Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.401917952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 14x^{4} + 49x^{2} - 18 \) |
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 | 1.2 | ||
Root | \(-2.26409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.26409 | −1.30718 | −0.653588 | − | 0.756851i | \(-0.726737\pi\) | ||||
−0.653588 | + | 0.756851i | \(0.726737\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.67831 | −1.64499 | −0.822494 | − | 0.568773i | \(-0.807418\pi\) | ||||
−0.822494 | + | 0.568773i | \(0.807418\pi\) | |||||||
\(6\) | −2.26409 | −0.924312 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.12612 | 0.708707 | ||||||||
\(10\) | −3.67831 | −1.16318 | ||||||||
\(11\) | −2.32803 | −0.701928 | −0.350964 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350964 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(12\) | −2.26409 | −0.653588 | ||||||||
\(13\) | −5.27088 | −1.46188 | −0.730940 | − | 0.682442i | \(-0.760918\pi\) | ||||
−0.730940 | + | 0.682442i | \(0.760918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.32803 | 2.15029 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.70655 | 1.14151 | 0.570753 | − | 0.821122i | \(-0.306652\pi\) | ||||
0.570753 | + | 0.821122i | \(0.306652\pi\) | |||||||
\(18\) | 2.12612 | 0.501131 | ||||||||
\(19\) | −5.94240 | −1.36328 | −0.681640 | − | 0.731688i | \(-0.738733\pi\) | ||||
−0.681640 | + | 0.731688i | \(0.738733\pi\) | |||||||
\(20\) | −3.67831 | −0.822494 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.32803 | −0.496338 | ||||||||
\(23\) | −8.65606 | −1.80491 | −0.902457 | − | 0.430780i | \(-0.858238\pi\) | ||||
−0.902457 | + | 0.430780i | \(0.858238\pi\) | |||||||
\(24\) | −2.26409 | −0.462156 | ||||||||
\(25\) | 8.52994 | 1.70599 | ||||||||
\(26\) | −5.27088 | −1.03370 | ||||||||
\(27\) | 1.97855 | 0.380772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 8.32803 | 1.52048 | ||||||||
\(31\) | 1.97855 | 0.355358 | 0.177679 | − | 0.984089i | \(-0.443141\pi\) | ||||
0.177679 | + | 0.984089i | \(0.443141\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.27088 | 0.917543 | ||||||||
\(34\) | 4.70655 | 0.807166 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.12612 | 0.354353 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −5.94240 | −0.963985 | ||||||||
\(39\) | 11.9338 | 1.91093 | ||||||||
\(40\) | −3.67831 | −0.581591 | ||||||||
\(41\) | −10.3634 | −1.61849 | −0.809246 | − | 0.587470i | \(-0.800124\pi\) | ||||
−0.809246 | + | 0.587470i | \(0.800124\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1860 | −1.85835 | −0.929174 | − | 0.369642i | \(-0.879480\pi\) | ||||
−0.929174 | + | 0.369642i | \(0.879480\pi\) | |||||||
\(44\) | −2.32803 | −0.350964 | ||||||||
\(45\) | −7.82052 | −1.16581 | ||||||||
\(46\) | −8.65606 | −1.27627 | ||||||||
\(47\) | 1.97855 | 0.288601 | 0.144300 | − | 0.989534i | \(-0.453907\pi\) | ||||
0.144300 | + | 0.989534i | \(0.453907\pi\) | |||||||
\(48\) | −2.26409 | −0.326794 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.52994 | 1.20632 | ||||||||
\(51\) | −10.6561 | −1.49215 | ||||||||
\(52\) | −5.27088 | −0.730940 | ||||||||
\(53\) | 6.32803 | 0.869222 | 0.434611 | − | 0.900618i | \(-0.356886\pi\) | ||||
0.434611 | + | 0.900618i | \(0.356886\pi\) | |||||||
\(54\) | 1.97855 | 0.269246 | ||||||||
\(55\) | 8.56321 | 1.15466 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.4542 | 1.78205 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 7.17825 | 0.934529 | 0.467265 | − | 0.884118i | \(-0.345240\pi\) | ||||
0.467265 | + | 0.884118i | \(0.345240\pi\) | |||||||
\(60\) | 8.32803 | 1.07514 | ||||||||
\(61\) | 11.1129 | 1.42286 | 0.711428 | − | 0.702759i | \(-0.248049\pi\) | ||||
0.711428 | + | 0.702759i | \(0.248049\pi\) | |||||||
\(62\) | 1.97855 | 0.251276 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 19.3879 | 2.40478 | ||||||||
\(66\) | 5.27088 | 0.648801 | ||||||||
\(67\) | −2.25224 | −0.275155 | −0.137577 | − | 0.990491i | \(-0.543932\pi\) | ||||
−0.137577 | + | 0.990491i | \(0.543932\pi\) | |||||||
\(68\) | 4.70655 | 0.570753 | ||||||||
\(69\) | 19.5981 | 2.35934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 2.12612 | 0.250566 | ||||||||
\(73\) | 7.17825 | 0.840151 | 0.420076 | − | 0.907489i | \(-0.362004\pi\) | ||||
0.420076 | + | 0.907489i | \(0.362004\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | −19.3126 | −2.23003 | ||||||||
\(76\) | −5.94240 | −0.681640 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.9338 | 1.35123 | ||||||||
\(79\) | 11.1261 | 1.25179 | 0.625893 | − | 0.779909i | \(-0.284735\pi\) | ||||
0.625893 | + | 0.779909i | \(0.284735\pi\) | |||||||
\(80\) | −3.67831 | −0.411247 | ||||||||
\(81\) | −10.8580 | −1.20644 | ||||||||
\(82\) | −10.3634 | −1.14445 | ||||||||
\(83\) | 10.3634 | 1.13753 | 0.568766 | − | 0.822500i | \(-0.307421\pi\) | ||||
0.568766 | + | 0.822500i | \(0.307421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3121 | −1.87776 | ||||||||
\(86\) | −12.1860 | −1.31405 | ||||||||
\(87\) | 2.26409 | 0.242736 | ||||||||
\(88\) | −2.32803 | −0.248169 | ||||||||
\(89\) | −5.83521 | −0.618531 | −0.309266 | − | 0.950976i | \(-0.600083\pi\) | ||||
−0.309266 | + | 0.950976i | \(0.600083\pi\) | |||||||
\(90\) | −7.82052 | −0.824355 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.65606 | −0.902457 | ||||||||
\(93\) | −4.47962 | −0.464515 | ||||||||
\(94\) | 1.97855 | 0.204072 | ||||||||
\(95\) | 21.8580 | 2.24258 | ||||||||
\(96\) | −2.26409 | −0.231078 | ||||||||
\(97\) | −4.13545 | −0.419892 | −0.209946 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209946 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.94967 | −0.497461 | ||||||||
\(100\) | 8.52994 | 0.852994 | ||||||||
\(101\) | −3.75624 | −0.373760 | −0.186880 | − | 0.982383i | \(-0.559838\pi\) | ||||
−0.186880 | + | 0.982383i | \(0.559838\pi\) | |||||||
\(102\) | −10.6561 | −1.05511 | ||||||||
\(103\) | −8.48528 | −0.836080 | −0.418040 | − | 0.908429i | \(-0.637283\pi\) | ||||
−0.418040 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(104\) | −5.27088 | −0.516852 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.32803 | 0.614633 | ||||||||
\(107\) | 4.65606 | 0.450119 | 0.225059 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225059 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(108\) | 1.97855 | 0.190386 | ||||||||
\(109\) | −10.9841 | −1.05209 | −0.526043 | − | 0.850458i | \(-0.676325\pi\) | ||||
−0.526043 | + | 0.850458i | \(0.676325\pi\) | |||||||
\(110\) | 8.56321 | 0.816470 | ||||||||
\(111\) | 4.52819 | 0.429796 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.8076 | 1.95742 | 0.978709 | − | 0.205251i | \(-0.0658010\pi\) | ||||
0.978709 | + | 0.205251i | \(0.0658010\pi\) | |||||||
\(114\) | 13.4542 | 1.26010 | ||||||||
\(115\) | 31.8397 | 2.96906 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −11.2065 | −1.03604 | ||||||||
\(118\) | 7.17825 | 0.660812 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.32803 | 0.760242 | ||||||||
\(121\) | −5.58027 | −0.507297 | ||||||||
\(122\) | 11.1129 | 1.00611 | ||||||||
\(123\) | 23.4637 | 2.11565 | ||||||||
\(124\) | 1.97855 | 0.177679 | ||||||||
\(125\) | −12.9842 | −1.16134 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.25224 | 0.199854 | 0.0999269 | − | 0.994995i | \(-0.468139\pi\) | ||||
0.0999269 | + | 0.994995i | \(0.468139\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 27.5903 | 2.42919 | ||||||||
\(130\) | 19.3879 | 1.70043 | ||||||||
\(131\) | −9.48427 | −0.828644 | −0.414322 | − | 0.910130i | \(-0.635981\pi\) | ||||
−0.414322 | + | 0.910130i | \(0.635981\pi\) | |||||||
\(132\) | 5.27088 | 0.458771 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.25224 | −0.194564 | ||||||||
\(135\) | −7.27770 | −0.626365 | ||||||||
\(136\) | 4.70655 | 0.403583 | ||||||||
\(137\) | 13.1605 | 1.12438 | 0.562190 | − | 0.827008i | \(-0.309959\pi\) | ||||
0.562190 | + | 0.827008i | \(0.309959\pi\) | |||||||
\(138\) | 19.5981 | 1.66830 | ||||||||
\(139\) | 8.66364 | 0.734840 | 0.367420 | − | 0.930055i | \(-0.380241\pi\) | ||||
0.367420 | + | 0.930055i | \(0.380241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.47962 | −0.377252 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | 12.2708 | 1.02613 | ||||||||
\(144\) | 2.12612 | 0.177177 | ||||||||
\(145\) | 3.67831 | 0.305467 | ||||||||
\(146\) | 7.17825 | 0.594077 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −5.12612 | −0.419948 | −0.209974 | − | 0.977707i | \(-0.567338\pi\) | ||||
−0.209974 | + | 0.977707i | \(0.567338\pi\) | |||||||
\(150\) | −19.3126 | −1.57687 | ||||||||
\(151\) | −15.0599 | −1.22556 | −0.612778 | − | 0.790255i | \(-0.709948\pi\) | ||||
−0.612778 | + | 0.790255i | \(0.709948\pi\) | |||||||
\(152\) | −5.94240 | −0.481992 | ||||||||
\(153\) | 10.0067 | 0.808992 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.27770 | −0.584559 | ||||||||
\(156\) | 11.9338 | 0.955466 | ||||||||
\(157\) | 8.12856 | 0.648730 | 0.324365 | − | 0.945932i | \(-0.394849\pi\) | ||||
0.324365 | + | 0.945932i | \(0.394849\pi\) | |||||||
\(158\) | 11.1261 | 0.885147 | ||||||||
\(159\) | −14.3273 | −1.13623 | ||||||||
\(160\) | −3.67831 | −0.290796 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.8580 | −0.853083 | ||||||||
\(163\) | 5.82355 | 0.456136 | 0.228068 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228068 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(164\) | −10.3634 | −0.809246 | ||||||||
\(165\) | −19.3879 | −1.50935 | ||||||||
\(166\) | 10.3634 | 0.804356 | ||||||||
\(167\) | 6.22795 | 0.481933 | 0.240967 | − | 0.970533i | \(-0.422536\pi\) | ||||
0.240967 | + | 0.970533i | \(0.422536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.7822 | 1.13709 | ||||||||
\(170\) | −17.3121 | −1.32778 | ||||||||
\(171\) | −12.6343 | −0.966166 | ||||||||
\(172\) | −12.1860 | −0.929174 | ||||||||
\(173\) | −2.36452 | −0.179771 | −0.0898856 | − | 0.995952i | \(-0.528650\pi\) | ||||
−0.0898856 | + | 0.995952i | \(0.528650\pi\) | |||||||
\(174\) | 2.26409 | 0.171640 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.32803 | −0.175482 | ||||||||
\(177\) | −16.2522 | −1.22159 | ||||||||
\(178\) | −5.83521 | −0.437368 | ||||||||
\(179\) | −8.50448 | −0.635655 | −0.317827 | − | 0.948149i | \(-0.602953\pi\) | ||||
−0.317827 | + | 0.948149i | \(0.602953\pi\) | |||||||
\(180\) | −7.82052 | −0.582907 | ||||||||
\(181\) | 7.99212 | 0.594050 | 0.297025 | − | 0.954870i | \(-0.404006\pi\) | ||||
0.297025 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.1605 | −1.85992 | ||||||||
\(184\) | −8.65606 | −0.638133 | ||||||||
\(185\) | 7.35661 | 0.540869 | ||||||||
\(186\) | −4.47962 | −0.328461 | ||||||||
\(187\) | −10.9570 | −0.801254 | ||||||||
\(188\) | 1.97855 | 0.144300 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.8580 | 1.58574 | ||||||||
\(191\) | 1.74776 | 0.126464 | 0.0632318 | − | 0.997999i | \(-0.479859\pi\) | ||||
0.0632318 | + | 0.997999i | \(0.479859\pi\) | |||||||
\(192\) | −2.26409 | −0.163397 | ||||||||
\(193\) | −7.49552 | −0.539539 | −0.269770 | − | 0.962925i | \(-0.586948\pi\) | ||||
−0.269770 | + | 0.962925i | \(0.586948\pi\) | |||||||
\(194\) | −4.13545 | −0.296908 | ||||||||
\(195\) | −43.8961 | −3.14346 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.6561 | 1.61418 | 0.807089 | − | 0.590430i | \(-0.201042\pi\) | ||||
0.807089 | + | 0.590430i | \(0.201042\pi\) | |||||||
\(198\) | −4.94967 | −0.351758 | ||||||||
\(199\) | 17.5417 | 1.24349 | 0.621747 | − | 0.783218i | \(-0.286423\pi\) | ||||
0.621747 | + | 0.783218i | \(0.286423\pi\) | |||||||
\(200\) | 8.52994 | 0.603158 | ||||||||
\(201\) | 5.09928 | 0.359675 | ||||||||
\(202\) | −3.75624 | −0.264288 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.6561 | −0.746074 | ||||||||
\(205\) | 38.1198 | 2.66240 | ||||||||
\(206\) | −8.48528 | −0.591198 | ||||||||
\(207\) | −18.4038 | −1.27915 | ||||||||
\(208\) | −5.27088 | −0.365470 | ||||||||
\(209\) | 13.8341 | 0.956924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4796 | −1.13450 | −0.567252 | − | 0.823544i | \(-0.691993\pi\) | ||||
−0.567252 | + | 0.823544i | \(0.691993\pi\) | |||||||
\(212\) | 6.32803 | 0.434611 | ||||||||
\(213\) | −18.1127 | −1.24107 | ||||||||
\(214\) | 4.65606 | 0.318282 | ||||||||
\(215\) | 44.8239 | 3.05696 | ||||||||
\(216\) | 1.97855 | 0.134623 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.9841 | −0.743937 | ||||||||
\(219\) | −16.2522 | −1.09822 | ||||||||
\(220\) | 8.56321 | 0.577332 | ||||||||
\(221\) | −24.8076 | −1.66874 | ||||||||
\(222\) | 4.52819 | 0.303912 | ||||||||
\(223\) | 21.0835 | 1.41186 | 0.705929 | − | 0.708283i | \(-0.250530\pi\) | ||||
0.705929 | + | 0.708283i | \(0.250530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.1357 | 1.20905 | ||||||||
\(226\) | 20.8076 | 1.38410 | ||||||||
\(227\) | −24.3047 | −1.61316 | −0.806579 | − | 0.591126i | \(-0.798684\pi\) | ||||
−0.806579 | + | 0.591126i | \(0.798684\pi\) | |||||||
\(228\) | 13.4542 | 0.891023 | ||||||||
\(229\) | −12.0857 | −0.798643 | −0.399321 | − | 0.916811i | \(-0.630754\pi\) | ||||
−0.399321 | + | 0.916811i | \(0.630754\pi\) | |||||||
\(230\) | 31.8397 | 2.09944 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 7.63060 | 0.499897 | 0.249949 | − | 0.968259i | \(-0.419586\pi\) | ||||
0.249949 | + | 0.968259i | \(0.419586\pi\) | |||||||
\(234\) | −11.2065 | −0.732593 | ||||||||
\(235\) | −7.27770 | −0.474745 | ||||||||
\(236\) | 7.17825 | 0.467265 | ||||||||
\(237\) | −25.1906 | −1.63630 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.504478 | 0.0326320 | 0.0163160 | − | 0.999867i | \(-0.494806\pi\) | ||||
0.0163160 | + | 0.999867i | \(0.494806\pi\) | |||||||
\(240\) | 8.32803 | 0.537572 | ||||||||
\(241\) | 21.8622 | 1.40827 | 0.704135 | − | 0.710066i | \(-0.251335\pi\) | ||||
0.704135 | + | 0.710066i | \(0.251335\pi\) | |||||||
\(242\) | −5.58027 | −0.358713 | ||||||||
\(243\) | 18.6478 | 1.19626 | ||||||||
\(244\) | 11.1129 | 0.711428 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 23.4637 | 1.49599 | ||||||||
\(247\) | 31.3217 | 1.99295 | ||||||||
\(248\) | 1.97855 | 0.125638 | ||||||||
\(249\) | −23.4637 | −1.48695 | ||||||||
\(250\) | −12.9842 | −0.821194 | ||||||||
\(251\) | −9.87024 | −0.623004 | −0.311502 | − | 0.950245i | \(-0.600832\pi\) | ||||
−0.311502 | + | 0.950245i | \(0.600832\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1516 | 1.26692 | ||||||||
\(254\) | 2.25224 | 0.141318 | ||||||||
\(255\) | 39.1963 | 2.45457 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.6772 | −0.728403 | −0.364201 | − | 0.931320i | \(-0.618658\pi\) | ||||
−0.364201 | + | 0.931320i | \(0.618658\pi\) | |||||||
\(258\) | 27.5903 | 1.71769 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 19.3879 | 1.20239 | ||||||||
\(261\) | −2.12612 | −0.131603 | ||||||||
\(262\) | −9.48427 | −0.585940 | ||||||||
\(263\) | −17.6815 | −1.09029 | −0.545145 | − | 0.838342i | \(-0.683525\pi\) | ||||
−0.545145 | + | 0.838342i | \(0.683525\pi\) | |||||||
\(264\) | 5.27088 | 0.324400 | ||||||||
\(265\) | −23.2764 | −1.42986 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2115 | 0.808529 | ||||||||
\(268\) | −2.25224 | −0.137577 | ||||||||
\(269\) | 4.32733 | 0.263842 | 0.131921 | − | 0.991260i | \(-0.457885\pi\) | ||||
0.131921 | + | 0.991260i | \(0.457885\pi\) | |||||||
\(270\) | −7.27770 | −0.442907 | ||||||||
\(271\) | −24.8690 | −1.51069 | −0.755343 | − | 0.655330i | \(-0.772530\pi\) | ||||
−0.755343 | + | 0.655330i | \(0.772530\pi\) | |||||||
\(272\) | 4.70655 | 0.285376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.1605 | 0.795057 | ||||||||
\(275\) | −19.8580 | −1.19748 | ||||||||
\(276\) | 19.5981 | 1.17967 | ||||||||
\(277\) | −5.64711 | −0.339302 | −0.169651 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169651 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(278\) | 8.66364 | 0.519611 | ||||||||
\(279\) | 4.20663 | 0.251844 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2274 | 0.848734 | 0.424367 | − | 0.905490i | \(-0.360497\pi\) | ||||
0.424367 | + | 0.905490i | \(0.360497\pi\) | |||||||
\(282\) | −4.47962 | −0.266757 | ||||||||
\(283\) | −18.2911 | −1.08729 | −0.543647 | − | 0.839314i | \(-0.682957\pi\) | ||||
−0.543647 | + | 0.839314i | \(0.682957\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | −49.4885 | −2.93145 | ||||||||
\(286\) | 12.2708 | 0.725586 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.12612 | 0.125283 | ||||||||
\(289\) | 5.15158 | 0.303034 | ||||||||
\(290\) | 3.67831 | 0.215998 | ||||||||
\(291\) | 9.36306 | 0.548872 | ||||||||
\(292\) | 7.17825 | 0.420076 | ||||||||
\(293\) | 7.71333 | 0.450618 | 0.225309 | − | 0.974287i | \(-0.427661\pi\) | ||||
0.225309 | + | 0.974287i | \(0.427661\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.4038 | −1.53729 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | −4.60612 | −0.267274 | ||||||||
\(298\) | −5.12612 | −0.296948 | ||||||||
\(299\) | 45.6251 | 2.63857 | ||||||||
\(300\) | −19.3126 | −1.11501 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.0599 | −0.866599 | ||||||||
\(303\) | 8.50448 | 0.488569 | ||||||||
\(304\) | −5.94240 | −0.340820 | ||||||||
\(305\) | −40.8765 | −2.34058 | ||||||||
\(306\) | 10.0067 | 0.572044 | ||||||||
\(307\) | −30.5034 | −1.74092 | −0.870460 | − | 0.492240i | \(-0.836178\pi\) | ||||
−0.870460 | + | 0.492240i | \(0.836178\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.2115 | 1.09290 | ||||||||
\(310\) | −7.27770 | −0.413346 | ||||||||
\(311\) | −6.32162 | −0.358466 | −0.179233 | − | 0.983807i | \(-0.557362\pi\) | ||||
−0.179233 | + | 0.983807i | \(0.557362\pi\) | |||||||
\(312\) | 11.9338 | 0.675616 | ||||||||
\(313\) | −30.5970 | −1.72945 | −0.864724 | − | 0.502248i | \(-0.832506\pi\) | ||||
−0.864724 | + | 0.502248i | \(0.832506\pi\) | |||||||
\(314\) | 8.12856 | 0.458721 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.1261 | 0.625893 | ||||||||
\(317\) | 33.2115 | 1.86534 | 0.932671 | − | 0.360728i | \(-0.117472\pi\) | ||||
0.932671 | + | 0.360728i | \(0.117472\pi\) | |||||||
\(318\) | −14.3273 | −0.803433 | ||||||||
\(319\) | 2.32803 | 0.130345 | ||||||||
\(320\) | −3.67831 | −0.205624 | ||||||||
\(321\) | −10.5418 | −0.588384 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.9682 | −1.55619 | ||||||||
\(324\) | −10.8580 | −0.603221 | ||||||||
\(325\) | −44.9603 | −2.49395 | ||||||||
\(326\) | 5.82355 | 0.322537 | ||||||||
\(327\) | 24.8690 | 1.37526 | ||||||||
\(328\) | −10.3634 | −0.572223 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −19.3879 | −1.06727 | ||||||||
\(331\) | 11.2459 | 0.618130 | 0.309065 | − | 0.951041i | \(-0.399984\pi\) | ||||
0.309065 | + | 0.951041i | \(0.399984\pi\) | |||||||
\(332\) | 10.3634 | 0.568766 | ||||||||
\(333\) | −4.25224 | −0.233021 | ||||||||
\(334\) | 6.22795 | 0.340778 | ||||||||
\(335\) | 8.28443 | 0.452627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000 | 0.544735 | 0.272367 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272367 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(338\) | 14.7822 | 0.804045 | ||||||||
\(339\) | −47.1105 | −2.55869 | ||||||||
\(340\) | −17.3121 | −0.938882 | ||||||||
\(341\) | −4.60612 | −0.249435 | ||||||||
\(342\) | −12.6343 | −0.683182 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.1860 | −0.657025 | ||||||||
\(345\) | −72.0880 | −3.88109 | ||||||||
\(346\) | −2.36452 | −0.127117 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 2.26409 | 0.121368 | ||||||||
\(349\) | 28.3622 | 1.51819 | 0.759097 | − | 0.650978i | \(-0.225641\pi\) | ||||
0.759097 | + | 0.650978i | \(0.225641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4287 | −0.556642 | ||||||||
\(352\) | −2.32803 | −0.124084 | ||||||||
\(353\) | 5.74155 | 0.305592 | 0.152796 | − | 0.988258i | \(-0.451172\pi\) | ||||
0.152796 | + | 0.988258i | \(0.451172\pi\) | |||||||
\(354\) | −16.2522 | −0.863797 | ||||||||
\(355\) | −29.4265 | −1.56179 | ||||||||
\(356\) | −5.83521 | −0.309266 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.50448 | −0.449476 | ||||||||
\(359\) | 16.4382 | 0.867577 | 0.433789 | − | 0.901015i | \(-0.357176\pi\) | ||||
0.433789 | + | 0.901015i | \(0.357176\pi\) | |||||||
\(360\) | −7.82052 | −0.412178 | ||||||||
\(361\) | 16.3121 | 0.858533 | ||||||||
\(362\) | 7.99212 | 0.420057 | ||||||||
\(363\) | 12.6343 | 0.663126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.4038 | −1.38204 | ||||||||
\(366\) | −25.1605 | −1.31516 | ||||||||
\(367\) | −14.0485 | −0.733324 | −0.366662 | − | 0.930354i | \(-0.619499\pi\) | ||||
−0.366662 | + | 0.930354i | \(0.619499\pi\) | |||||||
\(368\) | −8.65606 | −0.451228 | ||||||||
\(369\) | −22.0338 | −1.14704 | ||||||||
\(370\) | 7.35661 | 0.382452 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.47962 | −0.232257 | ||||||||
\(373\) | −17.4981 | −0.906019 | −0.453009 | − | 0.891506i | \(-0.649650\pi\) | ||||
−0.453009 | + | 0.891506i | \(0.649650\pi\) | |||||||
\(374\) | −10.9570 | −0.566572 | ||||||||
\(375\) | 29.3975 | 1.51808 | ||||||||
\(376\) | 1.97855 | 0.102036 | ||||||||
\(377\) | 5.27088 | 0.271464 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.89935 | −0.405762 | −0.202881 | − | 0.979203i | \(-0.565030\pi\) | ||||
−0.202881 | + | 0.979203i | \(0.565030\pi\) | |||||||
\(380\) | 21.8580 | 1.12129 | ||||||||
\(381\) | −5.09928 | −0.261244 | ||||||||
\(382\) | 1.74776 | 0.0894232 | ||||||||
\(383\) | 11.5146 | 0.588367 | 0.294183 | − | 0.955749i | \(-0.404952\pi\) | ||||
0.294183 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(384\) | −2.26409 | −0.115539 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.49552 | −0.381512 | ||||||||
\(387\) | −25.9089 | −1.31702 | ||||||||
\(388\) | −4.13545 | −0.209946 | ||||||||
\(389\) | 0.756717 | 0.0383671 | 0.0191835 | − | 0.999816i | \(-0.493893\pi\) | ||||
0.0191835 | + | 0.999816i | \(0.493893\pi\) | |||||||
\(390\) | −43.8961 | −2.22276 | ||||||||
\(391\) | −40.7402 | −2.06032 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4733 | 1.08318 | ||||||||
\(394\) | 22.6561 | 1.14140 | ||||||||
\(395\) | −40.9253 | −2.05917 | ||||||||
\(396\) | −4.94967 | −0.248730 | ||||||||
\(397\) | 27.4966 | 1.38001 | 0.690007 | − | 0.723803i | \(-0.257607\pi\) | ||||
0.690007 | + | 0.723803i | \(0.257607\pi\) | |||||||
\(398\) | 17.5417 | 0.879284 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.52994 | 0.426497 | ||||||||
\(401\) | 11.9242 | 0.595467 | 0.297733 | − | 0.954649i | \(-0.403769\pi\) | ||||
0.297733 | + | 0.954649i | \(0.403769\pi\) | |||||||
\(402\) | 5.09928 | 0.254329 | ||||||||
\(403\) | −10.4287 | −0.519490 | ||||||||
\(404\) | −3.75624 | −0.186880 | ||||||||
\(405\) | 39.9390 | 1.98458 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.65606 | 0.230792 | ||||||||
\(408\) | −10.6561 | −0.527554 | ||||||||
\(409\) | −36.7471 | −1.81703 | −0.908513 | − | 0.417858i | \(-0.862781\pi\) | ||||
−0.908513 | + | 0.417858i | \(0.862781\pi\) | |||||||
\(410\) | 38.1198 | 1.88260 | ||||||||
\(411\) | −29.7967 | −1.46976 | ||||||||
\(412\) | −8.48528 | −0.418040 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.4038 | −0.904499 | ||||||||
\(415\) | −38.1198 | −1.87123 | ||||||||
\(416\) | −5.27088 | −0.258426 | ||||||||
\(417\) | −19.6153 | −0.960565 | ||||||||
\(418\) | 13.8341 | 0.676648 | ||||||||
\(419\) | 1.16468 | 0.0568983 | 0.0284492 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284492 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.4128 | −1.23854 | −0.619272 | − | 0.785177i | \(-0.712572\pi\) | ||||
−0.619272 | + | 0.785177i | \(0.712572\pi\) | |||||||
\(422\) | −16.4796 | −0.802215 | ||||||||
\(423\) | 4.20663 | 0.204533 | ||||||||
\(424\) | 6.32803 | 0.307316 | ||||||||
\(425\) | 40.1466 | 1.94740 | ||||||||
\(426\) | −18.1127 | −0.877566 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.65606 | 0.225059 | ||||||||
\(429\) | −27.7822 | −1.34134 | ||||||||
\(430\) | 44.8239 | 2.16160 | ||||||||
\(431\) | 30.4038 | 1.46450 | 0.732250 | − | 0.681036i | \(-0.238470\pi\) | ||||
0.732250 | + | 0.681036i | \(0.238470\pi\) | |||||||
\(432\) | 1.97855 | 0.0951929 | ||||||||
\(433\) | 14.5349 | 0.698501 | 0.349251 | − | 0.937029i | \(-0.386436\pi\) | ||||
0.349251 | + | 0.937029i | \(0.386436\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.32803 | −0.399299 | ||||||||
\(436\) | −10.9841 | −0.526043 | ||||||||
\(437\) | 51.4378 | 2.46060 | ||||||||
\(438\) | −16.2522 | −0.776562 | ||||||||
\(439\) | −1.91413 | −0.0913566 | −0.0456783 | − | 0.998956i | \(-0.514545\pi\) | ||||
−0.0456783 | + | 0.998956i | \(0.514545\pi\) | |||||||
\(440\) | 8.56321 | 0.408235 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.8076 | −1.17998 | ||||||||
\(443\) | −37.1797 | −1.76646 | −0.883229 | − | 0.468941i | \(-0.844636\pi\) | ||||
−0.883229 | + | 0.468941i | \(0.844636\pi\) | |||||||
\(444\) | 4.52819 | 0.214898 | ||||||||
\(445\) | 21.4637 | 1.01748 | ||||||||
\(446\) | 21.0835 | 0.998334 | ||||||||
\(447\) | 11.6060 | 0.548946 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.2714 | −1.71175 | −0.855876 | − | 0.517182i | \(-0.826981\pi\) | ||||
−0.855876 | + | 0.517182i | \(0.826981\pi\) | |||||||
\(450\) | 18.1357 | 0.854924 | ||||||||
\(451\) | 24.1263 | 1.13606 | ||||||||
\(452\) | 20.8076 | 0.978709 | ||||||||
\(453\) | 34.0970 | 1.60202 | ||||||||
\(454\) | −24.3047 | −1.14068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.4542 | 0.630048 | ||||||||
\(457\) | −16.9592 | −0.793319 | −0.396660 | − | 0.917966i | \(-0.629831\pi\) | ||||
−0.396660 | + | 0.917966i | \(0.629831\pi\) | |||||||
\(458\) | −12.0857 | −0.564726 | ||||||||
\(459\) | 9.31213 | 0.434653 | ||||||||
\(460\) | 31.8397 | 1.48453 | ||||||||
\(461\) | −24.6974 | −1.15027 | −0.575137 | − | 0.818057i | \(-0.695051\pi\) | ||||
−0.575137 | + | 0.818057i | \(0.695051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.807647 | −0.0375345 | −0.0187673 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187673 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 16.4774 | 0.764121 | ||||||||
\(466\) | 7.63060 | 0.353481 | ||||||||
\(467\) | −27.4254 | −1.26910 | −0.634548 | − | 0.772883i | \(-0.718814\pi\) | ||||
−0.634548 | + | 0.772883i | \(0.718814\pi\) | |||||||
\(468\) | −11.2065 | −0.518022 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.27770 | −0.335695 | ||||||||
\(471\) | −18.4038 | −0.848003 | ||||||||
\(472\) | 7.17825 | 0.330406 | ||||||||
\(473\) | 28.3694 | 1.30443 | ||||||||
\(474\) | −25.1906 | −1.15704 | ||||||||
\(475\) | −50.6883 | −2.32574 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.4542 | 0.616023 | ||||||||
\(478\) | 0.504478 | 0.0230743 | ||||||||
\(479\) | 18.1420 | 0.828929 | 0.414465 | − | 0.910065i | \(-0.363969\pi\) | ||||
0.414465 | + | 0.910065i | \(0.363969\pi\) | |||||||
\(480\) | 8.32803 | 0.380121 | ||||||||
\(481\) | 10.5418 | 0.480663 | ||||||||
\(482\) | 21.8622 | 0.995797 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.58027 | −0.253649 | ||||||||
\(485\) | 15.2115 | 0.690717 | ||||||||
\(486\) | 18.6478 | 0.845883 | ||||||||
\(487\) | −17.8993 | −0.811097 | −0.405548 | − | 0.914074i | \(-0.632919\pi\) | ||||
−0.405548 | + | 0.914074i | \(0.632919\pi\) | |||||||
\(488\) | 11.1129 | 0.503055 | ||||||||
\(489\) | −13.1851 | −0.596249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1446 | 0.457821 | 0.228910 | − | 0.973447i | \(-0.426484\pi\) | ||||
0.228910 | + | 0.973447i | \(0.426484\pi\) | |||||||
\(492\) | 23.4637 | 1.05783 | ||||||||
\(493\) | −4.70655 | −0.211972 | ||||||||
\(494\) | 31.3217 | 1.40923 | ||||||||
\(495\) | 18.2064 | 0.818318 | ||||||||
\(496\) | 1.97855 | 0.0888394 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −23.4637 | −1.05143 | ||||||||
\(499\) | −24.1516 | −1.08117 | −0.540587 | − | 0.841288i | \(-0.681798\pi\) | ||||
−0.540587 | + | 0.841288i | \(0.681798\pi\) | |||||||
\(500\) | −12.9842 | −0.580672 | ||||||||
\(501\) | −14.1007 | −0.629971 | ||||||||
\(502\) | −9.87024 | −0.440530 | ||||||||
\(503\) | −33.9254 | −1.51266 | −0.756329 | − | 0.654191i | \(-0.773009\pi\) | ||||
−0.756329 | + | 0.654191i | \(0.773009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.8166 | 0.614831 | ||||||||
\(506\) | 20.1516 | 0.895847 | ||||||||
\(507\) | −33.4682 | −1.48638 | ||||||||
\(508\) | 2.25224 | 0.0999269 | ||||||||
\(509\) | 39.1183 | 1.73389 | 0.866945 | − | 0.498404i | \(-0.166080\pi\) | ||||
0.866945 | + | 0.498404i | \(0.166080\pi\) | |||||||
\(510\) | 39.1963 | 1.73564 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.7573 | −0.519098 | ||||||||
\(514\) | −11.6772 | −0.515059 | ||||||||
\(515\) | 31.2115 | 1.37534 | ||||||||
\(516\) | 27.5903 | 1.21459 | ||||||||
\(517\) | −4.60612 | −0.202577 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.35350 | 0.234992 | ||||||||
\(520\) | 19.3879 | 0.850216 | ||||||||
\(521\) | −14.7200 | −0.644894 | −0.322447 | − | 0.946587i | \(-0.604505\pi\) | ||||
−0.322447 | + | 0.946587i | \(0.604505\pi\) | |||||||
\(522\) | −2.12612 | −0.0930577 | ||||||||
\(523\) | −38.8035 | −1.69676 | −0.848380 | − | 0.529388i | \(-0.822422\pi\) | ||||
−0.848380 | + | 0.529388i | \(0.822422\pi\) | |||||||
\(524\) | −9.48427 | −0.414322 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6815 | −0.770951 | ||||||||
\(527\) | 9.31213 | 0.405643 | ||||||||
\(528\) | 5.27088 | 0.229386 | ||||||||
\(529\) | 51.9274 | 2.25771 | ||||||||
\(530\) | −23.2764 | −1.01106 | ||||||||
\(531\) | 15.2618 | 0.662307 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.6243 | 2.36604 | ||||||||
\(534\) | 13.2115 | 0.571716 | ||||||||
\(535\) | −17.1264 | −0.740440 | ||||||||
\(536\) | −2.25224 | −0.0972819 | ||||||||
\(537\) | 19.2549 | 0.830912 | ||||||||
\(538\) | 4.32733 | 0.186565 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.27770 | −0.313183 | ||||||||
\(541\) | 16.7758 | 0.721249 | 0.360625 | − | 0.932711i | \(-0.382564\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382564\pi\) | |||||||
\(542\) | −24.8690 | −1.06822 | ||||||||
\(543\) | −18.0949 | −0.776527 | ||||||||
\(544\) | 4.70655 | 0.201792 | ||||||||
\(545\) | 40.4029 | 1.73067 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.8993 | −0.850835 | −0.425417 | − | 0.904997i | \(-0.639873\pi\) | ||||
−0.425417 | + | 0.904997i | \(0.639873\pi\) | |||||||
\(548\) | 13.1605 | 0.562190 | ||||||||
\(549\) | 23.6273 | 1.00839 | ||||||||
\(550\) | −19.8580 | −0.846747 | ||||||||
\(551\) | 5.94240 | 0.253155 | ||||||||
\(552\) | 19.5981 | 0.834152 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.64711 | −0.239923 | ||||||||
\(555\) | −16.6561 | −0.707010 | ||||||||
\(556\) | 8.66364 | 0.367420 | ||||||||
\(557\) | 40.1198 | 1.69993 | 0.849965 | − | 0.526840i | \(-0.176623\pi\) | ||||
0.849965 | + | 0.526840i | \(0.176623\pi\) | |||||||
\(558\) | 4.20663 | 0.178081 | ||||||||
\(559\) | 64.2310 | 2.71668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.8076 | 1.04738 | ||||||||
\(562\) | 14.2274 | 0.600146 | ||||||||
\(563\) | 39.1895 | 1.65164 | 0.825820 | − | 0.563933i | \(-0.190712\pi\) | ||||
0.825820 | + | 0.563933i | \(0.190712\pi\) | |||||||
\(564\) | −4.47962 | −0.188626 | ||||||||
\(565\) | −76.5369 | −3.21993 | ||||||||
\(566\) | −18.2911 | −0.768833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | 41.2115 | 1.72767 | 0.863837 | − | 0.503771i | \(-0.168054\pi\) | ||||
0.863837 | + | 0.503771i | \(0.168054\pi\) | |||||||
\(570\) | −49.4885 | −2.07285 | ||||||||
\(571\) | −33.4128 | −1.39828 | −0.699141 | − | 0.714984i | \(-0.746434\pi\) | ||||
−0.699141 | + | 0.714984i | \(0.746434\pi\) | |||||||
\(572\) | 12.2708 | 0.513067 | ||||||||
\(573\) | −3.95709 | −0.165310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −73.8357 | −3.07916 | ||||||||
\(576\) | 2.12612 | 0.0885883 | ||||||||
\(577\) | 32.0765 | 1.33536 | 0.667682 | − | 0.744447i | \(-0.267287\pi\) | ||||
0.667682 | + | 0.744447i | \(0.267287\pi\) | |||||||
\(578\) | 5.15158 | 0.214278 | ||||||||
\(579\) | 16.9706 | 0.705273 | ||||||||
\(580\) | 3.67831 | 0.152733 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.36306 | 0.388111 | ||||||||
\(583\) | −14.7319 | −0.610131 | ||||||||
\(584\) | 7.17825 | 0.297038 | ||||||||
\(585\) | 41.2210 | 1.70428 | ||||||||
\(586\) | 7.71333 | 0.318635 | ||||||||
\(587\) | 28.2033 | 1.16407 | 0.582037 | − | 0.813162i | \(-0.302256\pi\) | ||||
0.582037 | + | 0.813162i | \(0.302256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.7573 | −0.484452 | ||||||||
\(590\) | −26.4038 | −1.08703 | ||||||||
\(591\) | −51.2954 | −2.11001 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 42.5890 | 1.74892 | 0.874461 | − | 0.485096i | \(-0.161215\pi\) | ||||
0.874461 | + | 0.485096i | \(0.161215\pi\) | |||||||
\(594\) | −4.60612 | −0.188991 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.12612 | −0.209974 | ||||||||
\(597\) | −39.7159 | −1.62547 | ||||||||
\(598\) | 45.6251 | 1.86575 | ||||||||
\(599\) | −10.3185 | −0.421601 | −0.210801 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210801 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(600\) | −19.3126 | −0.788433 | ||||||||
\(601\) | 34.2754 | 1.39812 | 0.699060 | − | 0.715063i | \(-0.253602\pi\) | ||||
0.699060 | + | 0.715063i | \(0.253602\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.78853 | −0.195004 | ||||||||
\(604\) | −15.0599 | −0.612778 | ||||||||
\(605\) | 20.5259 | 0.834498 | ||||||||
\(606\) | 8.50448 | 0.345471 | ||||||||
\(607\) | 11.6997 | 0.474875 | 0.237438 | − | 0.971403i | \(-0.423692\pi\) | ||||
0.237438 | + | 0.971403i | \(0.423692\pi\) | |||||||
\(608\) | −5.94240 | −0.240996 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40.8765 | −1.65504 | ||||||||
\(611\) | −10.4287 | −0.421899 | ||||||||
\(612\) | 10.0067 | 0.404496 | ||||||||
\(613\) | −14.1351 | −0.570910 | −0.285455 | − | 0.958392i | \(-0.592145\pi\) | ||||
−0.285455 | + | 0.958392i | \(0.592145\pi\) | |||||||
\(614\) | −30.5034 | −1.23102 | ||||||||
\(615\) | −86.3067 | −3.48022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0599 | −0.847839 | −0.423920 | − | 0.905700i | \(-0.639346\pi\) | ||||
−0.423920 | + | 0.905700i | \(0.639346\pi\) | |||||||
\(618\) | 19.2115 | 0.772799 | ||||||||
\(619\) | 10.0261 | 0.402983 | 0.201492 | − | 0.979490i | \(-0.435421\pi\) | ||||
0.201492 | + | 0.979490i | \(0.435421\pi\) | |||||||
\(620\) | −7.27770 | −0.292280 | ||||||||
\(621\) | −17.1264 | −0.687260 | ||||||||
\(622\) | −6.32162 | −0.253474 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.9338 | 0.477733 | ||||||||
\(625\) | 5.11021 | 0.204409 | ||||||||
\(626\) | −30.5970 | −1.22290 | ||||||||
\(627\) | −31.3217 | −1.25087 | ||||||||
\(628\) | 8.12856 | 0.324365 | ||||||||
\(629\) | −9.41309 | −0.375325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4038 | −0.573407 | −0.286704 | − | 0.958019i | \(-0.592559\pi\) | ||||
−0.286704 | + | 0.958019i | \(0.592559\pi\) | |||||||
\(632\) | 11.1261 | 0.442573 | ||||||||
\(633\) | 37.3114 | 1.48299 | ||||||||
\(634\) | 33.2115 | 1.31900 | ||||||||
\(635\) | −8.28443 | −0.328757 | ||||||||
\(636\) | −14.3273 | −0.568113 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.32803 | 0.0921676 | ||||||||
\(639\) | 17.0090 | 0.672864 | ||||||||
\(640\) | −3.67831 | −0.145398 | ||||||||
\(641\) | −40.2714 | −1.59062 | −0.795311 | − | 0.606201i | \(-0.792693\pi\) | ||||
−0.795311 | + | 0.606201i | \(0.792693\pi\) | |||||||
\(642\) | −10.5418 | −0.416050 | ||||||||
\(643\) | 2.23484 | 0.0881335 | 0.0440667 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440667 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −101.485 | −3.99599 | ||||||||
\(646\) | −27.9682 | −1.10039 | ||||||||
\(647\) | 11.1714 | 0.439192 | 0.219596 | − | 0.975591i | \(-0.429526\pi\) | ||||
0.219596 | + | 0.975591i | \(0.429526\pi\) | |||||||
\(648\) | −10.8580 | −0.426542 | ||||||||
\(649\) | −16.7112 | −0.655972 | ||||||||
\(650\) | −44.9603 | −1.76349 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.82355 | 0.228068 | ||||||||
\(653\) | 26.1516 | 1.02339 | 0.511695 | − | 0.859167i | \(-0.329018\pi\) | ||||
0.511695 | + | 0.859167i | \(0.329018\pi\) | |||||||
\(654\) | 24.8690 | 0.972455 | ||||||||
\(655\) | 34.8860 | 1.36311 | ||||||||
\(656\) | −10.3634 | −0.404623 | ||||||||
\(657\) | 15.2618 | 0.595421 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9751 | 0.856030 | 0.428015 | − | 0.903772i | \(-0.359213\pi\) | ||||
0.428015 | + | 0.903772i | \(0.359213\pi\) | |||||||
\(660\) | −19.3879 | −0.754674 | ||||||||
\(661\) | −16.1049 | −0.626410 | −0.313205 | − | 0.949686i | \(-0.601403\pi\) | ||||
−0.313205 | + | 0.949686i | \(0.601403\pi\) | |||||||
\(662\) | 11.2459 | 0.437084 | ||||||||
\(663\) | 56.1668 | 2.18134 | ||||||||
\(664\) | 10.3634 | 0.402178 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.25224 | −0.164771 | ||||||||
\(667\) | 8.65606 | 0.335164 | ||||||||
\(668\) | 6.22795 | 0.240967 | ||||||||
\(669\) | −47.7351 | −1.84554 | ||||||||
\(670\) | 8.28443 | 0.320055 | ||||||||
\(671\) | −25.8711 | −0.998742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.5395 | 1.67832 | 0.839162 | − | 0.543881i | \(-0.183046\pi\) | ||||
0.839162 | + | 0.543881i | \(0.183046\pi\) | |||||||
\(674\) | 10.0000 | 0.385186 | ||||||||
\(675\) | 16.8769 | 0.649592 | ||||||||
\(676\) | 14.7822 | 0.568545 | ||||||||
\(677\) | 12.0271 | 0.462241 | 0.231120 | − | 0.972925i | \(-0.425761\pi\) | ||||
0.231120 | + | 0.972925i | \(0.425761\pi\) | |||||||
\(678\) | −47.1105 | −1.80927 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −17.3121 | −0.663890 | ||||||||
\(681\) | 55.0281 | 2.10868 | ||||||||
\(682\) | −4.60612 | −0.176377 | ||||||||
\(683\) | −11.2115 | −0.428995 | −0.214498 | − | 0.976725i | \(-0.568811\pi\) | ||||
−0.214498 | + | 0.976725i | \(0.568811\pi\) | |||||||
\(684\) | −12.6343 | −0.483083 | ||||||||
\(685\) | −48.4085 | −1.84959 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.3631 | 1.04397 | ||||||||
\(688\) | −12.1860 | −0.464587 | ||||||||
\(689\) | −33.3543 | −1.27070 | ||||||||
\(690\) | −72.0880 | −2.74434 | ||||||||
\(691\) | 17.0904 | 0.650150 | 0.325075 | − | 0.945688i | \(-0.394610\pi\) | ||||
0.325075 | + | 0.945688i | \(0.394610\pi\) | |||||||
\(692\) | −2.36452 | −0.0898856 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | −31.8675 | −1.20880 | ||||||||
\(696\) | 2.26409 | 0.0858202 | ||||||||
\(697\) | −48.7758 | −1.84752 | ||||||||
\(698\) | 28.3622 | 1.07353 | ||||||||
\(699\) | −17.2764 | −0.653453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.4892 | −1.37818 | −0.689089 | − | 0.724677i | \(-0.741989\pi\) | ||||
−0.689089 | + | 0.724677i | \(0.741989\pi\) | |||||||
\(702\) | −10.4287 | −0.393605 | ||||||||
\(703\) | 11.8848 | 0.448244 | ||||||||
\(704\) | −2.32803 | −0.0877410 | ||||||||
\(705\) | 16.4774 | 0.620575 | ||||||||
\(706\) | 5.74155 | 0.216086 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.2522 | −0.610797 | ||||||||
\(709\) | 19.9433 | 0.748987 | 0.374494 | − | 0.927229i | \(-0.377817\pi\) | ||||
0.374494 | + | 0.927229i | \(0.377817\pi\) | |||||||
\(710\) | −29.4265 | −1.10436 | ||||||||
\(711\) | 23.6555 | 0.887149 | ||||||||
\(712\) | −5.83521 | −0.218684 | ||||||||
\(713\) | −17.1264 | −0.641390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.1357 | −1.68798 | ||||||||
\(716\) | −8.50448 | −0.317827 | ||||||||
\(717\) | −1.14219 | −0.0426557 | ||||||||
\(718\) | 16.4382 | 0.613470 | ||||||||
\(719\) | 33.2412 | 1.23969 | 0.619844 | − | 0.784725i | \(-0.287196\pi\) | ||||
0.619844 | + | 0.784725i | \(0.287196\pi\) | |||||||
\(720\) | −7.82052 | −0.291454 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.3121 | 0.607074 | ||||||||
\(723\) | −49.4981 | −1.84086 | ||||||||
\(724\) | 7.99212 | 0.297025 | ||||||||
\(725\) | −8.52994 | −0.316794 | ||||||||
\(726\) | 12.6343 | 0.468901 | ||||||||
\(727\) | −36.3192 | −1.34700 | −0.673502 | − | 0.739186i | \(-0.735211\pi\) | ||||
−0.673502 | + | 0.739186i | \(0.735211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.64650 | −0.357278 | ||||||||
\(730\) | −26.4038 | −0.977249 | ||||||||
\(731\) | −57.3540 | −2.12131 | ||||||||
\(732\) | −25.1605 | −0.929960 | ||||||||
\(733\) | −13.1558 | −0.485921 | −0.242961 | − | 0.970036i | \(-0.578119\pi\) | ||||
−0.242961 | + | 0.970036i | \(0.578119\pi\) | |||||||
\(734\) | −14.0485 | −0.518538 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.65606 | −0.319067 | ||||||||
\(737\) | 5.24328 | 0.193139 | ||||||||
\(738\) | −22.0338 | −0.811076 | ||||||||
\(739\) | 14.7414 | 0.542272 | 0.271136 | − | 0.962541i | \(-0.412601\pi\) | ||||
0.271136 | + | 0.962541i | \(0.412601\pi\) | |||||||
\(740\) | 7.35661 | 0.270435 | ||||||||
\(741\) | −70.9152 | −2.60514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.9274 | 1.86835 | 0.934173 | − | 0.356821i | \(-0.116139\pi\) | ||||
0.934173 | + | 0.356821i | \(0.116139\pi\) | |||||||
\(744\) | −4.47962 | −0.164231 | ||||||||
\(745\) | 18.8554 | 0.690810 | ||||||||
\(746\) | −17.4981 | −0.640652 | ||||||||
\(747\) | 22.0338 | 0.806176 | ||||||||
\(748\) | −10.9570 | −0.400627 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 29.3975 | 1.07344 | ||||||||
\(751\) | 10.1198 | 0.369276 | 0.184638 | − | 0.982807i | \(-0.440889\pi\) | ||||
0.184638 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(752\) | 1.97855 | 0.0721502 | ||||||||
\(753\) | 22.3471 | 0.814375 | ||||||||
\(754\) | 5.27088 | 0.191954 | ||||||||
\(755\) | 55.3949 | 2.01603 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.3631 | 1.50337 | 0.751683 | − | 0.659525i | \(-0.229242\pi\) | ||||
0.751683 | + | 0.659525i | \(0.229242\pi\) | |||||||
\(758\) | −7.89935 | −0.286917 | ||||||||
\(759\) | −45.6251 | −1.65609 | ||||||||
\(760\) | 21.8580 | 0.792872 | ||||||||
\(761\) | −24.2110 | −0.877649 | −0.438824 | − | 0.898573i | \(-0.644605\pi\) | ||||
−0.438824 | + | 0.898573i | \(0.644605\pi\) | |||||||
\(762\) | −5.09928 | −0.184727 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.74776 | 0.0632318 | ||||||||
\(765\) | −36.8076 | −1.33078 | ||||||||
\(766\) | 11.5146 | 0.416038 | ||||||||
\(767\) | −37.8357 | −1.36617 | ||||||||
\(768\) | −2.26409 | −0.0816984 | ||||||||
\(769\) | −3.99311 | −0.143995 | −0.0719976 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719976 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.4382 | 0.952150 | ||||||||
\(772\) | −7.49552 | −0.269770 | ||||||||
\(773\) | 2.42672 | 0.0872830 | 0.0436415 | − | 0.999047i | \(-0.486104\pi\) | ||||
0.0436415 | + | 0.999047i | \(0.486104\pi\) | |||||||
\(774\) | −25.9089 | −0.931276 | ||||||||
\(775\) | 16.8769 | 0.606236 | ||||||||
\(776\) | −4.13545 | −0.148454 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.756717 | 0.0271296 | ||||||||
\(779\) | 61.5835 | 2.20646 | ||||||||
\(780\) | −43.8961 | −1.57173 | ||||||||
\(781\) | −18.6243 | −0.666428 | ||||||||
\(782\) | −40.7402 | −1.45687 | ||||||||
\(783\) | −1.97855 | −0.0707075 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.8993 | −1.06715 | ||||||||
\(786\) | 21.4733 | 0.765926 | ||||||||
\(787\) | 50.2731 | 1.79204 | 0.896021 | − | 0.444011i | \(-0.146445\pi\) | ||||
0.896021 | + | 0.444011i | \(0.146445\pi\) | |||||||
\(788\) | 22.6561 | 0.807089 | ||||||||
\(789\) | 40.0326 | 1.42520 | ||||||||
\(790\) | −40.9253 | −1.45606 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.94967 | −0.175879 | ||||||||
\(793\) | −58.5745 | −2.08004 | ||||||||
\(794\) | 27.4966 | 0.975817 | ||||||||
\(795\) | 52.7000 | 1.86908 | ||||||||
\(796\) | 17.5417 | 0.621747 | ||||||||
\(797\) | 1.64125 | 0.0581361 | 0.0290681 | − | 0.999577i | \(-0.490746\pi\) | ||||
0.0290681 | + | 0.999577i | \(0.490746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.31213 | 0.329439 | ||||||||
\(800\) | 8.52994 | 0.301579 | ||||||||
\(801\) | −12.4064 | −0.438357 | ||||||||
\(802\) | 11.9242 | 0.421058 | ||||||||
\(803\) | −16.7112 | −0.589725 | ||||||||
\(804\) | 5.09928 | 0.179838 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.4287 | −0.367335 | ||||||||
\(807\) | −9.79749 | −0.344888 | ||||||||
\(808\) | −3.75624 | −0.132144 | ||||||||
\(809\) | −3.34394 | −0.117567 | −0.0587833 | − | 0.998271i | \(-0.518722\pi\) | ||||
−0.0587833 | + | 0.998271i | \(0.518722\pi\) | |||||||
\(810\) | 39.9390 | 1.40331 | ||||||||
\(811\) | 3.00679 | 0.105583 | 0.0527913 | − | 0.998606i | \(-0.483188\pi\) | ||||
0.0527913 | + | 0.998606i | \(0.483188\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.3058 | 1.97473 | ||||||||
\(814\) | 4.65606 | 0.163195 | ||||||||
\(815\) | −21.4208 | −0.750338 | ||||||||
\(816\) | −10.6561 | −0.373037 | ||||||||
\(817\) | 72.4141 | 2.53345 | ||||||||
\(818\) | −36.7471 | −1.28483 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.1198 | 1.33120 | ||||||||
\(821\) | 39.9433 | 1.39403 | 0.697016 | − | 0.717056i | \(-0.254511\pi\) | ||||
0.697016 | + | 0.717056i | \(0.254511\pi\) | |||||||
\(822\) | −29.7967 | −1.03928 | ||||||||
\(823\) | 17.0090 | 0.592895 | 0.296447 | − | 0.955049i | \(-0.404198\pi\) | ||||
0.296447 | + | 0.955049i | \(0.404198\pi\) | |||||||
\(824\) | −8.48528 | −0.295599 | ||||||||
\(825\) | 44.9603 | 1.56532 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0943 | 1.15080 | 0.575401 | − | 0.817872i | \(-0.304846\pi\) | ||||
0.575401 | + | 0.817872i | \(0.304846\pi\) | |||||||
\(828\) | −18.4038 | −0.639577 | ||||||||
\(829\) | 7.15576 | 0.248530 | 0.124265 | − | 0.992249i | \(-0.460343\pi\) | ||||
0.124265 | + | 0.992249i | \(0.460343\pi\) | |||||||
\(830\) | −38.1198 | −1.32316 | ||||||||
\(831\) | 12.7856 | 0.443527 | ||||||||
\(832\) | −5.27088 | −0.182735 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.6153 | −0.679222 | ||||||||
\(835\) | −22.9083 | −0.792774 | ||||||||
\(836\) | 13.8341 | 0.478462 | ||||||||
\(837\) | 3.91465 | 0.135310 | ||||||||
\(838\) | 1.16468 | 0.0402332 | ||||||||
\(839\) | −0.684186 | −0.0236207 | −0.0118104 | − | 0.999930i | \(-0.503759\pi\) | ||||
−0.0118104 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −25.4128 | −0.875782 | ||||||||
\(843\) | −32.2121 | −1.10944 | ||||||||
\(844\) | −16.4796 | −0.567252 | ||||||||
\(845\) | −54.3734 | −1.87050 | ||||||||
\(846\) | 4.20663 | 0.144627 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.32803 | 0.217305 | ||||||||
\(849\) | 41.4128 | 1.42128 | ||||||||
\(850\) | 40.1466 | 1.37702 | ||||||||
\(851\) | 17.3121 | 0.593452 | ||||||||
\(852\) | −18.1127 | −0.620533 | ||||||||
\(853\) | 32.6701 | 1.11860 | 0.559302 | − | 0.828964i | \(-0.311069\pi\) | ||||
0.559302 | + | 0.828964i | \(0.311069\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46.4727 | 1.58933 | ||||||||
\(856\) | 4.65606 | 0.159141 | ||||||||
\(857\) | −18.0475 | −0.616490 | −0.308245 | − | 0.951307i | \(-0.599742\pi\) | ||||
−0.308245 | + | 0.951307i | \(0.599742\pi\) | |||||||
\(858\) | −27.7822 | −0.948468 | ||||||||
\(859\) | −32.4490 | −1.10714 | −0.553572 | − | 0.832801i | \(-0.686736\pi\) | ||||
−0.553572 | + | 0.832801i | \(0.686736\pi\) | |||||||
\(860\) | 44.8239 | 1.52848 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.4038 | 1.03556 | ||||||||
\(863\) | 0.132467 | 0.00450922 | 0.00225461 | − | 0.999997i | \(-0.499282\pi\) | ||||
0.00225461 | + | 0.999997i | \(0.499282\pi\) | |||||||
\(864\) | 1.97855 | 0.0673115 | ||||||||
\(865\) | 8.69743 | 0.295722 | ||||||||
\(866\) | 14.5349 | 0.493915 | ||||||||
\(867\) | −11.6637 | −0.396119 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.9020 | −0.878664 | ||||||||
\(870\) | −8.32803 | −0.282347 | ||||||||
\(871\) | 11.8713 | 0.402243 | ||||||||
\(872\) | −10.9841 | −0.371968 | ||||||||
\(873\) | −8.79247 | −0.297580 | ||||||||
\(874\) | 51.4378 | 1.73991 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.2522 | −0.549112 | ||||||||
\(877\) | 1.56176 | 0.0527367 | 0.0263684 | − | 0.999652i | \(-0.491606\pi\) | ||||
0.0263684 | + | 0.999652i | \(0.491606\pi\) | |||||||
\(878\) | −1.91413 | −0.0645989 | ||||||||
\(879\) | −17.4637 | −0.589036 | ||||||||
\(880\) | 8.56321 | 0.288666 | ||||||||
\(881\) | −10.0202 | −0.337589 | −0.168795 | − | 0.985651i | \(-0.553987\pi\) | ||||
−0.168795 | + | 0.985651i | \(0.553987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.96819 | −0.200846 | −0.100423 | − | 0.994945i | \(-0.532020\pi\) | ||||
−0.100423 | + | 0.994945i | \(0.532020\pi\) | |||||||
\(884\) | −24.8076 | −0.834371 | ||||||||
\(885\) | 59.7807 | 2.00951 | ||||||||
\(886\) | −37.1797 | −1.24908 | ||||||||
\(887\) | −13.4481 | −0.451544 | −0.225772 | − | 0.974180i | \(-0.572490\pi\) | ||||
−0.225772 | + | 0.974180i | \(0.572490\pi\) | |||||||
\(888\) | 4.52819 | 0.151956 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.4637 | 0.719465 | ||||||||
\(891\) | 25.2777 | 0.846835 | ||||||||
\(892\) | 21.0835 | 0.705929 | ||||||||
\(893\) | −11.7573 | −0.393444 | ||||||||
\(894\) | 11.6060 | 0.388163 | ||||||||
\(895\) | 31.2821 | 1.04564 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −103.299 | −3.44907 | ||||||||
\(898\) | −36.2714 | −1.21039 | ||||||||
\(899\) | −1.97855 | −0.0659882 | ||||||||
\(900\) | 18.1357 | 0.604523 | ||||||||
\(901\) | 29.7832 | 0.992221 | ||||||||
\(902\) | 24.1263 | 0.803319 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.8076 | 0.692052 | ||||||||
\(905\) | −29.3975 | −0.977205 | ||||||||
\(906\) | 34.0970 | 1.13280 | ||||||||
\(907\) | 33.6841 | 1.11846 | 0.559232 | − | 0.829011i | \(-0.311096\pi\) | ||||
0.559232 | + | 0.829011i | \(0.311096\pi\) | |||||||
\(908\) | −24.3047 | −0.806579 | ||||||||
\(909\) | −7.98621 | −0.264886 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.5580 | −0.747380 | −0.373690 | − | 0.927554i | \(-0.621908\pi\) | ||||
−0.373690 | + | 0.927554i | \(0.621908\pi\) | |||||||
\(912\) | 13.4542 | 0.445511 | ||||||||
\(913\) | −24.1263 | −0.798465 | ||||||||
\(914\) | −16.9592 | −0.560962 | ||||||||
\(915\) | 92.5482 | 3.05955 | ||||||||
\(916\) | −12.0857 | −0.399321 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.31213 | 0.307346 | ||||||||
\(919\) | −24.0688 | −0.793958 | −0.396979 | − | 0.917828i | \(-0.629941\pi\) | ||||
−0.396979 | + | 0.917828i | \(0.629941\pi\) | |||||||
\(920\) | 31.8397 | 1.04972 | ||||||||
\(921\) | 69.0625 | 2.27569 | ||||||||
\(922\) | −24.6974 | −0.813366 | ||||||||
\(923\) | −42.1670 | −1.38795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0599 | −0.560926 | ||||||||
\(926\) | −0.807647 | −0.0265409 | ||||||||
\(927\) | −18.0407 | −0.592535 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 39.9944 | 1.31217 | 0.656087 | − | 0.754685i | \(-0.272210\pi\) | ||||
0.656087 | + | 0.754685i | \(0.272210\pi\) | |||||||
\(930\) | 16.4774 | 0.540315 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.63060 | 0.249949 | ||||||||
\(933\) | 14.3127 | 0.468578 | ||||||||
\(934\) | −27.4254 | −0.897387 | ||||||||
\(935\) | 40.3032 | 1.31805 | ||||||||
\(936\) | −11.2065 | −0.366297 | ||||||||
\(937\) | 49.8812 | 1.62955 | 0.814774 | − | 0.579778i | \(-0.196861\pi\) | ||||
0.814774 | + | 0.579778i | \(0.196861\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 69.2746 | 2.26069 | ||||||||
\(940\) | −7.27770 | −0.237373 | ||||||||
\(941\) | −13.1401 | −0.428354 | −0.214177 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214177 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(942\) | −18.4038 | −0.599629 | ||||||||
\(943\) | 89.7062 | 2.92124 | ||||||||
\(944\) | 7.17825 | 0.233632 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.3694 | 0.922369 | ||||||||
\(947\) | −27.2459 | −0.885373 | −0.442686 | − | 0.896677i | \(-0.645974\pi\) | ||||
−0.442686 | + | 0.896677i | \(0.645974\pi\) | |||||||
\(948\) | −25.1906 | −0.818152 | ||||||||
\(949\) | −37.8357 | −1.22820 | ||||||||
\(950\) | −50.6883 | −1.64455 | ||||||||
\(951\) | −75.1939 | −2.43833 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.3376 | 1.30666 | 0.653331 | − | 0.757072i | \(-0.273371\pi\) | ||||
0.653331 | + | 0.757072i | \(0.273371\pi\) | |||||||
\(954\) | 13.4542 | 0.435594 | ||||||||
\(955\) | −6.42880 | −0.208031 | ||||||||
\(956\) | 0.504478 | 0.0163160 | ||||||||
\(957\) | −5.27088 | −0.170383 | ||||||||
\(958\) | 18.1420 | 0.586141 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.32803 | 0.268786 | ||||||||
\(961\) | −27.0854 | −0.873721 | ||||||||
\(962\) | 10.5418 | 0.339880 | ||||||||
\(963\) | 9.89935 | 0.319002 | ||||||||
\(964\) | 21.8622 | 0.704135 | ||||||||
\(965\) | 27.5708 | 0.887536 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3879 | 1.52389 | 0.761946 | − | 0.647640i | \(-0.224244\pi\) | ||||
0.761946 | + | 0.647640i | \(0.224244\pi\) | |||||||
\(968\) | −5.58027 | −0.179357 | ||||||||
\(969\) | 63.3226 | 2.03421 | ||||||||
\(970\) | 15.2115 | 0.488411 | ||||||||
\(971\) | −9.55629 | −0.306676 | −0.153338 | − | 0.988174i | \(-0.549002\pi\) | ||||
−0.153338 | + | 0.988174i | \(0.549002\pi\) | |||||||
\(972\) | 18.6478 | 0.598129 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.8993 | −0.573532 | ||||||||
\(975\) | 101.794 | 3.26003 | ||||||||
\(976\) | 11.1129 | 0.355714 | ||||||||
\(977\) | 12.5485 | 0.401461 | 0.200730 | − | 0.979647i | \(-0.435668\pi\) | ||||
0.200730 | + | 0.979647i | \(0.435668\pi\) | |||||||
\(978\) | −13.1851 | −0.421612 | ||||||||
\(979\) | 13.5846 | 0.434164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.3535 | −0.745620 | ||||||||
\(982\) | 10.1446 | 0.323728 | ||||||||
\(983\) | −1.51464 | −0.0483095 | −0.0241548 | − | 0.999708i | \(-0.507689\pi\) | ||||
−0.0241548 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(984\) | 23.4637 | 0.747996 | ||||||||
\(985\) | −83.3360 | −2.65530 | ||||||||
\(986\) | −4.70655 | −0.149887 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.3217 | 0.996476 | ||||||||
\(989\) | 105.483 | 3.35416 | ||||||||
\(990\) | 18.2064 | 0.578638 | ||||||||
\(991\) | −2.53629 | −0.0805679 | −0.0402840 | − | 0.999188i | \(-0.512826\pi\) | ||||
−0.0402840 | + | 0.999188i | \(0.512826\pi\) | |||||||
\(992\) | 1.97855 | 0.0628189 | ||||||||
\(993\) | −25.4618 | −0.808004 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −64.5236 | −2.04554 | ||||||||
\(996\) | −23.4637 | −0.743476 | ||||||||
\(997\) | 29.0112 | 0.918795 | 0.459397 | − | 0.888231i | \(-0.348065\pi\) | ||||
0.459397 | + | 0.888231i | \(0.348065\pi\) | |||||||
\(998\) | −24.1516 | −0.764505 | ||||||||
\(999\) | −3.95709 | −0.125197 |
(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 | 2842.2.a.bb.1.2 | ✓ | 6 | |
7.6 | odd | 2 | inner | 2842.2.a.bb.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2842.2.a.bb.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2842.2.a.bb.1.5 | yes | 6 | 7.6 | odd | 2 | inner |