Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(17,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.s (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.17 |
Dual form | 360.2.s.b.233.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58114 | − | 1.58114i | 0.707107 | − | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23607 | − | 3.23607i | −1.22312 | − | 1.22312i | −0.966517 | − | 0.256601i | \(-0.917397\pi\) |
−0.256601 | − | 0.966517i | \(-0.582603\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.57649i | − | 1.37986i | −0.723874 | − | 0.689932i | \(-0.757640\pi\) | ||
0.723874 | − | 0.689932i | \(-0.242360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.23607 | + | 4.23607i | −1.17487 | + | 1.17487i | −0.193841 | + | 0.981033i | \(0.562095\pi\) |
−0.981033 | + | 0.193841i | \(0.937905\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.74806 | − | 1.74806i | 0.423968 | − | 0.423968i | −0.462600 | − | 0.886567i | \(-0.653083\pi\) |
0.886567 | + | 0.462600i | \(0.153083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.47214i | − | 0.567147i | −0.958951 | − | 0.283573i | \(-0.908480\pi\) | ||
0.958951 | − | 0.283573i | \(-0.0915200\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | + | 2.82843i | 0.589768 | + | 0.589768i | 0.937568 | − | 0.347801i | \(-0.113071\pi\) |
−0.347801 | + | 0.937568i | \(0.613071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 1.00000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.99070 | 1.11245 | 0.556223 | − | 0.831033i | \(-0.312250\pi\) | ||||
0.556223 | + | 0.831033i | \(0.312250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52786 | 0.274412 | 0.137206 | − | 0.990543i | \(-0.456188\pi\) | ||||
0.137206 | + | 0.990543i | \(0.456188\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2333 | −1.72975 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.23607 | + | 2.23607i | 0.367607 | + | 0.367607i | 0.866604 | − | 0.498997i | \(-0.166298\pi\) |
−0.498997 | + | 0.866604i | \(0.666298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.07107i | − | 1.10432i | −0.833740 | − | 0.552158i | \(-0.813805\pi\) | ||
0.833740 | − | 0.552158i | \(-0.186195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47214 | − | 2.47214i | 0.376997 | − | 0.376997i | −0.493020 | − | 0.870018i | \(-0.664107\pi\) |
0.870018 | + | 0.493020i | \(0.164107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.74806 | + | 1.74806i | −0.254981 | + | 0.254981i | −0.823009 | − | 0.568028i | \(-0.807707\pi\) |
0.568028 | + | 0.823009i | \(0.307707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.9443i | 1.99204i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.23607 | − | 7.23607i | −0.975711 | − | 0.975711i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.08036 | 0.140651 | 0.0703256 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703256 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4721 | 1.34082 | 0.670410 | − | 0.741991i | \(-0.266118\pi\) | ||||
0.670410 | + | 0.741991i | \(0.266118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.3956i | 1.66152i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.52786 | − | 1.52786i | −0.186658 | − | 0.186658i | 0.607591 | − | 0.794250i | \(-0.292136\pi\) |
−0.794250 | + | 0.607591i | \(0.792136\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6491i | 1.50117i | 0.660772 | + | 0.750587i | \(0.270229\pi\) | ||||
−0.660772 | + | 0.750587i | \(0.729771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.527864 | + | 0.527864i | −0.0617818 | + | 0.0617818i | −0.737323 | − | 0.675541i | \(-0.763910\pi\) |
0.675541 | + | 0.737323i | \(0.263910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.8098 | + | 14.8098i | −1.68774 | + | 1.68774i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4721i | 1.62824i | 0.580695 | + | 0.814121i | \(0.302781\pi\) | ||||
−0.580695 | + | 0.814121i | \(0.697219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.08036 | + | 1.08036i | 0.118585 | + | 0.118585i | 0.763909 | − | 0.645324i | \(-0.223278\pi\) |
−0.645324 | + | 0.763909i | \(0.723278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.52786i | − | 0.599581i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.746512 | 0.0791302 | 0.0395651 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395651 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27.4164 | 2.87402 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.90879 | − | 3.90879i | −0.401033 | − | 0.401033i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | + | 1.00000i | 0.101535 | + | 0.101535i | 0.756049 | − | 0.654515i | \(-0.227127\pi\) |
−0.654515 | + | 0.756049i | \(0.727127\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.9799i | − | 1.09254i | −0.837610 | − | 0.546268i | \(-0.816048\pi\) | ||
0.837610 | − | 0.546268i | \(-0.183952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1803 | + | 12.1803i | −1.20016 | + | 1.20016i | −0.226049 | + | 0.974116i | \(0.572581\pi\) |
−0.974116 | + | 0.226049i | \(0.927419\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2333 | − | 10.2333i | 0.989295 | − | 0.989295i | −0.0106485 | − | 0.999943i | \(-0.503390\pi\) |
0.999943 | + | 0.0106485i | \(0.00338957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.4164i | − | 1.47662i | −0.674459 | − | 0.738312i | \(-0.735623\pi\) | ||
0.674459 | − | 0.738312i | \(-0.264377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.16228 | + | 3.16228i | 0.297482 | + | 0.297482i | 0.840027 | − | 0.542545i | \(-0.182539\pi\) |
−0.542545 | + | 0.840027i | \(0.682539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427 | 0.834058 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.94427 | −0.904025 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | − | 7.90569i | −0.707107 | − | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.23607 | − | 7.23607i | −0.642097 | − | 0.642097i | 0.308973 | − | 0.951071i | \(-0.400015\pi\) |
−0.951071 | + | 0.308973i | \(0.900015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.41577i | − | 0.211066i | −0.994416 | − | 0.105533i | \(-0.966345\pi\) | ||
0.994416 | − | 0.105533i | \(-0.0336549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | + | 8.00000i | −0.693688 | + | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.81913 | + | 8.81913i | −0.753469 | + | 0.753469i | −0.975125 | − | 0.221656i | \(-0.928854\pi\) |
0.221656 | + | 0.975125i | \(0.428854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.94427i | 0.758643i | 0.925265 | + | 0.379322i | \(0.123843\pi\) | ||||
−0.925265 | + | 0.379322i | \(0.876157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.3863 | + | 19.3863i | 1.62117 | + | 1.62117i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.47214 | − | 9.47214i | 0.786618 | − | 0.786618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.4760 | 1.18592 | 0.592959 | − | 0.805232i | \(-0.297959\pi\) | ||||
0.592959 | + | 0.805232i | \(0.297959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.94427 | −0.402359 | −0.201180 | − | 0.979554i | \(-0.564477\pi\) | ||||
−0.201180 | + | 0.979554i | \(0.564477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.41577 | − | 2.41577i | 0.194039 | − | 0.194039i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.708204 | − | 0.708204i | −0.0565208 | − | 0.0565208i | 0.678281 | − | 0.734802i | \(-0.262725\pi\) |
−0.734802 | + | 0.678281i | \(0.762725\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 18.3060i | − | 1.44271i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.47214 | − | 2.47214i | 0.193633 | − | 0.193633i | −0.603631 | − | 0.797264i | \(-0.706280\pi\) |
0.797264 | + | 0.603631i | \(0.206280\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.32456 | − | 6.32456i | 0.489409 | − | 0.489409i | −0.418711 | − | 0.908120i | \(-0.637518\pi\) |
0.908120 | + | 0.418711i | \(0.137518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.8885i | − | 1.76066i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.99070 | − | 5.99070i | −0.455465 | − | 0.455465i | 0.441699 | − | 0.897163i | \(-0.354376\pi\) |
−0.897163 | + | 0.441699i | \(0.854376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.1803 | + | 16.1803i | −1.22312 | + | 1.22312i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7295 | 1.02619 | 0.513095 | − | 0.858332i | \(-0.328499\pi\) | ||||
0.513095 | + | 0.858332i | \(0.328499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4721 | −0.778388 | −0.389194 | − | 0.921156i | \(-0.627246\pi\) | ||||
−0.389194 | + | 0.921156i | \(0.627246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.07107 | 0.519875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00000 | − | 8.00000i | −0.585018 | − | 0.585018i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.3060i | − | 1.32457i | −0.749251 | − | 0.662287i | \(-0.769586\pi\) | ||
0.749251 | − | 0.662287i | \(-0.230414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.47214 | + | 1.47214i | −0.105967 | + | 0.105967i | −0.758102 | − | 0.652136i | \(-0.773873\pi\) |
0.652136 | + | 0.758102i | \(0.273873\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.82998 | − | 3.82998i | 0.272875 | − | 0.272875i | −0.557382 | − | 0.830256i | \(-0.688194\pi\) |
0.830256 | + | 0.557382i | \(0.188194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.3863 | − | 19.3863i | −1.36065 | − | 1.36065i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1803 | − | 11.1803i | −0.780869 | − | 0.780869i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 7.81758i | − | 0.533155i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.94427 | − | 4.94427i | −0.335639 | − | 0.335639i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8098i | 0.996217i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2361 | − | 19.2361i | 1.28814 | − | 1.28814i | 0.352228 | − | 0.935914i | \(-0.385424\pi\) |
0.935914 | − | 0.352228i | \(-0.114576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.4667 | − | 20.4667i | 1.35842 | − | 1.35842i | 0.482558 | − | 0.875864i | \(-0.339708\pi\) |
0.875864 | − | 0.482558i | \(-0.160292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8885i | 1.31427i | 0.753772 | + | 0.657136i | \(0.228232\pi\) | ||||
−0.753772 | + | 0.657136i | \(0.771768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5579 | − | 16.5579i | −1.08474 | − | 1.08474i | −0.996060 | − | 0.0886844i | \(-0.971734\pi\) |
−0.0886844 | − | 0.996060i | \(-0.528266\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.52786i | 0.360598i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6491 | 0.818203 | 0.409101 | − | 0.912489i | \(-0.365842\pi\) | ||||
0.409101 | + | 0.912489i | \(0.365842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.94427 | 0.189657 | 0.0948286 | − | 0.995494i | \(-0.469770\pi\) | ||||
0.0948286 | + | 0.995494i | \(0.469770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.0478 | + | 22.0478i | 1.40858 | + | 1.40858i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4721 | + | 10.4721i | 0.666326 | + | 0.666326i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.7000i | 1.93777i | 0.247513 | + | 0.968885i | \(0.420387\pi\) | ||||
−0.247513 | + | 0.968885i | \(0.579613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9443 | − | 12.9443i | 0.813799 | − | 0.813799i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.16228 | − | 3.16228i | 0.197257 | − | 0.197257i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) |
0.798823 | + | 0.601566i | \(0.205456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 14.4721i | − | 0.899255i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.1421 | + | 14.1421i | 0.872041 | + | 0.872041i | 0.992695 | − | 0.120653i | \(-0.0384989\pi\) |
−0.120653 | + | 0.992695i | \(0.538499\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3153 | −0.750875 | −0.375437 | − | 0.926848i | \(-0.622507\pi\) | ||||
−0.375437 | + | 0.926848i | \(0.622507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.9443 | −1.75824 | −0.879120 | − | 0.476601i | \(-0.841869\pi\) | ||||
−0.879120 | + | 0.476601i | \(0.841869\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.8825 | −1.37986 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1803 | + | 15.1803i | 0.912098 | + | 0.912098i | 0.996437 | − | 0.0843389i | \(-0.0268778\pi\) |
−0.0843389 | + | 0.996437i | \(0.526878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5595i | 1.04751i | 0.851869 | + | 0.523755i | \(0.175469\pi\) | ||||
−0.851869 | + | 0.523755i | \(0.824531\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | + | 8.00000i | −0.475551 | + | 0.475551i | −0.903705 | − | 0.428155i | \(-0.859164\pi\) |
0.428155 | + | 0.903705i | \(0.359164\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.8825 | + | 22.8825i | −1.35071 | + | 1.35071i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8885i | 0.640503i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.15143 | − | 8.15143i | −0.476212 | − | 0.476212i | 0.427706 | − | 0.903918i | \(-0.359322\pi\) |
−0.903918 | + | 0.427706i | \(0.859322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70820 | − | 1.70820i | 0.0994555 | − | 0.0994555i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9628 | −1.38581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | −0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5579 | − | 16.5579i | 0.948103 | − | 0.948103i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4721 | + | 10.4721i | 0.597676 | + | 0.597676i | 0.939694 | − | 0.342017i | \(-0.111110\pi\) |
−0.342017 | + | 0.939694i | \(0.611110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8098i | 0.839789i | 0.907573 | + | 0.419894i | \(0.137933\pi\) | ||||
−0.907573 | + | 0.419894i | \(0.862067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.47214 | + | 7.47214i | −0.422350 | + | 0.422350i | −0.886012 | − | 0.463662i | \(-0.846535\pi\) |
0.463662 | + | 0.886012i | \(0.346535\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.81758 | − | 7.81758i | 0.439079 | − | 0.439079i | −0.452623 | − | 0.891702i | \(-0.649512\pi\) |
0.891702 | + | 0.452623i | \(0.149512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.4164i | − | 1.53502i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.32145 | − | 4.32145i | −0.240452 | − | 0.240452i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1803 | + | 21.1803i | 1.17487 | + | 1.17487i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.3137 | 0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.52786 | −0.303839 | −0.151919 | − | 0.988393i | \(-0.548545\pi\) | ||||
−0.151919 | + | 0.988393i | \(0.548545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.83153 | −0.263975 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4164 | + | 14.4164i | 0.785312 | + | 0.785312i | 0.980722 | − | 0.195410i | \(-0.0626037\pi\) |
−0.195410 | + | 0.980722i | \(0.562604\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.99226i | − | 0.378652i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.4721 | − | 22.4721i | 1.21338 | − | 1.21338i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.99226 | + | 6.99226i | −0.375364 | + | 0.375364i | −0.869426 | − | 0.494062i | \(-0.835511\pi\) |
0.494062 | + | 0.869426i | \(0.335511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.52786i | − | 0.295900i | −0.988995 | − | 0.147950i | \(-0.952733\pi\) | ||
0.988995 | − | 0.147950i | \(-0.0472674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0540 | + | 20.0540i | 1.06737 | + | 1.06737i | 0.997560 | + | 0.0698078i | \(0.0222386\pi\) |
0.0698078 | + | 0.997560i | \(0.477761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.0000 | + | 20.0000i | 1.06149 | + | 1.06149i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.1158 | −1.74779 | −0.873893 | − | 0.486119i | \(-0.838412\pi\) | ||||
−0.873893 | + | 0.486119i | \(0.838412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8885 | 0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.66925i | 0.0873727i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29180 | + | 2.29180i | 0.119631 | + | 0.119631i | 0.764388 | − | 0.644757i | \(-0.223041\pi\) |
−0.644757 | + | 0.764388i | \(0.723041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2918 | − | 11.2918i | 0.584667 | − | 0.584667i | −0.351515 | − | 0.936182i | \(-0.614333\pi\) |
0.936182 | + | 0.351515i | \(0.114333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.3770 | + | 25.3770i | −1.30698 | + | 1.30698i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.9443i | − | 0.870369i | −0.900341 | − | 0.435184i | \(-0.856683\pi\) | ||
0.900341 | − | 0.435184i | \(-0.143317\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.90879 | + | 3.90879i | 0.199730 | + | 0.199730i | 0.799884 | − | 0.600154i | \(-0.204894\pi\) |
−0.600154 | + | 0.799884i | \(0.704894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.8328i | 2.38682i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.7974 | −0.953068 | −0.476534 | − | 0.879156i | \(-0.658107\pi\) | ||||
−0.476534 | + | 0.879156i | \(0.658107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.88854 | 0.500085 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.8825 | + | 22.8825i | 1.15134 | + | 1.15134i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.23607 | − | 6.23607i | −0.312979 | − | 0.312979i | 0.533083 | − | 0.846063i | \(-0.321033\pi\) |
−0.846063 | + | 0.533083i | \(0.821033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.5378i | 1.37517i | 0.726104 | + | 0.687585i | \(0.241329\pi\) | ||||
−0.726104 | + | 0.687585i | \(0.758671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.47214 | + | 6.47214i | −0.322400 | + | 0.322400i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2333 | − | 10.2333i | 0.507248 | − | 0.507248i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.8885i | − | 1.28011i | −0.768331 | − | 0.640053i | \(-0.778912\pi\) | ||
0.768331 | − | 0.640053i | \(-0.221088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.49613 | − | 3.49613i | −0.172033 | − | 0.172033i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.41641 | 0.167705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.40182 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.74032 | − | 8.74032i | −0.423968 | − | 0.423968i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.8885 | − | 33.8885i | −1.63998 | − | 1.63998i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.65685i | − | 0.272481i | −0.990676 | − | 0.136241i | \(-0.956498\pi\) | ||
0.990676 | − | 0.136241i | \(-0.0435020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4164 | + | 16.4164i | −0.788922 | + | 0.788922i | −0.981318 | − | 0.192395i | \(-0.938374\pi\) |
0.192395 | + | 0.981318i | \(0.438374\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.99226 | − | 6.99226i | 0.334485 | − | 0.334485i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9443i | 0.999616i | 0.866136 | + | 0.499808i | \(0.166596\pi\) | ||||
−0.866136 | + | 0.499808i | \(0.833404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.4667 | − | 20.4667i | −0.972402 | − | 0.972402i | 0.0272274 | − | 0.999629i | \(-0.491332\pi\) |
−0.999629 | + | 0.0272274i | \(0.991332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.18034 | − | 1.18034i | 0.0559535 | − | 0.0559535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.6938 | 1.82608 | 0.913038 | − | 0.407875i | \(-0.133730\pi\) | ||||
0.913038 | + | 0.407875i | \(0.133730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.3607 | −1.52380 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.3491 | − | 43.3491i | 2.03224 | − | 2.03224i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | + | 13.0000i | 0.608114 | + | 0.608114i | 0.942453 | − | 0.334339i | \(-0.108513\pi\) |
−0.334339 | + | 0.942453i | \(0.608513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 9.48683i | − | 0.441846i | −0.975291 | − | 0.220923i | \(-0.929093\pi\) | ||
0.975291 | − | 0.220923i | \(-0.0709069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6525 | − | 10.6525i | 0.495063 | − | 0.495063i | −0.414834 | − | 0.909897i | \(-0.636160\pi\) |
0.909897 | + | 0.414834i | \(0.136160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.57649 | + | 4.57649i | −0.211775 | + | 0.211775i | −0.805021 | − | 0.593246i | \(-0.797846\pi\) |
0.593246 | + | 0.805021i | \(0.297846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.88854i | 0.456611i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.3137 | − | 11.3137i | −0.520205 | − | 0.520205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.3607 | −0.567147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.5980 | −1.80928 | −0.904639 | − | 0.426179i | \(-0.859859\pi\) | ||||
−0.904639 | + | 0.426179i | \(0.859859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.9443 | −0.863784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.16228 | 0.143592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76393 | + | 8.76393i | 0.397132 | + | 0.397132i | 0.877220 | − | 0.480088i | \(-0.159395\pi\) |
−0.480088 | + | 0.877220i | \(0.659395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.7000i | 1.38547i | 0.721191 | + | 0.692737i | \(0.243595\pi\) | ||||
−0.721191 | + | 0.692737i | \(0.756405\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.4721 | − | 10.4721i | 0.471641 | − | 0.471641i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.9334 | − | 40.9334i | 1.83611 | − | 1.83611i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 26.4721i | − | 1.18506i | −0.805550 | − | 0.592528i | \(-0.798130\pi\) | ||
0.805550 | − | 0.592528i | \(-0.201870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.2070 | − | 29.2070i | −1.30228 | − | 1.30228i | −0.926854 | − | 0.375422i | \(-0.877498\pi\) |
−0.375422 | − | 0.926854i | \(-0.622502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3607 | − | 17.3607i | −0.772540 | − | 0.772540i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.9830 | −0.575460 | −0.287730 | − | 0.957712i | \(-0.592901\pi\) | ||||
−0.287730 | + | 0.957712i | \(0.592901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.41641 | 0.151133 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.5176i | 1.69729i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 8.00000i | 0.351840 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.24574i | − | 0.273631i | −0.990597 | − | 0.136816i | \(-0.956313\pi\) | ||
0.990597 | − | 0.136816i | \(-0.0436867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.88854 | + | 9.88854i | −0.432396 | + | 0.432396i | −0.889443 | − | 0.457047i | \(-0.848907\pi\) |
0.457047 | + | 0.889443i | \(0.348907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.67080 | − | 2.67080i | 0.116342 | − | 0.116342i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.9535 | + | 29.9535i | 1.29743 | + | 1.29743i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 32.3607i | − | 1.39907i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 63.8158 | 2.74874 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3050 | −1.08794 | −0.543972 | − | 0.839103i | \(-0.683080\pi\) | ||||
−0.543972 | + | 0.839103i | \(0.683080\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.3755 | − | 24.3755i | −1.04413 | − | 1.04413i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | + | 12.0000i | 0.513083 | + | 0.513083i | 0.915470 | − | 0.402387i | \(-0.131819\pi\) |
−0.402387 | + | 0.915470i | \(0.631819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 14.8098i | − | 0.630920i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.8328 | − | 46.8328i | 1.99153 | − | 1.99153i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.1235 | − | 26.1235i | 1.10689 | − | 1.10689i | 0.113333 | − | 0.993557i | \(-0.463847\pi\) |
0.993557 | − | 0.113333i | \(-0.0361527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.9443i | 0.885848i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.33540 | + | 1.33540i | 0.0562805 | + | 0.0562805i | 0.734687 | − | 0.678406i | \(-0.237329\pi\) |
−0.678406 | + | 0.734687i | \(0.737329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.3662 | −1.27302 | −0.636508 | − | 0.771270i | \(-0.719622\pi\) | ||||
−0.636508 | + | 0.771270i | \(0.719622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.41641 | −0.310367 | −0.155184 | − | 0.987886i | \(-0.549597\pi\) | ||||
−0.155184 | + | 0.987886i | \(0.549597\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.1421 | − | 14.1421i | 0.589768 | − | 0.589768i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0557 | − | 12.0557i | −0.501887 | − | 0.501887i | 0.410137 | − | 0.912024i | \(-0.365481\pi\) |
−0.912024 | + | 0.410137i | \(0.865481\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.99226i | − | 0.290088i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.8825 | − | 22.8825i | 0.944460 | − | 0.944460i | −0.0540767 | − | 0.998537i | \(-0.517222\pi\) |
0.998537 | + | 0.0540767i | \(0.0172216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.77709i | − | 0.155632i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.1359 | − | 22.1359i | −0.909014 | − | 0.909014i | 0.0871785 | − | 0.996193i | \(-0.472215\pi\) |
−0.996193 | + | 0.0871785i | \(0.972215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8885 | + | 17.8885i | −0.733359 | + | 0.733359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6491 | 0.516829 | 0.258414 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258414 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.8328 | −1.25770 | −0.628848 | − | 0.777528i | \(-0.716473\pi\) | ||||
−0.628848 | + | 0.777528i | \(0.716473\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.7233 | + | 15.7233i | −0.639242 | + | 0.639242i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6525 | + | 30.6525i | 1.24415 | + | 1.24415i | 0.958265 | + | 0.285880i | \(0.0922860\pi\) |
0.285880 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.8098i | − | 0.599142i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7082 | + | 26.7082i | −1.07873 | + | 1.07873i | −0.0821110 | + | 0.996623i | \(0.526166\pi\) |
−0.996623 | + | 0.0821110i | \(0.973834\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.5579 | + | 16.5579i | −0.666596 | + | 0.666596i | −0.956926 | − | 0.290330i | \(-0.906235\pi\) |
0.290330 | + | 0.956926i | \(0.406235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.88854i | 0.236681i | 0.992973 | + | 0.118340i | \(0.0377574\pi\) | ||||
−0.992973 | + | 0.118340i | \(0.962243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.41577 | − | 2.41577i | −0.0967856 | − | 0.0967856i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.81758 | 0.311707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.36068 | 0.332833 | 0.166417 | − | 0.986056i | \(-0.446780\pi\) | ||||
0.166417 | + | 0.986056i | \(0.446780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.8825 | −0.908063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −59.0689 | − | 59.0689i | −2.34039 | − | 2.34039i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.57804i | 0.220319i | 0.993914 | + | 0.110160i | \(0.0351362\pi\) | ||||
−0.993914 | + | 0.110160i | \(0.964864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.0000 | + | 20.0000i | −0.788723 | + | 0.788723i | −0.981285 | − | 0.192562i | \(-0.938320\pi\) |
0.192562 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.3755 | + | 24.3755i | −0.958299 | + | 0.958299i | −0.999165 | − | 0.0408656i | \(-0.986988\pi\) |
0.0408656 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.94427i | − | 0.194080i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3137 | + | 11.3137i | 0.442740 | + | 0.442740i | 0.892932 | − | 0.450192i | \(-0.148644\pi\) |
−0.450192 | + | 0.892932i | \(0.648644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.81966 | − | 3.81966i | −0.149246 | − | 0.149246i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.5316 | 1.38411 | 0.692057 | − | 0.721843i | \(-0.256705\pi\) | ||||
0.692057 | + | 0.721843i | \(0.256705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.3050 | 1.60658 | 0.803288 | − | 0.595591i | \(-0.203082\pi\) | ||||
0.803288 | + | 0.595591i | \(0.203082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.2982i | 0.981023i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.9443 | + | 16.9443i | 0.656085 | + | 0.656085i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 47.9256i | − | 1.85015i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4721 | − | 19.4721i | 0.750596 | − | 0.750596i | −0.223995 | − | 0.974590i | \(-0.571910\pi\) |
0.974590 | + | 0.223995i | \(0.0719098\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3060 | + | 18.3060i | −0.703555 | + | 0.703555i | −0.965172 | − | 0.261617i | \(-0.915744\pi\) |
0.261617 | + | 0.965172i | \(0.415744\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.47214i | − | 0.248378i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0649 | + | 15.0649i | 0.576441 | + | 0.576441i | 0.933921 | − | 0.357480i | \(-0.116364\pi\) |
−0.357480 | + | 0.933921i | \(0.616364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.8885i | 1.06557i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.3607 | −0.774557 | −0.387278 | − | 0.921963i | \(-0.626585\pi\) | ||||
−0.387278 | + | 0.921963i | \(0.626585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421 | + | 14.1421i | 0.536442 | + | 0.536442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3607 | − | 12.3607i | −0.468194 | − | 0.468194i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.6212i | 1.15655i | 0.815843 | + | 0.578274i | \(0.196273\pi\) | ||||
−0.815843 | + | 0.578274i | \(0.803727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.52786 | − | 5.52786i | 0.208487 | − | 0.208487i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.5316 | + | 35.5316i | −1.33630 | + | 1.33630i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.8885i | 0.596707i | 0.954455 | + | 0.298353i | \(0.0964374\pi\) | ||||
−0.954455 | + | 0.298353i | \(0.903563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.32145 | + | 4.32145i | 0.161840 | + | 0.161840i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.3050 | 2.29268 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.32145 | 0.161163 | 0.0805815 | − | 0.996748i | \(-0.474322\pi\) | ||||
0.0805815 | + | 0.996748i | \(0.474322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 78.8328 | 2.93589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 29.9535i | − | 1.11245i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.12461 | + | 9.12461i | 0.338413 | + | 0.338413i | 0.855770 | − | 0.517357i | \(-0.173084\pi\) |
−0.517357 | + | 0.855770i | \(0.673084\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.64290i | − | 0.319669i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1803 | − | 11.1803i | 0.412955 | − | 0.412955i | −0.469811 | − | 0.882767i | \(-0.655678\pi\) |
0.882767 | + | 0.469811i | \(0.155678\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.99226 | + | 6.99226i | −0.257563 | + | 0.257563i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.3607i | 0.454695i | 0.973814 | + | 0.227347i | \(0.0730053\pi\) | ||||
−0.973814 | + | 0.227347i | \(0.926995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.2070 | + | 29.2070i | 1.07150 | + | 1.07150i | 0.997239 | + | 0.0742626i | \(0.0236603\pi\) |
0.0742626 | + | 0.997239i | \(0.476340\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.8885 | − | 22.8885i | 0.838571 | − | 0.838571i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −66.2316 | −2.42005 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.3607 | 1.18086 | 0.590429 | − | 0.807090i | \(-0.298959\pi\) | ||||
0.590429 | + | 0.807090i | \(0.298959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.81758 | + | 7.81758i | −0.284511 | + | 0.284511i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7082 | + | 10.7082i | 0.389196 | + | 0.389196i | 0.874401 | − | 0.485204i | \(-0.161255\pi\) |
−0.485204 | + | 0.874401i | \(0.661255\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0447i | 0.944121i | 0.881566 | + | 0.472060i | \(0.156490\pi\) | ||||
−0.881566 | + | 0.472060i | \(0.843510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −49.8885 | + | 49.8885i | −1.80609 | + | 1.80609i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.57649 | + | 4.57649i | −0.165248 | + | 0.165248i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0000i | 1.15395i | 0.816762 | + | 0.576975i | \(0.195767\pi\) | ||||
−0.816762 | + | 0.576975i | \(0.804233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.81758 | − | 7.81758i | −0.281179 | − | 0.281179i | 0.552400 | − | 0.833579i | \(-0.313712\pi\) |
−0.833579 | + | 0.552400i | \(0.813712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.63932i | − | 0.274412i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.4806 | −0.626309 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.8885 | 2.07141 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.23954 | −0.0799325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.4721 | − | 30.4721i | −1.08621 | − | 1.08621i | −0.995915 | − | 0.0902997i | \(-0.971218\pi\) |
−0.0902997 | − | 0.995915i | \(-0.528782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 20.4667i | − | 0.727712i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.3607 | + | 44.3607i | −1.57529 | + | 1.57529i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.66925 | + | 1.66925i | −0.0591280 | + | 0.0591280i | −0.736052 | − | 0.676924i | \(-0.763312\pi\) |
0.676924 | + | 0.736052i | \(0.263312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.11146i | 0.216208i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.41577 | + | 2.41577i | 0.0852505 | + | 0.0852505i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.9443 | − | 28.9443i | −1.02015 | − | 1.02015i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.2272 | −0.640833 | −0.320416 | − | 0.947277i | \(-0.603823\pi\) | ||||
−0.320416 | + | 0.947277i | \(0.603823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8885 | −0.487693 | −0.243846 | − | 0.969814i | \(-0.578409\pi\) | ||||
−0.243846 | + | 0.969814i | \(0.578409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 7.81758i | − | 0.273838i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.11146 | − | 6.11146i | −0.213813 | − | 0.213813i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.32611i | 0.255683i | 0.991795 | + | 0.127841i | \(0.0408049\pi\) | ||||
−0.991795 | + | 0.127841i | \(0.959195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.1246 | − | 13.1246i | 0.457495 | − | 0.457495i | −0.440337 | − | 0.897832i | \(-0.645141\pi\) |
0.897832 | + | 0.440337i | \(0.145141\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.81758 | + | 7.81758i | −0.271844 | + | 0.271844i | −0.829842 | − | 0.557998i | \(-0.811570\pi\) |
0.557998 | + | 0.829842i | \(0.311570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.3607i | − | 1.26286i | −0.775433 | − | 0.631429i | \(-0.782469\pi\) | ||
0.775433 | − | 0.631429i | \(-0.217531\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.3755 | + | 24.3755i | 0.844560 | + | 0.844560i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.0000i | − | 0.692129i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.8021 | −0.752692 | −0.376346 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376346 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.88854 | 0.237536 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.1900 | − | 36.1900i | −1.24497 | − | 1.24497i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.1803 | + | 32.1803i | 1.10573 | + | 1.10573i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6491i | 0.433606i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1246 | + | 28.1246i | −0.962968 | + | 0.962968i | −0.999338 | − | 0.0363700i | \(-0.988421\pi\) |
0.0363700 | + | 0.999338i | \(0.488421\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.3755 | − | 24.3755i | 0.832651 | − | 0.832651i | −0.155228 | − | 0.987879i | \(-0.549611\pi\) |
0.987879 | + | 0.155228i | \(0.0496112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000i | 0.136478i | 0.997669 | + | 0.0682391i | \(0.0217381\pi\) | ||||
−0.997669 | + | 0.0682391i | \(0.978262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.9597 | + | 21.9597i | 0.747517 | + | 0.747517i | 0.974012 | − | 0.226495i | \(-0.0727267\pi\) |
−0.226495 | + | 0.974012i | \(0.572727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9443 | −0.644125 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.2316 | 2.24675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9443 | 0.438600 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.1667i | 1.72975i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.29180 | − | 7.29180i | −0.246226 | − | 0.246226i | 0.573194 | − | 0.819420i | \(-0.305704\pi\) |
−0.819420 | + | 0.573194i | \(0.805704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5378i | 0.927771i | 0.885895 | + | 0.463885i | \(0.153545\pi\) | ||||
−0.885895 | + | 0.463885i | \(0.846455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5279 | + | 13.5279i | −0.455249 | + | 0.455249i | −0.897092 | − | 0.441843i | \(-0.854325\pi\) |
0.441843 | + | 0.897092i | \(0.354325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.6166 | + | 27.6166i | −0.927274 | + | 0.927274i | −0.997529 | − | 0.0702554i | \(-0.977619\pi\) |
0.0702554 | + | 0.997529i | \(0.477619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.8328i | 1.57072i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.32145 | + | 4.32145i | 0.144612 | + | 0.144612i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7082 | − | 21.7082i | 0.725625 | − | 0.725625i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.15298 | 0.305269 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.5579 | + | 16.5579i | −0.550403 | + | 0.550403i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5279 | + | 25.5279i | 0.847639 | + | 0.847639i | 0.989838 | − | 0.142199i | \(-0.0454174\pi\) |
−0.142199 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.4450i | − | 1.00869i | −0.863503 | − | 0.504344i | \(-0.831734\pi\) | ||
0.863503 | − | 0.504344i | \(-0.168266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.94427 | − | 4.94427i | 0.163632 | − | 0.163632i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.81758 | + | 7.81758i | −0.258159 | + | 0.258159i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.4721i | 0.741287i | 0.928775 | + | 0.370644i | \(0.120863\pi\) | ||||
−0.928775 | + | 0.370644i | \(0.879137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.5825 | − | 53.5825i | −1.76369 | − | 1.76369i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1803 | − | 11.1803i | 0.367607 | − | 0.367607i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.08191 | 0.0683054 | 0.0341527 | − | 0.999417i | \(-0.489127\pi\) | ||||
0.0341527 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.4721 | 1.12978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.2982 | −0.827340 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | − | 19.0000i | −0.620703 | − | 0.620703i | 0.325008 | − | 0.945711i | \(-0.394633\pi\) |
−0.945711 | + | 0.325008i | \(0.894633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.49458i | 0.0813209i | 0.999173 | + | 0.0406604i | \(0.0129462\pi\) | ||||
−0.999173 | + | 0.0406604i | \(0.987054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.0000 | − | 20.0000i | 0.651290 | − | 0.651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.16073 | − | 2.16073i | 0.0702142 | − | 0.0702142i | −0.671128 | − | 0.741342i | \(-0.734190\pi\) |
0.741342 | + | 0.671128i | \(0.234190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.47214i | − | 0.145172i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.7851 | + | 34.7851i | 1.12680 | + | 1.12680i | 0.990695 | + | 0.136104i | \(0.0434581\pi\) |
0.136104 | + | 0.990695i | \(0.456542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.9443 | − | 28.9443i | −0.936615 | − | 0.936615i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.0786 | 1.84316 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6656 | −0.924698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.65530i | 0.149859i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.0689 | − | 34.0689i | −1.09558 | − | 1.09558i | −0.994921 | − | 0.100661i | \(-0.967904\pi\) |
−0.100661 | − | 0.994921i | \(-0.532096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 28.5393i | − | 0.915870i | −0.888986 | − | 0.457935i | \(-0.848589\pi\) | ||
0.888986 | − | 0.457935i | \(-0.151411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9443 | − | 28.9443i | 0.927911 | − | 0.927911i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0463 | − | 27.0463i | 0.865287 | − | 0.865287i | −0.126659 | − | 0.991946i | \(-0.540425\pi\) |
0.991946 | + | 0.126659i | \(0.0404254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.41641i | − | 0.109189i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7264 | + | 11.7264i | 0.374013 | + | 0.374013i | 0.868937 | − | 0.494923i | \(-0.164804\pi\) |
−0.494923 | + | 0.868937i | \(0.664804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 12.1115i | − | 0.385903i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9845 | 0.444682 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8328 | −0.725308 | −0.362654 | − | 0.931924i | \(-0.618129\pi\) | ||||
−0.362654 | + | 0.931924i | \(0.618129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6491 | + | 12.6491i | 0.401004 | + | 0.401004i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.6525 | + | 25.6525i | 0.812422 | + | 0.812422i | 0.984996 | − | 0.172574i | \(-0.0552085\pi\) |
−0.172574 | + | 0.984996i | \(0.555209\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 360.2.s.b.17.3 | yes | 8 | |
3.2 | odd | 2 | inner | 360.2.s.b.17.1 | ✓ | 8 | |
4.3 | odd | 2 | 720.2.w.e.17.4 | 8 | |||
5.2 | odd | 4 | 1800.2.s.e.593.3 | 8 | |||
5.3 | odd | 4 | inner | 360.2.s.b.233.1 | yes | 8 | |
5.4 | even | 2 | 1800.2.s.e.1457.3 | 8 | |||
8.3 | odd | 2 | 2880.2.w.o.2177.2 | 8 | |||
8.5 | even | 2 | 2880.2.w.m.2177.1 | 8 | |||
12.11 | even | 2 | 720.2.w.e.17.2 | 8 | |||
15.2 | even | 4 | 1800.2.s.e.593.4 | 8 | |||
15.8 | even | 4 | inner | 360.2.s.b.233.3 | yes | 8 | |
15.14 | odd | 2 | 1800.2.s.e.1457.4 | 8 | |||
20.3 | even | 4 | 720.2.w.e.593.2 | 8 | |||
20.7 | even | 4 | 3600.2.w.j.593.2 | 8 | |||
20.19 | odd | 2 | 3600.2.w.j.1457.2 | 8 | |||
24.5 | odd | 2 | 2880.2.w.m.2177.3 | 8 | |||
24.11 | even | 2 | 2880.2.w.o.2177.4 | 8 | |||
40.3 | even | 4 | 2880.2.w.o.2753.4 | 8 | |||
40.13 | odd | 4 | 2880.2.w.m.2753.3 | 8 | |||
60.23 | odd | 4 | 720.2.w.e.593.4 | 8 | |||
60.47 | odd | 4 | 3600.2.w.j.593.1 | 8 | |||
60.59 | even | 2 | 3600.2.w.j.1457.1 | 8 | |||
120.53 | even | 4 | 2880.2.w.m.2753.1 | 8 | |||
120.83 | odd | 4 | 2880.2.w.o.2753.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.s.b.17.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
360.2.s.b.17.3 | yes | 8 | 1.1 | even | 1 | trivial | |
360.2.s.b.233.1 | yes | 8 | 5.3 | odd | 4 | inner | |
360.2.s.b.233.3 | yes | 8 | 15.8 | even | 4 | inner | |
720.2.w.e.17.2 | 8 | 12.11 | even | 2 | |||
720.2.w.e.17.4 | 8 | 4.3 | odd | 2 | |||
720.2.w.e.593.2 | 8 | 20.3 | even | 4 | |||
720.2.w.e.593.4 | 8 | 60.23 | odd | 4 | |||
1800.2.s.e.593.3 | 8 | 5.2 | odd | 4 | |||
1800.2.s.e.593.4 | 8 | 15.2 | even | 4 | |||
1800.2.s.e.1457.3 | 8 | 5.4 | even | 2 | |||
1800.2.s.e.1457.4 | 8 | 15.14 | odd | 2 | |||
2880.2.w.m.2177.1 | 8 | 8.5 | even | 2 | |||
2880.2.w.m.2177.3 | 8 | 24.5 | odd | 2 | |||
2880.2.w.m.2753.1 | 8 | 120.53 | even | 4 | |||
2880.2.w.m.2753.3 | 8 | 40.13 | odd | 4 | |||
2880.2.w.o.2177.2 | 8 | 8.3 | odd | 2 | |||
2880.2.w.o.2177.4 | 8 | 24.11 | even | 2 | |||
2880.2.w.o.2753.2 | 8 | 120.83 | odd | 4 | |||
2880.2.w.o.2753.4 | 8 | 40.3 | even | 4 | |||
3600.2.w.j.593.1 | 8 | 60.47 | odd | 4 | |||
3600.2.w.j.593.2 | 8 | 20.7 | even | 4 | |||
3600.2.w.j.1457.1 | 8 | 60.59 | even | 2 | |||
3600.2.w.j.1457.2 | 8 | 20.19 | odd | 2 |