Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75477 | −1.94792 | −0.973959 | − | 0.226722i | \(-0.927199\pi\) | ||||
−0.973959 | + | 0.226722i | \(0.927199\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.58878 | 2.79439 | ||||||||
\(5\) | −0.0622071 | −0.0278199 | −0.0139099 | − | 0.999903i | \(-0.504428\pi\) | ||||
−0.0139099 | + | 0.999903i | \(0.504428\pi\) | |||||||
\(6\) | 2.75477 | 1.12463 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.88627 | −3.49532 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.171367 | 0.0541909 | ||||||||
\(11\) | 1.07439 | 0.323941 | 0.161970 | − | 0.986796i | \(-0.448215\pi\) | ||||
0.161970 | + | 0.986796i | \(0.448215\pi\) | |||||||
\(12\) | −5.58878 | −1.61334 | ||||||||
\(13\) | 6.04155 | 1.67562 | 0.837812 | − | 0.545959i | \(-0.183835\pi\) | ||||
0.837812 | + | 0.545959i | \(0.183835\pi\) | |||||||
\(14\) | −2.75477 | −0.736244 | ||||||||
\(15\) | 0.0622071 | 0.0160618 | ||||||||
\(16\) | 16.0569 | 4.01422 | ||||||||
\(17\) | −0.508785 | −0.123399 | −0.0616993 | − | 0.998095i | \(-0.519652\pi\) | ||||
−0.0616993 | + | 0.998095i | \(0.519652\pi\) | |||||||
\(18\) | −2.75477 | −0.649306 | ||||||||
\(19\) | −4.80180 | −1.10161 | −0.550805 | − | 0.834634i | \(-0.685679\pi\) | ||||
−0.550805 | + | 0.834634i | \(0.685679\pi\) | |||||||
\(20\) | −0.347662 | −0.0777396 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −2.95970 | −0.631010 | ||||||||
\(23\) | −4.88480 | −1.01855 | −0.509275 | − | 0.860604i | \(-0.670086\pi\) | ||||
−0.509275 | + | 0.860604i | \(0.670086\pi\) | |||||||
\(24\) | 9.88627 | 2.01803 | ||||||||
\(25\) | −4.99613 | −0.999226 | ||||||||
\(26\) | −16.6431 | −3.26398 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.58878 | 1.05618 | ||||||||
\(29\) | 1.19489 | 0.221885 | 0.110942 | − | 0.993827i | \(-0.464613\pi\) | ||||
0.110942 | + | 0.993827i | \(0.464613\pi\) | |||||||
\(30\) | −0.171367 | −0.0312871 | ||||||||
\(31\) | −8.60831 | −1.54610 | −0.773049 | − | 0.634347i | \(-0.781269\pi\) | ||||
−0.773049 | + | 0.634347i | \(0.781269\pi\) | |||||||
\(32\) | −24.4605 | −4.32405 | ||||||||
\(33\) | −1.07439 | −0.187027 | ||||||||
\(34\) | 1.40159 | 0.240370 | ||||||||
\(35\) | −0.0622071 | −0.0105149 | ||||||||
\(36\) | 5.58878 | 0.931463 | ||||||||
\(37\) | −1.69413 | −0.278514 | −0.139257 | − | 0.990256i | \(-0.544471\pi\) | ||||
−0.139257 | + | 0.990256i | \(0.544471\pi\) | |||||||
\(38\) | 13.2279 | 2.14585 | ||||||||
\(39\) | −6.04155 | −0.967422 | ||||||||
\(40\) | 0.614996 | 0.0972395 | ||||||||
\(41\) | −7.00680 | −1.09428 | −0.547139 | − | 0.837042i | \(-0.684283\pi\) | ||||
−0.547139 | + | 0.837042i | \(0.684283\pi\) | |||||||
\(42\) | 2.75477 | 0.425071 | ||||||||
\(43\) | 1.99737 | 0.304595 | 0.152298 | − | 0.988335i | \(-0.451333\pi\) | ||||
0.152298 | + | 0.988335i | \(0.451333\pi\) | |||||||
\(44\) | 6.00452 | 0.905216 | ||||||||
\(45\) | −0.0622071 | −0.00927329 | ||||||||
\(46\) | 13.4565 | 1.98405 | ||||||||
\(47\) | −5.71846 | −0.834123 | −0.417061 | − | 0.908878i | \(-0.636940\pi\) | ||||
−0.417061 | + | 0.908878i | \(0.636940\pi\) | |||||||
\(48\) | −16.0569 | −2.31761 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 13.7632 | 1.94641 | ||||||||
\(51\) | 0.508785 | 0.0712442 | ||||||||
\(52\) | 33.7649 | 4.68234 | ||||||||
\(53\) | 1.01255 | 0.139085 | 0.0695424 | − | 0.997579i | \(-0.477846\pi\) | ||||
0.0695424 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(54\) | 2.75477 | 0.374877 | ||||||||
\(55\) | −0.0668347 | −0.00901199 | ||||||||
\(56\) | −9.88627 | −1.32111 | ||||||||
\(57\) | 4.80180 | 0.636015 | ||||||||
\(58\) | −3.29164 | −0.432213 | ||||||||
\(59\) | −4.82268 | −0.627860 | −0.313930 | − | 0.949446i | \(-0.601646\pi\) | ||||
−0.313930 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(60\) | 0.347662 | 0.0448830 | ||||||||
\(61\) | 6.50953 | 0.833459 | 0.416730 | − | 0.909030i | \(-0.363176\pi\) | ||||
0.416730 | + | 0.909030i | \(0.363176\pi\) | |||||||
\(62\) | 23.7139 | 3.01167 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 35.2694 | 4.40867 | ||||||||
\(65\) | −0.375827 | −0.0466157 | ||||||||
\(66\) | 2.95970 | 0.364314 | ||||||||
\(67\) | −9.27574 | −1.13321 | −0.566606 | − | 0.823989i | \(-0.691744\pi\) | ||||
−0.566606 | + | 0.823989i | \(0.691744\pi\) | |||||||
\(68\) | −2.84349 | −0.344824 | ||||||||
\(69\) | 4.88480 | 0.588060 | ||||||||
\(70\) | 0.171367 | 0.0204822 | ||||||||
\(71\) | −4.83756 | −0.574113 | −0.287056 | − | 0.957914i | \(-0.592677\pi\) | ||||
−0.287056 | + | 0.957914i | \(0.592677\pi\) | |||||||
\(72\) | −9.88627 | −1.16511 | ||||||||
\(73\) | 10.1283 | 1.18542 | 0.592712 | − | 0.805414i | \(-0.298057\pi\) | ||||
0.592712 | + | 0.805414i | \(0.298057\pi\) | |||||||
\(74\) | 4.66695 | 0.542522 | ||||||||
\(75\) | 4.99613 | 0.576903 | ||||||||
\(76\) | −26.8362 | −3.07832 | ||||||||
\(77\) | 1.07439 | 0.122438 | ||||||||
\(78\) | 16.6431 | 1.88446 | ||||||||
\(79\) | 14.9495 | 1.68195 | 0.840975 | − | 0.541074i | \(-0.181982\pi\) | ||||
0.840975 | + | 0.541074i | \(0.181982\pi\) | |||||||
\(80\) | −0.998852 | −0.111675 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 19.3021 | 2.13156 | ||||||||
\(83\) | −7.77734 | −0.853673 | −0.426837 | − | 0.904329i | \(-0.640372\pi\) | ||||
−0.426837 | + | 0.904329i | \(0.640372\pi\) | |||||||
\(84\) | −5.58878 | −0.609785 | ||||||||
\(85\) | 0.0316501 | 0.00343293 | ||||||||
\(86\) | −5.50229 | −0.593327 | ||||||||
\(87\) | −1.19489 | −0.128105 | ||||||||
\(88\) | −10.6217 | −1.13228 | ||||||||
\(89\) | −11.8515 | −1.25625 | −0.628126 | − | 0.778112i | \(-0.716178\pi\) | ||||
−0.628126 | + | 0.778112i | \(0.716178\pi\) | |||||||
\(90\) | 0.171367 | 0.0180636 | ||||||||
\(91\) | 6.04155 | 0.633326 | ||||||||
\(92\) | −27.3000 | −2.84623 | ||||||||
\(93\) | 8.60831 | 0.892640 | ||||||||
\(94\) | 15.7531 | 1.62480 | ||||||||
\(95\) | 0.298707 | 0.0306466 | ||||||||
\(96\) | 24.4605 | 2.49649 | ||||||||
\(97\) | 18.5781 | 1.88632 | 0.943162 | − | 0.332334i | \(-0.107836\pi\) | ||||
0.943162 | + | 0.332334i | \(0.107836\pi\) | |||||||
\(98\) | −2.75477 | −0.278274 | ||||||||
\(99\) | 1.07439 | 0.107980 | ||||||||
\(100\) | −27.9223 | −2.79223 | ||||||||
\(101\) | 9.37959 | 0.933304 | 0.466652 | − | 0.884441i | \(-0.345460\pi\) | ||||
0.466652 | + | 0.884441i | \(0.345460\pi\) | |||||||
\(102\) | −1.40159 | −0.138778 | ||||||||
\(103\) | 2.58365 | 0.254574 | 0.127287 | − | 0.991866i | \(-0.459373\pi\) | ||||
0.127287 | + | 0.991866i | \(0.459373\pi\) | |||||||
\(104\) | −59.7283 | −5.85685 | ||||||||
\(105\) | 0.0622071 | 0.00607080 | ||||||||
\(106\) | −2.78935 | −0.270926 | ||||||||
\(107\) | 4.00965 | 0.387627 | 0.193814 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193814 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(108\) | −5.58878 | −0.537780 | ||||||||
\(109\) | −6.55630 | −0.627980 | −0.313990 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313990 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(110\) | 0.184114 | 0.0175546 | ||||||||
\(111\) | 1.69413 | 0.160800 | ||||||||
\(112\) | 16.0569 | 1.51723 | ||||||||
\(113\) | 16.4661 | 1.54900 | 0.774502 | − | 0.632572i | \(-0.218001\pi\) | ||||
0.774502 | + | 0.632572i | \(0.218001\pi\) | |||||||
\(114\) | −13.2279 | −1.23890 | ||||||||
\(115\) | 0.303869 | 0.0283360 | ||||||||
\(116\) | 6.67795 | 0.620032 | ||||||||
\(117\) | 6.04155 | 0.558541 | ||||||||
\(118\) | 13.2854 | 1.22302 | ||||||||
\(119\) | −0.508785 | −0.0466403 | ||||||||
\(120\) | −0.614996 | −0.0561412 | ||||||||
\(121\) | −9.84569 | −0.895062 | ||||||||
\(122\) | −17.9323 | −1.62351 | ||||||||
\(123\) | 7.00680 | 0.631782 | ||||||||
\(124\) | −48.1099 | −4.32040 | ||||||||
\(125\) | 0.621831 | 0.0556182 | ||||||||
\(126\) | −2.75477 | −0.245415 | ||||||||
\(127\) | 12.8824 | 1.14313 | 0.571563 | − | 0.820558i | \(-0.306337\pi\) | ||||
0.571563 | + | 0.820558i | \(0.306337\pi\) | |||||||
\(128\) | −48.2382 | −4.26369 | ||||||||
\(129\) | −1.99737 | −0.175858 | ||||||||
\(130\) | 1.03532 | 0.0908035 | ||||||||
\(131\) | 11.8402 | 1.03448 | 0.517242 | − | 0.855839i | \(-0.326959\pi\) | ||||
0.517242 | + | 0.855839i | \(0.326959\pi\) | |||||||
\(132\) | −6.00452 | −0.522627 | ||||||||
\(133\) | −4.80180 | −0.416369 | ||||||||
\(134\) | 25.5526 | 2.20741 | ||||||||
\(135\) | 0.0622071 | 0.00535394 | ||||||||
\(136\) | 5.02999 | 0.431318 | ||||||||
\(137\) | −2.48600 | −0.212393 | −0.106197 | − | 0.994345i | \(-0.533867\pi\) | ||||
−0.106197 | + | 0.994345i | \(0.533867\pi\) | |||||||
\(138\) | −13.4565 | −1.14549 | ||||||||
\(139\) | −7.31586 | −0.620523 | −0.310262 | − | 0.950651i | \(-0.600417\pi\) | ||||
−0.310262 | + | 0.950651i | \(0.600417\pi\) | |||||||
\(140\) | −0.347662 | −0.0293828 | ||||||||
\(141\) | 5.71846 | 0.481581 | ||||||||
\(142\) | 13.3264 | 1.11832 | ||||||||
\(143\) | 6.49098 | 0.542803 | ||||||||
\(144\) | 16.0569 | 1.33807 | ||||||||
\(145\) | −0.0743304 | −0.00617281 | ||||||||
\(146\) | −27.9011 | −2.30911 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −9.46812 | −0.778275 | ||||||||
\(149\) | −1.48707 | −0.121825 | −0.0609126 | − | 0.998143i | \(-0.519401\pi\) | ||||
−0.0609126 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(150\) | −13.7632 | −1.12376 | ||||||||
\(151\) | −2.24879 | −0.183004 | −0.0915021 | − | 0.995805i | \(-0.529167\pi\) | ||||
−0.0915021 | + | 0.995805i | \(0.529167\pi\) | |||||||
\(152\) | 47.4719 | 3.85048 | ||||||||
\(153\) | −0.508785 | −0.0411329 | ||||||||
\(154\) | −2.95970 | −0.238499 | ||||||||
\(155\) | 0.535498 | 0.0430123 | ||||||||
\(156\) | −33.7649 | −2.70335 | ||||||||
\(157\) | −8.58340 | −0.685030 | −0.342515 | − | 0.939512i | \(-0.611279\pi\) | ||||
−0.342515 | + | 0.939512i | \(0.611279\pi\) | |||||||
\(158\) | −41.1825 | −3.27630 | ||||||||
\(159\) | −1.01255 | −0.0803007 | ||||||||
\(160\) | 1.52162 | 0.120294 | ||||||||
\(161\) | −4.88480 | −0.384976 | ||||||||
\(162\) | −2.75477 | −0.216435 | ||||||||
\(163\) | −4.26636 | −0.334167 | −0.167084 | − | 0.985943i | \(-0.553435\pi\) | ||||
−0.167084 | + | 0.985943i | \(0.553435\pi\) | |||||||
\(164\) | −39.1594 | −3.05784 | ||||||||
\(165\) | 0.0668347 | 0.00520308 | ||||||||
\(166\) | 21.4248 | 1.66289 | ||||||||
\(167\) | −1.84955 | −0.143123 | −0.0715613 | − | 0.997436i | \(-0.522798\pi\) | ||||
−0.0715613 | + | 0.997436i | \(0.522798\pi\) | |||||||
\(168\) | 9.88627 | 0.762742 | ||||||||
\(169\) | 23.5003 | 1.80771 | ||||||||
\(170\) | −0.0871888 | −0.00668708 | ||||||||
\(171\) | −4.80180 | −0.367203 | ||||||||
\(172\) | 11.1628 | 0.851158 | ||||||||
\(173\) | 19.9150 | 1.51411 | 0.757056 | − | 0.653350i | \(-0.226637\pi\) | ||||
0.757056 | + | 0.653350i | \(0.226637\pi\) | |||||||
\(174\) | 3.29164 | 0.249539 | ||||||||
\(175\) | −4.99613 | −0.377672 | ||||||||
\(176\) | 17.2513 | 1.30037 | ||||||||
\(177\) | 4.82268 | 0.362495 | ||||||||
\(178\) | 32.6481 | 2.44708 | ||||||||
\(179\) | −7.55740 | −0.564866 | −0.282433 | − | 0.959287i | \(-0.591142\pi\) | ||||
−0.282433 | + | 0.959287i | \(0.591142\pi\) | |||||||
\(180\) | −0.347662 | −0.0259132 | ||||||||
\(181\) | 12.6026 | 0.936742 | 0.468371 | − | 0.883532i | \(-0.344841\pi\) | ||||
0.468371 | + | 0.883532i | \(0.344841\pi\) | |||||||
\(182\) | −16.6431 | −1.23367 | ||||||||
\(183\) | −6.50953 | −0.481198 | ||||||||
\(184\) | 48.2924 | 3.56016 | ||||||||
\(185\) | 0.105387 | 0.00774821 | ||||||||
\(186\) | −23.7139 | −1.73879 | ||||||||
\(187\) | −0.546634 | −0.0399738 | ||||||||
\(188\) | −31.9592 | −2.33086 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.822869 | −0.0596972 | ||||||||
\(191\) | 9.86937 | 0.714123 | 0.357061 | − | 0.934081i | \(-0.383779\pi\) | ||||
0.357061 | + | 0.934081i | \(0.383779\pi\) | |||||||
\(192\) | −35.2694 | −2.54535 | ||||||||
\(193\) | 22.3252 | 1.60700 | 0.803502 | − | 0.595302i | \(-0.202968\pi\) | ||||
0.803502 | + | 0.595302i | \(0.202968\pi\) | |||||||
\(194\) | −51.1785 | −3.67441 | ||||||||
\(195\) | 0.375827 | 0.0269136 | ||||||||
\(196\) | 5.58878 | 0.399198 | ||||||||
\(197\) | 13.1973 | 0.940270 | 0.470135 | − | 0.882595i | \(-0.344205\pi\) | ||||
0.470135 | + | 0.882595i | \(0.344205\pi\) | |||||||
\(198\) | −2.95970 | −0.210337 | ||||||||
\(199\) | −0.635396 | −0.0450421 | −0.0225210 | − | 0.999746i | \(-0.507169\pi\) | ||||
−0.0225210 | + | 0.999746i | \(0.507169\pi\) | |||||||
\(200\) | 49.3931 | 3.49262 | ||||||||
\(201\) | 9.27574 | 0.654260 | ||||||||
\(202\) | −25.8386 | −1.81800 | ||||||||
\(203\) | 1.19489 | 0.0838645 | ||||||||
\(204\) | 2.84349 | 0.199084 | ||||||||
\(205\) | 0.435873 | 0.0304427 | ||||||||
\(206\) | −7.11737 | −0.495890 | ||||||||
\(207\) | −4.88480 | −0.339517 | ||||||||
\(208\) | 97.0083 | 6.72632 | ||||||||
\(209\) | −5.15901 | −0.356856 | ||||||||
\(210\) | −0.171367 | −0.0118254 | ||||||||
\(211\) | 25.7898 | 1.77545 | 0.887723 | − | 0.460379i | \(-0.152286\pi\) | ||||
0.887723 | + | 0.460379i | \(0.152286\pi\) | |||||||
\(212\) | 5.65893 | 0.388657 | ||||||||
\(213\) | 4.83756 | 0.331464 | ||||||||
\(214\) | −11.0457 | −0.755067 | ||||||||
\(215\) | −0.124250 | −0.00847381 | ||||||||
\(216\) | 9.88627 | 0.672675 | ||||||||
\(217\) | −8.60831 | −0.584370 | ||||||||
\(218\) | 18.0611 | 1.22325 | ||||||||
\(219\) | −10.1283 | −0.684405 | ||||||||
\(220\) | −0.373524 | −0.0251830 | ||||||||
\(221\) | −3.07385 | −0.206770 | ||||||||
\(222\) | −4.66695 | −0.313225 | ||||||||
\(223\) | 15.7070 | 1.05182 | 0.525911 | − | 0.850540i | \(-0.323725\pi\) | ||||
0.525911 | + | 0.850540i | \(0.323725\pi\) | |||||||
\(224\) | −24.4605 | −1.63434 | ||||||||
\(225\) | −4.99613 | −0.333075 | ||||||||
\(226\) | −45.3605 | −3.01733 | ||||||||
\(227\) | −2.90291 | −0.192673 | −0.0963363 | − | 0.995349i | \(-0.530712\pi\) | ||||
−0.0963363 | + | 0.995349i | \(0.530712\pi\) | |||||||
\(228\) | 26.8362 | 1.77727 | ||||||||
\(229\) | 0.832421 | 0.0550079 | 0.0275040 | − | 0.999622i | \(-0.491244\pi\) | ||||
0.0275040 | + | 0.999622i | \(0.491244\pi\) | |||||||
\(230\) | −0.837091 | −0.0551961 | ||||||||
\(231\) | −1.07439 | −0.0706896 | ||||||||
\(232\) | −11.8130 | −0.775559 | ||||||||
\(233\) | 23.8340 | 1.56142 | 0.780709 | − | 0.624894i | \(-0.214858\pi\) | ||||
0.780709 | + | 0.624894i | \(0.214858\pi\) | |||||||
\(234\) | −16.6431 | −1.08799 | ||||||||
\(235\) | 0.355729 | 0.0232052 | ||||||||
\(236\) | −26.9529 | −1.75448 | ||||||||
\(237\) | −14.9495 | −0.971075 | ||||||||
\(238\) | 1.40159 | 0.0908515 | ||||||||
\(239\) | 0.0398658 | 0.00257871 | 0.00128935 | − | 0.999999i | \(-0.499590\pi\) | ||||
0.00128935 | + | 0.999999i | \(0.499590\pi\) | |||||||
\(240\) | 0.998852 | 0.0644756 | ||||||||
\(241\) | 17.5074 | 1.12775 | 0.563877 | − | 0.825859i | \(-0.309309\pi\) | ||||
0.563877 | + | 0.825859i | \(0.309309\pi\) | |||||||
\(242\) | 27.1226 | 1.74351 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 36.3803 | 2.32901 | ||||||||
\(245\) | −0.0622071 | −0.00397427 | ||||||||
\(246\) | −19.3021 | −1.23066 | ||||||||
\(247\) | −29.0103 | −1.84588 | ||||||||
\(248\) | 85.1040 | 5.40411 | ||||||||
\(249\) | 7.77734 | 0.492869 | ||||||||
\(250\) | −1.71300 | −0.108340 | ||||||||
\(251\) | 29.0199 | 1.83172 | 0.915860 | − | 0.401498i | \(-0.131510\pi\) | ||||
0.915860 | + | 0.401498i | \(0.131510\pi\) | |||||||
\(252\) | 5.58878 | 0.352060 | ||||||||
\(253\) | −5.24817 | −0.329950 | ||||||||
\(254\) | −35.4881 | −2.22672 | ||||||||
\(255\) | −0.0316501 | −0.00198201 | ||||||||
\(256\) | 62.3465 | 3.89666 | ||||||||
\(257\) | 25.5866 | 1.59605 | 0.798023 | − | 0.602626i | \(-0.205879\pi\) | ||||
0.798023 | + | 0.602626i | \(0.205879\pi\) | |||||||
\(258\) | 5.50229 | 0.342558 | ||||||||
\(259\) | −1.69413 | −0.105268 | ||||||||
\(260\) | −2.10042 | −0.130262 | ||||||||
\(261\) | 1.19489 | 0.0739616 | ||||||||
\(262\) | −32.6171 | −2.01509 | ||||||||
\(263\) | −2.33319 | −0.143871 | −0.0719353 | − | 0.997409i | \(-0.522918\pi\) | ||||
−0.0719353 | + | 0.997409i | \(0.522918\pi\) | |||||||
\(264\) | 10.6217 | 0.653720 | ||||||||
\(265\) | −0.0629880 | −0.00386932 | ||||||||
\(266\) | 13.2279 | 0.811054 | ||||||||
\(267\) | 11.8515 | 0.725297 | ||||||||
\(268\) | −51.8400 | −3.16664 | ||||||||
\(269\) | −18.4044 | −1.12213 | −0.561067 | − | 0.827770i | \(-0.689609\pi\) | ||||
−0.561067 | + | 0.827770i | \(0.689609\pi\) | |||||||
\(270\) | −0.171367 | −0.0104290 | ||||||||
\(271\) | 25.4471 | 1.54580 | 0.772901 | − | 0.634526i | \(-0.218805\pi\) | ||||
0.772901 | + | 0.634526i | \(0.218805\pi\) | |||||||
\(272\) | −8.16950 | −0.495349 | ||||||||
\(273\) | −6.04155 | −0.365651 | ||||||||
\(274\) | 6.84836 | 0.413724 | ||||||||
\(275\) | −5.36779 | −0.323690 | ||||||||
\(276\) | 27.3000 | 1.64327 | ||||||||
\(277\) | −14.0025 | −0.841329 | −0.420664 | − | 0.907216i | \(-0.638203\pi\) | ||||
−0.420664 | + | 0.907216i | \(0.638203\pi\) | |||||||
\(278\) | 20.1535 | 1.20873 | ||||||||
\(279\) | −8.60831 | −0.515366 | ||||||||
\(280\) | 0.614996 | 0.0367531 | ||||||||
\(281\) | −8.32382 | −0.496557 | −0.248279 | − | 0.968689i | \(-0.579865\pi\) | ||||
−0.248279 | + | 0.968689i | \(0.579865\pi\) | |||||||
\(282\) | −15.7531 | −0.938081 | ||||||||
\(283\) | −20.0741 | −1.19328 | −0.596640 | − | 0.802509i | \(-0.703498\pi\) | ||||
−0.596640 | + | 0.802509i | \(0.703498\pi\) | |||||||
\(284\) | −27.0360 | −1.60429 | ||||||||
\(285\) | −0.298707 | −0.0176938 | ||||||||
\(286\) | −17.8812 | −1.05734 | ||||||||
\(287\) | −7.00680 | −0.413598 | ||||||||
\(288\) | −24.4605 | −1.44135 | ||||||||
\(289\) | −16.7411 | −0.984773 | ||||||||
\(290\) | 0.204764 | 0.0120241 | ||||||||
\(291\) | −18.5781 | −1.08907 | ||||||||
\(292\) | 56.6046 | 3.31254 | ||||||||
\(293\) | 9.30777 | 0.543766 | 0.271883 | − | 0.962330i | \(-0.412354\pi\) | ||||
0.271883 | + | 0.962330i | \(0.412354\pi\) | |||||||
\(294\) | 2.75477 | 0.160662 | ||||||||
\(295\) | 0.300005 | 0.0174670 | ||||||||
\(296\) | 16.7486 | 0.973495 | ||||||||
\(297\) | −1.07439 | −0.0623424 | ||||||||
\(298\) | 4.09653 | 0.237306 | ||||||||
\(299\) | −29.5117 | −1.70671 | ||||||||
\(300\) | 27.9223 | 1.61209 | ||||||||
\(301\) | 1.99737 | 0.115126 | ||||||||
\(302\) | 6.19491 | 0.356477 | ||||||||
\(303\) | −9.37959 | −0.538843 | ||||||||
\(304\) | −77.1019 | −4.42210 | ||||||||
\(305\) | −0.404939 | −0.0231867 | ||||||||
\(306\) | 1.40159 | 0.0801235 | ||||||||
\(307\) | −0.0661153 | −0.00377340 | −0.00188670 | − | 0.999998i | \(-0.500601\pi\) | ||||
−0.00188670 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(308\) | 6.00452 | 0.342139 | ||||||||
\(309\) | −2.58365 | −0.146979 | ||||||||
\(310\) | −1.47518 | −0.0837844 | ||||||||
\(311\) | −25.7491 | −1.46010 | −0.730049 | − | 0.683395i | \(-0.760503\pi\) | ||||
−0.730049 | + | 0.683395i | \(0.760503\pi\) | |||||||
\(312\) | 59.7283 | 3.38145 | ||||||||
\(313\) | −24.2429 | −1.37029 | −0.685144 | − | 0.728408i | \(-0.740261\pi\) | ||||
−0.685144 | + | 0.728408i | \(0.740261\pi\) | |||||||
\(314\) | 23.6453 | 1.33438 | ||||||||
\(315\) | −0.0622071 | −0.00350498 | ||||||||
\(316\) | 83.5494 | 4.70002 | ||||||||
\(317\) | 31.7699 | 1.78437 | 0.892187 | − | 0.451666i | \(-0.149170\pi\) | ||||
0.892187 | + | 0.451666i | \(0.149170\pi\) | |||||||
\(318\) | 2.78935 | 0.156419 | ||||||||
\(319\) | 1.28377 | 0.0718775 | ||||||||
\(320\) | −2.19401 | −0.122649 | ||||||||
\(321\) | −4.00965 | −0.223797 | ||||||||
\(322\) | 13.4565 | 0.749902 | ||||||||
\(323\) | 2.44309 | 0.135937 | ||||||||
\(324\) | 5.58878 | 0.310488 | ||||||||
\(325\) | −30.1844 | −1.67433 | ||||||||
\(326\) | 11.7529 | 0.650931 | ||||||||
\(327\) | 6.55630 | 0.362564 | ||||||||
\(328\) | 69.2711 | 3.82485 | ||||||||
\(329\) | −5.71846 | −0.315269 | ||||||||
\(330\) | −0.184114 | −0.0101352 | ||||||||
\(331\) | −34.8179 | −1.91377 | −0.956883 | − | 0.290473i | \(-0.906187\pi\) | ||||
−0.956883 | + | 0.290473i | \(0.906187\pi\) | |||||||
\(332\) | −43.4658 | −2.38550 | ||||||||
\(333\) | −1.69413 | −0.0928378 | ||||||||
\(334\) | 5.09509 | 0.278791 | ||||||||
\(335\) | 0.577018 | 0.0315258 | ||||||||
\(336\) | −16.0569 | −0.875974 | ||||||||
\(337\) | 23.4163 | 1.27557 | 0.637784 | − | 0.770215i | \(-0.279851\pi\) | ||||
0.637784 | + | 0.770215i | \(0.279851\pi\) | |||||||
\(338\) | −64.7380 | −3.52128 | ||||||||
\(339\) | −16.4661 | −0.894318 | ||||||||
\(340\) | 0.176885 | 0.00959295 | ||||||||
\(341\) | −9.24868 | −0.500844 | ||||||||
\(342\) | 13.2279 | 0.715282 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −19.7465 | −1.06466 | ||||||||
\(345\) | −0.303869 | −0.0163598 | ||||||||
\(346\) | −54.8614 | −2.94937 | ||||||||
\(347\) | 24.2861 | 1.30375 | 0.651874 | − | 0.758327i | \(-0.273983\pi\) | ||||
0.651874 | + | 0.758327i | \(0.273983\pi\) | |||||||
\(348\) | −6.67795 | −0.357976 | ||||||||
\(349\) | −17.1955 | −0.920454 | −0.460227 | − | 0.887801i | \(-0.652232\pi\) | ||||
−0.460227 | + | 0.887801i | \(0.652232\pi\) | |||||||
\(350\) | 13.7632 | 0.735674 | ||||||||
\(351\) | −6.04155 | −0.322474 | ||||||||
\(352\) | −26.2801 | −1.40073 | ||||||||
\(353\) | −4.36982 | −0.232582 | −0.116291 | − | 0.993215i | \(-0.537101\pi\) | ||||
−0.116291 | + | 0.993215i | \(0.537101\pi\) | |||||||
\(354\) | −13.2854 | −0.706111 | ||||||||
\(355\) | 0.300931 | 0.0159717 | ||||||||
\(356\) | −66.2351 | −3.51045 | ||||||||
\(357\) | 0.508785 | 0.0269278 | ||||||||
\(358\) | 20.8189 | 1.10031 | ||||||||
\(359\) | 25.6589 | 1.35422 | 0.677112 | − | 0.735880i | \(-0.263231\pi\) | ||||
0.677112 | + | 0.735880i | \(0.263231\pi\) | |||||||
\(360\) | 0.614996 | 0.0324132 | ||||||||
\(361\) | 4.05732 | 0.213543 | ||||||||
\(362\) | −34.7172 | −1.82470 | ||||||||
\(363\) | 9.84569 | 0.516765 | ||||||||
\(364\) | 33.7649 | 1.76976 | ||||||||
\(365\) | −0.630051 | −0.0329784 | ||||||||
\(366\) | 17.9323 | 0.937335 | ||||||||
\(367\) | 13.3943 | 0.699177 | 0.349589 | − | 0.936903i | \(-0.386321\pi\) | ||||
0.349589 | + | 0.936903i | \(0.386321\pi\) | |||||||
\(368\) | −78.4345 | −4.08868 | ||||||||
\(369\) | −7.00680 | −0.364759 | ||||||||
\(370\) | −0.290318 | −0.0150929 | ||||||||
\(371\) | 1.01255 | 0.0525691 | ||||||||
\(372\) | 48.1099 | 2.49438 | ||||||||
\(373\) | −27.9726 | −1.44837 | −0.724184 | − | 0.689606i | \(-0.757784\pi\) | ||||
−0.724184 | + | 0.689606i | \(0.757784\pi\) | |||||||
\(374\) | 1.50585 | 0.0778658 | ||||||||
\(375\) | −0.621831 | −0.0321112 | ||||||||
\(376\) | 56.5342 | 2.91553 | ||||||||
\(377\) | 7.21896 | 0.371795 | ||||||||
\(378\) | 2.75477 | 0.141690 | ||||||||
\(379\) | −17.3497 | −0.891195 | −0.445598 | − | 0.895233i | \(-0.647009\pi\) | ||||
−0.445598 | + | 0.895233i | \(0.647009\pi\) | |||||||
\(380\) | 1.66940 | 0.0856386 | ||||||||
\(381\) | −12.8824 | −0.659985 | ||||||||
\(382\) | −27.1879 | −1.39105 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 48.2382 | 2.46165 | ||||||||
\(385\) | −0.0668347 | −0.00340621 | ||||||||
\(386\) | −61.5009 | −3.13031 | ||||||||
\(387\) | 1.99737 | 0.101532 | ||||||||
\(388\) | 103.829 | 5.27112 | ||||||||
\(389\) | 25.7331 | 1.30472 | 0.652360 | − | 0.757909i | \(-0.273779\pi\) | ||||
0.652360 | + | 0.757909i | \(0.273779\pi\) | |||||||
\(390\) | −1.03532 | −0.0524254 | ||||||||
\(391\) | 2.48531 | 0.125688 | ||||||||
\(392\) | −9.88627 | −0.499332 | ||||||||
\(393\) | −11.8402 | −0.597260 | ||||||||
\(394\) | −36.3556 | −1.83157 | ||||||||
\(395\) | −0.929966 | −0.0467917 | ||||||||
\(396\) | 6.00452 | 0.301739 | ||||||||
\(397\) | −24.5190 | −1.23057 | −0.615286 | − | 0.788304i | \(-0.710960\pi\) | ||||
−0.615286 | + | 0.788304i | \(0.710960\pi\) | |||||||
\(398\) | 1.75037 | 0.0877383 | ||||||||
\(399\) | 4.80180 | 0.240391 | ||||||||
\(400\) | −80.2222 | −4.01111 | ||||||||
\(401\) | 22.3210 | 1.11466 | 0.557329 | − | 0.830291i | \(-0.311826\pi\) | ||||
0.557329 | + | 0.830291i | \(0.311826\pi\) | |||||||
\(402\) | −25.5526 | −1.27445 | ||||||||
\(403\) | −52.0075 | −2.59068 | ||||||||
\(404\) | 52.4204 | 2.60801 | ||||||||
\(405\) | −0.0622071 | −0.00309110 | ||||||||
\(406\) | −3.29164 | −0.163361 | ||||||||
\(407\) | −1.82016 | −0.0902218 | ||||||||
\(408\) | −5.02999 | −0.249022 | ||||||||
\(409\) | −7.39770 | −0.365793 | −0.182896 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182896 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(410\) | −1.20073 | −0.0592999 | ||||||||
\(411\) | 2.48600 | 0.122625 | ||||||||
\(412\) | 14.4394 | 0.711380 | ||||||||
\(413\) | −4.82268 | −0.237309 | ||||||||
\(414\) | 13.4565 | 0.661351 | ||||||||
\(415\) | 0.483806 | 0.0237491 | ||||||||
\(416\) | −147.779 | −7.24547 | ||||||||
\(417\) | 7.31586 | 0.358259 | ||||||||
\(418\) | 14.2119 | 0.695127 | ||||||||
\(419\) | −14.3909 | −0.703040 | −0.351520 | − | 0.936180i | \(-0.614335\pi\) | ||||
−0.351520 | + | 0.936180i | \(0.614335\pi\) | |||||||
\(420\) | 0.347662 | 0.0169642 | ||||||||
\(421\) | 14.7365 | 0.718212 | 0.359106 | − | 0.933297i | \(-0.383082\pi\) | ||||
0.359106 | + | 0.933297i | \(0.383082\pi\) | |||||||
\(422\) | −71.0451 | −3.45842 | ||||||||
\(423\) | −5.71846 | −0.278041 | ||||||||
\(424\) | −10.0104 | −0.486146 | ||||||||
\(425\) | 2.54196 | 0.123303 | ||||||||
\(426\) | −13.3264 | −0.645665 | ||||||||
\(427\) | 6.50953 | 0.315018 | ||||||||
\(428\) | 22.4090 | 1.08318 | ||||||||
\(429\) | −6.49098 | −0.313387 | ||||||||
\(430\) | 0.342282 | 0.0165063 | ||||||||
\(431\) | −33.1881 | −1.59861 | −0.799307 | − | 0.600924i | \(-0.794800\pi\) | ||||
−0.799307 | + | 0.600924i | \(0.794800\pi\) | |||||||
\(432\) | −16.0569 | −0.772536 | ||||||||
\(433\) | 35.3732 | 1.69993 | 0.849963 | − | 0.526842i | \(-0.176624\pi\) | ||||
0.849963 | + | 0.526842i | \(0.176624\pi\) | |||||||
\(434\) | 23.7139 | 1.13831 | ||||||||
\(435\) | 0.0743304 | 0.00356387 | ||||||||
\(436\) | −36.6417 | −1.75482 | ||||||||
\(437\) | 23.4558 | 1.12204 | ||||||||
\(438\) | 27.9011 | 1.33317 | ||||||||
\(439\) | −13.2140 | −0.630672 | −0.315336 | − | 0.948980i | \(-0.602117\pi\) | ||||
−0.315336 | + | 0.948980i | \(0.602117\pi\) | |||||||
\(440\) | 0.660746 | 0.0314998 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 8.46776 | 0.402770 | ||||||||
\(443\) | 17.3294 | 0.823345 | 0.411672 | − | 0.911332i | \(-0.364945\pi\) | ||||
0.411672 | + | 0.911332i | \(0.364945\pi\) | |||||||
\(444\) | 9.46812 | 0.449337 | ||||||||
\(445\) | 0.737245 | 0.0349488 | ||||||||
\(446\) | −43.2694 | −2.04886 | ||||||||
\(447\) | 1.48707 | 0.0703358 | ||||||||
\(448\) | 35.2694 | 1.66632 | ||||||||
\(449\) | 19.7160 | 0.930458 | 0.465229 | − | 0.885190i | \(-0.345972\pi\) | ||||
0.465229 | + | 0.885190i | \(0.345972\pi\) | |||||||
\(450\) | 13.7632 | 0.648804 | ||||||||
\(451\) | −7.52803 | −0.354481 | ||||||||
\(452\) | 92.0256 | 4.32852 | ||||||||
\(453\) | 2.24879 | 0.105657 | ||||||||
\(454\) | 7.99685 | 0.375311 | ||||||||
\(455\) | −0.375827 | −0.0176191 | ||||||||
\(456\) | −47.4719 | −2.22308 | ||||||||
\(457\) | −13.0019 | −0.608203 | −0.304101 | − | 0.952640i | \(-0.598356\pi\) | ||||
−0.304101 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(458\) | −2.29313 | −0.107151 | ||||||||
\(459\) | 0.508785 | 0.0237481 | ||||||||
\(460\) | 1.69826 | 0.0791817 | ||||||||
\(461\) | −33.8132 | −1.57484 | −0.787420 | − | 0.616417i | \(-0.788584\pi\) | ||||
−0.787420 | + | 0.616417i | \(0.788584\pi\) | |||||||
\(462\) | 2.95970 | 0.137698 | ||||||||
\(463\) | 11.4436 | 0.531830 | 0.265915 | − | 0.963996i | \(-0.414326\pi\) | ||||
0.265915 | + | 0.963996i | \(0.414326\pi\) | |||||||
\(464\) | 19.1861 | 0.890693 | ||||||||
\(465\) | −0.535498 | −0.0248331 | ||||||||
\(466\) | −65.6573 | −3.04152 | ||||||||
\(467\) | −1.63772 | −0.0757848 | −0.0378924 | − | 0.999282i | \(-0.512064\pi\) | ||||
−0.0378924 | + | 0.999282i | \(0.512064\pi\) | |||||||
\(468\) | 33.7649 | 1.56078 | ||||||||
\(469\) | −9.27574 | −0.428314 | ||||||||
\(470\) | −0.979953 | −0.0452018 | ||||||||
\(471\) | 8.58340 | 0.395502 | ||||||||
\(472\) | 47.6783 | 2.19457 | ||||||||
\(473\) | 2.14595 | 0.0986709 | ||||||||
\(474\) | 41.1825 | 1.89157 | ||||||||
\(475\) | 23.9904 | 1.10076 | ||||||||
\(476\) | −2.84349 | −0.130331 | ||||||||
\(477\) | 1.01255 | 0.0463616 | ||||||||
\(478\) | −0.109821 | −0.00502311 | ||||||||
\(479\) | −17.0378 | −0.778476 | −0.389238 | − | 0.921137i | \(-0.627262\pi\) | ||||
−0.389238 | + | 0.921137i | \(0.627262\pi\) | |||||||
\(480\) | −1.52162 | −0.0694520 | ||||||||
\(481\) | −10.2352 | −0.466684 | ||||||||
\(482\) | −48.2290 | −2.19677 | ||||||||
\(483\) | 4.88480 | 0.222266 | ||||||||
\(484\) | −55.0253 | −2.50115 | ||||||||
\(485\) | −1.15569 | −0.0524773 | ||||||||
\(486\) | 2.75477 | 0.124959 | ||||||||
\(487\) | 10.1822 | 0.461398 | 0.230699 | − | 0.973025i | \(-0.425899\pi\) | ||||
0.230699 | + | 0.973025i | \(0.425899\pi\) | |||||||
\(488\) | −64.3549 | −2.91321 | ||||||||
\(489\) | 4.26636 | 0.192932 | ||||||||
\(490\) | 0.171367 | 0.00774155 | ||||||||
\(491\) | −9.69862 | −0.437693 | −0.218846 | − | 0.975759i | \(-0.570229\pi\) | ||||
−0.218846 | + | 0.975759i | \(0.570229\pi\) | |||||||
\(492\) | 39.1594 | 1.76544 | ||||||||
\(493\) | −0.607941 | −0.0273803 | ||||||||
\(494\) | 79.9169 | 3.59563 | ||||||||
\(495\) | −0.0668347 | −0.00300400 | ||||||||
\(496\) | −138.222 | −6.20637 | ||||||||
\(497\) | −4.83756 | −0.216994 | ||||||||
\(498\) | −21.4248 | −0.960068 | ||||||||
\(499\) | 14.2515 | 0.637984 | 0.318992 | − | 0.947757i | \(-0.396656\pi\) | ||||
0.318992 | + | 0.947757i | \(0.396656\pi\) | |||||||
\(500\) | 3.47527 | 0.155419 | ||||||||
\(501\) | 1.84955 | 0.0826319 | ||||||||
\(502\) | −79.9433 | −3.56804 | ||||||||
\(503\) | 0.233948 | 0.0104312 | 0.00521562 | − | 0.999986i | \(-0.498340\pi\) | ||||
0.00521562 | + | 0.999986i | \(0.498340\pi\) | |||||||
\(504\) | −9.88627 | −0.440369 | ||||||||
\(505\) | −0.583477 | −0.0259644 | ||||||||
\(506\) | 14.4575 | 0.642716 | ||||||||
\(507\) | −23.5003 | −1.04368 | ||||||||
\(508\) | 71.9968 | 3.19434 | ||||||||
\(509\) | 24.2402 | 1.07443 | 0.537213 | − | 0.843446i | \(-0.319477\pi\) | ||||
0.537213 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(510\) | 0.0871888 | 0.00386079 | ||||||||
\(511\) | 10.1283 | 0.448048 | ||||||||
\(512\) | −75.2741 | −3.32668 | ||||||||
\(513\) | 4.80180 | 0.212005 | ||||||||
\(514\) | −70.4852 | −3.10897 | ||||||||
\(515\) | −0.160721 | −0.00708223 | ||||||||
\(516\) | −11.1628 | −0.491416 | ||||||||
\(517\) | −6.14385 | −0.270206 | ||||||||
\(518\) | 4.66695 | 0.205054 | ||||||||
\(519\) | −19.9150 | −0.874173 | ||||||||
\(520\) | 3.71553 | 0.162937 | ||||||||
\(521\) | −12.9339 | −0.566643 | −0.283322 | − | 0.959025i | \(-0.591436\pi\) | ||||
−0.283322 | + | 0.959025i | \(0.591436\pi\) | |||||||
\(522\) | −3.29164 | −0.144071 | ||||||||
\(523\) | −5.15784 | −0.225537 | −0.112768 | − | 0.993621i | \(-0.535972\pi\) | ||||
−0.112768 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(524\) | 66.1723 | 2.89075 | ||||||||
\(525\) | 4.99613 | 0.218049 | ||||||||
\(526\) | 6.42741 | 0.280248 | ||||||||
\(527\) | 4.37978 | 0.190786 | ||||||||
\(528\) | −17.2513 | −0.750768 | ||||||||
\(529\) | 0.861235 | 0.0374450 | ||||||||
\(530\) | 0.173518 | 0.00753713 | ||||||||
\(531\) | −4.82268 | −0.209287 | ||||||||
\(532\) | −26.8362 | −1.16350 | ||||||||
\(533\) | −42.3319 | −1.83360 | ||||||||
\(534\) | −32.6481 | −1.41282 | ||||||||
\(535\) | −0.249429 | −0.0107837 | ||||||||
\(536\) | 91.7024 | 3.96094 | ||||||||
\(537\) | 7.55740 | 0.326126 | ||||||||
\(538\) | 50.6998 | 2.18583 | ||||||||
\(539\) | 1.07439 | 0.0462772 | ||||||||
\(540\) | 0.347662 | 0.0149610 | ||||||||
\(541\) | −4.79752 | −0.206261 | −0.103131 | − | 0.994668i | \(-0.532886\pi\) | ||||
−0.103131 | + | 0.994668i | \(0.532886\pi\) | |||||||
\(542\) | −70.1011 | −3.01110 | ||||||||
\(543\) | −12.6026 | −0.540828 | ||||||||
\(544\) | 12.4451 | 0.533581 | ||||||||
\(545\) | 0.407849 | 0.0174703 | ||||||||
\(546\) | 16.6431 | 0.712259 | ||||||||
\(547\) | 4.32095 | 0.184750 | 0.0923752 | − | 0.995724i | \(-0.470554\pi\) | ||||
0.0923752 | + | 0.995724i | \(0.470554\pi\) | |||||||
\(548\) | −13.8937 | −0.593509 | ||||||||
\(549\) | 6.50953 | 0.277820 | ||||||||
\(550\) | 14.7870 | 0.630522 | ||||||||
\(551\) | −5.73761 | −0.244430 | ||||||||
\(552\) | −48.2924 | −2.05546 | ||||||||
\(553\) | 14.9495 | 0.635718 | ||||||||
\(554\) | 38.5737 | 1.63884 | ||||||||
\(555\) | −0.105387 | −0.00447343 | ||||||||
\(556\) | −40.8867 | −1.73398 | ||||||||
\(557\) | −43.3862 | −1.83833 | −0.919167 | − | 0.393869i | \(-0.871137\pi\) | ||||
−0.919167 | + | 0.393869i | \(0.871137\pi\) | |||||||
\(558\) | 23.7139 | 1.00389 | ||||||||
\(559\) | 12.0672 | 0.510387 | ||||||||
\(560\) | −0.998852 | −0.0422092 | ||||||||
\(561\) | 0.546634 | 0.0230789 | ||||||||
\(562\) | 22.9302 | 0.967254 | ||||||||
\(563\) | 37.4142 | 1.57682 | 0.788411 | − | 0.615149i | \(-0.210904\pi\) | ||||
0.788411 | + | 0.615149i | \(0.210904\pi\) | |||||||
\(564\) | 31.9592 | 1.34572 | ||||||||
\(565\) | −1.02431 | −0.0430931 | ||||||||
\(566\) | 55.2995 | 2.32441 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 47.8254 | 2.00671 | ||||||||
\(569\) | −22.8628 | −0.958459 | −0.479229 | − | 0.877690i | \(-0.659084\pi\) | ||||
−0.479229 | + | 0.877690i | \(0.659084\pi\) | |||||||
\(570\) | 0.822869 | 0.0344662 | ||||||||
\(571\) | 8.08011 | 0.338142 | 0.169071 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169071 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(572\) | 36.2766 | 1.51680 | ||||||||
\(573\) | −9.86937 | −0.412299 | ||||||||
\(574\) | 19.3021 | 0.805656 | ||||||||
\(575\) | 24.4051 | 1.01776 | ||||||||
\(576\) | 35.2694 | 1.46956 | ||||||||
\(577\) | 30.7327 | 1.27942 | 0.639710 | − | 0.768616i | \(-0.279054\pi\) | ||||
0.639710 | + | 0.768616i | \(0.279054\pi\) | |||||||
\(578\) | 46.1180 | 1.91826 | ||||||||
\(579\) | −22.3252 | −0.927804 | ||||||||
\(580\) | −0.415416 | −0.0172492 | ||||||||
\(581\) | −7.77734 | −0.322658 | ||||||||
\(582\) | 51.1785 | 2.12142 | ||||||||
\(583\) | 1.08788 | 0.0450552 | ||||||||
\(584\) | −100.131 | −4.14344 | ||||||||
\(585\) | −0.375827 | −0.0155386 | ||||||||
\(586\) | −25.6408 | −1.05921 | ||||||||
\(587\) | 30.8287 | 1.27243 | 0.636217 | − | 0.771510i | \(-0.280498\pi\) | ||||
0.636217 | + | 0.771510i | \(0.280498\pi\) | |||||||
\(588\) | −5.58878 | −0.230477 | ||||||||
\(589\) | 41.3354 | 1.70320 | ||||||||
\(590\) | −0.826446 | −0.0340243 | ||||||||
\(591\) | −13.1973 | −0.542865 | ||||||||
\(592\) | −27.2024 | −1.11801 | ||||||||
\(593\) | −8.50164 | −0.349120 | −0.174560 | − | 0.984647i | \(-0.555850\pi\) | ||||
−0.174560 | + | 0.984647i | \(0.555850\pi\) | |||||||
\(594\) | 2.95970 | 0.121438 | ||||||||
\(595\) | 0.0316501 | 0.00129753 | ||||||||
\(596\) | −8.31088 | −0.340427 | ||||||||
\(597\) | 0.635396 | 0.0260050 | ||||||||
\(598\) | 81.2981 | 3.32453 | ||||||||
\(599\) | −12.3139 | −0.503131 | −0.251565 | − | 0.967840i | \(-0.580945\pi\) | ||||
−0.251565 | + | 0.967840i | \(0.580945\pi\) | |||||||
\(600\) | −49.3931 | −2.01646 | ||||||||
\(601\) | −34.8192 | −1.42030 | −0.710152 | − | 0.704048i | \(-0.751374\pi\) | ||||
−0.710152 | + | 0.704048i | \(0.751374\pi\) | |||||||
\(602\) | −5.50229 | −0.224257 | ||||||||
\(603\) | −9.27574 | −0.377737 | ||||||||
\(604\) | −12.5680 | −0.511385 | ||||||||
\(605\) | 0.612472 | 0.0249005 | ||||||||
\(606\) | 25.8386 | 1.04962 | ||||||||
\(607\) | 44.2362 | 1.79549 | 0.897746 | − | 0.440513i | \(-0.145204\pi\) | ||||
0.897746 | + | 0.440513i | \(0.145204\pi\) | |||||||
\(608\) | 117.455 | 4.76341 | ||||||||
\(609\) | −1.19489 | −0.0484192 | ||||||||
\(610\) | 1.11552 | 0.0451659 | ||||||||
\(611\) | −34.5483 | −1.39768 | ||||||||
\(612\) | −2.84349 | −0.114941 | ||||||||
\(613\) | 0.0580635 | 0.00234516 | 0.00117258 | − | 0.999999i | \(-0.499627\pi\) | ||||
0.00117258 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(614\) | 0.182133 | 0.00735027 | ||||||||
\(615\) | −0.435873 | −0.0175761 | ||||||||
\(616\) | −10.6217 | −0.427960 | ||||||||
\(617\) | −15.9111 | −0.640555 | −0.320278 | − | 0.947324i | \(-0.603776\pi\) | ||||
−0.320278 | + | 0.947324i | \(0.603776\pi\) | |||||||
\(618\) | 7.11737 | 0.286302 | ||||||||
\(619\) | 39.8889 | 1.60327 | 0.801636 | − | 0.597813i | \(-0.203963\pi\) | ||||
0.801636 | + | 0.597813i | \(0.203963\pi\) | |||||||
\(620\) | 2.99278 | 0.120193 | ||||||||
\(621\) | 4.88480 | 0.196020 | ||||||||
\(622\) | 70.9329 | 2.84415 | ||||||||
\(623\) | −11.8515 | −0.474818 | ||||||||
\(624\) | −97.0083 | −3.88344 | ||||||||
\(625\) | 24.9420 | 0.997679 | ||||||||
\(626\) | 66.7836 | 2.66921 | ||||||||
\(627\) | 5.15901 | 0.206031 | ||||||||
\(628\) | −47.9707 | −1.91424 | ||||||||
\(629\) | 0.861949 | 0.0343682 | ||||||||
\(630\) | 0.171367 | 0.00682741 | ||||||||
\(631\) | −5.43344 | −0.216302 | −0.108151 | − | 0.994134i | \(-0.534493\pi\) | ||||
−0.108151 | + | 0.994134i | \(0.534493\pi\) | |||||||
\(632\) | −147.795 | −5.87896 | ||||||||
\(633\) | −25.7898 | −1.02505 | ||||||||
\(634\) | −87.5188 | −3.47582 | ||||||||
\(635\) | −0.801376 | −0.0318017 | ||||||||
\(636\) | −5.65893 | −0.224391 | ||||||||
\(637\) | 6.04155 | 0.239375 | ||||||||
\(638\) | −3.53650 | −0.140012 | ||||||||
\(639\) | −4.83756 | −0.191371 | ||||||||
\(640\) | 3.00076 | 0.118615 | ||||||||
\(641\) | 28.7454 | 1.13537 | 0.567687 | − | 0.823245i | \(-0.307839\pi\) | ||||
0.567687 | + | 0.823245i | \(0.307839\pi\) | |||||||
\(642\) | 11.0457 | 0.435938 | ||||||||
\(643\) | 13.5003 | 0.532402 | 0.266201 | − | 0.963918i | \(-0.414232\pi\) | ||||
0.266201 | + | 0.963918i | \(0.414232\pi\) | |||||||
\(644\) | −27.3000 | −1.07577 | ||||||||
\(645\) | 0.124250 | 0.00489236 | ||||||||
\(646\) | −6.73015 | −0.264794 | ||||||||
\(647\) | 16.6769 | 0.655635 | 0.327817 | − | 0.944741i | \(-0.393687\pi\) | ||||
0.327817 | + | 0.944741i | \(0.393687\pi\) | |||||||
\(648\) | −9.88627 | −0.388369 | ||||||||
\(649\) | −5.18144 | −0.203389 | ||||||||
\(650\) | 83.1511 | 3.26145 | ||||||||
\(651\) | 8.60831 | 0.337386 | ||||||||
\(652\) | −23.8438 | −0.933793 | ||||||||
\(653\) | 10.1477 | 0.397111 | 0.198556 | − | 0.980090i | \(-0.436375\pi\) | ||||
0.198556 | + | 0.980090i | \(0.436375\pi\) | |||||||
\(654\) | −18.0611 | −0.706246 | ||||||||
\(655\) | −0.736546 | −0.0287792 | ||||||||
\(656\) | −112.507 | −4.39267 | ||||||||
\(657\) | 10.1283 | 0.395142 | ||||||||
\(658\) | 15.7531 | 0.614118 | ||||||||
\(659\) | 24.5050 | 0.954578 | 0.477289 | − | 0.878746i | \(-0.341619\pi\) | ||||
0.477289 | + | 0.878746i | \(0.341619\pi\) | |||||||
\(660\) | 0.373524 | 0.0145394 | ||||||||
\(661\) | 46.8349 | 1.82167 | 0.910834 | − | 0.412773i | \(-0.135440\pi\) | ||||
0.910834 | + | 0.412773i | \(0.135440\pi\) | |||||||
\(662\) | 95.9155 | 3.72786 | ||||||||
\(663\) | 3.07385 | 0.119378 | ||||||||
\(664\) | 76.8888 | 2.98386 | ||||||||
\(665\) | 0.298707 | 0.0115833 | ||||||||
\(666\) | 4.66695 | 0.180841 | ||||||||
\(667\) | −5.83677 | −0.226001 | ||||||||
\(668\) | −10.3367 | −0.399940 | ||||||||
\(669\) | −15.7070 | −0.607269 | ||||||||
\(670\) | −1.58955 | −0.0614098 | ||||||||
\(671\) | 6.99377 | 0.269991 | ||||||||
\(672\) | 24.4605 | 0.943584 | ||||||||
\(673\) | 12.2569 | 0.472468 | 0.236234 | − | 0.971696i | \(-0.424087\pi\) | ||||
0.236234 | + | 0.971696i | \(0.424087\pi\) | |||||||
\(674\) | −64.5067 | −2.48470 | ||||||||
\(675\) | 4.99613 | 0.192301 | ||||||||
\(676\) | 131.338 | 5.05146 | ||||||||
\(677\) | −18.4420 | −0.708784 | −0.354392 | − | 0.935097i | \(-0.615312\pi\) | ||||
−0.354392 | + | 0.935097i | \(0.615312\pi\) | |||||||
\(678\) | 45.3605 | 1.74206 | ||||||||
\(679\) | 18.5781 | 0.712963 | ||||||||
\(680\) | −0.312901 | −0.0119992 | ||||||||
\(681\) | 2.90291 | 0.111240 | ||||||||
\(682\) | 25.4780 | 0.975603 | ||||||||
\(683\) | 25.2948 | 0.967878 | 0.483939 | − | 0.875102i | \(-0.339206\pi\) | ||||
0.483939 | + | 0.875102i | \(0.339206\pi\) | |||||||
\(684\) | −26.8362 | −1.02611 | ||||||||
\(685\) | 0.154647 | 0.00590875 | ||||||||
\(686\) | −2.75477 | −0.105178 | ||||||||
\(687\) | −0.832421 | −0.0317588 | ||||||||
\(688\) | 32.0714 | 1.22271 | ||||||||
\(689\) | 6.11739 | 0.233054 | ||||||||
\(690\) | 0.837091 | 0.0318675 | ||||||||
\(691\) | −35.2927 | −1.34260 | −0.671298 | − | 0.741188i | \(-0.734263\pi\) | ||||
−0.671298 | + | 0.741188i | \(0.734263\pi\) | |||||||
\(692\) | 111.301 | 4.23102 | ||||||||
\(693\) | 1.07439 | 0.0408127 | ||||||||
\(694\) | −66.9028 | −2.53960 | ||||||||
\(695\) | 0.455099 | 0.0172629 | ||||||||
\(696\) | 11.8130 | 0.447769 | ||||||||
\(697\) | 3.56496 | 0.135032 | ||||||||
\(698\) | 47.3697 | 1.79297 | ||||||||
\(699\) | −23.8340 | −0.901485 | ||||||||
\(700\) | −27.9223 | −1.05536 | ||||||||
\(701\) | 24.9776 | 0.943390 | 0.471695 | − | 0.881762i | \(-0.343642\pi\) | ||||
0.471695 | + | 0.881762i | \(0.343642\pi\) | |||||||
\(702\) | 16.6431 | 0.628153 | ||||||||
\(703\) | 8.13489 | 0.306813 | ||||||||
\(704\) | 37.8931 | 1.42815 | ||||||||
\(705\) | −0.355729 | −0.0133975 | ||||||||
\(706\) | 12.0379 | 0.453051 | ||||||||
\(707\) | 9.37959 | 0.352756 | ||||||||
\(708\) | 26.9529 | 1.01295 | ||||||||
\(709\) | 17.0802 | 0.641461 | 0.320731 | − | 0.947170i | \(-0.396072\pi\) | ||||
0.320731 | + | 0.947170i | \(0.396072\pi\) | |||||||
\(710\) | −0.828996 | −0.0311117 | ||||||||
\(711\) | 14.9495 | 0.560650 | ||||||||
\(712\) | 117.167 | 4.39100 | ||||||||
\(713\) | 42.0498 | 1.57478 | ||||||||
\(714\) | −1.40159 | −0.0524531 | ||||||||
\(715\) | −0.403785 | −0.0151007 | ||||||||
\(716\) | −42.2366 | −1.57846 | ||||||||
\(717\) | −0.0398658 | −0.00148882 | ||||||||
\(718\) | −70.6844 | −2.63792 | ||||||||
\(719\) | −8.53982 | −0.318481 | −0.159241 | − | 0.987240i | \(-0.550905\pi\) | ||||
−0.159241 | + | 0.987240i | \(0.550905\pi\) | |||||||
\(720\) | −0.998852 | −0.0372250 | ||||||||
\(721\) | 2.58365 | 0.0962201 | ||||||||
\(722\) | −11.1770 | −0.415965 | ||||||||
\(723\) | −17.5074 | −0.651109 | ||||||||
\(724\) | 70.4330 | 2.61762 | ||||||||
\(725\) | −5.96981 | −0.221713 | ||||||||
\(726\) | −27.1226 | −1.00662 | ||||||||
\(727\) | 40.2408 | 1.49245 | 0.746225 | − | 0.665694i | \(-0.231865\pi\) | ||||
0.746225 | + | 0.665694i | \(0.231865\pi\) | |||||||
\(728\) | −59.7283 | −2.21368 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.73565 | 0.0642392 | ||||||||
\(731\) | −1.01623 | −0.0375867 | ||||||||
\(732\) | −36.3803 | −1.34465 | ||||||||
\(733\) | 4.90667 | 0.181232 | 0.0906160 | − | 0.995886i | \(-0.471116\pi\) | ||||
0.0906160 | + | 0.995886i | \(0.471116\pi\) | |||||||
\(734\) | −36.8983 | −1.36194 | ||||||||
\(735\) | 0.0622071 | 0.00229455 | ||||||||
\(736\) | 119.485 | 4.40426 | ||||||||
\(737\) | −9.96576 | −0.367094 | ||||||||
\(738\) | 19.3021 | 0.710522 | ||||||||
\(739\) | −12.7916 | −0.470548 | −0.235274 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235274 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(740\) | 0.588985 | 0.0216515 | ||||||||
\(741\) | 29.0103 | 1.06572 | ||||||||
\(742\) | −2.78935 | −0.102400 | ||||||||
\(743\) | −18.3697 | −0.673919 | −0.336960 | − | 0.941519i | \(-0.609399\pi\) | ||||
−0.336960 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(744\) | −85.1040 | −3.12006 | ||||||||
\(745\) | 0.0925061 | 0.00338916 | ||||||||
\(746\) | 77.0583 | 2.82130 | ||||||||
\(747\) | −7.77734 | −0.284558 | ||||||||
\(748\) | −3.05501 | −0.111702 | ||||||||
\(749\) | 4.00965 | 0.146509 | ||||||||
\(750\) | 1.71300 | 0.0625500 | ||||||||
\(751\) | −32.8771 | −1.19970 | −0.599851 | − | 0.800112i | \(-0.704774\pi\) | ||||
−0.599851 | + | 0.800112i | \(0.704774\pi\) | |||||||
\(752\) | −91.8205 | −3.34835 | ||||||||
\(753\) | −29.0199 | −1.05754 | ||||||||
\(754\) | −19.8866 | −0.724227 | ||||||||
\(755\) | 0.139891 | 0.00509115 | ||||||||
\(756\) | −5.58878 | −0.203262 | ||||||||
\(757\) | −10.0269 | −0.364435 | −0.182218 | − | 0.983258i | \(-0.558328\pi\) | ||||
−0.182218 | + | 0.983258i | \(0.558328\pi\) | |||||||
\(758\) | 47.7946 | 1.73598 | ||||||||
\(759\) | 5.24817 | 0.190497 | ||||||||
\(760\) | −2.95309 | −0.107120 | ||||||||
\(761\) | 7.45689 | 0.270312 | 0.135156 | − | 0.990824i | \(-0.456846\pi\) | ||||
0.135156 | + | 0.990824i | \(0.456846\pi\) | |||||||
\(762\) | 35.4881 | 1.28560 | ||||||||
\(763\) | −6.55630 | −0.237354 | ||||||||
\(764\) | 55.1577 | 1.99554 | ||||||||
\(765\) | 0.0316501 | 0.00114431 | ||||||||
\(766\) | 2.75477 | 0.0995340 | ||||||||
\(767\) | −29.1365 | −1.05206 | ||||||||
\(768\) | −62.3465 | −2.24974 | ||||||||
\(769\) | −32.4343 | −1.16961 | −0.584805 | − | 0.811174i | \(-0.698829\pi\) | ||||
−0.584805 | + | 0.811174i | \(0.698829\pi\) | |||||||
\(770\) | 0.184114 | 0.00663503 | ||||||||
\(771\) | −25.5866 | −0.921478 | ||||||||
\(772\) | 124.771 | 4.49059 | ||||||||
\(773\) | −38.4735 | −1.38380 | −0.691898 | − | 0.721995i | \(-0.743225\pi\) | ||||
−0.691898 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(774\) | −5.50229 | −0.197776 | ||||||||
\(775\) | 43.0082 | 1.54490 | ||||||||
\(776\) | −183.668 | −6.59331 | ||||||||
\(777\) | 1.69413 | 0.0607766 | ||||||||
\(778\) | −70.8889 | −2.54149 | ||||||||
\(779\) | 33.6453 | 1.20547 | ||||||||
\(780\) | 2.10042 | 0.0752069 | ||||||||
\(781\) | −5.19742 | −0.185978 | ||||||||
\(782\) | −6.84647 | −0.244829 | ||||||||
\(783\) | −1.19489 | −0.0427017 | ||||||||
\(784\) | 16.0569 | 0.573460 | ||||||||
\(785\) | 0.533949 | 0.0190574 | ||||||||
\(786\) | 32.6171 | 1.16341 | ||||||||
\(787\) | 10.3070 | 0.367404 | 0.183702 | − | 0.982982i | \(-0.441192\pi\) | ||||
0.183702 | + | 0.982982i | \(0.441192\pi\) | |||||||
\(788\) | 73.7568 | 2.62748 | ||||||||
\(789\) | 2.33319 | 0.0830638 | ||||||||
\(790\) | 2.56185 | 0.0911464 | ||||||||
\(791\) | 16.4661 | 0.585468 | ||||||||
\(792\) | −10.6217 | −0.377426 | ||||||||
\(793\) | 39.3276 | 1.39656 | ||||||||
\(794\) | 67.5442 | 2.39706 | ||||||||
\(795\) | 0.0629880 | 0.00223396 | ||||||||
\(796\) | −3.55109 | −0.125865 | ||||||||
\(797\) | −3.25265 | −0.115215 | −0.0576074 | − | 0.998339i | \(-0.518347\pi\) | ||||
−0.0576074 | + | 0.998339i | \(0.518347\pi\) | |||||||
\(798\) | −13.2279 | −0.468262 | ||||||||
\(799\) | 2.90947 | 0.102930 | ||||||||
\(800\) | 122.208 | 4.32070 | ||||||||
\(801\) | −11.8515 | −0.418751 | ||||||||
\(802\) | −61.4894 | −2.17127 | ||||||||
\(803\) | 10.8817 | 0.384007 | ||||||||
\(804\) | 51.8400 | 1.82826 | ||||||||
\(805\) | 0.303869 | 0.0107100 | ||||||||
\(806\) | 143.269 | 5.04643 | ||||||||
\(807\) | 18.4044 | 0.647864 | ||||||||
\(808\) | −92.7291 | −3.26220 | ||||||||
\(809\) | 52.7845 | 1.85580 | 0.927902 | − | 0.372825i | \(-0.121611\pi\) | ||||
0.927902 | + | 0.372825i | \(0.121611\pi\) | |||||||
\(810\) | 0.171367 | 0.00602121 | ||||||||
\(811\) | 28.6113 | 1.00468 | 0.502340 | − | 0.864670i | \(-0.332473\pi\) | ||||
0.502340 | + | 0.864670i | \(0.332473\pi\) | |||||||
\(812\) | 6.67795 | 0.234350 | ||||||||
\(813\) | −25.4471 | −0.892470 | ||||||||
\(814\) | 5.01412 | 0.175745 | ||||||||
\(815\) | 0.265398 | 0.00929650 | ||||||||
\(816\) | 8.16950 | 0.285990 | ||||||||
\(817\) | −9.59096 | −0.335545 | ||||||||
\(818\) | 20.3790 | 0.712534 | ||||||||
\(819\) | 6.04155 | 0.211109 | ||||||||
\(820\) | 2.43600 | 0.0850687 | ||||||||
\(821\) | 41.7489 | 1.45705 | 0.728523 | − | 0.685021i | \(-0.240207\pi\) | ||||
0.728523 | + | 0.685021i | \(0.240207\pi\) | |||||||
\(822\) | −6.84836 | −0.238864 | ||||||||
\(823\) | −17.7142 | −0.617478 | −0.308739 | − | 0.951147i | \(-0.599907\pi\) | ||||
−0.308739 | + | 0.951147i | \(0.599907\pi\) | |||||||
\(824\) | −25.5426 | −0.889820 | ||||||||
\(825\) | 5.36779 | 0.186882 | ||||||||
\(826\) | 13.2854 | 0.462258 | ||||||||
\(827\) | −36.6496 | −1.27443 | −0.637216 | − | 0.770685i | \(-0.719914\pi\) | ||||
−0.637216 | + | 0.770685i | \(0.719914\pi\) | |||||||
\(828\) | −27.3000 | −0.948742 | ||||||||
\(829\) | −16.8926 | −0.586704 | −0.293352 | − | 0.956005i | \(-0.594771\pi\) | ||||
−0.293352 | + | 0.956005i | \(0.594771\pi\) | |||||||
\(830\) | −1.33278 | −0.0462613 | ||||||||
\(831\) | 14.0025 | 0.485741 | ||||||||
\(832\) | 213.082 | 7.38728 | ||||||||
\(833\) | −0.508785 | −0.0176284 | ||||||||
\(834\) | −20.1535 | −0.697860 | ||||||||
\(835\) | 0.115055 | 0.00398165 | ||||||||
\(836\) | −28.8325 | −0.997194 | ||||||||
\(837\) | 8.60831 | 0.297547 | ||||||||
\(838\) | 39.6436 | 1.36947 | ||||||||
\(839\) | 32.4506 | 1.12032 | 0.560159 | − | 0.828385i | \(-0.310740\pi\) | ||||
0.560159 | + | 0.828385i | \(0.310740\pi\) | |||||||
\(840\) | −0.614996 | −0.0212194 | ||||||||
\(841\) | −27.5722 | −0.950767 | ||||||||
\(842\) | −40.5957 | −1.39902 | ||||||||
\(843\) | 8.32382 | 0.286688 | ||||||||
\(844\) | 144.134 | 4.96128 | ||||||||
\(845\) | −1.46189 | −0.0502904 | ||||||||
\(846\) | 15.7531 | 0.541601 | ||||||||
\(847\) | −9.84569 | −0.338302 | ||||||||
\(848\) | 16.2584 | 0.558317 | ||||||||
\(849\) | 20.0741 | 0.688941 | ||||||||
\(850\) | −7.00252 | −0.240184 | ||||||||
\(851\) | 8.27549 | 0.283680 | ||||||||
\(852\) | 27.0360 | 0.926239 | ||||||||
\(853\) | −4.83915 | −0.165689 | −0.0828446 | − | 0.996562i | \(-0.526401\pi\) | ||||
−0.0828446 | + | 0.996562i | \(0.526401\pi\) | |||||||
\(854\) | −17.9323 | −0.613630 | ||||||||
\(855\) | 0.298707 | 0.0102155 | ||||||||
\(856\) | −39.6404 | −1.35488 | ||||||||
\(857\) | 49.5352 | 1.69209 | 0.846045 | − | 0.533112i | \(-0.178978\pi\) | ||||
0.846045 | + | 0.533112i | \(0.178978\pi\) | |||||||
\(858\) | 17.8812 | 0.610453 | ||||||||
\(859\) | −7.46891 | −0.254836 | −0.127418 | − | 0.991849i | \(-0.540669\pi\) | ||||
−0.127418 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(860\) | −0.694408 | −0.0236791 | ||||||||
\(861\) | 7.00680 | 0.238791 | ||||||||
\(862\) | 91.4256 | 3.11397 | ||||||||
\(863\) | 29.2130 | 0.994421 | 0.497211 | − | 0.867630i | \(-0.334358\pi\) | ||||
0.497211 | + | 0.867630i | \(0.334358\pi\) | |||||||
\(864\) | 24.4605 | 0.832163 | ||||||||
\(865\) | −1.23886 | −0.0421224 | ||||||||
\(866\) | −97.4451 | −3.31132 | ||||||||
\(867\) | 16.7411 | 0.568559 | ||||||||
\(868\) | −48.1099 | −1.63296 | ||||||||
\(869\) | 16.0616 | 0.544852 | ||||||||
\(870\) | −0.204764 | −0.00694213 | ||||||||
\(871\) | −56.0398 | −1.89884 | ||||||||
\(872\) | 64.8174 | 2.19499 | ||||||||
\(873\) | 18.5781 | 0.628774 | ||||||||
\(874\) | −64.6155 | −2.18565 | ||||||||
\(875\) | 0.621831 | 0.0210217 | ||||||||
\(876\) | −56.6046 | −1.91249 | ||||||||
\(877\) | 4.74247 | 0.160142 | 0.0800709 | − | 0.996789i | \(-0.474485\pi\) | ||||
0.0800709 | + | 0.996789i | \(0.474485\pi\) | |||||||
\(878\) | 36.4017 | 1.22850 | ||||||||
\(879\) | −9.30777 | −0.313943 | ||||||||
\(880\) | −1.07316 | −0.0361761 | ||||||||
\(881\) | 7.63329 | 0.257172 | 0.128586 | − | 0.991698i | \(-0.458956\pi\) | ||||
0.128586 | + | 0.991698i | \(0.458956\pi\) | |||||||
\(882\) | −2.75477 | −0.0927580 | ||||||||
\(883\) | 52.4049 | 1.76356 | 0.881782 | − | 0.471657i | \(-0.156344\pi\) | ||||
0.881782 | + | 0.471657i | \(0.156344\pi\) | |||||||
\(884\) | −17.1791 | −0.577795 | ||||||||
\(885\) | −0.300005 | −0.0100846 | ||||||||
\(886\) | −47.7386 | −1.60381 | ||||||||
\(887\) | 7.01764 | 0.235629 | 0.117815 | − | 0.993036i | \(-0.462411\pi\) | ||||
0.117815 | + | 0.993036i | \(0.462411\pi\) | |||||||
\(888\) | −16.7486 | −0.562047 | ||||||||
\(889\) | 12.8824 | 0.432061 | ||||||||
\(890\) | −2.03094 | −0.0680774 | ||||||||
\(891\) | 1.07439 | 0.0359934 | ||||||||
\(892\) | 87.7832 | 2.93920 | ||||||||
\(893\) | 27.4589 | 0.918877 | ||||||||
\(894\) | −4.09653 | −0.137008 | ||||||||
\(895\) | 0.470124 | 0.0157145 | ||||||||
\(896\) | −48.2382 | −1.61153 | ||||||||
\(897\) | 29.5117 | 0.985368 | ||||||||
\(898\) | −54.3132 | −1.81246 | ||||||||
\(899\) | −10.2859 | −0.343055 | ||||||||
\(900\) | −27.9223 | −0.930742 | ||||||||
\(901\) | −0.515172 | −0.0171629 | ||||||||
\(902\) | 20.7380 | 0.690500 | ||||||||
\(903\) | −1.99737 | −0.0664682 | ||||||||
\(904\) | −162.789 | −5.41427 | ||||||||
\(905\) | −0.783970 | −0.0260601 | ||||||||
\(906\) | −6.19491 | −0.205812 | ||||||||
\(907\) | 17.5487 | 0.582696 | 0.291348 | − | 0.956617i | \(-0.405896\pi\) | ||||
0.291348 | + | 0.956617i | \(0.405896\pi\) | |||||||
\(908\) | −16.2237 | −0.538402 | ||||||||
\(909\) | 9.37959 | 0.311101 | ||||||||
\(910\) | 1.03532 | 0.0343205 | ||||||||
\(911\) | −21.6509 | −0.717327 | −0.358664 | − | 0.933467i | \(-0.616768\pi\) | ||||
−0.358664 | + | 0.933467i | \(0.616768\pi\) | |||||||
\(912\) | 77.1019 | 2.55310 | ||||||||
\(913\) | −8.35589 | −0.276540 | ||||||||
\(914\) | 35.8173 | 1.18473 | ||||||||
\(915\) | 0.404939 | 0.0133869 | ||||||||
\(916\) | 4.65222 | 0.153714 | ||||||||
\(917\) | 11.8402 | 0.390999 | ||||||||
\(918\) | −1.40159 | −0.0462593 | ||||||||
\(919\) | −8.50116 | −0.280427 | −0.140214 | − | 0.990121i | \(-0.544779\pi\) | ||||
−0.140214 | + | 0.990121i | \(0.544779\pi\) | |||||||
\(920\) | −3.00413 | −0.0990433 | ||||||||
\(921\) | 0.0661153 | 0.00217857 | ||||||||
\(922\) | 93.1478 | 3.06766 | ||||||||
\(923\) | −29.2263 | −0.961997 | ||||||||
\(924\) | −6.00452 | −0.197534 | ||||||||
\(925\) | 8.46410 | 0.278298 | ||||||||
\(926\) | −31.5246 | −1.03596 | ||||||||
\(927\) | 2.58365 | 0.0848581 | ||||||||
\(928\) | −29.2275 | −0.959440 | ||||||||
\(929\) | 50.4287 | 1.65451 | 0.827256 | − | 0.561825i | \(-0.189900\pi\) | ||||
0.827256 | + | 0.561825i | \(0.189900\pi\) | |||||||
\(930\) | 1.47518 | 0.0483729 | ||||||||
\(931\) | −4.80180 | −0.157373 | ||||||||
\(932\) | 133.203 | 4.36321 | ||||||||
\(933\) | 25.7491 | 0.842988 | ||||||||
\(934\) | 4.51156 | 0.147623 | ||||||||
\(935\) | 0.0340045 | 0.00111207 | ||||||||
\(936\) | −59.7283 | −1.95228 | ||||||||
\(937\) | −24.3609 | −0.795836 | −0.397918 | − | 0.917421i | \(-0.630267\pi\) | ||||
−0.397918 | + | 0.917421i | \(0.630267\pi\) | |||||||
\(938\) | 25.5526 | 0.834321 | ||||||||
\(939\) | 24.2429 | 0.791136 | ||||||||
\(940\) | 1.98809 | 0.0648443 | ||||||||
\(941\) | 55.4566 | 1.80783 | 0.903917 | − | 0.427708i | \(-0.140679\pi\) | ||||
0.903917 | + | 0.427708i | \(0.140679\pi\) | |||||||
\(942\) | −23.6453 | −0.770406 | ||||||||
\(943\) | 34.2268 | 1.11458 | ||||||||
\(944\) | −77.4371 | −2.52036 | ||||||||
\(945\) | 0.0622071 | 0.00202360 | ||||||||
\(946\) | −5.91160 | −0.192203 | ||||||||
\(947\) | −53.8777 | −1.75079 | −0.875394 | − | 0.483409i | \(-0.839398\pi\) | ||||
−0.875394 | + | 0.483409i | \(0.839398\pi\) | |||||||
\(948\) | −83.5494 | −2.71356 | ||||||||
\(949\) | 61.1904 | 1.98633 | ||||||||
\(950\) | −66.0882 | −2.14419 | ||||||||
\(951\) | −31.7699 | −1.03021 | ||||||||
\(952\) | 5.02999 | 0.163023 | ||||||||
\(953\) | −37.0182 | −1.19914 | −0.599568 | − | 0.800324i | \(-0.704661\pi\) | ||||
−0.599568 | + | 0.800324i | \(0.704661\pi\) | |||||||
\(954\) | −2.78935 | −0.0903087 | ||||||||
\(955\) | −0.613945 | −0.0198668 | ||||||||
\(956\) | 0.222801 | 0.00720590 | ||||||||
\(957\) | −1.28377 | −0.0414985 | ||||||||
\(958\) | 46.9352 | 1.51641 | ||||||||
\(959\) | −2.48600 | −0.0802770 | ||||||||
\(960\) | 2.19401 | 0.0708113 | ||||||||
\(961\) | 43.1030 | 1.39042 | ||||||||
\(962\) | 28.1956 | 0.909062 | ||||||||
\(963\) | 4.00965 | 0.129209 | ||||||||
\(964\) | 97.8452 | 3.15138 | ||||||||
\(965\) | −1.38879 | −0.0447067 | ||||||||
\(966\) | −13.4565 | −0.432956 | ||||||||
\(967\) | 14.8126 | 0.476341 | 0.238171 | − | 0.971223i | \(-0.423452\pi\) | ||||
0.238171 | + | 0.971223i | \(0.423452\pi\) | |||||||
\(968\) | 97.3371 | 3.12853 | ||||||||
\(969\) | −2.44309 | −0.0784833 | ||||||||
\(970\) | 3.18367 | 0.102222 | ||||||||
\(971\) | −57.8696 | −1.85713 | −0.928563 | − | 0.371176i | \(-0.878955\pi\) | ||||
−0.928563 | + | 0.371176i | \(0.878955\pi\) | |||||||
\(972\) | −5.58878 | −0.179260 | ||||||||
\(973\) | −7.31586 | −0.234536 | ||||||||
\(974\) | −28.0495 | −0.898765 | ||||||||
\(975\) | 30.1844 | 0.966673 | ||||||||
\(976\) | 104.523 | 3.34569 | ||||||||
\(977\) | −8.59063 | −0.274839 | −0.137419 | − | 0.990513i | \(-0.543881\pi\) | ||||
−0.137419 | + | 0.990513i | \(0.543881\pi\) | |||||||
\(978\) | −11.7529 | −0.375815 | ||||||||
\(979\) | −12.7331 | −0.406951 | ||||||||
\(980\) | −0.347662 | −0.0111057 | ||||||||
\(981\) | −6.55630 | −0.209327 | ||||||||
\(982\) | 26.7175 | 0.852590 | ||||||||
\(983\) | 9.43567 | 0.300951 | 0.150476 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150476 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(984\) | −69.2711 | −2.20828 | ||||||||
\(985\) | −0.820967 | −0.0261582 | ||||||||
\(986\) | 1.67474 | 0.0533345 | ||||||||
\(987\) | 5.71846 | 0.182020 | ||||||||
\(988\) | −162.132 | −5.15811 | ||||||||
\(989\) | −9.75673 | −0.310246 | ||||||||
\(990\) | 0.184114 | 0.00585154 | ||||||||
\(991\) | 37.9315 | 1.20493 | 0.602467 | − | 0.798144i | \(-0.294185\pi\) | ||||
0.602467 | + | 0.798144i | \(0.294185\pi\) | |||||||
\(992\) | 210.563 | 6.68540 | ||||||||
\(993\) | 34.8179 | 1.10491 | ||||||||
\(994\) | 13.3264 | 0.422687 | ||||||||
\(995\) | 0.0395262 | 0.00125306 | ||||||||
\(996\) | 43.4658 | 1.37727 | ||||||||
\(997\) | −43.8717 | −1.38943 | −0.694716 | − | 0.719284i | \(-0.744470\pi\) | ||||
−0.694716 | + | 0.719284i | \(0.744470\pi\) | |||||||
\(998\) | −39.2596 | −1.24274 | ||||||||
\(999\) | 1.69413 | 0.0535999 |
(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 | 8043.2.a.t.1.1 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.1 | ✓ | 52 | 1.1 | even | 1 | trivial |