Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 8x^{6} + 14x^{5} + 18x^{4} - 24x^{3} - 10x^{2} + 10x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.28873\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28873 | −1.61837 | −0.809187 | − | 0.587552i | \(-0.800092\pi\) | ||||
−0.809187 | + | 0.587552i | \(0.800092\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.23826 | 1.61913 | ||||||||
\(5\) | −2.92705 | −1.30902 | −0.654508 | − | 0.756055i | \(-0.727124\pi\) | ||||
−0.654508 | + | 0.756055i | \(0.727124\pi\) | |||||||
\(6\) | −2.28873 | −0.934368 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.83405 | −1.00199 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.69922 | 2.11848 | ||||||||
\(11\) | −0.608757 | −0.183547 | −0.0917736 | − | 0.995780i | \(-0.529254\pi\) | ||||
−0.0917736 | + | 0.995780i | \(0.529254\pi\) | |||||||
\(12\) | 3.23826 | 0.934806 | ||||||||
\(13\) | 3.41992 | 0.948516 | 0.474258 | − | 0.880386i | \(-0.342716\pi\) | ||||
0.474258 | + | 0.880386i | \(0.342716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.92705 | −0.755761 | ||||||||
\(16\) | 0.00982553 | 0.00245638 | ||||||||
\(17\) | 2.88681 | 0.700154 | 0.350077 | − | 0.936721i | \(-0.386155\pi\) | ||||
0.350077 | + | 0.936721i | \(0.386155\pi\) | |||||||
\(18\) | −2.28873 | −0.539458 | ||||||||
\(19\) | −2.02704 | −0.465034 | −0.232517 | − | 0.972592i | \(-0.574696\pi\) | ||||
−0.232517 | + | 0.972592i | \(0.574696\pi\) | |||||||
\(20\) | −9.47856 | −2.11947 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.39328 | 0.297048 | ||||||||
\(23\) | −3.71591 | −0.774821 | −0.387411 | − | 0.921907i | \(-0.626630\pi\) | ||||
−0.387411 | + | 0.921907i | \(0.626630\pi\) | |||||||
\(24\) | −2.83405 | −0.578497 | ||||||||
\(25\) | 3.56763 | 0.713525 | ||||||||
\(26\) | −7.82726 | −1.53505 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.68366 | −0.498343 | −0.249172 | − | 0.968459i | \(-0.580158\pi\) | ||||
−0.249172 | + | 0.968459i | \(0.580158\pi\) | |||||||
\(30\) | 6.69922 | 1.22310 | ||||||||
\(31\) | 0.845922 | 0.151932 | 0.0759661 | − | 0.997110i | \(-0.475796\pi\) | ||||
0.0759661 | + | 0.997110i | \(0.475796\pi\) | |||||||
\(32\) | 5.64560 | 0.998011 | ||||||||
\(33\) | −0.608757 | −0.105971 | ||||||||
\(34\) | −6.60711 | −1.13311 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.23826 | 0.539711 | ||||||||
\(37\) | 4.12496 | 0.678139 | 0.339069 | − | 0.940761i | \(-0.389888\pi\) | ||||
0.339069 | + | 0.940761i | \(0.389888\pi\) | |||||||
\(38\) | 4.63933 | 0.752599 | ||||||||
\(39\) | 3.41992 | 0.547626 | ||||||||
\(40\) | 8.29540 | 1.31162 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.717546 | 0.109425 | 0.0547124 | − | 0.998502i | \(-0.482576\pi\) | ||||
0.0547124 | + | 0.998502i | \(0.482576\pi\) | |||||||
\(44\) | −1.97132 | −0.297187 | ||||||||
\(45\) | −2.92705 | −0.436339 | ||||||||
\(46\) | 8.50470 | 1.25395 | ||||||||
\(47\) | −5.20024 | −0.758532 | −0.379266 | − | 0.925288i | \(-0.623824\pi\) | ||||
−0.379266 | + | 0.925288i | \(0.623824\pi\) | |||||||
\(48\) | 0.00982553 | 0.00141819 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.16531 | −1.15475 | ||||||||
\(51\) | 2.88681 | 0.404234 | ||||||||
\(52\) | 11.0746 | 1.53577 | ||||||||
\(53\) | 4.40902 | 0.605625 | 0.302813 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302813 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(54\) | −2.28873 | −0.311456 | ||||||||
\(55\) | 1.78186 | 0.240266 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.02704 | −0.268488 | ||||||||
\(58\) | 6.14216 | 0.806505 | ||||||||
\(59\) | −8.32320 | −1.08359 | −0.541794 | − | 0.840511i | \(-0.682255\pi\) | ||||
−0.541794 | + | 0.840511i | \(0.682255\pi\) | |||||||
\(60\) | −9.47856 | −1.22368 | ||||||||
\(61\) | −5.34616 | −0.684506 | −0.342253 | − | 0.939608i | \(-0.611190\pi\) | ||||
−0.342253 | + | 0.939608i | \(0.611190\pi\) | |||||||
\(62\) | −1.93608 | −0.245883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9409 | −1.61761 | ||||||||
\(65\) | −10.0103 | −1.24162 | ||||||||
\(66\) | 1.39328 | 0.171501 | ||||||||
\(67\) | 7.48135 | 0.913993 | 0.456996 | − | 0.889469i | \(-0.348925\pi\) | ||||
0.456996 | + | 0.889469i | \(0.348925\pi\) | |||||||
\(68\) | 9.34825 | 1.13364 | ||||||||
\(69\) | −3.71591 | −0.447343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.5145 | −1.24785 | −0.623923 | − | 0.781486i | \(-0.714462\pi\) | ||||
−0.623923 | + | 0.781486i | \(0.714462\pi\) | |||||||
\(72\) | −2.83405 | −0.333996 | ||||||||
\(73\) | 4.75212 | 0.556194 | 0.278097 | − | 0.960553i | \(-0.410296\pi\) | ||||
0.278097 | + | 0.960553i | \(0.410296\pi\) | |||||||
\(74\) | −9.44089 | −1.09748 | ||||||||
\(75\) | 3.56763 | 0.411954 | ||||||||
\(76\) | −6.56408 | −0.752952 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.82726 | −0.886263 | ||||||||
\(79\) | 0.682550 | 0.0767929 | 0.0383964 | − | 0.999263i | \(-0.487775\pi\) | ||||
0.0383964 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(80\) | −0.0287598 | −0.00321545 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.28873 | 0.252747 | ||||||||
\(83\) | −1.24939 | −0.137139 | −0.0685694 | − | 0.997646i | \(-0.521843\pi\) | ||||
−0.0685694 | + | 0.997646i | \(0.521843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.44983 | −0.916513 | ||||||||
\(86\) | −1.64227 | −0.177090 | ||||||||
\(87\) | −2.68366 | −0.287719 | ||||||||
\(88\) | 1.72525 | 0.183912 | ||||||||
\(89\) | −3.56714 | −0.378116 | −0.189058 | − | 0.981966i | \(-0.560543\pi\) | ||||
−0.189058 | + | 0.981966i | \(0.560543\pi\) | |||||||
\(90\) | 6.69922 | 0.706159 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.0331 | −1.25454 | ||||||||
\(93\) | 0.845922 | 0.0877181 | ||||||||
\(94\) | 11.9019 | 1.22759 | ||||||||
\(95\) | 5.93324 | 0.608738 | ||||||||
\(96\) | 5.64560 | 0.576202 | ||||||||
\(97\) | 13.5915 | 1.38001 | 0.690006 | − | 0.723804i | \(-0.257608\pi\) | ||||
0.690006 | + | 0.723804i | \(0.257608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.608757 | −0.0611824 | ||||||||
\(100\) | 11.5529 | 1.15529 | ||||||||
\(101\) | −7.00621 | −0.697144 | −0.348572 | − | 0.937282i | \(-0.613333\pi\) | ||||
−0.348572 | + | 0.937282i | \(0.613333\pi\) | |||||||
\(102\) | −6.60711 | −0.654201 | ||||||||
\(103\) | 12.9840 | 1.27935 | 0.639677 | − | 0.768644i | \(-0.279068\pi\) | ||||
0.639677 | + | 0.768644i | \(0.279068\pi\) | |||||||
\(104\) | −9.69222 | −0.950400 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0910 | −0.980127 | ||||||||
\(107\) | 10.9971 | 1.06313 | 0.531566 | − | 0.847017i | \(-0.321604\pi\) | ||||
0.531566 | + | 0.847017i | \(0.321604\pi\) | |||||||
\(108\) | 3.23826 | 0.311602 | ||||||||
\(109\) | 3.47454 | 0.332801 | 0.166400 | − | 0.986058i | \(-0.446786\pi\) | ||||
0.166400 | + | 0.986058i | \(0.446786\pi\) | |||||||
\(110\) | −4.07819 | −0.388841 | ||||||||
\(111\) | 4.12496 | 0.391523 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1226 | −1.42261 | −0.711307 | − | 0.702882i | \(-0.751896\pi\) | ||||
−0.711307 | + | 0.702882i | \(0.751896\pi\) | |||||||
\(114\) | 4.63933 | 0.434513 | ||||||||
\(115\) | 10.8767 | 1.01425 | ||||||||
\(116\) | −8.69040 | −0.806883 | ||||||||
\(117\) | 3.41992 | 0.316172 | ||||||||
\(118\) | 19.0495 | 1.75365 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.29540 | 0.757263 | ||||||||
\(121\) | −10.6294 | −0.966310 | ||||||||
\(122\) | 12.2359 | 1.10779 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 2.73932 | 0.245998 | ||||||||
\(125\) | 4.19263 | 0.375001 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.54115 | −0.491698 | −0.245849 | − | 0.969308i | \(-0.579067\pi\) | ||||
−0.245849 | + | 0.969308i | \(0.579067\pi\) | |||||||
\(128\) | 18.3269 | 1.61989 | ||||||||
\(129\) | 0.717546 | 0.0631764 | ||||||||
\(130\) | 22.9108 | 2.00941 | ||||||||
\(131\) | −0.469897 | −0.0410551 | −0.0205276 | − | 0.999789i | \(-0.506535\pi\) | ||||
−0.0205276 | + | 0.999789i | \(0.506535\pi\) | |||||||
\(132\) | −1.97132 | −0.171581 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.1228 | −1.47918 | ||||||||
\(135\) | −2.92705 | −0.251920 | ||||||||
\(136\) | −8.18135 | −0.701545 | ||||||||
\(137\) | −4.21932 | −0.360481 | −0.180241 | − | 0.983623i | \(-0.557688\pi\) | ||||
−0.180241 | + | 0.983623i | \(0.557688\pi\) | |||||||
\(138\) | 8.50470 | 0.723968 | ||||||||
\(139\) | 13.0636 | 1.10804 | 0.554021 | − | 0.832503i | \(-0.313093\pi\) | ||||
0.554021 | + | 0.832503i | \(0.313093\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.20024 | −0.437939 | ||||||||
\(142\) | 24.0649 | 2.01948 | ||||||||
\(143\) | −2.08190 | −0.174097 | ||||||||
\(144\) | 0.00982553 | 0.000818794 0 | ||||||||
\(145\) | 7.85521 | 0.652340 | ||||||||
\(146\) | −10.8763 | −0.900129 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.3577 | 1.09800 | ||||||||
\(149\) | 18.7649 | 1.53728 | 0.768639 | − | 0.639683i | \(-0.220934\pi\) | ||||
0.768639 | + | 0.639683i | \(0.220934\pi\) | |||||||
\(150\) | −8.16531 | −0.666695 | ||||||||
\(151\) | −12.1409 | −0.988010 | −0.494005 | − | 0.869459i | \(-0.664468\pi\) | ||||
−0.494005 | + | 0.869459i | \(0.664468\pi\) | |||||||
\(152\) | 5.74472 | 0.465958 | ||||||||
\(153\) | 2.88681 | 0.233385 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47606 | −0.198882 | ||||||||
\(156\) | 11.0746 | 0.886678 | ||||||||
\(157\) | 9.83418 | 0.784853 | 0.392427 | − | 0.919783i | \(-0.371636\pi\) | ||||
0.392427 | + | 0.919783i | \(0.371636\pi\) | |||||||
\(158\) | −1.56217 | −0.124280 | ||||||||
\(159\) | 4.40902 | 0.349658 | ||||||||
\(160\) | −16.5250 | −1.30641 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.28873 | −0.179819 | ||||||||
\(163\) | −9.56943 | −0.749536 | −0.374768 | − | 0.927119i | \(-0.622278\pi\) | ||||
−0.374768 | + | 0.927119i | \(0.622278\pi\) | |||||||
\(164\) | −3.23826 | −0.252866 | ||||||||
\(165\) | 1.78186 | 0.138718 | ||||||||
\(166\) | 2.85952 | 0.221942 | ||||||||
\(167\) | 0.912899 | 0.0706422 | 0.0353211 | − | 0.999376i | \(-0.488755\pi\) | ||||
0.0353211 | + | 0.999376i | \(0.488755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.30413 | −0.100318 | ||||||||
\(170\) | 19.3393 | 1.48326 | ||||||||
\(171\) | −2.02704 | −0.155011 | ||||||||
\(172\) | 2.32360 | 0.177173 | ||||||||
\(173\) | −3.91474 | −0.297632 | −0.148816 | − | 0.988865i | \(-0.547546\pi\) | ||||
−0.148816 | + | 0.988865i | \(0.547546\pi\) | |||||||
\(174\) | 6.14216 | 0.465636 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.00598136 | −0.000450862 0 | ||||||||
\(177\) | −8.32320 | −0.625610 | ||||||||
\(178\) | 8.16421 | 0.611933 | ||||||||
\(179\) | 16.6937 | 1.24775 | 0.623874 | − | 0.781525i | \(-0.285558\pi\) | ||||
0.623874 | + | 0.781525i | \(0.285558\pi\) | |||||||
\(180\) | −9.47856 | −0.706490 | ||||||||
\(181\) | 7.61276 | 0.565852 | 0.282926 | − | 0.959142i | \(-0.408695\pi\) | ||||
0.282926 | + | 0.959142i | \(0.408695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.34616 | −0.395200 | ||||||||
\(184\) | 10.5311 | 0.776360 | ||||||||
\(185\) | −12.0740 | −0.887695 | ||||||||
\(186\) | −1.93608 | −0.141961 | ||||||||
\(187\) | −1.75736 | −0.128511 | ||||||||
\(188\) | −16.8397 | −1.22816 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.5796 | −0.985165 | ||||||||
\(191\) | 3.70107 | 0.267800 | 0.133900 | − | 0.990995i | \(-0.457250\pi\) | ||||
0.133900 | + | 0.990995i | \(0.457250\pi\) | |||||||
\(192\) | −12.9409 | −0.933928 | ||||||||
\(193\) | −25.6969 | −1.84971 | −0.924853 | − | 0.380326i | \(-0.875812\pi\) | ||||
−0.924853 | + | 0.380326i | \(0.875812\pi\) | |||||||
\(194\) | −31.1073 | −2.23337 | ||||||||
\(195\) | −10.0103 | −0.716851 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0996 | −1.57453 | −0.787266 | − | 0.616614i | \(-0.788504\pi\) | ||||
−0.787266 | + | 0.616614i | \(0.788504\pi\) | |||||||
\(198\) | 1.39328 | 0.0990159 | ||||||||
\(199\) | −1.01277 | −0.0717935 | −0.0358968 | − | 0.999356i | \(-0.511429\pi\) | ||||
−0.0358968 | + | 0.999356i | \(0.511429\pi\) | |||||||
\(200\) | −10.1108 | −0.714943 | ||||||||
\(201\) | 7.48135 | 0.527694 | ||||||||
\(202\) | 16.0353 | 1.12824 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.34825 | 0.654508 | ||||||||
\(205\) | 2.92705 | 0.204434 | ||||||||
\(206\) | −29.7169 | −2.07047 | ||||||||
\(207\) | −3.71591 | −0.258274 | ||||||||
\(208\) | 0.0336026 | 0.00232992 | ||||||||
\(209\) | 1.23397 | 0.0853557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5270 | 0.931236 | 0.465618 | − | 0.884986i | \(-0.345832\pi\) | ||||
0.465618 | + | 0.884986i | \(0.345832\pi\) | |||||||
\(212\) | 14.2776 | 0.980587 | ||||||||
\(213\) | −10.5145 | −0.720444 | ||||||||
\(214\) | −25.1694 | −1.72055 | ||||||||
\(215\) | −2.10029 | −0.143239 | ||||||||
\(216\) | −2.83405 | −0.192832 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.95227 | −0.538596 | ||||||||
\(219\) | 4.75212 | 0.321119 | ||||||||
\(220\) | 5.77014 | 0.389023 | ||||||||
\(221\) | 9.87266 | 0.664107 | ||||||||
\(222\) | −9.44089 | −0.633631 | ||||||||
\(223\) | 14.5693 | 0.975634 | 0.487817 | − | 0.872946i | \(-0.337793\pi\) | ||||
0.487817 | + | 0.872946i | \(0.337793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56763 | 0.237842 | ||||||||
\(226\) | 34.6115 | 2.30232 | ||||||||
\(227\) | −6.91389 | −0.458891 | −0.229445 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229445 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(228\) | −6.56408 | −0.434717 | ||||||||
\(229\) | −10.7145 | −0.708037 | −0.354019 | − | 0.935238i | \(-0.615185\pi\) | ||||
−0.354019 | + | 0.935238i | \(0.615185\pi\) | |||||||
\(230\) | −24.8937 | −1.64144 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.60562 | 0.499333 | ||||||||
\(233\) | −18.4752 | −1.21035 | −0.605176 | − | 0.796092i | \(-0.706897\pi\) | ||||
−0.605176 | + | 0.796092i | \(0.706897\pi\) | |||||||
\(234\) | −7.82726 | −0.511684 | ||||||||
\(235\) | 15.2214 | 0.992932 | ||||||||
\(236\) | −26.9527 | −1.75447 | ||||||||
\(237\) | 0.682550 | 0.0443364 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2275 | 0.790930 | 0.395465 | − | 0.918481i | \(-0.370583\pi\) | ||||
0.395465 | + | 0.918481i | \(0.370583\pi\) | |||||||
\(240\) | −0.0287598 | −0.00185644 | ||||||||
\(241\) | −15.5057 | −0.998812 | −0.499406 | − | 0.866368i | \(-0.666448\pi\) | ||||
−0.499406 | + | 0.866368i | \(0.666448\pi\) | |||||||
\(242\) | 24.3278 | 1.56385 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −17.3123 | −1.10831 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.28873 | 0.145924 | ||||||||
\(247\) | −6.93231 | −0.441092 | ||||||||
\(248\) | −2.39738 | −0.152234 | ||||||||
\(249\) | −1.24939 | −0.0791771 | ||||||||
\(250\) | −9.59579 | −0.606891 | ||||||||
\(251\) | 8.42100 | 0.531529 | 0.265765 | − | 0.964038i | \(-0.414376\pi\) | ||||
0.265765 | + | 0.964038i | \(0.414376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.26209 | 0.142216 | ||||||||
\(254\) | 12.6822 | 0.795751 | ||||||||
\(255\) | −8.44983 | −0.529149 | ||||||||
\(256\) | −16.0635 | −1.00397 | ||||||||
\(257\) | −11.3723 | −0.709382 | −0.354691 | − | 0.934984i | \(-0.615414\pi\) | ||||
−0.354691 | + | 0.934984i | \(0.615414\pi\) | |||||||
\(258\) | −1.64227 | −0.102243 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −32.4159 | −2.01035 | ||||||||
\(261\) | −2.68366 | −0.166114 | ||||||||
\(262\) | 1.07547 | 0.0664425 | ||||||||
\(263\) | −15.9552 | −0.983839 | −0.491919 | − | 0.870641i | \(-0.663704\pi\) | ||||
−0.491919 | + | 0.870641i | \(0.663704\pi\) | |||||||
\(264\) | 1.72525 | 0.106182 | ||||||||
\(265\) | −12.9054 | −0.792773 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.56714 | −0.218305 | ||||||||
\(268\) | 24.2266 | 1.47988 | ||||||||
\(269\) | 10.9890 | 0.670010 | 0.335005 | − | 0.942216i | \(-0.391262\pi\) | ||||
0.335005 | + | 0.942216i | \(0.391262\pi\) | |||||||
\(270\) | 6.69922 | 0.407701 | ||||||||
\(271\) | −3.75539 | −0.228123 | −0.114062 | − | 0.993474i | \(-0.536386\pi\) | ||||
−0.114062 | + | 0.993474i | \(0.536386\pi\) | |||||||
\(272\) | 0.0283644 | 0.00171985 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.65687 | 0.583393 | ||||||||
\(275\) | −2.17182 | −0.130965 | ||||||||
\(276\) | −12.0331 | −0.724308 | ||||||||
\(277\) | −19.9041 | −1.19592 | −0.597961 | − | 0.801525i | \(-0.704022\pi\) | ||||
−0.597961 | + | 0.801525i | \(0.704022\pi\) | |||||||
\(278\) | −29.8990 | −1.79322 | ||||||||
\(279\) | 0.845922 | 0.0506440 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.65900 | 0.337588 | 0.168794 | − | 0.985651i | \(-0.446013\pi\) | ||||
0.168794 | + | 0.985651i | \(0.446013\pi\) | |||||||
\(282\) | 11.9019 | 0.708748 | ||||||||
\(283\) | −23.3837 | −1.39001 | −0.695007 | − | 0.719003i | \(-0.744599\pi\) | ||||
−0.695007 | + | 0.719003i | \(0.744599\pi\) | |||||||
\(284\) | −34.0488 | −2.02043 | ||||||||
\(285\) | 5.93324 | 0.351455 | ||||||||
\(286\) | 4.76490 | 0.281754 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.64560 | 0.332670 | ||||||||
\(289\) | −8.66634 | −0.509785 | ||||||||
\(290\) | −17.9784 | −1.05573 | ||||||||
\(291\) | 13.5915 | 0.796750 | ||||||||
\(292\) | 15.3886 | 0.900551 | ||||||||
\(293\) | −14.4856 | −0.846256 | −0.423128 | − | 0.906070i | \(-0.639068\pi\) | ||||
−0.423128 | + | 0.906070i | \(0.639068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.3624 | 1.41843 | ||||||||
\(296\) | −11.6903 | −0.679486 | ||||||||
\(297\) | −0.608757 | −0.0353237 | ||||||||
\(298\) | −42.9476 | −2.48789 | ||||||||
\(299\) | −12.7081 | −0.734930 | ||||||||
\(300\) | 11.5529 | 0.667008 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.7871 | 1.59897 | ||||||||
\(303\) | −7.00621 | −0.402496 | ||||||||
\(304\) | −0.0199167 | −0.00114230 | ||||||||
\(305\) | 15.6485 | 0.896030 | ||||||||
\(306\) | −6.60711 | −0.377703 | ||||||||
\(307\) | 6.70376 | 0.382604 | 0.191302 | − | 0.981531i | \(-0.438729\pi\) | ||||
0.191302 | + | 0.981531i | \(0.438729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9840 | 0.738635 | ||||||||
\(310\) | 5.66702 | 0.321865 | ||||||||
\(311\) | 7.41192 | 0.420291 | 0.210146 | − | 0.977670i | \(-0.432606\pi\) | ||||
0.210146 | + | 0.977670i | \(0.432606\pi\) | |||||||
\(312\) | −9.69222 | −0.548714 | ||||||||
\(313\) | 16.7688 | 0.947829 | 0.473914 | − | 0.880571i | \(-0.342841\pi\) | ||||
0.473914 | + | 0.880571i | \(0.342841\pi\) | |||||||
\(314\) | −22.5077 | −1.27019 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.21028 | 0.124338 | ||||||||
\(317\) | −6.67784 | −0.375065 | −0.187532 | − | 0.982258i | \(-0.560049\pi\) | ||||
−0.187532 | + | 0.982258i | \(0.560049\pi\) | |||||||
\(318\) | −10.0910 | −0.565877 | ||||||||
\(319\) | 1.63370 | 0.0914695 | ||||||||
\(320\) | 37.8786 | 2.11748 | ||||||||
\(321\) | 10.9971 | 0.613800 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.85167 | −0.325596 | ||||||||
\(324\) | 3.23826 | 0.179904 | ||||||||
\(325\) | 12.2010 | 0.676790 | ||||||||
\(326\) | 21.9018 | 1.21303 | ||||||||
\(327\) | 3.47454 | 0.192143 | ||||||||
\(328\) | 2.83405 | 0.156484 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.07819 | −0.224497 | ||||||||
\(331\) | −22.2105 | −1.22080 | −0.610399 | − | 0.792094i | \(-0.708991\pi\) | ||||
−0.610399 | + | 0.792094i | \(0.708991\pi\) | |||||||
\(332\) | −4.04587 | −0.222046 | ||||||||
\(333\) | 4.12496 | 0.226046 | ||||||||
\(334\) | −2.08937 | −0.114325 | ||||||||
\(335\) | −21.8983 | −1.19643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.06165 | −0.439146 | −0.219573 | − | 0.975596i | \(-0.570466\pi\) | ||||
−0.219573 | + | 0.975596i | \(0.570466\pi\) | |||||||
\(338\) | 2.98480 | 0.162352 | ||||||||
\(339\) | −15.1226 | −0.821346 | ||||||||
\(340\) | −27.3628 | −1.48396 | ||||||||
\(341\) | −0.514961 | −0.0278867 | ||||||||
\(342\) | 4.63933 | 0.250866 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.03356 | −0.109642 | ||||||||
\(345\) | 10.8767 | 0.585580 | ||||||||
\(346\) | 8.95976 | 0.481680 | ||||||||
\(347\) | 7.12163 | 0.382309 | 0.191154 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191154 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(348\) | −8.69040 | −0.465854 | ||||||||
\(349\) | −13.7173 | −0.734272 | −0.367136 | − | 0.930167i | \(-0.619662\pi\) | ||||
−0.367136 | + | 0.930167i | \(0.619662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.41992 | 0.182542 | ||||||||
\(352\) | −3.43680 | −0.183182 | ||||||||
\(353\) | 22.1845 | 1.18076 | 0.590380 | − | 0.807126i | \(-0.298978\pi\) | ||||
0.590380 | + | 0.807126i | \(0.298978\pi\) | |||||||
\(354\) | 19.0495 | 1.01247 | ||||||||
\(355\) | 30.7766 | 1.63345 | ||||||||
\(356\) | −11.5513 | −0.612220 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.2074 | −2.01932 | ||||||||
\(359\) | 6.04012 | 0.318785 | 0.159393 | − | 0.987215i | \(-0.449046\pi\) | ||||
0.159393 | + | 0.987215i | \(0.449046\pi\) | |||||||
\(360\) | 8.29540 | 0.437206 | ||||||||
\(361\) | −14.8911 | −0.783743 | ||||||||
\(362\) | −17.4235 | −0.915760 | ||||||||
\(363\) | −10.6294 | −0.557900 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.9097 | −0.728067 | ||||||||
\(366\) | 12.2359 | 0.639581 | ||||||||
\(367\) | −1.35316 | −0.0706345 | −0.0353172 | − | 0.999376i | \(-0.511244\pi\) | ||||
−0.0353172 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(368\) | −0.0365108 | −0.00190326 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 27.6340 | 1.43662 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.73932 | 0.142027 | ||||||||
\(373\) | −29.5094 | −1.52794 | −0.763970 | − | 0.645251i | \(-0.776753\pi\) | ||||
−0.763970 | + | 0.645251i | \(0.776753\pi\) | |||||||
\(374\) | 4.02212 | 0.207979 | ||||||||
\(375\) | 4.19263 | 0.216507 | ||||||||
\(376\) | 14.7377 | 0.760039 | ||||||||
\(377\) | −9.17791 | −0.472686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.78403 | −0.297106 | −0.148553 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148553 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(380\) | 19.2134 | 0.985627 | ||||||||
\(381\) | −5.54115 | −0.283882 | ||||||||
\(382\) | −8.47073 | −0.433400 | ||||||||
\(383\) | −8.68937 | −0.444006 | −0.222003 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222003 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(384\) | 18.3269 | 0.935242 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 58.8132 | 2.99351 | ||||||||
\(387\) | 0.717546 | 0.0364749 | ||||||||
\(388\) | 44.0130 | 2.23442 | ||||||||
\(389\) | −29.0515 | −1.47297 | −0.736484 | − | 0.676455i | \(-0.763516\pi\) | ||||
−0.736484 | + | 0.676455i | \(0.763516\pi\) | |||||||
\(390\) | 22.9108 | 1.16013 | ||||||||
\(391\) | −10.7271 | −0.542494 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.469897 | −0.0237032 | ||||||||
\(394\) | 50.5799 | 2.54818 | ||||||||
\(395\) | −1.99786 | −0.100523 | ||||||||
\(396\) | −1.97132 | −0.0990623 | ||||||||
\(397\) | −23.2522 | −1.16699 | −0.583497 | − | 0.812115i | \(-0.698316\pi\) | ||||
−0.583497 | + | 0.812115i | \(0.698316\pi\) | |||||||
\(398\) | 2.31796 | 0.116189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0350538 | 0.00175269 | ||||||||
\(401\) | 3.15628 | 0.157617 | 0.0788086 | − | 0.996890i | \(-0.474888\pi\) | ||||
0.0788086 | + | 0.996890i | \(0.474888\pi\) | |||||||
\(402\) | −17.1228 | −0.854006 | ||||||||
\(403\) | 2.89299 | 0.144110 | ||||||||
\(404\) | −22.6880 | −1.12877 | ||||||||
\(405\) | −2.92705 | −0.145446 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.51110 | −0.124470 | ||||||||
\(408\) | −8.18135 | −0.405037 | ||||||||
\(409\) | 5.39404 | 0.266718 | 0.133359 | − | 0.991068i | \(-0.457424\pi\) | ||||
0.133359 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(410\) | −6.69922 | −0.330851 | ||||||||
\(411\) | −4.21932 | −0.208124 | ||||||||
\(412\) | 42.0457 | 2.07144 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.50470 | 0.417983 | ||||||||
\(415\) | 3.65704 | 0.179517 | ||||||||
\(416\) | 19.3075 | 0.946629 | ||||||||
\(417\) | 13.0636 | 0.639728 | ||||||||
\(418\) | −2.82423 | −0.138137 | ||||||||
\(419\) | 18.6107 | 0.909193 | 0.454596 | − | 0.890698i | \(-0.349784\pi\) | ||||
0.454596 | + | 0.890698i | \(0.349784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8411 | −0.674575 | −0.337287 | − | 0.941402i | \(-0.609509\pi\) | ||||
−0.337287 | + | 0.941402i | \(0.609509\pi\) | |||||||
\(422\) | −30.9596 | −1.50709 | ||||||||
\(423\) | −5.20024 | −0.252844 | ||||||||
\(424\) | −12.4954 | −0.606828 | ||||||||
\(425\) | 10.2990 | 0.499577 | ||||||||
\(426\) | 24.0649 | 1.16595 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 35.6116 | 1.72135 | ||||||||
\(429\) | −2.08190 | −0.100515 | ||||||||
\(430\) | 4.80700 | 0.231814 | ||||||||
\(431\) | −6.67726 | −0.321632 | −0.160816 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160816 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(432\) | 0.00982553 | 0.000472731 0 | ||||||||
\(433\) | 33.1341 | 1.59232 | 0.796161 | − | 0.605084i | \(-0.206861\pi\) | ||||
0.796161 | + | 0.605084i | \(0.206861\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.85521 | 0.376628 | ||||||||
\(436\) | 11.2515 | 0.538848 | ||||||||
\(437\) | 7.53229 | 0.360318 | ||||||||
\(438\) | −10.8763 | −0.519690 | ||||||||
\(439\) | 4.72295 | 0.225414 | 0.112707 | − | 0.993628i | \(-0.464048\pi\) | ||||
0.112707 | + | 0.993628i | \(0.464048\pi\) | |||||||
\(440\) | −5.04988 | −0.240744 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.5958 | −1.07477 | ||||||||
\(443\) | 6.79271 | 0.322731 | 0.161366 | − | 0.986895i | \(-0.448410\pi\) | ||||
0.161366 | + | 0.986895i | \(0.448410\pi\) | |||||||
\(444\) | 13.3577 | 0.633928 | ||||||||
\(445\) | 10.4412 | 0.494960 | ||||||||
\(446\) | −33.3452 | −1.57894 | ||||||||
\(447\) | 18.7649 | 0.887548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.12828 | −0.194826 | −0.0974128 | − | 0.995244i | \(-0.531057\pi\) | ||||
−0.0974128 | + | 0.995244i | \(0.531057\pi\) | |||||||
\(450\) | −8.16531 | −0.384917 | ||||||||
\(451\) | 0.608757 | 0.0286652 | ||||||||
\(452\) | −48.9709 | −2.30340 | ||||||||
\(453\) | −12.1409 | −0.570428 | ||||||||
\(454\) | 15.8240 | 0.742657 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.74472 | 0.269021 | ||||||||
\(457\) | 15.7297 | 0.735806 | 0.367903 | − | 0.929864i | \(-0.380076\pi\) | ||||
0.367903 | + | 0.929864i | \(0.380076\pi\) | |||||||
\(458\) | 24.5227 | 1.14587 | ||||||||
\(459\) | 2.88681 | 0.134745 | ||||||||
\(460\) | 35.2215 | 1.64221 | ||||||||
\(461\) | −19.0027 | −0.885043 | −0.442522 | − | 0.896758i | \(-0.645916\pi\) | ||||
−0.442522 | + | 0.896758i | \(0.645916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.20764 | 0.427915 | 0.213958 | − | 0.976843i | \(-0.431365\pi\) | ||||
0.213958 | + | 0.976843i | \(0.431365\pi\) | |||||||
\(464\) | −0.0263684 | −0.00122412 | ||||||||
\(465\) | −2.47606 | −0.114824 | ||||||||
\(466\) | 42.2847 | 1.95880 | ||||||||
\(467\) | 28.8693 | 1.33591 | 0.667955 | − | 0.744202i | \(-0.267170\pi\) | ||||
0.667955 | + | 0.744202i | \(0.267170\pi\) | |||||||
\(468\) | 11.0746 | 0.511924 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −34.8375 | −1.60693 | ||||||||
\(471\) | 9.83418 | 0.453135 | ||||||||
\(472\) | 23.5883 | 1.08574 | ||||||||
\(473\) | −0.436811 | −0.0200846 | ||||||||
\(474\) | −1.56217 | −0.0717528 | ||||||||
\(475\) | −7.23171 | −0.331814 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.40902 | 0.201875 | ||||||||
\(478\) | −27.9853 | −1.28002 | ||||||||
\(479\) | −17.4001 | −0.795033 | −0.397517 | − | 0.917595i | \(-0.630128\pi\) | ||||
−0.397517 | + | 0.917595i | \(0.630128\pi\) | |||||||
\(480\) | −16.5250 | −0.754258 | ||||||||
\(481\) | 14.1070 | 0.643225 | ||||||||
\(482\) | 35.4884 | 1.61645 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −34.4209 | −1.56458 | ||||||||
\(485\) | −39.7831 | −1.80646 | ||||||||
\(486\) | −2.28873 | −0.103819 | ||||||||
\(487\) | −29.6791 | −1.34489 | −0.672443 | − | 0.740149i | \(-0.734755\pi\) | ||||
−0.672443 | + | 0.740149i | \(0.734755\pi\) | |||||||
\(488\) | 15.1513 | 0.685866 | ||||||||
\(489\) | −9.56943 | −0.432745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.7906 | 1.75059 | 0.875297 | − | 0.483585i | \(-0.160666\pi\) | ||||
0.875297 | + | 0.483585i | \(0.160666\pi\) | |||||||
\(492\) | −3.23826 | −0.145992 | ||||||||
\(493\) | −7.74721 | −0.348917 | ||||||||
\(494\) | 15.8662 | 0.713852 | ||||||||
\(495\) | 1.78186 | 0.0800888 | ||||||||
\(496\) | 0.00831164 | 0.000373204 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.85952 | 0.128138 | ||||||||
\(499\) | −6.03265 | −0.270058 | −0.135029 | − | 0.990842i | \(-0.543113\pi\) | ||||
−0.135029 | + | 0.990842i | \(0.543113\pi\) | |||||||
\(500\) | 13.5769 | 0.607175 | ||||||||
\(501\) | 0.912899 | 0.0407853 | ||||||||
\(502\) | −19.2734 | −0.860212 | ||||||||
\(503\) | −11.5833 | −0.516473 | −0.258237 | − | 0.966082i | \(-0.583141\pi\) | ||||
−0.258237 | + | 0.966082i | \(0.583141\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.5075 | 0.912573 | ||||||||
\(506\) | −5.17730 | −0.230159 | ||||||||
\(507\) | −1.30413 | −0.0579186 | ||||||||
\(508\) | −17.9437 | −0.796124 | ||||||||
\(509\) | −39.4142 | −1.74700 | −0.873501 | − | 0.486822i | \(-0.838156\pi\) | ||||
−0.873501 | + | 0.486822i | \(0.838156\pi\) | |||||||
\(510\) | 19.3393 | 0.856361 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.111163 | 0.00491276 | ||||||||
\(513\) | −2.02704 | −0.0894959 | ||||||||
\(514\) | 26.0280 | 1.14804 | ||||||||
\(515\) | −38.0049 | −1.67470 | ||||||||
\(516\) | 2.32360 | 0.102291 | ||||||||
\(517\) | 3.16568 | 0.139226 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.91474 | −0.171838 | ||||||||
\(520\) | 28.3696 | 1.24409 | ||||||||
\(521\) | 25.2288 | 1.10530 | 0.552648 | − | 0.833415i | \(-0.313617\pi\) | ||||
0.552648 | + | 0.833415i | \(0.313617\pi\) | |||||||
\(522\) | 6.14216 | 0.268835 | ||||||||
\(523\) | 10.4796 | 0.458242 | 0.229121 | − | 0.973398i | \(-0.426415\pi\) | ||||
0.229121 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(524\) | −1.52165 | −0.0664737 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.5170 | 1.59222 | ||||||||
\(527\) | 2.44201 | 0.106376 | ||||||||
\(528\) | −0.00598136 | −0.000260305 0 | ||||||||
\(529\) | −9.19200 | −0.399652 | ||||||||
\(530\) | 29.5370 | 1.28300 | ||||||||
\(531\) | −8.32320 | −0.361196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.41992 | −0.148133 | ||||||||
\(534\) | 8.16421 | 0.353300 | ||||||||
\(535\) | −32.1892 | −1.39166 | ||||||||
\(536\) | −21.2025 | −0.915809 | ||||||||
\(537\) | 16.6937 | 0.720388 | ||||||||
\(538\) | −25.1508 | −1.08433 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.47856 | −0.407892 | ||||||||
\(541\) | −31.8941 | −1.37123 | −0.685617 | − | 0.727962i | \(-0.740468\pi\) | ||||
−0.685617 | + | 0.727962i | \(0.740468\pi\) | |||||||
\(542\) | 8.59505 | 0.369189 | ||||||||
\(543\) | 7.61276 | 0.326695 | ||||||||
\(544\) | 16.2978 | 0.698761 | ||||||||
\(545\) | −10.1702 | −0.435642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.5699 | −1.26432 | −0.632158 | − | 0.774840i | \(-0.717831\pi\) | ||||
−0.632158 | + | 0.774840i | \(0.717831\pi\) | |||||||
\(548\) | −13.6633 | −0.583666 | ||||||||
\(549\) | −5.34616 | −0.228169 | ||||||||
\(550\) | 4.97069 | 0.211951 | ||||||||
\(551\) | 5.43988 | 0.231747 | ||||||||
\(552\) | 10.5311 | 0.448232 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.5551 | 1.93545 | ||||||||
\(555\) | −12.0740 | −0.512511 | ||||||||
\(556\) | 42.3034 | 1.79406 | ||||||||
\(557\) | −16.1913 | −0.686049 | −0.343025 | − | 0.939326i | \(-0.611451\pi\) | ||||
−0.343025 | + | 0.939326i | \(0.611451\pi\) | |||||||
\(558\) | −1.93608 | −0.0819610 | ||||||||
\(559\) | 2.45395 | 0.103791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75736 | −0.0741960 | ||||||||
\(562\) | −12.9519 | −0.546343 | ||||||||
\(563\) | 44.0238 | 1.85538 | 0.927692 | − | 0.373347i | \(-0.121790\pi\) | ||||
0.927692 | + | 0.373347i | \(0.121790\pi\) | |||||||
\(564\) | −16.8397 | −0.709081 | ||||||||
\(565\) | 44.2646 | 1.86222 | ||||||||
\(566\) | 53.5188 | 2.24956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.7987 | 1.25032 | ||||||||
\(569\) | −1.55627 | −0.0652423 | −0.0326211 | − | 0.999468i | \(-0.510385\pi\) | ||||
−0.0326211 | + | 0.999468i | \(0.510385\pi\) | |||||||
\(570\) | −13.5796 | −0.568785 | ||||||||
\(571\) | 2.77742 | 0.116231 | 0.0581156 | − | 0.998310i | \(-0.481491\pi\) | ||||
0.0581156 | + | 0.998310i | \(0.481491\pi\) | |||||||
\(572\) | −6.74175 | −0.281887 | ||||||||
\(573\) | 3.70107 | 0.154614 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.2570 | −0.552854 | ||||||||
\(576\) | −12.9409 | −0.539204 | ||||||||
\(577\) | −13.0836 | −0.544677 | −0.272339 | − | 0.962201i | \(-0.587797\pi\) | ||||
−0.272339 | + | 0.962201i | \(0.587797\pi\) | |||||||
\(578\) | 19.8349 | 0.825022 | ||||||||
\(579\) | −25.6969 | −1.06793 | ||||||||
\(580\) | 25.4372 | 1.05622 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −31.1073 | −1.28944 | ||||||||
\(583\) | −2.68402 | −0.111161 | ||||||||
\(584\) | −13.4677 | −0.557299 | ||||||||
\(585\) | −10.0103 | −0.413874 | ||||||||
\(586\) | 33.1535 | 1.36956 | ||||||||
\(587\) | −43.8023 | −1.80792 | −0.903958 | − | 0.427622i | \(-0.859352\pi\) | ||||
−0.903958 | + | 0.427622i | \(0.859352\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.71472 | −0.0706537 | ||||||||
\(590\) | −55.7589 | −2.29556 | ||||||||
\(591\) | −22.0996 | −0.909056 | ||||||||
\(592\) | 0.0405299 | 0.00166577 | ||||||||
\(593\) | 8.07068 | 0.331423 | 0.165712 | − | 0.986174i | \(-0.447008\pi\) | ||||
0.165712 | + | 0.986174i | \(0.447008\pi\) | |||||||
\(594\) | 1.39328 | 0.0571669 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 60.7656 | 2.48906 | ||||||||
\(597\) | −1.01277 | −0.0414500 | ||||||||
\(598\) | 29.0854 | 1.18939 | ||||||||
\(599\) | −41.8204 | −1.70874 | −0.854368 | − | 0.519669i | \(-0.826055\pi\) | ||||
−0.854368 | + | 0.519669i | \(0.826055\pi\) | |||||||
\(600\) | −10.1108 | −0.412772 | ||||||||
\(601\) | −4.99552 | −0.203772 | −0.101886 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101886 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.48135 | 0.304664 | ||||||||
\(604\) | −39.3153 | −1.59972 | ||||||||
\(605\) | 31.1128 | 1.26492 | ||||||||
\(606\) | 16.0353 | 0.651389 | ||||||||
\(607\) | 29.7455 | 1.20733 | 0.603667 | − | 0.797237i | \(-0.293706\pi\) | ||||
0.603667 | + | 0.797237i | \(0.293706\pi\) | |||||||
\(608\) | −11.4439 | −0.464110 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.8151 | −1.45011 | ||||||||
\(611\) | −17.7844 | −0.719480 | ||||||||
\(612\) | 9.34825 | 0.377880 | ||||||||
\(613\) | 1.91945 | 0.0775259 | 0.0387630 | − | 0.999248i | \(-0.487658\pi\) | ||||
0.0387630 | + | 0.999248i | \(0.487658\pi\) | |||||||
\(614\) | −15.3431 | −0.619196 | ||||||||
\(615\) | 2.92705 | 0.118030 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6186 | −0.508004 | −0.254002 | − | 0.967204i | \(-0.581747\pi\) | ||||
−0.254002 | + | 0.967204i | \(0.581747\pi\) | |||||||
\(618\) | −29.7169 | −1.19539 | ||||||||
\(619\) | −33.3246 | −1.33943 | −0.669714 | − | 0.742619i | \(-0.733583\pi\) | ||||
−0.669714 | + | 0.742619i | \(0.733583\pi\) | |||||||
\(620\) | −8.01813 | −0.322016 | ||||||||
\(621\) | −3.71591 | −0.149114 | ||||||||
\(622\) | −16.9638 | −0.680188 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.0336026 | 0.00134518 | ||||||||
\(625\) | −30.1102 | −1.20441 | ||||||||
\(626\) | −38.3792 | −1.53394 | ||||||||
\(627\) | 1.23397 | 0.0492801 | ||||||||
\(628\) | 31.8457 | 1.27078 | ||||||||
\(629\) | 11.9080 | 0.474801 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.318323 | 0.0126722 | 0.00633612 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633612 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(632\) | −1.93438 | −0.0769454 | ||||||||
\(633\) | 13.5270 | 0.537649 | ||||||||
\(634\) | 15.2837 | 0.606995 | ||||||||
\(635\) | 16.2192 | 0.643641 | ||||||||
\(636\) | 14.2776 | 0.566142 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.73908 | −0.148032 | ||||||||
\(639\) | −10.5145 | −0.415948 | ||||||||
\(640\) | −53.6439 | −2.12046 | ||||||||
\(641\) | 38.6465 | 1.52645 | 0.763223 | − | 0.646135i | \(-0.223616\pi\) | ||||
0.763223 | + | 0.646135i | \(0.223616\pi\) | |||||||
\(642\) | −25.1694 | −0.993358 | ||||||||
\(643\) | −42.9801 | −1.69497 | −0.847485 | − | 0.530819i | \(-0.821884\pi\) | ||||
−0.847485 | + | 0.530819i | \(0.821884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.10029 | −0.0826990 | ||||||||
\(646\) | 13.3929 | 0.526935 | ||||||||
\(647\) | −46.8808 | −1.84307 | −0.921536 | − | 0.388292i | \(-0.873065\pi\) | ||||
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(648\) | −2.83405 | −0.111332 | ||||||||
\(649\) | 5.06680 | 0.198889 | ||||||||
\(650\) | −27.9247 | −1.09530 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.9883 | −1.21360 | ||||||||
\(653\) | 4.47205 | 0.175005 | 0.0875024 | − | 0.996164i | \(-0.472111\pi\) | ||||
0.0875024 | + | 0.996164i | \(0.472111\pi\) | |||||||
\(654\) | −7.95227 | −0.310958 | ||||||||
\(655\) | 1.37541 | 0.0537418 | ||||||||
\(656\) | −0.00982553 | −0.000383623 0 | ||||||||
\(657\) | 4.75212 | 0.185398 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.5709 | −1.96996 | −0.984982 | − | 0.172657i | \(-0.944765\pi\) | ||||
−0.984982 | + | 0.172657i | \(0.944765\pi\) | |||||||
\(660\) | 5.77014 | 0.224602 | ||||||||
\(661\) | 19.5720 | 0.761263 | 0.380632 | − | 0.924727i | \(-0.375707\pi\) | ||||
0.380632 | + | 0.924727i | \(0.375707\pi\) | |||||||
\(662\) | 50.8337 | 1.97571 | ||||||||
\(663\) | 9.87266 | 0.383422 | ||||||||
\(664\) | 3.54084 | 0.137411 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.44089 | −0.365827 | ||||||||
\(667\) | 9.97224 | 0.386127 | ||||||||
\(668\) | 2.95621 | 0.114379 | ||||||||
\(669\) | 14.5693 | 0.563283 | ||||||||
\(670\) | 50.1192 | 1.93627 | ||||||||
\(671\) | 3.25451 | 0.125639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5808 | 0.754784 | 0.377392 | − | 0.926054i | \(-0.376821\pi\) | ||||
0.377392 | + | 0.926054i | \(0.376821\pi\) | |||||||
\(674\) | 18.4509 | 0.710702 | ||||||||
\(675\) | 3.56763 | 0.137318 | ||||||||
\(676\) | −4.22313 | −0.162428 | ||||||||
\(677\) | 2.92171 | 0.112291 | 0.0561453 | − | 0.998423i | \(-0.482119\pi\) | ||||
0.0561453 | + | 0.998423i | \(0.482119\pi\) | |||||||
\(678\) | 34.6115 | 1.32924 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 23.9472 | 0.918334 | ||||||||
\(681\) | −6.91389 | −0.264941 | ||||||||
\(682\) | 1.17860 | 0.0451311 | ||||||||
\(683\) | −26.8964 | −1.02916 | −0.514581 | − | 0.857442i | \(-0.672052\pi\) | ||||
−0.514581 | + | 0.857442i | \(0.672052\pi\) | |||||||
\(684\) | −6.56408 | −0.250984 | ||||||||
\(685\) | 12.3502 | 0.471876 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7145 | −0.408785 | ||||||||
\(688\) | 0.00705028 | 0.000268789 0 | ||||||||
\(689\) | 15.0785 | 0.574445 | ||||||||
\(690\) | −24.8937 | −0.947687 | ||||||||
\(691\) | −20.1551 | −0.766738 | −0.383369 | − | 0.923595i | \(-0.625236\pi\) | ||||
−0.383369 | + | 0.923595i | \(0.625236\pi\) | |||||||
\(692\) | −12.6770 | −0.481906 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.2994 | −0.618718 | ||||||||
\(695\) | −38.2379 | −1.45044 | ||||||||
\(696\) | 7.60562 | 0.288290 | ||||||||
\(697\) | −2.88681 | −0.109346 | ||||||||
\(698\) | 31.3952 | 1.18833 | ||||||||
\(699\) | −18.4752 | −0.698797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3666 | −1.18470 | −0.592351 | − | 0.805680i | \(-0.701800\pi\) | ||||
−0.592351 | + | 0.805680i | \(0.701800\pi\) | |||||||
\(702\) | −7.82726 | −0.295421 | ||||||||
\(703\) | −8.36144 | −0.315358 | ||||||||
\(704\) | 7.87786 | 0.296908 | ||||||||
\(705\) | 15.2214 | 0.573269 | ||||||||
\(706\) | −50.7741 | −1.91091 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −26.9527 | −1.01294 | ||||||||
\(709\) | −39.8398 | −1.49621 | −0.748107 | − | 0.663578i | \(-0.769037\pi\) | ||||
−0.748107 | + | 0.663578i | \(0.769037\pi\) | |||||||
\(710\) | −70.4391 | −2.64353 | ||||||||
\(711\) | 0.682550 | 0.0255976 | ||||||||
\(712\) | 10.1094 | 0.378867 | ||||||||
\(713\) | −3.14337 | −0.117720 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.09383 | 0.227896 | ||||||||
\(716\) | 54.0587 | 2.02027 | ||||||||
\(717\) | 12.2275 | 0.456644 | ||||||||
\(718\) | −13.8242 | −0.515913 | ||||||||
\(719\) | 36.5431 | 1.36283 | 0.681414 | − | 0.731899i | \(-0.261366\pi\) | ||||
0.681414 | + | 0.731899i | \(0.261366\pi\) | |||||||
\(720\) | −0.0287598 | −0.00107182 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.0817 | 1.26839 | ||||||||
\(723\) | −15.5057 | −0.576665 | ||||||||
\(724\) | 24.6521 | 0.916189 | ||||||||
\(725\) | −9.57429 | −0.355580 | ||||||||
\(726\) | 24.3278 | 0.902890 | ||||||||
\(727\) | 9.59428 | 0.355832 | 0.177916 | − | 0.984046i | \(-0.443064\pi\) | ||||
0.177916 | + | 0.984046i | \(0.443064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.8355 | 1.17828 | ||||||||
\(731\) | 2.07142 | 0.0766142 | ||||||||
\(732\) | −17.3123 | −0.639881 | ||||||||
\(733\) | −24.6790 | −0.911539 | −0.455769 | − | 0.890098i | \(-0.650636\pi\) | ||||
−0.455769 | + | 0.890098i | \(0.650636\pi\) | |||||||
\(734\) | 3.09702 | 0.114313 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.9786 | −0.773280 | ||||||||
\(737\) | −4.55433 | −0.167761 | ||||||||
\(738\) | 2.28873 | 0.0842491 | ||||||||
\(739\) | −13.7444 | −0.505597 | −0.252799 | − | 0.967519i | \(-0.581351\pi\) | ||||
−0.252799 | + | 0.967519i | \(0.581351\pi\) | |||||||
\(740\) | −39.0987 | −1.43729 | ||||||||
\(741\) | −6.93231 | −0.254665 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.8201 | 1.31411 | 0.657055 | − | 0.753842i | \(-0.271802\pi\) | ||||
0.657055 | + | 0.753842i | \(0.271802\pi\) | |||||||
\(744\) | −2.39738 | −0.0878923 | ||||||||
\(745\) | −54.9257 | −2.01232 | ||||||||
\(746\) | 67.5390 | 2.47278 | ||||||||
\(747\) | −1.24939 | −0.0457129 | ||||||||
\(748\) | −5.69081 | −0.208077 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.59579 | −0.350389 | ||||||||
\(751\) | −27.6537 | −1.00910 | −0.504549 | − | 0.863383i | \(-0.668341\pi\) | ||||
−0.504549 | + | 0.863383i | \(0.668341\pi\) | |||||||
\(752\) | −0.0510951 | −0.00186325 | ||||||||
\(753\) | 8.42100 | 0.306878 | ||||||||
\(754\) | 21.0057 | 0.764983 | ||||||||
\(755\) | 35.5369 | 1.29332 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.2987 | −1.93718 | −0.968588 | − | 0.248673i | \(-0.920006\pi\) | ||||
−0.968588 | + | 0.248673i | \(0.920006\pi\) | |||||||
\(758\) | 13.2381 | 0.480828 | ||||||||
\(759\) | 2.26209 | 0.0821086 | ||||||||
\(760\) | −16.8151 | −0.609947 | ||||||||
\(761\) | −45.7807 | −1.65955 | −0.829775 | − | 0.558098i | \(-0.811531\pi\) | ||||
−0.829775 | + | 0.558098i | \(0.811531\pi\) | |||||||
\(762\) | 12.6822 | 0.459427 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.9850 | 0.433603 | ||||||||
\(765\) | −8.44983 | −0.305504 | ||||||||
\(766\) | 19.8876 | 0.718568 | ||||||||
\(767\) | −28.4647 | −1.02780 | ||||||||
\(768\) | −16.0635 | −0.579643 | ||||||||
\(769\) | −38.4188 | −1.38542 | −0.692708 | − | 0.721218i | \(-0.743583\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3723 | −0.409562 | ||||||||
\(772\) | −83.2134 | −2.99492 | ||||||||
\(773\) | 3.82589 | 0.137608 | 0.0688039 | − | 0.997630i | \(-0.478082\pi\) | ||||
0.0688039 | + | 0.997630i | \(0.478082\pi\) | |||||||
\(774\) | −1.64227 | −0.0590301 | ||||||||
\(775\) | 3.01793 | 0.108407 | ||||||||
\(776\) | −38.5191 | −1.38275 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 66.4909 | 2.38381 | ||||||||
\(779\) | 2.02704 | 0.0726262 | ||||||||
\(780\) | −32.4159 | −1.16068 | ||||||||
\(781\) | 6.40079 | 0.229038 | ||||||||
\(782\) | 24.5514 | 0.877958 | ||||||||
\(783\) | −2.68366 | −0.0959062 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.7852 | −1.02739 | ||||||||
\(786\) | 1.07547 | 0.0383606 | ||||||||
\(787\) | −37.4452 | −1.33478 | −0.667389 | − | 0.744710i | \(-0.732588\pi\) | ||||
−0.667389 | + | 0.744710i | \(0.732588\pi\) | |||||||
\(788\) | −71.5644 | −2.54937 | ||||||||
\(789\) | −15.9552 | −0.568019 | ||||||||
\(790\) | 4.57255 | 0.162684 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.72525 | 0.0613039 | ||||||||
\(793\) | −18.2835 | −0.649265 | ||||||||
\(794\) | 53.2179 | 1.88863 | ||||||||
\(795\) | −12.9054 | −0.457708 | ||||||||
\(796\) | −3.27962 | −0.116243 | ||||||||
\(797\) | 47.4050 | 1.67917 | 0.839586 | − | 0.543227i | \(-0.182798\pi\) | ||||
0.839586 | + | 0.543227i | \(0.182798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.0121 | −0.531089 | ||||||||
\(800\) | 20.1414 | 0.712106 | ||||||||
\(801\) | −3.56714 | −0.126039 | ||||||||
\(802\) | −7.22386 | −0.255083 | ||||||||
\(803\) | −2.89289 | −0.102088 | ||||||||
\(804\) | 24.2266 | 0.854406 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.62126 | −0.233224 | ||||||||
\(807\) | 10.9890 | 0.386831 | ||||||||
\(808\) | 19.8559 | 0.698529 | ||||||||
\(809\) | −4.56961 | −0.160659 | −0.0803294 | − | 0.996768i | \(-0.525597\pi\) | ||||
−0.0803294 | + | 0.996768i | \(0.525597\pi\) | |||||||
\(810\) | 6.69922 | 0.235386 | ||||||||
\(811\) | 39.9591 | 1.40315 | 0.701577 | − | 0.712594i | \(-0.252480\pi\) | ||||
0.701577 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.75539 | −0.131707 | ||||||||
\(814\) | 5.74721 | 0.201440 | ||||||||
\(815\) | 28.0102 | 0.981155 | ||||||||
\(816\) | 0.0283644 | 0.000992953 0 | ||||||||
\(817\) | −1.45449 | −0.0508863 | ||||||||
\(818\) | −12.3455 | −0.431650 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.47856 | 0.331006 | ||||||||
\(821\) | 15.6877 | 0.547504 | 0.273752 | − | 0.961800i | \(-0.411735\pi\) | ||||
0.273752 | + | 0.961800i | \(0.411735\pi\) | |||||||
\(822\) | 9.65687 | 0.336822 | ||||||||
\(823\) | 29.8856 | 1.04175 | 0.520873 | − | 0.853634i | \(-0.325606\pi\) | ||||
0.520873 | + | 0.853634i | \(0.325606\pi\) | |||||||
\(824\) | −36.7973 | −1.28189 | ||||||||
\(825\) | −2.17182 | −0.0756130 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.79265 | −0.305750 | −0.152875 | − | 0.988246i | \(-0.548853\pi\) | ||||
−0.152875 | + | 0.988246i | \(0.548853\pi\) | |||||||
\(828\) | −12.0331 | −0.418179 | ||||||||
\(829\) | −18.1178 | −0.629258 | −0.314629 | − | 0.949215i | \(-0.601880\pi\) | ||||
−0.314629 | + | 0.949215i | \(0.601880\pi\) | |||||||
\(830\) | −8.36996 | −0.290525 | ||||||||
\(831\) | −19.9041 | −0.690466 | ||||||||
\(832\) | −44.2568 | −1.53433 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −29.8990 | −1.03532 | ||||||||
\(835\) | −2.67210 | −0.0924719 | ||||||||
\(836\) | 3.99593 | 0.138202 | ||||||||
\(837\) | 0.845922 | 0.0292394 | ||||||||
\(838\) | −42.5948 | −1.47141 | ||||||||
\(839\) | −21.3469 | −0.736977 | −0.368489 | − | 0.929632i | \(-0.620125\pi\) | ||||
−0.368489 | + | 0.929632i | \(0.620125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7980 | −0.751654 | ||||||||
\(842\) | 31.6785 | 1.09171 | ||||||||
\(843\) | 5.65900 | 0.194906 | ||||||||
\(844\) | 43.8039 | 1.50779 | ||||||||
\(845\) | 3.81726 | 0.131318 | ||||||||
\(846\) | 11.9019 | 0.409196 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.0433209 | 0.00148765 | ||||||||
\(849\) | −23.3837 | −0.802525 | ||||||||
\(850\) | −23.5717 | −0.808502 | ||||||||
\(851\) | −15.3280 | −0.525436 | ||||||||
\(852\) | −34.0488 | −1.16649 | ||||||||
\(853\) | −18.5830 | −0.636270 | −0.318135 | − | 0.948045i | \(-0.603057\pi\) | ||||
−0.318135 | + | 0.948045i | \(0.603057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.93324 | 0.202913 | ||||||||
\(856\) | −31.1664 | −1.06524 | ||||||||
\(857\) | 38.8453 | 1.32693 | 0.663465 | − | 0.748207i | \(-0.269085\pi\) | ||||
0.663465 | + | 0.748207i | \(0.269085\pi\) | |||||||
\(858\) | 4.76490 | 0.162671 | ||||||||
\(859\) | 10.3316 | 0.352511 | 0.176255 | − | 0.984344i | \(-0.443602\pi\) | ||||
0.176255 | + | 0.984344i | \(0.443602\pi\) | |||||||
\(860\) | −6.80131 | −0.231923 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.2824 | 0.520521 | ||||||||
\(863\) | −49.2323 | −1.67589 | −0.837944 | − | 0.545757i | \(-0.816242\pi\) | ||||
−0.837944 | + | 0.545757i | \(0.816242\pi\) | |||||||
\(864\) | 5.64560 | 0.192067 | ||||||||
\(865\) | 11.4586 | 0.389605 | ||||||||
\(866\) | −75.8348 | −2.57697 | ||||||||
\(867\) | −8.66634 | −0.294324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.415507 | −0.0140951 | ||||||||
\(870\) | −17.9784 | −0.609525 | ||||||||
\(871\) | 25.5856 | 0.866937 | ||||||||
\(872\) | −9.84701 | −0.333462 | ||||||||
\(873\) | 13.5915 | 0.460004 | ||||||||
\(874\) | −17.2393 | −0.583130 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.3886 | 0.519933 | ||||||||
\(877\) | −27.6814 | −0.934734 | −0.467367 | − | 0.884063i | \(-0.654797\pi\) | ||||
−0.467367 | + | 0.884063i | \(0.654797\pi\) | |||||||
\(878\) | −10.8095 | −0.364804 | ||||||||
\(879\) | −14.4856 | −0.488586 | ||||||||
\(880\) | 0.0175077 | 0.000590186 0 | ||||||||
\(881\) | 14.1997 | 0.478400 | 0.239200 | − | 0.970970i | \(-0.423115\pi\) | ||||
0.239200 | + | 0.970970i | \(0.423115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.5409 | 0.825869 | 0.412934 | − | 0.910761i | \(-0.364504\pi\) | ||||
0.412934 | + | 0.910761i | \(0.364504\pi\) | |||||||
\(884\) | 31.9703 | 1.07528 | ||||||||
\(885\) | 24.3624 | 0.818934 | ||||||||
\(886\) | −15.5466 | −0.522300 | ||||||||
\(887\) | −45.1211 | −1.51502 | −0.757510 | − | 0.652824i | \(-0.773584\pi\) | ||||
−0.757510 | + | 0.652824i | \(0.773584\pi\) | |||||||
\(888\) | −11.6903 | −0.392301 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −23.8970 | −0.801031 | ||||||||
\(891\) | −0.608757 | −0.0203941 | ||||||||
\(892\) | 47.1793 | 1.57968 | ||||||||
\(893\) | 10.5411 | 0.352744 | ||||||||
\(894\) | −42.9476 | −1.43638 | ||||||||
\(895\) | −48.8634 | −1.63332 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.7081 | −0.424312 | ||||||||
\(898\) | 9.44850 | 0.315300 | ||||||||
\(899\) | −2.27017 | −0.0757143 | ||||||||
\(900\) | 11.5529 | 0.385097 | ||||||||
\(901\) | 12.7280 | 0.424031 | ||||||||
\(902\) | −1.39328 | −0.0463911 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 42.8581 | 1.42544 | ||||||||
\(905\) | −22.2829 | −0.740710 | ||||||||
\(906\) | 27.7871 | 0.923165 | ||||||||
\(907\) | 43.3718 | 1.44014 | 0.720068 | − | 0.693903i | \(-0.244111\pi\) | ||||
0.720068 | + | 0.693903i | \(0.244111\pi\) | |||||||
\(908\) | −22.3890 | −0.743005 | ||||||||
\(909\) | −7.00621 | −0.232381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.89404 | 0.228410 | 0.114205 | − | 0.993457i | \(-0.463568\pi\) | ||||
0.114205 | + | 0.993457i | \(0.463568\pi\) | |||||||
\(912\) | −0.0199167 | −0.000659509 0 | ||||||||
\(913\) | 0.760577 | 0.0251714 | ||||||||
\(914\) | −36.0011 | −1.19081 | ||||||||
\(915\) | 15.6485 | 0.517323 | ||||||||
\(916\) | −34.6965 | −1.14641 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.60711 | −0.218067 | ||||||||
\(919\) | −21.2218 | −0.700043 | −0.350022 | − | 0.936742i | \(-0.613826\pi\) | ||||
−0.350022 | + | 0.936742i | \(0.613826\pi\) | |||||||
\(920\) | −30.8250 | −1.01627 | ||||||||
\(921\) | 6.70376 | 0.220896 | ||||||||
\(922\) | 43.4919 | 1.43233 | ||||||||
\(923\) | −35.9589 | −1.18360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.7163 | 0.483869 | ||||||||
\(926\) | −21.0738 | −0.692527 | ||||||||
\(927\) | 12.9840 | 0.426451 | ||||||||
\(928\) | −15.1509 | −0.497352 | ||||||||
\(929\) | −33.2194 | −1.08989 | −0.544947 | − | 0.838471i | \(-0.683450\pi\) | ||||
−0.544947 | + | 0.838471i | \(0.683450\pi\) | |||||||
\(930\) | 5.66702 | 0.185829 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −59.8276 | −1.95972 | ||||||||
\(933\) | 7.41192 | 0.242655 | ||||||||
\(934\) | −66.0738 | −2.16200 | ||||||||
\(935\) | 5.14389 | 0.168223 | ||||||||
\(936\) | −9.69222 | −0.316800 | ||||||||
\(937\) | −48.1152 | −1.57186 | −0.785928 | − | 0.618318i | \(-0.787814\pi\) | ||||
−0.785928 | + | 0.618318i | \(0.787814\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7688 | 0.547229 | ||||||||
\(940\) | 49.2908 | 1.60769 | ||||||||
\(941\) | 39.1978 | 1.27781 | 0.638906 | − | 0.769285i | \(-0.279387\pi\) | ||||
0.638906 | + | 0.769285i | \(0.279387\pi\) | |||||||
\(942\) | −22.5077 | −0.733342 | ||||||||
\(943\) | 3.71591 | 0.121007 | ||||||||
\(944\) | −0.0817798 | −0.00266171 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.999741 | 0.0325044 | ||||||||
\(947\) | 7.83468 | 0.254593 | 0.127296 | − | 0.991865i | \(-0.459370\pi\) | ||||
0.127296 | + | 0.991865i | \(0.459370\pi\) | |||||||
\(948\) | 2.21028 | 0.0717865 | ||||||||
\(949\) | 16.2519 | 0.527558 | ||||||||
\(950\) | 16.5514 | 0.536998 | ||||||||
\(951\) | −6.67784 | −0.216544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0595 | −0.844150 | −0.422075 | − | 0.906561i | \(-0.638698\pi\) | ||||
−0.422075 | + | 0.906561i | \(0.638698\pi\) | |||||||
\(954\) | −10.0910 | −0.326709 | ||||||||
\(955\) | −10.8332 | −0.350555 | ||||||||
\(956\) | 39.5958 | 1.28062 | ||||||||
\(957\) | 1.63370 | 0.0528099 | ||||||||
\(958\) | 39.8242 | 1.28666 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 37.8786 | 1.22253 | ||||||||
\(961\) | −30.2844 | −0.976917 | ||||||||
\(962\) | −32.2871 | −1.04098 | ||||||||
\(963\) | 10.9971 | 0.354378 | ||||||||
\(964\) | −50.2117 | −1.61721 | ||||||||
\(965\) | 75.2162 | 2.42130 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.2924 | −0.909821 | −0.454911 | − | 0.890537i | \(-0.650329\pi\) | ||||
−0.454911 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(968\) | 30.1243 | 0.968230 | ||||||||
\(969\) | −5.85167 | −0.187983 | ||||||||
\(970\) | 91.0527 | 2.92353 | ||||||||
\(971\) | −40.1883 | −1.28970 | −0.644851 | − | 0.764308i | \(-0.723081\pi\) | ||||
−0.644851 | + | 0.764308i | \(0.723081\pi\) | |||||||
\(972\) | 3.23826 | 0.103867 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 67.9272 | 2.17653 | ||||||||
\(975\) | 12.2010 | 0.390745 | ||||||||
\(976\) | −0.0525289 | −0.00168141 | ||||||||
\(977\) | 15.5653 | 0.497979 | 0.248989 | − | 0.968506i | \(-0.419902\pi\) | ||||
0.248989 | + | 0.968506i | \(0.419902\pi\) | |||||||
\(978\) | 21.9018 | 0.700342 | ||||||||
\(979\) | 2.17152 | 0.0694021 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.47454 | 0.110934 | ||||||||
\(982\) | −88.7810 | −2.83312 | ||||||||
\(983\) | 33.7929 | 1.07783 | 0.538913 | − | 0.842361i | \(-0.318835\pi\) | ||||
0.538913 | + | 0.842361i | \(0.318835\pi\) | |||||||
\(984\) | 2.83405 | 0.0903461 | ||||||||
\(985\) | 64.6867 | 2.06109 | ||||||||
\(986\) | 17.7312 | 0.564678 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.4487 | −0.714187 | ||||||||
\(989\) | −2.66634 | −0.0847846 | ||||||||
\(990\) | −4.07819 | −0.129614 | ||||||||
\(991\) | 46.8354 | 1.48777 | 0.743887 | − | 0.668305i | \(-0.232980\pi\) | ||||
0.743887 | + | 0.668305i | \(0.232980\pi\) | |||||||
\(992\) | 4.77574 | 0.151630 | ||||||||
\(993\) | −22.2105 | −0.704829 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.96443 | 0.0939789 | ||||||||
\(996\) | −4.04587 | −0.128198 | ||||||||
\(997\) | −8.38234 | −0.265472 | −0.132736 | − | 0.991151i | \(-0.542376\pi\) | ||||
−0.132736 | + | 0.991151i | \(0.542376\pi\) | |||||||
\(998\) | 13.8071 | 0.437055 | ||||||||
\(999\) | 4.12496 | 0.130508 |
(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 | 6027.2.a.ba.1.2 | yes | 8 | |
7.6 | odd | 2 | 6027.2.a.z.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.z.1.2 | ✓ | 8 | 7.6 | odd | 2 | ||
6027.2.a.ba.1.2 | yes | 8 | 1.1 | even | 1 | trivial |