Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.80306\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −1.80306 | −0.806352 | −0.403176 | − | 0.915122i | \(-0.632094\pi\) | ||||
−0.403176 | + | 0.915122i | \(0.632094\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.10861 | −1.55291 | −0.776455 | − | 0.630172i | \(-0.782984\pi\) | ||||
−0.776455 | + | 0.630172i | \(0.782984\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59144 | −0.781349 | −0.390675 | − | 0.920529i | \(-0.627758\pi\) | ||||
−0.390675 | + | 0.920529i | \(0.627758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46748 | −0.961707 | −0.480853 | − | 0.876801i | \(-0.659673\pi\) | ||||
−0.480853 | + | 0.876801i | \(0.659673\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.80306 | 0.465548 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.68470 | 0.408600 | 0.204300 | − | 0.978908i | \(-0.434508\pi\) | ||||
0.204300 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.49774 | −0.573021 | −0.286510 | − | 0.958077i | \(-0.592495\pi\) | ||||
−0.286510 | + | 0.958077i | \(0.592495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.10861 | 0.896573 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.91932 | −1.85981 | −0.929904 | − | 0.367803i | \(-0.880110\pi\) | ||||
−0.929904 | + | 0.367803i | \(0.880110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.74898 | −0.349796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.42158 | −0.821067 | −0.410534 | − | 0.911845i | \(-0.634658\pi\) | ||||
−0.410534 | + | 0.911845i | \(0.634658\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.95084 | −0.529987 | −0.264993 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264993 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.59144 | 0.451112 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.40807 | 1.25219 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.918154 | 0.150944 | 0.0754718 | − | 0.997148i | \(-0.475954\pi\) | ||||
0.0754718 | + | 0.997148i | \(0.475954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.46748 | 0.555242 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.83849 | −0.287125 | −0.143562 | − | 0.989641i | \(-0.545856\pi\) | ||||
−0.143562 | + | 0.989641i | \(0.545856\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.850997 | 0.129776 | 0.0648879 | − | 0.997893i | \(-0.479331\pi\) | ||||
0.0648879 | + | 0.997893i | \(0.479331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.80306 | −0.268784 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.74458 | −0.983798 | −0.491899 | − | 0.870652i | \(-0.663697\pi\) | ||||
−0.491899 | + | 0.870652i | \(0.663697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.88072 | 1.41153 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68470 | −0.235905 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.65455 | 0.639351 | 0.319676 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319676 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.67252 | 0.630043 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.49774 | 0.330834 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.23850 | 0.161239 | 0.0806194 | − | 0.996745i | \(-0.474310\pi\) | ||||
0.0806194 | + | 0.996745i | \(0.474310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.97208 | −1.02072 | −0.510360 | − | 0.859961i | \(-0.670488\pi\) | ||||
−0.510360 | + | 0.859961i | \(0.670488\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.10861 | −0.517637 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.25208 | 0.775475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.65708 | −0.202445 | −0.101223 | − | 0.994864i | \(-0.532275\pi\) | ||||
−0.101223 | + | 0.994864i | \(0.532275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.91932 | 1.07376 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.24057 | −0.740620 | −0.370310 | − | 0.928908i | \(-0.620749\pi\) | ||||
−0.370310 | + | 0.928908i | \(0.620749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.76409 | −0.557594 | −0.278797 | − | 0.960350i | \(-0.589936\pi\) | ||||
−0.278797 | + | 0.960350i | \(0.589936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.74898 | 0.201955 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.6472 | 1.21337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7193 | −1.20601 | −0.603007 | − | 0.797736i | \(-0.706031\pi\) | ||||
−0.603007 | + | 0.797736i | \(0.706031\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.69008 | −0.405039 | −0.202519 | − | 0.979278i | \(-0.564913\pi\) | ||||
−0.202519 | + | 0.979278i | \(0.564913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.03761 | −0.329475 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.42158 | 0.474044 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0739 | −1.27983 | −0.639916 | − | 0.768445i | \(-0.721031\pi\) | ||||
−0.639916 | + | 0.768445i | \(0.721031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.2466 | 1.49344 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.95084 | 0.305988 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.50357 | 0.462057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8662 | 1.50944 | 0.754719 | − | 0.656048i | \(-0.227773\pi\) | ||||
0.754719 | + | 0.656048i | \(0.227773\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.59144 | −0.260450 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.27675 | 0.127041 | 0.0635206 | − | 0.997981i | \(-0.479767\pi\) | ||||
0.0635206 | + | 0.997981i | \(0.479767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.26805 | 0.519077 | 0.259538 | − | 0.965733i | \(-0.416430\pi\) | ||||
0.259538 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.40807 | −0.722954 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.81076 | 0.755094 | 0.377547 | − | 0.925990i | \(-0.376768\pi\) | ||||
0.377547 | + | 0.925990i | \(0.376768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.01235 | −0.192748 | −0.0963739 | − | 0.995345i | \(-0.530724\pi\) | ||||
−0.0963739 | + | 0.995345i | \(0.530724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.918154 | −0.0871473 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.20964 | 0.772298 | 0.386149 | − | 0.922436i | \(-0.373805\pi\) | ||||
0.386149 | + | 0.922436i | \(0.373805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.0821 | 1.49966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.46748 | −0.320569 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92178 | −0.634519 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.28443 | −0.389494 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.83849 | 0.165771 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1688 | 1.08841 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.38074 | 0.832406 | 0.416203 | − | 0.909272i | \(-0.363361\pi\) | ||||
0.416203 | + | 0.909272i | \(0.363361\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.850997 | −0.0749261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.8572 | 1.73493 | 0.867465 | − | 0.497498i | \(-0.165748\pi\) | ||||
0.867465 | + | 0.497498i | \(0.165748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.2623 | 0.889850 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.80306 | 0.155183 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.44295 | 0.465023 | 0.232511 | − | 0.972594i | \(-0.425306\pi\) | ||||
0.232511 | + | 0.972594i | \(0.425306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0858 | −1.10992 | −0.554960 | − | 0.831877i | \(-0.687266\pi\) | ||||
−0.554960 | + | 0.831877i | \(0.687266\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.74458 | 0.567996 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.98578 | 0.751429 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.97238 | 0.662070 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.88072 | −0.814948 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.961230 | −0.0787470 | −0.0393735 | − | 0.999225i | \(-0.512536\pi\) | ||||
−0.0393735 | + | 0.999225i | \(0.512536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.62272 | −0.701707 | −0.350853 | − | 0.936430i | \(-0.614108\pi\) | ||||
−0.350853 | + | 0.936430i | \(0.614108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.68470 | 0.136200 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.32054 | 0.427356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.40121 | 0.271446 | 0.135723 | − | 0.990747i | \(-0.456664\pi\) | ||||
0.135723 | + | 0.990747i | \(0.456664\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.65455 | −0.369130 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.6461 | 2.88811 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.70291 | −0.211708 | −0.105854 | − | 0.994382i | \(-0.533758\pi\) | ||||
−0.105854 | + | 0.994382i | \(0.533758\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.67252 | −0.363755 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.976559 | −0.0751200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.49774 | −0.191007 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7489 | 1.04531 | 0.522654 | − | 0.852545i | \(-0.324942\pi\) | ||||
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.18588 | 0.543201 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.23850 | −0.0930912 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.148844 | 0.0111251 | 0.00556257 | − | 0.999985i | \(-0.498229\pi\) | ||||
0.00556257 | + | 0.999985i | \(0.498229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.10022 | 0.527755 | 0.263877 | − | 0.964556i | \(-0.414999\pi\) | ||||
0.263877 | + | 0.964556i | \(0.414999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.97208 | 0.589313 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.65549 | −0.121714 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.36580 | −0.319259 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.10861 | 0.298858 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.56545 | −0.402702 | −0.201351 | − | 0.979519i | \(-0.564533\pi\) | ||||
−0.201351 | + | 0.979519i | \(0.564533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.6812 | −1.20074 | −0.600371 | − | 0.799721i | \(-0.704981\pi\) | ||||
−0.600371 | + | 0.799721i | \(0.704981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.25208 | −0.447721 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0656 | 0.717145 | 0.358573 | − | 0.933502i | \(-0.383264\pi\) | ||||
0.358573 | + | 0.933502i | \(0.383264\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2270 | −1.00853 | −0.504263 | − | 0.863550i | \(-0.668236\pi\) | ||||
−0.504263 | + | 0.863550i | \(0.668236\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.65708 | 0.116882 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.1666 | 1.27504 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.31491 | 0.231524 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.91932 | −0.619936 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.47275 | 0.447729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4006 | 1.33560 | 0.667798 | − | 0.744343i | \(-0.267237\pi\) | ||||
0.667798 | + | 0.744343i | \(0.267237\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.24057 | 0.427597 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.53440 | −0.104645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1239 | 0.823022 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.76409 | 0.321927 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.84167 | −0.392953 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.50496 | −0.368640 | −0.184320 | − | 0.982866i | \(-0.559008\pi\) | ||||
−0.184320 | + | 0.982866i | \(0.559008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.74898 | −0.116599 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.7959 | −1.64576 | −0.822880 | − | 0.568215i | \(-0.807634\pi\) | ||||
−0.822880 | + | 0.568215i | \(0.807634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.8293 | −1.50860 | −0.754302 | − | 0.656528i | \(-0.772024\pi\) | ||||
−0.754302 | + | 0.656528i | \(0.772024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.6472 | −0.700537 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.2217 | 0.800672 | 0.400336 | − | 0.916368i | \(-0.368893\pi\) | ||||
0.400336 | + | 0.916368i | \(0.368893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1609 | 0.793288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.7193 | 0.696293 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.79185 | 0.504013 | 0.252007 | − | 0.967726i | \(-0.418910\pi\) | ||||
0.252007 | + | 0.967726i | \(0.418910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.1396 | −1.42613 | −0.713067 | − | 0.701096i | \(-0.752695\pi\) | ||||
−0.713067 | + | 0.701096i | \(0.752695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.8155 | −1.13819 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.66087 | 0.551078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.69008 | 0.233849 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1687 | −1.02056 | −0.510279 | − | 0.860009i | \(-0.670458\pi\) | ||||
−0.510279 | + | 0.860009i | \(0.670458\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.1139 | 1.45316 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.03761 | 0.190223 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3740 | 1.39565 | 0.697825 | − | 0.716268i | \(-0.254151\pi\) | ||||
0.697825 | + | 0.716268i | \(0.254151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.77234 | −0.234402 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.42158 | −0.273689 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4376 | −1.26023 | −0.630117 | − | 0.776500i | \(-0.716993\pi\) | ||||
−0.630117 | + | 0.776500i | \(0.716993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.39242 | −0.515542 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0739 | 0.738911 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.8017 | 1.02442 | 0.512209 | − | 0.858861i | \(-0.328827\pi\) | ||||
0.512209 | + | 0.858861i | \(0.328827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.49263 | −0.515890 | −0.257945 | − | 0.966160i | \(-0.583045\pi\) | ||||
−0.257945 | + | 0.966160i | \(0.583045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.2466 | −0.862241 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.53238 | 0.273313 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.1608 | −0.730670 | −0.365335 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365335 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.95084 | −0.176662 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5701 | −0.869178 | −0.434589 | − | 0.900629i | \(-0.643106\pi\) | ||||
−0.434589 | + | 0.900629i | \(0.643106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.16542 | 0.485384 | 0.242692 | − | 0.970103i | \(-0.421970\pi\) | ||||
0.242692 | + | 0.970103i | \(0.421970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.50357 | −0.266769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.55366 | 0.445879 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1618 | −0.833046 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8662 | −0.871474 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.2346 | 1.70791 | 0.853953 | − | 0.520350i | \(-0.174199\pi\) | ||||
0.853953 | + | 0.520350i | \(0.174199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.23309 | −0.130015 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.59144 | 0.150371 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.9276 | 1.78859 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.49642 | −0.201530 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.27675 | −0.0733473 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3741 | 0.823061 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8192 | 1.35943 | 0.679716 | − | 0.733475i | \(-0.262103\pi\) | ||||
0.679716 | + | 0.733475i | \(0.262103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.26805 | −0.299689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.4270 | −0.931492 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4875 | 0.705832 | 0.352916 | − | 0.935655i | \(-0.385190\pi\) | ||||
0.352916 | + | 0.935655i | \(0.385190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.40807 | 0.417398 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.38861 | −0.190323 | −0.0951617 | − | 0.995462i | \(-0.530337\pi\) | ||||
−0.0951617 | + | 0.995462i | \(0.530337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4583 | 0.641540 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.81076 | −0.435954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.20794 | −0.234136 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.06455 | 0.336401 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.01235 | 0.111283 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.7109 | 1.52775 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.83764 | 0.430795 | 0.215398 | − | 0.976526i | \(-0.430895\pi\) | ||||
0.215398 | + | 0.976526i | \(0.430895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.918154 | 0.0503145 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.98782 | 0.163242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0047 | −1.03525 | −0.517627 | − | 0.855606i | \(-0.673185\pi\) | ||||
−0.517627 | + | 0.855606i | \(0.673185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.20964 | −0.445887 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.64694 | 0.414105 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.8358 | −0.639071 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.0821 | −0.865829 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.2208 | 1.35392 | 0.676961 | − | 0.736019i | \(-0.263297\pi\) | ||||
0.676961 | + | 0.736019i | \(0.263297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.06370 | 0.0569387 | 0.0284693 | − | 0.999595i | \(-0.490937\pi\) | ||||
0.0284693 | + | 0.999595i | \(0.490937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.46748 | 0.185081 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0049 | 1.01153 | 0.505764 | − | 0.862672i | \(-0.331211\pi\) | ||||
0.505764 | + | 0.862672i | \(0.331211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2521 | 0.597201 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.92178 | 0.366340 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.4615 | 1.18547 | 0.592736 | − | 0.805397i | \(-0.298048\pi\) | ||||
0.592736 | + | 0.805397i | \(0.298048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7613 | −0.671647 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.28443 | 0.224874 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.58993 | 0.449618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.29449 | 0.328569 | 0.164285 | − | 0.986413i | \(-0.447468\pi\) | ||||
0.164285 | + | 0.986413i | \(0.447468\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.83849 | −0.0957082 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.1237 | −0.992855 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.9702 | −0.619794 | −0.309897 | − | 0.950770i | \(-0.600295\pi\) | ||||
−0.309897 | + | 0.950770i | \(0.600295\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1688 | −0.628394 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.3318 | 0.789626 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5730 | −0.954032 | −0.477016 | − | 0.878895i | \(-0.658282\pi\) | ||||
−0.477016 | + | 0.878895i | \(0.658282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.38074 | −0.480590 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.3120 | −1.49777 | −0.748886 | − | 0.662698i | \(-0.769411\pi\) | ||||
−0.748886 | + | 0.662698i | \(0.769411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.1976 | −0.978400 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.850997 | 0.0432586 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.9476 | 0.808573 | 0.404287 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404287 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.0264 | −0.759917 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.8572 | −1.00166 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.3275 | 0.972473 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9256 | −1.15060 | −0.575302 | − | 0.817941i | \(-0.695116\pi\) | ||||
−0.575302 | + | 0.817941i | \(0.695116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.2623 | −0.513755 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0031 | 1.04884 | 0.524421 | − | 0.851459i | \(-0.324282\pi\) | ||||
0.524421 | + | 0.851459i | \(0.324282\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2320 | 0.509692 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.80306 | −0.0895947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.37934 | −0.117940 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4707 | 1.70447 | 0.852234 | − | 0.523160i | \(-0.175247\pi\) | ||||
0.852234 | + | 0.523160i | \(0.175247\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.44295 | −0.268481 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.08851 | −0.250389 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.65343 | 0.326604 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0858 | 0.640812 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.80419 | −0.381260 | −0.190630 | − | 0.981662i | \(-0.561053\pi\) | ||||
−0.190630 | + | 0.981662i | \(0.561053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5378 | −1.39085 | −0.695424 | − | 0.718599i | \(-0.744783\pi\) | ||||
−0.695424 | + | 0.718599i | \(0.744783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.74458 | −0.327933 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.94650 | −0.142926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.7542 | 1.58509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.98578 | −0.433838 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9732 | 0.528559 | 0.264279 | − | 0.964446i | \(-0.414866\pi\) | ||||
0.264279 | + | 0.964446i | \(0.414866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.8851 | 0.907558 | 0.453779 | − | 0.891114i | \(-0.350076\pi\) | ||||
0.453779 | + | 0.891114i | \(0.350076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.97238 | −0.382246 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.2781 | 1.06571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.2125 | −1.20333 | −0.601665 | − | 0.798749i | \(-0.705496\pi\) | ||||
−0.601665 | + | 0.798749i | \(0.705496\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.88072 | 0.470510 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.2876 | −0.963893 | −0.481947 | − | 0.876201i | \(-0.660070\pi\) | ||||
−0.481947 | + | 0.876201i | \(0.660070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.7700 | 1.03200 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.961230 | 0.0454646 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.3700 | −1.24448 | −0.622240 | − | 0.782827i | \(-0.713777\pi\) | ||||
−0.622240 | + | 0.782827i | \(0.713777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.76435 | 0.224345 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.62272 | 0.405131 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.6874 | −1.20424 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0483 | −0.937818 | −0.468909 | − | 0.883247i | \(-0.655353\pi\) | ||||
−0.468909 | + | 0.883247i | \(0.655353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.68470 | −0.0786351 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0956 | −1.30854 | −0.654272 | − | 0.756260i | \(-0.727025\pi\) | ||||
−0.654272 | + | 0.756260i | \(0.727025\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.8772 | −1.10967 | −0.554834 | − | 0.831961i | \(-0.687218\pi\) | ||||
−0.554834 | + | 0.831961i | \(0.687218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.32054 | −0.246734 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.4385 | −1.54735 | −0.773674 | − | 0.633584i | \(-0.781583\pi\) | ||||
−0.773674 | + | 0.633584i | \(0.781583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.80832 | 0.314379 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.40121 | −0.156720 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.20531 | −0.101400 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.36849 | 0.200440 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.65455 | 0.213117 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.13119 | −0.143068 | −0.0715340 | − | 0.997438i | \(-0.522789\pi\) | ||||
−0.0715340 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.18368 | −0.145163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −36.6461 | −1.66745 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.8047 | −1.21714 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.2378 | −1.18895 | −0.594475 | − | 0.804114i | \(-0.702640\pi\) | ||||
−0.594475 | + | 0.804114i | \(0.702640\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.70291 | 0.122230 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.20065 | −0.234702 | −0.117351 | − | 0.993090i | \(-0.537440\pi\) | ||||
−0.117351 | + | 0.993090i | \(0.537440\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.44904 | −0.335488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.67252 | 0.210014 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.6401 | 1.15012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0631 | −1.48011 | −0.740053 | − | 0.672548i | \(-0.765200\pi\) | ||||
−0.740053 | + | 0.672548i | \(0.765200\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.7807 | 0.659040 | 0.329520 | − | 0.944149i | \(-0.393113\pi\) | ||||
0.329520 | + | 0.944149i | \(0.393113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.30205 | −0.102440 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.976559 | 0.0433705 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.0505 | 1.37629 | 0.688145 | − | 0.725573i | \(-0.258425\pi\) | ||||
0.688145 | + | 0.725573i | \(0.258425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.5738 | 0.865894 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.49774 | 0.110278 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.49861 | −0.418559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.4782 | 0.768689 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.7489 | −0.603509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.63406 | 0.159211 | 0.0796056 | − | 0.996826i | \(-0.474634\pi\) | ||||
0.0796056 | + | 0.996826i | \(0.474634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1659 | 1.14416 | 0.572078 | − | 0.820199i | \(-0.306137\pi\) | ||||
0.572078 | + | 0.820199i | \(0.306137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.18588 | −0.313617 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.97128 | −0.216553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.5543 | 2.45888 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.23850 | 0.0537462 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.37495 | 0.276130 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.0833 | −0.608872 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.148844 | −0.00642310 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.6053 | −1.10290 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.260024 | 0.0111793 | 0.00558966 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558966 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.10022 | −0.304699 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.62838 | 0.155423 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8527 | −1.19090 | −0.595448 | − | 0.803394i | \(-0.703025\pi\) | ||||
−0.595448 | + | 0.803394i | \(0.703025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.97208 | −0.340240 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0440 | 0.470489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.0414 | 1.87283 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.65549 | 0.0702714 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.13555 | 0.344714 | 0.172357 | − | 0.985035i | \(-0.444862\pi\) | ||||
0.172357 | + | 0.985035i | \(0.444862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.95082 | −0.124806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.36580 | 0.184324 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.9622 | −1.89493 | −0.947466 | − | 0.319856i | \(-0.896366\pi\) | ||||
−0.947466 | + | 0.319856i | \(0.896366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8025 | −0.622745 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.10861 | −0.172546 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.14797 | 0.341581 | 0.170790 | − | 0.985307i | \(-0.445368\pi\) | ||||
0.170790 | + | 0.985307i | \(0.445368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.71162 | 0.239024 | 0.119512 | − | 0.992833i | \(-0.461867\pi\) | ||||
0.119512 | + | 0.992833i | \(0.461867\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.56545 | 0.232500 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.5997 | 0.650553 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.28848 | 0.345054 | 0.172527 | − | 0.985005i | \(-0.444807\pi\) | ||||
0.172527 | + | 0.985005i | \(0.444807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.6812 | 0.693249 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.1611 | 0.628989 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0620 | −0.499556 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.25208 | 0.258492 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2682 | 1.33185 | 0.665925 | − | 0.746019i | \(-0.268037\pi\) | ||||
0.665925 | + | 0.746019i | \(0.268037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.37043 | 0.303693 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0656 | −0.414044 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.2913 | −1.07965 | −0.539826 | − | 0.841776i | \(-0.681510\pi\) | ||||
−0.539826 | + | 0.841776i | \(0.681510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4804 | 0.511646 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2270 | 0.582273 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.95363 | 0.0798233 | 0.0399117 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399117 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.855179 | −0.0348835 | −0.0174417 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174417 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.65708 | −0.0674817 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.72508 | 0.314069 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.8511 | −0.724553 | −0.362276 | − | 0.932071i | \(-0.618000\pi\) | ||||
−0.362276 | + | 0.932071i | \(0.618000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.1666 | −0.736147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3867 | 0.946125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0354 | 0.849611 | 0.424806 | − | 0.905285i | \(-0.360342\pi\) | ||||
0.424806 | + | 0.905285i | \(0.360342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.31491 | −0.133670 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.7077 | −1.19599 | −0.597993 | − | 0.801501i | \(-0.704035\pi\) | ||||
−0.597993 | + | 0.801501i | \(0.704035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.12602 | −0.286419 | −0.143209 | − | 0.989692i | \(-0.545742\pi\) | ||||
−0.143209 | + | 0.989692i | \(0.545742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.91932 | 0.357920 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 49.6070 | 1.98746 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.1962 | −0.527847 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.47275 | −0.258497 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.54681 | 0.0616755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8881 | −0.433447 | −0.216724 | − | 0.976233i | \(-0.569537\pi\) | ||||
−0.216724 | + | 0.976233i | \(0.569537\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.4006 | −0.771106 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9140 | −0.671213 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.2612 | −1.35748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.24057 | −0.246873 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00715 | 0.237268 | 0.118634 | − | 0.992938i | \(-0.462148\pi\) | ||||
0.118634 | + | 0.992938i | \(0.462148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8736 | 0.902045 | 0.451023 | − | 0.892513i | \(-0.351059\pi\) | ||||
0.451023 | + | 0.892513i | \(0.351059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.53440 | 0.0604169 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1587 | 0.753205 | 0.376602 | − | 0.926375i | \(-0.377092\pi\) | ||||
0.376602 | + | 0.926375i | \(0.377092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.20950 | −0.125984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.1239 | −0.475172 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.0547 | −1.13700 | −0.568499 | − | 0.822684i | \(-0.692475\pi\) | ||||
−0.568499 | + | 0.822684i | \(0.692475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.8037 | −1.39897 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.76409 | −0.185865 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.7083 | 0.728771 | 0.364386 | − | 0.931248i | \(-0.381279\pi\) | ||||
0.364386 | + | 0.931248i | \(0.381279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.65833 | −0.258979 | −0.129490 | − | 0.991581i | \(-0.541334\pi\) | ||||
−0.129490 | + | 0.991581i | \(0.541334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.84167 | 0.226872 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.5034 | −0.717533 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.4375 | 1.52703 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.50496 | 0.212834 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.6592 | 0.797539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7547 | −0.992772 | −0.496386 | − | 0.868102i | \(-0.665340\pi\) | ||||
−0.496386 | + | 0.868102i | \(0.665340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.74898 | 0.0673182 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.7352 | 0.451019 | 0.225510 | − | 0.974241i | \(-0.427595\pi\) | ||||
0.225510 | + | 0.974241i | \(0.427595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −61.0797 | −2.34402 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.7959 | 0.950180 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.4318 | −1.16444 | −0.582220 | − | 0.813031i | \(-0.697816\pi\) | ||||
−0.582220 | + | 0.813031i | \(0.697816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.81397 | −0.374972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.8293 | 0.870993 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.1396 | −0.614868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.5839 | −1.35368 | −0.676838 | − | 0.736132i | \(-0.736650\pi\) | ||||
−0.676838 | + | 0.736132i | \(0.736650\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.6472 | 0.404455 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.5944 | 0.894986 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.09731 | −0.117319 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.2217 | −0.462268 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.4767 | −0.433468 | −0.216734 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216734 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.29331 | −0.0864938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.1609 | −0.458005 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.24567 | −0.197284 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.41968 | 0.0908729 | 0.0454365 | − | 0.998967i | \(-0.485532\pi\) | ||||
0.0454365 | + | 0.998967i | \(0.485532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.7193 | −0.402005 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.3195 | 0.985673 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.2019 | −0.605916 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.79185 | −0.290992 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.9803 | 1.00620 | 0.503098 | − | 0.864229i | \(-0.332194\pi\) | ||||
0.503098 | + | 0.864229i | \(0.332194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.6444 | −0.806080 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.1396 | 0.823379 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.73325 | 0.287206 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.04133 | 0.298237 | 0.149118 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149118 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.43368 | 0.0530264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.1812 | −1.77961 | −0.889807 | − | 0.456336i | \(-0.849161\pi\) | ||||
−0.889807 | + | 0.456336i | \(0.849161\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.8155 | 0.657135 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.29424 | 0.158180 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.9605 | 0.807829 | 0.403915 | − | 0.914797i | \(-0.367649\pi\) | ||||
0.403915 | + | 0.914797i | \(0.367649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.66087 | −0.318165 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.55455 | 0.167090 | 0.0835451 | − | 0.996504i | \(-0.473376\pi\) | ||||
0.0835451 | + | 0.996504i | \(0.473376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.73315 | 0.0634979 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.69008 | −0.135013 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32.0914 | −1.17259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.3222 | 0.887530 | 0.443765 | − | 0.896143i | \(-0.353643\pi\) | ||||
0.443765 | + | 0.896143i | \(0.353643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.1687 | 0.589219 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.5473 | 0.565823 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.86234 | 0.358453 | 0.179226 | − | 0.983808i | \(-0.442641\pi\) | ||||
0.179226 | + | 0.983808i | \(0.442641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.1139 | −0.838982 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.04767 | −0.0379781 | −0.0189891 | − | 0.999820i | \(-0.506045\pi\) | ||||
−0.0189891 | + | 0.999820i | \(0.506045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.26796 | 0.299320 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.03761 | −0.109825 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.29447 | −0.155064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2840 | −0.406912 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.3740 | −0.805779 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.32588 | 0.0836561 | 0.0418280 | − | 0.999125i | \(-0.486682\pi\) | ||||
0.0418280 | + | 0.999125i | \(0.486682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.16096 | 0.185387 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.77234 | 0.135332 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.59208 | 0.164528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.1721 | 0.578683 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.42158 | 0.158015 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.13259 | −0.218882 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.04798 | −0.322526 | −0.161263 | − | 0.986912i | \(-0.551557\pi\) | ||||
−0.161263 | + | 0.986912i | \(0.551557\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.4376 | 0.727596 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.7303 | −1.19931 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.6431 | 0.981634 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.39242 | 0.297649 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.67319 | 0.200955 | 0.100477 | − | 0.994939i | \(-0.467963\pi\) | ||||
0.100477 | + | 0.994939i | \(0.467963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3626 | −0.401979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0739 | −0.426611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.3459 | 0.435676 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −66.0750 | −2.32884 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8017 | −0.591448 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.7932 | −1.32874 | −0.664369 | − | 0.747405i | \(-0.731300\pi\) | ||||
−0.664369 | + | 0.747405i | \(0.731300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.2974 | 0.607394 | 0.303697 | − | 0.952769i | \(-0.401779\pi\) | ||||
0.303697 | + | 0.952769i | \(0.401779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.49263 | 0.297849 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.87350 | 0.170711 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.12557 | −0.0743643 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.2466 | 0.497815 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.1038 | 0.457325 | 0.228662 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228662 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.47594 | −0.190879 | −0.0954396 | − | 0.995435i | \(-0.530426\pi\) | ||||
−0.0954396 | + | 0.995435i | \(0.530426\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.53238 | −0.157797 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.81367 | −0.0978411 | −0.0489205 | − | 0.998803i | \(-0.515578\pi\) | ||||
−0.0489205 | + | 0.998803i | \(0.515578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7545 | 0.408250 | 0.204125 | − | 0.978945i | \(-0.434565\pi\) | ||||
0.204125 | + | 0.978945i | \(0.434565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1608 | 0.421852 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.6460 | 0.576751 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.80306 | −0.0623974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.95084 | 0.101996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.1585 | −1.21381 | −0.606903 | − | 0.794776i | \(-0.707588\pi\) | ||||
−0.606903 | + | 0.794776i | \(0.707588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.44960 | −0.325848 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.5701 | 0.501820 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.76079 | 0.0605732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.6031 | 0.604849 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.16542 | −0.280236 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.18931 | −0.280726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.19930 | −0.178021 | −0.0890104 | − | 0.996031i | \(-0.528370\pi\) | ||||
−0.0890104 | + | 0.996031i | \(0.528370\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.50357 | 0.154019 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.20592 | 0.0411933 | 0.0205966 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205966 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2254 | −1.33835 | −0.669176 | − | 0.743104i | \(-0.733353\pi\) | ||||
−0.669176 | + | 0.743104i | \(0.733353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.55366 | −0.257428 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4008 | 0.592329 | 0.296164 | − | 0.955137i | \(-0.404292\pi\) | ||||
0.296164 | + | 0.955137i | \(0.404292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.7900 | −0.842886 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.1618 | 0.480959 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.7784 | 0.942319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.74591 | 0.194693 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.8662 | 0.503146 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.9969 | −1.69020 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.8185 | −1.74979 | −0.874893 | − | 0.484316i | \(-0.839068\pi\) | ||||
−0.874893 | + | 0.484316i | \(0.839068\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.2346 | −0.986060 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.7905 | −1.87963 | −0.939814 | − | 0.341686i | \(-0.889002\pi\) | ||||
−0.939814 | + | 0.341686i | \(0.889002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.6270 | 1.16529 | 0.582645 | − | 0.812727i | \(-0.302018\pi\) | ||||
0.582645 | + | 0.812727i | \(0.302018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.23309 | 0.0750643 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.25650 | −0.109343 | −0.0546713 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546713 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.5418 | −1.29265 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.59144 | −0.0868166 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8462 | 0.563736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.268375 | −0.00897079 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.9276 | −1.03264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.0474 | 0.435155 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.84151 | 0.261239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.49642 | 0.116354 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8021 | −0.425556 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.93813 | 0.0643547 | 0.0321773 | − | 0.999482i | \(-0.489756\pi\) | ||||
0.0321773 | + | 0.999482i | \(0.489756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.27675 | 0.0423471 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6161 | −0.749304 | −0.374652 | − | 0.927165i | \(-0.622238\pi\) | ||||
−0.374652 | + | 0.927165i | \(0.622238\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.56262 | 0.316477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.3741 | −0.475194 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −81.5855 | −2.69419 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.152045 | −0.00501549 | −0.00250774 | − | 0.999997i | \(-0.500798\pi\) | ||||
−0.00250774 | + | 0.999997i | \(0.500798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8192 | −0.784869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.6391 | 0.712259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.60583 | −0.0527994 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.26805 | 0.173026 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.4885 | −1.32838 | −0.664192 | − | 0.747562i | \(-0.731224\pi\) | ||||
−0.664192 | + | 0.747562i | \(0.731224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.6795 | −0.808836 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.4270 | 0.537797 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.87180 | 0.257435 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.3072 | −1.61079 | −0.805397 | − | 0.592735i | \(-0.798048\pi\) | ||||
−0.805397 | + | 0.592735i | \(0.798048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.4875 | −0.407513 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.8417 | −0.744618 | −0.372309 | − | 0.928109i | \(-0.621434\pi\) | ||||
−0.372309 | + | 0.928109i | \(0.621434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.3981 | 0.533996 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.40807 | −0.240985 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.8527 | 0.677622 | 0.338811 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338811 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.5194 | 0.536242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.38861 | 0.109883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6396 | −0.668581 | −0.334291 | − | 0.942470i | \(-0.608497\pi\) | ||||
−0.334291 | + | 0.942470i | \(0.608497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0348 | 0.324719 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.4583 | −0.370393 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.3630 | −0.722139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2925 | −0.719114 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.81076 | 0.251698 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.0773 | 0.968222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.8774 | 1.41100 | 0.705501 | − | 0.708709i | \(-0.250722\pi\) | ||||
0.705501 | + | 0.708709i | \(0.250722\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.20794 | 0.135179 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.54975 | 0.306466 | 0.153233 | − | 0.988190i | \(-0.451031\pi\) | ||||
0.153233 | + | 0.988190i | \(0.451031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53.7643 | 1.72361 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.06455 | −0.194221 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9627 | 0.382721 | 0.191360 | − | 0.981520i | \(-0.438710\pi\) | ||||
0.191360 | + | 0.981520i | \(0.438710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.2888 | 0.999995 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.01235 | −0.0642493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.2845 | −1.18919 | −0.594595 | − | 0.804025i | \(-0.702688\pi\) | ||||
−0.594595 | + | 0.804025i | \(0.702688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1489 | −0.578272 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.7109 | −0.882047 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.59032 | −0.241358 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.0389 | −1.46247 | −0.731237 | − | 0.682123i | \(-0.761057\pi\) | ||||
−0.731237 | + | 0.682123i | \(0.761057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.83764 | −0.248720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.6521 | 0.813228 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.30573 | −0.199705 | −0.0998523 | − | 0.995002i | \(-0.531837\pi\) | ||||
−0.0998523 | + | 0.995002i | \(0.531837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.918154 | −0.0290491 |
(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 | 4008.2.a.k.1.3 | ✓ | 11 | |
4.3 | odd | 2 | 8016.2.a.be.1.3 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.3 | ✓ | 11 | 1.1 | even | 1 | trivial | |
8016.2.a.be.1.3 | 11 | 4.3 | odd | 2 |