Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} - 760 x^{4} - 742 x^{3} + 366 x^{2} + 236 x - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.46794\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46794 | −1.03799 | −0.518996 | − | 0.854777i | \(-0.673694\pi\) | ||||
−0.518996 | + | 0.854777i | \(0.673694\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.154851 | 0.0774254 | ||||||||
\(5\) | 3.84216 | 1.71827 | 0.859133 | − | 0.511753i | \(-0.171004\pi\) | ||||
0.859133 | + | 0.511753i | \(0.171004\pi\) | |||||||
\(6\) | 1.46794 | 0.599284 | ||||||||
\(7\) | 2.46223 | 0.930637 | 0.465318 | − | 0.885143i | \(-0.345940\pi\) | ||||
0.465318 | + | 0.885143i | \(0.345940\pi\) | |||||||
\(8\) | 2.70857 | 0.957624 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.64006 | −1.78354 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.154851 | −0.0447016 | ||||||||
\(13\) | −4.64696 | −1.28884 | −0.644418 | − | 0.764674i | \(-0.722900\pi\) | ||||
−0.644418 | + | 0.764674i | \(0.722900\pi\) | |||||||
\(14\) | −3.61441 | −0.965993 | ||||||||
\(15\) | −3.84216 | −0.992041 | ||||||||
\(16\) | −4.28572 | −1.07143 | ||||||||
\(17\) | 5.70692 | 1.38413 | 0.692066 | − | 0.721834i | \(-0.256701\pi\) | ||||
0.692066 | + | 0.721834i | \(0.256701\pi\) | |||||||
\(18\) | −1.46794 | −0.345997 | ||||||||
\(19\) | 6.71196 | 1.53983 | 0.769914 | − | 0.638147i | \(-0.220299\pi\) | ||||
0.769914 | + | 0.638147i | \(0.220299\pi\) | |||||||
\(20\) | 0.594961 | 0.133037 | ||||||||
\(21\) | −2.46223 | −0.537304 | ||||||||
\(22\) | −1.46794 | −0.312966 | ||||||||
\(23\) | 2.93787 | 0.612588 | 0.306294 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306294 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(24\) | −2.70857 | −0.552885 | ||||||||
\(25\) | 9.76218 | 1.95244 | ||||||||
\(26\) | 6.82147 | 1.33780 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.381279 | 0.0720549 | ||||||||
\(29\) | 5.67137 | 1.05315 | 0.526573 | − | 0.850130i | \(-0.323477\pi\) | ||||
0.526573 | + | 0.850130i | \(0.323477\pi\) | |||||||
\(30\) | 5.64006 | 1.02973 | ||||||||
\(31\) | 0.232595 | 0.0417754 | 0.0208877 | − | 0.999782i | \(-0.493351\pi\) | ||||
0.0208877 | + | 0.999782i | \(0.493351\pi\) | |||||||
\(32\) | 0.874048 | 0.154511 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −8.37742 | −1.43672 | ||||||||
\(35\) | 9.46029 | 1.59908 | ||||||||
\(36\) | 0.154851 | 0.0258085 | ||||||||
\(37\) | 5.55034 | 0.912470 | 0.456235 | − | 0.889859i | \(-0.349198\pi\) | ||||
0.456235 | + | 0.889859i | \(0.349198\pi\) | |||||||
\(38\) | −9.85276 | −1.59833 | ||||||||
\(39\) | 4.64696 | 0.744109 | ||||||||
\(40\) | 10.4068 | 1.64545 | ||||||||
\(41\) | −4.35928 | −0.680806 | −0.340403 | − | 0.940280i | \(-0.610563\pi\) | ||||
−0.340403 | + | 0.940280i | \(0.610563\pi\) | |||||||
\(42\) | 3.61441 | 0.557716 | ||||||||
\(43\) | −9.35832 | −1.42713 | −0.713565 | − | 0.700589i | \(-0.752921\pi\) | ||||
−0.713565 | + | 0.700589i | \(0.752921\pi\) | |||||||
\(44\) | 0.154851 | 0.0233446 | ||||||||
\(45\) | 3.84216 | 0.572755 | ||||||||
\(46\) | −4.31262 | −0.635861 | ||||||||
\(47\) | 10.7428 | 1.56699 | 0.783497 | − | 0.621395i | \(-0.213434\pi\) | ||||
0.783497 | + | 0.621395i | \(0.213434\pi\) | |||||||
\(48\) | 4.28572 | 0.618591 | ||||||||
\(49\) | −0.937404 | −0.133915 | ||||||||
\(50\) | −14.3303 | −2.02661 | ||||||||
\(51\) | −5.70692 | −0.799129 | ||||||||
\(52\) | −0.719586 | −0.0997886 | ||||||||
\(53\) | −11.3834 | −1.56363 | −0.781816 | − | 0.623510i | \(-0.785706\pi\) | ||||
−0.781816 | + | 0.623510i | \(0.785706\pi\) | |||||||
\(54\) | 1.46794 | 0.199761 | ||||||||
\(55\) | 3.84216 | 0.518076 | ||||||||
\(56\) | 6.66913 | 0.891200 | ||||||||
\(57\) | −6.71196 | −0.889020 | ||||||||
\(58\) | −8.32523 | −1.09316 | ||||||||
\(59\) | −13.2037 | −1.71897 | −0.859485 | − | 0.511161i | \(-0.829216\pi\) | ||||
−0.859485 | + | 0.511161i | \(0.829216\pi\) | |||||||
\(60\) | −0.594961 | −0.0768091 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −0.341436 | −0.0433624 | ||||||||
\(63\) | 2.46223 | 0.310212 | ||||||||
\(64\) | 7.28839 | 0.911049 | ||||||||
\(65\) | −17.8544 | −2.21456 | ||||||||
\(66\) | 1.46794 | 0.180691 | ||||||||
\(67\) | 12.5899 | 1.53810 | 0.769049 | − | 0.639190i | \(-0.220730\pi\) | ||||
0.769049 | + | 0.639190i | \(0.220730\pi\) | |||||||
\(68\) | 0.883721 | 0.107167 | ||||||||
\(69\) | −2.93787 | −0.353678 | ||||||||
\(70\) | −13.8871 | −1.65983 | ||||||||
\(71\) | −0.299770 | −0.0355761 | −0.0177881 | − | 0.999842i | \(-0.505662\pi\) | ||||
−0.0177881 | + | 0.999842i | \(0.505662\pi\) | |||||||
\(72\) | 2.70857 | 0.319208 | ||||||||
\(73\) | −2.65468 | −0.310707 | −0.155353 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155353 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(74\) | −8.14757 | −0.947135 | ||||||||
\(75\) | −9.76218 | −1.12724 | ||||||||
\(76\) | 1.03935 | 0.119222 | ||||||||
\(77\) | 2.46223 | 0.280598 | ||||||||
\(78\) | −6.82147 | −0.772379 | ||||||||
\(79\) | −12.9557 | −1.45763 | −0.728815 | − | 0.684710i | \(-0.759929\pi\) | ||||
−0.728815 | + | 0.684710i | \(0.759929\pi\) | |||||||
\(80\) | −16.4664 | −1.84100 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.39917 | 0.706670 | ||||||||
\(83\) | −7.42505 | −0.815005 | −0.407502 | − | 0.913204i | \(-0.633600\pi\) | ||||
−0.407502 | + | 0.913204i | \(0.633600\pi\) | |||||||
\(84\) | −0.381279 | −0.0416009 | ||||||||
\(85\) | 21.9269 | 2.37831 | ||||||||
\(86\) | 13.7375 | 1.48135 | ||||||||
\(87\) | −5.67137 | −0.608035 | ||||||||
\(88\) | 2.70857 | 0.288735 | ||||||||
\(89\) | −3.40420 | −0.360845 | −0.180422 | − | 0.983589i | \(-0.557746\pi\) | ||||
−0.180422 | + | 0.983589i | \(0.557746\pi\) | |||||||
\(90\) | −5.64006 | −0.594515 | ||||||||
\(91\) | −11.4419 | −1.19944 | ||||||||
\(92\) | 0.454931 | 0.0474299 | ||||||||
\(93\) | −0.232595 | −0.0241190 | ||||||||
\(94\) | −15.7698 | −1.62653 | ||||||||
\(95\) | 25.7884 | 2.64583 | ||||||||
\(96\) | −0.874048 | −0.0892071 | ||||||||
\(97\) | −15.8330 | −1.60760 | −0.803798 | − | 0.594902i | \(-0.797191\pi\) | ||||
−0.803798 | + | 0.594902i | \(0.797191\pi\) | |||||||
\(98\) | 1.37605 | 0.139002 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.51168 | 0.151168 | ||||||||
\(101\) | 7.72797 | 0.768962 | 0.384481 | − | 0.923133i | \(-0.374380\pi\) | ||||
0.384481 | + | 0.923133i | \(0.374380\pi\) | |||||||
\(102\) | 8.37742 | 0.829489 | ||||||||
\(103\) | 16.1339 | 1.58972 | 0.794860 | − | 0.606793i | \(-0.207544\pi\) | ||||
0.794860 | + | 0.606793i | \(0.207544\pi\) | |||||||
\(104\) | −12.5866 | −1.23422 | ||||||||
\(105\) | −9.46029 | −0.923230 | ||||||||
\(106\) | 16.7102 | 1.62304 | ||||||||
\(107\) | 1.14677 | 0.110863 | 0.0554314 | − | 0.998462i | \(-0.482347\pi\) | ||||
0.0554314 | + | 0.998462i | \(0.482347\pi\) | |||||||
\(108\) | −0.154851 | −0.0149005 | ||||||||
\(109\) | 11.7557 | 1.12600 | 0.562998 | − | 0.826458i | \(-0.309648\pi\) | ||||
0.562998 | + | 0.826458i | \(0.309648\pi\) | |||||||
\(110\) | −5.64006 | −0.537759 | ||||||||
\(111\) | −5.55034 | −0.526815 | ||||||||
\(112\) | −10.5525 | −0.997113 | ||||||||
\(113\) | −16.4246 | −1.54509 | −0.772546 | − | 0.634959i | \(-0.781017\pi\) | ||||
−0.772546 | + | 0.634959i | \(0.781017\pi\) | |||||||
\(114\) | 9.85276 | 0.922795 | ||||||||
\(115\) | 11.2878 | 1.05259 | ||||||||
\(116\) | 0.878216 | 0.0815403 | ||||||||
\(117\) | −4.64696 | −0.429612 | ||||||||
\(118\) | 19.3822 | 1.78428 | ||||||||
\(119\) | 14.0518 | 1.28812 | ||||||||
\(120\) | −10.4068 | −0.950002 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.46794 | 0.132901 | ||||||||
\(123\) | 4.35928 | 0.393063 | ||||||||
\(124\) | 0.0360176 | 0.00323447 | ||||||||
\(125\) | 18.2970 | 1.63654 | ||||||||
\(126\) | −3.61441 | −0.321998 | ||||||||
\(127\) | 11.9297 | 1.05859 | 0.529295 | − | 0.848438i | \(-0.322457\pi\) | ||||
0.529295 | + | 0.848438i | \(0.322457\pi\) | |||||||
\(128\) | −12.4470 | −1.10017 | ||||||||
\(129\) | 9.35832 | 0.823954 | ||||||||
\(130\) | 26.2091 | 2.29869 | ||||||||
\(131\) | 20.8633 | 1.82283 | 0.911417 | − | 0.411485i | \(-0.134990\pi\) | ||||
0.911417 | + | 0.411485i | \(0.134990\pi\) | |||||||
\(132\) | −0.154851 | −0.0134780 | ||||||||
\(133\) | 16.5264 | 1.43302 | ||||||||
\(134\) | −18.4812 | −1.59653 | ||||||||
\(135\) | −3.84216 | −0.330680 | ||||||||
\(136\) | 15.4576 | 1.32548 | ||||||||
\(137\) | −19.1597 | −1.63692 | −0.818460 | − | 0.574564i | \(-0.805172\pi\) | ||||
−0.818460 | + | 0.574564i | \(0.805172\pi\) | |||||||
\(138\) | 4.31262 | 0.367115 | ||||||||
\(139\) | −2.58202 | −0.219004 | −0.109502 | − | 0.993987i | \(-0.534926\pi\) | ||||
−0.109502 | + | 0.993987i | \(0.534926\pi\) | |||||||
\(140\) | 1.46493 | 0.123809 | ||||||||
\(141\) | −10.7428 | −0.904705 | ||||||||
\(142\) | 0.440044 | 0.0369277 | ||||||||
\(143\) | −4.64696 | −0.388598 | ||||||||
\(144\) | −4.28572 | −0.357144 | ||||||||
\(145\) | 21.7903 | 1.80959 | ||||||||
\(146\) | 3.89691 | 0.322511 | ||||||||
\(147\) | 0.937404 | 0.0773158 | ||||||||
\(148\) | 0.859474 | 0.0706483 | ||||||||
\(149\) | 9.45719 | 0.774763 | 0.387382 | − | 0.921919i | \(-0.373380\pi\) | ||||
0.387382 | + | 0.921919i | \(0.373380\pi\) | |||||||
\(150\) | 14.3303 | 1.17006 | ||||||||
\(151\) | 6.16589 | 0.501773 | 0.250887 | − | 0.968016i | \(-0.419278\pi\) | ||||
0.250887 | + | 0.968016i | \(0.419278\pi\) | |||||||
\(152\) | 18.1798 | 1.47458 | ||||||||
\(153\) | 5.70692 | 0.461377 | ||||||||
\(154\) | −3.61441 | −0.291258 | ||||||||
\(155\) | 0.893668 | 0.0717811 | ||||||||
\(156\) | 0.719586 | 0.0576130 | ||||||||
\(157\) | 0.475244 | 0.0379286 | 0.0189643 | − | 0.999820i | \(-0.493963\pi\) | ||||
0.0189643 | + | 0.999820i | \(0.493963\pi\) | |||||||
\(158\) | 19.0182 | 1.51301 | ||||||||
\(159\) | 11.3834 | 0.902763 | ||||||||
\(160\) | 3.35823 | 0.265491 | ||||||||
\(161\) | 7.23372 | 0.570097 | ||||||||
\(162\) | −1.46794 | −0.115332 | ||||||||
\(163\) | 17.6623 | 1.38341 | 0.691707 | − | 0.722178i | \(-0.256859\pi\) | ||||
0.691707 | + | 0.722178i | \(0.256859\pi\) | |||||||
\(164\) | −0.675038 | −0.0527116 | ||||||||
\(165\) | −3.84216 | −0.299112 | ||||||||
\(166\) | 10.8995 | 0.845968 | ||||||||
\(167\) | −15.9865 | −1.23707 | −0.618536 | − | 0.785756i | \(-0.712274\pi\) | ||||
−0.618536 | + | 0.785756i | \(0.712274\pi\) | |||||||
\(168\) | −6.66913 | −0.514535 | ||||||||
\(169\) | 8.59425 | 0.661096 | ||||||||
\(170\) | −32.1874 | −2.46866 | ||||||||
\(171\) | 6.71196 | 0.513276 | ||||||||
\(172\) | −1.44914 | −0.110496 | ||||||||
\(173\) | −2.22261 | −0.168982 | −0.0844909 | − | 0.996424i | \(-0.526926\pi\) | ||||
−0.0844909 | + | 0.996424i | \(0.526926\pi\) | |||||||
\(174\) | 8.32523 | 0.631134 | ||||||||
\(175\) | 24.0368 | 1.81701 | ||||||||
\(176\) | −4.28572 | −0.323049 | ||||||||
\(177\) | 13.2037 | 0.992448 | ||||||||
\(178\) | 4.99717 | 0.374553 | ||||||||
\(179\) | −24.5110 | −1.83204 | −0.916020 | − | 0.401132i | \(-0.868617\pi\) | ||||
−0.916020 | + | 0.401132i | \(0.868617\pi\) | |||||||
\(180\) | 0.594961 | 0.0443458 | ||||||||
\(181\) | −14.1308 | −1.05034 | −0.525168 | − | 0.850999i | \(-0.675997\pi\) | ||||
−0.525168 | + | 0.850999i | \(0.675997\pi\) | |||||||
\(182\) | 16.7960 | 1.24501 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 7.95743 | 0.586629 | ||||||||
\(185\) | 21.3253 | 1.56787 | ||||||||
\(186\) | 0.341436 | 0.0250353 | ||||||||
\(187\) | 5.70692 | 0.417331 | ||||||||
\(188\) | 1.66353 | 0.121325 | ||||||||
\(189\) | −2.46223 | −0.179101 | ||||||||
\(190\) | −37.8558 | −2.74635 | ||||||||
\(191\) | −21.1658 | −1.53151 | −0.765753 | − | 0.643135i | \(-0.777633\pi\) | ||||
−0.765753 | + | 0.643135i | \(0.777633\pi\) | |||||||
\(192\) | −7.28839 | −0.525995 | ||||||||
\(193\) | −10.1194 | −0.728414 | −0.364207 | − | 0.931318i | \(-0.618660\pi\) | ||||
−0.364207 | + | 0.931318i | \(0.618660\pi\) | |||||||
\(194\) | 23.2419 | 1.66867 | ||||||||
\(195\) | 17.8544 | 1.27858 | ||||||||
\(196\) | −0.145158 | −0.0103684 | ||||||||
\(197\) | 4.80836 | 0.342582 | 0.171291 | − | 0.985221i | \(-0.445206\pi\) | ||||
0.171291 | + | 0.985221i | \(0.445206\pi\) | |||||||
\(198\) | −1.46794 | −0.104322 | ||||||||
\(199\) | 13.0978 | 0.928480 | 0.464240 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464240 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(200\) | 26.4415 | 1.86970 | ||||||||
\(201\) | −12.5899 | −0.888021 | ||||||||
\(202\) | −11.3442 | −0.798176 | ||||||||
\(203\) | 13.9642 | 0.980097 | ||||||||
\(204\) | −0.883721 | −0.0618729 | ||||||||
\(205\) | −16.7491 | −1.16980 | ||||||||
\(206\) | −23.6836 | −1.65011 | ||||||||
\(207\) | 2.93787 | 0.204196 | ||||||||
\(208\) | 19.9156 | 1.38090 | ||||||||
\(209\) | 6.71196 | 0.464276 | ||||||||
\(210\) | 13.8871 | 0.958304 | ||||||||
\(211\) | −6.36135 | −0.437933 | −0.218967 | − | 0.975732i | \(-0.570269\pi\) | ||||
−0.218967 | + | 0.975732i | \(0.570269\pi\) | |||||||
\(212\) | −1.76273 | −0.121065 | ||||||||
\(213\) | 0.299770 | 0.0205399 | ||||||||
\(214\) | −1.68340 | −0.115075 | ||||||||
\(215\) | −35.9561 | −2.45219 | ||||||||
\(216\) | −2.70857 | −0.184295 | ||||||||
\(217\) | 0.572704 | 0.0388777 | ||||||||
\(218\) | −17.2567 | −1.16877 | ||||||||
\(219\) | 2.65468 | 0.179387 | ||||||||
\(220\) | 0.594961 | 0.0401123 | ||||||||
\(221\) | −26.5198 | −1.78392 | ||||||||
\(222\) | 8.14757 | 0.546829 | ||||||||
\(223\) | 22.5356 | 1.50910 | 0.754548 | − | 0.656244i | \(-0.227856\pi\) | ||||
0.754548 | + | 0.656244i | \(0.227856\pi\) | |||||||
\(224\) | 2.15211 | 0.143794 | ||||||||
\(225\) | 9.76218 | 0.650812 | ||||||||
\(226\) | 24.1103 | 1.60379 | ||||||||
\(227\) | 27.1685 | 1.80323 | 0.901617 | − | 0.432535i | \(-0.142381\pi\) | ||||
0.901617 | + | 0.432535i | \(0.142381\pi\) | |||||||
\(228\) | −1.03935 | −0.0688327 | ||||||||
\(229\) | −24.6096 | −1.62625 | −0.813124 | − | 0.582090i | \(-0.802235\pi\) | ||||
−0.813124 | + | 0.582090i | \(0.802235\pi\) | |||||||
\(230\) | −16.5698 | −1.09258 | ||||||||
\(231\) | −2.46223 | −0.162003 | ||||||||
\(232\) | 15.3613 | 1.00852 | ||||||||
\(233\) | 24.0471 | 1.57538 | 0.787690 | − | 0.616071i | \(-0.211277\pi\) | ||||
0.787690 | + | 0.616071i | \(0.211277\pi\) | |||||||
\(234\) | 6.82147 | 0.445933 | ||||||||
\(235\) | 41.2754 | 2.69251 | ||||||||
\(236\) | −2.04460 | −0.133092 | ||||||||
\(237\) | 12.9557 | 0.841564 | ||||||||
\(238\) | −20.6272 | −1.33706 | ||||||||
\(239\) | 16.2704 | 1.05245 | 0.526224 | − | 0.850346i | \(-0.323607\pi\) | ||||
0.526224 | + | 0.850346i | \(0.323607\pi\) | |||||||
\(240\) | 16.4664 | 1.06290 | ||||||||
\(241\) | 1.53799 | 0.0990706 | 0.0495353 | − | 0.998772i | \(-0.484226\pi\) | ||||
0.0495353 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(242\) | −1.46794 | −0.0943628 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.154851 | −0.00991330 | ||||||||
\(245\) | −3.60165 | −0.230101 | ||||||||
\(246\) | −6.39917 | −0.407996 | ||||||||
\(247\) | −31.1902 | −1.98458 | ||||||||
\(248\) | 0.630001 | 0.0400051 | ||||||||
\(249\) | 7.42505 | 0.470543 | ||||||||
\(250\) | −26.8590 | −1.69871 | ||||||||
\(251\) | −22.8738 | −1.44378 | −0.721891 | − | 0.692006i | \(-0.756727\pi\) | ||||
−0.721891 | + | 0.692006i | \(0.756727\pi\) | |||||||
\(252\) | 0.381279 | 0.0240183 | ||||||||
\(253\) | 2.93787 | 0.184702 | ||||||||
\(254\) | −17.5121 | −1.09881 | ||||||||
\(255\) | −21.9269 | −1.37312 | ||||||||
\(256\) | 3.69471 | 0.230920 | ||||||||
\(257\) | −10.1026 | −0.630186 | −0.315093 | − | 0.949061i | \(-0.602036\pi\) | ||||
−0.315093 | + | 0.949061i | \(0.602036\pi\) | |||||||
\(258\) | −13.7375 | −0.855257 | ||||||||
\(259\) | 13.6662 | 0.849178 | ||||||||
\(260\) | −2.76476 | −0.171463 | ||||||||
\(261\) | 5.67137 | 0.351049 | ||||||||
\(262\) | −30.6261 | −1.89208 | ||||||||
\(263\) | −11.1552 | −0.687859 | −0.343929 | − | 0.938996i | \(-0.611758\pi\) | ||||
−0.343929 | + | 0.938996i | \(0.611758\pi\) | |||||||
\(264\) | −2.70857 | −0.166701 | ||||||||
\(265\) | −43.7368 | −2.68673 | ||||||||
\(266\) | −24.2598 | −1.48746 | ||||||||
\(267\) | 3.40420 | 0.208334 | ||||||||
\(268\) | 1.94955 | 0.119088 | ||||||||
\(269\) | 6.03952 | 0.368236 | 0.184118 | − | 0.982904i | \(-0.441057\pi\) | ||||
0.184118 | + | 0.982904i | \(0.441057\pi\) | |||||||
\(270\) | 5.64006 | 0.343243 | ||||||||
\(271\) | 4.26042 | 0.258802 | 0.129401 | − | 0.991592i | \(-0.458695\pi\) | ||||
0.129401 | + | 0.991592i | \(0.458695\pi\) | |||||||
\(272\) | −24.4583 | −1.48300 | ||||||||
\(273\) | 11.4419 | 0.692496 | ||||||||
\(274\) | 28.1252 | 1.69911 | ||||||||
\(275\) | 9.76218 | 0.588681 | ||||||||
\(276\) | −0.454931 | −0.0273837 | ||||||||
\(277\) | 8.39998 | 0.504706 | 0.252353 | − | 0.967635i | \(-0.418796\pi\) | ||||
0.252353 | + | 0.967635i | \(0.418796\pi\) | |||||||
\(278\) | 3.79026 | 0.227325 | ||||||||
\(279\) | 0.232595 | 0.0139251 | ||||||||
\(280\) | 25.6239 | 1.53132 | ||||||||
\(281\) | 12.3489 | 0.736671 | 0.368335 | − | 0.929693i | \(-0.379928\pi\) | ||||
0.368335 | + | 0.929693i | \(0.379928\pi\) | |||||||
\(282\) | 15.7698 | 0.939075 | ||||||||
\(283\) | 7.31966 | 0.435109 | 0.217554 | − | 0.976048i | \(-0.430192\pi\) | ||||
0.217554 | + | 0.976048i | \(0.430192\pi\) | |||||||
\(284\) | −0.0464196 | −0.00275450 | ||||||||
\(285\) | −25.7884 | −1.52757 | ||||||||
\(286\) | 6.82147 | 0.403362 | ||||||||
\(287\) | −10.7336 | −0.633583 | ||||||||
\(288\) | 0.874048 | 0.0515038 | ||||||||
\(289\) | 15.5689 | 0.915820 | ||||||||
\(290\) | −31.9869 | −1.87833 | ||||||||
\(291\) | 15.8330 | 0.928147 | ||||||||
\(292\) | −0.411079 | −0.0240566 | ||||||||
\(293\) | 16.8649 | 0.985255 | 0.492628 | − | 0.870240i | \(-0.336036\pi\) | ||||
0.492628 | + | 0.870240i | \(0.336036\pi\) | |||||||
\(294\) | −1.37605 | −0.0802531 | ||||||||
\(295\) | −50.7305 | −2.95365 | ||||||||
\(296\) | 15.0335 | 0.873803 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −13.8826 | −0.804197 | ||||||||
\(299\) | −13.6522 | −0.789525 | ||||||||
\(300\) | −1.51168 | −0.0872769 | ||||||||
\(301\) | −23.0424 | −1.32814 | ||||||||
\(302\) | −9.05117 | −0.520836 | ||||||||
\(303\) | −7.72797 | −0.443961 | ||||||||
\(304\) | −28.7656 | −1.64982 | ||||||||
\(305\) | −3.84216 | −0.220001 | ||||||||
\(306\) | −8.37742 | −0.478905 | ||||||||
\(307\) | 20.2128 | 1.15360 | 0.576802 | − | 0.816884i | \(-0.304300\pi\) | ||||
0.576802 | + | 0.816884i | \(0.304300\pi\) | |||||||
\(308\) | 0.381279 | 0.0217254 | ||||||||
\(309\) | −16.1339 | −0.917825 | ||||||||
\(310\) | −1.31185 | −0.0745082 | ||||||||
\(311\) | −27.5538 | −1.56243 | −0.781215 | − | 0.624262i | \(-0.785400\pi\) | ||||
−0.781215 | + | 0.624262i | \(0.785400\pi\) | |||||||
\(312\) | 12.5866 | 0.712577 | ||||||||
\(313\) | 18.0023 | 1.01755 | 0.508776 | − | 0.860899i | \(-0.330098\pi\) | ||||
0.508776 | + | 0.860899i | \(0.330098\pi\) | |||||||
\(314\) | −0.697630 | −0.0393695 | ||||||||
\(315\) | 9.46029 | 0.533027 | ||||||||
\(316\) | −2.00620 | −0.112858 | ||||||||
\(317\) | 29.5066 | 1.65726 | 0.828628 | − | 0.559799i | \(-0.189122\pi\) | ||||
0.828628 | + | 0.559799i | \(0.189122\pi\) | |||||||
\(318\) | −16.7102 | −0.937060 | ||||||||
\(319\) | 5.67137 | 0.317536 | ||||||||
\(320\) | 28.0032 | 1.56542 | ||||||||
\(321\) | −1.14677 | −0.0640066 | ||||||||
\(322\) | −10.6187 | −0.591756 | ||||||||
\(323\) | 38.3046 | 2.13133 | ||||||||
\(324\) | 0.154851 | 0.00860282 | ||||||||
\(325\) | −45.3645 | −2.51637 | ||||||||
\(326\) | −25.9271 | −1.43597 | ||||||||
\(327\) | −11.7557 | −0.650094 | ||||||||
\(328\) | −11.8074 | −0.651956 | ||||||||
\(329\) | 26.4512 | 1.45830 | ||||||||
\(330\) | 5.64006 | 0.310475 | ||||||||
\(331\) | 17.8450 | 0.980852 | 0.490426 | − | 0.871483i | \(-0.336841\pi\) | ||||
0.490426 | + | 0.871483i | \(0.336841\pi\) | |||||||
\(332\) | −1.14977 | −0.0631021 | ||||||||
\(333\) | 5.55034 | 0.304157 | ||||||||
\(334\) | 23.4672 | 1.28407 | ||||||||
\(335\) | 48.3723 | 2.64286 | ||||||||
\(336\) | 10.5525 | 0.575683 | ||||||||
\(337\) | −15.1235 | −0.823832 | −0.411916 | − | 0.911222i | \(-0.635140\pi\) | ||||
−0.411916 | + | 0.911222i | \(0.635140\pi\) | |||||||
\(338\) | −12.6159 | −0.686212 | ||||||||
\(339\) | 16.4246 | 0.892059 | ||||||||
\(340\) | 3.39540 | 0.184141 | ||||||||
\(341\) | 0.232595 | 0.0125957 | ||||||||
\(342\) | −9.85276 | −0.532776 | ||||||||
\(343\) | −19.5437 | −1.05526 | ||||||||
\(344\) | −25.3477 | −1.36665 | ||||||||
\(345\) | −11.2878 | −0.607713 | ||||||||
\(346\) | 3.26266 | 0.175402 | ||||||||
\(347\) | 11.2684 | 0.604920 | 0.302460 | − | 0.953162i | \(-0.402192\pi\) | ||||
0.302460 | + | 0.953162i | \(0.402192\pi\) | |||||||
\(348\) | −0.878216 | −0.0470773 | ||||||||
\(349\) | 6.44520 | 0.345004 | 0.172502 | − | 0.985009i | \(-0.444815\pi\) | ||||
0.172502 | + | 0.985009i | \(0.444815\pi\) | |||||||
\(350\) | −35.2845 | −1.88604 | ||||||||
\(351\) | 4.64696 | 0.248036 | ||||||||
\(352\) | 0.874048 | 0.0465869 | ||||||||
\(353\) | −22.9363 | −1.22078 | −0.610389 | − | 0.792102i | \(-0.708987\pi\) | ||||
−0.610389 | + | 0.792102i | \(0.708987\pi\) | |||||||
\(354\) | −19.3822 | −1.03015 | ||||||||
\(355\) | −1.15176 | −0.0611292 | ||||||||
\(356\) | −0.527143 | −0.0279385 | ||||||||
\(357\) | −14.0518 | −0.743699 | ||||||||
\(358\) | 35.9807 | 1.90164 | ||||||||
\(359\) | 11.2684 | 0.594724 | 0.297362 | − | 0.954765i | \(-0.403893\pi\) | ||||
0.297362 | + | 0.954765i | \(0.403893\pi\) | |||||||
\(360\) | 10.4068 | 0.548484 | ||||||||
\(361\) | 26.0504 | 1.37107 | ||||||||
\(362\) | 20.7432 | 1.09024 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.77179 | −0.0928669 | ||||||||
\(365\) | −10.1997 | −0.533877 | ||||||||
\(366\) | −1.46794 | −0.0767305 | ||||||||
\(367\) | 10.1541 | 0.530039 | 0.265020 | − | 0.964243i | \(-0.414622\pi\) | ||||
0.265020 | + | 0.964243i | \(0.414622\pi\) | |||||||
\(368\) | −12.5909 | −0.656346 | ||||||||
\(369\) | −4.35928 | −0.226935 | ||||||||
\(370\) | −31.3042 | −1.62743 | ||||||||
\(371\) | −28.0286 | −1.45517 | ||||||||
\(372\) | −0.0360176 | −0.00186742 | ||||||||
\(373\) | −24.8297 | −1.28563 | −0.642817 | − | 0.766020i | \(-0.722234\pi\) | ||||
−0.642817 | + | 0.766020i | \(0.722234\pi\) | |||||||
\(374\) | −8.37742 | −0.433186 | ||||||||
\(375\) | −18.2970 | −0.944855 | ||||||||
\(376\) | 29.0976 | 1.50059 | ||||||||
\(377\) | −26.3546 | −1.35733 | ||||||||
\(378\) | 3.61441 | 0.185905 | ||||||||
\(379\) | 12.2701 | 0.630271 | 0.315136 | − | 0.949047i | \(-0.397950\pi\) | ||||
0.315136 | + | 0.949047i | \(0.397950\pi\) | |||||||
\(380\) | 3.99335 | 0.204855 | ||||||||
\(381\) | −11.9297 | −0.611177 | ||||||||
\(382\) | 31.0702 | 1.58969 | ||||||||
\(383\) | −22.3129 | −1.14014 | −0.570068 | − | 0.821597i | \(-0.693083\pi\) | ||||
−0.570068 | + | 0.821597i | \(0.693083\pi\) | |||||||
\(384\) | 12.4470 | 0.635185 | ||||||||
\(385\) | 9.46029 | 0.482141 | ||||||||
\(386\) | 14.8547 | 0.756087 | ||||||||
\(387\) | −9.35832 | −0.475710 | ||||||||
\(388\) | −2.45175 | −0.124469 | ||||||||
\(389\) | 24.6635 | 1.25049 | 0.625245 | − | 0.780429i | \(-0.284999\pi\) | ||||
0.625245 | + | 0.780429i | \(0.284999\pi\) | |||||||
\(390\) | −26.2091 | −1.32715 | ||||||||
\(391\) | 16.7662 | 0.847903 | ||||||||
\(392\) | −2.53902 | −0.128240 | ||||||||
\(393\) | −20.8633 | −1.05241 | ||||||||
\(394\) | −7.05839 | −0.355597 | ||||||||
\(395\) | −49.7779 | −2.50460 | ||||||||
\(396\) | 0.154851 | 0.00778154 | ||||||||
\(397\) | −3.99794 | −0.200651 | −0.100325 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100325 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(398\) | −19.2268 | −0.963754 | ||||||||
\(399\) | −16.5264 | −0.827355 | ||||||||
\(400\) | −41.8380 | −2.09190 | ||||||||
\(401\) | 1.45172 | 0.0724952 | 0.0362476 | − | 0.999343i | \(-0.488460\pi\) | ||||
0.0362476 | + | 0.999343i | \(0.488460\pi\) | |||||||
\(402\) | 18.4812 | 0.921758 | ||||||||
\(403\) | −1.08086 | −0.0538416 | ||||||||
\(404\) | 1.19668 | 0.0595372 | ||||||||
\(405\) | 3.84216 | 0.190918 | ||||||||
\(406\) | −20.4987 | −1.01733 | ||||||||
\(407\) | 5.55034 | 0.275120 | ||||||||
\(408\) | −15.4576 | −0.765265 | ||||||||
\(409\) | 13.2091 | 0.653147 | 0.326574 | − | 0.945172i | \(-0.394106\pi\) | ||||
0.326574 | + | 0.945172i | \(0.394106\pi\) | |||||||
\(410\) | 24.5866 | 1.21425 | ||||||||
\(411\) | 19.1597 | 0.945076 | ||||||||
\(412\) | 2.49835 | 0.123085 | ||||||||
\(413\) | −32.5105 | −1.59974 | ||||||||
\(414\) | −4.31262 | −0.211954 | ||||||||
\(415\) | −28.5282 | −1.40039 | ||||||||
\(416\) | −4.06167 | −0.199140 | ||||||||
\(417\) | 2.58202 | 0.126442 | ||||||||
\(418\) | −9.85276 | −0.481914 | ||||||||
\(419\) | −12.6761 | −0.619267 | −0.309634 | − | 0.950856i | \(-0.600206\pi\) | ||||
−0.309634 | + | 0.950856i | \(0.600206\pi\) | |||||||
\(420\) | −1.46493 | −0.0714814 | ||||||||
\(421\) | −4.36098 | −0.212541 | −0.106271 | − | 0.994337i | \(-0.533891\pi\) | ||||
−0.106271 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(422\) | 9.33809 | 0.454571 | ||||||||
\(423\) | 10.7428 | 0.522332 | ||||||||
\(424\) | −30.8328 | −1.49737 | ||||||||
\(425\) | 55.7120 | 2.70243 | ||||||||
\(426\) | −0.440044 | −0.0213202 | ||||||||
\(427\) | −2.46223 | −0.119156 | ||||||||
\(428\) | 0.177579 | 0.00858359 | ||||||||
\(429\) | 4.64696 | 0.224357 | ||||||||
\(430\) | 52.7815 | 2.54535 | ||||||||
\(431\) | −1.72411 | −0.0830477 | −0.0415238 | − | 0.999138i | \(-0.513221\pi\) | ||||
−0.0415238 | + | 0.999138i | \(0.513221\pi\) | |||||||
\(432\) | 4.28572 | 0.206197 | ||||||||
\(433\) | −6.68214 | −0.321123 | −0.160561 | − | 0.987026i | \(-0.551330\pi\) | ||||
−0.160561 | + | 0.987026i | \(0.551330\pi\) | |||||||
\(434\) | −0.840696 | −0.0403547 | ||||||||
\(435\) | −21.7903 | −1.04476 | ||||||||
\(436\) | 1.82039 | 0.0871807 | ||||||||
\(437\) | 19.7189 | 0.943281 | ||||||||
\(438\) | −3.89691 | −0.186202 | ||||||||
\(439\) | −4.62223 | −0.220607 | −0.110303 | − | 0.993898i | \(-0.535182\pi\) | ||||
−0.110303 | + | 0.993898i | \(0.535182\pi\) | |||||||
\(440\) | 10.4068 | 0.496123 | ||||||||
\(441\) | −0.937404 | −0.0446383 | ||||||||
\(442\) | 38.9296 | 1.85169 | ||||||||
\(443\) | 24.7151 | 1.17425 | 0.587125 | − | 0.809497i | \(-0.300260\pi\) | ||||
0.587125 | + | 0.809497i | \(0.300260\pi\) | |||||||
\(444\) | −0.859474 | −0.0407888 | ||||||||
\(445\) | −13.0795 | −0.620027 | ||||||||
\(446\) | −33.0810 | −1.56643 | ||||||||
\(447\) | −9.45719 | −0.447310 | ||||||||
\(448\) | 17.9457 | 0.847856 | ||||||||
\(449\) | −17.0015 | −0.802350 | −0.401175 | − | 0.916002i | \(-0.631398\pi\) | ||||
−0.401175 | + | 0.916002i | \(0.631398\pi\) | |||||||
\(450\) | −14.3303 | −0.675537 | ||||||||
\(451\) | −4.35928 | −0.205271 | ||||||||
\(452\) | −2.54335 | −0.119629 | ||||||||
\(453\) | −6.16589 | −0.289699 | ||||||||
\(454\) | −39.8817 | −1.87174 | ||||||||
\(455\) | −43.9616 | −2.06095 | ||||||||
\(456\) | −18.1798 | −0.851347 | ||||||||
\(457\) | −31.3936 | −1.46853 | −0.734265 | − | 0.678863i | \(-0.762473\pi\) | ||||
−0.734265 | + | 0.678863i | \(0.762473\pi\) | |||||||
\(458\) | 36.1254 | 1.68803 | ||||||||
\(459\) | −5.70692 | −0.266376 | ||||||||
\(460\) | 1.74792 | 0.0814971 | ||||||||
\(461\) | 4.61978 | 0.215165 | 0.107582 | − | 0.994196i | \(-0.465689\pi\) | ||||
0.107582 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(462\) | 3.61441 | 0.168158 | ||||||||
\(463\) | 27.6857 | 1.28666 | 0.643331 | − | 0.765588i | \(-0.277552\pi\) | ||||
0.643331 | + | 0.765588i | \(0.277552\pi\) | |||||||
\(464\) | −24.3059 | −1.12837 | ||||||||
\(465\) | −0.893668 | −0.0414429 | ||||||||
\(466\) | −35.2998 | −1.63523 | ||||||||
\(467\) | 3.83606 | 0.177512 | 0.0887558 | − | 0.996053i | \(-0.471711\pi\) | ||||
0.0887558 | + | 0.996053i | \(0.471711\pi\) | |||||||
\(468\) | −0.719586 | −0.0332629 | ||||||||
\(469\) | 30.9992 | 1.43141 | ||||||||
\(470\) | −60.5899 | −2.79480 | ||||||||
\(471\) | −0.475244 | −0.0218981 | ||||||||
\(472\) | −35.7630 | −1.64613 | ||||||||
\(473\) | −9.35832 | −0.430296 | ||||||||
\(474\) | −19.0182 | −0.873536 | ||||||||
\(475\) | 65.5233 | 3.00641 | ||||||||
\(476\) | 2.17593 | 0.0997335 | ||||||||
\(477\) | −11.3834 | −0.521210 | ||||||||
\(478\) | −23.8841 | −1.09243 | ||||||||
\(479\) | 19.8463 | 0.906801 | 0.453400 | − | 0.891307i | \(-0.350211\pi\) | ||||
0.453400 | + | 0.891307i | \(0.350211\pi\) | |||||||
\(480\) | −3.35823 | −0.153282 | ||||||||
\(481\) | −25.7922 | −1.17602 | ||||||||
\(482\) | −2.25768 | −0.102834 | ||||||||
\(483\) | −7.23372 | −0.329146 | ||||||||
\(484\) | 0.154851 | 0.00703867 | ||||||||
\(485\) | −60.8329 | −2.76228 | ||||||||
\(486\) | 1.46794 | 0.0665872 | ||||||||
\(487\) | −18.7149 | −0.848054 | −0.424027 | − | 0.905650i | \(-0.639384\pi\) | ||||
−0.424027 | + | 0.905650i | \(0.639384\pi\) | |||||||
\(488\) | −2.70857 | −0.122611 | ||||||||
\(489\) | −17.6623 | −0.798715 | ||||||||
\(490\) | 5.28701 | 0.238843 | ||||||||
\(491\) | −33.1187 | −1.49463 | −0.747313 | − | 0.664472i | \(-0.768656\pi\) | ||||
−0.747313 | + | 0.664472i | \(0.768656\pi\) | |||||||
\(492\) | 0.675038 | 0.0304331 | ||||||||
\(493\) | 32.3661 | 1.45769 | ||||||||
\(494\) | 45.7854 | 2.05998 | ||||||||
\(495\) | 3.84216 | 0.172692 | ||||||||
\(496\) | −0.996839 | −0.0447594 | ||||||||
\(497\) | −0.738103 | −0.0331085 | ||||||||
\(498\) | −10.8995 | −0.488420 | ||||||||
\(499\) | 3.36699 | 0.150727 | 0.0753635 | − | 0.997156i | \(-0.475988\pi\) | ||||
0.0753635 | + | 0.997156i | \(0.475988\pi\) | |||||||
\(500\) | 2.83331 | 0.126709 | ||||||||
\(501\) | 15.9865 | 0.714224 | ||||||||
\(502\) | 33.5774 | 1.49863 | ||||||||
\(503\) | 15.7130 | 0.700609 | 0.350305 | − | 0.936636i | \(-0.386078\pi\) | ||||
0.350305 | + | 0.936636i | \(0.386078\pi\) | |||||||
\(504\) | 6.66913 | 0.297067 | ||||||||
\(505\) | 29.6921 | 1.32128 | ||||||||
\(506\) | −4.31262 | −0.191719 | ||||||||
\(507\) | −8.59425 | −0.381684 | ||||||||
\(508\) | 1.84732 | 0.0819617 | ||||||||
\(509\) | −7.97241 | −0.353371 | −0.176685 | − | 0.984267i | \(-0.556538\pi\) | ||||
−0.176685 | + | 0.984267i | \(0.556538\pi\) | |||||||
\(510\) | 32.1874 | 1.42528 | ||||||||
\(511\) | −6.53644 | −0.289155 | ||||||||
\(512\) | 19.4704 | 0.860480 | ||||||||
\(513\) | −6.71196 | −0.296340 | ||||||||
\(514\) | 14.8301 | 0.654127 | ||||||||
\(515\) | 61.9889 | 2.73156 | ||||||||
\(516\) | 1.44914 | 0.0637950 | ||||||||
\(517\) | 10.7428 | 0.472467 | ||||||||
\(518\) | −20.0612 | −0.881439 | ||||||||
\(519\) | 2.22261 | 0.0975617 | ||||||||
\(520\) | −48.3598 | −2.12072 | ||||||||
\(521\) | −19.8637 | −0.870244 | −0.435122 | − | 0.900372i | \(-0.643295\pi\) | ||||
−0.435122 | + | 0.900372i | \(0.643295\pi\) | |||||||
\(522\) | −8.32523 | −0.364386 | ||||||||
\(523\) | 10.5930 | 0.463197 | 0.231599 | − | 0.972811i | \(-0.425604\pi\) | ||||
0.231599 | + | 0.972811i | \(0.425604\pi\) | |||||||
\(524\) | 3.23070 | 0.141134 | ||||||||
\(525\) | −24.0368 | −1.04905 | ||||||||
\(526\) | 16.3752 | 0.713991 | ||||||||
\(527\) | 1.32740 | 0.0578226 | ||||||||
\(528\) | 4.28572 | 0.186512 | ||||||||
\(529\) | −14.3689 | −0.624736 | ||||||||
\(530\) | 64.2031 | 2.78880 | ||||||||
\(531\) | −13.2037 | −0.572990 | ||||||||
\(532\) | 2.55913 | 0.110952 | ||||||||
\(533\) | 20.2574 | 0.877446 | ||||||||
\(534\) | −4.99717 | −0.216249 | ||||||||
\(535\) | 4.40608 | 0.190492 | ||||||||
\(536\) | 34.1006 | 1.47292 | ||||||||
\(537\) | 24.5110 | 1.05773 | ||||||||
\(538\) | −8.86566 | −0.382226 | ||||||||
\(539\) | −0.937404 | −0.0403768 | ||||||||
\(540\) | −0.594961 | −0.0256030 | ||||||||
\(541\) | 0.967556 | 0.0415985 | 0.0207993 | − | 0.999784i | \(-0.493379\pi\) | ||||
0.0207993 | + | 0.999784i | \(0.493379\pi\) | |||||||
\(542\) | −6.25404 | −0.268634 | ||||||||
\(543\) | 14.1308 | 0.606412 | ||||||||
\(544\) | 4.98812 | 0.213864 | ||||||||
\(545\) | 45.1674 | 1.93476 | ||||||||
\(546\) | −16.7960 | −0.718804 | ||||||||
\(547\) | 2.94593 | 0.125959 | 0.0629794 | − | 0.998015i | \(-0.479940\pi\) | ||||
0.0629794 | + | 0.998015i | \(0.479940\pi\) | |||||||
\(548\) | −2.96689 | −0.126739 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −14.3303 | −0.611046 | ||||||||
\(551\) | 38.0660 | 1.62167 | ||||||||
\(552\) | −7.95743 | −0.338691 | ||||||||
\(553\) | −31.9000 | −1.35653 | ||||||||
\(554\) | −12.3307 | −0.523880 | ||||||||
\(555\) | −21.3253 | −0.905207 | ||||||||
\(556\) | −0.399828 | −0.0169565 | ||||||||
\(557\) | 0.0922439 | 0.00390850 | 0.00195425 | − | 0.999998i | \(-0.499378\pi\) | ||||
0.00195425 | + | 0.999998i | \(0.499378\pi\) | |||||||
\(558\) | −0.341436 | −0.0144541 | ||||||||
\(559\) | 43.4877 | 1.83934 | ||||||||
\(560\) | −40.5442 | −1.71330 | ||||||||
\(561\) | −5.70692 | −0.240946 | ||||||||
\(562\) | −18.1274 | −0.764658 | ||||||||
\(563\) | 16.5637 | 0.698079 | 0.349039 | − | 0.937108i | \(-0.386508\pi\) | ||||
0.349039 | + | 0.937108i | \(0.386508\pi\) | |||||||
\(564\) | −1.66353 | −0.0700471 | ||||||||
\(565\) | −63.1057 | −2.65488 | ||||||||
\(566\) | −10.7448 | −0.451639 | ||||||||
\(567\) | 2.46223 | 0.103404 | ||||||||
\(568\) | −0.811948 | −0.0340686 | ||||||||
\(569\) | −44.9171 | −1.88302 | −0.941512 | − | 0.336980i | \(-0.890594\pi\) | ||||
−0.941512 | + | 0.336980i | \(0.890594\pi\) | |||||||
\(570\) | 37.8558 | 1.58561 | ||||||||
\(571\) | 11.9694 | 0.500903 | 0.250452 | − | 0.968129i | \(-0.419421\pi\) | ||||
0.250452 | + | 0.968129i | \(0.419421\pi\) | |||||||
\(572\) | −0.719586 | −0.0300874 | ||||||||
\(573\) | 21.1658 | 0.884215 | ||||||||
\(574\) | 15.7563 | 0.657653 | ||||||||
\(575\) | 28.6800 | 1.19604 | ||||||||
\(576\) | 7.28839 | 0.303683 | ||||||||
\(577\) | 1.73895 | 0.0723935 | 0.0361967 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361967 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(578\) | −22.8543 | −0.950613 | ||||||||
\(579\) | 10.1194 | 0.420550 | ||||||||
\(580\) | 3.37424 | 0.140108 | ||||||||
\(581\) | −18.2822 | −0.758474 | ||||||||
\(582\) | −23.2419 | −0.963408 | ||||||||
\(583\) | −11.3834 | −0.471453 | ||||||||
\(584\) | −7.19039 | −0.297540 | ||||||||
\(585\) | −17.8544 | −0.738187 | ||||||||
\(586\) | −24.7566 | −1.02269 | ||||||||
\(587\) | 34.0791 | 1.40660 | 0.703298 | − | 0.710895i | \(-0.251710\pi\) | ||||
0.703298 | + | 0.710895i | \(0.251710\pi\) | |||||||
\(588\) | 0.145158 | 0.00598620 | ||||||||
\(589\) | 1.56117 | 0.0643269 | ||||||||
\(590\) | 74.4694 | 3.06586 | ||||||||
\(591\) | −4.80836 | −0.197790 | ||||||||
\(592\) | −23.7872 | −0.977648 | ||||||||
\(593\) | −19.1334 | −0.785714 | −0.392857 | − | 0.919600i | \(-0.628513\pi\) | ||||
−0.392857 | + | 0.919600i | \(0.628513\pi\) | |||||||
\(594\) | 1.46794 | 0.0602303 | ||||||||
\(595\) | 53.9891 | 2.21334 | ||||||||
\(596\) | 1.46445 | 0.0599863 | ||||||||
\(597\) | −13.0978 | −0.536058 | ||||||||
\(598\) | 20.0406 | 0.819520 | ||||||||
\(599\) | 11.7116 | 0.478521 | 0.239261 | − | 0.970955i | \(-0.423095\pi\) | ||||
0.239261 | + | 0.970955i | \(0.423095\pi\) | |||||||
\(600\) | −26.4415 | −1.07947 | ||||||||
\(601\) | −20.3403 | −0.829698 | −0.414849 | − | 0.909890i | \(-0.636166\pi\) | ||||
−0.414849 | + | 0.909890i | \(0.636166\pi\) | |||||||
\(602\) | 33.8248 | 1.37860 | ||||||||
\(603\) | 12.5899 | 0.512699 | ||||||||
\(604\) | 0.954793 | 0.0388500 | ||||||||
\(605\) | 3.84216 | 0.156206 | ||||||||
\(606\) | 11.3442 | 0.460827 | ||||||||
\(607\) | 18.2830 | 0.742085 | 0.371042 | − | 0.928616i | \(-0.379000\pi\) | ||||
0.371042 | + | 0.928616i | \(0.379000\pi\) | |||||||
\(608\) | 5.86657 | 0.237921 | ||||||||
\(609\) | −13.9642 | −0.565859 | ||||||||
\(610\) | 5.64006 | 0.228359 | ||||||||
\(611\) | −49.9213 | −2.01960 | ||||||||
\(612\) | 0.883721 | 0.0357223 | ||||||||
\(613\) | −33.4060 | −1.34925 | −0.674627 | − | 0.738158i | \(-0.735696\pi\) | ||||
−0.674627 | + | 0.738158i | \(0.735696\pi\) | |||||||
\(614\) | −29.6712 | −1.19743 | ||||||||
\(615\) | 16.7491 | 0.675387 | ||||||||
\(616\) | 6.66913 | 0.268707 | ||||||||
\(617\) | −37.0969 | −1.49347 | −0.746733 | − | 0.665124i | \(-0.768379\pi\) | ||||
−0.746733 | + | 0.665124i | \(0.768379\pi\) | |||||||
\(618\) | 23.6836 | 0.952694 | ||||||||
\(619\) | −35.5774 | −1.42998 | −0.714988 | − | 0.699137i | \(-0.753568\pi\) | ||||
−0.714988 | + | 0.699137i | \(0.753568\pi\) | |||||||
\(620\) | 0.138385 | 0.00555768 | ||||||||
\(621\) | −2.93787 | −0.117893 | ||||||||
\(622\) | 40.4473 | 1.62179 | ||||||||
\(623\) | −8.38194 | −0.335815 | ||||||||
\(624\) | −19.9156 | −0.797262 | ||||||||
\(625\) | 21.4892 | 0.859568 | ||||||||
\(626\) | −26.4263 | −1.05621 | ||||||||
\(627\) | −6.71196 | −0.268050 | ||||||||
\(628\) | 0.0735919 | 0.00293663 | ||||||||
\(629\) | 31.6753 | 1.26298 | ||||||||
\(630\) | −13.8871 | −0.553277 | ||||||||
\(631\) | 3.96808 | 0.157967 | 0.0789834 | − | 0.996876i | \(-0.474833\pi\) | ||||
0.0789834 | + | 0.996876i | \(0.474833\pi\) | |||||||
\(632\) | −35.0914 | −1.39586 | ||||||||
\(633\) | 6.36135 | 0.252841 | ||||||||
\(634\) | −43.3140 | −1.72022 | ||||||||
\(635\) | 45.8358 | 1.81894 | ||||||||
\(636\) | 1.76273 | 0.0698968 | ||||||||
\(637\) | 4.35608 | 0.172594 | ||||||||
\(638\) | −8.32523 | −0.329599 | ||||||||
\(639\) | −0.299770 | −0.0118587 | ||||||||
\(640\) | −47.8235 | −1.89039 | ||||||||
\(641\) | −4.20491 | −0.166084 | −0.0830419 | − | 0.996546i | \(-0.526464\pi\) | ||||
−0.0830419 | + | 0.996546i | \(0.526464\pi\) | |||||||
\(642\) | 1.68340 | 0.0664383 | ||||||||
\(643\) | 29.2183 | 1.15226 | 0.576129 | − | 0.817359i | \(-0.304563\pi\) | ||||
0.576129 | + | 0.817359i | \(0.304563\pi\) | |||||||
\(644\) | 1.12015 | 0.0441400 | ||||||||
\(645\) | 35.9561 | 1.41577 | ||||||||
\(646\) | −56.2289 | −2.21230 | ||||||||
\(647\) | 8.11234 | 0.318929 | 0.159464 | − | 0.987204i | \(-0.449023\pi\) | ||||
0.159464 | + | 0.987204i | \(0.449023\pi\) | |||||||
\(648\) | 2.70857 | 0.106403 | ||||||||
\(649\) | −13.2037 | −0.518289 | ||||||||
\(650\) | 66.5923 | 2.61197 | ||||||||
\(651\) | −0.572704 | −0.0224460 | ||||||||
\(652\) | 2.73501 | 0.107111 | ||||||||
\(653\) | −23.5399 | −0.921189 | −0.460595 | − | 0.887611i | \(-0.652364\pi\) | ||||
−0.460595 | + | 0.887611i | \(0.652364\pi\) | |||||||
\(654\) | 17.2567 | 0.674792 | ||||||||
\(655\) | 80.1600 | 3.13211 | ||||||||
\(656\) | 18.6827 | 0.729436 | ||||||||
\(657\) | −2.65468 | −0.103569 | ||||||||
\(658\) | −38.8288 | −1.51371 | ||||||||
\(659\) | −46.8281 | −1.82416 | −0.912082 | − | 0.410007i | \(-0.865526\pi\) | ||||
−0.912082 | + | 0.410007i | \(0.865526\pi\) | |||||||
\(660\) | −0.594961 | −0.0231588 | ||||||||
\(661\) | −45.2831 | −1.76131 | −0.880655 | − | 0.473758i | \(-0.842897\pi\) | ||||
−0.880655 | + | 0.473758i | \(0.842897\pi\) | |||||||
\(662\) | −26.1955 | −1.01812 | ||||||||
\(663\) | 26.5198 | 1.02995 | ||||||||
\(664\) | −20.1113 | −0.780468 | ||||||||
\(665\) | 63.4971 | 2.46231 | ||||||||
\(666\) | −8.14757 | −0.315712 | ||||||||
\(667\) | 16.6617 | 0.645145 | ||||||||
\(668\) | −2.47552 | −0.0957808 | ||||||||
\(669\) | −22.5356 | −0.871277 | ||||||||
\(670\) | −71.0077 | −2.74327 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −2.15211 | −0.0830195 | ||||||||
\(673\) | 42.7822 | 1.64913 | 0.824566 | − | 0.565765i | \(-0.191419\pi\) | ||||
0.824566 | + | 0.565765i | \(0.191419\pi\) | |||||||
\(674\) | 22.2005 | 0.855130 | ||||||||
\(675\) | −9.76218 | −0.375746 | ||||||||
\(676\) | 1.33083 | 0.0511856 | ||||||||
\(677\) | 32.8918 | 1.26414 | 0.632068 | − | 0.774913i | \(-0.282206\pi\) | ||||
0.632068 | + | 0.774913i | \(0.282206\pi\) | |||||||
\(678\) | −24.1103 | −0.925950 | ||||||||
\(679\) | −38.9845 | −1.49609 | ||||||||
\(680\) | 59.3905 | 2.27752 | ||||||||
\(681\) | −27.1685 | −1.04110 | ||||||||
\(682\) | −0.341436 | −0.0130743 | ||||||||
\(683\) | −29.9574 | −1.14629 | −0.573144 | − | 0.819455i | \(-0.694276\pi\) | ||||
−0.573144 | + | 0.819455i | \(0.694276\pi\) | |||||||
\(684\) | 1.03935 | 0.0397406 | ||||||||
\(685\) | −73.6144 | −2.81266 | ||||||||
\(686\) | 28.6891 | 1.09535 | ||||||||
\(687\) | 24.6096 | 0.938915 | ||||||||
\(688\) | 40.1072 | 1.52907 | ||||||||
\(689\) | 52.8983 | 2.01526 | ||||||||
\(690\) | 16.5698 | 0.630800 | ||||||||
\(691\) | −46.0051 | −1.75011 | −0.875057 | − | 0.484019i | \(-0.839177\pi\) | ||||
−0.875057 | + | 0.484019i | \(0.839177\pi\) | |||||||
\(692\) | −0.344173 | −0.0130835 | ||||||||
\(693\) | 2.46223 | 0.0935325 | ||||||||
\(694\) | −16.5414 | −0.627901 | ||||||||
\(695\) | −9.92054 | −0.376308 | ||||||||
\(696\) | −15.3613 | −0.582269 | ||||||||
\(697\) | −24.8781 | −0.942324 | ||||||||
\(698\) | −9.46117 | −0.358111 | ||||||||
\(699\) | −24.0471 | −0.909547 | ||||||||
\(700\) | 3.72211 | 0.140683 | ||||||||
\(701\) | −4.97041 | −0.187730 | −0.0938650 | − | 0.995585i | \(-0.529922\pi\) | ||||
−0.0938650 | + | 0.995585i | \(0.529922\pi\) | |||||||
\(702\) | −6.82147 | −0.257460 | ||||||||
\(703\) | 37.2536 | 1.40505 | ||||||||
\(704\) | 7.28839 | 0.274692 | ||||||||
\(705\) | −41.2754 | −1.55452 | ||||||||
\(706\) | 33.6692 | 1.26716 | ||||||||
\(707\) | 19.0281 | 0.715625 | ||||||||
\(708\) | 2.04460 | 0.0768407 | ||||||||
\(709\) | −31.0750 | −1.16704 | −0.583522 | − | 0.812097i | \(-0.698326\pi\) | ||||
−0.583522 | + | 0.812097i | \(0.698326\pi\) | |||||||
\(710\) | 1.69072 | 0.0634516 | ||||||||
\(711\) | −12.9557 | −0.485877 | ||||||||
\(712\) | −9.22052 | −0.345554 | ||||||||
\(713\) | 0.683335 | 0.0255911 | ||||||||
\(714\) | 20.6272 | 0.771953 | ||||||||
\(715\) | −17.8544 | −0.667715 | ||||||||
\(716\) | −3.79555 | −0.141846 | ||||||||
\(717\) | −16.2704 | −0.607631 | ||||||||
\(718\) | −16.5414 | −0.617318 | ||||||||
\(719\) | −37.4717 | −1.39746 | −0.698729 | − | 0.715386i | \(-0.746251\pi\) | ||||
−0.698729 | + | 0.715386i | \(0.746251\pi\) | |||||||
\(720\) | −16.4664 | −0.613667 | ||||||||
\(721\) | 39.7254 | 1.47945 | ||||||||
\(722\) | −38.2404 | −1.42316 | ||||||||
\(723\) | −1.53799 | −0.0571985 | ||||||||
\(724\) | −2.18817 | −0.0813226 | ||||||||
\(725\) | 55.3649 | 2.05620 | ||||||||
\(726\) | 1.46794 | 0.0544804 | ||||||||
\(727\) | −7.56311 | −0.280500 | −0.140250 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140250 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(728\) | −30.9912 | −1.14861 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.9726 | 0.554159 | ||||||||
\(731\) | −53.4072 | −1.97534 | ||||||||
\(732\) | 0.154851 | 0.00572345 | ||||||||
\(733\) | −12.6942 | −0.468869 | −0.234435 | − | 0.972132i | \(-0.575324\pi\) | ||||
−0.234435 | + | 0.972132i | \(0.575324\pi\) | |||||||
\(734\) | −14.9056 | −0.550176 | ||||||||
\(735\) | 3.60165 | 0.132849 | ||||||||
\(736\) | 2.56784 | 0.0946518 | ||||||||
\(737\) | 12.5899 | 0.463754 | ||||||||
\(738\) | 6.39917 | 0.235557 | ||||||||
\(739\) | 13.3928 | 0.492662 | 0.246331 | − | 0.969186i | \(-0.420775\pi\) | ||||
0.246331 | + | 0.969186i | \(0.420775\pi\) | |||||||
\(740\) | 3.30223 | 0.121393 | ||||||||
\(741\) | 31.1902 | 1.14580 | ||||||||
\(742\) | 41.1444 | 1.51046 | ||||||||
\(743\) | −3.77240 | −0.138396 | −0.0691980 | − | 0.997603i | \(-0.522044\pi\) | ||||
−0.0691980 | + | 0.997603i | \(0.522044\pi\) | |||||||
\(744\) | −0.630001 | −0.0230970 | ||||||||
\(745\) | 36.3360 | 1.33125 | ||||||||
\(746\) | 36.4486 | 1.33448 | ||||||||
\(747\) | −7.42505 | −0.271668 | ||||||||
\(748\) | 0.883721 | 0.0323120 | ||||||||
\(749\) | 2.82362 | 0.103173 | ||||||||
\(750\) | 26.8590 | 0.980751 | ||||||||
\(751\) | −9.51843 | −0.347332 | −0.173666 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173666 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(752\) | −46.0406 | −1.67893 | ||||||||
\(753\) | 22.8738 | 0.833568 | ||||||||
\(754\) | 38.6870 | 1.40890 | ||||||||
\(755\) | 23.6903 | 0.862179 | ||||||||
\(756\) | −0.381279 | −0.0138670 | ||||||||
\(757\) | −10.7916 | −0.392229 | −0.196114 | − | 0.980581i | \(-0.562832\pi\) | ||||
−0.196114 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(758\) | −18.0117 | −0.654216 | ||||||||
\(759\) | −2.93787 | −0.106638 | ||||||||
\(760\) | 69.8497 | 2.53371 | ||||||||
\(761\) | −22.1374 | −0.802480 | −0.401240 | − | 0.915973i | \(-0.631421\pi\) | ||||
−0.401240 | + | 0.915973i | \(0.631421\pi\) | |||||||
\(762\) | 17.5121 | 0.634396 | ||||||||
\(763\) | 28.9454 | 1.04789 | ||||||||
\(764\) | −3.27755 | −0.118577 | ||||||||
\(765\) | 21.9269 | 0.792768 | ||||||||
\(766\) | 32.7540 | 1.18345 | ||||||||
\(767\) | 61.3569 | 2.21547 | ||||||||
\(768\) | −3.69471 | −0.133322 | ||||||||
\(769\) | 19.4521 | 0.701460 | 0.350730 | − | 0.936477i | \(-0.385934\pi\) | ||||
0.350730 | + | 0.936477i | \(0.385934\pi\) | |||||||
\(770\) | −13.8871 | −0.500458 | ||||||||
\(771\) | 10.1026 | 0.363838 | ||||||||
\(772\) | −1.56700 | −0.0563977 | ||||||||
\(773\) | 39.4207 | 1.41786 | 0.708932 | − | 0.705277i | \(-0.249177\pi\) | ||||
0.708932 | + | 0.705277i | \(0.249177\pi\) | |||||||
\(774\) | 13.7375 | 0.493783 | ||||||||
\(775\) | 2.27064 | 0.0815637 | ||||||||
\(776\) | −42.8848 | −1.53947 | ||||||||
\(777\) | −13.6662 | −0.490273 | ||||||||
\(778\) | −36.2046 | −1.29800 | ||||||||
\(779\) | −29.2593 | −1.04832 | ||||||||
\(780\) | 2.76476 | 0.0989943 | ||||||||
\(781\) | −0.299770 | −0.0107266 | ||||||||
\(782\) | −24.6118 | −0.880116 | ||||||||
\(783\) | −5.67137 | −0.202678 | ||||||||
\(784\) | 4.01745 | 0.143480 | ||||||||
\(785\) | 1.82596 | 0.0651714 | ||||||||
\(786\) | 30.6261 | 1.09240 | ||||||||
\(787\) | −37.7502 | −1.34565 | −0.672824 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672824 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(788\) | 0.744578 | 0.0265245 | ||||||||
\(789\) | 11.1552 | 0.397135 | ||||||||
\(790\) | 73.0710 | 2.59975 | ||||||||
\(791\) | −40.4411 | −1.43792 | ||||||||
\(792\) | 2.70857 | 0.0962449 | ||||||||
\(793\) | 4.64696 | 0.165018 | ||||||||
\(794\) | 5.86874 | 0.208274 | ||||||||
\(795\) | 43.7368 | 1.55119 | ||||||||
\(796\) | 2.02821 | 0.0718879 | ||||||||
\(797\) | −20.3463 | −0.720705 | −0.360352 | − | 0.932816i | \(-0.617344\pi\) | ||||
−0.360352 | + | 0.932816i | \(0.617344\pi\) | |||||||
\(798\) | 24.2598 | 0.858787 | ||||||||
\(799\) | 61.3082 | 2.16893 | ||||||||
\(800\) | 8.53261 | 0.301673 | ||||||||
\(801\) | −3.40420 | −0.120282 | ||||||||
\(802\) | −2.13103 | −0.0752494 | ||||||||
\(803\) | −2.65468 | −0.0936816 | ||||||||
\(804\) | −1.94955 | −0.0687554 | ||||||||
\(805\) | 27.7931 | 0.979578 | ||||||||
\(806\) | 1.58664 | 0.0558870 | ||||||||
\(807\) | −6.03952 | −0.212601 | ||||||||
\(808\) | 20.9318 | 0.736377 | ||||||||
\(809\) | −3.16766 | −0.111369 | −0.0556844 | − | 0.998448i | \(-0.517734\pi\) | ||||
−0.0556844 | + | 0.998448i | \(0.517734\pi\) | |||||||
\(810\) | −5.64006 | −0.198172 | ||||||||
\(811\) | −14.3129 | −0.502593 | −0.251296 | − | 0.967910i | \(-0.580857\pi\) | ||||
−0.251296 | + | 0.967910i | \(0.580857\pi\) | |||||||
\(812\) | 2.16237 | 0.0758844 | ||||||||
\(813\) | −4.26042 | −0.149419 | ||||||||
\(814\) | −8.14757 | −0.285572 | ||||||||
\(815\) | 67.8612 | 2.37707 | ||||||||
\(816\) | 24.4583 | 0.856211 | ||||||||
\(817\) | −62.8126 | −2.19754 | ||||||||
\(818\) | −19.3902 | −0.677961 | ||||||||
\(819\) | −11.4419 | −0.399813 | ||||||||
\(820\) | −2.59360 | −0.0905726 | ||||||||
\(821\) | −14.3547 | −0.500982 | −0.250491 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250491 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(822\) | −28.1252 | −0.980980 | ||||||||
\(823\) | 21.5880 | 0.752509 | 0.376255 | − | 0.926516i | \(-0.377212\pi\) | ||||
0.376255 | + | 0.926516i | \(0.377212\pi\) | |||||||
\(824\) | 43.6998 | 1.52235 | ||||||||
\(825\) | −9.76218 | −0.339875 | ||||||||
\(826\) | 47.7235 | 1.66051 | ||||||||
\(827\) | 27.7946 | 0.966513 | 0.483257 | − | 0.875479i | \(-0.339454\pi\) | ||||
0.483257 | + | 0.875479i | \(0.339454\pi\) | |||||||
\(828\) | 0.454931 | 0.0158100 | ||||||||
\(829\) | 18.2361 | 0.633368 | 0.316684 | − | 0.948531i | \(-0.397431\pi\) | ||||
0.316684 | + | 0.948531i | \(0.397431\pi\) | |||||||
\(830\) | 41.8777 | 1.45360 | ||||||||
\(831\) | −8.39998 | −0.291392 | ||||||||
\(832\) | −33.8689 | −1.17419 | ||||||||
\(833\) | −5.34969 | −0.185356 | ||||||||
\(834\) | −3.79026 | −0.131246 | ||||||||
\(835\) | −61.4227 | −2.12562 | ||||||||
\(836\) | 1.03935 | 0.0359467 | ||||||||
\(837\) | −0.232595 | −0.00803967 | ||||||||
\(838\) | 18.6078 | 0.642794 | ||||||||
\(839\) | 25.3815 | 0.876268 | 0.438134 | − | 0.898910i | \(-0.355640\pi\) | ||||
0.438134 | + | 0.898910i | \(0.355640\pi\) | |||||||
\(840\) | −25.6239 | −0.884107 | ||||||||
\(841\) | 3.16442 | 0.109118 | ||||||||
\(842\) | 6.40166 | 0.220616 | ||||||||
\(843\) | −12.3489 | −0.425317 | ||||||||
\(844\) | −0.985060 | −0.0339072 | ||||||||
\(845\) | 33.0205 | 1.13594 | ||||||||
\(846\) | −15.7698 | −0.542175 | ||||||||
\(847\) | 2.46223 | 0.0846034 | ||||||||
\(848\) | 48.7861 | 1.67532 | ||||||||
\(849\) | −7.31966 | −0.251210 | ||||||||
\(850\) | −81.7819 | −2.80510 | ||||||||
\(851\) | 16.3062 | 0.558968 | ||||||||
\(852\) | 0.0464196 | 0.00159031 | ||||||||
\(853\) | −50.9440 | −1.74429 | −0.872144 | − | 0.489249i | \(-0.837271\pi\) | ||||
−0.872144 | + | 0.489249i | \(0.837271\pi\) | |||||||
\(854\) | 3.61441 | 0.123683 | ||||||||
\(855\) | 25.7884 | 0.881944 | ||||||||
\(856\) | 3.10612 | 0.106165 | ||||||||
\(857\) | 25.5195 | 0.871729 | 0.435865 | − | 0.900012i | \(-0.356443\pi\) | ||||
0.435865 | + | 0.900012i | \(0.356443\pi\) | |||||||
\(858\) | −6.82147 | −0.232881 | ||||||||
\(859\) | 19.5049 | 0.665497 | 0.332748 | − | 0.943016i | \(-0.392024\pi\) | ||||
0.332748 | + | 0.943016i | \(0.392024\pi\) | |||||||
\(860\) | −5.56784 | −0.189862 | ||||||||
\(861\) | 10.7336 | 0.365799 | ||||||||
\(862\) | 2.53090 | 0.0862027 | ||||||||
\(863\) | −23.2335 | −0.790876 | −0.395438 | − | 0.918493i | \(-0.629407\pi\) | ||||
−0.395438 | + | 0.918493i | \(0.629407\pi\) | |||||||
\(864\) | −0.874048 | −0.0297357 | ||||||||
\(865\) | −8.53962 | −0.290356 | ||||||||
\(866\) | 9.80898 | 0.333323 | ||||||||
\(867\) | −15.5689 | −0.528749 | ||||||||
\(868\) | 0.0886837 | 0.00301012 | ||||||||
\(869\) | −12.9557 | −0.439492 | ||||||||
\(870\) | 31.9869 | 1.08446 | ||||||||
\(871\) | −58.5047 | −1.98235 | ||||||||
\(872\) | 31.8413 | 1.07828 | ||||||||
\(873\) | −15.8330 | −0.535866 | ||||||||
\(874\) | −28.9461 | −0.979117 | ||||||||
\(875\) | 45.0516 | 1.52302 | ||||||||
\(876\) | 0.411079 | 0.0138891 | ||||||||
\(877\) | 7.94166 | 0.268171 | 0.134085 | − | 0.990970i | \(-0.457190\pi\) | ||||
0.134085 | + | 0.990970i | \(0.457190\pi\) | |||||||
\(878\) | 6.78516 | 0.228988 | ||||||||
\(879\) | −16.8649 | −0.568837 | ||||||||
\(880\) | −16.4664 | −0.555083 | ||||||||
\(881\) | 8.19164 | 0.275983 | 0.137992 | − | 0.990433i | \(-0.455935\pi\) | ||||
0.137992 | + | 0.990433i | \(0.455935\pi\) | |||||||
\(882\) | 1.37605 | 0.0463341 | ||||||||
\(883\) | 16.4576 | 0.553844 | 0.276922 | − | 0.960892i | \(-0.410686\pi\) | ||||
0.276922 | + | 0.960892i | \(0.410686\pi\) | |||||||
\(884\) | −4.10662 | −0.138121 | ||||||||
\(885\) | 50.7305 | 1.70529 | ||||||||
\(886\) | −36.2803 | −1.21886 | ||||||||
\(887\) | 13.3032 | 0.446679 | 0.223340 | − | 0.974741i | \(-0.428304\pi\) | ||||
0.223340 | + | 0.974741i | \(0.428304\pi\) | |||||||
\(888\) | −15.0335 | −0.504490 | ||||||||
\(889\) | 29.3737 | 0.985162 | ||||||||
\(890\) | 19.1999 | 0.643582 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 3.48966 | 0.116842 | ||||||||
\(893\) | 72.1050 | 2.41290 | ||||||||
\(894\) | 13.8826 | 0.464303 | ||||||||
\(895\) | −94.1752 | −3.14793 | ||||||||
\(896\) | −30.6475 | −1.02386 | ||||||||
\(897\) | 13.6522 | 0.455833 | ||||||||
\(898\) | 24.9572 | 0.832832 | ||||||||
\(899\) | 1.31913 | 0.0439956 | ||||||||
\(900\) | 1.51168 | 0.0503893 | ||||||||
\(901\) | −64.9642 | −2.16427 | ||||||||
\(902\) | 6.39917 | 0.213069 | ||||||||
\(903\) | 23.0424 | 0.766802 | ||||||||
\(904\) | −44.4871 | −1.47962 | ||||||||
\(905\) | −54.2928 | −1.80476 | ||||||||
\(906\) | 9.05117 | 0.300705 | ||||||||
\(907\) | 6.59934 | 0.219128 | 0.109564 | − | 0.993980i | \(-0.465055\pi\) | ||||
0.109564 | + | 0.993980i | \(0.465055\pi\) | |||||||
\(908\) | 4.20706 | 0.139616 | ||||||||
\(909\) | 7.72797 | 0.256321 | ||||||||
\(910\) | 64.5330 | 2.13925 | ||||||||
\(911\) | −45.1362 | −1.49543 | −0.747714 | − | 0.664021i | \(-0.768848\pi\) | ||||
−0.747714 | + | 0.664021i | \(0.768848\pi\) | |||||||
\(912\) | 28.7656 | 0.952524 | ||||||||
\(913\) | −7.42505 | −0.245733 | ||||||||
\(914\) | 46.0840 | 1.52432 | ||||||||
\(915\) | 3.84216 | 0.127018 | ||||||||
\(916\) | −3.81082 | −0.125913 | ||||||||
\(917\) | 51.3703 | 1.69640 | ||||||||
\(918\) | 8.37742 | 0.276496 | ||||||||
\(919\) | 22.6447 | 0.746979 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(920\) | 30.5737 | 1.00798 | ||||||||
\(921\) | −20.2128 | −0.666034 | ||||||||
\(922\) | −6.78156 | −0.223339 | ||||||||
\(923\) | 1.39302 | 0.0458518 | ||||||||
\(924\) | −0.381279 | −0.0125432 | ||||||||
\(925\) | 54.1834 | 1.78154 | ||||||||
\(926\) | −40.6409 | −1.33554 | ||||||||
\(927\) | 16.1339 | 0.529906 | ||||||||
\(928\) | 4.95705 | 0.162723 | ||||||||
\(929\) | −11.5176 | −0.377879 | −0.188940 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188940 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(930\) | 1.31185 | 0.0430173 | ||||||||
\(931\) | −6.29181 | −0.206206 | ||||||||
\(932\) | 3.72372 | 0.121974 | ||||||||
\(933\) | 27.5538 | 0.902070 | ||||||||
\(934\) | −5.63111 | −0.184255 | ||||||||
\(935\) | 21.9269 | 0.717086 | ||||||||
\(936\) | −12.5866 | −0.411407 | ||||||||
\(937\) | −7.74043 | −0.252869 | −0.126434 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126434 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(938\) | −45.5050 | −1.48579 | ||||||||
\(939\) | −18.0023 | −0.587484 | ||||||||
\(940\) | 6.39153 | 0.208469 | ||||||||
\(941\) | −31.6675 | −1.03233 | −0.516166 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516166 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(942\) | 0.697630 | 0.0227300 | ||||||||
\(943\) | −12.8070 | −0.417053 | ||||||||
\(944\) | 56.5872 | 1.84176 | ||||||||
\(945\) | −9.46029 | −0.307743 | ||||||||
\(946\) | 13.7375 | 0.446643 | ||||||||
\(947\) | 32.2734 | 1.04874 | 0.524372 | − | 0.851489i | \(-0.324300\pi\) | ||||
0.524372 | + | 0.851489i | \(0.324300\pi\) | |||||||
\(948\) | 2.00620 | 0.0651584 | ||||||||
\(949\) | 12.3362 | 0.400450 | ||||||||
\(950\) | −96.1843 | −3.12063 | ||||||||
\(951\) | −29.5066 | −0.956818 | ||||||||
\(952\) | 38.0602 | 1.23354 | ||||||||
\(953\) | 32.3994 | 1.04952 | 0.524759 | − | 0.851251i | \(-0.324155\pi\) | ||||
0.524759 | + | 0.851251i | \(0.324155\pi\) | |||||||
\(954\) | 16.7102 | 0.541012 | ||||||||
\(955\) | −81.3225 | −2.63153 | ||||||||
\(956\) | 2.51949 | 0.0814862 | ||||||||
\(957\) | −5.67137 | −0.183329 | ||||||||
\(958\) | −29.1332 | −0.941251 | ||||||||
\(959\) | −47.1755 | −1.52338 | ||||||||
\(960\) | −28.0032 | −0.903798 | ||||||||
\(961\) | −30.9459 | −0.998255 | ||||||||
\(962\) | 37.8614 | 1.22070 | ||||||||
\(963\) | 1.14677 | 0.0369542 | ||||||||
\(964\) | 0.238159 | 0.00767058 | ||||||||
\(965\) | −38.8805 | −1.25161 | ||||||||
\(966\) | 10.6187 | 0.341650 | ||||||||
\(967\) | −54.5762 | −1.75505 | −0.877526 | − | 0.479529i | \(-0.840808\pi\) | ||||
−0.877526 | + | 0.479529i | \(0.840808\pi\) | |||||||
\(968\) | 2.70857 | 0.0870567 | ||||||||
\(969\) | −38.3046 | −1.23052 | ||||||||
\(970\) | 89.2990 | 2.86722 | ||||||||
\(971\) | 3.84654 | 0.123441 | 0.0617207 | − | 0.998093i | \(-0.480341\pi\) | ||||
0.0617207 | + | 0.998093i | \(0.480341\pi\) | |||||||
\(972\) | −0.154851 | −0.00496684 | ||||||||
\(973\) | −6.35755 | −0.203814 | ||||||||
\(974\) | 27.4724 | 0.880272 | ||||||||
\(975\) | 45.3645 | 1.45283 | ||||||||
\(976\) | 4.28572 | 0.137183 | ||||||||
\(977\) | −3.97466 | −0.127161 | −0.0635804 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635804 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(978\) | 25.9271 | 0.829059 | ||||||||
\(979\) | −3.40420 | −0.108799 | ||||||||
\(980\) | −0.557719 | −0.0178157 | ||||||||
\(981\) | 11.7557 | 0.375332 | ||||||||
\(982\) | 48.6163 | 1.55141 | ||||||||
\(983\) | 3.16990 | 0.101104 | 0.0505521 | − | 0.998721i | \(-0.483902\pi\) | ||||
0.0505521 | + | 0.998721i | \(0.483902\pi\) | |||||||
\(984\) | 11.8074 | 0.376407 | ||||||||
\(985\) | 18.4745 | 0.588646 | ||||||||
\(986\) | −47.5115 | −1.51307 | ||||||||
\(987\) | −26.4512 | −0.841952 | ||||||||
\(988\) | −4.82983 | −0.153657 | ||||||||
\(989\) | −27.4935 | −0.874243 | ||||||||
\(990\) | −5.64006 | −0.179253 | ||||||||
\(991\) | 25.3534 | 0.805378 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(992\) | 0.203299 | 0.00645476 | ||||||||
\(993\) | −17.8450 | −0.566295 | ||||||||
\(994\) | 1.08349 | 0.0343663 | ||||||||
\(995\) | 50.3239 | 1.59537 | ||||||||
\(996\) | 1.14977 | 0.0364320 | ||||||||
\(997\) | 5.71711 | 0.181063 | 0.0905314 | − | 0.995894i | \(-0.471143\pi\) | ||||
0.0905314 | + | 0.995894i | \(0.471143\pi\) | |||||||
\(998\) | −4.94254 | −0.156453 | ||||||||
\(999\) | −5.55034 | −0.175605 |
(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 | 2013.2.a.e.1.3 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.11 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.3 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.11 | 13 | 3.2 | odd | 2 |