Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.454453 | −0.321347 | −0.160673 | − | 0.987008i | \(-0.551367\pi\) | ||||
−0.160673 | + | 0.987008i | \(0.551367\pi\) | |||||||
\(3\) | 2.93224 | 1.69293 | 0.846466 | − | 0.532443i | \(-0.178726\pi\) | ||||
0.846466 | + | 0.532443i | \(0.178726\pi\) | |||||||
\(4\) | −1.79347 | −0.896736 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.33257 | −0.544018 | ||||||||
\(7\) | 4.01407 | 1.51718 | 0.758588 | − | 0.651571i | \(-0.225890\pi\) | ||||
0.758588 | + | 0.651571i | \(0.225890\pi\) | |||||||
\(8\) | 1.72395 | 0.609510 | ||||||||
\(9\) | 5.59806 | 1.86602 | ||||||||
\(10\) | −0.454453 | −0.143711 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −5.25890 | −1.51811 | ||||||||
\(13\) | −2.54805 | −0.706702 | −0.353351 | − | 0.935491i | \(-0.614958\pi\) | ||||
−0.353351 | + | 0.935491i | \(0.614958\pi\) | |||||||
\(14\) | −1.82421 | −0.487539 | ||||||||
\(15\) | 2.93224 | 0.757102 | ||||||||
\(16\) | 2.80349 | 0.700872 | ||||||||
\(17\) | −3.98319 | −0.966066 | −0.483033 | − | 0.875602i | \(-0.660465\pi\) | ||||
−0.483033 | + | 0.875602i | \(0.660465\pi\) | |||||||
\(18\) | −2.54405 | −0.599639 | ||||||||
\(19\) | −5.22272 | −1.19817 | −0.599087 | − | 0.800684i | \(-0.704470\pi\) | ||||
−0.599087 | + | 0.800684i | \(0.704470\pi\) | |||||||
\(20\) | −1.79347 | −0.401033 | ||||||||
\(21\) | 11.7702 | 2.56847 | ||||||||
\(22\) | 0.454453 | 0.0968897 | ||||||||
\(23\) | 0.343009 | 0.0715223 | 0.0357612 | − | 0.999360i | \(-0.488614\pi\) | ||||
0.0357612 | + | 0.999360i | \(0.488614\pi\) | |||||||
\(24\) | 5.05506 | 1.03186 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.15797 | 0.227096 | ||||||||
\(27\) | 7.61814 | 1.46611 | ||||||||
\(28\) | −7.19912 | −1.36051 | ||||||||
\(29\) | 6.48025 | 1.20335 | 0.601676 | − | 0.798740i | \(-0.294500\pi\) | ||||
0.601676 | + | 0.798740i | \(0.294500\pi\) | |||||||
\(30\) | −1.33257 | −0.243292 | ||||||||
\(31\) | 7.89077 | 1.41722 | 0.708612 | − | 0.705598i | \(-0.249322\pi\) | ||||
0.708612 | + | 0.705598i | \(0.249322\pi\) | |||||||
\(32\) | −4.72196 | −0.834733 | ||||||||
\(33\) | −2.93224 | −0.510438 | ||||||||
\(34\) | 1.81017 | 0.310442 | ||||||||
\(35\) | 4.01407 | 0.678501 | ||||||||
\(36\) | −10.0400 | −1.67333 | ||||||||
\(37\) | 8.95232 | 1.47175 | 0.735876 | − | 0.677116i | \(-0.236770\pi\) | ||||
0.735876 | + | 0.677116i | \(0.236770\pi\) | |||||||
\(38\) | 2.37348 | 0.385030 | ||||||||
\(39\) | −7.47151 | −1.19640 | ||||||||
\(40\) | 1.72395 | 0.272581 | ||||||||
\(41\) | 4.00932 | 0.626151 | 0.313076 | − | 0.949728i | \(-0.398641\pi\) | ||||
0.313076 | + | 0.949728i | \(0.398641\pi\) | |||||||
\(42\) | −5.34902 | −0.825371 | ||||||||
\(43\) | −3.95029 | −0.602413 | −0.301207 | − | 0.953559i | \(-0.597389\pi\) | ||||
−0.301207 | + | 0.953559i | \(0.597389\pi\) | |||||||
\(44\) | 1.79347 | 0.270376 | ||||||||
\(45\) | 5.59806 | 0.834509 | ||||||||
\(46\) | −0.155881 | −0.0229835 | ||||||||
\(47\) | 4.50057 | 0.656476 | 0.328238 | − | 0.944595i | \(-0.393545\pi\) | ||||
0.328238 | + | 0.944595i | \(0.393545\pi\) | |||||||
\(48\) | 8.22051 | 1.18653 | ||||||||
\(49\) | 9.11274 | 1.30182 | ||||||||
\(50\) | −0.454453 | −0.0642694 | ||||||||
\(51\) | −11.6797 | −1.63549 | ||||||||
\(52\) | 4.56986 | 0.633725 | ||||||||
\(53\) | 0.587202 | 0.0806584 | 0.0403292 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403292 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(54\) | −3.46209 | −0.471130 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 6.92007 | 0.924733 | ||||||||
\(57\) | −15.3143 | −2.02843 | ||||||||
\(58\) | −2.94497 | −0.386694 | ||||||||
\(59\) | 11.5878 | 1.50860 | 0.754298 | − | 0.656532i | \(-0.227977\pi\) | ||||
0.754298 | + | 0.656532i | \(0.227977\pi\) | |||||||
\(60\) | −5.25890 | −0.678921 | ||||||||
\(61\) | 9.08260 | 1.16291 | 0.581454 | − | 0.813580i | \(-0.302484\pi\) | ||||
0.581454 | + | 0.813580i | \(0.302484\pi\) | |||||||
\(62\) | −3.58599 | −0.455421 | ||||||||
\(63\) | 22.4710 | 2.83108 | ||||||||
\(64\) | −3.46107 | −0.432633 | ||||||||
\(65\) | −2.54805 | −0.316047 | ||||||||
\(66\) | 1.33257 | 0.164028 | ||||||||
\(67\) | −3.80200 | −0.464489 | −0.232244 | − | 0.972657i | \(-0.574607\pi\) | ||||
−0.232244 | + | 0.972657i | \(0.574607\pi\) | |||||||
\(68\) | 7.14375 | 0.866307 | ||||||||
\(69\) | 1.00579 | 0.121082 | ||||||||
\(70\) | −1.82421 | −0.218034 | ||||||||
\(71\) | −0.695920 | −0.0825905 | −0.0412952 | − | 0.999147i | \(-0.513148\pi\) | ||||
−0.0412952 | + | 0.999147i | \(0.513148\pi\) | |||||||
\(72\) | 9.65080 | 1.13736 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | −4.06841 | −0.472943 | ||||||||
\(75\) | 2.93224 | 0.338586 | ||||||||
\(76\) | 9.36681 | 1.07445 | ||||||||
\(77\) | −4.01407 | −0.457445 | ||||||||
\(78\) | 3.39545 | 0.384459 | ||||||||
\(79\) | 10.3893 | 1.16889 | 0.584444 | − | 0.811434i | \(-0.301313\pi\) | ||||
0.584444 | + | 0.811434i | \(0.301313\pi\) | |||||||
\(80\) | 2.80349 | 0.313440 | ||||||||
\(81\) | 5.54408 | 0.616009 | ||||||||
\(82\) | −1.82205 | −0.201212 | ||||||||
\(83\) | −9.19674 | −1.00947 | −0.504737 | − | 0.863273i | \(-0.668410\pi\) | ||||
−0.504737 | + | 0.863273i | \(0.668410\pi\) | |||||||
\(84\) | −21.1096 | −2.30324 | ||||||||
\(85\) | −3.98319 | −0.432038 | ||||||||
\(86\) | 1.79522 | 0.193584 | ||||||||
\(87\) | 19.0017 | 2.03719 | ||||||||
\(88\) | −1.72395 | −0.183774 | ||||||||
\(89\) | 15.2413 | 1.61558 | 0.807789 | − | 0.589472i | \(-0.200664\pi\) | ||||
0.807789 | + | 0.589472i | \(0.200664\pi\) | |||||||
\(90\) | −2.54405 | −0.268167 | ||||||||
\(91\) | −10.2280 | −1.07219 | ||||||||
\(92\) | −0.615177 | −0.0641367 | ||||||||
\(93\) | 23.1377 | 2.39927 | ||||||||
\(94\) | −2.04530 | −0.210956 | ||||||||
\(95\) | −5.22272 | −0.535840 | ||||||||
\(96\) | −13.8460 | −1.41315 | ||||||||
\(97\) | −7.88949 | −0.801056 | −0.400528 | − | 0.916284i | \(-0.631173\pi\) | ||||
−0.400528 | + | 0.916284i | \(0.631173\pi\) | |||||||
\(98\) | −4.14131 | −0.418336 | ||||||||
\(99\) | −5.59806 | −0.562626 | ||||||||
\(100\) | −1.79347 | −0.179347 | ||||||||
\(101\) | 17.7507 | 1.76626 | 0.883131 | − | 0.469126i | \(-0.155431\pi\) | ||||
0.883131 | + | 0.469126i | \(0.155431\pi\) | |||||||
\(102\) | 5.30787 | 0.525558 | ||||||||
\(103\) | −14.1523 | −1.39446 | −0.697232 | − | 0.716846i | \(-0.745585\pi\) | ||||
−0.697232 | + | 0.716846i | \(0.745585\pi\) | |||||||
\(104\) | −4.39272 | −0.430742 | ||||||||
\(105\) | 11.7702 | 1.14866 | ||||||||
\(106\) | −0.266856 | −0.0259193 | ||||||||
\(107\) | 3.16194 | 0.305676 | 0.152838 | − | 0.988251i | \(-0.451159\pi\) | ||||
0.152838 | + | 0.988251i | \(0.451159\pi\) | |||||||
\(108\) | −13.6629 | −1.31472 | ||||||||
\(109\) | 2.34608 | 0.224714 | 0.112357 | − | 0.993668i | \(-0.464160\pi\) | ||||
0.112357 | + | 0.993668i | \(0.464160\pi\) | |||||||
\(110\) | 0.454453 | 0.0433304 | ||||||||
\(111\) | 26.2504 | 2.49158 | ||||||||
\(112\) | 11.2534 | 1.06335 | ||||||||
\(113\) | −7.71763 | −0.726013 | −0.363007 | − | 0.931787i | \(-0.618250\pi\) | ||||
−0.363007 | + | 0.931787i | \(0.618250\pi\) | |||||||
\(114\) | 6.95963 | 0.651829 | ||||||||
\(115\) | 0.343009 | 0.0319858 | ||||||||
\(116\) | −11.6222 | −1.07909 | ||||||||
\(117\) | −14.2641 | −1.31872 | ||||||||
\(118\) | −5.26609 | −0.484783 | ||||||||
\(119\) | −15.9888 | −1.46569 | ||||||||
\(120\) | 5.05506 | 0.461461 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.12761 | −0.373697 | ||||||||
\(123\) | 11.7563 | 1.06003 | ||||||||
\(124\) | −14.1519 | −1.27088 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −10.2120 | −0.909758 | ||||||||
\(127\) | 9.28633 | 0.824028 | 0.412014 | − | 0.911177i | \(-0.364825\pi\) | ||||
0.412014 | + | 0.911177i | \(0.364825\pi\) | |||||||
\(128\) | 11.0168 | 0.973758 | ||||||||
\(129\) | −11.5832 | −1.01984 | ||||||||
\(130\) | 1.15797 | 0.101561 | ||||||||
\(131\) | −19.0112 | −1.66102 | −0.830509 | − | 0.557006i | \(-0.811950\pi\) | ||||
−0.830509 | + | 0.557006i | \(0.811950\pi\) | |||||||
\(132\) | 5.25890 | 0.457729 | ||||||||
\(133\) | −20.9644 | −1.81784 | ||||||||
\(134\) | 1.72783 | 0.149262 | ||||||||
\(135\) | 7.61814 | 0.655665 | ||||||||
\(136\) | −6.86685 | −0.588827 | ||||||||
\(137\) | −1.59211 | −0.136023 | −0.0680115 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680115 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(138\) | −0.457083 | −0.0389095 | ||||||||
\(139\) | −14.9012 | −1.26390 | −0.631950 | − | 0.775009i | \(-0.717745\pi\) | ||||
−0.631950 | + | 0.775009i | \(0.717745\pi\) | |||||||
\(140\) | −7.19912 | −0.608437 | ||||||||
\(141\) | 13.1968 | 1.11137 | ||||||||
\(142\) | 0.316263 | 0.0265402 | ||||||||
\(143\) | 2.54805 | 0.213079 | ||||||||
\(144\) | 15.6941 | 1.30784 | ||||||||
\(145\) | 6.48025 | 0.538156 | ||||||||
\(146\) | 0.454453 | 0.0376108 | ||||||||
\(147\) | 26.7208 | 2.20389 | ||||||||
\(148\) | −16.0557 | −1.31977 | ||||||||
\(149\) | −20.0774 | −1.64480 | −0.822401 | − | 0.568909i | \(-0.807366\pi\) | ||||
−0.822401 | + | 0.568909i | \(0.807366\pi\) | |||||||
\(150\) | −1.33257 | −0.108804 | ||||||||
\(151\) | −15.8960 | −1.29360 | −0.646799 | − | 0.762661i | \(-0.723893\pi\) | ||||
−0.646799 | + | 0.762661i | \(0.723893\pi\) | |||||||
\(152\) | −9.00374 | −0.730300 | ||||||||
\(153\) | −22.2982 | −1.80270 | ||||||||
\(154\) | 1.82421 | 0.146999 | ||||||||
\(155\) | 7.89077 | 0.633802 | ||||||||
\(156\) | 13.3999 | 1.07285 | ||||||||
\(157\) | 19.3992 | 1.54822 | 0.774111 | − | 0.633050i | \(-0.218197\pi\) | ||||
0.774111 | + | 0.633050i | \(0.218197\pi\) | |||||||
\(158\) | −4.72145 | −0.375619 | ||||||||
\(159\) | 1.72182 | 0.136549 | ||||||||
\(160\) | −4.72196 | −0.373304 | ||||||||
\(161\) | 1.37686 | 0.108512 | ||||||||
\(162\) | −2.51953 | −0.197953 | ||||||||
\(163\) | −3.88963 | −0.304659 | −0.152330 | − | 0.988330i | \(-0.548678\pi\) | ||||
−0.152330 | + | 0.988330i | \(0.548678\pi\) | |||||||
\(164\) | −7.19061 | −0.561492 | ||||||||
\(165\) | −2.93224 | −0.228275 | ||||||||
\(166\) | 4.17949 | 0.324391 | ||||||||
\(167\) | 7.95012 | 0.615199 | 0.307599 | − | 0.951516i | \(-0.400474\pi\) | ||||
0.307599 | + | 0.951516i | \(0.400474\pi\) | |||||||
\(168\) | 20.2913 | 1.56551 | ||||||||
\(169\) | −6.50744 | −0.500572 | ||||||||
\(170\) | 1.81017 | 0.138834 | ||||||||
\(171\) | −29.2371 | −2.23582 | ||||||||
\(172\) | 7.08473 | 0.540206 | ||||||||
\(173\) | −19.6741 | −1.49579 | −0.747896 | − | 0.663816i | \(-0.768936\pi\) | ||||
−0.747896 | + | 0.663816i | \(0.768936\pi\) | |||||||
\(174\) | −8.63537 | −0.654646 | ||||||||
\(175\) | 4.01407 | 0.303435 | ||||||||
\(176\) | −2.80349 | −0.211321 | ||||||||
\(177\) | 33.9781 | 2.55395 | ||||||||
\(178\) | −6.92647 | −0.519161 | ||||||||
\(179\) | −15.8383 | −1.18381 | −0.591905 | − | 0.806008i | \(-0.701624\pi\) | ||||
−0.591905 | + | 0.806008i | \(0.701624\pi\) | |||||||
\(180\) | −10.0400 | −0.748335 | ||||||||
\(181\) | −8.72608 | −0.648604 | −0.324302 | − | 0.945954i | \(-0.605129\pi\) | ||||
−0.324302 | + | 0.945954i | \(0.605129\pi\) | |||||||
\(182\) | 4.64817 | 0.344545 | ||||||||
\(183\) | 26.6324 | 1.96872 | ||||||||
\(184\) | 0.591332 | 0.0435936 | ||||||||
\(185\) | 8.95232 | 0.658188 | ||||||||
\(186\) | −10.5150 | −0.770996 | ||||||||
\(187\) | 3.98319 | 0.291280 | ||||||||
\(188\) | −8.07165 | −0.588686 | ||||||||
\(189\) | 30.5797 | 2.22435 | ||||||||
\(190\) | 2.37348 | 0.172190 | ||||||||
\(191\) | 11.0526 | 0.799738 | 0.399869 | − | 0.916572i | \(-0.369056\pi\) | ||||
0.399869 | + | 0.916572i | \(0.369056\pi\) | |||||||
\(192\) | −10.1487 | −0.732419 | ||||||||
\(193\) | 1.62235 | 0.116779 | 0.0583895 | − | 0.998294i | \(-0.481403\pi\) | ||||
0.0583895 | + | 0.998294i | \(0.481403\pi\) | |||||||
\(194\) | 3.58540 | 0.257417 | ||||||||
\(195\) | −7.47151 | −0.535046 | ||||||||
\(196\) | −16.3435 | −1.16739 | ||||||||
\(197\) | 16.2364 | 1.15680 | 0.578399 | − | 0.815754i | \(-0.303678\pi\) | ||||
0.578399 | + | 0.815754i | \(0.303678\pi\) | |||||||
\(198\) | 2.54405 | 0.180798 | ||||||||
\(199\) | −20.4639 | −1.45065 | −0.725325 | − | 0.688407i | \(-0.758310\pi\) | ||||
−0.725325 | + | 0.688407i | \(0.758310\pi\) | |||||||
\(200\) | 1.72395 | 0.121902 | ||||||||
\(201\) | −11.1484 | −0.786348 | ||||||||
\(202\) | −8.06687 | −0.567583 | ||||||||
\(203\) | 26.0122 | 1.82570 | ||||||||
\(204\) | 20.9472 | 1.46660 | ||||||||
\(205\) | 4.00932 | 0.280023 | ||||||||
\(206\) | 6.43154 | 0.448106 | ||||||||
\(207\) | 1.92018 | 0.133462 | ||||||||
\(208\) | −7.14343 | −0.495308 | ||||||||
\(209\) | 5.22272 | 0.361263 | ||||||||
\(210\) | −5.34902 | −0.369117 | ||||||||
\(211\) | 16.9237 | 1.16508 | 0.582539 | − | 0.812803i | \(-0.302059\pi\) | ||||
0.582539 | + | 0.812803i | \(0.302059\pi\) | |||||||
\(212\) | −1.05313 | −0.0723294 | ||||||||
\(213\) | −2.04061 | −0.139820 | ||||||||
\(214\) | −1.43695 | −0.0982280 | ||||||||
\(215\) | −3.95029 | −0.269407 | ||||||||
\(216\) | 13.1333 | 0.893610 | ||||||||
\(217\) | 31.6741 | 2.15018 | ||||||||
\(218\) | −1.06618 | −0.0722111 | ||||||||
\(219\) | −2.93224 | −0.198143 | ||||||||
\(220\) | 1.79347 | 0.120916 | ||||||||
\(221\) | 10.1494 | 0.682721 | ||||||||
\(222\) | −11.9296 | −0.800660 | ||||||||
\(223\) | −10.2499 | −0.686387 | −0.343193 | − | 0.939265i | \(-0.611509\pi\) | ||||
−0.343193 | + | 0.939265i | \(0.611509\pi\) | |||||||
\(224\) | −18.9543 | −1.26644 | ||||||||
\(225\) | 5.59806 | 0.373204 | ||||||||
\(226\) | 3.50730 | 0.233302 | ||||||||
\(227\) | −20.5357 | −1.36300 | −0.681502 | − | 0.731816i | \(-0.738673\pi\) | ||||
−0.681502 | + | 0.731816i | \(0.738673\pi\) | |||||||
\(228\) | 27.4658 | 1.81897 | ||||||||
\(229\) | 8.20194 | 0.541999 | 0.271000 | − | 0.962579i | \(-0.412646\pi\) | ||||
0.271000 | + | 0.962579i | \(0.412646\pi\) | |||||||
\(230\) | −0.155881 | −0.0102785 | ||||||||
\(231\) | −11.7702 | −0.774424 | ||||||||
\(232\) | 11.1717 | 0.733456 | ||||||||
\(233\) | 17.8722 | 1.17085 | 0.585423 | − | 0.810728i | \(-0.300929\pi\) | ||||
0.585423 | + | 0.810728i | \(0.300929\pi\) | |||||||
\(234\) | 6.48238 | 0.423766 | ||||||||
\(235\) | 4.50057 | 0.293585 | ||||||||
\(236\) | −20.7823 | −1.35281 | ||||||||
\(237\) | 30.4640 | 1.97885 | ||||||||
\(238\) | 7.26616 | 0.470995 | ||||||||
\(239\) | 1.70551 | 0.110320 | 0.0551601 | − | 0.998478i | \(-0.482433\pi\) | ||||
0.0551601 | + | 0.998478i | \(0.482433\pi\) | |||||||
\(240\) | 8.22051 | 0.530632 | ||||||||
\(241\) | −14.1559 | −0.911863 | −0.455932 | − | 0.890015i | \(-0.650694\pi\) | ||||
−0.455932 | + | 0.890015i | \(0.650694\pi\) | |||||||
\(242\) | −0.454453 | −0.0292133 | ||||||||
\(243\) | −6.59782 | −0.423250 | ||||||||
\(244\) | −16.2894 | −1.04282 | ||||||||
\(245\) | 9.11274 | 0.582192 | ||||||||
\(246\) | −5.34269 | −0.340638 | ||||||||
\(247\) | 13.3078 | 0.846753 | ||||||||
\(248\) | 13.6033 | 0.863813 | ||||||||
\(249\) | −26.9671 | −1.70897 | ||||||||
\(250\) | −0.454453 | −0.0287421 | ||||||||
\(251\) | 6.81720 | 0.430298 | 0.215149 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215149 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(252\) | −40.3011 | −2.53873 | ||||||||
\(253\) | −0.343009 | −0.0215648 | ||||||||
\(254\) | −4.22020 | −0.264799 | ||||||||
\(255\) | −11.6797 | −0.731411 | ||||||||
\(256\) | 1.91551 | 0.119719 | ||||||||
\(257\) | 14.1277 | 0.881264 | 0.440632 | − | 0.897688i | \(-0.354754\pi\) | ||||
0.440632 | + | 0.897688i | \(0.354754\pi\) | |||||||
\(258\) | 5.26402 | 0.327724 | ||||||||
\(259\) | 35.9352 | 2.23291 | ||||||||
\(260\) | 4.56986 | 0.283411 | ||||||||
\(261\) | 36.2768 | 2.24548 | ||||||||
\(262\) | 8.63970 | 0.533763 | ||||||||
\(263\) | 10.9108 | 0.672787 | 0.336393 | − | 0.941722i | \(-0.390793\pi\) | ||||
0.336393 | + | 0.941722i | \(0.390793\pi\) | |||||||
\(264\) | −5.05506 | −0.311117 | ||||||||
\(265\) | 0.587202 | 0.0360716 | ||||||||
\(266\) | 9.52732 | 0.584157 | ||||||||
\(267\) | 44.6913 | 2.73506 | ||||||||
\(268\) | 6.81879 | 0.416524 | ||||||||
\(269\) | 28.5175 | 1.73874 | 0.869372 | − | 0.494158i | \(-0.164524\pi\) | ||||
0.869372 | + | 0.494158i | \(0.164524\pi\) | |||||||
\(270\) | −3.46209 | −0.210696 | ||||||||
\(271\) | 22.8996 | 1.39105 | 0.695526 | − | 0.718501i | \(-0.255172\pi\) | ||||
0.695526 | + | 0.718501i | \(0.255172\pi\) | |||||||
\(272\) | −11.1668 | −0.677089 | ||||||||
\(273\) | −29.9911 | −1.81515 | ||||||||
\(274\) | 0.723538 | 0.0437105 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −1.80385 | −0.108579 | ||||||||
\(277\) | 11.9686 | 0.719125 | 0.359562 | − | 0.933121i | \(-0.382926\pi\) | ||||
0.359562 | + | 0.933121i | \(0.382926\pi\) | |||||||
\(278\) | 6.77188 | 0.406150 | ||||||||
\(279\) | 44.1730 | 2.64457 | ||||||||
\(280\) | 6.92007 | 0.413553 | ||||||||
\(281\) | −13.0516 | −0.778595 | −0.389298 | − | 0.921112i | \(-0.627282\pi\) | ||||
−0.389298 | + | 0.921112i | \(0.627282\pi\) | |||||||
\(282\) | −5.99731 | −0.357135 | ||||||||
\(283\) | 19.1469 | 1.13816 | 0.569081 | − | 0.822281i | \(-0.307299\pi\) | ||||
0.569081 | + | 0.822281i | \(0.307299\pi\) | |||||||
\(284\) | 1.24811 | 0.0740619 | ||||||||
\(285\) | −15.3143 | −0.907141 | ||||||||
\(286\) | −1.15797 | −0.0684721 | ||||||||
\(287\) | 16.0937 | 0.949981 | ||||||||
\(288\) | −26.4338 | −1.55763 | ||||||||
\(289\) | −1.13417 | −0.0667156 | ||||||||
\(290\) | −2.94497 | −0.172935 | ||||||||
\(291\) | −23.1339 | −1.35613 | ||||||||
\(292\) | 1.79347 | 0.104955 | ||||||||
\(293\) | −26.5060 | −1.54850 | −0.774249 | − | 0.632882i | \(-0.781872\pi\) | ||||
−0.774249 | + | 0.632882i | \(0.781872\pi\) | |||||||
\(294\) | −12.1433 | −0.708214 | ||||||||
\(295\) | 11.5878 | 0.674665 | ||||||||
\(296\) | 15.4334 | 0.897048 | ||||||||
\(297\) | −7.61814 | −0.442050 | ||||||||
\(298\) | 9.12421 | 0.528552 | ||||||||
\(299\) | −0.874004 | −0.0505450 | ||||||||
\(300\) | −5.25890 | −0.303623 | ||||||||
\(301\) | −15.8567 | −0.913966 | ||||||||
\(302\) | 7.22398 | 0.415693 | ||||||||
\(303\) | 52.0494 | 2.99016 | ||||||||
\(304\) | −14.6418 | −0.839767 | ||||||||
\(305\) | 9.08260 | 0.520068 | ||||||||
\(306\) | 10.1335 | 0.579291 | ||||||||
\(307\) | −18.8383 | −1.07516 | −0.537581 | − | 0.843212i | \(-0.680662\pi\) | ||||
−0.537581 | + | 0.843212i | \(0.680662\pi\) | |||||||
\(308\) | 7.19912 | 0.410208 | ||||||||
\(309\) | −41.4979 | −2.36073 | ||||||||
\(310\) | −3.58599 | −0.203670 | ||||||||
\(311\) | −4.77177 | −0.270582 | −0.135291 | − | 0.990806i | \(-0.543197\pi\) | ||||
−0.135291 | + | 0.990806i | \(0.543197\pi\) | |||||||
\(312\) | −12.8805 | −0.729217 | ||||||||
\(313\) | −22.1675 | −1.25298 | −0.626490 | − | 0.779429i | \(-0.715509\pi\) | ||||
−0.626490 | + | 0.779429i | \(0.715509\pi\) | |||||||
\(314\) | −8.81601 | −0.497516 | ||||||||
\(315\) | 22.4710 | 1.26610 | ||||||||
\(316\) | −18.6329 | −1.04818 | ||||||||
\(317\) | −16.6837 | −0.937052 | −0.468526 | − | 0.883450i | \(-0.655215\pi\) | ||||
−0.468526 | + | 0.883450i | \(0.655215\pi\) | |||||||
\(318\) | −0.782487 | −0.0438797 | ||||||||
\(319\) | −6.48025 | −0.362825 | ||||||||
\(320\) | −3.46107 | −0.193480 | ||||||||
\(321\) | 9.27157 | 0.517489 | ||||||||
\(322\) | −0.625719 | −0.0348699 | ||||||||
\(323\) | 20.8031 | 1.15752 | ||||||||
\(324\) | −9.94316 | −0.552398 | ||||||||
\(325\) | −2.54805 | −0.141340 | ||||||||
\(326\) | 1.76765 | 0.0979012 | ||||||||
\(327\) | 6.87928 | 0.380425 | ||||||||
\(328\) | 6.91189 | 0.381645 | ||||||||
\(329\) | 18.0656 | 0.995989 | ||||||||
\(330\) | 1.33257 | 0.0733554 | ||||||||
\(331\) | −28.6451 | −1.57448 | −0.787239 | − | 0.616648i | \(-0.788490\pi\) | ||||
−0.787239 | + | 0.616648i | \(0.788490\pi\) | |||||||
\(332\) | 16.4941 | 0.905231 | ||||||||
\(333\) | 50.1156 | 2.74632 | ||||||||
\(334\) | −3.61296 | −0.197692 | ||||||||
\(335\) | −3.80200 | −0.207726 | ||||||||
\(336\) | 32.9977 | 1.80017 | ||||||||
\(337\) | −16.8036 | −0.915350 | −0.457675 | − | 0.889120i | \(-0.651318\pi\) | ||||
−0.457675 | + | 0.889120i | \(0.651318\pi\) | |||||||
\(338\) | 2.95733 | 0.160857 | ||||||||
\(339\) | −22.6300 | −1.22909 | ||||||||
\(340\) | 7.14375 | 0.387424 | ||||||||
\(341\) | −7.89077 | −0.427309 | ||||||||
\(342\) | 13.2869 | 0.718473 | ||||||||
\(343\) | 8.48069 | 0.457914 | ||||||||
\(344\) | −6.81012 | −0.367177 | ||||||||
\(345\) | 1.00579 | 0.0541497 | ||||||||
\(346\) | 8.94094 | 0.480668 | ||||||||
\(347\) | −19.7364 | −1.05951 | −0.529753 | − | 0.848152i | \(-0.677715\pi\) | ||||
−0.529753 | + | 0.848152i | \(0.677715\pi\) | |||||||
\(348\) | −34.0790 | −1.82683 | ||||||||
\(349\) | −8.95453 | −0.479325 | −0.239663 | − | 0.970856i | \(-0.577037\pi\) | ||||
−0.239663 | + | 0.970856i | \(0.577037\pi\) | |||||||
\(350\) | −1.82421 | −0.0975079 | ||||||||
\(351\) | −19.4114 | −1.03610 | ||||||||
\(352\) | 4.72196 | 0.251681 | ||||||||
\(353\) | −14.6499 | −0.779735 | −0.389867 | − | 0.920871i | \(-0.627479\pi\) | ||||
−0.389867 | + | 0.920871i | \(0.627479\pi\) | |||||||
\(354\) | −15.4415 | −0.820704 | ||||||||
\(355\) | −0.695920 | −0.0369356 | ||||||||
\(356\) | −27.3349 | −1.44875 | ||||||||
\(357\) | −46.8831 | −2.48132 | ||||||||
\(358\) | 7.19776 | 0.380413 | ||||||||
\(359\) | −28.2818 | −1.49265 | −0.746327 | − | 0.665579i | \(-0.768185\pi\) | ||||
−0.746327 | + | 0.665579i | \(0.768185\pi\) | |||||||
\(360\) | 9.65080 | 0.508642 | ||||||||
\(361\) | 8.27684 | 0.435623 | ||||||||
\(362\) | 3.96559 | 0.208427 | ||||||||
\(363\) | 2.93224 | 0.153903 | ||||||||
\(364\) | 18.3437 | 0.961472 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −12.1032 | −0.632643 | ||||||||
\(367\) | −6.95945 | −0.363280 | −0.181640 | − | 0.983365i | \(-0.558141\pi\) | ||||
−0.181640 | + | 0.983365i | \(0.558141\pi\) | |||||||
\(368\) | 0.961622 | 0.0501280 | ||||||||
\(369\) | 22.4444 | 1.16841 | ||||||||
\(370\) | −4.06841 | −0.211507 | ||||||||
\(371\) | 2.35707 | 0.122373 | ||||||||
\(372\) | −41.4968 | −2.15151 | ||||||||
\(373\) | −14.9021 | −0.771600 | −0.385800 | − | 0.922583i | \(-0.626074\pi\) | ||||
−0.385800 | + | 0.922583i | \(0.626074\pi\) | |||||||
\(374\) | −1.81017 | −0.0936019 | ||||||||
\(375\) | 2.93224 | 0.151420 | ||||||||
\(376\) | 7.75878 | 0.400129 | ||||||||
\(377\) | −16.5120 | −0.850412 | ||||||||
\(378\) | −13.8971 | −0.714787 | ||||||||
\(379\) | 30.8831 | 1.58636 | 0.793180 | − | 0.608987i | \(-0.208424\pi\) | ||||
0.793180 | + | 0.608987i | \(0.208424\pi\) | |||||||
\(380\) | 9.36681 | 0.480507 | ||||||||
\(381\) | 27.2298 | 1.39502 | ||||||||
\(382\) | −5.02289 | −0.256993 | ||||||||
\(383\) | 30.5292 | 1.55997 | 0.779985 | − | 0.625798i | \(-0.215226\pi\) | ||||
0.779985 | + | 0.625798i | \(0.215226\pi\) | |||||||
\(384\) | 32.3040 | 1.64851 | ||||||||
\(385\) | −4.01407 | −0.204576 | ||||||||
\(386\) | −0.737280 | −0.0375266 | ||||||||
\(387\) | −22.1139 | −1.12411 | ||||||||
\(388\) | 14.1496 | 0.718336 | ||||||||
\(389\) | 21.1418 | 1.07193 | 0.535965 | − | 0.844240i | \(-0.319948\pi\) | ||||
0.535965 | + | 0.844240i | \(0.319948\pi\) | |||||||
\(390\) | 3.39545 | 0.171935 | ||||||||
\(391\) | −1.36627 | −0.0690953 | ||||||||
\(392\) | 15.7100 | 0.793473 | ||||||||
\(393\) | −55.7455 | −2.81199 | ||||||||
\(394\) | −7.37870 | −0.371734 | ||||||||
\(395\) | 10.3893 | 0.522743 | ||||||||
\(396\) | 10.0400 | 0.504527 | ||||||||
\(397\) | 9.35012 | 0.469269 | 0.234634 | − | 0.972084i | \(-0.424611\pi\) | ||||
0.234634 | + | 0.972084i | \(0.424611\pi\) | |||||||
\(398\) | 9.29989 | 0.466161 | ||||||||
\(399\) | −61.4726 | −3.07748 | ||||||||
\(400\) | 2.80349 | 0.140174 | ||||||||
\(401\) | 27.1940 | 1.35800 | 0.679002 | − | 0.734137i | \(-0.262413\pi\) | ||||
0.679002 | + | 0.734137i | \(0.262413\pi\) | |||||||
\(402\) | 5.06642 | 0.252690 | ||||||||
\(403\) | −20.1061 | −1.00156 | ||||||||
\(404\) | −31.8354 | −1.58387 | ||||||||
\(405\) | 5.54408 | 0.275488 | ||||||||
\(406\) | −11.8213 | −0.586682 | ||||||||
\(407\) | −8.95232 | −0.443750 | ||||||||
\(408\) | −20.1353 | −0.996845 | ||||||||
\(409\) | −16.9629 | −0.838762 | −0.419381 | − | 0.907810i | \(-0.637753\pi\) | ||||
−0.419381 | + | 0.907810i | \(0.637753\pi\) | |||||||
\(410\) | −1.82205 | −0.0899846 | ||||||||
\(411\) | −4.66845 | −0.230278 | ||||||||
\(412\) | 25.3817 | 1.25047 | ||||||||
\(413\) | 46.5140 | 2.28881 | ||||||||
\(414\) | −0.872634 | −0.0428876 | ||||||||
\(415\) | −9.19674 | −0.451450 | ||||||||
\(416\) | 12.0318 | 0.589908 | ||||||||
\(417\) | −43.6938 | −2.13970 | ||||||||
\(418\) | −2.37348 | −0.116091 | ||||||||
\(419\) | 5.54865 | 0.271069 | 0.135535 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135535 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(420\) | −21.1096 | −1.03004 | ||||||||
\(421\) | 28.6696 | 1.39727 | 0.698637 | − | 0.715477i | \(-0.253790\pi\) | ||||
0.698637 | + | 0.715477i | \(0.253790\pi\) | |||||||
\(422\) | −7.69104 | −0.374394 | ||||||||
\(423\) | 25.1945 | 1.22500 | ||||||||
\(424\) | 1.01231 | 0.0491621 | ||||||||
\(425\) | −3.98319 | −0.193213 | ||||||||
\(426\) | 0.927360 | 0.0449307 | ||||||||
\(427\) | 36.4582 | 1.76433 | ||||||||
\(428\) | −5.67085 | −0.274111 | ||||||||
\(429\) | 7.47151 | 0.360728 | ||||||||
\(430\) | 1.79522 | 0.0865732 | ||||||||
\(431\) | 1.92806 | 0.0928715 | 0.0464357 | − | 0.998921i | \(-0.485214\pi\) | ||||
0.0464357 | + | 0.998921i | \(0.485214\pi\) | |||||||
\(432\) | 21.3574 | 1.02756 | ||||||||
\(433\) | −0.0632902 | −0.00304153 | −0.00152077 | − | 0.999999i | \(-0.500484\pi\) | ||||
−0.00152077 | + | 0.999999i | \(0.500484\pi\) | |||||||
\(434\) | −14.3944 | −0.690953 | ||||||||
\(435\) | 19.0017 | 0.911061 | ||||||||
\(436\) | −4.20763 | −0.201509 | ||||||||
\(437\) | −1.79144 | −0.0856962 | ||||||||
\(438\) | 1.33257 | 0.0636725 | ||||||||
\(439\) | −39.8008 | −1.89959 | −0.949794 | − | 0.312876i | \(-0.898708\pi\) | ||||
−0.949794 | + | 0.312876i | \(0.898708\pi\) | |||||||
\(440\) | −1.72395 | −0.0821863 | ||||||||
\(441\) | 51.0137 | 2.42922 | ||||||||
\(442\) | −4.61242 | −0.219390 | ||||||||
\(443\) | −33.6711 | −1.59976 | −0.799881 | − | 0.600159i | \(-0.795104\pi\) | ||||
−0.799881 | + | 0.600159i | \(0.795104\pi\) | |||||||
\(444\) | −47.0794 | −2.23429 | ||||||||
\(445\) | 15.2413 | 0.722508 | ||||||||
\(446\) | 4.65812 | 0.220568 | ||||||||
\(447\) | −58.8717 | −2.78454 | ||||||||
\(448\) | −13.8930 | −0.656381 | ||||||||
\(449\) | −35.7073 | −1.68513 | −0.842565 | − | 0.538595i | \(-0.818955\pi\) | ||||
−0.842565 | + | 0.538595i | \(0.818955\pi\) | |||||||
\(450\) | −2.54405 | −0.119928 | ||||||||
\(451\) | −4.00932 | −0.188792 | ||||||||
\(452\) | 13.8414 | 0.651043 | ||||||||
\(453\) | −46.6109 | −2.18997 | ||||||||
\(454\) | 9.33252 | 0.437997 | ||||||||
\(455\) | −10.2280 | −0.479498 | ||||||||
\(456\) | −26.4012 | −1.23635 | ||||||||
\(457\) | −17.1178 | −0.800737 | −0.400369 | − | 0.916354i | \(-0.631118\pi\) | ||||
−0.400369 | + | 0.916354i | \(0.631118\pi\) | |||||||
\(458\) | −3.72740 | −0.174170 | ||||||||
\(459\) | −30.3445 | −1.41636 | ||||||||
\(460\) | −0.615177 | −0.0286828 | ||||||||
\(461\) | 25.1811 | 1.17280 | 0.586399 | − | 0.810022i | \(-0.300545\pi\) | ||||
0.586399 | + | 0.810022i | \(0.300545\pi\) | |||||||
\(462\) | 5.34902 | 0.248859 | ||||||||
\(463\) | −9.26234 | −0.430458 | −0.215229 | − | 0.976564i | \(-0.569050\pi\) | ||||
−0.215229 | + | 0.976564i | \(0.569050\pi\) | |||||||
\(464\) | 18.1673 | 0.843397 | ||||||||
\(465\) | 23.1377 | 1.07298 | ||||||||
\(466\) | −8.12207 | −0.376247 | ||||||||
\(467\) | 14.4145 | 0.667024 | 0.333512 | − | 0.942746i | \(-0.391766\pi\) | ||||
0.333512 | + | 0.942746i | \(0.391766\pi\) | |||||||
\(468\) | 25.5823 | 1.18254 | ||||||||
\(469\) | −15.2615 | −0.704710 | ||||||||
\(470\) | −2.04530 | −0.0943426 | ||||||||
\(471\) | 56.8831 | 2.62104 | ||||||||
\(472\) | 19.9768 | 0.919505 | ||||||||
\(473\) | 3.95029 | 0.181634 | ||||||||
\(474\) | −13.8445 | −0.635897 | ||||||||
\(475\) | −5.22272 | −0.239635 | ||||||||
\(476\) | 28.6755 | 1.31434 | ||||||||
\(477\) | 3.28719 | 0.150510 | ||||||||
\(478\) | −0.775074 | −0.0354511 | ||||||||
\(479\) | 36.0074 | 1.64522 | 0.822609 | − | 0.568607i | \(-0.192517\pi\) | ||||
0.822609 | + | 0.568607i | \(0.192517\pi\) | |||||||
\(480\) | −13.8460 | −0.631978 | ||||||||
\(481\) | −22.8110 | −1.04009 | ||||||||
\(482\) | 6.43320 | 0.293024 | ||||||||
\(483\) | 4.03729 | 0.183703 | ||||||||
\(484\) | −1.79347 | −0.0815215 | ||||||||
\(485\) | −7.88949 | −0.358243 | ||||||||
\(486\) | 2.99840 | 0.136010 | ||||||||
\(487\) | 43.4785 | 1.97020 | 0.985100 | − | 0.171983i | \(-0.0550174\pi\) | ||||
0.985100 | + | 0.171983i | \(0.0550174\pi\) | |||||||
\(488\) | 15.6580 | 0.708804 | ||||||||
\(489\) | −11.4053 | −0.515767 | ||||||||
\(490\) | −4.14131 | −0.187085 | ||||||||
\(491\) | −15.4476 | −0.697141 | −0.348570 | − | 0.937283i | \(-0.613333\pi\) | ||||
−0.348570 | + | 0.937283i | \(0.613333\pi\) | |||||||
\(492\) | −21.0846 | −0.950569 | ||||||||
\(493\) | −25.8121 | −1.16252 | ||||||||
\(494\) | −6.04775 | −0.272101 | ||||||||
\(495\) | −5.59806 | −0.251614 | ||||||||
\(496\) | 22.1217 | 0.993293 | ||||||||
\(497\) | −2.79347 | −0.125304 | ||||||||
\(498\) | 12.2553 | 0.549172 | ||||||||
\(499\) | −11.4349 | −0.511899 | −0.255949 | − | 0.966690i | \(-0.582388\pi\) | ||||
−0.255949 | + | 0.966690i | \(0.582388\pi\) | |||||||
\(500\) | −1.79347 | −0.0802065 | ||||||||
\(501\) | 23.3117 | 1.04149 | ||||||||
\(502\) | −3.09810 | −0.138275 | ||||||||
\(503\) | 6.07764 | 0.270989 | 0.135494 | − | 0.990778i | \(-0.456738\pi\) | ||||
0.135494 | + | 0.990778i | \(0.456738\pi\) | |||||||
\(504\) | 38.7390 | 1.72557 | ||||||||
\(505\) | 17.7507 | 0.789897 | ||||||||
\(506\) | 0.155881 | 0.00692978 | ||||||||
\(507\) | −19.0814 | −0.847435 | ||||||||
\(508\) | −16.6548 | −0.738936 | ||||||||
\(509\) | −9.74848 | −0.432094 | −0.216047 | − | 0.976383i | \(-0.569316\pi\) | ||||
−0.216047 | + | 0.976383i | \(0.569316\pi\) | |||||||
\(510\) | 5.30787 | 0.235037 | ||||||||
\(511\) | −4.01407 | −0.177572 | ||||||||
\(512\) | −22.9041 | −1.01223 | ||||||||
\(513\) | −39.7875 | −1.75666 | ||||||||
\(514\) | −6.42039 | −0.283191 | ||||||||
\(515\) | −14.1523 | −0.623623 | ||||||||
\(516\) | 20.7742 | 0.914532 | ||||||||
\(517\) | −4.50057 | −0.197935 | ||||||||
\(518\) | −16.3309 | −0.717537 | ||||||||
\(519\) | −57.6892 | −2.53227 | ||||||||
\(520\) | −4.39272 | −0.192634 | ||||||||
\(521\) | 5.39978 | 0.236569 | 0.118284 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118284 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(522\) | −16.4861 | −0.721578 | ||||||||
\(523\) | −35.7850 | −1.56477 | −0.782383 | − | 0.622797i | \(-0.785996\pi\) | ||||
−0.782383 | + | 0.622797i | \(0.785996\pi\) | |||||||
\(524\) | 34.0961 | 1.48949 | ||||||||
\(525\) | 11.7702 | 0.513695 | ||||||||
\(526\) | −4.95843 | −0.216198 | ||||||||
\(527\) | −31.4305 | −1.36913 | ||||||||
\(528\) | −8.22051 | −0.357752 | ||||||||
\(529\) | −22.8823 | −0.994885 | ||||||||
\(530\) | −0.266856 | −0.0115915 | ||||||||
\(531\) | 64.8689 | 2.81507 | ||||||||
\(532\) | 37.5990 | 1.63012 | ||||||||
\(533\) | −10.2160 | −0.442502 | ||||||||
\(534\) | −20.3101 | −0.878904 | ||||||||
\(535\) | 3.16194 | 0.136702 | ||||||||
\(536\) | −6.55448 | −0.283110 | ||||||||
\(537\) | −46.4417 | −2.00411 | ||||||||
\(538\) | −12.9599 | −0.558740 | ||||||||
\(539\) | −9.11274 | −0.392514 | ||||||||
\(540\) | −13.6629 | −0.587959 | ||||||||
\(541\) | −2.55972 | −0.110051 | −0.0550256 | − | 0.998485i | \(-0.517524\pi\) | ||||
−0.0550256 | + | 0.998485i | \(0.517524\pi\) | |||||||
\(542\) | −10.4068 | −0.447010 | ||||||||
\(543\) | −25.5870 | −1.09804 | ||||||||
\(544\) | 18.8085 | 0.806408 | ||||||||
\(545\) | 2.34608 | 0.100495 | ||||||||
\(546\) | 13.6296 | 0.583291 | ||||||||
\(547\) | −1.16722 | −0.0499068 | −0.0249534 | − | 0.999689i | \(-0.507944\pi\) | ||||
−0.0249534 | + | 0.999689i | \(0.507944\pi\) | |||||||
\(548\) | 2.85540 | 0.121977 | ||||||||
\(549\) | 50.8449 | 2.17001 | ||||||||
\(550\) | 0.454453 | 0.0193779 | ||||||||
\(551\) | −33.8446 | −1.44183 | ||||||||
\(552\) | 1.73393 | 0.0738010 | ||||||||
\(553\) | 41.7034 | 1.77341 | ||||||||
\(554\) | −5.43918 | −0.231088 | ||||||||
\(555\) | 26.2504 | 1.11427 | ||||||||
\(556\) | 26.7248 | 1.13338 | ||||||||
\(557\) | −36.7799 | −1.55841 | −0.779207 | − | 0.626766i | \(-0.784378\pi\) | ||||
−0.779207 | + | 0.626766i | \(0.784378\pi\) | |||||||
\(558\) | −20.0746 | −0.849824 | ||||||||
\(559\) | 10.0655 | 0.425727 | ||||||||
\(560\) | 11.2534 | 0.475543 | ||||||||
\(561\) | 11.6797 | 0.493117 | ||||||||
\(562\) | 5.93135 | 0.250199 | ||||||||
\(563\) | 6.11013 | 0.257511 | 0.128756 | − | 0.991676i | \(-0.458902\pi\) | ||||
0.128756 | + | 0.991676i | \(0.458902\pi\) | |||||||
\(564\) | −23.6681 | −0.996605 | ||||||||
\(565\) | −7.71763 | −0.324683 | ||||||||
\(566\) | −8.70135 | −0.365745 | ||||||||
\(567\) | 22.2543 | 0.934594 | ||||||||
\(568\) | −1.19973 | −0.0503397 | ||||||||
\(569\) | −7.31923 | −0.306838 | −0.153419 | − | 0.988161i | \(-0.549028\pi\) | ||||
−0.153419 | + | 0.988161i | \(0.549028\pi\) | |||||||
\(570\) | 6.95963 | 0.291507 | ||||||||
\(571\) | 16.3404 | 0.683824 | 0.341912 | − | 0.939732i | \(-0.388926\pi\) | ||||
0.341912 | + | 0.939732i | \(0.388926\pi\) | |||||||
\(572\) | −4.56986 | −0.191075 | ||||||||
\(573\) | 32.4089 | 1.35390 | ||||||||
\(574\) | −7.31383 | −0.305273 | ||||||||
\(575\) | 0.343009 | 0.0143045 | ||||||||
\(576\) | −19.3753 | −0.807302 | ||||||||
\(577\) | 19.9481 | 0.830450 | 0.415225 | − | 0.909719i | \(-0.363703\pi\) | ||||
0.415225 | + | 0.909719i | \(0.363703\pi\) | |||||||
\(578\) | 0.515425 | 0.0214388 | ||||||||
\(579\) | 4.75712 | 0.197699 | ||||||||
\(580\) | −11.6222 | −0.482584 | ||||||||
\(581\) | −36.9163 | −1.53155 | ||||||||
\(582\) | 10.5133 | 0.435789 | ||||||||
\(583\) | −0.587202 | −0.0243194 | ||||||||
\(584\) | −1.72395 | −0.0713378 | ||||||||
\(585\) | −14.2641 | −0.589749 | ||||||||
\(586\) | 12.0457 | 0.497605 | ||||||||
\(587\) | −8.39196 | −0.346373 | −0.173187 | − | 0.984889i | \(-0.555406\pi\) | ||||
−0.173187 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(588\) | −47.9230 | −1.97631 | ||||||||
\(589\) | −41.2113 | −1.69808 | ||||||||
\(590\) | −5.26609 | −0.216801 | ||||||||
\(591\) | 47.6092 | 1.95838 | ||||||||
\(592\) | 25.0977 | 1.03151 | ||||||||
\(593\) | −37.2001 | −1.52763 | −0.763813 | − | 0.645438i | \(-0.776675\pi\) | ||||
−0.763813 | + | 0.645438i | \(0.776675\pi\) | |||||||
\(594\) | 3.46209 | 0.142051 | ||||||||
\(595\) | −15.9888 | −0.655477 | ||||||||
\(596\) | 36.0082 | 1.47495 | ||||||||
\(597\) | −60.0052 | −2.45585 | ||||||||
\(598\) | 0.397194 | 0.0162425 | ||||||||
\(599\) | −6.57215 | −0.268531 | −0.134265 | − | 0.990945i | \(-0.542867\pi\) | ||||
−0.134265 | + | 0.990945i | \(0.542867\pi\) | |||||||
\(600\) | 5.05506 | 0.206372 | ||||||||
\(601\) | −4.81474 | −0.196397 | −0.0981987 | − | 0.995167i | \(-0.531308\pi\) | ||||
−0.0981987 | + | 0.995167i | \(0.531308\pi\) | |||||||
\(602\) | 7.20613 | 0.293700 | ||||||||
\(603\) | −21.2838 | −0.866745 | ||||||||
\(604\) | 28.5090 | 1.16002 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −23.6540 | −0.960879 | ||||||||
\(607\) | 10.0570 | 0.408202 | 0.204101 | − | 0.978950i | \(-0.434573\pi\) | ||||
0.204101 | + | 0.978950i | \(0.434573\pi\) | |||||||
\(608\) | 24.6615 | 1.00016 | ||||||||
\(609\) | 76.2741 | 3.09078 | ||||||||
\(610\) | −4.12761 | −0.167122 | ||||||||
\(611\) | −11.4677 | −0.463933 | ||||||||
\(612\) | 39.9911 | 1.61655 | ||||||||
\(613\) | −31.3737 | −1.26717 | −0.633587 | − | 0.773672i | \(-0.718418\pi\) | ||||
−0.633587 | + | 0.773672i | \(0.718418\pi\) | |||||||
\(614\) | 8.56114 | 0.345500 | ||||||||
\(615\) | 11.7563 | 0.474061 | ||||||||
\(616\) | −6.92007 | −0.278818 | ||||||||
\(617\) | −13.9568 | −0.561878 | −0.280939 | − | 0.959726i | \(-0.590646\pi\) | ||||
−0.280939 | + | 0.959726i | \(0.590646\pi\) | |||||||
\(618\) | 18.8588 | 0.758614 | ||||||||
\(619\) | −25.5234 | −1.02587 | −0.512936 | − | 0.858427i | \(-0.671442\pi\) | ||||
−0.512936 | + | 0.858427i | \(0.671442\pi\) | |||||||
\(620\) | −14.1519 | −0.568353 | ||||||||
\(621\) | 2.61309 | 0.104860 | ||||||||
\(622\) | 2.16855 | 0.0869508 | ||||||||
\(623\) | 61.1797 | 2.45111 | ||||||||
\(624\) | −20.9463 | −0.838522 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0741 | 0.402641 | ||||||||
\(627\) | 15.3143 | 0.611594 | ||||||||
\(628\) | −34.7919 | −1.38835 | ||||||||
\(629\) | −35.6588 | −1.42181 | ||||||||
\(630\) | −10.2120 | −0.406856 | ||||||||
\(631\) | 20.6445 | 0.821846 | 0.410923 | − | 0.911670i | \(-0.365206\pi\) | ||||
0.410923 | + | 0.911670i | \(0.365206\pi\) | |||||||
\(632\) | 17.9107 | 0.712449 | ||||||||
\(633\) | 49.6245 | 1.97240 | ||||||||
\(634\) | 7.58197 | 0.301119 | ||||||||
\(635\) | 9.28633 | 0.368517 | ||||||||
\(636\) | −3.08804 | −0.122449 | ||||||||
\(637\) | −23.2197 | −0.919999 | ||||||||
\(638\) | 2.94497 | 0.116592 | ||||||||
\(639\) | −3.89580 | −0.154115 | ||||||||
\(640\) | 11.0168 | 0.435478 | ||||||||
\(641\) | 45.3629 | 1.79173 | 0.895863 | − | 0.444330i | \(-0.146558\pi\) | ||||
0.895863 | + | 0.444330i | \(0.146558\pi\) | |||||||
\(642\) | −4.21349 | −0.166293 | ||||||||
\(643\) | 45.4885 | 1.79389 | 0.896946 | − | 0.442140i | \(-0.145781\pi\) | ||||
0.896946 | + | 0.442140i | \(0.145781\pi\) | |||||||
\(644\) | −2.46936 | −0.0973065 | ||||||||
\(645\) | −11.5832 | −0.456088 | ||||||||
\(646\) | −9.45404 | −0.371964 | ||||||||
\(647\) | −8.30027 | −0.326317 | −0.163159 | − | 0.986600i | \(-0.552168\pi\) | ||||
−0.163159 | + | 0.986600i | \(0.552168\pi\) | |||||||
\(648\) | 9.55775 | 0.375464 | ||||||||
\(649\) | −11.5878 | −0.454859 | ||||||||
\(650\) | 1.15797 | 0.0454193 | ||||||||
\(651\) | 92.8762 | 3.64011 | ||||||||
\(652\) | 6.97594 | 0.273199 | ||||||||
\(653\) | 21.0375 | 0.823263 | 0.411631 | − | 0.911350i | \(-0.364959\pi\) | ||||
0.411631 | + | 0.911350i | \(0.364959\pi\) | |||||||
\(654\) | −3.12631 | −0.122248 | ||||||||
\(655\) | −19.0112 | −0.742829 | ||||||||
\(656\) | 11.2401 | 0.438852 | ||||||||
\(657\) | −5.59806 | −0.218401 | ||||||||
\(658\) | −8.20997 | −0.320058 | ||||||||
\(659\) | −20.9096 | −0.814522 | −0.407261 | − | 0.913312i | \(-0.633516\pi\) | ||||
−0.407261 | + | 0.913312i | \(0.633516\pi\) | |||||||
\(660\) | 5.25890 | 0.204702 | ||||||||
\(661\) | 8.89183 | 0.345852 | 0.172926 | − | 0.984935i | \(-0.444678\pi\) | ||||
0.172926 | + | 0.984935i | \(0.444678\pi\) | |||||||
\(662\) | 13.0179 | 0.505953 | ||||||||
\(663\) | 29.7605 | 1.15580 | ||||||||
\(664\) | −15.8548 | −0.615284 | ||||||||
\(665\) | −20.9644 | −0.812963 | ||||||||
\(666\) | −22.7752 | −0.882521 | ||||||||
\(667\) | 2.22279 | 0.0860666 | ||||||||
\(668\) | −14.2583 | −0.551671 | ||||||||
\(669\) | −30.0553 | −1.16201 | ||||||||
\(670\) | 1.72783 | 0.0667519 | ||||||||
\(671\) | −9.08260 | −0.350630 | ||||||||
\(672\) | −55.5786 | −2.14399 | ||||||||
\(673\) | 36.7588 | 1.41695 | 0.708474 | − | 0.705737i | \(-0.249384\pi\) | ||||
0.708474 | + | 0.705737i | \(0.249384\pi\) | |||||||
\(674\) | 7.63644 | 0.294145 | ||||||||
\(675\) | 7.61814 | 0.293222 | ||||||||
\(676\) | 11.6709 | 0.448881 | ||||||||
\(677\) | 4.83714 | 0.185906 | 0.0929532 | − | 0.995670i | \(-0.470369\pi\) | ||||
0.0929532 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(678\) | 10.2843 | 0.394965 | ||||||||
\(679\) | −31.6689 | −1.21534 | ||||||||
\(680\) | −6.86685 | −0.263332 | ||||||||
\(681\) | −60.2158 | −2.30747 | ||||||||
\(682\) | 3.58599 | 0.137314 | ||||||||
\(683\) | 11.8370 | 0.452929 | 0.226464 | − | 0.974019i | \(-0.427283\pi\) | ||||
0.226464 | + | 0.974019i | \(0.427283\pi\) | |||||||
\(684\) | 52.4360 | 2.00494 | ||||||||
\(685\) | −1.59211 | −0.0608313 | ||||||||
\(686\) | −3.85407 | −0.147149 | ||||||||
\(687\) | 24.0501 | 0.917568 | ||||||||
\(688\) | −11.0746 | −0.422215 | ||||||||
\(689\) | −1.49622 | −0.0570015 | ||||||||
\(690\) | −0.457083 | −0.0174008 | ||||||||
\(691\) | 9.08395 | 0.345570 | 0.172785 | − | 0.984960i | \(-0.444723\pi\) | ||||
0.172785 | + | 0.984960i | \(0.444723\pi\) | |||||||
\(692\) | 35.2849 | 1.34133 | ||||||||
\(693\) | −22.4710 | −0.853602 | ||||||||
\(694\) | 8.96927 | 0.340469 | ||||||||
\(695\) | −14.9012 | −0.565233 | ||||||||
\(696\) | 32.7581 | 1.24169 | ||||||||
\(697\) | −15.9699 | −0.604904 | ||||||||
\(698\) | 4.06941 | 0.154030 | ||||||||
\(699\) | 52.4056 | 1.98216 | ||||||||
\(700\) | −7.19912 | −0.272101 | ||||||||
\(701\) | 0.954313 | 0.0360439 | 0.0180219 | − | 0.999838i | \(-0.494263\pi\) | ||||
0.0180219 | + | 0.999838i | \(0.494263\pi\) | |||||||
\(702\) | 8.82157 | 0.332949 | ||||||||
\(703\) | −46.7555 | −1.76342 | ||||||||
\(704\) | 3.46107 | 0.130444 | ||||||||
\(705\) | 13.1968 | 0.497019 | ||||||||
\(706\) | 6.65769 | 0.250565 | ||||||||
\(707\) | 71.2526 | 2.67973 | ||||||||
\(708\) | −60.9388 | −2.29022 | ||||||||
\(709\) | −31.6264 | −1.18776 | −0.593878 | − | 0.804555i | \(-0.702404\pi\) | ||||
−0.593878 | + | 0.804555i | \(0.702404\pi\) | |||||||
\(710\) | 0.316263 | 0.0118691 | ||||||||
\(711\) | 58.1600 | 2.18117 | ||||||||
\(712\) | 26.2754 | 0.984711 | ||||||||
\(713\) | 2.70661 | 0.101363 | ||||||||
\(714\) | 21.3062 | 0.797363 | ||||||||
\(715\) | 2.54805 | 0.0952917 | ||||||||
\(716\) | 28.4055 | 1.06156 | ||||||||
\(717\) | 5.00097 | 0.186765 | ||||||||
\(718\) | 12.8527 | 0.479660 | ||||||||
\(719\) | 4.03832 | 0.150604 | 0.0753020 | − | 0.997161i | \(-0.476008\pi\) | ||||
0.0753020 | + | 0.997161i | \(0.476008\pi\) | |||||||
\(720\) | 15.6941 | 0.584884 | ||||||||
\(721\) | −56.8081 | −2.11565 | ||||||||
\(722\) | −3.76143 | −0.139986 | ||||||||
\(723\) | −41.5086 | −1.54372 | ||||||||
\(724\) | 15.6500 | 0.581627 | ||||||||
\(725\) | 6.48025 | 0.240671 | ||||||||
\(726\) | −1.33257 | −0.0494562 | ||||||||
\(727\) | −15.1500 | −0.561882 | −0.280941 | − | 0.959725i | \(-0.590646\pi\) | ||||
−0.280941 | + | 0.959725i | \(0.590646\pi\) | |||||||
\(728\) | −17.6327 | −0.653511 | ||||||||
\(729\) | −35.9787 | −1.33254 | ||||||||
\(730\) | 0.454453 | 0.0168201 | ||||||||
\(731\) | 15.7348 | 0.581971 | ||||||||
\(732\) | −47.7645 | −1.76543 | ||||||||
\(733\) | 32.9810 | 1.21818 | 0.609091 | − | 0.793101i | \(-0.291535\pi\) | ||||
0.609091 | + | 0.793101i | \(0.291535\pi\) | |||||||
\(734\) | 3.16274 | 0.116739 | ||||||||
\(735\) | 26.7208 | 0.985611 | ||||||||
\(736\) | −1.61968 | −0.0597020 | ||||||||
\(737\) | 3.80200 | 0.140049 | ||||||||
\(738\) | −10.1999 | −0.375465 | ||||||||
\(739\) | 33.4284 | 1.22968 | 0.614842 | − | 0.788650i | \(-0.289220\pi\) | ||||
0.614842 | + | 0.788650i | \(0.289220\pi\) | |||||||
\(740\) | −16.0557 | −0.590221 | ||||||||
\(741\) | 39.0216 | 1.43349 | ||||||||
\(742\) | −1.07118 | −0.0393242 | ||||||||
\(743\) | −11.0010 | −0.403589 | −0.201794 | − | 0.979428i | \(-0.564677\pi\) | ||||
−0.201794 | + | 0.979428i | \(0.564677\pi\) | |||||||
\(744\) | 39.8883 | 1.46238 | ||||||||
\(745\) | −20.0774 | −0.735577 | ||||||||
\(746\) | 6.77229 | 0.247951 | ||||||||
\(747\) | −51.4839 | −1.88370 | ||||||||
\(748\) | −7.14375 | −0.261201 | ||||||||
\(749\) | 12.6922 | 0.463764 | ||||||||
\(750\) | −1.33257 | −0.0486585 | ||||||||
\(751\) | −9.50545 | −0.346859 | −0.173429 | − | 0.984846i | \(-0.555485\pi\) | ||||
−0.173429 | + | 0.984846i | \(0.555485\pi\) | |||||||
\(752\) | 12.6173 | 0.460106 | ||||||||
\(753\) | 19.9897 | 0.728465 | ||||||||
\(754\) | 7.50393 | 0.273277 | ||||||||
\(755\) | −15.8960 | −0.578514 | ||||||||
\(756\) | −54.8439 | −1.99465 | ||||||||
\(757\) | −45.7176 | −1.66163 | −0.830817 | − | 0.556546i | \(-0.812126\pi\) | ||||
−0.830817 | + | 0.556546i | \(0.812126\pi\) | |||||||
\(758\) | −14.0349 | −0.509772 | ||||||||
\(759\) | −1.00579 | −0.0365077 | ||||||||
\(760\) | −9.00374 | −0.326600 | ||||||||
\(761\) | −44.6478 | −1.61848 | −0.809241 | − | 0.587477i | \(-0.800121\pi\) | ||||
−0.809241 | + | 0.587477i | \(0.800121\pi\) | |||||||
\(762\) | −12.3747 | −0.448287 | ||||||||
\(763\) | 9.41733 | 0.340930 | ||||||||
\(764\) | −19.8225 | −0.717154 | ||||||||
\(765\) | −22.2982 | −0.806191 | ||||||||
\(766\) | −13.8741 | −0.501292 | ||||||||
\(767\) | −29.5262 | −1.06613 | ||||||||
\(768\) | 5.61674 | 0.202677 | ||||||||
\(769\) | 26.5064 | 0.955844 | 0.477922 | − | 0.878402i | \(-0.341390\pi\) | ||||
0.477922 | + | 0.878402i | \(0.341390\pi\) | |||||||
\(770\) | 1.82421 | 0.0657398 | ||||||||
\(771\) | 41.4260 | 1.49192 | ||||||||
\(772\) | −2.90963 | −0.104720 | ||||||||
\(773\) | 23.9999 | 0.863217 | 0.431609 | − | 0.902061i | \(-0.357946\pi\) | ||||
0.431609 | + | 0.902061i | \(0.357946\pi\) | |||||||
\(774\) | 10.0497 | 0.361231 | ||||||||
\(775\) | 7.89077 | 0.283445 | ||||||||
\(776\) | −13.6011 | −0.488252 | ||||||||
\(777\) | 105.371 | 3.78016 | ||||||||
\(778\) | −9.60794 | −0.344461 | ||||||||
\(779\) | −20.9396 | −0.750239 | ||||||||
\(780\) | 13.3999 | 0.479795 | ||||||||
\(781\) | 0.695920 | 0.0249020 | ||||||||
\(782\) | 0.620906 | 0.0222036 | ||||||||
\(783\) | 49.3675 | 1.76425 | ||||||||
\(784\) | 25.5475 | 0.912410 | ||||||||
\(785\) | 19.3992 | 0.692386 | ||||||||
\(786\) | 25.3337 | 0.903624 | ||||||||
\(787\) | −44.6725 | −1.59240 | −0.796202 | − | 0.605031i | \(-0.793161\pi\) | ||||
−0.796202 | + | 0.605031i | \(0.793161\pi\) | |||||||
\(788\) | −29.1196 | −1.03734 | ||||||||
\(789\) | 31.9930 | 1.13898 | ||||||||
\(790\) | −4.72145 | −0.167982 | ||||||||
\(791\) | −30.9791 | −1.10149 | ||||||||
\(792\) | −9.65080 | −0.342926 | ||||||||
\(793\) | −23.1429 | −0.821829 | ||||||||
\(794\) | −4.24919 | −0.150798 | ||||||||
\(795\) | 1.72182 | 0.0610667 | ||||||||
\(796\) | 36.7015 | 1.30085 | ||||||||
\(797\) | 19.2437 | 0.681646 | 0.340823 | − | 0.940128i | \(-0.389294\pi\) | ||||
0.340823 | + | 0.940128i | \(0.389294\pi\) | |||||||
\(798\) | 27.9364 | 0.988939 | ||||||||
\(799\) | −17.9266 | −0.634199 | ||||||||
\(800\) | −4.72196 | −0.166947 | ||||||||
\(801\) | 85.3219 | 3.01470 | ||||||||
\(802\) | −12.3584 | −0.436390 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 19.9944 | 0.705146 | ||||||||
\(805\) | 1.37686 | 0.0485280 | ||||||||
\(806\) | 9.13727 | 0.321847 | ||||||||
\(807\) | 83.6204 | 2.94358 | ||||||||
\(808\) | 30.6014 | 1.07655 | ||||||||
\(809\) | 47.5771 | 1.67272 | 0.836361 | − | 0.548180i | \(-0.184679\pi\) | ||||
0.836361 | + | 0.548180i | \(0.184679\pi\) | |||||||
\(810\) | −2.51953 | −0.0885271 | ||||||||
\(811\) | −18.4707 | −0.648593 | −0.324296 | − | 0.945956i | \(-0.605128\pi\) | ||||
−0.324296 | + | 0.945956i | \(0.605128\pi\) | |||||||
\(812\) | −46.6521 | −1.63717 | ||||||||
\(813\) | 67.1472 | 2.35496 | ||||||||
\(814\) | 4.06841 | 0.142598 | ||||||||
\(815\) | −3.88963 | −0.136248 | ||||||||
\(816\) | −32.7439 | −1.14627 | ||||||||
\(817\) | 20.6313 | 0.721796 | ||||||||
\(818\) | 7.70884 | 0.269533 | ||||||||
\(819\) | −57.2572 | −2.00073 | ||||||||
\(820\) | −7.19061 | −0.251107 | ||||||||
\(821\) | 9.00762 | 0.314368 | 0.157184 | − | 0.987569i | \(-0.449758\pi\) | ||||
0.157184 | + | 0.987569i | \(0.449758\pi\) | |||||||
\(822\) | 2.12159 | 0.0739990 | ||||||||
\(823\) | −38.4563 | −1.34050 | −0.670251 | − | 0.742135i | \(-0.733813\pi\) | ||||
−0.670251 | + | 0.742135i | \(0.733813\pi\) | |||||||
\(824\) | −24.3979 | −0.849940 | ||||||||
\(825\) | −2.93224 | −0.102088 | ||||||||
\(826\) | −21.1384 | −0.735500 | ||||||||
\(827\) | 18.5542 | 0.645192 | 0.322596 | − | 0.946537i | \(-0.395444\pi\) | ||||
0.322596 | + | 0.946537i | \(0.395444\pi\) | |||||||
\(828\) | −3.44380 | −0.119680 | ||||||||
\(829\) | −25.4625 | −0.884349 | −0.442174 | − | 0.896929i | \(-0.645793\pi\) | ||||
−0.442174 | + | 0.896929i | \(0.645793\pi\) | |||||||
\(830\) | 4.17949 | 0.145072 | ||||||||
\(831\) | 35.0949 | 1.21743 | ||||||||
\(832\) | 8.81897 | 0.305743 | ||||||||
\(833\) | −36.2978 | −1.25764 | ||||||||
\(834\) | 19.8568 | 0.687585 | ||||||||
\(835\) | 7.95012 | 0.275125 | ||||||||
\(836\) | −9.36681 | −0.323958 | ||||||||
\(837\) | 60.1130 | 2.07781 | ||||||||
\(838\) | −2.52160 | −0.0871072 | ||||||||
\(839\) | −23.2802 | −0.803722 | −0.401861 | − | 0.915701i | \(-0.631637\pi\) | ||||
−0.401861 | + | 0.915701i | \(0.631637\pi\) | |||||||
\(840\) | 20.2913 | 0.700118 | ||||||||
\(841\) | 12.9937 | 0.448058 | ||||||||
\(842\) | −13.0290 | −0.449009 | ||||||||
\(843\) | −38.2706 | −1.31811 | ||||||||
\(844\) | −30.3522 | −1.04477 | ||||||||
\(845\) | −6.50744 | −0.223863 | ||||||||
\(846\) | −11.4497 | −0.393649 | ||||||||
\(847\) | 4.01407 | 0.137925 | ||||||||
\(848\) | 1.64622 | 0.0565313 | ||||||||
\(849\) | 56.1433 | 1.92683 | ||||||||
\(850\) | 1.81017 | 0.0620885 | ||||||||
\(851\) | 3.07073 | 0.105263 | ||||||||
\(852\) | 3.65977 | 0.125382 | ||||||||
\(853\) | −6.18516 | −0.211776 | −0.105888 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105888 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(854\) | −16.5685 | −0.566963 | ||||||||
\(855\) | −29.2371 | −0.999888 | ||||||||
\(856\) | 5.45104 | 0.186313 | ||||||||
\(857\) | −19.3546 | −0.661139 | −0.330570 | − | 0.943782i | \(-0.607241\pi\) | ||||
−0.330570 | + | 0.943782i | \(0.607241\pi\) | |||||||
\(858\) | −3.39545 | −0.115919 | ||||||||
\(859\) | −6.42562 | −0.219239 | −0.109620 | − | 0.993974i | \(-0.534963\pi\) | ||||
−0.109620 | + | 0.993974i | \(0.534963\pi\) | |||||||
\(860\) | 7.08473 | 0.241587 | ||||||||
\(861\) | 47.1907 | 1.60825 | ||||||||
\(862\) | −0.876213 | −0.0298439 | ||||||||
\(863\) | 14.3184 | 0.487404 | 0.243702 | − | 0.969850i | \(-0.421638\pi\) | ||||
0.243702 | + | 0.969850i | \(0.421638\pi\) | |||||||
\(864\) | −35.9726 | −1.22381 | ||||||||
\(865\) | −19.6741 | −0.668939 | ||||||||
\(866\) | 0.0287624 | 0.000977387 0 | ||||||||
\(867\) | −3.32565 | −0.112945 | ||||||||
\(868\) | −56.8066 | −1.92814 | ||||||||
\(869\) | −10.3893 | −0.352433 | ||||||||
\(870\) | −8.63537 | −0.292767 | ||||||||
\(871\) | 9.68769 | 0.328255 | ||||||||
\(872\) | 4.04454 | 0.136965 | ||||||||
\(873\) | −44.1658 | −1.49479 | ||||||||
\(874\) | 0.814126 | 0.0275382 | ||||||||
\(875\) | 4.01407 | 0.135700 | ||||||||
\(876\) | 5.25890 | 0.177682 | ||||||||
\(877\) | 20.4040 | 0.688995 | 0.344497 | − | 0.938787i | \(-0.388049\pi\) | ||||
0.344497 | + | 0.938787i | \(0.388049\pi\) | |||||||
\(878\) | 18.0876 | 0.610427 | ||||||||
\(879\) | −77.7221 | −2.62150 | ||||||||
\(880\) | −2.80349 | −0.0945056 | ||||||||
\(881\) | 2.90247 | 0.0977867 | 0.0488934 | − | 0.998804i | \(-0.484431\pi\) | ||||
0.0488934 | + | 0.998804i | \(0.484431\pi\) | |||||||
\(882\) | −23.1833 | −0.780623 | ||||||||
\(883\) | 49.7621 | 1.67463 | 0.837314 | − | 0.546722i | \(-0.184125\pi\) | ||||
0.837314 | + | 0.546722i | \(0.184125\pi\) | |||||||
\(884\) | −18.2026 | −0.612221 | ||||||||
\(885\) | 33.9781 | 1.14216 | ||||||||
\(886\) | 15.3019 | 0.514078 | ||||||||
\(887\) | 32.3733 | 1.08699 | 0.543495 | − | 0.839413i | \(-0.317101\pi\) | ||||
0.543495 | + | 0.839413i | \(0.317101\pi\) | |||||||
\(888\) | 45.2545 | 1.51864 | ||||||||
\(889\) | 37.2760 | 1.25020 | ||||||||
\(890\) | −6.92647 | −0.232176 | ||||||||
\(891\) | −5.54408 | −0.185734 | ||||||||
\(892\) | 18.3830 | 0.615508 | ||||||||
\(893\) | −23.5052 | −0.786573 | ||||||||
\(894\) | 26.7544 | 0.894802 | ||||||||
\(895\) | −15.8383 | −0.529416 | ||||||||
\(896\) | 44.2223 | 1.47736 | ||||||||
\(897\) | −2.56279 | −0.0855692 | ||||||||
\(898\) | 16.2273 | 0.541511 | ||||||||
\(899\) | 51.1342 | 1.70542 | ||||||||
\(900\) | −10.0400 | −0.334665 | ||||||||
\(901\) | −2.33894 | −0.0779214 | ||||||||
\(902\) | 1.82205 | 0.0606676 | ||||||||
\(903\) | −46.4958 | −1.54728 | ||||||||
\(904\) | −13.3048 | −0.442513 | ||||||||
\(905\) | −8.72608 | −0.290065 | ||||||||
\(906\) | 21.1825 | 0.703741 | ||||||||
\(907\) | 6.24920 | 0.207501 | 0.103751 | − | 0.994603i | \(-0.466916\pi\) | ||||
0.103751 | + | 0.994603i | \(0.466916\pi\) | |||||||
\(908\) | 36.8302 | 1.22225 | ||||||||
\(909\) | 99.3696 | 3.29588 | ||||||||
\(910\) | 4.64817 | 0.154085 | ||||||||
\(911\) | 18.8447 | 0.624351 | 0.312176 | − | 0.950024i | \(-0.398942\pi\) | ||||
0.312176 | + | 0.950024i | \(0.398942\pi\) | |||||||
\(912\) | −42.9335 | −1.42167 | ||||||||
\(913\) | 9.19674 | 0.304368 | ||||||||
\(914\) | 7.77924 | 0.257314 | ||||||||
\(915\) | 26.6324 | 0.880440 | ||||||||
\(916\) | −14.7100 | −0.486031 | ||||||||
\(917\) | −76.3123 | −2.52005 | ||||||||
\(918\) | 13.7902 | 0.455143 | ||||||||
\(919\) | 33.0120 | 1.08897 | 0.544483 | − | 0.838772i | \(-0.316726\pi\) | ||||
0.544483 | + | 0.838772i | \(0.316726\pi\) | |||||||
\(920\) | 0.591332 | 0.0194956 | ||||||||
\(921\) | −55.2386 | −1.82017 | ||||||||
\(922\) | −11.4436 | −0.376875 | ||||||||
\(923\) | 1.77324 | 0.0583668 | ||||||||
\(924\) | 21.1096 | 0.694454 | ||||||||
\(925\) | 8.95232 | 0.294351 | ||||||||
\(926\) | 4.20930 | 0.138326 | ||||||||
\(927\) | −79.2252 | −2.60210 | ||||||||
\(928\) | −30.5995 | −1.00448 | ||||||||
\(929\) | 1.26418 | 0.0414764 | 0.0207382 | − | 0.999785i | \(-0.493398\pi\) | ||||
0.0207382 | + | 0.999785i | \(0.493398\pi\) | |||||||
\(930\) | −10.5150 | −0.344800 | ||||||||
\(931\) | −47.5933 | −1.55981 | ||||||||
\(932\) | −32.0533 | −1.04994 | ||||||||
\(933\) | −13.9920 | −0.458078 | ||||||||
\(934\) | −6.55072 | −0.214346 | ||||||||
\(935\) | 3.98319 | 0.130264 | ||||||||
\(936\) | −24.5907 | −0.803773 | ||||||||
\(937\) | 22.1573 | 0.723848 | 0.361924 | − | 0.932208i | \(-0.382120\pi\) | ||||
0.361924 | + | 0.932208i | \(0.382120\pi\) | |||||||
\(938\) | 6.93563 | 0.226456 | ||||||||
\(939\) | −65.0005 | −2.12121 | ||||||||
\(940\) | −8.07165 | −0.263268 | ||||||||
\(941\) | 2.99531 | 0.0976443 | 0.0488221 | − | 0.998807i | \(-0.484453\pi\) | ||||
0.0488221 | + | 0.998807i | \(0.484453\pi\) | |||||||
\(942\) | −25.8507 | −0.842261 | ||||||||
\(943\) | 1.37523 | 0.0447838 | ||||||||
\(944\) | 32.4861 | 1.05733 | ||||||||
\(945\) | 30.5797 | 0.994759 | ||||||||
\(946\) | −1.79522 | −0.0583676 | ||||||||
\(947\) | −30.1720 | −0.980459 | −0.490230 | − | 0.871593i | \(-0.663087\pi\) | ||||
−0.490230 | + | 0.871593i | \(0.663087\pi\) | |||||||
\(948\) | −54.6363 | −1.77451 | ||||||||
\(949\) | 2.54805 | 0.0827132 | ||||||||
\(950\) | 2.37348 | 0.0770059 | ||||||||
\(951\) | −48.9208 | −1.58637 | ||||||||
\(952\) | −27.5640 | −0.893354 | ||||||||
\(953\) | −30.0505 | −0.973432 | −0.486716 | − | 0.873560i | \(-0.661805\pi\) | ||||
−0.486716 | + | 0.873560i | \(0.661805\pi\) | |||||||
\(954\) | −1.49387 | −0.0483660 | ||||||||
\(955\) | 11.0526 | 0.357654 | ||||||||
\(956\) | −3.05879 | −0.0989282 | ||||||||
\(957\) | −19.0017 | −0.614237 | ||||||||
\(958\) | −16.3637 | −0.528686 | ||||||||
\(959\) | −6.39083 | −0.206371 | ||||||||
\(960\) | −10.1487 | −0.327548 | ||||||||
\(961\) | 31.2643 | 1.00853 | ||||||||
\(962\) | 10.3665 | 0.334230 | ||||||||
\(963\) | 17.7007 | 0.570397 | ||||||||
\(964\) | 25.3883 | 0.817701 | ||||||||
\(965\) | 1.62235 | 0.0522252 | ||||||||
\(966\) | −1.83476 | −0.0590324 | ||||||||
\(967\) | −38.6126 | −1.24170 | −0.620848 | − | 0.783931i | \(-0.713212\pi\) | ||||
−0.620848 | + | 0.783931i | \(0.713212\pi\) | |||||||
\(968\) | 1.72395 | 0.0554100 | ||||||||
\(969\) | 60.9998 | 1.95960 | ||||||||
\(970\) | 3.58540 | 0.115120 | ||||||||
\(971\) | −15.8100 | −0.507369 | −0.253684 | − | 0.967287i | \(-0.581642\pi\) | ||||
−0.253684 | + | 0.967287i | \(0.581642\pi\) | |||||||
\(972\) | 11.8330 | 0.379544 | ||||||||
\(973\) | −59.8143 | −1.91756 | ||||||||
\(974\) | −19.7589 | −0.633117 | ||||||||
\(975\) | −7.47151 | −0.239280 | ||||||||
\(976\) | 25.4630 | 0.815049 | ||||||||
\(977\) | 18.9126 | 0.605066 | 0.302533 | − | 0.953139i | \(-0.402168\pi\) | ||||
0.302533 | + | 0.953139i | \(0.402168\pi\) | |||||||
\(978\) | 5.18319 | 0.165740 | ||||||||
\(979\) | −15.2413 | −0.487115 | ||||||||
\(980\) | −16.3435 | −0.522072 | ||||||||
\(981\) | 13.1335 | 0.419320 | ||||||||
\(982\) | 7.02021 | 0.224024 | ||||||||
\(983\) | −50.9819 | −1.62607 | −0.813035 | − | 0.582215i | \(-0.802186\pi\) | ||||
−0.813035 | + | 0.582215i | \(0.802186\pi\) | |||||||
\(984\) | 20.2674 | 0.646100 | ||||||||
\(985\) | 16.2364 | 0.517336 | ||||||||
\(986\) | 11.7304 | 0.373572 | ||||||||
\(987\) | 52.9728 | 1.68614 | ||||||||
\(988\) | −23.8671 | −0.759314 | ||||||||
\(989\) | −1.35498 | −0.0430860 | ||||||||
\(990\) | 2.54405 | 0.0808554 | ||||||||
\(991\) | −27.7207 | −0.880578 | −0.440289 | − | 0.897856i | \(-0.645124\pi\) | ||||
−0.440289 | + | 0.897856i | \(0.645124\pi\) | |||||||
\(992\) | −37.2599 | −1.18300 | ||||||||
\(993\) | −83.9945 | −2.66548 | ||||||||
\(994\) | 1.26950 | 0.0402661 | ||||||||
\(995\) | −20.4639 | −0.648750 | ||||||||
\(996\) | 48.3647 | 1.53250 | ||||||||
\(997\) | −12.8864 | −0.408116 | −0.204058 | − | 0.978959i | \(-0.565413\pi\) | ||||
−0.204058 | + | 0.978959i | \(0.565413\pi\) | |||||||
\(998\) | 5.19665 | 0.164497 | ||||||||
\(999\) | 68.2001 | 2.15776 |
(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 | 4015.2.a.i.1.15 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.i.1.15 | ✓ | 38 | 1.1 | even | 1 | trivial |