Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.15603 | −1.82213 | −0.911067 | − | 0.412258i | \(-0.864740\pi\) | ||||
−0.911067 | + | 0.412258i | \(0.864740\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.126707 | 0.0566651 | 0.0283326 | − | 0.999599i | \(-0.490980\pi\) | ||||
0.0283326 | + | 0.999599i | \(0.490980\pi\) | |||||||
\(6\) | −3.15603 | −1.28844 | ||||||||
\(7\) | 5.16404 | 1.95182 | 0.975912 | − | 0.218165i | \(-0.0700069\pi\) | ||||
0.975912 | + | 0.218165i | \(0.0700069\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.96052 | 2.32017 | ||||||||
\(10\) | 0.126707 | 0.0400683 | ||||||||
\(11\) | −3.20397 | −0.966035 | −0.483017 | − | 0.875611i | \(-0.660459\pi\) | ||||
−0.483017 | + | 0.875611i | \(0.660459\pi\) | |||||||
\(12\) | −3.15603 | −0.911067 | ||||||||
\(13\) | 0.276972 | 0.0768181 | 0.0384091 | − | 0.999262i | \(-0.487771\pi\) | ||||
0.0384091 | + | 0.999262i | \(0.487771\pi\) | |||||||
\(14\) | 5.16404 | 1.38015 | ||||||||
\(15\) | −0.399891 | −0.103251 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.29296 | 0.556124 | 0.278062 | − | 0.960563i | \(-0.410308\pi\) | ||||
0.278062 | + | 0.960563i | \(0.410308\pi\) | |||||||
\(18\) | 6.96052 | 1.64061 | ||||||||
\(19\) | −4.61432 | −1.05860 | −0.529299 | − | 0.848436i | \(-0.677545\pi\) | ||||
−0.529299 | + | 0.848436i | \(0.677545\pi\) | |||||||
\(20\) | 0.126707 | 0.0283326 | ||||||||
\(21\) | −16.2979 | −3.55648 | ||||||||
\(22\) | −3.20397 | −0.683090 | ||||||||
\(23\) | 0.949092 | 0.197899 | 0.0989497 | − | 0.995092i | \(-0.468452\pi\) | ||||
0.0989497 | + | 0.995092i | \(0.468452\pi\) | |||||||
\(24\) | −3.15603 | −0.644222 | ||||||||
\(25\) | −4.98395 | −0.996789 | ||||||||
\(26\) | 0.276972 | 0.0543186 | ||||||||
\(27\) | −12.4995 | −2.40553 | ||||||||
\(28\) | 5.16404 | 0.975912 | ||||||||
\(29\) | −4.64072 | −0.861760 | −0.430880 | − | 0.902409i | \(-0.641797\pi\) | ||||
−0.430880 | + | 0.902409i | \(0.641797\pi\) | |||||||
\(30\) | −0.399891 | −0.0730098 | ||||||||
\(31\) | 0.973237 | 0.174799 | 0.0873993 | − | 0.996173i | \(-0.472144\pi\) | ||||
0.0873993 | + | 0.996173i | \(0.472144\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 10.1118 | 1.76024 | ||||||||
\(34\) | 2.29296 | 0.393239 | ||||||||
\(35\) | 0.654321 | 0.110600 | ||||||||
\(36\) | 6.96052 | 1.16009 | ||||||||
\(37\) | 9.85731 | 1.62053 | 0.810266 | − | 0.586062i | \(-0.199323\pi\) | ||||
0.810266 | + | 0.586062i | \(0.199323\pi\) | |||||||
\(38\) | −4.61432 | −0.748541 | ||||||||
\(39\) | −0.874131 | −0.139973 | ||||||||
\(40\) | 0.126707 | 0.0200342 | ||||||||
\(41\) | 5.49741 | 0.858551 | 0.429275 | − | 0.903174i | \(-0.358769\pi\) | ||||
0.429275 | + | 0.903174i | \(0.358769\pi\) | |||||||
\(42\) | −16.2979 | −2.51481 | ||||||||
\(43\) | 6.34943 | 0.968279 | 0.484139 | − | 0.874991i | \(-0.339133\pi\) | ||||
0.484139 | + | 0.874991i | \(0.339133\pi\) | |||||||
\(44\) | −3.20397 | −0.483017 | ||||||||
\(45\) | 0.881947 | 0.131473 | ||||||||
\(46\) | 0.949092 | 0.139936 | ||||||||
\(47\) | 7.68155 | 1.12047 | 0.560235 | − | 0.828334i | \(-0.310711\pi\) | ||||
0.560235 | + | 0.828334i | \(0.310711\pi\) | |||||||
\(48\) | −3.15603 | −0.455533 | ||||||||
\(49\) | 19.6673 | 2.80962 | ||||||||
\(50\) | −4.98395 | −0.704836 | ||||||||
\(51\) | −7.23664 | −1.01333 | ||||||||
\(52\) | 0.276972 | 0.0384091 | ||||||||
\(53\) | 5.93359 | 0.815041 | 0.407521 | − | 0.913196i | \(-0.366393\pi\) | ||||
0.407521 | + | 0.913196i | \(0.366393\pi\) | |||||||
\(54\) | −12.4995 | −1.70097 | ||||||||
\(55\) | −0.405966 | −0.0547405 | ||||||||
\(56\) | 5.16404 | 0.690074 | ||||||||
\(57\) | 14.5629 | 1.92891 | ||||||||
\(58\) | −4.64072 | −0.609356 | ||||||||
\(59\) | −5.08216 | −0.661641 | −0.330820 | − | 0.943694i | \(-0.607325\pi\) | ||||
−0.330820 | + | 0.943694i | \(0.607325\pi\) | |||||||
\(60\) | −0.399891 | −0.0516257 | ||||||||
\(61\) | −3.09134 | −0.395805 | −0.197903 | − | 0.980222i | \(-0.563413\pi\) | ||||
−0.197903 | + | 0.980222i | \(0.563413\pi\) | |||||||
\(62\) | 0.973237 | 0.123601 | ||||||||
\(63\) | 35.9444 | 4.52857 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0350943 | 0.00435291 | ||||||||
\(66\) | 10.1118 | 1.24468 | ||||||||
\(67\) | 0.425022 | 0.0519247 | 0.0259623 | − | 0.999663i | \(-0.491735\pi\) | ||||
0.0259623 | + | 0.999663i | \(0.491735\pi\) | |||||||
\(68\) | 2.29296 | 0.278062 | ||||||||
\(69\) | −2.99536 | −0.360599 | ||||||||
\(70\) | 0.654321 | 0.0782063 | ||||||||
\(71\) | 1.39943 | 0.166081 | 0.0830406 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830406 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(72\) | 6.96052 | 0.820305 | ||||||||
\(73\) | −3.07623 | −0.360046 | −0.180023 | − | 0.983662i | \(-0.557617\pi\) | ||||
−0.180023 | + | 0.983662i | \(0.557617\pi\) | |||||||
\(74\) | 9.85731 | 1.14589 | ||||||||
\(75\) | 15.7295 | 1.81628 | ||||||||
\(76\) | −4.61432 | −0.529299 | ||||||||
\(77\) | −16.5455 | −1.88553 | ||||||||
\(78\) | −0.874131 | −0.0989758 | ||||||||
\(79\) | −14.3331 | −1.61259 | −0.806297 | − | 0.591510i | \(-0.798532\pi\) | ||||
−0.806297 | + | 0.591510i | \(0.798532\pi\) | |||||||
\(80\) | 0.126707 | 0.0141663 | ||||||||
\(81\) | 18.5672 | 2.06303 | ||||||||
\(82\) | 5.49741 | 0.607087 | ||||||||
\(83\) | 3.20258 | 0.351529 | 0.175764 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175764 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(84\) | −16.2979 | −1.77824 | ||||||||
\(85\) | 0.290534 | 0.0315129 | ||||||||
\(86\) | 6.34943 | 0.684676 | ||||||||
\(87\) | 14.6462 | 1.57024 | ||||||||
\(88\) | −3.20397 | −0.341545 | ||||||||
\(89\) | 14.2139 | 1.50667 | 0.753337 | − | 0.657635i | \(-0.228443\pi\) | ||||
0.753337 | + | 0.657635i | \(0.228443\pi\) | |||||||
\(90\) | 0.881947 | 0.0929654 | ||||||||
\(91\) | 1.43029 | 0.149936 | ||||||||
\(92\) | 0.949092 | 0.0989497 | ||||||||
\(93\) | −3.07156 | −0.318506 | ||||||||
\(94\) | 7.68155 | 0.792292 | ||||||||
\(95\) | −0.584667 | −0.0599856 | ||||||||
\(96\) | −3.15603 | −0.322111 | ||||||||
\(97\) | −12.5799 | −1.27730 | −0.638649 | − | 0.769498i | \(-0.720507\pi\) | ||||
−0.638649 | + | 0.769498i | \(0.720507\pi\) | |||||||
\(98\) | 19.6673 | 1.98670 | ||||||||
\(99\) | −22.3013 | −2.24137 | ||||||||
\(100\) | −4.98395 | −0.498395 | ||||||||
\(101\) | 0.599044 | 0.0596071 | 0.0298035 | − | 0.999556i | \(-0.490512\pi\) | ||||
0.0298035 | + | 0.999556i | \(0.490512\pi\) | |||||||
\(102\) | −7.23664 | −0.716534 | ||||||||
\(103\) | 7.14033 | 0.703557 | 0.351779 | − | 0.936083i | \(-0.385577\pi\) | ||||
0.351779 | + | 0.936083i | \(0.385577\pi\) | |||||||
\(104\) | 0.276972 | 0.0271593 | ||||||||
\(105\) | −2.06505 | −0.201529 | ||||||||
\(106\) | 5.93359 | 0.576321 | ||||||||
\(107\) | −18.9606 | −1.83299 | −0.916494 | − | 0.400049i | \(-0.868993\pi\) | ||||
−0.916494 | + | 0.400049i | \(0.868993\pi\) | |||||||
\(108\) | −12.4995 | −1.20276 | ||||||||
\(109\) | −11.0546 | −1.05884 | −0.529420 | − | 0.848360i | \(-0.677590\pi\) | ||||
−0.529420 | + | 0.848360i | \(0.677590\pi\) | |||||||
\(110\) | −0.405966 | −0.0387074 | ||||||||
\(111\) | −31.1100 | −2.95283 | ||||||||
\(112\) | 5.16404 | 0.487956 | ||||||||
\(113\) | 15.9633 | 1.50170 | 0.750849 | − | 0.660473i | \(-0.229644\pi\) | ||||
0.750849 | + | 0.660473i | \(0.229644\pi\) | |||||||
\(114\) | 14.5629 | 1.36394 | ||||||||
\(115\) | 0.120257 | 0.0112140 | ||||||||
\(116\) | −4.64072 | −0.430880 | ||||||||
\(117\) | 1.92787 | 0.178231 | ||||||||
\(118\) | −5.08216 | −0.467851 | ||||||||
\(119\) | 11.8409 | 1.08546 | ||||||||
\(120\) | −0.399891 | −0.0365049 | ||||||||
\(121\) | −0.734548 | −0.0667771 | ||||||||
\(122\) | −3.09134 | −0.279876 | ||||||||
\(123\) | −17.3500 | −1.56439 | ||||||||
\(124\) | 0.973237 | 0.0873993 | ||||||||
\(125\) | −1.26504 | −0.113148 | ||||||||
\(126\) | 35.9444 | 3.20218 | ||||||||
\(127\) | 10.2657 | 0.910933 | 0.455467 | − | 0.890253i | \(-0.349472\pi\) | ||||
0.455467 | + | 0.890253i | \(0.349472\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −20.0390 | −1.76433 | ||||||||
\(130\) | 0.0350943 | 0.00307797 | ||||||||
\(131\) | 16.8058 | 1.46833 | 0.734164 | − | 0.678972i | \(-0.237574\pi\) | ||||
0.734164 | + | 0.678972i | \(0.237574\pi\) | |||||||
\(132\) | 10.1118 | 0.880122 | ||||||||
\(133\) | −23.8285 | −2.06620 | ||||||||
\(134\) | 0.425022 | 0.0367163 | ||||||||
\(135\) | −1.58378 | −0.136310 | ||||||||
\(136\) | 2.29296 | 0.196620 | ||||||||
\(137\) | 4.73370 | 0.404427 | 0.202213 | − | 0.979341i | \(-0.435187\pi\) | ||||
0.202213 | + | 0.979341i | \(0.435187\pi\) | |||||||
\(138\) | −2.99536 | −0.254982 | ||||||||
\(139\) | −3.84059 | −0.325755 | −0.162877 | − | 0.986646i | \(-0.552078\pi\) | ||||
−0.162877 | + | 0.986646i | \(0.552078\pi\) | |||||||
\(140\) | 0.654321 | 0.0553002 | ||||||||
\(141\) | −24.2432 | −2.04165 | ||||||||
\(142\) | 1.39943 | 0.117437 | ||||||||
\(143\) | −0.887411 | −0.0742090 | ||||||||
\(144\) | 6.96052 | 0.580043 | ||||||||
\(145\) | −0.588012 | −0.0488317 | ||||||||
\(146\) | −3.07623 | −0.254591 | ||||||||
\(147\) | −62.0706 | −5.11950 | ||||||||
\(148\) | 9.85731 | 0.810266 | ||||||||
\(149\) | −11.2899 | −0.924901 | −0.462451 | − | 0.886645i | \(-0.653030\pi\) | ||||
−0.462451 | + | 0.886645i | \(0.653030\pi\) | |||||||
\(150\) | 15.7295 | 1.28431 | ||||||||
\(151\) | −1.17424 | −0.0955585 | −0.0477793 | − | 0.998858i | \(-0.515214\pi\) | ||||
−0.0477793 | + | 0.998858i | \(0.515214\pi\) | |||||||
\(152\) | −4.61432 | −0.374271 | ||||||||
\(153\) | 15.9602 | 1.29030 | ||||||||
\(154\) | −16.5455 | −1.33327 | ||||||||
\(155\) | 0.123316 | 0.00990498 | ||||||||
\(156\) | −0.874131 | −0.0699865 | ||||||||
\(157\) | 13.6147 | 1.08658 | 0.543288 | − | 0.839547i | \(-0.317179\pi\) | ||||
0.543288 | + | 0.839547i | \(0.317179\pi\) | |||||||
\(158\) | −14.3331 | −1.14028 | ||||||||
\(159\) | −18.7266 | −1.48511 | ||||||||
\(160\) | 0.126707 | 0.0100171 | ||||||||
\(161\) | 4.90115 | 0.386265 | ||||||||
\(162\) | 18.5672 | 1.45878 | ||||||||
\(163\) | 13.1528 | 1.03021 | 0.515104 | − | 0.857127i | \(-0.327753\pi\) | ||||
0.515104 | + | 0.857127i | \(0.327753\pi\) | |||||||
\(164\) | 5.49741 | 0.429275 | ||||||||
\(165\) | 1.28124 | 0.0997445 | ||||||||
\(166\) | 3.20258 | 0.248568 | ||||||||
\(167\) | 16.3881 | 1.26815 | 0.634074 | − | 0.773272i | \(-0.281381\pi\) | ||||
0.634074 | + | 0.773272i | \(0.281381\pi\) | |||||||
\(168\) | −16.2979 | −1.25741 | ||||||||
\(169\) | −12.9233 | −0.994099 | ||||||||
\(170\) | 0.290534 | 0.0222830 | ||||||||
\(171\) | −32.1180 | −2.45613 | ||||||||
\(172\) | 6.34943 | 0.484139 | ||||||||
\(173\) | 18.7770 | 1.42759 | 0.713796 | − | 0.700354i | \(-0.246974\pi\) | ||||
0.713796 | + | 0.700354i | \(0.246974\pi\) | |||||||
\(174\) | 14.6462 | 1.11033 | ||||||||
\(175\) | −25.7373 | −1.94556 | ||||||||
\(176\) | −3.20397 | −0.241509 | ||||||||
\(177\) | 16.0394 | 1.20560 | ||||||||
\(178\) | 14.2139 | 1.06538 | ||||||||
\(179\) | −6.43092 | −0.480670 | −0.240335 | − | 0.970690i | \(-0.577257\pi\) | ||||
−0.240335 | + | 0.970690i | \(0.577257\pi\) | |||||||
\(180\) | 0.881947 | 0.0657364 | ||||||||
\(181\) | 24.5274 | 1.82311 | 0.911555 | − | 0.411179i | \(-0.134883\pi\) | ||||
0.911555 | + | 0.411179i | \(0.134883\pi\) | |||||||
\(182\) | 1.43029 | 0.106020 | ||||||||
\(183\) | 9.75635 | 0.721210 | ||||||||
\(184\) | 0.949092 | 0.0699680 | ||||||||
\(185\) | 1.24899 | 0.0918277 | ||||||||
\(186\) | −3.07156 | −0.225218 | ||||||||
\(187\) | −7.34658 | −0.537235 | ||||||||
\(188\) | 7.68155 | 0.560235 | ||||||||
\(189\) | −64.5479 | −4.69517 | ||||||||
\(190\) | −0.584667 | −0.0424162 | ||||||||
\(191\) | 9.54659 | 0.690767 | 0.345384 | − | 0.938462i | \(-0.387749\pi\) | ||||
0.345384 | + | 0.938462i | \(0.387749\pi\) | |||||||
\(192\) | −3.15603 | −0.227767 | ||||||||
\(193\) | −5.97063 | −0.429775 | −0.214888 | − | 0.976639i | \(-0.568939\pi\) | ||||
−0.214888 | + | 0.976639i | \(0.568939\pi\) | |||||||
\(194\) | −12.5799 | −0.903187 | ||||||||
\(195\) | −0.110759 | −0.00793159 | ||||||||
\(196\) | 19.6673 | 1.40481 | ||||||||
\(197\) | 11.6397 | 0.829293 | 0.414646 | − | 0.909983i | \(-0.363905\pi\) | ||||
0.414646 | + | 0.909983i | \(0.363905\pi\) | |||||||
\(198\) | −22.3013 | −1.58489 | ||||||||
\(199\) | −13.0399 | −0.924375 | −0.462188 | − | 0.886782i | \(-0.652935\pi\) | ||||
−0.462188 | + | 0.886782i | \(0.652935\pi\) | |||||||
\(200\) | −4.98395 | −0.352418 | ||||||||
\(201\) | −1.34138 | −0.0946137 | ||||||||
\(202\) | 0.599044 | 0.0421486 | ||||||||
\(203\) | −23.9649 | −1.68200 | ||||||||
\(204\) | −7.23664 | −0.506666 | ||||||||
\(205\) | 0.696561 | 0.0486499 | ||||||||
\(206\) | 7.14033 | 0.497490 | ||||||||
\(207\) | 6.60617 | 0.459161 | ||||||||
\(208\) | 0.276972 | 0.0192045 | ||||||||
\(209\) | 14.7842 | 1.02264 | ||||||||
\(210\) | −2.06505 | −0.142502 | ||||||||
\(211\) | −22.7856 | −1.56862 | −0.784311 | − | 0.620368i | \(-0.786983\pi\) | ||||
−0.784311 | + | 0.620368i | \(0.786983\pi\) | |||||||
\(212\) | 5.93359 | 0.407521 | ||||||||
\(213\) | −4.41663 | −0.302622 | ||||||||
\(214\) | −18.9606 | −1.29612 | ||||||||
\(215\) | 0.804518 | 0.0548676 | ||||||||
\(216\) | −12.4995 | −0.850483 | ||||||||
\(217\) | 5.02584 | 0.341176 | ||||||||
\(218\) | −11.0546 | −0.748713 | ||||||||
\(219\) | 9.70868 | 0.656052 | ||||||||
\(220\) | −0.405966 | −0.0273702 | ||||||||
\(221\) | 0.635085 | 0.0427204 | ||||||||
\(222\) | −31.1100 | −2.08796 | ||||||||
\(223\) | −2.39151 | −0.160147 | −0.0800736 | − | 0.996789i | \(-0.525516\pi\) | ||||
−0.0800736 | + | 0.996789i | \(0.525516\pi\) | |||||||
\(224\) | 5.16404 | 0.345037 | ||||||||
\(225\) | −34.6908 | −2.31272 | ||||||||
\(226\) | 15.9633 | 1.06186 | ||||||||
\(227\) | −5.07995 | −0.337168 | −0.168584 | − | 0.985687i | \(-0.553920\pi\) | ||||
−0.168584 | + | 0.985687i | \(0.553920\pi\) | |||||||
\(228\) | 14.5629 | 0.964453 | ||||||||
\(229\) | 5.32645 | 0.351982 | 0.175991 | − | 0.984392i | \(-0.443687\pi\) | ||||
0.175991 | + | 0.984392i | \(0.443687\pi\) | |||||||
\(230\) | 0.120257 | 0.00792949 | ||||||||
\(231\) | 52.2179 | 3.43569 | ||||||||
\(232\) | −4.64072 | −0.304678 | ||||||||
\(233\) | 2.68052 | 0.175607 | 0.0878035 | − | 0.996138i | \(-0.472015\pi\) | ||||
0.0878035 | + | 0.996138i | \(0.472015\pi\) | |||||||
\(234\) | 1.92787 | 0.126029 | ||||||||
\(235\) | 0.973308 | 0.0634916 | ||||||||
\(236\) | −5.08216 | −0.330820 | ||||||||
\(237\) | 45.2355 | 2.93836 | ||||||||
\(238\) | 11.8409 | 0.767534 | ||||||||
\(239\) | −11.0564 | −0.715179 | −0.357590 | − | 0.933879i | \(-0.616401\pi\) | ||||
−0.357590 | + | 0.933879i | \(0.616401\pi\) | |||||||
\(240\) | −0.399891 | −0.0258129 | ||||||||
\(241\) | 5.22346 | 0.336472 | 0.168236 | − | 0.985747i | \(-0.446193\pi\) | ||||
0.168236 | + | 0.985747i | \(0.446193\pi\) | |||||||
\(242\) | −0.734548 | −0.0472185 | ||||||||
\(243\) | −21.1002 | −1.35358 | ||||||||
\(244\) | −3.09134 | −0.197903 | ||||||||
\(245\) | 2.49199 | 0.159207 | ||||||||
\(246\) | −17.3500 | −1.10619 | ||||||||
\(247\) | −1.27804 | −0.0813195 | ||||||||
\(248\) | 0.973237 | 0.0618006 | ||||||||
\(249\) | −10.1074 | −0.640532 | ||||||||
\(250\) | −1.26504 | −0.0800080 | ||||||||
\(251\) | −8.53704 | −0.538853 | −0.269427 | − | 0.963021i | \(-0.586834\pi\) | ||||
−0.269427 | + | 0.963021i | \(0.586834\pi\) | |||||||
\(252\) | 35.9444 | 2.26428 | ||||||||
\(253\) | −3.04087 | −0.191178 | ||||||||
\(254\) | 10.2657 | 0.644127 | ||||||||
\(255\) | −0.916934 | −0.0574206 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.55007 | 0.283825 | 0.141913 | − | 0.989879i | \(-0.454675\pi\) | ||||
0.141913 | + | 0.989879i | \(0.454675\pi\) | |||||||
\(258\) | −20.0390 | −1.24757 | ||||||||
\(259\) | 50.9036 | 3.16299 | ||||||||
\(260\) | 0.0350943 | 0.00217646 | ||||||||
\(261\) | −32.3018 | −1.99943 | ||||||||
\(262\) | 16.8058 | 1.03826 | ||||||||
\(263\) | 19.6713 | 1.21299 | 0.606493 | − | 0.795088i | \(-0.292576\pi\) | ||||
0.606493 | + | 0.795088i | \(0.292576\pi\) | |||||||
\(264\) | 10.1118 | 0.622340 | ||||||||
\(265\) | 0.751828 | 0.0461844 | ||||||||
\(266\) | −23.8285 | −1.46102 | ||||||||
\(267\) | −44.8596 | −2.74536 | ||||||||
\(268\) | 0.425022 | 0.0259623 | ||||||||
\(269\) | −5.55897 | −0.338936 | −0.169468 | − | 0.985536i | \(-0.554205\pi\) | ||||
−0.169468 | + | 0.985536i | \(0.554205\pi\) | |||||||
\(270\) | −1.58378 | −0.0963855 | ||||||||
\(271\) | 0.188715 | 0.0114636 | 0.00573181 | − | 0.999984i | \(-0.498175\pi\) | ||||
0.00573181 | + | 0.999984i | \(0.498175\pi\) | |||||||
\(272\) | 2.29296 | 0.139031 | ||||||||
\(273\) | −4.51405 | −0.273203 | ||||||||
\(274\) | 4.73370 | 0.285973 | ||||||||
\(275\) | 15.9684 | 0.962933 | ||||||||
\(276\) | −2.99536 | −0.180300 | ||||||||
\(277\) | 10.0013 | 0.600918 | 0.300459 | − | 0.953795i | \(-0.402860\pi\) | ||||
0.300459 | + | 0.953795i | \(0.402860\pi\) | |||||||
\(278\) | −3.84059 | −0.230344 | ||||||||
\(279\) | 6.77423 | 0.405563 | ||||||||
\(280\) | 0.654321 | 0.0391031 | ||||||||
\(281\) | 13.2302 | 0.789250 | 0.394625 | − | 0.918842i | \(-0.370874\pi\) | ||||
0.394625 | + | 0.918842i | \(0.370874\pi\) | |||||||
\(282\) | −24.2432 | −1.44366 | ||||||||
\(283\) | −14.8058 | −0.880111 | −0.440056 | − | 0.897970i | \(-0.645041\pi\) | ||||
−0.440056 | + | 0.897970i | \(0.645041\pi\) | |||||||
\(284\) | 1.39943 | 0.0830406 | ||||||||
\(285\) | 1.84523 | 0.109302 | ||||||||
\(286\) | −0.887411 | −0.0524737 | ||||||||
\(287\) | 28.3888 | 1.67574 | ||||||||
\(288\) | 6.96052 | 0.410152 | ||||||||
\(289\) | −11.7423 | −0.690726 | ||||||||
\(290\) | −0.588012 | −0.0345292 | ||||||||
\(291\) | 39.7026 | 2.32741 | ||||||||
\(292\) | −3.07623 | −0.180023 | ||||||||
\(293\) | 27.9134 | 1.63072 | 0.815358 | − | 0.578956i | \(-0.196540\pi\) | ||||
0.815358 | + | 0.578956i | \(0.196540\pi\) | |||||||
\(294\) | −62.0706 | −3.62003 | ||||||||
\(295\) | −0.643946 | −0.0374920 | ||||||||
\(296\) | 9.85731 | 0.572945 | ||||||||
\(297\) | 40.0481 | 2.32383 | ||||||||
\(298\) | −11.2899 | −0.654004 | ||||||||
\(299\) | 0.262872 | 0.0152023 | ||||||||
\(300\) | 15.7295 | 0.908142 | ||||||||
\(301\) | 32.7887 | 1.88991 | ||||||||
\(302\) | −1.17424 | −0.0675701 | ||||||||
\(303\) | −1.89060 | −0.108612 | ||||||||
\(304\) | −4.61432 | −0.264649 | ||||||||
\(305\) | −0.391694 | −0.0224284 | ||||||||
\(306\) | 15.9602 | 0.912382 | ||||||||
\(307\) | −11.6931 | −0.667360 | −0.333680 | − | 0.942686i | \(-0.608290\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608290\pi\) | |||||||
\(308\) | −16.5455 | −0.942765 | ||||||||
\(309\) | −22.5351 | −1.28198 | ||||||||
\(310\) | 0.123316 | 0.00700388 | ||||||||
\(311\) | 12.6235 | 0.715813 | 0.357907 | − | 0.933757i | \(-0.383491\pi\) | ||||
0.357907 | + | 0.933757i | \(0.383491\pi\) | |||||||
\(312\) | −0.874131 | −0.0494879 | ||||||||
\(313\) | −10.0057 | −0.565555 | −0.282777 | − | 0.959186i | \(-0.591256\pi\) | ||||
−0.282777 | + | 0.959186i | \(0.591256\pi\) | |||||||
\(314\) | 13.6147 | 0.768325 | ||||||||
\(315\) | 4.55441 | 0.256612 | ||||||||
\(316\) | −14.3331 | −0.806297 | ||||||||
\(317\) | −4.36072 | −0.244922 | −0.122461 | − | 0.992473i | \(-0.539079\pi\) | ||||
−0.122461 | + | 0.992473i | \(0.539079\pi\) | |||||||
\(318\) | −18.7266 | −1.05013 | ||||||||
\(319\) | 14.8687 | 0.832490 | ||||||||
\(320\) | 0.126707 | 0.00708314 | ||||||||
\(321\) | 59.8401 | 3.33995 | ||||||||
\(322\) | 4.90115 | 0.273130 | ||||||||
\(323\) | −10.5804 | −0.588711 | ||||||||
\(324\) | 18.5672 | 1.03151 | ||||||||
\(325\) | −1.38041 | −0.0765715 | ||||||||
\(326\) | 13.1528 | 0.728468 | ||||||||
\(327\) | 34.8887 | 1.92935 | ||||||||
\(328\) | 5.49741 | 0.303544 | ||||||||
\(329\) | 39.6679 | 2.18696 | ||||||||
\(330\) | 1.28124 | 0.0705300 | ||||||||
\(331\) | 22.9812 | 1.26316 | 0.631582 | − | 0.775309i | \(-0.282406\pi\) | ||||
0.631582 | + | 0.775309i | \(0.282406\pi\) | |||||||
\(332\) | 3.20258 | 0.175764 | ||||||||
\(333\) | 68.6120 | 3.75991 | ||||||||
\(334\) | 16.3881 | 0.896717 | ||||||||
\(335\) | 0.0538533 | 0.00294232 | ||||||||
\(336\) | −16.2979 | −0.889121 | ||||||||
\(337\) | 31.8141 | 1.73302 | 0.866512 | − | 0.499156i | \(-0.166357\pi\) | ||||
0.866512 | + | 0.499156i | \(0.166357\pi\) | |||||||
\(338\) | −12.9233 | −0.702934 | ||||||||
\(339\) | −50.3806 | −2.73630 | ||||||||
\(340\) | 0.290534 | 0.0157564 | ||||||||
\(341\) | −3.11823 | −0.168861 | ||||||||
\(342\) | −32.1180 | −1.73674 | ||||||||
\(343\) | 65.4146 | 3.53205 | ||||||||
\(344\) | 6.34943 | 0.342338 | ||||||||
\(345\) | −0.379534 | −0.0204334 | ||||||||
\(346\) | 18.7770 | 1.00946 | ||||||||
\(347\) | 28.0310 | 1.50478 | 0.752392 | − | 0.658716i | \(-0.228900\pi\) | ||||
0.752392 | + | 0.658716i | \(0.228900\pi\) | |||||||
\(348\) | 14.6462 | 0.785121 | ||||||||
\(349\) | 13.5611 | 0.725911 | 0.362955 | − | 0.931807i | \(-0.381768\pi\) | ||||
0.362955 | + | 0.931807i | \(0.381768\pi\) | |||||||
\(350\) | −25.7373 | −1.37572 | ||||||||
\(351\) | −3.46201 | −0.184788 | ||||||||
\(352\) | −3.20397 | −0.170772 | ||||||||
\(353\) | −0.301078 | −0.0160248 | −0.00801239 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00801239 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(354\) | 16.0394 | 0.852487 | ||||||||
\(355\) | 0.177317 | 0.00941102 | ||||||||
\(356\) | 14.2139 | 0.753337 | ||||||||
\(357\) | −37.3703 | −1.97785 | ||||||||
\(358\) | −6.43092 | −0.339885 | ||||||||
\(359\) | −25.4313 | −1.34221 | −0.671105 | − | 0.741362i | \(-0.734180\pi\) | ||||
−0.671105 | + | 0.741362i | \(0.734180\pi\) | |||||||
\(360\) | 0.881947 | 0.0464827 | ||||||||
\(361\) | 2.29193 | 0.120628 | ||||||||
\(362\) | 24.5274 | 1.28913 | ||||||||
\(363\) | 2.31825 | 0.121677 | ||||||||
\(364\) | 1.43029 | 0.0749678 | ||||||||
\(365\) | −0.389781 | −0.0204021 | ||||||||
\(366\) | 9.75635 | 0.509972 | ||||||||
\(367\) | 7.17017 | 0.374280 | 0.187140 | − | 0.982333i | \(-0.440078\pi\) | ||||
0.187140 | + | 0.982333i | \(0.440078\pi\) | |||||||
\(368\) | 0.949092 | 0.0494749 | ||||||||
\(369\) | 38.2648 | 1.99199 | ||||||||
\(370\) | 1.24899 | 0.0649320 | ||||||||
\(371\) | 30.6413 | 1.59082 | ||||||||
\(372\) | −3.07156 | −0.159253 | ||||||||
\(373\) | 28.5144 | 1.47642 | 0.738209 | − | 0.674573i | \(-0.235672\pi\) | ||||
0.738209 | + | 0.674573i | \(0.235672\pi\) | |||||||
\(374\) | −7.34658 | −0.379883 | ||||||||
\(375\) | 3.99249 | 0.206171 | ||||||||
\(376\) | 7.68155 | 0.396146 | ||||||||
\(377\) | −1.28535 | −0.0661988 | ||||||||
\(378\) | −64.5479 | −3.31999 | ||||||||
\(379\) | −15.5128 | −0.796841 | −0.398421 | − | 0.917203i | \(-0.630442\pi\) | ||||
−0.398421 | + | 0.917203i | \(0.630442\pi\) | |||||||
\(380\) | −0.584667 | −0.0299928 | ||||||||
\(381\) | −32.3988 | −1.65984 | ||||||||
\(382\) | 9.54659 | 0.488446 | ||||||||
\(383\) | 8.94598 | 0.457118 | 0.228559 | − | 0.973530i | \(-0.426599\pi\) | ||||
0.228559 | + | 0.973530i | \(0.426599\pi\) | |||||||
\(384\) | −3.15603 | −0.161055 | ||||||||
\(385\) | −2.09643 | −0.106844 | ||||||||
\(386\) | −5.97063 | −0.303897 | ||||||||
\(387\) | 44.1953 | 2.24657 | ||||||||
\(388\) | −12.5799 | −0.638649 | ||||||||
\(389\) | −19.0030 | −0.963488 | −0.481744 | − | 0.876312i | \(-0.659996\pi\) | ||||
−0.481744 | + | 0.876312i | \(0.659996\pi\) | |||||||
\(390\) | −0.110759 | −0.00560848 | ||||||||
\(391\) | 2.17623 | 0.110057 | ||||||||
\(392\) | 19.6673 | 0.993350 | ||||||||
\(393\) | −53.0395 | −2.67549 | ||||||||
\(394\) | 11.6397 | 0.586399 | ||||||||
\(395\) | −1.81610 | −0.0913779 | ||||||||
\(396\) | −22.3013 | −1.12068 | ||||||||
\(397\) | −7.25878 | −0.364308 | −0.182154 | − | 0.983270i | \(-0.558307\pi\) | ||||
−0.182154 | + | 0.983270i | \(0.558307\pi\) | |||||||
\(398\) | −13.0399 | −0.653632 | ||||||||
\(399\) | 75.2035 | 3.76488 | ||||||||
\(400\) | −4.98395 | −0.249197 | ||||||||
\(401\) | 17.3981 | 0.868820 | 0.434410 | − | 0.900715i | \(-0.356957\pi\) | ||||
0.434410 | + | 0.900715i | \(0.356957\pi\) | |||||||
\(402\) | −1.34138 | −0.0669020 | ||||||||
\(403\) | 0.269559 | 0.0134277 | ||||||||
\(404\) | 0.599044 | 0.0298035 | ||||||||
\(405\) | 2.35260 | 0.116902 | ||||||||
\(406\) | −23.9649 | −1.18936 | ||||||||
\(407\) | −31.5826 | −1.56549 | ||||||||
\(408\) | −7.23664 | −0.358267 | ||||||||
\(409\) | 27.3242 | 1.35109 | 0.675547 | − | 0.737317i | \(-0.263907\pi\) | ||||
0.675547 | + | 0.737317i | \(0.263907\pi\) | |||||||
\(410\) | 0.696561 | 0.0344007 | ||||||||
\(411\) | −14.9397 | −0.736920 | ||||||||
\(412\) | 7.14033 | 0.351779 | ||||||||
\(413\) | −26.2445 | −1.29141 | ||||||||
\(414\) | 6.60617 | 0.324676 | ||||||||
\(415\) | 0.405790 | 0.0199194 | ||||||||
\(416\) | 0.276972 | 0.0135797 | ||||||||
\(417\) | 12.1210 | 0.593569 | ||||||||
\(418\) | 14.7842 | 0.723117 | ||||||||
\(419\) | 5.09022 | 0.248674 | 0.124337 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124337 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(420\) | −2.06505 | −0.100764 | ||||||||
\(421\) | −22.2268 | −1.08327 | −0.541635 | − | 0.840614i | \(-0.682194\pi\) | ||||
−0.541635 | + | 0.840614i | \(0.682194\pi\) | |||||||
\(422\) | −22.7856 | −1.10918 | ||||||||
\(423\) | 53.4676 | 2.59968 | ||||||||
\(424\) | 5.93359 | 0.288161 | ||||||||
\(425\) | −11.4280 | −0.554338 | ||||||||
\(426\) | −4.41663 | −0.213986 | ||||||||
\(427\) | −15.9638 | −0.772542 | ||||||||
\(428\) | −18.9606 | −0.916494 | ||||||||
\(429\) | 2.80069 | 0.135219 | ||||||||
\(430\) | 0.804518 | 0.0387973 | ||||||||
\(431\) | −9.66923 | −0.465751 | −0.232875 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232875 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(432\) | −12.4995 | −0.601382 | ||||||||
\(433\) | −6.21118 | −0.298490 | −0.149245 | − | 0.988800i | \(-0.547684\pi\) | ||||
−0.149245 | + | 0.988800i | \(0.547684\pi\) | |||||||
\(434\) | 5.02584 | 0.241248 | ||||||||
\(435\) | 1.85578 | 0.0889780 | ||||||||
\(436\) | −11.0546 | −0.529420 | ||||||||
\(437\) | −4.37941 | −0.209496 | ||||||||
\(438\) | 9.70868 | 0.463899 | ||||||||
\(439\) | −27.4061 | −1.30802 | −0.654012 | − | 0.756485i | \(-0.726915\pi\) | ||||
−0.654012 | + | 0.756485i | \(0.726915\pi\) | |||||||
\(440\) | −0.405966 | −0.0193537 | ||||||||
\(441\) | 136.895 | 6.51879 | ||||||||
\(442\) | 0.635085 | 0.0302079 | ||||||||
\(443\) | 13.2401 | 0.629055 | 0.314527 | − | 0.949248i | \(-0.398154\pi\) | ||||
0.314527 | + | 0.949248i | \(0.398154\pi\) | |||||||
\(444\) | −31.1100 | −1.47641 | ||||||||
\(445\) | 1.80101 | 0.0853759 | ||||||||
\(446\) | −2.39151 | −0.113241 | ||||||||
\(447\) | 35.6311 | 1.68529 | ||||||||
\(448\) | 5.16404 | 0.243978 | ||||||||
\(449\) | −21.4786 | −1.01364 | −0.506818 | − | 0.862053i | \(-0.669178\pi\) | ||||
−0.506818 | + | 0.862053i | \(0.669178\pi\) | |||||||
\(450\) | −34.6908 | −1.63534 | ||||||||
\(451\) | −17.6136 | −0.829390 | ||||||||
\(452\) | 15.9633 | 0.750849 | ||||||||
\(453\) | 3.70594 | 0.174120 | ||||||||
\(454\) | −5.07995 | −0.238414 | ||||||||
\(455\) | 0.181228 | 0.00849612 | ||||||||
\(456\) | 14.5629 | 0.681971 | ||||||||
\(457\) | −3.44567 | −0.161182 | −0.0805909 | − | 0.996747i | \(-0.525681\pi\) | ||||
−0.0805909 | + | 0.996747i | \(0.525681\pi\) | |||||||
\(458\) | 5.32645 | 0.248889 | ||||||||
\(459\) | −28.6608 | −1.33777 | ||||||||
\(460\) | 0.120257 | 0.00560700 | ||||||||
\(461\) | −18.1362 | −0.844689 | −0.422345 | − | 0.906435i | \(-0.638793\pi\) | ||||
−0.422345 | + | 0.906435i | \(0.638793\pi\) | |||||||
\(462\) | 52.2179 | 2.42940 | ||||||||
\(463\) | 25.2513 | 1.17353 | 0.586763 | − | 0.809758i | \(-0.300402\pi\) | ||||
0.586763 | + | 0.809758i | \(0.300402\pi\) | |||||||
\(464\) | −4.64072 | −0.215440 | ||||||||
\(465\) | −0.389189 | −0.0180482 | ||||||||
\(466\) | 2.68052 | 0.124173 | ||||||||
\(467\) | 27.4955 | 1.27234 | 0.636171 | − | 0.771548i | \(-0.280517\pi\) | ||||
0.636171 | + | 0.771548i | \(0.280517\pi\) | |||||||
\(468\) | 1.92787 | 0.0891157 | ||||||||
\(469\) | 2.19483 | 0.101348 | ||||||||
\(470\) | 0.973308 | 0.0448953 | ||||||||
\(471\) | −42.9685 | −1.97989 | ||||||||
\(472\) | −5.08216 | −0.233925 | ||||||||
\(473\) | −20.3434 | −0.935391 | ||||||||
\(474\) | 45.2355 | 2.07774 | ||||||||
\(475\) | 22.9975 | 1.05520 | ||||||||
\(476\) | 11.8409 | 0.542728 | ||||||||
\(477\) | 41.3008 | 1.89104 | ||||||||
\(478\) | −11.0564 | −0.505708 | ||||||||
\(479\) | 2.36031 | 0.107845 | 0.0539227 | − | 0.998545i | \(-0.482828\pi\) | ||||
0.0539227 | + | 0.998545i | \(0.482828\pi\) | |||||||
\(480\) | −0.399891 | −0.0182525 | ||||||||
\(481\) | 2.73020 | 0.124486 | ||||||||
\(482\) | 5.22346 | 0.237922 | ||||||||
\(483\) | −15.4682 | −0.703826 | ||||||||
\(484\) | −0.734548 | −0.0333885 | ||||||||
\(485\) | −1.59397 | −0.0723783 | ||||||||
\(486\) | −21.1002 | −0.957125 | ||||||||
\(487\) | −29.1500 | −1.32091 | −0.660455 | − | 0.750865i | \(-0.729637\pi\) | ||||
−0.660455 | + | 0.750865i | \(0.729637\pi\) | |||||||
\(488\) | −3.09134 | −0.139938 | ||||||||
\(489\) | −41.5107 | −1.87718 | ||||||||
\(490\) | 2.49199 | 0.112577 | ||||||||
\(491\) | −15.4451 | −0.697029 | −0.348515 | − | 0.937303i | \(-0.613314\pi\) | ||||
−0.348515 | + | 0.937303i | \(0.613314\pi\) | |||||||
\(492\) | −17.3500 | −0.782197 | ||||||||
\(493\) | −10.6410 | −0.479245 | ||||||||
\(494\) | −1.27804 | −0.0575015 | ||||||||
\(495\) | −2.82574 | −0.127007 | ||||||||
\(496\) | 0.973237 | 0.0436996 | ||||||||
\(497\) | 7.22669 | 0.324161 | ||||||||
\(498\) | −10.1074 | −0.452925 | ||||||||
\(499\) | 37.4525 | 1.67660 | 0.838302 | − | 0.545206i | \(-0.183549\pi\) | ||||
0.838302 | + | 0.545206i | \(0.183549\pi\) | |||||||
\(500\) | −1.26504 | −0.0565742 | ||||||||
\(501\) | −51.7213 | −2.31074 | ||||||||
\(502\) | −8.53704 | −0.381027 | ||||||||
\(503\) | −1.16967 | −0.0521532 | −0.0260766 | − | 0.999660i | \(-0.508301\pi\) | ||||
−0.0260766 | + | 0.999660i | \(0.508301\pi\) | |||||||
\(504\) | 35.9444 | 1.60109 | ||||||||
\(505\) | 0.0759031 | 0.00337764 | ||||||||
\(506\) | −3.04087 | −0.135183 | ||||||||
\(507\) | 40.7863 | 1.81138 | ||||||||
\(508\) | 10.2657 | 0.455467 | ||||||||
\(509\) | 21.2307 | 0.941033 | 0.470516 | − | 0.882391i | \(-0.344068\pi\) | ||||
0.470516 | + | 0.882391i | \(0.344068\pi\) | |||||||
\(510\) | −0.916934 | −0.0406025 | ||||||||
\(511\) | −15.8858 | −0.702746 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 57.6767 | 2.54649 | ||||||||
\(514\) | 4.55007 | 0.200695 | ||||||||
\(515\) | 0.904730 | 0.0398672 | ||||||||
\(516\) | −20.0390 | −0.882167 | ||||||||
\(517\) | −24.6115 | −1.08241 | ||||||||
\(518\) | 50.9036 | 2.23657 | ||||||||
\(519\) | −59.2609 | −2.60126 | ||||||||
\(520\) | 0.0350943 | 0.00153899 | ||||||||
\(521\) | 15.7364 | 0.689425 | 0.344713 | − | 0.938708i | \(-0.387976\pi\) | ||||
0.344713 | + | 0.938708i | \(0.387976\pi\) | |||||||
\(522\) | −32.3018 | −1.41381 | ||||||||
\(523\) | −2.89234 | −0.126473 | −0.0632367 | − | 0.997999i | \(-0.520142\pi\) | ||||
−0.0632367 | + | 0.997999i | \(0.520142\pi\) | |||||||
\(524\) | 16.8058 | 0.734164 | ||||||||
\(525\) | 81.2276 | 3.54507 | ||||||||
\(526\) | 19.6713 | 0.857711 | ||||||||
\(527\) | 2.23159 | 0.0972097 | ||||||||
\(528\) | 10.1118 | 0.440061 | ||||||||
\(529\) | −22.0992 | −0.960836 | ||||||||
\(530\) | 0.751828 | 0.0326573 | ||||||||
\(531\) | −35.3745 | −1.53512 | ||||||||
\(532\) | −23.8285 | −1.03310 | ||||||||
\(533\) | 1.52263 | 0.0659523 | ||||||||
\(534\) | −44.8596 | −1.94126 | ||||||||
\(535\) | −2.40244 | −0.103867 | ||||||||
\(536\) | 0.425022 | 0.0183581 | ||||||||
\(537\) | 20.2962 | 0.875845 | ||||||||
\(538\) | −5.55897 | −0.239664 | ||||||||
\(539\) | −63.0136 | −2.71419 | ||||||||
\(540\) | −1.58378 | −0.0681549 | ||||||||
\(541\) | −18.1605 | −0.780783 | −0.390392 | − | 0.920649i | \(-0.627660\pi\) | ||||
−0.390392 | + | 0.920649i | \(0.627660\pi\) | |||||||
\(542\) | 0.188715 | 0.00810600 | ||||||||
\(543\) | −77.4093 | −3.32195 | ||||||||
\(544\) | 2.29296 | 0.0983098 | ||||||||
\(545\) | −1.40070 | −0.0599993 | ||||||||
\(546\) | −4.51405 | −0.193183 | ||||||||
\(547\) | −24.3052 | −1.03921 | −0.519607 | − | 0.854405i | \(-0.673922\pi\) | ||||
−0.519607 | + | 0.854405i | \(0.673922\pi\) | |||||||
\(548\) | 4.73370 | 0.202213 | ||||||||
\(549\) | −21.5173 | −0.918336 | ||||||||
\(550\) | 15.9684 | 0.680896 | ||||||||
\(551\) | 21.4137 | 0.912256 | ||||||||
\(552\) | −2.99536 | −0.127491 | ||||||||
\(553\) | −74.0165 | −3.14750 | ||||||||
\(554\) | 10.0013 | 0.424913 | ||||||||
\(555\) | −3.94185 | −0.167322 | ||||||||
\(556\) | −3.84059 | −0.162877 | ||||||||
\(557\) | 14.0010 | 0.593242 | 0.296621 | − | 0.954995i | \(-0.404140\pi\) | ||||
0.296621 | + | 0.954995i | \(0.404140\pi\) | |||||||
\(558\) | 6.77423 | 0.286776 | ||||||||
\(559\) | 1.75861 | 0.0743814 | ||||||||
\(560\) | 0.654321 | 0.0276501 | ||||||||
\(561\) | 23.1860 | 0.978914 | ||||||||
\(562\) | 13.2302 | 0.558084 | ||||||||
\(563\) | −25.1531 | −1.06008 | −0.530039 | − | 0.847973i | \(-0.677823\pi\) | ||||
−0.530039 | + | 0.847973i | \(0.677823\pi\) | |||||||
\(564\) | −24.2432 | −1.02082 | ||||||||
\(565\) | 2.02266 | 0.0850940 | ||||||||
\(566\) | −14.8058 | −0.622333 | ||||||||
\(567\) | 95.8819 | 4.02666 | ||||||||
\(568\) | 1.39943 | 0.0587186 | ||||||||
\(569\) | −37.9840 | −1.59237 | −0.796187 | − | 0.605051i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605051i | \(0.793153\pi\) | |||||||
\(570\) | 1.84523 | 0.0772880 | ||||||||
\(571\) | 16.5001 | 0.690508 | 0.345254 | − | 0.938509i | \(-0.387793\pi\) | ||||
0.345254 | + | 0.938509i | \(0.387793\pi\) | |||||||
\(572\) | −0.887411 | −0.0371045 | ||||||||
\(573\) | −30.1293 | −1.25867 | ||||||||
\(574\) | 28.3888 | 1.18493 | ||||||||
\(575\) | −4.73022 | −0.197264 | ||||||||
\(576\) | 6.96052 | 0.290021 | ||||||||
\(577\) | 0.833535 | 0.0347005 | 0.0173503 | − | 0.999849i | \(-0.494477\pi\) | ||||
0.0173503 | + | 0.999849i | \(0.494477\pi\) | |||||||
\(578\) | −11.7423 | −0.488417 | ||||||||
\(579\) | 18.8435 | 0.783108 | ||||||||
\(580\) | −0.588012 | −0.0244159 | ||||||||
\(581\) | 16.5382 | 0.686122 | ||||||||
\(582\) | 39.7026 | 1.64573 | ||||||||
\(583\) | −19.0111 | −0.787358 | ||||||||
\(584\) | −3.07623 | −0.127295 | ||||||||
\(585\) | 0.244274 | 0.0100995 | ||||||||
\(586\) | 27.9134 | 1.15309 | ||||||||
\(587\) | 6.27248 | 0.258893 | 0.129446 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129446 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(588\) | −62.0706 | −2.55975 | ||||||||
\(589\) | −4.49082 | −0.185041 | ||||||||
\(590\) | −0.643946 | −0.0265108 | ||||||||
\(591\) | −36.7352 | −1.51108 | ||||||||
\(592\) | 9.85731 | 0.405133 | ||||||||
\(593\) | 7.97567 | 0.327522 | 0.163761 | − | 0.986500i | \(-0.447637\pi\) | ||||
0.163761 | + | 0.986500i | \(0.447637\pi\) | |||||||
\(594\) | 40.0481 | 1.64319 | ||||||||
\(595\) | 1.50033 | 0.0615076 | ||||||||
\(596\) | −11.2899 | −0.462451 | ||||||||
\(597\) | 41.1544 | 1.68434 | ||||||||
\(598\) | 0.262872 | 0.0107496 | ||||||||
\(599\) | −8.52043 | −0.348135 | −0.174068 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174068 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(600\) | 15.7295 | 0.642153 | ||||||||
\(601\) | −25.6594 | −1.04667 | −0.523335 | − | 0.852127i | \(-0.675312\pi\) | ||||
−0.523335 | + | 0.852127i | \(0.675312\pi\) | |||||||
\(602\) | 32.7887 | 1.33637 | ||||||||
\(603\) | 2.95837 | 0.120474 | ||||||||
\(604\) | −1.17424 | −0.0477793 | ||||||||
\(605\) | −0.0930724 | −0.00378393 | ||||||||
\(606\) | −1.89060 | −0.0768003 | ||||||||
\(607\) | −33.8877 | −1.37546 | −0.687729 | − | 0.725968i | \(-0.741392\pi\) | ||||
−0.687729 | + | 0.725968i | \(0.741392\pi\) | |||||||
\(608\) | −4.61432 | −0.187135 | ||||||||
\(609\) | 75.6338 | 3.06483 | ||||||||
\(610\) | −0.391694 | −0.0158592 | ||||||||
\(611\) | 2.12757 | 0.0860724 | ||||||||
\(612\) | 15.9602 | 0.645152 | ||||||||
\(613\) | −16.7655 | −0.677154 | −0.338577 | − | 0.940939i | \(-0.609946\pi\) | ||||
−0.338577 | + | 0.940939i | \(0.609946\pi\) | |||||||
\(614\) | −11.6931 | −0.471895 | ||||||||
\(615\) | −2.19837 | −0.0886466 | ||||||||
\(616\) | −16.5455 | −0.666635 | ||||||||
\(617\) | 36.3913 | 1.46506 | 0.732530 | − | 0.680735i | \(-0.238340\pi\) | ||||
0.732530 | + | 0.680735i | \(0.238340\pi\) | |||||||
\(618\) | −22.5351 | −0.906494 | ||||||||
\(619\) | −8.33228 | −0.334903 | −0.167451 | − | 0.985880i | \(-0.553554\pi\) | ||||
−0.167451 | + | 0.985880i | \(0.553554\pi\) | |||||||
\(620\) | 0.123316 | 0.00495249 | ||||||||
\(621\) | −11.8632 | −0.476053 | ||||||||
\(622\) | 12.6235 | 0.506156 | ||||||||
\(623\) | 73.4013 | 2.94076 | ||||||||
\(624\) | −0.874131 | −0.0349932 | ||||||||
\(625\) | 24.7594 | 0.990377 | ||||||||
\(626\) | −10.0057 | −0.399907 | ||||||||
\(627\) | −46.6592 | −1.86339 | ||||||||
\(628\) | 13.6147 | 0.543288 | ||||||||
\(629\) | 22.6024 | 0.901217 | ||||||||
\(630\) | 4.55441 | 0.181452 | ||||||||
\(631\) | 26.1353 | 1.04043 | 0.520215 | − | 0.854036i | \(-0.325852\pi\) | ||||
0.520215 | + | 0.854036i | \(0.325852\pi\) | |||||||
\(632\) | −14.3331 | −0.570138 | ||||||||
\(633\) | 71.9118 | 2.85824 | ||||||||
\(634\) | −4.36072 | −0.173186 | ||||||||
\(635\) | 1.30074 | 0.0516182 | ||||||||
\(636\) | −18.7266 | −0.742557 | ||||||||
\(637\) | 5.44729 | 0.215830 | ||||||||
\(638\) | 14.8687 | 0.588659 | ||||||||
\(639\) | 9.74073 | 0.385337 | ||||||||
\(640\) | 0.126707 | 0.00500854 | ||||||||
\(641\) | 4.85837 | 0.191894 | 0.0959470 | − | 0.995386i | \(-0.469412\pi\) | ||||
0.0959470 | + | 0.995386i | \(0.469412\pi\) | |||||||
\(642\) | 59.8401 | 2.36170 | ||||||||
\(643\) | 14.2210 | 0.560821 | 0.280411 | − | 0.959880i | \(-0.409529\pi\) | ||||
0.280411 | + | 0.959880i | \(0.409529\pi\) | |||||||
\(644\) | 4.90115 | 0.193132 | ||||||||
\(645\) | −2.53908 | −0.0999762 | ||||||||
\(646\) | −10.5804 | −0.416282 | ||||||||
\(647\) | 27.7257 | 1.09001 | 0.545005 | − | 0.838433i | \(-0.316528\pi\) | ||||
0.545005 | + | 0.838433i | \(0.316528\pi\) | |||||||
\(648\) | 18.5672 | 0.729390 | ||||||||
\(649\) | 16.2831 | 0.639168 | ||||||||
\(650\) | −1.38041 | −0.0541442 | ||||||||
\(651\) | −15.8617 | −0.621668 | ||||||||
\(652\) | 13.1528 | 0.515104 | ||||||||
\(653\) | −7.83766 | −0.306712 | −0.153356 | − | 0.988171i | \(-0.549008\pi\) | ||||
−0.153356 | + | 0.988171i | \(0.549008\pi\) | |||||||
\(654\) | 34.8887 | 1.36426 | ||||||||
\(655\) | 2.12941 | 0.0832030 | ||||||||
\(656\) | 5.49741 | 0.214638 | ||||||||
\(657\) | −21.4122 | −0.835369 | ||||||||
\(658\) | 39.6679 | 1.54641 | ||||||||
\(659\) | −39.1494 | −1.52504 | −0.762522 | − | 0.646963i | \(-0.776039\pi\) | ||||
−0.762522 | + | 0.646963i | \(0.776039\pi\) | |||||||
\(660\) | 1.28124 | 0.0498723 | ||||||||
\(661\) | 7.86361 | 0.305859 | 0.152929 | − | 0.988237i | \(-0.451129\pi\) | ||||
0.152929 | + | 0.988237i | \(0.451129\pi\) | |||||||
\(662\) | 22.9812 | 0.893192 | ||||||||
\(663\) | −2.00435 | −0.0778423 | ||||||||
\(664\) | 3.20258 | 0.124284 | ||||||||
\(665\) | −3.01924 | −0.117081 | ||||||||
\(666\) | 68.6120 | 2.65866 | ||||||||
\(667\) | −4.40447 | −0.170542 | ||||||||
\(668\) | 16.3881 | 0.634074 | ||||||||
\(669\) | 7.54766 | 0.291810 | ||||||||
\(670\) | 0.0538533 | 0.00208053 | ||||||||
\(671\) | 9.90456 | 0.382361 | ||||||||
\(672\) | −16.2979 | −0.628704 | ||||||||
\(673\) | 48.5101 | 1.86993 | 0.934964 | − | 0.354742i | \(-0.115431\pi\) | ||||
0.934964 | + | 0.354742i | \(0.115431\pi\) | |||||||
\(674\) | 31.8141 | 1.22543 | ||||||||
\(675\) | 62.2968 | 2.39781 | ||||||||
\(676\) | −12.9233 | −0.497049 | ||||||||
\(677\) | 37.4073 | 1.43768 | 0.718840 | − | 0.695176i | \(-0.244673\pi\) | ||||
0.718840 | + | 0.695176i | \(0.244673\pi\) | |||||||
\(678\) | −50.3806 | −1.93485 | ||||||||
\(679\) | −64.9633 | −2.49306 | ||||||||
\(680\) | 0.290534 | 0.0111415 | ||||||||
\(681\) | 16.0325 | 0.614366 | ||||||||
\(682\) | −3.11823 | −0.119403 | ||||||||
\(683\) | −3.91544 | −0.149820 | −0.0749100 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749100 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(684\) | −32.1180 | −1.22806 | ||||||||
\(685\) | 0.599793 | 0.0229169 | ||||||||
\(686\) | 65.4146 | 2.49754 | ||||||||
\(687\) | −16.8104 | −0.641358 | ||||||||
\(688\) | 6.34943 | 0.242070 | ||||||||
\(689\) | 1.64344 | 0.0626100 | ||||||||
\(690\) | −0.379534 | −0.0144486 | ||||||||
\(691\) | 31.4259 | 1.19550 | 0.597749 | − | 0.801683i | \(-0.296062\pi\) | ||||
0.597749 | + | 0.801683i | \(0.296062\pi\) | |||||||
\(692\) | 18.7770 | 0.713796 | ||||||||
\(693\) | −115.165 | −4.37475 | ||||||||
\(694\) | 28.0310 | 1.06404 | ||||||||
\(695\) | −0.486631 | −0.0184590 | ||||||||
\(696\) | 14.6462 | 0.555164 | ||||||||
\(697\) | 12.6053 | 0.477461 | ||||||||
\(698\) | 13.5611 | 0.513296 | ||||||||
\(699\) | −8.45981 | −0.319979 | ||||||||
\(700\) | −25.7373 | −0.972778 | ||||||||
\(701\) | 30.8684 | 1.16588 | 0.582942 | − | 0.812514i | \(-0.301902\pi\) | ||||
0.582942 | + | 0.812514i | \(0.301902\pi\) | |||||||
\(702\) | −3.46201 | −0.130665 | ||||||||
\(703\) | −45.4848 | −1.71549 | ||||||||
\(704\) | −3.20397 | −0.120754 | ||||||||
\(705\) | −3.07179 | −0.115690 | ||||||||
\(706\) | −0.301078 | −0.0113312 | ||||||||
\(707\) | 3.09349 | 0.116343 | ||||||||
\(708\) | 16.0394 | 0.602799 | ||||||||
\(709\) | 50.8639 | 1.91023 | 0.955117 | − | 0.296230i | \(-0.0957293\pi\) | ||||
0.955117 | + | 0.296230i | \(0.0957293\pi\) | |||||||
\(710\) | 0.177317 | 0.00665460 | ||||||||
\(711\) | −99.7654 | −3.74150 | ||||||||
\(712\) | 14.2139 | 0.532690 | ||||||||
\(713\) | 0.923692 | 0.0345925 | ||||||||
\(714\) | −37.3703 | −1.39855 | ||||||||
\(715\) | −0.112441 | −0.00420506 | ||||||||
\(716\) | −6.43092 | −0.240335 | ||||||||
\(717\) | 34.8943 | 1.30315 | ||||||||
\(718\) | −25.4313 | −0.949086 | ||||||||
\(719\) | 52.5879 | 1.96120 | 0.980599 | − | 0.196025i | \(-0.0628035\pi\) | ||||
0.980599 | + | 0.196025i | \(0.0628035\pi\) | |||||||
\(720\) | 0.881947 | 0.0328682 | ||||||||
\(721\) | 36.8729 | 1.37322 | ||||||||
\(722\) | 2.29193 | 0.0852967 | ||||||||
\(723\) | −16.4854 | −0.613098 | ||||||||
\(724\) | 24.5274 | 0.911555 | ||||||||
\(725\) | 23.1291 | 0.858992 | ||||||||
\(726\) | 2.31825 | 0.0860385 | ||||||||
\(727\) | −7.98148 | −0.296017 | −0.148008 | − | 0.988986i | \(-0.547286\pi\) | ||||
−0.148008 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(728\) | 1.43029 | 0.0530102 | ||||||||
\(729\) | 10.8912 | 0.403377 | ||||||||
\(730\) | −0.389781 | −0.0144264 | ||||||||
\(731\) | 14.5590 | 0.538483 | ||||||||
\(732\) | 9.75635 | 0.360605 | ||||||||
\(733\) | −25.5918 | −0.945253 | −0.472627 | − | 0.881263i | \(-0.656694\pi\) | ||||
−0.472627 | + | 0.881263i | \(0.656694\pi\) | |||||||
\(734\) | 7.17017 | 0.264656 | ||||||||
\(735\) | −7.86479 | −0.290097 | ||||||||
\(736\) | 0.949092 | 0.0349840 | ||||||||
\(737\) | −1.36176 | −0.0501610 | ||||||||
\(738\) | 38.2648 | 1.40855 | ||||||||
\(739\) | 20.0865 | 0.738894 | 0.369447 | − | 0.929252i | \(-0.379547\pi\) | ||||
0.369447 | + | 0.929252i | \(0.379547\pi\) | |||||||
\(740\) | 1.24899 | 0.0459138 | ||||||||
\(741\) | 4.03352 | 0.148175 | ||||||||
\(742\) | 30.6413 | 1.12488 | ||||||||
\(743\) | −47.6511 | −1.74815 | −0.874074 | − | 0.485793i | \(-0.838531\pi\) | ||||
−0.874074 | + | 0.485793i | \(0.838531\pi\) | |||||||
\(744\) | −3.07156 | −0.112609 | ||||||||
\(745\) | −1.43051 | −0.0524097 | ||||||||
\(746\) | 28.5144 | 1.04398 | ||||||||
\(747\) | 22.2916 | 0.815607 | ||||||||
\(748\) | −7.34658 | −0.268618 | ||||||||
\(749\) | −97.9132 | −3.57767 | ||||||||
\(750\) | 3.99249 | 0.145785 | ||||||||
\(751\) | 5.80813 | 0.211942 | 0.105971 | − | 0.994369i | \(-0.466205\pi\) | ||||
0.105971 | + | 0.994369i | \(0.466205\pi\) | |||||||
\(752\) | 7.68155 | 0.280117 | ||||||||
\(753\) | 26.9431 | 0.981863 | ||||||||
\(754\) | −1.28535 | −0.0468096 | ||||||||
\(755\) | −0.148785 | −0.00541484 | ||||||||
\(756\) | −64.5479 | −2.34759 | ||||||||
\(757\) | 19.8269 | 0.720620 | 0.360310 | − | 0.932833i | \(-0.382671\pi\) | ||||
0.360310 | + | 0.932833i | \(0.382671\pi\) | |||||||
\(758\) | −15.5128 | −0.563452 | ||||||||
\(759\) | 9.59706 | 0.348351 | ||||||||
\(760\) | −0.584667 | −0.0212081 | ||||||||
\(761\) | 37.1860 | 1.34799 | 0.673995 | − | 0.738736i | \(-0.264577\pi\) | ||||
0.673995 | + | 0.738736i | \(0.264577\pi\) | |||||||
\(762\) | −32.3988 | −1.17369 | ||||||||
\(763\) | −57.0865 | −2.06667 | ||||||||
\(764\) | 9.54659 | 0.345384 | ||||||||
\(765\) | 2.02227 | 0.0731152 | ||||||||
\(766\) | 8.94598 | 0.323232 | ||||||||
\(767\) | −1.40761 | −0.0508260 | ||||||||
\(768\) | −3.15603 | −0.113883 | ||||||||
\(769\) | −22.5934 | −0.814739 | −0.407369 | − | 0.913263i | \(-0.633554\pi\) | ||||
−0.407369 | + | 0.913263i | \(0.633554\pi\) | |||||||
\(770\) | −2.09643 | −0.0755500 | ||||||||
\(771\) | −14.3601 | −0.517168 | ||||||||
\(772\) | −5.97063 | −0.214888 | ||||||||
\(773\) | −0.112206 | −0.00403578 | −0.00201789 | − | 0.999998i | \(-0.500642\pi\) | ||||
−0.00201789 | + | 0.999998i | \(0.500642\pi\) | |||||||
\(774\) | 44.1953 | 1.58857 | ||||||||
\(775\) | −4.85056 | −0.174237 | ||||||||
\(776\) | −12.5799 | −0.451593 | ||||||||
\(777\) | −160.653 | −5.76340 | ||||||||
\(778\) | −19.0030 | −0.681289 | ||||||||
\(779\) | −25.3668 | −0.908859 | ||||||||
\(780\) | −0.110759 | −0.00396579 | ||||||||
\(781\) | −4.48372 | −0.160440 | ||||||||
\(782\) | 2.17623 | 0.0778218 | ||||||||
\(783\) | 58.0066 | 2.07299 | ||||||||
\(784\) | 19.6673 | 0.702404 | ||||||||
\(785\) | 1.72509 | 0.0615709 | ||||||||
\(786\) | −53.0395 | −1.89186 | ||||||||
\(787\) | −47.4574 | −1.69167 | −0.845836 | − | 0.533443i | \(-0.820898\pi\) | ||||
−0.845836 | + | 0.533443i | \(0.820898\pi\) | |||||||
\(788\) | 11.6397 | 0.414646 | ||||||||
\(789\) | −62.0833 | −2.21022 | ||||||||
\(790\) | −1.81610 | −0.0646139 | ||||||||
\(791\) | 82.4350 | 2.93105 | ||||||||
\(792\) | −22.3013 | −0.792443 | ||||||||
\(793\) | −0.856213 | −0.0304050 | ||||||||
\(794\) | −7.25878 | −0.257605 | ||||||||
\(795\) | −2.37279 | −0.0841542 | ||||||||
\(796\) | −13.0399 | −0.462188 | ||||||||
\(797\) | 22.5840 | 0.799967 | 0.399983 | − | 0.916522i | \(-0.369016\pi\) | ||||
0.399983 | + | 0.916522i | \(0.369016\pi\) | |||||||
\(798\) | 75.2035 | 2.66218 | ||||||||
\(799\) | 17.6135 | 0.623120 | ||||||||
\(800\) | −4.98395 | −0.176209 | ||||||||
\(801\) | 98.9363 | 3.49574 | ||||||||
\(802\) | 17.3981 | 0.614348 | ||||||||
\(803\) | 9.85618 | 0.347817 | ||||||||
\(804\) | −1.34138 | −0.0473068 | ||||||||
\(805\) | 0.621011 | 0.0218878 | ||||||||
\(806\) | 0.269559 | 0.00949482 | ||||||||
\(807\) | 17.5443 | 0.617587 | ||||||||
\(808\) | 0.599044 | 0.0210743 | ||||||||
\(809\) | −6.94987 | −0.244344 | −0.122172 | − | 0.992509i | \(-0.538986\pi\) | ||||
−0.122172 | + | 0.992509i | \(0.538986\pi\) | |||||||
\(810\) | 2.35260 | 0.0826620 | ||||||||
\(811\) | 39.2392 | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(812\) | −23.9649 | −0.841001 | ||||||||
\(813\) | −0.595590 | −0.0208882 | ||||||||
\(814\) | −31.5826 | −1.10697 | ||||||||
\(815\) | 1.66656 | 0.0583769 | ||||||||
\(816\) | −7.23664 | −0.253333 | ||||||||
\(817\) | −29.2983 | −1.02502 | ||||||||
\(818\) | 27.3242 | 0.955368 | ||||||||
\(819\) | 9.95558 | 0.347876 | ||||||||
\(820\) | 0.696561 | 0.0243250 | ||||||||
\(821\) | 42.6889 | 1.48985 | 0.744927 | − | 0.667147i | \(-0.232485\pi\) | ||||
0.744927 | + | 0.667147i | \(0.232485\pi\) | |||||||
\(822\) | −14.9397 | −0.521081 | ||||||||
\(823\) | −44.6437 | −1.55618 | −0.778092 | − | 0.628151i | \(-0.783812\pi\) | ||||
−0.778092 | + | 0.628151i | \(0.783812\pi\) | |||||||
\(824\) | 7.14033 | 0.248745 | ||||||||
\(825\) | −50.3968 | −1.75459 | ||||||||
\(826\) | −26.2445 | −0.913162 | ||||||||
\(827\) | −45.1598 | −1.57036 | −0.785180 | − | 0.619268i | \(-0.787430\pi\) | ||||
−0.785180 | + | 0.619268i | \(0.787430\pi\) | |||||||
\(828\) | 6.60617 | 0.229580 | ||||||||
\(829\) | −31.9968 | −1.11129 | −0.555647 | − | 0.831418i | \(-0.687529\pi\) | ||||
−0.555647 | + | 0.831418i | \(0.687529\pi\) | |||||||
\(830\) | 0.405790 | 0.0140852 | ||||||||
\(831\) | −31.5643 | −1.09495 | ||||||||
\(832\) | 0.276972 | 0.00960227 | ||||||||
\(833\) | 45.0963 | 1.56250 | ||||||||
\(834\) | 12.1210 | 0.419717 | ||||||||
\(835\) | 2.07649 | 0.0718598 | ||||||||
\(836\) | 14.7842 | 0.511321 | ||||||||
\(837\) | −12.1650 | −0.420483 | ||||||||
\(838\) | 5.09022 | 0.175839 | ||||||||
\(839\) | 3.06882 | 0.105948 | 0.0529738 | − | 0.998596i | \(-0.483130\pi\) | ||||
0.0529738 | + | 0.998596i | \(0.483130\pi\) | |||||||
\(840\) | −2.06505 | −0.0712512 | ||||||||
\(841\) | −7.46374 | −0.257371 | ||||||||
\(842\) | −22.2268 | −0.765987 | ||||||||
\(843\) | −41.7550 | −1.43812 | ||||||||
\(844\) | −22.7856 | −0.784311 | ||||||||
\(845\) | −1.63747 | −0.0563308 | ||||||||
\(846\) | 53.4676 | 1.83825 | ||||||||
\(847\) | −3.79323 | −0.130337 | ||||||||
\(848\) | 5.93359 | 0.203760 | ||||||||
\(849\) | 46.7274 | 1.60368 | ||||||||
\(850\) | −11.4280 | −0.391976 | ||||||||
\(851\) | 9.35550 | 0.320702 | ||||||||
\(852\) | −4.41663 | −0.151311 | ||||||||
\(853\) | −11.6490 | −0.398855 | −0.199427 | − | 0.979913i | \(-0.563908\pi\) | ||||
−0.199427 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(854\) | −15.9638 | −0.546270 | ||||||||
\(855\) | −4.06958 | −0.139177 | ||||||||
\(856\) | −18.9606 | −0.648059 | ||||||||
\(857\) | 3.11166 | 0.106292 | 0.0531462 | − | 0.998587i | \(-0.483075\pi\) | ||||
0.0531462 | + | 0.998587i | \(0.483075\pi\) | |||||||
\(858\) | 2.80069 | 0.0956141 | ||||||||
\(859\) | 28.2804 | 0.964915 | 0.482457 | − | 0.875919i | \(-0.339744\pi\) | ||||
0.482457 | + | 0.875919i | \(0.339744\pi\) | |||||||
\(860\) | 0.804518 | 0.0274338 | ||||||||
\(861\) | −89.5960 | −3.05342 | ||||||||
\(862\) | −9.66923 | −0.329335 | ||||||||
\(863\) | 3.93034 | 0.133790 | 0.0668952 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668952 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(864\) | −12.4995 | −0.425242 | ||||||||
\(865\) | 2.37919 | 0.0808947 | ||||||||
\(866\) | −6.21118 | −0.211064 | ||||||||
\(867\) | 37.0592 | 1.25860 | ||||||||
\(868\) | 5.02584 | 0.170588 | ||||||||
\(869\) | 45.9227 | 1.55782 | ||||||||
\(870\) | 1.85578 | 0.0629169 | ||||||||
\(871\) | 0.117719 | 0.00398876 | ||||||||
\(872\) | −11.0546 | −0.374357 | ||||||||
\(873\) | −87.5628 | −2.96355 | ||||||||
\(874\) | −4.37941 | −0.148136 | ||||||||
\(875\) | −6.53270 | −0.220846 | ||||||||
\(876\) | 9.70868 | 0.328026 | ||||||||
\(877\) | 40.6211 | 1.37168 | 0.685838 | − | 0.727754i | \(-0.259436\pi\) | ||||
0.685838 | + | 0.727754i | \(0.259436\pi\) | |||||||
\(878\) | −27.4061 | −0.924912 | ||||||||
\(879\) | −88.0954 | −2.97138 | ||||||||
\(880\) | −0.405966 | −0.0136851 | ||||||||
\(881\) | −9.52411 | −0.320876 | −0.160438 | − | 0.987046i | \(-0.551291\pi\) | ||||
−0.160438 | + | 0.987046i | \(0.551291\pi\) | |||||||
\(882\) | 136.895 | 4.60948 | ||||||||
\(883\) | −8.35845 | −0.281284 | −0.140642 | − | 0.990061i | \(-0.544917\pi\) | ||||
−0.140642 | + | 0.990061i | \(0.544917\pi\) | |||||||
\(884\) | 0.635085 | 0.0213602 | ||||||||
\(885\) | 2.03231 | 0.0683154 | ||||||||
\(886\) | 13.2401 | 0.444809 | ||||||||
\(887\) | 8.13444 | 0.273128 | 0.136564 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136564 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(888\) | −31.1100 | −1.04398 | ||||||||
\(889\) | 53.0125 | 1.77798 | ||||||||
\(890\) | 1.80101 | 0.0603699 | ||||||||
\(891\) | −59.4889 | −1.99295 | ||||||||
\(892\) | −2.39151 | −0.0800736 | ||||||||
\(893\) | −35.4451 | −1.18613 | ||||||||
\(894\) | 35.6311 | 1.19168 | ||||||||
\(895\) | −0.814844 | −0.0272372 | ||||||||
\(896\) | 5.16404 | 0.172518 | ||||||||
\(897\) | −0.829631 | −0.0277006 | ||||||||
\(898\) | −21.4786 | −0.716749 | ||||||||
\(899\) | −4.51652 | −0.150634 | ||||||||
\(900\) | −34.6908 | −1.15636 | ||||||||
\(901\) | 13.6055 | 0.453264 | ||||||||
\(902\) | −17.6136 | −0.586467 | ||||||||
\(903\) | −103.482 | −3.44367 | ||||||||
\(904\) | 15.9633 | 0.530931 | ||||||||
\(905\) | 3.10780 | 0.103307 | ||||||||
\(906\) | 3.70594 | 0.123122 | ||||||||
\(907\) | −4.77501 | −0.158552 | −0.0792758 | − | 0.996853i | \(-0.525261\pi\) | ||||
−0.0792758 | + | 0.996853i | \(0.525261\pi\) | |||||||
\(908\) | −5.07995 | −0.168584 | ||||||||
\(909\) | 4.16965 | 0.138299 | ||||||||
\(910\) | 0.181228 | 0.00600766 | ||||||||
\(911\) | 8.45562 | 0.280147 | 0.140074 | − | 0.990141i | \(-0.455266\pi\) | ||||
0.140074 | + | 0.990141i | \(0.455266\pi\) | |||||||
\(912\) | 14.5629 | 0.482226 | ||||||||
\(913\) | −10.2610 | −0.339589 | ||||||||
\(914\) | −3.44567 | −0.113973 | ||||||||
\(915\) | 1.23620 | 0.0408675 | ||||||||
\(916\) | 5.32645 | 0.175991 | ||||||||
\(917\) | 86.7858 | 2.86592 | ||||||||
\(918\) | −28.6608 | −0.945949 | ||||||||
\(919\) | −23.2429 | −0.766712 | −0.383356 | − | 0.923601i | \(-0.625232\pi\) | ||||
−0.383356 | + | 0.923601i | \(0.625232\pi\) | |||||||
\(920\) | 0.120257 | 0.00396475 | ||||||||
\(921\) | 36.9037 | 1.21602 | ||||||||
\(922\) | −18.1362 | −0.597285 | ||||||||
\(923\) | 0.387601 | 0.0127581 | ||||||||
\(924\) | 52.2179 | 1.71784 | ||||||||
\(925\) | −49.1283 | −1.61533 | ||||||||
\(926\) | 25.2513 | 0.829809 | ||||||||
\(927\) | 49.7004 | 1.63237 | ||||||||
\(928\) | −4.64072 | −0.152339 | ||||||||
\(929\) | 35.3596 | 1.16011 | 0.580055 | − | 0.814577i | \(-0.303031\pi\) | ||||
0.580055 | + | 0.814577i | \(0.303031\pi\) | |||||||
\(930\) | −0.389189 | −0.0127620 | ||||||||
\(931\) | −90.7513 | −2.97425 | ||||||||
\(932\) | 2.68052 | 0.0878035 | ||||||||
\(933\) | −39.8401 | −1.30431 | ||||||||
\(934\) | 27.4955 | 0.899682 | ||||||||
\(935\) | −0.930864 | −0.0304425 | ||||||||
\(936\) | 1.92787 | 0.0630143 | ||||||||
\(937\) | 31.8521 | 1.04056 | 0.520281 | − | 0.853995i | \(-0.325827\pi\) | ||||
0.520281 | + | 0.853995i | \(0.325827\pi\) | |||||||
\(938\) | 2.19483 | 0.0716637 | ||||||||
\(939\) | 31.5782 | 1.03052 | ||||||||
\(940\) | 0.973308 | 0.0317458 | ||||||||
\(941\) | 55.2658 | 1.80161 | 0.900807 | − | 0.434219i | \(-0.142976\pi\) | ||||
0.900807 | + | 0.434219i | \(0.142976\pi\) | |||||||
\(942\) | −42.9685 | −1.39999 | ||||||||
\(943\) | 5.21755 | 0.169907 | ||||||||
\(944\) | −5.08216 | −0.165410 | ||||||||
\(945\) | −8.17868 | −0.266053 | ||||||||
\(946\) | −20.3434 | −0.661421 | ||||||||
\(947\) | −23.1857 | −0.753433 | −0.376717 | − | 0.926329i | \(-0.622947\pi\) | ||||
−0.376717 | + | 0.926329i | \(0.622947\pi\) | |||||||
\(948\) | 45.2355 | 1.46918 | ||||||||
\(949\) | −0.852030 | −0.0276581 | ||||||||
\(950\) | 22.9975 | 0.746138 | ||||||||
\(951\) | 13.7626 | 0.446281 | ||||||||
\(952\) | 11.8409 | 0.383767 | ||||||||
\(953\) | 34.9846 | 1.13326 | 0.566631 | − | 0.823972i | \(-0.308247\pi\) | ||||
0.566631 | + | 0.823972i | \(0.308247\pi\) | |||||||
\(954\) | 41.3008 | 1.33716 | ||||||||
\(955\) | 1.20962 | 0.0391424 | ||||||||
\(956\) | −11.0564 | −0.357590 | ||||||||
\(957\) | −46.9262 | −1.51691 | ||||||||
\(958\) | 2.36031 | 0.0762582 | ||||||||
\(959\) | 24.4450 | 0.789370 | ||||||||
\(960\) | −0.399891 | −0.0129064 | ||||||||
\(961\) | −30.0528 | −0.969445 | ||||||||
\(962\) | 2.73020 | 0.0880251 | ||||||||
\(963\) | −131.975 | −4.25285 | ||||||||
\(964\) | 5.22346 | 0.168236 | ||||||||
\(965\) | −0.756521 | −0.0243533 | ||||||||
\(966\) | −15.4682 | −0.497680 | ||||||||
\(967\) | −0.935053 | −0.0300693 | −0.0150346 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150346 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(968\) | −0.734548 | −0.0236093 | ||||||||
\(969\) | 33.3922 | 1.07271 | ||||||||
\(970\) | −1.59397 | −0.0511792 | ||||||||
\(971\) | −11.9326 | −0.382936 | −0.191468 | − | 0.981499i | \(-0.561325\pi\) | ||||
−0.191468 | + | 0.981499i | \(0.561325\pi\) | |||||||
\(972\) | −21.1002 | −0.676790 | ||||||||
\(973\) | −19.8330 | −0.635816 | ||||||||
\(974\) | −29.1500 | −0.934025 | ||||||||
\(975\) | 4.35662 | 0.139524 | ||||||||
\(976\) | −3.09134 | −0.0989513 | ||||||||
\(977\) | −17.9356 | −0.573812 | −0.286906 | − | 0.957959i | \(-0.592627\pi\) | ||||
−0.286906 | + | 0.957959i | \(0.592627\pi\) | |||||||
\(978\) | −41.5107 | −1.32737 | ||||||||
\(979\) | −45.5411 | −1.45550 | ||||||||
\(980\) | 2.49199 | 0.0796037 | ||||||||
\(981\) | −76.9458 | −2.45669 | ||||||||
\(982\) | −15.4451 | −0.492874 | ||||||||
\(983\) | 38.5877 | 1.23076 | 0.615378 | − | 0.788232i | \(-0.289004\pi\) | ||||
0.615378 | + | 0.788232i | \(0.289004\pi\) | |||||||
\(984\) | −17.3500 | −0.553097 | ||||||||
\(985\) | 1.47483 | 0.0469920 | ||||||||
\(986\) | −10.6410 | −0.338878 | ||||||||
\(987\) | −125.193 | −3.98493 | ||||||||
\(988\) | −1.27804 | −0.0406597 | ||||||||
\(989\) | 6.02619 | 0.191622 | ||||||||
\(990\) | −2.82574 | −0.0898078 | ||||||||
\(991\) | −57.1812 | −1.81642 | −0.908211 | − | 0.418512i | \(-0.862552\pi\) | ||||
−0.908211 | + | 0.418512i | \(0.862552\pi\) | |||||||
\(992\) | 0.973237 | 0.0309003 | ||||||||
\(993\) | −72.5295 | −2.30165 | ||||||||
\(994\) | 7.22669 | 0.229217 | ||||||||
\(995\) | −1.65225 | −0.0523799 | ||||||||
\(996\) | −10.1074 | −0.320266 | ||||||||
\(997\) | 33.9164 | 1.07414 | 0.537072 | − | 0.843537i | \(-0.319530\pi\) | ||||
0.537072 | + | 0.843537i | \(0.319530\pi\) | |||||||
\(998\) | 37.4525 | 1.18554 | ||||||||
\(999\) | −123.211 | −3.89824 |
(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 | 8026.2.a.d.1.6 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.d.1.6 | ✓ | 96 | 1.1 | even | 1 | trivial |