Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2591,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.b (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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.8 | ||
Root | \(1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2591 |
Dual form | 2880.2.b.a.2591.1 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.16228i | 1.19523i | 0.801784 | + | 0.597614i | \(0.203885\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.16228i | 1.55649i | 0.627964 | + | 0.778243i | \(0.283889\pi\) | ||||
−0.627964 | + | 0.778243i | \(0.716111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.05792i | 0.848115i | 0.905635 | + | 0.424058i | \(0.139395\pi\) | ||||
−0.905635 | + | 0.424058i | \(0.860605\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.30056i | 1.77065i | 0.464976 | + | 0.885323i | \(0.346063\pi\) | ||||
−0.464976 | + | 0.885323i | \(0.653937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.30056 | −1.67486 | −0.837432 | − | 0.546542i | \(-0.815944\pi\) | ||||
−0.837432 | + | 0.546542i | \(0.815944\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.32456 | 0.803050 | 0.401525 | − | 0.915848i | \(-0.368480\pi\) | ||||
0.401525 | + | 0.915848i | \(0.368480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.32456i | − 1.49513i | −0.664186 | − | 0.747567i | \(-0.731222\pi\) | ||||
0.664186 | − | 0.747567i | \(-0.268778\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.16228i | − 0.534522i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 11.5432i | − 1.89769i | −0.315741 | − | 0.948846i | \(-0.602253\pi\) | ||||
0.315741 | − | 0.948846i | \(-0.397747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 10.3585i | − 1.61772i | −0.587999 | − | 0.808862i | \(-0.700084\pi\) | ||||
0.587999 | − | 0.808862i | \(-0.299916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.18472 | 0.172809 | 0.0864045 | − | 0.996260i | \(-0.472462\pi\) | ||||
0.0864045 | + | 0.996260i | \(0.472462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3246 | −1.41819 | −0.709093 | − | 0.705115i | \(-0.750896\pi\) | ||||
−0.709093 | + | 0.705115i | \(0.750896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.16228i | − 0.696081i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.83772i | 0.890196i | 0.895482 | + | 0.445098i | \(0.146831\pi\) | ||||
−0.895482 | + | 0.445098i | \(0.853169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.48528i | − 1.08643i | −0.839594 | − | 0.543214i | \(-0.817207\pi\) | ||||
0.839594 | − | 0.543214i | \(-0.182793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.05792i | − 0.379289i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.11584 | 0.747169 | 0.373585 | − | 0.927596i | \(-0.378129\pi\) | ||||
0.373585 | + | 0.927596i | \(0.378129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.11584 | 0.725817 | 0.362909 | − | 0.931825i | \(-0.381784\pi\) | ||||
0.362909 | + | 0.931825i | \(0.381784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.3246 | −1.86036 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3246i | 1.38662i | 0.720639 | + | 0.693310i | \(0.243849\pi\) | ||||
−0.720639 | + | 0.693310i | \(0.756151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.3246i | 1.13327i | 0.823970 | + | 0.566634i | \(0.191754\pi\) | ||||
−0.823970 | + | 0.566634i | \(0.808246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 7.30056i | − 0.791857i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.87320i | 0.198559i | 0.995060 | + | 0.0992796i | \(0.0316538\pi\) | ||||
−0.995060 | + | 0.0992796i | \(0.968346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.67000 | −1.01369 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.30056 | 0.749022 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3246 | 1.25137 | 0.625684 | − | 0.780076i | \(-0.284820\pi\) | ||||
0.625684 | + | 0.780076i | \(0.284820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.16228i | 0.705720i | 0.935676 | + | 0.352860i | \(0.114791\pi\) | ||||
−0.935676 | + | 0.352860i | \(0.885209\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.67544i | 0.161971i | 0.996715 | + | 0.0809857i | \(0.0258068\pi\) | ||||
−0.996715 | + | 0.0809857i | \(0.974193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.48528i | − 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.18472i | − 0.111449i | −0.998446 | − | 0.0557245i | \(-0.982253\pi\) | ||||
0.998446 | − | 0.0557245i | \(-0.0177468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.0864 | −2.11633 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.6491 | −1.42265 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.83772i | − 0.784221i | −0.919918 | − | 0.392111i | \(-0.871745\pi\) | ||||
0.919918 | − | 0.392111i | \(-0.128255\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.48683i | − 0.304646i | −0.988331 | − | 0.152323i | \(-0.951325\pi\) | ||||
0.988331 | − | 0.152323i | \(-0.0486754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 23.0864i | − 2.00185i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.7858i | 1.34868i | 0.738423 | + | 0.674338i | \(0.235571\pi\) | ||||
−0.738423 | + | 0.674338i | \(0.764429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.7858 | −1.32008 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.32456 | −0.359135 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3246 | −1.33736 | −0.668680 | − | 0.743550i | \(-0.733140\pi\) | ||||
−0.668680 | + | 0.743550i | \(0.733140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.32456i | 0.668644i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.42736i | − 0.433150i | −0.976266 | − | 0.216575i | \(-0.930511\pi\) | ||||
0.976266 | − | 0.216575i | \(-0.0694887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.36944 | 0.183353 | 0.0916763 | − | 0.995789i | \(-0.470778\pi\) | ||||
0.0916763 | + | 0.995789i | \(0.470778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.64911 | 0.280701 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9737 | 1.44254 | 0.721271 | − | 0.692653i | \(-0.243558\pi\) | ||||
0.721271 | + | 0.692653i | \(0.243558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.16228i | 0.239046i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.48683i | 0.260618i | 0.991473 | + | 0.130309i | \(0.0415970\pi\) | ||||
−0.991473 | + | 0.130309i | \(0.958403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.11584i | 0.454587i | 0.973826 | + | 0.227294i | \(0.0729877\pi\) | ||||
−0.973826 | + | 0.227294i | \(0.927012\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.5432i | 0.848673i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.6875 | −2.75599 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6011 | 1.05650 | 0.528250 | − | 0.849089i | \(-0.322848\pi\) | ||||
0.528250 | + | 0.849089i | \(0.322848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.324555 | 0.0233620 | 0.0116810 | − | 0.999932i | \(-0.496282\pi\) | ||||
0.0116810 | + | 0.999932i | \(0.496282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6491 | 1.04371 | 0.521853 | − | 0.853035i | \(-0.325241\pi\) | ||||
0.521853 | + | 0.853035i | \(0.325241\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 6.64911i | − 0.471343i | −0.971833 | − | 0.235671i | \(-0.924271\pi\) | ||||
0.971833 | − | 0.235671i | \(-0.0757289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.6754i | 0.959828i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3585i | 0.723468i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 37.6875i | − 2.60690i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2317 | −0.842064 | −0.421032 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421032 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.48528 | 0.578691 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.3246 | 1.78703 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.3246 | −1.50171 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.48683i | − 0.367426i | −0.982980 | − | 0.183713i | \(-0.941188\pi\) | ||||
0.982980 | − | 0.183713i | \(-0.0588116\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.64911i | 0.574062i | 0.957921 | + | 0.287031i | \(0.0926682\pi\) | ||||
−0.957921 | + | 0.287031i | \(0.907332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.36944i | − 0.156577i | −0.996931 | − | 0.0782884i | \(-0.975055\pi\) | ||||
0.996931 | − | 0.0782884i | \(-0.0249455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 21.9017i | − 1.43483i | −0.696647 | − | 0.717414i | \(-0.745326\pi\) | ||||
0.696647 | − | 0.717414i | \(-0.254674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.18472 | −0.0772825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.36944 | −0.153266 | −0.0766331 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766331 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 22.3246i | − 1.42048i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4868i | 0.977520i | 0.872418 | + | 0.488760i | \(0.162551\pi\) | ||||
−0.872418 | + | 0.488760i | \(0.837449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1553i | 1.13250i | 0.824235 | + | 0.566248i | \(0.191605\pi\) | ||||
−0.824235 | + | 0.566248i | \(0.808395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.5028 | 2.26817 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.6011 | 0.900344 | 0.450172 | − | 0.892942i | \(-0.351363\pi\) | ||||
0.450172 | + | 0.892942i | \(0.351363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3246 | 0.634232 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9737 | −0.791018 | −0.395509 | − | 0.918462i | \(-0.629432\pi\) | ||||
−0.395509 | + | 0.918462i | \(0.629432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.64911i | 0.403905i | 0.979395 | + | 0.201952i | \(0.0647286\pi\) | ||||
−0.979395 | + | 0.201952i | \(0.935271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.16228i | 0.311297i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.1443i | 1.57086i | 0.618950 | + | 0.785430i | \(0.287558\pi\) | ||||
−0.618950 | + | 0.785430i | \(0.712442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3585i | 0.617935i | 0.951073 | + | 0.308968i | \(0.0999835\pi\) | ||||
−0.951073 | + | 0.308968i | \(0.900016\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.48528 | −0.504398 | −0.252199 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.7564 | 1.93355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.2982 | −2.13519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.83772i | − 0.398108i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 26.8328i | − 1.54662i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.48528i | 0.485866i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.36944 | 0.135231 | 0.0676154 | − | 0.997711i | \(-0.478461\pi\) | ||||
0.0676154 | + | 0.997711i | \(0.478461\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.2023 | −1.65591 | −0.827954 | − | 0.560796i | \(-0.810495\pi\) | ||||
−0.827954 | + | 0.560796i | \(0.810495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.9737 | −1.18550 | −0.592751 | − | 0.805386i | \(-0.701958\pi\) | ||||
−0.592751 | + | 0.805386i | \(0.701958\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.3246i | 1.24994i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 53.2982i | − 2.96559i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.05792i | 0.169623i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.74641i | 0.206546i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.93113 | 0.271039 | 0.135520 | − | 0.990775i | \(-0.456730\pi\) | ||||
0.135520 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.11584 | −0.334144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.35089 | 0.291482 | 0.145741 | − | 0.989323i | \(-0.453443\pi\) | ||||
0.145741 | + | 0.989323i | \(0.453443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.9737 | 2.32715 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6491i | 0.682988i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000i | 1.28839i | 0.764862 | + | 0.644194i | \(0.222807\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 20.7170i | − 1.10895i | −0.832199 | − | 0.554477i | \(-0.812918\pi\) | ||||
0.832199 | − | 0.554477i | \(-0.187082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.5323i | 1.03960i | 0.854289 | + | 0.519798i | \(0.173993\pi\) | ||||
−0.854289 | + | 0.519798i | \(0.826007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.11584 | −0.324595 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.8547 | −0.572890 | −0.286445 | − | 0.958097i | \(-0.592474\pi\) | ||||
−0.286445 | + | 0.958097i | \(0.592474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.2982 | 1.80517 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 25.4868i | − 1.33040i | −0.746664 | − | 0.665201i | \(-0.768346\pi\) | ||||
0.746664 | − | 0.665201i | \(-0.231654\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 32.6491i | − 1.69506i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.42736i | 0.281018i | 0.990079 | + | 0.140509i | \(0.0448739\pi\) | ||||
−0.990079 | + | 0.140509i | \(0.955126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.2242i | 0.681079i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.7564 | −1.67377 | −0.836887 | − | 0.547376i | \(-0.815627\pi\) | ||||
−0.836887 | + | 0.547376i | \(0.815627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3246 | 0.831976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.3246i | − 0.620116i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 0.688486i | − 0.0345541i | −0.999851 | − | 0.0172771i | \(-0.994500\pi\) | ||||
0.999851 | − | 0.0172771i | \(-0.00549973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.98905i | 0.398954i | 0.979903 | + | 0.199477i | \(0.0639243\pi\) | ||||
−0.979903 | + | 0.199477i | \(0.936076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.4558 | 1.26805 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 59.5892 | 2.95373 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.35089 | −0.264584 | −0.132292 | − | 0.991211i | \(-0.542234\pi\) | ||||
−0.132292 | + | 0.991211i | \(0.542234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.6228 | −1.06399 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 10.3246i | − 0.506812i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 15.4868i | − 0.756581i | −0.925687 | − | 0.378291i | \(-0.876512\pi\) | ||||
0.925687 | − | 0.378291i | \(-0.123488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6011i | 0.711615i | 0.934559 | + | 0.355808i | \(0.115794\pi\) | ||||
−0.934559 | + | 0.355808i | \(0.884206\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.30056i | 0.354129i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8328 | 1.29853 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.9487 | −1.58708 | −0.793541 | − | 0.608517i | \(-0.791765\pi\) | ||||
−0.793541 | + | 0.608517i | \(0.791765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2982 | 0.735186 | 0.367593 | − | 0.929987i | \(-0.380182\pi\) | ||||
0.367593 | + | 0.929987i | \(0.380182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.6491i | 1.65371i | 0.562414 | + | 0.826856i | \(0.309873\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.64911i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658709\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.87320i | − 0.0887984i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 33.4449i | − 1.57836i | −0.614161 | − | 0.789181i | \(-0.710505\pi\) | ||||
0.614161 | − | 0.789181i | \(-0.289495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.4734 | 2.51796 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.67000 | 0.453337 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.6228 | −1.38570 | −0.692848 | − | 0.721084i | \(-0.743644\pi\) | ||||
−0.692848 | + | 0.721084i | \(0.743644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.67544 | 0.357481 | 0.178741 | − | 0.983896i | \(-0.442798\pi\) | ||||
0.178741 | + | 0.983896i | \(0.442798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8377i | 1.34020i | 0.742270 | + | 0.670101i | \(0.233749\pi\) | ||||
−0.742270 | + | 0.670101i | \(0.766251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 25.6754i | − 1.18812i | −0.804422 | − | 0.594059i | \(-0.797525\pi\) | ||||
0.804422 | − | 0.594059i | \(-0.202475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3400i | 0.893038i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 43.8034i | − 2.01408i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.30056 | −0.334973 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.0570 | −1.83025 | −0.915125 | − | 0.403171i | \(-0.867908\pi\) | ||||
−0.915125 | + | 0.403171i | \(0.867908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.2982 | 1.60946 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3246 | −0.559629 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.83772i | − 0.400475i | −0.979747 | − | 0.200238i | \(-0.935829\pi\) | ||||
0.979747 | − | 0.200238i | \(-0.0641714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4868i | 1.24046i | 0.784419 | + | 0.620232i | \(0.212961\pi\) | ||||
−0.784419 | + | 0.620232i | \(0.787039\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.5717i | 1.42192i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.3400i | 0.867518i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0394 | 0.538959 | 0.269480 | − | 0.963006i | \(-0.413148\pi\) | ||||
0.269480 | + | 0.963006i | \(0.413148\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.18472 | 0.0528240 | 0.0264120 | − | 0.999651i | \(-0.491592\pi\) | ||||
0.0264120 | + | 0.999651i | \(0.491592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2982 | 0.500785 | 0.250392 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250392 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 6.32456i | − 0.279782i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 7.16228i | − 0.315608i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.11584i | 0.268975i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 12.7279i | − 0.557620i | −0.960346 | − | 0.278810i | \(-0.910060\pi\) | ||||
0.960346 | − | 0.278810i | \(-0.0899400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6011 | −0.638463 | −0.319231 | − | 0.947677i | \(-0.603425\pi\) | ||||
−0.319231 | + | 0.947677i | \(0.603425\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.7739 | 2.64735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.6754 | 1.37202 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.67544i | − 0.0724358i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 15.4868i | − 0.667065i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.3181i | 1.51844i | 0.650832 | + | 0.759222i | \(0.274420\pi\) | ||||
−0.650832 | + | 0.759222i | \(0.725580\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.48528i | 0.363470i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.8253 | 1.18972 | 0.594862 | − | 0.803828i | \(-0.297207\pi\) | ||||
0.594862 | + | 0.803828i | \(0.297207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.5717 | −1.34500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.9737 | −1.65733 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.3246 | 1.45438 | 0.727189 | − | 0.686437i | \(-0.240826\pi\) | ||||
0.727189 | + | 0.686437i | \(0.240826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 25.9473i | − 1.09746i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9473i | 1.59929i | 0.600473 | + | 0.799645i | \(0.294979\pi\) | ||||
−0.600473 | + | 0.799645i | \(0.705021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.18472i | 0.0498415i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 38.1838i | − 1.60075i | −0.599502 | − | 0.800373i | \(-0.704635\pi\) | ||||
0.599502 | − | 0.800373i | \(-0.295365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5323 | −0.817399 | −0.408700 | − | 0.912669i | \(-0.634018\pi\) | ||||
−0.408700 | + | 0.912669i | \(0.634018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6754 | 0.486055 | 0.243028 | − | 0.970019i | \(-0.421859\pi\) | ||||
0.243028 | + | 0.970019i | \(0.421859\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.6491 | −1.35451 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 53.2982i | − 2.20739i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 42.9737i | − 1.77371i | −0.462045 | − | 0.886857i | \(-0.652884\pi\) | ||||
0.462045 | − | 0.886857i | \(-0.347116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.7739i | 2.50415i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 3.55415i | − 0.145952i | −0.997334 | − | 0.0729758i | \(-0.976750\pi\) | ||||
0.997334 | − | 0.0729758i | \(-0.0232496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.0864 | 0.946450 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.74641 | 0.153074 | 0.0765370 | − | 0.997067i | \(-0.475614\pi\) | ||||
0.0765370 | + | 0.997067i | \(0.475614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.6491 | −1.49495 | −0.747474 | − | 0.664291i | \(-0.768734\pi\) | ||||
−0.747474 | + | 0.664291i | \(0.768734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6491 | 0.636227 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20.8377i | − 0.845777i | −0.906182 | − | 0.422889i | \(-0.861016\pi\) | ||||
0.906182 | − | 0.422889i | \(-0.138984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.62278i | 0.146562i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6590i | 0.713242i | 0.934249 | + | 0.356621i | \(0.116071\pi\) | ||||
−0.934249 | + | 0.356621i | \(0.883929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.2711i | 0.977119i | 0.872531 | + | 0.488559i | \(0.162477\pi\) | ||||
−0.872531 | + | 0.488559i | \(0.837523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.4339 | −1.66537 | −0.832685 | − | 0.553746i | \(-0.813198\pi\) | ||||
−0.832685 | + | 0.553746i | \(0.813198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.92359 | −0.237324 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 84.2719 | 3.36014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.9737i | 1.15342i | 0.816948 | + | 0.576712i | \(0.195664\pi\) | ||||
−0.816948 | + | 0.576712i | \(0.804336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.83772i | 0.350714i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9.17377i | − 0.363478i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.3585i | 0.409136i | 0.978852 | + | 0.204568i | \(0.0655789\pi\) | ||||
−0.978852 | + | 0.204568i | \(0.934421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.5717 | 1.24507 | 0.622533 | − | 0.782594i | \(-0.286104\pi\) | ||||
0.622533 | + | 0.782594i | \(0.286104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.0470 | −0.434301 | −0.217151 | − | 0.976138i | \(-0.569676\pi\) | ||||
−0.217151 | + | 0.976138i | \(0.569676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.2982 | −1.38558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.2982 | 0.911730 | 0.455865 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455865 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.48683i | 0.136242i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 27.4868i | − 1.07073i | −0.844619 | − | 0.535367i | \(-0.820173\pi\) | ||||
0.844619 | − | 0.535367i | \(-0.179827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.8253i | 1.08228i | 0.840933 | + | 0.541139i | \(0.182007\pi\) | ||||
−0.840933 | + | 0.541139i | \(0.817993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.0864i | 0.895252i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.8034 | 1.69101 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.35089 | 0.0520730 | 0.0260365 | − | 0.999661i | \(-0.491711\pi\) | ||||
0.0260365 | + | 0.999661i | \(0.491711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.9473 | −1.68903 | −0.844517 | − | 0.535529i | \(-0.820112\pi\) | ||||
−0.844517 | + | 0.535529i | \(0.820112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.9737i | 1.49567i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13.6754i | − 0.523276i | −0.965166 | − | 0.261638i | \(-0.915737\pi\) | ||||
0.965166 | − | 0.261638i | \(-0.0842627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 15.7858i | − 0.603146i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 31.5717i | − 1.20279i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.67000 | 0.367864 | 0.183932 | − | 0.982939i | \(-0.441117\pi\) | ||||
0.183932 | + | 0.982939i | \(0.441117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9706 | 0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 75.6228 | 2.86442 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 84.2719i | 3.17837i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.9737i | − 0.713578i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 14.6011i | − 0.548357i | −0.961679 | − | 0.274178i | \(-0.911594\pi\) | ||||
0.961679 | − | 0.274178i | \(-0.0884059\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.7858 | 0.590357 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4558 | −0.949343 | −0.474671 | − | 0.880163i | \(-0.657433\pi\) | ||||
−0.474671 | + | 0.880163i | \(0.657433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.6491 | −0.843497 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.32456 | 0.160610 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 27.8114i | − 1.03147i | −0.856749 | − | 0.515734i | \(-0.827519\pi\) | ||||
0.856749 | − | 0.515734i | \(-0.172481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 61.9473i | − 2.29120i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.17377i | 0.338841i | 0.985544 | + | 0.169420i | \(0.0541896\pi\) | ||||
−0.985544 | + | 0.169420i | \(0.945810\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.5717i | 1.16296i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.56169 | −0.0942333 | −0.0471166 | − | 0.998889i | \(-0.515003\pi\) | ||||
−0.0471166 | + | 0.998889i | \(0.515003\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.0470 | −0.405274 | −0.202637 | − | 0.979254i | \(-0.564951\pi\) | ||||
−0.202637 | + | 0.979254i | \(0.564951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3246 | 0.598085 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.29822 | −0.193593 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.97367i | 0.327454i | 0.986506 | + | 0.163727i | \(0.0523516\pi\) | ||||
−0.986506 | + | 0.163727i | \(0.947648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 10.0000i | − 0.363937i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.68095i | 0.0610952i | 0.999533 | + | 0.0305476i | \(0.00972512\pi\) | ||||
−0.999533 | + | 0.0305476i | \(0.990275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7279i | 0.461387i | 0.973026 | + | 0.230693i | \(0.0740994\pi\) | ||||
−0.973026 | + | 0.230693i | \(0.925901\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.8328 | 0.971413 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.9092 | −0.754988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.64911 | 0.167651 | 0.0838256 | − | 0.996480i | \(-0.473286\pi\) | ||||
0.0838256 | + | 0.996480i | \(0.473286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.2982 | 1.26959 | 0.634794 | − | 0.772681i | \(-0.281085\pi\) | ||||
0.634794 | + | 0.772681i | \(0.281085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 8.32456i | − 0.299027i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 75.6228i | 2.70947i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.5717i | 1.12972i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.42736i | 0.193711i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1728 | 1.64588 | 0.822942 | − | 0.568126i | \(-0.192331\pi\) | ||||
0.822942 | + | 0.568126i | \(0.192331\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.74641 | 0.133207 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9473 | 0.921417 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.6754 | −0.909471 | −0.454735 | − | 0.890627i | \(-0.650266\pi\) | ||||
−0.454735 | + | 0.890627i | \(0.650266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.64911i | 0.305984i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10.3246i | − 0.364346i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.87320i | 0.0658583i | 0.999458 | + | 0.0329292i | \(0.0104836\pi\) | ||||
−0.999458 | + | 0.0329292i | \(0.989516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.2023 | −1.02543 | −0.512715 | − | 0.858559i | \(-0.671360\pi\) | ||||
−0.512715 | + | 0.858559i | \(0.671360\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.9473 | 2.16726 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.6228 | −0.754640 | −0.377320 | − | 0.926083i | \(-0.623154\pi\) | ||||
−0.377320 | + | 0.926083i | \(0.623154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 46.7851i | − 1.63082i | −0.578881 | − | 0.815412i | \(-0.696510\pi\) | ||||
0.578881 | − | 0.815412i | \(-0.303490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9473i | 0.902277i | 0.892454 | + | 0.451139i | \(0.148982\pi\) | ||||
−0.892454 | + | 0.451139i | \(0.851018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.0864i | 0.801824i | 0.916117 | + | 0.400912i | \(0.131307\pi\) | ||||
−0.916117 | + | 0.400912i | \(0.868693\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 21.9017i | − 0.758849i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.36944 | −0.0819977 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.0864 | −0.797031 | −0.398516 | − | 0.917162i | \(-0.630475\pi\) | ||||
−0.398516 | + | 0.917162i | \(0.630475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.2982 | −0.355111 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.64911 | −0.125533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 49.4868i | − 1.70039i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3979i | 0.766890i | 0.923564 | + | 0.383445i | \(0.125262\pi\) | ||||
−0.923564 | + | 0.383445i | \(0.874738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.6406i | 0.910024i | 0.890485 | + | 0.455012i | \(0.150365\pi\) | ||||
−0.890485 | + | 0.455012i | \(0.849635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6656 | 1.83105 | 0.915524 | − | 0.402264i | \(-0.131776\pi\) | ||||
0.915524 | + | 0.402264i | \(0.131776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3400 | −0.658341 | −0.329171 | − | 0.944270i | \(-0.606769\pi\) | ||||
−0.329171 | + | 0.944270i | \(0.606769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9737 | −0.645124 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −63.6228 | −2.15825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7018i | 0.633686i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.16228i | − 0.106904i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6590i | 0.596304i | 0.954518 | + | 0.298152i | \(0.0963702\pi\) | ||||
−0.954518 | + | 0.298152i | \(0.903630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1.87320i | − 0.0631098i | −0.999502 | − | 0.0315549i | \(-0.989954\pi\) | ||||
0.999502 | − | 0.0315549i | \(-0.0100459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9706 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.36944 | 0.0795579 | 0.0397789 | − | 0.999209i | \(-0.487335\pi\) | ||||
0.0397789 | + | 0.999209i | \(0.487335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.9473 | 0.937323 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.64911 | −0.289431 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.48683i | − 0.116552i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 36.0000i | − 1.20067i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 75.3751i | − 2.51111i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.11584i | − 0.203298i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7170 | 0.687896 | 0.343948 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343948 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.5423 | 1.60828 | 0.804138 | − | 0.594442i | \(-0.202627\pi\) | ||||
0.804138 | + | 0.594442i | \(0.202627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −53.2982 | −1.76391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.0263 | 0.364122 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.02633i | 0.0998295i | 0.998753 | + | 0.0499148i | \(0.0158950\pi\) | ||||
−0.998753 | + | 0.0499148i | \(0.984105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.7018i | 0.615577i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 11.5432i | − 0.379538i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.98905i | 0.262112i | 0.991375 | + | 0.131056i | \(0.0418368\pi\) | ||||
−0.991375 | + | 0.131056i | \(0.958163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.9017 | 0.717799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.6875 | 1.23251 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.9473 | 0.650264 | 0.325132 | − | 0.945669i | \(-0.394591\pi\) | ||||
0.325132 | + | 0.945669i | \(0.394591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.5964i | − 1.51418i | −0.653310 | − | 0.757090i | \(-0.726620\pi\) | ||||
0.653310 | − | 0.757090i | \(-0.273380\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 6.11584i | − 0.198529i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6481i | 0.830823i | 0.909634 | + | 0.415412i | \(0.136362\pi\) | ||||
−0.909634 | + | 0.415412i | \(0.863638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.6011 | −0.472481 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.9192 | −1.61198 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.2982 | −1.23543 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.324555 | −0.0104478 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.13594i | 0.0686873i | 0.999410 | + | 0.0343437i | \(0.0109341\pi\) | ||||
−0.999410 | + | 0.0343437i | \(0.989066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 12.1359i | − 0.389461i | −0.980857 | − | 0.194730i | \(-0.937617\pi\) | ||||
0.980857 | − | 0.194730i | \(-0.0623832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 53.6656i | − 1.72044i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.2711i | 0.776502i | 0.921554 | + | 0.388251i | \(0.126921\pi\) | ||||
−0.921554 | + | 0.388251i | \(0.873079\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.67000 | −0.309055 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.55415 | 0.113360 | 0.0566800 | − | 0.998392i | \(-0.481949\pi\) | ||||
0.0566800 | + | 0.998392i | \(0.481949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6491 | −0.466759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 51.2982i | − 1.62954i | −0.579783 | − | 0.814771i | \(-0.696863\pi\) | ||||
0.579783 | − | 0.814771i | \(-0.303137\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.64911i | 0.210791i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 34.6296i | − 1.09673i | −0.836239 | − | 0.548365i | \(-0.815250\pi\) | ||||
0.836239 | − | 0.548365i | \(-0.184750\pi\) | |||||||
\(998\) | 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 | 2880.2.b.a.2591.8 | yes | 8 | |
3.2 | odd | 2 | 2880.2.b.d.2591.6 | yes | 8 | ||
4.3 | odd | 2 | inner | 2880.2.b.a.2591.2 | yes | 8 | |
8.3 | odd | 2 | 2880.2.b.d.2591.3 | yes | 8 | ||
8.5 | even | 2 | 2880.2.b.d.2591.5 | yes | 8 | ||
12.11 | even | 2 | 2880.2.b.d.2591.4 | yes | 8 | ||
24.5 | odd | 2 | inner | 2880.2.b.a.2591.7 | yes | 8 | |
24.11 | even | 2 | inner | 2880.2.b.a.2591.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.b.a.2591.1 | ✓ | 8 | 24.11 | even | 2 | inner | |
2880.2.b.a.2591.2 | yes | 8 | 4.3 | odd | 2 | inner | |
2880.2.b.a.2591.7 | yes | 8 | 24.5 | odd | 2 | inner | |
2880.2.b.a.2591.8 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.b.d.2591.3 | yes | 8 | 8.3 | odd | 2 | ||
2880.2.b.d.2591.4 | yes | 8 | 12.11 | even | 2 | ||
2880.2.b.d.2591.5 | yes | 8 | 8.5 | even | 2 | ||
2880.2.b.d.2591.6 | yes | 8 | 3.2 | odd | 2 |