Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9251,2,Mod(1,9251)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9251, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9251.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9251 = 11 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9251.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: | \(73.8696069099\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.35 | ||
Character | \(\chi\) | \(=\) | 9251.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.21557 | 1.56664 | 0.783321 | − | 0.621618i | \(-0.213524\pi\) | ||||
0.783321 | + | 0.621618i | \(0.213524\pi\) | |||||||
\(3\) | −2.66785 | −1.54028 | −0.770141 | − | 0.637873i | \(-0.779814\pi\) | ||||
−0.770141 | + | 0.637873i | \(0.779814\pi\) | |||||||
\(4\) | 2.90873 | 1.45436 | ||||||||
\(5\) | −0.0303185 | −0.0135588 | −0.00677942 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00677942 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(6\) | −5.91079 | −2.41307 | ||||||||
\(7\) | 2.76647 | 1.04563 | 0.522813 | − | 0.852447i | \(-0.324882\pi\) | ||||
0.522813 | + | 0.852447i | \(0.324882\pi\) | |||||||
\(8\) | 2.01335 | 0.711826 | ||||||||
\(9\) | 4.11741 | 1.37247 | ||||||||
\(10\) | −0.0671726 | −0.0212418 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −7.76005 | −2.24013 | ||||||||
\(13\) | −2.93677 | −0.814514 | −0.407257 | − | 0.913314i | \(-0.633515\pi\) | ||||
−0.407257 | + | 0.913314i | \(0.633515\pi\) | |||||||
\(14\) | 6.12929 | 1.63812 | ||||||||
\(15\) | 0.0808851 | 0.0208844 | ||||||||
\(16\) | −1.35675 | −0.339188 | ||||||||
\(17\) | 2.96861 | 0.719993 | 0.359997 | − | 0.932954i | \(-0.382778\pi\) | ||||
0.359997 | + | 0.932954i | \(0.382778\pi\) | |||||||
\(18\) | 9.12239 | 2.15017 | ||||||||
\(19\) | 0.00846514 | 0.00194204 | 0.000971018 | − | 1.00000i | \(-0.499691\pi\) | ||||
0.000971018 | 1.00000i | \(0.499691\pi\) | ||||||||
\(20\) | −0.0881882 | −0.0197195 | ||||||||
\(21\) | −7.38051 | −1.61056 | ||||||||
\(22\) | −2.21557 | −0.472360 | ||||||||
\(23\) | −2.03589 | −0.424512 | −0.212256 | − | 0.977214i | \(-0.568081\pi\) | ||||
−0.212256 | + | 0.977214i | \(0.568081\pi\) | |||||||
\(24\) | −5.37131 | −1.09641 | ||||||||
\(25\) | −4.99908 | −0.999816 | ||||||||
\(26\) | −6.50661 | −1.27605 | ||||||||
\(27\) | −2.98108 | −0.573709 | ||||||||
\(28\) | 8.04691 | 1.52072 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0.179206 | 0.0327184 | ||||||||
\(31\) | 8.46564 | 1.52047 | 0.760237 | − | 0.649646i | \(-0.225083\pi\) | ||||
0.760237 | + | 0.649646i | \(0.225083\pi\) | |||||||
\(32\) | −7.03267 | −1.24321 | ||||||||
\(33\) | 2.66785 | 0.464413 | ||||||||
\(34\) | 6.57714 | 1.12797 | ||||||||
\(35\) | −0.0838751 | −0.0141775 | ||||||||
\(36\) | 11.9764 | 1.99607 | ||||||||
\(37\) | −3.63138 | −0.596996 | −0.298498 | − | 0.954410i | \(-0.596486\pi\) | ||||
−0.298498 | + | 0.954410i | \(0.596486\pi\) | |||||||
\(38\) | 0.0187551 | 0.00304247 | ||||||||
\(39\) | 7.83486 | 1.25458 | ||||||||
\(40\) | −0.0610417 | −0.00965154 | ||||||||
\(41\) | 6.75803 | 1.05543 | 0.527714 | − | 0.849422i | \(-0.323049\pi\) | ||||
0.527714 | + | 0.849422i | \(0.323049\pi\) | |||||||
\(42\) | −16.3520 | −2.52317 | ||||||||
\(43\) | 4.50264 | 0.686645 | 0.343323 | − | 0.939217i | \(-0.388448\pi\) | ||||
0.343323 | + | 0.939217i | \(0.388448\pi\) | |||||||
\(44\) | −2.90873 | −0.438507 | ||||||||
\(45\) | −0.124834 | −0.0186091 | ||||||||
\(46\) | −4.51064 | −0.665058 | ||||||||
\(47\) | −11.9271 | −1.73975 | −0.869874 | − | 0.493275i | \(-0.835800\pi\) | ||||
−0.869874 | + | 0.493275i | \(0.835800\pi\) | |||||||
\(48\) | 3.61961 | 0.522445 | ||||||||
\(49\) | 0.653346 | 0.0933351 | ||||||||
\(50\) | −11.0758 | −1.56635 | ||||||||
\(51\) | −7.91979 | −1.10899 | ||||||||
\(52\) | −8.54228 | −1.18460 | ||||||||
\(53\) | −9.25328 | −1.27104 | −0.635518 | − | 0.772086i | \(-0.719213\pi\) | ||||
−0.635518 | + | 0.772086i | \(0.719213\pi\) | |||||||
\(54\) | −6.60477 | −0.898796 | ||||||||
\(55\) | 0.0303185 | 0.00408814 | ||||||||
\(56\) | 5.56987 | 0.744305 | ||||||||
\(57\) | −0.0225837 | −0.00299128 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.55322 | −0.592779 | −0.296389 | − | 0.955067i | \(-0.595783\pi\) | ||||
−0.296389 | + | 0.955067i | \(0.595783\pi\) | |||||||
\(60\) | 0.235273 | 0.0303736 | ||||||||
\(61\) | 2.45272 | 0.314038 | 0.157019 | − | 0.987596i | \(-0.449812\pi\) | ||||
0.157019 | + | 0.987596i | \(0.449812\pi\) | |||||||
\(62\) | 18.7562 | 2.38204 | ||||||||
\(63\) | 11.3907 | 1.43509 | ||||||||
\(64\) | −12.8678 | −1.60848 | ||||||||
\(65\) | 0.0890385 | 0.0110439 | ||||||||
\(66\) | 5.91079 | 0.727568 | ||||||||
\(67\) | 5.51636 | 0.673930 | 0.336965 | − | 0.941517i | \(-0.390600\pi\) | ||||
0.336965 | + | 0.941517i | \(0.390600\pi\) | |||||||
\(68\) | 8.63487 | 1.04713 | ||||||||
\(69\) | 5.43143 | 0.653868 | ||||||||
\(70\) | −0.185831 | −0.0222110 | ||||||||
\(71\) | 1.17364 | 0.139286 | 0.0696428 | − | 0.997572i | \(-0.477814\pi\) | ||||
0.0696428 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(72\) | 8.28978 | 0.976960 | ||||||||
\(73\) | −6.48168 | −0.758623 | −0.379312 | − | 0.925269i | \(-0.623839\pi\) | ||||
−0.379312 | + | 0.925269i | \(0.623839\pi\) | |||||||
\(74\) | −8.04557 | −0.935278 | ||||||||
\(75\) | 13.3368 | 1.54000 | ||||||||
\(76\) | 0.0246228 | 0.00282443 | ||||||||
\(77\) | −2.76647 | −0.315268 | ||||||||
\(78\) | 17.3586 | 1.96548 | ||||||||
\(79\) | −15.8454 | −1.78275 | −0.891376 | − | 0.453264i | \(-0.850259\pi\) | ||||
−0.891376 | + | 0.453264i | \(0.850259\pi\) | |||||||
\(80\) | 0.0411347 | 0.00459900 | ||||||||
\(81\) | −4.39917 | −0.488797 | ||||||||
\(82\) | 14.9729 | 1.65348 | ||||||||
\(83\) | −8.21870 | −0.902120 | −0.451060 | − | 0.892494i | \(-0.648954\pi\) | ||||
−0.451060 | + | 0.892494i | \(0.648954\pi\) | |||||||
\(84\) | −21.4679 | −2.34234 | ||||||||
\(85\) | −0.0900036 | −0.00976227 | ||||||||
\(86\) | 9.97588 | 1.07573 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.01335 | −0.214624 | ||||||||
\(89\) | 7.94101 | 0.841745 | 0.420873 | − | 0.907120i | \(-0.361724\pi\) | ||||
0.420873 | + | 0.907120i | \(0.361724\pi\) | |||||||
\(90\) | −0.276577 | −0.0291538 | ||||||||
\(91\) | −8.12449 | −0.851678 | ||||||||
\(92\) | −5.92184 | −0.617395 | ||||||||
\(93\) | −22.5850 | −2.34196 | ||||||||
\(94\) | −26.4253 | −2.72556 | ||||||||
\(95\) | −0.000256650 0 | −2.63317e−5 0 | ||||||||
\(96\) | 18.7621 | 1.91490 | ||||||||
\(97\) | 13.7773 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(98\) | 1.44753 | 0.146223 | ||||||||
\(99\) | −4.11741 | −0.413815 | ||||||||
\(100\) | −14.5410 | −1.45410 | ||||||||
\(101\) | −14.3761 | −1.43048 | −0.715239 | − | 0.698880i | \(-0.753682\pi\) | ||||
−0.715239 | + | 0.698880i | \(0.753682\pi\) | |||||||
\(102\) | −17.5468 | −1.73739 | ||||||||
\(103\) | −9.71486 | −0.957234 | −0.478617 | − | 0.878024i | \(-0.658862\pi\) | ||||
−0.478617 | + | 0.878024i | \(0.658862\pi\) | |||||||
\(104\) | −5.91275 | −0.579793 | ||||||||
\(105\) | 0.223766 | 0.0218373 | ||||||||
\(106\) | −20.5013 | −1.99126 | ||||||||
\(107\) | −5.18098 | −0.500864 | −0.250432 | − | 0.968134i | \(-0.580573\pi\) | ||||
−0.250432 | + | 0.968134i | \(0.580573\pi\) | |||||||
\(108\) | −8.67115 | −0.834382 | ||||||||
\(109\) | 14.4763 | 1.38658 | 0.693288 | − | 0.720661i | \(-0.256162\pi\) | ||||
0.693288 | + | 0.720661i | \(0.256162\pi\) | |||||||
\(110\) | 0.0671726 | 0.00640465 | ||||||||
\(111\) | 9.68798 | 0.919542 | ||||||||
\(112\) | −3.75341 | −0.354664 | ||||||||
\(113\) | 16.8906 | 1.58893 | 0.794466 | − | 0.607309i | \(-0.207751\pi\) | ||||
0.794466 | + | 0.607309i | \(0.207751\pi\) | |||||||
\(114\) | −0.0500356 | −0.00468627 | ||||||||
\(115\) | 0.0617250 | 0.00575588 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.0919 | −1.11790 | ||||||||
\(118\) | −10.0880 | −0.928671 | ||||||||
\(119\) | 8.21256 | 0.752844 | ||||||||
\(120\) | 0.162850 | 0.0148661 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.43415 | 0.491985 | ||||||||
\(123\) | −18.0294 | −1.62566 | ||||||||
\(124\) | 24.6242 | 2.21132 | ||||||||
\(125\) | 0.303157 | 0.0271152 | ||||||||
\(126\) | 25.2368 | 2.24827 | ||||||||
\(127\) | 22.0401 | 1.95575 | 0.977873 | − | 0.209201i | \(-0.0670863\pi\) | ||||
0.977873 | + | 0.209201i | \(0.0670863\pi\) | |||||||
\(128\) | −14.4442 | −1.27670 | ||||||||
\(129\) | −12.0123 | −1.05763 | ||||||||
\(130\) | 0.197271 | 0.0173018 | ||||||||
\(131\) | −3.43451 | −0.300074 | −0.150037 | − | 0.988680i | \(-0.547939\pi\) | ||||
−0.150037 | + | 0.988680i | \(0.547939\pi\) | |||||||
\(132\) | 7.76005 | 0.675425 | ||||||||
\(133\) | 0.0234185 | 0.00203064 | ||||||||
\(134\) | 12.2218 | 1.05581 | ||||||||
\(135\) | 0.0903817 | 0.00777882 | ||||||||
\(136\) | 5.97684 | 0.512510 | ||||||||
\(137\) | 9.74726 | 0.832765 | 0.416382 | − | 0.909190i | \(-0.363298\pi\) | ||||
0.416382 | + | 0.909190i | \(0.363298\pi\) | |||||||
\(138\) | 12.0337 | 1.02438 | ||||||||
\(139\) | −6.08833 | −0.516406 | −0.258203 | − | 0.966091i | \(-0.583130\pi\) | ||||
−0.258203 | + | 0.966091i | \(0.583130\pi\) | |||||||
\(140\) | −0.243970 | −0.0206192 | ||||||||
\(141\) | 31.8197 | 2.67970 | ||||||||
\(142\) | 2.60028 | 0.218211 | ||||||||
\(143\) | 2.93677 | 0.245585 | ||||||||
\(144\) | −5.58631 | −0.465525 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.3606 | −1.18849 | ||||||||
\(147\) | −1.74303 | −0.143762 | ||||||||
\(148\) | −10.5627 | −0.868249 | ||||||||
\(149\) | 3.75189 | 0.307366 | 0.153683 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153683 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(150\) | 29.5485 | 2.41263 | ||||||||
\(151\) | −19.6681 | −1.60057 | −0.800283 | − | 0.599623i | \(-0.795317\pi\) | ||||
−0.800283 | + | 0.599623i | \(0.795317\pi\) | |||||||
\(152\) | 0.0170433 | 0.00138239 | ||||||||
\(153\) | 12.2230 | 0.988169 | ||||||||
\(154\) | −6.12929 | −0.493912 | ||||||||
\(155\) | −0.256665 | −0.0206158 | ||||||||
\(156\) | 22.7895 | 1.82462 | ||||||||
\(157\) | −17.6082 | −1.40529 | −0.702644 | − | 0.711542i | \(-0.747997\pi\) | ||||
−0.702644 | + | 0.711542i | \(0.747997\pi\) | |||||||
\(158\) | −35.1066 | −2.79293 | ||||||||
\(159\) | 24.6863 | 1.95775 | ||||||||
\(160\) | 0.213220 | 0.0168565 | ||||||||
\(161\) | −5.63222 | −0.443881 | ||||||||
\(162\) | −9.74665 | −0.765769 | ||||||||
\(163\) | −16.1005 | −1.26109 | −0.630545 | − | 0.776153i | \(-0.717168\pi\) | ||||
−0.630545 | + | 0.776153i | \(0.717168\pi\) | |||||||
\(164\) | 19.6573 | 1.53498 | ||||||||
\(165\) | −0.0808851 | −0.00629689 | ||||||||
\(166\) | −18.2091 | −1.41330 | ||||||||
\(167\) | 11.0800 | 0.857395 | 0.428698 | − | 0.903448i | \(-0.358973\pi\) | ||||
0.428698 | + | 0.903448i | \(0.358973\pi\) | |||||||
\(168\) | −14.8596 | −1.14644 | ||||||||
\(169\) | −4.37536 | −0.336566 | ||||||||
\(170\) | −0.199409 | −0.0152940 | ||||||||
\(171\) | 0.0348544 | 0.00266539 | ||||||||
\(172\) | 13.0969 | 0.998633 | ||||||||
\(173\) | −13.7539 | −1.04569 | −0.522846 | − | 0.852427i | \(-0.675130\pi\) | ||||
−0.522846 | + | 0.852427i | \(0.675130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8298 | −1.04543 | ||||||||
\(176\) | 1.35675 | 0.102269 | ||||||||
\(177\) | 12.1473 | 0.913046 | ||||||||
\(178\) | 17.5938 | 1.31871 | ||||||||
\(179\) | −14.2759 | −1.06703 | −0.533514 | − | 0.845791i | \(-0.679129\pi\) | ||||
−0.533514 | + | 0.845791i | \(0.679129\pi\) | |||||||
\(180\) | −0.363107 | −0.0270644 | ||||||||
\(181\) | −25.1721 | −1.87102 | −0.935512 | − | 0.353295i | \(-0.885061\pi\) | ||||
−0.935512 | + | 0.353295i | \(0.885061\pi\) | |||||||
\(182\) | −18.0003 | −1.33427 | ||||||||
\(183\) | −6.54347 | −0.483708 | ||||||||
\(184\) | −4.09895 | −0.302179 | ||||||||
\(185\) | 0.110098 | 0.00809457 | ||||||||
\(186\) | −50.0386 | −3.66901 | ||||||||
\(187\) | −2.96861 | −0.217086 | ||||||||
\(188\) | −34.6927 | −2.53023 | ||||||||
\(189\) | −8.24706 | −0.599885 | ||||||||
\(190\) | −0.000568625 0 | −4.12524e−5 0 | ||||||||
\(191\) | −9.68243 | −0.700596 | −0.350298 | − | 0.936638i | \(-0.613920\pi\) | ||||
−0.350298 | + | 0.936638i | \(0.613920\pi\) | |||||||
\(192\) | 34.3294 | 2.47751 | ||||||||
\(193\) | −7.11012 | −0.511798 | −0.255899 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255899 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(194\) | 30.5244 | 2.19153 | ||||||||
\(195\) | −0.237541 | −0.0170107 | ||||||||
\(196\) | 1.90041 | 0.135743 | ||||||||
\(197\) | 17.0987 | 1.21823 | 0.609116 | − | 0.793081i | \(-0.291524\pi\) | ||||
0.609116 | + | 0.793081i | \(0.291524\pi\) | |||||||
\(198\) | −9.12239 | −0.648300 | ||||||||
\(199\) | 1.57365 | 0.111553 | 0.0557767 | − | 0.998443i | \(-0.482237\pi\) | ||||
0.0557767 | + | 0.998443i | \(0.482237\pi\) | |||||||
\(200\) | −10.0649 | −0.711696 | ||||||||
\(201\) | −14.7168 | −1.03804 | ||||||||
\(202\) | −31.8512 | −2.24105 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −23.0365 | −1.61288 | ||||||||
\(205\) | −0.204893 | −0.0143104 | ||||||||
\(206\) | −21.5239 | −1.49964 | ||||||||
\(207\) | −8.38258 | −0.582629 | ||||||||
\(208\) | 3.98447 | 0.276274 | ||||||||
\(209\) | −0.00846514 | −0.000585546 0 | ||||||||
\(210\) | 0.495768 | 0.0342112 | ||||||||
\(211\) | 11.5897 | 0.797865 | 0.398932 | − | 0.916980i | \(-0.369381\pi\) | ||||
0.398932 | + | 0.916980i | \(0.369381\pi\) | |||||||
\(212\) | −26.9153 | −1.84855 | ||||||||
\(213\) | −3.13110 | −0.214539 | ||||||||
\(214\) | −11.4788 | −0.784675 | ||||||||
\(215\) | −0.136513 | −0.00931011 | ||||||||
\(216\) | −6.00195 | −0.408381 | ||||||||
\(217\) | 23.4199 | 1.58985 | ||||||||
\(218\) | 32.0731 | 2.17227 | ||||||||
\(219\) | 17.2921 | 1.16849 | ||||||||
\(220\) | 0.0881882 | 0.00594565 | ||||||||
\(221\) | −8.71813 | −0.586445 | ||||||||
\(222\) | 21.4643 | 1.44059 | ||||||||
\(223\) | −25.0198 | −1.67545 | −0.837725 | − | 0.546093i | \(-0.816115\pi\) | ||||
−0.837725 | + | 0.546093i | \(0.816115\pi\) | |||||||
\(224\) | −19.4557 | −1.29994 | ||||||||
\(225\) | −20.5833 | −1.37222 | ||||||||
\(226\) | 37.4222 | 2.48929 | ||||||||
\(227\) | 10.9662 | 0.727850 | 0.363925 | − | 0.931428i | \(-0.381437\pi\) | ||||
0.363925 | + | 0.931428i | \(0.381437\pi\) | |||||||
\(228\) | −0.0656899 | −0.00435042 | ||||||||
\(229\) | −4.81531 | −0.318205 | −0.159102 | − | 0.987262i | \(-0.550860\pi\) | ||||
−0.159102 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(230\) | 0.136756 | 0.00901740 | ||||||||
\(231\) | 7.38051 | 0.485602 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8130 | −0.708380 | −0.354190 | − | 0.935173i | \(-0.615243\pi\) | ||||
−0.354190 | + | 0.935173i | \(0.615243\pi\) | |||||||
\(234\) | −26.7904 | −1.75134 | ||||||||
\(235\) | 0.361612 | 0.0235889 | ||||||||
\(236\) | −13.2441 | −0.862116 | ||||||||
\(237\) | 42.2732 | 2.74594 | ||||||||
\(238\) | 18.1955 | 1.17944 | ||||||||
\(239\) | 21.0838 | 1.36380 | 0.681900 | − | 0.731446i | \(-0.261154\pi\) | ||||
0.681900 | + | 0.731446i | \(0.261154\pi\) | |||||||
\(240\) | −0.109741 | −0.00708375 | ||||||||
\(241\) | −22.4730 | −1.44761 | −0.723806 | − | 0.690004i | \(-0.757609\pi\) | ||||
−0.723806 | + | 0.690004i | \(0.757609\pi\) | |||||||
\(242\) | 2.21557 | 0.142422 | ||||||||
\(243\) | 20.6795 | 1.32659 | ||||||||
\(244\) | 7.13429 | 0.456726 | ||||||||
\(245\) | −0.0198084 | −0.00126552 | ||||||||
\(246\) | −39.9453 | −2.54682 | ||||||||
\(247\) | −0.0248602 | −0.00158182 | ||||||||
\(248\) | 17.0443 | 1.08231 | ||||||||
\(249\) | 21.9262 | 1.38952 | ||||||||
\(250\) | 0.671664 | 0.0424797 | ||||||||
\(251\) | −20.8755 | −1.31765 | −0.658825 | − | 0.752296i | \(-0.728946\pi\) | ||||
−0.658825 | + | 0.752296i | \(0.728946\pi\) | |||||||
\(252\) | 33.1324 | 2.08715 | ||||||||
\(253\) | 2.03589 | 0.127995 | ||||||||
\(254\) | 48.8313 | 3.06395 | ||||||||
\(255\) | 0.240116 | 0.0150366 | ||||||||
\(256\) | −6.26637 | −0.391648 | ||||||||
\(257\) | 28.0070 | 1.74703 | 0.873513 | − | 0.486800i | \(-0.161836\pi\) | ||||
0.873513 | + | 0.486800i | \(0.161836\pi\) | |||||||
\(258\) | −26.6141 | −1.65692 | ||||||||
\(259\) | −10.0461 | −0.624235 | ||||||||
\(260\) | 0.258989 | 0.0160618 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.60937 | −0.470109 | ||||||||
\(263\) | 15.3563 | 0.946909 | 0.473455 | − | 0.880818i | \(-0.343007\pi\) | ||||
0.473455 | + | 0.880818i | \(0.343007\pi\) | |||||||
\(264\) | 5.37131 | 0.330581 | ||||||||
\(265\) | 0.280545 | 0.0172338 | ||||||||
\(266\) | 0.0518853 | 0.00318129 | ||||||||
\(267\) | −21.1854 | −1.29653 | ||||||||
\(268\) | 16.0456 | 0.980140 | ||||||||
\(269\) | −1.31269 | −0.0800361 | −0.0400181 | − | 0.999199i | \(-0.512742\pi\) | ||||
−0.0400181 | + | 0.999199i | \(0.512742\pi\) | |||||||
\(270\) | 0.200247 | 0.0121866 | ||||||||
\(271\) | −16.2781 | −0.988823 | −0.494411 | − | 0.869228i | \(-0.664616\pi\) | ||||
−0.494411 | + | 0.869228i | \(0.664616\pi\) | |||||||
\(272\) | −4.02767 | −0.244213 | ||||||||
\(273\) | 21.6749 | 1.31182 | ||||||||
\(274\) | 21.5957 | 1.30464 | ||||||||
\(275\) | 4.99908 | 0.301456 | ||||||||
\(276\) | 15.7986 | 0.950962 | ||||||||
\(277\) | −7.68366 | −0.461666 | −0.230833 | − | 0.972993i | \(-0.574145\pi\) | ||||
−0.230833 | + | 0.972993i | \(0.574145\pi\) | |||||||
\(278\) | −13.4891 | −0.809022 | ||||||||
\(279\) | 34.8565 | 2.08680 | ||||||||
\(280\) | −0.168870 | −0.0100919 | ||||||||
\(281\) | −9.58851 | −0.572002 | −0.286001 | − | 0.958229i | \(-0.592326\pi\) | ||||
−0.286001 | + | 0.958229i | \(0.592326\pi\) | |||||||
\(282\) | 70.4986 | 4.19813 | ||||||||
\(283\) | −2.00855 | −0.119396 | −0.0596979 | − | 0.998216i | \(-0.519014\pi\) | ||||
−0.0596979 | + | 0.998216i | \(0.519014\pi\) | |||||||
\(284\) | 3.41381 | 0.202572 | ||||||||
\(285\) | 0.000684703 0 | 4.05583e−5 0 | ||||||||
\(286\) | 6.50661 | 0.384744 | ||||||||
\(287\) | 18.6959 | 1.10358 | ||||||||
\(288\) | −28.9564 | −1.70627 | ||||||||
\(289\) | −8.18737 | −0.481610 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −36.7556 | −2.15465 | ||||||||
\(292\) | −18.8535 | −1.10332 | ||||||||
\(293\) | −11.3620 | −0.663774 | −0.331887 | − | 0.943319i | \(-0.607685\pi\) | ||||
−0.331887 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(294\) | −3.86179 | −0.225224 | ||||||||
\(295\) | 0.138047 | 0.00803739 | ||||||||
\(296\) | −7.31124 | −0.424957 | ||||||||
\(297\) | 2.98108 | 0.172980 | ||||||||
\(298\) | 8.31255 | 0.481533 | ||||||||
\(299\) | 5.97894 | 0.345771 | ||||||||
\(300\) | 38.7931 | 2.23972 | ||||||||
\(301\) | 12.4564 | 0.717975 | ||||||||
\(302\) | −43.5759 | −2.50751 | ||||||||
\(303\) | 38.3533 | 2.20334 | ||||||||
\(304\) | −0.0114851 | −0.000658715 0 | ||||||||
\(305\) | −0.0743626 | −0.00425799 | ||||||||
\(306\) | 27.0808 | 1.54811 | ||||||||
\(307\) | −27.1073 | −1.54709 | −0.773547 | − | 0.633739i | \(-0.781519\pi\) | ||||
−0.773547 | + | 0.633739i | \(0.781519\pi\) | |||||||
\(308\) | −8.04691 | −0.458515 | ||||||||
\(309\) | 25.9178 | 1.47441 | ||||||||
\(310\) | −0.568658 | −0.0322976 | ||||||||
\(311\) | 2.26559 | 0.128470 | 0.0642350 | − | 0.997935i | \(-0.479539\pi\) | ||||
0.0642350 | + | 0.997935i | \(0.479539\pi\) | |||||||
\(312\) | 15.7743 | 0.893045 | ||||||||
\(313\) | −19.9594 | −1.12817 | −0.564085 | − | 0.825716i | \(-0.690771\pi\) | ||||
−0.564085 | + | 0.825716i | \(0.690771\pi\) | |||||||
\(314\) | −39.0121 | −2.20158 | ||||||||
\(315\) | −0.345348 | −0.0194582 | ||||||||
\(316\) | −46.0901 | −2.59277 | ||||||||
\(317\) | −20.9086 | −1.17434 | −0.587171 | − | 0.809463i | \(-0.699758\pi\) | ||||
−0.587171 | + | 0.809463i | \(0.699758\pi\) | |||||||
\(318\) | 54.6942 | 3.06710 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.390133 | 0.0218091 | ||||||||
\(321\) | 13.8221 | 0.771473 | ||||||||
\(322\) | −12.4785 | −0.695402 | ||||||||
\(323\) | 0.0251297 | 0.00139825 | ||||||||
\(324\) | −12.7960 | −0.710888 | ||||||||
\(325\) | 14.6812 | 0.814365 | ||||||||
\(326\) | −35.6717 | −1.97567 | ||||||||
\(327\) | −38.6205 | −2.13572 | ||||||||
\(328\) | 13.6063 | 0.751281 | ||||||||
\(329\) | −32.9960 | −1.81913 | ||||||||
\(330\) | −0.179206 | −0.00986497 | ||||||||
\(331\) | 8.25543 | 0.453759 | 0.226880 | − | 0.973923i | \(-0.427148\pi\) | ||||
0.226880 | + | 0.973923i | \(0.427148\pi\) | |||||||
\(332\) | −23.9060 | −1.31201 | ||||||||
\(333\) | −14.9519 | −0.819359 | ||||||||
\(334\) | 24.5484 | 1.34323 | ||||||||
\(335\) | −0.167248 | −0.00913771 | ||||||||
\(336\) | 10.0135 | 0.546283 | ||||||||
\(337\) | 15.6393 | 0.851930 | 0.425965 | − | 0.904740i | \(-0.359935\pi\) | ||||
0.425965 | + | 0.904740i | \(0.359935\pi\) | |||||||
\(338\) | −9.69390 | −0.527279 | ||||||||
\(339\) | −45.0615 | −2.44740 | ||||||||
\(340\) | −0.261796 | −0.0141979 | ||||||||
\(341\) | −8.46564 | −0.458440 | ||||||||
\(342\) | 0.0772223 | 0.00417570 | ||||||||
\(343\) | −17.5578 | −0.948033 | ||||||||
\(344\) | 9.06538 | 0.488772 | ||||||||
\(345\) | −0.164673 | −0.00886569 | ||||||||
\(346\) | −30.4727 | −1.63822 | ||||||||
\(347\) | 24.8149 | 1.33213 | 0.666066 | − | 0.745893i | \(-0.267977\pi\) | ||||
0.666066 | + | 0.745893i | \(0.267977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3029 | −0.551502 | −0.275751 | − | 0.961229i | \(-0.588927\pi\) | ||||
−0.275751 | + | 0.961229i | \(0.588927\pi\) | |||||||
\(350\) | −30.6408 | −1.63782 | ||||||||
\(351\) | 8.75475 | 0.467294 | ||||||||
\(352\) | 7.03267 | 0.374843 | ||||||||
\(353\) | 18.0104 | 0.958595 | 0.479298 | − | 0.877652i | \(-0.340891\pi\) | ||||
0.479298 | + | 0.877652i | \(0.340891\pi\) | |||||||
\(354\) | 26.9131 | 1.43042 | ||||||||
\(355\) | −0.0355830 | −0.00188855 | ||||||||
\(356\) | 23.0982 | 1.22420 | ||||||||
\(357\) | −21.9098 | −1.15959 | ||||||||
\(358\) | −31.6291 | −1.67165 | ||||||||
\(359\) | −14.4949 | −0.765009 | −0.382505 | − | 0.923954i | \(-0.624938\pi\) | ||||
−0.382505 | + | 0.923954i | \(0.624938\pi\) | |||||||
\(360\) | −0.251334 | −0.0132464 | ||||||||
\(361\) | −18.9999 | −0.999996 | ||||||||
\(362\) | −55.7703 | −2.93122 | ||||||||
\(363\) | −2.66785 | −0.140026 | ||||||||
\(364\) | −23.6319 | −1.23865 | ||||||||
\(365\) | 0.196515 | 0.0102860 | ||||||||
\(366\) | −14.4975 | −0.757796 | ||||||||
\(367\) | 27.2063 | 1.42016 | 0.710078 | − | 0.704123i | \(-0.248660\pi\) | ||||
0.710078 | + | 0.704123i | \(0.248660\pi\) | |||||||
\(368\) | 2.76219 | 0.143989 | ||||||||
\(369\) | 27.8256 | 1.44854 | ||||||||
\(370\) | 0.243929 | 0.0126813 | ||||||||
\(371\) | −25.5989 | −1.32903 | ||||||||
\(372\) | −65.6937 | −3.40606 | ||||||||
\(373\) | −3.15392 | −0.163304 | −0.0816519 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816519 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(374\) | −6.57714 | −0.340096 | ||||||||
\(375\) | −0.808776 | −0.0417650 | ||||||||
\(376\) | −24.0134 | −1.23840 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −18.2719 | −0.939805 | ||||||||
\(379\) | 23.7889 | 1.22196 | 0.610978 | − | 0.791647i | \(-0.290776\pi\) | ||||
0.610978 | + | 0.791647i | \(0.290776\pi\) | |||||||
\(380\) | −0.000746525 0 | −3.82959e−5 0 | ||||||||
\(381\) | −58.7997 | −3.01240 | ||||||||
\(382\) | −21.4520 | −1.09758 | ||||||||
\(383\) | −28.9127 | −1.47737 | −0.738685 | − | 0.674050i | \(-0.764553\pi\) | ||||
−0.738685 | + | 0.674050i | \(0.764553\pi\) | |||||||
\(384\) | 38.5349 | 1.96648 | ||||||||
\(385\) | 0.0838751 | 0.00427467 | ||||||||
\(386\) | −15.7529 | −0.801803 | ||||||||
\(387\) | 18.5392 | 0.942400 | ||||||||
\(388\) | 40.0743 | 2.03447 | ||||||||
\(389\) | −8.64490 | −0.438314 | −0.219157 | − | 0.975690i | \(-0.570331\pi\) | ||||
−0.219157 | + | 0.975690i | \(0.570331\pi\) | |||||||
\(390\) | −0.526288 | −0.0266496 | ||||||||
\(391\) | −6.04375 | −0.305645 | ||||||||
\(392\) | 1.31541 | 0.0664384 | ||||||||
\(393\) | 9.16274 | 0.462199 | ||||||||
\(394\) | 37.8833 | 1.90853 | ||||||||
\(395\) | 0.480410 | 0.0241720 | ||||||||
\(396\) | −11.9764 | −0.601838 | ||||||||
\(397\) | −33.9319 | −1.70299 | −0.851496 | − | 0.524360i | \(-0.824304\pi\) | ||||
−0.851496 | + | 0.524360i | \(0.824304\pi\) | |||||||
\(398\) | 3.48653 | 0.174764 | ||||||||
\(399\) | −0.0624771 | −0.00312777 | ||||||||
\(400\) | 6.78252 | 0.339126 | ||||||||
\(401\) | 34.9361 | 1.74462 | 0.872312 | − | 0.488950i | \(-0.162620\pi\) | ||||
0.872312 | + | 0.488950i | \(0.162620\pi\) | |||||||
\(402\) | −32.6060 | −1.62624 | ||||||||
\(403\) | −24.8617 | −1.23845 | ||||||||
\(404\) | −41.8163 | −2.08044 | ||||||||
\(405\) | 0.133376 | 0.00662751 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.63138 | 0.180001 | ||||||||
\(408\) | −15.9453 | −0.789410 | ||||||||
\(409\) | 7.31308 | 0.361608 | 0.180804 | − | 0.983519i | \(-0.442130\pi\) | ||||
0.180804 | + | 0.983519i | \(0.442130\pi\) | |||||||
\(410\) | −0.453954 | −0.0224192 | ||||||||
\(411\) | −26.0042 | −1.28269 | ||||||||
\(412\) | −28.2579 | −1.39217 | ||||||||
\(413\) | −12.5963 | −0.619825 | ||||||||
\(414\) | −18.5721 | −0.912771 | ||||||||
\(415\) | 0.249178 | 0.0122317 | ||||||||
\(416\) | 20.6534 | 1.01261 | ||||||||
\(417\) | 16.2427 | 0.795411 | ||||||||
\(418\) | −0.0187551 | −0.000917340 0 | ||||||||
\(419\) | 12.3712 | 0.604371 | 0.302186 | − | 0.953249i | \(-0.402284\pi\) | ||||
0.302186 | + | 0.953249i | \(0.402284\pi\) | |||||||
\(420\) | 0.650875 | 0.0317594 | ||||||||
\(421\) | −3.04082 | −0.148201 | −0.0741003 | − | 0.997251i | \(-0.523608\pi\) | ||||
−0.0741003 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(422\) | 25.6776 | 1.24997 | ||||||||
\(423\) | −49.1088 | −2.38775 | ||||||||
\(424\) | −18.6301 | −0.904757 | ||||||||
\(425\) | −14.8403 | −0.719861 | ||||||||
\(426\) | −6.93715 | −0.336106 | ||||||||
\(427\) | 6.78536 | 0.328367 | ||||||||
\(428\) | −15.0701 | −0.728439 | ||||||||
\(429\) | −7.83486 | −0.378271 | ||||||||
\(430\) | −0.302454 | −0.0145856 | ||||||||
\(431\) | −29.6186 | −1.42668 | −0.713338 | − | 0.700820i | \(-0.752818\pi\) | ||||
−0.713338 | + | 0.700820i | \(0.752818\pi\) | |||||||
\(432\) | 4.04458 | 0.194595 | ||||||||
\(433\) | −21.2596 | −1.02167 | −0.510834 | − | 0.859679i | \(-0.670663\pi\) | ||||
−0.510834 | + | 0.859679i | \(0.670663\pi\) | |||||||
\(434\) | 51.8883 | 2.49072 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 42.1075 | 2.01659 | ||||||||
\(437\) | −0.0172341 | −0.000824417 0 | ||||||||
\(438\) | 38.3119 | 1.83061 | ||||||||
\(439\) | 13.9141 | 0.664084 | 0.332042 | − | 0.943265i | \(-0.392262\pi\) | ||||
0.332042 | + | 0.943265i | \(0.392262\pi\) | |||||||
\(440\) | 0.0610417 | 0.00291005 | ||||||||
\(441\) | 2.69009 | 0.128100 | ||||||||
\(442\) | −19.3156 | −0.918748 | ||||||||
\(443\) | 5.45297 | 0.259078 | 0.129539 | − | 0.991574i | \(-0.458650\pi\) | ||||
0.129539 | + | 0.991574i | \(0.458650\pi\) | |||||||
\(444\) | 28.1797 | 1.33735 | ||||||||
\(445\) | −0.240759 | −0.0114131 | ||||||||
\(446\) | −55.4330 | −2.62483 | ||||||||
\(447\) | −10.0095 | −0.473431 | ||||||||
\(448\) | −35.5985 | −1.68187 | ||||||||
\(449\) | −10.5672 | −0.498697 | −0.249348 | − | 0.968414i | \(-0.580216\pi\) | ||||
−0.249348 | + | 0.968414i | \(0.580216\pi\) | |||||||
\(450\) | −45.6036 | −2.14977 | ||||||||
\(451\) | −6.75803 | −0.318223 | ||||||||
\(452\) | 49.1301 | 2.31089 | ||||||||
\(453\) | 52.4714 | 2.46532 | ||||||||
\(454\) | 24.2962 | 1.14028 | ||||||||
\(455\) | 0.246322 | 0.0115478 | ||||||||
\(456\) | −0.0454689 | −0.00212927 | ||||||||
\(457\) | −3.77120 | −0.176409 | −0.0882046 | − | 0.996102i | \(-0.528113\pi\) | ||||
−0.0882046 | + | 0.996102i | \(0.528113\pi\) | |||||||
\(458\) | −10.6686 | −0.498512 | ||||||||
\(459\) | −8.84965 | −0.413066 | ||||||||
\(460\) | 0.179541 | 0.00837115 | ||||||||
\(461\) | −22.6499 | −1.05491 | −0.527455 | − | 0.849583i | \(-0.676854\pi\) | ||||
−0.527455 | + | 0.849583i | \(0.676854\pi\) | |||||||
\(462\) | 16.3520 | 0.760764 | ||||||||
\(463\) | −20.4484 | −0.950317 | −0.475158 | − | 0.879900i | \(-0.657609\pi\) | ||||
−0.475158 | + | 0.879900i | \(0.657609\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.684744 | 0.0317542 | ||||||||
\(466\) | −23.9568 | −1.10978 | ||||||||
\(467\) | 5.44385 | 0.251911 | 0.125956 | − | 0.992036i | \(-0.459800\pi\) | ||||
0.125956 | + | 0.992036i | \(0.459800\pi\) | |||||||
\(468\) | −35.1721 | −1.62583 | ||||||||
\(469\) | 15.2608 | 0.704679 | ||||||||
\(470\) | 0.801174 | 0.0369554 | ||||||||
\(471\) | 46.9760 | 2.16454 | ||||||||
\(472\) | −9.16722 | −0.421955 | ||||||||
\(473\) | −4.50264 | −0.207031 | ||||||||
\(474\) | 93.6591 | 4.30191 | ||||||||
\(475\) | −0.0423179 | −0.00194168 | ||||||||
\(476\) | 23.8881 | 1.09491 | ||||||||
\(477\) | −38.0996 | −1.74446 | ||||||||
\(478\) | 46.7126 | 2.13658 | ||||||||
\(479\) | 1.37366 | 0.0627640 | 0.0313820 | − | 0.999507i | \(-0.490009\pi\) | ||||
0.0313820 | + | 0.999507i | \(0.490009\pi\) | |||||||
\(480\) | −0.568838 | −0.0259638 | ||||||||
\(481\) | 10.6645 | 0.486262 | ||||||||
\(482\) | −49.7903 | −2.26789 | ||||||||
\(483\) | 15.0259 | 0.683702 | ||||||||
\(484\) | 2.90873 | 0.132215 | ||||||||
\(485\) | −0.417706 | −0.0189670 | ||||||||
\(486\) | 45.8169 | 2.07830 | ||||||||
\(487\) | −10.5262 | −0.476989 | −0.238494 | − | 0.971144i | \(-0.576654\pi\) | ||||
−0.238494 | + | 0.971144i | \(0.576654\pi\) | |||||||
\(488\) | 4.93818 | 0.223541 | ||||||||
\(489\) | 42.9537 | 1.94243 | ||||||||
\(490\) | −0.0438869 | −0.00198261 | ||||||||
\(491\) | −14.5072 | −0.654699 | −0.327350 | − | 0.944903i | \(-0.606156\pi\) | ||||
−0.327350 | + | 0.944903i | \(0.606156\pi\) | |||||||
\(492\) | −52.4427 | −2.36430 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −0.0550794 | −0.00247814 | ||||||||
\(495\) | 0.124834 | 0.00561085 | ||||||||
\(496\) | −11.4858 | −0.515726 | ||||||||
\(497\) | 3.24684 | 0.145641 | ||||||||
\(498\) | 48.5790 | 2.17688 | ||||||||
\(499\) | 22.6885 | 1.01568 | 0.507838 | − | 0.861453i | \(-0.330445\pi\) | ||||
0.507838 | + | 0.861453i | \(0.330445\pi\) | |||||||
\(500\) | 0.881801 | 0.0394354 | ||||||||
\(501\) | −29.5597 | −1.32063 | ||||||||
\(502\) | −46.2510 | −2.06429 | ||||||||
\(503\) | −21.2282 | −0.946521 | −0.473260 | − | 0.880923i | \(-0.656923\pi\) | ||||
−0.473260 | + | 0.880923i | \(0.656923\pi\) | |||||||
\(504\) | 22.9334 | 1.02154 | ||||||||
\(505\) | 0.435862 | 0.0193956 | ||||||||
\(506\) | 4.51064 | 0.200522 | ||||||||
\(507\) | 11.6728 | 0.518407 | ||||||||
\(508\) | 64.1088 | 2.84437 | ||||||||
\(509\) | −44.0902 | −1.95426 | −0.977132 | − | 0.212634i | \(-0.931796\pi\) | ||||
−0.977132 | + | 0.212634i | \(0.931796\pi\) | |||||||
\(510\) | 0.531993 | 0.0235570 | ||||||||
\(511\) | −17.9314 | −0.793237 | ||||||||
\(512\) | 15.0048 | 0.663126 | ||||||||
\(513\) | −0.0252352 | −0.00111416 | ||||||||
\(514\) | 62.0513 | 2.73696 | ||||||||
\(515\) | 0.294540 | 0.0129790 | ||||||||
\(516\) | −34.9407 | −1.53818 | ||||||||
\(517\) | 11.9271 | 0.524553 | ||||||||
\(518\) | −22.2578 | −0.977952 | ||||||||
\(519\) | 36.6934 | 1.61066 | ||||||||
\(520\) | 0.179266 | 0.00786131 | ||||||||
\(521\) | −9.15415 | −0.401051 | −0.200525 | − | 0.979689i | \(-0.564265\pi\) | ||||
−0.200525 | + | 0.979689i | \(0.564265\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.5781 | 1.55572 | 0.777861 | − | 0.628436i | \(-0.216305\pi\) | ||||
0.777861 | + | 0.628436i | \(0.216305\pi\) | |||||||
\(524\) | −9.99005 | −0.436417 | ||||||||
\(525\) | 36.8958 | 1.61026 | ||||||||
\(526\) | 34.0229 | 1.48347 | ||||||||
\(527\) | 25.1312 | 1.09473 | ||||||||
\(528\) | −3.61961 | −0.157523 | ||||||||
\(529\) | −18.8552 | −0.819790 | ||||||||
\(530\) | 0.621567 | 0.0269991 | ||||||||
\(531\) | −18.7475 | −0.813571 | ||||||||
\(532\) | 0.0681182 | 0.00295330 | ||||||||
\(533\) | −19.8468 | −0.859661 | ||||||||
\(534\) | −46.9376 | −2.03119 | ||||||||
\(535\) | 0.157079 | 0.00679114 | ||||||||
\(536\) | 11.1064 | 0.479721 | ||||||||
\(537\) | 38.0858 | 1.64352 | ||||||||
\(538\) | −2.90835 | −0.125388 | ||||||||
\(539\) | −0.653346 | −0.0281416 | ||||||||
\(540\) | 0.262896 | 0.0113132 | ||||||||
\(541\) | −6.79583 | −0.292175 | −0.146088 | − | 0.989272i | \(-0.546668\pi\) | ||||
−0.146088 | + | 0.989272i | \(0.546668\pi\) | |||||||
\(542\) | −36.0651 | −1.54913 | ||||||||
\(543\) | 67.1552 | 2.88191 | ||||||||
\(544\) | −20.8772 | −0.895104 | ||||||||
\(545\) | −0.438898 | −0.0188003 | ||||||||
\(546\) | 48.0221 | 2.05516 | ||||||||
\(547\) | −3.75643 | −0.160613 | −0.0803066 | − | 0.996770i | \(-0.525590\pi\) | ||||
−0.0803066 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(548\) | 28.3521 | 1.21114 | ||||||||
\(549\) | 10.0988 | 0.431008 | ||||||||
\(550\) | 11.0758 | 0.472273 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 10.9354 | 0.465440 | ||||||||
\(553\) | −43.8359 | −1.86409 | ||||||||
\(554\) | −17.0236 | −0.723265 | ||||||||
\(555\) | −0.293725 | −0.0124679 | ||||||||
\(556\) | −17.7093 | −0.751042 | ||||||||
\(557\) | 3.76382 | 0.159478 | 0.0797392 | − | 0.996816i | \(-0.474591\pi\) | ||||
0.0797392 | + | 0.996816i | \(0.474591\pi\) | |||||||
\(558\) | 77.2268 | 3.26927 | ||||||||
\(559\) | −13.2232 | −0.559283 | ||||||||
\(560\) | 0.113798 | 0.00480883 | ||||||||
\(561\) | 7.91979 | 0.334374 | ||||||||
\(562\) | −21.2440 | −0.896123 | ||||||||
\(563\) | 7.23739 | 0.305020 | 0.152510 | − | 0.988302i | \(-0.451264\pi\) | ||||
0.152510 | + | 0.988302i | \(0.451264\pi\) | |||||||
\(564\) | 92.5549 | 3.89726 | ||||||||
\(565\) | −0.512096 | −0.0215441 | ||||||||
\(566\) | −4.45007 | −0.187050 | ||||||||
\(567\) | −12.1702 | −0.511099 | ||||||||
\(568\) | 2.36295 | 0.0991472 | ||||||||
\(569\) | −44.8976 | −1.88220 | −0.941102 | − | 0.338123i | \(-0.890208\pi\) | ||||
−0.941102 | + | 0.338123i | \(0.890208\pi\) | |||||||
\(570\) | 0.00151700 | 6.35403e−5 0 | ||||||||
\(571\) | 37.8995 | 1.58604 | 0.793022 | − | 0.609192i | \(-0.208506\pi\) | ||||
0.793022 | + | 0.609192i | \(0.208506\pi\) | |||||||
\(572\) | 8.54228 | 0.357171 | ||||||||
\(573\) | 25.8312 | 1.07912 | ||||||||
\(574\) | 41.4220 | 1.72892 | ||||||||
\(575\) | 10.1776 | 0.424434 | ||||||||
\(576\) | −52.9822 | −2.20759 | ||||||||
\(577\) | −21.2375 | −0.884129 | −0.442064 | − | 0.896983i | \(-0.645754\pi\) | ||||
−0.442064 | + | 0.896983i | \(0.645754\pi\) | |||||||
\(578\) | −18.1397 | −0.754510 | ||||||||
\(579\) | 18.9687 | 0.788313 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.7368 | −0.943280 | ||||||||
\(582\) | −81.4345 | −3.37557 | ||||||||
\(583\) | 9.25328 | 0.383232 | ||||||||
\(584\) | −13.0499 | −0.540008 | ||||||||
\(585\) | 0.366608 | 0.0151574 | ||||||||
\(586\) | −25.1732 | −1.03990 | ||||||||
\(587\) | −18.8832 | −0.779393 | −0.389696 | − | 0.920943i | \(-0.627420\pi\) | ||||
−0.389696 | + | 0.920943i | \(0.627420\pi\) | |||||||
\(588\) | −5.06999 | −0.209083 | ||||||||
\(589\) | 0.0716628 | 0.00295281 | ||||||||
\(590\) | 0.305851 | 0.0125917 | ||||||||
\(591\) | −45.6167 | −1.87642 | ||||||||
\(592\) | 4.92689 | 0.202494 | ||||||||
\(593\) | 30.3319 | 1.24558 | 0.622791 | − | 0.782389i | \(-0.285999\pi\) | ||||
0.622791 | + | 0.782389i | \(0.285999\pi\) | |||||||
\(594\) | 6.60477 | 0.270997 | ||||||||
\(595\) | −0.248992 | −0.0102077 | ||||||||
\(596\) | 10.9132 | 0.447023 | ||||||||
\(597\) | −4.19827 | −0.171824 | ||||||||
\(598\) | 13.2467 | 0.541699 | ||||||||
\(599\) | −22.9082 | −0.936004 | −0.468002 | − | 0.883727i | \(-0.655026\pi\) | ||||
−0.468002 | + | 0.883727i | \(0.655026\pi\) | |||||||
\(600\) | 26.8516 | 1.09621 | ||||||||
\(601\) | 35.3358 | 1.44138 | 0.720688 | − | 0.693260i | \(-0.243826\pi\) | ||||
0.720688 | + | 0.693260i | \(0.243826\pi\) | |||||||
\(602\) | 27.5980 | 1.12481 | ||||||||
\(603\) | 22.7131 | 0.924949 | ||||||||
\(604\) | −57.2091 | −2.32781 | ||||||||
\(605\) | −0.0303185 | −0.00123262 | ||||||||
\(606\) | 84.9743 | 3.45184 | ||||||||
\(607\) | 37.8672 | 1.53698 | 0.768491 | − | 0.639861i | \(-0.221008\pi\) | ||||
0.768491 | + | 0.639861i | \(0.221008\pi\) | |||||||
\(608\) | −0.0595325 | −0.00241436 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.164755 | −0.00667075 | ||||||||
\(611\) | 35.0272 | 1.41705 | ||||||||
\(612\) | 35.5533 | 1.43716 | ||||||||
\(613\) | 27.2682 | 1.10135 | 0.550677 | − | 0.834719i | \(-0.314370\pi\) | ||||
0.550677 | + | 0.834719i | \(0.314370\pi\) | |||||||
\(614\) | −60.0579 | −2.42374 | ||||||||
\(615\) | 0.546624 | 0.0220420 | ||||||||
\(616\) | −5.56987 | −0.224416 | ||||||||
\(617\) | −11.4370 | −0.460437 | −0.230218 | − | 0.973139i | \(-0.573944\pi\) | ||||
−0.230218 | + | 0.973139i | \(0.573944\pi\) | |||||||
\(618\) | 57.4225 | 2.30987 | ||||||||
\(619\) | −32.6083 | −1.31064 | −0.655320 | − | 0.755351i | \(-0.727466\pi\) | ||||
−0.655320 | + | 0.755351i | \(0.727466\pi\) | |||||||
\(620\) | −0.746570 | −0.0299830 | ||||||||
\(621\) | 6.06914 | 0.243546 | ||||||||
\(622\) | 5.01957 | 0.201267 | ||||||||
\(623\) | 21.9685 | 0.880151 | ||||||||
\(624\) | −10.6300 | −0.425539 | ||||||||
\(625\) | 24.9862 | 0.999449 | ||||||||
\(626\) | −44.2213 | −1.76744 | ||||||||
\(627\) | 0.0225837 | 0.000901906 0 | ||||||||
\(628\) | −51.2175 | −2.04380 | ||||||||
\(629\) | −10.7802 | −0.429833 | ||||||||
\(630\) | −0.765141 | −0.0304840 | ||||||||
\(631\) | 41.1477 | 1.63806 | 0.819032 | − | 0.573748i | \(-0.194511\pi\) | ||||
0.819032 | + | 0.573748i | \(0.194511\pi\) | |||||||
\(632\) | −31.9024 | −1.26901 | ||||||||
\(633\) | −30.9194 | −1.22894 | ||||||||
\(634\) | −46.3243 | −1.83977 | ||||||||
\(635\) | −0.668223 | −0.0265176 | ||||||||
\(636\) | 71.8059 | 2.84729 | ||||||||
\(637\) | −1.91873 | −0.0760228 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.83236 | 0.191165 | ||||||||
\(640\) | 0.437926 | 0.0173105 | ||||||||
\(641\) | 20.4742 | 0.808683 | 0.404342 | − | 0.914608i | \(-0.367501\pi\) | ||||
0.404342 | + | 0.914608i | \(0.367501\pi\) | |||||||
\(642\) | 30.6237 | 1.20862 | ||||||||
\(643\) | 35.2092 | 1.38852 | 0.694259 | − | 0.719726i | \(-0.255732\pi\) | ||||
0.694259 | + | 0.719726i | \(0.255732\pi\) | |||||||
\(644\) | −16.3826 | −0.645564 | ||||||||
\(645\) | 0.364196 | 0.0143402 | ||||||||
\(646\) | 0.0556764 | 0.00219056 | ||||||||
\(647\) | 17.0854 | 0.671696 | 0.335848 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335848 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(648\) | −8.85706 | −0.347938 | ||||||||
\(649\) | 4.55322 | 0.178729 | ||||||||
\(650\) | 32.5271 | 1.27582 | ||||||||
\(651\) | −62.4808 | −2.44881 | ||||||||
\(652\) | −46.8320 | −1.83408 | ||||||||
\(653\) | 17.8368 | 0.698008 | 0.349004 | − | 0.937121i | \(-0.386520\pi\) | ||||
0.349004 | + | 0.937121i | \(0.386520\pi\) | |||||||
\(654\) | −85.5662 | −3.34590 | ||||||||
\(655\) | 0.104129 | 0.00406866 | ||||||||
\(656\) | −9.16898 | −0.357988 | ||||||||
\(657\) | −26.6877 | −1.04119 | ||||||||
\(658\) | −73.1047 | −2.84992 | ||||||||
\(659\) | −0.783162 | −0.0305077 | −0.0152538 | − | 0.999884i | \(-0.504856\pi\) | ||||
−0.0152538 | + | 0.999884i | \(0.504856\pi\) | |||||||
\(660\) | −0.235273 | −0.00915798 | ||||||||
\(661\) | −8.43300 | −0.328006 | −0.164003 | − | 0.986460i | \(-0.552441\pi\) | ||||
−0.164003 | + | 0.986460i | \(0.552441\pi\) | |||||||
\(662\) | 18.2904 | 0.710878 | ||||||||
\(663\) | 23.2586 | 0.903290 | ||||||||
\(664\) | −16.5471 | −0.642153 | ||||||||
\(665\) | −0.000710014 0 | −2.75332e−5 0 | ||||||||
\(666\) | −33.1269 | −1.28364 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 32.2287 | 1.24697 | ||||||||
\(669\) | 66.7490 | 2.58067 | ||||||||
\(670\) | −0.370548 | −0.0143155 | ||||||||
\(671\) | −2.45272 | −0.0946861 | ||||||||
\(672\) | 51.9047 | 2.00227 | ||||||||
\(673\) | 20.2296 | 0.779794 | 0.389897 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389897 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(674\) | 34.6500 | 1.33467 | ||||||||
\(675\) | 14.9026 | 0.573603 | ||||||||
\(676\) | −12.7267 | −0.489490 | ||||||||
\(677\) | −34.0656 | −1.30925 | −0.654623 | − | 0.755955i | \(-0.727173\pi\) | ||||
−0.654623 | + | 0.755955i | \(0.727173\pi\) | |||||||
\(678\) | −99.8366 | −3.83420 | ||||||||
\(679\) | 38.1144 | 1.46269 | ||||||||
\(680\) | −0.181209 | −0.00694904 | ||||||||
\(681\) | −29.2560 | −1.12109 | ||||||||
\(682\) | −18.7562 | −0.718211 | ||||||||
\(683\) | 3.06771 | 0.117383 | 0.0586913 | − | 0.998276i | \(-0.481307\pi\) | ||||
0.0586913 | + | 0.998276i | \(0.481307\pi\) | |||||||
\(684\) | 0.101382 | 0.00387644 | ||||||||
\(685\) | −0.295522 | −0.0112913 | ||||||||
\(686\) | −38.9005 | −1.48523 | ||||||||
\(687\) | 12.8465 | 0.490125 | ||||||||
\(688\) | −6.10896 | −0.232902 | ||||||||
\(689\) | 27.1748 | 1.03528 | ||||||||
\(690\) | −0.364843 | −0.0138893 | ||||||||
\(691\) | −13.6648 | −0.519834 | −0.259917 | − | 0.965631i | \(-0.583695\pi\) | ||||
−0.259917 | + | 0.965631i | \(0.583695\pi\) | |||||||
\(692\) | −40.0065 | −1.52082 | ||||||||
\(693\) | −11.3907 | −0.432696 | ||||||||
\(694\) | 54.9789 | 2.08697 | ||||||||
\(695\) | 0.184589 | 0.00700186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0619 | 0.759900 | ||||||||
\(698\) | −22.8268 | −0.864006 | ||||||||
\(699\) | 28.8473 | 1.09111 | ||||||||
\(700\) | −40.2271 | −1.52044 | ||||||||
\(701\) | 18.7324 | 0.707511 | 0.353756 | − | 0.935338i | \(-0.384904\pi\) | ||||
0.353756 | + | 0.935338i | \(0.384904\pi\) | |||||||
\(702\) | 19.3967 | 0.732082 | ||||||||
\(703\) | −0.0307402 | −0.00115939 | ||||||||
\(704\) | 12.8678 | 0.484975 | ||||||||
\(705\) | −0.964725 | −0.0363336 | ||||||||
\(706\) | 39.9031 | 1.50177 | ||||||||
\(707\) | −39.7711 | −1.49575 | ||||||||
\(708\) | 35.3332 | 1.32790 | ||||||||
\(709\) | −6.47528 | −0.243184 | −0.121592 | − | 0.992580i | \(-0.538800\pi\) | ||||
−0.121592 | + | 0.992580i | \(0.538800\pi\) | |||||||
\(710\) | −0.0788365 | −0.00295868 | ||||||||
\(711\) | −65.2422 | −2.44677 | ||||||||
\(712\) | 15.9880 | 0.599176 | ||||||||
\(713\) | −17.2351 | −0.645459 | ||||||||
\(714\) | −48.5427 | −1.81666 | ||||||||
\(715\) | −0.0890385 | −0.00332985 | ||||||||
\(716\) | −41.5246 | −1.55185 | ||||||||
\(717\) | −56.2484 | −2.10064 | ||||||||
\(718\) | −32.1143 | −1.19849 | ||||||||
\(719\) | 16.0143 | 0.597233 | 0.298616 | − | 0.954373i | \(-0.403475\pi\) | ||||
0.298616 | + | 0.954373i | \(0.403475\pi\) | |||||||
\(720\) | 0.169368 | 0.00631198 | ||||||||
\(721\) | −26.8759 | −1.00091 | ||||||||
\(722\) | −42.0956 | −1.56664 | ||||||||
\(723\) | 59.9545 | 2.22973 | ||||||||
\(724\) | −73.2187 | −2.72115 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.91079 | −0.219370 | ||||||||
\(727\) | −4.97936 | −0.184674 | −0.0923372 | − | 0.995728i | \(-0.529434\pi\) | ||||
−0.0923372 | + | 0.995728i | \(0.529434\pi\) | |||||||
\(728\) | −16.3574 | −0.606247 | ||||||||
\(729\) | −41.9724 | −1.55453 | ||||||||
\(730\) | 0.435391 | 0.0161145 | ||||||||
\(731\) | 13.3666 | 0.494380 | ||||||||
\(732\) | −19.0332 | −0.703487 | ||||||||
\(733\) | 40.3472 | 1.49026 | 0.745128 | − | 0.666921i | \(-0.232388\pi\) | ||||
0.745128 | + | 0.666921i | \(0.232388\pi\) | |||||||
\(734\) | 60.2773 | 2.22487 | ||||||||
\(735\) | 0.0528459 | 0.00194925 | ||||||||
\(736\) | 14.3177 | 0.527758 | ||||||||
\(737\) | −5.51636 | −0.203198 | ||||||||
\(738\) | 61.6494 | 2.26935 | ||||||||
\(739\) | 26.6762 | 0.981301 | 0.490650 | − | 0.871356i | \(-0.336759\pi\) | ||||
0.490650 | + | 0.871356i | \(0.336759\pi\) | |||||||
\(740\) | 0.320245 | 0.0117724 | ||||||||
\(741\) | 0.0663232 | 0.00243644 | ||||||||
\(742\) | −56.7161 | −2.08211 | ||||||||
\(743\) | −6.29958 | −0.231109 | −0.115555 | − | 0.993301i | \(-0.536865\pi\) | ||||
−0.115555 | + | 0.993301i | \(0.536865\pi\) | |||||||
\(744\) | −45.4715 | −1.66707 | ||||||||
\(745\) | −0.113751 | −0.00416753 | ||||||||
\(746\) | −6.98771 | −0.255838 | ||||||||
\(747\) | −33.8398 | −1.23813 | ||||||||
\(748\) | −8.63487 | −0.315722 | ||||||||
\(749\) | −14.3330 | −0.523717 | ||||||||
\(750\) | −1.79190 | −0.0654308 | ||||||||
\(751\) | 12.2284 | 0.446220 | 0.223110 | − | 0.974793i | \(-0.428379\pi\) | ||||
0.223110 | + | 0.974793i | \(0.428379\pi\) | |||||||
\(752\) | 16.1821 | 0.590102 | ||||||||
\(753\) | 55.6927 | 2.02955 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.596306 | 0.0217018 | ||||||||
\(756\) | −23.9885 | −0.872452 | ||||||||
\(757\) | −25.1248 | −0.913175 | −0.456587 | − | 0.889679i | \(-0.650928\pi\) | ||||
−0.456587 | + | 0.889679i | \(0.650928\pi\) | |||||||
\(758\) | 52.7060 | 1.91437 | ||||||||
\(759\) | −5.43143 | −0.197149 | ||||||||
\(760\) | −0.000516726 0 | −1.87436e−5 0 | ||||||||
\(761\) | 43.7418 | 1.58564 | 0.792819 | − | 0.609457i | \(-0.208612\pi\) | ||||
0.792819 | + | 0.609457i | \(0.208612\pi\) | |||||||
\(762\) | −130.275 | −4.71935 | ||||||||
\(763\) | 40.0481 | 1.44984 | ||||||||
\(764\) | −28.1636 | −1.01892 | ||||||||
\(765\) | −0.370582 | −0.0133984 | ||||||||
\(766\) | −64.0580 | −2.31451 | ||||||||
\(767\) | 13.3718 | 0.482827 | ||||||||
\(768\) | 16.7177 | 0.603249 | ||||||||
\(769\) | −33.3683 | −1.20329 | −0.601645 | − | 0.798763i | \(-0.705488\pi\) | ||||
−0.601645 | + | 0.798763i | \(0.705488\pi\) | |||||||
\(770\) | 0.185831 | 0.00669687 | ||||||||
\(771\) | −74.7183 | −2.69091 | ||||||||
\(772\) | −20.6814 | −0.744340 | ||||||||
\(773\) | −43.3898 | −1.56062 | −0.780311 | − | 0.625392i | \(-0.784939\pi\) | ||||
−0.780311 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(774\) | 41.0748 | 1.47640 | ||||||||
\(775\) | −42.3204 | −1.52019 | ||||||||
\(776\) | 27.7384 | 0.995752 | ||||||||
\(777\) | 26.8015 | 0.961498 | ||||||||
\(778\) | −19.1533 | −0.686680 | ||||||||
\(779\) | 0.0572077 | 0.00204968 | ||||||||
\(780\) | −0.690943 | −0.0247397 | ||||||||
\(781\) | −1.17364 | −0.0419962 | ||||||||
\(782\) | −13.3903 | −0.478837 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.886428 | −0.0316582 | ||||||||
\(785\) | 0.533854 | 0.0190541 | ||||||||
\(786\) | 20.3006 | 0.724100 | ||||||||
\(787\) | −4.95565 | −0.176650 | −0.0883250 | − | 0.996092i | \(-0.528151\pi\) | ||||
−0.0883250 | + | 0.996092i | \(0.528151\pi\) | |||||||
\(788\) | 49.7355 | 1.77175 | ||||||||
\(789\) | −40.9682 | −1.45851 | ||||||||
\(790\) | 1.06438 | 0.0378689 | ||||||||
\(791\) | 46.7272 | 1.66143 | ||||||||
\(792\) | −8.28978 | −0.294565 | ||||||||
\(793\) | −7.20307 | −0.255789 | ||||||||
\(794\) | −75.1783 | −2.66798 | ||||||||
\(795\) | −0.748452 | −0.0265449 | ||||||||
\(796\) | 4.57733 | 0.162239 | ||||||||
\(797\) | 18.3240 | 0.649071 | 0.324535 | − | 0.945874i | \(-0.394792\pi\) | ||||
0.324535 | + | 0.945874i | \(0.394792\pi\) | |||||||
\(798\) | −0.138422 | −0.00490009 | ||||||||
\(799\) | −35.4069 | −1.25261 | ||||||||
\(800\) | 35.1569 | 1.24298 | ||||||||
\(801\) | 32.6964 | 1.15527 | ||||||||
\(802\) | 77.4031 | 2.73320 | ||||||||
\(803\) | 6.48168 | 0.228734 | ||||||||
\(804\) | −42.8072 | −1.50969 | ||||||||
\(805\) | 0.170760 | 0.00601851 | ||||||||
\(806\) | −55.0826 | −1.94020 | ||||||||
\(807\) | 3.50206 | 0.123278 | ||||||||
\(808\) | −28.9442 | −1.01825 | ||||||||
\(809\) | 14.1728 | 0.498290 | 0.249145 | − | 0.968466i | \(-0.419850\pi\) | ||||
0.249145 | + | 0.968466i | \(0.419850\pi\) | |||||||
\(810\) | 0.295503 | 0.0103829 | ||||||||
\(811\) | −34.2009 | −1.20096 | −0.600479 | − | 0.799641i | \(-0.705023\pi\) | ||||
−0.600479 | + | 0.799641i | \(0.705023\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.4274 | 1.52307 | ||||||||
\(814\) | 8.04557 | 0.281997 | ||||||||
\(815\) | 0.488143 | 0.0170989 | ||||||||
\(816\) | 10.7452 | 0.376157 | ||||||||
\(817\) | 0.0381154 | 0.00133349 | ||||||||
\(818\) | 16.2026 | 0.566511 | ||||||||
\(819\) | −33.4518 | −1.16890 | ||||||||
\(820\) | −0.595979 | −0.0208125 | ||||||||
\(821\) | −50.3544 | −1.75738 | −0.878691 | − | 0.477391i | \(-0.841582\pi\) | ||||
−0.878691 | + | 0.477391i | \(0.841582\pi\) | |||||||
\(822\) | −57.6140 | −2.00952 | ||||||||
\(823\) | 47.9005 | 1.66971 | 0.834854 | − | 0.550472i | \(-0.185552\pi\) | ||||
0.834854 | + | 0.550472i | \(0.185552\pi\) | |||||||
\(824\) | −19.5594 | −0.681384 | ||||||||
\(825\) | −13.3368 | −0.464327 | ||||||||
\(826\) | −27.9080 | −0.971043 | ||||||||
\(827\) | 51.7450 | 1.79935 | 0.899674 | − | 0.436562i | \(-0.143804\pi\) | ||||
0.899674 | + | 0.436562i | \(0.143804\pi\) | |||||||
\(828\) | −24.3827 | −0.847356 | ||||||||
\(829\) | 23.3442 | 0.810779 | 0.405389 | − | 0.914144i | \(-0.367136\pi\) | ||||
0.405389 | + | 0.914144i | \(0.367136\pi\) | |||||||
\(830\) | 0.552071 | 0.0191627 | ||||||||
\(831\) | 20.4988 | 0.711096 | ||||||||
\(832\) | 37.7899 | 1.31013 | ||||||||
\(833\) | 1.93953 | 0.0672006 | ||||||||
\(834\) | 35.9869 | 1.24612 | ||||||||
\(835\) | −0.335928 | −0.0116253 | ||||||||
\(836\) | −0.0246228 | −0.000851597 0 | ||||||||
\(837\) | −25.2367 | −0.872309 | ||||||||
\(838\) | 27.4091 | 0.946833 | ||||||||
\(839\) | 55.9223 | 1.93065 | 0.965327 | − | 0.261045i | \(-0.0840672\pi\) | ||||
0.965327 | + | 0.261045i | \(0.0840672\pi\) | |||||||
\(840\) | 0.450519 | 0.0155444 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −6.73714 | −0.232177 | ||||||||
\(843\) | 25.5807 | 0.881045 | ||||||||
\(844\) | 33.7112 | 1.16039 | ||||||||
\(845\) | 0.132654 | 0.00456345 | ||||||||
\(846\) | −108.804 | −3.74075 | ||||||||
\(847\) | 2.76647 | 0.0950570 | ||||||||
\(848\) | 12.5544 | 0.431120 | ||||||||
\(849\) | 5.35850 | 0.183903 | ||||||||
\(850\) | −32.8797 | −1.12776 | ||||||||
\(851\) | 7.39308 | 0.253432 | ||||||||
\(852\) | −9.10751 | −0.312018 | ||||||||
\(853\) | 22.3983 | 0.766903 | 0.383451 | − | 0.923561i | \(-0.374735\pi\) | ||||
0.383451 | + | 0.923561i | \(0.374735\pi\) | |||||||
\(854\) | 15.0334 | 0.514433 | ||||||||
\(855\) | −0.00105673 | −3.61395e−5 0 | ||||||||
\(856\) | −10.4311 | −0.356529 | ||||||||
\(857\) | 30.5062 | 1.04207 | 0.521036 | − | 0.853535i | \(-0.325546\pi\) | ||||
0.521036 | + | 0.853535i | \(0.325546\pi\) | |||||||
\(858\) | −17.3586 | −0.592614 | ||||||||
\(859\) | 1.31566 | 0.0448896 | 0.0224448 | − | 0.999748i | \(-0.492855\pi\) | ||||
0.0224448 | + | 0.999748i | \(0.492855\pi\) | |||||||
\(860\) | −0.397079 | −0.0135403 | ||||||||
\(861\) | −49.8778 | −1.69983 | ||||||||
\(862\) | −65.6219 | −2.23509 | ||||||||
\(863\) | −10.2207 | −0.347915 | −0.173958 | − | 0.984753i | \(-0.555656\pi\) | ||||
−0.173958 | + | 0.984753i | \(0.555656\pi\) | |||||||
\(864\) | 20.9649 | 0.713242 | ||||||||
\(865\) | 0.416998 | 0.0141784 | ||||||||
\(866\) | −47.1019 | −1.60059 | ||||||||
\(867\) | 21.8427 | 0.741816 | ||||||||
\(868\) | 68.1222 | 2.31222 | ||||||||
\(869\) | 15.8454 | 0.537520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.2003 | −0.548926 | ||||||||
\(872\) | 29.1458 | 0.987001 | ||||||||
\(873\) | 56.7266 | 1.91991 | ||||||||
\(874\) | −0.0381832 | −0.00129157 | ||||||||
\(875\) | 0.838674 | 0.0283523 | ||||||||
\(876\) | 50.2981 | 1.69942 | ||||||||
\(877\) | −24.1790 | −0.816467 | −0.408234 | − | 0.912877i | \(-0.633855\pi\) | ||||
−0.408234 | + | 0.912877i | \(0.633855\pi\) | |||||||
\(878\) | 30.8276 | 1.04038 | ||||||||
\(879\) | 30.3120 | 1.02240 | ||||||||
\(880\) | −0.0411347 | −0.00138665 | ||||||||
\(881\) | −6.03785 | −0.203420 | −0.101710 | − | 0.994814i | \(-0.532431\pi\) | ||||
−0.101710 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(882\) | 5.96007 | 0.200686 | ||||||||
\(883\) | 40.6679 | 1.36858 | 0.684292 | − | 0.729208i | \(-0.260111\pi\) | ||||
0.684292 | + | 0.729208i | \(0.260111\pi\) | |||||||
\(884\) | −25.3587 | −0.852904 | ||||||||
\(885\) | −0.368287 | −0.0123798 | ||||||||
\(886\) | 12.0814 | 0.405883 | ||||||||
\(887\) | 8.68207 | 0.291515 | 0.145758 | − | 0.989320i | \(-0.453438\pi\) | ||||
0.145758 | + | 0.989320i | \(0.453438\pi\) | |||||||
\(888\) | 19.5053 | 0.654554 | ||||||||
\(889\) | 60.9733 | 2.04498 | ||||||||
\(890\) | −0.533418 | −0.0178802 | ||||||||
\(891\) | 4.39917 | 0.147378 | ||||||||
\(892\) | −72.7758 | −2.43671 | ||||||||
\(893\) | −0.100965 | −0.00337865 | ||||||||
\(894\) | −22.1766 | −0.741697 | ||||||||
\(895\) | 0.432822 | 0.0144676 | ||||||||
\(896\) | −39.9594 | −1.33495 | ||||||||
\(897\) | −15.9509 | −0.532585 | ||||||||
\(898\) | −23.4123 | −0.781279 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −59.8711 | −1.99570 | ||||||||
\(901\) | −27.4694 | −0.915137 | ||||||||
\(902\) | −14.9729 | −0.498542 | ||||||||
\(903\) | −33.2318 | −1.10588 | ||||||||
\(904\) | 34.0066 | 1.13104 | ||||||||
\(905\) | 0.763178 | 0.0253689 | ||||||||
\(906\) | 116.254 | 3.86228 | ||||||||
\(907\) | 25.8588 | 0.858627 | 0.429313 | − | 0.903156i | \(-0.358756\pi\) | ||||
0.429313 | + | 0.903156i | \(0.358756\pi\) | |||||||
\(908\) | 31.8976 | 1.05856 | ||||||||
\(909\) | −59.1924 | −1.96329 | ||||||||
\(910\) | 0.545743 | 0.0180912 | ||||||||
\(911\) | 32.9864 | 1.09289 | 0.546444 | − | 0.837496i | \(-0.315981\pi\) | ||||
0.546444 | + | 0.837496i | \(0.315981\pi\) | |||||||
\(912\) | 0.0306405 | 0.00101461 | ||||||||
\(913\) | 8.21870 | 0.271999 | ||||||||
\(914\) | −8.35534 | −0.276370 | ||||||||
\(915\) | 0.198388 | 0.00655851 | ||||||||
\(916\) | −14.0064 | −0.462785 | ||||||||
\(917\) | −9.50145 | −0.313766 | ||||||||
\(918\) | −19.6070 | −0.647126 | ||||||||
\(919\) | −7.22039 | −0.238179 | −0.119089 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119089 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(920\) | 0.124274 | 0.00409719 | ||||||||
\(921\) | 72.3181 | 2.38296 | ||||||||
\(922\) | −50.1823 | −1.65266 | ||||||||
\(923\) | −3.44672 | −0.113450 | ||||||||
\(924\) | 21.4679 | 0.706243 | ||||||||
\(925\) | 18.1536 | 0.596886 | ||||||||
\(926\) | −45.3047 | −1.48881 | ||||||||
\(927\) | −40.0001 | −1.31377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.2378 | −0.696790 | −0.348395 | − | 0.937348i | \(-0.613273\pi\) | ||||
−0.348395 | + | 0.937348i | \(0.613273\pi\) | |||||||
\(930\) | 1.51709 | 0.0497475 | ||||||||
\(931\) | 0.00553066 | 0.000181260 0 | ||||||||
\(932\) | −31.4520 | −1.03024 | ||||||||
\(933\) | −6.04426 | −0.197880 | ||||||||
\(934\) | 12.0612 | 0.394655 | ||||||||
\(935\) | 0.0900036 | 0.00294343 | ||||||||
\(936\) | −24.3452 | −0.795748 | ||||||||
\(937\) | 20.8523 | 0.681216 | 0.340608 | − | 0.940205i | \(-0.389367\pi\) | ||||
0.340608 | + | 0.940205i | \(0.389367\pi\) | |||||||
\(938\) | 33.8114 | 1.10398 | ||||||||
\(939\) | 53.2486 | 1.73770 | ||||||||
\(940\) | 1.05183 | 0.0343069 | ||||||||
\(941\) | −2.68677 | −0.0875863 | −0.0437932 | − | 0.999041i | \(-0.513944\pi\) | ||||
−0.0437932 | + | 0.999041i | \(0.513944\pi\) | |||||||
\(942\) | 104.078 | 3.39106 | ||||||||
\(943\) | −13.7586 | −0.448041 | ||||||||
\(944\) | 6.17759 | 0.201063 | ||||||||
\(945\) | 0.250038 | 0.00813374 | ||||||||
\(946\) | −9.97588 | −0.324344 | ||||||||
\(947\) | 55.6323 | 1.80781 | 0.903903 | − | 0.427737i | \(-0.140689\pi\) | ||||
0.903903 | + | 0.427737i | \(0.140689\pi\) | |||||||
\(948\) | 122.961 | 3.99360 | ||||||||
\(949\) | 19.0352 | 0.617910 | ||||||||
\(950\) | −0.0937581 | −0.00304191 | ||||||||
\(951\) | 55.7808 | 1.80882 | ||||||||
\(952\) | 16.5347 | 0.535894 | ||||||||
\(953\) | −7.95601 | −0.257721 | −0.128860 | − | 0.991663i | \(-0.541132\pi\) | ||||
−0.128860 | + | 0.991663i | \(0.541132\pi\) | |||||||
\(954\) | −84.4121 | −2.73294 | ||||||||
\(955\) | 0.293556 | 0.00949926 | ||||||||
\(956\) | 61.3271 | 1.98346 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.04342 | 0.0983286 | ||||||||
\(959\) | 26.9655 | 0.870761 | ||||||||
\(960\) | −1.04082 | −0.0335922 | ||||||||
\(961\) | 40.6670 | 1.31184 | ||||||||
\(962\) | 23.6280 | 0.761797 | ||||||||
\(963\) | −21.3322 | −0.687421 | ||||||||
\(964\) | −65.3678 | −2.10536 | ||||||||
\(965\) | 0.215568 | 0.00693938 | ||||||||
\(966\) | 33.2908 | 1.07112 | ||||||||
\(967\) | −25.1953 | −0.810227 | −0.405113 | − | 0.914266i | \(-0.632768\pi\) | ||||
−0.405113 | + | 0.914266i | \(0.632768\pi\) | |||||||
\(968\) | 2.01335 | 0.0647115 | ||||||||
\(969\) | −0.0670421 | −0.00215370 | ||||||||
\(970\) | −0.925454 | −0.0297145 | ||||||||
\(971\) | −37.9104 | −1.21660 | −0.608301 | − | 0.793706i | \(-0.708149\pi\) | ||||
−0.608301 | + | 0.793706i | \(0.708149\pi\) | |||||||
\(972\) | 60.1512 | 1.92935 | ||||||||
\(973\) | −16.8432 | −0.539968 | ||||||||
\(974\) | −23.3215 | −0.747270 | ||||||||
\(975\) | −39.1671 | −1.25435 | ||||||||
\(976\) | −3.32773 | −0.106518 | ||||||||
\(977\) | 35.7237 | 1.14290 | 0.571451 | − | 0.820636i | \(-0.306381\pi\) | ||||
0.571451 | + | 0.820636i | \(0.306381\pi\) | |||||||
\(978\) | 95.1667 | 3.04310 | ||||||||
\(979\) | −7.94101 | −0.253796 | ||||||||
\(980\) | −0.0576174 | −0.00184052 | ||||||||
\(981\) | 59.6047 | 1.90303 | ||||||||
\(982\) | −32.1416 | −1.02568 | ||||||||
\(983\) | 20.9846 | 0.669304 | 0.334652 | − | 0.942342i | \(-0.391381\pi\) | ||||
0.334652 | + | 0.942342i | \(0.391381\pi\) | |||||||
\(984\) | −36.2995 | −1.15719 | ||||||||
\(985\) | −0.518407 | −0.0165178 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 88.0282 | 2.80197 | ||||||||
\(988\) | −0.0723116 | −0.00230054 | ||||||||
\(989\) | −9.16686 | −0.291489 | ||||||||
\(990\) | 0.276577 | 0.00879019 | ||||||||
\(991\) | 0.284262 | 0.00902987 | 0.00451494 | − | 0.999990i | \(-0.498563\pi\) | ||||
0.00451494 | + | 0.999990i | \(0.498563\pi\) | |||||||
\(992\) | −59.5360 | −1.89027 | ||||||||
\(993\) | −22.0242 | −0.698917 | ||||||||
\(994\) | 7.19359 | 0.228167 | ||||||||
\(995\) | −0.0477108 | −0.00151253 | ||||||||
\(996\) | 63.7775 | 2.02087 | ||||||||
\(997\) | 17.3826 | 0.550511 | 0.275255 | − | 0.961371i | \(-0.411238\pi\) | ||||
0.275255 | + | 0.961371i | \(0.411238\pi\) | |||||||
\(998\) | 50.2678 | 1.59120 | ||||||||
\(999\) | 10.8254 | 0.342502 |
(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 | 9251.2.a.bb.1.35 | yes | 40 | |
29.28 | even | 2 | 9251.2.a.ba.1.6 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9251.2.a.ba.1.6 | ✓ | 40 | 29.28 | even | 2 | ||
9251.2.a.bb.1.35 | yes | 40 | 1.1 | even | 1 | trivial |