Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.865 |
Dual form | 2016.2.s.n.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.00000 | 1.29987 | 0.649934 | − | 0.759991i | \(-0.274797\pi\) | ||||
0.649934 | + | 0.759991i | \(0.274797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.50000 | + | 9.52628i | −0.987829 | + | 1.71097i | −0.359211 | + | 0.933257i | \(0.616954\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | + | 5.19615i | −1.01419 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.50000 | + | 9.52628i | −0.755483 | + | 1.30854i | 0.189651 | + | 0.981852i | \(0.439264\pi\) |
−0.945134 | + | 0.326683i | \(0.894069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 8.66025i | −0.610847 | + | 1.05802i | 0.380251 | + | 0.924883i | \(0.375838\pi\) |
−0.991098 | + | 0.133135i | \(0.957496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | − | 5.19615i | 0.351123 | − | 0.608164i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524664\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.50000 | − | 0.866025i | −0.284901 | − | 0.0986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | − | 9.52628i | −0.618798 | − | 1.07179i | −0.989705 | − | 0.143120i | \(-0.954286\pi\) |
0.370907 | − | 0.928670i | \(-0.379047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0000 | −1.20741 | −0.603703 | − | 0.797209i | \(-0.706309\pi\) | ||||
−0.603703 | + | 0.797209i | \(0.706309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | − | 10.3923i | −0.209657 | − | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | + | 13.8564i | 0.788263 | + | 1.36531i | 0.927030 | + | 0.374987i | \(0.122353\pi\) |
−0.138767 | + | 0.990325i | \(0.544314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.50000 | − | 6.06218i | −0.338358 | − | 0.586053i | 0.645766 | − | 0.763535i | \(-0.276538\pi\) |
−0.984124 | + | 0.177482i | \(0.943205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | + | 20.7846i | −1.11901 | + | 1.93817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0000 | + | 3.46410i | 0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 1.50000 | + | 2.59808i | 0.131056 | + | 0.226995i | 0.924084 | − | 0.382190i | \(-0.124830\pi\) |
−0.793028 | + | 0.609185i | \(0.791497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | + | 1.73205i | −0.0854358 | + | 0.147979i | −0.905577 | − | 0.424182i | \(-0.860562\pi\) |
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.0000 | −1.86602 | −0.933008 | − | 0.359856i | \(-0.882826\pi\) | ||||
−0.933008 | + | 0.359856i | \(0.882826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.5000 | + | 18.1865i | 0.871978 | + | 1.51031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.0000 | −2.65062 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | − | 10.3923i | 0.478852 | − | 0.829396i | −0.520854 | − | 0.853646i | \(-0.674386\pi\) |
0.999706 | + | 0.0242497i | \(0.00771967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | + | 13.8564i | −1.26098 | + | 1.09204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.0000 | 1.70241 | 0.851206 | − | 0.524832i | \(-0.175872\pi\) | ||||
0.851206 | + | 0.524832i | \(0.175872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0000 | 0.891953 | 0.445976 | − | 0.895045i | \(-0.352856\pi\) | ||||
0.445976 | + | 0.895045i | \(0.352856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | − | 10.3923i | 0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 3.46410i | 0.146254 | + | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | + | 20.7846i | 0.868290 | + | 1.50392i | 0.863743 | + | 0.503932i | \(0.168114\pi\) |
0.00454614 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | − | 16.4545i | 0.683825 | − | 1.18442i | −0.289980 | − | 0.957033i | \(-0.593649\pi\) |
0.973805 | − | 0.227387i | \(-0.0730182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | − | 17.3205i | 0.708881 | − | 1.22782i | −0.256391 | − | 0.966573i | \(-0.582534\pi\) |
0.965272 | − | 0.261245i | \(-0.0841331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.50000 | + | 18.1865i | 0.245652 | + | 1.27644i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | − | 5.19615i | −0.204598 | − | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.5000 | − | 9.52628i | −1.86682 | − | 0.646686i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | + | 13.8564i | −0.538138 | + | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | 0.602685 | 0.301342 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301342 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.50000 | + | 6.06218i | −0.232303 | + | 0.402361i | −0.958485 | − | 0.285141i | \(-0.907959\pi\) |
0.726182 | + | 0.687502i | \(0.241293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | + | 6.92820i | 0.264327 | + | 0.457829i | 0.967387 | − | 0.253302i | \(-0.0815167\pi\) |
−0.703060 | + | 0.711131i | \(0.748183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | + | 10.3923i | 0.393073 | + | 0.680823i | 0.992853 | − | 0.119342i | \(-0.0380786\pi\) |
−0.599780 | + | 0.800165i | \(0.704745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5000 | − | 12.9904i | −1.05415 | − | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0000 | 1.57799 | 0.788993 | − | 0.614402i | \(-0.210603\pi\) | ||||
0.788993 | + | 0.614402i | \(0.210603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0000 | − | 22.5167i | 0.801614 | − | 1.38844i | −0.116939 | − | 0.993139i | \(-0.537308\pi\) |
0.918553 | − | 0.395298i | \(-0.129359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.0000 | −2.02717 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5000 | − | 18.1865i | 0.640196 | − | 1.10885i | −0.345192 | − | 0.938532i | \(-0.612186\pi\) |
0.985389 | − | 0.170321i | \(-0.0544803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | + | 0.866025i | 0.0303728 | + | 0.0526073i | 0.880812 | − | 0.473466i | \(-0.156997\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | − | 3.46410i | −0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | + | 27.7128i | −0.961347 | + | 1.66510i | −0.242222 | + | 0.970221i | \(0.577876\pi\) |
−0.719125 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.00000 | − | 1.73205i | 0.0594438 | − | 0.102960i | −0.834772 | − | 0.550596i | \(-0.814401\pi\) |
0.894216 | + | 0.447636i | \(0.147734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | + | 10.3923i | 0.118056 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.00000 | 0.408944 | 0.204472 | − | 0.978872i | \(-0.434452\pi\) | ||||
0.204472 | + | 0.978872i | \(0.434452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.0000 | 1.22267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.0000 | − | 27.7128i | −0.925304 | − | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 5.19615i | −0.0576390 | − | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0000 | − | 25.9808i | 0.858898 | − | 1.48765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | − | 0.866025i | −0.0282617 | − | 0.0489506i | 0.851549 | − | 0.524276i | \(-0.175664\pi\) |
−0.879810 | + | 0.475325i | \(0.842331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.50000 | + | 14.7224i | 0.477408 | + | 0.826894i | 0.999665 | − | 0.0258939i | \(-0.00824321\pi\) |
−0.522257 | + | 0.852788i | \(0.674910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.50000 | + | 6.06218i | −0.195962 | + | 0.339417i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | − | 13.8564i | 0.443760 | − | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | − | 3.46410i | 0.220527 | − | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | − | 10.3923i | −0.329790 | − | 0.571213i | 0.652680 | − | 0.757634i | \(-0.273645\pi\) |
−0.982470 | + | 0.186421i | \(0.940311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.0000 | −1.63908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0000 | −0.817102 | −0.408551 | − | 0.912735i | \(-0.633966\pi\) | ||||
−0.408551 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.50000 | − | 9.52628i | −0.297842 | − | 0.515877i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | − | 15.5885i | −0.477670 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.00000 | + | 1.73205i | 0.0527780 | + | 0.0914141i | 0.891207 | − | 0.453596i | \(-0.149859\pi\) |
−0.838429 | + | 0.545010i | \(0.816526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0000 | 0.942163 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | \(-0.979666\pi\) |
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.5000 | − | 9.52628i | −1.42773 | − | 0.494580i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | + | 10.3923i | 0.310668 | + | 0.538093i | 0.978507 | − | 0.206213i | \(-0.0661139\pi\) |
−0.667839 | + | 0.744306i | \(0.732781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.0000 | −1.44207 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.00000 | + | 1.73205i | 0.0510976 | + | 0.0885037i | 0.890443 | − | 0.455095i | \(-0.150395\pi\) |
−0.839345 | + | 0.543599i | \(0.817061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50000 | − | 7.79423i | −0.0764471 | − | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.00000 | + | 5.19615i | −0.152106 | + | 0.263455i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.5000 | − | 28.5788i | 0.830205 | − | 1.43796i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | + | 3.46410i | 0.100377 | + | 0.173858i | 0.911840 | − | 0.410546i | \(-0.134662\pi\) |
−0.811463 | + | 0.584404i | \(0.801328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.00000 | + | 13.8564i | 0.399501 | + | 0.691956i | 0.993664 | − | 0.112388i | \(-0.0358501\pi\) |
−0.594163 | + | 0.804344i | \(0.702517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.0000 | − | 38.1051i | 1.09590 | − | 1.89815i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.50000 | + | 6.06218i | −0.173064 | + | 0.299755i | −0.939490 | − | 0.342578i | \(-0.888700\pi\) |
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.5000 | + | 6.06218i | 0.861119 | + | 0.298300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.5000 | − | 28.5788i | −0.809953 | − | 1.40288i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 13.8564i | 0.388057 | + | 0.672134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | − | 17.3205i | 0.967868 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.00000 | − | 6.92820i | 0.192673 | − | 0.333720i | −0.753462 | − | 0.657491i | \(-0.771618\pi\) |
0.946135 | + | 0.323772i | \(0.104951\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50000 | − | 12.9904i | −0.357955 | − | 0.619997i | 0.629664 | − | 0.776868i | \(-0.283193\pi\) |
−0.987619 | + | 0.156871i | \(0.949859\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5000 | − | 18.1865i | −0.498870 | − | 0.864068i | 0.501129 | − | 0.865373i | \(-0.332918\pi\) |
−0.999999 | + | 0.00130426i | \(0.999585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | + | 3.46410i | −0.0941763 | + | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | − | 20.7846i | 1.12514 | − | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.0000 | − | 8.66025i | −1.15439 | − | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00000 | − | 1.73205i | 0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | + | 13.8564i | 0.364769 | + | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5000 | + | 18.1865i | 0.476780 | + | 0.825808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.50000 | − | 2.59808i | 0.0679715 | − | 0.117730i | −0.830037 | − | 0.557709i | \(-0.811681\pi\) |
0.898008 | + | 0.439979i | \(0.145014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.0000 | 1.66979 | 0.834893 | − | 0.550412i | \(-0.185529\pi\) | ||||
0.834893 | + | 0.550412i | \(0.185529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0000 | − | 24.2487i | 0.630528 | − | 1.09211i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | − | 15.5885i | −0.134568 | − | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.00000 | − | 8.66025i | −0.223831 | − | 0.387686i | 0.732137 | − | 0.681157i | \(-0.238523\pi\) |
−0.955968 | + | 0.293471i | \(0.905190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.5000 | − | 37.2391i | −0.952971 | − | 1.65059i | −0.738945 | − | 0.673766i | \(-0.764676\pi\) |
−0.214026 | − | 0.976828i | \(-0.568658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0000 | + | 5.19615i | 0.663561 | + | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | + | 41.5692i | −1.05757 | + | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.00000 | − | 12.1244i | 0.306676 | − | 0.531178i | −0.670957 | − | 0.741496i | \(-0.734117\pi\) |
0.977633 | + | 0.210318i | \(0.0674500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | + | 17.3205i | 0.437269 | + | 0.757373i | 0.997478 | − | 0.0709788i | \(-0.0226123\pi\) |
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.0000 | + | 38.1051i | 0.958335 | + | 1.65989i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | −0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5000 | − | 18.1865i | 0.453955 | − | 0.786272i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | − | 6.92820i | 0.0430730 | − | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | + | 25.9808i | 0.644900 | + | 1.11700i | 0.984325 | + | 0.176367i | \(0.0564345\pi\) |
−0.339424 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.0000 | −1.28506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0000 | − | 19.0526i | 0.935535 | − | 0.810197i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.50000 | − | 16.4545i | 0.400377 | − | 0.693474i | −0.593394 | − | 0.804912i | \(-0.702212\pi\) |
0.993771 | + | 0.111438i | \(0.0355457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | − | 31.1769i | −0.757266 | − | 1.31162i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.0000 | −1.33449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | − | 14.7224i | 0.353860 | − | 0.612903i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.986922 | + | 0.161198i | \(0.0515357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.50000 | − | 28.5788i | −0.228178 | − | 1.18565i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.50000 | − | 9.52628i | −0.227787 | − | 0.394538i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0000 | 0.619116 | 0.309558 | − | 0.950881i | \(-0.399819\pi\) | ||||
0.309558 | + | 0.950881i | \(0.399819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | + | 31.1769i | 0.245976 | + | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.00000 | − | 15.5885i | 0.367730 | − | 0.636927i | −0.621480 | − | 0.783430i | \(-0.713468\pi\) |
0.989210 | + | 0.146503i | \(0.0468017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.0000 | −1.50926 | −0.754631 | − | 0.656150i | \(-0.772184\pi\) | ||||
−0.754631 | + | 0.656150i | \(0.772184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.0000 | + | 25.9808i | −0.609837 | + | 1.05627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5000 | + | 23.3827i | 0.547948 | + | 0.949074i | 0.998415 | + | 0.0562808i | \(0.0179242\pi\) |
−0.450467 | + | 0.892793i | \(0.648742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00000 | + | 6.92820i | 0.161823 | + | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0000 | −0.885687 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0000 | − | 19.0526i | 0.442127 | − | 0.765787i | −0.555720 | − | 0.831370i | \(-0.687557\pi\) |
0.997847 | + | 0.0655827i | \(0.0208906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | + | 10.3923i | −0.480770 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.0000 | −1.71180 | −0.855901 | − | 0.517139i | \(-0.826997\pi\) | ||||
−0.855901 | + | 0.517139i | \(0.826997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.5000 | + | 44.1673i | 1.01194 | + | 1.75273i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.0000 | − | 10.3923i | 1.03016 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.00000 | + | 8.66025i | −0.197488 | + | 0.342059i | −0.947713 | − | 0.319123i | \(-0.896612\pi\) |
0.750225 | + | 0.661182i | \(0.229945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.0000 | + | 25.9808i | −0.589711 | + | 1.02141i | 0.404559 | + | 0.914512i | \(0.367425\pi\) |
−0.994270 | + | 0.106897i | \(0.965908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.50000 | + | 6.06218i | 0.137387 | + | 0.237961i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5000 | + | 37.2391i | 0.841360 | + | 1.45728i | 0.888745 | + | 0.458402i | \(0.151578\pi\) |
−0.0473852 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.50000 | + | 7.79423i | −0.175830 | + | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0000 | − | 36.3731i | 0.816805 | − | 1.41475i | −0.0912190 | − | 0.995831i | \(-0.529076\pi\) |
0.908024 | − | 0.418917i | \(-0.137590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0000 | + | 48.4974i | 1.08416 | + | 1.87783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.0000 | 1.73462 | 0.867311 | − | 0.497766i | \(-0.165846\pi\) | ||||
0.867311 | + | 0.497766i | \(0.165846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.50000 | + | 12.9904i | 0.288248 | + | 0.499261i | 0.973392 | − | 0.229147i | \(-0.0735938\pi\) |
−0.685143 | + | 0.728408i | \(0.740260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.50000 | + | 18.1865i | 0.134318 | + | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5000 | − | 18.1865i | 0.401771 | − | 0.695888i | −0.592168 | − | 0.805814i | \(-0.701728\pi\) |
0.993940 | + | 0.109926i | \(0.0350613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.0000 | − | 38.1051i | 0.838133 | − | 1.45169i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | − | 17.3205i | −0.380418 | − | 0.658903i | 0.610704 | − | 0.791859i | \(-0.290887\pi\) |
−0.991122 | + | 0.132956i | \(0.957553\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.0000 | − | 57.1577i | −1.25176 | − | 2.16811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00000 | − | 13.8564i | 0.303022 | − | 0.524849i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.0000 | −1.24639 | −0.623196 | − | 0.782065i | \(-0.714166\pi\) | ||||
−0.623196 | + | 0.782065i | \(0.714166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0000 | + | 5.19615i | 0.564133 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | + | 29.4449i | 0.638448 | + | 1.10583i | 0.985773 | + | 0.168080i | \(0.0537568\pi\) |
−0.347325 | + | 0.937745i | \(0.612910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −88.0000 | −3.29563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.00000 | − | 15.5885i | −0.335643 | − | 0.581351i | 0.647965 | − | 0.761670i | \(-0.275620\pi\) |
−0.983608 | + | 0.180319i | \(0.942287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | + | 27.7128i | −1.19174 | + | 1.03208i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.0000 | + | 24.2487i | −0.519947 | + | 0.900575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.00000 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | − | 8.66025i | −0.184177 | − | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0000 | + | 29.4449i | −0.625355 | + | 1.08315i | 0.363117 | + | 0.931744i | \(0.381713\pi\) |
−0.988472 | + | 0.151403i | \(0.951621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.0000 | 1.83432 | 0.917161 | − | 0.398517i | \(-0.130475\pi\) | ||||
0.917161 | + | 0.398517i | \(0.130475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0000 | − | 12.1244i | 0.511549 | − | 0.443014i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50000 | + | 2.59808i | 0.0547358 | + | 0.0948051i | 0.892095 | − | 0.451848i | \(-0.149235\pi\) |
−0.837359 | + | 0.546653i | \(0.815902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.0000 | −1.20099 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | − | 10.3923i | −0.217500 | − | 0.376721i | 0.736543 | − | 0.676391i | \(-0.236457\pi\) |
−0.954043 | + | 0.299670i | \(0.903123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0000 | − | 8.66025i | −0.905061 | − | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0000 | + | 24.2487i | −0.505511 | + | 0.875570i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.00000 | −0.108183 | −0.0540914 | − | 0.998536i | \(-0.517226\pi\) | ||||
−0.0540914 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0000 | − | 25.9808i | 0.539513 | − | 0.934463i | −0.459418 | − | 0.888220i | \(-0.651942\pi\) |
0.998930 | − | 0.0462427i | \(-0.0147248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0000 | − | 38.1051i | −0.790263 | − | 1.36878i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | − | 5.19615i | 0.107348 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.0000 | 1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0000 | − | 29.4449i | 0.605985 | − | 1.04960i | −0.385911 | − | 0.922536i | \(-0.626113\pi\) |
0.991895 | − | 0.127060i | \(-0.0405540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | − | 31.1769i | −0.213335 | − | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | + | 34.6410i | 0.710221 | + | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0000 | 0.885545 | 0.442773 | − | 0.896634i | \(-0.353995\pi\) | ||||
0.442773 | + | 0.896634i | \(0.353995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60.0000 | − | 20.7846i | −2.11472 | − | 0.732561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.0000 | − | 34.6410i | 0.703163 | − | 1.21791i | −0.264188 | − | 0.964471i | \(-0.585104\pi\) |
0.967351 | − | 0.253442i | \(-0.0815627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | + | 20.7846i | −0.420342 | + | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5000 | + | 32.0429i | 0.645654 | + | 1.11831i | 0.984150 | + | 0.177338i | \(0.0567487\pi\) |
−0.338495 | + | 0.940968i | \(0.609918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0000 | + | 20.7846i | −0.416777 | + | 0.721879i | −0.995613 | − | 0.0935647i | \(-0.970174\pi\) |
0.578836 | + | 0.815444i | \(0.303507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | + | 27.7128i | −0.138592 | + | 0.960192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.0000 | + | 57.1577i | 1.14201 | + | 1.97802i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | + | 17.3205i | −0.687208 | + | 0.595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0000 | − | 27.7128i | 0.548473 | − | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0000 | −1.02718 | −0.513590 | − | 0.858036i | \(-0.671685\pi\) | ||||
−0.513590 | + | 0.858036i | \(0.671685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0000 | − | 29.4449i | −0.580033 | − | 1.00465i | −0.995475 | − | 0.0950262i | \(-0.969707\pi\) |
0.415442 | − | 0.909620i | \(-0.363627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.00000 | − | 15.5885i | −0.306364 | − | 0.530637i | 0.671200 | − | 0.741276i | \(-0.265779\pi\) |
−0.977564 | + | 0.210639i | \(0.932446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | 0.373149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | − | 34.6410i | 0.677674 | − | 1.17377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.50000 | + | 7.79423i | 0.0507093 | + | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.0000 | −1.74994 | −0.874970 | − | 0.484178i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00000 | − | 6.92820i | −0.134307 | − | 0.232626i | 0.791026 | − | 0.611783i | \(-0.209547\pi\) |
−0.925332 | + | 0.379157i | \(0.876214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.50000 | + | 44.1673i | 0.285081 | + | 1.48132i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.0000 | −1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.5000 | + | 66.6840i | −1.28405 | + | 2.22403i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.0000 | + | 38.1051i | 0.732926 | + | 1.26947i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.0000 | + | 31.1769i | 0.598340 | + | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | + | 27.7128i | −0.531271 | + | 0.920189i | 0.468063 | + | 0.883695i | \(0.344952\pi\) |
−0.999334 | + | 0.0364935i | \(0.988381\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.0000 | −1.92163 | −0.960813 | − | 0.277198i | \(-0.910594\pi\) | ||||
−0.960813 | + | 0.277198i | \(0.910594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.50000 | − | 9.52628i | 0.182023 | − | 0.315274i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | + | 5.19615i | −0.198137 | + | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | − | 6.92820i | −0.131948 | − | 0.228540i | 0.792480 | − | 0.609898i | \(-0.208790\pi\) |
−0.924427 | + | 0.381358i | \(0.875456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | 0.526077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.00000 | + | 10.3923i | −0.196221 | + | 0.339865i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0000 | −0.424691 | −0.212346 | − | 0.977195i | \(-0.568110\pi\) | ||||
−0.212346 | + | 0.977195i | \(0.568110\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5000 | + | 42.4352i | −0.798677 | + | 1.38335i | 0.121801 | + | 0.992555i | \(0.461133\pi\) |
−0.920478 | + | 0.390795i | \(0.872200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | + | 27.7128i | 0.521032 | + | 0.902453i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.0000 | − | 34.6410i | −0.649913 | − | 1.12568i | −0.983143 | − | 0.182836i | \(-0.941472\pi\) |
0.333231 | − | 0.942845i | \(-0.391861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0000 | + | 62.3538i | −1.16493 | + | 2.01772i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.00000 | − | 1.73205i | −0.161458 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.0000 | − | 77.9423i | −1.45161 | − | 2.51427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57.0000 | 1.83489 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.00000 | −0.160789 | −0.0803946 | − | 0.996763i | \(-0.525618\pi\) | ||||
−0.0803946 | + | 0.996763i | \(0.525618\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.5000 | − | 23.3827i | −0.433236 | − | 0.750386i | 0.563914 | − | 0.825833i | \(-0.309295\pi\) |
−0.997150 | + | 0.0754473i | \(0.975962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0000 | − | 57.1577i | −0.352644 | − | 1.83239i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0000 | − | 22.5167i | 0.415907 | − | 0.720372i | −0.579616 | − | 0.814890i | \(-0.696798\pi\) |
0.995523 | + | 0.0945177i | \(0.0301309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.0000 | + | 41.5692i | −0.765481 | + | 1.32585i | 0.174511 | + | 0.984655i | \(0.444166\pi\) |
−0.939992 | + | 0.341197i | \(0.889168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | − | 13.8564i | −0.254385 | − | 0.440608i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5000 | + | 19.9186i | −0.365310 | + | 0.632735i | −0.988826 | − | 0.149076i | \(-0.952370\pi\) |
0.623516 | + | 0.781810i | \(0.285704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.0000 | 1.90213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | + | 1.73205i | −0.0316703 | + | 0.0548546i | −0.881426 | − | 0.472322i | \(-0.843416\pi\) |
0.849756 | + | 0.527176i | \(0.176749\pi\) | |||||||
\(998\) | 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 | 2016.2.s.n.865.1 | 2 | ||
3.2 | odd | 2 | 672.2.q.a.193.1 | ✓ | 2 | ||
4.3 | odd | 2 | 2016.2.s.k.865.1 | 2 | |||
7.2 | even | 3 | inner | 2016.2.s.n.289.1 | 2 | ||
12.11 | even | 2 | 672.2.q.f.193.1 | yes | 2 | ||
21.2 | odd | 6 | 672.2.q.a.289.1 | yes | 2 | ||
21.11 | odd | 6 | 4704.2.a.bf.1.1 | 1 | |||
21.17 | even | 6 | 4704.2.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 1344.2.q.u.193.1 | 2 | |||
24.11 | even | 2 | 1344.2.q.k.193.1 | 2 | |||
28.23 | odd | 6 | 2016.2.s.k.289.1 | 2 | |||
84.11 | even | 6 | 4704.2.a.o.1.1 | 1 | |||
84.23 | even | 6 | 672.2.q.f.289.1 | yes | 2 | ||
84.59 | odd | 6 | 4704.2.a.s.1.1 | 1 | |||
168.11 | even | 6 | 9408.2.a.bt.1.1 | 1 | |||
168.53 | odd | 6 | 9408.2.a.e.1.1 | 1 | |||
168.59 | odd | 6 | 9408.2.a.bl.1.1 | 1 | |||
168.101 | even | 6 | 9408.2.a.dc.1.1 | 1 | |||
168.107 | even | 6 | 1344.2.q.k.961.1 | 2 | |||
168.149 | odd | 6 | 1344.2.q.u.961.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.a.193.1 | ✓ | 2 | 3.2 | odd | 2 | ||
672.2.q.a.289.1 | yes | 2 | 21.2 | odd | 6 | ||
672.2.q.f.193.1 | yes | 2 | 12.11 | even | 2 | ||
672.2.q.f.289.1 | yes | 2 | 84.23 | even | 6 | ||
1344.2.q.k.193.1 | 2 | 24.11 | even | 2 | |||
1344.2.q.k.961.1 | 2 | 168.107 | even | 6 | |||
1344.2.q.u.193.1 | 2 | 24.5 | odd | 2 | |||
1344.2.q.u.961.1 | 2 | 168.149 | odd | 6 | |||
2016.2.s.k.289.1 | 2 | 28.23 | odd | 6 | |||
2016.2.s.k.865.1 | 2 | 4.3 | odd | 2 | |||
2016.2.s.n.289.1 | 2 | 7.2 | even | 3 | inner | ||
2016.2.s.n.865.1 | 2 | 1.1 | even | 1 | trivial | ||
4704.2.a.b.1.1 | 1 | 21.17 | even | 6 | |||
4704.2.a.o.1.1 | 1 | 84.11 | even | 6 | |||
4704.2.a.s.1.1 | 1 | 84.59 | odd | 6 | |||
4704.2.a.bf.1.1 | 1 | 21.11 | odd | 6 | |||
9408.2.a.e.1.1 | 1 | 168.53 | odd | 6 | |||
9408.2.a.bl.1.1 | 1 | 168.59 | odd | 6 | |||
9408.2.a.bt.1.1 | 1 | 168.11 | even | 6 | |||
9408.2.a.dc.1.1 | 1 | 168.101 | even | 6 |