Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.95372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.27661 | 0.570918 | 0.285459 | − | 0.958391i | \(-0.407854\pi\) | ||||
0.285459 | + | 0.958391i | \(0.407854\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −5.23034 | −1.97688 | −0.988441 | − | 0.151609i | \(-0.951555\pi\) | ||||
−0.988441 | + | 0.151609i | \(0.951555\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.27661 | −0.403700 | ||||||||
\(11\) | −0.0462763 | −0.0139528 | −0.00697641 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697641 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.72448 | −1.58769 | −0.793843 | − | 0.608123i | \(-0.791923\pi\) | ||||
−0.793843 | + | 0.608123i | \(0.791923\pi\) | |||||||
\(14\) | 5.23034 | 1.39787 | ||||||||
\(15\) | 1.27661 | 0.329620 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.23034 | 1.26854 | 0.634271 | − | 0.773110i | \(-0.281300\pi\) | ||||
0.634271 | + | 0.773110i | \(0.281300\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 8.21863 | 1.88548 | 0.942742 | − | 0.333524i | \(-0.108238\pi\) | ||||
0.942742 | + | 0.333524i | \(0.108238\pi\) | |||||||
\(20\) | 1.27661 | 0.285459 | ||||||||
\(21\) | −5.23034 | −1.14135 | ||||||||
\(22\) | 0.0462763 | 0.00986614 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.37026 | −0.674052 | ||||||||
\(26\) | 5.72448 | 1.12266 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.23034 | −0.988441 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.27661 | −0.233076 | ||||||||
\(31\) | −4.18296 | −0.751282 | −0.375641 | − | 0.926765i | \(-0.622577\pi\) | ||||
−0.375641 | + | 0.926765i | \(0.622577\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.0462763 | −0.00805567 | ||||||||
\(34\) | −5.23034 | −0.896995 | ||||||||
\(35\) | −6.67711 | −1.12864 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.31965 | 1.03894 | 0.519472 | − | 0.854487i | \(-0.326129\pi\) | ||||
0.519472 | + | 0.854487i | \(0.326129\pi\) | |||||||
\(38\) | −8.21863 | −1.33324 | ||||||||
\(39\) | −5.72448 | −0.916651 | ||||||||
\(40\) | −1.27661 | −0.201850 | ||||||||
\(41\) | 7.07871 | 1.10551 | 0.552754 | − | 0.833344i | \(-0.313577\pi\) | ||||
0.552754 | + | 0.833344i | \(0.313577\pi\) | |||||||
\(42\) | 5.23034 | 0.807058 | ||||||||
\(43\) | −11.1691 | −1.70327 | −0.851637 | − | 0.524132i | \(-0.824390\pi\) | ||||
−0.851637 | + | 0.524132i | \(0.824390\pi\) | |||||||
\(44\) | −0.0462763 | −0.00697641 | ||||||||
\(45\) | 1.27661 | 0.190306 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 2.31118 | 0.337121 | 0.168560 | − | 0.985691i | \(-0.446088\pi\) | ||||
0.168560 | + | 0.985691i | \(0.446088\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 20.3564 | 2.90806 | ||||||||
\(50\) | 3.37026 | 0.476627 | ||||||||
\(51\) | 5.23034 | 0.732394 | ||||||||
\(52\) | −5.72448 | −0.793843 | ||||||||
\(53\) | 1.04304 | 0.143272 | 0.0716362 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716362 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.0590769 | −0.00796592 | ||||||||
\(56\) | 5.23034 | 0.698933 | ||||||||
\(57\) | 8.21863 | 1.08858 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 7.63193 | 0.993593 | 0.496796 | − | 0.867867i | \(-0.334510\pi\) | ||||
0.496796 | + | 0.867867i | \(0.334510\pi\) | |||||||
\(60\) | 1.27661 | 0.164810 | ||||||||
\(61\) | −5.95372 | −0.762296 | −0.381148 | − | 0.924514i | \(-0.624471\pi\) | ||||
−0.381148 | + | 0.924514i | \(0.624471\pi\) | |||||||
\(62\) | 4.18296 | 0.531237 | ||||||||
\(63\) | −5.23034 | −0.658960 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.30795 | −0.906439 | ||||||||
\(66\) | 0.0462763 | 0.00569622 | ||||||||
\(67\) | −9.46391 | −1.15620 | −0.578100 | − | 0.815966i | \(-0.696206\pi\) | ||||
−0.578100 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(68\) | 5.23034 | 0.634271 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 6.67711 | 0.798067 | ||||||||
\(71\) | −6.52548 | −0.774432 | −0.387216 | − | 0.921989i | \(-0.626563\pi\) | ||||
−0.387216 | + | 0.921989i | \(0.626563\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.12389 | −0.248582 | −0.124291 | − | 0.992246i | \(-0.539666\pi\) | ||||
−0.124291 | + | 0.992246i | \(0.539666\pi\) | |||||||
\(74\) | −6.31965 | −0.734645 | ||||||||
\(75\) | −3.37026 | −0.389164 | ||||||||
\(76\) | 8.21863 | 0.942742 | ||||||||
\(77\) | 0.242041 | 0.0275831 | ||||||||
\(78\) | 5.72448 | 0.648170 | ||||||||
\(79\) | −12.5846 | −1.41587 | −0.707937 | − | 0.706276i | \(-0.750374\pi\) | ||||
−0.707937 | + | 0.706276i | \(0.750374\pi\) | |||||||
\(80\) | 1.27661 | 0.142730 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.07871 | −0.781712 | ||||||||
\(83\) | −14.8266 | −1.62743 | −0.813715 | − | 0.581264i | \(-0.802559\pi\) | ||||
−0.813715 | + | 0.581264i | \(0.802559\pi\) | |||||||
\(84\) | −5.23034 | −0.570676 | ||||||||
\(85\) | 6.67711 | 0.724234 | ||||||||
\(86\) | 11.1691 | 1.20440 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0.0462763 | 0.00493307 | ||||||||
\(89\) | −16.4059 | −1.73902 | −0.869512 | − | 0.493911i | \(-0.835567\pi\) | ||||
−0.869512 | + | 0.493911i | \(0.835567\pi\) | |||||||
\(90\) | −1.27661 | −0.134567 | ||||||||
\(91\) | 29.9410 | 3.13867 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −4.18296 | −0.433753 | ||||||||
\(94\) | −2.31118 | −0.238380 | ||||||||
\(95\) | 10.4920 | 1.07646 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.4059 | −1.25963 | −0.629816 | − | 0.776745i | \(-0.716870\pi\) | ||||
−0.629816 | + | 0.776745i | \(0.716870\pi\) | |||||||
\(98\) | −20.3564 | −2.05631 | ||||||||
\(99\) | −0.0462763 | −0.00465094 | ||||||||
\(100\) | −3.37026 | −0.337026 | ||||||||
\(101\) | −13.2660 | −1.32002 | −0.660008 | − | 0.751258i | \(-0.729447\pi\) | ||||
−0.660008 | + | 0.751258i | \(0.729447\pi\) | |||||||
\(102\) | −5.23034 | −0.517880 | ||||||||
\(103\) | −3.03457 | −0.299005 | −0.149503 | − | 0.988761i | \(-0.547767\pi\) | ||||
−0.149503 | + | 0.988761i | \(0.547767\pi\) | |||||||
\(104\) | 5.72448 | 0.561332 | ||||||||
\(105\) | −6.67711 | −0.651619 | ||||||||
\(106\) | −1.04304 | −0.101309 | ||||||||
\(107\) | 1.85270 | 0.179108 | 0.0895538 | − | 0.995982i | \(-0.471456\pi\) | ||||
0.0895538 | + | 0.995982i | \(0.471456\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.37763 | −0.131953 | −0.0659766 | − | 0.997821i | \(-0.521016\pi\) | ||||
−0.0659766 | + | 0.997821i | \(0.521016\pi\) | |||||||
\(110\) | 0.0590769 | 0.00563276 | ||||||||
\(111\) | 6.31965 | 0.599835 | ||||||||
\(112\) | −5.23034 | −0.494220 | ||||||||
\(113\) | −13.0139 | −1.22424 | −0.612122 | − | 0.790763i | \(-0.709684\pi\) | ||||
−0.612122 | + | 0.790763i | \(0.709684\pi\) | |||||||
\(114\) | −8.21863 | −0.769745 | ||||||||
\(115\) | 1.27661 | 0.119045 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −5.72448 | −0.529229 | ||||||||
\(118\) | −7.63193 | −0.702576 | ||||||||
\(119\) | −27.3564 | −2.50776 | ||||||||
\(120\) | −1.27661 | −0.116538 | ||||||||
\(121\) | −10.9979 | −0.999805 | ||||||||
\(122\) | 5.95372 | 0.539025 | ||||||||
\(123\) | 7.07871 | 0.638265 | ||||||||
\(124\) | −4.18296 | −0.375641 | ||||||||
\(125\) | −10.6856 | −0.955747 | ||||||||
\(126\) | 5.23034 | 0.465955 | ||||||||
\(127\) | −19.2660 | −1.70958 | −0.854791 | − | 0.518973i | \(-0.826315\pi\) | ||||
−0.854791 | + | 0.518973i | \(0.826315\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.1691 | −0.983386 | ||||||||
\(130\) | 7.30795 | 0.640949 | ||||||||
\(131\) | −15.7836 | −1.37902 | −0.689508 | − | 0.724278i | \(-0.742173\pi\) | ||||
−0.689508 | + | 0.724278i | \(0.742173\pi\) | |||||||
\(132\) | −0.0462763 | −0.00402783 | ||||||||
\(133\) | −42.9862 | −3.72738 | ||||||||
\(134\) | 9.46391 | 0.817557 | ||||||||
\(135\) | 1.27661 | 0.109873 | ||||||||
\(136\) | −5.23034 | −0.448498 | ||||||||
\(137\) | 21.0452 | 1.79802 | 0.899008 | − | 0.437933i | \(-0.144289\pi\) | ||||
0.899008 | + | 0.437933i | \(0.144289\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 6.58456 | 0.558495 | 0.279247 | − | 0.960219i | \(-0.409915\pi\) | ||||
0.279247 | + | 0.960219i | \(0.409915\pi\) | |||||||
\(140\) | −6.67711 | −0.564319 | ||||||||
\(141\) | 2.31118 | 0.194637 | ||||||||
\(142\) | 6.52548 | 0.547606 | ||||||||
\(143\) | 0.264908 | 0.0221527 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.27661 | −0.106017 | ||||||||
\(146\) | 2.12389 | 0.175774 | ||||||||
\(147\) | 20.3564 | 1.67897 | ||||||||
\(148\) | 6.31965 | 0.519472 | ||||||||
\(149\) | −4.04628 | −0.331484 | −0.165742 | − | 0.986169i | \(-0.553002\pi\) | ||||
−0.165742 | + | 0.986169i | \(0.553002\pi\) | |||||||
\(150\) | 3.37026 | 0.275181 | ||||||||
\(151\) | 14.8979 | 1.21238 | 0.606188 | − | 0.795321i | \(-0.292698\pi\) | ||||
0.606188 | + | 0.795321i | \(0.292698\pi\) | |||||||
\(152\) | −8.21863 | −0.666619 | ||||||||
\(153\) | 5.23034 | 0.422848 | ||||||||
\(154\) | −0.242041 | −0.0195042 | ||||||||
\(155\) | −5.34002 | −0.428921 | ||||||||
\(156\) | −5.72448 | −0.458326 | ||||||||
\(157\) | 3.96867 | 0.316734 | 0.158367 | − | 0.987380i | \(-0.449377\pi\) | ||||
0.158367 | + | 0.987380i | \(0.449377\pi\) | |||||||
\(158\) | 12.5846 | 1.00117 | ||||||||
\(159\) | 1.04304 | 0.0827183 | ||||||||
\(160\) | −1.27661 | −0.100925 | ||||||||
\(161\) | −5.23034 | −0.412208 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.30112 | 0.336890 | 0.168445 | − | 0.985711i | \(-0.446126\pi\) | ||||
0.168445 | + | 0.985711i | \(0.446126\pi\) | |||||||
\(164\) | 7.07871 | 0.552754 | ||||||||
\(165\) | −0.0590769 | −0.00459913 | ||||||||
\(166\) | 14.8266 | 1.15077 | ||||||||
\(167\) | −1.77923 | −0.137681 | −0.0688404 | − | 0.997628i | \(-0.521930\pi\) | ||||
−0.0688404 | + | 0.997628i | \(0.521930\pi\) | |||||||
\(168\) | 5.23034 | 0.403529 | ||||||||
\(169\) | 19.7697 | 1.52075 | ||||||||
\(170\) | −6.67711 | −0.512111 | ||||||||
\(171\) | 8.21863 | 0.628494 | ||||||||
\(172\) | −11.1691 | −0.851637 | ||||||||
\(173\) | 6.30471 | 0.479338 | 0.239669 | − | 0.970855i | \(-0.422961\pi\) | ||||
0.239669 | + | 0.970855i | \(0.422961\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 17.6276 | 1.33252 | ||||||||
\(176\) | −0.0462763 | −0.00348821 | ||||||||
\(177\) | 7.63193 | 0.573651 | ||||||||
\(178\) | 16.4059 | 1.22968 | ||||||||
\(179\) | −10.9192 | −0.816136 | −0.408068 | − | 0.912952i | \(-0.633797\pi\) | ||||
−0.408068 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(180\) | 1.27661 | 0.0951531 | ||||||||
\(181\) | 25.2937 | 1.88007 | 0.940035 | − | 0.341079i | \(-0.110792\pi\) | ||||
0.940035 | + | 0.341079i | \(0.110792\pi\) | |||||||
\(182\) | −29.9410 | −2.21937 | ||||||||
\(183\) | −5.95372 | −0.440112 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 8.06774 | 0.593152 | ||||||||
\(186\) | 4.18296 | 0.306710 | ||||||||
\(187\) | −0.242041 | −0.0176998 | ||||||||
\(188\) | 2.31118 | 0.168560 | ||||||||
\(189\) | −5.23034 | −0.380451 | ||||||||
\(190\) | −10.4920 | −0.761170 | ||||||||
\(191\) | −13.0915 | −0.947268 | −0.473634 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473634 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −11.0196 | −0.793210 | −0.396605 | − | 0.917989i | \(-0.629812\pi\) | ||||
−0.396605 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(194\) | 12.4059 | 0.890694 | ||||||||
\(195\) | −7.30795 | −0.523333 | ||||||||
\(196\) | 20.3564 | 1.45403 | ||||||||
\(197\) | −21.6042 | −1.53923 | −0.769617 | − | 0.638505i | \(-0.779553\pi\) | ||||
−0.769617 | + | 0.638505i | \(0.779553\pi\) | |||||||
\(198\) | 0.0462763 | 0.00328871 | ||||||||
\(199\) | 9.40269 | 0.666539 | 0.333270 | − | 0.942832i | \(-0.391848\pi\) | ||||
0.333270 | + | 0.942832i | \(0.391848\pi\) | |||||||
\(200\) | 3.37026 | 0.238313 | ||||||||
\(201\) | −9.46391 | −0.667533 | ||||||||
\(202\) | 13.2660 | 0.933393 | ||||||||
\(203\) | 5.23034 | 0.367098 | ||||||||
\(204\) | 5.23034 | 0.366197 | ||||||||
\(205\) | 9.03676 | 0.631155 | ||||||||
\(206\) | 3.03457 | 0.211429 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −5.72448 | −0.396922 | ||||||||
\(209\) | −0.380328 | −0.0263078 | ||||||||
\(210\) | 6.67711 | 0.460764 | ||||||||
\(211\) | 16.5576 | 1.13987 | 0.569935 | − | 0.821690i | \(-0.306969\pi\) | ||||
0.569935 | + | 0.821690i | \(0.306969\pi\) | |||||||
\(212\) | 1.04304 | 0.0716362 | ||||||||
\(213\) | −6.52548 | −0.447119 | ||||||||
\(214\) | −1.85270 | −0.126648 | ||||||||
\(215\) | −14.2586 | −0.972431 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 21.8783 | 1.48520 | ||||||||
\(218\) | 1.37763 | 0.0933050 | ||||||||
\(219\) | −2.12389 | −0.143519 | ||||||||
\(220\) | −0.0590769 | −0.00398296 | ||||||||
\(221\) | −29.9410 | −2.01405 | ||||||||
\(222\) | −6.31965 | −0.424147 | ||||||||
\(223\) | −9.48678 | −0.635282 | −0.317641 | − | 0.948211i | \(-0.602891\pi\) | ||||
−0.317641 | + | 0.948211i | \(0.602891\pi\) | |||||||
\(224\) | 5.23034 | 0.349467 | ||||||||
\(225\) | −3.37026 | −0.224684 | ||||||||
\(226\) | 13.0139 | 0.865672 | ||||||||
\(227\) | −7.74356 | −0.513958 | −0.256979 | − | 0.966417i | \(-0.582727\pi\) | ||||
−0.256979 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(228\) | 8.21863 | 0.544292 | ||||||||
\(229\) | −15.3479 | −1.01422 | −0.507110 | − | 0.861881i | \(-0.669286\pi\) | ||||
−0.507110 | + | 0.861881i | \(0.669286\pi\) | |||||||
\(230\) | −1.27661 | −0.0841773 | ||||||||
\(231\) | 0.242041 | 0.0159251 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −1.69674 | −0.111157 | −0.0555786 | − | 0.998454i | \(-0.517700\pi\) | ||||
−0.0555786 | + | 0.998454i | \(0.517700\pi\) | |||||||
\(234\) | 5.72448 | 0.374221 | ||||||||
\(235\) | 2.95049 | 0.192468 | ||||||||
\(236\) | 7.63193 | 0.496796 | ||||||||
\(237\) | −12.5846 | −0.817455 | ||||||||
\(238\) | 27.3564 | 1.77325 | ||||||||
\(239\) | 0.315518 | 0.0204092 | 0.0102046 | − | 0.999948i | \(-0.496752\pi\) | ||||
0.0102046 | + | 0.999948i | \(0.496752\pi\) | |||||||
\(240\) | 1.27661 | 0.0824050 | ||||||||
\(241\) | 28.0591 | 1.80745 | 0.903724 | − | 0.428116i | \(-0.140823\pi\) | ||||
0.903724 | + | 0.428116i | \(0.140823\pi\) | |||||||
\(242\) | 10.9979 | 0.706969 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.95372 | −0.381148 | ||||||||
\(245\) | 25.9873 | 1.66026 | ||||||||
\(246\) | −7.07871 | −0.451322 | ||||||||
\(247\) | −47.0474 | −2.99356 | ||||||||
\(248\) | 4.18296 | 0.265618 | ||||||||
\(249\) | −14.8266 | −0.939598 | ||||||||
\(250\) | 10.6856 | 0.675815 | ||||||||
\(251\) | −10.6308 | −0.671012 | −0.335506 | − | 0.942038i | \(-0.608907\pi\) | ||||
−0.335506 | + | 0.942038i | \(0.608907\pi\) | |||||||
\(252\) | −5.23034 | −0.329480 | ||||||||
\(253\) | −0.0462763 | −0.00290937 | ||||||||
\(254\) | 19.2660 | 1.20886 | ||||||||
\(255\) | 6.67711 | 0.418137 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.4059 | −0.898617 | −0.449309 | − | 0.893377i | \(-0.648330\pi\) | ||||
−0.449309 | + | 0.893377i | \(0.648330\pi\) | |||||||
\(258\) | 11.1691 | 0.695359 | ||||||||
\(259\) | −33.0539 | −2.05387 | ||||||||
\(260\) | −7.30795 | −0.453220 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 15.7836 | 0.975112 | ||||||||
\(263\) | 6.92708 | 0.427142 | 0.213571 | − | 0.976928i | \(-0.431491\pi\) | ||||
0.213571 | + | 0.976928i | \(0.431491\pi\) | |||||||
\(264\) | 0.0462763 | 0.00284811 | ||||||||
\(265\) | 1.33156 | 0.0817968 | ||||||||
\(266\) | 42.9862 | 2.63565 | ||||||||
\(267\) | −16.4059 | −1.00403 | ||||||||
\(268\) | −9.46391 | −0.578100 | ||||||||
\(269\) | 16.8857 | 1.02954 | 0.514769 | − | 0.857329i | \(-0.327878\pi\) | ||||
0.514769 | + | 0.857329i | \(0.327878\pi\) | |||||||
\(270\) | −1.27661 | −0.0776922 | ||||||||
\(271\) | −10.5511 | −0.640933 | −0.320466 | − | 0.947260i | \(-0.603840\pi\) | ||||
−0.320466 | + | 0.947260i | \(0.603840\pi\) | |||||||
\(272\) | 5.23034 | 0.317136 | ||||||||
\(273\) | 29.9410 | 1.81211 | ||||||||
\(274\) | −21.0452 | −1.27139 | ||||||||
\(275\) | 0.155963 | 0.00940493 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 27.9075 | 1.67680 | 0.838400 | − | 0.545056i | \(-0.183492\pi\) | ||||
0.838400 | + | 0.545056i | \(0.183492\pi\) | |||||||
\(278\) | −6.58456 | −0.394916 | ||||||||
\(279\) | −4.18296 | −0.250427 | ||||||||
\(280\) | 6.67711 | 0.399034 | ||||||||
\(281\) | −20.1261 | −1.20062 | −0.600311 | − | 0.799767i | \(-0.704956\pi\) | ||||
−0.600311 | + | 0.799767i | \(0.704956\pi\) | |||||||
\(282\) | −2.31118 | −0.137629 | ||||||||
\(283\) | 9.74302 | 0.579162 | 0.289581 | − | 0.957153i | \(-0.406484\pi\) | ||||
0.289581 | + | 0.957153i | \(0.406484\pi\) | |||||||
\(284\) | −6.52548 | −0.387216 | ||||||||
\(285\) | 10.4920 | 0.621493 | ||||||||
\(286\) | −0.264908 | −0.0156643 | ||||||||
\(287\) | −37.0240 | −2.18546 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.3564 | 0.609201 | ||||||||
\(290\) | 1.27661 | 0.0749653 | ||||||||
\(291\) | −12.4059 | −0.727248 | ||||||||
\(292\) | −2.12389 | −0.124291 | ||||||||
\(293\) | −4.27337 | −0.249653 | −0.124827 | − | 0.992179i | \(-0.539837\pi\) | ||||
−0.124827 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(294\) | −20.3564 | −1.18721 | ||||||||
\(295\) | 9.74302 | 0.567260 | ||||||||
\(296\) | −6.31965 | −0.367322 | ||||||||
\(297\) | −0.0462763 | −0.00268522 | ||||||||
\(298\) | 4.04628 | 0.234394 | ||||||||
\(299\) | −5.72448 | −0.331055 | ||||||||
\(300\) | −3.37026 | −0.194582 | ||||||||
\(301\) | 58.4182 | 3.36717 | ||||||||
\(302\) | −14.8979 | −0.857280 | ||||||||
\(303\) | −13.2660 | −0.762112 | ||||||||
\(304\) | 8.21863 | 0.471371 | ||||||||
\(305\) | −7.60060 | −0.435209 | ||||||||
\(306\) | −5.23034 | −0.298998 | ||||||||
\(307\) | 0.157362 | 0.00898115 | 0.00449057 | − | 0.999990i | \(-0.498571\pi\) | ||||
0.00449057 | + | 0.999990i | \(0.498571\pi\) | |||||||
\(308\) | 0.242041 | 0.0137915 | ||||||||
\(309\) | −3.03457 | −0.172631 | ||||||||
\(310\) | 5.34002 | 0.303293 | ||||||||
\(311\) | 27.3420 | 1.55042 | 0.775212 | − | 0.631702i | \(-0.217643\pi\) | ||||
0.775212 | + | 0.631702i | \(0.217643\pi\) | |||||||
\(312\) | 5.72448 | 0.324085 | ||||||||
\(313\) | 3.04523 | 0.172127 | 0.0860633 | − | 0.996290i | \(-0.472571\pi\) | ||||
0.0860633 | + | 0.996290i | \(0.472571\pi\) | |||||||
\(314\) | −3.96867 | −0.223965 | ||||||||
\(315\) | −6.67711 | −0.376213 | ||||||||
\(316\) | −12.5846 | −0.707937 | ||||||||
\(317\) | 29.8585 | 1.67702 | 0.838510 | − | 0.544886i | \(-0.183427\pi\) | ||||
0.838510 | + | 0.544886i | \(0.183427\pi\) | |||||||
\(318\) | −1.04304 | −0.0584907 | ||||||||
\(319\) | 0.0462763 | 0.00259097 | ||||||||
\(320\) | 1.27661 | 0.0713648 | ||||||||
\(321\) | 1.85270 | 0.103408 | ||||||||
\(322\) | 5.23034 | 0.291475 | ||||||||
\(323\) | 42.9862 | 2.39182 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 19.2930 | 1.07018 | ||||||||
\(326\) | −4.30112 | −0.238217 | ||||||||
\(327\) | −1.37763 | −0.0761832 | ||||||||
\(328\) | −7.07871 | −0.390856 | ||||||||
\(329\) | −12.0883 | −0.666448 | ||||||||
\(330\) | 0.0590769 | 0.00325207 | ||||||||
\(331\) | −5.37982 | −0.295702 | −0.147851 | − | 0.989010i | \(-0.547236\pi\) | ||||
−0.147851 | + | 0.989010i | \(0.547236\pi\) | |||||||
\(332\) | −14.8266 | −0.813715 | ||||||||
\(333\) | 6.31965 | 0.346315 | ||||||||
\(334\) | 1.77923 | 0.0973550 | ||||||||
\(335\) | −12.0817 | −0.660096 | ||||||||
\(336\) | −5.23034 | −0.285338 | ||||||||
\(337\) | 27.8007 | 1.51440 | 0.757200 | − | 0.653183i | \(-0.226567\pi\) | ||||
0.757200 | + | 0.653183i | \(0.226567\pi\) | |||||||
\(338\) | −19.7697 | −1.07533 | ||||||||
\(339\) | −13.0139 | −0.706818 | ||||||||
\(340\) | 6.67711 | 0.362117 | ||||||||
\(341\) | 0.193572 | 0.0104825 | ||||||||
\(342\) | −8.21863 | −0.444413 | ||||||||
\(343\) | −69.8585 | −3.77201 | ||||||||
\(344\) | 11.1691 | 0.602198 | ||||||||
\(345\) | 1.27661 | 0.0687305 | ||||||||
\(346\) | −6.30471 | −0.338943 | ||||||||
\(347\) | 3.08304 | 0.165506 | 0.0827531 | − | 0.996570i | \(-0.473629\pi\) | ||||
0.0827531 | + | 0.996570i | \(0.473629\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | −18.7441 | −1.00335 | −0.501675 | − | 0.865056i | \(-0.667283\pi\) | ||||
−0.501675 | + | 0.865056i | \(0.667283\pi\) | |||||||
\(350\) | −17.6276 | −0.942235 | ||||||||
\(351\) | −5.72448 | −0.305550 | ||||||||
\(352\) | 0.0462763 | 0.00246653 | ||||||||
\(353\) | 8.21863 | 0.437434 | 0.218717 | − | 0.975788i | \(-0.429813\pi\) | ||||
0.218717 | + | 0.975788i | \(0.429813\pi\) | |||||||
\(354\) | −7.63193 | −0.405633 | ||||||||
\(355\) | −8.33051 | −0.442138 | ||||||||
\(356\) | −16.4059 | −0.869512 | ||||||||
\(357\) | −27.3564 | −1.44786 | ||||||||
\(358\) | 10.9192 | 0.577095 | ||||||||
\(359\) | 17.9089 | 0.945195 | 0.472598 | − | 0.881278i | \(-0.343316\pi\) | ||||
0.472598 | + | 0.881278i | \(0.343316\pi\) | |||||||
\(360\) | −1.27661 | −0.0672834 | ||||||||
\(361\) | 48.5459 | 2.55505 | ||||||||
\(362\) | −25.2937 | −1.32941 | ||||||||
\(363\) | −10.9979 | −0.577238 | ||||||||
\(364\) | 29.9410 | 1.56933 | ||||||||
\(365\) | −2.71138 | −0.141920 | ||||||||
\(366\) | 5.95372 | 0.311206 | ||||||||
\(367\) | −6.43726 | −0.336022 | −0.168011 | − | 0.985785i | \(-0.553734\pi\) | ||||
−0.168011 | + | 0.985785i | \(0.553734\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 7.07871 | 0.368503 | ||||||||
\(370\) | −8.06774 | −0.419422 | ||||||||
\(371\) | −5.45544 | −0.283232 | ||||||||
\(372\) | −4.18296 | −0.216877 | ||||||||
\(373\) | 7.85270 | 0.406598 | 0.203299 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203299 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(374\) | 0.242041 | 0.0125156 | ||||||||
\(375\) | −10.6856 | −0.551801 | ||||||||
\(376\) | −2.31118 | −0.119190 | ||||||||
\(377\) | 5.72448 | 0.294826 | ||||||||
\(378\) | 5.23034 | 0.269019 | ||||||||
\(379\) | 21.4432 | 1.10146 | 0.550732 | − | 0.834682i | \(-0.314348\pi\) | ||||
0.550732 | + | 0.834682i | \(0.314348\pi\) | |||||||
\(380\) | 10.4920 | 0.538229 | ||||||||
\(381\) | −19.2660 | −0.987027 | ||||||||
\(382\) | 13.0915 | 0.669820 | ||||||||
\(383\) | −30.9293 | −1.58041 | −0.790206 | − | 0.612841i | \(-0.790026\pi\) | ||||
−0.790206 | + | 0.612841i | \(0.790026\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0.308992 | 0.0157477 | ||||||||
\(386\) | 11.0196 | 0.560884 | ||||||||
\(387\) | −11.1691 | −0.567758 | ||||||||
\(388\) | −12.4059 | −0.629816 | ||||||||
\(389\) | 5.88977 | 0.298623 | 0.149312 | − | 0.988790i | \(-0.452294\pi\) | ||||
0.149312 | + | 0.988790i | \(0.452294\pi\) | |||||||
\(390\) | 7.30795 | 0.370052 | ||||||||
\(391\) | 5.23034 | 0.264509 | ||||||||
\(392\) | −20.3564 | −1.02815 | ||||||||
\(393\) | −15.7836 | −0.796175 | ||||||||
\(394\) | 21.6042 | 1.08840 | ||||||||
\(395\) | −16.0656 | −0.808348 | ||||||||
\(396\) | −0.0462763 | −0.00232547 | ||||||||
\(397\) | −9.54152 | −0.478875 | −0.239438 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239438 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(398\) | −9.40269 | −0.471314 | ||||||||
\(399\) | −42.9862 | −2.15200 | ||||||||
\(400\) | −3.37026 | −0.168513 | ||||||||
\(401\) | 34.2920 | 1.71246 | 0.856229 | − | 0.516596i | \(-0.172801\pi\) | ||||
0.856229 | + | 0.516596i | \(0.172801\pi\) | |||||||
\(402\) | 9.46391 | 0.472017 | ||||||||
\(403\) | 23.9453 | 1.19280 | ||||||||
\(404\) | −13.2660 | −0.660008 | ||||||||
\(405\) | 1.27661 | 0.0634354 | ||||||||
\(406\) | −5.23034 | −0.259577 | ||||||||
\(407\) | −0.292450 | −0.0144962 | ||||||||
\(408\) | −5.23034 | −0.258940 | ||||||||
\(409\) | −14.4942 | −0.716692 | −0.358346 | − | 0.933589i | \(-0.616659\pi\) | ||||
−0.358346 | + | 0.933589i | \(0.616659\pi\) | |||||||
\(410\) | −9.03676 | −0.446294 | ||||||||
\(411\) | 21.0452 | 1.03808 | ||||||||
\(412\) | −3.03457 | −0.149503 | ||||||||
\(413\) | −39.9176 | −1.96421 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −18.9278 | −0.929130 | ||||||||
\(416\) | 5.72448 | 0.280666 | ||||||||
\(417\) | 6.58456 | 0.322447 | ||||||||
\(418\) | 0.380328 | 0.0186024 | ||||||||
\(419\) | −7.11292 | −0.347489 | −0.173745 | − | 0.984791i | \(-0.555587\pi\) | ||||
−0.173745 | + | 0.984791i | \(0.555587\pi\) | |||||||
\(420\) | −6.67711 | −0.325810 | ||||||||
\(421\) | −14.1958 | −0.691859 | −0.345930 | − | 0.938260i | \(-0.612436\pi\) | ||||
−0.345930 | + | 0.938260i | \(0.612436\pi\) | |||||||
\(422\) | −16.5576 | −0.806009 | ||||||||
\(423\) | 2.31118 | 0.112374 | ||||||||
\(424\) | −1.04304 | −0.0506544 | ||||||||
\(425\) | −17.6276 | −0.855064 | ||||||||
\(426\) | 6.52548 | 0.316161 | ||||||||
\(427\) | 31.1400 | 1.50697 | ||||||||
\(428\) | 1.85270 | 0.0895538 | ||||||||
\(429\) | 0.264908 | 0.0127899 | ||||||||
\(430\) | 14.2586 | 0.687612 | ||||||||
\(431\) | 1.26022 | 0.0607027 | 0.0303513 | − | 0.999539i | \(-0.490337\pi\) | ||||
0.0303513 | + | 0.999539i | \(0.490337\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 1.34411 | 0.0645936 | 0.0322968 | − | 0.999478i | \(-0.489718\pi\) | ||||
0.0322968 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(434\) | −21.8783 | −1.05019 | ||||||||
\(435\) | −1.27661 | −0.0612089 | ||||||||
\(436\) | −1.37763 | −0.0659766 | ||||||||
\(437\) | 8.21863 | 0.393150 | ||||||||
\(438\) | 2.12389 | 0.101483 | ||||||||
\(439\) | −26.8893 | −1.28335 | −0.641677 | − | 0.766975i | \(-0.721761\pi\) | ||||
−0.641677 | + | 0.766975i | \(0.721761\pi\) | |||||||
\(440\) | 0.0590769 | 0.00281638 | ||||||||
\(441\) | 20.3564 | 0.969353 | ||||||||
\(442\) | 29.9410 | 1.42415 | ||||||||
\(443\) | 21.9410 | 1.04245 | 0.521224 | − | 0.853420i | \(-0.325476\pi\) | ||||
0.521224 | + | 0.853420i | \(0.325476\pi\) | |||||||
\(444\) | 6.31965 | 0.299917 | ||||||||
\(445\) | −20.9440 | −0.992841 | ||||||||
\(446\) | 9.48678 | 0.449212 | ||||||||
\(447\) | −4.04628 | −0.191382 | ||||||||
\(448\) | −5.23034 | −0.247110 | ||||||||
\(449\) | 11.2682 | 0.531779 | 0.265890 | − | 0.964004i | \(-0.414334\pi\) | ||||
0.265890 | + | 0.964004i | \(0.414334\pi\) | |||||||
\(450\) | 3.37026 | 0.158876 | ||||||||
\(451\) | −0.327576 | −0.0154250 | ||||||||
\(452\) | −13.0139 | −0.612122 | ||||||||
\(453\) | 14.8979 | 0.699966 | ||||||||
\(454\) | 7.74356 | 0.363423 | ||||||||
\(455\) | 38.2230 | 1.79192 | ||||||||
\(456\) | −8.21863 | −0.384873 | ||||||||
\(457\) | 19.1392 | 0.895296 | 0.447648 | − | 0.894210i | \(-0.352262\pi\) | ||||
0.447648 | + | 0.894210i | \(0.352262\pi\) | |||||||
\(458\) | 15.3479 | 0.717163 | ||||||||
\(459\) | 5.23034 | 0.244131 | ||||||||
\(460\) | 1.27661 | 0.0595224 | ||||||||
\(461\) | −39.2739 | −1.82917 | −0.914585 | − | 0.404395i | \(-0.867482\pi\) | ||||
−0.914585 | + | 0.404395i | \(0.867482\pi\) | |||||||
\(462\) | −0.242041 | −0.0112607 | ||||||||
\(463\) | −8.97390 | −0.417052 | −0.208526 | − | 0.978017i | \(-0.566867\pi\) | ||||
−0.208526 | + | 0.978017i | \(0.566867\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −5.34002 | −0.247638 | ||||||||
\(466\) | 1.69674 | 0.0786000 | ||||||||
\(467\) | −23.5666 | −1.09053 | −0.545266 | − | 0.838263i | \(-0.683571\pi\) | ||||
−0.545266 | + | 0.838263i | \(0.683571\pi\) | |||||||
\(468\) | −5.72448 | −0.264614 | ||||||||
\(469\) | 49.4994 | 2.28567 | ||||||||
\(470\) | −2.95049 | −0.136096 | ||||||||
\(471\) | 3.96867 | 0.182866 | ||||||||
\(472\) | −7.63193 | −0.351288 | ||||||||
\(473\) | 0.516865 | 0.0237655 | ||||||||
\(474\) | 12.5846 | 0.578028 | ||||||||
\(475\) | −27.6989 | −1.27091 | ||||||||
\(476\) | −27.3564 | −1.25388 | ||||||||
\(477\) | 1.04304 | 0.0477575 | ||||||||
\(478\) | −0.315518 | −0.0144314 | ||||||||
\(479\) | −9.70376 | −0.443376 | −0.221688 | − | 0.975118i | \(-0.571157\pi\) | ||||
−0.221688 | + | 0.975118i | \(0.571157\pi\) | |||||||
\(480\) | −1.27661 | −0.0582691 | ||||||||
\(481\) | −36.1767 | −1.64952 | ||||||||
\(482\) | −28.0591 | −1.27806 | ||||||||
\(483\) | −5.23034 | −0.237989 | ||||||||
\(484\) | −10.9979 | −0.499903 | ||||||||
\(485\) | −15.8376 | −0.719147 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −25.3856 | −1.15033 | −0.575165 | − | 0.818038i | \(-0.695062\pi\) | ||||
−0.575165 | + | 0.818038i | \(0.695062\pi\) | |||||||
\(488\) | 5.95372 | 0.269512 | ||||||||
\(489\) | 4.30112 | 0.194503 | ||||||||
\(490\) | −25.9873 | −1.17398 | ||||||||
\(491\) | −8.39726 | −0.378963 | −0.189482 | − | 0.981884i | \(-0.560681\pi\) | ||||
−0.189482 | + | 0.981884i | \(0.560681\pi\) | |||||||
\(492\) | 7.07871 | 0.319133 | ||||||||
\(493\) | −5.23034 | −0.235562 | ||||||||
\(494\) | 47.0474 | 2.11676 | ||||||||
\(495\) | −0.0590769 | −0.00265531 | ||||||||
\(496\) | −4.18296 | −0.187821 | ||||||||
\(497\) | 34.1305 | 1.53096 | ||||||||
\(498\) | 14.8266 | 0.664396 | ||||||||
\(499\) | 8.00867 | 0.358517 | 0.179259 | − | 0.983802i | \(-0.442630\pi\) | ||||
0.179259 | + | 0.983802i | \(0.442630\pi\) | |||||||
\(500\) | −10.6856 | −0.477874 | ||||||||
\(501\) | −1.77923 | −0.0794900 | ||||||||
\(502\) | 10.6308 | 0.474477 | ||||||||
\(503\) | −4.32812 | −0.192981 | −0.0964906 | − | 0.995334i | \(-0.530762\pi\) | ||||
−0.0964906 | + | 0.995334i | \(0.530762\pi\) | |||||||
\(504\) | 5.23034 | 0.232978 | ||||||||
\(505\) | −16.9355 | −0.753622 | ||||||||
\(506\) | 0.0462763 | 0.00205723 | ||||||||
\(507\) | 19.7697 | 0.878004 | ||||||||
\(508\) | −19.2660 | −0.854791 | ||||||||
\(509\) | 3.76015 | 0.166666 | 0.0833329 | − | 0.996522i | \(-0.473444\pi\) | ||||
0.0833329 | + | 0.996522i | \(0.473444\pi\) | |||||||
\(510\) | −6.67711 | −0.295667 | ||||||||
\(511\) | 11.1086 | 0.491417 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.21863 | 0.362861 | ||||||||
\(514\) | 14.4059 | 0.635418 | ||||||||
\(515\) | −3.87397 | −0.170708 | ||||||||
\(516\) | −11.1691 | −0.491693 | ||||||||
\(517\) | −0.106953 | −0.00470379 | ||||||||
\(518\) | 33.0539 | 1.45230 | ||||||||
\(519\) | 6.30471 | 0.276746 | ||||||||
\(520\) | 7.30795 | 0.320475 | ||||||||
\(521\) | 16.1261 | 0.706496 | 0.353248 | − | 0.935530i | \(-0.385077\pi\) | ||||
0.353248 | + | 0.935530i | \(0.385077\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 4.47561 | 0.195705 | 0.0978525 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978525 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(524\) | −15.7836 | −0.689508 | ||||||||
\(525\) | 17.6276 | 0.769331 | ||||||||
\(526\) | −6.92708 | −0.302035 | ||||||||
\(527\) | −21.8783 | −0.953034 | ||||||||
\(528\) | −0.0462763 | −0.00201392 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −1.33156 | −0.0578391 | ||||||||
\(531\) | 7.63193 | 0.331198 | ||||||||
\(532\) | −42.9862 | −1.86369 | ||||||||
\(533\) | −40.5219 | −1.75520 | ||||||||
\(534\) | 16.4059 | 0.709954 | ||||||||
\(535\) | 2.36519 | 0.102256 | ||||||||
\(536\) | 9.46391 | 0.408779 | ||||||||
\(537\) | −10.9192 | −0.471196 | ||||||||
\(538\) | −16.8857 | −0.727993 | ||||||||
\(539\) | −0.942019 | −0.0405756 | ||||||||
\(540\) | 1.27661 | 0.0549366 | ||||||||
\(541\) | −27.2703 | −1.17244 | −0.586222 | − | 0.810151i | \(-0.699385\pi\) | ||||
−0.586222 | + | 0.810151i | \(0.699385\pi\) | |||||||
\(542\) | 10.5511 | 0.453208 | ||||||||
\(543\) | 25.2937 | 1.08546 | ||||||||
\(544\) | −5.23034 | −0.224249 | ||||||||
\(545\) | −1.75870 | −0.0753345 | ||||||||
\(546\) | −29.9410 | −1.28136 | ||||||||
\(547\) | −16.6736 | −0.712910 | −0.356455 | − | 0.934312i | \(-0.616015\pi\) | ||||
−0.356455 | + | 0.934312i | \(0.616015\pi\) | |||||||
\(548\) | 21.0452 | 0.899008 | ||||||||
\(549\) | −5.95372 | −0.254099 | ||||||||
\(550\) | −0.155963 | −0.00665029 | ||||||||
\(551\) | −8.21863 | −0.350125 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 65.8215 | 2.79901 | ||||||||
\(554\) | −27.9075 | −1.18568 | ||||||||
\(555\) | 8.06774 | 0.342457 | ||||||||
\(556\) | 6.58456 | 0.279247 | ||||||||
\(557\) | −30.3989 | −1.28804 | −0.644022 | − | 0.765007i | \(-0.722735\pi\) | ||||
−0.644022 | + | 0.765007i | \(0.722735\pi\) | |||||||
\(558\) | 4.18296 | 0.177079 | ||||||||
\(559\) | 63.9374 | 2.70427 | ||||||||
\(560\) | −6.67711 | −0.282159 | ||||||||
\(561\) | −0.242041 | −0.0102190 | ||||||||
\(562\) | 20.1261 | 0.848967 | ||||||||
\(563\) | −18.1054 | −0.763052 | −0.381526 | − | 0.924358i | \(-0.624601\pi\) | ||||
−0.381526 | + | 0.924358i | \(0.624601\pi\) | |||||||
\(564\) | 2.31118 | 0.0973184 | ||||||||
\(565\) | −16.6137 | −0.698944 | ||||||||
\(566\) | −9.74302 | −0.409530 | ||||||||
\(567\) | −5.23034 | −0.219653 | ||||||||
\(568\) | 6.52548 | 0.273803 | ||||||||
\(569\) | 17.4154 | 0.730093 | 0.365047 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365047 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(570\) | −10.4920 | −0.439462 | ||||||||
\(571\) | 12.4669 | 0.521725 | 0.260863 | − | 0.965376i | \(-0.415993\pi\) | ||||
0.260863 | + | 0.965376i | \(0.415993\pi\) | |||||||
\(572\) | 0.264908 | 0.0110764 | ||||||||
\(573\) | −13.0915 | −0.546906 | ||||||||
\(574\) | 37.0240 | 1.54535 | ||||||||
\(575\) | −3.37026 | −0.140550 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −0.816482 | −0.0339906 | −0.0169953 | − | 0.999856i | \(-0.505410\pi\) | ||||
−0.0169953 | + | 0.999856i | \(0.505410\pi\) | |||||||
\(578\) | −10.3564 | −0.430770 | ||||||||
\(579\) | −11.0196 | −0.457960 | ||||||||
\(580\) | −1.27661 | −0.0530084 | ||||||||
\(581\) | 77.5481 | 3.21724 | ||||||||
\(582\) | 12.4059 | 0.514242 | ||||||||
\(583\) | −0.0482680 | −0.00199905 | ||||||||
\(584\) | 2.12389 | 0.0878871 | ||||||||
\(585\) | −7.30795 | −0.302146 | ||||||||
\(586\) | 4.27337 | 0.176531 | ||||||||
\(587\) | −35.5671 | −1.46801 | −0.734006 | − | 0.679143i | \(-0.762352\pi\) | ||||
−0.734006 | + | 0.679143i | \(0.762352\pi\) | |||||||
\(588\) | 20.3564 | 0.839484 | ||||||||
\(589\) | −34.3782 | −1.41653 | ||||||||
\(590\) | −9.74302 | −0.401114 | ||||||||
\(591\) | −21.6042 | −0.888678 | ||||||||
\(592\) | 6.31965 | 0.259736 | ||||||||
\(593\) | 0.405187 | 0.0166390 | 0.00831951 | − | 0.999965i | \(-0.497352\pi\) | ||||
0.00831951 | + | 0.999965i | \(0.497352\pi\) | |||||||
\(594\) | 0.0462763 | 0.00189874 | ||||||||
\(595\) | −34.9235 | −1.43173 | ||||||||
\(596\) | −4.04628 | −0.165742 | ||||||||
\(597\) | 9.40269 | 0.384827 | ||||||||
\(598\) | 5.72448 | 0.234092 | ||||||||
\(599\) | 5.62186 | 0.229703 | 0.114852 | − | 0.993383i | \(-0.463361\pi\) | ||||
0.114852 | + | 0.993383i | \(0.463361\pi\) | |||||||
\(600\) | 3.37026 | 0.137590 | ||||||||
\(601\) | −27.4656 | −1.12034 | −0.560172 | − | 0.828376i | \(-0.689265\pi\) | ||||
−0.560172 | + | 0.828376i | \(0.689265\pi\) | |||||||
\(602\) | −58.4182 | −2.38095 | ||||||||
\(603\) | −9.46391 | −0.385400 | ||||||||
\(604\) | 14.8979 | 0.606188 | ||||||||
\(605\) | −14.0400 | −0.570807 | ||||||||
\(606\) | 13.2660 | 0.538895 | ||||||||
\(607\) | −31.6554 | −1.28485 | −0.642426 | − | 0.766347i | \(-0.722072\pi\) | ||||
−0.642426 | + | 0.766347i | \(0.722072\pi\) | |||||||
\(608\) | −8.21863 | −0.333310 | ||||||||
\(609\) | 5.23034 | 0.211944 | ||||||||
\(610\) | 7.60060 | 0.307739 | ||||||||
\(611\) | −13.2303 | −0.535242 | ||||||||
\(612\) | 5.23034 | 0.211424 | ||||||||
\(613\) | 12.9448 | 0.522834 | 0.261417 | − | 0.965226i | \(-0.415810\pi\) | ||||
0.261417 | + | 0.965226i | \(0.415810\pi\) | |||||||
\(614\) | −0.157362 | −0.00635063 | ||||||||
\(615\) | 9.03676 | 0.364397 | ||||||||
\(616\) | −0.242041 | −0.00975209 | ||||||||
\(617\) | 27.1385 | 1.09256 | 0.546278 | − | 0.837604i | \(-0.316044\pi\) | ||||
0.546278 | + | 0.837604i | \(0.316044\pi\) | |||||||
\(618\) | 3.03457 | 0.122068 | ||||||||
\(619\) | 10.2122 | 0.410461 | 0.205231 | − | 0.978714i | \(-0.434206\pi\) | ||||
0.205231 | + | 0.978714i | \(0.434206\pi\) | |||||||
\(620\) | −5.34002 | −0.214460 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −27.3420 | −1.09631 | ||||||||
\(623\) | 85.8085 | 3.43785 | ||||||||
\(624\) | −5.72448 | −0.229163 | ||||||||
\(625\) | 3.20996 | 0.128399 | ||||||||
\(626\) | −3.04523 | −0.121712 | ||||||||
\(627\) | −0.380328 | −0.0151888 | ||||||||
\(628\) | 3.96867 | 0.158367 | ||||||||
\(629\) | 33.0539 | 1.31795 | ||||||||
\(630\) | 6.67711 | 0.266022 | ||||||||
\(631\) | −21.2532 | −0.846077 | −0.423038 | − | 0.906112i | \(-0.639036\pi\) | ||||
−0.423038 | + | 0.906112i | \(0.639036\pi\) | |||||||
\(632\) | 12.5846 | 0.500587 | ||||||||
\(633\) | 16.5576 | 0.658104 | ||||||||
\(634\) | −29.8585 | −1.18583 | ||||||||
\(635\) | −24.5952 | −0.976031 | ||||||||
\(636\) | 1.04304 | 0.0413592 | ||||||||
\(637\) | −116.530 | −4.61709 | ||||||||
\(638\) | −0.0462763 | −0.00183210 | ||||||||
\(639\) | −6.52548 | −0.258144 | ||||||||
\(640\) | −1.27661 | −0.0504625 | ||||||||
\(641\) | 25.5181 | 1.00790 | 0.503952 | − | 0.863731i | \(-0.331879\pi\) | ||||
0.503952 | + | 0.863731i | \(0.331879\pi\) | |||||||
\(642\) | −1.85270 | −0.0731204 | ||||||||
\(643\) | 1.66321 | 0.0655908 | 0.0327954 | − | 0.999462i | \(-0.489559\pi\) | ||||
0.0327954 | + | 0.999462i | \(0.489559\pi\) | |||||||
\(644\) | −5.23034 | −0.206104 | ||||||||
\(645\) | −14.2586 | −0.561433 | ||||||||
\(646\) | −42.9862 | −1.69127 | ||||||||
\(647\) | −3.16333 | −0.124363 | −0.0621817 | − | 0.998065i | \(-0.519806\pi\) | ||||
−0.0621817 | + | 0.998065i | \(0.519806\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.353177 | −0.0138634 | ||||||||
\(650\) | −19.2930 | −0.756734 | ||||||||
\(651\) | 21.8783 | 0.857478 | ||||||||
\(652\) | 4.30112 | 0.168445 | ||||||||
\(653\) | 8.19089 | 0.320534 | 0.160267 | − | 0.987074i | \(-0.448764\pi\) | ||||
0.160267 | + | 0.987074i | \(0.448764\pi\) | |||||||
\(654\) | 1.37763 | 0.0538697 | ||||||||
\(655\) | −20.1495 | −0.787306 | ||||||||
\(656\) | 7.07871 | 0.276377 | ||||||||
\(657\) | −2.12389 | −0.0828607 | ||||||||
\(658\) | 12.0883 | 0.471250 | ||||||||
\(659\) | 36.5432 | 1.42352 | 0.711761 | − | 0.702422i | \(-0.247898\pi\) | ||||
0.711761 | + | 0.702422i | \(0.247898\pi\) | |||||||
\(660\) | −0.0590769 | −0.00229956 | ||||||||
\(661\) | −15.5894 | −0.606359 | −0.303180 | − | 0.952933i | \(-0.598048\pi\) | ||||
−0.303180 | + | 0.952933i | \(0.598048\pi\) | |||||||
\(662\) | 5.37982 | 0.209093 | ||||||||
\(663\) | −29.9410 | −1.16281 | ||||||||
\(664\) | 14.8266 | 0.575384 | ||||||||
\(665\) | −54.8767 | −2.12803 | ||||||||
\(666\) | −6.31965 | −0.244882 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −1.77923 | −0.0688404 | ||||||||
\(669\) | −9.48678 | −0.366780 | ||||||||
\(670\) | 12.0817 | 0.466758 | ||||||||
\(671\) | 0.275516 | 0.0106362 | ||||||||
\(672\) | 5.23034 | 0.201765 | ||||||||
\(673\) | −36.4651 | −1.40562 | −0.702812 | − | 0.711375i | \(-0.748073\pi\) | ||||
−0.702812 | + | 0.711375i | \(0.748073\pi\) | |||||||
\(674\) | −27.8007 | −1.07084 | ||||||||
\(675\) | −3.37026 | −0.129721 | ||||||||
\(676\) | 19.7697 | 0.760374 | ||||||||
\(677\) | 31.8149 | 1.22275 | 0.611373 | − | 0.791343i | \(-0.290618\pi\) | ||||
0.611373 | + | 0.791343i | \(0.290618\pi\) | |||||||
\(678\) | 13.0139 | 0.499796 | ||||||||
\(679\) | 64.8872 | 2.49014 | ||||||||
\(680\) | −6.67711 | −0.256056 | ||||||||
\(681\) | −7.74356 | −0.296734 | ||||||||
\(682\) | −0.193572 | −0.00741226 | ||||||||
\(683\) | −49.1202 | −1.87953 | −0.939765 | − | 0.341820i | \(-0.888957\pi\) | ||||
−0.939765 | + | 0.341820i | \(0.888957\pi\) | |||||||
\(684\) | 8.21863 | 0.314247 | ||||||||
\(685\) | 26.8666 | 1.02652 | ||||||||
\(686\) | 69.8585 | 2.66721 | ||||||||
\(687\) | −15.3479 | −0.585561 | ||||||||
\(688\) | −11.1691 | −0.425819 | ||||||||
\(689\) | −5.97086 | −0.227472 | ||||||||
\(690\) | −1.27661 | −0.0485998 | ||||||||
\(691\) | 28.7776 | 1.09475 | 0.547376 | − | 0.836887i | \(-0.315627\pi\) | ||||
0.547376 | + | 0.836887i | \(0.315627\pi\) | |||||||
\(692\) | 6.30471 | 0.239669 | ||||||||
\(693\) | 0.242041 | 0.00919436 | ||||||||
\(694\) | −3.08304 | −0.117031 | ||||||||
\(695\) | 8.40593 | 0.318855 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 37.0240 | 1.40238 | ||||||||
\(698\) | 18.7441 | 0.709475 | ||||||||
\(699\) | −1.69674 | −0.0641766 | ||||||||
\(700\) | 17.6276 | 0.666261 | ||||||||
\(701\) | 12.1388 | 0.458477 | 0.229239 | − | 0.973370i | \(-0.426376\pi\) | ||||
0.229239 | + | 0.973370i | \(0.426376\pi\) | |||||||
\(702\) | 5.72448 | 0.216057 | ||||||||
\(703\) | 51.9389 | 1.95891 | ||||||||
\(704\) | −0.0462763 | −0.00174410 | ||||||||
\(705\) | 2.95049 | 0.111122 | ||||||||
\(706\) | −8.21863 | −0.309312 | ||||||||
\(707\) | 69.3857 | 2.60952 | ||||||||
\(708\) | 7.63193 | 0.286826 | ||||||||
\(709\) | −15.2887 | −0.574180 | −0.287090 | − | 0.957904i | \(-0.592688\pi\) | ||||
−0.287090 | + | 0.957904i | \(0.592688\pi\) | |||||||
\(710\) | 8.33051 | 0.312638 | ||||||||
\(711\) | −12.5846 | −0.471958 | ||||||||
\(712\) | 16.4059 | 0.614838 | ||||||||
\(713\) | −4.18296 | −0.156653 | ||||||||
\(714\) | 27.3564 | 1.02379 | ||||||||
\(715\) | 0.338185 | 0.0126474 | ||||||||
\(716\) | −10.9192 | −0.408068 | ||||||||
\(717\) | 0.315518 | 0.0117832 | ||||||||
\(718\) | −17.9089 | −0.668354 | ||||||||
\(719\) | 24.3170 | 0.906870 | 0.453435 | − | 0.891289i | \(-0.350198\pi\) | ||||
0.453435 | + | 0.891289i | \(0.350198\pi\) | |||||||
\(720\) | 1.27661 | 0.0475765 | ||||||||
\(721\) | 15.8718 | 0.591098 | ||||||||
\(722\) | −48.5459 | −1.80669 | ||||||||
\(723\) | 28.0591 | 1.04353 | ||||||||
\(724\) | 25.2937 | 0.940035 | ||||||||
\(725\) | 3.37026 | 0.125168 | ||||||||
\(726\) | 10.9979 | 0.408169 | ||||||||
\(727\) | 32.5489 | 1.20717 | 0.603587 | − | 0.797297i | \(-0.293738\pi\) | ||||
0.603587 | + | 0.797297i | \(0.293738\pi\) | |||||||
\(728\) | −29.9410 | −1.10969 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.71138 | 0.100353 | ||||||||
\(731\) | −58.4182 | −2.16068 | ||||||||
\(732\) | −5.95372 | −0.220056 | ||||||||
\(733\) | −8.97555 | −0.331519 | −0.165760 | − | 0.986166i | \(-0.553008\pi\) | ||||
−0.165760 | + | 0.986166i | \(0.553008\pi\) | |||||||
\(734\) | 6.43726 | 0.237604 | ||||||||
\(735\) | 25.9873 | 0.958554 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0.437955 | 0.0161323 | ||||||||
\(738\) | −7.07871 | −0.260571 | ||||||||
\(739\) | −50.5868 | −1.86087 | −0.930433 | − | 0.366463i | \(-0.880569\pi\) | ||||
−0.930433 | + | 0.366463i | \(0.880569\pi\) | |||||||
\(740\) | 8.06774 | 0.296576 | ||||||||
\(741\) | −47.0474 | −1.72833 | ||||||||
\(742\) | 5.45544 | 0.200276 | ||||||||
\(743\) | −20.9064 | −0.766982 | −0.383491 | − | 0.923545i | \(-0.625278\pi\) | ||||
−0.383491 | + | 0.923545i | \(0.625278\pi\) | |||||||
\(744\) | 4.18296 | 0.153355 | ||||||||
\(745\) | −5.16553 | −0.189250 | ||||||||
\(746\) | −7.85270 | −0.287508 | ||||||||
\(747\) | −14.8266 | −0.542477 | ||||||||
\(748\) | −0.242041 | −0.00884988 | ||||||||
\(749\) | −9.69027 | −0.354075 | ||||||||
\(750\) | 10.6856 | 0.390182 | ||||||||
\(751\) | −29.4760 | −1.07560 | −0.537798 | − | 0.843074i | \(-0.680744\pi\) | ||||
−0.537798 | + | 0.843074i | \(0.680744\pi\) | |||||||
\(752\) | 2.31118 | 0.0842802 | ||||||||
\(753\) | −10.6308 | −0.387409 | ||||||||
\(754\) | −5.72448 | −0.208473 | ||||||||
\(755\) | 19.0189 | 0.692168 | ||||||||
\(756\) | −5.23034 | −0.190225 | ||||||||
\(757\) | −6.71118 | −0.243922 | −0.121961 | − | 0.992535i | \(-0.538918\pi\) | ||||
−0.121961 | + | 0.992535i | \(0.538918\pi\) | |||||||
\(758\) | −21.4432 | −0.778853 | ||||||||
\(759\) | −0.0462763 | −0.00167972 | ||||||||
\(760\) | −10.4920 | −0.380585 | ||||||||
\(761\) | −21.3564 | −0.774169 | −0.387085 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387085 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(762\) | 19.2660 | 0.697934 | ||||||||
\(763\) | 7.20548 | 0.260856 | ||||||||
\(764\) | −13.0915 | −0.473634 | ||||||||
\(765\) | 6.67711 | 0.241411 | ||||||||
\(766\) | 30.9293 | 1.11752 | ||||||||
\(767\) | −43.6889 | −1.57751 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −11.9159 | −0.429699 | −0.214849 | − | 0.976647i | \(-0.568926\pi\) | ||||
−0.214849 | + | 0.976647i | \(0.568926\pi\) | |||||||
\(770\) | −0.308992 | −0.0111353 | ||||||||
\(771\) | −14.4059 | −0.518817 | ||||||||
\(772\) | −11.0196 | −0.396605 | ||||||||
\(773\) | −8.94256 | −0.321642 | −0.160821 | − | 0.986984i | \(-0.551414\pi\) | ||||
−0.160821 | + | 0.986984i | \(0.551414\pi\) | |||||||
\(774\) | 11.1691 | 0.401466 | ||||||||
\(775\) | 14.0977 | 0.506404 | ||||||||
\(776\) | 12.4059 | 0.445347 | ||||||||
\(777\) | −33.0539 | −1.18580 | ||||||||
\(778\) | −5.88977 | −0.211159 | ||||||||
\(779\) | 58.1773 | 2.08442 | ||||||||
\(780\) | −7.30795 | −0.261666 | ||||||||
\(781\) | 0.301975 | 0.0108055 | ||||||||
\(782\) | −5.23034 | −0.187036 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 20.3564 | 0.727015 | ||||||||
\(785\) | 5.06645 | 0.180829 | ||||||||
\(786\) | 15.7836 | 0.562981 | ||||||||
\(787\) | 18.6074 | 0.663283 | 0.331642 | − | 0.943405i | \(-0.392398\pi\) | ||||
0.331642 | + | 0.943405i | \(0.392398\pi\) | |||||||
\(788\) | −21.6042 | −0.769617 | ||||||||
\(789\) | 6.92708 | 0.246610 | ||||||||
\(790\) | 16.0656 | 0.571588 | ||||||||
\(791\) | 68.0671 | 2.42019 | ||||||||
\(792\) | 0.0462763 | 0.00164436 | ||||||||
\(793\) | 34.0820 | 1.21029 | ||||||||
\(794\) | 9.54152 | 0.338616 | ||||||||
\(795\) | 1.33156 | 0.0472254 | ||||||||
\(796\) | 9.40269 | 0.333270 | ||||||||
\(797\) | −17.3600 | −0.614921 | −0.307461 | − | 0.951561i | \(-0.599479\pi\) | ||||
−0.307461 | + | 0.951561i | \(0.599479\pi\) | |||||||
\(798\) | 42.9862 | 1.52170 | ||||||||
\(799\) | 12.0883 | 0.427652 | ||||||||
\(800\) | 3.37026 | 0.119157 | ||||||||
\(801\) | −16.4059 | −0.579675 | ||||||||
\(802\) | −34.2920 | −1.21089 | ||||||||
\(803\) | 0.0982856 | 0.00346842 | ||||||||
\(804\) | −9.46391 | −0.333766 | ||||||||
\(805\) | −6.67711 | −0.235337 | ||||||||
\(806\) | −23.9453 | −0.843437 | ||||||||
\(807\) | 16.8857 | 0.594404 | ||||||||
\(808\) | 13.2660 | 0.466696 | ||||||||
\(809\) | 35.7667 | 1.25749 | 0.628745 | − | 0.777612i | \(-0.283569\pi\) | ||||
0.628745 | + | 0.777612i | \(0.283569\pi\) | |||||||
\(810\) | −1.27661 | −0.0448556 | ||||||||
\(811\) | 34.2857 | 1.20393 | 0.601967 | − | 0.798521i | \(-0.294384\pi\) | ||||
0.601967 | + | 0.798521i | \(0.294384\pi\) | |||||||
\(812\) | 5.23034 | 0.183549 | ||||||||
\(813\) | −10.5511 | −0.370043 | ||||||||
\(814\) | 0.292450 | 0.0102504 | ||||||||
\(815\) | 5.49086 | 0.192336 | ||||||||
\(816\) | 5.23034 | 0.183098 | ||||||||
\(817\) | −91.7949 | −3.21150 | ||||||||
\(818\) | 14.4942 | 0.506778 | ||||||||
\(819\) | 29.9410 | 1.04622 | ||||||||
\(820\) | 9.03676 | 0.315577 | ||||||||
\(821\) | 4.50067 | 0.157075 | 0.0785373 | − | 0.996911i | \(-0.474975\pi\) | ||||
0.0785373 | + | 0.996911i | \(0.474975\pi\) | |||||||
\(822\) | −21.0452 | −0.734037 | ||||||||
\(823\) | −8.71133 | −0.303658 | −0.151829 | − | 0.988407i | \(-0.548516\pi\) | ||||
−0.151829 | + | 0.988407i | \(0.548516\pi\) | |||||||
\(824\) | 3.03457 | 0.105714 | ||||||||
\(825\) | 0.155963 | 0.00542994 | ||||||||
\(826\) | 39.9176 | 1.38891 | ||||||||
\(827\) | −50.5683 | −1.75843 | −0.879215 | − | 0.476424i | \(-0.841933\pi\) | ||||
−0.879215 | + | 0.476424i | \(0.841933\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 30.3973 | 1.05574 | 0.527870 | − | 0.849325i | \(-0.322991\pi\) | ||||
0.527870 | + | 0.849325i | \(0.322991\pi\) | |||||||
\(830\) | 18.9278 | 0.656994 | ||||||||
\(831\) | 27.9075 | 0.968100 | ||||||||
\(832\) | −5.72448 | −0.198461 | ||||||||
\(833\) | 106.471 | 3.68900 | ||||||||
\(834\) | −6.58456 | −0.228005 | ||||||||
\(835\) | −2.27138 | −0.0786045 | ||||||||
\(836\) | −0.380328 | −0.0131539 | ||||||||
\(837\) | −4.18296 | −0.144584 | ||||||||
\(838\) | 7.11292 | 0.245712 | ||||||||
\(839\) | 35.0937 | 1.21157 | 0.605785 | − | 0.795629i | \(-0.292859\pi\) | ||||
0.605785 | + | 0.795629i | \(0.292859\pi\) | |||||||
\(840\) | 6.67711 | 0.230382 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 14.1958 | 0.489218 | ||||||||
\(843\) | −20.1261 | −0.693179 | ||||||||
\(844\) | 16.5576 | 0.569935 | ||||||||
\(845\) | 25.2383 | 0.868223 | ||||||||
\(846\) | −2.31118 | −0.0794601 | ||||||||
\(847\) | 57.5225 | 1.97650 | ||||||||
\(848\) | 1.04304 | 0.0358181 | ||||||||
\(849\) | 9.74302 | 0.334379 | ||||||||
\(850\) | 17.6276 | 0.604622 | ||||||||
\(851\) | 6.31965 | 0.216635 | ||||||||
\(852\) | −6.52548 | −0.223559 | ||||||||
\(853\) | −19.1208 | −0.654685 | −0.327343 | − | 0.944906i | \(-0.606153\pi\) | ||||
−0.327343 | + | 0.944906i | \(0.606153\pi\) | |||||||
\(854\) | −31.1400 | −1.06559 | ||||||||
\(855\) | 10.4920 | 0.358819 | ||||||||
\(856\) | −1.85270 | −0.0633241 | ||||||||
\(857\) | −47.9424 | −1.63768 | −0.818841 | − | 0.574020i | \(-0.805383\pi\) | ||||
−0.818841 | + | 0.574020i | \(0.805383\pi\) | |||||||
\(858\) | −0.264908 | −0.00904380 | ||||||||
\(859\) | 6.54456 | 0.223297 | 0.111649 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111649 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(860\) | −14.2586 | −0.486215 | ||||||||
\(861\) | −37.0240 | −1.26178 | ||||||||
\(862\) | −1.26022 | −0.0429233 | ||||||||
\(863\) | 43.7670 | 1.48985 | 0.744923 | − | 0.667150i | \(-0.232486\pi\) | ||||
0.744923 | + | 0.667150i | \(0.232486\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 8.04867 | 0.273663 | ||||||||
\(866\) | −1.34411 | −0.0456746 | ||||||||
\(867\) | 10.3564 | 0.351722 | ||||||||
\(868\) | 21.8783 | 0.742598 | ||||||||
\(869\) | 0.582367 | 0.0197554 | ||||||||
\(870\) | 1.27661 | 0.0432812 | ||||||||
\(871\) | 54.1760 | 1.83568 | ||||||||
\(872\) | 1.37763 | 0.0466525 | ||||||||
\(873\) | −12.4059 | −0.419877 | ||||||||
\(874\) | −8.21863 | −0.277999 | ||||||||
\(875\) | 55.8892 | 1.88940 | ||||||||
\(876\) | −2.12389 | −0.0717595 | ||||||||
\(877\) | −3.52786 | −0.119127 | −0.0595637 | − | 0.998225i | \(-0.518971\pi\) | ||||
−0.0595637 | + | 0.998225i | \(0.518971\pi\) | |||||||
\(878\) | 26.8893 | 0.907469 | ||||||||
\(879\) | −4.27337 | −0.144137 | ||||||||
\(880\) | −0.0590769 | −0.00199148 | ||||||||
\(881\) | 53.9867 | 1.81886 | 0.909429 | − | 0.415859i | \(-0.136519\pi\) | ||||
0.909429 | + | 0.415859i | \(0.136519\pi\) | |||||||
\(882\) | −20.3564 | −0.685436 | ||||||||
\(883\) | 9.13340 | 0.307363 | 0.153682 | − | 0.988120i | \(-0.450887\pi\) | ||||
0.153682 | + | 0.988120i | \(0.450887\pi\) | |||||||
\(884\) | −29.9410 | −1.00702 | ||||||||
\(885\) | 9.74302 | 0.327508 | ||||||||
\(886\) | −21.9410 | −0.737121 | ||||||||
\(887\) | −53.6947 | −1.80289 | −0.901445 | − | 0.432894i | \(-0.857493\pi\) | ||||
−0.901445 | + | 0.432894i | \(0.857493\pi\) | |||||||
\(888\) | −6.31965 | −0.212074 | ||||||||
\(889\) | 100.768 | 3.37964 | ||||||||
\(890\) | 20.9440 | 0.702045 | ||||||||
\(891\) | −0.0462763 | −0.00155031 | ||||||||
\(892\) | −9.48678 | −0.317641 | ||||||||
\(893\) | 18.9948 | 0.635636 | ||||||||
\(894\) | 4.04628 | 0.135328 | ||||||||
\(895\) | −13.9395 | −0.465947 | ||||||||
\(896\) | 5.23034 | 0.174733 | ||||||||
\(897\) | −5.72448 | −0.191135 | ||||||||
\(898\) | −11.2682 | −0.376025 | ||||||||
\(899\) | 4.18296 | 0.139510 | ||||||||
\(900\) | −3.37026 | −0.112342 | ||||||||
\(901\) | 5.45544 | 0.181747 | ||||||||
\(902\) | 0.327576 | 0.0109071 | ||||||||
\(903\) | 58.4182 | 1.94404 | ||||||||
\(904\) | 13.0139 | 0.432836 | ||||||||
\(905\) | 32.2903 | 1.07337 | ||||||||
\(906\) | −14.8979 | −0.494951 | ||||||||
\(907\) | −36.1161 | −1.19921 | −0.599607 | − | 0.800295i | \(-0.704676\pi\) | ||||
−0.599607 | + | 0.800295i | \(0.704676\pi\) | |||||||
\(908\) | −7.74356 | −0.256979 | ||||||||
\(909\) | −13.2660 | −0.440006 | ||||||||
\(910\) | −38.2230 | −1.26708 | ||||||||
\(911\) | −55.3685 | −1.83444 | −0.917221 | − | 0.398380i | \(-0.869573\pi\) | ||||
−0.917221 | + | 0.398380i | \(0.869573\pi\) | |||||||
\(912\) | 8.21863 | 0.272146 | ||||||||
\(913\) | 0.686120 | 0.0227073 | ||||||||
\(914\) | −19.1392 | −0.633070 | ||||||||
\(915\) | −7.60060 | −0.251268 | ||||||||
\(916\) | −15.3479 | −0.507110 | ||||||||
\(917\) | 82.5533 | 2.72615 | ||||||||
\(918\) | −5.23034 | −0.172627 | ||||||||
\(919\) | 24.5938 | 0.811274 | 0.405637 | − | 0.914034i | \(-0.367050\pi\) | ||||
0.405637 | + | 0.914034i | \(0.367050\pi\) | |||||||
\(920\) | −1.27661 | −0.0420887 | ||||||||
\(921\) | 0.157362 | 0.00518527 | ||||||||
\(922\) | 39.2739 | 1.29342 | ||||||||
\(923\) | 37.3550 | 1.22956 | ||||||||
\(924\) | 0.242041 | 0.00796255 | ||||||||
\(925\) | −21.2989 | −0.700303 | ||||||||
\(926\) | 8.97390 | 0.294900 | ||||||||
\(927\) | −3.03457 | −0.0996684 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −29.1944 | −0.957836 | −0.478918 | − | 0.877860i | \(-0.658971\pi\) | ||||
−0.478918 | + | 0.877860i | \(0.658971\pi\) | |||||||
\(930\) | 5.34002 | 0.175106 | ||||||||
\(931\) | 167.302 | 5.48310 | ||||||||
\(932\) | −1.69674 | −0.0555786 | ||||||||
\(933\) | 27.3420 | 0.895137 | ||||||||
\(934\) | 23.5666 | 0.771122 | ||||||||
\(935\) | −0.308992 | −0.0101051 | ||||||||
\(936\) | 5.72448 | 0.187111 | ||||||||
\(937\) | 28.2143 | 0.921723 | 0.460861 | − | 0.887472i | \(-0.347541\pi\) | ||||
0.460861 | + | 0.887472i | \(0.347541\pi\) | |||||||
\(938\) | −49.4994 | −1.61621 | ||||||||
\(939\) | 3.04523 | 0.0993774 | ||||||||
\(940\) | 2.95049 | 0.0962342 | ||||||||
\(941\) | −19.2331 | −0.626980 | −0.313490 | − | 0.949591i | \(-0.601498\pi\) | ||||
−0.313490 | + | 0.949591i | \(0.601498\pi\) | |||||||
\(942\) | −3.96867 | −0.129306 | ||||||||
\(943\) | 7.07871 | 0.230514 | ||||||||
\(944\) | 7.63193 | 0.248398 | ||||||||
\(945\) | −6.67711 | −0.217206 | ||||||||
\(946\) | −0.516865 | −0.0168047 | ||||||||
\(947\) | 2.51322 | 0.0816688 | 0.0408344 | − | 0.999166i | \(-0.486998\pi\) | ||||
0.0408344 | + | 0.999166i | \(0.486998\pi\) | |||||||
\(948\) | −12.5846 | −0.408727 | ||||||||
\(949\) | 12.1582 | 0.394670 | ||||||||
\(950\) | 27.6989 | 0.898672 | ||||||||
\(951\) | 29.8585 | 0.968228 | ||||||||
\(952\) | 27.3564 | 0.886627 | ||||||||
\(953\) | 41.9061 | 1.35747 | 0.678736 | − | 0.734382i | \(-0.262528\pi\) | ||||
0.678736 | + | 0.734382i | \(0.262528\pi\) | |||||||
\(954\) | −1.04304 | −0.0337696 | ||||||||
\(955\) | −16.7128 | −0.540813 | ||||||||
\(956\) | 0.315518 | 0.0102046 | ||||||||
\(957\) | 0.0462763 | 0.00149590 | ||||||||
\(958\) | 9.70376 | 0.313514 | ||||||||
\(959\) | −110.074 | −3.55446 | ||||||||
\(960\) | 1.27661 | 0.0412025 | ||||||||
\(961\) | −13.5028 | −0.435575 | ||||||||
\(962\) | 36.1767 | 1.16638 | ||||||||
\(963\) | 1.85270 | 0.0597026 | ||||||||
\(964\) | 28.0591 | 0.903724 | ||||||||
\(965\) | −14.0678 | −0.452858 | ||||||||
\(966\) | 5.23034 | 0.168283 | ||||||||
\(967\) | −26.6116 | −0.855772 | −0.427886 | − | 0.903833i | \(-0.640741\pi\) | ||||
−0.427886 | + | 0.903833i | \(0.640741\pi\) | |||||||
\(968\) | 10.9979 | 0.353485 | ||||||||
\(969\) | 42.9862 | 1.38092 | ||||||||
\(970\) | 15.8376 | 0.508513 | ||||||||
\(971\) | 3.71168 | 0.119114 | 0.0595568 | − | 0.998225i | \(-0.481031\pi\) | ||||
0.0595568 | + | 0.998225i | \(0.481031\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −34.4395 | −1.10408 | ||||||||
\(974\) | 25.3856 | 0.813406 | ||||||||
\(975\) | 19.2930 | 0.617871 | ||||||||
\(976\) | −5.95372 | −0.190574 | ||||||||
\(977\) | 25.7520 | 0.823880 | 0.411940 | − | 0.911211i | \(-0.364851\pi\) | ||||
0.411940 | + | 0.911211i | \(0.364851\pi\) | |||||||
\(978\) | −4.30112 | −0.137535 | ||||||||
\(979\) | 0.759205 | 0.0242643 | ||||||||
\(980\) | 25.9873 | 0.830132 | ||||||||
\(981\) | −1.37763 | −0.0439844 | ||||||||
\(982\) | 8.39726 | 0.267967 | ||||||||
\(983\) | 11.1992 | 0.357199 | 0.178600 | − | 0.983922i | \(-0.442843\pi\) | ||||
0.178600 | + | 0.983922i | \(0.442843\pi\) | |||||||
\(984\) | −7.07871 | −0.225661 | ||||||||
\(985\) | −27.5802 | −0.878777 | ||||||||
\(986\) | 5.23034 | 0.166568 | ||||||||
\(987\) | −12.0883 | −0.384774 | ||||||||
\(988\) | −47.0474 | −1.49678 | ||||||||
\(989\) | −11.1691 | −0.355157 | ||||||||
\(990\) | 0.0590769 | 0.00187759 | ||||||||
\(991\) | −37.7659 | −1.19967 | −0.599836 | − | 0.800123i | \(-0.704768\pi\) | ||||
−0.599836 | + | 0.800123i | \(0.704768\pi\) | |||||||
\(992\) | 4.18296 | 0.132809 | ||||||||
\(993\) | −5.37982 | −0.170724 | ||||||||
\(994\) | −34.1305 | −1.08255 | ||||||||
\(995\) | 12.0036 | 0.380539 | ||||||||
\(996\) | −14.8266 | −0.469799 | ||||||||
\(997\) | 15.1634 | 0.480229 | 0.240115 | − | 0.970745i | \(-0.422815\pi\) | ||||
0.240115 | + | 0.970745i | \(0.422815\pi\) | |||||||
\(998\) | −8.00867 | −0.253510 | ||||||||
\(999\) | 6.31965 | 0.199945 |
(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 | 4002.2.a.bb.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.bb.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |