Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1079,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1764.1079");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.e (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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{12} - 10x^{10} + 4x^{8} - 40x^{6} + 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1079.15 | ||
Root | \(1.41135 - 0.0900240i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.i.1079.16 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41135 | − | 0.0900240i | 0.997972 | − | 0.0636566i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.98379 | − | 0.254110i | 0.991896 | − | 0.127055i | ||||
\(5\) | 2.48866i | 1.11296i | 0.830859 | + | 0.556482i | \(0.187849\pi\) | ||||
−0.830859 | + | 0.556482i | \(0.812151\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.77694 | − | 0.537226i | 0.981796 | − | 0.189938i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.224040 | + | 3.51237i | 0.0708475 | + | 1.11071i | ||||
\(11\) | −4.60787 | −1.38932 | −0.694662 | − | 0.719336i | \(-0.744446\pi\) | ||||
−0.694662 | + | 0.719336i | \(0.744446\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.22221 | 1.44838 | 0.724190 | − | 0.689600i | \(-0.242214\pi\) | ||||
0.724190 | + | 0.689600i | \(0.242214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.87086 | − | 1.00820i | 0.967714 | − | 0.252051i | ||||
\(17\) | 5.61101i | 1.36087i | 0.732809 | + | 0.680435i | \(0.238209\pi\) | ||||
−0.732809 | + | 0.680435i | \(0.761791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.19355i | 0.732651i | 0.930487 | + | 0.366326i | \(0.119384\pi\) | ||||
−0.930487 | + | 0.366326i | \(0.880616\pi\) | |||||||
\(20\) | 0.632394 | + | 4.93699i | 0.141408 | + | 1.10394i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.50329 | + | 0.414819i | −1.38651 | + | 0.0884397i | ||||
\(23\) | −0.718731 | −0.149866 | −0.0749329 | − | 0.997189i | \(-0.523874\pi\) | ||||
−0.0749329 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.19345 | −0.238691 | ||||||||
\(26\) | 7.37034 | − | 0.470124i | 1.44544 | − | 0.0921989i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.53656i | − | 0.842418i | −0.906964 | − | 0.421209i | \(-0.861606\pi\) | ||
0.906964 | − | 0.421209i | \(-0.138394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17715i | 0.211422i | 0.994397 | + | 0.105711i | \(0.0337119\pi\) | ||||
−0.994397 | + | 0.105711i | \(0.966288\pi\) | |||||||
\(32\) | 5.37235 | − | 1.77139i | 0.949707 | − | 0.313141i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.505125 | + | 7.91907i | 0.0866283 | + | 1.35811i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.71296 | 0.446007 | 0.223004 | − | 0.974818i | \(-0.428414\pi\) | ||||
0.223004 | + | 0.974818i | \(0.428414\pi\) | |||||||
\(38\) | 0.287496 | + | 4.50721i | 0.0466381 | + | 0.731165i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.33697 | + | 6.91087i | 0.211394 | + | 1.09270i | ||||
\(41\) | 3.83670i | 0.599192i | 0.954066 | + | 0.299596i | \(0.0968519\pi\) | ||||
−0.954066 | + | 0.299596i | \(0.903148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1773i | 1.70453i | 0.523113 | + | 0.852263i | \(0.324771\pi\) | ||||
−0.523113 | + | 0.852263i | \(0.675229\pi\) | |||||||
\(44\) | −9.14105 | + | 1.17091i | −1.37807 | + | 0.176521i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.01438 | + | 0.0647031i | −0.149562 | + | 0.00953995i | ||||
\(47\) | −5.41810 | −0.790312 | −0.395156 | − | 0.918614i | \(-0.629309\pi\) | ||||
−0.395156 | + | 0.918614i | \(0.629309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.68437 | + | 0.107439i | −0.238206 | + | 0.0151942i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.3598 | − | 1.32702i | 1.43664 | − | 0.184024i | ||||
\(53\) | − | 2.06823i | − | 0.284093i | −0.989860 | − | 0.142046i | \(-0.954632\pi\) | ||
0.989860 | − | 0.142046i | \(-0.0453682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 11.4674i | − | 1.54627i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.408399 | − | 6.40265i | −0.0536254 | − | 0.840709i | ||||
\(59\) | 4.11641 | 0.535912 | 0.267956 | − | 0.963431i | \(-0.413652\pi\) | ||||
0.267956 | + | 0.963431i | \(0.413652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01025 | −0.129349 | −0.0646747 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646747 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(62\) | 0.105972 | + | 1.66136i | 0.0134584 | + | 0.210993i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.42278 | − | 2.98369i | 0.927847 | − | 0.372961i | ||||
\(65\) | 12.9963i | 1.61200i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.6446i | − | 1.54478i | −0.635147 | − | 0.772391i | \(-0.719060\pi\) | ||
0.635147 | − | 0.772391i | \(-0.280940\pi\) | |||||||
\(68\) | 1.42581 | + | 11.1311i | 0.172905 | + | 1.34984i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.31012 | 0.867552 | 0.433776 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433776 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.63787 | 1.12803 | 0.564014 | − | 0.825765i | \(-0.309256\pi\) | ||||
0.564014 | + | 0.825765i | \(0.309256\pi\) | |||||||
\(74\) | 3.82892 | − | 0.244231i | 0.445103 | − | 0.0283913i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.811513 | + | 6.33534i | 0.0930870 | + | 0.726714i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.83951i | 0.994522i | 0.867601 | + | 0.497261i | \(0.165661\pi\) | ||||
−0.867601 | + | 0.497261i | \(0.834339\pi\) | |||||||
\(80\) | 2.50908 | + | 9.63326i | 0.280523 | + | 1.07703i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.345395 | + | 5.41491i | 0.0381425 | + | 0.597977i | ||||
\(83\) | −13.7657 | −1.51099 | −0.755493 | − | 0.655157i | \(-0.772603\pi\) | ||||
−0.755493 | + | 0.655157i | \(0.772603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.9639 | −1.51460 | ||||||||
\(86\) | 1.00623 | + | 15.7751i | 0.108504 | + | 1.70107i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.7958 | + | 2.47547i | −1.36403 | + | 0.263886i | ||||
\(89\) | − | 8.52595i | − | 0.903749i | −0.892082 | − | 0.451874i | \(-0.850756\pi\) | ||
0.892082 | − | 0.451874i | \(-0.149244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.42581 | + | 0.182637i | −0.148651 | + | 0.0190412i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.64682 | + | 0.487759i | −0.788709 | + | 0.0503085i | ||||
\(95\) | −7.94768 | −0.815415 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7232 | −1.08878 | −0.544388 | − | 0.838833i | \(-0.683238\pi\) | ||||
−0.544388 | + | 0.838833i | \(0.683238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.36756 | + | 0.303268i | −0.236756 | + | 0.0303268i | ||||
\(101\) | 3.83670i | 0.381766i | 0.981613 | + | 0.190883i | \(0.0611351\pi\) | ||||
−0.981613 | + | 0.190883i | \(0.938865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.6774i | − | 1.64327i | −0.570012 | − | 0.821636i | \(-0.693061\pi\) | ||
0.570012 | − | 0.821636i | \(-0.306939\pi\) | |||||||
\(104\) | 14.5018 | − | 2.80550i | 1.42201 | − | 0.275102i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.186190 | − | 2.91898i | −0.0180844 | − | 0.283517i | ||||
\(107\) | 5.73689 | 0.554606 | 0.277303 | − | 0.960783i | \(-0.410559\pi\) | ||||
0.277303 | + | 0.960783i | \(0.410559\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.82705 | −0.270782 | −0.135391 | − | 0.990792i | \(-0.543229\pi\) | ||||
−0.135391 | + | 0.990792i | \(0.543229\pi\) | |||||||
\(110\) | −1.03235 | − | 16.1845i | −0.0984302 | − | 1.54313i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.59651i | 0.526476i | 0.964731 | + | 0.263238i | \(0.0847904\pi\) | ||||
−0.964731 | + | 0.263238i | \(0.915210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.78868i | − | 0.166795i | ||||||
\(116\) | −1.15278 | − | 8.99958i | −0.107033 | − | 0.835590i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.80968 | − | 0.370576i | 0.534825 | − | 0.0341143i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2325 | 0.930224 | ||||||||
\(122\) | −1.42581 | + | 0.0909468i | −0.129087 | + | 0.00823394i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.299125 | + | 2.33522i | 0.0268622 | + | 0.209709i | ||||
\(125\) | 9.47322i | 0.847311i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.2266i | − | 1.35114i | −0.737294 | − | 0.675572i | \(-0.763897\pi\) | ||
0.737294 | − | 0.675572i | \(-0.236103\pi\) | |||||||
\(128\) | 10.2075 | − | 4.87924i | 0.902224 | − | 0.431268i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.16998 | + | 18.3423i | 0.102614 | + | 1.60873i | ||||
\(131\) | 4.15332 | 0.362877 | 0.181438 | − | 0.983402i | \(-0.441925\pi\) | ||||
0.181438 | + | 0.983402i | \(0.441925\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.13832 | − | 17.8459i | −0.0983356 | − | 1.54165i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.01438 | + | 15.5814i | 0.258481 | + | 1.33610i | ||||
\(137\) | − | 16.3317i | − | 1.39531i | −0.716433 | − | 0.697656i | \(-0.754226\pi\) | ||
0.716433 | − | 0.697656i | \(-0.245774\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.2903i | − | 0.872811i | −0.899750 | − | 0.436406i | \(-0.856251\pi\) | ||
0.899750 | − | 0.436406i | \(-0.143749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3171 | − | 0.658086i | 0.865792 | − | 0.0552254i | ||||
\(143\) | −24.0633 | −2.01227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2900 | 0.937581 | ||||||||
\(146\) | 13.6024 | − | 0.867640i | 1.12574 | − | 0.0718064i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.38194 | − | 0.689389i | 0.442393 | − | 0.0566674i | ||||
\(149\) | − | 5.65685i | − | 0.463428i | −0.972784 | − | 0.231714i | \(-0.925567\pi\) | ||
0.972784 | − | 0.231714i | \(-0.0744333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.1625i | − | 0.989767i | −0.868959 | − | 0.494884i | \(-0.835211\pi\) | ||
0.868959 | − | 0.494884i | \(-0.164789\pi\) | |||||||
\(152\) | 1.71566 | + | 8.86830i | 0.139158 | + | 0.719314i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.92953 | −0.235305 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.03901 | 0.561774 | 0.280887 | − | 0.959741i | \(-0.409371\pi\) | ||||
0.280887 | + | 0.959741i | \(0.409371\pi\) | |||||||
\(158\) | 0.795768 | + | 12.4756i | 0.0633079 | + | 0.992505i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.40840 | + | 13.3700i | 0.348515 | + | 1.05699i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.78868i | 0.140100i | 0.997543 | + | 0.0700502i | \(0.0223159\pi\) | ||||
−0.997543 | + | 0.0700502i | \(0.977684\pi\) | |||||||
\(164\) | 0.974943 | + | 7.61121i | 0.0761303 | + | 0.594336i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.4282 | + | 1.23925i | −1.50792 | + | 0.0961842i | ||||
\(167\) | −8.26973 | −0.639931 | −0.319965 | − | 0.947429i | \(-0.603671\pi\) | ||||
−0.319965 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.2715 | 1.09781 | ||||||||
\(170\) | −19.7079 | + | 1.25709i | −1.51153 | + | 0.0964143i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.84027 | + | 22.1735i | 0.216569 | + | 1.69071i | ||||
\(173\) | 19.3472i | 1.47094i | 0.677557 | + | 0.735470i | \(0.263039\pi\) | ||||
−0.677557 | + | 0.735470i | \(0.736961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.8364 | + | 4.64566i | −1.34447 | + | 0.350180i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.767540 | − | 12.0331i | −0.0575296 | − | 0.901916i | ||||
\(179\) | 12.0538 | 0.900941 | 0.450470 | − | 0.892791i | \(-0.351256\pi\) | ||||
0.450470 | + | 0.892791i | \(0.351256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7992 | 1.54599 | 0.772997 | − | 0.634410i | \(-0.218757\pi\) | ||||
0.772997 | + | 0.634410i | \(0.218757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.99587 | + | 0.386121i | −0.147138 | + | 0.0284652i | ||||
\(185\) | 6.75164i | 0.496390i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 25.8548i | − | 1.89069i | ||||||
\(188\) | −10.7484 | + | 1.37679i | −0.783907 | + | 0.100413i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.2169 | + | 0.715482i | −0.813761 | + | 0.0519065i | ||||
\(191\) | 10.6163 | 0.768169 | 0.384084 | − | 0.923298i | \(-0.374517\pi\) | ||||
0.384084 | + | 0.923298i | \(0.374517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9927 | 0.935233 | 0.467617 | − | 0.883931i | \(-0.345113\pi\) | ||||
0.467617 | + | 0.883931i | \(0.345113\pi\) | |||||||
\(194\) | −15.1341 | + | 0.965346i | −1.08657 | + | 0.0693078i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.18852i | − | 0.227173i | −0.993528 | − | 0.113586i | \(-0.963766\pi\) | ||
0.993528 | − | 0.113586i | \(-0.0362339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.0495i | − | 0.995940i | −0.867194 | − | 0.497970i | \(-0.834079\pi\) | ||
0.867194 | − | 0.497970i | \(-0.165921\pi\) | |||||||
\(200\) | −3.31415 | + | 0.641153i | −0.234345 | + | 0.0453364i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.345395 | + | 5.41491i | 0.0243019 | + | 0.380992i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.54826 | −0.666879 | ||||||||
\(206\) | −1.50137 | − | 23.5376i | −0.104605 | − | 1.63994i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.2144 | − | 5.26504i | 1.40162 | − | 0.365065i | ||||
\(209\) | − | 14.7155i | − | 1.01789i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.12962i | 0.628509i | 0.949339 | + | 0.314255i | \(0.101755\pi\) | ||||
−0.949339 | + | 0.314255i | \(0.898245\pi\) | |||||||
\(212\) | −0.525557 | − | 4.10293i | −0.0360954 | − | 0.281790i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.09673 | − | 0.516457i | 0.553481 | − | 0.0353043i | ||||
\(215\) | −27.8166 | −1.89708 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.98994 | + | 0.254502i | −0.270233 | + | 0.0172371i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.91399 | − | 22.7490i | −0.196461 | − | 1.53374i | ||||
\(221\) | 29.3019i | 1.97106i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.8384i | − | 1.59634i | −0.602434 | − | 0.798168i | \(-0.705802\pi\) | ||
0.602434 | − | 0.798168i | \(-0.294198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.503820 | + | 7.89861i | 0.0335136 | + | 0.525408i | ||||
\(227\) | 10.0124 | 0.664544 | 0.332272 | − | 0.943184i | \(-0.392185\pi\) | ||||
0.332272 | + | 0.943184i | \(0.392185\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.33630 | −0.352633 | −0.176316 | − | 0.984334i | \(-0.556418\pi\) | ||||
−0.176316 | + | 0.984334i | \(0.556418\pi\) | |||||||
\(230\) | −0.161024 | − | 2.52445i | −0.0106176 | − | 0.166457i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.43716 | − | 12.5977i | −0.160007 | − | 0.827082i | ||||
\(233\) | − | 8.76818i | − | 0.574423i | −0.957867 | − | 0.287211i | \(-0.907272\pi\) | ||
0.957867 | − | 0.287211i | \(-0.0927282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.4838i | − | 0.879589i | ||||||
\(236\) | 8.16611 | − | 1.04602i | 0.531568 | − | 0.0680902i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1385 | 0.849860 | 0.424930 | − | 0.905226i | \(-0.360299\pi\) | ||||
0.424930 | + | 0.905226i | \(0.360299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0638 | −1.42125 | −0.710627 | − | 0.703569i | \(-0.751588\pi\) | ||||
−0.710627 | + | 0.703569i | \(0.751588\pi\) | |||||||
\(242\) | 14.4415 | − | 0.921167i | 0.928337 | − | 0.0592149i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.00413 | + | 0.256715i | −0.128301 | + | 0.0164345i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.6774i | 1.06116i | ||||||||
\(248\) | 0.632394 | + | 3.26887i | 0.0401571 | + | 0.207573i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.852817 | + | 13.3700i | 0.0539369 | + | 0.845592i | ||||
\(251\) | −26.5149 | −1.67361 | −0.836804 | − | 0.547503i | \(-0.815579\pi\) | ||||
−0.836804 | + | 0.547503i | \(0.815579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.31182 | 0.208212 | ||||||||
\(254\) | −1.37076 | − | 21.4900i | −0.0860092 | − | 1.34840i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.9671 | − | 7.80521i | 0.872941 | − | 0.487826i | ||||
\(257\) | − | 16.9392i | − | 1.05664i | −0.849046 | − | 0.528320i | \(-0.822822\pi\) | ||
0.849046 | − | 0.528320i | \(-0.177178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.30250 | + | 25.7820i | 0.204812 | + | 1.59893i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.86176 | − | 0.373898i | 0.362141 | − | 0.0230995i | ||||
\(263\) | −13.9594 | −0.860772 | −0.430386 | − | 0.902645i | \(-0.641623\pi\) | ||||
−0.430386 | + | 0.902645i | \(0.641623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.14712 | 0.316185 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.21312 | − | 25.0842i | −0.196272 | − | 1.53226i | ||||
\(269\) | − | 15.5402i | − | 0.947500i | −0.880659 | − | 0.473750i | \(-0.842900\pi\) | ||
0.880659 | − | 0.473750i | \(-0.157100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.227723i | 0.0138332i | 0.999976 | + | 0.00691658i | \(0.00220163\pi\) | ||||
−0.999976 | + | 0.00691658i | \(0.997798\pi\) | |||||||
\(272\) | 5.65703 | + | 21.7194i | 0.343008 | + | 1.31693i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.47025 | − | 23.0497i | −0.0888208 | − | 1.39248i | ||||
\(275\) | 5.49927 | 0.331619 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1028 | −1.08769 | −0.543846 | − | 0.839185i | \(-0.683032\pi\) | ||||
−0.543846 | + | 0.839185i | \(0.683032\pi\) | |||||||
\(278\) | −0.926373 | − | 14.5232i | −0.0555602 | − | 0.871041i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.5594i | − | 0.987854i | −0.869503 | − | 0.493927i | \(-0.835561\pi\) | ||
0.869503 | − | 0.493927i | \(-0.164439\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.19355i | − | 0.189837i | −0.995485 | − | 0.0949185i | \(-0.969741\pi\) | ||
0.995485 | − | 0.0949185i | \(-0.0302590\pi\) | |||||||
\(284\) | 14.5018 | − | 1.85757i | 0.860521 | − | 0.110227i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.9616 | + | 2.16627i | −2.00819 | + | 0.128094i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4834 | −0.851966 | ||||||||
\(290\) | 15.9341 | − | 1.01637i | 0.935680 | − | 0.0596832i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.1195 | − | 2.44908i | 1.11889 | − | 0.143321i | ||||
\(293\) | − | 3.17751i | − | 0.185632i | −0.995683 | − | 0.0928160i | \(-0.970413\pi\) | ||
0.995683 | − | 0.0928160i | \(-0.0295868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2444i | 0.596451i | ||||||||
\(296\) | 7.53371 | − | 1.45747i | 0.437888 | − | 0.0847137i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.509253 | − | 7.98377i | −0.0295002 | − | 0.462488i | ||||
\(299\) | −3.75337 | −0.217063 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.09491 | − | 17.1654i | −0.0630052 | − | 0.987760i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.21975 | + | 12.3618i | 0.184665 | + | 0.708997i | ||||
\(305\) | − | 2.51418i | − | 0.143961i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8559i | 0.619579i | 0.950805 | + | 0.309790i | \(0.100259\pi\) | ||||
−0.950805 | + | 0.309790i | \(0.899741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.13458 | + | 0.263728i | −0.234828 | + | 0.0149787i | ||||
\(311\) | 18.6821 | 1.05936 | 0.529681 | − | 0.848197i | \(-0.322312\pi\) | ||||
0.529681 | + | 0.848197i | \(0.322312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8313 | −0.894839 | −0.447420 | − | 0.894324i | \(-0.647657\pi\) | ||||
−0.447420 | + | 0.894324i | \(0.647657\pi\) | |||||||
\(314\) | 9.93447 | − | 0.633680i | 0.560635 | − | 0.0357606i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.24621 | + | 17.5357i | 0.126359 | + | 0.986462i | ||||
\(317\) | 6.13829i | 0.344761i | 0.985030 | + | 0.172380i | \(0.0551458\pi\) | ||||
−0.985030 | + | 0.172380i | \(0.944854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.9039i | 1.17039i | ||||||||
\(320\) | 7.42539 | + | 18.4728i | 0.415092 | + | 1.03266i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.9191 | −0.997043 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23246 | −0.345715 | ||||||||
\(326\) | 0.161024 | + | 2.52445i | 0.00891831 | + | 0.139816i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.06117 | + | 10.6543i | 0.113809 | + | 0.588284i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.388432i | 0.0213501i | 0.999943 | + | 0.0106751i | \(0.00339804\pi\) | ||||
−0.999943 | + | 0.0106751i | \(0.996602\pi\) | |||||||
\(332\) | −27.3084 | + | 3.49801i | −1.49874 | + | 0.191978i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.6714 | + | 0.744474i | −0.638633 | + | 0.0407358i | ||||
\(335\) | 31.4681 | 1.71929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.10384 | 0.332497 | 0.166249 | − | 0.986084i | \(-0.446835\pi\) | ||||
0.166249 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(338\) | 20.1420 | − | 1.28477i | 1.09558 | − | 0.0698825i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −27.7015 | + | 3.54837i | −1.50233 | + | 0.192437i | ||||
\(341\) | − | 5.42415i | − | 0.293734i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.00475 | + | 31.0388i | 0.323754 | + | 1.67350i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.74171 | + | 27.3056i | 0.0936351 | + | 1.46796i | ||||
\(347\) | −29.0268 | −1.55824 | −0.779120 | − | 0.626874i | \(-0.784334\pi\) | ||||
−0.779120 | + | 0.626874i | \(0.784334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.2889 | −1.46074 | −0.730371 | − | 0.683050i | \(-0.760653\pi\) | ||||
−0.730371 | + | 0.683050i | \(0.760653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.7551 | + | 8.16234i | −1.31945 | + | 0.435054i | ||||
\(353\) | − | 30.2811i | − | 1.61170i | −0.592118 | − | 0.805851i | \(-0.701708\pi\) | ||
0.592118 | − | 0.805851i | \(-0.298292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.1924i | 0.965554i | ||||||||
\(356\) | −2.16653 | − | 16.9137i | −0.114826 | − | 0.896424i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.0120 | − | 1.08513i | 0.899113 | − | 0.0573508i | ||||
\(359\) | −20.7780 | −1.09662 | −0.548312 | − | 0.836274i | \(-0.684729\pi\) | ||||
−0.548312 | + | 0.836274i | \(0.684729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.80122 | 0.463222 | ||||||||
\(362\) | 29.3549 | − | 1.87243i | 1.54286 | − | 0.0984127i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.9854i | 1.25545i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.4825i | 1.06918i | 0.845112 | + | 0.534589i | \(0.179533\pi\) | ||||
−0.845112 | + | 0.534589i | \(0.820467\pi\) | |||||||
\(368\) | −2.78211 | + | 0.724626i | −0.145027 | + | 0.0377738i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.607810 | + | 9.52889i | 0.0315985 | + | 0.495384i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.9599 | −1.24060 | −0.620299 | − | 0.784365i | \(-0.712989\pi\) | ||||
−0.620299 | + | 0.784365i | \(0.712989\pi\) | |||||||
\(374\) | −2.32755 | − | 36.4900i | −0.120355 | − | 1.88686i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.0457 | + | 2.91074i | −0.775925 | + | 0.150110i | ||||
\(377\) | − | 23.6909i | − | 1.22014i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.00154i | − | 0.154179i | −0.997024 | − | 0.0770894i | \(-0.975437\pi\) | ||
0.997024 | − | 0.0770894i | \(-0.0245627\pi\) | |||||||
\(380\) | −15.7665 | + | 2.01958i | −0.808807 | + | 0.103603i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.9833 | − | 0.955722i | 0.766611 | − | 0.0488990i | ||||
\(383\) | 28.6815 | 1.46555 | 0.732777 | − | 0.680469i | \(-0.238224\pi\) | ||||
0.732777 | + | 0.680469i | \(0.238224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.3372 | − | 1.16965i | 0.933337 | − | 0.0595338i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.2726 | + | 2.72487i | −1.07995 | + | 0.138334i | ||||
\(389\) | 12.0942i | 0.613202i | 0.951838 | + | 0.306601i | \(0.0991918\pi\) | ||||
−0.951838 | + | 0.306601i | \(0.900808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.03281i | − | 0.203948i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.287044 | − | 4.50011i | −0.0144610 | − | 0.226712i | ||||
\(395\) | −21.9986 | −1.10687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.25829 | 0.263906 | 0.131953 | − | 0.991256i | \(-0.457875\pi\) | ||||
0.131953 | + | 0.991256i | \(0.457875\pi\) | |||||||
\(398\) | −1.26479 | − | 19.8286i | −0.0633981 | − | 0.993920i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.61968 | + | 1.20324i | −0.230984 | + | 0.0601621i | ||||
\(401\) | − | 18.5470i | − | 0.926193i | −0.886308 | − | 0.463096i | \(-0.846738\pi\) | ||
0.886308 | − | 0.463096i | \(-0.153262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.14732i | 0.306220i | ||||||||
\(404\) | 0.974943 | + | 7.61121i | 0.0485052 | + | 0.378672i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.5009 | −0.619649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5224 | −0.866429 | −0.433214 | − | 0.901291i | \(-0.642621\pi\) | ||||
−0.433214 | + | 0.901291i | \(0.642621\pi\) | |||||||
\(410\) | −13.4759 | + | 0.859573i | −0.665527 | + | 0.0424513i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.23789 | − | 33.0845i | −0.208786 | − | 1.62996i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 34.2583i | − | 1.68167i | ||||||
\(416\) | 28.0555 | − | 9.25058i | 1.37554 | − | 0.453547i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.32475 | − | 20.7686i | −0.0647954 | − | 1.01583i | ||||
\(419\) | 26.9149 | 1.31488 | 0.657439 | − | 0.753508i | \(-0.271640\pi\) | ||||
0.657439 | + | 0.753508i | \(0.271640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.71296 | −0.229695 | −0.114848 | − | 0.993383i | \(-0.536638\pi\) | ||||
−0.114848 | + | 0.993383i | \(0.536638\pi\) | |||||||
\(422\) | 0.821885 | + | 12.8850i | 0.0400087 | + | 0.627234i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.11110 | − | 5.74334i | −0.0539600 | − | 0.278921i | ||||
\(425\) | − | 6.69647i | − | 0.324827i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.3808 | − | 1.45780i | 0.550111 | − | 0.0704654i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −39.2589 | + | 2.50416i | −1.89323 | + | 0.120761i | ||||
\(431\) | −3.82093 | −0.184048 | −0.0920239 | − | 0.995757i | \(-0.529334\pi\) | ||||
−0.0920239 | + | 0.995757i | \(0.529334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.7992 | −1.67234 | −0.836172 | − | 0.548467i | \(-0.815212\pi\) | ||||
−0.836172 | + | 0.548467i | \(0.815212\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.60828 | + | 0.718381i | −0.268588 | + | 0.0344042i | ||||
\(437\) | − | 2.29531i | − | 0.109799i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.4814i | 1.69343i | 0.532044 | + | 0.846717i | \(0.321424\pi\) | ||||
−0.532044 | + | 0.846717i | \(0.678576\pi\) | |||||||
\(440\) | −6.16060 | − | 31.8444i | −0.293695 | − | 1.51812i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.63787 | + | 41.3550i | 0.125471 | + | 1.96706i | ||||
\(443\) | 10.9584 | 0.520648 | 0.260324 | − | 0.965521i | \(-0.416171\pi\) | ||||
0.260324 | + | 0.965521i | \(0.416171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.2182 | 1.00584 | ||||||||
\(446\) | −2.14603 | − | 33.6442i | −0.101617 | − | 1.59310i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1675i | 1.28211i | 0.767494 | + | 0.641056i | \(0.221503\pi\) | ||||
−0.767494 | + | 0.641056i | \(0.778497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.6790i | − | 0.832472i | ||||||
\(452\) | 1.42213 | + | 11.1023i | 0.0668913 | + | 0.522209i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1309 | − | 0.901354i | 0.663197 | − | 0.0423026i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.5614 | 1.80383 | 0.901914 | − | 0.431916i | \(-0.142162\pi\) | ||||
0.901914 | + | 0.431916i | \(0.142162\pi\) | |||||||
\(458\) | −7.53136 | + | 0.480395i | −0.351918 | + | 0.0224474i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.454522 | − | 3.54837i | −0.0211922 | − | 0.165444i | ||||
\(461\) | 13.5543i | 0.631287i | 0.948878 | + | 0.315643i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315643i | \(0.897780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7564i | 0.825212i | 0.910910 | + | 0.412606i | \(0.135381\pi\) | ||||
−0.910910 | + | 0.412606i | \(0.864619\pi\) | |||||||
\(464\) | −4.57377 | − | 17.5604i | −0.212332 | − | 0.815219i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.789347 | − | 12.3749i | −0.0365658 | − | 0.573258i | ||||
\(467\) | −10.7993 | −0.499732 | −0.249866 | − | 0.968280i | \(-0.580387\pi\) | ||||
−0.249866 | + | 0.968280i | \(0.580387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.21387 | − | 19.0304i | −0.0559916 | − | 0.877805i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.4310 | − | 2.21144i | 0.526156 | − | 0.101790i | ||||
\(473\) | − | 51.5037i | − | 2.36814i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.81135i | − | 0.174877i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.5430 | − | 1.18278i | 0.848136 | − | 0.0540992i | ||||
\(479\) | 18.9672 | 0.866634 | 0.433317 | − | 0.901242i | \(-0.357343\pi\) | ||||
0.433317 | + | 0.901242i | \(0.357343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1676 | 0.645988 | ||||||||
\(482\) | −31.1396 | + | 1.98627i | −1.41837 | + | 0.0904721i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.2991 | − | 2.60017i | 0.922685 | − | 0.118190i | ||||
\(485\) | − | 26.6865i | − | 1.21177i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.5316i | − | 0.658489i | −0.944245 | − | 0.329245i | \(-0.893206\pi\) | ||
0.944245 | − | 0.329245i | \(-0.106794\pi\) | |||||||
\(488\) | −2.80541 | + | 0.542733i | −0.126995 | + | 0.0245684i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.0025 | 1.17348 | 0.586738 | − | 0.809777i | \(-0.300412\pi\) | ||||
0.586738 | + | 0.809777i | \(0.300412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.4547 | 1.14642 | ||||||||
\(494\) | 1.50137 | + | 23.5376i | 0.0675497 | + | 1.05901i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.18680 | + | 4.55657i | 0.0532891 | + | 0.204596i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.74273i | − | 0.122781i | −0.998114 | − | 0.0613907i | \(-0.980446\pi\) | ||
0.998114 | − | 0.0613907i | \(-0.0195536\pi\) | |||||||
\(500\) | 2.40724 | + | 18.7929i | 0.107655 | + | 0.840444i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −37.4217 | + | 2.38698i | −1.67021 | + | 0.106536i | ||||
\(503\) | −21.5337 | −0.960139 | −0.480070 | − | 0.877230i | \(-0.659389\pi\) | ||||
−0.480070 | + | 0.877230i | \(0.659389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.54826 | −0.424892 | ||||||||
\(506\) | 4.67412 | − | 0.298143i | 0.207790 | − | 0.0132541i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.86923 | − | 30.2064i | −0.171669 | − | 1.34019i | ||||
\(509\) | 13.1345i | 0.582177i | 0.956696 | + | 0.291089i | \(0.0940175\pi\) | ||||
−0.956696 | + | 0.291089i | \(0.905983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.0097 | − | 12.2732i | 0.840117 | − | 0.542405i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.52494 | − | 23.9071i | −0.0672620 | − | 1.05450i | ||||
\(515\) | 41.5045 | 1.82890 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9659 | 1.09800 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.98196 | + | 36.0900i | 0.306179 | + | 1.58265i | ||||
\(521\) | − | 7.27913i | − | 0.318905i | −0.987206 | − | 0.159452i | \(-0.949027\pi\) | ||
0.987206 | − | 0.159452i | \(-0.0509728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.79029i | 0.122011i | 0.998137 | + | 0.0610055i | \(0.0194307\pi\) | ||||
−0.998137 | + | 0.0610055i | \(0.980569\pi\) | |||||||
\(524\) | 8.23931 | − | 1.05540i | 0.359936 | − | 0.0461053i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.7015 | + | 1.25668i | −0.859027 | + | 0.0547938i | ||||
\(527\) | −6.60499 | −0.287718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4834 | −0.977540 | ||||||||
\(530\) | 7.26437 | − | 0.463365i | 0.315544 | − | 0.0201273i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.0360i | 0.867858i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2772i | 0.617257i | ||||||||
\(536\) | −6.79300 | − | 35.1133i | −0.293413 | − | 1.51666i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.39899 | − | 21.9325i | −0.0603146 | − | 0.945578i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.607118 | 0.0261020 | 0.0130510 | − | 0.999915i | \(-0.495846\pi\) | ||||
0.0130510 | + | 0.999915i | \(0.495846\pi\) | |||||||
\(542\) | 0.0205005 | + | 0.321395i | 0.000880572 | + | 0.0138051i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.93929 | + | 30.1443i | 0.426144 | + | 1.29243i | ||||
\(545\) | − | 7.03558i | − | 0.301371i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.1295i | − | 0.475865i | −0.971282 | − | 0.237933i | \(-0.923530\pi\) | ||
0.971282 | − | 0.237933i | \(-0.0764697\pi\) | |||||||
\(548\) | −4.15005 | − | 32.3987i | −0.177281 | − | 1.38400i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.76138 | − | 0.495067i | 0.330946 | − | 0.0211097i | ||||
\(551\) | 14.4877 | 0.617198 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.5493 | + | 1.62969i | −1.08549 | + | 0.0692387i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.61487 | − | 20.4138i | −0.110895 | − | 0.865738i | ||||
\(557\) | 29.6533i | 1.25645i | 0.778031 | + | 0.628225i | \(0.216218\pi\) | ||||
−0.778031 | + | 0.628225i | \(0.783782\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.3703i | 2.46880i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.49075 | − | 23.3711i | −0.0628834 | − | 0.985850i | ||||
\(563\) | 32.8348 | 1.38382 | 0.691910 | − | 0.721983i | \(-0.256769\pi\) | ||||
0.691910 | + | 0.721983i | \(0.256769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.9278 | −0.585949 | ||||||||
\(566\) | −0.287496 | − | 4.50721i | −0.0120844 | − | 0.189452i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.2998 | − | 3.92718i | 0.851759 | − | 0.164781i | ||||
\(569\) | − | 9.16895i | − | 0.384382i | −0.981358 | − | 0.192191i | \(-0.938441\pi\) | ||
0.981358 | − | 0.192191i | \(-0.0615594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.4499i | 1.02320i | 0.859224 | + | 0.511599i | \(0.170947\pi\) | ||||
−0.859224 | + | 0.511599i | \(0.829053\pi\) | |||||||
\(572\) | −47.7365 | + | 6.11471i | −1.99596 | + | 0.255669i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.857772 | 0.0357716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0185 | −0.500337 | −0.250168 | − | 0.968202i | \(-0.580486\pi\) | ||||
−0.250168 | + | 0.968202i | \(0.580486\pi\) | |||||||
\(578\) | −20.4411 | + | 1.30386i | −0.850238 | + | 0.0542333i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.3969 | − | 2.86889i | 0.929983 | − | 0.119124i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.53012i | 0.394697i | ||||||||
\(584\) | 26.7638 | − | 5.17771i | 1.10749 | − | 0.214255i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.286052 | − | 4.48456i | −0.0118167 | − | 0.185256i | ||||
\(587\) | 18.8618 | 0.778510 | 0.389255 | − | 0.921130i | \(-0.372733\pi\) | ||||
0.389255 | + | 0.921130i | \(0.372733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.75929 | −0.154899 | ||||||||
\(590\) | 0.922240 | + | 14.4584i | 0.0379680 | + | 0.595241i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.5015 | − | 2.73521i | 0.431608 | − | 0.112416i | ||||
\(593\) | 8.83457i | 0.362792i | 0.983410 | + | 0.181396i | \(0.0580616\pi\) | ||||
−0.983410 | + | 0.181396i | \(0.941938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.43746 | − | 11.2220i | −0.0588808 | − | 0.459672i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.29729 | + | 0.337893i | −0.216622 | + | 0.0138175i | ||||
\(599\) | 27.8030 | 1.13600 | 0.568000 | − | 0.823028i | \(-0.307717\pi\) | ||||
0.568000 | + | 0.823028i | \(0.307717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1977 | −0.497556 | −0.248778 | − | 0.968561i | \(-0.580029\pi\) | ||||
−0.248778 | + | 0.968561i | \(0.580029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.09060 | − | 24.1278i | −0.125755 | − | 0.981746i | ||||
\(605\) | 25.4652i | 1.03531i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5180i | 0.426913i | 0.976953 | + | 0.213457i | \(0.0684722\pi\) | ||||
−0.976953 | + | 0.213457i | \(0.931528\pi\) | |||||||
\(608\) | 5.65703 | + | 17.1569i | 0.229423 | + | 0.695804i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.226336 | − | 3.54837i | −0.00916408 | − | 0.143669i | ||||
\(611\) | −28.2945 | −1.14467 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4103 | 1.59177 | 0.795884 | − | 0.605449i | \(-0.207006\pi\) | ||||
0.795884 | + | 0.605449i | \(0.207006\pi\) | |||||||
\(614\) | 0.977292 | + | 15.3214i | 0.0394403 | + | 0.618323i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 35.9618i | − | 1.44777i | −0.689922 | − | 0.723884i | \(-0.742355\pi\) | ||
0.689922 | − | 0.723884i | \(-0.257645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.4499i | 0.982726i | 0.870955 | + | 0.491363i | \(0.163501\pi\) | ||||
−0.870955 | + | 0.491363i | \(0.836499\pi\) | |||||||
\(620\) | −5.81157 | + | 0.744422i | −0.233398 | + | 0.0298967i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.3668 | − | 1.68183i | 1.05721 | − | 0.0674354i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5429 | −1.18172 | ||||||||
\(626\) | −22.3435 | + | 1.42520i | −0.893024 | + | 0.0569624i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.9639 | − | 1.78868i | 0.557221 | − | 0.0713762i | ||||
\(629\) | 15.2224i | 0.606958i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.08034i | 0.202245i | 0.994874 | + | 0.101123i | \(0.0322434\pi\) | ||||
−0.994874 | + | 0.101123i | \(0.967757\pi\) | |||||||
\(632\) | 4.74881 | + | 24.5468i | 0.188897 | + | 0.976418i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.552594 | + | 8.66325i | 0.0219463 | + | 0.344062i | ||||
\(635\) | 37.8939 | 1.50377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.88185 | + | 29.5026i | 0.0745031 | + | 1.16802i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.1428 | + | 25.4030i | 0.479986 | + | 1.00414i | ||||
\(641\) | 26.7077i | 1.05489i | 0.849589 | + | 0.527445i | \(0.176850\pi\) | ||||
−0.849589 | + | 0.527445i | \(0.823150\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3919i | 0.961924i | 0.876741 | + | 0.480962i | \(0.159713\pi\) | ||||
−0.876741 | + | 0.480962i | \(0.840287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.2900 | + | 1.61314i | −0.995021 | + | 0.0634683i | ||||
\(647\) | −4.83841 | −0.190218 | −0.0951088 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951088 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.9679 | −0.744555 | ||||||||
\(650\) | −8.79615 | + | 0.561071i | −0.345014 | + | 0.0220070i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.454522 | + | 3.54837i | 0.0178004 | + | 0.138965i | ||||
\(653\) | 22.5851i | 0.883821i | 0.897059 | + | 0.441911i | \(0.145699\pi\) | ||||
−0.897059 | + | 0.441911i | \(0.854301\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3362i | 0.403869i | ||||||||
\(656\) | 3.86817 | + | 14.8513i | 0.151027 | + | 0.579846i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4237 | −0.522911 | −0.261456 | − | 0.965215i | \(-0.584203\pi\) | ||||
−0.261456 | + | 0.965215i | \(0.584203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2037 | −0.552460 | −0.276230 | − | 0.961092i | \(-0.589085\pi\) | ||||
−0.276230 | + | 0.961092i | \(0.589085\pi\) | |||||||
\(662\) | 0.0349682 | + | 0.548211i | 0.00135908 | + | 0.0213068i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.2266 | + | 7.39531i | −1.48348 | + | 0.286994i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.26057i | 0.126250i | ||||||||
\(668\) | −16.4054 | + | 2.10142i | −0.634745 | + | 0.0813064i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44.4124 | − | 2.83289i | 1.71580 | − | 0.109444i | ||||
\(671\) | 4.65510 | 0.179708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3016 | 0.435643 | 0.217822 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217822 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(674\) | 8.61463 | − | 0.549492i | 0.331823 | − | 0.0211657i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.3116 | − | 3.62652i | 1.08891 | − | 0.139482i | ||||
\(677\) | − | 3.17751i | − | 0.122122i | −0.998134 | − | 0.0610608i | \(-0.980552\pi\) | ||
0.998134 | − | 0.0610608i | \(-0.0194484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −38.7770 | + | 7.50178i | −1.48703 | + | 0.287680i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.488303 | − | 7.65534i | −0.0186981 | − | 0.293138i | ||||
\(683\) | 6.26524 | 0.239733 | 0.119866 | − | 0.992790i | \(-0.461753\pi\) | ||||
0.119866 | + | 0.992790i | \(0.461753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6441 | 1.55293 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.2690 | + | 43.2658i | 0.429627 | + | 1.64949i | ||||
\(689\) | − | 10.8007i | − | 0.411474i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.1301i | − | 0.613619i | −0.951771 | − | 0.306809i | \(-0.900739\pi\) | ||
0.951771 | − | 0.306809i | \(-0.0992614\pi\) | |||||||
\(692\) | 4.91632 | + | 38.3808i | 0.186890 | + | 1.45902i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.9669 | + | 2.61311i | −1.55508 | + | 0.0991923i | ||||
\(695\) | 25.6091 | 0.971408 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5278 | −0.815422 | ||||||||
\(698\) | −38.5141 | + | 2.45666i | −1.45778 | + | 0.0929859i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.8903i | − | 1.92210i | −0.276373 | − | 0.961050i | \(-0.589133\pi\) | ||
0.276373 | − | 0.961050i | \(-0.410867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.66397i | 0.326768i | ||||||||
\(704\) | −34.2032 | + | 13.7484i | −1.28908 | + | 0.518164i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.72603 | − | 42.7371i | −0.102595 | − | 1.60843i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.3743 | 0.802727 | 0.401364 | − | 0.915919i | \(-0.368536\pi\) | ||||
0.401364 | + | 0.915919i | \(0.368536\pi\) | |||||||
\(710\) | 1.63776 | + | 25.6758i | 0.0614639 | + | 0.963596i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.58036 | − | 23.6760i | −0.171656 | − | 0.887297i | ||||
\(713\) | − | 0.846054i | − | 0.0316850i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 59.8854i | − | 2.23959i | ||||||
\(716\) | 23.9122 | − | 3.06298i | 0.893639 | − | 0.114469i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.3250 | + | 1.87052i | −1.09440 | + | 0.0698073i | ||||
\(719\) | 24.3853 | 0.909418 | 0.454709 | − | 0.890640i | \(-0.349743\pi\) | ||||
0.454709 | + | 0.890640i | \(0.349743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.4216 | − | 0.792321i | 0.462283 | − | 0.0294871i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 41.2613 | − | 5.28529i | 1.53346 | − | 0.196426i | ||||
\(725\) | 5.41417i | 0.201077i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.0825i | 1.37531i | 0.726037 | + | 0.687656i | \(0.241360\pi\) | ||||
−0.726037 | + | 0.687656i | \(0.758640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.15926 | + | 33.8517i | 0.0799180 | + | 1.25291i | ||||
\(731\) | −62.7161 | −2.31964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.1262 | 1.66678 | 0.833388 | − | 0.552689i | \(-0.186398\pi\) | ||||
0.833388 | + | 0.552689i | \(0.186398\pi\) | |||||||
\(734\) | 1.84392 | + | 28.9079i | 0.0680602 | + | 1.06701i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.86128 | + | 1.27315i | −0.142329 | + | 0.0469291i | ||||
\(737\) | 58.2646i | 2.14621i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0456i | 1.58346i | 0.610872 | + | 0.791729i | \(0.290819\pi\) | ||||
−0.610872 | + | 0.791729i | \(0.709181\pi\) | |||||||
\(740\) | 1.71566 | + | 13.3938i | 0.0630689 | + | 0.492367i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.52770 | 0.276165 | 0.138082 | − | 0.990421i | \(-0.455906\pi\) | ||||
0.138082 | + | 0.990421i | \(0.455906\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0780 | 0.515779 | ||||||||
\(746\) | −33.8158 | + | 2.15697i | −1.23808 | + | 0.0789723i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.56996 | − | 51.2905i | −0.240222 | − | 1.87537i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.0306i | − | 1.60670i | −0.595509 | − | 0.803349i | \(-0.703050\pi\) | ||
0.595509 | − | 0.803349i | \(-0.296950\pi\) | |||||||
\(752\) | −20.9727 | + | 5.46254i | −0.764796 | + | 0.199198i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.13275 | − | 33.4360i | −0.0776700 | − | 1.21767i | ||||
\(755\) | 30.2683 | 1.10158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.64185 | 0.277748 | 0.138874 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138874 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(758\) | −0.270211 | − | 4.23621i | −0.00981449 | − | 0.153866i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.0702 | + | 4.26970i | −0.800571 | + | 0.154878i | ||||
\(761\) | − | 17.4602i | − | 0.632932i | −0.948604 | − | 0.316466i | \(-0.897504\pi\) | ||
0.948604 | − | 0.316466i | \(-0.102496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.0605 | − | 2.69771i | 0.761943 | − | 0.0975996i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.4794 | − | 2.58202i | 1.46258 | − | 0.0932922i | ||||
\(767\) | 21.4968 | 0.776204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.13489 | 0.113047 | 0.0565235 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565235 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.7748 | − | 3.30157i | 0.927654 | − | 0.118826i | ||||
\(773\) | 19.0221i | 0.684179i | 0.939667 | + | 0.342090i | \(0.111135\pi\) | ||||
−0.939667 | + | 0.342090i | \(0.888865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.40487i | − | 0.0504645i | ||||||
\(776\) | −29.7777 | + | 5.76078i | −1.06896 | + | 0.206800i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.08877 | + | 17.0692i | 0.0390344 | + | 0.611959i | ||||
\(779\) | −12.2527 | −0.438999 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.6841 | −1.20531 | ||||||||
\(782\) | −0.363050 | − | 5.69169i | −0.0129826 | − | 0.203534i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.5177i | 0.625235i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.59842i | − | 0.163916i | −0.996636 | − | 0.0819581i | \(-0.973883\pi\) | ||
0.996636 | − | 0.0819581i | \(-0.0261174\pi\) | |||||||
\(788\) | −0.810235 | − | 6.32536i | −0.0288634 | − | 0.225332i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31.0476 | + | 1.98040i | −1.10462 | + | 0.0704594i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.27574 | −0.187347 | ||||||||
\(794\) | 7.42126 | − | 0.473372i | 0.263371 | − | 0.0167993i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.57011 | − | 27.8712i | −0.126539 | − | 0.987869i | ||||
\(797\) | 40.4802i | 1.43388i | 0.697134 | + | 0.716941i | \(0.254458\pi\) | ||||
−0.697134 | + | 0.716941i | \(0.745542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.4010i | − | 1.07551i | ||||||
\(800\) | −6.41165 | + | 2.11407i | −0.226686 | + | 0.0747437i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.66967 | − | 26.1762i | −0.0589583 | − | 0.924314i | ||||
\(803\) | −44.4100 | −1.56720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.553406 | + | 8.67599i | 0.0194929 | + | 0.305599i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.06117 | + | 10.6543i | 0.0725118 | + | 0.374816i | ||||
\(809\) | − | 9.86400i | − | 0.346800i | −0.984851 | − | 0.173400i | \(-0.944525\pi\) | ||
0.984851 | − | 0.173400i | \(-0.0554753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.0467i | − | 0.984854i | −0.870354 | − | 0.492427i | \(-0.836110\pi\) | ||
0.870354 | − | 0.492427i | \(-0.163890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.6432 | + | 1.12539i | −0.618392 | + | 0.0394447i | ||||
\(815\) | −4.45143 | −0.155927 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.6954 | −1.24882 | ||||||||
\(818\) | −24.7302 | + | 1.57744i | −0.864671 | + | 0.0551539i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.9418 | + | 2.42631i | −0.661475 | + | 0.0847303i | ||||
\(821\) | − | 26.5158i | − | 0.925408i | −0.886513 | − | 0.462704i | \(-0.846879\pi\) | ||
0.886513 | − | 0.462704i | \(-0.153121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 20.3844i | − | 0.710555i | −0.934761 | − | 0.355277i | \(-0.884386\pi\) | ||
0.934761 | − | 0.355277i | \(-0.115614\pi\) | |||||||
\(824\) | −8.95953 | − | 46.3121i | −0.312120 | − | 1.61336i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.5032 | −0.608645 | −0.304322 | − | 0.952569i | \(-0.598430\pi\) | ||||
−0.304322 | + | 0.952569i | \(0.598430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7983 | 0.375040 | 0.187520 | − | 0.982261i | \(-0.439955\pi\) | ||||
0.187520 | + | 0.982261i | \(0.439955\pi\) | |||||||
\(830\) | −3.08407 | − | 48.3503i | −0.107050 | − | 1.67826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 38.7633 | − | 15.5814i | 1.34388 | − | 0.540189i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.5806i | − | 0.712221i | ||||||
\(836\) | −3.73935 | − | 29.1924i | −0.129328 | − | 1.00964i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 37.9862 | − | 2.42299i | 1.31221 | − | 0.0837006i | ||||
\(839\) | −8.78448 | −0.303274 | −0.151637 | − | 0.988436i | \(-0.548454\pi\) | ||||
−0.151637 | + | 0.988436i | \(0.548454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.41964 | 0.290332 | ||||||||
\(842\) | −6.65161 | + | 0.424279i | −0.229230 | + | 0.0146216i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.31993 | + | 18.1113i | 0.0798552 | + | 0.623415i | ||||
\(845\) | 35.5169i | 1.22182i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.08519 | − | 8.00581i | −0.0716057 | − | 0.274921i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.602843 | − | 9.45104i | −0.0206774 | − | 0.324168i | ||||
\(851\) | −1.94989 | −0.0668413 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.87338 | 0.132622 | 0.0663110 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663110 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9310 | − | 3.08200i | 0.544510 | − | 0.105341i | ||||
\(857\) | 43.2775i | 1.47833i | 0.673524 | + | 0.739165i | \(0.264780\pi\) | ||||
−0.673524 | + | 0.739165i | \(0.735220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8903i | 0.542171i | 0.962555 | + | 0.271086i | \(0.0873826\pi\) | ||||
−0.962555 | + | 0.271086i | \(0.912617\pi\) | |||||||
\(860\) | −55.1824 | + | 7.06848i | −1.88170 | + | 0.241033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.39266 | + | 0.343976i | −0.183675 | + | 0.0117159i | ||||
\(863\) | 10.5584 | 0.359413 | 0.179707 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179707 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48.1487 | −1.63711 | ||||||||
\(866\) | −49.1137 | + | 3.13277i | −1.66895 | + | 0.106456i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 40.7313i | − | 1.38171i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 66.0327i | − | 2.23743i | ||||||
\(872\) | −7.85054 | + | 1.51876i | −0.265853 | + | 0.0514318i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.206633 | − | 3.23947i | −0.00698945 | − | 0.109577i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.75594 | −0.0592940 | −0.0296470 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296470 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(878\) | 3.19418 | + | 50.0765i | 0.107798 | + | 1.69000i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.5615 | − | 44.3888i | −0.389738 | − | 1.49635i | ||||
\(881\) | − | 39.9987i | − | 1.34759i | −0.738917 | − | 0.673796i | \(-0.764663\pi\) | ||
0.738917 | − | 0.673796i | \(-0.235337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.9005i | − | 0.535096i | −0.963545 | − | 0.267548i | \(-0.913787\pi\) | ||
0.963545 | − | 0.267548i | \(-0.0862133\pi\) | |||||||
\(884\) | 7.44589 | + | 58.1288i | 0.250433 | + | 1.95508i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.4661 | − | 0.986517i | 0.519592 | − | 0.0331427i | ||||
\(887\) | 33.3735 | 1.12057 | 0.560286 | − | 0.828299i | \(-0.310691\pi\) | ||||
0.560286 | + | 0.828299i | \(0.310691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 29.9462 | − | 1.91015i | 1.00380 | − | 0.0640284i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.05757 | − | 47.2904i | −0.202823 | − | 1.58340i | ||||
\(893\) | − | 17.3030i | − | 0.579023i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.9978i | 1.00272i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.44572 | + | 38.3427i | 0.0816148 | + | 1.27951i | ||||
\(899\) | 5.34020 | 0.178106 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6048 | 0.386613 | ||||||||
\(902\) | −1.59154 | − | 24.9512i | −0.0529923 | − | 0.830784i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00659 | + | 15.5412i | 0.0999977 | + | 0.516892i | ||||
\(905\) | 51.7623i | 1.72064i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.7879i | 1.22152i | 0.791815 | + | 0.610762i | \(0.209137\pi\) | ||||
−0.791815 | + | 0.610762i | \(0.790863\pi\) | |||||||
\(908\) | 19.8625 | − | 2.54424i | 0.659159 | − | 0.0844337i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.9066 | −1.55409 | −0.777043 | − | 0.629448i | \(-0.783281\pi\) | ||||
−0.777043 | + | 0.629448i | \(0.783281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63.4307 | 2.09925 | ||||||||
\(914\) | 54.4235 | − | 3.47145i | 1.80017 | − | 0.114826i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5861 | + | 1.35601i | −0.349775 | + | 0.0448037i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0153i | 0.594268i | 0.954836 | + | 0.297134i | \(0.0960309\pi\) | ||||
−0.954836 | + | 0.297134i | \(0.903969\pi\) | |||||||
\(920\) | −0.960926 | − | 4.96706i | −0.0316808 | − | 0.163759i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.22021 | + | 19.1298i | 0.0401856 | + | 0.630006i | ||||
\(923\) | 38.1750 | 1.25654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.23779 | −0.106458 | ||||||||
\(926\) | 1.59851 | + | 25.0605i | 0.0525302 | + | 0.823538i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.03602 | − | 24.3720i | −0.263795 | − | 0.800050i | ||||
\(929\) | − | 32.6340i | − | 1.07069i | −0.844635 | − | 0.535343i | \(-0.820182\pi\) | ||
0.844635 | − | 0.535343i | \(-0.179818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.22808 | − | 17.3942i | −0.0729833 | − | 0.569768i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.2416 | + | 0.972197i | −0.498719 | + | 0.0318113i | ||||
\(935\) | 64.3439 | 2.10427 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.08001 | 0.133288 | 0.0666441 | − | 0.997777i | \(-0.478771\pi\) | ||||
0.0666441 | + | 0.997777i | \(0.478771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.42638 | − | 26.7491i | −0.111756 | − | 0.872461i | ||||
\(941\) | 24.6956i | 0.805055i | 0.915408 | + | 0.402527i | \(0.131868\pi\) | ||||
−0.915408 | + | 0.402527i | \(0.868132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.75756i | − | 0.0897984i | ||||||
\(944\) | 15.9341 | − | 4.15018i | 0.518609 | − | 0.135077i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.63657 | − | 72.6895i | −0.150748 | − | 2.36334i | ||||
\(947\) | −36.9305 | −1.20008 | −0.600040 | − | 0.799970i | \(-0.704849\pi\) | ||||
−0.600040 | + | 0.799970i | \(0.704849\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.3310 | 1.63381 | ||||||||
\(950\) | −0.343113 | − | 5.37914i | −0.0111321 | − | 0.174522i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 61.5883i | 1.99504i | 0.0703720 | + | 0.997521i | \(0.477581\pi\) | ||||
−0.0703720 | + | 0.997521i | \(0.522419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.4204i | 0.854945i | ||||||||
\(956\) | 26.0641 | − | 3.33863i | 0.842972 | − | 0.107979i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.7693 | − | 1.70750i | 0.864876 | − | 0.0551669i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6143 | 0.955301 | ||||||||
\(962\) | 19.9954 | − | 1.27543i | 0.644678 | − | 0.0411214i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −43.7699 | + | 5.60663i | −1.40973 | + | 0.180577i | ||||
\(965\) | 32.3344i | 1.04088i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8368i | 0.734381i | 0.930146 | + | 0.367191i | \(0.119680\pi\) | ||||
−0.930146 | + | 0.367191i | \(0.880320\pi\) | |||||||
\(968\) | 28.4149 | − | 5.49714i | 0.913290 | − | 0.176685i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.40242 | − | 37.6638i | −0.0771371 | − | 1.20931i | ||||
\(971\) | −48.1874 | −1.54641 | −0.773203 | − | 0.634159i | \(-0.781347\pi\) | ||||
−0.773203 | + | 0.634159i | \(0.781347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.30819 | − | 20.5091i | −0.0419172 | − | 0.657154i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.91054 | + | 1.01854i | −0.125173 | + | 0.0326026i | ||||
\(977\) | − | 31.4737i | − | 1.00693i | −0.864015 | − | 0.503466i | \(-0.832058\pi\) | ||
0.864015 | − | 0.503466i | \(-0.167942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.2865i | 1.25560i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.6985 | − | 2.34085i | 1.17110 | − | 0.0746995i | ||||
\(983\) | 40.0880 | 1.27861 | 0.639304 | − | 0.768954i | \(-0.279223\pi\) | ||||
0.639304 | + | 0.768954i | \(0.279223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.93517 | 0.252835 | ||||||||
\(986\) | 35.9253 | − | 2.29153i | 1.14410 | − | 0.0729772i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.23789 | + | 33.0845i | 0.134825 | + | 1.05256i | ||||
\(989\) | − | 8.03350i | − | 0.255450i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.5681i | 1.63812i | 0.573711 | + | 0.819058i | \(0.305503\pi\) | ||||
−0.573711 | + | 0.819058i | \(0.694497\pi\) | |||||||
\(992\) | 2.08519 | + | 6.32406i | 0.0662049 | + | 0.200789i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.9644 | 1.10845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.5162 | −0.681424 | −0.340712 | − | 0.940168i | \(-0.610668\pi\) | ||||
−0.340712 | + | 0.940168i | \(0.610668\pi\) | |||||||
\(998\) | −0.246911 | − | 3.87094i | −0.00781584 | − | 0.122532i | ||||
\(999\) | 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 | 1764.2.e.i.1079.15 | 16 | ||
3.2 | odd | 2 | inner | 1764.2.e.i.1079.2 | 16 | ||
4.3 | odd | 2 | inner | 1764.2.e.i.1079.1 | 16 | ||
7.2 | even | 3 | 252.2.be.a.179.5 | yes | 32 | ||
7.4 | even | 3 | 252.2.be.a.107.7 | yes | 32 | ||
7.6 | odd | 2 | 1764.2.e.h.1079.15 | 16 | |||
12.11 | even | 2 | inner | 1764.2.e.i.1079.16 | 16 | ||
21.2 | odd | 6 | 252.2.be.a.179.12 | yes | 32 | ||
21.11 | odd | 6 | 252.2.be.a.107.10 | yes | 32 | ||
21.20 | even | 2 | 1764.2.e.h.1079.2 | 16 | |||
28.11 | odd | 6 | 252.2.be.a.107.12 | yes | 32 | ||
28.23 | odd | 6 | 252.2.be.a.179.10 | yes | 32 | ||
28.27 | even | 2 | 1764.2.e.h.1079.1 | 16 | |||
84.11 | even | 6 | 252.2.be.a.107.5 | ✓ | 32 | ||
84.23 | even | 6 | 252.2.be.a.179.7 | yes | 32 | ||
84.83 | odd | 2 | 1764.2.e.h.1079.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.be.a.107.5 | ✓ | 32 | 84.11 | even | 6 | ||
252.2.be.a.107.7 | yes | 32 | 7.4 | even | 3 | ||
252.2.be.a.107.10 | yes | 32 | 21.11 | odd | 6 | ||
252.2.be.a.107.12 | yes | 32 | 28.11 | odd | 6 | ||
252.2.be.a.179.5 | yes | 32 | 7.2 | even | 3 | ||
252.2.be.a.179.7 | yes | 32 | 84.23 | even | 6 | ||
252.2.be.a.179.10 | yes | 32 | 28.23 | odd | 6 | ||
252.2.be.a.179.12 | yes | 32 | 21.2 | odd | 6 | ||
1764.2.e.h.1079.1 | 16 | 28.27 | even | 2 | |||
1764.2.e.h.1079.2 | 16 | 21.20 | even | 2 | |||
1764.2.e.h.1079.15 | 16 | 7.6 | odd | 2 | |||
1764.2.e.h.1079.16 | 16 | 84.83 | odd | 2 | |||
1764.2.e.i.1079.1 | 16 | 4.3 | odd | 2 | inner | ||
1764.2.e.i.1079.2 | 16 | 3.2 | odd | 2 | inner | ||
1764.2.e.i.1079.15 | 16 | 1.1 | even | 1 | trivial | ||
1764.2.e.i.1079.16 | 16 | 12.11 | even | 2 | inner |