Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 83 x^{13} + 112 x^{12} - 668 x^{11} - 235 x^{10} + 2648 x^{9} + \cdots - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.716430\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.716430 | −0.506592 | −0.253296 | − | 0.967389i | \(-0.581515\pi\) | ||||
−0.253296 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.48673 | −0.743364 | ||||||||
\(5\) | −0.617976 | −0.276367 | −0.138184 | − | 0.990407i | \(-0.544126\pi\) | ||||
−0.138184 | + | 0.990407i | \(0.544126\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.49800 | 0.883175 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.442737 | 0.140006 | ||||||||
\(11\) | −2.03917 | −0.614833 | −0.307416 | − | 0.951575i | \(-0.599464\pi\) | ||||
−0.307416 | + | 0.951575i | \(0.599464\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.26367 | −0.627829 | −0.313915 | − | 0.949451i | \(-0.601641\pi\) | ||||
−0.313915 | + | 0.949451i | \(0.601641\pi\) | |||||||
\(14\) | 0.716430 | 0.191474 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.18382 | 0.295954 | ||||||||
\(17\) | 1.11795 | 0.271143 | 0.135572 | − | 0.990768i | \(-0.456713\pi\) | ||||
0.135572 | + | 0.990768i | \(0.456713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.92719 | 1.81862 | 0.909311 | − | 0.416117i | \(-0.136609\pi\) | ||||
0.909311 | + | 0.416117i | \(0.136609\pi\) | |||||||
\(20\) | 0.918763 | 0.205442 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.46092 | 0.311470 | ||||||||
\(23\) | −6.62633 | −1.38168 | −0.690842 | − | 0.723005i | \(-0.742760\pi\) | ||||
−0.690842 | + | 0.723005i | \(0.742760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61811 | −0.923621 | ||||||||
\(26\) | 1.62176 | 0.318054 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.48673 | 0.280965 | ||||||||
\(29\) | 3.70380 | 0.687778 | 0.343889 | − | 0.939010i | \(-0.388256\pi\) | ||||
0.343889 | + | 0.939010i | \(0.388256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50424 | −0.270170 | −0.135085 | − | 0.990834i | \(-0.543131\pi\) | ||||
−0.135085 | + | 0.990834i | \(0.543131\pi\) | |||||||
\(32\) | −5.84411 | −1.03310 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.800934 | −0.137359 | ||||||||
\(35\) | 0.617976 | 0.104457 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.29904 | 0.706757 | 0.353379 | − | 0.935480i | \(-0.385033\pi\) | ||||
0.353379 | + | 0.935480i | \(0.385033\pi\) | |||||||
\(38\) | −5.67928 | −0.921300 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.54370 | −0.244081 | ||||||||
\(41\) | 2.12378 | 0.331679 | 0.165839 | − | 0.986153i | \(-0.446967\pi\) | ||||
0.165839 | + | 0.986153i | \(0.446967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.68717 | −0.867285 | −0.433642 | − | 0.901085i | \(-0.642772\pi\) | ||||
−0.433642 | + | 0.901085i | \(0.642772\pi\) | |||||||
\(44\) | 3.03169 | 0.457044 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.74730 | 0.699951 | ||||||||
\(47\) | −7.25675 | −1.05851 | −0.529253 | − | 0.848464i | \(-0.677528\pi\) | ||||
−0.529253 | + | 0.848464i | \(0.677528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.30855 | 0.467899 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.36546 | 0.466706 | ||||||||
\(53\) | −7.02300 | −0.964683 | −0.482341 | − | 0.875983i | \(-0.660214\pi\) | ||||
−0.482341 | + | 0.875983i | \(0.660214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26016 | 0.169920 | ||||||||
\(56\) | −2.49800 | −0.333809 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.65351 | −0.348423 | ||||||||
\(59\) | 1.93188 | 0.251509 | 0.125754 | − | 0.992061i | \(-0.459865\pi\) | ||||
0.125754 | + | 0.992061i | \(0.459865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.43893 | 0.952457 | 0.476229 | − | 0.879322i | \(-0.342003\pi\) | ||||
0.476229 | + | 0.879322i | \(0.342003\pi\) | |||||||
\(62\) | 1.07768 | 0.136866 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.81927 | 0.227408 | ||||||||
\(65\) | 1.39890 | 0.173512 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4720 | 1.27936 | 0.639682 | − | 0.768640i | \(-0.279066\pi\) | ||||
0.639682 | + | 0.768640i | \(0.279066\pi\) | |||||||
\(68\) | −1.66209 | −0.201558 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.442737 | −0.0529172 | ||||||||
\(71\) | −9.88028 | −1.17257 | −0.586287 | − | 0.810104i | \(-0.699411\pi\) | ||||
−0.586287 | + | 0.810104i | \(0.699411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.42411 | 0.634845 | 0.317422 | − | 0.948284i | \(-0.397183\pi\) | ||||
0.317422 | + | 0.948284i | \(0.397183\pi\) | |||||||
\(74\) | −3.07996 | −0.358038 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.7856 | −1.35190 | ||||||||
\(77\) | 2.03917 | 0.232385 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1144 | 1.70050 | 0.850250 | − | 0.526378i | \(-0.176450\pi\) | ||||
0.850250 | + | 0.526378i | \(0.176450\pi\) | |||||||
\(80\) | −0.731571 | −0.0817921 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.52154 | −0.168026 | ||||||||
\(83\) | −8.98829 | −0.986593 | −0.493296 | − | 0.869861i | \(-0.664208\pi\) | ||||
−0.493296 | + | 0.869861i | \(0.664208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.690868 | −0.0749351 | ||||||||
\(86\) | 4.07446 | 0.439360 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.09384 | −0.543005 | ||||||||
\(89\) | −10.5005 | −1.11305 | −0.556523 | − | 0.830832i | \(-0.687865\pi\) | ||||
−0.556523 | + | 0.830832i | \(0.687865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.26367 | 0.237297 | ||||||||
\(92\) | 9.85155 | 1.02709 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.19896 | 0.536231 | ||||||||
\(95\) | −4.89882 | −0.502608 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4370 | −1.46585 | −0.732925 | − | 0.680309i | \(-0.761845\pi\) | ||||
−0.732925 | + | 0.680309i | \(0.761845\pi\) | |||||||
\(98\) | −0.716430 | −0.0723704 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.86587 | 0.686587 | ||||||||
\(101\) | −1.14263 | −0.113696 | −0.0568482 | − | 0.998383i | \(-0.518105\pi\) | ||||
−0.0568482 | + | 0.998383i | \(0.518105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3693 | −1.02171 | −0.510857 | − | 0.859666i | \(-0.670672\pi\) | ||||
−0.510857 | + | 0.859666i | \(0.670672\pi\) | |||||||
\(104\) | −5.65464 | −0.554483 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.03148 | 0.488701 | ||||||||
\(107\) | 9.21897 | 0.891231 | 0.445616 | − | 0.895224i | \(-0.352985\pi\) | ||||
0.445616 | + | 0.895224i | \(0.352985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.865135 | −0.0828649 | −0.0414324 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414324 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(110\) | −0.902815 | −0.0860800 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.18382 | −0.111860 | ||||||||
\(113\) | −16.4904 | −1.55128 | −0.775641 | − | 0.631174i | \(-0.782573\pi\) | ||||
−0.775641 | + | 0.631174i | \(0.782573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.09491 | 0.381853 | ||||||||
\(116\) | −5.50654 | −0.511269 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.38405 | −0.127413 | ||||||||
\(119\) | −1.11795 | −0.102482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.84179 | −0.621981 | ||||||||
\(122\) | −5.32947 | −0.482508 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.23640 | 0.200834 | ||||||||
\(125\) | 5.94376 | 0.531626 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 10.3849 | 0.917900 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00221 | −0.0878997 | ||||||||
\(131\) | −17.2493 | −1.50708 | −0.753538 | − | 0.657404i | \(-0.771654\pi\) | ||||
−0.753538 | + | 0.657404i | \(0.771654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.92719 | −0.687374 | ||||||||
\(134\) | −7.50249 | −0.648116 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.79264 | 0.239467 | ||||||||
\(137\) | 7.14706 | 0.610614 | 0.305307 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305307 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76101 | 0.743099 | 0.371550 | − | 0.928413i | \(-0.378827\pi\) | ||||
0.371550 | + | 0.928413i | \(0.378827\pi\) | |||||||
\(140\) | −0.918763 | −0.0776496 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.07853 | 0.594017 | ||||||||
\(143\) | 4.61601 | 0.386010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.28886 | −0.190079 | ||||||||
\(146\) | −3.88600 | −0.321607 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.39150 | −0.525378 | ||||||||
\(149\) | 21.4514 | 1.75737 | 0.878685 | − | 0.477402i | \(-0.158422\pi\) | ||||
0.878685 | + | 0.477402i | \(0.158422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.87577 | −0.315406 | −0.157703 | − | 0.987487i | \(-0.550409\pi\) | ||||
−0.157703 | + | 0.987487i | \(0.550409\pi\) | |||||||
\(152\) | 19.8021 | 1.60616 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.46092 | −0.117724 | ||||||||
\(155\) | 0.929586 | 0.0746661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2049 | −1.37310 | −0.686549 | − | 0.727084i | \(-0.740875\pi\) | ||||
−0.686549 | + | 0.727084i | \(0.740875\pi\) | |||||||
\(158\) | −10.8284 | −0.861461 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.61152 | 0.285516 | ||||||||
\(161\) | 6.62633 | 0.522228 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0674 | 1.72845 | 0.864225 | − | 0.503106i | \(-0.167809\pi\) | ||||
0.864225 | + | 0.503106i | \(0.167809\pi\) | |||||||
\(164\) | −3.15748 | −0.246558 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.43948 | 0.499800 | ||||||||
\(167\) | −17.4323 | −1.34895 | −0.674475 | − | 0.738298i | \(-0.735630\pi\) | ||||
−0.674475 | + | 0.738298i | \(0.735630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.87579 | −0.605830 | ||||||||
\(170\) | 0.494958 | 0.0379616 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.45527 | 0.644708 | ||||||||
\(173\) | 2.35715 | 0.179210 | 0.0896052 | − | 0.995977i | \(-0.471439\pi\) | ||||
0.0896052 | + | 0.995977i | \(0.471439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.61811 | 0.349096 | ||||||||
\(176\) | −2.41400 | −0.181962 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.52284 | 0.563861 | ||||||||
\(179\) | 19.6844 | 1.47128 | 0.735639 | − | 0.677374i | \(-0.236882\pi\) | ||||
0.735639 | + | 0.677374i | \(0.236882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.42604 | 0.403314 | 0.201657 | − | 0.979456i | \(-0.435367\pi\) | ||||
0.201657 | + | 0.979456i | \(0.435367\pi\) | |||||||
\(182\) | −1.62176 | −0.120213 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.5525 | −1.22027 | ||||||||
\(185\) | −2.65670 | −0.195325 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.27969 | −0.166708 | ||||||||
\(188\) | 10.7888 | 0.786856 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.50966 | 0.254617 | ||||||||
\(191\) | 11.8304 | 0.856015 | 0.428007 | − | 0.903775i | \(-0.359216\pi\) | ||||
0.428007 | + | 0.903775i | \(0.359216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0353 | −1.08227 | −0.541133 | − | 0.840937i | \(-0.682004\pi\) | ||||
−0.541133 | + | 0.840937i | \(0.682004\pi\) | |||||||
\(194\) | 10.3431 | 0.742589 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.48673 | −0.106195 | ||||||||
\(197\) | −1.48761 | −0.105988 | −0.0529941 | − | 0.998595i | \(-0.516876\pi\) | ||||
−0.0529941 | + | 0.998595i | \(0.516876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.11397 | 0.646072 | 0.323036 | − | 0.946387i | \(-0.395297\pi\) | ||||
0.323036 | + | 0.946387i | \(0.395297\pi\) | |||||||
\(200\) | −11.5360 | −0.815719 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.818617 | 0.0575977 | ||||||||
\(203\) | −3.70380 | −0.259956 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.31245 | −0.0916652 | ||||||||
\(206\) | 7.42885 | 0.517593 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.67977 | −0.185809 | ||||||||
\(209\) | −16.1649 | −1.11815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9309 | 1.02789 | 0.513944 | − | 0.857824i | \(-0.328184\pi\) | ||||
0.513944 | + | 0.857824i | \(0.328184\pi\) | |||||||
\(212\) | 10.4413 | 0.717110 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.60474 | −0.451491 | ||||||||
\(215\) | 3.51454 | 0.239689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50424 | 0.102115 | ||||||||
\(218\) | 0.619808 | 0.0419787 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.87351 | −0.126312 | ||||||||
\(221\) | −2.53068 | −0.170232 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.75342 | −0.117418 | −0.0587090 | − | 0.998275i | \(-0.518698\pi\) | ||||
−0.0587090 | + | 0.998275i | \(0.518698\pi\) | |||||||
\(224\) | 5.84411 | 0.390476 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8142 | 0.785868 | ||||||||
\(227\) | −0.504020 | −0.0334530 | −0.0167265 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167265 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5707 | 1.02894 | 0.514469 | − | 0.857509i | \(-0.327989\pi\) | ||||
0.514469 | + | 0.857509i | \(0.327989\pi\) | |||||||
\(230\) | −2.93372 | −0.193444 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.25207 | 0.607428 | ||||||||
\(233\) | −3.69340 | −0.241963 | −0.120981 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120981 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.48450 | 0.292537 | ||||||||
\(236\) | −2.87218 | −0.186963 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.800934 | 0.0519168 | ||||||||
\(239\) | 30.8421 | 1.99501 | 0.997506 | − | 0.0705784i | \(-0.0224845\pi\) | ||||
0.997506 | + | 0.0705784i | \(0.0224845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.61954 | −0.168739 | −0.0843695 | − | 0.996435i | \(-0.526888\pi\) | ||||
−0.0843695 | + | 0.996435i | \(0.526888\pi\) | |||||||
\(242\) | 4.90166 | 0.315091 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.0597 | −0.708022 | ||||||||
\(245\) | −0.617976 | −0.0394811 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.9445 | −1.14178 | ||||||||
\(248\) | −3.75759 | −0.238607 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.25829 | −0.269318 | ||||||||
\(251\) | 25.5776 | 1.61445 | 0.807223 | − | 0.590246i | \(-0.200969\pi\) | ||||
0.807223 | + | 0.590246i | \(0.200969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.5122 | 0.849505 | ||||||||
\(254\) | 0.716430 | 0.0449528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.0786 | −0.692409 | ||||||||
\(257\) | −18.4468 | −1.15068 | −0.575339 | − | 0.817915i | \(-0.695130\pi\) | ||||
−0.575339 | + | 0.817915i | \(0.695130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.29904 | −0.267129 | ||||||||
\(260\) | −2.07978 | −0.128982 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3579 | 0.763474 | ||||||||
\(263\) | −15.1320 | −0.933081 | −0.466540 | − | 0.884500i | \(-0.654500\pi\) | ||||
−0.466540 | + | 0.884500i | \(0.654500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.34005 | 0.266607 | ||||||||
\(266\) | 5.67928 | 0.348219 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.5691 | −0.951033 | ||||||||
\(269\) | 28.6078 | 1.74425 | 0.872124 | − | 0.489285i | \(-0.162742\pi\) | ||||
0.872124 | + | 0.489285i | \(0.162742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.03510 | 0.366606 | 0.183303 | − | 0.983056i | \(-0.441321\pi\) | ||||
0.183303 | + | 0.983056i | \(0.441321\pi\) | |||||||
\(272\) | 1.32345 | 0.0802459 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.12037 | −0.309333 | ||||||||
\(275\) | 9.41710 | 0.567872 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.2445 | 1.81722 | 0.908609 | − | 0.417648i | \(-0.137145\pi\) | ||||
0.908609 | + | 0.417648i | \(0.137145\pi\) | |||||||
\(278\) | −6.27665 | −0.376448 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.54370 | 0.0922539 | ||||||||
\(281\) | −0.763954 | −0.0455737 | −0.0227868 | − | 0.999740i | \(-0.507254\pi\) | ||||
−0.0227868 | + | 0.999740i | \(0.507254\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.57222 | −0.152903 | −0.0764514 | − | 0.997073i | \(-0.524359\pi\) | ||||
−0.0764514 | + | 0.997073i | \(0.524359\pi\) | |||||||
\(284\) | 14.6893 | 0.871649 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.30705 | −0.195550 | ||||||||
\(287\) | −2.12378 | −0.125363 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7502 | −0.926481 | ||||||||
\(290\) | 1.63981 | 0.0962928 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.06418 | −0.471921 | ||||||||
\(293\) | −7.68306 | −0.448849 | −0.224424 | − | 0.974491i | \(-0.572050\pi\) | ||||
−0.224424 | + | 0.974491i | \(0.572050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19385 | −0.0695089 | ||||||||
\(296\) | 10.7390 | 0.624191 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.3684 | −0.890270 | ||||||||
\(299\) | 14.9998 | 0.867462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.68717 | 0.327803 | ||||||||
\(302\) | 2.77672 | 0.159782 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.38434 | 0.538229 | ||||||||
\(305\) | −4.59708 | −0.263228 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6054 | −1.11894 | −0.559469 | − | 0.828851i | \(-0.688995\pi\) | ||||
−0.559469 | + | 0.828851i | \(0.688995\pi\) | |||||||
\(308\) | −3.03169 | −0.172747 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.665983 | −0.0378253 | ||||||||
\(311\) | 15.4474 | 0.875942 | 0.437971 | − | 0.898989i | \(-0.355697\pi\) | ||||
0.437971 | + | 0.898989i | \(0.355697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.138060 | 0.00780361 | 0.00390181 | − | 0.999992i | \(-0.498758\pi\) | ||||
0.00390181 | + | 0.999992i | \(0.498758\pi\) | |||||||
\(314\) | 12.3261 | 0.695601 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.4710 | −1.26409 | ||||||||
\(317\) | 16.5419 | 0.929086 | 0.464543 | − | 0.885551i | \(-0.346219\pi\) | ||||
0.464543 | + | 0.885551i | \(0.346219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.55266 | −0.422868 | ||||||||
\(320\) | −1.12426 | −0.0628482 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.74730 | −0.264557 | ||||||||
\(323\) | 8.86221 | 0.493107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.4539 | 0.579876 | ||||||||
\(326\) | −15.8097 | −0.875620 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.30519 | 0.292930 | ||||||||
\(329\) | 7.25675 | 0.400078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3281 | −1.00740 | −0.503702 | − | 0.863877i | \(-0.668029\pi\) | ||||
−0.503702 | + | 0.863877i | \(0.668029\pi\) | |||||||
\(332\) | 13.3631 | 0.733397 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4890 | 0.683368 | ||||||||
\(335\) | −6.47147 | −0.353574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8550 | 0.754730 | 0.377365 | − | 0.926065i | \(-0.376830\pi\) | ||||
0.377365 | + | 0.926065i | \(0.376830\pi\) | |||||||
\(338\) | 5.64245 | 0.306909 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.02713 | 0.0557041 | ||||||||
\(341\) | 3.06740 | 0.166109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −14.2065 | −0.765964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.68873 | −0.0907867 | ||||||||
\(347\) | −27.5408 | −1.47847 | −0.739235 | − | 0.673447i | \(-0.764813\pi\) | ||||
−0.739235 | + | 0.673447i | \(0.764813\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.4626 | −1.57710 | −0.788550 | − | 0.614971i | \(-0.789168\pi\) | ||||
−0.788550 | + | 0.614971i | \(0.789168\pi\) | |||||||
\(350\) | −3.30855 | −0.176849 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.9171 | 0.635186 | ||||||||
\(353\) | 29.9244 | 1.59272 | 0.796358 | − | 0.604825i | \(-0.206757\pi\) | ||||
0.796358 | + | 0.604825i | \(0.206757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.10578 | 0.324061 | ||||||||
\(356\) | 15.6113 | 0.827399 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.1025 | −0.745339 | ||||||||
\(359\) | −11.0464 | −0.583007 | −0.291504 | − | 0.956570i | \(-0.594156\pi\) | ||||
−0.291504 | + | 0.956570i | \(0.594156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.8403 | 2.30739 | ||||||||
\(362\) | −3.88737 | −0.204316 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.36546 | −0.176398 | ||||||||
\(365\) | −3.35197 | −0.175450 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6359 | 1.02499 | 0.512494 | − | 0.858691i | \(-0.328722\pi\) | ||||
0.512494 | + | 0.858691i | \(0.328722\pi\) | |||||||
\(368\) | −7.84436 | −0.408915 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.90334 | 0.0989500 | ||||||||
\(371\) | 7.02300 | 0.364616 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1118 | 0.523568 | 0.261784 | − | 0.965126i | \(-0.415689\pi\) | ||||
0.261784 | + | 0.965126i | \(0.415689\pi\) | |||||||
\(374\) | 1.63324 | 0.0844528 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.1273 | −0.934846 | ||||||||
\(377\) | −8.38418 | −0.431807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.47081 | 0.281017 | 0.140508 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140508 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(380\) | 7.28321 | 0.373621 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.47562 | −0.433651 | ||||||||
\(383\) | 9.87140 | 0.504405 | 0.252202 | − | 0.967674i | \(-0.418845\pi\) | ||||
0.252202 | + | 0.967674i | \(0.418845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.26016 | −0.0642236 | ||||||||
\(386\) | 10.7718 | 0.548268 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.4638 | 1.08966 | ||||||||
\(389\) | −7.86204 | −0.398621 | −0.199311 | − | 0.979936i | \(-0.563870\pi\) | ||||
−0.199311 | + | 0.979936i | \(0.563870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.40791 | −0.374634 | ||||||||
\(392\) | 2.49800 | 0.126168 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.06577 | 0.0536928 | ||||||||
\(395\) | −9.34033 | −0.469963 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7639 | −0.941732 | −0.470866 | − | 0.882205i | \(-0.656058\pi\) | ||||
−0.470866 | + | 0.882205i | \(0.656058\pi\) | |||||||
\(398\) | −6.52952 | −0.327295 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.46699 | −0.273349 | ||||||||
\(401\) | 10.4959 | 0.524138 | 0.262069 | − | 0.965049i | \(-0.415595\pi\) | ||||
0.262069 | + | 0.965049i | \(0.415595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.40511 | 0.169620 | ||||||||
\(404\) | 1.69879 | 0.0845178 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.65351 | 0.131692 | ||||||||
\(407\) | −8.76646 | −0.434537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2977 | 1.39923 | 0.699616 | − | 0.714519i | \(-0.253355\pi\) | ||||
0.699616 | + | 0.714519i | \(0.253355\pi\) | |||||||
\(410\) | 0.940275 | 0.0464369 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.4163 | 0.759505 | ||||||||
\(413\) | −1.93188 | −0.0950614 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.55455 | 0.272662 | ||||||||
\(416\) | 13.2292 | 0.648613 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.5810 | 0.566445 | ||||||||
\(419\) | 27.6457 | 1.35058 | 0.675290 | − | 0.737552i | \(-0.264018\pi\) | ||||
0.675290 | + | 0.737552i | \(0.264018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0977 | 1.07698 | 0.538488 | − | 0.842633i | \(-0.318996\pi\) | ||||
0.538488 | + | 0.842633i | \(0.318996\pi\) | |||||||
\(422\) | −10.6970 | −0.520720 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.5434 | −0.851984 | ||||||||
\(425\) | −5.16282 | −0.250434 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.43893 | −0.359995 | ||||||||
\(428\) | −13.7061 | −0.662509 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.51792 | −0.121425 | ||||||||
\(431\) | −20.1964 | −0.972827 | −0.486414 | − | 0.873729i | \(-0.661695\pi\) | ||||
−0.486414 | + | 0.873729i | \(0.661695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7722 | −0.709909 | −0.354954 | − | 0.934884i | \(-0.615504\pi\) | ||||
−0.354954 | + | 0.934884i | \(0.615504\pi\) | |||||||
\(434\) | −1.07768 | −0.0517305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.28622 | 0.0615988 | ||||||||
\(437\) | −52.5281 | −2.51276 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.567166 | −0.0270693 | −0.0135347 | − | 0.999908i | \(-0.504308\pi\) | ||||
−0.0135347 | + | 0.999908i | \(0.504308\pi\) | |||||||
\(440\) | 3.14787 | 0.150069 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.81305 | 0.0862381 | ||||||||
\(443\) | 7.32609 | 0.348073 | 0.174037 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174037 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.48904 | 0.307610 | ||||||||
\(446\) | 1.25621 | 0.0594830 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.81927 | −0.0859522 | ||||||||
\(449\) | 8.19856 | 0.386914 | 0.193457 | − | 0.981109i | \(-0.438030\pi\) | ||||
0.193457 | + | 0.981109i | \(0.438030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.33074 | −0.203927 | ||||||||
\(452\) | 24.5167 | 1.15317 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.361095 | 0.0169470 | ||||||||
\(455\) | −1.39890 | −0.0655812 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.2094 | −0.758243 | −0.379122 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379122 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(458\) | −11.1553 | −0.521252 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.08802 | −0.283856 | ||||||||
\(461\) | 31.9638 | 1.48870 | 0.744351 | − | 0.667788i | \(-0.232759\pi\) | ||||
0.744351 | + | 0.667788i | \(0.232759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0886 | 1.86308 | 0.931538 | − | 0.363645i | \(-0.118468\pi\) | ||||
0.931538 | + | 0.363645i | \(0.118468\pi\) | |||||||
\(464\) | 4.38462 | 0.203551 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.64606 | 0.122577 | ||||||||
\(467\) | 34.9976 | 1.61950 | 0.809749 | − | 0.586777i | \(-0.199603\pi\) | ||||
0.809749 | + | 0.586777i | \(0.199603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4720 | −0.483554 | ||||||||
\(470\) | −3.21283 | −0.148197 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.82582 | 0.222126 | ||||||||
\(473\) | 11.5971 | 0.533235 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.6086 | −1.67972 | ||||||||
\(476\) | 1.66209 | 0.0761818 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.0962 | −1.01066 | ||||||||
\(479\) | 31.4638 | 1.43762 | 0.718808 | − | 0.695209i | \(-0.244688\pi\) | ||||
0.718808 | + | 0.695209i | \(0.244688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.73161 | −0.443723 | ||||||||
\(482\) | 1.87671 | 0.0854820 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.1719 | 0.462358 | ||||||||
\(485\) | 8.92169 | 0.405113 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.4829 | −0.882857 | −0.441428 | − | 0.897297i | \(-0.645528\pi\) | ||||
−0.441428 | + | 0.897297i | \(0.645528\pi\) | |||||||
\(488\) | 18.5824 | 0.841187 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.442737 | 0.0200008 | ||||||||
\(491\) | −4.84336 | −0.218578 | −0.109289 | − | 0.994010i | \(-0.534857\pi\) | ||||
−0.109289 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.14067 | 0.186486 | ||||||||
\(494\) | 12.8560 | 0.578419 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.78075 | −0.0799579 | ||||||||
\(497\) | 9.88028 | 0.443191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1439 | −1.84185 | −0.920927 | − | 0.389735i | \(-0.872567\pi\) | ||||
−0.920927 | + | 0.389735i | \(0.872567\pi\) | |||||||
\(500\) | −8.83676 | −0.395192 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.3246 | −0.817867 | ||||||||
\(503\) | −7.38885 | −0.329452 | −0.164726 | − | 0.986339i | \(-0.552674\pi\) | ||||
−0.164726 | + | 0.986339i | \(0.552674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.706121 | 0.0314220 | ||||||||
\(506\) | −9.68054 | −0.430353 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.48673 | 0.0659629 | ||||||||
\(509\) | 8.13369 | 0.360520 | 0.180260 | − | 0.983619i | \(-0.442306\pi\) | ||||
0.180260 | + | 0.983619i | \(0.442306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.42411 | −0.239949 | ||||||||
\(512\) | −12.8327 | −0.567131 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.2158 | 0.582925 | ||||||||
\(515\) | 6.40796 | 0.282368 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7977 | 0.650804 | ||||||||
\(518\) | 3.07996 | 0.135326 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.49444 | 0.153241 | ||||||||
\(521\) | −28.9263 | −1.26728 | −0.633642 | − | 0.773626i | \(-0.718441\pi\) | ||||
−0.633642 | + | 0.773626i | \(0.718441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3728 | 0.759660 | 0.379830 | − | 0.925056i | \(-0.375982\pi\) | ||||
0.379830 | + | 0.925056i | \(0.375982\pi\) | |||||||
\(524\) | 25.6450 | 1.12031 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8410 | 0.472692 | ||||||||
\(527\) | −1.68167 | −0.0732547 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9082 | 0.909052 | ||||||||
\(530\) | −3.10934 | −0.135061 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.7856 | 0.510969 | ||||||||
\(533\) | −4.80754 | −0.208238 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.69710 | −0.246307 | ||||||||
\(536\) | 26.1591 | 1.12990 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.4955 | −0.883623 | ||||||||
\(539\) | −2.03917 | −0.0878332 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.8394 | 1.84181 | 0.920905 | − | 0.389787i | \(-0.127451\pi\) | ||||
0.920905 | + | 0.389787i | \(0.127451\pi\) | |||||||
\(542\) | −4.32373 | −0.185720 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.53344 | −0.280119 | ||||||||
\(545\) | 0.534633 | 0.0229012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.81661 | −0.291457 | −0.145729 | − | 0.989325i | \(-0.546553\pi\) | ||||
−0.145729 | + | 0.989325i | \(0.546553\pi\) | |||||||
\(548\) | −10.6257 | −0.453909 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.74669 | −0.287680 | ||||||||
\(551\) | 29.3607 | 1.25081 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1144 | −0.642729 | ||||||||
\(554\) | −21.6681 | −0.920589 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.0252 | −0.552393 | ||||||||
\(557\) | 1.16988 | 0.0495696 | 0.0247848 | − | 0.999693i | \(-0.492110\pi\) | ||||
0.0247848 | + | 0.999693i | \(0.492110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8739 | 0.544507 | ||||||||
\(560\) | 0.731571 | 0.0309145 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.547320 | 0.0230873 | ||||||||
\(563\) | 22.8170 | 0.961621 | 0.480810 | − | 0.876825i | \(-0.340343\pi\) | ||||
0.480810 | + | 0.876825i | \(0.340343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1907 | 0.428724 | ||||||||
\(566\) | 1.84282 | 0.0774594 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.6809 | −1.03559 | ||||||||
\(569\) | 5.19397 | 0.217743 | 0.108871 | − | 0.994056i | \(-0.465276\pi\) | ||||
0.108871 | + | 0.994056i | \(0.465276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.91405 | 0.289344 | 0.144672 | − | 0.989480i | \(-0.453787\pi\) | ||||
0.144672 | + | 0.989480i | \(0.453787\pi\) | |||||||
\(572\) | −6.86275 | −0.286946 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.52154 | 0.0635078 | ||||||||
\(575\) | 30.6011 | 1.27615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.8356 | 0.700873 | 0.350437 | − | 0.936586i | \(-0.386033\pi\) | ||||
0.350437 | + | 0.936586i | \(0.386033\pi\) | |||||||
\(578\) | 11.2839 | 0.469349 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.40291 | 0.141298 | ||||||||
\(581\) | 8.98829 | 0.372897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3211 | 0.593118 | ||||||||
\(584\) | 13.5494 | 0.560679 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.50437 | 0.227383 | ||||||||
\(587\) | 42.6694 | 1.76115 | 0.880576 | − | 0.473904i | \(-0.157156\pi\) | ||||
0.880576 | + | 0.473904i | \(0.157156\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.9244 | −0.491337 | ||||||||
\(590\) | 0.855313 | 0.0352127 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.08927 | 0.209168 | ||||||||
\(593\) | −23.0971 | −0.948486 | −0.474243 | − | 0.880394i | \(-0.657278\pi\) | ||||
−0.474243 | + | 0.880394i | \(0.657278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.690868 | 0.0283228 | ||||||||
\(596\) | −31.8924 | −1.30637 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.7463 | −0.439450 | ||||||||
\(599\) | 7.37647 | 0.301394 | 0.150697 | − | 0.988580i | \(-0.451848\pi\) | ||||
0.150697 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.20517 | −0.334696 | −0.167348 | − | 0.985898i | \(-0.553520\pi\) | ||||
−0.167348 | + | 0.985898i | \(0.553520\pi\) | |||||||
\(602\) | −4.07446 | −0.166062 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.76222 | 0.234461 | ||||||||
\(605\) | 4.22806 | 0.171895 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.57849 | 0.348190 | 0.174095 | − | 0.984729i | \(-0.444300\pi\) | ||||
0.174095 | + | 0.984729i | \(0.444300\pi\) | |||||||
\(608\) | −46.3274 | −1.87882 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.29349 | 0.133349 | ||||||||
\(611\) | 16.4269 | 0.664561 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3945 | 1.71230 | 0.856148 | − | 0.516730i | \(-0.172851\pi\) | ||||
0.856148 | + | 0.516730i | \(0.172851\pi\) | |||||||
\(614\) | 14.0459 | 0.566846 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.09384 | 0.205237 | ||||||||
\(617\) | 22.9614 | 0.924390 | 0.462195 | − | 0.886778i | \(-0.347062\pi\) | ||||
0.462195 | + | 0.886778i | \(0.347062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0297 | −0.644288 | −0.322144 | − | 0.946691i | \(-0.604403\pi\) | ||||
−0.322144 | + | 0.946691i | \(0.604403\pi\) | |||||||
\(620\) | −1.38204 | −0.0555041 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.0670 | −0.443746 | ||||||||
\(623\) | 10.5005 | 0.420692 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4174 | 0.776697 | ||||||||
\(626\) | −0.0989103 | −0.00395325 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.5790 | 1.02071 | ||||||||
\(629\) | 4.80612 | 0.191632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2130 | 1.12314 | 0.561571 | − | 0.827429i | \(-0.310197\pi\) | ||||
0.561571 | + | 0.827429i | \(0.310197\pi\) | |||||||
\(632\) | 37.7557 | 1.50184 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.8511 | −0.470668 | ||||||||
\(635\) | 0.617976 | 0.0245236 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.26367 | −0.0896899 | ||||||||
\(638\) | 5.41096 | 0.214222 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.41759 | −0.253678 | ||||||||
\(641\) | 27.3897 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318078\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5051 | 0.572026 | 0.286013 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286013 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(644\) | −9.85155 | −0.388205 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.34916 | −0.249804 | ||||||||
\(647\) | 13.0663 | 0.513690 | 0.256845 | − | 0.966453i | \(-0.417317\pi\) | ||||
0.256845 | + | 0.966453i | \(0.417317\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.93942 | −0.154636 | ||||||||
\(650\) | −7.48947 | −0.293761 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −32.8082 | −1.28487 | ||||||||
\(653\) | −28.8586 | −1.12932 | −0.564662 | − | 0.825323i | \(-0.690993\pi\) | ||||
−0.564662 | + | 0.825323i | \(0.690993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.6596 | 0.416507 | ||||||||
\(656\) | 2.51417 | 0.0981617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.19896 | −0.202676 | ||||||||
\(659\) | −41.5879 | −1.62004 | −0.810018 | − | 0.586405i | \(-0.800543\pi\) | ||||
−0.810018 | + | 0.586405i | \(0.800543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.4380 | 1.76733 | 0.883667 | − | 0.468115i | \(-0.155067\pi\) | ||||
0.883667 | + | 0.468115i | \(0.155067\pi\) | |||||||
\(662\) | 13.1308 | 0.510344 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.4527 | −0.871334 | ||||||||
\(665\) | 4.89882 | 0.189968 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.5426 | −0.950292 | ||||||||
\(668\) | 25.9170 | 1.00276 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.63636 | 0.179118 | ||||||||
\(671\) | −15.1692 | −0.585602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.1380 | −0.544980 | −0.272490 | − | 0.962159i | \(-0.587847\pi\) | ||||
−0.272490 | + | 0.962159i | \(0.587847\pi\) | |||||||
\(674\) | −9.92614 | −0.382341 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.7092 | 0.450352 | ||||||||
\(677\) | 36.8722 | 1.41711 | 0.708557 | − | 0.705654i | \(-0.249347\pi\) | ||||
0.708557 | + | 0.705654i | \(0.249347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4370 | 0.554039 | ||||||||
\(680\) | −1.72579 | −0.0661808 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.19758 | −0.0841496 | ||||||||
\(683\) | 13.3883 | 0.512289 | 0.256145 | − | 0.966638i | \(-0.417548\pi\) | ||||
0.256145 | + | 0.966638i | \(0.417548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.41671 | −0.168754 | ||||||||
\(686\) | 0.716430 | 0.0273534 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.73256 | −0.256677 | ||||||||
\(689\) | 15.8978 | 0.605656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6469 | 1.24195 | 0.620974 | − | 0.783831i | \(-0.286737\pi\) | ||||
0.620974 | + | 0.783831i | \(0.286737\pi\) | |||||||
\(692\) | −3.50443 | −0.133219 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.7311 | 0.748982 | ||||||||
\(695\) | −5.41410 | −0.205368 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.37428 | 0.0899324 | ||||||||
\(698\) | 21.1079 | 0.798947 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.86587 | −0.259505 | ||||||||
\(701\) | −36.7539 | −1.38817 | −0.694087 | − | 0.719891i | \(-0.744192\pi\) | ||||
−0.694087 | + | 0.719891i | \(0.744192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.0793 | 1.28532 | ||||||||
\(704\) | −3.70979 | −0.139818 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.4388 | −0.806858 | ||||||||
\(707\) | 1.14263 | 0.0429732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.1990 | −0.796146 | −0.398073 | − | 0.917354i | \(-0.630321\pi\) | ||||
−0.398073 | + | 0.917354i | \(0.630321\pi\) | |||||||
\(710\) | −4.37436 | −0.164167 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.2301 | −0.983015 | ||||||||
\(713\) | 9.96760 | 0.373289 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.85258 | −0.106681 | ||||||||
\(716\) | −29.2653 | −1.09370 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.91398 | 0.295347 | ||||||||
\(719\) | 17.8524 | 0.665782 | 0.332891 | − | 0.942965i | \(-0.391976\pi\) | ||||
0.332891 | + | 0.942965i | \(0.391976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3693 | 0.386172 | ||||||||
\(722\) | −31.4085 | −1.16890 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.06704 | −0.299809 | ||||||||
\(725\) | −17.1045 | −0.635246 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0525 | −0.966233 | −0.483116 | − | 0.875556i | \(-0.660495\pi\) | ||||
−0.483116 | + | 0.875556i | \(0.660495\pi\) | |||||||
\(728\) | 5.65464 | 0.209575 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.40145 | 0.0888818 | ||||||||
\(731\) | −6.35798 | −0.235158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.6871 | 1.79830 | 0.899150 | − | 0.437640i | \(-0.144186\pi\) | ||||
0.899150 | + | 0.437640i | \(0.144186\pi\) | |||||||
\(734\) | −14.0678 | −0.519251 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.7250 | 1.42742 | ||||||||
\(737\) | −21.3543 | −0.786594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.5162 | −1.78470 | −0.892349 | − | 0.451346i | \(-0.850944\pi\) | ||||
−0.892349 | + | 0.451346i | \(0.850944\pi\) | |||||||
\(740\) | 3.94980 | 0.145197 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.03148 | −0.184712 | ||||||||
\(743\) | −6.51240 | −0.238917 | −0.119458 | − | 0.992839i | \(-0.538116\pi\) | ||||
−0.119458 | + | 0.992839i | \(0.538116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.2565 | −0.485680 | ||||||||
\(746\) | −7.24438 | −0.265236 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.38928 | 0.123924 | ||||||||
\(749\) | −9.21897 | −0.336854 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.2954 | 1.65285 | 0.826427 | − | 0.563044i | \(-0.190370\pi\) | ||||
0.826427 | + | 0.563044i | \(0.190370\pi\) | |||||||
\(752\) | −8.59067 | −0.313269 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00667 | 0.218750 | ||||||||
\(755\) | 2.39514 | 0.0871679 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1126 | 1.16715 | 0.583577 | − | 0.812058i | \(-0.301653\pi\) | ||||
0.583577 | + | 0.812058i | \(0.301653\pi\) | |||||||
\(758\) | −3.91946 | −0.142361 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.2372 | −0.443891 | ||||||||
\(761\) | 17.0499 | 0.618059 | 0.309030 | − | 0.951052i | \(-0.399996\pi\) | ||||
0.309030 | + | 0.951052i | \(0.399996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.865135 | 0.0313200 | ||||||||
\(764\) | −17.5885 | −0.636330 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.07217 | −0.255528 | ||||||||
\(767\) | −4.37313 | −0.157905 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0262 | 0.830345 | 0.415172 | − | 0.909743i | \(-0.363721\pi\) | ||||
0.415172 | + | 0.909743i | \(0.363721\pi\) | |||||||
\(770\) | 0.902815 | 0.0325352 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.3534 | 0.804518 | ||||||||
\(773\) | 52.0454 | 1.87194 | 0.935972 | − | 0.352074i | \(-0.114524\pi\) | ||||
0.935972 | + | 0.352074i | \(0.114524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.94675 | 0.249534 | ||||||||
\(776\) | −36.0635 | −1.29460 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.63260 | 0.201939 | ||||||||
\(779\) | 16.8356 | 0.603198 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1476 | 0.720936 | ||||||||
\(782\) | 5.30725 | 0.189787 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.18382 | 0.0422792 | ||||||||
\(785\) | 10.6322 | 0.379479 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.25919 | −0.116178 | −0.0580888 | − | 0.998311i | \(-0.518501\pi\) | ||||
−0.0580888 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(788\) | 2.21168 | 0.0787878 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.69169 | 0.238080 | ||||||||
\(791\) | 16.4904 | 0.586330 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8393 | −0.597981 | ||||||||
\(794\) | 13.4430 | 0.477074 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.5500 | −0.480267 | ||||||||
\(797\) | 14.7367 | 0.522000 | 0.261000 | − | 0.965339i | \(-0.415948\pi\) | ||||
0.261000 | + | 0.965339i | \(0.415948\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.11270 | −0.287007 | ||||||||
\(800\) | 26.9887 | 0.954196 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.51955 | −0.265524 | ||||||||
\(803\) | −11.0607 | −0.390323 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.09491 | −0.144327 | ||||||||
\(806\) | −2.43952 | −0.0859285 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.85430 | −0.100414 | ||||||||
\(809\) | −18.9304 | −0.665557 | −0.332779 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332779 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.2689 | −1.69495 | −0.847475 | − | 0.530835i | \(-0.821878\pi\) | ||||
−0.847475 | + | 0.530835i | \(0.821878\pi\) | |||||||
\(812\) | 5.50654 | 0.193242 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.28056 | 0.220133 | ||||||||
\(815\) | −13.6371 | −0.477687 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.0833 | −1.57726 | ||||||||
\(818\) | −20.2733 | −0.708840 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.95125 | 0.0681406 | ||||||||
\(821\) | 24.4326 | 0.852704 | 0.426352 | − | 0.904557i | \(-0.359798\pi\) | ||||
0.426352 | + | 0.904557i | \(0.359798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8491 | 1.07533 | 0.537667 | − | 0.843157i | \(-0.319306\pi\) | ||||
0.537667 | + | 0.843157i | \(0.319306\pi\) | |||||||
\(824\) | −25.9024 | −0.902352 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.38405 | 0.0481574 | ||||||||
\(827\) | −20.5018 | −0.712917 | −0.356458 | − | 0.934311i | \(-0.616016\pi\) | ||||
−0.356458 | + | 0.934311i | \(0.616016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0508 | −0.835317 | −0.417659 | − | 0.908604i | \(-0.637149\pi\) | ||||
−0.417659 | + | 0.908604i | \(0.637149\pi\) | |||||||
\(830\) | −3.97944 | −0.138129 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.11822 | −0.142774 | ||||||||
\(833\) | 1.11795 | 0.0387347 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.7727 | 0.372806 | ||||||||
\(836\) | 24.0328 | 0.831191 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.8062 | −0.684194 | ||||||||
\(839\) | −44.0427 | −1.52052 | −0.760261 | − | 0.649618i | \(-0.774929\pi\) | ||||
−0.760261 | + | 0.649618i | \(0.774929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2819 | −0.526962 | ||||||||
\(842\) | −15.8314 | −0.545587 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.1982 | −0.764095 | ||||||||
\(845\) | 4.86705 | 0.167432 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.84179 | 0.235087 | ||||||||
\(848\) | −8.31394 | −0.285502 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.69880 | 0.126868 | ||||||||
\(851\) | −28.4868 | −0.976516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4780 | 0.906591 | 0.453295 | − | 0.891360i | \(-0.350248\pi\) | ||||
0.453295 | + | 0.891360i | \(0.350248\pi\) | |||||||
\(854\) | 5.32947 | 0.182371 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.0289 | 0.787113 | ||||||||
\(857\) | 40.8062 | 1.39391 | 0.696956 | − | 0.717114i | \(-0.254537\pi\) | ||||
0.696956 | + | 0.717114i | \(0.254537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8868 | −1.42916 | −0.714580 | − | 0.699554i | \(-0.753382\pi\) | ||||
−0.714580 | + | 0.699554i | \(0.753382\pi\) | |||||||
\(860\) | −5.22516 | −0.178176 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.4693 | 0.492827 | ||||||||
\(863\) | −4.40796 | −0.150049 | −0.0750244 | − | 0.997182i | \(-0.523903\pi\) | ||||
−0.0750244 | + | 0.997182i | \(0.523903\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.45666 | −0.0495279 | ||||||||
\(866\) | 10.5833 | 0.359635 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.23640 | −0.0759083 | ||||||||
\(869\) | −30.8208 | −1.04552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.7053 | −0.803222 | ||||||||
\(872\) | −2.16110 | −0.0731842 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.6327 | 1.27295 | ||||||||
\(875\) | −5.94376 | −0.200936 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5553 | −0.694102 | −0.347051 | − | 0.937846i | \(-0.612817\pi\) | ||||
−0.347051 | + | 0.937846i | \(0.612817\pi\) | |||||||
\(878\) | 0.406334 | 0.0137131 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.49180 | 0.0502884 | ||||||||
\(881\) | −29.0290 | −0.978012 | −0.489006 | − | 0.872280i | \(-0.662640\pi\) | ||||
−0.489006 | + | 0.872280i | \(0.662640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.9692 | 1.61429 | 0.807145 | − | 0.590353i | \(-0.201011\pi\) | ||||
0.807145 | + | 0.590353i | \(0.201011\pi\) | |||||||
\(884\) | 3.76243 | 0.126544 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.24863 | −0.176331 | ||||||||
\(887\) | 5.23890 | 0.175905 | 0.0879526 | − | 0.996125i | \(-0.471968\pi\) | ||||
0.0879526 | + | 0.996125i | \(0.471968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −4.64894 | −0.155833 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.60686 | 0.0872843 | ||||||||
\(893\) | −57.5257 | −1.92502 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1645 | −0.406613 | ||||||||
\(896\) | −10.3849 | −0.346934 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.87370 | −0.196008 | ||||||||
\(899\) | −5.57140 | −0.185817 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.85137 | −0.261567 | ||||||||
\(902\) | 3.10268 | 0.103308 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.1929 | −1.37005 | ||||||||
\(905\) | −3.35316 | −0.111463 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.2955 | 0.673901 | 0.336950 | − | 0.941522i | \(-0.390605\pi\) | ||||
0.336950 | + | 0.941522i | \(0.390605\pi\) | |||||||
\(908\) | 0.749341 | 0.0248678 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00221 | 0.0332230 | ||||||||
\(911\) | −3.65224 | −0.121004 | −0.0605021 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605021 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.3286 | 0.606589 | ||||||||
\(914\) | 11.6129 | 0.384120 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.1493 | −0.764876 | ||||||||
\(917\) | 17.2493 | 0.569621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3743 | 0.606112 | 0.303056 | − | 0.952973i | \(-0.401993\pi\) | ||||
0.303056 | + | 0.952973i | \(0.401993\pi\) | |||||||
\(920\) | 10.2291 | 0.337243 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.8998 | −0.754166 | ||||||||
\(923\) | 22.3657 | 0.736176 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8534 | −0.652776 | ||||||||
\(926\) | −28.7207 | −0.943820 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.6454 | −0.710545 | ||||||||
\(929\) | 34.1612 | 1.12079 | 0.560396 | − | 0.828225i | \(-0.310649\pi\) | ||||
0.560396 | + | 0.828225i | \(0.310649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.92719 | 0.259803 | ||||||||
\(932\) | 5.49108 | 0.179866 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.0734 | −0.820425 | ||||||||
\(935\) | 1.40880 | 0.0460726 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.3046 | 0.401973 | 0.200986 | − | 0.979594i | \(-0.435585\pi\) | ||||
0.200986 | + | 0.979594i | \(0.435585\pi\) | |||||||
\(938\) | 7.50249 | 0.244965 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.66724 | −0.217461 | ||||||||
\(941\) | 13.7984 | 0.449815 | 0.224908 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224908 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.0729 | −0.458275 | ||||||||
\(944\) | 2.28699 | 0.0744351 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.30851 | −0.270133 | ||||||||
\(947\) | −15.8853 | −0.516204 | −0.258102 | − | 0.966118i | \(-0.583097\pi\) | ||||
−0.258102 | + | 0.966118i | \(0.583097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2784 | −0.398574 | ||||||||
\(950\) | 26.2275 | 0.850932 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.79264 | −0.0905100 | ||||||||
\(953\) | −32.1393 | −1.04109 | −0.520546 | − | 0.853833i | \(-0.674272\pi\) | ||||
−0.520546 | + | 0.853833i | \(0.674272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.31088 | −0.236575 | ||||||||
\(956\) | −45.8539 | −1.48302 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.5416 | −0.728285 | ||||||||
\(959\) | −7.14706 | −0.230790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7373 | −0.927008 | ||||||||
\(962\) | 6.97202 | 0.224787 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.89454 | 0.125435 | ||||||||
\(965\) | 9.29147 | 0.299103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.50545 | −0.273517 | −0.136758 | − | 0.990604i | \(-0.543668\pi\) | ||||
−0.136758 | + | 0.990604i | \(0.543668\pi\) | |||||||
\(968\) | −17.0908 | −0.549318 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.39177 | −0.205227 | ||||||||
\(971\) | 48.7435 | 1.56425 | 0.782127 | − | 0.623120i | \(-0.214135\pi\) | ||||
0.782127 | + | 0.623120i | \(0.214135\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.76101 | −0.280865 | ||||||||
\(974\) | 13.9582 | 0.447249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.80633 | 0.281884 | ||||||||
\(977\) | −9.54315 | −0.305312 | −0.152656 | − | 0.988279i | \(-0.548783\pi\) | ||||
−0.152656 | + | 0.988279i | \(0.548783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.4122 | 0.684337 | ||||||||
\(980\) | 0.918763 | 0.0293488 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.46993 | 0.110730 | ||||||||
\(983\) | −27.1267 | −0.865206 | −0.432603 | − | 0.901584i | \(-0.642405\pi\) | ||||
−0.432603 | + | 0.901584i | \(0.642405\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.919311 | 0.0292917 | ||||||||
\(986\) | −2.96650 | −0.0944725 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.6787 | 0.848761 | ||||||||
\(989\) | 37.6850 | 1.19831 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.07844 | −0.256620 | −0.128310 | − | 0.991734i | \(-0.540955\pi\) | ||||
−0.128310 | + | 0.991734i | \(0.540955\pi\) | |||||||
\(992\) | 8.79096 | 0.279113 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.07853 | −0.224517 | ||||||||
\(995\) | −5.63222 | −0.178553 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4806 | 1.34538 | 0.672688 | − | 0.739927i | \(-0.265140\pi\) | ||||
0.672688 | + | 0.739927i | \(0.265140\pi\) | |||||||
\(998\) | 29.4767 | 0.933069 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.s.1.8 | 16 | ||
3.2 | odd | 2 | 2667.2.a.n.1.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.n.1.9 | ✓ | 16 | 3.2 | odd | 2 | ||
8001.2.a.s.1.8 | 16 | 1.1 | even | 1 | trivial |