Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(67,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.67 |
Dual form | 539.2.e.e.177.1 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 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 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.00000 | − | 1.73205i | −0.288675 | − | 0.500000i | ||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −3.00000 | + | 5.19615i | −0.727607 | + | 1.26025i | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 6.00000 | 1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | − | 2.59808i | −0.312772 | − | 0.541736i | 0.666190 | − | 0.745782i | \(-0.267924\pi\) |
−0.978961 | + | 0.204046i | \(0.934591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | − | 4.33013i | 0.449013 | − | 0.777714i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | −5.50000 | − | 9.52628i | −0.904194 | − | 1.56611i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
−0.0821995 | − | 0.996616i | \(-0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 4.00000 | − | 6.92820i | 0.554700 | − | 0.960769i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50000 | + | 7.79423i | −0.585850 | + | 1.01472i | 0.408919 | + | 0.912571i | \(0.365906\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(60\) | 3.00000 | − | 5.19615i | 0.387298 | − | 0.670820i | ||||
\(61\) | −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 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | + | 4.33013i | −0.305424 | + | 0.529009i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 6.00000 | + | 10.3923i | 0.727607 | + | 1.26025i | ||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | 6.00000 | − | 10.3923i | 0.670820 | − | 1.16190i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.0000 | −1.95237 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | 0.101535 | 0.0507673 | − | 0.998711i | \(-0.483833\pi\) | ||||
0.0507673 | + | 0.998711i | \(0.483833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 4.00000 | + | 6.92820i | 0.400000 | + | 0.692820i | ||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | − | 5.19615i | −0.290021 | − | 0.502331i | 0.683793 | − | 0.729676i | \(-0.260329\pi\) |
−0.973814 | + | 0.227345i | \(0.926996\pi\) | |||||||
\(108\) | 5.00000 | − | 8.66025i | 0.481125 | − | 0.833333i | ||||
\(109\) | −10.0000 | + | 17.3205i | −0.957826 | + | 1.65900i | −0.230063 | + | 0.973176i | \(0.573893\pi\) |
−0.727764 | + | 0.685828i | \(0.759440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0000 | −1.04407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | − | 7.79423i | 0.419627 | − | 0.726816i | ||||
\(116\) | −6.00000 | + | 10.3923i | −0.557086 | + | 0.964901i | ||||
\(117\) | 4.00000 | + | 6.92820i | 0.369800 | + | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00000 | + | 5.19615i | −0.270501 | + | 0.468521i | ||||
\(124\) | −5.00000 | − | 8.66025i | −0.449013 | − | 0.777714i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.50000 | + | 12.9904i | 0.645497 | + | 1.11803i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | − | 2.59808i | 0.128154 | − | 0.221969i | −0.794808 | − | 0.606861i | \(-0.792428\pi\) |
0.922961 | + | 0.384893i | \(0.125762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | 4.00000 | − | 6.92820i | 0.333333 | − | 0.577350i | ||||
\(145\) | −9.00000 | − | 15.5885i | −0.747409 | − | 1.29455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22.0000 | −1.80839 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.0000 | 1.20483 | ||||||||
\(156\) | −4.00000 | − | 6.92820i | −0.320256 | − | 0.554700i | ||||
\(157\) | −6.50000 | + | 11.2583i | −0.518756 | + | 0.898513i | 0.481006 | + | 0.876717i | \(0.340272\pi\) |
−0.999762 | + | 0.0217953i | \(0.993062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | −6.00000 | + | 10.3923i | −0.468521 | + | 0.811503i | ||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | −0.464294 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 8.00000 | − | 13.8564i | 0.609994 | − | 1.05654i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 4.50000 | + | 7.79423i | 0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.50000 | − | 12.9904i | 0.560576 | − | 0.970947i | −0.436870 | − | 0.899525i | \(-0.643913\pi\) |
0.997446 | − | 0.0714220i | \(-0.0227537\pi\) | |||||||
\(180\) | 6.00000 | + | 10.3923i | 0.447214 | + | 0.774597i | ||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.5000 | − | 28.5788i | 1.21310 | − | 2.10116i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5000 | + | 23.3827i | 0.976826 | + | 1.69191i | 0.673774 | + | 0.738938i | \(0.264672\pi\) |
0.303052 | + | 0.952974i | \(0.401994\pi\) | |||||||
\(192\) | −4.00000 | + | 6.92820i | −0.288675 | + | 0.500000i | ||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.50000 | + | 4.33013i | 0.176336 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | −9.00000 | − | 15.5885i | −0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | −8.00000 | − | 13.8564i | −0.554700 | − | 0.960769i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −6.00000 | − | 10.3923i | −0.412082 | − | 0.713746i | ||||
\(213\) | 4.50000 | − | 7.79423i | 0.308335 | − | 0.534052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.0000 | + | 20.7846i | 0.818393 | + | 1.41750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | − | 1.73205i | −0.0675737 | − | 0.117041i | ||||
\(220\) | 3.00000 | − | 5.19615i | 0.202260 | − | 0.350325i | ||||
\(221\) | −12.0000 | + | 20.7846i | −0.807207 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0000 | 1.27233 | 0.636167 | − | 0.771551i | \(-0.280519\pi\) | ||||
0.636167 | + | 0.771551i | \(0.280519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | 2.50000 | + | 4.33013i | 0.165205 | + | 0.286143i | 0.936728 | − | 0.350058i | \(-0.113838\pi\) |
−0.771523 | + | 0.636201i | \(0.780505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.00000 | + | 15.5885i | 0.585850 | + | 1.01472i | ||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | −6.00000 | − | 10.3923i | −0.387298 | − | 0.670820i | ||||
\(241\) | −14.0000 | + | 24.2487i | −0.901819 | + | 1.56200i | −0.0766885 | + | 0.997055i | \(0.524435\pi\) |
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | −20.0000 | −1.28037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 6.92820i | 0.254514 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | + | 10.3923i | −0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.00000 | + | 15.5885i | −0.563602 | + | 0.976187i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 24.0000 | 1.48842 | ||||||||
\(261\) | −6.00000 | − | 10.3923i | −0.371391 | − | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0000 | − | 25.9808i | 0.924940 | − | 1.60204i | 0.133281 | − | 0.991078i | \(-0.457449\pi\) |
0.791658 | − | 0.610964i | \(-0.209218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | 15.0000 | − | 25.9808i | 0.914566 | − | 1.58408i | 0.107031 | − | 0.994256i | \(-0.465866\pi\) |
0.807535 | − | 0.589819i | \(-0.200801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 24.0000 | 1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | −3.00000 | + | 5.19615i | −0.180579 | + | 0.312772i | ||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0000 | − | 27.7128i | 0.951101 | − | 1.64736i | 0.208053 | − | 0.978117i | \(-0.433287\pi\) |
0.743048 | − | 0.669238i | \(-0.233379\pi\) | |||||||
\(284\) | 9.00000 | − | 15.5885i | 0.534052 | − | 0.925005i | ||||
\(285\) | 3.00000 | + | 5.19615i | 0.177705 | + | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | − | 0.866025i | 0.0293105 | − | 0.0507673i | ||||
\(292\) | −2.00000 | − | 3.46410i | −0.117041 | − | 0.202721i | ||||
\(293\) | 30.0000 | 1.75262 | 0.876309 | − | 0.481749i | \(-0.159998\pi\) | ||||
0.876309 | + | 0.481749i | \(0.159998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.0000 | −1.57200 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.50000 | − | 4.33013i | 0.145065 | − | 0.251259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 8.00000 | 0.461880 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000 | + | 10.3923i | 0.344691 | + | 0.597022i | ||||
\(304\) | 4.00000 | − | 6.92820i | 0.229416 | − | 0.397360i | ||||
\(305\) | 15.0000 | − | 25.9808i | 0.858898 | − | 1.48765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.0000 | 1.12509 | ||||||||
\(317\) | −4.50000 | − | 7.79423i | −0.252745 | − | 0.437767i | 0.711535 | − | 0.702650i | \(-0.248000\pi\) |
−0.964281 | + | 0.264883i | \(0.914667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | −12.0000 | − | 20.7846i | −0.670820 | − | 1.16190i | ||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 1.00000 | + | 1.73205i | 0.0555556 | + | 0.0962250i | ||||
\(325\) | −8.00000 | + | 13.8564i | −0.443760 | + | 0.768615i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | + | 17.3205i | 0.553001 | + | 0.957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.500000 | + | 0.866025i | 0.0274825 | + | 0.0476011i | 0.879440 | − | 0.476011i | \(-0.157918\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | −12.0000 | + | 20.7846i | −0.658586 | + | 1.14070i | ||||
\(333\) | 11.0000 | − | 19.0526i | 0.602796 | − | 1.04407i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0000 | −0.819538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.50000 | + | 2.59808i | −0.0814688 | + | 0.141108i | ||||
\(340\) | −18.0000 | + | 31.1769i | −0.976187 | + | 1.69081i | ||||
\(341\) | −2.50000 | − | 4.33013i | −0.135383 | − | 0.234490i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.50000 | − | 7.79423i | −0.242272 | − | 0.419627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00000 | − | 15.5885i | 0.483145 | − | 0.836832i | −0.516667 | − | 0.856186i | \(-0.672828\pi\) |
0.999813 | + | 0.0193540i | \(0.00616095\pi\) | |||||||
\(348\) | 6.00000 | + | 10.3923i | 0.321634 | + | 0.557086i | ||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5000 | + | 23.3827i | 0.716506 | + | 1.24102i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | − | 20.7846i | −0.633336 | − | 1.09697i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.353529 | − | 0.935423i | \(-0.384981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.50000 | − | 14.7224i | 0.443696 | − | 0.768505i | −0.554264 | − | 0.832341i | \(-0.687000\pi\) |
0.997960 | + | 0.0638362i | \(0.0203335\pi\) | |||||||
\(368\) | −6.00000 | + | 10.3923i | −0.312772 | + | 0.541736i | ||||
\(369\) | −6.00000 | − | 10.3923i | −0.312348 | − | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | − | 2.59808i | 0.0774597 | − | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0000 | 0.565032 | 0.282516 | − | 0.959263i | \(-0.408831\pi\) | ||||
0.282516 | + | 0.959263i | \(0.408831\pi\) | |||||||
\(380\) | 6.00000 | + | 10.3923i | 0.307794 | + | 0.533114i | ||||
\(381\) | 1.00000 | − | 1.73205i | 0.0512316 | − | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.00000 | + | 13.8564i | 0.406663 | + | 0.704361i | ||||
\(388\) | 1.00000 | − | 1.73205i | 0.0507673 | − | 0.0879316i | ||||
\(389\) | −16.5000 | + | 28.5788i | −0.836583 | + | 1.44900i | 0.0561516 | + | 0.998422i | \(0.482117\pi\) |
−0.892735 | + | 0.450582i | \(0.851216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.0000 | + | 25.9808i | −0.754732 | + | 1.30723i | ||||
\(396\) | 2.00000 | − | 3.46410i | 0.100504 | − | 0.174078i | ||||
\(397\) | 1.00000 | + | 1.73205i | 0.0501886 | + | 0.0869291i | 0.890028 | − | 0.455905i | \(-0.150684\pi\) |
−0.839840 | + | 0.542834i | \(0.817351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000 | 0.800000 | ||||||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | − | 17.3205i | 0.498135 | − | 0.862796i | ||||
\(404\) | 12.0000 | + | 20.7846i | 0.597022 | + | 1.03407i | ||||
\(405\) | −3.00000 | −0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0000 | −0.545250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50000 | − | 2.59808i | −0.0739895 | − | 0.128154i | ||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | − | 31.1769i | −0.883585 | − | 1.53041i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | + | 12.1244i | −0.342791 | + | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | − | 20.7846i | −0.582086 | − | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −2.00000 | − | 3.46410i | −0.0965609 | − | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −10.0000 | − | 17.3205i | −0.481125 | − | 0.833333i | ||||
\(433\) | −11.0000 | −0.528626 | −0.264313 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | 20.0000 | + | 34.6410i | 0.957826 | + | 1.65900i | ||||
\(437\) | 3.00000 | − | 5.19615i | 0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0000 | + | 22.5167i | 0.620456 | + | 1.07466i | 0.989401 | + | 0.145210i | \(0.0463858\pi\) |
−0.368945 | + | 0.929451i | \(0.620281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.50000 | − | 7.79423i | −0.213801 | − | 0.370315i | 0.739100 | − | 0.673596i | \(-0.235251\pi\) |
−0.952901 | + | 0.303281i | \(0.901918\pi\) | |||||||
\(444\) | −11.0000 | + | 19.0526i | −0.522037 | + | 0.904194i | ||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −5.00000 | − | 8.66025i | −0.234920 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | − | 6.92820i | −0.187112 | − | 0.324088i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
−0.944286 | + | 0.329125i | \(0.893246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.0000 | + | 25.9808i | −0.700140 | + | 1.21268i | ||||
\(460\) | −9.00000 | − | 15.5885i | −0.419627 | − | 0.726816i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000 | 0.232370 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(464\) | 12.0000 | + | 20.7846i | 0.557086 | + | 0.964901i | ||||
\(465\) | 7.50000 | − | 12.9904i | 0.347804 | − | 0.602414i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.50000 | + | 12.9904i | 0.347059 | + | 0.601123i | 0.985726 | − | 0.168360i | \(-0.0538472\pi\) |
−0.638667 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(468\) | 16.0000 | 0.739600 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | + | 11.2583i | 0.299504 | + | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | −0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.0000 | − | 38.1051i | −1.00311 | − | 1.73744i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 1.50000 | + | 2.59808i | 0.0681115 | + | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.50000 | + | 9.52628i | −0.249229 | + | 0.431677i | −0.963312 | − | 0.268384i | \(-0.913510\pi\) |
0.714083 | + | 0.700061i | \(0.246844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 6.00000 | + | 10.3923i | 0.270501 | + | 0.468521i | ||||
\(493\) | 18.0000 | − | 31.1769i | 0.810679 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | −20.0000 | −0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 3.00000 | − | 5.19615i | 0.134164 | − | 0.232379i | ||||
\(501\) | −3.00000 | + | 5.19615i | −0.134030 | + | 0.232147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.50000 | − | 2.59808i | 0.0666173 | − | 0.115385i | ||||
\(508\) | 2.00000 | − | 3.46410i | 0.0887357 | − | 0.153695i | ||||
\(509\) | 10.5000 | + | 18.1865i | 0.465404 | + | 0.806104i | 0.999220 | − | 0.0394971i | \(-0.0125756\pi\) |
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.00000 | + | 8.66025i | 0.220755 | + | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | − | 10.3923i | 0.264392 | − | 0.457940i | ||||
\(516\) | −8.00000 | − | 13.8564i | −0.352180 | − | 0.609994i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | − | 2.59808i | 0.0657162 | − | 0.113824i | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0000 | + | 25.9808i | 0.653410 | + | 1.13174i | ||||
\(528\) | −2.00000 | + | 3.46410i | −0.0870388 | + | 0.150756i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | −1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 15.5885i | 0.389104 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.50000 | − | 12.9904i | −0.323649 | − | 0.560576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 30.0000 | 1.29099 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.50000 | − | 6.06218i | 0.150199 | − | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −60.0000 | −2.57012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −3.00000 | − | 5.19615i | −0.128154 | − | 0.221969i | ||||
\(549\) | 10.0000 | − | 17.3205i | 0.426790 | − | 0.739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.5000 | − | 28.5788i | −0.700386 | − | 1.21310i | ||||
\(556\) | −14.0000 | + | 24.2487i | −0.593732 | + | 1.02837i | ||||
\(557\) | −15.0000 | + | 25.9808i | −0.635570 | + | 1.10084i | 0.350824 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.0000 | 1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.50000 | − | 7.79423i | −0.189316 | − | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | + | 15.5885i | 0.377300 | + | 0.653502i | 0.990668 | − | 0.136295i | \(-0.0435194\pi\) |
−0.613369 | + | 0.789797i | \(0.710186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | −4.00000 | − | 6.92820i | −0.167248 | − | 0.289683i | ||||
\(573\) | 27.0000 | 1.12794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | −8.00000 | − | 13.8564i | −0.333333 | − | 0.577350i | ||||
\(577\) | 5.50000 | − | 9.52628i | 0.228968 | − | 0.396584i | −0.728535 | − | 0.685009i | \(-0.759798\pi\) |
0.957503 | + | 0.288425i | \(0.0931316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.00000 | + | 12.1244i | 0.290910 | + | 0.503871i | ||||
\(580\) | −36.0000 | −1.49482 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | −22.0000 | + | 38.1051i | −0.904194 | + | 1.56611i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | 8.00000 | + | 13.8564i | 0.327418 | + | 0.567105i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | 1.50000 | − | 2.59808i | 0.0609837 | − | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00000 | + | 12.1244i | 0.284121 | + | 0.492112i | 0.972396 | − | 0.233338i | \(-0.0749648\pi\) |
−0.688274 | + | 0.725450i | \(0.741632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.0000 | + | 20.7846i | −0.485071 | + | 0.840168i | ||||
\(613\) | 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 | ||||||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | + | 16.4545i | −0.381837 | + | 0.661361i | −0.991325 | − | 0.131434i | \(-0.958042\pi\) |
0.609488 | + | 0.792796i | \(0.291375\pi\) | |||||||
\(620\) | 15.0000 | − | 25.9808i | 0.602414 | − | 1.04341i | ||||
\(621\) | −7.50000 | − | 12.9904i | −0.300965 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.0000 | −0.640513 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.00000 | − | 1.73205i | 0.0399362 | − | 0.0691714i | ||||
\(628\) | 13.0000 | + | 22.5167i | 0.518756 | + | 0.898513i | ||||
\(629\) | 66.0000 | 2.63159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.00000 | − | 12.1244i | 0.278225 | − | 0.481900i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | + | 5.19615i | 0.119051 | + | 0.206203i | ||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50000 | + | 12.9904i | −0.296232 | + | 0.513089i | −0.975271 | − | 0.221013i | \(-0.929064\pi\) |
0.679039 | + | 0.734103i | \(0.262397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.0000 | 1.93237 | 0.966186 | − | 0.257847i | \(-0.0830131\pi\) | ||||
0.966186 | + | 0.257847i | \(0.0830131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | 0.944999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5000 | + | 28.5788i | −0.648682 | + | 1.12355i | 0.334756 | + | 0.942305i | \(0.391346\pi\) |
−0.983438 | + | 0.181245i | \(0.941987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50000 | + | 7.79423i | 0.176640 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.0000 | −1.56652 | ||||||||
\(653\) | −19.5000 | − | 33.7750i | −0.763094 | − | 1.32172i | −0.941248 | − | 0.337715i | \(-0.890346\pi\) |
0.178154 | − | 0.984003i | \(-0.442987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | − | 15.5885i | 0.351659 | − | 0.609091i | ||||
\(656\) | 12.0000 | + | 20.7846i | 0.468521 | + | 0.811503i | ||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.0000 | 1.16863 | 0.584317 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584317 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(660\) | −3.00000 | − | 5.19615i | −0.116775 | − | 0.202260i | ||||
\(661\) | −24.5000 | + | 42.4352i | −0.952940 | + | 1.65054i | −0.213925 | + | 0.976850i | \(0.568625\pi\) |
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.0000 | + | 20.7846i | 0.466041 | + | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | + | 15.5885i | 0.348481 | + | 0.603587i | ||||
\(668\) | −6.00000 | + | 10.3923i | −0.232147 | + | 0.402090i | ||||
\(669\) | 9.50000 | − | 16.4545i | 0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | −0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.0000 | + | 17.3205i | −0.384900 | + | 0.666667i | ||||
\(676\) | 3.00000 | − | 5.19615i | 0.115385 | − | 0.199852i | ||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | 4.00000 | + | 6.92820i | 0.152944 | + | 0.264906i | ||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.00000 | 0.190762 | ||||||||
\(688\) | −16.0000 | − | 27.7128i | −0.609994 | − | 1.05654i | ||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | + | 30.3109i | 0.665731 | + | 1.15308i | 0.979086 | + | 0.203445i | \(0.0652137\pi\) |
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.0000 | − | 36.3731i | −0.796575 | − | 1.37971i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0000 | − | 19.0526i | 0.414873 | − | 0.718581i | ||||
\(704\) | −4.00000 | + | 6.92820i | −0.150756 | + | 0.261116i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.0000 | 0.676481 | ||||||||
\(709\) | 0.500000 | + | 0.866025i | 0.0187779 | + | 0.0325243i | 0.875262 | − | 0.483650i | \(-0.160689\pi\) |
−0.856484 | + | 0.516174i | \(0.827356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0000 | + | 17.3205i | −0.375029 | + | 0.649570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.0000 | −0.561754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | −15.0000 | − | 25.9808i | −0.560576 | − | 0.970947i | ||||
\(717\) | −6.00000 | + | 10.3923i | −0.224074 | + | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5000 | − | 33.7750i | −0.727227 | − | 1.25959i | −0.958051 | − | 0.286599i | \(-0.907475\pi\) |
0.230823 | − | 0.972996i | \(-0.425858\pi\) | |||||||
\(720\) | 24.0000 | 0.894427 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.0000 | + | 24.2487i | 0.520666 | + | 0.901819i | ||||
\(724\) | 7.00000 | − | 12.1244i | 0.260153 | − | 0.450598i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.0000 | −0.630495 | −0.315248 | − | 0.949009i | \(-0.602088\pi\) | ||||
−0.315248 | + | 0.949009i | \(0.602088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0000 | + | 41.5692i | −0.887672 | + | 1.53749i | ||||
\(732\) | −10.0000 | + | 17.3205i | −0.369611 | + | 0.640184i | ||||
\(733\) | −2.00000 | − | 3.46410i | −0.0738717 | − | 0.127950i | 0.826723 | − | 0.562609i | \(-0.190202\pi\) |
−0.900595 | + | 0.434659i | \(0.856869\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.50000 | + | 4.33013i | 0.0920887 | + | 0.159502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0000 | − | 29.4449i | 0.625355 | − | 1.08315i | −0.363117 | − | 0.931744i | \(-0.618287\pi\) |
0.988472 | − | 0.151403i | \(-0.0483792\pi\) | |||||||
\(740\) | −33.0000 | − | 57.1577i | −1.21310 | − | 2.10116i | ||||
\(741\) | 8.00000 | 0.293887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000 | 0.880475 | 0.440237 | − | 0.897881i | \(-0.354894\pi\) | ||||
0.440237 | + | 0.897881i | \(0.354894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | − | 20.7846i | −0.439057 | − | 0.760469i | ||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.50000 | − | 7.79423i | 0.163989 | − | 0.284037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.50000 | + | 2.59808i | −0.0544466 | + | 0.0943042i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0000 | + | 41.5692i | 0.869999 | + | 1.50688i | 0.861996 | + | 0.506915i | \(0.169214\pi\) |
0.00800331 | + | 0.999968i | \(0.497452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 54.0000 | 1.95365 | ||||||||
\(765\) | −18.0000 | − | 31.1769i | −0.650791 | − | 1.12720i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0000 | + | 31.1769i | −0.649942 | + | 1.12573i | ||||
\(768\) | 8.00000 | + | 13.8564i | 0.288675 | + | 0.500000i | ||||
\(769\) | 40.0000 | 1.44244 | 0.721218 | − | 0.692708i | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 14.0000 | + | 24.2487i | 0.503871 | + | 0.872730i | ||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0000 | + | 17.3205i | 0.359211 | + | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.214972 | − | 0.372343i | ||||
\(780\) | 12.0000 | − | 20.7846i | 0.429669 | − | 0.744208i | ||||
\(781\) | 4.50000 | − | 7.79423i | 0.161023 | − | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.0000 | −1.07211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.0000 | −1.39197 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0000 | − | 43.3013i | 0.891154 | − | 1.54352i | 0.0526599 | − | 0.998613i | \(-0.483230\pi\) |
0.838494 | − | 0.544911i | \(-0.183437\pi\) | |||||||
\(788\) | 18.0000 | − | 31.1769i | 0.641223 | − | 1.11063i | ||||
\(789\) | −15.0000 | − | 25.9808i | −0.534014 | − | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | − | 34.6410i | −0.710221 | − | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.00000 | − | 15.5885i | 0.319197 | − | 0.552866i | ||||
\(796\) | 16.0000 | + | 27.7128i | 0.567105 | + | 0.982255i | ||||
\(797\) | 21.0000 | 0.743858 | 0.371929 | − | 0.928261i | \(-0.378696\pi\) | ||||
0.371929 | + | 0.928261i | \(0.378696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | − | 5.19615i | 0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | 10.0000 | 0.352673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0000 | − | 25.9808i | −0.528025 | − | 0.914566i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.0000 | − | 51.9615i | 1.05085 | − | 1.82013i | ||||
\(816\) | 12.0000 | − | 20.7846i | 0.420084 | − | 0.727607i | ||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.0000 | −1.25717 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5000 | + | 19.9186i | −0.400865 | + | 0.694318i | −0.993831 | − | 0.110910i | \(-0.964624\pi\) |
0.592966 | + | 0.805228i | \(0.297957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | −6.00000 | − | 10.3923i | −0.208514 | − | 0.361158i | ||||
\(829\) | −12.5000 | + | 21.6506i | −0.434143 | + | 0.751958i | −0.997225 | − | 0.0744432i | \(-0.976282\pi\) |
0.563082 | + | 0.826401i | \(0.309615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | + | 6.92820i | 0.138758 | + | 0.240337i | ||||
\(832\) | −32.0000 | −1.10940 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.311458 | − | 0.539461i | ||||
\(836\) | 2.00000 | − | 3.46410i | 0.0691714 | − | 0.119808i | ||||
\(837\) | 12.5000 | − | 21.6506i | 0.432063 | − | 0.748355i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.0000 | 0.517858 | 0.258929 | − | 0.965896i | \(-0.416631\pi\) | ||||
0.258929 | + | 0.965896i | \(0.416631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.00000 | − | 10.3923i | 0.206651 | − | 0.357930i | ||||
\(844\) | 14.0000 | − | 24.2487i | 0.481900 | − | 0.834675i | ||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.0000 | −0.824163 | ||||||||
\(849\) | −16.0000 | − | 27.7128i | −0.549119 | − | 0.951101i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.5000 | + | 28.5788i | −0.565613 | + | 0.979670i | ||||
\(852\) | −9.00000 | − | 15.5885i | −0.308335 | − | 0.534052i | ||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | −0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | + | 10.3923i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.50000 | − | 11.2583i | −0.221777 | − | 0.384129i | 0.733571 | − | 0.679613i | \(-0.237852\pi\) |
−0.955348 | + | 0.295484i | \(0.904519\pi\) | |||||||
\(860\) | 48.0000 | 1.63679 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | + | 10.3923i | 0.204242 | + | 0.353758i | 0.949891 | − | 0.312581i | \(-0.101194\pi\) |
−0.745649 | + | 0.666339i | \(0.767860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | 0.339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | + | 17.3205i | −0.338837 | + | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.00000 | + | 1.73205i | 0.0338449 | + | 0.0586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.0000 | − | 25.9808i | 0.505937 | − | 0.876309i | ||||
\(880\) | −6.00000 | − | 10.3923i | −0.202260 | − | 0.350325i | ||||
\(881\) | 9.00000 | 0.303218 | 0.151609 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151609 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 24.0000 | + | 41.5692i | 0.807207 | + | 1.39812i | ||||
\(885\) | −13.5000 | + | 23.3827i | −0.453798 | + | 0.786000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0000 | − | 36.3731i | −0.705111 | − | 1.22129i | −0.966651 | − | 0.256096i | \(-0.917564\pi\) |
0.261540 | − | 0.965193i | \(-0.415770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 19.0000 | − | 32.9090i | 0.636167 | − | 1.10187i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.0000 | 1.50418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.0000 | + | 25.9808i | −0.500278 | + | 0.866507i | ||||
\(900\) | −8.00000 | + | 13.8564i | −0.266667 | + | 0.461880i | ||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.5000 | + | 18.1865i | 0.349032 | + | 0.604541i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | + | 6.92820i | −0.132818 | + | 0.230047i | −0.924762 | − | 0.380547i | \(-0.875736\pi\) |
0.791944 | + | 0.610594i | \(0.209069\pi\) | |||||||
\(908\) | 12.0000 | + | 20.7846i | 0.398234 | + | 0.689761i | ||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | −4.00000 | − | 6.92820i | −0.132453 | − | 0.229416i | ||||
\(913\) | −6.00000 | + | 10.3923i | −0.198571 | + | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.0000 | − | 25.9808i | −0.495885 | − | 0.858898i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | 1.18495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.0000 | 1.44671 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | − | 6.92820i | 0.131377 | − | 0.227552i | ||||
\(928\) | 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 | ||||||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00000 | + | 15.5885i | −0.294331 | + | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.0000 | −0.653372 | −0.326686 | − | 0.945133i | \(-0.605932\pi\) | ||||
−0.326686 | + | 0.945133i | \(0.605932\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0000 | −0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | − | 15.5885i | 0.293392 | − | 0.508169i | −0.681218 | − | 0.732081i | \(-0.738549\pi\) |
0.974609 | + | 0.223912i | \(0.0718827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | 36.0000 | 1.17170 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | + | 23.3827i | 0.438691 | + | 0.759835i | 0.997589 | − | 0.0694014i | \(-0.0221089\pi\) |
−0.558898 | + | 0.829237i | \(0.688776\pi\) | |||||||
\(948\) | 10.0000 | − | 17.3205i | 0.324785 | − | 0.562544i | ||||
\(949\) | 4.00000 | − | 6.92820i | 0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | −0.291845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5000 | + | 70.1481i | −1.31055 | + | 2.26994i | ||||
\(956\) | −12.0000 | + | 20.7846i | −0.388108 | + | 0.672222i | ||||
\(957\) | 3.00000 | + | 5.19615i | 0.0969762 | + | 0.167968i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.0000 | −0.774597 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 28.0000 | + | 48.4974i | 0.901819 | + | 1.56200i | ||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0000 | 0.450210 | 0.225105 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225105 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.00000 | + | 10.3923i | −0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5000 | − | 33.7750i | −0.625785 | − | 1.08389i | −0.988389 | − | 0.151948i | \(-0.951445\pi\) |
0.362604 | − | 0.931943i | \(-0.381888\pi\) | |||||||
\(972\) | 32.0000 | 1.02640 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.00000 | + | 13.8564i | 0.256205 | + | 0.443760i | ||||
\(976\) | −20.0000 | + | 34.6410i | −0.640184 | + | 1.10883i | ||||
\(977\) | −4.50000 | + | 7.79423i | −0.143968 | + | 0.249359i | −0.928987 | − | 0.370111i | \(-0.879319\pi\) |
0.785020 | + | 0.619471i | \(0.212653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | −0.0958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.0000 | −1.27710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.5000 | − | 28.5788i | 0.526268 | − | 0.911523i | −0.473263 | − | 0.880921i | \(-0.656924\pi\) |
0.999532 | − | 0.0306024i | \(-0.00974257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0000 | + | 46.7654i | 0.860292 | + | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.0000 | 0.509028 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000 | 0.0317340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.0000 | −1.52170 | ||||||||
\(996\) | 12.0000 | + | 20.7846i | 0.380235 | + | 0.658586i | ||||
\(997\) | −14.0000 | + | 24.2487i | −0.443384 | + | 0.767964i | −0.997938 | − | 0.0641836i | \(-0.979556\pi\) |
0.554554 | + | 0.832148i | \(0.312889\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.5000 | − | 47.6314i | −0.870061 | − | 1.50699i |
(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 | 539.2.e.e.67.1 | 2 | ||
7.2 | even | 3 | inner | 539.2.e.e.177.1 | 2 | ||
7.3 | odd | 6 | 77.2.a.b.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 539.2.a.b.1.1 | 1 | |||
7.5 | odd | 6 | 539.2.e.d.177.1 | 2 | |||
7.6 | odd | 2 | 539.2.e.d.67.1 | 2 | |||
21.11 | odd | 6 | 4851.2.a.k.1.1 | 1 | |||
21.17 | even | 6 | 693.2.a.b.1.1 | 1 | |||
28.3 | even | 6 | 1232.2.a.d.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.s.1.1 | 1 | |||
35.3 | even | 12 | 1925.2.b.g.1849.2 | 2 | |||
35.17 | even | 12 | 1925.2.b.g.1849.1 | 2 | |||
35.24 | odd | 6 | 1925.2.a.f.1.1 | 1 | |||
56.3 | even | 6 | 4928.2.a.x.1.1 | 1 | |||
56.45 | odd | 6 | 4928.2.a.i.1.1 | 1 | |||
77.3 | odd | 30 | 847.2.f.f.372.1 | 4 | |||
77.10 | even | 6 | 847.2.a.c.1.1 | 1 | |||
77.17 | even | 30 | 847.2.f.g.729.1 | 4 | |||
77.24 | even | 30 | 847.2.f.g.323.1 | 4 | |||
77.31 | odd | 30 | 847.2.f.f.323.1 | 4 | |||
77.32 | odd | 6 | 5929.2.a.d.1.1 | 1 | |||
77.38 | odd | 30 | 847.2.f.f.729.1 | 4 | |||
77.52 | even | 30 | 847.2.f.g.372.1 | 4 | |||
77.59 | odd | 30 | 847.2.f.f.148.1 | 4 | |||
77.73 | even | 30 | 847.2.f.g.148.1 | 4 | |||
231.164 | odd | 6 | 7623.2.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.b.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
539.2.a.b.1.1 | 1 | 7.4 | even | 3 | |||
539.2.e.d.67.1 | 2 | 7.6 | odd | 2 | |||
539.2.e.d.177.1 | 2 | 7.5 | odd | 6 | |||
539.2.e.e.67.1 | 2 | 1.1 | even | 1 | trivial | ||
539.2.e.e.177.1 | 2 | 7.2 | even | 3 | inner | ||
693.2.a.b.1.1 | 1 | 21.17 | even | 6 | |||
847.2.a.c.1.1 | 1 | 77.10 | even | 6 | |||
847.2.f.f.148.1 | 4 | 77.59 | odd | 30 | |||
847.2.f.f.323.1 | 4 | 77.31 | odd | 30 | |||
847.2.f.f.372.1 | 4 | 77.3 | odd | 30 | |||
847.2.f.f.729.1 | 4 | 77.38 | odd | 30 | |||
847.2.f.g.148.1 | 4 | 77.73 | even | 30 | |||
847.2.f.g.323.1 | 4 | 77.24 | even | 30 | |||
847.2.f.g.372.1 | 4 | 77.52 | even | 30 | |||
847.2.f.g.729.1 | 4 | 77.17 | even | 30 | |||
1232.2.a.d.1.1 | 1 | 28.3 | even | 6 | |||
1925.2.a.f.1.1 | 1 | 35.24 | odd | 6 | |||
1925.2.b.g.1849.1 | 2 | 35.17 | even | 12 | |||
1925.2.b.g.1849.2 | 2 | 35.3 | even | 12 | |||
4851.2.a.k.1.1 | 1 | 21.11 | odd | 6 | |||
4928.2.a.i.1.1 | 1 | 56.45 | odd | 6 | |||
4928.2.a.x.1.1 | 1 | 56.3 | even | 6 | |||
5929.2.a.d.1.1 | 1 | 77.32 | odd | 6 | |||
7623.2.a.i.1.1 | 1 | 231.164 | odd | 6 | |||
8624.2.a.s.1.1 | 1 | 28.11 | odd | 6 |