Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [95,2,Mod(49,95)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(95, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("95.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.i (of order \(6\), 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: | \(0.758578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 95.49 |
Dual form | 95.2.i.a.64.1 |
$q$-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 \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −1.22474 | − | 0.707107i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 2.23205 | + | 0.133975i | 0.998203 | + | 0.0599153i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | −3.73205 | − | 2.46410i | −1.18018 | − | 0.779217i | ||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73205 | − | 1.00000i | 0.480384 | − | 0.277350i | −0.240192 | − | 0.970725i | \(-0.577210\pi\) |
0.720577 | + | 0.693375i | \(0.243877\pi\) | |||||||
\(14\) | −4.00000 | + | 6.92820i | −1.06904 | + | 1.85164i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 1.73205 | + | 1.00000i | 0.420084 | + | 0.242536i | 0.695113 | − | 0.718900i | \(-0.255354\pi\) |
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 6.00000i | 1.41421i | ||||||||
\(19\) | 3.50000 | + | 2.59808i | 0.802955 | + | 0.596040i | ||||
\(20\) | 2.00000 | + | 4.00000i | 0.447214 | + | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73205 | + | 1.00000i | 0.369274 | + | 0.213201i | ||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96410 | + | 0.598076i | 0.992820 | + | 0.119615i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.92820 | − | 4.00000i | 1.30931 | − | 0.755929i | ||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −6.92820 | + | 4.00000i | −1.22474 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 3.46410i | −0.342997 | − | 0.594089i | ||||
\(35\) | 0.535898 | − | 8.92820i | 0.0905834 | − | 1.50914i | ||||
\(36\) | 3.00000 | − | 5.19615i | 0.500000 | − | 0.866025i | ||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | −3.46410 | − | 8.00000i | −0.561951 | − | 1.29777i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205 | + | 1.00000i | 0.264135 | + | 0.152499i | 0.626219 | − | 0.779647i | \(-0.284601\pi\) |
−0.362084 | + | 0.932145i | \(0.617935\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | −3.00000 | − | 6.00000i | −0.447214 | − | 0.894427i | ||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | 5.19615 | − | 3.00000i | 0.757937 | − | 0.437595i | −0.0706177 | − | 0.997503i | \(-0.522497\pi\) |
0.828554 | + | 0.559908i | \(0.189164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | −8.00000 | − | 6.00000i | −1.13137 | − | 0.848528i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.46410 | + | 2.00000i | 0.480384 | + | 0.277350i | ||||
\(53\) | −3.46410 | + | 2.00000i | −0.475831 | + | 0.274721i | −0.718677 | − | 0.695344i | \(-0.755252\pi\) |
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.23205 | − | 0.133975i | −0.300970 | − | 0.0180651i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 18.0000i | − | 2.36352i | ||||||
\(59\) | 4.50000 | − | 7.79423i | 0.585850 | − | 1.01472i | −0.408919 | − | 0.912571i | \(-0.634094\pi\) |
0.994769 | − | 0.102151i | \(-0.0325726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 12.1244 | + | 7.00000i | 1.53979 | + | 0.889001i | ||||
\(63\) | −10.3923 | + | 6.00000i | −1.30931 | + | 0.755929i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 4.00000 | − | 2.00000i | 0.496139 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.66025 | + | 5.00000i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.85641 | + | 14.9282i | −1.17807 | + | 1.78426i | ||||
\(71\) | −0.500000 | + | 0.866025i | −0.0593391 | + | 0.102778i | −0.894169 | − | 0.447730i | \(-0.852233\pi\) |
0.834830 | + | 0.550508i | \(0.185566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66025 | + | 5.00000i | 1.01361 | + | 0.585206i | 0.912245 | − | 0.409644i | \(-0.134347\pi\) |
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 8.66025i | −0.114708 | + | 0.993399i | ||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 4.92820 | − | 7.46410i | 0.550990 | − | 0.834512i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 3.46410 | − | 2.00000i | 0.382546 | − | 0.220863i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.73205 | + | 2.46410i | 0.404798 | + | 0.267269i | ||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.50000 | − | 9.52628i | −0.582999 | − | 1.00978i | −0.995122 | − | 0.0986553i | \(-0.968546\pi\) |
0.412123 | − | 0.911128i | \(-0.364787\pi\) | |||||||
\(90\) | −0.803848 | + | 13.3923i | −0.0847330 | + | 1.41167i | ||||
\(91\) | −4.00000 | − | 6.92820i | −0.419314 | − | 0.726273i | ||||
\(92\) | −10.3923 | − | 6.00000i | −1.08347 | − | 0.625543i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | 7.46410 | + | 6.26795i | 0.765801 | + | 0.643078i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.19615 | + | 3.00000i | 0.527589 | + | 0.304604i | 0.740034 | − | 0.672569i | \(-0.234809\pi\) |
−0.212445 | + | 0.977173i | \(0.568143\pi\) | |||||||
\(98\) | 15.5885 | + | 9.00000i | 1.57467 | + | 0.909137i | ||||
\(99\) | 1.50000 | + | 2.59808i | 0.150756 | + | 0.261116i | ||||
\(100\) | 3.92820 | + | 9.19615i | 0.392820 | + | 0.919615i | ||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.0000i | − | 1.57653i | −0.615338 | − | 0.788263i | \(-0.710980\pi\) | ||
0.615338 | − | 0.788263i | \(-0.289020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | − | 10.0000i | − | 0.966736i | −0.875417 | − | 0.483368i | \(-0.839413\pi\) | ||
0.875417 | − | 0.483368i | \(-0.160587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.50000 | − | 12.9904i | 0.718370 | − | 1.24425i | −0.243276 | − | 0.969957i | \(-0.578222\pi\) |
0.961645 | − | 0.274296i | \(-0.0884447\pi\) | |||||||
\(110\) | 3.73205 | + | 2.46410i | 0.355837 | + | 0.234943i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.8564 | − | 8.00000i | −1.30931 | − | 0.755929i | ||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | + | 6.00000i | −1.11901 | + | 0.559503i | ||||
\(116\) | −9.00000 | + | 15.5885i | −0.835629 | + | 1.44735i | ||||
\(117\) | −5.19615 | − | 3.00000i | −0.480384 | − | 0.277350i | ||||
\(118\) | −15.5885 | + | 9.00000i | −1.43503 | + | 0.828517i | ||||
\(119\) | 4.00000 | − | 6.92820i | 0.366679 | − | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | − | 14.0000i | − | 1.26750i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.00000 | − | 12.1244i | −0.628619 | − | 1.08880i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 24.0000 | 2.13809 | ||||||||
\(127\) | −5.19615 | + | 3.00000i | −0.461084 | + | 0.266207i | −0.712500 | − | 0.701672i | \(-0.752437\pi\) |
0.251416 | + | 0.967879i | \(0.419104\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.92820 | − | 0.535898i | −0.783055 | − | 0.0470014i | ||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3923 | − | 14.0000i | 0.901127 | − | 1.21395i | ||||
\(134\) | 20.0000 | 1.72774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | + | 17.3205i | 0.848189 | + | 1.46911i | 0.882823 | + | 0.469706i | \(0.155640\pi\) |
−0.0346338 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(140\) | 16.0000 | − | 8.00000i | 1.35225 | − | 0.676123i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.73205 | − | 1.00000i | 0.145350 | − | 0.0839181i | ||||
\(143\) | −1.73205 | + | 1.00000i | −0.144841 | + | 0.0836242i | ||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 9.00000 | + | 18.0000i | 0.747409 | + | 1.49482i | ||||
\(146\) | −10.0000 | − | 17.3205i | −0.827606 | − | 1.43346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46410 | + | 2.00000i | −0.284747 | + | 0.164399i | ||||
\(149\) | −0.500000 | + | 0.866025i | −0.0409616 | + | 0.0709476i | −0.885779 | − | 0.464107i | \(-0.846375\pi\) |
0.844818 | + | 0.535054i | \(0.179709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.00000 | 0.732410 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 4.00000 | − | 6.92820i | 0.322329 | − | 0.558291i | ||||
\(155\) | −15.6244 | − | 0.937822i | −1.25498 | − | 0.0753277i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.46410 | − | 2.00000i | −0.276465 | − | 0.159617i | 0.355357 | − | 0.934731i | \(-0.384359\pi\) |
−0.631822 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(158\) | −1.73205 | + | 1.00000i | −0.137795 | + | 0.0795557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0000 | + | 8.00000i | −1.26491 | + | 0.632456i | ||||
\(161\) | 12.0000 | + | 20.7846i | 0.945732 | + | 1.63806i | ||||
\(162\) | 15.5885 | − | 9.00000i | 1.22474 | − | 0.707107i | ||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | −10.3923 | + | 6.00000i | −0.804181 | + | 0.464294i | −0.844931 | − | 0.534875i | \(-0.820359\pi\) |
0.0407502 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50000 | + | 7.79423i | −0.346154 | + | 0.599556i | ||||
\(170\) | −4.00000 | − | 8.00000i | −0.306786 | − | 0.613572i | ||||
\(171\) | 1.50000 | − | 12.9904i | 0.114708 | − | 0.993399i | ||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | −20.7846 | − | 12.0000i | −1.58022 | − | 0.912343i | −0.994826 | − | 0.101598i | \(-0.967605\pi\) |
−0.585399 | − | 0.810745i | \(-0.699062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.39230 | − | 19.8564i | 0.180841 | − | 1.50100i | ||||
\(176\) | −2.00000 | + | 3.46410i | −0.150756 | + | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 22.0000i | 1.64897i | ||||||||
\(179\) | −15.0000 | −1.12115 | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||||
−0.560576 | + | 0.828103i | \(0.689420\pi\) | |||||||
\(180\) | 7.39230 | − | 11.1962i | 0.550990 | − | 0.834512i | ||||
\(181\) | 3.00000 | + | 5.19615i | 0.222988 | + | 0.386227i | 0.955714 | − | 0.294297i | \(-0.0950855\pi\) |
−0.732726 | + | 0.680524i | \(0.761752\pi\) | |||||||
\(182\) | 16.0000i | 1.18600i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.267949 | + | 4.46410i | −0.0197000 | + | 0.328207i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73205 | − | 1.00000i | −0.126660 | − | 0.0731272i | ||||
\(188\) | 10.3923 | + | 6.00000i | 0.757937 | + | 0.437595i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.66025 | − | 18.3205i | −0.483186 | − | 1.32911i | ||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8564 | + | 8.00000i | 0.997406 | + | 0.575853i | 0.907480 | − | 0.420096i | \(-0.138004\pi\) |
0.0899262 | + | 0.995948i | \(0.471337\pi\) | |||||||
\(194\) | −6.00000 | − | 10.3923i | −0.430775 | − | 0.746124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.00000 | − | 15.5885i | −0.642857 | − | 1.11346i | ||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | − | 6.00000i | − | 0.426401i | ||||||
\(199\) | 6.50000 | + | 11.2583i | 0.460773 | + | 0.798082i | 0.999000 | − | 0.0447181i | \(-0.0142390\pi\) |
−0.538227 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.0000i | 2.11079i | ||||||||
\(203\) | 31.1769 | − | 18.0000i | 2.18819 | − | 1.26335i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.46410 | + | 3.73205i | −0.172100 | + | 0.260658i | ||||
\(206\) | −16.0000 | + | 27.7128i | −1.11477 | + | 1.93084i | ||||
\(207\) | 15.5885 | + | 9.00000i | 1.08347 | + | 0.625543i | ||||
\(208\) | − | 8.00000i | − | 0.554700i | ||||||
\(209\) | −3.50000 | − | 2.59808i | −0.242100 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.50000 | + | 4.33013i | −0.172107 | + | 0.298098i | −0.939156 | − | 0.343490i | \(-0.888391\pi\) |
0.767049 | + | 0.641588i | \(0.221724\pi\) | |||||||
\(212\) | −6.92820 | − | 4.00000i | −0.475831 | − | 0.274721i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.0000 | + | 17.3205i | −0.683586 | + | 1.18401i | ||||
\(215\) | 3.73205 | + | 2.46410i | 0.254524 | + | 0.168050i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.0000i | 1.90076i | ||||||||
\(218\) | −25.9808 | + | 15.0000i | −1.75964 | + | 1.01593i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | − | 4.00000i | −0.134840 | − | 0.269680i | ||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.73205 | − | 1.00000i | −0.115987 | − | 0.0669650i | 0.440884 | − | 0.897564i | \(-0.354665\pi\) |
−0.556871 | + | 0.830599i | \(0.687998\pi\) | |||||||
\(224\) | 16.0000 | + | 27.7128i | 1.06904 | + | 1.85164i | ||||
\(225\) | −5.89230 | − | 13.7942i | −0.392820 | − | 0.919615i | ||||
\(226\) | 12.0000 | − | 20.7846i | 0.798228 | − | 1.38257i | ||||
\(227\) | 14.0000i | 0.929213i | 0.885517 | + | 0.464606i | \(0.153804\pi\) | ||||
−0.885517 | + | 0.464606i | \(0.846196\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0000 | −1.12339 | −0.561696 | − | 0.827344i | \(-0.689851\pi\) | ||||
−0.561696 | + | 0.827344i | \(0.689851\pi\) | |||||||
\(230\) | 26.7846 | + | 1.60770i | 1.76612 | + | 0.106008i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.92820 | − | 4.00000i | −0.453882 | − | 0.262049i | 0.255586 | − | 0.966786i | \(-0.417731\pi\) |
−0.709468 | + | 0.704737i | \(0.751065\pi\) | |||||||
\(234\) | 6.00000 | + | 10.3923i | 0.392232 | + | 0.679366i | ||||
\(235\) | 12.0000 | − | 6.00000i | 0.782794 | − | 0.391397i | ||||
\(236\) | 18.0000 | 1.17170 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.8564 | + | 8.00000i | −0.898177 | + | 0.518563i | ||||
\(239\) | 19.0000 | 1.22901 | 0.614504 | − | 0.788914i | \(-0.289356\pi\) | ||||
0.614504 | + | 0.788914i | \(0.289356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 17.3205 | + | 10.0000i | 1.11340 | + | 0.642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.00000 | + | 12.1244i | −0.448129 | + | 0.776182i | ||||
\(245\) | −20.0885 | − | 1.20577i | −1.28340 | − | 0.0770339i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.66025 | + | 1.00000i | 0.551039 | + | 0.0636285i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.0526 | − | 14.4641i | −1.07850 | − | 0.914790i | ||||
\(251\) | −6.50000 | − | 11.2583i | −0.410276 | − | 0.710620i | 0.584643 | − | 0.811290i | \(-0.301234\pi\) |
−0.994920 | + | 0.100671i | \(0.967901\pi\) | |||||||
\(252\) | −20.7846 | − | 12.0000i | −1.30931 | − | 0.755929i | ||||
\(253\) | 5.19615 | − | 3.00000i | 0.326679 | − | 0.188608i | ||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −5.19615 | + | 3.00000i | −0.324127 | + | 0.187135i | −0.653231 | − | 0.757159i | \(-0.726587\pi\) |
0.329104 | + | 0.944294i | \(0.393253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 7.46410 | + | 4.92820i | 0.462904 | + | 0.305634i | ||||
\(261\) | 13.5000 | − | 23.3827i | 0.835629 | − | 1.44735i | ||||
\(262\) | 20.7846 | − | 12.0000i | 1.28408 | − | 0.741362i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | + | 4.00000i | −0.491436 | + | 0.245718i | ||||
\(266\) | −32.0000 | + | 13.8564i | −1.96205 | + | 0.849591i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.3205 | − | 10.0000i | −1.05802 | − | 0.610847i | ||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50000 | + | 2.59808i | −0.0911185 | + | 0.157822i | −0.907982 | − | 0.419009i | \(-0.862378\pi\) |
0.816864 | + | 0.576831i | \(0.195711\pi\) | |||||||
\(272\) | 6.92820 | − | 4.00000i | 0.420084 | − | 0.242536i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.0000 | −1.44989 | ||||||||
\(275\) | −4.96410 | − | 0.598076i | −0.299347 | − | 0.0360654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.0000i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | − | 40.0000i | − | 2.39904i | ||||||
\(279\) | 10.5000 | + | 18.1865i | 0.628619 | + | 1.08880i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.00000 | − | 8.66025i | −0.298275 | − | 0.516627i | 0.677466 | − | 0.735554i | \(-0.263078\pi\) |
−0.975741 | + | 0.218926i | \(0.929745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | + | 7.00000i | 0.720718 | + | 0.416107i | 0.815017 | − | 0.579437i | \(-0.196728\pi\) |
−0.0942988 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 6.92820 | + | 4.00000i | 0.408959 | + | 0.236113i | ||||
\(288\) | 20.7846 | + | 12.0000i | 1.22474 | + | 0.707107i | ||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 2.41154 | − | 40.1769i | 0.141611 | − | 2.35927i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.0000i | 1.17041i | ||||||||
\(293\) | − | 4.00000i | − | 0.233682i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) | ||
0.993151 | − | 0.116841i | \(-0.0372769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.0885 | − | 16.7942i | 0.645595 | − | 0.977798i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.73205 | − | 1.00000i | 0.100335 | − | 0.0579284i | ||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 6.92820i | 0.230556 | − | 0.399335i | ||||
\(302\) | −15.5885 | − | 9.00000i | −0.897015 | − | 0.517892i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000 | − | 6.92820i | 0.917663 | − | 0.397360i | ||||
\(305\) | 7.00000 | + | 14.0000i | 0.400819 | + | 0.801638i | ||||
\(306\) | −6.00000 | + | 10.3923i | −0.342997 | + | 0.594089i | ||||
\(307\) | −13.8564 | − | 8.00000i | −0.790827 | − | 0.456584i | 0.0494267 | − | 0.998778i | \(-0.484261\pi\) |
−0.840254 | + | 0.542194i | \(0.817594\pi\) | |||||||
\(308\) | −6.92820 | + | 4.00000i | −0.394771 | + | 0.227921i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 26.1244 | + | 17.2487i | 1.48376 | + | 0.979661i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.9808 | + | 15.0000i | −1.46852 | + | 0.847850i | −0.999378 | − | 0.0352727i | \(-0.988770\pi\) |
−0.469142 | + | 0.883123i | \(0.655437\pi\) | |||||||
\(314\) | 4.00000 | + | 6.92820i | 0.225733 | + | 0.390981i | ||||
\(315\) | −24.0000 | + | 12.0000i | −1.35225 | + | 0.676123i | ||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −1.73205 | + | 1.00000i | −0.0972817 | + | 0.0561656i | −0.547852 | − | 0.836576i | \(-0.684554\pi\) |
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | 17.8564 | + | 1.07180i | 0.998203 | + | 0.0599153i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 48.0000i | − | 2.67494i | ||||||
\(323\) | 3.46410 | + | 8.00000i | 0.192748 | + | 0.445132i | ||||
\(324\) | −18.0000 | −1.00000 | ||||||||
\(325\) | 9.19615 | − | 3.92820i | 0.510111 | − | 0.217898i | ||||
\(326\) | −4.00000 | + | 6.92820i | −0.221540 | + | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | −10.3923 | + | 6.00000i | −0.570352 | + | 0.329293i | ||||
\(333\) | 5.19615 | − | 3.00000i | 0.284747 | − | 0.164399i | ||||
\(334\) | 24.0000 | 1.31322 | ||||||||
\(335\) | −20.0000 | + | 10.0000i | −1.09272 | + | 0.546358i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.4449 | − | 17.0000i | −1.60396 | − | 0.926049i | −0.990684 | − | 0.136184i | \(-0.956516\pi\) |
−0.613280 | − | 0.789865i | \(-0.710150\pi\) | |||||||
\(338\) | 15.5885 | − | 9.00000i | 0.847900 | − | 0.489535i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.535898 | + | 8.92820i | −0.0290632 | + | 0.484200i | ||||
\(341\) | 7.00000 | 0.379071 | ||||||||
\(342\) | −15.5885 | + | 21.0000i | −0.842927 | + | 1.13555i | ||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | + | 41.5692i | 1.29025 | + | 2.23478i | ||||
\(347\) | 10.3923 | + | 6.00000i | 0.557888 | + | 0.322097i | 0.752297 | − | 0.658824i | \(-0.228946\pi\) |
−0.194409 | + | 0.980921i | \(0.562279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | −24.0000 | + | 32.0000i | −1.28285 | + | 1.71047i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.92820 | − | 4.00000i | 0.369274 | − | 0.213201i | ||||
\(353\) | 8.00000i | 0.425797i | 0.977074 | + | 0.212899i | \(0.0682904\pi\) | ||||
−0.977074 | + | 0.212899i | \(0.931710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.23205 | + | 1.86603i | −0.0653905 | + | 0.0990383i | ||||
\(356\) | 11.0000 | − | 19.0526i | 0.582999 | − | 1.00978i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.9808 | + | 15.0000i | 1.37313 | + | 0.792775i | ||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | − | 12.0000i | − | 0.630706i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | − | 13.8564i | 0.419314 | − | 0.726273i | ||||
\(365\) | 18.6603 | + | 12.3205i | 0.976722 | + | 0.644885i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8564 | + | 8.00000i | −0.723299 | + | 0.417597i | −0.815966 | − | 0.578101i | \(-0.803794\pi\) |
0.0926670 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 4.92820 | − | 7.46410i | 0.256205 | − | 0.388040i | ||||
\(371\) | 8.00000 | + | 13.8564i | 0.415339 | + | 0.719389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000i | 0.621336i | 0.950518 | + | 0.310668i | \(0.100553\pi\) | ||||
−0.950518 | + | 0.310668i | \(0.899447\pi\) | |||||||
\(374\) | 2.00000 | + | 3.46410i | 0.103418 | + | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.5885 | + | 9.00000i | 0.802846 | + | 0.463524i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | −3.39230 | + | 19.1962i | −0.174022 | + | 0.984742i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.19615 | + | 3.00000i | 0.265858 | + | 0.153493i | ||||
\(383\) | 5.19615 | + | 3.00000i | 0.265511 | + | 0.153293i | 0.626846 | − | 0.779143i | \(-0.284346\pi\) |
−0.361335 | + | 0.932436i | \(0.617679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.535898 | + | 8.92820i | −0.0273119 | + | 0.455023i | ||||
\(386\) | −16.0000 | − | 27.7128i | −0.814379 | − | 1.41055i | ||||
\(387\) | − | 6.00000i | − | 0.304997i | ||||||
\(388\) | 12.0000i | 0.609208i | ||||||||
\(389\) | −16.5000 | − | 28.5788i | −0.836583 | − | 1.44900i | −0.892735 | − | 0.450582i | \(-0.851216\pi\) |
0.0561516 | − | 0.998422i | \(-0.482117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0000 | + | 31.1769i | −0.906827 | + | 1.57067i | ||||
\(395\) | 1.23205 | − | 1.86603i | 0.0619912 | − | 0.0938899i | ||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 6.92820 | + | 4.00000i | 0.347717 | + | 0.200754i | 0.663679 | − | 0.748017i | \(-0.268994\pi\) |
−0.315963 | + | 0.948772i | \(0.602327\pi\) | |||||||
\(398\) | − | 26.0000i | − | 1.30326i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0000 | − | 16.0000i | 0.600000 | − | 0.800000i | ||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.1244 | + | 7.00000i | −0.603957 | + | 0.348695i | ||||
\(404\) | 15.0000 | − | 25.9808i | 0.746278 | − | 1.29259i | ||||
\(405\) | −11.0885 | + | 16.7942i | −0.550990 | + | 0.834512i | ||||
\(406\) | −72.0000 | −3.57330 | ||||||||
\(407\) | − | 2.00000i | − | 0.0991363i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | − | 4.33013i | −0.123617 | − | 0.214111i | 0.797574 | − | 0.603220i | \(-0.206116\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(410\) | 8.00000 | − | 4.00000i | 0.395092 | − | 0.197546i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.7128 | − | 16.0000i | 1.36531 | − | 0.788263i | ||||
\(413\) | −31.1769 | − | 18.0000i | −1.53412 | − | 0.885722i | ||||
\(414\) | −18.0000 | − | 31.1769i | −0.884652 | − | 1.53226i | ||||
\(415\) | −0.803848 | + | 13.3923i | −0.0394593 | + | 0.657402i | ||||
\(416\) | −8.00000 | + | 13.8564i | −0.392232 | + | 0.679366i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.46410 | + | 8.00000i | 0.169435 | + | 0.391293i | ||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.50000 | − | 12.9904i | 0.365528 | − | 0.633112i | −0.623333 | − | 0.781956i | \(-0.714222\pi\) |
0.988861 | + | 0.148844i | \(0.0475552\pi\) | |||||||
\(422\) | 8.66025 | − | 5.00000i | 0.421575 | − | 0.243396i | ||||
\(423\) | −15.5885 | − | 9.00000i | −0.757937 | − | 0.437595i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 6.00000i | 0.388057 | + | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.2487 | − | 14.0000i | 1.17348 | − | 0.677507i | ||||
\(428\) | 17.3205 | − | 10.0000i | 0.837218 | − | 0.483368i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.00000 | − | 8.00000i | −0.192897 | − | 0.385794i | ||||
\(431\) | −10.5000 | − | 18.1865i | −0.505767 | − | 0.876014i | −0.999978 | − | 0.00667224i | \(-0.997876\pi\) |
0.494211 | − | 0.869342i | \(-0.335457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46410 | − | 2.00000i | 0.166474 | − | 0.0961139i | −0.414448 | − | 0.910073i | \(-0.636025\pi\) |
0.580922 | + | 0.813959i | \(0.302692\pi\) | |||||||
\(434\) | 28.0000 | − | 48.4974i | 1.34404 | − | 2.32795i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.0000 | 1.43674 | ||||||||
\(437\) | −25.9808 | − | 3.00000i | −1.24283 | − | 0.143509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.50000 | + | 11.2583i | −0.310228 | + | 0.537331i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
0.668184 | + | 0.743996i | \(0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | −6.92820 | − | 4.00000i | −0.329541 | − | 0.190261i | ||||
\(443\) | −3.46410 | + | 2.00000i | −0.164584 | + | 0.0950229i | −0.580030 | − | 0.814595i | \(-0.696959\pi\) |
0.415445 | + | 0.909618i | \(0.363626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0000 | − | 22.0000i | −0.521450 | − | 1.04290i | ||||
\(446\) | 2.00000 | + | 3.46410i | 0.0947027 | + | 0.164030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 32.0000i | − | 1.51186i | ||||||
\(449\) | −31.0000 | −1.46298 | −0.731490 | − | 0.681852i | \(-0.761175\pi\) | ||||
−0.731490 | + | 0.681852i | \(0.761175\pi\) | |||||||
\(450\) | −3.58846 | + | 29.7846i | −0.169161 | + | 1.40406i | ||||
\(451\) | 1.00000 | − | 1.73205i | 0.0470882 | − | 0.0815591i | ||||
\(452\) | −20.7846 | + | 12.0000i | −0.977626 | + | 0.564433i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.0000 | − | 24.2487i | 0.657053 | − | 1.13805i | ||||
\(455\) | −8.00000 | − | 16.0000i | −0.375046 | − | 0.750092i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.0000i | 1.59045i | 0.606313 | + | 0.795226i | \(0.292648\pi\) | ||||
−0.606313 | + | 0.795226i | \(0.707352\pi\) | |||||||
\(458\) | 29.4449 | + | 17.0000i | 1.37587 | + | 0.794358i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.3923 | − | 14.7846i | −1.04405 | − | 0.689336i | ||||
\(461\) | 12.5000 | − | 21.6506i | 0.582183 | − | 1.00837i | −0.413037 | − | 0.910714i | \(-0.635532\pi\) |
0.995220 | − | 0.0976564i | \(-0.0311346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | 36.0000 | 1.67126 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.00000 | + | 13.8564i | 0.370593 | + | 0.641886i | ||||
\(467\) | 10.0000i | 0.462745i | 0.972865 | + | 0.231372i | \(0.0743216\pi\) | ||||
−0.972865 | + | 0.231372i | \(0.925678\pi\) | |||||||
\(468\) | − | 12.0000i | − | 0.554700i | ||||||
\(469\) | 20.0000 | + | 34.6410i | 0.923514 | + | 1.59957i | ||||
\(470\) | −26.7846 | − | 1.60770i | −1.23548 | − | 0.0741574i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.73205 | − | 1.00000i | −0.0796398 | − | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8205 | + | 14.9904i | 0.725895 | + | 0.687806i | ||||
\(476\) | 16.0000 | 0.733359 | ||||||||
\(477\) | 10.3923 | + | 6.00000i | 0.475831 | + | 0.274721i | ||||
\(478\) | −32.9090 | − | 19.0000i | −1.50522 | − | 0.869040i | ||||
\(479\) | 7.50000 | + | 12.9904i | 0.342684 | + | 0.593546i | 0.984930 | − | 0.172953i | \(-0.0553307\pi\) |
−0.642246 | + | 0.766498i | \(0.721997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | − | 17.3205i | −0.454545 | − | 0.787296i | ||||
\(485\) | 11.1962 | + | 7.39230i | 0.508391 | + | 0.335667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 38.0000i | − | 1.72194i | −0.508652 | − | 0.860972i | \(-0.669856\pi\) | ||
0.508652 | − | 0.860972i | \(-0.330144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 33.5885 | + | 22.1769i | 1.51737 | + | 1.00185i | ||||
\(491\) | −6.50000 | + | 11.2583i | −0.293341 | + | 0.508081i | −0.974598 | − | 0.223963i | \(-0.928100\pi\) |
0.681257 | + | 0.732045i | \(0.261434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000i | 0.810679i | ||||||||
\(494\) | −14.0000 | − | 10.3923i | −0.629890 | − | 0.467572i | ||||
\(495\) | 3.00000 | + | 6.00000i | 0.134840 | + | 0.269680i | ||||
\(496\) | −14.0000 | + | 24.2487i | −0.628619 | + | 1.08880i | ||||
\(497\) | 3.46410 | + | 2.00000i | 0.155386 | + | 0.0897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | − | 24.2487i | 0.626726 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153141i | \(-0.0489388\pi\) | |||||||
\(500\) | 7.53590 | + | 21.0526i | 0.337016 | + | 0.941499i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.0000i | 1.16044i | ||||||||
\(503\) | 22.5167 | − | 13.0000i | 1.00397 | − | 0.579641i | 0.0945483 | − | 0.995520i | \(-0.469859\pi\) |
0.909420 | + | 0.415879i | \(0.136526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.0000 | − | 30.0000i | −0.667491 | − | 1.33498i | ||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.3923 | − | 6.00000i | −0.461084 | − | 0.266207i | ||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | − | 34.6410i | 0.884748 | − | 1.53243i | ||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | 2.14359 | − | 35.7128i | 0.0944580 | − | 1.57369i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.19615 | + | 3.00000i | −0.228527 | + | 0.131940i | ||||
\(518\) | −13.8564 | − | 8.00000i | −0.608816 | − | 0.351500i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | 0.657162 | 0.328581 | − | 0.944476i | \(-0.393430\pi\) | ||||
0.328581 | + | 0.944476i | \(0.393430\pi\) | |||||||
\(522\) | −46.7654 | + | 27.0000i | −2.04686 | + | 1.18176i | ||||
\(523\) | −13.8564 | + | 8.00000i | −0.605898 | + | 0.349816i | −0.771358 | − | 0.636401i | \(-0.780422\pi\) |
0.165460 | + | 0.986216i | \(0.447089\pi\) | |||||||
\(524\) | −24.0000 | −1.04844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.1244 | − | 7.00000i | −0.528145 | − | 0.304925i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 17.8564 | + | 1.07180i | 0.775633 | + | 0.0465559i | ||||
\(531\) | −27.0000 | −1.17170 | ||||||||
\(532\) | 34.6410 | + | 4.00000i | 1.50188 | + | 0.173422i | ||||
\(533\) | 4.00000i | 0.173259i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.33975 | − | 22.3205i | 0.0579223 | − | 0.965000i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.19615 | + | 3.00000i | −0.224022 | + | 0.129339i | ||||
\(539\) | 9.00000 | 0.387657 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5000 | − | 19.9186i | −0.494424 | − | 0.856367i | 0.505556 | − | 0.862794i | \(-0.331288\pi\) |
−0.999979 | + | 0.00642713i | \(0.997954\pi\) | |||||||
\(542\) | 5.19615 | − | 3.00000i | 0.223194 | − | 0.128861i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.0000 | −0.685994 | ||||||||
\(545\) | 18.4808 | − | 27.9904i | 0.791629 | − | 1.19898i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0526 | − | 11.0000i | 0.814629 | − | 0.470326i | −0.0339321 | − | 0.999424i | \(-0.510803\pi\) |
0.848561 | + | 0.529098i | \(0.177470\pi\) | |||||||
\(548\) | 20.7846 | + | 12.0000i | 0.887875 | + | 0.512615i | ||||
\(549\) | 10.5000 | − | 18.1865i | 0.448129 | − | 0.776182i | ||||
\(550\) | 8.00000 | + | 6.00000i | 0.341121 | + | 0.255841i | ||||
\(551\) | −4.50000 | + | 38.9711i | −0.191706 | + | 1.66023i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.46410 | − | 2.00000i | −0.147309 | − | 0.0850487i | ||||
\(554\) | −28.0000 | + | 48.4974i | −1.18961 | + | 2.06046i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | + | 34.6410i | −0.848189 | + | 1.46911i | ||||
\(557\) | 12.1244 | − | 7.00000i | 0.513725 | − | 0.296600i | −0.220638 | − | 0.975356i | \(-0.570814\pi\) |
0.734364 | + | 0.678756i | \(0.237481\pi\) | |||||||
\(558\) | − | 42.0000i | − | 1.77800i | ||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −29.8564 | − | 19.7128i | −1.26166 | − | 0.833018i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.0000i | 0.843649i | ||||||||
\(563\) | 24.0000i | 1.01148i | 0.862686 | + | 0.505740i | \(0.168780\pi\) | ||||
−0.862686 | + | 0.505740i | \(0.831220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.60770 | + | 26.7846i | −0.0676362 | + | 1.12684i | ||||
\(566\) | −14.0000 | − | 24.2487i | −0.588464 | − | 1.01925i | ||||
\(567\) | 31.1769 | + | 18.0000i | 1.30931 | + | 0.755929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | −0.628833 | −0.314416 | − | 0.949285i | \(-0.601809\pi\) | ||||
−0.314416 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0000 | 0.544033 | 0.272017 | − | 0.962293i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962293i | \(0.412309\pi\) | |||||||
\(572\) | −3.46410 | − | 2.00000i | −0.144841 | − | 0.0836242i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.00000 | − | 13.8564i | −0.333914 | − | 0.578355i | ||||
\(575\) | −27.5885 | + | 11.7846i | −1.15052 | + | 0.491452i | ||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | 6.00000i | 0.249783i | 0.992170 | + | 0.124892i | \(0.0398583\pi\) | ||||
−0.992170 | + | 0.124892i | \(0.960142\pi\) | |||||||
\(578\) | 26.0000i | 1.08146i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −22.1769 | + | 33.5885i | −0.920846 | + | 1.39468i | ||||
\(581\) | 24.0000 | 0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.1962 | − | 7.39230i | −0.462904 | − | 0.305634i | ||||
\(586\) | −4.00000 | + | 6.92820i | −0.165238 | + | 0.286201i | ||||
\(587\) | 20.7846 | + | 12.0000i | 0.857873 | + | 0.495293i | 0.863299 | − | 0.504692i | \(-0.168394\pi\) |
−0.00542667 | + | 0.999985i | \(0.501727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.5000 | − | 18.1865i | −1.00950 | − | 0.749363i | ||||
\(590\) | −36.0000 | + | 18.0000i | −1.48210 | + | 0.741048i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.92820 | + | 4.00000i | 0.284747 | + | 0.164399i | ||||
\(593\) | 27.7128 | − | 16.0000i | 1.13803 | − | 0.657041i | 0.192087 | − | 0.981378i | \(-0.438474\pi\) |
0.945942 | + | 0.324337i | \(0.105141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.85641 | − | 14.9282i | 0.404073 | − | 0.611997i | ||||
\(596\) | −2.00000 | −0.0819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.7846 | − | 12.0000i | 0.849946 | − | 0.490716i | ||||
\(599\) | −6.00000 | − | 10.3923i | −0.245153 | − | 0.424618i | 0.717021 | − | 0.697051i | \(-0.245505\pi\) |
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | −13.8564 | + | 8.00000i | −0.564745 | + | 0.326056i | ||||
\(603\) | 25.9808 | + | 15.0000i | 1.05802 | + | 0.610847i | ||||
\(604\) | 9.00000 | + | 15.5885i | 0.366205 | + | 0.634285i | ||||
\(605\) | −22.3205 | − | 1.33975i | −0.907458 | − | 0.0544684i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | −34.6410 | − | 4.00000i | −1.40488 | − | 0.162221i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.87564 | − | 31.2487i | 0.0759426 | − | 1.26522i | ||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | 10.3923 | − | 6.00000i | 0.420084 | − | 0.242536i | ||||
\(613\) | 20.7846 | + | 12.0000i | 0.839482 | + | 0.484675i | 0.857088 | − | 0.515170i | \(-0.172271\pi\) |
−0.0176058 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5885 | − | 9.00000i | 0.627568 | − | 0.362326i | −0.152242 | − | 0.988343i | \(-0.548649\pi\) |
0.779809 | + | 0.626017i | \(0.215316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | −14.0000 | − | 28.0000i | −0.562254 | − | 1.12451i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.1051 | + | 22.0000i | −1.52665 | + | 0.881411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 60.0000 | 2.39808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.00000i | − | 0.319235i | ||||||
\(629\) | −2.00000 | + | 3.46410i | −0.0797452 | + | 0.138123i | ||||
\(630\) | 53.5692 | + | 3.21539i | 2.13425 | + | 0.128104i | ||||
\(631\) | −0.500000 | − | 0.866025i | −0.0199047 | − | 0.0344759i | 0.855901 | − | 0.517139i | \(-0.173003\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.00000 | 0.158860 | ||||||||
\(635\) | −12.0000 | + | 6.00000i | −0.476205 | + | 0.238103i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5885 | + | 9.00000i | −0.617637 | + | 0.356593i | ||||
\(638\) | 18.0000i | 0.712627i | ||||||||
\(639\) | 3.00000 | 0.118678 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | + | 18.1865i | −0.414725 | + | 0.718325i | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) |
0.580674 | + | 0.814136i | \(0.302789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.8372 | − | 23.0000i | −1.57102 | − | 0.907031i | −0.996044 | − | 0.0888646i | \(-0.971676\pi\) |
−0.574981 | − | 0.818167i | \(-0.694991\pi\) | |||||||
\(644\) | −24.0000 | + | 41.5692i | −0.945732 | + | 1.63806i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 17.3205i | 0.0786889 | − | 0.681466i | ||||
\(647\) | − | 6.00000i | − | 0.235884i | −0.993020 | − | 0.117942i | \(-0.962370\pi\) | ||
0.993020 | − | 0.117942i | \(-0.0376297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | + | 7.79423i | −0.176640 | + | 0.305950i | ||||
\(650\) | −19.8564 | − | 2.39230i | −0.778832 | − | 0.0938339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.92820 | − | 4.00000i | 0.271329 | − | 0.156652i | ||||
\(653\) | − | 10.0000i | − | 0.391330i | −0.980671 | − | 0.195665i | \(-0.937313\pi\) | ||
0.980671 | − | 0.195665i | \(-0.0626866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7846 | + | 22.3923i | −0.577683 | + | 0.874940i | ||||
\(656\) | 4.00000 | + | 6.92820i | 0.156174 | + | 0.270501i | ||||
\(657\) | − | 30.0000i | − | 1.17041i | ||||||
\(658\) | 48.0000i | 1.87123i | ||||||||
\(659\) | 10.0000 | + | 17.3205i | 0.389545 | + | 0.674711i | 0.992388 | − | 0.123148i | \(-0.0392990\pi\) |
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.50000 | + | 12.9904i | 0.291716 | + | 0.505267i | 0.974216 | − | 0.225619i | \(-0.0724404\pi\) |
−0.682499 | + | 0.730886i | \(0.739107\pi\) | |||||||
\(662\) | −34.6410 | − | 20.0000i | −1.34636 | − | 0.777322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.0718 | − | 29.8564i | 0.972243 | − | 1.15778i | ||||
\(666\) | −12.0000 | −0.464991 | ||||||||
\(667\) | −46.7654 | − | 27.0000i | −1.81076 | − | 1.04544i | ||||
\(668\) | −20.7846 | − | 12.0000i | −0.804181 | − | 0.464294i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44.6410 | + | 2.67949i | 1.72463 | + | 0.103518i | ||||
\(671\) | −3.50000 | − | 6.06218i | −0.135116 | − | 0.234028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000i | 0.770943i | 0.922720 | + | 0.385472i | \(0.125961\pi\) | ||||
−0.922720 | + | 0.385472i | \(0.874039\pi\) | |||||||
\(674\) | 34.0000 | + | 58.8897i | 1.30963 | + | 2.26835i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.0000 | −0.692308 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 20.7846i | 0.460518 | − | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.1244 | − | 7.00000i | −0.464266 | − | 0.268044i | ||||
\(683\) | − | 30.0000i | − | 1.14792i | −0.818884 | − | 0.573959i | \(-0.805407\pi\) | ||
0.818884 | − | 0.573959i | \(-0.194593\pi\) | |||||||
\(684\) | 24.0000 | − | 10.3923i | 0.917663 | − | 0.397360i | ||||
\(685\) | 24.0000 | − | 12.0000i | 0.916993 | − | 0.458496i | ||||
\(686\) | 8.00000 | − | 13.8564i | 0.305441 | − | 0.529040i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.92820 | − | 4.00000i | 0.264135 | − | 0.152499i | ||||
\(689\) | −4.00000 | + | 6.92820i | −0.152388 | + | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.00000 | 0.114125 | 0.0570627 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570627 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(692\) | − | 48.0000i | − | 1.82469i | ||||||
\(693\) | 10.3923 | − | 6.00000i | 0.394771 | − | 0.227921i | ||||
\(694\) | −12.0000 | − | 20.7846i | −0.455514 | − | 0.788973i | ||||
\(695\) | 20.0000 | + | 40.0000i | 0.758643 | + | 1.51729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.46410 | + | 2.00000i | −0.131212 | + | 0.0757554i | ||||
\(698\) | 24.2487 | + | 14.0000i | 0.917827 | + | 0.529908i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 36.7846 | − | 15.7128i | 1.39033 | − | 0.593889i | ||||
\(701\) | −3.00000 | + | 5.19615i | −0.113308 | + | 0.196256i | −0.917102 | − | 0.398652i | \(-0.869478\pi\) |
0.803794 | + | 0.594908i | \(0.202811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.19615 | + | 7.00000i | −0.195977 | + | 0.264010i | ||||
\(704\) | −8.00000 | −0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.00000 | − | 13.8564i | 0.301084 | − | 0.521493i | ||||
\(707\) | −51.9615 | + | 30.0000i | −1.95421 | + | 1.12827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5000 | + | 21.6506i | 0.469447 | + | 0.813107i | 0.999390 | − | 0.0349269i | \(-0.0111198\pi\) |
−0.529943 | + | 0.848034i | \(0.677787\pi\) | |||||||
\(710\) | 4.00000 | − | 2.00000i | 0.150117 | − | 0.0750587i | ||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.3731 | − | 21.0000i | 1.36218 | − | 0.786456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | + | 2.00000i | −0.149592 | + | 0.0747958i | ||||
\(716\) | −15.0000 | − | 25.9808i | −0.560576 | − | 0.970947i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.6410 | − | 20.0000i | 1.29279 | − | 0.746393i | ||||
\(719\) | −10.5000 | + | 18.1865i | −0.391584 | + | 0.678243i | −0.992659 | − | 0.120950i | \(-0.961406\pi\) |
0.601075 | + | 0.799193i | \(0.294739\pi\) | |||||||
\(720\) | −26.7846 | − | 1.60770i | −0.998203 | − | 0.0599153i | ||||
\(721\) | −64.0000 | −2.38348 | ||||||||
\(722\) | 8.66025 | − | 37.0000i | 0.322301 | − | 1.37700i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.00000 | + | 10.3923i | −0.222988 | + | 0.386227i | ||||
\(725\) | 17.6769 | + | 41.3827i | 0.656504 | + | 1.53691i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.92820 | − | 4.00000i | −0.256953 | − | 0.148352i | 0.365991 | − | 0.930618i | \(-0.380730\pi\) |
−0.622944 | + | 0.782267i | \(0.714063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −20.0000 | − | 40.0000i | −0.740233 | − | 1.48047i | ||||
\(731\) | 2.00000 | + | 3.46410i | 0.0739727 | + | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00000i | 0.221615i | 0.993842 | + | 0.110808i | \(0.0353437\pi\) | ||||
−0.993842 | + | 0.110808i | \(0.964656\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.0000 | − | 41.5692i | 0.884652 | − | 1.53226i | ||||
\(737\) | 8.66025 | − | 5.00000i | 0.319005 | − | 0.184177i | ||||
\(738\) | −10.3923 | − | 6.00000i | −0.382546 | − | 0.220863i | ||||
\(739\) | −14.5000 | + | 25.1147i | −0.533391 | + | 0.923861i | 0.465848 | + | 0.884865i | \(0.345749\pi\) |
−0.999239 | + | 0.0389959i | \(0.987584\pi\) | |||||||
\(740\) | −8.00000 | + | 4.00000i | −0.294086 | + | 0.147043i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 32.0000i | − | 1.17476i | ||||||
\(743\) | 43.3013 | + | 25.0000i | 1.58857 | + | 0.917161i | 0.993543 | + | 0.113455i | \(0.0361917\pi\) |
0.595026 | + | 0.803706i | \(0.297142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23205 | + | 1.86603i | −0.0451388 | + | 0.0683659i | ||||
\(746\) | 12.0000 | − | 20.7846i | 0.439351 | − | 0.760979i | ||||
\(747\) | 15.5885 | − | 9.00000i | 0.570352 | − | 0.329293i | ||||
\(748\) | − | 4.00000i | − | 0.146254i | ||||||
\(749\) | −40.0000 | −1.46157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5000 | − | 35.5070i | −0.748056 | − | 1.29567i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) |
0.200698 | − | 0.979653i | \(-0.435679\pi\) | |||||||
\(752\) | − | 24.0000i | − | 0.875190i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.0000 | − | 31.1769i | −0.655521 | − | 1.13540i | ||||
\(755\) | 20.0885 | + | 1.20577i | 0.731094 | + | 0.0438825i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5167 | − | 13.0000i | −0.818382 | − | 0.472493i | 0.0314762 | − | 0.999505i | \(-0.489979\pi\) |
−0.849858 | + | 0.527011i | \(0.823312\pi\) | |||||||
\(758\) | −50.2295 | − | 29.0000i | −1.82442 | − | 1.05333i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.9615 | − | 30.0000i | −1.88113 | − | 1.08607i | ||||
\(764\) | −3.00000 | − | 5.19615i | −0.108536 | − | 0.187990i | ||||
\(765\) | 0.803848 | − | 13.3923i | 0.0290632 | − | 0.484200i | ||||
\(766\) | −6.00000 | − | 10.3923i | −0.216789 | − | 0.375489i | ||||
\(767\) | − | 18.0000i | − | 0.649942i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | + | 4.33013i | 0.0901523 | + | 0.156148i | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 9.85641 | − | 14.9282i | 0.355200 | − | 0.537975i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.0000i | 1.15171i | ||||||||
\(773\) | −29.4449 | + | 17.0000i | −1.05906 | + | 0.611448i | −0.925172 | − | 0.379549i | \(-0.876079\pi\) |
−0.133887 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(774\) | −6.00000 | + | 10.3923i | −0.215666 | + | 0.373544i | ||||
\(775\) | −34.7487 | − | 4.18653i | −1.24821 | − | 0.150385i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 66.0000i | 2.36621i | ||||||||
\(779\) | −8.00000 | + | 3.46410i | −0.286630 | + | 0.124114i | ||||
\(780\) | 0 |