Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | 1.14059 | 0.658518 | 0.329259 | − | 0.944240i | \(-0.393201\pi\) | ||||
0.329259 | + | 0.944240i | \(0.393201\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.375030 | −0.167719 | −0.0838594 | − | 0.996478i | \(-0.526725\pi\) | ||||
−0.0838594 | + | 0.996478i | \(0.526725\pi\) | |||||||
\(6\) | −1.14059 | −0.465643 | ||||||||
\(7\) | 0.176944 | 0.0668787 | 0.0334394 | − | 0.999441i | \(-0.489354\pi\) | ||||
0.0334394 | + | 0.999441i | \(0.489354\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.69906 | −0.566353 | ||||||||
\(10\) | 0.375030 | 0.118595 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.14059 | 0.329259 | ||||||||
\(13\) | 5.77706 | 1.60227 | 0.801134 | − | 0.598485i | \(-0.204230\pi\) | ||||
0.801134 | + | 0.598485i | \(0.204230\pi\) | |||||||
\(14\) | −0.176944 | −0.0472904 | ||||||||
\(15\) | −0.427755 | −0.110446 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.61006 | −0.390496 | −0.195248 | − | 0.980754i | \(-0.562551\pi\) | ||||
−0.195248 | + | 0.980754i | \(0.562551\pi\) | |||||||
\(18\) | 1.69906 | 0.400472 | ||||||||
\(19\) | 5.31123 | 1.21848 | 0.609239 | − | 0.792986i | \(-0.291475\pi\) | ||||
0.609239 | + | 0.792986i | \(0.291475\pi\) | |||||||
\(20\) | −0.375030 | −0.0838594 | ||||||||
\(21\) | 0.201821 | 0.0440409 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 6.15672 | 1.28377 | 0.641883 | − | 0.766803i | \(-0.278154\pi\) | ||||
0.641883 | + | 0.766803i | \(0.278154\pi\) | |||||||
\(24\) | −1.14059 | −0.232821 | ||||||||
\(25\) | −4.85935 | −0.971870 | ||||||||
\(26\) | −5.77706 | −1.13297 | ||||||||
\(27\) | −5.35969 | −1.03147 | ||||||||
\(28\) | 0.176944 | 0.0334394 | ||||||||
\(29\) | 3.06238 | 0.568670 | 0.284335 | − | 0.958725i | \(-0.408227\pi\) | ||||
0.284335 | + | 0.958725i | \(0.408227\pi\) | |||||||
\(30\) | 0.427755 | 0.0780970 | ||||||||
\(31\) | 8.87367 | 1.59376 | 0.796879 | − | 0.604139i | \(-0.206483\pi\) | ||||
0.796879 | + | 0.604139i | \(0.206483\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.14059 | 0.198551 | ||||||||
\(34\) | 1.61006 | 0.276122 | ||||||||
\(35\) | −0.0663595 | −0.0112168 | ||||||||
\(36\) | −1.69906 | −0.283177 | ||||||||
\(37\) | −3.49928 | −0.575279 | −0.287639 | − | 0.957739i | \(-0.592870\pi\) | ||||
−0.287639 | + | 0.957739i | \(0.592870\pi\) | |||||||
\(38\) | −5.31123 | −0.861595 | ||||||||
\(39\) | 6.58924 | 1.05512 | ||||||||
\(40\) | 0.375030 | 0.0592975 | ||||||||
\(41\) | −11.5908 | −1.81018 | −0.905088 | − | 0.425223i | \(-0.860196\pi\) | ||||
−0.905088 | + | 0.425223i | \(0.860196\pi\) | |||||||
\(42\) | −0.201821 | −0.0311416 | ||||||||
\(43\) | 8.97270 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.637199 | 0.0949881 | ||||||||
\(46\) | −6.15672 | −0.907759 | ||||||||
\(47\) | 7.36380 | 1.07412 | 0.537061 | − | 0.843544i | \(-0.319535\pi\) | ||||
0.537061 | + | 0.843544i | \(0.319535\pi\) | |||||||
\(48\) | 1.14059 | 0.164630 | ||||||||
\(49\) | −6.96869 | −0.995527 | ||||||||
\(50\) | 4.85935 | 0.687216 | ||||||||
\(51\) | −1.83641 | −0.257149 | ||||||||
\(52\) | 5.77706 | 0.801134 | ||||||||
\(53\) | −11.0118 | −1.51259 | −0.756293 | − | 0.654233i | \(-0.772992\pi\) | ||||
−0.756293 | + | 0.654233i | \(0.772992\pi\) | |||||||
\(54\) | 5.35969 | 0.729361 | ||||||||
\(55\) | −0.375030 | −0.0505691 | ||||||||
\(56\) | −0.176944 | −0.0236452 | ||||||||
\(57\) | 6.05792 | 0.802391 | ||||||||
\(58\) | −3.06238 | −0.402111 | ||||||||
\(59\) | −10.0186 | −1.30431 | −0.652155 | − | 0.758086i | \(-0.726135\pi\) | ||||
−0.652155 | + | 0.758086i | \(0.726135\pi\) | |||||||
\(60\) | −0.427755 | −0.0552229 | ||||||||
\(61\) | 1.83225 | 0.234595 | 0.117298 | − | 0.993097i | \(-0.462577\pi\) | ||||
0.117298 | + | 0.993097i | \(0.462577\pi\) | |||||||
\(62\) | −8.87367 | −1.12696 | ||||||||
\(63\) | −0.300639 | −0.0378770 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.16657 | −0.268730 | ||||||||
\(66\) | −1.14059 | −0.140397 | ||||||||
\(67\) | 1.50796 | 0.184226 | 0.0921132 | − | 0.995749i | \(-0.470638\pi\) | ||||
0.0921132 | + | 0.995749i | \(0.470638\pi\) | |||||||
\(68\) | −1.61006 | −0.195248 | ||||||||
\(69\) | 7.02228 | 0.845383 | ||||||||
\(70\) | 0.0663595 | 0.00793148 | ||||||||
\(71\) | 8.55660 | 1.01548 | 0.507741 | − | 0.861510i | \(-0.330481\pi\) | ||||
0.507741 | + | 0.861510i | \(0.330481\pi\) | |||||||
\(72\) | 1.69906 | 0.200236 | ||||||||
\(73\) | −6.63706 | −0.776809 | −0.388404 | − | 0.921489i | \(-0.626974\pi\) | ||||
−0.388404 | + | 0.921489i | \(0.626974\pi\) | |||||||
\(74\) | 3.49928 | 0.406784 | ||||||||
\(75\) | −5.54252 | −0.639995 | ||||||||
\(76\) | 5.31123 | 0.609239 | ||||||||
\(77\) | 0.176944 | 0.0201647 | ||||||||
\(78\) | −6.58924 | −0.746085 | ||||||||
\(79\) | 2.84138 | 0.319680 | 0.159840 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159840 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(80\) | −0.375030 | −0.0419297 | ||||||||
\(81\) | −1.01601 | −0.112890 | ||||||||
\(82\) | 11.5908 | 1.27999 | ||||||||
\(83\) | 7.86977 | 0.863819 | 0.431910 | − | 0.901917i | \(-0.357840\pi\) | ||||
0.431910 | + | 0.901917i | \(0.357840\pi\) | |||||||
\(84\) | 0.201821 | 0.0220204 | ||||||||
\(85\) | 0.603820 | 0.0654935 | ||||||||
\(86\) | −8.97270 | −0.967551 | ||||||||
\(87\) | 3.49292 | 0.374480 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.885668 | 0.0938807 | 0.0469403 | − | 0.998898i | \(-0.485053\pi\) | ||||
0.0469403 | + | 0.998898i | \(0.485053\pi\) | |||||||
\(90\) | −0.637199 | −0.0671667 | ||||||||
\(91\) | 1.02222 | 0.107158 | ||||||||
\(92\) | 6.15672 | 0.641883 | ||||||||
\(93\) | 10.1212 | 1.04952 | ||||||||
\(94\) | −7.36380 | −0.759518 | ||||||||
\(95\) | −1.99187 | −0.204362 | ||||||||
\(96\) | −1.14059 | −0.116411 | ||||||||
\(97\) | 7.17673 | 0.728686 | 0.364343 | − | 0.931265i | \(-0.381294\pi\) | ||||
0.364343 | + | 0.931265i | \(0.381294\pi\) | |||||||
\(98\) | 6.96869 | 0.703944 | ||||||||
\(99\) | −1.69906 | −0.170762 | ||||||||
\(100\) | −4.85935 | −0.485935 | ||||||||
\(101\) | −14.6793 | −1.46064 | −0.730322 | − | 0.683103i | \(-0.760630\pi\) | ||||
−0.730322 | + | 0.683103i | \(0.760630\pi\) | |||||||
\(102\) | 1.83641 | 0.181832 | ||||||||
\(103\) | 5.93610 | 0.584901 | 0.292450 | − | 0.956281i | \(-0.405529\pi\) | ||||
0.292450 | + | 0.956281i | \(0.405529\pi\) | |||||||
\(104\) | −5.77706 | −0.566487 | ||||||||
\(105\) | −0.0756889 | −0.00738648 | ||||||||
\(106\) | 11.0118 | 1.06956 | ||||||||
\(107\) | −11.0816 | −1.07130 | −0.535649 | − | 0.844441i | \(-0.679933\pi\) | ||||
−0.535649 | + | 0.844441i | \(0.679933\pi\) | |||||||
\(108\) | −5.35969 | −0.515736 | ||||||||
\(109\) | 4.02602 | 0.385623 | 0.192811 | − | 0.981236i | \(-0.438239\pi\) | ||||
0.192811 | + | 0.981236i | \(0.438239\pi\) | |||||||
\(110\) | 0.375030 | 0.0357578 | ||||||||
\(111\) | −3.99124 | −0.378832 | ||||||||
\(112\) | 0.176944 | 0.0167197 | ||||||||
\(113\) | 20.8267 | 1.95921 | 0.979606 | − | 0.200928i | \(-0.0643958\pi\) | ||||
0.979606 | + | 0.200928i | \(0.0643958\pi\) | |||||||
\(114\) | −6.05792 | −0.567376 | ||||||||
\(115\) | −2.30896 | −0.215311 | ||||||||
\(116\) | 3.06238 | 0.284335 | ||||||||
\(117\) | −9.81558 | −0.907450 | ||||||||
\(118\) | 10.0186 | 0.922286 | ||||||||
\(119\) | −0.284890 | −0.0261159 | ||||||||
\(120\) | 0.427755 | 0.0390485 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.83225 | −0.165884 | ||||||||
\(123\) | −13.2203 | −1.19203 | ||||||||
\(124\) | 8.87367 | 0.796879 | ||||||||
\(125\) | 3.69756 | 0.330720 | ||||||||
\(126\) | 0.300639 | 0.0267831 | ||||||||
\(127\) | 5.71335 | 0.506978 | 0.253489 | − | 0.967338i | \(-0.418422\pi\) | ||||
0.253489 | + | 0.967338i | \(0.418422\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.2342 | 0.901067 | ||||||||
\(130\) | 2.16657 | 0.190021 | ||||||||
\(131\) | 12.9789 | 1.13397 | 0.566986 | − | 0.823727i | \(-0.308109\pi\) | ||||
0.566986 | + | 0.823727i | \(0.308109\pi\) | |||||||
\(132\) | 1.14059 | 0.0992754 | ||||||||
\(133\) | 0.939792 | 0.0814903 | ||||||||
\(134\) | −1.50796 | −0.130268 | ||||||||
\(135\) | 2.01005 | 0.172997 | ||||||||
\(136\) | 1.61006 | 0.138061 | ||||||||
\(137\) | −3.53736 | −0.302217 | −0.151109 | − | 0.988517i | \(-0.548284\pi\) | ||||
−0.151109 | + | 0.988517i | \(0.548284\pi\) | |||||||
\(138\) | −7.02228 | −0.597776 | ||||||||
\(139\) | 10.0260 | 0.850391 | 0.425195 | − | 0.905102i | \(-0.360205\pi\) | ||||
0.425195 | + | 0.905102i | \(0.360205\pi\) | |||||||
\(140\) | −0.0663595 | −0.00560841 | ||||||||
\(141\) | 8.39906 | 0.707329 | ||||||||
\(142\) | −8.55660 | −0.718054 | ||||||||
\(143\) | 5.77706 | 0.483102 | ||||||||
\(144\) | −1.69906 | −0.141588 | ||||||||
\(145\) | −1.14849 | −0.0953767 | ||||||||
\(146\) | 6.63706 | 0.549287 | ||||||||
\(147\) | −7.94840 | −0.655573 | ||||||||
\(148\) | −3.49928 | −0.287639 | ||||||||
\(149\) | 24.1445 | 1.97799 | 0.988996 | − | 0.147939i | \(-0.0472640\pi\) | ||||
0.988996 | + | 0.147939i | \(0.0472640\pi\) | |||||||
\(150\) | 5.54252 | 0.452545 | ||||||||
\(151\) | −0.198077 | −0.0161193 | −0.00805965 | − | 0.999968i | \(-0.502565\pi\) | ||||
−0.00805965 | + | 0.999968i | \(0.502565\pi\) | |||||||
\(152\) | −5.31123 | −0.430797 | ||||||||
\(153\) | 2.73558 | 0.221159 | ||||||||
\(154\) | −0.176944 | −0.0142586 | ||||||||
\(155\) | −3.32790 | −0.267303 | ||||||||
\(156\) | 6.58924 | 0.527562 | ||||||||
\(157\) | 20.2212 | 1.61383 | 0.806913 | − | 0.590670i | \(-0.201137\pi\) | ||||
0.806913 | + | 0.590670i | \(0.201137\pi\) | |||||||
\(158\) | −2.84138 | −0.226048 | ||||||||
\(159\) | −12.5599 | −0.996066 | ||||||||
\(160\) | 0.375030 | 0.0296488 | ||||||||
\(161\) | 1.08940 | 0.0858566 | ||||||||
\(162\) | 1.01601 | 0.0798255 | ||||||||
\(163\) | 11.7335 | 0.919039 | 0.459519 | − | 0.888168i | \(-0.348022\pi\) | ||||
0.459519 | + | 0.888168i | \(0.348022\pi\) | |||||||
\(164\) | −11.5908 | −0.905088 | ||||||||
\(165\) | −0.427755 | −0.0333007 | ||||||||
\(166\) | −7.86977 | −0.610813 | ||||||||
\(167\) | 19.8909 | 1.53920 | 0.769602 | − | 0.638524i | \(-0.220455\pi\) | ||||
0.769602 | + | 0.638524i | \(0.220455\pi\) | |||||||
\(168\) | −0.201821 | −0.0155708 | ||||||||
\(169\) | 20.3744 | 1.56726 | ||||||||
\(170\) | −0.603820 | −0.0463109 | ||||||||
\(171\) | −9.02409 | −0.690090 | ||||||||
\(172\) | 8.97270 | 0.684162 | ||||||||
\(173\) | 20.3715 | 1.54882 | 0.774408 | − | 0.632687i | \(-0.218048\pi\) | ||||
0.774408 | + | 0.632687i | \(0.218048\pi\) | |||||||
\(174\) | −3.49292 | −0.264797 | ||||||||
\(175\) | −0.859835 | −0.0649974 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −11.4271 | −0.858912 | ||||||||
\(178\) | −0.885668 | −0.0663836 | ||||||||
\(179\) | 11.3922 | 0.851491 | 0.425745 | − | 0.904843i | \(-0.360012\pi\) | ||||
0.425745 | + | 0.904843i | \(0.360012\pi\) | |||||||
\(180\) | 0.637199 | 0.0474940 | ||||||||
\(181\) | −8.49660 | −0.631547 | −0.315774 | − | 0.948835i | \(-0.602264\pi\) | ||||
−0.315774 | + | 0.948835i | \(0.602264\pi\) | |||||||
\(182\) | −1.02222 | −0.0757719 | ||||||||
\(183\) | 2.08984 | 0.154485 | ||||||||
\(184\) | −6.15672 | −0.453880 | ||||||||
\(185\) | 1.31234 | 0.0964850 | ||||||||
\(186\) | −10.1212 | −0.742122 | ||||||||
\(187\) | −1.61006 | −0.117739 | ||||||||
\(188\) | 7.36380 | 0.537061 | ||||||||
\(189\) | −0.948367 | −0.0689836 | ||||||||
\(190\) | 1.99187 | 0.144506 | ||||||||
\(191\) | −4.10814 | −0.297255 | −0.148627 | − | 0.988893i | \(-0.547486\pi\) | ||||
−0.148627 | + | 0.988893i | \(0.547486\pi\) | |||||||
\(192\) | 1.14059 | 0.0823148 | ||||||||
\(193\) | −19.8031 | −1.42546 | −0.712731 | − | 0.701438i | \(-0.752542\pi\) | ||||
−0.712731 | + | 0.701438i | \(0.752542\pi\) | |||||||
\(194\) | −7.17673 | −0.515259 | ||||||||
\(195\) | −2.47117 | −0.176964 | ||||||||
\(196\) | −6.96869 | −0.497764 | ||||||||
\(197\) | −1.00000 | −0.0712470 | ||||||||
\(198\) | 1.69906 | 0.120747 | ||||||||
\(199\) | 17.2853 | 1.22532 | 0.612661 | − | 0.790346i | \(-0.290099\pi\) | ||||
0.612661 | + | 0.790346i | \(0.290099\pi\) | |||||||
\(200\) | 4.85935 | 0.343608 | ||||||||
\(201\) | 1.71996 | 0.121316 | ||||||||
\(202\) | 14.6793 | 1.03283 | ||||||||
\(203\) | 0.541872 | 0.0380319 | ||||||||
\(204\) | −1.83641 | −0.128574 | ||||||||
\(205\) | 4.34690 | 0.303601 | ||||||||
\(206\) | −5.93610 | −0.413587 | ||||||||
\(207\) | −10.4606 | −0.727065 | ||||||||
\(208\) | 5.77706 | 0.400567 | ||||||||
\(209\) | 5.31123 | 0.367385 | ||||||||
\(210\) | 0.0756889 | 0.00522303 | ||||||||
\(211\) | −6.16750 | −0.424588 | −0.212294 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212294 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(212\) | −11.0118 | −0.756293 | ||||||||
\(213\) | 9.75955 | 0.668713 | ||||||||
\(214\) | 11.0816 | 0.757522 | ||||||||
\(215\) | −3.36504 | −0.229494 | ||||||||
\(216\) | 5.35969 | 0.364681 | ||||||||
\(217\) | 1.57015 | 0.106588 | ||||||||
\(218\) | −4.02602 | −0.272677 | ||||||||
\(219\) | −7.57014 | −0.511543 | ||||||||
\(220\) | −0.375030 | −0.0252845 | ||||||||
\(221\) | −9.30139 | −0.625679 | ||||||||
\(222\) | 3.99124 | 0.267874 | ||||||||
\(223\) | −21.1361 | −1.41538 | −0.707688 | − | 0.706525i | \(-0.750262\pi\) | ||||
−0.707688 | + | 0.706525i | \(0.750262\pi\) | |||||||
\(224\) | −0.176944 | −0.0118226 | ||||||||
\(225\) | 8.25633 | 0.550422 | ||||||||
\(226\) | −20.8267 | −1.38537 | ||||||||
\(227\) | −16.8202 | −1.11640 | −0.558199 | − | 0.829707i | \(-0.688507\pi\) | ||||
−0.558199 | + | 0.829707i | \(0.688507\pi\) | |||||||
\(228\) | 6.05792 | 0.401195 | ||||||||
\(229\) | 20.4813 | 1.35344 | 0.676720 | − | 0.736241i | \(-0.263401\pi\) | ||||
0.676720 | + | 0.736241i | \(0.263401\pi\) | |||||||
\(230\) | 2.30896 | 0.152248 | ||||||||
\(231\) | 0.201821 | 0.0132788 | ||||||||
\(232\) | −3.06238 | −0.201055 | ||||||||
\(233\) | −26.4406 | −1.73218 | −0.866091 | − | 0.499886i | \(-0.833375\pi\) | ||||
−0.866091 | + | 0.499886i | \(0.833375\pi\) | |||||||
\(234\) | 9.81558 | 0.641664 | ||||||||
\(235\) | −2.76165 | −0.180150 | ||||||||
\(236\) | −10.0186 | −0.652155 | ||||||||
\(237\) | 3.24084 | 0.210515 | ||||||||
\(238\) | 0.284890 | 0.0184667 | ||||||||
\(239\) | −22.1273 | −1.43130 | −0.715648 | − | 0.698461i | \(-0.753869\pi\) | ||||
−0.715648 | + | 0.698461i | \(0.753869\pi\) | |||||||
\(240\) | −0.427755 | −0.0276115 | ||||||||
\(241\) | 12.7215 | 0.819463 | 0.409731 | − | 0.912206i | \(-0.365622\pi\) | ||||
0.409731 | + | 0.912206i | \(0.365622\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 14.9202 | 0.957132 | ||||||||
\(244\) | 1.83225 | 0.117298 | ||||||||
\(245\) | 2.61347 | 0.166969 | ||||||||
\(246\) | 13.2203 | 0.842896 | ||||||||
\(247\) | 30.6833 | 1.95233 | ||||||||
\(248\) | −8.87367 | −0.563478 | ||||||||
\(249\) | 8.97616 | 0.568841 | ||||||||
\(250\) | −3.69756 | −0.233854 | ||||||||
\(251\) | −1.39768 | −0.0882206 | −0.0441103 | − | 0.999027i | \(-0.514045\pi\) | ||||
−0.0441103 | + | 0.999027i | \(0.514045\pi\) | |||||||
\(252\) | −0.300639 | −0.0189385 | ||||||||
\(253\) | 6.15672 | 0.387070 | ||||||||
\(254\) | −5.71335 | −0.358487 | ||||||||
\(255\) | 0.688709 | 0.0431287 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.1133 | −1.37939 | −0.689695 | − | 0.724100i | \(-0.742255\pi\) | ||||
−0.689695 | + | 0.724100i | \(0.742255\pi\) | |||||||
\(258\) | −10.2342 | −0.637150 | ||||||||
\(259\) | −0.619179 | −0.0384739 | ||||||||
\(260\) | −2.16657 | −0.134365 | ||||||||
\(261\) | −5.20317 | −0.322068 | ||||||||
\(262\) | −12.9789 | −0.801840 | ||||||||
\(263\) | 3.97155 | 0.244896 | 0.122448 | − | 0.992475i | \(-0.460925\pi\) | ||||
0.122448 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(264\) | −1.14059 | −0.0701983 | ||||||||
\(265\) | 4.12976 | 0.253689 | ||||||||
\(266\) | −0.939792 | −0.0576223 | ||||||||
\(267\) | 1.01018 | 0.0618221 | ||||||||
\(268\) | 1.50796 | 0.0921132 | ||||||||
\(269\) | 25.6677 | 1.56499 | 0.782495 | − | 0.622657i | \(-0.213947\pi\) | ||||
0.782495 | + | 0.622657i | \(0.213947\pi\) | |||||||
\(270\) | −2.01005 | −0.122328 | ||||||||
\(271\) | −0.364186 | −0.0221227 | −0.0110614 | − | 0.999939i | \(-0.503521\pi\) | ||||
−0.0110614 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(272\) | −1.61006 | −0.0976240 | ||||||||
\(273\) | 1.16593 | 0.0705653 | ||||||||
\(274\) | 3.53736 | 0.213700 | ||||||||
\(275\) | −4.85935 | −0.293030 | ||||||||
\(276\) | 7.02228 | 0.422691 | ||||||||
\(277\) | 18.9045 | 1.13586 | 0.567931 | − | 0.823076i | \(-0.307744\pi\) | ||||
0.567931 | + | 0.823076i | \(0.307744\pi\) | |||||||
\(278\) | −10.0260 | −0.601317 | ||||||||
\(279\) | −15.0769 | −0.902630 | ||||||||
\(280\) | 0.0663595 | 0.00396574 | ||||||||
\(281\) | −27.4959 | −1.64027 | −0.820135 | − | 0.572170i | \(-0.806102\pi\) | ||||
−0.820135 | + | 0.572170i | \(0.806102\pi\) | |||||||
\(282\) | −8.39906 | −0.500157 | ||||||||
\(283\) | 6.24017 | 0.370939 | 0.185470 | − | 0.982650i | \(-0.440619\pi\) | ||||
0.185470 | + | 0.982650i | \(0.440619\pi\) | |||||||
\(284\) | 8.55660 | 0.507741 | ||||||||
\(285\) | −2.27190 | −0.134576 | ||||||||
\(286\) | −5.77706 | −0.341605 | ||||||||
\(287\) | −2.05093 | −0.121062 | ||||||||
\(288\) | 1.69906 | 0.100118 | ||||||||
\(289\) | −14.4077 | −0.847513 | ||||||||
\(290\) | 1.14849 | 0.0674415 | ||||||||
\(291\) | 8.18568 | 0.479853 | ||||||||
\(292\) | −6.63706 | −0.388404 | ||||||||
\(293\) | −16.9894 | −0.992533 | −0.496267 | − | 0.868170i | \(-0.665296\pi\) | ||||
−0.496267 | + | 0.868170i | \(0.665296\pi\) | |||||||
\(294\) | 7.94840 | 0.463560 | ||||||||
\(295\) | 3.75728 | 0.218757 | ||||||||
\(296\) | 3.49928 | 0.203392 | ||||||||
\(297\) | −5.35969 | −0.311001 | ||||||||
\(298\) | −24.1445 | −1.39865 | ||||||||
\(299\) | 35.5678 | 2.05694 | ||||||||
\(300\) | −5.54252 | −0.319997 | ||||||||
\(301\) | 1.58767 | 0.0915118 | ||||||||
\(302\) | 0.198077 | 0.0113981 | ||||||||
\(303\) | −16.7430 | −0.961861 | ||||||||
\(304\) | 5.31123 | 0.304620 | ||||||||
\(305\) | −0.687148 | −0.0393460 | ||||||||
\(306\) | −2.73558 | −0.156383 | ||||||||
\(307\) | −30.2004 | −1.72363 | −0.861813 | − | 0.507226i | \(-0.830671\pi\) | ||||
−0.861813 | + | 0.507226i | \(0.830671\pi\) | |||||||
\(308\) | 0.176944 | 0.0100823 | ||||||||
\(309\) | 6.77064 | 0.385168 | ||||||||
\(310\) | 3.32790 | 0.189012 | ||||||||
\(311\) | 25.5594 | 1.44934 | 0.724670 | − | 0.689096i | \(-0.241992\pi\) | ||||
0.724670 | + | 0.689096i | \(0.241992\pi\) | |||||||
\(312\) | −6.58924 | −0.373042 | ||||||||
\(313\) | 26.4591 | 1.49556 | 0.747779 | − | 0.663948i | \(-0.231120\pi\) | ||||
0.747779 | + | 0.663948i | \(0.231120\pi\) | |||||||
\(314\) | −20.2212 | −1.14115 | ||||||||
\(315\) | 0.112749 | 0.00635268 | ||||||||
\(316\) | 2.84138 | 0.159840 | ||||||||
\(317\) | 26.8098 | 1.50579 | 0.752894 | − | 0.658142i | \(-0.228657\pi\) | ||||
0.752894 | + | 0.658142i | \(0.228657\pi\) | |||||||
\(318\) | 12.5599 | 0.704325 | ||||||||
\(319\) | 3.06238 | 0.171461 | ||||||||
\(320\) | −0.375030 | −0.0209648 | ||||||||
\(321\) | −12.6395 | −0.705469 | ||||||||
\(322\) | −1.08940 | −0.0607097 | ||||||||
\(323\) | −8.55137 | −0.475811 | ||||||||
\(324\) | −1.01601 | −0.0564451 | ||||||||
\(325\) | −28.0728 | −1.55720 | ||||||||
\(326\) | −11.7335 | −0.649859 | ||||||||
\(327\) | 4.59203 | 0.253940 | ||||||||
\(328\) | 11.5908 | 0.639994 | ||||||||
\(329\) | 1.30298 | 0.0718358 | ||||||||
\(330\) | 0.427755 | 0.0235471 | ||||||||
\(331\) | −2.24781 | −0.123551 | −0.0617753 | − | 0.998090i | \(-0.519676\pi\) | ||||
−0.0617753 | + | 0.998090i | \(0.519676\pi\) | |||||||
\(332\) | 7.86977 | 0.431910 | ||||||||
\(333\) | 5.94550 | 0.325811 | ||||||||
\(334\) | −19.8909 | −1.08838 | ||||||||
\(335\) | −0.565530 | −0.0308982 | ||||||||
\(336\) | 0.201821 | 0.0110102 | ||||||||
\(337\) | −20.0951 | −1.09465 | −0.547325 | − | 0.836920i | \(-0.684354\pi\) | ||||
−0.547325 | + | 0.836920i | \(0.684354\pi\) | |||||||
\(338\) | −20.3744 | −1.10822 | ||||||||
\(339\) | 23.7547 | 1.29018 | ||||||||
\(340\) | 0.603820 | 0.0327467 | ||||||||
\(341\) | 8.87367 | 0.480536 | ||||||||
\(342\) | 9.02409 | 0.487967 | ||||||||
\(343\) | −2.47168 | −0.133458 | ||||||||
\(344\) | −8.97270 | −0.483776 | ||||||||
\(345\) | −2.63357 | −0.141787 | ||||||||
\(346\) | −20.3715 | −1.09518 | ||||||||
\(347\) | 7.48401 | 0.401763 | 0.200881 | − | 0.979616i | \(-0.435619\pi\) | ||||
0.200881 | + | 0.979616i | \(0.435619\pi\) | |||||||
\(348\) | 3.49292 | 0.187240 | ||||||||
\(349\) | −3.60092 | −0.192753 | −0.0963764 | − | 0.995345i | \(-0.530725\pi\) | ||||
−0.0963764 | + | 0.995345i | \(0.530725\pi\) | |||||||
\(350\) | 0.859835 | 0.0459601 | ||||||||
\(351\) | −30.9633 | −1.65270 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −19.9929 | −1.06411 | −0.532057 | − | 0.846709i | \(-0.678581\pi\) | ||||
−0.532057 | + | 0.846709i | \(0.678581\pi\) | |||||||
\(354\) | 11.4271 | 0.607342 | ||||||||
\(355\) | −3.20899 | −0.170315 | ||||||||
\(356\) | 0.885668 | 0.0469403 | ||||||||
\(357\) | −0.324942 | −0.0171978 | ||||||||
\(358\) | −11.3922 | −0.602095 | ||||||||
\(359\) | 17.4829 | 0.922713 | 0.461357 | − | 0.887215i | \(-0.347363\pi\) | ||||
0.461357 | + | 0.887215i | \(0.347363\pi\) | |||||||
\(360\) | −0.637199 | −0.0335834 | ||||||||
\(361\) | 9.20912 | 0.484690 | ||||||||
\(362\) | 8.49660 | 0.446571 | ||||||||
\(363\) | 1.14059 | 0.0598653 | ||||||||
\(364\) | 1.02222 | 0.0535788 | ||||||||
\(365\) | 2.48910 | 0.130285 | ||||||||
\(366\) | −2.08984 | −0.109238 | ||||||||
\(367\) | 29.5756 | 1.54383 | 0.771917 | − | 0.635724i | \(-0.219298\pi\) | ||||
0.771917 | + | 0.635724i | \(0.219298\pi\) | |||||||
\(368\) | 6.15672 | 0.320941 | ||||||||
\(369\) | 19.6934 | 1.02520 | ||||||||
\(370\) | −1.31234 | −0.0682252 | ||||||||
\(371\) | −1.94848 | −0.101160 | ||||||||
\(372\) | 10.1212 | 0.524759 | ||||||||
\(373\) | 23.6488 | 1.22449 | 0.612244 | − | 0.790669i | \(-0.290267\pi\) | ||||
0.612244 | + | 0.790669i | \(0.290267\pi\) | |||||||
\(374\) | 1.61006 | 0.0832540 | ||||||||
\(375\) | 4.21739 | 0.217785 | ||||||||
\(376\) | −7.36380 | −0.379759 | ||||||||
\(377\) | 17.6916 | 0.911163 | ||||||||
\(378\) | 0.948367 | 0.0487787 | ||||||||
\(379\) | 22.9373 | 1.17821 | 0.589105 | − | 0.808057i | \(-0.299481\pi\) | ||||
0.589105 | + | 0.808057i | \(0.299481\pi\) | |||||||
\(380\) | −1.99187 | −0.102181 | ||||||||
\(381\) | 6.51658 | 0.333854 | ||||||||
\(382\) | 4.10814 | 0.210191 | ||||||||
\(383\) | −18.5190 | −0.946277 | −0.473139 | − | 0.880988i | \(-0.656879\pi\) | ||||
−0.473139 | + | 0.880988i | \(0.656879\pi\) | |||||||
\(384\) | −1.14059 | −0.0582054 | ||||||||
\(385\) | −0.0663595 | −0.00338200 | ||||||||
\(386\) | 19.8031 | 1.00795 | ||||||||
\(387\) | −15.2452 | −0.774955 | ||||||||
\(388\) | 7.17673 | 0.364343 | ||||||||
\(389\) | −18.5454 | −0.940288 | −0.470144 | − | 0.882590i | \(-0.655798\pi\) | ||||
−0.470144 | + | 0.882590i | \(0.655798\pi\) | |||||||
\(390\) | 2.47117 | 0.125132 | ||||||||
\(391\) | −9.91266 | −0.501305 | ||||||||
\(392\) | 6.96869 | 0.351972 | ||||||||
\(393\) | 14.8036 | 0.746742 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | −1.06560 | −0.0536163 | ||||||||
\(396\) | −1.69906 | −0.0853810 | ||||||||
\(397\) | 2.64088 | 0.132542 | 0.0662711 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662711 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(398\) | −17.2853 | −0.866434 | ||||||||
\(399\) | 1.07191 | 0.0536629 | ||||||||
\(400\) | −4.85935 | −0.242968 | ||||||||
\(401\) | −24.6618 | −1.23155 | −0.615777 | − | 0.787921i | \(-0.711158\pi\) | ||||
−0.615777 | + | 0.787921i | \(0.711158\pi\) | |||||||
\(402\) | −1.71996 | −0.0857837 | ||||||||
\(403\) | 51.2637 | 2.55363 | ||||||||
\(404\) | −14.6793 | −0.730322 | ||||||||
\(405\) | 0.381036 | 0.0189338 | ||||||||
\(406\) | −0.541872 | −0.0268926 | ||||||||
\(407\) | −3.49928 | −0.173453 | ||||||||
\(408\) | 1.83641 | 0.0909158 | ||||||||
\(409\) | −3.50713 | −0.173416 | −0.0867082 | − | 0.996234i | \(-0.527635\pi\) | ||||
−0.0867082 | + | 0.996234i | \(0.527635\pi\) | |||||||
\(410\) | −4.34690 | −0.214678 | ||||||||
\(411\) | −4.03467 | −0.199016 | ||||||||
\(412\) | 5.93610 | 0.292450 | ||||||||
\(413\) | −1.77273 | −0.0872305 | ||||||||
\(414\) | 10.4606 | 0.514112 | ||||||||
\(415\) | −2.95140 | −0.144879 | ||||||||
\(416\) | −5.77706 | −0.283244 | ||||||||
\(417\) | 11.4355 | 0.559998 | ||||||||
\(418\) | −5.31123 | −0.259781 | ||||||||
\(419\) | −4.67818 | −0.228544 | −0.114272 | − | 0.993449i | \(-0.536454\pi\) | ||||
−0.114272 | + | 0.993449i | \(0.536454\pi\) | |||||||
\(420\) | −0.0756889 | −0.00369324 | ||||||||
\(421\) | −26.2204 | −1.27791 | −0.638953 | − | 0.769246i | \(-0.720632\pi\) | ||||
−0.638953 | + | 0.769246i | \(0.720632\pi\) | |||||||
\(422\) | 6.16750 | 0.300229 | ||||||||
\(423\) | −12.5115 | −0.608332 | ||||||||
\(424\) | 11.0118 | 0.534780 | ||||||||
\(425\) | 7.82383 | 0.379511 | ||||||||
\(426\) | −9.75955 | −0.472852 | ||||||||
\(427\) | 0.324206 | 0.0156894 | ||||||||
\(428\) | −11.0816 | −0.535649 | ||||||||
\(429\) | 6.58924 | 0.318132 | ||||||||
\(430\) | 3.36504 | 0.162276 | ||||||||
\(431\) | −4.21940 | −0.203241 | −0.101621 | − | 0.994823i | \(-0.532403\pi\) | ||||
−0.101621 | + | 0.994823i | \(0.532403\pi\) | |||||||
\(432\) | −5.35969 | −0.257868 | ||||||||
\(433\) | −26.6218 | −1.27936 | −0.639681 | − | 0.768640i | \(-0.720934\pi\) | ||||
−0.639681 | + | 0.768640i | \(0.720934\pi\) | |||||||
\(434\) | −1.57015 | −0.0753694 | ||||||||
\(435\) | −1.30995 | −0.0628073 | ||||||||
\(436\) | 4.02602 | 0.192811 | ||||||||
\(437\) | 32.6997 | 1.56424 | ||||||||
\(438\) | 7.57014 | 0.361715 | ||||||||
\(439\) | 0.548668 | 0.0261865 | 0.0130932 | − | 0.999914i | \(-0.495832\pi\) | ||||
0.0130932 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(440\) | 0.375030 | 0.0178789 | ||||||||
\(441\) | 11.8402 | 0.563820 | ||||||||
\(442\) | 9.30139 | 0.442422 | ||||||||
\(443\) | 33.8396 | 1.60777 | 0.803883 | − | 0.594788i | \(-0.202764\pi\) | ||||
0.803883 | + | 0.594788i | \(0.202764\pi\) | |||||||
\(444\) | −3.99124 | −0.189416 | ||||||||
\(445\) | −0.332153 | −0.0157455 | ||||||||
\(446\) | 21.1361 | 1.00082 | ||||||||
\(447\) | 27.5389 | 1.30254 | ||||||||
\(448\) | 0.176944 | 0.00835984 | ||||||||
\(449\) | 0.977296 | 0.0461215 | 0.0230607 | − | 0.999734i | \(-0.492659\pi\) | ||||
0.0230607 | + | 0.999734i | \(0.492659\pi\) | |||||||
\(450\) | −8.25633 | −0.389207 | ||||||||
\(451\) | −11.5908 | −0.545789 | ||||||||
\(452\) | 20.8267 | 0.979606 | ||||||||
\(453\) | −0.225925 | −0.0106149 | ||||||||
\(454\) | 16.8202 | 0.789412 | ||||||||
\(455\) | −0.383363 | −0.0179723 | ||||||||
\(456\) | −6.05792 | −0.283688 | ||||||||
\(457\) | −0.113660 | −0.00531680 | −0.00265840 | − | 0.999996i | \(-0.500846\pi\) | ||||
−0.00265840 | + | 0.999996i | \(0.500846\pi\) | |||||||
\(458\) | −20.4813 | −0.957026 | ||||||||
\(459\) | 8.62940 | 0.402786 | ||||||||
\(460\) | −2.30896 | −0.107656 | ||||||||
\(461\) | 3.00340 | 0.139882 | 0.0699412 | − | 0.997551i | \(-0.477719\pi\) | ||||
0.0699412 | + | 0.997551i | \(0.477719\pi\) | |||||||
\(462\) | −0.201821 | −0.00938954 | ||||||||
\(463\) | 14.9797 | 0.696166 | 0.348083 | − | 0.937464i | \(-0.386833\pi\) | ||||
0.348083 | + | 0.937464i | \(0.386833\pi\) | |||||||
\(464\) | 3.06238 | 0.142168 | ||||||||
\(465\) | −3.79576 | −0.176024 | ||||||||
\(466\) | 26.4406 | 1.22484 | ||||||||
\(467\) | −26.3116 | −1.21756 | −0.608778 | − | 0.793341i | \(-0.708340\pi\) | ||||
−0.608778 | + | 0.793341i | \(0.708340\pi\) | |||||||
\(468\) | −9.81558 | −0.453725 | ||||||||
\(469\) | 0.266825 | 0.0123208 | ||||||||
\(470\) | 2.76165 | 0.127385 | ||||||||
\(471\) | 23.0640 | 1.06273 | ||||||||
\(472\) | 10.0186 | 0.461143 | ||||||||
\(473\) | 8.97270 | 0.412565 | ||||||||
\(474\) | −3.24084 | −0.148857 | ||||||||
\(475\) | −25.8091 | −1.18420 | ||||||||
\(476\) | −0.284890 | −0.0130579 | ||||||||
\(477\) | 18.7097 | 0.856659 | ||||||||
\(478\) | 22.1273 | 1.01208 | ||||||||
\(479\) | −25.7015 | −1.17433 | −0.587165 | − | 0.809467i | \(-0.699756\pi\) | ||||
−0.587165 | + | 0.809467i | \(0.699756\pi\) | |||||||
\(480\) | 0.427755 | 0.0195243 | ||||||||
\(481\) | −20.2156 | −0.921751 | ||||||||
\(482\) | −12.7215 | −0.579448 | ||||||||
\(483\) | 1.24255 | 0.0565381 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.69149 | −0.122214 | ||||||||
\(486\) | −14.9202 | −0.676795 | ||||||||
\(487\) | 15.4358 | 0.699464 | 0.349732 | − | 0.936850i | \(-0.386273\pi\) | ||||
0.349732 | + | 0.936850i | \(0.386273\pi\) | |||||||
\(488\) | −1.83225 | −0.0829419 | ||||||||
\(489\) | 13.3831 | 0.605204 | ||||||||
\(490\) | −2.61347 | −0.118065 | ||||||||
\(491\) | 13.1337 | 0.592717 | 0.296359 | − | 0.955077i | \(-0.404228\pi\) | ||||
0.296359 | + | 0.955077i | \(0.404228\pi\) | |||||||
\(492\) | −13.2203 | −0.596017 | ||||||||
\(493\) | −4.93061 | −0.222063 | ||||||||
\(494\) | −30.6833 | −1.38051 | ||||||||
\(495\) | 0.637199 | 0.0286400 | ||||||||
\(496\) | 8.87367 | 0.398439 | ||||||||
\(497\) | 1.51404 | 0.0679141 | ||||||||
\(498\) | −8.97616 | −0.402231 | ||||||||
\(499\) | 1.38739 | 0.0621080 | 0.0310540 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310540 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(500\) | 3.69756 | 0.165360 | ||||||||
\(501\) | 22.6873 | 1.01359 | ||||||||
\(502\) | 1.39768 | 0.0623814 | ||||||||
\(503\) | −31.6192 | −1.40983 | −0.704915 | − | 0.709292i | \(-0.749015\pi\) | ||||
−0.704915 | + | 0.709292i | \(0.749015\pi\) | |||||||
\(504\) | 0.300639 | 0.0133915 | ||||||||
\(505\) | 5.50518 | 0.244977 | ||||||||
\(506\) | −6.15672 | −0.273700 | ||||||||
\(507\) | 23.2388 | 1.03207 | ||||||||
\(508\) | 5.71335 | 0.253489 | ||||||||
\(509\) | −14.2574 | −0.631948 | −0.315974 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315974 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(510\) | −0.688709 | −0.0304966 | ||||||||
\(511\) | −1.17439 | −0.0519520 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −28.4665 | −1.25683 | ||||||||
\(514\) | 22.1133 | 0.975376 | ||||||||
\(515\) | −2.22622 | −0.0980988 | ||||||||
\(516\) | 10.2342 | 0.450533 | ||||||||
\(517\) | 7.36380 | 0.323860 | ||||||||
\(518\) | 0.619179 | 0.0272052 | ||||||||
\(519\) | 23.2355 | 1.01992 | ||||||||
\(520\) | 2.16657 | 0.0950106 | ||||||||
\(521\) | −28.0934 | −1.23079 | −0.615397 | − | 0.788217i | \(-0.711004\pi\) | ||||
−0.615397 | + | 0.788217i | \(0.711004\pi\) | |||||||
\(522\) | 5.20317 | 0.227737 | ||||||||
\(523\) | −13.8013 | −0.603487 | −0.301743 | − | 0.953389i | \(-0.597569\pi\) | ||||
−0.301743 | + | 0.953389i | \(0.597569\pi\) | |||||||
\(524\) | 12.9789 | 0.566986 | ||||||||
\(525\) | −0.980717 | −0.0428020 | ||||||||
\(526\) | −3.97155 | −0.173168 | ||||||||
\(527\) | −14.2871 | −0.622356 | ||||||||
\(528\) | 1.14059 | 0.0496377 | ||||||||
\(529\) | 14.9052 | 0.648053 | ||||||||
\(530\) | −4.12976 | −0.179385 | ||||||||
\(531\) | 17.0222 | 0.738700 | ||||||||
\(532\) | 0.939792 | 0.0407451 | ||||||||
\(533\) | −66.9607 | −2.90039 | ||||||||
\(534\) | −1.01018 | −0.0437149 | ||||||||
\(535\) | 4.15593 | 0.179677 | ||||||||
\(536\) | −1.50796 | −0.0651338 | ||||||||
\(537\) | 12.9938 | 0.560722 | ||||||||
\(538\) | −25.6677 | −1.10662 | ||||||||
\(539\) | −6.96869 | −0.300163 | ||||||||
\(540\) | 2.01005 | 0.0864986 | ||||||||
\(541\) | −1.42879 | −0.0614286 | −0.0307143 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307143 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(542\) | 0.364186 | 0.0156431 | ||||||||
\(543\) | −9.69112 | −0.415886 | ||||||||
\(544\) | 1.61006 | 0.0690306 | ||||||||
\(545\) | −1.50988 | −0.0646762 | ||||||||
\(546\) | −1.16593 | −0.0498972 | ||||||||
\(547\) | 3.66640 | 0.156764 | 0.0783820 | − | 0.996923i | \(-0.475025\pi\) | ||||
0.0783820 | + | 0.996923i | \(0.475025\pi\) | |||||||
\(548\) | −3.53736 | −0.151109 | ||||||||
\(549\) | −3.11310 | −0.132864 | ||||||||
\(550\) | 4.85935 | 0.207203 | ||||||||
\(551\) | 16.2650 | 0.692913 | ||||||||
\(552\) | −7.02228 | −0.298888 | ||||||||
\(553\) | 0.502766 | 0.0213798 | ||||||||
\(554\) | −18.9045 | −0.803175 | ||||||||
\(555\) | 1.49684 | 0.0635372 | ||||||||
\(556\) | 10.0260 | 0.425195 | ||||||||
\(557\) | −33.5713 | −1.42246 | −0.711231 | − | 0.702958i | \(-0.751862\pi\) | ||||
−0.711231 | + | 0.702958i | \(0.751862\pi\) | |||||||
\(558\) | 15.0769 | 0.638256 | ||||||||
\(559\) | 51.8358 | 2.19242 | ||||||||
\(560\) | −0.0663595 | −0.00280420 | ||||||||
\(561\) | −1.83641 | −0.0775333 | ||||||||
\(562\) | 27.4959 | 1.15985 | ||||||||
\(563\) | 45.5619 | 1.92021 | 0.960103 | − | 0.279646i | \(-0.0902172\pi\) | ||||
0.960103 | + | 0.279646i | \(0.0902172\pi\) | |||||||
\(564\) | 8.39906 | 0.353664 | ||||||||
\(565\) | −7.81065 | −0.328597 | ||||||||
\(566\) | −6.24017 | −0.262294 | ||||||||
\(567\) | −0.179778 | −0.00754996 | ||||||||
\(568\) | −8.55660 | −0.359027 | ||||||||
\(569\) | 24.0234 | 1.00711 | 0.503556 | − | 0.863962i | \(-0.332025\pi\) | ||||
0.503556 | + | 0.863962i | \(0.332025\pi\) | |||||||
\(570\) | 2.27190 | 0.0951596 | ||||||||
\(571\) | −37.8054 | −1.58211 | −0.791054 | − | 0.611747i | \(-0.790467\pi\) | ||||
−0.791054 | + | 0.611747i | \(0.790467\pi\) | |||||||
\(572\) | 5.77706 | 0.241551 | ||||||||
\(573\) | −4.68570 | −0.195748 | ||||||||
\(574\) | 2.05093 | 0.0856040 | ||||||||
\(575\) | −29.9177 | −1.24765 | ||||||||
\(576\) | −1.69906 | −0.0707942 | ||||||||
\(577\) | −39.3180 | −1.63683 | −0.818414 | − | 0.574629i | \(-0.805147\pi\) | ||||
−0.818414 | + | 0.574629i | \(0.805147\pi\) | |||||||
\(578\) | 14.4077 | 0.599282 | ||||||||
\(579\) | −22.5872 | −0.938693 | ||||||||
\(580\) | −1.14849 | −0.0476883 | ||||||||
\(581\) | 1.39251 | 0.0577711 | ||||||||
\(582\) | −8.18568 | −0.339307 | ||||||||
\(583\) | −11.0118 | −0.456062 | ||||||||
\(584\) | 6.63706 | 0.274643 | ||||||||
\(585\) | 3.68114 | 0.152196 | ||||||||
\(586\) | 16.9894 | 0.701827 | ||||||||
\(587\) | 31.7779 | 1.31162 | 0.655808 | − | 0.754928i | \(-0.272328\pi\) | ||||
0.655808 | + | 0.754928i | \(0.272328\pi\) | |||||||
\(588\) | −7.94840 | −0.327787 | ||||||||
\(589\) | 47.1301 | 1.94196 | ||||||||
\(590\) | −3.75728 | −0.154685 | ||||||||
\(591\) | −1.14059 | −0.0469175 | ||||||||
\(592\) | −3.49928 | −0.143820 | ||||||||
\(593\) | 48.3451 | 1.98530 | 0.992648 | − | 0.121038i | \(-0.0386223\pi\) | ||||
0.992648 | + | 0.121038i | \(0.0386223\pi\) | |||||||
\(594\) | 5.35969 | 0.219911 | ||||||||
\(595\) | 0.106843 | 0.00438012 | ||||||||
\(596\) | 24.1445 | 0.988996 | ||||||||
\(597\) | 19.7154 | 0.806897 | ||||||||
\(598\) | −35.5678 | −1.45447 | ||||||||
\(599\) | −32.3091 | −1.32011 | −0.660057 | − | 0.751215i | \(-0.729468\pi\) | ||||
−0.660057 | + | 0.751215i | \(0.729468\pi\) | |||||||
\(600\) | 5.54252 | 0.226272 | ||||||||
\(601\) | −4.59377 | −0.187384 | −0.0936919 | − | 0.995601i | \(-0.529867\pi\) | ||||
−0.0936919 | + | 0.995601i | \(0.529867\pi\) | |||||||
\(602\) | −1.58767 | −0.0647086 | ||||||||
\(603\) | −2.56211 | −0.104337 | ||||||||
\(604\) | −0.198077 | −0.00805965 | ||||||||
\(605\) | −0.375030 | −0.0152472 | ||||||||
\(606\) | 16.7430 | 0.680138 | ||||||||
\(607\) | −20.1052 | −0.816043 | −0.408021 | − | 0.912972i | \(-0.633781\pi\) | ||||
−0.408021 | + | 0.912972i | \(0.633781\pi\) | |||||||
\(608\) | −5.31123 | −0.215399 | ||||||||
\(609\) | 0.618052 | 0.0250447 | ||||||||
\(610\) | 0.687148 | 0.0278218 | ||||||||
\(611\) | 42.5411 | 1.72103 | ||||||||
\(612\) | 2.73558 | 0.110579 | ||||||||
\(613\) | 5.58115 | 0.225421 | 0.112710 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112710 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(614\) | 30.2004 | 1.21879 | ||||||||
\(615\) | 4.95802 | 0.199927 | ||||||||
\(616\) | −0.176944 | −0.00712929 | ||||||||
\(617\) | 13.6960 | 0.551378 | 0.275689 | − | 0.961247i | \(-0.411094\pi\) | ||||
0.275689 | + | 0.961247i | \(0.411094\pi\) | |||||||
\(618\) | −6.77064 | −0.272355 | ||||||||
\(619\) | 20.9151 | 0.840650 | 0.420325 | − | 0.907374i | \(-0.361916\pi\) | ||||
0.420325 | + | 0.907374i | \(0.361916\pi\) | |||||||
\(620\) | −3.32790 | −0.133652 | ||||||||
\(621\) | −32.9981 | −1.32417 | ||||||||
\(622\) | −25.5594 | −1.02484 | ||||||||
\(623\) | 0.156714 | 0.00627862 | ||||||||
\(624\) | 6.58924 | 0.263781 | ||||||||
\(625\) | 22.9101 | 0.916403 | ||||||||
\(626\) | −26.4591 | −1.05752 | ||||||||
\(627\) | 6.05792 | 0.241930 | ||||||||
\(628\) | 20.2212 | 0.806913 | ||||||||
\(629\) | 5.63404 | 0.224644 | ||||||||
\(630\) | −0.112749 | −0.00449202 | ||||||||
\(631\) | −9.86703 | −0.392800 | −0.196400 | − | 0.980524i | \(-0.562925\pi\) | ||||
−0.196400 | + | 0.980524i | \(0.562925\pi\) | |||||||
\(632\) | −2.84138 | −0.113024 | ||||||||
\(633\) | −7.03457 | −0.279599 | ||||||||
\(634\) | −26.8098 | −1.06475 | ||||||||
\(635\) | −2.14268 | −0.0850297 | ||||||||
\(636\) | −12.5599 | −0.498033 | ||||||||
\(637\) | −40.2586 | −1.59510 | ||||||||
\(638\) | −3.06238 | −0.121241 | ||||||||
\(639\) | −14.5382 | −0.575122 | ||||||||
\(640\) | 0.375030 | 0.0148244 | ||||||||
\(641\) | 44.8732 | 1.77239 | 0.886193 | − | 0.463317i | \(-0.153341\pi\) | ||||
0.886193 | + | 0.463317i | \(0.153341\pi\) | |||||||
\(642\) | 12.6395 | 0.498842 | ||||||||
\(643\) | 29.4827 | 1.16268 | 0.581342 | − | 0.813660i | \(-0.302528\pi\) | ||||
0.581342 | + | 0.813660i | \(0.302528\pi\) | |||||||
\(644\) | 1.08940 | 0.0429283 | ||||||||
\(645\) | −3.83812 | −0.151126 | ||||||||
\(646\) | 8.55137 | 0.336449 | ||||||||
\(647\) | 14.0866 | 0.553800 | 0.276900 | − | 0.960899i | \(-0.410693\pi\) | ||||
0.276900 | + | 0.960899i | \(0.410693\pi\) | |||||||
\(648\) | 1.01601 | 0.0399127 | ||||||||
\(649\) | −10.0186 | −0.393264 | ||||||||
\(650\) | 28.0728 | 1.10110 | ||||||||
\(651\) | 1.79089 | 0.0701905 | ||||||||
\(652\) | 11.7335 | 0.459519 | ||||||||
\(653\) | 17.9797 | 0.703601 | 0.351801 | − | 0.936075i | \(-0.385570\pi\) | ||||
0.351801 | + | 0.936075i | \(0.385570\pi\) | |||||||
\(654\) | −4.59203 | −0.179563 | ||||||||
\(655\) | −4.86749 | −0.190188 | ||||||||
\(656\) | −11.5908 | −0.452544 | ||||||||
\(657\) | 11.2768 | 0.439948 | ||||||||
\(658\) | −1.30298 | −0.0507956 | ||||||||
\(659\) | −33.0433 | −1.28719 | −0.643593 | − | 0.765368i | \(-0.722557\pi\) | ||||
−0.643593 | + | 0.765368i | \(0.722557\pi\) | |||||||
\(660\) | −0.427755 | −0.0166503 | ||||||||
\(661\) | 33.7044 | 1.31095 | 0.655474 | − | 0.755218i | \(-0.272469\pi\) | ||||
0.655474 | + | 0.755218i | \(0.272469\pi\) | |||||||
\(662\) | 2.24781 | 0.0873635 | ||||||||
\(663\) | −10.6090 | −0.412021 | ||||||||
\(664\) | −7.86977 | −0.305406 | ||||||||
\(665\) | −0.352451 | −0.0136674 | ||||||||
\(666\) | −5.94550 | −0.230383 | ||||||||
\(667\) | 18.8542 | 0.730039 | ||||||||
\(668\) | 19.8909 | 0.769602 | ||||||||
\(669\) | −24.1075 | −0.932052 | ||||||||
\(670\) | 0.565530 | 0.0218483 | ||||||||
\(671\) | 1.83225 | 0.0707331 | ||||||||
\(672\) | −0.201821 | −0.00778540 | ||||||||
\(673\) | −3.52827 | −0.136005 | −0.0680023 | − | 0.997685i | \(-0.521663\pi\) | ||||
−0.0680023 | + | 0.997685i | \(0.521663\pi\) | |||||||
\(674\) | 20.0951 | 0.774034 | ||||||||
\(675\) | 26.0446 | 1.00246 | ||||||||
\(676\) | 20.3744 | 0.783632 | ||||||||
\(677\) | 31.2837 | 1.20233 | 0.601166 | − | 0.799124i | \(-0.294703\pi\) | ||||
0.601166 | + | 0.799124i | \(0.294703\pi\) | |||||||
\(678\) | −23.7547 | −0.912293 | ||||||||
\(679\) | 1.26988 | 0.0487336 | ||||||||
\(680\) | −0.603820 | −0.0231554 | ||||||||
\(681\) | −19.1849 | −0.735168 | ||||||||
\(682\) | −8.87367 | −0.339790 | ||||||||
\(683\) | 12.2691 | 0.469464 | 0.234732 | − | 0.972060i | \(-0.424579\pi\) | ||||
0.234732 | + | 0.972060i | \(0.424579\pi\) | |||||||
\(684\) | −9.02409 | −0.345045 | ||||||||
\(685\) | 1.32662 | 0.0506875 | ||||||||
\(686\) | 2.47168 | 0.0943693 | ||||||||
\(687\) | 23.3607 | 0.891265 | ||||||||
\(688\) | 8.97270 | 0.342081 | ||||||||
\(689\) | −63.6158 | −2.42357 | ||||||||
\(690\) | 2.63357 | 0.100258 | ||||||||
\(691\) | 30.1833 | 1.14823 | 0.574113 | − | 0.818776i | \(-0.305347\pi\) | ||||
0.574113 | + | 0.818776i | \(0.305347\pi\) | |||||||
\(692\) | 20.3715 | 0.774408 | ||||||||
\(693\) | −0.300639 | −0.0114203 | ||||||||
\(694\) | −7.48401 | −0.284089 | ||||||||
\(695\) | −3.76004 | −0.142626 | ||||||||
\(696\) | −3.49292 | −0.132399 | ||||||||
\(697\) | 18.6618 | 0.706867 | ||||||||
\(698\) | 3.60092 | 0.136297 | ||||||||
\(699\) | −30.1578 | −1.14067 | ||||||||
\(700\) | −0.859835 | −0.0324987 | ||||||||
\(701\) | 5.77248 | 0.218024 | 0.109012 | − | 0.994040i | \(-0.465231\pi\) | ||||
0.109012 | + | 0.994040i | \(0.465231\pi\) | |||||||
\(702\) | 30.9633 | 1.16863 | ||||||||
\(703\) | −18.5855 | −0.700965 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −3.14990 | −0.118632 | ||||||||
\(706\) | 19.9929 | 0.752442 | ||||||||
\(707\) | −2.59742 | −0.0976860 | ||||||||
\(708\) | −11.4271 | −0.429456 | ||||||||
\(709\) | 31.3260 | 1.17647 | 0.588237 | − | 0.808689i | \(-0.299822\pi\) | ||||
0.588237 | + | 0.808689i | \(0.299822\pi\) | |||||||
\(710\) | 3.20899 | 0.120431 | ||||||||
\(711\) | −4.82767 | −0.181052 | ||||||||
\(712\) | −0.885668 | −0.0331918 | ||||||||
\(713\) | 54.6327 | 2.04601 | ||||||||
\(714\) | 0.324942 | 0.0121607 | ||||||||
\(715\) | −2.16657 | −0.0810253 | ||||||||
\(716\) | 11.3922 | 0.425745 | ||||||||
\(717\) | −25.2381 | −0.942535 | ||||||||
\(718\) | −17.4829 | −0.652457 | ||||||||
\(719\) | −24.2491 | −0.904339 | −0.452170 | − | 0.891932i | \(-0.649350\pi\) | ||||
−0.452170 | + | 0.891932i | \(0.649350\pi\) | |||||||
\(720\) | 0.637199 | 0.0237470 | ||||||||
\(721\) | 1.05036 | 0.0391174 | ||||||||
\(722\) | −9.20912 | −0.342728 | ||||||||
\(723\) | 14.5100 | 0.539631 | ||||||||
\(724\) | −8.49660 | −0.315774 | ||||||||
\(725\) | −14.8812 | −0.552674 | ||||||||
\(726\) | −1.14059 | −0.0423312 | ||||||||
\(727\) | −21.0147 | −0.779393 | −0.389697 | − | 0.920943i | \(-0.627420\pi\) | ||||
−0.389697 | + | 0.920943i | \(0.627420\pi\) | |||||||
\(728\) | −1.02222 | −0.0378860 | ||||||||
\(729\) | 20.0658 | 0.743180 | ||||||||
\(730\) | −2.48910 | −0.0921257 | ||||||||
\(731\) | −14.4465 | −0.534325 | ||||||||
\(732\) | 2.08984 | 0.0772426 | ||||||||
\(733\) | −23.0662 | −0.851970 | −0.425985 | − | 0.904730i | \(-0.640072\pi\) | ||||
−0.425985 | + | 0.904730i | \(0.640072\pi\) | |||||||
\(734\) | −29.5756 | −1.09165 | ||||||||
\(735\) | 2.98089 | 0.109952 | ||||||||
\(736\) | −6.15672 | −0.226940 | ||||||||
\(737\) | 1.50796 | 0.0555463 | ||||||||
\(738\) | −19.6934 | −0.724926 | ||||||||
\(739\) | 1.69074 | 0.0621950 | 0.0310975 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310975 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(740\) | 1.31234 | 0.0482425 | ||||||||
\(741\) | 34.9970 | 1.28565 | ||||||||
\(742\) | 1.94848 | 0.0715308 | ||||||||
\(743\) | −23.1676 | −0.849937 | −0.424969 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424969 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(744\) | −10.1212 | −0.371061 | ||||||||
\(745\) | −9.05492 | −0.331746 | ||||||||
\(746\) | −23.6488 | −0.865843 | ||||||||
\(747\) | −13.3712 | −0.489227 | ||||||||
\(748\) | −1.61006 | −0.0588695 | ||||||||
\(749\) | −1.96083 | −0.0716470 | ||||||||
\(750\) | −4.21739 | −0.153997 | ||||||||
\(751\) | 12.5875 | 0.459323 | 0.229661 | − | 0.973271i | \(-0.426238\pi\) | ||||
0.229661 | + | 0.973271i | \(0.426238\pi\) | |||||||
\(752\) | 7.36380 | 0.268530 | ||||||||
\(753\) | −1.59417 | −0.0580949 | ||||||||
\(754\) | −17.6916 | −0.644289 | ||||||||
\(755\) | 0.0742850 | 0.00270351 | ||||||||
\(756\) | −0.948367 | −0.0344918 | ||||||||
\(757\) | −25.9849 | −0.944439 | −0.472220 | − | 0.881481i | \(-0.656547\pi\) | ||||
−0.472220 | + | 0.881481i | \(0.656547\pi\) | |||||||
\(758\) | −22.9373 | −0.833120 | ||||||||
\(759\) | 7.02228 | 0.254893 | ||||||||
\(760\) | 1.99187 | 0.0722528 | ||||||||
\(761\) | −39.9523 | −1.44827 | −0.724135 | − | 0.689658i | \(-0.757761\pi\) | ||||
−0.724135 | + | 0.689658i | \(0.757761\pi\) | |||||||
\(762\) | −6.51658 | −0.236071 | ||||||||
\(763\) | 0.712382 | 0.0257900 | ||||||||
\(764\) | −4.10814 | −0.148627 | ||||||||
\(765\) | −1.02593 | −0.0370925 | ||||||||
\(766\) | 18.5190 | 0.669119 | ||||||||
\(767\) | −57.8780 | −2.08985 | ||||||||
\(768\) | 1.14059 | 0.0411574 | ||||||||
\(769\) | 15.2858 | 0.551220 | 0.275610 | − | 0.961270i | \(-0.411120\pi\) | ||||
0.275610 | + | 0.961270i | \(0.411120\pi\) | |||||||
\(770\) | 0.0663595 | 0.00239143 | ||||||||
\(771\) | −25.2221 | −0.908354 | ||||||||
\(772\) | −19.8031 | −0.712731 | ||||||||
\(773\) | 41.8515 | 1.50529 | 0.752647 | − | 0.658424i | \(-0.228777\pi\) | ||||
0.752647 | + | 0.658424i | \(0.228777\pi\) | |||||||
\(774\) | 15.2452 | 0.547976 | ||||||||
\(775\) | −43.1203 | −1.54893 | ||||||||
\(776\) | −7.17673 | −0.257629 | ||||||||
\(777\) | −0.706228 | −0.0253358 | ||||||||
\(778\) | 18.5454 | 0.664884 | ||||||||
\(779\) | −61.5613 | −2.20566 | ||||||||
\(780\) | −2.47117 | −0.0884820 | ||||||||
\(781\) | 8.55660 | 0.306179 | ||||||||
\(782\) | 9.91266 | 0.354476 | ||||||||
\(783\) | −16.4134 | −0.586568 | ||||||||
\(784\) | −6.96869 | −0.248882 | ||||||||
\(785\) | −7.58356 | −0.270669 | ||||||||
\(786\) | −14.8036 | −0.528026 | ||||||||
\(787\) | −2.30597 | −0.0821991 | −0.0410995 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0410995 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(788\) | −1.00000 | −0.0356235 | ||||||||
\(789\) | 4.52990 | 0.161269 | ||||||||
\(790\) | 1.06560 | 0.0379124 | ||||||||
\(791\) | 3.68517 | 0.131030 | ||||||||
\(792\) | 1.69906 | 0.0603735 | ||||||||
\(793\) | 10.5850 | 0.375884 | ||||||||
\(794\) | −2.64088 | −0.0937214 | ||||||||
\(795\) | 4.71035 | 0.167059 | ||||||||
\(796\) | 17.2853 | 0.612661 | ||||||||
\(797\) | −25.3488 | −0.897902 | −0.448951 | − | 0.893556i | \(-0.648202\pi\) | ||||
−0.448951 | + | 0.893556i | \(0.648202\pi\) | |||||||
\(798\) | −1.07191 | −0.0379454 | ||||||||
\(799\) | −11.8561 | −0.419440 | ||||||||
\(800\) | 4.85935 | 0.171804 | ||||||||
\(801\) | −1.50480 | −0.0531696 | ||||||||
\(802\) | 24.6618 | 0.870840 | ||||||||
\(803\) | −6.63706 | −0.234217 | ||||||||
\(804\) | 1.71996 | 0.0606582 | ||||||||
\(805\) | −0.408557 | −0.0143998 | ||||||||
\(806\) | −51.2637 | −1.80569 | ||||||||
\(807\) | 29.2763 | 1.03057 | ||||||||
\(808\) | 14.6793 | 0.516416 | ||||||||
\(809\) | 6.17589 | 0.217133 | 0.108566 | − | 0.994089i | \(-0.465374\pi\) | ||||
0.108566 | + | 0.994089i | \(0.465374\pi\) | |||||||
\(810\) | −0.381036 | −0.0133882 | ||||||||
\(811\) | −43.7164 | −1.53509 | −0.767545 | − | 0.640995i | \(-0.778522\pi\) | ||||
−0.767545 | + | 0.640995i | \(0.778522\pi\) | |||||||
\(812\) | 0.541872 | 0.0190160 | ||||||||
\(813\) | −0.415386 | −0.0145682 | ||||||||
\(814\) | 3.49928 | 0.122650 | ||||||||
\(815\) | −4.40042 | −0.154140 | ||||||||
\(816\) | −1.83641 | −0.0642872 | ||||||||
\(817\) | 47.6560 | 1.66727 | ||||||||
\(818\) | 3.50713 | 0.122624 | ||||||||
\(819\) | −1.73681 | −0.0606891 | ||||||||
\(820\) | 4.34690 | 0.151800 | ||||||||
\(821\) | −16.7716 | −0.585332 | −0.292666 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292666 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(822\) | 4.03467 | 0.140725 | ||||||||
\(823\) | 19.9978 | 0.697080 | 0.348540 | − | 0.937294i | \(-0.386678\pi\) | ||||
0.348540 | + | 0.937294i | \(0.386678\pi\) | |||||||
\(824\) | −5.93610 | −0.206794 | ||||||||
\(825\) | −5.54252 | −0.192966 | ||||||||
\(826\) | 1.77273 | 0.0616813 | ||||||||
\(827\) | 3.08574 | 0.107302 | 0.0536508 | − | 0.998560i | \(-0.482914\pi\) | ||||
0.0536508 | + | 0.998560i | \(0.482914\pi\) | |||||||
\(828\) | −10.4606 | −0.363532 | ||||||||
\(829\) | −41.5406 | −1.44276 | −0.721382 | − | 0.692537i | \(-0.756493\pi\) | ||||
−0.721382 | + | 0.692537i | \(0.756493\pi\) | |||||||
\(830\) | 2.95140 | 0.102445 | ||||||||
\(831\) | 21.5622 | 0.747986 | ||||||||
\(832\) | 5.77706 | 0.200284 | ||||||||
\(833\) | 11.2200 | 0.388749 | ||||||||
\(834\) | −11.4355 | −0.395978 | ||||||||
\(835\) | −7.45969 | −0.258153 | ||||||||
\(836\) | 5.31123 | 0.183693 | ||||||||
\(837\) | −47.5601 | −1.64392 | ||||||||
\(838\) | 4.67818 | 0.161605 | ||||||||
\(839\) | −10.8880 | −0.375895 | −0.187948 | − | 0.982179i | \(-0.560184\pi\) | ||||
−0.187948 | + | 0.982179i | \(0.560184\pi\) | |||||||
\(840\) | 0.0756889 | 0.00261151 | ||||||||
\(841\) | −19.6218 | −0.676614 | ||||||||
\(842\) | 26.2204 | 0.903615 | ||||||||
\(843\) | −31.3615 | −1.08015 | ||||||||
\(844\) | −6.16750 | −0.212294 | ||||||||
\(845\) | −7.64104 | −0.262860 | ||||||||
\(846\) | 12.5115 | 0.430156 | ||||||||
\(847\) | 0.176944 | 0.00607988 | ||||||||
\(848\) | −11.0118 | −0.378147 | ||||||||
\(849\) | 7.11746 | 0.244270 | ||||||||
\(850\) | −7.82383 | −0.268355 | ||||||||
\(851\) | −21.5441 | −0.738523 | ||||||||
\(852\) | 9.75955 | 0.334357 | ||||||||
\(853\) | −38.0063 | −1.30131 | −0.650655 | − | 0.759373i | \(-0.725506\pi\) | ||||
−0.650655 | + | 0.759373i | \(0.725506\pi\) | |||||||
\(854\) | −0.324206 | −0.0110941 | ||||||||
\(855\) | 3.38431 | 0.115741 | ||||||||
\(856\) | 11.0816 | 0.378761 | ||||||||
\(857\) | −29.0051 | −0.990796 | −0.495398 | − | 0.868666i | \(-0.664978\pi\) | ||||
−0.495398 | + | 0.868666i | \(0.664978\pi\) | |||||||
\(858\) | −6.58924 | −0.224953 | ||||||||
\(859\) | −26.7452 | −0.912535 | −0.456267 | − | 0.889843i | \(-0.650814\pi\) | ||||
−0.456267 | + | 0.889843i | \(0.650814\pi\) | |||||||
\(860\) | −3.36504 | −0.114747 | ||||||||
\(861\) | −2.33926 | −0.0797217 | ||||||||
\(862\) | 4.21940 | 0.143713 | ||||||||
\(863\) | −7.92679 | −0.269831 | −0.134916 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134916 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(864\) | 5.35969 | 0.182340 | ||||||||
\(865\) | −7.63993 | −0.259765 | ||||||||
\(866\) | 26.6218 | 0.904646 | ||||||||
\(867\) | −16.4333 | −0.558103 | ||||||||
\(868\) | 1.57015 | 0.0532942 | ||||||||
\(869\) | 2.84138 | 0.0963871 | ||||||||
\(870\) | 1.30995 | 0.0444115 | ||||||||
\(871\) | 8.71156 | 0.295180 | ||||||||
\(872\) | −4.02602 | −0.136338 | ||||||||
\(873\) | −12.1937 | −0.412694 | ||||||||
\(874\) | −32.6997 | −1.10609 | ||||||||
\(875\) | 0.654262 | 0.0221181 | ||||||||
\(876\) | −7.57014 | −0.255771 | ||||||||
\(877\) | −35.7593 | −1.20751 | −0.603753 | − | 0.797172i | \(-0.706329\pi\) | ||||
−0.603753 | + | 0.797172i | \(0.706329\pi\) | |||||||
\(878\) | −0.548668 | −0.0185167 | ||||||||
\(879\) | −19.3779 | −0.653601 | ||||||||
\(880\) | −0.375030 | −0.0126423 | ||||||||
\(881\) | −6.35043 | −0.213951 | −0.106976 | − | 0.994262i | \(-0.534117\pi\) | ||||
−0.106976 | + | 0.994262i | \(0.534117\pi\) | |||||||
\(882\) | −11.8402 | −0.398681 | ||||||||
\(883\) | 19.9632 | 0.671816 | 0.335908 | − | 0.941895i | \(-0.390957\pi\) | ||||
0.335908 | + | 0.941895i | \(0.390957\pi\) | |||||||
\(884\) | −9.30139 | −0.312840 | ||||||||
\(885\) | 4.28550 | 0.144056 | ||||||||
\(886\) | −33.8396 | −1.13686 | ||||||||
\(887\) | −9.65391 | −0.324147 | −0.162073 | − | 0.986779i | \(-0.551818\pi\) | ||||
−0.162073 | + | 0.986779i | \(0.551818\pi\) | |||||||
\(888\) | 3.99124 | 0.133937 | ||||||||
\(889\) | 1.01095 | 0.0339060 | ||||||||
\(890\) | 0.332153 | 0.0111338 | ||||||||
\(891\) | −1.01601 | −0.0340377 | ||||||||
\(892\) | −21.1361 | −0.707688 | ||||||||
\(893\) | 39.1108 | 1.30879 | ||||||||
\(894\) | −27.5389 | −0.921038 | ||||||||
\(895\) | −4.27241 | −0.142811 | ||||||||
\(896\) | −0.176944 | −0.00591130 | ||||||||
\(897\) | 40.5681 | 1.35453 | ||||||||
\(898\) | −0.977296 | −0.0326128 | ||||||||
\(899\) | 27.1746 | 0.906323 | ||||||||
\(900\) | 8.25633 | 0.275211 | ||||||||
\(901\) | 17.7296 | 0.590659 | ||||||||
\(902\) | 11.5908 | 0.385931 | ||||||||
\(903\) | 1.81088 | 0.0602622 | ||||||||
\(904\) | −20.8267 | −0.692686 | ||||||||
\(905\) | 3.18648 | 0.105922 | ||||||||
\(906\) | 0.225925 | 0.00750584 | ||||||||
\(907\) | −7.13100 | −0.236781 | −0.118390 | − | 0.992967i | \(-0.537773\pi\) | ||||
−0.118390 | + | 0.992967i | \(0.537773\pi\) | |||||||
\(908\) | −16.8202 | −0.558199 | ||||||||
\(909\) | 24.9410 | 0.827241 | ||||||||
\(910\) | 0.383363 | 0.0127084 | ||||||||
\(911\) | −0.408592 | −0.0135373 | −0.00676863 | − | 0.999977i | \(-0.502155\pi\) | ||||
−0.00676863 | + | 0.999977i | \(0.502155\pi\) | |||||||
\(912\) | 6.05792 | 0.200598 | ||||||||
\(913\) | 7.86977 | 0.260451 | ||||||||
\(914\) | 0.113660 | 0.00375954 | ||||||||
\(915\) | −0.783753 | −0.0259101 | ||||||||
\(916\) | 20.4813 | 0.676720 | ||||||||
\(917\) | 2.29655 | 0.0758386 | ||||||||
\(918\) | −8.62940 | −0.284813 | ||||||||
\(919\) | 27.7150 | 0.914232 | 0.457116 | − | 0.889407i | \(-0.348882\pi\) | ||||
0.457116 | + | 0.889407i | \(0.348882\pi\) | |||||||
\(920\) | 2.30896 | 0.0761241 | ||||||||
\(921\) | −34.4462 | −1.13504 | ||||||||
\(922\) | −3.00340 | −0.0989118 | ||||||||
\(923\) | 49.4320 | 1.62707 | ||||||||
\(924\) | 0.201821 | 0.00663941 | ||||||||
\(925\) | 17.0043 | 0.559097 | ||||||||
\(926\) | −14.9797 | −0.492264 | ||||||||
\(927\) | −10.0858 | −0.331261 | ||||||||
\(928\) | −3.06238 | −0.100528 | ||||||||
\(929\) | −49.5070 | −1.62427 | −0.812136 | − | 0.583468i | \(-0.801695\pi\) | ||||
−0.812136 | + | 0.583468i | \(0.801695\pi\) | |||||||
\(930\) | 3.79576 | 0.124468 | ||||||||
\(931\) | −37.0123 | −1.21303 | ||||||||
\(932\) | −26.4406 | −0.866091 | ||||||||
\(933\) | 29.1527 | 0.954417 | ||||||||
\(934\) | 26.3116 | 0.860942 | ||||||||
\(935\) | 0.603820 | 0.0197470 | ||||||||
\(936\) | 9.81558 | 0.320832 | ||||||||
\(937\) | −14.9508 | −0.488421 | −0.244211 | − | 0.969722i | \(-0.578529\pi\) | ||||
−0.244211 | + | 0.969722i | \(0.578529\pi\) | |||||||
\(938\) | −0.266825 | −0.00871213 | ||||||||
\(939\) | 30.1789 | 0.984852 | ||||||||
\(940\) | −2.76165 | −0.0900751 | ||||||||
\(941\) | 31.4853 | 1.02639 | 0.513196 | − | 0.858271i | \(-0.328461\pi\) | ||||
0.513196 | + | 0.858271i | \(0.328461\pi\) | |||||||
\(942\) | −23.0640 | −0.751467 | ||||||||
\(943\) | −71.3612 | −2.32384 | ||||||||
\(944\) | −10.0186 | −0.326077 | ||||||||
\(945\) | 0.355667 | 0.0115698 | ||||||||
\(946\) | −8.97270 | −0.291728 | ||||||||
\(947\) | 11.7996 | 0.383436 | 0.191718 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191718 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(948\) | 3.24084 | 0.105258 | ||||||||
\(949\) | −38.3427 | −1.24466 | ||||||||
\(950\) | 25.8091 | 0.837358 | ||||||||
\(951\) | 30.5789 | 0.991589 | ||||||||
\(952\) | 0.284890 | 0.00923335 | ||||||||
\(953\) | −22.0070 | −0.712877 | −0.356439 | − | 0.934319i | \(-0.616009\pi\) | ||||
−0.356439 | + | 0.934319i | \(0.616009\pi\) | |||||||
\(954\) | −18.7097 | −0.605749 | ||||||||
\(955\) | 1.54068 | 0.0498552 | ||||||||
\(956\) | −22.1273 | −0.715648 | ||||||||
\(957\) | 3.49292 | 0.112910 | ||||||||
\(958\) | 25.7015 | 0.830377 | ||||||||
\(959\) | −0.625916 | −0.0202119 | ||||||||
\(960\) | −0.427755 | −0.0138057 | ||||||||
\(961\) | 47.7420 | 1.54006 | ||||||||
\(962\) | 20.2156 | 0.651777 | ||||||||
\(963\) | 18.8283 | 0.606733 | ||||||||
\(964\) | 12.7215 | 0.409731 | ||||||||
\(965\) | 7.42678 | 0.239077 | ||||||||
\(966\) | −1.24255 | −0.0399785 | ||||||||
\(967\) | −26.5423 | −0.853542 | −0.426771 | − | 0.904360i | \(-0.640349\pi\) | ||||
−0.426771 | + | 0.904360i | \(0.640349\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −9.75358 | −0.313330 | ||||||||
\(970\) | 2.69149 | 0.0864186 | ||||||||
\(971\) | 37.2714 | 1.19609 | 0.598047 | − | 0.801461i | \(-0.295943\pi\) | ||||
0.598047 | + | 0.801461i | \(0.295943\pi\) | |||||||
\(972\) | 14.9202 | 0.478566 | ||||||||
\(973\) | 1.77404 | 0.0568730 | ||||||||
\(974\) | −15.4358 | −0.494595 | ||||||||
\(975\) | −32.0195 | −1.02544 | ||||||||
\(976\) | 1.83225 | 0.0586488 | ||||||||
\(977\) | −14.6805 | −0.469672 | −0.234836 | − | 0.972035i | \(-0.575455\pi\) | ||||
−0.234836 | + | 0.972035i | \(0.575455\pi\) | |||||||
\(978\) | −13.3831 | −0.427944 | ||||||||
\(979\) | 0.885668 | 0.0283061 | ||||||||
\(980\) | 2.61347 | 0.0834843 | ||||||||
\(981\) | −6.84045 | −0.218399 | ||||||||
\(982\) | −13.1337 | −0.419115 | ||||||||
\(983\) | 1.57010 | 0.0500785 | 0.0250393 | − | 0.999686i | \(-0.492029\pi\) | ||||
0.0250393 | + | 0.999686i | \(0.492029\pi\) | |||||||
\(984\) | 13.2203 | 0.421448 | ||||||||
\(985\) | 0.375030 | 0.0119495 | ||||||||
\(986\) | 4.93061 | 0.157023 | ||||||||
\(987\) | 1.48617 | 0.0473052 | ||||||||
\(988\) | 30.6833 | 0.976165 | ||||||||
\(989\) | 55.2424 | 1.75661 | ||||||||
\(990\) | −0.637199 | −0.0202515 | ||||||||
\(991\) | 24.8193 | 0.788411 | 0.394205 | − | 0.919022i | \(-0.371020\pi\) | ||||
0.394205 | + | 0.919022i | \(0.371020\pi\) | |||||||
\(992\) | −8.87367 | −0.281739 | ||||||||
\(993\) | −2.56382 | −0.0813604 | ||||||||
\(994\) | −1.51404 | −0.0480225 | ||||||||
\(995\) | −6.48251 | −0.205509 | ||||||||
\(996\) | 8.97616 | 0.284421 | ||||||||
\(997\) | −33.5113 | −1.06131 | −0.530657 | − | 0.847587i | \(-0.678055\pi\) | ||||
−0.530657 | + | 0.847587i | \(0.678055\pi\) | |||||||
\(998\) | −1.38739 | −0.0439170 | ||||||||
\(999\) | 18.7551 | 0.593384 |
(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 | 4334.2.a.h.1.18 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.h.1.18 | ✓ | 27 | 1.1 | even | 1 | trivial |