Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1 |
$q$-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 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.70156 | −1.77702 | −0.888512 | − | 0.458854i | \(-0.848260\pi\) | ||||
−0.888512 | + | 0.458854i | \(0.848260\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.70156 | 1.41757 | 0.708787 | − | 0.705422i | \(-0.249243\pi\) | ||||
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.70156 | 1.25655 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.701562 | 0.170154 | 0.0850769 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850769 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.70156 | −0.390365 | −0.195183 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195183 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.70156 | 1.02596 | ||||||||
\(22\) | −4.70156 | −1.00238 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.70156 | −0.888512 | ||||||||
\(29\) | −6.40312 | −1.18903 | −0.594515 | − | 0.804084i | \(-0.702656\pi\) | ||||
−0.594515 | + | 0.804084i | \(0.702656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1047 | −1.81486 | −0.907428 | − | 0.420208i | \(-0.861957\pi\) | ||||
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.70156 | −0.818437 | ||||||||
\(34\) | −0.701562 | −0.120317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.70156 | 0.279735 | 0.139868 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139868 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(38\) | 1.70156 | 0.276030 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.70156 | −0.578087 | −0.289043 | − | 0.957316i | \(-0.593337\pi\) | ||||
−0.289043 | + | 0.957316i | \(0.593337\pi\) | |||||||
\(42\) | −4.70156 | −0.725467 | ||||||||
\(43\) | 11.4031 | 1.73896 | 0.869480 | − | 0.493968i | \(-0.164454\pi\) | ||||
0.869480 | + | 0.493968i | \(0.164454\pi\) | |||||||
\(44\) | 4.70156 | 0.708787 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.00000 | −1.02105 | −0.510527 | − | 0.859861i | \(-0.670550\pi\) | ||||
−0.510527 | + | 0.859861i | \(0.670550\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 15.1047 | 2.15781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.701562 | −0.0982383 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −2.40312 | −0.330095 | −0.165047 | − | 0.986286i | \(-0.552778\pi\) | ||||
−0.165047 | + | 0.986286i | \(0.552778\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.70156 | 0.628273 | ||||||||
\(57\) | 1.70156 | 0.225377 | ||||||||
\(58\) | 6.40312 | 0.840771 | ||||||||
\(59\) | 2.70156 | 0.351713 | 0.175857 | − | 0.984416i | \(-0.443730\pi\) | ||||
0.175857 | + | 0.984416i | \(0.443730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1047 | 1.80592 | 0.902960 | − | 0.429725i | \(-0.141389\pi\) | ||||
0.902960 | + | 0.429725i | \(0.141389\pi\) | |||||||
\(62\) | 10.1047 | 1.28330 | ||||||||
\(63\) | −4.70156 | −0.592341 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.70156 | 0.578722 | ||||||||
\(67\) | 6.40312 | 0.782266 | 0.391133 | − | 0.920334i | \(-0.372083\pi\) | ||||
0.391133 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(68\) | 0.701562 | 0.0850769 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.70156 | −0.201938 | −0.100969 | − | 0.994890i | \(-0.532194\pi\) | ||||
−0.100969 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | −1.70156 | −0.197803 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.70156 | −0.195183 | ||||||||
\(77\) | −22.1047 | −2.51906 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.70156 | −0.641476 | −0.320738 | − | 0.947168i | \(-0.603931\pi\) | ||||
−0.320738 | + | 0.947168i | \(0.603931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.70156 | 0.408769 | ||||||||
\(83\) | 10.7016 | 1.17465 | 0.587325 | − | 0.809352i | \(-0.300181\pi\) | ||||
0.587325 | + | 0.809352i | \(0.300181\pi\) | |||||||
\(84\) | 4.70156 | 0.512982 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.4031 | −1.22963 | ||||||||
\(87\) | 6.40312 | 0.686487 | ||||||||
\(88\) | −4.70156 | −0.501188 | ||||||||
\(89\) | 11.4031 | 1.20873 | 0.604364 | − | 0.796708i | \(-0.293427\pi\) | ||||
0.604364 | + | 0.796708i | \(0.293427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70156 | −0.492858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.1047 | 1.04781 | ||||||||
\(94\) | 7.00000 | 0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 2.59688 | 0.263673 | 0.131836 | − | 0.991271i | \(-0.457913\pi\) | ||||
0.131836 | + | 0.991271i | \(0.457913\pi\) | |||||||
\(98\) | −15.1047 | −1.52580 | ||||||||
\(99\) | 4.70156 | 0.472525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.70156 | 0.666830 | 0.333415 | − | 0.942780i | \(-0.391799\pi\) | ||||
0.333415 | + | 0.942780i | \(0.391799\pi\) | |||||||
\(102\) | 0.701562 | 0.0694650 | ||||||||
\(103\) | −1.40312 | −0.138254 | −0.0691270 | − | 0.997608i | \(-0.522021\pi\) | ||||
−0.0691270 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.40312 | 0.233412 | ||||||||
\(107\) | −19.1047 | −1.84692 | −0.923460 | − | 0.383695i | \(-0.874651\pi\) | ||||
−0.923460 | + | 0.383695i | \(0.874651\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.29844 | 0.411716 | 0.205858 | − | 0.978582i | \(-0.434002\pi\) | ||||
0.205858 | + | 0.978582i | \(0.434002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.70156 | −0.161505 | ||||||||
\(112\) | −4.70156 | −0.444256 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | −1.70156 | −0.159366 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.40312 | −0.594515 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −2.70156 | −0.248699 | ||||||||
\(119\) | −3.29844 | −0.302367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1047 | 1.00952 | ||||||||
\(122\) | −14.1047 | −1.27698 | ||||||||
\(123\) | 3.70156 | 0.333759 | ||||||||
\(124\) | −10.1047 | −0.907428 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.70156 | 0.418848 | ||||||||
\(127\) | 6.29844 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.4031 | −1.00399 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.5078 | 1.96652 | 0.983258 | − | 0.182217i | \(-0.0583275\pi\) | ||||
0.983258 | + | 0.182217i | \(0.0583275\pi\) | |||||||
\(132\) | −4.70156 | −0.409218 | ||||||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | −6.40312 | −0.553146 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.701562 | −0.0601585 | ||||||||
\(137\) | −13.7016 | −1.17060 | −0.585302 | − | 0.810816i | \(-0.699024\pi\) | ||||
−0.585302 | + | 0.810816i | \(0.699024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.40312 | 0.797563 | 0.398781 | − | 0.917046i | \(-0.369433\pi\) | ||||
0.398781 | + | 0.917046i | \(0.369433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 1.70156 | 0.142792 | ||||||||
\(143\) | 4.70156 | 0.393164 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | −15.1047 | −1.24581 | ||||||||
\(148\) | 1.70156 | 0.139868 | ||||||||
\(149\) | 6.59688 | 0.540437 | 0.270219 | − | 0.962799i | \(-0.412904\pi\) | ||||
0.270219 | + | 0.962799i | \(0.412904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1047 | −1.14782 | −0.573912 | − | 0.818917i | \(-0.694575\pi\) | ||||
−0.573912 | + | 0.818917i | \(0.694575\pi\) | |||||||
\(152\) | 1.70156 | 0.138015 | ||||||||
\(153\) | 0.701562 | 0.0567179 | ||||||||
\(154\) | 22.1047 | 1.78125 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 22.7016 | 1.81178 | 0.905891 | − | 0.423511i | \(-0.139203\pi\) | ||||
0.905891 | + | 0.423511i | \(0.139203\pi\) | |||||||
\(158\) | 5.70156 | 0.453592 | ||||||||
\(159\) | 2.40312 | 0.190580 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 18.8062 | 1.47302 | 0.736510 | − | 0.676427i | \(-0.236473\pi\) | ||||
0.736510 | + | 0.676427i | \(0.236473\pi\) | |||||||
\(164\) | −3.70156 | −0.289043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7016 | −0.830602 | ||||||||
\(167\) | 1.10469 | 0.0854832 | 0.0427416 | − | 0.999086i | \(-0.486391\pi\) | ||||
0.0427416 | + | 0.999086i | \(0.486391\pi\) | |||||||
\(168\) | −4.70156 | −0.362733 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.70156 | −0.130122 | ||||||||
\(172\) | 11.4031 | 0.869480 | ||||||||
\(173\) | 0.193752 | 0.0147307 | 0.00736533 | − | 0.999973i | \(-0.497656\pi\) | ||||
0.00736533 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(174\) | −6.40312 | −0.485420 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.70156 | 0.354394 | ||||||||
\(177\) | −2.70156 | −0.203062 | ||||||||
\(178\) | −11.4031 | −0.854700 | ||||||||
\(179\) | −24.2094 | −1.80949 | −0.904747 | − | 0.425950i | \(-0.859940\pi\) | ||||
−0.904747 | + | 0.425950i | \(0.859940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2984 | 0.839806 | 0.419903 | − | 0.907569i | \(-0.362064\pi\) | ||||
0.419903 | + | 0.907569i | \(0.362064\pi\) | |||||||
\(182\) | 4.70156 | 0.348503 | ||||||||
\(183\) | −14.1047 | −1.04265 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.1047 | −0.740912 | ||||||||
\(187\) | 3.29844 | 0.241206 | ||||||||
\(188\) | −7.00000 | −0.510527 | ||||||||
\(189\) | 4.70156 | 0.341988 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8062 | −0.926628 | −0.463314 | − | 0.886194i | \(-0.653340\pi\) | ||||
−0.463314 | + | 0.886194i | \(0.653340\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −16.2094 | −1.16678 | −0.583388 | − | 0.812194i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812194i | \(0.698273\pi\) | |||||||
\(194\) | −2.59688 | −0.186445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.1047 | 1.07891 | ||||||||
\(197\) | 5.40312 | 0.384957 | 0.192478 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192478 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(198\) | −4.70156 | −0.334125 | ||||||||
\(199\) | 8.29844 | 0.588261 | 0.294130 | − | 0.955765i | \(-0.404970\pi\) | ||||
0.294130 | + | 0.955765i | \(0.404970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.40312 | −0.451642 | ||||||||
\(202\) | −6.70156 | −0.471520 | ||||||||
\(203\) | 30.1047 | 2.11293 | ||||||||
\(204\) | −0.701562 | −0.0491192 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.40312 | 0.0977603 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.80625 | 0.468561 | 0.234281 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234281 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(212\) | −2.40312 | −0.165047 | ||||||||
\(213\) | 1.70156 | 0.116589 | ||||||||
\(214\) | 19.1047 | 1.30597 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 47.5078 | 3.22504 | ||||||||
\(218\) | −4.29844 | −0.291127 | ||||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.701562 | 0.0471922 | ||||||||
\(222\) | 1.70156 | 0.114201 | ||||||||
\(223\) | −11.4031 | −0.763610 | −0.381805 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381805 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(224\) | 4.70156 | 0.314136 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 16.1047 | 1.06891 | 0.534453 | − | 0.845198i | \(-0.320518\pi\) | ||||
0.534453 | + | 0.845198i | \(0.320518\pi\) | |||||||
\(228\) | 1.70156 | 0.112689 | ||||||||
\(229\) | 15.7016 | 1.03759 | 0.518794 | − | 0.854899i | \(-0.326381\pi\) | ||||
0.518794 | + | 0.854899i | \(0.326381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.1047 | 1.45438 | ||||||||
\(232\) | 6.40312 | 0.420386 | ||||||||
\(233\) | 20.2094 | 1.32396 | 0.661980 | − | 0.749521i | \(-0.269716\pi\) | ||||
0.661980 | + | 0.749521i | \(0.269716\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.70156 | 0.175857 | ||||||||
\(237\) | 5.70156 | 0.370356 | ||||||||
\(238\) | 3.29844 | 0.213806 | ||||||||
\(239\) | 6.10469 | 0.394879 | 0.197440 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197440 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.59688 | −0.167279 | −0.0836397 | − | 0.996496i | \(-0.526654\pi\) | ||||
−0.0836397 | + | 0.996496i | \(0.526654\pi\) | |||||||
\(242\) | −11.1047 | −0.713836 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.1047 | 0.902960 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.70156 | −0.236003 | ||||||||
\(247\) | −1.70156 | −0.108268 | ||||||||
\(248\) | 10.1047 | 0.641648 | ||||||||
\(249\) | −10.7016 | −0.678184 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.298438 | 0.0188372 | 0.00941862 | − | 0.999956i | \(-0.497002\pi\) | ||||
0.00941862 | + | 0.999956i | \(0.497002\pi\) | |||||||
\(252\) | −4.70156 | −0.296171 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.29844 | −0.395199 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.2984 | 0.954290 | 0.477145 | − | 0.878824i | \(-0.341672\pi\) | ||||
0.477145 | + | 0.878824i | \(0.341672\pi\) | |||||||
\(258\) | 11.4031 | 0.709928 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.40312 | −0.396343 | ||||||||
\(262\) | −22.5078 | −1.39054 | ||||||||
\(263\) | −2.00000 | −0.123325 | −0.0616626 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616626 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(264\) | 4.70156 | 0.289361 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.00000 | −0.490511 | ||||||||
\(267\) | −11.4031 | −0.697860 | ||||||||
\(268\) | 6.40312 | 0.391133 | ||||||||
\(269\) | 31.2094 | 1.90287 | 0.951435 | − | 0.307851i | \(-0.0996099\pi\) | ||||
0.951435 | + | 0.307851i | \(0.0996099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5078 | 1.18502 | 0.592508 | − | 0.805565i | \(-0.298138\pi\) | ||||
0.592508 | + | 0.805565i | \(0.298138\pi\) | |||||||
\(272\) | 0.701562 | 0.0425385 | ||||||||
\(273\) | 4.70156 | 0.284551 | ||||||||
\(274\) | 13.7016 | 0.827742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | −9.40312 | −0.563962 | ||||||||
\(279\) | −10.1047 | −0.604952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.9109 | −1.30710 | −0.653548 | − | 0.756885i | \(-0.726720\pi\) | ||||
−0.653548 | + | 0.756885i | \(0.726720\pi\) | |||||||
\(282\) | −7.00000 | −0.416844 | ||||||||
\(283\) | −21.4031 | −1.27228 | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||||
−0.636142 | + | 0.771572i | \(0.719471\pi\) | |||||||
\(284\) | −1.70156 | −0.100969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.70156 | −0.278009 | ||||||||
\(287\) | 17.4031 | 1.02727 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.5078 | −0.971048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.59688 | −0.152232 | ||||||||
\(292\) | 12.0000 | 0.702247 | ||||||||
\(293\) | −21.4031 | −1.25038 | −0.625192 | − | 0.780471i | \(-0.714979\pi\) | ||||
−0.625192 | + | 0.780471i | \(0.714979\pi\) | |||||||
\(294\) | 15.1047 | 0.880923 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.70156 | −0.0989013 | ||||||||
\(297\) | −4.70156 | −0.272812 | ||||||||
\(298\) | −6.59688 | −0.382147 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.6125 | −3.09017 | ||||||||
\(302\) | 14.1047 | 0.811633 | ||||||||
\(303\) | −6.70156 | −0.384995 | ||||||||
\(304\) | −1.70156 | −0.0975913 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.701562 | −0.0401056 | ||||||||
\(307\) | 5.70156 | 0.325405 | 0.162703 | − | 0.986675i | \(-0.447979\pi\) | ||||
0.162703 | + | 0.986675i | \(0.447979\pi\) | |||||||
\(308\) | −22.1047 | −1.25953 | ||||||||
\(309\) | 1.40312 | 0.0798209 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 21.2094 | 1.19882 | 0.599412 | − | 0.800440i | \(-0.295401\pi\) | ||||
0.599412 | + | 0.800440i | \(0.295401\pi\) | |||||||
\(314\) | −22.7016 | −1.28112 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.70156 | −0.320738 | ||||||||
\(317\) | −1.19375 | −0.0670478 | −0.0335239 | − | 0.999438i | \(-0.510673\pi\) | ||||
−0.0335239 | + | 0.999438i | \(0.510673\pi\) | |||||||
\(318\) | −2.40312 | −0.134761 | ||||||||
\(319\) | −30.1047 | −1.68554 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.1047 | 1.06632 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.19375 | −0.0664221 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.8062 | −1.04158 | ||||||||
\(327\) | −4.29844 | −0.237704 | ||||||||
\(328\) | 3.70156 | 0.204385 | ||||||||
\(329\) | 32.9109 | 1.81444 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 10.7016 | 0.587325 | ||||||||
\(333\) | 1.70156 | 0.0932450 | ||||||||
\(334\) | −1.10469 | −0.0604457 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.70156 | 0.256491 | ||||||||
\(337\) | −8.10469 | −0.441490 | −0.220745 | − | 0.975332i | \(-0.570849\pi\) | ||||
−0.220745 | + | 0.975332i | \(0.570849\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −14.0000 | −0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −47.5078 | −2.57269 | ||||||||
\(342\) | 1.70156 | 0.0920099 | ||||||||
\(343\) | −38.1047 | −2.05746 | ||||||||
\(344\) | −11.4031 | −0.614815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.193752 | −0.0104161 | ||||||||
\(347\) | −10.5078 | −0.564089 | −0.282044 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282044 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(348\) | 6.40312 | 0.343243 | ||||||||
\(349\) | −11.4031 | −0.610395 | −0.305198 | − | 0.952289i | \(-0.598723\pi\) | ||||
−0.305198 | + | 0.952289i | \(0.598723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.70156 | −0.250594 | ||||||||
\(353\) | −14.5078 | −0.772173 | −0.386086 | − | 0.922463i | \(-0.626173\pi\) | ||||
−0.386086 | + | 0.922463i | \(0.626173\pi\) | |||||||
\(354\) | 2.70156 | 0.143586 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.4031 | 0.604364 | ||||||||
\(357\) | 3.29844 | 0.174572 | ||||||||
\(358\) | 24.2094 | 1.27951 | ||||||||
\(359\) | −34.6125 | −1.82678 | −0.913389 | − | 0.407088i | \(-0.866544\pi\) | ||||
−0.913389 | + | 0.407088i | \(0.866544\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1047 | −0.847615 | ||||||||
\(362\) | −11.2984 | −0.593833 | ||||||||
\(363\) | −11.1047 | −0.582845 | ||||||||
\(364\) | −4.70156 | −0.246429 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.1047 | 0.737264 | ||||||||
\(367\) | 2.29844 | 0.119977 | 0.0599887 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599887 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.70156 | −0.192696 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2984 | 0.586586 | ||||||||
\(372\) | 10.1047 | 0.523904 | ||||||||
\(373\) | −5.29844 | −0.274343 | −0.137171 | − | 0.990547i | \(-0.543801\pi\) | ||||
−0.137171 | + | 0.990547i | \(0.543801\pi\) | |||||||
\(374\) | −3.29844 | −0.170558 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | −6.40312 | −0.329778 | ||||||||
\(378\) | −4.70156 | −0.241822 | ||||||||
\(379\) | −13.8953 | −0.713754 | −0.356877 | − | 0.934151i | \(-0.616159\pi\) | ||||
−0.356877 | + | 0.934151i | \(0.616159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.29844 | −0.322679 | ||||||||
\(382\) | 12.8062 | 0.655225 | ||||||||
\(383\) | −32.5078 | −1.66107 | −0.830536 | − | 0.556965i | \(-0.811966\pi\) | ||||
−0.830536 | + | 0.556965i | \(0.811966\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.2094 | 0.825035 | ||||||||
\(387\) | 11.4031 | 0.579653 | ||||||||
\(388\) | 2.59688 | 0.131836 | ||||||||
\(389\) | −27.1047 | −1.37426 | −0.687131 | − | 0.726533i | \(-0.741130\pi\) | ||||
−0.687131 | + | 0.726533i | \(0.741130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −15.1047 | −0.762902 | ||||||||
\(393\) | −22.5078 | −1.13537 | ||||||||
\(394\) | −5.40312 | −0.272205 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.70156 | 0.236262 | ||||||||
\(397\) | 21.9109 | 1.09968 | 0.549839 | − | 0.835271i | \(-0.314689\pi\) | ||||
0.549839 | + | 0.835271i | \(0.314689\pi\) | |||||||
\(398\) | −8.29844 | −0.415963 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2094 | 0.909333 | 0.454666 | − | 0.890662i | \(-0.349759\pi\) | ||||
0.454666 | + | 0.890662i | \(0.349759\pi\) | |||||||
\(402\) | 6.40312 | 0.319359 | ||||||||
\(403\) | −10.1047 | −0.503350 | ||||||||
\(404\) | 6.70156 | 0.333415 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.1047 | −1.49407 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0.701562 | 0.0347325 | ||||||||
\(409\) | 29.4031 | 1.45389 | 0.726945 | − | 0.686695i | \(-0.240939\pi\) | ||||
0.726945 | + | 0.686695i | \(0.240939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.7016 | 0.675848 | ||||||||
\(412\) | −1.40312 | −0.0691270 | ||||||||
\(413\) | −12.7016 | −0.625003 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −9.40312 | −0.460473 | ||||||||
\(418\) | 8.00000 | 0.391293 | ||||||||
\(419\) | 9.91093 | 0.484181 | 0.242090 | − | 0.970254i | \(-0.422167\pi\) | ||||
0.242090 | + | 0.970254i | \(0.422167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.596876 | −0.0290899 | −0.0145450 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145450 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(422\) | −6.80625 | −0.331323 | ||||||||
\(423\) | −7.00000 | −0.340352 | ||||||||
\(424\) | 2.40312 | 0.116706 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.70156 | −0.0824410 | ||||||||
\(427\) | −66.3141 | −3.20916 | ||||||||
\(428\) | −19.1047 | −0.923460 | ||||||||
\(429\) | −4.70156 | −0.226994 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.3141 | 1.70102 | 0.850509 | − | 0.525960i | \(-0.176294\pi\) | ||||
0.850509 | + | 0.525960i | \(0.176294\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 11.1047 | 0.533657 | 0.266829 | − | 0.963744i | \(-0.414024\pi\) | ||||
0.266829 | + | 0.963744i | \(0.414024\pi\) | |||||||
\(434\) | −47.5078 | −2.28045 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.29844 | 0.205858 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.0000 | 0.573382 | ||||||||
\(439\) | −10.2984 | −0.491518 | −0.245759 | − | 0.969331i | \(-0.579037\pi\) | ||||
−0.245759 | + | 0.969331i | \(0.579037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.1047 | 0.719271 | ||||||||
\(442\) | −0.701562 | −0.0333699 | ||||||||
\(443\) | −32.5078 | −1.54449 | −0.772246 | − | 0.635323i | \(-0.780867\pi\) | ||||
−0.772246 | + | 0.635323i | \(0.780867\pi\) | |||||||
\(444\) | −1.70156 | −0.0807526 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.4031 | 0.539954 | ||||||||
\(447\) | −6.59688 | −0.312022 | ||||||||
\(448\) | −4.70156 | −0.222128 | ||||||||
\(449\) | 2.29844 | 0.108470 | 0.0542350 | − | 0.998528i | \(-0.482728\pi\) | ||||
0.0542350 | + | 0.998528i | \(0.482728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.4031 | −0.819481 | ||||||||
\(452\) | 14.0000 | 0.658505 | ||||||||
\(453\) | 14.1047 | 0.662696 | ||||||||
\(454\) | −16.1047 | −0.755830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.70156 | −0.0796829 | ||||||||
\(457\) | 2.59688 | 0.121477 | 0.0607384 | − | 0.998154i | \(-0.480654\pi\) | ||||
0.0607384 | + | 0.998154i | \(0.480654\pi\) | |||||||
\(458\) | −15.7016 | −0.733686 | ||||||||
\(459\) | −0.701562 | −0.0327461 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.2094 | 1.68644 | 0.843219 | − | 0.537570i | \(-0.180658\pi\) | ||||
0.843219 | + | 0.537570i | \(0.180658\pi\) | |||||||
\(462\) | −22.1047 | −1.02840 | ||||||||
\(463\) | 21.2984 | 0.989822 | 0.494911 | − | 0.868944i | \(-0.335201\pi\) | ||||
0.494911 | + | 0.868944i | \(0.335201\pi\) | |||||||
\(464\) | −6.40312 | −0.297258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.2094 | −0.936181 | ||||||||
\(467\) | −30.2984 | −1.40204 | −0.701022 | − | 0.713139i | \(-0.747273\pi\) | ||||
−0.701022 | + | 0.713139i | \(0.747273\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −30.1047 | −1.39011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.7016 | −1.04603 | ||||||||
\(472\) | −2.70156 | −0.124349 | ||||||||
\(473\) | 53.6125 | 2.46511 | ||||||||
\(474\) | −5.70156 | −0.261881 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.29844 | −0.151184 | ||||||||
\(477\) | −2.40312 | −0.110032 | ||||||||
\(478\) | −6.10469 | −0.279222 | ||||||||
\(479\) | −40.6125 | −1.85563 | −0.927816 | − | 0.373038i | \(-0.878316\pi\) | ||||
−0.927816 | + | 0.373038i | \(0.878316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.70156 | 0.0775846 | ||||||||
\(482\) | 2.59688 | 0.118284 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1047 | 0.504758 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 7.89531 | 0.357771 | 0.178885 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(488\) | −14.1047 | −0.638489 | ||||||||
\(489\) | −18.8062 | −0.850448 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.4031 | 1.50746 | 0.753731 | − | 0.657183i | \(-0.228252\pi\) | ||||
0.753731 | + | 0.657183i | \(0.228252\pi\) | |||||||
\(492\) | 3.70156 | 0.166879 | ||||||||
\(493\) | −4.49219 | −0.202318 | ||||||||
\(494\) | 1.70156 | 0.0765569 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1047 | −0.453714 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 10.7016 | 0.479548 | ||||||||
\(499\) | 17.2094 | 0.770397 | 0.385199 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385199 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.10469 | −0.0493537 | ||||||||
\(502\) | −0.298438 | −0.0133199 | ||||||||
\(503\) | 12.2094 | 0.544389 | 0.272195 | − | 0.962242i | \(-0.412251\pi\) | ||||
0.272195 | + | 0.962242i | \(0.412251\pi\) | |||||||
\(504\) | 4.70156 | 0.209424 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.29844 | 0.279448 | ||||||||
\(509\) | −5.40312 | −0.239489 | −0.119745 | − | 0.992805i | \(-0.538208\pi\) | ||||
−0.119745 | + | 0.992805i | \(0.538208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.4187 | −2.49582 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.70156 | 0.0751258 | ||||||||
\(514\) | −15.2984 | −0.674785 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.4031 | −0.501995 | ||||||||
\(517\) | −32.9109 | −1.44742 | ||||||||
\(518\) | 8.00000 | 0.351500 | ||||||||
\(519\) | −0.193752 | −0.00850475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.2094 | −1.58636 | −0.793181 | − | 0.608986i | \(-0.791576\pi\) | ||||
−0.793181 | + | 0.608986i | \(0.791576\pi\) | |||||||
\(522\) | 6.40312 | 0.280257 | ||||||||
\(523\) | 24.8062 | 1.08470 | 0.542351 | − | 0.840152i | \(-0.317534\pi\) | ||||
0.542351 | + | 0.840152i | \(0.317534\pi\) | |||||||
\(524\) | 22.5078 | 0.983258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | −7.08907 | −0.308805 | ||||||||
\(528\) | −4.70156 | −0.204609 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.70156 | 0.117238 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | −3.70156 | −0.160332 | ||||||||
\(534\) | 11.4031 | 0.493461 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.40312 | −0.276573 | ||||||||
\(537\) | 24.2094 | 1.04471 | ||||||||
\(538\) | −31.2094 | −1.34553 | ||||||||
\(539\) | 71.0156 | 3.05886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.79063 | −0.0769851 | −0.0384925 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384925 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(542\) | −19.5078 | −0.837932 | ||||||||
\(543\) | −11.2984 | −0.484862 | ||||||||
\(544\) | −0.701562 | −0.0300792 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.70156 | −0.201208 | ||||||||
\(547\) | 31.6125 | 1.35165 | 0.675826 | − | 0.737061i | \(-0.263787\pi\) | ||||
0.675826 | + | 0.737061i | \(0.263787\pi\) | |||||||
\(548\) | −13.7016 | −0.585302 | ||||||||
\(549\) | 14.1047 | 0.601973 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8953 | 0.464156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8062 | 1.13992 | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.40312 | 0.398781 | ||||||||
\(557\) | −16.8062 | −0.712104 | −0.356052 | − | 0.934466i | \(-0.615877\pi\) | ||||
−0.356052 | + | 0.934466i | \(0.615877\pi\) | |||||||
\(558\) | 10.1047 | 0.427765 | ||||||||
\(559\) | 11.4031 | 0.482301 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.29844 | −0.139260 | ||||||||
\(562\) | 21.9109 | 0.924257 | ||||||||
\(563\) | 32.5078 | 1.37004 | 0.685020 | − | 0.728524i | \(-0.259793\pi\) | ||||
0.685020 | + | 0.728524i | \(0.259793\pi\) | |||||||
\(564\) | 7.00000 | 0.294753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.4031 | 0.899640 | ||||||||
\(567\) | −4.70156 | −0.197447 | ||||||||
\(568\) | 1.70156 | 0.0713960 | ||||||||
\(569\) | −11.2984 | −0.473655 | −0.236828 | − | 0.971552i | \(-0.576108\pi\) | ||||
−0.236828 | + | 0.971552i | \(0.576108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 4.70156 | 0.196582 | ||||||||
\(573\) | 12.8062 | 0.534989 | ||||||||
\(574\) | −17.4031 | −0.726392 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −24.2094 | −1.00785 | −0.503925 | − | 0.863748i | \(-0.668111\pi\) | ||||
−0.503925 | + | 0.863748i | \(0.668111\pi\) | |||||||
\(578\) | 16.5078 | 0.686634 | ||||||||
\(579\) | 16.2094 | 0.673639 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.3141 | −2.08738 | ||||||||
\(582\) | 2.59688 | 0.107644 | ||||||||
\(583\) | −11.2984 | −0.467933 | ||||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4031 | 0.884155 | ||||||||
\(587\) | 7.50781 | 0.309881 | 0.154940 | − | 0.987924i | \(-0.450481\pi\) | ||||
0.154940 | + | 0.987924i | \(0.450481\pi\) | |||||||
\(588\) | −15.1047 | −0.622907 | ||||||||
\(589\) | 17.1938 | 0.708456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.40312 | −0.222255 | ||||||||
\(592\) | 1.70156 | 0.0699338 | ||||||||
\(593\) | −17.9109 | −0.735514 | −0.367757 | − | 0.929922i | \(-0.619874\pi\) | ||||
−0.367757 | + | 0.929922i | \(0.619874\pi\) | |||||||
\(594\) | 4.70156 | 0.192907 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.59688 | 0.270219 | ||||||||
\(597\) | −8.29844 | −0.339632 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.20937 | 0.335426 | 0.167713 | − | 0.985836i | \(-0.446362\pi\) | ||||
0.167713 | + | 0.985836i | \(0.446362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6125 | 0.432893 | 0.216446 | − | 0.976295i | \(-0.430553\pi\) | ||||
0.216446 | + | 0.976295i | \(0.430553\pi\) | |||||||
\(602\) | 53.6125 | 2.18508 | ||||||||
\(603\) | 6.40312 | 0.260755 | ||||||||
\(604\) | −14.1047 | −0.573912 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.70156 | 0.272232 | ||||||||
\(607\) | 35.1047 | 1.42486 | 0.712428 | − | 0.701746i | \(-0.247596\pi\) | ||||
0.712428 | + | 0.701746i | \(0.247596\pi\) | |||||||
\(608\) | 1.70156 | 0.0690075 | ||||||||
\(609\) | −30.1047 | −1.21990 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | −0.283190 | ||||||||
\(612\) | 0.701562 | 0.0283590 | ||||||||
\(613\) | 12.8062 | 0.517240 | 0.258620 | − | 0.965979i | \(-0.416732\pi\) | ||||
0.258620 | + | 0.965979i | \(0.416732\pi\) | |||||||
\(614\) | −5.70156 | −0.230096 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.1047 | 0.890623 | ||||||||
\(617\) | 27.1047 | 1.09119 | 0.545597 | − | 0.838048i | \(-0.316303\pi\) | ||||
0.545597 | + | 0.838048i | \(0.316303\pi\) | |||||||
\(618\) | −1.40312 | −0.0564419 | ||||||||
\(619\) | −13.1938 | −0.530302 | −0.265151 | − | 0.964207i | \(-0.585422\pi\) | ||||
−0.265151 | + | 0.964207i | \(0.585422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.0000 | −1.20289 | ||||||||
\(623\) | −53.6125 | −2.14794 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.2094 | −0.847697 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | 22.7016 | 0.905891 | ||||||||
\(629\) | 1.19375 | 0.0475980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6125 | 1.33809 | 0.669046 | − | 0.743221i | \(-0.266703\pi\) | ||||
0.669046 | + | 0.743221i | \(0.266703\pi\) | |||||||
\(632\) | 5.70156 | 0.226796 | ||||||||
\(633\) | −6.80625 | −0.270524 | ||||||||
\(634\) | 1.19375 | 0.0474099 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.40312 | 0.0952901 | ||||||||
\(637\) | 15.1047 | 0.598469 | ||||||||
\(638\) | 30.1047 | 1.19186 | ||||||||
\(639\) | −1.70156 | −0.0673128 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.50781 | 0.217545 | 0.108773 | − | 0.994067i | \(-0.465308\pi\) | ||||
0.108773 | + | 0.994067i | \(0.465308\pi\) | |||||||
\(642\) | −19.1047 | −0.754002 | ||||||||
\(643\) | 10.2984 | 0.406131 | 0.203065 | − | 0.979165i | \(-0.434910\pi\) | ||||
0.203065 | + | 0.979165i | \(0.434910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.19375 | 0.0469675 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 12.7016 | 0.498580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −47.5078 | −1.86198 | ||||||||
\(652\) | 18.8062 | 0.736510 | ||||||||
\(653\) | 21.2984 | 0.833472 | 0.416736 | − | 0.909027i | \(-0.363174\pi\) | ||||
0.416736 | + | 0.909027i | \(0.363174\pi\) | |||||||
\(654\) | 4.29844 | 0.168082 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.70156 | −0.144522 | ||||||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | −32.9109 | −1.28300 | ||||||||
\(659\) | −19.3141 | −0.752369 | −0.376184 | − | 0.926545i | \(-0.622764\pi\) | ||||
−0.376184 | + | 0.926545i | \(0.622764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1203 | −1.56050 | −0.780250 | − | 0.625468i | \(-0.784908\pi\) | ||||
−0.780250 | + | 0.625468i | \(0.784908\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | −0.701562 | −0.0272464 | ||||||||
\(664\) | −10.7016 | −0.415301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70156 | −0.0659342 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.10469 | 0.0427416 | ||||||||
\(669\) | 11.4031 | 0.440870 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 66.3141 | 2.56003 | ||||||||
\(672\) | −4.70156 | −0.181367 | ||||||||
\(673\) | −36.0156 | −1.38830 | −0.694150 | − | 0.719830i | \(-0.744220\pi\) | ||||
−0.694150 | + | 0.719830i | \(0.744220\pi\) | |||||||
\(674\) | 8.10469 | 0.312181 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −31.6125 | −1.21497 | −0.607483 | − | 0.794332i | \(-0.707821\pi\) | ||||
−0.607483 | + | 0.794332i | \(0.707821\pi\) | |||||||
\(678\) | 14.0000 | 0.537667 | ||||||||
\(679\) | −12.2094 | −0.468553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.1047 | −0.617133 | ||||||||
\(682\) | 47.5078 | 1.81917 | ||||||||
\(683\) | −44.7016 | −1.71046 | −0.855229 | − | 0.518251i | \(-0.826583\pi\) | ||||
−0.855229 | + | 0.518251i | \(0.826583\pi\) | |||||||
\(684\) | −1.70156 | −0.0650609 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 38.1047 | 1.45484 | ||||||||
\(687\) | −15.7016 | −0.599052 | ||||||||
\(688\) | 11.4031 | 0.434740 | ||||||||
\(689\) | −2.40312 | −0.0915517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1938 | −0.844290 | −0.422145 | − | 0.906528i | \(-0.638723\pi\) | ||||
−0.422145 | + | 0.906528i | \(0.638723\pi\) | |||||||
\(692\) | 0.193752 | 0.00736533 | ||||||||
\(693\) | −22.1047 | −0.839688 | ||||||||
\(694\) | 10.5078 | 0.398871 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.40312 | −0.242710 | ||||||||
\(697\) | −2.59688 | −0.0983637 | ||||||||
\(698\) | 11.4031 | 0.431615 | ||||||||
\(699\) | −20.2094 | −0.764389 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9109 | 1.16749 | 0.583745 | − | 0.811937i | \(-0.301587\pi\) | ||||
0.583745 | + | 0.811937i | \(0.301587\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −2.89531 | −0.109199 | ||||||||
\(704\) | 4.70156 | 0.177197 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5078 | 0.546009 | ||||||||
\(707\) | −31.5078 | −1.18497 | ||||||||
\(708\) | −2.70156 | −0.101531 | ||||||||
\(709\) | 15.6125 | 0.586340 | 0.293170 | − | 0.956060i | \(-0.405290\pi\) | ||||
0.293170 | + | 0.956060i | \(0.405290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.70156 | −0.213825 | ||||||||
\(712\) | −11.4031 | −0.427350 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −3.29844 | −0.123441 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.2094 | −0.904747 | ||||||||
\(717\) | −6.10469 | −0.227984 | ||||||||
\(718\) | 34.6125 | 1.29173 | ||||||||
\(719\) | −11.0156 | −0.410813 | −0.205407 | − | 0.978677i | \(-0.565852\pi\) | ||||
−0.205407 | + | 0.978677i | \(0.565852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.59688 | 0.245680 | ||||||||
\(722\) | 16.1047 | 0.599354 | ||||||||
\(723\) | 2.59688 | 0.0965788 | ||||||||
\(724\) | 11.2984 | 0.419903 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.1047 | 0.412134 | ||||||||
\(727\) | −7.79063 | −0.288938 | −0.144469 | − | 0.989509i | \(-0.546147\pi\) | ||||
−0.144469 | + | 0.989509i | \(0.546147\pi\) | |||||||
\(728\) | 4.70156 | 0.174251 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | −14.1047 | −0.521324 | ||||||||
\(733\) | −47.9109 | −1.76963 | −0.884815 | − | 0.465942i | \(-0.845716\pi\) | ||||
−0.884815 | + | 0.465942i | \(0.845716\pi\) | |||||||
\(734\) | −2.29844 | −0.0848369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1047 | 1.10892 | ||||||||
\(738\) | 3.70156 | 0.136256 | ||||||||
\(739\) | 4.61250 | 0.169673 | 0.0848367 | − | 0.996395i | \(-0.472963\pi\) | ||||
0.0848367 | + | 0.996395i | \(0.472963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.70156 | 0.0625084 | ||||||||
\(742\) | −11.2984 | −0.414779 | ||||||||
\(743\) | 30.6125 | 1.12306 | 0.561532 | − | 0.827455i | \(-0.310212\pi\) | ||||
0.561532 | + | 0.827455i | \(0.310212\pi\) | |||||||
\(744\) | −10.1047 | −0.370456 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.29844 | 0.193990 | ||||||||
\(747\) | 10.7016 | 0.391550 | ||||||||
\(748\) | 3.29844 | 0.120603 | ||||||||
\(749\) | 89.8219 | 3.28202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50781 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(752\) | −7.00000 | −0.255264 | ||||||||
\(753\) | −0.298438 | −0.0108757 | ||||||||
\(754\) | 6.40312 | 0.233188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.70156 | 0.170994 | ||||||||
\(757\) | 17.8953 | 0.650416 | 0.325208 | − | 0.945642i | \(-0.394566\pi\) | ||||
0.325208 | + | 0.945642i | \(0.394566\pi\) | |||||||
\(758\) | 13.8953 | 0.504701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.7172 | −0.968497 | −0.484249 | − | 0.874930i | \(-0.660907\pi\) | ||||
−0.484249 | + | 0.874930i | \(0.660907\pi\) | |||||||
\(762\) | 6.29844 | 0.228168 | ||||||||
\(763\) | −20.2094 | −0.731628 | ||||||||
\(764\) | −12.8062 | −0.463314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5078 | 1.17455 | ||||||||
\(767\) | 2.70156 | 0.0975478 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −8.00000 | −0.288487 | −0.144244 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144244 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2984 | −0.550960 | ||||||||
\(772\) | −16.2094 | −0.583388 | ||||||||
\(773\) | −26.5969 | −0.956623 | −0.478312 | − | 0.878190i | \(-0.658751\pi\) | ||||
−0.478312 | + | 0.878190i | \(0.658751\pi\) | |||||||
\(774\) | −11.4031 | −0.409877 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.59688 | −0.0932224 | ||||||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | 27.1047 | 0.971750 | ||||||||
\(779\) | 6.29844 | 0.225665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.40312 | 0.228829 | ||||||||
\(784\) | 15.1047 | 0.539453 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22.5078 | 0.802827 | ||||||||
\(787\) | −33.8953 | −1.20824 | −0.604119 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604119 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(788\) | 5.40312 | 0.192478 | ||||||||
\(789\) | 2.00000 | 0.0712019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.8219 | −2.34036 | ||||||||
\(792\) | −4.70156 | −0.167063 | ||||||||
\(793\) | 14.1047 | 0.500872 | ||||||||
\(794\) | −21.9109 | −0.777590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.29844 | 0.294130 | ||||||||
\(797\) | −2.91093 | −0.103111 | −0.0515553 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515553 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(798\) | 8.00000 | 0.283197 | ||||||||
\(799\) | −4.91093 | −0.173736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4031 | 0.402910 | ||||||||
\(802\) | −18.2094 | −0.642995 | ||||||||
\(803\) | 56.4187 | 1.99097 | ||||||||
\(804\) | −6.40312 | −0.225821 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.1047 | 0.355922 | ||||||||
\(807\) | −31.2094 | −1.09862 | ||||||||
\(808\) | −6.70156 | −0.235760 | ||||||||
\(809\) | 7.19375 | 0.252919 | 0.126459 | − | 0.991972i | \(-0.459639\pi\) | ||||
0.126459 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.7016 | 1.71014 | 0.855072 | − | 0.518510i | \(-0.173513\pi\) | ||||
0.855072 | + | 0.518510i | \(0.173513\pi\) | |||||||
\(812\) | 30.1047 | 1.05647 | ||||||||
\(813\) | −19.5078 | −0.684169 | ||||||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.701562 | −0.0245596 | ||||||||
\(817\) | −19.4031 | −0.678829 | ||||||||
\(818\) | −29.4031 | −1.02806 | ||||||||
\(819\) | −4.70156 | −0.164286 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.5969 | −0.718836 | −0.359418 | − | 0.933177i | \(-0.617025\pi\) | ||||
−0.359418 | + | 0.933177i | \(0.617025\pi\) | |||||||
\(822\) | −13.7016 | −0.477897 | ||||||||
\(823\) | −17.1047 | −0.596232 | −0.298116 | − | 0.954530i | \(-0.596358\pi\) | ||||
−0.298116 | + | 0.954530i | \(0.596358\pi\) | |||||||
\(824\) | 1.40312 | 0.0488801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.7016 | 0.441944 | ||||||||
\(827\) | −20.7016 | −0.719864 | −0.359932 | − | 0.932979i | \(-0.617200\pi\) | ||||
−0.359932 | + | 0.932979i | \(0.617200\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50781 | −0.191294 | −0.0956471 | − | 0.995415i | \(-0.530492\pi\) | ||||
−0.0956471 | + | 0.995415i | \(0.530492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.0000 | −0.763172 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 10.5969 | 0.367160 | ||||||||
\(834\) | 9.40312 | 0.325604 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.00000 | −0.276686 | ||||||||
\(837\) | 10.1047 | 0.349269 | ||||||||
\(838\) | −9.91093 | −0.342368 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0000 | 0.413793 | ||||||||
\(842\) | 0.596876 | 0.0205697 | ||||||||
\(843\) | 21.9109 | 0.754653 | ||||||||
\(844\) | 6.80625 | 0.234281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | −52.2094 | −1.79394 | ||||||||
\(848\) | −2.40312 | −0.0825236 | ||||||||
\(849\) | 21.4031 | 0.734553 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.70156 | 0.0582946 | ||||||||
\(853\) | −0.507811 | −0.0173871 | −0.00869355 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869355 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(854\) | 66.3141 | 2.26922 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1047 | 0.652985 | ||||||||
\(857\) | 7.61250 | 0.260038 | 0.130019 | − | 0.991512i | \(-0.458496\pi\) | ||||
0.130019 | + | 0.991512i | \(0.458496\pi\) | |||||||
\(858\) | 4.70156 | 0.160509 | ||||||||
\(859\) | −6.20937 | −0.211861 | −0.105931 | − | 0.994374i | \(-0.533782\pi\) | ||||
−0.105931 | + | 0.994374i | \(0.533782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.4031 | −0.593097 | ||||||||
\(862\) | −35.3141 | −1.20280 | ||||||||
\(863\) | −54.2250 | −1.84584 | −0.922920 | − | 0.384991i | \(-0.874204\pi\) | ||||
−0.922920 | + | 0.384991i | \(0.874204\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.1047 | −0.377353 | ||||||||
\(867\) | 16.5078 | 0.560635 | ||||||||
\(868\) | 47.5078 | 1.61252 | ||||||||
\(869\) | −26.8062 | −0.909340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.40312 | 0.216962 | ||||||||
\(872\) | −4.29844 | −0.145563 | ||||||||
\(873\) | 2.59688 | 0.0878909 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | 42.7172 | 1.44246 | 0.721228 | − | 0.692697i | \(-0.243578\pi\) | ||||
0.721228 | + | 0.692697i | \(0.243578\pi\) | |||||||
\(878\) | 10.2984 | 0.347555 | ||||||||
\(879\) | 21.4031 | 0.721909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7172 | −1.33811 | −0.669053 | − | 0.743215i | \(-0.733300\pi\) | ||||
−0.669053 | + | 0.743215i | \(0.733300\pi\) | |||||||
\(882\) | −15.1047 | −0.508601 | ||||||||
\(883\) | −45.6125 | −1.53498 | −0.767491 | − | 0.641059i | \(-0.778495\pi\) | ||||
−0.767491 | + | 0.641059i | \(0.778495\pi\) | |||||||
\(884\) | 0.701562 | 0.0235961 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.5078 | 1.09212 | ||||||||
\(887\) | 20.0000 | 0.671534 | 0.335767 | − | 0.941945i | \(-0.391004\pi\) | ||||
0.335767 | + | 0.941945i | \(0.391004\pi\) | |||||||
\(888\) | 1.70156 | 0.0571007 | ||||||||
\(889\) | −29.6125 | −0.993171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.70156 | 0.157508 | ||||||||
\(892\) | −11.4031 | −0.381805 | ||||||||
\(893\) | 11.9109 | 0.398584 | ||||||||
\(894\) | 6.59688 | 0.220633 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.70156 | 0.157068 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.29844 | −0.0766999 | ||||||||
\(899\) | 64.7016 | 2.15792 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.68594 | −0.0561668 | ||||||||
\(902\) | 17.4031 | 0.579461 | ||||||||
\(903\) | 53.6125 | 1.78411 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.1047 | −0.468597 | ||||||||
\(907\) | 25.0156 | 0.830630 | 0.415315 | − | 0.909678i | \(-0.363671\pi\) | ||||
0.415315 | + | 0.909678i | \(0.363671\pi\) | |||||||
\(908\) | 16.1047 | 0.534453 | ||||||||
\(909\) | 6.70156 | 0.222277 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2094 | 1.39846 | 0.699229 | − | 0.714897i | \(-0.253527\pi\) | ||||
0.699229 | + | 0.714897i | \(0.253527\pi\) | |||||||
\(912\) | 1.70156 | 0.0563444 | ||||||||
\(913\) | 50.3141 | 1.66515 | ||||||||
\(914\) | −2.59688 | −0.0858970 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.7016 | 0.518794 | ||||||||
\(917\) | −105.822 | −3.49455 | ||||||||
\(918\) | 0.701562 | 0.0231550 | ||||||||
\(919\) | −4.89531 | −0.161481 | −0.0807407 | − | 0.996735i | \(-0.525729\pi\) | ||||
−0.0807407 | + | 0.996735i | \(0.525729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.70156 | −0.187873 | ||||||||
\(922\) | −36.2094 | −1.19249 | ||||||||
\(923\) | −1.70156 | −0.0560076 | ||||||||
\(924\) | 22.1047 | 0.727191 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.2984 | −0.699910 | ||||||||
\(927\) | −1.40312 | −0.0460846 | ||||||||
\(928\) | 6.40312 | 0.210193 | ||||||||
\(929\) | 52.2984 | 1.71586 | 0.857928 | − | 0.513770i | \(-0.171751\pi\) | ||||
0.857928 | + | 0.513770i | \(0.171751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.7016 | −0.842335 | ||||||||
\(932\) | 20.2094 | 0.661980 | ||||||||
\(933\) | −30.0000 | −0.982156 | ||||||||
\(934\) | 30.2984 | 0.991395 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −14.9109 | −0.487119 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(938\) | 30.1047 | 0.982953 | ||||||||
\(939\) | −21.2094 | −0.692142 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.4187 | 0.926425 | 0.463212 | − | 0.886247i | \(-0.346697\pi\) | ||||
0.463212 | + | 0.886247i | \(0.346697\pi\) | |||||||
\(942\) | 22.7016 | 0.739657 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.70156 | 0.0879284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.6125 | −1.74309 | ||||||||
\(947\) | −47.5078 | −1.54380 | −0.771898 | − | 0.635746i | \(-0.780693\pi\) | ||||
−0.771898 | + | 0.635746i | \(0.780693\pi\) | |||||||
\(948\) | 5.70156 | 0.185178 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.19375 | 0.0387100 | ||||||||
\(952\) | 3.29844 | 0.106903 | ||||||||
\(953\) | 31.2984 | 1.01386 | 0.506928 | − | 0.861988i | \(-0.330781\pi\) | ||||
0.506928 | + | 0.861988i | \(0.330781\pi\) | |||||||
\(954\) | 2.40312 | 0.0778040 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.10469 | 0.197440 | ||||||||
\(957\) | 30.1047 | 0.973146 | ||||||||
\(958\) | 40.6125 | 1.31213 | ||||||||
\(959\) | 64.4187 | 2.08019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.1047 | 2.29370 | ||||||||
\(962\) | −1.70156 | −0.0548606 | ||||||||
\(963\) | −19.1047 | −0.615640 | ||||||||
\(964\) | −2.59688 | −0.0836397 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.8953 | −0.961368 | −0.480684 | − | 0.876894i | \(-0.659612\pi\) | ||||
−0.480684 | + | 0.876894i | \(0.659612\pi\) | |||||||
\(968\) | −11.1047 | −0.356918 | ||||||||
\(969\) | 1.19375 | 0.0383488 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8953 | −1.18403 | −0.592013 | − | 0.805928i | \(-0.701667\pi\) | ||||
−0.592013 | + | 0.805928i | \(0.701667\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −44.2094 | −1.41729 | ||||||||
\(974\) | −7.89531 | −0.252982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1047 | 0.451480 | ||||||||
\(977\) | 23.4031 | 0.748732 | 0.374366 | − | 0.927281i | \(-0.377860\pi\) | ||||
0.374366 | + | 0.927281i | \(0.377860\pi\) | |||||||
\(978\) | 18.8062 | 0.601358 | ||||||||
\(979\) | 53.6125 | 1.71346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.29844 | 0.137239 | ||||||||
\(982\) | −33.4031 | −1.06594 | ||||||||
\(983\) | 7.50781 | 0.239462 | 0.119731 | − | 0.992806i | \(-0.461797\pi\) | ||||
0.119731 | + | 0.992806i | \(0.461797\pi\) | |||||||
\(984\) | −3.70156 | −0.118001 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.49219 | 0.143060 | ||||||||
\(987\) | −32.9109 | −1.04757 | ||||||||
\(988\) | −1.70156 | −0.0541339 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.10469 | −0.289220 | −0.144610 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144610 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(992\) | 10.1047 | 0.320824 | ||||||||
\(993\) | 12.0000 | 0.380808 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.7016 | −0.339092 | ||||||||
\(997\) | 10.4922 | 0.332291 | 0.166145 | − | 0.986101i | \(-0.446868\pi\) | ||||
0.166145 | + | 0.986101i | \(0.446868\pi\) | |||||||
\(998\) | −17.2094 | −0.544753 | ||||||||
\(999\) | −1.70156 | −0.0538350 |
(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 | 1950.2.a.bc.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 5850.2.a.cj.1.1 | 2 | |||
5.2 | odd | 4 | 1950.2.e.p.1249.1 | 4 | |||
5.3 | odd | 4 | 1950.2.e.p.1249.4 | 4 | |||
5.4 | even | 2 | 1950.2.a.bg.1.2 | yes | 2 | ||
15.2 | even | 4 | 5850.2.e.bi.5149.3 | 4 | |||
15.8 | even | 4 | 5850.2.e.bi.5149.2 | 4 | |||
15.14 | odd | 2 | 5850.2.a.cg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.a.bc.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1950.2.a.bg.1.2 | yes | 2 | 5.4 | even | 2 | ||
1950.2.e.p.1249.1 | 4 | 5.2 | odd | 4 | |||
1950.2.e.p.1249.4 | 4 | 5.3 | odd | 4 | |||
5850.2.a.cg.1.2 | 2 | 15.14 | odd | 2 | |||
5850.2.a.cj.1.1 | 2 | 3.2 | odd | 2 | |||
5850.2.e.bi.5149.2 | 4 | 15.8 | even | 4 | |||
5850.2.e.bi.5149.3 | 4 | 15.2 | even | 4 |