Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} - 249 x^{6} + 2736 x^{5} - 801 x^{4} - 900 x^{3} + 429 x^{2} - 36 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.66914\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 2.17000 | 1.25285 | 0.626425 | − | 0.779482i | \(-0.284517\pi\) | ||||
0.626425 | + | 0.779482i | \(0.284517\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.20913 | −1.43517 | −0.717583 | − | 0.696473i | \(-0.754752\pi\) | ||||
−0.717583 | + | 0.696473i | \(0.754752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70252 | 0.643494 | 0.321747 | − | 0.946826i | \(-0.395730\pi\) | ||||
0.321747 | + | 0.946826i | \(0.395730\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.70890 | 0.569634 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56324 | 0.471335 | 0.235668 | − | 0.971834i | \(-0.424272\pi\) | ||||
0.235668 | + | 0.971834i | \(0.424272\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.34519 | −0.373088 | −0.186544 | − | 0.982447i | \(-0.559729\pi\) | ||||
−0.186544 | + | 0.982447i | \(0.559729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.96381 | −1.79805 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.30535 | −1.90538 | −0.952689 | − | 0.303947i | \(-0.901695\pi\) | ||||
−0.952689 | + | 0.303947i | \(0.901695\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.69448 | 0.806201 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.270390 | −0.0563801 | −0.0281901 | − | 0.999603i | \(-0.508974\pi\) | ||||
−0.0281901 | + | 0.999603i | \(0.508974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.29850 | 1.05970 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.80168 | −0.539184 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.47669 | 0.645605 | 0.322803 | − | 0.946466i | \(-0.395375\pi\) | ||||
0.322803 | + | 0.946466i | \(0.395375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.97386 | −1.43215 | −0.716073 | − | 0.698025i | \(-0.754062\pi\) | ||||
−0.716073 | + | 0.698025i | \(0.754062\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.39224 | 0.590512 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.46362 | −0.923520 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.41140 | 1.21843 | 0.609214 | − | 0.793006i | \(-0.291485\pi\) | ||||
0.609214 | + | 0.793006i | \(0.291485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.91906 | −0.467424 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.68101 | −0.418704 | −0.209352 | − | 0.977840i | \(-0.567135\pi\) | ||||
−0.209352 | + | 0.977840i | \(0.567135\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08191 | 0.469987 | 0.234993 | − | 0.971997i | \(-0.424493\pi\) | ||||
0.234993 | + | 0.971997i | \(0.424493\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.48409 | −0.817519 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.60815 | −0.380438 | −0.190219 | − | 0.981742i | \(-0.560920\pi\) | ||||
−0.190219 | + | 0.981742i | \(0.560920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.10141 | −0.585916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.17000 | 0.303861 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.06637 | −0.421198 | −0.210599 | − | 0.977573i | \(-0.567541\pi\) | ||||
−0.210599 | + | 0.977573i | \(0.567541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.01664 | −0.676444 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.0226 | −2.38715 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.954765 | −0.122245 | −0.0611226 | − | 0.998130i | \(-0.519468\pi\) | ||||
−0.0611226 | + | 0.998130i | \(0.519468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.90945 | 0.366556 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.31688 | 0.535444 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.38979 | −0.536298 | −0.268149 | − | 0.963377i | \(-0.586412\pi\) | ||||
−0.268149 | + | 0.963377i | \(0.586412\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.586746 | −0.0706359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9061 | −1.29431 | −0.647155 | − | 0.762358i | \(-0.724041\pi\) | ||||
−0.647155 | + | 0.762358i | \(0.724041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.18272 | −0.138426 | −0.0692132 | − | 0.997602i | \(-0.522049\pi\) | ||||
−0.0692132 | + | 0.997602i | \(0.522049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.4978 | 1.32765 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.66146 | 0.303301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0741392 | −0.00834132 | −0.00417066 | − | 0.999991i | \(-0.501328\pi\) | ||||
−0.00417066 | + | 0.999991i | \(0.501328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2064 | −1.24515 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.26055 | −0.906713 | −0.453357 | − | 0.891329i | \(-0.649774\pi\) | ||||
−0.453357 | + | 0.891329i | \(0.649774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20913 | −0.348079 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.54442 | 0.808847 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.83589 | −0.618603 | −0.309301 | − | 0.950964i | \(-0.600095\pi\) | ||||
−0.309301 | + | 0.950964i | \(0.600095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.29022 | −0.240080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.3033 | −1.79427 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.6529 | 2.73453 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.57873 | −0.566434 | −0.283217 | − | 0.959056i | \(-0.591402\pi\) | ||||
−0.283217 | + | 0.959056i | \(0.591402\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.67143 | 0.268488 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.24181 | −0.621083 | −0.310542 | − | 0.950560i | \(-0.600510\pi\) | ||||
−0.310542 | + | 0.950560i | \(0.600510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9810 | 1.57466 | 0.787329 | − | 0.616534i | \(-0.211464\pi\) | ||||
0.787329 | + | 0.616534i | \(0.211464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8561 | −1.15703 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.5421 | −1.88920 | −0.944602 | − | 0.328218i | \(-0.893552\pi\) | ||||
−0.944602 | + | 0.328218i | \(0.893552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.92754 | 0.184625 | 0.0923123 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923123 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.0827 | 1.52651 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6973 | 1.10038 | 0.550192 | − | 0.835038i | \(-0.314554\pi\) | ||||
0.550192 | + | 0.835038i | \(0.314554\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.867715 | 0.0809149 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.29880 | −0.212524 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.70252 | 0.156070 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.55628 | −0.777843 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.81780 | −0.524573 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.957936 | −0.0856804 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9148 | 1.76716 | 0.883578 | − | 0.468285i | \(-0.155128\pi\) | ||||
0.883578 | + | 0.468285i | \(0.155128\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.68775 | 0.588823 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.79773 | 0.157069 | 0.0785344 | − | 0.996911i | \(-0.474976\pi\) | ||||
0.0785344 | + | 0.996911i | \(0.474976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.1401 | −1.22610 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.99096 | 0.773819 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.05801 | −0.517571 | −0.258785 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258785 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2402 | 0.868562 | 0.434281 | − | 0.900777i | \(-0.357002\pi\) | ||||
0.434281 | + | 0.900777i | \(0.357002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.65969 | −0.476632 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.10286 | −0.175850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1571 | −0.926550 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.90006 | −0.734065 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.1741 | −1.07927 | −0.539634 | − | 0.841900i | \(-0.681437\pi\) | ||||
−0.539634 | + | 0.841900i | \(0.681437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7238 | −1.36096 | −0.680481 | − | 0.732766i | \(-0.738229\pi\) | ||||
−0.680481 | + | 0.732766i | \(0.738229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.70890 | 0.138157 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.5891 | 2.05537 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2040 | 1.37303 | 0.686513 | − | 0.727118i | \(-0.259141\pi\) | ||||
0.686513 | + | 0.727118i | \(0.259141\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.65402 | −0.527698 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.460345 | −0.0362803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.297541 | −0.0233052 | −0.0116526 | − | 0.999932i | \(-0.503709\pi\) | ||||
−0.0116526 | + | 0.999932i | \(0.503709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.8861 | −0.847483 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.11071 | −0.627625 | −0.313813 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313813 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1905 | −0.860805 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.1930 | −1.08537 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.30029 | 0.326945 | 0.163472 | − | 0.986548i | \(-0.447731\pi\) | ||||
0.163472 | + | 0.986548i | \(0.447731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.02083 | 0.681911 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.17000 | −0.163107 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.34978 | −0.474605 | −0.237302 | − | 0.971436i | \(-0.576263\pi\) | ||||
−0.237302 | + | 0.971436i | \(0.576263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.66110 | 0.197798 | 0.0988988 | − | 0.995097i | \(-0.468468\pi\) | ||||
0.0988988 | + | 0.995097i | \(0.468468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.07184 | −0.153155 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.7841 | −1.74865 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.56324 | 0.114316 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.76993 | −0.346962 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6624 | −0.988579 | −0.494289 | − | 0.869297i | \(-0.664572\pi\) | ||||
−0.494289 | + | 0.869297i | \(0.664572\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.7543 | −1.42195 | −0.710973 | − | 0.703220i | \(-0.751745\pi\) | ||||
−0.710973 | + | 0.703220i | \(0.751745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.36764 | 0.670831 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.6912 | 1.33170 | 0.665848 | − | 0.746088i | \(-0.268070\pi\) | ||||
0.665848 | + | 0.746088i | \(0.268070\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1404 | 0.718834 | 0.359417 | − | 0.933177i | \(-0.382976\pi\) | ||||
0.359417 | + | 0.933177i | \(0.382976\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.52584 | −0.671901 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.91915 | 0.415443 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.60371 | 0.600909 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.462069 | −0.0321160 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.9833 | −0.898071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6987 | 1.08074 | 0.540372 | − | 0.841426i | \(-0.318284\pi\) | ||||
0.540372 | + | 0.841426i | \(0.318284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.6661 | −1.62158 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.89024 | −0.674509 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.5757 | −0.921578 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.56649 | −0.173428 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.34519 | −0.0904872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.20369 | 0.616325 | 0.308162 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308162 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.05462 | 0.603642 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.1557 | −1.27141 | −0.635706 | − | 0.771931i | \(-0.719291\pi\) | ||||
−0.635706 | + | 0.771931i | \(0.719291\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3955 | −0.753036 | −0.376518 | − | 0.926409i | \(-0.622879\pi\) | ||||
−0.376518 | + | 0.926409i | \(0.622879\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.77536 | 0.379991 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4525 | 1.27438 | 0.637188 | − | 0.770708i | \(-0.280097\pi\) | ||||
0.637188 | + | 0.770708i | \(0.280097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.36989 | 0.545991 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.160882 | −0.0104504 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.34105 | 0.539538 | 0.269769 | − | 0.962925i | \(-0.413053\pi\) | ||||
0.269769 | + | 0.962925i | \(0.413053\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8279 | −1.66372 | −0.831861 | − | 0.554984i | \(-0.812724\pi\) | ||||
−0.831861 | + | 0.554984i | \(0.812724\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9128 | −1.02080 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1620 | 0.840886 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1723 | 0.710874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.9254 | −1.13598 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5608 | −1.42403 | −0.712014 | − | 0.702166i | \(-0.752217\pi\) | ||||
−0.712014 | + | 0.702166i | \(0.752217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.422684 | −0.0265739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.96381 | −0.436091 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0467 | −0.813829 | −0.406915 | − | 0.913466i | \(-0.633395\pi\) | ||||
−0.406915 | + | 0.913466i | \(0.633395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6181 | 0.784050 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.94132 | 0.367759 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.6859 | −1.27555 | −0.637775 | − | 0.770223i | \(-0.720145\pi\) | ||||
−0.637775 | + | 0.770223i | \(0.720145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.84036 | 0.604489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6639 | −0.775017 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.82717 | −0.355289 | −0.177644 | − | 0.984095i | \(-0.556848\pi\) | ||||
−0.177644 | + | 0.984095i | \(0.556848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.98666 | −0.181427 | −0.0907134 | − | 0.995877i | \(-0.528915\pi\) | ||||
−0.0907134 | + | 0.995877i | \(0.528915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.96977 | −0.300784 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.28284 | 0.499474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62682 | 0.157830 | 0.0789151 | − | 0.996881i | \(-0.474854\pi\) | ||||
0.0789151 | + | 0.996881i | \(0.474854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.6265 | −0.815800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.19113 | −0.428987 | −0.214494 | − | 0.976725i | \(-0.568810\pi\) | ||||
−0.214494 | + | 0.976725i | \(0.568810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7265 | −0.815956 | −0.407978 | − | 0.912992i | \(-0.633766\pi\) | ||||
−0.407978 | + | 0.912992i | \(0.633766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 57.8369 | 3.42596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.56449 | −0.269433 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1058 | −0.709657 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.54175 | 0.148490 | 0.0742452 | − | 0.997240i | \(-0.476345\pi\) | ||||
0.0742452 | + | 0.997240i | \(0.476345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.20913 | 0.186843 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.37971 | −0.254136 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.363725 | 0.0210348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.24703 | 0.302434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5447 | −0.778125 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.06396 | 0.175442 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.42090 | 0.309387 | 0.154694 | − | 0.987962i | \(-0.450561\pi\) | ||||
0.154694 | + | 0.987962i | \(0.450561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 34.6788 | 1.97281 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5270 | −1.22068 | −0.610342 | − | 0.792138i | \(-0.708968\pi\) | ||||
−0.610342 | + | 0.792138i | \(0.708968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0437 | 1.41555 | 0.707776 | − | 0.706437i | \(-0.249699\pi\) | ||||
0.707776 | + | 0.706437i | \(0.249699\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.33679 | −0.526069 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7274 | 0.939504 | 0.469752 | − | 0.882798i | \(-0.344343\pi\) | ||||
0.469752 | + | 0.882798i | \(0.344343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.43491 | 0.304296 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.4063 | −2.36689 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.30535 | −0.462122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.12749 | −0.395362 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.18276 | 0.231307 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.44044 | −0.244809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.8107 | 1.14386 | 0.571931 | − | 0.820302i | \(-0.306194\pi\) | ||||
0.571931 | + | 0.820302i | \(0.306194\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.6654 | 0.694058 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0874 | 0.769677 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3757 | 1.76362 | 0.881809 | − | 0.471606i | \(-0.156326\pi\) | ||||
0.881809 | + | 0.471606i | \(0.156326\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.3830 | 1.37862 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4651 | −0.675021 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9004 | −1.02053 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.88294 | 0.101374 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.4754 | 1.68969 | 0.844844 | − | 0.535013i | \(-0.179693\pi\) | ||||
0.844844 | + | 0.535013i | \(0.179693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0830546 | 0.00444581 | 0.00222291 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222291 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.76879 | 0.201163 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.3492 | 1.08308 | 0.541539 | − | 0.840676i | \(-0.317842\pi\) | ||||
0.541539 | + | 0.840676i | \(0.317842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.9989 | 1.85755 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.69448 | 0.195533 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.57604 | −0.452626 | −0.226313 | − | 0.974055i | \(-0.572667\pi\) | ||||
−0.226313 | + | 0.974055i | \(0.572667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.9788 | 2.63046 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.5671 | −0.974521 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.79549 | 0.198665 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.7526 | −1.81407 | −0.907036 | − | 0.421054i | \(-0.861660\pi\) | ||||
−0.907036 | + | 0.421054i | \(0.861660\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.58159 | −0.238508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.22056 | −0.271038 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.82563 | 0.198084 | 0.0990419 | − | 0.995083i | \(-0.468422\pi\) | ||||
0.0990419 | + | 0.995083i | \(0.468422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.07872 | −0.107345 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.67680 | −0.240868 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.1141 | 1.59823 | 0.799113 | − | 0.601181i | \(-0.205303\pi\) | ||||
0.799113 | + | 0.601181i | \(0.205303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 43.2152 | 2.21398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.3739 | 1.04106 | 0.520530 | − | 0.853844i | \(-0.325735\pi\) | ||||
0.520530 | + | 0.853844i | \(0.325735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.54096 | −0.435287 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.26668 | 0.267721 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.3645 | −0.931118 | −0.465559 | − | 0.885017i | \(-0.654147\pi\) | ||||
−0.465559 | + | 0.885017i | \(0.654147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.270390 | −0.0136742 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.90109 | 0.196784 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.237922 | 0.0119712 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3639 | 1.57411 | 0.787055 | − | 0.616882i | \(-0.211605\pi\) | ||||
0.787055 | + | 0.616882i | \(0.211605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.6839 | −1.53612 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0286 | −0.600682 | −0.300341 | − | 0.953832i | \(-0.597100\pi\) | ||||
−0.300341 | + | 0.953832i | \(0.597100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.7263 | 0.534317 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.9626 | 1.78700 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5858 | 0.574288 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.27287 | −0.0629394 | −0.0314697 | − | 0.999505i | \(-0.510019\pi\) | ||||
−0.0314697 | + | 0.999505i | \(0.510019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.1459 | −0.648438 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.70252 | −0.0837758 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.5092 | 1.30128 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.2212 | 1.08818 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4485 | 1.09668 | 0.548340 | − | 0.836256i | \(-0.315260\pi\) | ||||
0.548340 | + | 0.836256i | \(0.315260\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.3270 | 1.57552 | 0.787761 | − | 0.615981i | \(-0.211240\pi\) | ||||
0.787761 | + | 0.615981i | \(0.211240\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.45707 | −0.216710 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.29850 | 0.257015 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.62551 | −0.0786640 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.56320 | −0.220313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.2314 | −0.926345 | −0.463173 | − | 0.886268i | \(-0.653289\pi\) | ||||
−0.463173 | + | 0.886268i | \(0.653289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4820 | −1.17653 | −0.588265 | − | 0.808668i | \(-0.700189\pi\) | ||||
−0.588265 | + | 0.808668i | \(0.700189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.2110 | −1.16083 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.24568 | 0.107425 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1768 | 0.581168 | 0.290584 | − | 0.956849i | \(-0.406150\pi\) | ||||
0.290584 | + | 0.956849i | \(0.406150\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00891 | −0.333758 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.8064 | −1.74872 | −0.874362 | − | 0.485274i | \(-0.838720\pi\) | ||||
−0.874362 | + | 0.485274i | \(0.838720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7281 | 0.887797 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.5879 | −1.35216 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3308 | −0.487539 | −0.243770 | − | 0.969833i | \(-0.578384\pi\) | ||||
−0.243770 | + | 0.969833i | \(0.578384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.19107 | −0.197350 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36.2906 | −1.70508 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.34960 | 0.344555 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9065 | −0.837630 | −0.418815 | − | 0.908072i | \(-0.637554\pi\) | ||||
−0.418815 | + | 0.908072i | \(0.637554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.80168 | −0.130771 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9047 | −0.787330 | −0.393665 | − | 0.919254i | \(-0.628793\pi\) | ||||
−0.393665 | + | 0.919254i | \(0.628793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.4949 | 1.97490 | 0.987452 | − | 0.157922i | \(-0.0504795\pi\) | ||||
0.987452 | + | 0.157922i | \(0.0504795\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 55.5284 | 2.57507 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.64917 | −0.400236 | −0.200118 | − | 0.979772i | \(-0.564133\pi\) | ||||
−0.200118 | + | 0.979772i | \(0.564133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.47372 | −0.345104 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.3326 | 1.72020 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.81777 | 0.221521 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −44.0059 | −2.01913 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.24012 | −0.239929 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3819 | 0.748510 | 0.374255 | − | 0.927326i | \(-0.377898\pi\) | ||||
0.374255 | + | 0.927326i | \(0.377898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.96974 | −0.454581 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.998949 | −0.0454538 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.9029 | 0.812927 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.7254 | 1.80013 | 0.900064 | − | 0.435757i | \(-0.143519\pi\) | ||||
0.900064 | + | 0.435757i | \(0.143519\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.645664 | −0.0291979 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7675 | 0.846967 | 0.423484 | − | 0.905904i | \(-0.360807\pi\) | ||||
0.423484 | + | 0.905904i | \(0.360807\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.47669 | 0.156582 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.57295 | −0.385325 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.5678 | −0.832880 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2522 | 1.13045 | 0.565223 | − | 0.824938i | \(-0.308790\pi\) | ||||
0.565223 | + | 0.824938i | \(0.308790\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.6002 | −0.786321 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8627 | −0.618107 | −0.309053 | − | 0.951045i | \(-0.600012\pi\) | ||||
−0.309053 | + | 0.951045i | \(0.600012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0308 | 0.891358 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.2833 | −1.07846 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.0478 | −0.622656 | −0.311328 | − | 0.950302i | \(-0.600774\pi\) | ||||
−0.311328 | + | 0.950302i | \(0.600774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.01360 | −0.0890765 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.2690 | 1.02735 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −51.2852 | −2.25989 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.07717 | −0.179314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.33162 | 0.409613 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.73417 | −0.251219 | −0.125609 | − | 0.992080i | \(-0.540089\pi\) | ||||
−0.125609 | + | 0.992080i | \(0.540089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.07052 | 0.352899 | 0.176450 | − | 0.984310i | \(-0.443539\pi\) | ||||
0.176450 | + | 0.984310i | \(0.443539\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.5752 | 0.854332 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.97386 | −0.347347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9269 | −0.996821 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.70890 | −0.0741600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.60647 | 0.156214 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 62.7130 | 2.71132 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7790 | −0.594609 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.41150 | −0.276163 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.49022 | 0.279037 | 0.139518 | − | 0.990219i | \(-0.455445\pi\) | ||||
0.139518 | + | 0.990219i | \(0.455445\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.77458 | 0.247811 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.18572 | −0.264967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.491942 | 0.0210339 | 0.0105170 | − | 0.999945i | \(-0.496652\pi\) | ||||
0.0105170 | + | 0.999945i | \(0.496652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63160 | −0.0696350 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.8751 | −1.23012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.126224 | −0.00536758 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −51.6116 | −2.19079 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.0867 | 0.808727 | 0.404364 | − | 0.914598i | \(-0.367493\pi\) | ||||
0.404364 | + | 0.914598i | \(0.367493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.14575 | −0.175347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.39224 | 0.143220 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.43278 | 0.0603843 | 0.0301922 | − | 0.999544i | \(-0.490388\pi\) | ||||
0.0301922 | + | 0.999544i | \(0.490388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.5380 | −1.57923 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.0791 | −0.801247 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.6751 | 1.11828 | 0.559139 | − | 0.829074i | \(-0.311132\pi\) | ||||
0.559139 | + | 0.829074i | \(0.311132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3926 | 0.644158 | 0.322079 | − | 0.946713i | \(-0.395618\pi\) | ||||
0.322079 | + | 0.946713i | \(0.395618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.6475 | −1.23854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.43266 | −0.0597461 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.5558 | −1.56347 | −0.781733 | − | 0.623613i | \(-0.785664\pi\) | ||||
−0.781733 | + | 0.623613i | \(0.785664\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −42.8668 | −1.78148 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0638 | −0.583464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79347 | −0.198525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.37713 | 0.305007 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3466 | −0.922342 | −0.461171 | − | 0.887311i | \(-0.652571\pi\) | ||||
−0.461171 | + | 0.887311i | \(0.652571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.2257 | 2.72878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.5600 | 1.66841 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.76185 | 0.236611 | 0.118305 | − | 0.992977i | \(-0.462254\pi\) | ||||
0.118305 | + | 0.992977i | \(0.462254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.46362 | −0.223987 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0047 | 0.900592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.7931 | −0.563572 | −0.281786 | − | 0.959477i | \(-0.590927\pi\) | ||||
−0.281786 | + | 0.959477i | \(0.590927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9342 | −0.568389 | −0.284194 | − | 0.958767i | \(-0.591726\pi\) | ||||
−0.284194 | + | 0.958767i | \(0.591726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.50172 | −0.305494 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.4582 | 1.11633 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.8102 | 1.12878 | 0.564391 | − | 0.825508i | \(-0.309111\pi\) | ||||
0.564391 | + | 0.825508i | \(0.309111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.8446 | 0.520488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.50845 | 0.141937 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.181586 | −0.00733417 | −0.00366709 | − | 0.999993i | \(-0.501167\pi\) | ||||
−0.00366709 | + | 0.999993i | \(0.501167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.6701 | 0.752850 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.99176 | 0.160702 | 0.0803510 | − | 0.996767i | \(-0.474396\pi\) | ||||
0.0803510 | + | 0.996767i | \(0.474396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.2337 | −0.531907 | −0.265953 | − | 0.963986i | \(-0.585687\pi\) | ||||
−0.265953 | + | 0.963986i | \(0.585687\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.757546 | 0.0303993 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.93574 | −0.398067 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4184 | −0.936735 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.1737 | −1.12515 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.41140 | 0.295512 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.4711 | 0.934368 | 0.467184 | − | 0.884160i | \(-0.345269\pi\) | ||||
0.467184 | + | 0.884160i | \(0.345269\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.0662 | 1.35401 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −63.9092 | −2.53616 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.51717 | 0.218598 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.6374 | −0.737283 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.22616 | −0.245918 | −0.122959 | − | 0.992412i | \(-0.539238\pi\) | ||||
−0.122959 | + | 0.992412i | \(0.539238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.44042 | −0.135677 | −0.0678385 | − | 0.997696i | \(-0.521610\pi\) | ||||
−0.0678385 | + | 0.997696i | \(0.521610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.4618 | −0.845059 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.6489 | 1.08699 | 0.543495 | − | 0.839413i | \(-0.317101\pi\) | ||||
0.543495 | + | 0.839413i | \(0.317101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.56324 | −0.0613626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.4592 | −1.15460 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0889 | 0.473076 | 0.236538 | − | 0.971622i | \(-0.423987\pi\) | ||||
0.236538 | + | 0.971622i | \(0.423987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.76916 | −0.225420 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.02114 | −0.0788524 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.48788 | −0.291687 | −0.145843 | − | 0.989308i | \(-0.546590\pi\) | ||||
−0.145843 | + | 0.989308i | \(0.546590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4560 | 1.02902 | 0.514509 | − | 0.857485i | \(-0.327974\pi\) | ||||
0.514509 | + | 0.857485i | \(0.327974\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.91906 | −0.113367 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.3773 | 1.75965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.940061 | −0.0363993 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.9720 | 0.772163 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.49253 | −0.0576184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.39833 | 0.323732 | 0.161866 | − | 0.986813i | \(-0.448249\pi\) | ||||
0.161866 | + | 0.986813i | \(0.448249\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.8447 | −0.571374 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.2587 | −0.701740 | −0.350870 | − | 0.936424i | \(-0.614114\pi\) | ||||
−0.350870 | + | 0.936424i | \(0.614114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.49792 | −0.364497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.5680 | −1.59289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.5791 | 0.978758 | 0.489379 | − | 0.872071i | \(-0.337224\pi\) | ||||
0.489379 | + | 0.872071i | \(0.337224\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.4409 | 0.742800 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.7282 | −0.943441 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.12484 | 0.157144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2637 | −0.656741 | −0.328370 | − | 0.944549i | \(-0.606499\pi\) | ||||
−0.328370 | + | 0.944549i | \(0.606499\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.54817 | 0.172771 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.8621 | −1.24653 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68101 | −0.101551 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.2119 | 1.59660 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.3280 | 0.692240 | 0.346120 | − | 0.938190i | \(-0.387499\pi\) | ||||
0.346120 | + | 0.938190i | \(0.387499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −61.5543 | −2.32156 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.1627 | 0.684045 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6268 | −0.399663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.74511 | −0.103095 | −0.0515474 | − | 0.998671i | \(-0.516415\pi\) | ||||
−0.0515474 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.126697 | −0.00475150 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.15605 | 0.0807447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.74833 | 0.252373 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.1001 | 0.675960 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.11780 | −0.228155 | −0.114078 | − | 0.993472i | \(-0.536391\pi\) | ||||
−0.114078 | + | 0.993472i | \(0.536391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.2081 | 1.01328 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −56.0466 | −2.08439 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.4213 | 0.684148 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.88321 | −0.329460 | −0.164730 | − | 0.986339i | \(-0.552675\pi\) | ||||
−0.164730 | + | 0.986339i | \(0.552675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.911609 | −0.0337633 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.08191 | 0.113989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1133 | 0.964517 | 0.482259 | − | 0.876029i | \(-0.339817\pi\) | ||||
0.482259 | + | 0.876029i | \(0.339817\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.5614 | 1.05350 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.86230 | −0.252776 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.6675 | 0.797050 | 0.398525 | − | 0.917157i | \(-0.369522\pi\) | ||||
0.398525 | + | 0.917157i | \(0.369522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.2438 | 0.890619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.1589 | −0.629499 | −0.314749 | − | 0.949175i | \(-0.601920\pi\) | ||||
−0.314749 | + | 0.949175i | \(0.601920\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.2775 | 1.54893 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1165 | −0.516495 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.2709 | −1.21569 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.5615 | −1.88151 | −0.940753 | − | 0.339091i | \(-0.889880\pi\) | ||||
−0.940753 | + | 0.339091i | \(0.889880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −48.9570 | −1.78409 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.6687 | 1.95321 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.725707 | −0.0263763 | −0.0131881 | − | 0.999913i | \(-0.504198\pi\) | ||||
−0.0131881 | + | 0.999913i | \(0.504198\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.917225 | −0.0332932 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.5554 | −0.672633 | −0.336317 | − | 0.941749i | \(-0.609181\pi\) | ||||
−0.336317 | + | 0.941749i | \(0.609181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.28168 | 0.118805 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.48409 | −0.198278 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.34519 | 0.0485720 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.1388 | 1.62775 | 0.813874 | − | 0.581041i | \(-0.197355\pi\) | ||||
0.813874 | + | 0.581041i | \(0.197355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.3113 | −1.01961 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.4320 | 0.914724 | 0.457362 | − | 0.889281i | \(-0.348794\pi\) | ||||
0.457362 | + | 0.889281i | \(0.348794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.2495 | −1.51765 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.3813 | 0.982298 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.2668 | 0.797789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0488 | −0.610054 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.74058 | −0.348100 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −55.2097 | −1.97052 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7429 | −1.06022 | −0.530110 | − | 0.847929i | \(-0.677849\pi\) | ||||
−0.530110 | + | 0.847929i | \(0.677849\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −44.8885 | −1.59807 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.9149 | 0.708091 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.28434 | 0.0456082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.3536 | 0.757334 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.5190 | 1.54152 | 0.770761 | − | 0.637124i | \(-0.219876\pi\) | ||||
0.770761 | + | 0.637124i | \(0.219876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.60815 | −0.0922697 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.97296 | −0.352377 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.84887 | −0.0652452 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.47731 | 0.0520682 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.6450 | −0.445124 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.43994 | −0.120942 | −0.0604709 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604709 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.4132 | −1.24353 | −0.621763 | − | 0.783205i | \(-0.713583\pi\) | ||||
−0.621763 | + | 0.783205i | \(0.713583\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.48106 | −0.227301 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.954847 | 0.0334468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.5963 | −0.895503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.91376 | −0.136758 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3915 | −0.362666 | −0.181333 | − | 0.983422i | \(-0.558041\pi\) | ||||
−0.181333 | + | 0.983422i | \(0.558041\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.6806 | 0.755740 | 0.377870 | − | 0.925859i | \(-0.376657\pi\) | ||||
0.377870 | + | 0.925859i | \(0.376657\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.9738 | 0.625766 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.7237 | 1.72906 | 0.864531 | − | 0.502579i | \(-0.167615\pi\) | ||||
0.864531 | + | 0.502579i | \(0.167615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.31747 | −0.149952 | −0.0749760 | − | 0.997185i | \(-0.523888\pi\) | ||||
−0.0749760 | + | 0.997185i | \(0.523888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.70020 | 0.197738 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.10141 | −0.142105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.0283 | 0.900746 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3402 | 0.772191 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4729 | −0.879422 | −0.439711 | − | 0.898139i | \(-0.644919\pi\) | ||||
−0.439711 | + | 0.898139i | \(0.644919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.9126 | −0.583194 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.6048 | −0.537457 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.9116 | 1.23540 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5673 | −0.500537 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.7865 | −1.02227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00397 | −0.0686951 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.39660 | 0.150537 | 0.0752683 | − | 0.997163i | \(-0.476019\pi\) | ||||
0.0752683 | + | 0.997163i | \(0.476019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45.5472 | 1.55768 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.0133 | −1.60595 | −0.802973 | − | 0.596016i | \(-0.796749\pi\) | ||||
−0.802973 | + | 0.596016i | \(0.796749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4665 | 0.391233 | 0.195616 | − | 0.980681i | \(-0.437329\pi\) | ||||
0.195616 | + | 0.980681i | \(0.437329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.90495 | −0.337560 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0470 | 1.39726 | 0.698629 | − | 0.715485i | \(-0.253794\pi\) | ||||
0.698629 | + | 0.715485i | \(0.253794\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8002 | −0.469220 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.17000 | 0.0736971 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.115898 | −0.00393155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.90510 | 0.200087 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.53350 | −0.322660 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.63091 | −0.0551348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.7545 | −1.10604 | −0.553021 | − | 0.833167i | \(-0.686525\pi\) | ||||
−0.553021 | + | 0.833167i | \(0.686525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.51559 | 0.186036 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.4053 | −0.620090 | −0.310045 | − | 0.950722i | \(-0.600344\pi\) | ||||
−0.310045 | + | 0.950722i | \(0.600344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.3984 | 1.32586 | 0.662931 | − | 0.748680i | \(-0.269312\pi\) | ||||
0.662931 | + | 0.748680i | \(0.269312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.96381 | 0.234086 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.03073 | −0.236069 | −0.118034 | − | 0.993009i | \(-0.537659\pi\) | ||||
−0.118034 | + | 0.993009i | \(0.537659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.9055 | 1.13715 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.5182 | −0.586883 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.6616 | 0.724878 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.3773 | 0.681137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.789284 | 0.0263534 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.7226 | −0.924601 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.06637 | −0.102155 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.3861 | 0.378904 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.53980 | −0.283872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3275 | −1.10662 | −0.553311 | − | 0.832975i | \(-0.686636\pi\) | ||||
−0.553311 | + | 0.832975i | \(0.686636\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.6666 | −0.353790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.5422 | −0.912515 | −0.456258 | − | 0.889848i | \(-0.650810\pi\) | ||||
−0.456258 | + | 0.889848i | \(0.650810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9132 | −0.427366 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.64880 | 0.219803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.06069 | 0.101073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0702 | −0.826988 | −0.413494 | − | 0.910507i | \(-0.635692\pi\) | ||||
−0.413494 | + | 0.910507i | \(0.635692\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7634 | 0.387616 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6707 | 0.482892 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.2693 | 1.29117 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.3100 | 0.896978 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.1222 | −0.627380 | −0.313690 | − | 0.949525i | \(-0.601565\pi\) | ||||
−0.313690 | + | 0.949525i | \(0.601565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.0636 | 1.11639 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.7136 | −1.52933 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.01664 | −0.164062 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7035 | 1.06838 | 0.534188 | − | 0.845366i | \(-0.320617\pi\) | ||||
0.534188 | + | 0.845366i | \(0.320617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.3448 | 1.77347 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.4221 | 0.665742 | 0.332871 | − | 0.942972i | \(-0.391983\pi\) | ||||
0.332871 | + | 0.942972i | \(0.391983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.724918 | 0.0236066 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.3073 | 0.497947 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5386 | −0.504935 | −0.252468 | − | 0.967605i | \(-0.581242\pi\) | ||||
−0.252468 | + | 0.967605i | \(0.581242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.59098 | 0.0516453 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.2984 | 1.17706 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.9031 | 0.839085 | 0.419543 | − | 0.907736i | \(-0.362191\pi\) | ||||
0.419543 | + | 0.907736i | \(0.362191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.8445 | 1.41877 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.7937 | 0.381238 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.3139 | −0.333053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.5824 | 1.05104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.3955 | −1.07616 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 63.3941 | 2.04073 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.7864 | −0.957865 | −0.478933 | − | 0.877852i | \(-0.658976\pi\) | ||||
−0.478933 | + | 0.877852i | \(0.658976\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.0226 | −0.578970 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.28341 | 0.105369 | 0.0526847 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526847 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.4342 | 0.558914 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4667 | −0.495329 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.89636 | −0.316613 | −0.158306 | − | 0.987390i | \(-0.550603\pi\) | ||||
−0.158306 | + | 0.987390i | \(0.550603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.12290 | −0.291569 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.29397 | 0.105168 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.9896 | 1.14789 | 0.573945 | − | 0.818894i | \(-0.305412\pi\) | ||||
0.573945 | + | 0.818894i | \(0.305412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.9826 | −1.91120 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.63575 | −0.306709 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.833317 | −0.0264979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.7949 | −1.93121 | −0.965607 | − | 0.260005i | \(-0.916276\pi\) | ||||
−0.965607 | + | 0.260005i | \(0.916276\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.1593 | 1.43309 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.5419 | −1.03165 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.4164 | 0.583252 | 0.291626 | − | 0.956532i | \(-0.405804\pi\) | ||||
0.291626 | + | 0.956532i | \(0.405804\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.7644 | −0.656957 |
(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 | 4012.2.a.h.1.13 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.13 | ✓ | 15 | 1.1 | even | 1 | trivial |