Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.71784\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | −2.58633 | −1.15664 | −0.578320 | − | 0.815810i | \(-0.696292\pi\) | ||||
−0.578320 | + | 0.815810i | \(0.696292\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.26383 | 1.23361 | 0.616807 | − | 0.787115i | \(-0.288426\pi\) | ||||
0.616807 | + | 0.787115i | \(0.288426\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.58633 | −0.817868 | ||||||||
\(11\) | −5.04950 | −1.52248 | −0.761241 | − | 0.648469i | \(-0.775410\pi\) | ||||
−0.761241 | + | 0.648469i | \(0.775410\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.26383 | 0.872296 | ||||||||
\(15\) | 2.58633 | 0.667787 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.96813 | 0.962412 | 0.481206 | − | 0.876607i | \(-0.340199\pi\) | ||||
0.481206 | + | 0.876607i | \(0.340199\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.09958 | −0.252261 | −0.126130 | − | 0.992014i | \(-0.540256\pi\) | ||||
−0.126130 | + | 0.992014i | \(0.540256\pi\) | |||||||
\(20\) | −2.58633 | −0.578320 | ||||||||
\(21\) | −3.26383 | −0.712227 | ||||||||
\(22\) | −5.04950 | −1.07656 | ||||||||
\(23\) | 6.36847 | 1.32792 | 0.663959 | − | 0.747769i | \(-0.268875\pi\) | ||||
0.663959 | + | 0.747769i | \(0.268875\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.68909 | 0.337817 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.26383 | 0.616807 | ||||||||
\(29\) | 1.31929 | 0.244986 | 0.122493 | − | 0.992469i | \(-0.460911\pi\) | ||||
0.122493 | + | 0.992469i | \(0.460911\pi\) | |||||||
\(30\) | 2.58633 | 0.472197 | ||||||||
\(31\) | −9.20293 | −1.65289 | −0.826447 | − | 0.563014i | \(-0.809642\pi\) | ||||
−0.826447 | + | 0.563014i | \(0.809642\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.04950 | 0.879006 | ||||||||
\(34\) | 3.96813 | 0.680528 | ||||||||
\(35\) | −8.44134 | −1.42685 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.79533 | −1.44594 | −0.722971 | − | 0.690878i | \(-0.757224\pi\) | ||||
−0.722971 | + | 0.690878i | \(0.757224\pi\) | |||||||
\(38\) | −1.09958 | −0.178375 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.58633 | −0.408934 | ||||||||
\(41\) | 5.07728 | 0.792938 | 0.396469 | − | 0.918048i | \(-0.370235\pi\) | ||||
0.396469 | + | 0.918048i | \(0.370235\pi\) | |||||||
\(42\) | −3.26383 | −0.503620 | ||||||||
\(43\) | 3.38706 | 0.516523 | 0.258261 | − | 0.966075i | \(-0.416850\pi\) | ||||
0.258261 | + | 0.966075i | \(0.416850\pi\) | |||||||
\(44\) | −5.04950 | −0.761241 | ||||||||
\(45\) | −2.58633 | −0.385547 | ||||||||
\(46\) | 6.36847 | 0.938979 | ||||||||
\(47\) | 2.09076 | 0.304968 | 0.152484 | − | 0.988306i | \(-0.451273\pi\) | ||||
0.152484 | + | 0.988306i | \(0.451273\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.65261 | 0.521802 | ||||||||
\(50\) | 1.68909 | 0.238873 | ||||||||
\(51\) | −3.96813 | −0.555649 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 1.27373 | 0.174961 | 0.0874803 | − | 0.996166i | \(-0.472119\pi\) | ||||
0.0874803 | + | 0.996166i | \(0.472119\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 13.0597 | 1.76097 | ||||||||
\(56\) | 3.26383 | 0.436148 | ||||||||
\(57\) | 1.09958 | 0.145643 | ||||||||
\(58\) | 1.31929 | 0.173231 | ||||||||
\(59\) | −0.585224 | −0.0761897 | −0.0380949 | − | 0.999274i | \(-0.512129\pi\) | ||||
−0.0380949 | + | 0.999274i | \(0.512129\pi\) | |||||||
\(60\) | 2.58633 | 0.333893 | ||||||||
\(61\) | −3.12507 | −0.400124 | −0.200062 | − | 0.979783i | \(-0.564114\pi\) | ||||
−0.200062 | + | 0.979783i | \(0.564114\pi\) | |||||||
\(62\) | −9.20293 | −1.16877 | ||||||||
\(63\) | 3.26383 | 0.411204 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.58633 | 0.320794 | ||||||||
\(66\) | 5.04950 | 0.621551 | ||||||||
\(67\) | −2.90850 | −0.355330 | −0.177665 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177665 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(68\) | 3.96813 | 0.481206 | ||||||||
\(69\) | −6.36847 | −0.766673 | ||||||||
\(70\) | −8.44134 | −1.00893 | ||||||||
\(71\) | −1.22777 | −0.145710 | −0.0728548 | − | 0.997343i | \(-0.523211\pi\) | ||||
−0.0728548 | + | 0.997343i | \(0.523211\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.28463 | 0.969642 | 0.484821 | − | 0.874613i | \(-0.338885\pi\) | ||||
0.484821 | + | 0.874613i | \(0.338885\pi\) | |||||||
\(74\) | −8.79533 | −1.02244 | ||||||||
\(75\) | −1.68909 | −0.195039 | ||||||||
\(76\) | −1.09958 | −0.126130 | ||||||||
\(77\) | −16.4807 | −1.87815 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −6.38385 | −0.718239 | −0.359120 | − | 0.933292i | \(-0.616923\pi\) | ||||
−0.359120 | + | 0.933292i | \(0.616923\pi\) | |||||||
\(80\) | −2.58633 | −0.289160 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.07728 | 0.560692 | ||||||||
\(83\) | 11.7908 | 1.29421 | 0.647106 | − | 0.762400i | \(-0.275979\pi\) | ||||
0.647106 | + | 0.762400i | \(0.275979\pi\) | |||||||
\(84\) | −3.26383 | −0.356113 | ||||||||
\(85\) | −10.2629 | −1.11317 | ||||||||
\(86\) | 3.38706 | 0.365237 | ||||||||
\(87\) | −1.31929 | −0.141443 | ||||||||
\(88\) | −5.04950 | −0.538279 | ||||||||
\(89\) | −2.27017 | −0.240638 | −0.120319 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120319 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(90\) | −2.58633 | −0.272623 | ||||||||
\(91\) | −3.26383 | −0.342143 | ||||||||
\(92\) | 6.36847 | 0.663959 | ||||||||
\(93\) | 9.20293 | 0.954299 | ||||||||
\(94\) | 2.09076 | 0.215645 | ||||||||
\(95\) | 2.84387 | 0.291775 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −15.4982 | −1.57360 | −0.786801 | − | 0.617206i | \(-0.788264\pi\) | ||||
−0.786801 | + | 0.617206i | \(0.788264\pi\) | |||||||
\(98\) | 3.65261 | 0.368969 | ||||||||
\(99\) | −5.04950 | −0.507494 | ||||||||
\(100\) | 1.68909 | 0.168909 | ||||||||
\(101\) | −7.67767 | −0.763957 | −0.381978 | − | 0.924171i | \(-0.624757\pi\) | ||||
−0.381978 | + | 0.924171i | \(0.624757\pi\) | |||||||
\(102\) | −3.96813 | −0.392903 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 8.44134 | 0.823791 | ||||||||
\(106\) | 1.27373 | 0.123716 | ||||||||
\(107\) | −20.5151 | −1.98327 | −0.991634 | − | 0.129081i | \(-0.958797\pi\) | ||||
−0.991634 | + | 0.129081i | \(0.958797\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.38576 | 0.132732 | 0.0663660 | − | 0.997795i | \(-0.478859\pi\) | ||||
0.0663660 | + | 0.997795i | \(0.478859\pi\) | |||||||
\(110\) | 13.0597 | 1.24519 | ||||||||
\(111\) | 8.79533 | 0.834816 | ||||||||
\(112\) | 3.26383 | 0.308403 | ||||||||
\(113\) | −10.3227 | −0.971074 | −0.485537 | − | 0.874216i | \(-0.661376\pi\) | ||||
−0.485537 | + | 0.874216i | \(0.661376\pi\) | |||||||
\(114\) | 1.09958 | 0.102985 | ||||||||
\(115\) | −16.4709 | −1.53592 | ||||||||
\(116\) | 1.31929 | 0.122493 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −0.585224 | −0.0538743 | ||||||||
\(119\) | 12.9513 | 1.18724 | ||||||||
\(120\) | 2.58633 | 0.236098 | ||||||||
\(121\) | 14.4975 | 1.31795 | ||||||||
\(122\) | −3.12507 | −0.282931 | ||||||||
\(123\) | −5.07728 | −0.457803 | ||||||||
\(124\) | −9.20293 | −0.826447 | ||||||||
\(125\) | 8.56310 | 0.765907 | ||||||||
\(126\) | 3.26383 | 0.290765 | ||||||||
\(127\) | 18.6909 | 1.65855 | 0.829273 | − | 0.558844i | \(-0.188755\pi\) | ||||
0.829273 | + | 0.558844i | \(0.188755\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.38706 | −0.298214 | ||||||||
\(130\) | 2.58633 | 0.226836 | ||||||||
\(131\) | 5.07360 | 0.443283 | 0.221641 | − | 0.975128i | \(-0.428859\pi\) | ||||
0.221641 | + | 0.975128i | \(0.428859\pi\) | |||||||
\(132\) | 5.04950 | 0.439503 | ||||||||
\(133\) | −3.58884 | −0.311192 | ||||||||
\(134\) | −2.90850 | −0.251256 | ||||||||
\(135\) | 2.58633 | 0.222596 | ||||||||
\(136\) | 3.96813 | 0.340264 | ||||||||
\(137\) | 8.93266 | 0.763168 | 0.381584 | − | 0.924334i | \(-0.375379\pi\) | ||||
0.381584 | + | 0.924334i | \(0.375379\pi\) | |||||||
\(138\) | −6.36847 | −0.542120 | ||||||||
\(139\) | −7.90112 | −0.670164 | −0.335082 | − | 0.942189i | \(-0.608764\pi\) | ||||
−0.335082 | + | 0.942189i | \(0.608764\pi\) | |||||||
\(140\) | −8.44134 | −0.713424 | ||||||||
\(141\) | −2.09076 | −0.176074 | ||||||||
\(142\) | −1.22777 | −0.103032 | ||||||||
\(143\) | 5.04950 | 0.422261 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.41212 | −0.283361 | ||||||||
\(146\) | 8.28463 | 0.685641 | ||||||||
\(147\) | −3.65261 | −0.301262 | ||||||||
\(148\) | −8.79533 | −0.722971 | ||||||||
\(149\) | −19.9344 | −1.63309 | −0.816545 | − | 0.577282i | \(-0.804113\pi\) | ||||
−0.816545 | + | 0.577282i | \(0.804113\pi\) | |||||||
\(150\) | −1.68909 | −0.137913 | ||||||||
\(151\) | 9.91239 | 0.806659 | 0.403330 | − | 0.915055i | \(-0.367853\pi\) | ||||
0.403330 | + | 0.915055i | \(0.367853\pi\) | |||||||
\(152\) | −1.09958 | −0.0891877 | ||||||||
\(153\) | 3.96813 | 0.320804 | ||||||||
\(154\) | −16.4807 | −1.32806 | ||||||||
\(155\) | 23.8018 | 1.91180 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −11.9341 | −0.952443 | −0.476222 | − | 0.879325i | \(-0.657994\pi\) | ||||
−0.476222 | + | 0.879325i | \(0.657994\pi\) | |||||||
\(158\) | −6.38385 | −0.507872 | ||||||||
\(159\) | −1.27373 | −0.101014 | ||||||||
\(160\) | −2.58633 | −0.204467 | ||||||||
\(161\) | 20.7856 | 1.63814 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −16.2967 | −1.27646 | −0.638228 | − | 0.769847i | \(-0.720332\pi\) | ||||
−0.638228 | + | 0.769847i | \(0.720332\pi\) | |||||||
\(164\) | 5.07728 | 0.396469 | ||||||||
\(165\) | −13.0597 | −1.01669 | ||||||||
\(166\) | 11.7908 | 0.915146 | ||||||||
\(167\) | −1.14380 | −0.0885099 | −0.0442549 | − | 0.999020i | \(-0.514091\pi\) | ||||
−0.0442549 | + | 0.999020i | \(0.514091\pi\) | |||||||
\(168\) | −3.26383 | −0.251810 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −10.2629 | −0.787127 | ||||||||
\(171\) | −1.09958 | −0.0840869 | ||||||||
\(172\) | 3.38706 | 0.258261 | ||||||||
\(173\) | −7.53776 | −0.573085 | −0.286543 | − | 0.958067i | \(-0.592506\pi\) | ||||
−0.286543 | + | 0.958067i | \(0.592506\pi\) | |||||||
\(174\) | −1.31929 | −0.100015 | ||||||||
\(175\) | 5.51290 | 0.416736 | ||||||||
\(176\) | −5.04950 | −0.380621 | ||||||||
\(177\) | 0.585224 | 0.0439882 | ||||||||
\(178\) | −2.27017 | −0.170157 | ||||||||
\(179\) | −10.9526 | −0.818637 | −0.409319 | − | 0.912391i | \(-0.634234\pi\) | ||||
−0.409319 | + | 0.912391i | \(0.634234\pi\) | |||||||
\(180\) | −2.58633 | −0.192773 | ||||||||
\(181\) | 9.46537 | 0.703555 | 0.351778 | − | 0.936084i | \(-0.385577\pi\) | ||||
0.351778 | + | 0.936084i | \(0.385577\pi\) | |||||||
\(182\) | −3.26383 | −0.241931 | ||||||||
\(183\) | 3.12507 | 0.231012 | ||||||||
\(184\) | 6.36847 | 0.469490 | ||||||||
\(185\) | 22.7476 | 1.67244 | ||||||||
\(186\) | 9.20293 | 0.674791 | ||||||||
\(187\) | −20.0371 | −1.46526 | ||||||||
\(188\) | 2.09076 | 0.152484 | ||||||||
\(189\) | −3.26383 | −0.237409 | ||||||||
\(190\) | 2.84387 | 0.206316 | ||||||||
\(191\) | 10.3592 | 0.749566 | 0.374783 | − | 0.927113i | \(-0.377717\pi\) | ||||
0.374783 | + | 0.927113i | \(0.377717\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.0661 | −1.30043 | −0.650213 | − | 0.759752i | \(-0.725320\pi\) | ||||
−0.650213 | + | 0.759752i | \(0.725320\pi\) | |||||||
\(194\) | −15.4982 | −1.11271 | ||||||||
\(195\) | −2.58633 | −0.185211 | ||||||||
\(196\) | 3.65261 | 0.260901 | ||||||||
\(197\) | −16.6620 | −1.18712 | −0.593558 | − | 0.804791i | \(-0.702277\pi\) | ||||
−0.593558 | + | 0.804791i | \(0.702277\pi\) | |||||||
\(198\) | −5.04950 | −0.358853 | ||||||||
\(199\) | −8.32966 | −0.590474 | −0.295237 | − | 0.955424i | \(-0.595399\pi\) | ||||
−0.295237 | + | 0.955424i | \(0.595399\pi\) | |||||||
\(200\) | 1.68909 | 0.119436 | ||||||||
\(201\) | 2.90850 | 0.205150 | ||||||||
\(202\) | −7.67767 | −0.540199 | ||||||||
\(203\) | 4.30595 | 0.302218 | ||||||||
\(204\) | −3.96813 | −0.277825 | ||||||||
\(205\) | −13.1315 | −0.917145 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 6.36847 | 0.442639 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 5.55233 | 0.384063 | ||||||||
\(210\) | 8.44134 | 0.582508 | ||||||||
\(211\) | −21.5780 | −1.48549 | −0.742747 | − | 0.669573i | \(-0.766477\pi\) | ||||
−0.742747 | + | 0.669573i | \(0.766477\pi\) | |||||||
\(212\) | 1.27373 | 0.0874803 | ||||||||
\(213\) | 1.22777 | 0.0841254 | ||||||||
\(214\) | −20.5151 | −1.40238 | ||||||||
\(215\) | −8.76006 | −0.597431 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −30.0368 | −2.03903 | ||||||||
\(218\) | 1.38576 | 0.0938558 | ||||||||
\(219\) | −8.28463 | −0.559823 | ||||||||
\(220\) | 13.0597 | 0.880483 | ||||||||
\(221\) | −3.96813 | −0.266925 | ||||||||
\(222\) | 8.79533 | 0.590304 | ||||||||
\(223\) | −25.7402 | −1.72369 | −0.861847 | − | 0.507168i | \(-0.830692\pi\) | ||||
−0.861847 | + | 0.507168i | \(0.830692\pi\) | |||||||
\(224\) | 3.26383 | 0.218074 | ||||||||
\(225\) | 1.68909 | 0.112606 | ||||||||
\(226\) | −10.3227 | −0.686653 | ||||||||
\(227\) | −4.56547 | −0.303021 | −0.151510 | − | 0.988456i | \(-0.548414\pi\) | ||||
−0.151510 | + | 0.988456i | \(0.548414\pi\) | |||||||
\(228\) | 1.09958 | 0.0728214 | ||||||||
\(229\) | −4.72707 | −0.312374 | −0.156187 | − | 0.987728i | \(-0.549920\pi\) | ||||
−0.156187 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(230\) | −16.4709 | −1.08606 | ||||||||
\(231\) | 16.4807 | 1.08435 | ||||||||
\(232\) | 1.31929 | 0.0866157 | ||||||||
\(233\) | 2.72230 | 0.178344 | 0.0891720 | − | 0.996016i | \(-0.471578\pi\) | ||||
0.0891720 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −5.40739 | −0.352739 | ||||||||
\(236\) | −0.585224 | −0.0380949 | ||||||||
\(237\) | 6.38385 | 0.414676 | ||||||||
\(238\) | 12.9513 | 0.839509 | ||||||||
\(239\) | −3.50420 | −0.226668 | −0.113334 | − | 0.993557i | \(-0.536153\pi\) | ||||
−0.113334 | + | 0.993557i | \(0.536153\pi\) | |||||||
\(240\) | 2.58633 | 0.166947 | ||||||||
\(241\) | 5.54442 | 0.357147 | 0.178574 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178574 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(242\) | 14.4975 | 0.931934 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.12507 | −0.200062 | ||||||||
\(245\) | −9.44685 | −0.603537 | ||||||||
\(246\) | −5.07728 | −0.323716 | ||||||||
\(247\) | 1.09958 | 0.0699646 | ||||||||
\(248\) | −9.20293 | −0.584386 | ||||||||
\(249\) | −11.7908 | −0.747214 | ||||||||
\(250\) | 8.56310 | 0.541578 | ||||||||
\(251\) | 20.1646 | 1.27278 | 0.636389 | − | 0.771368i | \(-0.280427\pi\) | ||||
0.636389 | + | 0.771368i | \(0.280427\pi\) | |||||||
\(252\) | 3.26383 | 0.205602 | ||||||||
\(253\) | −32.1576 | −2.02173 | ||||||||
\(254\) | 18.6909 | 1.17277 | ||||||||
\(255\) | 10.2629 | 0.642686 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.76155 | −0.421774 | −0.210887 | − | 0.977510i | \(-0.567635\pi\) | ||||
−0.210887 | + | 0.977510i | \(0.567635\pi\) | |||||||
\(258\) | −3.38706 | −0.210869 | ||||||||
\(259\) | −28.7065 | −1.78373 | ||||||||
\(260\) | 2.58633 | 0.160397 | ||||||||
\(261\) | 1.31929 | 0.0816621 | ||||||||
\(262\) | 5.07360 | 0.313448 | ||||||||
\(263\) | −0.821275 | −0.0506420 | −0.0253210 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253210 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(264\) | 5.04950 | 0.310775 | ||||||||
\(265\) | −3.29429 | −0.202367 | ||||||||
\(266\) | −3.58884 | −0.220046 | ||||||||
\(267\) | 2.27017 | 0.138932 | ||||||||
\(268\) | −2.90850 | −0.177665 | ||||||||
\(269\) | 30.2037 | 1.84155 | 0.920776 | − | 0.390093i | \(-0.127557\pi\) | ||||
0.920776 | + | 0.390093i | \(0.127557\pi\) | |||||||
\(270\) | 2.58633 | 0.157399 | ||||||||
\(271\) | −11.3371 | −0.688681 | −0.344340 | − | 0.938845i | \(-0.611897\pi\) | ||||
−0.344340 | + | 0.938845i | \(0.611897\pi\) | |||||||
\(272\) | 3.96813 | 0.240603 | ||||||||
\(273\) | 3.26383 | 0.197536 | ||||||||
\(274\) | 8.93266 | 0.539641 | ||||||||
\(275\) | −8.52905 | −0.514321 | ||||||||
\(276\) | −6.36847 | −0.383337 | ||||||||
\(277\) | 21.7770 | 1.30845 | 0.654227 | − | 0.756299i | \(-0.272994\pi\) | ||||
0.654227 | + | 0.756299i | \(0.272994\pi\) | |||||||
\(278\) | −7.90112 | −0.473878 | ||||||||
\(279\) | −9.20293 | −0.550965 | ||||||||
\(280\) | −8.44134 | −0.504467 | ||||||||
\(281\) | −22.7937 | −1.35976 | −0.679879 | − | 0.733324i | \(-0.737968\pi\) | ||||
−0.679879 | + | 0.733324i | \(0.737968\pi\) | |||||||
\(282\) | −2.09076 | −0.124503 | ||||||||
\(283\) | −19.3591 | −1.15078 | −0.575391 | − | 0.817879i | \(-0.695150\pi\) | ||||
−0.575391 | + | 0.817879i | \(0.695150\pi\) | |||||||
\(284\) | −1.22777 | −0.0728548 | ||||||||
\(285\) | −2.84387 | −0.168456 | ||||||||
\(286\) | 5.04950 | 0.298583 | ||||||||
\(287\) | 16.5714 | 0.978179 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −1.25396 | −0.0737624 | ||||||||
\(290\) | −3.41212 | −0.200366 | ||||||||
\(291\) | 15.4982 | 0.908520 | ||||||||
\(292\) | 8.28463 | 0.484821 | ||||||||
\(293\) | 14.5669 | 0.851007 | 0.425504 | − | 0.904957i | \(-0.360097\pi\) | ||||
0.425504 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(294\) | −3.65261 | −0.213025 | ||||||||
\(295\) | 1.51358 | 0.0881241 | ||||||||
\(296\) | −8.79533 | −0.511218 | ||||||||
\(297\) | 5.04950 | 0.293002 | ||||||||
\(298\) | −19.9344 | −1.15477 | ||||||||
\(299\) | −6.36847 | −0.368298 | ||||||||
\(300\) | −1.68909 | −0.0975194 | ||||||||
\(301\) | 11.0548 | 0.637189 | ||||||||
\(302\) | 9.91239 | 0.570394 | ||||||||
\(303\) | 7.67767 | 0.441071 | ||||||||
\(304\) | −1.09958 | −0.0630652 | ||||||||
\(305\) | 8.08246 | 0.462800 | ||||||||
\(306\) | 3.96813 | 0.226843 | ||||||||
\(307\) | 5.93484 | 0.338719 | 0.169360 | − | 0.985554i | \(-0.445830\pi\) | ||||
0.169360 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(308\) | −16.4807 | −0.939077 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 23.8018 | 1.35185 | ||||||||
\(311\) | 13.6957 | 0.776610 | 0.388305 | − | 0.921531i | \(-0.373061\pi\) | ||||
0.388305 | + | 0.921531i | \(0.373061\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −21.2483 | −1.20103 | −0.600513 | − | 0.799615i | \(-0.705037\pi\) | ||||
−0.600513 | + | 0.799615i | \(0.705037\pi\) | |||||||
\(314\) | −11.9341 | −0.673479 | ||||||||
\(315\) | −8.44134 | −0.475616 | ||||||||
\(316\) | −6.38385 | −0.359120 | ||||||||
\(317\) | −26.2038 | −1.47175 | −0.735876 | − | 0.677116i | \(-0.763229\pi\) | ||||
−0.735876 | + | 0.677116i | \(0.763229\pi\) | |||||||
\(318\) | −1.27373 | −0.0714274 | ||||||||
\(319\) | −6.66177 | −0.372987 | ||||||||
\(320\) | −2.58633 | −0.144580 | ||||||||
\(321\) | 20.5151 | 1.14504 | ||||||||
\(322\) | 20.7856 | 1.15834 | ||||||||
\(323\) | −4.36327 | −0.242779 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.68909 | −0.0936936 | ||||||||
\(326\) | −16.2967 | −0.902591 | ||||||||
\(327\) | −1.38576 | −0.0766329 | ||||||||
\(328\) | 5.07728 | 0.280346 | ||||||||
\(329\) | 6.82389 | 0.376213 | ||||||||
\(330\) | −13.0597 | −0.718911 | ||||||||
\(331\) | −8.67449 | −0.476793 | −0.238397 | − | 0.971168i | \(-0.576622\pi\) | ||||
−0.238397 | + | 0.971168i | \(0.576622\pi\) | |||||||
\(332\) | 11.7908 | 0.647106 | ||||||||
\(333\) | −8.79533 | −0.481981 | ||||||||
\(334\) | −1.14380 | −0.0625859 | ||||||||
\(335\) | 7.52232 | 0.410989 | ||||||||
\(336\) | −3.26383 | −0.178057 | ||||||||
\(337\) | −2.76207 | −0.150460 | −0.0752299 | − | 0.997166i | \(-0.523969\pi\) | ||||
−0.0752299 | + | 0.997166i | \(0.523969\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 10.3227 | 0.560650 | ||||||||
\(340\) | −10.2629 | −0.556583 | ||||||||
\(341\) | 46.4702 | 2.51650 | ||||||||
\(342\) | −1.09958 | −0.0594584 | ||||||||
\(343\) | −10.9253 | −0.589912 | ||||||||
\(344\) | 3.38706 | 0.182618 | ||||||||
\(345\) | 16.4709 | 0.886766 | ||||||||
\(346\) | −7.53776 | −0.405233 | ||||||||
\(347\) | 0.174289 | 0.00935630 | 0.00467815 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467815 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(348\) | −1.31929 | −0.0707214 | ||||||||
\(349\) | −15.0994 | −0.808254 | −0.404127 | − | 0.914703i | \(-0.632425\pi\) | ||||
−0.404127 | + | 0.914703i | \(0.632425\pi\) | |||||||
\(350\) | 5.51290 | 0.294677 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −5.04950 | −0.269139 | ||||||||
\(353\) | −15.6514 | −0.833040 | −0.416520 | − | 0.909127i | \(-0.636750\pi\) | ||||
−0.416520 | + | 0.909127i | \(0.636750\pi\) | |||||||
\(354\) | 0.585224 | 0.0311043 | ||||||||
\(355\) | 3.17542 | 0.168534 | ||||||||
\(356\) | −2.27017 | −0.120319 | ||||||||
\(357\) | −12.9513 | −0.685456 | ||||||||
\(358\) | −10.9526 | −0.578864 | ||||||||
\(359\) | −1.43312 | −0.0756370 | −0.0378185 | − | 0.999285i | \(-0.512041\pi\) | ||||
−0.0378185 | + | 0.999285i | \(0.512041\pi\) | |||||||
\(360\) | −2.58633 | −0.136311 | ||||||||
\(361\) | −17.7909 | −0.936364 | ||||||||
\(362\) | 9.46537 | 0.497489 | ||||||||
\(363\) | −14.4975 | −0.760921 | ||||||||
\(364\) | −3.26383 | −0.171071 | ||||||||
\(365\) | −21.4268 | −1.12153 | ||||||||
\(366\) | 3.12507 | 0.163350 | ||||||||
\(367\) | −14.5873 | −0.761451 | −0.380726 | − | 0.924688i | \(-0.624326\pi\) | ||||
−0.380726 | + | 0.924688i | \(0.624326\pi\) | |||||||
\(368\) | 6.36847 | 0.331979 | ||||||||
\(369\) | 5.07728 | 0.264313 | ||||||||
\(370\) | 22.7476 | 1.18259 | ||||||||
\(371\) | 4.15725 | 0.215834 | ||||||||
\(372\) | 9.20293 | 0.477150 | ||||||||
\(373\) | 22.4462 | 1.16222 | 0.581110 | − | 0.813825i | \(-0.302619\pi\) | ||||
0.581110 | + | 0.813825i | \(0.302619\pi\) | |||||||
\(374\) | −20.0371 | −1.03609 | ||||||||
\(375\) | −8.56310 | −0.442197 | ||||||||
\(376\) | 2.09076 | 0.107823 | ||||||||
\(377\) | −1.31929 | −0.0679470 | ||||||||
\(378\) | −3.26383 | −0.167873 | ||||||||
\(379\) | 22.1475 | 1.13764 | 0.568821 | − | 0.822461i | \(-0.307400\pi\) | ||||
0.568821 | + | 0.822461i | \(0.307400\pi\) | |||||||
\(380\) | 2.84387 | 0.145888 | ||||||||
\(381\) | −18.6909 | −0.957561 | ||||||||
\(382\) | 10.3592 | 0.530023 | ||||||||
\(383\) | −25.4503 | −1.30045 | −0.650224 | − | 0.759743i | \(-0.725325\pi\) | ||||
−0.650224 | + | 0.759743i | \(0.725325\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 42.6246 | 2.17235 | ||||||||
\(386\) | −18.0661 | −0.919540 | ||||||||
\(387\) | 3.38706 | 0.172174 | ||||||||
\(388\) | −15.4982 | −0.786801 | ||||||||
\(389\) | 35.4634 | 1.79807 | 0.899034 | − | 0.437879i | \(-0.144270\pi\) | ||||
0.899034 | + | 0.437879i | \(0.144270\pi\) | |||||||
\(390\) | −2.58633 | −0.130964 | ||||||||
\(391\) | 25.2709 | 1.27800 | ||||||||
\(392\) | 3.65261 | 0.184485 | ||||||||
\(393\) | −5.07360 | −0.255929 | ||||||||
\(394\) | −16.6620 | −0.839418 | ||||||||
\(395\) | 16.5107 | 0.830744 | ||||||||
\(396\) | −5.04950 | −0.253747 | ||||||||
\(397\) | −22.8936 | −1.14900 | −0.574498 | − | 0.818506i | \(-0.694803\pi\) | ||||
−0.574498 | + | 0.818506i | \(0.694803\pi\) | |||||||
\(398\) | −8.32966 | −0.417528 | ||||||||
\(399\) | 3.58884 | 0.179667 | ||||||||
\(400\) | 1.68909 | 0.0844543 | ||||||||
\(401\) | 4.12648 | 0.206067 | 0.103033 | − | 0.994678i | \(-0.467145\pi\) | ||||
0.103033 | + | 0.994678i | \(0.467145\pi\) | |||||||
\(402\) | 2.90850 | 0.145063 | ||||||||
\(403\) | 9.20293 | 0.458430 | ||||||||
\(404\) | −7.67767 | −0.381978 | ||||||||
\(405\) | −2.58633 | −0.128516 | ||||||||
\(406\) | 4.30595 | 0.213701 | ||||||||
\(407\) | 44.4120 | 2.20142 | ||||||||
\(408\) | −3.96813 | −0.196452 | ||||||||
\(409\) | 29.2954 | 1.44856 | 0.724282 | − | 0.689504i | \(-0.242171\pi\) | ||||
0.724282 | + | 0.689504i | \(0.242171\pi\) | |||||||
\(410\) | −13.1315 | −0.648519 | ||||||||
\(411\) | −8.93266 | −0.440615 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −1.91008 | −0.0939887 | ||||||||
\(414\) | 6.36847 | 0.312993 | ||||||||
\(415\) | −30.4950 | −1.49694 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 7.90112 | 0.386920 | ||||||||
\(418\) | 5.55233 | 0.271573 | ||||||||
\(419\) | −0.0991300 | −0.00484282 | −0.00242141 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242141 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(420\) | 8.44134 | 0.411895 | ||||||||
\(421\) | 16.8298 | 0.820235 | 0.410118 | − | 0.912033i | \(-0.365488\pi\) | ||||
0.410118 | + | 0.912033i | \(0.365488\pi\) | |||||||
\(422\) | −21.5780 | −1.05040 | ||||||||
\(423\) | 2.09076 | 0.101656 | ||||||||
\(424\) | 1.27373 | 0.0618579 | ||||||||
\(425\) | 6.70251 | 0.325120 | ||||||||
\(426\) | 1.22777 | 0.0594857 | ||||||||
\(427\) | −10.1997 | −0.493599 | ||||||||
\(428\) | −20.5151 | −0.991634 | ||||||||
\(429\) | −5.04950 | −0.243792 | ||||||||
\(430\) | −8.76006 | −0.422447 | ||||||||
\(431\) | −19.7165 | −0.949708 | −0.474854 | − | 0.880065i | \(-0.657499\pi\) | ||||
−0.474854 | + | 0.880065i | \(0.657499\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 1.07818 | 0.0518142 | 0.0259071 | − | 0.999664i | \(-0.491753\pi\) | ||||
0.0259071 | + | 0.999664i | \(0.491753\pi\) | |||||||
\(434\) | −30.0368 | −1.44181 | ||||||||
\(435\) | 3.41212 | 0.163599 | ||||||||
\(436\) | 1.38576 | 0.0663660 | ||||||||
\(437\) | −7.00264 | −0.334981 | ||||||||
\(438\) | −8.28463 | −0.395855 | ||||||||
\(439\) | −30.2389 | −1.44322 | −0.721612 | − | 0.692298i | \(-0.756599\pi\) | ||||
−0.721612 | + | 0.692298i | \(0.756599\pi\) | |||||||
\(440\) | 13.0597 | 0.622595 | ||||||||
\(441\) | 3.65261 | 0.173934 | ||||||||
\(442\) | −3.96813 | −0.188745 | ||||||||
\(443\) | −8.66943 | −0.411897 | −0.205948 | − | 0.978563i | \(-0.566028\pi\) | ||||
−0.205948 | + | 0.978563i | \(0.566028\pi\) | |||||||
\(444\) | 8.79533 | 0.417408 | ||||||||
\(445\) | 5.87141 | 0.278332 | ||||||||
\(446\) | −25.7402 | −1.21884 | ||||||||
\(447\) | 19.9344 | 0.942864 | ||||||||
\(448\) | 3.26383 | 0.154202 | ||||||||
\(449\) | 3.28847 | 0.155193 | 0.0775964 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775964 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(450\) | 1.68909 | 0.0796243 | ||||||||
\(451\) | −25.6378 | −1.20724 | ||||||||
\(452\) | −10.3227 | −0.485537 | ||||||||
\(453\) | −9.91239 | −0.465725 | ||||||||
\(454\) | −4.56547 | −0.214268 | ||||||||
\(455\) | 8.44134 | 0.395736 | ||||||||
\(456\) | 1.09958 | 0.0514925 | ||||||||
\(457\) | −37.8667 | −1.77133 | −0.885665 | − | 0.464325i | \(-0.846297\pi\) | ||||
−0.885665 | + | 0.464325i | \(0.846297\pi\) | |||||||
\(458\) | −4.72707 | −0.220881 | ||||||||
\(459\) | −3.96813 | −0.185216 | ||||||||
\(460\) | −16.4709 | −0.767962 | ||||||||
\(461\) | −14.6597 | −0.682771 | −0.341386 | − | 0.939923i | \(-0.610896\pi\) | ||||
−0.341386 | + | 0.939923i | \(0.610896\pi\) | |||||||
\(462\) | 16.4807 | 0.766753 | ||||||||
\(463\) | −17.1345 | −0.796306 | −0.398153 | − | 0.917319i | \(-0.630349\pi\) | ||||
−0.398153 | + | 0.917319i | \(0.630349\pi\) | |||||||
\(464\) | 1.31929 | 0.0612466 | ||||||||
\(465\) | −23.8018 | −1.10378 | ||||||||
\(466\) | 2.72230 | 0.126108 | ||||||||
\(467\) | 10.8737 | 0.503173 | 0.251586 | − | 0.967835i | \(-0.419048\pi\) | ||||
0.251586 | + | 0.967835i | \(0.419048\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −9.49285 | −0.438339 | ||||||||
\(470\) | −5.40739 | −0.249424 | ||||||||
\(471\) | 11.9341 | 0.549893 | ||||||||
\(472\) | −0.585224 | −0.0269371 | ||||||||
\(473\) | −17.1030 | −0.786397 | ||||||||
\(474\) | 6.38385 | 0.293220 | ||||||||
\(475\) | −1.85728 | −0.0852180 | ||||||||
\(476\) | 12.9513 | 0.593622 | ||||||||
\(477\) | 1.27373 | 0.0583202 | ||||||||
\(478\) | −3.50420 | −0.160279 | ||||||||
\(479\) | −0.456662 | −0.0208654 | −0.0104327 | − | 0.999946i | \(-0.503321\pi\) | ||||
−0.0104327 | + | 0.999946i | \(0.503321\pi\) | |||||||
\(480\) | 2.58633 | 0.118049 | ||||||||
\(481\) | 8.79533 | 0.401032 | ||||||||
\(482\) | 5.54442 | 0.252541 | ||||||||
\(483\) | −20.7856 | −0.945779 | ||||||||
\(484\) | 14.4975 | 0.658977 | ||||||||
\(485\) | 40.0834 | 1.82009 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −19.4436 | −0.881074 | −0.440537 | − | 0.897734i | \(-0.645212\pi\) | ||||
−0.440537 | + | 0.897734i | \(0.645212\pi\) | |||||||
\(488\) | −3.12507 | −0.141465 | ||||||||
\(489\) | 16.2967 | 0.736962 | ||||||||
\(490\) | −9.44685 | −0.426765 | ||||||||
\(491\) | −37.6264 | −1.69805 | −0.849027 | − | 0.528350i | \(-0.822811\pi\) | ||||
−0.849027 | + | 0.528350i | \(0.822811\pi\) | |||||||
\(492\) | −5.07728 | −0.228902 | ||||||||
\(493\) | 5.23512 | 0.235778 | ||||||||
\(494\) | 1.09958 | 0.0494724 | ||||||||
\(495\) | 13.0597 | 0.586988 | ||||||||
\(496\) | −9.20293 | −0.413224 | ||||||||
\(497\) | −4.00724 | −0.179749 | ||||||||
\(498\) | −11.7908 | −0.528360 | ||||||||
\(499\) | 22.5980 | 1.01163 | 0.505814 | − | 0.862643i | \(-0.331192\pi\) | ||||
0.505814 | + | 0.862643i | \(0.331192\pi\) | |||||||
\(500\) | 8.56310 | 0.382954 | ||||||||
\(501\) | 1.14380 | 0.0511012 | ||||||||
\(502\) | 20.1646 | 0.899990 | ||||||||
\(503\) | 40.1851 | 1.79177 | 0.895883 | − | 0.444290i | \(-0.146544\pi\) | ||||
0.895883 | + | 0.444290i | \(0.146544\pi\) | |||||||
\(504\) | 3.26383 | 0.145383 | ||||||||
\(505\) | 19.8570 | 0.883623 | ||||||||
\(506\) | −32.1576 | −1.42958 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 18.6909 | 0.829273 | ||||||||
\(509\) | −14.6278 | −0.648365 | −0.324182 | − | 0.945995i | \(-0.605089\pi\) | ||||
−0.324182 | + | 0.945995i | \(0.605089\pi\) | |||||||
\(510\) | 10.2629 | 0.454448 | ||||||||
\(511\) | 27.0397 | 1.19616 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.09958 | 0.0485476 | ||||||||
\(514\) | −6.76155 | −0.298239 | ||||||||
\(515\) | −2.58633 | −0.113967 | ||||||||
\(516\) | −3.38706 | −0.149107 | ||||||||
\(517\) | −10.5573 | −0.464309 | ||||||||
\(518\) | −28.7065 | −1.26129 | ||||||||
\(519\) | 7.53776 | 0.330871 | ||||||||
\(520\) | 2.58633 | 0.113418 | ||||||||
\(521\) | 19.9760 | 0.875164 | 0.437582 | − | 0.899179i | \(-0.355835\pi\) | ||||
0.437582 | + | 0.899179i | \(0.355835\pi\) | |||||||
\(522\) | 1.31929 | 0.0577438 | ||||||||
\(523\) | −1.31871 | −0.0576632 | −0.0288316 | − | 0.999584i | \(-0.509179\pi\) | ||||
−0.0288316 | + | 0.999584i | \(0.509179\pi\) | |||||||
\(524\) | 5.07360 | 0.221641 | ||||||||
\(525\) | −5.51290 | −0.240603 | ||||||||
\(526\) | −0.821275 | −0.0358093 | ||||||||
\(527\) | −36.5184 | −1.59077 | ||||||||
\(528\) | 5.04950 | 0.219751 | ||||||||
\(529\) | 17.5574 | 0.763365 | ||||||||
\(530\) | −3.29429 | −0.143095 | ||||||||
\(531\) | −0.585224 | −0.0253966 | ||||||||
\(532\) | −3.58884 | −0.155596 | ||||||||
\(533\) | −5.07728 | −0.219922 | ||||||||
\(534\) | 2.27017 | 0.0982400 | ||||||||
\(535\) | 53.0587 | 2.29393 | ||||||||
\(536\) | −2.90850 | −0.125628 | ||||||||
\(537\) | 10.9526 | 0.472641 | ||||||||
\(538\) | 30.2037 | 1.30217 | ||||||||
\(539\) | −18.4439 | −0.794434 | ||||||||
\(540\) | 2.58633 | 0.111298 | ||||||||
\(541\) | −11.3795 | −0.489244 | −0.244622 | − | 0.969618i | \(-0.578664\pi\) | ||||
−0.244622 | + | 0.969618i | \(0.578664\pi\) | |||||||
\(542\) | −11.3371 | −0.486971 | ||||||||
\(543\) | −9.46537 | −0.406198 | ||||||||
\(544\) | 3.96813 | 0.170132 | ||||||||
\(545\) | −3.58404 | −0.153523 | ||||||||
\(546\) | 3.26383 | 0.139679 | ||||||||
\(547\) | −26.6627 | −1.14001 | −0.570007 | − | 0.821640i | \(-0.693060\pi\) | ||||
−0.570007 | + | 0.821640i | \(0.693060\pi\) | |||||||
\(548\) | 8.93266 | 0.381584 | ||||||||
\(549\) | −3.12507 | −0.133375 | ||||||||
\(550\) | −8.52905 | −0.363680 | ||||||||
\(551\) | −1.45067 | −0.0618004 | ||||||||
\(552\) | −6.36847 | −0.271060 | ||||||||
\(553\) | −20.8358 | −0.886029 | ||||||||
\(554\) | 21.7770 | 0.925216 | ||||||||
\(555\) | −22.7476 | −0.965582 | ||||||||
\(556\) | −7.90112 | −0.335082 | ||||||||
\(557\) | 11.4909 | 0.486886 | 0.243443 | − | 0.969915i | \(-0.421723\pi\) | ||||
0.243443 | + | 0.969915i | \(0.421723\pi\) | |||||||
\(558\) | −9.20293 | −0.389591 | ||||||||
\(559\) | −3.38706 | −0.143258 | ||||||||
\(560\) | −8.44134 | −0.356712 | ||||||||
\(561\) | 20.0371 | 0.845966 | ||||||||
\(562\) | −22.7937 | −0.961494 | ||||||||
\(563\) | 21.7841 | 0.918089 | 0.459044 | − | 0.888413i | \(-0.348192\pi\) | ||||
0.459044 | + | 0.888413i | \(0.348192\pi\) | |||||||
\(564\) | −2.09076 | −0.0880368 | ||||||||
\(565\) | 26.6978 | 1.12318 | ||||||||
\(566\) | −19.3591 | −0.813726 | ||||||||
\(567\) | 3.26383 | 0.137068 | ||||||||
\(568\) | −1.22777 | −0.0515161 | ||||||||
\(569\) | −8.16236 | −0.342184 | −0.171092 | − | 0.985255i | \(-0.554730\pi\) | ||||
−0.171092 | + | 0.985255i | \(0.554730\pi\) | |||||||
\(570\) | −2.84387 | −0.119117 | ||||||||
\(571\) | 25.6290 | 1.07254 | 0.536270 | − | 0.844046i | \(-0.319833\pi\) | ||||
0.536270 | + | 0.844046i | \(0.319833\pi\) | |||||||
\(572\) | 5.04950 | 0.211130 | ||||||||
\(573\) | −10.3592 | −0.432762 | ||||||||
\(574\) | 16.5714 | 0.691677 | ||||||||
\(575\) | 10.7569 | 0.448593 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.16724 | 0.381637 | 0.190819 | − | 0.981625i | \(-0.438886\pi\) | ||||
0.190819 | + | 0.981625i | \(0.438886\pi\) | |||||||
\(578\) | −1.25396 | −0.0521579 | ||||||||
\(579\) | 18.0661 | 0.750801 | ||||||||
\(580\) | −3.41212 | −0.141681 | ||||||||
\(581\) | 38.4833 | 1.59656 | ||||||||
\(582\) | 15.4982 | 0.642421 | ||||||||
\(583\) | −6.43172 | −0.266374 | ||||||||
\(584\) | 8.28463 | 0.342820 | ||||||||
\(585\) | 2.58633 | 0.106931 | ||||||||
\(586\) | 14.5669 | 0.601753 | ||||||||
\(587\) | 37.5871 | 1.55139 | 0.775693 | − | 0.631110i | \(-0.217400\pi\) | ||||
0.775693 | + | 0.631110i | \(0.217400\pi\) | |||||||
\(588\) | −3.65261 | −0.150631 | ||||||||
\(589\) | 10.1193 | 0.416960 | ||||||||
\(590\) | 1.51358 | 0.0623132 | ||||||||
\(591\) | 16.6620 | 0.685382 | ||||||||
\(592\) | −8.79533 | −0.361486 | ||||||||
\(593\) | 19.0589 | 0.782654 | 0.391327 | − | 0.920252i | \(-0.372016\pi\) | ||||
0.391327 | + | 0.920252i | \(0.372016\pi\) | |||||||
\(594\) | 5.04950 | 0.207184 | ||||||||
\(595\) | −33.4963 | −1.37322 | ||||||||
\(596\) | −19.9344 | −0.816545 | ||||||||
\(597\) | 8.32966 | 0.340910 | ||||||||
\(598\) | −6.36847 | −0.260426 | ||||||||
\(599\) | −22.5483 | −0.921298 | −0.460649 | − | 0.887582i | \(-0.652383\pi\) | ||||
−0.460649 | + | 0.887582i | \(0.652383\pi\) | |||||||
\(600\) | −1.68909 | −0.0689567 | ||||||||
\(601\) | −38.7686 | −1.58141 | −0.790703 | − | 0.612200i | \(-0.790285\pi\) | ||||
−0.790703 | + | 0.612200i | \(0.790285\pi\) | |||||||
\(602\) | 11.0548 | 0.450561 | ||||||||
\(603\) | −2.90850 | −0.118443 | ||||||||
\(604\) | 9.91239 | 0.403330 | ||||||||
\(605\) | −37.4952 | −1.52440 | ||||||||
\(606\) | 7.67767 | 0.311884 | ||||||||
\(607\) | 7.15081 | 0.290242 | 0.145121 | − | 0.989414i | \(-0.453643\pi\) | ||||
0.145121 | + | 0.989414i | \(0.453643\pi\) | |||||||
\(608\) | −1.09958 | −0.0445938 | ||||||||
\(609\) | −4.30595 | −0.174486 | ||||||||
\(610\) | 8.08246 | 0.327249 | ||||||||
\(611\) | −2.09076 | −0.0845830 | ||||||||
\(612\) | 3.96813 | 0.160402 | ||||||||
\(613\) | 24.1609 | 0.975848 | 0.487924 | − | 0.872886i | \(-0.337754\pi\) | ||||
0.487924 | + | 0.872886i | \(0.337754\pi\) | |||||||
\(614\) | 5.93484 | 0.239511 | ||||||||
\(615\) | 13.1315 | 0.529514 | ||||||||
\(616\) | −16.4807 | −0.664028 | ||||||||
\(617\) | 13.9374 | 0.561098 | 0.280549 | − | 0.959840i | \(-0.409483\pi\) | ||||
0.280549 | + | 0.959840i | \(0.409483\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −44.1988 | −1.77650 | −0.888250 | − | 0.459360i | \(-0.848079\pi\) | ||||
−0.888250 | + | 0.459360i | \(0.848079\pi\) | |||||||
\(620\) | 23.8018 | 0.955902 | ||||||||
\(621\) | −6.36847 | −0.255558 | ||||||||
\(622\) | 13.6957 | 0.549146 | ||||||||
\(623\) | −7.40947 | −0.296854 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −30.5924 | −1.22370 | ||||||||
\(626\) | −21.2483 | −0.849253 | ||||||||
\(627\) | −5.55233 | −0.221739 | ||||||||
\(628\) | −11.9341 | −0.476222 | ||||||||
\(629\) | −34.9010 | −1.39159 | ||||||||
\(630\) | −8.44134 | −0.336311 | ||||||||
\(631\) | −34.5081 | −1.37375 | −0.686873 | − | 0.726777i | \(-0.741017\pi\) | ||||
−0.686873 | + | 0.726777i | \(0.741017\pi\) | |||||||
\(632\) | −6.38385 | −0.253936 | ||||||||
\(633\) | 21.5780 | 0.857650 | ||||||||
\(634\) | −26.2038 | −1.04069 | ||||||||
\(635\) | −48.3407 | −1.91834 | ||||||||
\(636\) | −1.27373 | −0.0505068 | ||||||||
\(637\) | −3.65261 | −0.144722 | ||||||||
\(638\) | −6.66177 | −0.263742 | ||||||||
\(639\) | −1.22777 | −0.0485698 | ||||||||
\(640\) | −2.58633 | −0.102234 | ||||||||
\(641\) | −6.91448 | −0.273106 | −0.136553 | − | 0.990633i | \(-0.543602\pi\) | ||||
−0.136553 | + | 0.990633i | \(0.543602\pi\) | |||||||
\(642\) | 20.5151 | 0.809666 | ||||||||
\(643\) | −1.21092 | −0.0477541 | −0.0238771 | − | 0.999715i | \(-0.507601\pi\) | ||||
−0.0238771 | + | 0.999715i | \(0.507601\pi\) | |||||||
\(644\) | 20.7856 | 0.819068 | ||||||||
\(645\) | 8.76006 | 0.344927 | ||||||||
\(646\) | −4.36327 | −0.171671 | ||||||||
\(647\) | 28.9173 | 1.13686 | 0.568429 | − | 0.822733i | \(-0.307552\pi\) | ||||
0.568429 | + | 0.822733i | \(0.307552\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.95509 | 0.115998 | ||||||||
\(650\) | −1.68909 | −0.0662514 | ||||||||
\(651\) | 30.0368 | 1.17724 | ||||||||
\(652\) | −16.2967 | −0.638228 | ||||||||
\(653\) | −9.25548 | −0.362195 | −0.181097 | − | 0.983465i | \(-0.557965\pi\) | ||||
−0.181097 | + | 0.983465i | \(0.557965\pi\) | |||||||
\(654\) | −1.38576 | −0.0541876 | ||||||||
\(655\) | −13.1220 | −0.512719 | ||||||||
\(656\) | 5.07728 | 0.198235 | ||||||||
\(657\) | 8.28463 | 0.323214 | ||||||||
\(658\) | 6.82389 | 0.266023 | ||||||||
\(659\) | 2.44040 | 0.0950644 | 0.0475322 | − | 0.998870i | \(-0.484864\pi\) | ||||
0.0475322 | + | 0.998870i | \(0.484864\pi\) | |||||||
\(660\) | −13.0597 | −0.508347 | ||||||||
\(661\) | −33.4088 | −1.29945 | −0.649725 | − | 0.760169i | \(-0.725116\pi\) | ||||
−0.649725 | + | 0.760169i | \(0.725116\pi\) | |||||||
\(662\) | −8.67449 | −0.337144 | ||||||||
\(663\) | 3.96813 | 0.154109 | ||||||||
\(664\) | 11.7908 | 0.457573 | ||||||||
\(665\) | 9.28192 | 0.359938 | ||||||||
\(666\) | −8.79533 | −0.340812 | ||||||||
\(667\) | 8.40186 | 0.325321 | ||||||||
\(668\) | −1.14380 | −0.0442549 | ||||||||
\(669\) | 25.7402 | 0.995175 | ||||||||
\(670\) | 7.52232 | 0.290613 | ||||||||
\(671\) | 15.7801 | 0.609183 | ||||||||
\(672\) | −3.26383 | −0.125905 | ||||||||
\(673\) | 7.91974 | 0.305284 | 0.152642 | − | 0.988282i | \(-0.451222\pi\) | ||||
0.152642 | + | 0.988282i | \(0.451222\pi\) | |||||||
\(674\) | −2.76207 | −0.106391 | ||||||||
\(675\) | −1.68909 | −0.0650130 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 18.0533 | 0.693844 | 0.346922 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346922 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(678\) | 10.3227 | 0.396439 | ||||||||
\(679\) | −50.5835 | −1.94122 | ||||||||
\(680\) | −10.2629 | −0.393563 | ||||||||
\(681\) | 4.56547 | 0.174949 | ||||||||
\(682\) | 46.4702 | 1.77944 | ||||||||
\(683\) | −17.5773 | −0.672575 | −0.336287 | − | 0.941759i | \(-0.609171\pi\) | ||||
−0.336287 | + | 0.941759i | \(0.609171\pi\) | |||||||
\(684\) | −1.09958 | −0.0420435 | ||||||||
\(685\) | −23.1028 | −0.882711 | ||||||||
\(686\) | −10.9253 | −0.417131 | ||||||||
\(687\) | 4.72707 | 0.180349 | ||||||||
\(688\) | 3.38706 | 0.129131 | ||||||||
\(689\) | −1.27373 | −0.0485253 | ||||||||
\(690\) | 16.4709 | 0.627038 | ||||||||
\(691\) | 35.8248 | 1.36284 | 0.681421 | − | 0.731892i | \(-0.261362\pi\) | ||||
0.681421 | + | 0.731892i | \(0.261362\pi\) | |||||||
\(692\) | −7.53776 | −0.286543 | ||||||||
\(693\) | −16.4807 | −0.626052 | ||||||||
\(694\) | 0.174289 | 0.00661591 | ||||||||
\(695\) | 20.4349 | 0.775139 | ||||||||
\(696\) | −1.31929 | −0.0500076 | ||||||||
\(697\) | 20.1473 | 0.763134 | ||||||||
\(698\) | −15.0994 | −0.571522 | ||||||||
\(699\) | −2.72230 | −0.102967 | ||||||||
\(700\) | 5.51290 | 0.208368 | ||||||||
\(701\) | −32.3796 | −1.22296 | −0.611480 | − | 0.791260i | \(-0.709425\pi\) | ||||
−0.611480 | + | 0.791260i | \(0.709425\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 9.67116 | 0.364755 | ||||||||
\(704\) | −5.04950 | −0.190310 | ||||||||
\(705\) | 5.40739 | 0.203654 | ||||||||
\(706\) | −15.6514 | −0.589048 | ||||||||
\(707\) | −25.0586 | −0.942427 | ||||||||
\(708\) | 0.585224 | 0.0219941 | ||||||||
\(709\) | −15.6976 | −0.589536 | −0.294768 | − | 0.955569i | \(-0.595242\pi\) | ||||
−0.294768 | + | 0.955569i | \(0.595242\pi\) | |||||||
\(710\) | 3.17542 | 0.119171 | ||||||||
\(711\) | −6.38385 | −0.239413 | ||||||||
\(712\) | −2.27017 | −0.0850784 | ||||||||
\(713\) | −58.6085 | −2.19491 | ||||||||
\(714\) | −12.9513 | −0.484691 | ||||||||
\(715\) | −13.0597 | −0.488404 | ||||||||
\(716\) | −10.9526 | −0.409319 | ||||||||
\(717\) | 3.50420 | 0.130867 | ||||||||
\(718\) | −1.43312 | −0.0534834 | ||||||||
\(719\) | −7.74491 | −0.288836 | −0.144418 | − | 0.989517i | \(-0.546131\pi\) | ||||
−0.144418 | + | 0.989517i | \(0.546131\pi\) | |||||||
\(720\) | −2.58633 | −0.0963867 | ||||||||
\(721\) | 3.26383 | 0.121552 | ||||||||
\(722\) | −17.7909 | −0.662110 | ||||||||
\(723\) | −5.54442 | −0.206199 | ||||||||
\(724\) | 9.46537 | 0.351778 | ||||||||
\(725\) | 2.22840 | 0.0827606 | ||||||||
\(726\) | −14.4975 | −0.538052 | ||||||||
\(727\) | 5.63394 | 0.208951 | 0.104476 | − | 0.994527i | \(-0.466684\pi\) | ||||
0.104476 | + | 0.994527i | \(0.466684\pi\) | |||||||
\(728\) | −3.26383 | −0.120966 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.4268 | −0.793040 | ||||||||
\(731\) | 13.4403 | 0.497108 | ||||||||
\(732\) | 3.12507 | 0.115506 | ||||||||
\(733\) | −6.82775 | −0.252189 | −0.126094 | − | 0.992018i | \(-0.540244\pi\) | ||||
−0.126094 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(734\) | −14.5873 | −0.538427 | ||||||||
\(735\) | 9.44685 | 0.348452 | ||||||||
\(736\) | 6.36847 | 0.234745 | ||||||||
\(737\) | 14.6865 | 0.540983 | ||||||||
\(738\) | 5.07728 | 0.186897 | ||||||||
\(739\) | 42.6127 | 1.56753 | 0.783766 | − | 0.621056i | \(-0.213296\pi\) | ||||
0.783766 | + | 0.621056i | \(0.213296\pi\) | |||||||
\(740\) | 22.7476 | 0.836218 | ||||||||
\(741\) | −1.09958 | −0.0403941 | ||||||||
\(742\) | 4.15725 | 0.152617 | ||||||||
\(743\) | −28.8400 | −1.05804 | −0.529019 | − | 0.848610i | \(-0.677440\pi\) | ||||
−0.529019 | + | 0.848610i | \(0.677440\pi\) | |||||||
\(744\) | 9.20293 | 0.337396 | ||||||||
\(745\) | 51.5569 | 1.88890 | ||||||||
\(746\) | 22.4462 | 0.821814 | ||||||||
\(747\) | 11.7908 | 0.431404 | ||||||||
\(748\) | −20.0371 | −0.732628 | ||||||||
\(749\) | −66.9578 | −2.44659 | ||||||||
\(750\) | −8.56310 | −0.312680 | ||||||||
\(751\) | −5.01222 | −0.182899 | −0.0914493 | − | 0.995810i | \(-0.529150\pi\) | ||||
−0.0914493 | + | 0.995810i | \(0.529150\pi\) | |||||||
\(752\) | 2.09076 | 0.0762421 | ||||||||
\(753\) | −20.1646 | −0.734839 | ||||||||
\(754\) | −1.31929 | −0.0480458 | ||||||||
\(755\) | −25.6367 | −0.933015 | ||||||||
\(756\) | −3.26383 | −0.118704 | ||||||||
\(757\) | −20.1426 | −0.732097 | −0.366048 | − | 0.930596i | \(-0.619290\pi\) | ||||
−0.366048 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(758\) | 22.1475 | 0.804434 | ||||||||
\(759\) | 32.1576 | 1.16725 | ||||||||
\(760\) | 2.84387 | 0.103158 | ||||||||
\(761\) | 31.1012 | 1.12742 | 0.563708 | − | 0.825974i | \(-0.309374\pi\) | ||||
0.563708 | + | 0.825974i | \(0.309374\pi\) | |||||||
\(762\) | −18.6909 | −0.677098 | ||||||||
\(763\) | 4.52290 | 0.163740 | ||||||||
\(764\) | 10.3592 | 0.374783 | ||||||||
\(765\) | −10.2629 | −0.371055 | ||||||||
\(766\) | −25.4503 | −0.919556 | ||||||||
\(767\) | 0.585224 | 0.0211312 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 15.6768 | 0.565320 | 0.282660 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282660 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(770\) | 42.6246 | 1.53608 | ||||||||
\(771\) | 6.76155 | 0.243511 | ||||||||
\(772\) | −18.0661 | −0.650213 | ||||||||
\(773\) | −17.2048 | −0.618814 | −0.309407 | − | 0.950930i | \(-0.600131\pi\) | ||||
−0.309407 | + | 0.950930i | \(0.600131\pi\) | |||||||
\(774\) | 3.38706 | 0.121746 | ||||||||
\(775\) | −15.5445 | −0.558376 | ||||||||
\(776\) | −15.4982 | −0.556353 | ||||||||
\(777\) | 28.7065 | 1.02984 | ||||||||
\(778\) | 35.4634 | 1.27143 | ||||||||
\(779\) | −5.58288 | −0.200027 | ||||||||
\(780\) | −2.58633 | −0.0926054 | ||||||||
\(781\) | 6.19963 | 0.221840 | ||||||||
\(782\) | 25.2709 | 0.903685 | ||||||||
\(783\) | −1.31929 | −0.0471476 | ||||||||
\(784\) | 3.65261 | 0.130450 | ||||||||
\(785\) | 30.8654 | 1.10163 | ||||||||
\(786\) | −5.07360 | −0.180969 | ||||||||
\(787\) | −6.53585 | −0.232978 | −0.116489 | − | 0.993192i | \(-0.537164\pi\) | ||||
−0.116489 | + | 0.993192i | \(0.537164\pi\) | |||||||
\(788\) | −16.6620 | −0.593558 | ||||||||
\(789\) | 0.821275 | 0.0292381 | ||||||||
\(790\) | 16.5107 | 0.587425 | ||||||||
\(791\) | −33.6914 | −1.19793 | ||||||||
\(792\) | −5.04950 | −0.179426 | ||||||||
\(793\) | 3.12507 | 0.110975 | ||||||||
\(794\) | −22.8936 | −0.812463 | ||||||||
\(795\) | 3.29429 | 0.116836 | ||||||||
\(796\) | −8.32966 | −0.295237 | ||||||||
\(797\) | −38.2429 | −1.35463 | −0.677317 | − | 0.735691i | \(-0.736857\pi\) | ||||
−0.677317 | + | 0.735691i | \(0.736857\pi\) | |||||||
\(798\) | 3.58884 | 0.127044 | ||||||||
\(799\) | 8.29640 | 0.293505 | ||||||||
\(800\) | 1.68909 | 0.0597182 | ||||||||
\(801\) | −2.27017 | −0.0802126 | ||||||||
\(802\) | 4.12648 | 0.145711 | ||||||||
\(803\) | −41.8333 | −1.47626 | ||||||||
\(804\) | 2.90850 | 0.102575 | ||||||||
\(805\) | −53.7584 | −1.89473 | ||||||||
\(806\) | 9.20293 | 0.324159 | ||||||||
\(807\) | −30.2037 | −1.06322 | ||||||||
\(808\) | −7.67767 | −0.270099 | ||||||||
\(809\) | −8.21963 | −0.288987 | −0.144493 | − | 0.989506i | \(-0.546155\pi\) | ||||
−0.144493 | + | 0.989506i | \(0.546155\pi\) | |||||||
\(810\) | −2.58633 | −0.0908743 | ||||||||
\(811\) | 30.0048 | 1.05361 | 0.526805 | − | 0.849986i | \(-0.323390\pi\) | ||||
0.526805 | + | 0.849986i | \(0.323390\pi\) | |||||||
\(812\) | 4.30595 | 0.151109 | ||||||||
\(813\) | 11.3371 | 0.397610 | ||||||||
\(814\) | 44.4120 | 1.55664 | ||||||||
\(815\) | 42.1486 | 1.47640 | ||||||||
\(816\) | −3.96813 | −0.138912 | ||||||||
\(817\) | −3.72435 | −0.130298 | ||||||||
\(818\) | 29.2954 | 1.02429 | ||||||||
\(819\) | −3.26383 | −0.114048 | ||||||||
\(820\) | −13.1315 | −0.458572 | ||||||||
\(821\) | 8.96030 | 0.312717 | 0.156358 | − | 0.987700i | \(-0.450025\pi\) | ||||
0.156358 | + | 0.987700i | \(0.450025\pi\) | |||||||
\(822\) | −8.93266 | −0.311562 | ||||||||
\(823\) | −1.03466 | −0.0360661 | −0.0180331 | − | 0.999837i | \(-0.505740\pi\) | ||||
−0.0180331 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 8.52905 | 0.296943 | ||||||||
\(826\) | −1.91008 | −0.0664600 | ||||||||
\(827\) | −19.4171 | −0.675197 | −0.337599 | − | 0.941290i | \(-0.609615\pi\) | ||||
−0.337599 | + | 0.941290i | \(0.609615\pi\) | |||||||
\(828\) | 6.36847 | 0.221320 | ||||||||
\(829\) | 32.8890 | 1.14228 | 0.571141 | − | 0.820852i | \(-0.306501\pi\) | ||||
0.571141 | + | 0.820852i | \(0.306501\pi\) | |||||||
\(830\) | −30.4950 | −1.05850 | ||||||||
\(831\) | −21.7770 | −0.755436 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 14.4940 | 0.502188 | ||||||||
\(834\) | 7.90112 | 0.273593 | ||||||||
\(835\) | 2.95824 | 0.102374 | ||||||||
\(836\) | 5.55233 | 0.192031 | ||||||||
\(837\) | 9.20293 | 0.318100 | ||||||||
\(838\) | −0.0991300 | −0.00342439 | ||||||||
\(839\) | 42.0324 | 1.45112 | 0.725560 | − | 0.688158i | \(-0.241581\pi\) | ||||
0.725560 | + | 0.688158i | \(0.241581\pi\) | |||||||
\(840\) | 8.44134 | 0.291254 | ||||||||
\(841\) | −27.2595 | −0.939982 | ||||||||
\(842\) | 16.8298 | 0.579994 | ||||||||
\(843\) | 22.7937 | 0.785057 | ||||||||
\(844\) | −21.5780 | −0.742747 | ||||||||
\(845\) | −2.58633 | −0.0889723 | ||||||||
\(846\) | 2.09076 | 0.0718818 | ||||||||
\(847\) | 47.3174 | 1.62584 | ||||||||
\(848\) | 1.27373 | 0.0437402 | ||||||||
\(849\) | 19.3591 | 0.664404 | ||||||||
\(850\) | 6.70251 | 0.229894 | ||||||||
\(851\) | −56.0128 | −1.92009 | ||||||||
\(852\) | 1.22777 | 0.0420627 | ||||||||
\(853\) | −48.9872 | −1.67729 | −0.838644 | − | 0.544679i | \(-0.816651\pi\) | ||||
−0.838644 | + | 0.544679i | \(0.816651\pi\) | |||||||
\(854\) | −10.1997 | −0.349027 | ||||||||
\(855\) | 2.84387 | 0.0972583 | ||||||||
\(856\) | −20.5151 | −0.701191 | ||||||||
\(857\) | 3.80196 | 0.129873 | 0.0649363 | − | 0.997889i | \(-0.479316\pi\) | ||||
0.0649363 | + | 0.997889i | \(0.479316\pi\) | |||||||
\(858\) | −5.04950 | −0.172387 | ||||||||
\(859\) | 37.0815 | 1.26520 | 0.632602 | − | 0.774477i | \(-0.281987\pi\) | ||||
0.632602 | + | 0.774477i | \(0.281987\pi\) | |||||||
\(860\) | −8.76006 | −0.298715 | ||||||||
\(861\) | −16.5714 | −0.564752 | ||||||||
\(862\) | −19.7165 | −0.671545 | ||||||||
\(863\) | 38.0451 | 1.29507 | 0.647535 | − | 0.762035i | \(-0.275800\pi\) | ||||
0.647535 | + | 0.762035i | \(0.275800\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 19.4951 | 0.662854 | ||||||||
\(866\) | 1.07818 | 0.0366382 | ||||||||
\(867\) | 1.25396 | 0.0425867 | ||||||||
\(868\) | −30.0368 | −1.01952 | ||||||||
\(869\) | 32.2353 | 1.09351 | ||||||||
\(870\) | 3.41212 | 0.115682 | ||||||||
\(871\) | 2.90850 | 0.0985507 | ||||||||
\(872\) | 1.38576 | 0.0469279 | ||||||||
\(873\) | −15.4982 | −0.524534 | ||||||||
\(874\) | −7.00264 | −0.236868 | ||||||||
\(875\) | 27.9486 | 0.944834 | ||||||||
\(876\) | −8.28463 | −0.279912 | ||||||||
\(877\) | 6.54738 | 0.221089 | 0.110545 | − | 0.993871i | \(-0.464740\pi\) | ||||
0.110545 | + | 0.993871i | \(0.464740\pi\) | |||||||
\(878\) | −30.2389 | −1.02051 | ||||||||
\(879\) | −14.5669 | −0.491329 | ||||||||
\(880\) | 13.0597 | 0.440241 | ||||||||
\(881\) | −21.9076 | −0.738087 | −0.369043 | − | 0.929412i | \(-0.620315\pi\) | ||||
−0.369043 | + | 0.929412i | \(0.620315\pi\) | |||||||
\(882\) | 3.65261 | 0.122990 | ||||||||
\(883\) | 42.2700 | 1.42250 | 0.711249 | − | 0.702940i | \(-0.248130\pi\) | ||||
0.711249 | + | 0.702940i | \(0.248130\pi\) | |||||||
\(884\) | −3.96813 | −0.133463 | ||||||||
\(885\) | −1.51358 | −0.0508785 | ||||||||
\(886\) | −8.66943 | −0.291255 | ||||||||
\(887\) | 43.9327 | 1.47512 | 0.737558 | − | 0.675283i | \(-0.235979\pi\) | ||||
0.737558 | + | 0.675283i | \(0.235979\pi\) | |||||||
\(888\) | 8.79533 | 0.295152 | ||||||||
\(889\) | 61.0038 | 2.04600 | ||||||||
\(890\) | 5.87141 | 0.196810 | ||||||||
\(891\) | −5.04950 | −0.169165 | ||||||||
\(892\) | −25.7402 | −0.861847 | ||||||||
\(893\) | −2.29895 | −0.0769316 | ||||||||
\(894\) | 19.9344 | 0.666706 | ||||||||
\(895\) | 28.3271 | 0.946869 | ||||||||
\(896\) | 3.26383 | 0.109037 | ||||||||
\(897\) | 6.36847 | 0.212637 | ||||||||
\(898\) | 3.28847 | 0.109738 | ||||||||
\(899\) | −12.1413 | −0.404936 | ||||||||
\(900\) | 1.68909 | 0.0563029 | ||||||||
\(901\) | 5.05433 | 0.168384 | ||||||||
\(902\) | −25.6378 | −0.853644 | ||||||||
\(903\) | −11.0548 | −0.367881 | ||||||||
\(904\) | −10.3227 | −0.343326 | ||||||||
\(905\) | −24.4805 | −0.813761 | ||||||||
\(906\) | −9.91239 | −0.329317 | ||||||||
\(907\) | −3.52779 | −0.117138 | −0.0585691 | − | 0.998283i | \(-0.518654\pi\) | ||||
−0.0585691 | + | 0.998283i | \(0.518654\pi\) | |||||||
\(908\) | −4.56547 | −0.151510 | ||||||||
\(909\) | −7.67767 | −0.254652 | ||||||||
\(910\) | 8.44134 | 0.279828 | ||||||||
\(911\) | −20.9171 | −0.693016 | −0.346508 | − | 0.938047i | \(-0.612633\pi\) | ||||
−0.346508 | + | 0.938047i | \(0.612633\pi\) | |||||||
\(912\) | 1.09958 | 0.0364107 | ||||||||
\(913\) | −59.5379 | −1.97042 | ||||||||
\(914\) | −37.8667 | −1.25252 | ||||||||
\(915\) | −8.08246 | −0.267198 | ||||||||
\(916\) | −4.72707 | −0.156187 | ||||||||
\(917\) | 16.5594 | 0.546839 | ||||||||
\(918\) | −3.96813 | −0.130968 | ||||||||
\(919\) | 29.1550 | 0.961735 | 0.480868 | − | 0.876793i | \(-0.340322\pi\) | ||||
0.480868 | + | 0.876793i | \(0.340322\pi\) | |||||||
\(920\) | −16.4709 | −0.543031 | ||||||||
\(921\) | −5.93484 | −0.195560 | ||||||||
\(922\) | −14.6597 | −0.482792 | ||||||||
\(923\) | 1.22777 | 0.0404126 | ||||||||
\(924\) | 16.4807 | 0.542177 | ||||||||
\(925\) | −14.8561 | −0.488464 | ||||||||
\(926\) | −17.1345 | −0.563073 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 1.31929 | 0.0433079 | ||||||||
\(929\) | 32.5406 | 1.06762 | 0.533811 | − | 0.845604i | \(-0.320759\pi\) | ||||
0.533811 | + | 0.845604i | \(0.320759\pi\) | |||||||
\(930\) | −23.8018 | −0.780491 | ||||||||
\(931\) | −4.01634 | −0.131630 | ||||||||
\(932\) | 2.72230 | 0.0891720 | ||||||||
\(933\) | −13.6957 | −0.448376 | ||||||||
\(934\) | 10.8737 | 0.355797 | ||||||||
\(935\) | 51.8224 | 1.69477 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 18.2879 | 0.597440 | 0.298720 | − | 0.954341i | \(-0.403440\pi\) | ||||
0.298720 | + | 0.954341i | \(0.403440\pi\) | |||||||
\(938\) | −9.49285 | −0.309953 | ||||||||
\(939\) | 21.2483 | 0.693413 | ||||||||
\(940\) | −5.40739 | −0.176369 | ||||||||
\(941\) | −1.18747 | −0.0387103 | −0.0193551 | − | 0.999813i | \(-0.506161\pi\) | ||||
−0.0193551 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(942\) | 11.9341 | 0.388833 | ||||||||
\(943\) | 32.3345 | 1.05296 | ||||||||
\(944\) | −0.585224 | −0.0190474 | ||||||||
\(945\) | 8.44134 | 0.274597 | ||||||||
\(946\) | −17.1030 | −0.556066 | ||||||||
\(947\) | −34.0318 | −1.10589 | −0.552943 | − | 0.833219i | \(-0.686495\pi\) | ||||
−0.552943 | + | 0.833219i | \(0.686495\pi\) | |||||||
\(948\) | 6.38385 | 0.207338 | ||||||||
\(949\) | −8.28463 | −0.268930 | ||||||||
\(950\) | −1.85728 | −0.0602583 | ||||||||
\(951\) | 26.2038 | 0.849716 | ||||||||
\(952\) | 12.9513 | 0.419754 | ||||||||
\(953\) | −20.1190 | −0.651718 | −0.325859 | − | 0.945418i | \(-0.605654\pi\) | ||||
−0.325859 | + | 0.945418i | \(0.605654\pi\) | |||||||
\(954\) | 1.27373 | 0.0412386 | ||||||||
\(955\) | −26.7923 | −0.866978 | ||||||||
\(956\) | −3.50420 | −0.113334 | ||||||||
\(957\) | 6.66177 | 0.215344 | ||||||||
\(958\) | −0.456662 | −0.0147541 | ||||||||
\(959\) | 29.1547 | 0.941455 | ||||||||
\(960\) | 2.58633 | 0.0834733 | ||||||||
\(961\) | 53.6939 | 1.73206 | ||||||||
\(962\) | 8.79533 | 0.283573 | ||||||||
\(963\) | −20.5151 | −0.661089 | ||||||||
\(964\) | 5.54442 | 0.178574 | ||||||||
\(965\) | 46.7248 | 1.50413 | ||||||||
\(966\) | −20.7856 | −0.668766 | ||||||||
\(967\) | 28.8891 | 0.929011 | 0.464505 | − | 0.885570i | \(-0.346232\pi\) | ||||
0.464505 | + | 0.885570i | \(0.346232\pi\) | |||||||
\(968\) | 14.4975 | 0.465967 | ||||||||
\(969\) | 4.36327 | 0.140168 | ||||||||
\(970\) | 40.0834 | 1.28700 | ||||||||
\(971\) | −9.05129 | −0.290470 | −0.145235 | − | 0.989397i | \(-0.546394\pi\) | ||||
−0.145235 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −25.7879 | −0.826724 | ||||||||
\(974\) | −19.4436 | −0.623013 | ||||||||
\(975\) | 1.68909 | 0.0540941 | ||||||||
\(976\) | −3.12507 | −0.100031 | ||||||||
\(977\) | 16.1280 | 0.515980 | 0.257990 | − | 0.966148i | \(-0.416940\pi\) | ||||
0.257990 | + | 0.966148i | \(0.416940\pi\) | |||||||
\(978\) | 16.2967 | 0.521111 | ||||||||
\(979\) | 11.4633 | 0.366367 | ||||||||
\(980\) | −9.44685 | −0.301768 | ||||||||
\(981\) | 1.38576 | 0.0442440 | ||||||||
\(982\) | −37.6264 | −1.20071 | ||||||||
\(983\) | 43.7312 | 1.39481 | 0.697404 | − | 0.716678i | \(-0.254338\pi\) | ||||
0.697404 | + | 0.716678i | \(0.254338\pi\) | |||||||
\(984\) | −5.07728 | −0.161858 | ||||||||
\(985\) | 43.0933 | 1.37307 | ||||||||
\(986\) | 5.23512 | 0.166720 | ||||||||
\(987\) | −6.82389 | −0.217207 | ||||||||
\(988\) | 1.09958 | 0.0349823 | ||||||||
\(989\) | 21.5704 | 0.685899 | ||||||||
\(990\) | 13.0597 | 0.415063 | ||||||||
\(991\) | 22.8528 | 0.725942 | 0.362971 | − | 0.931800i | \(-0.381762\pi\) | ||||
0.362971 | + | 0.931800i | \(0.381762\pi\) | |||||||
\(992\) | −9.20293 | −0.292193 | ||||||||
\(993\) | 8.67449 | 0.275277 | ||||||||
\(994\) | −4.00724 | −0.127102 | ||||||||
\(995\) | 21.5432 | 0.682966 | ||||||||
\(996\) | −11.7908 | −0.373607 | ||||||||
\(997\) | 21.0694 | 0.667276 | 0.333638 | − | 0.942701i | \(-0.391724\pi\) | ||||
0.333638 | + | 0.942701i | \(0.391724\pi\) | |||||||
\(998\) | 22.5980 | 0.715328 | ||||||||
\(999\) | 8.79533 | 0.278272 |
(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 | 8034.2.a.u.1.3 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.u.1.3 | ✓ | 11 | 1.1 | even | 1 | trivial |