Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(3.38131\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | 3.38131 | 1.51217 | 0.756084 | − | 0.654475i | \(-0.227110\pi\) | ||||
0.756084 | + | 0.654475i | \(0.227110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18014 | 0.824014 | 0.412007 | − | 0.911181i | \(-0.364828\pi\) | ||||
0.412007 | + | 0.911181i | \(0.364828\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.42337 | 0.429162 | 0.214581 | − | 0.976706i | \(-0.431161\pi\) | ||||
0.214581 | + | 0.976706i | \(0.431161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00143 | 1.38715 | 0.693574 | − | 0.720386i | \(-0.256035\pi\) | ||||
0.693574 | + | 0.720386i | \(0.256035\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.38131 | 0.873051 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.50797 | 1.33588 | 0.667939 | − | 0.744216i | \(-0.267177\pi\) | ||||
0.667939 | + | 0.744216i | \(0.267177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.82733 | −1.79571 | −0.897856 | − | 0.440289i | \(-0.854876\pi\) | ||||
−0.897856 | + | 0.440289i | \(0.854876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.18014 | 0.475745 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.75758 | 1.61757 | 0.808784 | − | 0.588106i | \(-0.200126\pi\) | ||||
0.808784 | + | 0.588106i | \(0.200126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.43326 | 1.28665 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.29374 | 1.16872 | 0.584359 | − | 0.811495i | \(-0.301346\pi\) | ||||
0.584359 | + | 0.811495i | \(0.301346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.08688 | −1.63205 | −0.816026 | − | 0.578015i | \(-0.803828\pi\) | ||||
−0.816026 | + | 0.578015i | \(0.803828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42337 | 0.247777 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.37172 | 1.24605 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.72415 | 0.776646 | 0.388323 | − | 0.921523i | \(-0.373055\pi\) | ||||
0.388323 | + | 0.921523i | \(0.373055\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.00143 | 0.800870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8364 | −1.84853 | −0.924267 | − | 0.381748i | \(-0.875322\pi\) | ||||
−0.924267 | + | 0.381748i | \(0.875322\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.11615 | −1.08520 | −0.542601 | − | 0.839991i | \(-0.682560\pi\) | ||||
−0.542601 | + | 0.839991i | \(0.682560\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.38131 | 0.504056 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.21355 | −1.19807 | −0.599035 | − | 0.800723i | \(-0.704449\pi\) | ||||
−0.599035 | + | 0.800723i | \(0.704449\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.24700 | −0.321000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.50797 | 0.771270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8063 | −1.48436 | −0.742179 | − | 0.670201i | \(-0.766208\pi\) | ||||
−0.742179 | + | 0.670201i | \(0.766208\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.81285 | 0.648964 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.82733 | −1.03676 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.83956 | −0.890435 | −0.445218 | − | 0.895422i | \(-0.646874\pi\) | ||||
−0.445218 | + | 0.895422i | \(0.646874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.73720 | −0.222426 | −0.111213 | − | 0.993797i | \(-0.535474\pi\) | ||||
−0.111213 | + | 0.993797i | \(0.535474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.18014 | 0.274671 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9114 | 2.09760 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.61452 | −0.197245 | −0.0986225 | − | 0.995125i | \(-0.531444\pi\) | ||||
−0.0986225 | + | 0.995125i | \(0.531444\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.75758 | 0.933903 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0154 | 1.90068 | 0.950340 | − | 0.311214i | \(-0.100736\pi\) | ||||
0.950340 | + | 0.311214i | \(0.100736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43455 | 0.519025 | 0.259513 | − | 0.965740i | \(-0.416438\pi\) | ||||
0.259513 | + | 0.965740i | \(0.416438\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.43326 | 0.742849 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.10314 | 0.353635 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.26342 | 0.479673 | 0.239836 | − | 0.970813i | \(-0.422906\pi\) | ||||
0.239836 | + | 0.970813i | \(0.422906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.41440 | 0.484544 | 0.242272 | − | 0.970208i | \(-0.422107\pi\) | ||||
0.242272 | + | 0.970208i | \(0.422107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.6241 | 2.02007 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.29374 | 0.674759 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.56376 | −0.907757 | −0.453879 | − | 0.891064i | \(-0.649960\pi\) | ||||
−0.453879 | + | 0.891064i | \(0.649960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9038 | 1.14303 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.08688 | −0.942266 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.4666 | −2.71542 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.2977 | −1.04557 | −0.522786 | − | 0.852464i | \(-0.675107\pi\) | ||||
−0.522786 | + | 0.852464i | \(0.675107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.42337 | 0.143054 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.31154 | 0.528518 | 0.264259 | − | 0.964452i | \(-0.414873\pi\) | ||||
0.264259 | + | 0.964452i | \(0.414873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.971769 | −0.0957513 | −0.0478756 | − | 0.998853i | \(-0.515245\pi\) | ||||
−0.0478756 | + | 0.998853i | \(0.515245\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.37172 | 0.719406 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7609 | −1.33031 | −0.665156 | − | 0.746704i | \(-0.731635\pi\) | ||||
−0.665156 | + | 0.746704i | \(0.731635\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.15480 | −0.493741 | −0.246870 | − | 0.969049i | \(-0.579402\pi\) | ||||
−0.246870 | + | 0.969049i | \(0.579402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.72415 | 0.448397 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.9885 | −1.69221 | −0.846106 | − | 0.533015i | \(-0.821059\pi\) | ||||
−0.846106 | + | 0.533015i | \(0.821059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.2308 | 2.44603 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.00143 | 0.462383 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0081 | 1.10078 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.97402 | −0.815820 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.8364 | −1.06725 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.84630 | 0.433466 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.3783 | −1.45334 | −0.726668 | − | 0.686989i | \(-0.758932\pi\) | ||||
−0.726668 | + | 0.686989i | \(0.758932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.11615 | −0.626542 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0066 | −1.04902 | −0.524512 | − | 0.851403i | \(-0.675752\pi\) | ||||
−0.524512 | + | 0.851403i | \(0.675752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0647 | −1.47969 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.38131 | 0.291017 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.24650 | 0.619110 | 0.309555 | − | 0.950881i | \(-0.399820\pi\) | ||||
0.309555 | + | 0.950881i | \(0.399820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.39592 | −0.627314 | −0.313657 | − | 0.949536i | \(-0.601554\pi\) | ||||
−0.313657 | + | 0.949536i | \(0.601554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.21355 | −0.691706 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.11888 | 0.595310 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.2811 | 1.76730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.24700 | −0.185330 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.8445 | 1.95341 | 0.976707 | − | 0.214577i | \(-0.0688373\pi\) | ||||
0.976707 | + | 0.214577i | \(0.0688373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42298 | 0.115800 | 0.0579002 | − | 0.998322i | \(-0.481559\pi\) | ||||
0.0579002 | + | 0.998322i | \(0.481559\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.50797 | 0.445293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.7256 | −2.46794 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8822 | 1.58677 | 0.793386 | − | 0.608718i | \(-0.208316\pi\) | ||||
0.793386 | + | 0.608718i | \(0.208316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8063 | −0.856995 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.9126 | 1.33290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3419 | 1.12335 | 0.561674 | − | 0.827359i | \(-0.310158\pi\) | ||||
0.561674 | + | 0.827359i | \(0.310158\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.81285 | 0.374680 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0143 | 0.924179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.82733 | −0.598571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.94096 | −0.375654 | −0.187827 | − | 0.982202i | \(-0.560144\pi\) | ||||
−0.187827 | + | 0.982202i | \(0.560144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0254 | 1.06022 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.83956 | −0.514093 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.94308 | 0.145233 | 0.0726163 | − | 0.997360i | \(-0.476865\pi\) | ||||
0.0726163 | + | 0.997360i | \(0.476865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2531 | 0.836439 | 0.418220 | − | 0.908346i | \(-0.362654\pi\) | ||||
0.418220 | + | 0.908346i | \(0.362654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.73720 | −0.128418 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.9738 | 1.17442 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.83986 | 0.573308 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.18014 | 0.158582 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.97683 | −0.649541 | −0.324770 | − | 0.945793i | \(-0.605287\pi\) | ||||
−0.324770 | + | 0.945793i | \(0.605287\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0704 | −0.724884 | −0.362442 | − | 0.932006i | \(-0.618057\pi\) | ||||
−0.362442 | + | 0.932006i | \(0.618057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.9114 | 1.21105 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.4156 | −1.38330 | −0.691652 | − | 0.722231i | \(-0.743117\pi\) | ||||
−0.691652 | + | 0.722231i | \(0.743117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.98916 | 0.424560 | 0.212280 | − | 0.977209i | \(-0.431911\pi\) | ||||
0.212280 | + | 0.977209i | \(0.431911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.61452 | −0.113880 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.7212 | 0.963040 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −40.0225 | −2.79529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.75758 | 0.539189 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1412 | −0.770651 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53399 | −0.518661 | −0.259331 | − | 0.965789i | \(-0.583502\pi\) | ||||
−0.259331 | + | 0.965789i | \(0.583502\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0154 | 1.09736 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.0619 | −1.64101 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.8107 | −1.34484 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.43455 | 0.299659 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.5477 | 1.85306 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.15074 | 0.0770591 | 0.0385295 | − | 0.999257i | \(-0.487733\pi\) | ||||
0.0385295 | + | 0.999257i | \(0.487733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.43326 | 0.428884 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.0325 | −1.66147 | −0.830733 | − | 0.556671i | \(-0.812078\pi\) | ||||
−0.830733 | + | 0.556671i | \(0.812078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.40955 | 0.489637 | 0.244818 | − | 0.969569i | \(-0.421272\pi\) | ||||
0.244818 | + | 0.969569i | \(0.421272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.10314 | 0.204171 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.93657 | −0.192381 | −0.0961906 | − | 0.995363i | \(-0.530666\pi\) | ||||
−0.0961906 | + | 0.995363i | \(0.530666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.7726 | −1.81168 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.26342 | 0.276939 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.6134 | 1.72148 | 0.860738 | − | 0.509048i | \(-0.170002\pi\) | ||||
0.860738 | + | 0.509048i | \(0.170002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.8419 | 1.08488 | 0.542441 | − | 0.840094i | \(-0.317500\pi\) | ||||
0.542441 | + | 0.840094i | \(0.317500\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.59781 | −0.485406 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.1479 | −2.49092 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.41440 | 0.279751 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.78068 | 0.364873 | 0.182437 | − | 0.983218i | \(-0.441602\pi\) | ||||
0.182437 | + | 0.983218i | \(0.441602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0419 | 0.694198 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6241 | 1.16629 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.5244 | 1.77930 | 0.889651 | − | 0.456641i | \(-0.150948\pi\) | ||||
0.889651 | + | 0.456641i | \(0.150948\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.2993 | 0.639967 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.29374 | 0.389573 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.27282 | 0.263473 | 0.131737 | − | 0.991285i | \(-0.457945\pi\) | ||||
0.131737 | + | 0.991285i | \(0.457945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.5394 | −2.24460 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.56376 | −0.524094 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.38718 | 0.450404 | 0.225202 | − | 0.974312i | \(-0.427696\pi\) | ||||
0.225202 | + | 0.974312i | \(0.427696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7734 | 0.897420 | 0.448710 | − | 0.893677i | \(-0.351884\pi\) | ||||
0.448710 | + | 0.893677i | \(0.351884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9038 | 0.659929 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.15690 | 0.552182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.05325 | −0.123368 | −0.0616839 | − | 0.998096i | \(-0.519647\pi\) | ||||
−0.0616839 | + | 0.998096i | \(0.519647\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.08688 | −0.544018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3998 | 1.51523 | 0.757613 | − | 0.652704i | \(-0.226365\pi\) | ||||
0.757613 | + | 0.652704i | \(0.226365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.37163 | 0.140979 | 0.0704894 | − | 0.997513i | \(-0.477544\pi\) | ||||
0.0704894 | + | 0.997513i | \(0.477544\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −26.4666 | −1.56775 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.8050 | −1.52322 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.3377 | 0.784571 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.2977 | −0.603661 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.38097 | 0.489621 | 0.244811 | − | 0.969571i | \(-0.421274\pi\) | ||||
0.244811 | + | 0.969571i | \(0.421274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.1267 | −1.34649 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.42337 | 0.0825922 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 38.7990 | 2.24381 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5142 | −0.894222 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.31154 | 0.305140 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.87403 | −0.336346 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1839 | 1.32318 | 0.661588 | − | 0.749868i | \(-0.269883\pi\) | ||||
0.661588 | + | 0.749868i | \(0.269883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.971769 | −0.0552820 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1324 | 1.25501 | 0.627506 | − | 0.778612i | \(-0.284076\pi\) | ||||
0.627506 | + | 0.778612i | \(0.284076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.6297 | −1.44868 | −0.724338 | − | 0.689445i | \(-0.757854\pi\) | ||||
−0.724338 | + | 0.689445i | \(0.757854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.37172 | 0.415349 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.5554 | −1.94082 | −0.970412 | − | 0.241454i | \(-0.922376\pi\) | ||||
−0.970412 | + | 0.241454i | \(0.922376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.95830 | 0.501569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7609 | −0.768056 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.1127 | −2.39885 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.1755 | 1.78478 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.15480 | −0.285061 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.9067 | −0.987227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.70159 | −0.533247 | −0.266624 | − | 0.963801i | \(-0.585908\pi\) | ||||
−0.266624 | + | 0.963801i | \(0.585908\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.72415 | 0.258882 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.45920 | −0.298268 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.56357 | 0.412014 | 0.206007 | − | 0.978551i | \(-0.433953\pi\) | ||||
0.206007 | + | 0.978551i | \(0.433953\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.9885 | −0.976999 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.9340 | −0.700414 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1597 | −1.08852 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.2308 | 1.41222 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.21673 | −0.387415 | −0.193707 | − | 0.981059i | \(-0.562051\pi\) | ||||
−0.193707 | + | 0.981059i | \(0.562051\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2805 | 0.710889 | 0.355444 | − | 0.934697i | \(-0.384330\pi\) | ||||
0.355444 | + | 0.934697i | \(0.384330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00143 | 0.266957 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4226 | −0.874087 | −0.437043 | − | 0.899440i | \(-0.643974\pi\) | ||||
−0.437043 | + | 0.899440i | \(0.643974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.1531 | 2.87415 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.0081 | 0.635537 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.150138 | 0.00792397 | 0.00396198 | − | 0.999992i | \(-0.498739\pi\) | ||||
0.00396198 | + | 0.999992i | \(0.498739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.2671 | 2.22458 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.97402 | −0.471014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.9946 | 0.784853 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6880 | 1.13211 | 0.566053 | − | 0.824369i | \(-0.308470\pi\) | ||||
0.566053 | + | 0.824369i | \(0.308470\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.8364 | −0.616178 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.5592 | −1.22313 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.2389 | 0.892595 | 0.446298 | − | 0.894885i | \(-0.352742\pi\) | ||||
0.446298 | + | 0.894885i | \(0.352742\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.84630 | 0.250262 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.4777 | 1.62118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.48673 | −0.281834 | −0.140917 | − | 0.990021i | \(-0.545005\pi\) | ||||
−0.140917 | + | 0.990021i | \(0.545005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.3783 | −0.839084 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0351 | −0.768256 | −0.384128 | − | 0.923280i | \(-0.625498\pi\) | ||||
−0.384128 | + | 0.923280i | \(0.625498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.4927 | 0.534756 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.11615 | −0.361734 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5552 | −1.14359 | −0.571797 | − | 0.820395i | \(-0.693753\pi\) | ||||
−0.571797 | + | 0.820395i | \(0.693753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.7285 | 2.16087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0066 | −0.605655 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.4160 | 0.725346 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6044 | 0.732975 | 0.366488 | − | 0.930423i | \(-0.380560\pi\) | ||||
0.366488 | + | 0.930423i | \(0.380560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.0647 | −0.854301 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.53046 | −0.425991 | −0.212995 | − | 0.977053i | \(-0.568322\pi\) | ||||
−0.212995 | + | 0.977053i | \(0.568322\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.4474 | −2.26390 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.38131 | 0.168019 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.72421 | 0.333307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9598 | 1.62976 | 0.814879 | − | 0.579631i | \(-0.196803\pi\) | ||||
0.814879 | + | 0.579631i | \(0.196803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.24650 | 0.357444 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.9112 | −0.733731 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.9265 | 0.732711 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.39592 | −0.362180 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4830 | 1.09837 | 0.549183 | − | 0.835702i | \(-0.314939\pi\) | ||||
0.549183 | + | 0.835702i | \(0.314939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.13889 | −0.104243 | −0.0521215 | − | 0.998641i | \(-0.516598\pi\) | ||||
−0.0521215 | + | 0.998641i | \(0.516598\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.21355 | −0.399356 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.4342 | 1.71881 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.78734 | −0.183282 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.11888 | 0.343703 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.6297 | −1.81256 | −0.906278 | − | 0.422681i | \(-0.861089\pi\) | ||||
−0.906278 | + | 0.422681i | \(0.861089\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.34024 | 0.208579 | 0.104289 | − | 0.994547i | \(-0.466743\pi\) | ||||
0.104289 | + | 0.994547i | \(0.466743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.2811 | 1.02035 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −60.7212 | −2.90469 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.88893 | −0.185609 | −0.0928044 | − | 0.995684i | \(-0.529583\pi\) | ||||
−0.0928044 | + | 0.995684i | \(0.529583\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.24700 | −0.107000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.35696 | −0.207005 | −0.103503 | − | 0.994629i | \(-0.533005\pi\) | ||||
−0.103503 | + | 0.994629i | \(0.533005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.9567 | −1.37268 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.8445 | 1.12780 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.8021 | 0.887328 | 0.443664 | − | 0.896193i | \(-0.353678\pi\) | ||||
0.443664 | + | 0.896193i | \(0.353678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8475 | −0.793319 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.42298 | 0.0668573 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.8692 | 1.72845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5750 | 1.24313 | 0.621563 | − | 0.783364i | \(-0.286498\pi\) | ||||
0.621563 | + | 0.783364i | \(0.286498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.50797 | 0.257090 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0895 | 0.935662 | 0.467831 | − | 0.883818i | \(-0.345036\pi\) | ||||
0.467831 | + | 0.883818i | \(0.345036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0599 | 1.35053 | 0.675264 | − | 0.737576i | \(-0.264030\pi\) | ||||
0.675264 | + | 0.737576i | \(0.264030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30.7256 | −1.42486 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4129 | 1.17597 | 0.587984 | − | 0.808872i | \(-0.299922\pi\) | ||||
0.587984 | + | 0.808872i | \(0.299922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.51988 | −0.162533 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.8822 | 0.916124 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.1289 | −0.465727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −50.3553 | −2.31046 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.8063 | −0.494786 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.72548 | 0.124530 | 0.0622651 | − | 0.998060i | \(-0.480168\pi\) | ||||
0.0622651 | + | 0.998060i | \(0.480168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.6275 | 1.07732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.9126 | 0.769550 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.8197 | −1.58108 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1754 | 1.05018 | 0.525089 | − | 0.851047i | \(-0.324032\pi\) | ||||
0.525089 | + | 0.851047i | \(0.324032\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.3419 | 0.648565 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3994 | −1.01087 | −0.505434 | − | 0.862865i | \(-0.668668\pi\) | ||||
−0.505434 | + | 0.862865i | \(0.668668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.6657 | 1.56126 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.81285 | 0.216321 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.9158 | 1.56619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.4678 | −1.00580 | −0.502898 | − | 0.864346i | \(-0.667733\pi\) | ||||
−0.502898 | + | 0.864346i | \(0.667733\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.4958 | 1.53809 | 0.769046 | − | 0.639193i | \(-0.220731\pi\) | ||||
0.769046 | + | 0.639193i | \(0.220731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9600 | 0.799208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0143 | 0.533575 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.0445 | 1.59765 | 0.798823 | − | 0.601567i | \(-0.205457\pi\) | ||||
0.798823 | + | 0.601567i | \(0.205457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.66794 | 0.427684 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.82733 | −0.345585 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.28585 | −0.144792 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6909 | −0.514165 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.94096 | −0.216884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3650 | −0.673154 | −0.336577 | − | 0.941656i | \(-0.609269\pi\) | ||||
−0.336577 | + | 0.941656i | \(0.609269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7306 | 0.512941 | 0.256471 | − | 0.966552i | \(-0.417440\pi\) | ||||
0.256471 | + | 0.966552i | \(0.417440\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.0254 | 0.612118 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −50.0503 | −2.18022 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.1801 | 1.61653 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.83956 | −0.296812 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −59.1989 | −2.56419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.5297 | −2.01166 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.94308 | 0.0838501 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.19831 | −0.137761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9718 | −1.15961 | −0.579804 | − | 0.814756i | \(-0.696871\pi\) | ||||
−0.579804 | + | 0.814756i | \(0.696871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2531 | 0.482919 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.4300 | −0.746619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.4592 | 1.64440 | 0.822198 | − | 0.569202i | \(-0.192748\pi\) | ||||
0.822198 | + | 0.569202i | \(0.192748\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.73720 | −0.0741420 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.2632 | −2.09868 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.29485 | 0.395257 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.9738 | 0.678051 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.1906 | −0.643648 | −0.321824 | − | 0.946800i | \(-0.604296\pi\) | ||||
−0.321824 | + | 0.946800i | \(0.604296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.5909 | −1.50534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.83986 | 0.330999 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3816 | 0.563969 | 0.281985 | − | 0.959419i | \(-0.409007\pi\) | ||||
0.281985 | + | 0.959419i | \(0.409007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −60.8246 | −2.55891 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.18014 | 0.0915572 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.6459 | −0.823600 | −0.411800 | − | 0.911274i | \(-0.635100\pi\) | ||||
−0.411800 | + | 0.911274i | \(0.635100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.2035 | −0.636249 | −0.318124 | − | 0.948049i | \(-0.603053\pi\) | ||||
−0.318124 | + | 0.948049i | \(0.603053\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.97683 | −0.375013 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.9066 | 2.08125 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.699702 | 0.0291290 | 0.0145645 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145645 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0704 | −0.418512 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.62400 | 0.399271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.3813 | −0.637030 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.9114 | 0.699200 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.4446 | −0.513645 | −0.256822 | − | 0.966459i | \(-0.582676\pi\) | ||||
−0.256822 | + | 0.966459i | \(0.582676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.1260 | 2.93070 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.4156 | −0.798651 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.1187 | 0.702982 | 0.351491 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351491 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.6032 | 1.66457 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.98916 | 0.245120 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8211 | −0.687289 | −0.343645 | − | 0.939100i | \(-0.611662\pi\) | ||||
−0.343645 | + | 0.939100i | \(0.611662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.5830 | −0.921178 | −0.460589 | − | 0.887614i | \(-0.652362\pi\) | ||||
−0.460589 | + | 0.887614i | \(0.652362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.61452 | −0.0657484 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.3440 | −1.23366 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.60797 | −0.389976 | −0.194988 | − | 0.980806i | \(-0.562467\pi\) | ||||
−0.194988 | + | 0.980806i | \(0.562467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.7212 | 0.556012 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.0795 | −1.66190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.4590 | 1.27062 | 0.635308 | − | 0.772259i | \(-0.280873\pi\) | ||||
0.635308 | + | 0.772259i | \(0.280873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −40.0225 | −1.61386 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2764 | −0.615005 | −0.307503 | − | 0.951547i | \(-0.599493\pi\) | ||||
−0.307503 | + | 0.951547i | \(0.599493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1164 | 1.37126 | 0.685628 | − | 0.727952i | \(-0.259528\pi\) | ||||
0.685628 | + | 0.727952i | \(0.259528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.75758 | 0.311301 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6702 | −0.748005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.7795 | −0.631178 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.1412 | −0.444935 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.0205 | 1.03750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8395 | −1.18789 | −0.593946 | − | 0.804505i | \(-0.702431\pi\) | ||||
−0.593946 | + | 0.804505i | \(0.702431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.53399 | −0.299449 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −55.3800 | −2.19769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.2382 | −0.445275 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.0154 | 0.633560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.98414 | 0.0783690 | 0.0391845 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391845 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6832 | 0.618484 | 0.309242 | − | 0.950983i | \(-0.399925\pi\) | ||||
0.309242 | + | 0.950983i | \(0.399925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0619 | −0.947436 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.16451 | −0.360294 | −0.180147 | − | 0.983640i | \(-0.557657\pi\) | ||||
−0.180147 | + | 0.983640i | \(0.557657\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.73521 | −0.382141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.8107 | −0.776441 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0883 | 0.473050 | 0.236525 | − | 0.971625i | \(-0.423991\pi\) | ||||
0.236525 | + | 0.971625i | \(0.423991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.5982 | −1.58630 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.43455 | 0.173008 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.2128 | −1.64438 | −0.822188 | − | 0.569217i | \(-0.807247\pi\) | ||||
−0.822188 | + | 0.569217i | \(0.807247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0116 | −0.389404 | −0.194702 | − | 0.980862i | \(-0.562374\pi\) | ||||
−0.194702 | + | 0.980862i | \(0.562374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.5477 | 1.06987 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −57.7009 | −2.23754 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.8242 | 1.89048 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.15074 | 0.0444901 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.47268 | −0.0954567 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.8885 | 0.612457 | 0.306229 | − | 0.951958i | \(-0.400933\pi\) | ||||
0.306229 | + | 0.951958i | \(0.400933\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.43326 | 0.247616 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1756 | 1.19817 | 0.599087 | − | 0.800684i | \(-0.295530\pi\) | ||||
0.599087 | + | 0.800684i | \(0.295530\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4504 | −0.861566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.0325 | −0.959248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.7517 | 0.755780 | 0.377890 | − | 0.925851i | \(-0.376650\pi\) | ||||
0.377890 | + | 0.925851i | \(0.376650\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.5027 | 0.936199 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.40955 | 0.282692 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.0469 | −2.05902 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.7668 | −1.36063 | −0.680316 | − | 0.732919i | \(-0.738158\pi\) | ||||
−0.680316 | + | 0.732919i | \(0.738158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.10314 | 0.117878 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.0079 | −0.948604 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.1944 | −2.46942 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.93657 | −0.111071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.2240 | −0.877160 | −0.438580 | − | 0.898692i | \(-0.644518\pi\) | ||||
−0.438580 | + | 0.898692i | \(0.644518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.9775 | −1.39463 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.7726 | −1.04598 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5799 | 0.435506 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8679 | 0.746156 | 0.373078 | − | 0.927800i | \(-0.378302\pi\) | ||||
0.373078 | + | 0.927800i | \(0.378302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.26342 | 0.159891 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −70.4923 | −2.63996 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0711 | 0.900209 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.6134 | 0.993895 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.79193 | 0.216003 | 0.108001 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108001 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.11859 | −0.0789004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.8419 | 0.626357 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.4893 | 1.50373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2264 | −0.824331 | −0.412165 | − | 0.911109i | \(-0.635227\pi\) | ||||
−0.412165 | + | 0.911109i | \(0.635227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.1955 | −1.44970 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.28416 | −0.0843672 | −0.0421836 | − | 0.999110i | \(-0.513431\pi\) | ||||
−0.0421836 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.59781 | −0.280249 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.29806 | −0.0846500 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.67059 | 0.0614538 | 0.0307269 | − | 0.999528i | \(-0.490218\pi\) | ||||
0.0307269 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −39.1479 | −1.43813 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.4665 | −1.81475 | −0.907375 | − | 0.420323i | \(-0.861917\pi\) | ||||
−0.907375 | + | 0.420323i | \(0.861917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 80.6255 | 2.95389 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.41440 | 0.161515 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.0006 | −1.09620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.2975 | 1.39749 | 0.698747 | − | 0.715369i | \(-0.253741\pi\) | ||||
0.698747 | + | 0.715369i | \(0.253741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.78068 | 0.210660 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.81153 | 0.175110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.3444 | 1.10288 | 0.551442 | − | 0.834213i | \(-0.314078\pi\) | ||||
0.551442 | + | 0.834213i | \(0.314078\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.0419 | 0.400795 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5231 | 0.490214 | 0.245107 | − | 0.969496i | \(-0.421177\pi\) | ||||
0.245107 | + | 0.969496i | \(0.421177\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2382 | −0.406849 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.6241 | 0.673358 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −34.2076 | −1.23517 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8744 | 0.464261 | 0.232131 | − | 0.972685i | \(-0.425430\pi\) | ||||
0.232131 | + | 0.972685i | \(0.425430\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.5244 | 1.02728 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.91163 | −0.212627 | −0.106313 | − | 0.994333i | \(-0.533905\pi\) | ||||
−0.106313 | + | 0.994333i | \(0.533905\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −58.4583 | −2.09988 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.2993 | 0.369485 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 92.6473 | 3.31943 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.7958 | 0.815699 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.29374 | 0.224920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 67.2279 | 2.39947 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3311 | 0.938601 | 0.469301 | − | 0.883039i | \(-0.344506\pi\) | ||||
0.469301 | + | 0.883039i | \(0.344506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.27282 | 0.152116 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.2173 | −1.39441 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.68851 | −0.308538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.5394 | −1.29592 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.7848 | −1.79889 | −0.899445 | − | 0.437035i | \(-0.856029\pi\) | ||||
−0.899445 | + | 0.437035i | \(0.856029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.2400 | −1.60047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.56376 | −0.302586 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.31200 | 0.222746 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.1867 | 2.01557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.38718 | 0.260041 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.0939 | 0.776781 | 0.388391 | − | 0.921495i | \(-0.373031\pi\) | ||||
0.388391 | + | 0.921495i | \(0.373031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.9802 | −0.385567 | −0.192783 | − | 0.981241i | \(-0.561751\pi\) | ||||
−0.192783 | + | 0.981241i | \(0.561751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7734 | 0.518126 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.4946 | 1.69869 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.7004 | 1.94871 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.9038 | 0.381010 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.8208 | 0.796451 | 0.398226 | − | 0.917287i | \(-0.369626\pi\) | ||||
0.398226 | + | 0.917287i | \(0.369626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.73811 | 0.165160 | 0.0825802 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825802 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.15690 | 0.318802 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.6761 | 0.614658 | 0.307329 | − | 0.951603i | \(-0.400565\pi\) | ||||
0.307329 | + | 0.951603i | \(0.400565\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.25537 | −0.217258 | −0.108629 | − | 0.994082i | \(-0.534646\pi\) | ||||
−0.108629 | + | 0.994082i | \(0.534646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.05325 | −0.0712264 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.3764 | −0.428817 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.38131 | −0.117015 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.08688 | −0.314089 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.0898 | 1.07334 | 0.536669 | − | 0.843793i | \(-0.319682\pi\) | ||||
0.536669 | + | 0.843793i | \(0.319682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6111 | 0.365901 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.3998 | 0.874816 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.6242 | 1.39751 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.5646 | −0.672248 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.37163 | 0.0813941 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.6480 | 1.25628 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.71143 | −0.127077 | −0.0635385 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635385 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.4666 | −0.905140 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.9041 | −0.919026 | −0.459513 | − | 0.888171i | \(-0.651976\pi\) | ||||
−0.459513 | + | 0.888171i | \(0.651976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3548 | −0.523901 | −0.261950 | − | 0.965081i | \(-0.584366\pi\) | ||||
−0.261950 | + | 0.965081i | \(0.584366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.8050 | −0.879430 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.1838 | −1.77636 | −0.888179 | − | 0.459498i | \(-0.848029\pi\) | ||||
−0.888179 | + | 0.459498i | \(0.848029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7069 | −0.568052 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.3377 | 0.452972 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.06842 | 0.205857 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.07492 | −0.273608 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.2977 | −0.348524 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.5656 | 0.357183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.6674 | 1.64338 | 0.821691 | − | 0.569934i | \(-0.193031\pi\) | ||||
0.821691 | + | 0.569934i | \(0.193031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.38097 | 0.282683 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.713672 | −0.0240442 | −0.0120221 | − | 0.999928i | \(-0.503827\pi\) | ||||
−0.0120221 | + | 0.999928i | \(0.503827\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.62220 | −0.290160 | −0.145080 | − | 0.989420i | \(-0.546344\pi\) | ||||
−0.145080 | + | 0.989420i | \(0.546344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.1267 | −0.777395 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.51090 | 0.285768 | 0.142884 | − | 0.989739i | \(-0.454362\pi\) | ||||
0.142884 | + | 0.989739i | \(0.454362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.7069 | −1.19757 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.42337 | 0.0476846 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.2902 | 2.15139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.57016 | 0.219616 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.7990 | 1.29546 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −57.1905 | −1.90741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.5207 | −1.98292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.5142 | −0.516279 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.0504 | 1.26484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.3979 | −0.976143 | −0.488071 | − | 0.872804i | \(-0.662299\pi\) | ||||
−0.488071 | + | 0.872804i | \(0.662299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.31154 | 0.176173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.694625 | 0.0230140 | 0.0115070 | − | 0.999934i | \(-0.496337\pi\) | ||||
0.0115070 | + | 0.999934i | \(0.496337\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.28332 | 0.207947 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.87403 | −0.194189 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.1761 | −0.864412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.2759 | −1.49351 | −0.746757 | − | 0.665097i | \(-0.768390\pi\) | ||||
−0.746757 | + | 0.665097i | \(0.768390\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.1839 | 0.763936 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.1000 | 2.63652 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.3917 | 0.999273 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.971769 | −0.0319171 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.0209 | −1.64113 | −0.820566 | − | 0.571551i | \(-0.806342\pi\) | ||||
−0.820566 | + | 0.571551i | \(0.806342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.5880 | 0.576424 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.1324 | 0.724581 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.5090 | 0.866938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.3630 | −1.71062 | −0.855312 | − | 0.518114i | \(-0.826634\pi\) | ||||
−0.855312 | + | 0.518114i | \(0.826634\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.6297 | −0.836393 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.6749 | −1.61935 | −0.809677 | − | 0.586875i | \(-0.800358\pi\) | ||||
−0.809677 | + | 0.586875i | \(0.800358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −91.8218 | −2.99013 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.37172 | 0.239802 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.6023 | −1.02694 | −0.513468 | − | 0.858109i | \(-0.671640\pi\) | ||||
−0.513468 | + | 0.858109i | \(0.671640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1791 | 0.719965 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.5554 | −1.12054 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.2157 | −1.43229 | −0.716143 | − | 0.697953i | \(-0.754094\pi\) | ||||
−0.716143 | + | 0.697953i | \(0.754094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.3535 | −0.982215 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.95830 | 0.289581 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.7984 | 0.510156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.5715 | 1.66360 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.7609 | −0.443437 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.0512 | −1.09615 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8623 | −1.02462 | −0.512311 | − | 0.858800i | \(-0.671210\pi\) | ||||
−0.512311 | + | 0.858800i | \(0.671210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.1127 | −1.38498 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.6768 | 0.791917 | 0.395958 | − | 0.918268i | \(-0.370412\pi\) | ||||
0.395958 | + | 0.918268i | \(0.370412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.1241 | −0.516916 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.1755 | 1.03044 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.3621 | −0.875392 | −0.437696 | − | 0.899123i | \(-0.644205\pi\) | ||||
−0.437696 | + | 0.899123i | \(0.644205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1894 | −0.389574 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.15480 | −0.164580 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.2808 | −0.327906 | −0.163953 | − | 0.986468i | \(-0.552425\pi\) | ||||
−0.163953 | + | 0.986468i | \(0.552425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65.6502 | −2.09179 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.9067 | −0.569975 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.2041 | −1.75539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.86212 | 0.217982 | 0.108991 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108991 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.70159 | −0.307871 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.2512 | 0.642006 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.7713 | 1.32291 | 0.661456 | − | 0.749984i | \(-0.269939\pi\) | ||||
0.661456 | + | 0.749984i | \(0.269939\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.72415 | 0.149466 |
(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 | 4008.2.a.m.1.12 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.12 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.12 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.12 | 13 | 4.3 | odd | 2 |