Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13972 | −0.805906 | −0.402953 | − | 0.915221i | \(-0.632016\pi\) | ||||
−0.402953 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(3\) | 3.40925 | 1.96833 | 0.984165 | − | 0.177255i | \(-0.0567219\pi\) | ||||
0.984165 | + | 0.177255i | \(0.0567219\pi\) | |||||||
\(4\) | −0.701031 | −0.350516 | ||||||||
\(5\) | −0.104086 | −0.0465485 | −0.0232742 | − | 0.999729i | \(-0.507409\pi\) | ||||
−0.0232742 | + | 0.999729i | \(0.507409\pi\) | |||||||
\(6\) | −3.88560 | −1.58629 | ||||||||
\(7\) | 1.00506 | 0.379878 | 0.189939 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189939 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(8\) | 3.07843 | 1.08839 | ||||||||
\(9\) | 8.62297 | 2.87432 | ||||||||
\(10\) | 0.118629 | 0.0375137 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.38999 | −0.689930 | ||||||||
\(13\) | 1.47074 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(14\) | −1.14549 | −0.306146 | ||||||||
\(15\) | −0.354854 | −0.0916228 | ||||||||
\(16\) | −2.10649 | −0.526623 | ||||||||
\(17\) | −0.523035 | −0.126855 | −0.0634273 | − | 0.997986i | \(-0.520203\pi\) | ||||
−0.0634273 | + | 0.997986i | \(0.520203\pi\) | |||||||
\(18\) | −9.82779 | −2.31643 | ||||||||
\(19\) | 4.88589 | 1.12090 | 0.560450 | − | 0.828188i | \(-0.310628\pi\) | ||||
0.560450 | + | 0.828188i | \(0.310628\pi\) | |||||||
\(20\) | 0.0729673 | 0.0163160 | ||||||||
\(21\) | 3.42651 | 0.747725 | ||||||||
\(22\) | −1.13972 | −0.242990 | ||||||||
\(23\) | −3.18640 | −0.664409 | −0.332205 | − | 0.943207i | \(-0.607792\pi\) | ||||
−0.332205 | + | 0.943207i | \(0.607792\pi\) | |||||||
\(24\) | 10.4951 | 2.14231 | ||||||||
\(25\) | −4.98917 | −0.997833 | ||||||||
\(26\) | −1.67623 | −0.328736 | ||||||||
\(27\) | 19.1701 | 3.68928 | ||||||||
\(28\) | −0.704580 | −0.133153 | ||||||||
\(29\) | 4.16319 | 0.773084 | 0.386542 | − | 0.922272i | \(-0.373669\pi\) | ||||
0.386542 | + | 0.922272i | \(0.373669\pi\) | |||||||
\(30\) | 0.404435 | 0.0738393 | ||||||||
\(31\) | −7.69918 | −1.38281 | −0.691407 | − | 0.722466i | \(-0.743009\pi\) | ||||
−0.691407 | + | 0.722466i | \(0.743009\pi\) | |||||||
\(32\) | −3.75604 | −0.663980 | ||||||||
\(33\) | 3.40925 | 0.593474 | ||||||||
\(34\) | 0.596115 | 0.102233 | ||||||||
\(35\) | −0.104612 | −0.0176827 | ||||||||
\(36\) | −6.04497 | −1.00749 | ||||||||
\(37\) | 4.51585 | 0.742402 | 0.371201 | − | 0.928553i | \(-0.378946\pi\) | ||||
0.371201 | + | 0.928553i | \(0.378946\pi\) | |||||||
\(38\) | −5.56856 | −0.903340 | ||||||||
\(39\) | 5.01410 | 0.802899 | ||||||||
\(40\) | −0.320420 | −0.0506628 | ||||||||
\(41\) | −4.28457 | −0.669137 | −0.334569 | − | 0.942371i | \(-0.608591\pi\) | ||||
−0.334569 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(42\) | −3.90527 | −0.602596 | ||||||||
\(43\) | −7.09033 | −1.08127 | −0.540633 | − | 0.841259i | \(-0.681815\pi\) | ||||
−0.540633 | + | 0.841259i | \(0.681815\pi\) | |||||||
\(44\) | −0.701031 | −0.105684 | ||||||||
\(45\) | −0.897527 | −0.133795 | ||||||||
\(46\) | 3.63161 | 0.535451 | ||||||||
\(47\) | 7.07039 | 1.03132 | 0.515662 | − | 0.856792i | \(-0.327546\pi\) | ||||
0.515662 | + | 0.856792i | \(0.327546\pi\) | |||||||
\(48\) | −7.18155 | −1.03657 | ||||||||
\(49\) | −5.98985 | −0.855693 | ||||||||
\(50\) | 5.68627 | 0.804160 | ||||||||
\(51\) | −1.78315 | −0.249692 | ||||||||
\(52\) | −1.03103 | −0.142978 | ||||||||
\(53\) | −4.44226 | −0.610191 | −0.305095 | − | 0.952322i | \(-0.598688\pi\) | ||||
−0.305095 | + | 0.952322i | \(0.598688\pi\) | |||||||
\(54\) | −21.8486 | −2.97322 | ||||||||
\(55\) | −0.104086 | −0.0140349 | ||||||||
\(56\) | 3.09401 | 0.413455 | ||||||||
\(57\) | 16.6572 | 2.20630 | ||||||||
\(58\) | −4.74488 | −0.623033 | ||||||||
\(59\) | 3.97795 | 0.517885 | 0.258943 | − | 0.965893i | \(-0.416626\pi\) | ||||
0.258943 | + | 0.965893i | \(0.416626\pi\) | |||||||
\(60\) | 0.248763 | 0.0321152 | ||||||||
\(61\) | 14.0507 | 1.79900 | 0.899502 | − | 0.436916i | \(-0.143929\pi\) | ||||
0.899502 | + | 0.436916i | \(0.143929\pi\) | |||||||
\(62\) | 8.77494 | 1.11442 | ||||||||
\(63\) | 8.66662 | 1.09189 | ||||||||
\(64\) | 8.49383 | 1.06173 | ||||||||
\(65\) | −0.153082 | −0.0189875 | ||||||||
\(66\) | −3.88560 | −0.478284 | ||||||||
\(67\) | −12.2458 | −1.49607 | −0.748033 | − | 0.663662i | \(-0.769002\pi\) | ||||
−0.748033 | + | 0.663662i | \(0.769002\pi\) | |||||||
\(68\) | 0.366664 | 0.0444645 | ||||||||
\(69\) | −10.8632 | −1.30778 | ||||||||
\(70\) | 0.119229 | 0.0142506 | ||||||||
\(71\) | 11.2219 | 1.33180 | 0.665898 | − | 0.746043i | \(-0.268049\pi\) | ||||
0.665898 | + | 0.746043i | \(0.268049\pi\) | |||||||
\(72\) | 26.5452 | 3.12838 | ||||||||
\(73\) | 7.92036 | 0.927008 | 0.463504 | − | 0.886095i | \(-0.346592\pi\) | ||||
0.463504 | + | 0.886095i | \(0.346592\pi\) | |||||||
\(74\) | −5.14682 | −0.598306 | ||||||||
\(75\) | −17.0093 | −1.96406 | ||||||||
\(76\) | −3.42516 | −0.392893 | ||||||||
\(77\) | 1.00506 | 0.114537 | ||||||||
\(78\) | −5.71469 | −0.647061 | ||||||||
\(79\) | 12.9966 | 1.46223 | 0.731117 | − | 0.682252i | \(-0.238999\pi\) | ||||
0.731117 | + | 0.682252i | \(0.238999\pi\) | |||||||
\(80\) | 0.219256 | 0.0245135 | ||||||||
\(81\) | 39.4866 | 4.38740 | ||||||||
\(82\) | 4.88322 | 0.539262 | ||||||||
\(83\) | 1.05831 | 0.116164 | 0.0580822 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580822 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(84\) | −2.40209 | −0.262089 | ||||||||
\(85\) | 0.0544404 | 0.00590489 | ||||||||
\(86\) | 8.08101 | 0.871398 | ||||||||
\(87\) | 14.1933 | 1.52168 | ||||||||
\(88\) | 3.07843 | 0.328161 | ||||||||
\(89\) | −9.63567 | −1.02138 | −0.510690 | − | 0.859765i | \(-0.670610\pi\) | ||||
−0.510690 | + | 0.859765i | \(0.670610\pi\) | |||||||
\(90\) | 1.02293 | 0.107826 | ||||||||
\(91\) | 1.47818 | 0.154955 | ||||||||
\(92\) | 2.23376 | 0.232886 | ||||||||
\(93\) | −26.2484 | −2.72183 | ||||||||
\(94\) | −8.05829 | −0.831149 | ||||||||
\(95\) | −0.508551 | −0.0521762 | ||||||||
\(96\) | −12.8053 | −1.30693 | ||||||||
\(97\) | −3.03765 | −0.308426 | −0.154213 | − | 0.988038i | \(-0.549284\pi\) | ||||
−0.154213 | + | 0.988038i | \(0.549284\pi\) | |||||||
\(98\) | 6.82677 | 0.689608 | ||||||||
\(99\) | 8.62297 | 0.866641 | ||||||||
\(100\) | 3.49756 | 0.349756 | ||||||||
\(101\) | 12.8550 | 1.27912 | 0.639560 | − | 0.768742i | \(-0.279117\pi\) | ||||
0.639560 | + | 0.768742i | \(0.279117\pi\) | |||||||
\(102\) | 2.03230 | 0.201228 | ||||||||
\(103\) | −1.44393 | −0.142275 | −0.0711376 | − | 0.997467i | \(-0.522663\pi\) | ||||
−0.0711376 | + | 0.997467i | \(0.522663\pi\) | |||||||
\(104\) | 4.52755 | 0.443963 | ||||||||
\(105\) | −0.356650 | −0.0348055 | ||||||||
\(106\) | 5.06294 | 0.491757 | ||||||||
\(107\) | −1.13652 | −0.109872 | −0.0549359 | − | 0.998490i | \(-0.517495\pi\) | ||||
−0.0549359 | + | 0.998490i | \(0.517495\pi\) | |||||||
\(108\) | −13.4388 | −1.29315 | ||||||||
\(109\) | −11.3071 | −1.08302 | −0.541510 | − | 0.840695i | \(-0.682147\pi\) | ||||
−0.541510 | + | 0.840695i | \(0.682147\pi\) | |||||||
\(110\) | 0.118629 | 0.0113108 | ||||||||
\(111\) | 15.3957 | 1.46129 | ||||||||
\(112\) | −2.11716 | −0.200052 | ||||||||
\(113\) | −12.7882 | −1.20301 | −0.601507 | − | 0.798868i | \(-0.705433\pi\) | ||||
−0.601507 | + | 0.798868i | \(0.705433\pi\) | |||||||
\(114\) | −18.9846 | −1.77807 | ||||||||
\(115\) | 0.331658 | 0.0309273 | ||||||||
\(116\) | −2.91852 | −0.270978 | ||||||||
\(117\) | 12.6821 | 1.17246 | ||||||||
\(118\) | −4.53377 | −0.417367 | ||||||||
\(119\) | −0.525682 | −0.0481892 | ||||||||
\(120\) | −1.09239 | −0.0997212 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −16.0139 | −1.44983 | ||||||||
\(123\) | −14.6072 | −1.31708 | ||||||||
\(124\) | 5.39737 | 0.484698 | ||||||||
\(125\) | 1.03973 | 0.0929961 | ||||||||
\(126\) | −9.87754 | −0.879961 | ||||||||
\(127\) | −8.52712 | −0.756659 | −0.378330 | − | 0.925671i | \(-0.623501\pi\) | ||||
−0.378330 | + | 0.925671i | \(0.623501\pi\) | |||||||
\(128\) | −2.16854 | −0.191673 | ||||||||
\(129\) | −24.1727 | −2.12829 | ||||||||
\(130\) | 0.174472 | 0.0153022 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −2.38999 | −0.208022 | ||||||||
\(133\) | 4.91062 | 0.425805 | ||||||||
\(134\) | 13.9569 | 1.20569 | ||||||||
\(135\) | −1.99533 | −0.171731 | ||||||||
\(136\) | −1.61012 | −0.138067 | ||||||||
\(137\) | −19.4991 | −1.66592 | −0.832959 | − | 0.553334i | \(-0.813355\pi\) | ||||
−0.832959 | + | 0.553334i | \(0.813355\pi\) | |||||||
\(138\) | 12.3810 | 1.05394 | ||||||||
\(139\) | −4.36910 | −0.370583 | −0.185291 | − | 0.982684i | \(-0.559323\pi\) | ||||
−0.185291 | + | 0.982684i | \(0.559323\pi\) | |||||||
\(140\) | 0.0733366 | 0.00619808 | ||||||||
\(141\) | 24.1047 | 2.02998 | ||||||||
\(142\) | −12.7899 | −1.07330 | ||||||||
\(143\) | 1.47074 | 0.122989 | ||||||||
\(144\) | −18.1642 | −1.51368 | ||||||||
\(145\) | −0.433328 | −0.0359859 | ||||||||
\(146\) | −9.02702 | −0.747081 | ||||||||
\(147\) | −20.4209 | −1.68429 | ||||||||
\(148\) | −3.16575 | −0.260223 | ||||||||
\(149\) | 5.11776 | 0.419264 | 0.209632 | − | 0.977780i | \(-0.432773\pi\) | ||||
0.209632 | + | 0.977780i | \(0.432773\pi\) | |||||||
\(150\) | 19.3859 | 1.58285 | ||||||||
\(151\) | −3.61329 | −0.294045 | −0.147023 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147023 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(152\) | 15.0409 | 1.21997 | ||||||||
\(153\) | −4.51011 | −0.364621 | ||||||||
\(154\) | −1.14549 | −0.0923064 | ||||||||
\(155\) | 0.801374 | 0.0643679 | ||||||||
\(156\) | −3.51504 | −0.281429 | ||||||||
\(157\) | 14.0393 | 1.12046 | 0.560228 | − | 0.828339i | \(-0.310714\pi\) | ||||
0.560228 | + | 0.828339i | \(0.310714\pi\) | |||||||
\(158\) | −14.8125 | −1.17842 | ||||||||
\(159\) | −15.1448 | −1.20106 | ||||||||
\(160\) | 0.390949 | 0.0309073 | ||||||||
\(161\) | −3.20253 | −0.252394 | ||||||||
\(162\) | −45.0038 | −3.53584 | ||||||||
\(163\) | −12.4299 | −0.973586 | −0.486793 | − | 0.873517i | \(-0.661833\pi\) | ||||
−0.486793 | + | 0.873517i | \(0.661833\pi\) | |||||||
\(164\) | 3.00362 | 0.234543 | ||||||||
\(165\) | −0.354854 | −0.0276253 | ||||||||
\(166\) | −1.20618 | −0.0936175 | ||||||||
\(167\) | 17.1141 | 1.32433 | 0.662165 | − | 0.749358i | \(-0.269638\pi\) | ||||
0.662165 | + | 0.749358i | \(0.269638\pi\) | |||||||
\(168\) | 10.5482 | 0.813815 | ||||||||
\(169\) | −10.8369 | −0.833611 | ||||||||
\(170\) | −0.0620470 | −0.00475878 | ||||||||
\(171\) | 42.1309 | 3.22183 | ||||||||
\(172\) | 4.97054 | 0.379000 | ||||||||
\(173\) | 8.33709 | 0.633857 | 0.316929 | − | 0.948449i | \(-0.397348\pi\) | ||||
0.316929 | + | 0.948449i | \(0.397348\pi\) | |||||||
\(174\) | −16.1765 | −1.22633 | ||||||||
\(175\) | −5.01442 | −0.379055 | ||||||||
\(176\) | −2.10649 | −0.158783 | ||||||||
\(177\) | 13.5618 | 1.01937 | ||||||||
\(178\) | 10.9820 | 0.823135 | ||||||||
\(179\) | 7.07537 | 0.528838 | 0.264419 | − | 0.964408i | \(-0.414820\pi\) | ||||
0.264419 | + | 0.964408i | \(0.414820\pi\) | |||||||
\(180\) | 0.629194 | 0.0468974 | ||||||||
\(181\) | 13.6052 | 1.01127 | 0.505634 | − | 0.862748i | \(-0.331259\pi\) | ||||
0.505634 | + | 0.862748i | \(0.331259\pi\) | |||||||
\(182\) | −1.68472 | −0.124880 | ||||||||
\(183\) | 47.9022 | 3.54103 | ||||||||
\(184\) | −9.80909 | −0.723136 | ||||||||
\(185\) | −0.470035 | −0.0345577 | ||||||||
\(186\) | 29.9159 | 2.19354 | ||||||||
\(187\) | −0.523035 | −0.0382481 | ||||||||
\(188\) | −4.95657 | −0.361495 | ||||||||
\(189\) | 19.2671 | 1.40148 | ||||||||
\(190\) | 0.579607 | 0.0420491 | ||||||||
\(191\) | −24.4823 | −1.77148 | −0.885740 | − | 0.464182i | \(-0.846348\pi\) | ||||
−0.885740 | + | 0.464182i | \(0.846348\pi\) | |||||||
\(192\) | 28.9576 | 2.08983 | ||||||||
\(193\) | −23.2283 | −1.67201 | −0.836005 | − | 0.548722i | \(-0.815114\pi\) | ||||
−0.836005 | + | 0.548722i | \(0.815114\pi\) | |||||||
\(194\) | 3.46208 | 0.248563 | ||||||||
\(195\) | −0.521896 | −0.0373737 | ||||||||
\(196\) | 4.19907 | 0.299934 | ||||||||
\(197\) | −9.28048 | −0.661206 | −0.330603 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330603 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(198\) | −9.82779 | −0.698431 | ||||||||
\(199\) | −0.503697 | −0.0357061 | −0.0178531 | − | 0.999841i | \(-0.505683\pi\) | ||||
−0.0178531 | + | 0.999841i | \(0.505683\pi\) | |||||||
\(200\) | −15.3588 | −1.08603 | ||||||||
\(201\) | −41.7491 | −2.94475 | ||||||||
\(202\) | −14.6511 | −1.03085 | ||||||||
\(203\) | 4.18426 | 0.293678 | ||||||||
\(204\) | 1.25005 | 0.0875208 | ||||||||
\(205\) | 0.445962 | 0.0311473 | ||||||||
\(206\) | 1.64569 | 0.114660 | ||||||||
\(207\) | −27.4762 | −1.90973 | ||||||||
\(208\) | −3.09809 | −0.214814 | ||||||||
\(209\) | 4.88589 | 0.337964 | ||||||||
\(210\) | 0.406482 | 0.0280499 | ||||||||
\(211\) | −9.79724 | −0.674470 | −0.337235 | − | 0.941421i | \(-0.609492\pi\) | ||||
−0.337235 | + | 0.941421i | \(0.609492\pi\) | |||||||
\(212\) | 3.11416 | 0.213882 | ||||||||
\(213\) | 38.2583 | 2.62141 | ||||||||
\(214\) | 1.29532 | 0.0885464 | ||||||||
\(215\) | 0.738001 | 0.0503313 | ||||||||
\(216\) | 59.0137 | 4.01537 | ||||||||
\(217\) | −7.73816 | −0.525300 | ||||||||
\(218\) | 12.8869 | 0.872812 | ||||||||
\(219\) | 27.0025 | 1.82466 | ||||||||
\(220\) | 0.0729673 | 0.00491945 | ||||||||
\(221\) | −0.769246 | −0.0517451 | ||||||||
\(222\) | −17.5468 | −1.17766 | ||||||||
\(223\) | −7.42764 | −0.497392 | −0.248696 | − | 0.968582i | \(-0.580002\pi\) | ||||
−0.248696 | + | 0.968582i | \(0.580002\pi\) | |||||||
\(224\) | −3.77505 | −0.252231 | ||||||||
\(225\) | −43.0214 | −2.86809 | ||||||||
\(226\) | 14.5750 | 0.969515 | ||||||||
\(227\) | 21.0243 | 1.39543 | 0.697716 | − | 0.716374i | \(-0.254200\pi\) | ||||
0.697716 | + | 0.716374i | \(0.254200\pi\) | |||||||
\(228\) | −11.6772 | −0.773343 | ||||||||
\(229\) | −11.6483 | −0.769741 | −0.384870 | − | 0.922971i | \(-0.625754\pi\) | ||||
−0.384870 | + | 0.922971i | \(0.625754\pi\) | |||||||
\(230\) | −0.377998 | −0.0249245 | ||||||||
\(231\) | 3.42651 | 0.225447 | ||||||||
\(232\) | 12.8161 | 0.841416 | ||||||||
\(233\) | −1.58868 | −0.104078 | −0.0520390 | − | 0.998645i | \(-0.516572\pi\) | ||||
−0.0520390 | + | 0.998645i | \(0.516572\pi\) | |||||||
\(234\) | −14.4541 | −0.944893 | ||||||||
\(235\) | −0.735926 | −0.0480065 | ||||||||
\(236\) | −2.78867 | −0.181527 | ||||||||
\(237\) | 44.3087 | 2.87816 | ||||||||
\(238\) | 0.599132 | 0.0388360 | ||||||||
\(239\) | 20.8034 | 1.34566 | 0.672830 | − | 0.739797i | \(-0.265079\pi\) | ||||
0.672830 | + | 0.739797i | \(0.265079\pi\) | |||||||
\(240\) | 0.747496 | 0.0482507 | ||||||||
\(241\) | −7.99233 | −0.514831 | −0.257416 | − | 0.966301i | \(-0.582871\pi\) | ||||
−0.257416 | + | 0.966301i | \(0.582871\pi\) | |||||||
\(242\) | −1.13972 | −0.0732642 | ||||||||
\(243\) | 77.1095 | 4.94658 | ||||||||
\(244\) | −9.84996 | −0.630579 | ||||||||
\(245\) | 0.623457 | 0.0398312 | ||||||||
\(246\) | 16.6481 | 1.06144 | ||||||||
\(247\) | 7.18585 | 0.457225 | ||||||||
\(248\) | −23.7014 | −1.50504 | ||||||||
\(249\) | 3.60803 | 0.228650 | ||||||||
\(250\) | −1.18500 | −0.0749461 | ||||||||
\(251\) | 8.35603 | 0.527428 | 0.263714 | − | 0.964601i | \(-0.415053\pi\) | ||||
0.263714 | + | 0.964601i | \(0.415053\pi\) | |||||||
\(252\) | −6.07557 | −0.382725 | ||||||||
\(253\) | −3.18640 | −0.200327 | ||||||||
\(254\) | 9.71855 | 0.609796 | ||||||||
\(255\) | 0.185601 | 0.0116228 | ||||||||
\(256\) | −14.5161 | −0.907258 | ||||||||
\(257\) | 9.46958 | 0.590696 | 0.295348 | − | 0.955390i | \(-0.404564\pi\) | ||||
0.295348 | + | 0.955390i | \(0.404564\pi\) | |||||||
\(258\) | 27.5502 | 1.71520 | ||||||||
\(259\) | 4.53871 | 0.282022 | ||||||||
\(260\) | 0.107316 | 0.00665543 | ||||||||
\(261\) | 35.8990 | 2.22209 | ||||||||
\(262\) | 1.13972 | 0.0704123 | ||||||||
\(263\) | 5.47287 | 0.337471 | 0.168736 | − | 0.985661i | \(-0.446032\pi\) | ||||
0.168736 | + | 0.985661i | \(0.446032\pi\) | |||||||
\(264\) | 10.4951 | 0.645930 | ||||||||
\(265\) | 0.462375 | 0.0284035 | ||||||||
\(266\) | −5.59675 | −0.343159 | ||||||||
\(267\) | −32.8504 | −2.01041 | ||||||||
\(268\) | 8.58471 | 0.524395 | ||||||||
\(269\) | 3.78140 | 0.230556 | 0.115278 | − | 0.993333i | \(-0.463224\pi\) | ||||
0.115278 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(270\) | 2.27412 | 0.138399 | ||||||||
\(271\) | −31.1040 | −1.88943 | −0.944716 | − | 0.327891i | \(-0.893662\pi\) | ||||
−0.944716 | + | 0.327891i | \(0.893662\pi\) | |||||||
\(272\) | 1.10177 | 0.0668045 | ||||||||
\(273\) | 5.03948 | 0.305003 | ||||||||
\(274\) | 22.2235 | 1.34257 | ||||||||
\(275\) | −4.98917 | −0.300858 | ||||||||
\(276\) | 7.61545 | 0.458396 | ||||||||
\(277\) | −1.24461 | −0.0747812 | −0.0373906 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373906 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(278\) | 4.97957 | 0.298655 | ||||||||
\(279\) | −66.3898 | −3.97465 | ||||||||
\(280\) | −0.322042 | −0.0192457 | ||||||||
\(281\) | −5.99503 | −0.357633 | −0.178817 | − | 0.983882i | \(-0.557227\pi\) | ||||
−0.178817 | + | 0.983882i | \(0.557227\pi\) | |||||||
\(282\) | −27.4727 | −1.63598 | ||||||||
\(283\) | −0.258842 | −0.0153866 | −0.00769328 | − | 0.999970i | \(-0.502449\pi\) | ||||
−0.00769328 | + | 0.999970i | \(0.502449\pi\) | |||||||
\(284\) | −7.86691 | −0.466815 | ||||||||
\(285\) | −1.73378 | −0.102700 | ||||||||
\(286\) | −1.67623 | −0.0991176 | ||||||||
\(287\) | −4.30626 | −0.254190 | ||||||||
\(288\) | −32.3882 | −1.90849 | ||||||||
\(289\) | −16.7264 | −0.983908 | ||||||||
\(290\) | 0.493874 | 0.0290013 | ||||||||
\(291\) | −10.3561 | −0.607084 | ||||||||
\(292\) | −5.55242 | −0.324931 | ||||||||
\(293\) | 18.1873 | 1.06251 | 0.531256 | − | 0.847211i | \(-0.321720\pi\) | ||||
0.531256 | + | 0.847211i | \(0.321720\pi\) | |||||||
\(294\) | 23.2741 | 1.35738 | ||||||||
\(295\) | −0.414048 | −0.0241068 | ||||||||
\(296\) | 13.9017 | 0.808022 | ||||||||
\(297\) | 19.1701 | 1.11236 | ||||||||
\(298\) | −5.83283 | −0.337887 | ||||||||
\(299\) | −4.68635 | −0.271018 | ||||||||
\(300\) | 11.9241 | 0.688436 | ||||||||
\(301\) | −7.12622 | −0.410749 | ||||||||
\(302\) | 4.11815 | 0.236973 | ||||||||
\(303\) | 43.8258 | 2.51773 | ||||||||
\(304\) | −10.2921 | −0.590292 | ||||||||
\(305\) | −1.46247 | −0.0837410 | ||||||||
\(306\) | 5.14028 | 0.293850 | ||||||||
\(307\) | −1.68926 | −0.0964112 | −0.0482056 | − | 0.998837i | \(-0.515350\pi\) | ||||
−0.0482056 | + | 0.998837i | \(0.515350\pi\) | |||||||
\(308\) | −0.704580 | −0.0401472 | ||||||||
\(309\) | −4.92273 | −0.280044 | ||||||||
\(310\) | −0.913344 | −0.0518745 | ||||||||
\(311\) | −30.2079 | −1.71293 | −0.856467 | − | 0.516203i | \(-0.827345\pi\) | ||||
−0.856467 | + | 0.516203i | \(0.827345\pi\) | |||||||
\(312\) | 15.4355 | 0.873866 | ||||||||
\(313\) | 8.81226 | 0.498098 | 0.249049 | − | 0.968491i | \(-0.419882\pi\) | ||||
0.249049 | + | 0.968491i | \(0.419882\pi\) | |||||||
\(314\) | −16.0009 | −0.902982 | ||||||||
\(315\) | −0.902070 | −0.0508259 | ||||||||
\(316\) | −9.11104 | −0.512536 | ||||||||
\(317\) | 6.14160 | 0.344947 | 0.172473 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172473 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(318\) | 17.2608 | 0.967939 | ||||||||
\(319\) | 4.16319 | 0.233094 | ||||||||
\(320\) | −0.884085 | −0.0494219 | ||||||||
\(321\) | −3.87469 | −0.216264 | ||||||||
\(322\) | 3.64999 | 0.203406 | ||||||||
\(323\) | −2.55549 | −0.142191 | ||||||||
\(324\) | −27.6814 | −1.53785 | ||||||||
\(325\) | −7.33774 | −0.407025 | ||||||||
\(326\) | 14.1667 | 0.784618 | ||||||||
\(327\) | −38.5485 | −2.13174 | ||||||||
\(328\) | −13.1897 | −0.728281 | ||||||||
\(329\) | 7.10619 | 0.391777 | ||||||||
\(330\) | 0.404435 | 0.0222634 | ||||||||
\(331\) | 11.9166 | 0.654993 | 0.327497 | − | 0.944852i | \(-0.393795\pi\) | ||||
0.327497 | + | 0.944852i | \(0.393795\pi\) | |||||||
\(332\) | −0.741907 | −0.0407174 | ||||||||
\(333\) | 38.9401 | 2.13390 | ||||||||
\(334\) | −19.5053 | −1.06729 | ||||||||
\(335\) | 1.27461 | 0.0696396 | ||||||||
\(336\) | −7.21791 | −0.393769 | ||||||||
\(337\) | −28.7112 | −1.56400 | −0.781998 | − | 0.623281i | \(-0.785799\pi\) | ||||
−0.781998 | + | 0.623281i | \(0.785799\pi\) | |||||||
\(338\) | 12.3511 | 0.671812 | ||||||||
\(339\) | −43.5981 | −2.36793 | ||||||||
\(340\) | −0.0381644 | −0.00206976 | ||||||||
\(341\) | −7.69918 | −0.416934 | ||||||||
\(342\) | −48.0175 | −2.59649 | ||||||||
\(343\) | −13.0556 | −0.704937 | ||||||||
\(344\) | −21.8271 | −1.17684 | ||||||||
\(345\) | 1.13070 | 0.0608750 | ||||||||
\(346\) | −9.50197 | −0.510829 | ||||||||
\(347\) | −21.5606 | −1.15743 | −0.578717 | − | 0.815529i | \(-0.696446\pi\) | ||||
−0.578717 | + | 0.815529i | \(0.696446\pi\) | |||||||
\(348\) | −9.94997 | −0.533374 | ||||||||
\(349\) | −17.5173 | −0.937677 | −0.468839 | − | 0.883284i | \(-0.655327\pi\) | ||||
−0.468839 | + | 0.883284i | \(0.655327\pi\) | |||||||
\(350\) | 5.71505 | 0.305482 | ||||||||
\(351\) | 28.1941 | 1.50489 | ||||||||
\(352\) | −3.75604 | −0.200197 | ||||||||
\(353\) | 29.3367 | 1.56143 | 0.780717 | − | 0.624885i | \(-0.214854\pi\) | ||||
0.780717 | + | 0.624885i | \(0.214854\pi\) | |||||||
\(354\) | −15.4567 | −0.821516 | ||||||||
\(355\) | −1.16804 | −0.0619931 | ||||||||
\(356\) | 6.75491 | 0.358009 | ||||||||
\(357\) | −1.79218 | −0.0948523 | ||||||||
\(358\) | −8.06396 | −0.426194 | ||||||||
\(359\) | −12.0516 | −0.636059 | −0.318030 | − | 0.948081i | \(-0.603021\pi\) | ||||
−0.318030 | + | 0.948081i | \(0.603021\pi\) | |||||||
\(360\) | −2.76297 | −0.145621 | ||||||||
\(361\) | 4.87192 | 0.256417 | ||||||||
\(362\) | −15.5062 | −0.814987 | ||||||||
\(363\) | 3.40925 | 0.178939 | ||||||||
\(364\) | −1.03625 | −0.0543143 | ||||||||
\(365\) | −0.824395 | −0.0431508 | ||||||||
\(366\) | −54.5953 | −2.85374 | ||||||||
\(367\) | −23.4905 | −1.22619 | −0.613096 | − | 0.790009i | \(-0.710076\pi\) | ||||
−0.613096 | + | 0.790009i | \(0.710076\pi\) | |||||||
\(368\) | 6.71212 | 0.349893 | ||||||||
\(369\) | −36.9457 | −1.92332 | ||||||||
\(370\) | 0.535710 | 0.0278502 | ||||||||
\(371\) | −4.46474 | −0.231798 | ||||||||
\(372\) | 18.4010 | 0.954045 | ||||||||
\(373\) | −13.5774 | −0.703011 | −0.351506 | − | 0.936186i | \(-0.614330\pi\) | ||||
−0.351506 | + | 0.936186i | \(0.614330\pi\) | |||||||
\(374\) | 0.596115 | 0.0308244 | ||||||||
\(375\) | 3.54469 | 0.183047 | ||||||||
\(376\) | 21.7657 | 1.12248 | ||||||||
\(377\) | 6.12295 | 0.315348 | ||||||||
\(378\) | −21.9592 | −1.12946 | ||||||||
\(379\) | −19.6101 | −1.00730 | −0.503651 | − | 0.863907i | \(-0.668010\pi\) | ||||
−0.503651 | + | 0.863907i | \(0.668010\pi\) | |||||||
\(380\) | 0.356510 | 0.0182886 | ||||||||
\(381\) | −29.0710 | −1.48935 | ||||||||
\(382\) | 27.9031 | 1.42765 | ||||||||
\(383\) | −21.9292 | −1.12053 | −0.560264 | − | 0.828314i | \(-0.689300\pi\) | ||||
−0.560264 | + | 0.828314i | \(0.689300\pi\) | |||||||
\(384\) | −7.39307 | −0.377276 | ||||||||
\(385\) | −0.104612 | −0.00533155 | ||||||||
\(386\) | 26.4738 | 1.34748 | ||||||||
\(387\) | −61.1397 | −3.10791 | ||||||||
\(388\) | 2.12949 | 0.108108 | ||||||||
\(389\) | −16.0085 | −0.811662 | −0.405831 | − | 0.913948i | \(-0.633018\pi\) | ||||
−0.405831 | + | 0.913948i | \(0.633018\pi\) | |||||||
\(390\) | 0.594817 | 0.0301197 | ||||||||
\(391\) | 1.66660 | 0.0842834 | ||||||||
\(392\) | −18.4393 | −0.931326 | ||||||||
\(393\) | −3.40925 | −0.171974 | ||||||||
\(394\) | 10.5772 | 0.532870 | ||||||||
\(395\) | −1.35276 | −0.0680648 | ||||||||
\(396\) | −6.04497 | −0.303771 | ||||||||
\(397\) | 28.5338 | 1.43207 | 0.716035 | − | 0.698065i | \(-0.245955\pi\) | ||||
0.716035 | + | 0.698065i | \(0.245955\pi\) | |||||||
\(398\) | 0.574075 | 0.0287758 | ||||||||
\(399\) | 16.7415 | 0.838125 | ||||||||
\(400\) | 10.5096 | 0.525482 | ||||||||
\(401\) | 34.5253 | 1.72411 | 0.862054 | − | 0.506816i | \(-0.169178\pi\) | ||||
0.862054 | + | 0.506816i | \(0.169178\pi\) | |||||||
\(402\) | 47.5824 | 2.37319 | ||||||||
\(403\) | −11.3235 | −0.564062 | ||||||||
\(404\) | −9.01175 | −0.448351 | ||||||||
\(405\) | −4.10999 | −0.204227 | ||||||||
\(406\) | −4.76890 | −0.236676 | ||||||||
\(407\) | 4.51585 | 0.223843 | ||||||||
\(408\) | −5.48931 | −0.271761 | ||||||||
\(409\) | 1.88479 | 0.0931966 | 0.0465983 | − | 0.998914i | \(-0.485162\pi\) | ||||
0.0465983 | + | 0.998914i | \(0.485162\pi\) | |||||||
\(410\) | −0.508273 | −0.0251018 | ||||||||
\(411\) | −66.4772 | −3.27908 | ||||||||
\(412\) | 1.01224 | 0.0498697 | ||||||||
\(413\) | 3.99809 | 0.196733 | ||||||||
\(414\) | 31.3152 | 1.53906 | ||||||||
\(415\) | −0.110155 | −0.00540727 | ||||||||
\(416\) | −5.52414 | −0.270843 | ||||||||
\(417\) | −14.8954 | −0.729429 | ||||||||
\(418\) | −5.56856 | −0.272367 | ||||||||
\(419\) | −20.8076 | −1.01652 | −0.508259 | − | 0.861204i | \(-0.669711\pi\) | ||||
−0.508259 | + | 0.861204i | \(0.669711\pi\) | |||||||
\(420\) | 0.250023 | 0.0121999 | ||||||||
\(421\) | −11.7864 | −0.574434 | −0.287217 | − | 0.957866i | \(-0.592730\pi\) | ||||
−0.287217 | + | 0.957866i | \(0.592730\pi\) | |||||||
\(422\) | 11.1661 | 0.543559 | ||||||||
\(423\) | 60.9678 | 2.96435 | ||||||||
\(424\) | −13.6752 | −0.664125 | ||||||||
\(425\) | 2.60951 | 0.126580 | ||||||||
\(426\) | −43.6038 | −2.11261 | ||||||||
\(427\) | 14.1218 | 0.683402 | ||||||||
\(428\) | 0.796739 | 0.0385118 | ||||||||
\(429\) | 5.01410 | 0.242083 | ||||||||
\(430\) | −0.841117 | −0.0405623 | ||||||||
\(431\) | 13.7150 | 0.660630 | 0.330315 | − | 0.943871i | \(-0.392845\pi\) | ||||
0.330315 | + | 0.943871i | \(0.392845\pi\) | |||||||
\(432\) | −40.3816 | −1.94286 | ||||||||
\(433\) | −29.7123 | −1.42788 | −0.713942 | − | 0.700205i | \(-0.753092\pi\) | ||||
−0.713942 | + | 0.700205i | \(0.753092\pi\) | |||||||
\(434\) | 8.81936 | 0.423343 | ||||||||
\(435\) | −1.47732 | −0.0708321 | ||||||||
\(436\) | 7.92660 | 0.379615 | ||||||||
\(437\) | −15.5684 | −0.744736 | ||||||||
\(438\) | −30.7753 | −1.47050 | ||||||||
\(439\) | −24.5212 | −1.17033 | −0.585166 | − | 0.810914i | \(-0.698971\pi\) | ||||
−0.585166 | + | 0.810914i | \(0.698971\pi\) | |||||||
\(440\) | −0.320420 | −0.0152754 | ||||||||
\(441\) | −51.6503 | −2.45954 | ||||||||
\(442\) | 0.876727 | 0.0417017 | ||||||||
\(443\) | 21.4778 | 1.02044 | 0.510220 | − | 0.860044i | \(-0.329564\pi\) | ||||
0.510220 | + | 0.860044i | \(0.329564\pi\) | |||||||
\(444\) | −10.7928 | −0.512206 | ||||||||
\(445\) | 1.00293 | 0.0475437 | ||||||||
\(446\) | 8.46546 | 0.400851 | ||||||||
\(447\) | 17.4477 | 0.825249 | ||||||||
\(448\) | 8.53682 | 0.403327 | ||||||||
\(449\) | 0.818727 | 0.0386381 | 0.0193191 | − | 0.999813i | \(-0.493850\pi\) | ||||
0.0193191 | + | 0.999813i | \(0.493850\pi\) | |||||||
\(450\) | 49.0325 | 2.31141 | ||||||||
\(451\) | −4.28457 | −0.201752 | ||||||||
\(452\) | 8.96493 | 0.421675 | ||||||||
\(453\) | −12.3186 | −0.578778 | ||||||||
\(454\) | −23.9619 | −1.12459 | ||||||||
\(455\) | −0.153857 | −0.00721294 | ||||||||
\(456\) | 51.2780 | 2.40131 | ||||||||
\(457\) | 39.1336 | 1.83059 | 0.915296 | − | 0.402783i | \(-0.131957\pi\) | ||||
0.915296 | + | 0.402783i | \(0.131957\pi\) | |||||||
\(458\) | 13.2758 | 0.620339 | ||||||||
\(459\) | −10.0266 | −0.468002 | ||||||||
\(460\) | −0.232503 | −0.0108405 | ||||||||
\(461\) | 28.8028 | 1.34148 | 0.670740 | − | 0.741693i | \(-0.265977\pi\) | ||||
0.670740 | + | 0.741693i | \(0.265977\pi\) | |||||||
\(462\) | −3.90527 | −0.181689 | ||||||||
\(463\) | −22.9216 | −1.06526 | −0.532630 | − | 0.846348i | \(-0.678796\pi\) | ||||
−0.532630 | + | 0.846348i | \(0.678796\pi\) | |||||||
\(464\) | −8.76972 | −0.407124 | ||||||||
\(465\) | 2.73208 | 0.126697 | ||||||||
\(466\) | 1.81066 | 0.0838770 | ||||||||
\(467\) | 18.6223 | 0.861737 | 0.430868 | − | 0.902415i | \(-0.358207\pi\) | ||||
0.430868 | + | 0.902415i | \(0.358207\pi\) | |||||||
\(468\) | −8.89055 | −0.410966 | ||||||||
\(469\) | −12.3078 | −0.568322 | ||||||||
\(470\) | 0.838752 | 0.0386887 | ||||||||
\(471\) | 47.8633 | 2.20543 | ||||||||
\(472\) | 12.2458 | 0.563661 | ||||||||
\(473\) | −7.09033 | −0.326014 | ||||||||
\(474\) | −50.4996 | −2.31952 | ||||||||
\(475\) | −24.3765 | −1.11847 | ||||||||
\(476\) | 0.368520 | 0.0168911 | ||||||||
\(477\) | −38.3054 | −1.75389 | ||||||||
\(478\) | −23.7101 | −1.08448 | ||||||||
\(479\) | 26.0559 | 1.19053 | 0.595263 | − | 0.803531i | \(-0.297048\pi\) | ||||
0.595263 | + | 0.803531i | \(0.297048\pi\) | |||||||
\(480\) | 1.33284 | 0.0608357 | ||||||||
\(481\) | 6.64163 | 0.302832 | ||||||||
\(482\) | 9.10904 | 0.414905 | ||||||||
\(483\) | −10.9182 | −0.496795 | ||||||||
\(484\) | −0.701031 | −0.0318651 | ||||||||
\(485\) | 0.316175 | 0.0143568 | ||||||||
\(486\) | −87.8835 | −3.98647 | ||||||||
\(487\) | 3.78023 | 0.171298 | 0.0856492 | − | 0.996325i | \(-0.472704\pi\) | ||||
0.0856492 | + | 0.996325i | \(0.472704\pi\) | |||||||
\(488\) | 43.2540 | 1.95802 | ||||||||
\(489\) | −42.3766 | −1.91634 | ||||||||
\(490\) | −0.710568 | −0.0321002 | ||||||||
\(491\) | −0.00784829 | −0.000354188 0 | −0.000177094 | − | 1.00000i | \(-0.500056\pi\) | ||||
−0.000177094 | 1.00000i | \(0.500056\pi\) | ||||||||
\(492\) | 10.2401 | 0.461658 | ||||||||
\(493\) | −2.17749 | −0.0980693 | ||||||||
\(494\) | −8.18988 | −0.368480 | ||||||||
\(495\) | −0.897527 | −0.0403408 | ||||||||
\(496\) | 16.2183 | 0.728222 | ||||||||
\(497\) | 11.2787 | 0.505920 | ||||||||
\(498\) | −4.11216 | −0.184270 | ||||||||
\(499\) | 26.3236 | 1.17840 | 0.589202 | − | 0.807986i | \(-0.299442\pi\) | ||||
0.589202 | + | 0.807986i | \(0.299442\pi\) | |||||||
\(500\) | −0.728882 | −0.0325966 | ||||||||
\(501\) | 58.3462 | 2.60672 | ||||||||
\(502\) | −9.52356 | −0.425057 | ||||||||
\(503\) | −40.9573 | −1.82620 | −0.913098 | − | 0.407740i | \(-0.866317\pi\) | ||||
−0.913098 | + | 0.407740i | \(0.866317\pi\) | |||||||
\(504\) | 26.6796 | 1.18840 | ||||||||
\(505\) | −1.33802 | −0.0595411 | ||||||||
\(506\) | 3.63161 | 0.161445 | ||||||||
\(507\) | −36.9458 | −1.64082 | ||||||||
\(508\) | 5.97778 | 0.265221 | ||||||||
\(509\) | 35.8740 | 1.59009 | 0.795043 | − | 0.606553i | \(-0.207448\pi\) | ||||
0.795043 | + | 0.606553i | \(0.207448\pi\) | |||||||
\(510\) | −0.211533 | −0.00936686 | ||||||||
\(511\) | 7.96045 | 0.352150 | ||||||||
\(512\) | 20.8814 | 0.922838 | ||||||||
\(513\) | 93.6629 | 4.13532 | ||||||||
\(514\) | −10.7927 | −0.476046 | ||||||||
\(515\) | 0.150293 | 0.00662269 | ||||||||
\(516\) | 16.9458 | 0.745998 | ||||||||
\(517\) | 7.07039 | 0.310956 | ||||||||
\(518\) | −5.17288 | −0.227283 | ||||||||
\(519\) | 28.4232 | 1.24764 | ||||||||
\(520\) | −0.471253 | −0.0206658 | ||||||||
\(521\) | 16.6857 | 0.731015 | 0.365507 | − | 0.930808i | \(-0.380895\pi\) | ||||
0.365507 | + | 0.930808i | \(0.380895\pi\) | |||||||
\(522\) | −40.9149 | −1.79080 | ||||||||
\(523\) | −20.9358 | −0.915459 | −0.457730 | − | 0.889091i | \(-0.651337\pi\) | ||||
−0.457730 | + | 0.889091i | \(0.651337\pi\) | |||||||
\(524\) | 0.701031 | 0.0306247 | ||||||||
\(525\) | −17.0954 | −0.746105 | ||||||||
\(526\) | −6.23755 | −0.271970 | ||||||||
\(527\) | 4.02694 | 0.175416 | ||||||||
\(528\) | −7.18155 | −0.312537 | ||||||||
\(529\) | −12.8469 | −0.558560 | ||||||||
\(530\) | −0.526979 | −0.0228905 | ||||||||
\(531\) | 34.3018 | 1.48857 | ||||||||
\(532\) | −3.44250 | −0.149251 | ||||||||
\(533\) | −6.30147 | −0.272947 | ||||||||
\(534\) | 37.4403 | 1.62020 | ||||||||
\(535\) | 0.118296 | 0.00511437 | ||||||||
\(536\) | −37.6979 | −1.62830 | ||||||||
\(537\) | 24.1217 | 1.04093 | ||||||||
\(538\) | −4.30975 | −0.185806 | ||||||||
\(539\) | −5.98985 | −0.258001 | ||||||||
\(540\) | 1.39879 | 0.0601943 | ||||||||
\(541\) | −11.5182 | −0.495204 | −0.247602 | − | 0.968862i | \(-0.579643\pi\) | ||||
−0.247602 | + | 0.968862i | \(0.579643\pi\) | |||||||
\(542\) | 35.4499 | 1.52270 | ||||||||
\(543\) | 46.3836 | 1.99051 | ||||||||
\(544\) | 1.96454 | 0.0842289 | ||||||||
\(545\) | 1.17690 | 0.0504129 | ||||||||
\(546\) | −5.74362 | −0.245804 | ||||||||
\(547\) | −11.6750 | −0.499187 | −0.249593 | − | 0.968351i | \(-0.580297\pi\) | ||||
−0.249593 | + | 0.968351i | \(0.580297\pi\) | |||||||
\(548\) | 13.6695 | 0.583931 | ||||||||
\(549\) | 121.159 | 5.17092 | ||||||||
\(550\) | 5.68627 | 0.242463 | ||||||||
\(551\) | 20.3409 | 0.866550 | ||||||||
\(552\) | −33.4416 | −1.42337 | ||||||||
\(553\) | 13.0624 | 0.555470 | ||||||||
\(554\) | 1.41851 | 0.0602666 | ||||||||
\(555\) | −1.60247 | −0.0680209 | ||||||||
\(556\) | 3.06288 | 0.129895 | ||||||||
\(557\) | 10.0985 | 0.427888 | 0.213944 | − | 0.976846i | \(-0.431369\pi\) | ||||
0.213944 | + | 0.976846i | \(0.431369\pi\) | |||||||
\(558\) | 75.6660 | 3.20320 | ||||||||
\(559\) | −10.4280 | −0.441058 | ||||||||
\(560\) | 0.220365 | 0.00931214 | ||||||||
\(561\) | −1.78315 | −0.0752849 | ||||||||
\(562\) | 6.83267 | 0.288219 | ||||||||
\(563\) | 44.3884 | 1.87075 | 0.935374 | − | 0.353660i | \(-0.115063\pi\) | ||||
0.935374 | + | 0.353660i | \(0.115063\pi\) | |||||||
\(564\) | −16.8982 | −0.711541 | ||||||||
\(565\) | 1.33107 | 0.0559984 | ||||||||
\(566\) | 0.295008 | 0.0124001 | ||||||||
\(567\) | 39.6865 | 1.66668 | ||||||||
\(568\) | 34.5458 | 1.44951 | ||||||||
\(569\) | −40.5732 | −1.70092 | −0.850459 | − | 0.526042i | \(-0.823675\pi\) | ||||
−0.850459 | + | 0.526042i | \(0.823675\pi\) | |||||||
\(570\) | 1.97602 | 0.0827665 | ||||||||
\(571\) | 17.2145 | 0.720406 | 0.360203 | − | 0.932874i | \(-0.382707\pi\) | ||||
0.360203 | + | 0.932874i | \(0.382707\pi\) | |||||||
\(572\) | −1.03103 | −0.0431096 | ||||||||
\(573\) | −83.4663 | −3.48686 | ||||||||
\(574\) | 4.90794 | 0.204854 | ||||||||
\(575\) | 15.8975 | 0.662970 | ||||||||
\(576\) | 73.2420 | 3.05175 | ||||||||
\(577\) | 5.55353 | 0.231196 | 0.115598 | − | 0.993296i | \(-0.463122\pi\) | ||||
0.115598 | + | 0.993296i | \(0.463122\pi\) | |||||||
\(578\) | 19.0635 | 0.792937 | ||||||||
\(579\) | −79.1910 | −3.29107 | ||||||||
\(580\) | 0.303776 | 0.0126136 | ||||||||
\(581\) | 1.06366 | 0.0441282 | ||||||||
\(582\) | 11.8031 | 0.489253 | ||||||||
\(583\) | −4.44226 | −0.183980 | ||||||||
\(584\) | 24.3823 | 1.00894 | ||||||||
\(585\) | −1.32002 | −0.0545763 | ||||||||
\(586\) | −20.7285 | −0.856285 | ||||||||
\(587\) | −40.3244 | −1.66437 | −0.832184 | − | 0.554500i | \(-0.812910\pi\) | ||||
−0.832184 | + | 0.554500i | \(0.812910\pi\) | |||||||
\(588\) | 14.3157 | 0.590369 | ||||||||
\(589\) | −37.6174 | −1.55000 | ||||||||
\(590\) | 0.471900 | 0.0194278 | ||||||||
\(591\) | −31.6394 | −1.30147 | ||||||||
\(592\) | −9.51261 | −0.390966 | ||||||||
\(593\) | −40.6926 | −1.67104 | −0.835521 | − | 0.549458i | \(-0.814834\pi\) | ||||
−0.835521 | + | 0.549458i | \(0.814834\pi\) | |||||||
\(594\) | −21.8486 | −0.896458 | ||||||||
\(595\) | 0.0547160 | 0.00224314 | ||||||||
\(596\) | −3.58771 | −0.146958 | ||||||||
\(597\) | −1.71723 | −0.0702815 | ||||||||
\(598\) | 5.34114 | 0.218415 | ||||||||
\(599\) | −27.5848 | −1.12708 | −0.563541 | − | 0.826088i | \(-0.690561\pi\) | ||||
−0.563541 | + | 0.826088i | \(0.690561\pi\) | |||||||
\(600\) | −52.3619 | −2.13767 | ||||||||
\(601\) | −34.1958 | −1.39487 | −0.697437 | − | 0.716646i | \(-0.745676\pi\) | ||||
−0.697437 | + | 0.716646i | \(0.745676\pi\) | |||||||
\(602\) | 8.12192 | 0.331025 | ||||||||
\(603\) | −105.595 | −4.30018 | ||||||||
\(604\) | 2.53303 | 0.103067 | ||||||||
\(605\) | −0.104086 | −0.00423168 | ||||||||
\(606\) | −49.9493 | −2.02905 | ||||||||
\(607\) | 13.0452 | 0.529486 | 0.264743 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264743 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(608\) | −18.3516 | −0.744255 | ||||||||
\(609\) | 14.2652 | 0.578054 | ||||||||
\(610\) | 1.66681 | 0.0674873 | ||||||||
\(611\) | 10.3987 | 0.420686 | ||||||||
\(612\) | 3.16173 | 0.127805 | ||||||||
\(613\) | 31.6081 | 1.27664 | 0.638320 | − | 0.769771i | \(-0.279630\pi\) | ||||
0.638320 | + | 0.769771i | \(0.279630\pi\) | |||||||
\(614\) | 1.92529 | 0.0776983 | ||||||||
\(615\) | 1.52039 | 0.0613082 | ||||||||
\(616\) | 3.09401 | 0.124661 | ||||||||
\(617\) | 19.3884 | 0.780549 | 0.390274 | − | 0.920699i | \(-0.372380\pi\) | ||||
0.390274 | + | 0.920699i | \(0.372380\pi\) | |||||||
\(618\) | 5.61055 | 0.225689 | ||||||||
\(619\) | 15.3798 | 0.618165 | 0.309083 | − | 0.951035i | \(-0.399978\pi\) | ||||
0.309083 | + | 0.951035i | \(0.399978\pi\) | |||||||
\(620\) | −0.561788 | −0.0225620 | ||||||||
\(621\) | −61.0835 | −2.45119 | ||||||||
\(622\) | 34.4286 | 1.38046 | ||||||||
\(623\) | −9.68445 | −0.387999 | ||||||||
\(624\) | −10.5622 | −0.422825 | ||||||||
\(625\) | 24.8376 | 0.993504 | ||||||||
\(626\) | −10.0435 | −0.401420 | ||||||||
\(627\) | 16.6572 | 0.665225 | ||||||||
\(628\) | −9.84197 | −0.392737 | ||||||||
\(629\) | −2.36195 | −0.0941770 | ||||||||
\(630\) | 1.02811 | 0.0409609 | ||||||||
\(631\) | −0.0436089 | −0.00173604 | −0.000868022 | − | 1.00000i | \(-0.500276\pi\) | ||||
−0.000868022 | 1.00000i | \(0.500276\pi\) | ||||||||
\(632\) | 40.0091 | 1.59148 | ||||||||
\(633\) | −33.4012 | −1.32758 | ||||||||
\(634\) | −6.99973 | −0.277995 | ||||||||
\(635\) | 0.887550 | 0.0352213 | ||||||||
\(636\) | 10.6169 | 0.420989 | ||||||||
\(637\) | −8.80949 | −0.349045 | ||||||||
\(638\) | −4.74488 | −0.187852 | ||||||||
\(639\) | 96.7662 | 3.82801 | ||||||||
\(640\) | 0.225713 | 0.00892210 | ||||||||
\(641\) | −8.14772 | −0.321816 | −0.160908 | − | 0.986969i | \(-0.551442\pi\) | ||||
−0.160908 | + | 0.986969i | \(0.551442\pi\) | |||||||
\(642\) | 4.41607 | 0.174288 | ||||||||
\(643\) | 2.79586 | 0.110258 | 0.0551290 | − | 0.998479i | \(-0.482443\pi\) | ||||
0.0551290 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(644\) | 2.24507 | 0.0884682 | ||||||||
\(645\) | 2.51603 | 0.0990686 | ||||||||
\(646\) | 2.91255 | 0.114593 | ||||||||
\(647\) | −33.0032 | −1.29749 | −0.648744 | − | 0.761006i | \(-0.724706\pi\) | ||||
−0.648744 | + | 0.761006i | \(0.724706\pi\) | |||||||
\(648\) | 121.557 | 4.77520 | ||||||||
\(649\) | 3.97795 | 0.156148 | ||||||||
\(650\) | 8.36300 | 0.328024 | ||||||||
\(651\) | −26.3813 | −1.03396 | ||||||||
\(652\) | 8.71376 | 0.341257 | ||||||||
\(653\) | −5.02300 | −0.196565 | −0.0982826 | − | 0.995159i | \(-0.531335\pi\) | ||||
−0.0982826 | + | 0.995159i | \(0.531335\pi\) | |||||||
\(654\) | 43.9347 | 1.71798 | ||||||||
\(655\) | 0.104086 | 0.00406696 | ||||||||
\(656\) | 9.02541 | 0.352383 | ||||||||
\(657\) | 68.2970 | 2.66452 | ||||||||
\(658\) | −8.09908 | −0.315735 | ||||||||
\(659\) | −45.3118 | −1.76510 | −0.882549 | − | 0.470221i | \(-0.844174\pi\) | ||||
−0.882549 | + | 0.470221i | \(0.844174\pi\) | |||||||
\(660\) | 0.248763 | 0.00968310 | ||||||||
\(661\) | 35.9507 | 1.39832 | 0.699160 | − | 0.714965i | \(-0.253557\pi\) | ||||
0.699160 | + | 0.714965i | \(0.253557\pi\) | |||||||
\(662\) | −13.5816 | −0.527863 | ||||||||
\(663\) | −2.62255 | −0.101851 | ||||||||
\(664\) | 3.25792 | 0.126432 | ||||||||
\(665\) | −0.511125 | −0.0198206 | ||||||||
\(666\) | −44.3809 | −1.71972 | ||||||||
\(667\) | −13.2656 | −0.513644 | ||||||||
\(668\) | −11.9975 | −0.464198 | ||||||||
\(669\) | −25.3227 | −0.979031 | ||||||||
\(670\) | −1.45271 | −0.0561230 | ||||||||
\(671\) | 14.0507 | 0.542420 | ||||||||
\(672\) | −12.8701 | −0.496474 | ||||||||
\(673\) | −10.8923 | −0.419869 | −0.209934 | − | 0.977715i | \(-0.567325\pi\) | ||||
−0.209934 | + | 0.977715i | \(0.567325\pi\) | |||||||
\(674\) | 32.7228 | 1.26043 | ||||||||
\(675\) | −95.6427 | −3.68129 | ||||||||
\(676\) | 7.59703 | 0.292194 | ||||||||
\(677\) | −23.9805 | −0.921646 | −0.460823 | − | 0.887492i | \(-0.652446\pi\) | ||||
−0.460823 | + | 0.887492i | \(0.652446\pi\) | |||||||
\(678\) | 49.6898 | 1.90833 | ||||||||
\(679\) | −3.05302 | −0.117164 | ||||||||
\(680\) | 0.167591 | 0.00642681 | ||||||||
\(681\) | 71.6771 | 2.74667 | ||||||||
\(682\) | 8.77494 | 0.336010 | ||||||||
\(683\) | 5.82515 | 0.222893 | 0.111447 | − | 0.993770i | \(-0.464452\pi\) | ||||
0.111447 | + | 0.993770i | \(0.464452\pi\) | |||||||
\(684\) | −29.5351 | −1.12930 | ||||||||
\(685\) | 2.02957 | 0.0775460 | ||||||||
\(686\) | 14.8798 | 0.568112 | ||||||||
\(687\) | −39.7119 | −1.51510 | ||||||||
\(688\) | 14.9357 | 0.569419 | ||||||||
\(689\) | −6.53339 | −0.248902 | ||||||||
\(690\) | −1.28869 | −0.0490595 | ||||||||
\(691\) | 28.0781 | 1.06814 | 0.534070 | − | 0.845440i | \(-0.320662\pi\) | ||||
0.534070 | + | 0.845440i | \(0.320662\pi\) | |||||||
\(692\) | −5.84456 | −0.222177 | ||||||||
\(693\) | 8.66662 | 0.329218 | ||||||||
\(694\) | 24.5731 | 0.932782 | ||||||||
\(695\) | 0.454761 | 0.0172501 | ||||||||
\(696\) | 43.6931 | 1.65618 | ||||||||
\(697\) | 2.24098 | 0.0848831 | ||||||||
\(698\) | 19.9648 | 0.755680 | ||||||||
\(699\) | −5.41620 | −0.204860 | ||||||||
\(700\) | 3.51527 | 0.132865 | ||||||||
\(701\) | −32.4425 | −1.22534 | −0.612668 | − | 0.790341i | \(-0.709904\pi\) | ||||
−0.612668 | + | 0.790341i | \(0.709904\pi\) | |||||||
\(702\) | −32.1335 | −1.21280 | ||||||||
\(703\) | 22.0640 | 0.832158 | ||||||||
\(704\) | 8.49383 | 0.320123 | ||||||||
\(705\) | −2.50895 | −0.0944927 | ||||||||
\(706\) | −33.4357 | −1.25837 | ||||||||
\(707\) | 12.9201 | 0.485909 | ||||||||
\(708\) | −9.50727 | −0.357305 | ||||||||
\(709\) | −19.5920 | −0.735795 | −0.367897 | − | 0.929866i | \(-0.619922\pi\) | ||||
−0.367897 | + | 0.929866i | \(0.619922\pi\) | |||||||
\(710\) | 1.33124 | 0.0499606 | ||||||||
\(711\) | 112.069 | 4.20293 | ||||||||
\(712\) | −29.6627 | −1.11166 | ||||||||
\(713\) | 24.5326 | 0.918754 | ||||||||
\(714\) | 2.04259 | 0.0764420 | ||||||||
\(715\) | −0.153082 | −0.00572496 | ||||||||
\(716\) | −4.96006 | −0.185366 | ||||||||
\(717\) | 70.9239 | 2.64870 | ||||||||
\(718\) | 13.7355 | 0.512604 | ||||||||
\(719\) | −13.5736 | −0.506210 | −0.253105 | − | 0.967439i | \(-0.581452\pi\) | ||||
−0.253105 | + | 0.967439i | \(0.581452\pi\) | |||||||
\(720\) | 1.89063 | 0.0704597 | ||||||||
\(721\) | −1.45124 | −0.0540472 | ||||||||
\(722\) | −5.55264 | −0.206648 | ||||||||
\(723\) | −27.2478 | −1.01336 | ||||||||
\(724\) | −9.53768 | −0.354465 | ||||||||
\(725\) | −20.7708 | −0.771409 | ||||||||
\(726\) | −3.88560 | −0.144208 | ||||||||
\(727\) | −16.9885 | −0.630068 | −0.315034 | − | 0.949080i | \(-0.602016\pi\) | ||||
−0.315034 | + | 0.949080i | \(0.602016\pi\) | |||||||
\(728\) | 4.55047 | 0.168652 | ||||||||
\(729\) | 144.425 | 5.34909 | ||||||||
\(730\) | 0.939582 | 0.0347755 | ||||||||
\(731\) | 3.70849 | 0.137163 | ||||||||
\(732\) | −33.5810 | −1.24119 | ||||||||
\(733\) | −19.1559 | −0.707538 | −0.353769 | − | 0.935333i | \(-0.615100\pi\) | ||||
−0.353769 | + | 0.935333i | \(0.615100\pi\) | |||||||
\(734\) | 26.7726 | 0.988195 | ||||||||
\(735\) | 2.12552 | 0.0784010 | ||||||||
\(736\) | 11.9682 | 0.441154 | ||||||||
\(737\) | −12.2458 | −0.451081 | ||||||||
\(738\) | 42.1079 | 1.55001 | ||||||||
\(739\) | 35.2345 | 1.29612 | 0.648061 | − | 0.761589i | \(-0.275580\pi\) | ||||
0.648061 | + | 0.761589i | \(0.275580\pi\) | |||||||
\(740\) | 0.329509 | 0.0121130 | ||||||||
\(741\) | 24.4983 | 0.899969 | ||||||||
\(742\) | 5.08857 | 0.186807 | ||||||||
\(743\) | 27.6287 | 1.01360 | 0.506799 | − | 0.862064i | \(-0.330828\pi\) | ||||
0.506799 | + | 0.862064i | \(0.330828\pi\) | |||||||
\(744\) | −80.8038 | −2.96241 | ||||||||
\(745\) | −0.532685 | −0.0195161 | ||||||||
\(746\) | 15.4745 | 0.566561 | ||||||||
\(747\) | 9.12575 | 0.333894 | ||||||||
\(748\) | 0.366664 | 0.0134066 | ||||||||
\(749\) | −1.14228 | −0.0417379 | ||||||||
\(750\) | −4.03997 | −0.147519 | ||||||||
\(751\) | −38.2670 | −1.39638 | −0.698191 | − | 0.715911i | \(-0.746011\pi\) | ||||
−0.698191 | + | 0.715911i | \(0.746011\pi\) | |||||||
\(752\) | −14.8937 | −0.543119 | ||||||||
\(753\) | 28.4878 | 1.03815 | ||||||||
\(754\) | −6.97846 | −0.254141 | ||||||||
\(755\) | 0.376091 | 0.0136874 | ||||||||
\(756\) | −13.5069 | −0.491240 | ||||||||
\(757\) | −9.55929 | −0.347438 | −0.173719 | − | 0.984795i | \(-0.555578\pi\) | ||||
−0.173719 | + | 0.984795i | \(0.555578\pi\) | |||||||
\(758\) | 22.3501 | 0.811791 | ||||||||
\(759\) | −10.8632 | −0.394310 | ||||||||
\(760\) | −1.56554 | −0.0567880 | ||||||||
\(761\) | 24.1317 | 0.874775 | 0.437388 | − | 0.899273i | \(-0.355904\pi\) | ||||
0.437388 | + | 0.899273i | \(0.355904\pi\) | |||||||
\(762\) | 33.1329 | 1.20028 | ||||||||
\(763\) | −11.3643 | −0.411415 | ||||||||
\(764\) | 17.1629 | 0.620931 | ||||||||
\(765\) | 0.469438 | 0.0169726 | ||||||||
\(766\) | 24.9932 | 0.903040 | ||||||||
\(767\) | 5.85052 | 0.211250 | ||||||||
\(768\) | −49.4891 | −1.78578 | ||||||||
\(769\) | 1.54517 | 0.0557204 | 0.0278602 | − | 0.999612i | \(-0.491131\pi\) | ||||
0.0278602 | + | 0.999612i | \(0.491131\pi\) | |||||||
\(770\) | 0.119229 | 0.00429672 | ||||||||
\(771\) | 32.2841 | 1.16269 | ||||||||
\(772\) | 16.2838 | 0.586065 | ||||||||
\(773\) | 14.6467 | 0.526805 | 0.263403 | − | 0.964686i | \(-0.415155\pi\) | ||||
0.263403 | + | 0.964686i | \(0.415155\pi\) | |||||||
\(774\) | 69.6823 | 2.50468 | ||||||||
\(775\) | 38.4125 | 1.37982 | ||||||||
\(776\) | −9.35117 | −0.335688 | ||||||||
\(777\) | 15.4736 | 0.555112 | ||||||||
\(778\) | 18.2452 | 0.654123 | ||||||||
\(779\) | −20.9339 | −0.750036 | ||||||||
\(780\) | 0.365865 | 0.0131001 | ||||||||
\(781\) | 11.2219 | 0.401552 | ||||||||
\(782\) | −1.89946 | −0.0679245 | ||||||||
\(783\) | 79.8086 | 2.85213 | ||||||||
\(784\) | 12.6176 | 0.450628 | ||||||||
\(785\) | −1.46129 | −0.0521555 | ||||||||
\(786\) | 3.88560 | 0.138595 | ||||||||
\(787\) | −14.1284 | −0.503624 | −0.251812 | − | 0.967776i | \(-0.581027\pi\) | ||||
−0.251812 | + | 0.967776i | \(0.581027\pi\) | |||||||
\(788\) | 6.50590 | 0.231763 | ||||||||
\(789\) | 18.6584 | 0.664255 | ||||||||
\(790\) | 1.54177 | 0.0548538 | ||||||||
\(791\) | −12.8529 | −0.456998 | ||||||||
\(792\) | 26.5452 | 0.943242 | ||||||||
\(793\) | 20.6648 | 0.733830 | ||||||||
\(794\) | −32.5206 | −1.15411 | ||||||||
\(795\) | 1.57635 | 0.0559074 | ||||||||
\(796\) | 0.353108 | 0.0125156 | ||||||||
\(797\) | −9.00312 | −0.318907 | −0.159453 | − | 0.987205i | \(-0.550973\pi\) | ||||
−0.159453 | + | 0.987205i | \(0.550973\pi\) | |||||||
\(798\) | −19.0807 | −0.675450 | ||||||||
\(799\) | −3.69806 | −0.130828 | ||||||||
\(800\) | 18.7395 | 0.662541 | ||||||||
\(801\) | −83.0881 | −2.93577 | ||||||||
\(802\) | −39.3492 | −1.38947 | ||||||||
\(803\) | 7.92036 | 0.279503 | ||||||||
\(804\) | 29.2674 | 1.03218 | ||||||||
\(805\) | 0.333337 | 0.0117486 | ||||||||
\(806\) | 12.9056 | 0.454581 | ||||||||
\(807\) | 12.8917 | 0.453810 | ||||||||
\(808\) | 39.5731 | 1.39218 | ||||||||
\(809\) | −15.5861 | −0.547977 | −0.273989 | − | 0.961733i | \(-0.588343\pi\) | ||||
−0.273989 | + | 0.961733i | \(0.588343\pi\) | |||||||
\(810\) | 4.68425 | 0.164588 | ||||||||
\(811\) | 52.0440 | 1.82751 | 0.913756 | − | 0.406262i | \(-0.133168\pi\) | ||||
0.913756 | + | 0.406262i | \(0.133168\pi\) | |||||||
\(812\) | −2.93330 | −0.102939 | ||||||||
\(813\) | −106.041 | −3.71902 | ||||||||
\(814\) | −5.14682 | −0.180396 | ||||||||
\(815\) | 1.29377 | 0.0453189 | ||||||||
\(816\) | 3.75620 | 0.131493 | ||||||||
\(817\) | −34.6426 | −1.21199 | ||||||||
\(818\) | −2.14813 | −0.0751077 | ||||||||
\(819\) | 12.7463 | 0.445392 | ||||||||
\(820\) | −0.312633 | −0.0109176 | ||||||||
\(821\) | 34.8413 | 1.21597 | 0.607986 | − | 0.793948i | \(-0.291978\pi\) | ||||
0.607986 | + | 0.793948i | \(0.291978\pi\) | |||||||
\(822\) | 75.7656 | 2.64263 | ||||||||
\(823\) | 46.1931 | 1.61019 | 0.805094 | − | 0.593147i | \(-0.202115\pi\) | ||||
0.805094 | + | 0.593147i | \(0.202115\pi\) | |||||||
\(824\) | −4.44505 | −0.154851 | ||||||||
\(825\) | −17.0093 | −0.592188 | ||||||||
\(826\) | −4.55672 | −0.158548 | ||||||||
\(827\) | 42.6018 | 1.48141 | 0.740705 | − | 0.671830i | \(-0.234492\pi\) | ||||
0.740705 | + | 0.671830i | \(0.234492\pi\) | |||||||
\(828\) | 19.2617 | 0.669389 | ||||||||
\(829\) | −0.217175 | −0.00754282 | −0.00377141 | − | 0.999993i | \(-0.501200\pi\) | ||||
−0.00377141 | + | 0.999993i | \(0.501200\pi\) | |||||||
\(830\) | 0.125546 | 0.00435775 | ||||||||
\(831\) | −4.24317 | −0.147194 | ||||||||
\(832\) | 12.4922 | 0.433088 | ||||||||
\(833\) | 3.13290 | 0.108549 | ||||||||
\(834\) | 16.9766 | 0.587851 | ||||||||
\(835\) | −1.78133 | −0.0616456 | ||||||||
\(836\) | −3.42516 | −0.118462 | ||||||||
\(837\) | −147.594 | −5.10159 | ||||||||
\(838\) | 23.7149 | 0.819218 | ||||||||
\(839\) | 31.2991 | 1.08057 | 0.540283 | − | 0.841483i | \(-0.318317\pi\) | ||||
0.540283 | + | 0.841483i | \(0.318317\pi\) | |||||||
\(840\) | −1.09792 | −0.0378819 | ||||||||
\(841\) | −11.6679 | −0.402341 | ||||||||
\(842\) | 13.4332 | 0.462940 | ||||||||
\(843\) | −20.4385 | −0.703940 | ||||||||
\(844\) | 6.86817 | 0.236412 | ||||||||
\(845\) | 1.12797 | 0.0388033 | ||||||||
\(846\) | −69.4864 | −2.38899 | ||||||||
\(847\) | 1.00506 | 0.0345343 | ||||||||
\(848\) | 9.35758 | 0.321341 | ||||||||
\(849\) | −0.882457 | −0.0302858 | ||||||||
\(850\) | −2.97412 | −0.102011 | ||||||||
\(851\) | −14.3893 | −0.493259 | ||||||||
\(852\) | −26.8202 | −0.918846 | ||||||||
\(853\) | 6.56028 | 0.224620 | 0.112310 | − | 0.993673i | \(-0.464175\pi\) | ||||
0.112310 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(854\) | −16.0949 | −0.550758 | ||||||||
\(855\) | −4.38522 | −0.149971 | ||||||||
\(856\) | −3.49871 | −0.119583 | ||||||||
\(857\) | 26.9210 | 0.919604 | 0.459802 | − | 0.888021i | \(-0.347920\pi\) | ||||
0.459802 | + | 0.888021i | \(0.347920\pi\) | |||||||
\(858\) | −5.71469 | −0.195096 | ||||||||
\(859\) | 15.3834 | 0.524874 | 0.262437 | − | 0.964949i | \(-0.415474\pi\) | ||||
0.262437 | + | 0.964949i | \(0.415474\pi\) | |||||||
\(860\) | −0.517362 | −0.0176419 | ||||||||
\(861\) | −14.6811 | −0.500330 | ||||||||
\(862\) | −15.6313 | −0.532405 | ||||||||
\(863\) | −35.3756 | −1.20420 | −0.602101 | − | 0.798420i | \(-0.705669\pi\) | ||||
−0.602101 | + | 0.798420i | \(0.705669\pi\) | |||||||
\(864\) | −72.0035 | −2.44961 | ||||||||
\(865\) | −0.867771 | −0.0295051 | ||||||||
\(866\) | 33.8639 | 1.15074 | ||||||||
\(867\) | −57.0245 | −1.93666 | ||||||||
\(868\) | 5.42469 | 0.184126 | ||||||||
\(869\) | 12.9966 | 0.440880 | ||||||||
\(870\) | 1.68374 | 0.0570840 | ||||||||
\(871\) | −18.0104 | −0.610258 | ||||||||
\(872\) | −34.8079 | −1.17875 | ||||||||
\(873\) | −26.1935 | −0.886516 | ||||||||
\(874\) | 17.7436 | 0.600188 | ||||||||
\(875\) | 1.04499 | 0.0353272 | ||||||||
\(876\) | −18.9296 | −0.639571 | ||||||||
\(877\) | −10.1993 | −0.344405 | −0.172203 | − | 0.985062i | \(-0.555088\pi\) | ||||
−0.172203 | + | 0.985062i | \(0.555088\pi\) | |||||||
\(878\) | 27.9473 | 0.943177 | ||||||||
\(879\) | 62.0049 | 2.09137 | ||||||||
\(880\) | 0.219256 | 0.00739110 | ||||||||
\(881\) | 1.40982 | 0.0474981 | 0.0237491 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237491 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(882\) | 58.8670 | 1.98216 | ||||||||
\(883\) | 29.2312 | 0.983707 | 0.491853 | − | 0.870678i | \(-0.336320\pi\) | ||||
0.491853 | + | 0.870678i | \(0.336320\pi\) | |||||||
\(884\) | 0.539265 | 0.0181375 | ||||||||
\(885\) | −1.41159 | −0.0474501 | ||||||||
\(886\) | −24.4787 | −0.822379 | ||||||||
\(887\) | 20.9929 | 0.704874 | 0.352437 | − | 0.935836i | \(-0.385353\pi\) | ||||
0.352437 | + | 0.935836i | \(0.385353\pi\) | |||||||
\(888\) | 47.3944 | 1.59045 | ||||||||
\(889\) | −8.57028 | −0.287438 | ||||||||
\(890\) | −1.14307 | −0.0383157 | ||||||||
\(891\) | 39.4866 | 1.32285 | ||||||||
\(892\) | 5.20701 | 0.174344 | ||||||||
\(893\) | 34.5452 | 1.15601 | ||||||||
\(894\) | −19.8856 | −0.665073 | ||||||||
\(895\) | −0.736444 | −0.0246166 | ||||||||
\(896\) | −2.17951 | −0.0728124 | ||||||||
\(897\) | −15.9769 | −0.533453 | ||||||||
\(898\) | −0.933122 | −0.0311387 | ||||||||
\(899\) | −32.0531 | −1.06903 | ||||||||
\(900\) | 30.1594 | 1.00531 | ||||||||
\(901\) | 2.32346 | 0.0774055 | ||||||||
\(902\) | 4.88322 | 0.162594 | ||||||||
\(903\) | −24.2951 | −0.808489 | ||||||||
\(904\) | −39.3676 | −1.30935 | ||||||||
\(905\) | −1.41611 | −0.0470730 | ||||||||
\(906\) | 14.0398 | 0.466440 | ||||||||
\(907\) | 52.9372 | 1.75775 | 0.878876 | − | 0.477050i | \(-0.158294\pi\) | ||||
0.878876 | + | 0.477050i | \(0.158294\pi\) | |||||||
\(908\) | −14.7387 | −0.489121 | ||||||||
\(909\) | 110.848 | 3.67660 | ||||||||
\(910\) | 0.175355 | 0.00581295 | ||||||||
\(911\) | 13.8224 | 0.457957 | 0.228978 | − | 0.973431i | \(-0.426461\pi\) | ||||
0.228978 | + | 0.973431i | \(0.426461\pi\) | |||||||
\(912\) | −35.0883 | −1.16189 | ||||||||
\(913\) | 1.05831 | 0.0350249 | ||||||||
\(914\) | −44.6014 | −1.47528 | ||||||||
\(915\) | −4.98593 | −0.164830 | ||||||||
\(916\) | 8.16582 | 0.269806 | ||||||||
\(917\) | −1.00506 | −0.0331901 | ||||||||
\(918\) | 11.4276 | 0.377166 | ||||||||
\(919\) | 52.0476 | 1.71689 | 0.858446 | − | 0.512904i | \(-0.171430\pi\) | ||||
0.858446 | + | 0.512904i | \(0.171430\pi\) | |||||||
\(920\) | 1.02098 | 0.0336609 | ||||||||
\(921\) | −5.75911 | −0.189769 | ||||||||
\(922\) | −32.8272 | −1.08111 | ||||||||
\(923\) | 16.5045 | 0.543251 | ||||||||
\(924\) | −2.40209 | −0.0790229 | ||||||||
\(925\) | −22.5303 | −0.740793 | ||||||||
\(926\) | 26.1243 | 0.858499 | ||||||||
\(927\) | −12.4510 | −0.408945 | ||||||||
\(928\) | −15.6371 | −0.513312 | ||||||||
\(929\) | −19.0920 | −0.626389 | −0.313195 | − | 0.949689i | \(-0.601399\pi\) | ||||
−0.313195 | + | 0.949689i | \(0.601399\pi\) | |||||||
\(930\) | −3.11382 | −0.102106 | ||||||||
\(931\) | −29.2657 | −0.959146 | ||||||||
\(932\) | 1.11371 | 0.0364809 | ||||||||
\(933\) | −102.986 | −3.37162 | ||||||||
\(934\) | −21.2243 | −0.694479 | ||||||||
\(935\) | 0.0544404 | 0.00178039 | ||||||||
\(936\) | 39.0409 | 1.27609 | ||||||||
\(937\) | 2.45217 | 0.0801087 | 0.0400544 | − | 0.999198i | \(-0.487247\pi\) | ||||
0.0400544 | + | 0.999198i | \(0.487247\pi\) | |||||||
\(938\) | 14.0275 | 0.458014 | ||||||||
\(939\) | 30.0432 | 0.980422 | ||||||||
\(940\) | 0.515907 | 0.0168270 | ||||||||
\(941\) | 3.38460 | 0.110335 | 0.0551674 | − | 0.998477i | \(-0.482431\pi\) | ||||
0.0551674 | + | 0.998477i | \(0.482431\pi\) | |||||||
\(942\) | −54.5509 | −1.77737 | ||||||||
\(943\) | 13.6523 | 0.444581 | ||||||||
\(944\) | −8.37953 | −0.272730 | ||||||||
\(945\) | −2.00543 | −0.0652366 | ||||||||
\(946\) | 8.08101 | 0.262736 | ||||||||
\(947\) | 20.4572 | 0.664769 | 0.332385 | − | 0.943144i | \(-0.392147\pi\) | ||||
0.332385 | + | 0.943144i | \(0.392147\pi\) | |||||||
\(948\) | −31.0618 | −1.00884 | ||||||||
\(949\) | 11.6488 | 0.378135 | ||||||||
\(950\) | 27.7825 | 0.901383 | ||||||||
\(951\) | 20.9382 | 0.678969 | ||||||||
\(952\) | −1.61828 | −0.0524486 | ||||||||
\(953\) | −20.7523 | −0.672234 | −0.336117 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336117 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(954\) | 43.6576 | 1.41347 | ||||||||
\(955\) | 2.54826 | 0.0824597 | ||||||||
\(956\) | −14.5838 | −0.471675 | ||||||||
\(957\) | 14.1933 | 0.458805 | ||||||||
\(958\) | −29.6966 | −0.959452 | ||||||||
\(959\) | −19.5978 | −0.632846 | ||||||||
\(960\) | −3.01406 | −0.0972785 | ||||||||
\(961\) | 28.2774 | 0.912174 | ||||||||
\(962\) | −7.56962 | −0.244054 | ||||||||
\(963\) | −9.80020 | −0.315807 | ||||||||
\(964\) | 5.60287 | 0.180456 | ||||||||
\(965\) | 2.41773 | 0.0778295 | ||||||||
\(966\) | 12.4437 | 0.400370 | ||||||||
\(967\) | −39.7338 | −1.27775 | −0.638877 | − | 0.769309i | \(-0.720601\pi\) | ||||
−0.638877 | + | 0.769309i | \(0.720601\pi\) | |||||||
\(968\) | 3.07843 | 0.0989444 | ||||||||
\(969\) | −8.71230 | −0.279879 | ||||||||
\(970\) | −0.360352 | −0.0115702 | ||||||||
\(971\) | 1.99217 | 0.0639318 | 0.0319659 | − | 0.999489i | \(-0.489823\pi\) | ||||
0.0319659 | + | 0.999489i | \(0.489823\pi\) | |||||||
\(972\) | −54.0562 | −1.73385 | ||||||||
\(973\) | −4.39122 | −0.140776 | ||||||||
\(974\) | −4.30841 | −0.138050 | ||||||||
\(975\) | −25.0162 | −0.801159 | ||||||||
\(976\) | −29.5976 | −0.947397 | ||||||||
\(977\) | 14.1309 | 0.452086 | 0.226043 | − | 0.974117i | \(-0.427421\pi\) | ||||
0.226043 | + | 0.974117i | \(0.427421\pi\) | |||||||
\(978\) | 48.2976 | 1.54439 | ||||||||
\(979\) | −9.63567 | −0.307957 | ||||||||
\(980\) | −0.437063 | −0.0139615 | ||||||||
\(981\) | −97.5003 | −3.11295 | ||||||||
\(982\) | 0.00894488 | 0.000285443 0 | ||||||||
\(983\) | −4.82055 | −0.153752 | −0.0768758 | − | 0.997041i | \(-0.524494\pi\) | ||||
−0.0768758 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(984\) | −44.9671 | −1.43350 | ||||||||
\(985\) | 0.965964 | 0.0307782 | ||||||||
\(986\) | 2.48174 | 0.0790346 | ||||||||
\(987\) | 24.2267 | 0.771146 | ||||||||
\(988\) | −5.03751 | −0.160264 | ||||||||
\(989\) | 22.5926 | 0.718403 | ||||||||
\(990\) | 1.02293 | 0.0325109 | ||||||||
\(991\) | 44.8116 | 1.42349 | 0.711744 | − | 0.702439i | \(-0.247906\pi\) | ||||
0.711744 | + | 0.702439i | \(0.247906\pi\) | |||||||
\(992\) | 28.9184 | 0.918161 | ||||||||
\(993\) | 40.6265 | 1.28924 | ||||||||
\(994\) | −12.8546 | −0.407724 | ||||||||
\(995\) | 0.0524276 | 0.00166207 | ||||||||
\(996\) | −2.52934 | −0.0801453 | ||||||||
\(997\) | 30.0396 | 0.951364 | 0.475682 | − | 0.879617i | \(-0.342201\pi\) | ||||
0.475682 | + | 0.879617i | \(0.342201\pi\) | |||||||
\(998\) | −30.0016 | −0.949683 | ||||||||
\(999\) | 86.5693 | 2.73893 |
(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 | 1441.2.a.e.1.7 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.e.1.7 | ✓ | 28 | 1.1 | even | 1 | trivial |