Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2230,2,Mod(1,2230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2230.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2230 = 2 \cdot 5 \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2230.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: | \(17.8066396507\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.67955408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 30x^{2} + 24x + 4 \) |
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 | 1.6 | ||
Root | \(-2.13450\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.13450 | 1.23235 | 0.616176 | − | 0.787608i | \(-0.288681\pi\) | ||||
0.616176 | + | 0.787608i | \(0.288681\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.13450 | −0.871405 | ||||||||
\(7\) | 2.94362 | 1.11258 | 0.556292 | − | 0.830987i | \(-0.312224\pi\) | ||||
0.556292 | + | 0.830987i | \(0.312224\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.55608 | 0.518692 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.88769 | 1.47369 | 0.736846 | − | 0.676060i | \(-0.236314\pi\) | ||||
0.736846 | + | 0.676060i | \(0.236314\pi\) | |||||||
\(12\) | 2.13450 | 0.616176 | ||||||||
\(13\) | 1.18156 | 0.327707 | 0.163853 | − | 0.986485i | \(-0.447608\pi\) | ||||
0.163853 | + | 0.986485i | \(0.447608\pi\) | |||||||
\(14\) | −2.94362 | −0.786716 | ||||||||
\(15\) | −2.13450 | −0.551125 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.72348 | 0.418006 | 0.209003 | − | 0.977915i | \(-0.432978\pi\) | ||||
0.209003 | + | 0.977915i | \(0.432978\pi\) | |||||||
\(18\) | −1.55608 | −0.366770 | ||||||||
\(19\) | 3.50901 | 0.805022 | 0.402511 | − | 0.915415i | \(-0.368138\pi\) | ||||
0.402511 | + | 0.915415i | \(0.368138\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 6.28315 | 1.37110 | ||||||||
\(22\) | −4.88769 | −1.04206 | ||||||||
\(23\) | −1.51609 | −0.316126 | −0.158063 | − | 0.987429i | \(-0.550525\pi\) | ||||
−0.158063 | + | 0.987429i | \(0.550525\pi\) | |||||||
\(24\) | −2.13450 | −0.435702 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.18156 | −0.231723 | ||||||||
\(27\) | −3.08205 | −0.593141 | ||||||||
\(28\) | 2.94362 | 0.556292 | ||||||||
\(29\) | 5.12726 | 0.952108 | 0.476054 | − | 0.879416i | \(-0.342067\pi\) | ||||
0.476054 | + | 0.879416i | \(0.342067\pi\) | |||||||
\(30\) | 2.13450 | 0.389704 | ||||||||
\(31\) | −1.83007 | −0.328691 | −0.164345 | − | 0.986403i | \(-0.552551\pi\) | ||||
−0.164345 | + | 0.986403i | \(0.552551\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.4327 | 1.81611 | ||||||||
\(34\) | −1.72348 | −0.295575 | ||||||||
\(35\) | −2.94362 | −0.497563 | ||||||||
\(36\) | 1.55608 | 0.259346 | ||||||||
\(37\) | −9.24316 | −1.51957 | −0.759783 | − | 0.650177i | \(-0.774695\pi\) | ||||
−0.759783 | + | 0.650177i | \(0.774695\pi\) | |||||||
\(38\) | −3.50901 | −0.569236 | ||||||||
\(39\) | 2.52204 | 0.403850 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.682260 | 0.106551 | 0.0532756 | − | 0.998580i | \(-0.483034\pi\) | ||||
0.0532756 | + | 0.998580i | \(0.483034\pi\) | |||||||
\(42\) | −6.28315 | −0.969511 | ||||||||
\(43\) | −6.76997 | −1.03241 | −0.516206 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516206 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(44\) | 4.88769 | 0.736846 | ||||||||
\(45\) | −1.55608 | −0.231966 | ||||||||
\(46\) | 1.51609 | 0.223535 | ||||||||
\(47\) | 9.01802 | 1.31541 | 0.657707 | − | 0.753274i | \(-0.271527\pi\) | ||||
0.657707 | + | 0.753274i | \(0.271527\pi\) | |||||||
\(48\) | 2.13450 | 0.308088 | ||||||||
\(49\) | 1.66490 | 0.237843 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 3.67877 | 0.515131 | ||||||||
\(52\) | 1.18156 | 0.163853 | ||||||||
\(53\) | 9.35047 | 1.28439 | 0.642193 | − | 0.766543i | \(-0.278025\pi\) | ||||
0.642193 | + | 0.766543i | \(0.278025\pi\) | |||||||
\(54\) | 3.08205 | 0.419414 | ||||||||
\(55\) | −4.88769 | −0.659055 | ||||||||
\(56\) | −2.94362 | −0.393358 | ||||||||
\(57\) | 7.48997 | 0.992071 | ||||||||
\(58\) | −5.12726 | −0.673242 | ||||||||
\(59\) | −9.94967 | −1.29534 | −0.647669 | − | 0.761922i | \(-0.724256\pi\) | ||||
−0.647669 | + | 0.761922i | \(0.724256\pi\) | |||||||
\(60\) | −2.13450 | −0.275562 | ||||||||
\(61\) | −13.9563 | −1.78692 | −0.893461 | − | 0.449141i | \(-0.851730\pi\) | ||||
−0.893461 | + | 0.449141i | \(0.851730\pi\) | |||||||
\(62\) | 1.83007 | 0.232419 | ||||||||
\(63\) | 4.58049 | 0.577088 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.18156 | −0.146555 | ||||||||
\(66\) | −10.4327 | −1.28418 | ||||||||
\(67\) | 6.03189 | 0.736913 | 0.368456 | − | 0.929645i | \(-0.379886\pi\) | ||||
0.368456 | + | 0.929645i | \(0.379886\pi\) | |||||||
\(68\) | 1.72348 | 0.209003 | ||||||||
\(69\) | −3.23608 | −0.389578 | ||||||||
\(70\) | 2.94362 | 0.351830 | ||||||||
\(71\) | 10.6224 | 1.26065 | 0.630323 | − | 0.776333i | \(-0.282922\pi\) | ||||
0.630323 | + | 0.776333i | \(0.282922\pi\) | |||||||
\(72\) | −1.55608 | −0.183385 | ||||||||
\(73\) | −5.91560 | −0.692368 | −0.346184 | − | 0.938167i | \(-0.612523\pi\) | ||||
−0.346184 | + | 0.938167i | \(0.612523\pi\) | |||||||
\(74\) | 9.24316 | 1.07450 | ||||||||
\(75\) | 2.13450 | 0.246470 | ||||||||
\(76\) | 3.50901 | 0.402511 | ||||||||
\(77\) | 14.3875 | 1.63961 | ||||||||
\(78\) | −2.52204 | −0.285565 | ||||||||
\(79\) | 0.792340 | 0.0891452 | 0.0445726 | − | 0.999006i | \(-0.485807\pi\) | ||||
0.0445726 | + | 0.999006i | \(0.485807\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.2469 | −1.24965 | ||||||||
\(82\) | −0.682260 | −0.0753430 | ||||||||
\(83\) | 13.7940 | 1.51408 | 0.757042 | − | 0.653366i | \(-0.226644\pi\) | ||||
0.757042 | + | 0.653366i | \(0.226644\pi\) | |||||||
\(84\) | 6.28315 | 0.685548 | ||||||||
\(85\) | −1.72348 | −0.186938 | ||||||||
\(86\) | 6.76997 | 0.730025 | ||||||||
\(87\) | 10.9441 | 1.17333 | ||||||||
\(88\) | −4.88769 | −0.521029 | ||||||||
\(89\) | −4.20666 | −0.445905 | −0.222952 | − | 0.974829i | \(-0.571569\pi\) | ||||
−0.222952 | + | 0.974829i | \(0.571569\pi\) | |||||||
\(90\) | 1.55608 | 0.164025 | ||||||||
\(91\) | 3.47807 | 0.364601 | ||||||||
\(92\) | −1.51609 | −0.158063 | ||||||||
\(93\) | −3.90628 | −0.405063 | ||||||||
\(94\) | −9.01802 | −0.930138 | ||||||||
\(95\) | −3.50901 | −0.360017 | ||||||||
\(96\) | −2.13450 | −0.217851 | ||||||||
\(97\) | −11.0914 | −1.12616 | −0.563081 | − | 0.826402i | \(-0.690384\pi\) | ||||
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(98\) | −1.66490 | −0.168180 | ||||||||
\(99\) | 7.60561 | 0.764392 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.5689 | 1.84768 | 0.923838 | − | 0.382783i | \(-0.125034\pi\) | ||||
0.923838 | + | 0.382783i | \(0.125034\pi\) | |||||||
\(102\) | −3.67877 | −0.364253 | ||||||||
\(103\) | 14.5857 | 1.43717 | 0.718586 | − | 0.695438i | \(-0.244789\pi\) | ||||
0.718586 | + | 0.695438i | \(0.244789\pi\) | |||||||
\(104\) | −1.18156 | −0.115862 | ||||||||
\(105\) | −6.28315 | −0.613172 | ||||||||
\(106\) | −9.35047 | −0.908198 | ||||||||
\(107\) | 7.12063 | 0.688377 | 0.344188 | − | 0.938901i | \(-0.388154\pi\) | ||||
0.344188 | + | 0.938901i | \(0.388154\pi\) | |||||||
\(108\) | −3.08205 | −0.296571 | ||||||||
\(109\) | 5.01471 | 0.480322 | 0.240161 | − | 0.970733i | \(-0.422800\pi\) | ||||
0.240161 | + | 0.970733i | \(0.422800\pi\) | |||||||
\(110\) | 4.88769 | 0.466023 | ||||||||
\(111\) | −19.7295 | −1.87264 | ||||||||
\(112\) | 2.94362 | 0.278146 | ||||||||
\(113\) | −9.11501 | −0.857468 | −0.428734 | − | 0.903431i | \(-0.641040\pi\) | ||||
−0.428734 | + | 0.903431i | \(0.641040\pi\) | |||||||
\(114\) | −7.48997 | −0.701500 | ||||||||
\(115\) | 1.51609 | 0.141376 | ||||||||
\(116\) | 5.12726 | 0.476054 | ||||||||
\(117\) | 1.83860 | 0.169979 | ||||||||
\(118\) | 9.94967 | 0.915942 | ||||||||
\(119\) | 5.07328 | 0.465067 | ||||||||
\(120\) | 2.13450 | 0.194852 | ||||||||
\(121\) | 12.8895 | 1.17177 | ||||||||
\(122\) | 13.9563 | 1.26354 | ||||||||
\(123\) | 1.45628 | 0.131309 | ||||||||
\(124\) | −1.83007 | −0.164345 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.58049 | −0.408063 | ||||||||
\(127\) | 0.747627 | 0.0663411 | 0.0331706 | − | 0.999450i | \(-0.489440\pi\) | ||||
0.0331706 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −14.4505 | −1.27229 | ||||||||
\(130\) | 1.18156 | 0.103630 | ||||||||
\(131\) | 14.1204 | 1.23371 | 0.616853 | − | 0.787078i | \(-0.288407\pi\) | ||||
0.616853 | + | 0.787078i | \(0.288407\pi\) | |||||||
\(132\) | 10.4327 | 0.908054 | ||||||||
\(133\) | 10.3292 | 0.895654 | ||||||||
\(134\) | −6.03189 | −0.521076 | ||||||||
\(135\) | 3.08205 | 0.265261 | ||||||||
\(136\) | −1.72348 | −0.147788 | ||||||||
\(137\) | −12.0399 | −1.02864 | −0.514321 | − | 0.857598i | \(-0.671956\pi\) | ||||
−0.514321 | + | 0.857598i | \(0.671956\pi\) | |||||||
\(138\) | 3.23608 | 0.275474 | ||||||||
\(139\) | 9.71606 | 0.824106 | 0.412053 | − | 0.911160i | \(-0.364812\pi\) | ||||
0.412053 | + | 0.911160i | \(0.364812\pi\) | |||||||
\(140\) | −2.94362 | −0.248781 | ||||||||
\(141\) | 19.2489 | 1.62105 | ||||||||
\(142\) | −10.6224 | −0.891411 | ||||||||
\(143\) | 5.77511 | 0.482939 | ||||||||
\(144\) | 1.55608 | 0.129673 | ||||||||
\(145\) | −5.12726 | −0.425795 | ||||||||
\(146\) | 5.91560 | 0.489578 | ||||||||
\(147\) | 3.55372 | 0.293106 | ||||||||
\(148\) | −9.24316 | −0.759783 | ||||||||
\(149\) | −18.1445 | −1.48646 | −0.743229 | − | 0.669037i | \(-0.766707\pi\) | ||||
−0.743229 | + | 0.669037i | \(0.766707\pi\) | |||||||
\(150\) | −2.13450 | −0.174281 | ||||||||
\(151\) | 17.8080 | 1.44920 | 0.724599 | − | 0.689171i | \(-0.242025\pi\) | ||||
0.724599 | + | 0.689171i | \(0.242025\pi\) | |||||||
\(152\) | −3.50901 | −0.284618 | ||||||||
\(153\) | 2.68187 | 0.216816 | ||||||||
\(154\) | −14.3875 | −1.15938 | ||||||||
\(155\) | 1.83007 | 0.146995 | ||||||||
\(156\) | 2.52204 | 0.201925 | ||||||||
\(157\) | −8.54108 | −0.681653 | −0.340826 | − | 0.940126i | \(-0.610707\pi\) | ||||
−0.340826 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(158\) | −0.792340 | −0.0630352 | ||||||||
\(159\) | 19.9585 | 1.58282 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −4.46278 | −0.351717 | ||||||||
\(162\) | 11.2469 | 0.883636 | ||||||||
\(163\) | −15.6136 | −1.22295 | −0.611475 | − | 0.791264i | \(-0.709423\pi\) | ||||
−0.611475 | + | 0.791264i | \(0.709423\pi\) | |||||||
\(164\) | 0.682260 | 0.0532756 | ||||||||
\(165\) | −10.4327 | −0.812188 | ||||||||
\(166\) | −13.7940 | −1.07062 | ||||||||
\(167\) | −16.9665 | −1.31290 | −0.656452 | − | 0.754368i | \(-0.727944\pi\) | ||||
−0.656452 | + | 0.754368i | \(0.727944\pi\) | |||||||
\(168\) | −6.28315 | −0.484755 | ||||||||
\(169\) | −11.6039 | −0.892608 | ||||||||
\(170\) | 1.72348 | 0.132185 | ||||||||
\(171\) | 5.46028 | 0.417558 | ||||||||
\(172\) | −6.76997 | −0.516206 | ||||||||
\(173\) | 8.86101 | 0.673690 | 0.336845 | − | 0.941560i | \(-0.390640\pi\) | ||||
0.336845 | + | 0.941560i | \(0.390640\pi\) | |||||||
\(174\) | −10.9441 | −0.829671 | ||||||||
\(175\) | 2.94362 | 0.222517 | ||||||||
\(176\) | 4.88769 | 0.368423 | ||||||||
\(177\) | −21.2375 | −1.59631 | ||||||||
\(178\) | 4.20666 | 0.315302 | ||||||||
\(179\) | −20.7403 | −1.55020 | −0.775102 | − | 0.631836i | \(-0.782302\pi\) | ||||
−0.775102 | + | 0.631836i | \(0.782302\pi\) | |||||||
\(180\) | −1.55608 | −0.115983 | ||||||||
\(181\) | 10.9538 | 0.814188 | 0.407094 | − | 0.913386i | \(-0.366542\pi\) | ||||
0.407094 | + | 0.913386i | \(0.366542\pi\) | |||||||
\(182\) | −3.47807 | −0.257812 | ||||||||
\(183\) | −29.7897 | −2.20212 | ||||||||
\(184\) | 1.51609 | 0.111767 | ||||||||
\(185\) | 9.24316 | 0.679570 | ||||||||
\(186\) | 3.90628 | 0.286422 | ||||||||
\(187\) | 8.42385 | 0.616013 | ||||||||
\(188\) | 9.01802 | 0.657707 | ||||||||
\(189\) | −9.07239 | −0.659919 | ||||||||
\(190\) | 3.50901 | 0.254570 | ||||||||
\(191\) | 20.0091 | 1.44781 | 0.723904 | − | 0.689901i | \(-0.242346\pi\) | ||||
0.723904 | + | 0.689901i | \(0.242346\pi\) | |||||||
\(192\) | 2.13450 | 0.154044 | ||||||||
\(193\) | −4.39641 | −0.316461 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(194\) | 11.0914 | 0.796317 | ||||||||
\(195\) | −2.52204 | −0.180607 | ||||||||
\(196\) | 1.66490 | 0.118921 | ||||||||
\(197\) | −21.8553 | −1.55713 | −0.778565 | − | 0.627565i | \(-0.784052\pi\) | ||||
−0.778565 | + | 0.627565i | \(0.784052\pi\) | |||||||
\(198\) | −7.60561 | −0.540507 | ||||||||
\(199\) | −11.1500 | −0.790402 | −0.395201 | − | 0.918595i | \(-0.629325\pi\) | ||||
−0.395201 | + | 0.918595i | \(0.629325\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 12.8750 | 0.908136 | ||||||||
\(202\) | −18.5689 | −1.30650 | ||||||||
\(203\) | 15.0927 | 1.05930 | ||||||||
\(204\) | 3.67877 | 0.257565 | ||||||||
\(205\) | −0.682260 | −0.0476511 | ||||||||
\(206\) | −14.5857 | −1.01623 | ||||||||
\(207\) | −2.35914 | −0.163972 | ||||||||
\(208\) | 1.18156 | 0.0819266 | ||||||||
\(209\) | 17.1509 | 1.18636 | ||||||||
\(210\) | 6.28315 | 0.433578 | ||||||||
\(211\) | 6.35671 | 0.437614 | 0.218807 | − | 0.975768i | \(-0.429784\pi\) | ||||
0.218807 | + | 0.975768i | \(0.429784\pi\) | |||||||
\(212\) | 9.35047 | 0.642193 | ||||||||
\(213\) | 22.6735 | 1.55356 | ||||||||
\(214\) | −7.12063 | −0.486756 | ||||||||
\(215\) | 6.76997 | 0.461708 | ||||||||
\(216\) | 3.08205 | 0.209707 | ||||||||
\(217\) | −5.38704 | −0.365696 | ||||||||
\(218\) | −5.01471 | −0.339639 | ||||||||
\(219\) | −12.6268 | −0.853241 | ||||||||
\(220\) | −4.88769 | −0.329528 | ||||||||
\(221\) | 2.03640 | 0.136983 | ||||||||
\(222\) | 19.7295 | 1.32416 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | −2.94362 | −0.196679 | ||||||||
\(225\) | 1.55608 | 0.103738 | ||||||||
\(226\) | 9.11501 | 0.606321 | ||||||||
\(227\) | −4.24805 | −0.281953 | −0.140976 | − | 0.990013i | \(-0.545024\pi\) | ||||
−0.140976 | + | 0.990013i | \(0.545024\pi\) | |||||||
\(228\) | 7.48997 | 0.496035 | ||||||||
\(229\) | 7.33025 | 0.484397 | 0.242198 | − | 0.970227i | \(-0.422132\pi\) | ||||
0.242198 | + | 0.970227i | \(0.422132\pi\) | |||||||
\(230\) | −1.51609 | −0.0999678 | ||||||||
\(231\) | 30.7101 | 2.02057 | ||||||||
\(232\) | −5.12726 | −0.336621 | ||||||||
\(233\) | 13.9826 | 0.916030 | 0.458015 | − | 0.888945i | \(-0.348561\pi\) | ||||
0.458015 | + | 0.888945i | \(0.348561\pi\) | |||||||
\(234\) | −1.83860 | −0.120193 | ||||||||
\(235\) | −9.01802 | −0.588271 | ||||||||
\(236\) | −9.94967 | −0.647669 | ||||||||
\(237\) | 1.69125 | 0.109858 | ||||||||
\(238\) | −5.07328 | −0.328852 | ||||||||
\(239\) | 7.57521 | 0.490000 | 0.245000 | − | 0.969523i | \(-0.421212\pi\) | ||||
0.245000 | + | 0.969523i | \(0.421212\pi\) | |||||||
\(240\) | −2.13450 | −0.137781 | ||||||||
\(241\) | −23.0746 | −1.48637 | −0.743183 | − | 0.669089i | \(-0.766685\pi\) | ||||
−0.743183 | + | 0.669089i | \(0.766685\pi\) | |||||||
\(242\) | −12.8895 | −0.828567 | ||||||||
\(243\) | −14.7602 | −0.946868 | ||||||||
\(244\) | −13.9563 | −0.893461 | ||||||||
\(245\) | −1.66490 | −0.106367 | ||||||||
\(246\) | −1.45628 | −0.0928491 | ||||||||
\(247\) | 4.14611 | 0.263811 | ||||||||
\(248\) | 1.83007 | 0.116210 | ||||||||
\(249\) | 29.4432 | 1.86589 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −14.1193 | −0.891201 | −0.445600 | − | 0.895232i | \(-0.647010\pi\) | ||||
−0.445600 | + | 0.895232i | \(0.647010\pi\) | |||||||
\(252\) | 4.58049 | 0.288544 | ||||||||
\(253\) | −7.41015 | −0.465872 | ||||||||
\(254\) | −0.747627 | −0.0469103 | ||||||||
\(255\) | −3.67877 | −0.230374 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.62239 | 0.288337 | 0.144168 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144168 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(258\) | 14.4505 | 0.899648 | ||||||||
\(259\) | −27.2083 | −1.69064 | ||||||||
\(260\) | −1.18156 | −0.0732774 | ||||||||
\(261\) | 7.97840 | 0.493850 | ||||||||
\(262\) | −14.1204 | −0.872362 | ||||||||
\(263\) | 0.970610 | 0.0598503 | 0.0299252 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299252 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(264\) | −10.4327 | −0.642091 | ||||||||
\(265\) | −9.35047 | −0.574395 | ||||||||
\(266\) | −10.3292 | −0.633323 | ||||||||
\(267\) | −8.97910 | −0.549512 | ||||||||
\(268\) | 6.03189 | 0.368456 | ||||||||
\(269\) | −14.2768 | −0.870474 | −0.435237 | − | 0.900316i | \(-0.643335\pi\) | ||||
−0.435237 | + | 0.900316i | \(0.643335\pi\) | |||||||
\(270\) | −3.08205 | −0.187568 | ||||||||
\(271\) | 14.8530 | 0.902257 | 0.451128 | − | 0.892459i | \(-0.351022\pi\) | ||||
0.451128 | + | 0.892459i | \(0.351022\pi\) | |||||||
\(272\) | 1.72348 | 0.104502 | ||||||||
\(273\) | 7.42393 | 0.449317 | ||||||||
\(274\) | 12.0399 | 0.727359 | ||||||||
\(275\) | 4.88769 | 0.294739 | ||||||||
\(276\) | −3.23608 | −0.194789 | ||||||||
\(277\) | 11.1006 | 0.666972 | 0.333486 | − | 0.942755i | \(-0.391775\pi\) | ||||
0.333486 | + | 0.942755i | \(0.391775\pi\) | |||||||
\(278\) | −9.71606 | −0.582731 | ||||||||
\(279\) | −2.84773 | −0.170489 | ||||||||
\(280\) | 2.94362 | 0.175915 | ||||||||
\(281\) | 26.8121 | 1.59948 | 0.799738 | − | 0.600349i | \(-0.204972\pi\) | ||||
0.799738 | + | 0.600349i | \(0.204972\pi\) | |||||||
\(282\) | −19.2489 | −1.14626 | ||||||||
\(283\) | 3.27664 | 0.194776 | 0.0973879 | − | 0.995247i | \(-0.468951\pi\) | ||||
0.0973879 | + | 0.995247i | \(0.468951\pi\) | |||||||
\(284\) | 10.6224 | 0.630323 | ||||||||
\(285\) | −7.48997 | −0.443667 | ||||||||
\(286\) | −5.77511 | −0.341489 | ||||||||
\(287\) | 2.00831 | 0.118547 | ||||||||
\(288\) | −1.55608 | −0.0916926 | ||||||||
\(289\) | −14.0296 | −0.825271 | ||||||||
\(290\) | 5.12726 | 0.301083 | ||||||||
\(291\) | −23.6746 | −1.38783 | ||||||||
\(292\) | −5.91560 | −0.346184 | ||||||||
\(293\) | −23.5985 | −1.37864 | −0.689320 | − | 0.724457i | \(-0.742091\pi\) | ||||
−0.689320 | + | 0.724457i | \(0.742091\pi\) | |||||||
\(294\) | −3.55372 | −0.207257 | ||||||||
\(295\) | 9.94967 | 0.579292 | ||||||||
\(296\) | 9.24316 | 0.537248 | ||||||||
\(297\) | −15.0641 | −0.874108 | ||||||||
\(298\) | 18.1445 | 1.05108 | ||||||||
\(299\) | −1.79135 | −0.103596 | ||||||||
\(300\) | 2.13450 | 0.123235 | ||||||||
\(301\) | −19.9282 | −1.14864 | ||||||||
\(302\) | −17.8080 | −1.02474 | ||||||||
\(303\) | 39.6353 | 2.27699 | ||||||||
\(304\) | 3.50901 | 0.201255 | ||||||||
\(305\) | 13.9563 | 0.799136 | ||||||||
\(306\) | −2.68187 | −0.153312 | ||||||||
\(307\) | 0.150742 | 0.00860331 | 0.00430165 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00430165 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(308\) | 14.3875 | 0.819803 | ||||||||
\(309\) | 31.1331 | 1.77110 | ||||||||
\(310\) | −1.83007 | −0.103941 | ||||||||
\(311\) | 4.60390 | 0.261063 | 0.130532 | − | 0.991444i | \(-0.458332\pi\) | ||||
0.130532 | + | 0.991444i | \(0.458332\pi\) | |||||||
\(312\) | −2.52204 | −0.142782 | ||||||||
\(313\) | 17.7806 | 1.00502 | 0.502508 | − | 0.864573i | \(-0.332411\pi\) | ||||
0.502508 | + | 0.864573i | \(0.332411\pi\) | |||||||
\(314\) | 8.54108 | 0.482001 | ||||||||
\(315\) | −4.58049 | −0.258082 | ||||||||
\(316\) | 0.792340 | 0.0445726 | ||||||||
\(317\) | 23.8147 | 1.33757 | 0.668784 | − | 0.743457i | \(-0.266815\pi\) | ||||
0.668784 | + | 0.743457i | \(0.266815\pi\) | |||||||
\(318\) | −19.9585 | −1.11922 | ||||||||
\(319\) | 25.0604 | 1.40311 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 15.1990 | 0.848323 | ||||||||
\(322\) | 4.46278 | 0.248701 | ||||||||
\(323\) | 6.04772 | 0.336504 | ||||||||
\(324\) | −11.2469 | −0.624825 | ||||||||
\(325\) | 1.18156 | 0.0655413 | ||||||||
\(326\) | 15.6136 | 0.864756 | ||||||||
\(327\) | 10.7039 | 0.591926 | ||||||||
\(328\) | −0.682260 | −0.0376715 | ||||||||
\(329\) | 26.5456 | 1.46351 | ||||||||
\(330\) | 10.4327 | 0.574304 | ||||||||
\(331\) | 36.1186 | 1.98526 | 0.992629 | − | 0.121193i | \(-0.0386719\pi\) | ||||
0.992629 | + | 0.121193i | \(0.0386719\pi\) | |||||||
\(332\) | 13.7940 | 0.757042 | ||||||||
\(333\) | −14.3831 | −0.788186 | ||||||||
\(334\) | 16.9665 | 0.928363 | ||||||||
\(335\) | −6.03189 | −0.329557 | ||||||||
\(336\) | 6.28315 | 0.342774 | ||||||||
\(337\) | −11.2380 | −0.612172 | −0.306086 | − | 0.952004i | \(-0.599020\pi\) | ||||
−0.306086 | + | 0.952004i | \(0.599020\pi\) | |||||||
\(338\) | 11.6039 | 0.631169 | ||||||||
\(339\) | −19.4560 | −1.05670 | ||||||||
\(340\) | −1.72348 | −0.0934690 | ||||||||
\(341\) | −8.94482 | −0.484389 | ||||||||
\(342\) | −5.46028 | −0.295258 | ||||||||
\(343\) | −15.7045 | −0.847964 | ||||||||
\(344\) | 6.76997 | 0.365013 | ||||||||
\(345\) | 3.23608 | 0.174225 | ||||||||
\(346\) | −8.86101 | −0.476371 | ||||||||
\(347\) | −30.6989 | −1.64800 | −0.824001 | − | 0.566588i | \(-0.808263\pi\) | ||||
−0.824001 | + | 0.566588i | \(0.808263\pi\) | |||||||
\(348\) | 10.9441 | 0.586666 | ||||||||
\(349\) | 17.5626 | 0.940105 | 0.470052 | − | 0.882639i | \(-0.344235\pi\) | ||||
0.470052 | + | 0.882639i | \(0.344235\pi\) | |||||||
\(350\) | −2.94362 | −0.157343 | ||||||||
\(351\) | −3.64164 | −0.194376 | ||||||||
\(352\) | −4.88769 | −0.260515 | ||||||||
\(353\) | −10.6920 | −0.569079 | −0.284539 | − | 0.958664i | \(-0.591841\pi\) | ||||
−0.284539 | + | 0.958664i | \(0.591841\pi\) | |||||||
\(354\) | 21.2375 | 1.12876 | ||||||||
\(355\) | −10.6224 | −0.563778 | ||||||||
\(356\) | −4.20666 | −0.222952 | ||||||||
\(357\) | 10.8289 | 0.573126 | ||||||||
\(358\) | 20.7403 | 1.09616 | ||||||||
\(359\) | 23.0313 | 1.21554 | 0.607772 | − | 0.794111i | \(-0.292063\pi\) | ||||
0.607772 | + | 0.794111i | \(0.292063\pi\) | |||||||
\(360\) | 1.55608 | 0.0820124 | ||||||||
\(361\) | −6.68685 | −0.351940 | ||||||||
\(362\) | −10.9538 | −0.575718 | ||||||||
\(363\) | 27.5125 | 1.44403 | ||||||||
\(364\) | 3.47807 | 0.182300 | ||||||||
\(365\) | 5.91560 | 0.309636 | ||||||||
\(366\) | 29.7897 | 1.55713 | ||||||||
\(367\) | −27.3778 | −1.42911 | −0.714554 | − | 0.699580i | \(-0.753370\pi\) | ||||
−0.714554 | + | 0.699580i | \(0.753370\pi\) | |||||||
\(368\) | −1.51609 | −0.0790315 | ||||||||
\(369\) | 1.06165 | 0.0552672 | ||||||||
\(370\) | −9.24316 | −0.480529 | ||||||||
\(371\) | 27.5242 | 1.42899 | ||||||||
\(372\) | −3.90628 | −0.202531 | ||||||||
\(373\) | 0.673310 | 0.0348627 | 0.0174313 | − | 0.999848i | \(-0.494451\pi\) | ||||
0.0174313 | + | 0.999848i | \(0.494451\pi\) | |||||||
\(374\) | −8.42385 | −0.435587 | ||||||||
\(375\) | −2.13450 | −0.110225 | ||||||||
\(376\) | −9.01802 | −0.465069 | ||||||||
\(377\) | 6.05817 | 0.312012 | ||||||||
\(378\) | 9.07239 | 0.466633 | ||||||||
\(379\) | 2.85212 | 0.146503 | 0.0732517 | − | 0.997313i | \(-0.476662\pi\) | ||||
0.0732517 | + | 0.997313i | \(0.476662\pi\) | |||||||
\(380\) | −3.50901 | −0.180008 | ||||||||
\(381\) | 1.59581 | 0.0817556 | ||||||||
\(382\) | −20.0091 | −1.02375 | ||||||||
\(383\) | −17.1127 | −0.874419 | −0.437209 | − | 0.899360i | \(-0.644033\pi\) | ||||
−0.437209 | + | 0.899360i | \(0.644033\pi\) | |||||||
\(384\) | −2.13450 | −0.108926 | ||||||||
\(385\) | −14.3875 | −0.733254 | ||||||||
\(386\) | 4.39641 | 0.223772 | ||||||||
\(387\) | −10.5346 | −0.535503 | ||||||||
\(388\) | −11.0914 | −0.563081 | ||||||||
\(389\) | −35.3435 | −1.79199 | −0.895994 | − | 0.444065i | \(-0.853536\pi\) | ||||
−0.895994 | + | 0.444065i | \(0.853536\pi\) | |||||||
\(390\) | 2.52204 | 0.127709 | ||||||||
\(391\) | −2.61295 | −0.132143 | ||||||||
\(392\) | −1.66490 | −0.0840901 | ||||||||
\(393\) | 30.1400 | 1.52036 | ||||||||
\(394\) | 21.8553 | 1.10106 | ||||||||
\(395\) | −0.792340 | −0.0398669 | ||||||||
\(396\) | 7.60561 | 0.382196 | ||||||||
\(397\) | −9.06350 | −0.454884 | −0.227442 | − | 0.973792i | \(-0.573036\pi\) | ||||
−0.227442 | + | 0.973792i | \(0.573036\pi\) | |||||||
\(398\) | 11.1500 | 0.558899 | ||||||||
\(399\) | 22.0476 | 1.10376 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 3.16303 | 0.157954 | 0.0789772 | − | 0.996876i | \(-0.474835\pi\) | ||||
0.0789772 | + | 0.996876i | \(0.474835\pi\) | |||||||
\(402\) | −12.8750 | −0.642149 | ||||||||
\(403\) | −2.16234 | −0.107714 | ||||||||
\(404\) | 18.5689 | 0.923838 | ||||||||
\(405\) | 11.2469 | 0.558861 | ||||||||
\(406\) | −15.0927 | −0.749038 | ||||||||
\(407\) | −45.1777 | −2.23937 | ||||||||
\(408\) | −3.67877 | −0.182126 | ||||||||
\(409\) | 6.37643 | 0.315294 | 0.157647 | − | 0.987496i | \(-0.449609\pi\) | ||||
0.157647 | + | 0.987496i | \(0.449609\pi\) | |||||||
\(410\) | 0.682260 | 0.0336944 | ||||||||
\(411\) | −25.6992 | −1.26765 | ||||||||
\(412\) | 14.5857 | 0.718586 | ||||||||
\(413\) | −29.2881 | −1.44117 | ||||||||
\(414\) | 2.35914 | 0.115946 | ||||||||
\(415\) | −13.7940 | −0.677119 | ||||||||
\(416\) | −1.18156 | −0.0579309 | ||||||||
\(417\) | 20.7389 | 1.01559 | ||||||||
\(418\) | −17.1509 | −0.838880 | ||||||||
\(419\) | 3.85214 | 0.188189 | 0.0940946 | − | 0.995563i | \(-0.470004\pi\) | ||||
0.0940946 | + | 0.995563i | \(0.470004\pi\) | |||||||
\(420\) | −6.28315 | −0.306586 | ||||||||
\(421\) | −15.1353 | −0.737650 | −0.368825 | − | 0.929499i | \(-0.620240\pi\) | ||||
−0.368825 | + | 0.929499i | \(0.620240\pi\) | |||||||
\(422\) | −6.35671 | −0.309440 | ||||||||
\(423\) | 14.0327 | 0.682294 | ||||||||
\(424\) | −9.35047 | −0.454099 | ||||||||
\(425\) | 1.72348 | 0.0836013 | ||||||||
\(426\) | −22.6735 | −1.09853 | ||||||||
\(427\) | −41.0821 | −1.98810 | ||||||||
\(428\) | 7.12063 | 0.344188 | ||||||||
\(429\) | 12.3269 | 0.595151 | ||||||||
\(430\) | −6.76997 | −0.326477 | ||||||||
\(431\) | 26.3547 | 1.26946 | 0.634731 | − | 0.772733i | \(-0.281111\pi\) | ||||
0.634731 | + | 0.772733i | \(0.281111\pi\) | |||||||
\(432\) | −3.08205 | −0.148285 | ||||||||
\(433\) | −4.88170 | −0.234599 | −0.117300 | − | 0.993097i | \(-0.537424\pi\) | ||||
−0.117300 | + | 0.993097i | \(0.537424\pi\) | |||||||
\(434\) | 5.38704 | 0.258586 | ||||||||
\(435\) | −10.9441 | −0.524730 | ||||||||
\(436\) | 5.01471 | 0.240161 | ||||||||
\(437\) | −5.31996 | −0.254488 | ||||||||
\(438\) | 12.6268 | 0.603333 | ||||||||
\(439\) | −27.4018 | −1.30782 | −0.653909 | − | 0.756573i | \(-0.726872\pi\) | ||||
−0.653909 | + | 0.756573i | \(0.726872\pi\) | |||||||
\(440\) | 4.88769 | 0.233011 | ||||||||
\(441\) | 2.59071 | 0.123367 | ||||||||
\(442\) | −2.03640 | −0.0968619 | ||||||||
\(443\) | −21.0022 | −0.997842 | −0.498921 | − | 0.866647i | \(-0.666270\pi\) | ||||
−0.498921 | + | 0.866647i | \(0.666270\pi\) | |||||||
\(444\) | −19.7295 | −0.936320 | ||||||||
\(445\) | 4.20666 | 0.199415 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | −38.7294 | −1.83184 | ||||||||
\(448\) | 2.94362 | 0.139073 | ||||||||
\(449\) | −2.13623 | −0.100815 | −0.0504076 | − | 0.998729i | \(-0.516052\pi\) | ||||
−0.0504076 | + | 0.998729i | \(0.516052\pi\) | |||||||
\(450\) | −1.55608 | −0.0733541 | ||||||||
\(451\) | 3.33467 | 0.157024 | ||||||||
\(452\) | −9.11501 | −0.428734 | ||||||||
\(453\) | 38.0112 | 1.78592 | ||||||||
\(454\) | 4.24805 | 0.199371 | ||||||||
\(455\) | −3.47807 | −0.163055 | ||||||||
\(456\) | −7.48997 | −0.350750 | ||||||||
\(457\) | 3.99174 | 0.186726 | 0.0933628 | − | 0.995632i | \(-0.470238\pi\) | ||||
0.0933628 | + | 0.995632i | \(0.470238\pi\) | |||||||
\(458\) | −7.33025 | −0.342520 | ||||||||
\(459\) | −5.31187 | −0.247937 | ||||||||
\(460\) | 1.51609 | 0.0706879 | ||||||||
\(461\) | −9.81448 | −0.457106 | −0.228553 | − | 0.973531i | \(-0.573399\pi\) | ||||
−0.228553 | + | 0.973531i | \(0.573399\pi\) | |||||||
\(462\) | −30.7101 | −1.42876 | ||||||||
\(463\) | −5.92453 | −0.275336 | −0.137668 | − | 0.990478i | \(-0.543961\pi\) | ||||
−0.137668 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(464\) | 5.12726 | 0.238027 | ||||||||
\(465\) | 3.90628 | 0.181149 | ||||||||
\(466\) | −13.9826 | −0.647731 | ||||||||
\(467\) | 12.6924 | 0.587335 | 0.293667 | − | 0.955908i | \(-0.405124\pi\) | ||||
0.293667 | + | 0.955908i | \(0.405124\pi\) | |||||||
\(468\) | 1.83860 | 0.0849893 | ||||||||
\(469\) | 17.7556 | 0.819877 | ||||||||
\(470\) | 9.01802 | 0.415970 | ||||||||
\(471\) | −18.2309 | −0.840036 | ||||||||
\(472\) | 9.94967 | 0.457971 | ||||||||
\(473\) | −33.0895 | −1.52146 | ||||||||
\(474\) | −1.69125 | −0.0776815 | ||||||||
\(475\) | 3.50901 | 0.161004 | ||||||||
\(476\) | 5.07328 | 0.232534 | ||||||||
\(477\) | 14.5500 | 0.666200 | ||||||||
\(478\) | −7.57521 | −0.346482 | ||||||||
\(479\) | 33.2614 | 1.51975 | 0.759876 | − | 0.650068i | \(-0.225260\pi\) | ||||
0.759876 | + | 0.650068i | \(0.225260\pi\) | |||||||
\(480\) | 2.13450 | 0.0974260 | ||||||||
\(481\) | −10.9214 | −0.497972 | ||||||||
\(482\) | 23.0746 | 1.05102 | ||||||||
\(483\) | −9.52579 | −0.433439 | ||||||||
\(484\) | 12.8895 | 0.585885 | ||||||||
\(485\) | 11.0914 | 0.503635 | ||||||||
\(486\) | 14.7602 | 0.669537 | ||||||||
\(487\) | −34.5446 | −1.56537 | −0.782683 | − | 0.622421i | \(-0.786149\pi\) | ||||
−0.782683 | + | 0.622421i | \(0.786149\pi\) | |||||||
\(488\) | 13.9563 | 0.631772 | ||||||||
\(489\) | −33.3271 | −1.50710 | ||||||||
\(490\) | 1.66490 | 0.0752125 | ||||||||
\(491\) | −5.39981 | −0.243690 | −0.121845 | − | 0.992549i | \(-0.538881\pi\) | ||||
−0.121845 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(492\) | 1.45628 | 0.0656543 | ||||||||
\(493\) | 8.83674 | 0.397987 | ||||||||
\(494\) | −4.14611 | −0.186542 | ||||||||
\(495\) | −7.60561 | −0.341847 | ||||||||
\(496\) | −1.83007 | −0.0821726 | ||||||||
\(497\) | 31.2683 | 1.40257 | ||||||||
\(498\) | −29.4432 | −1.31938 | ||||||||
\(499\) | −30.0164 | −1.34372 | −0.671859 | − | 0.740679i | \(-0.734504\pi\) | ||||
−0.671859 | + | 0.740679i | \(0.734504\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −36.2148 | −1.61796 | ||||||||
\(502\) | 14.1193 | 0.630174 | ||||||||
\(503\) | −14.1772 | −0.632131 | −0.316066 | − | 0.948737i | \(-0.602362\pi\) | ||||
−0.316066 | + | 0.948737i | \(0.602362\pi\) | |||||||
\(504\) | −4.58049 | −0.204031 | ||||||||
\(505\) | −18.5689 | −0.826306 | ||||||||
\(506\) | 7.41015 | 0.329422 | ||||||||
\(507\) | −24.7685 | −1.10001 | ||||||||
\(508\) | 0.747627 | 0.0331706 | ||||||||
\(509\) | −38.7002 | −1.71536 | −0.857678 | − | 0.514187i | \(-0.828094\pi\) | ||||
−0.857678 | + | 0.514187i | \(0.828094\pi\) | |||||||
\(510\) | 3.67877 | 0.162899 | ||||||||
\(511\) | −17.4133 | −0.770318 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.8149 | −0.477492 | ||||||||
\(514\) | −4.62239 | −0.203885 | ||||||||
\(515\) | −14.5857 | −0.642723 | ||||||||
\(516\) | −14.4505 | −0.636147 | ||||||||
\(517\) | 44.0772 | 1.93852 | ||||||||
\(518\) | 27.2083 | 1.19547 | ||||||||
\(519\) | 18.9138 | 0.830224 | ||||||||
\(520\) | 1.18156 | 0.0518149 | ||||||||
\(521\) | 32.9341 | 1.44287 | 0.721434 | − | 0.692484i | \(-0.243484\pi\) | ||||
0.721434 | + | 0.692484i | \(0.243484\pi\) | |||||||
\(522\) | −7.97840 | −0.349205 | ||||||||
\(523\) | −0.100231 | −0.00438279 | −0.00219139 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219139 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(524\) | 14.1204 | 0.616853 | ||||||||
\(525\) | 6.28315 | 0.274219 | ||||||||
\(526\) | −0.970610 | −0.0423206 | ||||||||
\(527\) | −3.15410 | −0.137395 | ||||||||
\(528\) | 10.4327 | 0.454027 | ||||||||
\(529\) | −20.7015 | −0.900064 | ||||||||
\(530\) | 9.35047 | 0.406158 | ||||||||
\(531\) | −15.4824 | −0.671881 | ||||||||
\(532\) | 10.3292 | 0.447827 | ||||||||
\(533\) | 0.806133 | 0.0349175 | ||||||||
\(534\) | 8.97910 | 0.388564 | ||||||||
\(535\) | −7.12063 | −0.307851 | ||||||||
\(536\) | −6.03189 | −0.260538 | ||||||||
\(537\) | −44.2701 | −1.91040 | ||||||||
\(538\) | 14.2768 | 0.615518 | ||||||||
\(539\) | 8.13751 | 0.350507 | ||||||||
\(540\) | 3.08205 | 0.132630 | ||||||||
\(541\) | 21.7799 | 0.936389 | 0.468195 | − | 0.883625i | \(-0.344905\pi\) | ||||
0.468195 | + | 0.883625i | \(0.344905\pi\) | |||||||
\(542\) | −14.8530 | −0.637992 | ||||||||
\(543\) | 23.3808 | 1.00337 | ||||||||
\(544\) | −1.72348 | −0.0738938 | ||||||||
\(545\) | −5.01471 | −0.214807 | ||||||||
\(546\) | −7.42393 | −0.317715 | ||||||||
\(547\) | −31.5835 | −1.35041 | −0.675205 | − | 0.737630i | \(-0.735945\pi\) | ||||
−0.675205 | + | 0.737630i | \(0.735945\pi\) | |||||||
\(548\) | −12.0399 | −0.514321 | ||||||||
\(549\) | −21.7171 | −0.926862 | ||||||||
\(550\) | −4.88769 | −0.208412 | ||||||||
\(551\) | 17.9916 | 0.766468 | ||||||||
\(552\) | 3.23608 | 0.137737 | ||||||||
\(553\) | 2.33235 | 0.0991815 | ||||||||
\(554\) | −11.1006 | −0.471620 | ||||||||
\(555\) | 19.7295 | 0.837470 | ||||||||
\(556\) | 9.71606 | 0.412053 | ||||||||
\(557\) | −17.5855 | −0.745121 | −0.372560 | − | 0.928008i | \(-0.621520\pi\) | ||||
−0.372560 | + | 0.928008i | \(0.621520\pi\) | |||||||
\(558\) | 2.84773 | 0.120554 | ||||||||
\(559\) | −7.99915 | −0.338328 | ||||||||
\(560\) | −2.94362 | −0.124391 | ||||||||
\(561\) | 17.9807 | 0.759145 | ||||||||
\(562\) | −26.8121 | −1.13100 | ||||||||
\(563\) | −26.0481 | −1.09779 | −0.548897 | − | 0.835890i | \(-0.684952\pi\) | ||||
−0.548897 | + | 0.835890i | \(0.684952\pi\) | |||||||
\(564\) | 19.2489 | 0.810526 | ||||||||
\(565\) | 9.11501 | 0.383471 | ||||||||
\(566\) | −3.27664 | −0.137727 | ||||||||
\(567\) | −33.1065 | −1.39034 | ||||||||
\(568\) | −10.6224 | −0.445706 | ||||||||
\(569\) | −21.3159 | −0.893607 | −0.446804 | − | 0.894632i | \(-0.647438\pi\) | ||||
−0.446804 | + | 0.894632i | \(0.647438\pi\) | |||||||
\(570\) | 7.48997 | 0.313720 | ||||||||
\(571\) | −35.3663 | −1.48003 | −0.740017 | − | 0.672589i | \(-0.765182\pi\) | ||||
−0.740017 | + | 0.672589i | \(0.765182\pi\) | |||||||
\(572\) | 5.77511 | 0.241469 | ||||||||
\(573\) | 42.7094 | 1.78421 | ||||||||
\(574\) | −2.00831 | −0.0838254 | ||||||||
\(575\) | −1.51609 | −0.0632252 | ||||||||
\(576\) | 1.55608 | 0.0648365 | ||||||||
\(577\) | −1.38457 | −0.0576402 | −0.0288201 | − | 0.999585i | \(-0.509175\pi\) | ||||
−0.0288201 | + | 0.999585i | \(0.509175\pi\) | |||||||
\(578\) | 14.0296 | 0.583555 | ||||||||
\(579\) | −9.38413 | −0.389991 | ||||||||
\(580\) | −5.12726 | −0.212898 | ||||||||
\(581\) | 40.6042 | 1.68455 | ||||||||
\(582\) | 23.6746 | 0.981343 | ||||||||
\(583\) | 45.7022 | 1.89279 | ||||||||
\(584\) | 5.91560 | 0.244789 | ||||||||
\(585\) | −1.83860 | −0.0760168 | ||||||||
\(586\) | 23.5985 | 0.974846 | ||||||||
\(587\) | 25.7020 | 1.06084 | 0.530418 | − | 0.847736i | \(-0.322035\pi\) | ||||
0.530418 | + | 0.847736i | \(0.322035\pi\) | |||||||
\(588\) | 3.55372 | 0.146553 | ||||||||
\(589\) | −6.42174 | −0.264603 | ||||||||
\(590\) | −9.94967 | −0.409622 | ||||||||
\(591\) | −46.6502 | −1.91893 | ||||||||
\(592\) | −9.24316 | −0.379891 | ||||||||
\(593\) | −20.8407 | −0.855823 | −0.427911 | − | 0.903821i | \(-0.640751\pi\) | ||||
−0.427911 | + | 0.903821i | \(0.640751\pi\) | |||||||
\(594\) | 15.0641 | 0.618088 | ||||||||
\(595\) | −5.07328 | −0.207984 | ||||||||
\(596\) | −18.1445 | −0.743229 | ||||||||
\(597\) | −23.7996 | −0.974054 | ||||||||
\(598\) | 1.79135 | 0.0732538 | ||||||||
\(599\) | 38.4242 | 1.56997 | 0.784985 | − | 0.619514i | \(-0.212670\pi\) | ||||
0.784985 | + | 0.619514i | \(0.212670\pi\) | |||||||
\(600\) | −2.13450 | −0.0871405 | ||||||||
\(601\) | −12.0623 | −0.492033 | −0.246016 | − | 0.969266i | \(-0.579122\pi\) | ||||
−0.246016 | + | 0.969266i | \(0.579122\pi\) | |||||||
\(602\) | 19.9282 | 0.812214 | ||||||||
\(603\) | 9.38608 | 0.382231 | ||||||||
\(604\) | 17.8080 | 0.724599 | ||||||||
\(605\) | −12.8895 | −0.524032 | ||||||||
\(606\) | −39.6353 | −1.61007 | ||||||||
\(607\) | 24.8747 | 1.00963 | 0.504816 | − | 0.863227i | \(-0.331560\pi\) | ||||
0.504816 | + | 0.863227i | \(0.331560\pi\) | |||||||
\(608\) | −3.50901 | −0.142309 | ||||||||
\(609\) | 32.2153 | 1.30543 | ||||||||
\(610\) | −13.9563 | −0.565074 | ||||||||
\(611\) | 10.6554 | 0.431069 | ||||||||
\(612\) | 2.68187 | 0.108408 | ||||||||
\(613\) | −31.5893 | −1.27588 | −0.637941 | − | 0.770085i | \(-0.720214\pi\) | ||||
−0.637941 | + | 0.770085i | \(0.720214\pi\) | |||||||
\(614\) | −0.150742 | −0.00608346 | ||||||||
\(615\) | −1.45628 | −0.0587230 | ||||||||
\(616\) | −14.3875 | −0.579689 | ||||||||
\(617\) | −26.5252 | −1.06786 | −0.533932 | − | 0.845527i | \(-0.679286\pi\) | ||||
−0.533932 | + | 0.845527i | \(0.679286\pi\) | |||||||
\(618\) | −31.1331 | −1.25236 | ||||||||
\(619\) | 40.7097 | 1.63626 | 0.818130 | − | 0.575033i | \(-0.195011\pi\) | ||||
0.818130 | + | 0.575033i | \(0.195011\pi\) | |||||||
\(620\) | 1.83007 | 0.0734974 | ||||||||
\(621\) | 4.67266 | 0.187507 | ||||||||
\(622\) | −4.60390 | −0.184599 | ||||||||
\(623\) | −12.3828 | −0.496107 | ||||||||
\(624\) | 2.52204 | 0.100962 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.7806 | −0.710654 | ||||||||
\(627\) | 36.6086 | 1.46201 | ||||||||
\(628\) | −8.54108 | −0.340826 | ||||||||
\(629\) | −15.9304 | −0.635188 | ||||||||
\(630\) | 4.58049 | 0.182491 | ||||||||
\(631\) | 7.72316 | 0.307454 | 0.153727 | − | 0.988113i | \(-0.450872\pi\) | ||||
0.153727 | + | 0.988113i | \(0.450872\pi\) | |||||||
\(632\) | −0.792340 | −0.0315176 | ||||||||
\(633\) | 13.5684 | 0.539294 | ||||||||
\(634\) | −23.8147 | −0.945803 | ||||||||
\(635\) | −0.747627 | −0.0296687 | ||||||||
\(636\) | 19.9585 | 0.791408 | ||||||||
\(637\) | 1.96718 | 0.0779426 | ||||||||
\(638\) | −25.0604 | −0.992152 | ||||||||
\(639\) | 16.5292 | 0.653887 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −28.5017 | −1.12575 | −0.562876 | − | 0.826542i | \(-0.690305\pi\) | ||||
−0.562876 | + | 0.826542i | \(0.690305\pi\) | |||||||
\(642\) | −15.1990 | −0.599855 | ||||||||
\(643\) | 4.76526 | 0.187923 | 0.0939617 | − | 0.995576i | \(-0.470047\pi\) | ||||
0.0939617 | + | 0.995576i | \(0.470047\pi\) | |||||||
\(644\) | −4.46278 | −0.175858 | ||||||||
\(645\) | 14.4505 | 0.568987 | ||||||||
\(646\) | −6.04772 | −0.237944 | ||||||||
\(647\) | −37.4316 | −1.47159 | −0.735794 | − | 0.677206i | \(-0.763191\pi\) | ||||
−0.735794 | + | 0.677206i | \(0.763191\pi\) | |||||||
\(648\) | 11.2469 | 0.441818 | ||||||||
\(649\) | −48.6309 | −1.90893 | ||||||||
\(650\) | −1.18156 | −0.0463447 | ||||||||
\(651\) | −11.4986 | −0.450666 | ||||||||
\(652\) | −15.6136 | −0.611475 | ||||||||
\(653\) | 34.8685 | 1.36451 | 0.682254 | − | 0.731115i | \(-0.261000\pi\) | ||||
0.682254 | + | 0.731115i | \(0.261000\pi\) | |||||||
\(654\) | −10.7039 | −0.418555 | ||||||||
\(655\) | −14.1204 | −0.551730 | ||||||||
\(656\) | 0.682260 | 0.0266378 | ||||||||
\(657\) | −9.20511 | −0.359126 | ||||||||
\(658\) | −26.5456 | −1.03486 | ||||||||
\(659\) | 13.7645 | 0.536190 | 0.268095 | − | 0.963392i | \(-0.413606\pi\) | ||||
0.268095 | + | 0.963392i | \(0.413606\pi\) | |||||||
\(660\) | −10.4327 | −0.406094 | ||||||||
\(661\) | 6.88583 | 0.267828 | 0.133914 | − | 0.990993i | \(-0.457245\pi\) | ||||
0.133914 | + | 0.990993i | \(0.457245\pi\) | |||||||
\(662\) | −36.1186 | −1.40379 | ||||||||
\(663\) | 4.34670 | 0.168812 | ||||||||
\(664\) | −13.7940 | −0.535310 | ||||||||
\(665\) | −10.3292 | −0.400549 | ||||||||
\(666\) | 14.3831 | 0.557332 | ||||||||
\(667\) | −7.77336 | −0.300986 | ||||||||
\(668\) | −16.9665 | −0.656452 | ||||||||
\(669\) | 2.13450 | 0.0825244 | ||||||||
\(670\) | 6.03189 | 0.233032 | ||||||||
\(671\) | −68.2140 | −2.63337 | ||||||||
\(672\) | −6.28315 | −0.242378 | ||||||||
\(673\) | −19.6393 | −0.757038 | −0.378519 | − | 0.925593i | \(-0.623567\pi\) | ||||
−0.378519 | + | 0.925593i | \(0.623567\pi\) | |||||||
\(674\) | 11.2380 | 0.432871 | ||||||||
\(675\) | −3.08205 | −0.118628 | ||||||||
\(676\) | −11.6039 | −0.446304 | ||||||||
\(677\) | −25.3687 | −0.974999 | −0.487499 | − | 0.873123i | \(-0.662091\pi\) | ||||
−0.487499 | + | 0.873123i | \(0.662091\pi\) | |||||||
\(678\) | 19.4560 | 0.747201 | ||||||||
\(679\) | −32.6489 | −1.25295 | ||||||||
\(680\) | 1.72348 | 0.0660926 | ||||||||
\(681\) | −9.06744 | −0.347465 | ||||||||
\(682\) | 8.94482 | 0.342515 | ||||||||
\(683\) | −23.6002 | −0.903038 | −0.451519 | − | 0.892262i | \(-0.649118\pi\) | ||||
−0.451519 | + | 0.892262i | \(0.649118\pi\) | |||||||
\(684\) | 5.46028 | 0.208779 | ||||||||
\(685\) | 12.0399 | 0.460022 | ||||||||
\(686\) | 15.7045 | 0.599601 | ||||||||
\(687\) | 15.6464 | 0.596947 | ||||||||
\(688\) | −6.76997 | −0.258103 | ||||||||
\(689\) | 11.0482 | 0.420902 | ||||||||
\(690\) | −3.23608 | −0.123195 | ||||||||
\(691\) | 11.0977 | 0.422178 | 0.211089 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211089 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(692\) | 8.86101 | 0.336845 | ||||||||
\(693\) | 22.3880 | 0.850451 | ||||||||
\(694\) | 30.6989 | 1.16531 | ||||||||
\(695\) | −9.71606 | −0.368551 | ||||||||
\(696\) | −10.9441 | −0.414835 | ||||||||
\(697\) | 1.17586 | 0.0445390 | ||||||||
\(698\) | −17.5626 | −0.664754 | ||||||||
\(699\) | 29.8458 | 1.12887 | ||||||||
\(700\) | 2.94362 | 0.111258 | ||||||||
\(701\) | −36.4476 | −1.37661 | −0.688303 | − | 0.725423i | \(-0.741644\pi\) | ||||
−0.688303 | + | 0.725423i | \(0.741644\pi\) | |||||||
\(702\) | 3.64164 | 0.137445 | ||||||||
\(703\) | −32.4343 | −1.22328 | ||||||||
\(704\) | 4.88769 | 0.184212 | ||||||||
\(705\) | −19.2489 | −0.724957 | ||||||||
\(706\) | 10.6920 | 0.402399 | ||||||||
\(707\) | 54.6599 | 2.05570 | ||||||||
\(708\) | −21.2375 | −0.798156 | ||||||||
\(709\) | 39.9645 | 1.50090 | 0.750449 | − | 0.660928i | \(-0.229837\pi\) | ||||
0.750449 | + | 0.660928i | \(0.229837\pi\) | |||||||
\(710\) | 10.6224 | 0.398651 | ||||||||
\(711\) | 1.23294 | 0.0462389 | ||||||||
\(712\) | 4.20666 | 0.157651 | ||||||||
\(713\) | 2.77455 | 0.103908 | ||||||||
\(714\) | −10.8289 | −0.405262 | ||||||||
\(715\) | −5.77511 | −0.215977 | ||||||||
\(716\) | −20.7403 | −0.775102 | ||||||||
\(717\) | 16.1693 | 0.603852 | ||||||||
\(718\) | −23.0313 | −0.859520 | ||||||||
\(719\) | 31.5864 | 1.17798 | 0.588988 | − | 0.808142i | \(-0.299527\pi\) | ||||
0.588988 | + | 0.808142i | \(0.299527\pi\) | |||||||
\(720\) | −1.55608 | −0.0579915 | ||||||||
\(721\) | 42.9348 | 1.59898 | ||||||||
\(722\) | 6.68685 | 0.248859 | ||||||||
\(723\) | −49.2526 | −1.83173 | ||||||||
\(724\) | 10.9538 | 0.407094 | ||||||||
\(725\) | 5.12726 | 0.190422 | ||||||||
\(726\) | −27.5125 | −1.02109 | ||||||||
\(727\) | −10.7517 | −0.398758 | −0.199379 | − | 0.979922i | \(-0.563892\pi\) | ||||
−0.199379 | + | 0.979922i | \(0.563892\pi\) | |||||||
\(728\) | −3.47807 | −0.128906 | ||||||||
\(729\) | 2.23493 | 0.0827753 | ||||||||
\(730\) | −5.91560 | −0.218946 | ||||||||
\(731\) | −11.6679 | −0.431554 | ||||||||
\(732\) | −29.7897 | −1.10106 | ||||||||
\(733\) | 7.10675 | 0.262494 | 0.131247 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131247 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(734\) | 27.3778 | 1.01053 | ||||||||
\(735\) | −3.55372 | −0.131081 | ||||||||
\(736\) | 1.51609 | 0.0558837 | ||||||||
\(737\) | 29.4820 | 1.08598 | ||||||||
\(738\) | −1.06165 | −0.0390798 | ||||||||
\(739\) | −18.2706 | −0.672094 | −0.336047 | − | 0.941845i | \(-0.609090\pi\) | ||||
−0.336047 | + | 0.941845i | \(0.609090\pi\) | |||||||
\(740\) | 9.24316 | 0.339785 | ||||||||
\(741\) | 8.84987 | 0.325108 | ||||||||
\(742\) | −27.5242 | −1.01045 | ||||||||
\(743\) | −27.6208 | −1.01331 | −0.506655 | − | 0.862149i | \(-0.669118\pi\) | ||||
−0.506655 | + | 0.862149i | \(0.669118\pi\) | |||||||
\(744\) | 3.90628 | 0.143211 | ||||||||
\(745\) | 18.1445 | 0.664764 | ||||||||
\(746\) | −0.673310 | −0.0246516 | ||||||||
\(747\) | 21.4645 | 0.785343 | ||||||||
\(748\) | 8.42385 | 0.308006 | ||||||||
\(749\) | 20.9604 | 0.765877 | ||||||||
\(750\) | 2.13450 | 0.0779408 | ||||||||
\(751\) | −19.3759 | −0.707038 | −0.353519 | − | 0.935427i | \(-0.615015\pi\) | ||||
−0.353519 | + | 0.935427i | \(0.615015\pi\) | |||||||
\(752\) | 9.01802 | 0.328853 | ||||||||
\(753\) | −30.1375 | −1.09827 | ||||||||
\(754\) | −6.05817 | −0.220626 | ||||||||
\(755\) | −17.8080 | −0.648101 | ||||||||
\(756\) | −9.07239 | −0.329960 | ||||||||
\(757\) | −0.517273 | −0.0188006 | −0.00940030 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00940030 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(758\) | −2.85212 | −0.103594 | ||||||||
\(759\) | −15.8169 | −0.574119 | ||||||||
\(760\) | 3.50901 | 0.127285 | ||||||||
\(761\) | −16.6258 | −0.602685 | −0.301343 | − | 0.953516i | \(-0.597435\pi\) | ||||
−0.301343 | + | 0.953516i | \(0.597435\pi\) | |||||||
\(762\) | −1.59581 | −0.0578100 | ||||||||
\(763\) | 14.7614 | 0.534399 | ||||||||
\(764\) | 20.0091 | 0.723904 | ||||||||
\(765\) | −2.68187 | −0.0969633 | ||||||||
\(766\) | 17.1127 | 0.618307 | ||||||||
\(767\) | −11.7562 | −0.424490 | ||||||||
\(768\) | 2.13450 | 0.0770220 | ||||||||
\(769\) | −10.4927 | −0.378377 | −0.189188 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189188 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(770\) | 14.3875 | 0.518489 | ||||||||
\(771\) | 9.86648 | 0.355332 | ||||||||
\(772\) | −4.39641 | −0.158230 | ||||||||
\(773\) | −47.7679 | −1.71809 | −0.859045 | − | 0.511899i | \(-0.828942\pi\) | ||||
−0.859045 | + | 0.511899i | \(0.828942\pi\) | |||||||
\(774\) | 10.5346 | 0.378658 | ||||||||
\(775\) | −1.83007 | −0.0657381 | ||||||||
\(776\) | 11.0914 | 0.398158 | ||||||||
\(777\) | −58.0761 | −2.08347 | ||||||||
\(778\) | 35.3435 | 1.26713 | ||||||||
\(779\) | 2.39406 | 0.0857760 | ||||||||
\(780\) | −2.52204 | −0.0903036 | ||||||||
\(781\) | 51.9189 | 1.85780 | ||||||||
\(782\) | 2.61295 | 0.0934389 | ||||||||
\(783\) | −15.8025 | −0.564734 | ||||||||
\(784\) | 1.66490 | 0.0594607 | ||||||||
\(785\) | 8.54108 | 0.304844 | ||||||||
\(786\) | −30.1400 | −1.07506 | ||||||||
\(787\) | −40.7277 | −1.45179 | −0.725893 | − | 0.687808i | \(-0.758573\pi\) | ||||
−0.725893 | + | 0.687808i | \(0.758573\pi\) | |||||||
\(788\) | −21.8553 | −0.778565 | ||||||||
\(789\) | 2.07176 | 0.0737567 | ||||||||
\(790\) | 0.792340 | 0.0281902 | ||||||||
\(791\) | −26.8311 | −0.954005 | ||||||||
\(792\) | −7.60561 | −0.270254 | ||||||||
\(793\) | −16.4902 | −0.585586 | ||||||||
\(794\) | 9.06350 | 0.321652 | ||||||||
\(795\) | −19.9585 | −0.707857 | ||||||||
\(796\) | −11.1500 | −0.395201 | ||||||||
\(797\) | 31.2035 | 1.10528 | 0.552642 | − | 0.833419i | \(-0.313620\pi\) | ||||
0.552642 | + | 0.833419i | \(0.313620\pi\) | |||||||
\(798\) | −22.0476 | −0.780477 | ||||||||
\(799\) | 15.5424 | 0.549851 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −6.54588 | −0.231287 | ||||||||
\(802\) | −3.16303 | −0.111691 | ||||||||
\(803\) | −28.9136 | −1.02034 | ||||||||
\(804\) | 12.8750 | 0.454068 | ||||||||
\(805\) | 4.46278 | 0.157292 | ||||||||
\(806\) | 2.16234 | 0.0761653 | ||||||||
\(807\) | −30.4739 | −1.07273 | ||||||||
\(808\) | −18.5689 | −0.653252 | ||||||||
\(809\) | 33.5685 | 1.18021 | 0.590103 | − | 0.807328i | \(-0.299087\pi\) | ||||
0.590103 | + | 0.807328i | \(0.299087\pi\) | |||||||
\(810\) | −11.2469 | −0.395174 | ||||||||
\(811\) | 19.2935 | 0.677485 | 0.338742 | − | 0.940879i | \(-0.389998\pi\) | ||||
0.338742 | + | 0.940879i | \(0.389998\pi\) | |||||||
\(812\) | 15.0927 | 0.529650 | ||||||||
\(813\) | 31.7037 | 1.11190 | ||||||||
\(814\) | 45.1777 | 1.58348 | ||||||||
\(815\) | 15.6136 | 0.546920 | ||||||||
\(816\) | 3.67877 | 0.128783 | ||||||||
\(817\) | −23.7559 | −0.831114 | ||||||||
\(818\) | −6.37643 | −0.222947 | ||||||||
\(819\) | 5.41214 | 0.189116 | ||||||||
\(820\) | −0.682260 | −0.0238256 | ||||||||
\(821\) | 14.7134 | 0.513502 | 0.256751 | − | 0.966478i | \(-0.417348\pi\) | ||||
0.256751 | + | 0.966478i | \(0.417348\pi\) | |||||||
\(822\) | 25.6992 | 0.896363 | ||||||||
\(823\) | 21.4458 | 0.747553 | 0.373777 | − | 0.927519i | \(-0.378063\pi\) | ||||
0.373777 | + | 0.927519i | \(0.378063\pi\) | |||||||
\(824\) | −14.5857 | −0.508117 | ||||||||
\(825\) | 10.4327 | 0.363222 | ||||||||
\(826\) | 29.2881 | 1.01906 | ||||||||
\(827\) | 5.18881 | 0.180432 | 0.0902162 | − | 0.995922i | \(-0.471244\pi\) | ||||
0.0902162 | + | 0.995922i | \(0.471244\pi\) | |||||||
\(828\) | −2.35914 | −0.0819859 | ||||||||
\(829\) | −26.4094 | −0.917237 | −0.458618 | − | 0.888633i | \(-0.651655\pi\) | ||||
−0.458618 | + | 0.888633i | \(0.651655\pi\) | |||||||
\(830\) | 13.7940 | 0.478796 | ||||||||
\(831\) | 23.6942 | 0.821944 | ||||||||
\(832\) | 1.18156 | 0.0409633 | ||||||||
\(833\) | 2.86943 | 0.0994198 | ||||||||
\(834\) | −20.7389 | −0.718129 | ||||||||
\(835\) | 16.9665 | 0.587149 | ||||||||
\(836\) | 17.1509 | 0.593178 | ||||||||
\(837\) | 5.64038 | 0.194960 | ||||||||
\(838\) | −3.85214 | −0.133070 | ||||||||
\(839\) | 23.1884 | 0.800553 | 0.400277 | − | 0.916394i | \(-0.368914\pi\) | ||||
0.400277 | + | 0.916394i | \(0.368914\pi\) | |||||||
\(840\) | 6.28315 | 0.216789 | ||||||||
\(841\) | −2.71124 | −0.0934910 | ||||||||
\(842\) | 15.1353 | 0.521597 | ||||||||
\(843\) | 57.2304 | 1.97112 | ||||||||
\(844\) | 6.35671 | 0.218807 | ||||||||
\(845\) | 11.6039 | 0.399187 | ||||||||
\(846\) | −14.0327 | −0.482455 | ||||||||
\(847\) | 37.9417 | 1.30369 | ||||||||
\(848\) | 9.35047 | 0.321096 | ||||||||
\(849\) | 6.99397 | 0.240032 | ||||||||
\(850\) | −1.72348 | −0.0591150 | ||||||||
\(851\) | 14.0134 | 0.480374 | ||||||||
\(852\) | 22.6735 | 0.776780 | ||||||||
\(853\) | 0.587610 | 0.0201194 | 0.0100597 | − | 0.999949i | \(-0.496798\pi\) | ||||
0.0100597 | + | 0.999949i | \(0.496798\pi\) | |||||||
\(854\) | 41.0821 | 1.40580 | ||||||||
\(855\) | −5.46028 | −0.186738 | ||||||||
\(856\) | −7.12063 | −0.243378 | ||||||||
\(857\) | 20.8324 | 0.711623 | 0.355811 | − | 0.934558i | \(-0.384205\pi\) | ||||
0.355811 | + | 0.934558i | \(0.384205\pi\) | |||||||
\(858\) | −12.3269 | −0.420835 | ||||||||
\(859\) | −8.67562 | −0.296008 | −0.148004 | − | 0.988987i | \(-0.547285\pi\) | ||||
−0.148004 | + | 0.988987i | \(0.547285\pi\) | |||||||
\(860\) | 6.76997 | 0.230854 | ||||||||
\(861\) | 4.28674 | 0.146092 | ||||||||
\(862\) | −26.3547 | −0.897645 | ||||||||
\(863\) | −0.612338 | −0.0208442 | −0.0104221 | − | 0.999946i | \(-0.503318\pi\) | ||||
−0.0104221 | + | 0.999946i | \(0.503318\pi\) | |||||||
\(864\) | 3.08205 | 0.104854 | ||||||||
\(865\) | −8.86101 | −0.301283 | ||||||||
\(866\) | 4.88170 | 0.165887 | ||||||||
\(867\) | −29.9461 | −1.01702 | ||||||||
\(868\) | −5.38704 | −0.182848 | ||||||||
\(869\) | 3.87271 | 0.131373 | ||||||||
\(870\) | 10.9441 | 0.371040 | ||||||||
\(871\) | 7.12706 | 0.241491 | ||||||||
\(872\) | −5.01471 | −0.169820 | ||||||||
\(873\) | −17.2591 | −0.584131 | ||||||||
\(874\) | 5.31996 | 0.179950 | ||||||||
\(875\) | −2.94362 | −0.0995125 | ||||||||
\(876\) | −12.6268 | −0.426621 | ||||||||
\(877\) | 16.5942 | 0.560345 | 0.280172 | − | 0.959950i | \(-0.409608\pi\) | ||||
0.280172 | + | 0.959950i | \(0.409608\pi\) | |||||||
\(878\) | 27.4018 | 0.924768 | ||||||||
\(879\) | −50.3710 | −1.69897 | ||||||||
\(880\) | −4.88769 | −0.164764 | ||||||||
\(881\) | −25.2628 | −0.851124 | −0.425562 | − | 0.904929i | \(-0.639924\pi\) | ||||
−0.425562 | + | 0.904929i | \(0.639924\pi\) | |||||||
\(882\) | −2.59071 | −0.0872337 | ||||||||
\(883\) | −15.8970 | −0.534976 | −0.267488 | − | 0.963561i | \(-0.586194\pi\) | ||||
−0.267488 | + | 0.963561i | \(0.586194\pi\) | |||||||
\(884\) | 2.03640 | 0.0684917 | ||||||||
\(885\) | 21.2375 | 0.713892 | ||||||||
\(886\) | 21.0022 | 0.705581 | ||||||||
\(887\) | −33.8814 | −1.13762 | −0.568812 | − | 0.822467i | \(-0.692597\pi\) | ||||
−0.568812 | + | 0.822467i | \(0.692597\pi\) | |||||||
\(888\) | 19.7295 | 0.662078 | ||||||||
\(889\) | 2.20073 | 0.0738101 | ||||||||
\(890\) | −4.20666 | −0.141008 | ||||||||
\(891\) | −54.9711 | −1.84160 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | 31.6443 | 1.05894 | ||||||||
\(894\) | 38.7294 | 1.29531 | ||||||||
\(895\) | 20.7403 | 0.693272 | ||||||||
\(896\) | −2.94362 | −0.0983394 | ||||||||
\(897\) | −3.82363 | −0.127667 | ||||||||
\(898\) | 2.13623 | 0.0712871 | ||||||||
\(899\) | −9.38325 | −0.312949 | ||||||||
\(900\) | 1.55608 | 0.0518692 | ||||||||
\(901\) | 16.1154 | 0.536881 | ||||||||
\(902\) | −3.33467 | −0.111032 | ||||||||
\(903\) | −42.5367 | −1.41553 | ||||||||
\(904\) | 9.11501 | 0.303161 | ||||||||
\(905\) | −10.9538 | −0.364116 | ||||||||
\(906\) | −38.0112 | −1.26284 | ||||||||
\(907\) | 22.2997 | 0.740450 | 0.370225 | − | 0.928942i | \(-0.379281\pi\) | ||||
0.370225 | + | 0.928942i | \(0.379281\pi\) | |||||||
\(908\) | −4.24805 | −0.140976 | ||||||||
\(909\) | 28.8946 | 0.958375 | ||||||||
\(910\) | 3.47807 | 0.115297 | ||||||||
\(911\) | −7.50040 | −0.248499 | −0.124250 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124250 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(912\) | 7.48997 | 0.248018 | ||||||||
\(913\) | 67.4206 | 2.23130 | ||||||||
\(914\) | −3.99174 | −0.132035 | ||||||||
\(915\) | 29.7897 | 0.984817 | ||||||||
\(916\) | 7.33025 | 0.242198 | ||||||||
\(917\) | 41.5651 | 1.37260 | ||||||||
\(918\) | 5.31187 | 0.175318 | ||||||||
\(919\) | −3.96890 | −0.130922 | −0.0654610 | − | 0.997855i | \(-0.520852\pi\) | ||||
−0.0654610 | + | 0.997855i | \(0.520852\pi\) | |||||||
\(920\) | −1.51609 | −0.0499839 | ||||||||
\(921\) | 0.321759 | 0.0106023 | ||||||||
\(922\) | 9.81448 | 0.323223 | ||||||||
\(923\) | 12.5510 | 0.413122 | ||||||||
\(924\) | 30.7101 | 1.01029 | ||||||||
\(925\) | −9.24316 | −0.303913 | ||||||||
\(926\) | 5.92453 | 0.194692 | ||||||||
\(927\) | 22.6965 | 0.745450 | ||||||||
\(928\) | −5.12726 | −0.168310 | ||||||||
\(929\) | 3.10767 | 0.101959 | 0.0509797 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509797 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(930\) | −3.90628 | −0.128092 | ||||||||
\(931\) | 5.84215 | 0.191469 | ||||||||
\(932\) | 13.9826 | 0.458015 | ||||||||
\(933\) | 9.82700 | 0.321722 | ||||||||
\(934\) | −12.6924 | −0.415309 | ||||||||
\(935\) | −8.42385 | −0.275489 | ||||||||
\(936\) | −1.83860 | −0.0600965 | ||||||||
\(937\) | 0.216264 | 0.00706505 | 0.00353252 | − | 0.999994i | \(-0.498876\pi\) | ||||
0.00353252 | + | 0.999994i | \(0.498876\pi\) | |||||||
\(938\) | −17.7556 | −0.579741 | ||||||||
\(939\) | 37.9525 | 1.23853 | ||||||||
\(940\) | −9.01802 | −0.294135 | ||||||||
\(941\) | −45.0298 | −1.46793 | −0.733964 | − | 0.679188i | \(-0.762332\pi\) | ||||
−0.733964 | + | 0.679188i | \(0.762332\pi\) | |||||||
\(942\) | 18.2309 | 0.593995 | ||||||||
\(943\) | −1.03437 | −0.0336836 | ||||||||
\(944\) | −9.94967 | −0.323834 | ||||||||
\(945\) | 9.07239 | 0.295125 | ||||||||
\(946\) | 33.0895 | 1.07583 | ||||||||
\(947\) | 37.6716 | 1.22416 | 0.612081 | − | 0.790795i | \(-0.290333\pi\) | ||||
0.612081 | + | 0.790795i | \(0.290333\pi\) | |||||||
\(948\) | 1.69125 | 0.0549291 | ||||||||
\(949\) | −6.98965 | −0.226894 | ||||||||
\(950\) | −3.50901 | −0.113847 | ||||||||
\(951\) | 50.8324 | 1.64835 | ||||||||
\(952\) | −5.07328 | −0.164426 | ||||||||
\(953\) | −4.50584 | −0.145958 | −0.0729792 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729792 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(954\) | −14.5500 | −0.471075 | ||||||||
\(955\) | −20.0091 | −0.647479 | ||||||||
\(956\) | 7.57521 | 0.245000 | ||||||||
\(957\) | 53.4914 | 1.72913 | ||||||||
\(958\) | −33.2614 | −1.07463 | ||||||||
\(959\) | −35.4410 | −1.14445 | ||||||||
\(960\) | −2.13450 | −0.0688906 | ||||||||
\(961\) | −27.6508 | −0.891963 | ||||||||
\(962\) | 10.9214 | 0.352119 | ||||||||
\(963\) | 11.0802 | 0.357055 | ||||||||
\(964\) | −23.0746 | −0.743183 | ||||||||
\(965\) | 4.39641 | 0.141526 | ||||||||
\(966\) | 9.52579 | 0.306487 | ||||||||
\(967\) | 30.3005 | 0.974397 | 0.487199 | − | 0.873291i | \(-0.338019\pi\) | ||||
0.487199 | + | 0.873291i | \(0.338019\pi\) | |||||||
\(968\) | −12.8895 | −0.414283 | ||||||||
\(969\) | 12.9088 | 0.414692 | ||||||||
\(970\) | −11.0914 | −0.356124 | ||||||||
\(971\) | 4.64548 | 0.149081 | 0.0745403 | − | 0.997218i | \(-0.476251\pi\) | ||||
0.0745403 | + | 0.997218i | \(0.476251\pi\) | |||||||
\(972\) | −14.7602 | −0.473434 | ||||||||
\(973\) | 28.6004 | 0.916886 | ||||||||
\(974\) | 34.5446 | 1.10688 | ||||||||
\(975\) | 2.52204 | 0.0807700 | ||||||||
\(976\) | −13.9563 | −0.446730 | ||||||||
\(977\) | 37.7279 | 1.20702 | 0.603511 | − | 0.797355i | \(-0.293768\pi\) | ||||
0.603511 | + | 0.797355i | \(0.293768\pi\) | |||||||
\(978\) | 33.3271 | 1.06568 | ||||||||
\(979\) | −20.5608 | −0.657127 | ||||||||
\(980\) | −1.66490 | −0.0531833 | ||||||||
\(981\) | 7.80327 | 0.249139 | ||||||||
\(982\) | 5.39981 | 0.172315 | ||||||||
\(983\) | 31.7295 | 1.01201 | 0.506007 | − | 0.862530i | \(-0.331121\pi\) | ||||
0.506007 | + | 0.862530i | \(0.331121\pi\) | |||||||
\(984\) | −1.45628 | −0.0464246 | ||||||||
\(985\) | 21.8553 | 0.696369 | ||||||||
\(986\) | −8.83674 | −0.281419 | ||||||||
\(987\) | 56.6615 | 1.80356 | ||||||||
\(988\) | 4.14611 | 0.131905 | ||||||||
\(989\) | 10.2639 | 0.326372 | ||||||||
\(990\) | 7.60561 | 0.241722 | ||||||||
\(991\) | −43.2187 | −1.37289 | −0.686444 | − | 0.727182i | \(-0.740829\pi\) | ||||
−0.686444 | + | 0.727182i | \(0.740829\pi\) | |||||||
\(992\) | 1.83007 | 0.0581048 | ||||||||
\(993\) | 77.0950 | 2.44654 | ||||||||
\(994\) | −31.2683 | −0.991770 | ||||||||
\(995\) | 11.1500 | 0.353479 | ||||||||
\(996\) | 29.4432 | 0.932943 | ||||||||
\(997\) | 47.3007 | 1.49803 | 0.749015 | − | 0.662553i | \(-0.230527\pi\) | ||||
0.749015 | + | 0.662553i | \(0.230527\pi\) | |||||||
\(998\) | 30.0164 | 0.950152 | ||||||||
\(999\) | 28.4879 | 0.901317 |
(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 | 2230.2.a.p.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2230.2.a.p.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial |