Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, 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("7500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.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: | \(59.8878015160\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 7x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7500.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.32440 | −1.63447 | −0.817234 | − | 0.576306i | \(-0.804494\pi\) | ||||
−0.817234 | + | 0.576306i | \(0.804494\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.584296 | 0.176172 | 0.0880859 | − | 0.996113i | \(-0.471925\pi\) | ||||
0.0880859 | + | 0.996113i | \(0.471925\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.966262 | −0.267993 | −0.133996 | − | 0.990982i | \(-0.542781\pi\) | ||||
−0.133996 | + | 0.990982i | \(0.542781\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.32440 | 0.563749 | 0.281874 | − | 0.959451i | \(-0.409044\pi\) | ||||
0.281874 | + | 0.959451i | \(0.409044\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.37899 | −1.23402 | −0.617012 | − | 0.786954i | \(-0.711657\pi\) | ||||
−0.617012 | + | 0.786954i | \(0.711657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.32440 | −0.943661 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.35813 | 0.283191 | 0.141595 | − | 0.989925i | \(-0.454777\pi\) | ||||
0.141595 | + | 0.989925i | \(0.454777\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.706362 | −0.131168 | −0.0655841 | − | 0.997847i | \(-0.520891\pi\) | ||||
−0.0655841 | + | 0.997847i | \(0.520891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48817 | 1.52452 | 0.762260 | − | 0.647271i | \(-0.224090\pi\) | ||||
0.762260 | + | 0.647271i | \(0.224090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.584296 | 0.101713 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.11909 | 1.00597 | 0.502986 | − | 0.864295i | \(-0.332235\pi\) | ||||
0.502986 | + | 0.864295i | \(0.332235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.966262 | −0.154726 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0615 | 1.72752 | 0.863759 | − | 0.503905i | \(-0.168104\pi\) | ||||
0.863759 | + | 0.503905i | \(0.168104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.03076 | 1.07218 | 0.536090 | − | 0.844161i | \(-0.319901\pi\) | ||||
0.536090 | + | 0.844161i | \(0.319901\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.06932 | −1.32290 | −0.661448 | − | 0.749991i | \(-0.730058\pi\) | ||||
−0.661448 | + | 0.749991i | \(0.730058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7004 | 1.67149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.32440 | 0.325481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.90571 | −1.22329 | −0.611647 | − | 0.791131i | \(-0.709493\pi\) | ||||
−0.611647 | + | 0.791131i | \(0.709493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.37899 | −0.712464 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.29250 | −0.949403 | −0.474701 | − | 0.880147i | \(-0.657444\pi\) | ||||
−0.474701 | + | 0.880147i | \(0.657444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.81370 | −0.616331 | −0.308166 | − | 0.951333i | \(-0.599715\pi\) | ||||
−0.308166 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.32440 | −0.544823 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.376006 | 0.0459364 | 0.0229682 | − | 0.999736i | \(-0.492688\pi\) | ||||
0.0229682 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.35813 | 0.163500 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5605 | 1.25330 | 0.626648 | − | 0.779302i | \(-0.284426\pi\) | ||||
0.626648 | + | 0.779302i | \(0.284426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.213375 | −0.0249736 | −0.0124868 | − | 0.999922i | \(-0.503975\pi\) | ||||
−0.0124868 | + | 0.999922i | \(0.503975\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.52673 | −0.287947 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.02594 | −0.790480 | −0.395240 | − | 0.918578i | \(-0.629339\pi\) | ||||
−0.395240 | + | 0.918578i | \(0.629339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.1113 | −1.76844 | −0.884222 | − | 0.467068i | \(-0.845310\pi\) | ||||
−0.884222 | + | 0.467068i | \(0.845310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.706362 | −0.0757300 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0197 | −1.48609 | −0.743043 | − | 0.669243i | \(-0.766618\pi\) | ||||
−0.743043 | + | 0.669243i | \(0.766618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17850 | 0.438026 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.48817 | 0.880182 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7520 | −1.59937 | −0.799687 | − | 0.600417i | \(-0.795001\pi\) | ||||
−0.799687 | + | 0.600417i | \(0.795001\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.584296 | 0.0587239 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.14178 | 0.710634 | 0.355317 | − | 0.934746i | \(-0.384373\pi\) | ||||
0.355317 | + | 0.934746i | \(0.384373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.32553 | −0.130609 | −0.0653044 | − | 0.997865i | \(-0.520802\pi\) | ||||
−0.0653044 | + | 0.997865i | \(0.520802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.6796 | −1.70915 | −0.854573 | − | 0.519331i | \(-0.826181\pi\) | ||||
−0.854573 | + | 0.519331i | \(0.826181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.53978 | 0.339049 | 0.169524 | − | 0.985526i | \(-0.445777\pi\) | ||||
0.169524 | + | 0.985526i | \(0.445777\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.11909 | 0.580798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4882 | −1.64515 | −0.822574 | − | 0.568658i | \(-0.807463\pi\) | ||||
−0.822574 | + | 0.568658i | \(0.807463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.966262 | −0.0893309 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0516 | −0.921430 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6586 | −0.968964 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.0615 | 0.997383 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.5060 | −1.55341 | −0.776705 | − | 0.629865i | \(-0.783110\pi\) | ||||
−0.776705 | + | 0.629865i | \(0.783110\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.03076 | 0.619024 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.8660 | −1.64833 | −0.824166 | − | 0.566349i | \(-0.808355\pi\) | ||||
−0.824166 | + | 0.566349i | \(0.808355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.2609 | 2.01697 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2508 | −1.13209 | −0.566046 | − | 0.824374i | \(-0.691528\pi\) | ||||
−0.566046 | + | 0.824374i | \(0.691528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9026 | −1.43366 | −0.716829 | − | 0.697249i | \(-0.754407\pi\) | ||||
−0.716829 | + | 0.697249i | \(0.754407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.06932 | −0.763774 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.564582 | −0.0472128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.7004 | 0.965033 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.1625 | 0.996388 | 0.498194 | − | 0.867066i | \(-0.333997\pi\) | ||||
0.498194 | + | 0.867066i | \(0.333997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.84446 | −0.801131 | −0.400565 | − | 0.916268i | \(-0.631186\pi\) | ||||
−0.400565 | + | 0.916268i | \(0.631186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.32440 | 0.187916 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4804 | 1.47489 | 0.737447 | − | 0.675405i | \(-0.236031\pi\) | ||||
0.737447 | + | 0.675405i | \(0.236031\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.90571 | −0.706269 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.87311 | −0.462866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5368 | 1.13861 | 0.569305 | − | 0.822127i | \(-0.307212\pi\) | ||||
0.569305 | + | 0.822127i | \(0.307212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.49299 | 0.347678 | 0.173839 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173839 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0663 | −0.928180 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.37899 | −0.411341 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.99816 | −0.151917 | −0.0759586 | − | 0.997111i | \(-0.524202\pi\) | ||||
−0.0759586 | + | 0.997111i | \(0.524202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.29250 | −0.548138 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.9793 | 1.04486 | 0.522431 | − | 0.852681i | \(-0.325025\pi\) | ||||
0.522431 | + | 0.852681i | \(0.325025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5379 | 1.00627 | 0.503133 | − | 0.864209i | \(-0.332180\pi\) | ||||
0.503133 | + | 0.864209i | \(0.332180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.81370 | −0.355839 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.35813 | 0.0993166 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.32440 | −0.314554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.54547 | 0.184184 | 0.0920920 | − | 0.995751i | \(-0.470645\pi\) | ||||
0.0920920 | + | 0.995751i | \(0.470645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.60541 | −0.403486 | −0.201743 | − | 0.979438i | \(-0.564661\pi\) | ||||
−0.201743 | + | 0.979438i | \(0.564661\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.85621 | 0.559732 | 0.279866 | − | 0.960039i | \(-0.409710\pi\) | ||||
0.279866 | + | 0.960039i | \(0.409710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9970 | 1.20489 | 0.602443 | − | 0.798162i | \(-0.294194\pi\) | ||||
0.602443 | + | 0.798162i | \(0.294194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.376006 | 0.0265214 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.05459 | 0.214390 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.35813 | 0.0943969 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.14292 | −0.217400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9553 | −0.891881 | −0.445940 | − | 0.895063i | \(-0.647131\pi\) | ||||
−0.445940 | + | 0.895063i | \(0.647131\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5605 | 0.723591 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −36.7062 | −2.49178 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.213375 | −0.0144185 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24597 | −0.151081 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9801 | −1.27100 | −0.635501 | − | 0.772100i | \(-0.719207\pi\) | ||||
−0.635501 | + | 0.772100i | \(0.719207\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.385109 | 0.0255606 | 0.0127803 | − | 0.999918i | \(-0.495932\pi\) | ||||
0.0127803 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2685 | 0.678562 | 0.339281 | − | 0.940685i | \(-0.389816\pi\) | ||||
0.339281 | + | 0.940685i | \(0.389816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.52673 | −0.166246 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.6380 | 1.41755 | 0.708777 | − | 0.705433i | \(-0.249247\pi\) | ||||
0.708777 | + | 0.705433i | \(0.249247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.02594 | −0.456384 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71601 | −0.499107 | −0.249553 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249553 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.3264 | −1.63142 | −0.815708 | − | 0.578463i | \(-0.803653\pi\) | ||||
−0.815708 | + | 0.578463i | \(0.803653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.19751 | 0.330710 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.1113 | −1.02101 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.39913 | −0.151432 | −0.0757160 | − | 0.997129i | \(-0.524124\pi\) | ||||
−0.0757160 | + | 0.997129i | \(0.524124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.793552 | 0.0498902 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3086 | 0.892548 | 0.446274 | − | 0.894896i | \(-0.352751\pi\) | ||||
0.446274 | + | 0.894896i | \(0.352751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.4614 | −1.64423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.706362 | −0.0437227 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0805 | −0.806580 | −0.403290 | − | 0.915072i | \(-0.632133\pi\) | ||||
−0.403290 | + | 0.915072i | \(0.632133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.0197 | −0.857993 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.6749 | 1.87028 | 0.935141 | − | 0.354277i | \(-0.115273\pi\) | ||||
0.935141 | + | 0.354277i | \(0.115273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2362 | 0.864789 | 0.432395 | − | 0.901684i | \(-0.357669\pi\) | ||||
0.432395 | + | 0.901684i | \(0.357669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.17850 | 0.252894 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.1307 | −1.20953 | −0.604767 | − | 0.796402i | \(-0.706734\pi\) | ||||
−0.604767 | + | 0.796402i | \(0.706734\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.48817 | 0.508173 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.81651 | −0.585604 | −0.292802 | − | 0.956173i | \(-0.594588\pi\) | ||||
−0.292802 | + | 0.956173i | \(0.594588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.54547 | −0.389088 | −0.194544 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194544 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −47.8344 | −2.82357 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5972 | −0.682187 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.7520 | −0.923399 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.869428 | −0.0507925 | −0.0253963 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253963 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.584296 | 0.0339043 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.31231 | −0.0758930 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4038 | −1.75244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.14178 | 0.410285 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.7261 | −1.23997 | −0.619986 | − | 0.784613i | \(-0.712862\pi\) | ||||
−0.619986 | + | 0.784613i | \(0.712862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.32553 | −0.0754070 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9831 | 1.07643 | 0.538216 | − | 0.842807i | \(-0.319098\pi\) | ||||
0.538216 | + | 0.842807i | \(0.319098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.08210 | 0.343781 | 0.171890 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171890 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.97817 | −0.111105 | −0.0555526 | − | 0.998456i | \(-0.517692\pi\) | ||||
−0.0555526 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.412724 | −0.0231081 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6796 | −0.986776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5029 | −0.695680 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.53978 | 0.195750 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.2193 | 2.16223 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1307 | −0.721730 | −0.360865 | − | 0.932618i | \(-0.617519\pi\) | ||||
−0.360865 | + | 0.932618i | \(0.617519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.11909 | 0.335324 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4960 | −0.626225 | −0.313113 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313113 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.4882 | −0.949827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.95960 | 0.268577 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.3264 | −1.09752 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.7775 | −1.59854 | −0.799271 | − | 0.600971i | \(-0.794781\pi\) | ||||
−0.799271 | + | 0.600971i | \(0.794781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0870 | 0.539946 | 0.269973 | − | 0.962868i | \(-0.412985\pi\) | ||||
0.269973 | + | 0.962868i | \(0.412985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.966262 | −0.0515752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2620 | 0.759090 | 0.379545 | − | 0.925173i | \(-0.376081\pi\) | ||||
0.379545 | + | 0.925173i | \(0.376081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.0516 | −0.531988 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.60909 | −0.348815 | −0.174407 | − | 0.984674i | \(-0.555801\pi\) | ||||
−0.174407 | + | 0.984674i | \(0.555801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.93349 | 0.522815 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.6586 | −0.559431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.54259 | −0.498119 | −0.249060 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249060 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0615 | 0.575840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38.5118 | 1.99943 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.30338 | 0.0674866 | 0.0337433 | − | 0.999431i | \(-0.489257\pi\) | ||||
0.0337433 | + | 0.999431i | \(0.489257\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.682531 | 0.0351521 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2855 | 1.24746 | 0.623731 | − | 0.781639i | \(-0.285616\pi\) | ||||
0.623731 | + | 0.781639i | \(0.285616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.5060 | −0.896861 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1319 | −0.619910 | −0.309955 | − | 0.950751i | \(-0.600314\pi\) | ||||
−0.309955 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.03076 | 0.357394 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.2598 | −1.48353 | −0.741766 | − | 0.670659i | \(-0.766012\pi\) | ||||
−0.741766 | + | 0.670659i | \(0.766012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.15684 | 0.159648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8660 | −0.951664 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.29380 | −0.315877 | −0.157938 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157938 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.2609 | 1.16450 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3064 | 1.51343 | 0.756714 | − | 0.653747i | \(-0.226804\pi\) | ||||
0.756714 | + | 0.653747i | \(0.226804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.20179 | −0.408560 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.57536 | 0.177224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4761 | 0.913583 | 0.456792 | − | 0.889574i | \(-0.348998\pi\) | ||||
0.456792 | + | 0.889574i | \(0.348998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.2508 | −0.653614 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.5357 | 1.55177 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.9026 | −0.827722 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.4453 | −1.09653 | −0.548263 | − | 0.836306i | \(-0.684711\pi\) | ||||
−0.548263 | + | 0.836306i | \(0.684711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.25053 | −0.304632 | −0.152316 | − | 0.988332i | \(-0.548673\pi\) | ||||
−0.152316 | + | 0.988332i | \(0.548673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.06932 | −0.440965 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.8163 | 1.00737 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.564582 | −0.0272583 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.5914 | 1.66621 | 0.833104 | − | 0.553116i | \(-0.186561\pi\) | ||||
0.833104 | + | 0.553116i | \(0.186561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.93139 | 0.188930 | 0.0944652 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944652 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.30539 | −0.349464 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.98906 | 0.238115 | 0.119057 | − | 0.992887i | \(-0.462013\pi\) | ||||
0.119057 | + | 0.992887i | \(0.462013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7004 | 0.557162 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.92754 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1625 | 0.575265 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.87365 | 0.465966 | 0.232983 | − | 0.972481i | \(-0.425151\pi\) | ||||
0.232983 | + | 0.972481i | \(0.425151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.46320 | 0.304340 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.84446 | −0.462533 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6424 | −0.591387 | −0.295693 | − | 0.955283i | \(-0.595551\pi\) | ||||
−0.295693 | + | 0.955283i | \(0.595551\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.32440 | 0.108494 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.7747 | 1.85249 | 0.926246 | − | 0.376919i | \(-0.123016\pi\) | ||||
0.926246 | + | 0.376919i | \(0.123016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.41868 | −0.205354 | −0.102677 | − | 0.994715i | \(-0.532741\pi\) | ||||
−0.102677 | + | 0.994715i | \(0.532741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.2746 | 0.521728 | 0.260864 | − | 0.965376i | \(-0.415993\pi\) | ||||
0.260864 | + | 0.965376i | \(0.415993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.62600 | −0.0750816 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4804 | 0.851530 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.10804 | 0.188888 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.90571 | −0.407765 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.55895 | −0.253995 | −0.126997 | − | 0.991903i | \(-0.540534\pi\) | ||||
−0.126997 | + | 0.991903i | \(0.540534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.91264 | −0.269593 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.87311 | −0.267236 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6341 | 0.753761 | 0.376881 | − | 0.926262i | \(-0.376997\pi\) | ||||
0.376881 | + | 0.926262i | \(0.376997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.5368 | 0.657377 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05925 | 0.0478032 | 0.0239016 | − | 0.999714i | \(-0.492391\pi\) | ||||
0.0239016 | + | 0.999714i | \(0.492391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.64187 | −0.0739459 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.6676 | −2.04847 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9700 | 1.11781 | 0.558906 | − | 0.829231i | \(-0.311221\pi\) | ||||
0.558906 | + | 0.829231i | \(0.311221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.49299 | 0.200732 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.5464 | −0.559415 | −0.279708 | − | 0.960085i | \(-0.590238\pi\) | ||||
−0.279708 | + | 0.960085i | \(0.590238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0663 | −0.535885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.4275 | −0.683810 | −0.341905 | − | 0.939735i | \(-0.611072\pi\) | ||||
−0.341905 | + | 0.939735i | \(0.611072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.922717 | 0.0408186 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.37899 | −0.237488 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.29916 | −0.233057 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.99816 | −0.0877094 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.3403 | −0.847312 | −0.423656 | − | 0.905823i | \(-0.639253\pi\) | ||||
−0.423656 | + | 0.905823i | \(0.639253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.95039 | −0.303920 | −0.151960 | − | 0.988387i | \(-0.548558\pi\) | ||||
−0.151960 | + | 0.988387i | \(0.548558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.7299 | 0.859446 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1555 | −0.919803 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.29250 | −0.316468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.6883 | −0.462962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.9793 | 0.603252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.83649 | 0.294469 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.66780 | 0.243678 | 0.121839 | − | 0.992550i | \(-0.461121\pi\) | ||||
0.121839 | + | 0.992550i | \(0.461121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5379 | 0.580968 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3997 | −0.530172 | −0.265086 | − | 0.964225i | \(-0.585400\pi\) | ||||
−0.265086 | + | 0.964225i | \(0.585400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.81370 | −0.205444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.79951 | 0.161865 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3829 | 1.29201 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.8970 | −1.05492 | −0.527461 | − | 0.849579i | \(-0.676856\pi\) | ||||
−0.527461 | + | 0.849579i | \(0.676856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.79355 | −0.287337 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.35813 | 0.0573405 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0285 | 1.05482 | 0.527412 | − | 0.849609i | \(-0.323162\pi\) | ||||
0.527412 | + | 0.849609i | \(0.323162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.32440 | −0.181608 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.09245 | 0.0877199 | 0.0438600 | − | 0.999038i | \(-0.486034\pi\) | ||||
0.0438600 | + | 0.999038i | \(0.486034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5320 | −0.482598 | −0.241299 | − | 0.970451i | \(-0.577573\pi\) | ||||
−0.241299 | + | 0.970451i | \(0.577573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.54547 | 0.106339 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.84516 | 0.243337 | 0.121669 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121669 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.60541 | −0.232953 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 69.6716 | 2.89046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.20357 | −0.215510 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.20276 | 0.379838 | 0.189919 | − | 0.981800i | \(-0.439177\pi\) | ||||
0.189919 | + | 0.981800i | \(0.439177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.6577 | −1.88129 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.85621 | 0.323161 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.9033 | 0.612004 | 0.306002 | − | 0.952031i | \(-0.401009\pi\) | ||||
0.306002 | + | 0.952031i | \(0.401009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9970 | 0.695642 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.52244 | −0.307359 | −0.153679 | − | 0.988121i | \(-0.549112\pi\) | ||||
−0.153679 | + | 0.988121i | \(0.549112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6618 | 0.761232 | 0.380616 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380616 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.376006 | 0.0153121 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.810016 | −0.0328776 | −0.0164388 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164388 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.05459 | 0.123778 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.76333 | 0.354527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.99106 | −0.201587 | −0.100794 | − | 0.994907i | \(-0.532138\pi\) | ||||
−0.100794 | + | 0.994907i | \(0.532138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.6100 | 1.71541 | 0.857706 | − | 0.514140i | \(-0.171889\pi\) | ||||
0.857706 | + | 0.514140i | \(0.171889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9631 | 1.48567 | 0.742836 | − | 0.669473i | \(-0.233480\pi\) | ||||
0.742836 | + | 0.669473i | \(0.233480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.35813 | 0.0545001 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 60.6268 | 2.42896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.14292 | −0.125516 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2232 | 0.567115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.2368 | −1.32313 | −0.661567 | − | 0.749886i | \(-0.730108\pi\) | ||||
−0.661567 | + | 0.749886i | \(0.730108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9553 | −0.514928 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3056 | −0.447946 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5605 | 0.417766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.2363 | −1.07577 | −0.537885 | − | 0.843018i | \(-0.680777\pi\) | ||||
−0.537885 | + | 0.843018i | \(0.680777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8557 | 0.506978 | 0.253489 | − | 0.967338i | \(-0.418422\pi\) | ||||
0.253489 | + | 0.967338i | \(0.418422\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.8408 | −1.25179 | −0.625895 | − | 0.779907i | \(-0.715266\pi\) | ||||
−0.625895 | + | 0.779907i | \(0.715266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.26098 | −0.167258 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.7062 | −1.43863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5019 | 0.567504 | 0.283752 | − | 0.958898i | \(-0.408421\pi\) | ||||
0.283752 | + | 0.958898i | \(0.408421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.213375 | −0.00832454 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.2386 | 1.29479 | 0.647396 | − | 0.762154i | \(-0.275858\pi\) | ||||
0.647396 | + | 0.762154i | \(0.275858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8531 | −1.23894 | −0.619472 | − | 0.785019i | \(-0.712653\pi\) | ||||
−0.619472 | + | 0.785019i | \(0.712653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.24597 | −0.0872264 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.959335 | −0.0371456 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9801 | −0.733814 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.81262 | −0.108580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1914 | 1.00960 | 0.504802 | − | 0.863235i | \(-0.331566\pi\) | ||||
0.504802 | + | 0.863235i | \(0.331566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.8442 | 0.570509 | 0.285254 | − | 0.958452i | \(-0.407922\pi\) | ||||
0.285254 | + | 0.958452i | \(0.407922\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 68.1179 | 2.61413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.385109 | 0.0147574 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.62626 | 0.215283 | 0.107641 | − | 0.994190i | \(-0.465670\pi\) | ||||
0.107641 | + | 0.994190i | \(0.465670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2685 | 0.391768 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.60525 | 0.327834 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4090 | 1.30898 | 0.654491 | − | 0.756070i | \(-0.272883\pi\) | ||||
0.654491 | + | 0.756070i | \(0.272883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.52673 | −0.0959824 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.7113 | 0.973887 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.6380 | 0.818425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.86294 | 0.334749 | 0.167374 | − | 0.985893i | \(-0.446471\pi\) | ||||
0.167374 | + | 0.985893i | \(0.446471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9145 | −1.24139 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.8839 | −1.16151 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.53673 | 0.0577132 | 0.0288566 | − | 0.999584i | \(-0.490813\pi\) | ||||
0.0288566 | + | 0.999584i | \(0.490813\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.02594 | −0.263493 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5281 | 0.431730 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.71601 | −0.288160 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.1353 | −0.713625 | −0.356813 | − | 0.934176i | \(-0.616137\pi\) | ||||
−0.356813 | + | 0.934176i | \(0.616137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.73214 | 0.213476 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.3264 | −0.941899 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.8094 | −1.73606 | −0.868032 | − | 0.496507i | \(-0.834616\pi\) | ||||
−0.868032 | + | 0.496507i | \(0.834616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3423 | 0.604441 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.0044 | −1.88389 | −0.941945 | − | 0.335768i | \(-0.891004\pi\) | ||||
−0.941945 | + | 0.335768i | \(0.891004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.219699 | 0.00809270 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2056 | 0.485775 | 0.242887 | − | 0.970054i | \(-0.421905\pi\) | ||||
0.242887 | + | 0.970054i | \(0.421905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.19751 | 0.190935 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6063 | −0.389107 | −0.194553 | − | 0.980892i | \(-0.562326\pi\) | ||||
−0.194553 | + | 0.980892i | \(0.562326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.1113 | −0.589481 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 76.4534 | 2.79355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2581 | 1.03115 | 0.515577 | − | 0.856843i | \(-0.327578\pi\) | ||||
0.515577 | + | 0.856843i | \(0.327578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.39913 | −0.0874293 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.7474 | −1.00849 | −0.504247 | − | 0.863559i | \(-0.668230\pi\) | ||||
−0.504247 | + | 0.863559i | \(0.668230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.793552 | 0.0288041 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.1152 | −0.584177 | −0.292088 | − | 0.956391i | \(-0.594350\pi\) | ||||
−0.292088 | + | 0.956391i | \(0.594350\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3074 | −0.554165 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.04646 | 0.254433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.7435 | −1.25288 | −0.626441 | − | 0.779468i | \(-0.715489\pi\) | ||||
−0.626441 | + | 0.779468i | \(0.715489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3086 | 0.515313 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.4684 | −0.844101 | −0.422051 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422051 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.4614 | −0.949296 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.4997 | −2.13180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.17043 | 0.220795 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.706362 | −0.0252433 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.6217 | 0.913316 | 0.456658 | − | 0.889642i | \(-0.349046\pi\) | ||||
0.456658 | + | 0.889642i | \(0.349046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0805 | −0.465679 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 75.6258 | 2.68894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.65129 | 0.165172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.92304 | 0.0681177 | 0.0340588 | − | 0.999420i | \(-0.489157\pi\) | ||||
0.0340588 | + | 0.999420i | \(0.489157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.0807 | −0.745781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0197 | −0.495362 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.124674 | −0.00439965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.6749 | 1.07981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.4087 | −1.59648 | −0.798242 | − | 0.602336i | \(-0.794237\pi\) | ||||
−0.798242 | + | 0.602336i | \(0.794237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.9207 | −0.839970 | −0.419985 | − | 0.907531i | \(-0.637965\pi\) | ||||
−0.419985 | + | 0.907531i | \(0.637965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.2362 | 0.499286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.8184 | −1.32310 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.17850 | 0.146009 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.5862 | −1.10237 | −0.551184 | − | 0.834384i | \(-0.685824\pi\) | ||||
−0.551184 | + | 0.834384i | \(0.685824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.53252 | −0.297425 | −0.148713 | − | 0.988880i | \(-0.547513\pi\) | ||||
−0.148713 | + | 0.988880i | \(0.547513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.7933 | −0.618733 | −0.309366 | − | 0.950943i | \(-0.600117\pi\) | ||||
−0.309366 | + | 0.950943i | \(0.600117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0216 | −1.59840 | −0.799199 | − | 0.601067i | \(-0.794743\pi\) | ||||
−0.799199 | + | 0.601067i | \(0.794743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.1307 | −0.698325 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.1964 | 0.942298 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.48817 | 0.293394 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.01208 | 0.0349410 | 0.0174705 | − | 0.999847i | \(-0.494439\pi\) | ||||
0.0174705 | + | 0.999847i | \(0.494439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5011 | −0.982795 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.81651 | −0.338099 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.0920 | 1.58374 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.54547 | −0.224640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.31054 | 0.284882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.81334 | 0.336002 | 0.168001 | − | 0.985787i | \(-0.446269\pi\) | ||||
0.168001 | + | 0.985787i | \(0.446269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.3424 | 1.95878 | 0.979390 | − | 0.201979i | \(-0.0647372\pi\) | ||||
0.979390 | + | 0.201979i | \(0.0647372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7349 | 0.366271 | 0.183135 | − | 0.983088i | \(-0.441375\pi\) | ||||
0.183135 | + | 0.983088i | \(0.441375\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.8344 | −1.63019 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.63250 | −0.327894 | −0.163947 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163947 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.5972 | −0.393861 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.10522 | −0.139260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.363320 | −0.0123106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.7520 | −0.533125 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.703817 | 0.0237662 | 0.0118831 | − | 0.999929i | \(-0.496217\pi\) | ||||
0.0118831 | + | 0.999929i | \(0.496217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.869428 | −0.0293251 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.92656 | 0.334434 | 0.167217 | − | 0.985920i | \(-0.446522\pi\) | ||||
0.167217 | + | 0.985920i | \(0.446522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8403 | −0.566723 | −0.283361 | − | 0.959013i | \(-0.591450\pi\) | ||||
−0.283361 | + | 0.959013i | \(0.591450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.3918 | −1.55768 | −0.778842 | − | 0.627221i | \(-0.784192\pi\) | ||||
−0.778842 | + | 0.627221i | \(0.784192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 75.7030 | 2.53900 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.584296 | 0.0195746 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.7837 | 1.63249 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.31231 | −0.0438169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.99572 | −0.199968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7004 | −0.689630 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.4038 | −1.01177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.5101 | −0.946662 | −0.473331 | − | 0.880885i | \(-0.656949\pi\) | ||||
−0.473331 | + | 0.880885i | \(0.656949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.14178 | 0.236878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.50073 | −0.215379 | −0.107689 | − | 0.994185i | \(-0.534345\pi\) | ||||
−0.107689 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.41375 | −0.311550 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 81.5841 | 2.69414 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.8266 | 0.555058 | 0.277529 | − | 0.960717i | \(-0.410485\pi\) | ||||
0.277529 | + | 0.960717i | \(0.410485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.7261 | −0.715899 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.2042 | −0.335874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.32553 | −0.0435363 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.6407 | −1.03810 | −0.519049 | − | 0.854744i | \(-0.673714\pi\) | ||||
−0.519049 | + | 0.854744i | \(0.673714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −62.9363 | −2.06265 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9831 | 0.621479 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.35105 | 0.0768053 | 0.0384026 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384026 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.08210 | 0.198482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.29802 | 0.140111 | 0.0700557 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700557 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0230 | 0.489217 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.8418 | −0.904737 | −0.452369 | − | 0.891831i | \(-0.649421\pi\) | ||||
−0.452369 | + | 0.891831i | \(0.649421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.206176 | 0.00669275 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.97817 | −0.0641467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6209 | 1.44541 | 0.722707 | − | 0.691154i | \(-0.242898\pi\) | ||||
0.722707 | + | 0.691154i | \(0.242898\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.412724 | −0.0133415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.3017 | 1.85037 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0490 | 1.32416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.6796 | −0.569716 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.1855 | 1.77465 | 0.887323 | − | 0.461148i | \(-0.152562\pi\) | ||||
0.887323 | + | 0.461148i | \(0.152562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.5029 | −0.401651 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.19165 | −0.198699 | −0.0993497 | − | 0.995053i | \(-0.531676\pi\) | ||||
−0.0993497 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 73.0934 | 2.34327 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1646 | −0.773095 | −0.386548 | − | 0.922269i | \(-0.626333\pi\) | ||||
−0.386548 | + | 0.922269i | \(0.626333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.19166 | −0.261806 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.53978 | 0.113016 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.52304 | 0.303738 | 0.151869 | − | 0.988401i | \(-0.451471\pi\) | ||||
0.151869 | + | 0.988401i | \(0.451471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.2193 | 1.24836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.54872 | 0.303631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4117 | −0.330740 | −0.165370 | − | 0.986232i | \(-0.552882\pi\) | ||||
−0.165370 | + | 0.986232i | \(0.552882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.1307 | −0.416691 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.7687 | 1.82955 | 0.914777 | − | 0.403959i | \(-0.132366\pi\) | ||||
0.914777 | + | 0.403959i | \(0.132366\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.11909 | 0.193599 |
(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 | 7500.2.a.f.1.1 | 4 | ||
5.2 | odd | 4 | 7500.2.d.c.1249.1 | 8 | |||
5.3 | odd | 4 | 7500.2.d.c.1249.8 | 8 | |||
5.4 | even | 2 | 7500.2.a.e.1.4 | 4 | |||
25.2 | odd | 20 | 1500.2.o.b.649.1 | 16 | |||
25.9 | even | 10 | 300.2.m.b.181.1 | yes | 8 | ||
25.11 | even | 5 | 1500.2.m.a.601.1 | 8 | |||
25.12 | odd | 20 | 1500.2.o.b.349.3 | 16 | |||
25.13 | odd | 20 | 1500.2.o.b.349.2 | 16 | |||
25.14 | even | 10 | 300.2.m.b.121.1 | ✓ | 8 | ||
25.16 | even | 5 | 1500.2.m.a.901.1 | 8 | |||
25.23 | odd | 20 | 1500.2.o.b.649.4 | 16 | |||
75.14 | odd | 10 | 900.2.n.b.721.2 | 8 | |||
75.59 | odd | 10 | 900.2.n.b.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.121.1 | ✓ | 8 | 25.14 | even | 10 | ||
300.2.m.b.181.1 | yes | 8 | 25.9 | even | 10 | ||
900.2.n.b.181.2 | 8 | 75.59 | odd | 10 | |||
900.2.n.b.721.2 | 8 | 75.14 | odd | 10 | |||
1500.2.m.a.601.1 | 8 | 25.11 | even | 5 | |||
1500.2.m.a.901.1 | 8 | 25.16 | even | 5 | |||
1500.2.o.b.349.2 | 16 | 25.13 | odd | 20 | |||
1500.2.o.b.349.3 | 16 | 25.12 | odd | 20 | |||
1500.2.o.b.649.1 | 16 | 25.2 | odd | 20 | |||
1500.2.o.b.649.4 | 16 | 25.23 | odd | 20 | |||
7500.2.a.e.1.4 | 4 | 5.4 | even | 2 | |||
7500.2.a.f.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7500.2.d.c.1249.1 | 8 | 5.2 | odd | 4 | |||
7500.2.d.c.1249.8 | 8 | 5.3 | odd | 4 |