Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.284897.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 5x^{2} + 10x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.04177\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.26608 | 1.46064 | 0.730319 | − | 0.683107i | \(-0.239372\pi\) | ||||
0.730319 | + | 0.683107i | \(0.239372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.21058 | 1.59145 | 0.795726 | − | 0.605657i | \(-0.207090\pi\) | ||||
0.795726 | + | 0.605657i | \(0.207090\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64992 | −0.497469 | −0.248734 | − | 0.968572i | \(-0.580015\pi\) | ||||
−0.248734 | + | 0.968572i | \(0.580015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09727 | −1.41373 | −0.706864 | − | 0.707350i | \(-0.749891\pi\) | ||||
−0.706864 | + | 0.707350i | \(0.749891\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.26608 | −0.843299 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.91600 | −1.91991 | −0.959956 | − | 0.280150i | \(-0.909616\pi\) | ||||
−0.959956 | + | 0.280150i | \(0.909616\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.28918 | 0.525175 | 0.262587 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262587 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.21058 | −0.918825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.37812 | −0.495872 | −0.247936 | − | 0.968776i | \(-0.579752\pi\) | ||||
−0.247936 | + | 0.968776i | \(0.579752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.66730 | 1.13346 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.30523 | 0.613767 | 0.306883 | − | 0.951747i | \(-0.400714\pi\) | ||||
0.306883 | + | 0.951747i | \(0.400714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.02804 | −1.08267 | −0.541334 | − | 0.840808i | \(-0.682080\pi\) | ||||
−0.541334 | + | 0.840808i | \(0.682080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.64992 | 0.287214 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.7521 | 2.32453 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.25775 | −0.535571 | −0.267785 | − | 0.963479i | \(-0.586292\pi\) | ||||
−0.267785 | + | 0.963479i | \(0.586292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.09727 | 0.816216 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.76188 | −1.05603 | −0.528014 | − | 0.849236i | \(-0.677063\pi\) | ||||
−0.528014 | + | 0.849236i | \(0.677063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.995567 | −0.151822 | −0.0759112 | − | 0.997115i | \(-0.524187\pi\) | ||||
−0.0759112 | + | 0.997115i | \(0.524187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.26608 | 0.486879 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.03765 | 1.02655 | 0.513274 | − | 0.858225i | \(-0.328433\pi\) | ||||
0.513274 | + | 0.858225i | \(0.328433\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7290 | 1.53272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.91600 | 1.10846 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.78190 | −1.06893 | −0.534463 | − | 0.845192i | \(-0.679486\pi\) | ||||
−0.534463 | + | 0.845192i | \(0.679486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.38877 | −0.726622 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.28918 | −0.303210 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76900 | 0.360494 | 0.180247 | − | 0.983621i | \(-0.442310\pi\) | ||||
0.180247 | + | 0.983621i | \(0.442310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5958 | −1.74076 | −0.870379 | − | 0.492382i | \(-0.836126\pi\) | ||||
−0.870379 | + | 0.492382i | \(0.836126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.21058 | 0.530484 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.6481 | −2.06494 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5454 | −1.28833 | −0.644165 | − | 0.764887i | \(-0.722795\pi\) | ||||
−0.644165 | + | 0.764887i | \(0.722795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.37812 | 0.286292 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.104019 | 0.0123448 | 0.00617239 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617239 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12397 | −0.716756 | −0.358378 | − | 0.933577i | \(-0.616670\pi\) | ||||
−0.358378 | + | 0.933577i | \(0.616670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.66730 | −0.654404 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.94712 | −0.791698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.17407 | −0.357111 | −0.178555 | − | 0.983930i | \(-0.557142\pi\) | ||||
−0.178555 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1125 | 1.65882 | 0.829408 | − | 0.558643i | \(-0.188678\pi\) | ||||
0.829408 | + | 0.558643i | \(0.188678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.8543 | −2.80430 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.30523 | −0.354358 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.4567 | −1.21441 | −0.607205 | − | 0.794545i | \(-0.707709\pi\) | ||||
−0.607205 | + | 0.794545i | \(0.707709\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.4625 | −2.24988 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.02804 | 0.625078 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.47667 | 0.767090 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.758299 | −0.0769936 | −0.0384968 | − | 0.999259i | \(-0.512257\pi\) | ||||
−0.0384968 | + | 0.999259i | \(0.512257\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.64992 | −0.165823 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7478 | 1.56696 | 0.783480 | − | 0.621417i | \(-0.213443\pi\) | ||||
0.783480 | + | 0.621417i | \(0.213443\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.604753 | 0.0595880 | 0.0297940 | − | 0.999556i | \(-0.490515\pi\) | ||||
0.0297940 | + | 0.999556i | \(0.490515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.7521 | −1.34207 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7791 | −1.23540 | −0.617702 | − | 0.786412i | \(-0.711936\pi\) | ||||
−0.617702 | + | 0.786412i | \(0.711936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0076 | −1.05433 | −0.527166 | − | 0.849762i | \(-0.676745\pi\) | ||||
−0.527166 | + | 0.849762i | \(0.676745\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.25775 | 0.309212 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.2772 | −1.62531 | −0.812653 | − | 0.582748i | \(-0.801977\pi\) | ||||
−0.812653 | + | 0.582748i | \(0.801977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.76713 | −0.724289 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09727 | −0.471243 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −33.3310 | −3.05545 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.27777 | −0.752525 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.76188 | 0.609698 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.17947 | 0.194938 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.31722 | 0.471827 | 0.235914 | − | 0.971774i | \(-0.424192\pi\) | ||||
0.235914 | + | 0.971774i | \(0.424192\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.995567 | 0.0876548 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.15770 | 0.450631 | 0.225315 | − | 0.974286i | \(-0.427659\pi\) | ||||
0.225315 | + | 0.974286i | \(0.427659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.63880 | 0.835790 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.26608 | −0.281100 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.21320 | 0.787137 | 0.393568 | − | 0.919295i | \(-0.371240\pi\) | ||||
0.393568 | + | 0.919295i | \(0.371240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5130 | 1.06134 | 0.530671 | − | 0.847578i | \(-0.321940\pi\) | ||||
0.530671 | + | 0.847578i | \(0.321940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.03765 | −0.592677 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.41007 | 0.703286 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7952 | 0.896490 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7290 | −0.884915 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.57887 | −0.538962 | −0.269481 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0126 | −1.79136 | −0.895678 | − | 0.444702i | \(-0.853309\pi\) | ||||
−0.895678 | + | 0.444702i | \(0.853309\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.91600 | −0.639971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.6881 | −1.58138 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3950 | 0.989232 | 0.494616 | − | 0.869112i | \(-0.335309\pi\) | ||||
0.494616 | + | 0.869112i | \(0.335309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.78190 | 0.617145 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0133 | −0.789156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.575434 | −0.0450715 | −0.0225357 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225357 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.38877 | 0.419515 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9821 | 0.998626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.28918 | 0.175058 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.0978 | 1.29992 | 0.649960 | − | 0.759969i | \(-0.274786\pi\) | ||||
0.649960 | + | 0.759969i | \(0.274786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.8627 | 1.80385 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.76900 | −0.208131 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.74199 | −0.279689 | −0.139845 | − | 0.990173i | \(-0.544660\pi\) | ||||
−0.139845 | + | 0.990173i | \(0.544660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.68447 | 0.571182 | 0.285591 | − | 0.958352i | \(-0.407810\pi\) | ||||
0.285591 | + | 0.958352i | \(0.407810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.5958 | 1.00503 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.6401 | −0.782275 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.0608 | 0.955097 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.21058 | −0.306275 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8665 | 0.858628 | 0.429314 | − | 0.903155i | \(-0.358755\pi\) | ||||
0.429314 | + | 0.903155i | \(0.358755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.56592 | −0.544607 | −0.272303 | − | 0.962211i | \(-0.587785\pi\) | ||||
−0.272303 | + | 0.962211i | \(0.587785\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.6481 | 1.19220 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.2456 | 0.943710 | 0.471855 | − | 0.881676i | \(-0.343585\pi\) | ||||
0.471855 | + | 0.881676i | \(0.343585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.82206 | −0.200051 | −0.100025 | − | 0.994985i | \(-0.531892\pi\) | ||||
−0.100025 | + | 0.994985i | \(0.531892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5454 | 0.743818 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.9170 | 0.976780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0849 | −1.54247 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.37812 | −0.165291 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.77697 | −0.261258 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.97232 | −0.686523 | −0.343261 | − | 0.939240i | \(-0.611532\pi\) | ||||
−0.343261 | + | 0.939240i | \(0.611532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.104019 | −0.00712726 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.25160 | −0.221758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.3816 | −1.72301 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.12397 | 0.413819 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.3500 | 2.71423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.9399 | 1.53617 | 0.768085 | − | 0.640347i | \(-0.221210\pi\) | ||||
0.768085 | + | 0.640347i | \(0.221210\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.66730 | 0.377820 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.7876 | −1.71159 | −0.855793 | − | 0.517319i | \(-0.826930\pi\) | ||||
−0.855793 | + | 0.517319i | \(0.826930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1888 | 0.805460 | 0.402730 | − | 0.915319i | \(-0.368061\pi\) | ||||
0.402730 | + | 0.915319i | \(0.368061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.94712 | 0.457087 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.47149 | −0.554986 | −0.277493 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277493 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.9856 | 1.49941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.17407 | 0.206178 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.5250 | 1.13360 | 0.566798 | − | 0.823857i | \(-0.308182\pi\) | ||||
0.566798 | + | 0.823857i | \(0.308182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1764 | −1.62176 | −0.810878 | − | 0.585215i | \(-0.801010\pi\) | ||||
−0.810878 | + | 0.585215i | \(0.801010\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 35.0419 | 2.23874 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6686 | −0.742454 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.1125 | −0.957718 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.14668 | 0.135497 | 0.0677486 | − | 0.997702i | \(-0.478418\pi\) | ||||
0.0677486 | + | 0.997702i | \(0.478418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.92370 | 0.246681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.8543 | 1.61906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.7250 | −1.35517 | −0.677585 | − | 0.735444i | \(-0.736973\pi\) | ||||
−0.677585 | + | 0.735444i | \(0.736973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.7170 | −0.852335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.30523 | 0.204589 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.3272 | 1.13011 | 0.565053 | − | 0.825055i | \(-0.308856\pi\) | ||||
0.565053 | + | 0.825055i | \(0.308856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.4163 | −1.56131 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4567 | 0.701140 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.7577 | −1.14368 | −0.571838 | − | 0.820367i | \(-0.693769\pi\) | ||||
−0.571838 | + | 0.820367i | \(0.693769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6404 | −1.86127 | −0.930635 | − | 0.365950i | \(-0.880744\pi\) | ||||
−0.930635 | + | 0.365950i | \(0.880744\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.4625 | 1.29897 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.35058 | −0.563861 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6795 | 0.882005 | 0.441003 | − | 0.897506i | \(-0.354623\pi\) | ||||
0.441003 | + | 0.897506i | \(0.354623\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.02804 | −0.360889 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.5620 | 1.82318 | 0.911588 | − | 0.411106i | \(-0.134857\pi\) | ||||
0.911588 | + | 0.411106i | \(0.134857\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.0703 | 1.37139 | 0.685694 | − | 0.727890i | \(-0.259499\pi\) | ||||
0.685694 | + | 0.727890i | \(0.259499\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.47667 | −0.442880 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.4715 | −1.68062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.6631 | 2.68606 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.758299 | 0.0444523 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.9252 | 1.16404 | 0.582020 | − | 0.813174i | \(-0.302263\pi\) | ||||
0.582020 | + | 0.813174i | \(0.302263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.04380 | 0.526550 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.64992 | 0.0957379 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.1219 | 0.701028 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.19192 | −0.241618 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.7478 | −0.904685 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.4049 | −2.54262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.67492 | 0.209739 | 0.104869 | − | 0.994486i | \(-0.466558\pi\) | ||||
0.104869 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.604753 | −0.0344032 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.1759 | −1.88123 | −0.940615 | − | 0.339475i | \(-0.889751\pi\) | ||||
−0.940615 | + | 0.339475i | \(0.889751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2804 | 0.581082 | 0.290541 | − | 0.956863i | \(-0.406165\pi\) | ||||
0.290541 | + | 0.956863i | \(0.406165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.7521 | 0.774844 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4030 | 0.921281 | 0.460641 | − | 0.887587i | \(-0.347620\pi\) | ||||
0.460641 | + | 0.887587i | \(0.347620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.45336 | −0.305330 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7791 | 0.713261 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.1212 | −1.00829 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.8878 | −1.60240 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.0076 | 0.608719 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.6326 | 1.63370 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.20238 | −0.176018 | −0.0880092 | − | 0.996120i | \(-0.528051\pi\) | ||||
−0.0880092 | + | 0.996120i | \(0.528051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.25775 | −0.178524 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.4423 | −1.88178 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0805 | 0.875960 | 0.437980 | − | 0.898985i | \(-0.355694\pi\) | ||||
0.437980 | + | 0.898985i | \(0.355694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.2772 | 0.938371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.94577 | 0.538593 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7014 | 0.847793 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.76713 | 0.418168 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.541237 | −0.0290551 | −0.0145276 | − | 0.999894i | \(-0.504624\pi\) | ||||
−0.0145276 | + | 0.999894i | \(0.504624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6118 | 0.889212 | 0.444606 | − | 0.895726i | \(-0.353344\pi\) | ||||
0.444606 | + | 0.895726i | \(0.353344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.09727 | 0.272072 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8202 | 1.58717 | 0.793584 | − | 0.608461i | \(-0.208213\pi\) | ||||
0.793584 | + | 0.608461i | \(0.208213\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.339734 | 0.0180312 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.3310 | 1.76406 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.74911 | −0.356205 | −0.178102 | − | 0.984012i | \(-0.556996\pi\) | ||||
−0.178102 | + | 0.984012i | \(0.556996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7596 | −0.724191 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.27777 | 0.434470 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0014 | −1.04692 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1555 | 0.999910 | 0.499955 | − | 0.866051i | \(-0.333350\pi\) | ||||
0.499955 | + | 0.866051i | \(0.333350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.76188 | −0.352009 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.7664 | −1.70114 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.7032 | 0.916637 | 0.458319 | − | 0.888788i | \(-0.348452\pi\) | ||||
0.458319 | + | 0.888788i | \(0.348452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.17947 | −0.112547 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.8477 | −0.867699 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4738 | −0.589370 | −0.294685 | − | 0.955594i | \(-0.595215\pi\) | ||||
−0.294685 | + | 0.955594i | \(0.595215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.31722 | −0.272409 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.9550 | 1.58173 | 0.790864 | − | 0.611991i | \(-0.209631\pi\) | ||||
0.790864 | + | 0.611991i | \(0.209631\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.6899 | −1.15638 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.995567 | −0.0506075 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.92327 | −0.249620 | −0.124810 | − | 0.992181i | \(-0.539832\pi\) | ||||
−0.124810 | + | 0.992181i | \(0.539832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.8252 | 0.952031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.15770 | −0.260172 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3668 | −0.521609 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7967 | −1.14413 | −0.572066 | − | 0.820208i | \(-0.693858\pi\) | ||||
−0.572066 | + | 0.820208i | \(0.693858\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.63880 | −0.482544 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.15323 | 0.407153 | 0.203576 | − | 0.979059i | \(-0.434743\pi\) | ||||
0.203576 | + | 0.979059i | \(0.434743\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.7265 | 1.53060 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.26608 | 0.162293 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.37502 | 0.266430 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.8407 | −1.42608 | −0.713041 | − | 0.701122i | \(-0.752683\pi\) | ||||
−0.713041 | + | 0.701122i | \(0.752683\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.21320 | −0.454454 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6591 | 0.573708 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.3588 | 2.42293 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.5130 | −0.612766 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.28566 | −0.307075 | −0.153537 | − | 0.988143i | \(-0.549067\pi\) | ||||
−0.153537 | + | 0.988143i | \(0.549067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.48032 | −0.364569 | −0.182284 | − | 0.983246i | \(-0.558349\pi\) | ||||
−0.182284 | + | 0.983246i | \(0.558349\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.03765 | 0.342182 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.8624 | −2.17615 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −57.2461 | −2.77033 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.41007 | −0.406042 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.40836 | −0.0678384 | −0.0339192 | − | 0.999425i | \(-0.510799\pi\) | ||||
−0.0339192 | + | 0.999425i | \(0.510799\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.2424 | −1.64558 | −0.822791 | − | 0.568344i | \(-0.807584\pi\) | ||||
−0.822791 | + | 0.568344i | \(0.807584\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.7952 | −0.517589 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.44395 | −0.260420 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5156 | 1.64734 | 0.823669 | − | 0.567071i | \(-0.191924\pi\) | ||||
0.823669 | + | 0.567071i | \(0.191924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7290 | 0.510906 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.46501 | 0.259650 | 0.129825 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129825 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.4186 | −1.77381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.57887 | 0.311170 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.4100 | −1.38794 | −0.693971 | − | 0.720003i | \(-0.744141\pi\) | ||||
−0.693971 | + | 0.720003i | \(0.744141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1565 | 0.525341 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.0126 | 1.03424 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −70.0982 | −3.28626 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.1605 | −1.08340 | −0.541700 | − | 0.840572i | \(-0.682219\pi\) | ||||
−0.541700 | + | 0.840572i | \(0.682219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.91600 | 0.369487 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.6357 | −1.47342 | −0.736711 | − | 0.676208i | \(-0.763622\pi\) | ||||
−0.736711 | + | 0.676208i | \(0.763622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0045 | −0.883216 | −0.441608 | − | 0.897208i | \(-0.645592\pi\) | ||||
−0.441608 | + | 0.897208i | \(0.645592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.6881 | 0.913012 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.6469 | 1.64954 | 0.824772 | − | 0.565466i | \(-0.191304\pi\) | ||||
0.824772 | + | 0.565466i | \(0.191304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.4024 | −2.05031 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3950 | −0.571133 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.64260 | 0.0755270 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9735 | 0.595265 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.78190 | −0.356309 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.3089 | −1.29347 | −0.646733 | − | 0.762717i | \(-0.723865\pi\) | ||||
−0.646733 | + | 0.762717i | \(0.723865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.6056 | 0.757151 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0133 | 0.455620 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.47667 | −0.112460 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7102 | −0.575955 | −0.287978 | − | 0.957637i | \(-0.592983\pi\) | ||||
−0.287978 | + | 0.957637i | \(0.592983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.575434 | 0.0260220 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2050 | −1.54365 | −0.771826 | − | 0.635834i | \(-0.780656\pi\) | ||||
−0.771826 | + | 0.635834i | \(0.780656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.1642 | −1.17838 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.38877 | −0.242207 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.437980 | 0.0196461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.9349 | −1.83250 | −0.916248 | − | 0.400612i | \(-0.868798\pi\) | ||||
−0.916248 | + | 0.400612i | \(0.868798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.1601 | 0.542192 | 0.271096 | − | 0.962552i | \(-0.412614\pi\) | ||||
0.271096 | + | 0.962552i | \(0.412614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.4335 | 2.28876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9821 | −0.576557 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.63676 | 0.382818 | 0.191409 | − | 0.981510i | \(-0.438694\pi\) | ||||
0.191409 | + | 0.981510i | \(0.438694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.7855 | −1.14068 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.28918 | −0.101070 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.97517 | 0.0870365 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6115 | −0.510675 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0978 | −0.750509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.450632 | 0.0197426 | 0.00987128 | − | 0.999951i | \(-0.496858\pi\) | ||||
0.00987128 | + | 0.999951i | \(0.496858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6091 | 0.944901 | 0.472451 | − | 0.881357i | \(-0.343370\pi\) | ||||
0.472451 | + | 0.881357i | \(0.343370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.8627 | −1.04145 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.7179 | 2.07863 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3446 | −0.754111 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.76900 | 0.120165 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.4671 | 1.49294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.7377 | −1.80448 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.74199 | 0.161479 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.7020 | −0.762479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0014 | 1.80578 | 0.902890 | − | 0.429872i | \(-0.141441\pi\) | ||||
0.902890 | + | 0.429872i | \(0.141441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.68447 | −0.329772 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.9516 | −1.54000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.4897 | 0.491266 | 0.245633 | − | 0.969363i | \(-0.421004\pi\) | ||||
0.245633 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.5958 | −0.580253 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.56629 | 0.322335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3647 | −0.568324 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.6401 | 0.451647 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.64653 | 0.0697659 | 0.0348829 | − | 0.999391i | \(-0.488894\pi\) | ||||
0.0348829 | + | 0.999391i | \(0.488894\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.07467 | 0.214636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.0608 | −0.551425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.99544 | 0.421258 | 0.210629 | − | 0.977566i | \(-0.432449\pi\) | ||||
0.210629 | + | 0.977566i | \(0.432449\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.4289 | −2.37398 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.21058 | 0.176828 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.9807 | 1.55031 | 0.775156 | − | 0.631770i | \(-0.217671\pi\) | ||||
0.775156 | + | 0.631770i | \(0.217671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5674 | 1.19551 | 0.597755 | − | 0.801679i | \(-0.296060\pi\) | ||||
0.597755 | + | 0.801679i | \(0.296060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.8665 | −0.495729 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.4775 | −0.562051 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.46548 | 0.310792 | 0.155396 | − | 0.987852i | \(-0.450335\pi\) | ||||
0.155396 | + | 0.987852i | \(0.450335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.56592 | 0.314429 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.6326 | 2.63993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8395 | 0.531758 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.6481 | −0.688314 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.1153 | 1.11917 | 0.559585 | − | 0.828773i | \(-0.310961\pi\) | ||||
0.559585 | + | 0.828773i | \(0.310961\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7993 | −0.568590 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2456 | −0.544851 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.8939 | −1.35079 | −0.675395 | − | 0.737456i | \(-0.736027\pi\) | ||||
−0.675395 | + | 0.737456i | \(0.736027\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −108.862 | −4.46290 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.82206 | 0.115499 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4006 | 0.833545 | 0.416772 | − | 0.909011i | \(-0.363161\pi\) | ||||
0.416772 | + | 0.909011i | \(0.363161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.4674 | −1.40596 | −0.702978 | − | 0.711212i | \(-0.748147\pi\) | ||||
−0.702978 | + | 0.711212i | \(0.748147\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5454 | −0.429443 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.0359 | −1.09917 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.27037 | −0.295095 | −0.147548 | − | 0.989055i | \(-0.547138\pi\) | ||||
−0.147548 | + | 0.989055i | \(0.547138\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.9170 | −0.563944 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.8728 | −1.45126 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7901 | −0.476199 | −0.238100 | − | 0.971241i | \(-0.576525\pi\) | ||||
−0.238100 | + | 0.971241i | \(0.576525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.0849 | 0.890548 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.2396 | −1.13688 | −0.568442 | − | 0.822723i | \(-0.692454\pi\) | ||||
−0.568442 | + | 0.822723i | \(0.692454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3137 | −0.454735 | −0.227368 | − | 0.973809i | \(-0.573012\pi\) | ||||
−0.227368 | + | 0.973809i | \(0.573012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.37812 | 0.0954306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.2395 | −1.93267 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.2182 | −0.848728 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.77697 | 0.150838 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.7884 | 1.02825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4312 | −0.733733 | −0.366866 | − | 0.930274i | \(-0.619569\pi\) | ||||
−0.366866 | + | 0.930274i | \(0.619569\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.97232 | 0.396364 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.3665 | 0.689168 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −54.6887 | −2.16684 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.104019 | 0.00411492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.3952 | 1.51652 | 0.758260 | − | 0.651952i | \(-0.226050\pi\) | ||||
0.758260 | + | 0.651952i | \(0.226050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.5338 | −0.454849 | −0.227425 | − | 0.973796i | \(-0.573031\pi\) | ||||
−0.227425 | + | 0.973796i | \(0.573031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.25160 | 0.128032 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −49.8032 | −1.95797 | −0.978983 | − | 0.203942i | \(-0.934625\pi\) | ||||
−0.978983 | + | 0.203942i | \(0.934625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.56863 | −0.179334 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.3816 | 0.994782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.6308 | 0.650814 | 0.325407 | − | 0.945574i | \(-0.394499\pi\) | ||||
0.325407 | + | 0.945574i | \(0.394499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8455 | 0.658208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.12397 | −0.238919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.03596 | −0.196173 | −0.0980866 | − | 0.995178i | \(-0.531272\pi\) | ||||
−0.0980866 | + | 0.995178i | \(0.531272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.59712 | 0.256598 | 0.128299 | − | 0.991736i | \(-0.459048\pi\) | ||||
0.128299 | + | 0.991736i | \(0.459048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.3500 | −1.56706 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.4811 | 1.22079 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.86024 | −0.304350 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.9399 | −0.886909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4319 | 0.865973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7616 | 0.453377 | 0.226688 | − | 0.973967i | \(-0.427210\pi\) | ||||
0.226688 | + | 0.973967i | \(0.427210\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.66730 | −0.218135 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.322074 | −0.0123783 | −0.00618915 | − | 0.999981i | \(-0.501970\pi\) | ||||
−0.00618915 | + | 0.999981i | \(0.501970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.19288 | −0.122532 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.7876 | 0.988185 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.3210 | 0.433185 | 0.216593 | − | 0.976262i | \(-0.430506\pi\) | ||||
0.216593 | + | 0.976262i | \(0.430506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.0911 | 1.14972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.1888 | −0.465032 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.6664 | 1.51117 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.2991 | −1.11459 | −0.557295 | − | 0.830314i | \(-0.688161\pi\) | ||||
−0.557295 | + | 0.830314i | \(0.688161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.94712 | −0.263899 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.8686 | 1.55024 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.5271 | 2.02748 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.47149 | 0.320421 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6166 | 0.740910 | 0.370455 | − | 0.928850i | \(-0.379202\pi\) | ||||
0.370455 | + | 0.928850i | \(0.379202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.45759 | −0.281268 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.9856 | −0.865686 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 66.3073 | 2.49374 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.2453 | 0.797884 | 0.398942 | − | 0.916976i | \(-0.369378\pi\) | ||||
0.398942 | + | 0.916976i | \(0.369378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.17407 | −0.119037 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.3354 | 0.536864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.4680 | 1.02724 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.5250 | −0.654481 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.176660 | −0.00658832 | −0.00329416 | − | 0.999995i | \(-0.501049\pi\) | ||||
−0.00329416 | + | 0.999995i | \(0.501049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54636 | 0.0948315 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.1764 | 0.936321 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.7318 | 0.695680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.4701 | −1.20425 | −0.602125 | − | 0.798402i | \(-0.705679\pi\) | ||||
−0.602125 | + | 0.798402i | \(0.705679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.88091 | 0.291486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.7271 | −0.839445 | −0.419723 | − | 0.907652i | \(-0.637873\pi\) | ||||
−0.419723 | + | 0.907652i | \(0.637873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.0419 | −1.29254 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.3991 | 0.640904 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.53177 | −0.240275 | −0.120137 | − | 0.992757i | \(-0.538334\pi\) | ||||
−0.120137 | + | 0.992757i | \(0.538334\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6686 | 0.428656 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2769 | 0.487084 | 0.243542 | − | 0.969890i | \(-0.421691\pi\) | ||||
0.243542 | + | 0.969890i | \(0.421691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.4871 | −0.787228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.1125 | 0.552939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −53.8076 | −1.96609 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5336 | 1.73453 | 0.867263 | − | 0.497851i | \(-0.165877\pi\) | ||||
0.867263 | + | 0.497851i | \(0.165877\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.14668 | −0.0782294 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −71.8949 | −2.61652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.99499 | −0.0725093 | −0.0362546 | − | 0.999343i | \(-0.511543\pi\) | ||||
−0.0362546 | + | 0.999343i | \(0.511543\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.92370 | −0.142421 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.3966 | −0.848126 | −0.424063 | − | 0.905633i | \(-0.639397\pi\) | ||||
−0.424063 | + | 0.905633i | \(0.639397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.3482 | −1.67792 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.8543 | −0.934765 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.1144 | −0.509640 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.40764 | −0.158944 | −0.0794718 | − | 0.996837i | \(-0.525323\pi\) | ||||
−0.0794718 | + | 0.996837i | \(0.525323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7250 | 0.782408 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.4847 | −1.56404 | −0.782018 | − | 0.623256i | \(-0.785810\pi\) | ||||
−0.782018 | + | 0.623256i | \(0.785810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.1627 | −1.22716 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.7170 | 0.492096 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4792 | −0.554600 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.171623 | −0.00614114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.30523 | −0.118119 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.4832 | 1.44491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.63599 | −0.272194 | −0.136097 | − | 0.990696i | \(-0.543456\pi\) | ||||
−0.136097 | + | 0.990696i | \(0.543456\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.3272 | −0.652467 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.7473 | −2.58659 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 69.3012 | 2.46096 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.4163 | 0.901425 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.17701 | −0.0416920 | −0.0208460 | − | 0.999783i | \(-0.506636\pi\) | ||||
−0.0208460 | + | 0.999783i | \(0.506636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.7101 | −1.97088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4567 | −0.404803 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.1040 | 0.356564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.7042 | −1.15267 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.7577 | 0.660301 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.7537 | 1.78441 | 0.892203 | − | 0.451634i | \(-0.149159\pi\) | ||||
0.892203 | + | 0.451634i | \(0.149159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.42078 | −0.155235 | −0.0776174 | − | 0.996983i | \(-0.524731\pi\) | ||||
−0.0776174 | + | 0.996983i | \(0.524731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.6404 | 1.07460 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.87942 | −0.0658331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.27904 | −0.0797334 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.4625 | −0.749960 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7260 | 0.862943 | 0.431472 | − | 0.902127i | \(-0.357995\pi\) | ||||
0.431472 | + | 0.902127i | \(0.357995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.09032 | −0.177437 | −0.0887187 | − | 0.996057i | \(-0.528277\pi\) | ||||
−0.0887187 | + | 0.996057i | \(0.528277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.35058 | 0.325546 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.2760 | −1.12234 | −0.561172 | − | 0.827699i | \(-0.689650\pi\) | ||||
−0.561172 | + | 0.827699i | \(0.689650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.44996 | 0.328211 | 0.164105 | − | 0.986443i | \(-0.447526\pi\) | ||||
0.164105 | + | 0.986443i | \(0.447526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.6795 | −0.509226 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84.9309 | −2.94268 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.26608 | −0.113027 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.02804 | 0.208359 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.01604 | −0.0350776 | −0.0175388 | − | 0.999846i | \(-0.505583\pi\) | ||||
−0.0175388 | + | 0.999846i | \(0.505583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.0754 | −0.623291 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.5620 | −1.05261 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.4007 | 1.45863 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.8543 | −1.19761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.0703 | −0.791771 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.74732 | 0.265575 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2405 | 0.350629 | 0.175315 | − | 0.984512i | \(-0.443906\pi\) | ||||
0.175315 | + | 0.984512i | \(0.443906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.47667 | 0.255697 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5117 | 0.564030 | 0.282015 | − | 0.959410i | \(-0.408997\pi\) | ||||
0.282015 | + | 0.959410i | \(0.408997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4220 | 0.355592 | 0.177796 | − | 0.984067i | \(-0.443103\pi\) | ||||
0.177796 | + | 0.984067i | \(0.443103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.4715 | 0.970305 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.3376 | 0.590179 | 0.295089 | − | 0.955470i | \(-0.404651\pi\) | ||||
0.295089 | + | 0.955470i | \(0.404651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.8427 | 1.89871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −45.6631 | −1.55080 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.23695 | 0.177651 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.7529 | 1.82135 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.758299 | −0.0256645 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.17683 | 0.310234 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.7758 | −1.78211 | −0.891056 | − | 0.453893i | \(-0.850035\pi\) | ||||
−0.891056 | + | 0.453893i | \(0.850035\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.9252 | −0.672059 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.7239 | 0.630825 | 0.315412 | − | 0.948955i | \(-0.397857\pi\) | ||||
0.315412 | + | 0.948955i | \(0.397857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.18388 | −0.0398408 | −0.0199204 | − | 0.999802i | \(-0.506341\pi\) | ||||
−0.0199204 | + | 0.999802i | \(0.506341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.04380 | −0.304004 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.6215 | −1.66613 | −0.833063 | − | 0.553178i | \(-0.813415\pi\) | ||||
−0.833063 | + | 0.553178i | \(0.813415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.3886 | 0.750890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.64992 | −0.0552743 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.1105 | 0.539117 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.2216 | −0.408524 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.1219 | −0.404739 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.9241 | −0.664505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.6015 | 2.05225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.19192 | 0.139498 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.0981 | 0.834290 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7086 | 1.31850 | 0.659251 | − | 0.751923i | \(-0.270873\pi\) | ||||
0.659251 | + | 0.751923i | \(0.270873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7478 | 0.522320 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.0082 | −0.430980 | −0.215490 | − | 0.976506i | \(-0.569135\pi\) | ||||
−0.215490 | + | 0.976506i | \(0.569135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.9344 | −0.825210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.4049 | 1.46798 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.7169 | 0.717157 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.7415 | −0.684198 | −0.342099 | − | 0.939664i | \(-0.611138\pi\) | ||||
−0.342099 | + | 0.939664i | \(0.611138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.67492 | −0.121093 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.530212 | −0.0174521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.4627 | −0.607049 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.604753 | 0.0198627 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.5351 | −0.542500 | −0.271250 | − | 0.962509i | \(-0.587437\pi\) | ||||
−0.271250 | + | 0.962509i | \(0.587437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.5607 | 0.804945 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.1759 | 1.08613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.6575 | 1.39505 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6845 | 1.06776 | 0.533879 | − | 0.845561i | \(-0.320734\pi\) | ||||
0.533879 | + | 0.845561i | \(0.320734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.2804 | −0.335488 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2334 | −0.789987 | −0.394994 | − | 0.918684i | \(-0.629253\pi\) | ||||
−0.394994 | + | 0.918684i | \(0.629253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0806 | 0.523655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.7521 | −0.447357 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.7988 | 1.55325 | 0.776626 | − | 0.629962i | \(-0.216930\pi\) | ||||
0.776626 | + | 0.629962i | \(0.216930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2155 | 1.01330 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.4030 | −0.531902 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.6792 | −0.378325 | −0.189163 | − | 0.981946i | \(-0.560577\pi\) | ||||
−0.189163 | + | 0.981946i | \(0.560577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.7569 | 1.25414 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.45336 | 0.176282 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.7930 | 1.25269 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.33722 | 0.172169 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7791 | −0.411801 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.7109 | −0.795473 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.5374 | −1.72165 | −0.860823 | − | 0.508905i | \(-0.830051\pi\) | ||||
−0.860823 | + | 0.508905i | \(0.830051\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.1212 | 0.582136 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.8894 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.6872 | 1.68907 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.8878 | 0.925149 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.3200 | 1.73785 | 0.868925 | − | 0.494943i | \(-0.164811\pi\) | ||||
0.868925 | + | 0.494943i | \(0.164811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.9026 | 0.604131 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0076 | −0.351444 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.7846 | 1.36462 | 0.682309 | − | 0.731064i | \(-0.260976\pi\) | ||||
0.682309 | + | 0.731064i | \(0.260976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.2612 | 1.37842 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.6326 | −0.943217 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.36758 | 0.0752845 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.2570 | 1.34234 | 0.671169 | − | 0.741305i | \(-0.265793\pi\) | ||||
0.671169 | + | 0.741305i | \(0.265793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.20238 | 0.101624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.21709 | −0.292201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.6191 | 1.09640 | 0.548198 | − | 0.836348i | \(-0.315314\pi\) | ||||
0.548198 | + | 0.836348i | \(0.315314\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.25775 | 0.103071 |
(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 | 8016.2.a.s.1.5 | 5 | ||
4.3 | odd | 2 | 4008.2.a.f.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.f.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
8016.2.a.s.1.5 | 5 | 1.1 | even | 1 | trivial |