Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.546298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.546298 | −0.386291 | −0.193146 | − | 0.981170i | \(-0.561869\pi\) | ||||
−0.193146 | + | 0.981170i | \(0.561869\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.70156 | −0.850779 | ||||||||
\(5\) | −0.842631 | −0.376836 | −0.188418 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188418 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(6\) | 0.546298 | 0.223025 | ||||||||
\(7\) | −4.19208 | −1.58446 | −0.792228 | − | 0.610226i | \(-0.791079\pi\) | ||||
−0.792228 | + | 0.610226i | \(0.791079\pi\) | |||||||
\(8\) | 2.02216 | 0.714940 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.460328 | 0.145568 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.70156 | 0.491198 | ||||||||
\(13\) | −5.95974 | −1.65293 | −0.826467 | − | 0.562985i | \(-0.809653\pi\) | ||||
−0.826467 | + | 0.562985i | \(0.809653\pi\) | |||||||
\(14\) | 2.29012 | 0.612061 | ||||||||
\(15\) | 0.842631 | 0.217566 | ||||||||
\(16\) | 2.29842 | 0.574604 | ||||||||
\(17\) | 0.386200 | 0.0936672 | 0.0468336 | − | 0.998903i | \(-0.485087\pi\) | ||||
0.0468336 | + | 0.998903i | \(0.485087\pi\) | |||||||
\(18\) | −0.546298 | −0.128764 | ||||||||
\(19\) | −2.95453 | −0.677815 | −0.338907 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338907 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(20\) | 1.43379 | 0.320604 | ||||||||
\(21\) | 4.19208 | 0.914786 | ||||||||
\(22\) | 0.546298 | 0.116471 | ||||||||
\(23\) | −0.974992 | −0.203300 | −0.101650 | − | 0.994820i | \(-0.532412\pi\) | ||||
−0.101650 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(24\) | −2.02216 | −0.412771 | ||||||||
\(25\) | −4.28997 | −0.857995 | ||||||||
\(26\) | 3.25580 | 0.638514 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.13306 | 1.34802 | ||||||||
\(29\) | −10.0563 | −1.86741 | −0.933707 | − | 0.358038i | \(-0.883446\pi\) | ||||
−0.933707 | + | 0.358038i | \(0.883446\pi\) | |||||||
\(30\) | −0.460328 | −0.0840440 | ||||||||
\(31\) | −10.6290 | −1.90902 | −0.954512 | − | 0.298171i | \(-0.903623\pi\) | ||||
−0.954512 | + | 0.298171i | \(0.903623\pi\) | |||||||
\(32\) | −5.29993 | −0.936904 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −0.210980 | −0.0361828 | ||||||||
\(35\) | 3.53237 | 0.597080 | ||||||||
\(36\) | −1.70156 | −0.283593 | ||||||||
\(37\) | −3.16781 | −0.520785 | −0.260392 | − | 0.965503i | \(-0.583852\pi\) | ||||
−0.260392 | + | 0.965503i | \(0.583852\pi\) | |||||||
\(38\) | 1.61405 | 0.261834 | ||||||||
\(39\) | 5.95974 | 0.954322 | ||||||||
\(40\) | −1.70393 | −0.269415 | ||||||||
\(41\) | −1.29317 | −0.201959 | −0.100980 | − | 0.994888i | \(-0.532198\pi\) | ||||
−0.100980 | + | 0.994888i | \(0.532198\pi\) | |||||||
\(42\) | −2.29012 | −0.353374 | ||||||||
\(43\) | −4.99709 | −0.762050 | −0.381025 | − | 0.924565i | \(-0.624429\pi\) | ||||
−0.381025 | + | 0.924565i | \(0.624429\pi\) | |||||||
\(44\) | 1.70156 | 0.256520 | ||||||||
\(45\) | −0.842631 | −0.125612 | ||||||||
\(46\) | 0.532636 | 0.0785330 | ||||||||
\(47\) | 7.87272 | 1.14835 | 0.574177 | − | 0.818731i | \(-0.305322\pi\) | ||||
0.574177 | + | 0.818731i | \(0.305322\pi\) | |||||||
\(48\) | −2.29842 | −0.331748 | ||||||||
\(49\) | 10.5735 | 1.51050 | ||||||||
\(50\) | 2.34361 | 0.331436 | ||||||||
\(51\) | −0.386200 | −0.0540788 | ||||||||
\(52\) | 10.1408 | 1.40628 | ||||||||
\(53\) | 0.370002 | 0.0508237 | 0.0254119 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254119 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(54\) | 0.546298 | 0.0743418 | ||||||||
\(55\) | 0.842631 | 0.113620 | ||||||||
\(56\) | −8.47703 | −1.13279 | ||||||||
\(57\) | 2.95453 | 0.391337 | ||||||||
\(58\) | 5.49376 | 0.721366 | ||||||||
\(59\) | 13.7723 | 1.79299 | 0.896497 | − | 0.443049i | \(-0.146103\pi\) | ||||
0.896497 | + | 0.443049i | \(0.146103\pi\) | |||||||
\(60\) | −1.43379 | −0.185101 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 5.80661 | 0.737440 | ||||||||
\(63\) | −4.19208 | −0.528152 | ||||||||
\(64\) | −1.70149 | −0.212686 | ||||||||
\(65\) | 5.02186 | 0.622885 | ||||||||
\(66\) | −0.546298 | −0.0672447 | ||||||||
\(67\) | 9.80901 | 1.19836 | 0.599181 | − | 0.800614i | \(-0.295493\pi\) | ||||
0.599181 | + | 0.800614i | \(0.295493\pi\) | |||||||
\(68\) | −0.657141 | −0.0796901 | ||||||||
\(69\) | 0.974992 | 0.117375 | ||||||||
\(70\) | −1.92973 | −0.230647 | ||||||||
\(71\) | −4.36706 | −0.518274 | −0.259137 | − | 0.965841i | \(-0.583438\pi\) | ||||
−0.259137 | + | 0.965841i | \(0.583438\pi\) | |||||||
\(72\) | 2.02216 | 0.238313 | ||||||||
\(73\) | −2.06518 | −0.241711 | −0.120855 | − | 0.992670i | \(-0.538564\pi\) | ||||
−0.120855 | + | 0.992670i | \(0.538564\pi\) | |||||||
\(74\) | 1.73057 | 0.201175 | ||||||||
\(75\) | 4.28997 | 0.495363 | ||||||||
\(76\) | 5.02730 | 0.576671 | ||||||||
\(77\) | 4.19208 | 0.477731 | ||||||||
\(78\) | −3.25580 | −0.368646 | ||||||||
\(79\) | −8.67552 | −0.976072 | −0.488036 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488036 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(80\) | −1.93672 | −0.216531 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.706457 | 0.0780151 | ||||||||
\(83\) | −7.09673 | −0.778967 | −0.389483 | − | 0.921033i | \(-0.627346\pi\) | ||||
−0.389483 | + | 0.921033i | \(0.627346\pi\) | |||||||
\(84\) | −7.13306 | −0.778281 | ||||||||
\(85\) | −0.325424 | −0.0352972 | ||||||||
\(86\) | 2.72990 | 0.294373 | ||||||||
\(87\) | 10.0563 | 1.07815 | ||||||||
\(88\) | −2.02216 | −0.215562 | ||||||||
\(89\) | −7.42432 | −0.786976 | −0.393488 | − | 0.919330i | \(-0.628732\pi\) | ||||
−0.393488 | + | 0.919330i | \(0.628732\pi\) | |||||||
\(90\) | 0.460328 | 0.0485228 | ||||||||
\(91\) | 24.9837 | 2.61900 | ||||||||
\(92\) | 1.65901 | 0.172963 | ||||||||
\(93\) | 10.6290 | 1.10218 | ||||||||
\(94\) | −4.30086 | −0.443599 | ||||||||
\(95\) | 2.48957 | 0.255425 | ||||||||
\(96\) | 5.29993 | 0.540922 | ||||||||
\(97\) | −6.00940 | −0.610162 | −0.305081 | − | 0.952326i | \(-0.598684\pi\) | ||||
−0.305081 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(98\) | −5.77628 | −0.583493 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 7.29964 | 0.729964 | ||||||||
\(101\) | −18.1851 | −1.80948 | −0.904742 | − | 0.425961i | \(-0.859936\pi\) | ||||
−0.904742 | + | 0.425961i | \(0.859936\pi\) | |||||||
\(102\) | 0.210980 | 0.0208902 | ||||||||
\(103\) | 10.9494 | 1.07887 | 0.539436 | − | 0.842026i | \(-0.318637\pi\) | ||||
0.539436 | + | 0.842026i | \(0.318637\pi\) | |||||||
\(104\) | −12.0515 | −1.18175 | ||||||||
\(105\) | −3.53237 | −0.344724 | ||||||||
\(106\) | −0.202132 | −0.0196328 | ||||||||
\(107\) | 2.84318 | 0.274860 | 0.137430 | − | 0.990511i | \(-0.456116\pi\) | ||||
0.137430 | + | 0.990511i | \(0.456116\pi\) | |||||||
\(108\) | 1.70156 | 0.163733 | ||||||||
\(109\) | 19.4494 | 1.86291 | 0.931456 | − | 0.363855i | \(-0.118540\pi\) | ||||
0.931456 | + | 0.363855i | \(0.118540\pi\) | |||||||
\(110\) | −0.460328 | −0.0438905 | ||||||||
\(111\) | 3.16781 | 0.300675 | ||||||||
\(112\) | −9.63513 | −0.910434 | ||||||||
\(113\) | 8.08952 | 0.760998 | 0.380499 | − | 0.924781i | \(-0.375752\pi\) | ||||
0.380499 | + | 0.924781i | \(0.375752\pi\) | |||||||
\(114\) | −1.61405 | −0.151170 | ||||||||
\(115\) | 0.821558 | 0.0766107 | ||||||||
\(116\) | 17.1114 | 1.58876 | ||||||||
\(117\) | −5.95974 | −0.550978 | ||||||||
\(118\) | −7.52376 | −0.692618 | ||||||||
\(119\) | −1.61898 | −0.148411 | ||||||||
\(120\) | 1.70393 | 0.155547 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.546298 | −0.0494595 | ||||||||
\(123\) | 1.29317 | 0.116601 | ||||||||
\(124\) | 18.0859 | 1.62416 | ||||||||
\(125\) | 7.82802 | 0.700159 | ||||||||
\(126\) | 2.29012 | 0.204020 | ||||||||
\(127\) | 1.18990 | 0.105587 | 0.0527934 | − | 0.998605i | \(-0.483188\pi\) | ||||
0.0527934 | + | 0.998605i | \(0.483188\pi\) | |||||||
\(128\) | 11.5294 | 1.01906 | ||||||||
\(129\) | 4.99709 | 0.439970 | ||||||||
\(130\) | −2.74343 | −0.240615 | ||||||||
\(131\) | −0.232276 | −0.0202940 | −0.0101470 | − | 0.999949i | \(-0.503230\pi\) | ||||
−0.0101470 | + | 0.999949i | \(0.503230\pi\) | |||||||
\(132\) | −1.70156 | −0.148102 | ||||||||
\(133\) | 12.3856 | 1.07397 | ||||||||
\(134\) | −5.35865 | −0.462917 | ||||||||
\(135\) | 0.842631 | 0.0725221 | ||||||||
\(136\) | 0.780956 | 0.0669664 | ||||||||
\(137\) | −13.7946 | −1.17855 | −0.589276 | − | 0.807932i | \(-0.700587\pi\) | ||||
−0.589276 | + | 0.807932i | \(0.700587\pi\) | |||||||
\(138\) | −0.532636 | −0.0453410 | ||||||||
\(139\) | 10.2427 | 0.868777 | 0.434388 | − | 0.900726i | \(-0.356965\pi\) | ||||
0.434388 | + | 0.900726i | \(0.356965\pi\) | |||||||
\(140\) | −6.01053 | −0.507983 | ||||||||
\(141\) | −7.87272 | −0.663003 | ||||||||
\(142\) | 2.38572 | 0.200205 | ||||||||
\(143\) | 5.95974 | 0.498378 | ||||||||
\(144\) | 2.29842 | 0.191535 | ||||||||
\(145\) | 8.47377 | 0.703709 | ||||||||
\(146\) | 1.12820 | 0.0933708 | ||||||||
\(147\) | −10.5735 | −0.872087 | ||||||||
\(148\) | 5.39021 | 0.443073 | ||||||||
\(149\) | −2.70615 | −0.221697 | −0.110848 | − | 0.993837i | \(-0.535357\pi\) | ||||
−0.110848 | + | 0.993837i | \(0.535357\pi\) | |||||||
\(150\) | −2.34361 | −0.191355 | ||||||||
\(151\) | −15.6416 | −1.27290 | −0.636448 | − | 0.771319i | \(-0.719597\pi\) | ||||
−0.636448 | + | 0.771319i | \(0.719597\pi\) | |||||||
\(152\) | −5.97451 | −0.484597 | ||||||||
\(153\) | 0.386200 | 0.0312224 | ||||||||
\(154\) | −2.29012 | −0.184543 | ||||||||
\(155\) | 8.95632 | 0.719389 | ||||||||
\(156\) | −10.1408 | −0.811917 | ||||||||
\(157\) | 3.50083 | 0.279397 | 0.139698 | − | 0.990194i | \(-0.455387\pi\) | ||||
0.139698 | + | 0.990194i | \(0.455387\pi\) | |||||||
\(158\) | 4.73942 | 0.377048 | ||||||||
\(159\) | −0.370002 | −0.0293431 | ||||||||
\(160\) | 4.46589 | 0.353059 | ||||||||
\(161\) | 4.08724 | 0.322120 | ||||||||
\(162\) | −0.546298 | −0.0429213 | ||||||||
\(163\) | 16.8255 | 1.31788 | 0.658938 | − | 0.752197i | \(-0.271006\pi\) | ||||
0.658938 | + | 0.752197i | \(0.271006\pi\) | |||||||
\(164\) | 2.20040 | 0.171823 | ||||||||
\(165\) | −0.842631 | −0.0655987 | ||||||||
\(166\) | 3.87693 | 0.300908 | ||||||||
\(167\) | 18.1086 | 1.40129 | 0.700645 | − | 0.713510i | \(-0.252896\pi\) | ||||
0.700645 | + | 0.713510i | \(0.252896\pi\) | |||||||
\(168\) | 8.47703 | 0.654017 | ||||||||
\(169\) | 22.5185 | 1.73219 | ||||||||
\(170\) | 0.177778 | 0.0136350 | ||||||||
\(171\) | −2.95453 | −0.225938 | ||||||||
\(172\) | 8.50285 | 0.648336 | ||||||||
\(173\) | −9.84724 | −0.748672 | −0.374336 | − | 0.927293i | \(-0.622129\pi\) | ||||
−0.374336 | + | 0.927293i | \(0.622129\pi\) | |||||||
\(174\) | −5.49376 | −0.416481 | ||||||||
\(175\) | 17.9839 | 1.35945 | ||||||||
\(176\) | −2.29842 | −0.173250 | ||||||||
\(177\) | −13.7723 | −1.03519 | ||||||||
\(178\) | 4.05589 | 0.304002 | ||||||||
\(179\) | −10.0310 | −0.749749 | −0.374875 | − | 0.927075i | \(-0.622314\pi\) | ||||
−0.374875 | + | 0.927075i | \(0.622314\pi\) | |||||||
\(180\) | 1.43379 | 0.106868 | ||||||||
\(181\) | −13.2298 | −0.983362 | −0.491681 | − | 0.870775i | \(-0.663617\pi\) | ||||
−0.491681 | + | 0.870775i | \(0.663617\pi\) | |||||||
\(182\) | −13.6485 | −1.01170 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −1.97158 | −0.145347 | ||||||||
\(185\) | 2.66929 | 0.196250 | ||||||||
\(186\) | −5.80661 | −0.425761 | ||||||||
\(187\) | −0.386200 | −0.0282417 | ||||||||
\(188\) | −13.3959 | −0.976996 | ||||||||
\(189\) | 4.19208 | 0.304929 | ||||||||
\(190\) | −1.36005 | −0.0986684 | ||||||||
\(191\) | −26.0670 | −1.88614 | −0.943069 | − | 0.332596i | \(-0.892075\pi\) | ||||
−0.943069 | + | 0.332596i | \(0.892075\pi\) | |||||||
\(192\) | 1.70149 | 0.122794 | ||||||||
\(193\) | −1.64976 | −0.118752 | −0.0593760 | − | 0.998236i | \(-0.518911\pi\) | ||||
−0.0593760 | + | 0.998236i | \(0.518911\pi\) | |||||||
\(194\) | 3.28292 | 0.235700 | ||||||||
\(195\) | −5.02186 | −0.359623 | ||||||||
\(196\) | −17.9914 | −1.28510 | ||||||||
\(197\) | −15.0092 | −1.06936 | −0.534681 | − | 0.845054i | \(-0.679568\pi\) | ||||
−0.534681 | + | 0.845054i | \(0.679568\pi\) | |||||||
\(198\) | 0.546298 | 0.0388237 | ||||||||
\(199\) | 0.432727 | 0.0306752 | 0.0153376 | − | 0.999882i | \(-0.495118\pi\) | ||||
0.0153376 | + | 0.999882i | \(0.495118\pi\) | |||||||
\(200\) | −8.67499 | −0.613415 | ||||||||
\(201\) | −9.80901 | −0.691874 | ||||||||
\(202\) | 9.93448 | 0.698988 | ||||||||
\(203\) | 42.1569 | 2.95883 | ||||||||
\(204\) | 0.657141 | 0.0460091 | ||||||||
\(205\) | 1.08967 | 0.0761055 | ||||||||
\(206\) | −5.98162 | −0.416759 | ||||||||
\(207\) | −0.974992 | −0.0677666 | ||||||||
\(208\) | −13.6980 | −0.949783 | ||||||||
\(209\) | 2.95453 | 0.204369 | ||||||||
\(210\) | 1.92973 | 0.133164 | ||||||||
\(211\) | −5.99457 | −0.412683 | −0.206342 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206342 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(212\) | −0.629580 | −0.0432398 | ||||||||
\(213\) | 4.36706 | 0.299226 | ||||||||
\(214\) | −1.55322 | −0.106176 | ||||||||
\(215\) | 4.21070 | 0.287168 | ||||||||
\(216\) | −2.02216 | −0.137590 | ||||||||
\(217\) | 44.5576 | 3.02476 | ||||||||
\(218\) | −10.6252 | −0.719626 | ||||||||
\(219\) | 2.06518 | 0.139552 | ||||||||
\(220\) | −1.43379 | −0.0966658 | ||||||||
\(221\) | −2.30165 | −0.154826 | ||||||||
\(222\) | −1.73057 | −0.116148 | ||||||||
\(223\) | 1.20744 | 0.0808559 | 0.0404280 | − | 0.999182i | \(-0.487128\pi\) | ||||
0.0404280 | + | 0.999182i | \(0.487128\pi\) | |||||||
\(224\) | 22.2177 | 1.48448 | ||||||||
\(225\) | −4.28997 | −0.285998 | ||||||||
\(226\) | −4.41929 | −0.293967 | ||||||||
\(227\) | 3.17333 | 0.210621 | 0.105311 | − | 0.994439i | \(-0.466416\pi\) | ||||
0.105311 | + | 0.994439i | \(0.466416\pi\) | |||||||
\(228\) | −5.02730 | −0.332941 | ||||||||
\(229\) | −26.1824 | −1.73018 | −0.865091 | − | 0.501614i | \(-0.832740\pi\) | ||||
−0.865091 | + | 0.501614i | \(0.832740\pi\) | |||||||
\(230\) | −0.448816 | −0.0295940 | ||||||||
\(231\) | −4.19208 | −0.275818 | ||||||||
\(232\) | −20.3355 | −1.33509 | ||||||||
\(233\) | 15.3586 | 1.00617 | 0.503087 | − | 0.864236i | \(-0.332197\pi\) | ||||
0.503087 | + | 0.864236i | \(0.332197\pi\) | |||||||
\(234\) | 3.25580 | 0.212838 | ||||||||
\(235\) | −6.63380 | −0.432741 | ||||||||
\(236\) | −23.4343 | −1.52544 | ||||||||
\(237\) | 8.67552 | 0.563535 | ||||||||
\(238\) | 0.884445 | 0.0573301 | ||||||||
\(239\) | −6.48318 | −0.419362 | −0.209681 | − | 0.977770i | \(-0.567243\pi\) | ||||
−0.209681 | + | 0.977770i | \(0.567243\pi\) | |||||||
\(240\) | 1.93672 | 0.125014 | ||||||||
\(241\) | −2.05017 | −0.132063 | −0.0660315 | − | 0.997818i | \(-0.521034\pi\) | ||||
−0.0660315 | + | 0.997818i | \(0.521034\pi\) | |||||||
\(242\) | −0.546298 | −0.0351174 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.70156 | −0.108931 | ||||||||
\(245\) | −8.90955 | −0.569210 | ||||||||
\(246\) | −0.706457 | −0.0450421 | ||||||||
\(247\) | 17.6082 | 1.12038 | ||||||||
\(248\) | −21.4935 | −1.36484 | ||||||||
\(249\) | 7.09673 | 0.449737 | ||||||||
\(250\) | −4.27643 | −0.270465 | ||||||||
\(251\) | 0.403663 | 0.0254790 | 0.0127395 | − | 0.999919i | \(-0.495945\pi\) | ||||
0.0127395 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(252\) | 7.13306 | 0.449340 | ||||||||
\(253\) | 0.974992 | 0.0612972 | ||||||||
\(254\) | −0.650042 | −0.0407873 | ||||||||
\(255\) | 0.325424 | 0.0203788 | ||||||||
\(256\) | −2.89551 | −0.180969 | ||||||||
\(257\) | −3.52100 | −0.219634 | −0.109817 | − | 0.993952i | \(-0.535027\pi\) | ||||
−0.109817 | + | 0.993952i | \(0.535027\pi\) | |||||||
\(258\) | −2.72990 | −0.169956 | ||||||||
\(259\) | 13.2797 | 0.825160 | ||||||||
\(260\) | −8.54498 | −0.529937 | ||||||||
\(261\) | −10.0563 | −0.622471 | ||||||||
\(262\) | 0.126892 | 0.00783940 | ||||||||
\(263\) | 25.3122 | 1.56082 | 0.780408 | − | 0.625271i | \(-0.215012\pi\) | ||||
0.780408 | + | 0.625271i | \(0.215012\pi\) | |||||||
\(264\) | 2.02216 | 0.124455 | ||||||||
\(265\) | −0.311775 | −0.0191522 | ||||||||
\(266\) | −6.76623 | −0.414864 | ||||||||
\(267\) | 7.42432 | 0.454361 | ||||||||
\(268\) | −16.6906 | −1.01954 | ||||||||
\(269\) | 26.8357 | 1.63620 | 0.818100 | − | 0.575076i | \(-0.195028\pi\) | ||||
0.818100 | + | 0.575076i | \(0.195028\pi\) | |||||||
\(270\) | −0.460328 | −0.0280147 | ||||||||
\(271\) | −8.80885 | −0.535099 | −0.267550 | − | 0.963544i | \(-0.586214\pi\) | ||||
−0.267550 | + | 0.963544i | \(0.586214\pi\) | |||||||
\(272\) | 0.887648 | 0.0538215 | ||||||||
\(273\) | −24.9837 | −1.51208 | ||||||||
\(274\) | 7.53597 | 0.455264 | ||||||||
\(275\) | 4.28997 | 0.258695 | ||||||||
\(276\) | −1.65901 | −0.0998604 | ||||||||
\(277\) | 21.3581 | 1.28328 | 0.641641 | − | 0.767005i | \(-0.278254\pi\) | ||||
0.641641 | + | 0.767005i | \(0.278254\pi\) | |||||||
\(278\) | −5.59559 | −0.335601 | ||||||||
\(279\) | −10.6290 | −0.636342 | ||||||||
\(280\) | 7.14300 | 0.426876 | ||||||||
\(281\) | −29.9872 | −1.78889 | −0.894444 | − | 0.447181i | \(-0.852428\pi\) | ||||
−0.894444 | + | 0.447181i | \(0.852428\pi\) | |||||||
\(282\) | 4.30086 | 0.256112 | ||||||||
\(283\) | 10.0912 | 0.599862 | 0.299931 | − | 0.953961i | \(-0.403036\pi\) | ||||
0.299931 | + | 0.953961i | \(0.403036\pi\) | |||||||
\(284\) | 7.43080 | 0.440937 | ||||||||
\(285\) | −2.48957 | −0.147470 | ||||||||
\(286\) | −3.25580 | −0.192519 | ||||||||
\(287\) | 5.42107 | 0.319996 | ||||||||
\(288\) | −5.29993 | −0.312301 | ||||||||
\(289\) | −16.8508 | −0.991226 | ||||||||
\(290\) | −4.62921 | −0.271837 | ||||||||
\(291\) | 6.00940 | 0.352277 | ||||||||
\(292\) | 3.51402 | 0.205643 | ||||||||
\(293\) | −11.7387 | −0.685783 | −0.342892 | − | 0.939375i | \(-0.611406\pi\) | ||||
−0.342892 | + | 0.939375i | \(0.611406\pi\) | |||||||
\(294\) | 5.77628 | 0.336880 | ||||||||
\(295\) | −11.6049 | −0.675665 | ||||||||
\(296\) | −6.40580 | −0.372330 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 1.47837 | 0.0856395 | ||||||||
\(299\) | 5.81070 | 0.336041 | ||||||||
\(300\) | −7.29964 | −0.421445 | ||||||||
\(301\) | 20.9482 | 1.20743 | ||||||||
\(302\) | 8.54499 | 0.491709 | ||||||||
\(303\) | 18.1851 | 1.04471 | ||||||||
\(304\) | −6.79073 | −0.389475 | ||||||||
\(305\) | −0.842631 | −0.0482489 | ||||||||
\(306\) | −0.210980 | −0.0120609 | ||||||||
\(307\) | 12.1646 | 0.694269 | 0.347135 | − | 0.937815i | \(-0.387155\pi\) | ||||
0.347135 | + | 0.937815i | \(0.387155\pi\) | |||||||
\(308\) | −7.13306 | −0.406444 | ||||||||
\(309\) | −10.9494 | −0.622887 | ||||||||
\(310\) | −4.89282 | −0.277894 | ||||||||
\(311\) | −10.4238 | −0.591079 | −0.295539 | − | 0.955331i | \(-0.595499\pi\) | ||||
−0.295539 | + | 0.955331i | \(0.595499\pi\) | |||||||
\(312\) | 12.0515 | 0.682283 | ||||||||
\(313\) | −3.70708 | −0.209536 | −0.104768 | − | 0.994497i | \(-0.533410\pi\) | ||||
−0.104768 | + | 0.994497i | \(0.533410\pi\) | |||||||
\(314\) | −1.91250 | −0.107928 | ||||||||
\(315\) | 3.53237 | 0.199027 | ||||||||
\(316\) | 14.7619 | 0.830422 | ||||||||
\(317\) | −17.7635 | −0.997696 | −0.498848 | − | 0.866690i | \(-0.666243\pi\) | ||||
−0.498848 | + | 0.866690i | \(0.666243\pi\) | |||||||
\(318\) | 0.202132 | 0.0113350 | ||||||||
\(319\) | 10.0563 | 0.563046 | ||||||||
\(320\) | 1.43373 | 0.0801477 | ||||||||
\(321\) | −2.84318 | −0.158691 | ||||||||
\(322\) | −2.23285 | −0.124432 | ||||||||
\(323\) | −1.14104 | −0.0634890 | ||||||||
\(324\) | −1.70156 | −0.0945310 | ||||||||
\(325\) | 25.5671 | 1.41821 | ||||||||
\(326\) | −9.19176 | −0.509084 | ||||||||
\(327\) | −19.4494 | −1.07555 | ||||||||
\(328\) | −2.61499 | −0.144389 | ||||||||
\(329\) | −33.0030 | −1.81952 | ||||||||
\(330\) | 0.460328 | 0.0253402 | ||||||||
\(331\) | 25.2813 | 1.38959 | 0.694794 | − | 0.719209i | \(-0.255496\pi\) | ||||
0.694794 | + | 0.719209i | \(0.255496\pi\) | |||||||
\(332\) | 12.0755 | 0.662729 | ||||||||
\(333\) | −3.16781 | −0.173595 | ||||||||
\(334\) | −9.89273 | −0.541306 | ||||||||
\(335\) | −8.26538 | −0.451586 | ||||||||
\(336\) | 9.63513 | 0.525640 | ||||||||
\(337\) | −15.8267 | −0.862134 | −0.431067 | − | 0.902320i | \(-0.641863\pi\) | ||||
−0.431067 | + | 0.902320i | \(0.641863\pi\) | |||||||
\(338\) | −12.3018 | −0.669130 | ||||||||
\(339\) | −8.08952 | −0.439363 | ||||||||
\(340\) | 0.553727 | 0.0300301 | ||||||||
\(341\) | 10.6290 | 0.575593 | ||||||||
\(342\) | 1.61405 | 0.0872780 | ||||||||
\(343\) | −14.9804 | −0.808863 | ||||||||
\(344\) | −10.1049 | −0.544820 | ||||||||
\(345\) | −0.821558 | −0.0442312 | ||||||||
\(346\) | 5.37953 | 0.289205 | ||||||||
\(347\) | −14.2210 | −0.763424 | −0.381712 | − | 0.924281i | \(-0.624665\pi\) | ||||
−0.381712 | + | 0.924281i | \(0.624665\pi\) | |||||||
\(348\) | −17.1114 | −0.917269 | ||||||||
\(349\) | 20.6858 | 1.10728 | 0.553642 | − | 0.832755i | \(-0.313238\pi\) | ||||
0.553642 | + | 0.832755i | \(0.313238\pi\) | |||||||
\(350\) | −9.82457 | −0.525145 | ||||||||
\(351\) | 5.95974 | 0.318107 | ||||||||
\(352\) | 5.29993 | 0.282487 | ||||||||
\(353\) | −13.3604 | −0.711102 | −0.355551 | − | 0.934657i | \(-0.615707\pi\) | ||||
−0.355551 | + | 0.934657i | \(0.615707\pi\) | |||||||
\(354\) | 7.52376 | 0.399883 | ||||||||
\(355\) | 3.67981 | 0.195304 | ||||||||
\(356\) | 12.6329 | 0.669543 | ||||||||
\(357\) | 1.61898 | 0.0856854 | ||||||||
\(358\) | 5.47990 | 0.289622 | ||||||||
\(359\) | −10.9660 | −0.578761 | −0.289381 | − | 0.957214i | \(-0.593449\pi\) | ||||
−0.289381 | + | 0.957214i | \(0.593449\pi\) | |||||||
\(360\) | −1.70393 | −0.0898050 | ||||||||
\(361\) | −10.2708 | −0.540567 | ||||||||
\(362\) | 7.22741 | 0.379864 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −42.5112 | −2.22819 | ||||||||
\(365\) | 1.74018 | 0.0910854 | ||||||||
\(366\) | 0.546298 | 0.0285555 | ||||||||
\(367\) | −18.2275 | −0.951468 | −0.475734 | − | 0.879589i | \(-0.657818\pi\) | ||||
−0.475734 | + | 0.879589i | \(0.657818\pi\) | |||||||
\(368\) | −2.24094 | −0.116817 | ||||||||
\(369\) | −1.29317 | −0.0673198 | ||||||||
\(370\) | −1.45823 | −0.0758098 | ||||||||
\(371\) | −1.55108 | −0.0805279 | ||||||||
\(372\) | −18.0859 | −0.937708 | ||||||||
\(373\) | −14.3974 | −0.745467 | −0.372733 | − | 0.927938i | \(-0.621579\pi\) | ||||
−0.372733 | + | 0.927938i | \(0.621579\pi\) | |||||||
\(374\) | 0.210980 | 0.0109095 | ||||||||
\(375\) | −7.82802 | −0.404237 | ||||||||
\(376\) | 15.9199 | 0.821005 | ||||||||
\(377\) | 59.9331 | 3.08671 | ||||||||
\(378\) | −2.29012 | −0.117791 | ||||||||
\(379\) | 11.1418 | 0.572316 | 0.286158 | − | 0.958182i | \(-0.407622\pi\) | ||||
0.286158 | + | 0.958182i | \(0.407622\pi\) | |||||||
\(380\) | −4.23616 | −0.217310 | ||||||||
\(381\) | −1.18990 | −0.0609606 | ||||||||
\(382\) | 14.2403 | 0.728599 | ||||||||
\(383\) | −13.6433 | −0.697140 | −0.348570 | − | 0.937283i | \(-0.613333\pi\) | ||||
−0.348570 | + | 0.937283i | \(0.613333\pi\) | |||||||
\(384\) | −11.5294 | −0.588356 | ||||||||
\(385\) | −3.53237 | −0.180026 | ||||||||
\(386\) | 0.901260 | 0.0458729 | ||||||||
\(387\) | −4.99709 | −0.254017 | ||||||||
\(388\) | 10.2253 | 0.519113 | ||||||||
\(389\) | 23.6998 | 1.20163 | 0.600814 | − | 0.799389i | \(-0.294843\pi\) | ||||
0.600814 | + | 0.799389i | \(0.294843\pi\) | |||||||
\(390\) | 2.74343 | 0.138919 | ||||||||
\(391\) | −0.376542 | −0.0190425 | ||||||||
\(392\) | 21.3812 | 1.07992 | ||||||||
\(393\) | 0.232276 | 0.0117168 | ||||||||
\(394\) | 8.19951 | 0.413086 | ||||||||
\(395\) | 7.31026 | 0.367819 | ||||||||
\(396\) | 1.70156 | 0.0855065 | ||||||||
\(397\) | −19.8855 | −0.998023 | −0.499011 | − | 0.866595i | \(-0.666303\pi\) | ||||
−0.499011 | + | 0.866595i | \(0.666303\pi\) | |||||||
\(398\) | −0.236398 | −0.0118496 | ||||||||
\(399\) | −12.3856 | −0.620055 | ||||||||
\(400\) | −9.86014 | −0.493007 | ||||||||
\(401\) | −15.1693 | −0.757517 | −0.378758 | − | 0.925496i | \(-0.623649\pi\) | ||||
−0.378758 | + | 0.925496i | \(0.623649\pi\) | |||||||
\(402\) | 5.35865 | 0.267265 | ||||||||
\(403\) | 63.3461 | 3.15549 | ||||||||
\(404\) | 30.9430 | 1.53947 | ||||||||
\(405\) | −0.842631 | −0.0418707 | ||||||||
\(406\) | −23.0302 | −1.14297 | ||||||||
\(407\) | 3.16781 | 0.157022 | ||||||||
\(408\) | −0.780956 | −0.0386631 | ||||||||
\(409\) | −20.3853 | −1.00799 | −0.503995 | − | 0.863706i | \(-0.668137\pi\) | ||||
−0.503995 | + | 0.863706i | \(0.668137\pi\) | |||||||
\(410\) | −0.595282 | −0.0293989 | ||||||||
\(411\) | 13.7946 | 0.680437 | ||||||||
\(412\) | −18.6310 | −0.917882 | ||||||||
\(413\) | −57.7343 | −2.84092 | ||||||||
\(414\) | 0.532636 | 0.0261777 | ||||||||
\(415\) | 5.97992 | 0.293543 | ||||||||
\(416\) | 31.5862 | 1.54864 | ||||||||
\(417\) | −10.2427 | −0.501588 | ||||||||
\(418\) | −1.61405 | −0.0789459 | ||||||||
\(419\) | 19.1519 | 0.935633 | 0.467817 | − | 0.883826i | \(-0.345041\pi\) | ||||
0.467817 | + | 0.883826i | \(0.345041\pi\) | |||||||
\(420\) | 6.01053 | 0.293284 | ||||||||
\(421\) | −8.29681 | −0.404362 | −0.202181 | − | 0.979348i | \(-0.564803\pi\) | ||||
−0.202181 | + | 0.979348i | \(0.564803\pi\) | |||||||
\(422\) | 3.27482 | 0.159416 | ||||||||
\(423\) | 7.87272 | 0.382785 | ||||||||
\(424\) | 0.748202 | 0.0363359 | ||||||||
\(425\) | −1.65679 | −0.0803660 | ||||||||
\(426\) | −2.38572 | −0.115588 | ||||||||
\(427\) | −4.19208 | −0.202869 | ||||||||
\(428\) | −4.83783 | −0.233845 | ||||||||
\(429\) | −5.95974 | −0.287739 | ||||||||
\(430\) | −2.30030 | −0.110930 | ||||||||
\(431\) | −17.6981 | −0.852485 | −0.426243 | − | 0.904609i | \(-0.640163\pi\) | ||||
−0.426243 | + | 0.904609i | \(0.640163\pi\) | |||||||
\(432\) | −2.29842 | −0.110583 | ||||||||
\(433\) | 5.57917 | 0.268118 | 0.134059 | − | 0.990973i | \(-0.457199\pi\) | ||||
0.134059 | + | 0.990973i | \(0.457199\pi\) | |||||||
\(434\) | −24.3417 | −1.16844 | ||||||||
\(435\) | −8.47377 | −0.406286 | ||||||||
\(436\) | −33.0942 | −1.58493 | ||||||||
\(437\) | 2.88064 | 0.137800 | ||||||||
\(438\) | −1.12820 | −0.0539077 | ||||||||
\(439\) | −6.90623 | −0.329616 | −0.164808 | − | 0.986326i | \(-0.552701\pi\) | ||||
−0.164808 | + | 0.986326i | \(0.552701\pi\) | |||||||
\(440\) | 1.70393 | 0.0812317 | ||||||||
\(441\) | 10.5735 | 0.503500 | ||||||||
\(442\) | 1.25739 | 0.0598078 | ||||||||
\(443\) | 8.54914 | 0.406182 | 0.203091 | − | 0.979160i | \(-0.434901\pi\) | ||||
0.203091 | + | 0.979160i | \(0.434901\pi\) | |||||||
\(444\) | −5.39021 | −0.255808 | ||||||||
\(445\) | 6.25596 | 0.296561 | ||||||||
\(446\) | −0.659621 | −0.0312339 | ||||||||
\(447\) | 2.70615 | 0.127997 | ||||||||
\(448\) | 7.13276 | 0.336991 | ||||||||
\(449\) | −22.1028 | −1.04309 | −0.521547 | − | 0.853223i | \(-0.674645\pi\) | ||||
−0.521547 | + | 0.853223i | \(0.674645\pi\) | |||||||
\(450\) | 2.34361 | 0.110479 | ||||||||
\(451\) | 1.29317 | 0.0608930 | ||||||||
\(452\) | −13.7648 | −0.647441 | ||||||||
\(453\) | 15.6416 | 0.734907 | ||||||||
\(454\) | −1.73358 | −0.0813611 | ||||||||
\(455\) | −21.0520 | −0.986933 | ||||||||
\(456\) | 5.97451 | 0.279782 | ||||||||
\(457\) | −12.2492 | −0.572995 | −0.286497 | − | 0.958081i | \(-0.592491\pi\) | ||||
−0.286497 | + | 0.958081i | \(0.592491\pi\) | |||||||
\(458\) | 14.3034 | 0.668355 | ||||||||
\(459\) | −0.386200 | −0.0180263 | ||||||||
\(460\) | −1.39793 | −0.0651788 | ||||||||
\(461\) | −5.51693 | −0.256949 | −0.128475 | − | 0.991713i | \(-0.541008\pi\) | ||||
−0.128475 | + | 0.991713i | \(0.541008\pi\) | |||||||
\(462\) | 2.29012 | 0.106546 | ||||||||
\(463\) | −39.0620 | −1.81536 | −0.907682 | − | 0.419659i | \(-0.862150\pi\) | ||||
−0.907682 | + | 0.419659i | \(0.862150\pi\) | |||||||
\(464\) | −23.1136 | −1.07302 | ||||||||
\(465\) | −8.95632 | −0.415339 | ||||||||
\(466\) | −8.39037 | −0.388676 | ||||||||
\(467\) | −15.4534 | −0.715099 | −0.357550 | − | 0.933894i | \(-0.616388\pi\) | ||||
−0.357550 | + | 0.933894i | \(0.616388\pi\) | |||||||
\(468\) | 10.1408 | 0.468761 | ||||||||
\(469\) | −41.1201 | −1.89875 | ||||||||
\(470\) | 3.62403 | 0.167164 | ||||||||
\(471\) | −3.50083 | −0.161310 | ||||||||
\(472\) | 27.8496 | 1.28188 | ||||||||
\(473\) | 4.99709 | 0.229767 | ||||||||
\(474\) | −4.73942 | −0.217689 | ||||||||
\(475\) | 12.6748 | 0.581561 | ||||||||
\(476\) | 2.75479 | 0.126265 | ||||||||
\(477\) | 0.370002 | 0.0169412 | ||||||||
\(478\) | 3.54175 | 0.161996 | ||||||||
\(479\) | 19.2183 | 0.878106 | 0.439053 | − | 0.898461i | \(-0.355314\pi\) | ||||
0.439053 | + | 0.898461i | \(0.355314\pi\) | |||||||
\(480\) | −4.46589 | −0.203839 | ||||||||
\(481\) | 18.8793 | 0.860823 | ||||||||
\(482\) | 1.12000 | 0.0510148 | ||||||||
\(483\) | −4.08724 | −0.185976 | ||||||||
\(484\) | −1.70156 | −0.0773435 | ||||||||
\(485\) | 5.06370 | 0.229931 | ||||||||
\(486\) | 0.546298 | 0.0247806 | ||||||||
\(487\) | −5.36667 | −0.243187 | −0.121594 | − | 0.992580i | \(-0.538800\pi\) | ||||
−0.121594 | + | 0.992580i | \(0.538800\pi\) | |||||||
\(488\) | 2.02216 | 0.0915387 | ||||||||
\(489\) | −16.8255 | −0.760876 | ||||||||
\(490\) | 4.86727 | 0.219881 | ||||||||
\(491\) | −30.3986 | −1.37187 | −0.685936 | − | 0.727662i | \(-0.740607\pi\) | ||||
−0.685936 | + | 0.727662i | \(0.740607\pi\) | |||||||
\(492\) | −2.20040 | −0.0992019 | ||||||||
\(493\) | −3.88375 | −0.174915 | ||||||||
\(494\) | −9.61933 | −0.432794 | ||||||||
\(495\) | 0.842631 | 0.0378734 | ||||||||
\(496\) | −24.4299 | −1.09693 | ||||||||
\(497\) | 18.3070 | 0.821182 | ||||||||
\(498\) | −3.87693 | −0.173729 | ||||||||
\(499\) | −17.0924 | −0.765160 | −0.382580 | − | 0.923922i | \(-0.624964\pi\) | ||||
−0.382580 | + | 0.923922i | \(0.624964\pi\) | |||||||
\(500\) | −13.3198 | −0.595681 | ||||||||
\(501\) | −18.1086 | −0.809035 | ||||||||
\(502\) | −0.220521 | −0.00984231 | ||||||||
\(503\) | 32.1659 | 1.43421 | 0.717103 | − | 0.696967i | \(-0.245468\pi\) | ||||
0.717103 | + | 0.696967i | \(0.245468\pi\) | |||||||
\(504\) | −8.47703 | −0.377597 | ||||||||
\(505\) | 15.3233 | 0.681878 | ||||||||
\(506\) | −0.532636 | −0.0236786 | ||||||||
\(507\) | −22.5185 | −1.00008 | ||||||||
\(508\) | −2.02469 | −0.0898310 | ||||||||
\(509\) | 20.2801 | 0.898900 | 0.449450 | − | 0.893306i | \(-0.351620\pi\) | ||||
0.449450 | + | 0.893306i | \(0.351620\pi\) | |||||||
\(510\) | −0.177778 | −0.00787216 | ||||||||
\(511\) | 8.65739 | 0.382980 | ||||||||
\(512\) | −21.4770 | −0.949156 | ||||||||
\(513\) | 2.95453 | 0.130446 | ||||||||
\(514\) | 1.92352 | 0.0848428 | ||||||||
\(515\) | −9.22627 | −0.406558 | ||||||||
\(516\) | −8.50285 | −0.374317 | ||||||||
\(517\) | −7.87272 | −0.346242 | ||||||||
\(518\) | −7.25467 | −0.318752 | ||||||||
\(519\) | 9.84724 | 0.432246 | ||||||||
\(520\) | 10.1550 | 0.445325 | ||||||||
\(521\) | 27.3063 | 1.19631 | 0.598156 | − | 0.801380i | \(-0.295900\pi\) | ||||
0.598156 | + | 0.801380i | \(0.295900\pi\) | |||||||
\(522\) | 5.49376 | 0.240455 | ||||||||
\(523\) | −23.5138 | −1.02819 | −0.514093 | − | 0.857734i | \(-0.671871\pi\) | ||||
−0.514093 | + | 0.857734i | \(0.671871\pi\) | |||||||
\(524\) | 0.395230 | 0.0172657 | ||||||||
\(525\) | −17.9839 | −0.784881 | ||||||||
\(526\) | −13.8280 | −0.602929 | ||||||||
\(527\) | −4.10492 | −0.178813 | ||||||||
\(528\) | 2.29842 | 0.100026 | ||||||||
\(529\) | −22.0494 | −0.958669 | ||||||||
\(530\) | 0.170322 | 0.00739833 | ||||||||
\(531\) | 13.7723 | 0.597665 | ||||||||
\(532\) | −21.0748 | −0.913709 | ||||||||
\(533\) | 7.70696 | 0.333825 | ||||||||
\(534\) | −4.05589 | −0.175516 | ||||||||
\(535\) | −2.39575 | −0.103577 | ||||||||
\(536\) | 19.8353 | 0.856757 | ||||||||
\(537\) | 10.0310 | 0.432868 | ||||||||
\(538\) | −14.6603 | −0.632050 | ||||||||
\(539\) | −10.5735 | −0.455433 | ||||||||
\(540\) | −1.43379 | −0.0617003 | ||||||||
\(541\) | 21.3883 | 0.919556 | 0.459778 | − | 0.888034i | \(-0.347929\pi\) | ||||
0.459778 | + | 0.888034i | \(0.347929\pi\) | |||||||
\(542\) | 4.81226 | 0.206704 | ||||||||
\(543\) | 13.2298 | 0.567744 | ||||||||
\(544\) | −2.04683 | −0.0877572 | ||||||||
\(545\) | −16.3886 | −0.702012 | ||||||||
\(546\) | 13.6485 | 0.584104 | ||||||||
\(547\) | −18.4841 | −0.790322 | −0.395161 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395161 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(548\) | 23.4723 | 1.00269 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.34361 | −0.0999317 | ||||||||
\(551\) | 29.7117 | 1.26576 | ||||||||
\(552\) | 1.97158 | 0.0839162 | ||||||||
\(553\) | 36.3684 | 1.54654 | ||||||||
\(554\) | −11.6679 | −0.495721 | ||||||||
\(555\) | −2.66929 | −0.113305 | ||||||||
\(556\) | −17.4286 | −0.739137 | ||||||||
\(557\) | −24.4886 | −1.03762 | −0.518808 | − | 0.854891i | \(-0.673624\pi\) | ||||
−0.518808 | + | 0.854891i | \(0.673624\pi\) | |||||||
\(558\) | 5.80661 | 0.245813 | ||||||||
\(559\) | 29.7814 | 1.25962 | ||||||||
\(560\) | 8.11886 | 0.343084 | ||||||||
\(561\) | 0.386200 | 0.0163054 | ||||||||
\(562\) | 16.3820 | 0.691032 | ||||||||
\(563\) | −20.3211 | −0.856433 | −0.428216 | − | 0.903676i | \(-0.640858\pi\) | ||||
−0.428216 | + | 0.903676i | \(0.640858\pi\) | |||||||
\(564\) | 13.3959 | 0.564069 | ||||||||
\(565\) | −6.81648 | −0.286771 | ||||||||
\(566\) | −5.51283 | −0.231721 | ||||||||
\(567\) | −4.19208 | −0.176051 | ||||||||
\(568\) | −8.83086 | −0.370535 | ||||||||
\(569\) | −24.7529 | −1.03769 | −0.518847 | − | 0.854867i | \(-0.673639\pi\) | ||||
−0.518847 | + | 0.854867i | \(0.673639\pi\) | |||||||
\(570\) | 1.36005 | 0.0569663 | ||||||||
\(571\) | 10.7099 | 0.448195 | 0.224098 | − | 0.974567i | \(-0.428057\pi\) | ||||
0.224098 | + | 0.974567i | \(0.428057\pi\) | |||||||
\(572\) | −10.1408 | −0.424010 | ||||||||
\(573\) | 26.0670 | 1.08896 | ||||||||
\(574\) | −2.96152 | −0.123612 | ||||||||
\(575\) | 4.18269 | 0.174430 | ||||||||
\(576\) | −1.70149 | −0.0708953 | ||||||||
\(577\) | −4.97286 | −0.207023 | −0.103512 | − | 0.994628i | \(-0.533008\pi\) | ||||
−0.103512 | + | 0.994628i | \(0.533008\pi\) | |||||||
\(578\) | 9.20559 | 0.382902 | ||||||||
\(579\) | 1.64976 | 0.0685616 | ||||||||
\(580\) | −14.4186 | −0.598701 | ||||||||
\(581\) | 29.7500 | 1.23424 | ||||||||
\(582\) | −3.28292 | −0.136082 | ||||||||
\(583\) | −0.370002 | −0.0153239 | ||||||||
\(584\) | −4.17611 | −0.172809 | ||||||||
\(585\) | 5.02186 | 0.207628 | ||||||||
\(586\) | 6.41284 | 0.264912 | ||||||||
\(587\) | 2.13571 | 0.0881502 | 0.0440751 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440751 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(588\) | 17.9914 | 0.741953 | ||||||||
\(589\) | 31.4037 | 1.29397 | ||||||||
\(590\) | 6.33975 | 0.261003 | ||||||||
\(591\) | 15.0092 | 0.617397 | ||||||||
\(592\) | −7.28094 | −0.299245 | ||||||||
\(593\) | 13.9935 | 0.574646 | 0.287323 | − | 0.957834i | \(-0.407235\pi\) | ||||
0.287323 | + | 0.957834i | \(0.407235\pi\) | |||||||
\(594\) | −0.546298 | −0.0224149 | ||||||||
\(595\) | 1.36420 | 0.0559268 | ||||||||
\(596\) | 4.60468 | 0.188615 | ||||||||
\(597\) | −0.432727 | −0.0177103 | ||||||||
\(598\) | −3.17437 | −0.129810 | ||||||||
\(599\) | −27.2804 | −1.11465 | −0.557324 | − | 0.830295i | \(-0.688172\pi\) | ||||
−0.557324 | + | 0.830295i | \(0.688172\pi\) | |||||||
\(600\) | 8.67499 | 0.354155 | ||||||||
\(601\) | 38.7081 | 1.57894 | 0.789468 | − | 0.613791i | \(-0.210356\pi\) | ||||
0.789468 | + | 0.613791i | \(0.210356\pi\) | |||||||
\(602\) | −11.4440 | −0.466421 | ||||||||
\(603\) | 9.80901 | 0.399454 | ||||||||
\(604\) | 26.6151 | 1.08295 | ||||||||
\(605\) | −0.842631 | −0.0342578 | ||||||||
\(606\) | −9.93448 | −0.403561 | ||||||||
\(607\) | 27.3959 | 1.11197 | 0.555983 | − | 0.831194i | \(-0.312342\pi\) | ||||
0.555983 | + | 0.831194i | \(0.312342\pi\) | |||||||
\(608\) | 15.6588 | 0.635048 | ||||||||
\(609\) | −42.1569 | −1.70828 | ||||||||
\(610\) | 0.460328 | 0.0186381 | ||||||||
\(611\) | −46.9194 | −1.89815 | ||||||||
\(612\) | −0.657141 | −0.0265634 | ||||||||
\(613\) | 8.56875 | 0.346088 | 0.173044 | − | 0.984914i | \(-0.444640\pi\) | ||||
0.173044 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(614\) | −6.64549 | −0.268190 | ||||||||
\(615\) | −1.08967 | −0.0439395 | ||||||||
\(616\) | 8.47703 | 0.341549 | ||||||||
\(617\) | 45.6108 | 1.83622 | 0.918112 | − | 0.396322i | \(-0.129713\pi\) | ||||
0.918112 | + | 0.396322i | \(0.129713\pi\) | |||||||
\(618\) | 5.98162 | 0.240616 | ||||||||
\(619\) | 36.2410 | 1.45665 | 0.728325 | − | 0.685232i | \(-0.240299\pi\) | ||||
0.728325 | + | 0.685232i | \(0.240299\pi\) | |||||||
\(620\) | −15.2397 | −0.612041 | ||||||||
\(621\) | 0.974992 | 0.0391251 | ||||||||
\(622\) | 5.69450 | 0.228329 | ||||||||
\(623\) | 31.1233 | 1.24693 | ||||||||
\(624\) | 13.6980 | 0.548357 | ||||||||
\(625\) | 14.8537 | 0.594150 | ||||||||
\(626\) | 2.02517 | 0.0809421 | ||||||||
\(627\) | −2.95453 | −0.117992 | ||||||||
\(628\) | −5.95686 | −0.237705 | ||||||||
\(629\) | −1.22341 | −0.0487804 | ||||||||
\(630\) | −1.92973 | −0.0768822 | ||||||||
\(631\) | −5.90488 | −0.235070 | −0.117535 | − | 0.993069i | \(-0.537499\pi\) | ||||
−0.117535 | + | 0.993069i | \(0.537499\pi\) | |||||||
\(632\) | −17.5432 | −0.697833 | ||||||||
\(633\) | 5.99457 | 0.238263 | ||||||||
\(634\) | 9.70415 | 0.385401 | ||||||||
\(635\) | −1.00265 | −0.0397889 | ||||||||
\(636\) | 0.629580 | 0.0249645 | ||||||||
\(637\) | −63.0153 | −2.49676 | ||||||||
\(638\) | −5.49376 | −0.217500 | ||||||||
\(639\) | −4.36706 | −0.172758 | ||||||||
\(640\) | −9.71501 | −0.384020 | ||||||||
\(641\) | −27.6940 | −1.09385 | −0.546923 | − | 0.837183i | \(-0.684201\pi\) | ||||
−0.546923 | + | 0.837183i | \(0.684201\pi\) | |||||||
\(642\) | 1.55322 | 0.0613008 | ||||||||
\(643\) | 39.7962 | 1.56941 | 0.784704 | − | 0.619871i | \(-0.212815\pi\) | ||||
0.784704 | + | 0.619871i | \(0.212815\pi\) | |||||||
\(644\) | −6.95467 | −0.274053 | ||||||||
\(645\) | −4.21070 | −0.165796 | ||||||||
\(646\) | 0.623347 | 0.0245253 | ||||||||
\(647\) | 35.8326 | 1.40872 | 0.704362 | − | 0.709841i | \(-0.251233\pi\) | ||||
0.704362 | + | 0.709841i | \(0.251233\pi\) | |||||||
\(648\) | 2.02216 | 0.0794378 | ||||||||
\(649\) | −13.7723 | −0.540608 | ||||||||
\(650\) | −13.9673 | −0.547842 | ||||||||
\(651\) | −44.5576 | −1.74635 | ||||||||
\(652\) | −28.6296 | −1.12122 | ||||||||
\(653\) | 3.93565 | 0.154014 | 0.0770070 | − | 0.997031i | \(-0.475464\pi\) | ||||
0.0770070 | + | 0.997031i | \(0.475464\pi\) | |||||||
\(654\) | 10.6252 | 0.415477 | ||||||||
\(655\) | 0.195723 | 0.00764751 | ||||||||
\(656\) | −2.97224 | −0.116047 | ||||||||
\(657\) | −2.06518 | −0.0805703 | ||||||||
\(658\) | 18.0295 | 0.702864 | ||||||||
\(659\) | −1.14603 | −0.0446429 | −0.0223215 | − | 0.999751i | \(-0.507106\pi\) | ||||
−0.0223215 | + | 0.999751i | \(0.507106\pi\) | |||||||
\(660\) | 1.43379 | 0.0558100 | ||||||||
\(661\) | −21.1185 | −0.821414 | −0.410707 | − | 0.911767i | \(-0.634718\pi\) | ||||
−0.410707 | + | 0.911767i | \(0.634718\pi\) | |||||||
\(662\) | −13.8112 | −0.536786 | ||||||||
\(663\) | 2.30165 | 0.0893887 | ||||||||
\(664\) | −14.3507 | −0.556915 | ||||||||
\(665\) | −10.4365 | −0.404709 | ||||||||
\(666\) | 1.73057 | 0.0670582 | ||||||||
\(667\) | 9.80484 | 0.379645 | ||||||||
\(668\) | −30.8129 | −1.19219 | ||||||||
\(669\) | −1.20744 | −0.0466822 | ||||||||
\(670\) | 4.51536 | 0.174444 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −22.2177 | −0.857067 | ||||||||
\(673\) | −50.2053 | −1.93527 | −0.967636 | − | 0.252349i | \(-0.918797\pi\) | ||||
−0.967636 | + | 0.252349i | \(0.918797\pi\) | |||||||
\(674\) | 8.64609 | 0.333035 | ||||||||
\(675\) | 4.28997 | 0.165121 | ||||||||
\(676\) | −38.3165 | −1.47371 | ||||||||
\(677\) | −15.0864 | −0.579819 | −0.289910 | − | 0.957054i | \(-0.593625\pi\) | ||||
−0.289910 | + | 0.957054i | \(0.593625\pi\) | |||||||
\(678\) | 4.41929 | 0.169722 | ||||||||
\(679\) | 25.1918 | 0.966774 | ||||||||
\(680\) | −0.658057 | −0.0252353 | ||||||||
\(681\) | −3.17333 | −0.121602 | ||||||||
\(682\) | −5.80661 | −0.222346 | ||||||||
\(683\) | 48.5108 | 1.85621 | 0.928107 | − | 0.372314i | \(-0.121436\pi\) | ||||
0.928107 | + | 0.372314i | \(0.121436\pi\) | |||||||
\(684\) | 5.02730 | 0.192224 | ||||||||
\(685\) | 11.6238 | 0.444121 | ||||||||
\(686\) | 8.18375 | 0.312457 | ||||||||
\(687\) | 26.1824 | 0.998922 | ||||||||
\(688\) | −11.4854 | −0.437877 | ||||||||
\(689\) | −2.20512 | −0.0840083 | ||||||||
\(690\) | 0.448816 | 0.0170861 | ||||||||
\(691\) | −28.3558 | −1.07871 | −0.539353 | − | 0.842080i | \(-0.681331\pi\) | ||||
−0.539353 | + | 0.842080i | \(0.681331\pi\) | |||||||
\(692\) | 16.7557 | 0.636954 | ||||||||
\(693\) | 4.19208 | 0.159244 | ||||||||
\(694\) | 7.76891 | 0.294904 | ||||||||
\(695\) | −8.63084 | −0.327386 | ||||||||
\(696\) | 20.3355 | 0.770814 | ||||||||
\(697\) | −0.499422 | −0.0189170 | ||||||||
\(698\) | −11.3006 | −0.427734 | ||||||||
\(699\) | −15.3586 | −0.580915 | ||||||||
\(700\) | −30.6006 | −1.15660 | ||||||||
\(701\) | −4.65092 | −0.175663 | −0.0878313 | − | 0.996135i | \(-0.527994\pi\) | ||||
−0.0878313 | + | 0.996135i | \(0.527994\pi\) | |||||||
\(702\) | −3.25580 | −0.122882 | ||||||||
\(703\) | 9.35937 | 0.352995 | ||||||||
\(704\) | 1.70149 | 0.0641272 | ||||||||
\(705\) | 6.63380 | 0.249843 | ||||||||
\(706\) | 7.29876 | 0.274692 | ||||||||
\(707\) | 76.2332 | 2.86705 | ||||||||
\(708\) | 23.4343 | 0.880715 | ||||||||
\(709\) | 47.0222 | 1.76595 | 0.882977 | − | 0.469416i | \(-0.155536\pi\) | ||||
0.882977 | + | 0.469416i | \(0.155536\pi\) | |||||||
\(710\) | −2.01028 | −0.0754443 | ||||||||
\(711\) | −8.67552 | −0.325357 | ||||||||
\(712\) | −15.0131 | −0.562641 | ||||||||
\(713\) | 10.3632 | 0.388104 | ||||||||
\(714\) | −0.884445 | −0.0330995 | ||||||||
\(715\) | −5.02186 | −0.187807 | ||||||||
\(716\) | 17.0683 | 0.637871 | ||||||||
\(717\) | 6.48318 | 0.242119 | ||||||||
\(718\) | 5.99069 | 0.223570 | ||||||||
\(719\) | 8.60663 | 0.320973 | 0.160487 | − | 0.987038i | \(-0.448694\pi\) | ||||
0.160487 | + | 0.987038i | \(0.448694\pi\) | |||||||
\(720\) | −1.93672 | −0.0721771 | ||||||||
\(721\) | −45.9005 | −1.70943 | ||||||||
\(722\) | 5.61091 | 0.208816 | ||||||||
\(723\) | 2.05017 | 0.0762466 | ||||||||
\(724\) | 22.5112 | 0.836624 | ||||||||
\(725\) | 43.1414 | 1.60223 | ||||||||
\(726\) | 0.546298 | 0.0202750 | ||||||||
\(727\) | 29.4993 | 1.09407 | 0.547034 | − | 0.837110i | \(-0.315757\pi\) | ||||
0.547034 | + | 0.837110i | \(0.315757\pi\) | |||||||
\(728\) | 50.5209 | 1.87243 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.950659 | −0.0351855 | ||||||||
\(731\) | −1.92988 | −0.0713791 | ||||||||
\(732\) | 1.70156 | 0.0628914 | ||||||||
\(733\) | −42.0201 | −1.55205 | −0.776025 | − | 0.630702i | \(-0.782767\pi\) | ||||
−0.776025 | + | 0.630702i | \(0.782767\pi\) | |||||||
\(734\) | 9.95766 | 0.367544 | ||||||||
\(735\) | 8.90955 | 0.328634 | ||||||||
\(736\) | 5.16739 | 0.190473 | ||||||||
\(737\) | −9.80901 | −0.361320 | ||||||||
\(738\) | 0.706457 | 0.0260050 | ||||||||
\(739\) | 50.8992 | 1.87236 | 0.936179 | − | 0.351523i | \(-0.114336\pi\) | ||||
0.936179 | + | 0.351523i | \(0.114336\pi\) | |||||||
\(740\) | −4.54196 | −0.166966 | ||||||||
\(741\) | −17.6082 | −0.646854 | ||||||||
\(742\) | 0.847351 | 0.0311072 | ||||||||
\(743\) | −4.44260 | −0.162983 | −0.0814916 | − | 0.996674i | \(-0.525968\pi\) | ||||
−0.0814916 | + | 0.996674i | \(0.525968\pi\) | |||||||
\(744\) | 21.4935 | 0.787989 | ||||||||
\(745\) | 2.28029 | 0.0835433 | ||||||||
\(746\) | 7.86525 | 0.287967 | ||||||||
\(747\) | −7.09673 | −0.259656 | ||||||||
\(748\) | 0.657141 | 0.0240275 | ||||||||
\(749\) | −11.9188 | −0.435504 | ||||||||
\(750\) | 4.27643 | 0.156153 | ||||||||
\(751\) | 3.39662 | 0.123944 | 0.0619722 | − | 0.998078i | \(-0.480261\pi\) | ||||
0.0619722 | + | 0.998078i | \(0.480261\pi\) | |||||||
\(752\) | 18.0948 | 0.659849 | ||||||||
\(753\) | −0.403663 | −0.0147103 | ||||||||
\(754\) | −32.7414 | −1.19237 | ||||||||
\(755\) | 13.1801 | 0.479673 | ||||||||
\(756\) | −7.13306 | −0.259427 | ||||||||
\(757\) | 13.8258 | 0.502508 | 0.251254 | − | 0.967921i | \(-0.419157\pi\) | ||||
0.251254 | + | 0.967921i | \(0.419157\pi\) | |||||||
\(758\) | −6.08675 | −0.221081 | ||||||||
\(759\) | −0.974992 | −0.0353900 | ||||||||
\(760\) | 5.03431 | 0.182613 | ||||||||
\(761\) | −34.7597 | −1.26004 | −0.630018 | − | 0.776580i | \(-0.716953\pi\) | ||||
−0.630018 | + | 0.776580i | \(0.716953\pi\) | |||||||
\(762\) | 0.650042 | 0.0235485 | ||||||||
\(763\) | −81.5332 | −2.95170 | ||||||||
\(764\) | 44.3544 | 1.60469 | ||||||||
\(765\) | −0.325424 | −0.0117657 | ||||||||
\(766\) | 7.45331 | 0.269299 | ||||||||
\(767\) | −82.0790 | −2.96370 | ||||||||
\(768\) | 2.89551 | 0.104483 | ||||||||
\(769\) | −1.09955 | −0.0396507 | −0.0198254 | − | 0.999803i | \(-0.506311\pi\) | ||||
−0.0198254 | + | 0.999803i | \(0.506311\pi\) | |||||||
\(770\) | 1.92973 | 0.0695426 | ||||||||
\(771\) | 3.52100 | 0.126806 | ||||||||
\(772\) | 2.80716 | 0.101032 | ||||||||
\(773\) | −13.8425 | −0.497879 | −0.248939 | − | 0.968519i | \(-0.580082\pi\) | ||||
−0.248939 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(774\) | 2.72990 | 0.0981244 | ||||||||
\(775\) | 45.5981 | 1.63793 | ||||||||
\(776\) | −12.1519 | −0.436229 | ||||||||
\(777\) | −13.2797 | −0.476406 | ||||||||
\(778\) | −12.9472 | −0.464178 | ||||||||
\(779\) | 3.82071 | 0.136891 | ||||||||
\(780\) | 8.54498 | 0.305960 | ||||||||
\(781\) | 4.36706 | 0.156266 | ||||||||
\(782\) | 0.205704 | 0.00735596 | ||||||||
\(783\) | 10.0563 | 0.359384 | ||||||||
\(784\) | 24.3023 | 0.867939 | ||||||||
\(785\) | −2.94991 | −0.105287 | ||||||||
\(786\) | −0.126892 | −0.00452608 | ||||||||
\(787\) | −33.6766 | −1.20044 | −0.600220 | − | 0.799835i | \(-0.704920\pi\) | ||||
−0.600220 | + | 0.799835i | \(0.704920\pi\) | |||||||
\(788\) | 25.5391 | 0.909792 | ||||||||
\(789\) | −25.3122 | −0.901137 | ||||||||
\(790\) | −3.99358 | −0.142085 | ||||||||
\(791\) | −33.9119 | −1.20577 | ||||||||
\(792\) | −2.02216 | −0.0718542 | ||||||||
\(793\) | −5.95974 | −0.211637 | ||||||||
\(794\) | 10.8634 | 0.385528 | ||||||||
\(795\) | 0.311775 | 0.0110575 | ||||||||
\(796\) | −0.736310 | −0.0260978 | ||||||||
\(797\) | −1.47756 | −0.0523377 | −0.0261689 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261689 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(798\) | 6.76623 | 0.239522 | ||||||||
\(799\) | 3.04044 | 0.107563 | ||||||||
\(800\) | 22.7366 | 0.803859 | ||||||||
\(801\) | −7.42432 | −0.262325 | ||||||||
\(802\) | 8.28694 | 0.292622 | ||||||||
\(803\) | 2.06518 | 0.0728786 | ||||||||
\(804\) | 16.6906 | 0.588632 | ||||||||
\(805\) | −3.44403 | −0.121386 | ||||||||
\(806\) | −34.6059 | −1.21894 | ||||||||
\(807\) | −26.8357 | −0.944660 | ||||||||
\(808\) | −36.7731 | −1.29367 | ||||||||
\(809\) | 26.0611 | 0.916260 | 0.458130 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458130 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(810\) | 0.460328 | 0.0161743 | ||||||||
\(811\) | 21.1286 | 0.741925 | 0.370962 | − | 0.928648i | \(-0.379028\pi\) | ||||
0.370962 | + | 0.928648i | \(0.379028\pi\) | |||||||
\(812\) | −71.7324 | −2.51731 | ||||||||
\(813\) | 8.80885 | 0.308940 | ||||||||
\(814\) | −1.73057 | −0.0606564 | ||||||||
\(815\) | −14.1777 | −0.496623 | ||||||||
\(816\) | −0.887648 | −0.0310739 | ||||||||
\(817\) | 14.7640 | 0.516529 | ||||||||
\(818\) | 11.1365 | 0.389378 | ||||||||
\(819\) | 24.9837 | 0.873000 | ||||||||
\(820\) | −1.85413 | −0.0647490 | ||||||||
\(821\) | −46.0338 | −1.60659 | −0.803295 | − | 0.595582i | \(-0.796922\pi\) | ||||
−0.803295 | + | 0.595582i | \(0.796922\pi\) | |||||||
\(822\) | −7.53597 | −0.262847 | ||||||||
\(823\) | −23.0217 | −0.802488 | −0.401244 | − | 0.915971i | \(-0.631422\pi\) | ||||
−0.401244 | + | 0.915971i | \(0.631422\pi\) | |||||||
\(824\) | 22.1413 | 0.771329 | ||||||||
\(825\) | −4.28997 | −0.149358 | ||||||||
\(826\) | 31.5402 | 1.09742 | ||||||||
\(827\) | −15.9583 | −0.554923 | −0.277461 | − | 0.960737i | \(-0.589493\pi\) | ||||
−0.277461 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(828\) | 1.65901 | 0.0576544 | ||||||||
\(829\) | −36.0118 | −1.25074 | −0.625370 | − | 0.780328i | \(-0.715052\pi\) | ||||
−0.625370 | + | 0.780328i | \(0.715052\pi\) | |||||||
\(830\) | −3.26682 | −0.113393 | ||||||||
\(831\) | −21.3581 | −0.740904 | ||||||||
\(832\) | 10.1404 | 0.351556 | ||||||||
\(833\) | 4.08348 | 0.141484 | ||||||||
\(834\) | 5.59559 | 0.193759 | ||||||||
\(835\) | −15.2589 | −0.528056 | ||||||||
\(836\) | −5.02730 | −0.173873 | ||||||||
\(837\) | 10.6290 | 0.367392 | ||||||||
\(838\) | −10.4627 | −0.361427 | ||||||||
\(839\) | 34.2082 | 1.18100 | 0.590499 | − | 0.807038i | \(-0.298931\pi\) | ||||
0.590499 | + | 0.807038i | \(0.298931\pi\) | |||||||
\(840\) | −7.14300 | −0.246457 | ||||||||
\(841\) | 72.1298 | 2.48723 | ||||||||
\(842\) | 4.53253 | 0.156201 | ||||||||
\(843\) | 29.9872 | 1.03281 | ||||||||
\(844\) | 10.2001 | 0.351102 | ||||||||
\(845\) | −18.9748 | −0.652752 | ||||||||
\(846\) | −4.30086 | −0.147866 | ||||||||
\(847\) | −4.19208 | −0.144041 | ||||||||
\(848\) | 0.850419 | 0.0292035 | ||||||||
\(849\) | −10.0912 | −0.346330 | ||||||||
\(850\) | 0.905100 | 0.0310447 | ||||||||
\(851\) | 3.08859 | 0.105875 | ||||||||
\(852\) | −7.43080 | −0.254575 | ||||||||
\(853\) | 11.3190 | 0.387554 | 0.193777 | − | 0.981046i | \(-0.437926\pi\) | ||||
0.193777 | + | 0.981046i | \(0.437926\pi\) | |||||||
\(854\) | 2.29012 | 0.0783664 | ||||||||
\(855\) | 2.48957 | 0.0851417 | ||||||||
\(856\) | 5.74935 | 0.196509 | ||||||||
\(857\) | 43.3860 | 1.48204 | 0.741019 | − | 0.671485i | \(-0.234343\pi\) | ||||
0.741019 | + | 0.671485i | \(0.234343\pi\) | |||||||
\(858\) | 3.25580 | 0.111151 | ||||||||
\(859\) | −25.6339 | −0.874617 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(860\) | −7.16476 | −0.244316 | ||||||||
\(861\) | −5.42107 | −0.184750 | ||||||||
\(862\) | 9.66842 | 0.329308 | ||||||||
\(863\) | 16.0782 | 0.547309 | 0.273654 | − | 0.961828i | \(-0.411768\pi\) | ||||
0.273654 | + | 0.961828i | \(0.411768\pi\) | |||||||
\(864\) | 5.29993 | 0.180307 | ||||||||
\(865\) | 8.29759 | 0.282126 | ||||||||
\(866\) | −3.04789 | −0.103572 | ||||||||
\(867\) | 16.8508 | 0.572285 | ||||||||
\(868\) | −75.8173 | −2.57341 | ||||||||
\(869\) | 8.67552 | 0.294297 | ||||||||
\(870\) | 4.62921 | 0.156945 | ||||||||
\(871\) | −58.4592 | −1.98081 | ||||||||
\(872\) | 39.3296 | 1.33187 | ||||||||
\(873\) | −6.00940 | −0.203387 | ||||||||
\(874\) | −1.57369 | −0.0532308 | ||||||||
\(875\) | −32.8156 | −1.10937 | ||||||||
\(876\) | −3.51402 | −0.118728 | ||||||||
\(877\) | −17.4124 | −0.587974 | −0.293987 | − | 0.955809i | \(-0.594982\pi\) | ||||
−0.293987 | + | 0.955809i | \(0.594982\pi\) | |||||||
\(878\) | 3.77286 | 0.127328 | ||||||||
\(879\) | 11.7387 | 0.395937 | ||||||||
\(880\) | 1.93672 | 0.0652867 | ||||||||
\(881\) | −41.4135 | −1.39526 | −0.697628 | − | 0.716460i | \(-0.745761\pi\) | ||||
−0.697628 | + | 0.716460i | \(0.745761\pi\) | |||||||
\(882\) | −5.77628 | −0.194498 | ||||||||
\(883\) | −49.5096 | −1.66613 | −0.833066 | − | 0.553174i | \(-0.813416\pi\) | ||||
−0.833066 | + | 0.553174i | \(0.813416\pi\) | |||||||
\(884\) | 3.91639 | 0.131722 | ||||||||
\(885\) | 11.6049 | 0.390095 | ||||||||
\(886\) | −4.67038 | −0.156905 | ||||||||
\(887\) | −48.4377 | −1.62638 | −0.813190 | − | 0.581999i | \(-0.802271\pi\) | ||||
−0.813190 | + | 0.581999i | \(0.802271\pi\) | |||||||
\(888\) | 6.40580 | 0.214965 | ||||||||
\(889\) | −4.98816 | −0.167298 | ||||||||
\(890\) | −3.41762 | −0.114559 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −2.05452 | −0.0687905 | ||||||||
\(893\) | −23.2602 | −0.778372 | ||||||||
\(894\) | −1.47837 | −0.0494440 | ||||||||
\(895\) | 8.45240 | 0.282533 | ||||||||
\(896\) | −48.3320 | −1.61466 | ||||||||
\(897\) | −5.81070 | −0.194014 | ||||||||
\(898\) | 12.0747 | 0.402938 | ||||||||
\(899\) | 106.889 | 3.56494 | ||||||||
\(900\) | 7.29964 | 0.243321 | ||||||||
\(901\) | 0.142895 | 0.00476052 | ||||||||
\(902\) | −0.706457 | −0.0235224 | ||||||||
\(903\) | −20.9482 | −0.697112 | ||||||||
\(904\) | 16.3583 | 0.544068 | ||||||||
\(905\) | 11.1478 | 0.370566 | ||||||||
\(906\) | −8.54499 | −0.283888 | ||||||||
\(907\) | 50.1623 | 1.66561 | 0.832807 | − | 0.553564i | \(-0.186733\pi\) | ||||
0.832807 | + | 0.553564i | \(0.186733\pi\) | |||||||
\(908\) | −5.39960 | −0.179192 | ||||||||
\(909\) | −18.1851 | −0.603161 | ||||||||
\(910\) | 11.5007 | 0.381244 | ||||||||
\(911\) | −19.2889 | −0.639071 | −0.319536 | − | 0.947574i | \(-0.603527\pi\) | ||||
−0.319536 | + | 0.947574i | \(0.603527\pi\) | |||||||
\(912\) | 6.79073 | 0.224864 | ||||||||
\(913\) | 7.09673 | 0.234867 | ||||||||
\(914\) | 6.69173 | 0.221343 | ||||||||
\(915\) | 0.842631 | 0.0278565 | ||||||||
\(916\) | 44.5509 | 1.47200 | ||||||||
\(917\) | 0.973717 | 0.0321550 | ||||||||
\(918\) | 0.210980 | 0.00696339 | ||||||||
\(919\) | −43.7882 | −1.44444 | −0.722220 | − | 0.691663i | \(-0.756878\pi\) | ||||
−0.722220 | + | 0.691663i | \(0.756878\pi\) | |||||||
\(920\) | 1.66132 | 0.0547720 | ||||||||
\(921\) | −12.1646 | −0.400837 | ||||||||
\(922\) | 3.01389 | 0.0992572 | ||||||||
\(923\) | 26.0265 | 0.856673 | ||||||||
\(924\) | 7.13306 | 0.234660 | ||||||||
\(925\) | 13.5898 | 0.446830 | ||||||||
\(926\) | 21.3395 | 0.701259 | ||||||||
\(927\) | 10.9494 | 0.359624 | ||||||||
\(928\) | 53.2979 | 1.74959 | ||||||||
\(929\) | −27.0615 | −0.887858 | −0.443929 | − | 0.896062i | \(-0.646416\pi\) | ||||
−0.443929 | + | 0.896062i | \(0.646416\pi\) | |||||||
\(930\) | 4.89282 | 0.160442 | ||||||||
\(931\) | −31.2397 | −1.02384 | ||||||||
\(932\) | −26.1335 | −0.856032 | ||||||||
\(933\) | 10.4238 | 0.341260 | ||||||||
\(934\) | 8.44218 | 0.276237 | ||||||||
\(935\) | 0.325424 | 0.0106425 | ||||||||
\(936\) | −12.0515 | −0.393916 | ||||||||
\(937\) | 2.66965 | 0.0872137 | 0.0436068 | − | 0.999049i | \(-0.486115\pi\) | ||||
0.0436068 | + | 0.999049i | \(0.486115\pi\) | |||||||
\(938\) | 22.4639 | 0.733471 | ||||||||
\(939\) | 3.70708 | 0.120976 | ||||||||
\(940\) | 11.2878 | 0.368167 | ||||||||
\(941\) | −31.2522 | −1.01879 | −0.509397 | − | 0.860532i | \(-0.670132\pi\) | ||||
−0.509397 | + | 0.860532i | \(0.670132\pi\) | |||||||
\(942\) | 1.91250 | 0.0623125 | ||||||||
\(943\) | 1.26083 | 0.0410583 | ||||||||
\(944\) | 31.6544 | 1.03026 | ||||||||
\(945\) | −3.53237 | −0.114908 | ||||||||
\(946\) | −2.72990 | −0.0887568 | ||||||||
\(947\) | −6.67071 | −0.216769 | −0.108384 | − | 0.994109i | \(-0.534568\pi\) | ||||
−0.108384 | + | 0.994109i | \(0.534568\pi\) | |||||||
\(948\) | −14.7619 | −0.479444 | ||||||||
\(949\) | 12.3079 | 0.399532 | ||||||||
\(950\) | −6.92424 | −0.224652 | ||||||||
\(951\) | 17.7635 | 0.576020 | ||||||||
\(952\) | −3.27383 | −0.106105 | ||||||||
\(953\) | 14.3407 | 0.464540 | 0.232270 | − | 0.972651i | \(-0.425385\pi\) | ||||
0.232270 | + | 0.972651i | \(0.425385\pi\) | |||||||
\(954\) | −0.202132 | −0.00654425 | ||||||||
\(955\) | 21.9648 | 0.710765 | ||||||||
\(956\) | 11.0315 | 0.356785 | ||||||||
\(957\) | −10.0563 | −0.325075 | ||||||||
\(958\) | −10.4989 | −0.339205 | ||||||||
\(959\) | 57.8280 | 1.86736 | ||||||||
\(960\) | −1.43373 | −0.0462733 | ||||||||
\(961\) | 81.9756 | 2.64438 | ||||||||
\(962\) | −10.3137 | −0.332528 | ||||||||
\(963\) | 2.84318 | 0.0916201 | ||||||||
\(964\) | 3.48848 | 0.112356 | ||||||||
\(965\) | 1.39014 | 0.0447501 | ||||||||
\(966\) | 2.23285 | 0.0718408 | ||||||||
\(967\) | 33.8580 | 1.08880 | 0.544400 | − | 0.838826i | \(-0.316757\pi\) | ||||
0.544400 | + | 0.838826i | \(0.316757\pi\) | |||||||
\(968\) | 2.02216 | 0.0649945 | ||||||||
\(969\) | 1.14104 | 0.0366554 | ||||||||
\(970\) | −2.76629 | −0.0888203 | ||||||||
\(971\) | 23.2171 | 0.745074 | 0.372537 | − | 0.928017i | \(-0.378488\pi\) | ||||
0.372537 | + | 0.928017i | \(0.378488\pi\) | |||||||
\(972\) | 1.70156 | 0.0545775 | ||||||||
\(973\) | −42.9383 | −1.37654 | ||||||||
\(974\) | 2.93180 | 0.0939411 | ||||||||
\(975\) | −25.5671 | −0.818803 | ||||||||
\(976\) | 2.29842 | 0.0735705 | ||||||||
\(977\) | 11.4832 | 0.367381 | 0.183690 | − | 0.982984i | \(-0.441196\pi\) | ||||
0.183690 | + | 0.982984i | \(0.441196\pi\) | |||||||
\(978\) | 9.19176 | 0.293920 | ||||||||
\(979\) | 7.42432 | 0.237282 | ||||||||
\(980\) | 15.1601 | 0.484272 | ||||||||
\(981\) | 19.4494 | 0.620970 | ||||||||
\(982\) | 16.6067 | 0.529942 | ||||||||
\(983\) | −2.32576 | −0.0741803 | −0.0370901 | − | 0.999312i | \(-0.511809\pi\) | ||||
−0.0370901 | + | 0.999312i | \(0.511809\pi\) | |||||||
\(984\) | 2.61499 | 0.0833629 | ||||||||
\(985\) | 12.6472 | 0.402974 | ||||||||
\(986\) | 2.12169 | 0.0675683 | ||||||||
\(987\) | 33.0030 | 1.05050 | ||||||||
\(988\) | −29.9614 | −0.953199 | ||||||||
\(989\) | 4.87213 | 0.154925 | ||||||||
\(990\) | −0.460328 | −0.0146302 | ||||||||
\(991\) | −27.4890 | −0.873218 | −0.436609 | − | 0.899651i | \(-0.643821\pi\) | ||||
−0.436609 | + | 0.899651i | \(0.643821\pi\) | |||||||
\(992\) | 56.3330 | 1.78857 | ||||||||
\(993\) | −25.2813 | −0.802279 | ||||||||
\(994\) | −10.0011 | −0.317216 | ||||||||
\(995\) | −0.364629 | −0.0115595 | ||||||||
\(996\) | −12.0755 | −0.382627 | ||||||||
\(997\) | −0.204845 | −0.00648751 | −0.00324375 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324375 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(998\) | 9.33754 | 0.295575 | ||||||||
\(999\) | 3.16781 | 0.100225 |
(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 | 2013.2.a.h.1.6 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.6 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.9 | 14 | 3.2 | odd | 2 |