Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1875) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.209057\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33826 | −0.946294 | −0.473147 | − | 0.880984i | \(-0.656882\pi\) | ||||
−0.473147 | + | 0.880984i | \(0.656882\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.209057 | −0.104528 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27977 | 0.483709 | 0.241854 | − | 0.970313i | \(-0.422244\pi\) | ||||
0.241854 | + | 0.970313i | \(0.422244\pi\) | |||||||
\(8\) | 2.95630 | 1.04521 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16535 | −0.351367 | −0.175683 | − | 0.984447i | \(-0.556214\pi\) | ||||
−0.175683 | + | 0.984447i | \(0.556214\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.61048 | −1.00137 | −0.500683 | − | 0.865631i | \(-0.666918\pi\) | ||||
−0.500683 | + | 0.865631i | \(0.666918\pi\) | |||||||
\(14\) | −1.71267 | −0.457730 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.53818 | −0.884545 | ||||||||
\(17\) | −5.35772 | −1.29944 | −0.649718 | − | 0.760175i | \(-0.725113\pi\) | ||||
−0.649718 | + | 0.760175i | \(0.725113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.61048 | −1.74596 | −0.872982 | − | 0.487753i | \(-0.837817\pi\) | ||||
−0.872982 | + | 0.487753i | \(0.837817\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.55955 | 0.332496 | ||||||||
\(23\) | −3.41811 | −0.712726 | −0.356363 | − | 0.934348i | \(-0.615983\pi\) | ||||
−0.356363 | + | 0.934348i | \(0.615983\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.83176 | 0.947586 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.267545 | −0.0505613 | ||||||||
\(29\) | 3.21661 | 0.597310 | 0.298655 | − | 0.954361i | \(-0.403462\pi\) | ||||
0.298655 | + | 0.954361i | \(0.403462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.09306 | −0.196319 | −0.0981594 | − | 0.995171i | \(-0.531295\pi\) | ||||
−0.0981594 | + | 0.995171i | \(0.531295\pi\) | |||||||
\(32\) | −1.17758 | −0.208169 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.17002 | 1.22965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.80126 | −1.28252 | −0.641260 | − | 0.767324i | \(-0.721588\pi\) | ||||
−0.641260 | + | 0.767324i | \(0.721588\pi\) | |||||||
\(38\) | 10.1848 | 1.65219 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00565 | 0.469403 | 0.234702 | − | 0.972067i | \(-0.424589\pi\) | ||||
0.234702 | + | 0.972067i | \(0.424589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.42278 | −0.521970 | −0.260985 | − | 0.965343i | \(-0.584047\pi\) | ||||
−0.260985 | + | 0.965343i | \(0.584047\pi\) | |||||||
\(44\) | 0.243625 | 0.0367278 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.57433 | 0.674448 | ||||||||
\(47\) | 9.41462 | 1.37326 | 0.686632 | − | 0.727005i | \(-0.259088\pi\) | ||||
0.686632 | + | 0.727005i | \(0.259088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36218 | −0.766026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.754795 | 0.104671 | ||||||||
\(53\) | 7.64760 | 1.05048 | 0.525239 | − | 0.850954i | \(-0.323976\pi\) | ||||
0.525239 | + | 0.850954i | \(0.323976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.78339 | 0.505576 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.30467 | −0.565231 | ||||||||
\(59\) | −12.7500 | −1.65991 | −0.829954 | − | 0.557832i | \(-0.811634\pi\) | ||||
−0.829954 | + | 0.557832i | \(0.811634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1506 | −1.29965 | −0.649824 | − | 0.760085i | \(-0.725157\pi\) | ||||
−0.649824 | + | 0.760085i | \(0.725157\pi\) | |||||||
\(62\) | 1.46280 | 0.185775 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.65227 | 1.08153 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.78903 | 1.07375 | 0.536876 | − | 0.843661i | \(-0.319604\pi\) | ||||
0.536876 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(68\) | 1.12007 | 0.135828 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0647 | 1.78786 | 0.893928 | − | 0.448211i | \(-0.147939\pi\) | ||||
0.893928 | + | 0.448211i | \(0.147939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.1533 | 1.53948 | 0.769740 | − | 0.638357i | \(-0.220386\pi\) | ||||
0.769740 | + | 0.638357i | \(0.220386\pi\) | |||||||
\(74\) | 10.4401 | 1.21364 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59102 | 0.182503 | ||||||||
\(77\) | −1.49139 | −0.169959 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5155 | −1.29560 | −0.647798 | − | 0.761812i | \(-0.724310\pi\) | ||||
−0.647798 | + | 0.761812i | \(0.724310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.02234 | −0.444193 | ||||||||
\(83\) | 10.7189 | 1.17655 | 0.588277 | − | 0.808659i | \(-0.299806\pi\) | ||||
0.588277 | + | 0.808659i | \(0.299806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.58058 | 0.493937 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.44512 | −0.367252 | ||||||||
\(89\) | 4.51584 | 0.478678 | 0.239339 | − | 0.970936i | \(-0.423069\pi\) | ||||
0.239339 | + | 0.970936i | \(0.423069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.62059 | −0.484369 | ||||||||
\(92\) | 0.714580 | 0.0745002 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.5992 | −1.29951 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0135 | 1.82899 | 0.914496 | − | 0.404596i | \(-0.132588\pi\) | ||||
0.914496 | + | 0.404596i | \(0.132588\pi\) | |||||||
\(98\) | 7.17600 | 0.724885 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.54634 | 0.651385 | 0.325693 | − | 0.945476i | \(-0.394403\pi\) | ||||
0.325693 | + | 0.945476i | \(0.394403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1588 | 1.09951 | 0.549753 | − | 0.835327i | \(-0.314722\pi\) | ||||
0.549753 | + | 0.835327i | \(0.314722\pi\) | |||||||
\(104\) | −10.6736 | −1.04664 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2345 | −0.994061 | ||||||||
\(107\) | 3.72681 | 0.360284 | 0.180142 | − | 0.983641i | \(-0.442344\pi\) | ||||
0.180142 | + | 0.983641i | \(0.442344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.99533 | −0.670031 | −0.335016 | − | 0.942213i | \(-0.608742\pi\) | ||||
−0.335016 | + | 0.942213i | \(0.608742\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.52807 | −0.427862 | ||||||||
\(113\) | 5.59858 | 0.526670 | 0.263335 | − | 0.964704i | \(-0.415178\pi\) | ||||
0.263335 | + | 0.964704i | \(0.415178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.672455 | −0.0624359 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.0628 | 1.57076 | ||||||||
\(119\) | −6.85666 | −0.628549 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.64195 | −0.876541 | ||||||||
\(122\) | 13.5841 | 1.22985 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.228511 | 0.0205209 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.38919 | −0.389478 | −0.194739 | − | 0.980855i | \(-0.562386\pi\) | ||||
−0.194739 | + | 0.980855i | \(0.562386\pi\) | |||||||
\(128\) | −9.22384 | −0.815280 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.99244 | 0.436192 | 0.218096 | − | 0.975927i | \(-0.430015\pi\) | ||||
0.218096 | + | 0.975927i | \(0.430015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.73968 | −0.844537 | ||||||||
\(134\) | −11.7620 | −1.01608 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.8390 | −1.35818 | ||||||||
\(137\) | −12.2056 | −1.04279 | −0.521396 | − | 0.853315i | \(-0.674589\pi\) | ||||
−0.521396 | + | 0.853315i | \(0.674589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.20617 | −0.441582 | −0.220791 | − | 0.975321i | \(-0.570864\pi\) | ||||
−0.220791 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −20.1606 | −1.69184 | ||||||||
\(143\) | 4.20748 | 0.351847 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.6026 | −1.45680 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.63091 | 0.134060 | ||||||||
\(149\) | 21.6208 | 1.77124 | 0.885622 | − | 0.464406i | \(-0.153732\pi\) | ||||
0.885622 | + | 0.464406i | \(0.153732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8918 | 0.967743 | 0.483872 | − | 0.875139i | \(-0.339230\pi\) | ||||
0.483872 | + | 0.875139i | \(0.339230\pi\) | |||||||
\(152\) | −22.4988 | −1.82490 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.99586 | 0.160831 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1112 | −0.966579 | −0.483290 | − | 0.875461i | \(-0.660558\pi\) | ||||
−0.483290 | + | 0.875461i | \(0.660558\pi\) | |||||||
\(158\) | 15.4108 | 1.22601 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.37441 | −0.344752 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.26913 | 0.647688 | 0.323844 | − | 0.946111i | \(-0.395025\pi\) | ||||
0.323844 | + | 0.946111i | \(0.395025\pi\) | |||||||
\(164\) | −0.628351 | −0.0490660 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.3447 | −1.11337 | ||||||||
\(167\) | −6.26564 | −0.484849 | −0.242425 | − | 0.970170i | \(-0.577943\pi\) | ||||
−0.242425 | + | 0.970170i | \(0.577943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0355444 | 0.00273418 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.715557 | 0.0545607 | ||||||||
\(173\) | −6.65609 | −0.506053 | −0.253027 | − | 0.967459i | \(-0.581426\pi\) | ||||
−0.253027 | + | 0.967459i | \(0.581426\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.12323 | 0.310800 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.04337 | −0.452970 | ||||||||
\(179\) | −21.7154 | −1.62309 | −0.811544 | − | 0.584292i | \(-0.801372\pi\) | ||||
−0.811544 | + | 0.584292i | \(0.801372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9474 | 0.962375 | 0.481188 | − | 0.876618i | \(-0.340206\pi\) | ||||
0.481188 | + | 0.876618i | \(0.340206\pi\) | |||||||
\(182\) | 6.18356 | 0.458356 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.1050 | −0.744947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.24362 | 0.456579 | ||||||||
\(188\) | −1.96819 | −0.143545 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.7683 | −1.14095 | −0.570476 | − | 0.821314i | \(-0.693241\pi\) | ||||
−0.570476 | + | 0.821314i | \(0.693241\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.93514 | 0.499202 | 0.249601 | − | 0.968349i | \(-0.419701\pi\) | ||||
0.249601 | + | 0.968349i | \(0.419701\pi\) | |||||||
\(194\) | −24.1067 | −1.73076 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12100 | 0.0800715 | ||||||||
\(197\) | 7.43948 | 0.530041 | 0.265020 | − | 0.964243i | \(-0.414621\pi\) | ||||
0.265020 | + | 0.964243i | \(0.414621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2398 | −1.00943 | −0.504716 | − | 0.863285i | \(-0.668403\pi\) | ||||
−0.504716 | + | 0.863285i | \(0.668403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.76072 | −0.616402 | ||||||||
\(203\) | 4.11653 | 0.288924 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.9334 | −1.04046 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.7745 | 0.885754 | ||||||||
\(209\) | 8.86889 | 0.613474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.89569 | 0.474719 | 0.237360 | − | 0.971422i | \(-0.423718\pi\) | ||||
0.237360 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(212\) | −1.59878 | −0.109805 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.98744 | −0.340935 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.39886 | −0.0949611 | ||||||||
\(218\) | 9.36158 | 0.634046 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3439 | 1.30121 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3983 | 0.897219 | 0.448609 | − | 0.893728i | \(-0.351920\pi\) | ||||
0.448609 | + | 0.893728i | \(0.351920\pi\) | |||||||
\(224\) | −1.50703 | −0.100693 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.49236 | −0.498385 | ||||||||
\(227\) | 0.849831 | 0.0564053 | 0.0282026 | − | 0.999602i | \(-0.491022\pi\) | ||||
0.0282026 | + | 0.999602i | \(0.491022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.79561 | −0.581231 | −0.290615 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290615 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.50926 | 0.624314 | ||||||||
\(233\) | −21.2093 | −1.38947 | −0.694734 | − | 0.719267i | \(-0.744478\pi\) | ||||
−0.694734 | + | 0.719267i | \(0.744478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.66548 | 0.173508 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.17600 | 0.594792 | ||||||||
\(239\) | 16.7972 | 1.08652 | 0.543261 | − | 0.839564i | \(-0.317189\pi\) | ||||
0.543261 | + | 0.839564i | \(0.317189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.51860 | 0.613147 | 0.306573 | − | 0.951847i | \(-0.400817\pi\) | ||||
0.306573 | + | 0.951847i | \(0.400817\pi\) | |||||||
\(242\) | 12.9035 | 0.829465 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.12205 | 0.135850 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4775 | 1.74835 | ||||||||
\(248\) | −3.23140 | −0.205194 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9486 | −0.817309 | −0.408655 | − | 0.912689i | \(-0.634002\pi\) | ||||
−0.408655 | + | 0.912689i | \(0.634002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.98331 | 0.250428 | ||||||||
\(254\) | 5.87389 | 0.368560 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.96064 | −0.310040 | ||||||||
\(257\) | 16.6837 | 1.04070 | 0.520352 | − | 0.853952i | \(-0.325801\pi\) | ||||
0.520352 | + | 0.853952i | \(0.325801\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.98384 | −0.620366 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.68119 | −0.412765 | ||||||||
\(263\) | 9.45426 | 0.582975 | 0.291487 | − | 0.956575i | \(-0.405850\pi\) | ||||
0.291487 | + | 0.956575i | \(0.405850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.0342 | 0.799180 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.83741 | −0.112238 | ||||||||
\(269\) | −31.7384 | −1.93513 | −0.967563 | − | 0.252631i | \(-0.918704\pi\) | ||||
−0.967563 | + | 0.252631i | \(0.918704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0556 | 1.15755 | 0.578773 | − | 0.815489i | \(-0.303532\pi\) | ||||
0.578773 | + | 0.815489i | \(0.303532\pi\) | |||||||
\(272\) | 18.9566 | 1.14941 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.3342 | 0.986787 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.71929 | −0.163387 | −0.0816933 | − | 0.996658i | \(-0.526033\pi\) | ||||
−0.0816933 | + | 0.996658i | \(0.526033\pi\) | |||||||
\(278\) | 6.96722 | 0.417866 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6076 | 0.871416 | 0.435708 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435708 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0890 | 1.07528 | 0.537639 | − | 0.843175i | \(-0.319316\pi\) | ||||
0.537639 | + | 0.843175i | \(0.319316\pi\) | |||||||
\(284\) | −3.14939 | −0.186882 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.63070 | −0.332950 | ||||||||
\(287\) | 3.84655 | 0.227054 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7051 | 0.688536 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.74979 | −0.160920 | ||||||||
\(293\) | 0.293910 | 0.0171704 | 0.00858521 | − | 0.999963i | \(-0.497267\pi\) | ||||
0.00858521 | + | 0.999963i | \(0.497267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −23.0628 | −1.34050 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.9343 | −1.67612 | ||||||||
\(299\) | 12.3410 | 0.713700 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.38039 | −0.252481 | ||||||||
\(302\) | −15.9144 | −0.915769 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.9272 | 1.54438 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.34411 | −0.0767125 | −0.0383563 | − | 0.999264i | \(-0.512212\pi\) | ||||
−0.0383563 | + | 0.999264i | \(0.512212\pi\) | |||||||
\(308\) | 0.311785 | 0.0177656 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9569 | −1.13165 | −0.565826 | − | 0.824525i | \(-0.691443\pi\) | ||||
−0.565826 | + | 0.824525i | \(0.691443\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.1446 | 0.799500 | 0.399750 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399750 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(314\) | 16.2080 | 0.914668 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.40740 | 0.135427 | ||||||||
\(317\) | −17.5897 | −0.987937 | −0.493968 | − | 0.869480i | \(-0.664454\pi\) | ||||
−0.493968 | + | 0.869480i | \(0.664454\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.74849 | −0.209875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.85410 | 0.326236 | ||||||||
\(323\) | 40.7748 | 2.26877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.0662 | −0.612903 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.88558 | 0.490624 | ||||||||
\(329\) | 12.0486 | 0.664260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00683 | 0.440095 | 0.220048 | − | 0.975489i | \(-0.429379\pi\) | ||||
0.220048 | + | 0.975489i | \(0.429379\pi\) | |||||||
\(332\) | −2.24086 | −0.122983 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.38506 | 0.458810 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8474 | 0.590895 | 0.295448 | − | 0.955359i | \(-0.404531\pi\) | ||||
0.295448 | + | 0.955359i | \(0.404531\pi\) | |||||||
\(338\) | −0.0475677 | −0.00258734 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.27380 | 0.0689799 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8208 | −0.854242 | ||||||||
\(344\) | −10.1188 | −0.545567 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.90759 | 0.478875 | ||||||||
\(347\) | −1.86153 | −0.0999323 | −0.0499662 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499662 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4623 | 1.30944 | 0.654719 | − | 0.755872i | \(-0.272787\pi\) | ||||
0.654719 | + | 0.755872i | \(0.272787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.37229 | 0.0731436 | ||||||||
\(353\) | 37.3621 | 1.98858 | 0.994291 | − | 0.106704i | \(-0.0340299\pi\) | ||||
0.994291 | + | 0.106704i | \(0.0340299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.944068 | −0.0500355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.0609 | 1.53592 | ||||||||
\(359\) | 25.3360 | 1.33718 | 0.668592 | − | 0.743629i | \(-0.266897\pi\) | ||||
0.668592 | + | 0.743629i | \(0.266897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.9194 | 2.04839 | ||||||||
\(362\) | −17.3270 | −0.910689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.965966 | 0.0506304 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.7057 | 1.23743 | 0.618714 | − | 0.785616i | \(-0.287654\pi\) | ||||
0.618714 | + | 0.785616i | \(0.287654\pi\) | |||||||
\(368\) | 12.0939 | 0.630438 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.78719 | 0.508126 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.93244 | −0.151836 | −0.0759181 | − | 0.997114i | \(-0.524189\pi\) | ||||
−0.0759181 | + | 0.997114i | \(0.524189\pi\) | |||||||
\(374\) | −8.35560 | −0.432058 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.8324 | 1.43535 | ||||||||
\(377\) | −11.6135 | −0.598126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7349 | −0.910980 | −0.455490 | − | 0.890241i | \(-0.650536\pi\) | ||||
−0.455490 | + | 0.890241i | \(0.650536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.1021 | 1.07968 | ||||||||
\(383\) | 4.40524 | 0.225097 | 0.112549 | − | 0.993646i | \(-0.464099\pi\) | ||||
0.112549 | + | 0.993646i | \(0.464099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.28102 | −0.472392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.76584 | −0.191182 | ||||||||
\(389\) | 31.3215 | 1.58806 | 0.794031 | − | 0.607877i | \(-0.207979\pi\) | ||||
0.794031 | + | 0.607877i | \(0.207979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.3133 | 0.926142 | ||||||||
\(392\) | −15.8522 | −0.800657 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.95596 | −0.501574 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4281 | −0.824501 | −0.412250 | − | 0.911071i | \(-0.635257\pi\) | ||||
−0.412250 | + | 0.911071i | \(0.635257\pi\) | |||||||
\(398\) | 19.0566 | 0.955220 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.1813 | 0.758120 | 0.379060 | − | 0.925372i | \(-0.376247\pi\) | ||||
0.379060 | + | 0.925372i | \(0.376247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.94646 | 0.196587 | ||||||||
\(404\) | −1.36856 | −0.0680883 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.50900 | −0.273407 | ||||||||
\(407\) | 9.09122 | 0.450635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.8421 | −0.733897 | −0.366948 | − | 0.930241i | \(-0.619597\pi\) | ||||
−0.366948 | + | 0.930241i | \(0.619597\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.33282 | −0.114930 | ||||||||
\(413\) | −16.3171 | −0.802912 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.25162 | 0.208453 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.8689 | −0.580526 | ||||||||
\(419\) | 35.2636 | 1.72274 | 0.861370 | − | 0.507978i | \(-0.169607\pi\) | ||||
0.861370 | + | 0.507978i | \(0.169607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2827 | −0.549887 | −0.274943 | − | 0.961460i | \(-0.588659\pi\) | ||||
−0.274943 | + | 0.961460i | \(0.588659\pi\) | |||||||
\(422\) | −9.22824 | −0.449224 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.6086 | 1.09797 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9904 | −0.628651 | ||||||||
\(428\) | −0.779115 | −0.0376599 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8249 | −1.24394 | −0.621971 | − | 0.783041i | \(-0.713668\pi\) | ||||
−0.621971 | + | 0.783041i | \(0.713668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.99902 | −0.480522 | −0.240261 | − | 0.970708i | \(-0.577233\pi\) | ||||
−0.240261 | + | 0.970708i | \(0.577233\pi\) | |||||||
\(434\) | 1.87205 | 0.0898610 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.46242 | 0.0700373 | ||||||||
\(437\) | 26.0135 | 1.24439 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.20385 | 0.439276 | 0.219638 | − | 0.975581i | \(-0.429512\pi\) | ||||
0.219638 | + | 0.975581i | \(0.429512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.8872 | −1.23133 | ||||||||
\(443\) | 9.12790 | 0.433680 | 0.216840 | − | 0.976207i | \(-0.430425\pi\) | ||||
0.216840 | + | 0.976207i | \(0.430425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.9305 | −0.849032 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.0729 | 0.523147 | ||||||||
\(449\) | −35.4831 | −1.67455 | −0.837275 | − | 0.546781i | \(-0.815853\pi\) | ||||
−0.837275 | + | 0.546781i | \(0.815853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.50264 | −0.164933 | ||||||||
\(452\) | −1.17042 | −0.0550520 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.13730 | −0.0533759 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7516 | 0.877162 | 0.438581 | − | 0.898692i | \(-0.355481\pi\) | ||||
0.438581 | + | 0.898692i | \(0.355481\pi\) | |||||||
\(458\) | 11.7708 | 0.550015 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0877 | 0.749280 | 0.374640 | − | 0.927170i | \(-0.377766\pi\) | ||||
0.374640 | + | 0.927170i | \(0.377766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1040 | −0.980787 | −0.490393 | − | 0.871501i | \(-0.663147\pi\) | ||||
−0.490393 | + | 0.871501i | \(0.663147\pi\) | |||||||
\(464\) | −11.3810 | −0.528348 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.3836 | 1.31484 | ||||||||
\(467\) | −18.0122 | −0.833504 | −0.416752 | − | 0.909020i | \(-0.636832\pi\) | ||||
−0.416752 | + | 0.909020i | \(0.636832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2480 | 0.519383 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −37.6928 | −1.73495 | ||||||||
\(473\) | 3.98875 | 0.183403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.43343 | 0.0657012 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.4791 | −1.02817 | ||||||||
\(479\) | −7.31414 | −0.334191 | −0.167096 | − | 0.985941i | \(-0.553439\pi\) | ||||
−0.167096 | + | 0.985941i | \(0.553439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.1663 | 1.28427 | ||||||||
\(482\) | −12.7384 | −0.580217 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.01572 | 0.0916235 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9433 | 0.541202 | 0.270601 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270601 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(488\) | −30.0081 | −1.35840 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.1658 | −0.503904 | −0.251952 | − | 0.967740i | \(-0.581072\pi\) | ||||
−0.251952 | + | 0.967740i | \(0.581072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.2337 | −0.776167 | ||||||||
\(494\) | −36.7720 | −1.65445 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.86743 | 0.173653 | ||||||||
\(497\) | 19.2794 | 0.864801 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.6045 | 1.37005 | 0.685023 | − | 0.728522i | \(-0.259792\pi\) | ||||
0.685023 | + | 0.728522i | \(0.259792\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.3286 | 0.773414 | ||||||||
\(503\) | 1.90950 | 0.0851404 | 0.0425702 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425702 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.33070 | −0.236979 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.917591 | 0.0407115 | ||||||||
\(509\) | −2.52518 | −0.111927 | −0.0559634 | − | 0.998433i | \(-0.517823\pi\) | ||||
−0.0559634 | + | 0.998433i | \(0.517823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.8333 | 0.744660 | ||||||||
\(512\) | 25.0863 | 1.10867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.3272 | −0.984811 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.9714 | −0.482520 | ||||||||
\(518\) | 13.3610 | 0.587048 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.65479 | −0.160119 | −0.0800595 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800595 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.3215 | −1.58823 | −0.794114 | − | 0.607768i | \(-0.792065\pi\) | ||||
−0.794114 | + | 0.607768i | \(0.792065\pi\) | |||||||
\(524\) | −1.04370 | −0.0455945 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6523 | −0.551665 | ||||||||
\(527\) | 5.85629 | 0.255104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3165 | −0.492022 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.03615 | 0.0882782 | ||||||||
\(533\) | −10.8518 | −0.470044 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.9830 | 1.12229 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.4743 | 1.83120 | ||||||||
\(539\) | 6.24883 | 0.269156 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3159 | −0.572496 | −0.286248 | − | 0.958156i | \(-0.592408\pi\) | ||||
−0.286248 | + | 0.958156i | \(0.592408\pi\) | |||||||
\(542\) | −25.5014 | −1.09538 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.30914 | 0.270502 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6657 | −1.26841 | −0.634207 | − | 0.773163i | \(-0.718673\pi\) | ||||
−0.634207 | + | 0.773163i | \(0.718673\pi\) | |||||||
\(548\) | 2.55166 | 0.109001 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4800 | −1.04288 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7372 | −0.626691 | ||||||||
\(554\) | 3.63913 | 0.154612 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.08839 | 0.0461578 | ||||||||
\(557\) | 42.4585 | 1.79902 | 0.899512 | − | 0.436897i | \(-0.143922\pi\) | ||||
0.899512 | + | 0.436897i | \(0.143922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3579 | 0.522683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5488 | −0.824615 | ||||||||
\(563\) | 41.0132 | 1.72850 | 0.864250 | − | 0.503063i | \(-0.167794\pi\) | ||||
0.864250 | + | 0.503063i | \(0.167794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.2078 | −1.01753 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 44.5358 | 1.86868 | ||||||||
\(569\) | 29.0619 | 1.21834 | 0.609169 | − | 0.793040i | \(-0.291503\pi\) | ||||
0.609169 | + | 0.793040i | \(0.291503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.230751 | −0.00965665 | −0.00482832 | − | 0.999988i | \(-0.501537\pi\) | ||||
−0.00482832 | + | 0.999988i | \(0.501537\pi\) | |||||||
\(572\) | −0.879602 | −0.0367780 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.14768 | −0.214860 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.4944 | −1.56091 | −0.780456 | − | 0.625211i | \(-0.785013\pi\) | ||||
−0.780456 | + | 0.625211i | \(0.785013\pi\) | |||||||
\(578\) | −15.6645 | −0.651557 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.7178 | 0.569110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.91215 | −0.369103 | ||||||||
\(584\) | 38.8851 | 1.60908 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.393329 | −0.0162483 | ||||||||
\(587\) | 15.3719 | 0.634464 | 0.317232 | − | 0.948348i | \(-0.397247\pi\) | ||||
0.317232 | + | 0.948348i | \(0.397247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.31868 | 0.342765 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27.6023 | 1.13445 | ||||||||
\(593\) | −8.30710 | −0.341132 | −0.170566 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170566 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.51998 | −0.185145 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.5155 | −0.675369 | ||||||||
\(599\) | 29.0293 | 1.18610 | 0.593052 | − | 0.805164i | \(-0.297923\pi\) | ||||
0.593052 | + | 0.805164i | \(0.297923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.2988 | −1.76620 | −0.883098 | − | 0.469188i | \(-0.844547\pi\) | ||||
−0.883098 | + | 0.469188i | \(0.844547\pi\) | |||||||
\(602\) | 5.86210 | 0.238921 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.48607 | −0.101157 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4484 | 0.586443 | 0.293222 | − | 0.956044i | \(-0.405273\pi\) | ||||
0.293222 | + | 0.956044i | \(0.405273\pi\) | |||||||
\(608\) | 8.96194 | 0.363455 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.9913 | −1.37514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.63973 | −0.348955 | −0.174478 | − | 0.984661i | \(-0.555824\pi\) | ||||
−0.174478 | + | 0.984661i | \(0.555824\pi\) | |||||||
\(614\) | 1.79877 | 0.0725926 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.40898 | −0.177643 | ||||||||
\(617\) | 32.9268 | 1.32559 | 0.662793 | − | 0.748803i | \(-0.269371\pi\) | ||||
0.662793 | + | 0.748803i | \(0.269371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.82425 | 0.394870 | 0.197435 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197435 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.7075 | 1.07087 | ||||||||
\(623\) | 5.77925 | 0.231541 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.9292 | −0.756561 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.53193 | 0.101035 | ||||||||
\(629\) | 41.7969 | 1.66655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.88051 | 0.114671 | 0.0573356 | − | 0.998355i | \(-0.481739\pi\) | ||||
0.0573356 | + | 0.998355i | \(0.481739\pi\) | |||||||
\(632\) | −34.0432 | −1.35417 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.5396 | 0.934878 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.3600 | 0.767072 | ||||||||
\(638\) | 5.01646 | 0.198603 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.6464 | 0.736490 | 0.368245 | − | 0.929729i | \(-0.379959\pi\) | ||||
0.368245 | + | 0.929729i | \(0.379959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.96215 | 0.0773795 | 0.0386897 | − | 0.999251i | \(-0.487682\pi\) | ||||
0.0386897 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(644\) | 0.914501 | 0.0360364 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −54.5673 | −2.14692 | ||||||||
\(647\) | 1.72726 | 0.0679055 | 0.0339528 | − | 0.999423i | \(-0.489190\pi\) | ||||
0.0339528 | + | 0.999423i | \(0.489190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8582 | 0.583237 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.72872 | −0.0677018 | ||||||||
\(653\) | −8.37928 | −0.327907 | −0.163953 | − | 0.986468i | \(-0.552425\pi\) | ||||
−0.163953 | + | 0.986468i | \(0.552425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.6345 | −0.415208 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.1241 | −0.628585 | ||||||||
\(659\) | −31.2624 | −1.21781 | −0.608905 | − | 0.793243i | \(-0.708391\pi\) | ||||
−0.608905 | + | 0.793243i | \(0.708391\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8798 | −0.423175 | −0.211588 | − | 0.977359i | \(-0.567863\pi\) | ||||
−0.211588 | + | 0.977359i | \(0.567863\pi\) | |||||||
\(662\) | −10.7152 | −0.416459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.6883 | 1.22974 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9948 | −0.425719 | ||||||||
\(668\) | 1.30987 | 0.0506806 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8290 | 0.456653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9803 | 1.11711 | 0.558554 | − | 0.829468i | \(-0.311356\pi\) | ||||
0.558554 | + | 0.829468i | \(0.311356\pi\) | |||||||
\(674\) | −14.5166 | −0.559160 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.00743080 | −0.000285800 0 | ||||||||
\(677\) | 5.89919 | 0.226724 | 0.113362 | − | 0.993554i | \(-0.463838\pi\) | ||||
0.113362 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.0532 | 0.884699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.70467 | −0.0652752 | ||||||||
\(683\) | −45.9083 | −1.75663 | −0.878316 | − | 0.478081i | \(-0.841332\pi\) | ||||
−0.878316 | + | 0.478081i | \(0.841332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21.1723 | 0.808364 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.1104 | 0.461706 | ||||||||
\(689\) | −27.6115 | −1.05191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.9475 | 0.796880 | 0.398440 | − | 0.917194i | \(-0.369552\pi\) | ||||
0.398440 | + | 0.917194i | \(0.369552\pi\) | |||||||
\(692\) | 1.39150 | 0.0528970 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.49122 | 0.0945653 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.1034 | −0.609960 | ||||||||
\(698\) | −32.7370 | −1.23911 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.2223 | −1.97241 | −0.986204 | − | 0.165533i | \(-0.947065\pi\) | ||||
−0.986204 | + | 0.165533i | \(0.947065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.3713 | 2.23923 | ||||||||
\(704\) | −10.0829 | −0.380015 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −50.0002 | −1.88178 | ||||||||
\(707\) | 8.37783 | 0.315081 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.9974 | −1.76503 | −0.882513 | − | 0.470288i | \(-0.844150\pi\) | ||||
−0.882513 | + | 0.470288i | \(0.844150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.3502 | 0.500318 | ||||||||
\(713\) | 3.73619 | 0.139921 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.53976 | 0.169659 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.9062 | −1.26537 | ||||||||
\(719\) | 4.69037 | 0.174921 | 0.0874607 | − | 0.996168i | \(-0.472125\pi\) | ||||
0.0874607 | + | 0.996168i | \(0.472125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2807 | 0.531841 | ||||||||
\(722\) | −52.0843 | −1.93838 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.70675 | −0.100596 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7594 | 1.02954 | 0.514769 | − | 0.857329i | \(-0.327878\pi\) | ||||
0.514769 | + | 0.857329i | \(0.327878\pi\) | |||||||
\(728\) | −13.6598 | −0.506267 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3383 | 0.678267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6040 | −1.13038 | −0.565192 | − | 0.824960i | \(-0.691198\pi\) | ||||
−0.565192 | + | 0.824960i | \(0.691198\pi\) | |||||||
\(734\) | −31.7244 | −1.17097 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.02510 | 0.148367 | ||||||||
\(737\) | −10.2423 | −0.377281 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.93383 | 0.181494 | 0.0907469 | − | 0.995874i | \(-0.471075\pi\) | ||||
0.0907469 | + | 0.995874i | \(0.471075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.0978 | −0.480836 | ||||||||
\(743\) | −21.7109 | −0.796496 | −0.398248 | − | 0.917278i | \(-0.630382\pi\) | ||||
−0.398248 | + | 0.917278i | \(0.630382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.92438 | 0.143682 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.30527 | −0.0477255 | ||||||||
\(749\) | 4.76947 | 0.174273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.6080 | −1.22637 | −0.613186 | − | 0.789939i | \(-0.710112\pi\) | ||||
−0.613186 | + | 0.789939i | \(0.710112\pi\) | |||||||
\(752\) | −33.3106 | −1.21471 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.5419 | 0.566003 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.88834 | −0.177670 | −0.0888349 | − | 0.996046i | \(-0.528314\pi\) | ||||
−0.0888349 | + | 0.996046i | \(0.528314\pi\) | |||||||
\(758\) | 23.7339 | 0.862054 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.2366 | 1.09608 | 0.548038 | − | 0.836453i | \(-0.315375\pi\) | ||||
0.548038 | + | 0.836453i | \(0.315375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.95243 | −0.324100 | ||||||||
\(764\) | 3.29647 | 0.119262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.89536 | −0.213008 | ||||||||
\(767\) | 46.0336 | 1.66218 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.0523 | 1.84099 | 0.920497 | − | 0.390751i | \(-0.127785\pi\) | ||||
0.920497 | + | 0.390751i | \(0.127785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.44984 | −0.0521808 | ||||||||
\(773\) | 6.54233 | 0.235311 | 0.117656 | − | 0.993054i | \(-0.462462\pi\) | ||||
0.117656 | + | 0.993054i | \(0.462462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 53.2532 | 1.91168 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.9163 | −1.50277 | ||||||||
\(779\) | −22.8744 | −0.819561 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5557 | −0.628193 | ||||||||
\(782\) | −24.5080 | −0.876403 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.9724 | 0.677585 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9765 | 0.391269 | 0.195635 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195635 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(788\) | −1.55527 | −0.0554044 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.16491 | 0.254755 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.6484 | 1.30142 | ||||||||
\(794\) | 21.9850 | 0.780220 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.97693 | 0.105514 | ||||||||
\(797\) | −12.6891 | −0.449473 | −0.224736 | − | 0.974420i | \(-0.572152\pi\) | ||||
−0.224736 | + | 0.974420i | \(0.572152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.4409 | −1.78447 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.3166 | −0.717404 | ||||||||
\(803\) | −15.3283 | −0.540923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.28139 | −0.186029 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.3529 | 0.680833 | ||||||||
\(809\) | 17.7818 | 0.625174 | 0.312587 | − | 0.949889i | \(-0.398805\pi\) | ||||
0.312587 | + | 0.949889i | \(0.398805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0811 | 1.30210 | 0.651048 | − | 0.759037i | \(-0.274330\pi\) | ||||
0.651048 | + | 0.759037i | \(0.274330\pi\) | |||||||
\(812\) | −0.860590 | −0.0302008 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.1664 | −0.426433 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0490 | 0.911340 | ||||||||
\(818\) | 19.8627 | 0.694482 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.337853 | 0.0117911 | 0.00589557 | − | 0.999983i | \(-0.498123\pi\) | ||||
0.00589557 | + | 0.999983i | \(0.498123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6629 | 0.929409 | 0.464704 | − | 0.885466i | \(-0.346161\pi\) | ||||
0.464704 | + | 0.885466i | \(0.346161\pi\) | |||||||
\(824\) | 32.9886 | 1.14921 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.8365 | 0.759791 | ||||||||
\(827\) | 43.4655 | 1.51144 | 0.755722 | − | 0.654893i | \(-0.227286\pi\) | ||||
0.755722 | + | 0.654893i | \(0.227286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9493 | 0.658137 | 0.329068 | − | 0.944306i | \(-0.393265\pi\) | ||||
0.329068 | + | 0.944306i | \(0.393265\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31.2388 | −1.08301 | ||||||||
\(833\) | 28.7290 | 0.995402 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.85410 | −0.0641255 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.1919 | −1.63022 | ||||||||
\(839\) | −22.7357 | −0.784922 | −0.392461 | − | 0.919769i | \(-0.628376\pi\) | ||||
−0.392461 | + | 0.919769i | \(0.628376\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6534 | −0.643221 | ||||||||
\(842\) | 15.0992 | 0.520355 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.44159 | −0.0496217 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3395 | −0.423991 | ||||||||
\(848\) | −27.0586 | −0.929196 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.6656 | 0.914085 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.9922 | −1.23235 | −0.616175 | − | 0.787610i | \(-0.711318\pi\) | ||||
−0.616175 | + | 0.787610i | \(0.711318\pi\) | |||||||
\(854\) | 17.3846 | 0.594888 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0175 | 0.376572 | ||||||||
\(857\) | 20.1724 | 0.689076 | 0.344538 | − | 0.938772i | \(-0.388036\pi\) | ||||
0.344538 | + | 0.938772i | \(0.388036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.0077 | 1.33093 | 0.665464 | − | 0.746430i | \(-0.268234\pi\) | ||||
0.665464 | + | 0.746430i | \(0.268234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.5605 | 1.17713 | ||||||||
\(863\) | −24.4962 | −0.833861 | −0.416930 | − | 0.908938i | \(-0.636894\pi\) | ||||
−0.416930 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.3813 | 0.454715 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.292442 | 0.00992613 | ||||||||
\(869\) | 13.4196 | 0.455230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.7326 | −1.07522 | ||||||||
\(872\) | −20.6803 | −0.700322 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.8128 | −1.17756 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.2278 | 0.986952 | 0.493476 | − | 0.869759i | \(-0.335726\pi\) | ||||
0.493476 | + | 0.869759i | \(0.335726\pi\) | |||||||
\(878\) | −12.3172 | −0.415684 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.72194 | 0.125395 | 0.0626977 | − | 0.998033i | \(-0.480030\pi\) | ||||
0.0626977 | + | 0.998033i | \(0.480030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.01518 | −0.236080 | −0.118040 | − | 0.993009i | \(-0.537661\pi\) | ||||
−0.118040 | + | 0.993009i | \(0.537661\pi\) | |||||||
\(884\) | −4.04398 | −0.136014 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.2155 | −0.410388 | ||||||||
\(887\) | −27.4537 | −0.921806 | −0.460903 | − | 0.887451i | \(-0.652474\pi\) | ||||
−0.460903 | + | 0.887451i | \(0.652474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.61717 | −0.188394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.80101 | −0.0937849 | ||||||||
\(893\) | −71.6498 | −2.39767 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.8044 | −0.394358 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.4857 | 1.58462 | ||||||||
\(899\) | −3.51594 | −0.117263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.9737 | −1.36503 | ||||||||
\(902\) | 4.68744 | 0.156075 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.5511 | 0.550480 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.09167 | −0.202271 | −0.101135 | − | 0.994873i | \(-0.532248\pi\) | ||||
−0.101135 | + | 0.994873i | \(0.532248\pi\) | |||||||
\(908\) | −0.177663 | −0.00589595 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.77586 | 0.0919682 | 0.0459841 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459841 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4913 | −0.413402 | ||||||||
\(914\) | −25.0945 | −0.830053 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.83878 | 0.0607551 | ||||||||
\(917\) | 6.38919 | 0.210990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.7566 | −0.783659 | −0.391829 | − | 0.920038i | \(-0.628158\pi\) | ||||
−0.391829 | + | 0.920038i | \(0.628158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.5296 | −0.709039 | ||||||||
\(923\) | −54.3909 | −1.79030 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.2427 | 0.928112 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.78782 | −0.124341 | ||||||||
\(929\) | −28.7158 | −0.942136 | −0.471068 | − | 0.882097i | \(-0.656131\pi\) | ||||
−0.471068 | + | 0.882097i | \(0.656131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.8088 | 1.33745 | ||||||||
\(932\) | 4.43395 | 0.145239 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.1050 | 0.788739 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1368 | −0.429161 | −0.214580 | − | 0.976706i | \(-0.568838\pi\) | ||||
−0.214580 | + | 0.976706i | \(0.568838\pi\) | |||||||
\(938\) | −15.0527 | −0.491489 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.4446 | 1.28586 | 0.642929 | − | 0.765926i | \(-0.277719\pi\) | ||||
0.642929 | + | 0.765926i | \(0.277719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2736 | −0.334556 | ||||||||
\(944\) | 45.1118 | 1.46826 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.33799 | −0.173553 | ||||||||
\(947\) | −25.1266 | −0.816504 | −0.408252 | − | 0.912869i | \(-0.633862\pi\) | ||||
−0.408252 | + | 0.912869i | \(0.633862\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.4898 | −1.54158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.2703 | −0.656964 | ||||||||
\(953\) | 6.14850 | 0.199169 | 0.0995847 | − | 0.995029i | \(-0.468249\pi\) | ||||
0.0995847 | + | 0.995029i | \(0.468249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.51158 | −0.113573 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.78823 | 0.316243 | ||||||||
\(959\) | −15.6204 | −0.504407 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8052 | −0.961459 | ||||||||
\(962\) | −37.6938 | −1.21530 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.98993 | −0.0640913 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.4461 | −1.59008 | −0.795040 | − | 0.606557i | \(-0.792550\pi\) | ||||
−0.795040 | + | 0.606557i | \(0.792550\pi\) | |||||||
\(968\) | −28.5045 | −0.916168 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.7332 | −1.66020 | −0.830099 | − | 0.557616i | \(-0.811716\pi\) | ||||
−0.830099 | + | 0.557616i | \(0.811716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.66272 | −0.213597 | ||||||||
\(974\) | −15.9832 | −0.512136 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.9146 | 1.14960 | ||||||||
\(977\) | 36.3167 | 1.16187 | 0.580937 | − | 0.813948i | \(-0.302686\pi\) | ||||
0.580937 | + | 0.813948i | \(0.302686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.26254 | −0.168192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.9427 | 0.476841 | ||||||||
\(983\) | −52.0481 | −1.66008 | −0.830039 | − | 0.557706i | \(-0.811682\pi\) | ||||
−0.830039 | + | 0.557706i | \(0.811682\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 23.0632 | 0.734482 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.74435 | −0.182752 | ||||||||
\(989\) | 11.6995 | 0.372021 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.4843 | −0.936599 | −0.468300 | − | 0.883570i | \(-0.655133\pi\) | ||||
−0.468300 | + | 0.883570i | \(0.655133\pi\) | |||||||
\(992\) | 1.28716 | 0.0408674 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.8009 | −0.818356 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4390 | 1.34406 | 0.672029 | − | 0.740525i | \(-0.265423\pi\) | ||||
0.672029 | + | 0.740525i | \(0.265423\pi\) | |||||||
\(998\) | −40.9568 | −1.29647 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.j.1.2 | 4 | ||
3.2 | odd | 2 | 1875.2.a.g.1.3 | yes | 4 | ||
5.4 | even | 2 | 5625.2.a.m.1.3 | 4 | |||
15.2 | even | 4 | 1875.2.b.d.1249.6 | 8 | |||
15.8 | even | 4 | 1875.2.b.d.1249.3 | 8 | |||
15.14 | odd | 2 | 1875.2.a.f.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.f.1.2 | ✓ | 4 | 15.14 | odd | 2 | ||
1875.2.a.g.1.3 | yes | 4 | 3.2 | odd | 2 | ||
1875.2.b.d.1249.3 | 8 | 15.8 | even | 4 | |||
1875.2.b.d.1249.6 | 8 | 15.2 | even | 4 | |||
5625.2.a.j.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5625.2.a.m.1.3 | 4 | 5.4 | even | 2 |