Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(289,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.by (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: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1009 |
Dual form | 2160.2.by.b.289.2 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23205 | + | 1.86603i | 0.550990 | + | 0.834512i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) |
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615 | + | 3.00000i | 1.44115 | + | 0.832050i | 0.997927 | − | 0.0643593i | \(-0.0205004\pi\) |
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.866025 | − | 0.500000i | −0.180579 | − | 0.104257i | 0.406986 | − | 0.913434i | \(-0.366580\pi\) |
−0.587565 | + | 0.809177i | \(0.699913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.96410 | + | 4.59808i | −0.392820 | + | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50000 | − | 7.79423i | −0.835629 | − | 1.44735i | −0.893517 | − | 0.449029i | \(-0.851770\pi\) |
0.0578882 | − | 0.998323i | \(-0.481563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 1.00000i | −0.338062 | − | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.50000 | + | 9.52628i | −0.858956 | + | 1.48775i | 0.0139704 | + | 0.999902i | \(0.495553\pi\) |
−0.872926 | + | 0.487852i | \(0.837780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | − | 2.00000i | 0.528271 | − | 0.304997i | −0.212041 | − | 0.977261i | \(-0.568011\pi\) |
0.740312 | + | 0.672264i | \(0.234678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.06218 | − | 3.50000i | 0.884260 | − | 0.510527i | 0.0121990 | − | 0.999926i | \(-0.496117\pi\) |
0.872060 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 5.19615i | −0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | + | 4.00000i | −0.269680 | + | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.803848 | + | 13.3923i | 0.0997050 | + | 1.66111i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.52628 | + | 5.50000i | 1.16382 | + | 0.671932i | 0.952217 | − | 0.305424i | \(-0.0987981\pi\) |
0.211604 | + | 0.977356i | \(0.432131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.73205 | − | 1.00000i | −0.197386 | − | 0.113961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.52628 | + | 5.50000i | −1.04565 | + | 0.603703i | −0.921427 | − | 0.388552i | \(-0.872976\pi\) |
−0.124218 | + | 0.992255i | \(0.539642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.73205 | − | 2.46410i | 0.404798 | − | 0.267269i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.39230 | + | 11.1962i | 0.758434 | + | 1.14870i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820 | − | 4.00000i | 0.703452 | − | 0.406138i | −0.105180 | − | 0.994453i | \(-0.533542\pi\) |
0.808632 | + | 0.588315i | \(0.200208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.00000i | − | 0.290021i | −0.989430 | − | 0.145010i | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.133975 | − | 2.23205i | −0.0124932 | − | 0.208140i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | + | 1.73205i | 0.0916698 | + | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.0000i | − | 1.68598i | −0.537931 | − | 0.842989i | \(-0.680794\pi\) | ||
0.537931 | − | 0.842989i | \(-0.319206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19615 | + | 3.00000i | −0.450564 | + | 0.260133i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | + | 13.8564i | −0.678551 | + | 1.17529i | 0.296866 | + | 0.954919i | \(0.404058\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000i | 1.00349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | − | 18.0000i | 0.747409 | − | 1.49482i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | − | 0.866025i | 0.0409616 | − | 0.0709476i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) |
0.885779 | + | 0.464107i | \(0.153625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.46410 | + | 0.267949i | −0.358565 | + | 0.0215222i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410 | + | 2.00000i | 0.276465 | + | 0.159617i | 0.631822 | − | 0.775113i | \(-0.282307\pi\) |
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.59808 | − | 1.50000i | −0.201045 | − | 0.116073i | 0.396098 | − | 0.918208i | \(-0.370364\pi\) |
−0.597143 | + | 0.802135i | \(0.703697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 19.9186i | 0.884615 | + | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.46410 | − | 2.00000i | 0.263371 | − | 0.152057i | −0.362500 | − | 0.931984i | \(-0.618077\pi\) |
0.625871 | + | 0.779926i | \(0.284744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.598076 | − | 4.96410i | −0.0452103 | − | 0.375251i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.73205 | − | 2.46410i | 0.274386 | − | 0.181164i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410 | − | 2.00000i | 0.253320 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.66025 | + | 5.00000i | 0.623379 | + | 0.359908i | 0.778183 | − | 0.628037i | \(-0.216141\pi\) |
−0.154805 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.00000i | 0.569976i | 0.958531 | + | 0.284988i | \(0.0919897\pi\) | ||||
−0.958531 | + | 0.284988i | \(0.908010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.79423 | + | 4.50000i | 0.547048 | + | 0.315838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.5526 | + | 1.47372i | −1.71483 | + | 0.102929i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | + | 10.3923i | 0.415029 | + | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | − | 15.5885i | 0.619586 | − | 1.07315i | −0.369976 | − | 0.929041i | \(-0.620634\pi\) |
0.989561 | − | 0.144112i | \(-0.0460326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | + | 4.00000i | 0.545595 | + | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.9186 | + | 11.5000i | −1.33385 | + | 0.770097i | −0.985887 | − | 0.167412i | \(-0.946459\pi\) |
−0.347960 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.92820 | − | 4.00000i | 0.459841 | − | 0.265489i | −0.252136 | − | 0.967692i | \(-0.581133\pi\) |
0.711977 | + | 0.702202i | \(0.247800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | + | 6.06218i | −0.231287 | + | 0.400600i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0000 | + | 7.00000i | 0.913259 | + | 0.456630i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0000 | − | 24.2487i | 0.905585 | − | 1.56852i | 0.0854543 | − | 0.996342i | \(-0.472766\pi\) |
0.820130 | − | 0.572177i | \(-0.193901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3923 | + | 0.803848i | −0.855603 | + | 0.0513559i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.1769 | + | 18.0000i | 1.98374 | + | 1.14531i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.00000i | − | 0.125739i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.3923 | − | 6.00000i | −0.648254 | − | 0.374270i | 0.139533 | − | 0.990217i | \(-0.455440\pi\) |
−0.787787 | + | 0.615948i | \(0.788773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | + | 1.73205i | 0.0621370 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8564 | − | 8.00000i | 0.854423 | − | 0.493301i | −0.00771799 | − | 0.999970i | \(-0.502457\pi\) |
0.862141 | + | 0.506669i | \(0.169123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.92820 | + | 1.19615i | −0.598693 | + | 0.0721307i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0526 | − | 11.0000i | 1.14476 | − | 0.660926i | 0.197153 | − | 0.980373i | \(-0.436830\pi\) |
0.947604 | + | 0.319447i | \(0.103497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.50000 | − | 2.59808i | −0.0894825 | − | 0.154988i | 0.817810 | − | 0.575488i | \(-0.195188\pi\) |
−0.907293 | + | 0.420500i | \(0.861855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.866025 | + | 0.500000i | 0.0514799 | + | 0.0297219i | 0.525519 | − | 0.850782i | \(-0.323871\pi\) |
−0.474039 | + | 0.880504i | \(0.657204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.0000i | − | 0.649309i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.5885 | − | 9.00000i | −0.910687 | − | 0.525786i | −0.0300351 | − | 0.999549i | \(-0.509562\pi\) |
−0.880652 | + | 0.473763i | \(0.842895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.92820 | + | 0.535898i | −0.519820 | + | 0.0312012i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | + | 3.46410i | −0.115278 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | + | 14.0000i | −0.400819 | + | 0.801638i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.00000i | − | 0.513657i | −0.966457 | − | 0.256829i | \(-0.917322\pi\) | ||
0.966457 | − | 0.256829i | \(-0.0826776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0526 | + | 11.0000i | −1.07691 | + | 0.621757i | −0.930062 | − | 0.367402i | \(-0.880247\pi\) |
−0.146852 | + | 0.989158i | \(0.546914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.73205 | + | 1.00000i | −0.0972817 | + | 0.0561656i | −0.547852 | − | 0.836576i | \(-0.684554\pi\) |
0.450570 | + | 0.892741i | \(0.351221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | + | 18.0000i | −1.33128 | + | 0.998460i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.50000 | + | 6.06218i | −0.192961 | + | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.47372 | + | 24.5526i | 0.0805180 | + | 1.34145i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.92820 | + | 4.00000i | 0.377403 | + | 0.217894i | 0.676688 | − | 0.736270i | \(-0.263415\pi\) |
−0.299285 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.50000 | − | 9.52628i | −0.294408 | − | 0.509930i | 0.680439 | − | 0.732805i | \(-0.261789\pi\) |
−0.974847 | + | 0.222875i | \(0.928456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8564 | − | 8.00000i | 0.737502 | − | 0.425797i | −0.0836583 | − | 0.996495i | \(-0.526660\pi\) |
0.821160 | + | 0.570697i | \(0.193327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.39230 | − | 11.1962i | −0.392343 | − | 0.594230i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.46410 | − | 4.92820i | 0.390689 | − | 0.257954i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8564 | + | 8.00000i | −0.723299 | + | 0.417597i | −0.815966 | − | 0.578101i | \(-0.803794\pi\) |
0.0926670 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3923 | − | 6.00000i | −0.538093 | − | 0.310668i | 0.206213 | − | 0.978507i | \(-0.433886\pi\) |
−0.744306 | + | 0.667839i | \(0.767219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 54.0000i | − | 2.78114i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.7128 | − | 16.0000i | −1.41606 | − | 0.817562i | −0.420109 | − | 0.907474i | \(-0.638008\pi\) |
−0.995950 | + | 0.0899119i | \(0.971341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.267949 | − | 4.46410i | −0.0136560 | − | 0.227512i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.50000 | − | 16.4545i | −0.481669 | − | 0.834275i | 0.518110 | − | 0.855314i | \(-0.326636\pi\) |
−0.999779 | + | 0.0210389i | \(0.993303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | + | 1.73205i | −0.0505722 | + | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | + | 24.0000i | −0.603786 | + | 1.20757i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000i | 0.200754i | 0.994949 | + | 0.100377i | \(0.0320049\pi\) | ||||
−0.994949 | + | 0.100377i | \(0.967995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00000 | + | 8.66025i | −0.249688 | + | 0.432472i | −0.963439 | − | 0.267927i | \(-0.913661\pi\) |
0.713751 | + | 0.700399i | \(0.246995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | + | 6.00000i | −0.517678 | + | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.46410 | − | 2.00000i | 0.171709 | − | 0.0991363i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0000 | − | 32.9090i | 0.939490 | − | 1.62724i | 0.173064 | − | 0.984911i | \(-0.444633\pi\) |
0.766426 | − | 0.642333i | \(-0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.0000 | − | 11.0000i | −1.07994 | − | 0.539969i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0000 | − | 29.4449i | 0.830504 | − | 1.43848i | −0.0671345 | − | 0.997744i | \(-0.521386\pi\) |
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 19.0526i | −0.536107 | − | 0.928565i | −0.999109 | − | 0.0422075i | \(-0.986561\pi\) |
0.463002 | − | 0.886357i | \(-0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.19615 | + | 3.92820i | 0.446079 | + | 0.190546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.06218 | − | 3.50000i | −0.293369 | − | 0.169377i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.19615 | − | 3.00000i | −0.248566 | − | 0.143509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.23205 | + | 1.86603i | 0.0584048 | + | 0.0884581i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.0000 | −1.03594 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.39230 | − | 11.1962i | −0.346557 | − | 0.524884i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.66025 | − | 5.00000i | 0.405110 | − | 0.233890i | −0.283577 | − | 0.958950i | \(-0.591521\pi\) |
0.688686 | + | 0.725059i | \(0.258188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5000 | − | 18.1865i | −0.489034 | − | 0.847031i | 0.510887 | − | 0.859648i | \(-0.329317\pi\) |
−0.999920 | + | 0.0126168i | \(0.995984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1769 | + | 18.0000i | 1.44891 | + | 0.836531i | 0.998417 | − | 0.0562469i | \(-0.0179134\pi\) |
0.450497 | + | 0.892778i | \(0.351247\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 36.0000i | − | 1.66588i | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||
0.553362 | − | 0.832941i | \(-0.313345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0000 | −0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.92820 | + | 4.00000i | 0.318559 | + | 0.183920i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.7846 | + | 27.5885i | −0.540715 | + | 1.26585i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0000 | + | 24.2487i | 0.639676 | + | 1.10795i | 0.985504 | + | 0.169654i | \(0.0542649\pi\) |
−0.345827 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0000 | + | 8.00000i | 0.726523 | + | 0.363261i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.0000i | − | 0.543772i | −0.962329 | − | 0.271886i | \(-0.912353\pi\) | ||
0.962329 | − | 0.271886i | \(-0.0876473\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.5885 | + | 9.00000i | −0.702069 | + | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.19615 | − | 3.00000i | 0.233079 | − | 0.134568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0000 | − | 20.7846i | 0.537194 | − | 0.930447i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) |
0.999054 | − | 0.0434940i | \(-0.0138489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.0000i | 1.20387i | 0.798545 | + | 0.601935i | \(0.205603\pi\) | ||||
−0.798545 | + | 0.601935i | \(0.794397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | + | 4.00000i | −0.0889988 | + | 0.177998i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.50000 | − | 12.9904i | 0.332432 | − | 0.575789i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
0.982988 | + | 0.183669i | \(0.0587976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.07180 | − | 17.8564i | −0.0472290 | − | 0.786847i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1244 | + | 7.00000i | 0.533229 | + | 0.307860i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0000 | 1.62100 | 0.810500 | − | 0.585739i | \(-0.199196\pi\) | ||||
0.810500 | + | 0.585739i | \(0.199196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0000i | 1.26808i | 0.773300 | + | 0.634041i | \(0.218605\pi\) | ||||
−0.773300 | + | 0.634041i | \(0.781395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46410 | + | 2.00000i | 0.150899 | + | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | − | 19.0526i | −0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −57.1577 | + | 33.0000i | −2.47577 | + | 1.42939i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.59808 | − | 3.69615i | 0.242026 | − | 0.159799i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | −0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | −0.730887 | −0.365444 | − | 0.930834i | \(-0.619083\pi\) | ||||
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.62436 | − | 13.0622i | −0.369427 | − | 0.559522i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.3109 | − | 17.5000i | 1.29600 | − | 0.748246i | 0.316289 | − | 0.948663i | \(-0.397563\pi\) |
0.979711 | + | 0.200417i | \(0.0642296\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.0000 | − | 46.7654i | −1.15024 | − | 1.99227i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.3923 | − | 6.00000i | −0.441926 | − | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.0000i | − | 1.01691i | −0.861088 | − | 0.508456i | \(-0.830216\pi\) | ||
0.861088 | − | 0.508456i | \(-0.169784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.0429 | + | 18.5000i | 1.35045 | + | 0.779682i | 0.988312 | − | 0.152443i | \(-0.0487140\pi\) |
0.362137 | + | 0.932125i | \(0.382047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.60770 | + | 26.7846i | 0.0676362 | + | 1.12684i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.00000 | + | 1.73205i | 0.0419222 | + | 0.0726113i | 0.886225 | − | 0.463255i | \(-0.153319\pi\) |
−0.844303 | + | 0.535866i | \(0.819985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | − | 3.00000i | 0.166812 | − | 0.125109i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.0000i | − | 1.33218i | −0.745873 | − | 0.666089i | \(-0.767967\pi\) | ||
0.745873 | − | 0.666089i | \(-0.232033\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.50000 | − | 9.52628i | 0.228178 | − | 0.395217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.59808 | + | 1.50000i | −0.107234 | + | 0.0619116i | −0.552658 | − | 0.833408i | \(-0.686386\pi\) |
0.445424 | + | 0.895320i | \(0.353053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | + | 10.3923i | −0.247226 | + | 0.428207i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.0000i | 1.23195i | 0.787765 | + | 0.615976i | \(0.211238\pi\) | ||||
−0.787765 | + | 0.615976i | \(0.788762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | + | 4.00000i | −0.0819920 | + | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | + | 10.3923i | −0.245153 | + | 0.424618i | −0.962175 | − | 0.272433i | \(-0.912172\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | + | 19.0526i | 0.448699 | + | 0.777170i | 0.998302 | − | 0.0582563i | \(-0.0185541\pi\) |
−0.549602 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6244 | − | 0.937822i | 0.635220 | − | 0.0381279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.866025 | − | 0.500000i | −0.0351509 | − | 0.0202944i | 0.482322 | − | 0.875994i | \(-0.339794\pi\) |
−0.517472 | + | 0.855700i | \(0.673127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.0000 | 1.69914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.0000i | − | 1.37325i | −0.727013 | − | 0.686624i | \(-0.759092\pi\) | ||
0.727013 | − | 0.686624i | \(-0.240908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.7128 | + | 16.0000i | 1.11568 | + | 0.644136i | 0.940294 | − | 0.340365i | \(-0.110551\pi\) |
0.175382 | + | 0.984500i | \(0.443884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.866025 | + | 0.500000i | −0.0346966 | + | 0.0200321i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.4545 | − | 23.4090i | 1.40697 | − | 0.928956i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.1769 | + | 18.0000i | −1.23527 | + | 0.713186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.50000 | + | 11.2583i | 0.256735 | + | 0.444677i | 0.965365 | − | 0.260902i | \(-0.0840201\pi\) |
−0.708631 | + | 0.705580i | \(0.750687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5788 | − | 16.5000i | −1.12704 | − | 0.650696i | −0.183851 | − | 0.982954i | \(-0.558856\pi\) |
−0.943189 | + | 0.332258i | \(0.892190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.0000i | − | 1.29736i | −0.761060 | − | 0.648682i | \(-0.775321\pi\) | ||
0.761060 | − | 0.648682i | \(-0.224679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5167 | − | 13.0000i | −0.881145 | − | 0.508729i | −0.0101092 | − | 0.999949i | \(-0.503218\pi\) |
−0.871036 | + | 0.491220i | \(0.836551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.7846 | + | 1.60770i | −1.04656 | + | 0.0628178i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0000 | + | 17.3205i | 0.389545 | + | 0.674711i | 0.992388 | − | 0.123148i | \(-0.0392990\pi\) |
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | − | 6.00000i | −0.465340 | − | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000i | 0.348481i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.00000 | + | 12.1244i | −0.270232 | + | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.19615 | − | 3.00000i | 0.200297 | − | 0.115642i | −0.396497 | − | 0.918036i | \(-0.629774\pi\) |
0.596794 | + | 0.802395i | \(0.296441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0526 | − | 11.0000i | 0.732249 | − | 0.422764i | −0.0869952 | − | 0.996209i | \(-0.527726\pi\) |
0.819244 | + | 0.573444i | \(0.194393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | + | 6.92820i | −0.153506 | + | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.00000i | 0.153056i | 0.997067 | + | 0.0765279i | \(0.0243834\pi\) | ||||
−0.997067 | + | 0.0765279i | \(0.975617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | + | 12.0000i | 0.916993 | + | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | − | 38.1051i | −0.836919 | − | 1.44959i | −0.892458 | − | 0.451130i | \(-0.851021\pi\) |
0.0555386 | − | 0.998457i | \(-0.482312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.7128 | + | 2.14359i | −1.35466 | + | 0.0813111i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0526 | + | 11.0000i | 0.721667 | + | 0.416655i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.0000i | − | 0.452589i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.73205 | − | 1.00000i | −0.0651405 | − | 0.0376089i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5000 | − | 23.3827i | −0.507003 | − | 0.878155i | −0.999967 | − | 0.00810550i | \(-0.997420\pi\) |
0.492964 | − | 0.870050i | \(-0.335913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.73205 | − | 1.00000i | 0.0648658 | − | 0.0374503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.3923 | + | 14.7846i | −0.837425 | + | 0.552913i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.0000 | 1.64092 | 0.820462 | − | 0.571702i | \(-0.193717\pi\) | ||||
0.820462 | + | 0.571702i | \(0.193717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.6769 | − | 5.38269i | 1.65926 | − | 0.199908i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.1865 | − | 10.5000i | 0.674501 | − | 0.389423i | −0.123279 | − | 0.992372i | \(-0.539341\pi\) |
0.797780 | + | 0.602949i | \(0.206008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | − | 6.92820i | −0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.46410 | − | 2.00000i | −0.127950 | − | 0.0738717i | 0.434659 | − | 0.900595i | \(-0.356869\pi\) |
−0.562609 | + | 0.826723i | \(0.690202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.0000i | 0.810380i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0000 | 1.47142 | 0.735712 | − | 0.677295i | \(-0.236848\pi\) | ||||
0.735712 | + | 0.677295i | \(0.236848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.9904 | + | 7.50000i | 0.476571 | + | 0.275148i | 0.718986 | − | 0.695024i | \(-0.244606\pi\) |
−0.242415 | + | 0.970173i | \(0.577940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.23205 | − | 0.133975i | 0.0817760 | − | 0.00490845i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.50000 | + | 2.59808i | 0.0548088 | + | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0000 | − | 22.5167i | 0.474377 | − | 0.821645i | −0.525193 | − | 0.850983i | \(-0.676007\pi\) |
0.999570 | + | 0.0293387i | \(0.00934013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | + | 20.0000i | −0.363937 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000i | 0.363456i | 0.983349 | + | 0.181728i | \(0.0581691\pi\) | ||||
−0.983349 | + | 0.181728i | \(0.941831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | + | 7.79423i | −0.163125 | + | 0.282541i | −0.935988 | − | 0.352032i | \(-0.885491\pi\) |
0.772863 | + | 0.634573i | \(0.218824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.06218 | − | 3.50000i | 0.219466 | − | 0.126709i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7846 | + | 12.0000i | −0.750489 | + | 0.433295i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.50000 | + | 12.9904i | −0.270457 | + | 0.468445i | −0.968979 | − | 0.247143i | \(-0.920508\pi\) |
0.698522 | + | 0.715589i | \(0.253841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 12.0000i | − | 0.431610i | −0.976436 | − | 0.215805i | \(-0.930762\pi\) | ||
0.976436 | − | 0.215805i | \(-0.0692376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | − | 8.00000i | −0.215526 | − | 0.287368i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.0000 | + | 57.1577i | −1.18235 | + | 2.04789i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | − | 10.3923i | −0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.535898 | + | 8.92820i | 0.0191270 | + | 0.318661i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1051 | − | 22.0000i | −1.35830 | − | 0.784215i | −0.368906 | − | 0.929467i | \(-0.620268\pi\) |
−0.989395 | + | 0.145251i | \(0.953601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.0000i | 1.49146i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.73205 | + | 1.00000i | 0.0613524 | + | 0.0354218i | 0.530362 | − | 0.847771i | \(-0.322056\pi\) |
−0.469010 | + | 0.883193i | \(0.655389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.00000 | − | 12.1244i | −0.247642 | − | 0.428929i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.92820 | − | 4.00000i | 0.244491 | − | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.23205 | + | 1.86603i | 0.0434241 | + | 0.0657688i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.46410 | − | 4.92820i | 0.261456 | − | 0.172627i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.7846 | − | 12.0000i | 0.727161 | − | 0.419827i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5000 | − | 26.8468i | −0.540954 | − | 0.936959i | −0.998850 | − | 0.0479535i | \(-0.984730\pi\) |
0.457896 | − | 0.889006i | \(-0.348603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.9904 | + | 7.50000i | 0.452816 | + | 0.261434i | 0.709019 | − | 0.705190i | \(-0.249138\pi\) |
−0.256203 | + | 0.966623i | \(0.582471\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.0000i | 1.21707i | 0.793527 | + | 0.608535i | \(0.208242\pi\) | ||||
−0.793527 | + | 0.608535i | \(0.791758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.0000 | −0.520972 | −0.260486 | − | 0.965478i | \(-0.583883\pi\) | ||||
−0.260486 | + | 0.965478i | \(0.583883\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923 | + | 6.00000i | 0.360072 | + | 0.207888i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.401924 | − | 6.69615i | −0.0139091 | − | 0.231730i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.0000 | + | 32.9090i | 0.655953 | + | 1.13614i | 0.981654 | + | 0.190671i | \(0.0610663\pi\) |
−0.325701 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0000 | + | 46.0000i | −0.791224 | + | 1.58245i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.00000 | + | 1.73205i | −0.0342796 | + | 0.0593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8372 | − | 23.0000i | 1.36400 | − | 0.787505i | 0.373845 | − | 0.927491i | \(-0.378039\pi\) |
0.990153 | + | 0.139986i | \(0.0447058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | + | 12.1244i | −0.238837 | + | 0.413678i | −0.960381 | − | 0.278691i | \(-0.910099\pi\) |
0.721544 | + | 0.692369i | \(0.243433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 45.0000i | − | 1.53182i | −0.642949 | − | 0.765909i | \(-0.722289\pi\) | ||
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 4.00000i | 0.272008 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | + | 20.7846i | −0.407072 | + | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.0000 | + | 57.1577i | 1.11816 | + | 1.93671i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.52628 | − | 7.23205i | 0.288241 | − | 0.244488i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.8372 | + | 23.0000i | 1.34521 | + | 0.776655i | 0.987566 | − | 0.157205i | \(-0.0502483\pi\) |
0.357640 | + | 0.933860i | \(0.383582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.00000i | − | 0.100958i | −0.998725 | − | 0.0504790i | \(-0.983925\pi\) | ||
0.998725 | − | 0.0504790i | \(-0.0160748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.50000 | + | 16.4545i | 0.318620 | + | 0.551866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.3731 | − | 21.0000i | 1.21718 | − | 0.702738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.46410 | − | 3.73205i | −0.0823658 | − | 0.124749i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.0000 | 0.600334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.0167 | − | 24.2583i | −0.532412 | − | 0.806374i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5788 | − | 16.5000i | 0.948945 | − | 0.547874i | 0.0561918 | − | 0.998420i | \(-0.482104\pi\) |
0.892753 | + | 0.450546i | \(0.148771\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | − | 10.3923i | −0.198789 | − | 0.344312i | 0.749347 | − | 0.662177i | \(-0.230367\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.0526 | − | 11.0000i | −0.630548 | − | 0.364047i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 12.0000i | − | 0.396275i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.1769 | − | 18.0000i | −1.02620 | − | 0.592477i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.19615 | + | 3.92820i | 0.302368 | + | 0.129159i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | + | 31.1769i | −0.589926 | + | 1.02178i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | + | 4.00000i | 0.261628 | + | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 52.0000i | − | 1.69877i | −0.527777 | − | 0.849383i | \(-0.676974\pi\) | ||
0.527777 | − | 0.849383i | \(-0.323026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.5000 | + | 35.5070i | −0.668281 | + | 1.15750i | 0.310104 | + | 0.950703i | \(0.399636\pi\) |
−0.978385 | + | 0.206794i | \(0.933697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.52628 | − | 5.50000i | 0.310218 | − | 0.179105i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.1673 | − | 25.5000i | 1.43524 | − | 0.828639i | 0.437730 | − | 0.899106i | \(-0.355783\pi\) |
0.997514 | + | 0.0704677i | \(0.0224492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | − | 20.7846i | 0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.00000i | − | 0.0647864i | −0.999475 | − | 0.0323932i | \(-0.989687\pi\) | ||
0.999475 | − | 0.0323932i | \(-0.0103129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | − | 12.0000i | 0.194155 | − | 0.388311i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | + | 10.3923i | −0.193750 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.33975 | + | 22.3205i | 0.0431279 | + | 0.718523i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7224 | + | 8.50000i | 0.473441 | + | 0.273342i | 0.717679 | − | 0.696374i | \(-0.245204\pi\) |
−0.244238 | + | 0.969715i | \(0.578538\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.0000 | −1.34784 | −0.673922 | − | 0.738802i | \(-0.735392\pi\) | ||||
−0.673922 | + | 0.738802i | \(0.735392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16.0000i | − | 0.512936i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.7654 | − | 27.0000i | −1.49616 | − | 0.863807i | −0.496167 | − | 0.868227i | \(-0.665259\pi\) |
−0.999990 | + | 0.00442082i | \(0.998593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00000 | + | 1.73205i | 0.0319601 | + | 0.0553566i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.4545 | + | 9.50000i | −0.524816 | + | 0.303003i | −0.738903 | − | 0.673812i | \(-0.764656\pi\) |
0.214087 | + | 0.976815i | \(0.431323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.9282 | + | 9.85641i | −0.475652 | + | 0.314051i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.1769 | − | 33.5885i | −0.703055 | − | 1.06483i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))