Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, 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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.16228 | 0.599708 | 0.299854 | − | 0.953985i | \(-0.403062\pi\) | ||||
0.299854 | + | 0.953985i | \(0.403062\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.32456 | −1.29139 | −0.645697 | − | 0.763594i | \(-0.723433\pi\) | ||||
−0.645697 | + | 0.763594i | \(0.723433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −5.16228 | −1.07641 | −0.538205 | − | 0.842814i | \(-0.680897\pi\) | ||||
−0.538205 | + | 0.842814i | \(0.680897\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.16228 | 0.424058 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.16228 | −1.51570 | −0.757848 | − | 0.652431i | \(-0.773749\pi\) | ||||
−0.757848 | + | 0.652431i | \(0.773749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.32456 | 1.13592 | 0.567962 | − | 0.823055i | \(-0.307732\pi\) | ||||
0.567962 | + | 0.823055i | \(0.307732\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.32456 | −0.913154 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.4868 | 1.88842 | 0.944212 | − | 0.329339i | \(-0.106826\pi\) | ||||
0.944212 | + | 0.329339i | \(0.106826\pi\) | |||||||
\(38\) | 3.00000 | 0.486664 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16228 | 0.482243 | 0.241121 | − | 0.970495i | \(-0.422485\pi\) | ||||
0.241121 | + | 0.970495i | \(0.422485\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.16228 | −0.761136 | ||||||||
\(47\) | 8.48683 | 1.23793 | 0.618966 | − | 0.785418i | \(-0.287552\pi\) | ||||
0.618966 | + | 0.785418i | \(0.287552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.16228 | 0.299854 | ||||||||
\(53\) | 6.16228 | 0.846454 | 0.423227 | − | 0.906024i | \(-0.360897\pi\) | ||||
0.423227 | + | 0.906024i | \(0.360897\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.16228 | −1.07176 | ||||||||
\(59\) | −12.3246 | −1.60452 | −0.802260 | − | 0.596974i | \(-0.796369\pi\) | ||||
−0.802260 | + | 0.596974i | \(0.796369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1623 | −1.30115 | −0.650573 | − | 0.759444i | \(-0.725471\pi\) | ||||
−0.650573 | + | 0.759444i | \(0.725471\pi\) | |||||||
\(62\) | 6.32456 | 0.803219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4868 | −1.89202 | −0.946009 | − | 0.324141i | \(-0.894925\pi\) | ||||
−0.946009 | + | 0.324141i | \(0.894925\pi\) | |||||||
\(68\) | −5.32456 | −0.645697 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.32456 | −0.275874 | −0.137937 | − | 0.990441i | \(-0.544047\pi\) | ||||
−0.137937 | + | 0.990441i | \(0.544047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.32456 | −0.974316 | −0.487158 | − | 0.873314i | \(-0.661966\pi\) | ||||
−0.487158 | + | 0.873314i | \(0.661966\pi\) | |||||||
\(74\) | 11.4868 | 1.33532 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.00000 | 0.344124 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.48683 | 0.504808 | 0.252404 | − | 0.967622i | \(-0.418779\pi\) | ||||
0.252404 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.00000 | −0.441726 | ||||||||
\(83\) | −3.16228 | −0.347105 | −0.173553 | − | 0.984825i | \(-0.555525\pi\) | ||||
−0.173553 | + | 0.984825i | \(0.555525\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.16228 | 0.340997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | −5.00000 | −0.529999 | −0.264999 | − | 0.964249i | \(-0.585372\pi\) | ||||
−0.264999 | + | 0.964249i | \(0.585372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16228 | −0.226668 | ||||||||
\(92\) | −5.16228 | −0.538205 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.48683 | 0.875350 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.48683 | −0.760173 | −0.380086 | − | 0.924951i | \(-0.624106\pi\) | ||||
−0.380086 | + | 0.924951i | \(0.624106\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.48683 | 0.346953 | 0.173476 | − | 0.984838i | \(-0.444500\pi\) | ||||
0.173476 | + | 0.984838i | \(0.444500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.32456 | −0.623177 | −0.311588 | − | 0.950217i | \(-0.600861\pi\) | ||||
−0.311588 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(104\) | 2.16228 | 0.212029 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.16228 | 0.598533 | ||||||||
\(107\) | −4.32456 | −0.418071 | −0.209035 | − | 0.977908i | \(-0.567032\pi\) | ||||
−0.209035 | + | 0.977908i | \(0.567032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.48683 | −0.333978 | −0.166989 | − | 0.985959i | \(-0.553404\pi\) | ||||
−0.166989 | + | 0.985959i | \(0.553404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.6491 | 1.00178 | 0.500892 | − | 0.865510i | \(-0.333005\pi\) | ||||
0.500892 | + | 0.865510i | \(0.333005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.16228 | −0.757848 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.3246 | −1.13457 | ||||||||
\(119\) | 5.32456 | 0.488101 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −10.1623 | −0.920049 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32456 | 0.567962 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4868 | −1.28550 | −0.642749 | − | 0.766077i | \(-0.722206\pi\) | ||||
−0.642749 | + | 0.766077i | \(0.722206\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4868 | −1.17835 | −0.589175 | − | 0.808005i | \(-0.700547\pi\) | ||||
−0.589175 | + | 0.808005i | \(0.700547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | −15.4868 | −1.33786 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.32456 | −0.456577 | ||||||||
\(137\) | −21.4868 | −1.83574 | −0.917872 | − | 0.396877i | \(-0.870094\pi\) | ||||
−0.917872 | + | 0.396877i | \(0.870094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.324555 | −0.0275284 | −0.0137642 | − | 0.999905i | \(-0.504381\pi\) | ||||
−0.0137642 | + | 0.999905i | \(0.504381\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.32456 | −0.195072 | ||||||||
\(143\) | −4.32456 | −0.361637 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.32456 | −0.688945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.4868 | 0.944212 | ||||||||
\(149\) | 0.486833 | 0.0398829 | 0.0199415 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199415 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.83772 | −0.149552 | −0.0747759 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747759 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(152\) | 3.00000 | 0.243332 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.8377 | −1.42361 | −0.711803 | − | 0.702380i | \(-0.752121\pi\) | ||||
−0.711803 | + | 0.702380i | \(0.752121\pi\) | |||||||
\(158\) | 4.48683 | 0.356953 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.16228 | 0.406844 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3246 | 0.965334 | 0.482667 | − | 0.875804i | \(-0.339668\pi\) | ||||
0.482667 | + | 0.875804i | \(0.339668\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.16228 | −0.245440 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.32456 | −0.640350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.16228 | 0.241121 | ||||||||
\(173\) | 19.1623 | 1.45688 | 0.728440 | − | 0.685109i | \(-0.240245\pi\) | ||||
0.728440 | + | 0.685109i | \(0.240245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.00000 | −0.374766 | ||||||||
\(179\) | −25.3246 | −1.89285 | −0.946423 | − | 0.322929i | \(-0.895332\pi\) | ||||
−0.946423 | + | 0.322929i | \(0.895332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1623 | −1.20133 | −0.600666 | − | 0.799500i | \(-0.705098\pi\) | ||||
−0.600666 | + | 0.799500i | \(0.705098\pi\) | |||||||
\(182\) | −2.16228 | −0.160279 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.16228 | −0.380568 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6491 | 0.778740 | ||||||||
\(188\) | 8.48683 | 0.618966 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.3246 | 1.96686 | 0.983432 | − | 0.181276i | \(-0.0580227\pi\) | ||||
0.983432 | + | 0.181276i | \(0.0580227\pi\) | |||||||
\(194\) | −7.48683 | −0.537523 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.8114 | 1.34026 | 0.670128 | − | 0.742246i | \(-0.266239\pi\) | ||||
0.670128 | + | 0.742246i | \(0.266239\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1359 | 1.42740 | 0.713700 | − | 0.700452i | \(-0.247018\pi\) | ||||
0.713700 | + | 0.700452i | \(0.247018\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.48683 | 0.245333 | ||||||||
\(203\) | 8.16228 | 0.572880 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.32456 | −0.440653 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.16228 | 0.149927 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3246 | −0.848457 | −0.424229 | − | 0.905555i | \(-0.639455\pi\) | ||||
−0.424229 | + | 0.905555i | \(0.639455\pi\) | |||||||
\(212\) | 6.16228 | 0.423227 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.32456 | −0.295621 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.32456 | −0.429339 | ||||||||
\(218\) | −3.48683 | −0.236158 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.5132 | −0.774459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.16228 | −0.479622 | −0.239811 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239811 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.6491 | 0.708368 | ||||||||
\(227\) | 21.8114 | 1.44767 | 0.723836 | − | 0.689972i | \(-0.242377\pi\) | ||||
0.723836 | + | 0.689972i | \(0.242377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.1623 | 1.59669 | 0.798344 | − | 0.602202i | \(-0.205710\pi\) | ||||
0.798344 | + | 0.602202i | \(0.205710\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.16228 | −0.535880 | ||||||||
\(233\) | 3.48683 | 0.228430 | 0.114215 | − | 0.993456i | \(-0.463565\pi\) | ||||
0.114215 | + | 0.993456i | \(0.463565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.3246 | −0.802260 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.32456 | 0.345140 | ||||||||
\(239\) | 5.81139 | 0.375907 | 0.187954 | − | 0.982178i | \(-0.439814\pi\) | ||||
0.187954 | + | 0.982178i | \(0.439814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.51317 | −0.290719 | −0.145359 | − | 0.989379i | \(-0.546434\pi\) | ||||
−0.145359 | + | 0.989379i | \(0.546434\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.1623 | −0.650573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.48683 | 0.412747 | ||||||||
\(248\) | 6.32456 | 0.401610 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3246 | 1.03040 | 0.515198 | − | 0.857071i | \(-0.327718\pi\) | ||||
0.515198 | + | 0.857071i | \(0.327718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.3246 | 0.649099 | ||||||||
\(254\) | −14.4868 | −0.908985 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.0000 | −1.18519 | −0.592594 | − | 0.805502i | \(-0.701896\pi\) | ||||
−0.592594 | + | 0.805502i | \(0.701896\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4868 | −0.713757 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.4868 | −0.833219 | ||||||||
\(263\) | 3.67544 | 0.226638 | 0.113319 | − | 0.993559i | \(-0.463852\pi\) | ||||
0.113319 | + | 0.993559i | \(0.463852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.00000 | −0.183942 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.4868 | −0.946009 | ||||||||
\(269\) | 2.64911 | 0.161519 | 0.0807596 | − | 0.996734i | \(-0.474265\pi\) | ||||
0.0807596 | + | 0.996734i | \(0.474265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3246 | 0.627172 | 0.313586 | − | 0.949560i | \(-0.398470\pi\) | ||||
0.313586 | + | 0.949560i | \(0.398470\pi\) | |||||||
\(272\) | −5.32456 | −0.322849 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.4868 | −1.29807 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.32456 | 0.259837 | 0.129919 | − | 0.991525i | \(-0.458528\pi\) | ||||
0.129919 | + | 0.991525i | \(0.458528\pi\) | |||||||
\(278\) | −0.324555 | −0.0194655 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1623 | −0.904506 | −0.452253 | − | 0.891890i | \(-0.649380\pi\) | ||||
−0.452253 | + | 0.891890i | \(0.649380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.64911 | −0.216917 | −0.108459 | − | 0.994101i | \(-0.534591\pi\) | ||||
−0.108459 | + | 0.994101i | \(0.534591\pi\) | |||||||
\(284\) | −2.32456 | −0.137937 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.32456 | −0.255716 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3509 | 0.667699 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.32456 | −0.487158 | ||||||||
\(293\) | −20.1359 | −1.17635 | −0.588177 | − | 0.808732i | \(-0.700154\pi\) | ||||
−0.588177 | + | 0.808732i | \(0.700154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.4868 | 0.667659 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.486833 | 0.0282015 | ||||||||
\(299\) | −11.1623 | −0.645531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.16228 | −0.182271 | ||||||||
\(302\) | −1.83772 | −0.105749 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6491 | 1.06436 | 0.532180 | − | 0.846631i | \(-0.321373\pi\) | ||||
0.532180 | + | 0.846631i | \(0.321373\pi\) | |||||||
\(308\) | 2.00000 | 0.113961 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16228 | 0.0656958 | 0.0328479 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328479 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(314\) | −17.8377 | −1.00664 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.48683 | 0.252404 | ||||||||
\(317\) | −28.1623 | −1.58175 | −0.790876 | − | 0.611977i | \(-0.790374\pi\) | ||||
−0.790876 | + | 0.611977i | \(0.790374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3246 | 0.914000 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.16228 | 0.287682 | ||||||||
\(323\) | −15.9737 | −0.888799 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.3246 | 0.682594 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | −8.48683 | −0.467894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.8114 | −1.85844 | −0.929221 | − | 0.369524i | \(-0.879521\pi\) | ||||
−0.929221 | + | 0.369524i | \(0.879521\pi\) | |||||||
\(332\) | −3.16228 | −0.173553 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.675445 | −0.0367938 | −0.0183969 | − | 0.999831i | \(-0.505856\pi\) | ||||
−0.0183969 | + | 0.999831i | \(0.505856\pi\) | |||||||
\(338\) | −8.32456 | −0.452796 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.6491 | −0.684988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.16228 | 0.170499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.1623 | 1.03017 | ||||||||
\(347\) | −23.0000 | −1.23470 | −0.617352 | − | 0.786687i | \(-0.711795\pi\) | ||||
−0.617352 | + | 0.786687i | \(0.711795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8114 | 1.11401 | 0.557004 | − | 0.830510i | \(-0.311951\pi\) | ||||
0.557004 | + | 0.830510i | \(0.311951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | 24.0000 | 1.27739 | 0.638696 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638696 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.00000 | −0.264999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.3246 | −1.33844 | ||||||||
\(359\) | −22.0000 | −1.16112 | −0.580558 | − | 0.814219i | \(-0.697165\pi\) | ||||
−0.580558 | + | 0.814219i | \(0.697165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −16.1623 | −0.849470 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.16228 | −0.113334 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.4605 | 1.38123 | 0.690613 | − | 0.723224i | \(-0.257341\pi\) | ||||
0.690613 | + | 0.723224i | \(0.257341\pi\) | |||||||
\(368\) | −5.16228 | −0.269102 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.16228 | −0.319930 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.32456 | −0.431029 | −0.215515 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215515 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(374\) | 10.6491 | 0.550652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.48683 | 0.437675 | ||||||||
\(377\) | −17.6491 | −0.908975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1623 | −0.573368 | −0.286684 | − | 0.958025i | \(-0.592553\pi\) | ||||
−0.286684 | + | 0.958025i | \(0.592553\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6754 | 0.698783 | 0.349391 | − | 0.936977i | \(-0.386388\pi\) | ||||
0.349391 | + | 0.936977i | \(0.386388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.3246 | 1.39078 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.48683 | −0.380086 | ||||||||
\(389\) | 7.51317 | 0.380933 | 0.190466 | − | 0.981694i | \(-0.439000\pi\) | ||||
0.190466 | + | 0.981694i | \(0.439000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4868 | 1.39007 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8114 | 0.947704 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8114 | −0.642985 | −0.321493 | − | 0.946912i | \(-0.604185\pi\) | ||||
−0.321493 | + | 0.946912i | \(0.604185\pi\) | |||||||
\(398\) | 20.1359 | 1.00932 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.83772 | −0.141709 | −0.0708545 | − | 0.997487i | \(-0.522573\pi\) | ||||
−0.0708545 | + | 0.997487i | \(0.522573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6754 | 0.681222 | ||||||||
\(404\) | 3.48683 | 0.173476 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.16228 | 0.405087 | ||||||||
\(407\) | −22.9737 | −1.13876 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.1359 | −1.19345 | −0.596723 | − | 0.802447i | \(-0.703531\pi\) | ||||
−0.596723 | + | 0.802447i | \(0.703531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.32456 | −0.311588 | ||||||||
\(413\) | 12.3246 | 0.606452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.16228 | 0.106014 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | −24.1359 | −1.17912 | −0.589559 | − | 0.807725i | \(-0.700698\pi\) | ||||
−0.589559 | + | 0.807725i | \(0.700698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.6491 | −1.49375 | −0.746873 | − | 0.664967i | \(-0.768446\pi\) | ||||
−0.746873 | + | 0.664967i | \(0.768446\pi\) | |||||||
\(422\) | −12.3246 | −0.599950 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.16228 | 0.299267 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.1623 | 0.491787 | ||||||||
\(428\) | −4.32456 | −0.209035 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.97367 | 0.335910 | 0.167955 | − | 0.985795i | \(-0.446284\pi\) | ||||
0.167955 | + | 0.985795i | \(0.446284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6754 | −0.849428 | −0.424714 | − | 0.905328i | \(-0.639625\pi\) | ||||
−0.424714 | + | 0.905328i | \(0.639625\pi\) | |||||||
\(434\) | −6.32456 | −0.303588 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.48683 | −0.166989 | ||||||||
\(437\) | −15.4868 | −0.740836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.18861 | 0.104457 | 0.0522284 | − | 0.998635i | \(-0.483368\pi\) | ||||
0.0522284 | + | 0.998635i | \(0.483368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.5132 | −0.547626 | ||||||||
\(443\) | 34.6228 | 1.64498 | 0.822489 | − | 0.568781i | \(-0.192585\pi\) | ||||
0.822489 | + | 0.568781i | \(0.192585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.16228 | −0.339144 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −18.8377 | −0.889007 | −0.444504 | − | 0.895777i | \(-0.646620\pi\) | ||||
−0.444504 | + | 0.895777i | \(0.646620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 10.6491 | 0.500892 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.8114 | 1.02366 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.6228 | −1.52603 | −0.763015 | − | 0.646381i | \(-0.776282\pi\) | ||||
−0.763015 | + | 0.646381i | \(0.776282\pi\) | |||||||
\(458\) | 24.1623 | 1.12903 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.16228 | −0.0541327 | −0.0270663 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270663 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.51317 | 0.0703228 | 0.0351614 | − | 0.999382i | \(-0.488805\pi\) | ||||
0.0351614 | + | 0.999382i | \(0.488805\pi\) | |||||||
\(464\) | −8.16228 | −0.378924 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.48683 | 0.161524 | ||||||||
\(467\) | −2.32456 | −0.107568 | −0.0537838 | − | 0.998553i | \(-0.517128\pi\) | ||||
−0.0537838 | + | 0.998553i | \(0.517128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4868 | 0.715116 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.3246 | −0.567284 | ||||||||
\(473\) | −6.32456 | −0.290803 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.32456 | 0.244051 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.81139 | 0.265807 | ||||||||
\(479\) | −2.16228 | −0.0987970 | −0.0493985 | − | 0.998779i | \(-0.515730\pi\) | ||||
−0.0493985 | + | 0.998779i | \(0.515730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.8377 | 1.13250 | ||||||||
\(482\) | −4.51317 | −0.205569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9737 | −0.497264 | −0.248632 | − | 0.968598i | \(-0.579981\pi\) | ||||
−0.248632 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(488\) | −10.1623 | −0.460025 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.67544 | 0.211000 | 0.105500 | − | 0.994419i | \(-0.466356\pi\) | ||||
0.105500 | + | 0.994419i | \(0.466356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.4605 | 1.95736 | ||||||||
\(494\) | 6.48683 | 0.291856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.32456 | 0.283981 | ||||||||
\(497\) | 2.32456 | 0.104271 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1623 | 0.499692 | 0.249846 | − | 0.968286i | \(-0.419620\pi\) | ||||
0.249846 | + | 0.968286i | \(0.419620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.3246 | 0.728601 | ||||||||
\(503\) | 30.0000 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.3246 | 0.458982 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.4868 | −0.642749 | ||||||||
\(509\) | 0.513167 | 0.0227457 | 0.0113729 | − | 0.999935i | \(-0.496380\pi\) | ||||
0.0113729 | + | 0.999935i | \(0.496380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.32456 | 0.368257 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.0000 | −0.838054 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.9737 | −0.746501 | ||||||||
\(518\) | −11.4868 | −0.504702 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6754 | 0.818186 | 0.409093 | − | 0.912493i | \(-0.365845\pi\) | ||||
0.409093 | + | 0.912493i | \(0.365845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6754 | 0.641712 | 0.320856 | − | 0.947128i | \(-0.396029\pi\) | ||||
0.320856 | + | 0.947128i | \(0.396029\pi\) | |||||||
\(524\) | −13.4868 | −0.589175 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.67544 | 0.160257 | ||||||||
\(527\) | −33.6754 | −1.46693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.64911 | 0.158657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.00000 | −0.130066 | ||||||||
\(533\) | −8.64911 | −0.374635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.4868 | −0.668929 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.64911 | 0.114211 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8114 | 0.593798 | 0.296899 | − | 0.954909i | \(-0.404048\pi\) | ||||
0.296899 | + | 0.954909i | \(0.404048\pi\) | |||||||
\(542\) | 10.3246 | 0.443478 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.32456 | −0.228288 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2982 | −0.739619 | −0.369809 | − | 0.929108i | \(-0.620577\pi\) | ||||
−0.369809 | + | 0.929108i | \(0.620577\pi\) | |||||||
\(548\) | −21.4868 | −0.917872 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.4868 | −1.04317 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.48683 | −0.190800 | ||||||||
\(554\) | 4.32456 | 0.183733 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.324555 | −0.0137642 | ||||||||
\(557\) | 32.8114 | 1.39026 | 0.695132 | − | 0.718883i | \(-0.255346\pi\) | ||||
0.695132 | + | 0.718883i | \(0.255346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.83772 | 0.289205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.1623 | −0.639582 | ||||||||
\(563\) | 42.4605 | 1.78950 | 0.894748 | − | 0.446571i | \(-0.147355\pi\) | ||||
0.894748 | + | 0.446571i | \(0.147355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.64911 | −0.153384 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.32456 | −0.0975362 | ||||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2982 | −0.472816 | −0.236408 | − | 0.971654i | \(-0.575970\pi\) | ||||
−0.236408 | + | 0.971654i | \(0.575970\pi\) | |||||||
\(572\) | −4.32456 | −0.180819 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.0000 | 1.16566 | 0.582828 | − | 0.812596i | \(-0.301946\pi\) | ||||
0.582828 | + | 0.812596i | \(0.301946\pi\) | |||||||
\(578\) | 11.3509 | 0.472135 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.16228 | 0.131193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3246 | −0.510431 | ||||||||
\(584\) | −8.32456 | −0.344473 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.1359 | −0.831808 | ||||||||
\(587\) | 25.1623 | 1.03856 | 0.519279 | − | 0.854605i | \(-0.326200\pi\) | ||||
0.519279 | + | 0.854605i | \(0.326200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9737 | 0.781796 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.4868 | 0.472106 | ||||||||
\(593\) | 13.3246 | 0.547174 | 0.273587 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273587 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.486833 | 0.0199415 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.1623 | −0.456459 | ||||||||
\(599\) | 24.1359 | 0.986168 | 0.493084 | − | 0.869982i | \(-0.335870\pi\) | ||||
0.493084 | + | 0.869982i | \(0.335870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.3246 | −1.40013 | −0.700064 | − | 0.714080i | \(-0.746845\pi\) | ||||
−0.700064 | + | 0.714080i | \(0.746845\pi\) | |||||||
\(602\) | −3.16228 | −0.128885 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.83772 | −0.0747759 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.1623 | 1.10248 | 0.551241 | − | 0.834346i | \(-0.314154\pi\) | ||||
0.551241 | + | 0.834346i | \(0.314154\pi\) | |||||||
\(608\) | 3.00000 | 0.121666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.3509 | 0.742398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8114 | −0.800174 | −0.400087 | − | 0.916477i | \(-0.631020\pi\) | ||||
−0.400087 | + | 0.916477i | \(0.631020\pi\) | |||||||
\(614\) | 18.6491 | 0.752617 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −18.5132 | −0.745312 | −0.372656 | − | 0.927970i | \(-0.621553\pi\) | ||||
−0.372656 | + | 0.927970i | \(0.621553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9737 | −1.16455 | −0.582275 | − | 0.812992i | \(-0.697837\pi\) | ||||
−0.582275 | + | 0.812992i | \(0.697837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.0000 | −0.721734 | ||||||||
\(623\) | 5.00000 | 0.200321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.16228 | 0.0464540 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.8377 | −0.711803 | ||||||||
\(629\) | −61.1623 | −2.43870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.1623 | −1.20074 | −0.600371 | − | 0.799722i | \(-0.704980\pi\) | ||||
−0.600371 | + | 0.799722i | \(0.704980\pi\) | |||||||
\(632\) | 4.48683 | 0.178477 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.1623 | −1.11847 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.16228 | 0.0856726 | ||||||||
\(638\) | 16.3246 | 0.646295 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.32456 | −0.0918144 | −0.0459072 | − | 0.998946i | \(-0.514618\pi\) | ||||
−0.0459072 | + | 0.998946i | \(0.514618\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.6491 | 1.09037 | 0.545187 | − | 0.838314i | \(-0.316459\pi\) | ||||
0.545187 | + | 0.838314i | \(0.316459\pi\) | |||||||
\(644\) | 5.16228 | 0.203422 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.9737 | −0.628475 | ||||||||
\(647\) | 43.1359 | 1.69585 | 0.847924 | − | 0.530117i | \(-0.177852\pi\) | ||||
0.847924 | + | 0.530117i | \(0.177852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.6491 | 0.967562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3246 | 0.482667 | ||||||||
\(653\) | −40.4868 | −1.58437 | −0.792186 | − | 0.610280i | \(-0.791057\pi\) | ||||
−0.792186 | + | 0.610280i | \(0.791057\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.00000 | −0.156174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.48683 | −0.330851 | ||||||||
\(659\) | −31.6491 | −1.23287 | −0.616437 | − | 0.787404i | \(-0.711425\pi\) | ||||
−0.616437 | + | 0.787404i | \(0.711425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6491 | −0.880948 | −0.440474 | − | 0.897765i | \(-0.645190\pi\) | ||||
−0.440474 | + | 0.897765i | \(0.645190\pi\) | |||||||
\(662\) | −33.8114 | −1.31412 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.16228 | −0.122720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.1359 | 1.63151 | ||||||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.3246 | 0.784621 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.97367 | −0.114626 | −0.0573132 | − | 0.998356i | \(-0.518253\pi\) | ||||
−0.0573132 | + | 0.998356i | \(0.518253\pi\) | |||||||
\(674\) | −0.675445 | −0.0260172 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.32456 | −0.320175 | ||||||||
\(677\) | −16.3246 | −0.627404 | −0.313702 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313702 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.48683 | 0.287318 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.6491 | −0.484359 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.16228 | 0.120561 | ||||||||
\(689\) | 13.3246 | 0.507625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2982 | 1.03847 | 0.519237 | − | 0.854631i | \(-0.326216\pi\) | ||||
0.519237 | + | 0.854631i | \(0.326216\pi\) | |||||||
\(692\) | 19.1623 | 0.728440 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.0000 | −0.873068 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2982 | 0.806728 | ||||||||
\(698\) | 20.8114 | 0.787723 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.67544 | −0.138820 | −0.0694098 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694098 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4605 | 1.29970 | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | −3.48683 | −0.131136 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.32456 | −0.237524 | −0.118762 | − | 0.992923i | \(-0.537892\pi\) | ||||
−0.118762 | + | 0.992923i | \(0.537892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.00000 | −0.187383 | ||||||||
\(713\) | −32.6491 | −1.22272 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.3246 | −0.946423 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.0000 | −0.821033 | ||||||||
\(719\) | 8.16228 | 0.304402 | 0.152201 | − | 0.988350i | \(-0.451364\pi\) | ||||
0.152201 | + | 0.988350i | \(0.451364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.32456 | 0.235539 | ||||||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.1623 | −0.600666 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8377 | 0.698652 | 0.349326 | − | 0.937001i | \(-0.386411\pi\) | ||||
0.349326 | + | 0.937001i | \(0.386411\pi\) | |||||||
\(728\) | −2.16228 | −0.0801393 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.8377 | −0.622766 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1359 | 0.706802 | 0.353401 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353401 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(734\) | 26.4605 | 0.976675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.16228 | −0.190284 | ||||||||
\(737\) | 30.9737 | 1.14093 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.6491 | 0.686019 | 0.343009 | − | 0.939332i | \(-0.388554\pi\) | ||||
0.343009 | + | 0.939332i | \(0.388554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.16228 | −0.226224 | ||||||||
\(743\) | 11.2982 | 0.414492 | 0.207246 | − | 0.978289i | \(-0.433550\pi\) | ||||
0.207246 | + | 0.978289i | \(0.433550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.32456 | −0.304784 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.6491 | 0.389370 | ||||||||
\(749\) | 4.32456 | 0.158016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.9473 | 1.67664 | 0.838321 | − | 0.545177i | \(-0.183538\pi\) | ||||
0.838321 | + | 0.545177i | \(0.183538\pi\) | |||||||
\(752\) | 8.48683 | 0.309483 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.6491 | −0.642743 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1096 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(758\) | −11.1623 | −0.405432 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9473 | 1.26684 | 0.633420 | − | 0.773808i | \(-0.281651\pi\) | ||||
0.633420 | + | 0.773808i | \(0.281651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.48683 | 0.126232 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6754 | 0.494114 | ||||||||
\(767\) | −26.6491 | −0.962244 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.3246 | 0.983432 | ||||||||
\(773\) | 36.0000 | 1.29483 | 0.647415 | − | 0.762138i | \(-0.275850\pi\) | ||||
0.647415 | + | 0.762138i | \(0.275850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.48683 | −0.268762 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.51317 | 0.269360 | ||||||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.64911 | 0.166358 | ||||||||
\(782\) | 27.4868 | 0.982927 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9737 | −0.747630 | −0.373815 | − | 0.927503i | \(-0.621951\pi\) | ||||
−0.373815 | + | 0.927503i | \(0.621951\pi\) | |||||||
\(788\) | 18.8114 | 0.670128 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6491 | −0.378639 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.9737 | −0.780308 | ||||||||
\(794\) | −12.8114 | −0.454659 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.1359 | 0.713700 | ||||||||
\(797\) | −21.4868 | −0.761103 | −0.380551 | − | 0.924760i | \(-0.624266\pi\) | ||||
−0.380551 | + | 0.924760i | \(0.624266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.1886 | −1.59866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.83772 | −0.100203 | ||||||||
\(803\) | 16.6491 | 0.587534 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.6754 | 0.481697 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.48683 | 0.122666 | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.67544 | 0.129062 | 0.0645312 | − | 0.997916i | \(-0.479445\pi\) | ||||
0.0645312 | + | 0.997916i | \(0.479445\pi\) | |||||||
\(812\) | 8.16228 | 0.286440 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.9737 | −0.805227 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.48683 | 0.331902 | ||||||||
\(818\) | −24.1359 | −0.843893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4605 | −0.469775 | −0.234887 | − | 0.972023i | \(-0.575472\pi\) | ||||
−0.234887 | + | 0.972023i | \(0.575472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.2982 | 1.78814 | 0.894072 | − | 0.447924i | \(-0.147836\pi\) | ||||
0.894072 | + | 0.447924i | \(0.147836\pi\) | |||||||
\(824\) | −6.32456 | −0.220326 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.3246 | 0.428826 | ||||||||
\(827\) | −10.6228 | −0.369390 | −0.184695 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184695 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.1096 | −1.74038 | −0.870189 | − | 0.492717i | \(-0.836004\pi\) | ||||
−0.870189 | + | 0.492717i | \(0.836004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.16228 | 0.0749635 | ||||||||
\(833\) | −5.32456 | −0.184485 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.00000 | −0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.1359 | −0.833762 | ||||||||
\(839\) | 19.7851 | 0.683056 | 0.341528 | − | 0.939872i | \(-0.389056\pi\) | ||||
0.341528 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6228 | 1.29734 | ||||||||
\(842\) | −30.6491 | −1.05624 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.3246 | −0.424229 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | 6.16228 | 0.211613 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −59.2982 | −2.03272 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.6228 | −0.671871 | −0.335936 | − | 0.941885i | \(-0.609052\pi\) | ||||
−0.335936 | + | 0.941885i | \(0.609052\pi\) | |||||||
\(854\) | 10.1623 | 0.347746 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.32456 | −0.147810 | ||||||||
\(857\) | −43.5964 | −1.48923 | −0.744613 | − | 0.667496i | \(-0.767366\pi\) | ||||
−0.744613 | + | 0.667496i | \(0.767366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | 0.818869 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.97367 | 0.237524 | ||||||||
\(863\) | −39.8114 | −1.35520 | −0.677598 | − | 0.735433i | \(-0.736979\pi\) | ||||
−0.677598 | + | 0.735433i | \(0.736979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.6754 | −0.600636 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.32456 | −0.214669 | ||||||||
\(869\) | −8.97367 | −0.304411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4868 | −1.13466 | ||||||||
\(872\) | −3.48683 | −0.118079 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.4868 | −0.523850 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.9737 | −0.775766 | −0.387883 | − | 0.921709i | \(-0.626793\pi\) | ||||
−0.387883 | + | 0.921709i | \(0.626793\pi\) | |||||||
\(878\) | 2.18861 | 0.0738621 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9737 | 1.61627 | 0.808137 | − | 0.588995i | \(-0.200476\pi\) | ||||
0.808137 | + | 0.588995i | \(0.200476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0263 | 0.572982 | 0.286491 | − | 0.958083i | \(-0.407511\pi\) | ||||
0.286491 | + | 0.958083i | \(0.407511\pi\) | |||||||
\(884\) | −11.5132 | −0.387230 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.6228 | 1.16317 | ||||||||
\(887\) | −17.6754 | −0.593483 | −0.296742 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296742 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4868 | 0.485873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.16228 | −0.239811 | ||||||||
\(893\) | 25.4605 | 0.852003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.8377 | −0.628623 | ||||||||
\(899\) | −51.6228 | −1.72172 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.8114 | −1.09311 | ||||||||
\(902\) | 8.00000 | 0.266371 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6491 | 0.354184 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.9737 | 0.497192 | 0.248596 | − | 0.968607i | \(-0.420031\pi\) | ||||
0.248596 | + | 0.968607i | \(0.420031\pi\) | |||||||
\(908\) | 21.8114 | 0.723836 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.29822 | 0.175538 | 0.0877690 | − | 0.996141i | \(-0.472026\pi\) | ||||
0.0877690 | + | 0.996141i | \(0.472026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.32456 | 0.209312 | ||||||||
\(914\) | −32.6228 | −1.07907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.1623 | 0.798344 | ||||||||
\(917\) | 13.4868 | 0.445374 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.2982 | −0.900485 | −0.450243 | − | 0.892906i | \(-0.648663\pi\) | ||||
−0.450243 | + | 0.892906i | \(0.648663\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.16228 | −0.0382776 | ||||||||
\(923\) | −5.02633 | −0.165444 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.51317 | 0.0497258 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.16228 | −0.267940 | ||||||||
\(929\) | 36.2982 | 1.19091 | 0.595453 | − | 0.803390i | \(-0.296973\pi\) | ||||
0.595453 | + | 0.803390i | \(0.296973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | 3.48683 | 0.114215 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.32456 | −0.0760618 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.1359 | 1.04984 | 0.524918 | − | 0.851153i | \(-0.324096\pi\) | ||||
0.524918 | + | 0.851153i | \(0.324096\pi\) | |||||||
\(938\) | 15.4868 | 0.505663 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.7851 | −1.78594 | −0.892971 | − | 0.450114i | \(-0.851383\pi\) | ||||
−0.892971 | + | 0.450114i | \(0.851383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.6491 | 0.672428 | ||||||||
\(944\) | −12.3246 | −0.401130 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.32456 | −0.205629 | ||||||||
\(947\) | −46.0000 | −1.49480 | −0.747400 | − | 0.664375i | \(-0.768698\pi\) | ||||
−0.747400 | + | 0.664375i | \(0.768698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.32456 | 0.172570 | ||||||||
\(953\) | 44.7851 | 1.45073 | 0.725365 | − | 0.688364i | \(-0.241671\pi\) | ||||
0.725365 | + | 0.688364i | \(0.241671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.81139 | 0.187954 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.16228 | −0.0698600 | ||||||||
\(959\) | 21.4868 | 0.693846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.00000 | 0.290323 | ||||||||
\(962\) | 24.8377 | 0.800800 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.51317 | −0.145359 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.51317 | 0.112976 | 0.0564879 | − | 0.998403i | \(-0.482010\pi\) | ||||
0.0564879 | + | 0.998403i | \(0.482010\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.4605 | 0.335693 | 0.167847 | − | 0.985813i | \(-0.446319\pi\) | ||||
0.167847 | + | 0.985813i | \(0.446319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.324555 | 0.0104048 | ||||||||
\(974\) | −10.9737 | −0.351619 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.1623 | −0.325287 | ||||||||
\(977\) | 16.4605 | 0.526618 | 0.263309 | − | 0.964712i | \(-0.415186\pi\) | ||||
0.263309 | + | 0.964712i | \(0.415186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.67544 | 0.149199 | ||||||||
\(983\) | −36.4342 | −1.16207 | −0.581035 | − | 0.813879i | \(-0.697352\pi\) | ||||
−0.581035 | + | 0.813879i | \(0.697352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 43.4605 | 1.38406 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.48683 | 0.206374 | ||||||||
\(989\) | −16.3246 | −0.519091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.5132 | 1.25518 | 0.627589 | − | 0.778545i | \(-0.284042\pi\) | ||||
0.627589 | + | 0.778545i | \(0.284042\pi\) | |||||||
\(992\) | 6.32456 | 0.200805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.32456 | 0.0737304 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.9737 | −0.917605 | −0.458803 | − | 0.888538i | \(-0.651721\pi\) | ||||
−0.458803 | + | 0.888538i | \(0.651721\pi\) | |||||||
\(998\) | 11.1623 | 0.353336 | ||||||||
\(999\) | 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 | 9450.2.a.em.1.2 | yes | 2 | |
3.2 | odd | 2 | 9450.2.a.ee.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 9450.2.a.eh.1.1 | yes | 2 | ||
15.14 | odd | 2 | 9450.2.a.ex.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9450.2.a.ee.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
9450.2.a.eh.1.1 | yes | 2 | 5.4 | even | 2 | ||
9450.2.a.em.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9450.2.a.ex.1.1 | yes | 2 | 15.14 | odd | 2 |