Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,2,Mod(43,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, 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("126.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.00611506547\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.43 |
Dual form | 126.2.f.a.85.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 1.50000 | − | 0.866025i | 0.433013 | − | 0.250000i | ||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | −4.50000 | + | 2.59808i | −1.16190 | + | 0.670820i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 1.50000 | − | 2.59808i | 0.335410 | − | 0.580948i | ||||
\(21\) | −1.50000 | − | 0.866025i | −0.327327 | − | 0.188982i | ||||
\(22\) | −3.00000 | − | 5.19615i | −0.639602 | − | 1.10782i | ||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 5.19615i | 0.948683i | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 9.00000 | + | 5.19615i | 1.56670 | + | 0.904534i | ||||
\(34\) | 3.00000 | − | 5.19615i | 0.514496 | − | 0.891133i | ||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 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 | ||||
\(39\) | 3.00000 | − | 1.73205i | 0.480384 | − | 0.277350i | ||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | −1.50000 | + | 0.866025i | −0.231455 | + | 0.133631i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | −4.50000 | − | 7.79423i | −0.670820 | − | 1.16190i | ||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −1.50000 | − | 0.866025i | −0.216506 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | 10.3923i | 1.45521i | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 18.0000 | 2.42712 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | − | 12.1244i | − | 1.60591i | ||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 4.50000 | + | 2.59808i | 0.580948 | + | 0.335410i | ||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 9.00000 | − | 5.19615i | 1.10782 | − | 0.639602i | ||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 4.50000 | − | 2.59808i | 0.541736 | − | 0.312772i | ||||
\(70\) | −1.50000 | + | 2.59808i | −0.179284 | + | 0.310530i | ||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | −6.00000 | − | 3.46410i | −0.692820 | − | 0.400000i | ||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | 3.00000 | + | 5.19615i | 0.341882 | + | 0.592157i | ||||
\(78\) | − | 3.46410i | − | 0.392232i | ||||||
\(79\) | −2.50000 | + | 4.33013i | −0.281272 | + | 0.487177i | −0.971698 | − | 0.236225i | \(-0.924090\pi\) |
0.690426 | + | 0.723403i | \(0.257423\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | + | 10.3923i | −0.658586 | + | 1.14070i | 0.322396 | + | 0.946605i | \(0.395512\pi\) |
−0.980982 | + | 0.194099i | \(0.937822\pi\) | |||||||
\(84\) | 1.73205i | 0.188982i | ||||||||
\(85\) | 9.00000 | + | 15.5885i | 0.976187 | + | 1.69081i | ||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | −9.00000 | − | 5.19615i | −0.964901 | − | 0.557086i | ||||
\(88\) | −3.00000 | + | 5.19615i | −0.319801 | + | 0.553912i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −9.00000 | −0.948683 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −1.50000 | + | 2.59808i | −0.156386 | + | 0.270868i | ||||
\(93\) | 3.00000 | − | 1.73205i | 0.311086 | − | 0.179605i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5000 | − | 18.1865i | −1.07728 | − | 1.86590i | ||||
\(96\) | −1.50000 | + | 0.866025i | −0.153093 | + | 0.0883883i | ||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −9.00000 | + | 15.5885i | −0.904534 | + | 1.56670i | ||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | 9.00000 | + | 5.19615i | 0.891133 | + | 0.514496i | ||||
\(103\) | 5.00000 | + | 8.66025i | 0.492665 | + | 0.853320i | 0.999964 | − | 0.00844953i | \(-0.00268960\pi\) |
−0.507300 | + | 0.861770i | \(0.669356\pi\) | |||||||
\(104\) | 1.00000 | + | 1.73205i | 0.0980581 | + | 0.169842i | ||||
\(105\) | − | 5.19615i | − | 0.507093i | ||||||
\(106\) | 3.00000 | − | 5.19615i | 0.291386 | − | 0.504695i | ||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | −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 | ||||
\(111\) | 3.46410i | 0.328798i | ||||||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | −7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) |
0.260955 | − | 0.965351i | \(-0.415962\pi\) | |||||||
\(114\) | −10.5000 | − | 6.06218i | −0.983415 | − | 0.567775i | ||||
\(115\) | 4.50000 | − | 7.79423i | 0.419627 | − | 0.726816i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | 4.50000 | − | 2.59808i | 0.410792 | − | 0.237171i | ||||
\(121\) | −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 | ||||||||
\(126\) | −1.50000 | − | 2.59808i | −0.133631 | − | 0.231455i | ||||
\(127\) | 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 | ||||
\(129\) | −3.00000 | − | 1.73205i | −0.264135 | − | 0.152499i | ||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | 4.50000 | + | 7.79423i | 0.393167 | + | 0.680985i | 0.992865 | − | 0.119241i | \(-0.0380462\pi\) |
−0.599699 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(132\) | − | 10.3923i | − | 0.904534i | ||||||
\(133\) | 3.50000 | − | 6.06218i | 0.303488 | − | 0.525657i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 13.5000 | − | 7.79423i | 1.16190 | − | 0.670820i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | − | 5.19615i | − | 0.442326i | ||||||
\(139\) | −2.50000 | − | 4.33013i | −0.212047 | − | 0.367277i | 0.740308 | − | 0.672268i | \(-0.234680\pi\) |
−0.952355 | + | 0.304991i | \(0.901346\pi\) | |||||||
\(140\) | 1.50000 | + | 2.59808i | 0.126773 | + | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50000 | − | 2.59808i | 0.125877 | − | 0.218026i | ||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | −18.0000 | −1.49482 | ||||||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | 1.50000 | − | 0.866025i | 0.123718 | − | 0.0714286i | ||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | −6.00000 | + | 3.46410i | −0.489898 | + | 0.282843i | ||||
\(151\) | −11.5000 | + | 19.9186i | −0.935857 | + | 1.62095i | −0.162758 | + | 0.986666i | \(0.552039\pi\) |
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | −18.0000 | −1.45521 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 3.00000 | − | 5.19615i | 0.240966 | − | 0.417365i | ||||
\(156\) | −3.00000 | − | 1.73205i | −0.240192 | − | 0.138675i | ||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | 2.50000 | + | 4.33013i | 0.198889 | + | 0.344486i | ||||
\(159\) | 10.3923i | 0.824163i | ||||||||
\(160\) | −1.50000 | + | 2.59808i | −0.118585 | + | 0.205396i | ||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31.1769i | 2.42712i | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 1.50000 | + | 0.866025i | 0.115728 | + | 0.0668153i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 18.0000 | 1.38054 | ||||||||
\(171\) | 21.0000 | 1.60591 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | −9.00000 | + | 5.19615i | −0.682288 | + | 0.393919i | ||||
\(175\) | −2.00000 | − | 3.46410i | −0.151186 | − | 0.261861i | ||||
\(176\) | 3.00000 | + | 5.19615i | 0.226134 | + | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0000 | 1.34538 | 0.672692 | − | 0.739923i | \(-0.265138\pi\) | ||||
0.672692 | + | 0.739923i | \(0.265138\pi\) | |||||||
\(180\) | −4.50000 | + | 7.79423i | −0.335410 | + | 0.580948i | ||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 1.00000 | − | 1.73205i | 0.0741249 | − | 0.128388i | ||||
\(183\) | −7.50000 | − | 4.33013i | −0.554416 | − | 0.320092i | ||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | − | 3.46410i | − | 0.254000i | ||||||
\(187\) | 18.0000 | − | 31.1769i | 1.31629 | − | 2.27988i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | −21.0000 | −1.52350 | ||||||||
\(191\) | 4.50000 | − | 7.79423i | 0.325609 | − | 0.563971i | −0.656027 | − | 0.754738i | \(-0.727764\pi\) |
0.981635 | + | 0.190767i | \(0.0610975\pi\) | |||||||
\(192\) | 1.73205i | 0.125000i | ||||||||
\(193\) | −8.50000 | − | 14.7224i | −0.611843 | − | 1.05974i | −0.990930 | − | 0.134382i | \(-0.957095\pi\) |
0.379086 | − | 0.925361i | \(-0.376238\pi\) | |||||||
\(194\) | 1.00000 | + | 1.73205i | 0.0717958 | + | 0.124354i | ||||
\(195\) | 9.00000 | + | 5.19615i | 0.644503 | + | 0.372104i | ||||
\(196\) | −0.500000 | + | 0.866025i | −0.0357143 | + | 0.0618590i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 9.00000 | + | 15.5885i | 0.639602 | + | 1.10782i | ||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 2.00000 | − | 3.46410i | 0.141421 | − | 0.244949i | ||||
\(201\) | 12.0000 | − | 6.92820i | 0.846415 | − | 0.488678i | ||||
\(202\) | 4.50000 | + | 7.79423i | 0.316619 | + | 0.548400i | ||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | 9.00000 | − | 5.19615i | 0.630126 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.0000 | 0.696733 | ||||||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −21.0000 | + | 36.3731i | −1.45260 | + | 2.51598i | ||||
\(210\) | −4.50000 | − | 2.59808i | −0.310530 | − | 0.179284i | ||||
\(211\) | −4.00000 | − | 6.92820i | −0.275371 | − | 0.476957i | 0.694857 | − | 0.719148i | \(-0.255467\pi\) |
−0.970229 | + | 0.242190i | \(0.922134\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 5.19615i | 0.356034i | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −5.00000 | + | 8.66025i | −0.338643 | + | 0.586546i | ||||
\(219\) | 3.46410i | 0.234082i | ||||||||
\(220\) | −9.00000 | − | 15.5885i | −0.606780 | − | 1.05097i | ||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | 3.00000 | + | 1.73205i | 0.201347 | + | 0.116248i | ||||
\(223\) | 14.0000 | − | 24.2487i | 0.937509 | − | 1.62381i | 0.167412 | − | 0.985887i | \(-0.446459\pi\) |
0.770097 | − | 0.637927i | \(-0.220208\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 6.00000 | − | 10.3923i | 0.400000 | − | 0.692820i | ||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | 7.50000 | − | 12.9904i | 0.497792 | − | 0.862202i | −0.502204 | − | 0.864749i | \(-0.667477\pi\) |
0.999997 | + | 0.00254715i | \(0.000810783\pi\) | |||||||
\(228\) | −10.5000 | + | 6.06218i | −0.695379 | + | 0.401478i | ||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | −4.50000 | − | 7.79423i | −0.296721 | − | 0.513936i | ||||
\(231\) | −9.00000 | + | 5.19615i | −0.592157 | + | 0.341882i | ||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 6.00000 | 0.392232 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.50000 | − | 4.33013i | −0.487177 | − | 0.281272i | ||||
\(238\) | 3.00000 | + | 5.19615i | 0.194461 | + | 0.336817i | ||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | − | 5.19615i | − | 0.335410i | ||||||
\(241\) | −4.00000 | + | 6.92820i | −0.257663 | + | 0.446285i | −0.965615 | − | 0.259975i | \(-0.916286\pi\) |
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(242\) | −25.0000 | −1.60706 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 5.00000 | 0.320092 | ||||||||
\(245\) | 1.50000 | − | 2.59808i | 0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | + | 12.1244i | 0.445399 | + | 0.771454i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | −18.0000 | − | 10.3923i | −1.14070 | − | 0.658586i | ||||
\(250\) | 1.50000 | − | 2.59808i | 0.0948683 | − | 0.164317i | ||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 8.50000 | − | 14.7224i | 0.533337 | − | 0.923768i | ||||
\(255\) | −27.0000 | + | 15.5885i | −1.69081 | + | 0.976187i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | −3.00000 | + | 1.73205i | −0.186772 | + | 0.107833i | ||||
\(259\) | −1.00000 | + | 1.73205i | −0.0621370 | + | 0.107624i | ||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | 9.00000 | − | 15.5885i | 0.557086 | − | 0.964901i | ||||
\(262\) | 9.00000 | 0.556022 | ||||||||
\(263\) | 10.5000 | − | 18.1865i | 0.647458 | − | 1.12143i | −0.336270 | − | 0.941766i | \(-0.609166\pi\) |
0.983728 | − | 0.179664i | \(-0.0575011\pi\) | |||||||
\(264\) | −9.00000 | − | 5.19615i | −0.553912 | − | 0.319801i | ||||
\(265\) | 9.00000 | + | 15.5885i | 0.552866 | + | 0.957591i | ||||
\(266\) | −3.50000 | − | 6.06218i | −0.214599 | − | 0.371696i | ||||
\(267\) | 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 | \(0.588469\pi\) | |||||||
\(270\) | − | 15.5885i | − | 0.948683i | ||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | −3.00000 | + | 5.19615i | −0.181902 | + | 0.315063i | ||||
\(273\) | 3.46410i | 0.209657i | ||||||||
\(274\) | 3.00000 | + | 5.19615i | 0.181237 | + | 0.313911i | ||||
\(275\) | 12.0000 | + | 20.7846i | 0.723627 | + | 1.25336i | ||||
\(276\) | −4.50000 | − | 2.59808i | −0.270868 | − | 0.156386i | ||||
\(277\) | 8.00000 | − | 13.8564i | 0.480673 | − | 0.832551i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.999754 | + | 0.0221745i | \(0.00705893\pi\) | |||||||
\(278\) | −5.00000 | −0.299880 | ||||||||
\(279\) | 3.00000 | + | 5.19615i | 0.179605 | + | 0.311086i | ||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | 13.5000 | − | 23.3827i | 0.805342 | − | 1.39489i | −0.110717 | − | 0.993852i | \(-0.535315\pi\) |
0.916060 | − | 0.401042i | \(-0.131352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.50000 | + | 16.4545i | 0.564716 | + | 0.978117i | 0.997076 | + | 0.0764162i | \(0.0243478\pi\) |
−0.432360 | + | 0.901701i | \(0.642319\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 31.5000 | − | 18.1865i | 1.86590 | − | 1.07728i | ||||
\(286\) | −6.00000 | + | 10.3923i | −0.354787 | + | 0.614510i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | −9.00000 | + | 15.5885i | −0.528498 | + | 0.915386i | ||||
\(291\) | −3.00000 | − | 1.73205i | −0.175863 | − | 0.101535i | ||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | 1.50000 | + | 2.59808i | 0.0876309 | + | 0.151781i | 0.906509 | − | 0.422186i | \(-0.138737\pi\) |
−0.818878 | + | 0.573967i | \(0.805404\pi\) | |||||||
\(294\) | − | 1.73205i | − | 0.101015i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | −27.0000 | − | 15.5885i | −1.56670 | − | 0.904534i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 6.92820i | 0.400000i | ||||||||
\(301\) | −1.00000 | − | 1.73205i | −0.0576390 | − | 0.0998337i | ||||
\(302\) | 11.5000 | + | 19.9186i | 0.661751 | + | 1.14619i | ||||
\(303\) | −13.5000 | − | 7.79423i | −0.775555 | − | 0.447767i | ||||
\(304\) | 3.50000 | − | 6.06218i | 0.200739 | − | 0.347690i | ||||
\(305\) | −15.0000 | −0.858898 | ||||||||
\(306\) | −9.00000 | + | 15.5885i | −0.514496 | + | 0.891133i | ||||
\(307\) | −25.0000 | −1.42683 | −0.713413 | − | 0.700744i | \(-0.752851\pi\) | ||||
−0.713413 | + | 0.700744i | \(0.752851\pi\) | |||||||
\(308\) | 3.00000 | − | 5.19615i | 0.170941 | − | 0.296078i | ||||
\(309\) | −15.0000 | + | 8.66025i | −0.853320 | + | 0.492665i | ||||
\(310\) | −3.00000 | − | 5.19615i | −0.170389 | − | 0.295122i | ||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | −3.00000 | + | 1.73205i | −0.169842 | + | 0.0980581i | ||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | 9.00000 | 0.507093 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 9.00000 | + | 5.19615i | 0.504695 | + | 0.291386i | ||||
\(319\) | 18.0000 | + | 31.1769i | 1.00781 | + | 1.74557i | ||||
\(320\) | 1.50000 | + | 2.59808i | 0.0838525 | + | 0.145237i | ||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 1.50000 | − | 2.59808i | 0.0835917 | − | 0.144785i | ||||
\(323\) | −42.0000 | −2.33694 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | 1.00000 | − | 1.73205i | 0.0553849 | − | 0.0959294i | ||||
\(327\) | − | 17.3205i | − | 0.957826i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 27.0000 | + | 15.5885i | 1.48630 | + | 0.858116i | ||||
\(331\) | −13.0000 | + | 22.5167i | −0.714545 | + | 1.23763i | 0.248590 | + | 0.968609i | \(0.420033\pi\) |
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | − | 20.7846i | 0.655630 | − | 1.13558i | ||||
\(336\) | 1.50000 | − | 0.866025i | 0.0818317 | − | 0.0472456i | ||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | −4.50000 | − | 7.79423i | −0.244768 | − | 0.423950i | ||||
\(339\) | 22.5000 | − | 12.9904i | 1.22203 | − | 0.705541i | ||||
\(340\) | 9.00000 | − | 15.5885i | 0.488094 | − | 0.845403i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 10.5000 | − | 18.1865i | 0.567775 | − | 0.983415i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.00000 | − | 1.73205i | 0.0539164 | − | 0.0933859i | ||||
\(345\) | 13.5000 | + | 7.79423i | 0.726816 | + | 0.419627i | ||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | 12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | \(0.0561403\pi\) |
−0.340293 | + | 0.940319i | \(0.610526\pi\) | |||||||
\(348\) | 10.3923i | 0.557086i | ||||||||
\(349\) | −13.0000 | + | 22.5167i | −0.695874 | + | 1.20529i | 0.274011 | + | 0.961727i | \(0.411649\pi\) |
−0.969885 | + | 0.243563i | \(0.921684\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | −9.00000 | + | 5.19615i | −0.480384 | + | 0.277350i | ||||
\(352\) | 6.00000 | 0.319801 | ||||||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50000 | + | 7.79423i | 0.238835 | + | 0.413675i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.00000 | − | 5.19615i | −0.476331 | − | 0.275010i | ||||
\(358\) | 9.00000 | − | 15.5885i | 0.475665 | − | 0.823876i | ||||
\(359\) | −3.00000 | −0.158334 | −0.0791670 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791670 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(360\) | 4.50000 | + | 7.79423i | 0.237171 | + | 0.410792i | ||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −12.5000 | + | 21.6506i | −0.656985 | + | 1.13793i | ||||
\(363\) | 37.5000 | − | 21.6506i | 1.96824 | − | 1.13636i | ||||
\(364\) | −1.00000 | − | 1.73205i | −0.0524142 | − | 0.0907841i | ||||
\(365\) | 3.00000 | + | 5.19615i | 0.157027 | + | 0.271979i | ||||
\(366\) | −7.50000 | + | 4.33013i | −0.392031 | + | 0.226339i | ||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 3.00000 | 0.156386 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −3.00000 | + | 5.19615i | −0.155752 | + | 0.269771i | ||||
\(372\) | −3.00000 | − | 1.73205i | −0.155543 | − | 0.0898027i | ||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | −18.0000 | − | 31.1769i | −0.930758 | − | 1.61212i | ||||
\(375\) | 5.19615i | 0.268328i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 4.50000 | − | 2.59808i | 0.231455 | − | 0.133631i | ||||
\(379\) | 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 | ||||
\(381\) | 29.4449i | 1.50851i | ||||||||
\(382\) | −4.50000 | − | 7.79423i | −0.230240 | − | 0.398787i | ||||
\(383\) | 9.00000 | + | 15.5885i | 0.459879 | + | 0.796533i | 0.998954 | − | 0.0457244i | \(-0.0145596\pi\) |
−0.539076 | + | 0.842257i | \(0.681226\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | −9.00000 | + | 15.5885i | −0.458682 | + | 0.794461i | ||||
\(386\) | −17.0000 | −0.865277 | ||||||||
\(387\) | 3.00000 | − | 5.19615i | 0.152499 | − | 0.264135i | ||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | −12.0000 | + | 20.7846i | −0.608424 | + | 1.05382i | 0.383076 | + | 0.923717i | \(0.374865\pi\) |
−0.991500 | + | 0.130105i | \(0.958469\pi\) | |||||||
\(390\) | 9.00000 | − | 5.19615i | 0.455733 | − | 0.263117i | ||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | −13.5000 | + | 7.79423i | −0.680985 | + | 0.393167i | ||||
\(394\) | 9.00000 | − | 15.5885i | 0.453413 | − | 0.785335i | ||||
\(395\) | −15.0000 | −0.754732 | ||||||||
\(396\) | 18.0000 | 0.904534 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | 7.00000 | − | 12.1244i | 0.350878 | − | 0.607739i | ||||
\(399\) | 10.5000 | + | 6.06218i | 0.525657 | + | 0.303488i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | − | 13.8564i | − | 0.691095i | ||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 9.00000 | 0.447767 | ||||||||
\(405\) | 13.5000 | + | 23.3827i | 0.670820 | + | 1.16190i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 6.00000 | − | 10.3923i | 0.297409 | − | 0.515127i | ||||
\(408\) | − | 10.3923i | − | 0.514496i | ||||||
\(409\) | −16.0000 | − | 27.7128i | −0.791149 | − | 1.37031i | −0.925256 | − | 0.379344i | \(-0.876150\pi\) |
0.134107 | − | 0.990967i | \(-0.457183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | − | 5.19615i | −0.443937 | − | 0.256307i | ||||
\(412\) | 5.00000 | − | 8.66025i | 0.246332 | − | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.00000 | 0.442326 | ||||||||
\(415\) | −36.0000 | −1.76717 | ||||||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 7.50000 | − | 4.33013i | 0.367277 | − | 0.212047i | ||||
\(418\) | 21.0000 | + | 36.3731i | 1.02714 | + | 1.77906i | ||||
\(419\) | −7.50000 | − | 12.9904i | −0.366399 | − | 0.634622i | 0.622601 | − | 0.782540i | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | −4.50000 | + | 2.59808i | −0.219578 | + | 0.126773i | ||||
\(421\) | 5.00000 | − | 8.66025i | 0.243685 | − | 0.422075i | −0.718076 | − | 0.695965i | \(-0.754977\pi\) |
0.961761 | + | 0.273890i | \(0.0883103\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −12.0000 | + | 20.7846i | −0.582086 | + | 1.00820i | ||||
\(426\) | 4.50000 | + | 2.59808i | 0.218026 | + | 0.125877i | ||||
\(427\) | −2.50000 | − | 4.33013i | −0.120983 | − | 0.209550i | ||||
\(428\) | 6.00000 | + | 10.3923i | 0.290021 | + | 0.502331i | ||||
\(429\) | − | 20.7846i | − | 1.00349i | ||||||
\(430\) | −3.00000 | + | 5.19615i | −0.144673 | + | 0.250581i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 1.00000 | − | 1.73205i | 0.0480015 | − | 0.0831411i | ||||
\(435\) | − | 31.1769i | − | 1.49482i | ||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | 10.5000 | + | 18.1865i | 0.502283 | + | 0.869980i | ||||
\(438\) | 3.00000 | + | 1.73205i | 0.143346 | + | 0.0827606i | ||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | −18.0000 | −0.858116 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −9.00000 | + | 15.5885i | −0.427603 | + | 0.740630i | −0.996660 | − | 0.0816684i | \(-0.973975\pi\) |
0.569057 | + | 0.822298i | \(0.307309\pi\) | |||||||
\(444\) | 3.00000 | − | 1.73205i | 0.142374 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | − | 24.2487i | −0.662919 | − | 1.14821i | ||||
\(447\) | −9.00000 | + | 5.19615i | −0.425685 | + | 0.245770i | ||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | 33.0000 | 1.55737 | 0.778683 | − | 0.627417i | \(-0.215888\pi\) | ||||
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(450\) | −6.00000 | − | 10.3923i | −0.282843 | − | 0.489898i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.50000 | + | 12.9904i | −0.352770 | + | 0.611016i | ||||
\(453\) | −34.5000 | − | 19.9186i | −1.62095 | − | 0.935857i | ||||
\(454\) | −7.50000 | − | 12.9904i | −0.351992 | − | 0.609669i | ||||
\(455\) | 3.00000 | + | 5.19615i | 0.140642 | + | 0.243599i | ||||
\(456\) | 12.1244i | 0.567775i | ||||||||
\(457\) | −14.5000 | + | 25.1147i | −0.678281 | + | 1.17482i | 0.297217 | + | 0.954810i | \(0.403942\pi\) |
−0.975498 | + | 0.220008i | \(0.929392\pi\) | |||||||
\(458\) | 1.00000 | 0.0467269 | ||||||||
\(459\) | − | 31.1769i | − | 1.45521i | ||||||
\(460\) | −9.00000 | −0.419627 | ||||||||
\(461\) | 16.5000 | − | 28.5788i | 0.768482 | − | 1.33105i | −0.169904 | − | 0.985461i | \(-0.554346\pi\) |
0.938386 | − | 0.345589i | \(-0.112321\pi\) | |||||||
\(462\) | 10.3923i | 0.483494i | ||||||||
\(463\) | 6.50000 | + | 11.2583i | 0.302081 | + | 0.523219i | 0.976607 | − | 0.215032i | \(-0.0689855\pi\) |
−0.674526 | + | 0.738251i | \(0.735652\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 9.00000 | + | 5.19615i | 0.417365 | + | 0.240966i | ||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 3.00000 | − | 5.19615i | 0.138675 | − | 0.240192i | ||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.5000 | + | 11.2583i | −0.898513 | + | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | + | 10.3923i | 0.275880 | + | 0.477839i | ||||
\(474\) | −7.50000 | + | 4.33013i | −0.344486 | + | 0.198889i | ||||
\(475\) | 14.0000 | − | 24.2487i | 0.642364 | − | 1.11261i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 15.0000 | 0.686084 | ||||||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | −4.50000 | − | 2.59808i | −0.205396 | − | 0.118585i | ||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | 4.00000 | + | 6.92820i | 0.182195 | + | 0.315571i | ||||
\(483\) | 5.19615i | 0.236433i | ||||||||
\(484\) | −12.5000 | + | 21.6506i | −0.568182 | + | 0.984120i | ||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | 13.5000 | + | 7.79423i | 0.612372 | + | 0.353553i | ||||
\(487\) | 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 | ||||
\(489\) | 3.46410i | 0.156652i | ||||||||
\(490\) | −1.50000 | − | 2.59808i | −0.0677631 | − | 0.117369i | ||||
\(491\) | −9.00000 | − | 15.5885i | −0.406164 | − | 0.703497i | 0.588292 | − | 0.808649i | \(-0.299801\pi\) |
−0.994456 | + | 0.105151i | \(0.966467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | + | 31.1769i | −0.810679 | + | 1.40414i | ||||
\(494\) | 14.0000 | 0.629890 | ||||||||
\(495\) | −54.0000 | −2.42712 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −1.50000 | + | 2.59808i | −0.0672842 | + | 0.116540i | ||||
\(498\) | −18.0000 | + | 10.3923i | −0.806599 | + | 0.465690i | ||||
\(499\) | −16.0000 | − | 27.7128i | −0.716258 | − | 1.24060i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.246214 | − | 0.969216i | \(-0.420813\pi\) | |||||||
\(500\) | −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 | \(0.413794\pi\) | |||||||
\(504\) | −1.50000 | + | 2.59808i | −0.0668153 | + | 0.115728i | ||||
\(505\) | −27.0000 | −1.20148 | ||||||||
\(506\) | −9.00000 | + | 15.5885i | −0.400099 | + | 0.692991i | ||||
\(507\) | 13.5000 | + | 7.79423i | 0.599556 | + | 0.346154i | ||||
\(508\) | −8.50000 | − | 14.7224i | −0.377127 | − | 0.653202i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 31.1769i | 1.38054i | ||||||||
\(511\) | −1.00000 | + | 1.73205i | −0.0442374 | + | 0.0766214i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | −15.0000 | + | 25.9808i | −0.660979 | + | 1.14485i | ||||
\(516\) | 3.46410i | 0.152499i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.00000 | + | 1.73205i | 0.0439375 | + | 0.0761019i | ||||
\(519\) | 9.00000 | + | 5.19615i | 0.395056 | + | 0.228086i | ||||
\(520\) | −3.00000 | + | 5.19615i | −0.131559 | + | 0.227866i | ||||
\(521\) | 24.0000 | 1.05146 | 0.525730 | − | 0.850652i | \(-0.323792\pi\) | ||||
0.525730 | + | 0.850652i | \(0.323792\pi\) | |||||||
\(522\) | −9.00000 | − | 15.5885i | −0.393919 | − | 0.682288i | ||||
\(523\) | −13.0000 | −0.568450 | −0.284225 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284225 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(524\) | 4.50000 | − | 7.79423i | 0.196583 | − | 0.340492i | ||||
\(525\) | 6.00000 | − | 3.46410i | 0.261861 | − | 0.151186i | ||||
\(526\) | −10.5000 | − | 18.1865i | −0.457822 | − | 0.792971i | ||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | −9.00000 | + | 5.19615i | −0.391675 | + | 0.226134i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 18.0000 | 0.781870 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.00000 | −0.303488 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | − | 31.1769i | −0.778208 | − | 1.34790i | ||||
\(536\) | 4.00000 | + | 6.92820i | 0.172774 | + | 0.299253i | ||||
\(537\) | 31.1769i | 1.34538i | ||||||||
\(538\) | −4.50000 | + | 7.79423i | −0.194009 | + | 0.336033i | ||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | −13.5000 | − | 7.79423i | −0.580948 | − | 0.335410i | ||||
\(541\) | 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 | ||||
\(543\) | − | 43.3013i | − | 1.85824i | ||||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | −15.0000 | − | 25.9808i | −0.642529 | − | 1.11289i | ||||
\(546\) | 3.00000 | + | 1.73205i | 0.128388 | + | 0.0741249i | ||||
\(547\) | −16.0000 | + | 27.7128i | −0.684111 | + | 1.18491i | 0.289605 | + | 0.957146i | \(0.406476\pi\) |
−0.973715 | + | 0.227768i | \(0.926857\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | 7.50000 | − | 12.9904i | 0.320092 | − | 0.554416i | ||||
\(550\) | 24.0000 | 1.02336 | ||||||||
\(551\) | 21.0000 | − | 36.3731i | 0.894630 | − | 1.54954i | ||||
\(552\) | −4.50000 | + | 2.59808i | −0.191533 | + | 0.110581i | ||||
\(553\) | −2.50000 | − | 4.33013i | −0.106311 | − | 0.184136i | ||||
\(554\) | −8.00000 | − | 13.8564i | −0.339887 | − | 0.588702i | ||||
\(555\) | −9.00000 | + | 5.19615i | −0.382029 | + | 0.220564i | ||||
\(556\) | −2.50000 | + | 4.33013i | −0.106024 | + | 0.183638i | ||||
\(557\) | −24.0000 | −1.01691 | −0.508456 | − | 0.861088i | \(-0.669784\pi\) | ||||
−0.508456 | + | 0.861088i | \(0.669784\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 1.50000 | − | 2.59808i | 0.0633866 | − | 0.109789i | ||||
\(561\) | 54.0000 | + | 31.1769i | 2.27988 | + | 1.31629i | ||||
\(562\) | −13.5000 | − | 23.3827i | −0.569463 | − | 0.986339i | ||||
\(563\) | 16.5000 | + | 28.5788i | 0.695392 | + | 1.20445i | 0.970048 | + | 0.242912i | \(0.0781026\pi\) |
−0.274656 | + | 0.961542i | \(0.588564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5000 | − | 38.9711i | 0.946582 | − | 1.63953i | ||||
\(566\) | 19.0000 | 0.798630 | ||||||||
\(567\) | −4.50000 | + | 7.79423i | −0.188982 | + | 0.327327i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | − | 36.3731i | − | 1.52350i | ||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | 13.5000 | + | 7.79423i | 0.563971 | + | 0.325609i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | 25.5000 | − | 14.7224i | 1.05974 | − | 0.611843i | ||||
\(580\) | 9.00000 | + | 15.5885i | 0.373705 | + | 0.647275i | ||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | −3.00000 | + | 1.73205i | −0.124354 | + | 0.0717958i | ||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | −9.00000 | + | 15.5885i | −0.372104 | + | 0.644503i | ||||
\(586\) | 3.00000 | 0.123929 | ||||||||
\(587\) | 1.50000 | − | 2.59808i | 0.0619116 | − | 0.107234i | −0.833408 | − | 0.552658i | \(-0.813614\pi\) |
0.895320 | + | 0.445424i | \(0.146947\pi\) | |||||||
\(588\) | −1.50000 | − | 0.866025i | −0.0618590 | − | 0.0357143i | ||||
\(589\) | 7.00000 | + | 12.1244i | 0.288430 | + | 0.499575i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1769i | 1.28245i | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −27.0000 | + | 15.5885i | −1.10782 | + | 0.639602i | ||||
\(595\) | −18.0000 | −0.737928 | ||||||||
\(596\) | 3.00000 | − | 5.19615i | 0.122885 | − | 0.212843i | ||||
\(597\) | 24.2487i | 0.992434i | ||||||||
\(598\) | 3.00000 | + | 5.19615i | 0.122679 | + | 0.212486i | ||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | 6.00000 | + | 3.46410i | 0.244949 | + | 0.141421i | ||||
\(601\) | −7.00000 | + | 12.1244i | −0.285536 | + | 0.494563i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) |
0.687203 | + | 0.726465i | \(0.258838\pi\) | |||||||
\(602\) | −2.00000 | −0.0815139 | ||||||||
\(603\) | 12.0000 | + | 20.7846i | 0.488678 | + | 0.846415i | ||||
\(604\) | 23.0000 | 0.935857 | ||||||||
\(605\) | 37.5000 | − | 64.9519i | 1.52459 | − | 2.64067i | ||||
\(606\) | −13.5000 | + | 7.79423i | −0.548400 | + | 0.316619i | ||||
\(607\) | 11.0000 | + | 19.0526i | 0.446476 | + | 0.773320i | 0.998154 | − | 0.0607380i | \(-0.0193454\pi\) |
−0.551678 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(608\) | −3.50000 | − | 6.06218i | −0.141944 | − | 0.245854i | ||||
\(609\) | 9.00000 | − | 5.19615i | 0.364698 | − | 0.210559i | ||||
\(610\) | −7.50000 | + | 12.9904i | −0.303666 | + | 0.525965i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 9.00000 | + | 15.5885i | 0.363803 | + | 0.630126i | ||||
\(613\) | 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 | ||||||||
\(616\) | −3.00000 | − | 5.19615i | −0.120873 | − | 0.209359i | ||||
\(617\) | −21.0000 | − | 36.3731i | −0.845428 | − | 1.46432i | −0.885249 | − | 0.465118i | \(-0.846012\pi\) |
0.0398207 | − | 0.999207i | \(-0.487321\pi\) | |||||||
\(618\) | 17.3205i | 0.696733i | ||||||||
\(619\) | 3.50000 | − | 6.06218i | 0.140677 | − | 0.243659i | −0.787075 | − | 0.616858i | \(-0.788405\pi\) |
0.927752 | + | 0.373198i | \(0.121739\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | −13.5000 | + | 7.79423i | −0.541736 | + | 0.312772i | ||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.46410i | 0.138675i | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | −63.0000 | − | 36.3731i | −2.51598 | − | 1.45260i | ||||
\(628\) | 6.50000 | − | 11.2583i | 0.259378 | − | 0.449256i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 4.50000 | − | 7.79423i | 0.179284 | − | 0.310530i | ||||
\(631\) | −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 | ||||
\(633\) | 12.0000 | − | 6.92820i | 0.476957 | − | 0.275371i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 25.5000 | + | 44.1673i | 1.01194 | + | 1.75273i | ||||
\(636\) | 9.00000 | − | 5.19615i | 0.356873 | − | 0.206041i | ||||
\(637\) | −1.00000 | + | 1.73205i | −0.0396214 | + | 0.0686264i | ||||
\(638\) | 36.0000 | 1.42525 | ||||||||
\(639\) | −9.00000 | −0.356034 | ||||||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | −13.5000 | + | 23.3827i | −0.533218 | + | 0.923561i | 0.466029 | + | 0.884769i | \(0.345684\pi\) |
−0.999247 | + | 0.0387913i | \(0.987649\pi\) | |||||||
\(642\) | −18.0000 | − | 10.3923i | −0.710403 | − | 0.410152i | ||||
\(643\) | 2.00000 | + | 3.46410i | 0.0788723 | + | 0.136611i | 0.902764 | − | 0.430137i | \(-0.141535\pi\) |
−0.823891 | + | 0.566748i | \(0.808201\pi\) | |||||||
\(644\) | −1.50000 | − | 2.59808i | −0.0591083 | − | 0.102379i | ||||
\(645\) | − | 10.3923i | − | 0.409197i | ||||||
\(646\) | −21.0000 | + | 36.3731i | −0.826234 | + | 1.43108i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.00000 | − | 6.92820i | 0.156893 | − | 0.271746i | ||||
\(651\) | 3.46410i | 0.135769i | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 18.0000 | + | 31.1769i | 0.704394 | + | 1.22005i | 0.966910 | + | 0.255119i | \(0.0821147\pi\) |
−0.262515 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(654\) | −15.0000 | − | 8.66025i | −0.586546 | − | 0.338643i | ||||
\(655\) | −13.5000 | + | 23.3827i | −0.527489 | + | 0.913637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0000 | + | 36.3731i | −0.818044 | + | 1.41689i | 0.0890776 | + | 0.996025i | \(0.471608\pi\) |
−0.907122 | + | 0.420869i | \(0.861725\pi\) | |||||||
\(660\) | 27.0000 | − | 15.5885i | 1.05097 | − | 0.606780i | ||||
\(661\) | −2.50000 | − | 4.33013i | −0.0972387 | − | 0.168422i | 0.813302 | − | 0.581842i | \(-0.197668\pi\) |
−0.910541 | + | 0.413419i | \(0.864334\pi\) | |||||||
\(662\) | 13.0000 | + | 22.5167i | 0.505259 | + | 0.875135i | ||||
\(663\) | 18.0000 | − | 10.3923i | 0.699062 | − | 0.403604i | ||||
\(664\) | 6.00000 | − | 10.3923i | 0.232845 | − | 0.403300i | ||||
\(665\) | 21.0000 | 0.814345 | ||||||||
\(666\) | −3.00000 | + | 5.19615i | −0.116248 | + | 0.201347i | ||||
\(667\) | 18.0000 | 0.696963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.0000 | + | 24.2487i | 1.62381 | + | 0.937509i | ||||
\(670\) | −12.0000 | − | 20.7846i | −0.463600 | − | 0.802980i | ||||
\(671\) | 15.0000 | + | 25.9808i | 0.579069 | + | 1.00298i | ||||
\(672\) | − | 1.73205i | − | 0.0668153i | ||||||
\(673\) | 18.5000 | − | 32.0429i | 0.713123 | − | 1.23516i | −0.250557 | − | 0.968102i | \(-0.580614\pi\) |
0.963679 | − | 0.267063i | \(-0.0860531\pi\) | |||||||
\(674\) | 22.0000 | 0.847408 | ||||||||
\(675\) | 18.0000 | + | 10.3923i | 0.692820 | + | 0.400000i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −21.0000 | + | 36.3731i | −0.807096 | + | 1.39793i | 0.107772 | + | 0.994176i | \(0.465628\pi\) |
−0.914867 | + | 0.403755i | \(0.867705\pi\) | |||||||
\(678\) | − | 25.9808i | − | 0.997785i | ||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | −9.00000 | − | 15.5885i | −0.345134 | − | 0.597790i | ||||
\(681\) | 22.5000 | + | 12.9904i | 0.862202 | + | 0.497792i | ||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | −6.00000 | −0.229584 | −0.114792 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114792 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(684\) | −10.5000 | − | 18.1865i | −0.401478 | − | 0.695379i | ||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | −1.50000 | + | 0.866025i | −0.0572286 | + | 0.0330409i | ||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 13.5000 | − | 7.79423i | 0.513936 | − | 0.296721i | ||||
\(691\) | −23.5000 | + | 40.7032i | −0.893982 | + | 1.54842i | −0.0589228 | + | 0.998263i | \(0.518767\pi\) |
−0.835059 | + | 0.550160i | \(0.814567\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −9.00000 | − | 15.5885i | −0.341882 | − | 0.592157i | ||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 7.50000 | − | 12.9904i | 0.284491 | − | 0.492753i | ||||
\(696\) | 9.00000 | + | 5.19615i | 0.341144 | + | 0.196960i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 13.0000 | + | 22.5167i | 0.492057 | + | 0.852268i | ||||
\(699\) | 15.5885i | 0.589610i | ||||||||
\(700\) | −2.00000 | + | 3.46410i | −0.0755929 | + | 0.130931i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 10.3923i | 0.392232i | ||||||||
\(703\) | −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 | ||||
\(707\) | −4.50000 | − | 7.79423i | −0.169240 | − | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | − | 45.0333i | 0.976450 | − | 1.69126i | 0.301388 | − | 0.953502i | \(-0.402550\pi\) |
0.675063 | − | 0.737760i | \(-0.264116\pi\) | |||||||
\(710\) | 9.00000 | 0.337764 | ||||||||
\(711\) | 7.50000 | − | 12.9904i | 0.281272 | − | 0.487177i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | + | 5.19615i | −0.112351 | + | 0.194597i | ||||
\(714\) | −9.00000 | + | 5.19615i | −0.336817 | + | 0.194461i | ||||
\(715\) | −18.0000 | − | 31.1769i | −0.673162 | − | 1.16595i | ||||
\(716\) | −9.00000 | − | 15.5885i | −0.336346 | − | 0.582568i | ||||
\(717\) | −22.5000 | + | 12.9904i | −0.840278 | + | 0.485135i | ||||
\(718\) | −1.50000 | + | 2.59808i | −0.0559795 | + | 0.0969593i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 9.00000 | 0.335410 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 15.0000 | − | 25.9808i | 0.558242 | − | 0.966904i | ||||
\(723\) | −12.0000 | − | 6.92820i | −0.446285 | − | 0.257663i | ||||
\(724\) | 12.5000 | + | 21.6506i | 0.464559 | + | 0.804640i | ||||
\(725\) | −12.0000 | − | 20.7846i | −0.445669 | − | 0.771921i | ||||
\(726\) | − | 43.3013i | − | 1.60706i | ||||||
\(727\) | −4.00000 | + | 6.92820i | −0.148352 | + | 0.256953i | −0.930618 | − | 0.365991i | \(-0.880730\pi\) |
0.782267 | + | 0.622944i | \(0.214063\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | 8.66025i | 0.320092i | ||||||||
\(733\) | −14.5000 | − | 25.1147i | −0.535570 | − | 0.927634i | −0.999136 | − | 0.0415715i | \(-0.986764\pi\) |
0.463566 | − | 0.886062i | \(-0.346570\pi\) | |||||||
\(734\) | 4.00000 | + | 6.92820i | 0.147643 | + | 0.255725i | ||||
\(735\) | 4.50000 | + | 2.59808i | 0.165985 | + | 0.0958315i | ||||
\(736\) | 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 | ||||
\(741\) | −21.0000 | + | 12.1244i | −0.771454 | + | 0.445399i | ||||
\(742\) | 3.00000 | + | 5.19615i | 0.110133 | + | 0.190757i | ||||
\(743\) | −18.0000 | − | 31.1769i | −0.660356 | − | 1.14377i | −0.980522 | − | 0.196409i | \(-0.937072\pi\) |
0.320166 | − | 0.947361i | \(-0.396261\pi\) | |||||||
\(744\) | −3.00000 | + | 1.73205i | −0.109985 | + | 0.0635001i | ||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | −14.0000 | −0.512576 | ||||||||
\(747\) | 18.0000 | − | 31.1769i | 0.658586 | − | 1.14070i | ||||
\(748\) | −36.0000 | −1.31629 | ||||||||
\(749\) | 6.00000 | − | 10.3923i | 0.219235 | − | 0.379727i | ||||
\(750\) | 4.50000 | + | 2.59808i | 0.164317 | + | 0.0948683i | ||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.19615i | 0.189358i | ||||||||
\(754\) | 6.00000 | − | 10.3923i | 0.218507 | − | 0.378465i | ||||
\(755\) | −69.0000 | −2.51117 | ||||||||
\(756\) | − | 5.19615i | − | 0.188982i | ||||||
\(757\) | 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 | ||||
\(759\) | − | 31.1769i | − | 1.13165i | ||||||
\(760\) | 10.5000 | + | 18.1865i | 0.380875 | + | 0.659695i | ||||
\(761\) | 21.0000 | + | 36.3731i | 0.761249 | + | 1.31852i | 0.942207 | + | 0.335032i | \(0.108747\pi\) |
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(762\) | 25.5000 | + | 14.7224i | 0.923768 | + | 0.533337i | ||||
\(763\) | 5.00000 | − | 8.66025i | 0.181012 | − | 0.313522i | ||||
\(764\) | −9.00000 | −0.325609 | ||||||||
\(765\) | −27.0000 | − | 46.7654i | −0.976187 | − | 1.69081i | ||||
\(766\) | 18.0000 | 0.650366 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.50000 | − | 0.866025i | 0.0541266 | − | 0.0312500i | ||||
\(769\) | −7.00000 | − | 12.1244i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(770\) | 9.00000 | + | 15.5885i | 0.324337 | + | 0.561769i | ||||
\(771\) | 27.0000 | − | 15.5885i | 0.972381 | − | 0.561405i | ||||
\(772\) | −8.50000 | + | 14.7224i | −0.305922 | + | 0.529872i | ||||
\(773\) | −51.0000 | −1.83434 | −0.917171 | − | 0.398493i | \(-0.869533\pi\) | ||||
−0.917171 | + | 0.398493i | \(0.869533\pi\) | |||||||
\(774\) | −3.00000 | − | 5.19615i | −0.107833 | − | 0.186772i | ||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 1.00000 | − | 1.73205i | 0.0358979 | − | 0.0621770i | ||||
\(777\) | −3.00000 | − | 1.73205i | −0.107624 | − | 0.0621370i | ||||
\(778\) | 12.0000 | + | 20.7846i | 0.430221 | + | 0.745164i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | − | 10.3923i | − | 0.372104i | ||||||
\(781\) | 9.00000 | − | 15.5885i | 0.322045 | − | 0.557799i | ||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 27.0000 | + | 15.5885i | 0.964901 | + | 0.557086i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −19.5000 | + | 33.7750i | −0.695985 | + | 1.20548i | ||||
\(786\) | 15.5885i | 0.556022i | ||||||||
\(787\) | −10.0000 | − | 17.3205i | −0.356462 | − | 0.617409i | 0.630905 | − | 0.775860i | \(-0.282684\pi\) |
−0.987367 | + | 0.158450i | \(0.949350\pi\) | |||||||
\(788\) | −9.00000 | − | 15.5885i | −0.320612 | − | 0.555316i | ||||
\(789\) | 31.5000 | + | 18.1865i | 1.12143 | + | 0.647458i | ||||
\(790\) | −7.50000 | + | 12.9904i | −0.266838 | + | 0.462177i | ||||
\(791\) | 15.0000 | 0.533339 | ||||||||
\(792\) | 9.00000 | − | 15.5885i | 0.319801 | − | 0.553912i | ||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 13.0000 | − | 22.5167i | 0.461353 | − | 0.799086i | ||||
\(795\) | −27.0000 | + | 15.5885i | −0.957591 | + | 0.552866i | ||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | −1.50000 | − | 2.59808i | −0.0531327 | − | 0.0920286i | 0.838236 | − | 0.545308i | \(-0.183587\pi\) |
−0.891368 | + | 0.453279i | \(0.850254\pi\) | |||||||
\(798\) | 10.5000 | − | 6.06218i | 0.371696 | − | 0.214599i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.00000 | −0.105934 | ||||||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | −12.0000 | − | 6.92820i | −0.423207 | − | 0.244339i | ||||
\(805\) | 4.50000 | + | 7.79423i | 0.158604 | + | 0.274710i | ||||
\(806\) | 2.00000 | + | 3.46410i | 0.0704470 | + | 0.122018i | ||||
\(807\) | − | 15.5885i | − | 0.548740i | ||||||
\(808\) | 4.50000 | − | 7.79423i | 0.158309 | − | 0.274200i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 27.0000 | 0.948683 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −3.00000 | + | 5.19615i | −0.105279 | + | 0.182349i | ||||
\(813\) | − | 48.4974i | − | 1.70088i | ||||||
\(814\) | −6.00000 | − | 10.3923i | −0.210300 | − | 0.364250i | ||||
\(815\) | 3.00000 | + | 5.19615i | 0.105085 | + | 0.182013i | ||||
\(816\) | −9.00000 | − | 5.19615i | −0.315063 | − | 0.181902i | ||||
\(817\) | 7.00000 | − | 12.1244i | 0.244899 | − | 0.424178i | ||||
\(818\) | −32.0000 | −1.11885 | ||||||||
\(819\) | −6.00000 | −0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | − | 20.7846i | 0.418803 | − | 0.725388i | −0.577016 | − | 0.816733i | \(-0.695783\pi\) |
0.995819 | + | 0.0913446i | \(0.0291165\pi\) | |||||||
\(822\) | −9.00000 | + | 5.19615i | −0.313911 | + | 0.181237i | ||||
\(823\) | −4.00000 | − | 6.92820i | −0.139431 | − | 0.241502i | 0.787850 | − | 0.615867i | \(-0.211194\pi\) |
−0.927281 | + | 0.374365i | \(0.877861\pi\) | |||||||
\(824\) | −5.00000 | − | 8.66025i | −0.174183 | − | 0.301694i | ||||
\(825\) | −36.0000 | + | 20.7846i | −1.25336 | + | 0.723627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 4.50000 | − | 7.79423i | 0.156386 | − | 0.270868i | ||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −18.0000 | + | 31.1769i | −0.624789 | + | 1.08217i | ||||
\(831\) | 24.0000 | + | 13.8564i | 0.832551 | + | 0.480673i | ||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | −3.00000 | − | 5.19615i | −0.103944 | − | 0.180036i | ||||
\(834\) | − | 8.66025i | − | 0.299880i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 42.0000 | 1.45260 | ||||||||
\(837\) | −9.00000 | + | 5.19615i | −0.311086 | + | 0.179605i | ||||
\(838\) | −15.0000 | −0.518166 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 5.19615i | 0.179284i | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | 40.5000 | + | 23.3827i | 1.39489 | + | 0.805342i | ||||
\(844\) | −4.00000 | + | 6.92820i | −0.137686 | + | 0.238479i | ||||
\(845\) | 27.0000 | 0.928828 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | 0.859010 | ||||||||
\(848\) | −3.00000 | + | 5.19615i | −0.103020 | + | 0.178437i | ||||
\(849\) | −28.5000 | + | 16.4545i | −0.978117 | + | 0.564716i | ||||
\(850\) | 12.0000 | + | 20.7846i | 0.411597 | + | 0.712906i | ||||
\(851\) | −3.00000 | − | 5.19615i | −0.102839 | − | 0.178122i | ||||
\(852\) | 4.50000 | − | 2.59808i | 0.154167 | − | 0.0890086i | ||||
\(853\) | −17.5000 | + | 30.3109i | −0.599189 | + | 1.03783i | 0.393753 | + | 0.919216i | \(0.371177\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | −5.00000 | −0.171096 | ||||||||
\(855\) | 31.5000 | + | 54.5596i | 1.07728 | + | 1.86590i | ||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −27.0000 | + | 46.7654i | −0.922302 | + | 1.59747i | −0.126459 | + | 0.991972i | \(0.540361\pi\) |
−0.795843 | + | 0.605503i | \(0.792972\pi\) | |||||||
\(858\) | −18.0000 | − | 10.3923i | −0.614510 | − | 0.354787i | ||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 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 | \(-0.451048\pi\) | ||||
0.153182 | + | 0.988198i | \(0.451048\pi\) | |||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | 32.9090i | 1.11765i | ||||||||
\(868\) | −1.00000 | − | 1.73205i | −0.0339422 | − | 0.0587896i | ||||
\(869\) | 15.0000 | + | 25.9808i | 0.508840 | + | 0.881337i | ||||
\(870\) | −27.0000 | − | 15.5885i | −0.915386 | − | 0.528498i | ||||
\(871\) | −8.00000 | + | 13.8564i | −0.271070 | + | 0.469506i | ||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 3.00000 | − | 5.19615i | 0.101535 | − | 0.175863i | ||||
\(874\) | 21.0000 | 0.710336 | ||||||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 3.00000 | − | 1.73205i | 0.101361 | − | 0.0585206i | ||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | −4.50000 | + | 2.59808i | −0.151781 | + | 0.0876309i | ||||
\(880\) | −9.00000 | + | 15.5885i | −0.303390 | + | 0.525487i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | −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 | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | − | 3.46410i | − | 0.116248i | ||||||
\(889\) | −8.50000 | + | 14.7224i | −0.285081 | + | 0.493775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | − | 46.7654i | 0.904534 | − | 1.56670i | ||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 10.3923i | 0.347571i | ||||||||
\(895\) | 27.0000 | + | 46.7654i | 0.902510 | + | 1.56319i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −9.00000 | − | 5.19615i | −0.300501 | − | 0.173494i | ||||
\(898\) | 16.5000 | − | 28.5788i | 0.550612 | − | 0.953688i | ||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | −12.0000 | −0.400000 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.00000 | − | 1.73205i | 0.0998337 | − | 0.0576390i | ||||
\(904\) | 7.50000 | + | 12.9904i | 0.249446 | + | 0.432054i | ||||
\(905\) | −37.5000 | − | 64.9519i | −1.24654 | − | 2.15907i | ||||
\(906\) | −34.5000 | + | 19.9186i | −1.14619 | + | 0.661751i | ||||
\(907\) | −16.0000 | + | 27.7128i | −0.531271 | + | 0.920189i | 0.468063 | + | 0.883695i | \(0.344952\pi\) |
−0.999334 | + | 0.0364935i | \(0.988381\pi\) | |||||||
\(908\) | −15.0000 | −0.497792 | ||||||||
\(909\) | 13.5000 | − | 23.3827i | 0.447767 | − | 0.775555i | ||||
\(910\) | 6.00000 | 0.198898 | ||||||||
\(911\) | −7.50000 | + | 12.9904i | −0.248486 | + | 0.430391i | −0.963106 | − | 0.269122i | \(-0.913266\pi\) |
0.714620 | + | 0.699513i | \(0.246600\pi\) | |||||||
\(912\) | 10.5000 | + | 6.06218i | 0.347690 | + | 0.200739i | ||||
\(913\) | 36.0000 | + | 62.3538i | 1.19143 | + | 2.06361i | ||||
\(914\) | 14.5000 | + | 25.1147i | 0.479617 | + | 0.830722i | ||||
\(915\) | − | 25.9808i | − | 0.858898i | ||||||
\(916\) | 0.500000 | − | 0.866025i | 0.0165205 | − | 0.0286143i | ||||
\(917\) | −9.00000 | −0.297206 | ||||||||
\(918\) | −27.0000 | − | 15.5885i | −0.891133 | − | 0.514496i | ||||
\(919\) | 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 | ||||
\(921\) | − | 43.3013i | − | 1.42683i | ||||||
\(922\) | −16.5000 | − | 28.5788i | −0.543399 | − | 0.941194i | ||||
\(923\) | −3.00000 | − | 5.19615i | −0.0987462 | − | 0.171033i | ||||
\(924\) | 9.00000 | + | 5.19615i | 0.296078 | + | 0.170941i | ||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | 13.0000 | 0.427207 | ||||||||
\(927\) | −15.0000 | − | 25.9808i | −0.492665 | − | 0.853320i | ||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 9.00000 | − | 5.19615i | 0.295122 | − | 0.170389i | ||||
\(931\) | 3.50000 | + | 6.06218i | 0.114708 | + | 0.198680i | ||||
\(932\) | −4.50000 | − | 7.79423i | −0.147402 | − | 0.255308i | ||||
\(933\) | 18.0000 | − | 10.3923i | 0.589294 | − | 0.340229i | ||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 108.000 | 3.53198 | ||||||||
\(936\) | −3.00000 | − | 5.19615i | −0.0980581 | − | 0.169842i | ||||
\(937\) | 38.0000 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(938\) | 4.00000 | − | 6.92820i | 0.130605 | − | 0.226214i | ||||
\(939\) | 15.0000 | + | 8.66025i | 0.489506 | + | 0.282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5000 | − | 18.1865i | −0.342290 | − | 0.592864i | 0.642567 | − | 0.766229i | \(-0.277869\pi\) |
−0.984858 | + | 0.173365i | \(0.944536\pi\) | |||||||
\(942\) | 22.5167i | 0.733632i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.5885i | 0.507093i | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 12.0000 | − | 20.7846i | 0.389948 | − | 0.675409i | −0.602494 | − | 0.798123i | \(-0.705826\pi\) |
0.992442 | + | 0.122714i | \(0.0391598\pi\) | |||||||
\(948\) | 8.66025i | 0.281272i | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | −14.0000 | − | 24.2487i | −0.454220 | − | 0.786732i | ||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 3.00000 | − | 5.19615i | 0.0972306 | − | 0.168408i | ||||
\(953\) | 42.0000 | 1.36051 | 0.680257 | − | 0.732974i | \(-0.261868\pi\) | ||||
0.680257 | + | 0.732974i | \(0.261868\pi\) | |||||||
\(954\) | −9.00000 | + | 15.5885i | −0.291386 | + | 0.504695i | ||||
\(955\) | 27.0000 | 0.873699 | ||||||||
\(956\) | 7.50000 | − | 12.9904i | 0.242567 | − | 0.420139i | ||||
\(957\) | −54.0000 | + | 31.1769i | −1.74557 | + | 1.00781i | ||||
\(958\) | −3.00000 | − | 5.19615i | −0.0969256 | − | 0.167880i | ||||
\(959\) | −3.00000 | − | 5.19615i | −0.0968751 | − | 0.167793i | ||||
\(960\) | −4.50000 | + | 2.59808i | −0.145237 | + | 0.0838525i | ||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 36.0000 | 1.16008 | ||||||||
\(964\) | 8.00000 | 0.257663 | ||||||||
\(965\) | 25.5000 | − | 44.1673i | 0.820874 | − | 1.42180i | ||||
\(966\) | 4.50000 | + | 2.59808i | 0.144785 | + | 0.0835917i | ||||
\(967\) | −8.50000 | − | 14.7224i | −0.273342 | − | 0.473441i | 0.696374 | − | 0.717679i | \(-0.254796\pi\) |
−0.969715 | + | 0.244238i | \(0.921462\pi\) | |||||||
\(968\) | 12.5000 | + | 21.6506i | 0.401765 | + | 0.695878i | ||||
\(969\) | − | 72.7461i | − | 2.33694i | ||||||
\(970\) | −3.00000 | + | 5.19615i | −0.0963242 | + | 0.166838i | ||||
\(971\) | −15.0000 | −0.481373 | −0.240686 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(972\) | 13.5000 | − | 7.79423i | 0.433013 | − | 0.250000i | ||||
\(973\) | 5.00000 | 0.160293 | ||||||||
\(974\) | 14.5000 | − | 25.1147i | 0.464610 | − | 0.804728i | ||||
\(975\) | 13.8564i | 0.443760i | ||||||||
\(976\) | −2.50000 | − | 4.33013i | −0.0800230 | − | 0.138604i | ||||
\(977\) | −3.00000 | − | 5.19615i | −0.0959785 | − | 0.166240i | 0.814038 | − | 0.580812i | \(-0.197265\pi\) |
−0.910017 | + | 0.414572i | \(0.863931\pi\) | |||||||
\(978\) | 3.00000 | + | 1.73205i | 0.0959294 | + | 0.0553849i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.00000 | −0.0958315 | ||||||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | −18.0000 | −0.574403 | ||||||||
\(983\) | −9.00000 | + | 15.5885i | −0.287055 | + | 0.497195i | −0.973106 | − | 0.230360i | \(-0.926010\pi\) |
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(984\) | 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 | ||||||||
\(990\) | −27.0000 | + | 46.7654i | −0.858116 | + | 1.48630i | ||||
\(991\) | −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 | ||||
\(993\) | −39.0000 | − | 22.5167i | −1.23763 | − | 0.714545i | ||||
\(994\) | 1.50000 | + | 2.59808i | 0.0475771 | + | 0.0824060i | ||||
\(995\) | 21.0000 | + | 36.3731i | 0.665745 | + | 1.15310i | ||||
\(996\) | 20.7846i | 0.658586i | ||||||||
\(997\) | 27.5000 | − | 47.6314i | 0.870934 | − | 1.50850i | 0.00990158 | − | 0.999951i | \(-0.496848\pi\) |
0.861032 | − | 0.508551i | \(-0.169818\pi\) | |||||||
\(998\) | −32.0000 | −1.01294 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))