Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, 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("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.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: | \(64.1837531447\) |
Analytic rank: | \(1\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.53354 | −1.46274 | −0.731371 | − | 0.681980i | \(-0.761119\pi\) | ||||
−0.731371 | + | 0.681980i | \(0.761119\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.39163 | 0.622357 | 0.311179 | − | 0.950351i | \(-0.399276\pi\) | ||||
0.311179 | + | 0.950351i | \(0.399276\pi\) | |||||||
\(6\) | 2.53354 | 1.03431 | ||||||||
\(7\) | 4.71879 | 1.78353 | 0.891767 | − | 0.452496i | \(-0.149466\pi\) | ||||
0.891767 | + | 0.452496i | \(0.149466\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.41884 | 1.13961 | ||||||||
\(10\) | −1.39163 | −0.440073 | ||||||||
\(11\) | −2.76601 | −0.833984 | −0.416992 | − | 0.908910i | \(-0.636916\pi\) | ||||
−0.416992 | + | 0.908910i | \(0.636916\pi\) | |||||||
\(12\) | −2.53354 | −0.731371 | ||||||||
\(13\) | −2.19021 | −0.607455 | −0.303727 | − | 0.952759i | \(-0.598231\pi\) | ||||
−0.303727 | + | 0.952759i | \(0.598231\pi\) | |||||||
\(14\) | −4.71879 | −1.26115 | ||||||||
\(15\) | −3.52576 | −0.910348 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.13908 | 1.24641 | 0.623205 | − | 0.782058i | \(-0.285830\pi\) | ||||
0.623205 | + | 0.782058i | \(0.285830\pi\) | |||||||
\(18\) | −3.41884 | −0.805829 | ||||||||
\(19\) | −6.17334 | −1.41626 | −0.708130 | − | 0.706082i | \(-0.750461\pi\) | ||||
−0.708130 | + | 0.706082i | \(0.750461\pi\) | |||||||
\(20\) | 1.39163 | 0.311179 | ||||||||
\(21\) | −11.9552 | −2.60885 | ||||||||
\(22\) | 2.76601 | 0.589716 | ||||||||
\(23\) | 6.53406 | 1.36245 | 0.681223 | − | 0.732076i | \(-0.261448\pi\) | ||||
0.681223 | + | 0.732076i | \(0.261448\pi\) | |||||||
\(24\) | 2.53354 | 0.517157 | ||||||||
\(25\) | −3.06336 | −0.612671 | ||||||||
\(26\) | 2.19021 | 0.429536 | ||||||||
\(27\) | −1.06116 | −0.204220 | ||||||||
\(28\) | 4.71879 | 0.891767 | ||||||||
\(29\) | −3.72122 | −0.691012 | −0.345506 | − | 0.938416i | \(-0.612293\pi\) | ||||
−0.345506 | + | 0.938416i | \(0.612293\pi\) | |||||||
\(30\) | 3.52576 | 0.643713 | ||||||||
\(31\) | 0.253263 | 0.0454874 | 0.0227437 | − | 0.999741i | \(-0.492760\pi\) | ||||
0.0227437 | + | 0.999741i | \(0.492760\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.00781 | 1.21990 | ||||||||
\(34\) | −5.13908 | −0.881345 | ||||||||
\(35\) | 6.56682 | 1.10999 | ||||||||
\(36\) | 3.41884 | 0.569807 | ||||||||
\(37\) | 2.29806 | 0.377798 | 0.188899 | − | 0.981996i | \(-0.439508\pi\) | ||||
0.188899 | + | 0.981996i | \(0.439508\pi\) | |||||||
\(38\) | 6.17334 | 1.00145 | ||||||||
\(39\) | 5.54899 | 0.888550 | ||||||||
\(40\) | −1.39163 | −0.220037 | ||||||||
\(41\) | −11.3204 | −1.76795 | −0.883974 | − | 0.467536i | \(-0.845142\pi\) | ||||
−0.883974 | + | 0.467536i | \(0.845142\pi\) | |||||||
\(42\) | 11.9552 | 1.84474 | ||||||||
\(43\) | 2.00522 | 0.305793 | 0.152897 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152897 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(44\) | −2.76601 | −0.416992 | ||||||||
\(45\) | 4.75778 | 0.709247 | ||||||||
\(46\) | −6.53406 | −0.963395 | ||||||||
\(47\) | 7.02008 | 1.02398 | 0.511992 | − | 0.858990i | \(-0.328908\pi\) | ||||
0.511992 | + | 0.858990i | \(0.328908\pi\) | |||||||
\(48\) | −2.53354 | −0.365686 | ||||||||
\(49\) | 15.2669 | 2.18099 | ||||||||
\(50\) | 3.06336 | 0.433224 | ||||||||
\(51\) | −13.0201 | −1.82318 | ||||||||
\(52\) | −2.19021 | −0.303727 | ||||||||
\(53\) | −0.800200 | −0.109916 | −0.0549580 | − | 0.998489i | \(-0.517502\pi\) | ||||
−0.0549580 | + | 0.998489i | \(0.517502\pi\) | |||||||
\(54\) | 1.06116 | 0.144405 | ||||||||
\(55\) | −3.84927 | −0.519036 | ||||||||
\(56\) | −4.71879 | −0.630574 | ||||||||
\(57\) | 15.6404 | 2.07162 | ||||||||
\(58\) | 3.72122 | 0.488619 | ||||||||
\(59\) | 4.01802 | 0.523102 | 0.261551 | − | 0.965190i | \(-0.415766\pi\) | ||||
0.261551 | + | 0.965190i | \(0.415766\pi\) | |||||||
\(60\) | −3.52576 | −0.455174 | ||||||||
\(61\) | −3.35908 | −0.430086 | −0.215043 | − | 0.976605i | \(-0.568989\pi\) | ||||
−0.215043 | + | 0.976605i | \(0.568989\pi\) | |||||||
\(62\) | −0.253263 | −0.0321645 | ||||||||
\(63\) | 16.1328 | 2.03254 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.04797 | −0.378054 | ||||||||
\(66\) | −7.00781 | −0.862602 | ||||||||
\(67\) | −7.50851 | −0.917310 | −0.458655 | − | 0.888614i | \(-0.651669\pi\) | ||||
−0.458655 | + | 0.888614i | \(0.651669\pi\) | |||||||
\(68\) | 5.13908 | 0.623205 | ||||||||
\(69\) | −16.5543 | −1.99291 | ||||||||
\(70\) | −6.56682 | −0.784885 | ||||||||
\(71\) | −13.6153 | −1.61584 | −0.807918 | − | 0.589295i | \(-0.799405\pi\) | ||||
−0.807918 | + | 0.589295i | \(0.799405\pi\) | |||||||
\(72\) | −3.41884 | −0.402915 | ||||||||
\(73\) | 14.0968 | 1.64991 | 0.824953 | − | 0.565201i | \(-0.191201\pi\) | ||||
0.824953 | + | 0.565201i | \(0.191201\pi\) | |||||||
\(74\) | −2.29806 | −0.267144 | ||||||||
\(75\) | 7.76115 | 0.896180 | ||||||||
\(76\) | −6.17334 | −0.708130 | ||||||||
\(77\) | −13.0522 | −1.48744 | ||||||||
\(78\) | −5.54899 | −0.628300 | ||||||||
\(79\) | −16.6002 | −1.86766 | −0.933832 | − | 0.357713i | \(-0.883557\pi\) | ||||
−0.933832 | + | 0.357713i | \(0.883557\pi\) | |||||||
\(80\) | 1.39163 | 0.155589 | ||||||||
\(81\) | −7.56804 | −0.840893 | ||||||||
\(82\) | 11.3204 | 1.25013 | ||||||||
\(83\) | −17.3391 | −1.90322 | −0.951608 | − | 0.307314i | \(-0.900570\pi\) | ||||
−0.951608 | + | 0.307314i | \(0.900570\pi\) | |||||||
\(84\) | −11.9552 | −1.30442 | ||||||||
\(85\) | 7.15172 | 0.775713 | ||||||||
\(86\) | −2.00522 | −0.216228 | ||||||||
\(87\) | 9.42786 | 1.01077 | ||||||||
\(88\) | 2.76601 | 0.294858 | ||||||||
\(89\) | 14.1295 | 1.49773 | 0.748863 | − | 0.662725i | \(-0.230600\pi\) | ||||
0.748863 | + | 0.662725i | \(0.230600\pi\) | |||||||
\(90\) | −4.75778 | −0.501514 | ||||||||
\(91\) | −10.3351 | −1.08342 | ||||||||
\(92\) | 6.53406 | 0.681223 | ||||||||
\(93\) | −0.641654 | −0.0665364 | ||||||||
\(94\) | −7.02008 | −0.724066 | ||||||||
\(95\) | −8.59102 | −0.881420 | ||||||||
\(96\) | 2.53354 | 0.258579 | ||||||||
\(97\) | −10.0057 | −1.01592 | −0.507961 | − | 0.861380i | \(-0.669600\pi\) | ||||
−0.507961 | + | 0.861380i | \(0.669600\pi\) | |||||||
\(98\) | −15.2669 | −1.54219 | ||||||||
\(99\) | −9.45656 | −0.950420 | ||||||||
\(100\) | −3.06336 | −0.306336 | ||||||||
\(101\) | −18.5334 | −1.84414 | −0.922072 | − | 0.387017i | \(-0.873505\pi\) | ||||
−0.922072 | + | 0.387017i | \(0.873505\pi\) | |||||||
\(102\) | 13.0201 | 1.28918 | ||||||||
\(103\) | −2.45893 | −0.242285 | −0.121143 | − | 0.992635i | \(-0.538656\pi\) | ||||
−0.121143 | + | 0.992635i | \(0.538656\pi\) | |||||||
\(104\) | 2.19021 | 0.214768 | ||||||||
\(105\) | −16.6373 | −1.62364 | ||||||||
\(106\) | 0.800200 | 0.0777223 | ||||||||
\(107\) | −0.166982 | −0.0161428 | −0.00807140 | − | 0.999967i | \(-0.502569\pi\) | ||||
−0.00807140 | + | 0.999967i | \(0.502569\pi\) | |||||||
\(108\) | −1.06116 | −0.102110 | ||||||||
\(109\) | 9.02543 | 0.864479 | 0.432240 | − | 0.901759i | \(-0.357723\pi\) | ||||
0.432240 | + | 0.901759i | \(0.357723\pi\) | |||||||
\(110\) | 3.84927 | 0.367014 | ||||||||
\(111\) | −5.82223 | −0.552622 | ||||||||
\(112\) | 4.71879 | 0.445883 | ||||||||
\(113\) | −15.1876 | −1.42872 | −0.714362 | − | 0.699776i | \(-0.753283\pi\) | ||||
−0.714362 | + | 0.699776i | \(0.753283\pi\) | |||||||
\(114\) | −15.6404 | −1.46486 | ||||||||
\(115\) | 9.09301 | 0.847928 | ||||||||
\(116\) | −3.72122 | −0.345506 | ||||||||
\(117\) | −7.48799 | −0.692264 | ||||||||
\(118\) | −4.01802 | −0.369889 | ||||||||
\(119\) | 24.2502 | 2.22301 | ||||||||
\(120\) | 3.52576 | 0.321857 | ||||||||
\(121\) | −3.34918 | −0.304471 | ||||||||
\(122\) | 3.35908 | 0.304117 | ||||||||
\(123\) | 28.6807 | 2.58605 | ||||||||
\(124\) | 0.253263 | 0.0227437 | ||||||||
\(125\) | −11.2212 | −1.00366 | ||||||||
\(126\) | −16.1328 | −1.43722 | ||||||||
\(127\) | 11.5985 | 1.02920 | 0.514602 | − | 0.857429i | \(-0.327940\pi\) | ||||
0.514602 | + | 0.857429i | \(0.327940\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.08031 | −0.447296 | ||||||||
\(130\) | 3.04797 | 0.267325 | ||||||||
\(131\) | 4.18442 | 0.365594 | 0.182797 | − | 0.983151i | \(-0.441485\pi\) | ||||
0.182797 | + | 0.983151i | \(0.441485\pi\) | |||||||
\(132\) | 7.00781 | 0.609952 | ||||||||
\(133\) | −29.1307 | −2.52595 | ||||||||
\(134\) | 7.50851 | 0.648636 | ||||||||
\(135\) | −1.47674 | −0.127098 | ||||||||
\(136\) | −5.13908 | −0.440673 | ||||||||
\(137\) | 8.88632 | 0.759210 | 0.379605 | − | 0.925149i | \(-0.376060\pi\) | ||||
0.379605 | + | 0.925149i | \(0.376060\pi\) | |||||||
\(138\) | 16.5543 | 1.40920 | ||||||||
\(139\) | 4.84928 | 0.411311 | 0.205655 | − | 0.978624i | \(-0.434067\pi\) | ||||
0.205655 | + | 0.978624i | \(0.434067\pi\) | |||||||
\(140\) | 6.56682 | 0.554997 | ||||||||
\(141\) | −17.7857 | −1.49783 | ||||||||
\(142\) | 13.6153 | 1.14257 | ||||||||
\(143\) | 6.05815 | 0.506608 | ||||||||
\(144\) | 3.41884 | 0.284904 | ||||||||
\(145\) | −5.17857 | −0.430057 | ||||||||
\(146\) | −14.0968 | −1.16666 | ||||||||
\(147\) | −38.6795 | −3.19023 | ||||||||
\(148\) | 2.29806 | 0.188899 | ||||||||
\(149\) | 1.12039 | 0.0917856 | 0.0458928 | − | 0.998946i | \(-0.485387\pi\) | ||||
0.0458928 | + | 0.998946i | \(0.485387\pi\) | |||||||
\(150\) | −7.76115 | −0.633695 | ||||||||
\(151\) | −14.2465 | −1.15937 | −0.579683 | − | 0.814842i | \(-0.696824\pi\) | ||||
−0.579683 | + | 0.814842i | \(0.696824\pi\) | |||||||
\(152\) | 6.17334 | 0.500724 | ||||||||
\(153\) | 17.5697 | 1.42043 | ||||||||
\(154\) | 13.0522 | 1.05178 | ||||||||
\(155\) | 0.352450 | 0.0283094 | ||||||||
\(156\) | 5.54899 | 0.444275 | ||||||||
\(157\) | 5.69937 | 0.454859 | 0.227430 | − | 0.973795i | \(-0.426968\pi\) | ||||
0.227430 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(158\) | 16.6002 | 1.32064 | ||||||||
\(159\) | 2.02734 | 0.160779 | ||||||||
\(160\) | −1.39163 | −0.110018 | ||||||||
\(161\) | 30.8328 | 2.42997 | ||||||||
\(162\) | 7.56804 | 0.594601 | ||||||||
\(163\) | 21.1843 | 1.65928 | 0.829640 | − | 0.558299i | \(-0.188546\pi\) | ||||
0.829640 | + | 0.558299i | \(0.188546\pi\) | |||||||
\(164\) | −11.3204 | −0.883974 | ||||||||
\(165\) | 9.75230 | 0.759216 | ||||||||
\(166\) | 17.3391 | 1.34578 | ||||||||
\(167\) | −3.61223 | −0.279523 | −0.139761 | − | 0.990185i | \(-0.544634\pi\) | ||||
−0.139761 | + | 0.990185i | \(0.544634\pi\) | |||||||
\(168\) | 11.9552 | 0.922368 | ||||||||
\(169\) | −8.20298 | −0.630998 | ||||||||
\(170\) | −7.15172 | −0.548512 | ||||||||
\(171\) | −21.1057 | −1.61399 | ||||||||
\(172\) | 2.00522 | 0.152897 | ||||||||
\(173\) | −5.78462 | −0.439797 | −0.219898 | − | 0.975523i | \(-0.570573\pi\) | ||||
−0.219898 | + | 0.975523i | \(0.570573\pi\) | |||||||
\(174\) | −9.42786 | −0.714724 | ||||||||
\(175\) | −14.4553 | −1.09272 | ||||||||
\(176\) | −2.76601 | −0.208496 | ||||||||
\(177\) | −10.1798 | −0.765163 | ||||||||
\(178\) | −14.1295 | −1.05905 | ||||||||
\(179\) | 12.0434 | 0.900164 | 0.450082 | − | 0.892987i | \(-0.351395\pi\) | ||||
0.450082 | + | 0.892987i | \(0.351395\pi\) | |||||||
\(180\) | 4.75778 | 0.354624 | ||||||||
\(181\) | −17.4236 | −1.29509 | −0.647544 | − | 0.762028i | \(-0.724204\pi\) | ||||
−0.647544 | + | 0.762028i | \(0.724204\pi\) | |||||||
\(182\) | 10.3351 | 0.766091 | ||||||||
\(183\) | 8.51037 | 0.629105 | ||||||||
\(184\) | −6.53406 | −0.481697 | ||||||||
\(185\) | 3.19805 | 0.235126 | ||||||||
\(186\) | 0.641654 | 0.0470483 | ||||||||
\(187\) | −14.2148 | −1.03949 | ||||||||
\(188\) | 7.02008 | 0.511992 | ||||||||
\(189\) | −5.00738 | −0.364233 | ||||||||
\(190\) | 8.59102 | 0.623258 | ||||||||
\(191\) | 1.21193 | 0.0876924 | 0.0438462 | − | 0.999038i | \(-0.486039\pi\) | ||||
0.0438462 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(192\) | −2.53354 | −0.182843 | ||||||||
\(193\) | 0.959405 | 0.0690595 | 0.0345298 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345298 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(194\) | 10.0057 | 0.718365 | ||||||||
\(195\) | 7.72216 | 0.552996 | ||||||||
\(196\) | 15.2669 | 1.09050 | ||||||||
\(197\) | −8.73442 | −0.622302 | −0.311151 | − | 0.950360i | \(-0.600714\pi\) | ||||
−0.311151 | + | 0.950360i | \(0.600714\pi\) | |||||||
\(198\) | 9.45656 | 0.672049 | ||||||||
\(199\) | 15.2750 | 1.08281 | 0.541407 | − | 0.840760i | \(-0.317892\pi\) | ||||
0.541407 | + | 0.840760i | \(0.317892\pi\) | |||||||
\(200\) | 3.06336 | 0.216612 | ||||||||
\(201\) | 19.0231 | 1.34179 | ||||||||
\(202\) | 18.5334 | 1.30401 | ||||||||
\(203\) | −17.5596 | −1.23244 | ||||||||
\(204\) | −13.0201 | −0.911588 | ||||||||
\(205\) | −15.7538 | −1.10030 | ||||||||
\(206\) | 2.45893 | 0.171322 | ||||||||
\(207\) | 22.3389 | 1.55266 | ||||||||
\(208\) | −2.19021 | −0.151864 | ||||||||
\(209\) | 17.0755 | 1.18114 | ||||||||
\(210\) | 16.6373 | 1.14808 | ||||||||
\(211\) | −8.91288 | −0.613588 | −0.306794 | − | 0.951776i | \(-0.599256\pi\) | ||||
−0.306794 | + | 0.951776i | \(0.599256\pi\) | |||||||
\(212\) | −0.800200 | −0.0549580 | ||||||||
\(213\) | 34.4949 | 2.36355 | ||||||||
\(214\) | 0.166982 | 0.0114147 | ||||||||
\(215\) | 2.79053 | 0.190313 | ||||||||
\(216\) | 1.06116 | 0.0722027 | ||||||||
\(217\) | 1.19510 | 0.0811284 | ||||||||
\(218\) | −9.02543 | −0.611279 | ||||||||
\(219\) | −35.7149 | −2.41339 | ||||||||
\(220\) | −3.84927 | −0.259518 | ||||||||
\(221\) | −11.2557 | −0.757138 | ||||||||
\(222\) | 5.82223 | 0.390763 | ||||||||
\(223\) | 6.57988 | 0.440621 | 0.220311 | − | 0.975430i | \(-0.429293\pi\) | ||||
0.220311 | + | 0.975430i | \(0.429293\pi\) | |||||||
\(224\) | −4.71879 | −0.315287 | ||||||||
\(225\) | −10.4731 | −0.698209 | ||||||||
\(226\) | 15.1876 | 1.01026 | ||||||||
\(227\) | 6.55570 | 0.435117 | 0.217558 | − | 0.976047i | \(-0.430191\pi\) | ||||
0.217558 | + | 0.976047i | \(0.430191\pi\) | |||||||
\(228\) | 15.6404 | 1.03581 | ||||||||
\(229\) | 8.51214 | 0.562498 | 0.281249 | − | 0.959635i | \(-0.409251\pi\) | ||||
0.281249 | + | 0.959635i | \(0.409251\pi\) | |||||||
\(230\) | −9.09301 | −0.599576 | ||||||||
\(231\) | 33.0684 | 2.17574 | ||||||||
\(232\) | 3.72122 | 0.244310 | ||||||||
\(233\) | −17.4576 | −1.14368 | −0.571842 | − | 0.820364i | \(-0.693771\pi\) | ||||
−0.571842 | + | 0.820364i | \(0.693771\pi\) | |||||||
\(234\) | 7.48799 | 0.489505 | ||||||||
\(235\) | 9.76938 | 0.637284 | ||||||||
\(236\) | 4.01802 | 0.261551 | ||||||||
\(237\) | 42.0572 | 2.73191 | ||||||||
\(238\) | −24.2502 | −1.57191 | ||||||||
\(239\) | −25.5963 | −1.65569 | −0.827845 | − | 0.560958i | \(-0.810433\pi\) | ||||
−0.827845 | + | 0.560958i | \(0.810433\pi\) | |||||||
\(240\) | −3.52576 | −0.227587 | ||||||||
\(241\) | −21.5827 | −1.39026 | −0.695132 | − | 0.718882i | \(-0.744654\pi\) | ||||
−0.695132 | + | 0.718882i | \(0.744654\pi\) | |||||||
\(242\) | 3.34918 | 0.215293 | ||||||||
\(243\) | 22.3574 | 1.43423 | ||||||||
\(244\) | −3.35908 | −0.215043 | ||||||||
\(245\) | 21.2460 | 1.35736 | ||||||||
\(246\) | −28.6807 | −1.82861 | ||||||||
\(247\) | 13.5209 | 0.860314 | ||||||||
\(248\) | −0.253263 | −0.0160822 | ||||||||
\(249\) | 43.9294 | 2.78391 | ||||||||
\(250\) | 11.2212 | 0.709693 | ||||||||
\(251\) | 0.556712 | 0.0351394 | 0.0175697 | − | 0.999846i | \(-0.494407\pi\) | ||||
0.0175697 | + | 0.999846i | \(0.494407\pi\) | |||||||
\(252\) | 16.1328 | 1.01627 | ||||||||
\(253\) | −18.0733 | −1.13626 | ||||||||
\(254\) | −11.5985 | −0.727757 | ||||||||
\(255\) | −18.1192 | −1.13467 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.1754 | 1.94467 | 0.972333 | − | 0.233599i | \(-0.0750503\pi\) | ||||
0.972333 | + | 0.233599i | \(0.0750503\pi\) | |||||||
\(258\) | 5.08031 | 0.316286 | ||||||||
\(259\) | 10.8440 | 0.673816 | ||||||||
\(260\) | −3.04797 | −0.189027 | ||||||||
\(261\) | −12.7223 | −0.787488 | ||||||||
\(262\) | −4.18442 | −0.258514 | ||||||||
\(263\) | 12.2728 | 0.756773 | 0.378387 | − | 0.925648i | \(-0.376479\pi\) | ||||
0.378387 | + | 0.925648i | \(0.376479\pi\) | |||||||
\(264\) | −7.00781 | −0.431301 | ||||||||
\(265\) | −1.11358 | −0.0684070 | ||||||||
\(266\) | 29.1307 | 1.78611 | ||||||||
\(267\) | −35.7978 | −2.19079 | ||||||||
\(268\) | −7.50851 | −0.458655 | ||||||||
\(269\) | −23.1202 | −1.40966 | −0.704832 | − | 0.709374i | \(-0.748978\pi\) | ||||
−0.704832 | + | 0.709374i | \(0.748978\pi\) | |||||||
\(270\) | 1.47674 | 0.0898717 | ||||||||
\(271\) | 23.9570 | 1.45528 | 0.727642 | − | 0.685957i | \(-0.240616\pi\) | ||||
0.727642 | + | 0.685957i | \(0.240616\pi\) | |||||||
\(272\) | 5.13908 | 0.311603 | ||||||||
\(273\) | 26.1845 | 1.58476 | ||||||||
\(274\) | −8.88632 | −0.536842 | ||||||||
\(275\) | 8.47328 | 0.510958 | ||||||||
\(276\) | −16.5543 | −0.996453 | ||||||||
\(277\) | −11.6360 | −0.699138 | −0.349569 | − | 0.936911i | \(-0.613672\pi\) | ||||
−0.349569 | + | 0.936911i | \(0.613672\pi\) | |||||||
\(278\) | −4.84928 | −0.290841 | ||||||||
\(279\) | 0.865868 | 0.0518381 | ||||||||
\(280\) | −6.56682 | −0.392442 | ||||||||
\(281\) | 16.6857 | 0.995384 | 0.497692 | − | 0.867354i | \(-0.334181\pi\) | ||||
0.497692 | + | 0.867354i | \(0.334181\pi\) | |||||||
\(282\) | 17.7857 | 1.05912 | ||||||||
\(283\) | −6.71441 | −0.399130 | −0.199565 | − | 0.979885i | \(-0.563953\pi\) | ||||
−0.199565 | + | 0.979885i | \(0.563953\pi\) | |||||||
\(284\) | −13.6153 | −0.807918 | ||||||||
\(285\) | 21.7657 | 1.28929 | ||||||||
\(286\) | −6.05815 | −0.358226 | ||||||||
\(287\) | −53.4185 | −3.15319 | ||||||||
\(288\) | −3.41884 | −0.201457 | ||||||||
\(289\) | 9.41016 | 0.553539 | ||||||||
\(290\) | 5.17857 | 0.304096 | ||||||||
\(291\) | 25.3498 | 1.48603 | ||||||||
\(292\) | 14.0968 | 0.824953 | ||||||||
\(293\) | 5.47976 | 0.320131 | 0.160066 | − | 0.987106i | \(-0.448829\pi\) | ||||
0.160066 | + | 0.987106i | \(0.448829\pi\) | |||||||
\(294\) | 38.6795 | 2.25583 | ||||||||
\(295\) | 5.59161 | 0.325556 | ||||||||
\(296\) | −2.29806 | −0.133572 | ||||||||
\(297\) | 2.93518 | 0.170316 | ||||||||
\(298\) | −1.12039 | −0.0649022 | ||||||||
\(299\) | −14.3110 | −0.827624 | ||||||||
\(300\) | 7.76115 | 0.448090 | ||||||||
\(301\) | 9.46220 | 0.545392 | ||||||||
\(302\) | 14.2465 | 0.819796 | ||||||||
\(303\) | 46.9552 | 2.69751 | ||||||||
\(304\) | −6.17334 | −0.354065 | ||||||||
\(305\) | −4.67460 | −0.267667 | ||||||||
\(306\) | −17.5697 | −1.00439 | ||||||||
\(307\) | 27.5631 | 1.57311 | 0.786556 | − | 0.617519i | \(-0.211862\pi\) | ||||
0.786556 | + | 0.617519i | \(0.211862\pi\) | |||||||
\(308\) | −13.0522 | −0.743719 | ||||||||
\(309\) | 6.22980 | 0.354401 | ||||||||
\(310\) | −0.352450 | −0.0200178 | ||||||||
\(311\) | −6.31777 | −0.358248 | −0.179124 | − | 0.983827i | \(-0.557326\pi\) | ||||
−0.179124 | + | 0.983827i | \(0.557326\pi\) | |||||||
\(312\) | −5.54899 | −0.314150 | ||||||||
\(313\) | −8.46763 | −0.478619 | −0.239309 | − | 0.970943i | \(-0.576921\pi\) | ||||
−0.239309 | + | 0.970943i | \(0.576921\pi\) | |||||||
\(314\) | −5.69937 | −0.321634 | ||||||||
\(315\) | 22.4509 | 1.26497 | ||||||||
\(316\) | −16.6002 | −0.933832 | ||||||||
\(317\) | 0.996946 | 0.0559940 | 0.0279970 | − | 0.999608i | \(-0.491087\pi\) | ||||
0.0279970 | + | 0.999608i | \(0.491087\pi\) | |||||||
\(318\) | −2.02734 | −0.113688 | ||||||||
\(319\) | 10.2929 | 0.576293 | ||||||||
\(320\) | 1.39163 | 0.0777947 | ||||||||
\(321\) | 0.423057 | 0.0236128 | ||||||||
\(322\) | −30.8328 | −1.71825 | ||||||||
\(323\) | −31.7253 | −1.76524 | ||||||||
\(324\) | −7.56804 | −0.420447 | ||||||||
\(325\) | 6.70940 | 0.372170 | ||||||||
\(326\) | −21.1843 | −1.17329 | ||||||||
\(327\) | −22.8663 | −1.26451 | ||||||||
\(328\) | 11.3204 | 0.625064 | ||||||||
\(329\) | 33.1263 | 1.82631 | ||||||||
\(330\) | −9.75230 | −0.536847 | ||||||||
\(331\) | −14.4797 | −0.795878 | −0.397939 | − | 0.917412i | \(-0.630274\pi\) | ||||
−0.397939 | + | 0.917412i | \(0.630274\pi\) | |||||||
\(332\) | −17.3391 | −0.951608 | ||||||||
\(333\) | 7.85670 | 0.430545 | ||||||||
\(334\) | 3.61223 | 0.197653 | ||||||||
\(335\) | −10.4491 | −0.570895 | ||||||||
\(336\) | −11.9552 | −0.652212 | ||||||||
\(337\) | 18.8737 | 1.02812 | 0.514058 | − | 0.857755i | \(-0.328142\pi\) | ||||
0.514058 | + | 0.857755i | \(0.328142\pi\) | |||||||
\(338\) | 8.20298 | 0.446183 | ||||||||
\(339\) | 38.4783 | 2.08986 | ||||||||
\(340\) | 7.15172 | 0.387856 | ||||||||
\(341\) | −0.700529 | −0.0379358 | ||||||||
\(342\) | 21.1057 | 1.14126 | ||||||||
\(343\) | 39.0099 | 2.10634 | ||||||||
\(344\) | −2.00522 | −0.108114 | ||||||||
\(345\) | −23.0375 | −1.24030 | ||||||||
\(346\) | 5.78462 | 0.310983 | ||||||||
\(347\) | 19.9968 | 1.07348 | 0.536742 | − | 0.843747i | \(-0.319655\pi\) | ||||
0.536742 | + | 0.843747i | \(0.319655\pi\) | |||||||
\(348\) | 9.42786 | 0.505386 | ||||||||
\(349\) | −4.49839 | −0.240793 | −0.120397 | − | 0.992726i | \(-0.538417\pi\) | ||||
−0.120397 | + | 0.992726i | \(0.538417\pi\) | |||||||
\(350\) | 14.4553 | 0.772670 | ||||||||
\(351\) | 2.32416 | 0.124054 | ||||||||
\(352\) | 2.76601 | 0.147429 | ||||||||
\(353\) | −34.2822 | −1.82466 | −0.912328 | − | 0.409461i | \(-0.865717\pi\) | ||||
−0.912328 | + | 0.409461i | \(0.865717\pi\) | |||||||
\(354\) | 10.1798 | 0.541052 | ||||||||
\(355\) | −18.9475 | −1.00563 | ||||||||
\(356\) | 14.1295 | 0.748863 | ||||||||
\(357\) | −61.4390 | −3.25170 | ||||||||
\(358\) | −12.0434 | −0.636512 | ||||||||
\(359\) | −4.56154 | −0.240749 | −0.120374 | − | 0.992729i | \(-0.538410\pi\) | ||||
−0.120374 | + | 0.992729i | \(0.538410\pi\) | |||||||
\(360\) | −4.75778 | −0.250757 | ||||||||
\(361\) | 19.1101 | 1.00579 | ||||||||
\(362\) | 17.4236 | 0.915766 | ||||||||
\(363\) | 8.48529 | 0.445362 | ||||||||
\(364\) | −10.3351 | −0.541708 | ||||||||
\(365\) | 19.6176 | 1.02683 | ||||||||
\(366\) | −8.51037 | −0.444844 | ||||||||
\(367\) | 11.4321 | 0.596748 | 0.298374 | − | 0.954449i | \(-0.403556\pi\) | ||||
0.298374 | + | 0.954449i | \(0.403556\pi\) | |||||||
\(368\) | 6.53406 | 0.340611 | ||||||||
\(369\) | −38.7026 | −2.01478 | ||||||||
\(370\) | −3.19805 | −0.166259 | ||||||||
\(371\) | −3.77597 | −0.196039 | ||||||||
\(372\) | −0.641654 | −0.0332682 | ||||||||
\(373\) | −5.21755 | −0.270154 | −0.135077 | − | 0.990835i | \(-0.543128\pi\) | ||||
−0.135077 | + | 0.990835i | \(0.543128\pi\) | |||||||
\(374\) | 14.2148 | 0.735028 | ||||||||
\(375\) | 28.4295 | 1.46809 | ||||||||
\(376\) | −7.02008 | −0.362033 | ||||||||
\(377\) | 8.15024 | 0.419759 | ||||||||
\(378\) | 5.00738 | 0.257552 | ||||||||
\(379\) | 27.1167 | 1.39289 | 0.696445 | − | 0.717611i | \(-0.254764\pi\) | ||||
0.696445 | + | 0.717611i | \(0.254764\pi\) | |||||||
\(380\) | −8.59102 | −0.440710 | ||||||||
\(381\) | −29.3854 | −1.50546 | ||||||||
\(382\) | −1.21193 | −0.0620079 | ||||||||
\(383\) | −21.8116 | −1.11452 | −0.557261 | − | 0.830337i | \(-0.688148\pi\) | ||||
−0.557261 | + | 0.830337i | \(0.688148\pi\) | |||||||
\(384\) | 2.53354 | 0.129289 | ||||||||
\(385\) | −18.1639 | −0.925718 | ||||||||
\(386\) | −0.959405 | −0.0488325 | ||||||||
\(387\) | 6.85553 | 0.348486 | ||||||||
\(388\) | −10.0057 | −0.507961 | ||||||||
\(389\) | −1.21853 | −0.0617821 | −0.0308910 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308910 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(390\) | −7.72216 | −0.391027 | ||||||||
\(391\) | 33.5791 | 1.69817 | ||||||||
\(392\) | −15.2669 | −0.771097 | ||||||||
\(393\) | −10.6014 | −0.534770 | ||||||||
\(394\) | 8.73442 | 0.440034 | ||||||||
\(395\) | −23.1013 | −1.16235 | ||||||||
\(396\) | −9.45656 | −0.475210 | ||||||||
\(397\) | −15.7252 | −0.789225 | −0.394612 | − | 0.918848i | \(-0.629121\pi\) | ||||
−0.394612 | + | 0.918848i | \(0.629121\pi\) | |||||||
\(398\) | −15.2750 | −0.765666 | ||||||||
\(399\) | 73.8038 | 3.69481 | ||||||||
\(400\) | −3.06336 | −0.153168 | ||||||||
\(401\) | −35.7473 | −1.78514 | −0.892568 | − | 0.450914i | \(-0.851098\pi\) | ||||
−0.892568 | + | 0.450914i | \(0.851098\pi\) | |||||||
\(402\) | −19.0231 | −0.948788 | ||||||||
\(403\) | −0.554700 | −0.0276316 | ||||||||
\(404\) | −18.5334 | −0.922072 | ||||||||
\(405\) | −10.5319 | −0.523336 | ||||||||
\(406\) | 17.5596 | 0.871469 | ||||||||
\(407\) | −6.35646 | −0.315078 | ||||||||
\(408\) | 13.0201 | 0.644590 | ||||||||
\(409\) | 1.14419 | 0.0565765 | 0.0282882 | − | 0.999600i | \(-0.490994\pi\) | ||||
0.0282882 | + | 0.999600i | \(0.490994\pi\) | |||||||
\(410\) | 15.7538 | 0.778026 | ||||||||
\(411\) | −22.5139 | −1.11053 | ||||||||
\(412\) | −2.45893 | −0.121143 | ||||||||
\(413\) | 18.9602 | 0.932970 | ||||||||
\(414\) | −22.3389 | −1.09790 | ||||||||
\(415\) | −24.1297 | −1.18448 | ||||||||
\(416\) | 2.19021 | 0.107384 | ||||||||
\(417\) | −12.2859 | −0.601642 | ||||||||
\(418\) | −17.0755 | −0.835191 | ||||||||
\(419\) | −33.2960 | −1.62662 | −0.813308 | − | 0.581833i | \(-0.802336\pi\) | ||||
−0.813308 | + | 0.581833i | \(0.802336\pi\) | |||||||
\(420\) | −16.6373 | −0.811818 | ||||||||
\(421\) | −27.8954 | −1.35954 | −0.679768 | − | 0.733427i | \(-0.737920\pi\) | ||||
−0.679768 | + | 0.733427i | \(0.737920\pi\) | |||||||
\(422\) | 8.91288 | 0.433872 | ||||||||
\(423\) | 24.0006 | 1.16695 | ||||||||
\(424\) | 0.800200 | 0.0388611 | ||||||||
\(425\) | −15.7428 | −0.763640 | ||||||||
\(426\) | −34.4949 | −1.67128 | ||||||||
\(427\) | −15.8508 | −0.767072 | ||||||||
\(428\) | −0.166982 | −0.00807140 | ||||||||
\(429\) | −15.3486 | −0.741036 | ||||||||
\(430\) | −2.79053 | −0.134571 | ||||||||
\(431\) | 1.78701 | 0.0860771 | 0.0430385 | − | 0.999073i | \(-0.486296\pi\) | ||||
0.0430385 | + | 0.999073i | \(0.486296\pi\) | |||||||
\(432\) | −1.06116 | −0.0510550 | ||||||||
\(433\) | 5.92092 | 0.284541 | 0.142271 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142271 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(434\) | −1.19510 | −0.0573664 | ||||||||
\(435\) | 13.1201 | 0.629062 | ||||||||
\(436\) | 9.02543 | 0.432240 | ||||||||
\(437\) | −40.3369 | −1.92958 | ||||||||
\(438\) | 35.7149 | 1.70652 | ||||||||
\(439\) | 26.8472 | 1.28135 | 0.640674 | − | 0.767813i | \(-0.278655\pi\) | ||||
0.640674 | + | 0.767813i | \(0.278655\pi\) | |||||||
\(440\) | 3.84927 | 0.183507 | ||||||||
\(441\) | 52.1953 | 2.48549 | ||||||||
\(442\) | 11.2557 | 0.535378 | ||||||||
\(443\) | −4.13134 | −0.196286 | −0.0981430 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981430 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(444\) | −5.82223 | −0.276311 | ||||||||
\(445\) | 19.6631 | 0.932121 | ||||||||
\(446\) | −6.57988 | −0.311566 | ||||||||
\(447\) | −2.83855 | −0.134259 | ||||||||
\(448\) | 4.71879 | 0.222942 | ||||||||
\(449\) | 17.7201 | 0.836261 | 0.418131 | − | 0.908387i | \(-0.362685\pi\) | ||||
0.418131 | + | 0.908387i | \(0.362685\pi\) | |||||||
\(450\) | 10.4731 | 0.493708 | ||||||||
\(451\) | 31.3123 | 1.47444 | ||||||||
\(452\) | −15.1876 | −0.714362 | ||||||||
\(453\) | 36.0942 | 1.69585 | ||||||||
\(454\) | −6.55570 | −0.307674 | ||||||||
\(455\) | −14.3827 | −0.674272 | ||||||||
\(456\) | −15.6404 | −0.732430 | ||||||||
\(457\) | 35.9463 | 1.68150 | 0.840748 | − | 0.541426i | \(-0.182115\pi\) | ||||
0.840748 | + | 0.541426i | \(0.182115\pi\) | |||||||
\(458\) | −8.51214 | −0.397746 | ||||||||
\(459\) | −5.45338 | −0.254542 | ||||||||
\(460\) | 9.09301 | 0.423964 | ||||||||
\(461\) | −31.0691 | −1.44703 | −0.723516 | − | 0.690307i | \(-0.757475\pi\) | ||||
−0.723516 | + | 0.690307i | \(0.757475\pi\) | |||||||
\(462\) | −33.0684 | −1.53848 | ||||||||
\(463\) | 23.6141 | 1.09744 | 0.548721 | − | 0.836005i | \(-0.315115\pi\) | ||||
0.548721 | + | 0.836005i | \(0.315115\pi\) | |||||||
\(464\) | −3.72122 | −0.172753 | ||||||||
\(465\) | −0.892947 | −0.0414094 | ||||||||
\(466\) | 17.4576 | 0.808707 | ||||||||
\(467\) | 15.3694 | 0.711211 | 0.355606 | − | 0.934636i | \(-0.384275\pi\) | ||||
0.355606 | + | 0.934636i | \(0.384275\pi\) | |||||||
\(468\) | −7.48799 | −0.346132 | ||||||||
\(469\) | −35.4310 | −1.63605 | ||||||||
\(470\) | −9.76938 | −0.450628 | ||||||||
\(471\) | −14.4396 | −0.665342 | ||||||||
\(472\) | −4.01802 | −0.184944 | ||||||||
\(473\) | −5.54646 | −0.255026 | ||||||||
\(474\) | −42.0572 | −1.93175 | ||||||||
\(475\) | 18.9111 | 0.867702 | ||||||||
\(476\) | 24.2502 | 1.11151 | ||||||||
\(477\) | −2.73576 | −0.125262 | ||||||||
\(478\) | 25.5963 | 1.17075 | ||||||||
\(479\) | −40.1793 | −1.83584 | −0.917919 | − | 0.396768i | \(-0.870132\pi\) | ||||
−0.917919 | + | 0.396768i | \(0.870132\pi\) | |||||||
\(480\) | 3.52576 | 0.160928 | ||||||||
\(481\) | −5.03323 | −0.229496 | ||||||||
\(482\) | 21.5827 | 0.983065 | ||||||||
\(483\) | −78.1163 | −3.55442 | ||||||||
\(484\) | −3.34918 | −0.152235 | ||||||||
\(485\) | −13.9242 | −0.632266 | ||||||||
\(486\) | −22.3574 | −1.01415 | ||||||||
\(487\) | −38.6875 | −1.75310 | −0.876549 | − | 0.481313i | \(-0.840160\pi\) | ||||
−0.876549 | + | 0.481313i | \(0.840160\pi\) | |||||||
\(488\) | 3.35908 | 0.152058 | ||||||||
\(489\) | −53.6712 | −2.42710 | ||||||||
\(490\) | −21.2460 | −0.959795 | ||||||||
\(491\) | 42.2643 | 1.90736 | 0.953682 | − | 0.300818i | \(-0.0972595\pi\) | ||||
0.953682 | + | 0.300818i | \(0.0972595\pi\) | |||||||
\(492\) | 28.6807 | 1.29303 | ||||||||
\(493\) | −19.1236 | −0.861285 | ||||||||
\(494\) | −13.5209 | −0.608334 | ||||||||
\(495\) | −13.1601 | −0.591501 | ||||||||
\(496\) | 0.253263 | 0.0113719 | ||||||||
\(497\) | −64.2475 | −2.88190 | ||||||||
\(498\) | −43.9294 | −1.96852 | ||||||||
\(499\) | 2.54463 | 0.113913 | 0.0569567 | − | 0.998377i | \(-0.481860\pi\) | ||||
0.0569567 | + | 0.998377i | \(0.481860\pi\) | |||||||
\(500\) | −11.2212 | −0.501829 | ||||||||
\(501\) | 9.15175 | 0.408870 | ||||||||
\(502\) | −0.556712 | −0.0248473 | ||||||||
\(503\) | 0.501645 | 0.0223673 | 0.0111836 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111836 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(504\) | −16.1328 | −0.718612 | ||||||||
\(505\) | −25.7917 | −1.14772 | ||||||||
\(506\) | 18.0733 | 0.803456 | ||||||||
\(507\) | 20.7826 | 0.922988 | ||||||||
\(508\) | 11.5985 | 0.514602 | ||||||||
\(509\) | −34.0775 | −1.51046 | −0.755229 | − | 0.655461i | \(-0.772474\pi\) | ||||
−0.755229 | + | 0.655461i | \(0.772474\pi\) | |||||||
\(510\) | 18.1192 | 0.802331 | ||||||||
\(511\) | 66.5198 | 2.94266 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.55089 | 0.289229 | ||||||||
\(514\) | −31.1754 | −1.37509 | ||||||||
\(515\) | −3.42192 | −0.150788 | ||||||||
\(516\) | −5.08031 | −0.223648 | ||||||||
\(517\) | −19.4176 | −0.853987 | ||||||||
\(518\) | −10.8440 | −0.476460 | ||||||||
\(519\) | 14.6556 | 0.643309 | ||||||||
\(520\) | 3.04797 | 0.133662 | ||||||||
\(521\) | −10.9875 | −0.481372 | −0.240686 | − | 0.970603i | \(-0.577372\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577372\pi\) | |||||||
\(522\) | 12.7223 | 0.556838 | ||||||||
\(523\) | −9.13391 | −0.399398 | −0.199699 | − | 0.979857i | \(-0.563996\pi\) | ||||
−0.199699 | + | 0.979857i | \(0.563996\pi\) | |||||||
\(524\) | 4.18442 | 0.182797 | ||||||||
\(525\) | 36.6232 | 1.59837 | ||||||||
\(526\) | −12.2728 | −0.535119 | ||||||||
\(527\) | 1.30154 | 0.0566960 | ||||||||
\(528\) | 7.00781 | 0.304976 | ||||||||
\(529\) | 19.6939 | 0.856258 | ||||||||
\(530\) | 1.11358 | 0.0483710 | ||||||||
\(531\) | 13.7370 | 0.596134 | ||||||||
\(532\) | −29.1307 | −1.26297 | ||||||||
\(533\) | 24.7940 | 1.07395 | ||||||||
\(534\) | 35.7978 | 1.54912 | ||||||||
\(535\) | −0.232378 | −0.0100466 | ||||||||
\(536\) | 7.50851 | 0.324318 | ||||||||
\(537\) | −30.5124 | −1.31671 | ||||||||
\(538\) | 23.1202 | 0.996783 | ||||||||
\(539\) | −42.2285 | −1.81891 | ||||||||
\(540\) | −1.47674 | −0.0635489 | ||||||||
\(541\) | 1.53054 | 0.0658029 | 0.0329015 | − | 0.999459i | \(-0.489525\pi\) | ||||
0.0329015 | + | 0.999459i | \(0.489525\pi\) | |||||||
\(542\) | −23.9570 | −1.02904 | ||||||||
\(543\) | 44.1435 | 1.89438 | ||||||||
\(544\) | −5.13908 | −0.220336 | ||||||||
\(545\) | 12.5601 | 0.538015 | ||||||||
\(546\) | −26.1845 | −1.12059 | ||||||||
\(547\) | 20.9634 | 0.896331 | 0.448166 | − | 0.893951i | \(-0.352077\pi\) | ||||
0.448166 | + | 0.893951i | \(0.352077\pi\) | |||||||
\(548\) | 8.88632 | 0.379605 | ||||||||
\(549\) | −11.4842 | −0.490132 | ||||||||
\(550\) | −8.47328 | −0.361302 | ||||||||
\(551\) | 22.9723 | 0.978653 | ||||||||
\(552\) | 16.5543 | 0.704599 | ||||||||
\(553\) | −78.3326 | −3.33104 | ||||||||
\(554\) | 11.6360 | 0.494365 | ||||||||
\(555\) | −8.10241 | −0.343928 | ||||||||
\(556\) | 4.84928 | 0.205655 | ||||||||
\(557\) | 32.3469 | 1.37058 | 0.685290 | − | 0.728270i | \(-0.259675\pi\) | ||||
0.685290 | + | 0.728270i | \(0.259675\pi\) | |||||||
\(558\) | −0.865868 | −0.0366551 | ||||||||
\(559\) | −4.39185 | −0.185756 | ||||||||
\(560\) | 6.56682 | 0.277499 | ||||||||
\(561\) | 36.0137 | 1.52050 | ||||||||
\(562\) | −16.6857 | −0.703843 | ||||||||
\(563\) | −32.5250 | −1.37076 | −0.685382 | − | 0.728184i | \(-0.740365\pi\) | ||||
−0.685382 | + | 0.728184i | \(0.740365\pi\) | |||||||
\(564\) | −17.7857 | −0.748913 | ||||||||
\(565\) | −21.1355 | −0.889177 | ||||||||
\(566\) | 6.71441 | 0.282228 | ||||||||
\(567\) | −35.7120 | −1.49976 | ||||||||
\(568\) | 13.6153 | 0.571284 | ||||||||
\(569\) | −17.5976 | −0.737731 | −0.368865 | − | 0.929483i | \(-0.620254\pi\) | ||||
−0.368865 | + | 0.929483i | \(0.620254\pi\) | |||||||
\(570\) | −21.7657 | −0.911666 | ||||||||
\(571\) | 1.19428 | 0.0499790 | 0.0249895 | − | 0.999688i | \(-0.492045\pi\) | ||||
0.0249895 | + | 0.999688i | \(0.492045\pi\) | |||||||
\(572\) | 6.05815 | 0.253304 | ||||||||
\(573\) | −3.07048 | −0.128271 | ||||||||
\(574\) | 53.4185 | 2.22964 | ||||||||
\(575\) | −20.0162 | −0.834732 | ||||||||
\(576\) | 3.41884 | 0.142452 | ||||||||
\(577\) | 10.3514 | 0.430936 | 0.215468 | − | 0.976511i | \(-0.430872\pi\) | ||||
0.215468 | + | 0.976511i | \(0.430872\pi\) | |||||||
\(578\) | −9.41016 | −0.391411 | ||||||||
\(579\) | −2.43070 | −0.101016 | ||||||||
\(580\) | −5.17857 | −0.215028 | ||||||||
\(581\) | −81.8196 | −3.39445 | ||||||||
\(582\) | −25.3498 | −1.05078 | ||||||||
\(583\) | 2.21336 | 0.0916681 | ||||||||
\(584\) | −14.0968 | −0.583330 | ||||||||
\(585\) | −10.4205 | −0.430836 | ||||||||
\(586\) | −5.47976 | −0.226367 | ||||||||
\(587\) | −4.78956 | −0.197686 | −0.0988432 | − | 0.995103i | \(-0.531514\pi\) | ||||
−0.0988432 | + | 0.995103i | \(0.531514\pi\) | |||||||
\(588\) | −38.6795 | −1.59511 | ||||||||
\(589\) | −1.56348 | −0.0644221 | ||||||||
\(590\) | −5.59161 | −0.230203 | ||||||||
\(591\) | 22.1290 | 0.910267 | ||||||||
\(592\) | 2.29806 | 0.0944496 | ||||||||
\(593\) | 23.4098 | 0.961323 | 0.480662 | − | 0.876906i | \(-0.340397\pi\) | ||||
0.480662 | + | 0.876906i | \(0.340397\pi\) | |||||||
\(594\) | −2.93518 | −0.120432 | ||||||||
\(595\) | 33.7474 | 1.38351 | ||||||||
\(596\) | 1.12039 | 0.0458928 | ||||||||
\(597\) | −38.6998 | −1.58388 | ||||||||
\(598\) | 14.3110 | 0.585219 | ||||||||
\(599\) | −0.809170 | −0.0330618 | −0.0165309 | − | 0.999863i | \(-0.505262\pi\) | ||||
−0.0165309 | + | 0.999863i | \(0.505262\pi\) | |||||||
\(600\) | −7.76115 | −0.316848 | ||||||||
\(601\) | 19.0585 | 0.777411 | 0.388706 | − | 0.921362i | \(-0.372922\pi\) | ||||
0.388706 | + | 0.921362i | \(0.372922\pi\) | |||||||
\(602\) | −9.46220 | −0.385650 | ||||||||
\(603\) | −25.6704 | −1.04538 | ||||||||
\(604\) | −14.2465 | −0.579683 | ||||||||
\(605\) | −4.66083 | −0.189490 | ||||||||
\(606\) | −46.9552 | −1.90743 | ||||||||
\(607\) | −4.20146 | −0.170532 | −0.0852660 | − | 0.996358i | \(-0.527174\pi\) | ||||
−0.0852660 | + | 0.996358i | \(0.527174\pi\) | |||||||
\(608\) | 6.17334 | 0.250362 | ||||||||
\(609\) | 44.4881 | 1.80275 | ||||||||
\(610\) | 4.67460 | 0.189269 | ||||||||
\(611\) | −15.3755 | −0.622024 | ||||||||
\(612\) | 17.5697 | 0.710214 | ||||||||
\(613\) | −6.18511 | −0.249814 | −0.124907 | − | 0.992168i | \(-0.539863\pi\) | ||||
−0.124907 | + | 0.992168i | \(0.539863\pi\) | |||||||
\(614\) | −27.5631 | −1.11236 | ||||||||
\(615\) | 39.9130 | 1.60945 | ||||||||
\(616\) | 13.0522 | 0.525889 | ||||||||
\(617\) | −45.1203 | −1.81648 | −0.908238 | − | 0.418455i | \(-0.862572\pi\) | ||||
−0.908238 | + | 0.418455i | \(0.862572\pi\) | |||||||
\(618\) | −6.22980 | −0.250599 | ||||||||
\(619\) | 23.2152 | 0.933099 | 0.466549 | − | 0.884495i | \(-0.345497\pi\) | ||||
0.466549 | + | 0.884495i | \(0.345497\pi\) | |||||||
\(620\) | 0.352450 | 0.0141547 | ||||||||
\(621\) | −6.93367 | −0.278239 | ||||||||
\(622\) | 6.31777 | 0.253320 | ||||||||
\(623\) | 66.6742 | 2.67125 | ||||||||
\(624\) | 5.54899 | 0.222137 | ||||||||
\(625\) | −0.299058 | −0.0119623 | ||||||||
\(626\) | 8.46763 | 0.338435 | ||||||||
\(627\) | −43.2616 | −1.72770 | ||||||||
\(628\) | 5.69937 | 0.227430 | ||||||||
\(629\) | 11.8099 | 0.470892 | ||||||||
\(630\) | −22.4509 | −0.894466 | ||||||||
\(631\) | 0.147010 | 0.00585236 | 0.00292618 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292618 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(632\) | 16.6002 | 0.660319 | ||||||||
\(633\) | 22.5812 | 0.897521 | ||||||||
\(634\) | −0.996946 | −0.0395938 | ||||||||
\(635\) | 16.1409 | 0.640533 | ||||||||
\(636\) | 2.02734 | 0.0803893 | ||||||||
\(637\) | −33.4378 | −1.32485 | ||||||||
\(638\) | −10.2929 | −0.407501 | ||||||||
\(639\) | −46.5485 | −1.84143 | ||||||||
\(640\) | −1.39163 | −0.0550091 | ||||||||
\(641\) | 2.86159 | 0.113026 | 0.0565130 | − | 0.998402i | \(-0.482002\pi\) | ||||
0.0565130 | + | 0.998402i | \(0.482002\pi\) | |||||||
\(642\) | −0.423057 | −0.0166967 | ||||||||
\(643\) | −44.7087 | −1.76314 | −0.881569 | − | 0.472056i | \(-0.843512\pi\) | ||||
−0.881569 | + | 0.472056i | \(0.843512\pi\) | |||||||
\(644\) | 30.8328 | 1.21498 | ||||||||
\(645\) | −7.06993 | −0.278378 | ||||||||
\(646\) | 31.7253 | 1.24821 | ||||||||
\(647\) | −20.1785 | −0.793297 | −0.396649 | − | 0.917971i | \(-0.629827\pi\) | ||||
−0.396649 | + | 0.917971i | \(0.629827\pi\) | |||||||
\(648\) | 7.56804 | 0.297301 | ||||||||
\(649\) | −11.1139 | −0.436259 | ||||||||
\(650\) | −6.70940 | −0.263164 | ||||||||
\(651\) | −3.02783 | −0.118670 | ||||||||
\(652\) | 21.1843 | 0.829640 | ||||||||
\(653\) | −31.7629 | −1.24298 | −0.621489 | − | 0.783423i | \(-0.713472\pi\) | ||||
−0.621489 | + | 0.783423i | \(0.713472\pi\) | |||||||
\(654\) | 22.8663 | 0.894144 | ||||||||
\(655\) | 5.82317 | 0.227530 | ||||||||
\(656\) | −11.3204 | −0.441987 | ||||||||
\(657\) | 48.1948 | 1.88026 | ||||||||
\(658\) | −33.1263 | −1.29140 | ||||||||
\(659\) | −31.0390 | −1.20911 | −0.604553 | − | 0.796565i | \(-0.706648\pi\) | ||||
−0.604553 | + | 0.796565i | \(0.706648\pi\) | |||||||
\(660\) | 9.75230 | 0.379608 | ||||||||
\(661\) | −19.5650 | −0.760991 | −0.380496 | − | 0.924783i | \(-0.624247\pi\) | ||||
−0.380496 | + | 0.924783i | \(0.624247\pi\) | |||||||
\(662\) | 14.4797 | 0.562771 | ||||||||
\(663\) | 28.5167 | 1.10750 | ||||||||
\(664\) | 17.3391 | 0.672889 | ||||||||
\(665\) | −40.5392 | −1.57204 | ||||||||
\(666\) | −7.85670 | −0.304441 | ||||||||
\(667\) | −24.3146 | −0.941467 | ||||||||
\(668\) | −3.61223 | −0.139761 | ||||||||
\(669\) | −16.6704 | −0.644515 | ||||||||
\(670\) | 10.4491 | 0.403683 | ||||||||
\(671\) | 9.29125 | 0.358685 | ||||||||
\(672\) | 11.9552 | 0.461184 | ||||||||
\(673\) | −22.9077 | −0.883028 | −0.441514 | − | 0.897254i | \(-0.645558\pi\) | ||||
−0.441514 | + | 0.897254i | \(0.645558\pi\) | |||||||
\(674\) | −18.8737 | −0.726988 | ||||||||
\(675\) | 3.25071 | 0.125120 | ||||||||
\(676\) | −8.20298 | −0.315499 | ||||||||
\(677\) | −39.5681 | −1.52073 | −0.760364 | − | 0.649498i | \(-0.774979\pi\) | ||||
−0.760364 | + | 0.649498i | \(0.774979\pi\) | |||||||
\(678\) | −38.4783 | −1.47775 | ||||||||
\(679\) | −47.2146 | −1.81193 | ||||||||
\(680\) | −7.15172 | −0.274256 | ||||||||
\(681\) | −16.6091 | −0.636464 | ||||||||
\(682\) | 0.700529 | 0.0268247 | ||||||||
\(683\) | −38.2437 | −1.46336 | −0.731678 | − | 0.681651i | \(-0.761262\pi\) | ||||
−0.731678 | + | 0.681651i | \(0.761262\pi\) | |||||||
\(684\) | −21.1057 | −0.806995 | ||||||||
\(685\) | 12.3665 | 0.472500 | ||||||||
\(686\) | −39.0099 | −1.48941 | ||||||||
\(687\) | −21.5659 | −0.822789 | ||||||||
\(688\) | 2.00522 | 0.0764483 | ||||||||
\(689\) | 1.75261 | 0.0667690 | ||||||||
\(690\) | 23.0375 | 0.877024 | ||||||||
\(691\) | 28.1325 | 1.07021 | 0.535105 | − | 0.844786i | \(-0.320272\pi\) | ||||
0.535105 | + | 0.844786i | \(0.320272\pi\) | |||||||
\(692\) | −5.78462 | −0.219898 | ||||||||
\(693\) | −44.6235 | −1.69511 | ||||||||
\(694\) | −19.9968 | −0.759068 | ||||||||
\(695\) | 6.74842 | 0.255982 | ||||||||
\(696\) | −9.42786 | −0.357362 | ||||||||
\(697\) | −58.1764 | −2.20359 | ||||||||
\(698\) | 4.49839 | 0.170267 | ||||||||
\(699\) | 44.2296 | 1.67292 | ||||||||
\(700\) | −14.4553 | −0.546360 | ||||||||
\(701\) | −21.1791 | −0.799924 | −0.399962 | − | 0.916532i | \(-0.630977\pi\) | ||||
−0.399962 | + | 0.916532i | \(0.630977\pi\) | |||||||
\(702\) | −2.32416 | −0.0877197 | ||||||||
\(703\) | −14.1867 | −0.535061 | ||||||||
\(704\) | −2.76601 | −0.104248 | ||||||||
\(705\) | −24.7512 | −0.932182 | ||||||||
\(706\) | 34.2822 | 1.29023 | ||||||||
\(707\) | −87.4553 | −3.28909 | ||||||||
\(708\) | −10.1798 | −0.382582 | ||||||||
\(709\) | −51.3793 | −1.92959 | −0.964794 | − | 0.263005i | \(-0.915286\pi\) | ||||
−0.964794 | + | 0.263005i | \(0.915286\pi\) | |||||||
\(710\) | 18.9475 | 0.711086 | ||||||||
\(711\) | −56.7533 | −2.12842 | ||||||||
\(712\) | −14.1295 | −0.529526 | ||||||||
\(713\) | 1.65484 | 0.0619742 | ||||||||
\(714\) | 61.4390 | 2.29930 | ||||||||
\(715\) | 8.43072 | 0.315291 | ||||||||
\(716\) | 12.0434 | 0.450082 | ||||||||
\(717\) | 64.8494 | 2.42185 | ||||||||
\(718\) | 4.56154 | 0.170235 | ||||||||
\(719\) | 11.6311 | 0.433768 | 0.216884 | − | 0.976197i | \(-0.430411\pi\) | ||||
0.216884 | + | 0.976197i | \(0.430411\pi\) | |||||||
\(720\) | 4.75778 | 0.177312 | ||||||||
\(721\) | −11.6031 | −0.432124 | ||||||||
\(722\) | −19.1101 | −0.711204 | ||||||||
\(723\) | 54.6807 | 2.03360 | ||||||||
\(724\) | −17.4236 | −0.647544 | ||||||||
\(725\) | 11.3994 | 0.423363 | ||||||||
\(726\) | −8.48529 | −0.314919 | ||||||||
\(727\) | −12.9139 | −0.478950 | −0.239475 | − | 0.970903i | \(-0.576975\pi\) | ||||
−0.239475 | + | 0.970903i | \(0.576975\pi\) | |||||||
\(728\) | 10.3351 | 0.383045 | ||||||||
\(729\) | −33.9394 | −1.25702 | ||||||||
\(730\) | −19.6176 | −0.726080 | ||||||||
\(731\) | 10.3050 | 0.381144 | ||||||||
\(732\) | 8.51037 | 0.314552 | ||||||||
\(733\) | −4.29538 | −0.158653 | −0.0793267 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793267 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(734\) | −11.4321 | −0.421965 | ||||||||
\(735\) | −53.8276 | −1.98546 | ||||||||
\(736\) | −6.53406 | −0.240849 | ||||||||
\(737\) | 20.7686 | 0.765022 | ||||||||
\(738\) | 38.7026 | 1.42466 | ||||||||
\(739\) | −22.6438 | −0.832967 | −0.416484 | − | 0.909143i | \(-0.636738\pi\) | ||||
−0.416484 | + | 0.909143i | \(0.636738\pi\) | |||||||
\(740\) | 3.19805 | 0.117563 | ||||||||
\(741\) | −34.2558 | −1.25842 | ||||||||
\(742\) | 3.77597 | 0.138620 | ||||||||
\(743\) | 30.5830 | 1.12198 | 0.560991 | − | 0.827822i | \(-0.310420\pi\) | ||||
0.560991 | + | 0.827822i | \(0.310420\pi\) | |||||||
\(744\) | 0.641654 | 0.0235242 | ||||||||
\(745\) | 1.55917 | 0.0571234 | ||||||||
\(746\) | 5.21755 | 0.191028 | ||||||||
\(747\) | −59.2798 | −2.16893 | ||||||||
\(748\) | −14.2148 | −0.519743 | ||||||||
\(749\) | −0.787955 | −0.0287912 | ||||||||
\(750\) | −28.4295 | −1.03810 | ||||||||
\(751\) | 36.4686 | 1.33076 | 0.665380 | − | 0.746505i | \(-0.268270\pi\) | ||||
0.665380 | + | 0.746505i | \(0.268270\pi\) | |||||||
\(752\) | 7.02008 | 0.255996 | ||||||||
\(753\) | −1.41045 | −0.0513998 | ||||||||
\(754\) | −8.15024 | −0.296814 | ||||||||
\(755\) | −19.8259 | −0.721540 | ||||||||
\(756\) | −5.00738 | −0.182117 | ||||||||
\(757\) | 14.7458 | 0.535947 | 0.267973 | − | 0.963426i | \(-0.413646\pi\) | ||||
0.267973 | + | 0.963426i | \(0.413646\pi\) | |||||||
\(758\) | −27.1167 | −0.984921 | ||||||||
\(759\) | 45.7895 | 1.66205 | ||||||||
\(760\) | 8.59102 | 0.311629 | ||||||||
\(761\) | 41.5565 | 1.50642 | 0.753211 | − | 0.657779i | \(-0.228504\pi\) | ||||
0.753211 | + | 0.657779i | \(0.228504\pi\) | |||||||
\(762\) | 29.3854 | 1.06452 | ||||||||
\(763\) | 42.5891 | 1.54183 | ||||||||
\(764\) | 1.21193 | 0.0438462 | ||||||||
\(765\) | 24.4506 | 0.884013 | ||||||||
\(766\) | 21.8116 | 0.788086 | ||||||||
\(767\) | −8.80031 | −0.317761 | ||||||||
\(768\) | −2.53354 | −0.0914214 | ||||||||
\(769\) | 18.9906 | 0.684818 | 0.342409 | − | 0.939551i | \(-0.388757\pi\) | ||||
0.342409 | + | 0.939551i | \(0.388757\pi\) | |||||||
\(770\) | 18.1639 | 0.654581 | ||||||||
\(771\) | −78.9842 | −2.84454 | ||||||||
\(772\) | 0.959405 | 0.0345298 | ||||||||
\(773\) | 18.4500 | 0.663600 | 0.331800 | − | 0.943350i | \(-0.392344\pi\) | ||||
0.331800 | + | 0.943350i | \(0.392344\pi\) | |||||||
\(774\) | −6.85553 | −0.246417 | ||||||||
\(775\) | −0.775836 | −0.0278689 | ||||||||
\(776\) | 10.0057 | 0.359182 | ||||||||
\(777\) | −27.4739 | −0.985619 | ||||||||
\(778\) | 1.21853 | 0.0436865 | ||||||||
\(779\) | 69.8846 | 2.50387 | ||||||||
\(780\) | 7.72216 | 0.276498 | ||||||||
\(781\) | 37.6600 | 1.34758 | ||||||||
\(782\) | −33.5791 | −1.20078 | ||||||||
\(783\) | 3.94880 | 0.141119 | ||||||||
\(784\) | 15.2669 | 0.545248 | ||||||||
\(785\) | 7.93143 | 0.283085 | ||||||||
\(786\) | 10.6014 | 0.378140 | ||||||||
\(787\) | −25.7800 | −0.918958 | −0.459479 | − | 0.888189i | \(-0.651964\pi\) | ||||
−0.459479 | + | 0.888189i | \(0.651964\pi\) | |||||||
\(788\) | −8.73442 | −0.311151 | ||||||||
\(789\) | −31.0937 | −1.10696 | ||||||||
\(790\) | 23.1013 | 0.821908 | ||||||||
\(791\) | −71.6668 | −2.54818 | ||||||||
\(792\) | 9.45656 | 0.336024 | ||||||||
\(793\) | 7.35709 | 0.261258 | ||||||||
\(794\) | 15.7252 | 0.558066 | ||||||||
\(795\) | 2.82132 | 0.100062 | ||||||||
\(796\) | 15.2750 | 0.541407 | ||||||||
\(797\) | 26.4267 | 0.936081 | 0.468041 | − | 0.883707i | \(-0.344960\pi\) | ||||
0.468041 | + | 0.883707i | \(0.344960\pi\) | |||||||
\(798\) | −73.8038 | −2.61263 | ||||||||
\(799\) | 36.0768 | 1.27630 | ||||||||
\(800\) | 3.06336 | 0.108306 | ||||||||
\(801\) | 48.3066 | 1.70683 | ||||||||
\(802\) | 35.7473 | 1.26228 | ||||||||
\(803\) | −38.9919 | −1.37600 | ||||||||
\(804\) | 19.0231 | 0.670894 | ||||||||
\(805\) | 42.9080 | 1.51231 | ||||||||
\(806\) | 0.554700 | 0.0195385 | ||||||||
\(807\) | 58.5761 | 2.06198 | ||||||||
\(808\) | 18.5334 | 0.652004 | ||||||||
\(809\) | 35.2271 | 1.23852 | 0.619260 | − | 0.785186i | \(-0.287433\pi\) | ||||
0.619260 | + | 0.785186i | \(0.287433\pi\) | |||||||
\(810\) | 10.5319 | 0.370054 | ||||||||
\(811\) | 25.6753 | 0.901581 | 0.450791 | − | 0.892630i | \(-0.351142\pi\) | ||||
0.450791 | + | 0.892630i | \(0.351142\pi\) | |||||||
\(812\) | −17.5596 | −0.616222 | ||||||||
\(813\) | −60.6961 | −2.12870 | ||||||||
\(814\) | 6.35646 | 0.222794 | ||||||||
\(815\) | 29.4807 | 1.03266 | ||||||||
\(816\) | −13.0201 | −0.455794 | ||||||||
\(817\) | −12.3789 | −0.433083 | ||||||||
\(818\) | −1.14419 | −0.0400056 | ||||||||
\(819\) | −35.3342 | −1.23468 | ||||||||
\(820\) | −15.7538 | −0.550148 | ||||||||
\(821\) | −7.63648 | −0.266515 | −0.133258 | − | 0.991081i | \(-0.542544\pi\) | ||||
−0.133258 | + | 0.991081i | \(0.542544\pi\) | |||||||
\(822\) | 22.5139 | 0.785262 | ||||||||
\(823\) | −30.6017 | −1.06671 | −0.533355 | − | 0.845892i | \(-0.679069\pi\) | ||||
−0.533355 | + | 0.845892i | \(0.679069\pi\) | |||||||
\(824\) | 2.45893 | 0.0856608 | ||||||||
\(825\) | −21.4674 | −0.747400 | ||||||||
\(826\) | −18.9602 | −0.659709 | ||||||||
\(827\) | 13.0639 | 0.454275 | 0.227138 | − | 0.973863i | \(-0.427063\pi\) | ||||
0.227138 | + | 0.973863i | \(0.427063\pi\) | |||||||
\(828\) | 22.3389 | 0.776331 | ||||||||
\(829\) | 42.4264 | 1.47353 | 0.736765 | − | 0.676149i | \(-0.236353\pi\) | ||||
0.736765 | + | 0.676149i | \(0.236353\pi\) | |||||||
\(830\) | 24.1297 | 0.837554 | ||||||||
\(831\) | 29.4803 | 1.02266 | ||||||||
\(832\) | −2.19021 | −0.0759319 | ||||||||
\(833\) | 78.4580 | 2.71841 | ||||||||
\(834\) | 12.2859 | 0.425425 | ||||||||
\(835\) | −5.02690 | −0.173963 | ||||||||
\(836\) | 17.0755 | 0.590569 | ||||||||
\(837\) | −0.268752 | −0.00928944 | ||||||||
\(838\) | 33.2960 | 1.15019 | ||||||||
\(839\) | −20.2524 | −0.699191 | −0.349596 | − | 0.936901i | \(-0.613681\pi\) | ||||
−0.349596 | + | 0.936901i | \(0.613681\pi\) | |||||||
\(840\) | 16.6373 | 0.574042 | ||||||||
\(841\) | −15.1526 | −0.522502 | ||||||||
\(842\) | 27.8954 | 0.961337 | ||||||||
\(843\) | −42.2739 | −1.45599 | ||||||||
\(844\) | −8.91288 | −0.306794 | ||||||||
\(845\) | −11.4155 | −0.392706 | ||||||||
\(846\) | −24.0006 | −0.825156 | ||||||||
\(847\) | −15.8041 | −0.543034 | ||||||||
\(848\) | −0.800200 | −0.0274790 | ||||||||
\(849\) | 17.0113 | 0.583825 | ||||||||
\(850\) | 15.7428 | 0.539975 | ||||||||
\(851\) | 15.0157 | 0.514730 | ||||||||
\(852\) | 34.4949 | 1.18178 | ||||||||
\(853\) | −31.3101 | −1.07204 | −0.536018 | − | 0.844206i | \(-0.680072\pi\) | ||||
−0.536018 | + | 0.844206i | \(0.680072\pi\) | |||||||
\(854\) | 15.8508 | 0.542402 | ||||||||
\(855\) | −29.3714 | −1.00448 | ||||||||
\(856\) | 0.166982 | 0.00570734 | ||||||||
\(857\) | −46.2106 | −1.57852 | −0.789261 | − | 0.614057i | \(-0.789536\pi\) | ||||
−0.789261 | + | 0.614057i | \(0.789536\pi\) | |||||||
\(858\) | 15.3486 | 0.523992 | ||||||||
\(859\) | 11.6321 | 0.396881 | 0.198441 | − | 0.980113i | \(-0.436412\pi\) | ||||
0.198441 | + | 0.980113i | \(0.436412\pi\) | |||||||
\(860\) | 2.79053 | 0.0951563 | ||||||||
\(861\) | 135.338 | 4.61231 | ||||||||
\(862\) | −1.78701 | −0.0608657 | ||||||||
\(863\) | −36.7764 | −1.25188 | −0.625941 | − | 0.779871i | \(-0.715285\pi\) | ||||
−0.625941 | + | 0.779871i | \(0.715285\pi\) | |||||||
\(864\) | 1.06116 | 0.0361013 | ||||||||
\(865\) | −8.05008 | −0.273711 | ||||||||
\(866\) | −5.92092 | −0.201201 | ||||||||
\(867\) | −23.8410 | −0.809684 | ||||||||
\(868\) | 1.19510 | 0.0405642 | ||||||||
\(869\) | 45.9162 | 1.55760 | ||||||||
\(870\) | −13.1201 | −0.444814 | ||||||||
\(871\) | 16.4452 | 0.557225 | ||||||||
\(872\) | −9.02543 | −0.305640 | ||||||||
\(873\) | −34.2078 | −1.15776 | ||||||||
\(874\) | 40.3369 | 1.36442 | ||||||||
\(875\) | −52.9506 | −1.79006 | ||||||||
\(876\) | −35.7149 | −1.20669 | ||||||||
\(877\) | −2.78864 | −0.0941655 | −0.0470828 | − | 0.998891i | \(-0.514992\pi\) | ||||
−0.0470828 | + | 0.998891i | \(0.514992\pi\) | |||||||
\(878\) | −26.8472 | −0.906050 | ||||||||
\(879\) | −13.8832 | −0.468269 | ||||||||
\(880\) | −3.84927 | −0.129759 | ||||||||
\(881\) | −41.4499 | −1.39648 | −0.698241 | − | 0.715862i | \(-0.746034\pi\) | ||||
−0.698241 | + | 0.715862i | \(0.746034\pi\) | |||||||
\(882\) | −52.1953 | −1.75751 | ||||||||
\(883\) | −29.0427 | −0.977364 | −0.488682 | − | 0.872462i | \(-0.662522\pi\) | ||||
−0.488682 | + | 0.872462i | \(0.662522\pi\) | |||||||
\(884\) | −11.2557 | −0.378569 | ||||||||
\(885\) | −14.1666 | −0.476205 | ||||||||
\(886\) | 4.13134 | 0.138795 | ||||||||
\(887\) | −20.0790 | −0.674187 | −0.337093 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337093 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(888\) | 5.82223 | 0.195381 | ||||||||
\(889\) | 54.7310 | 1.83562 | ||||||||
\(890\) | −19.6631 | −0.659109 | ||||||||
\(891\) | 20.9333 | 0.701292 | ||||||||
\(892\) | 6.57988 | 0.220311 | ||||||||
\(893\) | −43.3373 | −1.45023 | ||||||||
\(894\) | 2.83855 | 0.0949352 | ||||||||
\(895\) | 16.7600 | 0.560224 | ||||||||
\(896\) | −4.71879 | −0.157644 | ||||||||
\(897\) | 36.2574 | 1.21060 | ||||||||
\(898\) | −17.7201 | −0.591326 | ||||||||
\(899\) | −0.942447 | −0.0314324 | ||||||||
\(900\) | −10.4731 | −0.349105 | ||||||||
\(901\) | −4.11229 | −0.137000 | ||||||||
\(902\) | −31.3123 | −1.04259 | ||||||||
\(903\) | −23.9729 | −0.797768 | ||||||||
\(904\) | 15.1876 | 0.505130 | ||||||||
\(905\) | −24.2473 | −0.806008 | ||||||||
\(906\) | −36.0942 | −1.19915 | ||||||||
\(907\) | −23.6438 | −0.785080 | −0.392540 | − | 0.919735i | \(-0.628404\pi\) | ||||
−0.392540 | + | 0.919735i | \(0.628404\pi\) | |||||||
\(908\) | 6.55570 | 0.217558 | ||||||||
\(909\) | −63.3629 | −2.10161 | ||||||||
\(910\) | 14.3827 | 0.476782 | ||||||||
\(911\) | 25.2248 | 0.835735 | 0.417867 | − | 0.908508i | \(-0.362778\pi\) | ||||
0.417867 | + | 0.908508i | \(0.362778\pi\) | |||||||
\(912\) | 15.6404 | 0.517906 | ||||||||
\(913\) | 47.9602 | 1.58725 | ||||||||
\(914\) | −35.9463 | −1.18900 | ||||||||
\(915\) | 11.8433 | 0.391528 | ||||||||
\(916\) | 8.51214 | 0.281249 | ||||||||
\(917\) | 19.7454 | 0.652049 | ||||||||
\(918\) | 5.45338 | 0.179988 | ||||||||
\(919\) | 21.3841 | 0.705398 | 0.352699 | − | 0.935737i | \(-0.385264\pi\) | ||||
0.352699 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(920\) | −9.09301 | −0.299788 | ||||||||
\(921\) | −69.8324 | −2.30106 | ||||||||
\(922\) | 31.0691 | 1.02321 | ||||||||
\(923\) | 29.8203 | 0.981547 | ||||||||
\(924\) | 33.0684 | 1.08787 | ||||||||
\(925\) | −7.03977 | −0.231466 | ||||||||
\(926\) | −23.6141 | −0.776009 | ||||||||
\(927\) | −8.40669 | −0.276112 | ||||||||
\(928\) | 3.72122 | 0.122155 | ||||||||
\(929\) | 6.05803 | 0.198758 | 0.0993788 | − | 0.995050i | \(-0.468314\pi\) | ||||
0.0993788 | + | 0.995050i | \(0.468314\pi\) | |||||||
\(930\) | 0.892947 | 0.0292809 | ||||||||
\(931\) | −94.2479 | −3.08885 | ||||||||
\(932\) | −17.4576 | −0.571842 | ||||||||
\(933\) | 16.0064 | 0.524024 | ||||||||
\(934\) | −15.3694 | −0.502902 | ||||||||
\(935\) | −19.7817 | −0.646932 | ||||||||
\(936\) | 7.48799 | 0.244752 | ||||||||
\(937\) | −40.3196 | −1.31718 | −0.658592 | − | 0.752500i | \(-0.728848\pi\) | ||||
−0.658592 | + | 0.752500i | \(0.728848\pi\) | |||||||
\(938\) | 35.4310 | 1.15686 | ||||||||
\(939\) | 21.4531 | 0.700096 | ||||||||
\(940\) | 9.76938 | 0.318642 | ||||||||
\(941\) | −33.3535 | −1.08729 | −0.543647 | − | 0.839314i | \(-0.682957\pi\) | ||||
−0.543647 | + | 0.839314i | \(0.682957\pi\) | |||||||
\(942\) | 14.4396 | 0.470468 | ||||||||
\(943\) | −73.9681 | −2.40873 | ||||||||
\(944\) | 4.01802 | 0.130775 | ||||||||
\(945\) | −6.96843 | −0.226683 | ||||||||
\(946\) | 5.54646 | 0.180331 | ||||||||
\(947\) | −37.9584 | −1.23348 | −0.616741 | − | 0.787166i | \(-0.711547\pi\) | ||||
−0.616741 | + | 0.787166i | \(0.711547\pi\) | |||||||
\(948\) | 42.0572 | 1.36595 | ||||||||
\(949\) | −30.8750 | −1.00224 | ||||||||
\(950\) | −18.9111 | −0.613558 | ||||||||
\(951\) | −2.52581 | −0.0819049 | ||||||||
\(952\) | −24.2502 | −0.785954 | ||||||||
\(953\) | −20.8214 | −0.674472 | −0.337236 | − | 0.941420i | \(-0.609492\pi\) | ||||
−0.337236 | + | 0.941420i | \(0.609492\pi\) | |||||||
\(954\) | 2.73576 | 0.0885734 | ||||||||
\(955\) | 1.68657 | 0.0545760 | ||||||||
\(956\) | −25.5963 | −0.827845 | ||||||||
\(957\) | −26.0776 | −0.842968 | ||||||||
\(958\) | 40.1793 | 1.29813 | ||||||||
\(959\) | 41.9327 | 1.35408 | ||||||||
\(960\) | −3.52576 | −0.113794 | ||||||||
\(961\) | −30.9359 | −0.997931 | ||||||||
\(962\) | 5.03323 | 0.162278 | ||||||||
\(963\) | −0.570887 | −0.0183966 | ||||||||
\(964\) | −21.5827 | −0.695132 | ||||||||
\(965\) | 1.33514 | 0.0429797 | ||||||||
\(966\) | 78.1163 | 2.51335 | ||||||||
\(967\) | 44.6289 | 1.43517 | 0.717585 | − | 0.696471i | \(-0.245248\pi\) | ||||
0.717585 | + | 0.696471i | \(0.245248\pi\) | |||||||
\(968\) | 3.34918 | 0.107647 | ||||||||
\(969\) | 80.3774 | 2.58209 | ||||||||
\(970\) | 13.9242 | 0.447080 | ||||||||
\(971\) | 54.7566 | 1.75722 | 0.878612 | − | 0.477537i | \(-0.158470\pi\) | ||||
0.878612 | + | 0.477537i | \(0.158470\pi\) | |||||||
\(972\) | 22.3574 | 0.717115 | ||||||||
\(973\) | 22.8827 | 0.733587 | ||||||||
\(974\) | 38.6875 | 1.23963 | ||||||||
\(975\) | −16.9985 | −0.544389 | ||||||||
\(976\) | −3.35908 | −0.107521 | ||||||||
\(977\) | 23.3875 | 0.748234 | 0.374117 | − | 0.927382i | \(-0.377946\pi\) | ||||
0.374117 | + | 0.927382i | \(0.377946\pi\) | |||||||
\(978\) | 53.6712 | 1.71622 | ||||||||
\(979\) | −39.0824 | −1.24908 | ||||||||
\(980\) | 21.2460 | 0.678678 | ||||||||
\(981\) | 30.8565 | 0.985173 | ||||||||
\(982\) | −42.2643 | −1.34871 | ||||||||
\(983\) | 48.1613 | 1.53611 | 0.768053 | − | 0.640387i | \(-0.221226\pi\) | ||||
0.768053 | + | 0.640387i | \(0.221226\pi\) | |||||||
\(984\) | −28.6807 | −0.914307 | ||||||||
\(985\) | −12.1551 | −0.387294 | ||||||||
\(986\) | 19.1236 | 0.609020 | ||||||||
\(987\) | −83.9269 | −2.67142 | ||||||||
\(988\) | 13.5209 | 0.430157 | ||||||||
\(989\) | 13.1022 | 0.416626 | ||||||||
\(990\) | 13.1601 | 0.418254 | ||||||||
\(991\) | 39.1554 | 1.24381 | 0.621906 | − | 0.783092i | \(-0.286358\pi\) | ||||
0.621906 | + | 0.783092i | \(0.286358\pi\) | |||||||
\(992\) | −0.253263 | −0.00804112 | ||||||||
\(993\) | 36.6850 | 1.16416 | ||||||||
\(994\) | 64.2475 | 2.03781 | ||||||||
\(995\) | 21.2572 | 0.673898 | ||||||||
\(996\) | 43.9294 | 1.39196 | ||||||||
\(997\) | 26.3336 | 0.833992 | 0.416996 | − | 0.908908i | \(-0.363083\pi\) | ||||
0.416996 | + | 0.908908i | \(0.363083\pi\) | |||||||
\(998\) | −2.54463 | −0.0805490 | ||||||||
\(999\) | −2.43860 | −0.0771540 |
(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 | 8038.2.a.c.1.15 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.c.1.15 | ✓ | 84 | 1.1 | even | 1 | trivial |