Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 18x^{6} + 85x^{4} - 38x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.568463\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −0.568463 | −0.328202 | −0.164101 | − | 0.986444i | \(-0.552472\pi\) | ||||
−0.164101 | + | 0.986444i | \(0.552472\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67685 | −0.892283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.17164 | 1.55931 | 0.779654 | − | 0.626211i | \(-0.215395\pi\) | ||||
0.779654 | + | 0.626211i | \(0.215395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51826 | −0.975789 | −0.487894 | − | 0.872903i | \(-0.662235\pi\) | ||||
−0.487894 | + | 0.872903i | \(0.662235\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.67251 | −0.648178 | −0.324089 | − | 0.946027i | \(-0.605058\pi\) | ||||
−0.324089 | + | 0.946027i | \(0.605058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.14964 | 1.86966 | 0.934828 | − | 0.355100i | \(-0.115553\pi\) | ||||
0.934828 | + | 0.355100i | \(0.115553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.87292 | 0.807560 | 0.403780 | − | 0.914856i | \(-0.367696\pi\) | ||||
0.403780 | + | 0.914856i | \(0.367696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.22708 | 0.621052 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.49479 | 0.277575 | 0.138788 | − | 0.990322i | \(-0.455679\pi\) | ||||
0.138788 | + | 0.990322i | \(0.455679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.447097 | −0.0803009 | −0.0401505 | − | 0.999194i | \(-0.512784\pi\) | ||||
−0.0401505 | + | 0.999194i | \(0.512784\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.93989 | −0.511769 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4563 | −1.71901 | −0.859506 | − | 0.511125i | \(-0.829229\pi\) | ||||
−0.859506 | + | 0.511125i | \(0.829229\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.46805 | −1.01014 | −0.505070 | − | 0.863078i | \(-0.668533\pi\) | ||||
−0.505070 | + | 0.863078i | \(0.668533\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.45634 | 1.28958 | 0.644790 | − | 0.764360i | \(-0.276945\pi\) | ||||
0.644790 | + | 0.764360i | \(0.276945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.07930 | −0.886758 | −0.443379 | − | 0.896334i | \(-0.646220\pi\) | ||||
−0.443379 | + | 0.896334i | \(0.646220\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.51922 | 0.212734 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.36771 | 1.01203 | 0.506016 | − | 0.862524i | \(-0.331118\pi\) | ||||
0.506016 | + | 0.862524i | \(0.331118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.63277 | −0.613626 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.544667 | −0.0709096 | −0.0354548 | − | 0.999371i | \(-0.511288\pi\) | ||||
−0.0354548 | + | 0.999371i | \(0.511288\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8238 | 1.51389 | 0.756943 | − | 0.653481i | \(-0.226692\pi\) | ||||
0.756943 | + | 0.653481i | \(0.226692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.60786 | −0.807278 | −0.403639 | − | 0.914918i | \(-0.632255\pi\) | ||||
−0.403639 | + | 0.914918i | \(0.632255\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.20161 | −0.265043 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.10265 | 0.368216 | 0.184108 | − | 0.982906i | \(-0.441060\pi\) | ||||
0.184108 | + | 0.982906i | \(0.441060\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.02547 | −0.120022 | −0.0600109 | − | 0.998198i | \(-0.519114\pi\) | ||||
−0.0600109 | + | 0.998198i | \(0.519114\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.08864 | 1.02255 | 0.511276 | − | 0.859417i | \(-0.329173\pi\) | ||||
0.511276 | + | 0.859417i | \(0.329173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.19607 | 0.688452 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.18253 | 0.788385 | 0.394192 | − | 0.919028i | \(-0.371024\pi\) | ||||
0.394192 | + | 0.919028i | \(0.371024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.849733 | −0.0911009 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.60841 | −0.594490 | −0.297245 | − | 0.954801i | \(-0.596068\pi\) | ||||
−0.297245 | + | 0.954801i | \(0.596068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.254158 | 0.0263550 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.2034 | −1.74674 | −0.873370 | − | 0.487058i | \(-0.838070\pi\) | ||||
−0.873370 | + | 0.487058i | \(0.838070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8437 | −1.39134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0630 | −1.79734 | −0.898669 | − | 0.438627i | \(-0.855465\pi\) | ||||
−0.898669 | + | 0.438627i | \(0.855465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.75099 | 0.763728 | 0.381864 | − | 0.924219i | \(-0.375282\pi\) | ||||
0.381864 | + | 0.924219i | \(0.375282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.82405 | 0.466359 | 0.233179 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233179 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.265064 | −0.0253885 | −0.0126943 | − | 0.999919i | \(-0.504041\pi\) | ||||
−0.0126943 | + | 0.999919i | \(0.504041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.94405 | 0.564184 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.14720 | −0.578280 | −0.289140 | − | 0.957287i | \(-0.593369\pi\) | ||||
−0.289140 | + | 0.957287i | \(0.593369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.41784 | 0.870680 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.7458 | 1.43144 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.67685 | 0.331530 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.710503 | 0.0630469 | 0.0315235 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315235 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.80712 | −0.423243 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.57951 | −0.574854 | −0.287427 | − | 0.957802i | \(-0.592800\pi\) | ||||
−0.287427 | + | 0.957802i | \(0.592800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.26027 | −0.705723 | −0.352861 | − | 0.935676i | \(-0.614791\pi\) | ||||
−0.352861 | + | 0.935676i | \(0.614791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.22532 | −0.528025 | −0.264012 | − | 0.964519i | \(-0.585046\pi\) | ||||
−0.264012 | + | 0.964519i | \(0.585046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.45586 | 0.291036 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.1952 | −1.52156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.63277 | 0.789148 | 0.394574 | − | 0.918864i | \(-0.370892\pi\) | ||||
0.394574 | + | 0.918864i | \(0.370892\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4075 | −1.33522 | −0.667611 | − | 0.744510i | \(-0.732683\pi\) | ||||
−0.667611 | + | 0.744510i | \(0.732683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.15390 | 0.578358 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.1722 | 1.53011 | 0.765053 | − | 0.643967i | \(-0.222713\pi\) | ||||
0.765053 | + | 0.643967i | \(0.222713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.18827 | −0.332152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.46114 | 0.349423 | 0.174712 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174712 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.27218 | −0.0984444 | −0.0492222 | − | 0.998788i | \(-0.515674\pi\) | ||||
−0.0492222 | + | 0.998788i | \(0.515674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.621868 | −0.0478360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.8154 | −1.66826 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.0336 | 1.29504 | 0.647520 | − | 0.762049i | \(-0.275806\pi\) | ||||
0.647520 | + | 0.762049i | \(0.275806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.309623 | 0.0232727 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4563 | 1.00577 | 0.502887 | − | 0.864352i | \(-0.332271\pi\) | ||||
0.502887 | + | 0.864352i | \(0.332271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7946 | 1.54565 | 0.772824 | − | 0.634620i | \(-0.218844\pi\) | ||||
0.772824 | + | 0.634620i | \(0.218844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.72141 | −0.496861 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8212 | −1.01071 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5834 | 1.19993 | 0.599967 | − | 0.800025i | \(-0.295180\pi\) | ||||
0.599967 | + | 0.800025i | \(0.295180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8442 | −1.42842 | −0.714208 | − | 0.699934i | \(-0.753213\pi\) | ||||
−0.714208 | + | 0.699934i | \(0.753213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.7856 | 1.90840 | 0.954198 | − | 0.299176i | \(-0.0967119\pi\) | ||||
0.954198 | + | 0.299176i | \(0.0967119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.46063 | −0.599758 | −0.299879 | − | 0.953977i | \(-0.596946\pi\) | ||||
−0.299879 | + | 0.953977i | \(0.596946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.75632 | 0.264951 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3672 | −0.720572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42.1470 | 2.91537 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.116657 | −0.00803097 | −0.00401548 | − | 0.999992i | \(-0.501278\pi\) | ||||
−0.00401548 | + | 0.999992i | \(0.501278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.76374 | −0.120849 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.582940 | 0.0393915 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.40257 | 0.632485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0117 | 1.00526 | 0.502628 | − | 0.864503i | \(-0.332366\pi\) | ||||
0.502628 | + | 0.864503i | \(0.332366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.2681 | 1.21249 | 0.606247 | − | 0.795276i | \(-0.292674\pi\) | ||||
0.606247 | + | 0.795276i | \(0.292674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.90773 | 0.588639 | 0.294320 | − | 0.955707i | \(-0.404907\pi\) | ||||
0.294320 | + | 0.955707i | \(0.404907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.4808 | 1.14520 | 0.572602 | − | 0.819834i | \(-0.305934\pi\) | ||||
0.572602 | + | 0.819834i | \(0.305934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.16656 | −0.335604 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.4184 | 1.70886 | 0.854432 | − | 0.519564i | \(-0.173906\pi\) | ||||
0.854432 | + | 0.519564i | \(0.173906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.91849 | −0.574490 | −0.287245 | − | 0.957857i | \(-0.592739\pi\) | ||||
−0.287245 | + | 0.957857i | \(0.592739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.2035 | −0.847004 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.6725 | −1.82439 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.08300 | −0.258750 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.3235 | 1.78776 | 0.893881 | − | 0.448303i | \(-0.147972\pi\) | ||||
0.893881 | + | 0.448303i | \(0.147972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0293 | 1.25923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.4808 | −0.840907 | −0.420454 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420454 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00132 | −0.247676 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.50521 | 0.401129 | 0.200564 | − | 0.979681i | \(-0.435722\pi\) | ||||
0.200564 | + | 0.979681i | \(0.435722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.18818 | 0.195113 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.758938 | −0.0462732 | −0.0231366 | − | 0.999732i | \(-0.507365\pi\) | ||||
−0.0231366 | + | 0.999732i | \(0.507365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3375 | 1.47840 | 0.739198 | − | 0.673488i | \(-0.235205\pi\) | ||||
0.739198 | + | 0.673488i | \(0.235205\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.3048 | 1.52042 | 0.760210 | − | 0.649677i | \(-0.225096\pi\) | ||||
0.760210 | + | 0.649677i | \(0.225096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.19681 | 0.0716512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6328 | 0.813263 | 0.406632 | − | 0.913592i | \(-0.366703\pi\) | ||||
0.406632 | + | 0.913592i | \(0.366703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.5081 | −1.51630 | −0.758150 | − | 0.652081i | \(-0.773896\pi\) | ||||
−0.758150 | + | 0.652081i | \(0.773896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.85771 | −0.579865 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.77950 | 0.573284 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.4197 | −1.19293 | −0.596466 | − | 0.802638i | \(-0.703429\pi\) | ||||
−0.596466 | + | 0.802638i | \(0.703429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.6893 | 0.968411 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.6259 | −0.788008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2682 | 0.589891 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.89877 | 0.279587 | 0.139794 | − | 0.990181i | \(-0.455356\pi\) | ||||
0.139794 | + | 0.990181i | \(0.455356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.40615 | −0.250657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.5072 | −1.61649 | −0.808247 | − | 0.588843i | \(-0.799584\pi\) | ||||
−0.808247 | + | 0.588843i | \(0.799584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0147396 | 0.000833133 0 | 0.000416567 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000416567 | 1.00000i | \(0.499867\pi\) | ||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.13750 | −0.288551 | −0.144275 | − | 0.989538i | \(-0.546085\pi\) | ||||
−0.144275 | + | 0.989538i | \(0.546085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.73051 | 0.432825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.74230 | −0.153060 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.7800 | −1.21187 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.150679 | 0.00833257 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7515 | 1.58032 | 0.790162 | − | 0.612898i | \(-0.209996\pi\) | ||||
0.790162 | + | 0.612898i | \(0.209996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.9901 | 1.53385 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.36723 | 0.183425 | 0.0917123 | − | 0.995786i | \(-0.470766\pi\) | ||||
0.0917123 | + | 0.995786i | \(0.470766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.49446 | 0.189793 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.31222 | −0.125214 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.1716 | −1.56602 | −0.783008 | − | 0.622012i | \(-0.786316\pi\) | ||||
−0.783008 | + | 0.622012i | \(0.786316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.81084 | −0.471634 | −0.235817 | − | 0.971798i | \(-0.575777\pi\) | ||||
−0.235817 | + | 0.971798i | \(0.575777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3537 | −0.606016 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.3000 | −1.82560 | −0.912802 | − | 0.408402i | \(-0.866086\pi\) | ||||
−0.912802 | + | 0.408402i | \(0.866086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.8485 | 1.20590 | 0.602949 | − | 0.797780i | \(-0.293992\pi\) | ||||
0.602949 | + | 0.797780i | \(0.293992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.4167 | 2.49562 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.95093 | −0.469802 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.7307 | −1.76073 | −0.880363 | − | 0.474300i | \(-0.842701\pi\) | ||||
−0.880363 | + | 0.474300i | \(0.842701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.3140 | 0.901331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2511 | 0.634335 | 0.317168 | − | 0.948369i | \(-0.397268\pi\) | ||||
0.317168 | + | 0.948369i | \(0.397268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.25905 | −0.270855 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7935 | 0.862624 | 0.431312 | − | 0.902203i | \(-0.358051\pi\) | ||||
0.431312 | + | 0.902203i | \(0.358051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.403895 | −0.0206922 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.7334 | 1.62150 | 0.810751 | − | 0.585391i | \(-0.199059\pi\) | ||||
0.810751 | + | 0.585391i | \(0.199059\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.6364 | −1.15067 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.19176 | 0.466041 | 0.233020 | − | 0.972472i | \(-0.425139\pi\) | ||||
0.233020 | + | 0.972472i | \(0.425139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3504 | −0.523443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.74021 | 0.188669 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.94777 | −0.499264 | −0.249632 | − | 0.968341i | \(-0.580310\pi\) | ||||
−0.249632 | + | 0.968341i | \(0.580310\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.5346 | 1.67464 | 0.837318 | − | 0.546716i | \(-0.184122\pi\) | ||||
0.837318 | + | 0.546716i | \(0.184122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.57300 | 0.0783568 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −54.0764 | −2.68047 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0063 | −0.939803 | −0.469902 | − | 0.882719i | \(-0.655711\pi\) | ||||
−0.469902 | + | 0.882719i | \(0.655711\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.69566 | 0.231620 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.53886 | 0.173299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6480 | −0.764455 | −0.382227 | − | 0.924068i | \(-0.624843\pi\) | ||||
−0.382227 | + | 0.924068i | \(0.624843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1026 | 0.833532 | 0.416766 | − | 0.909014i | \(-0.363163\pi\) | ||||
0.416766 | + | 0.909014i | \(0.363163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.2734 | 0.791239 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.3433 | 0.499378 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.4568 | 0.744529 | 0.372265 | − | 0.928127i | \(-0.378581\pi\) | ||||
0.372265 | + | 0.928127i | \(0.378581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2374 | 1.06866 | 0.534331 | − | 0.845275i | \(-0.320564\pi\) | ||||
0.534331 | + | 0.845275i | \(0.320564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.5629 | 1.50986 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3884 | 1.25945 | 0.629725 | − | 0.776818i | \(-0.283168\pi\) | ||||
0.629725 | + | 0.776818i | \(0.283168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.4075 | −1.20715 | −0.603573 | − | 0.797308i | \(-0.706257\pi\) | ||||
−0.603573 | + | 0.797308i | \(0.706257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.47588 | −0.259000 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.0751 | −0.900210 | −0.450105 | − | 0.892976i | \(-0.648613\pi\) | ||||
−0.450105 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.4504 | −1.57512 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.32705 | 0.438223 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.41179 | −0.346709 | −0.173354 | − | 0.984860i | \(-0.555461\pi\) | ||||
−0.173354 | + | 0.984860i | \(0.555461\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.62439 | −0.402552 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2283 | −1.08185 | −0.540925 | − | 0.841071i | \(-0.681926\pi\) | ||||
−0.540925 | + | 0.841071i | \(0.681926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6970 | 0.822448 | 0.411224 | − | 0.911534i | \(-0.365101\pi\) | ||||
0.411224 | + | 0.911534i | \(0.365101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.4726 | −1.31756 | −0.658778 | − | 0.752337i | \(-0.728926\pi\) | ||||
−0.658778 | + | 0.752337i | \(0.728926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.8987 | −0.502185 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.7332 | 2.01085 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.7222 | −0.903020 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.72987 | 0.0790398 | 0.0395199 | − | 0.999219i | \(-0.487417\pi\) | ||||
0.0395199 | + | 0.999219i | \(0.487417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.7881 | 1.67739 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.7079 | −1.52745 | −0.763725 | − | 0.645542i | \(-0.776632\pi\) | ||||
−0.763725 | + | 0.645542i | \(0.776632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.53599 | −0.114682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.11307 | −0.0953614 | −0.0476807 | − | 0.998863i | \(-0.515183\pi\) | ||||
−0.0476807 | + | 0.998863i | \(0.515183\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.99483 | −0.179918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.7250 | 0.793480 | 0.396740 | − | 0.917931i | \(-0.370141\pi\) | ||||
0.396740 | + | 0.917931i | \(0.370141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.723189 | 0.0323097 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0925 | 0.851292 | 0.425646 | − | 0.904890i | \(-0.360047\pi\) | ||||
0.425646 | + | 0.904890i | \(0.360047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.353509 | 0.0156999 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.98684 | −0.221038 | −0.110519 | − | 0.993874i | \(-0.535251\pi\) | ||||
−0.110519 | + | 0.993874i | \(0.535251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 26.2996 | 1.16115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.4400 | −1.38273 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.68296 | −0.425035 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.91181 | 0.215190 | 0.107595 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107595 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.82761 | −0.0799157 | −0.0399578 | − | 0.999201i | \(-0.512722\pi\) | ||||
−0.0399578 | + | 0.999201i | \(0.512722\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.19487 | 0.0520493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.00048 | −0.347847 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.45799 | 0.0632714 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.7563 | 0.985683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.64944 | −0.330098 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.7996 | 1.58214 | 0.791070 | − | 0.611726i | \(-0.209525\pi\) | ||||
0.791070 | + | 0.611726i | \(0.209525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.8209 | −0.507285 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6171 | −0.667738 | −0.333869 | − | 0.942619i | \(-0.608354\pi\) | ||||
−0.333869 | + | 0.942619i | \(0.608354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.6506 | −1.35081 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1820 | 0.518970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3184 | 0.521946 | 0.260973 | − | 0.965346i | \(-0.415957\pi\) | ||||
0.260973 | + | 0.965346i | \(0.415957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.7516 | −1.25836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.85687 | 0.331717 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.6317 | 1.75457 | 0.877283 | − | 0.479974i | \(-0.159354\pi\) | ||||
0.877283 | + | 0.479974i | \(0.159354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.6866 | 0.825303 | 0.412652 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412652 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.2022 | 1.01283 | 0.506415 | − | 0.862290i | \(-0.330970\pi\) | ||||
0.506415 | + | 0.862290i | \(0.330970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.42707 | −0.393821 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0144 | 1.08299 | 0.541497 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541497 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.2807 | 0.468809 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.1031 | 1.57807 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.4124 | 1.46163 | 0.730814 | − | 0.682577i | \(-0.239141\pi\) | ||||
0.730814 | + | 0.682577i | \(0.239141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.64368 | −0.150135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.2266 | −0.626340 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.31307 | −0.0949865 | −0.0474933 | − | 0.998872i | \(-0.515123\pi\) | ||||
−0.0474933 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.80956 | 0.196842 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.6861 | 0.640915 | 0.320458 | − | 0.947263i | \(-0.396163\pi\) | ||||
0.320458 | + | 0.947263i | \(0.396163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.58367 | −0.390926 | −0.195463 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195463 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.6882 | 0.720321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4711 | 0.952661 | 0.476330 | − | 0.879266i | \(-0.341967\pi\) | ||||
0.476330 | + | 0.879266i | \(0.341967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.3886 | 0.865288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5419 | 0.950847 | 0.475424 | − | 0.879757i | \(-0.342295\pi\) | ||||
0.475424 | + | 0.879757i | \(0.342295\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.9132 | 1.44581 | 0.722905 | − | 0.690947i | \(-0.242806\pi\) | ||||
0.722905 | + | 0.690947i | \(0.242806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2178 | 0.491075 | 0.245538 | − | 0.969387i | \(-0.421036\pi\) | ||||
0.245538 | + | 0.969387i | \(0.421036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.4982 | 0.501537 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −23.9590 | −0.956831 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.9447 | 1.11423 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6965 | −0.505439 | −0.252720 | − | 0.967540i | \(-0.581325\pi\) | ||||
−0.252720 | + | 0.967540i | \(0.581325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0663150 | 0.00263578 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.30532 | −0.328553 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.79423 | 0.110365 | 0.0551826 | − | 0.998476i | \(-0.482426\pi\) | ||||
0.0551826 | + | 0.998476i | \(0.482426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.6325 | 1.12916 | 0.564579 | − | 0.825379i | \(-0.309039\pi\) | ||||
0.564579 | + | 0.825379i | \(0.309039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.1744 | 1.26491 | 0.632454 | − | 0.774598i | \(-0.282048\pi\) | ||||
0.632454 | + | 0.774598i | \(0.282048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.81682 | −0.110570 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.8245 | 1.20626 | 0.603129 | − | 0.797644i | \(-0.293921\pi\) | ||||
0.603129 | + | 0.797644i | \(0.293921\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.74502 | 0.107093 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.839268 | −0.0326932 | −0.0163466 | − | 0.999866i | \(-0.505204\pi\) | ||||
−0.0163466 | + | 0.999866i | \(0.505204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5779 | −0.761494 | −0.380747 | − | 0.924679i | \(-0.624333\pi\) | ||||
−0.380747 | + | 0.924679i | \(0.624333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.34501 | −0.207583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.78920 | 0.224159 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.53359 | −0.329928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 61.1485 | 2.36061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.5346 | −1.25412 | −0.627058 | − | 0.778973i | \(-0.715741\pi\) | ||||
−0.627058 | + | 0.778973i | \(0.715741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6491 | 0.870476 | 0.435238 | − | 0.900315i | \(-0.356664\pi\) | ||||
0.435238 | + | 0.900315i | \(0.356664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3847 | −0.397944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.0891 | −0.883481 | −0.441740 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441740 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.06372 | −0.193193 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.9215 | −0.987530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.53450 | −0.172501 | −0.0862503 | − | 0.996274i | \(-0.527488\pi\) | ||||
−0.0862503 | + | 0.996274i | \(0.527488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.2859 | 0.654750 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.93718 | −0.375859 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.97198 | 0.150020 | 0.0750098 | − | 0.997183i | \(-0.476101\pi\) | ||||
0.0750098 | + | 0.997183i | \(0.476101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −85.2155 | −3.21396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.7661 | −1.90656 | −0.953280 | − | 0.302087i | \(-0.902317\pi\) | ||||
−0.953280 | + | 0.302087i | \(0.902317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.3289 | −0.912405 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.73157 | −0.0648478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.0179 | −0.560853 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3661 | 0.423885 | 0.211943 | − | 0.977282i | \(-0.432021\pi\) | ||||
0.211943 | + | 0.977282i | \(0.432021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.06983 | 0.188549 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5894 | 0.911971 | 0.455986 | − | 0.889987i | \(-0.349287\pi\) | ||||
0.455986 | + | 0.889987i | \(0.349287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.0825 | −0.410464 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.5996 | −0.835878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.85199 | −0.216148 | −0.108074 | − | 0.994143i | \(-0.534468\pi\) | ||||
−0.108074 | + | 0.994143i | \(0.534468\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.1734 | −1.25880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5699 | 1.60274 | 0.801372 | − | 0.598166i | \(-0.204104\pi\) | ||||
0.801372 | + | 0.598166i | \(0.204104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.2993 | 0.598769 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.5161 | −0.532545 | −0.266272 | − | 0.963898i | \(-0.585792\pi\) | ||||
−0.266272 | + | 0.963898i | \(0.585792\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.2265 | −0.703462 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.02886 | 0.0375437 | 0.0187719 | − | 0.999824i | \(-0.494024\pi\) | ||||
0.0187719 | + | 0.999824i | \(0.494024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.1009 | −0.586748 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.69565 | 0.134321 | 0.0671604 | − | 0.997742i | \(-0.478606\pi\) | ||||
0.0671604 | + | 0.997742i | \(0.478606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3859 | −0.413284 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.4192 | 0.631445 | 0.315723 | − | 0.948852i | \(-0.397753\pi\) | ||||
0.315723 | + | 0.948852i | \(0.397753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.91628 | 0.0691928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.23731 | 0.297045 | 0.148522 | − | 0.988909i | \(-0.452548\pi\) | ||||
0.148522 | + | 0.988909i | \(0.452548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.66332 | 0.275988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.62576 | 0.0944422 | 0.0472211 | − | 0.998884i | \(-0.484963\pi\) | ||||
0.0472211 | + | 0.998884i | \(0.484963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.7123 | −1.88861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0458 | 0.574162 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.82380 | 0.172389 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.7752 | 1.70300 | 0.851502 | − | 0.524352i | \(-0.175692\pi\) | ||||
0.851502 | + | 0.524352i | \(0.175692\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.69797 | −0.131651 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.5992 | −1.47723 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.8553 | −1.87223 | −0.936115 | − | 0.351695i | \(-0.885605\pi\) | ||||
−0.936115 | + | 0.351695i | \(0.885605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.2470 | 0.574777 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0129 | 0.530454 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.30335 | −0.187151 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.431428 | 0.0151870 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8381 | −0.978734 | −0.489367 | − | 0.872078i | \(-0.662772\pi\) | ||||
−0.489367 | + | 0.872078i | \(0.662772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.8629 | 1.68069 | 0.840347 | − | 0.542049i | \(-0.182351\pi\) | ||||
0.840347 | + | 0.542049i | \(0.182351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8350 | −0.485213 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68.9162 | 2.41107 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.50211 | 0.296726 | 0.148363 | − | 0.988933i | \(-0.452600\pi\) | ||||
0.148363 | + | 0.988933i | \(0.452600\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.7183 | 0.652479 | 0.326240 | − | 0.945287i | \(-0.394218\pi\) | ||||
0.326240 | + | 0.945287i | \(0.394218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.33788 | −0.0465227 | −0.0232613 | − | 0.999729i | \(-0.507405\pi\) | ||||
−0.0232613 | + | 0.999729i | \(0.507405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0296 | −0.383075 | −0.191538 | − | 0.981485i | \(-0.561347\pi\) | ||||
−0.191538 | + | 0.981485i | \(0.561347\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.3849 | −0.499006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.44282 | −0.0498711 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.0158 | 1.31245 | 0.656226 | − | 0.754564i | \(-0.272152\pi\) | ||||
0.656226 | + | 0.754564i | \(0.272152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7656 | −0.922952 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.74973 | −0.266915 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.5004 | 0.497653 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.4966 | −1.38821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.34877 | −0.285856 | −0.142928 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142928 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1431 | 0.346481 | 0.173240 | − | 0.984880i | \(-0.444576\pi\) | ||||
0.173240 | + | 0.984880i | \(0.444576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1015 | 0.651736 | 0.325868 | − | 0.945415i | \(-0.394344\pi\) | ||||
0.325868 | + | 0.945415i | \(0.394344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.39706 | −0.115637 | −0.0578186 | − | 0.998327i | \(-0.518414\pi\) | ||||
−0.0578186 | + | 0.998327i | \(0.518414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.60375 | 0.190313 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.0031 | 1.59447 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2481 | 0.787733 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.0509 | 1.55859 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5065 | 0.692457 | 0.346228 | − | 0.938150i | \(-0.387462\pi\) | ||||
0.346228 | + | 0.938150i | \(0.387462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.6079 | 0.391523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.11424 | 0.273376 | 0.136688 | − | 0.990614i | \(-0.456354\pi\) | ||||
0.136688 | + | 0.990614i | \(0.456354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8454 | −0.735156 | −0.367578 | − | 0.929993i | \(-0.619813\pi\) | ||||
−0.367578 | + | 0.929993i | \(0.619813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.5445 | −1.66354 | −0.831771 | − | 0.555119i | \(-0.812673\pi\) | ||||
−0.831771 | + | 0.555119i | \(0.812673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.0438 | 1.07351 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −49.5442 | −1.65793 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.74584 | 0.258626 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.668315 | −0.0222896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.6903 | −0.655977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.19487 | 0.172493 | 0.0862464 | − | 0.996274i | \(-0.472513\pi\) | ||||
0.0862464 | + | 0.996274i | \(0.472513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.3520 | 1.60373 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.0398 | −0.564553 | −0.282276 | − | 0.959333i | \(-0.591090\pi\) | ||||
−0.282276 | + | 0.959333i | \(0.591090\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.1454 | 1.22933 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.0267 | 1.55127 | 0.775634 | − | 0.631183i | \(-0.217430\pi\) | ||||
0.775634 | + | 0.631183i | \(0.217430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.78477 | −0.0917613 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9159 | −0.359301 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.7482 | −0.681461 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.6480 | −1.53047 | −0.765235 | − | 0.643751i | \(-0.777377\pi\) | ||||
−0.765235 | + | 0.643751i | \(0.777377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.2053 | 0.530537 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.8072 | −1.65980 | −0.829899 | − | 0.557914i | \(-0.811602\pi\) | ||||
−0.829899 | + | 0.557914i | \(0.811602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.00837894 | −0.000273436 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0221 | −0.978693 | −0.489346 | − | 0.872090i | \(-0.662765\pi\) | ||||
−0.489346 | + | 0.872090i | \(0.662765\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.0502 | −0.815748 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.7154 | −1.22559 | −0.612793 | − | 0.790243i | \(-0.709954\pi\) | ||||
−0.612793 | + | 0.790243i | \(0.709954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60786 | 0.117116 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.92048 | 0.0947031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3188 | 1.04691 | 0.523455 | − | 0.852053i | \(-0.324643\pi\) | ||||
0.523455 | + | 0.852053i | \(0.324643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.39451 | −0.142054 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8001 | −0.993552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.9133 | −0.416124 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0403 | 0.644451 | 0.322226 | − | 0.946663i | \(-0.395569\pi\) | ||||
0.322226 | + | 0.946663i | \(0.395569\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.3811 | 0.397739 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5658 | 0.531622 | 0.265811 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265811 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5796 | 1.36224 | 0.681121 | − | 0.732171i | \(-0.261493\pi\) | ||||
0.681121 | + | 0.732171i | \(0.261493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.0047 | −0.926993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.709536 | 0.0226537 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.0421 | −1.24525 | −0.622626 | − | 0.782520i | \(-0.713934\pi\) | ||||
−0.622626 | + | 0.782520i | \(0.713934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.7508 | 1.04141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5549 | −0.557650 | −0.278825 | − | 0.960342i | \(-0.589945\pi\) | ||||
−0.278825 | + | 0.960342i | \(0.589945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.3442 | −0.518666 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.1398 | 1.68296 | 0.841478 | − | 0.540292i | \(-0.181686\pi\) | ||||
0.841478 | + | 0.540292i | \(0.181686\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.7435 | −1.06760 |
(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 | 9800.2.a.da.1.3 | yes | 8 | |
5.4 | even | 2 | 9800.2.a.cz.1.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 9800.2.a.da.1.6 | yes | 8 | |
35.34 | odd | 2 | 9800.2.a.cz.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9800.2.a.cz.1.3 | ✓ | 8 | 35.34 | odd | 2 | ||
9800.2.a.cz.1.6 | yes | 8 | 5.4 | even | 2 | ||
9800.2.a.da.1.3 | yes | 8 | 1.1 | even | 1 | trivial | |
9800.2.a.da.1.6 | yes | 8 | 7.6 | odd | 2 | inner |