Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,2,Mod(215,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.34760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 227.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.227 |
Dual form | 294.2.f.a.215.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 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 | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | −0.866025 | − | 1.50000i | −0.250000 | − | 0.433013i | ||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 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 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | −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 | 0 | ||||||||
\(29\) | 3.00000i | 0.557086i | 0.960424 | + | 0.278543i | \(0.0898515\pi\) | ||||
−0.960424 | + | 0.278543i | \(0.910149\pi\) | |||||||
\(30\) | 2.59808 | − | 1.50000i | 0.474342 | − | 0.273861i | ||||
\(31\) | 1.50000 | + | 0.866025i | 0.269408 | + | 0.155543i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 4.50000 | − | 2.59808i | 0.783349 | − | 0.452267i | ||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −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 | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 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 | 0.928351 | − | 0.371706i | \(-0.121227\pi\) |
0.142269 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(54\) | −4.50000 | + | 2.59808i | −0.612372 | + | 0.353553i | ||||
\(55\) | 5.19615i | 0.700649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −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 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | −2.59808 | + | 1.50000i | −0.306186 | + | 0.176777i | ||||
\(73\) | −6.00000 | − | 3.46410i | −0.702247 | − | 0.405442i | 0.105937 | − | 0.994373i | \(-0.466216\pi\) |
−0.808184 | + | 0.588930i | \(0.799549\pi\) | |||||||
\(74\) | 1.73205 | + | 1.00000i | 0.201347 | + | 0.116248i | ||||
\(75\) | −1.73205 | − | 3.00000i | −0.200000 | − | 0.346410i | ||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −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 | \(0.657658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −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 | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | \(-0.915026\pi\) | ||
0.964579 | − | 0.263795i | \(-0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 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 | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −3.46410 | −0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | −2.59808 | + | 1.50000i | −0.251166 | + | 0.145010i | −0.620298 | − | 0.784366i | \(-0.712988\pi\) |
0.369132 | + | 0.929377i | \(0.379655\pi\) | |||||||
\(108\) | −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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 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 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 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 | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | 5.19615 | + | 9.00000i | 0.442326 | + | 0.766131i | ||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | −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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 15.5885 | − | 9.00000i | 1.27706 | − | 0.737309i | 0.300750 | − | 0.953703i | \(-0.402763\pi\) |
0.976306 | + | 0.216394i | \(0.0694297\pi\) | |||||||
\(150\) | −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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000i | 0.240966i | ||||||||
\(156\) | −5.19615 | + | 3.00000i | −0.416025 | + | 0.240192i | ||||
\(157\) | 18.0000 | + | 10.3923i | 1.43656 | + | 0.829396i | 0.997609 | − | 0.0691164i | \(-0.0220180\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0.866025 | + | 0.500000i | 0.0688973 | + | 0.0397779i | ||||
\(159\) | 13.5000 | − | 7.79423i | 1.07062 | − | 0.618123i | ||||
\(160\) | − | 1.73205i | − | 0.136931i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 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 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 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 | 0.0585225 | − | 0.998286i | \(-0.481361\pi\) |
−0.835280 | + | 0.549825i | \(0.814694\pi\) | |||||||
\(180\) | −2.59808 | − | 4.50000i | −0.193649 | − | 0.335410i | ||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −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 | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | −4.50000 | − | 7.79423i | −0.319801 | − | 0.553912i | ||||
\(199\) | −9.00000 | − | 5.19615i | −0.637993 | − | 0.368345i | 0.145848 | − | 0.989307i | \(-0.453409\pi\) |
−0.783841 | + | 0.620962i | \(0.786742\pi\) | |||||||
\(200\) | −1.73205 | − | 1.00000i | −0.122474 | − | 0.0707107i | ||||
\(201\) | 1.73205 | + | 3.00000i | 0.122169 | + | 0.211604i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 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 | \(0.335817\pi\) | ||||
−0.493228 | + | 0.869900i | \(0.664183\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −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 | −0.0480291 | − | 0.998846i | \(-0.515294\pi\) |
0.841011 | + | 0.541017i | \(0.181961\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −15.5885 | + | 9.00000i | −1.02123 | + | 0.589610i | −0.914461 | − | 0.404674i | \(-0.867385\pi\) |
−0.106773 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(234\) | −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 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | −1.50000 | − | 2.59808i | −0.0968246 | − | 0.167705i | ||||
\(241\) | 22.5000 | + | 12.9904i | 1.44935 | + | 0.836784i | 0.998443 | − | 0.0557856i | \(-0.0177663\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 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 | \(0.294652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −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 | −0.630412 | − | 0.776261i | \(-0.717114\pi\) |
0.357056 | + | 0.934083i | \(0.383781\pi\) | |||||||
\(272\) | 3.46410 | 0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −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 | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000i | 1.78965i | 0.446417 | + | 0.894825i | \(0.352700\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | 10.3923 | − | 6.00000i | 0.618853 | − | 0.357295i | ||||
\(283\) | −24.0000 | − | 13.8564i | −1.42665 | − | 0.823678i | −0.429797 | − | 0.902926i | \(-0.641415\pi\) |
−0.996855 | + | 0.0792477i | \(0.974748\pi\) | |||||||
\(284\) | −10.3923 | − | 6.00000i | −0.616670 | − | 0.356034i | ||||
\(285\) | −9.00000 | + | 5.19615i | −0.533114 | + | 0.307794i | ||||
\(286\) | − | 10.3923i | − | 0.614510i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | \(0.687868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 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 | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 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 | −0.541793 | − | 0.840512i | \(-0.682254\pi\) |
0.457008 | + | 0.889463i | \(0.348921\pi\) | |||||||
\(314\) | 20.7846 | 1.17294 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | −12.9904 | + | 7.50000i | −0.729612 | + | 0.421242i | −0.818280 | − | 0.574819i | \(-0.805072\pi\) |
0.0886679 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(318\) | 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 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 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 | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | 0.752297 | − | 0.658824i | \(-0.228946\pi\) |
−0.194409 | + | 0.980921i | \(0.562279\pi\) | |||||||
\(348\) | 4.50000 | − | 2.59808i | 0.241225 | − | 0.139272i | ||||
\(349\) | − | 10.3923i | − | 0.556287i | −0.960539 | − | 0.278144i | \(-0.910281\pi\) | ||
0.960539 | − | 0.278144i | \(-0.0897191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000i | 0.960769i | ||||||||
\(352\) | −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 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | 5.19615 | − | 3.00000i | 0.274242 | − | 0.158334i | −0.356572 | − | 0.934268i | \(-0.616054\pi\) |
0.630814 | + | 0.775934i | \(0.282721\pi\) | |||||||
\(360\) | −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 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.5000 | + | 11.2583i | 1.01789 | + | 0.587680i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | −10.3923 | − | 18.0000i | −0.541002 | − | 0.937043i | ||||
\(370\) | 3.46410i | 0.180090i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 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 | 0.840091 | − | 0.542445i | \(-0.182501\pi\) |
−0.0497253 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(390\) | −5.19615 | − | 9.00000i | −0.263117 | − | 0.455733i | ||||
\(391\) | − | 20.7846i | − | 1.05112i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −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 | 0.242967 | − | 0.970034i | \(-0.421879\pi\) |
0.961558 | + | 0.274601i | \(0.0885459\pi\) | |||||||
\(398\) | −10.3923 | −0.520919 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | −10.3923 | + | 6.00000i | −0.518967 | + | 0.299626i | −0.736512 | − | 0.676425i | \(-0.763528\pi\) |
0.217545 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(402\) | 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 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000i | 0.297409i | ||||||||
\(408\) | 5.19615 | − | 3.00000i | 0.257248 | − | 0.148522i | ||||
\(409\) | −7.50000 | − | 4.33013i | −0.370851 | − | 0.214111i | 0.302979 | − | 0.952997i | \(-0.402019\pi\) |
−0.673830 | + | 0.738886i | \(0.735352\pi\) | |||||||
\(410\) | 10.3923 | + | 6.00000i | 0.513239 | + | 0.296319i | ||||
\(411\) | −27.0000 | + | 15.5885i | −1.33181 | + | 0.768922i | ||||
\(412\) | − | 3.46410i | − | 0.170664i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | 0.908591 | − | 0.417687i | \(-0.137159\pi\) |
0.0925683 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(432\) | 2.59808 | + | 4.50000i | 0.125000 | + | 0.216506i | ||||
\(433\) | − | 34.6410i | − | 1.66474i | −0.554220 | − | 0.832370i | \(-0.686983\pi\) | ||
0.554220 | − | 0.832370i | \(-0.313017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 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 | \(0.667925\pi\) |
−0.999992 | + | 0.00395451i | \(0.998741\pi\) | |||||||
\(440\) | 5.19615 | 0.247717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | 7.79423 | − | 4.50000i | 0.370315 | − | 0.213801i | −0.303281 | − | 0.952901i | \(-0.598082\pi\) |
0.673596 | + | 0.739100i | \(0.264749\pi\) | |||||||
\(444\) | 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 | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 30.0000i | − | 1.41579i | −0.706319 | − | 0.707894i | \(-0.749646\pi\) | ||
0.706319 | − | 0.707894i | \(-0.250354\pi\) | |||||||
\(450\) | −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 | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(0.604583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −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 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0000i | 1.48927i | 0.667472 | + | 0.744635i | \(0.267376\pi\) | ||||
−0.667472 | + | 0.744635i | \(0.732624\pi\) | |||||||
\(492\) | −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 | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | \(0.176897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 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 | 0.444941 | − | 0.895560i | \(-0.353225\pi\) |
0.998048 | + | 0.0624496i | \(0.0198913\pi\) | |||||||
\(524\) | −5.19615 | −0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 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 | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −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 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | 0.554031 | − | 0.832496i | \(-0.313089\pi\) |
−0.443947 | + | 0.896053i | \(0.646422\pi\) | |||||||
\(558\) | −2.59808 | − | 4.50000i | −0.109985 | − | 0.190500i | ||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | −5.19615 | + | 3.00000i | −0.217834 | + | 0.125767i | −0.604947 | − | 0.796266i | \(-0.706806\pi\) |
0.387113 | + | 0.922032i | \(0.373472\pi\) | |||||||
\(570\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000i | 0.500435i | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | 1.50000 | + | 0.866025i | 0.0624458 | + | 0.0360531i | 0.530898 | − | 0.847436i | \(-0.321855\pi\) |
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(578\) | 4.33013 | + | 2.50000i | 0.180110 | + | 0.103986i | ||||
\(579\) | −19.9186 | − | 34.5000i | −0.827788 | − | 1.43377i | ||||
\(580\) | 5.19615i | 0.215758i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −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 | \(0.604255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 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 | −0.135686 | − | 0.990752i | \(-0.543324\pi\) |
−0.925859 | + | 0.377869i | \(0.876657\pi\) | |||||||
\(600\) | −3.00000 | + | 1.73205i | −0.122474 | + | 0.0707107i | ||||
\(601\) | 29.4449i | 1.20108i | 0.799594 | + | 0.600541i | \(0.205048\pi\) | ||||
−0.799594 | + | 0.600541i | \(0.794952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | −0.840484 | − | 0.541837i | \(-0.817729\pi\) |
0.0490029 | + | 0.998799i | \(0.484396\pi\) | |||||||
\(608\) | 3.46410 | 0.140488 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | −3.00000 | − | 5.19615i | −0.120678 | − | 0.209020i | ||||
\(619\) | −6.00000 | − | 3.46410i | −0.241160 | − | 0.139234i | 0.374550 | − | 0.927207i | \(-0.377797\pi\) |
−0.615710 | + | 0.787973i | \(0.711131\pi\) | |||||||
\(620\) | 2.59808 | + | 1.50000i | 0.104341 | + | 0.0602414i | ||||
\(621\) | 27.0000 | − | 15.5885i | 1.08347 | − | 0.625543i | ||||
\(622\) | 13.8564i | 0.555591i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 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 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | 0.0297987 | − | 0.999556i | \(-0.490513\pi\) |
−0.850741 | + | 0.525584i | \(0.823847\pi\) | |||||||
\(642\) | 2.59808 | + | 4.50000i | 0.102538 | + | 0.177601i | ||||
\(643\) | 17.3205i | 0.683054i | 0.939872 | + | 0.341527i | \(0.110944\pi\) | ||||
−0.939872 | + | 0.341527i | \(0.889056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0000 | −0.548282 | ||||||||
\(653\) | −2.59808 | + | 1.50000i | −0.101671 | + | 0.0586995i | −0.549973 | − | 0.835182i | \(-0.685362\pi\) |
0.448303 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(654\) | −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 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000i | 0.467454i | 0.972302 | + | 0.233727i | \(0.0750921\pi\) | ||||
−0.972302 | + | 0.233727i | \(0.924908\pi\) | |||||||
\(660\) | 7.79423 | − | 4.50000i | 0.303390 | − | 0.175162i | ||||
\(661\) | 6.00000 | + | 3.46410i | 0.233373 | + | 0.134738i | 0.612127 | − | 0.790759i | \(-0.290314\pi\) |
−0.378754 | + | 0.925497i | \(0.623647\pi\) | |||||||
\(662\) | 6.92820 | + | 4.00000i | 0.269272 | + | 0.155464i | ||||
\(663\) | 18.0000 | − | 10.3923i | 0.699062 | − | 0.403604i | ||||
\(664\) | 8.66025i | 0.336083i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 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 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 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 | 0.805814 | − | 0.592168i | \(-0.201728\pi\) |
−0.109926 | + | 0.993940i | \(0.535061\pi\) | |||||||
\(684\) | 9.00000 | − | 5.19615i | 0.344124 | − | 0.198680i | ||||
\(685\) | − | 31.1769i | − | 1.19121i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 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 | −0.381514 | − | 0.924363i | \(-0.624597\pi\) |
0.609765 | + | 0.792582i | \(0.291264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.00000i | − | 0.113308i | −0.998394 | − | 0.0566542i | \(-0.981957\pi\) | ||
0.998394 | − | 0.0566542i | \(-0.0180433\pi\) | |||||||
\(702\) | 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 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | \(-0.816140\pi\) | ||
0.837769 | − | 0.546025i | \(-0.183860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 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 | −0.938330 | − | 0.345740i | \(-0.887628\pi\) |
−0.169745 | + | 0.985488i | \(0.554294\pi\) | |||||||
\(734\) | 22.5167 | 0.831105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.0000i | − | 0.660356i | −0.943919 | − | 0.330178i | \(-0.892891\pi\) | ||
0.943919 | − | 0.330178i | \(-0.107109\pi\) | |||||||
\(744\) | −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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 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 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 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 | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.888379\pi\) | ||
0.939143 | − | 0.343526i | \(-0.111621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.0000i | 1.28490i | ||||||||
\(786\) | −7.79423 | + | 4.50000i | −0.278011 | + | 0.160510i | ||||
\(787\) | −36.0000 | − | 20.7846i | −1.28326 | − | 0.740891i | −0.305818 | − | 0.952090i | \(-0.598930\pi\) |
−0.977443 | + | 0.211199i | \(0.932263\pi\) | |||||||
\(788\) | −15.5885 | − | 9.00000i | −0.555316 | − | 0.320612i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.73205i | 0.0616236i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −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 | \(0.652202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 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 | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | 2.59808 | − | 1.50000i | 0.0906735 | − | 0.0523504i | −0.453978 | − | 0.891013i | \(-0.649995\pi\) |
0.544651 | + | 0.838663i | \(0.316662\pi\) | |||||||
\(822\) | −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 | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.00000i | − | 0.312961i | −0.987681 | − | 0.156480i | \(-0.949985\pi\) | ||
0.987681 | − | 0.156480i | \(-0.0500148\pi\) | |||||||
\(828\) | 15.5885 | − | 9.00000i | 0.541736 | − | 0.312772i | ||||
\(829\) | 15.0000 | + | 8.66025i | 0.520972 | + | 0.300783i | 0.737332 | − | 0.675530i | \(-0.236085\pi\) |
−0.216361 | + | 0.976314i | \(0.569419\pi\) | |||||||
\(830\) | −12.9904 | − | 7.50000i | −0.450903 | − | 0.260329i | ||||
\(831\) | 6.92820 | + | 12.0000i | 0.240337 | + | 0.416275i | ||||
\(832\) | 3.46410i | 0.120096i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | \(0.480955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 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 | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 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 | \(0.136264\pi\) | ||||
−0.909762 | + | 0.415130i | \(0.863736\pi\) | |||||||
\(854\) | 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 | −0.160437 | − | 0.987046i | \(-0.551290\pi\) |
0.774589 | + | 0.632465i | \(0.217957\pi\) | |||||||
\(860\) | −13.8564 | −0.472500 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | −46.7654 | + | 27.0000i | −1.59191 | + | 0.919091i | −0.598933 | + | 0.800799i | \(0.704408\pi\) |
−0.992979 | + | 0.118291i | \(0.962258\pi\) | |||||||
\(864\) | 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 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 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 | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | \(0.443987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 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 | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 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 | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 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 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 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 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.880113\pi\) | ||
0.929907 | − | 0.367794i | \(-0.119887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | −10.3923 | + | 6.00000i | −0.337705 | + | 0.194974i | −0.659256 | − | 0.751918i | \(-0.729129\pi\) |
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(948\) | 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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | −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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −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 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | 0.794164 | − | 0.607704i | \(-0.207909\pi\) |
−0.129205 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(978\) | −21.0000 | + | 12.1244i | −0.671506 | + | 0.387694i | ||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.0000i | − | 0.570638i | ||||||
\(996\) | 7.50000 | + | 12.9904i | 0.237647 | + | 0.411616i | ||||
\(997\) | −15.0000 | − | 8.66025i | −0.475055 | − | 0.274273i | 0.243299 | − | 0.969951i | \(-0.421771\pi\) |
−0.718353 | + | 0.695678i | \(0.755104\pi\) | |||||||
\(998\) | −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 \(a_p\))