Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.74657 | −1.22830 | −0.614151 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614151 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.74657 | −0.868541 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −5.49314 | −1.52352 | −0.761761 | − | 0.647858i | \(-0.775665\pi\) | ||||
−0.761761 | + | 0.647858i | \(0.775665\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.74657 | 0.709161 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 8.03677 | 1.84376 | 0.921881 | − | 0.387473i | \(-0.126652\pi\) | ||||
0.921881 | + | 0.387473i | \(0.126652\pi\) | |||||||
\(20\) | −2.74657 | −0.614151 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −1.29021 | −0.269026 | −0.134513 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134513 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.54364 | 0.508727 | ||||||||
\(26\) | −5.49314 | −1.07729 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54364 | 0.843732 | 0.421866 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421866 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(30\) | 2.74657 | 0.501452 | ||||||||
\(31\) | −5.08727 | −0.913701 | −0.456851 | − | 0.889543i | \(-0.651023\pi\) | ||||
−0.456851 | + | 0.889543i | \(0.651023\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.03677 | −0.663641 | −0.331821 | − | 0.943342i | \(-0.607663\pi\) | ||||
−0.331821 | + | 0.943342i | \(0.607663\pi\) | |||||||
\(38\) | 8.03677 | 1.30374 | ||||||||
\(39\) | 5.49314 | 0.879606 | ||||||||
\(40\) | −2.74657 | −0.434271 | ||||||||
\(41\) | −5.54364 | −0.865771 | −0.432885 | − | 0.901449i | \(-0.642505\pi\) | ||||
−0.432885 | + | 0.901449i | \(0.642505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.03677 | −0.615602 | −0.307801 | − | 0.951451i | \(-0.599593\pi\) | ||||
−0.307801 | + | 0.951451i | \(0.599593\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.74657 | −0.409434 | ||||||||
\(46\) | −1.29021 | −0.190230 | ||||||||
\(47\) | 9.29021 | 1.35512 | 0.677558 | − | 0.735469i | \(-0.263038\pi\) | ||||
0.677558 | + | 0.735469i | \(0.263038\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.54364 | 0.359725 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −5.49314 | −0.761761 | ||||||||
\(53\) | 5.49314 | 0.754540 | 0.377270 | − | 0.926103i | \(-0.376863\pi\) | ||||
0.377270 | + | 0.926103i | \(0.376863\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.74657 | −0.370347 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.03677 | −1.06450 | ||||||||
\(58\) | 4.54364 | 0.596609 | ||||||||
\(59\) | 9.52991 | 1.24069 | 0.620344 | − | 0.784330i | \(-0.286993\pi\) | ||||
0.620344 | + | 0.784330i | \(0.286993\pi\) | |||||||
\(60\) | 2.74657 | 0.354580 | ||||||||
\(61\) | 1.65929 | 0.212451 | 0.106225 | − | 0.994342i | \(-0.466123\pi\) | ||||
0.106225 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(62\) | −5.08727 | −0.646084 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.0873 | 1.87135 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 3.54364 | 0.432924 | 0.216462 | − | 0.976291i | \(-0.430548\pi\) | ||||
0.216462 | + | 0.976291i | \(0.430548\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 1.29021 | 0.155322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54364 | 0.301874 | 0.150937 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150937 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.58041 | 1.00426 | 0.502131 | − | 0.864792i | \(-0.332550\pi\) | ||||
0.502131 | + | 0.864792i | \(0.332550\pi\) | |||||||
\(74\) | −4.03677 | −0.469265 | ||||||||
\(75\) | −2.54364 | −0.293714 | ||||||||
\(76\) | 8.03677 | 0.921881 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.49314 | 0.621975 | ||||||||
\(79\) | 12.2397 | 1.37707 | 0.688537 | − | 0.725201i | \(-0.258253\pi\) | ||||
0.688537 | + | 0.725201i | \(0.258253\pi\) | |||||||
\(80\) | −2.74657 | −0.307076 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.54364 | −0.612192 | ||||||||
\(83\) | 14.5299 | 1.59486 | 0.797432 | − | 0.603408i | \(-0.206191\pi\) | ||||
0.797432 | + | 0.603408i | \(0.206191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.74657 | 0.297907 | ||||||||
\(86\) | −4.03677 | −0.435296 | ||||||||
\(87\) | −4.54364 | −0.487129 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 6.50686 | 0.689726 | 0.344863 | − | 0.938653i | \(-0.387925\pi\) | ||||
0.344863 | + | 0.938653i | \(0.387925\pi\) | |||||||
\(90\) | −2.74657 | −0.289514 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.29021 | −0.134513 | ||||||||
\(93\) | 5.08727 | 0.527526 | ||||||||
\(94\) | 9.29021 | 0.958212 | ||||||||
\(95\) | −22.0735 | −2.26470 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.0872743 | 0.00886136 | 0.00443068 | − | 0.999990i | \(-0.498590\pi\) | ||||
0.00443068 | + | 0.999990i | \(0.498590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 2.54364 | 0.254364 | ||||||||
\(101\) | −13.0230 | −1.29584 | −0.647921 | − | 0.761708i | \(-0.724361\pi\) | ||||
−0.647921 | + | 0.761708i | \(0.724361\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 18.0735 | 1.78084 | 0.890420 | − | 0.455140i | \(-0.150411\pi\) | ||||
0.890420 | + | 0.455140i | \(0.150411\pi\) | |||||||
\(104\) | −5.49314 | −0.538646 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.49314 | 0.533541 | ||||||||
\(107\) | 17.4426 | 1.68624 | 0.843122 | − | 0.537723i | \(-0.180715\pi\) | ||||
0.843122 | + | 0.537723i | \(0.180715\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.65929 | 0.158932 | 0.0794658 | − | 0.996838i | \(-0.474679\pi\) | ||||
0.0794658 | + | 0.996838i | \(0.474679\pi\) | |||||||
\(110\) | −2.74657 | −0.261875 | ||||||||
\(111\) | 4.03677 | 0.383154 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.08727 | −0.666715 | −0.333357 | − | 0.942801i | \(-0.608182\pi\) | ||||
−0.333357 | + | 0.942801i | \(0.608182\pi\) | |||||||
\(114\) | −8.03677 | −0.752713 | ||||||||
\(115\) | 3.54364 | 0.330446 | ||||||||
\(116\) | 4.54364 | 0.421866 | ||||||||
\(117\) | −5.49314 | −0.507841 | ||||||||
\(118\) | 9.52991 | 0.877299 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.74657 | 0.250726 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.65929 | 0.150225 | ||||||||
\(123\) | 5.54364 | 0.499853 | ||||||||
\(124\) | −5.08727 | −0.456851 | ||||||||
\(125\) | 6.74657 | 0.603431 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.78334 | −0.601924 | −0.300962 | − | 0.953636i | \(-0.597308\pi\) | ||||
−0.300962 | + | 0.953636i | \(0.597308\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.03677 | 0.355418 | ||||||||
\(130\) | 15.0873 | 1.32324 | ||||||||
\(131\) | 13.8990 | 1.21436 | 0.607181 | − | 0.794564i | \(-0.292300\pi\) | ||||
0.607181 | + | 0.794564i | \(0.292300\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.54364 | 0.306124 | ||||||||
\(135\) | 2.74657 | 0.236387 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 5.49314 | 0.469310 | 0.234655 | − | 0.972079i | \(-0.424604\pi\) | ||||
0.234655 | + | 0.972079i | \(0.424604\pi\) | |||||||
\(138\) | 1.29021 | 0.109830 | ||||||||
\(139\) | −13.6309 | −1.15616 | −0.578079 | − | 0.815981i | \(-0.696198\pi\) | ||||
−0.578079 | + | 0.815981i | \(0.696198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.29021 | −0.782376 | ||||||||
\(142\) | 2.54364 | 0.213457 | ||||||||
\(143\) | −5.49314 | −0.459359 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.4794 | −1.03636 | ||||||||
\(146\) | 8.58041 | 0.710120 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.03677 | −0.331821 | ||||||||
\(149\) | 16.0368 | 1.31378 | 0.656892 | − | 0.753985i | \(-0.271871\pi\) | ||||
0.656892 | + | 0.753985i | \(0.271871\pi\) | |||||||
\(150\) | −2.54364 | −0.207687 | ||||||||
\(151\) | −5.69607 | −0.463539 | −0.231770 | − | 0.972771i | \(-0.574452\pi\) | ||||
−0.231770 | + | 0.972771i | \(0.574452\pi\) | |||||||
\(152\) | 8.03677 | 0.651868 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.9725 | 1.12230 | ||||||||
\(156\) | 5.49314 | 0.439803 | ||||||||
\(157\) | −18.1103 | −1.44536 | −0.722680 | − | 0.691182i | \(-0.757090\pi\) | ||||
−0.722680 | + | 0.691182i | \(0.757090\pi\) | |||||||
\(158\) | 12.2397 | 0.973739 | ||||||||
\(159\) | −5.49314 | −0.435634 | ||||||||
\(160\) | −2.74657 | −0.217135 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −13.4426 | −1.05291 | −0.526454 | − | 0.850203i | \(-0.676479\pi\) | ||||
−0.526454 | + | 0.850203i | \(0.676479\pi\) | |||||||
\(164\) | −5.54364 | −0.432885 | ||||||||
\(165\) | 2.74657 | 0.213820 | ||||||||
\(166\) | 14.5299 | 1.12774 | ||||||||
\(167\) | −23.5667 | −1.82364 | −0.911822 | − | 0.410585i | \(-0.865325\pi\) | ||||
−0.911822 | + | 0.410585i | \(0.865325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.1745 | 1.32112 | ||||||||
\(170\) | 2.74657 | 0.210652 | ||||||||
\(171\) | 8.03677 | 0.614587 | ||||||||
\(172\) | −4.03677 | −0.307801 | ||||||||
\(173\) | 10.9127 | 0.829679 | 0.414840 | − | 0.909895i | \(-0.363838\pi\) | ||||
0.414840 | + | 0.909895i | \(0.363838\pi\) | |||||||
\(174\) | −4.54364 | −0.344452 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −9.52991 | −0.716312 | ||||||||
\(178\) | 6.50686 | 0.487710 | ||||||||
\(179\) | −12.9495 | −0.967891 | −0.483946 | − | 0.875098i | \(-0.660797\pi\) | ||||
−0.483946 | + | 0.875098i | \(0.660797\pi\) | |||||||
\(180\) | −2.74657 | −0.204717 | ||||||||
\(181\) | −7.59414 | −0.564468 | −0.282234 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282234 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.65929 | −0.122659 | ||||||||
\(184\) | −1.29021 | −0.0951152 | ||||||||
\(185\) | 11.0873 | 0.815153 | ||||||||
\(186\) | 5.08727 | 0.373017 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 9.29021 | 0.677558 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22.0735 | −1.60138 | ||||||||
\(191\) | 18.9863 | 1.37380 | 0.686899 | − | 0.726753i | \(-0.258971\pi\) | ||||
0.686899 | + | 0.726753i | \(0.258971\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −21.5667 | −1.55240 | −0.776202 | − | 0.630484i | \(-0.782856\pi\) | ||||
−0.776202 | + | 0.630484i | \(0.782856\pi\) | |||||||
\(194\) | 0.0872743 | 0.00626593 | ||||||||
\(195\) | −15.0873 | −1.08042 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.12405 | −0.222579 | −0.111290 | − | 0.993788i | \(-0.535498\pi\) | ||||
−0.111290 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 26.0735 | 1.84830 | 0.924152 | − | 0.382024i | \(-0.124773\pi\) | ||||
0.924152 | + | 0.382024i | \(0.124773\pi\) | |||||||
\(200\) | 2.54364 | 0.179862 | ||||||||
\(201\) | −3.54364 | −0.249949 | ||||||||
\(202\) | −13.0230 | −0.916298 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 15.2260 | 1.06343 | ||||||||
\(206\) | 18.0735 | 1.25924 | ||||||||
\(207\) | −1.29021 | −0.0896755 | ||||||||
\(208\) | −5.49314 | −0.380880 | ||||||||
\(209\) | 8.03677 | 0.555915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6677 | 1.07861 | 0.539304 | − | 0.842111i | \(-0.318687\pi\) | ||||
0.539304 | + | 0.842111i | \(0.318687\pi\) | |||||||
\(212\) | 5.49314 | 0.377270 | ||||||||
\(213\) | −2.54364 | −0.174287 | ||||||||
\(214\) | 17.4426 | 1.19235 | ||||||||
\(215\) | 11.0873 | 0.756146 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.65929 | 0.112382 | ||||||||
\(219\) | −8.58041 | −0.579810 | ||||||||
\(220\) | −2.74657 | −0.185174 | ||||||||
\(221\) | 5.49314 | 0.369508 | ||||||||
\(222\) | 4.03677 | 0.270931 | ||||||||
\(223\) | −2.40586 | −0.161108 | −0.0805542 | − | 0.996750i | \(-0.525669\pi\) | ||||
−0.0805542 | + | 0.996750i | \(0.525669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54364 | 0.169576 | ||||||||
\(226\) | −7.08727 | −0.471438 | ||||||||
\(227\) | −2.45636 | −0.163035 | −0.0815173 | − | 0.996672i | \(-0.525977\pi\) | ||||
−0.0815173 | + | 0.996672i | \(0.525977\pi\) | |||||||
\(228\) | −8.03677 | −0.532248 | ||||||||
\(229\) | 10.5804 | 0.699173 | 0.349587 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349587 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(230\) | 3.54364 | 0.233661 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.54364 | 0.298304 | ||||||||
\(233\) | −7.07355 | −0.463403 | −0.231702 | − | 0.972787i | \(-0.574429\pi\) | ||||
−0.231702 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(234\) | −5.49314 | −0.359098 | ||||||||
\(235\) | −25.5162 | −1.66449 | ||||||||
\(236\) | 9.52991 | 0.620344 | ||||||||
\(237\) | −12.2397 | −0.795054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.66769 | 0.495981 | 0.247991 | − | 0.968762i | \(-0.420230\pi\) | ||||
0.247991 | + | 0.968762i | \(0.420230\pi\) | |||||||
\(240\) | 2.74657 | 0.177290 | ||||||||
\(241\) | 25.0598 | 1.61424 | 0.807122 | − | 0.590384i | \(-0.201024\pi\) | ||||
0.807122 | + | 0.590384i | \(0.201024\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.65929 | 0.106225 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.54364 | 0.353449 | ||||||||
\(247\) | −44.1471 | −2.80901 | ||||||||
\(248\) | −5.08727 | −0.323042 | ||||||||
\(249\) | −14.5299 | −0.920796 | ||||||||
\(250\) | 6.74657 | 0.426690 | ||||||||
\(251\) | 25.0230 | 1.57944 | 0.789720 | − | 0.613467i | \(-0.210226\pi\) | ||||
0.789720 | + | 0.613467i | \(0.210226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.29021 | −0.0811145 | ||||||||
\(254\) | −6.78334 | −0.425625 | ||||||||
\(255\) | −2.74657 | −0.171997 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.5069 | 0.655400 | 0.327700 | − | 0.944782i | \(-0.393726\pi\) | ||||
0.327700 | + | 0.944782i | \(0.393726\pi\) | |||||||
\(258\) | 4.03677 | 0.251319 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.0873 | 0.935673 | ||||||||
\(261\) | 4.54364 | 0.281244 | ||||||||
\(262\) | 13.8990 | 0.858683 | ||||||||
\(263\) | 23.6402 | 1.45772 | 0.728860 | − | 0.684663i | \(-0.240051\pi\) | ||||
0.728860 | + | 0.684663i | \(0.240051\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −15.0873 | −0.926804 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.50686 | −0.398214 | ||||||||
\(268\) | 3.54364 | 0.216462 | ||||||||
\(269\) | 15.1524 | 0.923860 | 0.461930 | − | 0.886916i | \(-0.347157\pi\) | ||||
0.461930 | + | 0.886916i | \(0.347157\pi\) | |||||||
\(270\) | 2.74657 | 0.167151 | ||||||||
\(271\) | −18.9863 | −1.15333 | −0.576667 | − | 0.816979i | \(-0.695647\pi\) | ||||
−0.576667 | + | 0.816979i | \(0.695647\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.49314 | 0.331853 | ||||||||
\(275\) | 2.54364 | 0.153387 | ||||||||
\(276\) | 1.29021 | 0.0776612 | ||||||||
\(277\) | 24.4794 | 1.47083 | 0.735413 | − | 0.677620i | \(-0.236988\pi\) | ||||
0.735413 | + | 0.677620i | \(0.236988\pi\) | |||||||
\(278\) | −13.6309 | −0.817528 | ||||||||
\(279\) | −5.08727 | −0.304567 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0873 | −0.721066 | −0.360533 | − | 0.932746i | \(-0.617405\pi\) | ||||
−0.360533 | + | 0.932746i | \(0.617405\pi\) | |||||||
\(282\) | −9.29021 | −0.553224 | ||||||||
\(283\) | −4.68141 | −0.278281 | −0.139141 | − | 0.990273i | \(-0.544434\pi\) | ||||
−0.139141 | + | 0.990273i | \(0.544434\pi\) | |||||||
\(284\) | 2.54364 | 0.150937 | ||||||||
\(285\) | 22.0735 | 1.30752 | ||||||||
\(286\) | −5.49314 | −0.324816 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | −12.4794 | −0.732816 | ||||||||
\(291\) | −0.0872743 | −0.00511611 | ||||||||
\(292\) | 8.58041 | 0.502131 | ||||||||
\(293\) | 11.6309 | 0.679485 | 0.339743 | − | 0.940518i | \(-0.389660\pi\) | ||||
0.339743 | + | 0.940518i | \(0.389660\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.1745 | −1.52394 | ||||||||
\(296\) | −4.03677 | −0.234633 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 16.0368 | 0.928985 | ||||||||
\(299\) | 7.08727 | 0.409868 | ||||||||
\(300\) | −2.54364 | −0.146857 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.69607 | −0.327772 | ||||||||
\(303\) | 13.0230 | 0.748154 | ||||||||
\(304\) | 8.03677 | 0.460941 | ||||||||
\(305\) | −4.55736 | −0.260954 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 14.0735 | 0.803220 | 0.401610 | − | 0.915811i | \(-0.368451\pi\) | ||||
0.401610 | + | 0.915811i | \(0.368451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0735 | −1.02817 | ||||||||
\(310\) | 13.9725 | 0.793587 | ||||||||
\(311\) | −12.2765 | −0.696135 | −0.348068 | − | 0.937469i | \(-0.613162\pi\) | ||||
−0.348068 | + | 0.937469i | \(0.613162\pi\) | |||||||
\(312\) | 5.49314 | 0.310988 | ||||||||
\(313\) | −23.4564 | −1.32583 | −0.662916 | − | 0.748694i | \(-0.730681\pi\) | ||||
−0.662916 | + | 0.748694i | \(0.730681\pi\) | |||||||
\(314\) | −18.1103 | −1.02202 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.2397 | 0.688537 | ||||||||
\(317\) | −0.572020 | −0.0321278 | −0.0160639 | − | 0.999871i | \(-0.505114\pi\) | ||||
−0.0160639 | + | 0.999871i | \(0.505114\pi\) | |||||||
\(318\) | −5.49314 | −0.308040 | ||||||||
\(319\) | 4.54364 | 0.254395 | ||||||||
\(320\) | −2.74657 | −0.153538 | ||||||||
\(321\) | −17.4426 | −0.973553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.03677 | −0.447178 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −13.9725 | −0.775057 | ||||||||
\(326\) | −13.4426 | −0.744519 | ||||||||
\(327\) | −1.65929 | −0.0917592 | ||||||||
\(328\) | −5.54364 | −0.306096 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.74657 | 0.151194 | ||||||||
\(331\) | 7.71819 | 0.424230 | 0.212115 | − | 0.977245i | \(-0.431965\pi\) | ||||
0.212115 | + | 0.977245i | \(0.431965\pi\) | |||||||
\(332\) | 14.5299 | 0.797432 | ||||||||
\(333\) | −4.03677 | −0.221214 | ||||||||
\(334\) | −23.5667 | −1.28951 | ||||||||
\(335\) | −9.73284 | −0.531762 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.5530 | 1.55538 | 0.777689 | − | 0.628649i | \(-0.216392\pi\) | ||||
0.777689 | + | 0.628649i | \(0.216392\pi\) | |||||||
\(338\) | 17.1745 | 0.934172 | ||||||||
\(339\) | 7.08727 | 0.384928 | ||||||||
\(340\) | 2.74657 | 0.148954 | ||||||||
\(341\) | −5.08727 | −0.275491 | ||||||||
\(342\) | 8.03677 | 0.434579 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.03677 | −0.217648 | ||||||||
\(345\) | −3.54364 | −0.190783 | ||||||||
\(346\) | 10.9127 | 0.586672 | ||||||||
\(347\) | −23.4426 | −1.25847 | −0.629233 | − | 0.777216i | \(-0.716631\pi\) | ||||
−0.629233 | + | 0.777216i | \(0.716631\pi\) | |||||||
\(348\) | −4.54364 | −0.243565 | ||||||||
\(349\) | −25.7328 | −1.37745 | −0.688724 | − | 0.725024i | \(-0.741829\pi\) | ||||
−0.688724 | + | 0.725024i | \(0.741829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.49314 | 0.293202 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 18.4059 | 0.979645 | 0.489823 | − | 0.871822i | \(-0.337062\pi\) | ||||
0.489823 | + | 0.871822i | \(0.337062\pi\) | |||||||
\(354\) | −9.52991 | −0.506509 | ||||||||
\(355\) | −6.98627 | −0.370793 | ||||||||
\(356\) | 6.50686 | 0.344863 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9495 | −0.684402 | ||||||||
\(359\) | −31.9725 | −1.68745 | −0.843723 | − | 0.536778i | \(-0.819641\pi\) | ||||
−0.843723 | + | 0.536778i | \(0.819641\pi\) | |||||||
\(360\) | −2.74657 | −0.144757 | ||||||||
\(361\) | 45.5897 | 2.39946 | ||||||||
\(362\) | −7.59414 | −0.399139 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.5667 | −1.23354 | ||||||||
\(366\) | −1.65929 | −0.0867327 | ||||||||
\(367\) | −36.4794 | −1.90421 | −0.952105 | − | 0.305772i | \(-0.901086\pi\) | ||||
−0.952105 | + | 0.305772i | \(0.901086\pi\) | |||||||
\(368\) | −1.29021 | −0.0672566 | ||||||||
\(369\) | −5.54364 | −0.288590 | ||||||||
\(370\) | 11.0873 | 0.576400 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.08727 | 0.263763 | ||||||||
\(373\) | −20.3133 | −1.05178 | −0.525890 | − | 0.850552i | \(-0.676268\pi\) | ||||
−0.525890 | + | 0.850552i | \(0.676268\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | −6.74657 | −0.348391 | ||||||||
\(376\) | 9.29021 | 0.479106 | ||||||||
\(377\) | −24.9588 | −1.28544 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.44264 | 0.485036 | 0.242518 | − | 0.970147i | \(-0.422027\pi\) | ||||
0.242518 | + | 0.970147i | \(0.422027\pi\) | |||||||
\(380\) | −22.0735 | −1.13235 | ||||||||
\(381\) | 6.78334 | 0.347521 | ||||||||
\(382\) | 18.9863 | 0.971422 | ||||||||
\(383\) | −23.7045 | −1.21124 | −0.605621 | − | 0.795754i | \(-0.707075\pi\) | ||||
−0.605621 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.5667 | −1.09772 | ||||||||
\(387\) | −4.03677 | −0.205201 | ||||||||
\(388\) | 0.0872743 | 0.00443068 | ||||||||
\(389\) | −1.25343 | −0.0635515 | −0.0317758 | − | 0.999495i | \(-0.510116\pi\) | ||||
−0.0317758 | + | 0.999495i | \(0.510116\pi\) | |||||||
\(390\) | −15.0873 | −0.763974 | ||||||||
\(391\) | 1.29021 | 0.0652485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8990 | −0.701112 | ||||||||
\(394\) | −3.12405 | −0.157387 | ||||||||
\(395\) | −33.6172 | −1.69146 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −28.6172 | −1.43626 | −0.718128 | − | 0.695911i | \(-0.755001\pi\) | ||||
−0.718128 | + | 0.695911i | \(0.755001\pi\) | |||||||
\(398\) | 26.0735 | 1.30695 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.54364 | 0.127182 | ||||||||
\(401\) | 0.405862 | 0.0202678 | 0.0101339 | − | 0.999949i | \(-0.496774\pi\) | ||||
0.0101339 | + | 0.999949i | \(0.496774\pi\) | |||||||
\(402\) | −3.54364 | −0.176741 | ||||||||
\(403\) | 27.9451 | 1.39204 | ||||||||
\(404\) | −13.0230 | −0.647921 | ||||||||
\(405\) | −2.74657 | −0.136478 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.03677 | −0.200095 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 32.7550 | 1.61963 | 0.809814 | − | 0.586686i | \(-0.199568\pi\) | ||||
0.809814 | + | 0.586686i | \(0.199568\pi\) | |||||||
\(410\) | 15.2260 | 0.751957 | ||||||||
\(411\) | −5.49314 | −0.270956 | ||||||||
\(412\) | 18.0735 | 0.890420 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.29021 | −0.0634101 | ||||||||
\(415\) | −39.9074 | −1.95898 | ||||||||
\(416\) | −5.49314 | −0.269323 | ||||||||
\(417\) | 13.6309 | 0.667509 | ||||||||
\(418\) | 8.03677 | 0.393091 | ||||||||
\(419\) | 15.9358 | 0.778513 | 0.389257 | − | 0.921129i | \(-0.372732\pi\) | ||||
0.389257 | + | 0.921129i | \(0.372732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1240 | −1.32195 | −0.660973 | − | 0.750410i | \(-0.729856\pi\) | ||||
−0.660973 | + | 0.750410i | \(0.729856\pi\) | |||||||
\(422\) | 15.6677 | 0.762691 | ||||||||
\(423\) | 9.29021 | 0.451705 | ||||||||
\(424\) | 5.49314 | 0.266770 | ||||||||
\(425\) | −2.54364 | −0.123385 | ||||||||
\(426\) | −2.54364 | −0.123240 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17.4426 | 0.843122 | ||||||||
\(429\) | 5.49314 | 0.265211 | ||||||||
\(430\) | 11.0873 | 0.534676 | ||||||||
\(431\) | −40.6265 | −1.95691 | −0.978455 | − | 0.206461i | \(-0.933805\pi\) | ||||
−0.978455 | + | 0.206461i | \(0.933805\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −1.10100 | −0.0529107 | −0.0264554 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264554 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.4794 | 0.598342 | ||||||||
\(436\) | 1.65929 | 0.0794658 | ||||||||
\(437\) | −10.3691 | −0.496021 | ||||||||
\(438\) | −8.58041 | −0.409988 | ||||||||
\(439\) | −22.8569 | −1.09090 | −0.545450 | − | 0.838143i | \(-0.683641\pi\) | ||||
−0.545450 | + | 0.838143i | \(0.683641\pi\) | |||||||
\(440\) | −2.74657 | −0.130938 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.49314 | 0.261282 | ||||||||
\(443\) | −9.55736 | −0.454084 | −0.227042 | − | 0.973885i | \(-0.572905\pi\) | ||||
−0.227042 | + | 0.973885i | \(0.572905\pi\) | |||||||
\(444\) | 4.03677 | 0.191577 | ||||||||
\(445\) | −17.8715 | −0.847192 | ||||||||
\(446\) | −2.40586 | −0.113921 | ||||||||
\(447\) | −16.0368 | −0.758513 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.681412 | 0.0321578 | 0.0160789 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160789 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(450\) | 2.54364 | 0.119908 | ||||||||
\(451\) | −5.54364 | −0.261040 | ||||||||
\(452\) | −7.08727 | −0.333357 | ||||||||
\(453\) | 5.69607 | 0.267625 | ||||||||
\(454\) | −2.45636 | −0.115283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.03677 | −0.376356 | ||||||||
\(457\) | 18.1471 | 0.848885 | 0.424443 | − | 0.905455i | \(-0.360470\pi\) | ||||
0.424443 | + | 0.905455i | \(0.360470\pi\) | |||||||
\(458\) | 10.5804 | 0.494390 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 3.54364 | 0.165223 | ||||||||
\(461\) | 41.7045 | 1.94237 | 0.971185 | − | 0.238326i | \(-0.0765988\pi\) | ||||
0.971185 | + | 0.238326i | \(0.0765988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.5804 | −1.32824 | −0.664122 | − | 0.747624i | \(-0.731195\pi\) | ||||
−0.664122 | + | 0.747624i | \(0.731195\pi\) | |||||||
\(464\) | 4.54364 | 0.210933 | ||||||||
\(465\) | −13.9725 | −0.647961 | ||||||||
\(466\) | −7.07355 | −0.327676 | ||||||||
\(467\) | −5.38282 | −0.249087 | −0.124544 | − | 0.992214i | \(-0.539747\pi\) | ||||
−0.124544 | + | 0.992214i | \(0.539747\pi\) | |||||||
\(468\) | −5.49314 | −0.253920 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −25.5162 | −1.17697 | ||||||||
\(471\) | 18.1103 | 0.834480 | ||||||||
\(472\) | 9.52991 | 0.438650 | ||||||||
\(473\) | −4.03677 | −0.185611 | ||||||||
\(474\) | −12.2397 | −0.562188 | ||||||||
\(475\) | 20.4426 | 0.937972 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.49314 | 0.251513 | ||||||||
\(478\) | 7.66769 | 0.350712 | ||||||||
\(479\) | −14.4794 | −0.661581 | −0.330791 | − | 0.943704i | \(-0.607315\pi\) | ||||
−0.330791 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(480\) | 2.74657 | 0.125363 | ||||||||
\(481\) | 22.1745 | 1.01107 | ||||||||
\(482\) | 25.0598 | 1.14144 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −0.239705 | −0.0108844 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −8.43332 | −0.382150 | −0.191075 | − | 0.981575i | \(-0.561197\pi\) | ||||
−0.191075 | + | 0.981575i | \(0.561197\pi\) | |||||||
\(488\) | 1.65929 | 0.0751127 | ||||||||
\(489\) | 13.4426 | 0.607897 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6770 | −1.74547 | −0.872734 | − | 0.488195i | \(-0.837655\pi\) | ||||
−0.872734 | + | 0.488195i | \(0.837655\pi\) | |||||||
\(492\) | 5.54364 | 0.249926 | ||||||||
\(493\) | −4.54364 | −0.204635 | ||||||||
\(494\) | −44.1471 | −1.98627 | ||||||||
\(495\) | −2.74657 | −0.123449 | ||||||||
\(496\) | −5.08727 | −0.228425 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.5299 | −0.651101 | ||||||||
\(499\) | 38.0461 | 1.70318 | 0.851589 | − | 0.524211i | \(-0.175640\pi\) | ||||
0.851589 | + | 0.524211i | \(0.175640\pi\) | |||||||
\(500\) | 6.74657 | 0.301716 | ||||||||
\(501\) | 23.5667 | 1.05288 | ||||||||
\(502\) | 25.0230 | 1.11683 | ||||||||
\(503\) | −21.5667 | −0.961611 | −0.480805 | − | 0.876827i | \(-0.659656\pi\) | ||||
−0.480805 | + | 0.876827i | \(0.659656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.7687 | 1.59169 | ||||||||
\(506\) | −1.29021 | −0.0573566 | ||||||||
\(507\) | −17.1745 | −0.762748 | ||||||||
\(508\) | −6.78334 | −0.300962 | ||||||||
\(509\) | 26.6540 | 1.18142 | 0.590708 | − | 0.806885i | \(-0.298849\pi\) | ||||
0.590708 | + | 0.806885i | \(0.298849\pi\) | |||||||
\(510\) | −2.74657 | −0.121620 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −8.03677 | −0.354832 | ||||||||
\(514\) | 10.5069 | 0.463438 | ||||||||
\(515\) | −49.6402 | −2.18741 | ||||||||
\(516\) | 4.03677 | 0.177709 | ||||||||
\(517\) | 9.29021 | 0.408583 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9127 | −0.479015 | ||||||||
\(520\) | 15.0873 | 0.661621 | ||||||||
\(521\) | 23.9725 | 1.05026 | 0.525128 | − | 0.851023i | \(-0.324017\pi\) | ||||
0.525128 | + | 0.851023i | \(0.324017\pi\) | |||||||
\(522\) | 4.54364 | 0.198870 | ||||||||
\(523\) | −20.6814 | −0.904335 | −0.452168 | − | 0.891933i | \(-0.649349\pi\) | ||||
−0.452168 | + | 0.891933i | \(0.649349\pi\) | |||||||
\(524\) | 13.8990 | 0.607181 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.6402 | 1.03076 | ||||||||
\(527\) | 5.08727 | 0.221605 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −21.3354 | −0.927625 | ||||||||
\(530\) | −15.0873 | −0.655349 | ||||||||
\(531\) | 9.52991 | 0.413563 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.4520 | 1.31902 | ||||||||
\(534\) | −6.50686 | −0.281580 | ||||||||
\(535\) | −47.9074 | −2.07122 | ||||||||
\(536\) | 3.54364 | 0.153062 | ||||||||
\(537\) | 12.9495 | 0.558812 | ||||||||
\(538\) | 15.1524 | 0.653268 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.74657 | 0.118193 | ||||||||
\(541\) | 35.9074 | 1.54378 | 0.771890 | − | 0.635757i | \(-0.219312\pi\) | ||||
0.771890 | + | 0.635757i | \(0.219312\pi\) | |||||||
\(542\) | −18.9863 | −0.815530 | ||||||||
\(543\) | 7.59414 | 0.325896 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −4.55736 | −0.195216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12405 | −0.219088 | −0.109544 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109544 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(548\) | 5.49314 | 0.234655 | ||||||||
\(549\) | 1.65929 | 0.0708169 | ||||||||
\(550\) | 2.54364 | 0.108461 | ||||||||
\(551\) | 36.5162 | 1.55564 | ||||||||
\(552\) | 1.29021 | 0.0549148 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.4794 | 1.04003 | ||||||||
\(555\) | −11.0873 | −0.470629 | ||||||||
\(556\) | −13.6309 | −0.578079 | ||||||||
\(557\) | −12.8760 | −0.545572 | −0.272786 | − | 0.962075i | \(-0.587945\pi\) | ||||
−0.272786 | + | 0.962075i | \(0.587945\pi\) | |||||||
\(558\) | −5.08727 | −0.215361 | ||||||||
\(559\) | 22.1745 | 0.937883 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | −12.0873 | −0.509871 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | −9.29021 | −0.391188 | ||||||||
\(565\) | 19.4657 | 0.818927 | ||||||||
\(566\) | −4.68141 | −0.196774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.54364 | 0.106729 | ||||||||
\(569\) | 21.3554 | 0.895263 | 0.447632 | − | 0.894218i | \(-0.352268\pi\) | ||||
0.447632 | + | 0.894218i | \(0.352268\pi\) | |||||||
\(570\) | 22.0735 | 0.924559 | ||||||||
\(571\) | 7.45636 | 0.312039 | 0.156020 | − | 0.987754i | \(-0.450134\pi\) | ||||
0.156020 | + | 0.987754i | \(0.450134\pi\) | |||||||
\(572\) | −5.49314 | −0.229680 | ||||||||
\(573\) | −18.9863 | −0.793163 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.28181 | −0.136861 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.64464 | −0.234989 | −0.117495 | − | 0.993074i | \(-0.537486\pi\) | ||||
−0.117495 | + | 0.993074i | \(0.537486\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | 21.5667 | 0.896281 | ||||||||
\(580\) | −12.4794 | −0.518179 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.0872743 | −0.00361763 | ||||||||
\(583\) | 5.49314 | 0.227502 | ||||||||
\(584\) | 8.58041 | 0.355060 | ||||||||
\(585\) | 15.0873 | 0.623782 | ||||||||
\(586\) | 11.6309 | 0.480469 | ||||||||
\(587\) | 34.4059 | 1.42008 | 0.710041 | − | 0.704160i | \(-0.248676\pi\) | ||||
0.710041 | + | 0.704160i | \(0.248676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.8853 | −1.68465 | ||||||||
\(590\) | −26.1745 | −1.07759 | ||||||||
\(591\) | 3.12405 | 0.128506 | ||||||||
\(592\) | −4.03677 | −0.165910 | ||||||||
\(593\) | 18.7182 | 0.768664 | 0.384332 | − | 0.923195i | \(-0.374432\pi\) | ||||
0.384332 | + | 0.923195i | \(0.374432\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0368 | 0.656892 | ||||||||
\(597\) | −26.0735 | −1.06712 | ||||||||
\(598\) | 7.08727 | 0.289820 | ||||||||
\(599\) | 10.4143 | 0.425515 | 0.212757 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212757 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(600\) | −2.54364 | −0.103844 | ||||||||
\(601\) | −25.0873 | −1.02333 | −0.511666 | − | 0.859185i | \(-0.670971\pi\) | ||||
−0.511666 | + | 0.859185i | \(0.670971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.54364 | 0.144308 | ||||||||
\(604\) | −5.69607 | −0.231770 | ||||||||
\(605\) | −2.74657 | −0.111664 | ||||||||
\(606\) | 13.0230 | 0.529025 | ||||||||
\(607\) | −31.9074 | −1.29508 | −0.647541 | − | 0.762031i | \(-0.724202\pi\) | ||||
−0.647541 | + | 0.762031i | \(0.724202\pi\) | |||||||
\(608\) | 8.03677 | 0.325934 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.55736 | −0.184522 | ||||||||
\(611\) | −51.0324 | −2.06455 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 3.42798 | 0.138455 | 0.0692274 | − | 0.997601i | \(-0.477947\pi\) | ||||
0.0692274 | + | 0.997601i | \(0.477947\pi\) | |||||||
\(614\) | 14.0735 | 0.567962 | ||||||||
\(615\) | −15.2260 | −0.613971 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.7550 | 0.513495 | 0.256748 | − | 0.966478i | \(-0.417349\pi\) | ||||
0.256748 | + | 0.966478i | \(0.417349\pi\) | |||||||
\(618\) | −18.0735 | −0.727025 | ||||||||
\(619\) | 21.5897 | 0.867765 | 0.433882 | − | 0.900970i | \(-0.357143\pi\) | ||||
0.433882 | + | 0.900970i | \(0.357143\pi\) | |||||||
\(620\) | 13.9725 | 0.561151 | ||||||||
\(621\) | 1.29021 | 0.0517742 | ||||||||
\(622\) | −12.2765 | −0.492242 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.49314 | 0.219901 | ||||||||
\(625\) | −31.2481 | −1.24992 | ||||||||
\(626\) | −23.4564 | −0.937505 | ||||||||
\(627\) | −8.03677 | −0.320958 | ||||||||
\(628\) | −18.1103 | −0.722680 | ||||||||
\(629\) | 4.03677 | 0.160957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.23131 | 0.168446 | 0.0842230 | − | 0.996447i | \(-0.473159\pi\) | ||||
0.0842230 | + | 0.996447i | \(0.473159\pi\) | |||||||
\(632\) | 12.2397 | 0.486869 | ||||||||
\(633\) | −15.6677 | −0.622735 | ||||||||
\(634\) | −0.572020 | −0.0227178 | ||||||||
\(635\) | 18.6309 | 0.739345 | ||||||||
\(636\) | −5.49314 | −0.217817 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.54364 | 0.179884 | ||||||||
\(639\) | 2.54364 | 0.100625 | ||||||||
\(640\) | −2.74657 | −0.108568 | ||||||||
\(641\) | 4.07355 | 0.160895 | 0.0804477 | − | 0.996759i | \(-0.474365\pi\) | ||||
0.0804477 | + | 0.996759i | \(0.474365\pi\) | |||||||
\(642\) | −17.4426 | −0.688406 | ||||||||
\(643\) | 19.2618 | 0.759612 | 0.379806 | − | 0.925066i | \(-0.375991\pi\) | ||||
0.379806 | + | 0.925066i | \(0.375991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0873 | −0.436561 | ||||||||
\(646\) | −8.03677 | −0.316203 | ||||||||
\(647\) | 18.8937 | 0.742787 | 0.371393 | − | 0.928476i | \(-0.378880\pi\) | ||||
0.371393 | + | 0.928476i | \(0.378880\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 9.52991 | 0.374082 | ||||||||
\(650\) | −13.9725 | −0.548048 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.4426 | −0.526454 | ||||||||
\(653\) | −8.92112 | −0.349110 | −0.174555 | − | 0.984647i | \(-0.555849\pi\) | ||||
−0.174555 | + | 0.984647i | \(0.555849\pi\) | |||||||
\(654\) | −1.65929 | −0.0648835 | ||||||||
\(655\) | −38.1745 | −1.49160 | ||||||||
\(656\) | −5.54364 | −0.216443 | ||||||||
\(657\) | 8.58041 | 0.334754 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.4426 | 1.77019 | 0.885097 | − | 0.465407i | \(-0.154092\pi\) | ||||
0.885097 | + | 0.465407i | \(0.154092\pi\) | |||||||
\(660\) | 2.74657 | 0.106910 | ||||||||
\(661\) | 29.0230 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(662\) | 7.71819 | 0.299976 | ||||||||
\(663\) | −5.49314 | −0.213336 | ||||||||
\(664\) | 14.5299 | 0.563870 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.03677 | −0.156422 | ||||||||
\(667\) | −5.86223 | −0.226986 | ||||||||
\(668\) | −23.5667 | −0.911822 | ||||||||
\(669\) | 2.40586 | 0.0930160 | ||||||||
\(670\) | −9.73284 | −0.376012 | ||||||||
\(671\) | 1.65929 | 0.0640563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2481 | −0.626318 | −0.313159 | − | 0.949701i | \(-0.601387\pi\) | ||||
−0.313159 | + | 0.949701i | \(0.601387\pi\) | |||||||
\(674\) | 28.5530 | 1.09982 | ||||||||
\(675\) | −2.54364 | −0.0979046 | ||||||||
\(676\) | 17.1745 | 0.660560 | ||||||||
\(677\) | 3.88968 | 0.149493 | 0.0747463 | − | 0.997203i | \(-0.476185\pi\) | ||||
0.0747463 | + | 0.997203i | \(0.476185\pi\) | |||||||
\(678\) | 7.08727 | 0.272185 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.74657 | 0.105326 | ||||||||
\(681\) | 2.45636 | 0.0941280 | ||||||||
\(682\) | −5.08727 | −0.194802 | ||||||||
\(683\) | 5.80546 | 0.222140 | 0.111070 | − | 0.993813i | \(-0.464572\pi\) | ||||
0.111070 | + | 0.993813i | \(0.464572\pi\) | |||||||
\(684\) | 8.03677 | 0.307294 | ||||||||
\(685\) | −15.0873 | −0.576455 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5804 | −0.403668 | ||||||||
\(688\) | −4.03677 | −0.153901 | ||||||||
\(689\) | −30.1745 | −1.14956 | ||||||||
\(690\) | −3.54364 | −0.134904 | ||||||||
\(691\) | 6.35536 | 0.241769 | 0.120885 | − | 0.992667i | \(-0.461427\pi\) | ||||
0.120885 | + | 0.992667i | \(0.461427\pi\) | |||||||
\(692\) | 10.9127 | 0.414840 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.4426 | −0.889870 | ||||||||
\(695\) | 37.4382 | 1.42011 | ||||||||
\(696\) | −4.54364 | −0.172226 | ||||||||
\(697\) | 5.54364 | 0.209980 | ||||||||
\(698\) | −25.7328 | −0.974002 | ||||||||
\(699\) | 7.07355 | 0.267546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.86223 | 0.221413 | 0.110707 | − | 0.993853i | \(-0.464689\pi\) | ||||
0.110707 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(702\) | 5.49314 | 0.207325 | ||||||||
\(703\) | −32.4426 | −1.22360 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 25.5162 | 0.960995 | ||||||||
\(706\) | 18.4059 | 0.692714 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.52991 | −0.358156 | ||||||||
\(709\) | −13.4564 | −0.505364 | −0.252682 | − | 0.967549i | \(-0.581313\pi\) | ||||
−0.252682 | + | 0.967549i | \(0.581313\pi\) | |||||||
\(710\) | −6.98627 | −0.262190 | ||||||||
\(711\) | 12.2397 | 0.459025 | ||||||||
\(712\) | 6.50686 | 0.243855 | ||||||||
\(713\) | 6.56363 | 0.245810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0873 | 0.564232 | ||||||||
\(716\) | −12.9495 | −0.483946 | ||||||||
\(717\) | −7.66769 | −0.286355 | ||||||||
\(718\) | −31.9725 | −1.19320 | ||||||||
\(719\) | 24.2765 | 0.905360 | 0.452680 | − | 0.891673i | \(-0.350468\pi\) | ||||
0.452680 | + | 0.891673i | \(0.350468\pi\) | |||||||
\(720\) | −2.74657 | −0.102359 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 45.5897 | 1.69667 | ||||||||
\(723\) | −25.0598 | −0.931985 | ||||||||
\(724\) | −7.59414 | −0.282234 | ||||||||
\(725\) | 11.5574 | 0.429230 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 22.1471 | 0.821390 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.5667 | −0.872242 | ||||||||
\(731\) | 4.03677 | 0.149305 | ||||||||
\(732\) | −1.65929 | −0.0613293 | ||||||||
\(733\) | 5.32698 | 0.196756 | 0.0983782 | − | 0.995149i | \(-0.468635\pi\) | ||||
0.0983782 | + | 0.995149i | \(0.468635\pi\) | |||||||
\(734\) | −36.4794 | −1.34648 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.29021 | −0.0475576 | ||||||||
\(737\) | 3.54364 | 0.130532 | ||||||||
\(738\) | −5.54364 | −0.204064 | ||||||||
\(739\) | −25.2618 | −0.929271 | −0.464636 | − | 0.885502i | \(-0.653815\pi\) | ||||
−0.464636 | + | 0.885502i | \(0.653815\pi\) | |||||||
\(740\) | 11.0873 | 0.407576 | ||||||||
\(741\) | 44.1471 | 1.62178 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4196 | −0.932554 | −0.466277 | − | 0.884639i | \(-0.654405\pi\) | ||||
−0.466277 | + | 0.884639i | \(0.654405\pi\) | |||||||
\(744\) | 5.08727 | 0.186509 | ||||||||
\(745\) | −44.0461 | −1.61372 | ||||||||
\(746\) | −20.3133 | −0.743721 | ||||||||
\(747\) | 14.5299 | 0.531622 | ||||||||
\(748\) | −1.00000 | −0.0365636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.74657 | −0.246350 | ||||||||
\(751\) | −40.5530 | −1.47980 | −0.739899 | − | 0.672718i | \(-0.765127\pi\) | ||||
−0.739899 | + | 0.672718i | \(0.765127\pi\) | |||||||
\(752\) | 9.29021 | 0.338779 | ||||||||
\(753\) | −25.0230 | −0.911891 | ||||||||
\(754\) | −24.9588 | −0.908947 | ||||||||
\(755\) | 15.6446 | 0.569367 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3554 | 0.485409 | 0.242704 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242704 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(758\) | 9.44264 | 0.342972 | ||||||||
\(759\) | 1.29021 | 0.0468315 | ||||||||
\(760\) | −22.0735 | −0.800692 | ||||||||
\(761\) | −18.4564 | −0.669043 | −0.334521 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334521 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(762\) | 6.78334 | 0.245735 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.9863 | 0.686899 | ||||||||
\(765\) | 2.74657 | 0.0993024 | ||||||||
\(766\) | −23.7045 | −0.856477 | ||||||||
\(767\) | −52.3491 | −1.89022 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −49.9158 | −1.80001 | −0.900005 | − | 0.435881i | \(-0.856437\pi\) | ||||
−0.900005 | + | 0.435881i | \(0.856437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5069 | −0.378395 | ||||||||
\(772\) | −21.5667 | −0.776202 | ||||||||
\(773\) | 42.1387 | 1.51562 | 0.757812 | − | 0.652473i | \(-0.226268\pi\) | ||||
0.757812 | + | 0.652473i | \(0.226268\pi\) | |||||||
\(774\) | −4.03677 | −0.145099 | ||||||||
\(775\) | −12.9402 | −0.464825 | ||||||||
\(776\) | 0.0872743 | 0.00313296 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.25343 | −0.0449377 | ||||||||
\(779\) | −44.5530 | −1.59628 | ||||||||
\(780\) | −15.0873 | −0.540211 | ||||||||
\(781\) | 2.54364 | 0.0910185 | ||||||||
\(782\) | 1.29021 | 0.0461377 | ||||||||
\(783\) | −4.54364 | −0.162376 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.7412 | 1.77534 | ||||||||
\(786\) | −13.8990 | −0.495761 | ||||||||
\(787\) | 34.3584 | 1.22475 | 0.612373 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612373 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(788\) | −3.12405 | −0.111290 | ||||||||
\(789\) | −23.6402 | −0.841615 | ||||||||
\(790\) | −33.6172 | −1.19605 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −9.11473 | −0.323673 | ||||||||
\(794\) | −28.6172 | −1.01559 | ||||||||
\(795\) | 15.0873 | 0.535090 | ||||||||
\(796\) | 26.0735 | 0.924152 | ||||||||
\(797\) | 18.1387 | 0.642506 | 0.321253 | − | 0.946993i | \(-0.395896\pi\) | ||||
0.321253 | + | 0.946993i | \(0.395896\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.29021 | −0.328664 | ||||||||
\(800\) | 2.54364 | 0.0899312 | ||||||||
\(801\) | 6.50686 | 0.229909 | ||||||||
\(802\) | 0.405862 | 0.0143315 | ||||||||
\(803\) | 8.58041 | 0.302796 | ||||||||
\(804\) | −3.54364 | −0.124974 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27.9451 | 0.984324 | ||||||||
\(807\) | −15.1524 | −0.533391 | ||||||||
\(808\) | −13.0230 | −0.458149 | ||||||||
\(809\) | −17.5436 | −0.616801 | −0.308401 | − | 0.951257i | \(-0.599794\pi\) | ||||
−0.308401 | + | 0.951257i | \(0.599794\pi\) | |||||||
\(810\) | −2.74657 | −0.0965046 | ||||||||
\(811\) | 43.0873 | 1.51300 | 0.756499 | − | 0.653994i | \(-0.226908\pi\) | ||||
0.756499 | + | 0.653994i | \(0.226908\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.9863 | 0.665878 | ||||||||
\(814\) | −4.03677 | −0.141489 | ||||||||
\(815\) | 36.9211 | 1.29329 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −32.4426 | −1.13502 | ||||||||
\(818\) | 32.7550 | 1.14525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.2260 | 0.531714 | ||||||||
\(821\) | 2.10100 | 0.0733255 | 0.0366627 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366627 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(822\) | −5.49314 | −0.191595 | ||||||||
\(823\) | 19.7412 | 0.688136 | 0.344068 | − | 0.938945i | \(-0.388195\pi\) | ||||
0.344068 | + | 0.938945i | \(0.388195\pi\) | |||||||
\(824\) | 18.0735 | 0.629622 | ||||||||
\(825\) | −2.54364 | −0.0885581 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.7182 | 0.824762 | 0.412381 | − | 0.911011i | \(-0.364697\pi\) | ||||
0.412381 | + | 0.911011i | \(0.364697\pi\) | |||||||
\(828\) | −1.29021 | −0.0448377 | ||||||||
\(829\) | −39.9632 | −1.38798 | −0.693990 | − | 0.719985i | \(-0.744149\pi\) | ||||
−0.693990 | + | 0.719985i | \(0.744149\pi\) | |||||||
\(830\) | −39.9074 | −1.38521 | ||||||||
\(831\) | −24.4794 | −0.849181 | ||||||||
\(832\) | −5.49314 | −0.190440 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.6309 | 0.472000 | ||||||||
\(835\) | 64.7275 | 2.23999 | ||||||||
\(836\) | 8.03677 | 0.277958 | ||||||||
\(837\) | 5.08727 | 0.175842 | ||||||||
\(838\) | 15.9358 | 0.550492 | ||||||||
\(839\) | −29.0682 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.35536 | −0.288116 | ||||||||
\(842\) | −27.1240 | −0.934756 | ||||||||
\(843\) | 12.0873 | 0.416308 | ||||||||
\(844\) | 15.6677 | 0.539304 | ||||||||
\(845\) | −47.1711 | −1.62273 | ||||||||
\(846\) | 9.29021 | 0.319404 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.49314 | 0.188635 | ||||||||
\(849\) | 4.68141 | 0.160666 | ||||||||
\(850\) | −2.54364 | −0.0872460 | ||||||||
\(851\) | 5.20827 | 0.178537 | ||||||||
\(852\) | −2.54364 | −0.0871436 | ||||||||
\(853\) | −20.2397 | −0.692994 | −0.346497 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346497 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0735 | −0.754899 | ||||||||
\(856\) | 17.4426 | 0.596177 | ||||||||
\(857\) | 12.1608 | 0.415406 | 0.207703 | − | 0.978192i | \(-0.433401\pi\) | ||||
0.207703 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(858\) | 5.49314 | 0.187533 | ||||||||
\(859\) | 14.5299 | 0.495754 | 0.247877 | − | 0.968791i | \(-0.420267\pi\) | ||||
0.247877 | + | 0.968791i | \(0.420267\pi\) | |||||||
\(860\) | 11.0873 | 0.378073 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.6265 | −1.38374 | ||||||||
\(863\) | −13.5857 | −0.462464 | −0.231232 | − | 0.972899i | \(-0.574276\pi\) | ||||
−0.231232 | + | 0.972899i | \(0.574276\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −29.9725 | −1.01910 | ||||||||
\(866\) | −1.10100 | −0.0374135 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2397 | 0.415204 | ||||||||
\(870\) | 12.4794 | 0.423092 | ||||||||
\(871\) | −19.4657 | −0.659569 | ||||||||
\(872\) | 1.65929 | 0.0561908 | ||||||||
\(873\) | 0.0872743 | 0.00295379 | ||||||||
\(874\) | −10.3691 | −0.350740 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.58041 | −0.289905 | ||||||||
\(877\) | −2.06516 | −0.0697354 | −0.0348677 | − | 0.999392i | \(-0.511101\pi\) | ||||
−0.0348677 | + | 0.999392i | \(0.511101\pi\) | |||||||
\(878\) | −22.8569 | −0.771383 | ||||||||
\(879\) | −11.6309 | −0.392301 | ||||||||
\(880\) | −2.74657 | −0.0925868 | ||||||||
\(881\) | 3.08727 | 0.104013 | 0.0520065 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520065 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8927 | 0.736749 | 0.368375 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368375 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(884\) | 5.49314 | 0.184754 | ||||||||
\(885\) | 26.1745 | 0.879848 | ||||||||
\(886\) | −9.55736 | −0.321086 | ||||||||
\(887\) | −37.7412 | −1.26723 | −0.633613 | − | 0.773650i | \(-0.718429\pi\) | ||||
−0.633613 | + | 0.773650i | \(0.718429\pi\) | |||||||
\(888\) | 4.03677 | 0.135465 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17.8715 | −0.599056 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −2.40586 | −0.0805542 | ||||||||
\(893\) | 74.6633 | 2.49851 | ||||||||
\(894\) | −16.0368 | −0.536350 | ||||||||
\(895\) | 35.5667 | 1.18886 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.08727 | −0.236637 | ||||||||
\(898\) | 0.681412 | 0.0227390 | ||||||||
\(899\) | −23.1147 | −0.770919 | ||||||||
\(900\) | 2.54364 | 0.0847879 | ||||||||
\(901\) | −5.49314 | −0.183003 | ||||||||
\(902\) | −5.54364 | −0.184583 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.08727 | −0.235719 | ||||||||
\(905\) | 20.8578 | 0.693337 | ||||||||
\(906\) | 5.69607 | 0.189239 | ||||||||
\(907\) | 31.5897 | 1.04892 | 0.524460 | − | 0.851435i | \(-0.324267\pi\) | ||||
0.524460 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(908\) | −2.45636 | −0.0815173 | ||||||||
\(909\) | −13.0230 | −0.431947 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.7422 | −0.919139 | −0.459569 | − | 0.888142i | \(-0.651996\pi\) | ||||
−0.459569 | + | 0.888142i | \(0.651996\pi\) | |||||||
\(912\) | −8.03677 | −0.266124 | ||||||||
\(913\) | 14.5299 | 0.480870 | ||||||||
\(914\) | 18.1471 | 0.600253 | ||||||||
\(915\) | 4.55736 | 0.150662 | ||||||||
\(916\) | 10.5804 | 0.349587 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 18.9304 | 0.624457 | 0.312229 | − | 0.950007i | \(-0.398924\pi\) | ||||
0.312229 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(920\) | 3.54364 | 0.116830 | ||||||||
\(921\) | −14.0735 | −0.463739 | ||||||||
\(922\) | 41.7045 | 1.37346 | ||||||||
\(923\) | −13.9725 | −0.459912 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.2681 | −0.337613 | ||||||||
\(926\) | −28.5804 | −0.939211 | ||||||||
\(927\) | 18.0735 | 0.593613 | ||||||||
\(928\) | 4.54364 | 0.149152 | ||||||||
\(929\) | −13.7687 | −0.451736 | −0.225868 | − | 0.974158i | \(-0.572522\pi\) | ||||
−0.225868 | + | 0.974158i | \(0.572522\pi\) | |||||||
\(930\) | −13.9725 | −0.458178 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.07355 | −0.231702 | ||||||||
\(933\) | 12.2765 | 0.401914 | ||||||||
\(934\) | −5.38282 | −0.176131 | ||||||||
\(935\) | 2.74657 | 0.0898224 | ||||||||
\(936\) | −5.49314 | −0.179549 | ||||||||
\(937\) | 17.2618 | 0.563919 | 0.281960 | − | 0.959426i | \(-0.409016\pi\) | ||||
0.281960 | + | 0.959426i | \(0.409016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.4564 | 0.765469 | ||||||||
\(940\) | −25.5162 | −0.832246 | ||||||||
\(941\) | 37.6309 | 1.22673 | 0.613366 | − | 0.789799i | \(-0.289815\pi\) | ||||
0.613366 | + | 0.789799i | \(0.289815\pi\) | |||||||
\(942\) | 18.1103 | 0.590066 | ||||||||
\(943\) | 7.15243 | 0.232915 | ||||||||
\(944\) | 9.52991 | 0.310172 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.03677 | −0.131247 | ||||||||
\(947\) | −7.73191 | −0.251253 | −0.125627 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125627 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(948\) | −12.2397 | −0.397527 | ||||||||
\(949\) | −47.1334 | −1.53001 | ||||||||
\(950\) | 20.4426 | 0.663247 | ||||||||
\(951\) | 0.572020 | 0.0185490 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6770 | −0.669794 | −0.334897 | − | 0.942255i | \(-0.608702\pi\) | ||||
−0.334897 | + | 0.942255i | \(0.608702\pi\) | |||||||
\(954\) | 5.49314 | 0.177847 | ||||||||
\(955\) | −52.1471 | −1.68744 | ||||||||
\(956\) | 7.66769 | 0.247991 | ||||||||
\(957\) | −4.54364 | −0.146875 | ||||||||
\(958\) | −14.4794 | −0.467808 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.74657 | 0.0886451 | ||||||||
\(961\) | −5.11964 | −0.165150 | ||||||||
\(962\) | 22.1745 | 0.714936 | ||||||||
\(963\) | 17.4426 | 0.562081 | ||||||||
\(964\) | 25.0598 | 0.807122 | ||||||||
\(965\) | 59.2344 | 1.90682 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.7235 | 0.505634 | 0.252817 | − | 0.967514i | \(-0.418643\pi\) | ||||
0.252817 | + | 0.967514i | \(0.418643\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 8.03677 | 0.258178 | ||||||||
\(970\) | −0.239705 | −0.00769646 | ||||||||
\(971\) | −8.24810 | −0.264694 | −0.132347 | − | 0.991203i | \(-0.542251\pi\) | ||||
−0.132347 | + | 0.991203i | \(0.542251\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.43332 | −0.270221 | ||||||||
\(975\) | 13.9725 | 0.447480 | ||||||||
\(976\) | 1.65929 | 0.0531127 | ||||||||
\(977\) | −35.3354 | −1.13048 | −0.565239 | − | 0.824927i | \(-0.691216\pi\) | ||||
−0.565239 | + | 0.824927i | \(0.691216\pi\) | |||||||
\(978\) | 13.4426 | 0.429848 | ||||||||
\(979\) | 6.50686 | 0.207960 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.65929 | 0.0529772 | ||||||||
\(982\) | −38.6770 | −1.23423 | ||||||||
\(983\) | 9.14311 | 0.291620 | 0.145810 | − | 0.989313i | \(-0.453421\pi\) | ||||
0.145810 | + | 0.989313i | \(0.453421\pi\) | |||||||
\(984\) | 5.54364 | 0.176725 | ||||||||
\(985\) | 8.58041 | 0.273395 | ||||||||
\(986\) | −4.54364 | −0.144699 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −44.1471 | −1.40451 | ||||||||
\(989\) | 5.20827 | 0.165613 | ||||||||
\(990\) | −2.74657 | −0.0872917 | ||||||||
\(991\) | 35.4657 | 1.12660 | 0.563302 | − | 0.826251i | \(-0.309531\pi\) | ||||
0.563302 | + | 0.826251i | \(0.309531\pi\) | |||||||
\(992\) | −5.08727 | −0.161521 | ||||||||
\(993\) | −7.71819 | −0.244929 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71.6128 | −2.27028 | ||||||||
\(996\) | −14.5299 | −0.460398 | ||||||||
\(997\) | −45.4931 | −1.44078 | −0.720391 | − | 0.693568i | \(-0.756038\pi\) | ||||
−0.720391 | + | 0.693568i | \(0.756038\pi\) | |||||||
\(998\) | 38.0461 | 1.20433 | ||||||||
\(999\) | 4.03677 | 0.127718 |
(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 | 3234.2.a.bg.1.1 | 3 | ||
3.2 | odd | 2 | 9702.2.a.du.1.3 | 3 | |||
7.3 | odd | 6 | 462.2.i.f.331.1 | yes | 6 | ||
7.5 | odd | 6 | 462.2.i.f.67.1 | ✓ | 6 | ||
7.6 | odd | 2 | 3234.2.a.bi.1.3 | 3 | |||
21.5 | even | 6 | 1386.2.k.w.991.3 | 6 | |||
21.17 | even | 6 | 1386.2.k.w.793.3 | 6 | |||
21.20 | even | 2 | 9702.2.a.dt.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.f.67.1 | ✓ | 6 | 7.5 | odd | 6 | ||
462.2.i.f.331.1 | yes | 6 | 7.3 | odd | 6 | ||
1386.2.k.w.793.3 | 6 | 21.17 | even | 6 | |||
1386.2.k.w.991.3 | 6 | 21.5 | even | 6 | |||
3234.2.a.bg.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3234.2.a.bi.1.3 | 3 | 7.6 | odd | 2 | |||
9702.2.a.dt.1.1 | 3 | 21.20 | even | 2 | |||
9702.2.a.du.1.3 | 3 | 3.2 | odd | 2 |