Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.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: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.1 |
$q$-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 | ||||||||
\(3\) | 1.23607 | 0.713644 | 0.356822 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356822 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47214 | −0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.47214 | −1.95142 | −0.975711 | − | 0.219061i | \(-0.929701\pi\) | ||||
−0.975711 | + | 0.219061i | \(0.929701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.763932 | 0.211877 | 0.105938 | − | 0.994373i | \(-0.466215\pi\) | ||||
0.105938 | + | 0.994373i | \(0.466215\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.23607 | 0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.52786 | −1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.00000 | −1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23607 | 0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.944272 | 0.151205 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.47214 | −1.32313 | −0.661563 | − | 0.749890i | \(-0.730106\pi\) | ||||
−0.661563 | + | 0.749890i | \(0.730106\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.76393 | −0.710165 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4721 | 1.52752 | 0.763759 | − | 0.645501i | \(-0.223352\pi\) | ||||
0.763759 | + | 0.645501i | \(0.223352\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.52786 | 0.774056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.9443 | −2.82413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.52786 | −0.202371 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.23607 | −1.20243 | −0.601217 | − | 0.799086i | \(-0.705317\pi\) | ||||
−0.601217 | + | 0.799086i | \(0.705317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2361 | 1.43863 | 0.719316 | − | 0.694683i | \(-0.244456\pi\) | ||||
0.719316 | + | 0.694683i | \(0.244456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.47214 | −0.185472 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.47214 | 0.306631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.94427 | 0.595220 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94427 | −0.586777 | −0.293389 | − | 0.955993i | \(-0.594783\pi\) | ||||
−0.293389 | + | 0.955993i | \(0.594783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94427 | −0.344601 | −0.172300 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172300 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.76393 | 0.781032 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.23607 | −1.01379 | −0.506895 | − | 0.862008i | \(-0.669207\pi\) | ||||
−0.506895 | + | 0.862008i | \(0.669207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4721 | 1.56972 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.52786 | −0.592649 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.763932 | 0.0800818 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.05573 | −0.316864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4721 | 1.26635 | 0.633177 | − | 0.774007i | \(-0.281751\pi\) | ||||
0.633177 | + | 0.774007i | \(0.281751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.52786 | 0.957586 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.70820 | −0.169973 | −0.0849863 | − | 0.996382i | \(-0.527085\pi\) | ||||
−0.0849863 | + | 0.996382i | \(0.527085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.52786 | −0.544677 | −0.272338 | − | 0.962202i | \(-0.587797\pi\) | ||||
−0.272338 | + | 0.962202i | \(0.587797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.94427 | 0.864675 | 0.432338 | − | 0.901712i | \(-0.357689\pi\) | ||||
0.432338 | + | 0.901712i | \(0.357689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.47214 | 0.811483 | 0.405742 | − | 0.913988i | \(-0.367013\pi\) | ||||
0.405742 | + | 0.913988i | \(0.367013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.52786 | −0.524682 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.4721 | −1.17328 | −0.586640 | − | 0.809848i | \(-0.699550\pi\) | ||||
−0.586640 | + | 0.809848i | \(0.699550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9443 | 1.20706 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12461 | −0.103970 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.47214 | 0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8885 | 2.80805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.4721 | −0.944241 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94427 | 0.793676 | 0.396838 | − | 0.917889i | \(-0.370108\pi\) | ||||
0.396838 | + | 0.917889i | \(0.370108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7082 | 1.02295 | 0.511475 | − | 0.859298i | \(-0.329099\pi\) | ||||
0.511475 | + | 0.859298i | \(0.329099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.23607 | −0.107181 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.8885 | −1.53960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.9443 | 1.27678 | 0.638388 | − | 0.769715i | \(-0.279602\pi\) | ||||
0.638388 | + | 0.769715i | \(0.279602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.23607 | 0.104842 | 0.0524210 | − | 0.998625i | \(-0.483306\pi\) | ||||
0.0524210 | + | 0.998625i | \(0.483306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.94427 | −0.413461 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4721 | −1.20185 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.23607 | 0.101949 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.94427 | 0.241204 | 0.120602 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120602 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.58359 | −0.532252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.763932 | 0.0609684 | 0.0304842 | − | 0.999535i | \(-0.490295\pi\) | ||||
0.0304842 | + | 0.999535i | \(0.490295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.3607 | −0.980266 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.41641 | −0.267594 | −0.133797 | − | 0.991009i | \(-0.542717\pi\) | ||||
−0.133797 | + | 0.991009i | \(0.542717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.8885 | −2.01542 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.4164 | 1.81202 | 0.906008 | − | 0.423261i | \(-0.139114\pi\) | ||||
0.906008 | + | 0.423261i | \(0.139114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4164 | −0.955108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.81966 | 0.139153 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.70820 | 0.433987 | 0.216993 | − | 0.976173i | \(-0.430375\pi\) | ||||
0.216993 | + | 0.976173i | \(0.430375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.47214 | 0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.4164 | −0.858110 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.05573 | −0.527370 | −0.263685 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263685 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1803 | −0.905358 | −0.452679 | − | 0.891674i | \(-0.649532\pi\) | ||||
−0.452679 | + | 0.891674i | \(0.649532\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8885 | 1.02667 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.4721 | −1.06401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.9443 | −2.11661 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.52786 | −0.402093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.94427 | 0.357755 | 0.178877 | − | 0.983871i | \(-0.442753\pi\) | ||||
0.178877 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.472136 | 0.0339851 | 0.0169925 | − | 0.999856i | \(-0.494591\pi\) | ||||
0.0169925 | + | 0.999856i | \(0.494591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.05573 | 0.218825 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9443 | 0.779747 | 0.389874 | − | 0.920868i | \(-0.372519\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4164 | 1.09284 | 0.546420 | − | 0.837511i | \(-0.315990\pi\) | ||||
0.546420 | + | 0.837511i | \(0.315990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.94427 | 0.348742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.47214 | −0.313882 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.4164 | −1.91484 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.88854 | −0.409282 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.11146 | −0.418750 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.9443 | 1.42839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.47214 | −0.167820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.63932 | −0.245922 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.41641 | 0.229812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9443 | 0.866813 | 0.433406 | − | 0.901199i | \(-0.357312\pi\) | ||||
0.433406 | + | 0.901199i | \(0.357312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.05573 | −0.537049 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.2361 | −1.14400 | −0.571999 | − | 0.820254i | \(-0.693832\pi\) | ||||
−0.571999 | + | 0.820254i | \(0.693832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.5967 | 1.55932 | 0.779658 | − | 0.626205i | \(-0.215393\pi\) | ||||
0.779658 | + | 0.626205i | \(0.215393\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8885 | −1.04089 | −0.520447 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520447 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.8885 | 2.21064 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8885 | −0.898375 | −0.449188 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449188 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4721 | 0.803401 | 0.401700 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401700 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5967 | 0.872232 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.23607 | 0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.944272 | −0.0600826 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.4164 | −0.723485 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.29180 | 0.270896 | 0.135448 | − | 0.990784i | \(-0.456753\pi\) | ||||
0.135448 | + | 0.990784i | \(0.456753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.8885 | −1.62760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.8885 | 1.12022 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.47214 | −0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.58359 | 0.407514 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0557 | 0.681725 | 0.340863 | − | 0.940113i | \(-0.389281\pi\) | ||||
0.340863 | + | 0.940113i | \(0.389281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.3607 | −1.98790 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.41641 | −0.453877 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.18034 | −0.254880 | −0.127440 | − | 0.991846i | \(-0.540676\pi\) | ||||
−0.127440 | + | 0.991846i | \(0.540676\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.944272 | 0.0571499 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −35.4164 | −2.13569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.88854 | 0.473977 | 0.236988 | − | 0.971512i | \(-0.423840\pi\) | ||||
0.236988 | + | 0.971512i | \(0.423840\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.63932 | 0.217880 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.18034 | −0.367383 | −0.183692 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183692 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.94427 | −0.292873 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.47214 | −0.500094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4164 | 0.903726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7639 | −0.745677 | −0.372838 | − | 0.927896i | \(-0.621615\pi\) | ||||
−0.372838 | + | 0.927896i | \(0.621615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.8885 | −1.74018 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.7771 | 2.07600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.05573 | 0.176717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.47214 | 0.373048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.11146 | −0.121300 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.3607 | 2.08201 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.81966 | 0.103853 | 0.0519267 | − | 0.998651i | \(-0.483464\pi\) | ||||
0.0519267 | + | 0.998651i | \(0.483464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.83282 | −0.388705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.47214 | −0.478873 | −0.239437 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239437 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.76393 | −0.268417 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.05573 | 0.508620 | 0.254310 | − | 0.967123i | \(-0.418152\pi\) | ||||
0.254310 | + | 0.967123i | \(0.418152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.9443 | 1.62057 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0557 | 0.617071 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52786 | −0.307579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.18034 | 0.231884 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.4721 | 0.579110 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4721 | 0.577348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.4721 | 1.23518 | 0.617590 | − | 0.786500i | \(-0.288109\pi\) | ||||
0.617590 | + | 0.786500i | \(0.288109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.58359 | 0.360779 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9443 | 0.707221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3607 | 0.564382 | 0.282191 | − | 0.959358i | \(-0.408939\pi\) | ||||
0.282191 | + | 0.959358i | \(0.408939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.4164 | −0.837304 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0000 | 0.861411 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.47214 | 0.347442 | 0.173721 | − | 0.984795i | \(-0.444421\pi\) | ||||
0.173721 | + | 0.984795i | \(0.444421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6525 | 1.42667 | 0.713337 | − | 0.700821i | \(-0.247183\pi\) | ||||
0.713337 | + | 0.700821i | \(0.247183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.22291 | −0.225402 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8885 | −0.845662 | −0.422831 | − | 0.906209i | \(-0.638964\pi\) | ||||
−0.422831 | + | 0.906209i | \(0.638964\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | −0.849192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.52786 | 0.292566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.9443 | −0.894284 | −0.447142 | − | 0.894463i | \(-0.647558\pi\) | ||||
−0.447142 | + | 0.894463i | \(0.647558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 38.1803 | 2.00395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.52786 | −0.498711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.8328 | −1.19186 | −0.595932 | − | 0.803035i | \(-0.703217\pi\) | ||||
−0.595932 | + | 0.803035i | \(0.703217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.4721 | 0.649273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0000 | −0.519174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.94427 | 0.152449 | 0.0762243 | − | 0.997091i | \(-0.475713\pi\) | ||||
0.0762243 | + | 0.997091i | \(0.475713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.88854 | 0.0975240 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.41641 | −0.175954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.58359 | −0.235443 | −0.117722 | − | 0.993047i | \(-0.537559\pi\) | ||||
−0.117722 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0557 | 0.566402 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4164 | −0.787742 | −0.393871 | − | 0.919166i | \(-0.628864\pi\) | ||||
−0.393871 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.9443 | −1.06742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.52786 | −0.484329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.47214 | −0.226746 | −0.113373 | − | 0.993552i | \(-0.536166\pi\) | ||||
−0.113373 | + | 0.993552i | \(0.536166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8885 | 0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.4721 | 0.730023 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.8885 | 2.10764 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.2361 | −0.764676 | −0.382338 | − | 0.924022i | \(-0.624881\pi\) | ||||
−0.382338 | + | 0.924022i | \(0.624881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.52786 | −0.0764889 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.5279 | −1.17493 | −0.587463 | − | 0.809251i | \(-0.699873\pi\) | ||||
−0.587463 | + | 0.809251i | \(0.699873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.88854 | −0.0940751 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.81966 | −0.388562 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.9443 | 1.43471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.4164 | −1.05897 | −0.529487 | − | 0.848318i | \(-0.677615\pi\) | ||||
−0.529487 | + | 0.848318i | \(0.677615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.4721 | 0.911163 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.23607 | −0.454477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.8885 | −1.46717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.52786 | 0.0748198 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1803 | 1.08358 | 0.541790 | − | 0.840514i | \(-0.317747\pi\) | ||||
0.541790 | + | 0.840514i | \(0.317747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.4164 | −0.749571 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.4721 | 1.18707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2361 | 0.543751 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.11146 | −0.295064 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0000 | −1.34871 | −0.674356 | − | 0.738406i | \(-0.735579\pi\) | ||||
−0.674356 | + | 0.738406i | \(0.735579\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.41641 | 0.452524 | 0.226262 | − | 0.974067i | \(-0.427349\pi\) | ||||
0.226262 | + | 0.974067i | \(0.427349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.8885 | −0.857690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.94427 | −0.236517 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.8885 | −0.659865 | −0.329932 | − | 0.944005i | \(-0.607026\pi\) | ||||
−0.329932 | + | 0.944005i | \(0.607026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4164 | −0.920426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.63932 | 0.172134 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.88854 | −0.372283 | −0.186142 | − | 0.982523i | \(-0.559598\pi\) | ||||
−0.186142 | + | 0.982523i | \(0.559598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.8328 | 2.58198 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.0557 | −0.519443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.47214 | 0.115896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.52786 | −0.352139 | −0.176069 | − | 0.984378i | \(-0.556338\pi\) | ||||
−0.176069 | + | 0.984378i | \(0.556338\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.7214 | −1.15389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7082 | 1.01105 | 0.505526 | − | 0.862811i | \(-0.331298\pi\) | ||||
0.505526 | + | 0.862811i | \(0.331298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.7771 | −1.66270 | −0.831351 | − | 0.555748i | \(-0.812432\pi\) | ||||
−0.831351 | + | 0.555748i | \(0.812432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.88854 | −0.458570 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.0689 | −1.48397 | −0.741985 | − | 0.670416i | \(-0.766116\pi\) | ||||
−0.741985 | + | 0.670416i | \(0.766116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.944272 | 0.0435098 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.8885 | −1.92604 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.76393 | −0.310350 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.7214 | 0.674045 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.58359 | −0.392194 | −0.196097 | − | 0.980584i | \(-0.562827\pi\) | ||||
−0.196097 | + | 0.980584i | \(0.562827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.41641 | −0.155775 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.94427 | 0.224972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.3607 | 1.83268 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.22291 | −0.190967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.8885 | 1.70989 | 0.854943 | − | 0.518722i | \(-0.173592\pi\) | ||||
0.854943 | + | 0.518722i | \(0.173592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | −0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.8328 | 1.38583 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.94427 | −0.221781 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.8885 | 0.979866 | 0.489933 | − | 0.871760i | \(-0.337021\pi\) | ||||
0.489933 | + | 0.871760i | \(0.337021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.9443 | 1.29313 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.94427 | −0.220454 | −0.110227 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110227 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.52786 | −0.245987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3475 | −0.681607 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.1246 | −1.82282 | −0.911408 | − | 0.411503i | \(-0.865004\pi\) | ||||
−0.911408 | + | 0.411503i | \(0.865004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.94427 | −0.130247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.83282 | 0.301676 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8885 | −0.788263 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −67.7771 | −2.98083 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.05573 | 0.309712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.58359 | −0.288432 | −0.144216 | − | 0.989546i | \(-0.546066\pi\) | ||||
−0.144216 | + | 0.989546i | \(0.546066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.29180 | −0.187667 | −0.0938336 | − | 0.995588i | \(-0.529912\pi\) | ||||
−0.0938336 | + | 0.995588i | \(0.529912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.76393 | 0.295202 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.0557 | −0.481595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.5967 | 0.590049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.47214 | −0.280339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.9443 | 1.25137 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.72136 | −0.376354 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.47214 | −0.278775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.05573 | −0.217363 | −0.108681 | − | 0.994077i | \(-0.534663\pi\) | ||||
−0.108681 | + | 0.994077i | \(0.534663\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0557 | −0.646103 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.4164 | 1.17439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.58359 | −0.195980 | −0.0979901 | − | 0.995187i | \(-0.531241\pi\) | ||||
−0.0979901 | + | 0.995187i | \(0.531241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.5410 | −0.705954 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.52786 | 0.235495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.8885 | −0.759326 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.05573 | 0.383704 | 0.191852 | − | 0.981424i | \(-0.438551\pi\) | ||||
0.191852 | + | 0.981424i | \(0.438551\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.94427 | 0.209120 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.7771 | −1.51051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.8197 | −0.751009 | −0.375505 | − | 0.926821i | \(-0.622531\pi\) | ||||
−0.375505 | + | 0.926821i | \(0.622531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.3607 | −1.69799 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.41641 | −0.101480 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3607 | 1.10510 | 0.552549 | − | 0.833481i | \(-0.313655\pi\) | ||||
0.552549 | + | 0.833481i | \(0.313655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.4721 | −0.605640 | −0.302820 | − | 0.953048i | \(-0.597928\pi\) | ||||
−0.302820 | + | 0.953048i | \(0.597928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.11146 | 0.255310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.8885 | 0.912815 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.583592 | 0.0242533 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.23607 | −0.383177 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 64.7214 | 2.68048 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.63932 | −0.150467 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.70820 | −0.153054 | −0.0765270 | − | 0.997068i | \(-0.524383\pi\) | ||||
−0.0765270 | + | 0.997068i | \(0.524383\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.05573 | 0.125909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5279 | 0.556462 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8328 | 1.34828 | 0.674141 | − | 0.738603i | \(-0.264514\pi\) | ||||
0.674141 | + | 0.738603i | \(0.264514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.4721 | 0.593300 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.0557 | 0.779899 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8885 | 0.730906 | 0.365453 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365453 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7771 | 1.21463 | 0.607316 | − | 0.794460i | \(-0.292246\pi\) | ||||
0.607316 | + | 0.794460i | \(0.292246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.88854 | −0.239800 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 99.9574 | 4.06385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.88854 | 0.401364 | 0.200682 | − | 0.979656i | \(-0.435684\pi\) | ||||
0.200682 | + | 0.979656i | \(0.435684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.52786 | −0.224000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.4164 | 1.18812 | 0.594059 | − | 0.804422i | \(-0.297525\pi\) | ||||
0.594059 | + | 0.804422i | \(0.297525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.8885 | −1.36652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3607 | 1.38331 | 0.691654 | − | 0.722229i | \(-0.256882\pi\) | ||||
0.691654 | + | 0.722229i | \(0.256882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.0689 | −1.93205 | −0.966026 | − | 0.258446i | \(-0.916790\pi\) | ||||
−0.966026 | + | 0.258446i | \(0.916790\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.1115 | −0.887302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.88854 | 0.394910 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9443 | −1.78920 | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.8328 | −0.589551 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.9443 | 1.14862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.763932 | 0.0302681 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.27864 | 0.287939 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5836 | 0.576017 | 0.288009 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288009 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.7082 | −1.72368 | −0.861842 | − | 0.507177i | \(-0.830689\pi\) | ||||
−0.861842 | + | 0.507177i | \(0.830689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.8885 | 1.01936 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.3607 | −0.800461 | −0.400230 | − | 0.916415i | \(-0.631070\pi\) | ||||
−0.400230 | + | 0.916415i | \(0.631070\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 59.7771 | 2.34646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.05573 | −0.119763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.41641 | −0.368493 | −0.184246 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184246 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.8885 | 1.48043 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.33437 | 0.169100 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.3050 | 1.45319 | 0.726597 | − | 0.687064i | \(-0.241101\pi\) | ||||
0.726597 | + | 0.687064i | \(0.241101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6525 | −0.881079 | −0.440540 | − | 0.897733i | \(-0.645213\pi\) | ||||
−0.440540 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.22291 | 0.164004 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | −0.155113 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.8885 | −0.692647 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.7214 | −2.80738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.94427 | −0.113493 | −0.0567467 | − | 0.998389i | \(-0.518073\pi\) | ||||
−0.0567467 | + | 0.998389i | \(0.518073\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.2492 | −1.16429 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.8197 | 0.761731 | 0.380866 | − | 0.924630i | \(-0.375626\pi\) | ||||
0.380866 | + | 0.924630i | \(0.375626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.4721 | 0.478637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.3050 | −0.816408 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7771 | 0.909805 | 0.454902 | − | 0.890541i | \(-0.349674\pi\) | ||||
0.454902 | + | 0.890541i | \(0.349674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.3607 | 1.84777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.1672 | 1.11280 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.63932 | −0.291035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1803 | −0.539446 | −0.269723 | − | 0.962938i | \(-0.586932\pi\) | ||||
−0.269723 | + | 0.962938i | \(0.586932\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.52786 | 0.361934 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.8885 | −1.43513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.6393 | −0.742827 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.4164 | −1.56428 | −0.782138 | − | 0.623105i | \(-0.785871\pi\) | ||||
−0.782138 | + | 0.623105i | \(0.785871\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.52786 | 0.208487 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 41.8885 | 1.57761 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.70820 | −0.0642436 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.63932 | 0.0615660 | 0.0307830 | − | 0.999526i | \(-0.490200\pi\) | ||||
0.0307830 | + | 0.999526i | \(0.490200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.0557 | −0.714646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.88854 | −0.370329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.1672 | −0.641120 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.1935 | 1.90920 | 0.954598 | − | 0.297898i | \(-0.0962856\pi\) | ||||
0.954598 | + | 0.297898i | \(0.0962856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.52786 | −0.205868 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.4164 | 0.573342 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.4721 | −0.908872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3607 | 0.458432 | 0.229216 | − | 0.973376i | \(-0.426384\pi\) | ||||
0.229216 | + | 0.973376i | \(0.426384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.9443 | 1.07054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.76393 | −0.175960 | −0.0879799 | − | 0.996122i | \(-0.528041\pi\) | ||||
−0.0879799 | + | 0.996122i | \(0.528041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.00000 | 0.147542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.8885 | −0.953617 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.41641 | −0.125675 | −0.0628373 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628373 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.16718 | −0.0428776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9443 | 0.915117 | 0.457558 | − | 0.889180i | \(-0.348724\pi\) | ||||
0.457558 | + | 0.889180i | \(0.348724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.52786 | 0.349074 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5967 | 0.497479 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94427 | 0.326817 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.0000 | 1.31366 | 0.656829 | − | 0.754039i | \(-0.271897\pi\) | ||||
0.656829 | + | 0.754039i | \(0.271897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.30495 | 0.193323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.9443 | −1.05339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3050 | 1.42856 | 0.714281 | − | 0.699859i | \(-0.246754\pi\) | ||||
0.714281 | + | 0.699859i | \(0.246754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.0000 | −1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.52786 | −0.127885 | −0.0639425 | − | 0.997954i | \(-0.520367\pi\) | ||||
−0.0639425 | + | 0.997954i | \(0.520367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.47214 | 0.306712 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.3050 | −0.770282 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.05573 | −0.254768 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.3607 | −0.662103 | −0.331052 | − | 0.943613i | \(-0.607403\pi\) | ||||
−0.331052 | + | 0.943613i | \(0.607403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3050 | −0.623223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.1803 | 1.44519 | 0.722593 | − | 0.691274i | \(-0.242950\pi\) | ||||
0.722593 | + | 0.691274i | \(0.242950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.5279 | −0.485935 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.52786 | −0.198311 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.4721 | 0.375203 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.7214 | 0.883469 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.47214 | 0.0882343 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2918 | −0.438155 | −0.219078 | − | 0.975707i | \(-0.570305\pi\) | ||||
−0.219078 | + | 0.975707i | \(0.570305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.6656 | 0.486509 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.4721 | −0.443458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.58359 | 0.304812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −40.0000 | −1.41865 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.1803 | −1.84832 | −0.924161 | − | 0.382003i | \(-0.875235\pi\) | ||||
−0.924161 | + | 0.382003i | \(0.875235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.8328 | 1.65683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.83282 | 0.312092 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.0557 | 0.672462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.9443 | 0.456226 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.16718 | −0.181894 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.4164 | −0.612328 | −0.306164 | − | 0.951979i | \(-0.599046\pi\) | ||||
−0.306164 | + | 0.951979i | \(0.599046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.0132 | −1.86154 | −0.930772 | − | 0.365601i | \(-0.880864\pi\) | ||||
−0.930772 | + | 0.365601i | \(0.880864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.6656 | −1.04042 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0557 | −0.387265 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.12461 | −0.0392971 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.11146 | 0.143491 | 0.0717454 | − | 0.997423i | \(-0.477143\pi\) | ||||
0.0717454 | + | 0.997423i | \(0.477143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7771 | −0.689386 | −0.344693 | − | 0.938715i | \(-0.612017\pi\) | ||||
−0.344693 | + | 0.938715i | \(0.612017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −43.7771 | −1.52412 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0557 | 0.523539 | 0.261769 | − | 0.965130i | \(-0.415694\pi\) | ||||
0.261769 | + | 0.965130i | \(0.415694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.2361 | 0.390245 | 0.195122 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195122 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.75078 | 0.338251 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.47214 | 0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 75.7771 | 2.62237 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.6656 | 0.472353 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.5279 | −0.743224 | −0.371612 | − | 0.928388i | \(-0.621195\pi\) | ||||
−0.371612 | + | 0.928388i | \(0.621195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.1378 | 1.10688 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.1803 | −1.38225 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.8885 | 1.06134 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.63932 | −0.262181 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.8885 | −0.613211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7082 | 0.469360 | 0.234680 | − | 0.972073i | \(-0.424596\pi\) | ||||
0.234680 | + | 0.972073i | \(0.424596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.88854 | 0.201384 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5279 | −0.940334 | −0.470167 | − | 0.882577i | \(-0.655806\pi\) | ||||
−0.470167 | + | 0.882577i | \(0.655806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8197 | −1.15391 | −0.576956 | − | 0.816775i | \(-0.695760\pi\) | ||||
−0.576956 | + | 0.816775i | \(0.695760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4721 | −0.356889 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.9443 | −0.712951 | −0.356476 | − | 0.934305i | \(-0.616022\pi\) | ||||
−0.356476 | + | 0.934305i | \(0.616022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.4721 | 0.628071 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.70820 | 0.125937 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −83.7771 | −2.84194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.05573 | 0.103539 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.3607 | −0.621415 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.52786 | 0.0516512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4164 | 0.453040 | 0.226520 | − | 0.974007i | \(-0.427265\pi\) | ||||
0.226520 | + | 0.974007i | \(0.427265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7771 | −0.532148 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8328 | 0.836639 | 0.418319 | − | 0.908300i | \(-0.362619\pi\) | ||||
0.418319 | + | 0.908300i | \(0.362619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0557 | 0.775887 | 0.387944 | − | 0.921683i | \(-0.373186\pi\) | ||||
0.387944 | + | 0.921683i | \(0.373186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.9443 | −1.24187 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.3050 | −1.11827 | −0.559135 | − | 0.829076i | \(-0.688867\pi\) | ||||
−0.559135 | + | 0.829076i | \(0.688867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.94427 | 0.299981 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.6393 | 0.523937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.9443 | −0.433164 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.8328 | −0.763217 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.77709 | 0.126113 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.7214 | −1.48988 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.4164 | −1.31025 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.944272 | 0.0313540 | 0.0156770 | − | 0.999877i | \(-0.495010\pi\) | ||||
0.0156770 | + | 0.999877i | \(0.495010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.51471 | 0.0834076 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.8328 | −1.15406 | −0.577031 | − | 0.816722i | \(-0.695789\pi\) | ||||
−0.577031 | + | 0.816722i | \(0.695789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.7771 | 1.97833 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.9443 | 1.48581 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.7082 | 0.386639 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.7771 | −1.18018 | −0.590089 | − | 0.807338i | \(-0.700907\pi\) | ||||
−0.590089 | + | 0.807338i | \(0.700907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.24922 | 0.0741144 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.77709 | −0.124324 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4721 | −0.804639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.13777 | 0.267279 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.3050 | −1.55203 | −0.776013 | − | 0.630717i | \(-0.782761\pi\) | ||||
−0.776013 | + | 0.630717i | \(0.782761\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.23607 | −0.0405105 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.88854 | 0.323736 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −93.6656 | −3.06319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.05573 | −0.295838 | −0.147919 | − | 0.988999i | \(-0.547257\pi\) | ||||
−0.147919 | + | 0.988999i | \(0.547257\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.4721 | −0.341745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.5967 | −1.16042 | −0.580210 | − | 0.814467i | \(-0.697030\pi\) | ||||
−0.580210 | + | 0.814467i | \(0.697030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.8885 | −1.10356 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.8885 | −0.581914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.58359 | −0.148947 | −0.0744734 | − | 0.997223i | \(-0.523728\pi\) | ||||
−0.0744734 | + | 0.997223i | \(0.523728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.24922 | −0.0730129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1935 | 0.362974 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8885 | 1.68083 | 0.840417 | − | 0.541940i | \(-0.182310\pi\) | ||||
0.840417 | + | 0.541940i | \(0.182310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0000 | 0.517748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.7771 | 1.15651 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.9443 | 0.482576 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1672 | −0.424307 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.52786 | 0.0491837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8885 | 0.961151 | 0.480575 | − | 0.876953i | \(-0.340428\pi\) | ||||
0.480575 | + | 0.876953i | \(0.340428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.83282 | −0.219502 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7639 | 0.730529 | 0.365265 | − | 0.930904i | \(-0.380978\pi\) | ||||
0.365265 | + | 0.930904i | \(0.380978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.23607 | 0.0396265 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.16718 | 0.165482 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.8328 | −0.410558 | −0.205279 | − | 0.978703i | \(-0.565810\pi\) | ||||
−0.205279 | + | 0.978703i | \(0.565810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.8328 | 1.24110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.4721 | −0.398205 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.52786 | −0.176311 | −0.0881557 | − | 0.996107i | \(-0.528097\pi\) | ||||
−0.0881557 | + | 0.996107i | \(0.528097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.4164 | 1.12846 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.9443 | 0.412021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.8885 | 0.823208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.7771 | 0.881479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.8885 | 1.58157 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0689 | 0.572247 | 0.286124 | − | 0.958193i | \(-0.407633\pi\) | ||||
0.286124 | + | 0.958193i | \(0.407633\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.7214 | 0.782149 |
(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 | 224.2.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2016.2.a.r.1.1 | 2 | |||
4.3 | odd | 2 | 224.2.a.d.1.1 | yes | 2 | ||
5.4 | even | 2 | 5600.2.a.bk.1.1 | 2 | |||
7.2 | even | 3 | 1568.2.i.v.1537.1 | 4 | |||
7.3 | odd | 6 | 1568.2.i.n.961.2 | 4 | |||
7.4 | even | 3 | 1568.2.i.v.961.1 | 4 | |||
7.5 | odd | 6 | 1568.2.i.n.1537.2 | 4 | |||
7.6 | odd | 2 | 1568.2.a.v.1.1 | 2 | |||
8.3 | odd | 2 | 448.2.a.i.1.2 | 2 | |||
8.5 | even | 2 | 448.2.a.j.1.1 | 2 | |||
12.11 | even | 2 | 2016.2.a.o.1.1 | 2 | |||
16.3 | odd | 4 | 1792.2.b.m.897.2 | 4 | |||
16.5 | even | 4 | 1792.2.b.k.897.2 | 4 | |||
16.11 | odd | 4 | 1792.2.b.m.897.3 | 4 | |||
16.13 | even | 4 | 1792.2.b.k.897.3 | 4 | |||
20.19 | odd | 2 | 5600.2.a.z.1.2 | 2 | |||
24.5 | odd | 2 | 4032.2.a.bw.1.2 | 2 | |||
24.11 | even | 2 | 4032.2.a.bv.1.2 | 2 | |||
28.3 | even | 6 | 1568.2.i.w.961.1 | 4 | |||
28.11 | odd | 6 | 1568.2.i.m.961.2 | 4 | |||
28.19 | even | 6 | 1568.2.i.w.1537.1 | 4 | |||
28.23 | odd | 6 | 1568.2.i.m.1537.2 | 4 | |||
28.27 | even | 2 | 1568.2.a.k.1.2 | 2 | |||
56.13 | odd | 2 | 3136.2.a.bf.1.2 | 2 | |||
56.27 | even | 2 | 3136.2.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
224.2.a.d.1.1 | yes | 2 | 4.3 | odd | 2 | ||
448.2.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
448.2.a.j.1.1 | 2 | 8.5 | even | 2 | |||
1568.2.a.k.1.2 | 2 | 28.27 | even | 2 | |||
1568.2.a.v.1.1 | 2 | 7.6 | odd | 2 | |||
1568.2.i.m.961.2 | 4 | 28.11 | odd | 6 | |||
1568.2.i.m.1537.2 | 4 | 28.23 | odd | 6 | |||
1568.2.i.n.961.2 | 4 | 7.3 | odd | 6 | |||
1568.2.i.n.1537.2 | 4 | 7.5 | odd | 6 | |||
1568.2.i.v.961.1 | 4 | 7.4 | even | 3 | |||
1568.2.i.v.1537.1 | 4 | 7.2 | even | 3 | |||
1568.2.i.w.961.1 | 4 | 28.3 | even | 6 | |||
1568.2.i.w.1537.1 | 4 | 28.19 | even | 6 | |||
1792.2.b.k.897.2 | 4 | 16.5 | even | 4 | |||
1792.2.b.k.897.3 | 4 | 16.13 | even | 4 | |||
1792.2.b.m.897.2 | 4 | 16.3 | odd | 4 | |||
1792.2.b.m.897.3 | 4 | 16.11 | odd | 4 | |||
2016.2.a.o.1.1 | 2 | 12.11 | even | 2 | |||
2016.2.a.r.1.1 | 2 | 3.2 | odd | 2 | |||
3136.2.a.bf.1.2 | 2 | 56.13 | odd | 2 | |||
3136.2.a.by.1.1 | 2 | 56.27 | even | 2 | |||
4032.2.a.bv.1.2 | 2 | 24.11 | even | 2 | |||
4032.2.a.bw.1.2 | 2 | 24.5 | odd | 2 | |||
5600.2.a.z.1.2 | 2 | 20.19 | odd | 2 | |||
5600.2.a.bk.1.1 | 2 | 5.4 | even | 2 |