Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,2,Mod(55,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.c (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: | \(1.29357651274\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.109 |
Dual form | 162.2.c.a.55.1 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | −12.0000 | −2.02837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 2.00000 | + | 3.46410i | 0.324443 | + | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | − | 10.3923i | −0.875190 | − | 1.51587i | −0.856560 | − | 0.516047i | \(-0.827403\pi\) |
−0.0186297 | − | 0.999826i | \(-0.505930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 3.46410i | 0.267261 | + | 0.462910i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.50000 | + | 2.59808i | 0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | −1.50000 | + | 2.59808i | −0.181902 | + | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | + | 10.3923i | 0.717137 | + | 1.24212i | ||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | + | 13.8564i | 0.900070 | + | 1.55897i | 0.827401 | + | 0.561611i | \(0.189818\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | + | 10.3923i | −0.618853 | + | 1.07188i | ||||
\(95\) | 6.00000 | − | 10.3923i | 0.615587 | − | 1.06623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −3.00000 | − | 5.19615i | −0.298511 | − | 0.517036i | 0.677284 | − | 0.735721i | \(-0.263157\pi\) |
−0.975796 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 0.500000 | − | 0.866025i | 0.0490290 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | − | 3.46410i | 0.188982 | − | 0.327327i | ||||
\(113\) | −7.50000 | + | 12.9904i | −0.705541 | + | 1.22203i | 0.260955 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 0.500000 | − | 0.866025i | 0.0452679 | − | 0.0784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.50000 | − | 2.59808i | 0.131559 | − | 0.227866i | ||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | − | 13.8564i | −0.693688 | − | 1.20150i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | + | 17.3205i | −0.848189 | + | 1.46911i | 0.0346338 | + | 0.999400i | \(0.488974\pi\) |
−0.882823 | + | 0.469706i | \(0.844360\pi\) | |||||||
\(140\) | 6.00000 | − | 10.3923i | 0.507093 | − | 0.878310i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | − | 10.3923i | −0.503509 | − | 0.872103i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.0000 | −2.24223 | ||||||||
\(146\) | −5.50000 | − | 9.52628i | −0.455183 | − | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.500000 | − | 0.866025i | 0.0410997 | − | 0.0711868i | ||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | + | 10.3923i | 0.481932 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50000 | − | 11.2583i | 0.518756 | − | 0.898513i | −0.481006 | − | 0.876717i | \(-0.659728\pi\) |
0.999762 | − | 0.0217953i | \(-0.00693820\pi\) | |||||||
\(158\) | 8.00000 | − | 13.8564i | 0.636446 | − | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | − | 2.59808i | −0.118585 | − | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −1.50000 | − | 2.59808i | −0.114043 | − | 0.197528i | 0.803354 | − | 0.595502i | \(-0.203047\pi\) |
−0.917397 | + | 0.397974i | \(0.869713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | − | 13.8564i | 0.604743 | − | 1.04745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.50000 | − | 2.59808i | −0.112430 | − | 0.194734i | ||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −2.00000 | − | 3.46410i | −0.148250 | − | 0.256776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50000 | − | 2.59808i | 0.110282 | − | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 6.00000 | + | 10.3923i | 0.434145 | + | 0.751961i | 0.997225 | − | 0.0744412i | \(-0.0237173\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | − | 7.79423i | −0.321429 | − | 0.556731i | ||||
\(197\) | 3.00000 | 0.213741 | 0.106871 | − | 0.994273i | \(-0.465917\pi\) | ||||
0.106871 | + | 0.994273i | \(0.465917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.00000 | + | 5.19615i | −0.211079 | + | 0.365600i | ||||
\(203\) | −18.0000 | + | 31.1769i | −1.26335 | + | 2.18819i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 24.0000 | 1.63679 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | −5.50000 | − | 9.52628i | −0.372507 | − | 0.645201i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.50000 | − | 2.59808i | 0.100901 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0000 | 0.997785 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5000 | + | 19.9186i | −0.759941 | + | 1.31626i | 0.182939 | + | 0.983124i | \(0.441439\pi\) |
−0.942880 | + | 0.333133i | \(0.891894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50000 | + | 7.79423i | 0.295439 | + | 0.511716i | ||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.0000 | 2.34838 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | − | 10.3923i | 0.388922 | − | 0.673633i | ||||
\(239\) | 6.00000 | − | 10.3923i | 0.388108 | − | 0.672222i | −0.604087 | − | 0.796918i | \(-0.706462\pi\) |
0.992195 | + | 0.124696i | \(0.0397955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.50000 | + | 11.2583i | 0.418702 | + | 0.725213i | 0.995809 | − | 0.0914555i | \(-0.0291519\pi\) |
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −13.5000 | − | 23.3827i | −0.862483 | − | 1.49387i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | − | 3.46410i | −0.124274 | − | 0.215249i | ||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | 0.741362 | ||||||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | + | 15.5885i | −0.552866 | + | 0.957591i | ||||
\(266\) | −8.00000 | + | 13.8564i | −0.490511 | + | 0.849591i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | + | 3.46410i | 0.122169 | + | 0.211604i | ||||
\(269\) | −21.0000 | −1.28039 | −0.640196 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.50000 | − | 7.79423i | 0.271855 | − | 0.470867i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 20.0000 | 1.19952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.0000 | −0.717137 | ||||||||
\(281\) | −13.5000 | − | 23.3827i | −0.805342 | − | 1.39489i | −0.916060 | − | 0.401042i | \(-0.868648\pi\) |
0.110717 | − | 0.993852i | \(-0.464685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | − | 3.46410i | 0.118888 | − | 0.205919i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) |
0.919327 | + | 0.393494i | \(0.128734\pi\) | |||||||
\(284\) | −6.00000 | + | 10.3923i | −0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 13.5000 | + | 23.3827i | 0.792747 | + | 1.37308i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.50000 | + | 9.52628i | −0.321863 | + | 0.557483i | ||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.00000 | −0.521356 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | − | 27.7128i | 0.922225 | − | 1.59734i | ||||
\(302\) | −4.00000 | + | 6.92820i | −0.230174 | + | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | − | 10.3923i | 0.340777 | − | 0.590243i | ||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5000 | − | 19.9186i | −0.650018 | − | 1.12586i | −0.983118 | − | 0.182973i | \(-0.941428\pi\) |
0.333099 | − | 0.942892i | \(-0.391906\pi\) | |||||||
\(314\) | −13.0000 | −0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | 10.5000 | + | 18.1865i | 0.589739 | + | 1.02146i | 0.994266 | + | 0.106932i | \(0.0341026\pi\) |
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | − | 5.19615i | 0.165647 | − | 0.286910i | ||||
\(329\) | 24.0000 | − | 41.5692i | 1.32316 | − | 2.29179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | − | 17.3205i | −0.549650 | − | 0.952021i | −0.998298 | − | 0.0583130i | \(-0.981428\pi\) |
0.448649 | − | 0.893708i | \(-0.351905\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 6.00000 | + | 10.3923i | 0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.73205i | −0.0544735 | + | 0.0943508i | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.50000 | − | 7.79423i | −0.244047 | − | 0.422701i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −4.00000 | − | 6.92820i | −0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.50000 | + | 2.59808i | −0.0806405 | + | 0.139673i | ||||
\(347\) | 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 | ||||||||
\(349\) | −7.00000 | − | 12.1244i | −0.374701 | − | 0.649002i | 0.615581 | − | 0.788074i | \(-0.288921\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | −16.0000 | −0.855236 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0000 | + | 31.1769i | −0.955341 | + | 1.65470i | ||||
\(356\) | −1.50000 | + | 2.59808i | −0.0794998 | + | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | + | 3.46410i | −0.104828 | + | 0.181568i | ||||
\(365\) | −16.5000 | + | 28.5788i | −0.863649 | + | 1.49588i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.00000 | −0.155963 | ||||||||
\(371\) | 12.0000 | + | 20.7846i | 0.623009 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | − | 10.3923i | −0.309426 | − | 0.535942i | ||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 6.00000 | + | 10.3923i | 0.307794 | + | 0.533114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00000 | − | 10.3923i | 0.306987 | − | 0.531717i | ||||
\(383\) | −6.00000 | + | 10.3923i | −0.306586 | + | 0.531022i | −0.977613 | − | 0.210411i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.50000 | + | 7.79423i | −0.227284 | + | 0.393668i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | ||||
\(395\) | −48.0000 | −2.41514 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0000 | −1.25471 | −0.627357 | − | 0.778732i | \(-0.715863\pi\) | ||||
−0.627357 | + | 0.778732i | \(0.715863\pi\) | |||||||
\(398\) | 2.00000 | + | 3.46410i | 0.100251 | + | 0.173640i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 36.0000 | 1.78665 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5000 | − | 21.6506i | 0.618085 | − | 1.07056i | −0.371750 | − | 0.928333i | \(-0.621242\pi\) |
0.989835 | − | 0.142222i | \(-0.0454247\pi\) | |||||||
\(410\) | 9.00000 | − | 15.5885i | 0.444478 | − | 0.769859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00000 | + | 3.46410i | 0.0985329 | + | 0.170664i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.0000 | 1.76717 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | + | 20.7846i | −0.586238 | + | 1.01539i | 0.408481 | + | 0.912767i | \(0.366058\pi\) |
−0.994720 | + | 0.102628i | \(0.967275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.50000 | + | 11.2583i | 0.316791 | + | 0.548697i | 0.979817 | − | 0.199899i | \(-0.0640614\pi\) |
−0.663026 | + | 0.748596i | \(0.730728\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | + | 3.46410i | −0.0967868 | + | 0.167640i | ||||
\(428\) | 6.00000 | − | 10.3923i | 0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | − | 20.7846i | −0.578691 | − | 1.00232i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0000 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(434\) | −8.00000 | − | 13.8564i | −0.384012 | − | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.50000 | + | 9.52628i | −0.263402 | + | 0.456226i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00000 | −0.142695 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | + | 7.79423i | −0.213320 | + | 0.369482i | ||||
\(446\) | −4.00000 | + | 6.92820i | −0.189405 | + | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | + | 3.46410i | 0.0944911 | + | 0.163663i | ||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.50000 | − | 12.9904i | −0.352770 | − | 0.611016i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.00000 | + | 10.3923i | −0.281594 | + | 0.487735i | ||||
\(455\) | −6.00000 | + | 10.3923i | −0.281284 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | 23.0000 | 1.07472 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00000 | + | 15.5885i | 0.419172 | + | 0.726027i | 0.995856 | − | 0.0909401i | \(-0.0289872\pi\) |
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | + | 6.92820i | −0.185896 | + | 0.321981i | −0.943878 | − | 0.330294i | \(-0.892852\pi\) |
0.757982 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | 24.0000 | 1.11059 | 0.555294 | − | 0.831654i | \(-0.312606\pi\) | ||||
0.555294 | + | 0.831654i | \(0.312606\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | −18.0000 | − | 31.1769i | −0.830278 | − | 1.43808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | + | 13.8564i | 0.367065 | + | 0.635776i | ||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0000 | −0.548867 | ||||||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.500000 | + | 0.866025i | −0.0227980 | + | 0.0394874i | ||||
\(482\) | 6.50000 | − | 11.2583i | 0.296067 | − | 0.512803i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50000 | + | 9.52628i | 0.250000 | + | 0.433013i | ||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | −0.181257 | −0.0906287 | − | 0.995885i | \(-0.528888\pi\) | ||||
−0.0906287 | + | 0.995885i | \(0.528888\pi\) | |||||||
\(488\) | 0.500000 | + | 0.866025i | 0.0226339 | + | 0.0392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.5000 | + | 23.3827i | −0.609868 | + | 1.05632i | ||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5000 | + | 23.3827i | 0.608009 | + | 1.05310i | ||||
\(494\) | 4.00000 | 0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 24.0000 | + | 41.5692i | 1.07655 | + | 1.86463i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | − | 34.6410i | 0.895323 | − | 1.55074i | 0.0619186 | − | 0.998081i | \(-0.480278\pi\) |
0.833404 | − | 0.552664i | \(-0.186389\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | − | 20.7846i | −0.535586 | − | 0.927663i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.00000 | − | 13.8564i | 0.354943 | − | 0.614779i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0000 | + | 38.1051i | 0.973223 | + | 1.68567i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0000 | 0.661622 | ||||||||
\(515\) | 6.00000 | + | 10.3923i | 0.264392 | + | 0.457940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.00000 | + | 3.46410i | −0.0878750 | + | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.50000 | + | 2.59808i | 0.0657794 | + | 0.113933i | ||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0000 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(524\) | −6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | − | 10.3923i | 0.261612 | − | 0.453126i | ||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 18.0000 | 0.781870 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.0000 | 0.693688 | ||||||||
\(533\) | −3.00000 | − | 5.19615i | −0.129944 | − | 0.225070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | − | 31.1769i | 0.778208 | − | 1.34790i | ||||
\(536\) | 2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.5000 | + | 18.1865i | 0.452687 | + | 0.784077i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | −0.0429934 | −0.0214967 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214967 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(542\) | 8.00000 | + | 13.8564i | 0.343629 | + | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | −16.5000 | + | 28.5788i | −0.706782 | + | 1.22418i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0000 | − | 38.1051i | −0.940652 | − | 1.62926i | −0.764231 | − | 0.644942i | \(-0.776881\pi\) |
−0.176421 | − | 0.984315i | \(-0.556452\pi\) | |||||||
\(548\) | −9.00000 | −0.384461 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.0000 | − | 31.1769i | −0.766826 | − | 1.32818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | + | 55.4256i | −1.36078 | + | 2.35694i | ||||
\(554\) | 5.00000 | − | 8.66025i | 0.212430 | − | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | 3.00000 | 0.127114 | 0.0635570 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635570 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 6.00000 | + | 10.3923i | 0.253546 | + | 0.439155i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5000 | + | 23.3827i | −0.569463 | + | 0.986339i | ||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5000 | − | 38.9711i | −0.946582 | − | 1.63953i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | −7.50000 | − | 12.9904i | −0.314416 | − | 0.544585i | 0.664897 | − | 0.746935i | \(-0.268475\pi\) |
−0.979313 | + | 0.202350i | \(0.935142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 20.7846i | −0.500870 | − | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0000 | −1.04076 | −0.520382 | − | 0.853934i | \(-0.674210\pi\) | ||||
−0.520382 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.5000 | − | 23.3827i | 0.560557 | − | 0.970913i | ||||
\(581\) | 24.0000 | − | 41.5692i | 0.995688 | − | 1.72458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.0000 | 0.455183 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.00000 | −0.371787 | ||||||||
\(587\) | −12.0000 | − | 20.7846i | −0.495293 | − | 0.857873i | 0.504692 | − | 0.863299i | \(-0.331606\pi\) |
−0.999985 | + | 0.00542667i | \(0.998273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | + | 13.8564i | −0.329634 | + | 0.570943i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 4.50000 | + | 7.79423i | 0.184327 | + | 0.319264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0000 | + | 31.1769i | −0.735460 | + | 1.27385i | 0.219061 | + | 0.975711i | \(0.429701\pi\) |
−0.954521 | + | 0.298143i | \(0.903633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | − | 30.3109i | −0.713840 | − | 1.23641i | −0.963405 | − | 0.268049i | \(-0.913621\pi\) |
0.249565 | − | 0.968358i | \(-0.419712\pi\) | |||||||
\(602\) | −32.0000 | −1.30422 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 16.5000 | + | 28.5788i | 0.670820 | + | 1.16190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | + | 17.3205i | −0.405887 | + | 0.703018i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 2.00000 | − | 3.46410i | 0.0811107 | − | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.50000 | + | 2.59808i | 0.0607332 | + | 0.105193i | ||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50000 | + | 2.59808i | −0.0603877 | + | 0.104595i | −0.894639 | − | 0.446790i | \(-0.852567\pi\) |
0.834251 | + | 0.551385i | \(0.185900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | − | 6.92820i | −0.160774 | − | 0.278468i | 0.774373 | − | 0.632730i | \(-0.218066\pi\) |
−0.935146 | + | 0.354262i | \(0.884732\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 6.00000 | + | 10.3923i | 0.240385 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −11.5000 | + | 19.9186i | −0.459632 | + | 0.796107i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.50000 | + | 11.2583i | 0.259378 | + | 0.449256i | ||||
\(629\) | −3.00000 | −0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 8.00000 | + | 13.8564i | 0.318223 | + | 0.551178i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.5000 | − | 18.1865i | 0.417008 | − | 0.722280i | ||||
\(635\) | 24.0000 | − | 41.5692i | 0.952411 | − | 1.64962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50000 | + | 7.79423i | 0.178296 | + | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | 22.5000 | + | 38.9711i | 0.888697 | + | 1.53927i | 0.841417 | + | 0.540386i | \(0.181722\pi\) |
0.0472793 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | − | 3.46410i | 0.0788723 | − | 0.136611i | −0.823891 | − | 0.566748i | \(-0.808201\pi\) |
0.902764 | + | 0.430137i | \(0.141535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | −36.0000 | −1.41531 | −0.707653 | − | 0.706560i | \(-0.750246\pi\) | ||||
−0.707653 | + | 0.706560i | \(0.750246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | + | 3.46410i | 0.0784465 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | + | 6.92820i | −0.156652 | + | 0.271329i | ||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0000 | − | 31.1769i | −0.703318 | − | 1.21818i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −48.0000 | −1.87123 | ||||||||
\(659\) | 6.00000 | + | 10.3923i | 0.233727 | + | 0.404827i | 0.958902 | − | 0.283738i | \(-0.0915745\pi\) |
−0.725175 | + | 0.688565i | \(0.758241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.5000 | + | 19.9186i | −0.447298 | + | 0.774743i | −0.998209 | − | 0.0598209i | \(-0.980947\pi\) |
0.550911 | + | 0.834564i | \(0.314280\pi\) | |||||||
\(662\) | −10.0000 | + | 17.3205i | −0.388661 | + | 0.673181i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | − | 10.3923i | −0.232845 | − | 0.403300i | ||||
\(665\) | 48.0000 | 1.86136 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.00000 | + | 10.3923i | 0.232147 | + | 0.402090i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.00000 | − | 10.3923i | 0.231800 | − | 0.401490i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.50000 | − | 9.52628i | −0.212009 | − | 0.367211i | 0.740334 | − | 0.672239i | \(-0.234667\pi\) |
−0.952343 | + | 0.305028i | \(0.901334\pi\) | |||||||
\(674\) | 2.00000 | 0.0770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −3.00000 | − | 5.19615i | −0.115299 | − | 0.199704i | 0.802600 | − | 0.596518i | \(-0.203449\pi\) |
−0.917899 | + | 0.396813i | \(0.870116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | − | 6.92820i | 0.153506 | − | 0.265880i | ||||
\(680\) | −4.50000 | + | 7.79423i | −0.172567 | + | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.0000 | −1.03162 | ||||||||
\(686\) | 4.00000 | + | 6.92820i | 0.152721 | + | 0.264520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 3.00000 | − | 5.19615i | 0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0000 | + | 24.2487i | 0.532585 | + | 0.922464i | 0.999276 | + | 0.0380440i | \(0.0121127\pi\) |
−0.466691 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(692\) | 3.00000 | 0.114043 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −30.0000 | − | 51.9615i | −1.13796 | − | 1.97101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | −7.00000 | + | 12.1244i | −0.264954 | + | 0.458914i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.00000 | + | 13.8564i | 0.302372 | + | 0.523723i | ||||
\(701\) | 51.0000 | 1.92624 | 0.963122 | − | 0.269066i | \(-0.0867150\pi\) | ||||
0.963122 | + | 0.269066i | \(0.0867150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 12.0000 | − | 20.7846i | 0.451306 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.5000 | − | 40.7032i | −0.882561 | − | 1.52864i | −0.848484 | − | 0.529221i | \(-0.822484\pi\) |
−0.0340772 | − | 0.999419i | \(-0.510849\pi\) | |||||||
\(710\) | 36.0000 | 1.35106 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | 0.112430 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 1.50000 | + | 2.59808i | 0.0558242 | + | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | 18.0000 | − | 31.1769i | 0.668503 | − | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | + | 24.2487i | 0.519231 | + | 0.899335i | 0.999750 | + | 0.0223506i | \(0.00711500\pi\) |
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 33.0000 | 1.22138 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | + | 12.1244i | −0.258551 | + | 0.447823i | −0.965854 | − | 0.259087i | \(-0.916578\pi\) |
0.707303 | + | 0.706910i | \(0.249912\pi\) | |||||||
\(734\) | −4.00000 | + | 6.92820i | −0.147643 | + | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 1.50000 | + | 2.59808i | 0.0551411 | + | 0.0955072i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | − | 20.7846i | 0.440534 | − | 0.763027i | ||||
\(743\) | 6.00000 | − | 10.3923i | 0.220119 | − | 0.381257i | −0.734725 | − | 0.678365i | \(-0.762689\pi\) |
0.954844 | + | 0.297108i | \(0.0960222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | + | 23.3827i | 0.494602 | + | 0.856675i | ||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | − | 41.5692i | −0.876941 | − | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | −6.00000 | + | 10.3923i | −0.218797 | + | 0.378968i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.50000 | − | 7.79423i | −0.163880 | − | 0.283849i | ||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 14.0000 | + | 24.2487i | 0.508503 | + | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | − | 10.3923i | 0.217643 | − | 0.376969i | ||||
\(761\) | −7.50000 | + | 12.9904i | −0.271875 | + | 0.470901i | −0.969342 | − | 0.245716i | \(-0.920977\pi\) |
0.697467 | + | 0.716617i | \(0.254310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0000 | + | 38.1051i | 0.796453 | + | 1.37950i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5000 | − | 32.0429i | 0.667127 | − | 1.15550i | −0.311577 | − | 0.950221i | \(-0.600857\pi\) |
0.978704 | − | 0.205277i | \(-0.0658095\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.50000 | + | 11.2583i | 0.233940 | + | 0.405196i | ||||
\(773\) | 27.0000 | 0.971123 | 0.485561 | − | 0.874203i | \(-0.338615\pi\) | ||||
0.485561 | + | 0.874203i | \(0.338615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | −0.574737 | ||||||||
\(776\) | −1.00000 | − | 1.73205i | −0.0358979 | − | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.00000 | + | 5.19615i | −0.107555 | + | 0.186291i | ||||
\(779\) | −12.0000 | + | 20.7846i | −0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 19.5000 | + | 33.7750i | 0.695985 | + | 1.20548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.0000 | + | 27.7128i | −0.570338 | + | 0.987855i | 0.426193 | + | 0.904632i | \(0.359855\pi\) |
−0.996531 | + | 0.0832226i | \(0.973479\pi\) | |||||||
\(788\) | −1.50000 | + | 2.59808i | −0.0534353 | + | 0.0925526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.0000 | + | 41.5692i | 0.853882 | + | 1.47897i | ||||
\(791\) | −60.0000 | −2.13335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | 0.0355110 | ||||||||
\(794\) | 12.5000 | + | 21.6506i | 0.443608 | + | 0.768352i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | −25.5000 | + | 44.1673i | −0.903256 | + | 1.56449i | −0.0800155 | + | 0.996794i | \(0.525497\pi\) |
−0.823241 | + | 0.567692i | \(0.807836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.00000 | 0.105934 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | + | 3.46410i | −0.0704470 | + | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.00000 | − | 5.19615i | −0.105540 | − | 0.182800i | ||||
\(809\) | 39.0000 | 1.37117 | 0.685583 | − | 0.727994i | \(-0.259547\pi\) | ||||
0.685583 | + | 0.727994i | \(0.259547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −18.0000 | − | 31.1769i | −0.631676 | − | 1.09410i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | + | 20.7846i | −0.420342 | + | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | + | 27.7128i | 0.559769 | + | 0.969549i | ||||
\(818\) | −25.0000 | −0.874105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −7.50000 | − | 12.9904i | −0.261752 | − | 0.453367i | 0.704956 | − | 0.709251i | \(-0.250967\pi\) |
−0.966708 | + | 0.255884i | \(0.917634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.0000 | + | 38.1051i | −0.766872 | + | 1.32826i | 0.172379 | + | 0.985031i | \(0.444854\pi\) |
−0.939251 | + | 0.343230i | \(0.888479\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0000 | 1.66912 | 0.834562 | − | 0.550914i | \(-0.185721\pi\) | ||||
0.834562 | + | 0.550914i | \(0.185721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | −18.0000 | − | 31.1769i | −0.624789 | − | 1.08217i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.500000 | − | 0.866025i | 0.0173344 | − | 0.0300240i | ||||
\(833\) | −13.5000 | + | 23.3827i | −0.467747 | + | 0.810162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | + | 31.1769i | 0.622916 | + | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.0000 | 0.829066 | ||||||||
\(839\) | 12.0000 | + | 20.7846i | 0.414286 | + | 0.717564i | 0.995353 | − | 0.0962912i | \(-0.0306980\pi\) |
−0.581067 | + | 0.813856i | \(0.697365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 6.50000 | − | 11.2583i | 0.224005 | − | 0.387988i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −36.0000 | −1.23844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.0000 | 1.51186 | ||||||||
\(848\) | −3.00000 | − | 5.19615i | −0.103020 | − | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | + | 10.3923i | −0.205798 | + | 0.356453i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | + | 8.66025i | 0.171197 | + | 0.296521i | 0.938839 | − | 0.344358i | \(-0.111903\pi\) |
−0.767642 | + | 0.640879i | \(0.778570\pi\) | |||||||
\(854\) | 4.00000 | 0.136877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −19.5000 | − | 33.7750i | −0.666107 | − | 1.15373i | −0.978984 | − | 0.203938i | \(-0.934626\pi\) |
0.312877 | − | 0.949794i | \(-0.398707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0000 | − | 45.0333i | 0.887109 | − | 1.53652i | 0.0438309 | − | 0.999039i | \(-0.486044\pi\) |
0.843278 | − | 0.537478i | \(-0.180623\pi\) | |||||||
\(860\) | −12.0000 | + | 20.7846i | −0.409197 | + | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | − | 10.3923i | −0.204361 | − | 0.353963i | ||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | 0.306009 | ||||||||
\(866\) | −5.50000 | − | 9.52628i | −0.186898 | − | 0.323716i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.00000 | + | 13.8564i | −0.271538 | + | 0.470317i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | 11.0000 | 0.372507 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | − | 10.3923i | −0.202837 | − | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5000 | − | 21.6506i | 0.422095 | − | 0.731090i | −0.574049 | − | 0.818821i | \(-0.694628\pi\) |
0.996144 | + | 0.0877308i | \(0.0279615\pi\) | |||||||
\(878\) | 14.0000 | − | 24.2487i | 0.472477 | − | 0.818354i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 1.50000 | + | 2.59808i | 0.0504505 | + | 0.0873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | − | 55.4256i | −1.07325 | − | 1.85892i | ||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | 24.0000 | + | 41.5692i | 0.803129 | + | 1.39106i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | − | 31.1769i | 0.601674 | − | 1.04213i | ||||
\(896\) | 2.00000 | − | 3.46410i | 0.0668153 | − | 0.115728i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.00000 | − | 15.5885i | −0.300334 | − | 0.520194i | ||||
\(899\) | 36.0000 | 1.20067 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.50000 | + | 12.9904i | −0.249446 | + | 0.432054i | ||||
\(905\) | 15.0000 | − | 25.9808i | 0.498617 | − | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | + | 13.8564i | 0.265636 | + | 0.460094i | 0.967730 | − | 0.251990i | \(-0.0810849\pi\) |
−0.702094 | + | 0.712084i | \(0.747752\pi\) | |||||||
\(908\) | 12.0000 | 0.398234 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | 0.397796 | ||||||||
\(911\) | 12.0000 | + | 20.7846i | 0.397578 | + | 0.688625i | 0.993426 | − | 0.114472i | \(-0.0365176\pi\) |
−0.595849 | + | 0.803097i | \(0.703184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.5000 | − | 19.9186i | −0.379971 | − | 0.658129i | ||||
\(917\) | −48.0000 | −1.58510 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.00000 | − | 15.5885i | 0.296399 | − | 0.513378i | ||||
\(923\) | 6.00000 | − | 10.3923i | 0.197492 | − | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.00000 | −0.295439 | ||||||||
\(929\) | −1.50000 | − | 2.59808i | −0.0492134 | − | 0.0852401i | 0.840369 | − | 0.542014i | \(-0.182338\pi\) |
−0.889583 | + | 0.456774i | \(0.849005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | − | 31.1769i | 0.589926 | − | 1.02178i | ||||
\(932\) | 10.5000 | − | 18.1865i | 0.343939 | − | 0.595720i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | − | 20.7846i | −0.392652 | − | 0.680093i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0000 | −1.20874 | −0.604369 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604369 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(938\) | −8.00000 | − | 13.8564i | −0.261209 | − | 0.452428i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0000 | + | 31.1769i | −0.587095 | + | 1.01688i | ||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00000 | − | 10.3923i | −0.194974 | − | 0.337705i | 0.751918 | − | 0.659256i | \(-0.229129\pi\) |
−0.946892 | + | 0.321552i | \(0.895796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | − | 9.52628i | 0.178538 | − | 0.309236i | ||||
\(950\) | 8.00000 | − | 13.8564i | 0.259554 | − | 0.449561i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | −9.00000 | −0.291539 | −0.145769 | − | 0.989319i | \(-0.546566\pi\) | ||||
−0.145769 | + | 0.989319i | \(0.546566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0000 | −1.16493 | ||||||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.00000 | + | 10.3923i | −0.193851 | + | 0.335760i | ||||
\(959\) | −18.0000 | + | 31.1769i | −0.581250 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 1.00000 | 0.0322413 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.0000 | −0.418702 | ||||||||
\(965\) | 19.5000 | + | 33.7750i | 0.627727 | + | 1.08726i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000 | − | 3.46410i | 0.0643157 | − | 0.111398i | −0.832075 | − | 0.554664i | \(-0.812847\pi\) |
0.896390 | + | 0.443266i | \(0.146180\pi\) | |||||||
\(968\) | 5.50000 | − | 9.52628i | 0.176777 | − | 0.306186i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.00000 | − | 5.19615i | −0.0963242 | − | 0.166838i | ||||
\(971\) | 36.0000 | 1.15529 | 0.577647 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −80.0000 | −2.56468 | ||||||||
\(974\) | 2.00000 | + | 3.46410i | 0.0640841 | + | 0.110997i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.500000 | − | 0.866025i | 0.0160046 | − | 0.0277208i | ||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 27.0000 | 0.862483 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000 | + | 41.5692i | 0.765481 | + | 1.32585i | 0.939992 | + | 0.341197i | \(0.110832\pi\) |
−0.174511 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.50000 | + | 7.79423i | −0.143382 | + | 0.248345i | ||||
\(986\) | 13.5000 | − | 23.3827i | 0.429928 | − | 0.744656i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | − | 3.46410i | −0.0636285 | − | 0.110208i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.0000 | − | 41.5692i | 0.761234 | − | 1.31850i | ||||
\(995\) | 6.00000 | − | 10.3923i | 0.190213 | − | 0.329458i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5000 | + | 32.0429i | 0.585901 | + | 1.01481i | 0.994762 | + | 0.102214i | \(0.0325925\pi\) |
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(998\) | −40.0000 | −1.26618 | ||||||||
\(999\) | 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 | 162.2.c.a.109.1 | 2 | ||
3.2 | odd | 2 | 162.2.c.d.109.1 | 2 | |||
4.3 | odd | 2 | 1296.2.i.b.433.1 | 2 | |||
9.2 | odd | 6 | 162.2.c.d.55.1 | 2 | |||
9.4 | even | 3 | 162.2.a.d.1.1 | yes | 1 | ||
9.5 | odd | 6 | 162.2.a.a.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 162.2.c.a.55.1 | 2 | ||
12.11 | even | 2 | 1296.2.i.n.433.1 | 2 | |||
36.7 | odd | 6 | 1296.2.i.b.865.1 | 2 | |||
36.11 | even | 6 | 1296.2.i.n.865.1 | 2 | |||
36.23 | even | 6 | 1296.2.a.c.1.1 | 1 | |||
36.31 | odd | 6 | 1296.2.a.l.1.1 | 1 | |||
45.4 | even | 6 | 4050.2.a.r.1.1 | 1 | |||
45.13 | odd | 12 | 4050.2.c.n.649.1 | 2 | |||
45.14 | odd | 6 | 4050.2.a.bh.1.1 | 1 | |||
45.22 | odd | 12 | 4050.2.c.n.649.2 | 2 | |||
45.23 | even | 12 | 4050.2.c.g.649.2 | 2 | |||
45.32 | even | 12 | 4050.2.c.g.649.1 | 2 | |||
63.13 | odd | 6 | 7938.2.a.s.1.1 | 1 | |||
63.41 | even | 6 | 7938.2.a.n.1.1 | 1 | |||
72.5 | odd | 6 | 5184.2.a.y.1.1 | 1 | |||
72.13 | even | 6 | 5184.2.a.c.1.1 | 1 | |||
72.59 | even | 6 | 5184.2.a.bd.1.1 | 1 | |||
72.67 | odd | 6 | 5184.2.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.2.a.a.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
162.2.a.d.1.1 | yes | 1 | 9.4 | even | 3 | ||
162.2.c.a.55.1 | 2 | 9.7 | even | 3 | inner | ||
162.2.c.a.109.1 | 2 | 1.1 | even | 1 | trivial | ||
162.2.c.d.55.1 | 2 | 9.2 | odd | 6 | |||
162.2.c.d.109.1 | 2 | 3.2 | odd | 2 | |||
1296.2.a.c.1.1 | 1 | 36.23 | even | 6 | |||
1296.2.a.l.1.1 | 1 | 36.31 | odd | 6 | |||
1296.2.i.b.433.1 | 2 | 4.3 | odd | 2 | |||
1296.2.i.b.865.1 | 2 | 36.7 | odd | 6 | |||
1296.2.i.n.433.1 | 2 | 12.11 | even | 2 | |||
1296.2.i.n.865.1 | 2 | 36.11 | even | 6 | |||
4050.2.a.r.1.1 | 1 | 45.4 | even | 6 | |||
4050.2.a.bh.1.1 | 1 | 45.14 | odd | 6 | |||
4050.2.c.g.649.1 | 2 | 45.32 | even | 12 | |||
4050.2.c.g.649.2 | 2 | 45.23 | even | 12 | |||
4050.2.c.n.649.1 | 2 | 45.13 | odd | 12 | |||
4050.2.c.n.649.2 | 2 | 45.22 | odd | 12 | |||
5184.2.a.c.1.1 | 1 | 72.13 | even | 6 | |||
5184.2.a.h.1.1 | 1 | 72.67 | odd | 6 | |||
5184.2.a.y.1.1 | 1 | 72.5 | odd | 6 | |||
5184.2.a.bd.1.1 | 1 | 72.59 | even | 6 | |||
7938.2.a.n.1.1 | 1 | 63.41 | even | 6 | |||
7938.2.a.s.1.1 | 1 | 63.13 | odd | 6 |