Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.82843 | 1.17107 | 0.585533 | − | 0.810649i | \(-0.300885\pi\) | ||||
0.585533 | + | 0.810649i | \(0.300885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.65685 | −1.73442 | −0.867211 | − | 0.497941i | \(-0.834090\pi\) | ||||
−0.867211 | + | 0.497941i | \(0.834090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.343146 | 0.0535904 | 0.0267952 | − | 0.999641i | \(-0.491470\pi\) | ||||
0.0267952 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65685 | −0.241677 | −0.120839 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120839 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82843 | 0.676115 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843 | 0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.82843 | 1.03329 | 0.516645 | − | 0.856200i | \(-0.327181\pi\) | ||||
0.516645 | + | 0.856200i | \(0.327181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137 | 1.28932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.65685 | −0.636446 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.31371 | −0.802784 | −0.401392 | − | 0.915906i | \(-0.631473\pi\) | ||||
−0.401392 | + | 0.915906i | \(0.631473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.82843 | −0.517662 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.65685 | −0.811625 | −0.405812 | − | 0.913956i | \(-0.633011\pi\) | ||||
−0.405812 | + | 0.913956i | \(0.633011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.65685 | −1.00137 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.4853 | −1.87690 | −0.938448 | − | 0.345421i | \(-0.887736\pi\) | ||||
−0.938448 | + | 0.345421i | \(0.887736\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4853 | −1.04332 | −0.521662 | − | 0.853152i | \(-0.674688\pi\) | ||||
−0.521662 | + | 0.853152i | \(0.674688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6569 | 1.34565 | 0.672825 | − | 0.739802i | \(-0.265081\pi\) | ||||
0.672825 | + | 0.739802i | \(0.265081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.82843 | 0.276026 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4853 | −1.38744 | −0.693719 | − | 0.720246i | \(-0.744029\pi\) | ||||
−0.693719 | + | 0.720246i | \(0.744029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.65685 | 0.726756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.48528 | 0.233796 | 0.116898 | − | 0.993144i | \(-0.462705\pi\) | ||||
0.116898 | + | 0.993144i | \(0.462705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82843 | 0.263752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.343146 | 0.0309404 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6569 | −1.21185 | −0.605925 | − | 0.795522i | \(-0.707197\pi\) | ||||
−0.605925 | + | 0.795522i | \(0.707197\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.65685 | 0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.17157 | 0.451842 | 0.225921 | − | 0.974146i | \(-0.427461\pi\) | ||||
0.225921 | + | 0.974146i | \(0.427461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.31371 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6569 | 1.15836 | 0.579180 | − | 0.815200i | \(-0.303373\pi\) | ||||
0.579180 | + | 0.815200i | \(0.303373\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.65685 | −0.139532 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.82843 | −0.400979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.34315 | −0.355804 | −0.177902 | − | 0.984048i | \(-0.556931\pi\) | ||||
−0.177902 | + | 0.984048i | \(0.556931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9706 | 1.05553 | 0.527765 | − | 0.849391i | \(-0.323030\pi\) | ||||
0.527765 | + | 0.849391i | \(0.323030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.82843 | 0.390355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.65685 | −0.775657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.31371 | −0.104845 | −0.0524227 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524227 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9706 | 1.32924 | 0.664619 | − | 0.747183i | \(-0.268594\pi\) | ||||
0.664619 | + | 0.747183i | \(0.268594\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | 0.311400 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.31371 | −0.565952 | −0.282976 | − | 0.959127i | \(-0.591322\pi\) | ||||
−0.282976 | + | 0.959127i | \(0.591322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.82843 | 0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.48528 | −0.634220 | −0.317110 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317110 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.34315 | 0.620141 | 0.310071 | − | 0.950714i | \(-0.399647\pi\) | ||||
0.310071 | + | 0.950714i | \(0.399647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.65685 | 0.562943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.3137 | 1.41236 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.31371 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7990 | 1.28120 | 0.640600 | − | 0.767875i | \(-0.278686\pi\) | ||||
0.640600 | + | 0.767875i | \(0.278686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3137 | −0.948562 | −0.474281 | − | 0.880373i | \(-0.657292\pi\) | ||||
−0.474281 | + | 0.880373i | \(0.657292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9706 | −1.20301 | −0.601506 | − | 0.798869i | \(-0.705432\pi\) | ||||
−0.601506 | + | 0.798869i | \(0.705432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6569 | −0.958523 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.343146 | 0.0239663 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.65685 | 0.658592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.3137 | −1.85418 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.82843 | 0.596570 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.82843 | −0.324795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.82843 | −0.189405 | −0.0947027 | − | 0.995506i | \(-0.530190\pi\) | ||||
−0.0947027 | + | 0.995506i | \(0.530190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.6569 | 1.17193 | 0.585963 | − | 0.810338i | \(-0.300716\pi\) | ||||
0.585963 | + | 0.810338i | \(0.300716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.17157 | −0.209583 | −0.104792 | − | 0.994494i | \(-0.533418\pi\) | ||||
−0.104792 | + | 0.994494i | \(0.533418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.51472 | 0.623330 | 0.311665 | − | 0.950192i | \(-0.399113\pi\) | ||||
0.311665 | + | 0.950192i | \(0.399113\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.65685 | −0.108081 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | −0.367452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31371 | −0.0846234 | −0.0423117 | − | 0.999104i | \(-0.513472\pi\) | ||||
−0.0423117 | + | 0.999104i | \(0.513472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82843 | 0.179969 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.31371 | −0.463487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.8284 | 0.683484 | 0.341742 | − | 0.939794i | \(-0.388983\pi\) | ||||
0.341742 | + | 0.939794i | \(0.388983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137 | 0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.82843 | 0.302368 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.82843 | −0.550702 | −0.275351 | − | 0.961344i | \(-0.588794\pi\) | ||||
−0.275351 | + | 0.961344i | \(0.588794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6569 | 1.34569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.82843 | −0.298872 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1421 | −0.872041 | −0.436021 | − | 0.899937i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899937i | \(0.643613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.3137 | 0.817855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.65685 | −0.468592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4853 | −1.12707 | −0.563534 | − | 0.826093i | \(-0.690559\pi\) | ||||
−0.563534 | + | 0.826093i | \(0.690559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65685 | −0.100647 | −0.0503234 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503234 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.82843 | −0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.6274 | 1.96039 | 0.980196 | − | 0.198031i | \(-0.0634547\pi\) | ||||
0.980196 | + | 0.198031i | \(0.0634547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.65685 | −0.578141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.97056 | 0.415829 | 0.207914 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207914 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3431 | 0.852612 | 0.426306 | − | 0.904579i | \(-0.359815\pi\) | ||||
0.426306 | + | 0.904579i | \(0.359815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.970563 | 0.0572905 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4853 | −1.08363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0000 | −0.584206 | −0.292103 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292103 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.3137 | 1.57434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4853 | −0.602364 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6569 | 0.776911 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6274 | −0.829445 | −0.414722 | − | 0.909948i | \(-0.636121\pi\) | ||||
−0.414722 | + | 0.909948i | \(0.636121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.9706 | −1.29837 | −0.649186 | − | 0.760629i | \(-0.724891\pi\) | ||||
−0.649186 | + | 0.760629i | \(0.724891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3137 | −0.747772 | −0.373886 | − | 0.927475i | \(-0.621975\pi\) | ||||
−0.373886 | + | 0.927475i | \(0.621975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.3137 | −1.08136 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.6569 | −0.759888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.4853 | −0.801038 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.68629 | −0.258364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4853 | 1.34583 | 0.672916 | − | 0.739719i | \(-0.265041\pi\) | ||||
0.672916 | + | 0.739719i | \(0.265041\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65685 | 0.419593 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3431 | 0.672374 | 0.336187 | − | 0.941795i | \(-0.390863\pi\) | ||||
0.336187 | + | 0.941795i | \(0.390863\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.48528 | 0.134982 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −38.6274 | −2.09179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.82843 | 0.152277 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.65685 | 0.518407 | 0.259204 | − | 0.965823i | \(-0.416540\pi\) | ||||
0.259204 | + | 0.965823i | \(0.416540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8284 | 1.11492 | 0.557460 | − | 0.830204i | \(-0.311776\pi\) | ||||
0.557460 | + | 0.830204i | \(0.311776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.3137 | −1.34731 | −0.673656 | − | 0.739045i | \(-0.735277\pi\) | ||||
−0.673656 | + | 0.739045i | \(0.735277\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.6569 | 0.722797 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.82843 | 0.462101 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6569 | 0.712882 | 0.356441 | − | 0.934318i | \(-0.383990\pi\) | ||||
0.356441 | + | 0.934318i | \(0.383990\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.343146 | 0.0178635 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.6569 | 1.95505 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.31371 | −0.482246 | −0.241123 | − | 0.970495i | \(-0.577516\pi\) | ||||
−0.241123 | + | 0.970495i | \(0.577516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.82843 | 0.248677 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7990 | −1.01701 | −0.508503 | − | 0.861060i | \(-0.669801\pi\) | ||||
−0.508503 | + | 0.861060i | \(0.669801\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6569 | −0.699662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6274 | 0.543036 | 0.271518 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271518 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.3137 | 0.576600 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.65685 | 0.490885 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.85786 | −0.195601 | −0.0978007 | − | 0.995206i | \(-0.531181\pi\) | ||||
−0.0978007 | + | 0.995206i | \(0.531181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6569 | 0.690657 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.17157 | 0.260871 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.65685 | −0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6569 | 0.785795 | 0.392897 | − | 0.919582i | \(-0.371473\pi\) | ||||
0.392897 | + | 0.919582i | \(0.371473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.2843 | 1.31257 | 0.656287 | − | 0.754511i | \(-0.272126\pi\) | ||||
0.656287 | + | 0.754511i | \(0.272126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.65685 | 0.481042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.6274 | 1.51814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.343146 | −0.0169675 | −0.00848373 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848373 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.31371 | −0.459411 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3137 | 0.556711 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.31371 | −0.359016 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6569 | 0.668779 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4853 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.828427 | −0.0403751 | −0.0201875 | − | 0.999796i | \(-0.506426\pi\) | ||||
−0.0201875 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.65685 | −0.0805590 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.82843 | 0.234213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.65685 | −0.273754 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9706 | 1.20279 | 0.601395 | − | 0.798952i | \(-0.294612\pi\) | ||||
0.601395 | + | 0.798952i | \(0.294612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.34315 | −0.400946 | −0.200473 | − | 0.979699i | \(-0.564248\pi\) | ||||
−0.200473 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.82843 | −0.231505 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.9706 | 0.996342 | 0.498171 | − | 0.867079i | \(-0.334005\pi\) | ||||
0.498171 | + | 0.867079i | \(0.334005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.65685 | −0.362970 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.34315 | −0.205424 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.34315 | −0.204966 | −0.102483 | − | 0.994735i | \(-0.532679\pi\) | ||||
−0.102483 | + | 0.994735i | \(0.532679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37258 | 0.0646324 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9706 | 0.609410 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.82843 | −0.132599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1421 | 1.31643 | 0.658217 | − | 0.752828i | \(-0.271311\pi\) | ||||
0.658217 | + | 0.752828i | \(0.271311\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.82843 | 0.225372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.0000 | −1.58354 | −0.791769 | − | 0.610821i | \(-0.790840\pi\) | ||||
−0.791769 | + | 0.610821i | \(0.790840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1421 | −1.02903 | −0.514516 | − | 0.857481i | \(-0.672028\pi\) | ||||
−0.514516 | + | 0.857481i | \(0.672028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.65685 | −0.447826 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.31371 | −0.338438 | −0.169219 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169219 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.31371 | −0.0605325 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.6274 | 1.77609 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.6569 | −0.989527 | −0.494763 | − | 0.869028i | \(-0.664745\pi\) | ||||
−0.494763 | + | 0.869028i | \(0.664745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.65685 | −0.349123 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.00000 | 0.364013 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.4853 | −0.839373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.8284 | 0.490683 | 0.245341 | − | 0.969437i | \(-0.421100\pi\) | ||||
0.245341 | + | 0.969437i | \(0.421100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.9706 | 0.767435 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4853 | 1.10501 | 0.552503 | − | 0.833511i | \(-0.313673\pi\) | ||||
0.552503 | + | 0.833511i | \(0.313673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3137 | −1.05000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.00000 | 0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6274 | 1.01498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8284 | 0.842876 | 0.421438 | − | 0.906857i | \(-0.361525\pi\) | ||||
0.421438 | + | 0.906857i | \(0.361525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.31371 | −0.326752 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5147 | −0.691767 | −0.345884 | − | 0.938277i | \(-0.612421\pi\) | ||||
−0.345884 | + | 0.938277i | \(0.612421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4853 | −0.466589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3137 | −0.944714 | −0.472357 | − | 0.881407i | \(-0.656597\pi\) | ||||
−0.472357 | + | 0.881407i | \(0.656597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9706 | 1.10463 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.6569 | 0.601793 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.62742 | −0.291473 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.6569 | −1.56216 | −0.781078 | − | 0.624434i | \(-0.785330\pi\) | ||||
−0.781078 | + | 0.624434i | \(0.785330\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.6274 | 1.86397 | 0.931983 | − | 0.362501i | \(-0.118077\pi\) | ||||
0.931983 | + | 0.362501i | \(0.118077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82843 | 0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46.6274 | −2.03112 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.343146 | −0.0148633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.48528 | −0.366167 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.4558 | −1.69634 | −0.848170 | − | 0.529725i | \(-0.822295\pi\) | ||||
−0.848170 | + | 0.529725i | \(0.822295\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.34315 | 0.358039 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4853 | −0.620481 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3137 | −0.996822 | −0.498411 | − | 0.866941i | \(-0.666083\pi\) | ||||
−0.498411 | + | 0.866941i | \(0.666083\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6569 | 0.581802 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.0000 | −0.680389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.65685 | 0.325015 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.9411 | 1.69236 | 0.846180 | − | 0.532897i | \(-0.178897\pi\) | ||||
0.846180 | + | 0.532897i | \(0.178897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.65685 | −0.408441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.3137 | 0.815425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6569 | 1.08131 | 0.540654 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540654 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.48528 | 0.104557 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.2843 | −1.77265 | −0.886324 | − | 0.463065i | \(-0.846750\pi\) | ||||
−0.886324 | + | 0.463065i | \(0.846750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.9706 | 1.71456 | 0.857282 | − | 0.514847i | \(-0.172151\pi\) | ||||
0.857282 | + | 0.514847i | \(0.172151\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.31371 | −0.138432 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.82843 | 0.117954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4853 | 1.26912 | 0.634559 | − | 0.772874i | \(-0.281182\pi\) | ||||
0.634559 | + | 0.772874i | \(0.281182\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.7990 | 0.739701 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.6863 | −0.858212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53.2548 | 2.20559 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.6569 | 0.728776 | 0.364388 | − | 0.931247i | \(-0.381278\pi\) | ||||
0.364388 | + | 0.931247i | \(0.381278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3137 | 1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.3137 | −0.547653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.6569 | 0.642950 | 0.321475 | − | 0.946918i | \(-0.395821\pi\) | ||||
0.321475 | + | 0.946918i | \(0.395821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6569 | 0.559876 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.9706 | −0.694559 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3137 | −1.03257 | −0.516284 | − | 0.856418i | \(-0.672685\pi\) | ||||
−0.516284 | + | 0.856418i | \(0.672685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.65685 | −0.229605 | −0.114802 | − | 0.993388i | \(-0.536623\pi\) | ||||
−0.114802 | + | 0.993388i | \(0.536623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6569 | −0.553404 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.65685 | 0.0670291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.9706 | −1.89712 | −0.948562 | − | 0.316593i | \(-0.897461\pi\) | ||||
−0.948562 | + | 0.316593i | \(0.897461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.343146 | 0.0138370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.6274 | −1.15250 | −0.576248 | − | 0.817275i | \(-0.695484\pi\) | ||||
−0.576248 | + | 0.817275i | \(0.695484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.1716 | −1.17250 | −0.586252 | − | 0.810129i | \(-0.699397\pi\) | ||||
−0.586252 | + | 0.810129i | \(0.699397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843 | 0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.6569 | −0.867664 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.3137 | −0.451826 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.9706 | 1.47411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.6569 | −0.541956 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.6274 | 1.60469 | 0.802343 | − | 0.596863i | \(-0.203586\pi\) | ||||
0.802343 | + | 0.596863i | \(0.203586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6274 | −1.20783 | −0.603914 | − | 0.797050i | \(-0.706393\pi\) | ||||
−0.603914 | + | 0.797050i | \(0.706393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.65685 | 0.380238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.45584 | −0.371748 | −0.185874 | − | 0.982574i | \(-0.559512\pi\) | ||||
−0.185874 | + | 0.982574i | \(0.559512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.3137 | −1.07051 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.2843 | −0.715519 | −0.357759 | − | 0.933814i | \(-0.616459\pi\) | ||||
−0.357759 | + | 0.933814i | \(0.616459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.17157 | 0.202070 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.82843 | 0.344430 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.7990 | 1.70617 | 0.853083 | − | 0.521775i | \(-0.174730\pi\) | ||||
0.853083 | + | 0.521775i | \(0.174730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.828427 | −0.0322221 | −0.0161110 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161110 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.82843 | −0.187521 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6569 | −0.528796 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.82843 | −0.109353 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.00000 | −0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.2843 | −1.93258 | −0.966291 | − | 0.257453i | \(-0.917117\pi\) | ||||
−0.966291 | + | 0.257453i | \(0.917117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.2843 | −2.00649 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6569 | 0.676612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.9411 | −1.45178 | −0.725888 | − | 0.687812i | \(-0.758571\pi\) | ||||
−0.725888 | + | 0.687812i | \(0.758571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.31371 | −0.355859 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.17157 | −0.121003 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3137 | −0.507212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1716 | 1.10974 | 0.554869 | − | 0.831937i | \(-0.312768\pi\) | ||||
0.554869 | + | 0.831937i | \(0.312768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.3137 | 0.429772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.6569 | 0.518034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.65685 | 0.0627578 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.51472 | 0.359880 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4853 | −1.00034 | −0.500168 | − | 0.865929i | \(-0.666728\pi\) | ||||
−0.500168 | + | 0.865929i | \(0.666728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6569 | −0.816804 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.65685 | −0.0624007 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.6569 | −1.11536 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.7696 | 1.75647 | 0.878234 | − | 0.478232i | \(-0.158722\pi\) | ||||
0.878234 | + | 0.478232i | \(0.158722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.65685 | −0.212149 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.3137 | −1.02291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9706 | 0.633777 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.3431 | −0.982434 | −0.491217 | − | 0.871037i | \(-0.663448\pi\) | ||||
−0.491217 | + | 0.871037i | \(0.663448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.6274 | 1.43856 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.31371 | −0.0488573 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.82843 | −0.179323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6274 | 1.13591 | 0.567954 | − | 0.823060i | \(-0.307735\pi\) | ||||
0.567954 | + | 0.823060i | \(0.307735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.6274 | 1.72458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.9706 | 1.29167 | 0.645834 | − | 0.763478i | \(-0.276510\pi\) | ||||
0.645834 | + | 0.763478i | \(0.276510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.1127 | −1.43878 | −0.719392 | − | 0.694604i | \(-0.755579\pi\) | ||||
−0.719392 | + | 0.694604i | \(0.755579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.82843 | 0.103905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | 0.440237 | 0.220119 | − | 0.975473i | \(-0.429356\pi\) | ||||
0.220119 | + | 0.975473i | \(0.429356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.34315 | −0.159121 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.31371 | −0.267595 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.6863 | −1.04678 | −0.523389 | − | 0.852094i | \(-0.675332\pi\) | ||||
−0.523389 | + | 0.852094i | \(0.675332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.8284 | 0.394610 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.9706 | 0.472047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.3137 | 1.64695 | 0.823477 | − | 0.567349i | \(-0.192031\pi\) | ||||
0.823477 | + | 0.567349i | \(0.192031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3137 | 0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.9706 | −0.687682 | −0.343841 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343841 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.9706 | −1.48323 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.82843 | 0.174572 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.9411 | −1.15183 | −0.575913 | − | 0.817511i | \(-0.695353\pi\) | ||||
−0.575913 | + | 0.817511i | \(0.695353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.82843 | −0.317948 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.6863 | −1.10371 | −0.551855 | − | 0.833940i | \(-0.686080\pi\) | ||||
−0.551855 | + | 0.833940i | \(0.686080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.65685 | −0.346884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.6569 | 0.776935 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.970563 | −0.0347740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.82843 | −0.172554 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.31371 | −0.0468883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.6569 | −1.91266 | −0.956330 | − | 0.292289i | \(-0.905583\pi\) | ||||
−0.956330 | + | 0.292289i | \(0.905583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.1421 | −0.503473 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.02944 | 0.249938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.3137 | 0.472189 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.6274 | 1.15572 | 0.577861 | − | 0.816135i | \(-0.303887\pi\) | ||||
0.577861 | + | 0.816135i | \(0.303887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.3137 | 1.24619 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.4853 | −0.650713 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.68629 | −0.0944450 | −0.0472225 | − | 0.998884i | \(-0.515037\pi\) | ||||
−0.0472225 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.1127 | 1.65435 | 0.827175 | − | 0.561944i | \(-0.189946\pi\) | ||||
0.827175 | + | 0.561944i | \(0.189946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.65685 | −0.0581084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9706 | 0.594453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.3137 | −0.955586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.2843 | 1.47573 | 0.737866 | − | 0.674948i | \(-0.235834\pi\) | ||||
0.737866 | + | 0.674948i | \(0.235834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.65685 | −0.197186 | −0.0985928 | − | 0.995128i | \(-0.531434\pi\) | ||||
−0.0985928 | + | 0.995128i | \(0.531434\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.68629 | −0.302052 | −0.151026 | − | 0.988530i | \(-0.548258\pi\) | ||||
−0.151026 | + | 0.988530i | \(0.548258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6863 | 0.649002 | 0.324501 | − | 0.945885i | \(-0.394804\pi\) | ||||
0.324501 | + | 0.945885i | \(0.394804\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.6274 | 1.13183 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.82843 | 0.167295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.31371 | −0.253101 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.65685 | −0.333790 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.9706 | −0.862080 | −0.431040 | − | 0.902333i | \(-0.641853\pi\) | ||||
−0.431040 | + | 0.902333i | \(0.641853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.97056 | 0.240079 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.1421 | 0.485930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.3431 | 0.492255 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.6569 | 0.742387 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.02944 | 0.0352473 | 0.0176236 | − | 0.999845i | \(-0.494390\pi\) | ||||
0.0176236 | + | 0.999845i | \(0.494390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.82843 | −0.301573 | −0.150787 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150787 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | 0.272956 | 0.136478 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136478 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.970563 | 0.0330767 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.0000 | −0.680808 | −0.340404 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340404 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.31371 | 0.214425 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.4853 | −0.625632 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.3137 | 1.80028 | 0.900138 | − | 0.435605i | \(-0.143465\pi\) | ||||
0.900138 | + | 0.435605i | \(0.143465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.0000 | −0.337292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9706 | −0.773898 | −0.386949 | − | 0.922101i | \(-0.626471\pi\) | ||||
−0.386949 | + | 0.922101i | \(0.626471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.7696 | 0.965987 | 0.482994 | − | 0.875624i | \(-0.339549\pi\) | ||||
0.482994 | + | 0.875624i | \(0.339549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.6274 | −1.29552 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00000 | 0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.68629 | 0.156821 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.48528 | −0.283632 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.82843 | −0.0944384 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.6274 | 1.55511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64.2843 | 2.14162 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.3137 | 0.908943 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.34315 | 0.277336 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.3431 | −1.27316 | −0.636582 | − | 0.771209i | \(-0.719652\pi\) | ||||
−0.636582 | + | 0.771209i | \(0.719652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.4853 | −0.347775 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9706 | −0.827312 | −0.413656 | − | 0.910433i | \(-0.635748\pi\) | ||||
−0.413656 | + | 0.910433i | \(0.635748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.2548 | −0.968194 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.6274 | 0.483040 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.6274 | 0.746410 | 0.373205 | − | 0.927749i | \(-0.378259\pi\) | ||||
0.373205 | + | 0.927749i | \(0.378259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | −0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.00000 | −0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.65685 | 0.251756 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.6569 | 0.448550 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.2843 | 0.862359 | 0.431179 | − | 0.902266i | \(-0.358098\pi\) | ||||
0.431179 | + | 0.902266i | \(0.358098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6274 | −0.478880 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.3137 | 0.631626 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.9706 | −0.749616 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.6569 | −1.29278 | −0.646388 | − | 0.763009i | \(-0.723721\pi\) | ||||
−0.646388 | + | 0.763009i | \(0.723721\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.970563 | 0.0316059 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.82843 | 0.0920087 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.82843 | −0.286583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.3137 | −0.431727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.7401 | −1.93517 | −0.967586 | − | 0.252541i | \(-0.918734\pi\) | ||||
−0.967586 | + | 0.252541i | \(0.918734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.31371 | −0.107229 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.3137 | −0.624324 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.3431 | −0.850665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.2548 | 2.00822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.7990 | 0.572970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.7990 | −1.15122 | −0.575609 | − | 0.817725i | \(-0.695235\pi\) | ||||
−0.575609 | + | 0.817725i | \(0.695235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.6569 | −0.438721 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.17157 | −0.165964 | −0.0829818 | − | 0.996551i | \(-0.526444\pi\) | ||||
−0.0829818 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.6274 | 1.23834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.5980 | −1.20287 | −0.601433 | − | 0.798923i | \(-0.705403\pi\) | ||||
−0.601433 | + | 0.798923i | \(0.705403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.6274 | −0.978856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.4853 | −0.462479 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.6274 | −0.849283 | −0.424641 | − | 0.905362i | \(-0.639600\pi\) | ||||
−0.424641 | + | 0.905362i | \(0.639600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.3137 | −0.424210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.68629 | −0.149166 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.3137 | 0.868525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34315 | 0.0744325 | 0.0372162 | − | 0.999307i | \(-0.488151\pi\) | ||||
0.0372162 | + | 0.999307i | \(0.488151\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.4853 | 0.777017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.9706 | −0.538003 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.3137 | −0.801693 | −0.400847 | − | 0.916145i | \(-0.631284\pi\) | ||||
−0.400847 | + | 0.916145i | \(0.631284\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.65685 | 0.242252 |
(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 | 6240.2.a.bt.1.2 | yes | 2 | |
4.3 | odd | 2 | 6240.2.a.bn.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.bn.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
6240.2.a.bt.1.2 | yes | 2 | 1.1 | even | 1 | trivial |