Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 17 x^{10} + 49 x^{9} + 106 x^{8} - 277 x^{7} - 317 x^{6} + 644 x^{5} + 537 x^{4} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.07960\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −3.07960 | −1.77801 | −0.889005 | − | 0.457897i | \(-0.848603\pi\) | ||||
−0.889005 | + | 0.457897i | \(0.848603\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30205 | 1.02951 | 0.514755 | − | 0.857337i | \(-0.327883\pi\) | ||||
0.514755 | + | 0.857337i | \(0.327883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.712294 | 0.269222 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.48396 | 2.16132 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.51110 | −0.455613 | −0.227807 | − | 0.973706i | \(-0.573155\pi\) | ||||
−0.227807 | + | 0.973706i | \(0.573155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.395847 | −0.109788 | −0.0548940 | − | 0.998492i | \(-0.517482\pi\) | ||||
−0.0548940 | + | 0.998492i | \(0.517482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.08941 | −1.83048 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.429554 | −0.104182 | −0.0520910 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520910 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.54879 | 0.814147 | 0.407074 | − | 0.913395i | \(-0.366549\pi\) | ||||
0.407074 | + | 0.913395i | \(0.366549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.19358 | −0.478679 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.70189 | −0.563383 | −0.281692 | − | 0.959505i | \(-0.590896\pi\) | ||||
−0.281692 | + | 0.959505i | \(0.590896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.299450 | 0.0598899 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.7292 | −2.06484 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.745139 | 0.138369 | 0.0691844 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691844 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64289 | −1.19310 | −0.596549 | − | 0.802577i | \(-0.703462\pi\) | ||||
−0.596549 | + | 0.802577i | \(0.703462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.65358 | 0.810085 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.63974 | 0.277166 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.72578 | 0.612514 | 0.306257 | − | 0.951949i | \(-0.400923\pi\) | ||||
0.306257 | + | 0.951949i | \(0.400923\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.21905 | 0.195204 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.89250 | −1.54495 | −0.772475 | − | 0.635046i | \(-0.780981\pi\) | ||||
−0.772475 | + | 0.635046i | \(0.780981\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82527 | −0.430850 | −0.215425 | − | 0.976520i | \(-0.569114\pi\) | ||||
−0.215425 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.9264 | 2.22510 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.59694 | 0.524668 | 0.262334 | − | 0.964977i | \(-0.415508\pi\) | ||||
0.262334 | + | 0.964977i | \(0.415508\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.49264 | −0.927520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.32286 | 0.185237 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.92224 | −0.264039 | −0.132020 | − | 0.991247i | \(-0.542146\pi\) | ||||
−0.132020 | + | 0.991247i | \(0.542146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.47863 | −0.469058 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.9289 | −1.44756 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.45878 | −0.189916 | −0.0949582 | − | 0.995481i | \(-0.530272\pi\) | ||||
−0.0949582 | + | 0.995481i | \(0.530272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00869 | 0.129149 | 0.0645745 | − | 0.997913i | \(-0.479431\pi\) | ||||
0.0645745 | + | 0.997913i | \(0.479431\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.61849 | 0.581875 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.911260 | −0.113028 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.83566 | −0.346431 | −0.173216 | − | 0.984884i | \(-0.555416\pi\) | ||||
−0.173216 | + | 0.984884i | \(0.555416\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.32076 | 1.00170 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.09545 | −0.604719 | −0.302359 | − | 0.953194i | \(-0.597774\pi\) | ||||
−0.302359 | + | 0.953194i | \(0.597774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.35012 | −0.392102 | −0.196051 | − | 0.980594i | \(-0.562812\pi\) | ||||
−0.196051 | + | 0.980594i | \(0.562812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.922186 | −0.106485 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.07635 | −0.122661 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.70619 | 0.191961 | 0.0959807 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959807 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.5899 | 1.50999 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3575 | 1.46618 | 0.733089 | − | 0.680133i | \(-0.238078\pi\) | ||||
0.733089 | + | 0.680133i | \(0.238078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.988855 | −0.107256 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.29473 | −0.246021 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.06080 | 0.536444 | 0.268222 | − | 0.963357i | \(-0.413564\pi\) | ||||
0.268222 | + | 0.963357i | \(0.413564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.281959 | −0.0295573 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.4575 | 2.12134 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.16950 | 0.838173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.13167 | 0.317973 | 0.158987 | − | 0.987281i | \(-0.449177\pi\) | ||||
0.158987 | + | 0.987281i | \(0.449177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.79791 | −0.984727 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.41494 | 0.737814 | 0.368907 | − | 0.929466i | \(-0.379732\pi\) | ||||
0.368907 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.63961 | −0.260089 | −0.130044 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130044 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.04975 | −0.492805 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.4179 | 1.49051 | 0.745253 | − | 0.666782i | \(-0.232329\pi\) | ||||
0.745253 | + | 0.666782i | \(0.232329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.43631 | 0.520704 | 0.260352 | − | 0.965514i | \(-0.416161\pi\) | ||||
0.260352 | + | 0.965514i | \(0.416161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4739 | −1.08906 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.87439 | 0.364472 | 0.182236 | − | 0.983255i | \(-0.441667\pi\) | ||||
0.182236 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.21990 | −0.580009 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.56665 | −0.237287 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.305968 | −0.0280481 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.71658 | −0.792417 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.4650 | 2.74694 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8209 | −0.967852 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.28775 | −0.203005 | −0.101502 | − | 0.994835i | \(-0.532365\pi\) | ||||
−0.101502 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.70073 | 0.766056 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.18083 | −0.452651 | −0.226326 | − | 0.974052i | \(-0.572671\pi\) | ||||
−0.226326 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52778 | 0.219186 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.6993 | −2.12577 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.7514 | −1.17486 | −0.587430 | − | 0.809275i | \(-0.699860\pi\) | ||||
−0.587430 | + | 0.809275i | \(0.699860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.67322 | 0.481197 | 0.240598 | − | 0.970625i | \(-0.422656\pi\) | ||||
0.240598 | + | 0.970625i | \(0.422656\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0772 | −0.932866 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.598163 | 0.0500209 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.71535 | 0.142452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.9948 | 1.64914 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.45066 | −0.692305 | −0.346152 | − | 0.938178i | \(-0.612512\pi\) | ||||
−0.346152 | + | 0.938178i | \(0.612512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.13407 | 0.173668 | 0.0868342 | − | 0.996223i | \(-0.472325\pi\) | ||||
0.0868342 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.78521 | −0.225171 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2923 | −1.22831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39456 | −0.590150 | −0.295075 | − | 0.955474i | \(-0.595345\pi\) | ||||
−0.295075 | + | 0.955474i | \(0.595345\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.91973 | 0.469465 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.92454 | −0.151675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00349 | −0.548556 | −0.274278 | − | 0.961650i | \(-0.588439\pi\) | ||||
−0.274278 | + | 0.961650i | \(0.588439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.7128 | 0.833990 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19958 | 0.170209 | 0.0851044 | − | 0.996372i | \(-0.472878\pi\) | ||||
0.0851044 | + | 0.996372i | \(0.472878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8433 | −0.987947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.0102 | 1.75963 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2390 | −1.15860 | −0.579301 | − | 0.815114i | \(-0.696674\pi\) | ||||
−0.579301 | + | 0.815114i | \(0.696674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.213296 | 0.0161237 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.49245 | 0.337673 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.09641 | 0.156693 | 0.0783463 | − | 0.996926i | \(-0.475036\pi\) | ||||
0.0783463 | + | 0.996926i | \(0.475036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5678 | −1.45446 | −0.727232 | − | 0.686392i | \(-0.759194\pi\) | ||||
−0.727232 | + | 0.686392i | \(0.759194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10636 | −0.229628 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.57694 | 0.630589 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.649098 | 0.0474667 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.64237 | −0.555900 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9897 | −1.51876 | −0.759381 | − | 0.650647i | \(-0.774498\pi\) | ||||
−0.759381 | + | 0.650647i | \(0.774498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2173 | 1.45527 | 0.727636 | − | 0.685964i | \(-0.240619\pi\) | ||||
0.727636 | + | 0.685964i | \(0.240619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.80632 | 0.200965 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.79759 | 0.270567 | 0.135283 | − | 0.990807i | \(-0.456806\pi\) | ||||
0.135283 | + | 0.990807i | \(0.456806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.05182 | −0.358114 | −0.179057 | − | 0.983839i | \(-0.557305\pi\) | ||||
−0.179057 | + | 0.983839i | \(0.557305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.73272 | 0.615958 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.530758 | 0.0372519 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.7731 | −1.59054 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.5190 | −1.21765 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.36256 | −0.370936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.68214 | −0.460017 | −0.230009 | − | 0.973189i | \(-0.573875\pi\) | ||||
−0.230009 | + | 0.973189i | \(0.573875\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.6920 | 1.07520 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.50393 | −0.443564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.73169 | −0.321208 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3170 | 0.697161 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.170037 | 0.0114379 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1719 | −1.21688 | −0.608439 | − | 0.793600i | \(-0.708204\pi\) | ||||
−0.608439 | + | 0.793600i | \(0.708204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94162 | 0.129441 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.1983 | −1.14149 | −0.570745 | − | 0.821128i | \(-0.693345\pi\) | ||||
−0.570745 | + | 0.821128i | \(0.693345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.43323 | 0.160792 | 0.0803962 | − | 0.996763i | \(-0.474381\pi\) | ||||
0.0803962 | + | 0.996763i | \(0.474381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.31472 | 0.218093 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.0890 | 1.25056 | 0.625282 | − | 0.780399i | \(-0.284984\pi\) | ||||
0.625282 | + | 0.780399i | \(0.284984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.28036 | 0.540151 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.25439 | −0.341309 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5281 | −1.19848 | −0.599242 | − | 0.800568i | \(-0.704531\pi\) | ||||
−0.599242 | + | 0.800568i | \(0.704531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7960 | −1.59725 | −0.798627 | − | 0.601827i | \(-0.794440\pi\) | ||||
−0.798627 | + | 0.601827i | \(0.794440\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.66382 | −0.619934 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.9464 | −0.954890 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40477 | −0.0893837 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −41.1359 | −2.60688 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.08282 | 0.256685 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.04528 | 0.190703 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.2181 | −1.01166 | −0.505828 | − | 0.862634i | \(-0.668813\pi\) | ||||
−0.505828 | + | 0.862634i | \(0.668813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.65385 | 0.164902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.83145 | 0.299059 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.8251 | −0.914157 | −0.457079 | − | 0.889426i | \(-0.651104\pi\) | ||||
−0.457079 | + | 0.889426i | \(0.651104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.42509 | −0.271831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.5853 | −0.953803 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.01160 | −0.183621 | −0.0918104 | − | 0.995777i | \(-0.529265\pi\) | ||||
−0.0918104 | + | 0.995777i | \(0.529265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4544 | 1.12103 | 0.560513 | − | 0.828146i | \(-0.310604\pi\) | ||||
0.560513 | + | 0.828146i | \(0.310604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.868322 | 0.0525533 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.452498 | −0.0272866 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.15965 | −0.0696768 | −0.0348384 | − | 0.999393i | \(-0.511092\pi\) | ||||
−0.0348384 | + | 0.999393i | \(0.511092\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −43.0722 | −2.57867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.81889 | −0.406781 | −0.203390 | − | 0.979098i | \(-0.565196\pi\) | ||||
−0.203390 | + | 0.979098i | \(0.565196\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.8219 | 1.71329 | 0.856643 | − | 0.515909i | \(-0.172546\pi\) | ||||
0.856643 | + | 0.515909i | \(0.172546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −25.1588 | −1.49028 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.04637 | −0.415934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8155 | −0.989146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.64431 | −0.565359 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4663 | 0.669871 | 0.334936 | − | 0.942241i | \(-0.391285\pi\) | ||||
0.334936 | + | 0.942241i | \(0.391285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.35818 | −0.195521 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.2129 | 0.940769 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06953 | 0.0618528 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.01243 | −0.115994 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.8351 | −1.31184 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.32205 | 0.132960 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.14567 | −0.407825 | −0.203913 | − | 0.978989i | \(-0.565366\pi\) | ||||
−0.203913 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.12896 | 0.462440 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0251 | −0.625176 | −0.312588 | − | 0.949889i | \(-0.601196\pi\) | ||||
−0.312588 | + | 0.949889i | \(0.601196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.22496 | 0.0692390 | 0.0346195 | − | 0.999401i | \(-0.488978\pi\) | ||||
0.0346195 | + | 0.999401i | \(0.488978\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.6320 | 0.599046 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.9136 | −1.62395 | −0.811975 | − | 0.583693i | \(-0.801607\pi\) | ||||
−0.811975 | + | 0.583693i | \(0.801607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.12598 | −0.0630426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.4811 | −2.65014 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.52439 | −0.0848195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.118536 | −0.00657520 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.7417 | −0.925817 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.56208 | 0.141252 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.3623 | −1.83376 | −0.916878 | − | 0.399168i | \(-0.869299\pi\) | ||||
−0.916878 | + | 0.399168i | \(0.869299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.1578 | 1.32384 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.52784 | −0.356654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.44165 | −0.296425 | −0.148213 | − | 0.988956i | \(-0.547352\pi\) | ||||
−0.148213 | + | 0.988956i | \(0.547352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9316 | −0.648034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0381 | 0.543591 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.61072 | −0.518930 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.1548 | 1.03126 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.92005 | 0.371488 | 0.185744 | − | 0.982598i | \(-0.440531\pi\) | ||||
0.185744 | + | 0.982598i | \(0.440531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.99538 | 0.320925 | 0.160463 | − | 0.987042i | \(-0.448701\pi\) | ||||
0.160463 | + | 0.987042i | \(0.448701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24713 | 0.226695 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.0233 | 1.75765 | 0.878826 | − | 0.477143i | \(-0.158328\pi\) | ||||
0.878826 | + | 0.477143i | \(0.158328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7300 | −0.622564 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.942261 | 0.0498698 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.0172 | 0.950910 | 0.475455 | − | 0.879740i | \(-0.342283\pi\) | ||||
0.475455 | + | 0.879740i | \(0.342283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.40612 | −0.337164 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.8436 | 1.40892 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.71215 | −0.403673 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.42605 | 0.439836 | 0.219918 | − | 0.975518i | \(-0.429421\pi\) | ||||
0.219918 | + | 0.975518i | \(0.429421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −64.1426 | −3.33913 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.36920 | −0.0710851 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.72600 | 0.141147 | 0.0705734 | − | 0.997507i | \(-0.477517\pi\) | ||||
0.0705734 | + | 0.997507i | \(0.477517\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.3241 | 1.72085 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.294961 | −0.0151912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1909 | −1.39670 | −0.698352 | − | 0.715755i | \(-0.746083\pi\) | ||||
−0.698352 | + | 0.715755i | \(0.746083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.04536 | 0.360945 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3615 | −0.529448 | −0.264724 | − | 0.964324i | \(-0.585281\pi\) | ||||
−0.264724 | + | 0.964324i | \(0.585281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.47781 | −0.126281 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.3190 | −0.931206 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5212 | 0.685552 | 0.342776 | − | 0.939417i | \(-0.388633\pi\) | ||||
0.342776 | + | 0.939417i | \(0.388633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.16061 | 0.0586944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.9549 | 0.804819 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.92774 | 0.197626 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.58842 | −0.431041 | −0.215520 | − | 0.976499i | \(-0.569145\pi\) | ||||
−0.215520 | + | 0.976499i | \(0.569145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.78456 | −0.389715 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.2526 | 1.61062 | 0.805309 | − | 0.592855i | \(-0.201999\pi\) | ||||
0.805309 | + | 0.592855i | \(0.201999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.62956 | 0.130988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.2847 | 1.55455 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.63002 | −0.279070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.7277 | 1.17326 | 0.586629 | − | 0.809856i | \(-0.300455\pi\) | ||||
0.586629 | + | 0.809856i | \(0.300455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 42.3489 | 2.08891 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.03908 | −0.0511296 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.7497 | 1.50944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4713 | −0.855573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.49186 | −0.0728821 | −0.0364411 | − | 0.999336i | \(-0.511602\pi\) | ||||
−0.0364411 | + | 0.999336i | \(0.511602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.44375 | −0.362786 | −0.181393 | − | 0.983411i | \(-0.558061\pi\) | ||||
−0.181393 | + | 0.983411i | \(0.558061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.3225 | 1.13398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.128630 | −0.00623945 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.718481 | 0.0347697 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.84211 | −0.0889377 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.22174 | 0.347859 | 0.173930 | − | 0.984758i | \(-0.444354\pi\) | ||||
0.173930 | + | 0.984758i | \(0.444354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6499 | −0.704029 | −0.352015 | − | 0.935994i | \(-0.614503\pi\) | ||||
−0.352015 | + | 0.935994i | \(0.614503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.28260 | −0.253281 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.58844 | −0.458677 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.764670 | −0.0364957 | −0.0182479 | − | 0.999833i | \(-0.505809\pi\) | ||||
−0.0182479 | + | 0.999833i | \(0.505809\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.0980 | −2.00467 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.68748 | −0.270220 | −0.135110 | − | 0.990831i | \(-0.543139\pi\) | ||||
−0.135110 | + | 0.990831i | \(0.543139\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6502 | 0.552274 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.0247 | 1.23093 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.94999 | −0.139218 | −0.0696092 | − | 0.997574i | \(-0.522175\pi\) | ||||
−0.0696092 | + | 0.997574i | \(0.522175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9485 | 0.703899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.57210 | −0.308784 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.649085 | −0.0304296 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.08053 | 0.0973230 | 0.0486615 | − | 0.998815i | \(-0.484504\pi\) | ||||
0.0486615 | + | 0.998815i | \(0.484504\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.60878 | 0.215119 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.1677 | −1.54478 | −0.772388 | − | 0.635151i | \(-0.780938\pi\) | ||||
−0.772388 | + | 0.635151i | \(0.780938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5804 | −0.584661 | −0.292331 | − | 0.956317i | \(-0.594431\pi\) | ||||
−0.292331 | + | 0.956317i | \(0.594431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 47.0942 | 2.18394 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.0939 | 1.39258 | 0.696290 | − | 0.717760i | \(-0.254833\pi\) | ||||
0.696290 | + | 0.717760i | \(0.254833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.01982 | −0.0932668 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7723 | 1.04929 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.26927 | 0.196301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.06268 | 0.0487592 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4637 | −0.570674 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3676 | 1.20476 | 0.602382 | − | 0.798208i | \(-0.294218\pi\) | ||||
0.602382 | + | 0.798208i | \(0.294218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.47484 | −0.0672468 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.92683 | 0.269680 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.20927 | 0.327356 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.81613 | 0.172925 | 0.0864627 | − | 0.996255i | \(-0.472444\pi\) | ||||
0.0864627 | + | 0.996255i | \(0.472444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.5680 | 0.975338 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.80027 | −0.0812448 | −0.0406224 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406224 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.320077 | −0.0144155 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.5553 | −1.01379 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.62946 | −0.162803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.7273 | 1.01741 | 0.508706 | − | 0.860940i | \(-0.330124\pi\) | ||||
0.508706 | + | 0.860940i | \(0.330124\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.77385 | −0.302633 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.7113 | −1.85982 | −0.929908 | − | 0.367793i | \(-0.880114\pi\) | ||||
−0.929908 | + | 0.367793i | \(0.880114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0696 | 0.759586 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.5523 | 1.75658 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.4466 | −1.39384 | −0.696922 | − | 0.717147i | \(-0.745448\pi\) | ||||
−0.696922 | + | 0.717147i | \(0.745448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.38627 | −0.105562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.0758 | −1.68109 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.07652 | −0.267764 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.43534 | −0.239046 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.9302 | 2.06001 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.25679 | 0.142683 | 0.0713413 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713413 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.7011 | 1.56110 | 0.780551 | − | 0.625092i | \(-0.214939\pi\) | ||||
0.780551 | + | 0.625092i | \(0.214939\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.656867 | −0.0286680 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.85348 | 0.124299 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6998 | −0.682599 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.45865 | −0.410470 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.91591 | 0.169617 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.4929 | 1.53449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.45610 | −0.278601 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.81101 | 0.422590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.59852 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.2611 | 2.58605 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5147 | 0.536070 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.3069 | 0.739989 | 0.369994 | − | 0.929034i | \(-0.379360\pi\) | ||||
0.369994 | + | 0.929034i | \(0.379360\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.54029 | 0.279133 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.64434 | 0.112653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.21531 | 0.0516802 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.4136 | −1.12119 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.123004 | −0.00521185 | −0.00260592 | − | 0.999997i | \(-0.500829\pi\) | ||||
−0.00260592 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.11838 | 0.0473022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.99896 | −0.0843963 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.7444 | −1.59074 | −0.795368 | − | 0.606127i | \(-0.792722\pi\) | ||||
−0.795368 | + | 0.606127i | \(0.792722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.91905 | 0.375227 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.68000 | 0.406522 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4827 | −0.774833 | −0.387417 | − | 0.921905i | \(-0.626632\pi\) | ||||
−0.387417 | + | 0.921905i | \(0.626632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.19473 | −0.342939 | −0.171469 | − | 0.985189i | \(-0.554851\pi\) | ||||
−0.171469 | + | 0.985189i | \(0.554851\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 64.6400 | 2.70037 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.809080 | −0.0337410 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4995 | −1.35297 | −0.676485 | − | 0.736456i | \(-0.736498\pi\) | ||||
−0.676485 | + | 0.736456i | \(0.736498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −62.2612 | −2.58749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.51448 | 0.394727 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.90469 | 0.120300 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.90858 | −0.244290 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.88559 | 0.284199 | 0.142099 | − | 0.989852i | \(-0.454615\pi\) | ||||
0.142099 | + | 0.989852i | \(0.454615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.5742 | −0.971358 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6951 | −0.481071 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.1333 | −0.703580 | −0.351790 | − | 0.936079i | \(-0.614427\pi\) | ||||
−0.351790 | + | 0.936079i | \(0.614427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.704355 | −0.0288758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.5576 | 0.636730 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.4007 | −1.28300 | −0.641499 | − | 0.767124i | \(-0.721687\pi\) | ||||
−0.641499 | + | 0.767124i | \(0.721687\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.27675 | −0.0520796 | −0.0260398 | − | 0.999661i | \(-0.508290\pi\) | ||||
−0.0260398 | + | 0.999661i | \(0.508290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.3863 | −0.748749 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.0660 | −0.815800 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1430 | −0.695814 | −0.347907 | − | 0.937529i | \(-0.613107\pi\) | ||||
−0.347907 | + | 0.937529i | \(0.613107\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.63452 | −0.0662342 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.42384 | −0.0576023 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0454 | 1.09235 | 0.546177 | − | 0.837670i | \(-0.316083\pi\) | ||||
0.546177 | + | 0.837670i | \(0.316083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 70.1321 | 2.82800 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.89811 | 0.358224 | 0.179112 | − | 0.983829i | \(-0.442677\pi\) | ||||
0.179112 | + | 0.983829i | \(0.442677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.0279 | −1.04615 | −0.523075 | − | 0.852287i | \(-0.675215\pi\) | ||||
−0.523075 | + | 0.852287i | \(0.675215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9892 | 1.16330 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.60478 | 0.144422 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4076 | −1.05630 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.5146 | 0.659529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60042 | −0.0638130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.985930 | 0.0392493 | 0.0196246 | − | 0.999807i | \(-0.493753\pi\) | ||||
0.0196246 | + | 0.999807i | \(0.493753\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.5783 | 0.817916 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.26652 | −0.208996 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.57009 | 0.101831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.0387 | −1.30699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.41271 | −0.0557986 | −0.0278993 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0278993 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.02820 | 0.237729 | 0.118865 | − | 0.992910i | \(-0.462075\pi\) | ||||
0.118865 | + | 0.992910i | \(0.462075\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.0295 | 0.788662 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0548 | 0.434608 | 0.217304 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217304 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.20435 | 0.0865284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.5717 | 0.571111 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.1595 | 1.84549 | 0.922747 | − | 0.385406i | \(-0.125938\pi\) | ||||
0.922747 | + | 0.385406i | \(0.125938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9265 | −0.466009 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.7221 | −0.847458 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4701 | −0.836355 | −0.418177 | − | 0.908365i | \(-0.637331\pi\) | ||||
−0.418177 | + | 0.908365i | \(0.637331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7348 | −1.66219 | −0.831095 | − | 0.556131i | \(-0.812285\pi\) | ||||
−0.831095 | + | 0.556131i | \(0.812285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.523648 | −0.0203368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.81908 | 0.225654 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.01328 | −0.0779547 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.9622 | 2.16362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.52422 | −0.0588420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1134 | −1.43062 | −0.715308 | − | 0.698809i | \(-0.753714\pi\) | ||||
−0.715308 | + | 0.698809i | \(0.753714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.21286 | −0.123663 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.1386 | 1.00459 | 0.502295 | − | 0.864696i | \(-0.332489\pi\) | ||||
0.502295 | + | 0.864696i | \(0.332489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.23067 | 0.0856052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.9639 | 2.02958 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.89201 | −0.0723958 | −0.0361979 | − | 0.999345i | \(-0.511525\pi\) | ||||
−0.0361979 | + | 0.999345i | \(0.511525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.6564 | −1.20953 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.49339 | −0.285891 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.760910 | 0.0289884 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.3376 | 1.38235 | 0.691174 | − | 0.722688i | \(-0.257094\pi\) | ||||
0.691174 | + | 0.722688i | \(0.257094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.97899 | −0.265110 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0601 | 0.495396 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.24936 | 0.160956 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −58.7867 | −2.22352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.89204 | −0.109231 | −0.0546154 | − | 0.998507i | \(-0.517393\pi\) | ||||
−0.0546154 | + | 0.998507i | \(0.517393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2220 | 0.498677 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.5002 | −0.960394 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.28161 | 0.198636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2959 | 0.950007 | 0.475004 | − | 0.879984i | \(-0.342447\pi\) | ||||
0.475004 | + | 0.879984i | \(0.342447\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.0629 | 0.414890 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.9484 | 0.672172 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.37700 | 0.0514970 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 57.0593 | 2.13092 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.6826 | 1.36803 | 0.684015 | − | 0.729468i | \(-0.260232\pi\) | ||||
0.684015 | + | 0.729468i | \(0.260232\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.88018 | −0.0700215 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.3620 | 2.83993 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.223131 | 0.00828689 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.3058 | 1.64321 | 0.821606 | − | 0.570055i | \(-0.193078\pi\) | ||||
0.821606 | + | 0.570055i | \(0.193078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.0090 | −0.407739 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.21361 | 0.0448869 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8282 | −0.547692 | −0.273846 | − | 0.961774i | \(-0.588296\pi\) | ||||
−0.273846 | + | 0.961774i | \(0.588296\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 46.0290 | 1.69781 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.28496 | 0.157839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.3323 | −0.711151 | −0.355575 | − | 0.934648i | \(-0.615715\pi\) | ||||
−0.355575 | + | 0.934648i | \(0.615715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.32615 | 0.158925 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.06424 | −0.295848 | −0.147924 | − | 0.988999i | \(-0.547259\pi\) | ||||
−0.147924 | + | 0.988999i | \(0.547259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.4539 | −0.712734 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 86.6097 | 3.16888 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.9821 | 0.401277 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.3128 | −0.960168 | −0.480084 | − | 0.877223i | \(-0.659394\pi\) | ||||
−0.480084 | + | 0.877223i | \(0.659394\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.07960 | 0.112227 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.91275 | 0.178793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.7653 | 1.51799 | 0.758994 | − | 0.651098i | \(-0.225691\pi\) | ||||
0.758994 | + | 0.651098i | \(0.225691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.5735 | −0.456389 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.78112 | 0.354565 | 0.177283 | − | 0.984160i | \(-0.443269\pi\) | ||||
0.177283 | + | 0.984160i | \(0.443269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.87225 | 0.140185 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.41170 | −0.231816 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.577451 | 0.0208506 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.79710 | −0.353293 | −0.176646 | − | 0.984274i | \(-0.556525\pi\) | ||||
−0.176646 | + | 0.984274i | \(0.556525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49.9453 | 1.79874 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 53.9711 | 1.94120 | 0.970602 | − | 0.240688i | \(-0.0773732\pi\) | ||||
0.970602 | + | 0.240688i | \(0.0773732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.98921 | −0.0714545 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.17281 | −0.293198 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.1064 | −1.25782 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.69972 | 0.275518 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.99476 | −0.285710 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0227 | −0.607565 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.8702 | 0.601357 | 0.300679 | − | 0.953726i | \(-0.402787\pi\) | ||||
0.300679 | + | 0.953726i | \(0.402787\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.6556 | 1.62538 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.75970 | 0.0981237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.399285 | −0.0141790 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.6275 | 0.483318 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.12950 | −0.217118 | −0.108559 | − | 0.994090i | \(-0.534624\pi\) | ||||
−0.108559 | + | 0.994090i | \(0.534624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.54508 | −0.0546610 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.8141 | 1.15943 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.06236 | 0.178647 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.43040 | −0.156151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.27455 | 0.326480 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.7869 | 1.68010 | 0.840049 | − | 0.542511i | \(-0.182526\pi\) | ||||
0.840049 | + | 0.542511i | \(0.182526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.03214 | 0.0713582 | 0.0356791 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356791 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56.8323 | −1.99319 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1224 | −0.564744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0263 | −0.350776 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.82821 | −0.0638829 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.0399 | 1.32760 | 0.663801 | − | 0.747909i | \(-0.268942\pi\) | ||||
0.663801 | + | 0.747909i | \(0.268942\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2757 | 0.497618 | 0.248809 | − | 0.968553i | \(-0.419961\pi\) | ||||
0.248809 | + | 0.968553i | \(0.419961\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.39351 | 0.0485159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.47913 | 0.190528 | 0.0952640 | − | 0.995452i | \(-0.469630\pi\) | ||||
0.0952640 | + | 0.995452i | \(0.469630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7400 | 0.477209 | 0.238604 | − | 0.971117i | \(-0.423310\pi\) | ||||
0.238604 | + | 0.971117i | \(0.423310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.57127 | 0.123886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.78894 | 0.0966309 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.06356 | 0.175232 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 71.2731 | 2.46356 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6438 | 1.05794 | 0.528970 | − | 0.848640i | \(-0.322578\pi\) | ||||
0.528970 | + | 0.848640i | \(0.322578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4448 | −0.980854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.9995 | 0.723261 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.5660 | −1.01710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.20877 | −0.213336 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −88.7602 | −3.04624 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0667 | −0.345080 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7685 | 0.985016 | 0.492508 | − | 0.870308i | \(-0.336080\pi\) | ||||
0.492508 | + | 0.870308i | \(0.336080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.9707 | 1.81156 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.2623 | 0.418873 | 0.209437 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209437 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.1377 | −0.414134 | −0.207067 | − | 0.978327i | \(-0.566392\pi\) | ||||
−0.207067 | + | 0.978327i | \(0.566392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.7000 | 0.739535 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.6941 | 0.534235 | 0.267117 | − | 0.963664i | \(-0.413929\pi\) | ||||
0.267117 | + | 0.963664i | \(0.413929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0811 | −1.19279 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 51.7850 | 1.75871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.57822 | −0.0874602 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.12249 | 0.0380340 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.3056 | 0.687242 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.70767 | −0.260567 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.7093 | −1.47596 | −0.737980 | − | 0.674823i | \(-0.764220\pi\) | ||||
−0.737980 | + | 0.674823i | \(0.764220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −35.3118 | −1.19104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.9024 | −0.636837 | −0.318418 | − | 0.947950i | \(-0.603152\pi\) | ||||
−0.318418 | + | 0.947950i | \(0.603152\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.2292 | −0.478851 | −0.239425 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239425 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.3419 | 0.347638 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.9527 | −1.30790 | −0.653951 | − | 0.756537i | \(-0.726890\pi\) | ||||
−0.653951 | + | 0.756537i | \(0.726890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.62955 | −0.0546533 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5357 | −0.687971 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7648 | 0.427157 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.82604 | 0.161317 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.29374 | −0.109975 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.94987 | −0.165087 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.825703 | 0.0275082 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.19747 | 0.206239 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45.0462 | −1.49738 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.96523 | −0.164868 | −0.0824338 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824338 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.0782 | 1.59465 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.28560 | 0.108857 | 0.0544283 | − | 0.998518i | \(-0.482666\pi\) | ||||
0.0544283 | + | 0.998518i | \(0.482666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.1845 | −0.668010 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.15100 | −0.236405 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.69027 | −0.121864 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.8588 | −1.41378 | −0.706890 | − | 0.707323i | \(-0.749903\pi\) | ||||
−0.706890 | + | 0.707323i | \(0.749903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.0059 | 0.725117 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.01702 | 0.0663909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.11568 | 0.0366834 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1151 | −0.562135 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.1420 | 1.34982 | 0.674912 | − | 0.737898i | \(-0.264182\pi\) | ||||
0.674912 | + | 0.737898i | \(0.264182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.0410 | −0.755138 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.9530 | 1.11157 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.49426 | 0.0488674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.30255 | −0.205895 | −0.102948 | − | 0.994687i | \(-0.532827\pi\) | ||||
−0.102948 | + | 0.994687i | \(0.532827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.77240 | −0.123108 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.6507 | 1.84676 | 0.923380 | − | 0.383887i | \(-0.125415\pi\) | ||||
0.923380 | + | 0.383887i | \(0.125415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7285 | 0.870399 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.5931 | −0.572305 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.0247 | −1.52810 | −0.764049 | − | 0.645158i | \(-0.776792\pi\) | ||||
−0.764049 | + | 0.645158i | \(0.776792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.32613 | 0.0430481 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 89.0424 | 2.88740 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7475 | −0.574897 | −0.287449 | − | 0.957796i | \(-0.592807\pi\) | ||||
−0.287449 | + | 0.957796i | \(0.592807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.3194 | −1.56358 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.46757 | 0.112090 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.79503 | −0.316298 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1280 | 0.423482 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 99.9692 | 3.22146 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.5412 | 1.49822 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.7545 | −1.37489 | −0.687446 | − | 0.726235i | \(-0.741268\pi\) | ||||
−0.687446 | + | 0.726235i | \(0.741268\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.69453 | 0.150810 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.3399 | −0.460188 | −0.230094 | − | 0.973168i | \(-0.573903\pi\) | ||||
−0.230094 | + | 0.973168i | \(0.573903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.04100 | 0.129549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.365044 | 0.0116908 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.4834 | 0.687315 | 0.343657 | − | 0.939095i | \(-0.388334\pi\) | ||||
0.343657 | + | 0.939095i | \(0.388334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.64737 | −0.244411 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.2488 | 1.12541 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.2599 | −1.18841 | −0.594203 | − | 0.804315i | \(-0.702532\pi\) | ||||
−0.594203 | + | 0.804315i | \(0.702532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.74225 | 0.278551 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.89020 | −0.251148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.63359 | 0.242734 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9370 | 0.569788 | 0.284894 | − | 0.958559i | \(-0.408042\pi\) | ||||
0.284894 | + | 0.958559i | \(0.408042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 102.743 | 3.26044 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.6296 | −0.368682 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.1260 | 1.42915 | 0.714577 | − | 0.699557i | \(-0.246619\pi\) | ||||
0.714577 | + | 0.699557i | \(0.246619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.9747 | −1.26474 |
(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 | 4016.2.a.i.1.1 | 12 | ||
4.3 | odd | 2 | 2008.2.a.b.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.b.1.12 | ✓ | 12 | 4.3 | odd | 2 | ||
4016.2.a.i.1.1 | 12 | 1.1 | even | 1 | trivial |