Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2016) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23607 | −0.975711 | −0.487856 | − | 0.872924i | \(-0.662221\pi\) | ||||
−0.487856 | + | 0.872924i | \(0.662221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47214 | −0.567147 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.70820 | −1.19024 | −0.595121 | − | 0.803636i | \(-0.702896\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.52786 | −0.283717 | −0.141859 | − | 0.989887i | \(-0.545308\pi\) | ||||
−0.141859 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.23607 | −0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214 | 0.735215 | 0.367607 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367607 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.23607 | 1.13008 | 0.565042 | − | 0.825062i | \(-0.308860\pi\) | ||||
0.565042 | + | 0.825062i | \(0.308860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9443 | 1.97398 | 0.986991 | − | 0.160773i | \(-0.0513986\pi\) | ||||
0.986991 | + | 0.160773i | \(0.0513986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.52786 | −0.222862 | −0.111431 | − | 0.993772i | \(-0.535543\pi\) | ||||
−0.111431 | + | 0.993772i | \(0.535543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.4721 | 1.41206 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.47214 | −0.842600 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47214 | 0.572598 | 0.286299 | − | 0.958140i | \(-0.407575\pi\) | ||||
0.286299 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.23607 | −0.858763 | −0.429382 | − | 0.903123i | \(-0.641268\pi\) | ||||
−0.429382 | + | 0.903123i | \(0.641268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9443 | −1.74909 | −0.874547 | − | 0.484940i | \(-0.838841\pi\) | ||||
−0.874547 | + | 0.484940i | \(0.838841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.23607 | −0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.9443 | 1.42082 | 0.710409 | − | 0.703789i | \(-0.248510\pi\) | ||||
0.710409 | + | 0.703789i | \(0.248510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47214 | −0.268141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.29180 | 0.242930 | 0.121465 | − | 0.992596i | \(-0.461241\pi\) | ||||
0.121465 | + | 0.992596i | \(0.461241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | 0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.94427 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.7082 | −1.76203 | −0.881016 | − | 0.473086i | \(-0.843140\pi\) | ||||
−0.881016 | + | 0.473086i | \(0.843140\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4721 | 1.82011 | 0.910057 | − | 0.414484i | \(-0.136038\pi\) | ||||
0.910057 | + | 0.414484i | \(0.136038\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.2361 | −1.08623 | −0.543116 | − | 0.839658i | \(-0.682756\pi\) | ||||
−0.543116 | + | 0.839658i | \(0.682756\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9443 | 1.04827 | 0.524136 | − | 0.851635i | \(-0.324389\pi\) | ||||
0.524136 | + | 0.851635i | \(0.324389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9443 | 1.21769 | 0.608847 | − | 0.793287i | \(-0.291632\pi\) | ||||
0.608847 | + | 0.793287i | \(0.291632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.4721 | 1.72254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.763932 | 0.0700295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8885 | −1.58735 | −0.793676 | − | 0.608341i | \(-0.791835\pi\) | ||||
−0.793676 | + | 0.608341i | \(0.791835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0000 | 1.39793 | 0.698963 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698963 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47214 | −0.214361 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.52786 | 0.130534 | 0.0652671 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652671 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.94427 | −0.419368 | −0.209684 | − | 0.977769i | \(-0.567243\pi\) | ||||
−0.209684 | + | 0.977769i | \(0.567243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4721 | 1.21022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.94427 | 0.410599 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.8885 | 1.46549 | 0.732743 | − | 0.680505i | \(-0.238240\pi\) | ||||
0.732743 | + | 0.680505i | \(0.238240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4721 | −1.31462 | −0.657310 | − | 0.753620i | \(-0.728306\pi\) | ||||
−0.657310 | + | 0.753620i | \(0.728306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.70820 | −0.449869 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4164 | 0.883428 | 0.441714 | − | 0.897156i | \(-0.354371\pi\) | ||||
0.441714 | + | 0.897156i | \(0.354371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7082 | −1.34633 | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
−0.673165 | + | 0.739492i | \(0.735066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.47214 | 0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.180340 | 0.0134792 | 0.00673962 | − | 0.999977i | \(-0.497855\pi\) | ||||
0.00673962 | + | 0.999977i | \(0.497855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.4721 | −1.06401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.47214 | −0.180780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.6525 | 1.92851 | 0.964253 | − | 0.264984i | \(-0.0853668\pi\) | ||||
0.964253 | + | 0.264984i | \(0.0853668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4721 | 0.897764 | 0.448882 | − | 0.893591i | \(-0.351822\pi\) | ||||
0.448882 | + | 0.893591i | \(0.351822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.94427 | −0.352265 | −0.176132 | − | 0.984366i | \(-0.556359\pi\) | ||||
−0.176132 | + | 0.984366i | \(0.556359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52786 | −0.107235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.4164 | −1.63547 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0000 | 1.65223 | 0.826114 | − | 0.563503i | \(-0.190547\pi\) | ||||
0.826114 | + | 0.563503i | \(0.190547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −41.8885 | −2.85677 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.47214 | −0.167820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.41641 | −0.229812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9443 | 0.866813 | 0.433406 | − | 0.901199i | \(-0.357312\pi\) | ||||
0.433406 | + | 0.901199i | \(0.357312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3607 | 1.08590 | 0.542948 | − | 0.839766i | \(-0.317308\pi\) | ||||
0.542948 | + | 0.839766i | \(0.317308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.4721 | −0.824182 | −0.412091 | − | 0.911143i | \(-0.635201\pi\) | ||||
−0.412091 | + | 0.911143i | \(0.635201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.3607 | 1.59592 | 0.797961 | − | 0.602710i | \(-0.205912\pi\) | ||||
0.797961 | + | 0.602710i | \(0.205912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.94427 | 0.322529 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.76393 | −0.566892 | −0.283446 | − | 0.958988i | \(-0.591478\pi\) | ||||
−0.283446 | + | 0.958988i | \(0.591478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.88854 | 0.508146 | 0.254073 | − | 0.967185i | \(-0.418230\pi\) | ||||
0.254073 | + | 0.967185i | \(0.418230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.23607 | −0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0557 | 0.703459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.41641 | −0.215642 | −0.107821 | − | 0.994170i | \(-0.534387\pi\) | ||||
−0.107821 | + | 0.994170i | \(0.534387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.4721 | 1.16133 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.7082 | −1.85315 | −0.926573 | − | 0.376114i | \(-0.877260\pi\) | ||||
−0.926573 | + | 0.376114i | \(0.877260\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | 0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.1803 | 1.73767 | 0.868837 | − | 0.495098i | \(-0.164868\pi\) | ||||
0.868837 | + | 0.495098i | \(0.164868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8885 | 1.59032 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.23607 | −0.197307 | −0.0986533 | − | 0.995122i | \(-0.531453\pi\) | ||||
−0.0986533 | + | 0.995122i | \(0.531453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.41641 | 0.450515 | 0.225257 | − | 0.974299i | \(-0.427678\pi\) | ||||
0.225257 | + | 0.974299i | \(0.427678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.7082 | −1.06784 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5279 | 0.692642 | 0.346321 | − | 0.938116i | \(-0.387431\pi\) | ||||
0.346321 | + | 0.938116i | \(0.387431\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4164 | −0.681046 | −0.340523 | − | 0.940236i | \(-0.610604\pi\) | ||||
−0.340523 | + | 0.940236i | \(0.610604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.47214 | 0.146953 | 0.0734766 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734766 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.23607 | 0.427132 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.1803 | 1.88000 | 0.939998 | − | 0.341181i | \(-0.110827\pi\) | ||||
0.939998 | + | 0.341181i | \(0.110827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.9443 | 1.21942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.5279 | 1.47631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9443 | 0.746095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4721 | −0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4721 | 1.05426 | 0.527130 | − | 0.849785i | \(-0.323268\pi\) | ||||
0.527130 | + | 0.849785i | \(0.323268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4164 | −0.647365 | −0.323683 | − | 0.946166i | \(-0.604921\pi\) | ||||
−0.323683 | + | 0.946166i | \(0.604921\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8885 | −0.898074 | −0.449037 | − | 0.893513i | \(-0.648233\pi\) | ||||
−0.449037 | + | 0.893513i | \(0.648233\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9443 | 1.17635 | 0.588174 | − | 0.808735i | \(-0.299847\pi\) | ||||
0.588174 | + | 0.808735i | \(0.299847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.94427 | 0.276826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.88854 | −0.105081 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.4721 | −1.35747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.52786 | −0.0842339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8885 | −0.983243 | −0.491622 | − | 0.870809i | \(-0.663596\pi\) | ||||
−0.491622 | + | 0.870809i | \(0.663596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.8885 | −1.41444 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8885 | −0.647610 | −0.323805 | − | 0.946124i | \(-0.604962\pi\) | ||||
−0.323805 | + | 0.946124i | \(0.604962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7639 | −1.11467 | −0.557333 | − | 0.830289i | \(-0.688175\pi\) | ||||
−0.557333 | + | 0.830289i | \(0.688175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4721 | 1.09585 | 0.547924 | − | 0.836528i | \(-0.315418\pi\) | ||||
0.547924 | + | 0.836528i | \(0.315418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.1803 | −0.648294 | −0.324147 | − | 0.946007i | \(-0.605077\pi\) | ||||
−0.324147 | + | 0.946007i | \(0.605077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.4164 | 1.24281 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.7639 | 0.884766 | 0.442383 | − | 0.896826i | \(-0.354133\pi\) | ||||
0.442383 | + | 0.896826i | \(0.354133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.3607 | 2.53131 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00000 | −0.415339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8885 | 0.615565 | 0.307783 | − | 0.951457i | \(-0.400413\pi\) | ||||
0.307783 | + | 0.951457i | \(0.400413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.83282 | 0.351908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.0000 | −1.63512 | −0.817562 | − | 0.575841i | \(-0.804675\pi\) | ||||
−0.817562 | + | 0.575841i | \(0.804675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.4721 | 0.533709 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.52786 | −0.0774658 | −0.0387329 | − | 0.999250i | \(-0.512332\pi\) | ||||
−0.0387329 | + | 0.999250i | \(0.512332\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.36068 | −0.220529 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.8885 | −2.10764 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.472136 | −0.0236958 | −0.0118479 | − | 0.999930i | \(-0.503771\pi\) | ||||
−0.0118479 | + | 0.999930i | \(0.503771\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.5279 | −0.875300 | −0.437650 | − | 0.899145i | \(-0.644189\pi\) | ||||
−0.437650 | + | 0.899145i | \(0.644189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0557 | 0.550725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.4721 | −0.717357 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.47214 | −0.318473 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.8885 | −2.05623 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.47214 | −0.316185 | −0.158092 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158092 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4164 | 1.04377 | 0.521886 | − | 0.853015i | \(-0.325229\pi\) | ||||
0.521886 | + | 0.853015i | \(0.325229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.18034 | 0.202776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.47214 | 0.216422 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.12461 | −0.439517 | −0.219759 | − | 0.975554i | \(-0.570527\pi\) | ||||
−0.219759 | + | 0.975554i | \(0.570527\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.1115 | 0.675042 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8328 | −1.08975 | −0.544875 | − | 0.838517i | \(-0.683423\pi\) | ||||
−0.544875 | + | 0.838517i | \(0.683423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.81966 | −0.371523 | −0.185762 | − | 0.982595i | \(-0.559475\pi\) | ||||
−0.185762 | + | 0.982595i | \(0.559475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.41641 | −0.351571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9443 | 0.610878 | 0.305439 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305439 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.4164 | −1.10264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.4721 | 0.678464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.111456 | −0.00521370 | −0.00260685 | − | 0.999997i | \(-0.500830\pi\) | ||||
−0.00260685 | + | 0.999997i | \(0.500830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.70820 | −0.452156 | −0.226078 | − | 0.974109i | \(-0.572590\pi\) | ||||
−0.226078 | + | 0.974109i | \(0.572590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8885 | 0.831351 | 0.415676 | − | 0.909513i | \(-0.363545\pi\) | ||||
0.415676 | + | 0.909513i | \(0.363545\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.5279 | 1.18129 | 0.590644 | − | 0.806932i | \(-0.298874\pi\) | ||||
0.590644 | + | 0.806932i | \(0.298874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.8885 | −1.92604 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5279 | −0.620701 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4164 | 1.25269 | 0.626344 | − | 0.779547i | \(-0.284551\pi\) | ||||
0.626344 | + | 0.779547i | \(0.284551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.4721 | 1.02041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.8328 | 1.03465 | 0.517327 | − | 0.855788i | \(-0.326927\pi\) | ||||
0.517327 | + | 0.855788i | \(0.326927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0689 | 1.89854 | 0.949271 | − | 0.314459i | \(-0.101823\pi\) | ||||
0.949271 | + | 0.314459i | \(0.101823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.16718 | −0.0525673 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.23607 | −0.324582 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9443 | 1.29572 | 0.647862 | − | 0.761758i | \(-0.275663\pi\) | ||||
0.647862 | + | 0.761758i | \(0.275663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.9443 | −1.29056 | −0.645281 | − | 0.763946i | \(-0.723260\pi\) | ||||
−0.645281 | + | 0.763946i | \(0.723260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.3050 | 2.55004 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.12461 | −0.227144 | −0.113572 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113572 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9443 | −0.661096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −59.7771 | −2.63409 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.94427 | 0.217449 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.1246 | −1.10073 | −0.550365 | − | 0.834924i | \(-0.685511\pi\) | ||||
−0.550365 | + | 0.834924i | \(0.685511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.88854 | −0.0822663 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.58359 | 0.416678 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −32.3607 | −1.40170 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.3607 | 1.57201 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.23607 | −0.139387 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.3607 | −1.64925 | −0.824627 | − | 0.565677i | \(-0.808615\pi\) | ||||
−0.824627 | + | 0.565677i | \(0.808615\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.4164 | −1.51707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.8328 | −1.66037 | −0.830186 | − | 0.557487i | \(-0.811766\pi\) | ||||
−0.830186 | + | 0.557487i | \(0.811766\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.77709 | 0.160909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9443 | 0.887437 | 0.443719 | − | 0.896166i | \(-0.353659\pi\) | ||||
0.443719 | + | 0.896166i | \(0.353659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.8885 | −2.44842 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3050 | −1.23506 | −0.617528 | − | 0.786549i | \(-0.711866\pi\) | ||||
−0.617528 | + | 0.786549i | \(0.711866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.8885 | −1.76226 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.5279 | 0.734806 | 0.367403 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367403 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.9443 | −1.21128 | −0.605640 | − | 0.795739i | \(-0.707083\pi\) | ||||
−0.605640 | + | 0.795739i | \(0.707083\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.2361 | −1.30263 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9443 | 0.537019 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.8885 | 1.07219 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.4164 | 0.801401 | 0.400700 | − | 0.916209i | \(-0.368767\pi\) | ||||
0.400700 | + | 0.916209i | \(0.368767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.11146 | 0.251818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.1246 | −0.703224 | −0.351612 | − | 0.936146i | \(-0.614366\pi\) | ||||
−0.351612 | + | 0.936146i | \(0.614366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47214 | −0.101348 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7639 | 1.01183 | 0.505913 | − | 0.862584i | \(-0.331156\pi\) | ||||
0.505913 | + | 0.862584i | \(0.331156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.111456 | 0.00454639 | 0.00227320 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227320 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.70820 | 0.0694484 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9443 | −1.17481 | −0.587406 | − | 0.809292i | \(-0.699851\pi\) | ||||
−0.587406 | + | 0.809292i | \(0.699851\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.83282 | 0.276426 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.8328 | −0.518313 | −0.259156 | − | 0.965835i | \(-0.583444\pi\) | ||||
−0.259156 | + | 0.965835i | \(0.583444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.4721 | −1.87090 | −0.935449 | − | 0.353462i | \(-0.885004\pi\) | ||||
−0.935449 | + | 0.353462i | \(0.885004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0557 | −0.444367 | −0.222184 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222184 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.29180 | 0.0918189 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.41641 | 0.136221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8885 | 0.712132 | 0.356066 | − | 0.934461i | \(-0.384118\pi\) | ||||
0.356066 | + | 0.934461i | \(0.384118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 57.8885 | 2.29724 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 50.2492 | 1.98473 | 0.992363 | − | 0.123356i | \(-0.0393657\pi\) | ||||
0.992363 | + | 0.123356i | \(0.0393657\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4164 | 0.923453 | 0.461726 | − | 0.887022i | \(-0.347230\pi\) | ||||
0.461726 | + | 0.887022i | \(0.347230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.4721 | 1.19798 | 0.598992 | − | 0.800755i | \(-0.295568\pi\) | ||||
0.598992 | + | 0.800755i | \(0.295568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.9443 | 0.822135 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.4164 | −0.446759 | −0.223379 | − | 0.974732i | \(-0.571709\pi\) | ||||
−0.223379 | + | 0.974732i | \(0.571709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51.7771 | −2.02310 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.6525 | 1.19405 | 0.597025 | − | 0.802222i | \(-0.296349\pi\) | ||||
0.597025 | + | 0.802222i | \(0.296349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.4721 | −0.951856 | −0.475928 | − | 0.879484i | \(-0.657888\pi\) | ||||
−0.475928 | + | 0.879484i | \(0.657888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.72136 | 0.337692 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.4721 | −0.558691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.3050 | 1.66928 | 0.834642 | − | 0.550793i | \(-0.185675\pi\) | ||||
0.834642 | + | 0.550793i | \(0.185675\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.0132 | 1.19193 | 0.595966 | − | 0.803010i | \(-0.296769\pi\) | ||||
0.595966 | + | 0.803010i | \(0.296769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.94427 | −0.266497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.18034 | 0.313012 | 0.156506 | − | 0.987677i | \(-0.449977\pi\) | ||||
0.156506 | + | 0.987677i | \(0.449977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.94427 | −0.188911 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.7771 | 1.36300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.8885 | 1.59352 | 0.796758 | − | 0.604299i | \(-0.206547\pi\) | ||||
0.796758 | + | 0.604299i | \(0.206547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000 | 0.606915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.52786 | 0.209383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.4164 | 0.431192 | 0.215596 | − | 0.976483i | \(-0.430831\pi\) | ||||
0.215596 | + | 0.976483i | \(0.430831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.0557 | −0.416975 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.7082 | −0.665986 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.94427 | 0.110574 | 0.0552872 | − | 0.998470i | \(-0.482393\pi\) | ||||
0.0552872 | + | 0.998470i | \(0.482393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.1115 | 0.528478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46.8328 | −1.75145 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.0557 | −0.710659 | −0.355329 | − | 0.934741i | \(-0.615631\pi\) | ||||
−0.355329 | + | 0.934741i | \(0.615631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4721 | 0.687938 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.36068 | −0.310508 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3607 | 0.458432 | 0.229216 | − | 0.973376i | \(-0.426384\pi\) | ||||
0.229216 | + | 0.973376i | \(0.426384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.3050 | 1.74725 | 0.873624 | − | 0.486601i | \(-0.161764\pi\) | ||||
0.873624 | + | 0.486601i | \(0.161764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.8885 | −0.953617 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.4853 | 1.81544 | 0.907720 | − | 0.419577i | \(-0.137822\pi\) | ||||
0.907720 | + | 0.419577i | \(0.137822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.8885 | −2.12087 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2361 | −0.410557 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | −0.875772 | −0.437886 | − | 0.899030i | \(-0.644273\pi\) | ||||
−0.437886 | + | 0.899030i | \(0.644273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.88854 | −0.359881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.9443 | 0.688541 | 0.344271 | − | 0.938870i | \(-0.388126\pi\) | ||||
0.344271 | + | 0.938870i | \(0.388126\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1803 | 0.441537 | 0.220768 | − | 0.975326i | \(-0.429143\pi\) | ||||
0.220768 | + | 0.975326i | \(0.429143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9443 | 0.396209 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.9443 | 1.04512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8885 | 1.00569 | 0.502843 | − | 0.864378i | \(-0.332287\pi\) | ||||
0.502843 | + | 0.864378i | \(0.332287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.7639 | −0.746827 | −0.373413 | − | 0.927665i | \(-0.621813\pi\) | ||||
−0.373413 | + | 0.927665i | \(0.621813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.5279 | −0.485935 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.8885 | −0.640924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.4164 | 0.837905 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.3050 | 1.90254 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.16718 | 0.0416056 | 0.0208028 | − | 0.999784i | \(-0.493378\pi\) | ||||
0.0208028 | + | 0.999784i | \(0.493378\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.9443 | 0.460245 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.34752 | 0.0477318 | 0.0238659 | − | 0.999715i | \(-0.492403\pi\) | ||||
0.0238659 | + | 0.999715i | \(0.492403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.16718 | −0.0412920 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.3607 | 1.70661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4721 | 0.651057 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.0000 | 1.12506 | 0.562530 | − | 0.826777i | \(-0.309828\pi\) | ||||
0.562530 | + | 0.826777i | \(0.309828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.11146 | −0.214602 | −0.107301 | − | 0.994227i | \(-0.534221\pi\) | ||||
−0.107301 | + | 0.994227i | \(0.534221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.8885 | −0.906836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.9443 | −1.28936 | −0.644682 | − | 0.764451i | \(-0.723010\pi\) | ||||
−0.644682 | + | 0.764451i | \(0.723010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0557 | 0.664241 | 0.332120 | − | 0.943237i | \(-0.392236\pi\) | ||||
0.332120 | + | 0.943237i | \(0.392236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.8197 | 0.550103 | 0.275052 | − | 0.961429i | \(-0.411305\pi\) | ||||
0.275052 | + | 0.961429i | \(0.411305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5279 | −1.09501 | −0.547504 | − | 0.836803i | \(-0.684422\pi\) | ||||
−0.547504 | + | 0.836803i | \(0.684422\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.763932 | 0.0264687 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.9443 | −1.27851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.4721 | 0.499634 | 0.249817 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249817 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6656 | −0.919505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.6525 | −0.779269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.527864 | −0.0181376 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.5279 | −0.875084 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5836 | 0.636290 | 0.318145 | − | 0.948042i | \(-0.396940\pi\) | ||||
0.318145 | + | 0.948042i | \(0.396940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.1803 | 0.416072 | 0.208036 | − | 0.978121i | \(-0.433293\pi\) | ||||
0.208036 | + | 0.978121i | \(0.433293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.4721 | −1.17617 | −0.588087 | − | 0.808798i | \(-0.700119\pi\) | ||||
−0.588087 | + | 0.808798i | \(0.700119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1803 | 1.50392 | 0.751958 | − | 0.659211i | \(-0.229110\pi\) | ||||
0.751958 | + | 0.659211i | \(0.229110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.3050 | 1.94843 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.8885 | −1.42097 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.7771 | −1.21226 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.52786 | −0.0516512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.83282 | 0.298263 | 0.149131 | − | 0.988817i | \(-0.452352\pi\) | ||||
0.149131 | + | 0.988817i | \(0.452352\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.12461 | −0.0378891 | −0.0189446 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189446 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9443 | 0.435609 | 0.217805 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217805 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.4721 | −1.02315 | −0.511577 | − | 0.859237i | \(-0.670939\pi\) | ||||
−0.511577 | + | 0.859237i | \(0.670939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.8885 | −0.599963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.77709 | 0.126395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.583592 | −0.0195073 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.77709 | 0.125973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.11146 | −0.203602 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.4164 | −0.911352 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9443 | −0.429807 | −0.214904 | − | 0.976635i | \(-0.568944\pi\) | ||||
−0.214904 | + | 0.976635i | \(0.568944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1246 | −0.832416 | −0.416208 | − | 0.909270i | \(-0.636641\pi\) | ||||
−0.416208 | + | 0.909270i | \(0.636641\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.8885 | −1.38631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0000 | 0.528367 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.9443 | −1.48257 | −0.741287 | − | 0.671188i | \(-0.765784\pi\) | ||||
−0.741287 | + | 0.671188i | \(0.765784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.3607 | 1.06516 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.4721 | 0.804639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.2361 | 1.81224 | 0.906118 | − | 0.423024i | \(-0.139032\pi\) | ||||
0.906118 | + | 0.423024i | \(0.139032\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47214 | −0.0810210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9443 | 0.488208 | 0.244104 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244104 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4296 | 1.64396 | 0.821978 | − | 0.569519i | \(-0.192870\pi\) | ||||
0.821978 | + | 0.569519i | \(0.192870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.3050 | −1.34507 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.1246 | −0.946423 | −0.473211 | − | 0.880949i | \(-0.656905\pi\) | ||||
−0.473211 | + | 0.880949i | \(0.656905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.8328 | 2.16949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7771 | −0.640643 | −0.320321 | − | 0.947309i | \(-0.603791\pi\) | ||||
−0.320321 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −86.2492 | −2.79096 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.52786 | 0.0493373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40.3607 | −1.29926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7771 | −0.378726 | −0.189363 | − | 0.981907i | \(-0.560642\pi\) | ||||
−0.189363 | + | 0.981907i | \(0.560642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.88854 | −0.317338 | −0.158669 | − | 0.987332i | \(-0.550720\pi\) | ||||
−0.158669 | + | 0.987332i | \(0.550720\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.94427 | −0.158506 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.2492 | −1.60762 | −0.803808 | − | 0.594889i | \(-0.797196\pi\) | ||||
−0.803808 | + | 0.594889i | \(0.797196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.41641 | −0.237029 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.9443 | −0.412858 | −0.206429 | − | 0.978462i | \(-0.566184\pi\) | ||||
−0.206429 | + | 0.978462i | \(0.566184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −73.8885 | −2.34952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.16718 | −0.291205 | −0.145603 | − | 0.989343i | \(-0.546512\pi\) | ||||
−0.145603 | + | 0.989343i | \(0.546512\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.8885 | −0.820722 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.3607 | −1.59494 | −0.797469 | − | 0.603359i | \(-0.793828\pi\) | ||||
−0.797469 | + | 0.603359i | \(0.793828\pi\) | |||||||
\(998\) | 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 | 4032.2.a.bp.1.1 | 2 | ||
3.2 | odd | 2 | 4032.2.a.bx.1.2 | 2 | |||
4.3 | odd | 2 | 4032.2.a.bo.1.1 | 2 | |||
8.3 | odd | 2 | 2016.2.a.u.1.2 | yes | 2 | ||
8.5 | even | 2 | 2016.2.a.v.1.2 | yes | 2 | ||
12.11 | even | 2 | 4032.2.a.bu.1.2 | 2 | |||
24.5 | odd | 2 | 2016.2.a.q.1.1 | yes | 2 | ||
24.11 | even | 2 | 2016.2.a.p.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.a.p.1.1 | ✓ | 2 | 24.11 | even | 2 | ||
2016.2.a.q.1.1 | yes | 2 | 24.5 | odd | 2 | ||
2016.2.a.u.1.2 | yes | 2 | 8.3 | odd | 2 | ||
2016.2.a.v.1.2 | yes | 2 | 8.5 | even | 2 | ||
4032.2.a.bo.1.1 | 2 | 4.3 | odd | 2 | |||
4032.2.a.bp.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4032.2.a.bu.1.2 | 2 | 12.11 | even | 2 | |||
4032.2.a.bx.1.2 | 2 | 3.2 | odd | 2 |