Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 68.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.68 |
Dual form | 75.2.e.a.32.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 1.22474i | −0.866025 | − | 0.866025i | 0.126004 | − | 0.992030i | \(-0.459785\pi\) |
−0.992030 | + | 0.126004i | \(0.959785\pi\) | |||||||
\(3\) | 1.22474 | − | 1.22474i | 0.707107 | − | 0.707107i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −1.22474 | + | 1.22474i | −0.433013 | + | 0.433013i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 1.22474 | + | 1.22474i | 0.353553 | + | 0.353553i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 1.25000 | ||||||||
\(17\) | 4.89898 | + | 4.89898i | 1.18818 | + | 1.18818i | 0.977571 | + | 0.210606i | \(0.0675437\pi\) |
0.210606 | + | 0.977571i | \(0.432456\pi\) | |||||||
\(18\) | −3.67423 | + | 3.67423i | −0.866025 | + | 0.866025i | ||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.44949 | − | 2.44949i | 0.510754 | − | 0.510754i | −0.404004 | − | 0.914757i | \(-0.632382\pi\) |
0.914757 | + | 0.404004i | \(0.132382\pi\) | |||||||
\(24\) | 3.00000i | 0.612372i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −3.67423 | − | 3.67423i | −0.649519 | − | 0.649519i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 12.0000i | − | 2.05798i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 4.89898 | − | 4.89898i | 0.794719 | − | 0.794719i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −7.34847 | − | 7.34847i | −1.07188 | − | 1.07188i | −0.997208 | − | 0.0746766i | \(-0.976208\pi\) |
−0.0746766 | − | 0.997208i | \(-0.523792\pi\) | |||||||
\(48\) | 6.12372 | − | 6.12372i | 0.883883 | − | 0.883883i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | 1.68034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.79796 | + | 9.79796i | −1.34585 | + | 1.34585i | −0.455740 | + | 0.890113i | \(0.650625\pi\) |
−0.890113 | + | 0.455740i | \(0.849375\pi\) | |||||||
\(54\) | 9.00000i | 1.22474i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.89898 | + | 4.89898i | 0.648886 | + | 0.648886i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 9.79796 | + | 9.79796i | 1.24434 | + | 1.24434i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | −4.89898 | + | 4.89898i | −0.594089 | + | 0.594089i | ||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 3.67423 | + | 3.67423i | 0.433013 | + | 0.433013i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16.0000i | − | 1.80014i | −0.435745 | − | 0.900070i | \(-0.643515\pi\) | ||
0.435745 | − | 0.900070i | \(-0.356485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44949 | − | 2.44949i | 0.268866 | − | 0.268866i | −0.559777 | − | 0.828643i | \(-0.689113\pi\) |
0.828643 | + | 0.559777i | \(0.189113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.44949 | + | 2.44949i | 0.255377 | + | 0.255377i | ||||
\(93\) | −9.79796 | + | 9.79796i | −1.01600 | + | 1.01600i | ||||
\(94\) | 18.0000i | 1.85656i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.00000 | −0.918559 | ||||||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | 8.57321 | − | 8.57321i | 0.866025 | − | 0.866025i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −14.6969 | − | 14.6969i | −1.45521 | − | 1.45521i | ||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.0000 | 2.33109 | ||||||||
\(107\) | −7.34847 | − | 7.34847i | −0.710403 | − | 0.710403i | 0.256216 | − | 0.966620i | \(-0.417524\pi\) |
−0.966620 | + | 0.256216i | \(0.917524\pi\) | |||||||
\(108\) | 3.67423 | − | 3.67423i | 0.353553 | − | 0.353553i | ||||
\(109\) | 14.0000i | 1.34096i | 0.741929 | + | 0.670478i | \(0.233911\pi\) | ||||
−0.741929 | + | 0.670478i | \(0.766089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6969 | − | 14.6969i | 1.38257 | − | 1.38257i | 0.542545 | − | 0.840027i | \(-0.317461\pi\) |
0.840027 | − | 0.542545i | \(-0.182539\pi\) | |||||||
\(114\) | − | 12.0000i | − | 1.12390i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | −2.44949 | − | 2.44949i | −0.221766 | − | 0.221766i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.00000i | − | 0.718421i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | −8.57321 | + | 8.57321i | −0.757772 | + | 0.757772i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | −1.02899 | ||||||||
\(137\) | 4.89898 | + | 4.89898i | 0.418548 | + | 0.418548i | 0.884703 | − | 0.466155i | \(-0.154361\pi\) |
−0.466155 | + | 0.884703i | \(0.654361\pi\) | |||||||
\(138\) | −7.34847 | + | 7.34847i | −0.625543 | + | 0.625543i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 15.0000i | − | 1.25000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.57321 | + | 8.57321i | 0.707107 | + | 0.707107i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −4.89898 | − | 4.89898i | −0.397360 | − | 0.397360i | ||||
\(153\) | 14.6969 | − | 14.6969i | 1.18818 | − | 1.18818i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | −19.5959 | + | 19.5959i | −1.55897 | + | 1.55897i | ||||
\(159\) | 24.0000i | 1.90332i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.0227 | + | 11.0227i | 0.866025 | + | 0.866025i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 17.1464 | + | 17.1464i | 1.32683 | + | 1.32683i | 0.908120 | + | 0.418711i | \(0.137518\pi\) |
0.418711 | + | 0.908120i | \(0.362482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79796 | + | 9.79796i | −0.744925 | + | 0.744925i | −0.973521 | − | 0.228596i | \(-0.926586\pi\) |
0.228596 | + | 0.973521i | \(0.426586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.44949 | − | 2.44949i | 0.181071 | − | 0.181071i | ||||
\(184\) | 6.00000i | 0.442326i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 24.0000 | 1.75977 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.34847 | − | 7.34847i | 0.535942 | − | 0.535942i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −1.22474 | − | 1.22474i | −0.0883883 | − | 0.0883883i | ||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −19.5959 | − | 19.5959i | −1.39615 | − | 1.39615i | −0.810727 | − | 0.585424i | \(-0.800928\pi\) |
−0.585424 | − | 0.810727i | \(-0.699072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.0000i | − | 1.13421i | −0.823646 | − | 0.567105i | \(-0.808063\pi\) | ||
0.823646 | − | 0.567105i | \(-0.191937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0000i | 0.840168i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.34847 | − | 7.34847i | −0.510754 | − | 0.510754i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | −9.79796 | − | 9.79796i | −0.672927 | − | 0.672927i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000i | 1.23045i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.1464 | − | 17.1464i | 1.16130 | − | 1.16130i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.0000 | −2.39468 | ||||||||
\(227\) | 17.1464 | + | 17.1464i | 1.13805 | + | 1.13805i | 0.988800 | + | 0.149249i | \(0.0476855\pi\) |
0.149249 | + | 0.988800i | \(0.452314\pi\) | |||||||
\(228\) | −4.89898 | + | 4.89898i | −0.324443 | + | 0.324443i | ||||
\(229\) | − | 26.0000i | − | 1.71813i | −0.511868 | − | 0.859064i | \(-0.671046\pi\) | ||
0.511868 | − | 0.859064i | \(-0.328954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6969 | − | 14.6969i | 0.962828 | − | 0.962828i | −0.0365050 | − | 0.999333i | \(-0.511622\pi\) |
0.999333 | + | 0.0365050i | \(0.0116225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.5959 | − | 19.5959i | −1.27289 | − | 1.27289i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | −13.4722 | − | 13.4722i | −0.866025 | − | 0.866025i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.707107 | + | 0.707107i | ||||
\(244\) | 2.00000i | 0.128037i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.79796 | − | 9.79796i | 0.622171 | − | 0.622171i | ||||
\(249\) | − | 6.00000i | − | 0.380235i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 4.89898 | + | 4.89898i | 0.305590 | + | 0.305590i | 0.843196 | − | 0.537606i | \(-0.180671\pi\) |
−0.537606 | + | 0.843196i | \(0.680671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.0454 | + | 22.0454i | −1.35938 | + | 1.35938i | −0.484695 | + | 0.874683i | \(0.661069\pi\) |
−0.874683 | + | 0.484695i | \(0.838931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0000 | 1.94386 | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) | ||||
0.971931 | + | 0.235267i | \(0.0755965\pi\) | |||||||
\(272\) | 24.4949 | + | 24.4949i | 1.48522 | + | 1.48522i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 12.0000i | − | 0.724947i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 4.89898 | − | 4.89898i | 0.293821 | − | 0.293821i | ||||
\(279\) | 24.0000i | 1.43684i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 22.0454 | + | 22.0454i | 1.31278 | + | 1.31278i | ||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.0227 | + | 11.0227i | −0.649519 | + | 0.649519i | ||||
\(289\) | 31.0000i | 1.82353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.79796 | + | 9.79796i | −0.572403 | + | 0.572403i | −0.932799 | − | 0.360396i | \(-0.882641\pi\) |
0.360396 | + | 0.932799i | \(0.382641\pi\) | |||||||
\(294\) | − | 21.0000i | − | 1.22474i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.79796 | + | 9.79796i | 0.563809 | + | 0.563809i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.0000i | 1.14708i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −36.0000 | −2.05798 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −19.5959 | − | 19.5959i | −1.10062 | − | 1.10062i | −0.994336 | − | 0.106280i | \(-0.966106\pi\) |
−0.106280 | − | 0.994336i | \(-0.533894\pi\) | |||||||
\(318\) | 29.3939 | − | 29.3939i | 1.64833 | − | 1.64833i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5959 | + | 19.5959i | −1.09035 | + | 1.09035i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.1464 | + | 17.1464i | 0.948200 | + | 0.948200i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 2.44949 | + | 2.44949i | 0.134433 | + | 0.134433i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 42.0000i | − | 2.29814i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | −15.9217 | + | 15.9217i | −0.866025 | + | 0.866025i | ||||
\(339\) | − | 36.0000i | − | 1.95525i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −14.6969 | − | 14.6969i | −0.794719 | − | 0.794719i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | 1.29025 | ||||||||
\(347\) | −7.34847 | − | 7.34847i | −0.394486 | − | 0.394486i | 0.481797 | − | 0.876283i | \(-0.339984\pi\) |
−0.876283 | + | 0.481797i | \(0.839984\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.0000i | 1.81998i | 0.414632 | + | 0.909989i | \(0.363910\pi\) | ||||
−0.414632 | + | 0.909989i | \(0.636090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.6969 | − | 14.6969i | 0.782239 | − | 0.782239i | −0.197969 | − | 0.980208i | \(-0.563435\pi\) |
0.980208 | + | 0.197969i | \(0.0634346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −26.9444 | − | 26.9444i | −1.41617 | − | 1.41617i | ||||
\(363\) | 13.4722 | − | 13.4722i | 0.707107 | − | 0.707107i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(368\) | 12.2474 | − | 12.2474i | 0.638442 | − | 0.638442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.79796 | − | 9.79796i | −0.508001 | − | 0.508001i | ||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.0000 | 0.928279 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.9444 | − | 26.9444i | 1.37679 | − | 1.37679i | 0.526812 | − | 0.849982i | \(-0.323387\pi\) |
0.849982 | − | 0.526812i | \(-0.176613\pi\) | |||||||
\(384\) | 21.0000i | 1.07165i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −8.57321 | − | 8.57321i | −0.433013 | − | 0.433013i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 48.0000i | 2.41821i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | −19.5959 | + | 19.5959i | −0.982255 | + | 0.982255i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.6969 | + | 14.6969i | −0.727607 | + | 0.727607i | ||||
\(409\) | − | 26.0000i | − | 1.28562i | −0.766027 | − | 0.642809i | \(-0.777769\pi\) | ||
0.766027 | − | 0.642809i | \(-0.222231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.0000i | 0.884652i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.89898 | + | 4.89898i | 0.239904 | + | 0.239904i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0000 | −1.85201 | −0.926003 | − | 0.377515i | \(-0.876779\pi\) | ||||
−0.926003 | + | 0.377515i | \(0.876779\pi\) | |||||||
\(422\) | 34.2929 | + | 34.2929i | 1.66935 | + | 1.66935i | ||||
\(423\) | −22.0454 | + | 22.0454i | −1.07188 | + | 1.07188i | ||||
\(424\) | − | 24.0000i | − | 1.16554i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.34847 | − | 7.34847i | 0.355202 | − | 0.355202i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −18.3712 | − | 18.3712i | −0.883883 | − | 0.883883i | ||||
\(433\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | 9.79796 | + | 9.79796i | 0.468700 | + | 0.468700i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.0000i | − | 0.763638i | −0.924237 | − | 0.381819i | \(-0.875298\pi\) | ||
0.924237 | − | 0.381819i | \(-0.124702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.9444 | − | 26.9444i | 1.28017 | − | 1.28017i | 0.339595 | − | 0.940572i | \(-0.389710\pi\) |
0.940572 | − | 0.339595i | \(-0.110290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.6969 | + | 14.6969i | 0.691286 | + | 0.691286i | ||||
\(453\) | −9.79796 | + | 9.79796i | −0.460348 | + | 0.460348i | ||||
\(454\) | − | 42.0000i | − | 1.97116i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | −31.8434 | + | 31.8434i | −1.48794 | + | 1.48794i | ||||
\(459\) | − | 36.0000i | − | 1.68034i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −36.0000 | −1.66767 | ||||||||
\(467\) | 17.1464 | + | 17.1464i | 0.793442 | + | 0.793442i | 0.982052 | − | 0.188610i | \(-0.0603982\pi\) |
−0.188610 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 48.0000i | 2.20471i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.3939 | + | 29.3939i | 1.34585 | + | 1.34585i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.44949 | − | 2.44949i | −0.111571 | − | 0.111571i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.0000i | 0.500000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 27.0000 | 1.22474 | ||||||||
\(487\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(488\) | −2.44949 | + | 2.44949i | −0.110883 | + | 0.110883i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −40.0000 | −1.79605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.34847 | + | 7.34847i | −0.329293 | + | 0.329293i | ||||
\(499\) | 44.0000i | 1.96971i | 0.173379 | + | 0.984855i | \(0.444532\pi\) | ||||
−0.173379 | + | 0.984855i | \(0.555468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.0000 | 1.87642 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.44949 | − | 2.44949i | 0.109217 | − | 0.109217i | −0.650386 | − | 0.759604i | \(-0.725393\pi\) |
0.759604 | + | 0.650386i | \(0.225393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.9217 | − | 15.9217i | −0.707107 | − | 0.707107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.12372 | − | 6.12372i | −0.270633 | − | 0.270633i | ||||
\(513\) | 14.6969 | − | 14.6969i | 0.648886 | − | 0.648886i | ||||
\(514\) | − | 12.0000i | − | 0.529297i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.0000i | 1.05348i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 54.0000 | 2.35451 | ||||||||
\(527\) | −39.1918 | − | 39.1918i | −1.70722 | − | 1.70722i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000i | 0.478261i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | −39.1918 | − | 39.1918i | −1.68343 | − | 1.68343i | ||||
\(543\) | 26.9444 | − | 26.9444i | 1.15629 | − | 1.15629i | ||||
\(544\) | − | 36.0000i | − | 1.54349i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | −4.89898 | + | 4.89898i | −0.209274 | + | 0.209274i | ||||
\(549\) | − | 6.00000i | − | 0.256074i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 7.34847 | + | 7.34847i | 0.312772 | + | 0.312772i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 29.3939 | + | 29.3939i | 1.24546 | + | 1.24546i | 0.957704 | + | 0.287754i | \(0.0929086\pi\) |
0.287754 | + | 0.957704i | \(0.407091\pi\) | |||||||
\(558\) | 29.3939 | − | 29.3939i | 1.24434 | − | 1.24434i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0454 | + | 22.0454i | −0.929103 | + | 0.929103i | −0.997648 | − | 0.0685449i | \(-0.978164\pi\) |
0.0685449 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(564\) | − | 18.0000i | − | 0.757937i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 37.9671 | − | 37.9671i | 1.57922 | − | 1.57922i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | −31.8434 | − | 31.8434i | −1.31432 | − | 1.31432i | −0.918201 | − | 0.396116i | \(-0.870358\pi\) |
−0.396116 | − | 0.918201i | \(-0.629642\pi\) | |||||||
\(588\) | −8.57321 | + | 8.57321i | −0.353553 | + | 0.353553i | ||||
\(589\) | − | 32.0000i | − | 1.31854i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −48.0000 | −1.97446 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2929 | + | 34.2929i | −1.40824 | + | 1.40824i | −0.639190 | + | 0.769049i | \(0.720730\pi\) |
−0.769049 | + | 0.639190i | \(0.779270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5959 | − | 19.5959i | −0.802008 | − | 0.802008i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.0000 | −1.55005 | −0.775026 | − | 0.631929i | \(-0.782263\pi\) | ||||
−0.775026 | + | 0.631929i | \(0.782263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.00000i | − | 0.325515i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | 14.6969 | − | 14.6969i | 0.596040 | − | 0.596040i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 14.6969 | + | 14.6969i | 0.594089 | + | 0.594089i | ||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.89898 | + | 4.89898i | 0.197225 | + | 0.197225i | 0.798810 | − | 0.601584i | \(-0.205464\pi\) |
−0.601584 | + | 0.798810i | \(0.705464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.0000i | 1.76851i | 0.467005 | + | 0.884255i | \(0.345333\pi\) | ||||
−0.467005 | + | 0.884255i | \(0.654667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | −0.722315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 19.5959 | + | 19.5959i | 0.779484 | + | 0.779484i | ||||
\(633\) | −34.2929 | + | 34.2929i | −1.36302 | + | 1.36302i | ||||
\(634\) | 48.0000i | 1.90632i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.0000 | −0.951662 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 22.0454 | + | 22.0454i | 0.870063 | + | 0.870063i | ||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 48.0000 | 1.88853 | ||||||||
\(647\) | 17.1464 | + | 17.1464i | 0.674096 | + | 0.674096i | 0.958658 | − | 0.284562i | \(-0.0918482\pi\) |
−0.284562 | + | 0.958658i | \(0.591848\pi\) | |||||||
\(648\) | 11.0227 | − | 11.0227i | 0.433013 | − | 0.433013i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.79796 | + | 9.79796i | −0.383424 | + | 0.383424i | −0.872334 | − | 0.488910i | \(-0.837395\pi\) |
0.488910 | + | 0.872334i | \(0.337395\pi\) | |||||||
\(654\) | − | 42.0000i | − | 1.64233i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 34.2929 | + | 34.2929i | 1.33283 | + | 1.33283i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −17.1464 | + | 17.1464i | −0.663415 | + | 0.663415i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | 29.3939 | + | 29.3939i | 1.12970 | + | 1.12970i | 0.990226 | + | 0.139473i | \(0.0445407\pi\) |
0.139473 | + | 0.990226i | \(0.455459\pi\) | |||||||
\(678\) | −44.0908 | + | 44.0908i | −1.69330 | + | 1.69330i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.0000 | 1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.9444 | − | 26.9444i | 1.03100 | − | 1.03100i | 0.0314944 | − | 0.999504i | \(-0.489973\pi\) |
0.999504 | − | 0.0314944i | \(-0.0100266\pi\) | |||||||
\(684\) | 12.0000i | 0.458831i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.8434 | − | 31.8434i | −1.21490 | − | 1.21490i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 52.0000 | 1.97817 | 0.989087 | − | 0.147335i | \(-0.0470696\pi\) | ||||
0.989087 | + | 0.147335i | \(0.0470696\pi\) | |||||||
\(692\) | −9.79796 | − | 9.79796i | −0.372463 | − | 0.372463i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.0000i | 0.683271i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 41.6413 | − | 41.6413i | 1.57615 | − | 1.57615i | ||||
\(699\) | − | 36.0000i | − | 1.36165i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.0000 | −1.35488 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 26.0000i | − | 0.976450i | −0.872718 | − | 0.488225i | \(-0.837644\pi\) | ||
0.872718 | − | 0.488225i | \(-0.162356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.0000 | −1.80014 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.5959 | + | 19.5959i | −0.733873 | + | 0.733873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.67423 | − | 3.67423i | −0.136741 | − | 0.136741i | ||||
\(723\) | 2.44949 | − | 2.44949i | 0.0910975 | − | 0.0910975i | ||||
\(724\) | 22.0000i | 0.817624i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −33.0000 | −1.22474 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.44949 | + | 2.44949i | 0.0905357 | + | 0.0905357i | ||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.0000 | −0.663489 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0454 | + | 22.0454i | −0.808768 | + | 0.808768i | −0.984447 | − | 0.175680i | \(-0.943788\pi\) |
0.175680 | + | 0.984447i | \(0.443788\pi\) | |||||||
\(744\) | − | 24.0000i | − | 0.879883i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.34847 | − | 7.34847i | −0.268866 | − | 0.268866i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | −36.7423 | − | 36.7423i | −1.33986 | − | 1.33986i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | 4.89898 | − | 4.89898i | 0.177939 | − | 0.177939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −66.0000 | −2.38468 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 23.2702 | − | 23.2702i | 0.839689 | − | 0.839689i | ||||
\(769\) | − | 46.0000i | − | 1.65880i | −0.558653 | − | 0.829401i | \(-0.688682\pi\) | ||
0.558653 | − | 0.829401i | \(-0.311318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.1918 | − | 39.1918i | 1.40963 | − | 1.40963i | 0.647947 | − | 0.761686i | \(-0.275628\pi\) |
0.761686 | − | 0.647947i | \(-0.224372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −29.3939 | − | 29.3939i | −1.05112 | − | 1.05112i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 35.0000i | 1.25000i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | 19.5959 | − | 19.5959i | 0.698076 | − | 0.698076i | ||||
\(789\) | 54.0000i | 1.92245i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | −19.5959 | − | 19.5959i | −0.694123 | − | 0.694123i | 0.269013 | − | 0.963136i | \(-0.413302\pi\) |
−0.963136 | + | 0.269013i | \(0.913302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 72.0000i | − | 2.54718i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.0000 | 1.82597 | 0.912983 | − | 0.407997i | \(-0.133772\pi\) | ||||
0.912983 | + | 0.407997i | \(0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.1918 | − | 39.1918i | 1.37452 | − | 1.37452i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 60.0000 | 2.10042 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −31.8434 | + | 31.8434i | −1.11338 | + | 1.11338i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | −14.6969 | − | 14.6969i | −0.512615 | − | 0.512615i | ||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8434 | − | 31.8434i | −1.10730 | − | 1.10730i | −0.993504 | − | 0.113799i | \(-0.963698\pi\) |
−0.113799 | − | 0.993504i | \(-0.536302\pi\) | |||||||
\(828\) | 7.34847 | − | 7.34847i | 0.255377 | − | 0.255377i | ||||
\(829\) | 34.0000i | 1.18087i | 0.807086 | + | 0.590434i | \(0.201044\pi\) | ||||
−0.807086 | + | 0.590434i | \(0.798956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.2929 | + | 34.2929i | −1.18818 | + | 1.18818i | ||||
\(834\) | − | 12.0000i | − | 0.415526i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.3939 | + | 29.3939i | 1.01600 | + | 1.01600i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 46.5403 | + | 46.5403i | 1.60388 | + | 1.60388i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 28.0000i | − | 0.963800i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 54.0000 | 1.85656 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −48.9898 | + | 48.9898i | −1.68232 | + | 1.68232i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 4.89898 | + | 4.89898i | 0.167346 | + | 0.167346i | 0.785812 | − | 0.618466i | \(-0.212245\pi\) |
−0.618466 | + | 0.785812i | \(0.712245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9444 | − | 26.9444i | 0.917198 | − | 0.917198i | −0.0796271 | − | 0.996825i | \(-0.525373\pi\) |
0.996825 | + | 0.0796271i | \(0.0253730\pi\) | |||||||
\(864\) | 27.0000i | 0.918559i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.9671 | + | 37.9671i | 1.28943 | + | 1.28943i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.1464 | − | 17.1464i | −0.580651 | − | 0.580651i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 24.0000i | − | 0.811812i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | −19.5959 | + | 19.5959i | −0.661330 | + | 0.661330i | ||||
\(879\) | 24.0000i | 0.809500i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −25.7196 | − | 25.7196i | −0.866025 | − | 0.866025i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −66.0000 | −2.21731 | ||||||||
\(887\) | 41.6413 | + | 41.6413i | 1.39818 | + | 1.39818i | 0.805268 | + | 0.592911i | \(0.202021\pi\) |
0.592911 | + | 0.805268i | \(0.297979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.3939 | − | 29.3939i | 0.983629 | − | 0.983629i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −96.0000 | −3.19822 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36.0000i | 1.19734i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.0000 | 0.797347 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | −17.1464 | + | 17.1464i | −0.569024 | + | 0.569024i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 24.4949 | + | 24.4949i | 0.811107 | + | 0.811107i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −44.0908 | + | 44.0908i | −1.45521 | + | 1.45521i | ||||
\(919\) | − | 56.0000i | − | 1.84727i | −0.383274 | − | 0.923635i | \(-0.625203\pi\) | ||
0.383274 | − | 0.923635i | \(-0.374797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 14.6969 | + | 14.6969i | 0.481414 | + | 0.481414i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 42.0000i | − | 1.37428i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.6413 | + | 41.6413i | 1.35316 | + | 1.35316i | 0.882101 | + | 0.471060i | \(0.156129\pi\) |
0.471060 | + | 0.882101i | \(0.343871\pi\) | |||||||
\(948\) | 19.5959 | − | 19.5959i | 0.636446 | − | 0.636446i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.0000 | −1.55651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6969 | − | 14.6969i | 0.476081 | − | 0.476081i | −0.427795 | − | 0.903876i | \(-0.640710\pi\) |
0.903876 | + | 0.427795i | \(0.140710\pi\) | |||||||
\(954\) | − | 72.0000i | − | 2.33109i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.0454 | + | 22.0454i | −0.710403 | + | 0.710403i | ||||
\(964\) | 2.00000i | 0.0644157i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | −13.4722 | + | 13.4722i | −0.433013 | + | 0.433013i | ||||
\(969\) | 48.0000i | 1.54198i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | −11.0227 | − | 11.0227i | −0.353553 | − | 0.353553i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −44.0908 | − | 44.0908i | −1.41059 | − | 1.41059i | −0.755880 | − | 0.654710i | \(-0.772791\pi\) |
−0.654710 | − | 0.755880i | \(-0.727209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0000 | 1.34096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.44949 | − | 2.44949i | 0.0781266 | − | 0.0781266i | −0.666964 | − | 0.745090i | \(-0.732406\pi\) |
0.745090 | + | 0.666964i | \(0.232406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 29.3939 | + | 29.3939i | 0.933257 | + | 0.933257i | ||||
\(993\) | −34.2929 | + | 34.2929i | −1.08825 | + | 1.08825i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | 53.8888 | − | 53.8888i | 1.70582 | − | 1.70582i | ||||
\(999\) | 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 | 75.2.e.a.68.1 | yes | 4 | |
3.2 | odd | 2 | inner | 75.2.e.a.68.2 | yes | 4 | |
4.3 | odd | 2 | 1200.2.v.g.593.1 | 4 | |||
5.2 | odd | 4 | inner | 75.2.e.a.32.2 | yes | 4 | |
5.3 | odd | 4 | inner | 75.2.e.a.32.1 | ✓ | 4 | |
5.4 | even | 2 | inner | 75.2.e.a.68.2 | yes | 4 | |
12.11 | even | 2 | 1200.2.v.g.593.2 | 4 | |||
15.2 | even | 4 | inner | 75.2.e.a.32.1 | ✓ | 4 | |
15.8 | even | 4 | inner | 75.2.e.a.32.2 | yes | 4 | |
15.14 | odd | 2 | CM | 75.2.e.a.68.1 | yes | 4 | |
20.3 | even | 4 | 1200.2.v.g.257.1 | 4 | |||
20.7 | even | 4 | 1200.2.v.g.257.2 | 4 | |||
20.19 | odd | 2 | 1200.2.v.g.593.2 | 4 | |||
60.23 | odd | 4 | 1200.2.v.g.257.2 | 4 | |||
60.47 | odd | 4 | 1200.2.v.g.257.1 | 4 | |||
60.59 | even | 2 | 1200.2.v.g.593.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.e.a.32.1 | ✓ | 4 | 5.3 | odd | 4 | inner | |
75.2.e.a.32.1 | ✓ | 4 | 15.2 | even | 4 | inner | |
75.2.e.a.32.2 | yes | 4 | 5.2 | odd | 4 | inner | |
75.2.e.a.32.2 | yes | 4 | 15.8 | even | 4 | inner | |
75.2.e.a.68.1 | yes | 4 | 1.1 | even | 1 | trivial | |
75.2.e.a.68.1 | yes | 4 | 15.14 | odd | 2 | CM | |
75.2.e.a.68.2 | yes | 4 | 3.2 | odd | 2 | inner | |
75.2.e.a.68.2 | yes | 4 | 5.4 | even | 2 | inner | |
1200.2.v.g.257.1 | 4 | 20.3 | even | 4 | |||
1200.2.v.g.257.1 | 4 | 60.47 | odd | 4 | |||
1200.2.v.g.257.2 | 4 | 20.7 | even | 4 | |||
1200.2.v.g.257.2 | 4 | 60.23 | odd | 4 | |||
1200.2.v.g.593.1 | 4 | 4.3 | odd | 2 | |||
1200.2.v.g.593.1 | 4 | 60.59 | even | 2 | |||
1200.2.v.g.593.2 | 4 | 12.11 | even | 2 | |||
1200.2.v.g.593.2 | 4 | 20.19 | odd | 2 |