Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(289,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.r (of order \(6\), degree \(2\), not 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.289 |
Dual form | 1728.2.r.b.1441.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 1.73205i | 1.34164 | − | 0.774597i | 0.354593 | − | 0.935021i | \(-0.384620\pi\) |
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 1.73205i | −0.832050 | + | 0.480384i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
0.0225039 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | + | 3.00000i | 0.361158 | + | 0.625543i | 0.988152 | − | 0.153481i | \(-0.0490483\pi\) |
−0.626994 | + | 0.779024i | \(0.715715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.50000 | − | 6.06218i | 0.700000 | − | 1.21244i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | + | 3.46410i | 1.11417 | + | 0.643268i | 0.939907 | − | 0.341431i | \(-0.110912\pi\) |
0.174265 | + | 0.984699i | \(0.444245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | + | 6.00000i | 0.622171 | + | 1.07763i | 0.989081 | + | 0.147375i | \(0.0470825\pi\) |
−0.366910 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.3923i | − | 1.70848i | −0.519875 | − | 0.854242i | \(-0.674022\pi\) | ||
0.519875 | − | 0.854242i | \(-0.325978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.33013 | − | 2.50000i | −0.660338 | − | 0.381246i | 0.132068 | − | 0.991241i | \(-0.457838\pi\) |
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73205 | − | 3.00000i | 0.252646 | − | 0.437595i | −0.711608 | − | 0.702577i | \(-0.752033\pi\) |
0.964253 | + | 0.264982i | \(0.0853660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 13.8564i | − | 1.90332i | −0.307148 | − | 0.951662i | \(-0.599375\pi\) | ||
0.307148 | − | 0.951662i | \(-0.400625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3923 | 1.40130 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.79423 | + | 4.50000i | −1.01472 | + | 0.585850i | −0.912571 | − | 0.408919i | \(-0.865906\pi\) |
−0.102151 | + | 0.994769i | \(0.532573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 3.46410i | −0.768221 | − | 0.443533i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | + | 10.3923i | −0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | − | 2.50000i | 0.529009 | − | 0.305424i | −0.211604 | − | 0.977356i | \(-0.567869\pi\) |
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410 | 0.411113 | 0.205557 | − | 0.978645i | \(-0.434100\pi\) | ||||
0.205557 | + | 0.978645i | \(0.434100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.66025 | − | 15.0000i | 0.974355 | − | 1.68763i | 0.292306 | − | 0.956325i | \(-0.405577\pi\) |
0.682048 | − | 0.731307i | \(-0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3923 | − | 6.00000i | −1.14070 | − | 0.658586i | −0.194099 | − | 0.980982i | \(-0.562178\pi\) |
−0.946605 | + | 0.322396i | \(0.895512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | − | 5.19615i | 0.976187 | − | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.1244 | + | 21.0000i | 1.24393 | + | 2.15455i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 1.73205i | 0.298511 | + | 0.172345i | 0.641774 | − | 0.766894i | \(-0.278199\pi\) |
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | − | 3.00000i | −0.170664 | − | 0.295599i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000i | 0.290021i | 0.989430 | + | 0.145010i | \(0.0463216\pi\) | ||||
−0.989430 | + | 0.145010i | \(0.953678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.92820i | − | 0.663602i | −0.943349 | − | 0.331801i | \(-0.892344\pi\) | ||
0.943349 | − | 0.331801i | \(-0.107656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3923 | + | 6.00000i | 0.969087 | + | 0.559503i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.46410 | −0.307389 | −0.153695 | − | 0.988118i | \(-0.549117\pi\) | ||||
−0.153695 | + | 0.988118i | \(0.549117\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3923 | + | 6.00000i | −0.907980 | + | 0.524222i | −0.879781 | − | 0.475380i | \(-0.842311\pi\) |
−0.0281993 | + | 0.999602i | \(0.508977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.50000 | − | 12.9904i | 0.640768 | − | 1.10984i | −0.344493 | − | 0.938789i | \(-0.611949\pi\) |
0.985262 | − | 0.171054i | \(-0.0547174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33013 | + | 2.50000i | −0.367277 | + | 0.212047i | −0.672268 | − | 0.740308i | \(-0.734680\pi\) |
0.304991 | + | 0.952355i | \(0.401346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.3923 | −0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.0000 | 1.99309 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | + | 5.19615i | −0.737309 | + | 0.425685i | −0.821090 | − | 0.570799i | \(-0.806634\pi\) |
0.0837813 | + | 0.996484i | \(0.473300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.73205 | + | 3.00000i | −0.140952 | + | 0.244137i | −0.927855 | − | 0.372940i | \(-0.878350\pi\) |
0.786903 | + | 0.617076i | \(0.211683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.7846 | + | 12.0000i | 1.66946 | + | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | − | 3.46410i | 0.478852 | − | 0.276465i | −0.241086 | − | 0.970504i | \(-0.577504\pi\) |
0.719938 | + | 0.694038i | \(0.244170\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.66025 | + | 15.0000i | 0.670151 | + | 1.16073i | 0.977861 | + | 0.209255i | \(0.0671038\pi\) |
−0.307711 | + | 0.951480i | \(0.599563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | + | 3.46410i | 0.456172 | + | 0.263371i | 0.710433 | − | 0.703765i | \(-0.248499\pi\) |
−0.254262 | + | 0.967135i | \(0.581832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3923i | 0.772454i | 0.922404 | + | 0.386227i | \(0.126222\pi\) | ||||
−0.922404 | + | 0.386227i | \(0.873778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.0000 | − | 31.1769i | −1.32339 | − | 2.29217i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.79423 | + | 4.50000i | 0.569970 | + | 0.329073i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.46410 | − | 6.00000i | 0.250654 | − | 0.434145i | −0.713052 | − | 0.701111i | \(-0.752688\pi\) |
0.963706 | + | 0.266966i | \(0.0860212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | + | 6.06218i | 0.251936 | + | 0.436365i | 0.964059 | − | 0.265689i | \(-0.0855996\pi\) |
−0.712123 | + | 0.702055i | \(0.752266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 5.19615i | 0.628587 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5000 | + | 18.1865i | −0.726300 | + | 1.25799i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8564 | + | 8.00000i | −0.953914 | + | 0.550743i | −0.894295 | − | 0.447478i | \(-0.852322\pi\) |
−0.0596196 | + | 0.998221i | \(0.518989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.3205 | −1.18125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.00000 | + | 5.19615i | −0.605406 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.66025 | + | 15.0000i | −0.579934 | + | 1.00447i | 0.415553 | + | 0.909569i | \(0.363588\pi\) |
−0.995486 | + | 0.0949052i | \(0.969745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.79423 | + | 4.50000i | 0.517321 | + | 0.298675i | 0.735838 | − | 0.677158i | \(-0.236789\pi\) |
−0.218517 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.0000 | 1.76883 | 0.884414 | − | 0.466702i | \(-0.154558\pi\) | ||||
0.884414 | + | 0.466702i | \(0.154558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.0000i | − | 0.782794i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1244 | − | 21.0000i | −0.784259 | − | 1.35838i | −0.929441 | − | 0.368972i | \(-0.879710\pi\) |
0.145181 | − | 0.989405i | \(-0.453624\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | + | 14.7224i | −0.547533 | + | 0.948355i | 0.450910 | + | 0.892570i | \(0.351100\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.0000 | + | 12.1244i | 1.34164 | + | 0.774597i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.1244 | − | 21.0000i | −0.771454 | − | 1.33620i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.0000i | − | 0.946792i | −0.880850 | − | 0.473396i | \(-0.843028\pi\) | ||
0.880850 | − | 0.473396i | \(-0.156972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.3923i | 0.653359i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.50000 | + | 12.9904i | 0.467837 | + | 0.810318i | 0.999325 | − | 0.0367485i | \(-0.0117000\pi\) |
−0.531487 | + | 0.847066i | \(0.678367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.3923 | − | 18.0000i | 0.640817 | − | 1.10993i | −0.344434 | − | 0.938811i | \(-0.611929\pi\) |
0.985251 | − | 0.171117i | \(-0.0547376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0000 | − | 41.5692i | −1.47431 | − | 2.55358i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.7846i | − | 1.26726i | −0.773636 | − | 0.633630i | \(-0.781564\pi\) | ||
0.773636 | − | 0.633630i | \(-0.218436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.92820 | −0.420858 | −0.210429 | − | 0.977609i | \(-0.567486\pi\) | ||||
−0.210429 | + | 0.977609i | \(0.567486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.1865 | − | 10.5000i | 1.09669 | − | 0.633174i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0000 | − | 8.66025i | −0.901263 | − | 0.520344i | −0.0236530 | − | 0.999720i | \(-0.507530\pi\) |
−0.877610 | + | 0.479376i | \(0.840863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.46410 | − | 2.00000i | 0.205919 | − | 0.118888i | −0.393494 | − | 0.919327i | \(-0.628734\pi\) |
0.599414 | + | 0.800439i | \(0.295400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.0000 | + | 6.92820i | −0.701047 | + | 0.404750i | −0.807737 | − | 0.589542i | \(-0.799308\pi\) |
0.106690 | + | 0.994292i | \(0.465975\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.5885 | + | 27.0000i | −0.907595 | + | 1.57200i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3923 | − | 6.00000i | −0.601003 | − | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.0000i | − | 1.76926i | −0.466290 | − | 0.884632i | \(-0.654410\pi\) | ||
0.466290 | − | 0.884632i | \(-0.345590\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.92820 | − | 12.0000i | −0.392862 | − | 0.680458i | 0.599963 | − | 0.800027i | \(-0.295182\pi\) |
−0.992826 | + | 0.119570i | \(0.961848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.50000 | + | 6.06218i | −0.197832 | + | 0.342655i | −0.947825 | − | 0.318791i | \(-0.896723\pi\) |
0.749993 | + | 0.661445i | \(0.230057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | − | 5.19615i | −0.505490 | − | 0.291845i | 0.225488 | − | 0.974246i | \(-0.427602\pi\) |
−0.730978 | + | 0.682401i | \(0.760936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.3923 | + | 18.0000i | 0.581857 | + | 1.00781i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0000i | 1.16847i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.2487i | 1.34508i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.2487 | − | 14.0000i | −1.33283 | − | 0.769510i | −0.347097 | − | 0.937829i | \(-0.612833\pi\) |
−0.985732 | + | 0.168320i | \(0.946166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.66025 | − | 15.0000i | 0.473160 | − | 0.819538i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.50000 | + | 14.7224i | 0.463025 | + | 0.801982i | 0.999110 | − | 0.0421818i | \(-0.0134309\pi\) |
−0.536085 | + | 0.844164i | \(0.680098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7846i | 1.12555i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3827 | + | 13.5000i | −1.25525 | + | 0.724718i | −0.972147 | − | 0.234372i | \(-0.924697\pi\) |
−0.283101 | + | 0.959090i | \(0.591363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | + | 7.79423i | −0.239511 | + | 0.414845i | −0.960574 | − | 0.278024i | \(-0.910320\pi\) |
0.721063 | + | 0.692869i | \(0.243654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3923 | − | 6.00000i | 0.551566 | − | 0.318447i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7128 | −1.46263 | −0.731313 | − | 0.682042i | \(-0.761092\pi\) | ||||
−0.731313 | + | 0.682042i | \(0.761092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0000 | + | 12.1244i | −1.09919 | + | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.66025 | − | 15.0000i | 0.452062 | − | 0.782994i | −0.546452 | − | 0.837490i | \(-0.684022\pi\) |
0.998514 | + | 0.0544966i | \(0.0173554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | + | 12.1244i | −1.08734 | + | 0.627775i | −0.932867 | − | 0.360222i | \(-0.882701\pi\) |
−0.154472 | + | 0.987997i | \(0.549368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000i | 0.256833i | 0.991720 | + | 0.128416i | \(0.0409894\pi\) | ||||
−0.991720 | + | 0.128416i | \(0.959011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.73205 | − | 3.00000i | −0.0885037 | − | 0.153293i | 0.818375 | − | 0.574684i | \(-0.194875\pi\) |
−0.906879 | + | 0.421392i | \(0.861542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | − | 3.46410i | −0.304212 | − | 0.175637i | 0.340121 | − | 0.940382i | \(-0.389532\pi\) |
−0.644334 | + | 0.764745i | \(0.722865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.19615 | + | 9.00000i | 0.262781 | + | 0.455150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 60.0000i | − | 3.01893i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.46410i | − | 0.173858i | −0.996214 | − | 0.0869291i | \(-0.972295\pi\) | ||
0.996214 | − | 0.0869291i | \(-0.0277054\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7846 | − | 12.0000i | −1.03536 | − | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.5885 | − | 27.0000i | 0.772691 | − | 1.33834i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.500000 | + | 0.866025i | 0.0247234 | + | 0.0428222i | 0.878122 | − | 0.478436i | \(-0.158796\pi\) |
−0.853399 | + | 0.521258i | \(0.825463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.5692 | −2.04055 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1769 | − | 18.0000i | 1.52309 | − | 0.879358i | 0.523465 | − | 0.852047i | \(-0.324639\pi\) |
0.999627 | − | 0.0273103i | \(-0.00869423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.0000 | + | 15.5885i | 1.31590 | + | 0.759735i | 0.983066 | − | 0.183251i | \(-0.0586620\pi\) |
0.332833 | + | 0.942986i | \(0.391995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.5000 | − | 18.1865i | 0.509325 | − | 0.882176i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7128 | −1.33488 | −0.667440 | − | 0.744664i | \(-0.732610\pi\) | ||||
−0.667440 | + | 0.744664i | \(0.732610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0000 | −0.528626 | −0.264313 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.0000 | + | 12.1244i | −1.00457 | + | 0.579987i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5788 | + | 16.5000i | 1.35782 | + | 0.783939i | 0.989330 | − | 0.145692i | \(-0.0465410\pi\) |
0.368492 | + | 0.929631i | \(0.379874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | − | 10.3923i | 0.853282 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0000 | 1.27421 | 0.637104 | − | 0.770778i | \(-0.280132\pi\) | ||||
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000i | 0.423793i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.50000 | − | 11.2583i | 0.304057 | − | 0.526642i | −0.672994 | − | 0.739648i | \(-0.734992\pi\) |
0.977051 | + | 0.213006i | \(0.0683253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00000 | + | 5.19615i | 0.419172 | + | 0.242009i | 0.694723 | − | 0.719277i | \(-0.255527\pi\) |
−0.275551 | + | 0.961286i | \(0.588860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1244 | − | 21.0000i | −0.563467 | − | 0.975953i | −0.997191 | − | 0.0749070i | \(-0.976134\pi\) |
0.433724 | − | 0.901046i | \(-0.357199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.0000i | 1.24941i | 0.780860 | + | 0.624705i | \(0.214781\pi\) | ||||
−0.780860 | + | 0.624705i | \(0.785219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.50000 | − | 12.9904i | −0.344850 | − | 0.597298i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.4352 | + | 24.5000i | 1.94706 | + | 1.12414i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.3923 | + | 18.0000i | −0.474837 | + | 0.822441i | −0.999585 | − | 0.0288165i | \(-0.990826\pi\) |
0.524748 | + | 0.851258i | \(0.324159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | + | 31.1769i | 0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.46410i | 0.157297i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | −1.25579 | −0.627894 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627894 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.59808 | + | 1.50000i | −0.117250 | + | 0.0676941i | −0.557478 | − | 0.830192i | \(-0.688231\pi\) |
0.440228 | + | 0.897886i | \(0.354898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | + | 10.3923i | 0.810679 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.866025 | + | 0.500000i | −0.0387686 | + | 0.0223831i | −0.519259 | − | 0.854617i | \(-0.673792\pi\) |
0.480490 | + | 0.877000i | \(0.340459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.92820 | 0.308913 | 0.154457 | − | 0.988000i | \(-0.450637\pi\) | ||||
0.154457 | + | 0.988000i | \(0.450637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | − | 3.46410i | 0.265945 | − | 0.153544i | −0.361098 | − | 0.932528i | \(-0.617598\pi\) |
0.627044 | + | 0.778984i | \(0.284265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3923 | − | 6.00000i | −0.457940 | − | 0.264392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | − | 5.19615i | 0.395820 | − | 0.228527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | 0.394297 | 0.197149 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197149 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3923 | + | 18.0000i | 0.452696 | + | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.00000 | − | 5.19615i | −0.389833 | − | 0.225070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.19615 | + | 9.00000i | 0.224649 | + | 0.389104i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.0000i | 0.904534i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1769i | 1.34040i | 0.742180 | + | 0.670200i | \(0.233792\pi\) | ||||
−0.742180 | + | 0.670200i | \(0.766208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | − | 20.7846i | −0.514024 | − | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4545 | − | 9.50000i | −0.703543 | − | 0.406191i | 0.105123 | − | 0.994459i | \(-0.466476\pi\) |
−0.808666 | + | 0.588269i | \(0.799810\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.2487 | + | 42.0000i | −1.03303 | + | 1.78926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7846i | 0.880672i | 0.897833 | + | 0.440336i | \(0.145141\pi\) | ||||
−0.897833 | + | 0.440336i | \(0.854859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3205 | 0.732579 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.79423 | + | 4.50000i | −0.328488 | + | 0.189652i | −0.655169 | − | 0.755482i | \(-0.727403\pi\) |
0.326682 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 10.3923i | 0.757266 | + | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5000 | − | 33.7750i | 0.817483 | − | 1.41592i | −0.0900490 | − | 0.995937i | \(-0.528702\pi\) |
0.907532 | − | 0.419984i | \(-0.137964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0429 | − | 18.5000i | 1.34096 | − | 0.774201i | 0.354008 | − | 0.935243i | \(-0.384819\pi\) |
0.986948 | + | 0.161042i | \(0.0514853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.2487 | 1.01124 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | 0.291414 | 0.145707 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145707 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7846 | − | 36.0000i | 0.860811 | − | 1.49097i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.59808 | − | 1.50000i | −0.107234 | − | 0.0619116i | 0.445424 | − | 0.895320i | \(-0.353053\pi\) |
−0.552658 | + | 0.833408i | \(0.686386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0000 | + | 24.2487i | −1.73058 | + | 0.999151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.73205 | + | 3.00000i | 0.0707697 | + | 0.122577i | 0.899239 | − | 0.437458i | \(-0.144121\pi\) |
−0.828469 | + | 0.560035i | \(0.810788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.00000 | − | 3.46410i | −0.243935 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.3923 | − | 18.0000i | −0.421811 | − | 0.730597i | 0.574306 | − | 0.818641i | \(-0.305272\pi\) |
−0.996117 | + | 0.0880432i | \(0.971939\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.2487i | − | 0.979396i | −0.871892 | − | 0.489698i | \(-0.837107\pi\) | ||
0.871892 | − | 0.489698i | \(-0.162893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50000 | − | 2.59808i | −0.0603877 | − | 0.104595i | 0.834251 | − | 0.551385i | \(-0.185900\pi\) |
−0.894639 | + | 0.446790i | \(0.852567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.2583 | − | 6.50000i | −0.452510 | − | 0.261257i | 0.256379 | − | 0.966576i | \(-0.417470\pi\) |
−0.708890 | + | 0.705319i | \(0.750804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 31.1769i | − | 1.24310i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1769 | −1.24113 | −0.620567 | − | 0.784154i | \(-0.713097\pi\) | ||||
−0.620567 | + | 0.784154i | \(0.713097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3923 | + | 6.00000i | −0.412406 | + | 0.238103i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.0000 | − | 12.1244i | −0.832050 | − | 0.480384i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | + | 33.7750i | −0.770204 | + | 1.33403i | 0.167247 | + | 0.985915i | \(0.446512\pi\) |
−0.937451 | + | 0.348117i | \(0.886821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.4545 | − | 9.50000i | 0.648901 | − | 0.374643i | −0.139134 | − | 0.990274i | \(-0.544432\pi\) |
0.788035 | + | 0.615630i | \(0.211098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.6410 | 1.36188 | 0.680939 | − | 0.732340i | \(-0.261572\pi\) | ||||
0.680939 | + | 0.732340i | \(0.261572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0000 | −1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7846 | + | 36.0000i | −0.812122 | + | 1.40664i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3923 | − | 6.00000i | −0.404827 | − | 0.233727i | 0.283738 | − | 0.958902i | \(-0.408425\pi\) |
−0.688565 | + | 0.725175i | \(0.741759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0000 | − | 19.0526i | 1.28355 | − | 0.741059i | 0.306055 | − | 0.952014i | \(-0.400991\pi\) |
0.977496 | + | 0.210955i | \(0.0676574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0000i | 0.929284i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.3923 | − | 18.0000i | −0.401190 | − | 0.694882i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | + | 8.66025i | −0.192736 | + | 0.333828i | −0.946156 | − | 0.323711i | \(-0.895069\pi\) |
0.753420 | + | 0.657539i | \(0.228403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0000 | − | 6.92820i | −0.461197 | − | 0.266272i | 0.251350 | − | 0.967896i | \(-0.419125\pi\) |
−0.712548 | + | 0.701624i | \(0.752459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 45.0000i | − | 1.72188i | −0.508709 | − | 0.860939i | \(-0.669877\pi\) | ||
0.508709 | − | 0.860939i | \(-0.330123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 51.9615i | − | 1.98535i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0000 | + | 41.5692i | 0.914327 | + | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.2487 | − | 14.0000i | −0.922464 | − | 0.532585i | −0.0380440 | − | 0.999276i | \(-0.512113\pi\) |
−0.884420 | + | 0.466691i | \(0.845446\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.66025 | + | 15.0000i | −0.328502 | + | 0.568982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | + | 7.79423i | 0.170450 | + | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1769i | 1.17754i | 0.808302 | + | 0.588768i | \(0.200387\pi\) | ||||
−0.808302 | + | 0.588768i | \(0.799613\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.7461 | 2.74367 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.0000 | − | 13.8564i | −0.901339 | − | 0.520388i | −0.0237046 | − | 0.999719i | \(-0.507546\pi\) |
−0.877634 | + | 0.479331i | \(0.840879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | + | 20.7846i | −0.449404 | + | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.1769 | + | 18.0000i | −1.16595 | + | 0.673162i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.3923 | 0.387568 | 0.193784 | − | 0.981044i | \(-0.437924\pi\) | ||||
0.193784 | + | 0.981044i | \(0.437924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.0000 | − | 24.2487i | 1.55984 | − | 0.900575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5885 | − | 27.0000i | 0.578144 | − | 1.00137i | −0.417548 | − | 0.908655i | \(-0.637111\pi\) |
0.995692 | − | 0.0927199i | \(-0.0295561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9904 | − | 7.50000i | −0.480467 | − | 0.277398i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | − | 6.92820i | 0.443230 | − | 0.255899i | −0.261737 | − | 0.965139i | \(-0.584295\pi\) |
0.704967 | + | 0.709240i | \(0.250962\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0000 | 0.552532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.00000i | − | 0.0367856i | −0.999831 | − | 0.0183928i | \(-0.994145\pi\) | ||
0.999831 | − | 0.0183928i | \(-0.00585494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.92820 | − | 12.0000i | −0.254171 | − | 0.440237i | 0.710499 | − | 0.703698i | \(-0.248469\pi\) |
−0.964670 | + | 0.263461i | \(0.915136\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | + | 31.1769i | −0.659469 | + | 1.14223i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5885 | + | 27.0000i | 0.568831 | + | 0.985244i | 0.996682 | + | 0.0813947i | \(0.0259374\pi\) |
−0.427851 | + | 0.903849i | \(0.640729\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000i | 0.436725i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 27.7128i | − | 1.00724i | −0.863925 | − | 0.503620i | \(-0.832001\pi\) | ||
0.863925 | − | 0.503620i | \(-0.167999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5885 | − | 27.0000i | 0.562867 | − | 0.974913i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0000 | − | 43.3013i | −0.901523 | − | 1.56148i | −0.825518 | − | 0.564376i | \(-0.809117\pi\) |
−0.0760054 | − | 0.997107i | \(-0.524217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 24.2487i | − | 0.872166i | −0.899907 | − | 0.436083i | \(-0.856365\pi\) | ||
0.899907 | − | 0.436083i | \(-0.143635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.4974 | 1.74208 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1865 | + | 10.5000i | −0.651600 | + | 0.376202i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 5.19615i | 0.322045 | + | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | − | 20.7846i | 0.428298 | − | 0.741835i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.46410 | − | 2.00000i | 0.123482 | − | 0.0712923i | −0.436987 | − | 0.899468i | \(-0.643954\pi\) |
0.560469 | + | 0.828176i | \(0.310621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0000 | − | 12.1244i | 0.743858 | − | 0.429467i | −0.0796123 | − | 0.996826i | \(-0.525368\pi\) |
0.823470 | + | 0.567359i | \(0.192035\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.19615 | − | 9.00000i | 0.183827 | − | 0.318397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.1865 | − | 10.5000i | −0.641789 | − | 0.370537i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | −0.527372 | −0.263686 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263686 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.0000i | − | 0.877869i | −0.898519 | − | 0.438934i | \(-0.855356\pi\) | ||
0.898519 | − | 0.438934i | \(-0.144644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.92820 | + | 12.0000i | 0.242684 | + | 0.420342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.5000 | − | 30.3109i | 0.612247 | − | 1.06044i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | − | 6.92820i | −0.418803 | − | 0.241796i | 0.275762 | − | 0.961226i | \(-0.411070\pi\) |
−0.694565 | + | 0.719430i | \(0.744403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.5167 | + | 39.0000i | 0.784881 | + | 1.35945i | 0.929070 | + | 0.369904i | \(0.120610\pi\) |
−0.144188 | + | 0.989550i | \(0.546057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0000i | 1.66912i | 0.550914 | + | 0.834562i | \(0.314279\pi\) | ||||
−0.550914 | + | 0.834562i | \(0.685721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6410i | 1.20313i | 0.798823 | + | 0.601566i | \(0.205456\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5000 | + | 18.1865i | 0.363803 | + | 0.630126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.9615 | + | 30.0000i | 1.79820 | + | 1.03819i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.3205 | − | 30.0000i | 0.597970 | − | 1.03572i | −0.395150 | − | 0.918617i | \(-0.629307\pi\) |
0.993120 | − | 0.117098i | \(-0.0373593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.50000 | + | 16.4545i | 0.327586 | + | 0.567396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46410i | 0.119169i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.1769 | − | 18.0000i | 1.06873 | − | 0.617032i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | − | 12.1244i | −0.719026 | − | 0.415130i | 0.0953679 | − | 0.995442i | \(-0.469597\pi\) |
−0.814394 | + | 0.580312i | \(0.802931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.00000 | + | 15.5885i | −0.307434 | + | 0.532492i | −0.977800 | − | 0.209539i | \(-0.932804\pi\) |
0.670366 | + | 0.742030i | \(0.266137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.4545 | + | 9.50000i | −0.561420 | + | 0.324136i | −0.753715 | − | 0.657201i | \(-0.771740\pi\) |
0.192295 | + | 0.981337i | \(0.438407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.3205 | −0.589597 | −0.294798 | − | 0.955559i | \(-0.595253\pi\) | ||||
−0.294798 | + | 0.955559i | \(0.595253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.0000 | − | 25.9808i | 1.52652 | − | 0.881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.66025 | + | 15.0000i | −0.293442 | + | 0.508256i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.0000 | + | 20.7846i | −1.21563 | + | 0.701846i | −0.963981 | − | 0.265971i | \(-0.914307\pi\) |
−0.251653 | + | 0.967818i | \(0.580974\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.00000i | 0.0336527i | 0.999858 | + | 0.0168263i | \(0.00535624\pi\) | ||||
−0.999858 | + | 0.0168263i | \(0.994644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.5885 | + | 27.0000i | 0.523409 | + | 0.906571i | 0.999629 | + | 0.0272449i | \(0.00867339\pi\) |
−0.476220 | + | 0.879326i | \(0.657993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0000 | + | 12.1244i | 0.702738 | + | 0.405726i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7846 | − | 36.0000i | −0.694753 | − | 1.20335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000i | 1.60089i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.5692i | − | 1.38487i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | + | 31.1769i | 0.598340 | + | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.866025 | + | 0.500000i | 0.0287559 | + | 0.0166022i | 0.514309 | − | 0.857605i | \(-0.328048\pi\) |
−0.485553 | + | 0.874207i | \(0.661382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.2487 | + | 42.0000i | −0.803396 | + | 1.39152i | 0.113973 | + | 0.993484i | \(0.463642\pi\) |
−0.917369 | + | 0.398038i | \(0.869691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | − | 31.1769i | −0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3923 | 0.342811 | 0.171405 | − | 0.985201i | \(-0.445169\pi\) | ||||
0.171405 | + | 0.985201i | \(0.445169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.3923 | + | 6.00000i | −0.342067 | + | 0.197492i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −63.0000 | − | 36.3731i | −2.07143 | − | 1.19594i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0000 | − | 25.9808i | 0.492134 | − | 0.852401i | −0.507825 | − | 0.861460i | \(-0.669550\pi\) |
0.999959 | + | 0.00905914i | \(0.00288365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.4352 | + | 24.5000i | −1.39076 | + | 0.802955i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.1769 | 1.01959 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.0000 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.0000 | − | 27.7128i | 1.56476 | − | 0.903412i | 0.567991 | − | 0.823035i | \(-0.307721\pi\) |
0.996765 | − | 0.0803769i | \(-0.0256124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.19615 | + | 9.00000i | −0.169210 | + | 0.293080i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.1865 | − | 10.5000i | −0.590983 | − | 0.341204i | 0.174503 | − | 0.984657i | \(-0.444168\pi\) |
−0.765486 | + | 0.643452i | \(0.777501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | − | 12.1244i | 0.681689 | − | 0.393573i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.0000 | 0.680257 | 0.340128 | − | 0.940379i | \(-0.389529\pi\) | ||||
0.340128 | + | 0.940379i | \(0.389529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 24.0000i | − | 0.776622i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.50000 | + | 14.7224i | −0.274194 | + | 0.474917i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.0000 | + | 12.1244i | 0.676014 | + | 0.390297i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.92820 | + | 12.0000i | 0.222796 | + | 0.385894i | 0.955656 | − | 0.294486i | \(-0.0951483\pi\) |
−0.732860 | + | 0.680380i | \(0.761815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 36.0000i | − | 1.15529i | −0.816286 | − | 0.577647i | \(-0.803971\pi\) | ||
0.816286 | − | 0.577647i | \(-0.196029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.50000 | + | 7.79423i | 0.143968 | + | 0.249359i | 0.928987 | − | 0.370111i | \(-0.120681\pi\) |
−0.785020 | + | 0.619471i | \(0.787347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5885 | + | 9.00000i | 0.498209 | + | 0.287641i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.9808 | + | 45.0000i | −0.828658 | + | 1.43528i | 0.0704339 | + | 0.997516i | \(0.477562\pi\) |
−0.899092 | + | 0.437761i | \(0.855772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 17.3205i | − | 0.550760i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8564 | 0.440163 | 0.220082 | − | 0.975481i | \(-0.429368\pi\) | ||||
0.220082 | + | 0.975481i | \(0.429368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.7846 | − | 12.0000i | 0.658916 | − | 0.380426i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0000 | − | 10.3923i | −0.570066 | − | 0.329128i | 0.187110 | − | 0.982339i | \(-0.440088\pi\) |
−0.757176 | + | 0.653211i | \(0.773421\pi\) | |||||||
\(998\) | 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 | 1728.2.r.b.289.2 | 4 | ||
3.2 | odd | 2 | 576.2.r.a.97.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 1728.2.r.b.289.1 | 4 | ||
8.3 | odd | 2 | 1728.2.r.a.289.2 | 4 | |||
8.5 | even | 2 | 1728.2.r.a.289.1 | 4 | |||
9.2 | odd | 6 | 5184.2.d.c.2593.2 | 4 | |||
9.4 | even | 3 | 1728.2.r.a.1441.1 | 4 | |||
9.5 | odd | 6 | 576.2.r.b.481.1 | yes | 4 | ||
9.7 | even | 3 | 5184.2.d.j.2593.3 | 4 | |||
12.11 | even | 2 | 576.2.r.a.97.1 | ✓ | 4 | ||
24.5 | odd | 2 | 576.2.r.b.97.1 | yes | 4 | ||
24.11 | even | 2 | 576.2.r.b.97.2 | yes | 4 | ||
36.7 | odd | 6 | 5184.2.d.j.2593.4 | 4 | |||
36.11 | even | 6 | 5184.2.d.c.2593.1 | 4 | |||
36.23 | even | 6 | 576.2.r.b.481.2 | yes | 4 | ||
36.31 | odd | 6 | 1728.2.r.a.1441.2 | 4 | |||
72.5 | odd | 6 | 576.2.r.a.481.2 | yes | 4 | ||
72.11 | even | 6 | 5184.2.d.c.2593.4 | 4 | |||
72.13 | even | 6 | inner | 1728.2.r.b.1441.2 | 4 | ||
72.29 | odd | 6 | 5184.2.d.c.2593.3 | 4 | |||
72.43 | odd | 6 | 5184.2.d.j.2593.1 | 4 | |||
72.59 | even | 6 | 576.2.r.a.481.1 | yes | 4 | ||
72.61 | even | 6 | 5184.2.d.j.2593.2 | 4 | |||
72.67 | odd | 6 | inner | 1728.2.r.b.1441.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.a.97.1 | ✓ | 4 | 12.11 | even | 2 | ||
576.2.r.a.97.2 | yes | 4 | 3.2 | odd | 2 | ||
576.2.r.a.481.1 | yes | 4 | 72.59 | even | 6 | ||
576.2.r.a.481.2 | yes | 4 | 72.5 | odd | 6 | ||
576.2.r.b.97.1 | yes | 4 | 24.5 | odd | 2 | ||
576.2.r.b.97.2 | yes | 4 | 24.11 | even | 2 | ||
576.2.r.b.481.1 | yes | 4 | 9.5 | odd | 6 | ||
576.2.r.b.481.2 | yes | 4 | 36.23 | even | 6 | ||
1728.2.r.a.289.1 | 4 | 8.5 | even | 2 | |||
1728.2.r.a.289.2 | 4 | 8.3 | odd | 2 | |||
1728.2.r.a.1441.1 | 4 | 9.4 | even | 3 | |||
1728.2.r.a.1441.2 | 4 | 36.31 | odd | 6 | |||
1728.2.r.b.289.1 | 4 | 4.3 | odd | 2 | inner | ||
1728.2.r.b.289.2 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.r.b.1441.1 | 4 | 72.67 | odd | 6 | inner | ||
1728.2.r.b.1441.2 | 4 | 72.13 | even | 6 | inner | ||
5184.2.d.c.2593.1 | 4 | 36.11 | even | 6 | |||
5184.2.d.c.2593.2 | 4 | 9.2 | odd | 6 | |||
5184.2.d.c.2593.3 | 4 | 72.29 | odd | 6 | |||
5184.2.d.c.2593.4 | 4 | 72.11 | even | 6 | |||
5184.2.d.j.2593.1 | 4 | 72.43 | odd | 6 | |||
5184.2.d.j.2593.2 | 4 | 72.61 | even | 6 | |||
5184.2.d.j.2593.3 | 4 | 9.7 | even | 3 | |||
5184.2.d.j.2593.4 | 4 | 36.7 | odd | 6 |