Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,2,Mod(5,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("42.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.f (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: | \(0.335371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.17 |
Dual form | 42.2.f.a.5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 1.50000i | 0.387298 | + | 0.670820i | 0.992085 | − | 0.125567i | \(-0.0400750\pi\) |
−0.604787 | + | 0.796387i | \(0.706742\pi\) | |||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | −1.50000 | − | 0.866025i | −0.474342 | − | 0.273861i | ||||
\(11\) | −2.59808 | − | 1.50000i | −0.783349 | − | 0.452267i | 0.0542666 | − | 0.998526i | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | −0.866025 | − | 1.50000i | −0.250000 | − | 0.433013i | ||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 1.73205 | − | 2.00000i | 0.462910 | − | 0.534522i | ||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.73205 | + | 3.00000i | −0.420084 | + | 0.727607i | −0.995947 | − | 0.0899392i | \(-0.971333\pi\) |
0.575863 | + | 0.817546i | \(0.304666\pi\) | |||||||
\(18\) | 2.59808 | + | 1.50000i | 0.612372 | + | 0.353553i | ||||
\(19\) | 3.00000 | − | 1.73205i | 0.688247 | − | 0.397360i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | −0.866025 | + | 4.50000i | −0.188982 | + | 0.981981i | ||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | 5.19615 | − | 3.00000i | 1.08347 | − | 0.625543i | 0.151642 | − | 0.988436i | \(-0.451544\pi\) |
0.931831 | + | 0.362892i | \(0.118211\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 1.00000 | − | 1.73205i | 0.200000 | − | 0.346410i | ||||
\(26\) | −1.73205 | − | 3.00000i | −0.339683 | − | 0.588348i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | −2.59808 | + | 1.50000i | −0.474342 | + | 0.273861i | ||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | − | 3.46410i | − | 0.594089i | ||||||
\(35\) | −3.46410 | − | 3.00000i | −0.585540 | − | 0.507093i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | −1.73205 | + | 3.00000i | −0.280976 | + | 0.486664i | ||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | −1.50000 | + | 0.866025i | −0.237171 | + | 0.136931i | ||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | −1.50000 | − | 4.33013i | −0.231455 | − | 0.668153i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −2.59808 | + | 1.50000i | −0.391675 | + | 0.226134i | ||||
\(45\) | 2.59808 | − | 4.50000i | 0.387298 | − | 0.670820i | ||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 3.46410 | + | 6.00000i | 0.505291 | + | 0.875190i | 0.999981 | + | 0.00612051i | \(0.00194823\pi\) |
−0.494690 | + | 0.869069i | \(0.664718\pi\) | |||||||
\(48\) | −1.73205 | −0.250000 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 2.00000i | 0.282843i | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | −7.79423 | − | 4.50000i | −1.07062 | − | 0.618123i | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | − | 5.19615i | − | 0.700649i | ||||||
\(56\) | −0.866025 | − | 2.50000i | −0.115728 | − | 0.334077i | ||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | −0.866025 | + | 1.50000i | −0.112747 | + | 0.195283i | −0.916877 | − | 0.399170i | \(-0.869298\pi\) |
0.804130 | + | 0.594454i | \(0.202632\pi\) | |||||||
\(60\) | 1.50000 | − | 2.59808i | 0.193649 | − | 0.335410i | ||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 1.73205 | 0.219971 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.19615 | + | 3.00000i | −0.644503 | + | 0.372104i | ||||
\(66\) | 2.59808 | − | 4.50000i | 0.319801 | − | 0.553912i | ||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 1.73205 | + | 3.00000i | 0.210042 | + | 0.363803i | ||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | 4.50000 | + | 0.866025i | 0.537853 | + | 0.103510i | ||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 2.59808 | − | 1.50000i | 0.306186 | − | 0.176777i | ||||
\(73\) | 6.00000 | + | 3.46410i | 0.702247 | + | 0.405442i | 0.808184 | − | 0.588930i | \(-0.200451\pi\) |
−0.105937 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(74\) | −1.73205 | − | 1.00000i | −0.201347 | − | 0.116248i | ||||
\(75\) | −1.73205 | − | 3.00000i | −0.200000 | − | 0.346410i | ||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | 7.79423 | + | 1.50000i | 0.888235 | + | 0.170941i | ||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0.866025 | − | 1.50000i | 0.0968246 | − | 0.167705i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −6.00000 | + | 3.46410i | −0.662589 | + | 0.382546i | ||||
\(83\) | −8.66025 | −0.950586 | −0.475293 | − | 0.879827i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879827i | \(0.657658\pi\) | |||||||
\(84\) | 3.46410 | + | 3.00000i | 0.377964 | + | 0.327327i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 6.92820 | − | 4.00000i | 0.747087 | − | 0.431331i | ||||
\(87\) | −4.50000 | − | 2.59808i | −0.482451 | − | 0.278543i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −5.19615 | − | 9.00000i | −0.550791 | − | 0.953998i | −0.998218 | − | 0.0596775i | \(-0.980993\pi\) |
0.447427 | − | 0.894321i | \(-0.352341\pi\) | |||||||
\(90\) | 5.19615i | 0.547723i | ||||||||
\(91\) | −3.00000 | − | 8.66025i | −0.314485 | − | 0.907841i | ||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | −2.59808 | + | 1.50000i | −0.269408 | + | 0.155543i | ||||
\(94\) | −6.00000 | − | 3.46410i | −0.618853 | − | 0.357295i | ||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 5.19615i | 0.527589i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) | ||||
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | −2.59808 | + | 6.50000i | −0.262445 | + | 0.656599i | ||||
\(99\) | 9.00000i | 0.904534i | ||||||||
\(100\) | −1.00000 | − | 1.73205i | −0.100000 | − | 0.173205i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | −5.19615 | − | 3.00000i | −0.514496 | − | 0.297044i | ||||
\(103\) | −3.00000 | + | 1.73205i | −0.295599 | + | 0.170664i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
0.344865 | + | 0.938652i | \(0.387925\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | −7.50000 | + | 2.59808i | −0.731925 | + | 0.253546i | ||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | 2.59808 | − | 1.50000i | 0.251166 | − | 0.145010i | −0.369132 | − | 0.929377i | \(-0.620345\pi\) |
0.620298 | + | 0.784366i | \(0.287012\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 2.59808 | + | 4.50000i | 0.247717 | + | 0.429058i | ||||
\(111\) | 3.46410 | 0.328798 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | − | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | \(-0.809095\pi\) | ||
0.825479 | − | 0.564433i | \(-0.190905\pi\) | |||||||
\(114\) | 3.00000 | + | 5.19615i | 0.280976 | + | 0.486664i | ||||
\(115\) | 9.00000 | + | 5.19615i | 0.839254 | + | 0.484544i | ||||
\(116\) | −2.59808 | − | 1.50000i | −0.241225 | − | 0.139272i | ||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | − | 1.73205i | − | 0.159448i | ||||||
\(119\) | 1.73205 | − | 9.00000i | 0.158777 | − | 0.825029i | ||||
\(120\) | 3.00000i | 0.273861i | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | − | 10.3923i | 0.541002 | − | 0.937043i | ||||
\(124\) | −1.50000 | + | 0.866025i | −0.134704 | + | 0.0777714i | ||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | −7.79423 | − | 1.50000i | −0.694365 | − | 0.133631i | ||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −6.92820 | + | 12.0000i | −0.609994 | + | 1.05654i | ||||
\(130\) | 3.00000 | − | 5.19615i | 0.263117 | − | 0.455733i | ||||
\(131\) | −2.59808 | − | 4.50000i | −0.226995 | − | 0.393167i | 0.729921 | − | 0.683531i | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | 5.19615i | 0.452267i | ||||||||
\(133\) | −6.00000 | + | 6.92820i | −0.520266 | + | 0.600751i | ||||
\(134\) | − | 2.00000i | − | 0.172774i | ||||||
\(135\) | −4.50000 | − | 7.79423i | −0.387298 | − | 0.670820i | ||||
\(136\) | −3.00000 | − | 1.73205i | −0.257248 | − | 0.148522i | ||||
\(137\) | 15.5885 | + | 9.00000i | 1.33181 | + | 0.768922i | 0.985577 | − | 0.169226i | \(-0.0541268\pi\) |
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(138\) | 5.19615 | + | 9.00000i | 0.442326 | + | 0.766131i | ||||
\(139\) | 17.3205i | 1.46911i | 0.678551 | + | 0.734553i | \(0.262608\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | −4.33013 | + | 1.50000i | −0.365963 | + | 0.126773i | ||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | −6.00000 | − | 10.3923i | −0.503509 | − | 0.872103i | ||||
\(143\) | 5.19615 | − | 9.00000i | 0.434524 | − | 0.752618i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | 4.50000 | − | 2.59808i | 0.373705 | − | 0.215758i | ||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | −1.73205 | − | 12.0000i | −0.142857 | − | 0.989743i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −15.5885 | + | 9.00000i | −1.27706 | + | 0.737309i | −0.976306 | − | 0.216394i | \(-0.930570\pi\) |
−0.300750 | + | 0.953703i | \(0.597237\pi\) | |||||||
\(150\) | 3.00000 | + | 1.73205i | 0.244949 | + | 0.141421i | ||||
\(151\) | −3.50000 | + | 6.06218i | −0.284826 | + | 0.493333i | −0.972567 | − | 0.232623i | \(-0.925269\pi\) |
0.687741 | + | 0.725956i | \(0.258602\pi\) | |||||||
\(152\) | 1.73205 | + | 3.00000i | 0.140488 | + | 0.243332i | ||||
\(153\) | 10.3923 | 0.840168 | ||||||||
\(154\) | −7.50000 | + | 2.59808i | −0.604367 | + | 0.209359i | ||||
\(155\) | − | 3.00000i | − | 0.240966i | ||||||
\(156\) | 5.19615 | − | 3.00000i | 0.416025 | − | 0.240192i | ||||
\(157\) | −18.0000 | − | 10.3923i | −1.43656 | − | 0.829396i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | −0.866025 | − | 0.500000i | −0.0688973 | − | 0.0397779i | ||||
\(159\) | −13.5000 | + | 7.79423i | −1.07062 | + | 0.618123i | ||||
\(160\) | 1.73205i | 0.136931i | ||||||||
\(161\) | −10.3923 | + | 12.0000i | −0.819028 | + | 0.945732i | ||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | −7.00000 | − | 12.1244i | −0.548282 | − | 0.949653i | −0.998392 | − | 0.0566798i | \(-0.981949\pi\) |
0.450110 | − | 0.892973i | \(-0.351385\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | −7.79423 | − | 4.50000i | −0.606780 | − | 0.350325i | ||||
\(166\) | 7.50000 | − | 4.33013i | 0.582113 | − | 0.336083i | ||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | −4.50000 | − | 0.866025i | −0.347183 | − | 0.0668153i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.19615 | − | 3.00000i | 0.398527 | − | 0.230089i | ||||
\(171\) | −9.00000 | − | 5.19615i | −0.688247 | − | 0.397360i | ||||
\(172\) | −4.00000 | + | 6.92820i | −0.304997 | + | 0.528271i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 5.19615 | 0.393919 | ||||||||
\(175\) | −1.00000 | + | 5.19615i | −0.0755929 | + | 0.392792i | ||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | 9.00000 | + | 5.19615i | 0.674579 | + | 0.389468i | ||||
\(179\) | 10.3923 | + | 6.00000i | 0.776757 | + | 0.448461i | 0.835280 | − | 0.549825i | \(-0.185306\pi\) |
−0.0585225 | + | 0.998286i | \(0.518639\pi\) | |||||||
\(180\) | −2.59808 | − | 4.50000i | −0.193649 | − | 0.335410i | ||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 6.92820 | + | 6.00000i | 0.513553 | + | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | −1.73205 | + | 3.00000i | −0.127343 | + | 0.220564i | ||||
\(186\) | 1.50000 | − | 2.59808i | 0.109985 | − | 0.190500i | ||||
\(187\) | 9.00000 | − | 5.19615i | 0.658145 | − | 0.379980i | ||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 12.9904 | − | 4.50000i | 0.944911 | − | 0.327327i | ||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −0.866025 | + | 1.50000i | −0.0625000 | + | 0.108253i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | −2.59808 | − | 4.50000i | −0.186531 | − | 0.323081i | ||||
\(195\) | 10.3923i | 0.744208i | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | −4.50000 | − | 7.79423i | −0.319801 | − | 0.553912i | ||||
\(199\) | 9.00000 | + | 5.19615i | 0.637993 | + | 0.368345i | 0.783841 | − | 0.620962i | \(-0.213258\pi\) |
−0.145848 | + | 0.989307i | \(0.546591\pi\) | |||||||
\(200\) | 1.73205 | + | 1.00000i | 0.122474 | + | 0.0707107i | ||||
\(201\) | 1.73205 | + | 3.00000i | 0.122169 | + | 0.211604i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | + | 7.50000i | 0.182349 | + | 0.526397i | ||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 1.73205 | − | 3.00000i | 0.120678 | − | 0.209020i | ||||
\(207\) | −15.5885 | − | 9.00000i | −1.08347 | − | 0.625543i | ||||
\(208\) | 3.00000 | − | 1.73205i | 0.208013 | − | 0.120096i | ||||
\(209\) | −10.3923 | −0.718851 | ||||||||
\(210\) | 5.19615 | − | 6.00000i | 0.358569 | − | 0.414039i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −7.79423 | + | 4.50000i | −0.535310 | + | 0.309061i | ||||
\(213\) | 18.0000 | + | 10.3923i | 1.23334 | + | 0.712069i | ||||
\(214\) | −1.50000 | + | 2.59808i | −0.102538 | + | 0.177601i | ||||
\(215\) | −6.92820 | − | 12.0000i | −0.472500 | − | 0.818393i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 4.50000 | + | 0.866025i | 0.305480 | + | 0.0587896i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | 10.3923 | − | 6.00000i | 0.702247 | − | 0.405442i | ||||
\(220\) | −4.50000 | − | 2.59808i | −0.303390 | − | 0.175162i | ||||
\(221\) | −10.3923 | − | 6.00000i | −0.699062 | − | 0.403604i | ||||
\(222\) | −3.00000 | + | 1.73205i | −0.201347 | + | 0.116248i | ||||
\(223\) | − | 25.9808i | − | 1.73980i | −0.493228 | − | 0.869900i | \(-0.664183\pi\) | ||
0.493228 | − | 0.869900i | \(-0.335817\pi\) | |||||||
\(224\) | −2.59808 | − | 0.500000i | −0.173591 | − | 0.0334077i | ||||
\(225\) | −6.00000 | −0.400000 | ||||||||
\(226\) | 6.00000 | + | 10.3923i | 0.399114 | + | 0.691286i | ||||
\(227\) | 2.59808 | − | 4.50000i | 0.172440 | − | 0.298675i | −0.766832 | − | 0.641848i | \(-0.778168\pi\) |
0.939272 | + | 0.343172i | \(0.111501\pi\) | |||||||
\(228\) | −5.19615 | − | 3.00000i | −0.344124 | − | 0.198680i | ||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 9.00000 | − | 10.3923i | 0.592157 | − | 0.683763i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 15.5885 | − | 9.00000i | 1.02123 | − | 0.589610i | 0.106773 | − | 0.994283i | \(-0.465948\pi\) |
0.914461 | + | 0.404674i | \(0.132615\pi\) | |||||||
\(234\) | −5.19615 | + | 9.00000i | −0.339683 | + | 0.588348i | ||||
\(235\) | −6.00000 | + | 10.3923i | −0.391397 | + | 0.677919i | ||||
\(236\) | 0.866025 | + | 1.50000i | 0.0563735 | + | 0.0976417i | ||||
\(237\) | 1.73205 | 0.112509 | ||||||||
\(238\) | 3.00000 | + | 8.66025i | 0.194461 | + | 0.561361i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | −1.50000 | − | 2.59808i | −0.0968246 | − | 0.167705i | ||||
\(241\) | −22.5000 | − | 12.9904i | −1.44935 | − | 0.836784i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 1.73205 | + | 1.00000i | 0.111340 | + | 0.0642824i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.2583 | + | 4.50000i | 0.719268 | + | 0.287494i | ||||
\(246\) | 12.0000i | 0.765092i | ||||||||
\(247\) | 6.00000 | + | 10.3923i | 0.381771 | + | 0.661247i | ||||
\(248\) | 0.866025 | − | 1.50000i | 0.0549927 | − | 0.0952501i | ||||
\(249\) | −7.50000 | + | 12.9904i | −0.475293 | + | 0.823232i | ||||
\(250\) | −10.5000 | + | 6.06218i | −0.664078 | + | 0.383406i | ||||
\(251\) | 19.0526 | 1.20259 | 0.601293 | − | 0.799028i | \(-0.294652\pi\) | ||||
0.601293 | + | 0.799028i | \(0.294652\pi\) | |||||||
\(252\) | 7.50000 | − | 2.59808i | 0.472456 | − | 0.163663i | ||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −9.52628 | + | 5.50000i | −0.597732 | + | 0.345101i | ||||
\(255\) | −5.19615 | + | 9.00000i | −0.325396 | + | 0.563602i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.19615 | + | 9.00000i | 0.324127 | + | 0.561405i | 0.981335 | − | 0.192304i | \(-0.0615961\pi\) |
−0.657208 | + | 0.753709i | \(0.728263\pi\) | |||||||
\(258\) | − | 13.8564i | − | 0.862662i | ||||||
\(259\) | −4.00000 | − | 3.46410i | −0.248548 | − | 0.215249i | ||||
\(260\) | 6.00000i | 0.372104i | ||||||||
\(261\) | −7.79423 | + | 4.50000i | −0.482451 | + | 0.278543i | ||||
\(262\) | 4.50000 | + | 2.59808i | 0.278011 | + | 0.160510i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | −2.59808 | − | 4.50000i | −0.159901 | − | 0.276956i | ||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 1.73205 | − | 9.00000i | 0.106199 | − | 0.551825i | ||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | 1.00000 | + | 1.73205i | 0.0610847 | + | 0.105802i | ||||
\(269\) | 14.7224 | − | 25.5000i | 0.897643 | − | 1.55476i | 0.0671428 | − | 0.997743i | \(-0.478612\pi\) |
0.830500 | − | 0.557019i | \(-0.188055\pi\) | |||||||
\(270\) | 7.79423 | + | 4.50000i | 0.474342 | + | 0.273861i | ||||
\(271\) | 4.50000 | − | 2.59808i | 0.273356 | − | 0.157822i | −0.357056 | − | 0.934083i | \(-0.616219\pi\) |
0.630412 | + | 0.776261i | \(0.282886\pi\) | |||||||
\(272\) | 3.46410 | 0.210042 | ||||||||
\(273\) | −15.5885 | − | 3.00000i | −0.943456 | − | 0.181568i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −5.19615 | + | 3.00000i | −0.313340 | + | 0.180907i | ||||
\(276\) | −9.00000 | − | 5.19615i | −0.541736 | − | 0.312772i | ||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | −8.66025 | − | 15.0000i | −0.519408 | − | 0.899640i | ||||
\(279\) | 5.19615i | 0.311086i | ||||||||
\(280\) | 3.00000 | − | 3.46410i | 0.179284 | − | 0.207020i | ||||
\(281\) | − | 30.0000i | − | 1.78965i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||
0.446417 | − | 0.894825i | \(-0.352700\pi\) | |||||||
\(282\) | −10.3923 | + | 6.00000i | −0.618853 | + | 0.357295i | ||||
\(283\) | 24.0000 | + | 13.8564i | 1.42665 | + | 0.823678i | 0.996855 | − | 0.0792477i | \(-0.0252518\pi\) |
0.429797 | + | 0.902926i | \(0.358585\pi\) | |||||||
\(284\) | 10.3923 | + | 6.00000i | 0.616670 | + | 0.356034i | ||||
\(285\) | 9.00000 | − | 5.19615i | 0.533114 | − | 0.307794i | ||||
\(286\) | 10.3923i | 0.614510i | ||||||||
\(287\) | −17.3205 | + | 6.00000i | −1.02240 | + | 0.354169i | ||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | 2.50000 | + | 4.33013i | 0.147059 | + | 0.254713i | ||||
\(290\) | −2.59808 | + | 4.50000i | −0.152564 | + | 0.264249i | ||||
\(291\) | 7.79423 | + | 4.50000i | 0.456906 | + | 0.263795i | ||||
\(292\) | 6.00000 | − | 3.46410i | 0.351123 | − | 0.202721i | ||||
\(293\) | −19.0526 | −1.11306 | −0.556531 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556531 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(294\) | 7.50000 | + | 9.52628i | 0.437409 | + | 0.555584i | ||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | −1.73205 | + | 1.00000i | −0.100673 | + | 0.0581238i | ||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 9.00000 | − | 15.5885i | 0.521356 | − | 0.903015i | ||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | −3.46410 | −0.200000 | ||||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | − | 7.00000i | − | 0.402805i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | − | 1.73205i | −0.172062 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.00000 | + | 5.19615i | −0.514496 | + | 0.297044i | ||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | 5.19615 | − | 6.00000i | 0.296078 | − | 0.341882i | ||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 1.50000 | + | 2.59808i | 0.0851943 | + | 0.147561i | ||||
\(311\) | −6.92820 | + | 12.0000i | −0.392862 | + | 0.680458i | −0.992826 | − | 0.119570i | \(-0.961848\pi\) |
0.599963 | + | 0.800027i | \(0.295182\pi\) | |||||||
\(312\) | −3.00000 | + | 5.19615i | −0.169842 | + | 0.294174i | ||||
\(313\) | 1.50000 | − | 0.866025i | 0.0847850 | − | 0.0489506i | −0.457008 | − | 0.889463i | \(-0.651079\pi\) |
0.541793 | + | 0.840512i | \(0.317746\pi\) | |||||||
\(314\) | 20.7846 | 1.17294 | ||||||||
\(315\) | −2.59808 | + | 13.5000i | −0.146385 | + | 0.760639i | ||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | 12.9904 | − | 7.50000i | 0.729612 | − | 0.421242i | −0.0886679 | − | 0.996061i | \(-0.528261\pi\) |
0.818280 | + | 0.574819i | \(0.194928\pi\) | |||||||
\(318\) | 7.79423 | − | 13.5000i | 0.437079 | − | 0.757042i | ||||
\(319\) | −4.50000 | + | 7.79423i | −0.251952 | + | 0.436393i | ||||
\(320\) | −0.866025 | − | 1.50000i | −0.0484123 | − | 0.0838525i | ||||
\(321\) | − | 5.19615i | − | 0.290021i | ||||||
\(322\) | 3.00000 | − | 15.5885i | 0.167183 | − | 0.868711i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | 6.00000 | + | 3.46410i | 0.332820 | + | 0.192154i | ||||
\(326\) | 12.1244 | + | 7.00000i | 0.671506 | + | 0.387694i | ||||
\(327\) | −1.73205 | − | 3.00000i | −0.0957826 | − | 0.165900i | ||||
\(328\) | 6.92820i | 0.382546i | ||||||||
\(329\) | −13.8564 | − | 12.0000i | −0.763928 | − | 0.661581i | ||||
\(330\) | 9.00000 | 0.495434 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | −4.33013 | + | 7.50000i | −0.237647 | + | 0.411616i | ||||
\(333\) | 3.00000 | − | 5.19615i | 0.164399 | − | 0.284747i | ||||
\(334\) | 15.0000 | − | 8.66025i | 0.820763 | − | 0.473868i | ||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 4.33013 | − | 1.50000i | 0.236228 | − | 0.0818317i | ||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | −0.866025 | + | 0.500000i | −0.0471056 | + | 0.0271964i | ||||
\(339\) | −18.0000 | − | 10.3923i | −0.977626 | − | 0.564433i | ||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | 2.59808 | + | 4.50000i | 0.140694 | + | 0.243689i | ||||
\(342\) | 10.3923 | 0.561951 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | 15.5885 | − | 9.00000i | 0.839254 | − | 0.484544i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | −4.50000 | + | 2.59808i | −0.241225 | + | 0.139272i | ||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | −1.73205 | − | 5.00000i | −0.0925820 | − | 0.267261i | ||||
\(351\) | − | 18.0000i | − | 0.960769i | ||||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | −17.3205 | + | 30.0000i | −0.921878 | + | 1.59674i | −0.125370 | + | 0.992110i | \(0.540012\pi\) |
−0.796507 | + | 0.604629i | \(0.793321\pi\) | |||||||
\(354\) | −2.59808 | − | 1.50000i | −0.138086 | − | 0.0797241i | ||||
\(355\) | −18.0000 | + | 10.3923i | −0.955341 | + | 0.551566i | ||||
\(356\) | −10.3923 | −0.550791 | ||||||||
\(357\) | −12.0000 | − | 10.3923i | −0.635107 | − | 0.550019i | ||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −5.19615 | + | 3.00000i | −0.274242 | + | 0.158334i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) |
0.356572 | + | 0.934268i | \(0.383946\pi\) | |||||||
\(360\) | 4.50000 | + | 2.59808i | 0.237171 | + | 0.136931i | ||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | −3.46410 | − | 6.00000i | −0.182069 | − | 0.315353i | ||||
\(363\) | −3.46410 | −0.181818 | ||||||||
\(364\) | −9.00000 | − | 1.73205i | −0.471728 | − | 0.0907841i | ||||
\(365\) | 12.0000i | 0.628109i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.5000 | − | 11.2583i | −1.01789 | − | 0.587680i | −0.104399 | − | 0.994535i | \(-0.533292\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | −5.19615 | − | 3.00000i | −0.270868 | − | 0.156386i | ||||
\(369\) | −10.3923 | − | 18.0000i | −0.541002 | − | 0.937043i | ||||
\(370\) | − | 3.46410i | − | 0.180090i | ||||||
\(371\) | 23.3827 | + | 4.50000i | 1.21397 | + | 0.233628i | ||||
\(372\) | 3.00000i | 0.155543i | ||||||||
\(373\) | −16.0000 | − | 27.7128i | −0.828449 | − | 1.43492i | −0.899255 | − | 0.437425i | \(-0.855891\pi\) |
0.0708063 | − | 0.997490i | \(-0.477443\pi\) | |||||||
\(374\) | −5.19615 | + | 9.00000i | −0.268687 | + | 0.465379i | ||||
\(375\) | 10.5000 | − | 18.1865i | 0.542218 | − | 0.939149i | ||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | 10.3923 | 0.535231 | ||||||||
\(378\) | −9.00000 | + | 10.3923i | −0.462910 | + | 0.534522i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 5.19615 | − | 3.00000i | 0.266557 | − | 0.153897i | ||||
\(381\) | 9.52628 | − | 16.5000i | 0.488046 | − | 0.845321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.73205 | + | 3.00000i | 0.0885037 | + | 0.153293i | 0.906879 | − | 0.421392i | \(-0.138458\pi\) |
−0.818375 | + | 0.574684i | \(0.805125\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 4.50000 | + | 12.9904i | 0.229341 | + | 0.662051i | ||||
\(386\) | 23.0000i | 1.17067i | ||||||||
\(387\) | 12.0000 | + | 20.7846i | 0.609994 | + | 1.05654i | ||||
\(388\) | 4.50000 | + | 2.59808i | 0.228453 | + | 0.131897i | ||||
\(389\) | −15.5885 | − | 9.00000i | −0.790366 | − | 0.456318i | 0.0497253 | − | 0.998763i | \(-0.484165\pi\) |
−0.840091 | + | 0.542445i | \(0.817499\pi\) | |||||||
\(390\) | −5.19615 | − | 9.00000i | −0.263117 | − | 0.455733i | ||||
\(391\) | 20.7846i | 1.05112i | ||||||||
\(392\) | 4.33013 | + | 5.50000i | 0.218704 | + | 0.277792i | ||||
\(393\) | −9.00000 | −0.453990 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | −0.866025 | + | 1.50000i | −0.0435745 | + | 0.0754732i | ||||
\(396\) | 7.79423 | + | 4.50000i | 0.391675 | + | 0.226134i | ||||
\(397\) | −24.0000 | + | 13.8564i | −1.20453 | + | 0.695433i | −0.961558 | − | 0.274601i | \(-0.911454\pi\) |
−0.242967 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(398\) | −10.3923 | −0.520919 | ||||||||
\(399\) | 5.19615 | + | 15.0000i | 0.260133 | + | 0.750939i | ||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 10.3923 | − | 6.00000i | 0.518967 | − | 0.299626i | −0.217545 | − | 0.976050i | \(-0.569805\pi\) |
0.736512 | + | 0.676425i | \(0.236472\pi\) | |||||||
\(402\) | −3.00000 | − | 1.73205i | −0.149626 | − | 0.0863868i | ||||
\(403\) | 3.00000 | − | 5.19615i | 0.149441 | − | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.5885 | −0.774597 | ||||||||
\(406\) | −6.00000 | − | 5.19615i | −0.297775 | − | 0.257881i | ||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | −5.19615 | + | 3.00000i | −0.257248 | + | 0.148522i | ||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | −10.3923 | − | 6.00000i | −0.513239 | − | 0.296319i | ||||
\(411\) | 27.0000 | − | 15.5885i | 1.33181 | − | 0.768922i | ||||
\(412\) | 3.46410i | 0.170664i | ||||||||
\(413\) | 0.866025 | − | 4.50000i | 0.0426143 | − | 0.221431i | ||||
\(414\) | 18.0000 | 0.884652 | ||||||||
\(415\) | −7.50000 | − | 12.9904i | −0.368161 | − | 0.637673i | ||||
\(416\) | −1.73205 | + | 3.00000i | −0.0849208 | + | 0.147087i | ||||
\(417\) | 25.9808 | + | 15.0000i | 1.27228 | + | 0.734553i | ||||
\(418\) | 9.00000 | − | 5.19615i | 0.440204 | − | 0.254152i | ||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | −1.50000 | + | 7.79423i | −0.0731925 | + | 0.380319i | ||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | −3.46410 | + | 2.00000i | −0.168630 | + | 0.0973585i | ||||
\(423\) | 10.3923 | − | 18.0000i | 0.505291 | − | 0.875190i | ||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | 3.46410 | + | 6.00000i | 0.168034 | + | 0.291043i | ||||
\(426\) | −20.7846 | −1.00702 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 3.00000i | − | 0.145010i | ||||||
\(429\) | −9.00000 | − | 15.5885i | −0.434524 | − | 0.752618i | ||||
\(430\) | 12.0000 | + | 6.92820i | 0.578691 | + | 0.334108i | ||||
\(431\) | −20.7846 | − | 12.0000i | −1.00116 | − | 0.578020i | −0.0925683 | − | 0.995706i | \(-0.529508\pi\) |
−0.908591 | + | 0.417687i | \(0.862841\pi\) | |||||||
\(432\) | 2.59808 | + | 4.50000i | 0.125000 | + | 0.216506i | ||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | −4.33013 | + | 1.50000i | −0.207853 | + | 0.0720023i | ||||
\(435\) | − | 9.00000i | − | 0.431517i | ||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | 10.3923 | − | 18.0000i | 0.497131 | − | 0.861057i | ||||
\(438\) | −6.00000 | + | 10.3923i | −0.286691 | + | 0.496564i | ||||
\(439\) | 31.5000 | − | 18.1865i | 1.50341 | − | 0.867996i | 0.503421 | − | 0.864041i | \(-0.332075\pi\) |
0.999992 | − | 0.00395451i | \(-0.00125876\pi\) | |||||||
\(440\) | 5.19615 | 0.247717 | ||||||||
\(441\) | −19.5000 | − | 7.79423i | −0.928571 | − | 0.371154i | ||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 1.73205 | − | 3.00000i | 0.0821995 | − | 0.142374i | ||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | 12.9904 | + | 22.5000i | 0.615112 | + | 1.06541i | ||||
\(447\) | 31.1769i | 1.47462i | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 30.0000i | 1.41579i | 0.706319 | + | 0.707894i | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 5.19615 | − | 3.00000i | 0.244949 | − | 0.141421i | ||||
\(451\) | −18.0000 | − | 10.3923i | −0.847587 | − | 0.489355i | ||||
\(452\) | −10.3923 | − | 6.00000i | −0.488813 | − | 0.282216i | ||||
\(453\) | 6.06218 | + | 10.5000i | 0.284826 | + | 0.493333i | ||||
\(454\) | 5.19615i | 0.243868i | ||||||||
\(455\) | 10.3923 | − | 12.0000i | 0.487199 | − | 0.562569i | ||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 2.50000 | + | 4.33013i | 0.116945 | + | 0.202555i | 0.918556 | − | 0.395292i | \(-0.129357\pi\) |
−0.801611 | + | 0.597847i | \(0.796023\pi\) | |||||||
\(458\) | 6.92820 | − | 12.0000i | 0.323734 | − | 0.560723i | ||||
\(459\) | 9.00000 | − | 15.5885i | 0.420084 | − | 0.727607i | ||||
\(460\) | 9.00000 | − | 5.19615i | 0.419627 | − | 0.242272i | ||||
\(461\) | −13.8564 | −0.645357 | −0.322679 | − | 0.946509i | \(-0.604583\pi\) | ||||
−0.322679 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(462\) | −2.59808 | + | 13.5000i | −0.120873 | + | 0.628077i | ||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −2.59808 | + | 1.50000i | −0.120613 | + | 0.0696358i | ||||
\(465\) | −4.50000 | − | 2.59808i | −0.208683 | − | 0.120483i | ||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | −15.5885 | − | 27.0000i | −0.721348 | − | 1.24941i | −0.960460 | − | 0.278419i | \(-0.910190\pi\) |
0.239112 | − | 0.970992i | \(-0.423144\pi\) | |||||||
\(468\) | − | 10.3923i | − | 0.480384i | ||||||
\(469\) | 1.00000 | − | 5.19615i | 0.0461757 | − | 0.239936i | ||||
\(470\) | − | 12.0000i | − | 0.553519i | ||||||
\(471\) | −31.1769 | + | 18.0000i | −1.43656 | + | 0.829396i | ||||
\(472\) | −1.50000 | − | 0.866025i | −0.0690431 | − | 0.0398621i | ||||
\(473\) | 20.7846 | + | 12.0000i | 0.955677 | + | 0.551761i | ||||
\(474\) | −1.50000 | + | 0.866025i | −0.0688973 | + | 0.0397779i | ||||
\(475\) | − | 6.92820i | − | 0.317888i | ||||||
\(476\) | −6.92820 | − | 6.00000i | −0.317554 | − | 0.275010i | ||||
\(477\) | 27.0000i | 1.23625i | ||||||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | −3.46410 | + | 6.00000i | −0.158279 | + | 0.274147i | −0.934248 | − | 0.356624i | \(-0.883928\pi\) |
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(480\) | 2.59808 | + | 1.50000i | 0.118585 | + | 0.0684653i | ||||
\(481\) | −6.00000 | + | 3.46410i | −0.273576 | + | 0.157949i | ||||
\(482\) | 25.9808 | 1.18339 | ||||||||
\(483\) | 9.00000 | + | 25.9808i | 0.409514 | + | 1.18217i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | −7.79423 | + | 4.50000i | −0.353918 | + | 0.204334i | ||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | −0.500000 | + | 0.866025i | −0.0226572 | + | 0.0392434i | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2487 | −1.09656 | ||||||||
\(490\) | −12.0000 | + | 1.73205i | −0.542105 | + | 0.0782461i | ||||
\(491\) | − | 33.0000i | − | 1.48927i | −0.667472 | − | 0.744635i | \(-0.732624\pi\) | ||
0.667472 | − | 0.744635i | \(-0.267376\pi\) | |||||||
\(492\) | −6.00000 | − | 10.3923i | −0.270501 | − | 0.468521i | ||||
\(493\) | 9.00000 | + | 5.19615i | 0.405340 | + | 0.234023i | ||||
\(494\) | −10.3923 | − | 6.00000i | −0.467572 | − | 0.269953i | ||||
\(495\) | −13.5000 | + | 7.79423i | −0.606780 | + | 0.350325i | ||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −10.3923 | − | 30.0000i | −0.466159 | − | 1.34568i | ||||
\(498\) | − | 15.0000i | − | 0.672166i | ||||||
\(499\) | −11.0000 | − | 19.0526i | −0.492428 | − | 0.852910i | 0.507534 | − | 0.861632i | \(-0.330557\pi\) |
−0.999962 | + | 0.00872186i | \(0.997224\pi\) | |||||||
\(500\) | 6.06218 | − | 10.5000i | 0.271109 | − | 0.469574i | ||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | −16.5000 | + | 9.52628i | −0.736431 | + | 0.425179i | ||||
\(503\) | 38.1051 | 1.69902 | 0.849512 | − | 0.527570i | \(-0.176897\pi\) | ||||
0.849512 | + | 0.527570i | \(0.176897\pi\) | |||||||
\(504\) | −5.19615 | + | 6.00000i | −0.231455 | + | 0.267261i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.5885 | − | 9.00000i | 0.692991 | − | 0.400099i | ||||
\(507\) | 0.866025 | − | 1.50000i | 0.0384615 | − | 0.0666173i | ||||
\(508\) | 5.50000 | − | 9.52628i | 0.244023 | − | 0.422660i | ||||
\(509\) | 9.52628 | + | 16.5000i | 0.422245 | + | 0.731350i | 0.996159 | − | 0.0875661i | \(-0.0279089\pi\) |
−0.573914 | + | 0.818916i | \(0.694576\pi\) | |||||||
\(510\) | − | 10.3923i | − | 0.460179i | ||||||
\(511\) | −18.0000 | − | 3.46410i | −0.796273 | − | 0.153243i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −15.5885 | + | 9.00000i | −0.688247 | + | 0.397360i | ||||
\(514\) | −9.00000 | − | 5.19615i | −0.396973 | − | 0.229192i | ||||
\(515\) | −5.19615 | − | 3.00000i | −0.228970 | − | 0.132196i | ||||
\(516\) | 6.92820 | + | 12.0000i | 0.304997 | + | 0.528271i | ||||
\(517\) | − | 20.7846i | − | 0.914106i | ||||||
\(518\) | 5.19615 | + | 1.00000i | 0.228306 | + | 0.0439375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | − | 5.19615i | −0.131559 | − | 0.227866i | ||||
\(521\) | −13.8564 | + | 24.0000i | −0.607060 | + | 1.05146i | 0.384662 | + | 0.923057i | \(0.374318\pi\) |
−0.991722 | + | 0.128402i | \(0.959015\pi\) | |||||||
\(522\) | 4.50000 | − | 7.79423i | 0.196960 | − | 0.341144i | ||||
\(523\) | −33.0000 | + | 19.0526i | −1.44299 | + | 0.833110i | −0.998048 | − | 0.0624496i | \(-0.980109\pi\) |
−0.444941 | + | 0.895560i | \(0.646775\pi\) | |||||||
\(524\) | −5.19615 | −0.226995 | ||||||||
\(525\) | 6.92820 | + | 6.00000i | 0.302372 | + | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.19615 | − | 3.00000i | 0.226348 | − | 0.130682i | ||||
\(528\) | 4.50000 | + | 2.59808i | 0.195837 | + | 0.113067i | ||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 7.79423 | + | 13.5000i | 0.338560 | + | 0.586403i | ||||
\(531\) | 5.19615 | 0.225494 | ||||||||
\(532\) | 3.00000 | + | 8.66025i | 0.130066 | + | 0.375470i | ||||
\(533\) | 24.0000i | 1.03956i | ||||||||
\(534\) | 15.5885 | − | 9.00000i | 0.674579 | − | 0.389468i | ||||
\(535\) | 4.50000 | + | 2.59808i | 0.194552 | + | 0.112325i | ||||
\(536\) | −1.73205 | − | 1.00000i | −0.0748132 | − | 0.0431934i | ||||
\(537\) | 18.0000 | − | 10.3923i | 0.776757 | − | 0.448461i | ||||
\(538\) | 29.4449i | 1.26946i | ||||||||
\(539\) | −20.7846 | + | 3.00000i | −0.895257 | + | 0.129219i | ||||
\(540\) | −9.00000 | −0.387298 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | −2.59808 | + | 4.50000i | −0.111597 | + | 0.193292i | ||||
\(543\) | 10.3923 | + | 6.00000i | 0.445976 | + | 0.257485i | ||||
\(544\) | −3.00000 | + | 1.73205i | −0.128624 | + | 0.0742611i | ||||
\(545\) | 3.46410 | 0.148386 | ||||||||
\(546\) | 15.0000 | − | 5.19615i | 0.641941 | − | 0.222375i | ||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 15.5885 | − | 9.00000i | 0.665906 | − | 0.384461i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.00000 | − | 5.19615i | 0.127920 | − | 0.221565i | ||||
\(551\) | −5.19615 | − | 9.00000i | −0.221364 | − | 0.383413i | ||||
\(552\) | 10.3923 | 0.442326 | ||||||||
\(553\) | −2.00000 | − | 1.73205i | −0.0850487 | − | 0.0736543i | ||||
\(554\) | − | 8.00000i | − | 0.339887i | ||||||
\(555\) | 3.00000 | + | 5.19615i | 0.127343 | + | 0.220564i | ||||
\(556\) | 15.0000 | + | 8.66025i | 0.636142 | + | 0.367277i | ||||
\(557\) | −2.59808 | − | 1.50000i | −0.110084 | − | 0.0635570i | 0.443947 | − | 0.896053i | \(-0.353578\pi\) |
−0.554031 | + | 0.832496i | \(0.686911\pi\) | |||||||
\(558\) | −2.59808 | − | 4.50000i | −0.109985 | − | 0.190500i | ||||
\(559\) | − | 27.7128i | − | 1.17213i | ||||||
\(560\) | −0.866025 | + | 4.50000i | −0.0365963 | + | 0.190160i | ||||
\(561\) | − | 18.0000i | − | 0.759961i | ||||||
\(562\) | 15.0000 | + | 25.9808i | 0.632737 | + | 1.09593i | ||||
\(563\) | −12.9904 | + | 22.5000i | −0.547479 | + | 0.948262i | 0.450967 | + | 0.892541i | \(0.351079\pi\) |
−0.998446 | + | 0.0557214i | \(0.982254\pi\) | |||||||
\(564\) | 6.00000 | − | 10.3923i | 0.252646 | − | 0.437595i | ||||
\(565\) | 18.0000 | − | 10.3923i | 0.757266 | − | 0.437208i | ||||
\(566\) | −27.7128 | −1.16486 | ||||||||
\(567\) | 4.50000 | − | 23.3827i | 0.188982 | − | 0.981981i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 5.19615 | − | 3.00000i | 0.217834 | − | 0.125767i | −0.387113 | − | 0.922032i | \(-0.626528\pi\) |
0.604947 | + | 0.796266i | \(0.293194\pi\) | |||||||
\(570\) | −5.19615 | + | 9.00000i | −0.217643 | + | 0.376969i | ||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −5.19615 | − | 9.00000i | −0.217262 | − | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | − | 13.8564i | 0.500870 | − | 0.578355i | ||||
\(575\) | − | 12.0000i | − | 0.500435i | ||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −1.50000 | − | 0.866025i | −0.0624458 | − | 0.0360531i | 0.468452 | − | 0.883489i | \(-0.344812\pi\) |
−0.530898 | + | 0.847436i | \(0.678145\pi\) | |||||||
\(578\) | −4.33013 | − | 2.50000i | −0.180110 | − | 0.103986i | ||||
\(579\) | −19.9186 | − | 34.5000i | −0.827788 | − | 1.43377i | ||||
\(580\) | − | 5.19615i | − | 0.215758i | ||||||
\(581\) | 21.6506 | − | 7.50000i | 0.898220 | − | 0.311152i | ||||
\(582\) | −9.00000 | −0.373062 | ||||||||
\(583\) | 13.5000 | + | 23.3827i | 0.559113 | + | 0.968412i | ||||
\(584\) | −3.46410 | + | 6.00000i | −0.143346 | + | 0.248282i | ||||
\(585\) | 15.5885 | + | 9.00000i | 0.644503 | + | 0.372104i | ||||
\(586\) | 16.5000 | − | 9.52628i | 0.681609 | − | 0.393527i | ||||
\(587\) | −15.5885 | −0.643404 | −0.321702 | − | 0.946841i | \(-0.604255\pi\) | ||||
−0.321702 | + | 0.946841i | \(0.604255\pi\) | |||||||
\(588\) | −11.2583 | − | 4.50000i | −0.464286 | − | 0.185577i | ||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 2.59808 | − | 1.50000i | 0.106961 | − | 0.0617540i | ||||
\(591\) | 27.0000 | + | 15.5885i | 1.11063 | + | 0.641223i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −19.0526 | − | 33.0000i | −0.782395 | − | 1.35515i | −0.930543 | − | 0.366182i | \(-0.880665\pi\) |
0.148148 | − | 0.988965i | \(-0.452669\pi\) | |||||||
\(594\) | −15.5885 | −0.639602 | ||||||||
\(595\) | 15.0000 | − | 5.19615i | 0.614940 | − | 0.213021i | ||||
\(596\) | 18.0000i | 0.737309i | ||||||||
\(597\) | 15.5885 | − | 9.00000i | 0.637993 | − | 0.368345i | ||||
\(598\) | −18.0000 | − | 10.3923i | −0.736075 | − | 0.424973i | ||||
\(599\) | 25.9808 | + | 15.0000i | 1.06155 | + | 0.612883i | 0.925859 | − | 0.377869i | \(-0.123343\pi\) |
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(600\) | 3.00000 | − | 1.73205i | 0.122474 | − | 0.0707107i | ||||
\(601\) | − | 29.4449i | − | 1.20108i | −0.799594 | − | 0.600541i | \(-0.794952\pi\) | ||
0.799594 | − | 0.600541i | \(-0.205048\pi\) | |||||||
\(602\) | −13.8564 | + | 16.0000i | −0.564745 | + | 0.652111i | ||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | 3.50000 | + | 6.06218i | 0.142413 | + | 0.246667i | ||||
\(605\) | 1.73205 | − | 3.00000i | 0.0704179 | − | 0.121967i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5000 | − | 11.2583i | 0.791481 | − | 0.456962i | −0.0490029 | − | 0.998799i | \(-0.515604\pi\) |
0.840484 | + | 0.541837i | \(0.182271\pi\) | |||||||
\(608\) | 3.46410 | 0.140488 | ||||||||
\(609\) | 13.5000 | + | 2.59808i | 0.547048 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.7846 | + | 12.0000i | −0.840855 | + | 0.485468i | ||||
\(612\) | 5.19615 | − | 9.00000i | 0.210042 | − | 0.363803i | ||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 12.1244 | + | 21.0000i | 0.489299 | + | 0.847491i | ||||
\(615\) | 20.7846 | 0.838116 | ||||||||
\(616\) | −1.50000 | + | 7.79423i | −0.0604367 | + | 0.314038i | ||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | −3.00000 | − | 5.19615i | −0.120678 | − | 0.209020i | ||||
\(619\) | 6.00000 | + | 3.46410i | 0.241160 | + | 0.139234i | 0.615710 | − | 0.787973i | \(-0.288869\pi\) |
−0.374550 | + | 0.927207i | \(0.622203\pi\) | |||||||
\(620\) | −2.59808 | − | 1.50000i | −0.104341 | − | 0.0602414i | ||||
\(621\) | −27.0000 | + | 15.5885i | −1.08347 | + | 0.625543i | ||||
\(622\) | − | 13.8564i | − | 0.555591i | ||||||
\(623\) | 20.7846 | + | 18.0000i | 0.832718 | + | 0.721155i | ||||
\(624\) | − | 6.00000i | − | 0.240192i | ||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −0.866025 | + | 1.50000i | −0.0346133 | + | 0.0599521i | ||||
\(627\) | −9.00000 | + | 15.5885i | −0.359425 | + | 0.622543i | ||||
\(628\) | −18.0000 | + | 10.3923i | −0.718278 | + | 0.414698i | ||||
\(629\) | −6.92820 | −0.276246 | ||||||||
\(630\) | −4.50000 | − | 12.9904i | −0.179284 | − | 0.517549i | ||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | −0.866025 | + | 0.500000i | −0.0344486 | + | 0.0198889i | ||||
\(633\) | 3.46410 | − | 6.00000i | 0.137686 | − | 0.238479i | ||||
\(634\) | −7.50000 | + | 12.9904i | −0.297863 | + | 0.515914i | ||||
\(635\) | 9.52628 | + | 16.5000i | 0.378039 | + | 0.654783i | ||||
\(636\) | 15.5885i | 0.618123i | ||||||||
\(637\) | 15.0000 | + | 19.0526i | 0.594322 | + | 0.754890i | ||||
\(638\) | − | 9.00000i | − | 0.356313i | ||||||
\(639\) | 31.1769 | − | 18.0000i | 1.23334 | − | 0.712069i | ||||
\(640\) | 1.50000 | + | 0.866025i | 0.0592927 | + | 0.0342327i | ||||
\(641\) | 20.7846 | + | 12.0000i | 0.820943 | + | 0.473972i | 0.850741 | − | 0.525584i | \(-0.176153\pi\) |
−0.0297987 | + | 0.999556i | \(0.509487\pi\) | |||||||
\(642\) | 2.59808 | + | 4.50000i | 0.102538 | + | 0.177601i | ||||
\(643\) | − | 17.3205i | − | 0.683054i | −0.939872 | − | 0.341527i | \(-0.889056\pi\) | ||
0.939872 | − | 0.341527i | \(-0.110944\pi\) | |||||||
\(644\) | 5.19615 | + | 15.0000i | 0.204757 | + | 0.591083i | ||||
\(645\) | −24.0000 | −0.944999 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | −7.79423 | − | 4.50000i | −0.306186 | − | 0.176777i | ||||
\(649\) | 4.50000 | − | 2.59808i | 0.176640 | − | 0.101983i | ||||
\(650\) | −6.92820 | −0.271746 | ||||||||
\(651\) | 5.19615 | − | 6.00000i | 0.203653 | − | 0.235159i | ||||
\(652\) | −14.0000 | −0.548282 | ||||||||
\(653\) | 2.59808 | − | 1.50000i | 0.101671 | − | 0.0586995i | −0.448303 | − | 0.893882i | \(-0.647971\pi\) |
0.549973 | + | 0.835182i | \(0.314638\pi\) | |||||||
\(654\) | 3.00000 | + | 1.73205i | 0.117309 | + | 0.0677285i | ||||
\(655\) | 4.50000 | − | 7.79423i | 0.175830 | − | 0.304546i | ||||
\(656\) | −3.46410 | − | 6.00000i | −0.135250 | − | 0.234261i | ||||
\(657\) | − | 20.7846i | − | 0.810885i | ||||||
\(658\) | 18.0000 | + | 3.46410i | 0.701713 | + | 0.135045i | ||||
\(659\) | − | 12.0000i | − | 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | −7.79423 | + | 4.50000i | −0.303390 | + | 0.175162i | ||||
\(661\) | −6.00000 | − | 3.46410i | −0.233373 | − | 0.134738i | 0.378754 | − | 0.925497i | \(-0.376353\pi\) |
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(662\) | −6.92820 | − | 4.00000i | −0.269272 | − | 0.155464i | ||||
\(663\) | −18.0000 | + | 10.3923i | −0.699062 | + | 0.403604i | ||||
\(664\) | − | 8.66025i | − | 0.336083i | ||||||
\(665\) | −15.5885 | − | 3.00000i | −0.604494 | − | 0.116335i | ||||
\(666\) | 6.00000i | 0.232495i | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | −8.66025 | + | 15.0000i | −0.335075 | + | 0.580367i | ||||
\(669\) | −38.9711 | − | 22.5000i | −1.50671 | − | 0.869900i | ||||
\(670\) | 3.00000 | − | 1.73205i | 0.115900 | − | 0.0669150i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.00000 | + | 3.46410i | −0.115728 | + | 0.133631i | ||||
\(673\) | −41.0000 | −1.58043 | −0.790217 | − | 0.612827i | \(-0.790032\pi\) | ||||
−0.790217 | + | 0.612827i | \(0.790032\pi\) | |||||||
\(674\) | −11.2583 | + | 6.50000i | −0.433655 | + | 0.250371i | ||||
\(675\) | −5.19615 | + | 9.00000i | −0.200000 | + | 0.346410i | ||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | −2.59808 | − | 4.50000i | −0.0998522 | − | 0.172949i | 0.811771 | − | 0.583976i | \(-0.198504\pi\) |
−0.911623 | + | 0.411027i | \(0.865170\pi\) | |||||||
\(678\) | 20.7846 | 0.798228 | ||||||||
\(679\) | −4.50000 | − | 12.9904i | −0.172694 | − | 0.498525i | ||||
\(680\) | − | 6.00000i | − | 0.230089i | ||||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | −4.50000 | − | 2.59808i | −0.172314 | − | 0.0994855i | ||||
\(683\) | −18.1865 | − | 10.5000i | −0.695888 | − | 0.401771i | 0.109926 | − | 0.993940i | \(-0.464939\pi\) |
−0.805814 | + | 0.592168i | \(0.798272\pi\) | |||||||
\(684\) | −9.00000 | + | 5.19615i | −0.344124 | + | 0.198680i | ||||
\(685\) | 31.1769i | 1.19121i | ||||||||
\(686\) | 0.866025 | − | 18.5000i | 0.0330650 | − | 0.706333i | ||||
\(687\) | 24.0000i | 0.915657i | ||||||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | 15.5885 | − | 27.0000i | 0.593873 | − | 1.02862i | ||||
\(690\) | −9.00000 | + | 15.5885i | −0.342624 | + | 0.593442i | ||||
\(691\) | −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 | ||||||||
\(693\) | −7.79423 | − | 22.5000i | −0.296078 | − | 0.854704i | ||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −25.9808 | + | 15.0000i | −0.985506 | + | 0.568982i | ||||
\(696\) | 2.59808 | − | 4.50000i | 0.0984798 | − | 0.170572i | ||||
\(697\) | −12.0000 | + | 20.7846i | −0.454532 | + | 0.787273i | ||||
\(698\) | −5.19615 | − | 9.00000i | −0.196677 | − | 0.340655i | ||||
\(699\) | − | 31.1769i | − | 1.17922i | ||||||
\(700\) | 4.00000 | + | 3.46410i | 0.151186 | + | 0.130931i | ||||
\(701\) | 3.00000i | 0.113308i | 0.998394 | + | 0.0566542i | \(0.0180433\pi\) | ||||
−0.998394 | + | 0.0566542i | \(0.981957\pi\) | |||||||
\(702\) | 9.00000 | + | 15.5885i | 0.339683 | + | 0.588348i | ||||
\(703\) | 6.00000 | + | 3.46410i | 0.226294 | + | 0.130651i | ||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 10.3923 | + | 18.0000i | 0.391397 | + | 0.677919i | ||||
\(706\) | − | 34.6410i | − | 1.30373i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.00000 | 0.112747 | ||||||||
\(709\) | 19.0000 | + | 32.9090i | 0.713560 | + | 1.23592i | 0.963512 | + | 0.267664i | \(0.0862517\pi\) |
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(710\) | 10.3923 | − | 18.0000i | 0.390016 | − | 0.675528i | ||||
\(711\) | 1.50000 | − | 2.59808i | 0.0562544 | − | 0.0974355i | ||||
\(712\) | 9.00000 | − | 5.19615i | 0.337289 | − | 0.194734i | ||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | 15.5885 | + | 3.00000i | 0.583383 | + | 0.112272i | ||||
\(715\) | 18.0000 | 0.673162 | ||||||||
\(716\) | 10.3923 | − | 6.00000i | 0.388379 | − | 0.224231i | ||||
\(717\) | −9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | ||||
\(718\) | 3.00000 | − | 5.19615i | 0.111959 | − | 0.193919i | ||||
\(719\) | 22.5167 | + | 39.0000i | 0.839730 | + | 1.45445i | 0.890121 | + | 0.455725i | \(0.150620\pi\) |
−0.0503909 | + | 0.998730i | \(0.516047\pi\) | |||||||
\(720\) | −5.19615 | −0.193649 | ||||||||
\(721\) | 6.00000 | − | 6.92820i | 0.223452 | − | 0.258020i | ||||
\(722\) | − | 7.00000i | − | 0.260513i | ||||||
\(723\) | −38.9711 | + | 22.5000i | −1.44935 | + | 0.836784i | ||||
\(724\) | 6.00000 | + | 3.46410i | 0.222988 | + | 0.128742i | ||||
\(725\) | −5.19615 | − | 3.00000i | −0.192980 | − | 0.111417i | ||||
\(726\) | 3.00000 | − | 1.73205i | 0.111340 | − | 0.0642824i | ||||
\(727\) | 29.4449i | 1.09205i | 0.837769 | + | 0.546025i | \(0.183860\pi\) | ||||
−0.837769 | + | 0.546025i | \(0.816140\pi\) | |||||||
\(728\) | 8.66025 | − | 3.00000i | 0.320970 | − | 0.111187i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −6.00000 | − | 10.3923i | −0.222070 | − | 0.384636i | ||||
\(731\) | 13.8564 | − | 24.0000i | 0.512498 | − | 0.887672i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000 | − | 17.3205i | 1.10808 | − | 0.639748i | 0.169745 | − | 0.985488i | \(-0.445706\pi\) |
0.938330 | + | 0.345740i | \(0.112372\pi\) | |||||||
\(734\) | 22.5167 | 0.831105 | ||||||||
\(735\) | 16.5000 | − | 12.9904i | 0.608612 | − | 0.479157i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 5.19615 | − | 3.00000i | 0.191403 | − | 0.110506i | ||||
\(738\) | 18.0000 | + | 10.3923i | 0.662589 | + | 0.382546i | ||||
\(739\) | 5.00000 | − | 8.66025i | 0.183928 | − | 0.318573i | −0.759287 | − | 0.650756i | \(-0.774452\pi\) |
0.943215 | + | 0.332184i | \(0.107785\pi\) | |||||||
\(740\) | 1.73205 | + | 3.00000i | 0.0636715 | + | 0.110282i | ||||
\(741\) | 20.7846 | 0.763542 | ||||||||
\(742\) | −22.5000 | + | 7.79423i | −0.826001 | + | 0.286135i | ||||
\(743\) | 18.0000i | 0.660356i | 0.943919 | + | 0.330178i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330178i | \(0.892891\pi\) | |||||||
\(744\) | −1.50000 | − | 2.59808i | −0.0549927 | − | 0.0952501i | ||||
\(745\) | −27.0000 | − | 15.5885i | −0.989203 | − | 0.571117i | ||||
\(746\) | 27.7128 | + | 16.0000i | 1.01464 | + | 0.585802i | ||||
\(747\) | 12.9904 | + | 22.5000i | 0.475293 | + | 0.823232i | ||||
\(748\) | − | 10.3923i | − | 0.379980i | ||||||
\(749\) | −5.19615 | + | 6.00000i | −0.189863 | + | 0.219235i | ||||
\(750\) | 21.0000i | 0.766812i | ||||||||
\(751\) | 5.50000 | + | 9.52628i | 0.200698 | + | 0.347619i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 3.46410 | − | 6.00000i | 0.126323 | − | 0.218797i | ||||
\(753\) | 16.5000 | − | 28.5788i | 0.601293 | − | 1.04147i | ||||
\(754\) | −9.00000 | + | 5.19615i | −0.327761 | + | 0.189233i | ||||
\(755\) | −12.1244 | −0.441250 | ||||||||
\(756\) | 2.59808 | − | 13.5000i | 0.0944911 | − | 0.490990i | ||||
\(757\) | 4.00000 | 0.145382 | 0.0726912 | − | 0.997354i | \(-0.476841\pi\) | ||||
0.0726912 | + | 0.997354i | \(0.476841\pi\) | |||||||
\(758\) | −13.8564 | + | 8.00000i | −0.503287 | + | 0.290573i | ||||
\(759\) | −15.5885 | + | 27.0000i | −0.565825 | + | 0.980038i | ||||
\(760\) | −3.00000 | + | 5.19615i | −0.108821 | + | 0.188484i | ||||
\(761\) | −8.66025 | − | 15.0000i | −0.313934 | − | 0.543750i | 0.665276 | − | 0.746597i | \(-0.268314\pi\) |
−0.979210 | + | 0.202848i | \(0.934980\pi\) | |||||||
\(762\) | 19.0526i | 0.690201i | ||||||||
\(763\) | −1.00000 | + | 5.19615i | −0.0362024 | + | 0.188113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | + | 15.5885i | 0.325396 | + | 0.563602i | ||||
\(766\) | −3.00000 | − | 1.73205i | −0.108394 | − | 0.0625815i | ||||
\(767\) | −5.19615 | − | 3.00000i | −0.187622 | − | 0.108324i | ||||
\(768\) | 0.866025 | + | 1.50000i | 0.0312500 | + | 0.0541266i | ||||
\(769\) | 19.0526i | 0.687053i | 0.939143 | + | 0.343526i | \(0.111621\pi\) | ||||
−0.939143 | + | 0.343526i | \(0.888379\pi\) | |||||||
\(770\) | −10.3923 | − | 9.00000i | −0.374513 | − | 0.324337i | ||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | −11.5000 | − | 19.9186i | −0.413894 | − | 0.716886i | ||||
\(773\) | 13.8564 | − | 24.0000i | 0.498380 | − | 0.863220i | −0.501618 | − | 0.865089i | \(-0.667262\pi\) |
0.999998 | + | 0.00186926i | \(0.000595004\pi\) | |||||||
\(774\) | −20.7846 | − | 12.0000i | −0.747087 | − | 0.431331i | ||||
\(775\) | −3.00000 | + | 1.73205i | −0.107763 | + | 0.0622171i | ||||
\(776\) | −5.19615 | −0.186531 | ||||||||
\(777\) | −8.66025 | + | 3.00000i | −0.310685 | + | 0.107624i | ||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | 20.7846 | − | 12.0000i | 0.744686 | − | 0.429945i | ||||
\(780\) | 9.00000 | + | 5.19615i | 0.322252 | + | 0.186052i | ||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | −10.3923 | − | 18.0000i | −0.371628 | − | 0.643679i | ||||
\(783\) | 15.5885i | 0.557086i | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | − | 36.0000i | − | 1.28490i | ||||||
\(786\) | 7.79423 | − | 4.50000i | 0.278011 | − | 0.160510i | ||||
\(787\) | 36.0000 | + | 20.7846i | 1.28326 | + | 0.740891i | 0.977443 | − | 0.211199i | \(-0.0677367\pi\) |
0.305818 | + | 0.952090i | \(0.401070\pi\) | |||||||
\(788\) | 15.5885 | + | 9.00000i | 0.555316 | + | 0.320612i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 1.73205i | − | 0.0616236i | ||||||
\(791\) | 10.3923 | + | 30.0000i | 0.369508 | + | 1.06668i | ||||
\(792\) | −9.00000 | −0.319801 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.8564 | − | 24.0000i | 0.491745 | − | 0.851728i | ||||
\(795\) | −23.3827 | − | 13.5000i | −0.829298 | − | 0.478796i | ||||
\(796\) | 9.00000 | − | 5.19615i | 0.318997 | − | 0.184173i | ||||
\(797\) | −25.9808 | −0.920286 | −0.460143 | − | 0.887845i | \(-0.652202\pi\) | ||||
−0.460143 | + | 0.887845i | \(0.652202\pi\) | |||||||
\(798\) | −12.0000 | − | 10.3923i | −0.424795 | − | 0.367884i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 1.73205 | − | 1.00000i | 0.0612372 | − | 0.0353553i | ||||
\(801\) | −15.5885 | + | 27.0000i | −0.550791 | + | 0.953998i | ||||
\(802\) | −6.00000 | + | 10.3923i | −0.211867 | + | 0.366965i | ||||
\(803\) | −10.3923 | − | 18.0000i | −0.366736 | − | 0.635206i | ||||
\(804\) | 3.46410 | 0.122169 | ||||||||
\(805\) | −27.0000 | − | 5.19615i | −0.951625 | − | 0.183140i | ||||
\(806\) | 6.00000i | 0.211341i | ||||||||
\(807\) | −25.5000 | − | 44.1673i | −0.897643 | − | 1.55476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 13.5000 | − | 7.79423i | 0.474342 | − | 0.273861i | ||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 7.79423 | + | 1.50000i | 0.273524 | + | 0.0526397i | ||||
\(813\) | − | 9.00000i | − | 0.315644i | ||||||
\(814\) | 3.00000 | + | 5.19615i | 0.105150 | + | 0.182125i | ||||
\(815\) | 12.1244 | − | 21.0000i | 0.424698 | − | 0.735598i | ||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | −24.0000 | + | 13.8564i | −0.839654 | + | 0.484774i | ||||
\(818\) | −8.66025 | −0.302799 | ||||||||
\(819\) | −18.0000 | + | 20.7846i | −0.628971 | + | 0.726273i | ||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | −2.59808 | + | 1.50000i | −0.0906735 | + | 0.0523504i | −0.544651 | − | 0.838663i | \(-0.683338\pi\) |
0.453978 | + | 0.891013i | \(0.350005\pi\) | |||||||
\(822\) | −15.5885 | + | 27.0000i | −0.543710 | + | 0.941733i | ||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | −1.73205 | − | 3.00000i | −0.0603388 | − | 0.104510i | ||||
\(825\) | 10.3923i | 0.361814i | ||||||||
\(826\) | 1.50000 | + | 4.33013i | 0.0521917 | + | 0.150664i | ||||
\(827\) | 9.00000i | 0.312961i | 0.987681 | + | 0.156480i | \(0.0500148\pi\) | ||||
−0.987681 | + | 0.156480i | \(0.949985\pi\) | |||||||
\(828\) | −15.5885 | + | 9.00000i | −0.541736 | + | 0.312772i | ||||
\(829\) | −15.0000 | − | 8.66025i | −0.520972 | − | 0.300783i | 0.216361 | − | 0.976314i | \(-0.430581\pi\) |
−0.737332 | + | 0.675530i | \(0.763915\pi\) | |||||||
\(830\) | 12.9904 | + | 7.50000i | 0.450903 | + | 0.260329i | ||||
\(831\) | 6.92820 | + | 12.0000i | 0.240337 | + | 0.416275i | ||||
\(832\) | − | 3.46410i | − | 0.120096i | ||||||
\(833\) | 3.46410 | + | 24.0000i | 0.120024 | + | 0.831551i | ||||
\(834\) | −30.0000 | −1.03882 | ||||||||
\(835\) | −15.0000 | − | 25.9808i | −0.519096 | − | 0.899101i | ||||
\(836\) | −5.19615 | + | 9.00000i | −0.179713 | + | 0.311272i | ||||
\(837\) | 7.79423 | + | 4.50000i | 0.269408 | + | 0.155543i | ||||
\(838\) | −21.0000 | + | 12.1244i | −0.725433 | + | 0.418829i | ||||
\(839\) | 3.46410 | 0.119594 | 0.0597970 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597970 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(840\) | −2.59808 | − | 7.50000i | −0.0896421 | − | 0.258775i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −27.7128 | + | 16.0000i | −0.955047 | + | 0.551396i | ||||
\(843\) | −45.0000 | − | 25.9808i | −1.54988 | − | 0.894825i | ||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | 0.866025 | + | 1.50000i | 0.0297922 | + | 0.0516016i | ||||
\(846\) | 20.7846i | 0.714590i | ||||||||
\(847\) | 4.00000 | + | 3.46410i | 0.137442 | + | 0.119028i | ||||
\(848\) | 9.00000i | 0.309061i | ||||||||
\(849\) | 41.5692 | − | 24.0000i | 1.42665 | − | 0.823678i | ||||
\(850\) | −6.00000 | − | 3.46410i | −0.205798 | − | 0.118818i | ||||
\(851\) | 10.3923 | + | 6.00000i | 0.356244 | + | 0.205677i | ||||
\(852\) | 18.0000 | − | 10.3923i | 0.616670 | − | 0.356034i | ||||
\(853\) | − | 24.2487i | − | 0.830260i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) | ||
0.909762 | − | 0.415130i | \(-0.136264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.0000i | − | 0.615587i | ||||||
\(856\) | 1.50000 | + | 2.59808i | 0.0512689 | + | 0.0888004i | ||||
\(857\) | −6.92820 | + | 12.0000i | −0.236663 | + | 0.409912i | −0.959755 | − | 0.280840i | \(-0.909387\pi\) |
0.723092 | + | 0.690752i | \(0.242720\pi\) | |||||||
\(858\) | 15.5885 | + | 9.00000i | 0.532181 | + | 0.307255i | ||||
\(859\) | −18.0000 | + | 10.3923i | −0.614152 | + | 0.354581i | −0.774589 | − | 0.632465i | \(-0.782043\pi\) |
0.160437 | + | 0.987046i | \(0.448710\pi\) | |||||||
\(860\) | −13.8564 | −0.472500 | ||||||||
\(861\) | −6.00000 | + | 31.1769i | −0.204479 | + | 1.06251i | ||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | 46.7654 | − | 27.0000i | 1.59191 | − | 0.919091i | 0.598933 | − | 0.800799i | \(-0.295592\pi\) |
0.992979 | − | 0.118291i | \(-0.0377417\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.3205 | − | 30.0000i | −0.588575 | − | 1.01944i | ||||
\(867\) | 8.66025 | 0.294118 | ||||||||
\(868\) | 3.00000 | − | 3.46410i | 0.101827 | − | 0.117579i | ||||
\(869\) | − | 3.00000i | − | 0.101768i | ||||||
\(870\) | 4.50000 | + | 7.79423i | 0.152564 | + | 0.264249i | ||||
\(871\) | −6.00000 | − | 3.46410i | −0.203302 | − | 0.117377i | ||||
\(872\) | 1.73205 | + | 1.00000i | 0.0586546 | + | 0.0338643i | ||||
\(873\) | 13.5000 | − | 7.79423i | 0.456906 | − | 0.263795i | ||||
\(874\) | 20.7846i | 0.703050i | ||||||||
\(875\) | −30.3109 | + | 10.5000i | −1.02470 | + | 0.354965i | ||||
\(876\) | − | 12.0000i | − | 0.405442i | ||||||
\(877\) | −22.0000 | − | 38.1051i | −0.742887 | − | 1.28672i | −0.951175 | − | 0.308651i | \(-0.900123\pi\) |
0.208288 | − | 0.978068i | \(-0.433211\pi\) | |||||||
\(878\) | −18.1865 | + | 31.5000i | −0.613766 | + | 1.06307i | ||||
\(879\) | −16.5000 | + | 28.5788i | −0.556531 | + | 0.963940i | ||||
\(880\) | −4.50000 | + | 2.59808i | −0.151695 | + | 0.0875811i | ||||
\(881\) | 10.3923 | 0.350126 | 0.175063 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175063 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(882\) | 20.7846 | − | 3.00000i | 0.699854 | − | 0.101015i | ||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | −10.3923 | + | 6.00000i | −0.349531 | + | 0.201802i | ||||
\(885\) | −2.59808 | + | 4.50000i | −0.0873334 | + | 0.151266i | ||||
\(886\) | 4.50000 | − | 7.79423i | 0.151180 | − | 0.261852i | ||||
\(887\) | −12.1244 | − | 21.0000i | −0.407096 | − | 0.705111i | 0.587467 | − | 0.809248i | \(-0.300125\pi\) |
−0.994563 | + | 0.104137i | \(0.966792\pi\) | |||||||
\(888\) | 3.46410i | 0.116248i | ||||||||
\(889\) | −27.5000 | + | 9.52628i | −0.922320 | + | 0.319501i | ||||
\(890\) | 18.0000i | 0.603361i | ||||||||
\(891\) | 23.3827 | − | 13.5000i | 0.783349 | − | 0.452267i | ||||
\(892\) | −22.5000 | − | 12.9904i | −0.753356 | − | 0.434950i | ||||
\(893\) | 20.7846 | + | 12.0000i | 0.695530 | + | 0.401565i | ||||
\(894\) | −15.5885 | − | 27.0000i | −0.521356 | − | 0.903015i | ||||
\(895\) | 20.7846i | 0.694753i | ||||||||
\(896\) | −1.73205 | + | 2.00000i | −0.0578638 | + | 0.0668153i | ||||
\(897\) | 36.0000 | 1.20201 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | −2.59808 | + | 4.50000i | −0.0866507 | + | 0.150083i | ||||
\(900\) | −3.00000 | + | 5.19615i | −0.100000 | + | 0.173205i | ||||
\(901\) | 27.0000 | − | 15.5885i | 0.899500 | − | 0.519327i | ||||
\(902\) | 20.7846 | 0.692052 | ||||||||
\(903\) | 6.92820 | − | 36.0000i | 0.230556 | − | 1.19800i | ||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | −10.3923 | + | 6.00000i | −0.345452 | + | 0.199447i | ||||
\(906\) | −10.5000 | − | 6.06218i | −0.348839 | − | 0.201402i | ||||
\(907\) | 13.0000 | − | 22.5167i | 0.431658 | − | 0.747653i | −0.565358 | − | 0.824845i | \(-0.691262\pi\) |
0.997016 | + | 0.0771920i | \(0.0245954\pi\) | |||||||
\(908\) | −2.59808 | − | 4.50000i | −0.0862202 | − | 0.149338i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.00000 | + | 15.5885i | −0.0994490 | + | 0.516752i | ||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −5.19615 | + | 3.00000i | −0.172062 | + | 0.0993399i | ||||
\(913\) | 22.5000 | + | 12.9904i | 0.744641 | + | 0.429919i | ||||
\(914\) | −4.33013 | − | 2.50000i | −0.143228 | − | 0.0826927i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | 10.3923 | + | 9.00000i | 0.343184 | + | 0.297206i | ||||
\(918\) | 18.0000i | 0.594089i | ||||||||
\(919\) | 10.0000 | + | 17.3205i | 0.329870 | + | 0.571351i | 0.982486 | − | 0.186338i | \(-0.0596619\pi\) |
−0.652616 | + | 0.757689i | \(0.726329\pi\) | |||||||
\(920\) | −5.19615 | + | 9.00000i | −0.171312 | + | 0.296721i | ||||
\(921\) | −36.3731 | − | 21.0000i | −1.19853 | − | 0.691974i | ||||
\(922\) | 12.0000 | − | 6.92820i | 0.395199 | − | 0.228168i | ||||
\(923\) | −41.5692 | −1.36827 | ||||||||
\(924\) | −4.50000 | − | 12.9904i | −0.148039 | − | 0.427352i | ||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 3.46410 | − | 2.00000i | 0.113837 | − | 0.0657241i | ||||
\(927\) | 9.00000 | + | 5.19615i | 0.295599 | + | 0.170664i | ||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | 24.2487 | + | 42.0000i | 0.795574 | + | 1.37798i | 0.922474 | + | 0.386060i | \(0.126164\pi\) |
−0.126899 | + | 0.991916i | \(0.540503\pi\) | |||||||
\(930\) | 5.19615 | 0.170389 | ||||||||
\(931\) | 9.00000 | − | 22.5167i | 0.294963 | − | 0.737954i | ||||
\(932\) | − | 18.0000i | − | 0.589610i | ||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 27.0000 | + | 15.5885i | 0.883467 | + | 0.510070i | ||||
\(935\) | 15.5885 | + | 9.00000i | 0.509797 | + | 0.294331i | ||||
\(936\) | 5.19615 | + | 9.00000i | 0.169842 | + | 0.294174i | ||||
\(937\) | 22.5167i | 0.735587i | 0.929907 | + | 0.367794i | \(0.119887\pi\) | ||||
−0.929907 | + | 0.367794i | \(0.880113\pi\) | |||||||
\(938\) | 1.73205 | + | 5.00000i | 0.0565535 | + | 0.163256i | ||||
\(939\) | − | 3.00000i | − | 0.0979013i | ||||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | −16.4545 | + | 28.5000i | −0.536401 | + | 0.929073i | 0.462693 | + | 0.886518i | \(0.346883\pi\) |
−0.999094 | + | 0.0425550i | \(0.986450\pi\) | |||||||
\(942\) | 18.0000 | − | 31.1769i | 0.586472 | − | 1.01580i | ||||
\(943\) | 36.0000 | − | 20.7846i | 1.17232 | − | 0.676840i | ||||
\(944\) | 1.73205 | 0.0563735 | ||||||||
\(945\) | 18.0000 | + | 15.5885i | 0.585540 | + | 0.507093i | ||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | 10.3923 | − | 6.00000i | 0.337705 | − | 0.194974i | −0.321552 | − | 0.946892i | \(-0.604204\pi\) |
0.659256 | + | 0.751918i | \(0.270871\pi\) | |||||||
\(948\) | 0.866025 | − | 1.50000i | 0.0281272 | − | 0.0487177i | ||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 3.46410 | + | 6.00000i | 0.112390 | + | 0.194666i | ||||
\(951\) | − | 25.9808i | − | 0.842484i | ||||||
\(952\) | 9.00000 | + | 1.73205i | 0.291692 | + | 0.0561361i | ||||
\(953\) | − | 24.0000i | − | 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(954\) | −13.5000 | − | 23.3827i | −0.437079 | − | 0.757042i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.19615 | − | 3.00000i | −0.168056 | − | 0.0970269i | ||||
\(957\) | 7.79423 | + | 13.5000i | 0.251952 | + | 0.436393i | ||||
\(958\) | − | 6.92820i | − | 0.223840i | ||||||
\(959\) | −46.7654 | − | 9.00000i | −1.51013 | − | 0.290625i | ||||
\(960\) | −3.00000 | −0.0968246 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 3.46410 | − | 6.00000i | 0.111687 | − | 0.193448i | ||||
\(963\) | −7.79423 | − | 4.50000i | −0.251166 | − | 0.145010i | ||||
\(964\) | −22.5000 | + | 12.9904i | −0.724676 | + | 0.418392i | ||||
\(965\) | 39.8372 | 1.28240 | ||||||||
\(966\) | −20.7846 | − | 18.0000i | −0.668734 | − | 0.579141i | ||||
\(967\) | −7.00000 | −0.225105 | −0.112552 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112552 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | 18.0000 | + | 10.3923i | 0.578243 | + | 0.333849i | ||||
\(970\) | 4.50000 | − | 7.79423i | 0.144486 | − | 0.250258i | ||||
\(971\) | 4.33013 | + | 7.50000i | 0.138960 | + | 0.240686i | 0.927103 | − | 0.374806i | \(-0.122291\pi\) |
−0.788143 | + | 0.615492i | \(0.788957\pi\) | |||||||
\(972\) | 15.5885 | 0.500000 | ||||||||
\(973\) | −15.0000 | − | 43.3013i | −0.480878 | − | 1.38817i | ||||
\(974\) | − | 1.00000i | − | 0.0320421i | ||||||
\(975\) | 10.3923 | − | 6.00000i | 0.332820 | − | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.7846 | − | 12.0000i | −0.664959 | − | 0.383914i | 0.129205 | − | 0.991618i | \(-0.458757\pi\) |
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(978\) | 21.0000 | − | 12.1244i | 0.671506 | − | 0.387694i | ||||
\(979\) | 31.1769i | 0.996419i | ||||||||
\(980\) | 9.52628 | − | 7.50000i | 0.304306 | − | 0.239579i | ||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 16.5000 | + | 28.5788i | 0.526536 | + | 0.911987i | ||||
\(983\) | 6.92820 | − | 12.0000i | 0.220975 | − | 0.382741i | −0.734129 | − | 0.679010i | \(-0.762409\pi\) |
0.955104 | + | 0.296269i | \(0.0957426\pi\) | |||||||
\(984\) | 10.3923 | + | 6.00000i | 0.331295 | + | 0.191273i | ||||
\(985\) | −27.0000 | + | 15.5885i | −0.860292 | + | 0.496690i | ||||
\(986\) | −10.3923 | −0.330958 | ||||||||
\(987\) | −30.0000 | + | 10.3923i | −0.954911 | + | 0.330791i | ||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | −41.5692 | + | 24.0000i | −1.32182 | + | 0.763156i | ||||
\(990\) | 7.79423 | − | 13.5000i | 0.247717 | − | 0.429058i | ||||
\(991\) | 23.5000 | − | 40.7032i | 0.746502 | − | 1.29298i | −0.202988 | − | 0.979181i | \(-0.565065\pi\) |
0.949490 | − | 0.313798i | \(-0.101602\pi\) | |||||||
\(992\) | −0.866025 | − | 1.50000i | −0.0274963 | − | 0.0476250i | ||||
\(993\) | 13.8564 | 0.439720 | ||||||||
\(994\) | 24.0000 | + | 20.7846i | 0.761234 | + | 0.659248i | ||||
\(995\) | 18.0000i | 0.570638i | ||||||||
\(996\) | 7.50000 | + | 12.9904i | 0.237647 | + | 0.411616i | ||||
\(997\) | 15.0000 | + | 8.66025i | 0.475055 | + | 0.274273i | 0.718353 | − | 0.695678i | \(-0.244896\pi\) |
−0.243299 | + | 0.969951i | \(0.578229\pi\) | |||||||
\(998\) | 19.0526 | + | 11.0000i | 0.603098 | + | 0.348199i | ||||
\(999\) | −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 \(a_p\))