Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2883,2,Mod(1,2883)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2883, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2883.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2883 = 3 \cdot 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2883.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: | \(23.0208709027\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 2883.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.22192 | 1.57113 | 0.785566 | − | 0.618778i | \(-0.212372\pi\) | ||||
0.785566 | + | 0.618778i | \(0.212372\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.93691 | 1.46846 | ||||||||
\(5\) | 1.02426 | 0.458061 | 0.229030 | − | 0.973419i | \(-0.426444\pi\) | ||||
0.229030 | + | 0.973419i | \(0.426444\pi\) | |||||||
\(6\) | 2.22192 | 0.907093 | ||||||||
\(7\) | 0.246895 | 0.0933177 | 0.0466588 | − | 0.998911i | \(-0.485143\pi\) | ||||
0.0466588 | + | 0.998911i | \(0.485143\pi\) | |||||||
\(8\) | 2.08174 | 0.736005 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.27581 | 0.719674 | ||||||||
\(11\) | 4.88554 | 1.47305 | 0.736523 | − | 0.676413i | \(-0.236467\pi\) | ||||
0.736523 | + | 0.676413i | \(0.236467\pi\) | |||||||
\(12\) | 2.93691 | 0.847813 | ||||||||
\(13\) | 1.31401 | 0.364441 | 0.182220 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182220 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(14\) | 0.548581 | 0.146614 | ||||||||
\(15\) | 1.02426 | 0.264462 | ||||||||
\(16\) | −1.24838 | −0.312094 | ||||||||
\(17\) | 6.62178 | 1.60602 | 0.803009 | − | 0.595967i | \(-0.203231\pi\) | ||||
0.803009 | + | 0.595967i | \(0.203231\pi\) | |||||||
\(18\) | 2.22192 | 0.523711 | ||||||||
\(19\) | −5.60275 | −1.28536 | −0.642680 | − | 0.766135i | \(-0.722177\pi\) | ||||
−0.642680 | + | 0.766135i | \(0.722177\pi\) | |||||||
\(20\) | 3.00815 | 0.672642 | ||||||||
\(21\) | 0.246895 | 0.0538770 | ||||||||
\(22\) | 10.8553 | 2.31435 | ||||||||
\(23\) | −0.476794 | −0.0994184 | −0.0497092 | − | 0.998764i | \(-0.515829\pi\) | ||||
−0.0497092 | + | 0.998764i | \(0.515829\pi\) | |||||||
\(24\) | 2.08174 | 0.424933 | ||||||||
\(25\) | −3.95090 | −0.790180 | ||||||||
\(26\) | 2.91962 | 0.572585 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.725109 | 0.137033 | ||||||||
\(29\) | −6.57245 | −1.22047 | −0.610237 | − | 0.792219i | \(-0.708926\pi\) | ||||
−0.610237 | + | 0.792219i | \(0.708926\pi\) | |||||||
\(30\) | 2.27581 | 0.415504 | ||||||||
\(31\) | 0 | 0 | ||||||||
\(32\) | −6.93726 | −1.22635 | ||||||||
\(33\) | 4.88554 | 0.850463 | ||||||||
\(34\) | 14.7130 | 2.52327 | ||||||||
\(35\) | 0.252884 | 0.0427452 | ||||||||
\(36\) | 2.93691 | 0.489485 | ||||||||
\(37\) | 7.64106 | 1.25618 | 0.628091 | − | 0.778140i | \(-0.283837\pi\) | ||||
0.628091 | + | 0.778140i | \(0.283837\pi\) | |||||||
\(38\) | −12.4488 | −2.01947 | ||||||||
\(39\) | 1.31401 | 0.210410 | ||||||||
\(40\) | 2.13223 | 0.337135 | ||||||||
\(41\) | 10.2582 | 1.60207 | 0.801034 | − | 0.598619i | \(-0.204284\pi\) | ||||
0.801034 | + | 0.598619i | \(0.204284\pi\) | |||||||
\(42\) | 0.548581 | 0.0846478 | ||||||||
\(43\) | −7.93895 | −1.21068 | −0.605339 | − | 0.795968i | \(-0.706962\pi\) | ||||
−0.605339 | + | 0.795968i | \(0.706962\pi\) | |||||||
\(44\) | 14.3484 | 2.16310 | ||||||||
\(45\) | 1.02426 | 0.152687 | ||||||||
\(46\) | −1.05940 | −0.156199 | ||||||||
\(47\) | −1.81918 | −0.265354 | −0.132677 | − | 0.991159i | \(-0.542357\pi\) | ||||
−0.132677 | + | 0.991159i | \(0.542357\pi\) | |||||||
\(48\) | −1.24838 | −0.180188 | ||||||||
\(49\) | −6.93904 | −0.991292 | ||||||||
\(50\) | −8.77857 | −1.24148 | ||||||||
\(51\) | 6.62178 | 0.927235 | ||||||||
\(52\) | 3.85913 | 0.535165 | ||||||||
\(53\) | 12.9101 | 1.77334 | 0.886669 | − | 0.462405i | \(-0.153013\pi\) | ||||
0.886669 | + | 0.462405i | \(0.153013\pi\) | |||||||
\(54\) | 2.22192 | 0.302364 | ||||||||
\(55\) | 5.00404 | 0.674744 | ||||||||
\(56\) | 0.513971 | 0.0686823 | ||||||||
\(57\) | −5.60275 | −0.742102 | ||||||||
\(58\) | −14.6034 | −1.91752 | ||||||||
\(59\) | −0.877915 | −0.114295 | −0.0571474 | − | 0.998366i | \(-0.518200\pi\) | ||||
−0.0571474 | + | 0.998366i | \(0.518200\pi\) | |||||||
\(60\) | 3.00815 | 0.388350 | ||||||||
\(61\) | −7.43904 | −0.952471 | −0.476236 | − | 0.879318i | \(-0.657999\pi\) | ||||
−0.476236 | + | 0.879318i | \(0.657999\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.246895 | 0.0311059 | ||||||||
\(64\) | −12.9173 | −1.61466 | ||||||||
\(65\) | 1.34588 | 0.166936 | ||||||||
\(66\) | 10.8553 | 1.33619 | ||||||||
\(67\) | −0.438119 | −0.0535248 | −0.0267624 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267624 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(68\) | 19.4476 | 2.35837 | ||||||||
\(69\) | −0.476794 | −0.0573993 | ||||||||
\(70\) | 0.561887 | 0.0671583 | ||||||||
\(71\) | 4.43447 | 0.526275 | 0.263137 | − | 0.964758i | \(-0.415243\pi\) | ||||
0.263137 | + | 0.964758i | \(0.415243\pi\) | |||||||
\(72\) | 2.08174 | 0.245335 | ||||||||
\(73\) | −1.47426 | −0.172549 | −0.0862745 | − | 0.996271i | \(-0.527496\pi\) | ||||
−0.0862745 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(74\) | 16.9778 | 1.97363 | ||||||||
\(75\) | −3.95090 | −0.456211 | ||||||||
\(76\) | −16.4548 | −1.88749 | ||||||||
\(77\) | 1.20622 | 0.137461 | ||||||||
\(78\) | 2.91962 | 0.330582 | ||||||||
\(79\) | −15.8534 | −1.78364 | −0.891822 | − | 0.452386i | \(-0.850573\pi\) | ||||
−0.891822 | + | 0.452386i | \(0.850573\pi\) | |||||||
\(80\) | −1.27866 | −0.142958 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.7929 | 2.51706 | ||||||||
\(83\) | −8.53475 | −0.936810 | −0.468405 | − | 0.883514i | \(-0.655171\pi\) | ||||
−0.468405 | + | 0.883514i | \(0.655171\pi\) | |||||||
\(84\) | 0.725109 | 0.0791159 | ||||||||
\(85\) | 6.78240 | 0.735654 | ||||||||
\(86\) | −17.6397 | −1.90213 | ||||||||
\(87\) | −6.57245 | −0.704641 | ||||||||
\(88\) | 10.1704 | 1.08417 | ||||||||
\(89\) | 12.7810 | 1.35478 | 0.677391 | − | 0.735623i | \(-0.263110\pi\) | ||||
0.677391 | + | 0.735623i | \(0.263110\pi\) | |||||||
\(90\) | 2.27581 | 0.239891 | ||||||||
\(91\) | 0.324423 | 0.0340088 | ||||||||
\(92\) | −1.40030 | −0.145992 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.04206 | −0.416906 | ||||||||
\(95\) | −5.73865 | −0.588773 | ||||||||
\(96\) | −6.93726 | −0.708031 | ||||||||
\(97\) | 8.25122 | 0.837784 | 0.418892 | − | 0.908036i | \(-0.362419\pi\) | ||||
0.418892 | + | 0.908036i | \(0.362419\pi\) | |||||||
\(98\) | −15.4180 | −1.55745 | ||||||||
\(99\) | 4.88554 | 0.491015 | ||||||||
\(100\) | −11.6034 | −1.16034 | ||||||||
\(101\) | 0.491992 | 0.0489551 | 0.0244775 | − | 0.999700i | \(-0.492208\pi\) | ||||
0.0244775 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(102\) | 14.7130 | 1.45681 | ||||||||
\(103\) | 7.76258 | 0.764869 | 0.382435 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382435 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(104\) | 2.73542 | 0.268230 | ||||||||
\(105\) | 0.252884 | 0.0246789 | ||||||||
\(106\) | 28.6851 | 2.78615 | ||||||||
\(107\) | 9.99162 | 0.965926 | 0.482963 | − | 0.875641i | \(-0.339561\pi\) | ||||
0.482963 | + | 0.875641i | \(0.339561\pi\) | |||||||
\(108\) | 2.93691 | 0.282604 | ||||||||
\(109\) | 10.2578 | 0.982519 | 0.491259 | − | 0.871013i | \(-0.336537\pi\) | ||||
0.491259 | + | 0.871013i | \(0.336537\pi\) | |||||||
\(110\) | 11.1186 | 1.06011 | ||||||||
\(111\) | 7.64106 | 0.725257 | ||||||||
\(112\) | −0.308219 | −0.0291239 | ||||||||
\(113\) | −17.3944 | −1.63633 | −0.818165 | − | 0.574983i | \(-0.805009\pi\) | ||||
−0.818165 | + | 0.574983i | \(0.805009\pi\) | |||||||
\(114\) | −12.4488 | −1.16594 | ||||||||
\(115\) | −0.488359 | −0.0455397 | ||||||||
\(116\) | −19.3027 | −1.79221 | ||||||||
\(117\) | 1.31401 | 0.121480 | ||||||||
\(118\) | −1.95065 | −0.179572 | ||||||||
\(119\) | 1.63489 | 0.149870 | ||||||||
\(120\) | 2.13223 | 0.194645 | ||||||||
\(121\) | 12.8685 | 1.16986 | ||||||||
\(122\) | −16.5289 | −1.49646 | ||||||||
\(123\) | 10.2582 | 0.924954 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.16801 | −0.820012 | ||||||||
\(126\) | 0.548581 | 0.0488714 | ||||||||
\(127\) | 4.01005 | 0.355835 | 0.177917 | − | 0.984045i | \(-0.443064\pi\) | ||||
0.177917 | + | 0.984045i | \(0.443064\pi\) | |||||||
\(128\) | −14.8265 | −1.31049 | ||||||||
\(129\) | −7.93895 | −0.698985 | ||||||||
\(130\) | 2.99044 | 0.262279 | ||||||||
\(131\) | 0.291671 | 0.0254834 | 0.0127417 | − | 0.999919i | \(-0.495944\pi\) | ||||
0.0127417 | + | 0.999919i | \(0.495944\pi\) | |||||||
\(132\) | 14.3484 | 1.24887 | ||||||||
\(133\) | −1.38329 | −0.119947 | ||||||||
\(134\) | −0.973464 | −0.0840944 | ||||||||
\(135\) | 1.02426 | 0.0881539 | ||||||||
\(136\) | 13.7848 | 1.18204 | ||||||||
\(137\) | −0.382882 | −0.0327118 | −0.0163559 | − | 0.999866i | \(-0.505206\pi\) | ||||
−0.0163559 | + | 0.999866i | \(0.505206\pi\) | |||||||
\(138\) | −1.05940 | −0.0901818 | ||||||||
\(139\) | 4.82874 | 0.409568 | 0.204784 | − | 0.978807i | \(-0.434351\pi\) | ||||
0.204784 | + | 0.978807i | \(0.434351\pi\) | |||||||
\(140\) | 0.742697 | 0.0627694 | ||||||||
\(141\) | −1.81918 | −0.153202 | ||||||||
\(142\) | 9.85302 | 0.826847 | ||||||||
\(143\) | 6.41965 | 0.536838 | ||||||||
\(144\) | −1.24838 | −0.104031 | ||||||||
\(145\) | −6.73187 | −0.559051 | ||||||||
\(146\) | −3.27568 | −0.271097 | ||||||||
\(147\) | −6.93904 | −0.572323 | ||||||||
\(148\) | 22.4411 | 1.84465 | ||||||||
\(149\) | −4.72173 | −0.386819 | −0.193410 | − | 0.981118i | \(-0.561955\pi\) | ||||
−0.193410 | + | 0.981118i | \(0.561955\pi\) | |||||||
\(150\) | −8.77857 | −0.716767 | ||||||||
\(151\) | 10.7341 | 0.873531 | 0.436765 | − | 0.899575i | \(-0.356124\pi\) | ||||
0.436765 | + | 0.899575i | \(0.356124\pi\) | |||||||
\(152\) | −11.6635 | −0.946031 | ||||||||
\(153\) | 6.62178 | 0.535339 | ||||||||
\(154\) | 2.68011 | 0.215970 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.85913 | 0.308978 | ||||||||
\(157\) | −23.2962 | −1.85924 | −0.929618 | − | 0.368525i | \(-0.879863\pi\) | ||||
−0.929618 | + | 0.368525i | \(0.879863\pi\) | |||||||
\(158\) | −35.2249 | −2.80234 | ||||||||
\(159\) | 12.9101 | 1.02384 | ||||||||
\(160\) | −7.10553 | −0.561741 | ||||||||
\(161\) | −0.117718 | −0.00927749 | ||||||||
\(162\) | 2.22192 | 0.174570 | ||||||||
\(163\) | −22.9681 | −1.79900 | −0.899499 | − | 0.436922i | \(-0.856069\pi\) | ||||
−0.899499 | + | 0.436922i | \(0.856069\pi\) | |||||||
\(164\) | 30.1275 | 2.35256 | ||||||||
\(165\) | 5.00404 | 0.389564 | ||||||||
\(166\) | −18.9635 | −1.47185 | ||||||||
\(167\) | −3.08014 | −0.238348 | −0.119174 | − | 0.992873i | \(-0.538025\pi\) | ||||
−0.119174 | + | 0.992873i | \(0.538025\pi\) | |||||||
\(168\) | 0.513971 | 0.0396537 | ||||||||
\(169\) | −11.2734 | −0.867183 | ||||||||
\(170\) | 15.0699 | 1.15581 | ||||||||
\(171\) | −5.60275 | −0.428453 | ||||||||
\(172\) | −23.3160 | −1.77783 | ||||||||
\(173\) | −4.57393 | −0.347750 | −0.173875 | − | 0.984768i | \(-0.555629\pi\) | ||||
−0.173875 | + | 0.984768i | \(0.555629\pi\) | |||||||
\(174\) | −14.6034 | −1.10708 | ||||||||
\(175\) | −0.975459 | −0.0737378 | ||||||||
\(176\) | −6.09899 | −0.459729 | ||||||||
\(177\) | −0.877915 | −0.0659881 | ||||||||
\(178\) | 28.3983 | 2.12854 | ||||||||
\(179\) | 4.89854 | 0.366134 | 0.183067 | − | 0.983100i | \(-0.441397\pi\) | ||||
0.183067 | + | 0.983100i | \(0.441397\pi\) | |||||||
\(180\) | 3.00815 | 0.224214 | ||||||||
\(181\) | 20.2801 | 1.50741 | 0.753705 | − | 0.657213i | \(-0.228265\pi\) | ||||
0.753705 | + | 0.657213i | \(0.228265\pi\) | |||||||
\(182\) | 0.720841 | 0.0534323 | ||||||||
\(183\) | −7.43904 | −0.549910 | ||||||||
\(184\) | −0.992560 | −0.0731725 | ||||||||
\(185\) | 7.82640 | 0.575408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.3510 | 2.36574 | ||||||||
\(188\) | −5.34276 | −0.389661 | ||||||||
\(189\) | 0.246895 | 0.0179590 | ||||||||
\(190\) | −12.7508 | −0.925040 | ||||||||
\(191\) | −17.5005 | −1.26629 | −0.633147 | − | 0.774032i | \(-0.718237\pi\) | ||||
−0.633147 | + | 0.774032i | \(0.718237\pi\) | |||||||
\(192\) | −12.9173 | −0.932223 | ||||||||
\(193\) | −6.05965 | −0.436183 | −0.218091 | − | 0.975928i | \(-0.569983\pi\) | ||||
−0.218091 | + | 0.975928i | \(0.569983\pi\) | |||||||
\(194\) | 18.3335 | 1.31627 | ||||||||
\(195\) | 1.34588 | 0.0963806 | ||||||||
\(196\) | −20.3793 | −1.45567 | ||||||||
\(197\) | 10.5875 | 0.754330 | 0.377165 | − | 0.926146i | \(-0.376899\pi\) | ||||
0.377165 | + | 0.926146i | \(0.376899\pi\) | |||||||
\(198\) | 10.8553 | 0.771449 | ||||||||
\(199\) | −26.8385 | −1.90253 | −0.951265 | − | 0.308375i | \(-0.900215\pi\) | ||||
−0.951265 | + | 0.308375i | \(0.900215\pi\) | |||||||
\(200\) | −8.22473 | −0.581577 | ||||||||
\(201\) | −0.438119 | −0.0309025 | ||||||||
\(202\) | 1.09317 | 0.0769149 | ||||||||
\(203\) | −1.62271 | −0.113892 | ||||||||
\(204\) | 19.4476 | 1.36160 | ||||||||
\(205\) | 10.5071 | 0.733845 | ||||||||
\(206\) | 17.2478 | 1.20171 | ||||||||
\(207\) | −0.476794 | −0.0331395 | ||||||||
\(208\) | −1.64038 | −0.113740 | ||||||||
\(209\) | −27.3724 | −1.89339 | ||||||||
\(210\) | 0.561887 | 0.0387739 | ||||||||
\(211\) | 2.56528 | 0.176601 | 0.0883007 | − | 0.996094i | \(-0.471856\pi\) | ||||
0.0883007 | + | 0.996094i | \(0.471856\pi\) | |||||||
\(212\) | 37.9158 | 2.60407 | ||||||||
\(213\) | 4.43447 | 0.303845 | ||||||||
\(214\) | 22.2005 | 1.51760 | ||||||||
\(215\) | −8.13151 | −0.554564 | ||||||||
\(216\) | 2.08174 | 0.141644 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 22.7920 | 1.54367 | ||||||||
\(219\) | −1.47426 | −0.0996212 | ||||||||
\(220\) | 14.6964 | 0.990832 | ||||||||
\(221\) | 8.70109 | 0.585299 | ||||||||
\(222\) | 16.9778 | 1.13947 | ||||||||
\(223\) | −6.42752 | −0.430419 | −0.215209 | − | 0.976568i | \(-0.569043\pi\) | ||||
−0.215209 | + | 0.976568i | \(0.569043\pi\) | |||||||
\(224\) | −1.71278 | −0.114440 | ||||||||
\(225\) | −3.95090 | −0.263393 | ||||||||
\(226\) | −38.6490 | −2.57089 | ||||||||
\(227\) | −16.4348 | −1.09082 | −0.545409 | − | 0.838170i | \(-0.683625\pi\) | ||||
−0.545409 | + | 0.838170i | \(0.683625\pi\) | |||||||
\(228\) | −16.4548 | −1.08974 | ||||||||
\(229\) | −17.3692 | −1.14779 | −0.573896 | − | 0.818928i | \(-0.694569\pi\) | ||||
−0.573896 | + | 0.818928i | \(0.694569\pi\) | |||||||
\(230\) | −1.08509 | −0.0715489 | ||||||||
\(231\) | 1.20622 | 0.0793632 | ||||||||
\(232\) | −13.6821 | −0.898274 | ||||||||
\(233\) | −17.0566 | −1.11742 | −0.558708 | − | 0.829364i | \(-0.688703\pi\) | ||||
−0.558708 | + | 0.829364i | \(0.688703\pi\) | |||||||
\(234\) | 2.91962 | 0.190862 | ||||||||
\(235\) | −1.86330 | −0.121548 | ||||||||
\(236\) | −2.57836 | −0.167837 | ||||||||
\(237\) | −15.8534 | −1.02979 | ||||||||
\(238\) | 3.63258 | 0.235465 | ||||||||
\(239\) | 4.66639 | 0.301844 | 0.150922 | − | 0.988546i | \(-0.451776\pi\) | ||||
0.150922 | + | 0.988546i | \(0.451776\pi\) | |||||||
\(240\) | −1.27866 | −0.0825370 | ||||||||
\(241\) | −6.06181 | −0.390476 | −0.195238 | − | 0.980756i | \(-0.562548\pi\) | ||||
−0.195238 | + | 0.980756i | \(0.562548\pi\) | |||||||
\(242\) | 28.5927 | 1.83801 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −21.8478 | −1.39866 | ||||||||
\(245\) | −7.10735 | −0.454072 | ||||||||
\(246\) | 22.7929 | 1.45322 | ||||||||
\(247\) | −7.36207 | −0.468437 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.53475 | −0.540868 | ||||||||
\(250\) | −20.3705 | −1.28835 | ||||||||
\(251\) | −12.6354 | −0.797536 | −0.398768 | − | 0.917052i | \(-0.630562\pi\) | ||||
−0.398768 | + | 0.917052i | \(0.630562\pi\) | |||||||
\(252\) | 0.725109 | 0.0456776 | ||||||||
\(253\) | −2.32940 | −0.146448 | ||||||||
\(254\) | 8.91000 | 0.559063 | ||||||||
\(255\) | 6.78240 | 0.424730 | ||||||||
\(256\) | −7.10881 | −0.444301 | ||||||||
\(257\) | −14.0203 | −0.874565 | −0.437283 | − | 0.899324i | \(-0.644059\pi\) | ||||
−0.437283 | + | 0.899324i | \(0.644059\pi\) | |||||||
\(258\) | −17.6397 | −1.09820 | ||||||||
\(259\) | 1.88654 | 0.117224 | ||||||||
\(260\) | 3.95274 | 0.245138 | ||||||||
\(261\) | −6.57245 | −0.406824 | ||||||||
\(262\) | 0.648069 | 0.0400379 | ||||||||
\(263\) | −17.2115 | −1.06130 | −0.530652 | − | 0.847590i | \(-0.678053\pi\) | ||||
−0.530652 | + | 0.847590i | \(0.678053\pi\) | |||||||
\(264\) | 10.1704 | 0.625945 | ||||||||
\(265\) | 13.2232 | 0.812297 | ||||||||
\(266\) | −3.07356 | −0.188452 | ||||||||
\(267\) | 12.7810 | 0.782184 | ||||||||
\(268\) | −1.28672 | −0.0785987 | ||||||||
\(269\) | 13.6155 | 0.830152 | 0.415076 | − | 0.909787i | \(-0.363755\pi\) | ||||
0.415076 | + | 0.909787i | \(0.363755\pi\) | |||||||
\(270\) | 2.27581 | 0.138501 | ||||||||
\(271\) | 9.26824 | 0.563005 | 0.281503 | − | 0.959560i | \(-0.409167\pi\) | ||||
0.281503 | + | 0.959560i | \(0.409167\pi\) | |||||||
\(272\) | −8.26648 | −0.501229 | ||||||||
\(273\) | 0.324423 | 0.0196350 | ||||||||
\(274\) | −0.850732 | −0.0513946 | ||||||||
\(275\) | −19.3023 | −1.16397 | ||||||||
\(276\) | −1.40030 | −0.0842882 | ||||||||
\(277\) | −30.1569 | −1.81195 | −0.905975 | − | 0.423332i | \(-0.860860\pi\) | ||||
−0.905975 | + | 0.423332i | \(0.860860\pi\) | |||||||
\(278\) | 10.7291 | 0.643486 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.526438 | 0.0314607 | ||||||||
\(281\) | 0.251359 | 0.0149948 | 0.00749742 | − | 0.999972i | \(-0.497613\pi\) | ||||
0.00749742 | + | 0.999972i | \(0.497613\pi\) | |||||||
\(282\) | −4.04206 | −0.240701 | ||||||||
\(283\) | −8.47213 | −0.503616 | −0.251808 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251808 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(284\) | 13.0236 | 0.772811 | ||||||||
\(285\) | −5.73865 | −0.339928 | ||||||||
\(286\) | 14.2639 | 0.843443 | ||||||||
\(287\) | 2.53271 | 0.149501 | ||||||||
\(288\) | −6.93726 | −0.408782 | ||||||||
\(289\) | 26.8480 | 1.57929 | ||||||||
\(290\) | −14.9576 | −0.878343 | ||||||||
\(291\) | 8.25122 | 0.483695 | ||||||||
\(292\) | −4.32977 | −0.253381 | ||||||||
\(293\) | 16.5238 | 0.965329 | 0.482665 | − | 0.875805i | \(-0.339669\pi\) | ||||
0.482665 | + | 0.875805i | \(0.339669\pi\) | |||||||
\(294\) | −15.4180 | −0.899194 | ||||||||
\(295\) | −0.899209 | −0.0523540 | ||||||||
\(296\) | 15.9067 | 0.924556 | ||||||||
\(297\) | 4.88554 | 0.283488 | ||||||||
\(298\) | −10.4913 | −0.607744 | ||||||||
\(299\) | −0.626512 | −0.0362321 | ||||||||
\(300\) | −11.6034 | −0.669925 | ||||||||
\(301\) | −1.96009 | −0.112978 | ||||||||
\(302\) | 23.8503 | 1.37243 | ||||||||
\(303\) | 0.491992 | 0.0282642 | ||||||||
\(304\) | 6.99435 | 0.401153 | ||||||||
\(305\) | −7.61948 | −0.436290 | ||||||||
\(306\) | 14.7130 | 0.841089 | ||||||||
\(307\) | 3.54132 | 0.202114 | 0.101057 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101057 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(308\) | 3.54255 | 0.201855 | ||||||||
\(309\) | 7.76258 | 0.441597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.1123 | 1.42399 | 0.711993 | − | 0.702187i | \(-0.247793\pi\) | ||||
0.711993 | + | 0.702187i | \(0.247793\pi\) | |||||||
\(312\) | 2.73542 | 0.154863 | ||||||||
\(313\) | −1.25019 | −0.0706647 | −0.0353323 | − | 0.999376i | \(-0.511249\pi\) | ||||
−0.0353323 | + | 0.999376i | \(0.511249\pi\) | |||||||
\(314\) | −51.7621 | −2.92110 | ||||||||
\(315\) | 0.252884 | 0.0142484 | ||||||||
\(316\) | −46.5600 | −2.61920 | ||||||||
\(317\) | 16.8497 | 0.946371 | 0.473186 | − | 0.880963i | \(-0.343104\pi\) | ||||
0.473186 | + | 0.880963i | \(0.343104\pi\) | |||||||
\(318\) | 28.6851 | 1.60858 | ||||||||
\(319\) | −32.1099 | −1.79781 | ||||||||
\(320\) | −13.2306 | −0.739612 | ||||||||
\(321\) | 9.99162 | 0.557678 | ||||||||
\(322\) | −0.261560 | −0.0145762 | ||||||||
\(323\) | −37.1002 | −2.06431 | ||||||||
\(324\) | 2.93691 | 0.163162 | ||||||||
\(325\) | −5.19152 | −0.287974 | ||||||||
\(326\) | −51.0331 | −2.82646 | ||||||||
\(327\) | 10.2578 | 0.567257 | ||||||||
\(328\) | 21.3549 | 1.17913 | ||||||||
\(329\) | −0.449146 | −0.0247622 | ||||||||
\(330\) | 11.1186 | 0.612056 | ||||||||
\(331\) | 9.65338 | 0.530598 | 0.265299 | − | 0.964166i | \(-0.414529\pi\) | ||||
0.265299 | + | 0.964166i | \(0.414529\pi\) | |||||||
\(332\) | −25.0658 | −1.37566 | ||||||||
\(333\) | 7.64106 | 0.418727 | ||||||||
\(334\) | −6.84381 | −0.374476 | ||||||||
\(335\) | −0.448746 | −0.0245176 | ||||||||
\(336\) | −0.308219 | −0.0168147 | ||||||||
\(337\) | 7.25309 | 0.395101 | 0.197551 | − | 0.980293i | \(-0.436701\pi\) | ||||
0.197551 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(338\) | −25.0485 | −1.36246 | ||||||||
\(339\) | −17.3944 | −0.944736 | ||||||||
\(340\) | 19.9193 | 1.08028 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.4488 | −0.673156 | ||||||||
\(343\) | −3.44148 | −0.185823 | ||||||||
\(344\) | −16.5268 | −0.891065 | ||||||||
\(345\) | −0.488359 | −0.0262924 | ||||||||
\(346\) | −10.1629 | −0.546360 | ||||||||
\(347\) | 20.2729 | 1.08831 | 0.544154 | − | 0.838985i | \(-0.316851\pi\) | ||||
0.544154 | + | 0.838985i | \(0.316851\pi\) | |||||||
\(348\) | −19.3027 | −1.03473 | ||||||||
\(349\) | 25.6000 | 1.37034 | 0.685169 | − | 0.728384i | \(-0.259728\pi\) | ||||
0.685169 | + | 0.728384i | \(0.259728\pi\) | |||||||
\(350\) | −2.16739 | −0.115852 | ||||||||
\(351\) | 1.31401 | 0.0701367 | ||||||||
\(352\) | −33.8923 | −1.80646 | ||||||||
\(353\) | −8.02074 | −0.426901 | −0.213450 | − | 0.976954i | \(-0.568470\pi\) | ||||
−0.213450 | + | 0.976954i | \(0.568470\pi\) | |||||||
\(354\) | −1.95065 | −0.103676 | ||||||||
\(355\) | 4.54203 | 0.241066 | ||||||||
\(356\) | 37.5366 | 1.98944 | ||||||||
\(357\) | 1.63489 | 0.0865274 | ||||||||
\(358\) | 10.8841 | 0.575245 | ||||||||
\(359\) | 24.8239 | 1.31016 | 0.655079 | − | 0.755560i | \(-0.272635\pi\) | ||||
0.655079 | + | 0.755560i | \(0.272635\pi\) | |||||||
\(360\) | 2.13223 | 0.112378 | ||||||||
\(361\) | 12.3908 | 0.652148 | ||||||||
\(362\) | 45.0607 | 2.36834 | ||||||||
\(363\) | 12.8685 | 0.675420 | ||||||||
\(364\) | 0.952801 | 0.0499404 | ||||||||
\(365\) | −1.51002 | −0.0790380 | ||||||||
\(366\) | −16.5289 | −0.863980 | ||||||||
\(367\) | −13.4121 | −0.700107 | −0.350053 | − | 0.936730i | \(-0.613837\pi\) | ||||
−0.350053 | + | 0.936730i | \(0.613837\pi\) | |||||||
\(368\) | 0.595219 | 0.0310279 | ||||||||
\(369\) | 10.2582 | 0.534023 | ||||||||
\(370\) | 17.3896 | 0.904042 | ||||||||
\(371\) | 3.18744 | 0.165484 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5457 | 1.01204 | 0.506019 | − | 0.862522i | \(-0.331117\pi\) | ||||
0.506019 | + | 0.862522i | \(0.331117\pi\) | |||||||
\(374\) | 71.8811 | 3.71688 | ||||||||
\(375\) | −9.16801 | −0.473434 | ||||||||
\(376\) | −3.78704 | −0.195302 | ||||||||
\(377\) | −8.63627 | −0.444790 | ||||||||
\(378\) | 0.548581 | 0.0282159 | ||||||||
\(379\) | 32.9292 | 1.69146 | 0.845731 | − | 0.533610i | \(-0.179165\pi\) | ||||
0.845731 | + | 0.533610i | \(0.179165\pi\) | |||||||
\(380\) | −16.8539 | −0.864587 | ||||||||
\(381\) | 4.01005 | 0.205441 | ||||||||
\(382\) | −38.8847 | −1.98951 | ||||||||
\(383\) | 8.35280 | 0.426808 | 0.213404 | − | 0.976964i | \(-0.431545\pi\) | ||||
0.213404 | + | 0.976964i | \(0.431545\pi\) | |||||||
\(384\) | −14.8265 | −0.756614 | ||||||||
\(385\) | 1.23547 | 0.0629656 | ||||||||
\(386\) | −13.4640 | −0.685301 | ||||||||
\(387\) | −7.93895 | −0.403559 | ||||||||
\(388\) | 24.2331 | 1.23025 | ||||||||
\(389\) | −7.06102 | −0.358008 | −0.179004 | − | 0.983848i | \(-0.557288\pi\) | ||||
−0.179004 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(390\) | 2.99044 | 0.151427 | ||||||||
\(391\) | −3.15723 | −0.159668 | ||||||||
\(392\) | −14.4453 | −0.729596 | ||||||||
\(393\) | 0.291671 | 0.0147129 | ||||||||
\(394\) | 23.5246 | 1.18515 | ||||||||
\(395\) | −16.2379 | −0.817018 | ||||||||
\(396\) | 14.3484 | 0.721034 | ||||||||
\(397\) | −29.9950 | −1.50540 | −0.752702 | − | 0.658361i | \(-0.771250\pi\) | ||||
−0.752702 | + | 0.658361i | \(0.771250\pi\) | |||||||
\(398\) | −59.6329 | −2.98912 | ||||||||
\(399\) | −1.38329 | −0.0692513 | ||||||||
\(400\) | 4.93222 | 0.246611 | ||||||||
\(401\) | 24.7567 | 1.23629 | 0.618145 | − | 0.786064i | \(-0.287885\pi\) | ||||
0.618145 | + | 0.786064i | \(0.287885\pi\) | |||||||
\(402\) | −0.973464 | −0.0485520 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.44494 | 0.0718883 | ||||||||
\(405\) | 1.02426 | 0.0508957 | ||||||||
\(406\) | −3.60552 | −0.178939 | ||||||||
\(407\) | 37.3307 | 1.85041 | ||||||||
\(408\) | 13.7848 | 0.682450 | ||||||||
\(409\) | 3.87563 | 0.191637 | 0.0958187 | − | 0.995399i | \(-0.469453\pi\) | ||||
0.0958187 | + | 0.995399i | \(0.469453\pi\) | |||||||
\(410\) | 23.3458 | 1.15297 | ||||||||
\(411\) | −0.382882 | −0.0188862 | ||||||||
\(412\) | 22.7980 | 1.12318 | ||||||||
\(413\) | −0.216753 | −0.0106657 | ||||||||
\(414\) | −1.05940 | −0.0520665 | ||||||||
\(415\) | −8.74176 | −0.429116 | ||||||||
\(416\) | −9.11564 | −0.446931 | ||||||||
\(417\) | 4.82874 | 0.236464 | ||||||||
\(418\) | −60.8193 | −2.97477 | ||||||||
\(419\) | −30.5687 | −1.49338 | −0.746689 | − | 0.665174i | \(-0.768358\pi\) | ||||
−0.746689 | + | 0.665174i | \(0.768358\pi\) | |||||||
\(420\) | 0.742697 | 0.0362399 | ||||||||
\(421\) | 2.10232 | 0.102461 | 0.0512303 | − | 0.998687i | \(-0.483686\pi\) | ||||
0.0512303 | + | 0.998687i | \(0.483686\pi\) | |||||||
\(422\) | 5.69985 | 0.277464 | ||||||||
\(423\) | −1.81918 | −0.0884514 | ||||||||
\(424\) | 26.8754 | 1.30519 | ||||||||
\(425\) | −26.1620 | −1.26904 | ||||||||
\(426\) | 9.85302 | 0.477380 | ||||||||
\(427\) | −1.83666 | −0.0888824 | ||||||||
\(428\) | 29.3445 | 1.41842 | ||||||||
\(429\) | 6.41965 | 0.309943 | ||||||||
\(430\) | −18.0675 | −0.871294 | ||||||||
\(431\) | 10.1174 | 0.487340 | 0.243670 | − | 0.969858i | \(-0.421649\pi\) | ||||
0.243670 | + | 0.969858i | \(0.421649\pi\) | |||||||
\(432\) | −1.24838 | −0.0600626 | ||||||||
\(433\) | −16.4597 | −0.791003 | −0.395502 | − | 0.918465i | \(-0.629429\pi\) | ||||
−0.395502 | + | 0.918465i | \(0.629429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.73187 | −0.322768 | ||||||||
\(436\) | 30.1262 | 1.44278 | ||||||||
\(437\) | 2.67136 | 0.127788 | ||||||||
\(438\) | −3.27568 | −0.156518 | ||||||||
\(439\) | 39.1043 | 1.86634 | 0.933172 | − | 0.359429i | \(-0.117029\pi\) | ||||
0.933172 | + | 0.359429i | \(0.117029\pi\) | |||||||
\(440\) | 10.4171 | 0.496615 | ||||||||
\(441\) | −6.93904 | −0.330431 | ||||||||
\(442\) | 19.3331 | 0.919581 | ||||||||
\(443\) | −10.0114 | −0.475657 | −0.237828 | − | 0.971307i | \(-0.576436\pi\) | ||||
−0.237828 | + | 0.971307i | \(0.576436\pi\) | |||||||
\(444\) | 22.4411 | 1.06501 | ||||||||
\(445\) | 13.0910 | 0.620573 | ||||||||
\(446\) | −14.2814 | −0.676245 | ||||||||
\(447\) | −4.72173 | −0.223330 | ||||||||
\(448\) | −3.18921 | −0.150676 | ||||||||
\(449\) | 11.1113 | 0.524376 | 0.262188 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262188 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(450\) | −8.77857 | −0.413826 | ||||||||
\(451\) | 50.1170 | 2.35992 | ||||||||
\(452\) | −51.0859 | −2.40288 | ||||||||
\(453\) | 10.7341 | 0.504333 | ||||||||
\(454\) | −36.5168 | −1.71382 | ||||||||
\(455\) | 0.332292 | 0.0155781 | ||||||||
\(456\) | −11.6635 | −0.546191 | ||||||||
\(457\) | 19.7652 | 0.924578 | 0.462289 | − | 0.886729i | \(-0.347028\pi\) | ||||
0.462289 | + | 0.886729i | \(0.347028\pi\) | |||||||
\(458\) | −38.5930 | −1.80333 | ||||||||
\(459\) | 6.62178 | 0.309078 | ||||||||
\(460\) | −1.43427 | −0.0668730 | ||||||||
\(461\) | 24.7521 | 1.15282 | 0.576410 | − | 0.817161i | \(-0.304453\pi\) | ||||
0.576410 | + | 0.817161i | \(0.304453\pi\) | |||||||
\(462\) | 2.68011 | 0.124690 | ||||||||
\(463\) | 28.7717 | 1.33714 | 0.668568 | − | 0.743651i | \(-0.266908\pi\) | ||||
0.668568 | + | 0.743651i | \(0.266908\pi\) | |||||||
\(464\) | 8.20490 | 0.380903 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −37.8984 | −1.75561 | ||||||||
\(467\) | −4.28353 | −0.198218 | −0.0991091 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991091 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(468\) | 3.85913 | 0.178388 | ||||||||
\(469\) | −0.108170 | −0.00499480 | ||||||||
\(470\) | −4.14010 | −0.190968 | ||||||||
\(471\) | −23.2962 | −1.07343 | ||||||||
\(472\) | −1.82759 | −0.0841215 | ||||||||
\(473\) | −38.7860 | −1.78338 | ||||||||
\(474\) | −35.2249 | −1.61793 | ||||||||
\(475\) | 22.1359 | 1.01567 | ||||||||
\(476\) | 4.80152 | 0.220077 | ||||||||
\(477\) | 12.9101 | 0.591113 | ||||||||
\(478\) | 10.3683 | 0.474237 | ||||||||
\(479\) | −41.0615 | −1.87615 | −0.938075 | − | 0.346434i | \(-0.887393\pi\) | ||||
−0.938075 | + | 0.346434i | \(0.887393\pi\) | |||||||
\(480\) | −7.10553 | −0.324322 | ||||||||
\(481\) | 10.0404 | 0.457804 | ||||||||
\(482\) | −13.4688 | −0.613489 | ||||||||
\(483\) | −0.117718 | −0.00535636 | ||||||||
\(484\) | 37.7936 | 1.71789 | ||||||||
\(485\) | 8.45135 | 0.383756 | ||||||||
\(486\) | 2.22192 | 0.100788 | ||||||||
\(487\) | −25.1767 | −1.14086 | −0.570432 | − | 0.821345i | \(-0.693224\pi\) | ||||
−0.570432 | + | 0.821345i | \(0.693224\pi\) | |||||||
\(488\) | −15.4861 | −0.701024 | ||||||||
\(489\) | −22.9681 | −1.03865 | ||||||||
\(490\) | −15.7919 | −0.713407 | ||||||||
\(491\) | 26.7390 | 1.20672 | 0.603358 | − | 0.797471i | \(-0.293829\pi\) | ||||
0.603358 | + | 0.797471i | \(0.293829\pi\) | |||||||
\(492\) | 30.1275 | 1.35825 | ||||||||
\(493\) | −43.5213 | −1.96010 | ||||||||
\(494\) | −16.3579 | −0.735977 | ||||||||
\(495\) | 5.00404 | 0.224915 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.09485 | 0.0491107 | ||||||||
\(498\) | −18.9635 | −0.849774 | ||||||||
\(499\) | 10.1261 | 0.453308 | 0.226654 | − | 0.973975i | \(-0.427221\pi\) | ||||
0.226654 | + | 0.973975i | \(0.427221\pi\) | |||||||
\(500\) | −26.9256 | −1.20415 | ||||||||
\(501\) | −3.08014 | −0.137610 | ||||||||
\(502\) | −28.0747 | −1.25303 | ||||||||
\(503\) | −5.00755 | −0.223276 | −0.111638 | − | 0.993749i | \(-0.535610\pi\) | ||||
−0.111638 | + | 0.993749i | \(0.535610\pi\) | |||||||
\(504\) | 0.513971 | 0.0228941 | ||||||||
\(505\) | 0.503926 | 0.0224244 | ||||||||
\(506\) | −5.17572 | −0.230089 | ||||||||
\(507\) | −11.2734 | −0.500668 | ||||||||
\(508\) | 11.7772 | 0.522527 | ||||||||
\(509\) | 11.9995 | 0.531867 | 0.265933 | − | 0.963991i | \(-0.414320\pi\) | ||||
0.265933 | + | 0.963991i | \(0.414320\pi\) | |||||||
\(510\) | 15.0699 | 0.667307 | ||||||||
\(511\) | −0.363988 | −0.0161019 | ||||||||
\(512\) | 13.8579 | 0.612439 | ||||||||
\(513\) | −5.60275 | −0.247367 | ||||||||
\(514\) | −31.1520 | −1.37406 | ||||||||
\(515\) | 7.95086 | 0.350357 | ||||||||
\(516\) | −23.3160 | −1.02643 | ||||||||
\(517\) | −8.88765 | −0.390878 | ||||||||
\(518\) | 4.19174 | 0.184174 | ||||||||
\(519\) | −4.57393 | −0.200773 | ||||||||
\(520\) | 2.80177 | 0.122866 | ||||||||
\(521\) | −25.1157 | −1.10034 | −0.550169 | − | 0.835054i | \(-0.685437\pi\) | ||||
−0.550169 | + | 0.835054i | \(0.685437\pi\) | |||||||
\(522\) | −14.6034 | −0.639175 | ||||||||
\(523\) | 29.6809 | 1.29785 | 0.648927 | − | 0.760850i | \(-0.275218\pi\) | ||||
0.648927 | + | 0.760850i | \(0.275218\pi\) | |||||||
\(524\) | 0.856613 | 0.0374213 | ||||||||
\(525\) | −0.975459 | −0.0425725 | ||||||||
\(526\) | −38.2424 | −1.66745 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −6.09899 | −0.265425 | ||||||||
\(529\) | −22.7727 | −0.990116 | ||||||||
\(530\) | 29.3809 | 1.27623 | ||||||||
\(531\) | −0.877915 | −0.0380983 | ||||||||
\(532\) | −4.06261 | −0.176136 | ||||||||
\(533\) | 13.4794 | 0.583859 | ||||||||
\(534\) | 28.3983 | 1.22891 | ||||||||
\(535\) | 10.2340 | 0.442453 | ||||||||
\(536\) | −0.912048 | −0.0393945 | ||||||||
\(537\) | 4.89854 | 0.211388 | ||||||||
\(538\) | 30.2525 | 1.30428 | ||||||||
\(539\) | −33.9010 | −1.46022 | ||||||||
\(540\) | 3.00815 | 0.129450 | ||||||||
\(541\) | 5.45842 | 0.234676 | 0.117338 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117338 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(542\) | 20.5932 | 0.884556 | ||||||||
\(543\) | 20.2801 | 0.870303 | ||||||||
\(544\) | −45.9370 | −1.96953 | ||||||||
\(545\) | 10.5066 | 0.450053 | ||||||||
\(546\) | 0.720841 | 0.0308491 | ||||||||
\(547\) | −41.4354 | −1.77165 | −0.885826 | − | 0.464018i | \(-0.846407\pi\) | ||||
−0.885826 | + | 0.464018i | \(0.846407\pi\) | |||||||
\(548\) | −1.12449 | −0.0480359 | ||||||||
\(549\) | −7.43904 | −0.317490 | ||||||||
\(550\) | −42.8880 | −1.82875 | ||||||||
\(551\) | 36.8238 | 1.56875 | ||||||||
\(552\) | −0.992560 | −0.0422461 | ||||||||
\(553\) | −3.91412 | −0.166446 | ||||||||
\(554\) | −67.0060 | −2.84681 | ||||||||
\(555\) | 7.82640 | 0.332212 | ||||||||
\(556\) | 14.1816 | 0.601433 | ||||||||
\(557\) | −25.2936 | −1.07172 | −0.535861 | − | 0.844306i | \(-0.680013\pi\) | ||||
−0.535861 | + | 0.844306i | \(0.680013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4319 | −0.441221 | ||||||||
\(560\) | −0.315694 | −0.0133405 | ||||||||
\(561\) | 32.3510 | 1.36586 | ||||||||
\(562\) | 0.558499 | 0.0235589 | ||||||||
\(563\) | 10.2214 | 0.430779 | 0.215390 | − | 0.976528i | \(-0.430898\pi\) | ||||
0.215390 | + | 0.976528i | \(0.430898\pi\) | |||||||
\(564\) | −5.34276 | −0.224971 | ||||||||
\(565\) | −17.8163 | −0.749539 | ||||||||
\(566\) | −18.8244 | −0.791247 | ||||||||
\(567\) | 0.246895 | 0.0103686 | ||||||||
\(568\) | 9.23140 | 0.387341 | ||||||||
\(569\) | 23.2771 | 0.975828 | 0.487914 | − | 0.872892i | \(-0.337758\pi\) | ||||
0.487914 | + | 0.872892i | \(0.337758\pi\) | |||||||
\(570\) | −12.7508 | −0.534072 | ||||||||
\(571\) | 11.4224 | 0.478014 | 0.239007 | − | 0.971018i | \(-0.423178\pi\) | ||||
0.239007 | + | 0.971018i | \(0.423178\pi\) | |||||||
\(572\) | 18.8539 | 0.788322 | ||||||||
\(573\) | −17.5005 | −0.731095 | ||||||||
\(574\) | 5.62747 | 0.234886 | ||||||||
\(575\) | 1.88377 | 0.0785585 | ||||||||
\(576\) | −12.9173 | −0.538219 | ||||||||
\(577\) | −24.7326 | −1.02963 | −0.514816 | − | 0.857301i | \(-0.672140\pi\) | ||||
−0.514816 | + | 0.857301i | \(0.672140\pi\) | |||||||
\(578\) | 59.6540 | 2.48128 | ||||||||
\(579\) | −6.05965 | −0.251830 | ||||||||
\(580\) | −19.7709 | −0.820942 | ||||||||
\(581\) | −2.10719 | −0.0874209 | ||||||||
\(582\) | 18.3335 | 0.759948 | ||||||||
\(583\) | 63.0728 | 2.61221 | ||||||||
\(584\) | −3.06902 | −0.126997 | ||||||||
\(585\) | 1.34588 | 0.0556454 | ||||||||
\(586\) | 36.7144 | 1.51666 | ||||||||
\(587\) | −6.83184 | −0.281980 | −0.140990 | − | 0.990011i | \(-0.545029\pi\) | ||||
−0.140990 | + | 0.990011i | \(0.545029\pi\) | |||||||
\(588\) | −20.3793 | −0.840430 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.99797 | −0.0822550 | ||||||||
\(591\) | 10.5875 | 0.435513 | ||||||||
\(592\) | −9.53892 | −0.392047 | ||||||||
\(593\) | 38.6613 | 1.58763 | 0.793814 | − | 0.608160i | \(-0.208092\pi\) | ||||
0.793814 | + | 0.608160i | \(0.208092\pi\) | |||||||
\(594\) | 10.8553 | 0.445396 | ||||||||
\(595\) | 1.67454 | 0.0686495 | ||||||||
\(596\) | −13.8673 | −0.568027 | ||||||||
\(597\) | −26.8385 | −1.09843 | ||||||||
\(598\) | −1.39206 | −0.0569255 | ||||||||
\(599\) | 17.5339 | 0.716414 | 0.358207 | − | 0.933642i | \(-0.383388\pi\) | ||||
0.358207 | + | 0.933642i | \(0.383388\pi\) | |||||||
\(600\) | −8.22473 | −0.335773 | ||||||||
\(601\) | −23.6210 | −0.963522 | −0.481761 | − | 0.876303i | \(-0.660003\pi\) | ||||
−0.481761 | + | 0.876303i | \(0.660003\pi\) | |||||||
\(602\) | −4.35515 | −0.177503 | ||||||||
\(603\) | −0.438119 | −0.0178416 | ||||||||
\(604\) | 31.5252 | 1.28274 | ||||||||
\(605\) | 13.1806 | 0.535868 | ||||||||
\(606\) | 1.09317 | 0.0444068 | ||||||||
\(607\) | 17.4107 | 0.706679 | 0.353339 | − | 0.935495i | \(-0.385046\pi\) | ||||
0.353339 | + | 0.935495i | \(0.385046\pi\) | |||||||
\(608\) | 38.8678 | 1.57630 | ||||||||
\(609\) | −1.62271 | −0.0657554 | ||||||||
\(610\) | −16.9298 | −0.685469 | ||||||||
\(611\) | −2.39042 | −0.0967059 | ||||||||
\(612\) | 19.4476 | 0.786122 | ||||||||
\(613\) | 29.9514 | 1.20972 | 0.604862 | − | 0.796330i | \(-0.293228\pi\) | ||||
0.604862 | + | 0.796330i | \(0.293228\pi\) | |||||||
\(614\) | 7.86852 | 0.317548 | ||||||||
\(615\) | 10.5071 | 0.423685 | ||||||||
\(616\) | 2.51102 | 0.101172 | ||||||||
\(617\) | −10.7265 | −0.431832 | −0.215916 | − | 0.976412i | \(-0.569274\pi\) | ||||
−0.215916 | + | 0.976412i | \(0.569274\pi\) | |||||||
\(618\) | 17.2478 | 0.693808 | ||||||||
\(619\) | 6.91417 | 0.277904 | 0.138952 | − | 0.990299i | \(-0.455627\pi\) | ||||
0.138952 | + | 0.990299i | \(0.455627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.476794 | −0.0191331 | ||||||||
\(622\) | 55.7973 | 2.23727 | ||||||||
\(623\) | 3.15557 | 0.126425 | ||||||||
\(624\) | −1.64038 | −0.0656678 | ||||||||
\(625\) | 10.3641 | 0.414565 | ||||||||
\(626\) | −2.77781 | −0.111024 | ||||||||
\(627\) | −27.3724 | −1.09315 | ||||||||
\(628\) | −68.4187 | −2.73020 | ||||||||
\(629\) | 50.5974 | 2.01745 | ||||||||
\(630\) | 0.561887 | 0.0223861 | ||||||||
\(631\) | −35.8409 | −1.42680 | −0.713401 | − | 0.700756i | \(-0.752846\pi\) | ||||
−0.713401 | + | 0.700756i | \(0.752846\pi\) | |||||||
\(632\) | −33.0026 | −1.31277 | ||||||||
\(633\) | 2.56528 | 0.101961 | ||||||||
\(634\) | 37.4385 | 1.48687 | ||||||||
\(635\) | 4.10732 | 0.162994 | ||||||||
\(636\) | 37.9158 | 1.50346 | ||||||||
\(637\) | −9.11797 | −0.361267 | ||||||||
\(638\) | −71.3456 | −2.82460 | ||||||||
\(639\) | 4.43447 | 0.175425 | ||||||||
\(640\) | −15.1862 | −0.600286 | ||||||||
\(641\) | 0.559732 | 0.0221081 | 0.0110540 | − | 0.999939i | \(-0.496481\pi\) | ||||
0.0110540 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(642\) | 22.2005 | 0.876185 | ||||||||
\(643\) | −24.2021 | −0.954438 | −0.477219 | − | 0.878785i | \(-0.658355\pi\) | ||||
−0.477219 | + | 0.878785i | \(0.658355\pi\) | |||||||
\(644\) | −0.345728 | −0.0136236 | ||||||||
\(645\) | −8.13151 | −0.320178 | ||||||||
\(646\) | −82.4335 | −3.24330 | ||||||||
\(647\) | −21.7594 | −0.855451 | −0.427725 | − | 0.903909i | \(-0.640685\pi\) | ||||
−0.427725 | + | 0.903909i | \(0.640685\pi\) | |||||||
\(648\) | 2.08174 | 0.0817783 | ||||||||
\(649\) | −4.28909 | −0.168361 | ||||||||
\(650\) | −11.5351 | −0.452445 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −67.4552 | −2.64175 | ||||||||
\(653\) | 6.31383 | 0.247079 | 0.123540 | − | 0.992340i | \(-0.460575\pi\) | ||||
0.123540 | + | 0.992340i | \(0.460575\pi\) | |||||||
\(654\) | 22.7920 | 0.891236 | ||||||||
\(655\) | 0.298746 | 0.0116730 | ||||||||
\(656\) | −12.8062 | −0.499996 | ||||||||
\(657\) | −1.47426 | −0.0575163 | ||||||||
\(658\) | −0.997965 | −0.0389047 | ||||||||
\(659\) | −29.7780 | −1.15999 | −0.579994 | − | 0.814621i | \(-0.696945\pi\) | ||||
−0.579994 | + | 0.814621i | \(0.696945\pi\) | |||||||
\(660\) | 14.6964 | 0.572057 | ||||||||
\(661\) | 8.98626 | 0.349525 | 0.174762 | − | 0.984611i | \(-0.444084\pi\) | ||||
0.174762 | + | 0.984611i | \(0.444084\pi\) | |||||||
\(662\) | 21.4490 | 0.833639 | ||||||||
\(663\) | 8.70109 | 0.337922 | ||||||||
\(664\) | −17.7671 | −0.689497 | ||||||||
\(665\) | −1.41685 | −0.0549429 | ||||||||
\(666\) | 16.9778 | 0.657876 | ||||||||
\(667\) | 3.13370 | 0.121338 | ||||||||
\(668\) | −9.04609 | −0.350004 | ||||||||
\(669\) | −6.42752 | −0.248502 | ||||||||
\(670\) | −0.997075 | −0.0385204 | ||||||||
\(671\) | −36.3437 | −1.40303 | ||||||||
\(672\) | −1.71278 | −0.0660718 | ||||||||
\(673\) | 7.98073 | 0.307634 | 0.153817 | − | 0.988099i | \(-0.450843\pi\) | ||||
0.153817 | + | 0.988099i | \(0.450843\pi\) | |||||||
\(674\) | 16.1158 | 0.620756 | ||||||||
\(675\) | −3.95090 | −0.152070 | ||||||||
\(676\) | −33.1089 | −1.27342 | ||||||||
\(677\) | −15.1051 | −0.580534 | −0.290267 | − | 0.956946i | \(-0.593744\pi\) | ||||
−0.290267 | + | 0.956946i | \(0.593744\pi\) | |||||||
\(678\) | −38.6490 | −1.48430 | ||||||||
\(679\) | 2.03719 | 0.0781801 | ||||||||
\(680\) | 14.1192 | 0.541445 | ||||||||
\(681\) | −16.4348 | −0.629784 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.9185 | −0.570841 | −0.285420 | − | 0.958402i | \(-0.592133\pi\) | ||||
−0.285420 | + | 0.958402i | \(0.592133\pi\) | |||||||
\(684\) | −16.4548 | −0.629164 | ||||||||
\(685\) | −0.392169 | −0.0149840 | ||||||||
\(686\) | −7.64669 | −0.291952 | ||||||||
\(687\) | −17.3692 | −0.662678 | ||||||||
\(688\) | 9.91080 | 0.377846 | ||||||||
\(689\) | 16.9640 | 0.646277 | ||||||||
\(690\) | −1.08509 | −0.0413088 | ||||||||
\(691\) | 38.1161 | 1.45000 | 0.725002 | − | 0.688747i | \(-0.241839\pi\) | ||||
0.725002 | + | 0.688747i | \(0.241839\pi\) | |||||||
\(692\) | −13.4332 | −0.510655 | ||||||||
\(693\) | 1.20622 | 0.0458204 | ||||||||
\(694\) | 45.0448 | 1.70988 | ||||||||
\(695\) | 4.94586 | 0.187607 | ||||||||
\(696\) | −13.6821 | −0.518619 | ||||||||
\(697\) | 67.9278 | 2.57295 | ||||||||
\(698\) | 56.8811 | 2.15298 | ||||||||
\(699\) | −17.0566 | −0.645141 | ||||||||
\(700\) | −2.86484 | −0.108281 | ||||||||
\(701\) | −9.47697 | −0.357940 | −0.178970 | − | 0.983855i | \(-0.557277\pi\) | ||||
−0.178970 | + | 0.983855i | \(0.557277\pi\) | |||||||
\(702\) | 2.91962 | 0.110194 | ||||||||
\(703\) | −42.8109 | −1.61465 | ||||||||
\(704\) | −63.1078 | −2.37846 | ||||||||
\(705\) | −1.86330 | −0.0701760 | ||||||||
\(706\) | −17.8214 | −0.670717 | ||||||||
\(707\) | 0.121471 | 0.00456837 | ||||||||
\(708\) | −2.57836 | −0.0969006 | ||||||||
\(709\) | 30.2319 | 1.13538 | 0.567692 | − | 0.823241i | \(-0.307837\pi\) | ||||
0.567692 | + | 0.823241i | \(0.307837\pi\) | |||||||
\(710\) | 10.0920 | 0.378746 | ||||||||
\(711\) | −15.8534 | −0.594548 | ||||||||
\(712\) | 26.6067 | 0.997127 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 3.63258 | 0.135946 | ||||||||
\(715\) | 6.57536 | 0.245904 | ||||||||
\(716\) | 14.3866 | 0.537652 | ||||||||
\(717\) | 4.66639 | 0.174270 | ||||||||
\(718\) | 55.1567 | 2.05843 | ||||||||
\(719\) | −28.1739 | −1.05071 | −0.525355 | − | 0.850883i | \(-0.676067\pi\) | ||||
−0.525355 | + | 0.850883i | \(0.676067\pi\) | |||||||
\(720\) | −1.27866 | −0.0476527 | ||||||||
\(721\) | 1.91654 | 0.0713758 | ||||||||
\(722\) | 27.5313 | 1.02461 | ||||||||
\(723\) | −6.06181 | −0.225441 | ||||||||
\(724\) | 59.5609 | 2.21356 | ||||||||
\(725\) | 25.9671 | 0.964394 | ||||||||
\(726\) | 28.5927 | 1.06117 | ||||||||
\(727\) | 44.0194 | 1.63259 | 0.816294 | − | 0.577637i | \(-0.196025\pi\) | ||||
0.816294 | + | 0.577637i | \(0.196025\pi\) | |||||||
\(728\) | 0.675363 | 0.0250306 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.35513 | −0.124179 | ||||||||
\(731\) | −52.5700 | −1.94437 | ||||||||
\(732\) | −21.8478 | −0.807518 | ||||||||
\(733\) | 24.7799 | 0.915266 | 0.457633 | − | 0.889141i | \(-0.348697\pi\) | ||||
0.457633 | + | 0.889141i | \(0.348697\pi\) | |||||||
\(734\) | −29.8006 | −1.09996 | ||||||||
\(735\) | −7.10735 | −0.262159 | ||||||||
\(736\) | 3.30765 | 0.121921 | ||||||||
\(737\) | −2.14045 | −0.0788444 | ||||||||
\(738\) | 22.7929 | 0.839020 | ||||||||
\(739\) | 24.3667 | 0.896345 | 0.448173 | − | 0.893947i | \(-0.352075\pi\) | ||||
0.448173 | + | 0.893947i | \(0.352075\pi\) | |||||||
\(740\) | 22.9854 | 0.844961 | ||||||||
\(741\) | −7.36207 | −0.270452 | ||||||||
\(742\) | 7.08223 | 0.259997 | ||||||||
\(743\) | −19.2865 | −0.707553 | −0.353777 | − | 0.935330i | \(-0.615103\pi\) | ||||
−0.353777 | + | 0.935330i | \(0.615103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.83626 | −0.177187 | ||||||||
\(746\) | 43.4289 | 1.59004 | ||||||||
\(747\) | −8.53475 | −0.312270 | ||||||||
\(748\) | 95.0119 | 3.47398 | ||||||||
\(749\) | 2.46688 | 0.0901380 | ||||||||
\(750\) | −20.3705 | −0.743827 | ||||||||
\(751\) | −32.7485 | −1.19501 | −0.597505 | − | 0.801865i | \(-0.703841\pi\) | ||||
−0.597505 | + | 0.801865i | \(0.703841\pi\) | |||||||
\(752\) | 2.27102 | 0.0828155 | ||||||||
\(753\) | −12.6354 | −0.460458 | ||||||||
\(754\) | −19.1891 | −0.698824 | ||||||||
\(755\) | 10.9945 | 0.400130 | ||||||||
\(756\) | 0.725109 | 0.0263720 | ||||||||
\(757\) | 18.7991 | 0.683264 | 0.341632 | − | 0.939834i | \(-0.389020\pi\) | ||||
0.341632 | + | 0.939834i | \(0.389020\pi\) | |||||||
\(758\) | 73.1660 | 2.65751 | ||||||||
\(759\) | −2.32940 | −0.0845517 | ||||||||
\(760\) | −11.9464 | −0.433340 | ||||||||
\(761\) | −40.0426 | −1.45154 | −0.725772 | − | 0.687935i | \(-0.758517\pi\) | ||||
−0.725772 | + | 0.687935i | \(0.758517\pi\) | |||||||
\(762\) | 8.91000 | 0.322775 | ||||||||
\(763\) | 2.53260 | 0.0916863 | ||||||||
\(764\) | −51.3975 | −1.85950 | ||||||||
\(765\) | 6.78240 | 0.245218 | ||||||||
\(766\) | 18.5592 | 0.670572 | ||||||||
\(767\) | −1.15359 | −0.0416537 | ||||||||
\(768\) | −7.10881 | −0.256517 | ||||||||
\(769\) | −18.3446 | −0.661522 | −0.330761 | − | 0.943715i | \(-0.607305\pi\) | ||||
−0.330761 | + | 0.943715i | \(0.607305\pi\) | |||||||
\(770\) | 2.74512 | 0.0989272 | ||||||||
\(771\) | −14.0203 | −0.504930 | ||||||||
\(772\) | −17.7966 | −0.640515 | ||||||||
\(773\) | 19.0710 | 0.685935 | 0.342968 | − | 0.939347i | \(-0.388568\pi\) | ||||
0.342968 | + | 0.939347i | \(0.388568\pi\) | |||||||
\(774\) | −17.6397 | −0.634045 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.1769 | 0.616613 | ||||||||
\(777\) | 1.88654 | 0.0676793 | ||||||||
\(778\) | −15.6890 | −0.562478 | ||||||||
\(779\) | −57.4743 | −2.05923 | ||||||||
\(780\) | 3.95274 | 0.141531 | ||||||||
\(781\) | 21.6648 | 0.775227 | ||||||||
\(782\) | −7.01509 | −0.250859 | ||||||||
\(783\) | −6.57245 | −0.234880 | ||||||||
\(784\) | 8.66254 | 0.309377 | ||||||||
\(785\) | −23.8612 | −0.851643 | ||||||||
\(786\) | 0.648069 | 0.0231159 | ||||||||
\(787\) | −0.519440 | −0.0185160 | −0.00925802 | − | 0.999957i | \(-0.502947\pi\) | ||||
−0.00925802 | + | 0.999957i | \(0.502947\pi\) | |||||||
\(788\) | 31.0946 | 1.10770 | ||||||||
\(789\) | −17.2115 | −0.612744 | ||||||||
\(790\) | −36.0793 | −1.28364 | ||||||||
\(791\) | −4.29460 | −0.152699 | ||||||||
\(792\) | 10.1704 | 0.361390 | ||||||||
\(793\) | −9.77497 | −0.347120 | ||||||||
\(794\) | −66.6463 | −2.36519 | ||||||||
\(795\) | 13.2232 | 0.468980 | ||||||||
\(796\) | −78.8222 | −2.79378 | ||||||||
\(797\) | 25.5899 | 0.906442 | 0.453221 | − | 0.891398i | \(-0.350275\pi\) | ||||
0.453221 | + | 0.891398i | \(0.350275\pi\) | |||||||
\(798\) | −3.07356 | −0.108803 | ||||||||
\(799\) | −12.0462 | −0.426163 | ||||||||
\(800\) | 27.4084 | 0.969035 | ||||||||
\(801\) | 12.7810 | 0.451594 | ||||||||
\(802\) | 55.0073 | 1.94237 | ||||||||
\(803\) | −7.20255 | −0.254172 | ||||||||
\(804\) | −1.28672 | −0.0453790 | ||||||||
\(805\) | −0.120574 | −0.00424966 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6155 | 0.479288 | ||||||||
\(808\) | 1.02420 | 0.0360312 | ||||||||
\(809\) | −0.476507 | −0.0167531 | −0.00837655 | − | 0.999965i | \(-0.502666\pi\) | ||||
−0.00837655 | + | 0.999965i | \(0.502666\pi\) | |||||||
\(810\) | 2.27581 | 0.0799638 | ||||||||
\(811\) | −13.8014 | −0.484634 | −0.242317 | − | 0.970197i | \(-0.577907\pi\) | ||||
−0.242317 | + | 0.970197i | \(0.577907\pi\) | |||||||
\(812\) | −4.76574 | −0.167245 | ||||||||
\(813\) | 9.26824 | 0.325051 | ||||||||
\(814\) | 82.9456 | 2.90724 | ||||||||
\(815\) | −23.5252 | −0.824051 | ||||||||
\(816\) | −8.26648 | −0.289385 | ||||||||
\(817\) | 44.4799 | 1.55616 | ||||||||
\(818\) | 8.61132 | 0.301088 | ||||||||
\(819\) | 0.324423 | 0.0113363 | ||||||||
\(820\) | 30.8583 | 1.07762 | ||||||||
\(821\) | 4.57783 | 0.159767 | 0.0798836 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798836 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(822\) | −0.850732 | −0.0296727 | ||||||||
\(823\) | 41.4156 | 1.44366 | 0.721829 | − | 0.692071i | \(-0.243302\pi\) | ||||
0.721829 | + | 0.692071i | \(0.243302\pi\) | |||||||
\(824\) | 16.1596 | 0.562948 | ||||||||
\(825\) | −19.3023 | −0.672019 | ||||||||
\(826\) | −0.481607 | −0.0167572 | ||||||||
\(827\) | 42.8847 | 1.49125 | 0.745623 | − | 0.666368i | \(-0.232152\pi\) | ||||
0.745623 | + | 0.666368i | \(0.232152\pi\) | |||||||
\(828\) | −1.40030 | −0.0486638 | ||||||||
\(829\) | −24.6524 | −0.856213 | −0.428107 | − | 0.903728i | \(-0.640819\pi\) | ||||
−0.428107 | + | 0.903728i | \(0.640819\pi\) | |||||||
\(830\) | −19.4235 | −0.674198 | ||||||||
\(831\) | −30.1569 | −1.04613 | ||||||||
\(832\) | −16.9734 | −0.588447 | ||||||||
\(833\) | −45.9488 | −1.59203 | ||||||||
\(834\) | 10.7291 | 0.371517 | ||||||||
\(835\) | −3.15485 | −0.109178 | ||||||||
\(836\) | −80.3904 | −2.78036 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −67.9210 | −2.34629 | ||||||||
\(839\) | −32.2000 | −1.11167 | −0.555834 | − | 0.831293i | \(-0.687601\pi\) | ||||
−0.555834 | + | 0.831293i | \(0.687601\pi\) | |||||||
\(840\) | 0.526438 | 0.0181638 | ||||||||
\(841\) | 14.1971 | 0.489555 | ||||||||
\(842\) | 4.67117 | 0.160979 | ||||||||
\(843\) | 0.251359 | 0.00865728 | ||||||||
\(844\) | 7.53401 | 0.259331 | ||||||||
\(845\) | −11.5468 | −0.397223 | ||||||||
\(846\) | −4.04206 | −0.138969 | ||||||||
\(847\) | 3.17717 | 0.109169 | ||||||||
\(848\) | −16.1167 | −0.553449 | ||||||||
\(849\) | −8.47213 | −0.290763 | ||||||||
\(850\) | −58.1298 | −1.99383 | ||||||||
\(851\) | −3.64321 | −0.124888 | ||||||||
\(852\) | 13.0236 | 0.446183 | ||||||||
\(853\) | 43.8610 | 1.50177 | 0.750886 | − | 0.660431i | \(-0.229627\pi\) | ||||
0.750886 | + | 0.660431i | \(0.229627\pi\) | |||||||
\(854\) | −4.08091 | −0.139646 | ||||||||
\(855\) | −5.73865 | −0.196258 | ||||||||
\(856\) | 20.7999 | 0.710927 | ||||||||
\(857\) | −18.0501 | −0.616581 | −0.308290 | − | 0.951292i | \(-0.599757\pi\) | ||||
−0.308290 | + | 0.951292i | \(0.599757\pi\) | |||||||
\(858\) | 14.2639 | 0.486962 | ||||||||
\(859\) | −42.0106 | −1.43338 | −0.716692 | − | 0.697390i | \(-0.754345\pi\) | ||||
−0.716692 | + | 0.697390i | \(0.754345\pi\) | |||||||
\(860\) | −23.8815 | −0.814353 | ||||||||
\(861\) | 2.53271 | 0.0863145 | ||||||||
\(862\) | 22.4801 | 0.765676 | ||||||||
\(863\) | 16.3390 | 0.556186 | 0.278093 | − | 0.960554i | \(-0.410298\pi\) | ||||
0.278093 | + | 0.960554i | \(0.410298\pi\) | |||||||
\(864\) | −6.93726 | −0.236010 | ||||||||
\(865\) | −4.68487 | −0.159290 | ||||||||
\(866\) | −36.5721 | −1.24277 | ||||||||
\(867\) | 26.8480 | 0.911806 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −77.4523 | −2.62739 | ||||||||
\(870\) | −14.9576 | −0.507112 | ||||||||
\(871\) | −0.575693 | −0.0195066 | ||||||||
\(872\) | 21.3540 | 0.723139 | ||||||||
\(873\) | 8.25122 | 0.279261 | ||||||||
\(874\) | 5.93553 | 0.200772 | ||||||||
\(875\) | −2.26354 | −0.0765216 | ||||||||
\(876\) | −4.32977 | −0.146289 | ||||||||
\(877\) | 33.9713 | 1.14713 | 0.573564 | − | 0.819161i | \(-0.305560\pi\) | ||||
0.573564 | + | 0.819161i | \(0.305560\pi\) | |||||||
\(878\) | 86.8864 | 2.93227 | ||||||||
\(879\) | 16.5238 | 0.557333 | ||||||||
\(880\) | −6.24693 | −0.210584 | ||||||||
\(881\) | 47.4247 | 1.59778 | 0.798889 | − | 0.601478i | \(-0.205421\pi\) | ||||
0.798889 | + | 0.601478i | \(0.205421\pi\) | |||||||
\(882\) | −15.4180 | −0.519150 | ||||||||
\(883\) | 32.4675 | 1.09262 | 0.546310 | − | 0.837583i | \(-0.316032\pi\) | ||||
0.546310 | + | 0.837583i | \(0.316032\pi\) | |||||||
\(884\) | 25.5543 | 0.859485 | ||||||||
\(885\) | −0.899209 | −0.0302266 | ||||||||
\(886\) | −22.2445 | −0.747320 | ||||||||
\(887\) | 21.9399 | 0.736670 | 0.368335 | − | 0.929693i | \(-0.379928\pi\) | ||||
0.368335 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(888\) | 15.9067 | 0.533793 | ||||||||
\(889\) | 0.990063 | 0.0332057 | ||||||||
\(890\) | 29.0871 | 0.975002 | ||||||||
\(891\) | 4.88554 | 0.163672 | ||||||||
\(892\) | −18.8771 | −0.632051 | ||||||||
\(893\) | 10.1924 | 0.341075 | ||||||||
\(894\) | −10.4913 | −0.350881 | ||||||||
\(895\) | 5.01736 | 0.167712 | ||||||||
\(896\) | −3.66060 | −0.122292 | ||||||||
\(897\) | −0.626512 | −0.0209186 | ||||||||
\(898\) | 24.6884 | 0.823864 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −11.6034 | −0.386781 | ||||||||
\(901\) | 85.4878 | 2.84801 | ||||||||
\(902\) | 111.356 | 3.70774 | ||||||||
\(903\) | −1.96009 | −0.0652277 | ||||||||
\(904\) | −36.2106 | −1.20435 | ||||||||
\(905\) | 20.7720 | 0.690485 | ||||||||
\(906\) | 23.8503 | 0.792374 | ||||||||
\(907\) | 8.76232 | 0.290948 | 0.145474 | − | 0.989362i | \(-0.453529\pi\) | ||||
0.145474 | + | 0.989362i | \(0.453529\pi\) | |||||||
\(908\) | −48.2676 | −1.60182 | ||||||||
\(909\) | 0.491992 | 0.0163184 | ||||||||
\(910\) | 0.738325 | 0.0244752 | ||||||||
\(911\) | 23.6888 | 0.784845 | 0.392422 | − | 0.919785i | \(-0.371637\pi\) | ||||
0.392422 | + | 0.919785i | \(0.371637\pi\) | |||||||
\(912\) | 6.99435 | 0.231606 | ||||||||
\(913\) | −41.6968 | −1.37996 | ||||||||
\(914\) | 43.9167 | 1.45263 | ||||||||
\(915\) | −7.61948 | −0.251892 | ||||||||
\(916\) | −51.0119 | −1.68548 | ||||||||
\(917\) | 0.0720123 | 0.00237806 | ||||||||
\(918\) | 14.7130 | 0.485603 | ||||||||
\(919\) | 27.4194 | 0.904481 | 0.452241 | − | 0.891896i | \(-0.350625\pi\) | ||||
0.452241 | + | 0.891896i | \(0.350625\pi\) | |||||||
\(920\) | −1.01663 | −0.0335175 | ||||||||
\(921\) | 3.54132 | 0.116691 | ||||||||
\(922\) | 54.9970 | 1.81123 | ||||||||
\(923\) | 5.82694 | 0.191796 | ||||||||
\(924\) | 3.54255 | 0.116541 | ||||||||
\(925\) | −30.1891 | −0.992610 | ||||||||
\(926\) | 63.9284 | 2.10082 | ||||||||
\(927\) | 7.76258 | 0.254956 | ||||||||
\(928\) | 45.5948 | 1.49672 | ||||||||
\(929\) | 24.5453 | 0.805304 | 0.402652 | − | 0.915353i | \(-0.368088\pi\) | ||||
0.402652 | + | 0.915353i | \(0.368088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.8777 | 1.27417 | ||||||||
\(932\) | −50.0938 | −1.64088 | ||||||||
\(933\) | 25.1123 | 0.822139 | ||||||||
\(934\) | −9.51764 | −0.311427 | ||||||||
\(935\) | 33.1356 | 1.08365 | ||||||||
\(936\) | 2.73542 | 0.0894101 | ||||||||
\(937\) | −6.50507 | −0.212511 | −0.106256 | − | 0.994339i | \(-0.533886\pi\) | ||||
−0.106256 | + | 0.994339i | \(0.533886\pi\) | |||||||
\(938\) | −0.240344 | −0.00784750 | ||||||||
\(939\) | −1.25019 | −0.0407983 | ||||||||
\(940\) | −5.47235 | −0.178488 | ||||||||
\(941\) | 30.8349 | 1.00519 | 0.502595 | − | 0.864522i | \(-0.332379\pi\) | ||||
0.502595 | + | 0.864522i | \(0.332379\pi\) | |||||||
\(942\) | −51.7621 | −1.68650 | ||||||||
\(943\) | −4.89107 | −0.159275 | ||||||||
\(944\) | 1.09597 | 0.0356707 | ||||||||
\(945\) | 0.252884 | 0.00822631 | ||||||||
\(946\) | −86.1793 | −2.80193 | ||||||||
\(947\) | 28.8158 | 0.936389 | 0.468194 | − | 0.883625i | \(-0.344905\pi\) | ||||
0.468194 | + | 0.883625i | \(0.344905\pi\) | |||||||
\(948\) | −46.5600 | −1.51220 | ||||||||
\(949\) | −1.93719 | −0.0628839 | ||||||||
\(950\) | 49.1841 | 1.59574 | ||||||||
\(951\) | 16.8497 | 0.546388 | ||||||||
\(952\) | 3.40340 | 0.110305 | ||||||||
\(953\) | 24.6753 | 0.799312 | 0.399656 | − | 0.916665i | \(-0.369129\pi\) | ||||
0.399656 | + | 0.916665i | \(0.369129\pi\) | |||||||
\(954\) | 28.6851 | 0.928716 | ||||||||
\(955\) | −17.9250 | −0.580039 | ||||||||
\(956\) | 13.7048 | 0.443244 | ||||||||
\(957\) | −32.1099 | −1.03797 | ||||||||
\(958\) | −91.2353 | −2.94768 | ||||||||
\(959\) | −0.0945318 | −0.00305259 | ||||||||
\(960\) | −13.2306 | −0.427015 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 22.3090 | 0.719271 | ||||||||
\(963\) | 9.99162 | 0.321975 | ||||||||
\(964\) | −17.8030 | −0.573396 | ||||||||
\(965\) | −6.20662 | −0.199798 | ||||||||
\(966\) | −0.261560 | −0.00841555 | ||||||||
\(967\) | −31.0647 | −0.998973 | −0.499486 | − | 0.866322i | \(-0.666478\pi\) | ||||
−0.499486 | + | 0.866322i | \(0.666478\pi\) | |||||||
\(968\) | 26.7888 | 0.861024 | ||||||||
\(969\) | −37.1002 | −1.19183 | ||||||||
\(970\) | 18.7782 | 0.602932 | ||||||||
\(971\) | −43.4539 | −1.39450 | −0.697250 | − | 0.716828i | \(-0.745593\pi\) | ||||
−0.697250 | + | 0.716828i | \(0.745593\pi\) | |||||||
\(972\) | 2.93691 | 0.0942015 | ||||||||
\(973\) | 1.19219 | 0.0382199 | ||||||||
\(974\) | −55.9405 | −1.79245 | ||||||||
\(975\) | −5.19152 | −0.166262 | ||||||||
\(976\) | 9.28673 | 0.297261 | ||||||||
\(977\) | −30.7060 | −0.982372 | −0.491186 | − | 0.871055i | \(-0.663437\pi\) | ||||
−0.491186 | + | 0.871055i | \(0.663437\pi\) | |||||||
\(978\) | −51.0331 | −1.63186 | ||||||||
\(979\) | 62.4420 | 1.99566 | ||||||||
\(980\) | −20.8737 | −0.666785 | ||||||||
\(981\) | 10.2578 | 0.327506 | ||||||||
\(982\) | 59.4119 | 1.89591 | ||||||||
\(983\) | 56.0862 | 1.78887 | 0.894436 | − | 0.447196i | \(-0.147577\pi\) | ||||
0.894436 | + | 0.447196i | \(0.147577\pi\) | |||||||
\(984\) | 21.3549 | 0.680771 | ||||||||
\(985\) | 10.8443 | 0.345529 | ||||||||
\(986\) | −96.7007 | −3.07958 | ||||||||
\(987\) | −0.449146 | −0.0142965 | ||||||||
\(988\) | −21.6217 | −0.687879 | ||||||||
\(989\) | 3.78524 | 0.120364 | ||||||||
\(990\) | 11.1186 | 0.353371 | ||||||||
\(991\) | 16.8077 | 0.533915 | 0.266957 | − | 0.963708i | \(-0.413982\pi\) | ||||
0.266957 | + | 0.963708i | \(0.413982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.65338 | 0.306341 | ||||||||
\(994\) | 2.43266 | 0.0771594 | ||||||||
\(995\) | −27.4895 | −0.871475 | ||||||||
\(996\) | −25.0658 | −0.794240 | ||||||||
\(997\) | 39.4217 | 1.24850 | 0.624248 | − | 0.781226i | \(-0.285405\pi\) | ||||
0.624248 | + | 0.781226i | \(0.285405\pi\) | |||||||
\(998\) | 22.4994 | 0.712207 | ||||||||
\(999\) | 7.64106 | 0.241752 |
(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 | 2883.2.a.v.1.21 | yes | 24 | |
3.2 | odd | 2 | 8649.2.a.bu.1.4 | 24 | |||
31.30 | odd | 2 | 2883.2.a.u.1.21 | ✓ | 24 | ||
93.92 | even | 2 | 8649.2.a.bv.1.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2883.2.a.u.1.21 | ✓ | 24 | 31.30 | odd | 2 | ||
2883.2.a.v.1.21 | yes | 24 | 1.1 | even | 1 | trivial | |
8649.2.a.bu.1.4 | 24 | 3.2 | odd | 2 | |||
8649.2.a.bv.1.4 | 24 | 93.92 | even | 2 |