Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.86035 | −1.65143 | −0.825713 | − | 0.564090i | \(-0.809227\pi\) | ||||
−0.825713 | + | 0.564090i | \(0.809227\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.90727 | −1.30017 | −0.650086 | − | 0.759861i | \(-0.725267\pi\) | ||||
−0.650086 | + | 0.759861i | \(0.725267\pi\) | |||||||
\(6\) | 2.86035 | 1.16773 | ||||||||
\(7\) | 0.924767 | 0.349529 | 0.174765 | − | 0.984610i | \(-0.444084\pi\) | ||||
0.174765 | + | 0.984610i | \(0.444084\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.18162 | 1.72721 | ||||||||
\(10\) | 2.90727 | 0.919360 | ||||||||
\(11\) | −1.96179 | −0.591501 | −0.295750 | − | 0.955265i | \(-0.595570\pi\) | ||||
−0.295750 | + | 0.955265i | \(0.595570\pi\) | |||||||
\(12\) | −2.86035 | −0.825713 | ||||||||
\(13\) | 4.75038 | 1.31752 | 0.658759 | − | 0.752354i | \(-0.271082\pi\) | ||||
0.658759 | + | 0.752354i | \(0.271082\pi\) | |||||||
\(14\) | −0.924767 | −0.247154 | ||||||||
\(15\) | 8.31583 | 2.14714 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.12285 | −0.757403 | −0.378702 | − | 0.925519i | \(-0.623629\pi\) | ||||
−0.378702 | + | 0.925519i | \(0.623629\pi\) | |||||||
\(18\) | −5.18162 | −1.22132 | ||||||||
\(19\) | −2.40612 | −0.552003 | −0.276001 | − | 0.961157i | \(-0.589009\pi\) | ||||
−0.276001 | + | 0.961157i | \(0.589009\pi\) | |||||||
\(20\) | −2.90727 | −0.650086 | ||||||||
\(21\) | −2.64516 | −0.577221 | ||||||||
\(22\) | 1.96179 | 0.418254 | ||||||||
\(23\) | −5.24942 | −1.09458 | −0.547290 | − | 0.836943i | \(-0.684341\pi\) | ||||
−0.547290 | + | 0.836943i | \(0.684341\pi\) | |||||||
\(24\) | 2.86035 | 0.583867 | ||||||||
\(25\) | 3.45224 | 0.690447 | ||||||||
\(26\) | −4.75038 | −0.931626 | ||||||||
\(27\) | −6.24021 | −1.20093 | ||||||||
\(28\) | 0.924767 | 0.174765 | ||||||||
\(29\) | −6.70446 | −1.24499 | −0.622494 | − | 0.782625i | \(-0.713880\pi\) | ||||
−0.622494 | + | 0.782625i | \(0.713880\pi\) | |||||||
\(30\) | −8.31583 | −1.51826 | ||||||||
\(31\) | 5.39883 | 0.969659 | 0.484830 | − | 0.874609i | \(-0.338882\pi\) | ||||
0.484830 | + | 0.874609i | \(0.338882\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.61140 | 0.976820 | ||||||||
\(34\) | 3.12285 | 0.535565 | ||||||||
\(35\) | −2.68855 | −0.454448 | ||||||||
\(36\) | 5.18162 | 0.863604 | ||||||||
\(37\) | −1.56509 | −0.257299 | −0.128649 | − | 0.991690i | \(-0.541064\pi\) | ||||
−0.128649 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(38\) | 2.40612 | 0.390325 | ||||||||
\(39\) | −13.5878 | −2.17578 | ||||||||
\(40\) | 2.90727 | 0.459680 | ||||||||
\(41\) | 2.11925 | 0.330972 | 0.165486 | − | 0.986212i | \(-0.447081\pi\) | ||||
0.165486 | + | 0.986212i | \(0.447081\pi\) | |||||||
\(42\) | 2.64516 | 0.408157 | ||||||||
\(43\) | 0.246973 | 0.0376630 | 0.0188315 | − | 0.999823i | \(-0.494005\pi\) | ||||
0.0188315 | + | 0.999823i | \(0.494005\pi\) | |||||||
\(44\) | −1.96179 | −0.295750 | ||||||||
\(45\) | −15.0644 | −2.24567 | ||||||||
\(46\) | 5.24942 | 0.773985 | ||||||||
\(47\) | 10.1832 | 1.48538 | 0.742689 | − | 0.669637i | \(-0.233550\pi\) | ||||
0.742689 | + | 0.669637i | \(0.233550\pi\) | |||||||
\(48\) | −2.86035 | −0.412856 | ||||||||
\(49\) | −6.14481 | −0.877829 | ||||||||
\(50\) | −3.45224 | −0.488220 | ||||||||
\(51\) | 8.93246 | 1.25080 | ||||||||
\(52\) | 4.75038 | 0.658759 | ||||||||
\(53\) | 0.976945 | 0.134194 | 0.0670968 | − | 0.997746i | \(-0.478626\pi\) | ||||
0.0670968 | + | 0.997746i | \(0.478626\pi\) | |||||||
\(54\) | 6.24021 | 0.849186 | ||||||||
\(55\) | 5.70345 | 0.769053 | ||||||||
\(56\) | −0.924767 | −0.123577 | ||||||||
\(57\) | 6.88237 | 0.911592 | ||||||||
\(58\) | 6.70446 | 0.880339 | ||||||||
\(59\) | 7.22403 | 0.940489 | 0.470244 | − | 0.882536i | \(-0.344166\pi\) | ||||
0.470244 | + | 0.882536i | \(0.344166\pi\) | |||||||
\(60\) | 8.31583 | 1.07357 | ||||||||
\(61\) | 1.80157 | 0.230667 | 0.115333 | − | 0.993327i | \(-0.463206\pi\) | ||||
0.115333 | + | 0.993327i | \(0.463206\pi\) | |||||||
\(62\) | −5.39883 | −0.685653 | ||||||||
\(63\) | 4.79179 | 0.603709 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.8107 | −1.71300 | ||||||||
\(66\) | −5.61140 | −0.690716 | ||||||||
\(67\) | 6.89869 | 0.842809 | 0.421404 | − | 0.906873i | \(-0.361537\pi\) | ||||
0.421404 | + | 0.906873i | \(0.361537\pi\) | |||||||
\(68\) | −3.12285 | −0.378702 | ||||||||
\(69\) | 15.0152 | 1.80762 | ||||||||
\(70\) | 2.68855 | 0.321343 | ||||||||
\(71\) | 13.6869 | 1.62433 | 0.812167 | − | 0.583426i | \(-0.198288\pi\) | ||||
0.812167 | + | 0.583426i | \(0.198288\pi\) | |||||||
\(72\) | −5.18162 | −0.610660 | ||||||||
\(73\) | 8.90678 | 1.04246 | 0.521230 | − | 0.853416i | \(-0.325473\pi\) | ||||
0.521230 | + | 0.853416i | \(0.325473\pi\) | |||||||
\(74\) | 1.56509 | 0.181938 | ||||||||
\(75\) | −9.87461 | −1.14022 | ||||||||
\(76\) | −2.40612 | −0.276001 | ||||||||
\(77\) | −1.81419 | −0.206747 | ||||||||
\(78\) | 13.5878 | 1.53851 | ||||||||
\(79\) | −2.07547 | −0.233509 | −0.116754 | − | 0.993161i | \(-0.537249\pi\) | ||||
−0.116754 | + | 0.993161i | \(0.537249\pi\) | |||||||
\(80\) | −2.90727 | −0.325043 | ||||||||
\(81\) | 2.30435 | 0.256039 | ||||||||
\(82\) | −2.11925 | −0.234032 | ||||||||
\(83\) | −8.77630 | −0.963325 | −0.481662 | − | 0.876357i | \(-0.659967\pi\) | ||||
−0.481662 | + | 0.876357i | \(0.659967\pi\) | |||||||
\(84\) | −2.64516 | −0.288611 | ||||||||
\(85\) | 9.07899 | 0.984754 | ||||||||
\(86\) | −0.246973 | −0.0266318 | ||||||||
\(87\) | 19.1771 | 2.05601 | ||||||||
\(88\) | 1.96179 | 0.209127 | ||||||||
\(89\) | 8.42300 | 0.892836 | 0.446418 | − | 0.894824i | \(-0.352699\pi\) | ||||
0.446418 | + | 0.894824i | \(0.352699\pi\) | |||||||
\(90\) | 15.0644 | 1.58793 | ||||||||
\(91\) | 4.39299 | 0.460511 | ||||||||
\(92\) | −5.24942 | −0.547290 | ||||||||
\(93\) | −15.4426 | −1.60132 | ||||||||
\(94\) | −10.1832 | −1.05032 | ||||||||
\(95\) | 6.99526 | 0.717699 | ||||||||
\(96\) | 2.86035 | 0.291934 | ||||||||
\(97\) | 8.08147 | 0.820549 | 0.410275 | − | 0.911962i | \(-0.365433\pi\) | ||||
0.410275 | + | 0.911962i | \(0.365433\pi\) | |||||||
\(98\) | 6.14481 | 0.620719 | ||||||||
\(99\) | −10.1652 | −1.02164 | ||||||||
\(100\) | 3.45224 | 0.345224 | ||||||||
\(101\) | −15.8267 | −1.57482 | −0.787408 | − | 0.616432i | \(-0.788578\pi\) | ||||
−0.787408 | + | 0.616432i | \(0.788578\pi\) | |||||||
\(102\) | −8.93246 | −0.884446 | ||||||||
\(103\) | 6.34543 | 0.625233 | 0.312617 | − | 0.949879i | \(-0.398794\pi\) | ||||
0.312617 | + | 0.949879i | \(0.398794\pi\) | |||||||
\(104\) | −4.75038 | −0.465813 | ||||||||
\(105\) | 7.69020 | 0.750487 | ||||||||
\(106\) | −0.976945 | −0.0948892 | ||||||||
\(107\) | 5.74011 | 0.554918 | 0.277459 | − | 0.960738i | \(-0.410508\pi\) | ||||
0.277459 | + | 0.960738i | \(0.410508\pi\) | |||||||
\(108\) | −6.24021 | −0.600465 | ||||||||
\(109\) | 2.46460 | 0.236066 | 0.118033 | − | 0.993010i | \(-0.462341\pi\) | ||||
0.118033 | + | 0.993010i | \(0.462341\pi\) | |||||||
\(110\) | −5.70345 | −0.543802 | ||||||||
\(111\) | 4.47670 | 0.424910 | ||||||||
\(112\) | 0.924767 | 0.0873823 | ||||||||
\(113\) | 3.31855 | 0.312183 | 0.156092 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156092 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(114\) | −6.88237 | −0.644593 | ||||||||
\(115\) | 15.2615 | 1.42314 | ||||||||
\(116\) | −6.70446 | −0.622494 | ||||||||
\(117\) | 24.6147 | 2.27563 | ||||||||
\(118\) | −7.22403 | −0.665026 | ||||||||
\(119\) | −2.88791 | −0.264734 | ||||||||
\(120\) | −8.31583 | −0.759128 | ||||||||
\(121\) | −7.15140 | −0.650127 | ||||||||
\(122\) | −1.80157 | −0.163106 | ||||||||
\(123\) | −6.06181 | −0.546575 | ||||||||
\(124\) | 5.39883 | 0.484830 | ||||||||
\(125\) | 4.49978 | 0.402472 | ||||||||
\(126\) | −4.79179 | −0.426887 | ||||||||
\(127\) | 10.7675 | 0.955464 | 0.477732 | − | 0.878506i | \(-0.341459\pi\) | ||||
0.477732 | + | 0.878506i | \(0.341459\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.706430 | −0.0621977 | ||||||||
\(130\) | 13.8107 | 1.21127 | ||||||||
\(131\) | −16.1817 | −1.41380 | −0.706900 | − | 0.707314i | \(-0.749907\pi\) | ||||
−0.706900 | + | 0.707314i | \(0.749907\pi\) | |||||||
\(132\) | 5.61140 | 0.488410 | ||||||||
\(133\) | −2.22510 | −0.192941 | ||||||||
\(134\) | −6.89869 | −0.595956 | ||||||||
\(135\) | 18.1420 | 1.56142 | ||||||||
\(136\) | 3.12285 | 0.267782 | ||||||||
\(137\) | −14.6083 | −1.24807 | −0.624036 | − | 0.781396i | \(-0.714508\pi\) | ||||
−0.624036 | + | 0.781396i | \(0.714508\pi\) | |||||||
\(138\) | −15.0152 | −1.27818 | ||||||||
\(139\) | −12.4414 | −1.05527 | −0.527635 | − | 0.849471i | \(-0.676921\pi\) | ||||
−0.527635 | + | 0.849471i | \(0.676921\pi\) | |||||||
\(140\) | −2.68855 | −0.227224 | ||||||||
\(141\) | −29.1277 | −2.45299 | ||||||||
\(142\) | −13.6869 | −1.14858 | ||||||||
\(143\) | −9.31923 | −0.779313 | ||||||||
\(144\) | 5.18162 | 0.431802 | ||||||||
\(145\) | 19.4917 | 1.61870 | ||||||||
\(146\) | −8.90678 | −0.737130 | ||||||||
\(147\) | 17.5763 | 1.44967 | ||||||||
\(148\) | −1.56509 | −0.128649 | ||||||||
\(149\) | 16.3480 | 1.33928 | 0.669638 | − | 0.742687i | \(-0.266449\pi\) | ||||
0.669638 | + | 0.742687i | \(0.266449\pi\) | |||||||
\(150\) | 9.87461 | 0.806259 | ||||||||
\(151\) | 24.4659 | 1.99101 | 0.995504 | − | 0.0947174i | \(-0.0301947\pi\) | ||||
0.995504 | + | 0.0947174i | \(0.0301947\pi\) | |||||||
\(152\) | 2.40612 | 0.195162 | ||||||||
\(153\) | −16.1814 | −1.30819 | ||||||||
\(154\) | 1.81419 | 0.146192 | ||||||||
\(155\) | −15.6959 | −1.26072 | ||||||||
\(156\) | −13.5878 | −1.08789 | ||||||||
\(157\) | −2.38955 | −0.190707 | −0.0953535 | − | 0.995443i | \(-0.530398\pi\) | ||||
−0.0953535 | + | 0.995443i | \(0.530398\pi\) | |||||||
\(158\) | 2.07547 | 0.165115 | ||||||||
\(159\) | −2.79441 | −0.221611 | ||||||||
\(160\) | 2.90727 | 0.229840 | ||||||||
\(161\) | −4.85449 | −0.382588 | ||||||||
\(162\) | −2.30435 | −0.181047 | ||||||||
\(163\) | 17.0078 | 1.33215 | 0.666076 | − | 0.745884i | \(-0.267973\pi\) | ||||
0.666076 | + | 0.745884i | \(0.267973\pi\) | |||||||
\(164\) | 2.11925 | 0.165486 | ||||||||
\(165\) | −16.3139 | −1.27003 | ||||||||
\(166\) | 8.77630 | 0.681173 | ||||||||
\(167\) | −11.1082 | −0.859579 | −0.429789 | − | 0.902929i | \(-0.641412\pi\) | ||||
−0.429789 | + | 0.902929i | \(0.641412\pi\) | |||||||
\(168\) | 2.64516 | 0.204079 | ||||||||
\(169\) | 9.56611 | 0.735855 | ||||||||
\(170\) | −9.07899 | −0.696326 | ||||||||
\(171\) | −12.4676 | −0.953424 | ||||||||
\(172\) | 0.246973 | 0.0188315 | ||||||||
\(173\) | −7.43749 | −0.565462 | −0.282731 | − | 0.959199i | \(-0.591240\pi\) | ||||
−0.282731 | + | 0.959199i | \(0.591240\pi\) | |||||||
\(174\) | −19.1771 | −1.45382 | ||||||||
\(175\) | 3.19251 | 0.241331 | ||||||||
\(176\) | −1.96179 | −0.147875 | ||||||||
\(177\) | −20.6633 | −1.55315 | ||||||||
\(178\) | −8.42300 | −0.631331 | ||||||||
\(179\) | −2.56601 | −0.191792 | −0.0958962 | − | 0.995391i | \(-0.530572\pi\) | ||||
−0.0958962 | + | 0.995391i | \(0.530572\pi\) | |||||||
\(180\) | −15.0644 | −1.12283 | ||||||||
\(181\) | −17.2955 | −1.28556 | −0.642781 | − | 0.766050i | \(-0.722220\pi\) | ||||
−0.642781 | + | 0.766050i | \(0.722220\pi\) | |||||||
\(182\) | −4.39299 | −0.325630 | ||||||||
\(183\) | −5.15311 | −0.380929 | ||||||||
\(184\) | 5.24942 | 0.386993 | ||||||||
\(185\) | 4.55014 | 0.334533 | ||||||||
\(186\) | 15.4426 | 1.13230 | ||||||||
\(187\) | 6.12637 | 0.448005 | ||||||||
\(188\) | 10.1832 | 0.742689 | ||||||||
\(189\) | −5.77074 | −0.419760 | ||||||||
\(190\) | −6.99526 | −0.507490 | ||||||||
\(191\) | 7.03698 | 0.509178 | 0.254589 | − | 0.967049i | \(-0.418060\pi\) | ||||
0.254589 | + | 0.967049i | \(0.418060\pi\) | |||||||
\(192\) | −2.86035 | −0.206428 | ||||||||
\(193\) | −22.5963 | −1.62652 | −0.813258 | − | 0.581903i | \(-0.802308\pi\) | ||||
−0.813258 | + | 0.581903i | \(0.802308\pi\) | |||||||
\(194\) | −8.08147 | −0.580216 | ||||||||
\(195\) | 39.5033 | 2.82889 | ||||||||
\(196\) | −6.14481 | −0.438915 | ||||||||
\(197\) | 5.69244 | 0.405570 | 0.202785 | − | 0.979223i | \(-0.435001\pi\) | ||||
0.202785 | + | 0.979223i | \(0.435001\pi\) | |||||||
\(198\) | 10.1652 | 0.722412 | ||||||||
\(199\) | −26.8035 | −1.90005 | −0.950026 | − | 0.312170i | \(-0.898944\pi\) | ||||
−0.950026 | + | 0.312170i | \(0.898944\pi\) | |||||||
\(200\) | −3.45224 | −0.244110 | ||||||||
\(201\) | −19.7327 | −1.39184 | ||||||||
\(202\) | 15.8267 | 1.11356 | ||||||||
\(203\) | −6.20007 | −0.435159 | ||||||||
\(204\) | 8.93246 | 0.625398 | ||||||||
\(205\) | −6.16124 | −0.430320 | ||||||||
\(206\) | −6.34543 | −0.442107 | ||||||||
\(207\) | −27.2005 | −1.89057 | ||||||||
\(208\) | 4.75038 | 0.329380 | ||||||||
\(209\) | 4.72030 | 0.326510 | ||||||||
\(210\) | −7.69020 | −0.530674 | ||||||||
\(211\) | 9.11175 | 0.627279 | 0.313639 | − | 0.949542i | \(-0.398452\pi\) | ||||
0.313639 | + | 0.949542i | \(0.398452\pi\) | |||||||
\(212\) | 0.976945 | 0.0670968 | ||||||||
\(213\) | −39.1493 | −2.68247 | ||||||||
\(214\) | −5.74011 | −0.392386 | ||||||||
\(215\) | −0.718018 | −0.0489684 | ||||||||
\(216\) | 6.24021 | 0.424593 | ||||||||
\(217\) | 4.99266 | 0.338924 | ||||||||
\(218\) | −2.46460 | −0.166924 | ||||||||
\(219\) | −25.4765 | −1.72155 | ||||||||
\(220\) | 5.70345 | 0.384526 | ||||||||
\(221\) | −14.8347 | −0.997892 | ||||||||
\(222\) | −4.47670 | −0.300457 | ||||||||
\(223\) | 11.2314 | 0.752113 | 0.376057 | − | 0.926597i | \(-0.377280\pi\) | ||||
0.376057 | + | 0.926597i | \(0.377280\pi\) | |||||||
\(224\) | −0.924767 | −0.0617886 | ||||||||
\(225\) | 17.8882 | 1.19255 | ||||||||
\(226\) | −3.31855 | −0.220747 | ||||||||
\(227\) | −9.49489 | −0.630198 | −0.315099 | − | 0.949059i | \(-0.602038\pi\) | ||||
−0.315099 | + | 0.949059i | \(0.602038\pi\) | |||||||
\(228\) | 6.88237 | 0.455796 | ||||||||
\(229\) | −9.64030 | −0.637049 | −0.318524 | − | 0.947915i | \(-0.603187\pi\) | ||||
−0.318524 | + | 0.947915i | \(0.603187\pi\) | |||||||
\(230\) | −15.2615 | −1.00631 | ||||||||
\(231\) | 5.18924 | 0.341427 | ||||||||
\(232\) | 6.70446 | 0.440170 | ||||||||
\(233\) | 10.6424 | 0.697205 | 0.348603 | − | 0.937271i | \(-0.386656\pi\) | ||||
0.348603 | + | 0.937271i | \(0.386656\pi\) | |||||||
\(234\) | −24.6147 | −1.60911 | ||||||||
\(235\) | −29.6054 | −1.93125 | ||||||||
\(236\) | 7.22403 | 0.470244 | ||||||||
\(237\) | 5.93658 | 0.385622 | ||||||||
\(238\) | 2.88791 | 0.187195 | ||||||||
\(239\) | 6.03473 | 0.390354 | 0.195177 | − | 0.980768i | \(-0.437472\pi\) | ||||
0.195177 | + | 0.980768i | \(0.437472\pi\) | |||||||
\(240\) | 8.31583 | 0.536784 | ||||||||
\(241\) | −8.99086 | −0.579152 | −0.289576 | − | 0.957155i | \(-0.593514\pi\) | ||||
−0.289576 | + | 0.957155i | \(0.593514\pi\) | |||||||
\(242\) | 7.15140 | 0.459709 | ||||||||
\(243\) | 12.1294 | 0.778101 | ||||||||
\(244\) | 1.80157 | 0.115333 | ||||||||
\(245\) | 17.8646 | 1.14133 | ||||||||
\(246\) | 6.06181 | 0.386487 | ||||||||
\(247\) | −11.4300 | −0.727274 | ||||||||
\(248\) | −5.39883 | −0.342826 | ||||||||
\(249\) | 25.1033 | 1.59086 | ||||||||
\(250\) | −4.49978 | −0.284591 | ||||||||
\(251\) | −9.62109 | −0.607278 | −0.303639 | − | 0.952787i | \(-0.598202\pi\) | ||||
−0.303639 | + | 0.952787i | \(0.598202\pi\) | |||||||
\(252\) | 4.79179 | 0.301855 | ||||||||
\(253\) | 10.2982 | 0.647445 | ||||||||
\(254\) | −10.7675 | −0.675615 | ||||||||
\(255\) | −25.9691 | −1.62625 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.6742 | 1.72627 | 0.863135 | − | 0.504973i | \(-0.168498\pi\) | ||||
0.863135 | + | 0.504973i | \(0.168498\pi\) | |||||||
\(258\) | 0.706430 | 0.0439804 | ||||||||
\(259\) | −1.44734 | −0.0899334 | ||||||||
\(260\) | −13.8107 | −0.856500 | ||||||||
\(261\) | −34.7400 | −2.15035 | ||||||||
\(262\) | 16.1817 | 0.999707 | ||||||||
\(263\) | 9.78791 | 0.603548 | 0.301774 | − | 0.953379i | \(-0.402421\pi\) | ||||
0.301774 | + | 0.953379i | \(0.402421\pi\) | |||||||
\(264\) | −5.61140 | −0.345358 | ||||||||
\(265\) | −2.84024 | −0.174475 | ||||||||
\(266\) | 2.22510 | 0.136430 | ||||||||
\(267\) | −24.0928 | −1.47445 | ||||||||
\(268\) | 6.89869 | 0.421404 | ||||||||
\(269\) | −14.1504 | −0.862764 | −0.431382 | − | 0.902169i | \(-0.641974\pi\) | ||||
−0.431382 | + | 0.902169i | \(0.641974\pi\) | |||||||
\(270\) | −18.1420 | −1.10409 | ||||||||
\(271\) | −14.9984 | −0.911085 | −0.455543 | − | 0.890214i | \(-0.650555\pi\) | ||||
−0.455543 | + | 0.890214i | \(0.650555\pi\) | |||||||
\(272\) | −3.12285 | −0.189351 | ||||||||
\(273\) | −12.5655 | −0.760500 | ||||||||
\(274\) | 14.6083 | 0.882520 | ||||||||
\(275\) | −6.77255 | −0.408400 | ||||||||
\(276\) | 15.0152 | 0.903809 | ||||||||
\(277\) | −6.51546 | −0.391476 | −0.195738 | − | 0.980656i | \(-0.562710\pi\) | ||||
−0.195738 | + | 0.980656i | \(0.562710\pi\) | |||||||
\(278\) | 12.4414 | 0.746188 | ||||||||
\(279\) | 27.9747 | 1.67480 | ||||||||
\(280\) | 2.68855 | 0.160672 | ||||||||
\(281\) | 27.8508 | 1.66144 | 0.830719 | − | 0.556691i | \(-0.187929\pi\) | ||||
0.830719 | + | 0.556691i | \(0.187929\pi\) | |||||||
\(282\) | 29.1277 | 1.73453 | ||||||||
\(283\) | 7.40071 | 0.439927 | 0.219963 | − | 0.975508i | \(-0.429406\pi\) | ||||
0.219963 | + | 0.975508i | \(0.429406\pi\) | |||||||
\(284\) | 13.6869 | 0.812167 | ||||||||
\(285\) | −20.0089 | −1.18523 | ||||||||
\(286\) | 9.31923 | 0.551058 | ||||||||
\(287\) | 1.95981 | 0.115684 | ||||||||
\(288\) | −5.18162 | −0.305330 | ||||||||
\(289\) | −7.24779 | −0.426341 | ||||||||
\(290\) | −19.4917 | −1.14459 | ||||||||
\(291\) | −23.1159 | −1.35508 | ||||||||
\(292\) | 8.90678 | 0.521230 | ||||||||
\(293\) | 28.9410 | 1.69075 | 0.845376 | − | 0.534172i | \(-0.179377\pi\) | ||||
0.845376 | + | 0.534172i | \(0.179377\pi\) | |||||||
\(294\) | −17.5763 | −1.02507 | ||||||||
\(295\) | −21.0022 | −1.22280 | ||||||||
\(296\) | 1.56509 | 0.0909689 | ||||||||
\(297\) | 12.2420 | 0.710351 | ||||||||
\(298\) | −16.3480 | −0.947012 | ||||||||
\(299\) | −24.9368 | −1.44213 | ||||||||
\(300\) | −9.87461 | −0.570111 | ||||||||
\(301\) | 0.228392 | 0.0131643 | ||||||||
\(302\) | −24.4659 | −1.40786 | ||||||||
\(303\) | 45.2700 | 2.60069 | ||||||||
\(304\) | −2.40612 | −0.138001 | ||||||||
\(305\) | −5.23764 | −0.299907 | ||||||||
\(306\) | 16.1814 | 0.925032 | ||||||||
\(307\) | 22.1714 | 1.26539 | 0.632696 | − | 0.774401i | \(-0.281948\pi\) | ||||
0.632696 | + | 0.774401i | \(0.281948\pi\) | |||||||
\(308\) | −1.81419 | −0.103373 | ||||||||
\(309\) | −18.1502 | −1.03253 | ||||||||
\(310\) | 15.6959 | 0.891466 | ||||||||
\(311\) | −1.02105 | −0.0578982 | −0.0289491 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289491 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(312\) | 13.5878 | 0.769256 | ||||||||
\(313\) | −25.1728 | −1.42285 | −0.711424 | − | 0.702763i | \(-0.751950\pi\) | ||||
−0.711424 | + | 0.702763i | \(0.751950\pi\) | |||||||
\(314\) | 2.38955 | 0.134850 | ||||||||
\(315\) | −13.9311 | −0.784926 | ||||||||
\(316\) | −2.07547 | −0.116754 | ||||||||
\(317\) | −11.7399 | −0.659378 | −0.329689 | − | 0.944090i | \(-0.606944\pi\) | ||||
−0.329689 | + | 0.944090i | \(0.606944\pi\) | |||||||
\(318\) | 2.79441 | 0.156703 | ||||||||
\(319\) | 13.1527 | 0.736411 | ||||||||
\(320\) | −2.90727 | −0.162521 | ||||||||
\(321\) | −16.4187 | −0.916405 | ||||||||
\(322\) | 4.85449 | 0.270530 | ||||||||
\(323\) | 7.51397 | 0.418089 | ||||||||
\(324\) | 2.30435 | 0.128019 | ||||||||
\(325\) | 16.3994 | 0.909677 | ||||||||
\(326\) | −17.0078 | −0.941974 | ||||||||
\(327\) | −7.04962 | −0.389845 | ||||||||
\(328\) | −2.11925 | −0.117016 | ||||||||
\(329\) | 9.41712 | 0.519183 | ||||||||
\(330\) | 16.3139 | 0.898049 | ||||||||
\(331\) | −3.72572 | −0.204784 | −0.102392 | − | 0.994744i | \(-0.532650\pi\) | ||||
−0.102392 | + | 0.994744i | \(0.532650\pi\) | |||||||
\(332\) | −8.77630 | −0.481662 | ||||||||
\(333\) | −8.10970 | −0.444409 | ||||||||
\(334\) | 11.1082 | 0.607814 | ||||||||
\(335\) | −20.0564 | −1.09580 | ||||||||
\(336\) | −2.64516 | −0.144305 | ||||||||
\(337\) | 0.392319 | 0.0213710 | 0.0106855 | − | 0.999943i | \(-0.496599\pi\) | ||||
0.0106855 | + | 0.999943i | \(0.496599\pi\) | |||||||
\(338\) | −9.56611 | −0.520328 | ||||||||
\(339\) | −9.49223 | −0.515547 | ||||||||
\(340\) | 9.07899 | 0.492377 | ||||||||
\(341\) | −10.5914 | −0.573554 | ||||||||
\(342\) | 12.4676 | 0.674172 | ||||||||
\(343\) | −12.1559 | −0.656356 | ||||||||
\(344\) | −0.246973 | −0.0133159 | ||||||||
\(345\) | −43.6533 | −2.35021 | ||||||||
\(346\) | 7.43749 | 0.399842 | ||||||||
\(347\) | −26.2281 | −1.40800 | −0.703998 | − | 0.710202i | \(-0.748604\pi\) | ||||
−0.703998 | + | 0.710202i | \(0.748604\pi\) | |||||||
\(348\) | 19.1771 | 1.02800 | ||||||||
\(349\) | −5.24597 | −0.280810 | −0.140405 | − | 0.990094i | \(-0.544840\pi\) | ||||
−0.140405 | + | 0.990094i | \(0.544840\pi\) | |||||||
\(350\) | −3.19251 | −0.170647 | ||||||||
\(351\) | −29.6434 | −1.58225 | ||||||||
\(352\) | 1.96179 | 0.104564 | ||||||||
\(353\) | −6.45299 | −0.343458 | −0.171729 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(354\) | 20.6633 | 1.09824 | ||||||||
\(355\) | −39.7915 | −2.11191 | ||||||||
\(356\) | 8.42300 | 0.446418 | ||||||||
\(357\) | 8.26045 | 0.437189 | ||||||||
\(358\) | 2.56601 | 0.135618 | ||||||||
\(359\) | −30.6743 | −1.61893 | −0.809463 | − | 0.587170i | \(-0.800242\pi\) | ||||
−0.809463 | + | 0.587170i | \(0.800242\pi\) | |||||||
\(360\) | 15.0644 | 0.793963 | ||||||||
\(361\) | −13.2106 | −0.695293 | ||||||||
\(362\) | 17.2955 | 0.909030 | ||||||||
\(363\) | 20.4555 | 1.07364 | ||||||||
\(364\) | 4.39299 | 0.230255 | ||||||||
\(365\) | −25.8944 | −1.35538 | ||||||||
\(366\) | 5.15311 | 0.269358 | ||||||||
\(367\) | −3.99356 | −0.208462 | −0.104231 | − | 0.994553i | \(-0.533238\pi\) | ||||
−0.104231 | + | 0.994553i | \(0.533238\pi\) | |||||||
\(368\) | −5.24942 | −0.273645 | ||||||||
\(369\) | 10.9812 | 0.571657 | ||||||||
\(370\) | −4.55014 | −0.236550 | ||||||||
\(371\) | 0.903446 | 0.0469046 | ||||||||
\(372\) | −15.4426 | −0.800660 | ||||||||
\(373\) | −8.77963 | −0.454592 | −0.227296 | − | 0.973826i | \(-0.572989\pi\) | ||||
−0.227296 | + | 0.973826i | \(0.572989\pi\) | |||||||
\(374\) | −6.12637 | −0.316787 | ||||||||
\(375\) | −12.8709 | −0.664653 | ||||||||
\(376\) | −10.1832 | −0.525160 | ||||||||
\(377\) | −31.8488 | −1.64029 | ||||||||
\(378\) | 5.77074 | 0.296815 | ||||||||
\(379\) | 0.346627 | 0.0178050 | 0.00890252 | − | 0.999960i | \(-0.497166\pi\) | ||||
0.00890252 | + | 0.999960i | \(0.497166\pi\) | |||||||
\(380\) | 6.99526 | 0.358849 | ||||||||
\(381\) | −30.7990 | −1.57788 | ||||||||
\(382\) | −7.03698 | −0.360043 | ||||||||
\(383\) | −11.3843 | −0.581711 | −0.290855 | − | 0.956767i | \(-0.593940\pi\) | ||||
−0.290855 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(384\) | 2.86035 | 0.145967 | ||||||||
\(385\) | 5.27436 | 0.268806 | ||||||||
\(386\) | 22.5963 | 1.15012 | ||||||||
\(387\) | 1.27972 | 0.0650519 | ||||||||
\(388\) | 8.08147 | 0.410275 | ||||||||
\(389\) | 6.21366 | 0.315045 | 0.157522 | − | 0.987515i | \(-0.449649\pi\) | ||||
0.157522 | + | 0.987515i | \(0.449649\pi\) | |||||||
\(390\) | −39.5033 | −2.00033 | ||||||||
\(391\) | 16.3932 | 0.829039 | ||||||||
\(392\) | 6.14481 | 0.310360 | ||||||||
\(393\) | 46.2853 | 2.33478 | ||||||||
\(394\) | −5.69244 | −0.286781 | ||||||||
\(395\) | 6.03396 | 0.303601 | ||||||||
\(396\) | −10.1652 | −0.510822 | ||||||||
\(397\) | −26.0825 | −1.30904 | −0.654522 | − | 0.756043i | \(-0.727130\pi\) | ||||
−0.654522 | + | 0.756043i | \(0.727130\pi\) | |||||||
\(398\) | 26.8035 | 1.34354 | ||||||||
\(399\) | 6.36459 | 0.318628 | ||||||||
\(400\) | 3.45224 | 0.172612 | ||||||||
\(401\) | −11.2005 | −0.559328 | −0.279664 | − | 0.960098i | \(-0.590223\pi\) | ||||
−0.279664 | + | 0.960098i | \(0.590223\pi\) | |||||||
\(402\) | 19.7327 | 0.984177 | ||||||||
\(403\) | 25.6465 | 1.27754 | ||||||||
\(404\) | −15.8267 | −0.787408 | ||||||||
\(405\) | −6.69937 | −0.332894 | ||||||||
\(406\) | 6.20007 | 0.307704 | ||||||||
\(407\) | 3.07037 | 0.152192 | ||||||||
\(408\) | −8.93246 | −0.442223 | ||||||||
\(409\) | −33.1316 | −1.63825 | −0.819125 | − | 0.573615i | \(-0.805541\pi\) | ||||
−0.819125 | + | 0.573615i | \(0.805541\pi\) | |||||||
\(410\) | 6.16124 | 0.304282 | ||||||||
\(411\) | 41.7849 | 2.06110 | ||||||||
\(412\) | 6.34543 | 0.312617 | ||||||||
\(413\) | 6.68055 | 0.328728 | ||||||||
\(414\) | 27.2005 | 1.33683 | ||||||||
\(415\) | 25.5151 | 1.25249 | ||||||||
\(416\) | −4.75038 | −0.232907 | ||||||||
\(417\) | 35.5869 | 1.74270 | ||||||||
\(418\) | −4.72030 | −0.230878 | ||||||||
\(419\) | 4.70544 | 0.229876 | 0.114938 | − | 0.993373i | \(-0.463333\pi\) | ||||
0.114938 | + | 0.993373i | \(0.463333\pi\) | |||||||
\(420\) | 7.69020 | 0.375243 | ||||||||
\(421\) | 0.481440 | 0.0234640 | 0.0117320 | − | 0.999931i | \(-0.496266\pi\) | ||||
0.0117320 | + | 0.999931i | \(0.496266\pi\) | |||||||
\(422\) | −9.11175 | −0.443553 | ||||||||
\(423\) | 52.7657 | 2.56556 | ||||||||
\(424\) | −0.976945 | −0.0474446 | ||||||||
\(425\) | −10.7808 | −0.522947 | ||||||||
\(426\) | 39.1493 | 1.89679 | ||||||||
\(427\) | 1.66603 | 0.0806248 | ||||||||
\(428\) | 5.74011 | 0.277459 | ||||||||
\(429\) | 26.6563 | 1.28698 | ||||||||
\(430\) | 0.718018 | 0.0346259 | ||||||||
\(431\) | 3.93910 | 0.189740 | 0.0948700 | − | 0.995490i | \(-0.469756\pi\) | ||||
0.0948700 | + | 0.995490i | \(0.469756\pi\) | |||||||
\(432\) | −6.24021 | −0.300232 | ||||||||
\(433\) | −20.7600 | −0.997662 | −0.498831 | − | 0.866699i | \(-0.666237\pi\) | ||||
−0.498831 | + | 0.866699i | \(0.666237\pi\) | |||||||
\(434\) | −4.99266 | −0.239655 | ||||||||
\(435\) | −55.7532 | −2.67316 | ||||||||
\(436\) | 2.46460 | 0.118033 | ||||||||
\(437\) | 12.6308 | 0.604212 | ||||||||
\(438\) | 25.4765 | 1.21732 | ||||||||
\(439\) | −27.9455 | −1.33376 | −0.666882 | − | 0.745163i | \(-0.732371\pi\) | ||||
−0.666882 | + | 0.745163i | \(0.732371\pi\) | |||||||
\(440\) | −5.70345 | −0.271901 | ||||||||
\(441\) | −31.8401 | −1.51619 | ||||||||
\(442\) | 14.8347 | 0.705617 | ||||||||
\(443\) | 16.1926 | 0.769333 | 0.384667 | − | 0.923056i | \(-0.374316\pi\) | ||||
0.384667 | + | 0.923056i | \(0.374316\pi\) | |||||||
\(444\) | 4.47670 | 0.212455 | ||||||||
\(445\) | −24.4880 | −1.16084 | ||||||||
\(446\) | −11.2314 | −0.531824 | ||||||||
\(447\) | −46.7609 | −2.21172 | ||||||||
\(448\) | 0.924767 | 0.0436911 | ||||||||
\(449\) | 6.35882 | 0.300091 | 0.150046 | − | 0.988679i | \(-0.452058\pi\) | ||||
0.150046 | + | 0.988679i | \(0.452058\pi\) | |||||||
\(450\) | −17.8882 | −0.843257 | ||||||||
\(451\) | −4.15752 | −0.195770 | ||||||||
\(452\) | 3.31855 | 0.156092 | ||||||||
\(453\) | −69.9812 | −3.28800 | ||||||||
\(454\) | 9.49489 | 0.445617 | ||||||||
\(455\) | −12.7716 | −0.598743 | ||||||||
\(456\) | −6.88237 | −0.322296 | ||||||||
\(457\) | −6.02019 | −0.281613 | −0.140806 | − | 0.990037i | \(-0.544969\pi\) | ||||
−0.140806 | + | 0.990037i | \(0.544969\pi\) | |||||||
\(458\) | 9.64030 | 0.450461 | ||||||||
\(459\) | 19.4873 | 0.909588 | ||||||||
\(460\) | 15.2615 | 0.711571 | ||||||||
\(461\) | 20.1400 | 0.938011 | 0.469006 | − | 0.883195i | \(-0.344612\pi\) | ||||
0.469006 | + | 0.883195i | \(0.344612\pi\) | |||||||
\(462\) | −5.18924 | −0.241425 | ||||||||
\(463\) | 24.5324 | 1.14012 | 0.570059 | − | 0.821604i | \(-0.306920\pi\) | ||||
0.570059 | + | 0.821604i | \(0.306920\pi\) | |||||||
\(464\) | −6.70446 | −0.311247 | ||||||||
\(465\) | 44.8958 | 2.08199 | ||||||||
\(466\) | −10.6424 | −0.492998 | ||||||||
\(467\) | −33.1166 | −1.53245 | −0.766226 | − | 0.642571i | \(-0.777868\pi\) | ||||
−0.766226 | + | 0.642571i | \(0.777868\pi\) | |||||||
\(468\) | 24.6147 | 1.13781 | ||||||||
\(469\) | 6.37968 | 0.294586 | ||||||||
\(470\) | 29.6054 | 1.36560 | ||||||||
\(471\) | 6.83497 | 0.314939 | ||||||||
\(472\) | −7.22403 | −0.332513 | ||||||||
\(473\) | −0.484508 | −0.0222777 | ||||||||
\(474\) | −5.93658 | −0.272676 | ||||||||
\(475\) | −8.30651 | −0.381129 | ||||||||
\(476\) | −2.88791 | −0.132367 | ||||||||
\(477\) | 5.06216 | 0.231780 | ||||||||
\(478\) | −6.03473 | −0.276022 | ||||||||
\(479\) | 11.4385 | 0.522637 | 0.261319 | − | 0.965253i | \(-0.415843\pi\) | ||||
0.261319 | + | 0.965253i | \(0.415843\pi\) | |||||||
\(480\) | −8.31583 | −0.379564 | ||||||||
\(481\) | −7.43476 | −0.338996 | ||||||||
\(482\) | 8.99086 | 0.409523 | ||||||||
\(483\) | 13.8856 | 0.631815 | ||||||||
\(484\) | −7.15140 | −0.325063 | ||||||||
\(485\) | −23.4950 | −1.06686 | ||||||||
\(486\) | −12.1294 | −0.550200 | ||||||||
\(487\) | 21.3072 | 0.965520 | 0.482760 | − | 0.875753i | \(-0.339634\pi\) | ||||
0.482760 | + | 0.875753i | \(0.339634\pi\) | |||||||
\(488\) | −1.80157 | −0.0815530 | ||||||||
\(489\) | −48.6483 | −2.19995 | ||||||||
\(490\) | −17.8646 | −0.807042 | ||||||||
\(491\) | −10.6261 | −0.479548 | −0.239774 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239774 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(492\) | −6.06181 | −0.273288 | ||||||||
\(493\) | 20.9371 | 0.942958 | ||||||||
\(494\) | 11.4300 | 0.514260 | ||||||||
\(495\) | 29.5531 | 1.32831 | ||||||||
\(496\) | 5.39883 | 0.242415 | ||||||||
\(497\) | 12.6572 | 0.567752 | ||||||||
\(498\) | −25.1033 | −1.12491 | ||||||||
\(499\) | −14.2070 | −0.635993 | −0.317996 | − | 0.948092i | \(-0.603010\pi\) | ||||
−0.317996 | + | 0.948092i | \(0.603010\pi\) | |||||||
\(500\) | 4.49978 | 0.201236 | ||||||||
\(501\) | 31.7734 | 1.41953 | ||||||||
\(502\) | 9.62109 | 0.429410 | ||||||||
\(503\) | 42.8787 | 1.91187 | 0.955934 | − | 0.293581i | \(-0.0948471\pi\) | ||||
0.955934 | + | 0.293581i | \(0.0948471\pi\) | |||||||
\(504\) | −4.79179 | −0.213443 | ||||||||
\(505\) | 46.0126 | 2.04753 | ||||||||
\(506\) | −10.2982 | −0.457813 | ||||||||
\(507\) | −27.3625 | −1.21521 | ||||||||
\(508\) | 10.7675 | 0.477732 | ||||||||
\(509\) | −20.6702 | −0.916192 | −0.458096 | − | 0.888903i | \(-0.651468\pi\) | ||||
−0.458096 | + | 0.888903i | \(0.651468\pi\) | |||||||
\(510\) | 25.9691 | 1.14993 | ||||||||
\(511\) | 8.23670 | 0.364370 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 15.0147 | 0.662917 | ||||||||
\(514\) | −27.6742 | −1.22066 | ||||||||
\(515\) | −18.4479 | −0.812911 | ||||||||
\(516\) | −0.706430 | −0.0310989 | ||||||||
\(517\) | −19.9773 | −0.878602 | ||||||||
\(518\) | 1.44734 | 0.0635925 | ||||||||
\(519\) | 21.2739 | 0.933819 | ||||||||
\(520\) | 13.8107 | 0.605637 | ||||||||
\(521\) | −22.0184 | −0.964645 | −0.482322 | − | 0.875994i | \(-0.660207\pi\) | ||||
−0.482322 | + | 0.875994i | \(0.660207\pi\) | |||||||
\(522\) | 34.7400 | 1.52053 | ||||||||
\(523\) | −15.9562 | −0.697715 | −0.348858 | − | 0.937176i | \(-0.613430\pi\) | ||||
−0.348858 | + | 0.937176i | \(0.613430\pi\) | |||||||
\(524\) | −16.1817 | −0.706900 | ||||||||
\(525\) | −9.13172 | −0.398541 | ||||||||
\(526\) | −9.78791 | −0.426773 | ||||||||
\(527\) | −16.8598 | −0.734423 | ||||||||
\(528\) | 5.61140 | 0.244205 | ||||||||
\(529\) | 4.55644 | 0.198106 | ||||||||
\(530\) | 2.84024 | 0.123372 | ||||||||
\(531\) | 37.4322 | 1.62442 | ||||||||
\(532\) | −2.22510 | −0.0964705 | ||||||||
\(533\) | 10.0673 | 0.436061 | ||||||||
\(534\) | 24.0928 | 1.04260 | ||||||||
\(535\) | −16.6881 | −0.721488 | ||||||||
\(536\) | −6.89869 | −0.297978 | ||||||||
\(537\) | 7.33969 | 0.316731 | ||||||||
\(538\) | 14.1504 | 0.610067 | ||||||||
\(539\) | 12.0548 | 0.519237 | ||||||||
\(540\) | 18.1420 | 0.780708 | ||||||||
\(541\) | 21.3231 | 0.916750 | 0.458375 | − | 0.888759i | \(-0.348432\pi\) | ||||
0.458375 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(542\) | 14.9984 | 0.644235 | ||||||||
\(543\) | 49.4712 | 2.12301 | ||||||||
\(544\) | 3.12285 | 0.133891 | ||||||||
\(545\) | −7.16526 | −0.306926 | ||||||||
\(546\) | 12.5655 | 0.537755 | ||||||||
\(547\) | −6.58830 | −0.281695 | −0.140848 | − | 0.990031i | \(-0.544983\pi\) | ||||
−0.140848 | + | 0.990031i | \(0.544983\pi\) | |||||||
\(548\) | −14.6083 | −0.624036 | ||||||||
\(549\) | 9.33503 | 0.398409 | ||||||||
\(550\) | 6.77255 | 0.288782 | ||||||||
\(551\) | 16.1318 | 0.687237 | ||||||||
\(552\) | −15.0152 | −0.639090 | ||||||||
\(553\) | −1.91933 | −0.0816180 | ||||||||
\(554\) | 6.51546 | 0.276815 | ||||||||
\(555\) | −13.0150 | −0.552456 | ||||||||
\(556\) | −12.4414 | −0.527635 | ||||||||
\(557\) | −8.20766 | −0.347770 | −0.173885 | − | 0.984766i | \(-0.555632\pi\) | ||||
−0.173885 | + | 0.984766i | \(0.555632\pi\) | |||||||
\(558\) | −27.9747 | −1.18426 | ||||||||
\(559\) | 1.17322 | 0.0496217 | ||||||||
\(560\) | −2.68855 | −0.113612 | ||||||||
\(561\) | −17.5236 | −0.739846 | ||||||||
\(562\) | −27.8508 | −1.17481 | ||||||||
\(563\) | −24.2028 | −1.02003 | −0.510013 | − | 0.860167i | \(-0.670359\pi\) | ||||
−0.510013 | + | 0.860167i | \(0.670359\pi\) | |||||||
\(564\) | −29.1277 | −1.22650 | ||||||||
\(565\) | −9.64793 | −0.405892 | ||||||||
\(566\) | −7.40071 | −0.311075 | ||||||||
\(567\) | 2.13099 | 0.0894930 | ||||||||
\(568\) | −13.6869 | −0.574288 | ||||||||
\(569\) | −43.8335 | −1.83760 | −0.918798 | − | 0.394727i | \(-0.870839\pi\) | ||||
−0.918798 | + | 0.394727i | \(0.870839\pi\) | |||||||
\(570\) | 20.0089 | 0.838082 | ||||||||
\(571\) | −20.6604 | −0.864610 | −0.432305 | − | 0.901727i | \(-0.642300\pi\) | ||||
−0.432305 | + | 0.901727i | \(0.642300\pi\) | |||||||
\(572\) | −9.31923 | −0.389657 | ||||||||
\(573\) | −20.1282 | −0.840869 | ||||||||
\(574\) | −1.95981 | −0.0818011 | ||||||||
\(575\) | −18.1222 | −0.755750 | ||||||||
\(576\) | 5.18162 | 0.215901 | ||||||||
\(577\) | 38.8143 | 1.61586 | 0.807930 | − | 0.589279i | \(-0.200588\pi\) | ||||
0.807930 | + | 0.589279i | \(0.200588\pi\) | |||||||
\(578\) | 7.24779 | 0.301468 | ||||||||
\(579\) | 64.6334 | 2.68607 | ||||||||
\(580\) | 19.4917 | 0.809349 | ||||||||
\(581\) | −8.11604 | −0.336710 | ||||||||
\(582\) | 23.1159 | 0.958184 | ||||||||
\(583\) | −1.91656 | −0.0793756 | ||||||||
\(584\) | −8.90678 | −0.368565 | ||||||||
\(585\) | −71.5616 | −2.95871 | ||||||||
\(586\) | −28.9410 | −1.19554 | ||||||||
\(587\) | −24.1509 | −0.996815 | −0.498407 | − | 0.866943i | \(-0.666082\pi\) | ||||
−0.498407 | + | 0.866943i | \(0.666082\pi\) | |||||||
\(588\) | 17.5763 | 0.724835 | ||||||||
\(589\) | −12.9903 | −0.535255 | ||||||||
\(590\) | 21.0022 | 0.864648 | ||||||||
\(591\) | −16.2824 | −0.669768 | ||||||||
\(592\) | −1.56509 | −0.0643247 | ||||||||
\(593\) | 8.60652 | 0.353427 | 0.176714 | − | 0.984262i | \(-0.443453\pi\) | ||||
0.176714 | + | 0.984262i | \(0.443453\pi\) | |||||||
\(594\) | −12.2420 | −0.502294 | ||||||||
\(595\) | 8.39595 | 0.344200 | ||||||||
\(596\) | 16.3480 | 0.669638 | ||||||||
\(597\) | 76.6676 | 3.13780 | ||||||||
\(598\) | 24.9368 | 1.01974 | ||||||||
\(599\) | 43.4943 | 1.77713 | 0.888565 | − | 0.458750i | \(-0.151703\pi\) | ||||
0.888565 | + | 0.458750i | \(0.151703\pi\) | |||||||
\(600\) | 9.87461 | 0.403129 | ||||||||
\(601\) | 41.7126 | 1.70149 | 0.850747 | − | 0.525576i | \(-0.176150\pi\) | ||||
0.850747 | + | 0.525576i | \(0.176150\pi\) | |||||||
\(602\) | −0.228392 | −0.00930858 | ||||||||
\(603\) | 35.7464 | 1.45571 | ||||||||
\(604\) | 24.4659 | 0.995504 | ||||||||
\(605\) | 20.7911 | 0.845277 | ||||||||
\(606\) | −45.2700 | −1.83897 | ||||||||
\(607\) | 12.5991 | 0.511381 | 0.255690 | − | 0.966759i | \(-0.417697\pi\) | ||||
0.255690 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(608\) | 2.40612 | 0.0975812 | ||||||||
\(609\) | 17.7344 | 0.718633 | ||||||||
\(610\) | 5.23764 | 0.212066 | ||||||||
\(611\) | 48.3742 | 1.95701 | ||||||||
\(612\) | −16.1814 | −0.654096 | ||||||||
\(613\) | −17.0227 | −0.687542 | −0.343771 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343771 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(614\) | −22.1714 | −0.894767 | ||||||||
\(615\) | 17.6233 | 0.710642 | ||||||||
\(616\) | 1.81419 | 0.0730960 | ||||||||
\(617\) | 0.633973 | 0.0255228 | 0.0127614 | − | 0.999919i | \(-0.495938\pi\) | ||||
0.0127614 | + | 0.999919i | \(0.495938\pi\) | |||||||
\(618\) | 18.1502 | 0.730107 | ||||||||
\(619\) | −38.6596 | −1.55386 | −0.776931 | − | 0.629586i | \(-0.783225\pi\) | ||||
−0.776931 | + | 0.629586i | \(0.783225\pi\) | |||||||
\(620\) | −15.6959 | −0.630362 | ||||||||
\(621\) | 32.7575 | 1.31451 | ||||||||
\(622\) | 1.02105 | 0.0409402 | ||||||||
\(623\) | 7.78931 | 0.312072 | ||||||||
\(624\) | −13.5878 | −0.543946 | ||||||||
\(625\) | −30.3432 | −1.21373 | ||||||||
\(626\) | 25.1728 | 1.00611 | ||||||||
\(627\) | −13.5017 | −0.539207 | ||||||||
\(628\) | −2.38955 | −0.0953535 | ||||||||
\(629\) | 4.88754 | 0.194879 | ||||||||
\(630\) | 13.9311 | 0.555026 | ||||||||
\(631\) | −4.95319 | −0.197183 | −0.0985917 | − | 0.995128i | \(-0.531434\pi\) | ||||
−0.0985917 | + | 0.995128i | \(0.531434\pi\) | |||||||
\(632\) | 2.07547 | 0.0825577 | ||||||||
\(633\) | −26.0628 | −1.03590 | ||||||||
\(634\) | 11.7399 | 0.466251 | ||||||||
\(635\) | −31.3042 | −1.24227 | ||||||||
\(636\) | −2.79441 | −0.110805 | ||||||||
\(637\) | −29.1902 | −1.15656 | ||||||||
\(638\) | −13.1527 | −0.520721 | ||||||||
\(639\) | 70.9202 | 2.80556 | ||||||||
\(640\) | 2.90727 | 0.114920 | ||||||||
\(641\) | 6.03197 | 0.238248 | 0.119124 | − | 0.992879i | \(-0.461991\pi\) | ||||
0.119124 | + | 0.992879i | \(0.461991\pi\) | |||||||
\(642\) | 16.4187 | 0.647996 | ||||||||
\(643\) | 16.8039 | 0.662679 | 0.331340 | − | 0.943512i | \(-0.392499\pi\) | ||||
0.331340 | + | 0.943512i | \(0.392499\pi\) | |||||||
\(644\) | −4.85449 | −0.191294 | ||||||||
\(645\) | 2.05379 | 0.0808677 | ||||||||
\(646\) | −7.51397 | −0.295633 | ||||||||
\(647\) | 18.9646 | 0.745576 | 0.372788 | − | 0.927917i | \(-0.378402\pi\) | ||||
0.372788 | + | 0.927917i | \(0.378402\pi\) | |||||||
\(648\) | −2.30435 | −0.0905234 | ||||||||
\(649\) | −14.1720 | −0.556300 | ||||||||
\(650\) | −16.3994 | −0.643239 | ||||||||
\(651\) | −14.2808 | −0.559708 | ||||||||
\(652\) | 17.0078 | 0.666076 | ||||||||
\(653\) | −5.59835 | −0.219080 | −0.109540 | − | 0.993982i | \(-0.534938\pi\) | ||||
−0.109540 | + | 0.993982i | \(0.534938\pi\) | |||||||
\(654\) | 7.04962 | 0.275662 | ||||||||
\(655\) | 47.0445 | 1.83818 | ||||||||
\(656\) | 2.11925 | 0.0827429 | ||||||||
\(657\) | 46.1516 | 1.80054 | ||||||||
\(658\) | −9.41712 | −0.367118 | ||||||||
\(659\) | 27.7703 | 1.08178 | 0.540890 | − | 0.841094i | \(-0.318088\pi\) | ||||
0.540890 | + | 0.841094i | \(0.318088\pi\) | |||||||
\(660\) | −16.3139 | −0.635017 | ||||||||
\(661\) | −32.7324 | −1.27314 | −0.636571 | − | 0.771218i | \(-0.719648\pi\) | ||||
−0.636571 | + | 0.771218i | \(0.719648\pi\) | |||||||
\(662\) | 3.72572 | 0.144804 | ||||||||
\(663\) | 42.4326 | 1.64795 | ||||||||
\(664\) | 8.77630 | 0.340587 | ||||||||
\(665\) | 6.46899 | 0.250857 | ||||||||
\(666\) | 8.10970 | 0.314244 | ||||||||
\(667\) | 35.1946 | 1.36274 | ||||||||
\(668\) | −11.1082 | −0.429789 | ||||||||
\(669\) | −32.1259 | −1.24206 | ||||||||
\(670\) | 20.0564 | 0.774845 | ||||||||
\(671\) | −3.53429 | −0.136440 | ||||||||
\(672\) | 2.64516 | 0.102039 | ||||||||
\(673\) | −1.26633 | −0.0488134 | −0.0244067 | − | 0.999702i | \(-0.507770\pi\) | ||||
−0.0244067 | + | 0.999702i | \(0.507770\pi\) | |||||||
\(674\) | −0.392319 | −0.0151115 | ||||||||
\(675\) | −21.5427 | −0.829178 | ||||||||
\(676\) | 9.56611 | 0.367927 | ||||||||
\(677\) | −22.2235 | −0.854119 | −0.427059 | − | 0.904224i | \(-0.640450\pi\) | ||||
−0.427059 | + | 0.904224i | \(0.640450\pi\) | |||||||
\(678\) | 9.49223 | 0.364547 | ||||||||
\(679\) | 7.47348 | 0.286806 | ||||||||
\(680\) | −9.07899 | −0.348163 | ||||||||
\(681\) | 27.1587 | 1.04073 | ||||||||
\(682\) | 10.5914 | 0.405564 | ||||||||
\(683\) | 4.75350 | 0.181888 | 0.0909438 | − | 0.995856i | \(-0.471012\pi\) | ||||
0.0909438 | + | 0.995856i | \(0.471012\pi\) | |||||||
\(684\) | −12.4676 | −0.476712 | ||||||||
\(685\) | 42.4703 | 1.62271 | ||||||||
\(686\) | 12.1559 | 0.464114 | ||||||||
\(687\) | 27.5747 | 1.05204 | ||||||||
\(688\) | 0.246973 | 0.00941576 | ||||||||
\(689\) | 4.64086 | 0.176803 | ||||||||
\(690\) | 43.6533 | 1.66185 | ||||||||
\(691\) | −25.4118 | −0.966711 | −0.483355 | − | 0.875424i | \(-0.660582\pi\) | ||||
−0.483355 | + | 0.875424i | \(0.660582\pi\) | |||||||
\(692\) | −7.43749 | −0.282731 | ||||||||
\(693\) | −9.40047 | −0.357095 | ||||||||
\(694\) | 26.2281 | 0.995604 | ||||||||
\(695\) | 36.1707 | 1.37203 | ||||||||
\(696\) | −19.1771 | −0.726908 | ||||||||
\(697\) | −6.61811 | −0.250679 | ||||||||
\(698\) | 5.24597 | 0.198563 | ||||||||
\(699\) | −30.4410 | −1.15138 | ||||||||
\(700\) | 3.19251 | 0.120666 | ||||||||
\(701\) | −48.4592 | −1.83028 | −0.915139 | − | 0.403138i | \(-0.867920\pi\) | ||||
−0.915139 | + | 0.403138i | \(0.867920\pi\) | |||||||
\(702\) | 29.6434 | 1.11882 | ||||||||
\(703\) | 3.76580 | 0.142030 | ||||||||
\(704\) | −1.96179 | −0.0739376 | ||||||||
\(705\) | 84.6820 | 3.18931 | ||||||||
\(706\) | 6.45299 | 0.242862 | ||||||||
\(707\) | −14.6360 | −0.550444 | ||||||||
\(708\) | −20.6633 | −0.776574 | ||||||||
\(709\) | −12.0723 | −0.453386 | −0.226693 | − | 0.973966i | \(-0.572791\pi\) | ||||
−0.226693 | + | 0.973966i | \(0.572791\pi\) | |||||||
\(710\) | 39.7915 | 1.49335 | ||||||||
\(711\) | −10.7543 | −0.403318 | ||||||||
\(712\) | −8.42300 | −0.315665 | ||||||||
\(713\) | −28.3408 | −1.06137 | ||||||||
\(714\) | −8.26045 | −0.309139 | ||||||||
\(715\) | 27.0935 | 1.01324 | ||||||||
\(716\) | −2.56601 | −0.0958962 | ||||||||
\(717\) | −17.2614 | −0.644641 | ||||||||
\(718\) | 30.6743 | 1.14475 | ||||||||
\(719\) | −40.0619 | −1.49406 | −0.747028 | − | 0.664793i | \(-0.768520\pi\) | ||||
−0.747028 | + | 0.664793i | \(0.768520\pi\) | |||||||
\(720\) | −15.0644 | −0.561417 | ||||||||
\(721\) | 5.86804 | 0.218537 | ||||||||
\(722\) | 13.2106 | 0.491646 | ||||||||
\(723\) | 25.7171 | 0.956427 | ||||||||
\(724\) | −17.2955 | −0.642781 | ||||||||
\(725\) | −23.1454 | −0.859598 | ||||||||
\(726\) | −20.4555 | −0.759176 | ||||||||
\(727\) | 50.9079 | 1.88807 | 0.944034 | − | 0.329848i | \(-0.106997\pi\) | ||||
0.944034 | + | 0.329848i | \(0.106997\pi\) | |||||||
\(728\) | −4.39299 | −0.162815 | ||||||||
\(729\) | −41.6074 | −1.54101 | ||||||||
\(730\) | 25.8944 | 0.958396 | ||||||||
\(731\) | −0.771260 | −0.0285261 | ||||||||
\(732\) | −5.15311 | −0.190465 | ||||||||
\(733\) | 13.9213 | 0.514197 | 0.257098 | − | 0.966385i | \(-0.417234\pi\) | ||||
0.257098 | + | 0.966385i | \(0.417234\pi\) | |||||||
\(734\) | 3.99356 | 0.147405 | ||||||||
\(735\) | −51.0992 | −1.88482 | ||||||||
\(736\) | 5.24942 | 0.193496 | ||||||||
\(737\) | −13.5337 | −0.498522 | ||||||||
\(738\) | −10.9812 | −0.404222 | ||||||||
\(739\) | 24.9402 | 0.917440 | 0.458720 | − | 0.888581i | \(-0.348308\pi\) | ||||
0.458720 | + | 0.888581i | \(0.348308\pi\) | |||||||
\(740\) | 4.55014 | 0.167266 | ||||||||
\(741\) | 32.6939 | 1.20104 | ||||||||
\(742\) | −0.903446 | −0.0331665 | ||||||||
\(743\) | −16.3152 | −0.598547 | −0.299274 | − | 0.954167i | \(-0.596744\pi\) | ||||
−0.299274 | + | 0.954167i | \(0.596744\pi\) | |||||||
\(744\) | 15.4426 | 0.566152 | ||||||||
\(745\) | −47.5280 | −1.74129 | ||||||||
\(746\) | 8.77963 | 0.321445 | ||||||||
\(747\) | −45.4755 | −1.66386 | ||||||||
\(748\) | 6.12637 | 0.224002 | ||||||||
\(749\) | 5.30827 | 0.193960 | ||||||||
\(750\) | 12.8709 | 0.469981 | ||||||||
\(751\) | 8.63544 | 0.315112 | 0.157556 | − | 0.987510i | \(-0.449639\pi\) | ||||
0.157556 | + | 0.987510i | \(0.449639\pi\) | |||||||
\(752\) | 10.1832 | 0.371344 | ||||||||
\(753\) | 27.5197 | 1.00287 | ||||||||
\(754\) | 31.8488 | 1.15986 | ||||||||
\(755\) | −71.1291 | −2.58865 | ||||||||
\(756\) | −5.77074 | −0.209880 | ||||||||
\(757\) | −6.09659 | −0.221584 | −0.110792 | − | 0.993844i | \(-0.535339\pi\) | ||||
−0.110792 | + | 0.993844i | \(0.535339\pi\) | |||||||
\(758\) | −0.346627 | −0.0125901 | ||||||||
\(759\) | −29.4566 | −1.06921 | ||||||||
\(760\) | −6.99526 | −0.253745 | ||||||||
\(761\) | 0.318396 | 0.0115418 | 0.00577091 | − | 0.999983i | \(-0.498163\pi\) | ||||
0.00577091 | + | 0.999983i | \(0.498163\pi\) | |||||||
\(762\) | 30.7990 | 1.11573 | ||||||||
\(763\) | 2.27918 | 0.0825118 | ||||||||
\(764\) | 7.03698 | 0.254589 | ||||||||
\(765\) | 47.0439 | 1.70088 | ||||||||
\(766\) | 11.3843 | 0.411332 | ||||||||
\(767\) | 34.3169 | 1.23911 | ||||||||
\(768\) | −2.86035 | −0.103214 | ||||||||
\(769\) | −29.6649 | −1.06974 | −0.534872 | − | 0.844933i | \(-0.679640\pi\) | ||||
−0.534872 | + | 0.844933i | \(0.679640\pi\) | |||||||
\(770\) | −5.27436 | −0.190075 | ||||||||
\(771\) | −79.1580 | −2.85081 | ||||||||
\(772\) | −22.5963 | −0.813258 | ||||||||
\(773\) | 12.5021 | 0.449671 | 0.224835 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224835 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(774\) | −1.27972 | −0.0459986 | ||||||||
\(775\) | 18.6380 | 0.669498 | ||||||||
\(776\) | −8.08147 | −0.290108 | ||||||||
\(777\) | 4.13991 | 0.148518 | ||||||||
\(778\) | −6.21366 | −0.222770 | ||||||||
\(779\) | −5.09919 | −0.182697 | ||||||||
\(780\) | 39.5033 | 1.41445 | ||||||||
\(781\) | −26.8507 | −0.960794 | ||||||||
\(782\) | −16.3932 | −0.586219 | ||||||||
\(783\) | 41.8373 | 1.49514 | ||||||||
\(784\) | −6.14481 | −0.219457 | ||||||||
\(785\) | 6.94708 | 0.247952 | ||||||||
\(786\) | −46.2853 | −1.65094 | ||||||||
\(787\) | 20.5767 | 0.733479 | 0.366740 | − | 0.930324i | \(-0.380474\pi\) | ||||
0.366740 | + | 0.930324i | \(0.380474\pi\) | |||||||
\(788\) | 5.69244 | 0.202785 | ||||||||
\(789\) | −27.9969 | −0.996715 | ||||||||
\(790\) | −6.03396 | −0.214679 | ||||||||
\(791\) | 3.06889 | 0.109117 | ||||||||
\(792\) | 10.1652 | 0.361206 | ||||||||
\(793\) | 8.55812 | 0.303908 | ||||||||
\(794\) | 26.0825 | 0.925633 | ||||||||
\(795\) | 8.12410 | 0.288132 | ||||||||
\(796\) | −26.8035 | −0.950026 | ||||||||
\(797\) | −24.1437 | −0.855214 | −0.427607 | − | 0.903965i | \(-0.640643\pi\) | ||||
−0.427607 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(798\) | −6.36459 | −0.225304 | ||||||||
\(799\) | −31.8007 | −1.12503 | ||||||||
\(800\) | −3.45224 | −0.122055 | ||||||||
\(801\) | 43.6448 | 1.54211 | ||||||||
\(802\) | 11.2005 | 0.395505 | ||||||||
\(803\) | −17.4732 | −0.616616 | ||||||||
\(804\) | −19.7327 | −0.695918 | ||||||||
\(805\) | 14.1133 | 0.497430 | ||||||||
\(806\) | −25.6465 | −0.903360 | ||||||||
\(807\) | 40.4751 | 1.42479 | ||||||||
\(808\) | 15.8267 | 0.556782 | ||||||||
\(809\) | −7.60139 | −0.267251 | −0.133625 | − | 0.991032i | \(-0.542662\pi\) | ||||
−0.133625 | + | 0.991032i | \(0.542662\pi\) | |||||||
\(810\) | 6.69937 | 0.235392 | ||||||||
\(811\) | −16.7616 | −0.588580 | −0.294290 | − | 0.955716i | \(-0.595083\pi\) | ||||
−0.294290 | + | 0.955716i | \(0.595083\pi\) | |||||||
\(812\) | −6.20007 | −0.217580 | ||||||||
\(813\) | 42.9006 | 1.50459 | ||||||||
\(814\) | −3.07037 | −0.107616 | ||||||||
\(815\) | −49.4463 | −1.73203 | ||||||||
\(816\) | 8.93246 | 0.312699 | ||||||||
\(817\) | −0.594248 | −0.0207901 | ||||||||
\(818\) | 33.1316 | 1.15842 | ||||||||
\(819\) | 22.7628 | 0.795398 | ||||||||
\(820\) | −6.16124 | −0.215160 | ||||||||
\(821\) | −10.1763 | −0.355156 | −0.177578 | − | 0.984107i | \(-0.556826\pi\) | ||||
−0.177578 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(822\) | −41.7849 | −1.45742 | ||||||||
\(823\) | −36.4234 | −1.26964 | −0.634820 | − | 0.772660i | \(-0.718926\pi\) | ||||
−0.634820 | + | 0.772660i | \(0.718926\pi\) | |||||||
\(824\) | −6.34543 | −0.221053 | ||||||||
\(825\) | 19.3719 | 0.674442 | ||||||||
\(826\) | −6.68055 | −0.232446 | ||||||||
\(827\) | −34.4459 | −1.19780 | −0.598900 | − | 0.800824i | \(-0.704395\pi\) | ||||
−0.598900 | + | 0.800824i | \(0.704395\pi\) | |||||||
\(828\) | −27.2005 | −0.945284 | ||||||||
\(829\) | 19.9394 | 0.692524 | 0.346262 | − | 0.938138i | \(-0.387451\pi\) | ||||
0.346262 | + | 0.938138i | \(0.387451\pi\) | |||||||
\(830\) | −25.5151 | −0.885642 | ||||||||
\(831\) | 18.6365 | 0.646494 | ||||||||
\(832\) | 4.75038 | 0.164690 | ||||||||
\(833\) | 19.1893 | 0.664871 | ||||||||
\(834\) | −35.5869 | −1.23227 | ||||||||
\(835\) | 32.2946 | 1.11760 | ||||||||
\(836\) | 4.72030 | 0.163255 | ||||||||
\(837\) | −33.6899 | −1.16449 | ||||||||
\(838\) | −4.70544 | −0.162547 | ||||||||
\(839\) | 9.69550 | 0.334726 | 0.167363 | − | 0.985895i | \(-0.446475\pi\) | ||||
0.167363 | + | 0.985895i | \(0.446475\pi\) | |||||||
\(840\) | −7.69020 | −0.265337 | ||||||||
\(841\) | 15.9498 | 0.549994 | ||||||||
\(842\) | −0.481440 | −0.0165915 | ||||||||
\(843\) | −79.6631 | −2.74374 | ||||||||
\(844\) | 9.11175 | 0.313639 | ||||||||
\(845\) | −27.8113 | −0.956738 | ||||||||
\(846\) | −52.7657 | −1.81412 | ||||||||
\(847\) | −6.61337 | −0.227238 | ||||||||
\(848\) | 0.976945 | 0.0335484 | ||||||||
\(849\) | −21.1686 | −0.726506 | ||||||||
\(850\) | 10.7808 | 0.369779 | ||||||||
\(851\) | 8.21581 | 0.281634 | ||||||||
\(852\) | −39.1493 | −1.34123 | ||||||||
\(853\) | 20.0790 | 0.687492 | 0.343746 | − | 0.939063i | \(-0.388304\pi\) | ||||
0.343746 | + | 0.939063i | \(0.388304\pi\) | |||||||
\(854\) | −1.66603 | −0.0570103 | ||||||||
\(855\) | 36.2468 | 1.23961 | ||||||||
\(856\) | −5.74011 | −0.196193 | ||||||||
\(857\) | 20.9821 | 0.716733 | 0.358367 | − | 0.933581i | \(-0.383334\pi\) | ||||
0.358367 | + | 0.933581i | \(0.383334\pi\) | |||||||
\(858\) | −26.6563 | −0.910031 | ||||||||
\(859\) | −21.9135 | −0.747680 | −0.373840 | − | 0.927493i | \(-0.621959\pi\) | ||||
−0.373840 | + | 0.927493i | \(0.621959\pi\) | |||||||
\(860\) | −0.718018 | −0.0244842 | ||||||||
\(861\) | −5.60576 | −0.191044 | ||||||||
\(862\) | −3.93910 | −0.134166 | ||||||||
\(863\) | 30.8113 | 1.04883 | 0.524414 | − | 0.851463i | \(-0.324284\pi\) | ||||
0.524414 | + | 0.851463i | \(0.324284\pi\) | |||||||
\(864\) | 6.24021 | 0.212296 | ||||||||
\(865\) | 21.6228 | 0.735198 | ||||||||
\(866\) | 20.7600 | 0.705454 | ||||||||
\(867\) | 20.7312 | 0.704070 | ||||||||
\(868\) | 4.99266 | 0.169462 | ||||||||
\(869\) | 4.07163 | 0.138120 | ||||||||
\(870\) | 55.7532 | 1.89021 | ||||||||
\(871\) | 32.7714 | 1.11042 | ||||||||
\(872\) | −2.46460 | −0.0834618 | ||||||||
\(873\) | 41.8751 | 1.41726 | ||||||||
\(874\) | −12.6308 | −0.427242 | ||||||||
\(875\) | 4.16124 | 0.140676 | ||||||||
\(876\) | −25.4765 | −0.860773 | ||||||||
\(877\) | 17.7004 | 0.597701 | 0.298850 | − | 0.954300i | \(-0.403397\pi\) | ||||
0.298850 | + | 0.954300i | \(0.403397\pi\) | |||||||
\(878\) | 27.9455 | 0.943113 | ||||||||
\(879\) | −82.7815 | −2.79215 | ||||||||
\(880\) | 5.70345 | 0.192263 | ||||||||
\(881\) | −0.849879 | −0.0286332 | −0.0143166 | − | 0.999898i | \(-0.504557\pi\) | ||||
−0.0143166 | + | 0.999898i | \(0.504557\pi\) | |||||||
\(882\) | 31.8401 | 1.07211 | ||||||||
\(883\) | −15.8989 | −0.535040 | −0.267520 | − | 0.963552i | \(-0.586204\pi\) | ||||
−0.267520 | + | 0.963552i | \(0.586204\pi\) | |||||||
\(884\) | −14.8347 | −0.498946 | ||||||||
\(885\) | 60.0738 | 2.01936 | ||||||||
\(886\) | −16.1926 | −0.544001 | ||||||||
\(887\) | −8.57797 | −0.288020 | −0.144010 | − | 0.989576i | \(-0.546000\pi\) | ||||
−0.144010 | + | 0.989576i | \(0.546000\pi\) | |||||||
\(888\) | −4.47670 | −0.150228 | ||||||||
\(889\) | 9.95746 | 0.333962 | ||||||||
\(890\) | 24.4880 | 0.820838 | ||||||||
\(891\) | −4.52064 | −0.151447 | ||||||||
\(892\) | 11.2314 | 0.376057 | ||||||||
\(893\) | −24.5021 | −0.819933 | ||||||||
\(894\) | 46.7609 | 1.56392 | ||||||||
\(895\) | 7.46009 | 0.249363 | ||||||||
\(896\) | −0.924767 | −0.0308943 | ||||||||
\(897\) | 71.3279 | 2.38157 | ||||||||
\(898\) | −6.35882 | −0.212197 | ||||||||
\(899\) | −36.1963 | −1.20721 | ||||||||
\(900\) | 17.8882 | 0.596273 | ||||||||
\(901\) | −3.05085 | −0.101639 | ||||||||
\(902\) | 4.15752 | 0.138430 | ||||||||
\(903\) | −0.653283 | −0.0217399 | ||||||||
\(904\) | −3.31855 | −0.110373 | ||||||||
\(905\) | 50.2827 | 1.67145 | ||||||||
\(906\) | 69.9812 | 2.32497 | ||||||||
\(907\) | 41.9823 | 1.39400 | 0.697000 | − | 0.717071i | \(-0.254518\pi\) | ||||
0.697000 | + | 0.717071i | \(0.254518\pi\) | |||||||
\(908\) | −9.49489 | −0.315099 | ||||||||
\(909\) | −82.0081 | −2.72004 | ||||||||
\(910\) | 12.7716 | 0.423376 | ||||||||
\(911\) | 8.97259 | 0.297275 | 0.148638 | − | 0.988892i | \(-0.452511\pi\) | ||||
0.148638 | + | 0.988892i | \(0.452511\pi\) | |||||||
\(912\) | 6.88237 | 0.227898 | ||||||||
\(913\) | 17.2172 | 0.569807 | ||||||||
\(914\) | 6.02019 | 0.199130 | ||||||||
\(915\) | 14.9815 | 0.495273 | ||||||||
\(916\) | −9.64030 | −0.318524 | ||||||||
\(917\) | −14.9643 | −0.494164 | ||||||||
\(918\) | −19.4873 | −0.643176 | ||||||||
\(919\) | 14.1904 | 0.468097 | 0.234049 | − | 0.972225i | \(-0.424803\pi\) | ||||
0.234049 | + | 0.972225i | \(0.424803\pi\) | |||||||
\(920\) | −15.2615 | −0.503157 | ||||||||
\(921\) | −63.4182 | −2.08970 | ||||||||
\(922\) | −20.1400 | −0.663274 | ||||||||
\(923\) | 65.0179 | 2.14009 | ||||||||
\(924\) | 5.18924 | 0.170713 | ||||||||
\(925\) | −5.40305 | −0.177651 | ||||||||
\(926\) | −24.5324 | −0.806185 | ||||||||
\(927\) | 32.8796 | 1.07991 | ||||||||
\(928\) | 6.70446 | 0.220085 | ||||||||
\(929\) | −35.1994 | −1.15485 | −0.577427 | − | 0.816442i | \(-0.695943\pi\) | ||||
−0.577427 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(930\) | −44.8958 | −1.47219 | ||||||||
\(931\) | 14.7852 | 0.484564 | ||||||||
\(932\) | 10.6424 | 0.348603 | ||||||||
\(933\) | 2.92055 | 0.0956146 | ||||||||
\(934\) | 33.1166 | 1.08361 | ||||||||
\(935\) | −17.8110 | −0.582483 | ||||||||
\(936\) | −24.6147 | −0.804556 | ||||||||
\(937\) | 3.34155 | 0.109164 | 0.0545819 | − | 0.998509i | \(-0.482617\pi\) | ||||
0.0545819 | + | 0.998509i | \(0.482617\pi\) | |||||||
\(938\) | −6.37968 | −0.208304 | ||||||||
\(939\) | 72.0030 | 2.34973 | ||||||||
\(940\) | −29.6054 | −0.965623 | ||||||||
\(941\) | 5.63570 | 0.183719 | 0.0918593 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918593 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(942\) | −6.83497 | −0.222695 | ||||||||
\(943\) | −11.1249 | −0.362275 | ||||||||
\(944\) | 7.22403 | 0.235122 | ||||||||
\(945\) | 16.7771 | 0.545760 | ||||||||
\(946\) | 0.484508 | 0.0157527 | ||||||||
\(947\) | 13.7554 | 0.446990 | 0.223495 | − | 0.974705i | \(-0.428253\pi\) | ||||
0.223495 | + | 0.974705i | \(0.428253\pi\) | |||||||
\(948\) | 5.93658 | 0.192811 | ||||||||
\(949\) | 42.3106 | 1.37346 | ||||||||
\(950\) | 8.30651 | 0.269499 | ||||||||
\(951\) | 33.5802 | 1.08891 | ||||||||
\(952\) | 2.88791 | 0.0935977 | ||||||||
\(953\) | 16.7347 | 0.542090 | 0.271045 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271045 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(954\) | −5.06216 | −0.163893 | ||||||||
\(955\) | −20.4584 | −0.662018 | ||||||||
\(956\) | 6.03473 | 0.195177 | ||||||||
\(957\) | −37.6214 | −1.21613 | ||||||||
\(958\) | −11.4385 | −0.369560 | ||||||||
\(959\) | −13.5093 | −0.436237 | ||||||||
\(960\) | 8.31583 | 0.268392 | ||||||||
\(961\) | −1.85260 | −0.0597613 | ||||||||
\(962\) | 7.43476 | 0.239706 | ||||||||
\(963\) | 29.7431 | 0.958458 | ||||||||
\(964\) | −8.99086 | −0.289576 | ||||||||
\(965\) | 65.6936 | 2.11475 | ||||||||
\(966\) | −13.8856 | −0.446761 | ||||||||
\(967\) | −10.1650 | −0.326885 | −0.163443 | − | 0.986553i | \(-0.552260\pi\) | ||||
−0.163443 | + | 0.986553i | \(0.552260\pi\) | |||||||
\(968\) | 7.15140 | 0.229855 | ||||||||
\(969\) | −21.4926 | −0.690443 | ||||||||
\(970\) | 23.4950 | 0.754380 | ||||||||
\(971\) | 22.7207 | 0.729142 | 0.364571 | − | 0.931176i | \(-0.381216\pi\) | ||||
0.364571 | + | 0.931176i | \(0.381216\pi\) | |||||||
\(972\) | 12.1294 | 0.389050 | ||||||||
\(973\) | −11.5054 | −0.368847 | ||||||||
\(974\) | −21.3072 | −0.682726 | ||||||||
\(975\) | −46.9082 | −1.50226 | ||||||||
\(976\) | 1.80157 | 0.0576667 | ||||||||
\(977\) | −23.5699 | −0.754069 | −0.377034 | − | 0.926199i | \(-0.623056\pi\) | ||||
−0.377034 | + | 0.926199i | \(0.623056\pi\) | |||||||
\(978\) | 48.6483 | 1.55560 | ||||||||
\(979\) | −16.5241 | −0.528113 | ||||||||
\(980\) | 17.8646 | 0.570665 | ||||||||
\(981\) | 12.7706 | 0.407734 | ||||||||
\(982\) | 10.6261 | 0.339091 | ||||||||
\(983\) | −35.1370 | −1.12069 | −0.560347 | − | 0.828258i | \(-0.689332\pi\) | ||||
−0.560347 | + | 0.828258i | \(0.689332\pi\) | |||||||
\(984\) | 6.06181 | 0.193243 | ||||||||
\(985\) | −16.5495 | −0.527310 | ||||||||
\(986\) | −20.9371 | −0.666772 | ||||||||
\(987\) | −26.9363 | −0.857392 | ||||||||
\(988\) | −11.4300 | −0.363637 | ||||||||
\(989\) | −1.29647 | −0.0412252 | ||||||||
\(990\) | −29.5531 | −0.939260 | ||||||||
\(991\) | −42.0035 | −1.33428 | −0.667142 | − | 0.744931i | \(-0.732483\pi\) | ||||
−0.667142 | + | 0.744931i | \(0.732483\pi\) | |||||||
\(992\) | −5.39883 | −0.171413 | ||||||||
\(993\) | 10.6569 | 0.338185 | ||||||||
\(994\) | −12.6572 | −0.401461 | ||||||||
\(995\) | 77.9252 | 2.47039 | ||||||||
\(996\) | 25.1033 | 0.795430 | ||||||||
\(997\) | 35.3169 | 1.11850 | 0.559248 | − | 0.829000i | \(-0.311090\pi\) | ||||
0.559248 | + | 0.829000i | \(0.311090\pi\) | |||||||
\(998\) | 14.2070 | 0.449715 | ||||||||
\(999\) | 9.76648 | 0.308998 |
(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 | 4006.2.a.g.1.4 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.4 | ✓ | 40 | 1.1 | even | 1 | trivial |