Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(883,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("2646.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.f (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: | \(21.1284163748\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1765.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1765 |
Dual form | 2646.2.f.c.883.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 1.50000 | + | 2.59808i | 0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | + | 5.19615i | −0.639602 | + | 1.10782i | ||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | − | 5.19615i | −0.514496 | − | 0.891133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −3.50000 | − | 6.06218i | −0.567775 | − | 0.983415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | + | 1.73205i | 0.138675 | + | 0.240192i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.0000 | −2.42712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | −3.00000 | + | 5.19615i | −0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.50000 | + | 6.06218i | −0.401478 | + | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | − | 15.5885i | 0.976187 | − | 1.69081i | ||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | − | 5.19615i | −0.319801 | − | 0.553912i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.5000 | − | 18.1865i | 1.07728 | − | 1.86590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | + | 1.73205i | 0.101535 | + | 0.175863i | 0.912317 | − | 0.409484i | \(-0.134291\pi\) |
−0.810782 | + | 0.585348i | \(0.800958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | + | 8.66025i | −0.492665 | + | 0.853320i | −0.999964 | − | 0.00844953i | \(-0.997310\pi\) |
0.507300 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(104\) | 1.00000 | − | 1.73205i | 0.0980581 | − | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 9.00000 | + | 15.5885i | 0.858116 | + | 1.48630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.50000 | − | 12.9904i | 0.705541 | − | 1.22203i | −0.260955 | − | 0.965351i | \(-0.584038\pi\) |
0.966496 | − | 0.256681i | \(-0.0826291\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | − | 7.79423i | −0.419627 | − | 0.726816i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 2.50000 | − | 4.33013i | 0.226339 | − | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | + | 5.19615i | −0.263117 | + | 0.455733i | ||||
\(131\) | 4.50000 | − | 7.79423i | 0.393167 | − | 0.680985i | −0.599699 | − | 0.800226i | \(-0.704713\pi\) |
0.992865 | + | 0.119241i | \(0.0380462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | − | 4.33013i | 0.212047 | − | 0.367277i | −0.740308 | − | 0.672268i | \(-0.765320\pi\) |
0.952355 | + | 0.304991i | \(0.0986536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50000 | + | 2.59808i | 0.125877 | + | 0.218026i | ||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 1.00000 | + | 1.73205i | 0.0827606 | + | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | −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 | ||||||||
\(151\) | −11.5000 | − | 19.9186i | −0.935857 | − | 1.62095i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
−0.162758 | − | 0.986666i | \(-0.552039\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.50000 | + | 11.2583i | −0.518756 | + | 0.898513i | 0.481006 | + | 0.876717i | \(0.340272\pi\) |
−0.999762 | + | 0.0217953i | \(0.993062\pi\) | |||||||
\(158\) | −2.50000 | + | 4.33013i | −0.198889 | + | 0.344486i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.50000 | + | 2.59808i | 0.118585 | + | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | −18.0000 | −1.38054 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | + | 5.19615i | −0.226134 | + | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.0000 | 1.85824 | 0.929118 | − | 0.369784i | \(-0.120568\pi\) | ||||
0.929118 | + | 0.369784i | \(0.120568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.50000 | − | 2.59808i | 0.110581 | − | 0.191533i | ||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | − | 31.1769i | −1.31629 | − | 2.27988i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.0000 | −1.52350 | ||||||||
\(191\) | −4.50000 | − | 7.79423i | −0.325609 | − | 0.563971i | 0.656027 | − | 0.754738i | \(-0.272236\pi\) |
−0.981635 | + | 0.190767i | \(0.938902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | + | 14.7224i | −0.611843 | + | 1.05974i | 0.379086 | + | 0.925361i | \(0.376238\pi\) |
−0.990930 | + | 0.134382i | \(0.957095\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.50000 | + | 7.79423i | −0.316619 | + | 0.548400i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.0000 | 0.696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −21.0000 | − | 36.3731i | −1.45260 | − | 2.51598i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.00000 | + | 8.66025i | 0.338643 | + | 0.586546i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.00000 | − | 15.5885i | 0.606780 | − | 1.05097i | ||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0000 | − | 24.2487i | −0.937509 | − | 1.62381i | −0.770097 | − | 0.637927i | \(-0.779792\pi\) |
−0.167412 | − | 0.985887i | \(-0.553541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | 7.50000 | + | 12.9904i | 0.497792 | + | 0.862202i | 0.999997 | − | 0.00254715i | \(-0.000810783\pi\) |
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | −4.50000 | + | 7.79423i | −0.296721 | + | 0.513936i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | + | 6.92820i | 0.257663 | + | 0.446285i | 0.965615 | − | 0.259975i | \(-0.0837143\pi\) |
−0.707953 | + | 0.706260i | \(0.750381\pi\) | |||||||
\(242\) | 25.0000 | 1.60706 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | − | 12.1244i | 0.445399 | − | 0.771454i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −8.50000 | − | 14.7224i | −0.533337 | − | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.00000 | −0.556022 | ||||||||
\(263\) | −10.5000 | − | 18.1865i | −0.647458 | − | 1.12143i | −0.983728 | − | 0.179664i | \(-0.942499\pi\) |
0.336270 | − | 0.941766i | \(-0.390834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | + | 15.5885i | −0.552866 | + | 0.957591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | −9.00000 | −0.548740 | −0.274370 | − | 0.961624i | \(-0.588469\pi\) | ||||
−0.274370 | + | 0.961624i | \(0.588469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0000 | 1.70088 | 0.850439 | − | 0.526073i | \(-0.176336\pi\) | ||||
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | −3.00000 | − | 5.19615i | −0.181902 | − | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | − | 5.19615i | 0.181237 | − | 0.313911i | ||||
\(275\) | −12.0000 | + | 20.7846i | −0.723627 | + | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | −5.00000 | −0.299880 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5000 | − | 23.3827i | −0.805342 | − | 1.39489i | −0.916060 | − | 0.401042i | \(-0.868648\pi\) |
0.110717 | − | 0.993852i | \(-0.464685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.50000 | + | 16.4545i | −0.564716 | + | 0.978117i | 0.432360 | + | 0.901701i | \(0.357681\pi\) |
−0.997076 | + | 0.0764162i | \(0.975652\pi\) | |||||||
\(284\) | 1.50000 | − | 2.59808i | 0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | + | 10.3923i | 0.354787 | + | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | −9.00000 | − | 15.5885i | −0.528498 | − | 0.915386i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | − | 1.73205i | 0.0585206 | − | 0.101361i | ||||
\(293\) | 1.50000 | − | 2.59808i | 0.0876309 | − | 0.151781i | −0.818878 | − | 0.573967i | \(-0.805404\pi\) |
0.906509 | + | 0.422186i | \(0.138737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.5000 | + | 19.9186i | −0.661751 | + | 1.14619i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 6.06218i | −0.200739 | − | 0.347690i | ||||
\(305\) | 15.0000 | 0.858898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | − | 8.66025i | −0.282617 | − | 0.489506i | 0.689412 | − | 0.724370i | \(-0.257869\pi\) |
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | − | 31.1769i | 1.00781 | − | 1.74557i | ||||
\(320\) | 1.50000 | − | 2.59808i | 0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.0000 | 2.33694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | −0.443760 | ||||||||
\(326\) | −1.00000 | − | 1.73205i | −0.0553849 | − | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | − | 22.5167i | −0.714545 | − | 1.23763i | −0.963135 | − | 0.269019i | \(-0.913301\pi\) |
0.248590 | − | 0.968609i | \(-0.420033\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | + | 20.7846i | 0.655630 | + | 1.13558i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | + | 15.5885i | 0.488094 | + | 0.845403i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.00000 | − | 1.73205i | −0.0539164 | − | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | −12.0000 | + | 20.7846i | −0.644194 | + | 1.11578i | 0.340293 | + | 0.940319i | \(0.389474\pi\) |
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0000 | + | 22.5167i | 0.695874 | + | 1.20529i | 0.969885 | + | 0.243563i | \(0.0783162\pi\) |
−0.274011 | + | 0.961727i | \(0.588351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.00000 | 0.319801 | ||||||||
\(353\) | 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 | ||||||||
\(355\) | −4.50000 | + | 7.79423i | −0.238835 | + | 0.413675i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | + | 15.5885i | 0.475665 | + | 0.823876i | ||||
\(359\) | 3.00000 | 0.158334 | 0.0791670 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791670 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −12.5000 | − | 21.6506i | −0.656985 | − | 1.13793i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | + | 5.19615i | −0.157027 | + | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | + | 6.92820i | 0.208798 | + | 0.361649i | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | −3.00000 | −0.156386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | + | 12.1244i | −0.362446 | + | 0.627775i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | −18.0000 | + | 31.1769i | −0.930758 | + | 1.61212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 10.5000 | + | 18.1865i | 0.538639 | + | 0.932949i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.50000 | + | 7.79423i | −0.230240 | + | 0.398787i | ||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.0000 | 0.865277 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | −15.0000 | −0.754732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.0000 | −1.30490 | −0.652451 | − | 0.757831i | \(-0.726259\pi\) | ||||
−0.652451 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(398\) | 7.00000 | + | 12.1244i | 0.350878 | + | 0.607739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 9.00000 | 0.447767 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | − | 10.3923i | −0.297409 | − | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | − | 27.7128i | 0.791149 | − | 1.37031i | −0.134107 | − | 0.990967i | \(-0.542817\pi\) |
0.925256 | − | 0.379344i | \(-0.123850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.00000 | − | 8.66025i | −0.246332 | − | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.0000 | −1.76717 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.0000 | + | 36.3731i | −1.02714 | + | 1.77906i | ||||
\(419\) | −7.50000 | + | 12.9904i | −0.366399 | + | 0.634622i | −0.989000 | − | 0.147918i | \(-0.952743\pi\) |
0.622601 | + | 0.782540i | \(0.286076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −12.0000 | − | 20.7846i | −0.582086 | − | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.00000 | + | 10.3923i | −0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00000 | + | 5.19615i | 0.144673 | + | 0.250581i | ||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | 10.5000 | − | 18.1865i | 0.502283 | − | 0.869980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | −18.0000 | −0.858116 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 9.00000 | + | 15.5885i | 0.427603 | + | 0.740630i | 0.996660 | − | 0.0816684i | \(-0.0260248\pi\) |
−0.569057 | + | 0.822298i | \(0.692691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | + | 24.2487i | −0.662919 | + | 1.14821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.50000 | − | 12.9904i | 0.351992 | − | 0.609669i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5000 | − | 25.1147i | −0.678281 | − | 1.17482i | −0.975498 | − | 0.220008i | \(-0.929392\pi\) |
0.297217 | − | 0.954810i | \(-0.403942\pi\) | |||||||
\(458\) | 1.00000 | 0.0467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.00000 | 0.419627 | ||||||||
\(461\) | 16.5000 | + | 28.5788i | 0.768482 | + | 1.33105i | 0.938386 | + | 0.345589i | \(0.112321\pi\) |
−0.169904 | + | 0.985461i | \(0.554346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50000 | − | 11.2583i | 0.302081 | − | 0.523219i | −0.674526 | − | 0.738251i | \(-0.735652\pi\) |
0.976607 | + | 0.215032i | \(0.0689855\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | + | 7.79423i | 0.208458 | + | 0.361061i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | + | 10.3923i | −0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | − | 24.2487i | −0.642364 | − | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.0000 | 0.686084 | ||||||||
\(479\) | 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 | ||||||||
\(481\) | 2.00000 | − | 3.46410i | 0.0911922 | − | 0.157949i | ||||
\(482\) | 4.00000 | − | 6.92820i | 0.182195 | − | 0.315571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.0000 | 1.31412 | 0.657058 | − | 0.753840i | \(-0.271801\pi\) | ||||
0.657058 | + | 0.753840i | \(0.271801\pi\) | |||||||
\(488\) | 2.50000 | + | 4.33013i | 0.113170 | + | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | − | 15.5885i | 0.406164 | − | 0.703497i | −0.588292 | − | 0.808649i | \(-0.700199\pi\) |
0.994456 | + | 0.105151i | \(0.0335327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | + | 31.1769i | 0.810679 | + | 1.40414i | ||||
\(494\) | −14.0000 | −0.629890 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | + | 27.7128i | −0.716258 | + | 1.24060i | 0.246214 | + | 0.969216i | \(0.420813\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | −1.50000 | + | 2.59808i | −0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.50000 | − | 2.59808i | −0.0669483 | − | 0.115958i | ||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.50000 | + | 14.7224i | −0.377127 | + | 0.653202i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 15.0000 | + | 25.9808i | 0.660979 | + | 1.14485i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | − | 5.19615i | −0.131559 | − | 0.227866i | ||||
\(521\) | 24.0000 | 1.05146 | 0.525730 | − | 0.850652i | \(-0.323792\pi\) | ||||
0.525730 | + | 0.850652i | \(0.323792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0000 | 0.568450 | 0.284225 | − | 0.958758i | \(-0.408264\pi\) | ||||
0.284225 | + | 0.958758i | \(0.408264\pi\) | |||||||
\(524\) | 4.50000 | + | 7.79423i | 0.196583 | + | 0.340492i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.5000 | + | 18.1865i | −0.457822 | + | 0.792971i | ||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 18.0000 | 0.781870 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | − | 31.1769i | 0.778208 | − | 1.34790i | ||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.50000 | + | 7.79423i | 0.194009 | + | 0.336033i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | −14.0000 | − | 24.2487i | −0.601351 | − | 1.04157i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | −15.0000 | + | 25.9808i | −0.642529 | + | 1.11289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0000 | − | 27.7128i | −0.684111 | − | 1.18491i | −0.973715 | − | 0.227768i | \(-0.926857\pi\) |
0.289605 | − | 0.957146i | \(-0.406476\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.0000 | 1.02336 | ||||||||
\(551\) | 21.0000 | + | 36.3731i | 0.894630 | + | 1.54954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.00000 | − | 13.8564i | 0.339887 | − | 0.588702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5000 | + | 23.3827i | −0.569463 | + | 0.986339i | ||||
\(563\) | 16.5000 | − | 28.5788i | 0.695392 | − | 1.20445i | −0.274656 | − | 0.961542i | \(-0.588564\pi\) |
0.970048 | − | 0.242912i | \(-0.0781026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5000 | − | 38.9711i | −0.946582 | − | 1.63953i | ||||
\(566\) | 19.0000 | 0.798630 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −9.00000 | − | 15.5885i | −0.377300 | − | 0.653502i | 0.613369 | − | 0.789797i | \(-0.289814\pi\) |
−0.990668 | + | 0.136295i | \(0.956481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 6.00000 | − | 10.3923i | 0.250873 | − | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.00000 | 0.166522 | 0.0832611 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832611 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(578\) | −9.50000 | − | 16.4545i | −0.395148 | − | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.00000 | + | 15.5885i | −0.373705 | + | 0.647275i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | + | 31.1769i | 0.745484 | + | 1.29122i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.00000 | −0.123929 | ||||||||
\(587\) | 1.50000 | + | 2.59808i | 0.0619116 | + | 0.107234i | 0.895320 | − | 0.445424i | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00000 | − | 12.1244i | 0.288430 | − | 0.499575i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | + | 5.19615i | −0.122679 | + | 0.212486i | ||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | + | 12.1244i | 0.285536 | + | 0.494563i | 0.972739 | − | 0.231903i | \(-0.0744951\pi\) |
−0.687203 | + | 0.726465i | \(0.741162\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.0000 | 0.935857 | ||||||||
\(605\) | 37.5000 | + | 64.9519i | 1.52459 | + | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.0000 | + | 19.0526i | −0.446476 | + | 0.773320i | −0.998154 | − | 0.0607380i | \(-0.980655\pi\) |
0.551678 | + | 0.834058i | \(0.313988\pi\) | |||||||
\(608\) | −3.50000 | + | 6.06218i | −0.141944 | + | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.50000 | − | 12.9904i | −0.303666 | − | 0.525965i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | 0.323117 | 0.161558 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161558 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(614\) | −12.5000 | − | 21.6506i | −0.504459 | − | 0.873749i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0000 | − | 36.3731i | 0.845428 | − | 1.46432i | −0.0398207 | − | 0.999207i | \(-0.512679\pi\) |
0.885249 | − | 0.465118i | \(-0.153988\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.50000 | − | 6.06218i | −0.140677 | − | 0.243659i | 0.787075 | − | 0.616858i | \(-0.211595\pi\) |
−0.927752 | + | 0.373198i | \(0.878261\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −5.00000 | + | 8.66025i | −0.199840 | + | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.50000 | − | 11.2583i | −0.259378 | − | 0.449256i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.00000 | −0.278666 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(632\) | −2.50000 | − | 4.33013i | −0.0994447 | − | 0.172243i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 25.5000 | − | 44.1673i | 1.01194 | − | 1.75273i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −36.0000 | −1.42525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | 13.5000 | + | 23.3827i | 0.533218 | + | 0.923561i | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.00000 | + | 3.46410i | −0.0788723 | + | 0.136611i | −0.902764 | − | 0.430137i | \(-0.858465\pi\) |
0.823891 | + | 0.566748i | \(0.191799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0000 | − | 36.3731i | −0.826234 | − | 1.43108i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.00000 | + | 6.92820i | 0.156893 | + | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −18.0000 | + | 31.1769i | −0.704394 | + | 1.22005i | 0.262515 | + | 0.964928i | \(0.415448\pi\) |
−0.966910 | + | 0.255119i | \(0.917885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5000 | − | 23.3827i | −0.527489 | − | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.0000 | + | 36.3731i | 0.818044 | + | 1.41689i | 0.907122 | + | 0.420869i | \(0.138275\pi\) |
−0.0890776 | + | 0.996025i | \(0.528392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50000 | − | 4.33013i | 0.0972387 | − | 0.168422i | −0.813302 | − | 0.581842i | \(-0.802332\pi\) |
0.910541 | + | 0.413419i | \(0.135666\pi\) | |||||||
\(662\) | −13.0000 | + | 22.5167i | −0.505259 | + | 0.875135i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | − | 10.3923i | −0.232845 | − | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | 0.696963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.0000 | − | 20.7846i | 0.463600 | − | 0.802980i | ||||
\(671\) | 15.0000 | − | 25.9808i | 0.579069 | − | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5000 | + | 32.0429i | 0.713123 | + | 1.23516i | 0.963679 | + | 0.267063i | \(0.0860531\pi\) |
−0.250557 | + | 0.968102i | \(0.580614\pi\) | |||||||
\(674\) | −22.0000 | −0.847408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −21.0000 | − | 36.3731i | −0.807096 | − | 1.39793i | −0.914867 | − | 0.403755i | \(-0.867705\pi\) |
0.107772 | − | 0.994176i | \(-0.465628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.00000 | − | 15.5885i | 0.345134 | − | 0.597790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | + | 10.3923i | 0.229752 | + | 0.397942i | ||||
\(683\) | 6.00000 | 0.229584 | 0.114792 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5000 | + | 40.7032i | 0.893982 | + | 1.54842i | 0.835059 | + | 0.550160i | \(0.185433\pi\) |
0.0589228 | + | 0.998263i | \(0.481233\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −7.50000 | − | 12.9904i | −0.284491 | − | 0.492753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | −3.00000 | − | 5.19615i | −0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | − | 15.5885i | 0.338719 | − | 0.586679i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | + | 45.0333i | 0.976450 | + | 1.69126i | 0.675063 | + | 0.737760i | \(0.264116\pi\) |
0.301388 | + | 0.953502i | \(0.402550\pi\) | |||||||
\(710\) | 9.00000 | 0.337764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | − | 5.19615i | −0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | + | 31.1769i | −0.673162 | + | 1.16595i | ||||
\(716\) | 9.00000 | − | 15.5885i | 0.336346 | − | 0.582568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.50000 | − | 2.59808i | −0.0559795 | − | 0.0969593i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | − | 25.9808i | −0.558242 | − | 0.966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.5000 | + | 21.6506i | −0.464559 | + | 0.804640i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.00000 | + | 6.92820i | 0.148352 | + | 0.256953i | 0.930618 | − | 0.365991i | \(-0.119270\pi\) |
−0.782267 | + | 0.622944i | \(0.785937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5000 | − | 25.1147i | 0.535570 | − | 0.927634i | −0.463566 | − | 0.886062i | \(-0.653430\pi\) |
0.999136 | − | 0.0415715i | \(-0.0132364\pi\) | |||||||
\(734\) | 4.00000 | − | 6.92820i | 0.147643 | − | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.50000 | + | 2.59808i | 0.0552907 | + | 0.0957664i | ||||
\(737\) | 48.0000 | 1.76810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0000 | 0.956425 | 0.478213 | − | 0.878244i | \(-0.341285\pi\) | ||||
0.478213 | + | 0.878244i | \(0.341285\pi\) | |||||||
\(740\) | 3.00000 | + | 5.19615i | 0.110282 | + | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | − | 31.1769i | 0.660356 | − | 1.14377i | −0.320166 | − | 0.947361i | \(-0.603739\pi\) |
0.980522 | − | 0.196409i | \(-0.0629279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | 14.0000 | 0.512576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | 1.31629 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | − | 26.8468i | 0.565603 | − | 0.979653i | −0.431390 | − | 0.902165i | \(-0.641977\pi\) |
0.996993 | − | 0.0774878i | \(-0.0246899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | − | 10.3923i | −0.218507 | − | 0.378465i | ||||
\(755\) | −69.0000 | −2.51117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −1.00000 | − | 1.73205i | −0.0363216 | − | 0.0629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.5000 | − | 18.1865i | 0.380875 | − | 0.659695i | ||||
\(761\) | 21.0000 | − | 36.3731i | 0.761249 | − | 1.31852i | −0.180957 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335032i | \(-0.108747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.00000 | 0.325609 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | −0.650366 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00000 | − | 12.1244i | 0.252426 | − | 0.437215i | −0.711767 | − | 0.702416i | \(-0.752105\pi\) |
0.964193 | + | 0.265200i | \(0.0854381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.50000 | − | 14.7224i | −0.305922 | − | 0.529872i | ||||
\(773\) | −51.0000 | −1.83434 | −0.917171 | − | 0.398493i | \(-0.869533\pi\) | ||||
−0.917171 | + | 0.398493i | \(0.869533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0000 | − | 20.7846i | 0.430221 | − | 0.745164i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.5000 | + | 33.7750i | 0.695985 | + | 1.20548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | − | 17.3205i | 0.356462 | − | 0.617409i | −0.630905 | − | 0.775860i | \(-0.717316\pi\) |
0.987367 | + | 0.158450i | \(0.0506498\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.50000 | + | 12.9904i | 0.266838 | + | 0.462177i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 13.0000 | + | 22.5167i | 0.461353 | + | 0.799086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | − | 12.1244i | 0.248108 | − | 0.429736i | ||||
\(797\) | −1.50000 | + | 2.59808i | −0.0531327 | + | 0.0920286i | −0.891368 | − | 0.453279i | \(-0.850254\pi\) |
0.838236 | + | 0.545308i | \(0.183587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.00000 | −0.105934 | ||||||||
\(803\) | 6.00000 | + | 10.3923i | 0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | + | 3.46410i | −0.0704470 | + | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.50000 | − | 7.79423i | −0.158309 | − | 0.274200i | ||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.00000 | + | 10.3923i | −0.210300 | + | 0.364250i | ||||
\(815\) | 3.00000 | − | 5.19615i | 0.105085 | − | 0.182013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.00000 | − | 12.1244i | −0.244899 | − | 0.424178i | ||||
\(818\) | −32.0000 | −1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | − | 20.7846i | −0.418803 | − | 0.725388i | 0.577016 | − | 0.816733i | \(-0.304217\pi\) |
−0.995819 | + | 0.0913446i | \(0.970884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | −5.00000 | + | 8.66025i | −0.174183 | + | 0.301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 18.0000 | + | 31.1769i | 0.624789 | + | 1.08217i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | − | 1.73205i | 0.0346688 | − | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.0000 | 1.45260 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0000 | 0.518166 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 5.00000 | − | 8.66025i | 0.172311 | − | 0.298452i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | 27.0000 | 0.928828 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.0000 | + | 20.7846i | −0.411597 | + | 0.712906i | ||||
\(851\) | 3.00000 | − | 5.19615i | 0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5000 | + | 30.3109i | 0.599189 | + | 1.03783i | 0.992941 | + | 0.118609i | \(0.0378434\pi\) |
−0.393753 | + | 0.919216i | \(0.628823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −27.0000 | − | 46.7654i | −0.922302 | − | 1.59747i | −0.795843 | − | 0.605503i | \(-0.792972\pi\) |
−0.126459 | − | 0.991972i | \(-0.540361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | + | 3.46410i | −0.0682391 | + | 0.118194i | −0.898126 | − | 0.439738i | \(-0.855071\pi\) |
0.829887 | + | 0.557931i | \(0.188405\pi\) | |||||||
\(860\) | 3.00000 | − | 5.19615i | 0.102299 | − | 0.177187i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.00000 | + | 10.3923i | 0.204361 | + | 0.353963i | ||||
\(863\) | −9.00000 | −0.306364 | −0.153182 | − | 0.988198i | \(-0.548952\pi\) | ||||
−0.153182 | + | 0.988198i | \(0.548952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | 7.00000 | + | 12.1244i | 0.237870 | + | 0.412002i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.0000 | + | 25.9808i | −0.508840 | + | 0.881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | + | 13.8564i | 0.271070 | + | 0.469506i | ||||
\(872\) | −10.0000 | −0.338643 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.0000 | −0.710336 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | − | 19.0526i | 0.371444 | − | 0.643359i | −0.618344 | − | 0.785907i | \(-0.712196\pi\) |
0.989788 | + | 0.142548i | \(0.0455296\pi\) | |||||||
\(878\) | 4.00000 | − | 6.92820i | 0.134993 | − | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.00000 | + | 15.5885i | 0.303390 | + | 0.525487i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0000 | −1.14419 | −0.572096 | − | 0.820187i | \(-0.693869\pi\) | ||||
−0.572096 | + | 0.820187i | \(0.693869\pi\) | |||||||
\(884\) | 6.00000 | + | 10.3923i | 0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | − | 15.5885i | 0.302361 | − | 0.523704i | ||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.0000 | 0.937509 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0000 | + | 46.7654i | −0.902510 | + | 1.56319i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.5000 | + | 28.5788i | 0.550612 | + | 0.953688i | ||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.50000 | − | 12.9904i | 0.249446 | − | 0.432054i | ||||
\(905\) | 37.5000 | − | 64.9519i | 1.24654 | − | 2.15907i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | − | 27.7128i | −0.531271 | − | 0.920189i | −0.999334 | − | 0.0364935i | \(-0.988381\pi\) |
0.468063 | − | 0.883695i | \(-0.344952\pi\) | |||||||
\(908\) | −15.0000 | −0.497792 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.50000 | + | 12.9904i | 0.248486 | + | 0.430391i | 0.963106 | − | 0.269122i | \(-0.0867336\pi\) |
−0.714620 | + | 0.699513i | \(0.753400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | + | 62.3538i | −1.19143 | + | 2.06361i | ||||
\(914\) | −14.5000 | + | 25.1147i | −0.479617 | + | 0.830722i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.500000 | − | 0.866025i | −0.0165205 | − | 0.0286143i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0000 | 0.362857 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(920\) | −4.50000 | − | 7.79423i | −0.148361 | − | 0.256968i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.5000 | − | 28.5788i | 0.543399 | − | 0.941194i | ||||
\(923\) | −3.00000 | + | 5.19615i | −0.0987462 | + | 0.171033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | − | 6.92820i | −0.131519 | − | 0.227798i | ||||
\(926\) | −13.0000 | −0.427207 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.50000 | − | 7.79423i | 0.147402 | − | 0.255308i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | −108.000 | −3.53198 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5000 | + | 18.1865i | −0.342290 | + | 0.592864i | −0.984858 | − | 0.173365i | \(-0.944536\pi\) |
0.642567 | + | 0.766229i | \(0.277869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −12.0000 | − | 20.7846i | −0.389948 | − | 0.675409i | 0.602494 | − | 0.798123i | \(-0.294174\pi\) |
−0.992442 | + | 0.122714i | \(0.960840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | −14.0000 | + | 24.2487i | −0.454220 | + | 0.786732i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.0000 | −0.873699 | ||||||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.00000 | − | 5.19615i | 0.0969256 | − | 0.167880i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 25.5000 | + | 44.1673i | 0.820874 | + | 1.42180i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.50000 | + | 14.7224i | −0.273342 | + | 0.473441i | −0.969715 | − | 0.244238i | \(-0.921462\pi\) |
0.696374 | + | 0.717679i | \(0.254796\pi\) | |||||||
\(968\) | −12.5000 | + | 21.6506i | −0.401765 | + | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.00000 | − | 5.19615i | −0.0963242 | − | 0.166838i | ||||
\(971\) | −15.0000 | −0.481373 | −0.240686 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.5000 | − | 25.1147i | −0.464610 | − | 0.804728i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.50000 | − | 4.33013i | 0.0800230 | − | 0.138604i | ||||
\(977\) | 3.00000 | − | 5.19615i | 0.0959785 | − | 0.166240i | −0.814038 | − | 0.580812i | \(-0.802735\pi\) |
0.910017 | + | 0.414572i | \(0.136069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0000 | −0.574403 | ||||||||
\(983\) | −9.00000 | − | 15.5885i | −0.287055 | − | 0.497195i | 0.686050 | − | 0.727554i | \(-0.259343\pi\) |
−0.973106 | + | 0.230360i | \(0.926010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | + | 46.7654i | −0.860292 | + | 1.49007i | ||||
\(986\) | 18.0000 | − | 31.1769i | 0.573237 | − | 0.992875i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00000 | + | 12.1244i | 0.222700 | + | 0.385727i | ||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | + | 36.3731i | −0.665745 | + | 1.15310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.5000 | − | 47.6314i | −0.870934 | − | 1.50850i | −0.861032 | − | 0.508551i | \(-0.830182\pi\) |
−0.00990158 | − | 0.999951i | \(-0.503152\pi\) | |||||||
\(998\) | 32.0000 | 1.01294 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))