Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(161,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (of order \(2\), degree \(1\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(1.40126 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.161 |
Dual form | 1728.3.h.h.161.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.74597 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.66025 | 1.23718 | 0.618590 | − | 0.785714i | \(-0.287704\pi\) | ||||
0.618590 | + | 0.785714i | \(0.287704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.4164 | −1.21967 | −0.609837 | − | 0.792527i | \(-0.708765\pi\) | ||||
−0.609837 | + | 0.792527i | \(0.708765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615i | 0.399704i | 0.979826 | + | 0.199852i | \(0.0640461\pi\) | ||||
−0.979826 | + | 0.199852i | \(0.935954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.4164i | 0.789200i | 0.918853 | + | 0.394600i | \(0.129117\pi\) | ||||
−0.918853 | + | 0.394600i | \(0.870883\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 23.0000i | − 1.21053i | −0.796025 | − | 0.605263i | \(-0.793068\pi\) | ||||
0.796025 | − | 0.605263i | \(-0.206932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 7.74597i | − 0.336781i | −0.985720 | − | 0.168391i | \(-0.946143\pi\) | ||||
0.985720 | − | 0.168391i | \(-0.0538570\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 35.0000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −30.9839 | −1.06841 | −0.534205 | − | 0.845355i | \(-0.679389\pi\) | ||||
−0.534205 | + | 0.845355i | \(0.679389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 0.223490 | 0.111745 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111745 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −67.0820 | −1.91663 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 29.4449i | − 0.795807i | −0.917427 | − | 0.397904i | \(-0.869738\pi\) | ||||
0.917427 | − | 0.397904i | \(-0.130262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 80.4984i | 1.96338i | 0.190494 | + | 0.981688i | \(0.438991\pi\) | ||||
−0.190494 | + | 0.981688i | \(0.561009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.0000i | 0.883721i | 0.897084 | + | 0.441860i | \(0.145681\pi\) | ||||
−0.897084 | + | 0.441860i | \(0.854319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 54.2218i | − 1.15365i | −0.816866 | − | 0.576827i | \(-0.804291\pi\) | ||||
0.816866 | − | 0.576827i | \(-0.195709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26.0000 | 0.530612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 77.4597 | 1.46150 | 0.730752 | − | 0.682643i | \(-0.239170\pi\) | ||||
0.730752 | + | 0.682643i | \(0.239170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 103.923 | 1.88951 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.9149 | 1.59178 | 0.795889 | − | 0.605443i | \(-0.207004\pi\) | ||||
0.795889 | + | 0.605443i | \(0.207004\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 60.6218i | − 0.993800i | −0.867808 | − | 0.496900i | \(-0.834472\pi\) | ||||
0.867808 | − | 0.496900i | \(-0.165528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 40.2492i | − 0.619219i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 107.000i | 1.59701i | 0.601985 | + | 0.798507i | \(0.294377\pi\) | ||||
−0.601985 | + | 0.798507i | \(0.705623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 15.4919i | − 0.218196i | −0.994031 | − | 0.109098i | \(-0.965204\pi\) | ||||
0.994031 | − | 0.109098i | \(-0.0347963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −97.0000 | −1.32877 | −0.664384 | − | 0.747392i | \(-0.731306\pi\) | ||||
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −116.190 | −1.50895 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −67.5500 | −0.855063 | −0.427532 | − | 0.904000i | \(-0.640617\pi\) | ||||
−0.427532 | + | 0.904000i | \(0.640617\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 103.923i | − 1.22262i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 174.413i | − 1.95970i | −0.199735 | − | 0.979850i | \(-0.564008\pi\) | ||||
0.199735 | − | 0.979850i | \(-0.435992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45.0000i | 0.494505i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 178.157i | 1.87534i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 109.000 | 1.12371 | 0.561856 | − | 0.827235i | \(-0.310088\pi\) | ||||
0.561856 | + | 0.827235i | \(0.310088\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 170.411 | 1.68724 | 0.843620 | − | 0.536940i | \(-0.180420\pi\) | ||||
0.843620 | + | 0.536940i | \(0.180420\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 185.329 | 1.79931 | 0.899657 | − | 0.436596i | \(-0.143816\pi\) | ||||
0.899657 | + | 0.436596i | \(0.143816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4164 | 0.125387 | 0.0626935 | − | 0.998033i | \(-0.480031\pi\) | ||||
0.0626935 | + | 0.998033i | \(0.480031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 200.918i | − 1.84328i | −0.388042 | − | 0.921642i | \(-0.626848\pi\) | ||||
0.388042 | − | 0.921642i | \(-0.373152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4164i | 0.118729i | 0.998236 | + | 0.0593646i | \(0.0189075\pi\) | ||||
−0.998236 | + | 0.0593646i | \(0.981093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 60.0000i | 0.521739i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 116.190i | 0.976382i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.0000 | 0.487603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −77.4597 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 138.564 | 1.09106 | 0.545528 | − | 0.838093i | \(-0.316329\pi\) | ||||
0.545528 | + | 0.838093i | \(0.316329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 214.663 | 1.63865 | 0.819323 | − | 0.573333i | \(-0.194350\pi\) | ||||
0.819323 | + | 0.573333i | \(0.194350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 199.186i | − 1.49764i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 120.748i | − 0.881370i | −0.897662 | − | 0.440685i | \(-0.854736\pi\) | ||||
0.897662 | − | 0.440685i | \(-0.145264\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 49.0000i | 0.352518i | 0.984344 | + | 0.176259i | \(0.0563996\pi\) | ||||
−0.984344 | + | 0.176259i | \(0.943600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 69.7137i | − 0.487508i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 240.000 | 1.65517 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 139.427 | 0.935754 | 0.467877 | − | 0.883793i | \(-0.345019\pi\) | ||||
0.467877 | + | 0.883793i | \(0.345019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 164.545 | 1.08970 | 0.544850 | − | 0.838533i | \(-0.316586\pi\) | ||||
0.544850 | + | 0.838533i | \(0.316586\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −53.6656 | −0.346230 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 159.349i | 1.01496i | 0.861664 | + | 0.507480i | \(0.169423\pi\) | ||||
−0.861664 | + | 0.507480i | \(0.830577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 67.0820i | − 0.416659i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 97.0000i | 0.595092i | 0.954707 | + | 0.297546i | \(0.0961682\pi\) | ||||
−0.954707 | + | 0.297546i | \(0.903832\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 38.7298i | − 0.231915i | −0.993254 | − | 0.115958i | \(-0.963006\pi\) | ||||
0.993254 | − | 0.115958i | \(-0.0369937\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.000 | 0.840237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −77.4597 | −0.447744 | −0.223872 | − | 0.974619i | \(-0.571870\pi\) | ||||
−0.223872 | + | 0.974619i | \(0.571870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 303.109 | 1.73205 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.8328 | 0.149904 | 0.0749520 | − | 0.997187i | \(-0.476120\pi\) | ||||
0.0749520 | + | 0.997187i | \(0.476120\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 174.937i | 0.966503i | 0.875481 | + | 0.483252i | \(0.160544\pi\) | ||||
−0.875481 | + | 0.483252i | \(0.839456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 228.079i | 1.23286i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 180.000i | − 0.962567i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 178.157i | − 0.932760i | −0.884584 | − | 0.466380i | \(-0.845558\pi\) | ||||
0.884584 | − | 0.466380i | \(-0.154442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 59.0000 | 0.305699 | 0.152850 | − | 0.988249i | \(-0.451155\pi\) | ||||
0.152850 | + | 0.988249i | \(0.451155\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2379 | 0.117959 | 0.0589794 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589794 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 88.3346 | 0.443892 | 0.221946 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221946 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −268.328 | −1.32181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 623.538i | − 3.04165i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 308.577i | 1.47645i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.00000i | − 0.00473934i | −0.999997 | − | 0.00236967i | \(-0.999246\pi\) | ||||
0.999997 | − | 0.00236967i | \(-0.000754290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 294.347i | − 1.36905i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60.0000 | 0.276498 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −69.7137 | −0.315447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −48.4974 | −0.217477 | −0.108739 | − | 0.994070i | \(-0.534681\pi\) | ||||
−0.108739 | + | 0.994070i | \(0.534681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −80.4984 | −0.354619 | −0.177309 | − | 0.984155i | \(-0.556739\pi\) | ||||
−0.177309 | + | 0.984155i | \(0.556739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 235.559i | − 1.02864i | −0.857598 | − | 0.514321i | \(-0.828044\pi\) | ||||
0.857598 | − | 0.514321i | \(-0.171956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 295.161i | 1.26679i | 0.773831 | + | 0.633393i | \(0.218338\pi\) | ||||
−0.773831 | + | 0.633393i | \(0.781662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 420.000i | 1.78723i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 154.919i | − 0.648198i | −0.946023 | − | 0.324099i | \(-0.894939\pi\) | ||||
0.946023 | − | 0.324099i | \(-0.105061\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 299.000 | 1.24066 | 0.620332 | − | 0.784339i | \(-0.286998\pi\) | ||||
0.620332 | + | 0.784339i | \(0.286998\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −201.395 | −0.822021 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 119.512 | 0.483852 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −134.164 | −0.534518 | −0.267259 | − | 0.963625i | \(-0.586118\pi\) | ||||
−0.267259 | + | 0.963625i | \(0.586118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 103.923i | 0.410763i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 348.827i | − 1.35730i | −0.734461 | − | 0.678651i | \(-0.762565\pi\) | ||||
0.734461 | − | 0.678651i | \(-0.237435\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 255.000i | − 0.984556i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 464.758i | 1.76714i | 0.468298 | + | 0.883570i | \(0.344867\pi\) | ||||
−0.468298 | + | 0.883570i | \(0.655133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −600.000 | −2.26415 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −162.665 | −0.604704 | −0.302352 | − | 0.953196i | \(-0.597772\pi\) | ||||
−0.302352 | + | 0.953196i | \(0.597772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 226.899 | 0.837264 | 0.418632 | − | 0.908156i | \(-0.362510\pi\) | ||||
0.418632 | + | 0.908156i | \(0.362510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −469.574 | −1.70754 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 297.913i | − 1.07550i | −0.843105 | − | 0.537749i | \(-0.819275\pi\) | ||||
0.843105 | − | 0.537749i | \(-0.180725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 53.6656i | 0.190981i | 0.995430 | + | 0.0954904i | \(0.0304419\pi\) | ||||
−0.995430 | + | 0.0954904i | \(0.969558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 442.000i | 1.56184i | 0.624633 | + | 0.780919i | \(0.285249\pi\) | ||||
−0.624633 | + | 0.780919i | \(0.714751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 697.137i | 2.42905i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 109.000 | 0.377163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −85.2056 | −0.290804 | −0.145402 | − | 0.989373i | \(-0.546448\pi\) | ||||
−0.145402 | + | 0.989373i | \(0.546448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −727.461 | −2.46597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40.2492 | 0.134613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 329.090i | 1.09332i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 469.574i | 1.53959i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 302.000i | 0.983713i | 0.870676 | + | 0.491857i | \(0.163682\pi\) | ||||
−0.870676 | + | 0.491857i | \(0.836318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 596.439i | − 1.91781i | −0.283724 | − | 0.958906i | \(-0.591570\pi\) | ||||
0.283724 | − | 0.958906i | \(-0.408430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −563.000 | −1.79872 | −0.899361 | − | 0.437207i | \(-0.855968\pi\) | ||||
−0.899361 | + | 0.437207i | \(0.855968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 415.692 | 1.30311 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 308.577 | 0.955348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 181.865i | 0.559586i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 469.574i | − 1.42728i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 359.000i | − 1.08459i | −0.840187 | − | 0.542296i | \(-0.817555\pi\) | ||||
0.840187 | − | 0.542296i | \(-0.182445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 828.818i | − 2.47408i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 253.000 | 0.750742 | 0.375371 | − | 0.926875i | \(-0.377515\pi\) | ||||
0.375371 | + | 0.926875i | \(0.377515\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −92.9516 | −0.272585 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −199.186 | −0.580717 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 53.6656 | 0.154656 | 0.0773280 | − | 0.997006i | \(-0.475361\pi\) | ||||
0.0773280 | + | 0.997006i | \(0.475361\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 71.0141i | − 0.203479i | −0.994811 | − | 0.101739i | \(-0.967559\pi\) | ||||
0.994811 | − | 0.101739i | \(-0.0324408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 375.659i | − 1.06419i | −0.846684 | − | 0.532095i | \(-0.821405\pi\) | ||||
0.846684 | − | 0.532095i | \(-0.178595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 120.000i | 0.338028i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 379.552i | 1.05725i | 0.848856 | + | 0.528624i | \(0.177292\pi\) | ||||
−0.848856 | + | 0.528624i | \(0.822708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −168.000 | −0.465374 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 751.359 | 2.05852 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −334.286 | −0.910861 | −0.455430 | − | 0.890271i | \(-0.650515\pi\) | ||||
−0.455430 | + | 0.890271i | \(0.650515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 670.820 | 1.80814 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 233.827i | 0.626882i | 0.949608 | + | 0.313441i | \(0.101482\pi\) | ||||
−0.949608 | + | 0.313441i | \(0.898518\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 160.997i | − 0.427047i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 349.000i | − 0.920844i | −0.887700 | − | 0.460422i | \(-0.847698\pi\) | ||||
0.887700 | − | 0.460422i | \(-0.152302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 635.169i | 1.65841i | 0.558948 | + | 0.829203i | \(0.311205\pi\) | ||||
−0.558948 | + | 0.829203i | \(0.688795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 900.000 | 2.33766 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −224.633 | −0.577463 | −0.288731 | − | 0.957410i | \(-0.593233\pi\) | ||||
−0.288731 | + | 0.957410i | \(0.593233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 103.923 | 0.265788 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 523.240 | 1.32466 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 90.0666i | − 0.226868i | −0.993546 | − | 0.113434i | \(-0.963815\pi\) | ||||
0.993546 | − | 0.113434i | \(-0.0361851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 429.325i | − 1.07064i | −0.844651 | − | 0.535318i | \(-0.820192\pi\) | ||||
0.844651 | − | 0.535318i | \(-0.179808\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0000i | 0.0893300i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 395.044i | 0.970625i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −469.000 | −1.14670 | −0.573350 | − | 0.819311i | \(-0.694356\pi\) | ||||
−0.573350 | + | 0.819311i | \(0.694356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 813.327 | 1.96931 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −308.577 | −0.736462 | −0.368231 | − | 0.929734i | \(-0.620036\pi\) | ||||
−0.368231 | + | 0.929734i | \(0.620036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 154.153i | − 0.366158i | −0.983098 | − | 0.183079i | \(-0.941394\pi\) | ||||
0.983098 | − | 0.183079i | \(-0.0586064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 469.574i | 1.10488i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 525.000i | − 1.22951i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 317.585i | − 0.736855i | −0.929656 | − | 0.368428i | \(-0.879896\pi\) | ||||
0.929656 | − | 0.368428i | \(-0.120104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −398.000 | −0.919169 | −0.459584 | − | 0.888134i | \(-0.652002\pi\) | ||||
−0.459584 | + | 0.888134i | \(0.652002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −178.157 | −0.407682 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −769.031 | −1.75178 | −0.875889 | − | 0.482513i | \(-0.839724\pi\) | ||||
−0.875889 | + | 0.482513i | \(0.839724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 563.489 | 1.27198 | 0.635992 | − | 0.771695i | \(-0.280591\pi\) | ||||
0.635992 | + | 0.771695i | \(0.280591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1351.00i | 3.03595i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 40.2492i | − 0.0896419i | −0.998995 | − | 0.0448210i | \(-0.985728\pi\) | ||||
0.998995 | − | 0.0448210i | \(-0.0142717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1080.00i | − 2.39468i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 348.569i | − 0.766085i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 326.000 | 0.713348 | 0.356674 | − | 0.934229i | \(-0.383911\pi\) | ||||
0.356674 | + | 0.934229i | \(0.383911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 766.851 | 1.66345 | 0.831725 | − | 0.555187i | \(-0.187353\pi\) | ||||
0.831725 | + | 0.555187i | \(0.187353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −150.688 | −0.325461 | −0.162730 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162730 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −120.748 | −0.258560 | −0.129280 | − | 0.991608i | \(-0.541267\pi\) | ||||
−0.129280 | + | 0.991608i | \(0.541267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 926.647i | 1.97579i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 509.823i | − 1.07785i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 805.000i | − 1.69474i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 511.234i | 1.06729i | 0.845707 | + | 0.533647i | \(0.179179\pi\) | ||||
−0.845707 | + | 0.533647i | \(0.820821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 153.000 | 0.318087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −844.310 | −1.74085 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 472.850 | 0.970944 | 0.485472 | − | 0.874252i | \(-0.338648\pi\) | ||||
0.485472 | + | 0.874252i | \(0.338648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 415.909 | 0.847064 | 0.423532 | − | 0.905881i | \(-0.360790\pi\) | ||||
0.423532 | + | 0.905881i | \(0.360790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 415.692i | − 0.843189i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 134.164i | − 0.269948i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 506.000i | 1.01403i | 0.861938 | + | 0.507014i | \(0.169251\pi\) | ||||
−0.861938 | + | 0.507014i | \(0.830749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 286.601i | − 0.569783i | −0.958560 | − | 0.284891i | \(-0.908042\pi\) | ||||
0.958560 | − | 0.284891i | \(-0.0919575\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1320.00 | −2.61386 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −178.157 | −0.350014 | −0.175007 | − | 0.984567i | \(-0.555995\pi\) | ||||
−0.175007 | + | 0.984567i | \(0.555995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −840.045 | −1.64392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1435.56 | −2.78749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 727.461i | 1.40708i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 254.912i | − 0.489274i | −0.969615 | − | 0.244637i | \(-0.921331\pi\) | ||||
0.969615 | − | 0.244637i | \(-0.0786688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 839.000i | 1.60421i | 0.597185 | + | 0.802103i | \(0.296286\pi\) | ||||
−0.597185 | + | 0.802103i | \(0.703714\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 92.9516i | 0.176379i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 469.000 | 0.886578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −418.282 | −0.784770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −103.923 | −0.194249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −348.827 | −0.647174 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 510.955i | 0.944464i | 0.881474 | + | 0.472232i | \(0.156552\pi\) | ||||
−0.881474 | + | 0.472232i | \(0.843448\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1556.30i | 2.85560i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0000i | 0.0237660i | 0.999929 | + | 0.0118830i | \(0.00378256\pi\) | ||||
−0.999929 | + | 0.0118830i | \(0.996217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 712.629i | 1.29334i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −585.000 | −1.05787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −720.375 | −1.29331 | −0.646656 | − | 0.762782i | \(-0.723833\pi\) | ||||
−0.646656 | + | 0.762782i | \(0.723833\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −197.454 | −0.353227 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 348.827 | 0.619585 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 103.923i | − 0.183935i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 415.909i | − 0.730947i | −0.930822 | − | 0.365473i | \(-0.880907\pi\) | ||||
0.930822 | − | 0.365473i | \(-0.119093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 287.000i | − 0.502627i | −0.967906 | − | 0.251313i | \(-0.919137\pi\) | ||||
0.967906 | − | 0.251313i | \(-0.0808625\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 271.109i | − 0.471494i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 169.000 | 0.292894 | 0.146447 | − | 0.989218i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989218i | \(0.453216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1039.23 | −1.78256 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −442.741 | −0.754244 | −0.377122 | − | 0.926164i | \(-0.623086\pi\) | ||||
−0.377122 | + | 0.926164i | \(0.623086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 159.349i | − 0.270541i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 751.319i | − 1.26698i | −0.773751 | − | 0.633490i | \(-0.781622\pi\) | ||||
0.773751 | − | 0.633490i | \(-0.218378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 900.000i | − 1.51261i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 123.935i | − 0.206904i | −0.994634 | − | 0.103452i | \(-0.967011\pi\) | ||||
0.994634 | − | 0.103452i | \(-0.0329888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −346.000 | −0.575707 | −0.287854 | − | 0.957674i | \(-0.592942\pi\) | ||||
−0.287854 | + | 0.957674i | \(0.592942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −457.012 | −0.755392 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −698.016 | −1.14994 | −0.574972 | − | 0.818173i | \(-0.694987\pi\) | ||||
−0.574972 | + | 0.818173i | \(0.694987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 281.745 | 0.461120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 497.099i | − 0.810928i | −0.914111 | − | 0.405464i | \(-0.867110\pi\) | ||||
0.914111 | − | 0.405464i | \(-0.132890\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 818.401i | 1.32642i | 0.748434 | + | 0.663210i | \(0.230806\pi\) | ||||
−0.748434 | + | 0.663210i | \(0.769194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 277.000i | 0.447496i | 0.974647 | + | 0.223748i | \(0.0718293\pi\) | ||||
−0.974647 | + | 0.223748i | \(0.928171\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1510.46i | − 2.42450i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −275.000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 395.044 | 0.628051 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −278.860 | −0.441934 | −0.220967 | − | 0.975281i | \(-0.570921\pi\) | ||||
−0.220967 | + | 0.975281i | \(0.570921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1073.31 | −1.69026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 135.100i | 0.212088i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 778.152i | 1.21397i | 0.794715 | + | 0.606983i | \(0.207620\pi\) | ||||
−0.794715 | + | 0.606983i | \(0.792380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 466.000i | 0.724728i | 0.932037 | + | 0.362364i | \(0.118030\pi\) | ||||
−0.932037 | + | 0.362364i | \(0.881970\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 852.056i | − 1.31693i | −0.752610 | − | 0.658467i | \(-0.771205\pi\) | ||||
0.752610 | − | 0.658467i | \(-0.228795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1260.00 | −1.94145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −185.903 | −0.284691 | −0.142345 | − | 0.989817i | \(-0.545464\pi\) | ||||
−0.142345 | + | 0.989817i | \(0.545464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1662.77 | −2.53858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 295.161 | 0.447892 | 0.223946 | − | 0.974602i | \(-0.428106\pi\) | ||||
0.223946 | + | 0.974602i | \(0.428106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1124.10i | 1.70061i | 0.526293 | + | 0.850303i | \(0.323582\pi\) | ||||
−0.526293 | + | 0.850303i | \(0.676418\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1542.89i | 2.32013i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 240.000i | 0.359820i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 813.327i | 1.21211i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.0000 | 0.0549777 | 0.0274889 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274889 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 735.867 | 1.08695 | 0.543476 | − | 0.839425i | \(-0.317108\pi\) | ||||
0.543476 | + | 0.839425i | \(0.317108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 943.968 | 1.39023 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1153.81 | −1.68933 | −0.844664 | − | 0.535297i | \(-0.820200\pi\) | ||||
−0.844664 | + | 0.535297i | \(0.820200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 935.307i | 1.36541i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 402.492i | 0.584169i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 662.000i | − 0.958032i | −0.877806 | − | 0.479016i | \(-0.840994\pi\) | ||||
0.877806 | − | 0.479016i | \(-0.159006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 379.552i | − 0.546119i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1080.00 | −1.54950 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1045.71 | 1.49173 | 0.745867 | − | 0.666095i | \(-0.232035\pi\) | ||||
0.745867 | + | 0.666095i | \(0.232035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −677.232 | −0.963345 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1475.80 | 2.08742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 129.904i | 0.183221i | 0.995795 | + | 0.0916106i | \(0.0292015\pi\) | ||||
−0.995795 | + | 0.0916106i | \(0.970799\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 53.6656i | − 0.0752674i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 540.000i | 0.755245i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 92.9516i | 0.129279i | 0.997909 | + | 0.0646395i | \(0.0205897\pi\) | ||||
−0.997909 | + | 0.0646395i | \(0.979410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1605.00 | 2.22607 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1084.44 | −1.49577 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 810.600 | 1.11499 | 0.557496 | − | 0.830179i | \(-0.311762\pi\) | ||||
0.557496 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −509.823 | −0.697433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 658.179i | − 0.897925i | −0.893551 | − | 0.448963i | \(-0.851794\pi\) | ||||
0.893551 | − | 0.448963i | \(-0.148206\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1435.56i | − 1.94784i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 82.0000i | − 0.110961i | −0.998460 | − | 0.0554804i | \(-0.982331\pi\) | ||||
0.998460 | − | 0.0554804i | \(-0.0176690\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 704.883i | 0.948698i | 0.880337 | + | 0.474349i | \(0.157317\pi\) | ||||
−0.880337 | + | 0.474349i | \(0.842683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1080.00 | −1.44966 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 116.190 | 0.155126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 465.922 | 0.620402 | 0.310201 | − | 0.950671i | \(-0.399604\pi\) | ||||
0.310201 | + | 0.950671i | \(0.399604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1274.56 | −1.68816 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 147.224i | − 0.194484i | −0.995261 | − | 0.0972420i | \(-0.968998\pi\) | ||||
0.995261 | − | 0.0972420i | \(-0.0310021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 40.2492i | − 0.0528899i | −0.999650 | − | 0.0264450i | \(-0.991581\pi\) | ||||
0.999650 | − | 0.0264450i | \(-0.00841867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1740.00i | − 2.28047i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 487.996i | 0.636240i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 551.000 | 0.716515 | 0.358257 | − | 0.933623i | \(-0.383371\pi\) | ||||
0.358257 | + | 0.933623i | \(0.383371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 588.693 | 0.761570 | 0.380785 | − | 0.924664i | \(-0.375654\pi\) | ||||
0.380785 | + | 0.924664i | \(0.375654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 242.487 | 0.312887 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1851.46 | 2.37672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 207.846i | 0.266128i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 1234.31i | − 1.57237i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 71.0000i | − 0.0902160i | −0.998982 | − | 0.0451080i | \(-0.985637\pi\) | ||||
0.998982 | − | 0.0451080i | \(-0.0143632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 116.190i | 0.146889i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 315.000 | 0.397226 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −635.169 | −0.796950 | −0.398475 | − | 0.917179i | \(-0.630460\pi\) | ||||
−0.398475 | + | 0.917179i | \(0.630460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 727.461 | 0.910465 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1301.39 | 1.62066 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 519.615i | 0.645485i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1100.15i | − 1.35988i | −0.733266 | − | 0.679942i | \(-0.762005\pi\) | ||||
0.733266 | − | 0.679942i | \(-0.237995\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 974.000i | 1.20099i | 0.799630 | + | 0.600493i | \(0.205029\pi\) | ||||
−0.799630 | + | 0.600493i | \(0.794971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 751.359i | − 0.921913i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 874.000 | 1.06977 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 689.391 | 0.839697 | 0.419848 | − | 0.907594i | \(-0.362083\pi\) | ||||
0.419848 | + | 0.907594i | \(0.362083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −410.496 | −0.498780 | −0.249390 | − | 0.968403i | \(-0.580230\pi\) | ||||
−0.249390 | + | 0.968403i | \(0.580230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1033.06 | 1.24917 | 0.624585 | − | 0.780957i | \(-0.285268\pi\) | ||||
0.624585 | + | 0.780957i | \(0.285268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 348.142i | 0.419954i | 0.977706 | + | 0.209977i | \(0.0673390\pi\) | ||||
−0.977706 | + | 0.209977i | \(0.932661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 348.827i | 0.418759i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 300.000i | 0.359281i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 728.121i | − 0.867844i | −0.900951 | − | 0.433922i | \(-0.857129\pi\) | ||||
0.900951 | − | 0.433922i | \(-0.142871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 119.000 | 0.141498 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1099.93 | −1.30169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 510.955 | 0.603253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −228.079 | −0.268013 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1103.32i | − 1.29345i | −0.762722 | − | 0.646727i | \(-0.776137\pi\) | ||||
0.762722 | − | 0.646727i | \(-0.223863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.8328i | 0.0313102i | 0.999877 | + | 0.0156551i | \(0.00498337\pi\) | ||||
−0.999877 | + | 0.0156551i | \(0.995017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1549.00i | − 1.80326i | −0.432509 | − | 0.901630i | \(-0.642371\pi\) | ||||
0.432509 | − | 0.901630i | \(-0.357629\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1309.07i | 1.51688i | 0.651742 | + | 0.758441i | \(0.274038\pi\) | ||||
−0.651742 | + | 0.758441i | \(0.725962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 600.000 | 0.693642 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 906.278 | 1.04290 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −555.988 | −0.638333 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −670.820 | −0.766652 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 8.66025i | − 0.00987486i | −0.999988 | − | 0.00493743i | \(-0.998428\pi\) | ||||
0.999988 | − | 0.00493743i | \(-0.00157164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 389.076i | 0.441630i | 0.975316 | + | 0.220815i | \(0.0708717\pi\) | ||||
−0.975316 | + | 0.220815i | \(0.929128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 61.0000i | 0.0690827i | 0.999403 | + | 0.0345413i | \(0.0109970\pi\) | ||||
−0.999403 | + | 0.0345413i | \(0.989003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1208.37i | 1.36231i | 0.732138 | + | 0.681156i | \(0.238522\pi\) | ||||
−0.732138 | + | 0.681156i | \(0.761478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1200.00 | 1.34983 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1247.10 | −1.39653 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −207.846 | −0.232230 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −214.663 | −0.238779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1039.23i | 1.15342i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1355.06i | − 1.49730i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 433.000i | − 0.477398i | −0.971094 | − | 0.238699i | \(-0.923279\pi\) | ||||
0.971094 | − | 0.238699i | \(-0.0767209\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1595.67i | 1.75156i | 0.482712 | + | 0.875779i | \(0.339652\pi\) | ||||
−0.482712 | + | 0.875779i | \(0.660348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1859.03 | 2.02730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −145.492 | −0.158316 | −0.0791579 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791579 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.4984 | 0.0872139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1030.57i | − 1.11413i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 536.656i | − 0.577671i | −0.957379 | − | 0.288835i | \(-0.906732\pi\) | ||||
0.957379 | − | 0.288835i | \(-0.0932681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 598.000i | − 0.642320i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1394.27i | 1.49120i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 469.000 | 0.500534 | 0.250267 | − | 0.968177i | \(-0.419482\pi\) | ||||
0.250267 | + | 0.968177i | \(0.419482\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −472.504 | −0.502130 | −0.251065 | − | 0.967970i | \(-0.580781\pi\) | ||||
−0.251065 | + | 0.967970i | \(0.580781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 623.538 | 0.661228 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 576.906 | 0.609193 | 0.304596 | − | 0.952482i | \(-0.401478\pi\) | ||||
0.304596 | + | 0.952482i | \(0.401478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 504.027i | − 0.531114i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 845.234i | − 0.886919i | −0.896294 | − | 0.443459i | \(-0.853751\pi\) | ||||
0.896294 | − | 0.443459i | \(-0.146249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1380.00i | 1.44503i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1045.71i | − 1.09041i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −913.000 | −0.950052 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −457.012 | −0.473588 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 999.393 | 1.03350 | 0.516749 | − | 0.856137i | \(-0.327142\pi\) | ||||
0.516749 | + | 0.856137i | \(0.327142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 469.574 | 0.483599 | 0.241799 | − | 0.970326i | \(-0.422262\pi\) | ||||
0.241799 | + | 0.970326i | \(0.422262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 424.352i | 0.436128i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 536.656i | − 0.549290i | −0.961546 | − | 0.274645i | \(-0.911440\pi\) | ||||
0.961546 | − | 0.274645i | \(-0.0885603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2340.00i | 2.39019i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1231.61i | − 1.25291i | −0.779458 | − | 0.626454i | \(-0.784506\pi\) | ||||
0.779458 | − | 0.626454i | \(-0.215494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −180.000 | −0.182741 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 294.347 | 0.297621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.3013 | −0.0436945 | −0.0218473 | − | 0.999761i | \(-0.506955\pi\) | ||||
−0.0218473 | + | 0.999761i | \(0.506955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −684.237 | −0.687675 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1558.85i | − 1.56354i | −0.623569 | − | 0.781768i | \(-0.714318\pi\) | ||||
0.623569 | − | 0.781768i | \(-0.285682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.3.h.h.161.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.3.h.h.161.8 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.3.h.h.161.2 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.3.h.h.161.5 | yes | 8 | |
8.5 | even | 2 | inner | 1728.3.h.h.161.7 | yes | 8 | |
12.11 | even | 2 | inner | 1728.3.h.h.161.6 | yes | 8 | |
24.5 | odd | 2 | inner | 1728.3.h.h.161.3 | yes | 8 | |
24.11 | even | 2 | inner | 1728.3.h.h.161.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.h.h.161.1 | ✓ | 8 | 24.11 | even | 2 | inner | |
1728.3.h.h.161.2 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.3.h.h.161.3 | yes | 8 | 24.5 | odd | 2 | inner | |
1728.3.h.h.161.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.3.h.h.161.5 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.3.h.h.161.6 | yes | 8 | 12.11 | even | 2 | inner | |
1728.3.h.h.161.7 | yes | 8 | 8.5 | even | 2 | inner | |
1728.3.h.h.161.8 | yes | 8 | 3.2 | odd | 2 | inner |