Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.580017.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 7x^{3} - 4x^{2} + 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.470042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.470042 | 0.332370 | 0.166185 | − | 0.986095i | \(-0.446855\pi\) | ||||
0.166185 | + | 0.986095i | \(0.446855\pi\) | |||||||
\(3\) | −0.577925 | −0.333665 | −0.166832 | − | 0.985985i | \(-0.553354\pi\) | ||||
−0.166832 | + | 0.985985i | \(0.553354\pi\) | |||||||
\(4\) | −1.77906 | −0.889530 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.271649 | −0.110900 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.77632 | −0.628023 | ||||||||
\(9\) | −2.66600 | −0.888668 | ||||||||
\(10\) | −0.470042 | −0.148640 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.02816 | 0.296805 | ||||||||
\(13\) | −1.19839 | −0.332374 | −0.166187 | − | 0.986094i | \(-0.553146\pi\) | ||||
−0.166187 | + | 0.986094i | \(0.553146\pi\) | |||||||
\(14\) | 0.470042 | 0.125624 | ||||||||
\(15\) | 0.577925 | 0.149220 | ||||||||
\(16\) | 2.72318 | 0.680794 | ||||||||
\(17\) | 1.08534 | 0.263233 | 0.131616 | − | 0.991301i | \(-0.457983\pi\) | ||||
0.131616 | + | 0.991301i | \(0.457983\pi\) | |||||||
\(18\) | −1.25313 | −0.295367 | ||||||||
\(19\) | 6.29189 | 1.44346 | 0.721730 | − | 0.692175i | \(-0.243347\pi\) | ||||
0.721730 | + | 0.692175i | \(0.243347\pi\) | |||||||
\(20\) | 1.77906 | 0.397810 | ||||||||
\(21\) | −0.577925 | −0.126114 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.35986 | −1.32612 | −0.663061 | − | 0.748565i | \(-0.730743\pi\) | ||||
−0.663061 | + | 0.748565i | \(0.730743\pi\) | |||||||
\(24\) | 1.02658 | 0.209549 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.563295 | −0.110471 | ||||||||
\(27\) | 3.27452 | 0.630182 | ||||||||
\(28\) | −1.77906 | −0.336211 | ||||||||
\(29\) | 6.79931 | 1.26260 | 0.631300 | − | 0.775539i | \(-0.282522\pi\) | ||||
0.631300 | + | 0.775539i | \(0.282522\pi\) | |||||||
\(30\) | 0.271649 | 0.0495961 | ||||||||
\(31\) | 9.46531 | 1.70002 | 0.850010 | − | 0.526767i | \(-0.176596\pi\) | ||||
0.850010 | + | 0.526767i | \(0.176596\pi\) | |||||||
\(32\) | 4.83264 | 0.854299 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.510154 | 0.0874906 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.74298 | 0.790497 | ||||||||
\(37\) | −8.49980 | −1.39736 | −0.698680 | − | 0.715435i | \(-0.746229\pi\) | ||||
−0.698680 | + | 0.715435i | \(0.746229\pi\) | |||||||
\(38\) | 2.95746 | 0.479763 | ||||||||
\(39\) | 0.692581 | 0.110902 | ||||||||
\(40\) | 1.77632 | 0.280861 | ||||||||
\(41\) | 9.51571 | 1.48610 | 0.743052 | − | 0.669234i | \(-0.233377\pi\) | ||||
0.743052 | + | 0.669234i | \(0.233377\pi\) | |||||||
\(42\) | −0.271649 | −0.0419163 | ||||||||
\(43\) | −5.07339 | −0.773684 | −0.386842 | − | 0.922146i | \(-0.626434\pi\) | ||||
−0.386842 | + | 0.922146i | \(0.626434\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.66600 | 0.397424 | ||||||||
\(46\) | −2.98940 | −0.440763 | ||||||||
\(47\) | 3.89889 | 0.568712 | 0.284356 | − | 0.958719i | \(-0.408220\pi\) | ||||
0.284356 | + | 0.958719i | \(0.408220\pi\) | |||||||
\(48\) | −1.57379 | −0.227157 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.470042 | 0.0664740 | ||||||||
\(51\) | −0.627242 | −0.0878315 | ||||||||
\(52\) | 2.13201 | 0.295657 | ||||||||
\(53\) | −12.2191 | −1.67842 | −0.839210 | − | 0.543808i | \(-0.816982\pi\) | ||||
−0.839210 | + | 0.543808i | \(0.816982\pi\) | |||||||
\(54\) | 1.53916 | 0.209454 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.77632 | −0.237370 | ||||||||
\(57\) | −3.63624 | −0.481632 | ||||||||
\(58\) | 3.19596 | 0.419650 | ||||||||
\(59\) | −4.91466 | −0.639835 | −0.319917 | − | 0.947445i | \(-0.603655\pi\) | ||||
−0.319917 | + | 0.947445i | \(0.603655\pi\) | |||||||
\(60\) | −1.02816 | −0.132735 | ||||||||
\(61\) | −10.6033 | −1.35762 | −0.678810 | − | 0.734314i | \(-0.737504\pi\) | ||||
−0.678810 | + | 0.734314i | \(0.737504\pi\) | |||||||
\(62\) | 4.44909 | 0.565036 | ||||||||
\(63\) | −2.66600 | −0.335885 | ||||||||
\(64\) | −3.17481 | −0.396851 | ||||||||
\(65\) | 1.19839 | 0.148642 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.09350 | −0.622270 | −0.311135 | − | 0.950366i | \(-0.600709\pi\) | ||||
−0.311135 | + | 0.950366i | \(0.600709\pi\) | |||||||
\(68\) | −1.93088 | −0.234153 | ||||||||
\(69\) | 3.67552 | 0.442481 | ||||||||
\(70\) | −0.470042 | −0.0561808 | ||||||||
\(71\) | −7.24680 | −0.860037 | −0.430019 | − | 0.902820i | \(-0.641493\pi\) | ||||
−0.430019 | + | 0.902820i | \(0.641493\pi\) | |||||||
\(72\) | 4.73567 | 0.558104 | ||||||||
\(73\) | 10.2495 | 1.19962 | 0.599809 | − | 0.800143i | \(-0.295243\pi\) | ||||
0.599809 | + | 0.800143i | \(0.295243\pi\) | |||||||
\(74\) | −3.99527 | −0.464440 | ||||||||
\(75\) | −0.577925 | −0.0667330 | ||||||||
\(76\) | −11.1937 | −1.28400 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.325542 | 0.0368604 | ||||||||
\(79\) | −0.0718642 | −0.00808536 | −0.00404268 | − | 0.999992i | \(-0.501287\pi\) | ||||
−0.00404268 | + | 0.999992i | \(0.501287\pi\) | |||||||
\(80\) | −2.72318 | −0.304460 | ||||||||
\(81\) | 6.10558 | 0.678398 | ||||||||
\(82\) | 4.47278 | 0.493936 | ||||||||
\(83\) | −9.16537 | −1.00603 | −0.503015 | − | 0.864278i | \(-0.667776\pi\) | ||||
−0.503015 | + | 0.864278i | \(0.667776\pi\) | |||||||
\(84\) | 1.02816 | 0.112182 | ||||||||
\(85\) | −1.08534 | −0.117721 | ||||||||
\(86\) | −2.38471 | −0.257149 | ||||||||
\(87\) | −3.92949 | −0.421285 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.20656 | −0.339895 | −0.169947 | − | 0.985453i | \(-0.554360\pi\) | ||||
−0.169947 | + | 0.985453i | \(0.554360\pi\) | |||||||
\(90\) | 1.25313 | 0.132092 | ||||||||
\(91\) | −1.19839 | −0.125626 | ||||||||
\(92\) | 11.3146 | 1.17963 | ||||||||
\(93\) | −5.47024 | −0.567237 | ||||||||
\(94\) | 1.83264 | 0.189023 | ||||||||
\(95\) | −6.29189 | −0.645535 | ||||||||
\(96\) | −2.79290 | −0.285050 | ||||||||
\(97\) | −9.05358 | −0.919252 | −0.459626 | − | 0.888113i | \(-0.652017\pi\) | ||||
−0.459626 | + | 0.888113i | \(0.652017\pi\) | |||||||
\(98\) | 0.470042 | 0.0474814 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.77906 | −0.177906 | ||||||||
\(101\) | −2.41665 | −0.240466 | −0.120233 | − | 0.992746i | \(-0.538364\pi\) | ||||
−0.120233 | + | 0.992746i | \(0.538364\pi\) | |||||||
\(102\) | −0.294830 | −0.0291926 | ||||||||
\(103\) | −13.1214 | −1.29289 | −0.646443 | − | 0.762963i | \(-0.723744\pi\) | ||||
−0.646443 | + | 0.762963i | \(0.723744\pi\) | |||||||
\(104\) | 2.12873 | 0.208739 | ||||||||
\(105\) | 0.577925 | 0.0563997 | ||||||||
\(106\) | −5.74348 | −0.557856 | ||||||||
\(107\) | 13.6316 | 1.31782 | 0.658910 | − | 0.752222i | \(-0.271018\pi\) | ||||
0.658910 | + | 0.752222i | \(0.271018\pi\) | |||||||
\(108\) | −5.82557 | −0.560566 | ||||||||
\(109\) | 7.14569 | 0.684433 | 0.342217 | − | 0.939621i | \(-0.388822\pi\) | ||||
0.342217 | + | 0.939621i | \(0.388822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.91225 | 0.466250 | ||||||||
\(112\) | 2.72318 | 0.257316 | ||||||||
\(113\) | 10.9216 | 1.02742 | 0.513710 | − | 0.857964i | \(-0.328271\pi\) | ||||
0.513710 | + | 0.857964i | \(0.328271\pi\) | |||||||
\(114\) | −1.70919 | −0.160080 | ||||||||
\(115\) | 6.35986 | 0.593060 | ||||||||
\(116\) | −12.0964 | −1.12312 | ||||||||
\(117\) | 3.19492 | 0.295370 | ||||||||
\(118\) | −2.31010 | −0.212662 | ||||||||
\(119\) | 1.08534 | 0.0994926 | ||||||||
\(120\) | −1.02658 | −0.0937133 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.98402 | −0.451232 | ||||||||
\(123\) | −5.49936 | −0.495861 | ||||||||
\(124\) | −16.8394 | −1.51222 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.25313 | −0.111638 | ||||||||
\(127\) | −11.2229 | −0.995872 | −0.497936 | − | 0.867214i | \(-0.665909\pi\) | ||||
−0.497936 | + | 0.867214i | \(0.665909\pi\) | |||||||
\(128\) | −11.1576 | −0.986200 | ||||||||
\(129\) | 2.93204 | 0.258151 | ||||||||
\(130\) | 0.563295 | 0.0494043 | ||||||||
\(131\) | 17.3578 | 1.51656 | 0.758279 | − | 0.651930i | \(-0.226040\pi\) | ||||
0.758279 | + | 0.651930i | \(0.226040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.29189 | 0.545576 | ||||||||
\(134\) | −2.39416 | −0.206824 | ||||||||
\(135\) | −3.27452 | −0.281826 | ||||||||
\(136\) | −1.92790 | −0.165316 | ||||||||
\(137\) | 18.8358 | 1.60925 | 0.804627 | − | 0.593780i | \(-0.202365\pi\) | ||||
0.804627 | + | 0.593780i | \(0.202365\pi\) | |||||||
\(138\) | 1.72765 | 0.147067 | ||||||||
\(139\) | −20.0886 | −1.70390 | −0.851948 | − | 0.523626i | \(-0.824579\pi\) | ||||
−0.851948 | + | 0.523626i | \(0.824579\pi\) | |||||||
\(140\) | 1.77906 | 0.150358 | ||||||||
\(141\) | −2.25327 | −0.189759 | ||||||||
\(142\) | −3.40630 | −0.285851 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.26000 | −0.605000 | ||||||||
\(145\) | −6.79931 | −0.564652 | ||||||||
\(146\) | 4.81772 | 0.398717 | ||||||||
\(147\) | −0.577925 | −0.0476664 | ||||||||
\(148\) | 15.1217 | 1.24299 | ||||||||
\(149\) | −11.3747 | −0.931850 | −0.465925 | − | 0.884824i | \(-0.654278\pi\) | ||||
−0.465925 | + | 0.884824i | \(0.654278\pi\) | |||||||
\(150\) | −0.271649 | −0.0221800 | ||||||||
\(151\) | −12.8036 | −1.04195 | −0.520973 | − | 0.853573i | \(-0.674431\pi\) | ||||
−0.520973 | + | 0.853573i | \(0.674431\pi\) | |||||||
\(152\) | −11.1764 | −0.906526 | ||||||||
\(153\) | −2.89351 | −0.233926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.46531 | −0.760272 | ||||||||
\(156\) | −1.23214 | −0.0986504 | ||||||||
\(157\) | 8.23103 | 0.656908 | 0.328454 | − | 0.944520i | \(-0.393472\pi\) | ||||
0.328454 | + | 0.944520i | \(0.393472\pi\) | |||||||
\(158\) | −0.0337792 | −0.00268733 | ||||||||
\(159\) | 7.06171 | 0.560030 | ||||||||
\(160\) | −4.83264 | −0.382054 | ||||||||
\(161\) | −6.35986 | −0.501227 | ||||||||
\(162\) | 2.86988 | 0.225479 | ||||||||
\(163\) | 6.30685 | 0.493991 | 0.246995 | − | 0.969017i | \(-0.420557\pi\) | ||||
0.246995 | + | 0.969017i | \(0.420557\pi\) | |||||||
\(164\) | −16.9290 | −1.32193 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.30811 | −0.334374 | ||||||||
\(167\) | −9.35034 | −0.723551 | −0.361776 | − | 0.932265i | \(-0.617829\pi\) | ||||
−0.361776 | + | 0.932265i | \(0.617829\pi\) | |||||||
\(168\) | 1.02658 | 0.0792022 | ||||||||
\(169\) | −11.5639 | −0.889527 | ||||||||
\(170\) | −0.510154 | −0.0391270 | ||||||||
\(171\) | −16.7742 | −1.28276 | ||||||||
\(172\) | 9.02586 | 0.688216 | ||||||||
\(173\) | −6.98410 | −0.530991 | −0.265495 | − | 0.964112i | \(-0.585536\pi\) | ||||
−0.265495 | + | 0.964112i | \(0.585536\pi\) | |||||||
\(174\) | −1.84702 | −0.140023 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.84031 | 0.213490 | ||||||||
\(178\) | −1.50722 | −0.112971 | ||||||||
\(179\) | 13.0020 | 0.971812 | 0.485906 | − | 0.874011i | \(-0.338490\pi\) | ||||
0.485906 | + | 0.874011i | \(0.338490\pi\) | |||||||
\(180\) | −4.74298 | −0.353521 | ||||||||
\(181\) | −18.2396 | −1.35574 | −0.677871 | − | 0.735181i | \(-0.737097\pi\) | ||||
−0.677871 | + | 0.735181i | \(0.737097\pi\) | |||||||
\(182\) | −0.563295 | −0.0417542 | ||||||||
\(183\) | 6.12793 | 0.452990 | ||||||||
\(184\) | 11.2971 | 0.832836 | ||||||||
\(185\) | 8.49980 | 0.624918 | ||||||||
\(186\) | −2.57124 | −0.188533 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.93636 | −0.505886 | ||||||||
\(189\) | 3.27452 | 0.238186 | ||||||||
\(190\) | −2.95746 | −0.214556 | ||||||||
\(191\) | −14.8793 | −1.07663 | −0.538315 | − | 0.842743i | \(-0.680939\pi\) | ||||
−0.538315 | + | 0.842743i | \(0.680939\pi\) | |||||||
\(192\) | 1.83480 | 0.132415 | ||||||||
\(193\) | 4.87672 | 0.351034 | 0.175517 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175517 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(194\) | −4.25557 | −0.305532 | ||||||||
\(195\) | −0.692581 | −0.0495968 | ||||||||
\(196\) | −1.77906 | −0.127076 | ||||||||
\(197\) | −21.3123 | −1.51844 | −0.759220 | − | 0.650834i | \(-0.774420\pi\) | ||||
−0.759220 | + | 0.650834i | \(0.774420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.08916 | 0.0772085 | 0.0386042 | − | 0.999255i | \(-0.487709\pi\) | ||||
0.0386042 | + | 0.999255i | \(0.487709\pi\) | |||||||
\(200\) | −1.77632 | −0.125605 | ||||||||
\(201\) | 2.94366 | 0.207630 | ||||||||
\(202\) | −1.13593 | −0.0799237 | ||||||||
\(203\) | 6.79931 | 0.477218 | ||||||||
\(204\) | 1.11590 | 0.0781288 | ||||||||
\(205\) | −9.51571 | −0.664606 | ||||||||
\(206\) | −6.16759 | −0.429716 | ||||||||
\(207\) | 16.9554 | 1.17848 | ||||||||
\(208\) | −3.26344 | −0.226279 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.271649 | 0.0187456 | ||||||||
\(211\) | −22.9845 | −1.58232 | −0.791158 | − | 0.611612i | \(-0.790521\pi\) | ||||
−0.791158 | + | 0.611612i | \(0.790521\pi\) | |||||||
\(212\) | 21.7385 | 1.49301 | ||||||||
\(213\) | 4.18811 | 0.286964 | ||||||||
\(214\) | 6.40745 | 0.438004 | ||||||||
\(215\) | 5.07339 | 0.346002 | ||||||||
\(216\) | −5.81659 | −0.395769 | ||||||||
\(217\) | 9.46531 | 0.642547 | ||||||||
\(218\) | 3.35878 | 0.227485 | ||||||||
\(219\) | −5.92346 | −0.400271 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.30066 | −0.0874918 | ||||||||
\(222\) | 2.30896 | 0.154967 | ||||||||
\(223\) | −23.3688 | −1.56489 | −0.782447 | − | 0.622717i | \(-0.786029\pi\) | ||||
−0.782447 | + | 0.622717i | \(0.786029\pi\) | |||||||
\(224\) | 4.83264 | 0.322895 | ||||||||
\(225\) | −2.66600 | −0.177734 | ||||||||
\(226\) | 5.13363 | 0.341484 | ||||||||
\(227\) | −9.26282 | −0.614795 | −0.307398 | − | 0.951581i | \(-0.599458\pi\) | ||||
−0.307398 | + | 0.951581i | \(0.599458\pi\) | |||||||
\(228\) | 6.46909 | 0.428426 | ||||||||
\(229\) | 22.3739 | 1.47851 | 0.739255 | − | 0.673426i | \(-0.235178\pi\) | ||||
0.739255 | + | 0.673426i | \(0.235178\pi\) | |||||||
\(230\) | 2.98940 | 0.197115 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0777 | −0.792942 | ||||||||
\(233\) | −0.300984 | −0.0197181 | −0.00985907 | − | 0.999951i | \(-0.503138\pi\) | ||||
−0.00985907 | + | 0.999951i | \(0.503138\pi\) | |||||||
\(234\) | 1.50175 | 0.0981723 | ||||||||
\(235\) | −3.89889 | −0.254336 | ||||||||
\(236\) | 8.74348 | 0.569152 | ||||||||
\(237\) | 0.0415321 | 0.00269780 | ||||||||
\(238\) | 0.510154 | 0.0330684 | ||||||||
\(239\) | 17.8086 | 1.15194 | 0.575972 | − | 0.817469i | \(-0.304624\pi\) | ||||
0.575972 | + | 0.817469i | \(0.304624\pi\) | |||||||
\(240\) | 1.57379 | 0.101588 | ||||||||
\(241\) | −14.8175 | −0.954480 | −0.477240 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477240 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.3521 | −0.856540 | ||||||||
\(244\) | 18.8640 | 1.20764 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −2.58493 | −0.164809 | ||||||||
\(247\) | −7.54016 | −0.479769 | ||||||||
\(248\) | −16.8134 | −1.06765 | ||||||||
\(249\) | 5.29689 | 0.335677 | ||||||||
\(250\) | −0.470042 | −0.0297281 | ||||||||
\(251\) | 4.92595 | 0.310923 | 0.155462 | − | 0.987842i | \(-0.450313\pi\) | ||||
0.155462 | + | 0.987842i | \(0.450313\pi\) | |||||||
\(252\) | 4.74298 | 0.298780 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.27524 | −0.330998 | ||||||||
\(255\) | 0.627242 | 0.0392794 | ||||||||
\(256\) | 1.10508 | 0.0690674 | ||||||||
\(257\) | 10.6277 | 0.662940 | 0.331470 | − | 0.943466i | \(-0.392455\pi\) | ||||
0.331470 | + | 0.943466i | \(0.392455\pi\) | |||||||
\(258\) | 1.37818 | 0.0858018 | ||||||||
\(259\) | −8.49980 | −0.528152 | ||||||||
\(260\) | −2.13201 | −0.132222 | ||||||||
\(261\) | −18.1270 | −1.12203 | ||||||||
\(262\) | 8.15890 | 0.504059 | ||||||||
\(263\) | −6.62908 | −0.408766 | −0.204383 | − | 0.978891i | \(-0.565519\pi\) | ||||
−0.204383 | + | 0.978891i | \(0.565519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.2191 | 0.750612 | ||||||||
\(266\) | 2.95746 | 0.181333 | ||||||||
\(267\) | 1.85315 | 0.113411 | ||||||||
\(268\) | 9.06165 | 0.553528 | ||||||||
\(269\) | 14.6214 | 0.891480 | 0.445740 | − | 0.895163i | \(-0.352941\pi\) | ||||
0.445740 | + | 0.895163i | \(0.352941\pi\) | |||||||
\(270\) | −1.53916 | −0.0936705 | ||||||||
\(271\) | 5.00420 | 0.303984 | 0.151992 | − | 0.988382i | \(-0.451431\pi\) | ||||
0.151992 | + | 0.988382i | \(0.451431\pi\) | |||||||
\(272\) | 2.95556 | 0.179207 | ||||||||
\(273\) | 0.692581 | 0.0419169 | ||||||||
\(274\) | 8.85364 | 0.534868 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.53897 | −0.393600 | ||||||||
\(277\) | −3.50429 | −0.210552 | −0.105276 | − | 0.994443i | \(-0.533573\pi\) | ||||
−0.105276 | + | 0.994443i | \(0.533573\pi\) | |||||||
\(278\) | −9.44251 | −0.566324 | ||||||||
\(279\) | −25.2345 | −1.51075 | ||||||||
\(280\) | 1.77632 | 0.106155 | ||||||||
\(281\) | 9.42495 | 0.562245 | 0.281123 | − | 0.959672i | \(-0.409293\pi\) | ||||
0.281123 | + | 0.959672i | \(0.409293\pi\) | |||||||
\(282\) | −1.05913 | −0.0630703 | ||||||||
\(283\) | −15.9110 | −0.945812 | −0.472906 | − | 0.881113i | \(-0.656795\pi\) | ||||
−0.472906 | + | 0.881113i | \(0.656795\pi\) | |||||||
\(284\) | 12.8925 | 0.765029 | ||||||||
\(285\) | 3.63624 | 0.215392 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.51571 | 0.561695 | ||||||||
\(288\) | −12.8838 | −0.759188 | ||||||||
\(289\) | −15.8220 | −0.930709 | ||||||||
\(290\) | −3.19596 | −0.187673 | ||||||||
\(291\) | 5.23229 | 0.306722 | ||||||||
\(292\) | −18.2346 | −1.06710 | ||||||||
\(293\) | −15.3574 | −0.897187 | −0.448593 | − | 0.893736i | \(-0.648075\pi\) | ||||
−0.448593 | + | 0.893736i | \(0.648075\pi\) | |||||||
\(294\) | −0.271649 | −0.0158429 | ||||||||
\(295\) | 4.91466 | 0.286143 | ||||||||
\(296\) | 15.0984 | 0.877574 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.34658 | −0.309719 | ||||||||
\(299\) | 7.62161 | 0.440769 | ||||||||
\(300\) | 1.02816 | 0.0593610 | ||||||||
\(301\) | −5.07339 | −0.292425 | ||||||||
\(302\) | −6.01825 | −0.346312 | ||||||||
\(303\) | 1.39664 | 0.0802350 | ||||||||
\(304\) | 17.1339 | 0.982699 | ||||||||
\(305\) | 10.6033 | 0.607146 | ||||||||
\(306\) | −1.36007 | −0.0777501 | ||||||||
\(307\) | 16.0662 | 0.916944 | 0.458472 | − | 0.888709i | \(-0.348397\pi\) | ||||
0.458472 | + | 0.888709i | \(0.348397\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.58315 | 0.431391 | ||||||||
\(310\) | −4.44909 | −0.252692 | ||||||||
\(311\) | 3.67098 | 0.208162 | 0.104081 | − | 0.994569i | \(-0.466810\pi\) | ||||
0.104081 | + | 0.994569i | \(0.466810\pi\) | |||||||
\(312\) | −1.23024 | −0.0696489 | ||||||||
\(313\) | −4.45248 | −0.251669 | −0.125834 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125834 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(314\) | 3.86893 | 0.218336 | ||||||||
\(315\) | 2.66600 | 0.150212 | ||||||||
\(316\) | 0.127851 | 0.00719217 | ||||||||
\(317\) | −22.3020 | −1.25261 | −0.626304 | − | 0.779579i | \(-0.715433\pi\) | ||||
−0.626304 | + | 0.779579i | \(0.715433\pi\) | |||||||
\(318\) | 3.31930 | 0.186137 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.17481 | 0.177477 | ||||||||
\(321\) | −7.87806 | −0.439710 | ||||||||
\(322\) | −2.98940 | −0.166593 | ||||||||
\(323\) | 6.82882 | 0.379966 | ||||||||
\(324\) | −10.8622 | −0.603455 | ||||||||
\(325\) | −1.19839 | −0.0664749 | ||||||||
\(326\) | 2.96449 | 0.164188 | ||||||||
\(327\) | −4.12967 | −0.228371 | ||||||||
\(328\) | −16.9029 | −0.933308 | ||||||||
\(329\) | 3.89889 | 0.214953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.43313 | −0.463527 | −0.231763 | − | 0.972772i | \(-0.574450\pi\) | ||||
−0.231763 | + | 0.972772i | \(0.574450\pi\) | |||||||
\(332\) | 16.3057 | 0.894894 | ||||||||
\(333\) | 22.6605 | 1.24179 | ||||||||
\(334\) | −4.39506 | −0.240487 | ||||||||
\(335\) | 5.09350 | 0.278288 | ||||||||
\(336\) | −1.57379 | −0.0858573 | ||||||||
\(337\) | −30.2983 | −1.65045 | −0.825226 | − | 0.564803i | \(-0.808952\pi\) | ||||
−0.825226 | + | 0.564803i | \(0.808952\pi\) | |||||||
\(338\) | −5.43550 | −0.295652 | ||||||||
\(339\) | −6.31188 | −0.342814 | ||||||||
\(340\) | 1.93088 | 0.104717 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.88459 | −0.426350 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.01195 | 0.485892 | ||||||||
\(345\) | −3.67552 | −0.197883 | ||||||||
\(346\) | −3.28282 | −0.176485 | ||||||||
\(347\) | −1.68714 | −0.0905706 | −0.0452853 | − | 0.998974i | \(-0.514420\pi\) | ||||
−0.0452853 | + | 0.998974i | \(0.514420\pi\) | |||||||
\(348\) | 6.99079 | 0.374746 | ||||||||
\(349\) | 26.2092 | 1.40295 | 0.701474 | − | 0.712695i | \(-0.252526\pi\) | ||||
0.701474 | + | 0.712695i | \(0.252526\pi\) | |||||||
\(350\) | 0.470042 | 0.0251248 | ||||||||
\(351\) | −3.92417 | −0.209456 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.6788 | 0.940948 | 0.470474 | − | 0.882414i | \(-0.344083\pi\) | ||||
0.470474 | + | 0.882414i | \(0.344083\pi\) | |||||||
\(354\) | 1.33506 | 0.0709578 | ||||||||
\(355\) | 7.24680 | 0.384620 | ||||||||
\(356\) | 5.70466 | 0.302346 | ||||||||
\(357\) | −0.627242 | −0.0331972 | ||||||||
\(358\) | 6.11147 | 0.323001 | ||||||||
\(359\) | −7.06393 | −0.372820 | −0.186410 | − | 0.982472i | \(-0.559685\pi\) | ||||
−0.186410 | + | 0.982472i | \(0.559685\pi\) | |||||||
\(360\) | −4.73567 | −0.249592 | ||||||||
\(361\) | 20.5879 | 1.08358 | ||||||||
\(362\) | −8.57340 | −0.450608 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.13201 | 0.111748 | ||||||||
\(365\) | −10.2495 | −0.536486 | ||||||||
\(366\) | 2.88039 | 0.150560 | ||||||||
\(367\) | 9.09662 | 0.474840 | 0.237420 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237420 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(368\) | −17.3190 | −0.902816 | ||||||||
\(369\) | −25.3689 | −1.32065 | ||||||||
\(370\) | 3.99527 | 0.207704 | ||||||||
\(371\) | −12.2191 | −0.634383 | ||||||||
\(372\) | 9.73188 | 0.504574 | ||||||||
\(373\) | −33.9587 | −1.75832 | −0.879158 | − | 0.476531i | \(-0.841894\pi\) | ||||
−0.879158 | + | 0.476531i | \(0.841894\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.577925 | 0.0298439 | ||||||||
\(376\) | −6.92567 | −0.357164 | ||||||||
\(377\) | −8.14824 | −0.419656 | ||||||||
\(378\) | 1.53916 | 0.0791661 | ||||||||
\(379\) | 20.7225 | 1.06445 | 0.532223 | − | 0.846604i | \(-0.321357\pi\) | ||||
0.532223 | + | 0.846604i | \(0.321357\pi\) | |||||||
\(380\) | 11.1937 | 0.574223 | ||||||||
\(381\) | 6.48599 | 0.332288 | ||||||||
\(382\) | −6.99392 | −0.357840 | ||||||||
\(383\) | −17.5943 | −0.899028 | −0.449514 | − | 0.893273i | \(-0.648403\pi\) | ||||
−0.449514 | + | 0.893273i | \(0.648403\pi\) | |||||||
\(384\) | 6.44824 | 0.329060 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.29227 | 0.116673 | ||||||||
\(387\) | 13.5257 | 0.687548 | ||||||||
\(388\) | 16.1069 | 0.817702 | ||||||||
\(389\) | −23.3951 | −1.18618 | −0.593089 | − | 0.805137i | \(-0.702092\pi\) | ||||
−0.593089 | + | 0.805137i | \(0.702092\pi\) | |||||||
\(390\) | −0.325542 | −0.0164845 | ||||||||
\(391\) | −6.90258 | −0.349079 | ||||||||
\(392\) | −1.77632 | −0.0897176 | ||||||||
\(393\) | −10.0315 | −0.506022 | ||||||||
\(394\) | −10.0177 | −0.504684 | ||||||||
\(395\) | 0.0718642 | 0.00361588 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.31381 | 0.316881 | 0.158441 | − | 0.987369i | \(-0.449353\pi\) | ||||
0.158441 | + | 0.987369i | \(0.449353\pi\) | |||||||
\(398\) | 0.511951 | 0.0256618 | ||||||||
\(399\) | −3.63624 | −0.182040 | ||||||||
\(400\) | 2.72318 | 0.136159 | ||||||||
\(401\) | −29.4882 | −1.47257 | −0.736284 | − | 0.676672i | \(-0.763421\pi\) | ||||
−0.736284 | + | 0.676672i | \(0.763421\pi\) | |||||||
\(402\) | 1.38364 | 0.0690099 | ||||||||
\(403\) | −11.3432 | −0.565043 | ||||||||
\(404\) | 4.29937 | 0.213902 | ||||||||
\(405\) | −6.10558 | −0.303389 | ||||||||
\(406\) | 3.19596 | 0.158613 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.11418 | 0.0551602 | ||||||||
\(409\) | −22.1755 | −1.09651 | −0.548253 | − | 0.836313i | \(-0.684707\pi\) | ||||
−0.548253 | + | 0.836313i | \(0.684707\pi\) | |||||||
\(410\) | −4.47278 | −0.220895 | ||||||||
\(411\) | −10.8857 | −0.536952 | ||||||||
\(412\) | 23.3437 | 1.15006 | ||||||||
\(413\) | −4.91466 | −0.241835 | ||||||||
\(414\) | 7.96976 | 0.391692 | ||||||||
\(415\) | 9.16537 | 0.449910 | ||||||||
\(416\) | −5.79141 | −0.283947 | ||||||||
\(417\) | 11.6097 | 0.568530 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8536 | −1.16532 | −0.582662 | − | 0.812715i | \(-0.697989\pi\) | ||||
−0.582662 | + | 0.812715i | \(0.697989\pi\) | |||||||
\(420\) | −1.02816 | −0.0501692 | ||||||||
\(421\) | 15.7409 | 0.767162 | 0.383581 | − | 0.923507i | \(-0.374691\pi\) | ||||
0.383581 | + | 0.923507i | \(0.374691\pi\) | |||||||
\(422\) | −10.8037 | −0.525914 | ||||||||
\(423\) | −10.3945 | −0.505396 | ||||||||
\(424\) | 21.7050 | 1.05409 | ||||||||
\(425\) | 1.08534 | 0.0526465 | ||||||||
\(426\) | 1.96859 | 0.0953783 | ||||||||
\(427\) | −10.6033 | −0.513132 | ||||||||
\(428\) | −24.2515 | −1.17224 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.38471 | 0.115001 | ||||||||
\(431\) | 1.50575 | 0.0725294 | 0.0362647 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362647 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(432\) | 8.91710 | 0.429024 | ||||||||
\(433\) | 6.62788 | 0.318516 | 0.159258 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159258 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(434\) | 4.44909 | 0.213563 | ||||||||
\(435\) | 3.92949 | 0.188404 | ||||||||
\(436\) | −12.7126 | −0.608824 | ||||||||
\(437\) | −40.0156 | −1.91420 | ||||||||
\(438\) | −2.78428 | −0.133038 | ||||||||
\(439\) | 5.96524 | 0.284705 | 0.142353 | − | 0.989816i | \(-0.454533\pi\) | ||||
0.142353 | + | 0.989816i | \(0.454533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.66600 | −0.126953 | ||||||||
\(442\) | −0.611365 | −0.0290797 | ||||||||
\(443\) | 26.5172 | 1.25987 | 0.629936 | − | 0.776647i | \(-0.283081\pi\) | ||||
0.629936 | + | 0.776647i | \(0.283081\pi\) | |||||||
\(444\) | −8.73918 | −0.414743 | ||||||||
\(445\) | 3.20656 | 0.152005 | ||||||||
\(446\) | −10.9843 | −0.520124 | ||||||||
\(447\) | 6.57371 | 0.310926 | ||||||||
\(448\) | −3.17481 | −0.149995 | ||||||||
\(449\) | 37.4390 | 1.76686 | 0.883429 | − | 0.468565i | \(-0.155229\pi\) | ||||
0.883429 | + | 0.468565i | \(0.155229\pi\) | |||||||
\(450\) | −1.25313 | −0.0590733 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −19.4302 | −0.913922 | ||||||||
\(453\) | 7.39954 | 0.347661 | ||||||||
\(454\) | −4.35392 | −0.204339 | ||||||||
\(455\) | 1.19839 | 0.0561815 | ||||||||
\(456\) | 6.45912 | 0.302476 | ||||||||
\(457\) | −1.42603 | −0.0667069 | −0.0333535 | − | 0.999444i | \(-0.510619\pi\) | ||||
−0.0333535 | + | 0.999444i | \(0.510619\pi\) | |||||||
\(458\) | 10.5167 | 0.491412 | ||||||||
\(459\) | 3.55396 | 0.165885 | ||||||||
\(460\) | −11.3146 | −0.527545 | ||||||||
\(461\) | −0.554469 | −0.0258242 | −0.0129121 | − | 0.999917i | \(-0.504110\pi\) | ||||
−0.0129121 | + | 0.999917i | \(0.504110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2994 | 0.757495 | 0.378748 | − | 0.925500i | \(-0.376355\pi\) | ||||
0.378748 | + | 0.925500i | \(0.376355\pi\) | |||||||
\(464\) | 18.5157 | 0.859570 | ||||||||
\(465\) | 5.47024 | 0.253676 | ||||||||
\(466\) | −0.141475 | −0.00655372 | ||||||||
\(467\) | −22.7720 | −1.05376 | −0.526880 | − | 0.849939i | \(-0.676638\pi\) | ||||
−0.526880 | + | 0.849939i | \(0.676638\pi\) | |||||||
\(468\) | −5.68396 | −0.262741 | ||||||||
\(469\) | −5.09350 | −0.235196 | ||||||||
\(470\) | −1.83264 | −0.0845335 | ||||||||
\(471\) | −4.75691 | −0.219187 | ||||||||
\(472\) | 8.73001 | 0.401831 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.0195218 | 0.000896668 0 | ||||||||
\(475\) | 6.29189 | 0.288692 | ||||||||
\(476\) | −1.93088 | −0.0885017 | ||||||||
\(477\) | 32.5761 | 1.49156 | ||||||||
\(478\) | 8.37081 | 0.382872 | ||||||||
\(479\) | 14.7738 | 0.675033 | 0.337516 | − | 0.941320i | \(-0.390413\pi\) | ||||
0.337516 | + | 0.941320i | \(0.390413\pi\) | |||||||
\(480\) | 2.79290 | 0.127478 | ||||||||
\(481\) | 10.1861 | 0.464447 | ||||||||
\(482\) | −6.96486 | −0.317240 | ||||||||
\(483\) | 3.67552 | 0.167242 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.05358 | 0.411102 | ||||||||
\(486\) | −6.27607 | −0.284688 | ||||||||
\(487\) | −6.18415 | −0.280231 | −0.140115 | − | 0.990135i | \(-0.544747\pi\) | ||||
−0.140115 | + | 0.990135i | \(0.544747\pi\) | |||||||
\(488\) | 18.8349 | 0.852616 | ||||||||
\(489\) | −3.64488 | −0.164827 | ||||||||
\(490\) | −0.470042 | −0.0212343 | ||||||||
\(491\) | 36.2148 | 1.63435 | 0.817175 | − | 0.576389i | \(-0.195539\pi\) | ||||
0.817175 | + | 0.576389i | \(0.195539\pi\) | |||||||
\(492\) | 9.78370 | 0.441083 | ||||||||
\(493\) | 7.37953 | 0.332357 | ||||||||
\(494\) | −3.54420 | −0.159461 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.7757 | 1.15736 | ||||||||
\(497\) | −7.24680 | −0.325063 | ||||||||
\(498\) | 2.48976 | 0.111569 | ||||||||
\(499\) | −17.9874 | −0.805227 | −0.402614 | − | 0.915370i | \(-0.631898\pi\) | ||||
−0.402614 | + | 0.915370i | \(0.631898\pi\) | |||||||
\(500\) | 1.77906 | 0.0795620 | ||||||||
\(501\) | 5.40379 | 0.241424 | ||||||||
\(502\) | 2.31541 | 0.103342 | ||||||||
\(503\) | −20.1263 | −0.897389 | −0.448694 | − | 0.893685i | \(-0.648111\pi\) | ||||
−0.448694 | + | 0.893685i | \(0.648111\pi\) | |||||||
\(504\) | 4.73567 | 0.210943 | ||||||||
\(505\) | 2.41665 | 0.107540 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.68304 | 0.296804 | ||||||||
\(508\) | 19.9662 | 0.885858 | ||||||||
\(509\) | −22.3565 | −0.990936 | −0.495468 | − | 0.868626i | \(-0.665003\pi\) | ||||
−0.495468 | + | 0.868626i | \(0.665003\pi\) | |||||||
\(510\) | 0.294830 | 0.0130553 | ||||||||
\(511\) | 10.2495 | 0.453413 | ||||||||
\(512\) | 22.8346 | 1.00916 | ||||||||
\(513\) | 20.6030 | 0.909643 | ||||||||
\(514\) | 4.99549 | 0.220341 | ||||||||
\(515\) | 13.1214 | 0.578196 | ||||||||
\(516\) | −5.21627 | −0.229633 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.99527 | −0.175542 | ||||||||
\(519\) | 4.03628 | 0.177173 | ||||||||
\(520\) | −2.12873 | −0.0933509 | ||||||||
\(521\) | −4.65362 | −0.203879 | −0.101939 | − | 0.994791i | \(-0.532505\pi\) | ||||
−0.101939 | + | 0.994791i | \(0.532505\pi\) | |||||||
\(522\) | −8.52044 | −0.372930 | ||||||||
\(523\) | −28.6197 | −1.25145 | −0.625726 | − | 0.780043i | \(-0.715197\pi\) | ||||
−0.625726 | + | 0.780043i | \(0.715197\pi\) | |||||||
\(524\) | −30.8806 | −1.34902 | ||||||||
\(525\) | −0.577925 | −0.0252227 | ||||||||
\(526\) | −3.11595 | −0.135862 | ||||||||
\(527\) | 10.2730 | 0.447501 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.4478 | 0.758600 | ||||||||
\(530\) | 5.74348 | 0.249481 | ||||||||
\(531\) | 13.1025 | 0.568600 | ||||||||
\(532\) | −11.1937 | −0.485307 | ||||||||
\(533\) | −11.4036 | −0.493943 | ||||||||
\(534\) | 0.871058 | 0.0376944 | ||||||||
\(535\) | −13.6316 | −0.589347 | ||||||||
\(536\) | 9.04768 | 0.390800 | ||||||||
\(537\) | −7.51416 | −0.324260 | ||||||||
\(538\) | 6.87265 | 0.296301 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.82557 | 0.250693 | ||||||||
\(541\) | 1.53468 | 0.0659810 | 0.0329905 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329905 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(542\) | 2.35219 | 0.101035 | ||||||||
\(543\) | 10.5411 | 0.452363 | ||||||||
\(544\) | 5.24504 | 0.224879 | ||||||||
\(545\) | −7.14569 | −0.306088 | ||||||||
\(546\) | 0.325542 | 0.0139319 | ||||||||
\(547\) | 32.9352 | 1.40821 | 0.704104 | − | 0.710097i | \(-0.251349\pi\) | ||||
0.704104 | + | 0.710097i | \(0.251349\pi\) | |||||||
\(548\) | −33.5101 | −1.43148 | ||||||||
\(549\) | 28.2686 | 1.20647 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.7805 | 1.82251 | ||||||||
\(552\) | −6.52889 | −0.277888 | ||||||||
\(553\) | −0.0718642 | −0.00305598 | ||||||||
\(554\) | −1.64716 | −0.0699813 | ||||||||
\(555\) | −4.91225 | −0.208513 | ||||||||
\(556\) | 35.7389 | 1.51567 | ||||||||
\(557\) | 25.5992 | 1.08467 | 0.542337 | − | 0.840161i | \(-0.317539\pi\) | ||||
0.542337 | + | 0.840161i | \(0.317539\pi\) | |||||||
\(558\) | −11.8613 | −0.502129 | ||||||||
\(559\) | 6.07991 | 0.257153 | ||||||||
\(560\) | −2.72318 | −0.115075 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.43012 | 0.186874 | ||||||||
\(563\) | −14.5421 | −0.612876 | −0.306438 | − | 0.951891i | \(-0.599137\pi\) | ||||
−0.306438 | + | 0.951891i | \(0.599137\pi\) | |||||||
\(564\) | 4.00870 | 0.168797 | ||||||||
\(565\) | −10.9216 | −0.459476 | ||||||||
\(566\) | −7.47885 | −0.314359 | ||||||||
\(567\) | 6.10558 | 0.256410 | ||||||||
\(568\) | 12.8726 | 0.540123 | ||||||||
\(569\) | −4.43273 | −0.185830 | −0.0929148 | − | 0.995674i | \(-0.529618\pi\) | ||||
−0.0929148 | + | 0.995674i | \(0.529618\pi\) | |||||||
\(570\) | 1.70919 | 0.0715900 | ||||||||
\(571\) | 25.7504 | 1.07762 | 0.538811 | − | 0.842427i | \(-0.318874\pi\) | ||||
0.538811 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.59914 | 0.359234 | ||||||||
\(574\) | 4.47278 | 0.186690 | ||||||||
\(575\) | −6.35986 | −0.265224 | ||||||||
\(576\) | 8.46404 | 0.352668 | ||||||||
\(577\) | 42.5310 | 1.77059 | 0.885294 | − | 0.465031i | \(-0.153957\pi\) | ||||
0.885294 | + | 0.465031i | \(0.153957\pi\) | |||||||
\(578\) | −7.43703 | −0.309340 | ||||||||
\(579\) | −2.81838 | −0.117128 | ||||||||
\(580\) | 12.0964 | 0.502275 | ||||||||
\(581\) | −9.16537 | −0.380243 | ||||||||
\(582\) | 2.45940 | 0.101945 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −18.2064 | −0.753388 | ||||||||
\(585\) | −3.19492 | −0.132094 | ||||||||
\(586\) | −7.21861 | −0.298198 | ||||||||
\(587\) | 2.68746 | 0.110923 | 0.0554617 | − | 0.998461i | \(-0.482337\pi\) | ||||
0.0554617 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(588\) | 1.02816 | 0.0424007 | ||||||||
\(589\) | 59.5547 | 2.45391 | ||||||||
\(590\) | 2.31010 | 0.0951053 | ||||||||
\(591\) | 12.3169 | 0.506651 | ||||||||
\(592\) | −23.1465 | −0.951314 | ||||||||
\(593\) | 27.0766 | 1.11190 | 0.555952 | − | 0.831214i | \(-0.312354\pi\) | ||||
0.555952 | + | 0.831214i | \(0.312354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.08534 | −0.0444944 | ||||||||
\(596\) | 20.2362 | 0.828909 | ||||||||
\(597\) | −0.629452 | −0.0257618 | ||||||||
\(598\) | 3.58248 | 0.146498 | ||||||||
\(599\) | −16.1515 | −0.659933 | −0.329966 | − | 0.943993i | \(-0.607037\pi\) | ||||
−0.329966 | + | 0.943993i | \(0.607037\pi\) | |||||||
\(600\) | 1.02658 | 0.0419099 | ||||||||
\(601\) | 12.3469 | 0.503640 | 0.251820 | − | 0.967774i | \(-0.418971\pi\) | ||||
0.251820 | + | 0.967774i | \(0.418971\pi\) | |||||||
\(602\) | −2.38471 | −0.0971934 | ||||||||
\(603\) | 13.5793 | 0.552991 | ||||||||
\(604\) | 22.7785 | 0.926842 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.656481 | 0.0266677 | ||||||||
\(607\) | 13.0242 | 0.528635 | 0.264318 | − | 0.964436i | \(-0.414853\pi\) | ||||
0.264318 | + | 0.964436i | \(0.414853\pi\) | |||||||
\(608\) | 30.4065 | 1.23315 | ||||||||
\(609\) | −3.92949 | −0.159231 | ||||||||
\(610\) | 4.98402 | 0.201797 | ||||||||
\(611\) | −4.67241 | −0.189025 | ||||||||
\(612\) | 5.14773 | 0.208085 | ||||||||
\(613\) | −21.3235 | −0.861249 | −0.430624 | − | 0.902531i | \(-0.641707\pi\) | ||||
−0.430624 | + | 0.902531i | \(0.641707\pi\) | |||||||
\(614\) | 7.55177 | 0.304765 | ||||||||
\(615\) | 5.49936 | 0.221756 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.5851 | −1.55338 | −0.776688 | − | 0.629886i | \(-0.783102\pi\) | ||||
−0.776688 | + | 0.629886i | \(0.783102\pi\) | |||||||
\(618\) | 3.56440 | 0.143381 | ||||||||
\(619\) | −43.6172 | −1.75312 | −0.876561 | − | 0.481290i | \(-0.840168\pi\) | ||||
−0.876561 | + | 0.481290i | \(0.840168\pi\) | |||||||
\(620\) | 16.8394 | 0.676285 | ||||||||
\(621\) | −20.8255 | −0.835699 | ||||||||
\(622\) | 1.72552 | 0.0691870 | ||||||||
\(623\) | −3.20656 | −0.128468 | ||||||||
\(624\) | 1.88602 | 0.0755012 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.09285 | −0.0836472 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.6435 | −0.584339 | ||||||||
\(629\) | −9.22514 | −0.367831 | ||||||||
\(630\) | 1.25313 | 0.0499261 | ||||||||
\(631\) | 4.87238 | 0.193966 | 0.0969831 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969831 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(632\) | 0.127654 | 0.00507779 | ||||||||
\(633\) | 13.2833 | 0.527963 | ||||||||
\(634\) | −10.4829 | −0.416329 | ||||||||
\(635\) | 11.2229 | 0.445367 | ||||||||
\(636\) | −12.5632 | −0.498163 | ||||||||
\(637\) | −1.19839 | −0.0474821 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.3200 | 0.764287 | ||||||||
\(640\) | 11.1576 | 0.441042 | ||||||||
\(641\) | 34.8401 | 1.37610 | 0.688052 | − | 0.725662i | \(-0.258466\pi\) | ||||
0.688052 | + | 0.725662i | \(0.258466\pi\) | |||||||
\(642\) | −3.70302 | −0.146147 | ||||||||
\(643\) | −32.0891 | −1.26547 | −0.632735 | − | 0.774368i | \(-0.718068\pi\) | ||||
−0.632735 | + | 0.774368i | \(0.718068\pi\) | |||||||
\(644\) | 11.3146 | 0.445857 | ||||||||
\(645\) | −2.93204 | −0.115449 | ||||||||
\(646\) | 3.20983 | 0.126289 | ||||||||
\(647\) | 19.5279 | 0.767719 | 0.383860 | − | 0.923392i | \(-0.374595\pi\) | ||||
0.383860 | + | 0.923392i | \(0.374595\pi\) | |||||||
\(648\) | −10.8455 | −0.426050 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.563295 | −0.0220943 | ||||||||
\(651\) | −5.47024 | −0.214395 | ||||||||
\(652\) | −11.2203 | −0.439419 | ||||||||
\(653\) | 1.40985 | 0.0551716 | 0.0275858 | − | 0.999619i | \(-0.491218\pi\) | ||||
0.0275858 | + | 0.999619i | \(0.491218\pi\) | |||||||
\(654\) | −1.94112 | −0.0759038 | ||||||||
\(655\) | −17.3578 | −0.678226 | ||||||||
\(656\) | 25.9130 | 1.01173 | ||||||||
\(657\) | −27.3253 | −1.06606 | ||||||||
\(658\) | 1.83264 | 0.0714439 | ||||||||
\(659\) | −18.6595 | −0.726871 | −0.363435 | − | 0.931619i | \(-0.618396\pi\) | ||||
−0.363435 | + | 0.931619i | \(0.618396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.08885 | −0.0812468 | −0.0406234 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406234 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(662\) | −3.96393 | −0.154062 | ||||||||
\(663\) | 0.751683 | 0.0291930 | ||||||||
\(664\) | 16.2806 | 0.631810 | ||||||||
\(665\) | −6.29189 | −0.243989 | ||||||||
\(666\) | 10.6514 | 0.412733 | ||||||||
\(667\) | −43.2426 | −1.67436 | ||||||||
\(668\) | 16.6348 | 0.643621 | ||||||||
\(669\) | 13.5054 | 0.522150 | ||||||||
\(670\) | 2.39416 | 0.0924945 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.79290 | −0.107739 | ||||||||
\(673\) | −31.9112 | −1.23009 | −0.615043 | − | 0.788493i | \(-0.710861\pi\) | ||||
−0.615043 | + | 0.788493i | \(0.710861\pi\) | |||||||
\(674\) | −14.2415 | −0.548561 | ||||||||
\(675\) | 3.27452 | 0.126036 | ||||||||
\(676\) | 20.5728 | 0.791261 | ||||||||
\(677\) | −4.07020 | −0.156431 | −0.0782153 | − | 0.996936i | \(-0.524922\pi\) | ||||
−0.0782153 | + | 0.996936i | \(0.524922\pi\) | |||||||
\(678\) | −2.96685 | −0.113941 | ||||||||
\(679\) | −9.05358 | −0.347445 | ||||||||
\(680\) | 1.92790 | 0.0739317 | ||||||||
\(681\) | 5.35321 | 0.205136 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.8897 | 1.48807 | 0.744036 | − | 0.668139i | \(-0.232909\pi\) | ||||
0.744036 | + | 0.668139i | \(0.232909\pi\) | |||||||
\(684\) | 29.8423 | 1.14105 | ||||||||
\(685\) | −18.8358 | −0.719681 | ||||||||
\(686\) | 0.470042 | 0.0179463 | ||||||||
\(687\) | −12.9304 | −0.493327 | ||||||||
\(688\) | −13.8157 | −0.526720 | ||||||||
\(689\) | 14.6433 | 0.557864 | ||||||||
\(690\) | −1.72765 | −0.0657705 | ||||||||
\(691\) | −47.2979 | −1.79930 | −0.899649 | − | 0.436613i | \(-0.856178\pi\) | ||||
−0.899649 | + | 0.436613i | \(0.856178\pi\) | |||||||
\(692\) | 12.4251 | 0.472332 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.793029 | −0.0301030 | ||||||||
\(695\) | 20.0886 | 0.762005 | ||||||||
\(696\) | 6.98002 | 0.264577 | ||||||||
\(697\) | 10.3277 | 0.391191 | ||||||||
\(698\) | 12.3194 | 0.466298 | ||||||||
\(699\) | 0.173946 | 0.00657925 | ||||||||
\(700\) | −1.77906 | −0.0672422 | ||||||||
\(701\) | −13.4974 | −0.509791 | −0.254896 | − | 0.966969i | \(-0.582041\pi\) | ||||
−0.254896 | + | 0.966969i | \(0.582041\pi\) | |||||||
\(702\) | −1.84452 | −0.0696171 | ||||||||
\(703\) | −53.4799 | −2.01703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.25327 | 0.0848629 | ||||||||
\(706\) | 8.30979 | 0.312743 | ||||||||
\(707\) | −2.41665 | −0.0908876 | ||||||||
\(708\) | −5.05307 | −0.189906 | ||||||||
\(709\) | 16.3431 | 0.613776 | 0.306888 | − | 0.951746i | \(-0.400712\pi\) | ||||
0.306888 | + | 0.951746i | \(0.400712\pi\) | |||||||
\(710\) | 3.40630 | 0.127836 | ||||||||
\(711\) | 0.191590 | 0.00718520 | ||||||||
\(712\) | 5.69587 | 0.213462 | ||||||||
\(713\) | −60.1980 | −2.25443 | ||||||||
\(714\) | −0.294830 | −0.0110338 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.1313 | −0.864456 | ||||||||
\(717\) | −10.2920 | −0.384364 | ||||||||
\(718\) | −3.32035 | −0.123914 | ||||||||
\(719\) | 5.59133 | 0.208521 | 0.104261 | − | 0.994550i | \(-0.466752\pi\) | ||||
0.104261 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(720\) | 7.26000 | 0.270564 | ||||||||
\(721\) | −13.1214 | −0.488665 | ||||||||
\(722\) | 9.67720 | 0.360148 | ||||||||
\(723\) | 8.56341 | 0.318476 | ||||||||
\(724\) | 32.4494 | 1.20597 | ||||||||
\(725\) | 6.79931 | 0.252520 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1035 | 0.560159 | 0.280080 | − | 0.959977i | \(-0.409639\pi\) | ||||
0.280080 | + | 0.959977i | \(0.409639\pi\) | |||||||
\(728\) | 2.12873 | 0.0788959 | ||||||||
\(729\) | −10.6002 | −0.392601 | ||||||||
\(730\) | −4.81772 | −0.178312 | ||||||||
\(731\) | −5.50633 | −0.203659 | ||||||||
\(732\) | −10.9020 | −0.402948 | ||||||||
\(733\) | −13.0144 | −0.480696 | −0.240348 | − | 0.970687i | \(-0.577262\pi\) | ||||
−0.240348 | + | 0.970687i | \(0.577262\pi\) | |||||||
\(734\) | 4.27580 | 0.157823 | ||||||||
\(735\) | 0.577925 | 0.0213171 | ||||||||
\(736\) | −30.7349 | −1.13290 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −11.9245 | −0.438945 | ||||||||
\(739\) | 25.1956 | 0.926836 | 0.463418 | − | 0.886140i | \(-0.346623\pi\) | ||||
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(740\) | −15.1217 | −0.555883 | ||||||||
\(741\) | 4.35765 | 0.160082 | ||||||||
\(742\) | −5.74348 | −0.210850 | ||||||||
\(743\) | 38.2296 | 1.40251 | 0.701254 | − | 0.712911i | \(-0.252624\pi\) | ||||
0.701254 | + | 0.712911i | \(0.252624\pi\) | |||||||
\(744\) | 9.71688 | 0.356238 | ||||||||
\(745\) | 11.3747 | 0.416736 | ||||||||
\(746\) | −15.9620 | −0.584412 | ||||||||
\(747\) | 24.4349 | 0.894026 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.6316 | 0.498089 | ||||||||
\(750\) | 0.271649 | 0.00991922 | ||||||||
\(751\) | −24.3760 | −0.889494 | −0.444747 | − | 0.895656i | \(-0.646706\pi\) | ||||
−0.444747 | + | 0.895656i | \(0.646706\pi\) | |||||||
\(752\) | 10.6174 | 0.387176 | ||||||||
\(753\) | −2.84683 | −0.103744 | ||||||||
\(754\) | −3.83002 | −0.139481 | ||||||||
\(755\) | 12.8036 | 0.465972 | ||||||||
\(756\) | −5.82557 | −0.211874 | ||||||||
\(757\) | 28.9119 | 1.05082 | 0.525410 | − | 0.850849i | \(-0.323912\pi\) | ||||
0.525410 | + | 0.850849i | \(0.323912\pi\) | |||||||
\(758\) | 9.74047 | 0.353790 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.1764 | 0.405411 | ||||||||
\(761\) | 17.6334 | 0.639212 | 0.319606 | − | 0.947551i | \(-0.396449\pi\) | ||||
0.319606 | + | 0.947551i | \(0.396449\pi\) | |||||||
\(762\) | 3.04869 | 0.110442 | ||||||||
\(763\) | 7.14569 | 0.258691 | ||||||||
\(764\) | 26.4712 | 0.957696 | ||||||||
\(765\) | 2.89351 | 0.104615 | ||||||||
\(766\) | −8.27008 | −0.298810 | ||||||||
\(767\) | 5.88970 | 0.212665 | ||||||||
\(768\) | −0.638652 | −0.0230454 | ||||||||
\(769\) | −30.2925 | −1.09237 | −0.546187 | − | 0.837663i | \(-0.683921\pi\) | ||||
−0.546187 | + | 0.837663i | \(0.683921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.14203 | −0.221200 | ||||||||
\(772\) | −8.67599 | −0.312256 | ||||||||
\(773\) | −30.0549 | −1.08100 | −0.540500 | − | 0.841344i | \(-0.681765\pi\) | ||||
−0.540500 | + | 0.841344i | \(0.681765\pi\) | |||||||
\(774\) | 6.35763 | 0.228520 | ||||||||
\(775\) | 9.46531 | 0.340004 | ||||||||
\(776\) | 16.0820 | 0.577312 | ||||||||
\(777\) | 4.91225 | 0.176226 | ||||||||
\(778\) | −10.9967 | −0.394250 | ||||||||
\(779\) | 59.8718 | 2.14513 | ||||||||
\(780\) | 1.23214 | 0.0441178 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.24451 | −0.116023 | ||||||||
\(783\) | 22.2645 | 0.795668 | ||||||||
\(784\) | 2.72318 | 0.0972563 | ||||||||
\(785\) | −8.23103 | −0.293778 | ||||||||
\(786\) | −4.71523 | −0.168187 | ||||||||
\(787\) | 38.2530 | 1.36357 | 0.681787 | − | 0.731551i | \(-0.261203\pi\) | ||||
0.681787 | + | 0.731551i | \(0.261203\pi\) | |||||||
\(788\) | 37.9159 | 1.35070 | ||||||||
\(789\) | 3.83111 | 0.136391 | ||||||||
\(790\) | 0.0337792 | 0.00120181 | ||||||||
\(791\) | 10.9216 | 0.388329 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7070 | 0.451238 | ||||||||
\(794\) | 2.96776 | 0.105322 | ||||||||
\(795\) | −7.06171 | −0.250453 | ||||||||
\(796\) | −1.93768 | −0.0686793 | ||||||||
\(797\) | −12.7361 | −0.451135 | −0.225568 | − | 0.974228i | \(-0.572424\pi\) | ||||
−0.225568 | + | 0.974228i | \(0.572424\pi\) | |||||||
\(798\) | −1.70919 | −0.0605046 | ||||||||
\(799\) | 4.23161 | 0.149704 | ||||||||
\(800\) | 4.83264 | 0.170860 | ||||||||
\(801\) | 8.54870 | 0.302053 | ||||||||
\(802\) | −13.8607 | −0.489438 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.23695 | −0.184693 | ||||||||
\(805\) | 6.35986 | 0.224156 | ||||||||
\(806\) | −5.33177 | −0.187803 | ||||||||
\(807\) | −8.45004 | −0.297455 | ||||||||
\(808\) | 4.29274 | 0.151018 | ||||||||
\(809\) | 13.6911 | 0.481354 | 0.240677 | − | 0.970605i | \(-0.422631\pi\) | ||||
0.240677 | + | 0.970605i | \(0.422631\pi\) | |||||||
\(810\) | −2.86988 | −0.100837 | ||||||||
\(811\) | −42.2475 | −1.48351 | −0.741756 | − | 0.670670i | \(-0.766007\pi\) | ||||
−0.741756 | + | 0.670670i | \(0.766007\pi\) | |||||||
\(812\) | −12.0964 | −0.424500 | ||||||||
\(813\) | −2.89205 | −0.101429 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.30685 | −0.220919 | ||||||||
\(816\) | −1.70809 | −0.0597952 | ||||||||
\(817\) | −31.9212 | −1.11678 | ||||||||
\(818\) | −10.4234 | −0.364446 | ||||||||
\(819\) | 3.19492 | 0.111640 | ||||||||
\(820\) | 16.9290 | 0.591187 | ||||||||
\(821\) | −31.6222 | −1.10362 | −0.551810 | − | 0.833970i | \(-0.686063\pi\) | ||||
−0.551810 | + | 0.833970i | \(0.686063\pi\) | |||||||
\(822\) | −5.11674 | −0.178467 | ||||||||
\(823\) | 32.4818 | 1.13224 | 0.566122 | − | 0.824322i | \(-0.308443\pi\) | ||||
0.566122 | + | 0.824322i | \(0.308443\pi\) | |||||||
\(824\) | 23.3077 | 0.811962 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.31010 | −0.0803786 | ||||||||
\(827\) | −51.6677 | −1.79666 | −0.898330 | − | 0.439321i | \(-0.855219\pi\) | ||||
−0.898330 | + | 0.439321i | \(0.855219\pi\) | |||||||
\(828\) | −30.1647 | −1.04830 | ||||||||
\(829\) | 3.81406 | 0.132468 | 0.0662339 | − | 0.997804i | \(-0.478902\pi\) | ||||
0.0662339 | + | 0.997804i | \(0.478902\pi\) | |||||||
\(830\) | 4.30811 | 0.149537 | ||||||||
\(831\) | 2.02522 | 0.0702539 | ||||||||
\(832\) | 3.80467 | 0.131903 | ||||||||
\(833\) | 1.08534 | 0.0376047 | ||||||||
\(834\) | 5.45706 | 0.188962 | ||||||||
\(835\) | 9.35034 | 0.323582 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.9944 | 1.07132 | ||||||||
\(838\) | −11.2122 | −0.387319 | ||||||||
\(839\) | −34.9994 | −1.20831 | −0.604157 | − | 0.796865i | \(-0.706490\pi\) | ||||
−0.604157 | + | 0.796865i | \(0.706490\pi\) | |||||||
\(840\) | −1.02658 | −0.0354203 | ||||||||
\(841\) | 17.2306 | 0.594157 | ||||||||
\(842\) | 7.39887 | 0.254982 | ||||||||
\(843\) | −5.44691 | −0.187602 | ||||||||
\(844\) | 40.8907 | 1.40752 | ||||||||
\(845\) | 11.5639 | 0.397809 | ||||||||
\(846\) | −4.88583 | −0.167978 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −33.2747 | −1.14266 | ||||||||
\(849\) | 9.19537 | 0.315584 | ||||||||
\(850\) | 0.510154 | 0.0174981 | ||||||||
\(851\) | 54.0576 | 1.85307 | ||||||||
\(852\) | −7.45089 | −0.255263 | ||||||||
\(853\) | 51.6573 | 1.76871 | 0.884357 | − | 0.466812i | \(-0.154597\pi\) | ||||
0.884357 | + | 0.466812i | \(0.154597\pi\) | |||||||
\(854\) | −4.98402 | −0.170550 | ||||||||
\(855\) | 16.7742 | 0.573666 | ||||||||
\(856\) | −24.2141 | −0.827622 | ||||||||
\(857\) | 11.4832 | 0.392258 | 0.196129 | − | 0.980578i | \(-0.437163\pi\) | ||||
0.196129 | + | 0.980578i | \(0.437163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5148 | 0.392880 | 0.196440 | − | 0.980516i | \(-0.437062\pi\) | ||||
0.196440 | + | 0.980516i | \(0.437062\pi\) | |||||||
\(860\) | −9.02586 | −0.307779 | ||||||||
\(861\) | −5.49936 | −0.187418 | ||||||||
\(862\) | 0.707766 | 0.0241066 | ||||||||
\(863\) | −27.5849 | −0.938999 | −0.469500 | − | 0.882933i | \(-0.655566\pi\) | ||||
−0.469500 | + | 0.882933i | \(0.655566\pi\) | |||||||
\(864\) | 15.8246 | 0.538364 | ||||||||
\(865\) | 6.98410 | 0.237466 | ||||||||
\(866\) | 3.11538 | 0.105865 | ||||||||
\(867\) | 9.14395 | 0.310545 | ||||||||
\(868\) | −16.8394 | −0.571565 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.84702 | 0.0626200 | ||||||||
\(871\) | 6.10402 | 0.206827 | ||||||||
\(872\) | −12.6930 | −0.429840 | ||||||||
\(873\) | 24.1369 | 0.816910 | ||||||||
\(874\) | −18.8090 | −0.636224 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 10.5382 | 0.356053 | ||||||||
\(877\) | −50.2969 | −1.69841 | −0.849203 | − | 0.528067i | \(-0.822917\pi\) | ||||
−0.849203 | + | 0.528067i | \(0.822917\pi\) | |||||||
\(878\) | 2.80392 | 0.0946276 | ||||||||
\(879\) | 8.87540 | 0.299360 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.4455 | −0.992044 | −0.496022 | − | 0.868310i | \(-0.665207\pi\) | ||||
−0.496022 | + | 0.868310i | \(0.665207\pi\) | |||||||
\(882\) | −1.25313 | −0.0421952 | ||||||||
\(883\) | 27.3839 | 0.921542 | 0.460771 | − | 0.887519i | \(-0.347573\pi\) | ||||
0.460771 | + | 0.887519i | \(0.347573\pi\) | |||||||
\(884\) | 2.31395 | 0.0778266 | ||||||||
\(885\) | −2.84031 | −0.0954758 | ||||||||
\(886\) | 12.4642 | 0.418744 | ||||||||
\(887\) | −43.0693 | −1.44612 | −0.723062 | − | 0.690783i | \(-0.757266\pi\) | ||||
−0.723062 | + | 0.690783i | \(0.757266\pi\) | |||||||
\(888\) | −8.72571 | −0.292816 | ||||||||
\(889\) | −11.2229 | −0.376404 | ||||||||
\(890\) | 1.50722 | 0.0505221 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.5746 | 1.39202 | ||||||||
\(893\) | 24.5314 | 0.820912 | ||||||||
\(894\) | 3.08992 | 0.103342 | ||||||||
\(895\) | −13.0020 | −0.434608 | ||||||||
\(896\) | −11.1576 | −0.372749 | ||||||||
\(897\) | −4.40472 | −0.147069 | ||||||||
\(898\) | 17.5979 | 0.587251 | ||||||||
\(899\) | 64.3575 | 2.14644 | ||||||||
\(900\) | 4.74298 | 0.158099 | ||||||||
\(901\) | −13.2618 | −0.441815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.93204 | 0.0975720 | ||||||||
\(904\) | −19.4003 | −0.645244 | ||||||||
\(905\) | 18.2396 | 0.606306 | ||||||||
\(906\) | 3.47810 | 0.115552 | ||||||||
\(907\) | −30.1364 | −1.00066 | −0.500332 | − | 0.865834i | \(-0.666789\pi\) | ||||
−0.500332 | + | 0.865834i | \(0.666789\pi\) | |||||||
\(908\) | 16.4791 | 0.546879 | ||||||||
\(909\) | 6.44280 | 0.213694 | ||||||||
\(910\) | 0.563295 | 0.0186731 | ||||||||
\(911\) | 39.4333 | 1.30648 | 0.653242 | − | 0.757149i | \(-0.273409\pi\) | ||||
0.653242 | + | 0.757149i | \(0.273409\pi\) | |||||||
\(912\) | −9.90213 | −0.327892 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.670295 | −0.0221714 | ||||||||
\(915\) | −6.12793 | −0.202583 | ||||||||
\(916\) | −39.8045 | −1.31518 | ||||||||
\(917\) | 17.3578 | 0.573205 | ||||||||
\(918\) | 1.67051 | 0.0551350 | ||||||||
\(919\) | 16.9203 | 0.558149 | 0.279075 | − | 0.960269i | \(-0.409972\pi\) | ||||
0.279075 | + | 0.960269i | \(0.409972\pi\) | |||||||
\(920\) | −11.2971 | −0.372455 | ||||||||
\(921\) | −9.28503 | −0.305952 | ||||||||
\(922\) | −0.260624 | −0.00858319 | ||||||||
\(923\) | 8.68452 | 0.285854 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.49980 | −0.279472 | ||||||||
\(926\) | 7.66139 | 0.251769 | ||||||||
\(927\) | 34.9816 | 1.14895 | ||||||||
\(928\) | 32.8586 | 1.07864 | ||||||||
\(929\) | −41.8149 | −1.37190 | −0.685951 | − | 0.727648i | \(-0.740613\pi\) | ||||
−0.685951 | + | 0.727648i | \(0.740613\pi\) | |||||||
\(930\) | 2.57124 | 0.0843143 | ||||||||
\(931\) | 6.29189 | 0.206209 | ||||||||
\(932\) | 0.535469 | 0.0175399 | ||||||||
\(933\) | −2.12155 | −0.0694565 | ||||||||
\(934\) | −10.7038 | −0.350239 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.67519 | −0.185500 | ||||||||
\(937\) | 10.7732 | 0.351947 | 0.175973 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175973 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(938\) | −2.39416 | −0.0781721 | ||||||||
\(939\) | 2.57320 | 0.0839731 | ||||||||
\(940\) | 6.93636 | 0.226239 | ||||||||
\(941\) | 10.4374 | 0.340249 | 0.170125 | − | 0.985423i | \(-0.445583\pi\) | ||||
0.170125 | + | 0.985423i | \(0.445583\pi\) | |||||||
\(942\) | −2.23595 | −0.0728512 | ||||||||
\(943\) | −60.5186 | −1.97076 | ||||||||
\(944\) | −13.3835 | −0.435596 | ||||||||
\(945\) | −3.27452 | −0.106520 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.7372 | 0.836348 | 0.418174 | − | 0.908367i | \(-0.362670\pi\) | ||||
0.418174 | + | 0.908367i | \(0.362670\pi\) | |||||||
\(948\) | −0.0738881 | −0.00239978 | ||||||||
\(949\) | −12.2830 | −0.398723 | ||||||||
\(950\) | 2.95746 | 0.0959525 | ||||||||
\(951\) | 12.8889 | 0.417951 | ||||||||
\(952\) | −1.92790 | −0.0624837 | ||||||||
\(953\) | 22.0261 | 0.713496 | 0.356748 | − | 0.934201i | \(-0.383885\pi\) | ||||
0.356748 | + | 0.934201i | \(0.383885\pi\) | |||||||
\(954\) | 15.3121 | 0.495749 | ||||||||
\(955\) | 14.8793 | 0.481484 | ||||||||
\(956\) | −31.6826 | −1.02469 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.94431 | 0.224361 | ||||||||
\(959\) | 18.8358 | 0.608241 | ||||||||
\(960\) | −1.83480 | −0.0592179 | ||||||||
\(961\) | 58.5921 | 1.89007 | ||||||||
\(962\) | 4.78790 | 0.154368 | ||||||||
\(963\) | −36.3420 | −1.17110 | ||||||||
\(964\) | 26.3612 | 0.849039 | ||||||||
\(965\) | −4.87672 | −0.156987 | ||||||||
\(966\) | 1.72765 | 0.0555862 | ||||||||
\(967\) | −39.0647 | −1.25624 | −0.628118 | − | 0.778118i | \(-0.716174\pi\) | ||||
−0.628118 | + | 0.778118i | \(0.716174\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.94654 | −0.126781 | ||||||||
\(970\) | 4.25557 | 0.136638 | ||||||||
\(971\) | 27.4441 | 0.880723 | 0.440362 | − | 0.897820i | \(-0.354850\pi\) | ||||
0.440362 | + | 0.897820i | \(0.354850\pi\) | |||||||
\(972\) | 23.7543 | 0.761918 | ||||||||
\(973\) | −20.0886 | −0.644012 | ||||||||
\(974\) | −2.90681 | −0.0931403 | ||||||||
\(975\) | 0.692581 | 0.0221803 | ||||||||
\(976\) | −28.8748 | −0.924259 | ||||||||
\(977\) | 13.7037 | 0.438420 | 0.219210 | − | 0.975678i | \(-0.429652\pi\) | ||||
0.219210 | + | 0.975678i | \(0.429652\pi\) | |||||||
\(978\) | −1.71325 | −0.0547837 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.77906 | 0.0568300 | ||||||||
\(981\) | −19.0504 | −0.608234 | ||||||||
\(982\) | 17.0225 | 0.543209 | ||||||||
\(983\) | 26.5600 | 0.847133 | 0.423566 | − | 0.905865i | \(-0.360778\pi\) | ||||
0.423566 | + | 0.905865i | \(0.360778\pi\) | |||||||
\(984\) | 9.76862 | 0.311412 | ||||||||
\(985\) | 21.3123 | 0.679067 | ||||||||
\(986\) | 3.46869 | 0.110466 | ||||||||
\(987\) | −2.25327 | −0.0717222 | ||||||||
\(988\) | 13.4144 | 0.426769 | ||||||||
\(989\) | 32.2660 | 1.02600 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.9346 | −1.77682 | −0.888410 | − | 0.459051i | \(-0.848190\pi\) | ||||
−0.888410 | + | 0.459051i | \(0.848190\pi\) | |||||||
\(992\) | 45.7425 | 1.45232 | ||||||||
\(993\) | 4.87371 | 0.154663 | ||||||||
\(994\) | −3.40630 | −0.108041 | ||||||||
\(995\) | −1.08916 | −0.0345287 | ||||||||
\(996\) | −9.42349 | −0.298595 | ||||||||
\(997\) | −1.89634 | −0.0600578 | −0.0300289 | − | 0.999549i | \(-0.509560\pi\) | ||||
−0.0300289 | + | 0.999549i | \(0.509560\pi\) | |||||||
\(998\) | −8.45484 | −0.267633 | ||||||||
\(999\) | −27.8328 | −0.880591 |
(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 | 4235.2.a.bb.1.3 | yes | 5 | |
11.10 | odd | 2 | 4235.2.a.ba.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.ba.1.3 | ✓ | 5 | 11.10 | odd | 2 | ||
4235.2.a.bb.1.3 | yes | 5 | 1.1 | even | 1 | trivial |