Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.118870813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.14753\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15625 | −1.52470 | −0.762350 | − | 0.647164i | \(-0.775955\pi\) | ||||
−0.762350 | + | 0.647164i | \(0.775955\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.64943 | 1.32471 | ||||||||
\(5\) | −0.239094 | −0.106926 | −0.0534631 | − | 0.998570i | \(-0.517026\pi\) | ||||
−0.0534631 | + | 0.998570i | \(0.517026\pi\) | |||||||
\(6\) | −2.15625 | −0.880286 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.40032 | −0.495090 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.515547 | 0.163030 | ||||||||
\(11\) | −3.99784 | −1.20539 | −0.602697 | − | 0.797970i | \(-0.705907\pi\) | ||||
−0.602697 | + | 0.797970i | \(0.705907\pi\) | |||||||
\(12\) | 2.64943 | 0.764823 | ||||||||
\(13\) | −1.61682 | −0.448425 | −0.224213 | − | 0.974540i | \(-0.571981\pi\) | ||||
−0.224213 | + | 0.974540i | \(0.571981\pi\) | |||||||
\(14\) | −2.15625 | −0.576283 | ||||||||
\(15\) | −0.239094 | −0.0617338 | ||||||||
\(16\) | −2.27940 | −0.569849 | ||||||||
\(17\) | 4.61421 | 1.11911 | 0.559555 | − | 0.828793i | \(-0.310972\pi\) | ||||
0.559555 | + | 0.828793i | \(0.310972\pi\) | |||||||
\(18\) | −2.15625 | −0.508234 | ||||||||
\(19\) | −4.17289 | −0.957328 | −0.478664 | − | 0.877998i | \(-0.658879\pi\) | ||||
−0.478664 | + | 0.877998i | \(0.658879\pi\) | |||||||
\(20\) | −0.633462 | −0.141646 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 8.62035 | 1.83786 | ||||||||
\(23\) | 5.22408 | 1.08930 | 0.544648 | − | 0.838665i | \(-0.316663\pi\) | ||||
0.544648 | + | 0.838665i | \(0.316663\pi\) | |||||||
\(24\) | −1.40032 | −0.285840 | ||||||||
\(25\) | −4.94283 | −0.988567 | ||||||||
\(26\) | 3.48627 | 0.683714 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.64943 | 0.500694 | ||||||||
\(29\) | 9.10130 | 1.69007 | 0.845035 | − | 0.534712i | \(-0.179580\pi\) | ||||
0.845035 | + | 0.534712i | \(0.179580\pi\) | |||||||
\(30\) | 0.515547 | 0.0941256 | ||||||||
\(31\) | −6.57815 | −1.18147 | −0.590736 | − | 0.806865i | \(-0.701162\pi\) | ||||
−0.590736 | + | 0.806865i | \(0.701162\pi\) | |||||||
\(32\) | 7.71560 | 1.36394 | ||||||||
\(33\) | −3.99784 | −0.695934 | ||||||||
\(34\) | −9.94939 | −1.70631 | ||||||||
\(35\) | −0.239094 | −0.0404143 | ||||||||
\(36\) | 2.64943 | 0.441571 | ||||||||
\(37\) | −0.353708 | −0.0581492 | −0.0290746 | − | 0.999577i | \(-0.509256\pi\) | ||||
−0.0290746 | + | 0.999577i | \(0.509256\pi\) | |||||||
\(38\) | 8.99781 | 1.45964 | ||||||||
\(39\) | −1.61682 | −0.258898 | ||||||||
\(40\) | 0.334809 | 0.0529380 | ||||||||
\(41\) | −7.72038 | −1.20572 | −0.602860 | − | 0.797847i | \(-0.705972\pi\) | ||||
−0.602860 | + | 0.797847i | \(0.705972\pi\) | |||||||
\(42\) | −2.15625 | −0.332717 | ||||||||
\(43\) | −7.33166 | −1.11807 | −0.559034 | − | 0.829145i | \(-0.688828\pi\) | ||||
−0.559034 | + | 0.829145i | \(0.688828\pi\) | |||||||
\(44\) | −10.5920 | −1.59680 | ||||||||
\(45\) | −0.239094 | −0.0356420 | ||||||||
\(46\) | −11.2644 | −1.66085 | ||||||||
\(47\) | 3.52396 | 0.514023 | 0.257011 | − | 0.966408i | \(-0.417262\pi\) | ||||
0.257011 | + | 0.966408i | \(0.417262\pi\) | |||||||
\(48\) | −2.27940 | −0.329003 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.6580 | 1.50727 | ||||||||
\(51\) | 4.61421 | 0.646118 | ||||||||
\(52\) | −4.28365 | −0.594035 | ||||||||
\(53\) | −0.655025 | −0.0899745 | −0.0449873 | − | 0.998988i | \(-0.514325\pi\) | ||||
−0.0449873 | + | 0.998988i | \(0.514325\pi\) | |||||||
\(54\) | −2.15625 | −0.293429 | ||||||||
\(55\) | 0.955860 | 0.128888 | ||||||||
\(56\) | −1.40032 | −0.187126 | ||||||||
\(57\) | −4.17289 | −0.552713 | ||||||||
\(58\) | −19.6247 | −2.57685 | ||||||||
\(59\) | −11.8415 | −1.54163 | −0.770814 | − | 0.637060i | \(-0.780150\pi\) | ||||
−0.770814 | + | 0.637060i | \(0.780150\pi\) | |||||||
\(60\) | −0.633462 | −0.0817796 | ||||||||
\(61\) | −7.05891 | −0.903801 | −0.451901 | − | 0.892068i | \(-0.649254\pi\) | ||||
−0.451901 | + | 0.892068i | \(0.649254\pi\) | |||||||
\(62\) | 14.1842 | 1.80139 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −12.0780 | −1.50975 | ||||||||
\(65\) | 0.386572 | 0.0479484 | ||||||||
\(66\) | 8.62035 | 1.06109 | ||||||||
\(67\) | −0.167504 | −0.0204638 | −0.0102319 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102319 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(68\) | 12.2250 | 1.48250 | ||||||||
\(69\) | 5.22408 | 0.628905 | ||||||||
\(70\) | 0.515547 | 0.0616197 | ||||||||
\(71\) | 6.98566 | 0.829045 | 0.414523 | − | 0.910039i | \(-0.363949\pi\) | ||||
0.414523 | + | 0.910039i | \(0.363949\pi\) | |||||||
\(72\) | −1.40032 | −0.165030 | ||||||||
\(73\) | −2.79662 | −0.327320 | −0.163660 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163660 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(74\) | 0.762683 | 0.0886601 | ||||||||
\(75\) | −4.94283 | −0.570749 | ||||||||
\(76\) | −11.0558 | −1.26818 | ||||||||
\(77\) | −3.99784 | −0.455596 | ||||||||
\(78\) | 3.48627 | 0.394743 | ||||||||
\(79\) | 14.2526 | 1.60354 | 0.801770 | − | 0.597633i | \(-0.203892\pi\) | ||||
0.801770 | + | 0.597633i | \(0.203892\pi\) | |||||||
\(80\) | 0.544990 | 0.0609317 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.6471 | 1.83836 | ||||||||
\(83\) | −6.75526 | −0.741486 | −0.370743 | − | 0.928735i | \(-0.620897\pi\) | ||||
−0.370743 | + | 0.928735i | \(0.620897\pi\) | |||||||
\(84\) | 2.64943 | 0.289076 | ||||||||
\(85\) | −1.10323 | −0.119662 | ||||||||
\(86\) | 15.8089 | 1.70472 | ||||||||
\(87\) | 9.10130 | 0.975762 | ||||||||
\(88\) | 5.59827 | 0.596778 | ||||||||
\(89\) | −11.9943 | −1.27140 | −0.635698 | − | 0.771938i | \(-0.719288\pi\) | ||||
−0.635698 | + | 0.771938i | \(0.719288\pi\) | |||||||
\(90\) | 0.515547 | 0.0543434 | ||||||||
\(91\) | −1.61682 | −0.169489 | ||||||||
\(92\) | 13.8408 | 1.44300 | ||||||||
\(93\) | −6.57815 | −0.682123 | ||||||||
\(94\) | −7.59856 | −0.783731 | ||||||||
\(95\) | 0.997714 | 0.102363 | ||||||||
\(96\) | 7.71560 | 0.787471 | ||||||||
\(97\) | −1.79091 | −0.181840 | −0.0909199 | − | 0.995858i | \(-0.528981\pi\) | ||||
−0.0909199 | + | 0.995858i | \(0.528981\pi\) | |||||||
\(98\) | −2.15625 | −0.217814 | ||||||||
\(99\) | −3.99784 | −0.401798 | ||||||||
\(100\) | −13.0957 | −1.30957 | ||||||||
\(101\) | −11.0925 | −1.10375 | −0.551873 | − | 0.833928i | \(-0.686087\pi\) | ||||
−0.551873 | + | 0.833928i | \(0.686087\pi\) | |||||||
\(102\) | −9.94939 | −0.985137 | ||||||||
\(103\) | 14.5981 | 1.43839 | 0.719197 | − | 0.694806i | \(-0.244510\pi\) | ||||
0.719197 | + | 0.694806i | \(0.244510\pi\) | |||||||
\(104\) | 2.26407 | 0.222011 | ||||||||
\(105\) | −0.239094 | −0.0233332 | ||||||||
\(106\) | 1.41240 | 0.137184 | ||||||||
\(107\) | 10.6926 | 1.03369 | 0.516845 | − | 0.856079i | \(-0.327106\pi\) | ||||
0.516845 | + | 0.856079i | \(0.327106\pi\) | |||||||
\(108\) | 2.64943 | 0.254941 | ||||||||
\(109\) | −19.1750 | −1.83664 | −0.918318 | − | 0.395844i | \(-0.870452\pi\) | ||||
−0.918318 | + | 0.395844i | \(0.870452\pi\) | |||||||
\(110\) | −2.06107 | −0.196516 | ||||||||
\(111\) | −0.353708 | −0.0335725 | ||||||||
\(112\) | −2.27940 | −0.215383 | ||||||||
\(113\) | −13.9603 | −1.31327 | −0.656636 | − | 0.754208i | \(-0.728021\pi\) | ||||
−0.656636 | + | 0.754208i | \(0.728021\pi\) | |||||||
\(114\) | 8.99781 | 0.842722 | ||||||||
\(115\) | −1.24905 | −0.116474 | ||||||||
\(116\) | 24.1132 | 2.23886 | ||||||||
\(117\) | −1.61682 | −0.149475 | ||||||||
\(118\) | 25.5332 | 2.35052 | ||||||||
\(119\) | 4.61421 | 0.422984 | ||||||||
\(120\) | 0.334809 | 0.0305638 | ||||||||
\(121\) | 4.98272 | 0.452974 | ||||||||
\(122\) | 15.2208 | 1.37803 | ||||||||
\(123\) | −7.72038 | −0.696123 | ||||||||
\(124\) | −17.4283 | −1.56511 | ||||||||
\(125\) | 2.37727 | 0.212630 | ||||||||
\(126\) | −2.15625 | −0.192094 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 10.6120 | 0.937978 | ||||||||
\(129\) | −7.33166 | −0.645516 | ||||||||
\(130\) | −0.833547 | −0.0731069 | ||||||||
\(131\) | −1.23738 | −0.108111 | −0.0540553 | − | 0.998538i | \(-0.517215\pi\) | ||||
−0.0540553 | + | 0.998538i | \(0.517215\pi\) | |||||||
\(132\) | −10.5920 | −0.921913 | ||||||||
\(133\) | −4.17289 | −0.361836 | ||||||||
\(134\) | 0.361180 | 0.0312012 | ||||||||
\(135\) | −0.239094 | −0.0205779 | ||||||||
\(136\) | −6.46139 | −0.554059 | ||||||||
\(137\) | −5.10054 | −0.435769 | −0.217884 | − | 0.975975i | \(-0.569916\pi\) | ||||
−0.217884 | + | 0.975975i | \(0.569916\pi\) | |||||||
\(138\) | −11.2644 | −0.958892 | ||||||||
\(139\) | 12.5215 | 1.06206 | 0.531032 | − | 0.847352i | \(-0.321805\pi\) | ||||
0.531032 | + | 0.847352i | \(0.321805\pi\) | |||||||
\(140\) | −0.633462 | −0.0535373 | ||||||||
\(141\) | 3.52396 | 0.296771 | ||||||||
\(142\) | −15.0628 | −1.26405 | ||||||||
\(143\) | 6.46379 | 0.540529 | ||||||||
\(144\) | −2.27940 | −0.189950 | ||||||||
\(145\) | −2.17607 | −0.180713 | ||||||||
\(146\) | 6.03022 | 0.499065 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −0.937122 | −0.0770310 | ||||||||
\(149\) | 9.58767 | 0.785452 | 0.392726 | − | 0.919655i | \(-0.371532\pi\) | ||||
0.392726 | + | 0.919655i | \(0.371532\pi\) | |||||||
\(150\) | 10.6580 | 0.870222 | ||||||||
\(151\) | −17.1326 | −1.39423 | −0.697117 | − | 0.716957i | \(-0.745534\pi\) | ||||
−0.697117 | + | 0.716957i | \(0.745534\pi\) | |||||||
\(152\) | 5.84341 | 0.473963 | ||||||||
\(153\) | 4.61421 | 0.373036 | ||||||||
\(154\) | 8.62035 | 0.694648 | ||||||||
\(155\) | 1.57280 | 0.126330 | ||||||||
\(156\) | −4.28365 | −0.342966 | ||||||||
\(157\) | 7.98480 | 0.637257 | 0.318628 | − | 0.947880i | \(-0.396778\pi\) | ||||
0.318628 | + | 0.947880i | \(0.396778\pi\) | |||||||
\(158\) | −30.7322 | −2.44492 | ||||||||
\(159\) | −0.655025 | −0.0519468 | ||||||||
\(160\) | −1.84476 | −0.145841 | ||||||||
\(161\) | 5.22408 | 0.411715 | ||||||||
\(162\) | −2.15625 | −0.169411 | ||||||||
\(163\) | 5.01915 | 0.393130 | 0.196565 | − | 0.980491i | \(-0.437021\pi\) | ||||
0.196565 | + | 0.980491i | \(0.437021\pi\) | |||||||
\(164\) | −20.4546 | −1.59723 | ||||||||
\(165\) | 0.955860 | 0.0744136 | ||||||||
\(166\) | 14.5661 | 1.13055 | ||||||||
\(167\) | 7.58516 | 0.586958 | 0.293479 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293479 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(168\) | −1.40032 | −0.108037 | ||||||||
\(169\) | −10.3859 | −0.798915 | ||||||||
\(170\) | 2.37884 | 0.182449 | ||||||||
\(171\) | −4.17289 | −0.319109 | ||||||||
\(172\) | −19.4247 | −1.48112 | ||||||||
\(173\) | −4.01343 | −0.305135 | −0.152568 | − | 0.988293i | \(-0.548754\pi\) | ||||
−0.152568 | + | 0.988293i | \(0.548754\pi\) | |||||||
\(174\) | −19.6247 | −1.48775 | ||||||||
\(175\) | −4.94283 | −0.373643 | ||||||||
\(176\) | 9.11266 | 0.686893 | ||||||||
\(177\) | −11.8415 | −0.890059 | ||||||||
\(178\) | 25.8628 | 1.93850 | ||||||||
\(179\) | −24.8302 | −1.85590 | −0.927948 | − | 0.372711i | \(-0.878428\pi\) | ||||
−0.927948 | + | 0.372711i | \(0.878428\pi\) | |||||||
\(180\) | −0.633462 | −0.0472155 | ||||||||
\(181\) | 7.31346 | 0.543606 | 0.271803 | − | 0.962353i | \(-0.412380\pi\) | ||||
0.271803 | + | 0.962353i | \(0.412380\pi\) | |||||||
\(182\) | 3.48627 | 0.258420 | ||||||||
\(183\) | −7.05891 | −0.521810 | ||||||||
\(184\) | −7.31540 | −0.539299 | ||||||||
\(185\) | 0.0845694 | 0.00621767 | ||||||||
\(186\) | 14.1842 | 1.04003 | ||||||||
\(187\) | −18.4469 | −1.34897 | ||||||||
\(188\) | 9.33648 | 0.680933 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −2.15132 | −0.156073 | ||||||||
\(191\) | −12.4008 | −0.897293 | −0.448646 | − | 0.893709i | \(-0.648094\pi\) | ||||
−0.448646 | + | 0.893709i | \(0.648094\pi\) | |||||||
\(192\) | −12.0780 | −0.871654 | ||||||||
\(193\) | 16.0448 | 1.15493 | 0.577465 | − | 0.816415i | \(-0.304042\pi\) | ||||
0.577465 | + | 0.816415i | \(0.304042\pi\) | |||||||
\(194\) | 3.86166 | 0.277251 | ||||||||
\(195\) | 0.386572 | 0.0276830 | ||||||||
\(196\) | 2.64943 | 0.189245 | ||||||||
\(197\) | 12.1872 | 0.868304 | 0.434152 | − | 0.900840i | \(-0.357048\pi\) | ||||
0.434152 | + | 0.900840i | \(0.357048\pi\) | |||||||
\(198\) | 8.62035 | 0.612622 | ||||||||
\(199\) | 13.7816 | 0.976950 | 0.488475 | − | 0.872578i | \(-0.337553\pi\) | ||||
0.488475 | + | 0.872578i | \(0.337553\pi\) | |||||||
\(200\) | 6.92157 | 0.489429 | ||||||||
\(201\) | −0.167504 | −0.0118148 | ||||||||
\(202\) | 23.9183 | 1.68288 | ||||||||
\(203\) | 9.10130 | 0.638786 | ||||||||
\(204\) | 12.2250 | 0.855921 | ||||||||
\(205\) | 1.84590 | 0.128923 | ||||||||
\(206\) | −31.4772 | −2.19312 | ||||||||
\(207\) | 5.22408 | 0.363098 | ||||||||
\(208\) | 3.68537 | 0.255535 | ||||||||
\(209\) | 16.6826 | 1.15396 | ||||||||
\(210\) | 0.515547 | 0.0355761 | ||||||||
\(211\) | −12.3776 | −0.852111 | −0.426056 | − | 0.904697i | \(-0.640097\pi\) | ||||
−0.426056 | + | 0.904697i | \(0.640097\pi\) | |||||||
\(212\) | −1.73544 | −0.119190 | ||||||||
\(213\) | 6.98566 | 0.478649 | ||||||||
\(214\) | −23.0559 | −1.57607 | ||||||||
\(215\) | 1.75296 | 0.119551 | ||||||||
\(216\) | −1.40032 | −0.0952800 | ||||||||
\(217\) | −6.57815 | −0.446554 | ||||||||
\(218\) | 41.3462 | 2.80032 | ||||||||
\(219\) | −2.79662 | −0.188978 | ||||||||
\(220\) | 2.53248 | 0.170740 | ||||||||
\(221\) | −7.46034 | −0.501837 | ||||||||
\(222\) | 0.762683 | 0.0511879 | ||||||||
\(223\) | −16.9298 | −1.13370 | −0.566852 | − | 0.823819i | \(-0.691839\pi\) | ||||
−0.566852 | + | 0.823819i | \(0.691839\pi\) | |||||||
\(224\) | 7.71560 | 0.515520 | ||||||||
\(225\) | −4.94283 | −0.329522 | ||||||||
\(226\) | 30.1019 | 2.00235 | ||||||||
\(227\) | −14.4225 | −0.957256 | −0.478628 | − | 0.878018i | \(-0.658866\pi\) | ||||
−0.478628 | + | 0.878018i | \(0.658866\pi\) | |||||||
\(228\) | −11.0558 | −0.732186 | ||||||||
\(229\) | −16.4164 | −1.08483 | −0.542414 | − | 0.840111i | \(-0.682490\pi\) | ||||
−0.542414 | + | 0.840111i | \(0.682490\pi\) | |||||||
\(230\) | 2.69326 | 0.177588 | ||||||||
\(231\) | −3.99784 | −0.263039 | ||||||||
\(232\) | −12.7448 | −0.836736 | ||||||||
\(233\) | −7.64997 | −0.501167 | −0.250583 | − | 0.968095i | \(-0.580622\pi\) | ||||
−0.250583 | + | 0.968095i | \(0.580622\pi\) | |||||||
\(234\) | 3.48627 | 0.227905 | ||||||||
\(235\) | −0.842559 | −0.0549625 | ||||||||
\(236\) | −31.3731 | −2.04221 | ||||||||
\(237\) | 14.2526 | 0.925804 | ||||||||
\(238\) | −9.94939 | −0.644923 | ||||||||
\(239\) | 8.03695 | 0.519867 | 0.259933 | − | 0.965627i | \(-0.416299\pi\) | ||||
0.259933 | + | 0.965627i | \(0.416299\pi\) | |||||||
\(240\) | 0.544990 | 0.0351790 | ||||||||
\(241\) | −22.8036 | −1.46891 | −0.734456 | − | 0.678657i | \(-0.762562\pi\) | ||||
−0.734456 | + | 0.678657i | \(0.762562\pi\) | |||||||
\(242\) | −10.7440 | −0.690650 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −18.7021 | −1.19728 | ||||||||
\(245\) | −0.239094 | −0.0152752 | ||||||||
\(246\) | 16.6471 | 1.06138 | ||||||||
\(247\) | 6.74682 | 0.429290 | ||||||||
\(248\) | 9.21155 | 0.584934 | ||||||||
\(249\) | −6.75526 | −0.428097 | ||||||||
\(250\) | −5.12600 | −0.324197 | ||||||||
\(251\) | −2.22670 | −0.140548 | −0.0702739 | − | 0.997528i | \(-0.522387\pi\) | ||||
−0.0702739 | + | 0.997528i | \(0.522387\pi\) | |||||||
\(252\) | 2.64943 | 0.166898 | ||||||||
\(253\) | −20.8850 | −1.31303 | ||||||||
\(254\) | 2.15625 | 0.135295 | ||||||||
\(255\) | −1.10323 | −0.0690869 | ||||||||
\(256\) | 1.27383 | 0.0796142 | ||||||||
\(257\) | 12.7786 | 0.797110 | 0.398555 | − | 0.917144i | \(-0.369512\pi\) | ||||
0.398555 | + | 0.917144i | \(0.369512\pi\) | |||||||
\(258\) | 15.8089 | 0.984219 | ||||||||
\(259\) | −0.353708 | −0.0219783 | ||||||||
\(260\) | 1.02419 | 0.0635178 | ||||||||
\(261\) | 9.10130 | 0.563356 | ||||||||
\(262\) | 2.66811 | 0.164836 | ||||||||
\(263\) | 1.91222 | 0.117912 | 0.0589562 | − | 0.998261i | \(-0.481223\pi\) | ||||
0.0589562 | + | 0.998261i | \(0.481223\pi\) | |||||||
\(264\) | 5.59827 | 0.344550 | ||||||||
\(265\) | 0.156612 | 0.00962063 | ||||||||
\(266\) | 8.99781 | 0.551691 | ||||||||
\(267\) | −11.9943 | −0.734041 | ||||||||
\(268\) | −0.443788 | −0.0271087 | ||||||||
\(269\) | 7.78586 | 0.474712 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(270\) | 0.515547 | 0.0313752 | ||||||||
\(271\) | −10.3228 | −0.627064 | −0.313532 | − | 0.949578i | \(-0.601512\pi\) | ||||
−0.313532 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(272\) | −10.5176 | −0.637723 | ||||||||
\(273\) | −1.61682 | −0.0978544 | ||||||||
\(274\) | 10.9981 | 0.664417 | ||||||||
\(275\) | 19.7607 | 1.19161 | ||||||||
\(276\) | 13.8408 | 0.833118 | ||||||||
\(277\) | −13.1278 | −0.788776 | −0.394388 | − | 0.918944i | \(-0.629043\pi\) | ||||
−0.394388 | + | 0.918944i | \(0.629043\pi\) | |||||||
\(278\) | −26.9996 | −1.61933 | ||||||||
\(279\) | −6.57815 | −0.393824 | ||||||||
\(280\) | 0.334809 | 0.0200087 | ||||||||
\(281\) | 18.1404 | 1.08216 | 0.541081 | − | 0.840970i | \(-0.318015\pi\) | ||||
0.541081 | + | 0.840970i | \(0.318015\pi\) | |||||||
\(282\) | −7.59856 | −0.452487 | ||||||||
\(283\) | −19.1287 | −1.13708 | −0.568542 | − | 0.822655i | \(-0.692492\pi\) | ||||
−0.568542 | + | 0.822655i | \(0.692492\pi\) | |||||||
\(284\) | 18.5080 | 1.09825 | ||||||||
\(285\) | 0.997714 | 0.0590995 | ||||||||
\(286\) | −13.9376 | −0.824145 | ||||||||
\(287\) | −7.72038 | −0.455720 | ||||||||
\(288\) | 7.71560 | 0.454646 | ||||||||
\(289\) | 4.29089 | 0.252406 | ||||||||
\(290\) | 4.69215 | 0.275533 | ||||||||
\(291\) | −1.79091 | −0.104985 | ||||||||
\(292\) | −7.40944 | −0.433604 | ||||||||
\(293\) | −26.6893 | −1.55921 | −0.779603 | − | 0.626274i | \(-0.784579\pi\) | ||||
−0.779603 | + | 0.626274i | \(0.784579\pi\) | |||||||
\(294\) | −2.15625 | −0.125755 | ||||||||
\(295\) | 2.83122 | 0.164840 | ||||||||
\(296\) | 0.495306 | 0.0287891 | ||||||||
\(297\) | −3.99784 | −0.231978 | ||||||||
\(298\) | −20.6734 | −1.19758 | ||||||||
\(299\) | −8.44639 | −0.488468 | ||||||||
\(300\) | −13.0957 | −0.756079 | ||||||||
\(301\) | −7.33166 | −0.422590 | ||||||||
\(302\) | 36.9423 | 2.12579 | ||||||||
\(303\) | −11.0925 | −0.637249 | ||||||||
\(304\) | 9.51168 | 0.545532 | ||||||||
\(305\) | 1.68774 | 0.0966400 | ||||||||
\(306\) | −9.94939 | −0.568769 | ||||||||
\(307\) | 9.45867 | 0.539835 | 0.269917 | − | 0.962883i | \(-0.413004\pi\) | ||||
0.269917 | + | 0.962883i | \(0.413004\pi\) | |||||||
\(308\) | −10.5920 | −0.603534 | ||||||||
\(309\) | 14.5981 | 0.830458 | ||||||||
\(310\) | −3.39135 | −0.192616 | ||||||||
\(311\) | 1.98631 | 0.112633 | 0.0563167 | − | 0.998413i | \(-0.482064\pi\) | ||||
0.0563167 | + | 0.998413i | \(0.482064\pi\) | |||||||
\(312\) | 2.26407 | 0.128178 | ||||||||
\(313\) | −20.0441 | −1.13296 | −0.566480 | − | 0.824075i | \(-0.691695\pi\) | ||||
−0.566480 | + | 0.824075i | \(0.691695\pi\) | |||||||
\(314\) | −17.2173 | −0.971626 | ||||||||
\(315\) | −0.239094 | −0.0134714 | ||||||||
\(316\) | 37.7611 | 2.12423 | ||||||||
\(317\) | −27.2490 | −1.53046 | −0.765228 | − | 0.643760i | \(-0.777374\pi\) | ||||
−0.765228 | + | 0.643760i | \(0.777374\pi\) | |||||||
\(318\) | 1.41240 | 0.0792034 | ||||||||
\(319\) | −36.3855 | −2.03720 | ||||||||
\(320\) | 2.88778 | 0.161432 | ||||||||
\(321\) | 10.6926 | 0.596801 | ||||||||
\(322\) | −11.2644 | −0.627742 | ||||||||
\(323\) | −19.2546 | −1.07135 | ||||||||
\(324\) | 2.64943 | 0.147190 | ||||||||
\(325\) | 7.99168 | 0.443298 | ||||||||
\(326\) | −10.8226 | −0.599406 | ||||||||
\(327\) | −19.1750 | −1.06038 | ||||||||
\(328\) | 10.8110 | 0.596940 | ||||||||
\(329\) | 3.52396 | 0.194282 | ||||||||
\(330\) | −2.06107 | −0.113458 | ||||||||
\(331\) | 34.0423 | 1.87113 | 0.935567 | − | 0.353150i | \(-0.114889\pi\) | ||||
0.935567 | + | 0.353150i | \(0.114889\pi\) | |||||||
\(332\) | −17.8976 | −0.982256 | ||||||||
\(333\) | −0.353708 | −0.0193831 | ||||||||
\(334\) | −16.3555 | −0.894935 | ||||||||
\(335\) | 0.0400491 | 0.00218812 | ||||||||
\(336\) | −2.27940 | −0.124351 | ||||||||
\(337\) | −13.1131 | −0.714318 | −0.357159 | − | 0.934044i | \(-0.616255\pi\) | ||||
−0.357159 | + | 0.934044i | \(0.616255\pi\) | |||||||
\(338\) | 22.3946 | 1.21811 | ||||||||
\(339\) | −13.9603 | −0.758218 | ||||||||
\(340\) | −2.92292 | −0.158518 | ||||||||
\(341\) | 26.2984 | 1.42414 | ||||||||
\(342\) | 8.99781 | 0.486546 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.2667 | 0.553543 | ||||||||
\(345\) | −1.24905 | −0.0672464 | ||||||||
\(346\) | 8.65396 | 0.465240 | ||||||||
\(347\) | −8.22380 | −0.441477 | −0.220738 | − | 0.975333i | \(-0.570847\pi\) | ||||
−0.220738 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(348\) | 24.1132 | 1.29260 | ||||||||
\(349\) | −22.6433 | −1.21207 | −0.606035 | − | 0.795438i | \(-0.707241\pi\) | ||||
−0.606035 | + | 0.795438i | \(0.707241\pi\) | |||||||
\(350\) | 10.6580 | 0.569694 | ||||||||
\(351\) | −1.61682 | −0.0862995 | ||||||||
\(352\) | −30.8457 | −1.64408 | ||||||||
\(353\) | −22.9217 | −1.22000 | −0.610000 | − | 0.792401i | \(-0.708831\pi\) | ||||
−0.610000 | + | 0.792401i | \(0.708831\pi\) | |||||||
\(354\) | 25.5332 | 1.35707 | ||||||||
\(355\) | −1.67023 | −0.0886466 | ||||||||
\(356\) | −31.7781 | −1.68423 | ||||||||
\(357\) | 4.61421 | 0.244210 | ||||||||
\(358\) | 53.5402 | 2.82969 | ||||||||
\(359\) | 22.9728 | 1.21246 | 0.606230 | − | 0.795289i | \(-0.292681\pi\) | ||||
0.606230 | + | 0.795289i | \(0.292681\pi\) | |||||||
\(360\) | 0.334809 | 0.0176460 | ||||||||
\(361\) | −1.58696 | −0.0835240 | ||||||||
\(362\) | −15.7697 | −0.828836 | ||||||||
\(363\) | 4.98272 | 0.261525 | ||||||||
\(364\) | −4.28365 | −0.224524 | ||||||||
\(365\) | 0.668655 | 0.0349990 | ||||||||
\(366\) | 15.2208 | 0.795604 | ||||||||
\(367\) | −2.80411 | −0.146373 | −0.0731866 | − | 0.997318i | \(-0.523317\pi\) | ||||
−0.0731866 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(368\) | −11.9077 | −0.620734 | ||||||||
\(369\) | −7.72038 | −0.401907 | ||||||||
\(370\) | −0.182353 | −0.00948008 | ||||||||
\(371\) | −0.655025 | −0.0340072 | ||||||||
\(372\) | −17.4283 | −0.903617 | ||||||||
\(373\) | −35.2417 | −1.82475 | −0.912374 | − | 0.409358i | \(-0.865753\pi\) | ||||
−0.912374 | + | 0.409358i | \(0.865753\pi\) | |||||||
\(374\) | 39.7761 | 2.05677 | ||||||||
\(375\) | 2.37727 | 0.122762 | ||||||||
\(376\) | −4.93469 | −0.254487 | ||||||||
\(377\) | −14.7152 | −0.757870 | ||||||||
\(378\) | −2.15625 | −0.110906 | ||||||||
\(379\) | −8.26039 | −0.424308 | −0.212154 | − | 0.977236i | \(-0.568048\pi\) | ||||
−0.212154 | + | 0.977236i | \(0.568048\pi\) | |||||||
\(380\) | 2.64337 | 0.135602 | ||||||||
\(381\) | −1.00000 | −0.0512316 | ||||||||
\(382\) | 26.7393 | 1.36810 | ||||||||
\(383\) | −6.69505 | −0.342101 | −0.171050 | − | 0.985262i | \(-0.554716\pi\) | ||||
−0.171050 | + | 0.985262i | \(0.554716\pi\) | |||||||
\(384\) | 10.6120 | 0.541542 | ||||||||
\(385\) | 0.955860 | 0.0487151 | ||||||||
\(386\) | −34.5966 | −1.76092 | ||||||||
\(387\) | −7.33166 | −0.372689 | ||||||||
\(388\) | −4.74489 | −0.240885 | ||||||||
\(389\) | −13.4050 | −0.679658 | −0.339829 | − | 0.940487i | \(-0.610369\pi\) | ||||
−0.339829 | + | 0.940487i | \(0.610369\pi\) | |||||||
\(390\) | −0.833547 | −0.0422083 | ||||||||
\(391\) | 24.1050 | 1.21904 | ||||||||
\(392\) | −1.40032 | −0.0707271 | ||||||||
\(393\) | −1.23738 | −0.0624176 | ||||||||
\(394\) | −26.2787 | −1.32390 | ||||||||
\(395\) | −3.40771 | −0.171460 | ||||||||
\(396\) | −10.5920 | −0.532267 | ||||||||
\(397\) | 1.27937 | 0.0642097 | 0.0321048 | − | 0.999485i | \(-0.489779\pi\) | ||||
0.0321048 | + | 0.999485i | \(0.489779\pi\) | |||||||
\(398\) | −29.7165 | −1.48956 | ||||||||
\(399\) | −4.17289 | −0.208906 | ||||||||
\(400\) | 11.2667 | 0.563334 | ||||||||
\(401\) | −25.8637 | −1.29157 | −0.645785 | − | 0.763519i | \(-0.723470\pi\) | ||||
−0.645785 | + | 0.763519i | \(0.723470\pi\) | |||||||
\(402\) | 0.361180 | 0.0180140 | ||||||||
\(403\) | 10.6357 | 0.529802 | ||||||||
\(404\) | −29.3888 | −1.46215 | ||||||||
\(405\) | −0.239094 | −0.0118807 | ||||||||
\(406\) | −19.6247 | −0.973958 | ||||||||
\(407\) | 1.41407 | 0.0700927 | ||||||||
\(408\) | −6.46139 | −0.319886 | ||||||||
\(409\) | −8.40634 | −0.415667 | −0.207833 | − | 0.978164i | \(-0.566641\pi\) | ||||
−0.207833 | + | 0.978164i | \(0.566641\pi\) | |||||||
\(410\) | −3.98022 | −0.196569 | ||||||||
\(411\) | −5.10054 | −0.251591 | ||||||||
\(412\) | 38.6766 | 1.90546 | ||||||||
\(413\) | −11.8415 | −0.582681 | ||||||||
\(414\) | −11.2644 | −0.553616 | ||||||||
\(415\) | 1.61514 | 0.0792843 | ||||||||
\(416\) | −12.4747 | −0.611625 | ||||||||
\(417\) | 12.5215 | 0.613183 | ||||||||
\(418\) | −35.9718 | −1.75944 | ||||||||
\(419\) | 12.0193 | 0.587183 | 0.293592 | − | 0.955931i | \(-0.405149\pi\) | ||||
0.293592 | + | 0.955931i | \(0.405149\pi\) | |||||||
\(420\) | −0.633462 | −0.0309098 | ||||||||
\(421\) | 27.5197 | 1.34123 | 0.670614 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670614 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(422\) | 26.6893 | 1.29922 | ||||||||
\(423\) | 3.52396 | 0.171341 | ||||||||
\(424\) | 0.917247 | 0.0445455 | ||||||||
\(425\) | −22.8073 | −1.10631 | ||||||||
\(426\) | −15.0628 | −0.729797 | ||||||||
\(427\) | −7.05891 | −0.341605 | ||||||||
\(428\) | 28.3292 | 1.36934 | ||||||||
\(429\) | 6.46379 | 0.312075 | ||||||||
\(430\) | −3.77981 | −0.182279 | ||||||||
\(431\) | 35.4733 | 1.70869 | 0.854345 | − | 0.519707i | \(-0.173959\pi\) | ||||
0.854345 | + | 0.519707i | \(0.173959\pi\) | |||||||
\(432\) | −2.27940 | −0.109668 | ||||||||
\(433\) | 26.5237 | 1.27465 | 0.637323 | − | 0.770597i | \(-0.280042\pi\) | ||||
0.637323 | + | 0.770597i | \(0.280042\pi\) | |||||||
\(434\) | 14.1842 | 0.680862 | ||||||||
\(435\) | −2.17607 | −0.104334 | ||||||||
\(436\) | −50.8028 | −2.43301 | ||||||||
\(437\) | −21.7995 | −1.04281 | ||||||||
\(438\) | 6.03022 | 0.288135 | ||||||||
\(439\) | −32.6301 | −1.55735 | −0.778674 | − | 0.627428i | \(-0.784108\pi\) | ||||
−0.778674 | + | 0.627428i | \(0.784108\pi\) | |||||||
\(440\) | −1.33851 | −0.0638111 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 16.0864 | 0.765151 | ||||||||
\(443\) | 16.0947 | 0.764681 | 0.382340 | − | 0.924022i | \(-0.375118\pi\) | ||||
0.382340 | + | 0.924022i | \(0.375118\pi\) | |||||||
\(444\) | −0.937122 | −0.0444739 | ||||||||
\(445\) | 2.86777 | 0.135945 | ||||||||
\(446\) | 36.5050 | 1.72856 | ||||||||
\(447\) | 9.58767 | 0.453481 | ||||||||
\(448\) | −12.0780 | −0.570632 | ||||||||
\(449\) | 33.1478 | 1.56434 | 0.782171 | − | 0.623064i | \(-0.214112\pi\) | ||||
0.782171 | + | 0.623064i | \(0.214112\pi\) | |||||||
\(450\) | 10.6580 | 0.502423 | ||||||||
\(451\) | 30.8648 | 1.45337 | ||||||||
\(452\) | −36.9867 | −1.73971 | ||||||||
\(453\) | −17.1326 | −0.804962 | ||||||||
\(454\) | 31.0986 | 1.45953 | ||||||||
\(455\) | 0.386572 | 0.0181228 | ||||||||
\(456\) | 5.84341 | 0.273643 | ||||||||
\(457\) | −20.7795 | −0.972026 | −0.486013 | − | 0.873952i | \(-0.661549\pi\) | ||||
−0.486013 | + | 0.873952i | \(0.661549\pi\) | |||||||
\(458\) | 35.3980 | 1.65404 | ||||||||
\(459\) | 4.61421 | 0.215373 | ||||||||
\(460\) | −3.30925 | −0.154295 | ||||||||
\(461\) | 26.0027 | 1.21106 | 0.605532 | − | 0.795821i | \(-0.292960\pi\) | ||||
0.605532 | + | 0.795821i | \(0.292960\pi\) | |||||||
\(462\) | 8.62035 | 0.401055 | ||||||||
\(463\) | 1.40695 | 0.0653867 | 0.0326934 | − | 0.999465i | \(-0.489592\pi\) | ||||
0.0326934 | + | 0.999465i | \(0.489592\pi\) | |||||||
\(464\) | −20.7455 | −0.963084 | ||||||||
\(465\) | 1.57280 | 0.0729367 | ||||||||
\(466\) | 16.4953 | 0.764129 | ||||||||
\(467\) | −4.52880 | −0.209568 | −0.104784 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104784 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(468\) | −4.28365 | −0.198012 | ||||||||
\(469\) | −0.167504 | −0.00773460 | ||||||||
\(470\) | 1.81677 | 0.0838013 | ||||||||
\(471\) | 7.98480 | 0.367920 | ||||||||
\(472\) | 16.5819 | 0.763244 | ||||||||
\(473\) | 29.3108 | 1.34771 | ||||||||
\(474\) | −30.7322 | −1.41157 | ||||||||
\(475\) | 20.6259 | 0.946382 | ||||||||
\(476\) | 12.2250 | 0.560332 | ||||||||
\(477\) | −0.655025 | −0.0299915 | ||||||||
\(478\) | −17.3297 | −0.792641 | ||||||||
\(479\) | 1.74794 | 0.0798653 | 0.0399327 | − | 0.999202i | \(-0.487286\pi\) | ||||
0.0399327 | + | 0.999202i | \(0.487286\pi\) | |||||||
\(480\) | −1.84476 | −0.0842012 | ||||||||
\(481\) | 0.571882 | 0.0260756 | ||||||||
\(482\) | 49.1704 | 2.23965 | ||||||||
\(483\) | 5.22408 | 0.237704 | ||||||||
\(484\) | 13.2013 | 0.600061 | ||||||||
\(485\) | 0.428197 | 0.0194434 | ||||||||
\(486\) | −2.15625 | −0.0978096 | ||||||||
\(487\) | −25.2382 | −1.14365 | −0.571827 | − | 0.820375i | \(-0.693765\pi\) | ||||
−0.571827 | + | 0.820375i | \(0.693765\pi\) | |||||||
\(488\) | 9.88477 | 0.447463 | ||||||||
\(489\) | 5.01915 | 0.226974 | ||||||||
\(490\) | 0.515547 | 0.0232900 | ||||||||
\(491\) | −27.1705 | −1.22619 | −0.613093 | − | 0.790010i | \(-0.710075\pi\) | ||||
−0.613093 | + | 0.790010i | \(0.710075\pi\) | |||||||
\(492\) | −20.4546 | −0.922163 | ||||||||
\(493\) | 41.9953 | 1.89137 | ||||||||
\(494\) | −14.5478 | −0.654539 | ||||||||
\(495\) | 0.955860 | 0.0429627 | ||||||||
\(496\) | 14.9942 | 0.673260 | ||||||||
\(497\) | 6.98566 | 0.313350 | ||||||||
\(498\) | 14.5661 | 0.652720 | ||||||||
\(499\) | −18.9409 | −0.847909 | −0.423955 | − | 0.905683i | \(-0.639358\pi\) | ||||
−0.423955 | + | 0.905683i | \(0.639358\pi\) | |||||||
\(500\) | 6.29841 | 0.281673 | ||||||||
\(501\) | 7.58516 | 0.338880 | ||||||||
\(502\) | 4.80132 | 0.214293 | ||||||||
\(503\) | −2.52810 | −0.112722 | −0.0563611 | − | 0.998410i | \(-0.517950\pi\) | ||||
−0.0563611 | + | 0.998410i | \(0.517950\pi\) | |||||||
\(504\) | −1.40032 | −0.0623754 | ||||||||
\(505\) | 2.65216 | 0.118019 | ||||||||
\(506\) | 45.0334 | 2.00198 | ||||||||
\(507\) | −10.3859 | −0.461254 | ||||||||
\(508\) | −2.64943 | −0.117549 | ||||||||
\(509\) | 34.9093 | 1.54733 | 0.773663 | − | 0.633598i | \(-0.218422\pi\) | ||||
0.773663 | + | 0.633598i | \(0.218422\pi\) | |||||||
\(510\) | 2.37884 | 0.105337 | ||||||||
\(511\) | −2.79662 | −0.123715 | ||||||||
\(512\) | −23.9707 | −1.05937 | ||||||||
\(513\) | −4.17289 | −0.184238 | ||||||||
\(514\) | −27.5540 | −1.21535 | ||||||||
\(515\) | −3.49032 | −0.153802 | ||||||||
\(516\) | −19.4247 | −0.855124 | ||||||||
\(517\) | −14.0882 | −0.619600 | ||||||||
\(518\) | 0.762683 | 0.0335104 | ||||||||
\(519\) | −4.01343 | −0.176170 | ||||||||
\(520\) | −0.541327 | −0.0237387 | ||||||||
\(521\) | 8.56576 | 0.375273 | 0.187636 | − | 0.982239i | \(-0.439917\pi\) | ||||
0.187636 | + | 0.982239i | \(0.439917\pi\) | |||||||
\(522\) | −19.6247 | −0.858950 | ||||||||
\(523\) | 2.00260 | 0.0875675 | 0.0437838 | − | 0.999041i | \(-0.486059\pi\) | ||||
0.0437838 | + | 0.999041i | \(0.486059\pi\) | |||||||
\(524\) | −3.27835 | −0.143215 | ||||||||
\(525\) | −4.94283 | −0.215723 | ||||||||
\(526\) | −4.12322 | −0.179781 | ||||||||
\(527\) | −30.3530 | −1.32220 | ||||||||
\(528\) | 9.11266 | 0.396578 | ||||||||
\(529\) | 4.29098 | 0.186564 | ||||||||
\(530\) | −0.337696 | −0.0146686 | ||||||||
\(531\) | −11.8415 | −0.513876 | ||||||||
\(532\) | −11.0558 | −0.479328 | ||||||||
\(533\) | 12.4825 | 0.540676 | ||||||||
\(534\) | 25.8628 | 1.11919 | ||||||||
\(535\) | −2.55653 | −0.110528 | ||||||||
\(536\) | 0.234559 | 0.0101314 | ||||||||
\(537\) | −24.8302 | −1.07150 | ||||||||
\(538\) | −16.7883 | −0.723794 | ||||||||
\(539\) | −3.99784 | −0.172199 | ||||||||
\(540\) | −0.633462 | −0.0272599 | ||||||||
\(541\) | −14.8542 | −0.638632 | −0.319316 | − | 0.947648i | \(-0.603453\pi\) | ||||
−0.319316 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(542\) | 22.2585 | 0.956085 | ||||||||
\(543\) | 7.31346 | 0.313851 | ||||||||
\(544\) | 35.6014 | 1.52640 | ||||||||
\(545\) | 4.58464 | 0.196384 | ||||||||
\(546\) | 3.48627 | 0.149199 | ||||||||
\(547\) | 9.86356 | 0.421735 | 0.210868 | − | 0.977515i | \(-0.432371\pi\) | ||||
0.210868 | + | 0.977515i | \(0.432371\pi\) | |||||||
\(548\) | −13.5135 | −0.577268 | ||||||||
\(549\) | −7.05891 | −0.301267 | ||||||||
\(550\) | −42.6090 | −1.81685 | ||||||||
\(551\) | −37.9788 | −1.61795 | ||||||||
\(552\) | −7.31540 | −0.311364 | ||||||||
\(553\) | 14.2526 | 0.606081 | ||||||||
\(554\) | 28.3069 | 1.20265 | ||||||||
\(555\) | 0.0845694 | 0.00358977 | ||||||||
\(556\) | 33.1749 | 1.40693 | ||||||||
\(557\) | −1.50087 | −0.0635939 | −0.0317970 | − | 0.999494i | \(-0.510123\pi\) | ||||
−0.0317970 | + | 0.999494i | \(0.510123\pi\) | |||||||
\(558\) | 14.1842 | 0.600463 | ||||||||
\(559\) | 11.8540 | 0.501370 | ||||||||
\(560\) | 0.544990 | 0.0230300 | ||||||||
\(561\) | −18.4469 | −0.778827 | ||||||||
\(562\) | −39.1152 | −1.64997 | ||||||||
\(563\) | 40.5430 | 1.70868 | 0.854341 | − | 0.519713i | \(-0.173961\pi\) | ||||
0.854341 | + | 0.519713i | \(0.173961\pi\) | |||||||
\(564\) | 9.33648 | 0.393137 | ||||||||
\(565\) | 3.33782 | 0.140423 | ||||||||
\(566\) | 41.2463 | 1.73371 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −9.78219 | −0.410452 | ||||||||
\(569\) | 3.51593 | 0.147396 | 0.0736978 | − | 0.997281i | \(-0.476520\pi\) | ||||
0.0736978 | + | 0.997281i | \(0.476520\pi\) | |||||||
\(570\) | −2.15132 | −0.0901090 | ||||||||
\(571\) | −39.7252 | −1.66245 | −0.831224 | − | 0.555937i | \(-0.812359\pi\) | ||||
−0.831224 | + | 0.555937i | \(0.812359\pi\) | |||||||
\(572\) | 17.1253 | 0.716046 | ||||||||
\(573\) | −12.4008 | −0.518052 | ||||||||
\(574\) | 16.6471 | 0.694836 | ||||||||
\(575\) | −25.8217 | −1.07684 | ||||||||
\(576\) | −12.0780 | −0.503250 | ||||||||
\(577\) | 34.1969 | 1.42364 | 0.711818 | − | 0.702364i | \(-0.247872\pi\) | ||||
0.711818 | + | 0.702364i | \(0.247872\pi\) | |||||||
\(578\) | −9.25225 | −0.384843 | ||||||||
\(579\) | 16.0448 | 0.666799 | ||||||||
\(580\) | −5.76533 | −0.239392 | ||||||||
\(581\) | −6.75526 | −0.280256 | ||||||||
\(582\) | 3.86166 | 0.160071 | ||||||||
\(583\) | 2.61868 | 0.108455 | ||||||||
\(584\) | 3.91618 | 0.162053 | ||||||||
\(585\) | 0.386572 | 0.0159828 | ||||||||
\(586\) | 57.5489 | 2.37732 | ||||||||
\(587\) | −14.5520 | −0.600625 | −0.300313 | − | 0.953841i | \(-0.597091\pi\) | ||||
−0.300313 | + | 0.953841i | \(0.597091\pi\) | |||||||
\(588\) | 2.64943 | 0.109260 | ||||||||
\(589\) | 27.4499 | 1.13105 | ||||||||
\(590\) | −6.10483 | −0.251332 | ||||||||
\(591\) | 12.1872 | 0.501315 | ||||||||
\(592\) | 0.806240 | 0.0331363 | ||||||||
\(593\) | −22.6700 | −0.930947 | −0.465473 | − | 0.885062i | \(-0.654116\pi\) | ||||
−0.465473 | + | 0.885062i | \(0.654116\pi\) | |||||||
\(594\) | 8.62035 | 0.353697 | ||||||||
\(595\) | −1.10323 | −0.0452280 | ||||||||
\(596\) | 25.4018 | 1.04050 | ||||||||
\(597\) | 13.7816 | 0.564042 | ||||||||
\(598\) | 18.2126 | 0.744767 | ||||||||
\(599\) | 19.5665 | 0.799466 | 0.399733 | − | 0.916632i | \(-0.369103\pi\) | ||||
0.399733 | + | 0.916632i | \(0.369103\pi\) | |||||||
\(600\) | 6.92157 | 0.282572 | ||||||||
\(601\) | 7.31719 | 0.298475 | 0.149237 | − | 0.988801i | \(-0.452318\pi\) | ||||
0.149237 | + | 0.988801i | \(0.452318\pi\) | |||||||
\(602\) | 15.8089 | 0.644323 | ||||||||
\(603\) | −0.167504 | −0.00682127 | ||||||||
\(604\) | −45.3917 | −1.84696 | ||||||||
\(605\) | −1.19134 | −0.0484348 | ||||||||
\(606\) | 23.9183 | 0.971613 | ||||||||
\(607\) | 25.1482 | 1.02074 | 0.510368 | − | 0.859956i | \(-0.329509\pi\) | ||||
0.510368 | + | 0.859956i | \(0.329509\pi\) | |||||||
\(608\) | −32.1964 | −1.30574 | ||||||||
\(609\) | 9.10130 | 0.368803 | ||||||||
\(610\) | −3.63920 | −0.147347 | ||||||||
\(611\) | −5.69762 | −0.230501 | ||||||||
\(612\) | 12.2250 | 0.494166 | ||||||||
\(613\) | 40.8861 | 1.65137 | 0.825686 | − | 0.564129i | \(-0.190788\pi\) | ||||
0.825686 | + | 0.564129i | \(0.190788\pi\) | |||||||
\(614\) | −20.3953 | −0.823087 | ||||||||
\(615\) | 1.84590 | 0.0744338 | ||||||||
\(616\) | 5.59827 | 0.225561 | ||||||||
\(617\) | 23.3040 | 0.938185 | 0.469092 | − | 0.883149i | \(-0.344581\pi\) | ||||
0.469092 | + | 0.883149i | \(0.344581\pi\) | |||||||
\(618\) | −31.4772 | −1.26620 | ||||||||
\(619\) | 36.2218 | 1.45588 | 0.727939 | − | 0.685642i | \(-0.240478\pi\) | ||||
0.727939 | + | 0.685642i | \(0.240478\pi\) | |||||||
\(620\) | 4.16701 | 0.167351 | ||||||||
\(621\) | 5.22408 | 0.209635 | ||||||||
\(622\) | −4.28299 | −0.171732 | ||||||||
\(623\) | −11.9943 | −0.480543 | ||||||||
\(624\) | 3.68537 | 0.147533 | ||||||||
\(625\) | 24.1458 | 0.965831 | ||||||||
\(626\) | 43.2202 | 1.72743 | ||||||||
\(627\) | 16.6826 | 0.666237 | ||||||||
\(628\) | 21.1551 | 0.844182 | ||||||||
\(629\) | −1.63208 | −0.0650753 | ||||||||
\(630\) | 0.515547 | 0.0205399 | ||||||||
\(631\) | 44.1474 | 1.75748 | 0.878741 | − | 0.477299i | \(-0.158384\pi\) | ||||
0.878741 | + | 0.477299i | \(0.158384\pi\) | |||||||
\(632\) | −19.9582 | −0.793896 | ||||||||
\(633\) | −12.3776 | −0.491967 | ||||||||
\(634\) | 58.7557 | 2.33349 | ||||||||
\(635\) | 0.239094 | 0.00948816 | ||||||||
\(636\) | −1.73544 | −0.0688146 | ||||||||
\(637\) | −1.61682 | −0.0640608 | ||||||||
\(638\) | 78.4564 | 3.10612 | ||||||||
\(639\) | 6.98566 | 0.276348 | ||||||||
\(640\) | −2.53727 | −0.100294 | ||||||||
\(641\) | 20.5976 | 0.813557 | 0.406779 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406779 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(642\) | −23.0559 | −0.909943 | ||||||||
\(643\) | −3.13591 | −0.123668 | −0.0618342 | − | 0.998086i | \(-0.519695\pi\) | ||||
−0.0618342 | + | 0.998086i | \(0.519695\pi\) | |||||||
\(644\) | 13.8408 | 0.545404 | ||||||||
\(645\) | 1.75296 | 0.0690226 | ||||||||
\(646\) | 41.5178 | 1.63349 | ||||||||
\(647\) | 6.98764 | 0.274712 | 0.137356 | − | 0.990522i | \(-0.456139\pi\) | ||||
0.137356 | + | 0.990522i | \(0.456139\pi\) | |||||||
\(648\) | −1.40032 | −0.0550100 | ||||||||
\(649\) | 47.3403 | 1.85827 | ||||||||
\(650\) | −17.2321 | −0.675897 | ||||||||
\(651\) | −6.57815 | −0.257818 | ||||||||
\(652\) | 13.2979 | 0.520784 | ||||||||
\(653\) | 18.7511 | 0.733786 | 0.366893 | − | 0.930263i | \(-0.380422\pi\) | ||||
0.366893 | + | 0.930263i | \(0.380422\pi\) | |||||||
\(654\) | 41.3462 | 1.61677 | ||||||||
\(655\) | 0.295851 | 0.0115598 | ||||||||
\(656\) | 17.5978 | 0.687079 | ||||||||
\(657\) | −2.79662 | −0.109107 | ||||||||
\(658\) | −7.59856 | −0.296223 | ||||||||
\(659\) | 28.0273 | 1.09179 | 0.545895 | − | 0.837854i | \(-0.316190\pi\) | ||||
0.545895 | + | 0.837854i | \(0.316190\pi\) | |||||||
\(660\) | 2.53248 | 0.0985766 | ||||||||
\(661\) | −46.8900 | −1.82381 | −0.911905 | − | 0.410401i | \(-0.865389\pi\) | ||||
−0.911905 | + | 0.410401i | \(0.865389\pi\) | |||||||
\(662\) | −73.4038 | −2.85292 | ||||||||
\(663\) | −7.46034 | −0.289736 | ||||||||
\(664\) | 9.45956 | 0.367102 | ||||||||
\(665\) | 0.997714 | 0.0386897 | ||||||||
\(666\) | 0.762683 | 0.0295534 | ||||||||
\(667\) | 47.5459 | 1.84098 | ||||||||
\(668\) | 20.0963 | 0.777550 | ||||||||
\(669\) | −16.9298 | −0.654545 | ||||||||
\(670\) | −0.0863560 | −0.00333622 | ||||||||
\(671\) | 28.2204 | 1.08944 | ||||||||
\(672\) | 7.71560 | 0.297636 | ||||||||
\(673\) | 30.2264 | 1.16514 | 0.582571 | − | 0.812780i | \(-0.302047\pi\) | ||||
0.582571 | + | 0.812780i | \(0.302047\pi\) | |||||||
\(674\) | 28.2752 | 1.08912 | ||||||||
\(675\) | −4.94283 | −0.190250 | ||||||||
\(676\) | −27.5166 | −1.05833 | ||||||||
\(677\) | −4.66520 | −0.179298 | −0.0896491 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896491 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(678\) | 30.1019 | 1.15606 | ||||||||
\(679\) | −1.79091 | −0.0687290 | ||||||||
\(680\) | 1.54488 | 0.0592434 | ||||||||
\(681\) | −14.4225 | −0.552672 | ||||||||
\(682\) | −56.7060 | −2.17138 | ||||||||
\(683\) | −34.8003 | −1.33160 | −0.665798 | − | 0.746132i | \(-0.731909\pi\) | ||||
−0.665798 | + | 0.746132i | \(0.731909\pi\) | |||||||
\(684\) | −11.0558 | −0.422728 | ||||||||
\(685\) | 1.21951 | 0.0465951 | ||||||||
\(686\) | −2.15625 | −0.0823261 | ||||||||
\(687\) | −16.4164 | −0.626326 | ||||||||
\(688\) | 16.7118 | 0.637130 | ||||||||
\(689\) | 1.05906 | 0.0403469 | ||||||||
\(690\) | 2.69326 | 0.102531 | ||||||||
\(691\) | 36.6726 | 1.39509 | 0.697546 | − | 0.716540i | \(-0.254275\pi\) | ||||
0.697546 | + | 0.716540i | \(0.254275\pi\) | |||||||
\(692\) | −10.6333 | −0.404216 | ||||||||
\(693\) | −3.99784 | −0.151865 | ||||||||
\(694\) | 17.7326 | 0.673120 | ||||||||
\(695\) | −2.99383 | −0.113562 | ||||||||
\(696\) | −12.7448 | −0.483090 | ||||||||
\(697\) | −35.6234 | −1.34933 | ||||||||
\(698\) | 48.8247 | 1.84804 | ||||||||
\(699\) | −7.64997 | −0.289349 | ||||||||
\(700\) | −13.0957 | −0.494970 | ||||||||
\(701\) | −11.0457 | −0.417192 | −0.208596 | − | 0.978002i | \(-0.566889\pi\) | ||||
−0.208596 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(702\) | 3.48627 | 0.131581 | ||||||||
\(703\) | 1.47598 | 0.0556678 | ||||||||
\(704\) | 48.2859 | 1.81984 | ||||||||
\(705\) | −0.842559 | −0.0317326 | ||||||||
\(706\) | 49.4250 | 1.86014 | ||||||||
\(707\) | −11.0925 | −0.417177 | ||||||||
\(708\) | −31.3731 | −1.17907 | ||||||||
\(709\) | −7.73369 | −0.290445 | −0.145222 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145222 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(710\) | 3.60144 | 0.135160 | ||||||||
\(711\) | 14.2526 | 0.534513 | ||||||||
\(712\) | 16.7960 | 0.629455 | ||||||||
\(713\) | −34.3648 | −1.28697 | ||||||||
\(714\) | −9.94939 | −0.372347 | ||||||||
\(715\) | −1.54545 | −0.0577967 | ||||||||
\(716\) | −65.7857 | −2.45853 | ||||||||
\(717\) | 8.03695 | 0.300145 | ||||||||
\(718\) | −49.5353 | −1.84864 | ||||||||
\(719\) | −50.9775 | −1.90114 | −0.950571 | − | 0.310509i | \(-0.899501\pi\) | ||||
−0.950571 | + | 0.310509i | \(0.899501\pi\) | |||||||
\(720\) | 0.544990 | 0.0203106 | ||||||||
\(721\) | 14.5981 | 0.543662 | ||||||||
\(722\) | 3.42188 | 0.127349 | ||||||||
\(723\) | −22.8036 | −0.848076 | ||||||||
\(724\) | 19.3765 | 0.720121 | ||||||||
\(725\) | −44.9862 | −1.67075 | ||||||||
\(726\) | −10.7440 | −0.398747 | ||||||||
\(727\) | −6.89848 | −0.255850 | −0.127925 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127925 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(728\) | 2.26407 | 0.0839122 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.44179 | −0.0533630 | ||||||||
\(731\) | −33.8298 | −1.25124 | ||||||||
\(732\) | −18.7021 | −0.691248 | ||||||||
\(733\) | 6.77021 | 0.250063 | 0.125032 | − | 0.992153i | \(-0.460097\pi\) | ||||
0.125032 | + | 0.992153i | \(0.460097\pi\) | |||||||
\(734\) | 6.04636 | 0.223175 | ||||||||
\(735\) | −0.239094 | −0.00881912 | ||||||||
\(736\) | 40.3069 | 1.48573 | ||||||||
\(737\) | 0.669652 | 0.0246670 | ||||||||
\(738\) | 16.6471 | 0.612788 | ||||||||
\(739\) | 10.2163 | 0.375814 | 0.187907 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187907 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(740\) | 0.224060 | 0.00823662 | ||||||||
\(741\) | 6.74682 | 0.247851 | ||||||||
\(742\) | 1.41240 | 0.0518508 | ||||||||
\(743\) | 3.12087 | 0.114493 | 0.0572467 | − | 0.998360i | \(-0.481768\pi\) | ||||
0.0572467 | + | 0.998360i | \(0.481768\pi\) | |||||||
\(744\) | 9.21155 | 0.337712 | ||||||||
\(745\) | −2.29235 | −0.0839854 | ||||||||
\(746\) | 75.9901 | 2.78219 | ||||||||
\(747\) | −6.75526 | −0.247162 | ||||||||
\(748\) | −48.8736 | −1.78699 | ||||||||
\(749\) | 10.6926 | 0.390698 | ||||||||
\(750\) | −5.12600 | −0.187175 | ||||||||
\(751\) | 17.9651 | 0.655557 | 0.327778 | − | 0.944755i | \(-0.393700\pi\) | ||||
0.327778 | + | 0.944755i | \(0.393700\pi\) | |||||||
\(752\) | −8.03251 | −0.292916 | ||||||||
\(753\) | −2.22670 | −0.0811454 | ||||||||
\(754\) | 31.7296 | 1.15552 | ||||||||
\(755\) | 4.09631 | 0.149080 | ||||||||
\(756\) | 2.64943 | 0.0963587 | ||||||||
\(757\) | −41.8801 | −1.52216 | −0.761080 | − | 0.648658i | \(-0.775330\pi\) | ||||
−0.761080 | + | 0.648658i | \(0.775330\pi\) | |||||||
\(758\) | 17.8115 | 0.646942 | ||||||||
\(759\) | −20.8850 | −0.758078 | ||||||||
\(760\) | −1.39712 | −0.0506790 | ||||||||
\(761\) | 47.4903 | 1.72152 | 0.860761 | − | 0.509010i | \(-0.169988\pi\) | ||||
0.860761 | + | 0.509010i | \(0.169988\pi\) | |||||||
\(762\) | 2.15625 | 0.0781128 | ||||||||
\(763\) | −19.1750 | −0.694183 | ||||||||
\(764\) | −32.8551 | −1.18866 | ||||||||
\(765\) | −1.10323 | −0.0398873 | ||||||||
\(766\) | 14.4362 | 0.521602 | ||||||||
\(767\) | 19.1455 | 0.691305 | ||||||||
\(768\) | 1.27383 | 0.0459653 | ||||||||
\(769\) | 44.5562 | 1.60674 | 0.803369 | − | 0.595481i | \(-0.203039\pi\) | ||||
0.803369 | + | 0.595481i | \(0.203039\pi\) | |||||||
\(770\) | −2.06107 | −0.0742760 | ||||||||
\(771\) | 12.7786 | 0.460212 | ||||||||
\(772\) | 42.5095 | 1.52995 | ||||||||
\(773\) | 28.7248 | 1.03316 | 0.516580 | − | 0.856239i | \(-0.327205\pi\) | ||||
0.516580 | + | 0.856239i | \(0.327205\pi\) | |||||||
\(774\) | 15.8089 | 0.568239 | ||||||||
\(775\) | 32.5147 | 1.16796 | ||||||||
\(776\) | 2.50786 | 0.0900270 | ||||||||
\(777\) | −0.353708 | −0.0126892 | ||||||||
\(778\) | 28.9045 | 1.03628 | ||||||||
\(779\) | 32.2163 | 1.15427 | ||||||||
\(780\) | 1.02419 | 0.0366720 | ||||||||
\(781\) | −27.9275 | −0.999326 | ||||||||
\(782\) | −51.9764 | −1.85867 | ||||||||
\(783\) | 9.10130 | 0.325254 | ||||||||
\(784\) | −2.27940 | −0.0814070 | ||||||||
\(785\) | −1.90912 | −0.0681394 | ||||||||
\(786\) | 2.66811 | 0.0951682 | ||||||||
\(787\) | −6.88490 | −0.245420 | −0.122710 | − | 0.992443i | \(-0.539159\pi\) | ||||
−0.122710 | + | 0.992443i | \(0.539159\pi\) | |||||||
\(788\) | 32.2891 | 1.15025 | ||||||||
\(789\) | 1.91222 | 0.0680767 | ||||||||
\(790\) | 7.34788 | 0.261426 | ||||||||
\(791\) | −13.9603 | −0.496370 | ||||||||
\(792\) | 5.59827 | 0.198926 | ||||||||
\(793\) | 11.4130 | 0.405287 | ||||||||
\(794\) | −2.75864 | −0.0979006 | ||||||||
\(795\) | 0.156612 | 0.00555447 | ||||||||
\(796\) | 36.5132 | 1.29418 | ||||||||
\(797\) | 19.8500 | 0.703123 | 0.351562 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351562 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(798\) | 8.99781 | 0.318519 | ||||||||
\(799\) | 16.2603 | 0.575248 | ||||||||
\(800\) | −38.1370 | −1.34834 | ||||||||
\(801\) | −11.9943 | −0.423799 | ||||||||
\(802\) | 55.7686 | 1.96926 | ||||||||
\(803\) | 11.1804 | 0.394549 | ||||||||
\(804\) | −0.443788 | −0.0156512 | ||||||||
\(805\) | −1.24905 | −0.0440231 | ||||||||
\(806\) | −22.9332 | −0.807789 | ||||||||
\(807\) | 7.78586 | 0.274075 | ||||||||
\(808\) | 15.5331 | 0.546454 | ||||||||
\(809\) | −18.8305 | −0.662046 | −0.331023 | − | 0.943623i | \(-0.607394\pi\) | ||||
−0.331023 | + | 0.943623i | \(0.607394\pi\) | |||||||
\(810\) | 0.515547 | 0.0181145 | ||||||||
\(811\) | −47.7100 | −1.67533 | −0.837663 | − | 0.546188i | \(-0.816078\pi\) | ||||
−0.837663 | + | 0.546188i | \(0.816078\pi\) | |||||||
\(812\) | 24.1132 | 0.846208 | ||||||||
\(813\) | −10.3228 | −0.362036 | ||||||||
\(814\) | −3.04908 | −0.106870 | ||||||||
\(815\) | −1.20005 | −0.0420359 | ||||||||
\(816\) | −10.5176 | −0.368190 | ||||||||
\(817\) | 30.5942 | 1.07036 | ||||||||
\(818\) | 18.1262 | 0.633768 | ||||||||
\(819\) | −1.61682 | −0.0564963 | ||||||||
\(820\) | 4.89057 | 0.170786 | ||||||||
\(821\) | 25.1137 | 0.876475 | 0.438238 | − | 0.898859i | \(-0.355603\pi\) | ||||
0.438238 | + | 0.898859i | \(0.355603\pi\) | |||||||
\(822\) | 10.9981 | 0.383601 | ||||||||
\(823\) | 43.0088 | 1.49919 | 0.749597 | − | 0.661895i | \(-0.230247\pi\) | ||||
0.749597 | + | 0.661895i | \(0.230247\pi\) | |||||||
\(824\) | −20.4421 | −0.712134 | ||||||||
\(825\) | 19.7607 | 0.687978 | ||||||||
\(826\) | 25.5332 | 0.888413 | ||||||||
\(827\) | 13.8440 | 0.481403 | 0.240701 | − | 0.970599i | \(-0.422623\pi\) | ||||
0.240701 | + | 0.970599i | \(0.422623\pi\) | |||||||
\(828\) | 13.8408 | 0.481001 | ||||||||
\(829\) | 12.5853 | 0.437105 | 0.218553 | − | 0.975825i | \(-0.429867\pi\) | ||||
0.218553 | + | 0.975825i | \(0.429867\pi\) | |||||||
\(830\) | −3.48266 | −0.120885 | ||||||||
\(831\) | −13.1278 | −0.455400 | ||||||||
\(832\) | 19.5280 | 0.677010 | ||||||||
\(833\) | 4.61421 | 0.159873 | ||||||||
\(834\) | −26.9996 | −0.934920 | ||||||||
\(835\) | −1.81357 | −0.0627611 | ||||||||
\(836\) | 44.1992 | 1.52866 | ||||||||
\(837\) | −6.57815 | −0.227374 | ||||||||
\(838\) | −25.9167 | −0.895279 | ||||||||
\(839\) | −4.46813 | −0.154257 | −0.0771284 | − | 0.997021i | \(-0.524575\pi\) | ||||
−0.0771284 | + | 0.997021i | \(0.524575\pi\) | |||||||
\(840\) | 0.334809 | 0.0115520 | ||||||||
\(841\) | 53.8337 | 1.85633 | ||||||||
\(842\) | −59.3394 | −2.04497 | ||||||||
\(843\) | 18.1404 | 0.624787 | ||||||||
\(844\) | −32.7936 | −1.12880 | ||||||||
\(845\) | 2.48320 | 0.0854248 | ||||||||
\(846\) | −7.59856 | −0.261244 | ||||||||
\(847\) | 4.98272 | 0.171208 | ||||||||
\(848\) | 1.49306 | 0.0512719 | ||||||||
\(849\) | −19.1287 | −0.656495 | ||||||||
\(850\) | 49.1782 | 1.68680 | ||||||||
\(851\) | −1.84780 | −0.0633416 | ||||||||
\(852\) | 18.5080 | 0.634073 | ||||||||
\(853\) | −20.9580 | −0.717589 | −0.358795 | − | 0.933416i | \(-0.616812\pi\) | ||||
−0.358795 | + | 0.933416i | \(0.616812\pi\) | |||||||
\(854\) | 15.2208 | 0.520845 | ||||||||
\(855\) | 0.997714 | 0.0341211 | ||||||||
\(856\) | −14.9731 | −0.511769 | ||||||||
\(857\) | −3.36198 | −0.114843 | −0.0574216 | − | 0.998350i | \(-0.518288\pi\) | ||||
−0.0574216 | + | 0.998350i | \(0.518288\pi\) | |||||||
\(858\) | −13.9376 | −0.475820 | ||||||||
\(859\) | 31.0025 | 1.05779 | 0.528895 | − | 0.848687i | \(-0.322607\pi\) | ||||
0.528895 | + | 0.848687i | \(0.322607\pi\) | |||||||
\(860\) | 4.64432 | 0.158370 | ||||||||
\(861\) | −7.72038 | −0.263110 | ||||||||
\(862\) | −76.4894 | −2.60524 | ||||||||
\(863\) | 8.87723 | 0.302185 | 0.151092 | − | 0.988520i | \(-0.451721\pi\) | ||||
0.151092 | + | 0.988520i | \(0.451721\pi\) | |||||||
\(864\) | 7.71560 | 0.262490 | ||||||||
\(865\) | 0.959586 | 0.0326269 | ||||||||
\(866\) | −57.1917 | −1.94345 | ||||||||
\(867\) | 4.29089 | 0.145726 | ||||||||
\(868\) | −17.4283 | −0.591556 | ||||||||
\(869\) | −56.9795 | −1.93290 | ||||||||
\(870\) | 4.69215 | 0.159079 | ||||||||
\(871\) | 0.270823 | 0.00917650 | ||||||||
\(872\) | 26.8513 | 0.909299 | ||||||||
\(873\) | −1.79091 | −0.0606133 | ||||||||
\(874\) | 47.0053 | 1.58998 | ||||||||
\(875\) | 2.37727 | 0.0803665 | ||||||||
\(876\) | −7.40944 | −0.250342 | ||||||||
\(877\) | −19.3103 | −0.652061 | −0.326030 | − | 0.945359i | \(-0.605711\pi\) | ||||
−0.326030 | + | 0.945359i | \(0.605711\pi\) | |||||||
\(878\) | 70.3587 | 2.37449 | ||||||||
\(879\) | −26.6893 | −0.900208 | ||||||||
\(880\) | −2.17878 | −0.0734468 | ||||||||
\(881\) | 3.30078 | 0.111206 | 0.0556030 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556030 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(882\) | −2.15625 | −0.0726048 | ||||||||
\(883\) | 51.9315 | 1.74764 | 0.873818 | − | 0.486253i | \(-0.161637\pi\) | ||||
0.873818 | + | 0.486253i | \(0.161637\pi\) | |||||||
\(884\) | −19.7656 | −0.664790 | ||||||||
\(885\) | 2.83122 | 0.0951706 | ||||||||
\(886\) | −34.7042 | −1.16591 | ||||||||
\(887\) | 9.29948 | 0.312246 | 0.156123 | − | 0.987738i | \(-0.450100\pi\) | ||||
0.156123 | + | 0.987738i | \(0.450100\pi\) | |||||||
\(888\) | 0.495306 | 0.0166214 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −6.18364 | −0.207276 | ||||||||
\(891\) | −3.99784 | −0.133933 | ||||||||
\(892\) | −44.8543 | −1.50183 | ||||||||
\(893\) | −14.7051 | −0.492088 | ||||||||
\(894\) | −20.6734 | −0.691423 | ||||||||
\(895\) | 5.93675 | 0.198444 | ||||||||
\(896\) | 10.6120 | 0.354522 | ||||||||
\(897\) | −8.44639 | −0.282017 | ||||||||
\(898\) | −71.4750 | −2.38515 | ||||||||
\(899\) | −59.8698 | −1.99677 | ||||||||
\(900\) | −13.0957 | −0.436522 | ||||||||
\(901\) | −3.02242 | −0.100691 | ||||||||
\(902\) | −66.5524 | −2.21595 | ||||||||
\(903\) | −7.33166 | −0.243982 | ||||||||
\(904\) | 19.5489 | 0.650187 | ||||||||
\(905\) | −1.74861 | −0.0581256 | ||||||||
\(906\) | 36.9423 | 1.22733 | ||||||||
\(907\) | −31.2600 | −1.03797 | −0.518985 | − | 0.854783i | \(-0.673690\pi\) | ||||
−0.518985 | + | 0.854783i | \(0.673690\pi\) | |||||||
\(908\) | −38.2114 | −1.26809 | ||||||||
\(909\) | −11.0925 | −0.367916 | ||||||||
\(910\) | −0.833547 | −0.0276318 | ||||||||
\(911\) | −30.7338 | −1.01826 | −0.509128 | − | 0.860691i | \(-0.670032\pi\) | ||||
−0.509128 | + | 0.860691i | \(0.670032\pi\) | |||||||
\(912\) | 9.51168 | 0.314963 | ||||||||
\(913\) | 27.0065 | 0.893783 | ||||||||
\(914\) | 44.8059 | 1.48205 | ||||||||
\(915\) | 1.68774 | 0.0557951 | ||||||||
\(916\) | −43.4941 | −1.43709 | ||||||||
\(917\) | −1.23738 | −0.0408619 | ||||||||
\(918\) | −9.94939 | −0.328379 | ||||||||
\(919\) | 7.17530 | 0.236691 | 0.118346 | − | 0.992972i | \(-0.462241\pi\) | ||||
0.118346 | + | 0.992972i | \(0.462241\pi\) | |||||||
\(920\) | 1.74907 | 0.0576651 | ||||||||
\(921\) | 9.45867 | 0.311674 | ||||||||
\(922\) | −56.0683 | −1.84651 | ||||||||
\(923\) | −11.2946 | −0.371765 | ||||||||
\(924\) | −10.5920 | −0.348450 | ||||||||
\(925\) | 1.74832 | 0.0574844 | ||||||||
\(926\) | −3.03375 | −0.0996952 | ||||||||
\(927\) | 14.5981 | 0.479465 | ||||||||
\(928\) | 70.2220 | 2.30515 | ||||||||
\(929\) | 23.3488 | 0.766051 | 0.383025 | − | 0.923738i | \(-0.374882\pi\) | ||||
0.383025 | + | 0.923738i | \(0.374882\pi\) | |||||||
\(930\) | −3.39135 | −0.111207 | ||||||||
\(931\) | −4.17289 | −0.136761 | ||||||||
\(932\) | −20.2680 | −0.663902 | ||||||||
\(933\) | 1.98631 | 0.0650289 | ||||||||
\(934\) | 9.76524 | 0.319529 | ||||||||
\(935\) | 4.41053 | 0.144240 | ||||||||
\(936\) | 2.26407 | 0.0740036 | ||||||||
\(937\) | −54.8510 | −1.79191 | −0.895953 | − | 0.444150i | \(-0.853506\pi\) | ||||
−0.895953 | + | 0.444150i | \(0.853506\pi\) | |||||||
\(938\) | 0.361180 | 0.0117929 | ||||||||
\(939\) | −20.0441 | −0.654115 | ||||||||
\(940\) | −2.23230 | −0.0728095 | ||||||||
\(941\) | −2.79391 | −0.0910788 | −0.0455394 | − | 0.998963i | \(-0.514501\pi\) | ||||
−0.0455394 | + | 0.998963i | \(0.514501\pi\) | |||||||
\(942\) | −17.2173 | −0.560969 | ||||||||
\(943\) | −40.3319 | −1.31339 | ||||||||
\(944\) | 26.9914 | 0.878495 | ||||||||
\(945\) | −0.239094 | −0.00777773 | ||||||||
\(946\) | −63.2014 | −2.05486 | ||||||||
\(947\) | 6.53039 | 0.212209 | 0.106105 | − | 0.994355i | \(-0.466162\pi\) | ||||
0.106105 | + | 0.994355i | \(0.466162\pi\) | |||||||
\(948\) | 37.7611 | 1.22642 | ||||||||
\(949\) | 4.52163 | 0.146778 | ||||||||
\(950\) | −44.4747 | −1.44295 | ||||||||
\(951\) | −27.2490 | −0.883609 | ||||||||
\(952\) | −6.46139 | −0.209415 | ||||||||
\(953\) | 19.4446 | 0.629873 | 0.314937 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314937 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(954\) | 1.41240 | 0.0457281 | ||||||||
\(955\) | 2.96497 | 0.0959440 | ||||||||
\(956\) | 21.2933 | 0.688674 | ||||||||
\(957\) | −36.3855 | −1.17618 | ||||||||
\(958\) | −3.76899 | −0.121771 | ||||||||
\(959\) | −5.10054 | −0.164705 | ||||||||
\(960\) | 2.88778 | 0.0932026 | ||||||||
\(961\) | 12.2721 | 0.395874 | ||||||||
\(962\) | −1.23312 | −0.0397574 | ||||||||
\(963\) | 10.6926 | 0.344563 | ||||||||
\(964\) | −60.4165 | −1.94589 | ||||||||
\(965\) | −3.83622 | −0.123492 | ||||||||
\(966\) | −11.2644 | −0.362427 | ||||||||
\(967\) | −4.67554 | −0.150355 | −0.0751777 | − | 0.997170i | \(-0.523952\pi\) | ||||
−0.0751777 | + | 0.997170i | \(0.523952\pi\) | |||||||
\(968\) | −6.97742 | −0.224263 | ||||||||
\(969\) | −19.2546 | −0.618547 | ||||||||
\(970\) | −0.923301 | −0.0296454 | ||||||||
\(971\) | 4.75185 | 0.152494 | 0.0762470 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762470 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(972\) | 2.64943 | 0.0849804 | ||||||||
\(973\) | 12.5215 | 0.401422 | ||||||||
\(974\) | 54.4200 | 1.74373 | ||||||||
\(975\) | 7.99168 | 0.255938 | ||||||||
\(976\) | 16.0901 | 0.515030 | ||||||||
\(977\) | −37.3562 | −1.19513 | −0.597565 | − | 0.801821i | \(-0.703865\pi\) | ||||
−0.597565 | + | 0.801821i | \(0.703865\pi\) | |||||||
\(978\) | −10.8226 | −0.346067 | ||||||||
\(979\) | 47.9514 | 1.53253 | ||||||||
\(980\) | −0.633462 | −0.0202352 | ||||||||
\(981\) | −19.1750 | −0.612212 | ||||||||
\(982\) | 58.5864 | 1.86957 | ||||||||
\(983\) | 45.4192 | 1.44865 | 0.724324 | − | 0.689459i | \(-0.242152\pi\) | ||||
0.724324 | + | 0.689459i | \(0.242152\pi\) | |||||||
\(984\) | 10.8110 | 0.344643 | ||||||||
\(985\) | −2.91389 | −0.0928444 | ||||||||
\(986\) | −90.5524 | −2.88378 | ||||||||
\(987\) | 3.52396 | 0.112169 | ||||||||
\(988\) | 17.8752 | 0.568686 | ||||||||
\(989\) | −38.3011 | −1.21791 | ||||||||
\(990\) | −2.06107 | −0.0655053 | ||||||||
\(991\) | −8.11368 | −0.257739 | −0.128870 | − | 0.991662i | \(-0.541135\pi\) | ||||
−0.128870 | + | 0.991662i | \(0.541135\pi\) | |||||||
\(992\) | −50.7544 | −1.61145 | ||||||||
\(993\) | 34.0423 | 1.08030 | ||||||||
\(994\) | −15.0628 | −0.477764 | ||||||||
\(995\) | −3.29509 | −0.104461 | ||||||||
\(996\) | −17.8976 | −0.567106 | ||||||||
\(997\) | −33.0431 | −1.04648 | −0.523242 | − | 0.852184i | \(-0.675278\pi\) | ||||
−0.523242 | + | 0.852184i | \(0.675278\pi\) | |||||||
\(998\) | 40.8413 | 1.29281 | ||||||||
\(999\) | −0.353708 | −0.0111908 |
(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 | 2667.2.a.j.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 8001.2.a.l.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.j.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
8001.2.a.l.1.6 | 7 | 3.2 | odd | 2 |