Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
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 | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.554958 | 0.248185 | 0.124092 | − | 0.992271i | \(-0.460398\pi\) | ||||
0.124092 | + | 0.992271i | \(0.460398\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.554958 | 0.175493 | ||||||||
\(11\) | −0.356896 | −0.107608 | −0.0538041 | − | 0.998552i | \(-0.517135\pi\) | ||||
−0.0538041 | + | 0.998552i | \(0.517135\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.554958 | −0.143290 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.80194 | −0.922105 | −0.461053 | − | 0.887373i | \(-0.652528\pi\) | ||||
−0.461053 | + | 0.887373i | \(0.652528\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.74094 | 1.31706 | 0.658531 | − | 0.752554i | \(-0.271178\pi\) | ||||
0.658531 | + | 0.752554i | \(0.271178\pi\) | |||||||
\(20\) | 0.554958 | 0.124092 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −0.356896 | −0.0760905 | ||||||||
\(23\) | −2.44504 | −0.509826 | −0.254913 | − | 0.966964i | \(-0.582047\pi\) | ||||
−0.254913 | + | 0.966964i | \(0.582047\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.69202 | −0.938404 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 0.405813 | 0.0753576 | 0.0376788 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376788 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(30\) | −0.554958 | −0.101321 | ||||||||
\(31\) | −4.74094 | −0.851498 | −0.425749 | − | 0.904841i | \(-0.639989\pi\) | ||||
−0.425749 | + | 0.904841i | \(0.639989\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.356896 | 0.0621276 | ||||||||
\(34\) | −3.80194 | −0.652027 | ||||||||
\(35\) | −0.554958 | −0.0938050 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.54288 | 0.582445 | 0.291223 | − | 0.956655i | \(-0.405938\pi\) | ||||
0.291223 | + | 0.956655i | \(0.405938\pi\) | |||||||
\(38\) | 5.74094 | 0.931303 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.554958 | 0.0877466 | ||||||||
\(41\) | −3.26875 | −0.510493 | −0.255246 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −6.04892 | −0.922451 | −0.461226 | − | 0.887283i | \(-0.652590\pi\) | ||||
−0.461226 | + | 0.887283i | \(0.652590\pi\) | |||||||
\(44\) | −0.356896 | −0.0538041 | ||||||||
\(45\) | 0.554958 | 0.0827283 | ||||||||
\(46\) | −2.44504 | −0.360502 | ||||||||
\(47\) | 0.603875 | 0.0880843 | 0.0440421 | − | 0.999030i | \(-0.485976\pi\) | ||||
0.0440421 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.69202 | −0.663552 | ||||||||
\(51\) | 3.80194 | 0.532378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.35690 | −0.186384 | −0.0931920 | − | 0.995648i | \(-0.529707\pi\) | ||||
−0.0931920 | + | 0.995648i | \(0.529707\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.198062 | −0.0267067 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −5.74094 | −0.760406 | ||||||||
\(58\) | 0.405813 | 0.0532859 | ||||||||
\(59\) | 5.54288 | 0.721621 | 0.360811 | − | 0.932639i | \(-0.382500\pi\) | ||||
0.360811 | + | 0.932639i | \(0.382500\pi\) | |||||||
\(60\) | −0.554958 | −0.0716448 | ||||||||
\(61\) | 4.38404 | 0.561319 | 0.280660 | − | 0.959807i | \(-0.409447\pi\) | ||||
0.280660 | + | 0.959807i | \(0.409447\pi\) | |||||||
\(62\) | −4.74094 | −0.602100 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.356896 | 0.0439308 | ||||||||
\(67\) | −15.2959 | −1.86869 | −0.934346 | − | 0.356368i | \(-0.884015\pi\) | ||||
−0.934346 | + | 0.356368i | \(0.884015\pi\) | |||||||
\(68\) | −3.80194 | −0.461053 | ||||||||
\(69\) | 2.44504 | 0.294348 | ||||||||
\(70\) | −0.554958 | −0.0663302 | ||||||||
\(71\) | 7.42758 | 0.881492 | 0.440746 | − | 0.897632i | \(-0.354714\pi\) | ||||
0.440746 | + | 0.897632i | \(0.354714\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.2295 | −1.31432 | −0.657158 | − | 0.753753i | \(-0.728242\pi\) | ||||
−0.657158 | + | 0.753753i | \(0.728242\pi\) | |||||||
\(74\) | 3.54288 | 0.411851 | ||||||||
\(75\) | 4.69202 | 0.541788 | ||||||||
\(76\) | 5.74094 | 0.658531 | ||||||||
\(77\) | 0.356896 | 0.0406721 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.76271 | −0.198320 | −0.0991601 | − | 0.995071i | \(-0.531616\pi\) | ||||
−0.0991601 | + | 0.995071i | \(0.531616\pi\) | |||||||
\(80\) | 0.554958 | 0.0620462 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.26875 | −0.360973 | ||||||||
\(83\) | −11.4426 | −1.25599 | −0.627997 | − | 0.778216i | \(-0.716125\pi\) | ||||
−0.627997 | + | 0.778216i | \(0.716125\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −2.10992 | −0.228853 | ||||||||
\(86\) | −6.04892 | −0.652272 | ||||||||
\(87\) | −0.405813 | −0.0435077 | ||||||||
\(88\) | −0.356896 | −0.0380452 | ||||||||
\(89\) | 4.80194 | 0.509004 | 0.254502 | − | 0.967072i | \(-0.418088\pi\) | ||||
0.254502 | + | 0.967072i | \(0.418088\pi\) | |||||||
\(90\) | 0.554958 | 0.0584977 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.44504 | −0.254913 | ||||||||
\(93\) | 4.74094 | 0.491612 | ||||||||
\(94\) | 0.603875 | 0.0622850 | ||||||||
\(95\) | 3.18598 | 0.326875 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.65279 | 0.269350 | 0.134675 | − | 0.990890i | \(-0.457001\pi\) | ||||
0.134675 | + | 0.990890i | \(0.457001\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −0.356896 | −0.0358694 | ||||||||
\(100\) | −4.69202 | −0.469202 | ||||||||
\(101\) | −9.10752 | −0.906232 | −0.453116 | − | 0.891451i | \(-0.649688\pi\) | ||||
−0.453116 | + | 0.891451i | \(0.649688\pi\) | |||||||
\(102\) | 3.80194 | 0.376448 | ||||||||
\(103\) | 12.2784 | 1.20983 | 0.604915 | − | 0.796290i | \(-0.293207\pi\) | ||||
0.604915 | + | 0.796290i | \(0.293207\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.554958 | 0.0541584 | ||||||||
\(106\) | −1.35690 | −0.131793 | ||||||||
\(107\) | 6.08575 | 0.588332 | 0.294166 | − | 0.955754i | \(-0.404958\pi\) | ||||
0.294166 | + | 0.955754i | \(0.404958\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −20.2010 | −1.93491 | −0.967455 | − | 0.253044i | \(-0.918568\pi\) | ||||
−0.967455 | + | 0.253044i | \(0.918568\pi\) | |||||||
\(110\) | −0.198062 | −0.0188845 | ||||||||
\(111\) | −3.54288 | −0.336275 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.81700 | 0.265001 | 0.132501 | − | 0.991183i | \(-0.457699\pi\) | ||||
0.132501 | + | 0.991183i | \(0.457699\pi\) | |||||||
\(114\) | −5.74094 | −0.537688 | ||||||||
\(115\) | −1.35690 | −0.126531 | ||||||||
\(116\) | 0.405813 | 0.0376788 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.54288 | 0.510263 | ||||||||
\(119\) | 3.80194 | 0.348523 | ||||||||
\(120\) | −0.554958 | −0.0506605 | ||||||||
\(121\) | −10.8726 | −0.988420 | ||||||||
\(122\) | 4.38404 | 0.396913 | ||||||||
\(123\) | 3.26875 | 0.294733 | ||||||||
\(124\) | −4.74094 | −0.425749 | ||||||||
\(125\) | −5.37867 | −0.481083 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −1.40581 | −0.124746 | −0.0623729 | − | 0.998053i | \(-0.519867\pi\) | ||||
−0.0623729 | + | 0.998053i | \(0.519867\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.04892 | 0.532577 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.50365 | −0.830338 | −0.415169 | − | 0.909744i | \(-0.636277\pi\) | ||||
−0.415169 | + | 0.909744i | \(0.636277\pi\) | |||||||
\(132\) | 0.356896 | 0.0310638 | ||||||||
\(133\) | −5.74094 | −0.497803 | ||||||||
\(134\) | −15.2959 | −1.32136 | ||||||||
\(135\) | −0.554958 | −0.0477632 | ||||||||
\(136\) | −3.80194 | −0.326013 | ||||||||
\(137\) | 1.03684 | 0.0885829 | 0.0442914 | − | 0.999019i | \(-0.485897\pi\) | ||||
0.0442914 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(138\) | 2.44504 | 0.208136 | ||||||||
\(139\) | 8.74094 | 0.741397 | 0.370698 | − | 0.928753i | \(-0.379118\pi\) | ||||
0.370698 | + | 0.928753i | \(0.379118\pi\) | |||||||
\(140\) | −0.554958 | −0.0469025 | ||||||||
\(141\) | −0.603875 | −0.0508555 | ||||||||
\(142\) | 7.42758 | 0.623309 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.225209 | 0.0187026 | ||||||||
\(146\) | −11.2295 | −0.929362 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 3.54288 | 0.291223 | ||||||||
\(149\) | 9.38835 | 0.769124 | 0.384562 | − | 0.923099i | \(-0.374352\pi\) | ||||
0.384562 | + | 0.923099i | \(0.374352\pi\) | |||||||
\(150\) | 4.69202 | 0.383102 | ||||||||
\(151\) | 8.66248 | 0.704943 | 0.352471 | − | 0.935823i | \(-0.385341\pi\) | ||||
0.352471 | + | 0.935823i | \(0.385341\pi\) | |||||||
\(152\) | 5.74094 | 0.465652 | ||||||||
\(153\) | −3.80194 | −0.307368 | ||||||||
\(154\) | 0.356896 | 0.0287595 | ||||||||
\(155\) | −2.63102 | −0.211329 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.10992 | 0.567433 | 0.283717 | − | 0.958908i | \(-0.408433\pi\) | ||||
0.283717 | + | 0.958908i | \(0.408433\pi\) | |||||||
\(158\) | −1.76271 | −0.140234 | ||||||||
\(159\) | 1.35690 | 0.107609 | ||||||||
\(160\) | 0.554958 | 0.0438733 | ||||||||
\(161\) | 2.44504 | 0.192696 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −18.8931 | −1.47982 | −0.739910 | − | 0.672706i | \(-0.765132\pi\) | ||||
−0.739910 | + | 0.672706i | \(0.765132\pi\) | |||||||
\(164\) | −3.26875 | −0.255246 | ||||||||
\(165\) | 0.198062 | 0.0154191 | ||||||||
\(166\) | −11.4426 | −0.888122 | ||||||||
\(167\) | 3.13169 | 0.242337 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.10992 | −0.161823 | ||||||||
\(171\) | 5.74094 | 0.439021 | ||||||||
\(172\) | −6.04892 | −0.461226 | ||||||||
\(173\) | −4.39612 | −0.334231 | −0.167116 | − | 0.985937i | \(-0.553445\pi\) | ||||
−0.167116 | + | 0.985937i | \(0.553445\pi\) | |||||||
\(174\) | −0.405813 | −0.0307646 | ||||||||
\(175\) | 4.69202 | 0.354683 | ||||||||
\(176\) | −0.356896 | −0.0269020 | ||||||||
\(177\) | −5.54288 | −0.416628 | ||||||||
\(178\) | 4.80194 | 0.359920 | ||||||||
\(179\) | −16.9215 | −1.26478 | −0.632388 | − | 0.774652i | \(-0.717925\pi\) | ||||
−0.632388 | + | 0.774652i | \(0.717925\pi\) | |||||||
\(180\) | 0.554958 | 0.0413641 | ||||||||
\(181\) | −9.71917 | −0.722420 | −0.361210 | − | 0.932484i | \(-0.617636\pi\) | ||||
−0.361210 | + | 0.932484i | \(0.617636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.38404 | −0.324078 | ||||||||
\(184\) | −2.44504 | −0.180251 | ||||||||
\(185\) | 1.96615 | 0.144554 | ||||||||
\(186\) | 4.74094 | 0.347622 | ||||||||
\(187\) | 1.35690 | 0.0992261 | ||||||||
\(188\) | 0.603875 | 0.0440421 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 3.18598 | 0.231135 | ||||||||
\(191\) | 3.40581 | 0.246436 | 0.123218 | − | 0.992380i | \(-0.460679\pi\) | ||||
0.123218 | + | 0.992380i | \(0.460679\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −17.0804 | −1.22947 | −0.614736 | − | 0.788733i | \(-0.710738\pi\) | ||||
−0.614736 | + | 0.788733i | \(0.710738\pi\) | |||||||
\(194\) | 2.65279 | 0.190459 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.89977 | 0.277847 | 0.138924 | − | 0.990303i | \(-0.455636\pi\) | ||||
0.138924 | + | 0.990303i | \(0.455636\pi\) | |||||||
\(198\) | −0.356896 | −0.0253635 | ||||||||
\(199\) | 3.52111 | 0.249605 | 0.124802 | − | 0.992182i | \(-0.460170\pi\) | ||||
0.124802 | + | 0.992182i | \(0.460170\pi\) | |||||||
\(200\) | −4.69202 | −0.331776 | ||||||||
\(201\) | 15.2959 | 1.07889 | ||||||||
\(202\) | −9.10752 | −0.640803 | ||||||||
\(203\) | −0.405813 | −0.0284825 | ||||||||
\(204\) | 3.80194 | 0.266189 | ||||||||
\(205\) | −1.81402 | −0.126697 | ||||||||
\(206\) | 12.2784 | 0.855479 | ||||||||
\(207\) | −2.44504 | −0.169942 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.04892 | −0.141727 | ||||||||
\(210\) | 0.554958 | 0.0382957 | ||||||||
\(211\) | −3.18598 | −0.219332 | −0.109666 | − | 0.993968i | \(-0.534978\pi\) | ||||
−0.109666 | + | 0.993968i | \(0.534978\pi\) | |||||||
\(212\) | −1.35690 | −0.0931920 | ||||||||
\(213\) | −7.42758 | −0.508930 | ||||||||
\(214\) | 6.08575 | 0.416014 | ||||||||
\(215\) | −3.35690 | −0.228938 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 4.74094 | 0.321836 | ||||||||
\(218\) | −20.2010 | −1.36819 | ||||||||
\(219\) | 11.2295 | 0.758821 | ||||||||
\(220\) | −0.198062 | −0.0133534 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.54288 | −0.237782 | ||||||||
\(223\) | 3.35450 | 0.224634 | 0.112317 | − | 0.993672i | \(-0.464173\pi\) | ||||
0.112317 | + | 0.993672i | \(0.464173\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.69202 | −0.312801 | ||||||||
\(226\) | 2.81700 | 0.187384 | ||||||||
\(227\) | −10.8804 | −0.722157 | −0.361079 | − | 0.932535i | \(-0.617591\pi\) | ||||
−0.361079 | + | 0.932535i | \(0.617591\pi\) | |||||||
\(228\) | −5.74094 | −0.380203 | ||||||||
\(229\) | −12.0804 | −0.798294 | −0.399147 | − | 0.916887i | \(-0.630694\pi\) | ||||
−0.399147 | + | 0.916887i | \(0.630694\pi\) | |||||||
\(230\) | −1.35690 | −0.0894711 | ||||||||
\(231\) | −0.356896 | −0.0234820 | ||||||||
\(232\) | 0.405813 | 0.0266429 | ||||||||
\(233\) | −23.8810 | −1.56450 | −0.782248 | − | 0.622968i | \(-0.785927\pi\) | ||||
−0.782248 | + | 0.622968i | \(0.785927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.335126 | 0.0218612 | ||||||||
\(236\) | 5.54288 | 0.360811 | ||||||||
\(237\) | 1.76271 | 0.114500 | ||||||||
\(238\) | 3.80194 | 0.246443 | ||||||||
\(239\) | −17.4819 | −1.13081 | −0.565404 | − | 0.824814i | \(-0.691280\pi\) | ||||
−0.565404 | + | 0.824814i | \(0.691280\pi\) | |||||||
\(240\) | −0.554958 | −0.0358224 | ||||||||
\(241\) | −2.22521 | −0.143338 | −0.0716692 | − | 0.997428i | \(-0.522833\pi\) | ||||
−0.0716692 | + | 0.997428i | \(0.522833\pi\) | |||||||
\(242\) | −10.8726 | −0.698919 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.38404 | 0.280660 | ||||||||
\(245\) | 0.554958 | 0.0354550 | ||||||||
\(246\) | 3.26875 | 0.208408 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.74094 | −0.301050 | ||||||||
\(249\) | 11.4426 | 0.725148 | ||||||||
\(250\) | −5.37867 | −0.340177 | ||||||||
\(251\) | −8.30665 | −0.524311 | −0.262156 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262156 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 0.872625 | 0.0548615 | ||||||||
\(254\) | −1.40581 | −0.0882086 | ||||||||
\(255\) | 2.10992 | 0.132128 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.66248 | 0.290838 | 0.145419 | − | 0.989370i | \(-0.453547\pi\) | ||||
0.145419 | + | 0.989370i | \(0.453547\pi\) | |||||||
\(258\) | 6.04892 | 0.376589 | ||||||||
\(259\) | −3.54288 | −0.220144 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.405813 | 0.0251192 | ||||||||
\(262\) | −9.50365 | −0.587137 | ||||||||
\(263\) | −20.6015 | −1.27034 | −0.635171 | − | 0.772372i | \(-0.719070\pi\) | ||||
−0.635171 | + | 0.772372i | \(0.719070\pi\) | |||||||
\(264\) | 0.356896 | 0.0219654 | ||||||||
\(265\) | −0.753020 | −0.0462577 | ||||||||
\(266\) | −5.74094 | −0.352000 | ||||||||
\(267\) | −4.80194 | −0.293874 | ||||||||
\(268\) | −15.2959 | −0.934346 | ||||||||
\(269\) | 32.3032 | 1.96956 | 0.984780 | − | 0.173804i | \(-0.0556060\pi\) | ||||
0.984780 | + | 0.173804i | \(0.0556060\pi\) | |||||||
\(270\) | −0.554958 | −0.0337737 | ||||||||
\(271\) | −5.21850 | −0.317002 | −0.158501 | − | 0.987359i | \(-0.550666\pi\) | ||||
−0.158501 | + | 0.987359i | \(0.550666\pi\) | |||||||
\(272\) | −3.80194 | −0.230526 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.03684 | 0.0626375 | ||||||||
\(275\) | 1.67456 | 0.100980 | ||||||||
\(276\) | 2.44504 | 0.147174 | ||||||||
\(277\) | −6.27950 | −0.377299 | −0.188649 | − | 0.982045i | \(-0.560411\pi\) | ||||
−0.188649 | + | 0.982045i | \(0.560411\pi\) | |||||||
\(278\) | 8.74094 | 0.524247 | ||||||||
\(279\) | −4.74094 | −0.283833 | ||||||||
\(280\) | −0.554958 | −0.0331651 | ||||||||
\(281\) | 0.423272 | 0.0252503 | 0.0126251 | − | 0.999920i | \(-0.495981\pi\) | ||||
0.0126251 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(282\) | −0.603875 | −0.0359603 | ||||||||
\(283\) | 10.9946 | 0.653563 | 0.326781 | − | 0.945100i | \(-0.394036\pi\) | ||||
0.326781 | + | 0.945100i | \(0.394036\pi\) | |||||||
\(284\) | 7.42758 | 0.440746 | ||||||||
\(285\) | −3.18598 | −0.188721 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.26875 | 0.192948 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −2.54527 | −0.149722 | ||||||||
\(290\) | 0.225209 | 0.0132247 | ||||||||
\(291\) | −2.65279 | −0.155509 | ||||||||
\(292\) | −11.2295 | −0.657158 | ||||||||
\(293\) | −15.3177 | −0.894868 | −0.447434 | − | 0.894317i | \(-0.647662\pi\) | ||||
−0.447434 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 3.07606 | 0.179095 | ||||||||
\(296\) | 3.54288 | 0.205926 | ||||||||
\(297\) | 0.356896 | 0.0207092 | ||||||||
\(298\) | 9.38835 | 0.543853 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.69202 | 0.270894 | ||||||||
\(301\) | 6.04892 | 0.348654 | ||||||||
\(302\) | 8.66248 | 0.498470 | ||||||||
\(303\) | 9.10752 | 0.523214 | ||||||||
\(304\) | 5.74094 | 0.329265 | ||||||||
\(305\) | 2.43296 | 0.139311 | ||||||||
\(306\) | −3.80194 | −0.217342 | ||||||||
\(307\) | −19.8280 | −1.13164 | −0.565822 | − | 0.824527i | \(-0.691441\pi\) | ||||
−0.565822 | + | 0.824527i | \(0.691441\pi\) | |||||||
\(308\) | 0.356896 | 0.0203360 | ||||||||
\(309\) | −12.2784 | −0.698496 | ||||||||
\(310\) | −2.63102 | −0.149432 | ||||||||
\(311\) | 24.6461 | 1.39755 | 0.698776 | − | 0.715341i | \(-0.253729\pi\) | ||||
0.698776 | + | 0.715341i | \(0.253729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2034 | 0.633256 | 0.316628 | − | 0.948550i | \(-0.397449\pi\) | ||||
0.316628 | + | 0.948550i | \(0.397449\pi\) | |||||||
\(314\) | 7.10992 | 0.401236 | ||||||||
\(315\) | −0.554958 | −0.0312683 | ||||||||
\(316\) | −1.76271 | −0.0991601 | ||||||||
\(317\) | −24.8756 | −1.39715 | −0.698577 | − | 0.715535i | \(-0.746183\pi\) | ||||
−0.698577 | + | 0.715535i | \(0.746183\pi\) | |||||||
\(318\) | 1.35690 | 0.0760909 | ||||||||
\(319\) | −0.144833 | −0.00810909 | ||||||||
\(320\) | 0.554958 | 0.0310231 | ||||||||
\(321\) | −6.08575 | −0.339674 | ||||||||
\(322\) | 2.44504 | 0.136257 | ||||||||
\(323\) | −21.8267 | −1.21447 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.8931 | −1.04639 | ||||||||
\(327\) | 20.2010 | 1.11712 | ||||||||
\(328\) | −3.26875 | −0.180487 | ||||||||
\(329\) | −0.603875 | −0.0332927 | ||||||||
\(330\) | 0.198062 | 0.0109030 | ||||||||
\(331\) | 22.7289 | 1.24929 | 0.624645 | − | 0.780908i | \(-0.285243\pi\) | ||||
0.624645 | + | 0.780908i | \(0.285243\pi\) | |||||||
\(332\) | −11.4426 | −0.627997 | ||||||||
\(333\) | 3.54288 | 0.194148 | ||||||||
\(334\) | 3.13169 | 0.171358 | ||||||||
\(335\) | −8.48858 | −0.463781 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 10.5743 | 0.576021 | 0.288010 | − | 0.957627i | \(-0.407006\pi\) | ||||
0.288010 | + | 0.957627i | \(0.407006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.81700 | −0.152999 | ||||||||
\(340\) | −2.10992 | −0.114426 | ||||||||
\(341\) | 1.69202 | 0.0916281 | ||||||||
\(342\) | 5.74094 | 0.310434 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.04892 | −0.326136 | ||||||||
\(345\) | 1.35690 | 0.0730528 | ||||||||
\(346\) | −4.39612 | −0.236337 | ||||||||
\(347\) | 7.57002 | 0.406380 | 0.203190 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203190 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(348\) | −0.405813 | −0.0217539 | ||||||||
\(349\) | −5.50066 | −0.294444 | −0.147222 | − | 0.989103i | \(-0.547033\pi\) | ||||
−0.147222 | + | 0.989103i | \(0.547033\pi\) | |||||||
\(350\) | 4.69202 | 0.250799 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.356896 | −0.0190226 | ||||||||
\(353\) | −33.0508 | −1.75912 | −0.879559 | − | 0.475789i | \(-0.842162\pi\) | ||||
−0.879559 | + | 0.475789i | \(0.842162\pi\) | |||||||
\(354\) | −5.54288 | −0.294601 | ||||||||
\(355\) | 4.12200 | 0.218773 | ||||||||
\(356\) | 4.80194 | 0.254502 | ||||||||
\(357\) | −3.80194 | −0.201220 | ||||||||
\(358\) | −16.9215 | −0.894331 | ||||||||
\(359\) | −11.8702 | −0.626487 | −0.313243 | − | 0.949673i | \(-0.601416\pi\) | ||||
−0.313243 | + | 0.949673i | \(0.601416\pi\) | |||||||
\(360\) | 0.554958 | 0.0292489 | ||||||||
\(361\) | 13.9584 | 0.734651 | ||||||||
\(362\) | −9.71917 | −0.510828 | ||||||||
\(363\) | 10.8726 | 0.570665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.23191 | −0.326193 | ||||||||
\(366\) | −4.38404 | −0.229158 | ||||||||
\(367\) | −2.46980 | −0.128922 | −0.0644612 | − | 0.997920i | \(-0.520533\pi\) | ||||
−0.0644612 | + | 0.997920i | \(0.520533\pi\) | |||||||
\(368\) | −2.44504 | −0.127457 | ||||||||
\(369\) | −3.26875 | −0.170164 | ||||||||
\(370\) | 1.96615 | 0.102215 | ||||||||
\(371\) | 1.35690 | 0.0704465 | ||||||||
\(372\) | 4.74094 | 0.245806 | ||||||||
\(373\) | −9.28514 | −0.480766 | −0.240383 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240383 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(374\) | 1.35690 | 0.0701634 | ||||||||
\(375\) | 5.37867 | 0.277753 | ||||||||
\(376\) | 0.603875 | 0.0311425 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −0.292913 | −0.0150459 | −0.00752297 | − | 0.999972i | \(-0.502395\pi\) | ||||
−0.00752297 | + | 0.999972i | \(0.502395\pi\) | |||||||
\(380\) | 3.18598 | 0.163437 | ||||||||
\(381\) | 1.40581 | 0.0720220 | ||||||||
\(382\) | 3.40581 | 0.174257 | ||||||||
\(383\) | 28.2446 | 1.44323 | 0.721615 | − | 0.692294i | \(-0.243400\pi\) | ||||
0.721615 | + | 0.692294i | \(0.243400\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0.198062 | 0.0100942 | ||||||||
\(386\) | −17.0804 | −0.869368 | ||||||||
\(387\) | −6.04892 | −0.307484 | ||||||||
\(388\) | 2.65279 | 0.134675 | ||||||||
\(389\) | −23.1618 | −1.17435 | −0.587175 | − | 0.809460i | \(-0.699760\pi\) | ||||
−0.587175 | + | 0.809460i | \(0.699760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.29590 | 0.470114 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 9.50365 | 0.479396 | ||||||||
\(394\) | 3.89977 | 0.196468 | ||||||||
\(395\) | −0.978230 | −0.0492201 | ||||||||
\(396\) | −0.356896 | −0.0179347 | ||||||||
\(397\) | −21.8767 | −1.09796 | −0.548979 | − | 0.835836i | \(-0.684983\pi\) | ||||
−0.548979 | + | 0.835836i | \(0.684983\pi\) | |||||||
\(398\) | 3.52111 | 0.176497 | ||||||||
\(399\) | 5.74094 | 0.287406 | ||||||||
\(400\) | −4.69202 | −0.234601 | ||||||||
\(401\) | 15.3381 | 0.765949 | 0.382974 | − | 0.923759i | \(-0.374900\pi\) | ||||
0.382974 | + | 0.923759i | \(0.374900\pi\) | |||||||
\(402\) | 15.2959 | 0.762890 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9.10752 | −0.453116 | ||||||||
\(405\) | 0.554958 | 0.0275761 | ||||||||
\(406\) | −0.405813 | −0.0201402 | ||||||||
\(407\) | −1.26444 | −0.0626759 | ||||||||
\(408\) | 3.80194 | 0.188224 | ||||||||
\(409\) | 18.6383 | 0.921606 | 0.460803 | − | 0.887503i | \(-0.347562\pi\) | ||||
0.460803 | + | 0.887503i | \(0.347562\pi\) | |||||||
\(410\) | −1.81402 | −0.0895880 | ||||||||
\(411\) | −1.03684 | −0.0511433 | ||||||||
\(412\) | 12.2784 | 0.604915 | ||||||||
\(413\) | −5.54288 | −0.272747 | ||||||||
\(414\) | −2.44504 | −0.120167 | ||||||||
\(415\) | −6.35019 | −0.311719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.74094 | −0.428046 | ||||||||
\(418\) | −2.04892 | −0.100216 | ||||||||
\(419\) | 39.2258 | 1.91631 | 0.958153 | − | 0.286257i | \(-0.0924111\pi\) | ||||
0.958153 | + | 0.286257i | \(0.0924111\pi\) | |||||||
\(420\) | 0.554958 | 0.0270792 | ||||||||
\(421\) | −7.94139 | −0.387040 | −0.193520 | − | 0.981096i | \(-0.561990\pi\) | ||||
−0.193520 | + | 0.981096i | \(0.561990\pi\) | |||||||
\(422\) | −3.18598 | −0.155091 | ||||||||
\(423\) | 0.603875 | 0.0293614 | ||||||||
\(424\) | −1.35690 | −0.0658967 | ||||||||
\(425\) | 17.8388 | 0.865308 | ||||||||
\(426\) | −7.42758 | −0.359868 | ||||||||
\(427\) | −4.38404 | −0.212159 | ||||||||
\(428\) | 6.08575 | 0.294166 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.35690 | −0.161884 | ||||||||
\(431\) | 24.2674 | 1.16892 | 0.584460 | − | 0.811422i | \(-0.301306\pi\) | ||||
0.584460 | + | 0.811422i | \(0.301306\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −20.7832 | −0.998775 | −0.499387 | − | 0.866379i | \(-0.666441\pi\) | ||||
−0.499387 | + | 0.866379i | \(0.666441\pi\) | |||||||
\(434\) | 4.74094 | 0.227572 | ||||||||
\(435\) | −0.225209 | −0.0107980 | ||||||||
\(436\) | −20.2010 | −0.967455 | ||||||||
\(437\) | −14.0368 | −0.671473 | ||||||||
\(438\) | 11.2295 | 0.536567 | ||||||||
\(439\) | 38.5502 | 1.83990 | 0.919950 | − | 0.392036i | \(-0.128229\pi\) | ||||
0.919950 | + | 0.392036i | \(0.128229\pi\) | |||||||
\(440\) | −0.198062 | −0.00944225 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.59850 | −0.0759470 | −0.0379735 | − | 0.999279i | \(-0.512090\pi\) | ||||
−0.0379735 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(444\) | −3.54288 | −0.168137 | ||||||||
\(445\) | 2.66487 | 0.126327 | ||||||||
\(446\) | 3.35450 | 0.158840 | ||||||||
\(447\) | −9.38835 | −0.444054 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 26.2064 | 1.23676 | 0.618379 | − | 0.785880i | \(-0.287790\pi\) | ||||
0.618379 | + | 0.785880i | \(0.287790\pi\) | |||||||
\(450\) | −4.69202 | −0.221184 | ||||||||
\(451\) | 1.16660 | 0.0549332 | ||||||||
\(452\) | 2.81700 | 0.132501 | ||||||||
\(453\) | −8.66248 | −0.406999 | ||||||||
\(454\) | −10.8804 | −0.510642 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.74094 | −0.268844 | ||||||||
\(457\) | 11.1540 | 0.521764 | 0.260882 | − | 0.965371i | \(-0.415987\pi\) | ||||
0.260882 | + | 0.965371i | \(0.415987\pi\) | |||||||
\(458\) | −12.0804 | −0.564479 | ||||||||
\(459\) | 3.80194 | 0.177459 | ||||||||
\(460\) | −1.35690 | −0.0632656 | ||||||||
\(461\) | 17.9191 | 0.834578 | 0.417289 | − | 0.908774i | \(-0.362980\pi\) | ||||
0.417289 | + | 0.908774i | \(0.362980\pi\) | |||||||
\(462\) | −0.356896 | −0.0166043 | ||||||||
\(463\) | −11.5453 | −0.536554 | −0.268277 | − | 0.963342i | \(-0.586454\pi\) | ||||
−0.268277 | + | 0.963342i | \(0.586454\pi\) | |||||||
\(464\) | 0.405813 | 0.0188394 | ||||||||
\(465\) | 2.63102 | 0.122011 | ||||||||
\(466\) | −23.8810 | −1.10627 | ||||||||
\(467\) | −18.4620 | −0.854321 | −0.427160 | − | 0.904176i | \(-0.640486\pi\) | ||||
−0.427160 | + | 0.904176i | \(0.640486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2959 | 0.706299 | ||||||||
\(470\) | 0.335126 | 0.0154582 | ||||||||
\(471\) | −7.10992 | −0.327608 | ||||||||
\(472\) | 5.54288 | 0.255132 | ||||||||
\(473\) | 2.15883 | 0.0992633 | ||||||||
\(474\) | 1.76271 | 0.0809639 | ||||||||
\(475\) | −26.9366 | −1.23594 | ||||||||
\(476\) | 3.80194 | 0.174262 | ||||||||
\(477\) | −1.35690 | −0.0621280 | ||||||||
\(478\) | −17.4819 | −0.799602 | ||||||||
\(479\) | −35.8756 | −1.63920 | −0.819599 | − | 0.572937i | \(-0.805804\pi\) | ||||
−0.819599 | + | 0.572937i | \(0.805804\pi\) | |||||||
\(480\) | −0.554958 | −0.0253303 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.22521 | −0.101356 | ||||||||
\(483\) | −2.44504 | −0.111253 | ||||||||
\(484\) | −10.8726 | −0.494210 | ||||||||
\(485\) | 1.47219 | 0.0668487 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.90648 | −0.0863907 | −0.0431954 | − | 0.999067i | \(-0.513754\pi\) | ||||
−0.0431954 | + | 0.999067i | \(0.513754\pi\) | |||||||
\(488\) | 4.38404 | 0.198456 | ||||||||
\(489\) | 18.8931 | 0.854374 | ||||||||
\(490\) | 0.554958 | 0.0250705 | ||||||||
\(491\) | −17.7536 | −0.801209 | −0.400605 | − | 0.916251i | \(-0.631200\pi\) | ||||
−0.400605 | + | 0.916251i | \(0.631200\pi\) | |||||||
\(492\) | 3.26875 | 0.147367 | ||||||||
\(493\) | −1.54288 | −0.0694877 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.198062 | −0.00890224 | ||||||||
\(496\) | −4.74094 | −0.212874 | ||||||||
\(497\) | −7.42758 | −0.333173 | ||||||||
\(498\) | 11.4426 | 0.512757 | ||||||||
\(499\) | −24.8528 | −1.11256 | −0.556281 | − | 0.830994i | \(-0.687772\pi\) | ||||
−0.556281 | + | 0.830994i | \(0.687772\pi\) | |||||||
\(500\) | −5.37867 | −0.240541 | ||||||||
\(501\) | −3.13169 | −0.139913 | ||||||||
\(502\) | −8.30665 | −0.370744 | ||||||||
\(503\) | 42.3870 | 1.88994 | 0.944972 | − | 0.327151i | \(-0.106089\pi\) | ||||
0.944972 | + | 0.327151i | \(0.106089\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −5.05429 | −0.224913 | ||||||||
\(506\) | 0.872625 | 0.0387929 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.40581 | −0.0623729 | ||||||||
\(509\) | 2.93362 | 0.130031 | 0.0650153 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650153 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(510\) | 2.10992 | 0.0934287 | ||||||||
\(511\) | 11.2295 | 0.496765 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.74094 | −0.253469 | ||||||||
\(514\) | 4.66248 | 0.205653 | ||||||||
\(515\) | 6.81402 | 0.300262 | ||||||||
\(516\) | 6.04892 | 0.266289 | ||||||||
\(517\) | −0.215521 | −0.00947859 | ||||||||
\(518\) | −3.54288 | −0.155665 | ||||||||
\(519\) | 4.39612 | 0.192968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.1396 | −1.75855 | −0.879273 | − | 0.476318i | \(-0.841971\pi\) | ||||
−0.879273 | + | 0.476318i | \(0.841971\pi\) | |||||||
\(522\) | 0.405813 | 0.0177620 | ||||||||
\(523\) | −14.8418 | −0.648985 | −0.324492 | − | 0.945888i | \(-0.605193\pi\) | ||||
−0.324492 | + | 0.945888i | \(0.605193\pi\) | |||||||
\(524\) | −9.50365 | −0.415169 | ||||||||
\(525\) | −4.69202 | −0.204777 | ||||||||
\(526\) | −20.6015 | −0.898267 | ||||||||
\(527\) | 18.0248 | 0.785171 | ||||||||
\(528\) | 0.356896 | 0.0155319 | ||||||||
\(529\) | −17.0218 | −0.740077 | ||||||||
\(530\) | −0.753020 | −0.0327091 | ||||||||
\(531\) | 5.54288 | 0.240540 | ||||||||
\(532\) | −5.74094 | −0.248901 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.80194 | −0.207800 | ||||||||
\(535\) | 3.37734 | 0.146015 | ||||||||
\(536\) | −15.2959 | −0.660682 | ||||||||
\(537\) | 16.9215 | 0.730218 | ||||||||
\(538\) | 32.3032 | 1.39269 | ||||||||
\(539\) | −0.356896 | −0.0153726 | ||||||||
\(540\) | −0.554958 | −0.0238816 | ||||||||
\(541\) | −39.0127 | −1.67729 | −0.838643 | − | 0.544682i | \(-0.816650\pi\) | ||||
−0.838643 | + | 0.544682i | \(0.816650\pi\) | |||||||
\(542\) | −5.21850 | −0.224154 | ||||||||
\(543\) | 9.71917 | 0.417089 | ||||||||
\(544\) | −3.80194 | −0.163007 | ||||||||
\(545\) | −11.2107 | −0.480215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.0978 | 1.15862 | 0.579310 | − | 0.815107i | \(-0.303322\pi\) | ||||
0.579310 | + | 0.815107i | \(0.303322\pi\) | |||||||
\(548\) | 1.03684 | 0.0442914 | ||||||||
\(549\) | 4.38404 | 0.187106 | ||||||||
\(550\) | 1.67456 | 0.0714036 | ||||||||
\(551\) | 2.32975 | 0.0992506 | ||||||||
\(552\) | 2.44504 | 0.104068 | ||||||||
\(553\) | 1.76271 | 0.0749580 | ||||||||
\(554\) | −6.27950 | −0.266791 | ||||||||
\(555\) | −1.96615 | −0.0834583 | ||||||||
\(556\) | 8.74094 | 0.370698 | ||||||||
\(557\) | −32.2338 | −1.36579 | −0.682896 | − | 0.730516i | \(-0.739280\pi\) | ||||
−0.682896 | + | 0.730516i | \(0.739280\pi\) | |||||||
\(558\) | −4.74094 | −0.200700 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.554958 | −0.0234513 | ||||||||
\(561\) | −1.35690 | −0.0572882 | ||||||||
\(562\) | 0.423272 | 0.0178546 | ||||||||
\(563\) | 15.8237 | 0.666890 | 0.333445 | − | 0.942770i | \(-0.391789\pi\) | ||||
0.333445 | + | 0.942770i | \(0.391789\pi\) | |||||||
\(564\) | −0.603875 | −0.0254277 | ||||||||
\(565\) | 1.56332 | 0.0657693 | ||||||||
\(566\) | 10.9946 | 0.462138 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 7.42758 | 0.311654 | ||||||||
\(569\) | −22.0127 | −0.922819 | −0.461410 | − | 0.887187i | \(-0.652656\pi\) | ||||
−0.461410 | + | 0.887187i | \(0.652656\pi\) | |||||||
\(570\) | −3.18598 | −0.133446 | ||||||||
\(571\) | 10.0379 | 0.420073 | 0.210037 | − | 0.977694i | \(-0.432642\pi\) | ||||
0.210037 | + | 0.977694i | \(0.432642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.40581 | −0.142280 | ||||||||
\(574\) | 3.26875 | 0.136435 | ||||||||
\(575\) | 11.4722 | 0.478423 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −2.85325 | −0.118782 | −0.0593911 | − | 0.998235i | \(-0.518916\pi\) | ||||
−0.0593911 | + | 0.998235i | \(0.518916\pi\) | |||||||
\(578\) | −2.54527 | −0.105869 | ||||||||
\(579\) | 17.0804 | 0.709836 | ||||||||
\(580\) | 0.225209 | 0.00935131 | ||||||||
\(581\) | 11.4426 | 0.474721 | ||||||||
\(582\) | −2.65279 | −0.109962 | ||||||||
\(583\) | 0.484271 | 0.0200564 | ||||||||
\(584\) | −11.2295 | −0.464681 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.3177 | −0.632767 | ||||||||
\(587\) | 42.0514 | 1.73565 | 0.867824 | − | 0.496872i | \(-0.165518\pi\) | ||||
0.867824 | + | 0.496872i | \(0.165518\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −27.2174 | −1.12148 | ||||||||
\(590\) | 3.07606 | 0.126640 | ||||||||
\(591\) | −3.89977 | −0.160415 | ||||||||
\(592\) | 3.54288 | 0.145611 | ||||||||
\(593\) | 0.00909768 | 0.000373597 0 | 0.000186798 | − | 1.00000i | \(-0.499941\pi\) | ||||
0.000186798 | 1.00000i | \(0.499941\pi\) | ||||||||
\(594\) | 0.356896 | 0.0146436 | ||||||||
\(595\) | 2.10992 | 0.0864981 | ||||||||
\(596\) | 9.38835 | 0.384562 | ||||||||
\(597\) | −3.52111 | −0.144109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.13169 | 0.373111 | 0.186555 | − | 0.982444i | \(-0.440268\pi\) | ||||
0.186555 | + | 0.982444i | \(0.440268\pi\) | |||||||
\(600\) | 4.69202 | 0.191551 | ||||||||
\(601\) | −10.7791 | −0.439689 | −0.219844 | − | 0.975535i | \(-0.570555\pi\) | ||||
−0.219844 | + | 0.975535i | \(0.570555\pi\) | |||||||
\(602\) | 6.04892 | 0.246535 | ||||||||
\(603\) | −15.2959 | −0.622897 | ||||||||
\(604\) | 8.66248 | 0.352471 | ||||||||
\(605\) | −6.03385 | −0.245311 | ||||||||
\(606\) | 9.10752 | 0.369968 | ||||||||
\(607\) | −3.04354 | −0.123533 | −0.0617667 | − | 0.998091i | \(-0.519673\pi\) | ||||
−0.0617667 | + | 0.998091i | \(0.519673\pi\) | |||||||
\(608\) | 5.74094 | 0.232826 | ||||||||
\(609\) | 0.405813 | 0.0164444 | ||||||||
\(610\) | 2.43296 | 0.0985077 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.80194 | −0.153684 | ||||||||
\(613\) | −21.2228 | −0.857181 | −0.428591 | − | 0.903499i | \(-0.640990\pi\) | ||||
−0.428591 | + | 0.903499i | \(0.640990\pi\) | |||||||
\(614\) | −19.8280 | −0.800194 | ||||||||
\(615\) | 1.81402 | 0.0731483 | ||||||||
\(616\) | 0.356896 | 0.0143797 | ||||||||
\(617\) | −19.1019 | −0.769013 | −0.384506 | − | 0.923122i | \(-0.625628\pi\) | ||||
−0.384506 | + | 0.923122i | \(0.625628\pi\) | |||||||
\(618\) | −12.2784 | −0.493911 | ||||||||
\(619\) | −21.1454 | −0.849906 | −0.424953 | − | 0.905215i | \(-0.639709\pi\) | ||||
−0.424953 | + | 0.905215i | \(0.639709\pi\) | |||||||
\(620\) | −2.63102 | −0.105664 | ||||||||
\(621\) | 2.44504 | 0.0981162 | ||||||||
\(622\) | 24.6461 | 0.988218 | ||||||||
\(623\) | −4.80194 | −0.192386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.4752 | 0.819007 | ||||||||
\(626\) | 11.2034 | 0.447779 | ||||||||
\(627\) | 2.04892 | 0.0818259 | ||||||||
\(628\) | 7.10992 | 0.283717 | ||||||||
\(629\) | −13.4698 | −0.537076 | ||||||||
\(630\) | −0.554958 | −0.0221101 | ||||||||
\(631\) | −32.4359 | −1.29125 | −0.645627 | − | 0.763653i | \(-0.723404\pi\) | ||||
−0.645627 | + | 0.763653i | \(0.723404\pi\) | |||||||
\(632\) | −1.76271 | −0.0701168 | ||||||||
\(633\) | 3.18598 | 0.126631 | ||||||||
\(634\) | −24.8756 | −0.987937 | ||||||||
\(635\) | −0.780167 | −0.0309600 | ||||||||
\(636\) | 1.35690 | 0.0538044 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.144833 | −0.00573400 | ||||||||
\(639\) | 7.42758 | 0.293831 | ||||||||
\(640\) | 0.554958 | 0.0219366 | ||||||||
\(641\) | 18.4499 | 0.728729 | 0.364365 | − | 0.931256i | \(-0.381286\pi\) | ||||
0.364365 | + | 0.931256i | \(0.381286\pi\) | |||||||
\(642\) | −6.08575 | −0.240186 | ||||||||
\(643\) | −18.8334 | −0.742717 | −0.371358 | − | 0.928490i | \(-0.621108\pi\) | ||||
−0.371358 | + | 0.928490i | \(0.621108\pi\) | |||||||
\(644\) | 2.44504 | 0.0963481 | ||||||||
\(645\) | 3.35690 | 0.132178 | ||||||||
\(646\) | −21.8267 | −0.858760 | ||||||||
\(647\) | 47.8049 | 1.87941 | 0.939703 | − | 0.341992i | \(-0.111102\pi\) | ||||
0.939703 | + | 0.341992i | \(0.111102\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −1.97823 | −0.0776523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.74094 | −0.185812 | ||||||||
\(652\) | −18.8931 | −0.739910 | ||||||||
\(653\) | 41.1637 | 1.61086 | 0.805431 | − | 0.592690i | \(-0.201934\pi\) | ||||
0.805431 | + | 0.592690i | \(0.201934\pi\) | |||||||
\(654\) | 20.2010 | 0.789923 | ||||||||
\(655\) | −5.27413 | −0.206077 | ||||||||
\(656\) | −3.26875 | −0.127623 | ||||||||
\(657\) | −11.2295 | −0.438105 | ||||||||
\(658\) | −0.603875 | −0.0235415 | ||||||||
\(659\) | 31.9758 | 1.24560 | 0.622801 | − | 0.782380i | \(-0.285995\pi\) | ||||
0.622801 | + | 0.782380i | \(0.285995\pi\) | |||||||
\(660\) | 0.198062 | 0.00770956 | ||||||||
\(661\) | −43.2567 | −1.68249 | −0.841245 | − | 0.540655i | \(-0.818177\pi\) | ||||
−0.841245 | + | 0.540655i | \(0.818177\pi\) | |||||||
\(662\) | 22.7289 | 0.883382 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.4426 | −0.444061 | ||||||||
\(665\) | −3.18598 | −0.123547 | ||||||||
\(666\) | 3.54288 | 0.137284 | ||||||||
\(667\) | −0.992230 | −0.0384193 | ||||||||
\(668\) | 3.13169 | 0.121169 | ||||||||
\(669\) | −3.35450 | −0.129693 | ||||||||
\(670\) | −8.48858 | −0.327943 | ||||||||
\(671\) | −1.56465 | −0.0604025 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −12.6872 | −0.489057 | −0.244528 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244528 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(674\) | 10.5743 | 0.407308 | ||||||||
\(675\) | 4.69202 | 0.180596 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.39672 | −0.284279 | −0.142139 | − | 0.989847i | \(-0.545398\pi\) | ||||
−0.142139 | + | 0.989847i | \(0.545398\pi\) | |||||||
\(678\) | −2.81700 | −0.108186 | ||||||||
\(679\) | −2.65279 | −0.101805 | ||||||||
\(680\) | −2.10992 | −0.0809116 | ||||||||
\(681\) | 10.8804 | 0.416938 | ||||||||
\(682\) | 1.69202 | 0.0647909 | ||||||||
\(683\) | 5.76138 | 0.220453 | 0.110227 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110227 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(684\) | 5.74094 | 0.219510 | ||||||||
\(685\) | 0.575400 | 0.0219849 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 12.0804 | 0.460895 | ||||||||
\(688\) | −6.04892 | −0.230613 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.35690 | 0.0516561 | ||||||||
\(691\) | 3.84894 | 0.146420 | 0.0732102 | − | 0.997317i | \(-0.476676\pi\) | ||||
0.0732102 | + | 0.997317i | \(0.476676\pi\) | |||||||
\(692\) | −4.39612 | −0.167116 | ||||||||
\(693\) | 0.356896 | 0.0135574 | ||||||||
\(694\) | 7.57002 | 0.287354 | ||||||||
\(695\) | 4.85086 | 0.184003 | ||||||||
\(696\) | −0.405813 | −0.0153823 | ||||||||
\(697\) | 12.4276 | 0.470728 | ||||||||
\(698\) | −5.50066 | −0.208203 | ||||||||
\(699\) | 23.8810 | 0.903262 | ||||||||
\(700\) | 4.69202 | 0.177342 | ||||||||
\(701\) | 26.4776 | 1.00004 | 0.500022 | − | 0.866013i | \(-0.333325\pi\) | ||||
0.500022 | + | 0.866013i | \(0.333325\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.3394 | 0.767116 | ||||||||
\(704\) | −0.356896 | −0.0134510 | ||||||||
\(705\) | −0.335126 | −0.0126216 | ||||||||
\(706\) | −33.0508 | −1.24388 | ||||||||
\(707\) | 9.10752 | 0.342524 | ||||||||
\(708\) | −5.54288 | −0.208314 | ||||||||
\(709\) | 19.4886 | 0.731909 | 0.365955 | − | 0.930633i | \(-0.380743\pi\) | ||||
0.365955 | + | 0.930633i | \(0.380743\pi\) | |||||||
\(710\) | 4.12200 | 0.154696 | ||||||||
\(711\) | −1.76271 | −0.0661068 | ||||||||
\(712\) | 4.80194 | 0.179960 | ||||||||
\(713\) | 11.5918 | 0.434116 | ||||||||
\(714\) | −3.80194 | −0.142284 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.9215 | −0.632388 | ||||||||
\(717\) | 17.4819 | 0.652873 | ||||||||
\(718\) | −11.8702 | −0.442993 | ||||||||
\(719\) | 48.2140 | 1.79808 | 0.899039 | − | 0.437868i | \(-0.144266\pi\) | ||||
0.899039 | + | 0.437868i | \(0.144266\pi\) | |||||||
\(720\) | 0.554958 | 0.0206821 | ||||||||
\(721\) | −12.2784 | −0.457273 | ||||||||
\(722\) | 13.9584 | 0.519477 | ||||||||
\(723\) | 2.22521 | 0.0827564 | ||||||||
\(724\) | −9.71917 | −0.361210 | ||||||||
\(725\) | −1.90408 | −0.0707159 | ||||||||
\(726\) | 10.8726 | 0.403521 | ||||||||
\(727\) | −15.6987 | −0.582234 | −0.291117 | − | 0.956688i | \(-0.594027\pi\) | ||||
−0.291117 | + | 0.956688i | \(0.594027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.23191 | −0.230653 | ||||||||
\(731\) | 22.9976 | 0.850597 | ||||||||
\(732\) | −4.38404 | −0.162039 | ||||||||
\(733\) | 34.5478 | 1.27605 | 0.638026 | − | 0.770015i | \(-0.279751\pi\) | ||||
0.638026 | + | 0.770015i | \(0.279751\pi\) | |||||||
\(734\) | −2.46980 | −0.0911618 | ||||||||
\(735\) | −0.554958 | −0.0204699 | ||||||||
\(736\) | −2.44504 | −0.0901254 | ||||||||
\(737\) | 5.45904 | 0.201086 | ||||||||
\(738\) | −3.26875 | −0.120324 | ||||||||
\(739\) | −38.3739 | −1.41161 | −0.705803 | − | 0.708408i | \(-0.749414\pi\) | ||||
−0.705803 | + | 0.708408i | \(0.749414\pi\) | |||||||
\(740\) | 1.96615 | 0.0722770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.35690 | 0.0498132 | ||||||||
\(743\) | −20.3110 | −0.745137 | −0.372568 | − | 0.928005i | \(-0.621523\pi\) | ||||
−0.372568 | + | 0.928005i | \(0.621523\pi\) | |||||||
\(744\) | 4.74094 | 0.173811 | ||||||||
\(745\) | 5.21014 | 0.190885 | ||||||||
\(746\) | −9.28514 | −0.339953 | ||||||||
\(747\) | −11.4426 | −0.418665 | ||||||||
\(748\) | 1.35690 | 0.0496130 | ||||||||
\(749\) | −6.08575 | −0.222369 | ||||||||
\(750\) | 5.37867 | 0.196401 | ||||||||
\(751\) | 18.8552 | 0.688035 | 0.344017 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344017 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(752\) | 0.603875 | 0.0220211 | ||||||||
\(753\) | 8.30665 | 0.302711 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.80731 | 0.174956 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 3.10885 | 0.112993 | 0.0564966 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564966 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(758\) | −0.292913 | −0.0106391 | ||||||||
\(759\) | −0.872625 | −0.0316743 | ||||||||
\(760\) | 3.18598 | 0.115568 | ||||||||
\(761\) | 48.7928 | 1.76874 | 0.884370 | − | 0.466787i | \(-0.154589\pi\) | ||||
0.884370 | + | 0.466787i | \(0.154589\pi\) | |||||||
\(762\) | 1.40581 | 0.0509272 | ||||||||
\(763\) | 20.2010 | 0.731327 | ||||||||
\(764\) | 3.40581 | 0.123218 | ||||||||
\(765\) | −2.10992 | −0.0762842 | ||||||||
\(766\) | 28.2446 | 1.02052 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 9.82610 | 0.354338 | 0.177169 | − | 0.984180i | \(-0.443306\pi\) | ||||
0.177169 | + | 0.984180i | \(0.443306\pi\) | |||||||
\(770\) | 0.198062 | 0.00713767 | ||||||||
\(771\) | −4.66248 | −0.167915 | ||||||||
\(772\) | −17.0804 | −0.614736 | ||||||||
\(773\) | −4.30260 | −0.154754 | −0.0773769 | − | 0.997002i | \(-0.524654\pi\) | ||||
−0.0773769 | + | 0.997002i | \(0.524654\pi\) | |||||||
\(774\) | −6.04892 | −0.217424 | ||||||||
\(775\) | 22.2446 | 0.799049 | ||||||||
\(776\) | 2.65279 | 0.0952297 | ||||||||
\(777\) | 3.54288 | 0.127100 | ||||||||
\(778\) | −23.1618 | −0.830391 | ||||||||
\(779\) | −18.7657 | −0.672351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.65087 | −0.0948557 | ||||||||
\(782\) | 9.29590 | 0.332421 | ||||||||
\(783\) | −0.405813 | −0.0145026 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 3.94571 | 0.140828 | ||||||||
\(786\) | 9.50365 | 0.338984 | ||||||||
\(787\) | 30.7904 | 1.09756 | 0.548780 | − | 0.835967i | \(-0.315092\pi\) | ||||
0.548780 | + | 0.835967i | \(0.315092\pi\) | |||||||
\(788\) | 3.89977 | 0.138924 | ||||||||
\(789\) | 20.6015 | 0.733432 | ||||||||
\(790\) | −0.978230 | −0.0348039 | ||||||||
\(791\) | −2.81700 | −0.100161 | ||||||||
\(792\) | −0.356896 | −0.0126817 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.8767 | −0.776374 | ||||||||
\(795\) | 0.753020 | 0.0267069 | ||||||||
\(796\) | 3.52111 | 0.124802 | ||||||||
\(797\) | −9.83877 | −0.348507 | −0.174254 | − | 0.984701i | \(-0.555751\pi\) | ||||
−0.174254 | + | 0.984701i | \(0.555751\pi\) | |||||||
\(798\) | 5.74094 | 0.203227 | ||||||||
\(799\) | −2.29590 | −0.0812230 | ||||||||
\(800\) | −4.69202 | −0.165888 | ||||||||
\(801\) | 4.80194 | 0.169668 | ||||||||
\(802\) | 15.3381 | 0.541607 | ||||||||
\(803\) | 4.00777 | 0.141431 | ||||||||
\(804\) | 15.2959 | 0.539445 | ||||||||
\(805\) | 1.35690 | 0.0478243 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.3032 | −1.13713 | ||||||||
\(808\) | −9.10752 | −0.320402 | ||||||||
\(809\) | 32.8364 | 1.15447 | 0.577233 | − | 0.816580i | \(-0.304133\pi\) | ||||
0.577233 | + | 0.816580i | \(0.304133\pi\) | |||||||
\(810\) | 0.554958 | 0.0194992 | ||||||||
\(811\) | 27.1420 | 0.953083 | 0.476542 | − | 0.879152i | \(-0.341890\pi\) | ||||
0.476542 | + | 0.879152i | \(0.341890\pi\) | |||||||
\(812\) | −0.405813 | −0.0142413 | ||||||||
\(813\) | 5.21850 | 0.183021 | ||||||||
\(814\) | −1.26444 | −0.0443185 | ||||||||
\(815\) | −10.4849 | −0.367269 | ||||||||
\(816\) | 3.80194 | 0.133094 | ||||||||
\(817\) | −34.7265 | −1.21493 | ||||||||
\(818\) | 18.6383 | 0.651674 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.81402 | −0.0633483 | ||||||||
\(821\) | −30.8896 | −1.07805 | −0.539027 | − | 0.842288i | \(-0.681208\pi\) | ||||
−0.539027 | + | 0.842288i | \(0.681208\pi\) | |||||||
\(822\) | −1.03684 | −0.0361638 | ||||||||
\(823\) | −10.5284 | −0.366997 | −0.183499 | − | 0.983020i | \(-0.558742\pi\) | ||||
−0.183499 | + | 0.983020i | \(0.558742\pi\) | |||||||
\(824\) | 12.2784 | 0.427740 | ||||||||
\(825\) | −1.67456 | −0.0583008 | ||||||||
\(826\) | −5.54288 | −0.192861 | ||||||||
\(827\) | 46.2573 | 1.60852 | 0.804261 | − | 0.594276i | \(-0.202561\pi\) | ||||
0.804261 | + | 0.594276i | \(0.202561\pi\) | |||||||
\(828\) | −2.44504 | −0.0849711 | ||||||||
\(829\) | 14.8595 | 0.516091 | 0.258046 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258046 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(830\) | −6.35019 | −0.220418 | ||||||||
\(831\) | 6.27950 | 0.217834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.80194 | −0.131729 | ||||||||
\(834\) | −8.74094 | −0.302674 | ||||||||
\(835\) | 1.73795 | 0.0601444 | ||||||||
\(836\) | −2.04892 | −0.0708633 | ||||||||
\(837\) | 4.74094 | 0.163871 | ||||||||
\(838\) | 39.2258 | 1.35503 | ||||||||
\(839\) | −25.5284 | −0.881338 | −0.440669 | − | 0.897670i | \(-0.645259\pi\) | ||||
−0.440669 | + | 0.897670i | \(0.645259\pi\) | |||||||
\(840\) | 0.554958 | 0.0191479 | ||||||||
\(841\) | −28.8353 | −0.994321 | ||||||||
\(842\) | −7.94139 | −0.273679 | ||||||||
\(843\) | −0.423272 | −0.0145782 | ||||||||
\(844\) | −3.18598 | −0.109666 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.603875 | 0.0207617 | ||||||||
\(847\) | 10.8726 | 0.373588 | ||||||||
\(848\) | −1.35690 | −0.0465960 | ||||||||
\(849\) | −10.9946 | −0.377334 | ||||||||
\(850\) | 17.8388 | 0.611865 | ||||||||
\(851\) | −8.66248 | −0.296946 | ||||||||
\(852\) | −7.42758 | −0.254465 | ||||||||
\(853\) | −21.0640 | −0.721217 | −0.360609 | − | 0.932717i | \(-0.617431\pi\) | ||||
−0.360609 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(854\) | −4.38404 | −0.150019 | ||||||||
\(855\) | 3.18598 | 0.108958 | ||||||||
\(856\) | 6.08575 | 0.208007 | ||||||||
\(857\) | 32.2922 | 1.10308 | 0.551540 | − | 0.834149i | \(-0.314040\pi\) | ||||
0.551540 | + | 0.834149i | \(0.314040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.7700 | 0.845142 | 0.422571 | − | 0.906330i | \(-0.361128\pi\) | ||||
0.422571 | + | 0.906330i | \(0.361128\pi\) | |||||||
\(860\) | −3.35690 | −0.114469 | ||||||||
\(861\) | −3.26875 | −0.111399 | ||||||||
\(862\) | 24.2674 | 0.826552 | ||||||||
\(863\) | 1.51514 | 0.0515759 | 0.0257880 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257880 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −2.43967 | −0.0829511 | ||||||||
\(866\) | −20.7832 | −0.706240 | ||||||||
\(867\) | 2.54527 | 0.0864419 | ||||||||
\(868\) | 4.74094 | 0.160918 | ||||||||
\(869\) | 0.629104 | 0.0213409 | ||||||||
\(870\) | −0.225209 | −0.00763531 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.2010 | −0.684094 | ||||||||
\(873\) | 2.65279 | 0.0897834 | ||||||||
\(874\) | −14.0368 | −0.474803 | ||||||||
\(875\) | 5.37867 | 0.181832 | ||||||||
\(876\) | 11.2295 | 0.379410 | ||||||||
\(877\) | 16.0425 | 0.541716 | 0.270858 | − | 0.962619i | \(-0.412693\pi\) | ||||
0.270858 | + | 0.962619i | \(0.412693\pi\) | |||||||
\(878\) | 38.5502 | 1.30101 | ||||||||
\(879\) | 15.3177 | 0.516652 | ||||||||
\(880\) | −0.198062 | −0.00667668 | ||||||||
\(881\) | −18.8452 | −0.634911 | −0.317456 | − | 0.948273i | \(-0.602828\pi\) | ||||
−0.317456 | + | 0.948273i | \(0.602828\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 41.0092 | 1.38007 | 0.690035 | − | 0.723776i | \(-0.257595\pi\) | ||||
0.690035 | + | 0.723776i | \(0.257595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.07606 | −0.103401 | ||||||||
\(886\) | −1.59850 | −0.0537026 | ||||||||
\(887\) | −5.77107 | −0.193774 | −0.0968868 | − | 0.995295i | \(-0.530888\pi\) | ||||
−0.0968868 | + | 0.995295i | \(0.530888\pi\) | |||||||
\(888\) | −3.54288 | −0.118891 | ||||||||
\(889\) | 1.40581 | 0.0471495 | ||||||||
\(890\) | 2.66487 | 0.0893268 | ||||||||
\(891\) | −0.356896 | −0.0119565 | ||||||||
\(892\) | 3.35450 | 0.112317 | ||||||||
\(893\) | 3.46681 | 0.116012 | ||||||||
\(894\) | −9.38835 | −0.313994 | ||||||||
\(895\) | −9.39075 | −0.313898 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.2064 | 0.874520 | ||||||||
\(899\) | −1.92394 | −0.0641668 | ||||||||
\(900\) | −4.69202 | −0.156401 | ||||||||
\(901\) | 5.15883 | 0.171866 | ||||||||
\(902\) | 1.16660 | 0.0388436 | ||||||||
\(903\) | −6.04892 | −0.201295 | ||||||||
\(904\) | 2.81700 | 0.0936921 | ||||||||
\(905\) | −5.39373 | −0.179294 | ||||||||
\(906\) | −8.66248 | −0.287792 | ||||||||
\(907\) | 48.1618 | 1.59919 | 0.799593 | − | 0.600542i | \(-0.205048\pi\) | ||||
0.799593 | + | 0.600542i | \(0.205048\pi\) | |||||||
\(908\) | −10.8804 | −0.361079 | ||||||||
\(909\) | −9.10752 | −0.302077 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.32736 | 0.309029 | 0.154515 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154515 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(912\) | −5.74094 | −0.190101 | ||||||||
\(913\) | 4.08383 | 0.135155 | ||||||||
\(914\) | 11.1540 | 0.368943 | ||||||||
\(915\) | −2.43296 | −0.0804312 | ||||||||
\(916\) | −12.0804 | −0.399147 | ||||||||
\(917\) | 9.50365 | 0.313838 | ||||||||
\(918\) | 3.80194 | 0.125483 | ||||||||
\(919\) | −45.0877 | −1.48731 | −0.743653 | − | 0.668566i | \(-0.766908\pi\) | ||||
−0.743653 | + | 0.668566i | \(0.766908\pi\) | |||||||
\(920\) | −1.35690 | −0.0447355 | ||||||||
\(921\) | 19.8280 | 0.653355 | ||||||||
\(922\) | 17.9191 | 0.590136 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.356896 | −0.0117410 | ||||||||
\(925\) | −16.6233 | −0.546569 | ||||||||
\(926\) | −11.5453 | −0.379401 | ||||||||
\(927\) | 12.2784 | 0.403277 | ||||||||
\(928\) | 0.405813 | 0.0133215 | ||||||||
\(929\) | −31.1704 | −1.02267 | −0.511335 | − | 0.859382i | \(-0.670849\pi\) | ||||
−0.511335 | + | 0.859382i | \(0.670849\pi\) | |||||||
\(930\) | 2.63102 | 0.0862746 | ||||||||
\(931\) | 5.74094 | 0.188152 | ||||||||
\(932\) | −23.8810 | −0.782248 | ||||||||
\(933\) | −24.6461 | −0.806877 | ||||||||
\(934\) | −18.4620 | −0.604096 | ||||||||
\(935\) | 0.753020 | 0.0246264 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.4698 | 0.407370 | 0.203685 | − | 0.979036i | \(-0.434708\pi\) | ||||
0.203685 | + | 0.979036i | \(0.434708\pi\) | |||||||
\(938\) | 15.2959 | 0.499429 | ||||||||
\(939\) | −11.2034 | −0.365610 | ||||||||
\(940\) | 0.335126 | 0.0109306 | ||||||||
\(941\) | −10.9866 | −0.358153 | −0.179076 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179076 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(942\) | −7.10992 | −0.231654 | ||||||||
\(943\) | 7.99223 | 0.260263 | ||||||||
\(944\) | 5.54288 | 0.180405 | ||||||||
\(945\) | 0.554958 | 0.0180528 | ||||||||
\(946\) | 2.15883 | 0.0701897 | ||||||||
\(947\) | 57.7445 | 1.87644 | 0.938222 | − | 0.346033i | \(-0.112472\pi\) | ||||
0.938222 | + | 0.346033i | \(0.112472\pi\) | |||||||
\(948\) | 1.76271 | 0.0572501 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −26.9366 | −0.873939 | ||||||||
\(951\) | 24.8756 | 0.806647 | ||||||||
\(952\) | 3.80194 | 0.123222 | ||||||||
\(953\) | −38.7942 | −1.25667 | −0.628333 | − | 0.777944i | \(-0.716263\pi\) | ||||
−0.628333 | + | 0.777944i | \(0.716263\pi\) | |||||||
\(954\) | −1.35690 | −0.0439311 | ||||||||
\(955\) | 1.89008 | 0.0611617 | ||||||||
\(956\) | −17.4819 | −0.565404 | ||||||||
\(957\) | 0.144833 | 0.00468179 | ||||||||
\(958\) | −35.8756 | −1.15909 | ||||||||
\(959\) | −1.03684 | −0.0334812 | ||||||||
\(960\) | −0.554958 | −0.0179112 | ||||||||
\(961\) | −8.52350 | −0.274952 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.08575 | 0.196111 | ||||||||
\(964\) | −2.22521 | −0.0716692 | ||||||||
\(965\) | −9.47889 | −0.305136 | ||||||||
\(966\) | −2.44504 | −0.0786679 | ||||||||
\(967\) | −41.1588 | −1.32358 | −0.661789 | − | 0.749690i | \(-0.730203\pi\) | ||||
−0.661789 | + | 0.749690i | \(0.730203\pi\) | |||||||
\(968\) | −10.8726 | −0.349459 | ||||||||
\(969\) | 21.8267 | 0.701174 | ||||||||
\(970\) | 1.47219 | 0.0472691 | ||||||||
\(971\) | 30.9084 | 0.991898 | 0.495949 | − | 0.868352i | \(-0.334820\pi\) | ||||
0.495949 | + | 0.868352i | \(0.334820\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −8.74094 | −0.280222 | ||||||||
\(974\) | −1.90648 | −0.0610875 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.38404 | 0.140330 | ||||||||
\(977\) | −40.6249 | −1.29971 | −0.649853 | − | 0.760060i | \(-0.725170\pi\) | ||||
−0.649853 | + | 0.760060i | \(0.725170\pi\) | |||||||
\(978\) | 18.8931 | 0.604134 | ||||||||
\(979\) | −1.71379 | −0.0547730 | ||||||||
\(980\) | 0.554958 | 0.0177275 | ||||||||
\(981\) | −20.2010 | −0.644970 | ||||||||
\(982\) | −17.7536 | −0.566541 | ||||||||
\(983\) | 36.6335 | 1.16843 | 0.584214 | − | 0.811600i | \(-0.301403\pi\) | ||||
0.584214 | + | 0.811600i | \(0.301403\pi\) | |||||||
\(984\) | 3.26875 | 0.104204 | ||||||||
\(985\) | 2.16421 | 0.0689575 | ||||||||
\(986\) | −1.54288 | −0.0491352 | ||||||||
\(987\) | 0.603875 | 0.0192216 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.7899 | 0.470290 | ||||||||
\(990\) | −0.198062 | −0.00629483 | ||||||||
\(991\) | 0.754348 | 0.0239627 | 0.0119813 | − | 0.999928i | \(-0.496186\pi\) | ||||
0.0119813 | + | 0.999928i | \(0.496186\pi\) | |||||||
\(992\) | −4.74094 | −0.150525 | ||||||||
\(993\) | −22.7289 | −0.721278 | ||||||||
\(994\) | −7.42758 | −0.235589 | ||||||||
\(995\) | 1.95407 | 0.0619481 | ||||||||
\(996\) | 11.4426 | 0.362574 | ||||||||
\(997\) | 35.2336 | 1.11586 | 0.557929 | − | 0.829889i | \(-0.311596\pi\) | ||||
0.557929 | + | 0.829889i | \(0.311596\pi\) | |||||||
\(998\) | −24.8528 | −0.786701 | ||||||||
\(999\) | −3.54288 | −0.112092 |
(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 | 7098.2.a.cj.1.2 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.cc.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cc.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.cj.1.2 | yes | 3 | 1.1 | even | 1 | trivial |