Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.473620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.161383 | 0.114115 | 0.0570577 | − | 0.998371i | \(-0.481828\pi\) | ||||
0.0570577 | + | 0.998371i | \(0.481828\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97396 | −0.986978 | ||||||||
\(5\) | 2.08087 | 0.930592 | 0.465296 | − | 0.885155i | \(-0.345948\pi\) | ||||
0.465296 | + | 0.885155i | \(0.345948\pi\) | |||||||
\(6\) | −0.161383 | −0.0658845 | ||||||||
\(7\) | 3.66994 | 1.38711 | 0.693554 | − | 0.720405i | \(-0.256044\pi\) | ||||
0.693554 | + | 0.720405i | \(0.256044\pi\) | |||||||
\(8\) | −0.641331 | −0.226745 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.335818 | 0.106195 | ||||||||
\(11\) | 3.77836 | 1.13922 | 0.569609 | − | 0.821916i | \(-0.307095\pi\) | ||||
0.569609 | + | 0.821916i | \(0.307095\pi\) | |||||||
\(12\) | 1.97396 | 0.569832 | ||||||||
\(13\) | 3.51085 | 0.973735 | 0.486867 | − | 0.873476i | \(-0.338140\pi\) | ||||
0.486867 | + | 0.873476i | \(0.338140\pi\) | |||||||
\(14\) | 0.592268 | 0.158290 | ||||||||
\(15\) | −2.08087 | −0.537278 | ||||||||
\(16\) | 3.84441 | 0.961103 | ||||||||
\(17\) | 3.02517 | 0.733712 | 0.366856 | − | 0.930278i | \(-0.380434\pi\) | ||||
0.366856 | + | 0.930278i | \(0.380434\pi\) | |||||||
\(18\) | 0.161383 | 0.0380384 | ||||||||
\(19\) | −1.97558 | −0.453230 | −0.226615 | − | 0.973984i | \(-0.572766\pi\) | ||||
−0.226615 | + | 0.973984i | \(0.572766\pi\) | |||||||
\(20\) | −4.10754 | −0.918474 | ||||||||
\(21\) | −3.66994 | −0.800847 | ||||||||
\(22\) | 0.609764 | 0.130002 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.641331 | 0.130911 | ||||||||
\(25\) | −0.669990 | −0.133998 | ||||||||
\(26\) | 0.566593 | 0.111118 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −7.24430 | −1.36904 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −0.335818 | −0.0613116 | ||||||||
\(31\) | −3.58155 | −0.643266 | −0.321633 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321633 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(32\) | 1.90309 | 0.336421 | ||||||||
\(33\) | −3.77836 | −0.657728 | ||||||||
\(34\) | 0.488212 | 0.0837277 | ||||||||
\(35\) | 7.63666 | 1.29083 | ||||||||
\(36\) | −1.97396 | −0.328993 | ||||||||
\(37\) | 5.34560 | 0.878811 | 0.439406 | − | 0.898289i | \(-0.355189\pi\) | ||||
0.439406 | + | 0.898289i | \(0.355189\pi\) | |||||||
\(38\) | −0.318827 | −0.0517205 | ||||||||
\(39\) | −3.51085 | −0.562186 | ||||||||
\(40\) | −1.33452 | −0.211007 | ||||||||
\(41\) | −12.0312 | −1.87896 | −0.939480 | − | 0.342604i | \(-0.888691\pi\) | ||||
−0.939480 | + | 0.342604i | \(0.888691\pi\) | |||||||
\(42\) | −0.592268 | −0.0913890 | ||||||||
\(43\) | 3.68702 | 0.562266 | 0.281133 | − | 0.959669i | \(-0.409290\pi\) | ||||
0.281133 | + | 0.959669i | \(0.409290\pi\) | |||||||
\(44\) | −7.45831 | −1.12438 | ||||||||
\(45\) | 2.08087 | 0.310197 | ||||||||
\(46\) | −0.161383 | −0.0237947 | ||||||||
\(47\) | −0.138067 | −0.0201392 | −0.0100696 | − | 0.999949i | \(-0.503205\pi\) | ||||
−0.0100696 | + | 0.999949i | \(0.503205\pi\) | |||||||
\(48\) | −3.84441 | −0.554893 | ||||||||
\(49\) | 6.46848 | 0.924068 | ||||||||
\(50\) | −0.108125 | −0.0152912 | ||||||||
\(51\) | −3.02517 | −0.423609 | ||||||||
\(52\) | −6.93026 | −0.961054 | ||||||||
\(53\) | 3.01823 | 0.414586 | 0.207293 | − | 0.978279i | \(-0.433535\pi\) | ||||
0.207293 | + | 0.978279i | \(0.433535\pi\) | |||||||
\(54\) | −0.161383 | −0.0219615 | ||||||||
\(55\) | 7.86226 | 1.06015 | ||||||||
\(56\) | −2.35365 | −0.314519 | ||||||||
\(57\) | 1.97558 | 0.261672 | ||||||||
\(58\) | 0.161383 | 0.0211907 | ||||||||
\(59\) | 9.43156 | 1.22788 | 0.613942 | − | 0.789351i | \(-0.289583\pi\) | ||||
0.613942 | + | 0.789351i | \(0.289583\pi\) | |||||||
\(60\) | 4.10754 | 0.530281 | ||||||||
\(61\) | −10.8624 | −1.39079 | −0.695394 | − | 0.718628i | \(-0.744770\pi\) | ||||
−0.695394 | + | 0.718628i | \(0.744770\pi\) | |||||||
\(62\) | −0.578003 | −0.0734065 | ||||||||
\(63\) | 3.66994 | 0.462369 | ||||||||
\(64\) | −7.38169 | −0.922712 | ||||||||
\(65\) | 7.30561 | 0.906150 | ||||||||
\(66\) | −0.609764 | −0.0750568 | ||||||||
\(67\) | 4.57266 | 0.558639 | 0.279320 | − | 0.960198i | \(-0.409891\pi\) | ||||
0.279320 | + | 0.960198i | \(0.409891\pi\) | |||||||
\(68\) | −5.97155 | −0.724157 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.23243 | 0.147304 | ||||||||
\(71\) | −3.28228 | −0.389535 | −0.194768 | − | 0.980849i | \(-0.562395\pi\) | ||||
−0.194768 | + | 0.980849i | \(0.562395\pi\) | |||||||
\(72\) | −0.641331 | −0.0755815 | ||||||||
\(73\) | 1.53135 | 0.179231 | 0.0896153 | − | 0.995976i | \(-0.471436\pi\) | ||||
0.0896153 | + | 0.995976i | \(0.471436\pi\) | |||||||
\(74\) | 0.862691 | 0.100286 | ||||||||
\(75\) | 0.669990 | 0.0773638 | ||||||||
\(76\) | 3.89971 | 0.447328 | ||||||||
\(77\) | 13.8664 | 1.58022 | ||||||||
\(78\) | −0.566593 | −0.0641540 | ||||||||
\(79\) | 7.31941 | 0.823498 | 0.411749 | − | 0.911297i | \(-0.364918\pi\) | ||||
0.411749 | + | 0.911297i | \(0.364918\pi\) | |||||||
\(80\) | 7.99971 | 0.894395 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.94164 | −0.214418 | ||||||||
\(83\) | 5.82693 | 0.639588 | 0.319794 | − | 0.947487i | \(-0.396386\pi\) | ||||
0.319794 | + | 0.947487i | \(0.396386\pi\) | |||||||
\(84\) | 7.24430 | 0.790418 | ||||||||
\(85\) | 6.29498 | 0.682786 | ||||||||
\(86\) | 0.595024 | 0.0641631 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −2.42318 | −0.258311 | ||||||||
\(89\) | 6.06380 | 0.642761 | 0.321381 | − | 0.946950i | \(-0.395853\pi\) | ||||
0.321381 | + | 0.946950i | \(0.395853\pi\) | |||||||
\(90\) | 0.335818 | 0.0353983 | ||||||||
\(91\) | 12.8846 | 1.35067 | ||||||||
\(92\) | 1.97396 | 0.205799 | ||||||||
\(93\) | 3.58155 | 0.371390 | ||||||||
\(94\) | −0.0222817 | −0.00229819 | ||||||||
\(95\) | −4.11093 | −0.421772 | ||||||||
\(96\) | −1.90309 | −0.194233 | ||||||||
\(97\) | −13.5506 | −1.37585 | −0.687926 | − | 0.725781i | \(-0.741479\pi\) | ||||
−0.687926 | + | 0.725781i | \(0.741479\pi\) | |||||||
\(98\) | 1.04391 | 0.105450 | ||||||||
\(99\) | 3.77836 | 0.379739 | ||||||||
\(100\) | 1.32253 | 0.132253 | ||||||||
\(101\) | −5.39674 | −0.536996 | −0.268498 | − | 0.963280i | \(-0.586527\pi\) | ||||
−0.268498 | + | 0.963280i | \(0.586527\pi\) | |||||||
\(102\) | −0.488212 | −0.0483402 | ||||||||
\(103\) | 7.28928 | 0.718234 | 0.359117 | − | 0.933293i | \(-0.383078\pi\) | ||||
0.359117 | + | 0.933293i | \(0.383078\pi\) | |||||||
\(104\) | −2.25162 | −0.220789 | ||||||||
\(105\) | −7.63666 | −0.745262 | ||||||||
\(106\) | 0.487093 | 0.0473106 | ||||||||
\(107\) | −5.92929 | −0.573207 | −0.286603 | − | 0.958049i | \(-0.592526\pi\) | ||||
−0.286603 | + | 0.958049i | \(0.592526\pi\) | |||||||
\(108\) | 1.97396 | 0.189944 | ||||||||
\(109\) | 16.9282 | 1.62143 | 0.810715 | − | 0.585441i | \(-0.199078\pi\) | ||||
0.810715 | + | 0.585441i | \(0.199078\pi\) | |||||||
\(110\) | 1.26884 | 0.120979 | ||||||||
\(111\) | −5.34560 | −0.507382 | ||||||||
\(112\) | 14.1088 | 1.33315 | ||||||||
\(113\) | 6.48668 | 0.610215 | 0.305108 | − | 0.952318i | \(-0.401308\pi\) | ||||
0.305108 | + | 0.952318i | \(0.401308\pi\) | |||||||
\(114\) | 0.318827 | 0.0298608 | ||||||||
\(115\) | −2.08087 | −0.194042 | ||||||||
\(116\) | −1.97396 | −0.183277 | ||||||||
\(117\) | 3.51085 | 0.324578 | ||||||||
\(118\) | 1.52210 | 0.140120 | ||||||||
\(119\) | 11.1022 | 1.01774 | ||||||||
\(120\) | 1.33452 | 0.121825 | ||||||||
\(121\) | 3.27598 | 0.297816 | ||||||||
\(122\) | −1.75301 | −0.158710 | ||||||||
\(123\) | 12.0312 | 1.08482 | ||||||||
\(124\) | 7.06982 | 0.634889 | ||||||||
\(125\) | −11.7985 | −1.05529 | ||||||||
\(126\) | 0.592268 | 0.0527634 | ||||||||
\(127\) | 8.62092 | 0.764983 | 0.382492 | − | 0.923959i | \(-0.375066\pi\) | ||||
0.382492 | + | 0.923959i | \(0.375066\pi\) | |||||||
\(128\) | −4.99746 | −0.441717 | ||||||||
\(129\) | −3.68702 | −0.324624 | ||||||||
\(130\) | 1.17901 | 0.103406 | ||||||||
\(131\) | −4.57907 | −0.400075 | −0.200037 | − | 0.979788i | \(-0.564106\pi\) | ||||
−0.200037 | + | 0.979788i | \(0.564106\pi\) | |||||||
\(132\) | 7.45831 | 0.649162 | ||||||||
\(133\) | −7.25028 | −0.628679 | ||||||||
\(134\) | 0.737952 | 0.0637493 | ||||||||
\(135\) | −2.08087 | −0.179093 | ||||||||
\(136\) | −1.94013 | −0.166365 | ||||||||
\(137\) | −0.365639 | −0.0312387 | −0.0156193 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156193 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(138\) | 0.161383 | 0.0137379 | ||||||||
\(139\) | −12.2183 | −1.03634 | −0.518172 | − | 0.855277i | \(-0.673387\pi\) | ||||
−0.518172 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(140\) | −15.0744 | −1.27402 | ||||||||
\(141\) | 0.138067 | 0.0116273 | ||||||||
\(142\) | −0.529706 | −0.0444519 | ||||||||
\(143\) | 13.2652 | 1.10930 | ||||||||
\(144\) | 3.84441 | 0.320368 | ||||||||
\(145\) | 2.08087 | 0.172807 | ||||||||
\(146\) | 0.247134 | 0.0204530 | ||||||||
\(147\) | −6.46848 | −0.533511 | ||||||||
\(148\) | −10.5520 | −0.867367 | ||||||||
\(149\) | 2.72205 | 0.222999 | 0.111499 | − | 0.993764i | \(-0.464435\pi\) | ||||
0.111499 | + | 0.993764i | \(0.464435\pi\) | |||||||
\(150\) | 0.108125 | 0.00882840 | ||||||||
\(151\) | −14.3704 | −1.16945 | −0.584724 | − | 0.811232i | \(-0.698797\pi\) | ||||
−0.584724 | + | 0.811232i | \(0.698797\pi\) | |||||||
\(152\) | 1.26700 | 0.102767 | ||||||||
\(153\) | 3.02517 | 0.244571 | ||||||||
\(154\) | 2.23780 | 0.180327 | ||||||||
\(155\) | −7.45273 | −0.598618 | ||||||||
\(156\) | 6.93026 | 0.554865 | ||||||||
\(157\) | −9.48437 | −0.756936 | −0.378468 | − | 0.925614i | \(-0.623549\pi\) | ||||
−0.378468 | + | 0.925614i | \(0.623549\pi\) | |||||||
\(158\) | 1.18123 | 0.0939738 | ||||||||
\(159\) | −3.01823 | −0.239361 | ||||||||
\(160\) | 3.96007 | 0.313071 | ||||||||
\(161\) | −3.66994 | −0.289232 | ||||||||
\(162\) | 0.161383 | 0.0126795 | ||||||||
\(163\) | 20.6148 | 1.61468 | 0.807339 | − | 0.590088i | \(-0.200907\pi\) | ||||
0.807339 | + | 0.590088i | \(0.200907\pi\) | |||||||
\(164\) | 23.7491 | 1.85449 | ||||||||
\(165\) | −7.86226 | −0.612076 | ||||||||
\(166\) | 0.940370 | 0.0729869 | ||||||||
\(167\) | 13.3426 | 1.03248 | 0.516241 | − | 0.856443i | \(-0.327331\pi\) | ||||
0.516241 | + | 0.856443i | \(0.327331\pi\) | |||||||
\(168\) | 2.35365 | 0.181588 | ||||||||
\(169\) | −0.673934 | −0.0518411 | ||||||||
\(170\) | 1.01591 | 0.0779164 | ||||||||
\(171\) | −1.97558 | −0.151077 | ||||||||
\(172\) | −7.27802 | −0.554944 | ||||||||
\(173\) | 9.60604 | 0.730334 | 0.365167 | − | 0.930942i | \(-0.381012\pi\) | ||||
0.365167 | + | 0.930942i | \(0.381012\pi\) | |||||||
\(174\) | −0.161383 | −0.0122344 | ||||||||
\(175\) | −2.45883 | −0.185870 | ||||||||
\(176\) | 14.5256 | 1.09490 | ||||||||
\(177\) | −9.43156 | −0.708920 | ||||||||
\(178\) | 0.978597 | 0.0733489 | ||||||||
\(179\) | 10.3216 | 0.771473 | 0.385737 | − | 0.922609i | \(-0.373947\pi\) | ||||
0.385737 | + | 0.922609i | \(0.373947\pi\) | |||||||
\(180\) | −4.10754 | −0.306158 | ||||||||
\(181\) | 9.34390 | 0.694527 | 0.347263 | − | 0.937768i | \(-0.387111\pi\) | ||||
0.347263 | + | 0.937768i | \(0.387111\pi\) | |||||||
\(182\) | 2.07936 | 0.154133 | ||||||||
\(183\) | 10.8624 | 0.802972 | ||||||||
\(184\) | 0.641331 | 0.0472795 | ||||||||
\(185\) | 11.1235 | 0.817815 | ||||||||
\(186\) | 0.578003 | 0.0423812 | ||||||||
\(187\) | 11.4302 | 0.835857 | ||||||||
\(188\) | 0.272538 | 0.0198769 | ||||||||
\(189\) | −3.66994 | −0.266949 | ||||||||
\(190\) | −0.663436 | −0.0481307 | ||||||||
\(191\) | −0.626325 | −0.0453193 | −0.0226597 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226597 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(192\) | 7.38169 | 0.532728 | ||||||||
\(193\) | −0.516976 | −0.0372128 | −0.0186064 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186064 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(194\) | −2.18684 | −0.157006 | ||||||||
\(195\) | −7.30561 | −0.523166 | ||||||||
\(196\) | −12.7685 | −0.912035 | ||||||||
\(197\) | −0.0598105 | −0.00426132 | −0.00213066 | − | 0.999998i | \(-0.500678\pi\) | ||||
−0.00213066 | + | 0.999998i | \(0.500678\pi\) | |||||||
\(198\) | 0.609764 | 0.0433341 | ||||||||
\(199\) | −5.54830 | −0.393308 | −0.196654 | − | 0.980473i | \(-0.563008\pi\) | ||||
−0.196654 | + | 0.980473i | \(0.563008\pi\) | |||||||
\(200\) | 0.429685 | 0.0303833 | ||||||||
\(201\) | −4.57266 | −0.322531 | ||||||||
\(202\) | −0.870945 | −0.0612795 | ||||||||
\(203\) | 3.66994 | 0.257579 | ||||||||
\(204\) | 5.97155 | 0.418092 | ||||||||
\(205\) | −25.0354 | −1.74855 | ||||||||
\(206\) | 1.17637 | 0.0819615 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 13.4971 | 0.935859 | ||||||||
\(209\) | −7.46446 | −0.516328 | ||||||||
\(210\) | −1.23243 | −0.0850458 | ||||||||
\(211\) | −10.0930 | −0.694833 | −0.347416 | − | 0.937711i | \(-0.612941\pi\) | ||||
−0.347416 | + | 0.937711i | \(0.612941\pi\) | |||||||
\(212\) | −5.95785 | −0.409187 | ||||||||
\(213\) | 3.28228 | 0.224898 | ||||||||
\(214\) | −0.956890 | −0.0654117 | ||||||||
\(215\) | 7.67220 | 0.523240 | ||||||||
\(216\) | 0.641331 | 0.0436370 | ||||||||
\(217\) | −13.1441 | −0.892279 | ||||||||
\(218\) | 2.73194 | 0.185030 | ||||||||
\(219\) | −1.53135 | −0.103479 | ||||||||
\(220\) | −15.5198 | −1.04634 | ||||||||
\(221\) | 10.6209 | 0.714440 | ||||||||
\(222\) | −0.862691 | −0.0579000 | ||||||||
\(223\) | −2.65301 | −0.177659 | −0.0888293 | − | 0.996047i | \(-0.528313\pi\) | ||||
−0.0888293 | + | 0.996047i | \(0.528313\pi\) | |||||||
\(224\) | 6.98422 | 0.466653 | ||||||||
\(225\) | −0.669990 | −0.0446660 | ||||||||
\(226\) | 1.04684 | 0.0696349 | ||||||||
\(227\) | −2.02512 | −0.134412 | −0.0672059 | − | 0.997739i | \(-0.521408\pi\) | ||||
−0.0672059 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(228\) | −3.89971 | −0.258265 | ||||||||
\(229\) | −1.74269 | −0.115160 | −0.0575800 | − | 0.998341i | \(-0.518338\pi\) | ||||
−0.0575800 | + | 0.998341i | \(0.518338\pi\) | |||||||
\(230\) | −0.335818 | −0.0221432 | ||||||||
\(231\) | −13.8664 | −0.912339 | ||||||||
\(232\) | −0.641331 | −0.0421054 | ||||||||
\(233\) | 10.8194 | 0.708802 | 0.354401 | − | 0.935093i | \(-0.384685\pi\) | ||||
0.354401 | + | 0.935093i | \(0.384685\pi\) | |||||||
\(234\) | 0.566593 | 0.0370394 | ||||||||
\(235\) | −0.287299 | −0.0187413 | ||||||||
\(236\) | −18.6175 | −1.21189 | ||||||||
\(237\) | −7.31941 | −0.475447 | ||||||||
\(238\) | 1.79171 | 0.116139 | ||||||||
\(239\) | 13.5515 | 0.876572 | 0.438286 | − | 0.898836i | \(-0.355586\pi\) | ||||
0.438286 | + | 0.898836i | \(0.355586\pi\) | |||||||
\(240\) | −7.99971 | −0.516379 | ||||||||
\(241\) | −17.0852 | −1.10055 | −0.550277 | − | 0.834982i | \(-0.685478\pi\) | ||||
−0.550277 | + | 0.834982i | \(0.685478\pi\) | |||||||
\(242\) | 0.528689 | 0.0339854 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 21.4419 | 1.37268 | ||||||||
\(245\) | 13.4600 | 0.859931 | ||||||||
\(246\) | 1.94164 | 0.123794 | ||||||||
\(247\) | −6.93598 | −0.441326 | ||||||||
\(248\) | 2.29696 | 0.145857 | ||||||||
\(249\) | −5.82693 | −0.369267 | ||||||||
\(250\) | −1.90408 | −0.120425 | ||||||||
\(251\) | 14.0710 | 0.888151 | 0.444076 | − | 0.895989i | \(-0.353532\pi\) | ||||
0.444076 | + | 0.895989i | \(0.353532\pi\) | |||||||
\(252\) | −7.24430 | −0.456348 | ||||||||
\(253\) | −3.77836 | −0.237543 | ||||||||
\(254\) | 1.39127 | 0.0872963 | ||||||||
\(255\) | −6.29498 | −0.394207 | ||||||||
\(256\) | 13.9569 | 0.872305 | ||||||||
\(257\) | 2.08470 | 0.130040 | 0.0650201 | − | 0.997884i | \(-0.479289\pi\) | ||||
0.0650201 | + | 0.997884i | \(0.479289\pi\) | |||||||
\(258\) | −0.595024 | −0.0370446 | ||||||||
\(259\) | 19.6180 | 1.21901 | ||||||||
\(260\) | −14.4210 | −0.894350 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −0.738986 | −0.0456547 | ||||||||
\(263\) | −22.5597 | −1.39109 | −0.695545 | − | 0.718483i | \(-0.744837\pi\) | ||||
−0.695545 | + | 0.718483i | \(0.744837\pi\) | |||||||
\(264\) | 2.42318 | 0.149136 | ||||||||
\(265\) | 6.28054 | 0.385810 | ||||||||
\(266\) | −1.17008 | −0.0717419 | ||||||||
\(267\) | −6.06380 | −0.371098 | ||||||||
\(268\) | −9.02623 | −0.551365 | ||||||||
\(269\) | 21.7650 | 1.32704 | 0.663518 | − | 0.748160i | \(-0.269062\pi\) | ||||
0.663518 | + | 0.748160i | \(0.269062\pi\) | |||||||
\(270\) | −0.335818 | −0.0204372 | ||||||||
\(271\) | −19.0602 | −1.15782 | −0.578911 | − | 0.815391i | \(-0.696522\pi\) | ||||
−0.578911 | + | 0.815391i | \(0.696522\pi\) | |||||||
\(272\) | 11.6300 | 0.705172 | ||||||||
\(273\) | −12.8846 | −0.779812 | ||||||||
\(274\) | −0.0590081 | −0.00356481 | ||||||||
\(275\) | −2.53146 | −0.152653 | ||||||||
\(276\) | −1.97396 | −0.118818 | ||||||||
\(277\) | −5.11613 | −0.307399 | −0.153699 | − | 0.988118i | \(-0.549119\pi\) | ||||
−0.153699 | + | 0.988118i | \(0.549119\pi\) | |||||||
\(278\) | −1.97183 | −0.118263 | ||||||||
\(279\) | −3.58155 | −0.214422 | ||||||||
\(280\) | −4.89763 | −0.292689 | ||||||||
\(281\) | −7.01306 | −0.418364 | −0.209182 | − | 0.977877i | \(-0.567080\pi\) | ||||
−0.209182 | + | 0.977877i | \(0.567080\pi\) | |||||||
\(282\) | 0.0222817 | 0.00132686 | ||||||||
\(283\) | −18.5054 | −1.10003 | −0.550014 | − | 0.835155i | \(-0.685378\pi\) | ||||
−0.550014 | + | 0.835155i | \(0.685378\pi\) | |||||||
\(284\) | 6.47907 | 0.384462 | ||||||||
\(285\) | 4.11093 | 0.243510 | ||||||||
\(286\) | 2.14079 | 0.126588 | ||||||||
\(287\) | −44.1539 | −2.60632 | ||||||||
\(288\) | 1.90309 | 0.112140 | ||||||||
\(289\) | −7.84835 | −0.461667 | ||||||||
\(290\) | 0.335818 | 0.0197199 | ||||||||
\(291\) | 13.5506 | 0.794348 | ||||||||
\(292\) | −3.02281 | −0.176897 | ||||||||
\(293\) | 7.86714 | 0.459603 | 0.229802 | − | 0.973237i | \(-0.426192\pi\) | ||||
0.229802 | + | 0.973237i | \(0.426192\pi\) | |||||||
\(294\) | −1.04391 | −0.0608818 | ||||||||
\(295\) | 19.6258 | 1.14266 | ||||||||
\(296\) | −3.42830 | −0.199266 | ||||||||
\(297\) | −3.77836 | −0.219243 | ||||||||
\(298\) | 0.439294 | 0.0254476 | ||||||||
\(299\) | −3.51085 | −0.203038 | ||||||||
\(300\) | −1.32253 | −0.0763564 | ||||||||
\(301\) | 13.5312 | 0.779923 | ||||||||
\(302\) | −2.31915 | −0.133452 | ||||||||
\(303\) | 5.39674 | 0.310035 | ||||||||
\(304\) | −7.59496 | −0.435601 | ||||||||
\(305\) | −22.6032 | −1.29426 | ||||||||
\(306\) | 0.488212 | 0.0279092 | ||||||||
\(307\) | −1.52335 | −0.0869424 | −0.0434712 | − | 0.999055i | \(-0.513842\pi\) | ||||
−0.0434712 | + | 0.999055i | \(0.513842\pi\) | |||||||
\(308\) | −27.3716 | −1.55964 | ||||||||
\(309\) | −7.28928 | −0.414673 | ||||||||
\(310\) | −1.20275 | −0.0683115 | ||||||||
\(311\) | 15.6060 | 0.884936 | 0.442468 | − | 0.896784i | \(-0.354103\pi\) | ||||
0.442468 | + | 0.896784i | \(0.354103\pi\) | |||||||
\(312\) | 2.25162 | 0.127473 | ||||||||
\(313\) | −8.42755 | −0.476353 | −0.238177 | − | 0.971222i | \(-0.576550\pi\) | ||||
−0.238177 | + | 0.971222i | \(0.576550\pi\) | |||||||
\(314\) | −1.53062 | −0.0863780 | ||||||||
\(315\) | 7.63666 | 0.430277 | ||||||||
\(316\) | −14.4482 | −0.812774 | ||||||||
\(317\) | −8.28338 | −0.465241 | −0.232621 | − | 0.972568i | \(-0.574730\pi\) | ||||
−0.232621 | + | 0.972568i | \(0.574730\pi\) | |||||||
\(318\) | −0.487093 | −0.0273148 | ||||||||
\(319\) | 3.77836 | 0.211547 | ||||||||
\(320\) | −15.3603 | −0.858668 | ||||||||
\(321\) | 5.92929 | 0.330941 | ||||||||
\(322\) | −0.592268 | −0.0330058 | ||||||||
\(323\) | −5.97648 | −0.332540 | ||||||||
\(324\) | −1.97396 | −0.109664 | ||||||||
\(325\) | −2.35224 | −0.130479 | ||||||||
\(326\) | 3.32689 | 0.184259 | ||||||||
\(327\) | −16.9282 | −0.936133 | ||||||||
\(328\) | 7.71599 | 0.426044 | ||||||||
\(329\) | −0.506698 | −0.0279352 | ||||||||
\(330\) | −1.26884 | −0.0698473 | ||||||||
\(331\) | −21.2067 | −1.16563 | −0.582814 | − | 0.812605i | \(-0.698048\pi\) | ||||
−0.582814 | + | 0.812605i | \(0.698048\pi\) | |||||||
\(332\) | −11.5021 | −0.631260 | ||||||||
\(333\) | 5.34560 | 0.292937 | ||||||||
\(334\) | 2.15328 | 0.117822 | ||||||||
\(335\) | 9.51510 | 0.519865 | ||||||||
\(336\) | −14.1088 | −0.769696 | ||||||||
\(337\) | −13.8277 | −0.753242 | −0.376621 | − | 0.926367i | \(-0.622914\pi\) | ||||
−0.376621 | + | 0.926367i | \(0.622914\pi\) | |||||||
\(338\) | −0.108762 | −0.00591587 | ||||||||
\(339\) | −6.48668 | −0.352308 | ||||||||
\(340\) | −12.4260 | −0.673895 | ||||||||
\(341\) | −13.5324 | −0.732819 | ||||||||
\(342\) | −0.318827 | −0.0172402 | ||||||||
\(343\) | −1.95065 | −0.105325 | ||||||||
\(344\) | −2.36460 | −0.127491 | ||||||||
\(345\) | 2.08087 | 0.112030 | ||||||||
\(346\) | 1.55026 | 0.0833423 | ||||||||
\(347\) | 33.5066 | 1.79873 | 0.899365 | − | 0.437198i | \(-0.144029\pi\) | ||||
0.899365 | + | 0.437198i | \(0.144029\pi\) | |||||||
\(348\) | 1.97396 | 0.105815 | ||||||||
\(349\) | −20.9451 | −1.12117 | −0.560584 | − | 0.828098i | \(-0.689423\pi\) | ||||
−0.560584 | + | 0.828098i | \(0.689423\pi\) | |||||||
\(350\) | −0.396814 | −0.0212106 | ||||||||
\(351\) | −3.51085 | −0.187395 | ||||||||
\(352\) | 7.19054 | 0.383257 | ||||||||
\(353\) | 33.6831 | 1.79277 | 0.896386 | − | 0.443275i | \(-0.146183\pi\) | ||||
0.896386 | + | 0.443275i | \(0.146183\pi\) | |||||||
\(354\) | −1.52210 | −0.0808986 | ||||||||
\(355\) | −6.82999 | −0.362498 | ||||||||
\(356\) | −11.9697 | −0.634391 | ||||||||
\(357\) | −11.1022 | −0.587591 | ||||||||
\(358\) | 1.66574 | 0.0880370 | ||||||||
\(359\) | −1.33233 | −0.0703176 | −0.0351588 | − | 0.999382i | \(-0.511194\pi\) | ||||
−0.0351588 | + | 0.999382i | \(0.511194\pi\) | |||||||
\(360\) | −1.33452 | −0.0703356 | ||||||||
\(361\) | −15.0971 | −0.794583 | ||||||||
\(362\) | 1.50795 | 0.0792562 | ||||||||
\(363\) | −3.27598 | −0.171944 | ||||||||
\(364\) | −25.4337 | −1.33309 | ||||||||
\(365\) | 3.18653 | 0.166791 | ||||||||
\(366\) | 1.75301 | 0.0916314 | ||||||||
\(367\) | 14.0175 | 0.731708 | 0.365854 | − | 0.930672i | \(-0.380777\pi\) | ||||
0.365854 | + | 0.930672i | \(0.380777\pi\) | |||||||
\(368\) | −3.84441 | −0.200404 | ||||||||
\(369\) | −12.0312 | −0.626320 | ||||||||
\(370\) | 1.79515 | 0.0933252 | ||||||||
\(371\) | 11.0767 | 0.575075 | ||||||||
\(372\) | −7.06982 | −0.366553 | ||||||||
\(373\) | −17.5045 | −0.906347 | −0.453173 | − | 0.891422i | \(-0.649708\pi\) | ||||
−0.453173 | + | 0.891422i | \(0.649708\pi\) | |||||||
\(374\) | 1.84464 | 0.0953841 | ||||||||
\(375\) | 11.7985 | 0.609272 | ||||||||
\(376\) | 0.0885467 | 0.00456645 | ||||||||
\(377\) | 3.51085 | 0.180818 | ||||||||
\(378\) | −0.592268 | −0.0304630 | ||||||||
\(379\) | −26.0033 | −1.33570 | −0.667851 | − | 0.744295i | \(-0.732786\pi\) | ||||
−0.667851 | + | 0.744295i | \(0.732786\pi\) | |||||||
\(380\) | 8.11479 | 0.416280 | ||||||||
\(381\) | −8.62092 | −0.441663 | ||||||||
\(382\) | −0.101079 | −0.00517163 | ||||||||
\(383\) | −19.8921 | −1.01644 | −0.508219 | − | 0.861228i | \(-0.669696\pi\) | ||||
−0.508219 | + | 0.861228i | \(0.669696\pi\) | |||||||
\(384\) | 4.99746 | 0.255025 | ||||||||
\(385\) | 28.8540 | 1.47054 | ||||||||
\(386\) | −0.0834314 | −0.00424655 | ||||||||
\(387\) | 3.68702 | 0.187422 | ||||||||
\(388\) | 26.7482 | 1.35793 | ||||||||
\(389\) | −6.92622 | −0.351173 | −0.175587 | − | 0.984464i | \(-0.556182\pi\) | ||||
−0.175587 | + | 0.984464i | \(0.556182\pi\) | |||||||
\(390\) | −1.17901 | −0.0597012 | ||||||||
\(391\) | −3.02517 | −0.152989 | ||||||||
\(392\) | −4.14843 | −0.209528 | ||||||||
\(393\) | 4.57907 | 0.230983 | ||||||||
\(394\) | −0.00965242 | −0.000486282 0 | ||||||||
\(395\) | 15.2307 | 0.766341 | ||||||||
\(396\) | −7.45831 | −0.374794 | ||||||||
\(397\) | −23.2007 | −1.16441 | −0.582205 | − | 0.813042i | \(-0.697810\pi\) | ||||
−0.582205 | + | 0.813042i | \(0.697810\pi\) | |||||||
\(398\) | −0.895403 | −0.0448825 | ||||||||
\(399\) | 7.25028 | 0.362968 | ||||||||
\(400\) | −2.57572 | −0.128786 | ||||||||
\(401\) | 12.9918 | 0.648778 | 0.324389 | − | 0.945924i | \(-0.394841\pi\) | ||||
0.324389 | + | 0.945924i | \(0.394841\pi\) | |||||||
\(402\) | −0.737952 | −0.0368057 | ||||||||
\(403\) | −12.5743 | −0.626370 | ||||||||
\(404\) | 10.6529 | 0.530003 | ||||||||
\(405\) | 2.08087 | 0.103399 | ||||||||
\(406\) | 0.592268 | 0.0293938 | ||||||||
\(407\) | 20.1976 | 1.00116 | ||||||||
\(408\) | 1.94013 | 0.0960510 | ||||||||
\(409\) | −32.0911 | −1.58680 | −0.793402 | − | 0.608699i | \(-0.791692\pi\) | ||||
−0.793402 | + | 0.608699i | \(0.791692\pi\) | |||||||
\(410\) | −4.04029 | −0.199536 | ||||||||
\(411\) | 0.365639 | 0.0180357 | ||||||||
\(412\) | −14.3887 | −0.708881 | ||||||||
\(413\) | 34.6133 | 1.70321 | ||||||||
\(414\) | −0.161383 | −0.00793156 | ||||||||
\(415\) | 12.1251 | 0.595196 | ||||||||
\(416\) | 6.68145 | 0.327585 | ||||||||
\(417\) | 12.2183 | 0.598333 | ||||||||
\(418\) | −1.20464 | −0.0589209 | ||||||||
\(419\) | 28.0069 | 1.36823 | 0.684113 | − | 0.729376i | \(-0.260189\pi\) | ||||
0.684113 | + | 0.729376i | \(0.260189\pi\) | |||||||
\(420\) | 15.0744 | 0.735557 | ||||||||
\(421\) | −23.7699 | −1.15847 | −0.579237 | − | 0.815159i | \(-0.696650\pi\) | ||||
−0.579237 | + | 0.815159i | \(0.696650\pi\) | |||||||
\(422\) | −1.62885 | −0.0792911 | ||||||||
\(423\) | −0.138067 | −0.00671305 | ||||||||
\(424\) | −1.93568 | −0.0940051 | ||||||||
\(425\) | −2.02683 | −0.0983159 | ||||||||
\(426\) | 0.529706 | 0.0256643 | ||||||||
\(427\) | −39.8644 | −1.92917 | ||||||||
\(428\) | 11.7042 | 0.565742 | ||||||||
\(429\) | −13.2652 | −0.640452 | ||||||||
\(430\) | 1.23817 | 0.0597097 | ||||||||
\(431\) | 3.63777 | 0.175225 | 0.0876126 | − | 0.996155i | \(-0.472076\pi\) | ||||
0.0876126 | + | 0.996155i | \(0.472076\pi\) | |||||||
\(432\) | −3.84441 | −0.184964 | ||||||||
\(433\) | 39.2350 | 1.88552 | 0.942758 | − | 0.333478i | \(-0.108222\pi\) | ||||
0.942758 | + | 0.333478i | \(0.108222\pi\) | |||||||
\(434\) | −2.12124 | −0.101823 | ||||||||
\(435\) | −2.08087 | −0.0997700 | ||||||||
\(436\) | −33.4156 | −1.60032 | ||||||||
\(437\) | 1.97558 | 0.0945050 | ||||||||
\(438\) | −0.247134 | −0.0118085 | ||||||||
\(439\) | 28.2038 | 1.34609 | 0.673046 | − | 0.739601i | \(-0.264986\pi\) | ||||
0.673046 | + | 0.739601i | \(0.264986\pi\) | |||||||
\(440\) | −5.04231 | −0.240383 | ||||||||
\(441\) | 6.46848 | 0.308023 | ||||||||
\(442\) | 1.71404 | 0.0815286 | ||||||||
\(443\) | −24.3212 | −1.15553 | −0.577767 | − | 0.816202i | \(-0.696076\pi\) | ||||
−0.577767 | + | 0.816202i | \(0.696076\pi\) | |||||||
\(444\) | 10.5520 | 0.500775 | ||||||||
\(445\) | 12.6180 | 0.598149 | ||||||||
\(446\) | −0.428152 | −0.0202736 | ||||||||
\(447\) | −2.72205 | −0.128748 | ||||||||
\(448\) | −27.0904 | −1.27990 | ||||||||
\(449\) | 40.9877 | 1.93433 | 0.967164 | − | 0.254152i | \(-0.0817962\pi\) | ||||
0.967164 | + | 0.254152i | \(0.0817962\pi\) | |||||||
\(450\) | −0.108125 | −0.00509708 | ||||||||
\(451\) | −45.4582 | −2.14054 | ||||||||
\(452\) | −12.8044 | −0.602269 | ||||||||
\(453\) | 14.3704 | 0.675181 | ||||||||
\(454\) | −0.326821 | −0.0153384 | ||||||||
\(455\) | 26.8112 | 1.25693 | ||||||||
\(456\) | −1.26700 | −0.0593328 | ||||||||
\(457\) | 9.80944 | 0.458866 | 0.229433 | − | 0.973324i | \(-0.426313\pi\) | ||||
0.229433 | + | 0.973324i | \(0.426313\pi\) | |||||||
\(458\) | −0.281241 | −0.0131415 | ||||||||
\(459\) | −3.02517 | −0.141203 | ||||||||
\(460\) | 4.10754 | 0.191515 | ||||||||
\(461\) | −24.6215 | −1.14674 | −0.573369 | − | 0.819297i | \(-0.694364\pi\) | ||||
−0.573369 | + | 0.819297i | \(0.694364\pi\) | |||||||
\(462\) | −2.23780 | −0.104112 | ||||||||
\(463\) | 10.1126 | 0.469972 | 0.234986 | − | 0.971999i | \(-0.424495\pi\) | ||||
0.234986 | + | 0.971999i | \(0.424495\pi\) | |||||||
\(464\) | 3.84441 | 0.178472 | ||||||||
\(465\) | 7.45273 | 0.345612 | ||||||||
\(466\) | 1.74607 | 0.0808852 | ||||||||
\(467\) | 0.219921 | 0.0101767 | 0.00508836 | − | 0.999987i | \(-0.498380\pi\) | ||||
0.00508836 | + | 0.999987i | \(0.498380\pi\) | |||||||
\(468\) | −6.93026 | −0.320351 | ||||||||
\(469\) | 16.7814 | 0.774893 | ||||||||
\(470\) | −0.0463654 | −0.00213867 | ||||||||
\(471\) | 9.48437 | 0.437017 | ||||||||
\(472\) | −6.04875 | −0.278416 | ||||||||
\(473\) | 13.9309 | 0.640543 | ||||||||
\(474\) | −1.18123 | −0.0542558 | ||||||||
\(475\) | 1.32362 | 0.0607319 | ||||||||
\(476\) | −21.9152 | −1.00448 | ||||||||
\(477\) | 3.01823 | 0.138195 | ||||||||
\(478\) | 2.18698 | 0.100030 | ||||||||
\(479\) | −16.9614 | −0.774984 | −0.387492 | − | 0.921873i | \(-0.626659\pi\) | ||||
−0.387492 | + | 0.921873i | \(0.626659\pi\) | |||||||
\(480\) | −3.96007 | −0.180752 | ||||||||
\(481\) | 18.7676 | 0.855729 | ||||||||
\(482\) | −2.75727 | −0.125590 | ||||||||
\(483\) | 3.66994 | 0.166988 | ||||||||
\(484\) | −6.46664 | −0.293938 | ||||||||
\(485\) | −28.1969 | −1.28036 | ||||||||
\(486\) | −0.161383 | −0.00732050 | ||||||||
\(487\) | 28.0531 | 1.27121 | 0.635603 | − | 0.772016i | \(-0.280752\pi\) | ||||
0.635603 | + | 0.772016i | \(0.280752\pi\) | |||||||
\(488\) | 6.96639 | 0.315354 | ||||||||
\(489\) | −20.6148 | −0.932235 | ||||||||
\(490\) | 2.17223 | 0.0981313 | ||||||||
\(491\) | 37.9620 | 1.71320 | 0.856601 | − | 0.515980i | \(-0.172572\pi\) | ||||
0.856601 | + | 0.515980i | \(0.172572\pi\) | |||||||
\(492\) | −23.7491 | −1.07069 | ||||||||
\(493\) | 3.02517 | 0.136247 | ||||||||
\(494\) | −1.11935 | −0.0503620 | ||||||||
\(495\) | 7.86226 | 0.353382 | ||||||||
\(496\) | −13.7690 | −0.618244 | ||||||||
\(497\) | −12.0458 | −0.540327 | ||||||||
\(498\) | −0.940370 | −0.0421390 | ||||||||
\(499\) | 5.03700 | 0.225487 | 0.112744 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112744 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(500\) | 23.2897 | 1.04155 | ||||||||
\(501\) | −13.3426 | −0.596104 | ||||||||
\(502\) | 2.27082 | 0.101352 | ||||||||
\(503\) | −19.3933 | −0.864706 | −0.432353 | − | 0.901704i | \(-0.642317\pi\) | ||||
−0.432353 | + | 0.901704i | \(0.642317\pi\) | |||||||
\(504\) | −2.35365 | −0.104840 | ||||||||
\(505\) | −11.2299 | −0.499724 | ||||||||
\(506\) | −0.609764 | −0.0271073 | ||||||||
\(507\) | 0.673934 | 0.0299305 | ||||||||
\(508\) | −17.0173 | −0.755021 | ||||||||
\(509\) | −26.5066 | −1.17488 | −0.587442 | − | 0.809266i | \(-0.699865\pi\) | ||||
−0.587442 | + | 0.809266i | \(0.699865\pi\) | |||||||
\(510\) | −1.01591 | −0.0449850 | ||||||||
\(511\) | 5.61996 | 0.248612 | ||||||||
\(512\) | 12.2473 | 0.541260 | ||||||||
\(513\) | 1.97558 | 0.0872242 | ||||||||
\(514\) | 0.336436 | 0.0148396 | ||||||||
\(515\) | 15.1680 | 0.668383 | ||||||||
\(516\) | 7.27802 | 0.320397 | ||||||||
\(517\) | −0.521667 | −0.0229429 | ||||||||
\(518\) | 3.16603 | 0.139107 | ||||||||
\(519\) | −9.60604 | −0.421658 | ||||||||
\(520\) | −4.68531 | −0.205465 | ||||||||
\(521\) | −14.1503 | −0.619936 | −0.309968 | − | 0.950747i | \(-0.600318\pi\) | ||||
−0.309968 | + | 0.950747i | \(0.600318\pi\) | |||||||
\(522\) | 0.161383 | 0.00706356 | ||||||||
\(523\) | −2.42020 | −0.105828 | −0.0529139 | − | 0.998599i | \(-0.516851\pi\) | ||||
−0.0529139 | + | 0.998599i | \(0.516851\pi\) | |||||||
\(524\) | 9.03887 | 0.394865 | ||||||||
\(525\) | 2.45883 | 0.107312 | ||||||||
\(526\) | −3.64076 | −0.158745 | ||||||||
\(527\) | −10.8348 | −0.471971 | ||||||||
\(528\) | −14.5256 | −0.632144 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 1.01358 | 0.0440269 | ||||||||
\(531\) | 9.43156 | 0.409295 | ||||||||
\(532\) | 14.3117 | 0.620492 | ||||||||
\(533\) | −42.2398 | −1.82961 | ||||||||
\(534\) | −0.978597 | −0.0423480 | ||||||||
\(535\) | −12.3381 | −0.533422 | ||||||||
\(536\) | −2.93259 | −0.126668 | ||||||||
\(537\) | −10.3216 | −0.445410 | ||||||||
\(538\) | 3.51251 | 0.151435 | ||||||||
\(539\) | 24.4402 | 1.05271 | ||||||||
\(540\) | 4.10754 | 0.176760 | ||||||||
\(541\) | 21.1409 | 0.908919 | 0.454459 | − | 0.890768i | \(-0.349833\pi\) | ||||
0.454459 | + | 0.890768i | \(0.349833\pi\) | |||||||
\(542\) | −3.07600 | −0.132125 | ||||||||
\(543\) | −9.34390 | −0.400985 | ||||||||
\(544\) | 5.75716 | 0.246836 | ||||||||
\(545\) | 35.2254 | 1.50889 | ||||||||
\(546\) | −2.07936 | −0.0889886 | ||||||||
\(547\) | 19.9428 | 0.852692 | 0.426346 | − | 0.904560i | \(-0.359801\pi\) | ||||
0.426346 | + | 0.904560i | \(0.359801\pi\) | |||||||
\(548\) | 0.721755 | 0.0308319 | ||||||||
\(549\) | −10.8624 | −0.463596 | ||||||||
\(550\) | −0.408536 | −0.0174200 | ||||||||
\(551\) | −1.97558 | −0.0841627 | ||||||||
\(552\) | −0.641331 | −0.0272968 | ||||||||
\(553\) | 26.8618 | 1.14228 | ||||||||
\(554\) | −0.825660 | −0.0350789 | ||||||||
\(555\) | −11.1235 | −0.472166 | ||||||||
\(556\) | 24.1184 | 1.02285 | ||||||||
\(557\) | 11.3239 | 0.479809 | 0.239904 | − | 0.970797i | \(-0.422884\pi\) | ||||
0.239904 | + | 0.970797i | \(0.422884\pi\) | |||||||
\(558\) | −0.578003 | −0.0244688 | ||||||||
\(559\) | 12.9446 | 0.547497 | ||||||||
\(560\) | 29.3585 | 1.24062 | ||||||||
\(561\) | −11.4302 | −0.482582 | ||||||||
\(562\) | −1.13179 | −0.0477418 | ||||||||
\(563\) | −5.82702 | −0.245580 | −0.122790 | − | 0.992433i | \(-0.539184\pi\) | ||||
−0.122790 | + | 0.992433i | \(0.539184\pi\) | |||||||
\(564\) | −0.272538 | −0.0114759 | ||||||||
\(565\) | 13.4979 | 0.567862 | ||||||||
\(566\) | −2.98646 | −0.125530 | ||||||||
\(567\) | 3.66994 | 0.154123 | ||||||||
\(568\) | 2.10503 | 0.0883250 | ||||||||
\(569\) | −17.5619 | −0.736235 | −0.368117 | − | 0.929779i | \(-0.619998\pi\) | ||||
−0.368117 | + | 0.929779i | \(0.619998\pi\) | |||||||
\(570\) | 0.663436 | 0.0277883 | ||||||||
\(571\) | −5.56698 | −0.232971 | −0.116485 | − | 0.993192i | \(-0.537163\pi\) | ||||
−0.116485 | + | 0.993192i | \(0.537163\pi\) | |||||||
\(572\) | −26.1850 | −1.09485 | ||||||||
\(573\) | 0.626325 | 0.0261651 | ||||||||
\(574\) | −7.12570 | −0.297421 | ||||||||
\(575\) | 0.669990 | 0.0279405 | ||||||||
\(576\) | −7.38169 | −0.307571 | ||||||||
\(577\) | 14.3262 | 0.596407 | 0.298203 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298203 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(578\) | −1.26659 | −0.0526833 | ||||||||
\(579\) | 0.516976 | 0.0214848 | ||||||||
\(580\) | −4.10754 | −0.170556 | ||||||||
\(581\) | 21.3845 | 0.887178 | ||||||||
\(582\) | 2.18684 | 0.0906473 | ||||||||
\(583\) | 11.4040 | 0.472303 | ||||||||
\(584\) | −0.982100 | −0.0406396 | ||||||||
\(585\) | 7.30561 | 0.302050 | ||||||||
\(586\) | 1.26963 | 0.0524478 | ||||||||
\(587\) | 41.9005 | 1.72942 | 0.864709 | − | 0.502272i | \(-0.167503\pi\) | ||||
0.864709 | + | 0.502272i | \(0.167503\pi\) | |||||||
\(588\) | 12.7685 | 0.526564 | ||||||||
\(589\) | 7.07565 | 0.291547 | ||||||||
\(590\) | 3.16728 | 0.130395 | ||||||||
\(591\) | 0.0598105 | 0.00246027 | ||||||||
\(592\) | 20.5507 | 0.844628 | ||||||||
\(593\) | −42.7475 | −1.75543 | −0.877714 | − | 0.479185i | \(-0.840932\pi\) | ||||
−0.877714 | + | 0.479185i | \(0.840932\pi\) | |||||||
\(594\) | −0.609764 | −0.0250189 | ||||||||
\(595\) | 23.1022 | 0.947098 | ||||||||
\(596\) | −5.37320 | −0.220095 | ||||||||
\(597\) | 5.54830 | 0.227077 | ||||||||
\(598\) | −0.566593 | −0.0231697 | ||||||||
\(599\) | 5.56292 | 0.227295 | 0.113647 | − | 0.993521i | \(-0.463747\pi\) | ||||
0.113647 | + | 0.993521i | \(0.463747\pi\) | |||||||
\(600\) | −0.429685 | −0.0175418 | ||||||||
\(601\) | 11.5568 | 0.471413 | 0.235706 | − | 0.971824i | \(-0.424260\pi\) | ||||
0.235706 | + | 0.971824i | \(0.424260\pi\) | |||||||
\(602\) | 2.18371 | 0.0890012 | ||||||||
\(603\) | 4.57266 | 0.186213 | ||||||||
\(604\) | 28.3666 | 1.15422 | ||||||||
\(605\) | 6.81688 | 0.277146 | ||||||||
\(606\) | 0.870945 | 0.0353797 | ||||||||
\(607\) | −1.34211 | −0.0544745 | −0.0272372 | − | 0.999629i | \(-0.508671\pi\) | ||||
−0.0272372 | + | 0.999629i | \(0.508671\pi\) | |||||||
\(608\) | −3.75971 | −0.152476 | ||||||||
\(609\) | −3.66994 | −0.148714 | ||||||||
\(610\) | −3.64779 | −0.147695 | ||||||||
\(611\) | −0.484733 | −0.0196102 | ||||||||
\(612\) | −5.97155 | −0.241386 | ||||||||
\(613\) | −33.3794 | −1.34818 | −0.674090 | − | 0.738649i | \(-0.735464\pi\) | ||||
−0.674090 | + | 0.738649i | \(0.735464\pi\) | |||||||
\(614\) | −0.245844 | −0.00992147 | ||||||||
\(615\) | 25.0354 | 1.00952 | ||||||||
\(616\) | −8.89292 | −0.358306 | ||||||||
\(617\) | −35.6912 | −1.43687 | −0.718436 | − | 0.695593i | \(-0.755142\pi\) | ||||
−0.718436 | + | 0.695593i | \(0.755142\pi\) | |||||||
\(618\) | −1.17637 | −0.0473205 | ||||||||
\(619\) | −37.9577 | −1.52565 | −0.762825 | − | 0.646605i | \(-0.776188\pi\) | ||||
−0.762825 | + | 0.646605i | \(0.776188\pi\) | |||||||
\(620\) | 14.7114 | 0.590823 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 2.51855 | 0.100985 | ||||||||
\(623\) | 22.2538 | 0.891579 | ||||||||
\(624\) | −13.4971 | −0.540318 | ||||||||
\(625\) | −21.2012 | −0.848046 | ||||||||
\(626\) | −1.36007 | −0.0543592 | ||||||||
\(627\) | 7.46446 | 0.298102 | ||||||||
\(628\) | 18.7217 | 0.747078 | ||||||||
\(629\) | 16.1713 | 0.644794 | ||||||||
\(630\) | 1.23243 | 0.0491012 | ||||||||
\(631\) | 33.9249 | 1.35053 | 0.675264 | − | 0.737576i | \(-0.264030\pi\) | ||||
0.675264 | + | 0.737576i | \(0.264030\pi\) | |||||||
\(632\) | −4.69416 | −0.186724 | ||||||||
\(633\) | 10.0930 | 0.401162 | ||||||||
\(634\) | −1.33680 | −0.0530912 | ||||||||
\(635\) | 17.9390 | 0.711888 | ||||||||
\(636\) | 5.95785 | 0.236244 | ||||||||
\(637\) | 22.7099 | 0.899797 | ||||||||
\(638\) | 0.609764 | 0.0241408 | ||||||||
\(639\) | −3.28228 | −0.129845 | ||||||||
\(640\) | −10.3990 | −0.411058 | ||||||||
\(641\) | −33.6357 | −1.32853 | −0.664266 | − | 0.747496i | \(-0.731256\pi\) | ||||
−0.664266 | + | 0.747496i | \(0.731256\pi\) | |||||||
\(642\) | 0.956890 | 0.0377654 | ||||||||
\(643\) | −9.50885 | −0.374992 | −0.187496 | − | 0.982265i | \(-0.560037\pi\) | ||||
−0.187496 | + | 0.982265i | \(0.560037\pi\) | |||||||
\(644\) | 7.24430 | 0.285466 | ||||||||
\(645\) | −7.67220 | −0.302093 | ||||||||
\(646\) | −0.964505 | −0.0379479 | ||||||||
\(647\) | 32.0048 | 1.25824 | 0.629120 | − | 0.777309i | \(-0.283416\pi\) | ||||
0.629120 | + | 0.777309i | \(0.283416\pi\) | |||||||
\(648\) | −0.641331 | −0.0251938 | ||||||||
\(649\) | 35.6358 | 1.39883 | ||||||||
\(650\) | −0.379612 | −0.0148896 | ||||||||
\(651\) | 13.1441 | 0.515157 | ||||||||
\(652\) | −40.6927 | −1.59365 | ||||||||
\(653\) | −37.8578 | −1.48149 | −0.740745 | − | 0.671786i | \(-0.765527\pi\) | ||||
−0.740745 | + | 0.671786i | \(0.765527\pi\) | |||||||
\(654\) | −2.73194 | −0.106827 | ||||||||
\(655\) | −9.52843 | −0.372307 | ||||||||
\(656\) | −46.2529 | −1.80587 | ||||||||
\(657\) | 1.53135 | 0.0597435 | ||||||||
\(658\) | −0.0817727 | −0.00318783 | ||||||||
\(659\) | 19.1091 | 0.744383 | 0.372192 | − | 0.928156i | \(-0.378606\pi\) | ||||
0.372192 | + | 0.928156i | \(0.378606\pi\) | |||||||
\(660\) | 15.5198 | 0.604105 | ||||||||
\(661\) | −42.2818 | −1.64457 | −0.822286 | − | 0.569074i | \(-0.807302\pi\) | ||||
−0.822286 | + | 0.569074i | \(0.807302\pi\) | |||||||
\(662\) | −3.42242 | −0.133016 | ||||||||
\(663\) | −10.6209 | −0.412482 | ||||||||
\(664\) | −3.73699 | −0.145023 | ||||||||
\(665\) | −15.0869 | −0.585044 | ||||||||
\(666\) | 0.862691 | 0.0334286 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −26.3377 | −1.01904 | ||||||||
\(669\) | 2.65301 | 0.102571 | ||||||||
\(670\) | 1.53558 | 0.0593246 | ||||||||
\(671\) | −41.0420 | −1.58441 | ||||||||
\(672\) | −6.98422 | −0.269422 | ||||||||
\(673\) | 31.7136 | 1.22247 | 0.611234 | − | 0.791450i | \(-0.290673\pi\) | ||||
0.611234 | + | 0.791450i | \(0.290673\pi\) | |||||||
\(674\) | −2.23156 | −0.0859565 | ||||||||
\(675\) | 0.669990 | 0.0257879 | ||||||||
\(676\) | 1.33032 | 0.0511660 | ||||||||
\(677\) | −6.06261 | −0.233005 | −0.116502 | − | 0.993190i | \(-0.537168\pi\) | ||||
−0.116502 | + | 0.993190i | \(0.537168\pi\) | |||||||
\(678\) | −1.04684 | −0.0402037 | ||||||||
\(679\) | −49.7298 | −1.90845 | ||||||||
\(680\) | −4.03716 | −0.154818 | ||||||||
\(681\) | 2.02512 | 0.0776027 | ||||||||
\(682\) | −2.18390 | −0.0836259 | ||||||||
\(683\) | 25.3602 | 0.970379 | 0.485190 | − | 0.874409i | \(-0.338751\pi\) | ||||
0.485190 | + | 0.874409i | \(0.338751\pi\) | |||||||
\(684\) | 3.89971 | 0.149109 | ||||||||
\(685\) | −0.760847 | −0.0290705 | ||||||||
\(686\) | −0.314803 | −0.0120192 | ||||||||
\(687\) | 1.74269 | 0.0664877 | ||||||||
\(688\) | 14.1744 | 0.540395 | ||||||||
\(689\) | 10.5966 | 0.403697 | ||||||||
\(690\) | 0.335818 | 0.0127844 | ||||||||
\(691\) | −32.7346 | −1.24528 | −0.622642 | − | 0.782507i | \(-0.713941\pi\) | ||||
−0.622642 | + | 0.782507i | \(0.713941\pi\) | |||||||
\(692\) | −18.9619 | −0.720823 | ||||||||
\(693\) | 13.8664 | 0.526739 | ||||||||
\(694\) | 5.40742 | 0.205263 | ||||||||
\(695\) | −25.4247 | −0.964413 | ||||||||
\(696\) | 0.641331 | 0.0243096 | ||||||||
\(697\) | −36.3965 | −1.37861 | ||||||||
\(698\) | −3.38020 | −0.127942 | ||||||||
\(699\) | −10.8194 | −0.409227 | ||||||||
\(700\) | 4.85361 | 0.183449 | ||||||||
\(701\) | −2.21763 | −0.0837587 | −0.0418793 | − | 0.999123i | \(-0.513335\pi\) | ||||
−0.0418793 | + | 0.999123i | \(0.513335\pi\) | |||||||
\(702\) | −0.566593 | −0.0213847 | ||||||||
\(703\) | −10.5607 | −0.398304 | ||||||||
\(704\) | −27.8907 | −1.05117 | ||||||||
\(705\) | 0.287299 | 0.0108203 | ||||||||
\(706\) | 5.43590 | 0.204583 | ||||||||
\(707\) | −19.8057 | −0.744871 | ||||||||
\(708\) | 18.6175 | 0.699688 | ||||||||
\(709\) | −21.0149 | −0.789232 | −0.394616 | − | 0.918846i | \(-0.629122\pi\) | ||||
−0.394616 | + | 0.918846i | \(0.629122\pi\) | |||||||
\(710\) | −1.10225 | −0.0413666 | ||||||||
\(711\) | 7.31941 | 0.274499 | ||||||||
\(712\) | −3.88890 | −0.145743 | ||||||||
\(713\) | 3.58155 | 0.134130 | ||||||||
\(714\) | −1.79171 | −0.0670531 | ||||||||
\(715\) | 27.6032 | 1.03230 | ||||||||
\(716\) | −20.3744 | −0.761427 | ||||||||
\(717\) | −13.5515 | −0.506089 | ||||||||
\(718\) | −0.215016 | −0.00802432 | ||||||||
\(719\) | 29.7877 | 1.11089 | 0.555447 | − | 0.831552i | \(-0.312547\pi\) | ||||
0.555447 | + | 0.831552i | \(0.312547\pi\) | |||||||
\(720\) | 7.99971 | 0.298132 | ||||||||
\(721\) | 26.7512 | 0.996268 | ||||||||
\(722\) | −2.43642 | −0.0906741 | ||||||||
\(723\) | 17.0852 | 0.635406 | ||||||||
\(724\) | −18.4444 | −0.685482 | ||||||||
\(725\) | −0.669990 | −0.0248828 | ||||||||
\(726\) | −0.528689 | −0.0196215 | ||||||||
\(727\) | 52.4598 | 1.94563 | 0.972813 | − | 0.231590i | \(-0.0743928\pi\) | ||||
0.972813 | + | 0.231590i | \(0.0743928\pi\) | |||||||
\(728\) | −8.26330 | −0.306258 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.514253 | 0.0190334 | ||||||||
\(731\) | 11.1539 | 0.412541 | ||||||||
\(732\) | −21.4419 | −0.792516 | ||||||||
\(733\) | 43.1979 | 1.59555 | 0.797776 | − | 0.602954i | \(-0.206010\pi\) | ||||
0.797776 | + | 0.602954i | \(0.206010\pi\) | |||||||
\(734\) | 2.26219 | 0.0834991 | ||||||||
\(735\) | −13.4600 | −0.496481 | ||||||||
\(736\) | −1.90309 | −0.0701487 | ||||||||
\(737\) | 17.2771 | 0.636412 | ||||||||
\(738\) | −1.94164 | −0.0714727 | ||||||||
\(739\) | −7.29686 | −0.268419 | −0.134210 | − | 0.990953i | \(-0.542850\pi\) | ||||
−0.134210 | + | 0.990953i | \(0.542850\pi\) | |||||||
\(740\) | −21.9573 | −0.807165 | ||||||||
\(741\) | 6.93598 | 0.254800 | ||||||||
\(742\) | 1.78760 | 0.0656249 | ||||||||
\(743\) | −30.7316 | −1.12743 | −0.563716 | − | 0.825969i | \(-0.690629\pi\) | ||||
−0.563716 | + | 0.825969i | \(0.690629\pi\) | |||||||
\(744\) | −2.29696 | −0.0842106 | ||||||||
\(745\) | 5.66422 | 0.207521 | ||||||||
\(746\) | −2.82493 | −0.103428 | ||||||||
\(747\) | 5.82693 | 0.213196 | ||||||||
\(748\) | −22.5626 | −0.824972 | ||||||||
\(749\) | −21.7602 | −0.795099 | ||||||||
\(750\) | 1.90408 | 0.0695273 | ||||||||
\(751\) | −34.1301 | −1.24543 | −0.622713 | − | 0.782450i | \(-0.713970\pi\) | ||||
−0.622713 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(752\) | −0.530787 | −0.0193558 | ||||||||
\(753\) | −14.0710 | −0.512774 | ||||||||
\(754\) | 0.566593 | 0.0206341 | ||||||||
\(755\) | −29.9029 | −1.08828 | ||||||||
\(756\) | 7.24430 | 0.263473 | ||||||||
\(757\) | −15.6198 | −0.567710 | −0.283855 | − | 0.958867i | \(-0.591613\pi\) | ||||
−0.283855 | + | 0.958867i | \(0.591613\pi\) | |||||||
\(758\) | −4.19651 | −0.152424 | ||||||||
\(759\) | 3.77836 | 0.137146 | ||||||||
\(760\) | 2.63646 | 0.0956346 | ||||||||
\(761\) | −9.03111 | −0.327377 | −0.163689 | − | 0.986512i | \(-0.552339\pi\) | ||||
−0.163689 | + | 0.986512i | \(0.552339\pi\) | |||||||
\(762\) | −1.39127 | −0.0504006 | ||||||||
\(763\) | 62.1256 | 2.24910 | ||||||||
\(764\) | 1.23634 | 0.0447292 | ||||||||
\(765\) | 6.29498 | 0.227595 | ||||||||
\(766\) | −3.21026 | −0.115991 | ||||||||
\(767\) | 33.1128 | 1.19563 | ||||||||
\(768\) | −13.9569 | −0.503626 | ||||||||
\(769\) | 23.4779 | 0.846635 | 0.423318 | − | 0.905981i | \(-0.360865\pi\) | ||||
0.423318 | + | 0.905981i | \(0.360865\pi\) | |||||||
\(770\) | 4.65657 | 0.167811 | ||||||||
\(771\) | −2.08470 | −0.0750787 | ||||||||
\(772\) | 1.02049 | 0.0367282 | ||||||||
\(773\) | −21.4602 | −0.771871 | −0.385935 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385935 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(774\) | 0.595024 | 0.0213877 | ||||||||
\(775\) | 2.39960 | 0.0861963 | ||||||||
\(776\) | 8.69039 | 0.311967 | ||||||||
\(777\) | −19.6180 | −0.703793 | ||||||||
\(778\) | −1.11778 | −0.0400743 | ||||||||
\(779\) | 23.7687 | 0.851601 | ||||||||
\(780\) | 14.4210 | 0.516353 | ||||||||
\(781\) | −12.4016 | −0.443765 | ||||||||
\(782\) | −0.488212 | −0.0174584 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 24.8675 | 0.888125 | ||||||||
\(785\) | −19.7357 | −0.704398 | ||||||||
\(786\) | 0.738986 | 0.0263587 | ||||||||
\(787\) | 28.7283 | 1.02405 | 0.512026 | − | 0.858970i | \(-0.328895\pi\) | ||||
0.512026 | + | 0.858970i | \(0.328895\pi\) | |||||||
\(788\) | 0.118063 | 0.00420583 | ||||||||
\(789\) | 22.5597 | 0.803146 | ||||||||
\(790\) | 2.45799 | 0.0874513 | ||||||||
\(791\) | 23.8057 | 0.846434 | ||||||||
\(792\) | −2.42318 | −0.0861038 | ||||||||
\(793\) | −38.1363 | −1.35426 | ||||||||
\(794\) | −3.74421 | −0.132877 | ||||||||
\(795\) | −6.28054 | −0.222748 | ||||||||
\(796\) | 10.9521 | 0.388186 | ||||||||
\(797\) | −21.6103 | −0.765475 | −0.382737 | − | 0.923857i | \(-0.625019\pi\) | ||||
−0.382737 | + | 0.923857i | \(0.625019\pi\) | |||||||
\(798\) | 1.17008 | 0.0414202 | ||||||||
\(799\) | −0.417676 | −0.0147763 | ||||||||
\(800\) | −1.27505 | −0.0450798 | ||||||||
\(801\) | 6.06380 | 0.214254 | ||||||||
\(802\) | 2.09666 | 0.0740355 | ||||||||
\(803\) | 5.78598 | 0.204183 | ||||||||
\(804\) | 9.02623 | 0.318330 | ||||||||
\(805\) | −7.63666 | −0.269157 | ||||||||
\(806\) | −2.02928 | −0.0714784 | ||||||||
\(807\) | −21.7650 | −0.766165 | ||||||||
\(808\) | 3.46110 | 0.121761 | ||||||||
\(809\) | −38.6195 | −1.35779 | −0.678895 | − | 0.734235i | \(-0.737541\pi\) | ||||
−0.678895 | + | 0.734235i | \(0.737541\pi\) | |||||||
\(810\) | 0.335818 | 0.0117994 | ||||||||
\(811\) | 25.4982 | 0.895363 | 0.447681 | − | 0.894193i | \(-0.352250\pi\) | ||||
0.447681 | + | 0.894193i | \(0.352250\pi\) | |||||||
\(812\) | −7.24430 | −0.254225 | ||||||||
\(813\) | 19.0602 | 0.668469 | ||||||||
\(814\) | 3.25956 | 0.114247 | ||||||||
\(815\) | 42.8967 | 1.50261 | ||||||||
\(816\) | −11.6300 | −0.407131 | ||||||||
\(817\) | −7.28402 | −0.254836 | ||||||||
\(818\) | −5.17897 | −0.181079 | ||||||||
\(819\) | 12.8846 | 0.450225 | ||||||||
\(820\) | 49.4187 | 1.72578 | ||||||||
\(821\) | 27.1559 | 0.947747 | 0.473874 | − | 0.880593i | \(-0.342855\pi\) | ||||
0.473874 | + | 0.880593i | \(0.342855\pi\) | |||||||
\(822\) | 0.0590081 | 0.00205814 | ||||||||
\(823\) | −15.3728 | −0.535861 | −0.267930 | − | 0.963438i | \(-0.586340\pi\) | ||||
−0.267930 | + | 0.963438i | \(0.586340\pi\) | |||||||
\(824\) | −4.67484 | −0.162856 | ||||||||
\(825\) | 2.53146 | 0.0881342 | ||||||||
\(826\) | 5.58601 | 0.194362 | ||||||||
\(827\) | −4.88039 | −0.169708 | −0.0848539 | − | 0.996393i | \(-0.527042\pi\) | ||||
−0.0848539 | + | 0.996393i | \(0.527042\pi\) | |||||||
\(828\) | 1.97396 | 0.0685997 | ||||||||
\(829\) | 27.6304 | 0.959645 | 0.479823 | − | 0.877366i | \(-0.340701\pi\) | ||||
0.479823 | + | 0.877366i | \(0.340701\pi\) | |||||||
\(830\) | 1.95679 | 0.0679210 | ||||||||
\(831\) | 5.11613 | 0.177477 | ||||||||
\(832\) | −25.9160 | −0.898476 | ||||||||
\(833\) | 19.5682 | 0.678000 | ||||||||
\(834\) | 1.97183 | 0.0682790 | ||||||||
\(835\) | 27.7642 | 0.960820 | ||||||||
\(836\) | 14.7345 | 0.509604 | ||||||||
\(837\) | 3.58155 | 0.123797 | ||||||||
\(838\) | 4.51985 | 0.156136 | ||||||||
\(839\) | 18.3181 | 0.632411 | 0.316206 | − | 0.948691i | \(-0.397591\pi\) | ||||
0.316206 | + | 0.948691i | \(0.397591\pi\) | |||||||
\(840\) | 4.89763 | 0.168984 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −3.83607 | −0.132200 | ||||||||
\(843\) | 7.01306 | 0.241543 | ||||||||
\(844\) | 19.9232 | 0.685784 | ||||||||
\(845\) | −1.40237 | −0.0482429 | ||||||||
\(846\) | −0.0222817 | −0.000766062 0 | ||||||||
\(847\) | 12.0227 | 0.413104 | ||||||||
\(848\) | 11.6033 | 0.398460 | ||||||||
\(849\) | 18.5054 | 0.635102 | ||||||||
\(850\) | −0.327098 | −0.0112194 | ||||||||
\(851\) | −5.34560 | −0.183245 | ||||||||
\(852\) | −6.47907 | −0.221969 | ||||||||
\(853\) | −38.3460 | −1.31294 | −0.656472 | − | 0.754351i | \(-0.727952\pi\) | ||||
−0.656472 | + | 0.754351i | \(0.727952\pi\) | |||||||
\(854\) | −6.43346 | −0.220148 | ||||||||
\(855\) | −4.11093 | −0.140591 | ||||||||
\(856\) | 3.80264 | 0.129972 | ||||||||
\(857\) | 6.81213 | 0.232698 | 0.116349 | − | 0.993208i | \(-0.462881\pi\) | ||||
0.116349 | + | 0.993208i | \(0.462881\pi\) | |||||||
\(858\) | −2.14079 | −0.0730854 | ||||||||
\(859\) | −18.6302 | −0.635656 | −0.317828 | − | 0.948148i | \(-0.602953\pi\) | ||||
−0.317828 | + | 0.948148i | \(0.602953\pi\) | |||||||
\(860\) | −15.1446 | −0.516426 | ||||||||
\(861\) | 44.1539 | 1.50476 | ||||||||
\(862\) | 0.587076 | 0.0199959 | ||||||||
\(863\) | −15.8372 | −0.539105 | −0.269552 | − | 0.962986i | \(-0.586876\pi\) | ||||
−0.269552 | + | 0.962986i | \(0.586876\pi\) | |||||||
\(864\) | −1.90309 | −0.0647443 | ||||||||
\(865\) | 19.9889 | 0.679643 | ||||||||
\(866\) | 6.33189 | 0.215166 | ||||||||
\(867\) | 7.84835 | 0.266544 | ||||||||
\(868\) | 25.9458 | 0.880659 | ||||||||
\(869\) | 27.6554 | 0.938144 | ||||||||
\(870\) | −0.335818 | −0.0113853 | ||||||||
\(871\) | 16.0539 | 0.543966 | ||||||||
\(872\) | −10.8566 | −0.367651 | ||||||||
\(873\) | −13.5506 | −0.458617 | ||||||||
\(874\) | 0.318827 | 0.0107845 | ||||||||
\(875\) | −43.2998 | −1.46380 | ||||||||
\(876\) | 3.02281 | 0.102131 | ||||||||
\(877\) | −45.1404 | −1.52428 | −0.762141 | − | 0.647411i | \(-0.775852\pi\) | ||||
−0.762141 | + | 0.647411i | \(0.775852\pi\) | |||||||
\(878\) | 4.55162 | 0.153610 | ||||||||
\(879\) | −7.86714 | −0.265352 | ||||||||
\(880\) | 30.2258 | 1.01891 | ||||||||
\(881\) | −54.7405 | −1.84425 | −0.922127 | − | 0.386887i | \(-0.873550\pi\) | ||||
−0.922127 | + | 0.386887i | \(0.873550\pi\) | |||||||
\(882\) | 1.04391 | 0.0351501 | ||||||||
\(883\) | −47.5964 | −1.60175 | −0.800874 | − | 0.598833i | \(-0.795631\pi\) | ||||
−0.800874 | + | 0.598833i | \(0.795631\pi\) | |||||||
\(884\) | −20.9652 | −0.705137 | ||||||||
\(885\) | −19.6258 | −0.659715 | ||||||||
\(886\) | −3.92504 | −0.131864 | ||||||||
\(887\) | 3.05499 | 0.102577 | 0.0512883 | − | 0.998684i | \(-0.483667\pi\) | ||||
0.0512883 | + | 0.998684i | \(0.483667\pi\) | |||||||
\(888\) | 3.42830 | 0.115046 | ||||||||
\(889\) | 31.6383 | 1.06111 | ||||||||
\(890\) | 2.03633 | 0.0682580 | ||||||||
\(891\) | 3.77836 | 0.126580 | ||||||||
\(892\) | 5.23692 | 0.175345 | ||||||||
\(893\) | 0.272763 | 0.00912767 | ||||||||
\(894\) | −0.439294 | −0.0146922 | ||||||||
\(895\) | 21.4779 | 0.717927 | ||||||||
\(896\) | −18.3404 | −0.612709 | ||||||||
\(897\) | 3.51085 | 0.117224 | ||||||||
\(898\) | 6.61474 | 0.220737 | ||||||||
\(899\) | −3.58155 | −0.119451 | ||||||||
\(900\) | 1.32253 | 0.0440844 | ||||||||
\(901\) | 9.13066 | 0.304186 | ||||||||
\(902\) | −7.33620 | −0.244269 | ||||||||
\(903\) | −13.5312 | −0.450289 | ||||||||
\(904\) | −4.16011 | −0.138363 | ||||||||
\(905\) | 19.4434 | 0.646321 | ||||||||
\(906\) | 2.31915 | 0.0770485 | ||||||||
\(907\) | −24.3521 | −0.808599 | −0.404300 | − | 0.914627i | \(-0.632485\pi\) | ||||
−0.404300 | + | 0.914627i | \(0.632485\pi\) | |||||||
\(908\) | 3.99749 | 0.132661 | ||||||||
\(909\) | −5.39674 | −0.178999 | ||||||||
\(910\) | 4.32688 | 0.143435 | ||||||||
\(911\) | 8.64600 | 0.286455 | 0.143227 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143227 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(912\) | 7.59496 | 0.251494 | ||||||||
\(913\) | 22.0162 | 0.728630 | ||||||||
\(914\) | 1.58308 | 0.0523637 | ||||||||
\(915\) | 22.6032 | 0.747240 | ||||||||
\(916\) | 3.43999 | 0.113660 | ||||||||
\(917\) | −16.8049 | −0.554947 | ||||||||
\(918\) | −0.488212 | −0.0161134 | ||||||||
\(919\) | 38.3295 | 1.26437 | 0.632187 | − | 0.774816i | \(-0.282157\pi\) | ||||
0.632187 | + | 0.774816i | \(0.282157\pi\) | |||||||
\(920\) | 1.33452 | 0.0439980 | ||||||||
\(921\) | 1.52335 | 0.0501962 | ||||||||
\(922\) | −3.97351 | −0.130860 | ||||||||
\(923\) | −11.5236 | −0.379304 | ||||||||
\(924\) | 27.3716 | 0.900458 | ||||||||
\(925\) | −3.58150 | −0.117759 | ||||||||
\(926\) | 1.63201 | 0.0536311 | ||||||||
\(927\) | 7.28928 | 0.239411 | ||||||||
\(928\) | 1.90309 | 0.0624719 | ||||||||
\(929\) | 34.5501 | 1.13355 | 0.566776 | − | 0.823872i | \(-0.308191\pi\) | ||||
0.566776 | + | 0.823872i | \(0.308191\pi\) | |||||||
\(930\) | 1.20275 | 0.0394397 | ||||||||
\(931\) | −12.7790 | −0.418816 | ||||||||
\(932\) | −21.3570 | −0.699572 | ||||||||
\(933\) | −15.6060 | −0.510918 | ||||||||
\(934\) | 0.0354916 | 0.00116132 | ||||||||
\(935\) | 23.7847 | 0.777842 | ||||||||
\(936\) | −2.25162 | −0.0735964 | ||||||||
\(937\) | 31.5802 | 1.03168 | 0.515839 | − | 0.856685i | \(-0.327480\pi\) | ||||
0.515839 | + | 0.856685i | \(0.327480\pi\) | |||||||
\(938\) | 2.70824 | 0.0884272 | ||||||||
\(939\) | 8.42755 | 0.275023 | ||||||||
\(940\) | 0.567116 | 0.0184973 | ||||||||
\(941\) | −17.7672 | −0.579195 | −0.289597 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289597 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(942\) | 1.53062 | 0.0498703 | ||||||||
\(943\) | 12.0312 | 0.391790 | ||||||||
\(944\) | 36.2588 | 1.18012 | ||||||||
\(945\) | −7.63666 | −0.248421 | ||||||||
\(946\) | 2.24821 | 0.0730958 | ||||||||
\(947\) | −0.409000 | −0.0132907 | −0.00664535 | − | 0.999978i | \(-0.502115\pi\) | ||||
−0.00664535 | + | 0.999978i | \(0.502115\pi\) | |||||||
\(948\) | 14.4482 | 0.469255 | ||||||||
\(949\) | 5.37633 | 0.174523 | ||||||||
\(950\) | 0.213611 | 0.00693045 | ||||||||
\(951\) | 8.28338 | 0.268607 | ||||||||
\(952\) | −7.12018 | −0.230766 | ||||||||
\(953\) | −15.6870 | −0.508151 | −0.254076 | − | 0.967184i | \(-0.581771\pi\) | ||||
−0.254076 | + | 0.967184i | \(0.581771\pi\) | |||||||
\(954\) | 0.487093 | 0.0157702 | ||||||||
\(955\) | −1.30330 | −0.0421738 | ||||||||
\(956\) | −26.7500 | −0.865157 | ||||||||
\(957\) | −3.77836 | −0.122137 | ||||||||
\(958\) | −2.73728 | −0.0884376 | ||||||||
\(959\) | −1.34187 | −0.0433314 | ||||||||
\(960\) | 15.3603 | 0.495752 | ||||||||
\(961\) | −18.1725 | −0.586209 | ||||||||
\(962\) | 3.02878 | 0.0976518 | ||||||||
\(963\) | −5.92929 | −0.191069 | ||||||||
\(964\) | 33.7254 | 1.08622 | ||||||||
\(965\) | −1.07576 | −0.0346299 | ||||||||
\(966\) | 0.592268 | 0.0190559 | ||||||||
\(967\) | 48.0986 | 1.54675 | 0.773373 | − | 0.633951i | \(-0.218568\pi\) | ||||
0.773373 | + | 0.633951i | \(0.218568\pi\) | |||||||
\(968\) | −2.10099 | −0.0675283 | ||||||||
\(969\) | 5.97648 | 0.191992 | ||||||||
\(970\) | −4.55052 | −0.146108 | ||||||||
\(971\) | −24.7927 | −0.795636 | −0.397818 | − | 0.917464i | \(-0.630232\pi\) | ||||
−0.397818 | + | 0.917464i | \(0.630232\pi\) | |||||||
\(972\) | 1.97396 | 0.0633146 | ||||||||
\(973\) | −44.8405 | −1.43752 | ||||||||
\(974\) | 4.52730 | 0.145064 | ||||||||
\(975\) | 2.35224 | 0.0753318 | ||||||||
\(976\) | −41.7595 | −1.33669 | ||||||||
\(977\) | −26.6260 | −0.851841 | −0.425921 | − | 0.904761i | \(-0.640050\pi\) | ||||
−0.425921 | + | 0.904761i | \(0.640050\pi\) | |||||||
\(978\) | −3.32689 | −0.106382 | ||||||||
\(979\) | 22.9112 | 0.732245 | ||||||||
\(980\) | −26.5695 | −0.848733 | ||||||||
\(981\) | 16.9282 | 0.540477 | ||||||||
\(982\) | 6.12644 | 0.195503 | ||||||||
\(983\) | 6.74470 | 0.215123 | 0.107561 | − | 0.994198i | \(-0.465696\pi\) | ||||
0.107561 | + | 0.994198i | \(0.465696\pi\) | |||||||
\(984\) | −7.71599 | −0.245977 | ||||||||
\(985\) | −0.124458 | −0.00396555 | ||||||||
\(986\) | 0.488212 | 0.0155479 | ||||||||
\(987\) | 0.506698 | 0.0161284 | ||||||||
\(988\) | 13.6913 | 0.435579 | ||||||||
\(989\) | −3.68702 | −0.117240 | ||||||||
\(990\) | 1.26884 | 0.0403263 | ||||||||
\(991\) | 40.4589 | 1.28522 | 0.642610 | − | 0.766193i | \(-0.277851\pi\) | ||||
0.642610 | + | 0.766193i | \(0.277851\pi\) | |||||||
\(992\) | −6.81600 | −0.216408 | ||||||||
\(993\) | 21.2067 | 0.672976 | ||||||||
\(994\) | −1.94399 | −0.0616596 | ||||||||
\(995\) | −11.5453 | −0.366010 | ||||||||
\(996\) | 11.5021 | 0.364458 | ||||||||
\(997\) | −29.3174 | −0.928491 | −0.464246 | − | 0.885706i | \(-0.653675\pi\) | ||||
−0.464246 | + | 0.885706i | \(0.653675\pi\) | |||||||
\(998\) | 0.812889 | 0.0257316 | ||||||||
\(999\) | −5.34560 | −0.169127 |
(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 | 2001.2.a.k.1.4 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.k.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.k.1.7 | 10 | 3.2 | odd | 2 |