Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(169,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.r (of order \(3\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.337 |
Dual form | 504.2.r.b.169.1 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 5.19615i | 0.832050 | − | 1.44115i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
0.896410 | − | 0.443227i | \(-0.146166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410i | 0.894427i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | − | 0.866025i | −0.327327 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | + | 3.46410i | 0.371391 | + | 0.643268i | 0.989780 | − | 0.142605i | \(-0.0455477\pi\) |
−0.618389 | + | 0.785872i | \(0.712214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | + | 8.66025i | −0.898027 | + | 1.55543i | −0.0680129 | + | 0.997684i | \(0.521666\pi\) |
−0.830014 | + | 0.557743i | \(0.811667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | + | 2.59808i | 0.783349 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 10.3923i | − | 1.66410i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.50000 | + | 6.06218i | −0.546608 | + | 0.946753i | 0.451896 | + | 0.892071i | \(0.350748\pi\) |
−0.998504 | + | 0.0546823i | \(0.982585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | + | 5.19615i | 0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | − | 6.92820i | −0.583460 | − | 1.01058i | −0.995066 | − | 0.0992202i | \(-0.968365\pi\) |
0.411606 | − | 0.911362i | \(-0.364968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5000 | − | 6.06218i | 1.47029 | − | 0.848875i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50000 | − | 0.866025i | 0.198680 | − | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50000 | + | 7.79423i | −0.585850 | + | 1.01472i | 0.408919 | + | 0.912571i | \(0.365906\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50000 | + | 7.79423i | −0.549762 | + | 0.952217i | 0.448528 | + | 0.893769i | \(0.351948\pi\) |
−0.998290 | + | 0.0584478i | \(0.981385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0000 | 1.52153 | 0.760767 | − | 0.649025i | \(-0.224823\pi\) | ||||
0.760767 | + | 0.649025i | \(0.224823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.50000 | + | 0.866025i | 0.173205 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | − | 2.59808i | 0.170941 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | + | 12.1244i | −0.759257 | + | 1.31507i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000 | + | 3.46410i | 0.643268 | + | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.3205i | 1.79605i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | + | 1.73205i | −0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | − | 6.06218i | −0.355371 | − | 0.615521i | 0.631810 | − | 0.775123i | \(-0.282312\pi\) |
−0.987181 | + | 0.159602i | \(0.948979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 5.19615i | −0.295599 | + | 0.511992i | −0.975124 | − | 0.221660i | \(-0.928852\pi\) |
0.679525 | + | 0.733652i | \(0.262186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | − | 1.73205i | 0.292770 | − | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00000 | −0.870063 | −0.435031 | − | 0.900415i | \(-0.643263\pi\) | ||||
−0.435031 | + | 0.900415i | \(0.643263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | + | 5.19615i | −0.854242 | + | 0.493197i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.00000 | − | 15.5885i | −0.832050 | − | 1.44115i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.50000 | − | 6.06218i | −0.320844 | − | 0.555719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.1244i | 1.09322i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.5000 | − | 9.52628i | −1.45274 | − | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.500000 | − | 0.866025i | −0.0433555 | − | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | + | 5.19615i | 0.774597 | + | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.50000 | − | 4.33013i | −0.213589 | − | 0.369948i | 0.739246 | − | 0.673436i | \(-0.235182\pi\) |
−0.952835 | + | 0.303488i | \(0.901849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.50000 | + | 2.59808i | −0.127228 | + | 0.220366i | −0.922602 | − | 0.385754i | \(-0.873941\pi\) |
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0000 | − | 6.92820i | −1.01058 | − | 0.583460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.0000 | 1.50524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205i | 0.142857i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.00000 | + | 13.8564i | −0.655386 | + | 1.13516i | 0.326411 | + | 0.945228i | \(0.394160\pi\) |
−0.981797 | + | 0.189933i | \(0.939173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.5000 | − | 18.1865i | 0.848875 | − | 1.47029i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0000 | − | 17.3205i | −0.803219 | − | 1.39122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | − | 5.19615i | 0.239426 | − | 0.414698i | −0.721124 | − | 0.692806i | \(-0.756374\pi\) |
0.960550 | + | 0.278108i | \(0.0897074\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 3.46410i | −0.475831 | + | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00000 | + | 5.19615i | −0.700649 | + | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | + | 10.3923i | −0.464294 | + | 0.804181i | −0.999169 | − | 0.0407502i | \(-0.987025\pi\) |
0.534875 | + | 0.844931i | \(0.320359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 2.59808i | 0.114708 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0000 | + | 19.0526i | 0.836315 | + | 1.44854i | 0.892956 | + | 0.450145i | \(0.148628\pi\) |
−0.0566411 | + | 0.998395i | \(0.518039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.5885i | 1.17170i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | − | 3.46410i | −0.443533 | − | 0.256074i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | − | 10.3923i | 0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5000 | + | 18.1865i | 0.767836 | + | 1.32993i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | + | 2.59808i | −0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0000 | + | 17.3205i | 0.723575 | + | 1.25327i | 0.959558 | + | 0.281511i | \(0.0908356\pi\) |
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.0000 | + | 10.3923i | 1.28901 | + | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.5885i | 1.09952i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | − | 3.46410i | 0.140372 | − | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00000 | − | 12.1244i | −0.488901 | − | 0.846802i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | − | 10.3923i | −0.417029 | − | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.50000 | + | 2.59808i | 0.103757 | + | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.0000 | 1.50039 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0000 | 0.678844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.5000 | − | 11.2583i | 1.31769 | − | 0.760767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0000 | − | 36.3731i | 1.41261 | − | 2.44672i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000 | + | 10.3923i | 0.401790 | + | 0.695920i | 0.993942 | − | 0.109906i | \(-0.0350549\pi\) |
−0.592152 | + | 0.805826i | \(0.701722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.50000 | − | 9.52628i | −0.365048 | − | 0.632281i | 0.623736 | − | 0.781635i | \(-0.285614\pi\) |
−0.988784 | + | 0.149354i | \(0.952281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 5.19615i | − | 0.341882i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0000 | −0.851658 | −0.425829 | − | 0.904804i | \(-0.640018\pi\) | ||||
−0.425829 | + | 0.904804i | \(0.640018\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.0000 | − | 8.66025i | −0.974355 | − | 0.562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.00000 | − | 8.66025i | 0.323423 | − | 0.560185i | −0.657769 | − | 0.753220i | \(-0.728500\pi\) |
0.981192 | + | 0.193035i | \(0.0618330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5000 | + | 25.1147i | 0.934027 | + | 1.61778i | 0.776360 | + | 0.630290i | \(0.217064\pi\) |
0.157667 | + | 0.987492i | \(0.449603\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | − | 1.73205i | −0.0638877 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.00000 | −0.315597 | −0.157799 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157799 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.2487i | 1.51851i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5000 | − | 23.3827i | 0.842107 | − | 1.45857i | −0.0460033 | − | 0.998941i | \(-0.514648\pi\) |
0.888110 | − | 0.459631i | \(-0.152018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | + | 5.19615i | 0.186411 | + | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 5.19615i | 0.184988 | + | 0.320408i | 0.943572 | − | 0.331166i | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | − | 6.92820i | 0.245718 | − | 0.425596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0000 | − | 8.66025i | 0.917985 | − | 0.529999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0000 | 1.57939 | 0.789694 | − | 0.613501i | \(-0.210239\pi\) | ||||
0.789694 | + | 0.613501i | \(0.210239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | + | 5.19615i | −0.544705 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0000 | + | 25.9808i | 0.898027 | + | 1.55543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | − | 5.19615i | −0.178965 | − | 0.309976i | 0.762561 | − | 0.646916i | \(-0.223942\pi\) |
−0.941526 | + | 0.336939i | \(0.890608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0000 | + | 17.3205i | −0.594438 | + | 1.02960i | 0.399188 | + | 0.916869i | \(0.369292\pi\) |
−0.993626 | + | 0.112728i | \(0.964041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.46410i | 0.205196i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.00000 | 0.413197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.5000 | − | 6.06218i | −0.615521 | − | 0.355371i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | − | 15.5885i | −0.524000 | − | 0.907595i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | − | 7.79423i | 0.783349 | − | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.50000 | + | 9.52628i | −0.317015 | + | 0.549086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.0000 | + | 10.3923i | 1.03407 | + | 0.597022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0000 | −0.970241 | −0.485121 | − | 0.874447i | \(-0.661224\pi\) | ||||
−0.485121 | + | 0.874447i | \(0.661224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3923i | 0.591198i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | − | 25.9808i | 0.850572 | − | 1.47323i | −0.0301210 | − | 0.999546i | \(-0.509589\pi\) |
0.880693 | − | 0.473688i | \(-0.157077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.50000 | + | 11.2583i | 0.367402 | + | 0.636358i | 0.989158 | − | 0.146852i | \(-0.0469141\pi\) |
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | − | 5.19615i | 0.169031 | − | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 10.3923i | −0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5000 | + | 7.79423i | −0.753497 | + | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.00000 | 0.389490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.00000 | + | 1.73205i | −0.165900 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | + | 6.92820i | −0.220527 | + | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | − | 27.7128i | −0.879440 | − | 1.52323i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
−0.0274825 | − | 0.999622i | \(-0.508749\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.00000 | + | 15.5885i | −0.493197 | + | 0.854242i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.00000 | − | 15.5885i | −0.491723 | − | 0.851688i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5000 | − | 21.6506i | 0.680918 | − | 1.17939i | −0.293783 | − | 0.955872i | \(-0.594914\pi\) |
0.974701 | − | 0.223513i | \(-0.0717525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3923i | 0.564433i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.0000 | −1.62459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | + | 6.92820i | 0.646058 | + | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.50000 | + | 7.79423i | −0.241573 | + | 0.418416i | −0.961162 | − | 0.275983i | \(-0.910997\pi\) |
0.719590 | + | 0.694399i | \(0.244330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | − | 22.5167i | −0.695874 | − | 1.20529i | −0.969885 | − | 0.243563i | \(-0.921684\pi\) |
0.274011 | − | 0.961727i | \(-0.411649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | − | 15.5885i | −1.44115 | − | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5000 | − | 18.1865i | −0.558859 | − | 0.967972i | −0.997592 | − | 0.0693543i | \(-0.977906\pi\) |
0.438733 | − | 0.898617i | \(-0.355427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5000 | − | 6.06218i | −0.555719 | − | 0.320844i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.46410i | − | 0.181818i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0000 | + | 22.5167i | −0.680451 | + | 1.17858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.00000 | − | 1.73205i | −0.0521996 | − | 0.0904123i | 0.838745 | − | 0.544524i | \(-0.183290\pi\) |
−0.890945 | + | 0.454112i | \(0.849957\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.5000 | + | 18.1865i | 0.546608 | + | 0.946753i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | + | 3.46410i | 0.103835 | + | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00000 | + | 12.1244i | −0.362446 | + | 0.627775i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.625917 | + | 0.779890i | \(0.284725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | + | 10.3923i | −0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0000 | 1.38690 | 0.693448 | − | 0.720506i | \(-0.256091\pi\) | ||||
0.693448 | + | 0.720506i | \(0.256091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | + | 3.46410i | −0.307389 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | + | 10.3923i | −0.306586 | + | 0.531022i | −0.977613 | − | 0.210411i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | + | 5.19615i | 0.152894 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −33.0000 | −1.67748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.00000 | + | 6.92820i | 0.202808 | + | 0.351274i | 0.949432 | − | 0.313972i | \(-0.101660\pi\) |
−0.746624 | + | 0.665246i | \(0.768327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | − | 24.2487i | 0.708010 | − | 1.22631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.92820i | − | 0.349482i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.0000 | 1.00631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0000 | 1.70641 | 0.853206 | − | 0.521575i | \(-0.174655\pi\) | ||||
0.853206 | + | 0.521575i | \(0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.50000 | − | 0.866025i | −0.0750939 | − | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5000 | + | 28.5788i | −0.823971 | + | 1.42716i | 0.0787327 | + | 0.996896i | \(0.474913\pi\) |
−0.902703 | + | 0.430263i | \(0.858421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.0000 | + | 51.9615i | 1.49441 | + | 2.58839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.00000 | − | 15.5885i | −0.446113 | − | 0.772691i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.50000 | + | 12.9904i | −0.370851 | + | 0.642333i | −0.989697 | − | 0.143180i | \(-0.954267\pi\) |
0.618846 | + | 0.785513i | \(0.287601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.50000 | − | 4.33013i | −0.369948 | − | 0.213589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.00000 | 0.442861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.19615i | 0.254457i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | + | 17.3205i | −0.488532 | + | 0.846162i | −0.999913 | − | 0.0131919i | \(-0.995801\pi\) |
0.511381 | + | 0.859354i | \(0.329134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | + | 17.3205i | 0.487370 | + | 0.844150i | 0.999895 | − | 0.0145228i | \(-0.00462290\pi\) |
−0.512524 | + | 0.858673i | \(0.671290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.0000 | −1.16692 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.50000 | + | 6.06218i | 0.169775 | + | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | + | 3.46410i | −0.0967868 | + | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.0000 | − | 15.5885i | 1.30357 | − | 0.752618i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | −0.240285 | −0.120142 | − | 0.992757i | \(-0.538335\pi\) | ||||
−0.120142 | + | 0.992757i | \(0.538335\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | + | 6.92820i | −0.575356 | + | 0.332182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | − | 3.46410i | 0.0956730 | − | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.50000 | − | 9.52628i | −0.261313 | − | 0.452607i | 0.705278 | − | 0.708931i | \(-0.250822\pi\) |
−0.966591 | + | 0.256323i | \(0.917489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | + | 17.3205i | −0.474045 | + | 0.821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.7128i | 1.31077i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0000 | −1.08544 | −0.542719 | − | 0.839915i | \(-0.682605\pi\) | ||||
−0.542719 | + | 0.839915i | \(0.682605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.0000 | −0.988851 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.0000 | − | 8.66025i | −0.704761 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 10.3923i | 0.281284 | − | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | − | 21.6506i | −0.584725 | − | 1.01277i | −0.994910 | − | 0.100771i | \(-0.967869\pi\) |
0.410184 | − | 0.912003i | \(-0.365464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 36.3731i | − | 1.69775i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | − | 25.9808i | −0.698620 | − | 1.21004i | −0.968945 | − | 0.247276i | \(-0.920465\pi\) |
0.270326 | − | 0.962769i | \(-0.412869\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | − | 13.8564i | 0.371792 | − | 0.643962i | −0.618050 | − | 0.786139i | \(-0.712077\pi\) |
0.989841 | + | 0.142177i | \(0.0454103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30.0000 | − | 17.3205i | −1.39122 | − | 0.803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0000 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.00000 | 0.415581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 10.3923i | − | 0.478852i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.5000 | − | 28.5788i | 0.758671 | − | 1.31406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | + | 0.866025i | 0.0229416 | + | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0000 | + | 17.3205i | 0.456912 | + | 0.791394i | 0.998796 | − | 0.0490589i | \(-0.0156222\pi\) |
−0.541884 | + | 0.840453i | \(0.682289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | + | 31.1769i | −0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | + | 3.46410i | −0.273009 | + | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | − | 3.46410i | 0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.5000 | + | 18.1865i | −0.473858 | + | 0.820747i | −0.999552 | − | 0.0299272i | \(-0.990472\pi\) |
0.525694 | + | 0.850674i | \(0.323806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0000 | + | 24.2487i | 0.630528 | + | 1.09211i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.00000 | + | 15.5885i | −0.404520 | + | 0.700649i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.50000 | − | 14.7224i | 0.380512 | − | 0.659067i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) |
0.991136 | + | 0.132855i | \(0.0424144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.0000 | 0.980932 | 0.490466 | − | 0.871460i | \(-0.336827\pi\) | ||||
0.490466 | + | 0.871460i | \(0.336827\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.5000 | − | 19.9186i | −1.53220 | − | 0.884615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0000 | − | 36.3731i | 0.930809 | − | 1.61221i | 0.148866 | − | 0.988857i | \(-0.452438\pi\) |
0.781943 | − | 0.623350i | \(-0.214229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.50000 | − | 11.2583i | −0.287543 | − | 0.498039i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.19615i | − | 0.229416i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.00000 | − | 10.3923i | −0.264392 | − | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | − | 20.7846i | 0.527759 | − | 0.914106i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.0000 | + | 19.0526i | 1.44854 | + | 0.836315i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.73205i | − | 0.0755929i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.0000 | + | 60.6218i | −1.52462 | + | 2.64073i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.5000 | + | 23.3827i | 0.585850 | + | 1.01472i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.0000 | + | 36.3731i | 0.909611 | + | 1.57549i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 15.5885i | 0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.0000 | + | 13.8564i | −1.03568 | + | 0.597948i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0000 | −1.37579 | −0.687894 | − | 0.725811i | \(-0.741464\pi\) | ||||
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0000 | − | 6.92820i | 0.514969 | − | 0.297318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | − | 3.46410i | 0.0856706 | − | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.50000 | + | 14.7224i | 0.363434 | + | 0.629486i | 0.988524 | − | 0.151067i | \(-0.0482710\pi\) |
−0.625090 | + | 0.780553i | \(0.714938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.0000 | −0.512148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.00000 | + | 3.46410i | 0.0852029 | + | 0.147576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | + | 8.66025i | −0.212622 | + | 0.368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 20.7846i | − | 0.882258i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.00000 | 0.169485 | 0.0847427 | − | 0.996403i | \(-0.472993\pi\) | ||||
0.0847427 | + | 0.996403i | \(0.472993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −66.0000 | −2.79150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.5000 | + | 18.1865i | 1.32993 | + | 0.767836i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.50000 | − | 14.7224i | 0.358232 | − | 0.620477i | −0.629433 | − | 0.777055i | \(-0.716713\pi\) |
0.987666 | + | 0.156578i | \(0.0500463\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | − | 10.3923i | −0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | + | 7.79423i | −0.188982 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5000 | − | 32.0429i | 0.774201 | − | 1.34096i | −0.161042 | − | 0.986948i | \(-0.551485\pi\) |
0.935243 | − | 0.354008i | \(-0.115181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.0000 | + | 17.3205i | 1.25327 | + | 0.723575i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0000 | −0.624458 | −0.312229 | − | 0.950007i | \(-0.601076\pi\) | ||||
−0.312229 | + | 0.950007i | \(0.601076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 25.9808i | − | 1.07972i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.0000 | 1.48842 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5000 | + | 19.9186i | 0.474656 | + | 0.822128i | 0.999579 | − | 0.0290218i | \(-0.00923921\pi\) |
−0.524923 | + | 0.851150i | \(0.675906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | + | 5.19615i | −0.370211 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.0000 | 0.573944 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.0000 | − | 12.1244i | 0.859473 | − | 0.496217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | + | 13.8564i | −0.326871 | + | 0.566157i | −0.981889 | − | 0.189456i | \(-0.939328\pi\) |
0.655018 | + | 0.755613i | \(0.272661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5000 | + | 19.9186i | 0.469095 | + | 0.812496i | 0.999376 | − | 0.0353259i | \(-0.0112469\pi\) |
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5000 | + | 23.3827i | 0.549762 | + | 0.952217i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | + | 3.46410i | 0.0813116 | + | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 6.92820i | − | 0.280745i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.0000 | − | 12.1244i | −0.846802 | − | 0.488901i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.50000 | − | 7.79423i | 0.181163 | − | 0.313784i | −0.761114 | − | 0.648618i | \(-0.775347\pi\) |
0.942277 | + | 0.334835i | \(0.108680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.5000 | − | 18.1865i | −0.422031 | − | 0.730978i | 0.574107 | − | 0.818780i | \(-0.305349\pi\) |
−0.996138 | + | 0.0878015i | \(0.972016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 10.3923i | −0.722315 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.00000 | − | 8.66025i | −0.200321 | − | 0.346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.50000 | + | 2.59808i | 0.179713 | + | 0.103757i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.0000 | −1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.8564i | 0.550743i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | − | 6.92820i | 0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5000 | − | 21.6506i | −0.493720 | − | 0.855149i | 0.506254 | − | 0.862385i | \(-0.331030\pi\) |
−0.999974 | + | 0.00723604i | \(0.997697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.5000 | + | 21.6506i | −0.492952 | + | 0.853818i | −0.999967 | − | 0.00811944i | \(-0.997415\pi\) |
0.507015 | + | 0.861937i | \(0.330749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.0000 | − | 19.0526i | 1.29937 | − | 0.750194i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0000 | −1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | − | 8.66025i | 0.587896 | − | 0.339422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.0000 | − | 19.0526i | 0.430463 | − | 0.745584i | −0.566450 | − | 0.824096i | \(-0.691684\pi\) |
0.996913 | + | 0.0785119i | \(0.0250169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | + | 6.92820i | 0.156293 | + | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.5000 | − | 33.7750i | 0.760767 | − | 1.31769i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0000 | + | 34.6410i | 0.779089 | + | 1.34942i | 0.932467 | + | 0.361255i | \(0.117652\pi\) |
−0.153378 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | − | 24.2487i | 0.544537 | − | 0.943166i | −0.454099 | − | 0.890951i | \(-0.650039\pi\) |
0.998636 | − | 0.0522143i | \(-0.0166279\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 72.7461i | − | 2.82523i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.0000 | + | 10.3923i | 0.695920 | + | 0.401790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000 | − | 10.3923i | 0.231627 | − | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | + | 43.3013i | 0.963679 | + | 1.66914i | 0.713123 | + | 0.701039i | \(0.247280\pi\) |
0.250557 | + | 0.968102i | \(0.419386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | − | 2.59808i | 0.173205 | − | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | − | 5.19615i | −0.115299 | − | 0.199704i | 0.802600 | − | 0.596518i | \(-0.203449\pi\) |
−0.917899 | + | 0.396813i | \(0.870116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.50000 | + | 6.06218i | −0.134318 | + | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.5000 | − | 9.52628i | −0.632281 | − | 0.365048i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.0000 | 1.03313 | 0.516563 | − | 0.856249i | \(-0.327211\pi\) | ||||
0.516563 | + | 0.856249i | \(0.327211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2487i | 0.925146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | + | 13.8564i | 0.304334 | + | 0.527123i | 0.977113 | − | 0.212721i | \(-0.0682327\pi\) |
−0.672779 | + | 0.739844i | \(0.734899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.50000 | − | 7.79423i | −0.170941 | − | 0.296078i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.00000 | − | 5.19615i | −0.113796 | − | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.5000 | + | 42.4352i | −0.928004 | + | 1.60735i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.5000 | + | 11.2583i | −0.737558 | + | 0.425829i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.0000 | − | 13.8564i | 0.903892 | − | 0.521862i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | − | 10.3923i | 0.225653 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0000 | − | 24.2487i | −0.525781 | − | 0.910679i | −0.999549 | − | 0.0300298i | \(-0.990440\pi\) |
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.0000 | −1.12509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.0000 | + | 34.6410i | 0.749006 | + | 1.29732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | + | 31.1769i | −0.673162 | + | 1.16595i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 17.3205i | − | 0.646846i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0000 | 1.11881 | 0.559406 | − | 0.828894i | \(-0.311029\pi\) | ||||
0.559406 | + | 0.828894i | \(0.311029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.5000 | + | 25.1147i | 1.61778 | + | 0.934027i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | + | 3.46410i | −0.0742781 | + | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.0000 | − | 22.5167i | −0.482143 | − | 0.835097i | 0.517647 | − | 0.855595i | \(-0.326808\pi\) |
−0.999790 | + | 0.0204978i | \(0.993475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.5000 | − | 66.6840i | −1.42397 | − | 2.46640i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | + | 19.0526i | −0.406294 | + | 0.703722i | −0.994471 | − | 0.105010i | \(-0.966513\pi\) |
0.588177 | + | 0.808732i | \(0.299846\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | − | 1.73205i | −0.110657 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.0000 | −0.994558 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0000 | 0.698926 | 0.349463 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349463 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 10.3923i | − | 0.381771i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.00000 | + | 1.73205i | −0.0366864 | + | 0.0635428i | −0.883786 | − | 0.467892i | \(-0.845014\pi\) |
0.847099 | + | 0.531435i | \(0.178347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.0000 | − | 27.7128i | −0.586195 | − | 1.01532i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.50000 | + | 7.79423i | 0.164426 | + | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0000 | − | 29.4449i | 0.620339 | − | 1.07446i | −0.369084 | − | 0.929396i | \(-0.620328\pi\) |
0.989423 | − | 0.145062i | \(-0.0463382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.50000 | + | 4.33013i | −0.273315 | + | 0.157799i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0000 | 0.581530 | 0.290765 | − | 0.956795i | \(-0.406090\pi\) | ||||
0.290765 | + | 0.956795i | \(0.406090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.0000 | − | 10.3923i | 0.653359 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | + | 1.73205i | 0.0362024 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.0000 | + | 36.3731i | 0.759257 | + | 1.31507i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.0000 | + | 46.7654i | 0.974913 | + | 1.68860i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0000 | − | 22.5167i | 0.468792 | − | 0.811972i | −0.530572 | − | 0.847640i | \(-0.678023\pi\) |
0.999364 | + | 0.0356685i | \(0.0113561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 46.7654i | − | 1.68421i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.00000 | 0.143870 | 0.0719350 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719350 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | −0.359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.00000 | + | 5.19615i | 0.322873 | + | 0.186411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.50000 | + | 6.06218i | −0.125401 | + | 0.217200i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.0000 | − | 10.3923i | 0.643268 | − | 0.371391i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.00000 | + | 10.3923i | 0.214149 | + | 0.370917i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | + | 3.46410i | −0.0712923 | + | 0.123482i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
0.828176 | + | 0.560469i | \(0.189379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.00000 | + | 5.19615i | 0.320408 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 13.8564i | − | 0.491436i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.00000 | + | 10.3923i | −0.212531 | + | 0.368114i | −0.952506 | − | 0.304520i | \(-0.901504\pi\) |
0.739975 | + | 0.672634i | \(0.234837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.0000 | − | 48.4974i | −0.990569 | − | 1.71572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0000 | − | 25.9808i | 0.529999 | − | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5000 | + | 33.7750i | 0.688140 | + | 1.19189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | − | 6.92820i | 0.140981 | − | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.0000 | + | 10.3923i | −0.633630 | + | 0.365826i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.0000 | 1.58212 | 0.791058 | − | 0.611741i | \(-0.209531\pi\) | ||||
0.791058 | + | 0.611741i | \(0.209531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0000 | 0.526721 | 0.263361 | − | 0.964697i | \(-0.415169\pi\) | ||||
0.263361 | + | 0.964697i | \(0.415169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.0000 | − | 22.5167i | 1.36779 | − | 0.789694i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.50000 | − | 9.52628i | −0.192421 | − | 0.333282i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.00000 | + | 15.5885i | −0.314485 | + | 0.544705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | − | 39.8372i | 0.801730 | − | 1.38864i | −0.116747 | − | 0.993162i | \(-0.537247\pi\) |
0.918477 | − | 0.395475i | \(-0.129420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.19615i | 0.180907i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.0000 | −0.972480 | −0.486240 | − | 0.873825i | \(-0.661632\pi\) | ||||
−0.486240 | + | 0.873825i | \(0.661632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0000 | − | 8.66025i | −0.520344 | − | 0.300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.50000 | + | 6.06218i | −0.121268 | + | 0.210042i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | − | 20.7846i | −0.415277 | − | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.0000 | + | 25.9808i | 1.55543 | + | 0.898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.0000 | + | 31.1769i | 0.621429 | + | 1.07635i | 0.989220 | + | 0.146438i | \(0.0467809\pi\) |
−0.367791 | + | 0.929909i | \(0.619886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.00000 | − | 5.19615i | −0.309976 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.0000 | 1.58245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.6410i | 1.18888i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | + | 38.1051i | 0.753266 | + | 1.30469i | 0.946232 | + | 0.323489i | \(0.104856\pi\) |
−0.192966 | + | 0.981205i | \(0.561811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | + | 5.19615i | 0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | − | 25.9808i | −0.512390 | − | 0.887486i | −0.999897 | − | 0.0143666i | \(-0.995427\pi\) |
0.487507 | − | 0.873119i | \(-0.337907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.50000 | − | 9.52628i | 0.187658 | − | 0.325032i | −0.756811 | − | 0.653633i | \(-0.773244\pi\) |
0.944469 | + | 0.328601i | \(0.106577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5000 | − | 6.06218i | 0.357839 | − | 0.206598i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.0000 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.0000 | −1.49604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.0000 | − | 27.7128i | 1.63017 | − | 0.941176i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.0000 | − | 25.9808i | 0.508840 | − | 0.881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.0000 | + | 46.7654i | 0.914860 | + | 1.58458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.0000 | −0.710742 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0000 | + | 27.7128i | −0.540282 | + | 0.935795i | 0.458606 | + | 0.888640i | \(0.348349\pi\) |
−0.998888 | + | 0.0471555i | \(0.984984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.0000 | −1.28025 | −0.640126 | − | 0.768270i | \(-0.721118\pi\) | ||||
−0.640126 | + | 0.768270i | \(0.721118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.0000 | − | 15.5885i | −0.907595 | − | 0.524000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.00000 | + | 15.5885i | −0.302190 | + | 0.523409i | −0.976632 | − | 0.214919i | \(-0.931051\pi\) |
0.674441 | + | 0.738328i | \(0.264385\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | + | 3.46410i | 0.0670778 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5000 | − | 23.3827i | 0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.00000 | − | 6.92820i | −0.133855 | − | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0000 | − | 27.7128i | 0.534821 | − | 0.926337i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | − | 20.7846i | −1.20201 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.0000 | −1.33407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.0000 | −0.932815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.0526i | 0.634029i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.00000 | + | 13.8564i | −0.265929 | + | 0.460603i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5000 | + | 47.6314i | 0.913123 | + | 1.58157i | 0.809627 | + | 0.586945i | \(0.199669\pi\) |
0.103495 | + | 0.994630i | \(0.466997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.0000 | 1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | + | 27.7128i | 0.530104 | + | 0.918166i | 0.999383 | + | 0.0351168i | \(0.0111803\pi\) |
−0.469280 | + | 0.883050i | \(0.655486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000 | − | 6.92820i | 0.396708 | − | 0.229039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.5000 | + | 14.7224i | −0.840254 | + | 0.485121i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | − | 5.19615i | −0.0986394 | − | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.00000 | + | 15.5885i | 0.295599 | + | 0.511992i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.0000 | − | 39.8372i | −0.754606 | − | 1.30702i | −0.945570 | − | 0.325418i | \(-0.894495\pi\) |
0.190965 | − | 0.981597i | \(-0.438838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.500000 | + | 0.866025i | −0.0163868 | + | 0.0283828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 51.9615i | − | 1.70114i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −42.0000 | −1.37355 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.5000 | + | 11.2583i | 0.636358 | + | 0.367402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.00000 | − | 10.3923i | 0.195594 | − | 0.338779i | −0.751501 | − | 0.659732i | \(-0.770670\pi\) |
0.947095 | + | 0.320953i | \(0.104003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.0000 | + | 24.2487i | 0.455903 | + | 0.789647i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 10.3923i | − | 0.338062i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.50000 | + | 14.7224i | 0.276213 | + | 0.478415i | 0.970440 | − | 0.241341i | \(-0.0775872\pi\) |
−0.694228 | + | 0.719756i | \(0.744254\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.0000 | − | 67.5500i | 1.26599 | − | 2.19277i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0000 | −1.13376 | −0.566881 | − | 0.823800i | \(-0.691850\pi\) | ||||
−0.566881 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.0000 | −1.29437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7846i | 0.671871i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.50000 | + | 4.33013i | −0.0807292 | + | 0.139827i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5000 | + | 23.3827i | −0.435031 | + | 0.753497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.0000 | + | 25.9808i | 0.482867 | + | 0.836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.00000 | + | 5.19615i | −0.0964735 | + | 0.167097i | −0.910223 | − | 0.414119i | \(-0.864090\pi\) |
0.813749 | + | 0.581216i | \(0.197423\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5000 | − | 6.06218i | 0.337309 | − | 0.194745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00000 | 0.0961756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.00000 | − | 5.19615i | 0.288231 | − | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.5000 | + | 28.5788i | −0.527882 | + | 0.914318i | 0.471590 | + | 0.881818i | \(0.343680\pi\) |
−0.999472 | + | 0.0325001i | \(0.989653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0000 | + | 25.9808i | 0.479402 | + | 0.830349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | + | 5.19615i | −0.0957826 | + | 0.165900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | − | 10.3923i | 0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8564i | 0.441054i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.0000 | −1.39912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000 | 1.14358 | 0.571789 | − | 0.820401i | \(-0.306250\pi\) | ||||
0.571789 | + | 0.820401i | \(0.306250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.0000 | − | 27.7128i | −1.52323 | − | 0.879440i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0000 | + | 24.2487i | −0.443830 | + | 0.768736i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0000 | + | 32.9090i | 0.601736 | + | 1.04224i | 0.992558 | + | 0.121771i | \(0.0388574\pi\) |
−0.390822 | + | 0.920466i | \(0.627809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.1769i | 0.986394i |
(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 | 504.2.r.b.337.1 | yes | 2 | |
3.2 | odd | 2 | 1512.2.r.b.1009.1 | 2 | |||
4.3 | odd | 2 | 1008.2.r.b.337.1 | 2 | |||
9.2 | odd | 6 | 1512.2.r.b.505.1 | 2 | |||
9.4 | even | 3 | 4536.2.a.h.1.1 | 1 | |||
9.5 | odd | 6 | 4536.2.a.c.1.1 | 1 | |||
9.7 | even | 3 | inner | 504.2.r.b.169.1 | ✓ | 2 | |
12.11 | even | 2 | 3024.2.r.d.1009.1 | 2 | |||
36.7 | odd | 6 | 1008.2.r.b.673.1 | 2 | |||
36.11 | even | 6 | 3024.2.r.d.2017.1 | 2 | |||
36.23 | even | 6 | 9072.2.a.d.1.1 | 1 | |||
36.31 | odd | 6 | 9072.2.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.b.169.1 | ✓ | 2 | 9.7 | even | 3 | inner | |
504.2.r.b.337.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1008.2.r.b.337.1 | 2 | 4.3 | odd | 2 | |||
1008.2.r.b.673.1 | 2 | 36.7 | odd | 6 | |||
1512.2.r.b.505.1 | 2 | 9.2 | odd | 6 | |||
1512.2.r.b.1009.1 | 2 | 3.2 | odd | 2 | |||
3024.2.r.d.1009.1 | 2 | 12.11 | even | 2 | |||
3024.2.r.d.2017.1 | 2 | 36.11 | even | 6 | |||
4536.2.a.c.1.1 | 1 | 9.5 | odd | 6 | |||
4536.2.a.h.1.1 | 1 | 9.4 | even | 3 | |||
9072.2.a.d.1.1 | 1 | 36.23 | even | 6 | |||
9072.2.a.s.1.1 | 1 | 36.31 | odd | 6 |