Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, 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("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.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: | \(48.0859120972\) |
Analytic rank: | \(1\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-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 | ||||||||
\(3\) | −1.52904 | −0.882791 | −0.441395 | − | 0.897313i | \(-0.645516\pi\) | ||||
−0.441395 | + | 0.897313i | \(0.645516\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.77354 | −1.68758 | −0.843788 | − | 0.536676i | \(-0.819680\pi\) | ||||
−0.843788 | + | 0.536676i | \(0.819680\pi\) | |||||||
\(6\) | −1.52904 | −0.624227 | ||||||||
\(7\) | 0.908453 | 0.343363 | 0.171682 | − | 0.985153i | \(-0.445080\pi\) | ||||
0.171682 | + | 0.985153i | \(0.445080\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.662042 | −0.220681 | ||||||||
\(10\) | −3.77354 | −1.19330 | ||||||||
\(11\) | −2.19947 | −0.663167 | −0.331583 | − | 0.943426i | \(-0.607583\pi\) | ||||
−0.331583 | + | 0.943426i | \(0.607583\pi\) | |||||||
\(12\) | −1.52904 | −0.441395 | ||||||||
\(13\) | −1.27619 | −0.353953 | −0.176976 | − | 0.984215i | \(-0.556632\pi\) | ||||
−0.176976 | + | 0.984215i | \(0.556632\pi\) | |||||||
\(14\) | 0.908453 | 0.242794 | ||||||||
\(15\) | 5.76988 | 1.48978 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0603416 | 0.0146350 | 0.00731749 | − | 0.999973i | \(-0.497671\pi\) | ||||
0.00731749 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(18\) | −0.662042 | −0.156045 | ||||||||
\(19\) | 4.24736 | 0.974411 | 0.487206 | − | 0.873287i | \(-0.338016\pi\) | ||||
0.487206 | + | 0.873287i | \(0.338016\pi\) | |||||||
\(20\) | −3.77354 | −0.843788 | ||||||||
\(21\) | −1.38906 | −0.303118 | ||||||||
\(22\) | −2.19947 | −0.468930 | ||||||||
\(23\) | −1.92041 | −0.400432 | −0.200216 | − | 0.979752i | \(-0.564164\pi\) | ||||
−0.200216 | + | 0.979752i | \(0.564164\pi\) | |||||||
\(24\) | −1.52904 | −0.312114 | ||||||||
\(25\) | 9.23957 | 1.84791 | ||||||||
\(26\) | −1.27619 | −0.250282 | ||||||||
\(27\) | 5.59940 | 1.07761 | ||||||||
\(28\) | 0.908453 | 0.171682 | ||||||||
\(29\) | 9.79145 | 1.81823 | 0.909114 | − | 0.416548i | \(-0.136760\pi\) | ||||
0.909114 | + | 0.416548i | \(0.136760\pi\) | |||||||
\(30\) | 5.76988 | 1.05343 | ||||||||
\(31\) | 7.27484 | 1.30660 | 0.653300 | − | 0.757099i | \(-0.273384\pi\) | ||||
0.653300 | + | 0.757099i | \(0.273384\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.36308 | 0.585437 | ||||||||
\(34\) | 0.0603416 | 0.0103485 | ||||||||
\(35\) | −3.42808 | −0.579451 | ||||||||
\(36\) | −0.662042 | −0.110340 | ||||||||
\(37\) | −6.02467 | −0.990450 | −0.495225 | − | 0.868765i | \(-0.664914\pi\) | ||||
−0.495225 | + | 0.868765i | \(0.664914\pi\) | |||||||
\(38\) | 4.24736 | 0.689013 | ||||||||
\(39\) | 1.95135 | 0.312466 | ||||||||
\(40\) | −3.77354 | −0.596648 | ||||||||
\(41\) | −4.25253 | −0.664133 | −0.332067 | − | 0.943256i | \(-0.607746\pi\) | ||||
−0.332067 | + | 0.943256i | \(0.607746\pi\) | |||||||
\(42\) | −1.38906 | −0.214337 | ||||||||
\(43\) | 12.3544 | 1.88403 | 0.942017 | − | 0.335565i | \(-0.108927\pi\) | ||||
0.942017 | + | 0.335565i | \(0.108927\pi\) | |||||||
\(44\) | −2.19947 | −0.331583 | ||||||||
\(45\) | 2.49824 | 0.372415 | ||||||||
\(46\) | −1.92041 | −0.283149 | ||||||||
\(47\) | −5.29910 | −0.772953 | −0.386476 | − | 0.922299i | \(-0.626308\pi\) | ||||
−0.386476 | + | 0.922299i | \(0.626308\pi\) | |||||||
\(48\) | −1.52904 | −0.220698 | ||||||||
\(49\) | −6.17471 | −0.882102 | ||||||||
\(50\) | 9.23957 | 1.30667 | ||||||||
\(51\) | −0.0922646 | −0.0129196 | ||||||||
\(52\) | −1.27619 | −0.176976 | ||||||||
\(53\) | −1.73521 | −0.238350 | −0.119175 | − | 0.992873i | \(-0.538025\pi\) | ||||
−0.119175 | + | 0.992873i | \(0.538025\pi\) | |||||||
\(54\) | 5.59940 | 0.761982 | ||||||||
\(55\) | 8.29980 | 1.11914 | ||||||||
\(56\) | 0.908453 | 0.121397 | ||||||||
\(57\) | −6.49438 | −0.860201 | ||||||||
\(58\) | 9.79145 | 1.28568 | ||||||||
\(59\) | −5.60111 | −0.729202 | −0.364601 | − | 0.931164i | \(-0.618795\pi\) | ||||
−0.364601 | + | 0.931164i | \(0.618795\pi\) | |||||||
\(60\) | 5.76988 | 0.744888 | ||||||||
\(61\) | −5.24714 | −0.671828 | −0.335914 | − | 0.941893i | \(-0.609045\pi\) | ||||
−0.335914 | + | 0.941893i | \(0.609045\pi\) | |||||||
\(62\) | 7.27484 | 0.923906 | ||||||||
\(63\) | −0.601434 | −0.0757736 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.81577 | 0.597322 | ||||||||
\(66\) | 3.36308 | 0.413967 | ||||||||
\(67\) | −0.803318 | −0.0981410 | −0.0490705 | − | 0.998795i | \(-0.515626\pi\) | ||||
−0.0490705 | + | 0.998795i | \(0.515626\pi\) | |||||||
\(68\) | 0.0603416 | 0.00731749 | ||||||||
\(69\) | 2.93638 | 0.353498 | ||||||||
\(70\) | −3.42808 | −0.409734 | ||||||||
\(71\) | −4.81511 | −0.571448 | −0.285724 | − | 0.958312i | \(-0.592234\pi\) | ||||
−0.285724 | + | 0.958312i | \(0.592234\pi\) | |||||||
\(72\) | −0.662042 | −0.0780224 | ||||||||
\(73\) | 2.23818 | 0.261959 | 0.130980 | − | 0.991385i | \(-0.458188\pi\) | ||||
0.130980 | + | 0.991385i | \(0.458188\pi\) | |||||||
\(74\) | −6.02467 | −0.700354 | ||||||||
\(75\) | −14.1277 | −1.63132 | ||||||||
\(76\) | 4.24736 | 0.487206 | ||||||||
\(77\) | −1.99812 | −0.227707 | ||||||||
\(78\) | 1.95135 | 0.220947 | ||||||||
\(79\) | 8.73390 | 0.982640 | 0.491320 | − | 0.870979i | \(-0.336515\pi\) | ||||
0.491320 | + | 0.870979i | \(0.336515\pi\) | |||||||
\(80\) | −3.77354 | −0.421894 | ||||||||
\(81\) | −6.57558 | −0.730619 | ||||||||
\(82\) | −4.25253 | −0.469613 | ||||||||
\(83\) | 1.24574 | 0.136738 | 0.0683689 | − | 0.997660i | \(-0.478221\pi\) | ||||
0.0683689 | + | 0.997660i | \(0.478221\pi\) | |||||||
\(84\) | −1.38906 | −0.151559 | ||||||||
\(85\) | −0.227701 | −0.0246977 | ||||||||
\(86\) | 12.3544 | 1.33221 | ||||||||
\(87\) | −14.9715 | −1.60511 | ||||||||
\(88\) | −2.19947 | −0.234465 | ||||||||
\(89\) | −3.82706 | −0.405667 | −0.202834 | − | 0.979213i | \(-0.565015\pi\) | ||||
−0.202834 | + | 0.979213i | \(0.565015\pi\) | |||||||
\(90\) | 2.49824 | 0.263337 | ||||||||
\(91\) | −1.15936 | −0.121534 | ||||||||
\(92\) | −1.92041 | −0.200216 | ||||||||
\(93\) | −11.1235 | −1.15345 | ||||||||
\(94\) | −5.29910 | −0.546560 | ||||||||
\(95\) | −16.0276 | −1.64439 | ||||||||
\(96\) | −1.52904 | −0.156057 | ||||||||
\(97\) | 4.34112 | 0.440774 | 0.220387 | − | 0.975412i | \(-0.429268\pi\) | ||||
0.220387 | + | 0.975412i | \(0.429268\pi\) | |||||||
\(98\) | −6.17471 | −0.623740 | ||||||||
\(99\) | 1.45614 | 0.146348 | ||||||||
\(100\) | 9.23957 | 0.923957 | ||||||||
\(101\) | −10.2852 | −1.02342 | −0.511708 | − | 0.859159i | \(-0.670987\pi\) | ||||
−0.511708 | + | 0.859159i | \(0.670987\pi\) | |||||||
\(102\) | −0.0922646 | −0.00913555 | ||||||||
\(103\) | −6.32214 | −0.622939 | −0.311469 | − | 0.950256i | \(-0.600821\pi\) | ||||
−0.311469 | + | 0.950256i | \(0.600821\pi\) | |||||||
\(104\) | −1.27619 | −0.125141 | ||||||||
\(105\) | 5.24167 | 0.511534 | ||||||||
\(106\) | −1.73521 | −0.168539 | ||||||||
\(107\) | −0.853040 | −0.0824665 | −0.0412332 | − | 0.999150i | \(-0.513129\pi\) | ||||
−0.0412332 | + | 0.999150i | \(0.513129\pi\) | |||||||
\(108\) | 5.59940 | 0.538803 | ||||||||
\(109\) | −5.91086 | −0.566158 | −0.283079 | − | 0.959097i | \(-0.591356\pi\) | ||||
−0.283079 | + | 0.959097i | \(0.591356\pi\) | |||||||
\(110\) | 8.29980 | 0.791354 | ||||||||
\(111\) | 9.21196 | 0.874360 | ||||||||
\(112\) | 0.908453 | 0.0858408 | ||||||||
\(113\) | 7.51312 | 0.706775 | 0.353387 | − | 0.935477i | \(-0.385030\pi\) | ||||
0.353387 | + | 0.935477i | \(0.385030\pi\) | |||||||
\(114\) | −6.49438 | −0.608254 | ||||||||
\(115\) | 7.24672 | 0.675760 | ||||||||
\(116\) | 9.79145 | 0.909114 | ||||||||
\(117\) | 0.844894 | 0.0781105 | ||||||||
\(118\) | −5.60111 | −0.515624 | ||||||||
\(119\) | 0.0548175 | 0.00502511 | ||||||||
\(120\) | 5.76988 | 0.526716 | ||||||||
\(121\) | −6.16231 | −0.560210 | ||||||||
\(122\) | −5.24714 | −0.475054 | ||||||||
\(123\) | 6.50228 | 0.586291 | ||||||||
\(124\) | 7.27484 | 0.653300 | ||||||||
\(125\) | −15.9982 | −1.43092 | ||||||||
\(126\) | −0.601434 | −0.0535800 | ||||||||
\(127\) | −8.02104 | −0.711752 | −0.355876 | − | 0.934533i | \(-0.615818\pi\) | ||||
−0.355876 | + | 0.934533i | \(0.615818\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −18.8904 | −1.66321 | ||||||||
\(130\) | 4.81577 | 0.422371 | ||||||||
\(131\) | −16.6949 | −1.45864 | −0.729320 | − | 0.684172i | \(-0.760164\pi\) | ||||
−0.729320 | + | 0.684172i | \(0.760164\pi\) | |||||||
\(132\) | 3.36308 | 0.292719 | ||||||||
\(133\) | 3.85853 | 0.334577 | ||||||||
\(134\) | −0.803318 | −0.0693961 | ||||||||
\(135\) | −21.1295 | −1.81854 | ||||||||
\(136\) | 0.0603416 | 0.00517425 | ||||||||
\(137\) | −18.5136 | −1.58172 | −0.790862 | − | 0.611995i | \(-0.790367\pi\) | ||||
−0.790862 | + | 0.611995i | \(0.790367\pi\) | |||||||
\(138\) | 2.93638 | 0.249961 | ||||||||
\(139\) | 5.05033 | 0.428364 | 0.214182 | − | 0.976794i | \(-0.431292\pi\) | ||||
0.214182 | + | 0.976794i | \(0.431292\pi\) | |||||||
\(140\) | −3.42808 | −0.289726 | ||||||||
\(141\) | 8.10252 | 0.682356 | ||||||||
\(142\) | −4.81511 | −0.404075 | ||||||||
\(143\) | 2.80696 | 0.234730 | ||||||||
\(144\) | −0.662042 | −0.0551702 | ||||||||
\(145\) | −36.9484 | −3.06840 | ||||||||
\(146\) | 2.23818 | 0.185233 | ||||||||
\(147\) | 9.44137 | 0.778711 | ||||||||
\(148\) | −6.02467 | −0.495225 | ||||||||
\(149\) | 5.04022 | 0.412911 | 0.206455 | − | 0.978456i | \(-0.433807\pi\) | ||||
0.206455 | + | 0.978456i | \(0.433807\pi\) | |||||||
\(150\) | −14.1277 | −1.15352 | ||||||||
\(151\) | 10.1333 | 0.824632 | 0.412316 | − | 0.911041i | \(-0.364720\pi\) | ||||
0.412316 | + | 0.911041i | \(0.364720\pi\) | |||||||
\(152\) | 4.24736 | 0.344506 | ||||||||
\(153\) | −0.0399486 | −0.00322966 | ||||||||
\(154\) | −1.99812 | −0.161013 | ||||||||
\(155\) | −27.4519 | −2.20499 | ||||||||
\(156\) | 1.95135 | 0.156233 | ||||||||
\(157\) | −0.534403 | −0.0426500 | −0.0213250 | − | 0.999773i | \(-0.506788\pi\) | ||||
−0.0213250 | + | 0.999773i | \(0.506788\pi\) | |||||||
\(158\) | 8.73390 | 0.694831 | ||||||||
\(159\) | 2.65321 | 0.210413 | ||||||||
\(160\) | −3.77354 | −0.298324 | ||||||||
\(161\) | −1.74460 | −0.137494 | ||||||||
\(162\) | −6.57558 | −0.516626 | ||||||||
\(163\) | −7.96805 | −0.624106 | −0.312053 | − | 0.950065i | \(-0.601017\pi\) | ||||
−0.312053 | + | 0.950065i | \(0.601017\pi\) | |||||||
\(164\) | −4.25253 | −0.332067 | ||||||||
\(165\) | −12.6907 | −0.987970 | ||||||||
\(166\) | 1.24574 | 0.0966882 | ||||||||
\(167\) | −12.9722 | −1.00382 | −0.501911 | − | 0.864919i | \(-0.667369\pi\) | ||||
−0.501911 | + | 0.864919i | \(0.667369\pi\) | |||||||
\(168\) | −1.38906 | −0.107168 | ||||||||
\(169\) | −11.3713 | −0.874717 | ||||||||
\(170\) | −0.227701 | −0.0174639 | ||||||||
\(171\) | −2.81193 | −0.215034 | ||||||||
\(172\) | 12.3544 | 0.942017 | ||||||||
\(173\) | 3.44804 | 0.262149 | 0.131075 | − | 0.991373i | \(-0.458157\pi\) | ||||
0.131075 | + | 0.991373i | \(0.458157\pi\) | |||||||
\(174\) | −14.9715 | −1.13499 | ||||||||
\(175\) | 8.39372 | 0.634506 | ||||||||
\(176\) | −2.19947 | −0.165792 | ||||||||
\(177\) | 8.56431 | 0.643733 | ||||||||
\(178\) | −3.82706 | −0.286850 | ||||||||
\(179\) | 23.3164 | 1.74275 | 0.871374 | − | 0.490619i | \(-0.163229\pi\) | ||||
0.871374 | + | 0.490619i | \(0.163229\pi\) | |||||||
\(180\) | 2.49824 | 0.186208 | ||||||||
\(181\) | 5.03003 | 0.373879 | 0.186940 | − | 0.982371i | \(-0.440143\pi\) | ||||
0.186940 | + | 0.982371i | \(0.440143\pi\) | |||||||
\(182\) | −1.15936 | −0.0859377 | ||||||||
\(183\) | 8.02308 | 0.593083 | ||||||||
\(184\) | −1.92041 | −0.141574 | ||||||||
\(185\) | 22.7343 | 1.67146 | ||||||||
\(186\) | −11.1235 | −0.815616 | ||||||||
\(187\) | −0.132720 | −0.00970543 | ||||||||
\(188\) | −5.29910 | −0.386476 | ||||||||
\(189\) | 5.08680 | 0.370010 | ||||||||
\(190\) | −16.0276 | −1.16276 | ||||||||
\(191\) | 11.7699 | 0.851640 | 0.425820 | − | 0.904808i | \(-0.359986\pi\) | ||||
0.425820 | + | 0.904808i | \(0.359986\pi\) | |||||||
\(192\) | −1.52904 | −0.110349 | ||||||||
\(193\) | −13.0136 | −0.936740 | −0.468370 | − | 0.883532i | \(-0.655159\pi\) | ||||
−0.468370 | + | 0.883532i | \(0.655159\pi\) | |||||||
\(194\) | 4.34112 | 0.311675 | ||||||||
\(195\) | −7.36349 | −0.527311 | ||||||||
\(196\) | −6.17471 | −0.441051 | ||||||||
\(197\) | 17.3836 | 1.23853 | 0.619263 | − | 0.785183i | \(-0.287431\pi\) | ||||
0.619263 | + | 0.785183i | \(0.287431\pi\) | |||||||
\(198\) | 1.45614 | 0.103484 | ||||||||
\(199\) | 17.6285 | 1.24965 | 0.624825 | − | 0.780765i | \(-0.285170\pi\) | ||||
0.624825 | + | 0.780765i | \(0.285170\pi\) | |||||||
\(200\) | 9.23957 | 0.653336 | ||||||||
\(201\) | 1.22830 | 0.0866379 | ||||||||
\(202\) | −10.2852 | −0.723664 | ||||||||
\(203\) | 8.89508 | 0.624312 | ||||||||
\(204\) | −0.0922646 | −0.00645981 | ||||||||
\(205\) | 16.0471 | 1.12078 | ||||||||
\(206\) | −6.32214 | −0.440484 | ||||||||
\(207\) | 1.27139 | 0.0883677 | ||||||||
\(208\) | −1.27619 | −0.0884882 | ||||||||
\(209\) | −9.34196 | −0.646197 | ||||||||
\(210\) | 5.24167 | 0.361709 | ||||||||
\(211\) | 9.47712 | 0.652432 | 0.326216 | − | 0.945295i | \(-0.394226\pi\) | ||||
0.326216 | + | 0.945295i | \(0.394226\pi\) | |||||||
\(212\) | −1.73521 | −0.119175 | ||||||||
\(213\) | 7.36248 | 0.504469 | ||||||||
\(214\) | −0.853040 | −0.0583126 | ||||||||
\(215\) | −46.6199 | −3.17945 | ||||||||
\(216\) | 5.59940 | 0.380991 | ||||||||
\(217\) | 6.60886 | 0.448638 | ||||||||
\(218\) | −5.91086 | −0.400334 | ||||||||
\(219\) | −3.42227 | −0.231255 | ||||||||
\(220\) | 8.29980 | 0.559572 | ||||||||
\(221\) | −0.0770076 | −0.00518009 | ||||||||
\(222\) | 9.21196 | 0.618266 | ||||||||
\(223\) | 25.6987 | 1.72091 | 0.860455 | − | 0.509527i | \(-0.170180\pi\) | ||||
0.860455 | + | 0.509527i | \(0.170180\pi\) | |||||||
\(224\) | 0.908453 | 0.0606986 | ||||||||
\(225\) | −6.11698 | −0.407799 | ||||||||
\(226\) | 7.51312 | 0.499765 | ||||||||
\(227\) | −22.5818 | −1.49881 | −0.749404 | − | 0.662113i | \(-0.769660\pi\) | ||||
−0.749404 | + | 0.662113i | \(0.769660\pi\) | |||||||
\(228\) | −6.49438 | −0.430101 | ||||||||
\(229\) | −3.19706 | −0.211268 | −0.105634 | − | 0.994405i | \(-0.533687\pi\) | ||||
−0.105634 | + | 0.994405i | \(0.533687\pi\) | |||||||
\(230\) | 7.24672 | 0.477835 | ||||||||
\(231\) | 3.05520 | 0.201018 | ||||||||
\(232\) | 9.79145 | 0.642840 | ||||||||
\(233\) | −9.21154 | −0.603468 | −0.301734 | − | 0.953392i | \(-0.597565\pi\) | ||||
−0.301734 | + | 0.953392i | \(0.597565\pi\) | |||||||
\(234\) | 0.844894 | 0.0552325 | ||||||||
\(235\) | 19.9963 | 1.30442 | ||||||||
\(236\) | −5.60111 | −0.364601 | ||||||||
\(237\) | −13.3545 | −0.867465 | ||||||||
\(238\) | 0.0548175 | 0.00355329 | ||||||||
\(239\) | −18.4190 | −1.19143 | −0.595714 | − | 0.803197i | \(-0.703131\pi\) | ||||
−0.595714 | + | 0.803197i | \(0.703131\pi\) | |||||||
\(240\) | 5.76988 | 0.372444 | ||||||||
\(241\) | −18.5921 | −1.19762 | −0.598810 | − | 0.800891i | \(-0.704360\pi\) | ||||
−0.598810 | + | 0.800891i | \(0.704360\pi\) | |||||||
\(242\) | −6.16231 | −0.396128 | ||||||||
\(243\) | −6.74390 | −0.432621 | ||||||||
\(244\) | −5.24714 | −0.335914 | ||||||||
\(245\) | 23.3005 | 1.48861 | ||||||||
\(246\) | 6.50228 | 0.414570 | ||||||||
\(247\) | −5.42046 | −0.344895 | ||||||||
\(248\) | 7.27484 | 0.461953 | ||||||||
\(249\) | −1.90478 | −0.120711 | ||||||||
\(250\) | −15.9982 | −1.01181 | ||||||||
\(251\) | 21.8270 | 1.37771 | 0.688853 | − | 0.724901i | \(-0.258114\pi\) | ||||
0.688853 | + | 0.724901i | \(0.258114\pi\) | |||||||
\(252\) | −0.601434 | −0.0378868 | ||||||||
\(253\) | 4.22389 | 0.265553 | ||||||||
\(254\) | −8.02104 | −0.503285 | ||||||||
\(255\) | 0.348164 | 0.0218029 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7083 | −1.41650 | −0.708251 | − | 0.705961i | \(-0.750515\pi\) | ||||
−0.708251 | + | 0.705961i | \(0.750515\pi\) | |||||||
\(258\) | −18.8904 | −1.17607 | ||||||||
\(259\) | −5.47314 | −0.340084 | ||||||||
\(260\) | 4.81577 | 0.298661 | ||||||||
\(261\) | −6.48235 | −0.401247 | ||||||||
\(262\) | −16.6949 | −1.03141 | ||||||||
\(263\) | −15.0907 | −0.930530 | −0.465265 | − | 0.885172i | \(-0.654041\pi\) | ||||
−0.465265 | + | 0.885172i | \(0.654041\pi\) | |||||||
\(264\) | 3.36308 | 0.206983 | ||||||||
\(265\) | 6.54789 | 0.402234 | ||||||||
\(266\) | 3.85853 | 0.236582 | ||||||||
\(267\) | 5.85172 | 0.358119 | ||||||||
\(268\) | −0.803318 | −0.0490705 | ||||||||
\(269\) | −5.69049 | −0.346955 | −0.173478 | − | 0.984838i | \(-0.555500\pi\) | ||||
−0.173478 | + | 0.984838i | \(0.555500\pi\) | |||||||
\(270\) | −21.1295 | −1.28590 | ||||||||
\(271\) | −22.5694 | −1.37099 | −0.685496 | − | 0.728076i | \(-0.740415\pi\) | ||||
−0.685496 | + | 0.728076i | \(0.740415\pi\) | |||||||
\(272\) | 0.0603416 | 0.00365875 | ||||||||
\(273\) | 1.77271 | 0.107289 | ||||||||
\(274\) | −18.5136 | −1.11845 | ||||||||
\(275\) | −20.3222 | −1.22547 | ||||||||
\(276\) | 2.93638 | 0.176749 | ||||||||
\(277\) | −10.7753 | −0.647422 | −0.323711 | − | 0.946156i | \(-0.604931\pi\) | ||||
−0.323711 | + | 0.946156i | \(0.604931\pi\) | |||||||
\(278\) | 5.05033 | 0.302899 | ||||||||
\(279\) | −4.81625 | −0.288341 | ||||||||
\(280\) | −3.42808 | −0.204867 | ||||||||
\(281\) | 4.44325 | 0.265062 | 0.132531 | − | 0.991179i | \(-0.457690\pi\) | ||||
0.132531 | + | 0.991179i | \(0.457690\pi\) | |||||||
\(282\) | 8.10252 | 0.482498 | ||||||||
\(283\) | −17.7140 | −1.05299 | −0.526494 | − | 0.850179i | \(-0.676494\pi\) | ||||
−0.526494 | + | 0.850179i | \(0.676494\pi\) | |||||||
\(284\) | −4.81511 | −0.285724 | ||||||||
\(285\) | 24.5068 | 1.45166 | ||||||||
\(286\) | 2.80696 | 0.165979 | ||||||||
\(287\) | −3.86322 | −0.228039 | ||||||||
\(288\) | −0.662042 | −0.0390112 | ||||||||
\(289\) | −16.9964 | −0.999786 | ||||||||
\(290\) | −36.9484 | −2.16968 | ||||||||
\(291\) | −6.63775 | −0.389112 | ||||||||
\(292\) | 2.23818 | 0.130980 | ||||||||
\(293\) | −16.7408 | −0.978010 | −0.489005 | − | 0.872281i | \(-0.662640\pi\) | ||||
−0.489005 | + | 0.872281i | \(0.662640\pi\) | |||||||
\(294\) | 9.44137 | 0.550632 | ||||||||
\(295\) | 21.1360 | 1.23058 | ||||||||
\(296\) | −6.02467 | −0.350177 | ||||||||
\(297\) | −12.3157 | −0.714632 | ||||||||
\(298\) | 5.04022 | 0.291972 | ||||||||
\(299\) | 2.45081 | 0.141734 | ||||||||
\(300\) | −14.1277 | −0.815661 | ||||||||
\(301\) | 11.2234 | 0.646908 | ||||||||
\(302\) | 10.1333 | 0.583103 | ||||||||
\(303\) | 15.7265 | 0.903462 | ||||||||
\(304\) | 4.24736 | 0.243603 | ||||||||
\(305\) | 19.8003 | 1.13376 | ||||||||
\(306\) | −0.0399486 | −0.00228371 | ||||||||
\(307\) | 8.62774 | 0.492411 | 0.246206 | − | 0.969218i | \(-0.420816\pi\) | ||||
0.246206 | + | 0.969218i | \(0.420816\pi\) | |||||||
\(308\) | −1.99812 | −0.113853 | ||||||||
\(309\) | 9.66679 | 0.549924 | ||||||||
\(310\) | −27.4519 | −1.55916 | ||||||||
\(311\) | −7.71915 | −0.437713 | −0.218856 | − | 0.975757i | \(-0.570233\pi\) | ||||
−0.218856 | + | 0.975757i | \(0.570233\pi\) | |||||||
\(312\) | 1.95135 | 0.110473 | ||||||||
\(313\) | 15.5017 | 0.876206 | 0.438103 | − | 0.898925i | \(-0.355651\pi\) | ||||
0.438103 | + | 0.898925i | \(0.355651\pi\) | |||||||
\(314\) | −0.534403 | −0.0301581 | ||||||||
\(315\) | 2.26953 | 0.127874 | ||||||||
\(316\) | 8.73390 | 0.491320 | ||||||||
\(317\) | 18.5157 | 1.03995 | 0.519974 | − | 0.854182i | \(-0.325942\pi\) | ||||
0.519974 | + | 0.854182i | \(0.325942\pi\) | |||||||
\(318\) | 2.65321 | 0.148784 | ||||||||
\(319\) | −21.5361 | −1.20579 | ||||||||
\(320\) | −3.77354 | −0.210947 | ||||||||
\(321\) | 1.30433 | 0.0728006 | ||||||||
\(322\) | −1.74460 | −0.0972227 | ||||||||
\(323\) | 0.256292 | 0.0142605 | ||||||||
\(324\) | −6.57558 | −0.365310 | ||||||||
\(325\) | −11.7915 | −0.654074 | ||||||||
\(326\) | −7.96805 | −0.441309 | ||||||||
\(327\) | 9.03794 | 0.499799 | ||||||||
\(328\) | −4.25253 | −0.234807 | ||||||||
\(329\) | −4.81398 | −0.265403 | ||||||||
\(330\) | −12.6907 | −0.698600 | ||||||||
\(331\) | 12.0588 | 0.662809 | 0.331405 | − | 0.943489i | \(-0.392478\pi\) | ||||
0.331405 | + | 0.943489i | \(0.392478\pi\) | |||||||
\(332\) | 1.24574 | 0.0683689 | ||||||||
\(333\) | 3.98859 | 0.218573 | ||||||||
\(334\) | −12.9722 | −0.709809 | ||||||||
\(335\) | 3.03135 | 0.165620 | ||||||||
\(336\) | −1.38906 | −0.0757794 | ||||||||
\(337\) | 0.332736 | 0.0181253 | 0.00906265 | − | 0.999959i | \(-0.497115\pi\) | ||||
0.00906265 | + | 0.999959i | \(0.497115\pi\) | |||||||
\(338\) | −11.3713 | −0.618519 | ||||||||
\(339\) | −11.4878 | −0.623934 | ||||||||
\(340\) | −0.227701 | −0.0123488 | ||||||||
\(341\) | −16.0008 | −0.866494 | ||||||||
\(342\) | −2.81193 | −0.152052 | ||||||||
\(343\) | −11.9686 | −0.646244 | ||||||||
\(344\) | 12.3544 | 0.666107 | ||||||||
\(345\) | −11.0805 | −0.596555 | ||||||||
\(346\) | 3.44804 | 0.185368 | ||||||||
\(347\) | −7.20839 | −0.386967 | −0.193483 | − | 0.981104i | \(-0.561979\pi\) | ||||
−0.193483 | + | 0.981104i | \(0.561979\pi\) | |||||||
\(348\) | −14.9715 | −0.802557 | ||||||||
\(349\) | 18.5322 | 0.992007 | 0.496003 | − | 0.868321i | \(-0.334800\pi\) | ||||
0.496003 | + | 0.868321i | \(0.334800\pi\) | |||||||
\(350\) | 8.39372 | 0.448663 | ||||||||
\(351\) | −7.14593 | −0.381421 | ||||||||
\(352\) | −2.19947 | −0.117232 | ||||||||
\(353\) | −1.12923 | −0.0601030 | −0.0300515 | − | 0.999548i | \(-0.509567\pi\) | ||||
−0.0300515 | + | 0.999548i | \(0.509567\pi\) | |||||||
\(354\) | 8.56431 | 0.455188 | ||||||||
\(355\) | 18.1700 | 0.964362 | ||||||||
\(356\) | −3.82706 | −0.202834 | ||||||||
\(357\) | −0.0838181 | −0.00443612 | ||||||||
\(358\) | 23.3164 | 1.23231 | ||||||||
\(359\) | −8.06913 | −0.425872 | −0.212936 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212936 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(360\) | 2.49824 | 0.131669 | ||||||||
\(361\) | −0.959936 | −0.0505230 | ||||||||
\(362\) | 5.03003 | 0.264372 | ||||||||
\(363\) | 9.42241 | 0.494548 | ||||||||
\(364\) | −1.15936 | −0.0607671 | ||||||||
\(365\) | −8.44586 | −0.442077 | ||||||||
\(366\) | 8.02308 | 0.419373 | ||||||||
\(367\) | −25.6227 | −1.33750 | −0.668748 | − | 0.743489i | \(-0.733170\pi\) | ||||
−0.668748 | + | 0.743489i | \(0.733170\pi\) | |||||||
\(368\) | −1.92041 | −0.100108 | ||||||||
\(369\) | 2.81535 | 0.146561 | ||||||||
\(370\) | 22.7343 | 1.18190 | ||||||||
\(371\) | −1.57636 | −0.0818405 | ||||||||
\(372\) | −11.1235 | −0.576727 | ||||||||
\(373\) | −23.6666 | −1.22541 | −0.612706 | − | 0.790311i | \(-0.709919\pi\) | ||||
−0.612706 | + | 0.790311i | \(0.709919\pi\) | |||||||
\(374\) | −0.132720 | −0.00686278 | ||||||||
\(375\) | 24.4618 | 1.26320 | ||||||||
\(376\) | −5.29910 | −0.273280 | ||||||||
\(377\) | −12.4958 | −0.643566 | ||||||||
\(378\) | 5.08680 | 0.261637 | ||||||||
\(379\) | 16.3583 | 0.840268 | 0.420134 | − | 0.907462i | \(-0.361983\pi\) | ||||
0.420134 | + | 0.907462i | \(0.361983\pi\) | |||||||
\(380\) | −16.0276 | −0.822197 | ||||||||
\(381\) | 12.2645 | 0.628328 | ||||||||
\(382\) | 11.7699 | 0.602200 | ||||||||
\(383\) | 10.7888 | 0.551281 | 0.275640 | − | 0.961261i | \(-0.411110\pi\) | ||||
0.275640 | + | 0.961261i | \(0.411110\pi\) | |||||||
\(384\) | −1.52904 | −0.0780284 | ||||||||
\(385\) | 7.53998 | 0.384273 | ||||||||
\(386\) | −13.0136 | −0.662375 | ||||||||
\(387\) | −8.17915 | −0.415770 | ||||||||
\(388\) | 4.34112 | 0.220387 | ||||||||
\(389\) | −7.82434 | −0.396710 | −0.198355 | − | 0.980130i | \(-0.563560\pi\) | ||||
−0.198355 | + | 0.980130i | \(0.563560\pi\) | |||||||
\(390\) | −7.36349 | −0.372865 | ||||||||
\(391\) | −0.115880 | −0.00586032 | ||||||||
\(392\) | −6.17471 | −0.311870 | ||||||||
\(393\) | 25.5272 | 1.28767 | ||||||||
\(394\) | 17.3836 | 0.875771 | ||||||||
\(395\) | −32.9577 | −1.65828 | ||||||||
\(396\) | 1.45614 | 0.0731740 | ||||||||
\(397\) | 1.81287 | 0.0909856 | 0.0454928 | − | 0.998965i | \(-0.485514\pi\) | ||||
0.0454928 | + | 0.998965i | \(0.485514\pi\) | |||||||
\(398\) | 17.6285 | 0.883636 | ||||||||
\(399\) | −5.89984 | −0.295361 | ||||||||
\(400\) | 9.23957 | 0.461979 | ||||||||
\(401\) | 6.36350 | 0.317778 | 0.158889 | − | 0.987296i | \(-0.449209\pi\) | ||||
0.158889 | + | 0.987296i | \(0.449209\pi\) | |||||||
\(402\) | 1.22830 | 0.0612623 | ||||||||
\(403\) | −9.28412 | −0.462475 | ||||||||
\(404\) | −10.2852 | −0.511708 | ||||||||
\(405\) | 24.8132 | 1.23298 | ||||||||
\(406\) | 8.89508 | 0.441455 | ||||||||
\(407\) | 13.2511 | 0.656834 | ||||||||
\(408\) | −0.0922646 | −0.00456778 | ||||||||
\(409\) | 18.0756 | 0.893778 | 0.446889 | − | 0.894589i | \(-0.352532\pi\) | ||||
0.446889 | + | 0.894589i | \(0.352532\pi\) | |||||||
\(410\) | 16.0471 | 0.792508 | ||||||||
\(411\) | 28.3080 | 1.39633 | ||||||||
\(412\) | −6.32214 | −0.311469 | ||||||||
\(413\) | −5.08835 | −0.250381 | ||||||||
\(414\) | 1.27139 | 0.0624854 | ||||||||
\(415\) | −4.70084 | −0.230755 | ||||||||
\(416\) | −1.27619 | −0.0625706 | ||||||||
\(417\) | −7.72215 | −0.378155 | ||||||||
\(418\) | −9.34196 | −0.456930 | ||||||||
\(419\) | −18.7947 | −0.918183 | −0.459092 | − | 0.888389i | \(-0.651825\pi\) | ||||
−0.459092 | + | 0.888389i | \(0.651825\pi\) | |||||||
\(420\) | 5.24167 | 0.255767 | ||||||||
\(421\) | −22.2817 | −1.08594 | −0.542971 | − | 0.839751i | \(-0.682701\pi\) | ||||
−0.542971 | + | 0.839751i | \(0.682701\pi\) | |||||||
\(422\) | 9.47712 | 0.461339 | ||||||||
\(423\) | 3.50822 | 0.170576 | ||||||||
\(424\) | −1.73521 | −0.0842694 | ||||||||
\(425\) | 0.557530 | 0.0270442 | ||||||||
\(426\) | 7.36248 | 0.356713 | ||||||||
\(427\) | −4.76678 | −0.230681 | ||||||||
\(428\) | −0.853040 | −0.0412332 | ||||||||
\(429\) | −4.29195 | −0.207217 | ||||||||
\(430\) | −46.6199 | −2.24821 | ||||||||
\(431\) | 28.3379 | 1.36499 | 0.682495 | − | 0.730890i | \(-0.260895\pi\) | ||||
0.682495 | + | 0.730890i | \(0.260895\pi\) | |||||||
\(432\) | 5.59940 | 0.269401 | ||||||||
\(433\) | −30.3557 | −1.45880 | −0.729401 | − | 0.684087i | \(-0.760201\pi\) | ||||
−0.729401 | + | 0.684087i | \(0.760201\pi\) | |||||||
\(434\) | 6.60886 | 0.317235 | ||||||||
\(435\) | 56.4955 | 2.70875 | ||||||||
\(436\) | −5.91086 | −0.283079 | ||||||||
\(437\) | −8.15666 | −0.390186 | ||||||||
\(438\) | −3.42227 | −0.163522 | ||||||||
\(439\) | −21.7396 | −1.03757 | −0.518787 | − | 0.854904i | \(-0.673616\pi\) | ||||
−0.518787 | + | 0.854904i | \(0.673616\pi\) | |||||||
\(440\) | 8.29980 | 0.395677 | ||||||||
\(441\) | 4.08792 | 0.194663 | ||||||||
\(442\) | −0.0770076 | −0.00366288 | ||||||||
\(443\) | −6.34107 | −0.301273 | −0.150637 | − | 0.988589i | \(-0.548132\pi\) | ||||
−0.150637 | + | 0.988589i | \(0.548132\pi\) | |||||||
\(444\) | 9.21196 | 0.437180 | ||||||||
\(445\) | 14.4415 | 0.684595 | ||||||||
\(446\) | 25.6987 | 1.21687 | ||||||||
\(447\) | −7.70669 | −0.364514 | ||||||||
\(448\) | 0.908453 | 0.0429204 | ||||||||
\(449\) | −17.0265 | −0.803531 | −0.401765 | − | 0.915743i | \(-0.631603\pi\) | ||||
−0.401765 | + | 0.915743i | \(0.631603\pi\) | |||||||
\(450\) | −6.11698 | −0.288357 | ||||||||
\(451\) | 9.35333 | 0.440431 | ||||||||
\(452\) | 7.51312 | 0.353387 | ||||||||
\(453\) | −15.4941 | −0.727978 | ||||||||
\(454\) | −22.5818 | −1.05982 | ||||||||
\(455\) | 4.37490 | 0.205098 | ||||||||
\(456\) | −6.49438 | −0.304127 | ||||||||
\(457\) | 21.1408 | 0.988923 | 0.494462 | − | 0.869199i | \(-0.335365\pi\) | ||||
0.494462 | + | 0.869199i | \(0.335365\pi\) | |||||||
\(458\) | −3.19706 | −0.149389 | ||||||||
\(459\) | 0.337877 | 0.0157707 | ||||||||
\(460\) | 7.24672 | 0.337880 | ||||||||
\(461\) | 39.8194 | 1.85457 | 0.927287 | − | 0.374351i | \(-0.122135\pi\) | ||||
0.927287 | + | 0.374351i | \(0.122135\pi\) | |||||||
\(462\) | 3.05520 | 0.142141 | ||||||||
\(463\) | −18.1193 | −0.842077 | −0.421038 | − | 0.907043i | \(-0.638334\pi\) | ||||
−0.421038 | + | 0.907043i | \(0.638334\pi\) | |||||||
\(464\) | 9.79145 | 0.454557 | ||||||||
\(465\) | 41.9750 | 1.94654 | ||||||||
\(466\) | −9.21154 | −0.426716 | ||||||||
\(467\) | 14.9161 | 0.690237 | 0.345118 | − | 0.938559i | \(-0.387839\pi\) | ||||
0.345118 | + | 0.938559i | \(0.387839\pi\) | |||||||
\(468\) | 0.844894 | 0.0390552 | ||||||||
\(469\) | −0.729777 | −0.0336980 | ||||||||
\(470\) | 19.9963 | 0.922362 | ||||||||
\(471\) | 0.817122 | 0.0376510 | ||||||||
\(472\) | −5.60111 | −0.257812 | ||||||||
\(473\) | −27.1733 | −1.24943 | ||||||||
\(474\) | −13.3545 | −0.613391 | ||||||||
\(475\) | 39.2438 | 1.80063 | ||||||||
\(476\) | 0.0548175 | 0.00251256 | ||||||||
\(477\) | 1.14878 | 0.0525992 | ||||||||
\(478\) | −18.4190 | −0.842467 | ||||||||
\(479\) | 9.18330 | 0.419596 | 0.209798 | − | 0.977745i | \(-0.432719\pi\) | ||||
0.209798 | + | 0.977745i | \(0.432719\pi\) | |||||||
\(480\) | 5.76988 | 0.263358 | ||||||||
\(481\) | 7.68866 | 0.350573 | ||||||||
\(482\) | −18.5921 | −0.846845 | ||||||||
\(483\) | 2.66756 | 0.121378 | ||||||||
\(484\) | −6.16231 | −0.280105 | ||||||||
\(485\) | −16.3814 | −0.743841 | ||||||||
\(486\) | −6.74390 | −0.305910 | ||||||||
\(487\) | 24.2431 | 1.09856 | 0.549280 | − | 0.835638i | \(-0.314902\pi\) | ||||
0.549280 | + | 0.835638i | \(0.314902\pi\) | |||||||
\(488\) | −5.24714 | −0.237527 | ||||||||
\(489\) | 12.1835 | 0.550955 | ||||||||
\(490\) | 23.3005 | 1.05261 | ||||||||
\(491\) | −16.3967 | −0.739971 | −0.369985 | − | 0.929038i | \(-0.620637\pi\) | ||||
−0.369985 | + | 0.929038i | \(0.620637\pi\) | |||||||
\(492\) | 6.50228 | 0.293145 | ||||||||
\(493\) | 0.590832 | 0.0266097 | ||||||||
\(494\) | −5.42046 | −0.243878 | ||||||||
\(495\) | −5.49481 | −0.246973 | ||||||||
\(496\) | 7.27484 | 0.326650 | ||||||||
\(497\) | −4.37430 | −0.196214 | ||||||||
\(498\) | −1.90478 | −0.0853554 | ||||||||
\(499\) | −2.03407 | −0.0910576 | −0.0455288 | − | 0.998963i | \(-0.514497\pi\) | ||||
−0.0455288 | + | 0.998963i | \(0.514497\pi\) | |||||||
\(500\) | −15.9982 | −0.715460 | ||||||||
\(501\) | 19.8350 | 0.886164 | ||||||||
\(502\) | 21.8270 | 0.974186 | ||||||||
\(503\) | −5.30342 | −0.236468 | −0.118234 | − | 0.992986i | \(-0.537723\pi\) | ||||
−0.118234 | + | 0.992986i | \(0.537723\pi\) | |||||||
\(504\) | −0.601434 | −0.0267900 | ||||||||
\(505\) | 38.8116 | 1.72709 | ||||||||
\(506\) | 4.22389 | 0.187775 | ||||||||
\(507\) | 17.3872 | 0.772192 | ||||||||
\(508\) | −8.02104 | −0.355876 | ||||||||
\(509\) | −22.5760 | −1.00066 | −0.500331 | − | 0.865834i | \(-0.666788\pi\) | ||||
−0.500331 | + | 0.865834i | \(0.666788\pi\) | |||||||
\(510\) | 0.348164 | 0.0154169 | ||||||||
\(511\) | 2.03328 | 0.0899472 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 23.7827 | 1.05003 | ||||||||
\(514\) | −22.7083 | −1.00162 | ||||||||
\(515\) | 23.8568 | 1.05126 | ||||||||
\(516\) | −18.8904 | −0.831604 | ||||||||
\(517\) | 11.6552 | 0.512596 | ||||||||
\(518\) | −5.47314 | −0.240476 | ||||||||
\(519\) | −5.27218 | −0.231423 | ||||||||
\(520\) | 4.81577 | 0.211185 | ||||||||
\(521\) | −26.6847 | −1.16908 | −0.584540 | − | 0.811365i | \(-0.698725\pi\) | ||||
−0.584540 | + | 0.811365i | \(0.698725\pi\) | |||||||
\(522\) | −6.48235 | −0.283725 | ||||||||
\(523\) | −35.3765 | −1.54691 | −0.773454 | − | 0.633853i | \(-0.781472\pi\) | ||||
−0.773454 | + | 0.633853i | \(0.781472\pi\) | |||||||
\(524\) | −16.6949 | −0.729320 | ||||||||
\(525\) | −12.8343 | −0.560136 | ||||||||
\(526\) | −15.0907 | −0.657984 | ||||||||
\(527\) | 0.438976 | 0.0191221 | ||||||||
\(528\) | 3.36308 | 0.146359 | ||||||||
\(529\) | −19.3120 | −0.839654 | ||||||||
\(530\) | 6.54789 | 0.284422 | ||||||||
\(531\) | 3.70817 | 0.160921 | ||||||||
\(532\) | 3.85853 | 0.167288 | ||||||||
\(533\) | 5.42705 | 0.235072 | ||||||||
\(534\) | 5.85172 | 0.253229 | ||||||||
\(535\) | 3.21898 | 0.139168 | ||||||||
\(536\) | −0.803318 | −0.0346981 | ||||||||
\(537\) | −35.6516 | −1.53848 | ||||||||
\(538\) | −5.69049 | −0.245334 | ||||||||
\(539\) | 13.5811 | 0.584980 | ||||||||
\(540\) | −21.1295 | −0.909271 | ||||||||
\(541\) | −36.1096 | −1.55247 | −0.776237 | − | 0.630441i | \(-0.782874\pi\) | ||||
−0.776237 | + | 0.630441i | \(0.782874\pi\) | |||||||
\(542\) | −22.5694 | −0.969438 | ||||||||
\(543\) | −7.69111 | −0.330057 | ||||||||
\(544\) | 0.0603416 | 0.00258712 | ||||||||
\(545\) | 22.3049 | 0.955435 | ||||||||
\(546\) | 1.77271 | 0.0758650 | ||||||||
\(547\) | 12.6531 | 0.541007 | 0.270503 | − | 0.962719i | \(-0.412810\pi\) | ||||
0.270503 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(548\) | −18.5136 | −0.790862 | ||||||||
\(549\) | 3.47383 | 0.148259 | ||||||||
\(550\) | −20.3222 | −0.866542 | ||||||||
\(551\) | 41.5878 | 1.77170 | ||||||||
\(552\) | 2.93638 | 0.124980 | ||||||||
\(553\) | 7.93434 | 0.337402 | ||||||||
\(554\) | −10.7753 | −0.457797 | ||||||||
\(555\) | −34.7617 | −1.47555 | ||||||||
\(556\) | 5.05033 | 0.214182 | ||||||||
\(557\) | 21.4239 | 0.907761 | 0.453881 | − | 0.891063i | \(-0.350039\pi\) | ||||
0.453881 | + | 0.891063i | \(0.350039\pi\) | |||||||
\(558\) | −4.81625 | −0.203888 | ||||||||
\(559\) | −15.7667 | −0.666859 | ||||||||
\(560\) | −3.42808 | −0.144863 | ||||||||
\(561\) | 0.202934 | 0.00856786 | ||||||||
\(562\) | 4.44325 | 0.187427 | ||||||||
\(563\) | −37.7516 | −1.59104 | −0.795519 | − | 0.605928i | \(-0.792802\pi\) | ||||
−0.795519 | + | 0.605928i | \(0.792802\pi\) | |||||||
\(564\) | 8.10252 | 0.341178 | ||||||||
\(565\) | −28.3510 | −1.19274 | ||||||||
\(566\) | −17.7140 | −0.744574 | ||||||||
\(567\) | −5.97360 | −0.250868 | ||||||||
\(568\) | −4.81511 | −0.202037 | ||||||||
\(569\) | −5.82436 | −0.244170 | −0.122085 | − | 0.992520i | \(-0.538958\pi\) | ||||
−0.122085 | + | 0.992520i | \(0.538958\pi\) | |||||||
\(570\) | 24.5068 | 1.02648 | ||||||||
\(571\) | 13.9771 | 0.584921 | 0.292461 | − | 0.956278i | \(-0.405526\pi\) | ||||
0.292461 | + | 0.956278i | \(0.405526\pi\) | |||||||
\(572\) | 2.80696 | 0.117365 | ||||||||
\(573\) | −17.9966 | −0.751820 | ||||||||
\(574\) | −3.86322 | −0.161248 | ||||||||
\(575\) | −17.7437 | −0.739965 | ||||||||
\(576\) | −0.662042 | −0.0275851 | ||||||||
\(577\) | −24.8095 | −1.03283 | −0.516416 | − | 0.856338i | \(-0.672734\pi\) | ||||
−0.516416 | + | 0.856338i | \(0.672734\pi\) | |||||||
\(578\) | −16.9964 | −0.706955 | ||||||||
\(579\) | 19.8983 | 0.826946 | ||||||||
\(580\) | −36.9484 | −1.53420 | ||||||||
\(581\) | 1.13170 | 0.0469507 | ||||||||
\(582\) | −6.63775 | −0.275143 | ||||||||
\(583\) | 3.81656 | 0.158066 | ||||||||
\(584\) | 2.23818 | 0.0926166 | ||||||||
\(585\) | −3.18824 | −0.131817 | ||||||||
\(586\) | −16.7408 | −0.691558 | ||||||||
\(587\) | 26.6909 | 1.10165 | 0.550825 | − | 0.834621i | \(-0.314313\pi\) | ||||
0.550825 | + | 0.834621i | \(0.314313\pi\) | |||||||
\(588\) | 9.44137 | 0.389356 | ||||||||
\(589\) | 30.8989 | 1.27317 | ||||||||
\(590\) | 21.1360 | 0.870155 | ||||||||
\(591\) | −26.5801 | −1.09336 | ||||||||
\(592\) | −6.02467 | −0.247613 | ||||||||
\(593\) | 13.3126 | 0.546684 | 0.273342 | − | 0.961917i | \(-0.411871\pi\) | ||||
0.273342 | + | 0.961917i | \(0.411871\pi\) | |||||||
\(594\) | −12.3157 | −0.505321 | ||||||||
\(595\) | −0.206856 | −0.00848026 | ||||||||
\(596\) | 5.04022 | 0.206455 | ||||||||
\(597\) | −26.9546 | −1.10318 | ||||||||
\(598\) | 2.45081 | 0.100221 | ||||||||
\(599\) | 20.3987 | 0.833470 | 0.416735 | − | 0.909028i | \(-0.363174\pi\) | ||||
0.416735 | + | 0.909028i | \(0.363174\pi\) | |||||||
\(600\) | −14.1277 | −0.576759 | ||||||||
\(601\) | −31.4856 | −1.28432 | −0.642162 | − | 0.766569i | \(-0.721963\pi\) | ||||
−0.642162 | + | 0.766569i | \(0.721963\pi\) | |||||||
\(602\) | 11.2234 | 0.457433 | ||||||||
\(603\) | 0.531830 | 0.0216578 | ||||||||
\(604\) | 10.1333 | 0.412316 | ||||||||
\(605\) | 23.2537 | 0.945397 | ||||||||
\(606\) | 15.7265 | 0.638844 | ||||||||
\(607\) | 10.4307 | 0.423370 | 0.211685 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211685 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(608\) | 4.24736 | 0.172253 | ||||||||
\(609\) | −13.6009 | −0.551137 | ||||||||
\(610\) | 19.8003 | 0.801690 | ||||||||
\(611\) | 6.76268 | 0.273589 | ||||||||
\(612\) | −0.0399486 | −0.00161483 | ||||||||
\(613\) | 24.2024 | 0.977527 | 0.488764 | − | 0.872416i | \(-0.337448\pi\) | ||||
0.488764 | + | 0.872416i | \(0.337448\pi\) | |||||||
\(614\) | 8.62774 | 0.348187 | ||||||||
\(615\) | −24.5366 | −0.989411 | ||||||||
\(616\) | −1.99812 | −0.0805065 | ||||||||
\(617\) | −21.4118 | −0.862008 | −0.431004 | − | 0.902350i | \(-0.641841\pi\) | ||||
−0.431004 | + | 0.902350i | \(0.641841\pi\) | |||||||
\(618\) | 9.66679 | 0.388855 | ||||||||
\(619\) | −12.1478 | −0.488261 | −0.244131 | − | 0.969742i | \(-0.578503\pi\) | ||||
−0.244131 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(620\) | −27.4519 | −1.10249 | ||||||||
\(621\) | −10.7531 | −0.431508 | ||||||||
\(622\) | −7.71915 | −0.309510 | ||||||||
\(623\) | −3.47670 | −0.139291 | ||||||||
\(624\) | 1.95135 | 0.0781165 | ||||||||
\(625\) | 14.1718 | 0.566873 | ||||||||
\(626\) | 15.5017 | 0.619571 | ||||||||
\(627\) | 14.2842 | 0.570457 | ||||||||
\(628\) | −0.534403 | −0.0213250 | ||||||||
\(629\) | −0.363538 | −0.0144952 | ||||||||
\(630\) | 2.26953 | 0.0904204 | ||||||||
\(631\) | 12.7341 | 0.506937 | 0.253469 | − | 0.967344i | \(-0.418429\pi\) | ||||
0.253469 | + | 0.967344i | \(0.418429\pi\) | |||||||
\(632\) | 8.73390 | 0.347416 | ||||||||
\(633\) | −14.4909 | −0.575961 | ||||||||
\(634\) | 18.5157 | 0.735354 | ||||||||
\(635\) | 30.2677 | 1.20114 | ||||||||
\(636\) | 2.65321 | 0.105207 | ||||||||
\(637\) | 7.88014 | 0.312222 | ||||||||
\(638\) | −21.5361 | −0.852620 | ||||||||
\(639\) | 3.18780 | 0.126107 | ||||||||
\(640\) | −3.77354 | −0.149162 | ||||||||
\(641\) | 11.7600 | 0.464494 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(642\) | 1.30433 | 0.0514778 | ||||||||
\(643\) | −10.5960 | −0.417866 | −0.208933 | − | 0.977930i | \(-0.566999\pi\) | ||||
−0.208933 | + | 0.977930i | \(0.566999\pi\) | |||||||
\(644\) | −1.74460 | −0.0687469 | ||||||||
\(645\) | 71.2836 | 2.80679 | ||||||||
\(646\) | 0.256292 | 0.0100837 | ||||||||
\(647\) | −49.6333 | −1.95129 | −0.975643 | − | 0.219366i | \(-0.929601\pi\) | ||||
−0.975643 | + | 0.219366i | \(0.929601\pi\) | |||||||
\(648\) | −6.57558 | −0.258313 | ||||||||
\(649\) | 12.3195 | 0.483582 | ||||||||
\(650\) | −11.7915 | −0.462500 | ||||||||
\(651\) | −10.1052 | −0.396054 | ||||||||
\(652\) | −7.96805 | −0.312053 | ||||||||
\(653\) | 19.2194 | 0.752112 | 0.376056 | − | 0.926597i | \(-0.377280\pi\) | ||||
0.376056 | + | 0.926597i | \(0.377280\pi\) | |||||||
\(654\) | 9.03794 | 0.353411 | ||||||||
\(655\) | 62.9988 | 2.46157 | ||||||||
\(656\) | −4.25253 | −0.166033 | ||||||||
\(657\) | −1.48177 | −0.0578094 | ||||||||
\(658\) | −4.81398 | −0.187669 | ||||||||
\(659\) | −43.4523 | −1.69266 | −0.846331 | − | 0.532657i | \(-0.821193\pi\) | ||||
−0.846331 | + | 0.532657i | \(0.821193\pi\) | |||||||
\(660\) | −12.6907 | −0.493985 | ||||||||
\(661\) | −34.7821 | −1.35287 | −0.676434 | − | 0.736503i | \(-0.736476\pi\) | ||||
−0.676434 | + | 0.736503i | \(0.736476\pi\) | |||||||
\(662\) | 12.0588 | 0.468677 | ||||||||
\(663\) | 0.117748 | 0.00457294 | ||||||||
\(664\) | 1.24574 | 0.0483441 | ||||||||
\(665\) | −14.5603 | −0.564624 | ||||||||
\(666\) | 3.98859 | 0.154555 | ||||||||
\(667\) | −18.8036 | −0.728077 | ||||||||
\(668\) | −12.9722 | −0.501911 | ||||||||
\(669\) | −39.2942 | −1.51920 | ||||||||
\(670\) | 3.03135 | 0.117111 | ||||||||
\(671\) | 11.5410 | 0.445534 | ||||||||
\(672\) | −1.38906 | −0.0535841 | ||||||||
\(673\) | 45.6657 | 1.76028 | 0.880141 | − | 0.474712i | \(-0.157448\pi\) | ||||
0.880141 | + | 0.474712i | \(0.157448\pi\) | |||||||
\(674\) | 0.332736 | 0.0128165 | ||||||||
\(675\) | 51.7361 | 1.99132 | ||||||||
\(676\) | −11.3713 | −0.437359 | ||||||||
\(677\) | −0.957601 | −0.0368036 | −0.0184018 | − | 0.999831i | \(-0.505858\pi\) | ||||
−0.0184018 | + | 0.999831i | \(0.505858\pi\) | |||||||
\(678\) | −11.4878 | −0.441188 | ||||||||
\(679\) | 3.94371 | 0.151346 | ||||||||
\(680\) | −0.227701 | −0.00873194 | ||||||||
\(681\) | 34.5285 | 1.32313 | ||||||||
\(682\) | −16.0008 | −0.612704 | ||||||||
\(683\) | 15.8152 | 0.605152 | 0.302576 | − | 0.953125i | \(-0.402153\pi\) | ||||
0.302576 | + | 0.953125i | \(0.402153\pi\) | |||||||
\(684\) | −2.81193 | −0.107517 | ||||||||
\(685\) | 69.8617 | 2.66928 | ||||||||
\(686\) | −11.9686 | −0.456964 | ||||||||
\(687\) | 4.88843 | 0.186505 | ||||||||
\(688\) | 12.3544 | 0.471009 | ||||||||
\(689\) | 2.21447 | 0.0843646 | ||||||||
\(690\) | −11.0805 | −0.421828 | ||||||||
\(691\) | 41.4021 | 1.57501 | 0.787504 | − | 0.616309i | \(-0.211373\pi\) | ||||
0.787504 | + | 0.616309i | \(0.211373\pi\) | |||||||
\(692\) | 3.44804 | 0.131075 | ||||||||
\(693\) | 1.32284 | 0.0502505 | ||||||||
\(694\) | −7.20839 | −0.273627 | ||||||||
\(695\) | −19.0576 | −0.722896 | ||||||||
\(696\) | −14.9715 | −0.567494 | ||||||||
\(697\) | −0.256604 | −0.00971958 | ||||||||
\(698\) | 18.5322 | 0.701455 | ||||||||
\(699\) | 14.0848 | 0.532736 | ||||||||
\(700\) | 8.39372 | 0.317253 | ||||||||
\(701\) | −35.0104 | −1.32233 | −0.661163 | − | 0.750243i | \(-0.729937\pi\) | ||||
−0.661163 | + | 0.750243i | \(0.729937\pi\) | |||||||
\(702\) | −7.14593 | −0.269706 | ||||||||
\(703\) | −25.5890 | −0.965106 | ||||||||
\(704\) | −2.19947 | −0.0828958 | ||||||||
\(705\) | −30.5752 | −1.15153 | ||||||||
\(706\) | −1.12923 | −0.0424992 | ||||||||
\(707\) | −9.34363 | −0.351403 | ||||||||
\(708\) | 8.56431 | 0.321866 | ||||||||
\(709\) | 17.9260 | 0.673224 | 0.336612 | − | 0.941643i | \(-0.390719\pi\) | ||||
0.336612 | + | 0.941643i | \(0.390719\pi\) | |||||||
\(710\) | 18.1700 | 0.681907 | ||||||||
\(711\) | −5.78220 | −0.216850 | ||||||||
\(712\) | −3.82706 | −0.143425 | ||||||||
\(713\) | −13.9707 | −0.523205 | ||||||||
\(714\) | −0.0838181 | −0.00313681 | ||||||||
\(715\) | −10.5922 | −0.396124 | ||||||||
\(716\) | 23.3164 | 0.871374 | ||||||||
\(717\) | 28.1634 | 1.05178 | ||||||||
\(718\) | −8.06913 | −0.301137 | ||||||||
\(719\) | −35.1556 | −1.31108 | −0.655541 | − | 0.755160i | \(-0.727559\pi\) | ||||
−0.655541 | + | 0.755160i | \(0.727559\pi\) | |||||||
\(720\) | 2.49824 | 0.0931038 | ||||||||
\(721\) | −5.74337 | −0.213894 | ||||||||
\(722\) | −0.959936 | −0.0357251 | ||||||||
\(723\) | 28.4280 | 1.05725 | ||||||||
\(724\) | 5.03003 | 0.186940 | ||||||||
\(725\) | 90.4688 | 3.35993 | ||||||||
\(726\) | 9.42241 | 0.349698 | ||||||||
\(727\) | −17.9918 | −0.667279 | −0.333639 | − | 0.942701i | \(-0.608277\pi\) | ||||
−0.333639 | + | 0.942701i | \(0.608277\pi\) | |||||||
\(728\) | −1.15936 | −0.0429689 | ||||||||
\(729\) | 30.0384 | 1.11253 | ||||||||
\(730\) | −8.44586 | −0.312595 | ||||||||
\(731\) | 0.745486 | 0.0275728 | ||||||||
\(732\) | 8.02308 | 0.296542 | ||||||||
\(733\) | 12.1596 | 0.449125 | 0.224563 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224563 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(734\) | −25.6227 | −0.945753 | ||||||||
\(735\) | −35.6274 | −1.31413 | ||||||||
\(736\) | −1.92041 | −0.0707871 | ||||||||
\(737\) | 1.76688 | 0.0650838 | ||||||||
\(738\) | 2.81535 | 0.103635 | ||||||||
\(739\) | 32.1446 | 1.18246 | 0.591229 | − | 0.806504i | \(-0.298643\pi\) | ||||
0.591229 | + | 0.806504i | \(0.298643\pi\) | |||||||
\(740\) | 22.7343 | 0.835730 | ||||||||
\(741\) | 8.28809 | 0.304471 | ||||||||
\(742\) | −1.57636 | −0.0578700 | ||||||||
\(743\) | −46.8272 | −1.71792 | −0.858961 | − | 0.512041i | \(-0.828889\pi\) | ||||
−0.858961 | + | 0.512041i | \(0.828889\pi\) | |||||||
\(744\) | −11.1235 | −0.407808 | ||||||||
\(745\) | −19.0194 | −0.696819 | ||||||||
\(746\) | −23.6666 | −0.866497 | ||||||||
\(747\) | −0.824732 | −0.0301754 | ||||||||
\(748\) | −0.132720 | −0.00485272 | ||||||||
\(749\) | −0.774947 | −0.0283159 | ||||||||
\(750\) | 24.4618 | 0.893219 | ||||||||
\(751\) | 27.2361 | 0.993859 | 0.496929 | − | 0.867791i | \(-0.334461\pi\) | ||||
0.496929 | + | 0.867791i | \(0.334461\pi\) | |||||||
\(752\) | −5.29910 | −0.193238 | ||||||||
\(753\) | −33.3743 | −1.21623 | ||||||||
\(754\) | −12.4958 | −0.455070 | ||||||||
\(755\) | −38.2382 | −1.39163 | ||||||||
\(756\) | 5.08680 | 0.185005 | ||||||||
\(757\) | 45.1707 | 1.64176 | 0.820878 | − | 0.571104i | \(-0.193485\pi\) | ||||
0.820878 | + | 0.571104i | \(0.193485\pi\) | |||||||
\(758\) | 16.3583 | 0.594159 | ||||||||
\(759\) | −6.45848 | −0.234428 | ||||||||
\(760\) | −16.0276 | −0.581381 | ||||||||
\(761\) | 11.5698 | 0.419406 | 0.209703 | − | 0.977765i | \(-0.432750\pi\) | ||||
0.209703 | + | 0.977765i | \(0.432750\pi\) | |||||||
\(762\) | 12.2645 | 0.444295 | ||||||||
\(763\) | −5.36974 | −0.194398 | ||||||||
\(764\) | 11.7699 | 0.425820 | ||||||||
\(765\) | 0.150748 | 0.00545029 | ||||||||
\(766\) | 10.7888 | 0.389814 | ||||||||
\(767\) | 7.14810 | 0.258103 | ||||||||
\(768\) | −1.52904 | −0.0551744 | ||||||||
\(769\) | −0.637726 | −0.0229970 | −0.0114985 | − | 0.999934i | \(-0.503660\pi\) | ||||
−0.0114985 | + | 0.999934i | \(0.503660\pi\) | |||||||
\(770\) | 7.53998 | 0.271722 | ||||||||
\(771\) | 34.7218 | 1.25047 | ||||||||
\(772\) | −13.0136 | −0.468370 | ||||||||
\(773\) | −32.1925 | −1.15788 | −0.578942 | − | 0.815369i | \(-0.696534\pi\) | ||||
−0.578942 | + | 0.815369i | \(0.696534\pi\) | |||||||
\(774\) | −8.17915 | −0.293994 | ||||||||
\(775\) | 67.2164 | 2.41449 | ||||||||
\(776\) | 4.34112 | 0.155837 | ||||||||
\(777\) | 8.36863 | 0.300223 | ||||||||
\(778\) | −7.82434 | −0.280516 | ||||||||
\(779\) | −18.0620 | −0.647139 | ||||||||
\(780\) | −7.36349 | −0.263655 | ||||||||
\(781\) | 10.5907 | 0.378965 | ||||||||
\(782\) | −0.115880 | −0.00414387 | ||||||||
\(783\) | 54.8263 | 1.95933 | ||||||||
\(784\) | −6.17471 | −0.220525 | ||||||||
\(785\) | 2.01659 | 0.0719751 | ||||||||
\(786\) | 25.5272 | 0.910523 | ||||||||
\(787\) | −10.8708 | −0.387504 | −0.193752 | − | 0.981051i | \(-0.562066\pi\) | ||||
−0.193752 | + | 0.981051i | \(0.562066\pi\) | |||||||
\(788\) | 17.3836 | 0.619263 | ||||||||
\(789\) | 23.0742 | 0.821463 | ||||||||
\(790\) | −32.9577 | −1.17258 | ||||||||
\(791\) | 6.82532 | 0.242680 | ||||||||
\(792\) | 1.45614 | 0.0517418 | ||||||||
\(793\) | 6.69637 | 0.237795 | ||||||||
\(794\) | 1.81287 | 0.0643365 | ||||||||
\(795\) | −10.0120 | −0.355088 | ||||||||
\(796\) | 17.6285 | 0.624825 | ||||||||
\(797\) | 16.5443 | 0.586028 | 0.293014 | − | 0.956108i | \(-0.405342\pi\) | ||||
0.293014 | + | 0.956108i | \(0.405342\pi\) | |||||||
\(798\) | −5.89984 | −0.208852 | ||||||||
\(799\) | −0.319756 | −0.0113122 | ||||||||
\(800\) | 9.23957 | 0.326668 | ||||||||
\(801\) | 2.53367 | 0.0895229 | ||||||||
\(802\) | 6.36350 | 0.224703 | ||||||||
\(803\) | −4.92283 | −0.173723 | ||||||||
\(804\) | 1.22830 | 0.0433190 | ||||||||
\(805\) | 6.58331 | 0.232031 | ||||||||
\(806\) | −9.28412 | −0.327019 | ||||||||
\(807\) | 8.70098 | 0.306289 | ||||||||
\(808\) | −10.2852 | −0.361832 | ||||||||
\(809\) | 34.8306 | 1.22458 | 0.612290 | − | 0.790633i | \(-0.290249\pi\) | ||||
0.612290 | + | 0.790633i | \(0.290249\pi\) | |||||||
\(810\) | 24.8132 | 0.871846 | ||||||||
\(811\) | −30.3987 | −1.06744 | −0.533721 | − | 0.845661i | \(-0.679207\pi\) | ||||
−0.533721 | + | 0.845661i | \(0.679207\pi\) | |||||||
\(812\) | 8.89508 | 0.312156 | ||||||||
\(813\) | 34.5094 | 1.21030 | ||||||||
\(814\) | 13.2511 | 0.464451 | ||||||||
\(815\) | 30.0677 | 1.05323 | ||||||||
\(816\) | −0.0922646 | −0.00322991 | ||||||||
\(817\) | 52.4737 | 1.83582 | ||||||||
\(818\) | 18.0756 | 0.631997 | ||||||||
\(819\) | 0.767547 | 0.0268203 | ||||||||
\(820\) | 16.0471 | 0.560388 | ||||||||
\(821\) | 35.3608 | 1.23410 | 0.617050 | − | 0.786924i | \(-0.288328\pi\) | ||||
0.617050 | + | 0.786924i | \(0.288328\pi\) | |||||||
\(822\) | 28.3080 | 0.987355 | ||||||||
\(823\) | 10.0750 | 0.351192 | 0.175596 | − | 0.984462i | \(-0.443815\pi\) | ||||
0.175596 | + | 0.984462i | \(0.443815\pi\) | |||||||
\(824\) | −6.32214 | −0.220242 | ||||||||
\(825\) | 31.0734 | 1.08184 | ||||||||
\(826\) | −5.08835 | −0.177046 | ||||||||
\(827\) | −4.31639 | −0.150096 | −0.0750479 | − | 0.997180i | \(-0.523911\pi\) | ||||
−0.0750479 | + | 0.997180i | \(0.523911\pi\) | |||||||
\(828\) | 1.27139 | 0.0441838 | ||||||||
\(829\) | −21.1360 | −0.734083 | −0.367041 | − | 0.930205i | \(-0.619629\pi\) | ||||
−0.367041 | + | 0.930205i | \(0.619629\pi\) | |||||||
\(830\) | −4.70084 | −0.163169 | ||||||||
\(831\) | 16.4758 | 0.571538 | ||||||||
\(832\) | −1.27619 | −0.0442441 | ||||||||
\(833\) | −0.372592 | −0.0129095 | ||||||||
\(834\) | −7.72215 | −0.267396 | ||||||||
\(835\) | 48.9512 | 1.69403 | ||||||||
\(836\) | −9.34196 | −0.323098 | ||||||||
\(837\) | 40.7348 | 1.40800 | ||||||||
\(838\) | −18.7947 | −0.649254 | ||||||||
\(839\) | −29.2828 | −1.01096 | −0.505478 | − | 0.862840i | \(-0.668684\pi\) | ||||
−0.505478 | + | 0.862840i | \(0.668684\pi\) | |||||||
\(840\) | 5.24167 | 0.180855 | ||||||||
\(841\) | 66.8726 | 2.30595 | ||||||||
\(842\) | −22.2817 | −0.767877 | ||||||||
\(843\) | −6.79391 | −0.233995 | ||||||||
\(844\) | 9.47712 | 0.326216 | ||||||||
\(845\) | 42.9101 | 1.47615 | ||||||||
\(846\) | 3.50822 | 0.120615 | ||||||||
\(847\) | −5.59817 | −0.192355 | ||||||||
\(848\) | −1.73521 | −0.0595875 | ||||||||
\(849\) | 27.0854 | 0.929567 | ||||||||
\(850\) | 0.557530 | 0.0191231 | ||||||||
\(851\) | 11.5698 | 0.396608 | ||||||||
\(852\) | 7.36248 | 0.252234 | ||||||||
\(853\) | 24.6755 | 0.844874 | 0.422437 | − | 0.906392i | \(-0.361175\pi\) | ||||
0.422437 | + | 0.906392i | \(0.361175\pi\) | |||||||
\(854\) | −4.76678 | −0.163116 | ||||||||
\(855\) | 10.6109 | 0.362886 | ||||||||
\(856\) | −0.853040 | −0.0291563 | ||||||||
\(857\) | 38.6637 | 1.32073 | 0.660364 | − | 0.750946i | \(-0.270402\pi\) | ||||
0.660364 | + | 0.750946i | \(0.270402\pi\) | |||||||
\(858\) | −4.29195 | −0.146525 | ||||||||
\(859\) | 13.7469 | 0.469040 | 0.234520 | − | 0.972111i | \(-0.424648\pi\) | ||||
0.234520 | + | 0.972111i | \(0.424648\pi\) | |||||||
\(860\) | −46.6199 | −1.58973 | ||||||||
\(861\) | 5.90702 | 0.201311 | ||||||||
\(862\) | 28.3379 | 0.965194 | ||||||||
\(863\) | −13.2484 | −0.450982 | −0.225491 | − | 0.974245i | \(-0.572399\pi\) | ||||
−0.225491 | + | 0.974245i | \(0.572399\pi\) | |||||||
\(864\) | 5.59940 | 0.190496 | ||||||||
\(865\) | −13.0113 | −0.442397 | ||||||||
\(866\) | −30.3557 | −1.03153 | ||||||||
\(867\) | 25.9881 | 0.882602 | ||||||||
\(868\) | 6.60886 | 0.224319 | ||||||||
\(869\) | −19.2100 | −0.651654 | ||||||||
\(870\) | 56.4955 | 1.91538 | ||||||||
\(871\) | 1.02519 | 0.0347373 | ||||||||
\(872\) | −5.91086 | −0.200167 | ||||||||
\(873\) | −2.87401 | −0.0972704 | ||||||||
\(874\) | −8.15666 | −0.275903 | ||||||||
\(875\) | −14.5336 | −0.491325 | ||||||||
\(876\) | −3.42227 | −0.115628 | ||||||||
\(877\) | 43.6137 | 1.47273 | 0.736366 | − | 0.676584i | \(-0.236540\pi\) | ||||
0.736366 | + | 0.676584i | \(0.236540\pi\) | |||||||
\(878\) | −21.7396 | −0.733675 | ||||||||
\(879\) | 25.5974 | 0.863378 | ||||||||
\(880\) | 8.29980 | 0.279786 | ||||||||
\(881\) | 37.7943 | 1.27332 | 0.636660 | − | 0.771144i | \(-0.280315\pi\) | ||||
0.636660 | + | 0.771144i | \(0.280315\pi\) | |||||||
\(882\) | 4.08792 | 0.137647 | ||||||||
\(883\) | −32.2356 | −1.08481 | −0.542407 | − | 0.840116i | \(-0.682487\pi\) | ||||
−0.542407 | + | 0.840116i | \(0.682487\pi\) | |||||||
\(884\) | −0.0770076 | −0.00259005 | ||||||||
\(885\) | −32.3177 | −1.08635 | ||||||||
\(886\) | −6.34107 | −0.213032 | ||||||||
\(887\) | 18.9140 | 0.635069 | 0.317535 | − | 0.948247i | \(-0.397145\pi\) | ||||
0.317535 | + | 0.948247i | \(0.397145\pi\) | |||||||
\(888\) | 9.21196 | 0.309133 | ||||||||
\(889\) | −7.28674 | −0.244390 | ||||||||
\(890\) | 14.4415 | 0.484081 | ||||||||
\(891\) | 14.4628 | 0.484522 | ||||||||
\(892\) | 25.6987 | 0.860455 | ||||||||
\(893\) | −22.5072 | −0.753174 | ||||||||
\(894\) | −7.70669 | −0.257750 | ||||||||
\(895\) | −87.9852 | −2.94102 | ||||||||
\(896\) | 0.908453 | 0.0303493 | ||||||||
\(897\) | −3.74739 | −0.125122 | ||||||||
\(898\) | −17.0265 | −0.568182 | ||||||||
\(899\) | 71.2313 | 2.37570 | ||||||||
\(900\) | −6.11698 | −0.203899 | ||||||||
\(901\) | −0.104705 | −0.00348825 | ||||||||
\(902\) | 9.35333 | 0.311432 | ||||||||
\(903\) | −17.1611 | −0.571084 | ||||||||
\(904\) | 7.51312 | 0.249883 | ||||||||
\(905\) | −18.9810 | −0.630950 | ||||||||
\(906\) | −15.4941 | −0.514758 | ||||||||
\(907\) | −10.2967 | −0.341896 | −0.170948 | − | 0.985280i | \(-0.554683\pi\) | ||||
−0.170948 | + | 0.985280i | \(0.554683\pi\) | |||||||
\(908\) | −22.5818 | −0.749404 | ||||||||
\(909\) | 6.80923 | 0.225848 | ||||||||
\(910\) | 4.37490 | 0.145026 | ||||||||
\(911\) | 10.3128 | 0.341678 | 0.170839 | − | 0.985299i | \(-0.445352\pi\) | ||||
0.170839 | + | 0.985299i | \(0.445352\pi\) | |||||||
\(912\) | −6.49438 | −0.215050 | ||||||||
\(913\) | −2.73997 | −0.0906799 | ||||||||
\(914\) | 21.1408 | 0.699274 | ||||||||
\(915\) | −30.2754 | −1.00087 | ||||||||
\(916\) | −3.19706 | −0.105634 | ||||||||
\(917\) | −15.1665 | −0.500843 | ||||||||
\(918\) | 0.337877 | 0.0111516 | ||||||||
\(919\) | 22.7858 | 0.751635 | 0.375817 | − | 0.926694i | \(-0.377362\pi\) | ||||
0.375817 | + | 0.926694i | \(0.377362\pi\) | |||||||
\(920\) | 7.24672 | 0.238917 | ||||||||
\(921\) | −13.1921 | −0.434696 | ||||||||
\(922\) | 39.8194 | 1.31138 | ||||||||
\(923\) | 6.14501 | 0.202266 | ||||||||
\(924\) | 3.05520 | 0.100509 | ||||||||
\(925\) | −55.6654 | −1.83027 | ||||||||
\(926\) | −18.1193 | −0.595438 | ||||||||
\(927\) | 4.18552 | 0.137470 | ||||||||
\(928\) | 9.79145 | 0.321420 | ||||||||
\(929\) | 9.89839 | 0.324756 | 0.162378 | − | 0.986729i | \(-0.448084\pi\) | ||||
0.162378 | + | 0.986729i | \(0.448084\pi\) | |||||||
\(930\) | 41.9750 | 1.37641 | ||||||||
\(931\) | −26.2262 | −0.859530 | ||||||||
\(932\) | −9.21154 | −0.301734 | ||||||||
\(933\) | 11.8029 | 0.386409 | ||||||||
\(934\) | 14.9161 | 0.488071 | ||||||||
\(935\) | 0.500823 | 0.0163787 | ||||||||
\(936\) | 0.844894 | 0.0276162 | ||||||||
\(937\) | −43.5402 | −1.42240 | −0.711199 | − | 0.702991i | \(-0.751847\pi\) | ||||
−0.711199 | + | 0.702991i | \(0.751847\pi\) | |||||||
\(938\) | −0.729777 | −0.0238281 | ||||||||
\(939\) | −23.7026 | −0.773506 | ||||||||
\(940\) | 19.9963 | 0.652209 | ||||||||
\(941\) | 51.7914 | 1.68835 | 0.844176 | − | 0.536067i | \(-0.180090\pi\) | ||||
0.844176 | + | 0.536067i | \(0.180090\pi\) | |||||||
\(942\) | 0.817122 | 0.0266233 | ||||||||
\(943\) | 8.16658 | 0.265941 | ||||||||
\(944\) | −5.60111 | −0.182301 | ||||||||
\(945\) | −19.1952 | −0.624420 | ||||||||
\(946\) | −27.1733 | −0.883479 | ||||||||
\(947\) | 12.0036 | 0.390064 | 0.195032 | − | 0.980797i | \(-0.437519\pi\) | ||||
0.195032 | + | 0.980797i | \(0.437519\pi\) | |||||||
\(948\) | −13.3545 | −0.433733 | ||||||||
\(949\) | −2.85636 | −0.0927213 | ||||||||
\(950\) | 39.2438 | 1.27324 | ||||||||
\(951\) | −28.3113 | −0.918056 | ||||||||
\(952\) | 0.0548175 | 0.00177665 | ||||||||
\(953\) | −11.5510 | −0.374173 | −0.187086 | − | 0.982343i | \(-0.559904\pi\) | ||||
−0.187086 | + | 0.982343i | \(0.559904\pi\) | |||||||
\(954\) | 1.14878 | 0.0371932 | ||||||||
\(955\) | −44.4141 | −1.43721 | ||||||||
\(956\) | −18.4190 | −0.595714 | ||||||||
\(957\) | 32.9294 | 1.06446 | ||||||||
\(958\) | 9.18330 | 0.296699 | ||||||||
\(959\) | −16.8187 | −0.543105 | ||||||||
\(960\) | 5.76988 | 0.186222 | ||||||||
\(961\) | 21.9234 | 0.707205 | ||||||||
\(962\) | 7.68866 | 0.247892 | ||||||||
\(963\) | 0.564748 | 0.0181988 | ||||||||
\(964\) | −18.5921 | −0.598810 | ||||||||
\(965\) | 49.1073 | 1.58082 | ||||||||
\(966\) | 2.66756 | 0.0858273 | ||||||||
\(967\) | −14.4846 | −0.465793 | −0.232896 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232896 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(968\) | −6.16231 | −0.198064 | ||||||||
\(969\) | −0.391881 | −0.0125890 | ||||||||
\(970\) | −16.3814 | −0.525975 | ||||||||
\(971\) | −43.2229 | −1.38709 | −0.693545 | − | 0.720413i | \(-0.743952\pi\) | ||||
−0.693545 | + | 0.720413i | \(0.743952\pi\) | |||||||
\(972\) | −6.74390 | −0.216311 | ||||||||
\(973\) | 4.58799 | 0.147084 | ||||||||
\(974\) | 24.2431 | 0.776800 | ||||||||
\(975\) | 18.0296 | 0.577411 | ||||||||
\(976\) | −5.24714 | −0.167957 | ||||||||
\(977\) | 4.26551 | 0.136466 | 0.0682328 | − | 0.997669i | \(-0.478264\pi\) | ||||
0.0682328 | + | 0.997669i | \(0.478264\pi\) | |||||||
\(978\) | 12.1835 | 0.389584 | ||||||||
\(979\) | 8.41752 | 0.269025 | ||||||||
\(980\) | 23.3005 | 0.744307 | ||||||||
\(981\) | 3.91324 | 0.124940 | ||||||||
\(982\) | −16.3967 | −0.523238 | ||||||||
\(983\) | 12.5647 | 0.400752 | 0.200376 | − | 0.979719i | \(-0.435784\pi\) | ||||
0.200376 | + | 0.979719i | \(0.435784\pi\) | |||||||
\(984\) | 6.50228 | 0.207285 | ||||||||
\(985\) | −65.5975 | −2.09011 | ||||||||
\(986\) | 0.590832 | 0.0188159 | ||||||||
\(987\) | 7.36076 | 0.234296 | ||||||||
\(988\) | −5.42046 | −0.172448 | ||||||||
\(989\) | −23.7255 | −0.754428 | ||||||||
\(990\) | −5.49481 | −0.174637 | ||||||||
\(991\) | −29.5747 | −0.939471 | −0.469735 | − | 0.882807i | \(-0.655651\pi\) | ||||
−0.469735 | + | 0.882807i | \(0.655651\pi\) | |||||||
\(992\) | 7.27484 | 0.230977 | ||||||||
\(993\) | −18.4383 | −0.585122 | ||||||||
\(994\) | −4.37430 | −0.138744 | ||||||||
\(995\) | −66.5217 | −2.10888 | ||||||||
\(996\) | −1.90478 | −0.0603554 | ||||||||
\(997\) | 13.6944 | 0.433705 | 0.216852 | − | 0.976204i | \(-0.430421\pi\) | ||||
0.216852 | + | 0.976204i | \(0.430421\pi\) | |||||||
\(998\) | −2.03407 | −0.0643875 | ||||||||
\(999\) | −33.7346 | −1.06731 |
(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 | 6022.2.a.b.1.19 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.b.1.19 | ✓ | 54 | 1.1 | even | 1 | trivial |