Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.21768\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.51387 | −1.07047 | −0.535233 | − | 0.844705i | \(-0.679776\pi\) | ||||
−0.535233 | + | 0.844705i | \(0.679776\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.291794 | 0.145897 | ||||||||
\(5\) | 3.80505 | 1.70167 | 0.850835 | − | 0.525433i | \(-0.176097\pi\) | ||||
0.850835 | + | 0.525433i | \(0.176097\pi\) | |||||||
\(6\) | 1.51387 | 0.618034 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.58600 | 0.914288 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.76034 | −1.82158 | ||||||||
\(11\) | 1.15660 | 0.348727 | 0.174363 | − | 0.984681i | \(-0.444213\pi\) | ||||
0.174363 | + | 0.984681i | \(0.444213\pi\) | |||||||
\(12\) | −0.291794 | −0.0842336 | ||||||||
\(13\) | −4.56081 | −1.26494 | −0.632470 | − | 0.774585i | \(-0.717959\pi\) | ||||
−0.632470 | + | 0.774585i | \(0.717959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.80505 | −0.982460 | ||||||||
\(16\) | −4.49844 | −1.12461 | ||||||||
\(17\) | −6.92527 | −1.67963 | −0.839813 | − | 0.542876i | \(-0.817335\pi\) | ||||
−0.839813 | + | 0.542876i | \(0.817335\pi\) | |||||||
\(18\) | −1.51387 | −0.356822 | ||||||||
\(19\) | 2.40606 | 0.551987 | 0.275994 | − | 0.961159i | \(-0.410993\pi\) | ||||
0.275994 | + | 0.961159i | \(0.410993\pi\) | |||||||
\(20\) | 1.11029 | 0.248268 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.75093 | −0.373300 | ||||||||
\(23\) | 3.28488 | 0.684944 | 0.342472 | − | 0.939528i | \(-0.388736\pi\) | ||||
0.342472 | + | 0.939528i | \(0.388736\pi\) | |||||||
\(24\) | −2.58600 | −0.527864 | ||||||||
\(25\) | 9.47840 | 1.89568 | ||||||||
\(26\) | 6.90445 | 1.35407 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.28140 | 0.237950 | 0.118975 | − | 0.992897i | \(-0.462039\pi\) | ||||
0.118975 | + | 0.992897i | \(0.462039\pi\) | |||||||
\(30\) | 5.76034 | 1.05169 | ||||||||
\(31\) | −0.334671 | −0.0601087 | −0.0300544 | − | 0.999548i | \(-0.509568\pi\) | ||||
−0.0300544 | + | 0.999548i | \(0.509568\pi\) | |||||||
\(32\) | 1.63805 | 0.289569 | ||||||||
\(33\) | −1.15660 | −0.201337 | ||||||||
\(34\) | 10.4839 | 1.79798 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.291794 | 0.0486323 | ||||||||
\(37\) | 1.13227 | 0.186145 | 0.0930724 | − | 0.995659i | \(-0.470331\pi\) | ||||
0.0930724 | + | 0.995659i | \(0.470331\pi\) | |||||||
\(38\) | −3.64245 | −0.590883 | ||||||||
\(39\) | 4.56081 | 0.730313 | ||||||||
\(40\) | 9.83985 | 1.55582 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.12116 | 0.323474 | 0.161737 | − | 0.986834i | \(-0.448290\pi\) | ||||
0.161737 | + | 0.986834i | \(0.448290\pi\) | |||||||
\(44\) | 0.337487 | 0.0508781 | ||||||||
\(45\) | 3.80505 | 0.567223 | ||||||||
\(46\) | −4.97287 | −0.733209 | ||||||||
\(47\) | −7.39779 | −1.07908 | −0.539540 | − | 0.841960i | \(-0.681402\pi\) | ||||
−0.539540 | + | 0.841960i | \(0.681402\pi\) | |||||||
\(48\) | 4.49844 | 0.649294 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.3490 | −2.02926 | ||||||||
\(51\) | 6.92527 | 0.969732 | ||||||||
\(52\) | −1.33082 | −0.184551 | ||||||||
\(53\) | −2.25189 | −0.309322 | −0.154661 | − | 0.987968i | \(-0.549428\pi\) | ||||
−0.154661 | + | 0.987968i | \(0.549428\pi\) | |||||||
\(54\) | 1.51387 | 0.206011 | ||||||||
\(55\) | 4.40090 | 0.593418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.40606 | −0.318690 | ||||||||
\(58\) | −1.93987 | −0.254717 | ||||||||
\(59\) | −12.9132 | −1.68115 | −0.840575 | − | 0.541696i | \(-0.817782\pi\) | ||||
−0.840575 | + | 0.541696i | \(0.817782\pi\) | |||||||
\(60\) | −1.11029 | −0.143338 | ||||||||
\(61\) | 2.57480 | 0.329669 | 0.164834 | − | 0.986321i | \(-0.447291\pi\) | ||||
0.164834 | + | 0.986321i | \(0.447291\pi\) | |||||||
\(62\) | 0.506648 | 0.0643443 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.51709 | 0.814637 | ||||||||
\(65\) | −17.3541 | −2.15251 | ||||||||
\(66\) | 1.75093 | 0.215525 | ||||||||
\(67\) | −6.21525 | −0.759313 | −0.379657 | − | 0.925127i | \(-0.623958\pi\) | ||||
−0.379657 | + | 0.925127i | \(0.623958\pi\) | |||||||
\(68\) | −2.02075 | −0.245052 | ||||||||
\(69\) | −3.28488 | −0.395453 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.30854 | 0.273973 | 0.136986 | − | 0.990573i | \(-0.456258\pi\) | ||||
0.136986 | + | 0.990573i | \(0.456258\pi\) | |||||||
\(72\) | 2.58600 | 0.304763 | ||||||||
\(73\) | 11.9079 | 1.39371 | 0.696855 | − | 0.717212i | \(-0.254582\pi\) | ||||
0.696855 | + | 0.717212i | \(0.254582\pi\) | |||||||
\(74\) | −1.71411 | −0.199262 | ||||||||
\(75\) | −9.47840 | −1.09447 | ||||||||
\(76\) | 0.702072 | 0.0805332 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.90445 | −0.781775 | ||||||||
\(79\) | −12.7517 | −1.43467 | −0.717337 | − | 0.696727i | \(-0.754639\pi\) | ||||
−0.717337 | + | 0.696727i | \(0.754639\pi\) | |||||||
\(80\) | −17.1168 | −1.91372 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.51387 | 0.167179 | ||||||||
\(83\) | 2.58930 | 0.284213 | 0.142106 | − | 0.989851i | \(-0.454612\pi\) | ||||
0.142106 | + | 0.989851i | \(0.454612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.3510 | −2.85817 | ||||||||
\(86\) | −3.21115 | −0.346267 | ||||||||
\(87\) | −1.28140 | −0.137380 | ||||||||
\(88\) | 2.99095 | 0.318837 | ||||||||
\(89\) | −9.21039 | −0.976299 | −0.488150 | − | 0.872760i | \(-0.662328\pi\) | ||||
−0.488150 | + | 0.872760i | \(0.662328\pi\) | |||||||
\(90\) | −5.76034 | −0.607193 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.958507 | 0.0999312 | ||||||||
\(93\) | 0.334671 | 0.0347038 | ||||||||
\(94\) | 11.1993 | 1.15512 | ||||||||
\(95\) | 9.15516 | 0.939300 | ||||||||
\(96\) | −1.63805 | −0.167183 | ||||||||
\(97\) | −12.8974 | −1.30953 | −0.654766 | − | 0.755832i | \(-0.727233\pi\) | ||||
−0.654766 | + | 0.755832i | \(0.727233\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.15660 | 0.116242 | ||||||||
\(100\) | 2.76574 | 0.276574 | ||||||||
\(101\) | 0.177513 | 0.0176632 | 0.00883162 | − | 0.999961i | \(-0.497189\pi\) | ||||
0.00883162 | + | 0.999961i | \(0.497189\pi\) | |||||||
\(102\) | −10.4839 | −1.03807 | ||||||||
\(103\) | −14.5341 | −1.43209 | −0.716046 | − | 0.698053i | \(-0.754050\pi\) | ||||
−0.716046 | + | 0.698053i | \(0.754050\pi\) | |||||||
\(104\) | −11.7942 | −1.15652 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.40907 | 0.331118 | ||||||||
\(107\) | −12.0732 | −1.16716 | −0.583579 | − | 0.812056i | \(-0.698348\pi\) | ||||
−0.583579 | + | 0.812056i | \(0.698348\pi\) | |||||||
\(108\) | −0.291794 | −0.0280779 | ||||||||
\(109\) | 17.0080 | 1.62907 | 0.814537 | − | 0.580111i | \(-0.196991\pi\) | ||||
0.814537 | + | 0.580111i | \(0.196991\pi\) | |||||||
\(110\) | −6.66238 | −0.635233 | ||||||||
\(111\) | −1.13227 | −0.107471 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.63814 | 0.154103 | 0.0770516 | − | 0.997027i | \(-0.475449\pi\) | ||||
0.0770516 | + | 0.997027i | \(0.475449\pi\) | |||||||
\(114\) | 3.64245 | 0.341147 | ||||||||
\(115\) | 12.4991 | 1.16555 | ||||||||
\(116\) | 0.373905 | 0.0347162 | ||||||||
\(117\) | −4.56081 | −0.421647 | ||||||||
\(118\) | 19.5488 | 1.79961 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.83985 | −0.898251 | ||||||||
\(121\) | −9.66229 | −0.878390 | ||||||||
\(122\) | −3.89790 | −0.352899 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −0.0976550 | −0.00876968 | ||||||||
\(125\) | 17.0405 | 1.52415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.7696 | −1.84300 | −0.921502 | − | 0.388374i | \(-0.873037\pi\) | ||||
−0.921502 | + | 0.388374i | \(0.873037\pi\) | |||||||
\(128\) | −13.1421 | −1.16161 | ||||||||
\(129\) | −2.12116 | −0.186758 | ||||||||
\(130\) | 26.2718 | 2.30419 | ||||||||
\(131\) | 12.0351 | 1.05151 | 0.525756 | − | 0.850636i | \(-0.323783\pi\) | ||||
0.525756 | + | 0.850636i | \(0.323783\pi\) | |||||||
\(132\) | −0.337487 | −0.0293745 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.40906 | 0.812819 | ||||||||
\(135\) | −3.80505 | −0.327487 | ||||||||
\(136\) | −17.9087 | −1.53566 | ||||||||
\(137\) | −6.50063 | −0.555386 | −0.277693 | − | 0.960670i | \(-0.589570\pi\) | ||||
−0.277693 | + | 0.960670i | \(0.589570\pi\) | |||||||
\(138\) | 4.97287 | 0.423318 | ||||||||
\(139\) | 23.1305 | 1.96191 | 0.980954 | − | 0.194243i | \(-0.0622249\pi\) | ||||
0.980954 | + | 0.194243i | \(0.0622249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.39779 | 0.623007 | ||||||||
\(142\) | −3.49482 | −0.293279 | ||||||||
\(143\) | −5.27501 | −0.441118 | ||||||||
\(144\) | −4.49844 | −0.374870 | ||||||||
\(145\) | 4.87579 | 0.404912 | ||||||||
\(146\) | −18.0269 | −1.49192 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.330391 | 0.0271580 | ||||||||
\(149\) | −5.20043 | −0.426036 | −0.213018 | − | 0.977048i | \(-0.568329\pi\) | ||||
−0.213018 | + | 0.977048i | \(0.568329\pi\) | |||||||
\(150\) | 14.3490 | 1.17159 | ||||||||
\(151\) | −10.2898 | −0.837370 | −0.418685 | − | 0.908131i | \(-0.637509\pi\) | ||||
−0.418685 | + | 0.908131i | \(0.637509\pi\) | |||||||
\(152\) | 6.22205 | 0.504675 | ||||||||
\(153\) | −6.92527 | −0.559875 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.27344 | −0.102285 | ||||||||
\(156\) | 1.33082 | 0.106550 | ||||||||
\(157\) | 4.03587 | 0.322097 | 0.161049 | − | 0.986946i | \(-0.448512\pi\) | ||||
0.161049 | + | 0.986946i | \(0.448512\pi\) | |||||||
\(158\) | 19.3043 | 1.53577 | ||||||||
\(159\) | 2.25189 | 0.178587 | ||||||||
\(160\) | 6.23287 | 0.492752 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.51387 | −0.118941 | ||||||||
\(163\) | 6.84917 | 0.536468 | 0.268234 | − | 0.963354i | \(-0.413560\pi\) | ||||
0.268234 | + | 0.963354i | \(0.413560\pi\) | |||||||
\(164\) | −0.291794 | −0.0227853 | ||||||||
\(165\) | −4.40090 | −0.342610 | ||||||||
\(166\) | −3.91986 | −0.304240 | ||||||||
\(167\) | 2.72776 | 0.211080 | 0.105540 | − | 0.994415i | \(-0.466343\pi\) | ||||
0.105540 | + | 0.994415i | \(0.466343\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80095 | 0.600073 | ||||||||
\(170\) | 39.8919 | 3.05957 | ||||||||
\(171\) | 2.40606 | 0.183996 | ||||||||
\(172\) | 0.618941 | 0.0471938 | ||||||||
\(173\) | −3.57517 | −0.271815 | −0.135908 | − | 0.990722i | \(-0.543395\pi\) | ||||
−0.135908 | + | 0.990722i | \(0.543395\pi\) | |||||||
\(174\) | 1.93987 | 0.147061 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.20288 | −0.392182 | ||||||||
\(177\) | 12.9132 | 0.970612 | ||||||||
\(178\) | 13.9433 | 1.04510 | ||||||||
\(179\) | 13.3401 | 0.997084 | 0.498542 | − | 0.866865i | \(-0.333869\pi\) | ||||
0.498542 | + | 0.866865i | \(0.333869\pi\) | |||||||
\(180\) | 1.11029 | 0.0827561 | ||||||||
\(181\) | −6.15975 | −0.457850 | −0.228925 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228925 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.57480 | −0.190334 | ||||||||
\(184\) | 8.49468 | 0.626236 | ||||||||
\(185\) | 4.30836 | 0.316757 | ||||||||
\(186\) | −0.506648 | −0.0371492 | ||||||||
\(187\) | −8.00974 | −0.585730 | ||||||||
\(188\) | −2.15863 | −0.157434 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.8597 | −1.00549 | ||||||||
\(191\) | 23.8691 | 1.72711 | 0.863554 | − | 0.504256i | \(-0.168233\pi\) | ||||
0.863554 | + | 0.504256i | \(0.168233\pi\) | |||||||
\(192\) | −6.51709 | −0.470331 | ||||||||
\(193\) | −21.6807 | −1.56061 | −0.780304 | − | 0.625400i | \(-0.784936\pi\) | ||||
−0.780304 | + | 0.625400i | \(0.784936\pi\) | |||||||
\(194\) | 19.5249 | 1.40181 | ||||||||
\(195\) | 17.3541 | 1.24275 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.1707 | 1.57959 | 0.789797 | − | 0.613368i | \(-0.210186\pi\) | ||||
0.789797 | + | 0.613368i | \(0.210186\pi\) | |||||||
\(198\) | −1.75093 | −0.124433 | ||||||||
\(199\) | −7.79167 | −0.552337 | −0.276168 | − | 0.961109i | \(-0.589065\pi\) | ||||
−0.276168 | + | 0.961109i | \(0.589065\pi\) | |||||||
\(200\) | 24.5111 | 1.73320 | ||||||||
\(201\) | 6.21525 | 0.438390 | ||||||||
\(202\) | −0.268732 | −0.0189079 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.02075 | 0.141481 | ||||||||
\(205\) | −3.80505 | −0.265756 | ||||||||
\(206\) | 22.0028 | 1.53301 | ||||||||
\(207\) | 3.28488 | 0.228315 | ||||||||
\(208\) | 20.5165 | 1.42257 | ||||||||
\(209\) | 2.78283 | 0.192493 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.81577 | 0.538060 | 0.269030 | − | 0.963132i | \(-0.413297\pi\) | ||||
0.269030 | + | 0.963132i | \(0.413297\pi\) | |||||||
\(212\) | −0.657089 | −0.0451291 | ||||||||
\(213\) | −2.30854 | −0.158178 | ||||||||
\(214\) | 18.2772 | 1.24940 | ||||||||
\(215\) | 8.07111 | 0.550445 | ||||||||
\(216\) | −2.58600 | −0.175955 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.7479 | −1.74387 | ||||||||
\(219\) | −11.9079 | −0.804658 | ||||||||
\(220\) | 1.28416 | 0.0865778 | ||||||||
\(221\) | 31.5848 | 2.12463 | ||||||||
\(222\) | 1.71411 | 0.115044 | ||||||||
\(223\) | 22.6963 | 1.51986 | 0.759929 | − | 0.650006i | \(-0.225234\pi\) | ||||
0.759929 | + | 0.650006i | \(0.225234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.47840 | 0.631893 | ||||||||
\(226\) | −2.47992 | −0.164962 | ||||||||
\(227\) | −1.16540 | −0.0773504 | −0.0386752 | − | 0.999252i | \(-0.512314\pi\) | ||||
−0.0386752 | + | 0.999252i | \(0.512314\pi\) | |||||||
\(228\) | −0.702072 | −0.0464959 | ||||||||
\(229\) | −24.8081 | −1.63936 | −0.819682 | − | 0.572819i | \(-0.805850\pi\) | ||||
−0.819682 | + | 0.572819i | \(0.805850\pi\) | |||||||
\(230\) | −18.9220 | −1.24768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.31370 | 0.217555 | ||||||||
\(233\) | −18.9135 | −1.23906 | −0.619531 | − | 0.784972i | \(-0.712677\pi\) | ||||
−0.619531 | + | 0.784972i | \(0.712677\pi\) | |||||||
\(234\) | 6.90445 | 0.451358 | ||||||||
\(235\) | −28.1490 | −1.83624 | ||||||||
\(236\) | −3.76798 | −0.245275 | ||||||||
\(237\) | 12.7517 | 0.828309 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.69526 | 0.368396 | 0.184198 | − | 0.982889i | \(-0.441031\pi\) | ||||
0.184198 | + | 0.982889i | \(0.441031\pi\) | |||||||
\(240\) | 17.1168 | 1.10488 | ||||||||
\(241\) | 12.4796 | 0.803884 | 0.401942 | − | 0.915665i | \(-0.368335\pi\) | ||||
0.401942 | + | 0.915665i | \(0.368335\pi\) | |||||||
\(242\) | 14.6274 | 0.940286 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.751310 | 0.0480977 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.51387 | −0.0965206 | ||||||||
\(247\) | −10.9736 | −0.698230 | ||||||||
\(248\) | −0.865459 | −0.0549567 | ||||||||
\(249\) | −2.58930 | −0.164090 | ||||||||
\(250\) | −25.7971 | −1.63155 | ||||||||
\(251\) | −29.7508 | −1.87785 | −0.938926 | − | 0.344120i | \(-0.888177\pi\) | ||||
−0.938926 | + | 0.344120i | \(0.888177\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.79927 | 0.238858 | ||||||||
\(254\) | 31.4424 | 1.97287 | ||||||||
\(255\) | 26.3510 | 1.65016 | ||||||||
\(256\) | 6.86124 | 0.428827 | ||||||||
\(257\) | 4.66090 | 0.290739 | 0.145369 | − | 0.989377i | \(-0.453563\pi\) | ||||
0.145369 | + | 0.989377i | \(0.453563\pi\) | |||||||
\(258\) | 3.21115 | 0.199918 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.06382 | −0.314045 | ||||||||
\(261\) | 1.28140 | 0.0793166 | ||||||||
\(262\) | −18.2195 | −1.12561 | ||||||||
\(263\) | 24.2173 | 1.49330 | 0.746650 | − | 0.665217i | \(-0.231661\pi\) | ||||
0.746650 | + | 0.665217i | \(0.231661\pi\) | |||||||
\(264\) | −2.99095 | −0.184080 | ||||||||
\(265\) | −8.56857 | −0.526363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.21039 | 0.563667 | ||||||||
\(268\) | −1.81357 | −0.110782 | ||||||||
\(269\) | −26.7174 | −1.62899 | −0.814495 | − | 0.580170i | \(-0.802986\pi\) | ||||
−0.814495 | + | 0.580170i | \(0.802986\pi\) | |||||||
\(270\) | 5.76034 | 0.350563 | ||||||||
\(271\) | −21.2293 | −1.28959 | −0.644795 | − | 0.764356i | \(-0.723057\pi\) | ||||
−0.644795 | + | 0.764356i | \(0.723057\pi\) | |||||||
\(272\) | 31.1530 | 1.88893 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.84108 | 0.594522 | ||||||||
\(275\) | 10.9627 | 0.661074 | ||||||||
\(276\) | −0.958507 | −0.0576953 | ||||||||
\(277\) | −8.30807 | −0.499184 | −0.249592 | − | 0.968351i | \(-0.580296\pi\) | ||||
−0.249592 | + | 0.968351i | \(0.580296\pi\) | |||||||
\(278\) | −35.0166 | −2.10015 | ||||||||
\(279\) | −0.334671 | −0.0200362 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0193 | −1.13460 | −0.567300 | − | 0.823511i | \(-0.692012\pi\) | ||||
−0.567300 | + | 0.823511i | \(0.692012\pi\) | |||||||
\(282\) | −11.1993 | −0.666907 | ||||||||
\(283\) | 8.80867 | 0.523621 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(284\) | 0.673617 | 0.0399718 | ||||||||
\(285\) | −9.15516 | −0.542305 | ||||||||
\(286\) | 7.98566 | 0.472202 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.63805 | 0.0965232 | ||||||||
\(289\) | 30.9594 | 1.82114 | ||||||||
\(290\) | −7.38130 | −0.433445 | ||||||||
\(291\) | 12.8974 | 0.756058 | ||||||||
\(292\) | 3.47464 | 0.203338 | ||||||||
\(293\) | −30.0047 | −1.75289 | −0.876446 | − | 0.481500i | \(-0.840092\pi\) | ||||
−0.876446 | + | 0.481500i | \(0.840092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.1352 | −2.86076 | ||||||||
\(296\) | 2.92806 | 0.170190 | ||||||||
\(297\) | −1.15660 | −0.0671125 | ||||||||
\(298\) | 7.87276 | 0.456056 | ||||||||
\(299\) | −14.9817 | −0.866413 | ||||||||
\(300\) | −2.76574 | −0.159680 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.5774 | 0.896376 | ||||||||
\(303\) | −0.177513 | −0.0101979 | ||||||||
\(304\) | −10.8235 | −0.620771 | ||||||||
\(305\) | 9.79723 | 0.560988 | ||||||||
\(306\) | 10.4839 | 0.599327 | ||||||||
\(307\) | −26.3241 | −1.50240 | −0.751199 | − | 0.660076i | \(-0.770524\pi\) | ||||
−0.751199 | + | 0.660076i | \(0.770524\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.5341 | 0.826819 | ||||||||
\(310\) | 1.92782 | 0.109493 | ||||||||
\(311\) | 21.2895 | 1.20721 | 0.603607 | − | 0.797282i | \(-0.293730\pi\) | ||||
0.603607 | + | 0.797282i | \(0.293730\pi\) | |||||||
\(312\) | 11.7942 | 0.667717 | ||||||||
\(313\) | −14.8092 | −0.837065 | −0.418532 | − | 0.908202i | \(-0.637455\pi\) | ||||
−0.418532 | + | 0.908202i | \(0.637455\pi\) | |||||||
\(314\) | −6.10977 | −0.344794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.72085 | −0.209314 | ||||||||
\(317\) | 3.95277 | 0.222010 | 0.111005 | − | 0.993820i | \(-0.464593\pi\) | ||||
0.111005 | + | 0.993820i | \(0.464593\pi\) | |||||||
\(318\) | −3.40907 | −0.191171 | ||||||||
\(319\) | 1.48206 | 0.0829795 | ||||||||
\(320\) | 24.7979 | 1.38624 | ||||||||
\(321\) | 12.0732 | 0.673859 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.6626 | −0.927132 | ||||||||
\(324\) | 0.291794 | 0.0162108 | ||||||||
\(325\) | −43.2291 | −2.39792 | ||||||||
\(326\) | −10.3687 | −0.574271 | ||||||||
\(327\) | −17.0080 | −0.940547 | ||||||||
\(328\) | −2.58600 | −0.142788 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.66238 | 0.366752 | ||||||||
\(331\) | 30.9459 | 1.70094 | 0.850470 | − | 0.526023i | \(-0.176317\pi\) | ||||
0.850470 | + | 0.526023i | \(0.176317\pi\) | |||||||
\(332\) | 0.755542 | 0.0414658 | ||||||||
\(333\) | 1.13227 | 0.0620483 | ||||||||
\(334\) | −4.12946 | −0.225954 | ||||||||
\(335\) | −23.6493 | −1.29210 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.5965 | 1.77564 | 0.887822 | − | 0.460188i | \(-0.152218\pi\) | ||||
0.887822 | + | 0.460188i | \(0.152218\pi\) | |||||||
\(338\) | −11.8096 | −0.642357 | ||||||||
\(339\) | −1.63814 | −0.0889715 | ||||||||
\(340\) | −7.68906 | −0.416998 | ||||||||
\(341\) | −0.387079 | −0.0209615 | ||||||||
\(342\) | −3.64245 | −0.196961 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.48531 | 0.295748 | ||||||||
\(345\) | −12.4991 | −0.672930 | ||||||||
\(346\) | 5.41234 | 0.290969 | ||||||||
\(347\) | −24.1324 | −1.29549 | −0.647747 | − | 0.761855i | \(-0.724289\pi\) | ||||
−0.647747 | + | 0.761855i | \(0.724289\pi\) | |||||||
\(348\) | −0.373905 | −0.0200434 | ||||||||
\(349\) | −24.9455 | −1.33530 | −0.667651 | − | 0.744474i | \(-0.732700\pi\) | ||||
−0.667651 | + | 0.744474i | \(0.732700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.56081 | 0.243438 | ||||||||
\(352\) | 1.89456 | 0.100981 | ||||||||
\(353\) | −35.1182 | −1.86916 | −0.934578 | − | 0.355759i | \(-0.884222\pi\) | ||||
−0.934578 | + | 0.355759i | \(0.884222\pi\) | |||||||
\(354\) | −19.5488 | −1.03901 | ||||||||
\(355\) | 8.78410 | 0.466211 | ||||||||
\(356\) | −2.68754 | −0.142439 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.1951 | −1.06734 | ||||||||
\(359\) | −2.09790 | −0.110723 | −0.0553614 | − | 0.998466i | \(-0.517631\pi\) | ||||
−0.0553614 | + | 0.998466i | \(0.517631\pi\) | |||||||
\(360\) | 9.83985 | 0.518605 | ||||||||
\(361\) | −13.2109 | −0.695310 | ||||||||
\(362\) | 9.32504 | 0.490113 | ||||||||
\(363\) | 9.66229 | 0.507139 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.3100 | 2.37163 | ||||||||
\(366\) | 3.89790 | 0.203746 | ||||||||
\(367\) | 15.7507 | 0.822180 | 0.411090 | − | 0.911595i | \(-0.365148\pi\) | ||||
0.411090 | + | 0.911595i | \(0.365148\pi\) | |||||||
\(368\) | −14.7768 | −0.770295 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −6.52229 | −0.339077 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0976550 | 0.00506318 | ||||||||
\(373\) | −10.4347 | −0.540289 | −0.270144 | − | 0.962820i | \(-0.587071\pi\) | ||||
−0.270144 | + | 0.962820i | \(0.587071\pi\) | |||||||
\(374\) | 12.1257 | 0.627004 | ||||||||
\(375\) | −17.0405 | −0.879969 | ||||||||
\(376\) | −19.1307 | −0.986589 | ||||||||
\(377\) | −5.84421 | −0.300992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0415 | −0.669895 | −0.334947 | − | 0.942237i | \(-0.608719\pi\) | ||||
−0.334947 | + | 0.942237i | \(0.608719\pi\) | |||||||
\(380\) | 2.67142 | 0.137041 | ||||||||
\(381\) | 20.7696 | 1.06406 | ||||||||
\(382\) | −36.1347 | −1.84881 | ||||||||
\(383\) | 13.8502 | 0.707714 | 0.353857 | − | 0.935299i | \(-0.384870\pi\) | ||||
0.353857 | + | 0.935299i | \(0.384870\pi\) | |||||||
\(384\) | 13.1421 | 0.670656 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.8216 | 1.67058 | ||||||||
\(387\) | 2.12116 | 0.107825 | ||||||||
\(388\) | −3.76338 | −0.191057 | ||||||||
\(389\) | 29.4776 | 1.49458 | 0.747288 | − | 0.664500i | \(-0.231356\pi\) | ||||
0.747288 | + | 0.664500i | \(0.231356\pi\) | |||||||
\(390\) | −26.2718 | −1.33032 | ||||||||
\(391\) | −22.7487 | −1.15045 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0351 | −0.607090 | ||||||||
\(394\) | −33.5634 | −1.69090 | ||||||||
\(395\) | −48.5207 | −2.44134 | ||||||||
\(396\) | 0.337487 | 0.0169594 | ||||||||
\(397\) | −25.5717 | −1.28341 | −0.641703 | − | 0.766954i | \(-0.721772\pi\) | ||||
−0.641703 | + | 0.766954i | \(0.721772\pi\) | |||||||
\(398\) | 11.7955 | 0.591257 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −42.6381 | −2.13190 | ||||||||
\(401\) | 6.69303 | 0.334234 | 0.167117 | − | 0.985937i | \(-0.446554\pi\) | ||||
0.167117 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(402\) | −9.40906 | −0.469281 | ||||||||
\(403\) | 1.52637 | 0.0760339 | ||||||||
\(404\) | 0.0517973 | 0.00257701 | ||||||||
\(405\) | 3.80505 | 0.189074 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.30958 | 0.0649136 | ||||||||
\(408\) | 17.9087 | 0.886615 | ||||||||
\(409\) | −18.9785 | −0.938425 | −0.469212 | − | 0.883085i | \(-0.655462\pi\) | ||||
−0.469212 | + | 0.883085i | \(0.655462\pi\) | |||||||
\(410\) | 5.76034 | 0.284483 | ||||||||
\(411\) | 6.50063 | 0.320652 | ||||||||
\(412\) | −4.24097 | −0.208938 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.97287 | −0.244403 | ||||||||
\(415\) | 9.85242 | 0.483636 | ||||||||
\(416\) | −7.47084 | −0.366288 | ||||||||
\(417\) | −23.1305 | −1.13271 | ||||||||
\(418\) | −4.21284 | −0.206057 | ||||||||
\(419\) | 38.3019 | 1.87117 | 0.935586 | − | 0.353099i | \(-0.114872\pi\) | ||||
0.935586 | + | 0.353099i | \(0.114872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7293 | 0.669124 | 0.334562 | − | 0.942374i | \(-0.391412\pi\) | ||||
0.334562 | + | 0.942374i | \(0.391412\pi\) | |||||||
\(422\) | −11.8320 | −0.575974 | ||||||||
\(423\) | −7.39779 | −0.359693 | ||||||||
\(424\) | −5.82339 | −0.282809 | ||||||||
\(425\) | −65.6405 | −3.18403 | ||||||||
\(426\) | 3.49482 | 0.169325 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.52288 | −0.170285 | ||||||||
\(429\) | 5.27501 | 0.254680 | ||||||||
\(430\) | −12.2186 | −0.589233 | ||||||||
\(431\) | −1.39769 | −0.0673244 | −0.0336622 | − | 0.999433i | \(-0.510717\pi\) | ||||
−0.0336622 | + | 0.999433i | \(0.510717\pi\) | |||||||
\(432\) | 4.49844 | 0.216431 | ||||||||
\(433\) | 19.3022 | 0.927605 | 0.463802 | − | 0.885939i | \(-0.346485\pi\) | ||||
0.463802 | + | 0.885939i | \(0.346485\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.87579 | −0.233776 | ||||||||
\(436\) | 4.96284 | 0.237677 | ||||||||
\(437\) | 7.90359 | 0.378080 | ||||||||
\(438\) | 18.0269 | 0.861359 | ||||||||
\(439\) | −2.98535 | −0.142483 | −0.0712416 | − | 0.997459i | \(-0.522696\pi\) | ||||
−0.0712416 | + | 0.997459i | \(0.522696\pi\) | |||||||
\(440\) | 11.3807 | 0.542555 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −47.8152 | −2.27434 | ||||||||
\(443\) | 35.3757 | 1.68075 | 0.840374 | − | 0.542007i | \(-0.182335\pi\) | ||||
0.840374 | + | 0.542007i | \(0.182335\pi\) | |||||||
\(444\) | −0.330391 | −0.0156797 | ||||||||
\(445\) | −35.0460 | −1.66134 | ||||||||
\(446\) | −34.3592 | −1.62696 | ||||||||
\(447\) | 5.20043 | 0.245972 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.7278 | −1.16698 | −0.583489 | − | 0.812121i | \(-0.698313\pi\) | ||||
−0.583489 | + | 0.812121i | \(0.698313\pi\) | |||||||
\(450\) | −14.3490 | −0.676420 | ||||||||
\(451\) | −1.15660 | −0.0544619 | ||||||||
\(452\) | 0.477999 | 0.0224832 | ||||||||
\(453\) | 10.2898 | 0.483456 | ||||||||
\(454\) | 1.76426 | 0.0828010 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.22205 | −0.291374 | ||||||||
\(457\) | −9.46161 | −0.442595 | −0.221298 | − | 0.975206i | \(-0.571029\pi\) | ||||
−0.221298 | + | 0.975206i | \(0.571029\pi\) | |||||||
\(458\) | 37.5561 | 1.75488 | ||||||||
\(459\) | 6.92527 | 0.323244 | ||||||||
\(460\) | 3.64716 | 0.170050 | ||||||||
\(461\) | −20.5811 | −0.958557 | −0.479279 | − | 0.877663i | \(-0.659102\pi\) | ||||
−0.479279 | + | 0.877663i | \(0.659102\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.1195 | −1.26035 | −0.630175 | − | 0.776453i | \(-0.717017\pi\) | ||||
−0.630175 | + | 0.776453i | \(0.717017\pi\) | |||||||
\(464\) | −5.76430 | −0.267601 | ||||||||
\(465\) | 1.27344 | 0.0590544 | ||||||||
\(466\) | 28.6325 | 1.32637 | ||||||||
\(467\) | 6.72518 | 0.311204 | 0.155602 | − | 0.987820i | \(-0.450268\pi\) | ||||
0.155602 | + | 0.987820i | \(0.450268\pi\) | |||||||
\(468\) | −1.33082 | −0.0615169 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 42.6138 | 1.96563 | ||||||||
\(471\) | −4.03587 | −0.185963 | ||||||||
\(472\) | −33.3934 | −1.53705 | ||||||||
\(473\) | 2.45332 | 0.112804 | ||||||||
\(474\) | −19.3043 | −0.886676 | ||||||||
\(475\) | 22.8056 | 1.04639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.25189 | −0.103107 | ||||||||
\(478\) | −8.62186 | −0.394355 | ||||||||
\(479\) | 18.3927 | 0.840382 | 0.420191 | − | 0.907436i | \(-0.361963\pi\) | ||||
0.420191 | + | 0.907436i | \(0.361963\pi\) | |||||||
\(480\) | −6.23287 | −0.284490 | ||||||||
\(481\) | −5.16408 | −0.235462 | ||||||||
\(482\) | −18.8925 | −0.860531 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.81940 | −0.128154 | ||||||||
\(485\) | −49.0752 | −2.22839 | ||||||||
\(486\) | 1.51387 | 0.0686704 | ||||||||
\(487\) | 8.31877 | 0.376960 | 0.188480 | − | 0.982077i | \(-0.439644\pi\) | ||||
0.188480 | + | 0.982077i | \(0.439644\pi\) | |||||||
\(488\) | 6.65842 | 0.301412 | ||||||||
\(489\) | −6.84917 | −0.309730 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.703140 | −0.0317323 | −0.0158661 | − | 0.999874i | \(-0.505051\pi\) | ||||
−0.0158661 | + | 0.999874i | \(0.505051\pi\) | |||||||
\(492\) | 0.291794 | 0.0131551 | ||||||||
\(493\) | −8.87404 | −0.399667 | ||||||||
\(494\) | 16.6125 | 0.747432 | ||||||||
\(495\) | 4.40090 | 0.197806 | ||||||||
\(496\) | 1.50550 | 0.0675989 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.91986 | 0.175653 | ||||||||
\(499\) | −25.1798 | −1.12720 | −0.563601 | − | 0.826047i | \(-0.690584\pi\) | ||||
−0.563601 | + | 0.826047i | \(0.690584\pi\) | |||||||
\(500\) | 4.97232 | 0.222369 | ||||||||
\(501\) | −2.72776 | −0.121867 | ||||||||
\(502\) | 45.0387 | 2.01018 | ||||||||
\(503\) | −9.10380 | −0.405918 | −0.202959 | − | 0.979187i | \(-0.565056\pi\) | ||||
−0.202959 | + | 0.979187i | \(0.565056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.675447 | 0.0300570 | ||||||||
\(506\) | −5.75159 | −0.255689 | ||||||||
\(507\) | −7.80095 | −0.346452 | ||||||||
\(508\) | −6.06044 | −0.268889 | ||||||||
\(509\) | 8.52853 | 0.378021 | 0.189010 | − | 0.981975i | \(-0.439472\pi\) | ||||
0.189010 | + | 0.981975i | \(0.439472\pi\) | |||||||
\(510\) | −39.8919 | −1.76644 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15.8972 | 0.702565 | ||||||||
\(513\) | −2.40606 | −0.106230 | ||||||||
\(514\) | −7.05598 | −0.311226 | ||||||||
\(515\) | −55.3031 | −2.43695 | ||||||||
\(516\) | −0.618941 | −0.0272474 | ||||||||
\(517\) | −8.55625 | −0.376304 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.57517 | 0.156933 | ||||||||
\(520\) | −44.8776 | −1.96801 | ||||||||
\(521\) | 29.7200 | 1.30206 | 0.651029 | − | 0.759053i | \(-0.274338\pi\) | ||||
0.651029 | + | 0.759053i | \(0.274338\pi\) | |||||||
\(522\) | −1.93987 | −0.0849058 | ||||||||
\(523\) | 23.3081 | 1.01919 | 0.509597 | − | 0.860413i | \(-0.329795\pi\) | ||||
0.509597 | + | 0.860413i | \(0.329795\pi\) | |||||||
\(524\) | 3.51177 | 0.153412 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.6617 | −1.59853 | ||||||||
\(527\) | 2.31769 | 0.100960 | ||||||||
\(528\) | 5.20288 | 0.226426 | ||||||||
\(529\) | −12.2096 | −0.530852 | ||||||||
\(530\) | 12.9717 | 0.563454 | ||||||||
\(531\) | −12.9132 | −0.560383 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.56081 | 0.197550 | ||||||||
\(534\) | −13.9433 | −0.603386 | ||||||||
\(535\) | −45.9390 | −1.98612 | ||||||||
\(536\) | −16.0726 | −0.694231 | ||||||||
\(537\) | −13.3401 | −0.575667 | ||||||||
\(538\) | 40.4466 | 1.74378 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.11029 | −0.0477793 | ||||||||
\(541\) | 22.9665 | 0.987407 | 0.493704 | − | 0.869630i | \(-0.335643\pi\) | ||||
0.493704 | + | 0.869630i | \(0.335643\pi\) | |||||||
\(542\) | 32.1384 | 1.38046 | ||||||||
\(543\) | 6.15975 | 0.264340 | ||||||||
\(544\) | −11.3440 | −0.486368 | ||||||||
\(545\) | 64.7164 | 2.77215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0779 | −0.815711 | −0.407856 | − | 0.913046i | \(-0.633723\pi\) | ||||
−0.407856 | + | 0.913046i | \(0.633723\pi\) | |||||||
\(548\) | −1.89684 | −0.0810291 | ||||||||
\(549\) | 2.57480 | 0.109890 | ||||||||
\(550\) | −16.5960 | −0.707657 | ||||||||
\(551\) | 3.08312 | 0.131345 | ||||||||
\(552\) | −8.49468 | −0.361558 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.5773 | 0.534359 | ||||||||
\(555\) | −4.30836 | −0.182880 | ||||||||
\(556\) | 6.74935 | 0.286236 | ||||||||
\(557\) | −1.60892 | −0.0681723 | −0.0340861 | − | 0.999419i | \(-0.510852\pi\) | ||||
−0.0340861 | + | 0.999419i | \(0.510852\pi\) | |||||||
\(558\) | 0.506648 | 0.0214481 | ||||||||
\(559\) | −9.67419 | −0.409175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00974 | 0.338171 | ||||||||
\(562\) | 28.7928 | 1.21455 | ||||||||
\(563\) | 40.0650 | 1.68854 | 0.844268 | − | 0.535921i | \(-0.180035\pi\) | ||||
0.844268 | + | 0.535921i | \(0.180035\pi\) | |||||||
\(564\) | 2.15863 | 0.0908948 | ||||||||
\(565\) | 6.23320 | 0.262233 | ||||||||
\(566\) | −13.3352 | −0.560519 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.96987 | 0.250490 | ||||||||
\(569\) | 0.910623 | 0.0381753 | 0.0190876 | − | 0.999818i | \(-0.493924\pi\) | ||||
0.0190876 | + | 0.999818i | \(0.493924\pi\) | |||||||
\(570\) | 13.8597 | 0.580519 | ||||||||
\(571\) | 0.733915 | 0.0307134 | 0.0153567 | − | 0.999882i | \(-0.495112\pi\) | ||||
0.0153567 | + | 0.999882i | \(0.495112\pi\) | |||||||
\(572\) | −1.53921 | −0.0643578 | ||||||||
\(573\) | −23.8691 | −0.997146 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.1354 | 1.29843 | ||||||||
\(576\) | 6.51709 | 0.271546 | ||||||||
\(577\) | −31.6908 | −1.31930 | −0.659652 | − | 0.751571i | \(-0.729296\pi\) | ||||
−0.659652 | + | 0.751571i | \(0.729296\pi\) | |||||||
\(578\) | −46.8684 | −1.94947 | ||||||||
\(579\) | 21.6807 | 0.901017 | ||||||||
\(580\) | 1.42273 | 0.0590754 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −19.5249 | −0.809334 | ||||||||
\(583\) | −2.60453 | −0.107869 | ||||||||
\(584\) | 30.7937 | 1.27425 | ||||||||
\(585\) | −17.3541 | −0.717503 | ||||||||
\(586\) | 45.4231 | 1.87641 | ||||||||
\(587\) | −20.9045 | −0.862823 | −0.431411 | − | 0.902155i | \(-0.641984\pi\) | ||||
−0.431411 | + | 0.902155i | \(0.641984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.805238 | −0.0331792 | ||||||||
\(590\) | 74.3841 | 3.06235 | ||||||||
\(591\) | −22.1707 | −0.911979 | ||||||||
\(592\) | −5.09347 | −0.209340 | ||||||||
\(593\) | 1.44402 | 0.0592987 | 0.0296494 | − | 0.999560i | \(-0.490561\pi\) | ||||
0.0296494 | + | 0.999560i | \(0.490561\pi\) | |||||||
\(594\) | 1.75093 | 0.0718416 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.51745 | −0.0621573 | ||||||||
\(597\) | 7.79167 | 0.318892 | ||||||||
\(598\) | 22.6803 | 0.927465 | ||||||||
\(599\) | 10.3458 | 0.422719 | 0.211360 | − | 0.977408i | \(-0.432211\pi\) | ||||
0.211360 | + | 0.977408i | \(0.432211\pi\) | |||||||
\(600\) | −24.5111 | −1.00066 | ||||||||
\(601\) | 8.35641 | 0.340865 | 0.170432 | − | 0.985369i | \(-0.445484\pi\) | ||||
0.170432 | + | 0.985369i | \(0.445484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.21525 | −0.253104 | ||||||||
\(604\) | −3.00249 | −0.122170 | ||||||||
\(605\) | −36.7655 | −1.49473 | ||||||||
\(606\) | 0.268732 | 0.0109165 | ||||||||
\(607\) | −0.600544 | −0.0243753 | −0.0121877 | − | 0.999926i | \(-0.503880\pi\) | ||||
−0.0121877 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(608\) | 3.94125 | 0.159839 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.8317 | −0.600518 | ||||||||
\(611\) | 33.7399 | 1.36497 | ||||||||
\(612\) | −2.02075 | −0.0816841 | ||||||||
\(613\) | −20.2750 | −0.818899 | −0.409449 | − | 0.912333i | \(-0.634279\pi\) | ||||
−0.409449 | + | 0.912333i | \(0.634279\pi\) | |||||||
\(614\) | 39.8512 | 1.60827 | ||||||||
\(615\) | 3.80505 | 0.153434 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.4448 | −0.943854 | −0.471927 | − | 0.881638i | \(-0.656441\pi\) | ||||
−0.471927 | + | 0.881638i | \(0.656441\pi\) | |||||||
\(618\) | −22.0028 | −0.885081 | ||||||||
\(619\) | 10.3180 | 0.414716 | 0.207358 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207358 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(620\) | −0.371582 | −0.0149231 | ||||||||
\(621\) | −3.28488 | −0.131818 | ||||||||
\(622\) | −32.2294 | −1.29228 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −20.5165 | −0.821318 | ||||||||
\(625\) | 17.4481 | 0.697923 | ||||||||
\(626\) | 22.4191 | 0.896049 | ||||||||
\(627\) | −2.78283 | −0.111136 | ||||||||
\(628\) | 1.17764 | 0.0469930 | ||||||||
\(629\) | −7.84131 | −0.312654 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.95019 | 0.236873 | 0.118437 | − | 0.992962i | \(-0.462212\pi\) | ||||
0.118437 | + | 0.992962i | \(0.462212\pi\) | |||||||
\(632\) | −32.9757 | −1.31170 | ||||||||
\(633\) | −7.81577 | −0.310649 | ||||||||
\(634\) | −5.98397 | −0.237654 | ||||||||
\(635\) | −79.0293 | −3.13618 | ||||||||
\(636\) | 0.657089 | 0.0260553 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.24364 | −0.0888267 | ||||||||
\(639\) | 2.30854 | 0.0913243 | ||||||||
\(640\) | −50.0064 | −1.97668 | ||||||||
\(641\) | −18.7783 | −0.741697 | −0.370848 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370848 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(642\) | −18.2772 | −0.721343 | ||||||||
\(643\) | −26.6022 | −1.04909 | −0.524543 | − | 0.851384i | \(-0.675764\pi\) | ||||
−0.524543 | + | 0.851384i | \(0.675764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.07111 | −0.317800 | ||||||||
\(646\) | 25.2250 | 0.992463 | ||||||||
\(647\) | −23.5755 | −0.926847 | −0.463424 | − | 0.886137i | \(-0.653379\pi\) | ||||
−0.463424 | + | 0.886137i | \(0.653379\pi\) | |||||||
\(648\) | 2.58600 | 0.101588 | ||||||||
\(649\) | −14.9353 | −0.586261 | ||||||||
\(650\) | 65.4432 | 2.56689 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.99855 | 0.0782691 | ||||||||
\(653\) | −17.2768 | −0.676093 | −0.338046 | − | 0.941129i | \(-0.609766\pi\) | ||||
−0.338046 | + | 0.941129i | \(0.609766\pi\) | |||||||
\(654\) | 25.7479 | 1.00682 | ||||||||
\(655\) | 45.7941 | 1.78933 | ||||||||
\(656\) | 4.49844 | 0.175635 | ||||||||
\(657\) | 11.9079 | 0.464570 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.3358 | 1.25963 | 0.629813 | − | 0.776747i | \(-0.283132\pi\) | ||||
0.629813 | + | 0.776747i | \(0.283132\pi\) | |||||||
\(660\) | −1.28416 | −0.0499857 | ||||||||
\(661\) | −41.8828 | −1.62905 | −0.814525 | − | 0.580128i | \(-0.803002\pi\) | ||||
−0.814525 | + | 0.580128i | \(0.803002\pi\) | |||||||
\(662\) | −46.8480 | −1.82080 | ||||||||
\(663\) | −31.5848 | −1.22665 | ||||||||
\(664\) | 6.69593 | 0.259852 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.71411 | −0.0664205 | ||||||||
\(667\) | 4.20924 | 0.162982 | ||||||||
\(668\) | 0.795943 | 0.0307960 | ||||||||
\(669\) | −22.6963 | −0.877490 | ||||||||
\(670\) | 35.8019 | 1.38315 | ||||||||
\(671\) | 2.97800 | 0.114964 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.0621 | −1.23590 | −0.617951 | − | 0.786217i | \(-0.712037\pi\) | ||||
−0.617951 | + | 0.786217i | \(0.712037\pi\) | |||||||
\(674\) | −49.3467 | −1.90077 | ||||||||
\(675\) | −9.47840 | −0.364824 | ||||||||
\(676\) | 2.27627 | 0.0875488 | ||||||||
\(677\) | 39.2517 | 1.50857 | 0.754283 | − | 0.656549i | \(-0.227984\pi\) | ||||
0.754283 | + | 0.656549i | \(0.227984\pi\) | |||||||
\(678\) | 2.47992 | 0.0952409 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −68.1436 | −2.61319 | ||||||||
\(681\) | 1.16540 | 0.0446583 | ||||||||
\(682\) | 0.585987 | 0.0224386 | ||||||||
\(683\) | −15.5806 | −0.596176 | −0.298088 | − | 0.954538i | \(-0.596349\pi\) | ||||
−0.298088 | + | 0.954538i | \(0.596349\pi\) | |||||||
\(684\) | 0.702072 | 0.0268444 | ||||||||
\(685\) | −24.7352 | −0.945084 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.8081 | 0.946487 | ||||||||
\(688\) | −9.54191 | −0.363782 | ||||||||
\(689\) | 10.2705 | 0.391273 | ||||||||
\(690\) | 18.9220 | 0.720348 | ||||||||
\(691\) | −18.0215 | −0.685569 | −0.342784 | − | 0.939414i | \(-0.611370\pi\) | ||||
−0.342784 | + | 0.939414i | \(0.611370\pi\) | |||||||
\(692\) | −1.04321 | −0.0396570 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.5332 | 1.38678 | ||||||||
\(695\) | 88.0129 | 3.33852 | ||||||||
\(696\) | −3.31370 | −0.125605 | ||||||||
\(697\) | 6.92527 | 0.262313 | ||||||||
\(698\) | 37.7642 | 1.42940 | ||||||||
\(699\) | 18.9135 | 0.715373 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.16472 | −0.195069 | −0.0975344 | − | 0.995232i | \(-0.531096\pi\) | ||||
−0.0975344 | + | 0.995232i | \(0.531096\pi\) | |||||||
\(702\) | −6.90445 | −0.260592 | ||||||||
\(703\) | 2.72432 | 0.102750 | ||||||||
\(704\) | 7.53764 | 0.284086 | ||||||||
\(705\) | 28.1490 | 1.06015 | ||||||||
\(706\) | 53.1643 | 2.00087 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.76798 | 0.141609 | ||||||||
\(709\) | 11.3643 | 0.426796 | 0.213398 | − | 0.976965i | \(-0.431547\pi\) | ||||
0.213398 | + | 0.976965i | \(0.431547\pi\) | |||||||
\(710\) | −13.2980 | −0.499063 | ||||||||
\(711\) | −12.7517 | −0.478224 | ||||||||
\(712\) | −23.8180 | −0.892619 | ||||||||
\(713\) | −1.09935 | −0.0411711 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.0717 | −0.750637 | ||||||||
\(716\) | 3.89255 | 0.145472 | ||||||||
\(717\) | −5.69526 | −0.212693 | ||||||||
\(718\) | 3.17594 | 0.118525 | ||||||||
\(719\) | −30.5843 | −1.14060 | −0.570302 | − | 0.821435i | \(-0.693174\pi\) | ||||
−0.570302 | + | 0.821435i | \(0.693174\pi\) | |||||||
\(720\) | −17.1168 | −0.637906 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.9995 | 0.744306 | ||||||||
\(723\) | −12.4796 | −0.464123 | ||||||||
\(724\) | −1.79738 | −0.0667990 | ||||||||
\(725\) | 12.1456 | 0.451077 | ||||||||
\(726\) | −14.6274 | −0.542874 | ||||||||
\(727\) | −18.0711 | −0.670221 | −0.335111 | − | 0.942179i | \(-0.608774\pi\) | ||||
−0.335111 | + | 0.942179i | \(0.608774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −68.5933 | −2.53875 | ||||||||
\(731\) | −14.6896 | −0.543315 | ||||||||
\(732\) | −0.751310 | −0.0277692 | ||||||||
\(733\) | 49.3640 | 1.82330 | 0.911651 | − | 0.410966i | \(-0.134808\pi\) | ||||
0.911651 | + | 0.410966i | \(0.134808\pi\) | |||||||
\(734\) | −23.8445 | −0.880115 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.38080 | 0.198339 | ||||||||
\(737\) | −7.18853 | −0.264793 | ||||||||
\(738\) | 1.51387 | 0.0557262 | ||||||||
\(739\) | −9.21630 | −0.339027 | −0.169514 | − | 0.985528i | \(-0.554220\pi\) | ||||
−0.169514 | + | 0.985528i | \(0.554220\pi\) | |||||||
\(740\) | 1.25715 | 0.0462139 | ||||||||
\(741\) | 10.9736 | 0.403124 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.8911 | −1.75696 | −0.878478 | − | 0.477783i | \(-0.841440\pi\) | ||||
−0.878478 | + | 0.477783i | \(0.841440\pi\) | |||||||
\(744\) | 0.865459 | 0.0317293 | ||||||||
\(745\) | −19.7879 | −0.724972 | ||||||||
\(746\) | 15.7968 | 0.578361 | ||||||||
\(747\) | 2.58930 | 0.0947376 | ||||||||
\(748\) | −2.33719 | −0.0854562 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 25.7971 | 0.941977 | ||||||||
\(751\) | −0.992350 | −0.0362114 | −0.0181057 | − | 0.999836i | \(-0.505764\pi\) | ||||
−0.0181057 | + | 0.999836i | \(0.505764\pi\) | |||||||
\(752\) | 33.2786 | 1.21354 | ||||||||
\(753\) | 29.7508 | 1.08418 | ||||||||
\(754\) | 8.84736 | 0.322202 | ||||||||
\(755\) | −39.1531 | −1.42493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.2370 | 0.626490 | 0.313245 | − | 0.949672i | \(-0.398584\pi\) | ||||
0.313245 | + | 0.949672i | \(0.398584\pi\) | |||||||
\(758\) | 19.7430 | 0.717100 | ||||||||
\(759\) | −3.79927 | −0.137905 | ||||||||
\(760\) | 23.6752 | 0.858791 | ||||||||
\(761\) | 25.0256 | 0.907177 | 0.453589 | − | 0.891211i | \(-0.350144\pi\) | ||||
0.453589 | + | 0.891211i | \(0.350144\pi\) | |||||||
\(762\) | −31.4424 | −1.13904 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.96486 | 0.251980 | ||||||||
\(765\) | −26.3510 | −0.952723 | ||||||||
\(766\) | −20.9674 | −0.757584 | ||||||||
\(767\) | 58.8944 | 2.12655 | ||||||||
\(768\) | −6.86124 | −0.247584 | ||||||||
\(769\) | −12.7073 | −0.458239 | −0.229119 | − | 0.973398i | \(-0.573585\pi\) | ||||
−0.229119 | + | 0.973398i | \(0.573585\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.66090 | −0.167858 | ||||||||
\(772\) | −6.32628 | −0.227688 | ||||||||
\(773\) | −47.3022 | −1.70134 | −0.850671 | − | 0.525699i | \(-0.823804\pi\) | ||||
−0.850671 | + | 0.525699i | \(0.823804\pi\) | |||||||
\(774\) | −3.21115 | −0.115422 | ||||||||
\(775\) | −3.17215 | −0.113947 | ||||||||
\(776\) | −33.3526 | −1.19729 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.6252 | −1.59989 | ||||||||
\(779\) | −2.40606 | −0.0862059 | ||||||||
\(780\) | 5.06382 | 0.181314 | ||||||||
\(781\) | 2.67004 | 0.0955417 | ||||||||
\(782\) | 34.4385 | 1.23152 | ||||||||
\(783\) | −1.28140 | −0.0457935 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.3567 | 0.548103 | ||||||||
\(786\) | 18.2195 | 0.649869 | ||||||||
\(787\) | −41.5945 | −1.48269 | −0.741343 | − | 0.671127i | \(-0.765811\pi\) | ||||
−0.741343 | + | 0.671127i | \(0.765811\pi\) | |||||||
\(788\) | 6.46927 | 0.230458 | ||||||||
\(789\) | −24.2173 | −0.862158 | ||||||||
\(790\) | 73.4539 | 2.61337 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.99095 | 0.106279 | ||||||||
\(793\) | −11.7431 | −0.417011 | ||||||||
\(794\) | 38.7121 | 1.37384 | ||||||||
\(795\) | 8.56857 | 0.303896 | ||||||||
\(796\) | −2.27356 | −0.0805842 | ||||||||
\(797\) | −50.4009 | −1.78529 | −0.892645 | − | 0.450760i | \(-0.851153\pi\) | ||||
−0.892645 | + | 0.450760i | \(0.851153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.2317 | 1.81245 | ||||||||
\(800\) | 15.5261 | 0.548931 | ||||||||
\(801\) | −9.21039 | −0.325433 | ||||||||
\(802\) | −10.1324 | −0.357786 | ||||||||
\(803\) | 13.7726 | 0.486024 | ||||||||
\(804\) | 1.81357 | 0.0639597 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.31072 | −0.0813917 | ||||||||
\(807\) | 26.7174 | 0.940498 | ||||||||
\(808\) | 0.459049 | 0.0161493 | ||||||||
\(809\) | 18.2063 | 0.640098 | 0.320049 | − | 0.947401i | \(-0.396301\pi\) | ||||
0.320049 | + | 0.947401i | \(0.396301\pi\) | |||||||
\(810\) | −5.76034 | −0.202398 | ||||||||
\(811\) | −47.0365 | −1.65168 | −0.825838 | − | 0.563908i | \(-0.809297\pi\) | ||||
−0.825838 | + | 0.563908i | \(0.809297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.2293 | 0.744545 | ||||||||
\(814\) | −1.98254 | −0.0694878 | ||||||||
\(815\) | 26.0614 | 0.912892 | ||||||||
\(816\) | −31.1530 | −1.09057 | ||||||||
\(817\) | 5.10363 | 0.178553 | ||||||||
\(818\) | 28.7309 | 1.00455 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.11029 | −0.0387730 | ||||||||
\(821\) | −52.1811 | −1.82113 | −0.910566 | − | 0.413364i | \(-0.864354\pi\) | ||||
−0.910566 | + | 0.413364i | \(0.864354\pi\) | |||||||
\(822\) | −9.84108 | −0.343247 | ||||||||
\(823\) | −4.29085 | −0.149570 | −0.0747848 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747848 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(824\) | −37.5853 | −1.30934 | ||||||||
\(825\) | −10.9627 | −0.381671 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0862 | 1.60257 | 0.801287 | − | 0.598280i | \(-0.204149\pi\) | ||||
0.801287 | + | 0.598280i | \(0.204149\pi\) | |||||||
\(828\) | 0.958507 | 0.0333104 | ||||||||
\(829\) | −12.1577 | −0.422256 | −0.211128 | − | 0.977458i | \(-0.567714\pi\) | ||||
−0.211128 | + | 0.977458i | \(0.567714\pi\) | |||||||
\(830\) | −14.9153 | −0.517716 | ||||||||
\(831\) | 8.30807 | 0.288204 | ||||||||
\(832\) | −29.7232 | −1.03047 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 35.0166 | 1.21252 | ||||||||
\(835\) | 10.3793 | 0.359189 | ||||||||
\(836\) | 0.812014 | 0.0280841 | ||||||||
\(837\) | 0.334671 | 0.0115679 | ||||||||
\(838\) | −57.9840 | −2.00303 | ||||||||
\(839\) | −4.79517 | −0.165548 | −0.0827739 | − | 0.996568i | \(-0.526378\pi\) | ||||
−0.0827739 | + | 0.996568i | \(0.526378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3580 | −0.943380 | ||||||||
\(842\) | −20.7843 | −0.716274 | ||||||||
\(843\) | 19.0193 | 0.655061 | ||||||||
\(844\) | 2.28059 | 0.0785012 | ||||||||
\(845\) | 29.6830 | 1.02113 | ||||||||
\(846\) | 11.1993 | 0.385039 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.1300 | 0.347866 | ||||||||
\(849\) | −8.80867 | −0.302313 | ||||||||
\(850\) | 99.3710 | 3.40840 | ||||||||
\(851\) | 3.71938 | 0.127499 | ||||||||
\(852\) | −0.673617 | −0.0230777 | ||||||||
\(853\) | −5.26286 | −0.180197 | −0.0900984 | − | 0.995933i | \(-0.528718\pi\) | ||||
−0.0900984 | + | 0.995933i | \(0.528718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.15516 | 0.313100 | ||||||||
\(856\) | −31.2212 | −1.06712 | ||||||||
\(857\) | −0.907168 | −0.0309883 | −0.0154941 | − | 0.999880i | \(-0.504932\pi\) | ||||
−0.0154941 | + | 0.999880i | \(0.504932\pi\) | |||||||
\(858\) | −7.98566 | −0.272626 | ||||||||
\(859\) | 28.1280 | 0.959715 | 0.479858 | − | 0.877346i | \(-0.340688\pi\) | ||||
0.479858 | + | 0.877346i | \(0.340688\pi\) | |||||||
\(860\) | 2.35510 | 0.0803083 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.11592 | 0.0720685 | ||||||||
\(863\) | 4.62233 | 0.157346 | 0.0786730 | − | 0.996900i | \(-0.474932\pi\) | ||||
0.0786730 | + | 0.996900i | \(0.474932\pi\) | |||||||
\(864\) | −1.63805 | −0.0557277 | ||||||||
\(865\) | −13.6037 | −0.462540 | ||||||||
\(866\) | −29.2210 | −0.992969 | ||||||||
\(867\) | −30.9594 | −1.05144 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.7485 | −0.500309 | ||||||||
\(870\) | 7.38130 | 0.250249 | ||||||||
\(871\) | 28.3465 | 0.960486 | ||||||||
\(872\) | 43.9827 | 1.48944 | ||||||||
\(873\) | −12.8974 | −0.436510 | ||||||||
\(874\) | −11.9650 | −0.404722 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.47464 | −0.117397 | ||||||||
\(877\) | −33.5121 | −1.13162 | −0.565812 | − | 0.824534i | \(-0.691437\pi\) | ||||
−0.565812 | + | 0.824534i | \(0.691437\pi\) | |||||||
\(878\) | 4.51943 | 0.152523 | ||||||||
\(879\) | 30.0047 | 1.01203 | ||||||||
\(880\) | −19.7972 | −0.667364 | ||||||||
\(881\) | 5.55431 | 0.187129 | 0.0935647 | − | 0.995613i | \(-0.470174\pi\) | ||||
0.0935647 | + | 0.995613i | \(0.470174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.3288 | 1.12160 | 0.560802 | − | 0.827950i | \(-0.310493\pi\) | ||||
0.560802 | + | 0.827950i | \(0.310493\pi\) | |||||||
\(884\) | 9.21626 | 0.309976 | ||||||||
\(885\) | 49.1352 | 1.65166 | ||||||||
\(886\) | −53.5541 | −1.79918 | ||||||||
\(887\) | −31.4901 | −1.05733 | −0.528667 | − | 0.848829i | \(-0.677308\pi\) | ||||
−0.528667 | + | 0.848829i | \(0.677308\pi\) | |||||||
\(888\) | −2.92806 | −0.0982592 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 53.0550 | 1.77841 | ||||||||
\(891\) | 1.15660 | 0.0387474 | ||||||||
\(892\) | 6.62265 | 0.221743 | ||||||||
\(893\) | −17.7995 | −0.595638 | ||||||||
\(894\) | −7.87276 | −0.263304 | ||||||||
\(895\) | 50.7597 | 1.69671 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.9817 | 0.500224 | ||||||||
\(898\) | 37.4346 | 1.24921 | ||||||||
\(899\) | −0.428848 | −0.0143029 | ||||||||
\(900\) | 2.76574 | 0.0921913 | ||||||||
\(901\) | 15.5950 | 0.519544 | ||||||||
\(902\) | 1.75093 | 0.0582996 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.23622 | 0.140895 | ||||||||
\(905\) | −23.4381 | −0.779110 | ||||||||
\(906\) | −15.5774 | −0.517523 | ||||||||
\(907\) | −24.1540 | −0.802021 | −0.401010 | − | 0.916074i | \(-0.631341\pi\) | ||||
−0.401010 | + | 0.916074i | \(0.631341\pi\) | |||||||
\(908\) | −0.340057 | −0.0112852 | ||||||||
\(909\) | 0.177513 | 0.00588775 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5342 | 0.448407 | 0.224203 | − | 0.974542i | \(-0.428022\pi\) | ||||
0.224203 | + | 0.974542i | \(0.428022\pi\) | |||||||
\(912\) | 10.8235 | 0.358402 | ||||||||
\(913\) | 2.99477 | 0.0991126 | ||||||||
\(914\) | 14.3236 | 0.473783 | ||||||||
\(915\) | −9.79723 | −0.323886 | ||||||||
\(916\) | −7.23884 | −0.239178 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10.4839 | −0.346022 | ||||||||
\(919\) | −6.10358 | −0.201339 | −0.100669 | − | 0.994920i | \(-0.532098\pi\) | ||||
−0.100669 | + | 0.994920i | \(0.532098\pi\) | |||||||
\(920\) | 32.3227 | 1.06565 | ||||||||
\(921\) | 26.3241 | 0.867410 | ||||||||
\(922\) | 31.1571 | 1.02610 | ||||||||
\(923\) | −10.5288 | −0.346559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7322 | 0.352871 | ||||||||
\(926\) | 41.0553 | 1.34916 | ||||||||
\(927\) | −14.5341 | −0.477364 | ||||||||
\(928\) | 2.09900 | 0.0689030 | ||||||||
\(929\) | −34.5625 | −1.13396 | −0.566979 | − | 0.823732i | \(-0.691888\pi\) | ||||
−0.566979 | + | 0.823732i | \(0.691888\pi\) | |||||||
\(930\) | −1.92782 | −0.0632157 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.51883 | −0.180775 | ||||||||
\(933\) | −21.2895 | −0.696985 | ||||||||
\(934\) | −10.1810 | −0.333133 | ||||||||
\(935\) | −30.4775 | −0.996719 | ||||||||
\(936\) | −11.7942 | −0.385506 | ||||||||
\(937\) | 3.45162 | 0.112759 | 0.0563797 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563797 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.8092 | 0.483280 | ||||||||
\(940\) | −8.21370 | −0.267901 | ||||||||
\(941\) | 33.2147 | 1.08277 | 0.541384 | − | 0.840775i | \(-0.317900\pi\) | ||||
0.541384 | + | 0.840775i | \(0.317900\pi\) | |||||||
\(942\) | 6.10977 | 0.199067 | ||||||||
\(943\) | −3.28488 | −0.106970 | ||||||||
\(944\) | 58.0891 | 1.89064 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.71400 | −0.120753 | ||||||||
\(947\) | 29.1330 | 0.946694 | 0.473347 | − | 0.880876i | \(-0.343046\pi\) | ||||
0.473347 | + | 0.880876i | \(0.343046\pi\) | |||||||
\(948\) | 3.72085 | 0.120848 | ||||||||
\(949\) | −54.3094 | −1.76296 | ||||||||
\(950\) | −34.5246 | −1.12013 | ||||||||
\(951\) | −3.95277 | −0.128177 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7997 | 1.22445 | 0.612226 | − | 0.790683i | \(-0.290274\pi\) | ||||
0.612226 | + | 0.790683i | \(0.290274\pi\) | |||||||
\(954\) | 3.40907 | 0.110373 | ||||||||
\(955\) | 90.8231 | 2.93897 | ||||||||
\(956\) | 1.66184 | 0.0537478 | ||||||||
\(957\) | −1.48206 | −0.0479082 | ||||||||
\(958\) | −27.8440 | −0.899600 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.7979 | −0.800348 | ||||||||
\(961\) | −30.8880 | −0.996387 | ||||||||
\(962\) | 7.81774 | 0.252054 | ||||||||
\(963\) | −12.0732 | −0.389053 | ||||||||
\(964\) | 3.64148 | 0.117284 | ||||||||
\(965\) | −82.4960 | −2.65564 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.1460 | 0.551379 | 0.275690 | − | 0.961247i | \(-0.411094\pi\) | ||||
0.275690 | + | 0.961247i | \(0.411094\pi\) | |||||||
\(968\) | −24.9866 | −0.803101 | ||||||||
\(969\) | 16.6626 | 0.535280 | ||||||||
\(970\) | 74.2933 | 2.38541 | ||||||||
\(971\) | −10.5979 | −0.340104 | −0.170052 | − | 0.985435i | \(-0.554394\pi\) | ||||
−0.170052 | + | 0.985435i | \(0.554394\pi\) | |||||||
\(972\) | −0.291794 | −0.00935929 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.5935 | −0.403522 | ||||||||
\(975\) | 43.2291 | 1.38444 | ||||||||
\(976\) | −11.5826 | −0.370749 | ||||||||
\(977\) | 26.8876 | 0.860209 | 0.430105 | − | 0.902779i | \(-0.358477\pi\) | ||||
0.430105 | + | 0.902779i | \(0.358477\pi\) | |||||||
\(978\) | 10.3687 | 0.331555 | ||||||||
\(979\) | −10.6527 | −0.340462 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0080 | 0.543025 | ||||||||
\(982\) | 1.06446 | 0.0339683 | ||||||||
\(983\) | −27.7596 | −0.885392 | −0.442696 | − | 0.896672i | \(-0.645978\pi\) | ||||
−0.442696 | + | 0.896672i | \(0.645978\pi\) | |||||||
\(984\) | 2.58600 | 0.0824386 | ||||||||
\(985\) | 84.3605 | 2.68795 | ||||||||
\(986\) | 13.4341 | 0.427830 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.20202 | −0.101870 | ||||||||
\(989\) | 6.96774 | 0.221561 | ||||||||
\(990\) | −6.66238 | −0.211744 | ||||||||
\(991\) | 12.1510 | 0.385988 | 0.192994 | − | 0.981200i | \(-0.438180\pi\) | ||||
0.192994 | + | 0.981200i | \(0.438180\pi\) | |||||||
\(992\) | −0.548209 | −0.0174057 | ||||||||
\(993\) | −30.9459 | −0.982039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6477 | −0.939894 | ||||||||
\(996\) | −0.755542 | −0.0239403 | ||||||||
\(997\) | 15.7997 | 0.500382 | 0.250191 | − | 0.968197i | \(-0.419507\pi\) | ||||
0.250191 | + | 0.968197i | \(0.419507\pi\) | |||||||
\(998\) | 38.1188 | 1.20663 | ||||||||
\(999\) | −1.13227 | −0.0358236 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6027.2.a.bb.1.3 | 8 | ||
7.2 | even | 3 | 861.2.i.d.739.6 | yes | 16 | ||
7.4 | even | 3 | 861.2.i.d.247.6 | ✓ | 16 | ||
7.6 | odd | 2 | 6027.2.a.bc.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.6 | ✓ | 16 | 7.4 | even | 3 | ||
861.2.i.d.739.6 | yes | 16 | 7.2 | even | 3 | ||
6027.2.a.bb.1.3 | 8 | 1.1 | even | 1 | trivial | ||
6027.2.a.bc.1.3 | 8 | 7.6 | odd | 2 |