Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), 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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.2.i.f.541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | + | 7.79423i | −0.938315 | + | 1.62521i | −0.169701 | + | 0.985496i | \(0.554280\pi\) |
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | − | 6.06218i | 0.628619 | − | 1.08880i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 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 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | + | 20.7846i | −1.36753 | + | 2.36863i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.50000 | + | 7.79423i | 0.493939 | + | 0.855528i | 0.999976 | − | 0.00698436i | \(-0.00222321\pi\) |
−0.506036 | + | 0.862512i | \(0.668890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50000 | + | 2.59808i | −0.162698 | + | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.50000 | − | 6.06218i | 0.359092 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | − | 6.92820i | −0.406138 | − | 0.703452i | 0.588315 | − | 0.808632i | \(-0.299792\pi\) |
−0.994453 | + | 0.105180i | \(0.966458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.0000 | − | 24.2487i | −1.21395 | − | 2.10263i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.0000 | 2.00698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50000 | + | 6.06218i | 0.281127 | + | 0.486926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | − | 8.66025i | 0.399043 | − | 0.691164i | −0.594565 | − | 0.804048i | \(-0.702676\pi\) |
0.993608 | + | 0.112884i | \(0.0360089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −36.0000 | −2.83720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0000 | −1.72317 | −0.861586 | − | 0.507611i | \(-0.830529\pi\) | ||||
−0.861586 | + | 0.507611i | \(0.830529\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.50000 | − | 7.79423i | −0.342129 | − | 0.592584i | 0.642699 | − | 0.766119i | \(-0.277815\pi\) |
−0.984828 | + | 0.173534i | \(0.944481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | + | 1.73205i | −0.0735215 | + | 0.127343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | + | 15.5885i | 0.658145 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | + | 6.92820i | −0.287926 | + | 0.498703i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
0.685388 | + | 0.728178i | \(0.259632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0000 | − | 36.3731i | −1.45260 | − | 2.51598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.0000 | 1.90076 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00000 | − | 12.1244i | −0.468755 | − | 0.811907i | 0.530607 | − | 0.847618i | \(-0.321964\pi\) |
−0.999362 | + | 0.0357107i | \(0.988630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.50000 | − | 12.9904i | −0.497792 | − | 0.862202i | 0.502204 | − | 0.864749i | \(-0.332523\pi\) |
−0.999997 | + | 0.00254715i | \(0.999189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5000 | − | 21.6506i | 0.826023 | − | 1.43071i | −0.0751115 | − | 0.997175i | \(-0.523931\pi\) |
0.901135 | − | 0.433539i | \(-0.142735\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | − | 15.5885i | 0.582162 | − | 1.00833i | −0.413061 | − | 0.910703i | \(-0.635540\pi\) |
0.995223 | − | 0.0976302i | \(-0.0311262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | + | 21.6506i | 0.805196 | + | 1.39464i | 0.916159 | + | 0.400815i | \(0.131273\pi\) |
−0.110963 | + | 0.993825i | \(0.535394\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.50000 | − | 7.79423i | −0.287494 | − | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0000 | + | 24.2487i | −0.890799 | + | 1.54291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −54.0000 | −3.39495 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.50000 | − | 12.9904i | 0.467837 | − | 0.810318i | −0.531487 | − | 0.847066i | \(-0.678367\pi\) |
0.999325 | + | 0.0367485i | \(0.0117000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | + | 6.92820i | 0.248548 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.50000 | − | 7.79423i | 0.276433 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | − | 5.19615i | 0.180907 | − | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 19.0526i | 0.660926 | + | 1.14476i | 0.980373 | + | 0.197153i | \(0.0631696\pi\) |
−0.319447 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | − | 20.7846i | −0.715860 | − | 1.23991i | −0.962627 | − | 0.270831i | \(-0.912702\pi\) |
0.246767 | − | 0.969075i | \(-0.420632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.00000 | + | 1.73205i | −0.0594438 | + | 0.102960i | −0.894216 | − | 0.447636i | \(-0.852266\pi\) |
0.834772 | + | 0.550596i | \(0.185599\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.50000 | − | 12.9904i | 0.438155 | − | 0.758906i | −0.559393 | − | 0.828903i | \(-0.688966\pi\) |
0.997547 | + | 0.0699967i | \(0.0222989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | − | 10.3923i | −0.349334 | − | 0.605063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0000 | + | 31.1769i | 1.04097 | + | 1.80301i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 6.92820i | 0.230556 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.0000 | −1.94048 | −0.970241 | − | 0.242140i | \(-0.922151\pi\) | ||||
−0.970241 | + | 0.242140i | \(0.922151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | − | 17.3205i | −0.565233 | − | 0.979013i | −0.997028 | − | 0.0770410i | \(-0.975453\pi\) |
0.431795 | − | 0.901972i | \(-0.357881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | + | 7.79423i | 0.252745 | + | 0.437767i | 0.964281 | − | 0.264883i | \(-0.0853332\pi\) |
−0.711535 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.0000 | −1.16847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(335\) | −1.00000 | − | 1.73205i | −0.0546358 | − | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | − | 24.2487i | 0.762629 | − | 1.32091i | −0.178863 | − | 0.983874i | \(-0.557242\pi\) |
0.941491 | − | 0.337037i | \(-0.109425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.0000 | 2.27443 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.50000 | + | 16.4545i | 0.508523 | + | 0.880788i | 0.999951 | + | 0.00987003i | \(0.00314178\pi\) |
−0.491428 | + | 0.870918i | \(0.663525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | + | 1.73205i | −0.0523424 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0000 | − | 31.1769i | −0.934513 | − | 1.61862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | − | 3.46410i | 0.103556 | − | 0.179364i | −0.809591 | − | 0.586994i | \(-0.800311\pi\) |
0.913147 | + | 0.407630i | \(0.133645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.50000 | + | 7.79423i | −0.229939 | + | 0.398266i | −0.957790 | − | 0.287469i | \(-0.907186\pi\) |
0.727851 | + | 0.685736i | \(0.240519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | − | 20.7846i | −0.611577 | − | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5000 | + | 23.3827i | −0.682724 | + | 1.18251i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | −0.0503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | − | 24.2487i | −0.697390 | − | 1.20791i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | + | 10.3923i | 0.297409 | + | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.50000 | + | 14.7224i | −0.420298 | + | 0.727977i | −0.995968 | − | 0.0897044i | \(-0.971408\pi\) |
0.575670 | + | 0.817682i | \(0.304741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −48.0000 | −2.36193 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0000 | − | 25.9808i | 0.732798 | − | 1.26924i | −0.222885 | − | 0.974845i | \(-0.571547\pi\) |
0.955683 | − | 0.294398i | \(-0.0951193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5000 | + | 32.0429i | 0.901635 | + | 1.56168i | 0.825372 | + | 0.564590i | \(0.190966\pi\) |
0.0762630 | + | 0.997088i | \(0.475701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.0000 | + | 24.2487i | −0.677507 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0000 | 1.73406 | 0.867029 | − | 0.498257i | \(-0.166026\pi\) | ||||
0.867029 | + | 0.498257i | \(0.166026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.5000 | − | 54.5596i | 1.50685 | − | 2.60994i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.5000 | − | 23.3827i | −0.641404 | − | 1.11094i | −0.985119 | − | 0.171871i | \(-0.945019\pi\) |
0.343715 | − | 0.939074i | \(-0.388315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.00000 | + | 13.8564i | −0.375046 | + | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | − | 6.92820i | −0.187112 | − | 0.324088i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
−0.944286 | + | 0.329125i | \(0.893246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.00000 | − | 5.19615i | −0.139724 | − | 0.242009i | 0.787668 | − | 0.616100i | \(-0.211288\pi\) |
−0.927392 | + | 0.374091i | \(0.877955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.0000 | −1.52706 | −0.763529 | − | 0.645774i | \(-0.776535\pi\) | ||||
−0.763529 | + | 0.645774i | \(0.776535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | − | 10.3923i | 0.275880 | − | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | + | 6.06218i | 0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.00000 | + | 5.19615i | 0.137073 | + | 0.237418i | 0.926388 | − | 0.376571i | \(-0.122897\pi\) |
−0.789314 | + | 0.613990i | \(0.789564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | − | 6.92820i | 0.182384 | − | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.00000 | 0.363261 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.0000 | 1.72194 | 0.860972 | − | 0.508652i | \(-0.169856\pi\) | ||||
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | + | 25.9808i | −0.676941 | + | 1.17250i | 0.298957 | + | 0.954267i | \(0.403361\pi\) |
−0.975898 | + | 0.218229i | \(0.929972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | − | 20.7846i | −0.538274 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | + | 4.33013i | −0.111915 | + | 0.193843i | −0.916542 | − | 0.399937i | \(-0.869032\pi\) |
0.804627 | + | 0.593780i | \(0.202365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.0000 | 1.47140 | 0.735699 | − | 0.677309i | \(-0.236854\pi\) | ||||
0.735699 | + | 0.677309i | \(0.236854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.00000 | + | 10.3923i | −0.265945 | + | 0.460631i | −0.967811 | − | 0.251679i | \(-0.919017\pi\) |
0.701866 | + | 0.712309i | \(0.252351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | + | 3.46410i | 0.0881305 | + | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0000 | 1.39926 | 0.699631 | − | 0.714504i | \(-0.253348\pi\) | ||||
0.699631 | + | 0.714504i | \(0.253348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.5000 | − | 18.1865i | 0.457387 | − | 0.792218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | − | 20.7846i | −0.519778 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | + | 10.3923i | −0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −54.0000 | −2.32594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.50000 | + | 4.33013i | −0.107088 | + | 0.185482i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0000 | − | 22.5167i | −0.555840 | − | 0.962743i | −0.997838 | − | 0.0657267i | \(-0.979063\pi\) |
0.441998 | − | 0.897016i | \(-0.354270\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 3.46410i | −0.0850487 | + | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000 | + | 31.1769i | 0.754599 | + | 1.30700i | 0.945573 | + | 0.325409i | \(0.105502\pi\) |
−0.190974 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.50000 | − | 6.06218i | 0.146470 | − | 0.253694i | −0.783450 | − | 0.621455i | \(-0.786542\pi\) |
0.929921 | + | 0.367760i | \(0.119875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.00000 | 0.375326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | + | 31.1769i | −0.746766 | + | 1.29344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0000 | − | 46.7654i | −1.11823 | − | 1.93682i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5000 | + | 33.7750i | 0.804851 | + | 1.39404i | 0.916392 | + | 0.400283i | \(0.131088\pi\) |
−0.111540 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.5000 | + | 42.4352i | −1.00950 | + | 1.74851i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.0000 | 0.862367 | 0.431183 | − | 0.902264i | \(-0.358096\pi\) | ||||
0.431183 | + | 0.902264i | \(0.358096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0000 | − | 31.1769i | 0.735460 | − | 1.27385i | −0.219061 | − | 0.975711i | \(-0.570299\pi\) |
0.954521 | − | 0.298143i | \(-0.0963673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | + | 6.06218i | 0.142768 | + | 0.247281i | 0.928538 | − | 0.371237i | \(-0.121066\pi\) |
−0.785770 | + | 0.618519i | \(0.787733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.5000 | − | 21.6506i | −0.508197 | − | 0.880223i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.50000 | + | 12.9904i | −0.301939 | + | 0.522973i | −0.976575 | − | 0.215177i | \(-0.930967\pi\) |
0.674636 | + | 0.738150i | \(0.264300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | − | 17.3205i | −0.401934 | − | 0.696170i | 0.592025 | − | 0.805919i | \(-0.298329\pi\) |
−0.993959 | + | 0.109749i | \(0.964995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | + | 20.7846i | 0.480770 | + | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0000 | 0.915616 | 0.457808 | − | 0.889051i | \(-0.348635\pi\) | ||||
0.457808 | + | 0.889051i | \(0.348635\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00000 | + | 1.73205i | −0.0396838 | + | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000 | + | 31.1769i | 0.713186 | + | 1.23527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | − | 3.46410i | 0.0788723 | − | 0.136611i | −0.823891 | − | 0.566748i | \(-0.808201\pi\) |
0.902764 | + | 0.430137i | \(0.141535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.0000 | −1.06148 | −0.530740 | − | 0.847535i | \(-0.678086\pi\) | ||||
−0.530740 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −72.0000 | −2.82625 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.50000 | − | 7.79423i | 0.176099 | − | 0.305012i | −0.764442 | − | 0.644692i | \(-0.776986\pi\) |
0.940541 | + | 0.339680i | \(0.110319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | − | 5.19615i | −0.117220 | − | 0.203030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | − | 20.7846i | −0.467454 | − | 0.809653i | 0.531855 | − | 0.846836i | \(-0.321495\pi\) |
−0.999309 | + | 0.0371821i | \(0.988162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.0000 | 1.08579 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0000 | + | 36.3731i | −0.810696 | + | 1.40417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | + | 24.2487i | 0.539660 | + | 0.934719i | 0.998922 | + | 0.0464181i | \(0.0147807\pi\) |
−0.459262 | + | 0.888301i | \(0.651886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.0000 | + | 25.9808i | 0.576497 | + | 0.998522i | 0.995877 | + | 0.0907112i | \(0.0289140\pi\) |
−0.419380 | + | 0.907811i | \(0.637753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0000 | − | 27.7128i | 0.614024 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.0000 | 1.49229 | 0.746147 | − | 0.665782i | \(-0.231902\pi\) | ||||
0.746147 | + | 0.665782i | \(0.231902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | + | 31.1769i | −0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5000 | + | 32.0429i | 0.703773 | + | 1.21897i | 0.967132 | + | 0.254273i | \(0.0818362\pi\) |
−0.263359 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0000 | + | 41.5692i | −0.902613 | + | 1.56337i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0000 | + | 39.8372i | 0.863783 | + | 1.49612i | 0.868250 | + | 0.496126i | \(0.165245\pi\) |
−0.00446726 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.5000 | + | 54.5596i | 1.17968 | + | 2.04327i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | + | 20.7846i | −0.448775 | + | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | + | 24.2487i | 0.519231 | + | 0.899335i | 0.999750 | + | 0.0223506i | \(0.00711500\pi\) |
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | − | 5.19615i | −0.110959 | − | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0000 | − | 34.6410i | 0.738717 | − | 1.27950i | −0.214356 | − | 0.976756i | \(-0.568765\pi\) |
0.953073 | − | 0.302740i | \(-0.0979013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0000 | 0.404642 | 0.202321 | − | 0.979319i | \(-0.435152\pi\) | ||||
0.202321 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | − | 20.7846i | 0.440237 | − | 0.762513i | −0.557470 | − | 0.830197i | \(-0.688228\pi\) |
0.997707 | + | 0.0676840i | \(0.0215610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000 | + | 41.5692i | 0.876941 | + | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | + | 19.9186i | −0.419641 | + | 0.726839i | −0.995903 | − | 0.0904254i | \(-0.971177\pi\) |
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | + | 17.3205i | 0.362024 | + | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | + | 41.5692i | 0.866590 | + | 1.50098i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.50000 | + | 4.33013i | −0.0901523 | + | 0.156148i | −0.907575 | − | 0.419890i | \(-0.862069\pi\) |
0.817423 | + | 0.576038i | \(0.195402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.00000 | −0.323708 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.00000 | −0.251447 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.0000 | + | 36.3731i | −0.752403 | + | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.00000 | + | 8.66025i | 0.178458 | + | 0.309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.0000 | + | 22.5167i | −0.463400 | + | 0.802632i | −0.999128 | − | 0.0417585i | \(-0.986704\pi\) |
0.535728 | + | 0.844391i | \(0.320037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.0000 | 0.994309 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.50000 | − | 2.59808i | 0.0531327 | − | 0.0920286i | −0.838236 | − | 0.545308i | \(-0.816413\pi\) |
0.891368 | + | 0.453279i | \(0.149746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||