Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7168,2,Mod(1,7168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7168, 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("7168.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.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: | \(57.2367681689\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 24x^{10} + 221x^{8} - 968x^{6} + 2008x^{4} - 1640x^{2} + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 112) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.75510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7168.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.90620 | −1.67790 | −0.838949 | − | 0.544210i | \(-0.816829\pi\) | ||||
−0.838949 | + | 0.544210i | \(0.816829\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.85750 | −1.72513 | −0.862563 | − | 0.505950i | \(-0.831142\pi\) | ||||
−0.862563 | + | 0.505950i | \(0.831142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.44602 | 1.81534 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30053 | 0.392125 | 0.196063 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196063 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59251 | 0.441682 | 0.220841 | − | 0.975310i | \(-0.429120\pi\) | ||||
0.220841 | + | 0.975310i | \(0.429120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.2107 | 2.89458 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50885 | 0.365950 | 0.182975 | − | 0.983118i | \(-0.441427\pi\) | ||||
0.182975 | + | 0.983118i | \(0.441427\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.06859 | −0.474567 | −0.237283 | − | 0.971440i | \(-0.576257\pi\) | ||||
−0.237283 | + | 0.971440i | \(0.576257\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.90620 | −0.634186 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.77031 | 0.994677 | 0.497339 | − | 0.867556i | \(-0.334311\pi\) | ||||
0.497339 | + | 0.867556i | \(0.334311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.88030 | 1.97606 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.10863 | −1.36806 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.79924 | 1.07689 | 0.538446 | − | 0.842660i | \(-0.319011\pi\) | ||||
0.538446 | + | 0.842660i | \(0.319011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.10999 | 0.738176 | 0.369088 | − | 0.929394i | \(-0.379670\pi\) | ||||
0.369088 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.77961 | −0.657946 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.85750 | −0.652036 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.34005 | 0.384702 | 0.192351 | − | 0.981326i | \(-0.438389\pi\) | ||||
0.192351 | + | 0.981326i | \(0.438389\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.62815 | −0.741097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.45533 | 1.16433 | 0.582163 | − | 0.813072i | \(-0.302206\pi\) | ||||
0.582163 | + | 0.813072i | \(0.302206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.04676 | 1.22712 | 0.613560 | − | 0.789648i | \(-0.289737\pi\) | ||||
0.613560 | + | 0.789648i | \(0.289737\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21.0080 | −3.13169 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.59748 | −0.524747 | −0.262373 | − | 0.964966i | \(-0.584505\pi\) | ||||
−0.262373 | + | 0.964966i | \(0.584505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.38503 | −0.614027 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.955604 | −0.131262 | −0.0656312 | − | 0.997844i | \(-0.520906\pi\) | ||||
−0.0656312 | + | 0.997844i | \(0.520906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.01680 | −0.676466 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.01174 | 0.796275 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.60998 | −0.209601 | −0.104801 | − | 0.994493i | \(-0.533420\pi\) | ||||
−0.104801 | + | 0.994493i | \(0.533420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55209 | −0.582835 | −0.291418 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291418 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.44602 | 0.686134 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.14310 | −0.761957 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.15866 | −0.263722 | −0.131861 | − | 0.991268i | \(-0.542095\pi\) | ||||
−0.131861 | + | 0.991268i | \(0.542095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.8635 | −1.66897 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8202 | −1.64016 | −0.820079 | − | 0.572251i | \(-0.806070\pi\) | ||||
−0.820079 | + | 0.572251i | \(0.806070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4749 | −1.69416 | −0.847078 | − | 0.531468i | \(-0.821641\pi\) | ||||
−0.847078 | + | 0.531468i | \(0.821641\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −28.7142 | −3.31563 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.30053 | 0.148209 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.77961 | 0.200222 | 0.100111 | − | 0.994976i | \(-0.468080\pi\) | ||||
0.100111 | + | 0.994976i | \(0.468080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.32107 | 0.480119 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1276 | 1.11165 | 0.555827 | − | 0.831298i | \(-0.312402\pi\) | ||||
0.555827 | + | 0.831298i | \(0.312402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.82039 | −0.631310 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.8538 | −1.80692 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.45899 | 0.896651 | 0.448325 | − | 0.893870i | \(-0.352021\pi\) | ||||
0.448325 | + | 0.893870i | \(0.352021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59251 | 0.166940 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.9445 | −1.23858 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.97958 | 0.818688 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2227 | 1.64717 | 0.823585 | − | 0.567194i | \(-0.191971\pi\) | ||||
0.823585 | + | 0.567194i | \(0.191971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.08273 | 0.711841 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.3574 | 1.62762 | 0.813812 | − | 0.581128i | \(-0.197388\pi\) | ||||
0.813812 | + | 0.581128i | \(0.197388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1875 | −1.69354 | −0.846768 | − | 0.531963i | \(-0.821455\pi\) | ||||
−0.846768 | + | 0.531963i | \(0.821455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.2107 | 1.09405 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.80030 | 0.560736 | 0.280368 | − | 0.959893i | \(-0.409543\pi\) | ||||
0.280368 | + | 0.959893i | \(0.409543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.62944 | 0.443420 | 0.221710 | − | 0.975113i | \(-0.428836\pi\) | ||||
0.221710 | + | 0.975113i | \(0.428836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.80066 | −0.645490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.17193 | 0.862822 | 0.431411 | − | 0.902155i | \(-0.358016\pi\) | ||||
0.431411 | + | 0.902155i | \(0.358016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.4014 | −1.71594 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.67283 | 0.801803 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50885 | 0.138316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.30861 | −0.846238 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.6667 | −1.95362 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.8257 | −1.68383 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9787 | −1.15167 | −0.575835 | − | 0.817566i | \(-0.695323\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.3855 | −2.05898 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.64445 | −0.842639 | −0.421320 | − | 0.906912i | \(-0.638433\pi\) | ||||
−0.421320 | + | 0.906912i | \(0.638433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.06859 | −0.179369 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.4215 | 2.36007 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.6543 | 1.93548 | 0.967742 | − | 0.251943i | \(-0.0810694\pi\) | ||||
0.967742 | + | 0.251943i | \(0.0810694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.40067 | −0.797355 | −0.398677 | − | 0.917091i | \(-0.630531\pi\) | ||||
−0.398677 | + | 0.917091i | \(0.630531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4550 | 0.880471 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.07111 | 0.173195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.3706 | −1.85778 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.90620 | −0.239700 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9889 | 0.900243 | 0.450122 | − | 0.892967i | \(-0.351381\pi\) | ||||
0.450122 | + | 0.892967i | \(0.351381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.46829 | −0.445004 | −0.222502 | − | 0.974932i | \(-0.571422\pi\) | ||||
−0.222502 | + | 0.974932i | \(0.571422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.21724 | 0.664324 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.8543 | −1.27345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.94395 | −0.633996 | −0.316998 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.316998 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.77718 | 0.220245 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.77031 | 0.375953 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.93440 | −0.699796 | −0.349898 | − | 0.936788i | \(-0.613784\pi\) | ||||
−0.349898 | + | 0.936788i | \(0.613784\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.5799 | 1.13504 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.8175 | −0.914463 | −0.457231 | − | 0.889348i | \(-0.651159\pi\) | ||||
−0.457231 | + | 0.889348i | \(0.651159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4639 | −0.804917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2656 | −0.861500 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.97416 | −0.606264 | −0.303132 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303132 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.88030 | 0.746880 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.67893 | 0.351690 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.5856 | −1.23966 | −0.619832 | − | 0.784734i | \(-0.712799\pi\) | ||||
−0.619832 | + | 0.784734i | \(0.712799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.91953 | −0.439995 | −0.219998 | − | 0.975500i | \(-0.570605\pi\) | ||||
−0.219998 | + | 0.975500i | \(0.570605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2293 | 0.977937 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.02674 | −0.663659 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.96231 | 0.143498 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.10863 | −0.517077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3676 | 0.894891 | 0.447445 | − | 0.894311i | \(-0.352334\pi\) | ||||
0.447445 | + | 0.894311i | \(0.352334\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.6837 | 1.70479 | 0.852395 | − | 0.522898i | \(-0.175149\pi\) | ||||
0.852395 | + | 0.522898i | \(0.175149\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.8531 | 1.27849 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1496 | 1.15061 | 0.575306 | − | 0.817938i | \(-0.304883\pi\) | ||||
0.575306 | + | 0.817938i | \(0.304883\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.49683 | 0.389660 | 0.194830 | − | 0.980837i | \(-0.437585\pi\) | ||||
0.194830 | + | 0.980837i | \(0.437585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.27351 | 0.442499 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.79924 | 0.407027 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.7589 | −2.00861 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.9792 | 1.80568 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.69027 | −0.186090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.28393 | −0.0883893 | −0.0441946 | − | 0.999023i | \(-0.514072\pi\) | ||||
−0.0441946 | + | 0.999023i | \(0.514072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.1644 | 2.75202 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.0404 | −2.11694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.10999 | 0.279004 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.0669 | 2.84262 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.40286 | 0.161634 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.20318 | −0.214501 | −0.107250 | − | 0.994232i | \(-0.534205\pi\) | ||||
−0.107250 | + | 0.994232i | \(0.534205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 53.8083 | 3.58722 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.5064 | −1.29468 | −0.647342 | − | 0.762200i | \(-0.724119\pi\) | ||||
−0.647342 | + | 0.762200i | \(0.724119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.93029 | −0.656212 | −0.328106 | − | 0.944641i | \(-0.606410\pi\) | ||||
−0.328106 | + | 0.944641i | \(0.606410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.77961 | −0.248680 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.93857 | −0.192512 | −0.0962561 | − | 0.995357i | \(-0.530687\pi\) | ||||
−0.0962561 | + | 0.995357i | \(0.530687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8773 | 0.905254 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.17192 | −0.335952 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2109 | −1.04859 | −0.524297 | − | 0.851536i | \(-0.675672\pi\) | ||||
−0.524297 | + | 0.851536i | \(0.675672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1166 | 0.909329 | 0.454665 | − | 0.890663i | \(-0.349759\pi\) | ||||
0.454665 | + | 0.890663i | \(0.349759\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.76798 | 0.562466 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.85750 | −0.246447 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.29424 | −0.209608 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.4330 | −1.86524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0772 | 1.26726 | 0.633632 | − | 0.773635i | \(-0.281563\pi\) | ||||
0.633632 | + | 0.773635i | \(0.281563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.20394 | 0.390038 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.9153 | 1.05927 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.23679 | −0.201905 | −0.100953 | − | 0.994891i | \(-0.532189\pi\) | ||||
−0.100953 | + | 0.994891i | \(0.532189\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.34005 | 0.145404 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.5828 | 1.95493 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.0161 | 1.48090 | 0.740448 | − | 0.672114i | \(-0.234614\pi\) | ||||
0.740448 | + | 0.672114i | \(0.234614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.68624 | 0.226444 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.5835 | −1.50449 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.123749 | 0.00754513 | 0.00377257 | − | 0.999993i | \(-0.498799\pi\) | ||||
0.00377257 | + | 0.999993i | \(0.498799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1138 | 0.614372 | 0.307186 | − | 0.951650i | \(-0.400613\pi\) | ||||
0.307186 | + | 0.951650i | \(0.400613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.62815 | −0.280109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.8497 | 0.774863 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5677 | −0.935370 | −0.467685 | − | 0.883895i | \(-0.654912\pi\) | ||||
−0.467685 | + | 0.883895i | \(0.654912\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.3831 | 1.34004 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.21999 | −0.251743 | −0.125872 | − | 0.992047i | \(-0.540173\pi\) | ||||
−0.125872 | + | 0.992047i | \(0.540173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.4525 | 1.39410 | 0.697052 | − | 0.717020i | \(-0.254495\pi\) | ||||
0.697052 | + | 0.717020i | \(0.254495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.1903 | −1.37367 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.45533 | 0.440074 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7234 | −0.866080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −47.1466 | −2.76378 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.1261 | 1.11736 | 0.558680 | − | 0.829383i | \(-0.311308\pi\) | ||||
0.558680 | + | 0.829383i | \(0.311308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.21049 | 0.361589 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.24501 | −0.536450 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.59675 | 0.439331 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.04676 | 0.463808 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −47.5380 | −2.73099 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.5597 | 1.00546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6344 | 0.721085 | 0.360543 | − | 0.932743i | \(-0.382592\pi\) | ||||
0.360543 | + | 0.932743i | \(0.382592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 49.9504 | 2.84158 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.7737 | −1.12126 | −0.560631 | − | 0.828066i | \(-0.689442\pi\) | ||||
−0.560631 | + | 0.828066i | \(0.689442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.72743 | 0.493303 | 0.246652 | − | 0.969104i | \(-0.420670\pi\) | ||||
0.246652 | + | 0.969104i | \(0.420670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.0080 | −1.18367 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.8980 | 1.51074 | 0.755370 | − | 0.655298i | \(-0.227457\pi\) | ||||
0.755370 | + | 0.655298i | \(0.227457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.54211 | 0.422277 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8569 | −0.940858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.12119 | −0.173668 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.7345 | 0.872790 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.4541 | −0.744013 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.59748 | −0.198336 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5833 | 1.73597 | 0.867987 | − | 0.496586i | \(-0.165413\pi\) | ||||
0.867987 | + | 0.496586i | \(0.165413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7440 | 0.698365 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.32703 | 0.454954 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.4825 | 1.27918 | 0.639588 | − | 0.768718i | \(-0.279105\pi\) | ||||
0.639588 | + | 0.768718i | \(0.279105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.6555 | −1.44773 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.34518 | 0.289458 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 53.4784 | 2.87918 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.90552 | 0.478074 | 0.239037 | − | 0.971011i | \(-0.423168\pi\) | ||||
0.239037 | + | 0.971011i | \(0.423168\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.81511 | 0.525391 | 0.262695 | − | 0.964879i | \(-0.415389\pi\) | ||||
0.262695 | + | 0.964879i | \(0.415389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3206 | −0.604246 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0934 | 1.60171 | 0.800856 | − | 0.598857i | \(-0.204378\pi\) | ||||
0.800856 | + | 0.598857i | \(0.204378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 53.3115 | 2.82948 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.38503 | −0.232080 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3716 | 0.547394 | 0.273697 | − | 0.961816i | \(-0.411754\pi\) | ||||
0.273697 | + | 0.961816i | \(0.411754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7209 | −0.774786 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.0527 | 1.41990 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 55.8368 | 2.92263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.12973 | 0.424368 | 0.212184 | − | 0.977230i | \(-0.431942\pi\) | ||||
0.212184 | + | 0.977230i | \(0.431942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40.6019 | 2.11365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.955604 | −0.0496125 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.50693 | −0.233360 | −0.116680 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116680 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 54.7115 | 2.82529 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.23534 | 0.475644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.18664 | 0.0609535 | 0.0304767 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304767 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 37.7187 | 1.93239 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.3749 | −1.75647 | −0.878237 | − | 0.478225i | \(-0.841280\pi\) | ||||
−0.878237 | + | 0.478225i | \(0.841280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.01680 | −0.255680 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43.8228 | 2.22764 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.5044 | −0.786104 | −0.393052 | − | 0.919516i | \(-0.628581\pi\) | ||||
−0.393052 | + | 0.919516i | \(0.628581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.19768 | 0.364003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.0287 | 1.41386 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.86486 | −0.345408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3882 | −1.87646 | −0.938231 | − | 0.346009i | \(-0.887537\pi\) | ||||
−0.938231 | + | 0.346009i | \(0.887537\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.01174 | 0.300963 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.97625 | −0.248502 | −0.124251 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124251 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.54520 | 0.326039 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.6685 | −0.828266 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.04331 | 0.150851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06359 | 0.200932 | 0.100466 | − | 0.994941i | \(-0.467967\pi\) | ||||
0.100466 | + | 0.994941i | \(0.467967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −65.8379 | −3.24754 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.60998 | −0.0792219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.0674 | −1.91774 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.3203 | 1.33788 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.780982 | 0.0381535 | 0.0190767 | − | 0.999818i | \(-0.493927\pi\) | ||||
0.0190767 | + | 0.999818i | \(0.493927\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.34237 | 0.260371 | 0.130186 | − | 0.991490i | \(-0.458443\pi\) | ||||
0.130186 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.5920 | −0.952593 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.9079 | 0.723140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.55209 | −0.220291 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.01906 | −0.290603 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.18186 | −0.0569283 | −0.0284641 | − | 0.999595i | \(-0.509062\pi\) | ||||
−0.0284641 | + | 0.999595i | \(0.509062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.2584 | 0.733273 | 0.366637 | − | 0.930364i | \(-0.380509\pi\) | ||||
0.366637 | + | 0.930364i | \(0.380509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 65.0135 | 3.11716 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.86780 | −0.472041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.34502 | −0.207376 | −0.103688 | − | 0.994610i | \(-0.533064\pi\) | ||||
−0.103688 | + | 0.994610i | \(0.533064\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.44602 | 0.259334 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.10081 | 0.289858 | 0.144929 | − | 0.989442i | \(-0.453705\pi\) | ||||
0.144929 | + | 0.989442i | \(0.453705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.6305 | −1.54684 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.9359 | −1.51052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.72499 | 0.175793 | 0.0878967 | − | 0.996130i | \(-0.471985\pi\) | ||||
0.0878967 | + | 0.996130i | \(0.471985\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.69590 | 0.456562 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.8920 | 0.746670 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.14310 | −0.287993 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7451 | −0.502636 | −0.251318 | − | 0.967905i | \(-0.580864\pi\) | ||||
−0.251318 | + | 0.967905i | \(0.580864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.7259 | −0.500641 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.1551 | −0.519545 | −0.259772 | − | 0.965670i | \(-0.583648\pi\) | ||||
−0.259772 | + | 0.965670i | \(0.583648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.3485 | −1.27099 | −0.635496 | − | 0.772104i | \(-0.719204\pi\) | ||||
−0.635496 | + | 0.772104i | \(0.719204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 46.0758 | 2.13671 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.1100 | −0.745481 | −0.372740 | − | 0.927936i | \(-0.621582\pi\) | ||||
−0.372740 | + | 0.927936i | \(0.621582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.15866 | −0.0996777 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.0867 | 1.06378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.4651 | 0.481185 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.4383 | −0.937772 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.20424 | −0.238286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3880 | 0.520330 | 0.260165 | − | 0.965564i | \(-0.416223\pi\) | ||||
0.260165 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.72655 | 0.169916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8635 | −0.630810 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −62.5792 | −2.84157 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3531 | −1.42075 | −0.710373 | − | 0.703826i | \(-0.751474\pi\) | ||||
−0.710373 | + | 0.703826i | \(0.751474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.9652 | 1.17419 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6767 | 1.29416 | 0.647082 | − | 0.762421i | \(-0.275989\pi\) | ||||
0.647082 | + | 0.762421i | \(0.275989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.75020 | 0.394089 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.3216 | −1.22802 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.8202 | −0.619921 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1866 | 1.17227 | 0.586136 | − | 0.810213i | \(-0.300649\pi\) | ||||
0.586136 | + | 0.810213i | \(0.300649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.3440 | 1.53438 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.9854 | 1.42616 | 0.713080 | − | 0.701082i | \(-0.247299\pi\) | ||||
0.713080 | + | 0.701082i | \(0.247299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63.0987 | −2.80786 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.4103 | 1.35057 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2030 | 0.762511 | 0.381255 | − | 0.924470i | \(-0.375492\pi\) | ||||
0.381255 | + | 0.924470i | \(0.375492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4749 | −0.640331 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.7048 | 0.649234 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 66.3008 | 2.92156 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.67864 | −0.205766 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.1745 | 1.01725 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4322 | 1.50850 | 0.754251 | − | 0.656586i | \(-0.228000\pi\) | ||||
0.754251 | + | 0.656586i | \(0.228000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.7833 | −0.952516 | −0.476258 | − | 0.879306i | \(-0.658007\pi\) | ||||
−0.476258 | + | 0.879306i | \(0.658007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −28.7142 | −1.25319 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.20137 | 0.270136 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.244184 | −0.0106167 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.76798 | −0.380498 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.8727 | 0.514262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.3747 | −0.967341 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 48.2011 | 2.08003 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.30053 | 0.0560179 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5400 | −1.44200 | −0.720999 | − | 0.692936i | \(-0.756317\pi\) | ||||
−0.720999 | + | 0.692936i | \(0.756317\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.2034 | 0.738267 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.8581 | −0.764956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4310 | 1.68595 | 0.842973 | − | 0.537956i | \(-0.180803\pi\) | ||||
0.842973 | + | 0.537956i | \(0.180803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.7908 | −1.05804 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.9963 | −0.511058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.77961 | 0.0756769 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.2335 | 1.11355 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.390243 | −0.0165351 | −0.00826756 | − | 0.999966i | \(-0.502632\pi\) | ||||
−0.00826756 | + | 0.999966i | \(0.502632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8145 | 0.541997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.70288 | −0.240776 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.6449 | 0.827935 | 0.413967 | − | 0.910292i | \(-0.364143\pi\) | ||||
0.413967 | + | 0.910292i | \(0.364143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.3807 | −1.48848 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.32107 | 0.181468 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.08076 | −0.338763 | −0.169381 | − | 0.985551i | \(-0.554177\pi\) | ||||
−0.169381 | + | 0.985551i | \(0.554177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6889 | 0.447315 | 0.223657 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223657 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.9429 | −1.50153 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.1320 | 1.96554 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.95969 | 0.0815831 | 0.0407915 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407915 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −68.8297 | −2.86046 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.1276 | 0.420166 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.24279 | −0.0514713 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33.4554 | −1.38321 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.8082 | 1.43669 | 0.718343 | − | 0.695689i | \(-0.244901\pi\) | ||||
0.718343 | + | 0.695689i | \(0.244901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.50189 | −0.350314 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.9341 | −1.93061 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.5483 | −0.679558 | −0.339779 | − | 0.940505i | \(-0.610352\pi\) | ||||
−0.339779 | + | 0.940505i | \(0.610352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.82039 | −0.238613 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.9749 | −0.653809 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.2649 | −0.419412 | −0.209706 | − | 0.977764i | \(-0.567251\pi\) | ||||
−0.209706 | + | 0.977764i | \(0.567251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.6586 | 1.45455 | 0.727273 | − | 0.686348i | \(-0.240787\pi\) | ||||
0.727273 | + | 0.686348i | \(0.240787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7561 | −0.478746 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.9080 | 1.45987 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1111 | 0.938052 | 0.469026 | − | 0.883184i | \(-0.344605\pi\) | ||||
0.469026 | + | 0.883184i | \(0.344605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.8538 | −0.682950 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.72902 | −0.231771 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0706 | 1.53766 | 0.768829 | − | 0.639455i | \(-0.220840\pi\) | ||||
0.768829 | + | 0.639455i | \(0.220840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 83.5793 | 3.37024 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.9337 | −1.92974 | −0.964869 | − | 0.262732i | \(-0.915377\pi\) | ||||
−0.964869 | + | 0.262732i | \(0.915377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.72832 | 0.230240 | 0.115120 | − | 0.993352i | \(-0.463275\pi\) | ||||
0.115120 | + | 0.993352i | \(0.463275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.9103 | −1.36078 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.45899 | 0.338902 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2188 | 0.928752 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.81847 | 0.312239 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.53079 | 0.140782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.35784 | −0.0938640 | −0.0469320 | − | 0.998898i | \(-0.514944\pi\) | ||||
−0.0469320 | + | 0.998898i | \(0.514944\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.73136 | 0.148308 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.0652 | 1.98678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.59251 | 0.0630975 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −75.2652 | −2.97744 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.8415 | −1.96862 | −0.984311 | − | 0.176440i | \(-0.943542\pi\) | ||||
−0.984311 | + | 0.176440i | \(0.943542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.59806 | −0.339074 | −0.169537 | − | 0.985524i | \(-0.554227\pi\) | ||||
−0.169537 | + | 0.985524i | \(0.554227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 90.2097 | 3.55200 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.463264 | −0.0182128 | −0.00910640 | − | 0.999959i | \(-0.502899\pi\) | ||||
−0.00910640 | + | 0.999959i | \(0.502899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09383 | −0.0821901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9445 | −0.468141 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.38568 | −0.367290 | −0.183645 | − | 0.982993i | \(-0.558790\pi\) | ||||
−0.183645 | + | 0.982993i | \(0.558790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.2034 | 1.45366 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −78.8305 | −3.07547 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.54670 | 0.255023 | 0.127512 | − | 0.991837i | \(-0.459301\pi\) | ||||
0.127512 | + | 0.991837i | \(0.459301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.19204 | −0.124156 | −0.0620780 | − | 0.998071i | \(-0.519773\pi\) | ||||
−0.0620780 | + | 0.998071i | \(0.519773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.98320 | −0.271205 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.97958 | 0.309435 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.6642 | 1.07116 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.30910 | 0.359910 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.92014 | −0.228544 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.82222 | 0.262977 | 0.131489 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131489 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −70.2354 | −2.70336 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.75773 | −0.259721 | −0.129860 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129860 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.2227 | 0.622571 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 56.6895 | 2.17235 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.3991 | −1.58409 | −0.792046 | − | 0.610461i | \(-0.790984\pi\) | ||||
−0.792046 | + | 0.610461i | \(0.790984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −87.3888 | −3.33895 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.8594 | 1.10106 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.52181 | −0.0579762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.57700 | 0.250201 | 0.125100 | − | 0.992144i | \(-0.460075\pi\) | ||||
0.125100 | + | 0.992144i | \(0.460075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.08273 | 0.269051 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.2631 | 1.37554 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.2490 | 0.426086 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.54009 | 0.323016 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.67390 | −0.214300 | −0.107150 | − | 0.994243i | \(-0.534173\pi\) | ||||
−0.107150 | + | 0.994243i | \(0.534173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.84060 | −0.182567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −40.3302 | −1.51892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.3574 | 0.615184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.9282 | −1.91265 | −0.956325 | − | 0.292306i | \(-0.905578\pi\) | ||||
−0.956325 | + | 0.292306i | \(0.905578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.69181 | 0.363471 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.6059 | 0.734248 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.98930 | −0.298783 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.1121 | 1.75943 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.62249 | −0.284271 | −0.142135 | − | 0.989847i | \(-0.545397\pi\) | ||||
−0.142135 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.1875 | −0.640096 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.0257 | −1.52576 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57.2983 | 2.12800 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4856 | 0.945207 | 0.472604 | − | 0.881275i | \(-0.343314\pi\) | ||||
0.472604 | + | 0.881275i | \(0.343314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.4448 | −1.42388 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1414 | 0.449065 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1775 | −0.782210 | −0.391105 | − | 0.920346i | \(-0.627907\pi\) | ||||
−0.391105 | + | 0.920346i | \(0.627907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.2107 | 0.413512 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.80741 | −0.103412 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4538 | −0.642048 | −0.321024 | − | 0.947071i | \(-0.604027\pi\) | ||||
−0.321024 | + | 0.947071i | \(0.604027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.57374 | 0.351700 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6724 | 0.391531 | 0.195766 | − | 0.980651i | \(-0.437281\pi\) | ||||
0.195766 | + | 0.980651i | \(0.437281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.3896 | −1.55303 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 55.1554 | 2.01803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.80030 | 0.211938 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.82952 | 0.103251 | 0.0516254 | − | 0.998667i | \(-0.483560\pi\) | ||||
0.0516254 | + | 0.998667i | \(0.483560\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −58.3485 | −2.12634 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.0939 | 0.767687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1452 | 0.804881 | 0.402440 | − | 0.915446i | \(-0.368162\pi\) | ||||
0.402440 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0299 | −0.654444 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.79367 | 0.173770 | 0.0868852 | − | 0.996218i | \(-0.472309\pi\) | ||||
0.0868852 | + | 0.996218i | \(0.472309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.62944 | 0.167597 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.6980 | −1.14604 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.56390 | −0.0925772 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5489 | 0.488585 | 0.244293 | − | 0.969702i | \(-0.421444\pi\) | ||||
0.244293 | + | 0.969702i | \(0.421444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.40677 | 0.338777 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.5593 | −0.955273 | −0.477637 | − | 0.878558i | \(-0.658506\pi\) | ||||
−0.477637 | + | 0.878558i | \(0.658506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.6080 | 1.45868 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.80066 | −0.243972 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4220 | −0.552551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.9736 | −0.643148 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.2247 | −1.47325 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.6438 | 1.09372 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.6253 | −1.23426 | −0.617129 | − | 0.786862i | \(-0.711704\pi\) | ||||
−0.617129 | + | 0.786862i | \(0.711704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −69.7956 | −2.48479 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.17193 | 0.326116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.24923 | −0.257428 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7130 | −0.379950 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.9878 | −0.885113 | −0.442557 | − | 0.896741i | \(-0.645928\pi\) | ||||
−0.442557 | + | 0.896741i | \(0.645928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.42807 | −0.192031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 46.0678 | 1.62773 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.8251 | −0.664322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.4014 | −0.648566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.359641 | −0.0126600 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.99378 | 0.105256 | 0.0526278 | − | 0.998614i | \(-0.483240\pi\) | ||||
0.0526278 | + | 0.998614i | \(0.483240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.23328 | −0.113536 | −0.0567680 | − | 0.998387i | \(-0.518080\pi\) | ||||
−0.0567680 | + | 0.998387i | \(0.518080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3929 | −1.03085 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.4644 | 1.20724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.6454 | −0.582351 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.67283 | 0.303053 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.4948 | −1.41328 | −0.706639 | − | 0.707574i | \(-0.749790\pi\) | ||||
−0.706639 | + | 0.707574i | \(0.749790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.0492 | −1.43088 | −0.715442 | − | 0.698672i | \(-0.753775\pi\) | ||||
−0.715442 | + | 0.698672i | \(0.753775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −37.3437 | −1.30014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.8481 | 1.00315 | 0.501573 | − | 0.865116i | \(-0.332755\pi\) | ||||
0.501573 | + | 0.865116i | \(0.332755\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.1476 | −0.908144 | −0.454072 | − | 0.890965i | \(-0.650029\pi\) | ||||
−0.454072 | + | 0.890965i | \(0.650029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.2428 | 1.56945 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.50885 | 0.0522786 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.5859 | 1.57756 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.2164 | −1.00987 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.9862 | −1.44953 | −0.724763 | − | 0.688999i | \(-0.758051\pi\) | ||||
−0.724763 | + | 0.688999i | \(0.758051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.63123 | 0.159698 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.2641 | 0.422399 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.3646 | 1.38858 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.30861 | −0.319848 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −68.1577 | −2.33916 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1628 | 0.382654 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5345 | 0.531891 | 0.265945 | − | 0.963988i | \(-0.414316\pi\) | ||||
0.265945 | + | 0.963988i | \(0.414316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.4570 | 1.48620 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.3215 | 1.61647 | 0.808237 | − | 0.588858i | \(-0.200422\pi\) | ||||
0.808237 | + | 0.588858i | \(0.200422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.22844 | −0.246631 | −0.123316 | − | 0.992367i | \(-0.539353\pi\) | ||||
−0.123316 | + | 0.992367i | \(0.539353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.6667 | −0.738399 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.1105 | 0.344167 | 0.172084 | − | 0.985082i | \(-0.444950\pi\) | ||||
0.172084 | + | 0.985082i | \(0.444950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.7603 | 1.04588 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.7891 | 1.45319 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.31445 | 0.0785122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.43769 | −0.116482 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 88.3493 | 2.99017 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.8257 | −0.636426 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.8306 | 1.81773 | 0.908865 | − | 0.417089i | \(-0.136950\pi\) | ||||
0.908865 | + | 0.417089i | \(0.136950\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.5844 | −1.87482 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.5769 | 0.726946 | 0.363473 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363473 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.5046 | −1.02656 | −0.513281 | − | 0.858221i | \(-0.671570\pi\) | ||||
−0.513281 | + | 0.858221i | \(0.671570\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.0490 | −0.606709 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.7110 | −1.13191 | −0.565953 | − | 0.824437i | \(-0.691492\pi\) | ||||
−0.565953 | + | 0.824437i | \(0.691492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9787 | −0.435291 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.61970 | 0.188267 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.44171 | 0.249027 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.9788 | 2.13858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.0777 | −0.737153 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.8349 | 0.794937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.44186 | −0.0480355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.3855 | −0.778222 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.8346 | 0.759047 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.30668 | 0.0433876 | 0.0216938 | − | 0.999765i | \(-0.493094\pi\) | ||||
0.0216938 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 89.0829 | 2.95469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9873 | 0.993522 | 0.496761 | − | 0.867887i | \(-0.334523\pi\) | ||||
0.496761 | + | 0.867887i | \(0.334523\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1713 | 0.435908 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −51.0320 | −1.68707 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.64445 | −0.318488 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.0725 | −0.431220 | −0.215610 | − | 0.976480i | \(-0.569174\pi\) | ||||
−0.215610 | + | 0.976480i | \(0.569174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.7182 | −1.20991 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.0088 | −0.724428 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.1204 | 0.760194 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −93.6035 | −3.07434 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.7057 | −0.679333 | −0.339667 | − | 0.940546i | \(-0.610314\pi\) | ||||
−0.339667 | + | 0.940546i | \(0.610314\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06859 | −0.0677953 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57.4663 | 1.88136 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.56961 | −0.247553 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.93799 | −0.193986 | −0.0969929 | − | 0.995285i | \(-0.530922\pi\) | ||||
−0.0969929 | + | 0.995285i | \(0.530922\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3637 | −0.827712 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.7927 | 0.645223 | 0.322611 | − | 0.946532i | \(-0.395439\pi\) | ||||
0.322611 | + | 0.946532i | \(0.395439\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.5642 | 1.15813 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.4215 | 0.892023 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.8069 | 1.39104 | 0.695518 | − | 0.718509i | \(-0.255175\pi\) | ||||
0.695518 | + | 0.718509i | \(0.255175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.0514 | −0.748279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −78.1710 | −2.53487 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.689500 | −0.0223351 | −0.0111675 | − | 0.999938i | \(-0.503555\pi\) | ||||
−0.0111675 | + | 0.999938i | \(0.503555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.7081 | −1.54380 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.9189 | −0.708537 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.6543 | 0.731544 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1080 | −0.455096 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.5886 | 1.01793 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −91.3599 | −2.94098 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1022 | 0.453497 | 0.226749 | − | 0.973953i | \(-0.427190\pi\) | ||||
0.226749 | + | 0.973953i | \(0.427190\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.07083 | 0.291397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.360949 | −0.0115834 | −0.00579171 | − | 0.999983i | \(-0.501844\pi\) | ||||
−0.00579171 | + | 0.999983i | \(0.501844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.40067 | −0.301372 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45.7275 | −1.46445 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.83910 | 0.314781 | 0.157390 | − | 0.987536i | \(-0.449692\pi\) | ||||
0.157390 | + | 0.987536i | \(0.449692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.0012 | 0.351600 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.2120 | 0.804958 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6489 | 0.849968 | 0.424984 | − | 0.905201i | \(-0.360280\pi\) | ||||
0.424984 | + | 0.905201i | \(0.360280\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −62.2971 | −1.98495 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.4550 | 0.332787 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.3855 | 1.22059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8287 | 0.534583 | 0.267291 | − | 0.963616i | \(-0.413871\pi\) | ||||
0.267291 | + | 0.963616i | \(0.413871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −91.7875 | −2.91279 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.2040 | −0.672212 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.4607 | 1.15472 | 0.577361 | − | 0.816489i | \(-0.304083\pi\) | ||||
0.577361 | + | 0.816489i | \(0.304083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.6346 | −0.526294 |
(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 | 7168.2.a.bj.1.2 | 12 | ||
4.3 | odd | 2 | 7168.2.a.bi.1.11 | 12 | |||
8.3 | odd | 2 | 7168.2.a.bi.1.2 | 12 | |||
8.5 | even | 2 | inner | 7168.2.a.bj.1.11 | 12 | ||
32.3 | odd | 8 | 448.2.m.d.337.6 | 12 | |||
32.5 | even | 8 | 896.2.m.g.225.6 | 12 | |||
32.11 | odd | 8 | 448.2.m.d.113.6 | 12 | |||
32.13 | even | 8 | 896.2.m.g.673.6 | 12 | |||
32.19 | odd | 8 | 896.2.m.h.673.1 | 12 | |||
32.21 | even | 8 | 112.2.m.d.85.3 | yes | 12 | ||
32.27 | odd | 8 | 896.2.m.h.225.1 | 12 | |||
32.29 | even | 8 | 112.2.m.d.29.3 | ✓ | 12 | ||
224.53 | even | 24 | 784.2.x.l.373.5 | 24 | |||
224.61 | odd | 24 | 784.2.x.m.557.5 | 24 | |||
224.93 | even | 24 | 784.2.x.l.557.5 | 24 | |||
224.117 | odd | 24 | 784.2.x.m.165.2 | 24 | |||
224.125 | odd | 8 | 784.2.m.h.589.3 | 12 | |||
224.149 | even | 24 | 784.2.x.l.165.2 | 24 | |||
224.157 | odd | 24 | 784.2.x.m.765.2 | 24 | |||
224.181 | odd | 8 | 784.2.m.h.197.3 | 12 | |||
224.213 | odd | 24 | 784.2.x.m.373.5 | 24 | |||
224.221 | even | 24 | 784.2.x.l.765.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.3 | ✓ | 12 | 32.29 | even | 8 | ||
112.2.m.d.85.3 | yes | 12 | 32.21 | even | 8 | ||
448.2.m.d.113.6 | 12 | 32.11 | odd | 8 | |||
448.2.m.d.337.6 | 12 | 32.3 | odd | 8 | |||
784.2.m.h.197.3 | 12 | 224.181 | odd | 8 | |||
784.2.m.h.589.3 | 12 | 224.125 | odd | 8 | |||
784.2.x.l.165.2 | 24 | 224.149 | even | 24 | |||
784.2.x.l.373.5 | 24 | 224.53 | even | 24 | |||
784.2.x.l.557.5 | 24 | 224.93 | even | 24 | |||
784.2.x.l.765.2 | 24 | 224.221 | even | 24 | |||
784.2.x.m.165.2 | 24 | 224.117 | odd | 24 | |||
784.2.x.m.373.5 | 24 | 224.213 | odd | 24 | |||
784.2.x.m.557.5 | 24 | 224.61 | odd | 24 | |||
784.2.x.m.765.2 | 24 | 224.157 | odd | 24 | |||
896.2.m.g.225.6 | 12 | 32.5 | even | 8 | |||
896.2.m.g.673.6 | 12 | 32.13 | even | 8 | |||
896.2.m.h.225.1 | 12 | 32.27 | odd | 8 | |||
896.2.m.h.673.1 | 12 | 32.19 | odd | 8 | |||
7168.2.a.bi.1.2 | 12 | 8.3 | odd | 2 | |||
7168.2.a.bi.1.11 | 12 | 4.3 | odd | 2 | |||
7168.2.a.bj.1.2 | 12 | 1.1 | even | 1 | trivial | ||
7168.2.a.bj.1.11 | 12 | 8.5 | even | 2 | inner |