Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(299,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.899 |
Dual form | 1050.2.u.a.299.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 1.50000 | − | 0.866025i | 0.433013 | − | 0.250000i | ||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 1.73205 | − | 2.00000i | 0.462910 | − | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | − | 1.73205i | −0.727607 | − | 0.420084i | 0.0899392 | − | 0.995947i | \(-0.471333\pi\) |
−0.817546 | + | 0.575863i | \(0.804666\pi\) | |||||||
\(18\) | 1.50000 | − | 2.59808i | 0.353553 | − | 0.612372i | ||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.866025 | − | 4.50000i | 0.188982 | − | 0.981981i | ||||
\(22\) | − | 3.00000i | − | 0.639602i | ||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | −1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.73205 | + | 3.00000i | 0.339683 | + | 0.588348i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.59808 | − | 0.500000i | −0.490990 | − | 0.0944911i | ||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.59808 | − | 4.50000i | −0.452267 | − | 0.783349i | ||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 1.73205 | − | 1.00000i | 0.284747 | − | 0.164399i | −0.350823 | − | 0.936442i | \(-0.614098\pi\) |
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(38\) | 3.00000 | + | 1.73205i | 0.486664 | + | 0.280976i | ||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | −4.33013 | + | 1.50000i | −0.668153 | + | 0.231455i | ||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −2.59808 | + | 1.50000i | −0.391675 | + | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −6.00000 | + | 3.46410i | −0.875190 | + | 0.505291i | −0.869069 | − | 0.494690i | \(-0.835282\pi\) |
−0.00612051 | + | 0.999981i | \(0.501948\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 1.73205 | − | 3.00000i | 0.240192 | − | 0.416025i | ||||
\(53\) | −4.50000 | + | 7.79423i | −0.618123 | + | 1.07062i | 0.371706 | + | 0.928351i | \(0.378773\pi\) |
−0.989828 | + | 0.142269i | \(0.954560\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.866025 | + | 2.50000i | 0.115728 | + | 0.334077i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −2.59808 | + | 1.50000i | −0.341144 | + | 0.196960i | ||||
\(59\) | −0.866025 | + | 1.50000i | −0.112747 | + | 0.195283i | −0.916877 | − | 0.399170i | \(-0.869298\pi\) |
0.804130 | + | 0.594454i | \(0.202632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 1.73205i | 0.219971i | ||||||||
\(63\) | −5.19615 | + | 6.00000i | −0.654654 | + | 0.755929i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.59808 | + | 4.50000i | −0.319801 | + | 0.553912i | ||||
\(67\) | 1.73205 | + | 1.00000i | 0.211604 | + | 0.122169i | 0.602056 | − | 0.798454i | \(-0.294348\pi\) |
−0.390453 | + | 0.920623i | \(0.627682\pi\) | |||||||
\(68\) | 3.00000 | − | 1.73205i | 0.363803 | − | 0.210042i | ||||
\(69\) | 10.3923i | 1.25109i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 1.50000 | + | 2.59808i | 0.176777 | + | 0.306186i | ||||
\(73\) | −3.46410 | + | 6.00000i | −0.405442 | + | 0.702247i | −0.994373 | − | 0.105937i | \(-0.966216\pi\) |
0.588930 | + | 0.808184i | \(0.299549\pi\) | |||||||
\(74\) | −1.73205 | − | 1.00000i | −0.201347 | − | 0.116248i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | −1.50000 | + | 7.79423i | −0.170941 | + | 0.888235i | ||||
\(78\) | − | 6.00000i | − | 0.679366i | ||||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 3.46410 | + | 6.00000i | 0.382546 | + | 0.662589i | ||||
\(83\) | 8.66025i | 0.950586i | 0.879827 | + | 0.475293i | \(0.157658\pi\) | ||||
−0.879827 | + | 0.475293i | \(0.842342\pi\) | |||||||
\(84\) | 3.46410 | + | 3.00000i | 0.377964 | + | 0.327327i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.92820 | + | 4.00000i | −0.747087 | + | 0.431331i | ||||
\(87\) | −2.59808 | + | 4.50000i | −0.278543 | + | 0.482451i | ||||
\(88\) | 2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | ||||
\(89\) | −5.19615 | − | 9.00000i | −0.550791 | − | 0.953998i | −0.998218 | − | 0.0596775i | \(-0.980993\pi\) |
0.447427 | − | 0.894321i | \(-0.352341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | − | 8.66025i | −0.314485 | − | 0.907841i | ||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 1.50000 | + | 2.59808i | 0.155543 | + | 0.269408i | ||||
\(94\) | 6.00000 | + | 3.46410i | 0.618853 | + | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 5.19615 | 0.527589 | 0.263795 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263795 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(98\) | 6.50000 | + | 2.59808i | 0.656599 | + | 0.262445i | ||||
\(99\) | 9.00000i | 0.904534i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 3.00000 | − | 5.19615i | 0.297044 | − | 0.514496i | ||||
\(103\) | −1.73205 | − | 3.00000i | −0.170664 | − | 0.295599i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 4.50000 | + | 2.59808i | 0.433013 | + | 0.250000i | ||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46410 | −0.328798 | ||||||||
\(112\) | 1.73205 | − | 2.00000i | 0.163663 | − | 0.188982i | ||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | −3.00000 | − | 5.19615i | −0.280976 | − | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.59808 | + | 1.50000i | 0.241225 | + | 0.139272i | ||||
\(117\) | −5.19615 | − | 9.00000i | −0.480384 | − | 0.832050i | ||||
\(118\) | 1.73205 | 0.159448 | ||||||||
\(119\) | 1.73205 | − | 9.00000i | 0.158777 | − | 0.825029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3923 | + | 6.00000i | 0.937043 | + | 0.541002i | ||||
\(124\) | 1.50000 | − | 0.866025i | 0.134704 | − | 0.0777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.79423 | + | 1.50000i | 0.694365 | + | 0.133631i | ||||
\(127\) | − | 11.0000i | − | 0.976092i | −0.872818 | − | 0.488046i | \(-0.837710\pi\) | ||
0.872818 | − | 0.488046i | \(-0.162290\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.92820 | + | 12.0000i | −0.609994 | + | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | + | 4.50000i | 0.226995 | + | 0.393167i | 0.956916 | − | 0.290365i | \(-0.0937766\pi\) |
−0.729921 | + | 0.683531i | \(0.760443\pi\) | |||||||
\(132\) | 5.19615 | 0.452267 | ||||||||
\(133\) | −6.92820 | − | 6.00000i | −0.600751 | − | 0.520266i | ||||
\(134\) | − | 2.00000i | − | 0.172774i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 1.73205i | −0.257248 | − | 0.148522i | ||||
\(137\) | −9.00000 | + | 15.5885i | −0.768922 | + | 1.33181i | 0.169226 | + | 0.985577i | \(0.445873\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(138\) | 9.00000 | − | 5.19615i | 0.766131 | − | 0.442326i | ||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | −10.3923 | + | 6.00000i | −0.872103 | + | 0.503509i | ||||
\(143\) | −9.00000 | − | 5.19615i | −0.752618 | − | 0.434524i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.92820 | 0.573382 | ||||||||
\(147\) | 12.0000 | − | 1.73205i | 0.989743 | − | 0.142857i | ||||
\(148\) | 2.00000i | 0.164399i | ||||||||
\(149\) | −15.5885 | + | 9.00000i | −1.27706 | + | 0.737309i | −0.976306 | − | 0.216394i | \(-0.930570\pi\) |
−0.300750 | + | 0.953703i | \(0.597237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | + | 6.06218i | −0.284826 | + | 0.493333i | −0.972567 | − | 0.232623i | \(-0.925269\pi\) |
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(152\) | −3.00000 | + | 1.73205i | −0.243332 | + | 0.140488i | ||||
\(153\) | − | 10.3923i | − | 0.840168i | ||||||
\(154\) | 7.50000 | − | 2.59808i | 0.604367 | − | 0.209359i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.19615 | + | 3.00000i | −0.416025 | + | 0.240192i | ||||
\(157\) | −10.3923 | + | 18.0000i | −0.829396 | + | 1.43656i | 0.0691164 | + | 0.997609i | \(0.477982\pi\) |
−0.898513 | + | 0.438948i | \(0.855351\pi\) | |||||||
\(158\) | −0.500000 | + | 0.866025i | −0.0397779 | + | 0.0688973i | ||||
\(159\) | 13.5000 | − | 7.79423i | 1.07062 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | − | 12.0000i | 0.819028 | − | 0.945732i | ||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 12.1244 | − | 7.00000i | 0.949653 | − | 0.548282i | 0.0566798 | − | 0.998392i | \(-0.481949\pi\) |
0.892973 | + | 0.450110i | \(0.148615\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.50000 | − | 4.33013i | 0.582113 | − | 0.336083i | ||||
\(167\) | − | 17.3205i | − | 1.34030i | −0.742225 | − | 0.670151i | \(-0.766230\pi\) | ||
0.742225 | − | 0.670151i | \(-0.233770\pi\) | |||||||
\(168\) | 0.866025 | − | 4.50000i | 0.0668153 | − | 0.347183i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.00000 | − | 5.19615i | −0.688247 | − | 0.397360i | ||||
\(172\) | 6.92820 | + | 4.00000i | 0.528271 | + | 0.304997i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 5.19615 | 0.393919 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | 2.59808 | − | 1.50000i | 0.195283 | − | 0.112747i | ||||
\(178\) | −5.19615 | + | 9.00000i | −0.389468 | + | 0.674579i | ||||
\(179\) | 10.3923 | + | 6.00000i | 0.776757 | + | 0.448461i | 0.835280 | − | 0.549825i | \(-0.185306\pi\) |
−0.0585225 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | −6.00000 | + | 6.92820i | −0.444750 | + | 0.513553i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | − | 2.59808i | 0.109985 | − | 0.190500i | ||||
\(187\) | −5.19615 | − | 9.00000i | −0.379980 | − | 0.658145i | ||||
\(188\) | − | 6.92820i | − | 0.505291i | ||||||
\(189\) | 12.9904 | − | 4.50000i | 0.944911 | − | 0.327327i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −1.50000 | − | 0.866025i | −0.108253 | − | 0.0625000i | ||||
\(193\) | 19.9186 | + | 11.5000i | 1.43377 | + | 0.827788i | 0.997406 | − | 0.0719816i | \(-0.0229323\pi\) |
0.436365 | + | 0.899770i | \(0.356266\pi\) | |||||||
\(194\) | −2.59808 | − | 4.50000i | −0.186531 | − | 0.323081i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 7.79423 | − | 4.50000i | 0.553912 | − | 0.319801i | ||||
\(199\) | −9.00000 | − | 5.19615i | −0.637993 | − | 0.368345i | 0.145848 | − | 0.989307i | \(-0.453409\pi\) |
−0.783841 | + | 0.620962i | \(0.786742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.73205 | − | 3.00000i | −0.122169 | − | 0.211604i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.50000 | − | 2.59808i | 0.526397 | − | 0.182349i | ||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.73205 | + | 3.00000i | −0.120678 | + | 0.209020i | ||||
\(207\) | 9.00000 | − | 15.5885i | 0.625543 | − | 1.08347i | ||||
\(208\) | 1.73205 | + | 3.00000i | 0.120096 | + | 0.208013i | ||||
\(209\) | −10.3923 | −0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | −10.3923 | + | 18.0000i | −0.712069 | + | 1.23334i | ||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 0.866025 | − | 4.50000i | 0.0587896 | − | 0.305480i | ||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 10.3923 | − | 6.00000i | 0.702247 | − | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923 | + | 6.00000i | 0.699062 | + | 0.403604i | ||||
\(222\) | 1.73205 | + | 3.00000i | 0.116248 | + | 0.201347i | ||||
\(223\) | 25.9808 | 1.73980 | 0.869900 | − | 0.493228i | \(-0.164183\pi\) | ||||
0.869900 | + | 0.493228i | \(0.164183\pi\) | |||||||
\(224\) | −2.59808 | − | 0.500000i | −0.173591 | − | 0.0334077i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | + | 10.3923i | 0.399114 | + | 0.691286i | ||||
\(227\) | 4.50000 | + | 2.59808i | 0.298675 | + | 0.172440i | 0.641848 | − | 0.766832i | \(-0.278168\pi\) |
−0.343172 | + | 0.939272i | \(0.611501\pi\) | |||||||
\(228\) | −3.00000 | + | 5.19615i | −0.198680 | + | 0.344124i | ||||
\(229\) | 12.0000 | − | 6.92820i | 0.792982 | − | 0.457829i | −0.0480291 | − | 0.998846i | \(-0.515294\pi\) |
0.841011 | + | 0.541017i | \(0.181961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.00000 | − | 10.3923i | 0.592157 | − | 0.683763i | ||||
\(232\) | − | 3.00000i | − | 0.196960i | ||||||
\(233\) | −9.00000 | − | 15.5885i | −0.589610 | − | 1.02123i | −0.994283 | − | 0.106773i | \(-0.965948\pi\) |
0.404674 | − | 0.914461i | \(-0.367385\pi\) | |||||||
\(234\) | −5.19615 | + | 9.00000i | −0.339683 | + | 0.588348i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.866025 | − | 1.50000i | −0.0563735 | − | 0.0976417i | ||||
\(237\) | 1.73205i | 0.112509i | ||||||||
\(238\) | −8.66025 | + | 3.00000i | −0.561361 | + | 0.194461i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5000 | − | 12.9904i | −1.44935 | − | 0.836784i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 12.0000i | − | 0.765092i | ||||||
\(247\) | 10.3923 | − | 6.00000i | 0.661247 | − | 0.381771i | ||||
\(248\) | −1.50000 | − | 0.866025i | −0.0952501 | − | 0.0549927i | ||||
\(249\) | 7.50000 | − | 12.9904i | 0.475293 | − | 0.823232i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0526 | −1.20259 | −0.601293 | − | 0.799028i | \(-0.705348\pi\) | ||||
−0.601293 | + | 0.799028i | \(0.705348\pi\) | |||||||
\(252\) | −2.59808 | − | 7.50000i | −0.163663 | − | 0.472456i | ||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | −9.52628 | + | 5.50000i | −0.597732 | + | 0.345101i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.00000 | + | 5.19615i | −0.561405 | + | 0.324127i | −0.753709 | − | 0.657208i | \(-0.771737\pi\) |
0.192304 | + | 0.981335i | \(0.438404\pi\) | |||||||
\(258\) | 13.8564 | 0.862662 | ||||||||
\(259\) | 4.00000 | + | 3.46410i | 0.248548 | + | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.79423 | − | 4.50000i | 0.482451 | − | 0.278543i | ||||
\(262\) | 2.59808 | − | 4.50000i | 0.160510 | − | 0.278011i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −2.59808 | − | 4.50000i | −0.159901 | − | 0.276956i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.73205 | + | 9.00000i | −0.106199 | + | 0.551825i | ||||
\(267\) | 18.0000i | 1.10158i | ||||||||
\(268\) | −1.73205 | + | 1.00000i | −0.105802 | + | 0.0610847i | ||||
\(269\) | 14.7224 | − | 25.5000i | 0.897643 | − | 1.55476i | 0.0671428 | − | 0.997743i | \(-0.478612\pi\) |
0.830500 | − | 0.557019i | \(-0.188055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.50000 | − | 2.59808i | 0.273356 | − | 0.157822i | −0.357056 | − | 0.934083i | \(-0.616219\pi\) |
0.630412 | + | 0.776261i | \(0.282886\pi\) | |||||||
\(272\) | 3.46410i | 0.210042i | ||||||||
\(273\) | −3.00000 | + | 15.5885i | −0.181568 | + | 0.943456i | ||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.00000 | − | 5.19615i | −0.541736 | − | 0.312772i | ||||
\(277\) | 6.92820 | + | 4.00000i | 0.416275 | + | 0.240337i | 0.693482 | − | 0.720473i | \(-0.256075\pi\) |
−0.277207 | + | 0.960810i | \(0.589409\pi\) | |||||||
\(278\) | −15.0000 | + | 8.66025i | −0.899640 | + | 0.519408i | ||||
\(279\) | − | 5.19615i | − | 0.311086i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000i | 1.78965i | 0.446417 | + | 0.894825i | \(0.352700\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | −6.00000 | − | 10.3923i | −0.357295 | − | 0.618853i | ||||
\(283\) | −13.8564 | + | 24.0000i | −0.823678 | + | 1.42665i | 0.0792477 | + | 0.996855i | \(0.474748\pi\) |
−0.902926 | + | 0.429797i | \(0.858585\pi\) | |||||||
\(284\) | 10.3923 | + | 6.00000i | 0.616670 | + | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.3923i | 0.614510i | ||||||||
\(287\) | −6.00000 | − | 17.3205i | −0.354169 | − | 1.02240i | ||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | −2.50000 | − | 4.33013i | −0.147059 | − | 0.254713i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.79423 | − | 4.50000i | −0.456906 | − | 0.263795i | ||||
\(292\) | −3.46410 | − | 6.00000i | −0.202721 | − | 0.351123i | ||||
\(293\) | 19.0526i | 1.11306i | 0.830827 | + | 0.556531i | \(0.187868\pi\) | ||||
−0.830827 | + | 0.556531i | \(0.812132\pi\) | |||||||
\(294\) | −7.50000 | − | 9.52628i | −0.437409 | − | 0.555584i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.73205 | − | 1.00000i | 0.100673 | − | 0.0581238i | ||||
\(297\) | 7.79423 | − | 13.5000i | 0.452267 | − | 0.783349i | ||||
\(298\) | 15.5885 | + | 9.00000i | 0.903015 | + | 0.521356i | ||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | 7.00000 | 0.402805 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | + | 1.73205i | 0.172062 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.00000 | + | 5.19615i | −0.514496 | + | 0.297044i | ||||
\(307\) | −24.2487 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(308\) | −6.00000 | − | 5.19615i | −0.341882 | − | 0.296078i | ||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.92820 | − | 12.0000i | 0.392862 | − | 0.680458i | −0.599963 | − | 0.800027i | \(-0.704818\pi\) |
0.992826 | + | 0.119570i | \(0.0381515\pi\) | |||||||
\(312\) | 5.19615 | + | 3.00000i | 0.294174 | + | 0.169842i | ||||
\(313\) | 0.866025 | + | 1.50000i | 0.0489506 | + | 0.0847850i | 0.889463 | − | 0.457008i | \(-0.151079\pi\) |
−0.840512 | + | 0.541793i | \(0.817746\pi\) | |||||||
\(314\) | 20.7846 | 1.17294 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | 7.50000 | + | 12.9904i | 0.421242 | + | 0.729612i | 0.996061 | − | 0.0886679i | \(-0.0282610\pi\) |
−0.574819 | + | 0.818280i | \(0.694928\pi\) | |||||||
\(318\) | −13.5000 | − | 7.79423i | −0.757042 | − | 0.437079i | ||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.19615i | − | 0.290021i | ||||||
\(322\) | −15.5885 | − | 3.00000i | −0.868711 | − | 0.167183i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.1244 | − | 7.00000i | −0.671506 | − | 0.387694i | ||||
\(327\) | 3.00000 | − | 1.73205i | 0.165900 | − | 0.0957826i | ||||
\(328\) | −6.92820 | −0.382546 | ||||||||
\(329\) | −13.8564 | − | 12.0000i | −0.763928 | − | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | −7.50000 | − | 4.33013i | −0.411616 | − | 0.237647i | ||||
\(333\) | 5.19615 | + | 3.00000i | 0.284747 | + | 0.164399i | ||||
\(334\) | −15.0000 | + | 8.66025i | −0.820763 | + | 0.473868i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.33013 | + | 1.50000i | −0.236228 | + | 0.0818317i | ||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | 0.500000 | + | 0.866025i | 0.0271964 | + | 0.0471056i | ||||
\(339\) | 18.0000 | + | 10.3923i | 0.977626 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59808 | − | 4.50000i | −0.140694 | − | 0.243689i | ||||
\(342\) | 10.3923i | 0.561951i | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | −2.59808 | − | 4.50000i | −0.139272 | − | 0.241225i | ||||
\(349\) | − | 10.3923i | − | 0.556287i | −0.960539 | − | 0.278144i | \(-0.910281\pi\) | ||
0.960539 | − | 0.278144i | \(-0.0897191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000i | 0.960769i | ||||||||
\(352\) | −2.59808 | + | 1.50000i | −0.138478 | + | 0.0799503i | ||||
\(353\) | 30.0000 | + | 17.3205i | 1.59674 | + | 0.921878i | 0.992110 | + | 0.125370i | \(0.0400119\pi\) |
0.604629 | + | 0.796507i | \(0.293321\pi\) | |||||||
\(354\) | −2.59808 | − | 1.50000i | −0.138086 | − | 0.0797241i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | −10.3923 | + | 12.0000i | −0.550019 | + | 0.635107i | ||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | −5.19615 | + | 3.00000i | −0.274242 | + | 0.158334i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) |
0.356572 | + | 0.934268i | \(0.383946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 6.00000 | − | 3.46410i | 0.315353 | − | 0.182069i | ||||
\(363\) | 3.46410i | 0.181818i | ||||||||
\(364\) | 9.00000 | + | 1.73205i | 0.471728 | + | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2583 | + | 19.5000i | −0.587680 | + | 1.01789i | 0.406855 | + | 0.913493i | \(0.366625\pi\) |
−0.994535 | + | 0.104399i | \(0.966708\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | −10.3923 | − | 18.0000i | −0.541002 | − | 0.937043i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.3827 | − | 4.50000i | −1.21397 | − | 0.233628i | ||||
\(372\) | −3.00000 | −0.155543 | ||||||||
\(373\) | 27.7128 | − | 16.0000i | 1.43492 | − | 0.828449i | 0.437425 | − | 0.899255i | \(-0.355891\pi\) |
0.997490 | + | 0.0708063i | \(0.0225572\pi\) | |||||||
\(374\) | −5.19615 | + | 9.00000i | −0.268687 | + | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | 10.3923i | 0.535231i | ||||||||
\(378\) | −10.3923 | − | 9.00000i | −0.534522 | − | 0.462910i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.52628 | + | 16.5000i | −0.488046 | + | 0.845321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | − | 1.73205i | 0.153293 | − | 0.0885037i | −0.421392 | − | 0.906879i | \(-0.638458\pi\) |
0.574684 | + | 0.818375i | \(0.305125\pi\) | |||||||
\(384\) | 1.73205i | 0.0883883i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 23.0000i | − | 1.17067i | ||||||
\(387\) | 20.7846 | − | 12.0000i | 1.05654 | − | 0.609994i | ||||
\(388\) | −2.59808 | + | 4.50000i | −0.131897 | + | 0.228453i | ||||
\(389\) | −15.5885 | − | 9.00000i | −0.790366 | − | 0.456318i | 0.0497253 | − | 0.998763i | \(-0.484165\pi\) |
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7846i | 1.05112i | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | − | 9.00000i | − | 0.453990i | ||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.79423 | − | 4.50000i | −0.391675 | − | 0.226134i | ||||
\(397\) | 13.8564 | + | 24.0000i | 0.695433 | + | 1.20453i | 0.970034 | + | 0.242967i | \(0.0781208\pi\) |
−0.274601 | + | 0.961558i | \(0.588546\pi\) | |||||||
\(398\) | 10.3923i | 0.520919i | ||||||||
\(399\) | 5.19615 | + | 15.0000i | 0.260133 | + | 0.750939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3923 | + | 6.00000i | −0.518967 | + | 0.299626i | −0.736512 | − | 0.676425i | \(-0.763528\pi\) |
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(402\) | −1.73205 | + | 3.00000i | −0.0863868 | + | 0.149626i | ||||
\(403\) | 5.19615 | + | 3.00000i | 0.258839 | + | 0.149441i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | − | 5.19615i | −0.297775 | − | 0.257881i | ||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 3.00000 | + | 5.19615i | 0.148522 | + | 0.257248i | ||||
\(409\) | −7.50000 | − | 4.33013i | −0.370851 | − | 0.214111i | 0.302979 | − | 0.952997i | \(-0.402019\pi\) |
−0.673830 | + | 0.738886i | \(0.735352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.0000 | − | 15.5885i | 1.33181 | − | 0.768922i | ||||
\(412\) | 3.46410 | 0.170664 | ||||||||
\(413\) | −4.50000 | − | 0.866025i | −0.221431 | − | 0.0426143i | ||||
\(414\) | −18.0000 | −0.884652 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.73205 | − | 3.00000i | 0.0849208 | − | 0.147087i | ||||
\(417\) | −15.0000 | + | 25.9808i | −0.734553 | + | 1.27228i | ||||
\(418\) | 5.19615 | + | 9.00000i | 0.254152 | + | 0.440204i | ||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | −2.00000 | − | 3.46410i | −0.0973585 | − | 0.168630i | ||||
\(423\) | −18.0000 | − | 10.3923i | −0.875190 | − | 0.505291i | ||||
\(424\) | −4.50000 | + | 7.79423i | −0.218539 | + | 0.378521i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.7846 | 1.00702 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.00000 | −0.145010 | ||||||||
\(429\) | 9.00000 | + | 15.5885i | 0.434524 | + | 0.752618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7846 | + | 12.0000i | 1.00116 | + | 0.578020i | 0.908591 | − | 0.417687i | \(-0.137159\pi\) |
0.0925683 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | −34.6410 | −1.66474 | −0.832370 | − | 0.554220i | \(-0.813017\pi\) | ||||
−0.832370 | + | 0.554220i | \(0.813017\pi\) | |||||||
\(434\) | −4.33013 | + | 1.50000i | −0.207853 | + | 0.0720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | 18.0000 | + | 10.3923i | 0.861057 | + | 0.497131i | ||||
\(438\) | −10.3923 | − | 6.00000i | −0.496564 | − | 0.286691i | ||||
\(439\) | −31.5000 | + | 18.1865i | −1.50341 | + | 0.867996i | −0.503421 | + | 0.864041i | \(0.667925\pi\) |
−0.999992 | + | 0.00395451i | \(0.998741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.5000 | − | 7.79423i | −0.928571 | − | 0.371154i | ||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | 4.50000 | + | 7.79423i | 0.213801 | + | 0.370315i | 0.952901 | − | 0.303281i | \(-0.0980821\pi\) |
−0.739100 | + | 0.673596i | \(0.764749\pi\) | |||||||
\(444\) | 1.73205 | − | 3.00000i | 0.0821995 | − | 0.142374i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.9904 | − | 22.5000i | −0.615112 | − | 1.06541i | ||||
\(447\) | 31.1769 | 1.47462 | ||||||||
\(448\) | 0.866025 | + | 2.50000i | 0.0409159 | + | 0.118114i | ||||
\(449\) | 30.0000i | 1.41579i | 0.706319 | + | 0.707894i | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | − | 10.3923i | −0.847587 | − | 0.489355i | ||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 10.5000 | − | 6.06218i | 0.493333 | − | 0.284826i | ||||
\(454\) | − | 5.19615i | − | 0.243868i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 4.33013 | − | 2.50000i | 0.202555 | − | 0.116945i | −0.395292 | − | 0.918556i | \(-0.629357\pi\) |
0.597847 | + | 0.801611i | \(0.296023\pi\) | |||||||
\(458\) | −12.0000 | − | 6.92820i | −0.560723 | − | 0.323734i | ||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564 | 0.645357 | 0.322679 | − | 0.946509i | \(-0.395417\pi\) | ||||
0.322679 | + | 0.946509i | \(0.395417\pi\) | |||||||
\(462\) | −13.5000 | − | 2.59808i | −0.628077 | − | 0.120873i | ||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | −2.59808 | + | 1.50000i | −0.120613 | + | 0.0696358i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | 27.0000 | − | 15.5885i | 1.24941 | − | 0.721348i | 0.278419 | − | 0.960460i | \(-0.410190\pi\) |
0.970992 | + | 0.239112i | \(0.0768563\pi\) | |||||||
\(468\) | 10.3923 | 0.480384 | ||||||||
\(469\) | −1.00000 | + | 5.19615i | −0.0461757 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.1769 | − | 18.0000i | 1.43656 | − | 0.829396i | ||||
\(472\) | −0.866025 | + | 1.50000i | −0.0398621 | + | 0.0690431i | ||||
\(473\) | 12.0000 | − | 20.7846i | 0.551761 | − | 0.955677i | ||||
\(474\) | 1.50000 | − | 0.866025i | 0.0688973 | − | 0.0397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.92820 | + | 6.00000i | 0.317554 | + | 0.275010i | ||||
\(477\) | −27.0000 | −1.23625 | ||||||||
\(478\) | −5.19615 | + | 3.00000i | −0.237666 | + | 0.137217i | ||||
\(479\) | −3.46410 | + | 6.00000i | −0.158279 | + | 0.274147i | −0.934248 | − | 0.356624i | \(-0.883928\pi\) |
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 3.46410i | −0.273576 | + | 0.157949i | ||||
\(482\) | 25.9808i | 1.18339i | ||||||||
\(483\) | −25.9808 | + | 9.00000i | −1.18217 | + | 0.409514i | ||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 0.866025 | + | 0.500000i | 0.0392434 | + | 0.0226572i | 0.519493 | − | 0.854475i | \(-0.326121\pi\) |
−0.480250 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2487 | −1.09656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0000i | 1.48927i | 0.667472 | + | 0.744635i | \(0.267376\pi\) | ||||
−0.667472 | + | 0.744635i | \(0.732624\pi\) | |||||||
\(492\) | −10.3923 | + | 6.00000i | −0.468521 | + | 0.270501i | ||||
\(493\) | −5.19615 | + | 9.00000i | −0.234023 | + | 0.405340i | ||||
\(494\) | −10.3923 | − | 6.00000i | −0.467572 | − | 0.269953i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | 30.0000 | − | 10.3923i | 1.34568 | − | 0.466159i | ||||
\(498\) | −15.0000 | −0.672166 | ||||||||
\(499\) | 11.0000 | + | 19.0526i | 0.492428 | + | 0.852910i | 0.999962 | − | 0.00872186i | \(-0.00277629\pi\) |
−0.507534 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | 9.52628 | + | 16.5000i | 0.425179 | + | 0.736431i | ||||
\(503\) | − | 38.1051i | − | 1.69902i | −0.527570 | − | 0.849512i | \(-0.676897\pi\) | ||
0.527570 | − | 0.849512i | \(-0.323103\pi\) | |||||||
\(504\) | −5.19615 | + | 6.00000i | −0.231455 | + | 0.267261i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.5885 | + | 9.00000i | −0.692991 | + | 0.400099i | ||||
\(507\) | 1.50000 | + | 0.866025i | 0.0666173 | + | 0.0384615i | ||||
\(508\) | 9.52628 | + | 5.50000i | 0.422660 | + | 0.244023i | ||||
\(509\) | 9.52628 | + | 16.5000i | 0.422245 | + | 0.731350i | 0.996159 | − | 0.0875661i | \(-0.0279089\pi\) |
−0.573914 | + | 0.818916i | \(0.694576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0000 | − | 3.46410i | −0.796273 | − | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.00000 | + | 15.5885i | 0.397360 | + | 0.688247i | ||||
\(514\) | 9.00000 | + | 5.19615i | 0.396973 | + | 0.229192i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.92820 | − | 12.0000i | −0.304997 | − | 0.528271i | ||||
\(517\) | −20.7846 | −0.914106 | ||||||||
\(518\) | 1.00000 | − | 5.19615i | 0.0439375 | − | 0.228306i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8564 | − | 24.0000i | 0.607060 | − | 1.05146i | −0.384662 | − | 0.923057i | \(-0.625682\pi\) |
0.991722 | − | 0.128402i | \(-0.0409847\pi\) | |||||||
\(522\) | −7.79423 | − | 4.50000i | −0.341144 | − | 0.196960i | ||||
\(523\) | −19.0526 | − | 33.0000i | −0.833110 | − | 1.44299i | −0.895560 | − | 0.444941i | \(-0.853225\pi\) |
0.0624496 | − | 0.998048i | \(-0.480109\pi\) | |||||||
\(524\) | −5.19615 | −0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | −2.59808 | + | 4.50000i | −0.113067 | + | 0.195837i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.19615 | −0.225494 | ||||||||
\(532\) | 8.66025 | − | 3.00000i | 0.375470 | − | 0.130066i | ||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 15.5885 | − | 9.00000i | 0.674579 | − | 0.389468i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.73205 | + | 1.00000i | 0.0748132 | + | 0.0431934i | ||||
\(537\) | −10.3923 | − | 18.0000i | −0.448461 | − | 0.776757i | ||||
\(538\) | −29.4449 | −1.26946 | ||||||||
\(539\) | −20.7846 | + | 3.00000i | −0.895257 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | −4.50000 | − | 2.59808i | −0.193292 | − | 0.111597i | ||||
\(543\) | 6.00000 | − | 10.3923i | 0.257485 | − | 0.445976i | ||||
\(544\) | 3.00000 | − | 1.73205i | 0.128624 | − | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.0000 | − | 5.19615i | 0.641941 | − | 0.222375i | ||||
\(547\) | − | 2.00000i | − | 0.0855138i | −0.999086 | − | 0.0427569i | \(-0.986386\pi\) | ||
0.999086 | − | 0.0427569i | \(-0.0136141\pi\) | |||||||
\(548\) | −9.00000 | − | 15.5885i | −0.384461 | − | 0.665906i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.19615 | + | 9.00000i | 0.221364 | + | 0.383413i | ||||
\(552\) | 10.3923i | 0.442326i | ||||||||
\(553\) | 1.73205 | − | 2.00000i | 0.0736543 | − | 0.0850487i | ||||
\(554\) | − | 8.00000i | − | 0.339887i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.0000 | + | 8.66025i | 0.636142 | + | 0.367277i | ||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | −4.50000 | + | 2.59808i | −0.190500 | + | 0.109985i | ||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000i | 0.759961i | ||||||||
\(562\) | 25.9808 | − | 15.0000i | 1.09593 | − | 0.632737i | ||||
\(563\) | 22.5000 | + | 12.9904i | 0.948262 | + | 0.547479i | 0.892541 | − | 0.450967i | \(-0.148921\pi\) |
0.0557214 | + | 0.998446i | \(0.482254\pi\) | |||||||
\(564\) | −6.00000 | + | 10.3923i | −0.252646 | + | 0.437595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.7128 | 1.16486 | ||||||||
\(567\) | −23.3827 | − | 4.50000i | −0.981981 | − | 0.188982i | ||||
\(568\) | − | 12.0000i | − | 0.503509i | ||||||
\(569\) | 5.19615 | − | 3.00000i | 0.217834 | − | 0.125767i | −0.387113 | − | 0.922032i | \(-0.626528\pi\) |
0.604947 | + | 0.796266i | \(0.293194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 9.00000 | − | 5.19615i | 0.376309 | − | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | + | 13.8564i | −0.500870 | + | 0.578355i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −0.866025 | + | 1.50000i | −0.0360531 | + | 0.0624458i | −0.883489 | − | 0.468452i | \(-0.844812\pi\) |
0.847436 | + | 0.530898i | \(0.178145\pi\) | |||||||
\(578\) | −2.50000 | + | 4.33013i | −0.103986 | + | 0.180110i | ||||
\(579\) | −19.9186 | − | 34.5000i | −0.827788 | − | 1.43377i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6506 | + | 7.50000i | −0.898220 | + | 0.311152i | ||||
\(582\) | 9.00000i | 0.373062i | ||||||||
\(583\) | −23.3827 | + | 13.5000i | −0.968412 | + | 0.559113i | ||||
\(584\) | −3.46410 | + | 6.00000i | −0.143346 | + | 0.248282i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.5000 | − | 9.52628i | 0.681609 | − | 0.393527i | ||||
\(587\) | − | 15.5885i | − | 0.643404i | −0.946841 | − | 0.321702i | \(-0.895745\pi\) | ||
0.946841 | − | 0.321702i | \(-0.104255\pi\) | |||||||
\(588\) | −4.50000 | + | 11.2583i | −0.185577 | + | 0.464286i | ||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.0000 | + | 15.5885i | 1.11063 | + | 0.641223i | ||||
\(592\) | −1.73205 | − | 1.00000i | −0.0711868 | − | 0.0410997i | ||||
\(593\) | −33.0000 | + | 19.0526i | −1.35515 | + | 0.782395i | −0.988965 | − | 0.148148i | \(-0.952669\pi\) |
−0.366182 | + | 0.930543i | \(0.619335\pi\) | |||||||
\(594\) | −15.5885 | −0.639602 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.0000i | − | 0.737309i | ||||||
\(597\) | 9.00000 | + | 15.5885i | 0.368345 | + | 0.637993i | ||||
\(598\) | 10.3923 | − | 18.0000i | 0.424973 | − | 0.736075i | ||||
\(599\) | 25.9808 | + | 15.0000i | 1.06155 | + | 0.612883i | 0.925859 | − | 0.377869i | \(-0.123343\pi\) |
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.4449i | − | 1.20108i | −0.799594 | − | 0.600541i | \(-0.794952\pi\) | ||
0.799594 | − | 0.600541i | \(-0.205048\pi\) | |||||||
\(602\) | −16.0000 | − | 13.8564i | −0.652111 | − | 0.564745i | ||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | −3.50000 | − | 6.06218i | −0.142413 | − | 0.246667i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2583 | − | 19.5000i | −0.456962 | − | 0.791481i | 0.541837 | − | 0.840484i | \(-0.317729\pi\) |
−0.998799 | + | 0.0490029i | \(0.984396\pi\) | |||||||
\(608\) | − | 3.46410i | − | 0.140488i | ||||||
\(609\) | −13.5000 | − | 2.59808i | −0.547048 | − | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846 | − | 12.0000i | 0.840855 | − | 0.485468i | ||||
\(612\) | 9.00000 | + | 5.19615i | 0.363803 | + | 0.210042i | ||||
\(613\) | −1.73205 | − | 1.00000i | −0.0699569 | − | 0.0403896i | 0.464614 | − | 0.885514i | \(-0.346193\pi\) |
−0.534570 | + | 0.845124i | \(0.679527\pi\) | |||||||
\(614\) | 12.1244 | + | 21.0000i | 0.489299 | + | 0.847491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50000 | + | 7.79423i | −0.0604367 | + | 0.314038i | ||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 5.19615 | − | 3.00000i | 0.209020 | − | 0.120678i | ||||
\(619\) | −6.00000 | − | 3.46410i | −0.241160 | − | 0.139234i | 0.374550 | − | 0.927207i | \(-0.377797\pi\) |
−0.615710 | + | 0.787973i | \(0.711131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | + | 15.5885i | −1.08347 | + | 0.625543i | ||||
\(622\) | −13.8564 | −0.555591 | ||||||||
\(623\) | 18.0000 | − | 20.7846i | 0.721155 | − | 0.832718i | ||||
\(624\) | − | 6.00000i | − | 0.240192i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.866025 | − | 1.50000i | 0.0346133 | − | 0.0599521i | ||||
\(627\) | 15.5885 | + | 9.00000i | 0.622543 | + | 0.359425i | ||||
\(628\) | −10.3923 | − | 18.0000i | −0.414698 | − | 0.718278i | ||||
\(629\) | −6.92820 | −0.276246 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | −0.500000 | − | 0.866025i | −0.0198889 | − | 0.0344486i | ||||
\(633\) | −6.00000 | − | 3.46410i | −0.238479 | − | 0.137686i | ||||
\(634\) | 7.50000 | − | 12.9904i | 0.297863 | − | 0.515914i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.5885i | 0.618123i | ||||||||
\(637\) | 19.0526 | − | 15.0000i | 0.754890 | − | 0.594322i | ||||
\(638\) | −9.00000 | −0.356313 | ||||||||
\(639\) | 31.1769 | − | 18.0000i | 1.23334 | − | 0.712069i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7846 | − | 12.0000i | −0.820943 | − | 0.473972i | 0.0297987 | − | 0.999556i | \(-0.490513\pi\) |
−0.850741 | + | 0.525584i | \(0.823847\pi\) | |||||||
\(642\) | −4.50000 | + | 2.59808i | −0.177601 | + | 0.102538i | ||||
\(643\) | 17.3205 | 0.683054 | 0.341527 | − | 0.939872i | \(-0.389056\pi\) | ||||
0.341527 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(644\) | 5.19615 | + | 15.0000i | 0.204757 | + | 0.591083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | −4.50000 | + | 7.79423i | −0.176777 | + | 0.306186i | ||||
\(649\) | −4.50000 | + | 2.59808i | −0.176640 | + | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.19615 | + | 6.00000i | −0.203653 | + | 0.235159i | ||||
\(652\) | 14.0000i | 0.548282i | ||||||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | −3.00000 | − | 1.73205i | −0.117309 | − | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.46410 | + | 6.00000i | 0.135250 | + | 0.234261i | ||||
\(657\) | −20.7846 | −0.810885 | ||||||||
\(658\) | −3.46410 | + | 18.0000i | −0.135045 | + | 0.701713i | ||||
\(659\) | − | 12.0000i | − | 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.00000 | − | 3.46410i | −0.233373 | − | 0.134738i | 0.378754 | − | 0.925497i | \(-0.376353\pi\) |
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(662\) | 4.00000 | − | 6.92820i | 0.155464 | − | 0.269272i | ||||
\(663\) | −10.3923 | − | 18.0000i | −0.403604 | − | 0.699062i | ||||
\(664\) | 8.66025i | 0.336083i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 6.00000i | − | 0.232495i | ||||||
\(667\) | −15.5885 | + | 9.00000i | −0.603587 | + | 0.348481i | ||||
\(668\) | 15.0000 | + | 8.66025i | 0.580367 | + | 0.335075i | ||||
\(669\) | −38.9711 | − | 22.5000i | −1.50671 | − | 0.869900i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.46410 | + | 3.00000i | 0.133631 | + | 0.115728i | ||||
\(673\) | − | 41.0000i | − | 1.58043i | −0.612827 | − | 0.790217i | \(-0.709968\pi\) | ||
0.612827 | − | 0.790217i | \(-0.290032\pi\) | |||||||
\(674\) | −11.2583 | + | 6.50000i | −0.433655 | + | 0.250371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | 4.50000 | − | 2.59808i | 0.172949 | − | 0.0998522i | −0.411027 | − | 0.911623i | \(-0.634830\pi\) |
0.583976 | + | 0.811771i | \(0.301496\pi\) | |||||||
\(678\) | − | 20.7846i | − | 0.798228i | ||||||
\(679\) | 4.50000 | + | 12.9904i | 0.172694 | + | 0.498525i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | −2.59808 | + | 4.50000i | −0.0994855 | + | 0.172314i | ||||
\(683\) | −10.5000 | + | 18.1865i | −0.401771 | + | 0.695888i | −0.993940 | − | 0.109926i | \(-0.964939\pi\) |
0.592168 | + | 0.805814i | \(0.298272\pi\) | |||||||
\(684\) | 9.00000 | − | 5.19615i | 0.344124 | − | 0.198680i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.866025 | + | 18.5000i | −0.0330650 | + | 0.706333i | ||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | −6.92820 | + | 4.00000i | −0.264135 | + | 0.152499i | ||||
\(689\) | 15.5885 | − | 27.0000i | 0.593873 | − | 1.02862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | + | 3.46410i | −0.228251 | + | 0.131781i | −0.609765 | − | 0.792582i | \(-0.708736\pi\) |
0.381514 | + | 0.924363i | \(0.375403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.5000 | + | 7.79423i | −0.854704 | + | 0.296078i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.59808 | + | 4.50000i | −0.0984798 | + | 0.170572i | ||||
\(697\) | 20.7846 | + | 12.0000i | 0.787273 | + | 0.454532i | ||||
\(698\) | −9.00000 | + | 5.19615i | −0.340655 | + | 0.196677i | ||||
\(699\) | 31.1769i | 1.17922i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.00000i | − | 0.113308i | −0.998394 | − | 0.0566542i | \(-0.981957\pi\) | ||
0.998394 | − | 0.0566542i | \(-0.0180433\pi\) | |||||||
\(702\) | 15.5885 | − | 9.00000i | 0.588348 | − | 0.339683i | ||||
\(703\) | −3.46410 | + | 6.00000i | −0.130651 | + | 0.226294i | ||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 34.6410i | − | 1.30373i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.00000i | 0.112747i | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | −5.19615 | − | 9.00000i | −0.194734 | − | 0.337289i | ||||
\(713\) | 10.3923i | 0.389195i | ||||||||
\(714\) | 15.5885 | + | 3.00000i | 0.583383 | + | 0.112272i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.3923 | + | 6.00000i | −0.388379 | + | 0.224231i | ||||
\(717\) | −5.19615 | + | 9.00000i | −0.194054 | + | 0.336111i | ||||
\(718\) | 5.19615 | + | 3.00000i | 0.193919 | + | 0.111959i | ||||
\(719\) | 22.5167 | + | 39.0000i | 0.839730 | + | 1.45445i | 0.890121 | + | 0.455725i | \(0.150620\pi\) |
−0.0503909 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | − | 6.92820i | 0.223452 | − | 0.258020i | ||||
\(722\) | 7.00000 | 0.260513 | ||||||||
\(723\) | 22.5000 | + | 38.9711i | 0.836784 | + | 1.44935i | ||||
\(724\) | −6.00000 | − | 3.46410i | −0.222988 | − | 0.128742i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.00000 | − | 1.73205i | 0.111340 | − | 0.0642824i | ||||
\(727\) | 29.4449 | 1.09205 | 0.546025 | − | 0.837769i | \(-0.316140\pi\) | ||||
0.546025 | + | 0.837769i | \(0.316140\pi\) | |||||||
\(728\) | −3.00000 | − | 8.66025i | −0.111187 | − | 0.320970i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8564 | + | 24.0000i | −0.512498 | + | 0.887672i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3205 | + | 30.0000i | 0.639748 | + | 1.10808i | 0.985488 | + | 0.169745i | \(0.0542944\pi\) |
−0.345740 | + | 0.938330i | \(0.612372\pi\) | |||||||
\(734\) | 22.5167 | 0.831105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 3.00000 | + | 5.19615i | 0.110506 | + | 0.191403i | ||||
\(738\) | −10.3923 | + | 18.0000i | −0.382546 | + | 0.662589i | ||||
\(739\) | −5.00000 | + | 8.66025i | −0.183928 | + | 0.318573i | −0.943215 | − | 0.332184i | \(-0.892215\pi\) |
0.759287 | + | 0.650756i | \(0.225548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.7846 | −0.763542 | ||||||||
\(742\) | 7.79423 | + | 22.5000i | 0.286135 | + | 0.826001i | ||||
\(743\) | 18.0000 | 0.660356 | 0.330178 | − | 0.943919i | \(-0.392891\pi\) | ||||
0.330178 | + | 0.943919i | \(0.392891\pi\) | |||||||
\(744\) | 1.50000 | + | 2.59808i | 0.0549927 | + | 0.0952501i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −27.7128 | − | 16.0000i | −1.01464 | − | 0.585802i | ||||
\(747\) | −22.5000 | + | 12.9904i | −0.823232 | + | 0.475293i | ||||
\(748\) | 10.3923 | 0.379980 | ||||||||
\(749\) | −5.19615 | + | 6.00000i | −0.189863 | + | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.50000 | + | 9.52628i | 0.200698 | + | 0.347619i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 6.00000 | + | 3.46410i | 0.218797 | + | 0.126323i | ||||
\(753\) | 28.5788 | + | 16.5000i | 1.04147 | + | 0.601293i | ||||
\(754\) | 9.00000 | − | 5.19615i | 0.327761 | − | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.59808 | + | 13.5000i | −0.0944911 | + | 0.490990i | ||||
\(757\) | − | 4.00000i | − | 0.145382i | −0.997354 | − | 0.0726912i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726912i | \(-0.0231588\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | −15.5885 | + | 27.0000i | −0.565825 | + | 0.980038i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.66025 | + | 15.0000i | 0.313934 | + | 0.543750i | 0.979210 | − | 0.202848i | \(-0.0650196\pi\) |
−0.665276 | + | 0.746597i | \(0.731686\pi\) | |||||||
\(762\) | 19.0526 | 0.690201 | ||||||||
\(763\) | −5.19615 | − | 1.00000i | −0.188113 | − | 0.0362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | − | 1.73205i | −0.108394 | − | 0.0625815i | ||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | 1.50000 | − | 0.866025i | 0.0541266 | − | 0.0312500i | ||||
\(769\) | − | 19.0526i | − | 0.687053i | −0.939143 | − | 0.343526i | \(-0.888379\pi\) | ||
0.939143 | − | 0.343526i | \(-0.111621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | −19.9186 | + | 11.5000i | −0.716886 | + | 0.413894i | ||||
\(773\) | −24.0000 | − | 13.8564i | −0.863220 | − | 0.498380i | 0.00186926 | − | 0.999998i | \(-0.499405\pi\) |
−0.865089 | + | 0.501618i | \(0.832738\pi\) | |||||||
\(774\) | −20.7846 | − | 12.0000i | −0.747087 | − | 0.431331i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.19615 | 0.186531 | ||||||||
\(777\) | −3.00000 | − | 8.66025i | −0.107624 | − | 0.310685i | ||||
\(778\) | 18.0000i | 0.645331i | ||||||||
\(779\) | 20.7846 | − | 12.0000i | 0.744686 | − | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 18.0000 | − | 10.3923i | 0.643679 | − | 0.371628i | ||||
\(783\) | −15.5885 | −0.557086 | ||||||||
\(784\) | 6.50000 | + | 2.59808i | 0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.79423 | + | 4.50000i | −0.278011 | + | 0.160510i | ||||
\(787\) | 20.7846 | − | 36.0000i | 0.740891 | − | 1.28326i | −0.211199 | − | 0.977443i | \(-0.567737\pi\) |
0.952090 | − | 0.305818i | \(-0.0989300\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3923 | − | 30.0000i | −0.369508 | − | 1.06668i | ||||
\(792\) | 9.00000i | 0.319801i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.8564 | − | 24.0000i | 0.491745 | − | 0.851728i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.00000 | − | 5.19615i | 0.318997 | − | 0.184173i | ||||
\(797\) | − | 25.9808i | − | 0.920286i | −0.887845 | − | 0.460143i | \(-0.847798\pi\) | ||
0.887845 | − | 0.460143i | \(-0.152202\pi\) | |||||||
\(798\) | 10.3923 | − | 12.0000i | 0.367884 | − | 0.424795i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5885 | − | 27.0000i | 0.550791 | − | 0.953998i | ||||
\(802\) | 10.3923 | + | 6.00000i | 0.366965 | + | 0.211867i | ||||
\(803\) | −18.0000 | + | 10.3923i | −0.635206 | + | 0.366736i | ||||
\(804\) | 3.46410 | 0.122169 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.00000i | − | 0.211341i | ||||||
\(807\) | −44.1673 | + | 25.5000i | −1.55476 | + | 0.897643i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | −1.50000 | + | 7.79423i | −0.0526397 | + | 0.273524i | ||||
\(813\) | −9.00000 | −0.315644 | ||||||||
\(814\) | −3.00000 | − | 5.19615i | −0.105150 | − | 0.182125i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 13.8564 | + | 24.0000i | 0.484774 | + | 0.839654i | ||||
\(818\) | 8.66025i | 0.302799i | ||||||||
\(819\) | 18.0000 | − | 20.7846i | 0.628971 | − | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.59808 | − | 1.50000i | 0.0906735 | − | 0.0523504i | −0.453978 | − | 0.891013i | \(-0.649995\pi\) |
0.544651 | + | 0.838663i | \(0.316662\pi\) | |||||||
\(822\) | −27.0000 | − | 15.5885i | −0.941733 | − | 0.543710i | ||||
\(823\) | −6.92820 | − | 4.00000i | −0.241502 | − | 0.139431i | 0.374365 | − | 0.927281i | \(-0.377861\pi\) |
−0.615867 | + | 0.787850i | \(0.711194\pi\) | |||||||
\(824\) | −1.73205 | − | 3.00000i | −0.0603388 | − | 0.104510i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.50000 | + | 4.33013i | 0.0521917 | + | 0.150664i | ||||
\(827\) | −9.00000 | −0.312961 | −0.156480 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156480 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(828\) | 9.00000 | + | 15.5885i | 0.312772 | + | 0.541736i | ||||
\(829\) | 15.0000 | + | 8.66025i | 0.520972 | + | 0.300783i | 0.737332 | − | 0.675530i | \(-0.236085\pi\) |
−0.216361 | + | 0.976314i | \(0.569419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.92820 | − | 12.0000i | −0.240337 | − | 0.416275i | ||||
\(832\) | −3.46410 | −0.120096 | ||||||||
\(833\) | 24.0000 | − | 3.46410i | 0.831551 | − | 0.120024i | ||||
\(834\) | 30.0000 | 1.03882 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.19615 | − | 9.00000i | 0.179713 | − | 0.311272i | ||||
\(837\) | −4.50000 | + | 7.79423i | −0.155543 | + | 0.269408i | ||||
\(838\) | −12.1244 | − | 21.0000i | −0.418829 | − | 0.725433i | ||||
\(839\) | 3.46410 | 0.119594 | 0.0597970 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597970 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −16.0000 | − | 27.7128i | −0.551396 | − | 0.955047i | ||||
\(843\) | 25.9808 | − | 45.0000i | 0.894825 | − | 1.54988i | ||||
\(844\) | −2.00000 | + | 3.46410i | −0.0688428 | + | 0.119239i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 20.7846i | 0.714590i | ||||||||
\(847\) | 3.46410 | − | 4.00000i | 0.119028 | − | 0.137442i | ||||
\(848\) | 9.00000 | 0.309061 | ||||||||
\(849\) | 41.5692 | − | 24.0000i | 1.42665 | − | 0.823678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3923 | − | 6.00000i | −0.356244 | − | 0.205677i | ||||
\(852\) | −10.3923 | − | 18.0000i | −0.356034 | − | 0.616670i | ||||
\(853\) | 24.2487 | 0.830260 | 0.415130 | − | 0.909762i | \(-0.363736\pi\) | ||||
0.415130 | + | 0.909762i | \(0.363736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.50000 | + | 2.59808i | 0.0512689 | + | 0.0888004i | ||||
\(857\) | −12.0000 | − | 6.92820i | −0.409912 | − | 0.236663i | 0.280840 | − | 0.959755i | \(-0.409387\pi\) |
−0.690752 | + | 0.723092i | \(0.742720\pi\) | |||||||
\(858\) | 9.00000 | − | 15.5885i | 0.307255 | − | 0.532181i | ||||
\(859\) | 18.0000 | − | 10.3923i | 0.614152 | − | 0.354581i | −0.160437 | − | 0.987046i | \(-0.551290\pi\) |
0.774589 | + | 0.632465i | \(0.217957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | + | 31.1769i | −0.204479 | + | 1.06251i | ||||
\(862\) | − | 24.0000i | − | 0.817443i | ||||||
\(863\) | −27.0000 | − | 46.7654i | −0.919091 | − | 1.59191i | −0.800799 | − | 0.598933i | \(-0.795592\pi\) |
−0.118291 | − | 0.992979i | \(-0.537742\pi\) | |||||||
\(864\) | 4.50000 | + | 2.59808i | 0.153093 | + | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.3205 | + | 30.0000i | 0.588575 | + | 1.01944i | ||||
\(867\) | 8.66025i | 0.294118i | ||||||||
\(868\) | 3.46410 | + | 3.00000i | 0.117579 | + | 0.101827i | ||||
\(869\) | − | 3.00000i | − | 0.101768i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | − | 3.46410i | −0.203302 | − | 0.117377i | ||||
\(872\) | −1.00000 | + | 1.73205i | −0.0338643 | + | 0.0586546i | ||||
\(873\) | 7.79423 | + | 13.5000i | 0.263795 | + | 0.456906i | ||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000i | 0.405442i | ||||||||
\(877\) | −38.1051 | + | 22.0000i | −1.28672 | + | 0.742887i | −0.978068 | − | 0.208288i | \(-0.933211\pi\) |
−0.308651 | + | 0.951175i | \(0.599877\pi\) | |||||||
\(878\) | 31.5000 | + | 18.1865i | 1.06307 | + | 0.613766i | ||||
\(879\) | 16.5000 | − | 28.5788i | 0.556531 | − | 0.963940i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3923 | −0.350126 | −0.175063 | − | 0.984557i | \(-0.556013\pi\) | ||||
−0.175063 | + | 0.984557i | \(0.556013\pi\) | |||||||
\(882\) | 3.00000 | + | 20.7846i | 0.101015 | + | 0.699854i | ||||
\(883\) | 52.0000i | 1.74994i | 0.484178 | + | 0.874970i | \(0.339119\pi\) | ||||
−0.484178 | + | 0.874970i | \(0.660881\pi\) | |||||||
\(884\) | −10.3923 | + | 6.00000i | −0.349531 | + | 0.201802i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50000 | − | 7.79423i | 0.151180 | − | 0.261852i | ||||
\(887\) | 21.0000 | − | 12.1244i | 0.705111 | − | 0.407096i | −0.104137 | − | 0.994563i | \(-0.533208\pi\) |
0.809248 | + | 0.587467i | \(0.199875\pi\) | |||||||
\(888\) | −3.46410 | −0.116248 | ||||||||
\(889\) | 27.5000 | − | 9.52628i | 0.922320 | − | 0.319501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.3827 | + | 13.5000i | −0.783349 | + | 0.452267i | ||||
\(892\) | −12.9904 | + | 22.5000i | −0.434950 | + | 0.753356i | ||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | −15.5885 | − | 27.0000i | −0.521356 | − | 0.903015i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.73205 | − | 2.00000i | 0.0578638 | − | 0.0668153i | ||||
\(897\) | − | 36.0000i | − | 1.20201i | ||||||
\(898\) | 25.9808 | − | 15.0000i | 0.866989 | − | 0.500556i | ||||
\(899\) | −2.59808 | + | 4.50000i | −0.0866507 | + | 0.150083i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | − | 15.5885i | 0.899500 | − | 0.519327i | ||||
\(902\) | 20.7846i | 0.692052i | ||||||||
\(903\) | −36.0000 | − | 6.92820i | −1.19800 | − | 0.230556i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.5000 | − | 6.06218i | −0.348839 | − | 0.201402i | ||||
\(907\) | −22.5167 | − | 13.0000i | −0.747653 | − | 0.431658i | 0.0771920 | − | 0.997016i | \(-0.475405\pi\) |
−0.824845 | + | 0.565358i | \(0.808738\pi\) | |||||||
\(908\) | −4.50000 | + | 2.59808i | −0.149338 | + | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −3.00000 | − | 5.19615i | −0.0993399 | − | 0.172062i | ||||
\(913\) | −12.9904 | + | 22.5000i | −0.429919 | + | 0.744641i | ||||
\(914\) | −4.33013 | − | 2.50000i | −0.143228 | − | 0.0826927i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −9.00000 | + | 10.3923i | −0.297206 | + | 0.343184i | ||||
\(918\) | 18.0000 | 0.594089 | ||||||||
\(919\) | −10.0000 | − | 17.3205i | −0.329870 | − | 0.571351i | 0.652616 | − | 0.757689i | \(-0.273671\pi\) |
−0.982486 | + | 0.186338i | \(0.940338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.3731 | + | 21.0000i | 1.19853 | + | 0.691974i | ||||
\(922\) | −6.92820 | − | 12.0000i | −0.228168 | − | 0.395199i | ||||
\(923\) | 41.5692i | 1.36827i | ||||||||
\(924\) | 4.50000 | + | 12.9904i | 0.148039 | + | 0.427352i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.46410 | + | 2.00000i | −0.113837 | + | 0.0657241i | ||||
\(927\) | 5.19615 | − | 9.00000i | 0.170664 | − | 0.295599i | ||||
\(928\) | 2.59808 | + | 1.50000i | 0.0852860 | + | 0.0492399i | ||||
\(929\) | 24.2487 | + | 42.0000i | 0.795574 | + | 1.37798i | 0.922474 | + | 0.386060i | \(0.126164\pi\) |
−0.126899 | + | 0.991916i | \(0.540503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.00000 | − | 22.5167i | 0.294963 | − | 0.737954i | ||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | −20.7846 | + | 12.0000i | −0.680458 | + | 0.392862i | ||||
\(934\) | −27.0000 | − | 15.5885i | −0.883467 | − | 0.510070i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.19615 | − | 9.00000i | −0.169842 | − | 0.294174i | ||||
\(937\) | 22.5167 | 0.735587 | 0.367794 | − | 0.929907i | \(-0.380113\pi\) | ||||
0.367794 | + | 0.929907i | \(0.380113\pi\) | |||||||
\(938\) | 5.00000 | − | 1.73205i | 0.163256 | − | 0.0565535i | ||||
\(939\) | − | 3.00000i | − | 0.0979013i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4545 | − | 28.5000i | 0.536401 | − | 0.929073i | −0.462693 | − | 0.886518i | \(-0.653117\pi\) |
0.999094 | − | 0.0425550i | \(-0.0135498\pi\) | |||||||
\(942\) | −31.1769 | − | 18.0000i | −1.01580 | − | 0.586472i | ||||
\(943\) | 20.7846 | + | 36.0000i | 0.676840 | + | 1.17232i | ||||
\(944\) | 1.73205 | 0.0563735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | 6.00000 | + | 10.3923i | 0.194974 | + | 0.337705i | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | −1.50000 | − | 0.866025i | −0.0487177 | − | 0.0281272i | ||||
\(949\) | 12.0000 | − | 20.7846i | 0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 25.9808i | − | 0.842484i | ||||||
\(952\) | 1.73205 | − | 9.00000i | 0.0561361 | − | 0.291692i | ||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 13.5000 | + | 23.3827i | 0.437079 | + | 0.757042i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.19615 | + | 3.00000i | 0.168056 | + | 0.0970269i | ||||
\(957\) | −13.5000 | + | 7.79423i | −0.436393 | + | 0.251952i | ||||
\(958\) | 6.92820 | 0.223840 | ||||||||
\(959\) | −46.7654 | − | 9.00000i | −1.51013 | − | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 6.00000 | + | 3.46410i | 0.193448 | + | 0.111687i | ||||
\(963\) | −4.50000 | + | 7.79423i | −0.145010 | + | 0.251166i | ||||
\(964\) | 22.5000 | − | 12.9904i | 0.724676 | − | 0.418392i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.7846 | + | 18.0000i | 0.668734 | + | 0.579141i | ||||
\(967\) | 7.00000i | 0.225105i | 0.993646 | + | 0.112552i | \(0.0359026\pi\) | ||||
−0.993646 | + | 0.112552i | \(0.964097\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | −18.0000 | − | 10.3923i | −0.578243 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.33013 | − | 7.50000i | −0.138960 | − | 0.240686i | 0.788143 | − | 0.615492i | \(-0.211043\pi\) |
−0.927103 | + | 0.374806i | \(0.877709\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | 43.3013 | − | 15.0000i | 1.38817 | − | 0.480878i | ||||
\(974\) | − | 1.00000i | − | 0.0320421i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000 | − | 20.7846i | 0.383914 | − | 0.664959i | −0.607704 | − | 0.794164i | \(-0.707909\pi\) |
0.991618 | + | 0.129205i | \(0.0412426\pi\) | |||||||
\(978\) | 12.1244 | + | 21.0000i | 0.387694 | + | 0.671506i | ||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 28.5788 | − | 16.5000i | 0.911987 | − | 0.526536i | ||||
\(983\) | −12.0000 | − | 6.92820i | −0.382741 | − | 0.220975i | 0.296269 | − | 0.955104i | \(-0.404257\pi\) |
−0.679010 | + | 0.734129i | \(0.737591\pi\) | |||||||
\(984\) | 10.3923 | + | 6.00000i | 0.331295 | + | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.3923 | 0.330958 | ||||||||
\(987\) | 10.3923 | + | 30.0000i | 0.330791 | + | 0.954911i | ||||
\(988\) | 12.0000i | 0.381771i | ||||||||
\(989\) | −41.5692 | + | 24.0000i | −1.32182 | + | 0.763156i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5000 | − | 40.7032i | 0.746502 | − | 1.29298i | −0.202988 | − | 0.979181i | \(-0.565065\pi\) |
0.949490 | − | 0.313798i | \(-0.101602\pi\) | |||||||
\(992\) | 1.50000 | − | 0.866025i | 0.0476250 | − | 0.0274963i | ||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | −24.0000 | − | 20.7846i | −0.761234 | − | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.50000 | + | 12.9904i | 0.237647 | + | 0.411616i | ||||
\(997\) | 8.66025 | − | 15.0000i | 0.274273 | − | 0.475055i | −0.695678 | − | 0.718353i | \(-0.744896\pi\) |
0.969951 | + | 0.243299i | \(0.0782295\pi\) | |||||||
\(998\) | 11.0000 | − | 19.0526i | 0.348199 | − | 0.603098i | ||||
\(999\) | −5.19615 | − | 9.00000i | −0.164399 | − | 0.284747i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))