Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (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: | \(0.910294583043\) |
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 | 7.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.7 |
Dual form | 114.2.e.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.50000 | − | 2.59808i | 0.416025 | − | 0.720577i | −0.579510 | − | 0.814965i | \(-0.696756\pi\) |
0.995535 | + | 0.0943882i | \(0.0300895\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 0.866025i | 0.109109 | + | 0.188982i | ||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.500000 | + | 0.866025i | −0.0944911 | + | 0.163663i | ||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 2.00000 | − | 3.46410i | 0.342997 | − | 0.594089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 3.50000 | + | 2.59808i | 0.567775 | + | 0.421464i | ||||
\(39\) | 3.00000 | 0.480384 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | − | 3.46410i | −0.312348 | − | 0.541002i | 0.666523 | − | 0.745485i | \(-0.267782\pi\) |
−0.978870 | + | 0.204483i | \(0.934449\pi\) | |||||||
\(42\) | −0.500000 | + | 0.866025i | −0.0771517 | + | 0.133631i | ||||
\(43\) | 4.50000 | + | 7.79423i | 0.686244 | + | 1.18861i | 0.973044 | + | 0.230618i | \(0.0740749\pi\) |
−0.286801 | + | 0.957990i | \(0.592592\pi\) | |||||||
\(44\) | 1.00000 | − | 1.73205i | 0.150756 | − | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −5.00000 | + | 8.66025i | −0.729325 | + | 1.26323i | 0.227844 | + | 0.973698i | \(0.426832\pi\) |
−0.957169 | + | 0.289530i | \(0.906501\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | 1.50000 | + | 2.59808i | 0.208013 | + | 0.360288i | ||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.50000 | + | 2.59808i | 0.463586 | + | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | + | 12.1244i | 0.911322 | + | 1.57846i | 0.812198 | + | 0.583382i | \(0.198271\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | + | 9.52628i | −0.704203 | + | 1.21972i | 0.262776 | + | 0.964857i | \(0.415362\pi\) |
−0.966978 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(62\) | −1.50000 | − | 2.59808i | −0.190500 | − | 0.329956i | ||||
\(63\) | −0.500000 | + | 0.866025i | −0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.00000 | − | 12.1244i | −0.830747 | − | 1.43890i | −0.897447 | − | 0.441123i | \(-0.854580\pi\) |
0.0666994 | − | 0.997773i | \(-0.478753\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 5.50000 | + | 9.52628i | 0.643726 | + | 1.11497i | 0.984594 | + | 0.174855i | \(0.0559458\pi\) |
−0.340868 | + | 0.940111i | \(0.610721\pi\) | |||||||
\(74\) | −2.50000 | − | 4.33013i | −0.290619 | − | 0.503367i | ||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | −0.500000 | + | 4.33013i | −0.0573539 | + | 0.496700i | ||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 1.50000 | + | 2.59808i | 0.169842 | + | 0.294174i | ||||
\(79\) | −0.500000 | − | 0.866025i | −0.0562544 | − | 0.0974355i | 0.836527 | − | 0.547926i | \(-0.184582\pi\) |
−0.892781 | + | 0.450490i | \(0.851249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.00000 | − | 3.46410i | 0.220863 | − | 0.382546i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.50000 | + | 7.79423i | −0.485247 | + | 0.840473i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 7.00000 | − | 12.1244i | 0.741999 | − | 1.28518i | −0.209585 | − | 0.977790i | \(-0.567211\pi\) |
0.951584 | − | 0.307389i | \(-0.0994552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50000 | − | 2.59808i | 0.157243 | − | 0.272352i | ||||
\(92\) | −2.00000 | − | 3.46410i | −0.208514 | − | 0.361158i | ||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | −10.0000 | −1.03142 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | −3.00000 | − | 5.19615i | −0.303046 | − | 0.524891i | ||||
\(99\) | 1.00000 | − | 1.73205i | 0.100504 | − | 0.174078i | ||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | −3.00000 | −0.295599 | −0.147799 | − | 0.989017i | \(-0.547219\pi\) | ||||
−0.147799 | + | 0.989017i | \(0.547219\pi\) | |||||||
\(104\) | −1.50000 | + | 2.59808i | −0.147087 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | −10.0000 | −0.966736 | −0.483368 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.50000 | − | 4.33013i | −0.237289 | − | 0.410997i | ||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | −0.500000 | + | 4.33013i | −0.0468293 | + | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.50000 | + | 2.59808i | 0.138675 | + | 0.240192i | ||||
\(118\) | −7.00000 | + | 12.1244i | −0.644402 | + | 1.11614i | ||||
\(119\) | −2.00000 | − | 3.46410i | −0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −11.0000 | −0.995893 | ||||||||
\(123\) | 2.00000 | − | 3.46410i | 0.180334 | − | 0.312348i | ||||
\(124\) | 1.50000 | − | 2.59808i | 0.134704 | − | 0.233314i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 4.00000 | − | 6.92820i | 0.354943 | − | 0.614779i | −0.632166 | − | 0.774833i | \(-0.717834\pi\) |
0.987108 | + | 0.160055i | \(0.0511671\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.50000 | + | 7.79423i | −0.396203 | + | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 4.00000 | − | 1.73205i | 0.346844 | − | 0.150188i | ||||
\(134\) | −3.00000 | −0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | −2.00000 | − | 3.46410i | −0.170251 | − | 0.294884i | ||||
\(139\) | 9.50000 | − | 16.4545i | 0.805779 | − | 1.39565i | −0.109984 | − | 0.993933i | \(-0.535080\pi\) |
0.915764 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | −0.842152 | ||||||||
\(142\) | 7.00000 | − | 12.1244i | 0.587427 | − | 1.01745i | ||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.50000 | + | 9.52628i | −0.455183 | + | 0.788400i | ||||
\(147\) | −3.00000 | − | 5.19615i | −0.247436 | − | 0.428571i | ||||
\(148\) | 2.50000 | − | 4.33013i | 0.205499 | − | 0.355934i | ||||
\(149\) | 11.0000 | + | 19.0526i | 0.901155 | + | 1.56085i | 0.825997 | + | 0.563675i | \(0.190613\pi\) |
0.0751583 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(150\) | 2.50000 | + | 4.33013i | 0.204124 | + | 0.353553i | ||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | −4.00000 | + | 1.73205i | −0.324443 | + | 0.140488i | ||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | −1.00000 | − | 1.73205i | −0.0805823 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.50000 | + | 2.59808i | −0.120096 | + | 0.208013i | ||||
\(157\) | 10.5000 | + | 18.1865i | 0.837991 | + | 1.45144i | 0.891572 | + | 0.452880i | \(0.149603\pi\) |
−0.0535803 | + | 0.998564i | \(0.517063\pi\) | |||||||
\(158\) | 0.500000 | − | 0.866025i | 0.0397779 | − | 0.0688973i | ||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | + | 3.46410i | −0.157622 | + | 0.273009i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | + | 6.92820i | 0.310460 | + | 0.537733i | ||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | −0.500000 | − | 0.866025i | −0.0385758 | − | 0.0668153i | ||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | + | 4.33013i | −0.0382360 | + | 0.331133i | ||||
\(172\) | −9.00000 | −0.686244 | ||||||||
\(173\) | 12.0000 | + | 20.7846i | 0.912343 | + | 1.58022i | 0.810745 | + | 0.585399i | \(0.199062\pi\) |
0.101598 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 4.33013i | 0.188982 | − | 0.327327i | ||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | −7.00000 | + | 12.1244i | −0.526152 | + | 0.911322i | ||||
\(178\) | 14.0000 | 1.04934 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.00000 | − | 15.5885i | 0.668965 | − | 1.15868i | −0.309229 | − | 0.950988i | \(-0.600071\pi\) |
0.978194 | − | 0.207693i | \(-0.0665956\pi\) | |||||||
\(182\) | 3.00000 | 0.222375 | ||||||||
\(183\) | −11.0000 | −0.813143 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | − | 2.59808i | 0.109985 | − | 0.190500i | ||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | −5.00000 | − | 8.66025i | −0.364662 | − | 0.631614i | ||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 6.50000 | + | 11.2583i | 0.467880 | + | 0.810392i | 0.999326 | − | 0.0366998i | \(-0.0116845\pi\) |
−0.531446 | + | 0.847092i | \(0.678351\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | −2.50000 | + | 4.33013i | −0.177220 | + | 0.306955i | −0.940927 | − | 0.338608i | \(-0.890044\pi\) |
0.763707 | + | 0.645563i | \(0.223377\pi\) | |||||||
\(200\) | −2.50000 | + | 4.33013i | −0.176777 | + | 0.306186i | ||||
\(201\) | −3.00000 | −0.211604 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.00000 | + | 3.46410i | 0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.50000 | − | 2.59808i | −0.104510 | − | 0.181017i | ||||
\(207\) | −2.00000 | − | 3.46410i | −0.139010 | − | 0.240772i | ||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | −8.00000 | + | 3.46410i | −0.553372 | + | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5000 | − | 21.6506i | −0.860535 | − | 1.49049i | −0.871413 | − | 0.490550i | \(-0.836796\pi\) |
0.0108774 | − | 0.999941i | \(-0.496538\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 7.00000 | − | 12.1244i | 0.479632 | − | 0.830747i | ||||
\(214\) | −5.00000 | − | 8.66025i | −0.341793 | − | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 7.00000 | − | 12.1244i | 0.474100 | − | 0.821165i | ||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 2.50000 | − | 4.33013i | 0.167789 | − | 0.290619i | ||||
\(223\) | −4.50000 | − | 7.79423i | −0.301342 | − | 0.521940i | 0.675098 | − | 0.737728i | \(-0.264101\pi\) |
−0.976440 | + | 0.215788i | \(0.930768\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | 2.50000 | + | 4.33013i | 0.166667 | + | 0.288675i | ||||
\(226\) | 5.00000 | + | 8.66025i | 0.332595 | + | 0.576072i | ||||
\(227\) | 8.00000 | 0.530979 | 0.265489 | − | 0.964114i | \(-0.414466\pi\) | ||||
0.265489 | + | 0.964114i | \(0.414466\pi\) | |||||||
\(228\) | −4.00000 | + | 1.73205i | −0.264906 | + | 0.114708i | ||||
\(229\) | −11.0000 | −0.726900 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | − | 1.73205i | −0.0657952 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.00000 | − | 15.5885i | −0.589610 | − | 1.02123i | −0.994283 | − | 0.106773i | \(-0.965948\pi\) |
0.404674 | − | 0.914461i | \(-0.367385\pi\) | |||||||
\(234\) | −1.50000 | + | 2.59808i | −0.0980581 | + | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | 0.500000 | − | 0.866025i | 0.0324785 | − | 0.0562544i | ||||
\(238\) | 2.00000 | − | 3.46410i | 0.129641 | − | 0.224544i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5000 | + | 21.6506i | −0.805196 | + | 1.39464i | 0.110963 | + | 0.993825i | \(0.464606\pi\) |
−0.916159 | + | 0.400815i | \(0.868727\pi\) | |||||||
\(242\) | −3.50000 | − | 6.06218i | −0.224989 | − | 0.389692i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.50000 | − | 9.52628i | −0.352101 | − | 0.609858i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | 1.50000 | − | 12.9904i | 0.0954427 | − | 0.826558i | ||||
\(248\) | 3.00000 | 0.190500 | ||||||||
\(249\) | 4.00000 | + | 6.92820i | 0.253490 | + | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | − | 15.5885i | 0.568075 | − | 0.983935i | −0.428681 | − | 0.903456i | \(-0.641022\pi\) |
0.996756 | − | 0.0804789i | \(-0.0256450\pi\) | |||||||
\(252\) | −0.500000 | − | 0.866025i | −0.0314970 | − | 0.0545545i | ||||
\(253\) | 4.00000 | − | 6.92820i | 0.251478 | − | 0.435572i | ||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | −9.00000 | −0.560316 | ||||||||
\(259\) | −5.00000 | −0.310685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | −9.00000 | − | 15.5885i | −0.554964 | − | 0.961225i | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | 1.00000 | + | 1.73205i | 0.0615457 | + | 0.106600i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.50000 | + | 2.59808i | 0.214599 | + | 0.159298i | ||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | −2.00000 | + | 3.46410i | −0.121268 | + | 0.210042i | ||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −5.00000 | + | 8.66025i | −0.301511 | + | 0.522233i | ||||
\(276\) | 2.00000 | − | 3.46410i | 0.120386 | − | 0.208514i | ||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 19.0000 | 1.13954 | ||||||||
\(279\) | 1.50000 | − | 2.59808i | 0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.00000 | − | 6.92820i | 0.238620 | − | 0.413302i | −0.721699 | − | 0.692207i | \(-0.756638\pi\) |
0.960319 | + | 0.278906i | \(0.0899716\pi\) | |||||||
\(282\) | −5.00000 | − | 8.66025i | −0.297746 | − | 0.515711i | ||||
\(283\) | 10.0000 | + | 17.3205i | 0.594438 | + | 1.02960i | 0.993626 | + | 0.112728i | \(0.0359589\pi\) |
−0.399188 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(284\) | 14.0000 | 0.830747 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −2.00000 | − | 3.46410i | −0.118056 | − | 0.204479i | ||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.00000 | − | 1.73205i | 0.0586210 | − | 0.101535i | ||||
\(292\) | −11.0000 | −0.643726 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 3.00000 | − | 5.19615i | 0.174964 | − | 0.303046i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.00000 | 0.290619 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −11.0000 | + | 19.0526i | −0.637213 | + | 1.10369i | ||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | −2.50000 | + | 4.33013i | −0.144338 | + | 0.250000i | ||||
\(301\) | 4.50000 | + | 7.79423i | 0.259376 | + | 0.449252i | ||||
\(302\) | −10.0000 | − | 17.3205i | −0.575435 | − | 0.996683i | ||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | −3.50000 | − | 2.59808i | −0.200739 | − | 0.149010i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | + | 3.46410i | 0.114332 | + | 0.198030i | ||||
\(307\) | 6.00000 | + | 10.3923i | 0.342438 | + | 0.593120i | 0.984885 | − | 0.173210i | \(-0.0554140\pi\) |
−0.642447 | + | 0.766330i | \(0.722081\pi\) | |||||||
\(308\) | 1.00000 | − | 1.73205i | 0.0569803 | − | 0.0986928i | ||||
\(309\) | −1.50000 | − | 2.59808i | −0.0853320 | − | 0.147799i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | 0.567048 | 0.283524 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283524 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(312\) | −3.00000 | −0.169842 | ||||||||
\(313\) | −3.00000 | + | 5.19615i | −0.169570 | + | 0.293704i | −0.938269 | − | 0.345907i | \(-0.887571\pi\) |
0.768699 | + | 0.639611i | \(0.220905\pi\) | |||||||
\(314\) | −10.5000 | + | 18.1865i | −0.592549 | + | 1.02633i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | −6.00000 | + | 10.3923i | −0.336994 | + | 0.583690i | −0.983866 | − | 0.178908i | \(-0.942743\pi\) |
0.646872 | + | 0.762598i | \(0.276077\pi\) | |||||||
\(318\) | 2.00000 | + | 3.46410i | 0.112154 | + | 0.194257i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.00000 | − | 8.66025i | −0.279073 | − | 0.483368i | ||||
\(322\) | −4.00000 | −0.222911 | ||||||||
\(323\) | −14.0000 | − | 10.3923i | −0.778981 | − | 0.578243i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.50000 | − | 12.9904i | −0.416025 | − | 0.720577i | ||||
\(326\) | 5.50000 | + | 9.52628i | 0.304617 | + | 0.527612i | ||||
\(327\) | 7.00000 | − | 12.1244i | 0.387101 | − | 0.670478i | ||||
\(328\) | 2.00000 | + | 3.46410i | 0.110432 | + | 0.191273i | ||||
\(329\) | −5.00000 | + | 8.66025i | −0.275659 | + | 0.477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0000 | 0.824475 | 0.412237 | − | 0.911077i | \(-0.364747\pi\) | ||||
0.412237 | + | 0.911077i | \(0.364747\pi\) | |||||||
\(332\) | −4.00000 | + | 6.92820i | −0.219529 | + | 0.380235i | ||||
\(333\) | 2.50000 | − | 4.33013i | 0.136999 | − | 0.237289i | ||||
\(334\) | −6.00000 | −0.328305 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.500000 | − | 0.866025i | 0.0272772 | − | 0.0472456i | ||||
\(337\) | 9.50000 | + | 16.4545i | 0.517498 | + | 0.896333i | 0.999793 | + | 0.0203242i | \(0.00646983\pi\) |
−0.482295 | + | 0.876009i | \(0.660197\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | 5.00000 | + | 8.66025i | 0.271563 | + | 0.470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | −4.00000 | + | 1.73205i | −0.216295 | + | 0.0936586i | ||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −4.50000 | − | 7.79423i | −0.242624 | − | 0.420237i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | + | 20.7846i | −0.645124 | + | 1.11739i | ||||
\(347\) | −8.00000 | − | 13.8564i | −0.429463 | − | 0.743851i | 0.567363 | − | 0.823468i | \(-0.307964\pi\) |
−0.996826 | + | 0.0796169i | \(0.974630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.0000 | −1.55233 | −0.776167 | − | 0.630527i | \(-0.782839\pi\) | ||||
−0.776167 | + | 0.630527i | \(0.782839\pi\) | |||||||
\(350\) | 5.00000 | 0.267261 | ||||||||
\(351\) | −1.50000 | + | 2.59808i | −0.0800641 | + | 0.138675i | ||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | −12.0000 | −0.638696 | −0.319348 | − | 0.947638i | \(-0.603464\pi\) | ||||
−0.319348 | + | 0.947638i | \(0.603464\pi\) | |||||||
\(354\) | −14.0000 | −0.744092 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.00000 | + | 12.1244i | 0.370999 | + | 0.642590i | ||||
\(357\) | 2.00000 | − | 3.46410i | 0.105851 | − | 0.183340i | ||||
\(358\) | 2.00000 | + | 3.46410i | 0.105703 | + | 0.183083i | ||||
\(359\) | 18.0000 | + | 31.1769i | 0.950004 | + | 1.64545i | 0.745409 | + | 0.666608i | \(0.232254\pi\) |
0.204595 | + | 0.978847i | \(0.434412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 18.0000 | 0.946059 | ||||||||
\(363\) | −3.50000 | − | 6.06218i | −0.183702 | − | 0.318182i | ||||
\(364\) | 1.50000 | + | 2.59808i | 0.0786214 | + | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.50000 | − | 9.52628i | −0.287490 | − | 0.497947i | ||||
\(367\) | −11.5000 | + | 19.9186i | −0.600295 | + | 1.03974i | 0.392481 | + | 0.919760i | \(0.371617\pi\) |
−0.992776 | + | 0.119982i | \(0.961716\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | − | 3.46410i | 0.103835 | − | 0.179847i | ||||
\(372\) | 3.00000 | 0.155543 | ||||||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.00000 | − | 8.66025i | 0.257855 | − | 0.446619i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.500000 | − | 0.866025i | −0.0257172 | − | 0.0445435i | ||||
\(379\) | −13.0000 | −0.667765 | −0.333883 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333883 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | −4.00000 | − | 6.92820i | −0.204658 | − | 0.354478i | ||||
\(383\) | −7.00000 | − | 12.1244i | −0.357683 | − | 0.619526i | 0.629890 | − | 0.776684i | \(-0.283100\pi\) |
−0.987573 | + | 0.157159i | \(0.949767\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.50000 | + | 11.2583i | −0.330841 | + | 0.573034i | ||||
\(387\) | −9.00000 | −0.457496 | ||||||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | 8.00000 | − | 13.8564i | 0.405616 | − | 0.702548i | −0.588777 | − | 0.808296i | \(-0.700390\pi\) |
0.994393 | + | 0.105748i | \(0.0337237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | −3.00000 | + | 5.19615i | −0.151330 | + | 0.262111i | ||||
\(394\) | −1.00000 | − | 1.73205i | −0.0503793 | − | 0.0872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | −7.50000 | − | 12.9904i | −0.376414 | − | 0.651969i | 0.614123 | − | 0.789210i | \(-0.289510\pi\) |
−0.990538 | + | 0.137241i | \(0.956176\pi\) | |||||||
\(398\) | −5.00000 | −0.250627 | ||||||||
\(399\) | 3.50000 | + | 2.59808i | 0.175219 | + | 0.130066i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | −1.50000 | − | 2.59808i | −0.0748132 | − | 0.129580i | ||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | 5.00000 | + | 8.66025i | 0.248759 | + | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | 15.0000 | − | 25.9808i | 0.741702 | − | 1.28467i | −0.210017 | − | 0.977698i | \(-0.567352\pi\) |
0.951720 | − | 0.306968i | \(-0.0993146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 1.50000 | − | 2.59808i | 0.0738997 | − | 0.127998i | ||||
\(413\) | 7.00000 | + | 12.1244i | 0.344447 | + | 0.596601i | ||||
\(414\) | 2.00000 | − | 3.46410i | 0.0982946 | − | 0.170251i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.50000 | − | 2.59808i | −0.0735436 | − | 0.127381i | ||||
\(417\) | 19.0000 | 0.930434 | ||||||||
\(418\) | −7.00000 | − | 5.19615i | −0.342381 | − | 0.254152i | ||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 8.66025i | −0.243685 | − | 0.422075i | 0.718076 | − | 0.695965i | \(-0.245023\pi\) |
−0.961761 | + | 0.273890i | \(0.911690\pi\) | |||||||
\(422\) | 12.5000 | − | 21.6506i | 0.608490 | − | 1.05394i | ||||
\(423\) | −5.00000 | − | 8.66025i | −0.243108 | − | 0.421076i | ||||
\(424\) | −2.00000 | + | 3.46410i | −0.0971286 | + | 0.168232i | ||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 14.0000 | 0.678302 | ||||||||
\(427\) | −5.50000 | + | 9.52628i | −0.266164 | + | 0.461009i | ||||
\(428\) | 5.00000 | − | 8.66025i | 0.241684 | − | 0.418609i | ||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.00000 | − | 8.66025i | 0.240842 | − | 0.417150i | −0.720113 | − | 0.693857i | \(-0.755910\pi\) |
0.960954 | + | 0.276707i | \(0.0892433\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 4.50000 | − | 7.79423i | 0.216256 | − | 0.374567i | −0.737404 | − | 0.675452i | \(-0.763949\pi\) |
0.953660 | + | 0.300885i | \(0.0972820\pi\) | |||||||
\(434\) | −1.50000 | − | 2.59808i | −0.0720023 | − | 0.124712i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −2.00000 | + | 17.3205i | −0.0956730 | + | 0.828552i | ||||
\(438\) | −11.0000 | −0.525600 | ||||||||
\(439\) | −9.50000 | − | 16.4545i | −0.453410 | − | 0.785330i | 0.545185 | − | 0.838316i | \(-0.316459\pi\) |
−0.998595 | + | 0.0529862i | \(0.983126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | − | 5.19615i | 0.142857 | − | 0.247436i | ||||
\(442\) | −6.00000 | − | 10.3923i | −0.285391 | − | 0.494312i | ||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | 5.00000 | 0.237289 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.50000 | − | 7.79423i | 0.213081 | − | 0.369067i | ||||
\(447\) | −11.0000 | + | 19.0526i | −0.520282 | + | 0.901155i | ||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −36.0000 | −1.69895 | −0.849473 | − | 0.527633i | \(-0.823080\pi\) | ||||
−0.849473 | + | 0.527633i | \(0.823080\pi\) | |||||||
\(450\) | −2.50000 | + | 4.33013i | −0.117851 | + | 0.204124i | ||||
\(451\) | 4.00000 | + | 6.92820i | 0.188353 | + | 0.326236i | ||||
\(452\) | −5.00000 | + | 8.66025i | −0.235180 | + | 0.407344i | ||||
\(453\) | −10.0000 | − | 17.3205i | −0.469841 | − | 0.813788i | ||||
\(454\) | 4.00000 | + | 6.92820i | 0.187729 | + | 0.325157i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.50000 | − | 2.59808i | −0.163903 | − | 0.121666i | ||||
\(457\) | 5.00000 | 0.233890 | 0.116945 | − | 0.993138i | \(-0.462690\pi\) | ||||
0.116945 | + | 0.993138i | \(0.462690\pi\) | |||||||
\(458\) | −5.50000 | − | 9.52628i | −0.256998 | − | 0.445134i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.00000 | − | 5.19615i | −0.139724 | − | 0.242009i | 0.787668 | − | 0.616100i | \(-0.211288\pi\) |
−0.927392 | + | 0.374091i | \(0.877955\pi\) | |||||||
\(462\) | 1.00000 | − | 1.73205i | 0.0465242 | − | 0.0805823i | ||||
\(463\) | −9.00000 | −0.418265 | −0.209133 | − | 0.977887i | \(-0.567064\pi\) | ||||
−0.209133 | + | 0.977887i | \(0.567064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.00000 | − | 15.5885i | 0.416917 | − | 0.722121i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −1.50000 | + | 2.59808i | −0.0692636 | + | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5000 | + | 18.1865i | −0.483814 | + | 0.837991i | ||||
\(472\) | −7.00000 | − | 12.1244i | −0.322201 | − | 0.558069i | ||||
\(473\) | −9.00000 | − | 15.5885i | −0.413820 | − | 0.716758i | ||||
\(474\) | 1.00000 | 0.0459315 | ||||||||
\(475\) | 2.50000 | − | 21.6506i | 0.114708 | − | 0.993399i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 2.00000 | + | 3.46410i | 0.0915737 | + | 0.158610i | ||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | −3.00000 | + | 5.19615i | −0.137073 | + | 0.237418i | −0.926388 | − | 0.376571i | \(-0.877103\pi\) |
0.789314 | + | 0.613990i | \(0.210436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | + | 12.9904i | −0.341971 | + | 0.592310i | ||||
\(482\) | −25.0000 | −1.13872 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | 5.50000 | − | 9.52628i | 0.248973 | − | 0.431234i | ||||
\(489\) | 5.50000 | + | 9.52628i | 0.248719 | + | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | − | 25.9808i | −0.676941 | − | 1.17250i | −0.975898 | − | 0.218229i | \(-0.929972\pi\) |
0.298957 | − | 0.954267i | \(-0.403361\pi\) | |||||||
\(492\) | 2.00000 | + | 3.46410i | 0.0901670 | + | 0.156174i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 12.0000 | − | 5.19615i | 0.539906 | − | 0.233786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | + | 2.59808i | 0.0673520 | + | 0.116657i | ||||
\(497\) | −7.00000 | − | 12.1244i | −0.313993 | − | 0.543852i | ||||
\(498\) | −4.00000 | + | 6.92820i | −0.179244 | + | 0.310460i | ||||
\(499\) | −2.50000 | − | 4.33013i | −0.111915 | − | 0.193843i | 0.804627 | − | 0.593780i | \(-0.202365\pi\) |
−0.916542 | + | 0.399937i | \(0.869032\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 18.0000 | 0.803379 | ||||||||
\(503\) | −8.00000 | + | 13.8564i | −0.356702 | + | 0.617827i | −0.987408 | − | 0.158196i | \(-0.949432\pi\) |
0.630705 | + | 0.776022i | \(0.282766\pi\) | |||||||
\(504\) | 0.500000 | − | 0.866025i | 0.0222718 | − | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.00000 | 0.355643 | ||||||||
\(507\) | −2.00000 | + | 3.46410i | −0.0888231 | + | 0.153846i | ||||
\(508\) | 4.00000 | + | 6.92820i | 0.177471 | + | 0.307389i | ||||
\(509\) | −13.0000 | + | 22.5167i | −0.576215 | + | 0.998033i | 0.419694 | + | 0.907666i | \(0.362138\pi\) |
−0.995908 | + | 0.0903676i | \(0.971196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.50000 | + | 9.52628i | 0.243306 | + | 0.421418i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.00000 | + | 1.73205i | −0.176604 | + | 0.0764719i | ||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.50000 | − | 7.79423i | −0.198101 | − | 0.343122i | ||||
\(517\) | 10.0000 | − | 17.3205i | 0.439799 | − | 0.761755i | ||||
\(518\) | −2.50000 | − | 4.33013i | −0.109844 | − | 0.190255i | ||||
\(519\) | −12.0000 | + | 20.7846i | −0.526742 | + | 0.912343i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.0000 | 1.48957 | 0.744784 | − | 0.667306i | \(-0.232553\pi\) | ||||
0.744784 | + | 0.667306i | \(0.232553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.5000 | + | 32.0429i | −0.808949 | + | 1.40114i | 0.104644 | + | 0.994510i | \(0.466630\pi\) |
−0.913593 | + | 0.406630i | \(0.866704\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 9.00000 | − | 15.5885i | 0.392419 | − | 0.679689i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.0000 | −0.607548 | ||||||||
\(532\) | −0.500000 | + | 4.33013i | −0.0216777 | + | 0.187735i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 7.00000 | + | 12.1244i | 0.302920 | + | 0.524672i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.50000 | − | 2.59808i | 0.0647901 | − | 0.112220i | ||||
\(537\) | 2.00000 | + | 3.46410i | 0.0863064 | + | 0.149487i | ||||
\(538\) | 1.00000 | − | 1.73205i | 0.0431131 | − | 0.0746740i | ||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.5000 | − | 26.8468i | 0.666397 | − | 1.15423i | −0.312507 | − | 0.949915i | \(-0.601169\pi\) |
0.978905 | − | 0.204318i | \(-0.0654977\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | 18.0000 | 0.772454 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | + | 2.59808i | 0.0641941 | + | 0.111187i | ||||
\(547\) | −5.50000 | + | 9.52628i | −0.235163 | + | 0.407314i | −0.959320 | − | 0.282321i | \(-0.908896\pi\) |
0.724157 | + | 0.689635i | \(0.242229\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | −5.50000 | − | 9.52628i | −0.234734 | − | 0.406572i | ||||
\(550\) | −10.0000 | −0.426401 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.00000 | 0.170251 | ||||||||
\(553\) | −0.500000 | − | 0.866025i | −0.0212622 | − | 0.0368271i | ||||
\(554\) | −1.00000 | − | 1.73205i | −0.0424859 | − | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | −17.0000 | + | 29.4449i | −0.720313 | + | 1.24762i | 0.240561 | + | 0.970634i | \(0.422669\pi\) |
−0.960874 | + | 0.276985i | \(0.910665\pi\) | |||||||
\(558\) | 3.00000 | 0.127000 | ||||||||
\(559\) | 27.0000 | 1.14198 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | + | 6.92820i | −0.168880 | + | 0.292509i | ||||
\(562\) | 8.00000 | 0.337460 | ||||||||
\(563\) | −6.00000 | −0.252870 | −0.126435 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126435 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(564\) | 5.00000 | − | 8.66025i | 0.210538 | − | 0.364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.0000 | + | 17.3205i | −0.420331 | + | 0.728035i | ||||
\(567\) | −0.500000 | − | 0.866025i | −0.0209980 | − | 0.0363696i | ||||
\(568\) | 7.00000 | + | 12.1244i | 0.293713 | + | 0.508727i | ||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | −4.00000 | − | 6.92820i | −0.167102 | − | 0.289430i | ||||
\(574\) | 2.00000 | − | 3.46410i | 0.0834784 | − | 0.144589i | ||||
\(575\) | 10.0000 | + | 17.3205i | 0.417029 | + | 0.722315i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −6.50000 | + | 11.2583i | −0.270131 | + | 0.467880i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | −4.00000 | + | 6.92820i | −0.165663 | + | 0.286937i | ||||
\(584\) | −5.50000 | − | 9.52628i | −0.227592 | − | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.00000 | + | 12.1244i | 0.289167 | + | 0.500853i | ||||
\(587\) | 1.00000 | + | 1.73205i | 0.0412744 | + | 0.0714894i | 0.885925 | − | 0.463829i | \(-0.153525\pi\) |
−0.844650 | + | 0.535319i | \(0.820192\pi\) | |||||||
\(588\) | 6.00000 | 0.247436 | ||||||||
\(589\) | −12.0000 | + | 5.19615i | −0.494451 | + | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.00000 | − | 1.73205i | −0.0411345 | − | 0.0712470i | ||||
\(592\) | 2.50000 | + | 4.33013i | 0.102749 | + | 0.177967i | ||||
\(593\) | −17.0000 | + | 29.4449i | −0.698106 | + | 1.20916i | 0.271016 | + | 0.962575i | \(0.412640\pi\) |
−0.969122 | + | 0.246581i | \(0.920693\pi\) | |||||||
\(594\) | 1.00000 | + | 1.73205i | 0.0410305 | + | 0.0710669i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.0000 | −0.901155 | ||||||||
\(597\) | −5.00000 | −0.204636 | ||||||||
\(598\) | −6.00000 | + | 10.3923i | −0.245358 | + | 0.424973i | ||||
\(599\) | 23.0000 | − | 39.8372i | 0.939755 | − | 1.62770i | 0.173826 | − | 0.984776i | \(-0.444387\pi\) |
0.765928 | − | 0.642926i | \(-0.222280\pi\) | |||||||
\(600\) | −5.00000 | −0.204124 | ||||||||
\(601\) | 27.0000 | 1.10135 | 0.550676 | − | 0.834719i | \(-0.314370\pi\) | ||||
0.550676 | + | 0.834719i | \(0.314370\pi\) | |||||||
\(602\) | −4.50000 | + | 7.79423i | −0.183406 | + | 0.317669i | ||||
\(603\) | −1.50000 | − | 2.59808i | −0.0610847 | − | 0.105802i | ||||
\(604\) | 10.0000 | − | 17.3205i | 0.406894 | − | 0.704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.00000 | + | 8.66025i | 0.203111 | + | 0.351799i | ||||
\(607\) | 5.00000 | 0.202944 | 0.101472 | − | 0.994838i | \(-0.467645\pi\) | ||||
0.101472 | + | 0.994838i | \(0.467645\pi\) | |||||||
\(608\) | 0.500000 | − | 4.33013i | 0.0202777 | − | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | + | 25.9808i | 0.606835 | + | 1.05107i | ||||
\(612\) | −2.00000 | + | 3.46410i | −0.0808452 | + | 0.140028i | ||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | −6.00000 | + | 10.3923i | −0.242140 | + | 0.419399i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | 21.0000 | − | 36.3731i | 0.845428 | − | 1.46432i | −0.0398207 | − | 0.999207i | \(-0.512679\pi\) |
0.885249 | − | 0.465118i | \(-0.153988\pi\) | |||||||
\(618\) | 1.50000 | − | 2.59808i | 0.0603388 | − | 0.104510i | ||||
\(619\) | 1.00000 | 0.0401934 | 0.0200967 | − | 0.999798i | \(-0.493603\pi\) | ||||
0.0200967 | + | 0.999798i | \(0.493603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | − | 3.46410i | 0.0802572 | − | 0.139010i | ||||
\(622\) | 5.00000 | + | 8.66025i | 0.200482 | + | 0.347245i | ||||
\(623\) | 7.00000 | − | 12.1244i | 0.280449 | − | 0.485752i | ||||
\(624\) | −1.50000 | − | 2.59808i | −0.0600481 | − | 0.104006i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | −7.00000 | − | 5.19615i | −0.279553 | − | 0.207514i | ||||
\(628\) | −21.0000 | −0.837991 | ||||||||
\(629\) | 10.0000 | + | 17.3205i | 0.398726 | + | 0.690614i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.50000 | + | 14.7224i | −0.338380 | + | 0.586091i | −0.984128 | − | 0.177459i | \(-0.943212\pi\) |
0.645748 | + | 0.763550i | \(0.276545\pi\) | |||||||
\(632\) | 0.500000 | + | 0.866025i | 0.0198889 | + | 0.0344486i | ||||
\(633\) | 12.5000 | − | 21.6506i | 0.496830 | − | 0.860535i | ||||
\(634\) | −12.0000 | −0.476581 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.00000 | + | 3.46410i | −0.0793052 | + | 0.137361i | ||||
\(637\) | −9.00000 | + | 15.5885i | −0.356593 | + | 0.617637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0000 | 0.553831 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 5.00000 | − | 8.66025i | 0.197334 | − | 0.341793i | ||||
\(643\) | −18.5000 | − | 32.0429i | −0.729569 | − | 1.26365i | −0.957066 | − | 0.289871i | \(-0.906387\pi\) |
0.227497 | − | 0.973779i | \(-0.426946\pi\) | |||||||
\(644\) | −2.00000 | − | 3.46410i | −0.0788110 | − | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 17.3205i | 0.0786889 | − | 0.681466i | ||||
\(647\) | 48.0000 | 1.88707 | 0.943537 | − | 0.331266i | \(-0.107476\pi\) | ||||
0.943537 | + | 0.331266i | \(0.107476\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −14.0000 | − | 24.2487i | −0.549548 | − | 0.951845i | ||||
\(650\) | 7.50000 | − | 12.9904i | 0.294174 | − | 0.509525i | ||||
\(651\) | −1.50000 | − | 2.59808i | −0.0587896 | − | 0.101827i | ||||
\(652\) | −5.50000 | + | 9.52628i | −0.215397 | + | 0.373078i | ||||
\(653\) | −42.0000 | −1.64359 | −0.821794 | − | 0.569785i | \(-0.807026\pi\) | ||||
−0.821794 | + | 0.569785i | \(0.807026\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | + | 3.46410i | −0.0780869 | + | 0.135250i | ||||
\(657\) | −11.0000 | −0.429151 | ||||||||
\(658\) | −10.0000 | −0.389841 | ||||||||
\(659\) | 7.00000 | − | 12.1244i | 0.272681 | − | 0.472298i | −0.696866 | − | 0.717201i | \(-0.745423\pi\) |
0.969548 | + | 0.244903i | \(0.0787562\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | + | 8.66025i | −0.194477 | + | 0.336845i | −0.946729 | − | 0.322031i | \(-0.895634\pi\) |
0.752252 | + | 0.658876i | \(0.228968\pi\) | |||||||
\(662\) | 7.50000 | + | 12.9904i | 0.291496 | + | 0.504885i | ||||
\(663\) | −6.00000 | − | 10.3923i | −0.233021 | − | 0.403604i | ||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.00000 | 0.193746 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −3.00000 | − | 5.19615i | −0.116073 | − | 0.201045i | ||||
\(669\) | 4.50000 | − | 7.79423i | 0.173980 | − | 0.301342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0000 | − | 19.0526i | 0.424650 | − | 0.735516i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | −9.50000 | + | 16.4545i | −0.365926 | + | 0.633803i | ||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | −5.00000 | + | 8.66025i | −0.192024 | + | 0.332595i | ||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | + | 6.92820i | 0.153280 | + | 0.265489i | ||||
\(682\) | 3.00000 | + | 5.19615i | 0.114876 | + | 0.198971i | ||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | −3.50000 | − | 2.59808i | −0.133826 | − | 0.0993399i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | − | 11.2583i | −0.248171 | − | 0.429845i | ||||
\(687\) | −5.50000 | − | 9.52628i | −0.209838 | − | 0.363450i | ||||
\(688\) | 4.50000 | − | 7.79423i | 0.171561 | − | 0.297152i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | 0.152167 | 0.0760836 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760836 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(692\) | −24.0000 | −0.912343 | ||||||||
\(693\) | 1.00000 | − | 1.73205i | 0.0379869 | − | 0.0657952i | ||||
\(694\) | 8.00000 | − | 13.8564i | 0.303676 | − | 0.525982i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | + | 13.8564i | −0.303022 | + | 0.524849i | ||||
\(698\) | −14.5000 | − | 25.1147i | −0.548833 | − | 0.950607i | ||||
\(699\) | 9.00000 | − | 15.5885i | 0.340411 | − | 0.589610i | ||||
\(700\) | 2.50000 | + | 4.33013i | 0.0944911 | + | 0.163663i | ||||
\(701\) | 22.0000 | + | 38.1051i | 0.830929 | + | 1.43921i | 0.897303 | + | 0.441416i | \(0.145524\pi\) |
−0.0663742 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(702\) | −3.00000 | −0.113228 | ||||||||
\(703\) | −20.0000 | + | 8.66025i | −0.754314 | + | 0.326628i | ||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | − | 10.3923i | −0.225813 | − | 0.391120i | ||||
\(707\) | 5.00000 | − | 8.66025i | 0.188044 | − | 0.325702i | ||||
\(708\) | −7.00000 | − | 12.1244i | −0.263076 | − | 0.455661i | ||||
\(709\) | 15.5000 | − | 26.8468i | 0.582115 | − | 1.00825i | −0.413114 | − | 0.910679i | \(-0.635559\pi\) |
0.995228 | − | 0.0975728i | \(-0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −7.00000 | + | 12.1244i | −0.262336 | + | 0.454379i | ||||
\(713\) | 6.00000 | − | 10.3923i | 0.224702 | − | 0.389195i | ||||
\(714\) | 4.00000 | 0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.00000 | + | 3.46410i | −0.0747435 | + | 0.129460i | ||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | −18.0000 | + | 31.1769i | −0.671754 | + | 1.16351i | ||||
\(719\) | −20.0000 | − | 34.6410i | −0.745874 | − | 1.29189i | −0.949785 | − | 0.312903i | \(-0.898699\pi\) |
0.203911 | − | 0.978989i | \(-0.434635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | 18.5000 | + | 4.33013i | 0.688499 | + | 0.161151i | ||||
\(723\) | −25.0000 | −0.929760 | ||||||||
\(724\) | 9.00000 | + | 15.5885i | 0.334482 | + | 0.579340i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.50000 | − | 6.06218i | 0.129897 | − | 0.224989i | ||||
\(727\) | −8.50000 | − | 14.7224i | −0.315248 | − | 0.546025i | 0.664243 | − | 0.747517i | \(-0.268754\pi\) |
−0.979490 | + | 0.201492i | \(0.935421\pi\) | |||||||
\(728\) | −1.50000 | + | 2.59808i | −0.0555937 | + | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0000 | − | 31.1769i | 0.665754 | − | 1.15312i | ||||
\(732\) | 5.50000 | − | 9.52628i | 0.203286 | − | 0.352101i | ||||
\(733\) | −2.00000 | −0.0738717 | −0.0369358 | − | 0.999318i | \(-0.511760\pi\) | ||||
−0.0369358 | + | 0.999318i | \(0.511760\pi\) | |||||||
\(734\) | −23.0000 | −0.848945 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | + | 3.46410i | 0.0737210 | + | 0.127688i | ||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 2.00000 | + | 3.46410i | 0.0736210 | + | 0.127515i | ||||
\(739\) | 2.50000 | + | 4.33013i | 0.0919640 | + | 0.159286i | 0.908337 | − | 0.418238i | \(-0.137352\pi\) |
−0.816373 | + | 0.577524i | \(0.804019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | − | 5.19615i | 0.440831 | − | 0.190885i | ||||
\(742\) | 4.00000 | 0.146845 | ||||||||
\(743\) | 9.00000 | + | 15.5885i | 0.330178 | + | 0.571885i | 0.982547 | − | 0.186017i | \(-0.0595579\pi\) |
−0.652369 | + | 0.757902i | \(0.726225\pi\) | |||||||
\(744\) | 1.50000 | + | 2.59808i | 0.0549927 | + | 0.0952501i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.0000 | + | 22.5167i | 0.475964 | + | 0.824394i | ||||
\(747\) | −4.00000 | + | 6.92820i | −0.146352 | + | 0.253490i | ||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | −10.0000 | −0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | + | 11.2583i | −0.237188 | + | 0.410822i | −0.959906 | − | 0.280321i | \(-0.909559\pi\) |
0.722718 | + | 0.691143i | \(0.242893\pi\) | |||||||
\(752\) | 10.0000 | 0.364662 | ||||||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | − | 0.866025i | 0.0181848 | − | 0.0314970i | ||||
\(757\) | −2.50000 | − | 4.33013i | −0.0908640 | − | 0.157381i | 0.817011 | − | 0.576622i | \(-0.195630\pi\) |
−0.907875 | + | 0.419241i | \(0.862296\pi\) | |||||||
\(758\) | −6.50000 | − | 11.2583i | −0.236091 | − | 0.408921i | ||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.0000 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(762\) | 4.00000 | + | 6.92820i | 0.144905 | + | 0.250982i | ||||
\(763\) | −7.00000 | − | 12.1244i | −0.253417 | − | 0.438931i | ||||
\(764\) | 4.00000 | − | 6.92820i | 0.144715 | − | 0.250654i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | − | 12.1244i | 0.252920 | − | 0.438071i | ||||
\(767\) | 42.0000 | 1.51653 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −13.5000 | + | 23.3827i | −0.486822 | + | 0.843201i | −0.999885 | − | 0.0151499i | \(-0.995177\pi\) |
0.513063 | + | 0.858351i | \(0.328511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | −13.0000 | −0.467880 | ||||||||
\(773\) | 9.00000 | − | 15.5885i | 0.323708 | − | 0.560678i | −0.657542 | − | 0.753418i | \(-0.728404\pi\) |
0.981250 | + | 0.192740i | \(0.0617373\pi\) | |||||||
\(774\) | −4.50000 | − | 7.79423i | −0.161749 | − | 0.280158i | ||||
\(775\) | −7.50000 | + | 12.9904i | −0.269408 | + | 0.466628i | ||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | −2.50000 | − | 4.33013i | −0.0896870 | − | 0.155342i | ||||
\(778\) | 16.0000 | 0.573628 | ||||||||
\(779\) | −14.0000 | − | 10.3923i | −0.501602 | − | 0.372343i | ||||
\(780\) | 0 | 0 |