Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 10 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70156 | 1.02109 | 0.510547 | − | 0.859850i | \(-0.329443\pi\) | ||||
0.510547 | + | 0.859850i | \(0.329443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.701562 | 0.211529 | 0.105764 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.701562 | −0.170154 | −0.0850769 | − | 0.996374i | \(-0.527114\pi\) | ||||
−0.0850769 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70156 | −0.589529 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.70156 | 1.39737 | 0.698686 | − | 0.715428i | \(-0.253768\pi\) | ||||
0.698686 | + | 0.715428i | \(0.253768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.40312 | 1.74612 | 0.873058 | − | 0.487616i | \(-0.162133\pi\) | ||||
0.873058 | + | 0.487616i | \(0.162133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.40312 | −1.68885 | −0.844425 | − | 0.535673i | \(-0.820058\pi\) | ||||
−0.844425 | + | 0.535673i | \(0.820058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.701562 | −0.122126 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.70156 | −0.456647 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.70156 | −1.10173 | −0.550865 | − | 0.834594i | \(-0.685702\pi\) | ||||
−0.550865 | + | 0.834594i | \(0.685702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7016 | 1.67130 | 0.835652 | − | 0.549260i | \(-0.185090\pi\) | ||||
0.835652 | + | 0.549260i | \(0.185090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.40312 | −0.204667 | −0.102333 | − | 0.994750i | \(-0.532631\pi\) | ||||
−0.102333 | + | 0.994750i | \(0.532631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.298438 | 0.0426340 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.701562 | 0.0982383 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7016 | 1.46997 | 0.734986 | − | 0.678082i | \(-0.237189\pi\) | ||||
0.734986 | + | 0.678082i | \(0.237189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.701562 | −0.0945986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.8062 | −1.92761 | −0.963805 | − | 0.266609i | \(-0.914097\pi\) | ||||
−0.963805 | + | 0.266609i | \(0.914097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.70156 | 0.345900 | 0.172950 | − | 0.984931i | \(-0.444670\pi\) | ||||
0.172950 | + | 0.984931i | \(0.444670\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.70156 | 0.340365 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.70156 | −0.806773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5078 | 1.84044 | 0.920219 | − | 0.391403i | \(-0.128010\pi\) | ||||
0.920219 | + | 0.391403i | \(0.128010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4031 | 1.56872 | 0.784359 | − | 0.620308i | \(-0.212992\pi\) | ||||
0.784359 | + | 0.620308i | \(0.212992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.89531 | 0.215991 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.70156 | 0.528967 | 0.264484 | − | 0.964390i | \(-0.414799\pi\) | ||||
0.264484 | + | 0.964390i | \(0.414799\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.701562 | 0.0760951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.40312 | −1.00812 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.10469 | 0.859095 | 0.429548 | − | 0.903044i | \(-0.358673\pi\) | ||||
0.429548 | + | 0.903044i | \(0.358673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70156 | −0.283201 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.40312 | 0.975059 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1047 | 1.83825 | 0.919126 | − | 0.393963i | \(-0.128896\pi\) | ||||
0.919126 | + | 0.393963i | \(0.128896\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.701562 | 0.0705096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.80625 | −0.677247 | −0.338624 | − | 0.940922i | \(-0.609961\pi\) | ||||
−0.338624 | + | 0.940922i | \(0.609961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | 1.18240 | 0.591198 | − | 0.806527i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806527i | \(0.298655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.70156 | 0.263645 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.1047 | 1.75025 | 0.875123 | − | 0.483900i | \(-0.160780\pi\) | ||||
0.875123 | + | 0.483900i | \(0.160780\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8062 | 1.03505 | 0.517525 | − | 0.855668i | \(-0.326853\pi\) | ||||
0.517525 | + | 0.855668i | \(0.326853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.70156 | 0.636084 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.59688 | 0.620582 | 0.310291 | − | 0.950642i | \(-0.399574\pi\) | ||||
0.310291 | + | 0.950642i | \(0.399574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.70156 | −0.624924 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.89531 | −0.173743 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5078 | −0.955256 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.7016 | −0.964927 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4031 | −1.18933 | −0.594667 | − | 0.803972i | \(-0.702716\pi\) | ||||
−0.594667 | + | 0.803972i | \(0.702716\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8062 | −1.11889 | −0.559444 | − | 0.828868i | \(-0.688985\pi\) | ||||
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.40312 | −0.468510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.70156 | −0.398781 | −0.199391 | − | 0.979920i | \(-0.563896\pi\) | ||||
−0.199391 | + | 0.979920i | \(0.563896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.40312 | 0.118164 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.701562 | −0.0586676 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.40312 | −0.780887 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.298438 | −0.0246147 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.29844 | 0.106372 | 0.0531861 | − | 0.998585i | \(-0.483062\pi\) | ||||
0.0531861 | + | 0.998585i | \(0.483062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.701562 | −0.0567179 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.40312 | 0.755277 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.80625 | 0.702815 | 0.351408 | − | 0.936223i | \(-0.385703\pi\) | ||||
0.351408 | + | 0.936223i | \(0.385703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7016 | −0.848689 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.1047 | 1.42685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2984 | 0.884962 | 0.442481 | − | 0.896778i | \(-0.354098\pi\) | ||||
0.442481 | + | 0.896778i | \(0.354098\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.701562 | 0.0546165 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.8062 | −1.76480 | −0.882400 | − | 0.470500i | \(-0.844074\pi\) | ||||
−0.882400 | + | 0.470500i | \(0.844074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.70156 | 0.204219 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.8062 | 1.11291 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.0000 | −1.64436 | −0.822179 | − | 0.569230i | \(-0.807242\pi\) | ||||
−0.822179 | + | 0.569230i | \(0.807242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.29844 | −0.0965121 | −0.0482561 | − | 0.998835i | \(-0.515366\pi\) | ||||
−0.0482561 | + | 0.998835i | \(0.515366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.70156 | −0.199705 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.70156 | 0.492709 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.492189 | −0.0359925 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.70156 | −0.196510 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1047 | −1.59113 | −0.795565 | − | 0.605868i | \(-0.792826\pi\) | ||||
−0.795565 | + | 0.605868i | \(0.792826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.2094 | −1.01238 | −0.506188 | − | 0.862423i | \(-0.668946\pi\) | ||||
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.80625 | 0.198930 | 0.0994648 | − | 0.995041i | \(-0.468287\pi\) | ||||
0.0994648 | + | 0.995041i | \(0.468287\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.4031 | 1.78295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7016 | −0.747430 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.70156 | 0.465791 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.40312 | −0.0970561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5078 | −1.06258 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.4031 | −1.72448 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.4031 | −0.905699 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.701562 | 0.0471922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.40312 | 0.227890 | 0.113945 | − | 0.993487i | \(-0.463651\pi\) | ||||
0.113945 | + | 0.993487i | \(0.463651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5969 | −0.703339 | −0.351670 | − | 0.936124i | \(-0.614386\pi\) | ||||
−0.351670 | + | 0.936124i | \(0.614386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.4031 | −1.67869 | −0.839343 | − | 0.543602i | \(-0.817060\pi\) | ||||
−0.839343 | + | 0.543602i | \(0.817060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.89531 | −0.124702 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1047 | −0.661980 | −0.330990 | − | 0.943634i | \(-0.607383\pi\) | ||||
−0.330990 | + | 0.943634i | \(0.607383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.40312 | 0.0915297 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.70156 | −0.305399 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.10469 | −0.394879 | −0.197440 | − | 0.980315i | \(-0.563263\pi\) | ||||
−0.197440 | + | 0.980315i | \(0.563263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.298438 | −0.0190665 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2094 | −1.14937 | −0.574683 | − | 0.818376i | \(-0.694875\pi\) | ||||
−0.574683 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.70156 | 0.295585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.701562 | −0.0439335 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2094 | 1.26063 | 0.630313 | − | 0.776341i | \(-0.282927\pi\) | ||||
0.630313 | + | 0.776341i | \(0.282927\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.1047 | −1.12497 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.40312 | 0.582039 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.59688 | 0.283456 | 0.141728 | − | 0.989906i | \(-0.454734\pi\) | ||||
0.141728 | + | 0.989906i | \(0.454734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7016 | −0.657392 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.10469 | −0.495999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8062 | −0.902753 | −0.451376 | − | 0.892334i | \(-0.649067\pi\) | ||||
−0.451376 | + | 0.892334i | \(0.649067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.59688 | −0.400732 | −0.200366 | − | 0.979721i | \(-0.564213\pi\) | ||||
−0.200366 | + | 0.979721i | \(0.564213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.70156 | 0.163506 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.701562 | 0.0423058 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.80625 | 0.529116 | 0.264558 | − | 0.964370i | \(-0.414774\pi\) | ||||
0.264558 | + | 0.964370i | \(0.414774\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.40312 | −0.562950 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.9109 | 1.70656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5078 | −0.971048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1047 | −1.06132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.4031 | 0.899860 | 0.449930 | − | 0.893064i | \(-0.351449\pi\) | ||||
0.449930 | + | 0.893064i | \(0.351449\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.8062 | 0.862053 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.701562 | −0.0407088 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.70156 | −0.387561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8062 | 0.622862 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.80625 | 0.391009 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.70156 | −0.154691 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8953 | −0.793047 | −0.396524 | − | 0.918024i | \(-0.629784\pi\) | ||||
−0.396524 | + | 0.918024i | \(0.629784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8062 | 0.949945 | 0.474973 | − | 0.880001i | \(-0.342458\pi\) | ||||
0.474973 | + | 0.880001i | \(0.342458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.70156 | −0.152216 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2094 | 0.798078 | 0.399039 | − | 0.916934i | \(-0.369344\pi\) | ||||
0.399039 | + | 0.916934i | \(0.369344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.59688 | 0.369354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1047 | −1.01051 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.40312 | 0.0780719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8062 | −0.597587 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.79063 | −0.208984 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.2094 | −0.781018 | −0.390509 | − | 0.920599i | \(-0.627701\pi\) | ||||
−0.390509 | + | 0.920599i | \(0.627701\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.70156 | −0.367243 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.20937 | −0.338246 | −0.169123 | − | 0.985595i | \(-0.554094\pi\) | ||||
−0.169123 | + | 0.985595i | \(0.554094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.59688 | −0.358293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.59688 | −0.357241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1047 | −0.977561 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.70156 | 0.360800 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.10469 | 0.327717 | 0.163858 | − | 0.986484i | \(-0.447606\pi\) | ||||
0.163858 | + | 0.986484i | \(0.447606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.8062 | −1.86314 | −0.931568 | − | 0.363567i | \(-0.881559\pi\) | ||||
−0.931568 | + | 0.363567i | \(0.881559\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.8062 | 0.681608 | 0.340804 | − | 0.940134i | \(-0.389301\pi\) | ||||
0.340804 | + | 0.940134i | \(0.389301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5078 | −0.823069 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.89531 | 0.100311 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.6125 | −1.14066 | −0.570332 | − | 0.821414i | \(-0.693185\pi\) | ||||
−0.570332 | + | 0.821414i | \(0.693185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5078 | 0.551517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.4031 | −0.701552 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.19375 | 0.0623133 | 0.0311567 | − | 0.999515i | \(-0.490081\pi\) | ||||
0.0311567 | + | 0.999515i | \(0.490081\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7016 | 0.557101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.9109 | 1.50098 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.59688 | −0.445129 | −0.222565 | − | 0.974918i | \(-0.571443\pi\) | ||||
−0.222565 | + | 0.974918i | \(0.571443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.40312 | −0.484286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.6125 | 0.801960 | 0.400980 | − | 0.916087i | \(-0.368670\pi\) | ||||
0.400980 | + | 0.916087i | \(0.368670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4031 | 0.686663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.40312 | −0.276087 | −0.138043 | − | 0.990426i | \(-0.544081\pi\) | ||||
−0.138043 | + | 0.990426i | \(0.544081\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.89531 | −0.0965941 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6125 | 1.29861 | 0.649303 | − | 0.760530i | \(-0.275061\pi\) | ||||
0.649303 | + | 0.760530i | \(0.275061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.70156 | −0.237768 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.8062 | 0.645990 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.70156 | −0.236561 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7016 | −1.13936 | −0.569679 | − | 0.821867i | \(-0.692933\pi\) | ||||
−0.569679 | + | 0.821867i | \(0.692933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.40312 | 0.270495 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.806248 | 0.0402621 | 0.0201311 | − | 0.999797i | \(-0.493592\pi\) | ||||
0.0201311 | + | 0.999797i | \(0.493592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.40312 | 0.468403 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.70156 | −0.233048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.80625 | −0.237654 | −0.118827 | − | 0.992915i | \(-0.537913\pi\) | ||||
−0.118827 | + | 0.992915i | \(0.537913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.0000 | −1.96827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.70156 | 0.230236 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.6125 | 1.34896 | 0.674479 | − | 0.738294i | \(-0.264368\pi\) | ||||
0.674479 | + | 0.738294i | \(0.264368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.6125 | −1.24828 | −0.624138 | − | 0.781314i | \(-0.714550\pi\) | ||||
−0.624138 | + | 0.781314i | \(0.714550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.40312 | −0.0682222 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.701562 | −0.0340308 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.29844 | 0.353196 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.701562 | 0.0338717 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5969 | 0.605367 | 0.302684 | − | 0.953091i | \(-0.402117\pi\) | ||||
0.302684 | + | 0.953091i | \(0.402117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.40312 | 0.450845 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.4031 | −0.641158 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.89531 | −0.0904584 | −0.0452292 | − | 0.998977i | \(-0.514402\pi\) | ||||
−0.0452292 | + | 0.998977i | \(0.514402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.298438 | 0.0142113 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.3141 | −1.25022 | −0.625109 | − | 0.780537i | \(-0.714946\pi\) | ||||
−0.625109 | + | 0.780537i | \(0.714946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.10469 | −0.384199 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.29844 | −0.0614140 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.89531 | 0.183831 | 0.0919156 | − | 0.995767i | \(-0.470701\pi\) | ||||
0.0919156 | + | 0.995767i | \(0.470701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.50781 | 0.353529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.70156 | 0.126651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.29844 | 0.341407 | 0.170703 | − | 0.985322i | \(-0.445396\pi\) | ||||
0.170703 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.701562 | 0.0327461 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.8953 | 0.926617 | 0.463309 | − | 0.886197i | \(-0.346662\pi\) | ||||
0.463309 | + | 0.886197i | \(0.346662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.10469 | −0.190761 | −0.0953805 | − | 0.995441i | \(-0.530407\pi\) | ||||
−0.0953805 | + | 0.995441i | \(0.530407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.40312 | −0.436059 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.1047 | 0.837785 | 0.418892 | − | 0.908036i | \(-0.362418\pi\) | ||||
0.418892 | + | 0.908036i | \(0.362418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8062 | −0.498986 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.80625 | −0.405771 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.80625 | 0.129031 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7016 | 0.489991 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.7016 | −1.31141 | −0.655704 | − | 0.755018i | \(-0.727628\pi\) | ||||
−0.655704 | + | 0.755018i | \(0.727628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.70156 | 0.305565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.1047 | −0.823792 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.1047 | −0.822091 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.3141 | −1.64555 | −0.822774 | − | 0.568369i | \(-0.807574\pi\) | ||||
−0.822774 | + | 0.568369i | \(0.807574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2984 | −0.510933 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.20937 | −0.280225 | −0.140113 | − | 0.990136i | \(-0.544746\pi\) | ||||
−0.140113 | + | 0.990136i | \(0.544746\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.59688 | −0.297108 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.701562 | −0.0315329 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.8953 | 1.87926 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1938 | 0.680166 | 0.340083 | − | 0.940395i | \(-0.389545\pi\) | ||||
0.340083 | + | 0.940395i | \(0.389545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.8062 | 1.01891 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.4031 | 1.40020 | 0.700098 | − | 0.714047i | \(-0.253140\pi\) | ||||
0.700098 | + | 0.714047i | \(0.253140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.80625 | 0.302874 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.3141 | −1.43230 | −0.716148 | − | 0.697949i | \(-0.754096\pi\) | ||||
−0.716148 | + | 0.697949i | \(0.754096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.2094 | 1.60181 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | −0.528783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.984379 | −0.0432929 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.70156 | −0.117906 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.59688 | 0.287364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.9109 | 0.952649 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8062 | −0.642536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7016 | −0.463536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1047 | −0.782734 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.0000 | 0.949370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.209373 | 0.00901832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.2094 | 1.72874 | 0.864368 | − | 0.502860i | \(-0.167719\pi\) | ||||
0.864368 | + | 0.502860i | \(0.167719\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.29844 | 0.0557213 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.8062 | −0.462889 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.6125 | −1.09511 | −0.547556 | − | 0.836769i | \(-0.684442\pi\) | ||||
−0.547556 | + | 0.836769i | \(0.684442\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.70156 | 0.115300 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.8062 | −0.801173 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7016 | 0.540125 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.70156 | −0.284465 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.00000 | 0.0847427 | 0.0423714 | − | 0.999102i | \(-0.486509\pi\) | ||||
0.0423714 | + | 0.999102i | \(0.486509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.492189 | 0.0207803 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.1047 | 0.931601 | 0.465801 | − | 0.884890i | \(-0.345766\pi\) | ||||
0.465801 | + | 0.884890i | \(0.345766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.59688 | −0.277533 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.70156 | 0.113455 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.4031 | −1.14880 | −0.574399 | − | 0.818575i | \(-0.694764\pi\) | ||||
−0.574399 | + | 0.818575i | \(0.694764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.3141 | 1.10121 | 0.550605 | − | 0.834766i | \(-0.314397\pi\) | ||||
0.550605 | + | 0.834766i | \(0.314397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.70156 | 0.279474 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.5078 | −1.31169 | −0.655844 | − | 0.754897i | \(-0.727687\pi\) | ||||
−0.655844 | + | 0.754897i | \(0.727687\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.1047 | 0.918639 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8062 | 0.448319 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.50781 | 0.310942 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.2094 | −0.999228 | −0.499614 | − | 0.866248i | \(-0.666525\pi\) | ||||
−0.499614 | + | 0.866248i | \(0.666525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8062 | 0.774898 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2094 | 0.584495 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.40312 | −0.139750 | −0.0698748 | − | 0.997556i | \(-0.522260\pi\) | ||||
−0.0698748 | + | 0.997556i | \(0.522260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89531 | 0.0777003 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.80625 | −0.114852 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.8062 | −1.74902 | −0.874508 | − | 0.485011i | \(-0.838816\pi\) | ||||
−0.874508 | + | 0.485011i | \(0.838816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.29844 | 0.379291 | 0.189646 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189646 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.5078 | 0.427203 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.6125 | −1.68900 | −0.844500 | − | 0.535556i | \(-0.820102\pi\) | ||||
−0.844500 | + | 0.535556i | \(0.820102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.4031 | −1.02939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.40312 | 0.0567643 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.7172 | −1.84650 | −0.923250 | − | 0.384200i | \(-0.874477\pi\) | ||||
−0.923250 | + | 0.384200i | \(0.874477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.7016 | 0.431529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.6125 | 1.59216 | 0.796080 | − | 0.605191i | \(-0.206903\pi\) | ||||
0.796080 | + | 0.605191i | \(0.206903\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.70156 | −0.268924 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8953 | 0.877217 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.40312 | 0.0560354 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.70156 | 0.187464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.4031 | 0.531887 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.298438 | −0.0118245 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.5078 | 0.613480 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2094 | −0.403246 | −0.201623 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201623 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.2984 | 1.23429 | 0.617145 | − | 0.786849i | \(-0.288289\pi\) | ||||
0.617145 | + | 0.786849i | \(0.288289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.1047 | 0.790397 | 0.395198 | − | 0.918596i | \(-0.370676\pi\) | ||||
0.395198 | + | 0.918596i | \(0.370676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3875 | −0.407745 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.4031 | 0.995627 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6125 | 0.610964 | 0.305482 | − | 0.952198i | \(-0.401182\pi\) | ||||
0.305482 | + | 0.952198i | \(0.401182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8062 | 0.500382 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.4031 | 0.522906 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.4031 | −1.06747 | −0.533737 | − | 0.845650i | \(-0.679213\pi\) | ||||
−0.533737 | + | 0.845650i | \(0.679213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | −0.466746 | −0.233373 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.701562 | −0.0272464 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.40312 | 0.209524 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.0156 | 2.43997 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.40312 | −0.131572 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.89531 | 0.0731678 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.19375 | −0.123110 | −0.0615550 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615550 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.10469 | −0.157756 | −0.0788780 | − | 0.996884i | \(-0.525134\pi\) | ||||
−0.0788780 | + | 0.996884i | \(0.525134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.9109 | 1.87703 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5969 | 0.406073 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.0000 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4031 | 0.969190 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.7016 | −0.407697 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | −0.380418 | −0.190209 | − | 0.981744i | \(-0.560917\pi\) | ||||
−0.190209 | + | 0.981744i | \(0.560917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.89531 | 0.0719970 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.70156 | 0.178340 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.50781 | −0.284379 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.1047 | 0.382194 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.6125 | −0.967371 | −0.483685 | − | 0.875242i | \(-0.660702\pi\) | ||||
−0.483685 | + | 0.875242i | \(0.660702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4031 | 0.505508 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40312 | −0.0528447 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.3875 | −0.691533 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.8062 | 1.60762 | 0.803811 | − | 0.594884i | \(-0.202802\pi\) | ||||
0.803811 | + | 0.594884i | \(0.202802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.70156 | 0.176322 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −63.0156 | −2.35995 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.701562 | 0.0262369 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.10469 | 0.227984 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.19375 | 0.342869 | 0.171435 | − | 0.985196i | \(-0.445160\pi\) | ||||
0.171435 | + | 0.985196i | \(0.445160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.4187 | 1.20734 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.40312 | 0.349223 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.40312 | −0.348743 | −0.174371 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174371 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.80625 | −0.103793 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.7172 | 1.54086 | 0.770430 | − | 0.637525i | \(-0.220042\pi\) | ||||
0.770430 | + | 0.637525i | \(0.220042\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.298438 | 0.0110080 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.80625 | −0.103369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.80625 | −0.323943 | −0.161972 | − | 0.986795i | \(-0.551785\pi\) | ||||
−0.161972 | + | 0.986795i | \(0.551785\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5969 | −0.388762 | −0.194381 | − | 0.980926i | \(-0.562270\pi\) | ||||
−0.194381 | + | 0.980926i | \(0.562270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.29844 | −0.0475711 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.9109 | 1.78717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.3141 | −1.54406 | −0.772031 | − | 0.635585i | \(-0.780759\pi\) | ||||
−0.772031 | + | 0.635585i | \(0.780759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.2094 | 0.663586 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.4031 | −1.72290 | −0.861448 | − | 0.507846i | \(-0.830442\pi\) | ||||
−0.861448 | + | 0.507846i | \(0.830442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.70156 | −0.170656 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.1938 | 1.05688 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.701562 | 0.0253650 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8062 | 0.534623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.4031 | 1.85364 | 0.926822 | − | 0.375501i | \(-0.122529\pi\) | ||||
0.926822 | + | 0.375501i | \(0.122529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.2094 | −0.727823 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.5969 | −1.17243 | −0.586214 | − | 0.810156i | \(-0.699382\pi\) | ||||
−0.586214 | + | 0.810156i | \(0.699382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.40312 | −0.337770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.1047 | 0.649502 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.4031 | −0.766847 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8797 | 0.389306 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.40312 | −0.336040 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.80625 | −0.314308 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.19375 | 0.185137 | 0.0925686 | − | 0.995706i | \(-0.470492\pi\) | ||||
0.0925686 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.59688 | −0.163653 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.8219 | 0.633673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.70156 | −0.0959353 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.7016 | 0.379545 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.7016 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.984379 | 0.0348248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.10469 | 0.286365 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.40312 | 0.331829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.1047 | −0.638106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.8062 | 0.521205 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.806248 | −0.0283462 | −0.0141731 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141731 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2094 | −0.498959 | −0.249479 | − | 0.968380i | \(-0.580259\pi\) | ||||
−0.249479 | + | 0.968380i | \(0.580259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.59688 | 0.231363 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.2984 | −0.395767 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.70156 | −0.0944002 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.49219 | −0.0869780 | −0.0434890 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434890 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | 0.139431 | 0.0697156 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697156 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.701562 | −0.0244253 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5969 | 1.20305 | 0.601526 | − | 0.798854i | \(-0.294560\pi\) | ||||
0.601526 | + | 0.798854i | \(0.294560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.6125 | −1.65365 | −0.826825 | − | 0.562459i | \(-0.809855\pi\) | ||||
−0.826825 | + | 0.562459i | \(0.809855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.80625 | −0.305485 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.209373 | −0.00725433 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.8062 | 0.789243 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.40312 | 0.325020 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.1203 | 1.55773 | 0.778863 | − | 0.627194i | \(-0.215797\pi\) | ||||
0.778863 | + | 0.627194i | \(0.215797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.4187 | 2.04892 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.0000 | −0.344418 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.3875 | −0.975406 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.9109 | −1.53953 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7172 | −0.743582 | −0.371791 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371791 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.7016 | 0.433877 | 0.216939 | − | 0.976185i | \(-0.430393\pi\) | ||||
0.216939 | + | 0.976185i | \(0.430393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.2984 | 1.06789 | 0.533944 | − | 0.845520i | \(-0.320709\pi\) | ||||
0.533944 | + | 0.845520i | \(0.320709\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.9109 | −0.985282 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.4031 | 0.456248 | 0.228124 | − | 0.973632i | \(-0.426741\pi\) | ||||
0.228124 | + | 0.973632i | \(0.426741\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5078 | 0.560635 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.29844 | 0.111892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.1047 | 0.612751 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.70156 | −0.0913295 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.61250 | −0.121985 | −0.0609927 | − | 0.998138i | \(-0.519427\pi\) | ||||
−0.0609927 | + | 0.998138i | \(0.519427\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.4031 | −0.519534 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8062 | −0.431453 | −0.215727 | − | 0.976454i | \(-0.569212\pi\) | ||||
−0.215727 | + | 0.976454i | \(0.569212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.6125 | −0.592708 | −0.296354 | − | 0.955078i | \(-0.595771\pi\) | ||||
−0.296354 | + | 0.955078i | \(0.595771\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.8062 | −0.497707 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.4922 | 0.620907 | 0.310453 | − | 0.950589i | \(-0.399519\pi\) | ||||
0.310453 | + | 0.950589i | \(0.399519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.2094 | −1.21442 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.701562 | 0.0235032 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.80625 | 0.0939075 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0000 | 0.735379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.70156 | 0.223759 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −88.4187 | −2.94893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.50781 | −0.250121 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8062 | −0.359609 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.29844 | 0.0431615 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.2094 | −0.538223 | −0.269112 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269112 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.80625 | −0.225749 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.80625 | 0.225501 | 0.112751 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112751 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.80625 | 0.0928733 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.70156 | 0.0893109 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.5969 | −1.14249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.08907 | 0.233847 | 0.116923 | − | 0.993141i | \(-0.462697\pi\) | ||||
0.116923 | + | 0.993141i | \(0.462697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.8953 | 0.457866 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.5078 | −0.510446 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.70156 | −0.220346 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | 0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.10469 | 0.265906 | 0.132953 | − | 0.991122i | \(-0.457554\pi\) | ||||
0.132953 | + | 0.991122i | \(0.457554\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.596876 | −0.0195618 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.492189 | 0.0160963 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.8062 | 1.72510 | 0.862552 | − | 0.505968i | \(-0.168864\pi\) | ||||
0.862552 | + | 0.505968i | \(0.168864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8062 | −0.548451 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.7016 | −1.78322 | −0.891610 | − | 0.452804i | \(-0.850424\pi\) | ||||
−0.891610 | + | 0.452804i | \(0.850424\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71.7172 | 2.33543 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.70156 | 0.0878818 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.61250 | −0.312364 | −0.156182 | − | 0.987728i | \(-0.549919\pi\) | ||||
−0.156182 | + | 0.987728i | \(0.549919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4031 | −0.435084 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.2094 | −0.460770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.91093 | 0.159081 | 0.0795404 | − | 0.996832i | \(-0.474655\pi\) | ||||
0.0795404 | + | 0.996832i | \(0.474655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.59688 | −0.213247 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.6281 | 1.57028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.4187 | 1.85222 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.1047 | 0.583415 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.1047 | 0.711575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.8219 | 1.28058 | 0.640292 | − | 0.768131i | \(-0.278813\pi\) | ||||
0.640292 | + | 0.768131i | \(0.278813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.40312 | −0.0450748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0156 | 1.82972 | 0.914859 | − | 0.403773i | \(-0.132301\pi\) | ||||
0.914859 | + | 0.403773i | \(0.132301\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.7016 | −0.407193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.2094 | 0.838512 | 0.419256 | − | 0.907868i | \(-0.362291\pi\) | ||||
0.419256 | + | 0.907868i | \(0.362291\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.68594 | 0.181723 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.8062 | 0.345017 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0000 | −0.637901 | −0.318950 | − | 0.947771i | \(-0.603330\pi\) | ||||
−0.318950 | + | 0.947771i | \(0.603330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2094 | 0.452748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.79063 | 0.120657 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.8062 | 0.852389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7172 | 0.880465 | 0.440233 | − | 0.897884i | \(-0.354896\pi\) | ||||
0.440233 | + | 0.897884i | \(0.354896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.2094 | 0.450921 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.80625 | −0.0889641 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.4031 | −1.62795 | −0.813977 | − | 0.580898i | \(-0.802702\pi\) | ||||
−0.813977 | + | 0.580898i | \(0.802702\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.70156 | 0.212028 |
(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 | 1560.2.a.m.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4680.2.a.bb.1.2 | 2 | |||
4.3 | odd | 2 | 3120.2.a.bf.1.1 | 2 | |||
5.4 | even | 2 | 7800.2.a.be.1.1 | 2 | |||
12.11 | even | 2 | 9360.2.a.ct.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.m.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3120.2.a.bf.1.1 | 2 | 4.3 | odd | 2 | |||
4680.2.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
7800.2.a.be.1.1 | 2 | 5.4 | even | 2 | |||
9360.2.a.ct.1.1 | 2 | 12.11 | even | 2 |