Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + \cdots + 1496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.89261\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(5\) | −2.89261 | −1.29362 | −0.646808 | − | 0.762653i | \(-0.723896\pi\) | ||||
−0.646808 | + | 0.762653i | \(0.723896\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.19999 | −1.58745 | −0.793723 | − | 0.608280i | \(-0.791860\pi\) | ||||
−0.793723 | + | 0.608280i | \(0.791860\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.89261 | 0.914724 | ||||||||
\(11\) | −5.07383 | −1.52982 | −0.764909 | − | 0.644139i | \(-0.777216\pi\) | ||||
−0.764909 | + | 0.644139i | \(0.777216\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.31548 | 1.19690 | 0.598450 | − | 0.801160i | \(-0.295784\pi\) | ||||
0.598450 | + | 0.801160i | \(0.295784\pi\) | |||||||
\(14\) | 4.19999 | 1.12249 | ||||||||
\(15\) | 2.89261 | 0.746869 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.164752 | −0.0399582 | −0.0199791 | − | 0.999800i | \(-0.506360\pi\) | ||||
−0.0199791 | + | 0.999800i | \(0.506360\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.89261 | −0.646808 | ||||||||
\(21\) | 4.19999 | 0.916512 | ||||||||
\(22\) | 5.07383 | 1.08174 | ||||||||
\(23\) | −6.57103 | −1.37015 | −0.685077 | − | 0.728471i | \(-0.740231\pi\) | ||||
−0.685077 | + | 0.728471i | \(0.740231\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.36720 | 0.673441 | ||||||||
\(26\) | −4.31548 | −0.846336 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.19999 | −0.793723 | ||||||||
\(29\) | 2.51473 | 0.466974 | 0.233487 | − | 0.972360i | \(-0.424986\pi\) | ||||
0.233487 | + | 0.972360i | \(0.424986\pi\) | |||||||
\(30\) | −2.89261 | −0.528116 | ||||||||
\(31\) | 9.86954 | 1.77262 | 0.886311 | − | 0.463091i | \(-0.153260\pi\) | ||||
0.886311 | + | 0.463091i | \(0.153260\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.07383 | 0.883240 | ||||||||
\(34\) | 0.164752 | 0.0282547 | ||||||||
\(35\) | 12.1489 | 2.05354 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.06505 | −0.175093 | −0.0875464 | − | 0.996160i | \(-0.527903\pi\) | ||||
−0.0875464 | + | 0.996160i | \(0.527903\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −4.31548 | −0.691030 | ||||||||
\(40\) | 2.89261 | 0.457362 | ||||||||
\(41\) | −9.53136 | −1.48855 | −0.744274 | − | 0.667874i | \(-0.767204\pi\) | ||||
−0.744274 | + | 0.667874i | \(0.767204\pi\) | |||||||
\(42\) | −4.19999 | −0.648072 | ||||||||
\(43\) | 11.9616 | 1.82412 | 0.912060 | − | 0.410057i | \(-0.134491\pi\) | ||||
0.912060 | + | 0.410057i | \(0.134491\pi\) | |||||||
\(44\) | −5.07383 | −0.764909 | ||||||||
\(45\) | −2.89261 | −0.431205 | ||||||||
\(46\) | 6.57103 | 0.968845 | ||||||||
\(47\) | −2.21548 | −0.323161 | −0.161581 | − | 0.986860i | \(-0.551659\pi\) | ||||
−0.161581 | + | 0.986860i | \(0.551659\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 10.6399 | 1.51998 | ||||||||
\(50\) | −3.36720 | −0.476194 | ||||||||
\(51\) | 0.164752 | 0.0230699 | ||||||||
\(52\) | 4.31548 | 0.598450 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 14.6766 | 1.97900 | ||||||||
\(56\) | 4.19999 | 0.561247 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −2.51473 | −0.330201 | ||||||||
\(59\) | 7.39486 | 0.962729 | 0.481364 | − | 0.876521i | \(-0.340141\pi\) | ||||
0.481364 | + | 0.876521i | \(0.340141\pi\) | |||||||
\(60\) | 2.89261 | 0.373435 | ||||||||
\(61\) | −2.35917 | −0.302061 | −0.151031 | − | 0.988529i | \(-0.548259\pi\) | ||||
−0.151031 | + | 0.988529i | \(0.548259\pi\) | |||||||
\(62\) | −9.86954 | −1.25343 | ||||||||
\(63\) | −4.19999 | −0.529148 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.4830 | −1.54833 | ||||||||
\(66\) | −5.07383 | −0.624545 | ||||||||
\(67\) | −8.01730 | −0.979469 | −0.489735 | − | 0.871872i | \(-0.662906\pi\) | ||||
−0.489735 | + | 0.871872i | \(0.662906\pi\) | |||||||
\(68\) | −0.164752 | −0.0199791 | ||||||||
\(69\) | 6.57103 | 0.791058 | ||||||||
\(70\) | −12.1489 | −1.45207 | ||||||||
\(71\) | 12.1481 | 1.44171 | 0.720856 | − | 0.693085i | \(-0.243749\pi\) | ||||
0.720856 | + | 0.693085i | \(0.243749\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.402131 | 0.0470659 | 0.0235329 | − | 0.999723i | \(-0.492509\pi\) | ||||
0.0235329 | + | 0.999723i | \(0.492509\pi\) | |||||||
\(74\) | 1.06505 | 0.123809 | ||||||||
\(75\) | −3.36720 | −0.388811 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 21.3100 | 2.42850 | ||||||||
\(78\) | 4.31548 | 0.488632 | ||||||||
\(79\) | −9.61531 | −1.08181 | −0.540903 | − | 0.841085i | \(-0.681918\pi\) | ||||
−0.540903 | + | 0.841085i | \(0.681918\pi\) | |||||||
\(80\) | −2.89261 | −0.323404 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.53136 | 1.05256 | ||||||||
\(83\) | 14.9921 | 1.64560 | 0.822799 | − | 0.568333i | \(-0.192412\pi\) | ||||
0.822799 | + | 0.568333i | \(0.192412\pi\) | |||||||
\(84\) | 4.19999 | 0.458256 | ||||||||
\(85\) | 0.476563 | 0.0516906 | ||||||||
\(86\) | −11.9616 | −1.28985 | ||||||||
\(87\) | −2.51473 | −0.269608 | ||||||||
\(88\) | 5.07383 | 0.540872 | ||||||||
\(89\) | 9.04557 | 0.958828 | 0.479414 | − | 0.877589i | \(-0.340849\pi\) | ||||
0.479414 | + | 0.877589i | \(0.340849\pi\) | |||||||
\(90\) | 2.89261 | 0.304908 | ||||||||
\(91\) | −18.1250 | −1.90001 | ||||||||
\(92\) | −6.57103 | −0.685077 | ||||||||
\(93\) | −9.86954 | −1.02342 | ||||||||
\(94\) | 2.21548 | 0.228510 | ||||||||
\(95\) | 2.89261 | 0.296776 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.2021 | 1.44200 | 0.721001 | − | 0.692934i | \(-0.243682\pi\) | ||||
0.721001 | + | 0.692934i | \(0.243682\pi\) | |||||||
\(98\) | −10.6399 | −1.07479 | ||||||||
\(99\) | −5.07383 | −0.509939 | ||||||||
\(100\) | 3.36720 | 0.336720 | ||||||||
\(101\) | 19.4631 | 1.93665 | 0.968327 | − | 0.249686i | \(-0.0803274\pi\) | ||||
0.968327 | + | 0.249686i | \(0.0803274\pi\) | |||||||
\(102\) | −0.164752 | −0.0163129 | ||||||||
\(103\) | 2.15342 | 0.212183 | 0.106092 | − | 0.994356i | \(-0.466166\pi\) | ||||
0.106092 | + | 0.994356i | \(0.466166\pi\) | |||||||
\(104\) | −4.31548 | −0.423168 | ||||||||
\(105\) | −12.1489 | −1.18561 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −2.32310 | −0.224582 | −0.112291 | − | 0.993675i | \(-0.535819\pi\) | ||||
−0.112291 | + | 0.993675i | \(0.535819\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.97372 | −0.667961 | −0.333981 | − | 0.942580i | \(-0.608392\pi\) | ||||
−0.333981 | + | 0.942580i | \(0.608392\pi\) | |||||||
\(110\) | −14.6766 | −1.39936 | ||||||||
\(111\) | 1.06505 | 0.101090 | ||||||||
\(112\) | −4.19999 | −0.396861 | ||||||||
\(113\) | −4.23773 | −0.398652 | −0.199326 | − | 0.979933i | \(-0.563875\pi\) | ||||
−0.199326 | + | 0.979933i | \(0.563875\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 19.0074 | 1.77245 | ||||||||
\(116\) | 2.51473 | 0.233487 | ||||||||
\(117\) | 4.31548 | 0.398966 | ||||||||
\(118\) | −7.39486 | −0.680752 | ||||||||
\(119\) | 0.691956 | 0.0634315 | ||||||||
\(120\) | −2.89261 | −0.264058 | ||||||||
\(121\) | 14.7438 | 1.34034 | ||||||||
\(122\) | 2.35917 | 0.213590 | ||||||||
\(123\) | 9.53136 | 0.859414 | ||||||||
\(124\) | 9.86954 | 0.886311 | ||||||||
\(125\) | 4.72305 | 0.422442 | ||||||||
\(126\) | 4.19999 | 0.374164 | ||||||||
\(127\) | −13.2802 | −1.17843 | −0.589216 | − | 0.807976i | \(-0.700563\pi\) | ||||
−0.589216 | + | 0.807976i | \(0.700563\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.9616 | −1.05316 | ||||||||
\(130\) | 12.4830 | 1.09483 | ||||||||
\(131\) | −20.5119 | −1.79213 | −0.896066 | − | 0.443921i | \(-0.853587\pi\) | ||||
−0.896066 | + | 0.443921i | \(0.853587\pi\) | |||||||
\(132\) | 5.07383 | 0.441620 | ||||||||
\(133\) | 4.19999 | 0.364185 | ||||||||
\(134\) | 8.01730 | 0.692589 | ||||||||
\(135\) | 2.89261 | 0.248956 | ||||||||
\(136\) | 0.164752 | 0.0141274 | ||||||||
\(137\) | 21.2098 | 1.81208 | 0.906039 | − | 0.423194i | \(-0.139091\pi\) | ||||
0.906039 | + | 0.423194i | \(0.139091\pi\) | |||||||
\(138\) | −6.57103 | −0.559363 | ||||||||
\(139\) | −12.0035 | −1.01812 | −0.509061 | − | 0.860730i | \(-0.670007\pi\) | ||||
−0.509061 | + | 0.860730i | \(0.670007\pi\) | |||||||
\(140\) | 12.1489 | 1.02677 | ||||||||
\(141\) | 2.21548 | 0.186577 | ||||||||
\(142\) | −12.1481 | −1.01944 | ||||||||
\(143\) | −21.8960 | −1.83104 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.27414 | −0.604085 | ||||||||
\(146\) | −0.402131 | −0.0332806 | ||||||||
\(147\) | −10.6399 | −0.877562 | ||||||||
\(148\) | −1.06505 | −0.0875464 | ||||||||
\(149\) | 10.1141 | 0.828578 | 0.414289 | − | 0.910145i | \(-0.364030\pi\) | ||||
0.414289 | + | 0.910145i | \(0.364030\pi\) | |||||||
\(150\) | 3.36720 | 0.274931 | ||||||||
\(151\) | 22.9799 | 1.87007 | 0.935037 | − | 0.354550i | \(-0.115366\pi\) | ||||
0.935037 | + | 0.354550i | \(0.115366\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −0.164752 | −0.0133194 | ||||||||
\(154\) | −21.3100 | −1.71721 | ||||||||
\(155\) | −28.5487 | −2.29309 | ||||||||
\(156\) | −4.31548 | −0.345515 | ||||||||
\(157\) | −18.2952 | −1.46012 | −0.730059 | − | 0.683384i | \(-0.760507\pi\) | ||||
−0.730059 | + | 0.683384i | \(0.760507\pi\) | |||||||
\(158\) | 9.61531 | 0.764953 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | 2.89261 | 0.228681 | ||||||||
\(161\) | 27.5982 | 2.17504 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.7938 | 1.86368 | 0.931838 | − | 0.362875i | \(-0.118205\pi\) | ||||
0.931838 | + | 0.362875i | \(0.118205\pi\) | |||||||
\(164\) | −9.53136 | −0.744274 | ||||||||
\(165\) | −14.6766 | −1.14257 | ||||||||
\(166\) | −14.9921 | −1.16361 | ||||||||
\(167\) | −6.90049 | −0.533976 | −0.266988 | − | 0.963700i | \(-0.586028\pi\) | ||||
−0.266988 | + | 0.963700i | \(0.586028\pi\) | |||||||
\(168\) | −4.19999 | −0.324036 | ||||||||
\(169\) | 5.62338 | 0.432568 | ||||||||
\(170\) | −0.476563 | −0.0365507 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 11.9616 | 0.912060 | ||||||||
\(173\) | −13.0432 | −0.991653 | −0.495827 | − | 0.868422i | \(-0.665135\pi\) | ||||
−0.495827 | + | 0.868422i | \(0.665135\pi\) | |||||||
\(174\) | 2.51473 | 0.190641 | ||||||||
\(175\) | −14.1422 | −1.06905 | ||||||||
\(176\) | −5.07383 | −0.382454 | ||||||||
\(177\) | −7.39486 | −0.555832 | ||||||||
\(178\) | −9.04557 | −0.677994 | ||||||||
\(179\) | −13.7443 | −1.02730 | −0.513648 | − | 0.858001i | \(-0.671706\pi\) | ||||
−0.513648 | + | 0.858001i | \(0.671706\pi\) | |||||||
\(180\) | −2.89261 | −0.215603 | ||||||||
\(181\) | 10.6985 | 0.795211 | 0.397606 | − | 0.917556i | \(-0.369841\pi\) | ||||
0.397606 | + | 0.917556i | \(0.369841\pi\) | |||||||
\(182\) | 18.1250 | 1.34351 | ||||||||
\(183\) | 2.35917 | 0.174395 | ||||||||
\(184\) | 6.57103 | 0.484422 | ||||||||
\(185\) | 3.08077 | 0.226503 | ||||||||
\(186\) | 9.86954 | 0.723670 | ||||||||
\(187\) | 0.835923 | 0.0611288 | ||||||||
\(188\) | −2.21548 | −0.161581 | ||||||||
\(189\) | 4.19999 | 0.305504 | ||||||||
\(190\) | −2.89261 | −0.209852 | ||||||||
\(191\) | −12.9853 | −0.939583 | −0.469792 | − | 0.882777i | \(-0.655671\pi\) | ||||
−0.469792 | + | 0.882777i | \(0.655671\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −5.55372 | −0.399765 | −0.199883 | − | 0.979820i | \(-0.564056\pi\) | ||||
−0.199883 | + | 0.979820i | \(0.564056\pi\) | |||||||
\(194\) | −14.2021 | −1.01965 | ||||||||
\(195\) | 12.4830 | 0.893927 | ||||||||
\(196\) | 10.6399 | 0.759991 | ||||||||
\(197\) | −15.1348 | −1.07831 | −0.539156 | − | 0.842206i | \(-0.681257\pi\) | ||||
−0.539156 | + | 0.842206i | \(0.681257\pi\) | |||||||
\(198\) | 5.07383 | 0.360581 | ||||||||
\(199\) | −3.14427 | −0.222891 | −0.111446 | − | 0.993771i | \(-0.535548\pi\) | ||||
−0.111446 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(200\) | −3.36720 | −0.238097 | ||||||||
\(201\) | 8.01730 | 0.565497 | ||||||||
\(202\) | −19.4631 | −1.36942 | ||||||||
\(203\) | −10.5618 | −0.741296 | ||||||||
\(204\) | 0.164752 | 0.0115349 | ||||||||
\(205\) | 27.5705 | 1.92561 | ||||||||
\(206\) | −2.15342 | −0.150036 | ||||||||
\(207\) | −6.57103 | −0.456718 | ||||||||
\(208\) | 4.31548 | 0.299225 | ||||||||
\(209\) | 5.07383 | 0.350964 | ||||||||
\(210\) | 12.1489 | 0.838356 | ||||||||
\(211\) | −20.4722 | −1.40936 | −0.704681 | − | 0.709524i | \(-0.748910\pi\) | ||||
−0.704681 | + | 0.709524i | \(0.748910\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | −12.1481 | −0.832373 | ||||||||
\(214\) | 2.32310 | 0.158804 | ||||||||
\(215\) | −34.6001 | −2.35971 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −41.4519 | −2.81394 | ||||||||
\(218\) | 6.97372 | 0.472320 | ||||||||
\(219\) | −0.402131 | −0.0271735 | ||||||||
\(220\) | 14.6766 | 0.989498 | ||||||||
\(221\) | −0.710984 | −0.0478260 | ||||||||
\(222\) | −1.06505 | −0.0714813 | ||||||||
\(223\) | 1.30931 | 0.0876777 | 0.0438389 | − | 0.999039i | \(-0.486041\pi\) | ||||
0.0438389 | + | 0.999039i | \(0.486041\pi\) | |||||||
\(224\) | 4.19999 | 0.280623 | ||||||||
\(225\) | 3.36720 | 0.224480 | ||||||||
\(226\) | 4.23773 | 0.281890 | ||||||||
\(227\) | −29.3497 | −1.94801 | −0.974005 | − | 0.226528i | \(-0.927262\pi\) | ||||
−0.974005 | + | 0.226528i | \(0.927262\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 11.8618 | 0.783852 | 0.391926 | − | 0.919997i | \(-0.371809\pi\) | ||||
0.391926 | + | 0.919997i | \(0.371809\pi\) | |||||||
\(230\) | −19.0074 | −1.25331 | ||||||||
\(231\) | −21.3100 | −1.40210 | ||||||||
\(232\) | −2.51473 | −0.165100 | ||||||||
\(233\) | −6.53013 | −0.427803 | −0.213901 | − | 0.976855i | \(-0.568617\pi\) | ||||
−0.213901 | + | 0.976855i | \(0.568617\pi\) | |||||||
\(234\) | −4.31548 | −0.282112 | ||||||||
\(235\) | 6.40853 | 0.418046 | ||||||||
\(236\) | 7.39486 | 0.481364 | ||||||||
\(237\) | 9.61531 | 0.624581 | ||||||||
\(238\) | −0.691956 | −0.0448528 | ||||||||
\(239\) | −22.3102 | −1.44313 | −0.721564 | − | 0.692347i | \(-0.756577\pi\) | ||||
−0.721564 | + | 0.692347i | \(0.756577\pi\) | |||||||
\(240\) | 2.89261 | 0.186717 | ||||||||
\(241\) | 8.77862 | 0.565481 | 0.282740 | − | 0.959196i | \(-0.408757\pi\) | ||||
0.282740 | + | 0.959196i | \(0.408757\pi\) | |||||||
\(242\) | −14.7438 | −0.947764 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.35917 | −0.151031 | ||||||||
\(245\) | −30.7770 | −1.96627 | ||||||||
\(246\) | −9.53136 | −0.607697 | ||||||||
\(247\) | −4.31548 | −0.274588 | ||||||||
\(248\) | −9.86954 | −0.626716 | ||||||||
\(249\) | −14.9921 | −0.950086 | ||||||||
\(250\) | −4.72305 | −0.298712 | ||||||||
\(251\) | 13.4594 | 0.849552 | 0.424776 | − | 0.905299i | \(-0.360353\pi\) | ||||
0.424776 | + | 0.905299i | \(0.360353\pi\) | |||||||
\(252\) | −4.19999 | −0.264574 | ||||||||
\(253\) | 33.3403 | 2.09608 | ||||||||
\(254\) | 13.2802 | 0.833277 | ||||||||
\(255\) | −0.476563 | −0.0298436 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.35628 | −0.458872 | −0.229436 | − | 0.973324i | \(-0.573688\pi\) | ||||
−0.229436 | + | 0.973324i | \(0.573688\pi\) | |||||||
\(258\) | 11.9616 | 0.744694 | ||||||||
\(259\) | 4.47318 | 0.277950 | ||||||||
\(260\) | −12.4830 | −0.774164 | ||||||||
\(261\) | 2.51473 | 0.155658 | ||||||||
\(262\) | 20.5119 | 1.26723 | ||||||||
\(263\) | −22.7323 | −1.40173 | −0.700867 | − | 0.713292i | \(-0.747203\pi\) | ||||
−0.700867 | + | 0.713292i | \(0.747203\pi\) | |||||||
\(264\) | −5.07383 | −0.312273 | ||||||||
\(265\) | 2.89261 | 0.177692 | ||||||||
\(266\) | −4.19999 | −0.257518 | ||||||||
\(267\) | −9.04557 | −0.553580 | ||||||||
\(268\) | −8.01730 | −0.489735 | ||||||||
\(269\) | 19.1670 | 1.16863 | 0.584316 | − | 0.811526i | \(-0.301363\pi\) | ||||
0.584316 | + | 0.811526i | \(0.301363\pi\) | |||||||
\(270\) | −2.89261 | −0.176039 | ||||||||
\(271\) | −10.0217 | −0.608776 | −0.304388 | − | 0.952548i | \(-0.598452\pi\) | ||||
−0.304388 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(272\) | −0.164752 | −0.00998955 | ||||||||
\(273\) | 18.1250 | 1.09697 | ||||||||
\(274\) | −21.2098 | −1.28133 | ||||||||
\(275\) | −17.0846 | −1.03024 | ||||||||
\(276\) | 6.57103 | 0.395529 | ||||||||
\(277\) | 26.3575 | 1.58367 | 0.791836 | − | 0.610734i | \(-0.209126\pi\) | ||||
0.791836 | + | 0.610734i | \(0.209126\pi\) | |||||||
\(278\) | 12.0035 | 0.719922 | ||||||||
\(279\) | 9.86954 | 0.590874 | ||||||||
\(280\) | −12.1489 | −0.726037 | ||||||||
\(281\) | 25.1508 | 1.50037 | 0.750186 | − | 0.661227i | \(-0.229964\pi\) | ||||
0.750186 | + | 0.661227i | \(0.229964\pi\) | |||||||
\(282\) | −2.21548 | −0.131930 | ||||||||
\(283\) | 21.5774 | 1.28264 | 0.641322 | − | 0.767272i | \(-0.278386\pi\) | ||||
0.641322 | + | 0.767272i | \(0.278386\pi\) | |||||||
\(284\) | 12.1481 | 0.720856 | ||||||||
\(285\) | −2.89261 | −0.171344 | ||||||||
\(286\) | 21.8960 | 1.29474 | ||||||||
\(287\) | 40.0316 | 2.36299 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9729 | −0.998403 | ||||||||
\(290\) | 7.27414 | 0.427152 | ||||||||
\(291\) | −14.2021 | −0.832541 | ||||||||
\(292\) | 0.402131 | 0.0235329 | ||||||||
\(293\) | 4.48113 | 0.261790 | 0.130895 | − | 0.991396i | \(-0.458215\pi\) | ||||
0.130895 | + | 0.991396i | \(0.458215\pi\) | |||||||
\(294\) | 10.6399 | 0.620530 | ||||||||
\(295\) | −21.3905 | −1.24540 | ||||||||
\(296\) | 1.06505 | 0.0619046 | ||||||||
\(297\) | 5.07383 | 0.294413 | ||||||||
\(298\) | −10.1141 | −0.585893 | ||||||||
\(299\) | −28.3571 | −1.63994 | ||||||||
\(300\) | −3.36720 | −0.194406 | ||||||||
\(301\) | −50.2383 | −2.89569 | ||||||||
\(302\) | −22.9799 | −1.32234 | ||||||||
\(303\) | −19.4631 | −1.11813 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 6.82417 | 0.390751 | ||||||||
\(306\) | 0.164752 | 0.00941824 | ||||||||
\(307\) | −25.9747 | −1.48245 | −0.741227 | − | 0.671254i | \(-0.765756\pi\) | ||||
−0.741227 | + | 0.671254i | \(0.765756\pi\) | |||||||
\(308\) | 21.3100 | 1.21425 | ||||||||
\(309\) | −2.15342 | −0.122504 | ||||||||
\(310\) | 28.5487 | 1.62146 | ||||||||
\(311\) | 19.4275 | 1.10163 | 0.550817 | − | 0.834626i | \(-0.314316\pi\) | ||||
0.550817 | + | 0.834626i | \(0.314316\pi\) | |||||||
\(312\) | 4.31548 | 0.244316 | ||||||||
\(313\) | −16.6025 | −0.938428 | −0.469214 | − | 0.883085i | \(-0.655463\pi\) | ||||
−0.469214 | + | 0.883085i | \(0.655463\pi\) | |||||||
\(314\) | 18.2952 | 1.03246 | ||||||||
\(315\) | 12.1489 | 0.684515 | ||||||||
\(316\) | −9.61531 | −0.540903 | ||||||||
\(317\) | −22.4533 | −1.26110 | −0.630551 | − | 0.776148i | \(-0.717171\pi\) | ||||
−0.630551 | + | 0.776148i | \(0.717171\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −12.7593 | −0.714385 | ||||||||
\(320\) | −2.89261 | −0.161702 | ||||||||
\(321\) | 2.32310 | 0.129663 | ||||||||
\(322\) | −27.5982 | −1.53799 | ||||||||
\(323\) | 0.164752 | 0.00916704 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 14.5311 | 0.806040 | ||||||||
\(326\) | −23.7938 | −1.31782 | ||||||||
\(327\) | 6.97372 | 0.385648 | ||||||||
\(328\) | 9.53136 | 0.526281 | ||||||||
\(329\) | 9.30499 | 0.513001 | ||||||||
\(330\) | 14.6766 | 0.807921 | ||||||||
\(331\) | 2.79548 | 0.153653 | 0.0768267 | − | 0.997044i | \(-0.475521\pi\) | ||||
0.0768267 | + | 0.997044i | \(0.475521\pi\) | |||||||
\(332\) | 14.9921 | 0.822799 | ||||||||
\(333\) | −1.06505 | −0.0583642 | ||||||||
\(334\) | 6.90049 | 0.377578 | ||||||||
\(335\) | 23.1909 | 1.26706 | ||||||||
\(336\) | 4.19999 | 0.229128 | ||||||||
\(337\) | −18.2672 | −0.995077 | −0.497538 | − | 0.867442i | \(-0.665763\pi\) | ||||
−0.497538 | + | 0.867442i | \(0.665763\pi\) | |||||||
\(338\) | −5.62338 | −0.305872 | ||||||||
\(339\) | 4.23773 | 0.230162 | ||||||||
\(340\) | 0.476563 | 0.0258453 | ||||||||
\(341\) | −50.0764 | −2.71179 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −15.2874 | −0.825444 | ||||||||
\(344\) | −11.9616 | −0.644924 | ||||||||
\(345\) | −19.0074 | −1.02333 | ||||||||
\(346\) | 13.0432 | 0.701205 | ||||||||
\(347\) | −4.25132 | −0.228223 | −0.114111 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114111 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(348\) | −2.51473 | −0.134804 | ||||||||
\(349\) | 35.4354 | 1.89681 | 0.948406 | − | 0.317057i | \(-0.102695\pi\) | ||||
0.948406 | + | 0.317057i | \(0.102695\pi\) | |||||||
\(350\) | 14.1422 | 0.755933 | ||||||||
\(351\) | −4.31548 | −0.230343 | ||||||||
\(352\) | 5.07383 | 0.270436 | ||||||||
\(353\) | 19.5956 | 1.04297 | 0.521484 | − | 0.853261i | \(-0.325378\pi\) | ||||
0.521484 | + | 0.853261i | \(0.325378\pi\) | |||||||
\(354\) | 7.39486 | 0.393032 | ||||||||
\(355\) | −35.1397 | −1.86502 | ||||||||
\(356\) | 9.04557 | 0.479414 | ||||||||
\(357\) | −0.691956 | −0.0366222 | ||||||||
\(358\) | 13.7443 | 0.726408 | ||||||||
\(359\) | −14.0420 | −0.741110 | −0.370555 | − | 0.928810i | \(-0.620833\pi\) | ||||
−0.370555 | + | 0.928810i | \(0.620833\pi\) | |||||||
\(360\) | 2.89261 | 0.152454 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −10.6985 | −0.562299 | ||||||||
\(363\) | −14.7438 | −0.773846 | ||||||||
\(364\) | −18.1250 | −0.950006 | ||||||||
\(365\) | −1.16321 | −0.0608851 | ||||||||
\(366\) | −2.35917 | −0.123316 | ||||||||
\(367\) | −2.72418 | −0.142201 | −0.0711006 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0711006 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(368\) | −6.57103 | −0.342538 | ||||||||
\(369\) | −9.53136 | −0.496183 | ||||||||
\(370\) | −3.08077 | −0.160162 | ||||||||
\(371\) | 4.19999 | 0.218052 | ||||||||
\(372\) | −9.86954 | −0.511712 | ||||||||
\(373\) | 13.4646 | 0.697173 | 0.348586 | − | 0.937277i | \(-0.386662\pi\) | ||||
0.348586 | + | 0.937277i | \(0.386662\pi\) | |||||||
\(374\) | −0.835923 | −0.0432246 | ||||||||
\(375\) | −4.72305 | −0.243897 | ||||||||
\(376\) | 2.21548 | 0.114255 | ||||||||
\(377\) | 10.8523 | 0.558921 | ||||||||
\(378\) | −4.19999 | −0.216024 | ||||||||
\(379\) | −2.12113 | −0.108955 | −0.0544777 | − | 0.998515i | \(-0.517349\pi\) | ||||
−0.0544777 | + | 0.998515i | \(0.517349\pi\) | |||||||
\(380\) | 2.89261 | 0.148388 | ||||||||
\(381\) | 13.2802 | 0.680367 | ||||||||
\(382\) | 12.9853 | 0.664386 | ||||||||
\(383\) | 12.0871 | 0.617621 | 0.308811 | − | 0.951124i | \(-0.400069\pi\) | ||||
0.308811 | + | 0.951124i | \(0.400069\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −61.6416 | −3.14155 | ||||||||
\(386\) | 5.55372 | 0.282677 | ||||||||
\(387\) | 11.9616 | 0.608040 | ||||||||
\(388\) | 14.2021 | 0.721001 | ||||||||
\(389\) | 18.2322 | 0.924410 | 0.462205 | − | 0.886773i | \(-0.347058\pi\) | ||||
0.462205 | + | 0.886773i | \(0.347058\pi\) | |||||||
\(390\) | −12.4830 | −0.632102 | ||||||||
\(391\) | 1.08259 | 0.0547489 | ||||||||
\(392\) | −10.6399 | −0.537395 | ||||||||
\(393\) | 20.5119 | 1.03469 | ||||||||
\(394\) | 15.1348 | 0.762482 | ||||||||
\(395\) | 27.8133 | 1.39944 | ||||||||
\(396\) | −5.07383 | −0.254970 | ||||||||
\(397\) | 0.303597 | 0.0152371 | 0.00761854 | − | 0.999971i | \(-0.497575\pi\) | ||||
0.00761854 | + | 0.999971i | \(0.497575\pi\) | |||||||
\(398\) | 3.14427 | 0.157608 | ||||||||
\(399\) | −4.19999 | −0.210262 | ||||||||
\(400\) | 3.36720 | 0.168360 | ||||||||
\(401\) | 6.29918 | 0.314566 | 0.157283 | − | 0.987554i | \(-0.449726\pi\) | ||||
0.157283 | + | 0.987554i | \(0.449726\pi\) | |||||||
\(402\) | −8.01730 | −0.399867 | ||||||||
\(403\) | 42.5918 | 2.12165 | ||||||||
\(404\) | 19.4631 | 0.968327 | ||||||||
\(405\) | −2.89261 | −0.143735 | ||||||||
\(406\) | 10.5618 | 0.524175 | ||||||||
\(407\) | 5.40387 | 0.267860 | ||||||||
\(408\) | −0.164752 | −0.00815644 | ||||||||
\(409\) | 35.9705 | 1.77862 | 0.889312 | − | 0.457300i | \(-0.151184\pi\) | ||||
0.889312 | + | 0.457300i | \(0.151184\pi\) | |||||||
\(410\) | −27.5705 | −1.36161 | ||||||||
\(411\) | −21.2098 | −1.04620 | ||||||||
\(412\) | 2.15342 | 0.106092 | ||||||||
\(413\) | −31.0583 | −1.52828 | ||||||||
\(414\) | 6.57103 | 0.322948 | ||||||||
\(415\) | −43.3663 | −2.12877 | ||||||||
\(416\) | −4.31548 | −0.211584 | ||||||||
\(417\) | 12.0035 | 0.587813 | ||||||||
\(418\) | −5.07383 | −0.248169 | ||||||||
\(419\) | −31.9649 | −1.56159 | −0.780793 | − | 0.624789i | \(-0.785185\pi\) | ||||
−0.780793 | + | 0.624789i | \(0.785185\pi\) | |||||||
\(420\) | −12.1489 | −0.592807 | ||||||||
\(421\) | 13.1293 | 0.639885 | 0.319942 | − | 0.947437i | \(-0.396336\pi\) | ||||
0.319942 | + | 0.947437i | \(0.396336\pi\) | |||||||
\(422\) | 20.4722 | 0.996570 | ||||||||
\(423\) | −2.21548 | −0.107720 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −0.554753 | −0.0269095 | ||||||||
\(426\) | 12.1481 | 0.588576 | ||||||||
\(427\) | 9.90850 | 0.479506 | ||||||||
\(428\) | −2.32310 | −0.112291 | ||||||||
\(429\) | 21.8960 | 1.05715 | ||||||||
\(430\) | 34.6001 | 1.66857 | ||||||||
\(431\) | 18.8667 | 0.908779 | 0.454389 | − | 0.890803i | \(-0.349857\pi\) | ||||
0.454389 | + | 0.890803i | \(0.349857\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.9897 | −0.768418 | −0.384209 | − | 0.923246i | \(-0.625526\pi\) | ||||
−0.384209 | + | 0.923246i | \(0.625526\pi\) | |||||||
\(434\) | 41.4519 | 1.98976 | ||||||||
\(435\) | 7.27414 | 0.348769 | ||||||||
\(436\) | −6.97372 | −0.333981 | ||||||||
\(437\) | 6.57103 | 0.314335 | ||||||||
\(438\) | 0.402131 | 0.0192146 | ||||||||
\(439\) | 36.3616 | 1.73545 | 0.867723 | − | 0.497048i | \(-0.165583\pi\) | ||||
0.867723 | + | 0.497048i | \(0.165583\pi\) | |||||||
\(440\) | −14.6766 | −0.699680 | ||||||||
\(441\) | 10.6399 | 0.506661 | ||||||||
\(442\) | 0.710984 | 0.0338181 | ||||||||
\(443\) | 9.83169 | 0.467118 | 0.233559 | − | 0.972343i | \(-0.424963\pi\) | ||||
0.233559 | + | 0.972343i | \(0.424963\pi\) | |||||||
\(444\) | 1.06505 | 0.0505449 | ||||||||
\(445\) | −26.1653 | −1.24035 | ||||||||
\(446\) | −1.30931 | −0.0619975 | ||||||||
\(447\) | −10.1141 | −0.478380 | ||||||||
\(448\) | −4.19999 | −0.198431 | ||||||||
\(449\) | 2.21385 | 0.104478 | 0.0522391 | − | 0.998635i | \(-0.483364\pi\) | ||||
0.0522391 | + | 0.998635i | \(0.483364\pi\) | |||||||
\(450\) | −3.36720 | −0.158731 | ||||||||
\(451\) | 48.3605 | 2.27721 | ||||||||
\(452\) | −4.23773 | −0.199326 | ||||||||
\(453\) | −22.9799 | −1.07969 | ||||||||
\(454\) | 29.3497 | 1.37745 | ||||||||
\(455\) | 52.4285 | 2.45788 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −33.7502 | −1.57877 | −0.789384 | − | 0.613900i | \(-0.789600\pi\) | ||||
−0.789384 | + | 0.613900i | \(0.789600\pi\) | |||||||
\(458\) | −11.8618 | −0.554267 | ||||||||
\(459\) | 0.164752 | 0.00768996 | ||||||||
\(460\) | 19.0074 | 0.886226 | ||||||||
\(461\) | 27.9582 | 1.30214 | 0.651071 | − | 0.759017i | \(-0.274320\pi\) | ||||
0.651071 | + | 0.759017i | \(0.274320\pi\) | |||||||
\(462\) | 21.3100 | 0.991432 | ||||||||
\(463\) | −34.4387 | −1.60050 | −0.800251 | − | 0.599666i | \(-0.795300\pi\) | ||||
−0.800251 | + | 0.599666i | \(0.795300\pi\) | |||||||
\(464\) | 2.51473 | 0.116744 | ||||||||
\(465\) | 28.5487 | 1.32392 | ||||||||
\(466\) | 6.53013 | 0.302502 | ||||||||
\(467\) | −21.8458 | −1.01090 | −0.505452 | − | 0.862855i | \(-0.668674\pi\) | ||||
−0.505452 | + | 0.862855i | \(0.668674\pi\) | |||||||
\(468\) | 4.31548 | 0.199483 | ||||||||
\(469\) | 33.6726 | 1.55485 | ||||||||
\(470\) | −6.40853 | −0.295603 | ||||||||
\(471\) | 18.2952 | 0.842999 | ||||||||
\(472\) | −7.39486 | −0.340376 | ||||||||
\(473\) | −60.6909 | −2.79057 | ||||||||
\(474\) | −9.61531 | −0.441646 | ||||||||
\(475\) | −3.36720 | −0.154498 | ||||||||
\(476\) | 0.691956 | 0.0317157 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 22.3102 | 1.02045 | ||||||||
\(479\) | −12.2579 | −0.560076 | −0.280038 | − | 0.959989i | \(-0.590347\pi\) | ||||
−0.280038 | + | 0.959989i | \(0.590347\pi\) | |||||||
\(480\) | −2.89261 | −0.132029 | ||||||||
\(481\) | −4.59619 | −0.209568 | ||||||||
\(482\) | −8.77862 | −0.399855 | ||||||||
\(483\) | −27.5982 | −1.25576 | ||||||||
\(484\) | 14.7438 | 0.670171 | ||||||||
\(485\) | −41.0811 | −1.86540 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 7.38220 | 0.334519 | 0.167260 | − | 0.985913i | \(-0.446508\pi\) | ||||
0.167260 | + | 0.985913i | \(0.446508\pi\) | |||||||
\(488\) | 2.35917 | 0.106795 | ||||||||
\(489\) | −23.7938 | −1.07599 | ||||||||
\(490\) | 30.7770 | 1.39036 | ||||||||
\(491\) | 18.0802 | 0.815947 | 0.407973 | − | 0.912994i | \(-0.366236\pi\) | ||||
0.407973 | + | 0.912994i | \(0.366236\pi\) | |||||||
\(492\) | 9.53136 | 0.429707 | ||||||||
\(493\) | −0.414307 | −0.0186594 | ||||||||
\(494\) | 4.31548 | 0.194163 | ||||||||
\(495\) | 14.6766 | 0.659665 | ||||||||
\(496\) | 9.86954 | 0.443155 | ||||||||
\(497\) | −51.0218 | −2.28864 | ||||||||
\(498\) | 14.9921 | 0.671812 | ||||||||
\(499\) | 7.19500 | 0.322093 | 0.161046 | − | 0.986947i | \(-0.448513\pi\) | ||||
0.161046 | + | 0.986947i | \(0.448513\pi\) | |||||||
\(500\) | 4.72305 | 0.211221 | ||||||||
\(501\) | 6.90049 | 0.308291 | ||||||||
\(502\) | −13.4594 | −0.600724 | ||||||||
\(503\) | −7.01264 | −0.312678 | −0.156339 | − | 0.987703i | \(-0.549969\pi\) | ||||
−0.156339 | + | 0.987703i | \(0.549969\pi\) | |||||||
\(504\) | 4.19999 | 0.187082 | ||||||||
\(505\) | −56.2993 | −2.50528 | ||||||||
\(506\) | −33.3403 | −1.48216 | ||||||||
\(507\) | −5.62338 | −0.249743 | ||||||||
\(508\) | −13.2802 | −0.589216 | ||||||||
\(509\) | −35.5288 | −1.57479 | −0.787393 | − | 0.616452i | \(-0.788570\pi\) | ||||
−0.787393 | + | 0.616452i | \(0.788570\pi\) | |||||||
\(510\) | 0.476563 | 0.0211026 | ||||||||
\(511\) | −1.68894 | −0.0747145 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 7.35628 | 0.324471 | ||||||||
\(515\) | −6.22902 | −0.274483 | ||||||||
\(516\) | −11.9616 | −0.526578 | ||||||||
\(517\) | 11.2410 | 0.494378 | ||||||||
\(518\) | −4.47318 | −0.196540 | ||||||||
\(519\) | 13.0432 | 0.572531 | ||||||||
\(520\) | 12.4830 | 0.547416 | ||||||||
\(521\) | −19.9271 | −0.873022 | −0.436511 | − | 0.899699i | \(-0.643786\pi\) | ||||
−0.436511 | + | 0.899699i | \(0.643786\pi\) | |||||||
\(522\) | −2.51473 | −0.110067 | ||||||||
\(523\) | −28.6054 | −1.25083 | −0.625414 | − | 0.780293i | \(-0.715070\pi\) | ||||
−0.625414 | + | 0.780293i | \(0.715070\pi\) | |||||||
\(524\) | −20.5119 | −0.896066 | ||||||||
\(525\) | 14.1422 | 0.617216 | ||||||||
\(526\) | 22.7323 | 0.991175 | ||||||||
\(527\) | −1.62603 | −0.0708308 | ||||||||
\(528\) | 5.07383 | 0.220810 | ||||||||
\(529\) | 20.1784 | 0.877321 | ||||||||
\(530\) | −2.89261 | −0.125647 | ||||||||
\(531\) | 7.39486 | 0.320910 | ||||||||
\(532\) | 4.19999 | 0.182092 | ||||||||
\(533\) | −41.1324 | −1.78164 | ||||||||
\(534\) | 9.04557 | 0.391440 | ||||||||
\(535\) | 6.71982 | 0.290523 | ||||||||
\(536\) | 8.01730 | 0.346295 | ||||||||
\(537\) | 13.7443 | 0.593109 | ||||||||
\(538\) | −19.1670 | −0.826348 | ||||||||
\(539\) | −53.9849 | −2.32530 | ||||||||
\(540\) | 2.89261 | 0.124478 | ||||||||
\(541\) | −16.5564 | −0.711815 | −0.355908 | − | 0.934521i | \(-0.615828\pi\) | ||||
−0.355908 | + | 0.934521i | \(0.615828\pi\) | |||||||
\(542\) | 10.0217 | 0.430469 | ||||||||
\(543\) | −10.6985 | −0.459115 | ||||||||
\(544\) | 0.164752 | 0.00706368 | ||||||||
\(545\) | 20.1723 | 0.864085 | ||||||||
\(546\) | −18.1250 | −0.775677 | ||||||||
\(547\) | −14.5329 | −0.621381 | −0.310691 | − | 0.950511i | \(-0.600560\pi\) | ||||
−0.310691 | + | 0.950511i | \(0.600560\pi\) | |||||||
\(548\) | 21.2098 | 0.906039 | ||||||||
\(549\) | −2.35917 | −0.100687 | ||||||||
\(550\) | 17.0846 | 0.728490 | ||||||||
\(551\) | −2.51473 | −0.107131 | ||||||||
\(552\) | −6.57103 | −0.279681 | ||||||||
\(553\) | 40.3842 | 1.71731 | ||||||||
\(554\) | −26.3575 | −1.11982 | ||||||||
\(555\) | −3.08077 | −0.130771 | ||||||||
\(556\) | −12.0035 | −0.509061 | ||||||||
\(557\) | −36.3376 | −1.53967 | −0.769836 | − | 0.638241i | \(-0.779662\pi\) | ||||
−0.769836 | + | 0.638241i | \(0.779662\pi\) | |||||||
\(558\) | −9.86954 | −0.417811 | ||||||||
\(559\) | 51.6199 | 2.18329 | ||||||||
\(560\) | 12.1489 | 0.513386 | ||||||||
\(561\) | −0.835923 | −0.0352927 | ||||||||
\(562\) | −25.1508 | −1.06092 | ||||||||
\(563\) | −25.6272 | −1.08006 | −0.540029 | − | 0.841646i | \(-0.681587\pi\) | ||||
−0.540029 | + | 0.841646i | \(0.681587\pi\) | |||||||
\(564\) | 2.21548 | 0.0932886 | ||||||||
\(565\) | 12.2581 | 0.515702 | ||||||||
\(566\) | −21.5774 | −0.906966 | ||||||||
\(567\) | −4.19999 | −0.176383 | ||||||||
\(568\) | −12.1481 | −0.509722 | ||||||||
\(569\) | −13.8891 | −0.582259 | −0.291130 | − | 0.956684i | \(-0.594031\pi\) | ||||
−0.291130 | + | 0.956684i | \(0.594031\pi\) | |||||||
\(570\) | 2.89261 | 0.121158 | ||||||||
\(571\) | −13.8942 | −0.581456 | −0.290728 | − | 0.956806i | \(-0.593897\pi\) | ||||
−0.290728 | + | 0.956806i | \(0.593897\pi\) | |||||||
\(572\) | −21.8960 | −0.915519 | ||||||||
\(573\) | 12.9853 | 0.542469 | ||||||||
\(574\) | −40.0316 | −1.67089 | ||||||||
\(575\) | −22.1260 | −0.922717 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −9.46687 | −0.394111 | −0.197056 | − | 0.980392i | \(-0.563138\pi\) | ||||
−0.197056 | + | 0.980392i | \(0.563138\pi\) | |||||||
\(578\) | 16.9729 | 0.705978 | ||||||||
\(579\) | 5.55372 | 0.230805 | ||||||||
\(580\) | −7.27414 | −0.302042 | ||||||||
\(581\) | −62.9666 | −2.61230 | ||||||||
\(582\) | 14.2021 | 0.588695 | ||||||||
\(583\) | 5.07383 | 0.210137 | ||||||||
\(584\) | −0.402131 | −0.0166403 | ||||||||
\(585\) | −12.4830 | −0.516109 | ||||||||
\(586\) | −4.48113 | −0.185114 | ||||||||
\(587\) | 7.96978 | 0.328948 | 0.164474 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164474 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(588\) | −10.6399 | −0.438781 | ||||||||
\(589\) | −9.86954 | −0.406667 | ||||||||
\(590\) | 21.3905 | 0.880631 | ||||||||
\(591\) | 15.1348 | 0.622564 | ||||||||
\(592\) | −1.06505 | −0.0437732 | ||||||||
\(593\) | 28.5880 | 1.17397 | 0.586984 | − | 0.809598i | \(-0.300315\pi\) | ||||
0.586984 | + | 0.809598i | \(0.300315\pi\) | |||||||
\(594\) | −5.07383 | −0.208182 | ||||||||
\(595\) | −2.00156 | −0.0820559 | ||||||||
\(596\) | 10.1141 | 0.414289 | ||||||||
\(597\) | 3.14427 | 0.128686 | ||||||||
\(598\) | 28.3571 | 1.15961 | ||||||||
\(599\) | −46.9205 | −1.91712 | −0.958560 | − | 0.284892i | \(-0.908042\pi\) | ||||
−0.958560 | + | 0.284892i | \(0.908042\pi\) | |||||||
\(600\) | 3.36720 | 0.137465 | ||||||||
\(601\) | 20.2150 | 0.824587 | 0.412293 | − | 0.911051i | \(-0.364728\pi\) | ||||
0.412293 | + | 0.911051i | \(0.364728\pi\) | |||||||
\(602\) | 50.2383 | 2.04756 | ||||||||
\(603\) | −8.01730 | −0.326490 | ||||||||
\(604\) | 22.9799 | 0.935037 | ||||||||
\(605\) | −42.6480 | −1.73389 | ||||||||
\(606\) | 19.4631 | 0.790636 | ||||||||
\(607\) | −26.0644 | −1.05792 | −0.528962 | − | 0.848646i | \(-0.677418\pi\) | ||||
−0.528962 | + | 0.848646i | \(0.677418\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 10.5618 | 0.427987 | ||||||||
\(610\) | −6.82417 | −0.276303 | ||||||||
\(611\) | −9.56087 | −0.386792 | ||||||||
\(612\) | −0.164752 | −0.00665970 | ||||||||
\(613\) | −40.0784 | −1.61875 | −0.809375 | − | 0.587292i | \(-0.800194\pi\) | ||||
−0.809375 | + | 0.587292i | \(0.800194\pi\) | |||||||
\(614\) | 25.9747 | 1.04825 | ||||||||
\(615\) | −27.5705 | −1.11175 | ||||||||
\(616\) | −21.3100 | −0.858605 | ||||||||
\(617\) | −3.89038 | −0.156621 | −0.0783103 | − | 0.996929i | \(-0.524953\pi\) | ||||
−0.0783103 | + | 0.996929i | \(0.524953\pi\) | |||||||
\(618\) | 2.15342 | 0.0866234 | ||||||||
\(619\) | −39.9122 | −1.60421 | −0.802104 | − | 0.597184i | \(-0.796286\pi\) | ||||
−0.802104 | + | 0.597184i | \(0.796286\pi\) | |||||||
\(620\) | −28.5487 | −1.14655 | ||||||||
\(621\) | 6.57103 | 0.263686 | ||||||||
\(622\) | −19.4275 | −0.778973 | ||||||||
\(623\) | −37.9912 | −1.52209 | ||||||||
\(624\) | −4.31548 | −0.172758 | ||||||||
\(625\) | −30.4980 | −1.21992 | ||||||||
\(626\) | 16.6025 | 0.663569 | ||||||||
\(627\) | −5.07383 | −0.202629 | ||||||||
\(628\) | −18.2952 | −0.730059 | ||||||||
\(629\) | 0.175469 | 0.00699639 | ||||||||
\(630\) | −12.1489 | −0.484025 | ||||||||
\(631\) | 12.8924 | 0.513239 | 0.256619 | − | 0.966513i | \(-0.417391\pi\) | ||||
0.256619 | + | 0.966513i | \(0.417391\pi\) | |||||||
\(632\) | 9.61531 | 0.382476 | ||||||||
\(633\) | 20.4722 | 0.813696 | ||||||||
\(634\) | 22.4533 | 0.891733 | ||||||||
\(635\) | 38.4146 | 1.52444 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | 45.9162 | 1.81927 | ||||||||
\(638\) | 12.7593 | 0.505146 | ||||||||
\(639\) | 12.1481 | 0.480571 | ||||||||
\(640\) | 2.89261 | 0.114341 | ||||||||
\(641\) | 14.9520 | 0.590569 | 0.295284 | − | 0.955409i | \(-0.404586\pi\) | ||||
0.295284 | + | 0.955409i | \(0.404586\pi\) | |||||||
\(642\) | −2.32310 | −0.0916854 | ||||||||
\(643\) | 26.4447 | 1.04288 | 0.521438 | − | 0.853289i | \(-0.325396\pi\) | ||||
0.521438 | + | 0.853289i | \(0.325396\pi\) | |||||||
\(644\) | 27.5982 | 1.08752 | ||||||||
\(645\) | 34.6001 | 1.36238 | ||||||||
\(646\) | −0.164752 | −0.00648208 | ||||||||
\(647\) | 29.4064 | 1.15608 | 0.578042 | − | 0.816007i | \(-0.303817\pi\) | ||||
0.578042 | + | 0.816007i | \(0.303817\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −37.5203 | −1.47280 | ||||||||
\(650\) | −14.5311 | −0.569957 | ||||||||
\(651\) | 41.4519 | 1.62463 | ||||||||
\(652\) | 23.7938 | 0.931838 | ||||||||
\(653\) | 44.8056 | 1.75338 | 0.876690 | − | 0.481056i | \(-0.159747\pi\) | ||||
0.876690 | + | 0.481056i | \(0.159747\pi\) | |||||||
\(654\) | −6.97372 | −0.272694 | ||||||||
\(655\) | 59.3329 | 2.31833 | ||||||||
\(656\) | −9.53136 | −0.372137 | ||||||||
\(657\) | 0.402131 | 0.0156886 | ||||||||
\(658\) | −9.30499 | −0.362746 | ||||||||
\(659\) | 11.0523 | 0.430536 | 0.215268 | − | 0.976555i | \(-0.430937\pi\) | ||||
0.215268 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(660\) | −14.6766 | −0.571287 | ||||||||
\(661\) | −32.1873 | −1.25194 | −0.625971 | − | 0.779846i | \(-0.715297\pi\) | ||||
−0.625971 | + | 0.779846i | \(0.715297\pi\) | |||||||
\(662\) | −2.79548 | −0.108649 | ||||||||
\(663\) | 0.710984 | 0.0276123 | ||||||||
\(664\) | −14.9921 | −0.581806 | ||||||||
\(665\) | −12.1489 | −0.471115 | ||||||||
\(666\) | 1.06505 | 0.0412697 | ||||||||
\(667\) | −16.5244 | −0.639826 | ||||||||
\(668\) | −6.90049 | −0.266988 | ||||||||
\(669\) | −1.30931 | −0.0506208 | ||||||||
\(670\) | −23.1909 | −0.895944 | ||||||||
\(671\) | 11.9700 | 0.462099 | ||||||||
\(672\) | −4.19999 | −0.162018 | ||||||||
\(673\) | 8.10843 | 0.312557 | 0.156279 | − | 0.987713i | \(-0.450050\pi\) | ||||
0.156279 | + | 0.987713i | \(0.450050\pi\) | |||||||
\(674\) | 18.2672 | 0.703625 | ||||||||
\(675\) | −3.36720 | −0.129604 | ||||||||
\(676\) | 5.62338 | 0.216284 | ||||||||
\(677\) | 29.3481 | 1.12794 | 0.563971 | − | 0.825795i | \(-0.309273\pi\) | ||||
0.563971 | + | 0.825795i | \(0.309273\pi\) | |||||||
\(678\) | −4.23773 | −0.162749 | ||||||||
\(679\) | −59.6485 | −2.28910 | ||||||||
\(680\) | −0.476563 | −0.0182754 | ||||||||
\(681\) | 29.3497 | 1.12468 | ||||||||
\(682\) | 50.0764 | 1.91752 | ||||||||
\(683\) | 30.4604 | 1.16554 | 0.582768 | − | 0.812639i | \(-0.301970\pi\) | ||||
0.582768 | + | 0.812639i | \(0.301970\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −61.3518 | −2.34413 | ||||||||
\(686\) | 15.2874 | 0.583677 | ||||||||
\(687\) | −11.8618 | −0.452557 | ||||||||
\(688\) | 11.9616 | 0.456030 | ||||||||
\(689\) | −4.31548 | −0.164407 | ||||||||
\(690\) | 19.0074 | 0.723600 | ||||||||
\(691\) | 18.2783 | 0.695340 | 0.347670 | − | 0.937617i | \(-0.386973\pi\) | ||||
0.347670 | + | 0.937617i | \(0.386973\pi\) | |||||||
\(692\) | −13.0432 | −0.495827 | ||||||||
\(693\) | 21.3100 | 0.809500 | ||||||||
\(694\) | 4.25132 | 0.161378 | ||||||||
\(695\) | 34.7214 | 1.31706 | ||||||||
\(696\) | 2.51473 | 0.0953207 | ||||||||
\(697\) | 1.57031 | 0.0594797 | ||||||||
\(698\) | −35.4354 | −1.34125 | ||||||||
\(699\) | 6.53013 | 0.246992 | ||||||||
\(700\) | −14.1422 | −0.534525 | ||||||||
\(701\) | −29.1262 | −1.10008 | −0.550041 | − | 0.835137i | \(-0.685388\pi\) | ||||
−0.550041 | + | 0.835137i | \(0.685388\pi\) | |||||||
\(702\) | 4.31548 | 0.162877 | ||||||||
\(703\) | 1.06505 | 0.0401690 | ||||||||
\(704\) | −5.07383 | −0.191227 | ||||||||
\(705\) | −6.40853 | −0.241359 | ||||||||
\(706\) | −19.5956 | −0.737490 | ||||||||
\(707\) | −81.7449 | −3.07433 | ||||||||
\(708\) | −7.39486 | −0.277916 | ||||||||
\(709\) | −7.13353 | −0.267905 | −0.133953 | − | 0.990988i | \(-0.542767\pi\) | ||||
−0.133953 | + | 0.990988i | \(0.542767\pi\) | |||||||
\(710\) | 35.1397 | 1.31877 | ||||||||
\(711\) | −9.61531 | −0.360602 | ||||||||
\(712\) | −9.04557 | −0.338997 | ||||||||
\(713\) | −64.8530 | −2.42876 | ||||||||
\(714\) | 0.691956 | 0.0258958 | ||||||||
\(715\) | 63.3367 | 2.36866 | ||||||||
\(716\) | −13.7443 | −0.513648 | ||||||||
\(717\) | 22.3102 | 0.833191 | ||||||||
\(718\) | 14.0420 | 0.524044 | ||||||||
\(719\) | 2.23576 | 0.0833796 | 0.0416898 | − | 0.999131i | \(-0.486726\pi\) | ||||
0.0416898 | + | 0.999131i | \(0.486726\pi\) | |||||||
\(720\) | −2.89261 | −0.107801 | ||||||||
\(721\) | −9.04435 | −0.336829 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −8.77862 | −0.326480 | ||||||||
\(724\) | 10.6985 | 0.397606 | ||||||||
\(725\) | 8.46761 | 0.314479 | ||||||||
\(726\) | 14.7438 | 0.547192 | ||||||||
\(727\) | 27.1373 | 1.00647 | 0.503233 | − | 0.864151i | \(-0.332144\pi\) | ||||
0.503233 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(728\) | 18.1250 | 0.671756 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.16321 | 0.0430523 | ||||||||
\(731\) | −1.97069 | −0.0728886 | ||||||||
\(732\) | 2.35917 | 0.0871976 | ||||||||
\(733\) | 29.5464 | 1.09132 | 0.545661 | − | 0.838006i | \(-0.316279\pi\) | ||||
0.545661 | + | 0.838006i | \(0.316279\pi\) | |||||||
\(734\) | 2.72418 | 0.100551 | ||||||||
\(735\) | 30.7770 | 1.13523 | ||||||||
\(736\) | 6.57103 | 0.242211 | ||||||||
\(737\) | 40.6784 | 1.49841 | ||||||||
\(738\) | 9.53136 | 0.350854 | ||||||||
\(739\) | −6.27892 | −0.230974 | −0.115487 | − | 0.993309i | \(-0.536843\pi\) | ||||
−0.115487 | + | 0.993309i | \(0.536843\pi\) | |||||||
\(740\) | 3.08077 | 0.113251 | ||||||||
\(741\) | 4.31548 | 0.158533 | ||||||||
\(742\) | −4.19999 | −0.154186 | ||||||||
\(743\) | 39.2227 | 1.43894 | 0.719470 | − | 0.694523i | \(-0.244385\pi\) | ||||
0.719470 | + | 0.694523i | \(0.244385\pi\) | |||||||
\(744\) | 9.86954 | 0.361835 | ||||||||
\(745\) | −29.2561 | −1.07186 | ||||||||
\(746\) | −13.4646 | −0.492975 | ||||||||
\(747\) | 14.9921 | 0.548532 | ||||||||
\(748\) | 0.835923 | 0.0305644 | ||||||||
\(749\) | 9.75698 | 0.356512 | ||||||||
\(750\) | 4.72305 | 0.172461 | ||||||||
\(751\) | 34.3063 | 1.25185 | 0.625927 | − | 0.779882i | \(-0.284721\pi\) | ||||
0.625927 | + | 0.779882i | \(0.284721\pi\) | |||||||
\(752\) | −2.21548 | −0.0807903 | ||||||||
\(753\) | −13.4594 | −0.490489 | ||||||||
\(754\) | −10.8523 | −0.395217 | ||||||||
\(755\) | −66.4718 | −2.41916 | ||||||||
\(756\) | 4.19999 | 0.152752 | ||||||||
\(757\) | −6.27235 | −0.227972 | −0.113986 | − | 0.993482i | \(-0.536362\pi\) | ||||
−0.113986 | + | 0.993482i | \(0.536362\pi\) | |||||||
\(758\) | 2.12113 | 0.0770431 | ||||||||
\(759\) | −33.3403 | −1.21017 | ||||||||
\(760\) | −2.89261 | −0.104926 | ||||||||
\(761\) | 15.0822 | 0.546731 | 0.273365 | − | 0.961910i | \(-0.411863\pi\) | ||||
0.273365 | + | 0.961910i | \(0.411863\pi\) | |||||||
\(762\) | −13.2802 | −0.481092 | ||||||||
\(763\) | 29.2895 | 1.06035 | ||||||||
\(764\) | −12.9853 | −0.469792 | ||||||||
\(765\) | 0.476563 | 0.0172302 | ||||||||
\(766\) | −12.0871 | −0.436724 | ||||||||
\(767\) | 31.9124 | 1.15229 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −5.17273 | −0.186533 | −0.0932667 | − | 0.995641i | \(-0.529731\pi\) | ||||
−0.0932667 | + | 0.995641i | \(0.529731\pi\) | |||||||
\(770\) | 61.6416 | 2.22141 | ||||||||
\(771\) | 7.35628 | 0.264930 | ||||||||
\(772\) | −5.55372 | −0.199883 | ||||||||
\(773\) | −15.2176 | −0.547339 | −0.273669 | − | 0.961824i | \(-0.588237\pi\) | ||||
−0.273669 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(774\) | −11.9616 | −0.429949 | ||||||||
\(775\) | 33.2327 | 1.19376 | ||||||||
\(776\) | −14.2021 | −0.509825 | ||||||||
\(777\) | −4.47318 | −0.160475 | ||||||||
\(778\) | −18.2322 | −0.653657 | ||||||||
\(779\) | 9.53136 | 0.341496 | ||||||||
\(780\) | 12.4830 | 0.446964 | ||||||||
\(781\) | −61.6373 | −2.20556 | ||||||||
\(782\) | −1.08259 | −0.0387133 | ||||||||
\(783\) | −2.51473 | −0.0898692 | ||||||||
\(784\) | 10.6399 | 0.379996 | ||||||||
\(785\) | 52.9210 | 1.88883 | ||||||||
\(786\) | −20.5119 | −0.731635 | ||||||||
\(787\) | 13.3623 | 0.476314 | 0.238157 | − | 0.971227i | \(-0.423457\pi\) | ||||
0.238157 | + | 0.971227i | \(0.423457\pi\) | |||||||
\(788\) | −15.1348 | −0.539156 | ||||||||
\(789\) | 22.7323 | 0.809291 | ||||||||
\(790\) | −27.8133 | −0.989555 | ||||||||
\(791\) | 17.7984 | 0.632838 | ||||||||
\(792\) | 5.07383 | 0.180291 | ||||||||
\(793\) | −10.1810 | −0.361537 | ||||||||
\(794\) | −0.303597 | −0.0107742 | ||||||||
\(795\) | −2.89261 | −0.102590 | ||||||||
\(796\) | −3.14427 | −0.111446 | ||||||||
\(797\) | −36.0017 | −1.27524 | −0.637622 | − | 0.770349i | \(-0.720082\pi\) | ||||
−0.637622 | + | 0.770349i | \(0.720082\pi\) | |||||||
\(798\) | 4.19999 | 0.148678 | ||||||||
\(799\) | 0.365005 | 0.0129129 | ||||||||
\(800\) | −3.36720 | −0.119049 | ||||||||
\(801\) | 9.04557 | 0.319609 | ||||||||
\(802\) | −6.29918 | −0.222432 | ||||||||
\(803\) | −2.04034 | −0.0720022 | ||||||||
\(804\) | 8.01730 | 0.282748 | ||||||||
\(805\) | −79.8309 | −2.81367 | ||||||||
\(806\) | −42.5918 | −1.50023 | ||||||||
\(807\) | −19.1670 | −0.674710 | ||||||||
\(808\) | −19.4631 | −0.684710 | ||||||||
\(809\) | 33.4734 | 1.17686 | 0.588432 | − | 0.808547i | \(-0.299746\pi\) | ||||
0.588432 | + | 0.808547i | \(0.299746\pi\) | |||||||
\(810\) | 2.89261 | 0.101636 | ||||||||
\(811\) | −17.0307 | −0.598030 | −0.299015 | − | 0.954248i | \(-0.596658\pi\) | ||||
−0.299015 | + | 0.954248i | \(0.596658\pi\) | |||||||
\(812\) | −10.5618 | −0.370648 | ||||||||
\(813\) | 10.0217 | 0.351477 | ||||||||
\(814\) | −5.40387 | −0.189406 | ||||||||
\(815\) | −68.8263 | −2.41088 | ||||||||
\(816\) | 0.164752 | 0.00576747 | ||||||||
\(817\) | −11.9616 | −0.418482 | ||||||||
\(818\) | −35.9705 | −1.25768 | ||||||||
\(819\) | −18.1250 | −0.633337 | ||||||||
\(820\) | 27.5705 | 0.962804 | ||||||||
\(821\) | 28.3759 | 0.990324 | 0.495162 | − | 0.868801i | \(-0.335109\pi\) | ||||
0.495162 | + | 0.868801i | \(0.335109\pi\) | |||||||
\(822\) | 21.2098 | 0.739778 | ||||||||
\(823\) | 40.6574 | 1.41723 | 0.708613 | − | 0.705597i | \(-0.249321\pi\) | ||||
0.708613 | + | 0.705597i | \(0.249321\pi\) | |||||||
\(824\) | −2.15342 | −0.0750181 | ||||||||
\(825\) | 17.0846 | 0.594810 | ||||||||
\(826\) | 31.0583 | 1.08066 | ||||||||
\(827\) | −49.3362 | −1.71559 | −0.857793 | − | 0.513995i | \(-0.828165\pi\) | ||||
−0.857793 | + | 0.513995i | \(0.828165\pi\) | |||||||
\(828\) | −6.57103 | −0.228359 | ||||||||
\(829\) | 0.520715 | 0.0180852 | 0.00904258 | − | 0.999959i | \(-0.497122\pi\) | ||||
0.00904258 | + | 0.999959i | \(0.497122\pi\) | |||||||
\(830\) | 43.3663 | 1.50527 | ||||||||
\(831\) | −26.3575 | −0.914333 | ||||||||
\(832\) | 4.31548 | 0.149612 | ||||||||
\(833\) | −1.75294 | −0.0607358 | ||||||||
\(834\) | −12.0035 | −0.415647 | ||||||||
\(835\) | 19.9604 | 0.690759 | ||||||||
\(836\) | 5.07383 | 0.175482 | ||||||||
\(837\) | −9.86954 | −0.341141 | ||||||||
\(838\) | 31.9649 | 1.10421 | ||||||||
\(839\) | −44.9576 | −1.55211 | −0.776055 | − | 0.630665i | \(-0.782782\pi\) | ||||
−0.776055 | + | 0.630665i | \(0.782782\pi\) | |||||||
\(840\) | 12.1489 | 0.419178 | ||||||||
\(841\) | −22.6761 | −0.781935 | ||||||||
\(842\) | −13.1293 | −0.452467 | ||||||||
\(843\) | −25.1508 | −0.866240 | ||||||||
\(844\) | −20.4722 | −0.704681 | ||||||||
\(845\) | −16.2663 | −0.559576 | ||||||||
\(846\) | 2.21548 | 0.0761699 | ||||||||
\(847\) | −61.9235 | −2.12772 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | −21.5774 | −0.740535 | ||||||||
\(850\) | 0.554753 | 0.0190279 | ||||||||
\(851\) | 6.99845 | 0.239904 | ||||||||
\(852\) | −12.1481 | −0.416186 | ||||||||
\(853\) | 31.7249 | 1.08624 | 0.543121 | − | 0.839655i | \(-0.317243\pi\) | ||||
0.543121 | + | 0.839655i | \(0.317243\pi\) | |||||||
\(854\) | −9.90850 | −0.339062 | ||||||||
\(855\) | 2.89261 | 0.0989252 | ||||||||
\(856\) | 2.32310 | 0.0794019 | ||||||||
\(857\) | 41.9051 | 1.43145 | 0.715725 | − | 0.698383i | \(-0.246097\pi\) | ||||
0.715725 | + | 0.698383i | \(0.246097\pi\) | |||||||
\(858\) | −21.8960 | −0.747518 | ||||||||
\(859\) | −36.6132 | −1.24923 | −0.624613 | − | 0.780934i | \(-0.714743\pi\) | ||||
−0.624613 | + | 0.780934i | \(0.714743\pi\) | |||||||
\(860\) | −34.6001 | −1.17985 | ||||||||
\(861\) | −40.0316 | −1.36427 | ||||||||
\(862\) | −18.8667 | −0.642604 | ||||||||
\(863\) | 30.8006 | 1.04847 | 0.524233 | − | 0.851575i | \(-0.324352\pi\) | ||||
0.524233 | + | 0.851575i | \(0.324352\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 37.7288 | 1.28282 | ||||||||
\(866\) | 15.9897 | 0.543354 | ||||||||
\(867\) | 16.9729 | 0.576428 | ||||||||
\(868\) | −41.4519 | −1.40697 | ||||||||
\(869\) | 48.7864 | 1.65497 | ||||||||
\(870\) | −7.27414 | −0.246617 | ||||||||
\(871\) | −34.5985 | −1.17233 | ||||||||
\(872\) | 6.97372 | 0.236160 | ||||||||
\(873\) | 14.2021 | 0.480668 | ||||||||
\(874\) | −6.57103 | −0.222268 | ||||||||
\(875\) | −19.8367 | −0.670604 | ||||||||
\(876\) | −0.402131 | −0.0135867 | ||||||||
\(877\) | −30.8781 | −1.04268 | −0.521339 | − | 0.853350i | \(-0.674567\pi\) | ||||
−0.521339 | + | 0.853350i | \(0.674567\pi\) | |||||||
\(878\) | −36.3616 | −1.22715 | ||||||||
\(879\) | −4.48113 | −0.151145 | ||||||||
\(880\) | 14.6766 | 0.494749 | ||||||||
\(881\) | 29.4034 | 0.990626 | 0.495313 | − | 0.868715i | \(-0.335053\pi\) | ||||
0.495313 | + | 0.868715i | \(0.335053\pi\) | |||||||
\(882\) | −10.6399 | −0.358263 | ||||||||
\(883\) | −27.0905 | −0.911667 | −0.455833 | − | 0.890065i | \(-0.650659\pi\) | ||||
−0.455833 | + | 0.890065i | \(0.650659\pi\) | |||||||
\(884\) | −0.710984 | −0.0239130 | ||||||||
\(885\) | 21.3905 | 0.719033 | ||||||||
\(886\) | −9.83169 | −0.330302 | ||||||||
\(887\) | 16.8178 | 0.564686 | 0.282343 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282343 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(888\) | −1.06505 | −0.0357407 | ||||||||
\(889\) | 55.7768 | 1.87069 | ||||||||
\(890\) | 26.1653 | 0.877063 | ||||||||
\(891\) | −5.07383 | −0.169980 | ||||||||
\(892\) | 1.30931 | 0.0438389 | ||||||||
\(893\) | 2.21548 | 0.0741383 | ||||||||
\(894\) | 10.1141 | 0.338265 | ||||||||
\(895\) | 39.7569 | 1.32893 | ||||||||
\(896\) | 4.19999 | 0.140312 | ||||||||
\(897\) | 28.3571 | 0.946817 | ||||||||
\(898\) | −2.21385 | −0.0738772 | ||||||||
\(899\) | 24.8193 | 0.827768 | ||||||||
\(900\) | 3.36720 | 0.112240 | ||||||||
\(901\) | 0.164752 | 0.00548868 | ||||||||
\(902\) | −48.3605 | −1.61023 | ||||||||
\(903\) | 50.2383 | 1.67183 | ||||||||
\(904\) | 4.23773 | 0.140945 | ||||||||
\(905\) | −30.9465 | −1.02870 | ||||||||
\(906\) | 22.9799 | 0.763454 | ||||||||
\(907\) | −12.1895 | −0.404747 | −0.202373 | − | 0.979308i | \(-0.564865\pi\) | ||||
−0.202373 | + | 0.979308i | \(0.564865\pi\) | |||||||
\(908\) | −29.3497 | −0.974005 | ||||||||
\(909\) | 19.4631 | 0.645551 | ||||||||
\(910\) | −52.4285 | −1.73799 | ||||||||
\(911\) | 9.37909 | 0.310743 | 0.155372 | − | 0.987856i | \(-0.450343\pi\) | ||||
0.155372 | + | 0.987856i | \(0.450343\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −76.0674 | −2.51746 | ||||||||
\(914\) | 33.7502 | 1.11636 | ||||||||
\(915\) | −6.82417 | −0.225600 | ||||||||
\(916\) | 11.8618 | 0.391926 | ||||||||
\(917\) | 86.1496 | 2.84491 | ||||||||
\(918\) | −0.164752 | −0.00543762 | ||||||||
\(919\) | 37.3252 | 1.23125 | 0.615623 | − | 0.788041i | \(-0.288904\pi\) | ||||
0.615623 | + | 0.788041i | \(0.288904\pi\) | |||||||
\(920\) | −19.0074 | −0.626656 | ||||||||
\(921\) | 25.9747 | 0.855896 | ||||||||
\(922\) | −27.9582 | −0.920754 | ||||||||
\(923\) | 52.4248 | 1.72558 | ||||||||
\(924\) | −21.3100 | −0.701048 | ||||||||
\(925\) | −3.58623 | −0.117915 | ||||||||
\(926\) | 34.4387 | 1.13173 | ||||||||
\(927\) | 2.15342 | 0.0707277 | ||||||||
\(928\) | −2.51473 | −0.0825501 | ||||||||
\(929\) | −37.0078 | −1.21418 | −0.607092 | − | 0.794631i | \(-0.707664\pi\) | ||||
−0.607092 | + | 0.794631i | \(0.707664\pi\) | |||||||
\(930\) | −28.5487 | −0.936150 | ||||||||
\(931\) | −10.6399 | −0.348708 | ||||||||
\(932\) | −6.53013 | −0.213901 | ||||||||
\(933\) | −19.4275 | −0.636029 | ||||||||
\(934\) | 21.8458 | 0.714817 | ||||||||
\(935\) | −2.41800 | −0.0790771 | ||||||||
\(936\) | −4.31548 | −0.141056 | ||||||||
\(937\) | 1.39487 | 0.0455683 | 0.0227842 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227842 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(938\) | −33.6726 | −1.09945 | ||||||||
\(939\) | 16.6025 | 0.541801 | ||||||||
\(940\) | 6.40853 | 0.209023 | ||||||||
\(941\) | 18.6777 | 0.608874 | 0.304437 | − | 0.952532i | \(-0.401532\pi\) | ||||
0.304437 | + | 0.952532i | \(0.401532\pi\) | |||||||
\(942\) | −18.2952 | −0.596090 | ||||||||
\(943\) | 62.6308 | 2.03954 | ||||||||
\(944\) | 7.39486 | 0.240682 | ||||||||
\(945\) | −12.1489 | −0.395205 | ||||||||
\(946\) | 60.6909 | 1.97323 | ||||||||
\(947\) | 5.60661 | 0.182190 | 0.0910951 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910951 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(948\) | 9.61531 | 0.312291 | ||||||||
\(949\) | 1.73539 | 0.0563331 | ||||||||
\(950\) | 3.36720 | 0.109246 | ||||||||
\(951\) | 22.4533 | 0.728097 | ||||||||
\(952\) | −0.691956 | −0.0224264 | ||||||||
\(953\) | 12.3673 | 0.400616 | 0.200308 | − | 0.979733i | \(-0.435806\pi\) | ||||
0.200308 | + | 0.979733i | \(0.435806\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 37.5614 | 1.21546 | ||||||||
\(956\) | −22.3102 | −0.721564 | ||||||||
\(957\) | 12.7593 | 0.412450 | ||||||||
\(958\) | 12.2579 | 0.396033 | ||||||||
\(959\) | −89.0810 | −2.87658 | ||||||||
\(960\) | 2.89261 | 0.0933586 | ||||||||
\(961\) | 66.4078 | 2.14219 | ||||||||
\(962\) | 4.59619 | 0.148187 | ||||||||
\(963\) | −2.32310 | −0.0748608 | ||||||||
\(964\) | 8.77862 | 0.282740 | ||||||||
\(965\) | 16.0647 | 0.517143 | ||||||||
\(966\) | 27.5982 | 0.887958 | ||||||||
\(967\) | −54.8024 | −1.76233 | −0.881163 | − | 0.472812i | \(-0.843239\pi\) | ||||
−0.881163 | + | 0.472812i | \(0.843239\pi\) | |||||||
\(968\) | −14.7438 | −0.473882 | ||||||||
\(969\) | −0.164752 | −0.00529259 | ||||||||
\(970\) | 41.0811 | 1.31903 | ||||||||
\(971\) | −5.23079 | −0.167864 | −0.0839321 | − | 0.996471i | \(-0.526748\pi\) | ||||
−0.0839321 | + | 0.996471i | \(0.526748\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 50.4145 | 1.61621 | ||||||||
\(974\) | −7.38220 | −0.236541 | ||||||||
\(975\) | −14.5311 | −0.465368 | ||||||||
\(976\) | −2.35917 | −0.0755153 | ||||||||
\(977\) | 42.6129 | 1.36331 | 0.681653 | − | 0.731675i | \(-0.261261\pi\) | ||||
0.681653 | + | 0.731675i | \(0.261261\pi\) | |||||||
\(978\) | 23.7938 | 0.760842 | ||||||||
\(979\) | −45.8957 | −1.46683 | ||||||||
\(980\) | −30.7770 | −0.983136 | ||||||||
\(981\) | −6.97372 | −0.222654 | ||||||||
\(982\) | −18.0802 | −0.576962 | ||||||||
\(983\) | −46.7968 | −1.49259 | −0.746293 | − | 0.665617i | \(-0.768168\pi\) | ||||
−0.746293 | + | 0.665617i | \(0.768168\pi\) | |||||||
\(984\) | −9.53136 | −0.303849 | ||||||||
\(985\) | 43.7792 | 1.39492 | ||||||||
\(986\) | 0.414307 | 0.0131942 | ||||||||
\(987\) | −9.30499 | −0.296181 | ||||||||
\(988\) | −4.31548 | −0.137294 | ||||||||
\(989\) | −78.5997 | −2.49932 | ||||||||
\(990\) | −14.6766 | −0.466454 | ||||||||
\(991\) | 38.4547 | 1.22156 | 0.610778 | − | 0.791802i | \(-0.290857\pi\) | ||||
0.610778 | + | 0.791802i | \(0.290857\pi\) | |||||||
\(992\) | −9.86954 | −0.313358 | ||||||||
\(993\) | −2.79548 | −0.0887118 | ||||||||
\(994\) | 51.0218 | 1.61831 | ||||||||
\(995\) | 9.09515 | 0.288336 | ||||||||
\(996\) | −14.9921 | −0.475043 | ||||||||
\(997\) | 9.74444 | 0.308609 | 0.154305 | − | 0.988023i | \(-0.450686\pi\) | ||||
0.154305 | + | 0.988023i | \(0.450686\pi\) | |||||||
\(998\) | −7.19500 | −0.227754 | ||||||||
\(999\) | 1.06505 | 0.0336966 |
(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 | 6042.2.a.be.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.be.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial |