Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(269,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.t (of order \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.593 |
Dual form | 756.2.t.d.269.2 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.12132 | − | 3.67423i | 0.948683 | − | 1.64317i | 0.200480 | − | 0.979698i | \(-0.435750\pi\) |
0.748203 | − | 0.663470i | \(-0.230917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12132 | + | 3.67423i | 0.514496 | + | 0.891133i | 0.999859 | + | 0.0168199i | \(0.00535420\pi\) |
−0.485363 | + | 0.874313i | \(0.661312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | − | 0.866025i | −0.344124 | − | 0.198680i | 0.317970 | − | 0.948101i | \(-0.396999\pi\) |
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.36396 | − | 3.67423i | −1.32698 | − | 0.766131i | −0.342147 | − | 0.939647i | \(-0.611154\pi\) |
−0.984831 | + | 0.173516i | \(0.944487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.50000 | − | 11.2583i | −1.30000 | − | 2.25167i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.34847i | 1.36458i | 0.731083 | + | 0.682288i | \(0.239015\pi\) | ||||
−0.731083 | + | 0.682288i | \(0.760985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 0.866025i | −0.269408 | + | 0.155543i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.48528 | + | 7.34847i | −1.43427 | + | 1.24212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | − | 6.92820i | 0.657596 | − | 1.13899i | −0.323640 | − | 0.946180i | \(-0.604907\pi\) |
0.981236 | − | 0.192809i | \(-0.0617599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264 | 0.662589 | 0.331295 | − | 0.943527i | \(-0.392515\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.12132 | − | 3.67423i | 0.309426 | − | 0.535942i | −0.668811 | − | 0.743433i | \(-0.733196\pi\) |
0.978237 | + | 0.207491i | \(0.0665296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.36396 | − | 3.67423i | 0.874157 | − | 0.504695i | 0.00542976 | − | 0.999985i | \(-0.498272\pi\) |
0.868728 | + | 0.495290i | \(0.164938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264 | + | 7.34847i | 0.552345 | + | 0.956689i | 0.998105 | + | 0.0615367i | \(0.0196001\pi\) |
−0.445760 | + | 0.895152i | \(0.647067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | − | 2.59808i | −0.576166 | − | 0.332650i | 0.183442 | − | 0.983030i | \(-0.441276\pi\) |
−0.759608 | + | 0.650381i | \(0.774609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.7279 | − | 7.34847i | −1.57870 | − | 0.911465i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.6969i | − | 1.74421i | −0.489323 | − | 0.872103i | \(-0.662756\pi\) | ||
0.489323 | − | 0.872103i | \(-0.337244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.50000 | + | 4.33013i | −0.877809 | + | 0.506803i | −0.869935 | − | 0.493166i | \(-0.835840\pi\) |
−0.00787336 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.9706 | 1.86276 | 0.931381 | − | 0.364047i | \(-0.118605\pi\) | ||||
0.931381 | + | 0.364047i | \(0.118605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | 1.95237 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.36396 | − | 11.0227i | 0.674579 | − | 1.16840i | −0.302013 | − | 0.953304i | \(-0.597659\pi\) |
0.976592 | − | 0.215101i | \(-0.0690079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 8.66025i | −0.314485 | + | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.36396 | + | 3.67423i | −0.652929 | + | 0.376969i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.5885i | − | 1.58277i | −0.611319 | − | 0.791384i | \(-0.709361\pi\) | ||
0.611319 | − | 0.791384i | \(-0.290639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | + | 3.46410i | 0.591198 | + | 0.341328i | 0.765571 | − | 0.643352i | \(-0.222457\pi\) |
−0.174373 | + | 0.984680i | \(0.555790\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7279 | + | 7.34847i | 1.23045 | + | 0.710403i | 0.967125 | − | 0.254302i | \(-0.0818459\pi\) |
0.263330 | + | 0.964706i | \(0.415179\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.500000 | − | 0.866025i | −0.0478913 | − | 0.0829502i | 0.841086 | − | 0.540901i | \(-0.181917\pi\) |
−0.888977 | + | 0.457951i | \(0.848583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6969i | 1.38257i | 0.722581 | + | 0.691286i | \(0.242955\pi\) | ||||
−0.722581 | + | 0.691286i | \(0.757045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.0000 | + | 15.5885i | −2.51776 | + | 1.45363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.12132 | − | 11.0227i | −0.194461 | − | 1.01045i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −33.9411 | −3.03579 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.36396 | + | 11.0227i | −0.556022 | + | 0.963058i | 0.441801 | + | 0.897113i | \(0.354340\pi\) |
−0.997823 | + | 0.0659452i | \(0.978994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 3.46410i | 0.260133 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.36396 | + | 3.67423i | −0.543710 | + | 0.313911i | −0.746581 | − | 0.665294i | \(-0.768306\pi\) |
0.202871 | + | 0.979205i | \(0.434973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8564i | 1.17529i | 0.809121 | + | 0.587643i | \(0.199944\pi\) | ||||
−0.809121 | + | 0.587643i | \(0.800056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.0000 | + | 15.5885i | 2.24223 | + | 1.29455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36396 | + | 3.67423i | 0.521356 | + | 0.301005i | 0.737489 | − | 0.675359i | \(-0.236011\pi\) |
−0.216133 | + | 0.976364i | \(0.569345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.500000 | − | 0.866025i | −0.0406894 | − | 0.0704761i | 0.844963 | − | 0.534824i | \(-0.179622\pi\) |
−0.885653 | + | 0.464348i | \(0.846289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.34847i | 0.590243i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | − | 5.19615i | 0.718278 | − | 0.414698i | −0.0958404 | − | 0.995397i | \(-0.530554\pi\) |
0.814119 | + | 0.580699i | \(0.197221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7279 | + | 14.6969i | 1.00310 | + | 1.15828i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50000 | − | 6.06218i | 0.274141 | − | 0.474826i | −0.695777 | − | 0.718258i | \(-0.744940\pi\) |
0.969918 | + | 0.243432i | \(0.0782731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.48528 | 0.656611 | 0.328305 | − | 0.944572i | \(-0.393522\pi\) | ||||
0.328305 | + | 0.944572i | \(0.393522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.36396 | + | 11.0227i | −0.483843 | + | 0.838041i | −0.999828 | − | 0.0185571i | \(-0.994093\pi\) |
0.515985 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.50000 | + | 33.7750i | 0.491354 | + | 2.55315i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.36396 | − | 3.67423i | 0.475665 | − | 0.274625i | −0.242943 | − | 0.970040i | \(-0.578113\pi\) |
0.718608 | + | 0.695415i | \(0.244780\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0526i | 1.41617i | 0.706129 | + | 0.708083i | \(0.250440\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.9706 | − | 29.3939i | −1.24770 | − | 2.16108i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.36396 | + | 3.67423i | 0.460480 | + | 0.265858i | 0.712246 | − | 0.701930i | \(-0.247678\pi\) |
−0.251766 | + | 0.967788i | \(0.581011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | − | 13.8564i | −0.575853 | − | 0.997406i | −0.995948 | − | 0.0899262i | \(-0.971337\pi\) |
0.420096 | − | 0.907480i | \(-0.361996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.6969i | − | 1.04711i | −0.851991 | − | 0.523557i | \(-0.824605\pi\) | ||
0.851991 | − | 0.523557i | \(-0.175395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5000 | + | 7.79423i | −0.956990 | + | 0.552518i | −0.895245 | − | 0.445574i | \(-0.853000\pi\) |
−0.0617444 | + | 0.998092i | \(0.519666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.36396 | − | 18.3712i | 0.446663 | − | 1.28940i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | − | 15.5885i | 0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0000 | 0.894957 | 0.447478 | − | 0.894295i | \(-0.352322\pi\) | ||||
0.447478 | + | 0.894295i | \(0.352322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.6066 | + | 18.3712i | −0.723364 | + | 1.25290i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.50000 | − | 0.866025i | 0.305480 | − | 0.0587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7279 | − | 7.34847i | 0.856173 | − | 0.494312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7846i | 1.39184i | 0.718119 | + | 0.695920i | \(0.245003\pi\) | ||||
−0.718119 | + | 0.695920i | \(0.754997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.36396 | − | 11.0227i | −0.422391 | − | 0.731603i | 0.573782 | − | 0.819008i | \(-0.305476\pi\) |
−0.996173 | + | 0.0874056i | \(0.972142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.50000 | − | 4.33013i | −0.495614 | − | 0.286143i | 0.231287 | − | 0.972886i | \(-0.425707\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.0919 | + | 11.0227i | 1.25075 | + | 0.722121i | 0.971259 | − | 0.238027i | \(-0.0765006\pi\) |
0.279492 | + | 0.960148i | \(0.409834\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 15.5885i | −0.587095 | − | 1.01688i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.0454i | − | 1.42600i | −0.701165 | − | 0.712999i | \(-0.747336\pi\) | ||
0.701165 | − | 0.712999i | \(-0.252664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | + | 2.59808i | −0.289870 | + | 0.167357i | −0.637883 | − | 0.770133i | \(-0.720190\pi\) |
0.348013 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.5772 | − | 11.0227i | 1.76184 | − | 0.704215i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 5.19615i | −0.190885 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.24264 | −0.267793 | −0.133897 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133897 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | + | 13.8564i | −0.994192 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7279 | + | 7.34847i | −0.784837 | + | 0.453126i | −0.838142 | − | 0.545452i | \(-0.816358\pi\) |
0.0533046 | + | 0.998578i | \(0.483025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 31.1769i | − | 1.91518i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.24264 | + | 7.34847i | 0.258678 | + | 0.448044i | 0.965888 | − | 0.258960i | \(-0.0833797\pi\) |
−0.707210 | + | 0.707004i | \(0.750046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.50000 | + | 2.59808i | 0.273356 | + | 0.157822i | 0.630412 | − | 0.776261i | \(-0.282886\pi\) |
−0.357056 | + | 0.934083i | \(0.616219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5000 | − | 19.9186i | −0.690968 | − | 1.19679i | −0.971521 | − | 0.236953i | \(-0.923851\pi\) |
0.280553 | − | 0.959839i | \(-0.409482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.50000 | + | 4.33013i | −0.445829 | + | 0.257399i | −0.706067 | − | 0.708145i | \(-0.749532\pi\) |
0.260238 | + | 0.965544i | \(0.416199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6066 | − | 3.67423i | −0.626088 | − | 0.216883i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.48528 | −0.495715 | −0.247858 | − | 0.968796i | \(-0.579727\pi\) | ||||
−0.247858 | + | 0.968796i | \(0.579727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.0000 | 2.09600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7279 | + | 22.0454i | −0.736075 | + | 1.27492i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5000 | + | 4.33013i | 0.720488 | + | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.0919 | + | 11.0227i | −1.09320 | + | 0.631158i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.9090i | − | 1.87821i | −0.343625 | − | 0.939107i | \(-0.611655\pi\) | ||
0.343625 | − | 0.939107i | \(-0.388345\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.48528 | + | 14.6969i | 0.481156 | + | 0.833387i | 0.999766 | − | 0.0216240i | \(-0.00688367\pi\) |
−0.518610 | + | 0.855011i | \(0.673550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.5000 | + | 16.4545i | 1.61092 | + | 0.930062i | 0.989158 | + | 0.146852i | \(0.0469141\pi\) |
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7279 | + | 7.34847i | 0.714871 | + | 0.412731i | 0.812862 | − | 0.582456i | \(-0.197908\pi\) |
−0.0979908 | + | 0.995187i | \(0.531242\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.34847i | − | 0.408880i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39.0000 | + | 22.5167i | −2.16333 | + | 1.24900i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.48528 | + | 7.34847i | −0.467809 | + | 0.405134i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50000 | − | 4.33013i | 0.137412 | − | 0.238005i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.926516 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.48528 | −0.463600 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.00000 | 0.381314 | 0.190657 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190657 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7279 | + | 7.34847i | −0.683271 | + | 0.394486i | −0.801086 | − | 0.598549i | \(-0.795744\pi\) |
0.117816 | + | 0.993035i | \(0.462411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.19615i | − | 0.278144i | −0.990282 | − | 0.139072i | \(-0.955588\pi\) | ||
0.990282 | − | 0.139072i | \(-0.0444119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.24264 | − | 7.34847i | −0.225813 | − | 0.391120i | 0.730750 | − | 0.682645i | \(-0.239170\pi\) |
−0.956563 | + | 0.291526i | \(0.905837\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −54.0000 | − | 31.1769i | −2.86602 | − | 1.65470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.7423i | 1.92318i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5000 | − | 9.52628i | 0.861293 | − | 0.497268i | −0.00315207 | − | 0.999995i | \(-0.501003\pi\) |
0.864445 | + | 0.502727i | \(0.167670\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.0919 | + | 3.67423i | −0.991201 | + | 0.190757i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.4558 | 1.31104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.24264 | − | 7.34847i | 0.216789 | − | 0.375489i | −0.737036 | − | 0.675854i | \(-0.763775\pi\) |
0.953824 | + | 0.300365i | \(0.0971084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.0919 | − | 11.0227i | 0.967997 | − | 0.558873i | 0.0693719 | − | 0.997591i | \(-0.477900\pi\) |
0.898625 | + | 0.438718i | \(0.144567\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 31.1769i | − | 1.57668i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.48528 | − | 14.6969i | −0.426941 | − | 0.739483i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | + | 4.33013i | 0.376414 | + | 0.217323i | 0.676257 | − | 0.736666i | \(-0.263601\pi\) |
−0.299843 | + | 0.953989i | \(0.596934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | + | 5.19615i | 0.149441 | + | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0000 | + | 8.66025i | −0.741702 | + | 0.428222i | −0.822688 | − | 0.568493i | \(-0.807527\pi\) |
0.0809857 | + | 0.996715i | \(0.474193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.24264 | − | 22.0454i | −0.208767 | − | 1.08478i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.0000 | − | 62.3538i | 1.76717 | − | 3.06083i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.24264 | −0.207267 | −0.103633 | − | 0.994616i | \(-0.533047\pi\) | ||||
−0.103633 | + | 0.994616i | \(0.533047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.5772 | − | 47.7650i | 1.33769 | − | 2.31695i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.00000 | + | 10.3923i | 0.435541 | + | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.4558 | − | 14.6969i | 1.22616 | − | 0.707927i | 0.259939 | − | 0.965625i | \(-0.416297\pi\) |
0.966225 | + | 0.257698i | \(0.0829641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1244i | 0.582659i | 0.956623 | + | 0.291330i | \(0.0940977\pi\) | ||||
−0.956623 | + | 0.291330i | \(0.905902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.36396 | + | 11.0227i | 0.304430 | + | 0.527287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.0919 | − | 11.0227i | −0.907083 | − | 0.523704i | −0.0275914 | − | 0.999619i | \(-0.508784\pi\) |
−0.879491 | + | 0.475915i | \(0.842117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0000 | − | 46.7654i | −1.27992 | − | 2.21689i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.34847i | 0.346796i | 0.984852 | + | 0.173398i | \(0.0554746\pi\) | ||||
−0.984852 | + | 0.173398i | \(0.944525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.4558 | + | 29.3939i | 1.19339 | + | 1.37801i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | − | 19.9186i | 0.537947 | − | 0.931752i | −0.461067 | − | 0.887365i | \(-0.652533\pi\) |
0.999014 | − | 0.0443868i | \(-0.0141334\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.48528 | −0.395199 | −0.197599 | − | 0.980283i | \(-0.563315\pi\) | ||||
−0.197599 | + | 0.980283i | \(0.563315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | −0.325318 | −0.162659 | − | 0.986682i | \(-0.552007\pi\) | ||||
−0.162659 | + | 0.986682i | \(0.552007\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7279 | − | 22.0454i | 0.588978 | − | 1.02014i | −0.405389 | − | 0.914144i | \(-0.632864\pi\) |
0.994367 | − | 0.105995i | \(-0.0338029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | + | 5.19615i | 0.0461757 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.5167i | 1.03314i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6066 | + | 18.3712i | 0.484628 | + | 0.839400i | 0.999844 | − | 0.0176600i | \(-0.00562165\pi\) |
−0.515216 | + | 0.857060i | \(0.672288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | − | 13.8564i | −1.09431 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −57.2756 | − | 33.0681i | −2.60075 | − | 1.50155i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | − | 0.866025i | −0.0226572 | − | 0.0392434i | 0.854475 | − | 0.519493i | \(-0.173879\pi\) |
−0.877132 | + | 0.480250i | \(0.840546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 29.3939i | − | 1.32653i | −0.748386 | − | 0.663264i | \(-0.769171\pi\) | ||
0.748386 | − | 0.663264i | \(-0.230829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.0000 | + | 15.5885i | −1.21602 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.7279 | + | 36.7423i | −0.570925 | + | 1.64812i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | + | 21.6506i | −0.559577 | + | 0.969216i | 0.437955 | + | 0.898997i | \(0.355703\pi\) |
−0.997532 | + | 0.0702185i | \(0.977630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.6985 | 1.32419 | 0.662095 | − | 0.749420i | \(-0.269668\pi\) | ||||
0.662095 | + | 0.749420i | \(0.269668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.48528 | + | 14.6969i | −0.376103 | + | 0.651430i | −0.990492 | − | 0.137574i | \(-0.956070\pi\) |
0.614388 | + | 0.789004i | \(0.289403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.5000 | − | 4.33013i | 0.995341 | − | 0.191554i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.4558 | − | 14.6969i | 1.12172 | − | 0.647624i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.24264 | + | 7.34847i | 0.185873 | + | 0.321942i | 0.943871 | − | 0.330316i | \(-0.107155\pi\) |
−0.757997 | + | 0.652258i | \(0.773822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.00000 | + | 1.73205i | 0.131181 | + | 0.0757373i | 0.564154 | − | 0.825669i | \(-0.309202\pi\) |
−0.432973 | + | 0.901407i | \(0.642536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.36396 | − | 3.67423i | −0.277218 | − | 0.160052i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.5000 | + | 26.8468i | 0.673913 | + | 1.16725i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14.6969i | − | 0.636595i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.0000 | − | 31.1769i | 2.33462 | − | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5000 | + | 30.3109i | −0.752384 | + | 1.30317i | 0.194281 | + | 0.980946i | \(0.437763\pi\) |
−0.946664 | + | 0.322221i | \(0.895571\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.24264 | −0.181735 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.36396 | − | 11.0227i | 0.271114 | − | 0.469583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | + | 6.92820i | −0.340195 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0919 | + | 11.0227i | −0.808949 | + | 0.467047i | −0.846591 | − | 0.532244i | \(-0.821349\pi\) |
0.0376417 | + | 0.999291i | \(0.488015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3205i | 0.732579i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0919 | + | 33.0681i | 0.804627 | + | 1.39365i | 0.916543 | + | 0.399937i | \(0.130968\pi\) |
−0.111916 | + | 0.993718i | \(0.535699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.0000 | + | 31.1769i | 2.27180 | + | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.7279 | − | 7.34847i | −0.533582 | − | 0.308064i | 0.208892 | − | 0.977939i | \(-0.433014\pi\) |
−0.742474 | + | 0.669875i | \(0.766348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.50000 | − | 9.52628i | −0.230168 | − | 0.398662i | 0.727690 | − | 0.685907i | \(-0.240594\pi\) |
−0.957857 | + | 0.287244i | \(0.907261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 95.5301i | 3.98388i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | − | 1.73205i | 0.124892 | − | 0.0721062i | −0.436253 | − | 0.899824i | \(-0.643695\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.4264 | − | 14.6969i | −1.76014 | − | 0.609732i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.7279 | −0.525338 | −0.262669 | − | 0.964886i | \(-0.584603\pi\) | ||||
−0.262669 | + | 0.964886i | \(0.584603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.48528 | + | 14.6969i | −0.348449 | + | 0.603531i | −0.985974 | − | 0.166898i | \(-0.946625\pi\) |
0.637525 | + | 0.770429i | \(0.279958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.0000 | − | 15.5885i | −1.84482 | − | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.0919 | + | 11.0227i | −0.780073 | + | 0.450375i | −0.836456 | − | 0.548034i | \(-0.815377\pi\) |
0.0563830 | + | 0.998409i | \(0.482043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.1244i | − | 0.494563i | −0.968944 | − | 0.247281i | \(-0.920463\pi\) | ||
0.968944 | − | 0.247281i | \(-0.0795372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.3345 | + | 40.4166i | 0.948683 | + | 1.64317i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.50000 | − | 4.33013i | −0.304416 | − | 0.175754i | 0.340009 | − | 0.940422i | \(-0.389570\pi\) |
−0.644425 | + | 0.764668i | \(0.722903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.7279 | − | 7.34847i | −0.514917 | − | 0.297287i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50000 | + | 6.06218i | 0.141364 | + | 0.244849i | 0.928010 | − | 0.372554i | \(-0.121518\pi\) |
−0.786647 | + | 0.617403i | \(0.788185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.3939i | − | 1.18335i | −0.806176 | − | 0.591676i | \(-0.798466\pi\) | ||
0.806176 | − | 0.591676i | \(-0.201534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | + | 6.92820i | −0.482321 | + | 0.278468i | −0.721383 | − | 0.692536i | \(-0.756493\pi\) |
0.239062 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.4558 | + | 22.0454i | −1.01987 | + | 0.883231i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −39.5000 | + | 68.4160i | −1.58000 | + | 2.73664i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.9411 | 1.35332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.0624 | − | 62.4620i | 1.43109 | − | 2.47873i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | − | 19.0526i | 0.594322 | − | 0.754890i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.8198 | + | 18.3712i | −1.25681 | + | 0.725618i | −0.972452 | − | 0.233102i | \(-0.925113\pi\) |
−0.284354 | + | 0.958719i | \(0.591779\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 19.0526i | − | 0.751360i | −0.926750 | − | 0.375680i | \(-0.877409\pi\) | ||
0.926750 | − | 0.375680i | \(-0.122591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7279 | − | 22.0454i | −0.500386 | − | 0.866694i | −1.00000 | 0.000446060i | \(-0.999858\pi\) | |
0.499614 | − | 0.866248i | \(-0.333475\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.36396 | − | 3.67423i | −0.249041 | − | 0.143784i | 0.370284 | − | 0.928919i | \(-0.379260\pi\) |
−0.619325 | + | 0.785135i | \(0.712594\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0000 | + | 46.7654i | 1.05498 | + | 1.82727i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.0454i | − | 0.858767i | −0.903122 | − | 0.429384i | \(-0.858731\pi\) | ||
0.903122 | − | 0.429384i | \(-0.141269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5000 | − | 14.7224i | 0.991835 | − | 0.572636i | 0.0860127 | − | 0.996294i | \(-0.472587\pi\) |
0.905822 | + | 0.423658i | \(0.139254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.0919 | − | 3.67423i | 0.740351 | − | 0.142481i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.0000 | − | 46.7654i | 1.04544 | − | 1.81076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | −0.192736 | −0.0963679 | − | 0.995346i | \(-0.530723\pi\) | ||||
−0.0963679 | + | 0.995346i | \(0.530723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.7279 | + | 22.0454i | −0.489174 | + | 0.847274i | −0.999922 | − | 0.0124562i | \(-0.996035\pi\) |
0.510749 | + | 0.859730i | \(0.329368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.5000 | + | 38.9711i | −0.518082 | + | 1.49558i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7279 | + | 7.34847i | −0.487020 | + | 0.281181i | −0.723338 | − | 0.690495i | \(-0.757393\pi\) |
0.236317 | + | 0.971676i | \(0.424060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.1769i | 1.19121i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.7279 | − | 22.0454i | −0.484895 | − | 0.839863i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.50000 | − | 0.866025i | −0.0570627 | − | 0.0329452i | 0.471197 | − | 0.882028i | \(-0.343822\pi\) |
−0.528260 | + | 0.849083i | \(0.677155\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50.9117 | + | 29.3939i | 1.93119 | + | 1.11497i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.34847i | 0.277548i | 0.990324 | + | 0.138774i | \(0.0443161\pi\) | ||||
−0.990324 | + | 0.138774i | \(0.955684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | + | 6.92820i | −0.452589 | + | 0.261302i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.5000 | + | 32.0429i | −0.694782 | + | 1.20340i | 0.275472 | + | 0.961309i | \(0.411166\pi\) |
−0.970254 | + | 0.242089i | \(0.922167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.7279 | 0.476664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.24264 | − | 7.34847i | 0.158224 | − | 0.274052i | −0.776004 | − | 0.630727i | \(-0.782757\pi\) |
0.934228 | + | 0.356676i | \(0.116090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | − | 13.8564i | −0.446903 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 82.7315 | − | 47.7650i | 3.07257 | − | 1.77395i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5167i | 0.835097i | 0.908655 | + | 0.417548i | \(0.137111\pi\) | ||||
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6066 | − | 18.3712i | −0.392299 | − | 0.679482i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.50000 | − | 0.866025i | −0.0554038 | − | 0.0319874i | 0.472042 | − | 0.881576i | \(-0.343517\pi\) |
−0.527446 | + | 0.849589i | \(0.676850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.5000 | + | 32.0429i | 0.680534 | + | 1.17872i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.34847i | − | 0.269589i | −0.990874 | − | 0.134795i | \(-0.956963\pi\) | ||
0.990874 | − | 0.134795i | \(-0.0430375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.0000 | − | 15.5885i | 0.989203 | − | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.4558 | − | 29.3939i | −0.930136 | − | 1.07403i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.50000 | − | 9.52628i | 0.200698 | − | 0.347619i | −0.748056 | − | 0.663636i | \(-0.769012\pi\) |
0.948753 | + | 0.316017i | \(0.102346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.24264 | −0.154406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.0000 | −1.70824 | −0.854122 | − | 0.520073i | \(-0.825905\pi\) | ||||
−0.854122 | + | 0.520073i | \(0.825905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.48528 | + | 14.6969i | −0.307591 | + | 0.532764i | −0.977835 | − | 0.209377i | \(-0.932856\pi\) |
0.670244 | + | 0.742141i | \(0.266190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.500000 | + | 2.59808i | 0.0181012 | + | 0.0940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.4558 | − | 14.6969i | 0.919157 | − | 0.530676i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.3013i | 1.56148i | 0.624854 | + | 0.780742i | \(0.285159\pi\) | ||||
−0.624854 | + | 0.780742i | \(0.714841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.8492 | + | 25.7196i | 0.534090 | + | 0.925071i | 0.999207 | + | 0.0398218i | \(0.0126790\pi\) |
−0.465117 | + | 0.885249i | \(0.653988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.5000 | + | 11.2583i | 0.700461 | + | 0.404411i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.36396 | − | 3.67423i | −0.228013 | − | 0.131643i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 44.0908i | − | 1.57367i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.5000 | − | 12.9904i | 0.802038 | − | 0.463057i | −0.0421450 | − | 0.999112i | \(-0.513419\pi\) |
0.844183 | + | 0.536054i | \(0.180086\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.7279 | − | 36.7423i | 0.452553 | − | 1.30641i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.00000 | + | 15.5885i | −0.319599 | + | 0.553562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.0000 | − | 15.5885i | 2.85487 | − | 0.549421i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.4558 | + | 14.6969i | −0.894980 | + | 0.516717i | −0.875568 | − | 0.483095i | \(-0.839513\pi\) |
−0.0194117 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7846i | 0.729846i | 0.931038 | + | 0.364923i | \(0.118905\pi\) | ||||
−0.931038 | + | 0.364923i | \(0.881095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8492 | − | 25.7196i | −0.520146 | − | 0.900920i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.50000 | + | 4.33013i | 0.262392 | + | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4558 | + | 14.6969i | 0.888415 | + | 0.512927i | 0.873424 | − | 0.486961i | \(-0.161895\pi\) |
0.0149913 | + | 0.999888i | \(0.495228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5000 | + | 26.8468i | 0.540296 | + | 0.935820i | 0.998887 | + | 0.0471726i | \(0.0150211\pi\) |
−0.458591 | + | 0.888648i | \(0.651646\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3939i | 1.02213i | 0.859543 | + | 0.511063i | \(0.170748\pi\) | ||||
−0.859543 | + | 0.511063i | \(0.829252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50000 | + | 0.866025i | −0.0520972 | + | 0.0300783i | −0.525822 | − | 0.850594i | \(-0.676242\pi\) |
0.473725 | + | 0.880673i | \(0.342909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.24264 | + | 29.3939i | −0.146999 | + | 1.01844i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | − | 31.1769i | 0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4264 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.12132 | − | 3.67423i | 0.0729756 | − | 0.126398i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0000 | − | 19.0526i | 0.755929 | − | 0.654654i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.9117 | + | 29.3939i | −1.74523 | + | 1.00761i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.0526i | 0.652347i | 0.945310 | + | 0.326174i | \(0.105759\pi\) | ||||
−0.945310 | + | 0.326174i | \(0.894241\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.24264 | − | 7.34847i | −0.144926 | − | 0.251019i | 0.784419 | − | 0.620231i | \(-0.212961\pi\) |
−0.929345 | + | 0.369212i | \(0.879628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.5000 | − | 18.1865i | −1.07477 | − | 0.620517i | −0.145286 | − | 0.989390i | \(-0.546410\pi\) |
−0.929480 | + | 0.368873i | \(0.879744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.5477 | − | 25.7196i | −1.51642 | − | 0.875507i | −0.999814 | − | 0.0192849i | \(-0.993861\pi\) |
−0.516608 | − | 0.856222i | \(-0.672806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.0000 | + | 46.7654i | 0.918028 | + | 1.59007i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 3.46410i | −0.203302 | + | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 84.8528 | + | 29.3939i | 2.86855 | + | 0.993694i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5000 | + | 19.9186i | −0.388327 | + | 0.672603i | −0.992225 | − | 0.124459i | \(-0.960280\pi\) |
0.603897 | + | 0.797062i | \(0.293614\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.1838 | 1.28644 | 0.643222 | − | 0.765680i | \(-0.277597\pi\) | ||||
0.643222 | + | 0.765680i | \(0.277597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.0000 | −1.17784 | −0.588922 | − | 0.808190i | \(-0.700447\pi\) | ||||
−0.588922 | + | 0.808190i | \(0.700447\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.6985 | + | 51.4393i | −0.997178 | + | 1.72716i | −0.433568 | + | 0.901121i | \(0.642746\pi\) |
−0.563610 | + | 0.826041i | \(0.690588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.5000 | − | 14.7224i | −1.42540 | − | 0.493775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.36396 | + | 3.67423i | −0.212962 | + | 0.122954i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.1769i | − | 1.04213i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.36396 | − | 11.0227i | −0.212250 | − | 0.367628i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | + | 15.5885i | 0.899500 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 70.0036 | + | 40.4166i | 2.32700 | + | 1.34349i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0000 | − | 34.6410i | −0.664089 | − | 1.15024i | −0.979531 | − | 0.201291i | \(-0.935486\pi\) |
0.315442 | − | 0.948945i | \(-0.397847\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0454i | 0.730397i | 0.930930 | + | 0.365198i | \(0.118999\pi\) | ||||
−0.930930 | + | 0.365198i | \(0.881001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.4558 | − | 22.0454i | 0.840626 | − | 0.728003i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.9117 | −1.67578 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −104.000 | −3.41950 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.3345 | + | 40.4166i | −0.765581 | + | 1.32603i | 0.174358 | + | 0.984682i | \(0.444215\pi\) |
−0.939939 | + | 0.341343i | \(0.889118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.50000 | − | 11.2583i | −0.147482 | − | 0.368977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.1051i | − | 1.24484i | −0.782683 | − | 0.622420i | \(-0.786150\pi\) | ||
0.782683 | − | 0.622420i | \(-0.213850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.24264 | + | 7.34847i | 0.138306 | + | 0.239553i | 0.926856 | − | 0.375418i | \(-0.122501\pi\) |
−0.788549 | + | 0.614971i | \(0.789168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.0000 | − | 15.5885i | −0.879241 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.8198 | − | 18.3712i | −1.03400 | − | 0.596983i | −0.115875 | − | 0.993264i | \(-0.536967\pi\) |
−0.918129 | + | 0.396281i | \(0.870301\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.0000 | + | 25.9808i | 0.486921 | + | 0.843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 51.4393i | − | 1.66628i | −0.553061 | − | 0.833141i | \(-0.686540\pi\) | ||
0.553061 | − | 0.833141i | \(-0.313460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.0000 | − | 15.5885i | 0.873699 | − | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.0919 | − | 3.67423i | 0.616509 | − | 0.118647i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −67.8823 | −2.18521 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0000 | 1.22200 | 0.610999 | − | 0.791632i | \(-0.290768\pi\) | ||||
0.610999 | + | 0.791632i | \(0.290768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.5772 | + | 47.7650i | −0.884993 | + | 1.53285i | −0.0392720 | + | 0.999229i | \(0.512504\pi\) |
−0.845721 | + | 0.533625i | \(0.820829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | − | 34.6410i | 0.384702 | − | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7279 | + | 7.34847i | −0.407202 | + | 0.235098i | −0.689587 | − | 0.724203i | \(-0.742208\pi\) |
0.282385 | + | 0.959301i | \(0.408875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2132 | − | 36.7423i | −0.676596 | − | 1.17190i | −0.976000 | − | 0.217772i | \(-0.930121\pi\) |
0.299404 | − | 0.954127i | \(-0.403212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.0000 | − | 31.1769i | −1.72058 | − | 0.993379i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.8198 | + | 18.3712i | 1.01181 | + | 0.584169i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.0000 | + | 22.5167i | 0.412959 | + | 0.715265i | 0.995212 | − | 0.0977423i | \(-0.0311621\pi\) |
−0.582253 | + | 0.813008i | \(0.697829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 66.1362i | 2.09666i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.5000 | − | 26.8468i | 1.47267 | − | 0.850246i | 0.473142 | − | 0.880986i | \(-0.343120\pi\) |
0.999527 | + | 0.0307397i | \(0.00978629\pi\) | |||||||
\(998\) | 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 | 756.2.t.d.593.2 | yes | 4 | |
3.2 | odd | 2 | inner | 756.2.t.d.593.1 | yes | 4 | |
7.2 | even | 3 | 5292.2.f.d.2645.1 | 4 | |||
7.3 | odd | 6 | inner | 756.2.t.d.269.1 | ✓ | 4 | |
7.5 | odd | 6 | 5292.2.f.d.2645.4 | 4 | |||
9.2 | odd | 6 | 2268.2.w.g.1349.1 | 4 | |||
9.4 | even | 3 | 2268.2.bm.h.593.1 | 4 | |||
9.5 | odd | 6 | 2268.2.bm.h.593.2 | 4 | |||
9.7 | even | 3 | 2268.2.w.g.1349.2 | 4 | |||
21.2 | odd | 6 | 5292.2.f.d.2645.3 | 4 | |||
21.5 | even | 6 | 5292.2.f.d.2645.2 | 4 | |||
21.17 | even | 6 | inner | 756.2.t.d.269.2 | yes | 4 | |
63.31 | odd | 6 | 2268.2.w.g.269.1 | 4 | |||
63.38 | even | 6 | 2268.2.bm.h.1025.1 | 4 | |||
63.52 | odd | 6 | 2268.2.bm.h.1025.2 | 4 | |||
63.59 | even | 6 | 2268.2.w.g.269.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.t.d.269.1 | ✓ | 4 | 7.3 | odd | 6 | inner | |
756.2.t.d.269.2 | yes | 4 | 21.17 | even | 6 | inner | |
756.2.t.d.593.1 | yes | 4 | 3.2 | odd | 2 | inner | |
756.2.t.d.593.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2268.2.w.g.269.1 | 4 | 63.31 | odd | 6 | |||
2268.2.w.g.269.2 | 4 | 63.59 | even | 6 | |||
2268.2.w.g.1349.1 | 4 | 9.2 | odd | 6 | |||
2268.2.w.g.1349.2 | 4 | 9.7 | even | 3 | |||
2268.2.bm.h.593.1 | 4 | 9.4 | even | 3 | |||
2268.2.bm.h.593.2 | 4 | 9.5 | odd | 6 | |||
2268.2.bm.h.1025.1 | 4 | 63.38 | even | 6 | |||
2268.2.bm.h.1025.2 | 4 | 63.52 | odd | 6 | |||
5292.2.f.d.2645.1 | 4 | 7.2 | even | 3 | |||
5292.2.f.d.2645.2 | 4 | 21.5 | even | 6 | |||
5292.2.f.d.2645.3 | 4 | 21.2 | odd | 6 | |||
5292.2.f.d.2645.4 | 4 | 7.5 | odd | 6 |