Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.88474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(5\) | 3.43697 | 1.53706 | 0.768531 | − | 0.639813i | \(-0.220988\pi\) | ||||
0.768531 | + | 0.639813i | \(0.220988\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70832 | 1.02365 | 0.511824 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511824 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.43697 | 0.887423 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.375819 | −0.0911495 | −0.0455747 | − | 0.998961i | \(-0.514512\pi\) | ||||
−0.0455747 | + | 0.998961i | \(0.514512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70832 | 0.621331 | 0.310666 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310666 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.70832 | 0.591004 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.938844 | 0.195763 | 0.0978813 | − | 0.995198i | \(-0.468793\pi\) | ||||
0.0978813 | + | 0.995198i | \(0.468793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.81279 | 1.36256 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.728654 | 0.135308 | 0.0676539 | − | 0.997709i | \(-0.478449\pi\) | ||||
0.0676539 | + | 0.997709i | \(0.478449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.85361 | −1.23095 | −0.615473 | − | 0.788158i | \(-0.711035\pi\) | ||||
−0.615473 | + | 0.788158i | \(0.711035\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.30843 | 1.57341 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.89179 | 1.62620 | 0.813100 | − | 0.582124i | \(-0.197778\pi\) | ||||
0.813100 | + | 0.582124i | \(0.197778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.83063 | −0.442070 | −0.221035 | − | 0.975266i | \(-0.570944\pi\) | ||||
−0.221035 | + | 0.975266i | \(0.570944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.62418 | −0.247685 | −0.123843 | − | 0.992302i | \(-0.539522\pi\) | ||||
−0.123843 | + | 0.992302i | \(0.539522\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.43697 | 0.512354 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.10447 | −0.161104 | −0.0805520 | − | 0.996750i | \(-0.525668\pi\) | ||||
−0.0805520 | + | 0.996750i | \(0.525668\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.334998 | 0.0478568 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.375819 | −0.0526252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1683 | 1.67144 | 0.835721 | − | 0.549155i | \(-0.185050\pi\) | ||||
0.835721 | + | 0.549155i | \(0.185050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.43697 | −0.463442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.70832 | 0.358726 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.62933 | 0.342309 | 0.171155 | − | 0.985244i | \(-0.445250\pi\) | ||||
0.171155 | + | 0.985244i | \(0.445250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.10447 | −0.397487 | −0.198744 | − | 0.980052i | \(-0.563686\pi\) | ||||
−0.198744 | + | 0.980052i | \(0.563686\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.70832 | 0.341216 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.43697 | −0.426304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.73130 | −0.578021 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.938844 | 0.113024 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.108213 | 0.0128426 | 0.00642128 | − | 0.999979i | \(-0.497956\pi\) | ||||
0.00642128 | + | 0.999979i | \(0.497956\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7046 | 1.60400 | 0.802000 | − | 0.597324i | \(-0.203769\pi\) | ||||
0.802000 | + | 0.597324i | \(0.203769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.81279 | 0.786674 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.70832 | −0.308642 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.03708 | −0.904242 | −0.452121 | − | 0.891957i | \(-0.649333\pi\) | ||||
−0.452121 | + | 0.891957i | \(0.649333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.99626 | 0.548411 | 0.274205 | − | 0.961671i | \(-0.411585\pi\) | ||||
0.274205 | + | 0.961671i | \(0.411585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29168 | −0.140102 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.728654 | 0.0781199 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.33250 | 0.671244 | 0.335622 | − | 0.941997i | \(-0.391054\pi\) | ||||
0.335622 | + | 0.941997i | \(0.391054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70832 | −0.283909 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.85361 | −0.710687 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.30843 | 0.955024 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3951 | 1.56313 | 0.781566 | − | 0.623823i | \(-0.214421\pi\) | ||||
0.781566 | + | 0.623823i | \(0.214421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.750232 | 0.0746509 | 0.0373254 | − | 0.999303i | \(-0.488116\pi\) | ||||
0.0373254 | + | 0.999303i | \(0.488116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.17202 | −0.115482 | −0.0577412 | − | 0.998332i | \(-0.518390\pi\) | ||||
−0.0577412 | + | 0.998332i | \(0.518390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.30843 | 0.908409 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4129 | 1.00665 | 0.503327 | − | 0.864096i | \(-0.332109\pi\) | ||||
0.503327 | + | 0.864096i | \(0.332109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.99891 | −0.861939 | −0.430970 | − | 0.902366i | \(-0.641828\pi\) | ||||
−0.430970 | + | 0.902366i | \(0.641828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.89179 | 0.938887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.78731 | 0.826641 | 0.413320 | − | 0.910586i | \(-0.364369\pi\) | ||||
0.413320 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.22678 | 0.300899 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.01784 | −0.0933050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.83063 | −0.255229 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.23052 | 0.557275 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6842 | 1.39175 | 0.695876 | − | 0.718162i | \(-0.255016\pi\) | ||||
0.695876 | + | 0.718162i | \(0.255016\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.62418 | −0.143001 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.6613 | −1.19359 | −0.596795 | − | 0.802394i | \(-0.703559\pi\) | ||||
−0.596795 | + | 0.802394i | \(0.703559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.33500 | 0.636025 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.43697 | 0.295808 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9543 | −0.935893 | −0.467947 | − | 0.883757i | \(-0.655006\pi\) | ||||
−0.467947 | + | 0.883757i | \(0.655006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.51597 | −0.467858 | −0.233929 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233929 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.10447 | −0.0930134 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50437 | 0.207976 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.334998 | 0.0276301 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.95294 | −0.405761 | −0.202880 | − | 0.979204i | \(-0.565030\pi\) | ||||
−0.202880 | + | 0.979204i | \(0.565030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.124960 | −0.0101691 | −0.00508456 | − | 0.999987i | \(-0.501618\pi\) | ||||
−0.00508456 | + | 0.999987i | \(0.501618\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.375819 | −0.0303832 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.5557 | −1.89204 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3517 | −1.06559 | −0.532793 | − | 0.846246i | \(-0.678857\pi\) | ||||
−0.532793 | + | 0.846246i | \(0.678857\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.1683 | 0.965007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.54269 | 0.200392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0804 | 1.10286 | 0.551431 | − | 0.834221i | \(-0.314082\pi\) | ||||
0.551431 | + | 0.834221i | \(0.314082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.43697 | −0.267568 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1645 | −1.48300 | −0.741498 | − | 0.670955i | \(-0.765884\pi\) | ||||
−0.741498 | + | 0.670955i | \(0.765884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.70832 | 0.207110 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.4115 | 0.791571 | 0.395786 | − | 0.918343i | \(-0.370472\pi\) | ||||
0.395786 | + | 0.918343i | \(0.370472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.4512 | 1.39478 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.62933 | 0.197632 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.273842 | −0.0204679 | −0.0102340 | − | 0.999948i | \(-0.503258\pi\) | ||||
−0.0102340 | + | 0.999948i | \(0.503258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3517 | 1.28975 | 0.644873 | − | 0.764290i | \(-0.276910\pi\) | ||||
0.644873 | + | 0.764290i | \(0.276910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10447 | −0.229489 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.9978 | 2.49957 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.375819 | 0.0274826 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.70832 | 0.197001 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.49298 | 0.252743 | 0.126372 | − | 0.991983i | \(-0.459667\pi\) | ||||
0.126372 | + | 0.991983i | \(0.459667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.33765 | 0.240249 | 0.120125 | − | 0.992759i | \(-0.461671\pi\) | ||||
0.120125 | + | 0.992759i | \(0.461671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.43697 | −0.246127 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4103 | 1.59666 | 0.798332 | − | 0.602217i | \(-0.205716\pi\) | ||||
0.798332 | + | 0.602217i | \(0.205716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12231 | −0.433999 | −0.217000 | − | 0.976172i | \(-0.569627\pi\) | ||||
−0.217000 | + | 0.976172i | \(0.569627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.73130 | −0.333720 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.97343 | 0.138508 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.72881 | −0.679489 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.938844 | 0.0652542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.70832 | −0.187338 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.6983 | −1.21840 | −0.609202 | − | 0.793015i | \(-0.708510\pi\) | ||||
−0.609202 | + | 0.793015i | \(0.708510\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.108213 | 0.00741465 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.58227 | −0.380708 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.5618 | −1.26006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.7046 | 0.926070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.375819 | 0.0252803 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5111 | −1.70835 | −0.854176 | − | 0.519984i | \(-0.825938\pi\) | ||||
−0.854176 | + | 0.519984i | \(0.825938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.81279 | 0.454186 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.3339 | −0.951375 | −0.475687 | − | 0.879614i | \(-0.657801\pi\) | ||||
−0.475687 | + | 0.879614i | \(0.657801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2321 | −1.13873 | −0.569364 | − | 0.822086i | \(-0.692810\pi\) | ||||
−0.569364 | + | 0.822086i | \(0.692810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.70832 | −0.178194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.64576 | 0.500890 | 0.250445 | − | 0.968131i | \(-0.419423\pi\) | ||||
0.250445 | + | 0.968131i | \(0.419423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.79605 | −0.247627 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.03708 | −0.522065 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4919 | −0.678664 | −0.339332 | − | 0.940667i | \(-0.610201\pi\) | ||||
−0.339332 | + | 0.940667i | \(0.610201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3772 | −0.668456 | −0.334228 | − | 0.942492i | \(-0.608476\pi\) | ||||
−0.334228 | + | 0.942492i | \(0.608476\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.15138 | 0.0735589 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.70832 | −0.172326 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.99626 | 0.316625 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.53521 | 0.538738 | 0.269369 | − | 0.963037i | \(-0.413185\pi\) | ||||
0.269369 | + | 0.963037i | \(0.413185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.938844 | −0.0590246 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.29168 | −0.0808881 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.29433 | 0.0807380 | 0.0403690 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403690 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.7901 | 1.66466 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.728654 | 0.0451026 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4204 | −0.765873 | −0.382937 | − | 0.923775i | \(-0.625087\pi\) | ||||
−0.382937 | + | 0.923775i | \(0.625087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.8221 | 2.56911 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.33250 | 0.387543 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.5774 | −1.43754 | −0.718771 | − | 0.695247i | \(-0.755295\pi\) | ||||
−0.718771 | + | 0.695247i | \(0.755295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.871300 | −0.0529277 | −0.0264638 | − | 0.999650i | \(-0.508425\pi\) | ||||
−0.0264638 | + | 0.999650i | \(0.508425\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.70832 | −0.163915 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.81279 | −0.410827 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2499 | 1.09653 | 0.548266 | − | 0.836304i | \(-0.315288\pi\) | ||||
0.548266 | + | 0.836304i | \(0.315288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.85361 | −0.410315 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.4578 | −1.87661 | −0.938307 | − | 0.345804i | \(-0.887606\pi\) | ||||
−0.938307 | + | 0.345804i | \(0.887606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.89693 | 0.528868 | 0.264434 | − | 0.964404i | \(-0.414815\pi\) | ||||
0.264434 | + | 0.964404i | \(0.414815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.30843 | 0.551384 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.66626 | −0.452525 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8588 | −0.991692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3951 | 0.902475 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1656 | 0.593882 | 0.296941 | − | 0.954896i | \(-0.404033\pi\) | ||||
0.296941 | + | 0.954896i | \(0.404033\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.03693 | 0.526150 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.938844 | −0.0542948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.39880 | −0.253543 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.750232 | 0.0430997 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.6700 | −0.610962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.2116 | −0.696953 | −0.348476 | − | 0.937318i | \(-0.613301\pi\) | ||||
−0.348476 | + | 0.937318i | \(0.613301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17202 | −0.0666738 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9811 | −0.792794 | −0.396397 | − | 0.918079i | \(-0.629740\pi\) | ||||
−0.396397 | + | 0.918079i | \(0.629740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1465 | 0.573516 | 0.286758 | − | 0.958003i | \(-0.407422\pi\) | ||||
0.286758 | + | 0.958003i | \(0.407422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.30843 | 0.524470 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.74540 | −0.491191 | −0.245595 | − | 0.969372i | \(-0.578983\pi\) | ||||
−0.245595 | + | 0.969372i | \(0.578983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.728654 | −0.0407968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4129 | 0.581191 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.01784 | −0.0566340 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.81279 | −0.377906 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.99891 | −0.497641 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.99127 | −0.164914 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8320 | −0.595383 | −0.297691 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297691 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.89179 | 0.542067 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.2614 | −0.888454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.3707 | −0.837294 | −0.418647 | − | 0.908149i | \(-0.637496\pi\) | ||||
−0.418647 | + | 0.908149i | \(0.637496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.78731 | 0.477261 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.85361 | 0.371144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0510 | −0.974660 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.22678 | 0.173724 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.7176 | −1.54164 | −0.770820 | − | 0.637052i | \(-0.780153\pi\) | ||||
−0.770820 | + | 0.637052i | \(0.780153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4486 | −1.20164 | −0.600822 | − | 0.799383i | \(-0.705160\pi\) | ||||
−0.600822 | + | 0.799383i | \(0.705160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3109 | 1.18749 | 0.593745 | − | 0.804653i | \(-0.297649\pi\) | ||||
0.593745 | + | 0.804653i | \(0.297649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.371926 | 0.0197398 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.01784 | −0.0538697 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.75803 | 0.303897 | 0.151949 | − | 0.988388i | \(-0.451445\pi\) | ||||
0.151949 | + | 0.988388i | \(0.451445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.6650 | −0.613947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.1023 | 2.46545 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.07634 | −0.108384 | −0.0541921 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541921 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.83063 | −0.147357 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.9556 | 1.71097 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.4129 | −1.47116 | −0.735582 | − | 0.677436i | \(-0.763091\pi\) | ||||
−0.735582 | + | 0.677436i | \(0.763091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.23052 | 0.321743 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.728654 | −0.0375276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.24213 | 0.269270 | 0.134635 | − | 0.990895i | \(-0.457014\pi\) | ||||
0.134635 | + | 0.990895i | \(0.457014\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.6842 | 0.803528 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.83702 | 0.298258 | 0.149129 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149129 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.30843 | −0.474401 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.62418 | −0.0825618 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.9941 | 1.67287 | 0.836433 | − | 0.548069i | \(-0.184637\pi\) | ||||
0.836433 | + | 0.548069i | \(0.184637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.352835 | −0.0178437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.6613 | −0.689120 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.6232 | −1.38988 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6472 | 0.684932 | 0.342466 | − | 0.939530i | \(-0.388738\pi\) | ||||
0.342466 | + | 0.939530i | \(0.388738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.33500 | 0.367209 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4689 | 0.722543 | 0.361271 | − | 0.932461i | \(-0.382343\pi\) | ||||
0.361271 | + | 0.932461i | \(0.382343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.85361 | 0.341403 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.43697 | 0.170785 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.89179 | −0.490318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.2879 | −0.607600 | −0.303800 | − | 0.952736i | \(-0.598255\pi\) | ||||
−0.303800 | + | 0.952736i | \(0.598255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9543 | −0.540338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.12106 | 0.350404 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.1720 | 0.842941 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.51597 | −0.270118 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.17973 | 0.301899 | 0.150950 | − | 0.988541i | \(-0.451767\pi\) | ||||
0.150950 | + | 0.988541i | \(0.451767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0726 | −0.637120 | −0.318560 | − | 0.947903i | \(-0.603199\pi\) | ||||
−0.318560 | + | 0.947903i | \(0.603199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.10447 | −0.0537013 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.56038 | −0.124196 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.40791 | −0.406887 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.4092 | 0.742233 | 0.371117 | − | 0.928586i | \(-0.378975\pi\) | ||||
0.371117 | + | 0.928586i | \(0.378975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.07790 | −0.244028 | −0.122014 | − | 0.992528i | \(-0.538935\pi\) | ||||
−0.122014 | + | 0.992528i | \(0.538935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.50437 | 0.120075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.54269 | 0.121633 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6270 | 1.03220 | 0.516100 | − | 0.856528i | \(-0.327383\pi\) | ||||
0.516100 | + | 0.856528i | \(0.327383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.334998 | 0.0159523 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.2437 | −1.76950 | −0.884751 | − | 0.466065i | \(-0.845671\pi\) | ||||
−0.884751 | + | 0.466065i | \(0.845671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.7646 | 1.03174 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.95294 | −0.234266 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.4332 | −0.775532 | −0.387766 | − | 0.921758i | \(-0.626753\pi\) | ||||
−0.387766 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.83063 | 0.133289 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.124960 | −0.00587114 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.30843 | −0.436386 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.9059 | 1.11827 | 0.559135 | − | 0.829077i | \(-0.311133\pi\) | ||||
0.559135 | + | 0.829077i | \(0.311133\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.375819 | −0.0175417 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1619 | 0.519861 | 0.259930 | − | 0.965627i | \(-0.416300\pi\) | ||||
0.259930 | + | 0.965627i | \(0.416300\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2524 | 0.522944 | 0.261472 | − | 0.965211i | \(-0.415792\pi\) | ||||
0.261472 | + | 0.965211i | \(0.415792\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23.5557 | −1.09237 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.9736 | 1.10937 | 0.554683 | − | 0.832062i | \(-0.312840\pi\) | ||||
0.554683 | + | 0.832062i | \(0.312840\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8139 | −0.591690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3517 | −0.615216 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.62418 | 0.0746799 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.4512 | 0.846600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.1683 | 0.557147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.16719 | −0.236095 | −0.118047 | − | 0.993008i | \(-0.537663\pi\) | ||||
−0.118047 | + | 0.993008i | \(0.537663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.89179 | −0.451027 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.54269 | 0.115696 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 52.9124 | 2.40263 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.38065 | 0.107878 | 0.0539388 | − | 0.998544i | \(-0.482822\pi\) | ||||
0.0539388 | + | 0.998544i | \(0.482822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0804 | 0.636738 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.48918 | −0.157464 | −0.0787322 | − | 0.996896i | \(-0.525087\pi\) | ||||
−0.0787322 | + | 0.996896i | \(0.525087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.273842 | −0.0123332 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.43697 | −0.154481 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.293076 | 0.0131463 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.1048 | −1.52674 | −0.763370 | − | 0.645961i | \(-0.776457\pi\) | ||||
−0.763370 | + | 0.645961i | \(0.776457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.1645 | −0.856208 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.6218 | 1.45454 | 0.727268 | − | 0.686353i | \(-0.240790\pi\) | ||||
0.727268 | + | 0.686353i | \(0.240790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.57853 | 0.114743 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.8299 | 1.72110 | 0.860552 | − | 0.509363i | \(-0.170119\pi\) | ||||
0.860552 | + | 0.509363i | \(0.170119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.1164 | 1.64193 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.70832 | 0.119575 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.02820 | −0.177504 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.10447 | 0.0485747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.4115 | 0.457014 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.3366 | 0.628096 | 0.314048 | − | 0.949407i | \(-0.398315\pi\) | ||||
0.314048 | + | 0.949407i | \(0.398315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4500 | 0.631854 | 0.315927 | − | 0.948784i | \(-0.397685\pi\) | ||||
0.315927 | + | 0.948784i | \(0.397685\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.4512 | 0.805277 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.57572 | 0.112200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1186 | −0.961677 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.62933 | 0.114103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.83063 | 0.122608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.7889 | 1.54729 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.273842 | −0.0118172 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.334998 | −0.0144294 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.0770 | −1.80903 | −0.904515 | − | 0.426441i | \(-0.859767\pi\) | ||||
−0.904515 | + | 0.426441i | \(0.859767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3517 | 0.744635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.9290 | −1.32485 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.3098 | −0.996656 | −0.498328 | − | 0.866988i | \(-0.666053\pi\) | ||||
−0.498328 | + | 0.866988i | \(0.666053\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.10447 | −0.132496 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.97343 | 0.0840709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.7670 | −0.925627 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.9978 | 1.44313 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.0374 | −1.65407 | −0.827034 | − | 0.562152i | \(-0.809973\pi\) | ||||
−0.827034 | + | 0.562152i | \(0.809973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.62418 | 0.0686955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.375819 | 0.0158671 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.08008 | −0.214100 | −0.107050 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107050 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.2018 | 1.27060 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.70832 | 0.113739 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6664 | −0.698692 | −0.349346 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349346 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.5863 | 1.23815 | 0.619075 | − | 0.785332i | \(-0.287508\pi\) | ||||
0.619075 | + | 0.785332i | \(0.287508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.49298 | 0.145922 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.39615 | 0.266738 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.41009 | 0.183594 | 0.0917972 | − | 0.995778i | \(-0.470739\pi\) | ||||
0.0917972 | + | 0.995778i | \(0.470739\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.33765 | 0.138708 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5315 | 0.561380 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.1683 | −0.503959 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.43697 | −0.142101 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.91618 | 0.161638 | 0.0808189 | − | 0.996729i | \(-0.474246\pi\) | ||||
0.0808189 | + | 0.996729i | \(0.474246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.5618 | −0.764825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4103 | 0.921835 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.96323 | 0.285946 | 0.142973 | − | 0.989727i | \(-0.454334\pi\) | ||||
0.142973 | + | 0.989727i | \(0.454334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.49828 | −0.143416 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.12231 | −0.250570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.8221 | 1.38193 | 0.690966 | − | 0.722887i | \(-0.257185\pi\) | ||||
0.690966 | + | 0.722887i | \(0.257185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2934 | 1.23569 | 0.617847 | − | 0.786299i | \(-0.288005\pi\) | ||||
0.617847 | + | 0.786299i | \(0.288005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.73130 | −0.192674 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43697 | 0.139733 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.60634 | 0.349321 | 0.174660 | − | 0.984629i | \(-0.444117\pi\) | ||||
0.174660 | + | 0.984629i | \(0.444117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.97343 | 0.0799674 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10447 | 0.0446822 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.58975 | −0.387326 | −0.193663 | − | 0.981068i | \(-0.562037\pi\) | ||||
−0.193663 | + | 0.981068i | \(0.562037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.72881 | −0.392303 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.1073 | −1.13156 | −0.565778 | − | 0.824558i | \(-0.691424\pi\) | ||||
−0.565778 | + | 0.824558i | \(0.691424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.33780 | −0.174351 | −0.0871754 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871754 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.938844 | 0.0376745 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.1504 | 0.687118 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.6498 | −0.505993 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.70832 | −0.108160 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.71752 | −0.148227 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.6321 | 0.940780 | 0.470390 | − | 0.882459i | \(-0.344113\pi\) | ||||
0.470390 | + | 0.882459i | \(0.344113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.6983 | −0.703446 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 53.9064 | 2.13921 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.334998 | −0.0132731 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.108213 | 0.00428085 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.92740 | −0.115625 | −0.0578126 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578126 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.6334 | −0.774268 | −0.387134 | − | 0.922024i | \(-0.626535\pi\) | ||||
−0.387134 | + | 0.922024i | \(0.626535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.58227 | −0.219802 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.4855 | 1.15919 | 0.579597 | − | 0.814903i | \(-0.303210\pi\) | ||||
0.579597 | + | 0.814903i | \(0.303210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.62933 | −0.103210 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.5618 | −0.727494 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7554 | 0.538290 | 0.269145 | − | 0.963100i | \(-0.413259\pi\) | ||||
0.269145 | + | 0.963100i | \(0.413259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.9534 | −1.83462 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.7046 | 0.534667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.35658 | −0.130754 | −0.0653768 | − | 0.997861i | \(-0.520825\pi\) | ||||
−0.0653768 | + | 0.997861i | \(0.520825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.49298 | −0.0580704 | −0.0290352 | − | 0.999578i | \(-0.509243\pi\) | ||||
−0.0290352 | + | 0.999578i | \(0.509243\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.375819 | 0.0145956 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.2102 | 0.977610 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.684093 | 0.0264882 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.5111 | −0.986318 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.10447 | 0.119847 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.0725376 | −0.00279612 | −0.00139806 | − | 0.999999i | \(-0.500445\pi\) | ||||
−0.00139806 | + | 0.999999i | \(0.500445\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.81279 | 0.262225 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.81404 | −0.377184 | −0.188592 | − | 0.982056i | \(-0.560392\pi\) | ||||
−0.188592 | + | 0.982056i | \(0.560392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.6948 | 1.60010 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.3339 | −0.549277 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6115 | 0.979996 | 0.489998 | − | 0.871723i | \(-0.336997\pi\) | ||||
0.489998 | + | 0.871723i | \(0.336997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.6498 | −1.43853 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.2321 | −0.657445 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.1683 | −0.463574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.6920 | 1.39583 | 0.697914 | − | 0.716182i | \(-0.254112\pi\) | ||||
0.697914 | + | 0.716182i | \(0.254112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.70832 | −0.102881 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9582 | −0.719127 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.06380 | 0.0402945 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.64576 | 0.289189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.94141 | −0.262173 | −0.131087 | − | 0.991371i | \(-0.541847\pi\) | ||||
−0.131087 | + | 0.991371i | \(0.541847\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.7901 | 1.01041 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.79605 | −0.142967 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.03187 | 0.0764163 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.1098 | 0.867906 | 0.433953 | − | 0.900936i | \(-0.357118\pi\) | ||||
0.433953 | + | 0.900936i | \(0.357118\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.03708 | −0.301414 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.43448 | −0.240973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.43697 | 0.128536 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.4919 | −0.391827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.2868 | 1.09222 | 0.546108 | − | 0.837715i | \(-0.316109\pi\) | ||||
0.546108 | + | 0.837715i | \(0.316109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.17420 | −0.118213 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3772 | −0.385933 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.96417 | 0.184365 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.5277 | 1.42891 | 0.714457 | − | 0.699679i | \(-0.246674\pi\) | ||||
0.714457 | + | 0.699679i | \(0.246674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.610398 | 0.0225764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.9545 | −1.54962 | −0.774812 | − | 0.632191i | \(-0.782156\pi\) | ||||
−0.774812 | + | 0.632191i | \(0.782156\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15138 | 0.0424692 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.73130 | 0.174280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.5407 | −1.27060 | −0.635300 | − | 0.772266i | \(-0.719123\pi\) | ||||
−0.635300 | + | 0.772266i | \(0.719123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.70832 | −0.0994926 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.881429 | −0.0323365 | −0.0161682 | − | 0.999869i | \(-0.505147\pi\) | ||||
−0.0161682 | + | 0.999869i | \(0.505147\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0231 | −0.623679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.99626 | 0.182804 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.2015 | 1.03046 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2040 | 1.32110 | 0.660551 | − | 0.750782i | \(-0.270323\pi\) | ||||
0.660551 | + | 0.750782i | \(0.270323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.53521 | 0.311040 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.429485 | −0.0156306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.1353 | −1.34971 | −0.674853 | − | 0.737952i | \(-0.735793\pi\) | ||||
−0.674853 | + | 0.737952i | \(0.735793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.938844 | −0.0340779 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.7825 | −0.753364 | −0.376682 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376682 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.3719 | −0.882323 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.29168 | −0.0467008 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.62933 | −0.0949395 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.4501 | −1.85534 | −0.927670 | − | 0.373402i | \(-0.878191\pi\) | ||||
−0.927670 | + | 0.373402i | \(0.878191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29433 | 0.0466141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.8730 | −1.54204 | −0.771018 | − | 0.636814i | \(-0.780252\pi\) | ||||
−0.771018 | + | 0.636814i | \(0.780252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.6923 | −1.67724 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.7901 | 0.961090 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.66626 | −0.274672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.108213 | −0.00387217 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.728654 | 0.0260400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −45.8896 | −1.63787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5429 | 1.01744 | 0.508721 | − | 0.860931i | \(-0.330118\pi\) | ||||
0.508721 | + | 0.860931i | \(0.330118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4204 | −0.442177 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.7989 | 0.846190 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.10447 | 0.110243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.8221 | 1.48328 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8702 | 1.34143 | 0.670716 | − | 0.741714i | \(-0.265987\pi\) | ||||
0.670716 | + | 0.741714i | \(0.265987\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.415082 | 0.0146845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.33250 | 0.223748 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7046 | −0.483624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.73916 | 0.308015 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.5774 | −0.829965 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.13494 | −0.110219 | −0.0551093 | − | 0.998480i | \(-0.517551\pi\) | ||||
−0.0551093 | + | 0.998480i | \(0.517551\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.9455 | −1.71871 | −0.859354 | − | 0.511381i | \(-0.829134\pi\) | ||||
−0.859354 | + | 0.511381i | \(0.829134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.871300 | −0.0305578 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.3940 | 1.69517 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.39880 | −0.153895 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.70832 | −0.0946364 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.7077 | 1.66501 | 0.832505 | − | 0.554017i | \(-0.186906\pi\) | ||||
0.832505 | + | 0.554017i | \(0.186906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.8361 | 1.35374 | 0.676871 | − | 0.736102i | \(-0.263336\pi\) | ||||
0.676871 | + | 0.736102i | \(0.263336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.81279 | −0.237191 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.78092 | −0.0619288 | −0.0309644 | − | 0.999520i | \(-0.509858\pi\) | ||||
−0.0309644 | + | 0.999520i | \(0.509858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.3216 | −1.46989 | −0.734945 | − | 0.678127i | \(-0.762792\pi\) | ||||
−0.734945 | + | 0.678127i | \(0.762792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2499 | 0.633083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.125898 | −0.00436212 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.8680 | −2.27946 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.85361 | −0.236896 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.83546 | 0.305034 | 0.152517 | − | 0.988301i | \(-0.451262\pi\) | ||||
0.152517 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4691 | −0.981692 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.4578 | −1.08346 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43697 | 0.118236 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.70832 | 0.0930590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.89693 | 0.305342 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.28685 | 0.318349 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6753 | 0.433994 | 0.216997 | − | 0.976172i | \(-0.430374\pi\) | ||||
0.216997 | + | 0.976172i | \(0.430374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.30843 | 0.318341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.756850 | 0.0258535 | 0.0129268 | − | 0.999916i | \(-0.495885\pi\) | ||||
0.0129268 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8727 | −0.541569 | −0.270785 | − | 0.962640i | \(-0.587283\pi\) | ||||
−0.270785 | + | 0.962640i | \(0.587283\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.66626 | −0.261265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.47134 | −0.0841254 | −0.0420627 | − | 0.999115i | \(-0.513393\pi\) | ||||
−0.0420627 | + | 0.999115i | \(0.513393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.7840 | 1.21669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8588 | −0.572554 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.03708 | 0.272639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.73130 | 0.160314 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.3951 | 0.521044 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.8743 | 0.570454 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.66407 | 0.258797 | 0.129399 | − | 0.991593i | \(-0.458695\pi\) | ||||
0.129399 | + | 0.991593i | \(0.458695\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1656 | 0.342878 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.7544 | −0.497090 | −0.248545 | − | 0.968620i | \(-0.579952\pi\) | ||||
−0.248545 | + | 0.968620i | \(0.579952\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.45887 | 0.217358 | 0.108679 | − | 0.994077i | \(-0.465338\pi\) | ||||
0.108679 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.03693 | 0.303773 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.1889 | 1.04722 | 0.523611 | − | 0.851958i | \(-0.324585\pi\) | ||||
0.523611 | + | 0.851958i | \(0.324585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.4780 | 1.42466 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.99127 | −0.100099 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.941188 | −0.0314605 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.938844 | −0.0313471 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.99392 | −0.166556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.57307 | −0.152351 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.39880 | −0.146383 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59.6375 | 1.98242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4204 | −1.07650 | −0.538251 | − | 0.842785i | \(-0.680915\pi\) | ||||
−0.538251 | + | 0.842785i | \(0.680915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.750232 | 0.0248836 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.2083 | −1.63034 | −0.815172 | − | 0.579219i | \(-0.803358\pi\) | ||||
−0.815172 | + | 0.579219i | \(0.803358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.99626 | −0.165352 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.6700 | −0.352739 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.9991 | −1.22182 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2692 | −0.503683 | −0.251842 | − | 0.967768i | \(-0.581036\pi\) | ||||
−0.251842 | + | 0.967768i | \(0.581036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.2116 | −0.402386 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.108213 | −0.00356188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 67.3907 | 2.21579 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.17202 | −0.0384941 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.3644 | −0.700944 | −0.350472 | − | 0.936573i | \(-0.613979\pi\) | ||||
−0.350472 | + | 0.936573i | \(0.613979\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.907281 | 0.0297349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.9811 | −0.457720 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.29168 | 0.0422425 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.74128 | 0.122222 | 0.0611111 | − | 0.998131i | \(-0.480536\pi\) | ||||
0.0611111 | + | 0.998131i | \(0.480536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.1465 | 0.331120 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.50063 | −0.179315 | −0.0896576 | − | 0.995973i | \(-0.528577\pi\) | ||||
−0.0896576 | + | 0.995973i | \(0.528577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.65752 | −0.0865408 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.30843 | 0.302803 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7939 | 1.52060 | 0.760299 | − | 0.649573i | \(-0.225052\pi\) | ||||
0.760299 | + | 0.649573i | \(0.225052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.7046 | −0.444869 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.74540 | −0.283589 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5138 | −0.696900 | −0.348450 | − | 0.937327i | \(-0.613292\pi\) | ||||
−0.348450 | + | 0.937327i | \(0.613292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0053 | 0.388482 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.728654 | −0.0235541 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.6679 | −0.958026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.9720 | 0.515227 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.4129 | 0.335551 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4714 | 0.369278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.0271 | −1.76955 | −0.884776 | − | 0.466016i | \(-0.845689\pi\) | ||||
−0.884776 | + | 0.466016i | \(0.845689\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.01784 | −0.0326977 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.4346 | −0.655779 | −0.327889 | − | 0.944716i | \(-0.606337\pi\) | ||||
−0.327889 | + | 0.944716i | \(0.606337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.9390 | −0.478923 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.81279 | −0.218184 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1567 | 0.964800 | 0.482400 | − | 0.875951i | \(-0.339765\pi\) | ||||
0.482400 | + | 0.875951i | \(0.339765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.33250 | −0.202388 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.99891 | −0.287313 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.4871 | 0.844806 | 0.422403 | − | 0.906408i | \(-0.361187\pi\) | ||||
0.422403 | + | 0.906408i | \(0.361187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 77.0235 | 2.45417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.99127 | −0.0952131 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.52485 | −0.0484875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.7072 | 0.943681 | 0.471841 | − | 0.881684i | \(-0.343590\pi\) | ||||
0.471841 | + | 0.881684i | \(0.343590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.8320 | −0.343744 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0422 | −0.667083 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9444 | 0.441623 | 0.220811 | − | 0.975317i | \(-0.429129\pi\) | ||||
0.220811 | + | 0.975317i | \(0.429129\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.89179 | 0.312962 |
(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 | 6864.2.a.cc.1.3 | 4 | ||
4.3 | odd | 2 | 3432.2.a.t.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.t.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
6864.2.a.cc.1.3 | 4 | 1.1 | even | 1 | trivial |