Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38315 | −1.68514 | −0.842572 | − | 0.538584i | \(-0.818959\pi\) | ||||
−0.842572 | + | 0.538584i | \(0.818959\pi\) | |||||||
\(3\) | −2.49497 | −1.44047 | −0.720236 | − | 0.693729i | \(-0.755966\pi\) | ||||
−0.720236 | + | 0.693729i | \(0.755966\pi\) | |||||||
\(4\) | 3.67942 | 1.83971 | ||||||||
\(5\) | −2.67299 | −1.19540 | −0.597698 | − | 0.801722i | \(-0.703918\pi\) | ||||
−0.597698 | + | 0.801722i | \(0.703918\pi\) | |||||||
\(6\) | 5.94590 | 2.42740 | ||||||||
\(7\) | −2.23204 | −0.843632 | −0.421816 | − | 0.906682i | \(-0.638607\pi\) | ||||
−0.421816 | + | 0.906682i | \(0.638607\pi\) | |||||||
\(8\) | −4.00231 | −1.41503 | ||||||||
\(9\) | 3.22488 | 1.07496 | ||||||||
\(10\) | 6.37013 | 2.01441 | ||||||||
\(11\) | −3.56753 | −1.07565 | −0.537826 | − | 0.843056i | \(-0.680754\pi\) | ||||
−0.537826 | + | 0.843056i | \(0.680754\pi\) | |||||||
\(12\) | −9.18004 | −2.65005 | ||||||||
\(13\) | 0.171041 | 0.0474383 | 0.0237192 | − | 0.999719i | \(-0.492449\pi\) | ||||
0.0237192 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(14\) | 5.31929 | 1.42164 | ||||||||
\(15\) | 6.66902 | 1.72193 | ||||||||
\(16\) | 2.17928 | 0.544820 | ||||||||
\(17\) | 3.04647 | 0.738878 | 0.369439 | − | 0.929255i | \(-0.379550\pi\) | ||||
0.369439 | + | 0.929255i | \(0.379550\pi\) | |||||||
\(18\) | −7.68537 | −1.81146 | ||||||||
\(19\) | 3.24564 | 0.744601 | 0.372301 | − | 0.928112i | \(-0.378569\pi\) | ||||
0.372301 | + | 0.928112i | \(0.378569\pi\) | |||||||
\(20\) | −9.83503 | −2.19918 | ||||||||
\(21\) | 5.56887 | 1.21523 | ||||||||
\(22\) | 8.50198 | 1.81263 | ||||||||
\(23\) | −1.37245 | −0.286176 | −0.143088 | − | 0.989710i | \(-0.545703\pi\) | ||||
−0.143088 | + | 0.989710i | \(0.545703\pi\) | |||||||
\(24\) | 9.98564 | 2.03831 | ||||||||
\(25\) | 2.14485 | 0.428970 | ||||||||
\(26\) | −0.407618 | −0.0799404 | ||||||||
\(27\) | −0.561058 | −0.107976 | ||||||||
\(28\) | −8.21261 | −1.55204 | ||||||||
\(29\) | 3.33676 | 0.619621 | 0.309811 | − | 0.950798i | \(-0.399734\pi\) | ||||
0.309811 | + | 0.950798i | \(0.399734\pi\) | |||||||
\(30\) | −15.8933 | −2.90170 | ||||||||
\(31\) | −6.95962 | −1.24998 | −0.624992 | − | 0.780631i | \(-0.714898\pi\) | ||||
−0.624992 | + | 0.780631i | \(0.714898\pi\) | |||||||
\(32\) | 2.81106 | 0.496931 | ||||||||
\(33\) | 8.90089 | 1.54945 | ||||||||
\(34\) | −7.26021 | −1.24512 | ||||||||
\(35\) | 5.96621 | 1.00847 | ||||||||
\(36\) | 11.8657 | 1.97761 | ||||||||
\(37\) | −4.36072 | −0.716898 | −0.358449 | − | 0.933549i | \(-0.616694\pi\) | ||||
−0.358449 | + | 0.933549i | \(0.616694\pi\) | |||||||
\(38\) | −7.73486 | −1.25476 | ||||||||
\(39\) | −0.426743 | −0.0683335 | ||||||||
\(40\) | 10.6981 | 1.69152 | ||||||||
\(41\) | 8.86840 | 1.38501 | 0.692506 | − | 0.721412i | \(-0.256507\pi\) | ||||
0.692506 | + | 0.721412i | \(0.256507\pi\) | |||||||
\(42\) | −13.2715 | −2.04783 | ||||||||
\(43\) | 8.33722 | 1.27141 | 0.635707 | − | 0.771930i | \(-0.280709\pi\) | ||||
0.635707 | + | 0.771930i | \(0.280709\pi\) | |||||||
\(44\) | −13.1264 | −1.97889 | ||||||||
\(45\) | −8.62005 | −1.28500 | ||||||||
\(46\) | 3.27076 | 0.482247 | ||||||||
\(47\) | 4.76900 | 0.695629 | 0.347815 | − | 0.937563i | \(-0.386924\pi\) | ||||
0.347815 | + | 0.937563i | \(0.386924\pi\) | |||||||
\(48\) | −5.43724 | −0.784797 | ||||||||
\(49\) | −2.01800 | −0.288286 | ||||||||
\(50\) | −5.11151 | −0.722877 | ||||||||
\(51\) | −7.60086 | −1.06433 | ||||||||
\(52\) | 0.629332 | 0.0872727 | ||||||||
\(53\) | 4.79417 | 0.658530 | 0.329265 | − | 0.944237i | \(-0.393199\pi\) | ||||
0.329265 | + | 0.944237i | \(0.393199\pi\) | |||||||
\(54\) | 1.33709 | 0.181955 | ||||||||
\(55\) | 9.53597 | 1.28583 | ||||||||
\(56\) | 8.93331 | 1.19376 | ||||||||
\(57\) | −8.09778 | −1.07258 | ||||||||
\(58\) | −7.95201 | −1.04415 | ||||||||
\(59\) | −2.55132 | −0.332154 | −0.166077 | − | 0.986113i | \(-0.553110\pi\) | ||||
−0.166077 | + | 0.986113i | \(0.553110\pi\) | |||||||
\(60\) | 24.5381 | 3.16786 | ||||||||
\(61\) | −12.5381 | −1.60534 | −0.802670 | − | 0.596423i | \(-0.796588\pi\) | ||||
−0.802670 | + | 0.596423i | \(0.796588\pi\) | |||||||
\(62\) | 16.5858 | 2.10640 | ||||||||
\(63\) | −7.19805 | −0.906869 | ||||||||
\(64\) | −11.0578 | −1.38222 | ||||||||
\(65\) | −0.457191 | −0.0567075 | ||||||||
\(66\) | −21.2122 | −2.61104 | ||||||||
\(67\) | 4.09006 | 0.499680 | 0.249840 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249840 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(68\) | 11.2092 | 1.35932 | ||||||||
\(69\) | 3.42422 | 0.412228 | ||||||||
\(70\) | −14.2184 | −1.69942 | ||||||||
\(71\) | −0.238225 | −0.0282721 | −0.0141360 | − | 0.999900i | \(-0.504500\pi\) | ||||
−0.0141360 | + | 0.999900i | \(0.504500\pi\) | |||||||
\(72\) | −12.9069 | −1.52110 | ||||||||
\(73\) | −4.75265 | −0.556256 | −0.278128 | − | 0.960544i | \(-0.589714\pi\) | ||||
−0.278128 | + | 0.960544i | \(0.589714\pi\) | |||||||
\(74\) | 10.3923 | 1.20808 | ||||||||
\(75\) | −5.35134 | −0.617920 | ||||||||
\(76\) | 11.9421 | 1.36985 | ||||||||
\(77\) | 7.96288 | 0.907454 | ||||||||
\(78\) | 1.01699 | 0.115152 | ||||||||
\(79\) | −13.4382 | −1.51192 | −0.755959 | − | 0.654619i | \(-0.772829\pi\) | ||||
−0.755959 | + | 0.654619i | \(0.772829\pi\) | |||||||
\(80\) | −5.82518 | −0.651275 | ||||||||
\(81\) | −8.27480 | −0.919423 | ||||||||
\(82\) | −21.1348 | −2.33394 | ||||||||
\(83\) | 12.3750 | 1.35833 | 0.679166 | − | 0.733985i | \(-0.262342\pi\) | ||||
0.679166 | + | 0.733985i | \(0.262342\pi\) | |||||||
\(84\) | 20.4902 | 2.23566 | ||||||||
\(85\) | −8.14318 | −0.883252 | ||||||||
\(86\) | −19.8689 | −2.14252 | ||||||||
\(87\) | −8.32512 | −0.892547 | ||||||||
\(88\) | 14.2784 | 1.52208 | ||||||||
\(89\) | 17.0413 | 1.80637 | 0.903187 | − | 0.429248i | \(-0.141221\pi\) | ||||
0.903187 | + | 0.429248i | \(0.141221\pi\) | |||||||
\(90\) | 20.5429 | 2.16541 | ||||||||
\(91\) | −0.381771 | −0.0400205 | ||||||||
\(92\) | −5.04982 | −0.526480 | ||||||||
\(93\) | 17.3640 | 1.80057 | ||||||||
\(94\) | −11.3652 | −1.17224 | ||||||||
\(95\) | −8.67555 | −0.890093 | ||||||||
\(96\) | −7.01352 | −0.715814 | ||||||||
\(97\) | −9.50023 | −0.964603 | −0.482301 | − | 0.876005i | \(-0.660199\pi\) | ||||
−0.482301 | + | 0.876005i | \(0.660199\pi\) | |||||||
\(98\) | 4.80920 | 0.485802 | ||||||||
\(99\) | −11.5049 | −1.15628 | ||||||||
\(100\) | 7.89181 | 0.789181 | ||||||||
\(101\) | −14.9381 | −1.48640 | −0.743198 | − | 0.669071i | \(-0.766692\pi\) | ||||
−0.743198 | + | 0.669071i | \(0.766692\pi\) | |||||||
\(102\) | 18.1140 | 1.79355 | ||||||||
\(103\) | 10.1803 | 1.00310 | 0.501548 | − | 0.865130i | \(-0.332764\pi\) | ||||
0.501548 | + | 0.865130i | \(0.332764\pi\) | |||||||
\(104\) | −0.684560 | −0.0671266 | ||||||||
\(105\) | −14.8855 | −1.45268 | ||||||||
\(106\) | −11.4252 | −1.10972 | ||||||||
\(107\) | 13.8725 | 1.34111 | 0.670555 | − | 0.741860i | \(-0.266056\pi\) | ||||
0.670555 | + | 0.741860i | \(0.266056\pi\) | |||||||
\(108\) | −2.06437 | −0.198644 | ||||||||
\(109\) | −8.28011 | −0.793091 | −0.396545 | − | 0.918015i | \(-0.629791\pi\) | ||||
−0.396545 | + | 0.918015i | \(0.629791\pi\) | |||||||
\(110\) | −22.7257 | −2.16681 | ||||||||
\(111\) | 10.8799 | 1.03267 | ||||||||
\(112\) | −4.86424 | −0.459627 | ||||||||
\(113\) | −11.4873 | −1.08063 | −0.540315 | − | 0.841463i | \(-0.681695\pi\) | ||||
−0.540315 | + | 0.841463i | \(0.681695\pi\) | |||||||
\(114\) | 19.2982 | 1.80745 | ||||||||
\(115\) | 3.66854 | 0.342093 | ||||||||
\(116\) | 12.2773 | 1.13992 | ||||||||
\(117\) | 0.551587 | 0.0509942 | ||||||||
\(118\) | 6.08019 | 0.559727 | ||||||||
\(119\) | −6.79985 | −0.623341 | ||||||||
\(120\) | −26.6915 | −2.43659 | ||||||||
\(121\) | 1.72730 | 0.157027 | ||||||||
\(122\) | 29.8802 | 2.70523 | ||||||||
\(123\) | −22.1264 | −1.99507 | ||||||||
\(124\) | −25.6073 | −2.29961 | ||||||||
\(125\) | 7.63177 | 0.682606 | ||||||||
\(126\) | 17.1541 | 1.52820 | ||||||||
\(127\) | 0.455660 | 0.0404333 | 0.0202166 | − | 0.999796i | \(-0.493564\pi\) | ||||
0.0202166 | + | 0.999796i | \(0.493564\pi\) | |||||||
\(128\) | 20.7302 | 1.83231 | ||||||||
\(129\) | −20.8011 | −1.83144 | ||||||||
\(130\) | 1.08956 | 0.0955604 | ||||||||
\(131\) | −16.2877 | −1.42306 | −0.711532 | − | 0.702654i | \(-0.751998\pi\) | ||||
−0.711532 | + | 0.702654i | \(0.751998\pi\) | |||||||
\(132\) | 32.7501 | 2.85053 | ||||||||
\(133\) | −7.24440 | −0.628169 | ||||||||
\(134\) | −9.74723 | −0.842033 | ||||||||
\(135\) | 1.49970 | 0.129074 | ||||||||
\(136\) | −12.1929 | −1.04553 | ||||||||
\(137\) | 2.07152 | 0.176982 | 0.0884908 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884908 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(138\) | −8.16044 | −0.694663 | ||||||||
\(139\) | 19.9400 | 1.69129 | 0.845643 | − | 0.533748i | \(-0.179217\pi\) | ||||
0.845643 | + | 0.533748i | \(0.179217\pi\) | |||||||
\(140\) | 21.9522 | 1.85530 | ||||||||
\(141\) | −11.8985 | −1.00203 | ||||||||
\(142\) | 0.567726 | 0.0476425 | ||||||||
\(143\) | −0.610196 | −0.0510271 | ||||||||
\(144\) | 7.02790 | 0.585659 | ||||||||
\(145\) | −8.91912 | −0.740692 | ||||||||
\(146\) | 11.3263 | 0.937370 | ||||||||
\(147\) | 5.03485 | 0.415267 | ||||||||
\(148\) | −16.0449 | −1.31888 | ||||||||
\(149\) | −8.57850 | −0.702778 | −0.351389 | − | 0.936230i | \(-0.614291\pi\) | ||||
−0.351389 | + | 0.936230i | \(0.614291\pi\) | |||||||
\(150\) | 12.7531 | 1.04128 | ||||||||
\(151\) | 7.11675 | 0.579153 | 0.289576 | − | 0.957155i | \(-0.406486\pi\) | ||||
0.289576 | + | 0.957155i | \(0.406486\pi\) | |||||||
\(152\) | −12.9901 | −1.05363 | ||||||||
\(153\) | 9.82450 | 0.794264 | ||||||||
\(154\) | −18.9768 | −1.52919 | ||||||||
\(155\) | 18.6030 | 1.49423 | ||||||||
\(156\) | −1.57017 | −0.125714 | ||||||||
\(157\) | −22.3094 | −1.78049 | −0.890243 | − | 0.455486i | \(-0.849466\pi\) | ||||
−0.890243 | + | 0.455486i | \(0.849466\pi\) | |||||||
\(158\) | 32.0253 | 2.54780 | ||||||||
\(159\) | −11.9613 | −0.948594 | ||||||||
\(160\) | −7.51393 | −0.594029 | ||||||||
\(161\) | 3.06336 | 0.241427 | ||||||||
\(162\) | 19.7201 | 1.54936 | ||||||||
\(163\) | −1.08447 | −0.0849421 | −0.0424711 | − | 0.999098i | \(-0.513523\pi\) | ||||
−0.0424711 | + | 0.999098i | \(0.513523\pi\) | |||||||
\(164\) | 32.6306 | 2.54802 | ||||||||
\(165\) | −23.7920 | −1.85220 | ||||||||
\(166\) | −29.4915 | −2.28898 | ||||||||
\(167\) | 2.54198 | 0.196704 | 0.0983520 | − | 0.995152i | \(-0.468643\pi\) | ||||
0.0983520 | + | 0.995152i | \(0.468643\pi\) | |||||||
\(168\) | −22.2883 | −1.71958 | ||||||||
\(169\) | −12.9707 | −0.997750 | ||||||||
\(170\) | 19.4064 | 1.48841 | ||||||||
\(171\) | 10.4668 | 0.800416 | ||||||||
\(172\) | 30.6761 | 2.33903 | ||||||||
\(173\) | −11.3261 | −0.861106 | −0.430553 | − | 0.902565i | \(-0.641682\pi\) | ||||
−0.430553 | + | 0.902565i | \(0.641682\pi\) | |||||||
\(174\) | 19.8400 | 1.50407 | ||||||||
\(175\) | −4.78740 | −0.361893 | ||||||||
\(176\) | −7.77465 | −0.586036 | ||||||||
\(177\) | 6.36548 | 0.478458 | ||||||||
\(178\) | −40.6120 | −3.04400 | ||||||||
\(179\) | 8.72191 | 0.651907 | 0.325953 | − | 0.945386i | \(-0.394315\pi\) | ||||
0.325953 | + | 0.945386i | \(0.394315\pi\) | |||||||
\(180\) | −31.7168 | −2.36403 | ||||||||
\(181\) | −24.2768 | −1.80448 | −0.902239 | − | 0.431236i | \(-0.858078\pi\) | ||||
−0.902239 | + | 0.431236i | \(0.858078\pi\) | |||||||
\(182\) | 0.909818 | 0.0674402 | ||||||||
\(183\) | 31.2822 | 2.31245 | ||||||||
\(184\) | 5.49297 | 0.404947 | ||||||||
\(185\) | 11.6561 | 0.856977 | ||||||||
\(186\) | −41.3811 | −3.03421 | ||||||||
\(187\) | −10.8684 | −0.794776 | ||||||||
\(188\) | 17.5471 | 1.27976 | ||||||||
\(189\) | 1.25230 | 0.0910917 | ||||||||
\(190\) | 20.6752 | 1.49993 | ||||||||
\(191\) | 2.12136 | 0.153496 | 0.0767480 | − | 0.997051i | \(-0.475546\pi\) | ||||
0.0767480 | + | 0.997051i | \(0.475546\pi\) | |||||||
\(192\) | 27.5888 | 1.99105 | ||||||||
\(193\) | 8.52268 | 0.613476 | 0.306738 | − | 0.951794i | \(-0.400762\pi\) | ||||
0.306738 | + | 0.951794i | \(0.400762\pi\) | |||||||
\(194\) | 22.6405 | 1.62549 | ||||||||
\(195\) | 1.14068 | 0.0816856 | ||||||||
\(196\) | −7.42506 | −0.530361 | ||||||||
\(197\) | −8.78306 | −0.625767 | −0.312883 | − | 0.949792i | \(-0.601295\pi\) | ||||
−0.312883 | + | 0.949792i | \(0.601295\pi\) | |||||||
\(198\) | 27.4178 | 1.94850 | ||||||||
\(199\) | 0.326298 | 0.0231307 | 0.0115653 | − | 0.999933i | \(-0.496319\pi\) | ||||
0.0115653 | + | 0.999933i | \(0.496319\pi\) | |||||||
\(200\) | −8.58436 | −0.607006 | ||||||||
\(201\) | −10.2046 | −0.719775 | ||||||||
\(202\) | 35.5998 | 2.50479 | ||||||||
\(203\) | −7.44778 | −0.522732 | ||||||||
\(204\) | −27.9667 | −1.95806 | ||||||||
\(205\) | −23.7051 | −1.65564 | ||||||||
\(206\) | −24.2612 | −1.69036 | ||||||||
\(207\) | −4.42598 | −0.307627 | ||||||||
\(208\) | 0.372747 | 0.0258453 | ||||||||
\(209\) | −11.5789 | −0.800932 | ||||||||
\(210\) | 35.4745 | 2.44797 | ||||||||
\(211\) | 21.7473 | 1.49715 | 0.748574 | − | 0.663051i | \(-0.230739\pi\) | ||||
0.748574 | + | 0.663051i | \(0.230739\pi\) | |||||||
\(212\) | 17.6398 | 1.21150 | ||||||||
\(213\) | 0.594364 | 0.0407251 | ||||||||
\(214\) | −33.0604 | −2.25996 | ||||||||
\(215\) | −22.2853 | −1.51984 | ||||||||
\(216\) | 2.24553 | 0.152789 | ||||||||
\(217\) | 15.5341 | 1.05453 | ||||||||
\(218\) | 19.7328 | 1.33647 | ||||||||
\(219\) | 11.8577 | 0.801270 | ||||||||
\(220\) | 35.0868 | 2.36555 | ||||||||
\(221\) | 0.521073 | 0.0350511 | ||||||||
\(222\) | −25.9284 | −1.74020 | ||||||||
\(223\) | −11.1124 | −0.744145 | −0.372072 | − | 0.928204i | \(-0.621353\pi\) | ||||
−0.372072 | + | 0.928204i | \(0.621353\pi\) | |||||||
\(224\) | −6.27441 | −0.419226 | ||||||||
\(225\) | 6.91688 | 0.461125 | ||||||||
\(226\) | 27.3759 | 1.82102 | ||||||||
\(227\) | −21.6852 | −1.43930 | −0.719650 | − | 0.694337i | \(-0.755698\pi\) | ||||
−0.719650 | + | 0.694337i | \(0.755698\pi\) | |||||||
\(228\) | −29.7951 | −1.97323 | ||||||||
\(229\) | 9.11007 | 0.602011 | 0.301005 | − | 0.953622i | \(-0.402678\pi\) | ||||
0.301005 | + | 0.953622i | \(0.402678\pi\) | |||||||
\(230\) | −8.74269 | −0.576476 | ||||||||
\(231\) | −19.8671 | −1.30716 | ||||||||
\(232\) | −13.3548 | −0.876782 | ||||||||
\(233\) | −14.5692 | −0.954463 | −0.477231 | − | 0.878778i | \(-0.658360\pi\) | ||||
−0.477231 | + | 0.878778i | \(0.658360\pi\) | |||||||
\(234\) | −1.31452 | −0.0859326 | ||||||||
\(235\) | −12.7475 | −0.831552 | ||||||||
\(236\) | −9.38738 | −0.611067 | ||||||||
\(237\) | 33.5279 | 2.17787 | ||||||||
\(238\) | 16.2051 | 1.05042 | ||||||||
\(239\) | −14.9631 | −0.967881 | −0.483940 | − | 0.875101i | \(-0.660795\pi\) | ||||
−0.483940 | + | 0.875101i | \(0.660795\pi\) | |||||||
\(240\) | 14.5337 | 0.938143 | ||||||||
\(241\) | −10.6052 | −0.683143 | −0.341572 | − | 0.939856i | \(-0.610959\pi\) | ||||
−0.341572 | + | 0.939856i | \(0.610959\pi\) | |||||||
\(242\) | −4.11642 | −0.264614 | ||||||||
\(243\) | 22.3286 | 1.43238 | ||||||||
\(244\) | −46.1329 | −2.95336 | ||||||||
\(245\) | 5.39408 | 0.344615 | ||||||||
\(246\) | 52.7306 | 3.36198 | ||||||||
\(247\) | 0.555139 | 0.0353226 | ||||||||
\(248\) | 27.8545 | 1.76876 | ||||||||
\(249\) | −30.8752 | −1.95664 | ||||||||
\(250\) | −18.1877 | −1.15029 | ||||||||
\(251\) | −17.5875 | −1.11011 | −0.555056 | − | 0.831813i | \(-0.687303\pi\) | ||||
−0.555056 | + | 0.831813i | \(0.687303\pi\) | |||||||
\(252\) | −26.4846 | −1.66838 | ||||||||
\(253\) | 4.89626 | 0.307825 | ||||||||
\(254\) | −1.08591 | −0.0681359 | ||||||||
\(255\) | 20.3170 | 1.27230 | ||||||||
\(256\) | −27.2877 | −1.70548 | ||||||||
\(257\) | −15.6901 | −0.978724 | −0.489362 | − | 0.872081i | \(-0.662770\pi\) | ||||
−0.489362 | + | 0.872081i | \(0.662770\pi\) | |||||||
\(258\) | 49.5723 | 3.08623 | ||||||||
\(259\) | 9.73330 | 0.604798 | ||||||||
\(260\) | −1.68220 | −0.104325 | ||||||||
\(261\) | 10.7606 | 0.666067 | ||||||||
\(262\) | 38.8161 | 2.39807 | ||||||||
\(263\) | −8.97221 | −0.553250 | −0.276625 | − | 0.960978i | \(-0.589216\pi\) | ||||
−0.276625 | + | 0.960978i | \(0.589216\pi\) | |||||||
\(264\) | −35.6241 | −2.19251 | ||||||||
\(265\) | −12.8148 | −0.787204 | ||||||||
\(266\) | 17.2645 | 1.05856 | ||||||||
\(267\) | −42.5175 | −2.60203 | ||||||||
\(268\) | 15.0490 | 0.919266 | ||||||||
\(269\) | −0.339949 | −0.0207271 | −0.0103635 | − | 0.999946i | \(-0.503299\pi\) | ||||
−0.0103635 | + | 0.999946i | \(0.503299\pi\) | |||||||
\(270\) | −3.57402 | −0.217508 | ||||||||
\(271\) | −7.45834 | −0.453062 | −0.226531 | − | 0.974004i | \(-0.572738\pi\) | ||||
−0.226531 | + | 0.974004i | \(0.572738\pi\) | |||||||
\(272\) | 6.63911 | 0.402555 | ||||||||
\(273\) | 0.952507 | 0.0576483 | ||||||||
\(274\) | −4.93674 | −0.298239 | ||||||||
\(275\) | −7.65183 | −0.461423 | ||||||||
\(276\) | 12.5991 | 0.758379 | ||||||||
\(277\) | −23.7532 | −1.42719 | −0.713595 | − | 0.700559i | \(-0.752934\pi\) | ||||
−0.713595 | + | 0.700559i | \(0.752934\pi\) | |||||||
\(278\) | −47.5200 | −2.85006 | ||||||||
\(279\) | −22.4439 | −1.34368 | ||||||||
\(280\) | −23.8786 | −1.42702 | ||||||||
\(281\) | 12.7096 | 0.758193 | 0.379097 | − | 0.925357i | \(-0.376235\pi\) | ||||
0.379097 | + | 0.925357i | \(0.376235\pi\) | |||||||
\(282\) | 28.3559 | 1.68857 | ||||||||
\(283\) | 11.6001 | 0.689554 | 0.344777 | − | 0.938685i | \(-0.387955\pi\) | ||||
0.344777 | + | 0.938685i | \(0.387955\pi\) | |||||||
\(284\) | −0.876529 | −0.0520124 | ||||||||
\(285\) | 21.6452 | 1.28215 | ||||||||
\(286\) | 1.45419 | 0.0859880 | ||||||||
\(287\) | −19.7946 | −1.16844 | ||||||||
\(288\) | 9.06533 | 0.534180 | ||||||||
\(289\) | −7.71900 | −0.454059 | ||||||||
\(290\) | 21.2556 | 1.24817 | ||||||||
\(291\) | 23.7028 | 1.38948 | ||||||||
\(292\) | −17.4870 | −1.02335 | ||||||||
\(293\) | −6.10147 | −0.356452 | −0.178226 | − | 0.983990i | \(-0.557036\pi\) | ||||
−0.178226 | + | 0.983990i | \(0.557036\pi\) | |||||||
\(294\) | −11.9988 | −0.699785 | ||||||||
\(295\) | 6.81965 | 0.397055 | ||||||||
\(296\) | 17.4530 | 1.01443 | ||||||||
\(297\) | 2.00159 | 0.116144 | ||||||||
\(298\) | 20.4439 | 1.18428 | ||||||||
\(299\) | −0.234746 | −0.0135757 | ||||||||
\(300\) | −19.6898 | −1.13679 | ||||||||
\(301\) | −18.6090 | −1.07261 | ||||||||
\(302\) | −16.9603 | −0.975955 | ||||||||
\(303\) | 37.2701 | 2.14111 | ||||||||
\(304\) | 7.07316 | 0.405673 | ||||||||
\(305\) | 33.5142 | 1.91902 | ||||||||
\(306\) | −23.4133 | −1.33845 | ||||||||
\(307\) | 0.405309 | 0.0231322 | 0.0115661 | − | 0.999933i | \(-0.496318\pi\) | ||||
0.0115661 | + | 0.999933i | \(0.496318\pi\) | |||||||
\(308\) | 29.2988 | 1.66945 | ||||||||
\(309\) | −25.3996 | −1.44493 | ||||||||
\(310\) | −44.3337 | −2.51798 | ||||||||
\(311\) | −11.6930 | −0.663048 | −0.331524 | − | 0.943447i | \(-0.607563\pi\) | ||||
−0.331524 | + | 0.943447i | \(0.607563\pi\) | |||||||
\(312\) | 1.70796 | 0.0966940 | ||||||||
\(313\) | 18.2376 | 1.03085 | 0.515426 | − | 0.856934i | \(-0.327634\pi\) | ||||
0.515426 | + | 0.856934i | \(0.327634\pi\) | |||||||
\(314\) | 53.1668 | 3.00037 | ||||||||
\(315\) | 19.2403 | 1.08407 | ||||||||
\(316\) | −49.4448 | −2.78149 | ||||||||
\(317\) | 27.0250 | 1.51788 | 0.758939 | − | 0.651162i | \(-0.225718\pi\) | ||||
0.758939 | + | 0.651162i | \(0.225718\pi\) | |||||||
\(318\) | 28.5057 | 1.59852 | ||||||||
\(319\) | −11.9040 | −0.666497 | ||||||||
\(320\) | 29.5572 | 1.65230 | ||||||||
\(321\) | −34.6116 | −1.93183 | ||||||||
\(322\) | −7.30046 | −0.406839 | ||||||||
\(323\) | 9.88776 | 0.550170 | ||||||||
\(324\) | −30.4465 | −1.69147 | ||||||||
\(325\) | 0.366858 | 0.0203496 | ||||||||
\(326\) | 2.58445 | 0.143140 | ||||||||
\(327\) | 20.6586 | 1.14242 | ||||||||
\(328\) | −35.4941 | −1.95983 | ||||||||
\(329\) | −10.6446 | −0.586855 | ||||||||
\(330\) | 56.6999 | 3.12122 | ||||||||
\(331\) | −21.1684 | −1.16352 | −0.581761 | − | 0.813360i | \(-0.697636\pi\) | ||||
−0.581761 | + | 0.813360i | \(0.697636\pi\) | |||||||
\(332\) | 45.5327 | 2.49893 | ||||||||
\(333\) | −14.0628 | −0.770636 | ||||||||
\(334\) | −6.05792 | −0.331474 | ||||||||
\(335\) | −10.9327 | −0.597315 | ||||||||
\(336\) | 12.1361 | 0.662080 | ||||||||
\(337\) | −13.5243 | −0.736717 | −0.368358 | − | 0.929684i | \(-0.620080\pi\) | ||||
−0.368358 | + | 0.929684i | \(0.620080\pi\) | |||||||
\(338\) | 30.9113 | 1.68135 | ||||||||
\(339\) | 28.6604 | 1.55662 | ||||||||
\(340\) | −29.9622 | −1.62493 | ||||||||
\(341\) | 24.8287 | 1.34455 | ||||||||
\(342\) | −24.9440 | −1.34882 | ||||||||
\(343\) | 20.1285 | 1.08684 | ||||||||
\(344\) | −33.3681 | −1.79909 | ||||||||
\(345\) | −9.15289 | −0.492775 | ||||||||
\(346\) | 26.9918 | 1.45109 | ||||||||
\(347\) | −6.02881 | −0.323643 | −0.161822 | − | 0.986820i | \(-0.551737\pi\) | ||||
−0.161822 | + | 0.986820i | \(0.551737\pi\) | |||||||
\(348\) | −30.6316 | −1.64203 | ||||||||
\(349\) | −12.2753 | −0.657081 | −0.328540 | − | 0.944490i | \(-0.606557\pi\) | ||||
−0.328540 | + | 0.944490i | \(0.606557\pi\) | |||||||
\(350\) | 11.4091 | 0.609842 | ||||||||
\(351\) | −0.0959641 | −0.00512219 | ||||||||
\(352\) | −10.0286 | −0.534524 | ||||||||
\(353\) | 3.07296 | 0.163557 | 0.0817785 | − | 0.996651i | \(-0.473940\pi\) | ||||
0.0817785 | + | 0.996651i | \(0.473940\pi\) | |||||||
\(354\) | −15.1699 | −0.806271 | ||||||||
\(355\) | 0.636772 | 0.0337963 | ||||||||
\(356\) | 62.7020 | 3.32320 | ||||||||
\(357\) | 16.9654 | 0.897905 | ||||||||
\(358\) | −20.7857 | −1.09856 | ||||||||
\(359\) | −13.4613 | −0.710463 | −0.355231 | − | 0.934778i | \(-0.615598\pi\) | ||||
−0.355231 | + | 0.934778i | \(0.615598\pi\) | |||||||
\(360\) | 34.5001 | 1.81831 | ||||||||
\(361\) | −8.46581 | −0.445569 | ||||||||
\(362\) | 57.8553 | 3.04080 | ||||||||
\(363\) | −4.30956 | −0.226194 | ||||||||
\(364\) | −1.40469 | −0.0736260 | ||||||||
\(365\) | 12.7038 | 0.664945 | ||||||||
\(366\) | −74.5503 | −3.89681 | ||||||||
\(367\) | −18.3817 | −0.959516 | −0.479758 | − | 0.877401i | \(-0.659275\pi\) | ||||
−0.479758 | + | 0.877401i | \(0.659275\pi\) | |||||||
\(368\) | −2.99095 | −0.155914 | ||||||||
\(369\) | 28.5995 | 1.48883 | ||||||||
\(370\) | −27.7784 | −1.44413 | ||||||||
\(371\) | −10.7008 | −0.555557 | ||||||||
\(372\) | 63.8895 | 3.31252 | ||||||||
\(373\) | 6.94259 | 0.359473 | 0.179737 | − | 0.983715i | \(-0.442475\pi\) | ||||
0.179737 | + | 0.983715i | \(0.442475\pi\) | |||||||
\(374\) | 25.9011 | 1.33931 | ||||||||
\(375\) | −19.0410 | −0.983275 | ||||||||
\(376\) | −19.0870 | −0.984336 | ||||||||
\(377\) | 0.570724 | 0.0293938 | ||||||||
\(378\) | −2.98443 | −0.153503 | ||||||||
\(379\) | 11.3470 | 0.582856 | 0.291428 | − | 0.956593i | \(-0.405870\pi\) | ||||
0.291428 | + | 0.956593i | \(0.405870\pi\) | |||||||
\(380\) | −31.9210 | −1.63751 | ||||||||
\(381\) | −1.13686 | −0.0582430 | ||||||||
\(382\) | −5.05552 | −0.258663 | ||||||||
\(383\) | −36.1993 | −1.84970 | −0.924849 | − | 0.380335i | \(-0.875809\pi\) | ||||
−0.924849 | + | 0.380335i | \(0.875809\pi\) | |||||||
\(384\) | −51.7212 | −2.63939 | ||||||||
\(385\) | −21.2847 | −1.08477 | ||||||||
\(386\) | −20.3108 | −1.03379 | ||||||||
\(387\) | 26.8865 | 1.36672 | ||||||||
\(388\) | −34.9553 | −1.77459 | ||||||||
\(389\) | 27.9468 | 1.41696 | 0.708480 | − | 0.705731i | \(-0.249381\pi\) | ||||
0.708480 | + | 0.705731i | \(0.249381\pi\) | |||||||
\(390\) | −2.71841 | −0.137652 | ||||||||
\(391\) | −4.18113 | −0.211449 | ||||||||
\(392\) | 8.07665 | 0.407933 | ||||||||
\(393\) | 40.6374 | 2.04988 | ||||||||
\(394\) | 20.9314 | 1.05451 | ||||||||
\(395\) | 35.9202 | 1.80734 | ||||||||
\(396\) | −42.3312 | −2.12722 | ||||||||
\(397\) | 27.5452 | 1.38245 | 0.691226 | − | 0.722639i | \(-0.257071\pi\) | ||||
0.691226 | + | 0.722639i | \(0.257071\pi\) | |||||||
\(398\) | −0.777619 | −0.0389785 | ||||||||
\(399\) | 18.0746 | 0.904860 | ||||||||
\(400\) | 4.67423 | 0.233712 | ||||||||
\(401\) | −32.8563 | −1.64077 | −0.820384 | − | 0.571813i | \(-0.806240\pi\) | ||||
−0.820384 | + | 0.571813i | \(0.806240\pi\) | |||||||
\(402\) | 24.3191 | 1.21292 | ||||||||
\(403\) | −1.19038 | −0.0592971 | ||||||||
\(404\) | −54.9635 | −2.73454 | ||||||||
\(405\) | 22.1184 | 1.09907 | ||||||||
\(406\) | 17.7492 | 0.880878 | ||||||||
\(407\) | 15.5570 | 0.771133 | ||||||||
\(408\) | 30.4210 | 1.50606 | ||||||||
\(409\) | 11.6168 | 0.574415 | 0.287208 | − | 0.957868i | \(-0.407273\pi\) | ||||
0.287208 | + | 0.957868i | \(0.407273\pi\) | |||||||
\(410\) | 56.4929 | 2.78999 | ||||||||
\(411\) | −5.16837 | −0.254937 | ||||||||
\(412\) | 37.4576 | 1.84540 | ||||||||
\(413\) | 5.69465 | 0.280216 | ||||||||
\(414\) | 10.5478 | 0.518395 | ||||||||
\(415\) | −33.0782 | −1.62374 | ||||||||
\(416\) | 0.480808 | 0.0235735 | ||||||||
\(417\) | −49.7497 | −2.43625 | ||||||||
\(418\) | 27.5944 | 1.34969 | ||||||||
\(419\) | 15.3202 | 0.748441 | 0.374221 | − | 0.927340i | \(-0.377910\pi\) | ||||
0.374221 | + | 0.927340i | \(0.377910\pi\) | |||||||
\(420\) | −54.7700 | −2.67250 | ||||||||
\(421\) | 22.4446 | 1.09388 | 0.546941 | − | 0.837171i | \(-0.315792\pi\) | ||||
0.546941 | + | 0.837171i | \(0.315792\pi\) | |||||||
\(422\) | −51.8272 | −2.52291 | ||||||||
\(423\) | 15.3794 | 0.747773 | ||||||||
\(424\) | −19.1878 | −0.931840 | ||||||||
\(425\) | 6.53423 | 0.316957 | ||||||||
\(426\) | −1.41646 | −0.0686277 | ||||||||
\(427\) | 27.9856 | 1.35432 | ||||||||
\(428\) | 51.0429 | 2.46725 | ||||||||
\(429\) | 1.52242 | 0.0735031 | ||||||||
\(430\) | 53.1092 | 2.56115 | ||||||||
\(431\) | −21.9342 | −1.05653 | −0.528265 | − | 0.849079i | \(-0.677157\pi\) | ||||
−0.528265 | + | 0.849079i | \(0.677157\pi\) | |||||||
\(432\) | −1.22270 | −0.0588273 | ||||||||
\(433\) | 36.7281 | 1.76504 | 0.882520 | − | 0.470274i | \(-0.155845\pi\) | ||||
0.882520 | + | 0.470274i | \(0.155845\pi\) | |||||||
\(434\) | −37.0202 | −1.77703 | ||||||||
\(435\) | 22.2529 | 1.06695 | ||||||||
\(436\) | −30.4660 | −1.45906 | ||||||||
\(437\) | −4.45448 | −0.213087 | ||||||||
\(438\) | −28.2588 | −1.35026 | ||||||||
\(439\) | 33.6811 | 1.60751 | 0.803755 | − | 0.594960i | \(-0.202832\pi\) | ||||
0.803755 | + | 0.594960i | \(0.202832\pi\) | |||||||
\(440\) | −38.1659 | −1.81949 | ||||||||
\(441\) | −6.50779 | −0.309895 | ||||||||
\(442\) | −1.24180 | −0.0590662 | ||||||||
\(443\) | 12.0761 | 0.573752 | 0.286876 | − | 0.957968i | \(-0.407383\pi\) | ||||
0.286876 | + | 0.957968i | \(0.407383\pi\) | |||||||
\(444\) | 40.0316 | 1.89981 | ||||||||
\(445\) | −45.5511 | −2.15933 | ||||||||
\(446\) | 26.4827 | 1.25399 | ||||||||
\(447\) | 21.4031 | 1.01233 | ||||||||
\(448\) | 24.6813 | 1.16608 | ||||||||
\(449\) | 28.7540 | 1.35698 | 0.678492 | − | 0.734608i | \(-0.262634\pi\) | ||||
0.678492 | + | 0.734608i | \(0.262634\pi\) | |||||||
\(450\) | −16.4840 | −0.777063 | ||||||||
\(451\) | −31.6383 | −1.48979 | ||||||||
\(452\) | −42.2664 | −1.98805 | ||||||||
\(453\) | −17.7561 | −0.834253 | ||||||||
\(454\) | 51.6792 | 2.42543 | ||||||||
\(455\) | 1.02047 | 0.0478403 | ||||||||
\(456\) | 32.4098 | 1.51773 | ||||||||
\(457\) | 31.7539 | 1.48538 | 0.742692 | − | 0.669634i | \(-0.233549\pi\) | ||||
0.742692 | + | 0.669634i | \(0.233549\pi\) | |||||||
\(458\) | −21.7107 | −1.01447 | ||||||||
\(459\) | −1.70925 | −0.0797809 | ||||||||
\(460\) | 13.4981 | 0.629351 | ||||||||
\(461\) | −35.4539 | −1.65125 | −0.825626 | − | 0.564217i | \(-0.809178\pi\) | ||||
−0.825626 | + | 0.564217i | \(0.809178\pi\) | |||||||
\(462\) | 47.3464 | 2.20276 | ||||||||
\(463\) | 2.79877 | 0.130070 | 0.0650348 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650348 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(464\) | 7.27173 | 0.337582 | ||||||||
\(465\) | −46.4138 | −2.15239 | ||||||||
\(466\) | 34.7207 | 1.60841 | ||||||||
\(467\) | 35.2041 | 1.62905 | 0.814527 | − | 0.580126i | \(-0.196997\pi\) | ||||
0.814527 | + | 0.580126i | \(0.196997\pi\) | |||||||
\(468\) | 2.02952 | 0.0938145 | ||||||||
\(469\) | −9.12917 | −0.421546 | ||||||||
\(470\) | 30.3791 | 1.40128 | ||||||||
\(471\) | 55.6613 | 2.56474 | ||||||||
\(472\) | 10.2112 | 0.470008 | ||||||||
\(473\) | −29.7433 | −1.36760 | ||||||||
\(474\) | −79.9022 | −3.67003 | ||||||||
\(475\) | 6.96142 | 0.319412 | ||||||||
\(476\) | −25.0195 | −1.14677 | ||||||||
\(477\) | 15.4606 | 0.707893 | ||||||||
\(478\) | 35.6593 | 1.63102 | ||||||||
\(479\) | 2.50788 | 0.114588 | 0.0572940 | − | 0.998357i | \(-0.481753\pi\) | ||||
0.0572940 | + | 0.998357i | \(0.481753\pi\) | |||||||
\(480\) | 18.7470 | 0.855681 | ||||||||
\(481\) | −0.745863 | −0.0340084 | ||||||||
\(482\) | 25.2739 | 1.15119 | ||||||||
\(483\) | −7.64300 | −0.347768 | ||||||||
\(484\) | 6.35546 | 0.288885 | ||||||||
\(485\) | 25.3940 | 1.15308 | ||||||||
\(486\) | −53.2124 | −2.41376 | ||||||||
\(487\) | 16.6538 | 0.754655 | 0.377328 | − | 0.926080i | \(-0.376843\pi\) | ||||
0.377328 | + | 0.926080i | \(0.376843\pi\) | |||||||
\(488\) | 50.1814 | 2.27160 | ||||||||
\(489\) | 2.70572 | 0.122357 | ||||||||
\(490\) | −12.8549 | −0.580726 | ||||||||
\(491\) | 6.26557 | 0.282761 | 0.141381 | − | 0.989955i | \(-0.454846\pi\) | ||||
0.141381 | + | 0.989955i | \(0.454846\pi\) | |||||||
\(492\) | −81.4123 | −3.67035 | ||||||||
\(493\) | 10.1654 | 0.457825 | ||||||||
\(494\) | −1.32298 | −0.0595237 | ||||||||
\(495\) | 30.7523 | 1.38221 | ||||||||
\(496\) | −15.1669 | −0.681016 | ||||||||
\(497\) | 0.531727 | 0.0238512 | ||||||||
\(498\) | 73.5804 | 3.29722 | ||||||||
\(499\) | −30.2723 | −1.35518 | −0.677588 | − | 0.735442i | \(-0.736975\pi\) | ||||
−0.677588 | + | 0.735442i | \(0.736975\pi\) | |||||||
\(500\) | 28.0805 | 1.25580 | ||||||||
\(501\) | −6.34215 | −0.283347 | ||||||||
\(502\) | 41.9137 | 1.87070 | ||||||||
\(503\) | 21.4391 | 0.955923 | 0.477962 | − | 0.878381i | \(-0.341376\pi\) | ||||
0.477962 | + | 0.878381i | \(0.341376\pi\) | |||||||
\(504\) | 28.8088 | 1.28325 | ||||||||
\(505\) | 39.9293 | 1.77683 | ||||||||
\(506\) | −11.6685 | −0.518730 | ||||||||
\(507\) | 32.3616 | 1.43723 | ||||||||
\(508\) | 1.67656 | 0.0743855 | ||||||||
\(509\) | 16.0886 | 0.713116 | 0.356558 | − | 0.934273i | \(-0.383950\pi\) | ||||
0.356558 | + | 0.934273i | \(0.383950\pi\) | |||||||
\(510\) | −48.4185 | −2.14401 | ||||||||
\(511\) | 10.6081 | 0.469275 | ||||||||
\(512\) | 23.5704 | 1.04167 | ||||||||
\(513\) | −1.82099 | −0.0803989 | ||||||||
\(514\) | 37.3920 | 1.64929 | ||||||||
\(515\) | −27.2118 | −1.19910 | ||||||||
\(516\) | −76.5360 | −3.36931 | ||||||||
\(517\) | −17.0136 | −0.748255 | ||||||||
\(518\) | −23.1959 | −1.01917 | ||||||||
\(519\) | 28.2582 | 1.24040 | ||||||||
\(520\) | 1.82982 | 0.0802429 | ||||||||
\(521\) | 21.8917 | 0.959094 | 0.479547 | − | 0.877516i | \(-0.340801\pi\) | ||||
0.479547 | + | 0.877516i | \(0.340801\pi\) | |||||||
\(522\) | −25.6443 | −1.12242 | ||||||||
\(523\) | 34.7802 | 1.52083 | 0.760416 | − | 0.649436i | \(-0.224995\pi\) | ||||
0.760416 | + | 0.649436i | \(0.224995\pi\) | |||||||
\(524\) | −59.9293 | −2.61802 | ||||||||
\(525\) | 11.9444 | 0.521297 | ||||||||
\(526\) | 21.3822 | 0.932306 | ||||||||
\(527\) | −21.2023 | −0.923586 | ||||||||
\(528\) | 19.3975 | 0.844169 | ||||||||
\(529\) | −21.1164 | −0.918104 | ||||||||
\(530\) | 30.5395 | 1.32655 | ||||||||
\(531\) | −8.22770 | −0.357052 | ||||||||
\(532\) | −26.6552 | −1.15565 | ||||||||
\(533\) | 1.51686 | 0.0657026 | ||||||||
\(534\) | 101.326 | 4.38479 | ||||||||
\(535\) | −37.0811 | −1.60316 | ||||||||
\(536\) | −16.3697 | −0.707062 | ||||||||
\(537\) | −21.7609 | −0.939053 | ||||||||
\(538\) | 0.810151 | 0.0349281 | ||||||||
\(539\) | 7.19928 | 0.310095 | ||||||||
\(540\) | 5.51802 | 0.237458 | ||||||||
\(541\) | −4.86709 | −0.209252 | −0.104626 | − | 0.994512i | \(-0.533365\pi\) | ||||
−0.104626 | + | 0.994512i | \(0.533365\pi\) | |||||||
\(542\) | 17.7744 | 0.763475 | ||||||||
\(543\) | 60.5698 | 2.59930 | ||||||||
\(544\) | 8.56383 | 0.367171 | ||||||||
\(545\) | 22.1326 | 0.948057 | ||||||||
\(546\) | −2.26997 | −0.0971457 | ||||||||
\(547\) | −30.1606 | −1.28957 | −0.644787 | − | 0.764363i | \(-0.723054\pi\) | ||||
−0.644787 | + | 0.764363i | \(0.723054\pi\) | |||||||
\(548\) | 7.62197 | 0.325595 | ||||||||
\(549\) | −40.4338 | −1.72567 | ||||||||
\(550\) | 18.2355 | 0.777564 | ||||||||
\(551\) | 10.8299 | 0.461371 | ||||||||
\(552\) | −13.7048 | −0.583315 | ||||||||
\(553\) | 29.9946 | 1.27550 | ||||||||
\(554\) | 56.6074 | 2.40502 | ||||||||
\(555\) | −29.0817 | −1.23445 | ||||||||
\(556\) | 73.3675 | 3.11148 | ||||||||
\(557\) | −15.7159 | −0.665906 | −0.332953 | − | 0.942943i | \(-0.608045\pi\) | ||||
−0.332953 | + | 0.942943i | \(0.608045\pi\) | |||||||
\(558\) | 53.4872 | 2.26430 | ||||||||
\(559\) | 1.42601 | 0.0603138 | ||||||||
\(560\) | 13.0020 | 0.549436 | ||||||||
\(561\) | 27.1163 | 1.14485 | ||||||||
\(562\) | −30.2890 | −1.27766 | ||||||||
\(563\) | −5.15528 | −0.217269 | −0.108635 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108635 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(564\) | −43.7796 | −1.84345 | ||||||||
\(565\) | 30.7053 | 1.29178 | ||||||||
\(566\) | −27.6448 | −1.16200 | ||||||||
\(567\) | 18.4697 | 0.775654 | ||||||||
\(568\) | 0.953449 | 0.0400058 | ||||||||
\(569\) | 17.5813 | 0.737045 | 0.368523 | − | 0.929619i | \(-0.379864\pi\) | ||||
0.368523 | + | 0.929619i | \(0.379864\pi\) | |||||||
\(570\) | −51.5839 | −2.16061 | ||||||||
\(571\) | 23.9075 | 1.00050 | 0.500248 | − | 0.865882i | \(-0.333242\pi\) | ||||
0.500248 | + | 0.865882i | \(0.333242\pi\) | |||||||
\(572\) | −2.24516 | −0.0938750 | ||||||||
\(573\) | −5.29272 | −0.221107 | ||||||||
\(574\) | 47.1736 | 1.96899 | ||||||||
\(575\) | −2.94370 | −0.122761 | ||||||||
\(576\) | −35.6599 | −1.48583 | ||||||||
\(577\) | −6.80087 | −0.283124 | −0.141562 | − | 0.989929i | \(-0.545212\pi\) | ||||
−0.141562 | + | 0.989929i | \(0.545212\pi\) | |||||||
\(578\) | 18.3956 | 0.765154 | ||||||||
\(579\) | −21.2638 | −0.883695 | ||||||||
\(580\) | −32.8172 | −1.36266 | ||||||||
\(581\) | −27.6215 | −1.14593 | ||||||||
\(582\) | −56.4874 | −2.34148 | ||||||||
\(583\) | −17.1034 | −0.708350 | ||||||||
\(584\) | 19.0216 | 0.787118 | ||||||||
\(585\) | −1.47438 | −0.0609583 | ||||||||
\(586\) | 14.5407 | 0.600673 | ||||||||
\(587\) | −12.2824 | −0.506947 | −0.253474 | − | 0.967342i | \(-0.581573\pi\) | ||||
−0.253474 | + | 0.967342i | \(0.581573\pi\) | |||||||
\(588\) | 18.5253 | 0.763971 | ||||||||
\(589\) | −22.5884 | −0.930740 | ||||||||
\(590\) | −16.2523 | −0.669095 | ||||||||
\(591\) | 21.9135 | 0.901399 | ||||||||
\(592\) | −9.50323 | −0.390580 | ||||||||
\(593\) | −14.2660 | −0.585833 | −0.292917 | − | 0.956138i | \(-0.594626\pi\) | ||||
−0.292917 | + | 0.956138i | \(0.594626\pi\) | |||||||
\(594\) | −4.77011 | −0.195720 | ||||||||
\(595\) | 18.1759 | 0.745139 | ||||||||
\(596\) | −31.5639 | −1.29291 | ||||||||
\(597\) | −0.814105 | −0.0333191 | ||||||||
\(598\) | 0.559434 | 0.0228770 | ||||||||
\(599\) | 0.498134 | 0.0203532 | 0.0101766 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101766 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(600\) | 21.4177 | 0.874375 | ||||||||
\(601\) | −21.6279 | −0.882221 | −0.441110 | − | 0.897453i | \(-0.645415\pi\) | ||||
−0.441110 | + | 0.897453i | \(0.645415\pi\) | |||||||
\(602\) | 44.3481 | 1.80749 | ||||||||
\(603\) | 13.1899 | 0.537135 | ||||||||
\(604\) | 26.1855 | 1.06547 | ||||||||
\(605\) | −4.61705 | −0.187710 | ||||||||
\(606\) | −88.8204 | −3.60808 | ||||||||
\(607\) | −24.1356 | −0.979633 | −0.489817 | − | 0.871826i | \(-0.662936\pi\) | ||||
−0.489817 | + | 0.871826i | \(0.662936\pi\) | |||||||
\(608\) | 9.12371 | 0.370015 | ||||||||
\(609\) | 18.5820 | 0.752981 | ||||||||
\(610\) | −79.8694 | −3.23382 | ||||||||
\(611\) | 0.815695 | 0.0329995 | ||||||||
\(612\) | 36.1484 | 1.46121 | ||||||||
\(613\) | −29.3641 | −1.18600 | −0.593002 | − | 0.805201i | \(-0.702057\pi\) | ||||
−0.593002 | + | 0.805201i | \(0.702057\pi\) | |||||||
\(614\) | −0.965913 | −0.0389811 | ||||||||
\(615\) | 59.1436 | 2.38490 | ||||||||
\(616\) | −31.8699 | −1.28407 | ||||||||
\(617\) | 14.0470 | 0.565512 | 0.282756 | − | 0.959192i | \(-0.408751\pi\) | ||||
0.282756 | + | 0.959192i | \(0.408751\pi\) | |||||||
\(618\) | 60.5311 | 2.43492 | ||||||||
\(619\) | −14.5848 | −0.586214 | −0.293107 | − | 0.956080i | \(-0.594689\pi\) | ||||
−0.293107 | + | 0.956080i | \(0.594689\pi\) | |||||||
\(620\) | 68.4480 | 2.74894 | ||||||||
\(621\) | 0.770024 | 0.0309000 | ||||||||
\(622\) | 27.8662 | 1.11733 | ||||||||
\(623\) | −38.0368 | −1.52391 | ||||||||
\(624\) | −0.929992 | −0.0372295 | ||||||||
\(625\) | −31.1239 | −1.24495 | ||||||||
\(626\) | −43.4631 | −1.73713 | ||||||||
\(627\) | 28.8891 | 1.15372 | ||||||||
\(628\) | −82.0857 | −3.27558 | ||||||||
\(629\) | −13.2848 | −0.529700 | ||||||||
\(630\) | −45.8525 | −1.82681 | ||||||||
\(631\) | 15.8228 | 0.629895 | 0.314947 | − | 0.949109i | \(-0.398013\pi\) | ||||
0.314947 | + | 0.949109i | \(0.398013\pi\) | |||||||
\(632\) | 53.7839 | 2.13941 | ||||||||
\(633\) | −54.2589 | −2.15660 | ||||||||
\(634\) | −64.4048 | −2.55784 | ||||||||
\(635\) | −1.21797 | −0.0483338 | ||||||||
\(636\) | −44.0107 | −1.74514 | ||||||||
\(637\) | −0.345161 | −0.0136758 | ||||||||
\(638\) | 28.3691 | 1.12314 | ||||||||
\(639\) | −0.768246 | −0.0303913 | ||||||||
\(640\) | −55.4115 | −2.19033 | ||||||||
\(641\) | 1.27998 | 0.0505564 | 0.0252782 | − | 0.999680i | \(-0.491953\pi\) | ||||
0.0252782 | + | 0.999680i | \(0.491953\pi\) | |||||||
\(642\) | 82.4847 | 3.25541 | ||||||||
\(643\) | 30.2649 | 1.19353 | 0.596765 | − | 0.802416i | \(-0.296452\pi\) | ||||
0.596765 | + | 0.802416i | \(0.296452\pi\) | |||||||
\(644\) | 11.2714 | 0.444155 | ||||||||
\(645\) | 55.6011 | 2.18929 | ||||||||
\(646\) | −23.5640 | −0.927115 | ||||||||
\(647\) | 14.0216 | 0.551246 | 0.275623 | − | 0.961266i | \(-0.411116\pi\) | ||||
0.275623 | + | 0.961266i | \(0.411116\pi\) | |||||||
\(648\) | 33.1183 | 1.30101 | ||||||||
\(649\) | 9.10193 | 0.357282 | ||||||||
\(650\) | −0.874279 | −0.0342921 | ||||||||
\(651\) | −38.7572 | −1.51901 | ||||||||
\(652\) | −3.99021 | −0.156269 | ||||||||
\(653\) | 31.7172 | 1.24119 | 0.620595 | − | 0.784131i | \(-0.286891\pi\) | ||||
0.620595 | + | 0.784131i | \(0.286891\pi\) | |||||||
\(654\) | −49.2327 | −1.92515 | ||||||||
\(655\) | 43.5368 | 1.70112 | ||||||||
\(656\) | 19.3267 | 0.754582 | ||||||||
\(657\) | −15.3267 | −0.597952 | ||||||||
\(658\) | 25.3677 | 0.988935 | ||||||||
\(659\) | 48.4984 | 1.88923 | 0.944614 | − | 0.328182i | \(-0.106436\pi\) | ||||
0.944614 | + | 0.328182i | \(0.106436\pi\) | |||||||
\(660\) | −87.5405 | −3.40751 | ||||||||
\(661\) | 34.9661 | 1.36003 | 0.680013 | − | 0.733201i | \(-0.261974\pi\) | ||||
0.680013 | + | 0.733201i | \(0.261974\pi\) | |||||||
\(662\) | 50.4476 | 1.96070 | ||||||||
\(663\) | −1.30006 | −0.0504902 | ||||||||
\(664\) | −49.5285 | −1.92208 | ||||||||
\(665\) | 19.3642 | 0.750911 | ||||||||
\(666\) | 33.5138 | 1.29863 | ||||||||
\(667\) | −4.57954 | −0.177320 | ||||||||
\(668\) | 9.35299 | 0.361878 | ||||||||
\(669\) | 27.7252 | 1.07192 | ||||||||
\(670\) | 26.0542 | 1.00656 | ||||||||
\(671\) | 44.7301 | 1.72679 | ||||||||
\(672\) | 15.6545 | 0.603884 | ||||||||
\(673\) | −24.0260 | −0.926135 | −0.463067 | − | 0.886323i | \(-0.653251\pi\) | ||||
−0.463067 | + | 0.886323i | \(0.653251\pi\) | |||||||
\(674\) | 32.2305 | 1.24147 | ||||||||
\(675\) | −1.20339 | −0.0463184 | ||||||||
\(676\) | −47.7248 | −1.83557 | ||||||||
\(677\) | −38.3303 | −1.47315 | −0.736576 | − | 0.676354i | \(-0.763559\pi\) | ||||
−0.736576 | + | 0.676354i | \(0.763559\pi\) | |||||||
\(678\) | −68.3020 | −2.62312 | ||||||||
\(679\) | 21.2049 | 0.813769 | ||||||||
\(680\) | 32.5915 | 1.24983 | ||||||||
\(681\) | 54.1040 | 2.07327 | ||||||||
\(682\) | −59.1705 | −2.26576 | ||||||||
\(683\) | 23.5458 | 0.900955 | 0.450478 | − | 0.892788i | \(-0.351254\pi\) | ||||
0.450478 | + | 0.892788i | \(0.351254\pi\) | |||||||
\(684\) | 38.5117 | 1.47253 | ||||||||
\(685\) | −5.53713 | −0.211563 | ||||||||
\(686\) | −47.9694 | −1.83148 | ||||||||
\(687\) | −22.7294 | −0.867179 | ||||||||
\(688\) | 18.1691 | 0.692692 | ||||||||
\(689\) | 0.820002 | 0.0312396 | ||||||||
\(690\) | 21.8127 | 0.830397 | ||||||||
\(691\) | −27.3120 | −1.03900 | −0.519499 | − | 0.854471i | \(-0.673881\pi\) | ||||
−0.519499 | + | 0.854471i | \(0.673881\pi\) | |||||||
\(692\) | −41.6734 | −1.58418 | ||||||||
\(693\) | 25.6793 | 0.975476 | ||||||||
\(694\) | 14.3676 | 0.545385 | ||||||||
\(695\) | −53.2993 | −2.02176 | ||||||||
\(696\) | 33.3197 | 1.26298 | ||||||||
\(697\) | 27.0174 | 1.02336 | ||||||||
\(698\) | 29.2539 | 1.10728 | ||||||||
\(699\) | 36.3498 | 1.37488 | ||||||||
\(700\) | −17.6148 | −0.665778 | ||||||||
\(701\) | −52.1011 | −1.96783 | −0.983917 | − | 0.178628i | \(-0.942834\pi\) | ||||
−0.983917 | + | 0.178628i | \(0.942834\pi\) | |||||||
\(702\) | 0.228697 | 0.00863162 | ||||||||
\(703\) | −14.1533 | −0.533803 | ||||||||
\(704\) | 39.4489 | 1.48679 | ||||||||
\(705\) | 31.8045 | 1.19783 | ||||||||
\(706\) | −7.32333 | −0.275617 | ||||||||
\(707\) | 33.3424 | 1.25397 | ||||||||
\(708\) | 23.4212 | 0.880224 | ||||||||
\(709\) | 0.596094 | 0.0223868 | 0.0111934 | − | 0.999937i | \(-0.496437\pi\) | ||||
0.0111934 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(710\) | −1.51752 | −0.0569517 | ||||||||
\(711\) | −43.3366 | −1.62525 | ||||||||
\(712\) | −68.2045 | −2.55607 | ||||||||
\(713\) | 9.55172 | 0.357715 | ||||||||
\(714\) | −40.4312 | −1.51310 | ||||||||
\(715\) | 1.63104 | 0.0609976 | ||||||||
\(716\) | 32.0916 | 1.19932 | ||||||||
\(717\) | 37.3324 | 1.39421 | ||||||||
\(718\) | 32.0804 | 1.19723 | ||||||||
\(719\) | 36.8292 | 1.37350 | 0.686749 | − | 0.726895i | \(-0.259037\pi\) | ||||
0.686749 | + | 0.726895i | \(0.259037\pi\) | |||||||
\(720\) | −18.7855 | −0.700094 | ||||||||
\(721\) | −22.7229 | −0.846244 | ||||||||
\(722\) | 20.1753 | 0.750847 | ||||||||
\(723\) | 26.4597 | 0.984048 | ||||||||
\(724\) | −89.3244 | −3.31971 | ||||||||
\(725\) | 7.15686 | 0.265799 | ||||||||
\(726\) | 10.2704 | 0.381169 | ||||||||
\(727\) | 5.47852 | 0.203187 | 0.101594 | − | 0.994826i | \(-0.467606\pi\) | ||||
0.101594 | + | 0.994826i | \(0.467606\pi\) | |||||||
\(728\) | 1.52797 | 0.0566302 | ||||||||
\(729\) | −30.8847 | −1.14388 | ||||||||
\(730\) | −30.2750 | −1.12053 | ||||||||
\(731\) | 25.3991 | 0.939421 | ||||||||
\(732\) | 115.100 | 4.25423 | ||||||||
\(733\) | 34.9544 | 1.29107 | 0.645535 | − | 0.763731i | \(-0.276634\pi\) | ||||
0.645535 | + | 0.763731i | \(0.276634\pi\) | |||||||
\(734\) | 43.8063 | 1.61692 | ||||||||
\(735\) | −13.4581 | −0.496408 | ||||||||
\(736\) | −3.85804 | −0.142209 | ||||||||
\(737\) | −14.5914 | −0.537482 | ||||||||
\(738\) | −68.1570 | −2.50889 | ||||||||
\(739\) | 16.7379 | 0.615714 | 0.307857 | − | 0.951433i | \(-0.400388\pi\) | ||||
0.307857 | + | 0.951433i | \(0.400388\pi\) | |||||||
\(740\) | 42.8878 | 1.57659 | ||||||||
\(741\) | −1.38505 | −0.0508813 | ||||||||
\(742\) | 25.5016 | 0.936194 | ||||||||
\(743\) | −37.3283 | −1.36944 | −0.684722 | − | 0.728805i | \(-0.740076\pi\) | ||||
−0.684722 | + | 0.728805i | \(0.740076\pi\) | |||||||
\(744\) | −69.4962 | −2.54786 | ||||||||
\(745\) | 22.9302 | 0.840098 | ||||||||
\(746\) | −16.5452 | −0.605764 | ||||||||
\(747\) | 39.9078 | 1.46015 | ||||||||
\(748\) | −39.9894 | −1.46216 | ||||||||
\(749\) | −30.9641 | −1.13140 | ||||||||
\(750\) | 45.3777 | 1.65696 | ||||||||
\(751\) | −9.92872 | −0.362304 | −0.181152 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181152 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(752\) | 10.3930 | 0.378993 | ||||||||
\(753\) | 43.8802 | 1.59908 | ||||||||
\(754\) | −1.36012 | −0.0495327 | ||||||||
\(755\) | −19.0230 | −0.692317 | ||||||||
\(756\) | 4.60775 | 0.167582 | ||||||||
\(757\) | −0.302253 | −0.0109856 | −0.00549279 | − | 0.999985i | \(-0.501748\pi\) | ||||
−0.00549279 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(758\) | −27.0416 | −0.982197 | ||||||||
\(759\) | −12.2160 | −0.443414 | ||||||||
\(760\) | 34.7222 | 1.25951 | ||||||||
\(761\) | 21.5937 | 0.782769 | 0.391385 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391385 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(762\) | 2.70931 | 0.0981478 | ||||||||
\(763\) | 18.4815 | 0.669077 | ||||||||
\(764\) | 7.80536 | 0.282388 | ||||||||
\(765\) | −26.2607 | −0.949459 | ||||||||
\(766\) | 86.2685 | 3.11701 | ||||||||
\(767\) | −0.436382 | −0.0157568 | ||||||||
\(768\) | 68.0820 | 2.45670 | ||||||||
\(769\) | −4.25428 | −0.153413 | −0.0767067 | − | 0.997054i | \(-0.524440\pi\) | ||||
−0.0767067 | + | 0.997054i | \(0.524440\pi\) | |||||||
\(770\) | 50.7246 | 1.82799 | ||||||||
\(771\) | 39.1464 | 1.40982 | ||||||||
\(772\) | 31.3585 | 1.12862 | ||||||||
\(773\) | 21.6549 | 0.778872 | 0.389436 | − | 0.921054i | \(-0.372670\pi\) | ||||
0.389436 | + | 0.921054i | \(0.372670\pi\) | |||||||
\(774\) | −64.0747 | −2.30312 | ||||||||
\(775\) | −14.9273 | −0.536206 | ||||||||
\(776\) | 38.0229 | 1.36494 | ||||||||
\(777\) | −24.2843 | −0.871194 | ||||||||
\(778\) | −66.6015 | −2.38778 | ||||||||
\(779\) | 28.7837 | 1.03128 | ||||||||
\(780\) | 4.19703 | 0.150278 | ||||||||
\(781\) | 0.849875 | 0.0304109 | ||||||||
\(782\) | 9.96427 | 0.356322 | ||||||||
\(783\) | −1.87212 | −0.0669040 | ||||||||
\(784\) | −4.39778 | −0.157064 | ||||||||
\(785\) | 59.6328 | 2.12838 | ||||||||
\(786\) | −96.8450 | −3.45435 | ||||||||
\(787\) | 38.9198 | 1.38734 | 0.693670 | − | 0.720293i | \(-0.255993\pi\) | ||||
0.693670 | + | 0.720293i | \(0.255993\pi\) | |||||||
\(788\) | −32.3165 | −1.15123 | ||||||||
\(789\) | 22.3854 | 0.796942 | ||||||||
\(790\) | −85.6032 | −3.04563 | ||||||||
\(791\) | 25.6400 | 0.911654 | ||||||||
\(792\) | 46.0460 | 1.63617 | ||||||||
\(793\) | −2.14453 | −0.0761546 | ||||||||
\(794\) | −65.6443 | −2.32963 | ||||||||
\(795\) | 31.9724 | 1.13395 | ||||||||
\(796\) | 1.20059 | 0.0425537 | ||||||||
\(797\) | 0.932362 | 0.0330260 | 0.0165130 | − | 0.999864i | \(-0.494744\pi\) | ||||
0.0165130 | + | 0.999864i | \(0.494744\pi\) | |||||||
\(798\) | −43.0745 | −1.52482 | ||||||||
\(799\) | 14.5286 | 0.513985 | ||||||||
\(800\) | 6.02932 | 0.213168 | ||||||||
\(801\) | 54.9560 | 1.94178 | ||||||||
\(802\) | 78.3017 | 2.76493 | ||||||||
\(803\) | 16.9552 | 0.598337 | ||||||||
\(804\) | −37.5469 | −1.32418 | ||||||||
\(805\) | −8.18832 | −0.288600 | ||||||||
\(806\) | 2.83686 | 0.0999242 | ||||||||
\(807\) | 0.848164 | 0.0298568 | ||||||||
\(808\) | 59.7869 | 2.10330 | ||||||||
\(809\) | −41.2075 | −1.44878 | −0.724389 | − | 0.689392i | \(-0.757878\pi\) | ||||
−0.724389 | + | 0.689392i | \(0.757878\pi\) | |||||||
\(810\) | −52.7116 | −1.85210 | ||||||||
\(811\) | 38.7356 | 1.36019 | 0.680096 | − | 0.733123i | \(-0.261938\pi\) | ||||
0.680096 | + | 0.733123i | \(0.261938\pi\) | |||||||
\(812\) | −27.4035 | −0.961675 | ||||||||
\(813\) | 18.6083 | 0.652623 | ||||||||
\(814\) | −37.0748 | −1.29947 | ||||||||
\(815\) | 2.89877 | 0.101539 | ||||||||
\(816\) | −16.5644 | −0.579870 | ||||||||
\(817\) | 27.0596 | 0.946697 | ||||||||
\(818\) | −27.6847 | −0.967972 | ||||||||
\(819\) | −1.23116 | −0.0430203 | ||||||||
\(820\) | −87.2210 | −3.04589 | ||||||||
\(821\) | 29.3522 | 1.02440 | 0.512200 | − | 0.858866i | \(-0.328831\pi\) | ||||
0.512200 | + | 0.858866i | \(0.328831\pi\) | |||||||
\(822\) | 12.3170 | 0.429605 | ||||||||
\(823\) | −27.0107 | −0.941535 | −0.470768 | − | 0.882257i | \(-0.656023\pi\) | ||||
−0.470768 | + | 0.882257i | \(0.656023\pi\) | |||||||
\(824\) | −40.7448 | −1.41941 | ||||||||
\(825\) | 19.0911 | 0.664667 | ||||||||
\(826\) | −13.5712 | −0.472204 | ||||||||
\(827\) | 12.9494 | 0.450295 | 0.225147 | − | 0.974325i | \(-0.427714\pi\) | ||||
0.225147 | + | 0.974325i | \(0.427714\pi\) | |||||||
\(828\) | −16.2850 | −0.565944 | ||||||||
\(829\) | −0.270202 | −0.00938449 | −0.00469225 | − | 0.999989i | \(-0.501494\pi\) | ||||
−0.00469225 | + | 0.999989i | \(0.501494\pi\) | |||||||
\(830\) | 78.8303 | 2.73624 | ||||||||
\(831\) | 59.2634 | 2.05583 | ||||||||
\(832\) | −1.89133 | −0.0655701 | ||||||||
\(833\) | −6.14778 | −0.213008 | ||||||||
\(834\) | 118.561 | 4.10543 | ||||||||
\(835\) | −6.79466 | −0.235139 | ||||||||
\(836\) | −42.6038 | −1.47348 | ||||||||
\(837\) | 3.90475 | 0.134968 | ||||||||
\(838\) | −36.5104 | −1.26123 | ||||||||
\(839\) | 6.54256 | 0.225874 | 0.112937 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112937 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(840\) | 59.5764 | 2.05558 | ||||||||
\(841\) | −17.8660 | −0.616070 | ||||||||
\(842\) | −53.4889 | −1.84335 | ||||||||
\(843\) | −31.7102 | −1.09216 | ||||||||
\(844\) | 80.0175 | 2.75432 | ||||||||
\(845\) | 34.6706 | 1.19271 | ||||||||
\(846\) | −36.6515 | −1.26010 | ||||||||
\(847\) | −3.85541 | −0.132473 | ||||||||
\(848\) | 10.4478 | 0.358780 | ||||||||
\(849\) | −28.9419 | −0.993283 | ||||||||
\(850\) | −15.5721 | −0.534118 | ||||||||
\(851\) | 5.98487 | 0.205159 | ||||||||
\(852\) | 2.18691 | 0.0749224 | ||||||||
\(853\) | −1.50858 | −0.0516528 | −0.0258264 | − | 0.999666i | \(-0.508222\pi\) | ||||
−0.0258264 | + | 0.999666i | \(0.508222\pi\) | |||||||
\(854\) | −66.6939 | −2.28222 | ||||||||
\(855\) | −27.9776 | −0.956813 | ||||||||
\(856\) | −55.5222 | −1.89771 | ||||||||
\(857\) | 19.2304 | 0.656897 | 0.328448 | − | 0.944522i | \(-0.393474\pi\) | ||||
0.328448 | + | 0.944522i | \(0.393474\pi\) | |||||||
\(858\) | −3.62816 | −0.123863 | ||||||||
\(859\) | −28.0626 | −0.957485 | −0.478743 | − | 0.877955i | \(-0.658907\pi\) | ||||
−0.478743 | + | 0.877955i | \(0.658907\pi\) | |||||||
\(860\) | −81.9968 | −2.79607 | ||||||||
\(861\) | 49.3870 | 1.68310 | ||||||||
\(862\) | 52.2724 | 1.78041 | ||||||||
\(863\) | −15.6969 | −0.534328 | −0.267164 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267164 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(864\) | −1.57717 | −0.0536564 | ||||||||
\(865\) | 30.2745 | 1.02936 | ||||||||
\(866\) | −87.5287 | −2.97435 | ||||||||
\(867\) | 19.2587 | 0.654059 | ||||||||
\(868\) | 57.1566 | 1.94002 | ||||||||
\(869\) | 47.9413 | 1.62630 | ||||||||
\(870\) | −53.0321 | −1.79796 | ||||||||
\(871\) | 0.699569 | 0.0237040 | ||||||||
\(872\) | 33.1396 | 1.12225 | ||||||||
\(873\) | −30.6371 | −1.03691 | ||||||||
\(874\) | 10.6157 | 0.359082 | ||||||||
\(875\) | −17.0344 | −0.575868 | ||||||||
\(876\) | 43.6295 | 1.47410 | ||||||||
\(877\) | −14.6274 | −0.493934 | −0.246967 | − | 0.969024i | \(-0.579434\pi\) | ||||
−0.246967 | + | 0.969024i | \(0.579434\pi\) | |||||||
\(878\) | −80.2672 | −2.70889 | ||||||||
\(879\) | 15.2230 | 0.513459 | ||||||||
\(880\) | 20.7815 | 0.700545 | ||||||||
\(881\) | 24.6365 | 0.830024 | 0.415012 | − | 0.909816i | \(-0.363777\pi\) | ||||
0.415012 | + | 0.909816i | \(0.363777\pi\) | |||||||
\(882\) | 15.5091 | 0.522218 | ||||||||
\(883\) | 21.6211 | 0.727609 | 0.363804 | − | 0.931475i | \(-0.381478\pi\) | ||||
0.363804 | + | 0.931475i | \(0.381478\pi\) | |||||||
\(884\) | 1.91724 | 0.0644839 | ||||||||
\(885\) | −17.0148 | −0.571947 | ||||||||
\(886\) | −28.7792 | −0.966855 | ||||||||
\(887\) | −19.8445 | −0.666314 | −0.333157 | − | 0.942871i | \(-0.608114\pi\) | ||||
−0.333157 | + | 0.942871i | \(0.608114\pi\) | |||||||
\(888\) | −43.5446 | −1.46126 | ||||||||
\(889\) | −1.01705 | −0.0341108 | ||||||||
\(890\) | 108.555 | 3.63878 | ||||||||
\(891\) | 29.5206 | 0.988979 | ||||||||
\(892\) | −40.8873 | −1.36901 | ||||||||
\(893\) | 15.4785 | 0.517967 | ||||||||
\(894\) | −51.0069 | −1.70592 | ||||||||
\(895\) | −23.3136 | −0.779286 | ||||||||
\(896\) | −46.2706 | −1.54579 | ||||||||
\(897\) | 0.585683 | 0.0195554 | ||||||||
\(898\) | −68.5251 | −2.28671 | ||||||||
\(899\) | −23.2226 | −0.774516 | ||||||||
\(900\) | 25.4501 | 0.848337 | ||||||||
\(901\) | 14.6053 | 0.486574 | ||||||||
\(902\) | 75.3990 | 2.51051 | ||||||||
\(903\) | 46.4289 | 1.54506 | ||||||||
\(904\) | 45.9756 | 1.52912 | ||||||||
\(905\) | 64.8915 | 2.15707 | ||||||||
\(906\) | 42.3154 | 1.40584 | ||||||||
\(907\) | −57.5316 | −1.91031 | −0.955153 | − | 0.296114i | \(-0.904309\pi\) | ||||
−0.955153 | + | 0.296114i | \(0.904309\pi\) | |||||||
\(908\) | −79.7890 | −2.64789 | ||||||||
\(909\) | −48.1735 | −1.59782 | ||||||||
\(910\) | −2.43193 | −0.0806178 | ||||||||
\(911\) | 12.7535 | 0.422543 | 0.211271 | − | 0.977427i | \(-0.432240\pi\) | ||||
0.211271 | + | 0.977427i | \(0.432240\pi\) | |||||||
\(912\) | −17.6473 | −0.584361 | ||||||||
\(913\) | −44.1482 | −1.46109 | ||||||||
\(914\) | −75.6743 | −2.50308 | ||||||||
\(915\) | −83.6169 | −2.76429 | ||||||||
\(916\) | 33.5198 | 1.10752 | ||||||||
\(917\) | 36.3548 | 1.20054 | ||||||||
\(918\) | 4.07340 | 0.134442 | ||||||||
\(919\) | −1.67382 | −0.0552142 | −0.0276071 | − | 0.999619i | \(-0.508789\pi\) | ||||
−0.0276071 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(920\) | −14.6826 | −0.484072 | ||||||||
\(921\) | −1.01123 | −0.0333213 | ||||||||
\(922\) | 84.4921 | 2.78260 | ||||||||
\(923\) | −0.0407463 | −0.00134118 | ||||||||
\(924\) | −73.0995 | −2.40480 | ||||||||
\(925\) | −9.35310 | −0.307528 | ||||||||
\(926\) | −6.66989 | −0.219186 | ||||||||
\(927\) | 32.8302 | 1.07829 | ||||||||
\(928\) | 9.37985 | 0.307909 | ||||||||
\(929\) | 1.56230 | 0.0512573 | 0.0256287 | − | 0.999672i | \(-0.491841\pi\) | ||||
0.0256287 | + | 0.999672i | \(0.491841\pi\) | |||||||
\(930\) | 110.611 | 3.62708 | ||||||||
\(931\) | −6.54970 | −0.214658 | ||||||||
\(932\) | −53.6063 | −1.75593 | ||||||||
\(933\) | 29.1736 | 0.955102 | ||||||||
\(934\) | −83.8968 | −2.74519 | ||||||||
\(935\) | 29.0511 | 0.950072 | ||||||||
\(936\) | −2.20762 | −0.0721583 | ||||||||
\(937\) | −41.5510 | −1.35741 | −0.678706 | − | 0.734410i | \(-0.737459\pi\) | ||||
−0.678706 | + | 0.734410i | \(0.737459\pi\) | |||||||
\(938\) | 21.7562 | 0.710366 | ||||||||
\(939\) | −45.5023 | −1.48491 | ||||||||
\(940\) | −46.9032 | −1.52981 | ||||||||
\(941\) | −5.02999 | −0.163973 | −0.0819864 | − | 0.996633i | \(-0.526126\pi\) | ||||
−0.0819864 | + | 0.996633i | \(0.526126\pi\) | |||||||
\(942\) | −132.649 | −4.32195 | ||||||||
\(943\) | −12.1714 | −0.396357 | ||||||||
\(944\) | −5.56004 | −0.180964 | ||||||||
\(945\) | −3.34739 | −0.108891 | ||||||||
\(946\) | 70.8829 | 2.30460 | ||||||||
\(947\) | 32.6372 | 1.06057 | 0.530284 | − | 0.847820i | \(-0.322085\pi\) | ||||
0.530284 | + | 0.847820i | \(0.322085\pi\) | |||||||
\(948\) | 123.363 | 4.00665 | ||||||||
\(949\) | −0.812899 | −0.0263878 | ||||||||
\(950\) | −16.5901 | −0.538255 | ||||||||
\(951\) | −67.4267 | −2.18646 | ||||||||
\(952\) | 27.2151 | 0.882046 | ||||||||
\(953\) | −38.9007 | −1.26012 | −0.630058 | − | 0.776548i | \(-0.716969\pi\) | ||||
−0.630058 | + | 0.776548i | \(0.716969\pi\) | |||||||
\(954\) | −36.8450 | −1.19290 | ||||||||
\(955\) | −5.67035 | −0.183488 | ||||||||
\(956\) | −55.0554 | −1.78062 | ||||||||
\(957\) | 29.7002 | 0.960070 | ||||||||
\(958\) | −5.97667 | −0.193097 | ||||||||
\(959\) | −4.62371 | −0.149307 | ||||||||
\(960\) | −73.7444 | −2.38009 | ||||||||
\(961\) | 17.4363 | 0.562460 | ||||||||
\(962\) | 1.77751 | 0.0573091 | ||||||||
\(963\) | 44.7372 | 1.44164 | ||||||||
\(964\) | −39.0211 | −1.25678 | ||||||||
\(965\) | −22.7810 | −0.733346 | ||||||||
\(966\) | 18.2144 | 0.586040 | ||||||||
\(967\) | −21.9054 | −0.704430 | −0.352215 | − | 0.935919i | \(-0.614571\pi\) | ||||
−0.352215 | + | 0.935919i | \(0.614571\pi\) | |||||||
\(968\) | −6.91319 | −0.222198 | ||||||||
\(969\) | −24.6697 | −0.792504 | ||||||||
\(970\) | −60.5178 | −1.94311 | ||||||||
\(971\) | −50.0639 | −1.60663 | −0.803314 | − | 0.595556i | \(-0.796932\pi\) | ||||
−0.803314 | + | 0.595556i | \(0.796932\pi\) | |||||||
\(972\) | 82.1561 | 2.63516 | ||||||||
\(973\) | −44.5068 | −1.42682 | ||||||||
\(974\) | −39.6885 | −1.27170 | ||||||||
\(975\) | −0.915300 | −0.0293131 | ||||||||
\(976\) | −27.3240 | −0.874621 | ||||||||
\(977\) | 53.3465 | 1.70671 | 0.853353 | − | 0.521333i | \(-0.174565\pi\) | ||||
0.853353 | + | 0.521333i | \(0.174565\pi\) | |||||||
\(978\) | −6.44814 | −0.206189 | ||||||||
\(979\) | −60.7954 | −1.94303 | ||||||||
\(980\) | 19.8471 | 0.633992 | ||||||||
\(981\) | −26.7023 | −0.852540 | ||||||||
\(982\) | −14.9318 | −0.476493 | ||||||||
\(983\) | −48.7942 | −1.55629 | −0.778147 | − | 0.628082i | \(-0.783840\pi\) | ||||
−0.778147 | + | 0.628082i | \(0.783840\pi\) | |||||||
\(984\) | 88.5567 | 2.82308 | ||||||||
\(985\) | 23.4770 | 0.748039 | ||||||||
\(986\) | −24.2256 | −0.771500 | ||||||||
\(987\) | 26.5579 | 0.845348 | ||||||||
\(988\) | 2.04259 | 0.0649834 | ||||||||
\(989\) | −11.4424 | −0.363848 | ||||||||
\(990\) | −73.2875 | −2.32923 | ||||||||
\(991\) | −4.87308 | −0.154798 | −0.0773992 | − | 0.997000i | \(-0.524662\pi\) | ||||
−0.0773992 | + | 0.997000i | \(0.524662\pi\) | |||||||
\(992\) | −19.5639 | −0.621155 | ||||||||
\(993\) | 52.8146 | 1.67602 | ||||||||
\(994\) | −1.26719 | −0.0401927 | ||||||||
\(995\) | −0.872191 | −0.0276503 | ||||||||
\(996\) | −113.603 | −3.59964 | ||||||||
\(997\) | 28.5128 | 0.903009 | 0.451504 | − | 0.892269i | \(-0.350888\pi\) | ||||
0.451504 | + | 0.892269i | \(0.350888\pi\) | |||||||
\(998\) | 72.1436 | 2.28367 | ||||||||
\(999\) | 2.44662 | 0.0774076 |
(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 | 6037.2.a.b.1.19 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.19 | ✓ | 259 | 1.1 | even | 1 | trivial |