Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5850,2,Mod(5149,5850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5850.5149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5850.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(46.7124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1950) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5149.2 | ||
Root | \(3.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5850.5149 |
Dual form | 5850.2.e.bi.5149.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5850\mathbb{Z}\right)^\times\).
\(n\) | \(2251\) | \(3251\) | \(3277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.70156i | 1.77702i | 0.458854 | + | 0.888512i | \(0.348260\pi\) | ||||
−0.458854 | + | 0.888512i | \(0.651740\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.70156 | −1.41757 | −0.708787 | − | 0.705422i | \(-0.750757\pi\) | ||||
−0.708787 | + | 0.705422i | \(0.750757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 4.70156 | 1.25655 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.701562i | 0.170154i | 0.996374 | + | 0.0850769i | \(0.0271136\pi\) | ||||
−0.996374 | + | 0.0850769i | \(0.972886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.70156 | 0.390365 | 0.195183 | − | 0.980767i | \(-0.437470\pi\) | ||||
0.195183 | + | 0.980767i | \(0.437470\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.70156i | 1.00238i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 4.70156i | − 0.888512i | ||||||||
\(29\) | −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 | \(0.861957\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.701562 | 0.120317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.70156i | − 0.279735i | −0.990170 | − | 0.139868i | \(-0.955332\pi\) | ||||
0.990170 | − | 0.139868i | \(-0.0446677\pi\) | |||||||
\(38\) | − 1.70156i | − 0.276030i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.70156 | 0.578087 | 0.289043 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289043 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4031i | 1.73896i | 0.493968 | + | 0.869480i | \(0.335546\pi\) | ||||
−0.493968 | + | 0.869480i | \(0.664454\pi\) | |||||||
\(44\) | 4.70156 | 0.708787 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 7.00000i | − 1.02105i | −0.859861 | − | 0.510527i | \(-0.829450\pi\) | ||||
0.859861 | − | 0.510527i | \(-0.170550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.1047 | −2.15781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 1.00000i | − 0.138675i | ||||||||
\(53\) | 2.40312i | 0.330095i | 0.986286 | + | 0.165047i | \(0.0527777\pi\) | ||||
−0.986286 | + | 0.165047i | \(0.947222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.70156 | −0.628273 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.40312i | 0.840771i | ||||||||
\(59\) | 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 | \(0.141389\pi\) | |||||||
\(62\) | 10.1047i | 1.28330i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.40312i | − 0.782266i | −0.920334 | − | 0.391133i | \(-0.872083\pi\) | ||||
0.920334 | − | 0.391133i | \(-0.127917\pi\) | |||||||
\(68\) | − 0.701562i | − 0.0850769i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70156 | 0.201938 | 0.100969 | − | 0.994890i | \(-0.467806\pi\) | ||||
0.100969 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000i | 1.40449i | 0.711934 | + | 0.702247i | \(0.247820\pi\) | ||||
−0.711934 | + | 0.702247i | \(0.752180\pi\) | |||||||
\(74\) | −1.70156 | −0.197803 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.70156 | −0.195183 | ||||||||
\(77\) | − 22.1047i | − 2.51906i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.70156 | 0.641476 | 0.320738 | − | 0.947168i | \(-0.396069\pi\) | ||||
0.320738 | + | 0.947168i | \(0.396069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 3.70156i | − 0.408769i | ||||||||
\(83\) | − 10.7016i | − 1.17465i | −0.809352 | − | 0.587325i | \(-0.800181\pi\) | ||||
0.809352 | − | 0.587325i | \(-0.199819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.4031 | 1.22963 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 4.70156i | − 0.501188i | ||||||||
\(89\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 2.59688i | − 0.263673i | −0.991271 | − | 0.131836i | \(-0.957913\pi\) | ||||
0.991271 | − | 0.131836i | \(-0.0420874\pi\) | |||||||
\(98\) | 15.1047i | 1.52580i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.70156 | −0.666830 | −0.333415 | − | 0.942780i | \(-0.608201\pi\) | ||||
−0.333415 | + | 0.942780i | \(0.608201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.40312i | − 0.138254i | −0.997608 | − | 0.0691270i | \(-0.977979\pi\) | ||||
0.997608 | − | 0.0691270i | \(-0.0220214\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.40312 | 0.233412 | ||||||||
\(107\) | − 19.1047i | − 1.84692i | −0.383695 | − | 0.923460i | \(-0.625349\pi\) | ||||
0.383695 | − | 0.923460i | \(-0.374651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.29844 | −0.411716 | −0.205858 | − | 0.978582i | \(-0.565998\pi\) | ||||
−0.205858 | + | 0.978582i | \(0.565998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.70156i | 0.444256i | ||||||||
\(113\) | − 14.0000i | − 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.40312 | 0.594515 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 2.70156i | − 0.248699i | ||||||||
\(119\) | −3.29844 | −0.302367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1047 | 1.00952 | ||||||||
\(122\) | − 14.1047i | − 1.27698i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.1047 | 0.907428 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 6.29844i | − 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||||
0.960161 | − | 0.279448i | \(-0.0901515\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.5078 | −1.96652 | −0.983258 | − | 0.182217i | \(-0.941673\pi\) | ||||
−0.983258 | + | 0.182217i | \(0.941673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −6.40312 | −0.553146 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.701562 | −0.0601585 | ||||||||
\(137\) | − 13.7016i | − 1.17060i | −0.810816 | − | 0.585302i | \(-0.800976\pi\) | ||||
0.810816 | − | 0.585302i | \(-0.199024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.40312 | −0.797563 | −0.398781 | − | 0.917046i | \(-0.630567\pi\) | ||||
−0.398781 | + | 0.917046i | \(0.630567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1.70156i | − 0.142792i | ||||||||
\(143\) | − 4.70156i | − 0.393164i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.70156i | 0.139868i | ||||||||
\(149\) | 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 | \(0.694575\pi\) | |||||||
\(152\) | 1.70156i | 0.138015i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.1047 | −1.78125 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 22.7016i | − 1.81178i | −0.423511 | − | 0.905891i | \(-0.639203\pi\) | ||||
0.423511 | − | 0.905891i | \(-0.360797\pi\) | |||||||
\(158\) | − 5.70156i | − 0.453592i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8062i | 1.47302i | 0.676427 | + | 0.736510i | \(0.263527\pi\) | ||||
−0.676427 | + | 0.736510i | \(0.736473\pi\) | |||||||
\(164\) | −3.70156 | −0.289043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7016 | −0.830602 | ||||||||
\(167\) | 1.10469i | 0.0854832i | 0.999086 | + | 0.0427416i | \(0.0136092\pi\) | ||||
−0.999086 | + | 0.0427416i | \(0.986391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 11.4031i | − 0.869480i | ||||||||
\(173\) | − 0.193752i | − 0.0147307i | −0.999973 | − | 0.00736533i | \(-0.997656\pi\) | ||||
0.999973 | − | 0.00736533i | \(-0.00234448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.70156 | −0.354394 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 11.4031i | − 0.854700i | ||||||||
\(179\) | −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 | \(0.362064\pi\) | |||||||
\(182\) | 4.70156i | 0.348503i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.29844i | − 0.241206i | ||||||||
\(188\) | 7.00000i | 0.510527i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8062 | 0.926628 | 0.463314 | − | 0.886194i | \(-0.346660\pi\) | ||||
0.463314 | + | 0.886194i | \(0.346660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 16.2094i | − 1.16678i | −0.812194 | − | 0.583388i | \(-0.801727\pi\) | ||||
0.812194 | − | 0.583388i | \(-0.198273\pi\) | |||||||
\(194\) | −2.59688 | −0.186445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.1047 | 1.07891 | ||||||||
\(197\) | 5.40312i | 0.384957i | 0.981301 | + | 0.192478i | \(0.0616525\pi\) | ||||
−0.981301 | + | 0.192478i | \(0.938347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.29844 | −0.588261 | −0.294130 | − | 0.955765i | \(-0.595030\pi\) | ||||
−0.294130 | + | 0.955765i | \(0.595030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.70156i | 0.471520i | ||||||||
\(203\) | − 30.1047i | − 2.11293i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.40312 | −0.0977603 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.80625 | 0.468561 | 0.234281 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234281 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(212\) | − 2.40312i | − 0.165047i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.1047 | −1.30597 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 47.5078i | − 3.22504i | ||||||||
\(218\) | 4.29844i | 0.291127i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.701562 | −0.0471922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 11.4031i | − 0.763610i | −0.924243 | − | 0.381805i | \(-0.875303\pi\) | ||||
0.924243 | − | 0.381805i | \(-0.124697\pi\) | |||||||
\(224\) | 4.70156 | 0.314136 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 16.1047i | 1.06891i | 0.845198 | + | 0.534453i | \(0.179482\pi\) | ||||
−0.845198 | + | 0.534453i | \(0.820518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7016 | −1.03759 | −0.518794 | − | 0.854899i | \(-0.673619\pi\) | ||||
−0.518794 | + | 0.854899i | \(0.673619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 6.40312i | − 0.420386i | ||||||||
\(233\) | − 20.2094i | − 1.32396i | −0.749521 | − | 0.661980i | \(-0.769716\pi\) | ||||
0.749521 | − | 0.661980i | \(-0.230284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.70156 | −0.175857 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.29844i | 0.213806i | ||||||||
\(239\) | 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 | \(0.526654\pi\) | |||||||
\(242\) | − 11.1047i | − 0.713836i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.1047 | −0.902960 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.70156i | 0.108268i | ||||||||
\(248\) | − 10.1047i | − 0.641648i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.298438 | −0.0188372 | −0.00941862 | − | 0.999956i | \(-0.502998\pi\) | ||||
−0.00941862 | + | 0.999956i | \(0.502998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.29844 | −0.395199 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.2984i | 0.954290i | 0.878824 | + | 0.477145i | \(0.158328\pi\) | ||||
−0.878824 | + | 0.477145i | \(0.841672\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.5078i | 1.39054i | ||||||||
\(263\) | 2.00000i | 0.123325i | 0.998097 | + | 0.0616626i | \(0.0196403\pi\) | ||||
−0.998097 | + | 0.0616626i | \(0.980360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.40312i | 0.391133i | ||||||||
\(269\) | 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 | \(0.298138\pi\) | |||||||
\(272\) | 0.701562i | 0.0425385i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.7016 | −0.827742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 22.0000i | − 1.32185i | −0.750451 | − | 0.660926i | \(-0.770164\pi\) | ||||
0.750451 | − | 0.660926i | \(-0.229836\pi\) | |||||||
\(278\) | 9.40312i | 0.563962i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9109 | 1.30710 | 0.653548 | − | 0.756885i | \(-0.273280\pi\) | ||||
0.653548 | + | 0.756885i | \(0.273280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.4031i | − 1.27228i | −0.771572 | − | 0.636142i | \(-0.780529\pi\) | ||||
0.771572 | − | 0.636142i | \(-0.219471\pi\) | |||||||
\(284\) | −1.70156 | −0.100969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.70156 | −0.278009 | ||||||||
\(287\) | 17.4031i | 1.02727i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5078 | 0.971048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 12.0000i | − 0.702247i | ||||||||
\(293\) | 21.4031i | 1.25038i | 0.780471 | + | 0.625192i | \(0.214979\pi\) | ||||
−0.780471 | + | 0.625192i | \(0.785021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.70156 | 0.0989013 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 6.59688i | − 0.382147i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.6125 | −3.09017 | ||||||||
\(302\) | 14.1047i | 0.811633i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.70156 | 0.0975913 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.70156i | − 0.325405i | −0.986675 | − | 0.162703i | \(-0.947979\pi\) | ||||
0.986675 | − | 0.162703i | \(-0.0520211\pi\) | |||||||
\(308\) | 22.1047i | 1.25953i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0000 | −1.70114 | −0.850572 | − | 0.525859i | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2094i | 1.19882i | 0.800440 | + | 0.599412i | \(0.204599\pi\) | ||||
−0.800440 | + | 0.599412i | \(0.795401\pi\) | |||||||
\(314\) | −22.7016 | −1.28112 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.70156 | −0.320738 | ||||||||
\(317\) | − 1.19375i | − 0.0670478i | −0.999438 | − | 0.0335239i | \(-0.989327\pi\) | ||||
0.999438 | − | 0.0335239i | \(-0.0106730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.1047 | 1.68554 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.19375i | 0.0664221i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.8062 | 1.04158 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.70156i | 0.204385i | ||||||||
\(329\) | 32.9109 | 1.81444 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 10.7016i | 0.587325i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.10469 | 0.0604457 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.10469i | 0.441490i | 0.975332 | + | 0.220745i | \(0.0708489\pi\) | ||||
−0.975332 | + | 0.220745i | \(0.929151\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.5078 | 2.57269 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 38.1047i | − 2.05746i | ||||||||
\(344\) | −11.4031 | −0.614815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.193752 | −0.0104161 | ||||||||
\(347\) | − 10.5078i | − 0.564089i | −0.959401 | − | 0.282044i | \(-0.908987\pi\) | ||||
0.959401 | − | 0.282044i | \(-0.0910126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4031 | 0.610395 | 0.305198 | − | 0.952289i | \(-0.401277\pi\) | ||||
0.305198 | + | 0.952289i | \(0.401277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.70156i | 0.250594i | ||||||||
\(353\) | 14.5078i | 0.772173i | 0.922463 | + | 0.386086i | \(0.126173\pi\) | ||||
−0.922463 | + | 0.386086i | \(0.873827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.4031 | −0.604364 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.2094i | 1.27951i | ||||||||
\(359\) | −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 | ||||||||
\(362\) | − 11.2984i | − 0.593833i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.70156 | 0.246429 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.29844i | − 0.119977i | −0.998199 | − | 0.0599887i | \(-0.980894\pi\) | ||||
0.998199 | − | 0.0599887i | \(-0.0191065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2984 | −0.586586 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.29844i | − 0.274343i | −0.990547 | − | 0.137171i | \(-0.956199\pi\) | ||||
0.990547 | − | 0.137171i | \(-0.0438011\pi\) | |||||||
\(374\) | −3.29844 | −0.170558 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | − 6.40312i | − 0.329778i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.8953 | 0.713754 | 0.356877 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356877 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 12.8062i | − 0.655225i | ||||||||
\(383\) | 32.5078i | 1.66107i | 0.556965 | + | 0.830536i | \(0.311966\pi\) | ||||
−0.556965 | + | 0.830536i | \(0.688034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2094 | −0.825035 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.59688i | 0.131836i | ||||||||
\(389\) | −27.1047 | −1.37426 | −0.687131 | − | 0.726533i | \(-0.741130\pi\) | ||||
−0.687131 | + | 0.726533i | \(0.741130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 15.1047i | − 0.762902i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.40312 | 0.272205 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 21.9109i | − 1.09968i | −0.835271 | − | 0.549839i | \(-0.814689\pi\) | ||||
0.835271 | − | 0.549839i | \(-0.185311\pi\) | |||||||
\(398\) | 8.29844i | 0.415963i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2094 | −0.909333 | −0.454666 | − | 0.890662i | \(-0.650241\pi\) | ||||
−0.454666 | + | 0.890662i | \(0.650241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 10.1047i | − 0.503350i | ||||||||
\(404\) | 6.70156 | 0.333415 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.1047 | −1.49407 | ||||||||
\(407\) | 8.00000i | 0.396545i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4031 | −1.45389 | −0.726945 | − | 0.686695i | \(-0.759061\pi\) | ||||
−0.726945 | + | 0.686695i | \(0.759061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.40312i | 0.0691270i | ||||||||
\(413\) | 12.7016i | 0.625003i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000i | 0.391293i | ||||||||
\(419\) | 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 | \(0.504630\pi\) | |||||||
\(422\) | − 6.80625i | − 0.331323i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.40312 | −0.116706 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 66.3141i | 3.20916i | ||||||||
\(428\) | 19.1047i | 0.923460i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.3141 | −1.70102 | −0.850509 | − | 0.525960i | \(-0.823706\pi\) | ||||
−0.850509 | + | 0.525960i | \(0.823706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1047i | 0.533657i | 0.963744 | + | 0.266829i | \(0.0859758\pi\) | ||||
−0.963744 | + | 0.266829i | \(0.914024\pi\) | |||||||
\(434\) | −47.5078 | −2.28045 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.29844 | 0.205858 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2984 | 0.491518 | 0.245759 | − | 0.969331i | \(-0.420963\pi\) | ||||
0.245759 | + | 0.969331i | \(0.420963\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.701562i | 0.0333699i | ||||||||
\(443\) | 32.5078i | 1.54449i | 0.635323 | + | 0.772246i | \(0.280867\pi\) | ||||
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.4031 | −0.539954 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 4.70156i | − 0.222128i | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 14.0000i | 0.658505i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.1047 | 0.755830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.59688i | − 0.121477i | −0.998154 | − | 0.0607384i | \(-0.980654\pi\) | ||||
0.998154 | − | 0.0607384i | \(-0.0193455\pi\) | |||||||
\(458\) | 15.7016i | 0.733686i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.2094 | −1.68644 | −0.843219 | − | 0.537570i | \(-0.819342\pi\) | ||||
−0.843219 | + | 0.537570i | \(0.819342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2984i | 0.989822i | 0.868944 | + | 0.494911i | \(0.164799\pi\) | ||||
−0.868944 | + | 0.494911i | \(0.835201\pi\) | |||||||
\(464\) | −6.40312 | −0.297258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.2094 | −0.936181 | ||||||||
\(467\) | − 30.2984i | − 1.40204i | −0.713139 | − | 0.701022i | \(-0.752727\pi\) | ||||
0.713139 | − | 0.701022i | \(-0.247273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.1047 | 1.39011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.70156i | 0.124349i | ||||||||
\(473\) | − 53.6125i | − 2.46511i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.29844 | 0.151184 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 6.10469i | − 0.279222i | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 2.59688i | 0.118284i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.1047 | −0.504758 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7.89531i | − 0.357771i | −0.983870 | − | 0.178885i | \(-0.942751\pi\) | ||||
0.983870 | − | 0.178885i | \(-0.0572491\pi\) | |||||||
\(488\) | 14.1047i | 0.638489i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.4031 | −1.50746 | −0.753731 | − | 0.657183i | \(-0.771748\pi\) | ||||
−0.753731 | + | 0.657183i | \(0.771748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.49219i | − 0.202318i | ||||||||
\(494\) | 1.70156 | 0.0765569 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1047 | −0.453714 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.2094 | −0.770397 | −0.385199 | − | 0.922834i | \(-0.625867\pi\) | ||||
−0.385199 | + | 0.922834i | \(0.625867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.298438i | 0.0133199i | ||||||||
\(503\) | − 12.2094i | − 0.544389i | −0.962242 | − | 0.272195i | \(-0.912251\pi\) | ||||
0.962242 | − | 0.272195i | \(-0.0877494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.29844i | 0.279448i | ||||||||
\(509\) | −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 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.2984 | 0.674785 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.9109i | 1.44742i | ||||||||
\(518\) | − 8.00000i | − 0.351500i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2094 | 1.58636 | 0.793181 | − | 0.608986i | \(-0.208424\pi\) | ||||
0.793181 | + | 0.608986i | \(0.208424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8062i | 1.08470i | 0.840152 | + | 0.542351i | \(0.182466\pi\) | ||||
−0.840152 | + | 0.542351i | \(0.817534\pi\) | |||||||
\(524\) | 22.5078 | 0.983258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | − 7.08907i | − 0.308805i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 8.00000i | − 0.346844i | ||||||||
\(533\) | 3.70156i | 0.160332i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.40312 | 0.276573 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 31.2094i | − 1.34553i | ||||||||
\(539\) | 71.0156 | 3.05886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.79063 | −0.0769851 | −0.0384925 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384925 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(542\) | − 19.5078i | − 0.837932i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.701562 | 0.0300792 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 31.6125i | − 1.35165i | −0.737061 | − | 0.675826i | \(-0.763787\pi\) | ||||
0.737061 | − | 0.675826i | \(-0.236213\pi\) | |||||||
\(548\) | 13.7016i | 0.585302i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.8953 | −0.464156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8062i | 1.13992i | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.40312 | 0.398781 | ||||||||
\(557\) | − 16.8062i | − 0.712104i | −0.934466 | − | 0.356052i | \(-0.884123\pi\) | ||||
0.934466 | − | 0.356052i | \(-0.115877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.4031 | −0.482301 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 21.9109i | − 0.924257i | ||||||||
\(563\) | − 32.5078i | − 1.37004i | −0.728524 | − | 0.685020i | \(-0.759793\pi\) | ||||
0.728524 | − | 0.685020i | \(-0.240207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.4031 | −0.899640 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.70156i | 0.0713960i | ||||||||
\(569\) | −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 | \(0.184323\pi\) | |||||||
\(572\) | 4.70156i | 0.196582i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.4031 | 0.726392 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.2094i | 1.00785i | 0.863748 | + | 0.503925i | \(0.168111\pi\) | ||||
−0.863748 | + | 0.503925i | \(0.831889\pi\) | |||||||
\(578\) | − 16.5078i | − 0.686634i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.3141 | 2.08738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 11.2984i | − 0.467933i | ||||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4031 | 0.884155 | ||||||||
\(587\) | 7.50781i | 0.309881i | 0.987924 | + | 0.154940i | \(0.0495185\pi\) | ||||
−0.987924 | + | 0.154940i | \(0.950481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.1938 | −0.708456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 1.70156i | − 0.0699338i | ||||||||
\(593\) | 17.9109i | 0.735514i | 0.929922 | + | 0.367757i | \(0.119874\pi\) | ||||
−0.929922 | + | 0.367757i | \(0.880126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.59688 | −0.270219 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | \(0.430553\pi\) | |||||||
\(602\) | 53.6125i | 2.18508i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.1047 | 0.573912 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 35.1047i | − 1.42486i | −0.701746 | − | 0.712428i | \(-0.747596\pi\) | ||||
0.701746 | − | 0.712428i | \(-0.252404\pi\) | |||||||
\(608\) | − 1.70156i | − 0.0690075i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.00000 | 0.283190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.8062i | 0.517240i | 0.965979 | + | 0.258620i | \(0.0832677\pi\) | ||||
−0.965979 | + | 0.258620i | \(0.916732\pi\) | |||||||
\(614\) | −5.70156 | −0.230096 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.1047 | 0.890623 | ||||||||
\(617\) | 27.1047i | 1.09119i | 0.838048 | + | 0.545597i | \(0.183697\pi\) | ||||
−0.838048 | + | 0.545597i | \(0.816303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1938 | 0.530302 | 0.265151 | − | 0.964207i | \(-0.414578\pi\) | ||||
0.265151 | + | 0.964207i | \(0.414578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.0000i | 1.20289i | ||||||||
\(623\) | 53.6125i | 2.14794i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.2094 | 0.847697 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.7016i | 0.905891i | ||||||||
\(629\) | 1.19375 | 0.0475980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6125 | 1.33809 | 0.669046 | − | 0.743221i | \(-0.266703\pi\) | ||||
0.669046 | + | 0.743221i | \(0.266703\pi\) | |||||||
\(632\) | 5.70156i | 0.226796i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.19375 | −0.0474099 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 15.1047i | − 0.598469i | ||||||||
\(638\) | − 30.1047i | − 1.19186i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.50781 | −0.217545 | −0.108773 | − | 0.994067i | \(-0.534692\pi\) | ||||
−0.108773 | + | 0.994067i | \(0.534692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2984i | 0.406131i | 0.979165 | + | 0.203065i | \(0.0650904\pi\) | ||||
−0.979165 | + | 0.203065i | \(0.934910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.19375 | 0.0469675 | ||||||||
\(647\) | 24.0000i | 0.943537i | 0.881722 | + | 0.471769i | \(0.156384\pi\) | ||||
−0.881722 | + | 0.471769i | \(0.843616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.7016 | −0.498580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 18.8062i | − 0.736510i | ||||||||
\(653\) | − 21.2984i | − 0.833472i | −0.909027 | − | 0.416736i | \(-0.863174\pi\) | ||||
0.909027 | − | 0.416736i | \(-0.136826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.70156 | 0.144522 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 32.9109i | − 1.28300i | ||||||||
\(659\) | −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 | \(0.784908\pi\) | |||||||
\(662\) | 12.0000i | 0.466393i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.7016 | 0.415301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − 1.10469i | − 0.0427416i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −66.3141 | −2.56003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 36.0156i | − 1.38830i | −0.719830 | − | 0.694150i | \(-0.755780\pi\) | ||||
0.719830 | − | 0.694150i | \(-0.244220\pi\) | |||||||
\(674\) | 8.10469 | 0.312181 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − 31.6125i | − 1.21497i | −0.794332 | − | 0.607483i | \(-0.792179\pi\) | ||||
0.794332 | − | 0.607483i | \(-0.207821\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2094 | 0.468553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 47.5078i | − 1.81917i | ||||||||
\(683\) | 44.7016i | 1.71046i | 0.518251 | + | 0.855229i | \(0.326583\pi\) | ||||
−0.518251 | + | 0.855229i | \(0.673417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −38.1047 | −1.45484 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.4031i | 0.434740i | ||||||||
\(689\) | −2.40312 | −0.0915517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1938 | −0.844290 | −0.422145 | − | 0.906528i | \(-0.638723\pi\) | ||||
−0.422145 | + | 0.906528i | \(0.638723\pi\) | |||||||
\(692\) | 0.193752i | 0.00736533i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.5078 | −0.398871 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.59688i | 0.0983637i | ||||||||
\(698\) | − 11.4031i | − 0.431615i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9109 | −1.16749 | −0.583745 | − | 0.811937i | \(-0.698413\pi\) | ||||
−0.583745 | + | 0.811937i | \(0.698413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.89531i | − 0.109199i | ||||||||
\(704\) | 4.70156 | 0.177197 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5078 | 0.546009 | ||||||||
\(707\) | − 31.5078i | − 1.18497i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6125 | −0.586340 | −0.293170 | − | 0.956060i | \(-0.594710\pi\) | ||||
−0.293170 | + | 0.956060i | \(0.594710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.4031i | 0.427350i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.2094 | 0.904747 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.6125i | 1.29173i | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 16.1047i | 0.599354i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2984 | −0.419903 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.79063i | 0.288938i | 0.989509 | + | 0.144469i | \(0.0461475\pi\) | ||||
−0.989509 | + | 0.144469i | \(0.953853\pi\) | |||||||
\(728\) | − 4.70156i | − 0.174251i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 47.9109i | − 1.76963i | −0.465942 | − | 0.884815i | \(-0.654284\pi\) | ||||
0.465942 | − | 0.884815i | \(-0.345716\pi\) | |||||||
\(734\) | −2.29844 | −0.0848369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1047i | 1.10892i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.61250 | −0.169673 | −0.0848367 | − | 0.996395i | \(-0.527037\pi\) | ||||
−0.0848367 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.2984i | 0.414779i | ||||||||
\(743\) | − 30.6125i | − 1.12306i | −0.827455 | − | 0.561532i | \(-0.810212\pi\) | ||||
0.827455 | − | 0.561532i | \(-0.189788\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.29844 | −0.193990 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.29844i | 0.120603i | ||||||||
\(749\) | 89.8219 | 3.28202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50781 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(752\) | − 7.00000i | − 0.255264i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.40312 | −0.233188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 17.8953i | − 0.650416i | −0.945642 | − | 0.325208i | \(-0.894566\pi\) | ||||
0.945642 | − | 0.325208i | \(-0.105434\pi\) | |||||||
\(758\) | − 13.8953i | − 0.504701i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.7172 | 0.968497 | 0.484249 | − | 0.874930i | \(-0.339093\pi\) | ||||
0.484249 | + | 0.874930i | \(0.339093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 20.2094i | − 0.731628i | ||||||||
\(764\) | −12.8062 | −0.463314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5078 | 1.17455 | ||||||||
\(767\) | 2.70156i | 0.0975478i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.2094i | 0.583388i | ||||||||
\(773\) | 26.5969i | 0.956623i | 0.878190 | + | 0.478312i | \(0.158751\pi\) | ||||
−0.878190 | + | 0.478312i | \(0.841249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.59688 | 0.0932224 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.1047i | 0.971750i | ||||||||
\(779\) | 6.29844 | 0.225665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.1047 | −0.539453 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.8953i | 1.20824i | 0.796894 | + | 0.604119i | \(0.206475\pi\) | ||||
−0.796894 | + | 0.604119i | \(0.793525\pi\) | |||||||
\(788\) | − 5.40312i | − 0.192478i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 65.8219 | 2.34036 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1047i | 0.500872i | ||||||||
\(794\) | −21.9109 | −0.777590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.29844 | 0.294130 | ||||||||
\(797\) | − 2.91093i | − 0.103111i | −0.998670 | − | 0.0515553i | \(-0.983582\pi\) | ||||
0.998670 | − | 0.0515553i | \(-0.0164178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.91093 | 0.173736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2094i | 0.642995i | ||||||||
\(803\) | − 56.4187i | − 1.99097i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.1047 | −0.355922 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 6.70156i | − 0.235760i | ||||||||
\(809\) | 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 | \(0.173513\pi\) | |||||||
\(812\) | 30.1047i | 1.05647i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4031i | 0.678829i | ||||||||
\(818\) | 29.4031i | 1.02806i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5969 | 0.718836 | 0.359418 | − | 0.933177i | \(-0.382975\pi\) | ||||
0.359418 | + | 0.933177i | \(0.382975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 17.1047i | − 0.596232i | −0.954530 | − | 0.298116i | \(-0.903642\pi\) | ||||
0.954530 | − | 0.298116i | \(-0.0963582\pi\) | |||||||
\(824\) | 1.40312 | 0.0488801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.7016 | 0.441944 | ||||||||
\(827\) | − 20.7016i | − 0.719864i | −0.932979 | − | 0.359932i | \(-0.882800\pi\) | ||||
0.932979 | − | 0.359932i | \(-0.117200\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50781 | 0.191294 | 0.0956471 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956471 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1.00000i | − 0.0346688i | ||||||||
\(833\) | − 10.5969i | − 0.367160i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 9.91093i | − 0.342368i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0000 | 0.413793 | ||||||||
\(842\) | 0.596876i | 0.0205697i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.80625 | −0.234281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.2094i | 1.79394i | ||||||||
\(848\) | 2.40312i | 0.0825236i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 0.507811i | − 0.0173871i | −0.999962 | − | 0.00869355i | \(-0.997233\pi\) | ||||
0.999962 | − | 0.00869355i | \(-0.00276728\pi\) | |||||||
\(854\) | 66.3141 | 2.26922 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1047 | 0.652985 | ||||||||
\(857\) | 7.61250i | 0.260038i | 0.991512 | + | 0.130019i | \(0.0415038\pi\) | ||||
−0.991512 | + | 0.130019i | \(0.958496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.20937 | 0.211861 | 0.105931 | − | 0.994374i | \(-0.466218\pi\) | ||||
0.105931 | + | 0.994374i | \(0.466218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.3141i | 1.20280i | ||||||||
\(863\) | 54.2250i | 1.84584i | 0.384991 | + | 0.922920i | \(0.374204\pi\) | ||||
−0.384991 | + | 0.922920i | \(0.625796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.1047 | 0.377353 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 47.5078i | 1.61252i | ||||||||
\(869\) | −26.8062 | −0.909340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.40312 | 0.216962 | ||||||||
\(872\) | − 4.29844i | − 0.145563i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 42.7172i | − 1.44246i | −0.692697 | − | 0.721228i | \(-0.743578\pi\) | ||||
0.692697 | − | 0.721228i | \(-0.256422\pi\) | |||||||
\(878\) | − 10.2984i | − 0.347555i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7172 | 1.33811 | 0.669053 | − | 0.743215i | \(-0.266700\pi\) | ||||
0.669053 | + | 0.743215i | \(0.266700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 45.6125i | − 1.53498i | −0.641059 | − | 0.767491i | \(-0.721505\pi\) | ||||
0.641059 | − | 0.767491i | \(-0.278495\pi\) | |||||||
\(884\) | 0.701562 | 0.0235961 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.5078 | 1.09212 | ||||||||
\(887\) | 20.0000i | 0.671534i | 0.941945 | + | 0.335767i | \(0.108996\pi\) | ||||
−0.941945 | + | 0.335767i | \(0.891004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.6125 | 0.993171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.4031i | 0.381805i | ||||||||
\(893\) | − 11.9109i | − 0.398584i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.70156 | −0.157068 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 2.29844i | − 0.0766999i | ||||||||
\(899\) | 64.7016 | 2.15792 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.68594 | −0.0561668 | ||||||||
\(902\) | 17.4031i | 0.579461i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 25.0156i | − 0.830630i | −0.909678 | − | 0.415315i | \(-0.863671\pi\) | ||||
0.909678 | − | 0.415315i | \(-0.136329\pi\) | |||||||
\(908\) | − 16.1047i | − 0.534453i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2094 | −1.39846 | −0.699229 | − | 0.714897i | \(-0.746473\pi\) | ||||
−0.699229 | + | 0.714897i | \(0.746473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.3141i | 1.66515i | ||||||||
\(914\) | −2.59688 | −0.0858970 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.7016 | 0.518794 | ||||||||
\(917\) | − 105.822i | − 3.49455i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.89531 | 0.161481 | 0.0807407 | − | 0.996735i | \(-0.474271\pi\) | ||||
0.0807407 | + | 0.996735i | \(0.474271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.2094i | 1.19249i | ||||||||
\(923\) | 1.70156i | 0.0560076i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.2984 | 0.699910 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.40312i | 0.210193i | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 20.2094i | 0.661980i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.2984 | −0.991395 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9109i | 0.487119i | 0.969886 | + | 0.243560i | \(0.0783151\pi\) | ||||
−0.969886 | + | 0.243560i | \(0.921685\pi\) | |||||||
\(938\) | − 30.1047i | − 0.982953i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.4187 | −0.926425 | −0.463212 | − | 0.886247i | \(-0.653303\pi\) | ||||
−0.463212 | + | 0.886247i | \(0.653303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.70156 | 0.0879284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.6125 | −1.74309 | ||||||||
\(947\) | − 47.5078i | − 1.54380i | −0.635746 | − | 0.771898i | \(-0.719307\pi\) | ||||
0.635746 | − | 0.771898i | \(-0.280693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 3.29844i | − 0.106903i | ||||||||
\(953\) | − 31.2984i | − 1.01386i | −0.861988 | − | 0.506928i | \(-0.830781\pi\) | ||||
0.861988 | − | 0.506928i | \(-0.169219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.10469 | −0.197440 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.6125i | 1.31213i | ||||||||
\(959\) | 64.4187 | 2.08019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.1047 | 2.29370 | ||||||||
\(962\) | − 1.70156i | − 0.0548606i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.59688 | 0.0836397 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8953i | 0.961368i | 0.876894 | + | 0.480684i | \(0.159612\pi\) | ||||
−0.876894 | + | 0.480684i | \(0.840388\pi\) | |||||||
\(968\) | 11.1047i | 0.356918i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8953 | 1.18403 | 0.592013 | − | 0.805928i | \(-0.298333\pi\) | ||||
0.592013 | + | 0.805928i | \(0.298333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 44.2094i | − 1.41729i | ||||||||
\(974\) | −7.89531 | −0.252982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1047 | 0.451480 | ||||||||
\(977\) | 23.4031i | 0.748732i | 0.927281 | + | 0.374366i | \(0.122140\pi\) | ||||
−0.927281 | + | 0.374366i | \(0.877860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.6125 | −1.71346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.4031i | 1.06594i | ||||||||
\(983\) | − 7.50781i | − 0.239462i | −0.992806 | − | 0.119731i | \(-0.961797\pi\) | ||||
0.992806 | − | 0.119731i | \(-0.0382032\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.49219 | −0.143060 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 1.70156i | − 0.0541339i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.10469 | −0.289220 | −0.144610 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144610 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(992\) | 10.1047i | 0.320824i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 10.4922i | − 0.332291i | −0.986101 | − | 0.166145i | \(-0.946868\pi\) | ||||
0.986101 | − | 0.166145i | \(-0.0531321\pi\) | |||||||
\(998\) | 17.2094i | 0.544753i | ||||||||
\(999\) | 0 | 0 |
(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 | 5850.2.e.bi.5149.2 | 4 | ||
3.2 | odd | 2 | 1950.2.e.p.1249.4 | 4 | |||
5.2 | odd | 4 | 5850.2.a.cj.1.1 | 2 | |||
5.3 | odd | 4 | 5850.2.a.cg.1.2 | 2 | |||
5.4 | even | 2 | inner | 5850.2.e.bi.5149.3 | 4 | ||
15.2 | even | 4 | 1950.2.a.bc.1.1 | ✓ | 2 | ||
15.8 | even | 4 | 1950.2.a.bg.1.2 | yes | 2 | ||
15.14 | odd | 2 | 1950.2.e.p.1249.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.a.bc.1.1 | ✓ | 2 | 15.2 | even | 4 | ||
1950.2.a.bg.1.2 | yes | 2 | 15.8 | even | 4 | ||
1950.2.e.p.1249.1 | 4 | 15.14 | odd | 2 | |||
1950.2.e.p.1249.4 | 4 | 3.2 | odd | 2 | |||
5850.2.a.cg.1.2 | 2 | 5.3 | odd | 4 | |||
5850.2.a.cj.1.1 | 2 | 5.2 | odd | 4 | |||
5850.2.e.bi.5149.2 | 4 | 1.1 | even | 1 | trivial | ||
5850.2.e.bi.5149.3 | 4 | 5.4 | even | 2 | inner |