Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.57500224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 12x^{3} + 11x^{2} - 18x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.72058\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −1.72058 | −0.993376 | −0.496688 | − | 0.867929i | \(-0.665451\pi\) | ||||
−0.496688 | + | 0.867929i | \(0.665451\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.22719 | −0.996031 | −0.498015 | − | 0.867168i | \(-0.665938\pi\) | ||||
−0.498015 | + | 0.867168i | \(0.665938\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.96772 | 0.743729 | 0.371864 | − | 0.928287i | \(-0.378719\pi\) | ||||
0.371864 | + | 0.928287i | \(0.378719\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0396114 | −0.0132038 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.04754 | 1.95464 | 0.977318 | − | 0.211779i | \(-0.0679257\pi\) | ||||
0.977318 | + | 0.211779i | \(0.0679257\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.83206 | 0.989433 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.60817 | −1.84525 | −0.922627 | − | 0.385694i | \(-0.873962\pi\) | ||||
−0.922627 | + | 0.385694i | \(0.873962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.38562 | −0.738803 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.60084 | 1.37637 | 0.688185 | − | 0.725535i | \(-0.258408\pi\) | ||||
0.688185 | + | 0.725535i | \(0.258408\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0396114 | −0.00792229 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.22989 | 1.00649 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.25147 | −1.16087 | −0.580435 | − | 0.814307i | \(-0.697117\pi\) | ||||
−0.580435 | + | 0.814307i | \(0.697117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.36962 | −0.964413 | −0.482206 | − | 0.876058i | \(-0.660164\pi\) | ||||
−0.482206 | + | 0.876058i | \(0.660164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.72058 | 0.299514 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.38250 | −0.740777 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.61473 | 1.25185 | 0.625927 | − | 0.779881i | \(-0.284721\pi\) | ||||
0.625927 | + | 0.779881i | \(0.284721\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.1258 | −1.94169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.40485 | −1.46879 | −0.734396 | − | 0.678722i | \(-0.762534\pi\) | ||||
−0.734396 | + | 0.678722i | \(0.762534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.26919 | −0.956042 | −0.478021 | − | 0.878348i | \(-0.658646\pi\) | ||||
−0.478021 | + | 0.878348i | \(0.658646\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0882223 | 0.0131514 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4279 | 1.52107 | 0.760535 | − | 0.649297i | \(-0.224937\pi\) | ||||
0.760535 | + | 0.649297i | \(0.224937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.12807 | −0.446867 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.0905 | 1.83303 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.34870 | 0.597340 | 0.298670 | − | 0.954356i | \(-0.403457\pi\) | ||||
0.298670 | + | 0.954356i | \(0.403457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.22719 | 0.300315 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.72058 | −0.227896 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.10518 | −0.274071 | −0.137035 | − | 0.990566i | \(-0.543757\pi\) | ||||
−0.137035 | + | 0.990566i | \(0.543757\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.77442 | −1.12345 | −0.561725 | − | 0.827324i | \(-0.689862\pi\) | ||||
−0.561725 | + | 0.827324i | \(0.689862\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0779443 | −0.00982006 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.6962 | −1.94688 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7675 | 1.68197 | 0.840984 | − | 0.541060i | \(-0.181977\pi\) | ||||
0.840984 | + | 0.541060i | \(0.181977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.3573 | −1.36725 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.14707 | −0.136132 | −0.0680659 | − | 0.997681i | \(-0.521683\pi\) | ||||
−0.0680659 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.04471 | −0.707480 | −0.353740 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353740 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0681546 | 0.00786981 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.96772 | −0.224243 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.68740 | 0.639882 | 0.319941 | − | 0.947437i | \(-0.396337\pi\) | ||||
0.319941 | + | 0.947437i | \(0.396337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.87960 | −0.986622 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.02439 | −0.990555 | −0.495277 | − | 0.868735i | \(-0.664934\pi\) | ||||
−0.495277 | + | 0.868735i | \(0.664934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9449 | 1.83793 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.7561 | 1.15318 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.83170 | −0.512160 | −0.256080 | − | 0.966656i | \(-0.582431\pi\) | ||||
−0.256080 | + | 0.966656i | \(0.582431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8676 | 1.45372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.23885 | 0.958025 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.22719 | −0.228505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0691 | 1.22543 | 0.612717 | − | 0.790303i | \(-0.290077\pi\) | ||||
0.612717 | + | 0.790303i | \(0.290077\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0396114 | 0.00398110 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1105 | 1.70256 | 0.851280 | − | 0.524712i | \(-0.175827\pi\) | ||||
0.851280 | + | 0.524712i | \(0.175827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.4053 | 1.12379 | 0.561897 | − | 0.827207i | \(-0.310072\pi\) | ||||
0.561897 | + | 0.827207i | \(0.310072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.54043 | 0.735870 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.56007 | 0.634186 | 0.317093 | − | 0.948394i | \(-0.397293\pi\) | ||||
0.317093 | + | 0.948394i | \(0.397293\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.49644 | −0.143333 | −0.0716663 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716663 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.1017 | −1.24356 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.54633 | 0.333611 | 0.166805 | − | 0.985990i | \(-0.446655\pi\) | ||||
0.166805 | + | 0.985990i | \(0.446655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.7013 | −1.37091 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.279163 | −0.0258086 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.9708 | −1.37237 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.1818 | 1.45906 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2242 | 1.00392 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.70447 | 0.417454 | 0.208727 | − | 0.977974i | \(-0.433068\pi\) | ||||
0.208727 | + | 0.977974i | \(0.433068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7866 | 0.949710 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.53122 | 0.133784 | 0.0668918 | − | 0.997760i | \(-0.478692\pi\) | ||||
0.0668918 | + | 0.997760i | \(0.478692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.96772 | 0.170623 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.6480 | −1.00250 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.4781 | −1.40782 | −0.703910 | − | 0.710289i | \(-0.748564\pi\) | ||||
−0.703910 | + | 0.710289i | \(0.748564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.61989 | −0.222216 | −0.111108 | − | 0.993808i | \(-0.535440\pi\) | ||||
−0.111108 | + | 0.993808i | \(0.535440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.9421 | −1.51099 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.04754 | −0.589345 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.9232 | 1.15626 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.38209 | 0.443907 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0818 | 0.907860 | 0.453930 | − | 0.891037i | \(-0.350022\pi\) | ||||
0.453930 | + | 0.891037i | \(0.350022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.83904 | 0.149659 | 0.0748293 | − | 0.997196i | \(-0.476159\pi\) | ||||
0.0748293 | + | 0.997196i | \(0.476159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.301371 | 0.0243644 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.9592 | 0.960585 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.36554 | −0.188791 | −0.0943954 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943954 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.48228 | −0.593384 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9886 | 1.02365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2217 | 1.50556 | 0.752781 | − | 0.658271i | \(-0.228712\pi\) | ||||
0.752781 | + | 0.658271i | \(0.228712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.83206 | −0.298325 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.0347 | −1.00865 | −0.504326 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504326 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.6678 | 2.82060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0396114 | −0.00302916 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.9243 | 0.982614 | 0.491307 | − | 0.870987i | \(-0.336519\pi\) | ||||
0.491307 | + | 0.870987i | \(0.336519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0779443 | −0.00589204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.62212 | 0.272255 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.25316 | 0.542126 | 0.271063 | − | 0.962562i | \(-0.412625\pi\) | ||||
0.271063 | + | 0.962562i | \(0.412625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.4890 | 1.67159 | 0.835797 | − | 0.549039i | \(-0.185006\pi\) | ||||
0.835797 | + | 0.549039i | \(0.185006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0971 | 1.11601 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.9595 | −1.24689 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.60817 | 0.556365 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.2910 | 0.748558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.63679 | −0.118434 | −0.0592169 | − | 0.998245i | \(-0.518860\pi\) | ||||
−0.0592169 | + | 0.998245i | \(0.518860\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.67334 | 0.624321 | 0.312160 | − | 0.950029i | \(-0.398947\pi\) | ||||
0.312160 | + | 0.950029i | \(0.398947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 27.0066 | 1.93398 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.4678 | 1.03079 | 0.515393 | − | 0.856954i | \(-0.327646\pi\) | ||||
0.515393 | + | 0.856954i | \(0.327646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.92883 | 0.632948 | 0.316474 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316474 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.6881 | −1.67083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3012 | −0.863372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.9464 | 1.46296 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.261469 | −0.0181733 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9296 | 0.958953 | 0.479477 | − | 0.877555i | \(-0.340827\pi\) | ||||
0.479477 | + | 0.877555i | \(0.340827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.97362 | 0.135230 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.9627 | 0.952248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5659 | −0.717262 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.4004 | 0.702794 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −53.6189 | −3.60680 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.23753 | 0.0828713 | 0.0414356 | − | 0.999141i | \(-0.486807\pi\) | ||||
0.0414356 | + | 0.999141i | \(0.486807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.00156907 | 0.000104604 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.4085 | 1.28819 | 0.644093 | − | 0.764947i | \(-0.277235\pi\) | ||||
0.644093 | + | 0.764947i | \(0.277235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6297 | −0.900675 | −0.450338 | − | 0.892858i | \(-0.648696\pi\) | ||||
−0.450338 | + | 0.892858i | \(0.648696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.38562 | 0.222757 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.87370 | 0.450311 | 0.225156 | − | 0.974323i | \(-0.427711\pi\) | ||||
0.225156 | + | 0.974323i | \(0.427711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.2250 | −1.51503 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.78561 | −0.635644 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.9021 | −1.74015 | −0.870075 | − | 0.492919i | \(-0.835930\pi\) | ||||
−0.870075 | + | 0.492919i | \(0.835930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2375 | 0.659453 | 0.329727 | − | 0.944076i | \(-0.393043\pi\) | ||||
0.329727 | + | 0.944076i | \(0.393043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.411627 | −0.0264059 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.96682 | 0.445094 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.04754 | 0.448424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5272 | 0.983994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.8369 | 0.936498 | 0.468249 | − | 0.883596i | \(-0.344885\pi\) | ||||
0.468249 | + | 0.883596i | \(0.344885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.60084 | −0.414991 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −29.1550 | −1.82576 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.88893 | 0.367341 | 0.183671 | − | 0.982988i | \(-0.441202\pi\) | ||||
0.183671 | + | 0.982988i | \(0.441202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9837 | 0.931041 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.247630 | 0.0153279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7421 | −1.03236 | −0.516181 | − | 0.856480i | \(-0.672647\pi\) | ||||
−0.516181 | + | 0.856480i | \(0.672647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.68540 | −0.594969 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.31332 | 0.508767 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.63411 | 0.587402 | 0.293701 | − | 0.955897i | \(-0.405113\pi\) | ||||
0.293701 | + | 0.955897i | \(0.405113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.2625 | −1.59533 | −0.797667 | − | 0.603098i | \(-0.793933\pi\) | ||||
−0.797667 | + | 0.603098i | \(0.793933\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −23.8603 | −1.44409 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0396114 | 0.00238866 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.1065 | 1.62867 | 0.814336 | − | 0.580394i | \(-0.197101\pi\) | ||||
0.814336 | + | 0.580394i | \(0.197101\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.212698 | 0.0127339 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.2426 | −1.50585 | −0.752925 | − | 0.658106i | \(-0.771358\pi\) | ||||
−0.752925 | + | 0.658106i | \(0.771358\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.88126 | −0.230717 | −0.115359 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115359 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.83206 | 0.226992 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.5061 | −1.09238 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8843 | 2.40496 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.7659 | −1.21732 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.16065 | 0.535171 | 0.267585 | − | 0.963534i | \(-0.413774\pi\) | ||||
0.267585 | + | 0.963534i | \(0.413774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.68864 | 0.272983 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.22989 | −0.303469 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 46.5197 | 2.69030 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.3360 | −0.711036 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.4400 | −1.69128 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5423 | 1.11899 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.45110 | 0.425256 | 0.212628 | − | 0.977133i | \(-0.431798\pi\) | ||||
0.212628 | + | 0.977133i | \(0.431798\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.6236 | −1.11635 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1280 | 1.59499 | 0.797496 | − | 0.603324i | \(-0.206157\pi\) | ||||
0.797496 | + | 0.603324i | \(0.206157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.71407 | −0.209932 | −0.104966 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104966 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.173597 | 0.00978108 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.79790 | 0.269477 | 0.134739 | − | 0.990881i | \(-0.456981\pi\) | ||||
0.134739 | + | 0.990881i | \(0.456981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.25147 | 0.350015 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.2871 | −0.629985 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.60817 | −0.423330 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.279163 | −0.0154852 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.57474 | 0.142383 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.5193 | 1.13126 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.44840 | −0.519331 | −0.259665 | − | 0.965699i | \(-0.583612\pi\) | ||||
−0.259665 | + | 0.965699i | \(0.583612\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.301631 | −0.0165293 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.6629 | −1.67529 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1381 | −1.47831 | −0.739155 | − | 0.673536i | \(-0.764775\pi\) | ||||
−0.739155 | + | 0.673536i | \(0.764775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.10174 | −0.331401 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.36962 | 0.290781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9292 | −1.07608 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.2948 | 1.36183 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.46828 | −0.293553 | −0.146776 | − | 0.989170i | \(-0.546890\pi\) | ||||
−0.146776 | + | 0.989170i | \(0.546890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.27557 | 0.175337 | 0.0876687 | − | 0.996150i | \(-0.472058\pi\) | ||||
0.0876687 | + | 0.996150i | \(0.472058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.8578 | 1.96733 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6340 | 0.885340 | 0.442670 | − | 0.896685i | \(-0.354031\pi\) | ||||
0.442670 | + | 0.896685i | \(0.354031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.55474 | 0.135592 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.7584 | 1.36328 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1556 | 1.53877 | 0.769387 | − | 0.638783i | \(-0.220562\pi\) | ||||
0.769387 | + | 0.638783i | \(0.220562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.72058 | −0.0903069 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4627 | 0.704672 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9369 | 1.45830 | 0.729148 | − | 0.684356i | \(-0.239917\pi\) | ||||
0.729148 | + | 0.684356i | \(0.239917\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.372540 | 0.0193936 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.55704 | 0.444259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7198 | 0.762163 | 0.381082 | − | 0.924541i | \(-0.375552\pi\) | ||||
0.381082 | + | 0.924541i | \(0.375552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.3121 | −0.997272 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −44.0575 | −2.26908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.342859 | −0.0176115 | −0.00880574 | − | 0.999961i | \(-0.502803\pi\) | ||||
−0.00880574 | + | 0.999961i | \(0.502803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.09441 | −0.414689 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.3669 | 1.60277 | 0.801386 | − | 0.598148i | \(-0.204096\pi\) | ||||
0.801386 | + | 0.598148i | \(0.204096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.38250 | 0.223353 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.248332 | 0.0126234 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.0391 | −1.62445 | −0.812225 | − | 0.583345i | \(-0.801744\pi\) | ||||
−0.812225 | + | 0.583345i | \(0.801744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.2203 | −2.53975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.63459 | −0.132897 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.6669 | −0.637342 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.4621 | −1.67941 | −0.839706 | − | 0.543041i | \(-0.817273\pi\) | ||||
−0.839706 | + | 0.543041i | \(0.817273\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.38562 | −0.169493 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.41337 | 0.470081 | 0.235041 | − | 0.971986i | \(-0.424478\pi\) | ||||
0.235041 | + | 0.971986i | \(0.424478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.8426 | −1.88507 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.7766 | 0.982706 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.61473 | −0.377448 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0101 | −0.494966 | −0.247483 | − | 0.968892i | \(-0.579603\pi\) | ||||
−0.247483 | + | 0.968892i | \(0.579603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.3519 | 1.39849 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.14240 | −0.203834 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0990 | 0.986623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.50772 | 0.220744 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.41377 | −0.313333 | −0.156667 | − | 0.987652i | \(-0.550075\pi\) | ||||
−0.156667 | + | 0.987652i | \(0.550075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1476 | 0.494565 | 0.247282 | − | 0.968943i | \(-0.420462\pi\) | ||||
0.247282 | + | 0.968943i | \(0.420462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.413065 | −0.0200839 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.301371 | 0.0146186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.2656 | −0.835542 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.1258 | 0.585441 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.59530 | −0.269516 | −0.134758 | − | 0.990879i | \(-0.543026\pi\) | ||||
−0.134758 | + | 0.990879i | \(0.543026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.1228 | −1.63984 | −0.819918 | − | 0.572481i | \(-0.805981\pi\) | ||||
−0.819918 | + | 0.572481i | \(0.805981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.9560 | −1.14860 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.60084 | 0.315761 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.28891 | −0.300153 | −0.150077 | − | 0.988674i | \(-0.547952\pi\) | ||||
−0.150077 | + | 0.988674i | \(0.547952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.123907 | 0.00590035 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1169 | 1.05081 | 0.525403 | − | 0.850853i | \(-0.323914\pi\) | ||||
0.525403 | + | 0.850853i | \(0.323914\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.7611 | 0.510127 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.0672 | −0.901847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.54479 | 0.167289 | 0.0836444 | − | 0.996496i | \(-0.473344\pi\) | ||||
0.0836444 | + | 0.996496i | \(0.473344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.40485 | 0.442857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.16421 | −0.148667 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.8858 | −1.44795 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.0898 | 1.36076 | 0.680382 | − | 0.732858i | \(-0.261814\pi\) | ||||
0.680382 | + | 0.732858i | \(0.261814\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.7899 | −1.85723 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5291 | 0.676688 | 0.338344 | − | 0.941023i | \(-0.390133\pi\) | ||||
0.338344 | + | 0.941023i | \(0.390133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6005 | 0.957386 | 0.478693 | − | 0.877982i | \(-0.341111\pi\) | ||||
0.478693 | + | 0.877982i | \(0.341111\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.5767 | −0.954222 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8174 | −0.546846 | −0.273423 | − | 0.961894i | \(-0.588156\pi\) | ||||
−0.273423 | + | 0.961894i | \(0.588156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.0906 | 1.25093 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.07010 | 0.187540 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.26919 | 0.288258 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0396114 | −0.00181750 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.172258 | −0.00788717 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.0255 | 1.78312 | 0.891561 | − | 0.452901i | \(-0.149611\pi\) | ||||
0.891561 | + | 0.452901i | \(0.149611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.6651 | 2.44692 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.3479 | −1.01687 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.8803 | −1.22057 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.3964 | 1.33208 | 0.666039 | − | 0.745917i | \(-0.267989\pi\) | ||||
0.666039 | + | 0.745917i | \(0.267989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.0725 | −1.49559 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.5585 | −1.74012 | −0.870061 | − | 0.492943i | \(-0.835921\pi\) | ||||
−0.870061 | + | 0.492943i | \(0.835921\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 47.5623 | 2.14210 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0882223 | −0.00396530 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.25711 | −0.101245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4393 | −0.601626 | −0.300813 | − | 0.953683i | \(-0.597258\pi\) | ||||
−0.300813 | + | 0.953683i | \(0.597258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4272 | 1.00197 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.4840 | 0.734984 | 0.367492 | − | 0.930027i | \(-0.380217\pi\) | ||||
0.367492 | + | 0.930027i | \(0.380217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.1084 | −1.69580 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −63.0898 | −2.80192 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.6969 | −0.917374 | −0.458687 | − | 0.888598i | \(-0.651680\pi\) | ||||
−0.458687 | + | 0.888598i | \(0.651680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.8943 | −0.526173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.22989 | 0.230905 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.4017 | −1.11933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4279 | −0.458620 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.2372 | −0.976105 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5616 | 0.550334 | 0.275167 | − | 0.961396i | \(-0.411267\pi\) | ||||
0.275167 | + | 0.961396i | \(0.411267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.5981 | −1.77523 | −0.887616 | − | 0.460584i | \(-0.847640\pi\) | ||||
−0.887616 | + | 0.460584i | \(0.847640\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.134109 | 0.00585301 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.8530 | 1.77959 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5711 | 0.894396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0833891 | 0.00361878 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −66.2810 | −2.87095 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6105 | −0.631669 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.4796 | −0.538535 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.12807 | 0.134736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6583 | −0.716197 | −0.358099 | − | 0.933684i | \(-0.616575\pi\) | ||||
−0.358099 | + | 0.933684i | \(0.616575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.6941 | −1.66052 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.33285 | 0.142764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.5756 | −1.05078 | −0.525389 | − | 0.850862i | \(-0.676080\pi\) | ||||
−0.525389 | + | 0.850862i | \(0.676080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.347567 | 0.0148338 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.25147 | −0.266322 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1912 | 0.475899 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.1801 | 1.23863 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.4752 | −0.909934 | −0.454967 | − | 0.890508i | \(-0.650349\pi\) | ||||
−0.454967 | + | 0.890508i | \(0.650349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.1823 | −1.86871 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.0905 | −0.552680 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.9440 | −0.882686 | −0.441343 | − | 0.897338i | \(-0.645498\pi\) | ||||
−0.441343 | + | 0.897338i | \(0.645498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.89837 | −0.332287 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.4726 | −0.733779 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.1031 | −0.884687 | −0.442343 | − | 0.896846i | \(-0.645853\pi\) | ||||
−0.442343 | + | 0.896846i | \(0.645853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.6827 | 1.15848 | 0.579242 | − | 0.815156i | \(-0.303349\pi\) | ||||
0.579242 | + | 0.815156i | \(0.303349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.81622 | 0.117649 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.261469 | −0.0109040 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.9430 | 0.663714 | 0.331857 | − | 0.943330i | \(-0.392325\pi\) | ||||
0.331857 | + | 0.943330i | \(0.392325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.9232 | −0.620185 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.7575 | −0.736704 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.34870 | −0.180105 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.621750 | 0.0257062 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.93504 | −0.286240 | −0.143120 | − | 0.989705i | \(-0.545713\pi\) | ||||
−0.143120 | + | 0.989705i | \(0.545713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.36962 | −0.221251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.8929 | −1.02396 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0536 | −0.536049 | −0.268024 | − | 0.963412i | \(-0.586371\pi\) | ||||
−0.268024 | + | 0.963412i | \(0.586371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33.3428 | 1.36692 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.3627 | −0.628755 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5165 | −0.879142 | −0.439571 | − | 0.898208i | \(-0.644870\pi\) | ||||
−0.439571 | + | 0.898208i | \(0.644870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9862 | −0.692883 | −0.346442 | − | 0.938072i | \(-0.612610\pi\) | ||||
−0.346442 | + | 0.938072i | \(0.612610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.545351 | −0.0222084 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.22719 | −0.0905483 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.55167 | 0.347102 | 0.173551 | − | 0.984825i | \(-0.444476\pi\) | ||||
0.173551 | + | 0.984825i | \(0.444476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.1651 | 0.857653 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 73.4912 | 2.97314 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.17578 | 0.0878790 | 0.0439395 | − | 0.999034i | \(-0.486009\pi\) | ||||
0.0439395 | + | 0.999034i | \(0.486009\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.0400 | −1.45327 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.5625 | 1.59273 | 0.796364 | − | 0.604818i | \(-0.206754\pi\) | ||||
0.796364 | + | 0.604818i | \(0.206754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.42787 | 0.0975844 | 0.0487922 | − | 0.998809i | \(-0.484463\pi\) | ||||
0.0487922 | + | 0.998809i | \(0.484463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.5217 | 1.38531 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.50745 | −0.380908 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8004 | −0.992015 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.72058 | 0.0687133 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −57.9342 | −2.30999 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9436 | 0.475467 | 0.237733 | − | 0.971330i | \(-0.423596\pi\) | ||||
0.237733 | + | 0.971330i | \(0.423596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.9670 | −0.952601 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4778 | −0.415798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0452 | −0.873462 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0454370 | 0.00179746 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0294 | 1.02810 | 0.514050 | − | 0.857760i | \(-0.328145\pi\) | ||||
0.514050 | + | 0.857760i | \(0.328145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.6765 | 1.48582 | 0.742909 | − | 0.669393i | \(-0.233446\pi\) | ||||
0.742909 | + | 0.669393i | \(0.233446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0239 | −0.945940 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.3030 | −1.46653 | −0.733266 | − | 0.679941i | \(-0.762005\pi\) | ||||
−0.733266 | + | 0.679941i | \(0.762005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.10518 | 0.0826354 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.1795 | 0.712511 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.67401 | 0.104642 | 0.0523210 | − | 0.998630i | \(-0.483338\pi\) | ||||
0.0523210 | + | 0.998630i | \(0.483338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.41033 | −0.133253 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.239440 | 0.00934143 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.7451 | 1.70407 | 0.852034 | − | 0.523486i | \(-0.175369\pi\) | ||||
0.852034 | + | 0.523486i | \(0.175369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.6277 | −1.69692 | −0.848460 | − | 0.529260i | \(-0.822470\pi\) | ||||
−0.848460 | + | 0.529260i | \(0.822470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 92.2555 | 3.58291 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.38250 | −0.169946 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.2650 | −1.59779 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.12927 | −0.0823224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.77442 | 0.338733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.3184 | −1.36142 | −0.680712 | − | 0.732551i | \(-0.738329\pi\) | ||||
−0.680712 | + | 0.732551i | \(0.738329\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.207163 | −0.00797372 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.8219 | −0.684952 | −0.342476 | − | 0.939527i | \(-0.611265\pi\) | ||||
−0.342476 | + | 0.939527i | \(0.611265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.7487 | 0.911390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.3938 | −1.27965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.3781 | 0.703220 | 0.351610 | − | 0.936147i | \(-0.385634\pi\) | ||||
0.351610 | + | 0.936147i | \(0.385634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.6999 | 1.40223 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.4509 | 0.894709 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.6476 | 1.16758 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.93938 | 0.111819 | 0.0559097 | − | 0.998436i | \(-0.482194\pi\) | ||||
0.0559097 | + | 0.998436i | \(0.482194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0779443 | 0.00296086 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.83500 | 0.221334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 71.5538 | 2.71029 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.8267 | −0.447328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4261 | 1.75349 | 0.876744 | − | 0.480956i | \(-0.159710\pi\) | ||||
0.876744 | + | 0.480956i | \(0.159710\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.61473 | 0.287195 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.9604 | 1.50500 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.6687 | 1.26624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.55669 | 0.321353 | 0.160677 | − | 0.987007i | \(-0.448632\pi\) | ||||
0.160677 | + | 0.987007i | \(0.448632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.225286 | −0.00844888 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.4440 | −1.32739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.6962 | 0.587006 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 46.2871 | 1.72862 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.29599 | −0.0483324 | −0.0241662 | − | 0.999708i | \(-0.507693\pi\) | ||||
−0.0241662 | + | 0.999708i | \(0.507693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.4424 | 0.835798 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.6144 | −0.655085 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.247630 | 0.00919674 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.2174 | −0.453119 | −0.226559 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226559 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.3470 | 1.01285 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.6971 | 1.76414 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.2105 | −0.709556 | −0.354778 | − | 0.934951i | \(-0.615444\pi\) | ||||
−0.354778 | + | 0.934951i | \(0.615444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.9870 | −0.442145 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.7675 | −0.507132 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7110 | 1.09294 | 0.546469 | − | 0.837480i | \(-0.315972\pi\) | ||||
0.546469 | + | 0.837480i | \(0.315972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1258 | −0.445454 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.71120 | 0.282896 | 0.141448 | − | 0.989946i | \(-0.454824\pi\) | ||||
0.141448 | + | 0.989946i | \(0.454824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.6814 | −0.904257 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.357469 | 0.0130791 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9084 | 0.471662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.3681 | 1.21762 | 0.608809 | − | 0.793317i | \(-0.291647\pi\) | ||||
0.608809 | + | 0.793317i | \(0.291647\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.5281 | −0.930295 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.09589 | −0.149065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.7593 | −1.66315 | −0.831575 | − | 0.555412i | \(-0.812561\pi\) | ||||
−0.831575 | + | 0.555412i | \(0.812561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3573 | 0.412242 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.9488 | 1.30314 | 0.651572 | − | 0.758587i | \(-0.274110\pi\) | ||||
0.651572 | + | 0.758587i | \(0.274110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.94457 | −0.106601 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.671211 | −0.0242677 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.8363 | −0.535708 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.5476 | −0.740964 | −0.370482 | − | 0.928840i | \(-0.620807\pi\) | ||||
−0.370482 | + | 0.928840i | \(0.620807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1324 | −0.364908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1888 | −0.402434 | −0.201217 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201217 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.212698 | 0.00764036 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.7806 | −0.924874 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.40485 | −0.336964 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.14707 | 0.0410453 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.6945 | −1.16841 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.26852 | 0.188041 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3619 | 0.868409 | 0.434205 | − | 0.900814i | \(-0.357029\pi\) | ||||
0.434205 | + | 0.900814i | \(0.357029\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.8061 | 1.02552 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.97820 | 0.248116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.8380 | −2.19593 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.6645 | 0.591028 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.6680 | −0.732097 | −0.366048 | − | 0.930596i | \(-0.619290\pi\) | ||||
−0.366048 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −79.3375 | −2.80676 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.191391 | 0.00676246 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.04471 | 0.213313 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.9282 | −1.01958 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5762 | −0.583511 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4564 | −0.578577 | −0.289289 | − | 0.957242i | \(-0.593419\pi\) | ||||
−0.289289 | + | 0.957242i | \(0.593419\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7377 | 0.763312 | 0.381656 | − | 0.924304i | \(-0.375354\pi\) | ||||
0.381656 | + | 0.924304i | \(0.375354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.1867 | 1.58477 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.8105 | −1.49959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.26919 | −0.219331 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.549315 | −0.0191946 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.84811 | 0.0993997 | 0.0496998 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496998 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.30793 | −0.0804494 | −0.0402247 | − | 0.999191i | \(-0.512807\pi\) | ||||
−0.0402247 | + | 0.999191i | \(0.512807\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0681546 | −0.00237284 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.2836 | −1.40080 | −0.700398 | − | 0.713752i | \(-0.746994\pi\) | ||||
−0.700398 | + | 0.713752i | \(0.746994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6009 | −0.437647 | −0.218824 | − | 0.975764i | \(-0.570222\pi\) | ||||
−0.218824 | + | 0.975764i | \(0.570222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.6388 | −1.61788 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.7989 | 0.824583 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.0307 | 1.00465 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.0825 | −0.970674 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.5744 | −0.365068 | −0.182534 | − | 0.983200i | \(-0.558430\pi\) | ||||
−0.182534 | + | 0.983200i | \(0.558430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0809 | 0.347617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.4319 | 1.49588 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −81.6662 | −2.80940 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.96772 | 0.0676117 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.67802 | 0.229189 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.2636 | 1.72302 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.84636 | −0.165936 | −0.0829681 | − | 0.996552i | \(-0.526440\pi\) | ||||
−0.0829681 | + | 0.996552i | \(0.526440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0882223 | 0.00301714 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.1185 | −1.37042 | −0.685211 | − | 0.728344i | \(-0.740290\pi\) | ||||
−0.685211 | + | 0.728344i | \(0.740290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7826 | −1.22089 | −0.610443 | − | 0.792060i | \(-0.709008\pi\) | ||||
−0.610443 | + | 0.792060i | \(0.709008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.8412 | 1.08515 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.8507 | 1.28845 | 0.644226 | − | 0.764835i | \(-0.277180\pi\) | ||||
0.644226 | + | 0.764835i | \(0.277180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.7848 | −0.978714 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −70.3446 | −2.38903 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.68740 | −0.192932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 97.0270 | 3.28763 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.478075 | −0.0161804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.0861 | 0.746646 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.9970 | 0.675250 | 0.337625 | − | 0.941281i | \(-0.390377\pi\) | ||||
0.337625 | + | 0.941281i | \(0.390377\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7616 | −0.531626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.6003 | 0.997261 | 0.498631 | − | 0.866815i | \(-0.333836\pi\) | ||||
0.498631 | + | 0.866815i | \(0.333836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.3489 | 0.449225 | 0.224612 | − | 0.974448i | \(-0.427888\pi\) | ||||
0.224612 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.06716 | −0.271175 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.8492 | 0.867931 | 0.433966 | − | 0.900929i | \(-0.357114\pi\) | ||||
0.433966 | + | 0.900929i | \(0.357114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.25709 | 0.310473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.87960 | 0.297478 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.4279 | 0.348957 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.1542 | −0.539975 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −80.0407 | −2.67248 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.5680 | 1.11956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.0857 | −1.10224 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.2251 | 0.706327 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −50.0873 | −1.66496 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.2165 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287993\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.677772 | −0.0224803 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.0666 | −0.863624 | −0.431812 | − | 0.901964i | \(-0.642126\pi\) | ||||
−0.431812 | + | 0.901964i | \(0.642126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.02439 | 0.298664 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.6241 | −1.11158 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.01302 | 0.0994988 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.4079 | −0.772154 | −0.386077 | − | 0.922467i | \(-0.626170\pi\) | ||||
−0.386077 | + | 0.922467i | \(0.626170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.8202 | −0.422440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.08400 | −0.266088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.301631 | −0.00991755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.451779 | −0.0148384 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4027 | −0.833436 | −0.416718 | − | 0.909036i | \(-0.636820\pi\) | ||||
−0.416718 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.12807 | −0.102518 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.3964 | −1.58443 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.9449 | −0.554157 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2309 | 1.54297 | 0.771483 | − | 0.636249i | \(-0.219515\pi\) | ||||
0.771483 | + | 0.636249i | \(0.219515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.39035 | 0.208541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.11795 | −0.297237 | −0.148618 | − | 0.988895i | \(-0.547483\pi\) | ||||
−0.148618 | + | 0.988895i | \(0.547483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.0799 | −2.02160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.9200 | −0.745587 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.4205 | 1.67094 | 0.835471 | − | 0.549535i | \(-0.185195\pi\) | ||||
0.835471 | + | 0.549535i | \(0.185195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.6003 | −1.38287 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.25517 | −0.267692 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.6292 | 0.668247 | 0.334123 | − | 0.942529i | \(-0.391560\pi\) | ||||
0.334123 | + | 0.942529i | \(0.391560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.64544 | 0.117964 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.7561 | −0.347697 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.4243 | −1.04704 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.16716 | −0.0699083 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.259854 | −0.00837367 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.3172 | −0.621843 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.7119 | 1.01978 | 0.509892 | − | 0.860238i | \(-0.329685\pi\) | ||||
0.509892 | + | 0.860238i | \(0.329685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.0905 | 0.420526 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.6220 | −0.661791 | −0.330896 | − | 0.943667i | \(-0.607351\pi\) | ||||
−0.330896 | + | 0.943667i | \(0.607351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.15521 | −0.165269 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.480322 | 0.0153826 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.1819 | 1.25354 | 0.626771 | − | 0.779204i | \(-0.284376\pi\) | ||||
0.626771 | + | 0.779204i | \(0.284376\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.83170 | 0.154422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0592760 | 0.00189254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.917754 | 0.0292718 | 0.0146359 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146359 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.2225 | −1.02669 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.3050 | −1.12377 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.3819 | −1.31587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.64141 | −0.0839070 | −0.0419535 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419535 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.2567 | 0.515891 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.8862 | −0.630436 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.656840 | 0.0208023 | 0.0104012 | − | 0.999946i | \(-0.496689\pi\) | ||||
0.0104012 | + | 0.999946i | \(0.496689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.8242 | 1.25998 |
(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 | 3344.2.a.y.1.1 | 6 | ||
4.3 | odd | 2 | 1672.2.a.h.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.h.1.6 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.y.1.1 | 6 | 1.1 | even | 1 | trivial |