Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.271 |
Dual form | 324.3.f.b.55.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −1.00000 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 1.00000 | ||||||||
\(5\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | −0.268466 | − | 0.963289i | \(-0.586517\pi\) |
0.968466 | − | 0.249146i | \(-0.0801500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.50000 | + | 4.33013i | −1.07143 | + | 0.618590i | −0.928571 | − | 0.371154i | \(-0.878962\pi\) |
−0.142857 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.00000 | + | 12.1244i | −0.700000 | + | 1.21244i | ||||
\(11\) | −7.50000 | + | 4.33013i | −0.681818 | + | 0.393648i | −0.800540 | − | 0.599280i | \(-0.795454\pi\) |
0.118722 | + | 0.992928i | \(0.462120\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | + | 17.3205i | −0.769231 | + | 1.33235i | 0.168750 | + | 0.985659i | \(0.446027\pi\) |
−0.937981 | + | 0.346688i | \(0.887306\pi\) | |||||||
\(14\) | 15.0000 | − | 8.66025i | 1.07143 | − | 0.618590i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 1.00000 | ||||||||
\(17\) | 8.00000 | 0.470588 | 0.235294 | − | 0.971924i | \(-0.424395\pi\) | ||||
0.235294 | + | 0.971924i | \(0.424395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.3923i | 0.546963i | 0.961877 | + | 0.273482i | \(0.0881753\pi\) | ||||
−0.961877 | + | 0.273482i | \(0.911825\pi\) | |||||||
\(20\) | 14.0000 | − | 24.2487i | 0.700000 | − | 1.21244i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.0000 | − | 8.66025i | 0.681818 | − | 0.393648i | ||||
\(23\) | −3.00000 | − | 1.73205i | −0.130435 | − | 0.0753066i | 0.433363 | − | 0.901220i | \(-0.357327\pi\) |
−0.563798 | + | 0.825913i | \(0.690660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.0000 | − | 20.7846i | −0.480000 | − | 0.831384i | ||||
\(26\) | 20.0000 | − | 34.6410i | 0.769231 | − | 1.33235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −30.0000 | + | 17.3205i | −1.07143 | + | 0.618590i | ||||
\(29\) | 5.00000 | + | 8.66025i | 0.172414 | + | 0.298629i | 0.939263 | − | 0.343198i | \(-0.111510\pi\) |
−0.766849 | + | 0.641827i | \(0.778177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.5000 | + | 26.8468i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −32.0000 | −1.00000 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.0000 | −0.470588 | ||||||||
\(35\) | 60.6218i | 1.73205i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −0.270270 | −0.135135 | − | 0.990827i | \(-0.543147\pi\) | ||||
−0.135135 | + | 0.990827i | \(0.543147\pi\) | |||||||
\(38\) | − | 20.7846i | − | 0.546963i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −28.0000 | + | 48.4974i | −0.700000 | + | 1.21244i | ||||
\(41\) | −25.0000 | + | 43.3013i | −0.609756 | + | 1.05613i | 0.381524 | + | 0.924359i | \(0.375399\pi\) |
−0.991280 | + | 0.131770i | \(0.957934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15.0000 | − | 8.66025i | 0.348837 | − | 0.201401i | −0.315336 | − | 0.948980i | \(-0.602117\pi\) |
0.664173 | + | 0.747579i | \(0.268784\pi\) | |||||||
\(44\) | −30.0000 | + | 17.3205i | −0.681818 | + | 0.393648i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 3.46410i | 0.130435 | + | 0.0753066i | ||||
\(47\) | −75.0000 | + | 43.3013i | −1.59574 | + | 0.921304i | −0.603450 | + | 0.797401i | \(0.706208\pi\) |
−0.992294 | + | 0.123903i | \(0.960459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0000 | − | 22.5167i | 0.265306 | − | 0.459524i | ||||
\(50\) | 24.0000 | + | 41.5692i | 0.480000 | + | 0.831384i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −40.0000 | + | 69.2820i | −0.769231 | + | 1.33235i | ||||
\(53\) | 47.0000 | 0.886792 | 0.443396 | − | 0.896326i | \(-0.353773\pi\) | ||||
0.443396 | + | 0.896326i | \(0.353773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 60.6218i | 1.10221i | ||||||||
\(56\) | 60.0000 | − | 34.6410i | 1.07143 | − | 0.618590i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0000 | − | 17.3205i | −0.172414 | − | 0.298629i | ||||
\(59\) | −30.0000 | − | 17.3205i | −0.508475 | − | 0.293568i | 0.223732 | − | 0.974651i | \(-0.428176\pi\) |
−0.732206 | + | 0.681083i | \(0.761509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.0000 | + | 55.4256i | 0.524590 | + | 0.908617i | 0.999590 | + | 0.0286310i | \(0.00911476\pi\) |
−0.475000 | + | 0.879986i | \(0.657552\pi\) | |||||||
\(62\) | −93.0000 | − | 53.6936i | −1.50000 | − | 0.866025i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 70.0000 | + | 121.244i | 1.07692 | + | 1.86529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −75.0000 | − | 43.3013i | −1.11940 | − | 0.646288i | −0.178155 | − | 0.984003i | \(-0.557013\pi\) |
−0.941248 | + | 0.337715i | \(0.890346\pi\) | |||||||
\(68\) | 32.0000 | 0.470588 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 121.244i | − | 1.73205i | ||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.0000 | −0.753425 | −0.376712 | − | 0.926330i | \(-0.622945\pi\) | ||||
−0.376712 | + | 0.926330i | \(0.622945\pi\) | |||||||
\(74\) | 20.0000 | 0.270270 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 41.5692i | 0.546963i | ||||||||
\(77\) | 37.5000 | − | 64.9519i | 0.487013 | − | 0.843531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | − | 3.46410i | 0.0759494 | − | 0.0438494i | −0.461544 | − | 0.887117i | \(-0.652704\pi\) |
0.537494 | + | 0.843268i | \(0.319371\pi\) | |||||||
\(80\) | 56.0000 | − | 96.9948i | 0.700000 | − | 1.21244i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 50.0000 | − | 86.6025i | 0.609756 | − | 1.05613i | ||||
\(83\) | −25.5000 | + | 14.7224i | −0.307229 | + | 0.177379i | −0.645686 | − | 0.763603i | \(-0.723428\pi\) |
0.338457 | + | 0.940982i | \(0.390095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.0000 | − | 48.4974i | 0.329412 | − | 0.570558i | ||||
\(86\) | −30.0000 | + | 17.3205i | −0.348837 | + | 0.201401i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 60.0000 | − | 34.6410i | 0.681818 | − | 0.393648i | ||||
\(89\) | −10.0000 | −0.112360 | −0.0561798 | − | 0.998421i | \(-0.517892\pi\) | ||||
−0.0561798 | + | 0.998421i | \(0.517892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 173.205i | − | 1.90335i | ||||||
\(92\) | −12.0000 | − | 6.92820i | −0.130435 | − | 0.0753066i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 150.000 | − | 86.6025i | 1.59574 | − | 0.921304i | ||||
\(95\) | 63.0000 | + | 36.3731i | 0.663158 | + | 0.382874i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5000 | + | 21.6506i | 0.128866 | + | 0.223202i | 0.923237 | − | 0.384230i | \(-0.125533\pi\) |
−0.794372 | + | 0.607432i | \(0.792200\pi\) | |||||||
\(98\) | −26.0000 | + | 45.0333i | −0.265306 | + | 0.459524i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −48.0000 | − | 83.1384i | −0.480000 | − | 0.831384i | ||||
\(101\) | −77.5000 | − | 134.234i | −0.767327 | − | 1.32905i | −0.939008 | − | 0.343896i | \(-0.888253\pi\) |
0.171681 | − | 0.985153i | \(-0.445080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −120.000 | − | 69.2820i | −1.16505 | − | 0.672641i | −0.212540 | − | 0.977152i | \(-0.568174\pi\) |
−0.952509 | + | 0.304511i | \(0.901507\pi\) | |||||||
\(104\) | 80.0000 | − | 138.564i | 0.769231 | − | 1.33235i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −94.0000 | −0.886792 | ||||||||
\(107\) | 129.904i | 1.21405i | 0.794681 | + | 0.607027i | \(0.207638\pi\) | ||||
−0.794681 | + | 0.607027i | \(0.792362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 134.000 | 1.22936 | 0.614679 | − | 0.788777i | \(-0.289286\pi\) | ||||
0.614679 | + | 0.788777i | \(0.289286\pi\) | |||||||
\(110\) | − | 121.244i | − | 1.10221i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −120.000 | + | 69.2820i | −1.07143 | + | 0.618590i | ||||
\(113\) | −37.0000 | + | 64.0859i | −0.327434 | + | 0.567132i | −0.982002 | − | 0.188871i | \(-0.939517\pi\) |
0.654568 | + | 0.756003i | \(0.272850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.0000 | + | 12.1244i | −0.182609 | + | 0.105429i | ||||
\(116\) | 20.0000 | + | 34.6410i | 0.172414 | + | 0.298629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60.0000 | + | 34.6410i | 0.508475 | + | 0.293568i | ||||
\(119\) | −60.0000 | + | 34.6410i | −0.504202 | + | 0.291101i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.0000 | + | 39.8372i | −0.190083 | + | 0.329233i | ||||
\(122\) | −64.0000 | − | 110.851i | −0.524590 | − | 0.908617i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 186.000 | + | 107.387i | 1.50000 | + | 0.866025i | ||||
\(125\) | 7.00000 | 0.0560000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 25.9808i | − | 0.204573i | −0.994755 | − | 0.102286i | \(-0.967384\pi\) | ||
0.994755 | − | 0.102286i | \(-0.0326158\pi\) | |||||||
\(128\) | −128.000 | −1.00000 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −140.000 | − | 242.487i | −1.07692 | − | 1.86529i | ||||
\(131\) | −142.500 | − | 82.2724i | −1.08779 | − | 0.628034i | −0.154800 | − | 0.987946i | \(-0.549473\pi\) |
−0.932986 | + | 0.359912i | \(0.882807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.0000 | − | 77.9423i | −0.338346 | − | 0.586032i | ||||
\(134\) | 150.000 | + | 86.6025i | 1.11940 | + | 0.646288i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −64.0000 | −0.470588 | ||||||||
\(137\) | −31.0000 | − | 53.6936i | −0.226277 | − | 0.391924i | 0.730425 | − | 0.682993i | \(-0.239322\pi\) |
−0.956702 | + | 0.291070i | \(0.905989\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 150.000 | + | 86.6025i | 1.07914 | + | 0.623040i | 0.930663 | − | 0.365877i | \(-0.119231\pi\) |
0.148473 | + | 0.988916i | \(0.452564\pi\) | |||||||
\(140\) | 242.487i | 1.73205i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 173.205i | − | 1.21122i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 70.0000 | 0.482759 | ||||||||
\(146\) | 110.000 | 0.753425 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −40.0000 | −0.270270 | ||||||||
\(149\) | 57.5000 | − | 99.5929i | 0.385906 | − | 0.668409i | −0.605988 | − | 0.795473i | \(-0.707222\pi\) |
0.991894 | + | 0.127065i | \(0.0405556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 37.5000 | − | 21.6506i | 0.248344 | − | 0.143382i | −0.370662 | − | 0.928768i | \(-0.620869\pi\) |
0.619006 | + | 0.785386i | \(0.287536\pi\) | |||||||
\(152\) | − | 83.1384i | − | 0.546963i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −75.0000 | + | 129.904i | −0.487013 | + | 0.843531i | ||||
\(155\) | 325.500 | − | 187.928i | 2.10000 | − | 1.21244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 17.3205i | −0.0636943 | + | 0.110322i | −0.896114 | − | 0.443824i | \(-0.853622\pi\) |
0.832420 | + | 0.554146i | \(0.186955\pi\) | |||||||
\(158\) | −12.0000 | + | 6.92820i | −0.0759494 | + | 0.0438494i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −112.000 | + | 193.990i | −0.700000 | + | 1.21244i | ||||
\(161\) | 30.0000 | 0.186335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 103.923i | 0.637565i | 0.947828 | + | 0.318782i | \(0.103274\pi\) | ||||
−0.947828 | + | 0.318782i | \(0.896726\pi\) | |||||||
\(164\) | −100.000 | + | 173.205i | −0.609756 | + | 1.05613i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 51.0000 | − | 29.4449i | 0.307229 | − | 0.177379i | ||||
\(167\) | 213.000 | + | 122.976i | 1.27545 | + | 0.736381i | 0.976008 | − | 0.217734i | \(-0.0698665\pi\) |
0.299441 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −115.500 | − | 200.052i | −0.683432 | − | 1.18374i | ||||
\(170\) | −56.0000 | + | 96.9948i | −0.329412 | + | 0.570558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60.0000 | − | 34.6410i | 0.348837 | − | 0.201401i | ||||
\(173\) | 63.5000 | + | 109.985i | 0.367052 | + | 0.635753i | 0.989103 | − | 0.147224i | \(-0.0470338\pi\) |
−0.622051 | + | 0.782977i | \(0.713700\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 180.000 | + | 103.923i | 1.02857 | + | 0.593846i | ||||
\(176\) | −120.000 | + | 69.2820i | −0.681818 | + | 0.393648i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.0000 | 0.112360 | ||||||||
\(179\) | − | 233.827i | − | 1.30630i | −0.757231 | − | 0.653148i | \(-0.773448\pi\) | ||
0.757231 | − | 0.653148i | \(-0.226552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56.0000 | 0.309392 | 0.154696 | − | 0.987962i | \(-0.450560\pi\) | ||||
0.154696 | + | 0.987962i | \(0.450560\pi\) | |||||||
\(182\) | 346.410i | 1.90335i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.0000 | + | 13.8564i | 0.130435 | + | 0.0753066i | ||||
\(185\) | −35.0000 | + | 60.6218i | −0.189189 | + | 0.327685i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −60.0000 | + | 34.6410i | −0.320856 | + | 0.185246i | ||||
\(188\) | −300.000 | + | 173.205i | −1.59574 | + | 0.921304i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −126.000 | − | 72.7461i | −0.663158 | − | 0.382874i | ||||
\(191\) | −30.0000 | + | 17.3205i | −0.157068 | + | 0.0906833i | −0.576474 | − | 0.817116i | \(-0.695572\pi\) |
0.419406 | + | 0.907799i | \(0.362238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −32.5000 | + | 56.2917i | −0.168394 | + | 0.291667i | −0.937855 | − | 0.347027i | \(-0.887191\pi\) |
0.769462 | + | 0.638693i | \(0.220525\pi\) | |||||||
\(194\) | −25.0000 | − | 43.3013i | −0.128866 | − | 0.223202i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 52.0000 | − | 90.0666i | 0.265306 | − | 0.459524i | ||||
\(197\) | −253.000 | −1.28426 | −0.642132 | − | 0.766594i | \(-0.721950\pi\) | ||||
−0.642132 | + | 0.766594i | \(0.721950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 129.904i | − | 0.652783i | −0.945235 | − | 0.326391i | \(-0.894167\pi\) | ||
0.945235 | − | 0.326391i | \(-0.105833\pi\) | |||||||
\(200\) | 96.0000 | + | 166.277i | 0.480000 | + | 0.831384i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 155.000 | + | 268.468i | 0.767327 | + | 1.32905i | ||||
\(203\) | −75.0000 | − | 43.3013i | −0.369458 | − | 0.213307i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 175.000 | + | 303.109i | 0.853659 | + | 1.47858i | ||||
\(206\) | 240.000 | + | 138.564i | 1.16505 | + | 0.672641i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −160.000 | + | 277.128i | −0.769231 | + | 1.33235i | ||||
\(209\) | −45.0000 | − | 77.9423i | −0.215311 | − | 0.372930i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −129.000 | − | 74.4782i | −0.611374 | − | 0.352977i | 0.162129 | − | 0.986770i | \(-0.448164\pi\) |
−0.773503 | + | 0.633792i | \(0.781497\pi\) | |||||||
\(212\) | 188.000 | 0.886792 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 259.808i | − | 1.21405i | ||||||
\(215\) | − | 121.244i | − | 0.563924i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −465.000 | −2.14286 | ||||||||
\(218\) | −268.000 | −1.22936 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 242.487i | 1.10221i | ||||||||
\(221\) | −80.0000 | + | 138.564i | −0.361991 | + | 0.626987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −30.0000 | + | 17.3205i | −0.134529 | + | 0.0776704i | −0.565754 | − | 0.824574i | \(-0.691415\pi\) |
0.431225 | + | 0.902244i | \(0.358082\pi\) | |||||||
\(224\) | 240.000 | − | 138.564i | 1.07143 | − | 0.618590i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 74.0000 | − | 128.172i | 0.327434 | − | 0.567132i | ||||
\(227\) | 78.0000 | − | 45.0333i | 0.343612 | − | 0.198385i | −0.318256 | − | 0.948005i | \(-0.603097\pi\) |
0.661868 | + | 0.749620i | \(0.269764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.0000 | + | 126.440i | −0.318777 | + | 0.552138i | −0.980233 | − | 0.197846i | \(-0.936606\pi\) |
0.661456 | + | 0.749984i | \(0.269939\pi\) | |||||||
\(230\) | 42.0000 | − | 24.2487i | 0.182609 | − | 0.105429i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −40.0000 | − | 69.2820i | −0.172414 | − | 0.298629i | ||||
\(233\) | −334.000 | −1.43348 | −0.716738 | − | 0.697342i | \(-0.754366\pi\) | ||||
−0.716738 | + | 0.697342i | \(0.754366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 606.218i | 2.57965i | ||||||||
\(236\) | −120.000 | − | 69.2820i | −0.508475 | − | 0.293568i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 120.000 | − | 69.2820i | 0.504202 | − | 0.291101i | ||||
\(239\) | 15.0000 | + | 8.66025i | 0.0627615 | + | 0.0362354i | 0.531052 | − | 0.847339i | \(-0.321797\pi\) |
−0.468291 | + | 0.883574i | \(0.655130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −67.0000 | − | 116.047i | −0.278008 | − | 0.481524i | 0.692881 | − | 0.721052i | \(-0.256341\pi\) |
−0.970890 | + | 0.239527i | \(0.923008\pi\) | |||||||
\(242\) | 46.0000 | − | 79.6743i | 0.190083 | − | 0.329233i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 128.000 | + | 221.703i | 0.524590 | + | 0.908617i | ||||
\(245\) | −91.0000 | − | 157.617i | −0.371429 | − | 0.643333i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −180.000 | − | 103.923i | −0.728745 | − | 0.420741i | ||||
\(248\) | −372.000 | − | 214.774i | −1.50000 | − | 0.866025i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.0000 | −0.0560000 | ||||||||
\(251\) | 207.846i | 0.828072i | 0.910260 | + | 0.414036i | \(0.135881\pi\) | ||||
−0.910260 | + | 0.414036i | \(0.864119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | 0.118577 | ||||||||
\(254\) | 51.9615i | 0.204573i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 1.00000 | ||||||||
\(257\) | 134.000 | − | 232.095i | 0.521401 | − | 0.903093i | −0.478289 | − | 0.878202i | \(-0.658743\pi\) |
0.999690 | − | 0.0248904i | \(-0.00792367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 75.0000 | − | 43.3013i | 0.289575 | − | 0.167186i | ||||
\(260\) | 280.000 | + | 484.974i | 1.07692 | + | 1.86529i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 285.000 | + | 164.545i | 1.08779 | + | 0.628034i | ||||
\(263\) | 375.000 | − | 216.506i | 1.42586 | − | 0.823218i | 0.429065 | − | 0.903274i | \(-0.358843\pi\) |
0.996790 | + | 0.0800555i | \(0.0255098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 164.500 | − | 284.922i | 0.620755 | − | 1.07518i | ||||
\(266\) | 90.0000 | + | 155.885i | 0.338346 | + | 0.586032i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −300.000 | − | 173.205i | −1.11940 | − | 0.646288i | ||||
\(269\) | 350.000 | 1.30112 | 0.650558 | − | 0.759457i | \(-0.274535\pi\) | ||||
0.650558 | + | 0.759457i | \(0.274535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 36.3731i | − | 0.134218i | −0.997746 | − | 0.0671090i | \(-0.978622\pi\) | ||
0.997746 | − | 0.0671090i | \(-0.0213775\pi\) | |||||||
\(272\) | 128.000 | 0.470588 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 62.0000 | + | 107.387i | 0.226277 | + | 0.391924i | ||||
\(275\) | 180.000 | + | 103.923i | 0.654545 | + | 0.377902i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 260.000 | + | 450.333i | 0.938628 | + | 1.62575i | 0.768033 | + | 0.640410i | \(0.221236\pi\) |
0.170595 | + | 0.985341i | \(0.445431\pi\) | |||||||
\(278\) | −300.000 | − | 173.205i | −1.07914 | − | 0.623040i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 484.974i | − | 1.73205i | ||||||
\(281\) | −220.000 | − | 381.051i | −0.782918 | − | 1.35605i | −0.930235 | − | 0.366965i | \(-0.880397\pi\) |
0.147317 | − | 0.989089i | \(-0.452936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 285.000 | + | 164.545i | 1.00707 | + | 0.581430i | 0.910332 | − | 0.413880i | \(-0.135827\pi\) |
0.0967355 | + | 0.995310i | \(0.469160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 346.410i | 1.21122i | ||||||||
\(287\) | − | 433.013i | − | 1.50876i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −225.000 | −0.778547 | ||||||||
\(290\) | −140.000 | −0.482759 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −220.000 | −0.753425 | ||||||||
\(293\) | −109.000 | + | 188.794i | −0.372014 | + | 0.644347i | −0.989875 | − | 0.141940i | \(-0.954666\pi\) |
0.617862 | + | 0.786287i | \(0.287999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −210.000 | + | 121.244i | −0.711864 | + | 0.410995i | ||||
\(296\) | 80.0000 | 0.270270 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −115.000 | + | 199.186i | −0.385906 | + | 0.668409i | ||||
\(299\) | 60.0000 | − | 34.6410i | 0.200669 | − | 0.115856i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −75.0000 | + | 129.904i | −0.249169 | + | 0.431574i | ||||
\(302\) | −75.0000 | + | 43.3013i | −0.248344 | + | 0.143382i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 166.277i | 0.546963i | ||||||||
\(305\) | 448.000 | 1.46885 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 207.846i | − | 0.677023i | −0.940962 | − | 0.338512i | \(-0.890077\pi\) | ||
0.940962 | − | 0.338512i | \(-0.109923\pi\) | |||||||
\(308\) | 150.000 | − | 259.808i | 0.487013 | − | 0.843531i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −651.000 | + | 375.855i | −2.10000 | + | 1.21244i | ||||
\(311\) | −255.000 | − | 147.224i | −0.819936 | − | 0.473390i | 0.0304586 | − | 0.999536i | \(-0.490303\pi\) |
−0.850394 | + | 0.526146i | \(0.823637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −242.500 | − | 420.022i | −0.774760 | − | 1.34192i | −0.934929 | − | 0.354835i | \(-0.884537\pi\) |
0.160169 | − | 0.987090i | \(-0.448796\pi\) | |||||||
\(314\) | 20.0000 | − | 34.6410i | 0.0636943 | − | 0.110322i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.0000 | − | 13.8564i | 0.0759494 | − | 0.0438494i | ||||
\(317\) | 108.500 | + | 187.928i | 0.342271 | + | 0.592831i | 0.984854 | − | 0.173385i | \(-0.0554705\pi\) |
−0.642583 | + | 0.766216i | \(0.722137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −75.0000 | − | 43.3013i | −0.235110 | − | 0.135741i | ||||
\(320\) | 224.000 | − | 387.979i | 0.700000 | − | 1.21244i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −60.0000 | −0.186335 | ||||||||
\(323\) | 83.1384i | 0.257395i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 480.000 | 1.47692 | ||||||||
\(326\) | − | 207.846i | − | 0.637565i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 200.000 | − | 346.410i | 0.609756 | − | 1.05613i | ||||
\(329\) | 375.000 | − | 649.519i | 1.13982 | − | 1.97422i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 375.000 | − | 216.506i | 1.13293 | − | 0.654098i | 0.188260 | − | 0.982119i | \(-0.439715\pi\) |
0.944670 | + | 0.328021i | \(0.106382\pi\) | |||||||
\(332\) | −102.000 | + | 58.8897i | −0.307229 | + | 0.177379i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −426.000 | − | 245.951i | −1.27545 | − | 0.736381i | ||||
\(335\) | −525.000 | + | 303.109i | −1.56716 | + | 0.904803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 155.000 | − | 268.468i | 0.459941 | − | 0.796641i | −0.539017 | − | 0.842295i | \(-0.681204\pi\) |
0.998957 | + | 0.0456545i | \(0.0145373\pi\) | |||||||
\(338\) | 231.000 | + | 400.104i | 0.683432 | + | 1.18374i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 112.000 | − | 193.990i | 0.329412 | − | 0.570558i | ||||
\(341\) | −465.000 | −1.36364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 199.186i | − | 0.580717i | ||||||
\(344\) | −120.000 | + | 69.2820i | −0.348837 | + | 0.201401i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −127.000 | − | 219.970i | −0.367052 | − | 0.635753i | ||||
\(347\) | −187.500 | − | 108.253i | −0.540346 | − | 0.311969i | 0.204873 | − | 0.978789i | \(-0.434322\pi\) |
−0.745219 | + | 0.666820i | \(0.767655\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −37.0000 | − | 64.0859i | −0.106017 | − | 0.183627i | 0.808136 | − | 0.588996i | \(-0.200477\pi\) |
−0.914153 | + | 0.405369i | \(0.867143\pi\) | |||||||
\(350\) | −360.000 | − | 207.846i | −1.02857 | − | 0.593846i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 240.000 | − | 138.564i | 0.681818 | − | 0.393648i | ||||
\(353\) | 197.000 | + | 341.214i | 0.558074 | + | 0.966612i | 0.997657 | + | 0.0684103i | \(0.0217927\pi\) |
−0.439584 | + | 0.898202i | \(0.644874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −40.0000 | −0.112360 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 467.654i | 1.30630i | ||||||||
\(359\) | 571.577i | 1.59214i | 0.605207 | + | 0.796068i | \(0.293090\pi\) | ||||
−0.605207 | + | 0.796068i | \(0.706910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | 0.700831 | ||||||||
\(362\) | −112.000 | −0.309392 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 692.820i | − | 1.90335i | ||||||
\(365\) | −192.500 | + | 333.420i | −0.527397 | + | 0.913479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 487.500 | − | 281.458i | 1.32834 | − | 0.766916i | 0.343295 | − | 0.939228i | \(-0.388457\pi\) |
0.985043 | + | 0.172311i | \(0.0551235\pi\) | |||||||
\(368\) | −48.0000 | − | 27.7128i | −0.130435 | − | 0.0753066i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 70.0000 | − | 121.244i | 0.189189 | − | 0.327685i | ||||
\(371\) | −352.500 | + | 203.516i | −0.950135 | + | 0.548561i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0000 | − | 34.6410i | 0.0536193 | − | 0.0928714i | −0.837970 | − | 0.545716i | \(-0.816258\pi\) |
0.891589 | + | 0.452845i | \(0.149591\pi\) | |||||||
\(374\) | 120.000 | − | 69.2820i | 0.320856 | − | 0.185246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 600.000 | − | 346.410i | 1.59574 | − | 0.921304i | ||||
\(377\) | −200.000 | −0.530504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 685.892i | − | 1.80974i | −0.425686 | − | 0.904871i | \(-0.639967\pi\) | ||
0.425686 | − | 0.904871i | \(-0.360033\pi\) | |||||||
\(380\) | 252.000 | + | 145.492i | 0.663158 | + | 0.382874i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 60.0000 | − | 34.6410i | 0.157068 | − | 0.0906833i | ||||
\(383\) | 312.000 | + | 180.133i | 0.814621 | + | 0.470322i | 0.848558 | − | 0.529102i | \(-0.177471\pi\) |
−0.0339368 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −262.500 | − | 454.663i | −0.681818 | − | 1.18094i | ||||
\(386\) | 65.0000 | − | 112.583i | 0.168394 | − | 0.291667i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 50.0000 | + | 86.6025i | 0.128866 | + | 0.223202i | ||||
\(389\) | 237.500 | + | 411.362i | 0.610540 | + | 1.05749i | 0.991150 | + | 0.132750i | \(0.0423808\pi\) |
−0.380610 | + | 0.924736i | \(0.624286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | − | 13.8564i | −0.0613811 | − | 0.0354384i | ||||
\(392\) | −104.000 | + | 180.133i | −0.265306 | + | 0.459524i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 506.000 | 1.28426 | ||||||||
\(395\) | − | 48.4974i | − | 0.122778i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 260.000 | 0.654912 | 0.327456 | − | 0.944866i | \(-0.393809\pi\) | ||||
0.327456 | + | 0.944866i | \(0.393809\pi\) | |||||||
\(398\) | 259.808i | 0.652783i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −192.000 | − | 332.554i | −0.480000 | − | 0.831384i | ||||
\(401\) | −370.000 | + | 640.859i | −0.922693 | + | 1.59815i | −0.127464 | + | 0.991843i | \(0.540684\pi\) |
−0.795230 | + | 0.606308i | \(0.792650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −930.000 | + | 536.936i | −2.30769 | + | 1.33235i | ||||
\(404\) | −310.000 | − | 536.936i | −0.767327 | − | 1.32905i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 150.000 | + | 86.6025i | 0.369458 | + | 0.213307i | ||||
\(407\) | 75.0000 | − | 43.3013i | 0.184275 | − | 0.106391i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −329.500 | + | 570.711i | −0.805623 | + | 1.39538i | 0.110246 | + | 0.993904i | \(0.464836\pi\) |
−0.915869 | + | 0.401476i | \(0.868497\pi\) | |||||||
\(410\) | −350.000 | − | 606.218i | −0.853659 | − | 1.47858i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −480.000 | − | 277.128i | −1.16505 | − | 0.672641i | ||||
\(413\) | 300.000 | 0.726392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 206.114i | 0.496660i | ||||||||
\(416\) | 320.000 | − | 554.256i | 0.769231 | − | 1.33235i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 90.0000 | + | 155.885i | 0.215311 | + | 0.372930i | ||||
\(419\) | 510.000 | + | 294.449i | 1.21718 | + | 0.702741i | 0.964315 | − | 0.264759i | \(-0.0852924\pi\) |
0.252869 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 248.000 | + | 429.549i | 0.589074 | + | 1.02031i | 0.994354 | + | 0.106113i | \(0.0338405\pi\) |
−0.405280 | + | 0.914192i | \(0.632826\pi\) | |||||||
\(422\) | 258.000 | + | 148.956i | 0.611374 | + | 0.352977i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −376.000 | −0.886792 | ||||||||
\(425\) | −96.0000 | − | 166.277i | −0.225882 | − | 0.391240i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −480.000 | − | 277.128i | −1.12412 | − | 0.649012i | ||||
\(428\) | 519.615i | 1.21405i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 242.487i | 0.563924i | ||||||||
\(431\) | 571.577i | 1.32616i | 0.748547 | + | 0.663082i | \(0.230752\pi\) | ||||
−0.748547 | + | 0.663082i | \(0.769248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −235.000 | −0.542725 | −0.271363 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(434\) | 930.000 | 2.14286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 536.000 | 1.22936 | ||||||||
\(437\) | 18.0000 | − | 31.1769i | 0.0411899 | − | 0.0713431i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −358.500 | + | 206.980i | −0.816629 | + | 0.471481i | −0.849253 | − | 0.527987i | \(-0.822947\pi\) |
0.0326238 | + | 0.999468i | \(0.489614\pi\) | |||||||
\(440\) | − | 484.974i | − | 1.10221i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 160.000 | − | 277.128i | 0.361991 | − | 0.626987i | ||||
\(443\) | −498.000 | + | 287.520i | −1.12415 | + | 0.649030i | −0.942458 | − | 0.334325i | \(-0.891492\pi\) |
−0.181695 | + | 0.983355i | \(0.558159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.0000 | + | 60.6218i | −0.0786517 | + | 0.136229i | ||||
\(446\) | 60.0000 | − | 34.6410i | 0.134529 | − | 0.0776704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −480.000 | + | 277.128i | −1.07143 | + | 0.618590i | ||||
\(449\) | 470.000 | 1.04677 | 0.523385 | − | 0.852096i | \(-0.324669\pi\) | ||||
0.523385 | + | 0.852096i | \(0.324669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 433.013i | − | 0.960117i | ||||||
\(452\) | −148.000 | + | 256.344i | −0.327434 | + | 0.567132i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −156.000 | + | 90.0666i | −0.343612 | + | 0.198385i | ||||
\(455\) | −1050.00 | − | 606.218i | −2.30769 | − | 1.33235i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 162.500 | + | 281.458i | 0.355580 | + | 0.615882i | 0.987217 | − | 0.159382i | \(-0.0509501\pi\) |
−0.631637 | + | 0.775264i | \(0.717617\pi\) | |||||||
\(458\) | 146.000 | − | 252.879i | 0.318777 | − | 0.552138i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −84.0000 | + | 48.4974i | −0.182609 | + | 0.105429i | ||||
\(461\) | 327.500 | + | 567.247i | 0.710412 | + | 1.23047i | 0.964703 | + | 0.263342i | \(0.0848248\pi\) |
−0.254290 | + | 0.967128i | \(0.581842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −142.500 | − | 82.2724i | −0.307775 | − | 0.177694i | 0.338155 | − | 0.941090i | \(-0.390197\pi\) |
−0.645931 | + | 0.763396i | \(0.723530\pi\) | |||||||
\(464\) | 80.0000 | + | 138.564i | 0.172414 | + | 0.298629i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 668.000 | 1.43348 | ||||||||
\(467\) | − | 57.1577i | − | 0.122393i | −0.998126 | − | 0.0611967i | \(-0.980508\pi\) | ||
0.998126 | − | 0.0611967i | \(-0.0194917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 750.000 | 1.59915 | ||||||||
\(470\) | − | 1212.44i | − | 2.57965i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 240.000 | + | 138.564i | 0.508475 | + | 0.293568i | ||||
\(473\) | −75.0000 | + | 129.904i | −0.158562 | + | 0.274638i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 216.000 | − | 124.708i | 0.454737 | − | 0.262542i | ||||
\(476\) | −240.000 | + | 138.564i | −0.504202 | + | 0.291101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0000 | − | 17.3205i | −0.0627615 | − | 0.0362354i | ||||
\(479\) | 285.000 | − | 164.545i | 0.594990 | − | 0.343517i | −0.172078 | − | 0.985083i | \(-0.555048\pi\) |
0.767068 | + | 0.641566i | \(0.221715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.000 | − | 173.205i | 0.207900 | − | 0.360094i | ||||
\(482\) | 134.000 | + | 232.095i | 0.278008 | + | 0.481524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −92.0000 | + | 159.349i | −0.190083 | + | 0.329233i | ||||
\(485\) | 175.000 | 0.360825 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 519.615i | 1.06697i | 0.845809 | + | 0.533486i | \(0.179118\pi\) | ||||
−0.845809 | + | 0.533486i | \(0.820882\pi\) | |||||||
\(488\) | −256.000 | − | 443.405i | −0.524590 | − | 0.908617i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 182.000 | + | 315.233i | 0.371429 | + | 0.643333i | ||||
\(491\) | −187.500 | − | 108.253i | −0.381874 | − | 0.220475i | 0.296759 | − | 0.954952i | \(-0.404094\pi\) |
−0.678633 | + | 0.734477i | \(0.737427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0000 | + | 69.2820i | 0.0811359 | + | 0.140532i | ||||
\(494\) | 360.000 | + | 207.846i | 0.728745 | + | 0.420741i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 744.000 | + | 429.549i | 1.50000 | + | 0.866025i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.0000 | − | 22.5167i | −0.0781563 | − | 0.0451236i | 0.460413 | − | 0.887705i | \(-0.347701\pi\) |
−0.538569 | + | 0.842581i | \(0.681035\pi\) | |||||||
\(500\) | 28.0000 | 0.0560000 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 415.692i | − | 0.828072i | ||||||
\(503\) | 384.515i | 0.764444i | 0.924071 | + | 0.382222i | \(0.124841\pi\) | ||||
−0.924071 | + | 0.382222i | \(0.875159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1085.00 | −2.14851 | ||||||||
\(506\) | −60.0000 | −0.118577 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 103.923i | − | 0.204573i | ||||||
\(509\) | 132.500 | − | 229.497i | 0.260314 | − | 0.450878i | −0.706011 | − | 0.708201i | \(-0.749507\pi\) |
0.966325 | + | 0.257323i | \(0.0828405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 412.500 | − | 238.157i | 0.807241 | − | 0.466061i | ||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −268.000 | + | 464.190i | −0.521401 | + | 0.903093i | ||||
\(515\) | −840.000 | + | 484.974i | −1.63107 | + | 0.941698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 375.000 | − | 649.519i | 0.725338 | − | 1.25632i | ||||
\(518\) | −150.000 | + | 86.6025i | −0.289575 | + | 0.167186i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −560.000 | − | 969.948i | −1.07692 | − | 1.86529i | ||||
\(521\) | 380.000 | 0.729367 | 0.364683 | − | 0.931132i | \(-0.381177\pi\) | ||||
0.364683 | + | 0.931132i | \(0.381177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 623.538i | 1.19223i | 0.802898 | + | 0.596117i | \(0.203291\pi\) | ||||
−0.802898 | + | 0.596117i | \(0.796709\pi\) | |||||||
\(524\) | −570.000 | − | 329.090i | −1.08779 | − | 0.628034i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −750.000 | + | 433.013i | −1.42586 | + | 0.823218i | ||||
\(527\) | 372.000 | + | 214.774i | 0.705882 | + | 0.407541i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −258.500 | − | 447.735i | −0.488658 | − | 0.846380i | ||||
\(530\) | −329.000 | + | 569.845i | −0.620755 | + | 1.07518i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −180.000 | − | 311.769i | −0.338346 | − | 0.586032i | ||||
\(533\) | −500.000 | − | 866.025i | −0.938086 | − | 1.62481i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 787.500 | + | 454.663i | 1.47196 | + | 0.849838i | ||||
\(536\) | 600.000 | + | 346.410i | 1.11940 | + | 0.646288i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −700.000 | −1.30112 | ||||||||
\(539\) | 225.167i | 0.417749i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −532.000 | −0.983364 | −0.491682 | − | 0.870775i | \(-0.663618\pi\) | ||||
−0.491682 | + | 0.870775i | \(0.663618\pi\) | |||||||
\(542\) | 72.7461i | 0.134218i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −256.000 | −0.470588 | ||||||||
\(545\) | 469.000 | − | 812.332i | 0.860550 | − | 1.49052i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 780.000 | − | 450.333i | 1.42596 | − | 0.823278i | 0.429161 | − | 0.903228i | \(-0.358809\pi\) |
0.996799 | + | 0.0799498i | \(0.0254760\pi\) | |||||||
\(548\) | −124.000 | − | 214.774i | −0.226277 | − | 0.391924i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −360.000 | − | 207.846i | −0.654545 | − | 0.377902i | ||||
\(551\) | −90.0000 | + | 51.9615i | −0.163339 | + | 0.0943040i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 51.9615i | −0.0542495 | + | 0.0939630i | ||||
\(554\) | −520.000 | − | 900.666i | −0.938628 | − | 1.62575i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 600.000 | + | 346.410i | 1.07914 | + | 0.623040i | ||||
\(557\) | 89.0000 | 0.159785 | 0.0798923 | − | 0.996804i | \(-0.474542\pi\) | ||||
0.0798923 | + | 0.996804i | \(0.474542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 346.410i | 0.619696i | ||||||||
\(560\) | 969.948i | 1.73205i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 440.000 | + | 762.102i | 0.782918 | + | 1.35605i | ||||
\(563\) | 262.500 | + | 151.554i | 0.466252 | + | 0.269191i | 0.714670 | − | 0.699462i | \(-0.246577\pi\) |
−0.248417 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 259.000 | + | 448.601i | 0.458407 | + | 0.793984i | ||||
\(566\) | −570.000 | − | 329.090i | −1.00707 | − | 0.581430i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 50.0000 | + | 86.6025i | 0.0878735 | + | 0.152201i | 0.906612 | − | 0.421965i | \(-0.138660\pi\) |
−0.818739 | + | 0.574166i | \(0.805326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 294.000 | + | 169.741i | 0.514886 | + | 0.297270i | 0.734840 | − | 0.678241i | \(-0.237257\pi\) |
−0.219954 | + | 0.975510i | \(0.570591\pi\) | |||||||
\(572\) | − | 692.820i | − | 1.21122i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 866.025i | 1.50876i | ||||||||
\(575\) | 83.1384i | 0.144589i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −730.000 | −1.26516 | −0.632582 | − | 0.774493i | \(-0.718005\pi\) | ||||
−0.632582 | + | 0.774493i | \(0.718005\pi\) | |||||||
\(578\) | 450.000 | 0.778547 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 280.000 | 0.482759 | ||||||||
\(581\) | 127.500 | − | 220.836i | 0.219449 | − | 0.380097i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −352.500 | + | 203.516i | −0.604631 | + | 0.349084i | ||||
\(584\) | 440.000 | 0.753425 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 218.000 | − | 377.587i | 0.372014 | − | 0.644347i | ||||
\(587\) | 694.500 | − | 400.970i | 1.18313 | − | 0.683083i | 0.226397 | − | 0.974035i | \(-0.427305\pi\) |
0.956738 | + | 0.290952i | \(0.0939720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −279.000 | + | 483.242i | −0.473684 | + | 0.820445i | ||||
\(590\) | 420.000 | − | 242.487i | 0.711864 | − | 0.410995i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −160.000 | −0.270270 | ||||||||
\(593\) | −982.000 | −1.65599 | −0.827993 | − | 0.560738i | \(-0.810517\pi\) | ||||
−0.827993 | + | 0.560738i | \(0.810517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 484.974i | 0.815083i | ||||||||
\(596\) | 230.000 | − | 398.372i | 0.385906 | − | 0.668409i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −120.000 | + | 69.2820i | −0.200669 | + | 0.115856i | ||||
\(599\) | 195.000 | + | 112.583i | 0.325543 | + | 0.187952i | 0.653860 | − | 0.756615i | \(-0.273148\pi\) |
−0.328318 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −125.500 | − | 217.372i | −0.208819 | − | 0.361684i | 0.742524 | − | 0.669819i | \(-0.233629\pi\) |
−0.951343 | + | 0.308135i | \(0.900295\pi\) | |||||||
\(602\) | 150.000 | − | 259.808i | 0.249169 | − | 0.431574i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 150.000 | − | 86.6025i | 0.248344 | − | 0.143382i | ||||
\(605\) | 161.000 | + | 278.860i | 0.266116 | + | 0.460926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 330.000 | + | 190.526i | 0.543657 | + | 0.313881i | 0.746560 | − | 0.665318i | \(-0.231704\pi\) |
−0.202903 | + | 0.979199i | \(0.565037\pi\) | |||||||
\(608\) | − | 332.554i | − | 0.546963i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −896.000 | −1.46885 | ||||||||
\(611\) | − | 1732.05i | − | 2.83478i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 650.000 | 1.06036 | 0.530179 | − | 0.847885i | \(-0.322125\pi\) | ||||
0.530179 | + | 0.847885i | \(0.322125\pi\) | |||||||
\(614\) | 415.692i | 0.677023i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −300.000 | + | 519.615i | −0.487013 | + | 0.843531i | ||||
\(617\) | −379.000 | + | 656.447i | −0.614263 | + | 1.06393i | 0.376251 | + | 0.926518i | \(0.377213\pi\) |
−0.990513 | + | 0.137416i | \(0.956120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 150.000 | − | 86.6025i | 0.242326 | − | 0.139907i | −0.373919 | − | 0.927461i | \(-0.621986\pi\) |
0.616245 | + | 0.787554i | \(0.288653\pi\) | |||||||
\(620\) | 1302.00 | − | 751.710i | 2.10000 | − | 1.21244i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 510.000 | + | 294.449i | 0.819936 | + | 0.473390i | ||||
\(623\) | 75.0000 | − | 43.3013i | 0.120385 | − | 0.0695044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 324.500 | − | 562.050i | 0.519200 | − | 0.899281i | ||||
\(626\) | 485.000 | + | 840.045i | 0.774760 | + | 1.34192i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.0000 | + | 69.2820i | −0.0636943 | + | 0.110322i | ||||
\(629\) | −80.0000 | −0.127186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 119.512i | − | 0.189400i | −0.995506 | − | 0.0947001i | \(-0.969811\pi\) | ||
0.995506 | − | 0.0947001i | \(-0.0301892\pi\) | |||||||
\(632\) | −48.0000 | + | 27.7128i | −0.0759494 | + | 0.0438494i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −217.000 | − | 375.855i | −0.342271 | − | 0.592831i | ||||
\(635\) | −157.500 | − | 90.9327i | −0.248031 | − | 0.143201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 260.000 | + | 450.333i | 0.408163 | + | 0.706960i | ||||
\(638\) | 150.000 | + | 86.6025i | 0.235110 | + | 0.135741i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −448.000 | + | 775.959i | −0.700000 | + | 1.21244i | ||||
\(641\) | 455.000 | + | 788.083i | 0.709828 | + | 1.22946i | 0.964921 | + | 0.262542i | \(0.0845609\pi\) |
−0.255092 | + | 0.966917i | \(0.582106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0000 | − | 17.3205i | −0.0466563 | − | 0.0269370i | 0.476490 | − | 0.879180i | \(-0.341909\pi\) |
−0.523147 | + | 0.852243i | \(0.675242\pi\) | |||||||
\(644\) | 120.000 | 0.186335 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 166.277i | − | 0.257395i | ||||||
\(647\) | 914.523i | 1.41348i | 0.707472 | + | 0.706741i | \(0.249835\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 300.000 | 0.462250 | ||||||||
\(650\) | −960.000 | −1.47692 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 415.692i | 0.637565i | ||||||||
\(653\) | 51.5000 | − | 89.2006i | 0.0788668 | − | 0.136601i | −0.823894 | − | 0.566743i | \(-0.808203\pi\) |
0.902761 | + | 0.430142i | \(0.141536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −997.500 | + | 575.907i | −1.52290 | + | 0.879247i | ||||
\(656\) | −400.000 | + | 692.820i | −0.609756 | + | 1.05613i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −750.000 | + | 1299.04i | −1.13982 | + | 1.97422i | ||||
\(659\) | −52.5000 | + | 30.3109i | −0.0796662 | + | 0.0459953i | −0.539304 | − | 0.842111i | \(-0.681313\pi\) |
0.459638 | + | 0.888106i | \(0.347979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −289.000 | + | 500.563i | −0.437216 | + | 0.757281i | −0.997474 | − | 0.0710377i | \(-0.977369\pi\) |
0.560257 | + | 0.828319i | \(0.310702\pi\) | |||||||
\(662\) | −750.000 | + | 433.013i | −1.13293 | + | 0.654098i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 204.000 | − | 117.779i | 0.307229 | − | 0.177379i | ||||
\(665\) | −630.000 | −0.947368 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.6410i | − | 0.0519356i | ||||||
\(668\) | 852.000 | + | 491.902i | 1.27545 | + | 0.736381i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1050.00 | − | 606.218i | 1.56716 | − | 0.904803i | ||||
\(671\) | −480.000 | − | 277.128i | −0.715350 | − | 0.413008i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −422.500 | − | 731.791i | −0.627786 | − | 1.08736i | −0.987995 | − | 0.154486i | \(-0.950628\pi\) |
0.360209 | − | 0.932872i | \(-0.382705\pi\) | |||||||
\(674\) | −310.000 | + | 536.936i | −0.459941 | + | 0.796641i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −462.000 | − | 800.207i | −0.683432 | − | 1.18374i | ||||
\(677\) | −577.000 | − | 999.393i | −0.852290 | − | 1.47621i | −0.879137 | − | 0.476569i | \(-0.841880\pi\) |
0.0268475 | − | 0.999640i | \(-0.491453\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −187.500 | − | 108.253i | −0.276141 | − | 0.159430i | ||||
\(680\) | −224.000 | + | 387.979i | −0.329412 | + | 0.570558i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 930.000 | 1.36364 | ||||||||
\(683\) | 187.061i | 0.273882i | 0.990579 | + | 0.136941i | \(0.0437271\pi\) | ||||
−0.990579 | + | 0.136941i | \(0.956273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −434.000 | −0.633577 | ||||||||
\(686\) | 398.372i | 0.580717i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 240.000 | − | 138.564i | 0.348837 | − | 0.201401i | ||||
\(689\) | −470.000 | + | 814.064i | −0.682148 | + | 1.18152i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −426.000 | + | 245.951i | −0.616498 | + | 0.355935i | −0.775504 | − | 0.631342i | \(-0.782504\pi\) |
0.159006 | + | 0.987278i | \(0.449171\pi\) | |||||||
\(692\) | 254.000 | + | 439.941i | 0.367052 | + | 0.635753i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 375.000 | + | 216.506i | 0.540346 | + | 0.311969i | ||||
\(695\) | 1050.00 | − | 606.218i | 1.51079 | − | 0.872256i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −200.000 | + | 346.410i | −0.286944 | + | 0.497002i | ||||
\(698\) | 74.0000 | + | 128.172i | 0.106017 | + | 0.183627i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 720.000 | + | 415.692i | 1.02857 | + | 0.593846i | ||||
\(701\) | 215.000 | 0.306705 | 0.153352 | − | 0.988172i | \(-0.450993\pi\) | ||||
0.153352 | + | 0.988172i | \(0.450993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 103.923i | − | 0.147828i | ||||||
\(704\) | −480.000 | + | 277.128i | −0.681818 | + | 0.393648i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −394.000 | − | 682.428i | −0.558074 | − | 0.966612i | ||||
\(707\) | 1162.50 | + | 671.170i | 1.64427 | + | 0.949321i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 266.000 | + | 460.726i | 0.375176 | + | 0.649824i | 0.990353 | − | 0.138565i | \(-0.0442488\pi\) |
−0.615177 | + | 0.788389i | \(0.710916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 80.0000 | 0.112360 | ||||||||
\(713\) | −93.0000 | − | 161.081i | −0.130435 | − | 0.225920i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1050.00 | − | 606.218i | −1.46853 | − | 0.847857i | ||||
\(716\) | − | 935.307i | − | 1.30630i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 1143.15i | − | 1.59214i | ||||||
\(719\) | − | 1143.15i | − | 1.58992i | −0.606661 | − | 0.794961i | \(-0.707491\pi\) | ||
0.606661 | − | 0.794961i | \(-0.292509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1200.00 | 1.66436 | ||||||||
\(722\) | −506.000 | −0.700831 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 224.000 | 0.309392 | ||||||||
\(725\) | 120.000 | − | 207.846i | 0.165517 | − | 0.286684i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1072.50 | − | 619.208i | 1.47524 | − | 0.851731i | 0.475630 | − | 0.879645i | \(-0.342220\pi\) |
0.999610 | + | 0.0279146i | \(0.00888665\pi\) | |||||||
\(728\) | 1385.64i | 1.90335i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 385.000 | − | 666.840i | 0.527397 | − | 0.913479i | ||||
\(731\) | 120.000 | − | 69.2820i | 0.164159 | − | 0.0947771i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −475.000 | + | 822.724i | −0.648022 | + | 1.12241i | 0.335573 | + | 0.942014i | \(0.391070\pi\) |
−0.983595 | + | 0.180392i | \(0.942263\pi\) | |||||||
\(734\) | −975.000 | + | 562.917i | −1.32834 | + | 0.766916i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 96.0000 | + | 55.4256i | 0.130435 | + | 0.0753066i | ||||
\(737\) | 750.000 | 1.01764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 581.969i | − | 0.787509i | −0.919216 | − | 0.393754i | \(-0.871176\pi\) | ||
0.919216 | − | 0.393754i | \(-0.128824\pi\) | |||||||
\(740\) | −140.000 | + | 242.487i | −0.189189 | + | 0.327685i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 705.000 | − | 407.032i | 0.950135 | − | 0.548561i | ||||
\(743\) | −750.000 | − | 433.013i | −1.00942 | − | 0.582790i | −0.0983991 | − | 0.995147i | \(-0.531372\pi\) |
−0.911022 | + | 0.412357i | \(0.864706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −402.500 | − | 697.150i | −0.540268 | − | 0.935772i | ||||
\(746\) | −40.0000 | + | 69.2820i | −0.0536193 | + | 0.0928714i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −240.000 | + | 138.564i | −0.320856 | + | 0.185246i | ||||
\(749\) | −562.500 | − | 974.279i | −0.751001 | − | 1.30077i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −151.500 | − | 87.4686i | −0.201731 | − | 0.116469i | 0.395732 | − | 0.918366i | \(-0.370491\pi\) |
−0.597463 | + | 0.801897i | \(0.703824\pi\) | |||||||
\(752\) | −1200.00 | + | 692.820i | −1.59574 | + | 0.921304i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 400.000 | 0.530504 | ||||||||
\(755\) | − | 303.109i | − | 0.401469i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 830.000 | 1.09643 | 0.548217 | − | 0.836336i | \(-0.315307\pi\) | ||||
0.548217 | + | 0.836336i | \(0.315307\pi\) | |||||||
\(758\) | 1371.78i | 1.80974i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −504.000 | − | 290.985i | −0.663158 | − | 0.382874i | ||||
\(761\) | −280.000 | + | 484.974i | −0.367937 | + | 0.637285i | −0.989243 | − | 0.146283i | \(-0.953269\pi\) |
0.621306 | + | 0.783568i | \(0.286602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1005.00 | + | 580.237i | −1.31717 | + | 0.760468i | ||||
\(764\) | −120.000 | + | 69.2820i | −0.157068 | + | 0.0906833i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −624.000 | − | 360.267i | −0.814621 | − | 0.470322i | ||||
\(767\) | 600.000 | − | 346.410i | 0.782269 | − | 0.451643i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 165.500 | − | 286.654i | 0.215215 | − | 0.372763i | −0.738124 | − | 0.674665i | \(-0.764288\pi\) |
0.953339 | + | 0.301902i | \(0.0976216\pi\) | |||||||
\(770\) | 525.000 | + | 909.327i | 0.681818 | + | 1.18094i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −130.000 | + | 225.167i | −0.168394 | + | 0.291667i | ||||
\(773\) | −298.000 | −0.385511 | −0.192755 | − | 0.981247i | \(-0.561742\pi\) | ||||
−0.192755 | + | 0.981247i | \(0.561742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1288.65i | − | 1.66277i | ||||||
\(776\) | −100.000 | − | 173.205i | −0.128866 | − | 0.223202i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −475.000 | − | 822.724i | −0.610540 | − | 1.05749i | ||||
\(779\) | −450.000 | − | 259.808i | −0.577664 | − | 0.333514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 48.0000 | + | 27.7128i | 0.0613811 | + | 0.0354384i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 208.000 | − | 360.267i | 0.265306 | − | 0.459524i | ||||
\(785\) | 70.0000 | + | 121.244i | 0.0891720 | + | 0.154450i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 960.000 | + | 554.256i | 1.21982 | + | 0.704265i | 0.964880 | − | 0.262692i | \(-0.0846102\pi\) |
0.254942 | + | 0.966956i | \(0.417944\pi\) | |||||||
\(788\) | −1012.00 | −1.28426 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 96.9948i | 0.122778i | ||||||||
\(791\) | − | 640.859i | − | 0.810188i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1280.00 | −1.61412 | ||||||||
\(794\) | −520.000 | −0.654912 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 519.615i | − | 0.652783i | ||||||
\(797\) | 651.500 | − | 1128.43i | 0.817440 | − | 1.41585i | −0.0901219 | − | 0.995931i | \(-0.528726\pi\) |
0.907562 | − | 0.419918i | \(-0.137941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −600.000 | + | 346.410i | −0.750939 | + | 0.433555i | ||||
\(800\) | 384.000 | + | 665.108i | 0.480000 | + | 0.831384i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 740.000 | − | 1281.72i | 0.922693 | − | 1.59815i | ||||
\(803\) | 412.500 | − | 238.157i | 0.513699 | − | 0.296584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 105.000 | − | 181.865i | 0.130435 | − | 0.225920i | ||||
\(806\) | 1860.00 | − | 1073.87i | 2.30769 | − | 1.33235i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 620.000 | + | 1073.87i | 0.767327 | + | 1.32905i | ||||
\(809\) | 170.000 | 0.210136 | 0.105068 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105068 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 779.423i | − | 0.961064i | −0.876977 | − | 0.480532i | \(-0.840444\pi\) | ||
0.876977 | − | 0.480532i | \(-0.159556\pi\) | |||||||
\(812\) | −300.000 | − | 173.205i | −0.369458 | − | 0.213307i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −150.000 | + | 86.6025i | −0.184275 | + | 0.106391i | ||||
\(815\) | 630.000 | + | 363.731i | 0.773006 | + | 0.446295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 90.0000 | + | 155.885i | 0.110159 | + | 0.190801i | ||||
\(818\) | 659.000 | − | 1141.42i | 0.805623 | − | 1.39538i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 700.000 | + | 1212.44i | 0.853659 | + | 1.47858i | ||||
\(821\) | 545.000 | + | 943.968i | 0.663825 | + | 1.14978i | 0.979603 | + | 0.200945i | \(0.0644012\pi\) |
−0.315778 | + | 0.948833i | \(0.602265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −817.500 | − | 471.984i | −0.993317 | − | 0.573492i | −0.0870530 | − | 0.996204i | \(-0.527745\pi\) |
−0.906264 | + | 0.422712i | \(0.861078\pi\) | |||||||
\(824\) | 960.000 | + | 554.256i | 1.16505 | + | 0.672641i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −600.000 | −0.726392 | ||||||||
\(827\) | 83.1384i | 0.100530i | 0.998736 | + | 0.0502651i | \(0.0160066\pi\) | ||||
−0.998736 | + | 0.0502651i | \(0.983993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 542.000 | 0.653800 | 0.326900 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326900 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(830\) | − | 412.228i | − | 0.496660i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −640.000 | + | 1108.51i | −0.769231 | + | 1.33235i | ||||
\(833\) | 104.000 | − | 180.133i | 0.124850 | − | 0.216246i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1491.00 | − | 860.829i | 1.78563 | − | 1.03093i | ||||
\(836\) | −180.000 | − | 311.769i | −0.215311 | − | 0.372930i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1020.00 | − | 588.897i | −1.21718 | − | 0.702741i | ||||
\(839\) | 600.000 | − | 346.410i | 0.715137 | − | 0.412885i | −0.0978231 | − | 0.995204i | \(-0.531188\pi\) |
0.812960 | + | 0.582319i | \(0.197855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 370.500 | − | 641.725i | 0.440547 | − | 0.763050i | ||||
\(842\) | −496.000 | − | 859.097i | −0.589074 | − | 1.02031i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −516.000 | − | 297.913i | −0.611374 | − | 0.352977i | ||||
\(845\) | −1617.00 | −1.91361 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 398.372i | − | 0.470333i | ||||||
\(848\) | 752.000 | 0.886792 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 192.000 | + | 332.554i | 0.225882 | + | 0.391240i | ||||
\(851\) | 30.0000 | + | 17.3205i | 0.0352526 | + | 0.0203531i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −145.000 | − | 251.147i | −0.169988 | − | 0.294428i | 0.768427 | − | 0.639937i | \(-0.221040\pi\) |
−0.938415 | + | 0.345509i | \(0.887706\pi\) | |||||||
\(854\) | 960.000 | + | 554.256i | 1.12412 | + | 0.649012i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 1039.23i | − | 1.21405i | ||||||
\(857\) | −184.000 | − | 318.697i | −0.214702 | − | 0.371876i | 0.738478 | − | 0.674278i | \(-0.235545\pi\) |
−0.953180 | + | 0.302402i | \(0.902212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 924.000 | + | 533.472i | 1.07567 | + | 0.621038i | 0.929725 | − | 0.368255i | \(-0.120045\pi\) |
0.145944 | + | 0.989293i | \(0.453378\pi\) | |||||||
\(860\) | − | 484.974i | − | 0.563924i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1143.15i | − | 1.32616i | ||||||
\(863\) | − | 1018.45i | − | 1.18012i | −0.807358 | − | 0.590061i | \(-0.799104\pi\) | ||
0.807358 | − | 0.590061i | \(-0.200896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 889.000 | 1.02775 | ||||||||
\(866\) | 470.000 | 0.542725 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1860.00 | −2.14286 | ||||||||
\(869\) | −30.0000 | + | 51.9615i | −0.0345224 | + | 0.0597946i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1500.00 | − | 866.025i | 1.72216 | − | 0.994289i | ||||
\(872\) | −1072.00 | −1.22936 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.0000 | + | 62.3538i | −0.0411899 | + | 0.0713431i | ||||
\(875\) | −52.5000 | + | 30.3109i | −0.0600000 | + | 0.0346410i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 665.000 | − | 1151.81i | 0.758267 | − | 1.31336i | −0.185467 | − | 0.982651i | \(-0.559380\pi\) |
0.943734 | − | 0.330706i | \(-0.107287\pi\) | |||||||
\(878\) | 717.000 | − | 413.960i | 0.816629 | − | 0.471481i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 969.948i | 1.10221i | ||||||||
\(881\) | −1060.00 | −1.20318 | −0.601589 | − | 0.798806i | \(-0.705466\pi\) | ||||
−0.601589 | + | 0.798806i | \(0.705466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1506.88i | 1.70655i | 0.521461 | + | 0.853275i | \(0.325387\pi\) | ||||
−0.521461 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(884\) | −320.000 | + | 554.256i | −0.361991 | + | 0.626987i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 996.000 | − | 575.041i | 1.12415 | − | 0.649030i | ||||
\(887\) | 618.000 | + | 356.802i | 0.696731 | + | 0.402258i | 0.806129 | − | 0.591740i | \(-0.201559\pi\) |
−0.109398 | + | 0.993998i | \(0.534892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 112.500 | + | 194.856i | 0.126547 | + | 0.219185i | ||||
\(890\) | 70.0000 | − | 121.244i | 0.0786517 | − | 0.136229i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −120.000 | + | 69.2820i | −0.134529 | + | 0.0776704i | ||||
\(893\) | −450.000 | − | 779.423i | −0.503919 | − | 0.872814i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1417.50 | − | 818.394i | −1.58380 | − | 0.914407i | ||||
\(896\) | 960.000 | − | 554.256i | 1.07143 | − | 0.618590i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −940.000 | −1.04677 | ||||||||
\(899\) | 536.936i | 0.597259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 376.000 | 0.417314 | ||||||||
\(902\) | 866.025i | 0.960117i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 296.000 | − | 512.687i | 0.327434 | − | 0.567132i | ||||
\(905\) | 196.000 | − | 339.482i | 0.216575 | − | 0.375118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1155.00 | + | 666.840i | −1.27343 | + | 0.735215i | −0.975632 | − | 0.219415i | \(-0.929585\pi\) |
−0.297797 | + | 0.954629i | \(0.596252\pi\) | |||||||
\(908\) | 312.000 | − | 180.133i | 0.343612 | − | 0.198385i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2100.00 | + | 1212.44i | 2.30769 | + | 1.33235i | ||||
\(911\) | −1335.00 | + | 770.763i | −1.46542 | + | 0.846062i | −0.999253 | − | 0.0386335i | \(-0.987700\pi\) |
−0.466169 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 127.500 | − | 220.836i | 0.139650 | − | 0.241880i | ||||
\(914\) | −325.000 | − | 562.917i | −0.355580 | − | 0.615882i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −292.000 | + | 505.759i | −0.318777 | + | 0.552138i | ||||
\(917\) | 1425.00 | 1.55398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 909.327i | 0.989474i | 0.869043 | + | 0.494737i | \(0.164736\pi\) | ||||
−0.869043 | + | 0.494737i | \(0.835264\pi\) | |||||||
\(920\) | 168.000 | − | 96.9948i | 0.182609 | − | 0.105429i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −655.000 | − | 1134.49i | −0.710412 | − | 1.23047i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 120.000 | + | 207.846i | 0.129730 | + | 0.224698i | ||||
\(926\) | 285.000 | + | 164.545i | 0.307775 | + | 0.177694i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −160.000 | − | 277.128i | −0.172414 | − | 0.298629i | ||||
\(929\) | −670.000 | − | 1160.47i | −0.721206 | − | 1.24916i | −0.960517 | − | 0.278222i | \(-0.910255\pi\) |
0.239311 | − | 0.970943i | \(-0.423078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 234.000 | + | 135.100i | 0.251343 | + | 0.145113i | ||||
\(932\) | −1336.00 | −1.43348 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 114.315i | 0.122393i | ||||||||
\(935\) | 484.974i | 0.518689i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1225.00 | −1.30736 | −0.653682 | − | 0.756769i | \(-0.726777\pi\) | ||||
−0.653682 | + | 0.756769i | \(0.726777\pi\) | |||||||
\(938\) | −1500.00 | −1.59915 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2424.87i | 2.57965i | ||||||||
\(941\) | 57.5000 | − | 99.5929i | 0.0611052 | − | 0.105837i | −0.833854 | − | 0.551984i | \(-0.813871\pi\) |
0.894960 | + | 0.446147i | \(0.147204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 150.000 | − | 86.6025i | 0.159067 | − | 0.0918373i | ||||
\(944\) | −480.000 | − | 277.128i | −0.508475 | − | 0.293568i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 150.000 | − | 259.808i | 0.158562 | − | 0.274638i | ||||
\(947\) | 595.500 | − | 343.812i | 0.628828 | − | 0.363054i | −0.151470 | − | 0.988462i | \(-0.548401\pi\) |
0.780298 | + | 0.625408i | \(0.215067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 550.000 | − | 952.628i | 0.579557 | − | 1.00382i | ||||
\(950\) | −432.000 | + | 249.415i | −0.454737 | + | 0.262542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 480.000 | − | 277.128i | 0.504202 | − | 0.291101i | ||||
\(953\) | 44.0000 | 0.0461700 | 0.0230850 | − | 0.999734i | \(-0.492651\pi\) | ||||
0.0230850 | + | 0.999734i | \(0.492651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 242.487i | 0.253913i | ||||||||
\(956\) | 60.0000 | + | 34.6410i | 0.0627615 | + | 0.0362354i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −570.000 | + | 329.090i | −0.594990 | + | 0.343517i | ||||
\(959\) | 465.000 | + | 268.468i | 0.484880 | + | 0.279946i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | + | 1664.50i | 1.00000 | + | 1.73205i | ||||
\(962\) | −200.000 | + | 346.410i | −0.207900 | + | 0.360094i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −268.000 | − | 464.190i | −0.278008 | − | 0.481524i | ||||
\(965\) | 227.500 | + | 394.042i | 0.235751 | + | 0.408333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 217.500 | + | 125.574i | 0.224922 | + | 0.129859i | 0.608227 | − | 0.793763i | \(-0.291881\pi\) |
−0.383305 | + | 0.923622i | \(0.625214\pi\) | |||||||
\(968\) | 184.000 | − | 318.697i | 0.190083 | − | 0.329233i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −350.000 | −0.360825 | ||||||||
\(971\) | 337.750i | 0.347837i | 0.984760 | + | 0.173919i | \(0.0556430\pi\) | ||||
−0.984760 | + | 0.173919i | \(0.944357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1500.00 | −1.54162 | ||||||||
\(974\) | − | 1039.23i | − | 1.06697i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 512.000 | + | 886.810i | 0.524590 | + | 0.908617i | ||||
\(977\) | 173.000 | − | 299.645i | 0.177073 | − | 0.306699i | −0.763804 | − | 0.645448i | \(-0.776671\pi\) |
0.940877 | + | 0.338749i | \(0.110004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.0000 | − | 43.3013i | 0.0766088 | − | 0.0442301i | ||||
\(980\) | −364.000 | − | 630.466i | −0.371429 | − | 0.643333i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 375.000 | + | 216.506i | 0.381874 | + | 0.220475i | ||||
\(983\) | −687.000 | + | 396.640i | −0.698881 | + | 0.403499i | −0.806931 | − | 0.590646i | \(-0.798873\pi\) |
0.108050 | + | 0.994146i | \(0.465539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −885.500 | + | 1533.73i | −0.898985 | + | 1.55709i | ||||
\(986\) | −80.0000 | − | 138.564i | −0.0811359 | − | 0.140532i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −720.000 | − | 415.692i | −0.728745 | − | 0.420741i | ||||
\(989\) | −60.0000 | −0.0606673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1054.82i | − | 1.06440i | −0.846619 | − | 0.532199i | \(-0.821366\pi\) | ||
0.846619 | − | 0.532199i | \(-0.178634\pi\) | |||||||
\(992\) | −1488.00 | − | 859.097i | −1.50000 | − | 0.866025i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −787.500 | − | 454.663i | −0.791457 | − | 0.456948i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −130.000 | − | 225.167i | −0.130391 | − | 0.225844i | 0.793436 | − | 0.608653i | \(-0.208290\pi\) |
−0.923827 | + | 0.382809i | \(0.874957\pi\) | |||||||
\(998\) | 78.0000 | + | 45.0333i | 0.0781563 | + | 0.0451236i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.3.f.b.271.1 | 2 | ||
3.2 | odd | 2 | 324.3.f.i.271.1 | 2 | |||
4.3 | odd | 2 | 324.3.f.h.271.1 | 2 | |||
9.2 | odd | 6 | 324.3.f.c.55.1 | 2 | |||
9.4 | even | 3 | 108.3.d.b.55.1 | yes | 2 | ||
9.5 | odd | 6 | 108.3.d.a.55.2 | yes | 2 | ||
9.7 | even | 3 | 324.3.f.h.55.1 | 2 | |||
12.11 | even | 2 | 324.3.f.c.271.1 | 2 | |||
36.7 | odd | 6 | inner | 324.3.f.b.55.1 | 2 | ||
36.11 | even | 6 | 324.3.f.i.55.1 | 2 | |||
36.23 | even | 6 | 108.3.d.a.55.1 | ✓ | 2 | ||
36.31 | odd | 6 | 108.3.d.b.55.2 | yes | 2 | ||
72.5 | odd | 6 | 1728.3.g.a.703.1 | 2 | |||
72.13 | even | 6 | 1728.3.g.f.703.1 | 2 | |||
72.59 | even | 6 | 1728.3.g.a.703.2 | 2 | |||
72.67 | odd | 6 | 1728.3.g.f.703.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.a.55.1 | ✓ | 2 | 36.23 | even | 6 | ||
108.3.d.a.55.2 | yes | 2 | 9.5 | odd | 6 | ||
108.3.d.b.55.1 | yes | 2 | 9.4 | even | 3 | ||
108.3.d.b.55.2 | yes | 2 | 36.31 | odd | 6 | ||
324.3.f.b.55.1 | 2 | 36.7 | odd | 6 | inner | ||
324.3.f.b.271.1 | 2 | 1.1 | even | 1 | trivial | ||
324.3.f.c.55.1 | 2 | 9.2 | odd | 6 | |||
324.3.f.c.271.1 | 2 | 12.11 | even | 2 | |||
324.3.f.h.55.1 | 2 | 9.7 | even | 3 | |||
324.3.f.h.271.1 | 2 | 4.3 | odd | 2 | |||
324.3.f.i.55.1 | 2 | 36.11 | even | 6 | |||
324.3.f.i.271.1 | 2 | 3.2 | odd | 2 | |||
1728.3.g.a.703.1 | 2 | 72.5 | odd | 6 | |||
1728.3.g.a.703.2 | 2 | 72.59 | even | 6 | |||
1728.3.g.f.703.1 | 2 | 72.13 | even | 6 | |||
1728.3.g.f.703.2 | 2 | 72.67 | odd | 6 |