Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} - 137 x^{8} - 121665 x^{7} + 60168 x^{6} + 172218 x^{5} - 138024 x^{4} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.282383\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.282383 | 0.126286 | 0.0631428 | − | 0.998005i | \(-0.479888\pi\) | ||||
0.0631428 | + | 0.998005i | \(0.479888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.02462 | 1.89913 | 0.949565 | − | 0.313571i | \(-0.101525\pi\) | ||||
0.949565 | + | 0.313571i | \(0.101525\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61549 | 0.487089 | 0.243545 | − | 0.969890i | \(-0.421690\pi\) | ||||
0.243545 | + | 0.969890i | \(0.421690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.572564 | 0.158801 | 0.0794004 | − | 0.996843i | \(-0.474699\pi\) | ||||
0.0794004 | + | 0.996843i | \(0.474699\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.282383 | −0.0729110 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.464906 | −0.112756 | −0.0563781 | − | 0.998409i | \(-0.517955\pi\) | ||||
−0.0563781 | + | 0.998409i | \(0.517955\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.460906 | 0.105739 | 0.0528695 | − | 0.998601i | \(-0.483163\pi\) | ||||
0.0528695 | + | 0.998601i | \(0.483163\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.02462 | −1.09646 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92026 | −0.984052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.38151 | −0.248127 | −0.124064 | − | 0.992274i | \(-0.539593\pi\) | ||||
−0.124064 | + | 0.992274i | \(0.539593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.61549 | −0.281221 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41887 | 0.239833 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.37755 | 0.719665 | 0.359832 | − | 0.933017i | \(-0.382834\pi\) | ||||
0.359832 | + | 0.933017i | \(0.382834\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.572564 | −0.0916836 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.95258 | 0.461115 | 0.230557 | − | 0.973059i | \(-0.425945\pi\) | ||||
0.230557 | + | 0.973059i | \(0.425945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.06819 | −0.925390 | −0.462695 | − | 0.886518i | \(-0.653117\pi\) | ||||
−0.462695 | + | 0.886518i | \(0.653117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.282383 | 0.0420952 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.36723 | 0.928756 | 0.464378 | − | 0.885637i | \(-0.346278\pi\) | ||||
0.464378 | + | 0.885637i | \(0.346278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.2468 | 2.60669 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.464906 | 0.0650998 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.96026 | −0.818705 | −0.409353 | − | 0.912376i | \(-0.634245\pi\) | ||||
−0.409353 | + | 0.912376i | \(0.634245\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.456188 | 0.0615124 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.460906 | −0.0610484 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.5554 | 1.63457 | 0.817284 | − | 0.576235i | \(-0.195479\pi\) | ||||
0.817284 | + | 0.576235i | \(0.195479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.82665 | 1.00210 | 0.501050 | − | 0.865418i | \(-0.332947\pi\) | ||||
0.501050 | + | 0.865418i | \(0.332947\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.02462 | 0.633043 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.161682 | 0.0200542 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.23458 | −0.517336 | −0.258668 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258668 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.7536 | 1.63225 | 0.816126 | − | 0.577873i | \(-0.196117\pi\) | ||||
0.816126 | + | 0.577873i | \(0.196117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.71699 | 0.669123 | 0.334561 | − | 0.942374i | \(-0.391412\pi\) | ||||
0.334561 | + | 0.942374i | \(0.391412\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.92026 | 0.568143 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.11724 | 0.925046 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.81674 | −0.654435 | −0.327217 | − | 0.944949i | \(-0.606111\pi\) | ||||
−0.327217 | + | 0.944949i | \(0.606111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1920 | 1.44802 | 0.724008 | − | 0.689792i | \(-0.242298\pi\) | ||||
0.724008 | + | 0.689792i | \(0.242298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.131282 | −0.0142395 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.33893 | 0.565926 | 0.282963 | − | 0.959131i | \(-0.408683\pi\) | ||||
0.282963 | + | 0.959131i | \(0.408683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.87692 | 0.301583 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.38151 | 0.143256 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.130152 | 0.0133533 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.5054 | −1.77740 | −0.888702 | − | 0.458486i | \(-0.848392\pi\) | ||||
−0.888702 | + | 0.458486i | \(0.848392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.61549 | 0.162363 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.9008 | 1.18417 | 0.592085 | − | 0.805876i | \(-0.298305\pi\) | ||||
0.592085 | + | 0.805876i | \(0.298305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.02283 | −0.691980 | −0.345990 | − | 0.938238i | \(-0.612457\pi\) | ||||
−0.345990 | + | 0.938238i | \(0.612457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41887 | −0.138467 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4809 | −1.30325 | −0.651626 | − | 0.758540i | \(-0.725913\pi\) | ||||
−0.651626 | + | 0.758540i | \(0.725913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.29204 | −0.698451 | −0.349226 | − | 0.937039i | \(-0.613555\pi\) | ||||
−0.349226 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.37755 | −0.415499 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.9016 | −1.96625 | −0.983127 | − | 0.182925i | \(-0.941443\pi\) | ||||
−0.983127 | + | 0.182925i | \(0.941443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.282383 | 0.0263324 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.572564 | 0.0529336 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.33598 | −0.214139 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.39018 | −0.762744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.95258 | −0.266225 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.80131 | −0.250557 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5052 | 1.64207 | 0.821037 | − | 0.570874i | \(-0.193396\pi\) | ||||
0.821037 | + | 0.570874i | \(0.193396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.06819 | 0.534274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6604 | 1.54300 | 0.771498 | − | 0.636232i | \(-0.219508\pi\) | ||||
0.771498 | + | 0.636232i | \(0.219508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.31588 | 0.200812 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.282383 | −0.0243037 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0006 | −1.11072 | −0.555358 | − | 0.831612i | \(-0.687419\pi\) | ||||
−0.555358 | + | 0.831612i | \(0.687419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.446628 | −0.0378825 | −0.0189412 | − | 0.999821i | \(-0.506030\pi\) | ||||
−0.0189412 | + | 0.999821i | \(0.506030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.36723 | −0.536217 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.924973 | 0.0773501 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.282383 | 0.0234506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.2468 | −1.50497 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.48939 | −0.203939 | −0.101969 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101969 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.97623 | 0.567717 | 0.283859 | − | 0.958866i | \(-0.408385\pi\) | ||||
0.283859 | + | 0.958866i | \(0.408385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.464906 | −0.0375854 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.390116 | −0.0313349 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.517289 | 0.0412842 | 0.0206421 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206421 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.96026 | 0.472680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.02462 | 0.395996 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5780 | 0.906858 | 0.453429 | − | 0.891292i | \(-0.350200\pi\) | ||||
0.453429 | + | 0.891292i | \(0.350200\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.456188 | −0.0355142 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.90578 | −0.689150 | −0.344575 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344575 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6722 | −0.974782 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.460906 | 0.0352463 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0923 | 1.37553 | 0.687765 | − | 0.725933i | \(-0.258592\pi\) | ||||
0.687765 | + | 0.725933i | \(0.258592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.7225 | −1.86884 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.5554 | −0.943719 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.62128 | 0.569641 | 0.284820 | − | 0.958581i | \(-0.408066\pi\) | ||||
0.284820 | + | 0.958581i | \(0.408066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.9090 | 1.55415 | 0.777075 | − | 0.629408i | \(-0.216702\pi\) | ||||
0.777075 | + | 0.629408i | \(0.216702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.82665 | −0.578563 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.23615 | 0.0908833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.751052 | −0.0549224 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.02462 | −0.365488 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.10381 | 0.369299 | 0.184649 | − | 0.982804i | \(-0.440885\pi\) | ||||
0.184649 | + | 0.982804i | \(0.440885\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.73467 | −0.556754 | −0.278377 | − | 0.960472i | \(-0.589796\pi\) | ||||
−0.278377 | + | 0.960472i | \(0.589796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.161682 | −0.0115783 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0993 | −0.719545 | −0.359772 | − | 0.933040i | \(-0.617146\pi\) | ||||
−0.359772 | + | 0.933040i | \(0.617146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0031 | −0.850880 | −0.425440 | − | 0.904987i | \(-0.639881\pi\) | ||||
−0.425440 | + | 0.904987i | \(0.639881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.23458 | 0.298684 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.02462 | 0.352659 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.833758 | 0.0582322 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.744590 | 0.0515043 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.53376 | 0.587488 | 0.293744 | − | 0.955884i | \(-0.405099\pi\) | ||||
0.293744 | + | 0.955884i | \(0.405099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.7536 | −0.942382 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.71355 | −0.116863 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.94159 | −0.471226 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.71699 | −0.386318 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.266188 | −0.0179058 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.1107 | −1.27975 | −0.639874 | − | 0.768480i | \(-0.721013\pi\) | ||||
−0.639874 | + | 0.768480i | \(0.721013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.92026 | −0.328017 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.2099 | 0.810402 | 0.405201 | − | 0.914228i | \(-0.367202\pi\) | ||||
0.405201 | + | 0.914228i | \(0.367202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.4713 | −1.81536 | −0.907678 | − | 0.419668i | \(-0.862147\pi\) | ||||
−0.907678 | + | 0.419668i | \(0.862147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.11724 | −0.534075 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.9922 | 1.44076 | 0.720378 | − | 0.693582i | \(-0.243968\pi\) | ||||
0.720378 | + | 0.693582i | \(0.243968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79800 | 0.117288 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.81674 | 0.377838 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.93422 | 0.254483 | 0.127242 | − | 0.991872i | \(-0.459388\pi\) | ||||
0.127242 | + | 0.991872i | \(0.459388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.44231 | 0.479401 | 0.239701 | − | 0.970847i | \(-0.422951\pi\) | ||||
0.239701 | + | 0.970847i | \(0.422951\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.15260 | 0.329188 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.263898 | 0.0167914 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1920 | −0.836012 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5898 | −1.23650 | −0.618250 | − | 0.785982i | \(-0.712158\pi\) | ||||
−0.618250 | + | 0.785982i | \(0.712158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61549 | 0.101565 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.131282 | 0.00822117 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.9223 | 1.11796 | 0.558982 | − | 0.829180i | \(-0.311192\pi\) | ||||
0.558982 | + | 0.829180i | \(0.311192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.9955 | 1.36674 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2174 | 0.630034 | 0.315017 | − | 0.949086i | \(-0.397990\pi\) | ||||
0.315017 | + | 0.949086i | \(0.397990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68308 | −0.103391 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.33893 | −0.326737 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.1372 | 1.34973 | 0.674865 | − | 0.737942i | \(-0.264202\pi\) | ||||
0.674865 | + | 0.737942i | \(0.264202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0849 | −1.94902 | −0.974510 | − | 0.224345i | \(-0.927976\pi\) | ||||
−0.974510 | + | 0.224345i | \(0.927976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.87692 | −0.174119 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.94864 | −0.479321 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0334 | 0.963353 | 0.481677 | − | 0.876349i | \(-0.340028\pi\) | ||||
0.481677 | + | 0.876349i | \(0.340028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.38151 | −0.0827091 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2874 | 0.911970 | 0.455985 | − | 0.889987i | \(-0.349287\pi\) | ||||
0.455985 | + | 0.889987i | \(0.349287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.5611 | 0.865566 | 0.432783 | − | 0.901498i | \(-0.357532\pi\) | ||||
0.432783 | + | 0.901498i | \(0.357532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.130152 | −0.00770954 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.8356 | 0.875717 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7839 | −0.987286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.5054 | 1.02618 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1553 | 1.52801 | 0.764005 | − | 0.645210i | \(-0.223230\pi\) | ||||
0.764005 | + | 0.645210i | \(0.223230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.54542 | 0.206422 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.61549 | −0.0937404 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.572564 | 0.0331122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4904 | −1.75744 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9008 | −0.683681 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.21012 | 0.126551 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.8745 | −1.30551 | −0.652757 | − | 0.757567i | \(-0.726388\pi\) | ||||
−0.652757 | + | 0.757567i | \(0.726388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.02283 | 0.399515 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.38071 | −0.361817 | −0.180908 | − | 0.983500i | \(-0.557904\pi\) | ||||
−0.180908 | + | 0.983500i | \(0.557904\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.6435 | 1.78859 | 0.894297 | − | 0.447474i | \(-0.147676\pi\) | ||||
0.894297 | + | 0.447474i | \(0.147676\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41887 | 0.0799442 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.40227 | −0.0787591 | −0.0393796 | − | 0.999224i | \(-0.512538\pi\) | ||||
−0.0393796 | + | 0.999224i | \(0.512538\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.61549 | 0.0904502 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.4809 | 0.752433 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.214278 | −0.0119227 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.81716 | −0.156268 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.29204 | 0.403251 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.9929 | 1.76383 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.04905 | 0.387451 | 0.193725 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193725 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.37755 | 0.239888 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.19577 | −0.0653321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3534 | −0.945299 | −0.472649 | − | 0.881251i | \(-0.656702\pi\) | ||||
−0.472649 | + | 0.881251i | \(0.656702\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.9016 | 1.13522 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.23183 | −0.120860 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.5112 | 3.05132 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.282383 | −0.0152030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4903 | −0.831561 | −0.415780 | − | 0.909465i | \(-0.636492\pi\) | ||||
−0.415780 | + | 0.909465i | \(0.636492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.84281 | 0.152172 | 0.0760861 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760861 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.572564 | −0.0305612 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.16169 | 0.327954 | 0.163977 | − | 0.986464i | \(-0.447568\pi\) | ||||
0.163977 | + | 0.986464i | \(0.447568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.88379 | 0.206130 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.33598 | 0.123633 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.4172 | −1.55258 | −0.776290 | − | 0.630376i | \(-0.782901\pi\) | ||||
−0.776290 | + | 0.630376i | \(0.782901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7876 | −0.988819 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.39018 | 0.440370 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.61438 | 0.0845006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.7282 | −1.81280 | −0.906398 | − | 0.422424i | \(-0.861179\pi\) | ||||
−0.906398 | + | 0.422424i | \(0.861179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.95258 | 0.153705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.9481 | −1.55483 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8611 | 1.54615 | 0.773075 | − | 0.634315i | \(-0.218718\pi\) | ||||
0.773075 | + | 0.634315i | \(0.218718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.80131 | 0.144659 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.572564 | 0.0294886 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2483 | −0.731885 | −0.365943 | − | 0.930637i | \(-0.619253\pi\) | ||||
−0.365943 | + | 0.930637i | \(0.619253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.5052 | −0.948052 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.1526 | 0.672065 | 0.336032 | − | 0.941850i | \(-0.390915\pi\) | ||||
0.336032 | + | 0.941850i | \(0.390915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.29217 | 0.116820 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.06819 | −0.308463 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.65181 | −0.387962 | −0.193981 | − | 0.981005i | \(-0.562140\pi\) | ||||
−0.193981 | + | 0.981005i | \(0.562140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.464906 | −0.0235113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.6604 | −0.890849 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.64255 | −0.0826457 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9480 | 0.750219 | 0.375110 | − | 0.926980i | \(-0.377605\pi\) | ||||
0.375110 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.31588 | −0.115939 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.7956 | −1.23823 | −0.619116 | − | 0.785299i | \(-0.712509\pi\) | ||||
−0.619116 | + | 0.785299i | \(0.712509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.791005 | −0.0394028 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.282383 | 0.0140317 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.07190 | 0.350541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0219 | 1.53393 | 0.766967 | − | 0.641687i | \(-0.221765\pi\) | ||||
0.766967 | + | 0.641687i | \(0.221765\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0006 | 0.641272 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 63.0860 | 3.10426 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.72521 | 0.182863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.446628 | 0.0218714 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.8412 | −1.40899 | −0.704493 | − | 0.709711i | \(-0.748825\pi\) | ||||
−0.704493 | + | 0.709711i | \(0.748825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.1017 | 1.95444 | 0.977218 | − | 0.212237i | \(-0.0680749\pi\) | ||||
0.977218 | + | 0.212237i | \(0.0680749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.36723 | 0.309585 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.28746 | 0.110958 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.3260 | 1.90312 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.924973 | −0.0446581 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.6024 | 1.04055 | 0.520275 | − | 0.853999i | \(-0.325829\pi\) | ||||
0.520275 | + | 0.853999i | \(0.325829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1522 | −0.583999 | −0.291999 | − | 0.956418i | \(-0.594321\pi\) | ||||
−0.291999 | + | 0.956418i | \(0.594321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.282383 | −0.0135392 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.460906 | 0.0220481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2017 | −0.486900 | −0.243450 | − | 0.969913i | \(-0.578279\pi\) | ||||
−0.243450 | + | 0.969913i | \(0.578279\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.2468 | 0.868897 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8464 | 0.610353 | 0.305177 | − | 0.952296i | \(-0.401284\pi\) | ||||
0.305177 | + | 0.952296i | \(0.401284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50763 | 0.0714683 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.48939 | 0.117744 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.82169 | −0.274743 | −0.137371 | − | 0.990520i | \(-0.543865\pi\) | ||||
−0.137371 | + | 0.990520i | \(0.543865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.76987 | 0.224604 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.97623 | −0.327772 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.812394 | 0.0380856 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.03855 | 0.376028 | 0.188014 | − | 0.982166i | \(-0.439795\pi\) | ||||
0.188014 | + | 0.982166i | \(0.439795\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.464906 | 0.0216999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0979 | 1.40180 | 0.700901 | − | 0.713259i | \(-0.252782\pi\) | ||||
0.700901 | + | 0.713259i | \(0.252782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.1863 | 1.72820 | 0.864098 | − | 0.503324i | \(-0.167890\pi\) | ||||
0.864098 | + | 0.503324i | \(0.167890\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.390116 | 0.0180912 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.9455 | −1.47826 | −0.739130 | − | 0.673563i | \(-0.764763\pi\) | ||||
−0.739130 | + | 0.673563i | \(0.764763\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.2772 | −0.982488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.517289 | −0.0238354 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.80311 | −0.450748 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.26778 | −0.104053 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.96026 | −0.272902 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.62267 | −0.439671 | −0.219835 | − | 0.975537i | \(-0.570552\pi\) | ||||
−0.219835 | + | 0.975537i | \(0.570552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50643 | 0.114283 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.02462 | −0.228628 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.94323 | −0.224460 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.9992 | 1.54065 | 0.770324 | − | 0.637652i | \(-0.220094\pi\) | ||||
0.770324 | + | 0.637652i | \(0.220094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.5780 | −0.523575 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8256 | −0.714200 | −0.357100 | − | 0.934066i | \(-0.616235\pi\) | ||||
−0.357100 | + | 0.934066i | \(0.616235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.464906 | −0.0209383 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.456188 | 0.0205041 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 69.1067 | 3.09986 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2102 | −0.591369 | −0.295684 | − | 0.955286i | \(-0.595548\pi\) | ||||
−0.295684 | + | 0.955286i | \(0.595548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.90578 | 0.397881 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.5178 | −1.04861 | −0.524303 | − | 0.851532i | \(-0.675674\pi\) | ||||
−0.524303 | + | 0.851532i | \(0.675674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.36057 | 0.149544 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6722 | 0.562791 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8420 | 0.746508 | 0.373254 | − | 0.927729i | \(-0.378242\pi\) | ||||
0.373254 | + | 0.927729i | \(0.378242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.7257 | 1.27075 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.460906 | −0.0203495 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.98313 | −0.0873871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2862 | 0.452387 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0923 | −0.794163 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.3149 | 1.67861 | 0.839303 | − | 0.543665i | \(-0.182964\pi\) | ||||
0.839303 | + | 0.543665i | \(0.182964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.4290 | −0.499754 | −0.249877 | − | 0.968278i | \(-0.580390\pi\) | ||||
−0.249877 | + | 0.968278i | \(0.580390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.7225 | 1.07898 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.642274 | 0.0279779 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5554 | 0.544856 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.69054 | 0.0732254 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.80679 | −0.164582 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.62128 | −0.328882 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.4776 | 1.26969 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.53527 | 0.0660065 | 0.0330033 | − | 0.999455i | \(-0.489493\pi\) | ||||
0.0330033 | + | 0.999455i | \(0.489493\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.9090 | −0.897289 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.05915 | −0.0882043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.7104 | −1.56962 | −0.784812 | − | 0.619735i | \(-0.787240\pi\) | ||||
−0.784812 | + | 0.619735i | \(0.787240\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.82665 | 0.334033 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.460906 | 0.0196352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.2270 | −1.24286 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.23615 | −0.0524715 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7739 | −0.541246 | −0.270623 | − | 0.962685i | \(-0.587230\pi\) | ||||
−0.270623 | + | 0.962685i | \(0.587230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.47443 | −0.146953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.751052 | 0.0317094 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4675 | −0.694024 | −0.347012 | − | 0.937861i | \(-0.612804\pi\) | ||||
−0.347012 | + | 0.937861i | \(0.612804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.90225 | −0.248310 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.02462 | 0.211014 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.85212 | 0.119567 | 0.0597836 | − | 0.998211i | \(-0.480959\pi\) | ||||
0.0597836 | + | 0.998211i | \(0.480959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.9188 | 0.833574 | 0.416787 | − | 0.909004i | \(-0.363156\pi\) | ||||
0.416787 | + | 0.909004i | \(0.363156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.10381 | −0.213215 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.92026 | −0.205189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6175 | −0.816689 | −0.408344 | − | 0.912828i | \(-0.633894\pi\) | ||||
−0.408344 | + | 0.912828i | \(0.633894\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.73467 | 0.321442 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.2851 | 2.74997 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.62876 | −0.398783 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.161682 | 0.00668475 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.1057 | −1.40769 | −0.703846 | − | 0.710353i | \(-0.748535\pi\) | ||||
−0.703846 | + | 0.710353i | \(0.748535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.636747 | −0.0262367 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0993 | 0.415429 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.9271 | −1.51641 | −0.758206 | − | 0.652015i | \(-0.773924\pi\) | ||||
−0.758206 | + | 0.652015i | \(0.773924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.659641 | −0.0270426 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0031 | 0.491256 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.2603 | 0.623520 | 0.311760 | − | 0.950161i | \(-0.399082\pi\) | ||||
0.311760 | + | 0.950161i | \(0.399082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7506 | 1.13197 | 0.565985 | − | 0.824415i | \(-0.308496\pi\) | ||||
0.565985 | + | 0.824415i | \(0.308496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.23458 | −0.172445 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.36925 | −0.0963236 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3706 | 1.15153 | 0.575764 | − | 0.817616i | \(-0.304705\pi\) | ||||
0.575764 | + | 0.817616i | \(0.304705\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.02462 | −0.203608 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.64565 | 0.147487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.47568 | 0.382719 | 0.191360 | − | 0.981520i | \(-0.438710\pi\) | ||||
0.191360 | + | 0.981520i | \(0.438710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.833758 | −0.0336204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8218 | 0.475930 | 0.237965 | − | 0.971274i | \(-0.423520\pi\) | ||||
0.237965 | + | 0.971274i | \(0.423520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5351 | −0.905763 | −0.452881 | − | 0.891571i | \(-0.649604\pi\) | ||||
−0.452881 | + | 0.891571i | \(0.649604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.8261 | 1.07477 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8103 | 0.952410 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.744590 | −0.0297360 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.03515 | −0.0811467 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.6995 | −1.06289 | −0.531445 | − | 0.847093i | \(-0.678351\pi\) | ||||
−0.531445 | + | 0.847093i | \(0.678351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.53376 | −0.339186 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.22557 | 0.207370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.4475 | 0.413945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7536 | 0.544084 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.8910 | −0.785647 | −0.392823 | − | 0.919614i | \(-0.628502\pi\) | ||||
−0.392823 | + | 0.919614i | \(0.628502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.1460 | 1.78039 | 0.890193 | − | 0.455584i | \(-0.150570\pi\) | ||||
0.890193 | + | 0.455584i | \(0.150570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.71355 | 0.0674711 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.74463 | 0.343787 | 0.171893 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171893 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2831 | 0.796181 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.94159 | 0.272062 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.6687 | 0.691431 | 0.345715 | − | 0.938339i | \(-0.387636\pi\) | ||||
0.345715 | + | 0.938339i | \(0.387636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.98700 | 0.194858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.71699 | 0.223041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.656514 | −0.0255741 | −0.0127871 | − | 0.999918i | \(-0.504070\pi\) | ||||
−0.0127871 | + | 0.999918i | \(0.504070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0189 | 0.545271 | 0.272636 | − | 0.962117i | \(-0.412105\pi\) | ||||
0.272636 | + | 0.962117i | \(0.412105\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.266188 | 0.0103379 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.653965 | 0.0253597 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.1107 | 0.738863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.6439 | 0.488112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4264 | 0.787381 | 0.393690 | − | 0.919243i | \(-0.371198\pi\) | ||||
0.393690 | + | 0.919243i | \(0.371198\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.92026 | 0.189381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.54817 | −0.328533 | −0.164266 | − | 0.986416i | \(-0.552526\pi\) | ||||
−0.164266 | + | 0.986416i | \(0.552526\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −87.9580 | −3.37552 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2099 | −0.467886 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7783 | 0.986379 | 0.493190 | − | 0.869922i | \(-0.335831\pi\) | ||||
0.493190 | + | 0.869922i | \(0.335831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.67115 | −0.140267 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.4713 | 1.04810 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.41263 | −0.130011 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9673 | −0.721552 | −0.360776 | − | 0.932653i | \(-0.617488\pi\) | ||||
−0.360776 | + | 0.932653i | \(0.617488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.11724 | 0.308349 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.126120 | −0.00478401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.37267 | −0.0519936 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.9922 | −0.831821 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.08092 | 0.267443 | 0.133721 | − | 0.991019i | \(-0.457307\pi\) | ||||
0.133721 | + | 0.991019i | \(0.457307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.01764 | 0.0760966 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.79800 | −0.0677165 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 59.7968 | 2.24889 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.2787 | −1.32492 | −0.662460 | − | 0.749097i | \(-0.730488\pi\) | ||||
−0.662460 | + | 0.749097i | \(0.730488\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.81674 | −0.218145 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.38151 | −0.0517381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.261197 | 0.00976821 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.93422 | −0.146926 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.2543 | 1.79958 | 0.899791 | − | 0.436320i | \(-0.143719\pi\) | ||||
0.899791 | + | 0.436320i | \(0.143719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.2871 | −1.31416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.44231 | −0.276782 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.92026 | −0.182734 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1997 | −0.786252 | −0.393126 | − | 0.919485i | \(-0.628606\pi\) | ||||
−0.393126 | + | 0.919485i | \(0.628606\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.82114 | 0.104343 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6692 | −0.394075 | −0.197037 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197037 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.15260 | −0.190057 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.84093 | −0.251989 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.9145 | 1.94649 | 0.973245 | − | 0.229770i | \(-0.0737973\pi\) | ||||
0.973245 | + | 0.229770i | \(0.0737973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.263898 | −0.00969454 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1119 | 0.811207 | 0.405604 | − | 0.914049i | \(-0.367061\pi\) | ||||
0.405604 | + | 0.914049i | \(0.367061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.702962 | −0.0257545 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1920 | 0.482672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.7367 | −2.47504 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.2527 | 1.54182 | 0.770912 | − | 0.636941i | \(-0.219801\pi\) | ||||
0.770912 | + | 0.636941i | \(0.219801\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.5898 | 0.713893 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.96997 | 0.0716945 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.4263 | 1.46932 | 0.734660 | − | 0.678435i | \(-0.237342\pi\) | ||||
0.734660 | + | 0.678435i | \(0.237342\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.61549 | −0.0586387 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.7959 | −0.862600 | −0.431300 | − | 0.902209i | \(-0.641945\pi\) | ||||
−0.431300 | + | 0.902209i | \(0.641945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.6398 | −1.32645 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.131282 | −0.00474650 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.18875 | 0.259571 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.6196 | 0.671438 | 0.335719 | − | 0.941962i | \(-0.391021\pi\) | ||||
0.335719 | + | 0.941962i | \(0.391021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.9223 | −0.645456 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.1632 | −1.69634 | −0.848172 | − | 0.529722i | \(-0.822296\pi\) | ||||
−0.848172 | + | 0.529722i | \(0.822296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.79741 | 0.244170 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.9955 | −0.789086 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.36086 | 0.0487578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.2189 | 0.795053 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.146074 | 0.00521359 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.70101 | 0.345804 | 0.172902 | − | 0.984939i | \(-0.444686\pi\) | ||||
0.172902 | + | 0.984939i | \(0.444686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.2174 | −0.363750 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −105.022 | −3.73417 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.48126 | 0.159134 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.68308 | 0.0596926 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0633 | 0.746101 | 0.373051 | − | 0.927811i | \(-0.378312\pi\) | ||||
0.373051 | + | 0.927811i | \(0.378312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.96016 | −0.104723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.33893 | 0.188642 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.23575 | 0.325923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.41887 | 0.0500086 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.1372 | −0.779266 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.3066 | 1.48742 | 0.743710 | − | 0.668502i | \(-0.233064\pi\) | ||||
0.743710 | + | 0.668502i | \(0.233064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.9537 | −0.419751 | −0.209875 | − | 0.977728i | \(-0.567306\pi\) | ||||
−0.209875 | + | 0.977728i | \(0.567306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0849 | 1.12527 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.26943 | 0.114523 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.79686 | −0.0978498 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.87692 | 0.100528 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.3877 | 0.816237 | 0.408119 | − | 0.912929i | \(-0.366185\pi\) | ||||
0.408119 | + | 0.912929i | \(0.366185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.90370 | 0.170932 | 0.0854662 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854662 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.94864 | 0.276736 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.5936 | 1.34203 | 0.671015 | − | 0.741444i | \(-0.265858\pi\) | ||||
0.671015 | + | 0.741444i | \(0.265858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.4487 | 0.640749 | 0.320374 | − | 0.947291i | \(-0.396191\pi\) | ||||
0.320374 | + | 0.947291i | \(0.396191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0334 | −0.556192 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.48307 | −0.293921 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.51484 | −0.0870297 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.38151 | 0.0477521 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.9978 | 1.41540 | 0.707701 | − | 0.706512i | \(-0.249732\pi\) | ||||
0.707701 | + | 0.706512i | \(0.249732\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.2874 | −0.526526 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.57841 | −0.123101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.1575 | −1.44855 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5611 | −0.499735 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.37755 | 0.150061 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.1282 | −1.51092 | −0.755460 | − | 0.655194i | \(-0.772587\pi\) | ||||
−0.755460 | + | 0.655194i | \(0.772587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.130152 | 0.00445110 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.99764 | −0.102398 | −0.0511988 | − | 0.998688i | \(-0.516304\pi\) | ||||
−0.0511988 | + | 0.998688i | \(0.516304\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.4605 | −1.10754 | −0.553769 | − | 0.832670i | \(-0.686811\pi\) | ||||
−0.553769 | + | 0.832670i | \(0.686811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.8356 | −0.505595 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.6335 | 1.51934 | 0.759671 | − | 0.650307i | \(-0.225360\pi\) | ||||
0.759671 | + | 0.650307i | \(0.225360\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.10896 | 0.173710 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.7839 | 0.570010 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.39691 | −0.318768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.42457 | −0.0821533 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.5054 | −0.592468 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.0756 | −0.475841 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.6728 | 1.54226 | 0.771131 | − | 0.636676i | \(-0.219691\pi\) | ||||
0.771131 | + | 0.636676i | \(0.219691\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.1553 | −0.882197 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0982 | −0.744507 | −0.372253 | − | 0.928131i | \(-0.621415\pi\) | ||||
−0.372253 | + | 0.928131i | \(0.621415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.1538 | −0.678228 | −0.339114 | − | 0.940745i | \(-0.610127\pi\) | ||||
−0.339114 | + | 0.940745i | \(0.610127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.54542 | −0.119178 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.9783 | −1.64453 | −0.822265 | − | 0.569105i | \(-0.807290\pi\) | ||||
−0.822265 | + | 0.569105i | \(0.807290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 92.9819 | 3.11851 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.61549 | 0.0541210 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.93469 | 0.0982057 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.15212 | 0.0719375 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.572564 | −0.0191174 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38151 | −0.0460761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.77096 | 0.0923141 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.4904 | 1.01466 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.90434 | 0.196267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.2718 | −1.17118 | −0.585590 | − | 0.810607i | \(-0.699137\pi\) | ||||
−0.585590 | + | 0.810607i | \(0.699137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.9008 | 0.394723 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.5058 | −0.977571 | −0.488785 | − | 0.872404i | \(-0.662560\pi\) | ||||
−0.488785 | + | 0.872404i | \(0.662560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.3117 | 0.705313 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.21012 | −0.0730642 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 88.7368 | 2.93035 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.33449 | −0.109995 | −0.0549974 | − | 0.998486i | \(-0.517515\pi\) | ||||
−0.0549974 | + | 0.998486i | \(0.517515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.8745 | 0.753739 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.87482 | 0.259203 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.5387 | −0.708188 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.02283 | −0.230660 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.51004 | 0.0823518 | 0.0411759 | − | 0.999152i | \(-0.486890\pi\) | ||||
0.0411759 | + | 0.999152i | \(0.486890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.41007 | 0.275629 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.38071 | 0.208895 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.212084 | −0.00693590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.9088 | −1.10775 | −0.553877 | − | 0.832599i | \(-0.686852\pi\) | ||||
−0.553877 | + | 0.832599i | \(0.686852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.6435 | −1.03265 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.53677 | −0.245692 | −0.122846 | − | 0.992426i | \(-0.539202\pi\) | ||||
−0.122846 | + | 0.992426i | \(0.539202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.95258 | 0.0961491 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41887 | −0.0461558 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.77706 | −0.122738 | −0.0613690 | − | 0.998115i | \(-0.519547\pi\) | ||||
−0.0613690 | + | 0.998115i | \(0.519547\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.27334 | 0.106257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.40227 | 0.0454716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.9850 | −1.65157 | −0.825783 | − | 0.563988i | \(-0.809266\pi\) | ||||
−0.825783 | + | 0.563988i | \(0.809266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.44123 | 0.0466371 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.61549 | −0.0522215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −65.3231 | −2.10939 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0914 | −0.938433 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4809 | −0.434417 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.18414 | −0.0703100 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.7322 | −0.538070 | −0.269035 | − | 0.963130i | \(-0.586705\pi\) | ||||
−0.269035 | + | 0.963130i | \(0.586705\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.214278 | 0.00688359 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4629 | −0.464136 | −0.232068 | − | 0.972700i | \(-0.574549\pi\) | ||||
−0.232068 | + | 0.972700i | \(0.574549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.24414 | −0.0719437 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.81716 | 0.0902215 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.2710 | 0.392583 | 0.196292 | − | 0.980546i | \(-0.437110\pi\) | ||||
0.196292 | + | 0.980546i | \(0.437110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.62501 | 0.275656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.29204 | −0.232817 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.6017 | −0.848461 | −0.424231 | − | 0.905554i | \(-0.639455\pi\) | ||||
−0.424231 | + | 0.905554i | \(0.639455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.85187 | −0.0908681 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.9929 | −1.01835 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.06819 | −0.192957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.3584 | −1.66322 | −0.831610 | − | 0.555360i | \(-0.812581\pi\) | ||||
−0.831610 | + | 0.555360i | \(0.812581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.04905 | −0.223695 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.38949 | −0.107454 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.1603 | −1.74694 | −0.873472 | − | 0.486875i | \(-0.838137\pi\) | ||||
−0.873472 | + | 0.486875i | \(0.838137\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.37755 | −0.138500 |
(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 | 8004.2.a.i.1.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.9 | ✓ | 16 | 1.1 | even | 1 | trivial |