Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 14x^{5} + 13x^{4} + 50x^{3} - 53x^{2} - 25x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.11867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.11867 | −1.80056 | −0.900281 | − | 0.435309i | \(-0.856639\pi\) | ||||
−0.900281 | + | 0.435309i | \(0.856639\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20110 | −0.984361 | −0.492181 | − | 0.870493i | \(-0.663800\pi\) | ||||
−0.492181 | + | 0.870493i | \(0.663800\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.72607 | 2.24202 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.34957 | 1.31145 | 0.655723 | − | 0.755002i | \(-0.272364\pi\) | ||||
0.655723 | + | 0.755002i | \(0.272364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.54473 | 0.428430 | 0.214215 | − | 0.976787i | \(-0.431281\pi\) | ||||
0.214215 | + | 0.976787i | \(0.431281\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.86449 | 1.77240 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.501805 | −0.121706 | −0.0608528 | − | 0.998147i | \(-0.519382\pi\) | ||||
−0.0608528 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.34060 | −0.905077 | −0.452538 | − | 0.891745i | \(-0.649481\pi\) | ||||
−0.452538 | + | 0.891745i | \(0.649481\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.155164 | −0.0310329 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.6204 | −2.23634 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.841822 | −0.156322 | −0.0781612 | − | 0.996941i | \(-0.524905\pi\) | ||||
−0.0781612 | + | 0.996941i | \(0.524905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.98025 | 0.355663 | 0.177831 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177831 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.5649 | −2.36134 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2903 | −1.69172 | −0.845858 | − | 0.533408i | \(-0.820911\pi\) | ||||
−0.845858 | + | 0.533408i | \(0.820911\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.81748 | −0.771415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.41225 | −0.845252 | −0.422626 | − | 0.906304i | \(-0.638892\pi\) | ||||
−0.422626 | + | 0.906304i | \(0.638892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.20752 | 1.09914 | 0.549568 | − | 0.835449i | \(-0.314792\pi\) | ||||
0.549568 | + | 0.835449i | \(0.314792\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.8047 | −2.20696 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.28281 | −0.916442 | −0.458221 | − | 0.888838i | \(-0.651513\pi\) | ||||
−0.458221 | + | 0.888838i | \(0.651513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.56496 | 0.219138 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0386 | 1.37890 | 0.689452 | − | 0.724332i | \(-0.257852\pi\) | ||||
0.689452 | + | 0.724332i | \(0.257852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.57384 | −1.29094 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.11867 | 0.413077 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.10666 | 1.05540 | 0.527698 | − | 0.849432i | \(-0.323055\pi\) | ||||
0.527698 | + | 0.849432i | \(0.323055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28281 | 0.292283 | 0.146142 | − | 0.989264i | \(-0.453314\pi\) | ||||
0.146142 | + | 0.989264i | \(0.453314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.40009 | −0.421730 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.01951 | 0.124553 | 0.0622765 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622765 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5369 | 1.62965 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7182 | 1.86541 | 0.932704 | − | 0.360643i | \(-0.117443\pi\) | ||||
0.932704 | + | 0.360643i | \(0.117443\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.86509 | −0.218292 | −0.109146 | − | 0.994026i | \(-0.534812\pi\) | ||||
−0.109146 | + | 0.994026i | \(0.534812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.483906 | 0.0558766 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.43201 | −0.386131 | −0.193065 | − | 0.981186i | \(-0.561843\pi\) | ||||
−0.193065 | + | 0.981186i | \(0.561843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.0618 | 1.78465 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.4222 | −1.69281 | −0.846403 | − | 0.532544i | \(-0.821236\pi\) | ||||
−0.846403 | + | 0.532544i | \(0.821236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10452 | 0.119802 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.62536 | 0.281468 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1018 | −1.70679 | −0.853396 | − | 0.521263i | \(-0.825461\pi\) | ||||
−0.853396 | + | 0.521263i | \(0.825461\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.17573 | −0.640393 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.20110 | 0.225828 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.96899 | 0.199921 | 0.0999603 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999603 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.2555 | 2.94029 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.55769 | 0.652515 | 0.326257 | − | 0.945281i | \(-0.394212\pi\) | ||||
0.326257 | + | 0.945281i | \(0.394212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.59106 | 0.747970 | 0.373985 | − | 0.927435i | \(-0.377991\pi\) | ||||
0.373985 | + | 0.927435i | \(0.377991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9802 | 1.35152 | 0.675761 | − | 0.737121i | \(-0.263815\pi\) | ||||
0.675761 | + | 0.737121i | \(0.263815\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.39598 | 0.516841 | 0.258421 | − | 0.966032i | \(-0.416798\pi\) | ||||
0.258421 | + | 0.966032i | \(0.416798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 32.0920 | 3.04604 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.25894 | −0.588792 | −0.294396 | − | 0.955684i | \(-0.595118\pi\) | ||||
−0.294396 | + | 0.955684i | \(0.595118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.55408 | 0.890923 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3899 | 0.960550 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.91879 | 0.719890 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8790 | 1.52193 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3470 | 1.01491 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.86813 | −0.254505 | −0.127252 | − | 0.991870i | \(-0.540616\pi\) | ||||
−0.127252 | + | 0.991870i | \(0.540616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.4778 | −1.97906 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4456 | 1.34949 | 0.674744 | − | 0.738052i | \(-0.264254\pi\) | ||||
0.674744 | + | 0.738052i | \(0.264254\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.5776 | 2.20137 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.74936 | −0.149458 | −0.0747291 | − | 0.997204i | \(-0.523809\pi\) | ||||
−0.0747291 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7725 | 1.67708 | 0.838541 | − | 0.544838i | \(-0.183409\pi\) | ||||
0.838541 | + | 0.544838i | \(0.183409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.5940 | 1.65011 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.71890 | 0.561863 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.85293 | 0.153878 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.360002 | 0.0294925 | 0.0147463 | − | 0.999891i | \(-0.495306\pi\) | ||||
0.0147463 | + | 0.999891i | \(0.495306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2118 | −0.912400 | −0.456200 | − | 0.889877i | \(-0.650790\pi\) | ||||
−0.456200 | + | 0.889877i | \(0.650790\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.37518 | −0.272867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.35872 | −0.350101 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9976 | −0.957510 | −0.478755 | − | 0.877949i | \(-0.658912\pi\) | ||||
−0.478755 | + | 0.877949i | \(0.658912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −31.3069 | −2.48280 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9969 | −1.56627 | −0.783137 | − | 0.621849i | \(-0.786382\pi\) | ||||
−0.783137 | + | 0.621849i | \(0.786382\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29.8576 | 2.32441 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.0364 | 1.31831 | 0.659157 | − | 0.752005i | \(-0.270913\pi\) | ||||
0.659157 | + | 0.752005i | \(0.270913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6138 | −0.816448 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.72607 | −0.514356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2051 | 1.08000 | 0.539998 | − | 0.841666i | \(-0.318425\pi\) | ||||
0.539998 | + | 0.841666i | \(0.318425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.2819 | −1.90031 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00060 | −0.0747887 | −0.0373943 | − | 0.999301i | \(-0.511906\pi\) | ||||
−0.0373943 | + | 0.999301i | \(0.511906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.62945 | −0.269775 | −0.134887 | − | 0.990861i | \(-0.543067\pi\) | ||||
−0.134887 | + | 0.990861i | \(0.543067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.11931 | −0.526275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.6500 | 1.66526 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.18264 | −0.159610 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.3220 | −1.47045 | −0.735225 | − | 0.677823i | \(-0.762924\pi\) | ||||
−0.735225 | + | 0.677823i | \(0.762924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8275 | 0.923345 | 0.461672 | − | 0.887051i | \(-0.347250\pi\) | ||||
0.461672 | + | 0.887051i | \(0.347250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.6038 | 0.759351 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.8124 | −1.19783 | −0.598916 | − | 0.800812i | \(-0.704402\pi\) | ||||
−0.598916 | + | 0.800812i | \(0.704402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8072 | −0.766101 | −0.383050 | − | 0.923727i | \(-0.625126\pi\) | ||||
−0.383050 | + | 0.923727i | \(0.625126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.17951 | −0.224265 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.9129 | 0.832034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −29.1952 | −2.02920 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.34957 | −0.300866 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.73499 | 0.188285 | 0.0941424 | − | 0.995559i | \(-0.469989\pi\) | ||||
0.0941424 | + | 0.995559i | \(0.469989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −49.0198 | −3.35878 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.8645 | −1.08195 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.81659 | 0.393049 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.775151 | −0.0521423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.9765 | 1.67255 | 0.836274 | − | 0.548312i | \(-0.184729\pi\) | ||||
0.836274 | + | 0.548312i | \(0.184729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.04365 | −0.0695764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.3570 | −1.48388 | −0.741942 | − | 0.670464i | \(-0.766095\pi\) | ||||
−0.741942 | + | 0.670464i | \(0.766095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.989096 | −0.0653613 | −0.0326807 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326807 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.9343 | −0.912865 | −0.456433 | − | 0.889758i | \(-0.650873\pi\) | ||||
−0.456433 | + | 0.889758i | \(0.650873\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8291 | 0.902110 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.7033 | 0.695253 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.0277 | 1.74827 | 0.874137 | − | 0.485680i | \(-0.161428\pi\) | ||||
0.874137 | + | 0.485680i | \(0.161428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.82837 | −0.246607 | −0.123304 | − | 0.992369i | \(-0.539349\pi\) | ||||
−0.123304 | + | 0.992369i | \(0.539349\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2304 | −0.977028 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.54473 | −0.0982886 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 48.0966 | 3.04800 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.8968 | 0.940277 | 0.470138 | − | 0.882593i | \(-0.344204\pi\) | ||||
0.470138 | + | 0.882593i | \(0.344204\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.8797 | −1.18696 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.44464 | −0.215711 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.0665 | −1.87550 | −0.937748 | − | 0.347316i | \(-0.887093\pi\) | ||||
−0.937748 | + | 0.347316i | \(0.887093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.66216 | −0.350479 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.43780 | −0.0886587 | −0.0443293 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443293 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.0959 | −1.35734 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 50.2163 | 3.07319 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6249 | 1.07461 | 0.537304 | − | 0.843389i | \(-0.319443\pi\) | ||||
0.537304 | + | 0.843389i | \(0.319443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.9275 | −0.846038 | −0.423019 | − | 0.906121i | \(-0.639030\pi\) | ||||
−0.423019 | + | 0.906121i | \(0.639030\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.674899 | −0.0406979 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6415 | −1.84107 | −0.920534 | − | 0.390662i | \(-0.872246\pi\) | ||||
−0.920534 | + | 0.390662i | \(0.872246\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.3193 | 0.797405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.0208 | −1.49261 | −0.746307 | − | 0.665602i | \(-0.768175\pi\) | ||||
−0.746307 | + | 0.665602i | \(0.768175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1751 | −0.604848 | −0.302424 | − | 0.953173i | \(-0.597796\pi\) | ||||
−0.302424 | + | 0.953173i | \(0.597796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.86449 | −0.406617 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7482 | −0.985188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.14062 | −0.359969 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.222616 | 0.0130054 | 0.00650269 | − | 0.999979i | \(-0.497930\pi\) | ||||
0.00650269 | + | 0.999979i | \(0.497930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8436 | −1.03889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −50.5437 | −2.93284 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.70503 | −0.387762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.4512 | −1.17489 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.02468 | −0.287713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3870 | 1.04940 | 0.524702 | − | 0.851286i | \(-0.324177\pi\) | ||||
0.524702 | + | 0.851286i | \(0.324177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.6740 | −1.34677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.88655 | −0.220386 | −0.110193 | − | 0.993910i | \(-0.535147\pi\) | ||||
−0.110193 | + | 0.993910i | \(0.535147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9972 | 1.13031 | 0.565153 | − | 0.824986i | \(-0.308817\pi\) | ||||
0.565153 | + | 0.824986i | \(0.308817\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.7799 | 0.886289 | 0.443145 | − | 0.896450i | \(-0.353863\pi\) | ||||
0.443145 | + | 0.896450i | \(0.353863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.66157 | −0.205008 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −43.5997 | −2.43350 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.501805 | 0.0279212 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.239686 | −0.0132954 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8283 | −0.930605 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9796 | −0.713426 | −0.356713 | − | 0.934214i | \(-0.616103\pi\) | ||||
−0.356713 | + | 0.934214i | \(0.616103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −69.2134 | −3.79287 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.24404 | −0.122605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.777311 | 0.0423428 | 0.0211714 | − | 0.999776i | \(-0.493260\pi\) | ||||
0.0211714 | + | 0.999776i | \(0.493260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.5195 | 1.06016 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.61323 | 0.466433 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.7960 | −1.60416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.44512 | 0.507041 | 0.253520 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253520 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7146 | 0.734124 | 0.367062 | − | 0.930197i | \(-0.380364\pi\) | ||||
0.367062 | + | 0.930197i | \(0.380364\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.9503 | −0.958116 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1481 | −1.12560 | −0.562800 | − | 0.826593i | \(-0.690276\pi\) | ||||
−0.562800 | + | 0.826593i | \(0.690276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.5973 | −1.83624 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.0313 | 1.74333 | 0.871663 | − | 0.490105i | \(-0.163042\pi\) | ||||
0.871663 | + | 0.490105i | \(0.163042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.6961 | −1.29621 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.10525 | 0.214878 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.13804 | 0.268203 | 0.134102 | − | 0.990968i | \(-0.457185\pi\) | ||||
0.134102 | + | 0.990968i | \(0.457185\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.4032 | −1.89508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7740 | 0.609637 | 0.304818 | − | 0.952411i | \(-0.401404\pi\) | ||||
0.304818 | + | 0.952411i | \(0.401404\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −35.3876 | −1.82741 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.30038 | −0.0669732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.74286 | −0.500457 | −0.250229 | − | 0.968187i | \(-0.580506\pi\) | ||||
−0.250229 | + | 0.968187i | \(0.580506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.94472 | 0.458252 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.06400 | −0.360954 | −0.180477 | − | 0.983579i | \(-0.557764\pi\) | ||||
−0.180477 | + | 0.983579i | \(0.557764\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 48.4783 | 2.46429 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.8735 | 1.97096 | 0.985482 | − | 0.169780i | \(-0.0543058\pi\) | ||||
0.985482 | + | 0.169780i | \(0.0543058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17813 | 0.110153 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.1697 | −2.42984 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.55419 | 0.380092 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.128974 | −0.00647300 | −0.00323650 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323650 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8905 | 1.19304 | 0.596519 | − | 0.802599i | \(-0.296550\pi\) | ||||
0.596519 | + | 0.802599i | \(0.296550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.05894 | 0.152377 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.3537 | −1.75674 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.7585 | −2.21859 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2603 | 0.804019 | 0.402010 | − | 0.915635i | \(-0.368312\pi\) | ||||
0.402010 | + | 0.915635i | \(0.368312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.45568 | 0.269109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.9458 | 1.66633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −61.6638 | −3.01969 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.4603 | −1.63464 | −0.817321 | − | 0.576183i | \(-0.804542\pi\) | ||||
−0.817321 | + | 0.576183i | \(0.804542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.51777 | 0.171446 | 0.0857228 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857228 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −42.2586 | −2.05468 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0778622 | 0.00377687 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.9540 | −1.01167 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.3251 | 1.79789 | 0.898944 | − | 0.438063i | \(-0.144335\pi\) | ||||
0.898944 | + | 0.438063i | \(0.144335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.8020 | −1.91276 | −0.956381 | − | 0.292122i | \(-0.905639\pi\) | ||||
−0.956381 | + | 0.292122i | \(0.905639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.77868 | −0.277067 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.34060 | 0.207639 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.08123 | 0.147059 | 0.0735295 | − | 0.997293i | \(-0.476574\pi\) | ||||
0.0735295 | + | 0.997293i | \(0.476574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.09741 | −0.147162 | −0.0735811 | − | 0.997289i | \(-0.523443\pi\) | ||||
−0.0735811 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.4418 | 1.68010 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.12273 | −0.0531031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.0834 | −1.04218 | −0.521090 | − | 0.853502i | \(-0.674474\pi\) | ||||
−0.521090 | + | 0.853502i | \(0.674474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.5410 | −1.10850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 34.9657 | 1.64283 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.7201 | −1.48380 | −0.741901 | − | 0.670509i | \(-0.766076\pi\) | ||||
−0.741901 | + | 0.670509i | \(0.766076\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.83116 | 0.272175 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.0976 | −1.58808 | −0.794042 | − | 0.607862i | \(-0.792027\pi\) | ||||
−0.794042 | + | 0.607862i | \(0.792027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.2606 | −0.476849 | −0.238425 | − | 0.971161i | \(-0.576631\pi\) | ||||
−0.238425 | + | 0.971161i | \(0.576631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.5934 | 0.630378 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.8661 | 1.24322 | 0.621608 | − | 0.783329i | \(-0.286480\pi\) | ||||
0.621608 | + | 0.783329i | \(0.286480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.4164 | 1.72406 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.3496 | 1.44146 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.155164 | 0.00711943 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 67.5201 | 3.09153 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.9824 | 1.87253 | 0.936266 | − | 0.351292i | \(-0.114257\pi\) | ||||
0.936266 | + | 0.351292i | \(0.114257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8957 | −0.724782 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.33394 | −0.196794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4823 | −1.15471 | −0.577357 | − | 0.816492i | \(-0.695916\pi\) | ||||
−0.577357 | + | 0.816492i | \(0.695916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 62.3635 | 2.82017 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2626 | −0.643662 | −0.321831 | − | 0.946797i | \(-0.604298\pi\) | ||||
−0.321831 | + | 0.946797i | \(0.604298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.422431 | 0.0190253 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −64.3943 | −2.89431 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5353 | −1.41171 | −0.705857 | − | 0.708354i | \(-0.749438\pi\) | ||||
−0.705857 | + | 0.708354i | \(0.749438\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.1308 | −2.37371 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.55492 | −0.203094 | −0.101547 | − | 0.994831i | \(-0.532379\pi\) | ||||
−0.101547 | + | 0.994831i | \(0.532379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.4341 | −0.642310 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.1010 | 1.47007 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.3362 | −1.34463 | −0.672315 | − | 0.740265i | \(-0.734700\pi\) | ||||
−0.672315 | + | 0.740265i | \(0.734700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.6204 | 0.513052 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.7087 | −0.736272 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.3275 | −1.20186 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.3011 | −1.94460 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7954 | −0.604389 | −0.302194 | − | 0.953246i | \(-0.597719\pi\) | ||||
−0.302194 | + | 0.953246i | \(0.597719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.4907 | −0.502453 | −0.251226 | − | 0.967928i | \(-0.580834\pi\) | ||||
−0.251226 | + | 0.967928i | \(0.580834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.993698 | −0.0432862 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.15922 | −0.180836 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54.5260 | 2.36623 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.36045 | −0.362131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.7719 | −1.33039 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.12055 | 0.134662 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.98566 | 0.300337 | 0.150168 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150168 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.3190 | 0.485746 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8771 | −0.508759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.85429 | 0.293068 | 0.146534 | − | 0.989206i | \(-0.453188\pi\) | ||||
0.146534 | + | 0.989206i | \(0.453188\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3543 | 0.655307 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.841822 | 0.0358628 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −70.6377 | −2.99840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.5860 | −1.16885 | −0.584427 | − | 0.811446i | \(-0.698681\pi\) | ||||
−0.584427 | + | 0.811446i | \(0.698681\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1336 | 0.470903 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.80692 | 0.287388 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.1433 | −1.05967 | −0.529833 | − | 0.848102i | \(-0.677745\pi\) | ||||
−0.529833 | + | 0.848102i | \(0.677745\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7766 | 0.579584 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.67717 | −0.196077 | −0.0980386 | − | 0.995183i | \(-0.531257\pi\) | ||||
−0.0980386 | + | 0.995183i | \(0.531257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.3339 | −1.77162 | −0.885810 | − | 0.464048i | \(-0.846397\pi\) | ||||
−0.885810 | + | 0.464048i | \(0.846397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 63.3776 | 2.64764 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.673506 | 0.0280871 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.41497 | 0.391950 | 0.195975 | − | 0.980609i | \(-0.437213\pi\) | ||||
0.195975 | + | 0.980609i | \(0.437213\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.0047 | −1.66254 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.6635 | 1.80836 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.8693 | −0.945528 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.8912 | 1.60521 | 0.802605 | − | 0.596511i | \(-0.203447\pi\) | ||||
0.802605 | + | 0.596511i | \(0.203447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.98025 | −0.0815947 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.4322 | 2.15677 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.4540 | −1.00421 | −0.502103 | − | 0.864808i | \(-0.667440\pi\) | ||||
−0.502103 | + | 0.864808i | \(0.667440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.7040 | 1.37941 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.1789 | −1.39651 | −0.698256 | − | 0.715848i | \(-0.746040\pi\) | ||||
−0.698256 | + | 0.715848i | \(0.746040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.6474 | 1.69883 | 0.849416 | − | 0.527723i | \(-0.176954\pi\) | ||||
0.849416 | + | 0.527723i | \(0.176954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.85730 | 0.279251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.4300 | −0.708632 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.4909 | 0.425813 | 0.212907 | − | 0.977073i | \(-0.431707\pi\) | ||||
0.212907 | + | 0.977073i | \(0.431707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.70522 | −0.392631 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.6237 | 1.11571 | 0.557856 | − | 0.829938i | \(-0.311624\pi\) | ||||
0.557856 | + | 0.829938i | \(0.311624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −37.1524 | −1.49813 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.1542 | −1.57629 | −0.788145 | − | 0.615490i | \(-0.788958\pi\) | ||||
−0.788145 | + | 0.615490i | \(0.788958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.2527 | −0.492479 | −0.246240 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246240 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 50.4393 | 2.02406 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2001 | −0.968004 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.5649 | 0.541728 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.16373 | 0.205891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.41216 | −0.0562171 | −0.0281086 | − | 0.999605i | \(-0.508948\pi\) | ||||
−0.0281086 | + | 0.999605i | \(0.508948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.52953 | −0.339018 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.31303 | 0.250525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 105.722 | 4.18229 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3286 | −0.447455 | −0.223727 | − | 0.974652i | \(-0.571823\pi\) | ||||
−0.223727 | + | 0.974652i | \(0.571823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.3850 | −1.11939 | −0.559697 | − | 0.828698i | \(-0.689082\pi\) | ||||
−0.559697 | + | 0.828698i | \(0.689082\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.4760 | 1.94811 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.50503 | 0.255739 | 0.127869 | − | 0.991791i | \(-0.459186\pi\) | ||||
0.127869 | + | 0.991791i | \(0.459186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.2605 | 1.38410 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7378 | 1.08546 | 0.542732 | − | 0.839906i | \(-0.317390\pi\) | ||||
0.542732 | + | 0.839906i | \(0.317390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.9973 | −1.32838 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.5447 | −0.489416 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.46434 | −0.329724 | −0.164862 | − | 0.986317i | \(-0.552718\pi\) | ||||
−0.164862 | + | 0.986317i | \(0.552718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3620 | −0.480825 | −0.240413 | − | 0.970671i | \(-0.577283\pi\) | ||||
−0.240413 | + | 0.970671i | \(0.577283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.41744 | 0.0938855 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.65401 | 0.141484 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −77.8932 | −3.01153 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.92924 | 0.383314 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.2778 | 1.43696 | 0.718478 | − | 0.695550i | \(-0.244839\pi\) | ||||
0.718478 | + | 0.695550i | \(0.244839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.80307 | 0.0694001 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.98829 | −0.307015 | −0.153507 | − | 0.988147i | \(-0.549057\pi\) | ||||
−0.153507 | + | 0.988147i | \(0.549057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 69.7239 | 2.67183 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0709 | 0.538406 | 0.269203 | − | 0.963083i | \(-0.413240\pi\) | ||||
0.269203 | + | 0.963083i | \(0.413240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.85052 | 0.147121 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.08466 | 0.117687 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.5068 | 0.590763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.1189 | 1.52620 | 0.763098 | − | 0.646283i | \(-0.223678\pi\) | ||||
0.763098 | + | 0.646283i | \(0.223678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.5212 | −1.65085 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.71590 | 0.102872 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.4564 | 1.64367 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3588 | −1.18440 | −0.592202 | − | 0.805789i | \(-0.701741\pi\) | ||||
−0.592202 | + | 0.805789i | \(0.701741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2903 | 0.388106 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −43.1283 | −1.62430 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7701 | −0.704927 | −0.352463 | − | 0.935826i | \(-0.614656\pi\) | ||||
−0.352463 | + | 0.935826i | \(0.614656\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.0839 | −0.865715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.59546 | −0.321902 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7890 | −0.553076 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −84.2902 | −3.14788 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.68396 | 0.286563 | 0.143282 | − | 0.989682i | \(-0.454235\pi\) | ||||
0.143282 | + | 0.989682i | \(0.454235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.9394 | 0.444032 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.130621 | 0.00485113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4165 | −0.645940 | −0.322970 | − | 0.946409i | \(-0.604681\pi\) | ||||
−0.322970 | + | 0.946409i | \(0.604681\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.687103 | −0.0254482 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.61677 | −0.133771 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9404 | 0.884259 | 0.442129 | − | 0.896951i | \(-0.354223\pi\) | ||||
0.442129 | + | 0.896951i | \(0.354223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.43443 | 0.163345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.36626 | 0.0870443 | 0.0435222 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435222 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.81748 | 0.176975 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.4020 | −1.22540 | −0.612701 | − | 0.790315i | \(-0.709917\pi\) | ||||
−0.612701 | + | 0.790315i | \(0.709917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.792400 | −0.0290313 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −103.731 | −3.79531 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6008 | −0.934187 | −0.467093 | − | 0.884208i | \(-0.654699\pi\) | ||||
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.4581 | −1.69303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.6782 | 0.898131 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5879 | −0.530206 | −0.265103 | − | 0.964220i | \(-0.585406\pi\) | ||||
−0.265103 | + | 0.964220i | \(0.585406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 58.8796 | 2.13719 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.2613 | −1.35072 | −0.675360 | − | 0.737488i | \(-0.736012\pi\) | ||||
−0.675360 | + | 0.737488i | \(0.736012\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.42910 | 0.268600 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5226 | 0.452164 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0987 | 1.15751 | 0.578754 | − | 0.815502i | \(-0.303539\pi\) | ||||
0.578754 | + | 0.815502i | \(0.303539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 93.7673 | 3.37695 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.277139 | −0.00996798 | −0.00498399 | − | 0.999988i | \(-0.501586\pi\) | ||||
−0.00498399 | + | 0.999988i | \(0.501586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.307264 | −0.0110372 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.41225 | 0.193914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 68.3675 | 2.44638 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.78229 | 0.349590 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.4078 | 0.942536 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.9949 | −1.56825 | −0.784125 | − | 0.620603i | \(-0.786888\pi\) | ||||
−0.784125 | + | 0.620603i | \(0.786888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.48402 | 0.159635 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.52631 | 0.125223 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 68.9096 | 2.44397 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0980 | 0.357691 | 0.178846 | − | 0.983877i | \(-0.442764\pi\) | ||||
0.178846 | + | 0.983877i | \(0.442764\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.15274 | 0.111536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −108.302 | −3.82667 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.11234 | −0.286278 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.9661 | −1.93490 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.53900 | −0.0892663 | −0.0446332 | − | 0.999003i | \(-0.514212\pi\) | ||||
−0.0446332 | + | 0.999003i | \(0.514212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5896 | −1.28483 | −0.642417 | − | 0.766355i | \(-0.722068\pi\) | ||||
−0.642417 | + | 0.766355i | \(0.722068\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.4353 | 1.52334 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.0150 | 1.54178 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.20752 | −0.252159 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1081 | 1.12058 | 0.560291 | − | 0.828296i | \(-0.310689\pi\) | ||||
0.560291 | + | 0.828296i | \(0.310689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.43495 | −0.0848769 | −0.0424385 | − | 0.999099i | \(-0.513513\pi\) | ||||
−0.0424385 | + | 0.999099i | \(0.513513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.10478 | 0.0732791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3568 | 0.568782 | 0.284391 | − | 0.958708i | \(-0.408209\pi\) | ||||
0.284391 | + | 0.958708i | \(0.408209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.1942 | −0.666641 | −0.333320 | − | 0.942814i | \(-0.608169\pi\) | ||||
−0.333320 | + | 0.942814i | \(0.608169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 95.5606 | 3.31496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.4987 | −1.29770 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.0112 | −0.795384 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.4871 | 1.95015 | 0.975075 | − | 0.221875i | \(-0.0712178\pi\) | ||||
0.975075 | + | 0.221875i | \(0.0712178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2913 | −0.975563 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 78.0314 | 2.68755 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.3621 | 0.803680 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.7328 | 1.08907 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.6661 | 1.53113 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3163 | −1.03801 | −0.519004 | − | 0.854772i | \(-0.673697\pi\) | ||||
−0.519004 | + | 0.854772i | \(0.673697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.8047 | 0.506312 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.5463 | −1.65831 | −0.829155 | − | 0.559018i | \(-0.811178\pi\) | ||||
−0.829155 | + | 0.559018i | \(0.811178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.60363 | −0.122954 | −0.0614772 | − | 0.998108i | \(-0.519581\pi\) | ||||
−0.0614772 | + | 0.998108i | \(0.519581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.8163 | 0.436272 | 0.218136 | − | 0.975918i | \(-0.430002\pi\) | ||||
0.218136 | + | 0.975918i | \(0.430002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.2669 | −1.06311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 52.2320 | 1.77389 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9278 | −0.506390 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.57486 | 0.0533622 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2436 | 0.448227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.0967 | −0.644849 | −0.322424 | − | 0.946595i | \(-0.604498\pi\) | ||||
−0.322424 | + | 0.946595i | \(0.604498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.694265 | −0.0234170 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.01077 | −0.0340538 | −0.0170269 | − | 0.999855i | \(-0.505420\pi\) | ||||
−0.0170269 | + | 0.999855i | \(0.505420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.4066 | −1.49440 | −0.747201 | − | 0.664598i | \(-0.768603\pi\) | ||||
−0.747201 | + | 0.664598i | \(0.768603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 55.6481 | 1.87059 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.2738 | 1.21795 | 0.608977 | − | 0.793188i | \(-0.291580\pi\) | ||||
0.608977 | + | 0.793188i | \(0.291580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 69.8621 | 2.34047 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.28281 | 0.210246 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.20243 | 0.0736191 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.9107 | 0.698190 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.66702 | −0.0555981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.03740 | −0.167820 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.98877 | 0.265556 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.4622 | 1.40993 | 0.704967 | − | 0.709240i | \(-0.250962\pi\) | ||||
0.704967 | + | 0.709240i | \(0.250962\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.1075 | 1.46295 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2424 | −1.39955 | −0.699777 | − | 0.714361i | \(-0.746717\pi\) | ||||
−0.699777 | + | 0.714361i | \(0.746717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.0799 | −2.22002 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.6703 | 0.518044 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5501 | −0.974769 | −0.487385 | − | 0.873187i | \(-0.662049\pi\) | ||||
−0.487385 | + | 0.873187i | \(0.662049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57.3430 | −1.88952 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.2803 | 0.799196 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.59669 | 0.0524988 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 51.0580 | 1.67697 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.71420 | −0.0890500 | −0.0445250 | − | 0.999008i | \(-0.514177\pi\) | ||||
−0.0445250 | + | 0.999008i | \(0.514177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1208 | 0.396819 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.80420 | 0.157114 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.9699 | −1.37110 | −0.685548 | − | 0.728027i | \(-0.740438\pi\) | ||||
−0.685548 | + | 0.728027i | \(0.740438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.3644 | −2.03519 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.6164 | −0.541680 | −0.270840 | − | 0.962624i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4924 | 0.765018 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.6824 | −0.769575 | −0.384788 | − | 0.923005i | \(-0.625725\pi\) | ||||
−0.384788 | + | 0.923005i | \(0.625725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.88105 | −0.0935229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.2123 | −1.59582 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.2096 | 1.69124 | 0.845618 | − | 0.533789i | \(-0.179232\pi\) | ||||
0.845618 | + | 0.533789i | \(0.179232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.7308 | 1.44745 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.4192 | 0.369130 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0786 | −0.873504 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 94.0321 | 3.03014 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.2346 | −0.908905 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.9479 | −1.54190 | −0.770951 | − | 0.636894i | \(-0.780219\pi\) | ||||
−0.770951 | + | 0.636894i | \(0.780219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.56496 | −0.0502738 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.9180 | 0.350375 | 0.175188 | − | 0.984535i | \(-0.443947\pi\) | ||||
0.175188 | + | 0.984535i | \(0.443947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.747502 | 0.0239392 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.3984 | 0.684596 | 0.342298 | − | 0.939592i | \(-0.388795\pi\) | ||||
0.342298 | + | 0.939592i | \(0.388795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70.0362 | −2.23837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.2938 | 1.15877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.57428 | −0.273477 | −0.136739 | − | 0.990607i | \(-0.543662\pi\) | ||||
−0.136739 | + | 0.990607i | \(0.543662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.0057 | 1.17910 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31.2849 | −0.994803 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5165 | −1.60471 | −0.802355 | − | 0.596847i | \(-0.796420\pi\) | ||||
−0.802355 | + | 0.596847i | \(0.796420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.4792 | 1.28457 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.7877 | 0.754120 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.5524 | −0.809253 | −0.404627 | − | 0.914482i | \(-0.632599\pi\) | ||||
−0.404627 | + | 0.914482i | \(0.632599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 119.577 | 3.78326 |
(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 | 7448.2.a.bo.1.1 | ✓ | 7 | |
7.6 | odd | 2 | 7448.2.a.bp.1.7 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7448.2.a.bo.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
7448.2.a.bp.1.7 | yes | 7 | 7.6 | odd | 2 |