Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.15754\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15754 | −1.52561 | −0.762806 | − | 0.646628i | \(-0.776179\pi\) | ||||
−0.762806 | + | 0.646628i | \(0.776179\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.65498 | 1.32749 | ||||||||
\(5\) | 0.710210 | 0.317616 | 0.158808 | − | 0.987310i | \(-0.449235\pi\) | ||||
0.158808 | + | 0.987310i | \(0.449235\pi\) | |||||||
\(6\) | −2.15754 | −0.880812 | ||||||||
\(7\) | 2.30964 | 0.872963 | 0.436482 | − | 0.899713i | \(-0.356224\pi\) | ||||
0.436482 | + | 0.899713i | \(0.356224\pi\) | |||||||
\(8\) | −1.41315 | −0.499622 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.53231 | −0.484558 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.65498 | 0.766427 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.98315 | −1.33180 | ||||||||
\(15\) | 0.710210 | 0.183375 | ||||||||
\(16\) | −2.26104 | −0.565261 | ||||||||
\(17\) | −6.68027 | −1.62020 | −0.810102 | − | 0.586289i | \(-0.800588\pi\) | ||||
−0.810102 | + | 0.586289i | \(0.800588\pi\) | |||||||
\(18\) | −2.15754 | −0.508537 | ||||||||
\(19\) | −0.242517 | −0.0556372 | −0.0278186 | − | 0.999613i | \(-0.508856\pi\) | ||||
−0.0278186 | + | 0.999613i | \(0.508856\pi\) | |||||||
\(20\) | 1.88559 | 0.421631 | ||||||||
\(21\) | 2.30964 | 0.504005 | ||||||||
\(22\) | −2.15754 | −0.459989 | ||||||||
\(23\) | 9.53531 | 1.98825 | 0.994125 | − | 0.108242i | \(-0.0345220\pi\) | ||||
0.994125 | + | 0.108242i | \(0.0345220\pi\) | |||||||
\(24\) | −1.41315 | −0.288457 | ||||||||
\(25\) | −4.49560 | −0.899120 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 6.13206 | 1.15885 | ||||||||
\(29\) | −2.95273 | −0.548308 | −0.274154 | − | 0.961686i | \(-0.588398\pi\) | ||||
−0.274154 | + | 0.961686i | \(0.588398\pi\) | |||||||
\(30\) | −1.53231 | −0.279760 | ||||||||
\(31\) | −4.02017 | −0.722044 | −0.361022 | − | 0.932557i | \(-0.617572\pi\) | ||||
−0.361022 | + | 0.932557i | \(0.617572\pi\) | |||||||
\(32\) | 7.70458 | 1.36199 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 14.4130 | 2.47180 | ||||||||
\(35\) | 1.64033 | 0.277267 | ||||||||
\(36\) | 2.65498 | 0.442497 | ||||||||
\(37\) | 3.42304 | 0.562744 | 0.281372 | − | 0.959599i | \(-0.409211\pi\) | ||||
0.281372 | + | 0.959599i | \(0.409211\pi\) | |||||||
\(38\) | 0.523240 | 0.0848807 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00363 | −0.158688 | ||||||||
\(41\) | 9.46022 | 1.47744 | 0.738719 | − | 0.674013i | \(-0.235431\pi\) | ||||
0.738719 | + | 0.674013i | \(0.235431\pi\) | |||||||
\(42\) | −4.98315 | −0.768916 | ||||||||
\(43\) | −11.8791 | −1.81155 | −0.905776 | − | 0.423757i | \(-0.860711\pi\) | ||||
−0.905776 | + | 0.423757i | \(0.860711\pi\) | |||||||
\(44\) | 2.65498 | 0.400253 | ||||||||
\(45\) | 0.710210 | 0.105872 | ||||||||
\(46\) | −20.5728 | −3.03330 | ||||||||
\(47\) | −12.9178 | −1.88426 | −0.942130 | − | 0.335249i | \(-0.891180\pi\) | ||||
−0.942130 | + | 0.335249i | \(0.891180\pi\) | |||||||
\(48\) | −2.26104 | −0.326353 | ||||||||
\(49\) | −1.66555 | −0.237935 | ||||||||
\(50\) | 9.69944 | 1.37171 | ||||||||
\(51\) | −6.68027 | −0.935425 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.78954 | 0.932615 | 0.466307 | − | 0.884623i | \(-0.345584\pi\) | ||||
0.466307 | + | 0.884623i | \(0.345584\pi\) | |||||||
\(54\) | −2.15754 | −0.293604 | ||||||||
\(55\) | 0.710210 | 0.0957647 | ||||||||
\(56\) | −3.26386 | −0.436152 | ||||||||
\(57\) | −0.242517 | −0.0321221 | ||||||||
\(58\) | 6.37063 | 0.836504 | ||||||||
\(59\) | 7.81320 | 1.01719 | 0.508596 | − | 0.861005i | \(-0.330165\pi\) | ||||
0.508596 | + | 0.861005i | \(0.330165\pi\) | |||||||
\(60\) | 1.88559 | 0.243429 | ||||||||
\(61\) | 0.910585 | 0.116588 | 0.0582942 | − | 0.998299i | \(-0.481434\pi\) | ||||
0.0582942 | + | 0.998299i | \(0.481434\pi\) | |||||||
\(62\) | 8.67368 | 1.10156 | ||||||||
\(63\) | 2.30964 | 0.290988 | ||||||||
\(64\) | −12.1009 | −1.51261 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.15754 | −0.265575 | ||||||||
\(67\) | 9.32216 | 1.13888 | 0.569442 | − | 0.822032i | \(-0.307159\pi\) | ||||
0.569442 | + | 0.822032i | \(0.307159\pi\) | |||||||
\(68\) | −17.7360 | −2.15080 | ||||||||
\(69\) | 9.53531 | 1.14792 | ||||||||
\(70\) | −3.53908 | −0.423001 | ||||||||
\(71\) | 12.9704 | 1.53930 | 0.769650 | − | 0.638466i | \(-0.220431\pi\) | ||||
0.769650 | + | 0.638466i | \(0.220431\pi\) | |||||||
\(72\) | −1.41315 | −0.166541 | ||||||||
\(73\) | 8.51665 | 0.996798 | 0.498399 | − | 0.866948i | \(-0.333921\pi\) | ||||
0.498399 | + | 0.866948i | \(0.333921\pi\) | |||||||
\(74\) | −7.38534 | −0.858529 | ||||||||
\(75\) | −4.49560 | −0.519107 | ||||||||
\(76\) | −0.643877 | −0.0738578 | ||||||||
\(77\) | 2.30964 | 0.263208 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82360 | 0.205172 | 0.102586 | − | 0.994724i | \(-0.467288\pi\) | ||||
0.102586 | + | 0.994724i | \(0.467288\pi\) | |||||||
\(80\) | −1.60581 | −0.179536 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −20.4108 | −2.25400 | ||||||||
\(83\) | 4.64671 | 0.510042 | 0.255021 | − | 0.966935i | \(-0.417918\pi\) | ||||
0.255021 | + | 0.966935i | \(0.417918\pi\) | |||||||
\(84\) | 6.13206 | 0.669062 | ||||||||
\(85\) | −4.74440 | −0.514602 | ||||||||
\(86\) | 25.6297 | 2.76372 | ||||||||
\(87\) | −2.95273 | −0.316566 | ||||||||
\(88\) | −1.41315 | −0.150642 | ||||||||
\(89\) | 14.7714 | 1.56576 | 0.782881 | − | 0.622171i | \(-0.213749\pi\) | ||||
0.782881 | + | 0.622171i | \(0.213749\pi\) | |||||||
\(90\) | −1.53231 | −0.161519 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 25.3161 | 2.63938 | ||||||||
\(93\) | −4.02017 | −0.416872 | ||||||||
\(94\) | 27.8707 | 2.87465 | ||||||||
\(95\) | −0.172238 | −0.0176712 | ||||||||
\(96\) | 7.70458 | 0.786345 | ||||||||
\(97\) | 1.86542 | 0.189405 | 0.0947025 | − | 0.995506i | \(-0.469810\pi\) | ||||
0.0947025 | + | 0.995506i | \(0.469810\pi\) | |||||||
\(98\) | 3.59349 | 0.362997 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −11.9357 | −1.19357 | ||||||||
\(101\) | −2.45086 | −0.243870 | −0.121935 | − | 0.992538i | \(-0.538910\pi\) | ||||
−0.121935 | + | 0.992538i | \(0.538910\pi\) | |||||||
\(102\) | 14.4130 | 1.42709 | ||||||||
\(103\) | 10.2811 | 1.01302 | 0.506512 | − | 0.862233i | \(-0.330934\pi\) | ||||
0.506512 | + | 0.862233i | \(0.330934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64033 | 0.160080 | ||||||||
\(106\) | −14.6487 | −1.42281 | ||||||||
\(107\) | 19.6690 | 1.90148 | 0.950739 | − | 0.309993i | \(-0.100327\pi\) | ||||
0.950739 | + | 0.309993i | \(0.100327\pi\) | |||||||
\(108\) | 2.65498 | 0.255476 | ||||||||
\(109\) | 1.27506 | 0.122128 | 0.0610642 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610642 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(110\) | −1.53231 | −0.146100 | ||||||||
\(111\) | 3.42304 | 0.324900 | ||||||||
\(112\) | −5.22220 | −0.493452 | ||||||||
\(113\) | −0.638739 | −0.0600875 | −0.0300438 | − | 0.999549i | \(-0.509565\pi\) | ||||
−0.0300438 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(114\) | 0.523240 | 0.0490059 | ||||||||
\(115\) | 6.77207 | 0.631499 | ||||||||
\(116\) | −7.83943 | −0.727873 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8573 | −1.55184 | ||||||||
\(119\) | −15.4290 | −1.41438 | ||||||||
\(120\) | −1.00363 | −0.0916185 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.96462 | −0.177869 | ||||||||
\(123\) | 9.46022 | 0.853000 | ||||||||
\(124\) | −10.6735 | −0.958506 | ||||||||
\(125\) | −6.74387 | −0.603190 | ||||||||
\(126\) | −4.98315 | −0.443934 | ||||||||
\(127\) | 10.3681 | 0.920021 | 0.460010 | − | 0.887914i | \(-0.347846\pi\) | ||||
0.460010 | + | 0.887914i | \(0.347846\pi\) | |||||||
\(128\) | 10.6989 | 0.945660 | ||||||||
\(129\) | −11.8791 | −1.04590 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.68692 | −0.496868 | −0.248434 | − | 0.968649i | \(-0.579916\pi\) | ||||
−0.248434 | + | 0.968649i | \(0.579916\pi\) | |||||||
\(132\) | 2.65498 | 0.231086 | ||||||||
\(133\) | −0.560127 | −0.0485692 | ||||||||
\(134\) | −20.1129 | −1.73749 | ||||||||
\(135\) | 0.710210 | 0.0611251 | ||||||||
\(136\) | 9.44019 | 0.809490 | ||||||||
\(137\) | 4.86363 | 0.415528 | 0.207764 | − | 0.978179i | \(-0.433381\pi\) | ||||
0.207764 | + | 0.978179i | \(0.433381\pi\) | |||||||
\(138\) | −20.5728 | −1.75127 | ||||||||
\(139\) | −4.41515 | −0.374488 | −0.187244 | − | 0.982313i | \(-0.559956\pi\) | ||||
−0.187244 | + | 0.982313i | \(0.559956\pi\) | |||||||
\(140\) | 4.35505 | 0.368069 | ||||||||
\(141\) | −12.9178 | −1.08788 | ||||||||
\(142\) | −27.9841 | −2.34837 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.26104 | −0.188420 | ||||||||
\(145\) | −2.09706 | −0.174151 | ||||||||
\(146\) | −18.3750 | −1.52073 | ||||||||
\(147\) | −1.66555 | −0.137372 | ||||||||
\(148\) | 9.08810 | 0.747037 | ||||||||
\(149\) | 9.50356 | 0.778562 | 0.389281 | − | 0.921119i | \(-0.372724\pi\) | ||||
0.389281 | + | 0.921119i | \(0.372724\pi\) | |||||||
\(150\) | 9.69944 | 0.791956 | ||||||||
\(151\) | 15.2126 | 1.23798 | 0.618991 | − | 0.785398i | \(-0.287542\pi\) | ||||
0.618991 | + | 0.785398i | \(0.287542\pi\) | |||||||
\(152\) | 0.342711 | 0.0277976 | ||||||||
\(153\) | −6.68027 | −0.540068 | ||||||||
\(154\) | −4.98315 | −0.401554 | ||||||||
\(155\) | −2.85516 | −0.229332 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1949 | 1.61173 | 0.805866 | − | 0.592098i | \(-0.201700\pi\) | ||||
0.805866 | + | 0.592098i | \(0.201700\pi\) | |||||||
\(158\) | −3.93450 | −0.313012 | ||||||||
\(159\) | 6.78954 | 0.538445 | ||||||||
\(160\) | 5.47187 | 0.432589 | ||||||||
\(161\) | 22.0232 | 1.73567 | ||||||||
\(162\) | −2.15754 | −0.169512 | ||||||||
\(163\) | −16.4974 | −1.29217 | −0.646087 | − | 0.763264i | \(-0.723596\pi\) | ||||
−0.646087 | + | 0.763264i | \(0.723596\pi\) | |||||||
\(164\) | 25.1167 | 1.96129 | ||||||||
\(165\) | 0.710210 | 0.0552898 | ||||||||
\(166\) | −10.0255 | −0.778126 | ||||||||
\(167\) | −5.50507 | −0.425995 | −0.212998 | − | 0.977053i | \(-0.568323\pi\) | ||||
−0.212998 | + | 0.977053i | \(0.568323\pi\) | |||||||
\(168\) | −3.26386 | −0.251812 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 10.2362 | 0.785082 | ||||||||
\(171\) | −0.242517 | −0.0185457 | ||||||||
\(172\) | −31.5389 | −2.40482 | ||||||||
\(173\) | −12.7126 | −0.966524 | −0.483262 | − | 0.875476i | \(-0.660548\pi\) | ||||
−0.483262 | + | 0.875476i | \(0.660548\pi\) | |||||||
\(174\) | 6.37063 | 0.482956 | ||||||||
\(175\) | −10.3832 | −0.784899 | ||||||||
\(176\) | −2.26104 | −0.170432 | ||||||||
\(177\) | 7.81320 | 0.587276 | ||||||||
\(178\) | −31.8698 | −2.38875 | ||||||||
\(179\) | 24.4279 | 1.82583 | 0.912913 | − | 0.408154i | \(-0.133828\pi\) | ||||
0.912913 | + | 0.408154i | \(0.133828\pi\) | |||||||
\(180\) | 1.88559 | 0.140544 | ||||||||
\(181\) | 0.931324 | 0.0692248 | 0.0346124 | − | 0.999401i | \(-0.488980\pi\) | ||||
0.0346124 | + | 0.999401i | \(0.488980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.910585 | 0.0673124 | ||||||||
\(184\) | −13.4748 | −0.993374 | ||||||||
\(185\) | 2.43108 | 0.178736 | ||||||||
\(186\) | 8.67368 | 0.635985 | ||||||||
\(187\) | −6.68027 | −0.488510 | ||||||||
\(188\) | −34.2966 | −2.50134 | ||||||||
\(189\) | 2.30964 | 0.168002 | ||||||||
\(190\) | 0.371610 | 0.0269594 | ||||||||
\(191\) | 4.68209 | 0.338784 | 0.169392 | − | 0.985549i | \(-0.445820\pi\) | ||||
0.169392 | + | 0.985549i | \(0.445820\pi\) | |||||||
\(192\) | −12.1009 | −0.873304 | ||||||||
\(193\) | −10.2671 | −0.739039 | −0.369520 | − | 0.929223i | \(-0.620478\pi\) | ||||
−0.369520 | + | 0.929223i | \(0.620478\pi\) | |||||||
\(194\) | −4.02473 | −0.288959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.42200 | −0.315857 | ||||||||
\(197\) | 11.5842 | 0.825341 | 0.412671 | − | 0.910880i | \(-0.364596\pi\) | ||||
0.412671 | + | 0.910880i | \(0.364596\pi\) | |||||||
\(198\) | −2.15754 | −0.153330 | ||||||||
\(199\) | 17.2330 | 1.22162 | 0.610808 | − | 0.791779i | \(-0.290845\pi\) | ||||
0.610808 | + | 0.791779i | \(0.290845\pi\) | |||||||
\(200\) | 6.35294 | 0.449221 | ||||||||
\(201\) | 9.32216 | 0.657535 | ||||||||
\(202\) | 5.28783 | 0.372050 | ||||||||
\(203\) | −6.81975 | −0.478652 | ||||||||
\(204\) | −17.7360 | −1.24177 | ||||||||
\(205\) | 6.71875 | 0.469258 | ||||||||
\(206\) | −22.1818 | −1.54548 | ||||||||
\(207\) | 9.53531 | 0.662750 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.242517 | −0.0167752 | ||||||||
\(210\) | −3.53908 | −0.244220 | ||||||||
\(211\) | −10.6905 | −0.735967 | −0.367983 | − | 0.929832i | \(-0.619952\pi\) | ||||
−0.367983 | + | 0.929832i | \(0.619952\pi\) | |||||||
\(212\) | 18.0261 | 1.23804 | ||||||||
\(213\) | 12.9704 | 0.888716 | ||||||||
\(214\) | −42.4367 | −2.90092 | ||||||||
\(215\) | −8.43668 | −0.575377 | ||||||||
\(216\) | −1.41315 | −0.0961523 | ||||||||
\(217\) | −9.28516 | −0.630318 | ||||||||
\(218\) | −2.75099 | −0.186320 | ||||||||
\(219\) | 8.51665 | 0.575502 | ||||||||
\(220\) | 1.88559 | 0.127127 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.38534 | −0.495672 | ||||||||
\(223\) | −5.33992 | −0.357587 | −0.178794 | − | 0.983887i | \(-0.557219\pi\) | ||||
−0.178794 | + | 0.983887i | \(0.557219\pi\) | |||||||
\(224\) | 17.7948 | 1.18897 | ||||||||
\(225\) | −4.49560 | −0.299707 | ||||||||
\(226\) | 1.37811 | 0.0916702 | ||||||||
\(227\) | −7.82431 | −0.519318 | −0.259659 | − | 0.965700i | \(-0.583610\pi\) | ||||
−0.259659 | + | 0.965700i | \(0.583610\pi\) | |||||||
\(228\) | −0.643877 | −0.0426418 | ||||||||
\(229\) | −10.6805 | −0.705784 | −0.352892 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(230\) | −14.6110 | −0.963422 | ||||||||
\(231\) | 2.30964 | 0.151963 | ||||||||
\(232\) | 4.17263 | 0.273947 | ||||||||
\(233\) | 15.4509 | 1.01222 | 0.506112 | − | 0.862468i | \(-0.331082\pi\) | ||||
0.506112 | + | 0.862468i | \(0.331082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.17437 | −0.598470 | ||||||||
\(236\) | 20.7439 | 1.35031 | ||||||||
\(237\) | 1.82360 | 0.118456 | ||||||||
\(238\) | 33.2888 | 2.15779 | ||||||||
\(239\) | −16.9365 | −1.09553 | −0.547765 | − | 0.836632i | \(-0.684521\pi\) | ||||
−0.547765 | + | 0.836632i | \(0.684521\pi\) | |||||||
\(240\) | −1.60581 | −0.103655 | ||||||||
\(241\) | −0.0799646 | −0.00515098 | −0.00257549 | − | 0.999997i | \(-0.500820\pi\) | ||||
−0.00257549 | + | 0.999997i | \(0.500820\pi\) | |||||||
\(242\) | −2.15754 | −0.138692 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.41758 | 0.154770 | ||||||||
\(245\) | −1.18289 | −0.0755720 | ||||||||
\(246\) | −20.4108 | −1.30135 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.68108 | 0.360749 | ||||||||
\(249\) | 4.64671 | 0.294473 | ||||||||
\(250\) | 14.5502 | 0.920234 | ||||||||
\(251\) | −7.57174 | −0.477924 | −0.238962 | − | 0.971029i | \(-0.576807\pi\) | ||||
−0.238962 | + | 0.971029i | \(0.576807\pi\) | |||||||
\(252\) | 6.13206 | 0.386283 | ||||||||
\(253\) | 9.53531 | 0.599480 | ||||||||
\(254\) | −22.3696 | −1.40359 | ||||||||
\(255\) | −4.74440 | −0.297106 | ||||||||
\(256\) | 1.11835 | 0.0698970 | ||||||||
\(257\) | 23.0242 | 1.43621 | 0.718105 | − | 0.695935i | \(-0.245010\pi\) | ||||
0.718105 | + | 0.695935i | \(0.245010\pi\) | |||||||
\(258\) | 25.6297 | 1.59564 | ||||||||
\(259\) | 7.90600 | 0.491255 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.95273 | −0.182769 | ||||||||
\(262\) | 12.2698 | 0.758028 | ||||||||
\(263\) | −5.95047 | −0.366922 | −0.183461 | − | 0.983027i | \(-0.558730\pi\) | ||||
−0.183461 | + | 0.983027i | \(0.558730\pi\) | |||||||
\(264\) | −1.41315 | −0.0869731 | ||||||||
\(265\) | 4.82200 | 0.296213 | ||||||||
\(266\) | 1.20850 | 0.0740977 | ||||||||
\(267\) | 14.7714 | 0.903994 | ||||||||
\(268\) | 24.7502 | 1.51186 | ||||||||
\(269\) | −1.17571 | −0.0716841 | −0.0358420 | − | 0.999357i | \(-0.511411\pi\) | ||||
−0.0358420 | + | 0.999357i | \(0.511411\pi\) | |||||||
\(270\) | −1.53231 | −0.0932532 | ||||||||
\(271\) | −7.12706 | −0.432938 | −0.216469 | − | 0.976290i | \(-0.569454\pi\) | ||||
−0.216469 | + | 0.976290i | \(0.569454\pi\) | |||||||
\(272\) | 15.1044 | 0.915837 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4935 | −0.633934 | ||||||||
\(275\) | −4.49560 | −0.271095 | ||||||||
\(276\) | 25.3161 | 1.52385 | ||||||||
\(277\) | −11.9736 | −0.719426 | −0.359713 | − | 0.933063i | \(-0.617125\pi\) | ||||
−0.359713 | + | 0.933063i | \(0.617125\pi\) | |||||||
\(278\) | 9.52586 | 0.571323 | ||||||||
\(279\) | −4.02017 | −0.240681 | ||||||||
\(280\) | −2.31803 | −0.138529 | ||||||||
\(281\) | 18.7901 | 1.12092 | 0.560461 | − | 0.828181i | \(-0.310624\pi\) | ||||
0.560461 | + | 0.828181i | \(0.310624\pi\) | |||||||
\(282\) | 27.8707 | 1.65968 | ||||||||
\(283\) | 10.5237 | 0.625568 | 0.312784 | − | 0.949824i | \(-0.398738\pi\) | ||||
0.312784 | + | 0.949824i | \(0.398738\pi\) | |||||||
\(284\) | 34.4361 | 2.04341 | ||||||||
\(285\) | −0.172238 | −0.0102025 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.8497 | 1.28975 | ||||||||
\(288\) | 7.70458 | 0.453997 | ||||||||
\(289\) | 27.6260 | 1.62506 | ||||||||
\(290\) | 4.52448 | 0.265687 | ||||||||
\(291\) | 1.86542 | 0.109353 | ||||||||
\(292\) | 22.6115 | 1.32324 | ||||||||
\(293\) | −14.0111 | −0.818540 | −0.409270 | − | 0.912413i | \(-0.634217\pi\) | ||||
−0.409270 | + | 0.912413i | \(0.634217\pi\) | |||||||
\(294\) | 3.59349 | 0.209576 | ||||||||
\(295\) | 5.54901 | 0.323076 | ||||||||
\(296\) | −4.83725 | −0.281159 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −20.5043 | −1.18778 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −11.9357 | −0.689110 | ||||||||
\(301\) | −27.4366 | −1.58142 | ||||||||
\(302\) | −32.8217 | −1.88868 | ||||||||
\(303\) | −2.45086 | −0.140798 | ||||||||
\(304\) | 0.548341 | 0.0314495 | ||||||||
\(305\) | 0.646706 | 0.0370303 | ||||||||
\(306\) | 14.4130 | 0.823934 | ||||||||
\(307\) | 2.52126 | 0.143896 | 0.0719481 | − | 0.997408i | \(-0.477078\pi\) | ||||
0.0719481 | + | 0.997408i | \(0.477078\pi\) | |||||||
\(308\) | 6.13206 | 0.349406 | ||||||||
\(309\) | 10.2811 | 0.584870 | ||||||||
\(310\) | 6.16013 | 0.349872 | ||||||||
\(311\) | −22.9380 | −1.30069 | −0.650347 | − | 0.759638i | \(-0.725376\pi\) | ||||
−0.650347 | + | 0.759638i | \(0.725376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6566 | −1.22410 | −0.612051 | − | 0.790818i | \(-0.709655\pi\) | ||||
−0.612051 | + | 0.790818i | \(0.709655\pi\) | |||||||
\(314\) | −43.5714 | −2.45888 | ||||||||
\(315\) | 1.64033 | 0.0924222 | ||||||||
\(316\) | 4.84163 | 0.272363 | ||||||||
\(317\) | 26.6050 | 1.49429 | 0.747143 | − | 0.664664i | \(-0.231425\pi\) | ||||
0.747143 | + | 0.664664i | \(0.231425\pi\) | |||||||
\(318\) | −14.6487 | −0.821458 | ||||||||
\(319\) | −2.95273 | −0.165321 | ||||||||
\(320\) | −8.59415 | −0.480428 | ||||||||
\(321\) | 19.6690 | 1.09782 | ||||||||
\(322\) | −47.5159 | −2.64796 | ||||||||
\(323\) | 1.62008 | 0.0901435 | ||||||||
\(324\) | 2.65498 | 0.147499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.5937 | 1.97135 | ||||||||
\(327\) | 1.27506 | 0.0705108 | ||||||||
\(328\) | −13.3687 | −0.738161 | ||||||||
\(329\) | −29.8356 | −1.64489 | ||||||||
\(330\) | −1.53231 | −0.0843507 | ||||||||
\(331\) | −24.7670 | −1.36132 | −0.680659 | − | 0.732600i | \(-0.738307\pi\) | ||||
−0.680659 | + | 0.732600i | \(0.738307\pi\) | |||||||
\(332\) | 12.3369 | 0.677076 | ||||||||
\(333\) | 3.42304 | 0.187581 | ||||||||
\(334\) | 11.8774 | 0.649903 | ||||||||
\(335\) | 6.62069 | 0.361727 | ||||||||
\(336\) | −5.22220 | −0.284894 | ||||||||
\(337\) | −28.2890 | −1.54100 | −0.770499 | − | 0.637441i | \(-0.779993\pi\) | ||||
−0.770499 | + | 0.637441i | \(0.779993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.638739 | −0.0346916 | ||||||||
\(340\) | −12.5963 | −0.683129 | ||||||||
\(341\) | −4.02017 | −0.217704 | ||||||||
\(342\) | 0.523240 | 0.0282936 | ||||||||
\(343\) | −20.0143 | −1.08067 | ||||||||
\(344\) | 16.7869 | 0.905091 | ||||||||
\(345\) | 6.77207 | 0.364596 | ||||||||
\(346\) | 27.4280 | 1.47454 | ||||||||
\(347\) | −18.0814 | −0.970661 | −0.485331 | − | 0.874331i | \(-0.661301\pi\) | ||||
−0.485331 | + | 0.874331i | \(0.661301\pi\) | |||||||
\(348\) | −7.83943 | −0.420238 | ||||||||
\(349\) | 21.0326 | 1.12585 | 0.562924 | − | 0.826508i | \(-0.309676\pi\) | ||||
0.562924 | + | 0.826508i | \(0.309676\pi\) | |||||||
\(350\) | 22.4022 | 1.19745 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.70458 | 0.410655 | ||||||||
\(353\) | 2.20127 | 0.117162 | 0.0585810 | − | 0.998283i | \(-0.481342\pi\) | ||||
0.0585810 | + | 0.998283i | \(0.481342\pi\) | |||||||
\(354\) | −16.8573 | −0.895955 | ||||||||
\(355\) | 9.21169 | 0.488906 | ||||||||
\(356\) | 39.2177 | 2.07853 | ||||||||
\(357\) | −15.4290 | −0.816591 | ||||||||
\(358\) | −52.7041 | −2.78550 | ||||||||
\(359\) | −7.76540 | −0.409842 | −0.204921 | − | 0.978778i | \(-0.565694\pi\) | ||||
−0.204921 | + | 0.978778i | \(0.565694\pi\) | |||||||
\(360\) | −1.00363 | −0.0528959 | ||||||||
\(361\) | −18.9412 | −0.996905 | ||||||||
\(362\) | −2.00937 | −0.105610 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.04861 | 0.316599 | ||||||||
\(366\) | −1.96462 | −0.102692 | ||||||||
\(367\) | −11.9604 | −0.624326 | −0.312163 | − | 0.950028i | \(-0.601054\pi\) | ||||
−0.312163 | + | 0.950028i | \(0.601054\pi\) | |||||||
\(368\) | −21.5597 | −1.12388 | ||||||||
\(369\) | 9.46022 | 0.492480 | ||||||||
\(370\) | −5.24514 | −0.272682 | ||||||||
\(371\) | 15.6814 | 0.814138 | ||||||||
\(372\) | −10.6735 | −0.553394 | ||||||||
\(373\) | 14.1243 | 0.731330 | 0.365665 | − | 0.930747i | \(-0.380842\pi\) | ||||
0.365665 | + | 0.930747i | \(0.380842\pi\) | |||||||
\(374\) | 14.4130 | 0.745276 | ||||||||
\(375\) | −6.74387 | −0.348252 | ||||||||
\(376\) | 18.2548 | 0.941418 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.98315 | −0.256305 | ||||||||
\(379\) | −3.34432 | −0.171786 | −0.0858931 | − | 0.996304i | \(-0.527374\pi\) | ||||
−0.0858931 | + | 0.996304i | \(0.527374\pi\) | |||||||
\(380\) | −0.457288 | −0.0234584 | ||||||||
\(381\) | 10.3681 | 0.531174 | ||||||||
\(382\) | −10.1018 | −0.516853 | ||||||||
\(383\) | −5.63621 | −0.287997 | −0.143998 | − | 0.989578i | \(-0.545996\pi\) | ||||
−0.143998 | + | 0.989578i | \(0.545996\pi\) | |||||||
\(384\) | 10.6989 | 0.545977 | ||||||||
\(385\) | 1.64033 | 0.0835991 | ||||||||
\(386\) | 22.1516 | 1.12749 | ||||||||
\(387\) | −11.8791 | −0.603850 | ||||||||
\(388\) | 4.95266 | 0.251433 | ||||||||
\(389\) | 14.3490 | 0.727523 | 0.363761 | − | 0.931492i | \(-0.381492\pi\) | ||||
0.363761 | + | 0.931492i | \(0.381492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −63.6984 | −3.22137 | ||||||||
\(392\) | 2.35366 | 0.118878 | ||||||||
\(393\) | −5.68692 | −0.286867 | ||||||||
\(394\) | −24.9934 | −1.25915 | ||||||||
\(395\) | 1.29514 | 0.0651657 | ||||||||
\(396\) | 2.65498 | 0.133418 | ||||||||
\(397\) | −14.8769 | −0.746648 | −0.373324 | − | 0.927701i | \(-0.621782\pi\) | ||||
−0.373324 | + | 0.927701i | \(0.621782\pi\) | |||||||
\(398\) | −37.1809 | −1.86371 | ||||||||
\(399\) | −0.560127 | −0.0280414 | ||||||||
\(400\) | 10.1647 | 0.508237 | ||||||||
\(401\) | 19.6380 | 0.980675 | 0.490337 | − | 0.871533i | \(-0.336874\pi\) | ||||
0.490337 | + | 0.871533i | \(0.336874\pi\) | |||||||
\(402\) | −20.1129 | −1.00314 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.50698 | −0.323734 | ||||||||
\(405\) | 0.710210 | 0.0352906 | ||||||||
\(406\) | 14.7139 | 0.730237 | ||||||||
\(407\) | 3.42304 | 0.169674 | ||||||||
\(408\) | 9.44019 | 0.467359 | ||||||||
\(409\) | 23.1731 | 1.14584 | 0.572918 | − | 0.819613i | \(-0.305811\pi\) | ||||
0.572918 | + | 0.819613i | \(0.305811\pi\) | |||||||
\(410\) | −14.4960 | −0.715905 | ||||||||
\(411\) | 4.86363 | 0.239905 | ||||||||
\(412\) | 27.2961 | 1.34478 | ||||||||
\(413\) | 18.0457 | 0.887971 | ||||||||
\(414\) | −20.5728 | −1.01110 | ||||||||
\(415\) | 3.30014 | 0.161997 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.41515 | −0.216211 | ||||||||
\(418\) | 0.523240 | 0.0255925 | ||||||||
\(419\) | −3.70294 | −0.180900 | −0.0904502 | − | 0.995901i | \(-0.528831\pi\) | ||||
−0.0904502 | + | 0.995901i | \(0.528831\pi\) | |||||||
\(420\) | 4.35505 | 0.212505 | ||||||||
\(421\) | 23.7239 | 1.15623 | 0.578116 | − | 0.815955i | \(-0.303788\pi\) | ||||
0.578116 | + | 0.815955i | \(0.303788\pi\) | |||||||
\(422\) | 23.0653 | 1.12280 | ||||||||
\(423\) | −12.9178 | −0.628086 | ||||||||
\(424\) | −9.59460 | −0.465955 | ||||||||
\(425\) | 30.0318 | 1.45676 | ||||||||
\(426\) | −27.9841 | −1.35583 | ||||||||
\(427\) | 2.10313 | 0.101777 | ||||||||
\(428\) | 52.2209 | 2.52419 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.2025 | 0.877802 | ||||||||
\(431\) | −31.0695 | −1.49656 | −0.748282 | − | 0.663381i | \(-0.769121\pi\) | ||||
−0.748282 | + | 0.663381i | \(0.769121\pi\) | |||||||
\(432\) | −2.26104 | −0.108784 | ||||||||
\(433\) | 23.0541 | 1.10791 | 0.553954 | − | 0.832547i | \(-0.313118\pi\) | ||||
0.553954 | + | 0.832547i | \(0.313118\pi\) | |||||||
\(434\) | 20.0331 | 0.961620 | ||||||||
\(435\) | −2.09706 | −0.100546 | ||||||||
\(436\) | 3.38525 | 0.162124 | ||||||||
\(437\) | −2.31247 | −0.110621 | ||||||||
\(438\) | −18.3750 | −0.877992 | ||||||||
\(439\) | 2.39273 | 0.114199 | 0.0570994 | − | 0.998368i | \(-0.481815\pi\) | ||||
0.0570994 | + | 0.998368i | \(0.481815\pi\) | |||||||
\(440\) | −1.00363 | −0.0478462 | ||||||||
\(441\) | −1.66555 | −0.0793118 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1624 | −0.815411 | −0.407705 | − | 0.913113i | \(-0.633671\pi\) | ||||
−0.407705 | + | 0.913113i | \(0.633671\pi\) | |||||||
\(444\) | 9.08810 | 0.431302 | ||||||||
\(445\) | 10.4908 | 0.497311 | ||||||||
\(446\) | 11.5211 | 0.545539 | ||||||||
\(447\) | 9.50356 | 0.449503 | ||||||||
\(448\) | −27.9487 | −1.32045 | ||||||||
\(449\) | 29.0646 | 1.37164 | 0.685822 | − | 0.727769i | \(-0.259443\pi\) | ||||
0.685822 | + | 0.727769i | \(0.259443\pi\) | |||||||
\(450\) | 9.69944 | 0.457236 | ||||||||
\(451\) | 9.46022 | 0.445465 | ||||||||
\(452\) | −1.69584 | −0.0797656 | ||||||||
\(453\) | 15.2126 | 0.714749 | ||||||||
\(454\) | 16.8813 | 0.792277 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.342711 | 0.0160489 | ||||||||
\(457\) | −31.9111 | −1.49274 | −0.746369 | − | 0.665532i | \(-0.768205\pi\) | ||||
−0.746369 | + | 0.665532i | \(0.768205\pi\) | |||||||
\(458\) | 23.0435 | 1.07675 | ||||||||
\(459\) | −6.68027 | −0.311808 | ||||||||
\(460\) | 17.9797 | 0.838308 | ||||||||
\(461\) | −0.706685 | −0.0329136 | −0.0164568 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164568 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(462\) | −4.98315 | −0.231837 | ||||||||
\(463\) | 25.7813 | 1.19816 | 0.599079 | − | 0.800690i | \(-0.295533\pi\) | ||||
0.599079 | + | 0.800690i | \(0.295533\pi\) | |||||||
\(464\) | 6.67624 | 0.309937 | ||||||||
\(465\) | −2.85516 | −0.132405 | ||||||||
\(466\) | −33.3360 | −1.54426 | ||||||||
\(467\) | 37.3541 | 1.72854 | 0.864270 | − | 0.503028i | \(-0.167781\pi\) | ||||
0.864270 | + | 0.503028i | \(0.167781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.5309 | 0.994203 | ||||||||
\(470\) | 19.7941 | 0.913033 | ||||||||
\(471\) | 20.1949 | 0.930533 | ||||||||
\(472\) | −11.0412 | −0.508212 | ||||||||
\(473\) | −11.8791 | −0.546203 | ||||||||
\(474\) | −3.93450 | −0.180718 | ||||||||
\(475\) | 1.09026 | 0.0500245 | ||||||||
\(476\) | −40.9638 | −1.87757 | ||||||||
\(477\) | 6.78954 | 0.310872 | ||||||||
\(478\) | 36.5411 | 1.67135 | ||||||||
\(479\) | 1.74064 | 0.0795318 | 0.0397659 | − | 0.999209i | \(-0.487339\pi\) | ||||
0.0397659 | + | 0.999209i | \(0.487339\pi\) | |||||||
\(480\) | 5.47187 | 0.249756 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.172527 | 0.00785839 | ||||||||
\(483\) | 22.0232 | 1.00209 | ||||||||
\(484\) | 2.65498 | 0.120681 | ||||||||
\(485\) | 1.32484 | 0.0601580 | ||||||||
\(486\) | −2.15754 | −0.0978680 | ||||||||
\(487\) | 5.69783 | 0.258193 | 0.129097 | − | 0.991632i | \(-0.458792\pi\) | ||||
0.129097 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(488\) | −1.28679 | −0.0582502 | ||||||||
\(489\) | −16.4974 | −0.746037 | ||||||||
\(490\) | 2.55213 | 0.115293 | ||||||||
\(491\) | −27.7388 | −1.25183 | −0.625917 | − | 0.779890i | \(-0.715275\pi\) | ||||
−0.625917 | + | 0.779890i | \(0.715275\pi\) | |||||||
\(492\) | 25.1167 | 1.13235 | ||||||||
\(493\) | 19.7250 | 0.888370 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.710210 | 0.0319216 | ||||||||
\(496\) | 9.08977 | 0.408143 | ||||||||
\(497\) | 29.9569 | 1.34375 | ||||||||
\(498\) | −10.0255 | −0.449251 | ||||||||
\(499\) | 8.27073 | 0.370249 | 0.185124 | − | 0.982715i | \(-0.440731\pi\) | ||||
0.185124 | + | 0.982715i | \(0.440731\pi\) | |||||||
\(500\) | −17.9048 | −0.800729 | ||||||||
\(501\) | −5.50507 | −0.245948 | ||||||||
\(502\) | 16.3363 | 0.729126 | ||||||||
\(503\) | −12.7099 | −0.566706 | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||||
−0.283353 | + | 0.959016i | \(0.591447\pi\) | |||||||
\(504\) | −3.26386 | −0.145384 | ||||||||
\(505\) | −1.74062 | −0.0774568 | ||||||||
\(506\) | −20.5728 | −0.914573 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.5271 | 1.22132 | ||||||||
\(509\) | 5.55978 | 0.246433 | 0.123216 | − | 0.992380i | \(-0.460679\pi\) | ||||
0.123216 | + | 0.992380i | \(0.460679\pi\) | |||||||
\(510\) | 10.2362 | 0.453268 | ||||||||
\(511\) | 19.6704 | 0.870168 | ||||||||
\(512\) | −23.8107 | −1.05230 | ||||||||
\(513\) | −0.242517 | −0.0107074 | ||||||||
\(514\) | −49.6756 | −2.19110 | ||||||||
\(515\) | 7.30172 | 0.321752 | ||||||||
\(516\) | −31.5389 | −1.38842 | ||||||||
\(517\) | −12.9178 | −0.568126 | ||||||||
\(518\) | −17.0575 | −0.749464 | ||||||||
\(519\) | −12.7126 | −0.558023 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.41425 | −0.193392 | −0.0966958 | − | 0.995314i | \(-0.530827\pi\) | ||||
−0.0966958 | + | 0.995314i | \(0.530827\pi\) | |||||||
\(522\) | 6.37063 | 0.278835 | ||||||||
\(523\) | 15.5162 | 0.678474 | 0.339237 | − | 0.940701i | \(-0.389831\pi\) | ||||
0.339237 | + | 0.940701i | \(0.389831\pi\) | |||||||
\(524\) | −15.0986 | −0.659587 | ||||||||
\(525\) | −10.3832 | −0.453162 | ||||||||
\(526\) | 12.8384 | 0.559780 | ||||||||
\(527\) | 26.8558 | 1.16986 | ||||||||
\(528\) | −2.26104 | −0.0983992 | ||||||||
\(529\) | 67.9221 | 2.95314 | ||||||||
\(530\) | −10.4037 | −0.451906 | ||||||||
\(531\) | 7.81320 | 0.339064 | ||||||||
\(532\) | −1.48713 | −0.0644751 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −31.8698 | −1.37914 | ||||||||
\(535\) | 13.9691 | 0.603939 | ||||||||
\(536\) | −13.1736 | −0.569011 | ||||||||
\(537\) | 24.4279 | 1.05414 | ||||||||
\(538\) | 2.53663 | 0.109362 | ||||||||
\(539\) | −1.66555 | −0.0717402 | ||||||||
\(540\) | 1.88559 | 0.0811430 | ||||||||
\(541\) | −27.9827 | −1.20307 | −0.601536 | − | 0.798846i | \(-0.705444\pi\) | ||||
−0.601536 | + | 0.798846i | \(0.705444\pi\) | |||||||
\(542\) | 15.3769 | 0.660495 | ||||||||
\(543\) | 0.931324 | 0.0399669 | ||||||||
\(544\) | −51.4687 | −2.20670 | ||||||||
\(545\) | 0.905559 | 0.0387899 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1470 | −1.03245 | −0.516226 | − | 0.856453i | \(-0.672663\pi\) | ||||
−0.516226 | + | 0.856453i | \(0.672663\pi\) | |||||||
\(548\) | 12.9128 | 0.551609 | ||||||||
\(549\) | 0.910585 | 0.0388628 | ||||||||
\(550\) | 9.69944 | 0.413586 | ||||||||
\(551\) | 0.716086 | 0.0305063 | ||||||||
\(552\) | −13.4748 | −0.573524 | ||||||||
\(553\) | 4.21188 | 0.179107 | ||||||||
\(554\) | 25.8336 | 1.09756 | ||||||||
\(555\) | 2.43108 | 0.103193 | ||||||||
\(556\) | −11.7221 | −0.497129 | ||||||||
\(557\) | 19.1326 | 0.810675 | 0.405337 | − | 0.914167i | \(-0.367154\pi\) | ||||
0.405337 | + | 0.914167i | \(0.367154\pi\) | |||||||
\(558\) | 8.67368 | 0.367186 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.70886 | −0.156728 | ||||||||
\(561\) | −6.68027 | −0.282041 | ||||||||
\(562\) | −40.5404 | −1.71009 | ||||||||
\(563\) | −3.91199 | −0.164871 | −0.0824353 | − | 0.996596i | \(-0.526270\pi\) | ||||
−0.0824353 | + | 0.996596i | \(0.526270\pi\) | |||||||
\(564\) | −34.2966 | −1.44415 | ||||||||
\(565\) | −0.453639 | −0.0190847 | ||||||||
\(566\) | −22.7053 | −0.954373 | ||||||||
\(567\) | 2.30964 | 0.0969959 | ||||||||
\(568\) | −18.3290 | −0.769069 | ||||||||
\(569\) | −15.8002 | −0.662377 | −0.331189 | − | 0.943565i | \(-0.607450\pi\) | ||||
−0.331189 | + | 0.943565i | \(0.607450\pi\) | |||||||
\(570\) | 0.371610 | 0.0155650 | ||||||||
\(571\) | 20.2458 | 0.847262 | 0.423631 | − | 0.905835i | \(-0.360755\pi\) | ||||
0.423631 | + | 0.905835i | \(0.360755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.68209 | 0.195597 | ||||||||
\(574\) | −47.1417 | −1.96766 | ||||||||
\(575\) | −42.8669 | −1.78768 | ||||||||
\(576\) | −12.1009 | −0.504202 | ||||||||
\(577\) | −7.07073 | −0.294358 | −0.147179 | − | 0.989110i | \(-0.547019\pi\) | ||||
−0.147179 | + | 0.989110i | \(0.547019\pi\) | |||||||
\(578\) | −59.6042 | −2.47921 | ||||||||
\(579\) | −10.2671 | −0.426685 | ||||||||
\(580\) | −5.56764 | −0.231184 | ||||||||
\(581\) | 10.7322 | 0.445248 | ||||||||
\(582\) | −4.02473 | −0.166830 | ||||||||
\(583\) | 6.78954 | 0.281194 | ||||||||
\(584\) | −12.0353 | −0.498023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.2296 | 1.24877 | ||||||||
\(587\) | 27.1767 | 1.12170 | 0.560851 | − | 0.827917i | \(-0.310474\pi\) | ||||
0.560851 | + | 0.827917i | \(0.310474\pi\) | |||||||
\(588\) | −4.42200 | −0.182360 | ||||||||
\(589\) | 0.974959 | 0.0401725 | ||||||||
\(590\) | −11.9722 | −0.492889 | ||||||||
\(591\) | 11.5842 | 0.476511 | ||||||||
\(592\) | −7.73963 | −0.318097 | ||||||||
\(593\) | 20.0431 | 0.823070 | 0.411535 | − | 0.911394i | \(-0.364993\pi\) | ||||
0.411535 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(594\) | −2.15754 | −0.0885249 | ||||||||
\(595\) | −10.9579 | −0.449228 | ||||||||
\(596\) | 25.2318 | 1.03353 | ||||||||
\(597\) | 17.2330 | 0.705300 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.5855 | −1.00454 | −0.502268 | − | 0.864712i | \(-0.667501\pi\) | ||||
−0.502268 | + | 0.864712i | \(0.667501\pi\) | |||||||
\(600\) | 6.35294 | 0.259358 | ||||||||
\(601\) | −34.1098 | −1.39137 | −0.695683 | − | 0.718349i | \(-0.744898\pi\) | ||||
−0.695683 | + | 0.718349i | \(0.744898\pi\) | |||||||
\(602\) | 59.1955 | 2.41263 | ||||||||
\(603\) | 9.32216 | 0.379628 | ||||||||
\(604\) | 40.3891 | 1.64341 | ||||||||
\(605\) | 0.710210 | 0.0288741 | ||||||||
\(606\) | 5.28783 | 0.214803 | ||||||||
\(607\) | 20.9453 | 0.850143 | 0.425071 | − | 0.905160i | \(-0.360249\pi\) | ||||
0.425071 | + | 0.905160i | \(0.360249\pi\) | |||||||
\(608\) | −1.86849 | −0.0757773 | ||||||||
\(609\) | −6.81975 | −0.276350 | ||||||||
\(610\) | −1.39530 | −0.0564938 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −17.7360 | −0.716935 | ||||||||
\(613\) | −22.2792 | −0.899848 | −0.449924 | − | 0.893067i | \(-0.648549\pi\) | ||||
−0.449924 | + | 0.893067i | \(0.648549\pi\) | |||||||
\(614\) | −5.43973 | −0.219530 | ||||||||
\(615\) | 6.71875 | 0.270926 | ||||||||
\(616\) | −3.26386 | −0.131505 | ||||||||
\(617\) | 27.4366 | 1.10456 | 0.552279 | − | 0.833660i | \(-0.313758\pi\) | ||||
0.552279 | + | 0.833660i | \(0.313758\pi\) | |||||||
\(618\) | −22.1818 | −0.892284 | ||||||||
\(619\) | −47.9288 | −1.92642 | −0.963211 | − | 0.268747i | \(-0.913390\pi\) | ||||
−0.963211 | + | 0.268747i | \(0.913390\pi\) | |||||||
\(620\) | −7.58040 | −0.304436 | ||||||||
\(621\) | 9.53531 | 0.382639 | ||||||||
\(622\) | 49.4896 | 1.98435 | ||||||||
\(623\) | 34.1166 | 1.36685 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6884 | 0.707538 | ||||||||
\(626\) | 46.7250 | 1.86751 | ||||||||
\(627\) | −0.242517 | −0.00968519 | ||||||||
\(628\) | 53.6171 | 2.13956 | ||||||||
\(629\) | −22.8668 | −0.911760 | ||||||||
\(630\) | −3.53908 | −0.141000 | ||||||||
\(631\) | 23.8277 | 0.948567 | 0.474284 | − | 0.880372i | \(-0.342707\pi\) | ||||
0.474284 | + | 0.880372i | \(0.342707\pi\) | |||||||
\(632\) | −2.57702 | −0.102508 | ||||||||
\(633\) | −10.6905 | −0.424911 | ||||||||
\(634\) | −57.4013 | −2.27970 | ||||||||
\(635\) | 7.36353 | 0.292213 | ||||||||
\(636\) | 18.0261 | 0.714781 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.37063 | 0.252216 | ||||||||
\(639\) | 12.9704 | 0.513100 | ||||||||
\(640\) | 7.59848 | 0.300356 | ||||||||
\(641\) | −8.30355 | −0.327970 | −0.163985 | − | 0.986463i | \(-0.552435\pi\) | ||||
−0.163985 | + | 0.986463i | \(0.552435\pi\) | |||||||
\(642\) | −42.4367 | −1.67484 | ||||||||
\(643\) | 29.9185 | 1.17987 | 0.589934 | − | 0.807451i | \(-0.299154\pi\) | ||||
0.589934 | + | 0.807451i | \(0.299154\pi\) | |||||||
\(644\) | 58.4710 | 2.30408 | ||||||||
\(645\) | −8.43668 | −0.332194 | ||||||||
\(646\) | −3.49538 | −0.137524 | ||||||||
\(647\) | 5.87308 | 0.230895 | 0.115447 | − | 0.993314i | \(-0.463170\pi\) | ||||
0.115447 | + | 0.993314i | \(0.463170\pi\) | |||||||
\(648\) | −1.41315 | −0.0555136 | ||||||||
\(649\) | 7.81320 | 0.306695 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.28516 | −0.363914 | ||||||||
\(652\) | −43.8002 | −1.71535 | ||||||||
\(653\) | −5.43262 | −0.212595 | −0.106297 | − | 0.994334i | \(-0.533900\pi\) | ||||
−0.106297 | + | 0.994334i | \(0.533900\pi\) | |||||||
\(654\) | −2.75099 | −0.107572 | ||||||||
\(655\) | −4.03891 | −0.157813 | ||||||||
\(656\) | −21.3900 | −0.835138 | ||||||||
\(657\) | 8.51665 | 0.332266 | ||||||||
\(658\) | 64.3715 | 2.50946 | ||||||||
\(659\) | 26.5954 | 1.03601 | 0.518004 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518004 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(660\) | 1.88559 | 0.0733966 | ||||||||
\(661\) | −27.7763 | −1.08037 | −0.540187 | − | 0.841545i | \(-0.681646\pi\) | ||||
−0.540187 | + | 0.841545i | \(0.681646\pi\) | |||||||
\(662\) | 53.4359 | 2.07684 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.56647 | −0.254828 | ||||||||
\(665\) | −0.397808 | −0.0154263 | ||||||||
\(666\) | −7.38534 | −0.286176 | ||||||||
\(667\) | −28.1552 | −1.09017 | ||||||||
\(668\) | −14.6158 | −0.565504 | ||||||||
\(669\) | −5.33992 | −0.206453 | ||||||||
\(670\) | −14.2844 | −0.551855 | ||||||||
\(671\) | 0.910585 | 0.0351527 | ||||||||
\(672\) | 17.7948 | 0.686450 | ||||||||
\(673\) | 3.00054 | 0.115663 | 0.0578313 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578313 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(674\) | 61.0346 | 2.35096 | ||||||||
\(675\) | −4.49560 | −0.173036 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.1724 | −0.967452 | −0.483726 | − | 0.875219i | \(-0.660717\pi\) | ||||
−0.483726 | + | 0.875219i | \(0.660717\pi\) | |||||||
\(678\) | 1.37811 | 0.0529258 | ||||||||
\(679\) | 4.30846 | 0.165344 | ||||||||
\(680\) | 6.70452 | 0.257107 | ||||||||
\(681\) | −7.82431 | −0.299828 | ||||||||
\(682\) | 8.67368 | 0.332132 | ||||||||
\(683\) | 39.1652 | 1.49861 | 0.749307 | − | 0.662223i | \(-0.230387\pi\) | ||||
0.749307 | + | 0.662223i | \(0.230387\pi\) | |||||||
\(684\) | −0.643877 | −0.0246193 | ||||||||
\(685\) | 3.45420 | 0.131978 | ||||||||
\(686\) | 43.1817 | 1.64869 | ||||||||
\(687\) | −10.6805 | −0.407485 | ||||||||
\(688\) | 26.8592 | 1.02400 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −14.6110 | −0.556232 | ||||||||
\(691\) | 33.3472 | 1.26859 | 0.634294 | − | 0.773092i | \(-0.281291\pi\) | ||||
0.634294 | + | 0.773092i | \(0.281291\pi\) | |||||||
\(692\) | −33.7518 | −1.28305 | ||||||||
\(693\) | 2.30964 | 0.0877361 | ||||||||
\(694\) | 39.0114 | 1.48085 | ||||||||
\(695\) | −3.13568 | −0.118943 | ||||||||
\(696\) | 4.17263 | 0.158163 | ||||||||
\(697\) | −63.1969 | −2.39375 | ||||||||
\(698\) | −45.3787 | −1.71761 | ||||||||
\(699\) | 15.4509 | 0.584408 | ||||||||
\(700\) | −27.5673 | −1.04195 | ||||||||
\(701\) | 8.45704 | 0.319418 | 0.159709 | − | 0.987164i | \(-0.448944\pi\) | ||||
0.159709 | + | 0.987164i | \(0.448944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.830144 | −0.0313095 | ||||||||
\(704\) | −12.1009 | −0.456068 | ||||||||
\(705\) | −9.17437 | −0.345527 | ||||||||
\(706\) | −4.74934 | −0.178744 | ||||||||
\(707\) | −5.66061 | −0.212889 | ||||||||
\(708\) | 20.7439 | 0.779603 | ||||||||
\(709\) | −7.03783 | −0.264311 | −0.132156 | − | 0.991229i | \(-0.542190\pi\) | ||||
−0.132156 | + | 0.991229i | \(0.542190\pi\) | |||||||
\(710\) | −19.8746 | −0.745880 | ||||||||
\(711\) | 1.82360 | 0.0683905 | ||||||||
\(712\) | −20.8741 | −0.782290 | ||||||||
\(713\) | −38.3336 | −1.43560 | ||||||||
\(714\) | 33.2888 | 1.24580 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 64.8555 | 2.42377 | ||||||||
\(717\) | −16.9365 | −0.632504 | ||||||||
\(718\) | 16.7542 | 0.625260 | ||||||||
\(719\) | −5.52947 | −0.206215 | −0.103107 | − | 0.994670i | \(-0.532879\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532879\pi\) | |||||||
\(720\) | −1.60581 | −0.0598452 | ||||||||
\(721\) | 23.7456 | 0.884333 | ||||||||
\(722\) | 40.8664 | 1.52089 | ||||||||
\(723\) | −0.0799646 | −0.00297392 | ||||||||
\(724\) | 2.47265 | 0.0918952 | ||||||||
\(725\) | 13.2743 | 0.492995 | ||||||||
\(726\) | −2.15754 | −0.0800738 | ||||||||
\(727\) | −38.7533 | −1.43728 | −0.718640 | − | 0.695383i | \(-0.755235\pi\) | ||||
−0.718640 | + | 0.695383i | \(0.755235\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.0501 | −0.483006 | ||||||||
\(731\) | 79.3558 | 2.93508 | ||||||||
\(732\) | 2.41758 | 0.0893565 | ||||||||
\(733\) | 9.60595 | 0.354804 | 0.177402 | − | 0.984138i | \(-0.443231\pi\) | ||||
0.177402 | + | 0.984138i | \(0.443231\pi\) | |||||||
\(734\) | 25.8050 | 0.952480 | ||||||||
\(735\) | −1.18289 | −0.0436315 | ||||||||
\(736\) | 73.4655 | 2.70798 | ||||||||
\(737\) | 9.32216 | 0.343386 | ||||||||
\(738\) | −20.4108 | −0.751332 | ||||||||
\(739\) | 21.6659 | 0.796995 | 0.398497 | − | 0.917169i | \(-0.369532\pi\) | ||||
0.398497 | + | 0.917169i | \(0.369532\pi\) | |||||||
\(740\) | 6.45446 | 0.237271 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.8333 | −1.24206 | ||||||||
\(743\) | 12.3149 | 0.451790 | 0.225895 | − | 0.974152i | \(-0.427469\pi\) | ||||
0.225895 | + | 0.974152i | \(0.427469\pi\) | |||||||
\(744\) | 5.68108 | 0.208279 | ||||||||
\(745\) | 6.74952 | 0.247283 | ||||||||
\(746\) | −30.4738 | −1.11572 | ||||||||
\(747\) | 4.64671 | 0.170014 | ||||||||
\(748\) | −17.7360 | −0.648492 | ||||||||
\(749\) | 45.4285 | 1.65992 | ||||||||
\(750\) | 14.5502 | 0.531297 | ||||||||
\(751\) | 2.50813 | 0.0915231 | 0.0457616 | − | 0.998952i | \(-0.485429\pi\) | ||||
0.0457616 | + | 0.998952i | \(0.485429\pi\) | |||||||
\(752\) | 29.2078 | 1.06510 | ||||||||
\(753\) | −7.57174 | −0.275930 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.8041 | 0.393202 | ||||||||
\(756\) | 6.13206 | 0.223021 | ||||||||
\(757\) | 2.89889 | 0.105362 | 0.0526809 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526809 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(758\) | 7.21551 | 0.262079 | ||||||||
\(759\) | 9.53531 | 0.346110 | ||||||||
\(760\) | 0.243397 | 0.00882894 | ||||||||
\(761\) | −33.6764 | −1.22077 | −0.610384 | − | 0.792105i | \(-0.708985\pi\) | ||||
−0.610384 | + | 0.792105i | \(0.708985\pi\) | |||||||
\(762\) | −22.3696 | −0.810365 | ||||||||
\(763\) | 2.94493 | 0.106614 | ||||||||
\(764\) | 12.4309 | 0.449733 | ||||||||
\(765\) | −4.74440 | −0.171534 | ||||||||
\(766\) | 12.1604 | 0.439371 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.11835 | 0.0403551 | ||||||||
\(769\) | 25.1224 | 0.905935 | 0.452968 | − | 0.891527i | \(-0.350365\pi\) | ||||
0.452968 | + | 0.891527i | \(0.350365\pi\) | |||||||
\(770\) | −3.53908 | −0.127540 | ||||||||
\(771\) | 23.0242 | 0.829196 | ||||||||
\(772\) | −27.2588 | −0.981067 | ||||||||
\(773\) | 31.6336 | 1.13778 | 0.568891 | − | 0.822413i | \(-0.307373\pi\) | ||||
0.568891 | + | 0.822413i | \(0.307373\pi\) | |||||||
\(774\) | 25.6297 | 0.921241 | ||||||||
\(775\) | 18.0731 | 0.649204 | ||||||||
\(776\) | −2.63611 | −0.0946310 | ||||||||
\(777\) | 7.90600 | 0.283626 | ||||||||
\(778\) | −30.9585 | −1.10992 | ||||||||
\(779\) | −2.29426 | −0.0822005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9704 | 0.464117 | ||||||||
\(782\) | 137.432 | 4.91456 | ||||||||
\(783\) | −2.95273 | −0.105522 | ||||||||
\(784\) | 3.76587 | 0.134495 | ||||||||
\(785\) | 14.3426 | 0.511911 | ||||||||
\(786\) | 12.2698 | 0.437648 | ||||||||
\(787\) | 23.2041 | 0.827137 | 0.413569 | − | 0.910473i | \(-0.364282\pi\) | ||||
0.413569 | + | 0.910473i | \(0.364282\pi\) | |||||||
\(788\) | 30.7559 | 1.09563 | ||||||||
\(789\) | −5.95047 | −0.211842 | ||||||||
\(790\) | −2.79432 | −0.0994175 | ||||||||
\(791\) | −1.47526 | −0.0524542 | ||||||||
\(792\) | −1.41315 | −0.0502139 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 32.0974 | 1.13909 | ||||||||
\(795\) | 4.82200 | 0.171019 | ||||||||
\(796\) | 45.7533 | 1.62168 | ||||||||
\(797\) | 16.5706 | 0.586960 | 0.293480 | − | 0.955965i | \(-0.405187\pi\) | ||||
0.293480 | + | 0.955965i | \(0.405187\pi\) | |||||||
\(798\) | 1.20850 | 0.0427803 | ||||||||
\(799\) | 86.2946 | 3.05288 | ||||||||
\(800\) | −34.6367 | −1.22459 | ||||||||
\(801\) | 14.7714 | 0.521921 | ||||||||
\(802\) | −42.3698 | −1.49613 | ||||||||
\(803\) | 8.51665 | 0.300546 | ||||||||
\(804\) | 24.7502 | 0.872871 | ||||||||
\(805\) | 15.6411 | 0.551275 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.17571 | −0.0413868 | ||||||||
\(808\) | 3.46342 | 0.121843 | ||||||||
\(809\) | 8.97637 | 0.315592 | 0.157796 | − | 0.987472i | \(-0.449561\pi\) | ||||
0.157796 | + | 0.987472i | \(0.449561\pi\) | |||||||
\(810\) | −1.53231 | −0.0538398 | ||||||||
\(811\) | 2.09499 | 0.0735651 | 0.0367826 | − | 0.999323i | \(-0.488289\pi\) | ||||
0.0367826 | + | 0.999323i | \(0.488289\pi\) | |||||||
\(812\) | −18.1063 | −0.635406 | ||||||||
\(813\) | −7.12706 | −0.249957 | ||||||||
\(814\) | −7.38534 | −0.258856 | ||||||||
\(815\) | −11.7166 | −0.410414 | ||||||||
\(816\) | 15.1044 | 0.528759 | ||||||||
\(817\) | 2.88089 | 0.100790 | ||||||||
\(818\) | −49.9969 | −1.74810 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.8381 | 0.622935 | ||||||||
\(821\) | −32.8066 | −1.14496 | −0.572480 | − | 0.819919i | \(-0.694018\pi\) | ||||
−0.572480 | + | 0.819919i | \(0.694018\pi\) | |||||||
\(822\) | −10.4935 | −0.366002 | ||||||||
\(823\) | −6.37447 | −0.222200 | −0.111100 | − | 0.993809i | \(-0.535437\pi\) | ||||
−0.111100 | + | 0.993809i | \(0.535437\pi\) | |||||||
\(824\) | −14.5287 | −0.506130 | ||||||||
\(825\) | −4.49560 | −0.156517 | ||||||||
\(826\) | −38.9343 | −1.35470 | ||||||||
\(827\) | −14.7476 | −0.512825 | −0.256413 | − | 0.966567i | \(-0.582541\pi\) | ||||
−0.256413 | + | 0.966567i | \(0.582541\pi\) | |||||||
\(828\) | 25.3161 | 0.879794 | ||||||||
\(829\) | −25.4837 | −0.885085 | −0.442542 | − | 0.896748i | \(-0.645923\pi\) | ||||
−0.442542 | + | 0.896748i | \(0.645923\pi\) | |||||||
\(830\) | −7.12018 | −0.247145 | ||||||||
\(831\) | −11.9736 | −0.415361 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1263 | 0.385504 | ||||||||
\(834\) | 9.52586 | 0.329854 | ||||||||
\(835\) | −3.90976 | −0.135303 | ||||||||
\(836\) | −0.643877 | −0.0222690 | ||||||||
\(837\) | −4.02017 | −0.138957 | ||||||||
\(838\) | 7.98924 | 0.275984 | ||||||||
\(839\) | −41.7953 | −1.44293 | −0.721467 | − | 0.692449i | \(-0.756532\pi\) | ||||
−0.721467 | + | 0.692449i | \(0.756532\pi\) | |||||||
\(840\) | −2.31803 | −0.0799795 | ||||||||
\(841\) | −20.2814 | −0.699359 | ||||||||
\(842\) | −51.1852 | −1.76396 | ||||||||
\(843\) | 18.7901 | 0.647165 | ||||||||
\(844\) | −28.3831 | −0.976988 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 27.8707 | 0.958216 | ||||||||
\(847\) | 2.30964 | 0.0793603 | ||||||||
\(848\) | −15.3514 | −0.527170 | ||||||||
\(849\) | 10.5237 | 0.361172 | ||||||||
\(850\) | −64.7949 | −2.22245 | ||||||||
\(851\) | 32.6397 | 1.11888 | ||||||||
\(852\) | 34.4361 | 1.17976 | ||||||||
\(853\) | −25.2825 | −0.865655 | −0.432827 | − | 0.901477i | \(-0.642484\pi\) | ||||
−0.432827 | + | 0.901477i | \(0.642484\pi\) | |||||||
\(854\) | −4.53758 | −0.155273 | ||||||||
\(855\) | −0.172238 | −0.00589041 | ||||||||
\(856\) | −27.7952 | −0.950021 | ||||||||
\(857\) | −26.8626 | −0.917609 | −0.458804 | − | 0.888537i | \(-0.651722\pi\) | ||||
−0.458804 | + | 0.888537i | \(0.651722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.11713 | 0.208714 | 0.104357 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104357 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(860\) | −22.3992 | −0.763807 | ||||||||
\(861\) | 21.8497 | 0.744637 | ||||||||
\(862\) | 67.0336 | 2.28318 | ||||||||
\(863\) | 32.1517 | 1.09446 | 0.547228 | − | 0.836984i | \(-0.315683\pi\) | ||||
0.547228 | + | 0.836984i | \(0.315683\pi\) | |||||||
\(864\) | 7.70458 | 0.262115 | ||||||||
\(865\) | −9.02865 | −0.306983 | ||||||||
\(866\) | −49.7401 | −1.69024 | ||||||||
\(867\) | 27.6260 | 0.938228 | ||||||||
\(868\) | −24.6519 | −0.836740 | ||||||||
\(869\) | 1.82360 | 0.0618616 | ||||||||
\(870\) | 4.52448 | 0.153394 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.80184 | −0.0610180 | ||||||||
\(873\) | 1.86542 | 0.0631350 | ||||||||
\(874\) | 4.98925 | 0.168764 | ||||||||
\(875\) | −15.5759 | −0.526563 | ||||||||
\(876\) | 22.6115 | 0.763973 | ||||||||
\(877\) | −17.9062 | −0.604648 | −0.302324 | − | 0.953205i | \(-0.597763\pi\) | ||||
−0.302324 | + | 0.953205i | \(0.597763\pi\) | |||||||
\(878\) | −5.16241 | −0.174223 | ||||||||
\(879\) | −14.0111 | −0.472584 | ||||||||
\(880\) | −1.60581 | −0.0541320 | ||||||||
\(881\) | 40.5751 | 1.36701 | 0.683504 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683504 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(882\) | 3.59349 | 0.120999 | ||||||||
\(883\) | −24.6601 | −0.829879 | −0.414940 | − | 0.909849i | \(-0.636197\pi\) | ||||
−0.414940 | + | 0.909849i | \(0.636197\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.54901 | 0.186528 | ||||||||
\(886\) | 37.0286 | 1.24400 | ||||||||
\(887\) | 27.2662 | 0.915510 | 0.457755 | − | 0.889078i | \(-0.348654\pi\) | ||||
0.457755 | + | 0.889078i | \(0.348654\pi\) | |||||||
\(888\) | −4.83725 | −0.162327 | ||||||||
\(889\) | 23.9466 | 0.803144 | ||||||||
\(890\) | −22.6343 | −0.758703 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −14.1774 | −0.474693 | ||||||||
\(893\) | 3.13279 | 0.104835 | ||||||||
\(894\) | −20.5043 | −0.685767 | ||||||||
\(895\) | 17.3489 | 0.579911 | ||||||||
\(896\) | 24.7107 | 0.825526 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −62.7081 | −2.09260 | ||||||||
\(899\) | 11.8705 | 0.395902 | ||||||||
\(900\) | −11.9357 | −0.397858 | ||||||||
\(901\) | −45.3560 | −1.51103 | ||||||||
\(902\) | −20.4108 | −0.679606 | ||||||||
\(903\) | −27.4366 | −0.913032 | ||||||||
\(904\) | 0.902631 | 0.0300211 | ||||||||
\(905\) | 0.661436 | 0.0219869 | ||||||||
\(906\) | −32.8217 | −1.09043 | ||||||||
\(907\) | 0.121526 | 0.00403521 | 0.00201760 | − | 0.999998i | \(-0.499358\pi\) | ||||
0.00201760 | + | 0.999998i | \(0.499358\pi\) | |||||||
\(908\) | −20.7734 | −0.689389 | ||||||||
\(909\) | −2.45086 | −0.0812898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.6736 | −1.34758 | −0.673788 | − | 0.738925i | \(-0.735334\pi\) | ||||
−0.673788 | + | 0.738925i | \(0.735334\pi\) | |||||||
\(912\) | 0.548341 | 0.0181574 | ||||||||
\(913\) | 4.64671 | 0.153784 | ||||||||
\(914\) | 68.8495 | 2.27734 | ||||||||
\(915\) | 0.646706 | 0.0213795 | ||||||||
\(916\) | −28.3564 | −0.936921 | ||||||||
\(917\) | −13.1347 | −0.433748 | ||||||||
\(918\) | 14.4130 | 0.475698 | ||||||||
\(919\) | −26.0713 | −0.860012 | −0.430006 | − | 0.902826i | \(-0.641489\pi\) | ||||
−0.430006 | + | 0.902826i | \(0.641489\pi\) | |||||||
\(920\) | −9.56992 | −0.315511 | ||||||||
\(921\) | 2.52126 | 0.0830785 | ||||||||
\(922\) | 1.52470 | 0.0502134 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.13206 | 0.201730 | ||||||||
\(925\) | −15.3886 | −0.505975 | ||||||||
\(926\) | −55.6242 | −1.82792 | ||||||||
\(927\) | 10.2811 | 0.337675 | ||||||||
\(928\) | −22.7495 | −0.746790 | ||||||||
\(929\) | −26.9849 | −0.885346 | −0.442673 | − | 0.896683i | \(-0.645970\pi\) | ||||
−0.442673 | + | 0.896683i | \(0.645970\pi\) | |||||||
\(930\) | 6.16013 | 0.201999 | ||||||||
\(931\) | 0.403923 | 0.0132381 | ||||||||
\(932\) | 41.0219 | 1.34372 | ||||||||
\(933\) | −22.9380 | −0.750956 | ||||||||
\(934\) | −80.5929 | −2.63708 | ||||||||
\(935\) | −4.74440 | −0.155158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.9915 | 1.04512 | 0.522559 | − | 0.852603i | \(-0.324977\pi\) | ||||
0.522559 | + | 0.852603i | \(0.324977\pi\) | |||||||
\(938\) | −46.4537 | −1.51677 | ||||||||
\(939\) | −21.6566 | −0.706736 | ||||||||
\(940\) | −24.3578 | −0.794463 | ||||||||
\(941\) | −31.7257 | −1.03423 | −0.517115 | − | 0.855916i | \(-0.672994\pi\) | ||||
−0.517115 | + | 0.855916i | \(0.672994\pi\) | |||||||
\(942\) | −43.5714 | −1.41963 | ||||||||
\(943\) | 90.2062 | 2.93752 | ||||||||
\(944\) | −17.6660 | −0.574979 | ||||||||
\(945\) | 1.64033 | 0.0533600 | ||||||||
\(946\) | 25.6297 | 0.833294 | ||||||||
\(947\) | −46.5444 | −1.51249 | −0.756245 | − | 0.654289i | \(-0.772968\pi\) | ||||
−0.756245 | + | 0.654289i | \(0.772968\pi\) | |||||||
\(948\) | 4.84163 | 0.157249 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.35228 | −0.0763180 | ||||||||
\(951\) | 26.6050 | 0.862726 | ||||||||
\(952\) | 21.8035 | 0.706655 | ||||||||
\(953\) | 37.1054 | 1.20196 | 0.600981 | − | 0.799263i | \(-0.294777\pi\) | ||||
0.600981 | + | 0.799263i | \(0.294777\pi\) | |||||||
\(954\) | −14.6487 | −0.474269 | ||||||||
\(955\) | 3.32527 | 0.107603 | ||||||||
\(956\) | −44.9660 | −1.45430 | ||||||||
\(957\) | −2.95273 | −0.0954481 | ||||||||
\(958\) | −3.75550 | −0.121335 | ||||||||
\(959\) | 11.2332 | 0.362740 | ||||||||
\(960\) | −8.59415 | −0.277375 | ||||||||
\(961\) | −14.8382 | −0.478653 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.6690 | 0.633826 | ||||||||
\(964\) | −0.212305 | −0.00683787 | ||||||||
\(965\) | −7.29177 | −0.234730 | ||||||||
\(966\) | −47.5159 | −1.52880 | ||||||||
\(967\) | 33.1854 | 1.06717 | 0.533586 | − | 0.845746i | \(-0.320844\pi\) | ||||
0.533586 | + | 0.845746i | \(0.320844\pi\) | |||||||
\(968\) | −1.41315 | −0.0454202 | ||||||||
\(969\) | 1.62008 | 0.0520444 | ||||||||
\(970\) | −2.85840 | −0.0917777 | ||||||||
\(971\) | 23.0990 | 0.741283 | 0.370642 | − | 0.928776i | \(-0.379138\pi\) | ||||
0.370642 | + | 0.928776i | \(0.379138\pi\) | |||||||
\(972\) | 2.65498 | 0.0851585 | ||||||||
\(973\) | −10.1974 | −0.326914 | ||||||||
\(974\) | −12.2933 | −0.393903 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.05887 | −0.0659028 | ||||||||
\(977\) | 32.4063 | 1.03677 | 0.518385 | − | 0.855147i | \(-0.326533\pi\) | ||||
0.518385 | + | 0.855147i | \(0.326533\pi\) | |||||||
\(978\) | 35.5937 | 1.13816 | ||||||||
\(979\) | 14.7714 | 0.472095 | ||||||||
\(980\) | −3.14055 | −0.100321 | ||||||||
\(981\) | 1.27506 | 0.0407095 | ||||||||
\(982\) | 59.8475 | 1.90981 | ||||||||
\(983\) | −1.17252 | −0.0373976 | −0.0186988 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186988 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(984\) | −13.3687 | −0.426178 | ||||||||
\(985\) | 8.22723 | 0.262141 | ||||||||
\(986\) | −42.5575 | −1.35531 | ||||||||
\(987\) | −29.8356 | −0.949677 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −113.271 | −3.60182 | ||||||||
\(990\) | −1.53231 | −0.0486999 | ||||||||
\(991\) | −4.78159 | −0.151892 | −0.0759462 | − | 0.997112i | \(-0.524198\pi\) | ||||
−0.0759462 | + | 0.997112i | \(0.524198\pi\) | |||||||
\(992\) | −30.9737 | −0.983416 | ||||||||
\(993\) | −24.7670 | −0.785958 | ||||||||
\(994\) | −64.6333 | −2.05004 | ||||||||
\(995\) | 12.2391 | 0.388004 | ||||||||
\(996\) | 12.3369 | 0.390910 | ||||||||
\(997\) | 55.7577 | 1.76586 | 0.882932 | − | 0.469502i | \(-0.155566\pi\) | ||||
0.882932 | + | 0.469502i | \(0.155566\pi\) | |||||||
\(998\) | −17.8444 | −0.564856 | ||||||||
\(999\) | 3.42304 | 0.108300 |
(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 | 5577.2.a.y.1.1 | 7 | ||
13.5 | odd | 4 | 429.2.b.b.298.12 | yes | 14 | ||
13.8 | odd | 4 | 429.2.b.b.298.3 | ✓ | 14 | ||
13.12 | even | 2 | 5577.2.a.x.1.7 | 7 | |||
39.5 | even | 4 | 1287.2.b.c.298.3 | 14 | |||
39.8 | even | 4 | 1287.2.b.c.298.12 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.3 | ✓ | 14 | 13.8 | odd | 4 | ||
429.2.b.b.298.12 | yes | 14 | 13.5 | odd | 4 | ||
1287.2.b.c.298.3 | 14 | 39.5 | even | 4 | |||
1287.2.b.c.298.12 | 14 | 39.8 | even | 4 | |||
5577.2.a.x.1.7 | 7 | 13.12 | even | 2 | |||
5577.2.a.y.1.1 | 7 | 1.1 | even | 1 | trivial |