Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.38569.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 5x^{3} + 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 501) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.275834\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.81885 | 0.813415 | 0.406707 | − | 0.913559i | \(-0.366677\pi\) | ||||
0.406707 | + | 0.913559i | \(0.366677\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.619101 | 0.233998 | 0.116999 | − | 0.993132i | \(-0.462673\pi\) | ||||
0.116999 | + | 0.993132i | \(0.462673\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.67008 | 1.40808 | 0.704042 | − | 0.710159i | \(-0.251377\pi\) | ||||
0.704042 | + | 0.710159i | \(0.251377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.78748 | 0.773109 | 0.386554 | − | 0.922267i | \(-0.373665\pi\) | ||||
0.386554 | + | 0.922267i | \(0.373665\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.81885 | 0.469625 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.683131 | −0.165684 | −0.0828418 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828418 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.92392 | 1.35904 | 0.679520 | − | 0.733657i | \(-0.262188\pi\) | ||||
0.679520 | + | 0.733657i | \(0.262188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.619101 | 0.135099 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.31476 | 1.52523 | 0.762617 | − | 0.646851i | \(-0.223914\pi\) | ||||
0.762617 | + | 0.646851i | \(0.223914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.69178 | −0.338357 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.09331 | 1.31720 | 0.658598 | − | 0.752495i | \(-0.271150\pi\) | ||||
0.658598 | + | 0.752495i | \(0.271150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.05098 | 1.26639 | 0.633197 | − | 0.773991i | \(-0.281742\pi\) | ||||
0.633197 | + | 0.773991i | \(0.281742\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.67008 | 0.812957 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.12605 | 0.190337 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.99322 | −1.31408 | −0.657039 | − | 0.753857i | \(-0.728191\pi\) | ||||
−0.657039 | + | 0.753857i | \(0.728191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.78748 | 0.446355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0577645 | 0.00902130 | 0.00451065 | − | 0.999990i | \(-0.498564\pi\) | ||||
0.00451065 | + | 0.999990i | \(0.498564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.15534 | 1.24368 | 0.621839 | − | 0.783146i | \(-0.286386\pi\) | ||||
0.621839 | + | 0.783146i | \(0.286386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.81885 | 0.271138 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.68571 | −0.245887 | −0.122943 | − | 0.992414i | \(-0.539233\pi\) | ||||
−0.122943 | + | 0.992414i | \(0.539233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61671 | −0.945245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.683131 | −0.0956575 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0094 | −1.37490 | −0.687451 | − | 0.726231i | \(-0.741270\pi\) | ||||
−0.687451 | + | 0.726231i | \(0.741270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.49418 | 1.14536 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.92392 | 0.784642 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.9921 | −1.56124 | −0.780621 | − | 0.625005i | \(-0.785097\pi\) | ||||
−0.780621 | + | 0.625005i | \(0.785097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.90480 | 0.627995 | 0.313998 | − | 0.949424i | \(-0.398332\pi\) | ||||
0.313998 | + | 0.949424i | \(0.398332\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.619101 | 0.0779994 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.07002 | 0.628858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0368 | −1.34837 | −0.674183 | − | 0.738565i | \(-0.735504\pi\) | ||||
−0.674183 | + | 0.738565i | \(0.735504\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.31476 | 0.880594 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.2933 | −1.81498 | −0.907488 | − | 0.420078i | \(-0.862003\pi\) | ||||
−0.907488 | + | 0.420078i | \(0.862003\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.47053 | −0.640277 | −0.320139 | − | 0.947371i | \(-0.603729\pi\) | ||||
−0.320139 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.69178 | −0.195350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.89125 | 0.329489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.58093 | 0.965430 | 0.482715 | − | 0.875778i | \(-0.339651\pi\) | ||||
0.482715 | + | 0.875778i | \(0.339651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.86623 | −0.204846 | −0.102423 | − | 0.994741i | \(-0.532660\pi\) | ||||
−0.102423 | + | 0.994741i | \(0.532660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.24251 | −0.134769 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.09331 | 0.760483 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.14998 | −0.545897 | −0.272948 | − | 0.962029i | \(-0.587999\pi\) | ||||
−0.272948 | + | 0.962029i | \(0.587999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72573 | 0.180906 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.05098 | 0.731153 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.7747 | 1.10546 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4675 | 1.06282 | 0.531408 | − | 0.847116i | \(-0.321663\pi\) | ||||
0.531408 | + | 0.847116i | \(0.321663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.67008 | 0.469361 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.04032 | −0.402027 | −0.201014 | − | 0.979588i | \(-0.564424\pi\) | ||||
−0.201014 | + | 0.979588i | \(0.564424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5828 | −1.23982 | −0.619910 | − | 0.784673i | \(-0.712831\pi\) | ||||
−0.619910 | + | 0.784673i | \(0.712831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.12605 | 0.109891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.37816 | −0.326579 | −0.163289 | − | 0.986578i | \(-0.552210\pi\) | ||||
−0.163289 | + | 0.986578i | \(0.552210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0236 | −1.53478 | −0.767390 | − | 0.641180i | \(-0.778445\pi\) | ||||
−0.767390 | + | 0.641180i | \(0.778445\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.99322 | −0.758683 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.17791 | 0.581169 | 0.290584 | − | 0.956849i | \(-0.406150\pi\) | ||||
0.290584 | + | 0.956849i | \(0.406150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.3045 | 1.24065 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.78748 | 0.257703 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.422927 | −0.0387696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8097 | 0.982698 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0577645 | 0.00520845 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1714 | −1.08864 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.59133 | −0.762357 | −0.381179 | − | 0.924501i | \(-0.624482\pi\) | ||||
−0.381179 | + | 0.924501i | \(0.624482\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.15534 | 0.718037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.93595 | 0.518626 | 0.259313 | − | 0.965793i | \(-0.416504\pi\) | ||||
0.259313 | + | 0.965793i | \(0.416504\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.66750 | 0.318013 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.81885 | 0.156542 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.7914 | 1.60545 | 0.802727 | − | 0.596346i | \(-0.203382\pi\) | ||||
0.802727 | + | 0.596346i | \(0.203382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.45851 | −0.547803 | −0.273902 | − | 0.961758i | \(-0.588314\pi\) | ||||
−0.273902 | + | 0.961758i | \(0.588314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.68571 | −0.141963 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.0178 | 1.08860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.9017 | 1.07143 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.61671 | −0.545737 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.6797 | −1.36645 | −0.683226 | − | 0.730207i | \(-0.739424\pi\) | ||||
−0.683226 | + | 0.730207i | \(0.739424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.4080 | 1.74216 | 0.871079 | − | 0.491143i | \(-0.163421\pi\) | ||||
0.871079 | + | 0.491143i | \(0.163421\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.683131 | −0.0552279 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8247 | 1.03010 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.23856 | −0.577700 | −0.288850 | − | 0.957374i | \(-0.593273\pi\) | ||||
−0.288850 | + | 0.957374i | \(0.593273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.0094 | −0.793800 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.52858 | 0.356902 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00975 | 0.627372 | 0.313686 | − | 0.949527i | \(-0.398436\pi\) | ||||
0.313686 | + | 0.949527i | \(0.398436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.49418 | 0.661271 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.22994 | −0.402303 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.92392 | 0.453013 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3124 | 1.31624 | 0.658119 | − | 0.752914i | \(-0.271353\pi\) | ||||
0.658119 | + | 0.752914i | \(0.271353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.04738 | −0.0791748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.9921 | −0.901384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.93567 | 0.294166 | 0.147083 | − | 0.989124i | \(-0.453012\pi\) | ||||
0.147083 | + | 0.989124i | \(0.453012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.48440 | 0.333323 | 0.166661 | − | 0.986014i | \(-0.446701\pi\) | ||||
0.166661 | + | 0.986014i | \(0.446701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.90480 | 0.362573 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.5385 | −1.06889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.19028 | −0.233296 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.619101 | 0.0450330 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.9079 | −1.15105 | −0.575526 | − | 0.817784i | \(-0.695203\pi\) | ||||
−0.575526 | + | 0.817784i | \(0.695203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1335 | −1.59320 | −0.796602 | − | 0.604505i | \(-0.793371\pi\) | ||||
−0.796602 | + | 0.604505i | \(0.793371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.07002 | 0.363071 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.75941 | 0.695329 | 0.347665 | − | 0.937619i | \(-0.386975\pi\) | ||||
0.347665 | + | 0.937619i | \(0.386975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.36374 | −0.167561 | −0.0837804 | − | 0.996484i | \(-0.526699\pi\) | ||||
−0.0837804 | + | 0.996484i | \(0.526699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0368 | −0.778479 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.39148 | 0.308221 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.105065 | 0.00733806 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.31476 | 0.508411 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.6652 | 1.91364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.75868 | −0.465286 | −0.232643 | − | 0.972562i | \(-0.574737\pi\) | ||||
−0.232643 | + | 0.972562i | \(0.574737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.2933 | −1.04788 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.8333 | 1.01163 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.36527 | 0.296334 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.47053 | −0.369664 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.90422 | −0.128091 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.39260 | −0.562010 | −0.281005 | − | 0.959706i | \(-0.590668\pi\) | ||||
−0.281005 | + | 0.959706i | \(0.590668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.69178 | −0.112786 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.8113 | −1.64678 | −0.823392 | − | 0.567474i | \(-0.807921\pi\) | ||||
−0.823392 | + | 0.567474i | \(0.807921\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.3000 | −1.60579 | −0.802894 | − | 0.596121i | \(-0.796708\pi\) | ||||
−0.802894 | + | 0.596121i | \(0.796708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.89125 | 0.190230 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.67691 | −0.633955 | −0.316978 | − | 0.948433i | \(-0.602668\pi\) | ||||
−0.316978 | + | 0.948433i | \(0.602668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.06606 | −0.200008 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.58093 | 0.557391 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1035 | 1.68849 | 0.844247 | − | 0.535954i | \(-0.180048\pi\) | ||||
0.844247 | + | 0.535954i | \(0.180048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.1384 | 1.94138 | 0.970692 | − | 0.240328i | \(-0.0772549\pi\) | ||||
0.970692 | + | 0.240328i | \(0.0772549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0348 | −0.768876 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.5128 | 1.05069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.86623 | −0.118268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4290 | 1.16323 | 0.581615 | − | 0.813464i | \(-0.302421\pi\) | ||||
0.581615 | + | 0.813464i | \(0.302421\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.1606 | 2.14766 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.24251 | −0.0778092 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.06747 | 0.253722 | 0.126861 | − | 0.991921i | \(-0.459510\pi\) | ||||
0.126861 | + | 0.991921i | \(0.459510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.94861 | −0.307492 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.09331 | 0.439065 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.51519 | 0.0934309 | 0.0467154 | − | 0.998908i | \(-0.485125\pi\) | ||||
0.0467154 | + | 0.998908i | \(0.485125\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.2057 | −1.11836 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.14998 | −0.315174 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.06255 | −0.552554 | −0.276277 | − | 0.961078i | \(-0.589101\pi\) | ||||
−0.276277 | + | 0.961078i | \(0.589101\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1878 | 0.618867 | 0.309434 | − | 0.950921i | \(-0.399861\pi\) | ||||
0.309434 | + | 0.950921i | \(0.399861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.72573 | 0.104446 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.90077 | −0.476434 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6810 | −1.18252 | −0.591259 | − | 0.806481i | \(-0.701369\pi\) | ||||
−0.591259 | + | 0.806481i | \(0.701369\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.05098 | 0.422131 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3377 | 1.03428 | 0.517140 | − | 0.855901i | \(-0.326997\pi\) | ||||
0.517140 | + | 0.855901i | \(0.326997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.34287 | 0.0798255 | 0.0399128 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399128 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7747 | 0.638239 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0357621 | 0.00211097 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5333 | −0.972549 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4675 | 0.613617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.09037 | −0.472645 | −0.236322 | − | 0.971675i | \(-0.575942\pi\) | ||||
−0.236322 | + | 0.971675i | \(0.575942\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8119 | −1.26994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.67008 | 0.270986 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.3898 | 1.17917 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.04897 | 0.291018 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.04032 | −0.232110 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.92110 | 0.510821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.90434 | 0.451125 | 0.225562 | − | 0.974229i | \(-0.427578\pi\) | ||||
0.225562 | + | 0.974229i | \(0.427578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.5828 | −0.715810 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4753 | −0.707412 | −0.353706 | − | 0.935357i | \(-0.615079\pi\) | ||||
−0.353706 | + | 0.935357i | \(0.615079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1389 | −0.968750 | −0.484375 | − | 0.874860i | \(-0.660953\pi\) | ||||
−0.484375 | + | 0.874860i | \(0.660953\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.12605 | 0.0634458 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.78055 | 0.268502 | 0.134251 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134251 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.1264 | 1.85472 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.37816 | −0.188550 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.04681 | −0.225171 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.71582 | −0.261586 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.0236 | −0.886106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.04363 | −0.0575370 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.6964 | 1.79716 | 0.898578 | − | 0.438814i | \(-0.144601\pi\) | ||||
0.898578 | + | 0.438814i | \(0.144601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.99322 | −0.438026 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.0744 | −1.09678 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3364 | 0.563057 | 0.281528 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281528 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.17791 | 0.335538 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.9287 | 1.78319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.43012 | −0.455184 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.3045 | 0.716288 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.69508 | −0.520459 | −0.260230 | − | 0.965547i | \(-0.583798\pi\) | ||||
−0.260230 | + | 0.965547i | \(0.583798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0235 | 1.33948 | 0.669739 | − | 0.742597i | \(-0.266406\pi\) | ||||
0.669739 | + | 0.742597i | \(0.266406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.78748 | 0.148785 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.64539 | −0.140800 | −0.0704000 | − | 0.997519i | \(-0.522428\pi\) | ||||
−0.0704000 | + | 0.997519i | \(0.522428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.8162 | −1.47633 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.422927 | −0.0223837 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.6453 | −1.03684 | −0.518420 | − | 0.855126i | \(-0.673479\pi\) | ||||
−0.518420 | + | 0.855126i | \(0.673479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0928 | 0.846988 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8097 | 0.567361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.95008 | −0.520811 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.7060 | −1.75944 | −0.879720 | − | 0.475492i | \(-0.842270\pi\) | ||||
−0.879720 | + | 0.475492i | \(0.842270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0577645 | 0.00300710 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.19685 | −0.321724 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7459 | 1.22952 | 0.614758 | − | 0.788715i | \(-0.289254\pi\) | ||||
0.614758 | + | 0.788715i | \(0.289254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1714 | −0.628526 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7725 | 1.01834 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.74820 | 0.141166 | 0.0705828 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705828 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.59133 | −0.440147 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.50394 | −0.179043 | −0.0895215 | − | 0.995985i | \(-0.528534\pi\) | ||||
−0.0895215 | + | 0.995985i | \(0.528534\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.25876 | 0.268011 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.15534 | 0.414559 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.6535 | −0.996474 | −0.498237 | − | 0.867041i | \(-0.666019\pi\) | ||||
−0.498237 | + | 0.867041i | \(0.666019\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.99694 | −0.252706 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.93595 | 0.299429 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6074 | 0.785295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.07024 | −0.455222 | −0.227611 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227611 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.66750 | 0.183605 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.06991 | 0.203242 | 0.101621 | − | 0.994823i | \(-0.467597\pi\) | ||||
0.101621 | + | 0.994823i | \(0.467597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.6545 | 0.979060 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.81885 | 0.0903794 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.3290 | −1.85033 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.7756 | 0.977840 | 0.488920 | − | 0.872329i | \(-0.337391\pi\) | ||||
0.488920 | + | 0.872329i | \(0.337391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.7914 | 0.926910 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.42434 | −0.365328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39440 | −0.166625 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.45851 | −0.316274 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.6280 | 1.34972 | 0.674859 | − | 0.737947i | \(-0.264204\pi\) | ||||
0.674859 | + | 0.737947i | \(0.264204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8302 | 1.60005 | 0.800023 | − | 0.599970i | \(-0.204821\pi\) | ||||
0.800023 | + | 0.599970i | \(0.204821\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.68571 | −0.0819622 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.15571 | 0.0560601 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.03657 | 0.146950 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.0178 | 0.628504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.8163 | 1.33987 | 0.669933 | − | 0.742422i | \(-0.266323\pi\) | ||||
0.669933 | + | 0.742422i | \(0.266323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.9632 | −0.574914 | −0.287457 | − | 0.957794i | \(-0.592810\pi\) | ||||
−0.287457 | + | 0.957794i | \(0.592810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.9017 | 0.618588 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.3320 | 2.07285 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.14418 | −0.293246 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.61671 | −0.315082 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.9791 | −1.42435 | −0.712174 | − | 0.702003i | \(-0.752289\pi\) | ||||
−0.712174 | + | 0.702003i | \(0.752289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.36704 | −0.444040 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.6797 | −0.788922 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.51936 | 0.0717032 | 0.0358516 | − | 0.999357i | \(-0.488586\pi\) | ||||
0.0358516 | + | 0.999357i | \(0.488586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.269765 | 0.0127027 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.4080 | 1.00584 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.13885 | 0.147152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4960 | 0.958764 | 0.479382 | − | 0.877606i | \(-0.340861\pi\) | ||||
0.479382 | + | 0.877606i | \(0.340861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.683131 | −0.0318858 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9837 | −1.44306 | −0.721528 | − | 0.692385i | \(-0.756560\pi\) | ||||
−0.721528 | + | 0.692385i | \(0.756560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1283 | 0.470700 | 0.235350 | − | 0.971911i | \(-0.424376\pi\) | ||||
0.235350 | + | 0.971911i | \(0.424376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.8247 | 0.594730 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.95900 | 0.368298 | 0.184149 | − | 0.982898i | \(-0.441047\pi\) | ||||
0.184149 | + | 0.982898i | \(0.441047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.83292 | −0.315515 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.23856 | −0.333535 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.0861 | 1.75120 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0220 | −0.459840 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0094 | −0.458300 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.1206 | −0.919332 | −0.459666 | − | 0.888092i | \(-0.652031\pi\) | ||||
−0.459666 | + | 0.888092i | \(0.652031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2810 | −1.01592 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.52858 | 0.206057 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.0388 | 0.864509 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0083 | −1.08792 | −0.543959 | − | 0.839112i | \(-0.683075\pi\) | ||||
−0.543959 | + | 0.839112i | \(0.683075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00975 | 0.362213 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.8846 | 0.626605 | 0.313302 | − | 0.949653i | \(-0.398565\pi\) | ||||
0.313302 | + | 0.949653i | \(0.398565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.84566 | −0.218238 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.49418 | 0.381785 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.46807 | −0.424701 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.2272 | −1.48746 | −0.743728 | − | 0.668483i | \(-0.766944\pi\) | ||||
−0.743728 | + | 0.668483i | \(0.766944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.8540 | 1.86618 | 0.933089 | − | 0.359645i | \(-0.117102\pi\) | ||||
0.933089 | + | 0.359645i | \(0.117102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.34874 | −0.327015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.22994 | −0.232270 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.7891 | −0.921459 | −0.460730 | − | 0.887541i | \(-0.652412\pi\) | ||||
−0.460730 | + | 0.887541i | \(0.652412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.38681 | −0.149824 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.92392 | 0.261547 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.8862 | −1.00849 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.87243 | −0.346229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.3124 | 0.759930 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.82338 | −0.0798837 | −0.0399418 | − | 0.999202i | \(-0.512717\pi\) | ||||
−0.0399418 | + | 0.999202i | \(0.512717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0009 | −0.699671 | −0.349835 | − | 0.936811i | \(-0.613763\pi\) | ||||
−0.349835 | + | 0.936811i | \(0.613763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.04738 | −0.0457116 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.81674 | −0.209821 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.5058 | 1.32634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.9921 | −0.520414 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.161018 | 0.00697445 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.14436 | −0.265644 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.93567 | 0.169837 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.9006 | −1.33098 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.31528 | −0.400495 | −0.200248 | − | 0.979745i | \(-0.564175\pi\) | ||||
−0.200248 | + | 0.979745i | \(0.564175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.48440 | 0.192444 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.1445 | −1.24841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.41218 | −0.0603806 | −0.0301903 | − | 0.999544i | \(-0.509611\pi\) | ||||
−0.0301903 | + | 0.999544i | \(0.509611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.90480 | 0.209332 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.0202 | 1.79012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.31246 | 0.225909 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.5385 | −0.617124 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.5817 | −0.490733 | −0.245366 | − | 0.969430i | \(-0.578908\pi\) | ||||
−0.245366 | + | 0.969430i | \(0.578908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.7329 | 0.961498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.19028 | −0.134694 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.5357 | 1.75052 | 0.875261 | − | 0.483651i | \(-0.160690\pi\) | ||||
0.875261 | + | 0.483651i | \(0.160690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2367 | 0.472731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.619101 | 0.0259998 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7077 | −0.448889 | −0.224444 | − | 0.974487i | \(-0.572057\pi\) | ||||
−0.224444 | + | 0.974487i | \(0.572057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.47801 | −0.271096 | −0.135548 | − | 0.990771i | \(-0.543280\pi\) | ||||
−0.135548 | + | 0.990771i | \(0.543280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.9079 | −0.664560 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.3750 | −0.516073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.6512 | −1.35929 | −0.679643 | − | 0.733543i | \(-0.737865\pi\) | ||||
−0.679643 | + | 0.733543i | \(0.737865\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.1335 | −0.919836 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.15539 | −0.0479335 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.7449 | −1.93598 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.07002 | 0.209619 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9818 | 1.07238 | 0.536192 | − | 0.844096i | \(-0.319862\pi\) | ||||
0.536192 | + | 0.844096i | \(0.319862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.7694 | 1.72108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.75941 | 0.401449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.56680 | 0.105406 | 0.0527028 | − | 0.998610i | \(-0.483216\pi\) | ||||
0.0527028 | + | 0.998610i | \(0.483216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.769241 | −0.0315358 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.36374 | −0.0967413 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.6505 | −0.884616 | −0.442308 | − | 0.896863i | \(-0.645840\pi\) | ||||
−0.442308 | + | 0.896863i | \(0.645840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8211 | −0.482193 | −0.241096 | − | 0.970501i | \(-0.577507\pi\) | ||||
−0.241096 | + | 0.970501i | \(0.577507\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.0368 | −0.449455 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.6612 | 0.799341 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8427 | −0.440093 | −0.220046 | − | 0.975489i | \(-0.570621\pi\) | ||||
−0.220046 | + | 0.975489i | \(0.570621\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.39148 | 0.177952 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.69890 | −0.190097 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.90481 | 0.117324 | 0.0586620 | − | 0.998278i | \(-0.481317\pi\) | ||||
0.0586620 | + | 0.998278i | \(0.481317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.105065 | 0.00423663 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.16820 | 0.369098 | 0.184549 | − | 0.982823i | \(-0.440918\pi\) | ||||
0.184549 | + | 0.982823i | \(0.440918\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5746 | −0.585801 | −0.292901 | − | 0.956143i | \(-0.594621\pi\) | ||||
−0.292901 | + | 0.956143i | \(0.594621\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.31476 | 0.293531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.18836 | −0.127739 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.6790 | −0.547158 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.6652 | 1.10484 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.46041 | 0.217721 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9869 | 1.07433 | 0.537166 | − | 0.843476i | \(-0.319495\pi\) | ||||
0.537166 | + | 0.843476i | \(0.319495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.75868 | −0.268633 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6263 | −0.620113 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.4440 | −0.730777 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.2933 | −0.604992 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2044 | 0.403051 | 0.201526 | − | 0.979483i | \(-0.435410\pi\) | ||||
0.201526 | + | 0.979483i | \(0.435410\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.56619 | 0.298382 | 0.149191 | − | 0.988808i | \(-0.452333\pi\) | ||||
0.149191 | + | 0.988808i | \(0.452333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.8333 | 0.584062 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.5945 | 0.927594 | 0.463797 | − | 0.885942i | \(-0.346487\pi\) | ||||
0.463797 | + | 0.885942i | \(0.346487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −56.0042 | −2.19836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.36527 | 0.171088 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.8469 | 1.67673 | 0.838365 | − | 0.545110i | \(-0.183512\pi\) | ||||
0.838365 | + | 0.545110i | \(0.183512\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7966 | 0.421858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.47053 | −0.213426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.8220 | 0.577383 | 0.288691 | − | 0.957422i | \(-0.406780\pi\) | ||||
0.288691 | + | 0.957422i | \(0.406780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.7271 | −1.00067 | −0.500333 | − | 0.865833i | \(-0.666789\pi\) | ||||
−0.500333 | + | 0.865833i | \(0.666789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.90422 | −0.0739536 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.67064 | 0.258676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.8859 | 2.00903 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.39260 | −0.324477 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.9058 | 0.884270 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.2272 | −1.24227 | −0.621134 | − | 0.783704i | \(-0.713328\pi\) | ||||
−0.621134 | + | 0.783704i | \(0.713328\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.69178 | −0.0651168 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.72394 | −0.143123 | −0.0715613 | − | 0.997436i | \(-0.522798\pi\) | ||||
−0.0715613 | + | 0.997436i | \(0.522798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.48045 | 0.248697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.8113 | −0.950771 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.93647 | 0.150625 | 0.0753124 | − | 0.997160i | \(-0.476005\pi\) | ||||
0.0753124 | + | 0.997160i | \(0.476005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.1787 | 1.30590 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.3000 | −0.927103 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.9011 | −1.06295 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.7531 | 1.85465 | 0.927327 | − | 0.374252i | \(-0.122100\pi\) | ||||
0.927327 | + | 0.374252i | \(0.122100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.89125 | 0.109830 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.7471 | −0.445591 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0394607 | −0.00149468 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.67691 | −0.366014 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3833 | 1.14756 | 0.573782 | − | 0.819008i | \(-0.305476\pi\) | ||||
0.573782 | + | 0.819008i | \(0.305476\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.3512 | −1.78588 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.06606 | −0.115475 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.50137 | −0.0940736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0956 | −0.942486 | −0.471243 | − | 0.882003i | \(-0.656195\pi\) | ||||
−0.471243 | + | 0.882003i | \(0.656195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.58093 | 0.321810 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.5763 | 1.93155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.6774 | 0.885484 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.1035 | 0.974852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.84414 | 0.329831 | 0.164915 | − | 0.986308i | \(-0.447265\pi\) | ||||
0.164915 | + | 0.986308i | \(0.447265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.79002 | −0.290116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.1384 | 1.12086 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0003 | −0.445682 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5581 | −0.428667 | −0.214333 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214333 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.57116 | −0.206057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.2694 | −1.78287 | −0.891435 | − | 0.453149i | \(-0.850300\pi\) | ||||
−0.891435 | + | 0.453149i | \(0.850300\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.0348 | −0.443911 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.5430 | −1.89861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.05064 | −0.222576 | −0.111288 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111288 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5128 | 0.606613 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.4999 | 1.63254 | 0.816271 | − | 0.577669i | \(-0.196037\pi\) | ||||
0.816271 | + | 0.577669i | \(0.196037\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.3378 | −1.11149 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.86623 | −0.0682820 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09142 | −0.0764188 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.98102 | 0.327722 | 0.163861 | − | 0.986483i | \(-0.447605\pi\) | ||||
0.163861 | + | 0.986483i | \(0.447605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.4290 | 0.671592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.9379 | 1.41710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2948 | −1.17378 | −0.586888 | − | 0.809668i | \(-0.699647\pi\) | ||||
−0.586888 | + | 0.809668i | \(0.699647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 34.1606 | 1.23995 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0185 | 1.01567 | 0.507836 | − | 0.861454i | \(-0.330446\pi\) | ||||
0.507836 | + | 0.861454i | \(0.330446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.92021 | −0.359136 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.24251 | −0.0449231 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.4279 | −1.20701 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.3092 | −1.70601 | −0.853006 | − | 0.521901i | \(-0.825223\pi\) | ||||
−0.853006 | + | 0.521901i | \(0.825223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.06747 | 0.146486 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.0787 | 0.506376 | 0.253188 | − | 0.967417i | \(-0.418521\pi\) | ||||
0.253188 | + | 0.967417i | \(0.418521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.9287 | −0.428493 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.94861 | −0.177530 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.342192 | 0.0122603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.4208 | −2.55564 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.09331 | 0.253494 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1659 | −0.469910 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.04701 | −0.322491 | −0.161246 | − | 0.986914i | \(-0.551551\pi\) | ||||
−0.161246 | + | 0.986914i | \(0.551551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.51519 | 0.0539423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.82475 | 0.135992 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6720 | 0.485509 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.2057 | −0.645688 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6386 | −0.872745 | −0.436373 | − | 0.899766i | \(-0.643737\pi\) | ||||
−0.436373 | + | 0.899766i | \(0.643737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.15156 | 0.0407394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.14998 | −0.181966 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.5478 | −0.901564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.23680 | 0.290309 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.06255 | −0.319017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.9517 | 1.01789 | 0.508943 | − | 0.860800i | \(-0.330036\pi\) | ||||
0.508943 | + | 0.860800i | \(0.330036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.30951 | 0.116213 | 0.0581063 | − | 0.998310i | \(-0.481494\pi\) | ||||
0.0581063 | + | 0.998310i | \(0.481494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.1878 | 0.357303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.5685 | 0.510314 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.3115 | 1.69021 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.72573 | 0.0603020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.08580 | −0.317097 | −0.158548 | − | 0.987351i | \(-0.550681\pi\) | ||||
−0.158548 | + | 0.987351i | \(0.550681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.7110 | −1.80253 | −0.901265 | − | 0.433268i | \(-0.857360\pi\) | ||||
−0.901265 | + | 0.433268i | \(0.857360\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.90077 | −0.275069 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4035 | −0.431311 | −0.215655 | − | 0.976470i | \(-0.569189\pi\) | ||||
−0.215655 | + | 0.976470i | \(0.569189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.9171 | −0.622287 | −0.311144 | − | 0.950363i | \(-0.600712\pi\) | ||||
−0.311144 | + | 0.950363i | \(0.600712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.6810 | −0.682728 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.52008 | 0.156612 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.81885 | 0.0629439 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.05098 | 0.243718 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.6292 | 1.19553 | 0.597766 | − | 0.801670i | \(-0.296055\pi\) | ||||
0.597766 | + | 0.801670i | \(0.296055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3151 | 0.735004 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3377 | 0.597142 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.51247 | −0.327239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.69228 | 0.229950 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.34287 | 0.0460873 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.4685 | −2.00427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8267 | 0.781571 | 0.390786 | − | 0.920482i | \(-0.372203\pi\) | ||||
0.390786 | + | 0.920482i | \(0.372203\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.7747 | 0.368488 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.9758 | 1.22891 | 0.614455 | − | 0.788952i | \(-0.289376\pi\) | ||||
0.614455 | + | 0.788952i | \(0.289376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.4850 | 1.75664 | 0.878322 | − | 0.478069i | \(-0.158663\pi\) | ||||
0.878322 | + | 0.478069i | \(0.158663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0357621 | 0.00121877 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.1692 | 0.584447 | 0.292224 | − | 0.956350i | \(-0.405605\pi\) | ||||
0.292224 | + | 0.956350i | \(0.405605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.4887 | 1.07065 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.5333 | −0.561501 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.0737 | 1.35941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.7650 | −1.04243 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.4675 | 0.354272 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.53529 | −0.254739 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8184 | 0.702986 | 0.351493 | − | 0.936190i | \(-0.385674\pi\) | ||||
0.351493 | + | 0.936190i | \(0.385674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.09037 | −0.272882 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.4316 | −0.620977 | −0.310489 | − | 0.950577i | \(-0.600493\pi\) | ||||
−0.310489 | + | 0.950577i | \(0.600493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.6082 | 1.70310 | 0.851550 | − | 0.524273i | \(-0.175663\pi\) | ||||
0.851550 | + | 0.524273i | \(0.175663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.8119 | −0.733199 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.8658 | −1.23783 | −0.618917 | − | 0.785457i | \(-0.712428\pi\) | ||||
−0.618917 | + | 0.785457i | \(0.712428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.31890 | −0.178390 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.67008 | 0.156454 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.98603 | −0.334170 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.15839 | 0.239279 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.3898 | 0.680795 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.0148 | 1.66809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.83775 | 0.227799 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.04897 | 0.168019 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.15645 | 0.271129 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.73808 | 0.290143 | 0.145072 | − | 0.989421i | \(-0.453659\pi\) | ||||
0.145072 | + | 0.989421i | \(0.453659\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.04032 | −0.134009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4824 | 1.07619 | 0.538095 | − | 0.842884i | \(-0.319144\pi\) | ||||
0.538095 | + | 0.842884i | \(0.319144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.71547 | −0.288440 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.92110 | 0.294922 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.67495 | 0.121358 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.42216 | 0.277821 | 0.138911 | − | 0.990305i | \(-0.455640\pi\) | ||||
0.138911 | + | 0.990305i | \(0.455640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.90434 | 0.260457 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.6297 | −1.40317 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5228 | 0.444627 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.5828 | −0.413273 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.7866 | 0.813221 | 0.406611 | − | 0.913602i | \(-0.366711\pi\) | ||||
0.406611 | + | 0.913602i | \(0.366711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.1969 | −1.28463 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.4753 | −0.408425 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.80264 | −0.189767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7372 | −1.33083 | −0.665413 | − | 0.746476i | \(-0.731744\pi\) | ||||
−0.665413 | + | 0.746476i | \(0.731744\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.1389 | −0.559308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.5064 | 0.505494 | 0.252747 | − | 0.967532i | \(-0.418666\pi\) | ||||
0.252747 | + | 0.967532i | \(0.418666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.422534 | 0.0137596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.12605 | 0.0366305 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.98267 | 0.324393 | 0.162197 | − | 0.986758i | \(-0.448142\pi\) | ||||
0.162197 | + | 0.986758i | \(0.448142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2490 | −0.495004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.78055 | 0.155020 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.25373 | 0.234971 | 0.117486 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117486 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.9340 | −0.936282 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.1264 | 1.07082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.6337 | 0.375673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.7164 | 0.603754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.37816 | −0.108860 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40.2575 | −1.29593 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.7965 | −0.540138 | −0.270069 | − | 0.962841i | \(-0.587046\pi\) | ||||
−0.270069 | + | 0.962841i | \(0.587046\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.04681 | −0.130002 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.1516 | 1.09598 | 0.547988 | − | 0.836486i | \(-0.315394\pi\) | ||||
0.547988 | + | 0.836486i | \(0.315394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.99847 | −0.128185 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.71582 | −0.151027 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.4062 | −1.00477 | −0.502387 | − | 0.864643i | \(-0.667545\pi\) | ||||
−0.502387 | + | 0.864643i | \(0.667545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0508 | −0.768668 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0236 | −0.511593 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.4807 | 0.398073 | 0.199037 | − | 0.979992i | \(-0.436219\pi\) | ||||
0.199037 | + | 0.979992i | \(0.436219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.7509 | 0.565591 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.04363 | −0.0332190 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 59.6543 | 1.89690 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.0705 | −1.39995 | −0.699973 | − | 0.714169i | \(-0.746805\pi\) | ||||
−0.699973 | + | 0.714169i | \(0.746805\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.6964 | 1.03759 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.29928 | −0.136296 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.6923 | 0.338627 | 0.169314 | − | 0.985562i | \(-0.445845\pi\) | ||||
0.169314 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.99322 | −0.252894 |
(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 | 8016.2.a.u.1.4 | 5 | ||
4.3 | odd | 2 | 501.2.a.c.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 1503.2.a.c.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
501.2.a.c.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
1503.2.a.c.1.3 | 5 | 12.11 | even | 2 | |||
8016.2.a.u.1.4 | 5 | 1.1 | even | 1 | trivial |