Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.70156 | 1.65539 | 0.827694 | − | 0.561179i | \(-0.189652\pi\) | ||||
0.827694 | + | 0.561179i | \(0.189652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.70156 | −1.17054 | ||||||||
\(11\) | −5.70156 | −1.71909 | −0.859543 | − | 0.511064i | \(-0.829252\pi\) | ||||
−0.859543 | + | 0.511064i | \(0.829252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.70156 | −0.897761 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.70156 | 1.30803 | 0.654014 | − | 0.756482i | \(-0.273084\pi\) | ||||
0.654014 | + | 0.756482i | \(0.273084\pi\) | |||||||
\(20\) | 3.70156 | 0.827694 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.70156 | 1.21558 | ||||||||
\(23\) | 1.70156 | 0.354800 | 0.177400 | − | 0.984139i | \(-0.443231\pi\) | ||||
0.177400 | + | 0.984139i | \(0.443231\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70156 | 1.74031 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.70156 | 0.687363 | 0.343681 | − | 0.939086i | \(-0.388326\pi\) | ||||
0.343681 | + | 0.939086i | \(0.388326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.70156 | 0.634813 | ||||||||
\(35\) | 3.70156 | 0.625678 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.29844 | 0.706659 | 0.353329 | − | 0.935499i | \(-0.385049\pi\) | ||||
0.353329 | + | 0.935499i | \(0.385049\pi\) | |||||||
\(38\) | −5.70156 | −0.924916 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.70156 | −0.585268 | ||||||||
\(41\) | 9.40312 | 1.46852 | 0.734261 | − | 0.678868i | \(-0.237529\pi\) | ||||
0.734261 | + | 0.678868i | \(0.237529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.10469 | 1.38845 | 0.694226 | − | 0.719757i | \(-0.255747\pi\) | ||||
0.694226 | + | 0.719757i | \(0.255747\pi\) | |||||||
\(44\) | −5.70156 | −0.859543 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.70156 | −0.250882 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.70156 | −1.23059 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.1047 | −2.84576 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.70156 | −0.486039 | ||||||||
\(59\) | −10.8062 | −1.40685 | −0.703427 | − | 0.710768i | \(-0.748348\pi\) | ||||
−0.703427 | + | 0.710768i | \(0.748348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.70156 | 0.986084 | 0.493042 | − | 0.870006i | \(-0.335885\pi\) | ||||
0.493042 | + | 0.870006i | \(0.335885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.70156 | 0.459122 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.40312 | −0.904436 | −0.452218 | − | 0.891908i | \(-0.649367\pi\) | ||||
−0.452218 | + | 0.891908i | \(0.649367\pi\) | |||||||
\(68\) | −3.70156 | −0.448880 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.70156 | −0.442421 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.70156 | −0.901400 | −0.450700 | − | 0.892676i | \(-0.648826\pi\) | ||||
−0.450700 | + | 0.892676i | \(0.648826\pi\) | |||||||
\(74\) | −4.29844 | −0.499683 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.70156 | 0.654014 | ||||||||
\(77\) | −5.70156 | −0.649753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.40312 | −0.382881 | −0.191441 | − | 0.981504i | \(-0.561316\pi\) | ||||
−0.191441 | + | 0.981504i | \(0.561316\pi\) | |||||||
\(80\) | 3.70156 | 0.413847 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.40312 | −1.03840 | ||||||||
\(83\) | 0.596876 | 0.0655156 | 0.0327578 | − | 0.999463i | \(-0.489571\pi\) | ||||
0.0327578 | + | 0.999463i | \(0.489571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.7016 | −1.48614 | ||||||||
\(86\) | −9.10469 | −0.981784 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.70156 | 0.607789 | ||||||||
\(89\) | −16.8062 | −1.78146 | −0.890729 | − | 0.454534i | \(-0.849806\pi\) | ||||
−0.890729 | + | 0.454534i | \(0.849806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 1.70156 | 0.177400 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 21.1047 | 2.16530 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8062 | 1.70642 | 0.853208 | − | 0.521571i | \(-0.174654\pi\) | ||||
0.853208 | + | 0.521571i | \(0.174654\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.70156 | 0.870156 | ||||||||
\(101\) | −9.40312 | −0.935646 | −0.467823 | − | 0.883822i | \(-0.654961\pi\) | ||||
−0.467823 | + | 0.883822i | \(0.654961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.70156 | −0.955923 | −0.477962 | − | 0.878381i | \(-0.658624\pi\) | ||||
−0.477962 | + | 0.878381i | \(0.658624\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −7.40312 | −0.715687 | −0.357844 | − | 0.933782i | \(-0.616488\pi\) | ||||
−0.357844 | + | 0.933782i | \(0.616488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7016 | 1.50394 | 0.751968 | − | 0.659199i | \(-0.229105\pi\) | ||||
0.751968 | + | 0.659199i | \(0.229105\pi\) | |||||||
\(110\) | 21.1047 | 2.01225 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 20.8062 | 1.95729 | 0.978644 | − | 0.205564i | \(-0.0659030\pi\) | ||||
0.978644 | + | 0.205564i | \(0.0659030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.29844 | 0.587332 | ||||||||
\(116\) | 3.70156 | 0.343681 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8062 | 0.994796 | ||||||||
\(119\) | −3.70156 | −0.339322 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.5078 | 1.95526 | ||||||||
\(122\) | −7.70156 | −0.697267 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.7016 | 1.22550 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4031 | −1.72175 | −0.860874 | − | 0.508817i | \(-0.830083\pi\) | ||||
−0.860874 | + | 0.508817i | \(0.830083\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.70156 | −0.324648 | ||||||||
\(131\) | 13.7016 | 1.19711 | 0.598556 | − | 0.801081i | \(-0.295742\pi\) | ||||
0.598556 | + | 0.801081i | \(0.295742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.70156 | 0.494388 | ||||||||
\(134\) | 7.40312 | 0.639533 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.70156 | 0.317406 | ||||||||
\(137\) | 12.2984 | 1.05073 | 0.525363 | − | 0.850878i | \(-0.323929\pi\) | ||||
0.525363 | + | 0.850878i | \(0.323929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.8062 | −1.59513 | −0.797563 | − | 0.603236i | \(-0.793878\pi\) | ||||
−0.797563 | + | 0.603236i | \(0.793878\pi\) | |||||||
\(140\) | 3.70156 | 0.312839 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | −5.70156 | −0.476789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.7016 | 1.13785 | ||||||||
\(146\) | 7.70156 | 0.637386 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.29844 | 0.353329 | ||||||||
\(149\) | −2.59688 | −0.212744 | −0.106372 | − | 0.994326i | \(-0.533923\pi\) | ||||
−0.106372 | + | 0.994326i | \(0.533923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.70156 | 0.138471 | 0.0692356 | − | 0.997600i | \(-0.477944\pi\) | ||||
0.0692356 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(152\) | −5.70156 | −0.462458 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.70156 | 0.459445 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.895314 | 0.0714538 | 0.0357269 | − | 0.999362i | \(-0.488625\pi\) | ||||
0.0357269 | + | 0.999362i | \(0.488625\pi\) | |||||||
\(158\) | 3.40312 | 0.270738 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.70156 | −0.292634 | ||||||||
\(161\) | 1.70156 | 0.134102 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.40312 | −0.579857 | −0.289929 | − | 0.957048i | \(-0.593632\pi\) | ||||
−0.289929 | + | 0.957048i | \(0.593632\pi\) | |||||||
\(164\) | 9.40312 | 0.734261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.596876 | −0.0463265 | ||||||||
\(167\) | −9.70156 | −0.750729 | −0.375365 | − | 0.926877i | \(-0.622483\pi\) | ||||
−0.375365 | + | 0.926877i | \(0.622483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 13.7016 | 1.05086 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.10469 | 0.694226 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.70156 | 0.657776 | ||||||||
\(176\) | −5.70156 | −0.429771 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.8062 | 1.25968 | ||||||||
\(179\) | 10.8062 | 0.807697 | 0.403848 | − | 0.914826i | \(-0.367672\pi\) | ||||
0.403848 | + | 0.914826i | \(0.367672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.8062 | −1.24920 | −0.624599 | − | 0.780945i | \(-0.714738\pi\) | ||||
−0.624599 | + | 0.780945i | \(0.714738\pi\) | |||||||
\(182\) | −1.00000 | −0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.70156 | −0.125441 | ||||||||
\(185\) | 15.9109 | 1.16980 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.1047 | 1.54333 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.1047 | −1.53109 | ||||||||
\(191\) | −6.29844 | −0.455739 | −0.227869 | − | 0.973692i | \(-0.573176\pi\) | ||||
−0.227869 | + | 0.973692i | \(0.573176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.40312 | −0.100999 | −0.0504995 | − | 0.998724i | \(-0.516081\pi\) | ||||
−0.0504995 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(194\) | −16.8062 | −1.20662 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −9.40312 | −0.669945 | −0.334972 | − | 0.942228i | \(-0.608727\pi\) | ||||
−0.334972 | + | 0.942228i | \(0.608727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.89531 | 0.205243 | 0.102622 | − | 0.994720i | \(-0.467277\pi\) | ||||
0.102622 | + | 0.994720i | \(0.467277\pi\) | |||||||
\(200\) | −8.70156 | −0.615293 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.40312 | 0.661602 | ||||||||
\(203\) | 3.70156 | 0.259799 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.8062 | 2.43097 | ||||||||
\(206\) | 9.70156 | 0.675940 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −32.5078 | −2.24861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2984 | −1.25972 | −0.629858 | − | 0.776710i | \(-0.716887\pi\) | ||||
−0.629858 | + | 0.776710i | \(0.716887\pi\) | |||||||
\(212\) | 2.00000 | 0.137361 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.40312 | 0.506067 | ||||||||
\(215\) | 33.7016 | 2.29843 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.7016 | −1.06344 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.1047 | −1.42288 | ||||||||
\(221\) | −3.70156 | −0.248994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.40312 | −0.227890 | −0.113945 | − | 0.993487i | \(-0.536349\pi\) | ||||
−0.113945 | + | 0.993487i | \(0.536349\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.8062 | −1.38401 | ||||||||
\(227\) | −8.59688 | −0.570595 | −0.285297 | − | 0.958439i | \(-0.592092\pi\) | ||||
−0.285297 | + | 0.958439i | \(0.592092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | −6.29844 | −0.415307 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.70156 | −0.243019 | ||||||||
\(233\) | −20.2094 | −1.32396 | −0.661980 | − | 0.749521i | \(-0.730284\pi\) | ||||
−0.661980 | + | 0.749521i | \(0.730284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.6125 | 1.93171 | ||||||||
\(236\) | −10.8062 | −0.703427 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.70156 | 0.239937 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.806248 | 0.0519350 | 0.0259675 | − | 0.999663i | \(-0.491733\pi\) | ||||
0.0259675 | + | 0.999663i | \(0.491733\pi\) | |||||||
\(242\) | −21.5078 | −1.38257 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.70156 | 0.493042 | ||||||||
\(245\) | 3.70156 | 0.236484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.70156 | 0.362782 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.7016 | −0.866563 | ||||||||
\(251\) | 28.5078 | 1.79940 | 0.899699 | − | 0.436512i | \(-0.143786\pi\) | ||||
0.899699 | + | 0.436512i | \(0.143786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.70156 | −0.609932 | ||||||||
\(254\) | 19.4031 | 1.21746 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.29844 | 0.267092 | ||||||||
\(260\) | 3.70156 | 0.229561 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.7016 | −0.846485 | ||||||||
\(263\) | 1.19375 | 0.0736099 | 0.0368049 | − | 0.999322i | \(-0.488282\pi\) | ||||
0.0368049 | + | 0.999322i | \(0.488282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.40312 | 0.454770 | ||||||||
\(266\) | −5.70156 | −0.349585 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.40312 | −0.452218 | ||||||||
\(269\) | −20.8062 | −1.26858 | −0.634290 | − | 0.773095i | \(-0.718707\pi\) | ||||
−0.634290 | + | 0.773095i | \(0.718707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.2094 | −1.59211 | −0.796053 | − | 0.605227i | \(-0.793082\pi\) | ||||
−0.796053 | + | 0.605227i | \(0.793082\pi\) | |||||||
\(272\) | −3.70156 | −0.224440 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.2984 | −0.742976 | ||||||||
\(275\) | −49.6125 | −2.99175 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.6125 | −1.41874 | −0.709369 | − | 0.704838i | \(-0.751020\pi\) | ||||
−0.709369 | + | 0.704838i | \(0.751020\pi\) | |||||||
\(278\) | 18.8062 | 1.12792 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.70156 | −0.221211 | ||||||||
\(281\) | 12.8062 | 0.763957 | 0.381978 | − | 0.924171i | \(-0.375243\pi\) | ||||
0.381978 | + | 0.924171i | \(0.375243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.70156 | 0.337140 | ||||||||
\(287\) | 9.40312 | 0.555049 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.29844 | −0.194026 | ||||||||
\(290\) | −13.7016 | −0.804583 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.70156 | −0.450700 | ||||||||
\(293\) | −12.8062 | −0.748149 | −0.374075 | − | 0.927399i | \(-0.622040\pi\) | ||||
−0.374075 | + | 0.927399i | \(0.622040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −40.0000 | −2.32889 | ||||||||
\(296\) | −4.29844 | −0.249842 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.59688 | 0.150433 | ||||||||
\(299\) | 1.70156 | 0.0984039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.10469 | 0.524785 | ||||||||
\(302\) | −1.70156 | −0.0979139 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.70156 | 0.327007 | ||||||||
\(305\) | 28.5078 | 1.63235 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.8062 | 1.07333 | 0.536665 | − | 0.843796i | \(-0.319684\pi\) | ||||
0.536665 | + | 0.843796i | \(0.319684\pi\) | |||||||
\(308\) | −5.70156 | −0.324877 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.4031 | −1.55389 | −0.776944 | − | 0.629569i | \(-0.783231\pi\) | ||||
−0.776944 | + | 0.629569i | \(0.783231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2094 | −0.916208 | −0.458104 | − | 0.888899i | \(-0.651471\pi\) | ||||
−0.458104 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(314\) | −0.895314 | −0.0505255 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.40312 | −0.191441 | ||||||||
\(317\) | 5.40312 | 0.303470 | 0.151735 | − | 0.988421i | \(-0.451514\pi\) | ||||
0.151735 | + | 0.988421i | \(0.451514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.1047 | −1.18164 | ||||||||
\(320\) | 3.70156 | 0.206924 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.70156 | −0.0948243 | ||||||||
\(323\) | −21.1047 | −1.17430 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.70156 | 0.482676 | ||||||||
\(326\) | 7.40312 | 0.410021 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.40312 | −0.519201 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.20937 | −0.341298 | −0.170649 | − | 0.985332i | \(-0.554586\pi\) | ||||
−0.170649 | + | 0.985332i | \(0.554586\pi\) | |||||||
\(332\) | 0.596876 | 0.0327578 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.70156 | 0.530846 | ||||||||
\(335\) | −27.4031 | −1.49719 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.50781 | 0.136609 | 0.0683046 | − | 0.997665i | \(-0.478241\pi\) | ||||
0.0683046 | + | 0.997665i | \(0.478241\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.7016 | −0.743072 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −9.10469 | −0.490892 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −4.00000 | −0.214731 | −0.107366 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.0000 | 1.60586 | 0.802932 | − | 0.596071i | \(-0.203272\pi\) | ||||
0.802932 | + | 0.596071i | \(0.203272\pi\) | |||||||
\(350\) | −8.70156 | −0.465118 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.70156 | 0.303894 | ||||||||
\(353\) | 4.80625 | 0.255811 | 0.127905 | − | 0.991786i | \(-0.459175\pi\) | ||||
0.127905 | + | 0.991786i | \(0.459175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.6125 | 1.57167 | ||||||||
\(356\) | −16.8062 | −0.890729 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8062 | −0.571128 | ||||||||
\(359\) | −1.19375 | −0.0630038 | −0.0315019 | − | 0.999504i | \(-0.510029\pi\) | ||||
−0.0315019 | + | 0.999504i | \(0.510029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5078 | 0.710937 | ||||||||
\(362\) | 16.8062 | 0.883317 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | −28.5078 | −1.49217 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6125 | 1.12816 | 0.564082 | − | 0.825719i | \(-0.309230\pi\) | ||||
0.564082 | + | 0.825719i | \(0.309230\pi\) | |||||||
\(368\) | 1.70156 | 0.0887001 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.9109 | −0.827170 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.59688 | −0.341573 | −0.170787 | − | 0.985308i | \(-0.554631\pi\) | ||||
−0.170787 | + | 0.985308i | \(0.554631\pi\) | |||||||
\(374\) | −21.1047 | −1.09130 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 3.70156 | 0.190640 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6125 | 1.72656 | 0.863279 | − | 0.504727i | \(-0.168407\pi\) | ||||
0.863279 | + | 0.504727i | \(0.168407\pi\) | |||||||
\(380\) | 21.1047 | 1.08265 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.29844 | 0.322256 | ||||||||
\(383\) | 27.9109 | 1.42618 | 0.713091 | − | 0.701071i | \(-0.247295\pi\) | ||||
0.713091 | + | 0.701071i | \(0.247295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.1047 | −1.07559 | ||||||||
\(386\) | 1.40312 | 0.0714171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.8062 | 0.853208 | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.29844 | −0.318526 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.40312 | 0.473723 | ||||||||
\(395\) | −12.5969 | −0.633818 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.8062 | −1.24499 | −0.622495 | − | 0.782624i | \(-0.713881\pi\) | ||||
−0.622495 | + | 0.782624i | \(0.713881\pi\) | |||||||
\(398\) | −2.89531 | −0.145129 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.70156 | 0.435078 | ||||||||
\(401\) | 20.8062 | 1.03901 | 0.519507 | − | 0.854466i | \(-0.326116\pi\) | ||||
0.519507 | + | 0.854466i | \(0.326116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9.40312 | −0.467823 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.70156 | −0.183705 | ||||||||
\(407\) | −24.5078 | −1.21481 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.7016 | 0.578605 | 0.289303 | − | 0.957238i | \(-0.406577\pi\) | ||||
0.289303 | + | 0.957238i | \(0.406577\pi\) | |||||||
\(410\) | −34.8062 | −1.71896 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.70156 | −0.477962 | ||||||||
\(413\) | −10.8062 | −0.531741 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.20937 | 0.108454 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 32.5078 | 1.59001 | ||||||||
\(419\) | −14.8953 | −0.727684 | −0.363842 | − | 0.931461i | \(-0.618535\pi\) | ||||
−0.363842 | + | 0.931461i | \(0.618535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6125 | −1.54070 | −0.770349 | − | 0.637622i | \(-0.779918\pi\) | ||||
−0.770349 | + | 0.637622i | \(0.779918\pi\) | |||||||
\(422\) | 18.2984 | 0.890754 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | −32.2094 | −1.56238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.70156 | 0.372705 | ||||||||
\(428\) | −7.40312 | −0.357844 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −33.7016 | −1.62523 | ||||||||
\(431\) | −26.2094 | −1.26246 | −0.631231 | − | 0.775595i | \(-0.717450\pi\) | ||||
−0.631231 | + | 0.775595i | \(0.717450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.2094 | −1.16343 | −0.581714 | − | 0.813393i | \(-0.697618\pi\) | ||||
−0.581714 | + | 0.813393i | \(0.697618\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.7016 | 0.751968 | ||||||||
\(437\) | 9.70156 | 0.464089 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.5078 | −1.55151 | −0.775757 | − | 0.631032i | \(-0.782632\pi\) | ||||
−0.775757 | + | 0.631032i | \(0.782632\pi\) | |||||||
\(440\) | 21.1047 | 1.00613 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.70156 | 0.176065 | ||||||||
\(443\) | 38.2094 | 1.81538 | 0.907691 | − | 0.419639i | \(-0.137843\pi\) | ||||
0.907691 | + | 0.419639i | \(0.137843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −62.2094 | −2.94901 | ||||||||
\(446\) | 3.40312 | 0.161143 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 27.1047 | 1.27915 | 0.639575 | − | 0.768729i | \(-0.279111\pi\) | ||||
0.639575 | + | 0.768729i | \(0.279111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.6125 | −2.52451 | ||||||||
\(452\) | 20.8062 | 0.978644 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.59688 | 0.403471 | ||||||||
\(455\) | 3.70156 | 0.173532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4031 | 0.626972 | 0.313486 | − | 0.949593i | \(-0.398503\pi\) | ||||
0.313486 | + | 0.949593i | \(0.398503\pi\) | |||||||
\(458\) | −6.00000 | −0.280362 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.29844 | 0.293666 | ||||||||
\(461\) | −37.3141 | −1.73789 | −0.868944 | − | 0.494910i | \(-0.835201\pi\) | ||||
−0.868944 | + | 0.494910i | \(0.835201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3141 | 1.08350 | 0.541748 | − | 0.840541i | \(-0.317763\pi\) | ||||
0.541748 | + | 0.840541i | \(0.317763\pi\) | |||||||
\(464\) | 3.70156 | 0.171841 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.2094 | 0.936181 | ||||||||
\(467\) | 36.5078 | 1.68938 | 0.844690 | − | 0.535256i | \(-0.179785\pi\) | ||||
0.844690 | + | 0.535256i | \(0.179785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.40312 | −0.341845 | ||||||||
\(470\) | −29.6125 | −1.36592 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.8062 | 0.497398 | ||||||||
\(473\) | −51.9109 | −2.38687 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 49.6125 | 2.27638 | ||||||||
\(476\) | −3.70156 | −0.169661 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | 24.5078 | 1.11979 | 0.559895 | − | 0.828563i | \(-0.310841\pi\) | ||||
0.559895 | + | 0.828563i | \(0.310841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.29844 | 0.195992 | ||||||||
\(482\) | −0.806248 | −0.0367236 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5078 | 0.977628 | ||||||||
\(485\) | 62.2094 | 2.82478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | −7.70156 | −0.348633 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.70156 | −0.167220 | ||||||||
\(491\) | −39.4031 | −1.77824 | −0.889119 | − | 0.457676i | \(-0.848682\pi\) | ||||
−0.889119 | + | 0.457676i | \(0.848682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.7016 | −0.617087 | ||||||||
\(494\) | −5.70156 | −0.256525 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8062 | −1.20001 | −0.600006 | − | 0.799995i | \(-0.704835\pi\) | ||||
−0.600006 | + | 0.799995i | \(0.704835\pi\) | |||||||
\(500\) | 13.7016 | 0.612752 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.5078 | −1.27237 | ||||||||
\(503\) | 20.5969 | 0.918369 | 0.459185 | − | 0.888341i | \(-0.348142\pi\) | ||||
0.459185 | + | 0.888341i | \(0.348142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.8062 | −1.54886 | ||||||||
\(506\) | 9.70156 | 0.431287 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.4031 | −0.860874 | ||||||||
\(509\) | 5.91093 | 0.261998 | 0.130999 | − | 0.991383i | \(-0.458182\pi\) | ||||
0.130999 | + | 0.991383i | \(0.458182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.70156 | −0.340697 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | −35.9109 | −1.58242 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.6125 | −2.00604 | ||||||||
\(518\) | −4.29844 | −0.188863 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.70156 | −0.162324 | ||||||||
\(521\) | 7.70156 | 0.337412 | 0.168706 | − | 0.985666i | \(-0.446041\pi\) | ||||
0.168706 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6125 | 0.770141 | 0.385070 | − | 0.922887i | \(-0.374177\pi\) | ||||
0.385070 | + | 0.922887i | \(0.374177\pi\) | |||||||
\(524\) | 13.7016 | 0.598556 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.19375 | −0.0520500 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1047 | −0.874117 | ||||||||
\(530\) | −7.40312 | −0.321571 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.70156 | 0.247194 | ||||||||
\(533\) | 9.40312 | 0.407295 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.4031 | −1.18474 | ||||||||
\(536\) | 7.40312 | 0.319766 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.8062 | 0.897021 | ||||||||
\(539\) | −5.70156 | −0.245584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.298438 | −0.0128308 | −0.00641542 | − | 0.999979i | \(-0.502042\pi\) | ||||
−0.00641542 | + | 0.999979i | \(0.502042\pi\) | |||||||
\(542\) | 26.2094 | 1.12579 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.70156 | 0.158703 | ||||||||
\(545\) | 58.1203 | 2.48960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.6125 | −1.77922 | −0.889611 | − | 0.456719i | \(-0.849024\pi\) | ||||
−0.889611 | + | 0.456719i | \(0.849024\pi\) | |||||||
\(548\) | 12.2984 | 0.525363 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 49.6125 | 2.11548 | ||||||||
\(551\) | 21.1047 | 0.899090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.40312 | −0.144716 | ||||||||
\(554\) | 23.6125 | 1.00320 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8062 | −0.797563 | ||||||||
\(557\) | 37.4031 | 1.58482 | 0.792411 | − | 0.609988i | \(-0.208826\pi\) | ||||
0.792411 | + | 0.609988i | \(0.208826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.10469 | 0.385087 | ||||||||
\(560\) | 3.70156 | 0.156420 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.8062 | −0.540199 | ||||||||
\(563\) | −2.29844 | −0.0968676 | −0.0484338 | − | 0.998826i | \(-0.515423\pi\) | ||||
−0.0484338 | + | 0.998826i | \(0.515423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 77.0156 | 3.24007 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | −26.0000 | −1.08998 | −0.544988 | − | 0.838444i | \(-0.683466\pi\) | ||||
−0.544988 | + | 0.838444i | \(0.683466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8062 | −1.12181 | −0.560903 | − | 0.827881i | \(-0.689546\pi\) | ||||
−0.560903 | + | 0.827881i | \(0.689546\pi\) | |||||||
\(572\) | −5.70156 | −0.238394 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.40312 | −0.392479 | ||||||||
\(575\) | 14.8062 | 0.617463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.8062 | 0.699653 | 0.349827 | − | 0.936814i | \(-0.386240\pi\) | ||||
0.349827 | + | 0.936814i | \(0.386240\pi\) | |||||||
\(578\) | 3.29844 | 0.137197 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.7016 | 0.568926 | ||||||||
\(581\) | 0.596876 | 0.0247626 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.4031 | −0.472269 | ||||||||
\(584\) | 7.70156 | 0.318693 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.8062 | 0.529021 | ||||||||
\(587\) | 29.0156 | 1.19760 | 0.598801 | − | 0.800898i | \(-0.295644\pi\) | ||||
0.598801 | + | 0.800898i | \(0.295644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 40.0000 | 1.64677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.29844 | 0.176665 | ||||||||
\(593\) | −8.80625 | −0.361629 | −0.180815 | − | 0.983517i | \(-0.557873\pi\) | ||||
−0.180815 | + | 0.983517i | \(0.557873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.7016 | −0.561709 | ||||||||
\(596\) | −2.59688 | −0.106372 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.70156 | −0.0695820 | ||||||||
\(599\) | −17.7016 | −0.723266 | −0.361633 | − | 0.932320i | \(-0.617781\pi\) | ||||
−0.361633 | + | 0.932320i | \(0.617781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.59688 | −0.105929 | −0.0529644 | − | 0.998596i | \(-0.516867\pi\) | ||||
−0.0529644 | + | 0.998596i | \(0.516867\pi\) | |||||||
\(602\) | −9.10469 | −0.371079 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.70156 | 0.0692356 | ||||||||
\(605\) | 79.6125 | 3.23671 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5078 | −0.994741 | −0.497371 | − | 0.867538i | \(-0.665701\pi\) | ||||
−0.497371 | + | 0.867538i | \(0.665701\pi\) | |||||||
\(608\) | −5.70156 | −0.231229 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.5078 | −1.15425 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.91093 | −0.238740 | −0.119370 | − | 0.992850i | \(-0.538088\pi\) | ||||
−0.119370 | + | 0.992850i | \(0.538088\pi\) | |||||||
\(614\) | −18.8062 | −0.758958 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.70156 | 0.229722 | ||||||||
\(617\) | −13.9109 | −0.560033 | −0.280017 | − | 0.959995i | \(-0.590340\pi\) | ||||
−0.280017 | + | 0.959995i | \(0.590340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.7016 | 0.550712 | 0.275356 | − | 0.961342i | \(-0.411204\pi\) | ||||
0.275356 | + | 0.961342i | \(0.411204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.4031 | 1.09877 | ||||||||
\(623\) | −16.8062 | −0.673328 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.20937 | 0.288375 | ||||||||
\(626\) | 16.2094 | 0.647857 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.895314 | 0.0357269 | ||||||||
\(629\) | −15.9109 | −0.634411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5078 | 0.975641 | 0.487820 | − | 0.872944i | \(-0.337792\pi\) | ||||
0.487820 | + | 0.872944i | \(0.337792\pi\) | |||||||
\(632\) | 3.40312 | 0.135369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.40312 | −0.214585 | ||||||||
\(635\) | −71.8219 | −2.85016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 21.1047 | 0.835543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.70156 | −0.146317 | ||||||||
\(641\) | 23.1938 | 0.916098 | 0.458049 | − | 0.888927i | \(-0.348548\pi\) | ||||
0.458049 | + | 0.888927i | \(0.348548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3141 | −0.446183 | −0.223091 | − | 0.974798i | \(-0.571615\pi\) | ||||
−0.223091 | + | 0.974798i | \(0.571615\pi\) | |||||||
\(644\) | 1.70156 | 0.0670509 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.1047 | 0.830353 | ||||||||
\(647\) | 8.00000 | 0.314512 | 0.157256 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157256 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.6125 | 2.41850 | ||||||||
\(650\) | −8.70156 | −0.341303 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.40312 | −0.289929 | ||||||||
\(653\) | −22.5078 | −0.880799 | −0.440399 | − | 0.897802i | \(-0.645163\pi\) | ||||
−0.440399 | + | 0.897802i | \(0.645163\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.7172 | 1.98168 | ||||||||
\(656\) | 9.40312 | 0.367130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.00000 | −0.311872 | ||||||||
\(659\) | −29.0156 | −1.13029 | −0.565144 | − | 0.824992i | \(-0.691179\pi\) | ||||
−0.565144 | + | 0.824992i | \(0.691179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4187 | 1.02757 | 0.513785 | − | 0.857919i | \(-0.328243\pi\) | ||||
0.513785 | + | 0.857919i | \(0.328243\pi\) | |||||||
\(662\) | 6.20937 | 0.241334 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.596876 | −0.0231633 | ||||||||
\(665\) | 21.1047 | 0.818405 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.29844 | 0.243876 | ||||||||
\(668\) | −9.70156 | −0.375365 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.4031 | 1.05868 | ||||||||
\(671\) | −43.9109 | −1.69516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.91093 | −0.0736611 | −0.0368306 | − | 0.999322i | \(-0.511726\pi\) | ||||
−0.0368306 | + | 0.999322i | \(0.511726\pi\) | |||||||
\(674\) | −2.50781 | −0.0965973 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8062 | 0.644965 | ||||||||
\(680\) | 13.7016 | 0.525431 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.5078 | 0.784710 | 0.392355 | − | 0.919814i | \(-0.371661\pi\) | ||||
0.392355 | + | 0.919814i | \(0.371661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.5234 | 1.73936 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.10469 | 0.347113 | ||||||||
\(689\) | 2.00000 | 0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.61250 | −0.0613423 | −0.0306711 | − | 0.999530i | \(-0.509764\pi\) | ||||
−0.0306711 | + | 0.999530i | \(0.509764\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | −69.6125 | −2.64055 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.8062 | −1.31838 | ||||||||
\(698\) | −30.0000 | −1.13552 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.70156 | 0.328888 | ||||||||
\(701\) | −28.8062 | −1.08800 | −0.543998 | − | 0.839086i | \(-0.683090\pi\) | ||||
−0.543998 | + | 0.839086i | \(0.683090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.5078 | 0.924330 | ||||||||
\(704\) | −5.70156 | −0.214886 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.80625 | −0.180886 | ||||||||
\(707\) | −9.40312 | −0.353641 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.387503 | 0.0145530 | 0.00727649 | − | 0.999974i | \(-0.497684\pi\) | ||||
0.00727649 | + | 0.999974i | \(0.497684\pi\) | |||||||
\(710\) | −29.6125 | −1.11134 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.8062 | 0.629841 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.1047 | −0.789271 | ||||||||
\(716\) | 10.8062 | 0.403848 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.19375 | 0.0445504 | ||||||||
\(719\) | −33.0156 | −1.23127 | −0.615637 | − | 0.788030i | \(-0.711101\pi\) | ||||
−0.615637 | + | 0.788030i | \(0.711101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70156 | −0.361305 | ||||||||
\(722\) | −13.5078 | −0.502709 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.8062 | −0.624599 | ||||||||
\(725\) | 32.2094 | 1.19623 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.89531 | −0.107381 | −0.0536906 | − | 0.998558i | \(-0.517098\pi\) | ||||
−0.0536906 | + | 0.998558i | \(0.517098\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 28.5078 | 1.05512 | ||||||||
\(731\) | −33.7016 | −1.24650 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.4031 | 1.23377 | 0.616886 | − | 0.787052i | \(-0.288394\pi\) | ||||
0.616886 | + | 0.787052i | \(0.288394\pi\) | |||||||
\(734\) | −21.6125 | −0.797732 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.70156 | −0.0627204 | ||||||||
\(737\) | 42.2094 | 1.55480 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.79063 | 0.0658693 | 0.0329346 | − | 0.999458i | \(-0.489515\pi\) | ||||
0.0329346 | + | 0.999458i | \(0.489515\pi\) | |||||||
\(740\) | 15.9109 | 0.584898 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00000 | −0.0734223 | ||||||||
\(743\) | 41.0156 | 1.50472 | 0.752359 | − | 0.658754i | \(-0.228916\pi\) | ||||
0.752359 | + | 0.658754i | \(0.228916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.61250 | −0.352175 | ||||||||
\(746\) | 6.59688 | 0.241529 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.1047 | 0.771664 | ||||||||
\(749\) | −7.40312 | −0.270504 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.19375 | 0.335485 | 0.167742 | − | 0.985831i | \(-0.446352\pi\) | ||||
0.167742 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.70156 | −0.134803 | ||||||||
\(755\) | 6.29844 | 0.229224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.4187 | −1.68712 | −0.843559 | − | 0.537037i | \(-0.819544\pi\) | ||||
−0.843559 | + | 0.537037i | \(0.819544\pi\) | |||||||
\(758\) | −33.6125 | −1.22086 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.1047 | −0.765547 | ||||||||
\(761\) | −45.4031 | −1.64586 | −0.822931 | − | 0.568141i | \(-0.807663\pi\) | ||||
−0.822931 | + | 0.568141i | \(0.807663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.7016 | 0.568435 | ||||||||
\(764\) | −6.29844 | −0.227869 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.9109 | −1.00846 | ||||||||
\(767\) | −10.8062 | −0.390191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.08907 | 0.219577 | 0.109789 | − | 0.993955i | \(-0.464983\pi\) | ||||
0.109789 | + | 0.993955i | \(0.464983\pi\) | |||||||
\(770\) | 21.1047 | 0.760560 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.40312 | −0.0504995 | ||||||||
\(773\) | −29.3141 | −1.05435 | −0.527177 | − | 0.849756i | \(-0.676749\pi\) | ||||
−0.527177 | + | 0.849756i | \(0.676749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.8062 | −0.603309 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.0000 | 0.501924 | ||||||||
\(779\) | 53.6125 | 1.92087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.6125 | −1.63214 | ||||||||
\(782\) | 6.29844 | 0.225232 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 3.31406 | 0.118284 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.9109 | −0.852333 | −0.426166 | − | 0.904645i | \(-0.640136\pi\) | ||||
−0.426166 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(788\) | −9.40312 | −0.334972 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.5969 | 0.448177 | ||||||||
\(791\) | 20.8062 | 0.739785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.70156 | 0.273490 | ||||||||
\(794\) | 24.8062 | 0.880341 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.89531 | 0.102622 | ||||||||
\(797\) | 53.4031 | 1.89164 | 0.945818 | − | 0.324698i | \(-0.105263\pi\) | ||||
0.945818 | + | 0.324698i | \(0.105263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.6125 | −1.04761 | ||||||||
\(800\) | −8.70156 | −0.307647 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.8062 | −0.734694 | ||||||||
\(803\) | 43.9109 | 1.54958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.29844 | 0.221991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.40312 | 0.330801 | ||||||||
\(809\) | −39.6125 | −1.39270 | −0.696351 | − | 0.717702i | \(-0.745194\pi\) | ||||
−0.696351 | + | 0.717702i | \(0.745194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.1047 | −1.44338 | −0.721690 | − | 0.692216i | \(-0.756635\pi\) | ||||
−0.721690 | + | 0.692216i | \(0.756635\pi\) | |||||||
\(812\) | 3.70156 | 0.129899 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.5078 | 0.858998 | ||||||||
\(815\) | −27.4031 | −0.959890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.9109 | 1.81613 | ||||||||
\(818\) | −11.7016 | −0.409136 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 34.8062 | 1.21549 | ||||||||
\(821\) | −41.4031 | −1.44498 | −0.722489 | − | 0.691382i | \(-0.757002\pi\) | ||||
−0.722489 | + | 0.691382i | \(0.757002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8062 | 1.07384 | 0.536919 | − | 0.843634i | \(-0.319588\pi\) | ||||
0.536919 | + | 0.843634i | \(0.319588\pi\) | |||||||
\(824\) | 9.70156 | 0.337970 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8062 | 0.375997 | ||||||||
\(827\) | −8.08907 | −0.281284 | −0.140642 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140642 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3141 | 0.740268 | 0.370134 | − | 0.928978i | \(-0.379312\pi\) | ||||
0.370134 | + | 0.928978i | \(0.379312\pi\) | |||||||
\(830\) | −2.20937 | −0.0766884 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −3.70156 | −0.128252 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.9109 | −1.24275 | ||||||||
\(836\) | −32.5078 | −1.12431 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.8953 | 0.514550 | ||||||||
\(839\) | −9.19375 | −0.317404 | −0.158702 | − | 0.987327i | \(-0.550731\pi\) | ||||
−0.158702 | + | 0.987327i | \(0.550731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2984 | −0.527532 | ||||||||
\(842\) | 31.6125 | 1.08944 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.2984 | −0.629858 | ||||||||
\(845\) | 3.70156 | 0.127338 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5078 | 0.739017 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.2094 | 1.10477 | ||||||||
\(851\) | 7.31406 | 0.250723 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.2094 | 0.554998 | 0.277499 | − | 0.960726i | \(-0.410494\pi\) | ||||
0.277499 | + | 0.960726i | \(0.410494\pi\) | |||||||
\(854\) | −7.70156 | −0.263542 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.40312 | 0.253034 | ||||||||
\(857\) | −8.80625 | −0.300816 | −0.150408 | − | 0.988624i | \(-0.548059\pi\) | ||||
−0.150408 | + | 0.988624i | \(0.548059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1938 | 0.450165 | 0.225082 | − | 0.974340i | \(-0.427735\pi\) | ||||
0.225082 | + | 0.974340i | \(0.427735\pi\) | |||||||
\(860\) | 33.7016 | 1.14921 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.2094 | 0.892695 | ||||||||
\(863\) | 35.4031 | 1.20514 | 0.602568 | − | 0.798067i | \(-0.294144\pi\) | ||||
0.602568 | + | 0.798067i | \(0.294144\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 66.6281 | 2.26542 | ||||||||
\(866\) | 24.2094 | 0.822668 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.4031 | 0.658206 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.40312 | −0.250845 | ||||||||
\(872\) | −15.7016 | −0.531722 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.70156 | −0.328160 | ||||||||
\(875\) | 13.7016 | 0.463197 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.6125 | 1.74283 | 0.871415 | − | 0.490546i | \(-0.163203\pi\) | ||||
0.871415 | + | 0.490546i | \(0.163203\pi\) | |||||||
\(878\) | 32.5078 | 1.09709 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21.1047 | −0.711439 | ||||||||
\(881\) | −49.3141 | −1.66143 | −0.830716 | − | 0.556696i | \(-0.812069\pi\) | ||||
−0.830716 | + | 0.556696i | \(0.812069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1047 | 1.11406 | 0.557031 | − | 0.830492i | \(-0.311941\pi\) | ||||
0.557031 | + | 0.830492i | \(0.311941\pi\) | |||||||
\(884\) | −3.70156 | −0.124497 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.2094 | −1.28367 | ||||||||
\(887\) | 8.00000 | 0.268614 | 0.134307 | − | 0.990940i | \(-0.457119\pi\) | ||||
0.134307 | + | 0.990940i | \(0.457119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.4031 | −0.650760 | ||||||||
\(890\) | 62.2094 | 2.08526 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.40312 | −0.113945 | ||||||||
\(893\) | 45.6125 | 1.52636 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.0000 | 1.33705 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.1047 | −0.904495 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.40312 | −0.246634 | ||||||||
\(902\) | 53.6125 | 1.78510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.8062 | −0.692006 | ||||||||
\(905\) | −62.2094 | −2.06791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.6125 | 0.850449 | 0.425225 | − | 0.905088i | \(-0.360195\pi\) | ||||
0.425225 | + | 0.905088i | \(0.360195\pi\) | |||||||
\(908\) | −8.59688 | −0.285297 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.70156 | −0.122706 | ||||||||
\(911\) | 3.91093 | 0.129575 | 0.0647875 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647875 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.40312 | −0.112627 | ||||||||
\(914\) | −13.4031 | −0.443336 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | 0.198246 | ||||||||
\(917\) | 13.7016 | 0.452465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4031 | −0.903946 | −0.451973 | − | 0.892032i | \(-0.649280\pi\) | ||||
−0.451973 | + | 0.892032i | \(0.649280\pi\) | |||||||
\(920\) | −6.29844 | −0.207653 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 37.3141 | 1.22887 | ||||||||
\(923\) | 8.00000 | 0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.4031 | 1.22981 | ||||||||
\(926\) | −23.3141 | −0.766148 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.70156 | −0.121510 | ||||||||
\(929\) | 31.0156 | 1.01759 | 0.508795 | − | 0.860888i | \(-0.330091\pi\) | ||||
0.508795 | + | 0.860888i | \(0.330091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.70156 | 0.186861 | ||||||||
\(932\) | −20.2094 | −0.661980 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.5078 | −1.19457 | ||||||||
\(935\) | 78.1203 | 2.55481 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.19375 | 0.104335 | 0.0521677 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521677 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(938\) | 7.40312 | 0.241721 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.6125 | 0.965853 | ||||||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | −10.8062 | −0.351713 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 51.9109 | 1.68777 | ||||||||
\(947\) | −36.5078 | −1.18634 | −0.593172 | − | 0.805076i | \(-0.702125\pi\) | ||||
−0.593172 | + | 0.805076i | \(0.702125\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.70156 | −0.250003 | ||||||||
\(950\) | −49.6125 | −1.60964 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.70156 | 0.119968 | ||||||||
\(953\) | −49.8219 | −1.61389 | −0.806944 | − | 0.590628i | \(-0.798880\pi\) | ||||
−0.806944 | + | 0.590628i | \(0.798880\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.3141 | −0.754425 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.5078 | −0.791811 | ||||||||
\(959\) | 12.2984 | 0.397137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −4.29844 | −0.138587 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.806248 | 0.0259675 | ||||||||
\(965\) | −5.19375 | −0.167193 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.7172 | 0.601904 | 0.300952 | − | 0.953639i | \(-0.402696\pi\) | ||||
0.300952 | + | 0.953639i | \(0.402696\pi\) | |||||||
\(968\) | −21.5078 | −0.691287 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −62.2094 | −1.99742 | ||||||||
\(971\) | −29.1938 | −0.936872 | −0.468436 | − | 0.883497i | \(-0.655182\pi\) | ||||
−0.468436 | + | 0.883497i | \(0.655182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.8062 | −0.602901 | ||||||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.70156 | 0.246521 | ||||||||
\(977\) | −28.7172 | −0.918744 | −0.459372 | − | 0.888244i | \(-0.651926\pi\) | ||||
−0.459372 | + | 0.888244i | \(0.651926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95.8219 | 3.06248 | ||||||||
\(980\) | 3.70156 | 0.118242 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.4031 | 1.25740 | ||||||||
\(983\) | 18.8953 | 0.602667 | 0.301333 | − | 0.953519i | \(-0.402568\pi\) | ||||
0.301333 | + | 0.953519i | \(0.402568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.8062 | −1.10902 | ||||||||
\(986\) | 13.7016 | 0.436347 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.70156 | 0.181391 | ||||||||
\(989\) | 15.4922 | 0.492623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.4031 | −1.63287 | −0.816437 | − | 0.577434i | \(-0.804054\pi\) | ||||
−0.816437 | + | 0.577434i | \(0.804054\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 10.7172 | 0.339758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8062 | 0.405578 | 0.202789 | − | 0.979222i | \(-0.434999\pi\) | ||||
0.202789 | + | 0.979222i | \(0.434999\pi\) | |||||||
\(998\) | 26.8062 | 0.848537 | ||||||||
\(999\) | 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 | 1638.2.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 546.2.a.i.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 4368.2.a.bg.1.1 | 2 | |||
21.20 | even | 2 | 3822.2.a.bt.1.2 | 2 | |||
39.38 | odd | 2 | 7098.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.a.i.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1638.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3822.2.a.bt.1.2 | 2 | 21.20 | even | 2 | |||
4368.2.a.bg.1.1 | 2 | 12.11 | even | 2 | |||
7098.2.a.bh.1.2 | 2 | 39.38 | odd | 2 |