Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.864716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0.864716 | 0.499244 | 0.249622 | − | 0.968343i | \(-0.419694\pi\) | ||||
0.249622 | + | 0.968343i | \(0.419694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.40497 | −0.628323 | −0.314162 | − | 0.949370i | \(-0.601723\pi\) | ||||
−0.314162 | + | 0.949370i | \(0.601723\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45790 | −0.929000 | −0.464500 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464500 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.25227 | −0.750755 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26992 | 0.382896 | 0.191448 | − | 0.981503i | \(-0.438682\pi\) | ||||
0.191448 | + | 0.981503i | \(0.438682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.79248 | 1.05185 | 0.525923 | − | 0.850532i | \(-0.323720\pi\) | ||||
0.525923 | + | 0.850532i | \(0.323720\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.21490 | −0.313687 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.52341 | 1.49657 | 0.748286 | − | 0.663376i | \(-0.230877\pi\) | ||||
0.748286 | + | 0.663376i | \(0.230877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.12539 | −0.463798 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.32346 | 0.275961 | 0.137981 | − | 0.990435i | \(-0.455939\pi\) | ||||
0.137981 | + | 0.990435i | \(0.455939\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.02605 | −0.605210 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.54172 | −0.874054 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.10007 | −1.31845 | −0.659225 | − | 0.751946i | \(-0.729115\pi\) | ||||
−0.659225 | + | 0.751946i | \(0.729115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.91840 | 1.24258 | 0.621291 | − | 0.783580i | \(-0.286609\pi\) | ||||
0.621291 | + | 0.783580i | \(0.286609\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.09812 | 0.191158 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.45329 | 0.583712 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.38301 | 1.04936 | 0.524681 | − | 0.851299i | \(-0.324185\pi\) | ||||
0.524681 | + | 0.851299i | \(0.324185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.27942 | 0.525127 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.21762 | −1.12720 | −0.563601 | − | 0.826047i | \(-0.690585\pi\) | ||||
−0.563601 | + | 0.826047i | \(0.690585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.21157 | 1.40475 | 0.702376 | − | 0.711807i | \(-0.252123\pi\) | ||||
0.702376 | + | 0.711807i | \(0.252123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16437 | 0.471717 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3544 | −1.65621 | −0.828103 | − | 0.560576i | \(-0.810580\pi\) | ||||
−0.828103 | + | 0.560576i | \(0.810580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.958714 | −0.136959 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.864716 | −0.121084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1634 | −1.67077 | −0.835385 | − | 0.549665i | \(-0.814755\pi\) | ||||
−0.835385 | + | 0.549665i | \(0.814755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.78421 | −0.240582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.64089 | 0.747155 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.31997 | −0.297042 | −0.148521 | − | 0.988909i | \(-0.547451\pi\) | ||||
−0.148521 | + | 0.988909i | \(0.547451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.53585 | 0.697452 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.32834 | −0.660899 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.7359 | −1.80027 | −0.900137 | − | 0.435607i | \(-0.856534\pi\) | ||||
−0.900137 | + | 0.435607i | \(0.856534\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.14442 | 0.137772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.56458 | −0.304359 | −0.152180 | − | 0.988353i | \(-0.548629\pi\) | ||||
−0.152180 | + | 0.988353i | \(0.548629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.85616 | 0.568370 | 0.284185 | − | 0.958769i | \(-0.408277\pi\) | ||||
0.284185 | + | 0.958769i | \(0.408277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.61667 | −0.302147 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.12134 | −0.355710 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.22521 | 1.03792 | 0.518958 | − | 0.854799i | \(-0.326320\pi\) | ||||
0.518958 | + | 0.854799i | \(0.326320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.82950 | 0.314389 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.6201 | −1.38524 | −0.692619 | − | 0.721304i | \(-0.743543\pi\) | ||||
−0.692619 | + | 0.721304i | \(0.743543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40497 | 0.152391 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.13954 | −0.658228 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0483 | 1.06512 | 0.532558 | − | 0.846393i | \(-0.321231\pi\) | ||||
0.532558 | + | 0.846393i | \(0.321231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.32155 | −0.977164 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.98245 | 0.620351 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.16521 | −0.940331 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.67250 | −0.677490 | −0.338745 | − | 0.940878i | \(-0.610002\pi\) | ||||
−0.338745 | + | 0.940878i | \(0.610002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.86020 | −0.287461 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4085 | 1.33420 | 0.667100 | − | 0.744969i | \(-0.267536\pi\) | ||||
0.667100 | + | 0.744969i | \(0.267536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7335 | 1.05760 | 0.528800 | − | 0.848746i | \(-0.322642\pi\) | ||||
0.528800 | + | 0.848746i | \(0.322642\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.98611 | 0.291415 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.7214 | −1.51985 | −0.759924 | − | 0.650012i | \(-0.774764\pi\) | ||||
−0.759924 | + | 0.650012i | \(0.774764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8611 | −1.04030 | −0.520152 | − | 0.854074i | \(-0.674125\pi\) | ||||
−0.520152 | + | 0.854074i | \(0.674125\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.51949 | 0.523887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.1816 | −1.14595 | −0.572975 | − | 0.819573i | \(-0.694211\pi\) | ||||
−0.572975 | + | 0.819573i | \(0.694211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.85943 | −0.173393 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.54168 | −0.789678 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.45790 | 0.225316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.38730 | −0.853391 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.24119 | −0.562749 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2764 | 1.00859 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4744 | −1.55060 | −0.775302 | − | 0.631591i | \(-0.782402\pi\) | ||||
−0.775302 | + | 0.631591i | \(0.782402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.96539 | 0.701314 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.99832 | −0.698816 | −0.349408 | − | 0.936971i | \(-0.613617\pi\) | ||||
−0.349408 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0339 | −1.39032 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.38099 | 0.549189 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.95226 | 0.337665 | 0.168832 | − | 0.985645i | \(-0.446000\pi\) | ||||
0.168832 | + | 0.985645i | \(0.446000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9735 | −0.930756 | −0.465378 | − | 0.885112i | \(-0.654082\pi\) | ||||
−0.465378 | + | 0.885112i | \(0.654082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.81831 | −0.826851 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.81615 | 0.402747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.97541 | 0.828413 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.829015 | −0.0683760 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.9686 | −1.30820 | −0.654100 | − | 0.756408i | \(-0.726953\pi\) | ||||
−0.654100 | + | 0.756408i | \(0.726953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.3823 | −1.82145 | −0.910724 | − | 0.413015i | \(-0.864476\pi\) | ||||
−0.910724 | + | 0.413015i | \(0.864476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.25227 | 0.182085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.72017 | −0.780743 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.8758 | −1.58626 | −0.793129 | − | 0.609054i | \(-0.791549\pi\) | ||||
−0.793129 | + | 0.609054i | \(0.791549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5179 | −0.834122 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.25295 | −0.256368 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.77046 | −0.216999 | −0.108500 | − | 0.994096i | \(-0.534605\pi\) | ||||
−0.108500 | + | 0.994096i | \(0.534605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.54283 | −0.120109 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.7982 | 1.91895 | 0.959473 | − | 0.281801i | \(-0.0909319\pi\) | ||||
0.959473 | + | 0.281801i | \(0.0909319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.38291 | 0.106378 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6924 | −1.12356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.8989 | −0.828630 | −0.414315 | − | 0.910133i | \(-0.635979\pi\) | ||||
−0.414315 | + | 0.910133i | \(0.635979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.43773 | 0.562240 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.864716 | 0.0649960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.69364 | −0.126589 | −0.0632943 | − | 0.997995i | \(-0.520161\pi\) | ||||
−0.0632943 | + | 0.997995i | \(0.520161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.29745 | 0.0964390 | 0.0482195 | − | 0.998837i | \(-0.484645\pi\) | ||||
0.0482195 | + | 0.998837i | \(0.484645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00612 | −0.148296 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.96797 | −0.659338 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26992 | −0.0928659 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.1631 | 0.811996 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.465653 | −0.0336935 | −0.0168467 | − | 0.999858i | \(-0.505363\pi\) | ||||
−0.0168467 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1778 | −0.948560 | −0.474280 | − | 0.880374i | \(-0.657292\pi\) | ||||
−0.474280 | + | 0.880374i | \(0.657292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.60750 | −0.329950 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3903 | 1.52400 | 0.761998 | − | 0.647580i | \(-0.224219\pi\) | ||||
0.761998 | + | 0.647580i | \(0.224219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.46123 | 0.670689 | 0.335344 | − | 0.942096i | \(-0.391147\pi\) | ||||
0.335344 | + | 0.942096i | \(0.391147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.7423 | −0.898776 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.4513 | 1.22484 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1406 | 0.708248 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.98080 | −0.207180 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.28421 | 0.573031 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.28272 | −0.363678 | −0.181839 | − | 0.983328i | \(-0.558205\pi\) | ||||
−0.181839 | + | 0.983328i | \(0.558205\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.21763 | −0.151949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.9420 | −0.882638 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0048 | −1.15436 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.19920 | 0.283756 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.79248 | −0.255110 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4443 | 1.50298 | 0.751492 | − | 0.659742i | \(-0.229335\pi\) | ||||
0.751492 | + | 0.659742i | \(0.229335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.81547 | 0.454365 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.16577 | −0.0773751 | −0.0386875 | − | 0.999251i | \(-0.512318\pi\) | ||||
−0.0386875 | + | 0.999251i | \(0.512318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.41708 | −0.291889 | −0.145944 | − | 0.989293i | \(-0.546622\pi\) | ||||
−0.145944 | + | 0.989293i | \(0.546622\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.69908 | −0.177586 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.7157 | 1.48815 | 0.744076 | − | 0.668095i | \(-0.232890\pi\) | ||||
0.744076 | + | 0.668095i | \(0.232890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9526 | 1.04063 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.97718 | 0.518174 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9563 | −0.773388 | −0.386694 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386694 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8737 | 0.829268 | 0.414634 | − | 0.909988i | \(-0.363910\pi\) | ||||
0.414634 | + | 0.909988i | \(0.363910\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0719 | 1.03101 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.34697 | 0.0860546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.7399 | 1.57416 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9128 | −0.691572 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6277 | −0.860175 | −0.430088 | − | 0.902787i | \(-0.641517\pi\) | ||||
−0.430088 | + | 0.902787i | \(0.641517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.68070 | 0.105664 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.21490 | 0.0760802 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.6606 | −1.22640 | −0.613199 | − | 0.789929i | \(-0.710117\pi\) | ||||
−0.613199 | + | 0.789929i | \(0.710117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.6888 | −0.974856 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.9912 | 0.989833 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.48341 | 0.338121 | 0.169061 | − | 0.985606i | \(-0.445927\pi\) | ||||
0.169061 | + | 0.985606i | \(0.445927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.0892 | 1.04978 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.68892 | 0.531753 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.1449 | 0.618546 | 0.309273 | − | 0.950973i | \(-0.399914\pi\) | ||||
0.309273 | + | 0.950973i | \(0.399914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.54207 | −0.215165 | −0.107583 | − | 0.994196i | \(-0.534311\pi\) | ||||
−0.107583 | + | 0.994196i | \(0.534311\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.06049 | −0.487843 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.84285 | −0.231732 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2177 | 1.15468 | 0.577339 | − | 0.816504i | \(-0.304091\pi\) | ||||
0.577339 | + | 0.816504i | \(0.304091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.5821 | −0.932875 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.71710 | 0.579674 | 0.289837 | − | 0.957076i | \(-0.406399\pi\) | ||||
0.289837 | + | 0.957076i | \(0.406399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.43775 | 0.323241 | 0.161620 | − | 0.986853i | \(-0.448328\pi\) | ||||
0.161620 | + | 0.986853i | \(0.448328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.92531 | −0.469455 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7402 | 1.04717 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.76982 | −0.338233 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.9884 | −0.758793 | −0.379396 | − | 0.925234i | \(-0.623868\pi\) | ||||
−0.379396 | + | 0.925234i | \(0.623868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.40497 | −0.0818007 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.76763 | −0.334672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.01922 | 0.290269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.6411 | −1.30501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.5946 | 0.666091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.25950 | 0.186638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8146 | −0.788438 | −0.394219 | − | 0.919016i | \(-0.628985\pi\) | ||||
−0.394219 | + | 0.919016i | \(0.628985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.28140 | 0.528000 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0508 | −1.02357 | −0.511784 | − | 0.859114i | \(-0.671015\pi\) | ||||
−0.511784 | + | 0.859114i | \(0.671015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8897 | −1.35033 | −0.675164 | − | 0.737668i | \(-0.735927\pi\) | ||||
−0.675164 | + | 0.737668i | \(0.735927\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.77773 | −0.438225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.54912 | 0.480166 | 0.240083 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240083 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.01653 | −0.504829 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5946 | −0.758775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.52341 | −0.362972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4762 | −0.636587 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.39176 | −0.519366 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.9080 | 1.53862 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.8675 | 0.652298 | 0.326149 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326149 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.3762 | −0.787814 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.7035 | 1.13115 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.29403 | −0.342858 | −0.171429 | − | 0.985197i | \(-0.554838\pi\) | ||||
−0.171429 | + | 0.985197i | \(0.554838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.5336 | −0.572109 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.78582 | 0.475779 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5617 | 1.05623 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.60788 | −0.0865654 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.19978 | 0.171773 | 0.0858866 | − | 0.996305i | \(-0.472628\pi\) | ||||
0.0858866 | + | 0.996305i | \(0.472628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.2383 | 1.40450 | 0.702252 | − | 0.711929i | \(-0.252178\pi\) | ||||
0.702252 | + | 0.711929i | \(0.252178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.2244 | −0.919370 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1625 | 0.594119 | 0.297059 | − | 0.954859i | \(-0.403994\pi\) | ||||
0.297059 | + | 0.954859i | \(0.403994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.60316 | 0.191236 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.12539 | 0.112487 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.3590 | −1.65506 | −0.827532 | − | 0.561418i | \(-0.810256\pi\) | ||||
−0.827532 | + | 0.561418i | \(0.810256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.5548 | 1.23973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.11735 | −0.426050 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.82278 | −0.357120 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.85347 | −0.462147 | −0.231074 | − | 0.972936i | \(-0.574224\pi\) | ||||
−0.231074 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.2560 | 0.846253 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.8964 | 1.55215 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.6779 | −1.64022 | −0.820111 | − | 0.572205i | \(-0.806088\pi\) | ||||
−0.820111 | + | 0.572205i | \(0.806088\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.75087 | 0.503533 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.9269 | −1.38680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.2687 | 1.45206 | 0.726032 | − | 0.687661i | \(-0.241362\pi\) | ||||
0.726032 | + | 0.687661i | \(0.241362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.1104 | −0.774129 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.9554 | 0.815285 | 0.407643 | − | 0.913142i | \(-0.366351\pi\) | ||||
0.407643 | + | 0.913142i | \(0.366351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.38541 | 0.223501 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.7469 | −1.05462 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9543 | 0.656810 | 0.328405 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328405 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.32346 | −0.0669305 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.91627 | −0.348880 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9612 | −0.652147 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.98957 | 0.501362 | 0.250681 | − | 0.968070i | \(-0.419345\pi\) | ||||
0.250681 | + | 0.968070i | \(0.419345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.8648 | −0.694107 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.07820 | 0.403406 | 0.201703 | − | 0.979447i | \(-0.435352\pi\) | ||||
0.201703 | + | 0.979447i | \(0.435352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.2379 | 1.30700 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.97538 | −0.197538 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.10593 | 0.401796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.07272 | −0.250830 | −0.125415 | − | 0.992104i | \(-0.540026\pi\) | ||||
−0.125415 | + | 0.992104i | \(0.540026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.41759 | 0.168577 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.45790 | −0.120945 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7309 | 0.870377 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.48892 | −0.464674 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.11139 | −0.103148 | −0.0515742 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515742 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8083 | 0.867922 | 0.433961 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433961 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.5731 | 1.24341 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.02605 | 0.146785 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.70226 | 0.275952 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.16461 | 0.201069 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.9057 | −0.910656 | −0.455328 | − | 0.890324i | \(-0.650478\pi\) | ||||
−0.455328 | + | 0.890324i | \(0.650478\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.41653 | 0.212245 | 0.106122 | − | 0.994353i | \(-0.466156\pi\) | ||||
0.106122 | + | 0.994353i | \(0.466156\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.62590 | 0.413580 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.63350 | 0.412996 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8955 | 1.18820 | 0.594099 | − | 0.804392i | \(-0.297509\pi\) | ||||
0.594099 | + | 0.804392i | \(0.297509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.15928 | 0.102823 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.6050 | −0.978975 | −0.489487 | − | 0.872010i | \(-0.662816\pi\) | ||||
−0.489487 | + | 0.872010i | \(0.662816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1176 | −0.669238 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.8083 | −0.653111 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5452 | 0.922396 | 0.461198 | − | 0.887297i | \(-0.347420\pi\) | ||||
0.461198 | + | 0.887297i | \(0.347420\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.16581 | −0.431601 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.3544 | −0.909347 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.0965 | 0.613975 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.66545 | 0.171462 | 0.0857312 | − | 0.996318i | \(-0.472677\pi\) | ||||
0.0857312 | + | 0.996318i | \(0.472677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.54172 | 0.211989 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.5705 | −1.14436 | −0.572181 | − | 0.820127i | \(-0.693903\pi\) | ||||
−0.572181 | + | 0.820127i | \(0.693903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.5385 | 1.18688 | 0.593439 | − | 0.804879i | \(-0.297770\pi\) | ||||
0.593439 | + | 0.804879i | \(0.297770\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.40519 | −0.389781 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.2767 | −0.892020 | −0.446010 | − | 0.895028i | \(-0.647155\pi\) | ||||
−0.446010 | + | 0.895028i | \(0.647155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.2194 | 1.67245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.1869 | −0.791930 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6980 | 0.537873 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.7401 | −0.905740 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.3952 | 1.25434 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.38871 | 0.337599 | 0.168799 | − | 0.985650i | \(-0.446011\pi\) | ||||
0.168799 | + | 0.985650i | \(0.446011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.2075 | 1.10377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.81288 | −0.127990 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.37469 | 0.425683 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.1498 | −1.41153 | −0.705767 | − | 0.708444i | \(-0.749397\pi\) | ||||
−0.705767 | + | 0.708444i | \(0.749397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.39566 | −0.108336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5165 | −0.564860 | −0.282430 | − | 0.959288i | \(-0.591140\pi\) | ||||
−0.282430 | + | 0.959288i | \(0.591140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.10007 | 0.319771 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.01851 | 0.180618 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.30348 | 0.282750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.205806 | 0.00921315 | 0.00460657 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460657 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4434 | 0.958022 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5155 | −0.468863 | −0.234431 | − | 0.972133i | \(-0.575323\pi\) | ||||
−0.234431 | + | 0.972133i | \(0.575323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8386 | −0.838308 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.19583 | 0.0531086 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.6417 | −0.604658 | −0.302329 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302329 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9360 | −0.528016 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.6275 | −1.30808 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0802 | −0.664515 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4192 | −0.634154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.42448 | −0.413689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.08894 | 0.354383 | 0.177191 | − | 0.984176i | \(-0.443299\pi\) | ||||
0.177191 | + | 0.984176i | \(0.443299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.32178 | 0.407613 | 0.203807 | − | 0.979011i | \(-0.434669\pi\) | ||||
0.203807 | + | 0.979011i | \(0.434669\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.43153 | 0.280695 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.91840 | −0.301370 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.2484 | −0.923845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.25227 | −0.0977400 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.3727 | −1.18564 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0882 | 0.954956 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.46452 | −0.0631986 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.21749 | −0.0524411 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.687310 | −0.0295498 | −0.0147749 | − | 0.999891i | \(-0.504703\pi\) | ||||
−0.0147749 | + | 0.999891i | \(0.504703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.12193 | 0.0481466 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.2596 | 0.653647 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.5431 | −1.13490 | −0.567450 | − | 0.823408i | \(-0.692070\pi\) | ||||
−0.567450 | + | 0.823408i | \(0.692070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.22519 | 0.223006 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.3166 | −1.97315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.6747 | −0.964225 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.75474 | −0.329171 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.41792 | 0.399050 | 0.199525 | − | 0.979893i | \(-0.436060\pi\) | ||||
0.199525 | + | 0.979893i | \(0.436060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.9347 | 1.47758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.09812 | −0.0463627 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8884 | −1.09107 | −0.545533 | − | 0.838090i | \(-0.683673\pi\) | ||||
−0.545533 | + | 0.838090i | \(0.683673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1149 | 0.720027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.95464 | −0.292067 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.6163 | −1.19966 | −0.599830 | − | 0.800128i | \(-0.704765\pi\) | ||||
−0.599830 | + | 0.800128i | \(0.704765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.4796 | −1.35923 | −0.679614 | − | 0.733570i | \(-0.737853\pi\) | ||||
−0.679614 | + | 0.733570i | \(0.737853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.402658 | −0.0168213 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00487 | −0.167015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5525 | −0.689091 | −0.344546 | − | 0.938770i | \(-0.611967\pi\) | ||||
−0.344546 | + | 0.938770i | \(0.611967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3951 | −0.473563 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.0190 | 1.28689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.4466 | −0.639731 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0008 | 0.496173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.7234 | 0.896622 | 0.448311 | − | 0.893878i | \(-0.352026\pi\) | ||||
0.448311 | + | 0.893878i | \(0.352026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.1315 | 1.85961 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.4965 | 0.760846 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.4114 | 0.879260 | 0.439630 | − | 0.898179i | \(-0.355109\pi\) | ||||
0.439630 | + | 0.898179i | \(0.355109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.45329 | −0.141571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.18128 | 0.334837 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7962 | 1.09486 | 0.547431 | − | 0.836851i | \(-0.315606\pi\) | ||||
0.547431 | + | 0.836851i | \(0.315606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.5975 | 0.921772 | 0.460886 | − | 0.887459i | \(-0.347532\pi\) | ||||
0.460886 | + | 0.887459i | \(0.347532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.1891 | 1.35157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.1889 | 0.536205 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.8772 | −1.21268 | −0.606340 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606340 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.0904 | 0.611494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.0613 | −1.74207 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.4094 | 1.91485 | 0.957423 | − | 0.288688i | \(-0.0932190\pi\) | ||||
0.957423 | + | 0.288688i | \(0.0932190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.76871 | 0.353588 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.4721 | −1.22676 | −0.613380 | − | 0.789788i | \(-0.710190\pi\) | ||||
−0.613380 | + | 0.789788i | \(0.710190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.9767 | −0.521577 | −0.260788 | − | 0.965396i | \(-0.583982\pi\) | ||||
−0.260788 | + | 0.965396i | \(0.583982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.01081 | −0.241205 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.6977 | −0.989493 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.712781 | −0.0285112 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.16349 | 0.286082 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.38301 | −0.254507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.03775 | −0.240359 | −0.120179 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120179 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.56805 | −0.181564 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.5511 | 0.974280 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.63590 | −0.144060 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.77611 | 0.228499 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3185 | 0.644540 | 0.322270 | − | 0.946648i | \(-0.395554\pi\) | ||||
0.322270 | + | 0.946648i | \(0.395554\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.4448 | −0.411904 | −0.205952 | − | 0.978562i | \(-0.566029\pi\) | ||||
−0.205952 | + | 0.978562i | \(0.566029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.1912 | −0.440652 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7049 | 0.892620 | 0.446310 | − | 0.894878i | \(-0.352738\pi\) | ||||
0.446310 | + | 0.894878i | \(0.352738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26992 | 0.0498488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7043 | −0.576306 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.2960 | −0.442045 | −0.221023 | − | 0.975269i | \(-0.570939\pi\) | ||||
−0.221023 | + | 0.975269i | \(0.570939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.2374 | 0.439083 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.9374 | −0.426707 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.6163 | −1.15369 | −0.576843 | − | 0.816855i | \(-0.695716\pi\) | ||||
−0.576843 | + | 0.816855i | \(0.695716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.20393 | 0.202409 | 0.101205 | − | 0.994866i | \(-0.467730\pi\) | ||||
0.101205 | + | 0.994866i | \(0.467730\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.27942 | −0.127362 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.5272 | 0.873567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.39669 | −0.363841 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.4080 | 0.750356 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.94618 | −0.113736 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.50186 | −0.289175 | −0.144588 | − | 0.989492i | \(-0.546186\pi\) | ||||
−0.144588 | + | 0.989492i | \(0.546186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.7435 | 0.528986 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.95163 | 0.228740 | 0.114370 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114370 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.4004 | 0.629388 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.00806 | −0.0386290 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.0962 | 0.807222 | 0.403611 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403611 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.55283 | −0.212163 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.81952 | −0.145724 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −46.1294 | −1.75739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8962 | 0.909053 | 0.454527 | − | 0.890733i | \(-0.349808\pi\) | ||||
0.454527 | + | 0.890733i | \(0.349808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.03010 | 0.267051 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.4174 | 0.584816 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.21762 | 0.273387 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.6426 | 0.742951 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5315 | −1.00208 | −0.501041 | − | 0.865424i | \(-0.667049\pi\) | ||||
−0.501041 | + | 0.865424i | \(0.667049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.6390 | 1.57044 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.7945 | 0.519530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.9569 | −1.23947 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.9766 | 1.05068 | 0.525341 | − | 0.850892i | \(-0.323938\pi\) | ||||
0.525341 | + | 0.850892i | \(0.323938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.7776 | −0.779222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.15626 | 0.342905 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.76657 | −0.253055 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3388 | −0.386110 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.10331 | 0.264909 | 0.132454 | − | 0.991189i | \(-0.457714\pi\) | ||||
0.132454 | + | 0.991189i | \(0.457714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.3818 | −0.982510 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1321 | 0.414007 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.4852 | 0.797939 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.9008 | 0.663903 | 0.331951 | − | 0.943296i | \(-0.392293\pi\) | ||||
0.331951 | + | 0.943296i | \(0.392293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.40910 | 0.200337 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.21157 | −0.340702 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.3404 | 1.74856 | 0.874278 | − | 0.485425i | \(-0.161335\pi\) | ||||
0.874278 | + | 0.485425i | \(0.161335\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.16474 | 0.0429622 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.7134 | −0.689317 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2291 | −0.449855 | −0.224928 | − | 0.974375i | \(-0.572215\pi\) | ||||
−0.224928 | + | 0.974375i | \(0.572215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.3930 | 0.785891 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −54.1701 | −1.98731 | −0.993654 | − | 0.112478i | \(-0.964121\pi\) | ||||
−0.993654 | + | 0.112478i | \(0.964121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.4355 | 0.821973 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.4239 | 1.03997 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.6418 | 1.41194 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3321 | 0.778419 | 0.389209 | − | 0.921149i | \(-0.372748\pi\) | ||||
0.389209 | + | 0.921149i | \(0.372748\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.7841 | −0.429437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.4466 | 1.14446 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.5162 | −0.745676 | −0.372838 | − | 0.927897i | \(-0.621615\pi\) | ||||
−0.372838 | + | 0.927897i | \(0.621615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.45333 | 0.0527524 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.0095 | 1.26909 | 0.634547 | − | 0.772884i | \(-0.281187\pi\) | ||||
0.634547 | + | 0.772884i | \(0.281187\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.6955 | 0.966443 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.16437 | −0.114408 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.79248 | 0.136939 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.7151 | −1.72065 | −0.860325 | − | 0.509745i | \(-0.829740\pi\) | ||||
−0.860325 | + | 0.509745i | \(0.829740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.0009 | −0.612271 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0274 | 0.468564 | 0.234282 | − | 0.972169i | \(-0.424726\pi\) | ||||
0.234282 | + | 0.972169i | \(0.424726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.9354 | −0.752022 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5664 | −0.486691 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.0834 | −1.68694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.25681 | −0.116538 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.2465 | 1.15240 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.9249 | 0.996683 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.7483 | −1.80898 | −0.904491 | − | 0.426493i | \(-0.859749\pi\) | ||||
−0.904491 | + | 0.426493i | \(0.859749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.74159 | 0.168805 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.9412 | 1.06459 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.79845 | −0.312442 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.7773 | 0.524098 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.9689 | 1.09698 | 0.548488 | − | 0.836159i | \(-0.315204\pi\) | ||||
0.548488 | + | 0.836159i | \(0.315204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.3544 | 0.401689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6314 | −0.799642 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.16694 | 0.217627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.57031 | 0.161082 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.77247 | 0.308805 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.2100 | 1.55434 | 0.777171 | − | 0.629289i | \(-0.216654\pi\) | ||||
0.777171 | + | 0.629289i | \(0.216654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.4611 | 1.52612 | 0.763062 | − | 0.646325i | \(-0.223695\pi\) | ||||
0.763062 | + | 0.646325i | \(0.223695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.06288 | −0.107420 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.89243 | 0.136346 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 60.0908 | 2.10231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.9946 | 0.733611 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9757 | 0.383053 | 0.191527 | − | 0.981487i | \(-0.438656\pi\) | ||||
0.191527 | + | 0.981487i | \(0.438656\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.9430 | −1.74090 | −0.870452 | − | 0.492254i | \(-0.836173\pi\) | ||||
−0.870452 | + | 0.492254i | \(0.836173\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.32297 | −0.115691 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.81677 | 0.132722 | 0.0663610 | − | 0.997796i | \(-0.478861\pi\) | ||||
0.0663610 | + | 0.997796i | \(0.478861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8265 | 1.00119 | 0.500594 | − | 0.865682i | \(-0.333115\pi\) | ||||
0.500594 | + | 0.865682i | \(0.333115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.6178 | 0.576466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.958714 | 0.0332175 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.8409 | −1.20572 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.4214 | −1.08608 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.2710 | 0.976023 | 0.488011 | − | 0.872837i | \(-0.337722\pi\) | ||||
0.488011 | + | 0.872837i | \(0.337722\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4110 | 0.738309 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.40253 | 0.289399 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.94296 | −0.0668398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.0731 | 0.792800 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.70211 | 0.161376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.44770 | 0.289583 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.3536 | 1.89527 | 0.947635 | − | 0.319354i | \(-0.103466\pi\) | ||||
0.947635 | + | 0.319354i | \(0.103466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.6425 | 0.705959 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0285 | 0.820797 | 0.410399 | − | 0.911906i | \(-0.365390\pi\) | ||||
0.410399 | + | 0.911906i | \(0.365390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.9380 | −1.49914 | −0.749572 | − | 0.661923i | \(-0.769741\pi\) | ||||
−0.749572 | + | 0.661923i | \(0.769741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.3402 | 0.522794 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.5113 | −1.34498 | −0.672490 | − | 0.740106i | \(-0.734775\pi\) | ||||
−0.672490 | + | 0.740106i | \(0.734775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.3127 | 0.520648 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.864716 | 0.0293673 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.7153 | 0.397414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −55.8855 | −1.89361 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0282 | 0.508629 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.7163 | −0.936981 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −56.9846 | −1.92423 | −0.962117 | − | 0.272638i | \(-0.912104\pi\) | ||||
−0.962117 | + | 0.272638i | \(0.912104\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.2313 | −0.378823 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.94417 | 0.0991915 | 0.0495958 | − | 0.998769i | \(-0.484207\pi\) | ||||
0.0495958 | + | 0.998769i | \(0.484207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.9659 | −1.81610 | −0.908049 | − | 0.418864i | \(-0.862428\pi\) | ||||
−0.908049 | + | 0.418864i | \(0.862428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.21490 | −0.0408385 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.3259 | 1.15255 | 0.576276 | − | 0.817255i | \(-0.304505\pi\) | ||||
0.576276 | + | 0.817255i | \(0.304505\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.9504 | 1.44051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.59325 | 0.120378 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −74.0692 | −2.47863 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.37952 | 0.0795385 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.34020 | 0.144915 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49.1211 | −1.63828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.1634 | 0.405221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.5782 | −0.651520 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.82289 | −0.0605949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.9132 | 1.65734 | 0.828671 | − | 0.559736i | \(-0.189097\pi\) | ||||
0.828671 | + | 0.559736i | \(0.189097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.1996 | −1.00166 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2761 | 0.439857 | 0.219929 | − | 0.975516i | \(-0.429418\pi\) | ||||
0.219929 | + | 0.975516i | \(0.429418\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0266 | −0.530402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.81854 | 0.0931781 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.6591 | 0.649200 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.56725 | −0.117673 | −0.0588363 | − | 0.998268i | \(-0.518739\pi\) | ||||
−0.0588363 | + | 0.998268i | \(0.518739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.9457 | −0.393623 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.72610 | −0.320139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.3153 | −0.635084 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.1746 | −0.793999 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.8713 | −1.17690 | −0.588450 | − | 0.808534i | \(-0.700262\pi\) | ||||
−0.588450 | + | 0.808534i | \(0.700262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.25408 | −0.204969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.6088 | −0.511010 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.78421 | 0.0583498 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.19755 | −0.0717907 | −0.0358953 | − | 0.999356i | \(-0.511428\pi\) | ||||
−0.0358953 | + | 0.999356i | \(0.511428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.6578 | −0.674143 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.1909 | −0.788599 | −0.394300 | − | 0.918982i | \(-0.629013\pi\) | ||||
−0.394300 | + | 0.918982i | \(0.629013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.55226 | −0.311064 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.6839 | −0.510196 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3571 | 0.401552 | 0.200776 | − | 0.979637i | \(-0.435654\pi\) | ||||
0.200776 | + | 0.979637i | \(0.435654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.4169 | 0.597838 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.39256 | 0.239720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.8634 | 1.77720 | 0.888600 | − | 0.458682i | \(-0.151678\pi\) | ||||
0.888600 | + | 0.458682i | \(0.151678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.654230 | 0.0211704 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.79674 | −0.252033 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.71428 | −0.313691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.8642 | 0.544008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.4088 | 1.14103 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.5145 | 0.596003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.44333 | 0.175046 | 0.0875228 | − | 0.996163i | \(-0.472105\pi\) | ||||
0.0875228 | + | 0.996163i | \(0.472105\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.64089 | −0.181212 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.3852 | −0.622102 | −0.311051 | − | 0.950393i | \(-0.600681\pi\) | ||||
−0.311051 | + | 0.950393i | \(0.600681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.9717 | 0.864672 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.92368 | −0.317812 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0326 | −0.960827 | −0.480413 | − | 0.877042i | \(-0.659513\pi\) | ||||
−0.480413 | + | 0.877042i | \(0.659513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7605 | 0.407829 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.4621 | 0.781014 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.9831 | 0.764943 | 0.382471 | − | 0.923967i | \(-0.375073\pi\) | ||||
0.382471 | + | 0.923967i | \(0.375073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.0528 | −0.957562 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.1325 | 0.768144 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1912 | 0.387657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.0186 | 1.39830 | 0.699148 | − | 0.714977i | \(-0.253563\pi\) | ||||
0.699148 | + | 0.714977i | \(0.253563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.2620 | 0.325656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.2928 | −0.421409 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.1800 | 1.81091 | 0.905454 | − | 0.424445i | \(-0.139531\pi\) | ||||
0.905454 | + | 0.424445i | \(0.139531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.9899 | −0.917198 |
(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 | 4012.2.a.g.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |