Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6975,2,Mod(1,6975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6975.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6975 = 3^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6975.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: | \(55.6956554098\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 20x^{14} + 152x^{12} - 571x^{10} + 1130x^{8} - 1138x^{6} + 492x^{4} - 43x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 1395) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-1.11940\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6975.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33304 | 0.942602 | 0.471301 | − | 0.881972i | \(-0.343785\pi\) | ||||
0.471301 | + | 0.881972i | \(0.343785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.223003 | −0.111501 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.26227 | 0.855056 | 0.427528 | − | 0.904002i | \(-0.359385\pi\) | ||||
0.427528 | + | 0.904002i | \(0.359385\pi\) | |||||||
\(8\) | −2.96335 | −1.04770 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.88845 | 1.47392 | 0.736962 | − | 0.675935i | \(-0.236260\pi\) | ||||
0.736962 | + | 0.675935i | \(0.236260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.07923 | 1.68607 | 0.843037 | − | 0.537855i | \(-0.180765\pi\) | ||||
0.843037 | + | 0.537855i | \(0.180765\pi\) | |||||||
\(14\) | 3.01569 | 0.805977 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.50426 | −0.876066 | ||||||||
\(17\) | 4.32765 | 1.04961 | 0.524805 | − | 0.851222i | \(-0.324138\pi\) | ||||
0.524805 | + | 0.851222i | \(0.324138\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.22973 | −1.65861 | −0.829307 | − | 0.558793i | \(-0.811265\pi\) | ||||
−0.829307 | + | 0.558793i | \(0.811265\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.51650 | 1.38932 | ||||||||
\(23\) | 4.12776 | 0.860697 | 0.430348 | − | 0.902663i | \(-0.358391\pi\) | ||||
0.430348 | + | 0.902663i | \(0.358391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.10386 | 1.58930 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.504492 | −0.0953400 | ||||||||
\(29\) | 4.04025 | 0.750256 | 0.375128 | − | 0.926973i | \(-0.377599\pi\) | ||||
0.375128 | + | 0.926973i | \(0.377599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.25538 | 0.221922 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.76894 | 0.989365 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.36881 | −1.04703 | −0.523513 | − | 0.852018i | \(-0.675379\pi\) | ||||
−0.523513 | + | 0.852018i | \(0.675379\pi\) | |||||||
\(38\) | −9.63753 | −1.56341 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.39034 | −1.31035 | −0.655175 | − | 0.755477i | \(-0.727405\pi\) | ||||
−0.655175 | + | 0.755477i | \(0.727405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.73252 | 0.874202 | 0.437101 | − | 0.899412i | \(-0.356005\pi\) | ||||
0.437101 | + | 0.899412i | \(0.356005\pi\) | |||||||
\(44\) | −1.09014 | −0.164345 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.50247 | 0.811294 | ||||||||
\(47\) | 10.7510 | 1.56819 | 0.784094 | − | 0.620642i | \(-0.213128\pi\) | ||||
0.784094 | + | 0.620642i | \(0.213128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.88216 | −0.268880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.35569 | −0.188000 | ||||||||
\(53\) | −9.22059 | −1.26655 | −0.633273 | − | 0.773929i | \(-0.718289\pi\) | ||||
−0.633273 | + | 0.773929i | \(0.718289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.70389 | −0.895845 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.38582 | 0.707193 | ||||||||
\(59\) | −0.990591 | −0.128964 | −0.0644820 | − | 0.997919i | \(-0.520540\pi\) | ||||
−0.0644820 | + | 0.997919i | \(0.520540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2960 | 1.31827 | 0.659137 | − | 0.752023i | \(-0.270922\pi\) | ||||
0.659137 | + | 0.752023i | \(0.270922\pi\) | |||||||
\(62\) | −1.33304 | −0.169296 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.68200 | 1.08525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6127 | 1.41872 | 0.709361 | − | 0.704845i | \(-0.248984\pi\) | ||||
0.709361 | + | 0.704845i | \(0.248984\pi\) | |||||||
\(68\) | −0.965080 | −0.117033 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.62456 | 1.14223 | 0.571113 | − | 0.820872i | \(-0.306512\pi\) | ||||
0.571113 | + | 0.820872i | \(0.306512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.35569 | −0.158671 | −0.0793355 | − | 0.996848i | \(-0.525280\pi\) | ||||
−0.0793355 | + | 0.996848i | \(0.525280\pi\) | |||||||
\(74\) | −8.48988 | −0.986929 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.61225 | 0.184938 | ||||||||
\(77\) | 11.0590 | 1.26029 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.231061 | 0.0259964 | 0.0129982 | − | 0.999916i | \(-0.495862\pi\) | ||||
0.0129982 | + | 0.999916i | \(0.495862\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.1847 | −1.23514 | ||||||||
\(83\) | −4.96163 | −0.544609 | −0.272305 | − | 0.962211i | \(-0.587786\pi\) | ||||
−0.272305 | + | 0.962211i | \(0.587786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.64169 | 0.824024 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14.4862 | −1.54423 | ||||||||
\(89\) | −17.8808 | −1.89536 | −0.947678 | − | 0.319227i | \(-0.896577\pi\) | ||||
−0.947678 | + | 0.319227i | \(0.896577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7528 | 1.44169 | ||||||||
\(92\) | −0.920502 | −0.0959690 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.3315 | 1.47818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.43207 | −0.856147 | −0.428073 | − | 0.903744i | \(-0.640807\pi\) | ||||
−0.428073 | + | 0.903744i | \(0.640807\pi\) | |||||||
\(98\) | −2.50899 | −0.253446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.64222 | −0.859933 | −0.429967 | − | 0.902845i | \(-0.641475\pi\) | ||||
−0.429967 | + | 0.902845i | \(0.641475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17265 | −0.509676 | −0.254838 | − | 0.966984i | \(-0.582022\pi\) | ||||
−0.254838 | + | 0.966984i | \(0.582022\pi\) | |||||||
\(104\) | −18.0149 | −1.76651 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.2914 | −1.19385 | ||||||||
\(107\) | −4.66258 | −0.450749 | −0.225375 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225375 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1486 | 1.06784 | 0.533922 | − | 0.845533i | \(-0.320717\pi\) | ||||
0.533922 | + | 0.845533i | \(0.320717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.92757 | −0.749085 | ||||||||
\(113\) | 1.41328 | 0.132950 | 0.0664749 | − | 0.997788i | \(-0.478825\pi\) | ||||
0.0664749 | + | 0.997788i | \(0.478825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.900989 | −0.0836547 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.32050 | −0.121562 | ||||||||
\(119\) | 9.79030 | 0.897475 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.8969 | 1.17245 | ||||||||
\(122\) | 13.7251 | 1.24261 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.223003 | 0.0200263 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.918410 | −0.0814957 | −0.0407479 | − | 0.999169i | \(-0.512974\pi\) | ||||
−0.0407479 | + | 0.999169i | \(0.512974\pi\) | |||||||
\(128\) | 9.06270 | 0.801037 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.93833 | −0.169353 | −0.0846765 | − | 0.996408i | \(-0.526986\pi\) | ||||
−0.0846765 | + | 0.996408i | \(0.526986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.3556 | −1.41821 | ||||||||
\(134\) | 15.4803 | 1.33729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.8244 | −1.09968 | ||||||||
\(137\) | −2.29555 | −0.196122 | −0.0980608 | − | 0.995180i | \(-0.531264\pi\) | ||||
−0.0980608 | + | 0.995180i | \(0.531264\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7174 | 0.993858 | 0.496929 | − | 0.867791i | \(-0.334461\pi\) | ||||
0.496929 | + | 0.867791i | \(0.334461\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.8299 | 1.07666 | ||||||||
\(143\) | 29.7180 | 2.48514 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.80718 | −0.149564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.42026 | 0.116745 | ||||||||
\(149\) | 17.8708 | 1.46403 | 0.732017 | − | 0.681286i | \(-0.238579\pi\) | ||||
0.732017 | + | 0.681286i | \(0.238579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0489 | −1.14328 | −0.571641 | − | 0.820504i | \(-0.693693\pi\) | ||||
−0.571641 | + | 0.820504i | \(0.693693\pi\) | |||||||
\(152\) | 21.4243 | 1.73774 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.7421 | 1.18795 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8631 | 1.74486 | 0.872432 | − | 0.488735i | \(-0.162541\pi\) | ||||
0.872432 | + | 0.488735i | \(0.162541\pi\) | |||||||
\(158\) | 0.308014 | 0.0245043 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.33808 | 0.735944 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.27928 | 0.100201 | 0.0501003 | − | 0.998744i | \(-0.484046\pi\) | ||||
0.0501003 | + | 0.998744i | \(0.484046\pi\) | |||||||
\(164\) | 1.87107 | 0.146106 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.61405 | −0.513350 | ||||||||
\(167\) | −4.95546 | −0.383465 | −0.191733 | − | 0.981447i | \(-0.561411\pi\) | ||||
−0.191733 | + | 0.981447i | \(0.561411\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.9570 | 1.84285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.27837 | −0.0974748 | ||||||||
\(173\) | 7.89629 | 0.600344 | 0.300172 | − | 0.953885i | \(-0.402956\pi\) | ||||
0.300172 | + | 0.953885i | \(0.402956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.1304 | −1.29125 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23.8358 | −1.78657 | ||||||||
\(179\) | −2.80603 | −0.209733 | −0.104866 | − | 0.994486i | \(-0.533441\pi\) | ||||
−0.104866 | + | 0.994486i | \(0.533441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6229 | −1.38423 | −0.692114 | − | 0.721788i | \(-0.743320\pi\) | ||||
−0.692114 | + | 0.721788i | \(0.743320\pi\) | |||||||
\(182\) | 18.3331 | 1.35894 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.2320 | −0.901755 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.1555 | 1.54705 | ||||||||
\(188\) | −2.39750 | −0.174855 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.26507 | −0.453324 | −0.226662 | − | 0.973973i | \(-0.572781\pi\) | ||||
−0.226662 | + | 0.973973i | \(0.572781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.7905 | 1.71248 | 0.856238 | − | 0.516581i | \(-0.172795\pi\) | ||||
0.856238 | + | 0.516581i | \(0.172795\pi\) | |||||||
\(194\) | −11.2403 | −0.807005 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.419727 | 0.0299805 | ||||||||
\(197\) | 8.02750 | 0.571936 | 0.285968 | − | 0.958239i | \(-0.407685\pi\) | ||||
0.285968 | + | 0.958239i | \(0.407685\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.61898 | −0.114767 | −0.0573833 | − | 0.998352i | \(-0.518276\pi\) | ||||
−0.0573833 | + | 0.998352i | \(0.518276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.5204 | −0.810575 | ||||||||
\(203\) | 9.14013 | 0.641511 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.89535 | −0.480422 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.3032 | −1.47711 | ||||||||
\(209\) | −35.3422 | −2.44467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4962 | 0.929117 | 0.464559 | − | 0.885542i | \(-0.346213\pi\) | ||||
0.464559 | + | 0.885542i | \(0.346213\pi\) | |||||||
\(212\) | 2.05622 | 0.141222 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.21541 | −0.424877 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.26227 | −0.153573 | ||||||||
\(218\) | 14.8616 | 1.00655 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.3088 | 1.76972 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.9475 | 1.33579 | 0.667893 | − | 0.744258i | \(-0.267197\pi\) | ||||
0.667893 | + | 0.744258i | \(0.267197\pi\) | |||||||
\(224\) | 2.84000 | 0.189756 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.88395 | 0.125319 | ||||||||
\(227\) | −10.0990 | −0.670297 | −0.335148 | − | 0.942165i | \(-0.608786\pi\) | ||||
−0.335148 | + | 0.942165i | \(0.608786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2799 | 1.34014 | 0.670068 | − | 0.742300i | \(-0.266265\pi\) | ||||
0.670068 | + | 0.742300i | \(0.266265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.9727 | −0.786046 | ||||||||
\(233\) | −7.32867 | −0.480117 | −0.240058 | − | 0.970758i | \(-0.577167\pi\) | ||||
−0.240058 | + | 0.970758i | \(0.577167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.220905 | 0.0143797 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.0509 | 0.845962 | ||||||||
\(239\) | 25.1464 | 1.62658 | 0.813291 | − | 0.581857i | \(-0.197673\pi\) | ||||
0.813291 | + | 0.581857i | \(0.197673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7421 | 1.07845 | 0.539225 | − | 0.842162i | \(-0.318717\pi\) | ||||
0.539225 | + | 0.842162i | \(0.318717\pi\) | |||||||
\(242\) | 17.1922 | 1.10515 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.29605 | −0.146990 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.9512 | −2.79655 | ||||||||
\(248\) | 2.96335 | 0.188173 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1763 | −0.642324 | −0.321162 | − | 0.947024i | \(-0.604073\pi\) | ||||
−0.321162 | + | 0.947024i | \(0.604073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1783 | 1.26860 | ||||||||
\(254\) | −1.22428 | −0.0768180 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.28306 | −0.330191 | ||||||||
\(257\) | 4.80511 | 0.299735 | 0.149867 | − | 0.988706i | \(-0.452115\pi\) | ||||
0.149867 | + | 0.988706i | \(0.452115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4079 | −0.895266 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.58388 | −0.159633 | ||||||||
\(263\) | 24.3858 | 1.50370 | 0.751848 | − | 0.659337i | \(-0.229163\pi\) | ||||
0.751848 | + | 0.659337i | \(0.229163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.8026 | −1.33681 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.58968 | −0.158190 | ||||||||
\(269\) | 5.68385 | 0.346551 | 0.173275 | − | 0.984873i | \(-0.444565\pi\) | ||||
0.173275 | + | 0.984873i | \(0.444565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.83393 | −0.475877 | −0.237939 | − | 0.971280i | \(-0.576472\pi\) | ||||
−0.237939 | + | 0.971280i | \(0.576472\pi\) | |||||||
\(272\) | −15.1652 | −0.919528 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.06005 | −0.184865 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.61928 | −0.0972928 | −0.0486464 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486464 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(278\) | 15.6198 | 0.936812 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.528423 | 0.0315231 | 0.0157615 | − | 0.999876i | \(-0.494983\pi\) | ||||
0.0157615 | + | 0.999876i | \(0.494983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.346702 | −0.0206093 | −0.0103046 | − | 0.999947i | \(-0.503280\pi\) | ||||
−0.0103046 | + | 0.999947i | \(0.503280\pi\) | |||||||
\(284\) | −2.14631 | −0.127360 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 39.6153 | 2.34250 | ||||||||
\(287\) | −18.9812 | −1.12042 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.72859 | 0.101682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.302322 | 0.0176921 | ||||||||
\(293\) | −3.47069 | −0.202760 | −0.101380 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101380 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.8730 | 1.09697 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.8225 | 1.38000 | ||||||||
\(299\) | 25.0936 | 1.45120 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9685 | 0.747491 | ||||||||
\(302\) | −18.7277 | −1.07766 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25.3349 | 1.45306 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.2489 | −1.55518 | −0.777589 | − | 0.628773i | \(-0.783557\pi\) | ||||
−0.777589 | + | 0.628773i | \(0.783557\pi\) | |||||||
\(308\) | −2.46618 | −0.140524 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.76440 | 0.326869 | 0.163435 | − | 0.986554i | \(-0.447743\pi\) | ||||
0.163435 | + | 0.986554i | \(0.447743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.238264 | −0.0134675 | −0.00673374 | − | 0.999977i | \(-0.502143\pi\) | ||||
−0.00673374 | + | 0.999977i | \(0.502143\pi\) | |||||||
\(314\) | 29.1444 | 1.64471 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0515273 | −0.00289864 | ||||||||
\(317\) | −19.9231 | −1.11900 | −0.559498 | − | 0.828832i | \(-0.689006\pi\) | ||||
−0.559498 | + | 0.828832i | \(0.689006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.7506 | 1.10582 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.4480 | 0.693702 | ||||||||
\(323\) | −31.2878 | −1.74090 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.70533 | 0.0944494 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.8635 | 1.37286 | ||||||||
\(329\) | 24.3215 | 1.34089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5579 | 1.34982 | 0.674912 | − | 0.737898i | \(-0.264182\pi\) | ||||
0.674912 | + | 0.737898i | \(0.264182\pi\) | |||||||
\(332\) | 1.10646 | 0.0607247 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.60583 | −0.361455 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6863 | 0.691067 | 0.345533 | − | 0.938406i | \(-0.387698\pi\) | ||||
0.345533 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(338\) | 31.9357 | 1.73707 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.88845 | −0.264724 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0938 | −1.08496 | ||||||||
\(344\) | −16.9875 | −0.915904 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5261 | 0.565886 | ||||||||
\(347\) | −4.44092 | −0.238401 | −0.119201 | − | 0.992870i | \(-0.538033\pi\) | ||||
−0.119201 | + | 0.992870i | \(0.538033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.6583 | 1.96227 | 0.981137 | − | 0.193315i | \(-0.0619239\pi\) | ||||
0.981137 | + | 0.193315i | \(0.0619239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.13686 | 0.327096 | ||||||||
\(353\) | −22.1918 | −1.18115 | −0.590575 | − | 0.806983i | \(-0.701099\pi\) | ||||
−0.590575 | + | 0.806983i | \(0.701099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.98746 | 0.211335 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.74055 | −0.197694 | ||||||||
\(359\) | −28.6249 | −1.51076 | −0.755382 | − | 0.655284i | \(-0.772549\pi\) | ||||
−0.755382 | + | 0.655284i | \(0.772549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.2690 | 1.75100 | ||||||||
\(362\) | −24.8251 | −1.30478 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.06692 | −0.160750 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2622 | 0.901077 | 0.450539 | − | 0.892757i | \(-0.351232\pi\) | ||||
0.450539 | + | 0.892757i | \(0.351232\pi\) | |||||||
\(368\) | −14.4647 | −0.754027 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.8594 | −1.08297 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4593 | −1.11112 | −0.555560 | − | 0.831477i | \(-0.687496\pi\) | ||||
−0.555560 | + | 0.831477i | \(0.687496\pi\) | |||||||
\(374\) | 28.2012 | 1.45825 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.8589 | −1.64300 | ||||||||
\(377\) | 24.5616 | 1.26499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.91234 | −0.252330 | −0.126165 | − | 0.992009i | \(-0.540267\pi\) | ||||
−0.126165 | + | 0.992009i | \(0.540267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.35159 | −0.427305 | ||||||||
\(383\) | 15.1473 | 0.773991 | 0.386995 | − | 0.922082i | \(-0.373513\pi\) | ||||
0.386995 | + | 0.922082i | \(0.373513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.7137 | 1.61418 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.88038 | 0.0954616 | ||||||||
\(389\) | 17.4614 | 0.885330 | 0.442665 | − | 0.896687i | \(-0.354033\pi\) | ||||
0.442665 | + | 0.896687i | \(0.354033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8635 | 0.903396 | ||||||||
\(392\) | 5.57749 | 0.281706 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.7010 | 0.539108 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.79511 | 0.391225 | 0.195613 | − | 0.980681i | \(-0.437330\pi\) | ||||
0.195613 | + | 0.980681i | \(0.437330\pi\) | |||||||
\(398\) | −2.15817 | −0.108179 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.18319 | 0.258836 | 0.129418 | − | 0.991590i | \(-0.458689\pi\) | ||||
0.129418 | + | 0.991590i | \(0.458689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.07923 | −0.302828 | ||||||||
\(404\) | 1.92724 | 0.0958839 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.1842 | 0.604690 | ||||||||
\(407\) | −31.1336 | −1.54324 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.6314 | −1.36629 | −0.683143 | − | 0.730285i | \(-0.739387\pi\) | ||||
−0.683143 | + | 0.730285i | \(0.739387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.15352 | 0.0568296 | ||||||||
\(413\) | −2.24098 | −0.110271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.63174 | 0.374177 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −47.1126 | −2.30435 | ||||||||
\(419\) | 36.1293 | 1.76503 | 0.882517 | − | 0.470281i | \(-0.155847\pi\) | ||||
0.882517 | + | 0.470281i | \(0.155847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6662 | 0.909734 | 0.454867 | − | 0.890559i | \(-0.349687\pi\) | ||||
0.454867 | + | 0.890559i | \(0.349687\pi\) | |||||||
\(422\) | 17.9910 | 0.875788 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.3239 | 1.32696 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.2924 | 1.12720 | ||||||||
\(428\) | 1.03977 | 0.0502592 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.0240 | −1.83155 | −0.915777 | − | 0.401688i | \(-0.868424\pi\) | ||||
−0.915777 | + | 0.401688i | \(0.868424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.79863 | −0.326721 | −0.163361 | − | 0.986566i | \(-0.552233\pi\) | ||||
−0.163361 | + | 0.986566i | \(0.552233\pi\) | |||||||
\(434\) | −3.01569 | −0.144758 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.48618 | −0.119066 | ||||||||
\(437\) | −29.8426 | −1.42756 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.7446 | 1.75373 | 0.876863 | − | 0.480741i | \(-0.159632\pi\) | ||||
0.876863 | + | 0.480741i | \(0.159632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.0707 | 1.66814 | ||||||||
\(443\) | −15.2695 | −0.725478 | −0.362739 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362739 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.5909 | 1.25911 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.6410 | 0.927949 | ||||||||
\(449\) | −23.2699 | −1.09817 | −0.549087 | − | 0.835765i | \(-0.685024\pi\) | ||||
−0.549087 | + | 0.835765i | \(0.685024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.0157 | −1.93136 | ||||||||
\(452\) | −0.315165 | −0.0148241 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.4624 | −0.631823 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.2102 | −1.64707 | −0.823533 | − | 0.567268i | \(-0.808000\pi\) | ||||
−0.823533 | + | 0.567268i | \(0.808000\pi\) | |||||||
\(458\) | 27.0340 | 1.26321 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.4127 | −1.60276 | −0.801378 | − | 0.598158i | \(-0.795900\pi\) | ||||
−0.801378 | + | 0.598158i | \(0.795900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0471 | 0.978141 | 0.489071 | − | 0.872244i | \(-0.337336\pi\) | ||||
0.489071 | + | 0.872244i | \(0.337336\pi\) | |||||||
\(464\) | −14.1581 | −0.657274 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.76941 | −0.452559 | ||||||||
\(467\) | −8.48587 | −0.392679 | −0.196340 | − | 0.980536i | \(-0.562905\pi\) | ||||
−0.196340 | + | 0.980536i | \(0.562905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2711 | 1.21309 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.93547 | 0.135116 | ||||||||
\(473\) | 28.0232 | 1.28851 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.18327 | −0.100070 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 33.5211 | 1.53322 | ||||||||
\(479\) | 34.1647 | 1.56102 | 0.780512 | − | 0.625141i | \(-0.214959\pi\) | ||||
0.780512 | + | 0.625141i | \(0.214959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7175 | −1.76536 | ||||||||
\(482\) | 22.3178 | 1.01655 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.87606 | −0.130730 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.39095 | −0.244287 | −0.122144 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122144 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(488\) | −30.5108 | −1.38116 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9004 | −0.898094 | −0.449047 | − | 0.893508i | \(-0.648236\pi\) | ||||
−0.449047 | + | 0.893508i | \(0.648236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.4848 | 0.787477 | ||||||||
\(494\) | −58.5887 | −2.63603 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.50426 | 0.157346 | ||||||||
\(497\) | 21.7733 | 0.976666 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.6783 | −1.23905 | −0.619526 | − | 0.784976i | \(-0.712675\pi\) | ||||
−0.619526 | + | 0.784976i | \(0.712675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.5655 | −0.605456 | ||||||||
\(503\) | −15.4069 | −0.686960 | −0.343480 | − | 0.939160i | \(-0.611606\pi\) | ||||
−0.343480 | + | 0.939160i | \(0.611606\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.8985 | 1.19579 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.204808 | 0.00908689 | ||||||||
\(509\) | −31.1678 | −1.38149 | −0.690744 | − | 0.723099i | \(-0.742717\pi\) | ||||
−0.690744 | + | 0.723099i | \(0.742717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.06692 | −0.135673 | ||||||||
\(512\) | −25.1679 | −1.11228 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.40541 | 0.282530 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.5555 | 2.31139 | ||||||||
\(518\) | −19.2064 | −0.843879 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.324182 | −0.0142027 | −0.00710134 | − | 0.999975i | \(-0.502260\pi\) | ||||
−0.00710134 | + | 0.999975i | \(0.502260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3521 | −1.54584 | −0.772921 | − | 0.634503i | \(-0.781205\pi\) | ||||
−0.772921 | + | 0.634503i | \(0.781205\pi\) | |||||||
\(524\) | 0.432254 | 0.0188831 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.5073 | 1.41739 | ||||||||
\(527\) | −4.32765 | −0.188516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.96163 | −0.259201 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.64734 | 0.158132 | ||||||||
\(533\) | −51.0068 | −2.20935 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.4127 | −1.48640 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.57681 | 0.326659 | ||||||||
\(539\) | −9.20083 | −0.396308 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.1201 | 1.38095 | 0.690476 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690476 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(542\) | −10.4429 | −0.448563 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.43285 | 0.232932 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.9253 | −1.23676 | −0.618378 | − | 0.785880i | \(-0.712210\pi\) | ||||
−0.618378 | + | 0.785880i | \(0.712210\pi\) | |||||||
\(548\) | 0.511913 | 0.0218679 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.2100 | −1.24439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.522721 | 0.0222284 | ||||||||
\(554\) | −2.15856 | −0.0917084 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.61302 | −0.110817 | ||||||||
\(557\) | 17.6366 | 0.747286 | 0.373643 | − | 0.927573i | \(-0.378109\pi\) | ||||
0.373643 | + | 0.927573i | \(0.378109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.8493 | 1.47397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.704410 | 0.0297137 | ||||||||
\(563\) | −17.8325 | −0.751551 | −0.375776 | − | 0.926711i | \(-0.622624\pi\) | ||||
−0.375776 | + | 0.926711i | \(0.622624\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.462168 | −0.0194264 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.5210 | −1.19671 | ||||||||
\(569\) | −11.6624 | −0.488915 | −0.244458 | − | 0.969660i | \(-0.578610\pi\) | ||||
−0.244458 | + | 0.969660i | \(0.578610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.7640 | −0.994494 | −0.497247 | − | 0.867609i | \(-0.665656\pi\) | ||||
−0.497247 | + | 0.867609i | \(0.665656\pi\) | |||||||
\(572\) | −6.62720 | −0.277097 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25.3027 | −1.05611 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1226 | −0.421410 | −0.210705 | − | 0.977550i | \(-0.567576\pi\) | ||||
−0.210705 | + | 0.977550i | \(0.567576\pi\) | |||||||
\(578\) | 2.30429 | 0.0958457 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.2245 | −0.465671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.0744 | −1.86679 | ||||||||
\(584\) | 4.01737 | 0.166240 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.62657 | −0.191122 | ||||||||
\(587\) | −38.7269 | −1.59843 | −0.799215 | − | 0.601045i | \(-0.794751\pi\) | ||||
−0.799215 | + | 0.601045i | \(0.794751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.22973 | 0.297896 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.3180 | 0.917264 | ||||||||
\(593\) | 6.62601 | 0.272097 | 0.136049 | − | 0.990702i | \(-0.456560\pi\) | ||||
0.136049 | + | 0.990702i | \(0.456560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.98524 | −0.163242 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 33.4507 | 1.36790 | ||||||||
\(599\) | −24.7616 | −1.01173 | −0.505866 | − | 0.862612i | \(-0.668827\pi\) | ||||
−0.505866 | + | 0.862612i | \(0.668827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0843 | 1.06400 | 0.532000 | − | 0.846744i | \(-0.321441\pi\) | ||||
0.532000 | + | 0.846744i | \(0.321441\pi\) | |||||||
\(602\) | 17.2875 | 0.704587 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.13294 | 0.127478 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.2003 | −1.26638 | −0.633191 | − | 0.773996i | \(-0.718255\pi\) | ||||
−0.633191 | + | 0.773996i | \(0.718255\pi\) | |||||||
\(608\) | −9.07607 | −0.368083 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 65.3575 | 2.64408 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.85422 | −0.236450 | −0.118225 | − | 0.992987i | \(-0.537720\pi\) | ||||
−0.118225 | + | 0.992987i | \(0.537720\pi\) | |||||||
\(614\) | −36.3239 | −1.46591 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −32.7716 | −1.32041 | ||||||||
\(617\) | −18.4986 | −0.744724 | −0.372362 | − | 0.928088i | \(-0.621452\pi\) | ||||
−0.372362 | + | 0.928088i | \(0.621452\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.6560 | 0.548882 | 0.274441 | − | 0.961604i | \(-0.411507\pi\) | ||||
0.274441 | + | 0.961604i | \(0.411507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.68418 | 0.308108 | ||||||||
\(623\) | −40.4510 | −1.62064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.317616 | −0.0126945 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.87553 | −0.194555 | ||||||||
\(629\) | −27.5620 | −1.09897 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6705 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(632\) | −0.684715 | −0.0272365 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.5584 | −1.05477 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.4421 | −0.453351 | ||||||||
\(638\) | 26.3283 | 1.04235 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.814903 | 0.0321867 | 0.0160934 | − | 0.999870i | \(-0.494877\pi\) | ||||
0.0160934 | + | 0.999870i | \(0.494877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.6000 | −1.36449 | −0.682245 | − | 0.731124i | \(-0.738996\pi\) | ||||
−0.682245 | + | 0.731124i | \(0.738996\pi\) | |||||||
\(644\) | −2.08242 | −0.0820588 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −41.7079 | −1.64098 | ||||||||
\(647\) | 17.9892 | 0.707227 | 0.353614 | − | 0.935392i | \(-0.384953\pi\) | ||||
0.353614 | + | 0.935392i | \(0.384953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.84245 | −0.190083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.285282 | −0.0111725 | ||||||||
\(653\) | 1.86147 | 0.0728450 | 0.0364225 | − | 0.999336i | \(-0.488404\pi\) | ||||
0.0364225 | + | 0.999336i | \(0.488404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 29.4020 | 1.14795 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.4216 | 1.26392 | ||||||||
\(659\) | 2.06422 | 0.0804105 | 0.0402053 | − | 0.999191i | \(-0.487199\pi\) | ||||
0.0402053 | + | 0.999191i | \(0.487199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.31667 | −0.284586 | −0.142293 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142293 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(662\) | 32.7367 | 1.27235 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.7031 | 0.570589 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.6772 | 0.645743 | ||||||||
\(668\) | 1.10508 | 0.0427569 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.3317 | 1.94303 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.9205 | 0.922069 | 0.461035 | − | 0.887382i | \(-0.347478\pi\) | ||||
0.461035 | + | 0.887382i | \(0.347478\pi\) | |||||||
\(674\) | 16.9114 | 0.651401 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.34248 | −0.205480 | ||||||||
\(677\) | −25.4349 | −0.977543 | −0.488772 | − | 0.872412i | \(-0.662555\pi\) | ||||
−0.488772 | + | 0.872412i | \(0.662555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.0756 | −0.732053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.51650 | −0.249530 | ||||||||
\(683\) | −6.87665 | −0.263128 | −0.131564 | − | 0.991308i | \(-0.542000\pi\) | ||||
−0.131564 | + | 0.991308i | \(0.542000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.7858 | −1.02269 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0883 | −0.765858 | ||||||||
\(689\) | −56.0541 | −2.13549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.85648 | −0.298875 | −0.149437 | − | 0.988771i | \(-0.547746\pi\) | ||||
−0.149437 | + | 0.988771i | \(0.547746\pi\) | |||||||
\(692\) | −1.76090 | −0.0669393 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.91993 | −0.224717 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.3105 | −1.37536 | ||||||||
\(698\) | 48.8670 | 1.84964 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5943 | 0.664527 | 0.332263 | − | 0.943187i | \(-0.392188\pi\) | ||||
0.332263 | + | 0.943187i | \(0.392188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.0448 | 1.73661 | ||||||||
\(704\) | 42.4415 | 1.59958 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.5825 | −1.11335 | ||||||||
\(707\) | −19.5510 | −0.735291 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7814 | −0.968240 | −0.484120 | − | 0.875002i | \(-0.660860\pi\) | ||||
−0.484120 | + | 0.875002i | \(0.660860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 52.9870 | 1.98577 | ||||||||
\(713\) | −4.12776 | −0.154586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.625753 | 0.0233855 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.1582 | −1.42405 | ||||||||
\(719\) | 4.52192 | 0.168639 | 0.0843196 | − | 0.996439i | \(-0.473128\pi\) | ||||
0.0843196 | + | 0.996439i | \(0.473128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.7019 | −0.435802 | ||||||||
\(722\) | 44.3490 | 1.65050 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.15296 | 0.154343 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6527 | 1.02558 | 0.512792 | − | 0.858513i | \(-0.328611\pi\) | ||||
0.512792 | + | 0.858513i | \(0.328611\pi\) | |||||||
\(728\) | −40.7545 | −1.51046 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.8084 | 0.917571 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.9649 | −1.84550 | −0.922748 | − | 0.385403i | \(-0.874063\pi\) | ||||
−0.922748 | + | 0.385403i | \(0.874063\pi\) | |||||||
\(734\) | 23.0111 | 0.849357 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.18190 | 0.191008 | ||||||||
\(737\) | 56.7683 | 2.09109 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2507 | 0.634576 | 0.317288 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317288 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.8065 | −1.02081 | ||||||||
\(743\) | −23.2895 | −0.854411 | −0.427205 | − | 0.904155i | \(-0.640502\pi\) | ||||
−0.427205 | + | 0.904155i | \(0.640502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.6061 | −1.04734 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.71774 | −0.172498 | ||||||||
\(749\) | −10.5480 | −0.385416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5346 | −0.384412 | −0.192206 | − | 0.981355i | \(-0.561564\pi\) | ||||
−0.192206 | + | 0.981355i | \(0.561564\pi\) | |||||||
\(752\) | −37.6742 | −1.37384 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.7416 | 1.19238 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.00662 | 0.291006 | 0.145503 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145503 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(758\) | −6.54835 | −0.237847 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.9494 | −0.723165 | −0.361582 | − | 0.932340i | \(-0.617763\pi\) | ||||
−0.361582 | + | 0.932340i | \(0.617763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.2212 | 0.913067 | ||||||||
\(764\) | 1.39713 | 0.0505464 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.1920 | 0.729565 | ||||||||
\(767\) | −6.02203 | −0.217443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.5543 | 1.85910 | 0.929548 | − | 0.368700i | \(-0.120197\pi\) | ||||
0.929548 | + | 0.368700i | \(0.120197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.30535 | −0.190944 | ||||||||
\(773\) | 14.8224 | 0.533123 | 0.266562 | − | 0.963818i | \(-0.414112\pi\) | ||||
0.266562 | + | 0.963818i | \(0.414112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.9872 | 0.896988 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.2768 | 0.834514 | ||||||||
\(779\) | 60.6599 | 2.17337 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.0492 | 1.68355 | ||||||||
\(782\) | 23.8128 | 0.851543 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.59557 | 0.235556 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8528 | 0.565092 | 0.282546 | − | 0.959254i | \(-0.408821\pi\) | ||||
0.282546 | + | 0.959254i | \(0.408821\pi\) | |||||||
\(788\) | −1.79016 | −0.0637717 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.19720 | 0.113679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.5920 | 2.22271 | ||||||||
\(794\) | 10.3912 | 0.368770 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.361038 | 0.0127966 | ||||||||
\(797\) | 30.3453 | 1.07489 | 0.537444 | − | 0.843300i | \(-0.319390\pi\) | ||||
0.537444 | + | 0.843300i | \(0.319390\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.5264 | 1.64599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.90940 | 0.243979 | ||||||||
\(803\) | −6.62720 | −0.233869 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.10386 | −0.285446 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.6100 | 0.900955 | ||||||||
\(809\) | 35.0670 | 1.23289 | 0.616444 | − | 0.787399i | \(-0.288573\pi\) | ||||
0.616444 | + | 0.787399i | \(0.288573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.53788 | −0.124232 | −0.0621158 | − | 0.998069i | \(-0.519785\pi\) | ||||
−0.0621158 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(812\) | −2.03828 | −0.0715294 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −41.5024 | −1.45466 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.4446 | −1.44996 | ||||||||
\(818\) | −36.8338 | −1.28786 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.7938 | 1.59821 | 0.799107 | − | 0.601189i | \(-0.205306\pi\) | ||||
0.799107 | + | 0.601189i | \(0.205306\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.82724 | −0.342556 | −0.171278 | − | 0.985223i | \(-0.554790\pi\) | ||||
−0.171278 | + | 0.985223i | \(0.554790\pi\) | |||||||
\(824\) | 15.3284 | 0.533989 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.98732 | −0.103942 | ||||||||
\(827\) | −29.5330 | −1.02696 | −0.513481 | − | 0.858101i | \(-0.671644\pi\) | ||||
−0.513481 | + | 0.858101i | \(0.671644\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.36400 | −0.325225 | −0.162613 | − | 0.986690i | \(-0.551992\pi\) | ||||
−0.162613 | + | 0.986690i | \(0.551992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 52.7799 | 1.82981 | ||||||||
\(833\) | −8.14532 | −0.282219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.88141 | 0.272584 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 48.1619 | 1.66372 | ||||||||
\(839\) | −34.0552 | −1.17572 | −0.587858 | − | 0.808964i | \(-0.700028\pi\) | ||||
−0.587858 | + | 0.808964i | \(0.700028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6763 | −0.437115 | ||||||||
\(842\) | 24.8828 | 0.857517 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.00969 | −0.103598 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.1763 | 1.00251 | ||||||||
\(848\) | 32.3114 | 1.10958 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.2889 | −0.901172 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.2952 | −0.420980 | −0.210490 | − | 0.977596i | \(-0.567506\pi\) | ||||
−0.210490 | + | 0.977596i | \(0.567506\pi\) | |||||||
\(854\) | 31.0497 | 1.06250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.8169 | 0.472251 | ||||||||
\(857\) | −46.3090 | −1.58189 | −0.790943 | − | 0.611890i | \(-0.790410\pi\) | ||||
−0.790943 | + | 0.611890i | \(0.790410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6495 | −0.568072 | −0.284036 | − | 0.958814i | \(-0.591674\pi\) | ||||
−0.284036 | + | 0.958814i | \(0.591674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −50.6876 | −1.72643 | ||||||||
\(863\) | 27.5142 | 0.936595 | 0.468298 | − | 0.883571i | \(-0.344867\pi\) | ||||
0.468298 | + | 0.883571i | \(0.344867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.06284 | −0.307968 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.504492 | 0.0171236 | ||||||||
\(869\) | 1.12953 | 0.0383167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.5965 | 2.39207 | ||||||||
\(872\) | −33.0373 | −1.11878 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −39.7814 | −1.34562 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.4839 | −0.826762 | −0.413381 | − | 0.910558i | \(-0.635652\pi\) | ||||
−0.413381 | + | 0.910558i | \(0.635652\pi\) | |||||||
\(878\) | 48.9821 | 1.65307 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9948 | −1.34746 | −0.673730 | − | 0.738978i | \(-0.735309\pi\) | ||||
−0.673730 | + | 0.738978i | \(0.735309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.9829 | −1.41284 | −0.706418 | − | 0.707795i | \(-0.749690\pi\) | ||||
−0.706418 | + | 0.707795i | \(0.749690\pi\) | |||||||
\(884\) | −5.86694 | −0.197327 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.3549 | −0.683837 | ||||||||
\(887\) | −47.6126 | −1.59867 | −0.799337 | − | 0.600883i | \(-0.794816\pi\) | ||||
−0.799337 | + | 0.600883i | \(0.794816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.07769 | −0.0696834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.44836 | −0.148942 | ||||||||
\(893\) | −77.7265 | −2.60102 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.5022 | 0.684931 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.0197 | −1.03514 | ||||||||
\(899\) | −4.04025 | −0.134750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.9035 | −1.32938 | ||||||||
\(902\) | −54.6756 | −1.82050 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.18803 | −0.139292 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.5631 | 1.47969 | 0.739846 | − | 0.672776i | \(-0.234898\pi\) | ||||
0.739846 | + | 0.672776i | \(0.234898\pi\) | |||||||
\(908\) | 2.25212 | 0.0747391 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.19070 | −0.238239 | −0.119119 | − | 0.992880i | \(-0.538007\pi\) | ||||
−0.119119 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2547 | −0.802712 | ||||||||
\(914\) | −46.9367 | −1.55253 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.52249 | −0.149427 | ||||||||
\(917\) | −4.38503 | −0.144806 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.5933 | −1.14113 | −0.570564 | − | 0.821253i | \(-0.693275\pi\) | ||||
−0.570564 | + | 0.821253i | \(0.693275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −45.8735 | −1.51076 | ||||||||
\(923\) | 58.5099 | 1.92588 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.0566 | 0.921998 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.07206 | 0.166498 | ||||||||
\(929\) | −26.5992 | −0.872691 | −0.436345 | − | 0.899779i | \(-0.643727\pi\) | ||||
−0.436345 | + | 0.899779i | \(0.643727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6075 | 0.445968 | ||||||||
\(932\) | 1.63431 | 0.0535337 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.3120 | −0.370140 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12555 | −0.0367702 | −0.0183851 | − | 0.999831i | \(-0.505852\pi\) | ||||
−0.0183851 | + | 0.999831i | \(0.505852\pi\) | |||||||
\(938\) | 35.0204 | 1.14346 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.70702 | 0.120845 | 0.0604227 | − | 0.998173i | \(-0.480755\pi\) | ||||
0.0604227 | + | 0.998173i | \(0.480755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.6333 | −1.12781 | ||||||||
\(944\) | 3.47129 | 0.112981 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.3560 | 1.21455 | ||||||||
\(947\) | 5.91493 | 0.192209 | 0.0961047 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961047 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.24152 | −0.267531 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.0121 | −0.940288 | ||||||||
\(953\) | −35.3239 | −1.14425 | −0.572127 | − | 0.820165i | \(-0.693881\pi\) | ||||
−0.572127 | + | 0.820165i | \(0.693881\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.60771 | −0.181366 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45.5429 | 1.47142 | ||||||||
\(959\) | −5.19313 | −0.167695 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −51.6119 | −1.66404 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.73353 | −0.120249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.9475 | 0.641469 | 0.320735 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320735 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(968\) | −38.2182 | −1.22838 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.0305 | −0.995818 | −0.497909 | − | 0.867229i | \(-0.665899\pi\) | ||||
−0.497909 | + | 0.867229i | \(0.665899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.5079 | 0.849804 | ||||||||
\(974\) | −7.18636 | −0.230266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.0801 | −1.15489 | ||||||||
\(977\) | 17.1868 | 0.549853 | 0.274927 | − | 0.961465i | \(-0.411346\pi\) | ||||
0.274927 | + | 0.961465i | \(0.411346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −87.4092 | −2.79361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.5281 | −0.846545 | ||||||||
\(983\) | −36.9855 | −1.17965 | −0.589827 | − | 0.807530i | \(-0.700804\pi\) | ||||
−0.589827 | + | 0.807530i | \(0.700804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 23.3080 | 0.742277 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.80125 | 0.311819 | ||||||||
\(989\) | 23.6625 | 0.752423 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.4903 | 1.09562 | 0.547809 | − | 0.836603i | \(-0.315462\pi\) | ||||
0.547809 | + | 0.836603i | \(0.315462\pi\) | |||||||
\(992\) | −1.25538 | −0.0398584 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.0247 | 0.920608 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.7422 | 1.51201 | 0.756005 | − | 0.654566i | \(-0.227149\pi\) | ||||
0.756005 | + | 0.654566i | \(0.227149\pi\) | |||||||
\(998\) | −36.8963 | −1.16793 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6975.2.a.ck.1.14 | 16 | ||
3.2 | odd | 2 | inner | 6975.2.a.ck.1.4 | 16 | ||
5.2 | odd | 4 | 1395.2.c.g.559.14 | yes | 16 | ||
5.3 | odd | 4 | 1395.2.c.g.559.4 | yes | 16 | ||
5.4 | even | 2 | inner | 6975.2.a.ck.1.3 | 16 | ||
15.2 | even | 4 | 1395.2.c.g.559.3 | ✓ | 16 | ||
15.8 | even | 4 | 1395.2.c.g.559.13 | yes | 16 | ||
15.14 | odd | 2 | inner | 6975.2.a.ck.1.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1395.2.c.g.559.3 | ✓ | 16 | 15.2 | even | 4 | ||
1395.2.c.g.559.4 | yes | 16 | 5.3 | odd | 4 | ||
1395.2.c.g.559.13 | yes | 16 | 15.8 | even | 4 | ||
1395.2.c.g.559.14 | yes | 16 | 5.2 | odd | 4 | ||
6975.2.a.ck.1.3 | 16 | 5.4 | even | 2 | inner | ||
6975.2.a.ck.1.4 | 16 | 3.2 | odd | 2 | inner | ||
6975.2.a.ck.1.13 | 16 | 15.14 | odd | 2 | inner | ||
6975.2.a.ck.1.14 | 16 | 1.1 | even | 1 | trivial |