Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(65,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.910294583043\) |
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: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.65 |
Dual form | 114.2.h.d.107.1 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.00000 | + | 1.73205i | 1.34164 | + | 0.774597i | 0.987048 | − | 0.160424i | \(-0.0512862\pi\) |
0.354593 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 3.00000 | − | 1.73205i | 0.948683 | − | 0.547723i | ||||
\(11\) | − | 1.73205i | − | 0.522233i | −0.965307 | − | 0.261116i | \(-0.915909\pi\) | ||
0.965307 | − | 0.261116i | \(-0.0840907\pi\) | |||||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | −3.00000 | + | 1.73205i | −0.832050 | + | 0.480384i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
0.0225039 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(14\) | −1.00000 | + | 1.73205i | −0.267261 | + | 0.462910i | ||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.00000 | + | 3.46410i | 1.45521 | + | 0.840168i | 0.998770 | − | 0.0495842i | \(-0.0157896\pi\) |
0.456444 | + | 0.889752i | \(0.349123\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | 0.500000 | + | 4.33013i | 0.114708 | + | 0.993399i | ||||
\(20\) | − | 3.46410i | − | 0.774597i | ||||||
\(21\) | 3.46410i | 0.755929i | ||||||||
\(22\) | −1.50000 | − | 0.866025i | −0.319801 | − | 0.184637i | ||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | 3.50000 | + | 6.06218i | 0.700000 | + | 1.21244i | ||||
\(26\) | 3.46410i | 0.679366i | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 1.00000 | + | 1.73205i | 0.188982 | + | 0.327327i | ||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | −3.00000 | − | 5.19615i | −0.547723 | − | 0.948683i | ||||
\(31\) | − | 6.92820i | − | 1.24434i | −0.782881 | − | 0.622171i | \(-0.786251\pi\) | ||
0.782881 | − | 0.622171i | \(-0.213749\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 6.00000 | − | 3.46410i | 1.02899 | − | 0.594089i | ||||
\(35\) | −6.00000 | − | 3.46410i | −1.01419 | − | 0.585540i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | − | 6.92820i | − | 1.13899i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | 4.00000 | + | 1.73205i | 0.648886 | + | 0.280976i | ||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | −3.00000 | − | 1.73205i | −0.474342 | − | 0.273861i | ||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 3.00000 | + | 1.73205i | 0.462910 | + | 0.267261i | ||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | −1.50000 | + | 0.866025i | −0.226134 | + | 0.130558i | ||||
\(45\) | −9.00000 | − | 5.19615i | −1.34164 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 1.73205i | −0.437595 | + | 0.252646i | −0.702577 | − | 0.711608i | \(-0.747967\pi\) |
0.264982 | + | 0.964253i | \(0.414634\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 7.00000 | 0.989949 | ||||||||
\(51\) | 6.00000 | − | 10.3923i | 0.840168 | − | 1.45521i | ||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 4.50000 | + | 2.59808i | 0.612372 | + | 0.353553i | ||||
\(55\) | 3.00000 | − | 5.19615i | 0.404520 | − | 0.700649i | ||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 7.50000 | − | 0.866025i | 0.993399 | − | 0.114708i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | −6.00000 | −0.774597 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | −6.00000 | − | 3.46410i | −0.762001 | − | 0.439941i | ||||
\(63\) | 6.00000 | 0.755929 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | 4.50000 | − | 2.59808i | 0.549762 | − | 0.317406i | −0.199264 | − | 0.979946i | \(-0.563855\pi\) |
0.749026 | + | 0.662540i | \(0.230522\pi\) | |||||||
\(68\) | − | 6.92820i | − | 0.840168i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | + | 3.46410i | −0.717137 | + | 0.414039i | ||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | −2.50000 | + | 4.33013i | −0.292603 | + | 0.506803i | −0.974424 | − | 0.224716i | \(-0.927855\pi\) |
0.681822 | + | 0.731519i | \(0.261188\pi\) | |||||||
\(74\) | −6.00000 | − | 3.46410i | −0.697486 | − | 0.402694i | ||||
\(75\) | 10.5000 | − | 6.06218i | 1.21244 | − | 0.700000i | ||||
\(76\) | 3.50000 | − | 2.59808i | 0.401478 | − | 0.298020i | ||||
\(77\) | 3.46410i | 0.394771i | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −12.0000 | − | 6.92820i | −1.35011 | − | 0.779484i | −0.361842 | − | 0.932240i | \(-0.617852\pi\) |
−0.988264 | + | 0.152756i | \(0.951185\pi\) | |||||||
\(80\) | −3.00000 | + | 1.73205i | −0.335410 | + | 0.193649i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | − | 5.19615i | − | 0.570352i | −0.958475 | − | 0.285176i | \(-0.907948\pi\) | ||
0.958475 | − | 0.285176i | \(-0.0920520\pi\) | |||||||
\(84\) | 3.00000 | − | 1.73205i | 0.327327 | − | 0.188982i | ||||
\(85\) | 12.0000 | + | 20.7846i | 1.30158 | + | 2.25441i | ||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | −9.00000 | + | 5.19615i | −0.964901 | + | 0.557086i | ||||
\(88\) | 1.73205i | 0.184637i | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | −9.00000 | + | 5.19615i | −0.948683 | + | 0.547723i | ||||
\(91\) | 6.00000 | − | 3.46410i | 0.628971 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0000 | −1.24434 | ||||||||
\(94\) | 3.46410i | 0.357295i | ||||||||
\(95\) | −6.00000 | + | 13.8564i | −0.615587 | + | 1.42164i | ||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 7.50000 | + | 4.33013i | 0.761510 | + | 0.439658i | 0.829837 | − | 0.558005i | \(-0.188433\pi\) |
−0.0683279 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(98\) | −1.50000 | + | 2.59808i | −0.151523 | + | 0.262445i | ||||
\(99\) | 5.19615i | 0.522233i | ||||||||
\(100\) | 3.50000 | − | 6.06218i | 0.350000 | − | 0.606218i | ||||
\(101\) | 9.00000 | − | 5.19615i | 0.895533 | − | 0.517036i | 0.0197851 | − | 0.999804i | \(-0.493702\pi\) |
0.875748 | + | 0.482768i | \(0.160368\pi\) | |||||||
\(102\) | −6.00000 | − | 10.3923i | −0.594089 | − | 1.02899i | ||||
\(103\) | 10.3923i | 1.02398i | 0.858990 | + | 0.511992i | \(0.171092\pi\) | ||||
−0.858990 | + | 0.511992i | \(0.828908\pi\) | |||||||
\(104\) | 3.00000 | − | 1.73205i | 0.294174 | − | 0.169842i | ||||
\(105\) | −6.00000 | + | 10.3923i | −0.585540 | + | 1.01419i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 4.50000 | − | 2.59808i | 0.433013 | − | 0.250000i | ||||
\(109\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | −3.00000 | − | 5.19615i | −0.286039 | − | 0.495434i | ||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 1.00000 | − | 1.73205i | 0.0944911 | − | 0.163663i | ||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 3.00000 | − | 6.92820i | 0.280976 | − | 0.648886i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 9.00000 | − | 5.19615i | 0.832050 | − | 0.480384i | ||||
\(118\) | −1.50000 | − | 2.59808i | −0.138086 | − | 0.239172i | ||||
\(119\) | −12.0000 | − | 6.92820i | −1.10004 | − | 0.635107i | ||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 4.50000 | + | 2.59808i | 0.405751 | + | 0.234261i | ||||
\(124\) | −6.00000 | + | 3.46410i | −0.538816 | + | 0.311086i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 3.00000 | − | 5.19615i | 0.267261 | − | 0.462910i | ||||
\(127\) | −9.00000 | + | 5.19615i | −0.798621 | + | 0.461084i | −0.842989 | − | 0.537931i | \(-0.819206\pi\) |
0.0443678 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 12.0000 | + | 6.92820i | 1.05654 | + | 0.609994i | ||||
\(130\) | −6.00000 | + | 10.3923i | −0.526235 | + | 0.911465i | ||||
\(131\) | 16.5000 | + | 9.52628i | 1.44161 | + | 0.832315i | 0.997957 | − | 0.0638831i | \(-0.0203485\pi\) |
0.443654 | + | 0.896198i | \(0.353682\pi\) | |||||||
\(132\) | 1.50000 | + | 2.59808i | 0.130558 | + | 0.226134i | ||||
\(133\) | −1.00000 | − | 8.66025i | −0.0867110 | − | 0.750939i | ||||
\(134\) | − | 5.19615i | − | 0.448879i | ||||||
\(135\) | −9.00000 | + | 15.5885i | −0.774597 | + | 1.34164i | ||||
\(136\) | −6.00000 | − | 3.46410i | −0.514496 | − | 0.297044i | ||||
\(137\) | 1.50000 | − | 0.866025i | 0.128154 | − | 0.0739895i | −0.434553 | − | 0.900646i | \(-0.643094\pi\) |
0.562706 | + | 0.826657i | \(0.309760\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | − | 0.866025i | −0.0424094 | − | 0.0734553i | 0.844042 | − | 0.536278i | \(-0.180170\pi\) |
−0.886451 | + | 0.462822i | \(0.846837\pi\) | |||||||
\(140\) | 6.92820i | 0.585540i | ||||||||
\(141\) | 3.00000 | + | 5.19615i | 0.252646 | + | 0.437595i | ||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 3.00000 | + | 5.19615i | 0.250873 | + | 0.434524i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | − | 20.7846i | − | 1.72607i | ||||||
\(146\) | 2.50000 | + | 4.33013i | 0.206901 | + | 0.358364i | ||||
\(147\) | 5.19615i | 0.428571i | ||||||||
\(148\) | −6.00000 | + | 3.46410i | −0.493197 | + | 0.284747i | ||||
\(149\) | 6.00000 | + | 3.46410i | 0.491539 | + | 0.283790i | 0.725213 | − | 0.688525i | \(-0.241741\pi\) |
−0.233674 | + | 0.972315i | \(0.575075\pi\) | |||||||
\(150\) | − | 12.1244i | − | 0.989949i | ||||||
\(151\) | 6.92820i | 0.563809i | 0.959442 | + | 0.281905i | \(0.0909662\pi\) | ||||
−0.959442 | + | 0.281905i | \(0.909034\pi\) | |||||||
\(152\) | −0.500000 | − | 4.33013i | −0.0405554 | − | 0.351220i | ||||
\(153\) | −18.0000 | − | 10.3923i | −1.45521 | − | 0.840168i | ||||
\(154\) | 3.00000 | + | 1.73205i | 0.241747 | + | 0.139573i | ||||
\(155\) | 12.0000 | − | 20.7846i | 0.963863 | − | 1.66946i | ||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | 10.0000 | − | 17.3205i | 0.798087 | − | 1.38233i | −0.122774 | − | 0.992435i | \(-0.539179\pi\) |
0.920860 | − | 0.389892i | \(-0.127488\pi\) | |||||||
\(158\) | −12.0000 | + | 6.92820i | −0.954669 | + | 0.551178i | ||||
\(159\) | 9.00000 | − | 5.19615i | 0.713746 | − | 0.412082i | ||||
\(160\) | 3.46410i | 0.273861i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | −17.0000 | −1.33154 | −0.665771 | − | 0.746156i | \(-0.731897\pi\) | ||||
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | −9.00000 | − | 5.19615i | −0.700649 | − | 0.404520i | ||||
\(166\) | −4.50000 | − | 2.59808i | −0.349268 | − | 0.201650i | ||||
\(167\) | 6.00000 | + | 10.3923i | 0.464294 | + | 0.804181i | 0.999169 | − | 0.0407502i | \(-0.0129748\pi\) |
−0.534875 | + | 0.844931i | \(0.679641\pi\) | |||||||
\(168\) | − | 3.46410i | − | 0.267261i | ||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 24.0000 | 1.84072 | ||||||||
\(171\) | −1.50000 | − | 12.9904i | −0.114708 | − | 0.993399i | ||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | 10.3923i | 0.787839i | ||||||||
\(175\) | −7.00000 | − | 12.1244i | −0.529150 | − | 0.916515i | ||||
\(176\) | 1.50000 | + | 0.866025i | 0.113067 | + | 0.0652791i | ||||
\(177\) | −4.50000 | − | 2.59808i | −0.338241 | − | 0.195283i | ||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | −3.00000 | −0.224231 | −0.112115 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(180\) | 10.3923i | 0.774597i | ||||||||
\(181\) | 6.00000 | − | 3.46410i | 0.445976 | − | 0.257485i | −0.260153 | − | 0.965567i | \(-0.583773\pi\) |
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(182\) | − | 6.92820i | − | 0.513553i | ||||||
\(183\) | −15.0000 | + | 8.66025i | −1.10883 | + | 0.640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | − | 20.7846i | 0.882258 | − | 1.52811i | ||||
\(186\) | −6.00000 | + | 10.3923i | −0.439941 | + | 0.762001i | ||||
\(187\) | 6.00000 | − | 10.3923i | 0.438763 | − | 0.759961i | ||||
\(188\) | 3.00000 | + | 1.73205i | 0.218797 | + | 0.126323i | ||||
\(189\) | − | 10.3923i | − | 0.755929i | ||||||
\(190\) | 9.00000 | + | 12.1244i | 0.652929 | + | 0.879593i | ||||
\(191\) | 6.92820i | 0.501307i | 0.968077 | + | 0.250654i | \(0.0806455\pi\) | ||||
−0.968077 | + | 0.250654i | \(0.919354\pi\) | |||||||
\(192\) | − | 1.73205i | − | 0.125000i | ||||||
\(193\) | 18.0000 | + | 10.3923i | 1.29567 | + | 0.748054i | 0.979653 | − | 0.200700i | \(-0.0643215\pi\) |
0.316016 | + | 0.948754i | \(0.397655\pi\) | |||||||
\(194\) | 7.50000 | − | 4.33013i | 0.538469 | − | 0.310885i | ||||
\(195\) | 20.7846i | 1.48842i | ||||||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | 20.7846i | 1.48084i | 0.672143 | + | 0.740421i | \(0.265374\pi\) | ||||
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(198\) | 4.50000 | + | 2.59808i | 0.319801 | + | 0.184637i | ||||
\(199\) | −7.00000 | − | 12.1244i | −0.496217 | − | 0.859473i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
−0.999990 | + | 0.00436292i | \(0.998611\pi\) | |||||||
\(200\) | −3.50000 | − | 6.06218i | −0.247487 | − | 0.428661i | ||||
\(201\) | −4.50000 | − | 7.79423i | −0.317406 | − | 0.549762i | ||||
\(202\) | − | 10.3923i | − | 0.731200i | ||||||
\(203\) | 6.00000 | + | 10.3923i | 0.421117 | + | 0.729397i | ||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | −9.00000 | + | 5.19615i | −0.628587 | + | 0.362915i | ||||
\(206\) | 9.00000 | + | 5.19615i | 0.627060 | + | 0.362033i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.46410i | − | 0.240192i | ||||||
\(209\) | 7.50000 | − | 0.866025i | 0.518786 | − | 0.0599042i | ||||
\(210\) | 6.00000 | + | 10.3923i | 0.414039 | + | 0.717137i | ||||
\(211\) | 9.00000 | + | 5.19615i | 0.619586 | + | 0.357718i | 0.776708 | − | 0.629861i | \(-0.216888\pi\) |
−0.157122 | + | 0.987579i | \(0.550222\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | −9.00000 | − | 5.19615i | −0.616670 | − | 0.356034i | ||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | −24.0000 | + | 13.8564i | −1.63679 | + | 0.944999i | ||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 13.8564i | 0.940634i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.50000 | + | 4.33013i | 0.506803 | + | 0.292603i | ||||
\(220\) | −6.00000 | −0.404520 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | −6.00000 | + | 10.3923i | −0.402694 | + | 0.697486i | ||||
\(223\) | 12.0000 | + | 6.92820i | 0.803579 | + | 0.463947i | 0.844721 | − | 0.535207i | \(-0.179766\pi\) |
−0.0411418 | + | 0.999153i | \(0.513100\pi\) | |||||||
\(224\) | −1.00000 | − | 1.73205i | −0.0668153 | − | 0.115728i | ||||
\(225\) | −10.5000 | − | 18.1865i | −0.700000 | − | 1.21244i | ||||
\(226\) | −7.50000 | + | 12.9904i | −0.498893 | + | 0.864107i | ||||
\(227\) | −21.0000 | −1.39382 | −0.696909 | − | 0.717159i | \(-0.745442\pi\) | ||||
−0.696909 | + | 0.717159i | \(0.745442\pi\) | |||||||
\(228\) | −4.50000 | − | 6.06218i | −0.298020 | − | 0.401478i | ||||
\(229\) | 4.00000 | 0.264327 | 0.132164 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | 1.50000 | + | 0.866025i | 0.0982683 | + | 0.0567352i | 0.548329 | − | 0.836263i | \(-0.315264\pi\) |
−0.450060 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(234\) | − | 10.3923i | − | 0.679366i | ||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | −3.00000 | −0.195283 | ||||||||
\(237\) | −12.0000 | + | 20.7846i | −0.779484 | + | 1.35011i | ||||
\(238\) | −12.0000 | + | 6.92820i | −0.777844 | + | 0.449089i | ||||
\(239\) | 6.92820i | 0.448148i | 0.974572 | + | 0.224074i | \(0.0719358\pi\) | ||||
−0.974572 | + | 0.224074i | \(0.928064\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | 4.50000 | − | 2.59808i | 0.289870 | − | 0.167357i | −0.348013 | − | 0.937490i | \(-0.613143\pi\) |
0.637883 | + | 0.770133i | \(0.279810\pi\) | |||||||
\(242\) | 4.00000 | − | 6.92820i | 0.257130 | − | 0.445362i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | −5.00000 | + | 8.66025i | −0.320092 | + | 0.554416i | ||||
\(245\) | −9.00000 | − | 5.19615i | −0.574989 | − | 0.331970i | ||||
\(246\) | 4.50000 | − | 2.59808i | 0.286910 | − | 0.165647i | ||||
\(247\) | −9.00000 | − | 12.1244i | −0.572656 | − | 0.771454i | ||||
\(248\) | 6.92820i | 0.439941i | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 6.00000 | + | 3.46410i | 0.379473 | + | 0.219089i | ||||
\(251\) | 7.50000 | − | 4.33013i | 0.473396 | − | 0.273315i | −0.244264 | − | 0.969709i | \(-0.578546\pi\) |
0.717660 | + | 0.696393i | \(0.245213\pi\) | |||||||
\(252\) | −3.00000 | − | 5.19615i | −0.188982 | − | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.3923i | 0.652071i | ||||||||
\(255\) | 36.0000 | − | 20.7846i | 2.25441 | − | 1.30158i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | 12.0000 | − | 6.92820i | 0.747087 | − | 0.431331i | ||||
\(259\) | 13.8564i | 0.860995i | ||||||||
\(260\) | 6.00000 | + | 10.3923i | 0.372104 | + | 0.644503i | ||||
\(261\) | 9.00000 | + | 15.5885i | 0.557086 | + | 0.964901i | ||||
\(262\) | 16.5000 | − | 9.52628i | 1.01937 | − | 0.588536i | ||||
\(263\) | −3.00000 | − | 1.73205i | −0.184988 | − | 0.106803i | 0.404646 | − | 0.914473i | \(-0.367395\pi\) |
−0.589634 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(264\) | 3.00000 | 0.184637 | ||||||||
\(265\) | 20.7846i | 1.27679i | ||||||||
\(266\) | −8.00000 | − | 3.46410i | −0.490511 | − | 0.212398i | ||||
\(267\) | −9.00000 | + | 5.19615i | −0.550791 | + | 0.317999i | ||||
\(268\) | −4.50000 | − | 2.59808i | −0.274881 | − | 0.158703i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 9.00000 | + | 15.5885i | 0.547723 | + | 0.948683i | ||||
\(271\) | −13.0000 | + | 22.5167i | −0.789694 | + | 1.36779i | 0.136461 | + | 0.990645i | \(0.456427\pi\) |
−0.926155 | + | 0.377144i | \(0.876906\pi\) | |||||||
\(272\) | −6.00000 | + | 3.46410i | −0.363803 | + | 0.210042i | ||||
\(273\) | −6.00000 | − | 10.3923i | −0.363137 | − | 0.628971i | ||||
\(274\) | − | 1.73205i | − | 0.104637i | ||||||
\(275\) | 10.5000 | − | 6.06218i | 0.633174 | − | 0.365563i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | −1.00000 | −0.0599760 | ||||||||
\(279\) | 20.7846i | 1.24434i | ||||||||
\(280\) | 6.00000 | + | 3.46410i | 0.358569 | + | 0.207020i | ||||
\(281\) | 7.50000 | + | 12.9904i | 0.447412 | + | 0.774941i | 0.998217 | − | 0.0596933i | \(-0.0190123\pi\) |
−0.550804 | + | 0.834634i | \(0.685679\pi\) | |||||||
\(282\) | 6.00000 | 0.357295 | ||||||||
\(283\) | 0.500000 | − | 0.866025i | 0.0297219 | − | 0.0514799i | −0.850782 | − | 0.525519i | \(-0.823871\pi\) |
0.880504 | + | 0.474039i | \(0.157204\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 24.0000 | + | 10.3923i | 1.42164 | + | 0.615587i | ||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | 3.00000 | − | 5.19615i | 0.177084 | − | 0.306719i | ||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | 15.5000 | + | 26.8468i | 0.911765 | + | 1.57922i | ||||
\(290\) | −18.0000 | − | 10.3923i | −1.05700 | − | 0.610257i | ||||
\(291\) | 7.50000 | − | 12.9904i | 0.439658 | − | 0.761510i | ||||
\(292\) | 5.00000 | 0.292603 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 4.50000 | + | 2.59808i | 0.262445 | + | 0.151523i | ||||
\(295\) | 9.00000 | − | 5.19615i | 0.524000 | − | 0.302532i | ||||
\(296\) | 6.92820i | 0.402694i | ||||||||
\(297\) | 9.00000 | 0.522233 | ||||||||
\(298\) | 6.00000 | − | 3.46410i | 0.347571 | − | 0.200670i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.5000 | − | 6.06218i | −0.606218 | − | 0.350000i | ||||
\(301\) | 8.00000 | − | 13.8564i | 0.461112 | − | 0.798670i | ||||
\(302\) | 6.00000 | + | 3.46410i | 0.345261 | + | 0.199337i | ||||
\(303\) | −9.00000 | − | 15.5885i | −0.517036 | − | 0.895533i | ||||
\(304\) | −4.00000 | − | 1.73205i | −0.229416 | − | 0.0993399i | ||||
\(305\) | − | 34.6410i | − | 1.98354i | ||||||
\(306\) | −18.0000 | + | 10.3923i | −1.02899 | + | 0.594089i | ||||
\(307\) | −4.50000 | − | 2.59808i | −0.256829 | − | 0.148280i | 0.366058 | − | 0.930592i | \(-0.380707\pi\) |
−0.622887 | + | 0.782312i | \(0.714040\pi\) | |||||||
\(308\) | 3.00000 | − | 1.73205i | 0.170941 | − | 0.0986928i | ||||
\(309\) | 18.0000 | 1.02398 | ||||||||
\(310\) | −12.0000 | − | 20.7846i | −0.681554 | − | 1.18049i | ||||
\(311\) | − | 13.8564i | − | 0.785725i | −0.919597 | − | 0.392862i | \(-0.871485\pi\) | ||
0.919597 | − | 0.392862i | \(-0.128515\pi\) | |||||||
\(312\) | −3.00000 | − | 5.19615i | −0.169842 | − | 0.294174i | ||||
\(313\) | −15.5000 | − | 26.8468i | −0.876112 | − | 1.51747i | −0.855574 | − | 0.517681i | \(-0.826795\pi\) |
−0.0205381 | − | 0.999789i | \(-0.506538\pi\) | |||||||
\(314\) | −10.0000 | − | 17.3205i | −0.564333 | − | 0.977453i | ||||
\(315\) | 18.0000 | + | 10.3923i | 1.01419 | + | 0.585540i | ||||
\(316\) | 13.8564i | 0.779484i | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | − | 10.3923i | − | 0.582772i | ||||||
\(319\) | −9.00000 | + | 5.19615i | −0.503903 | + | 0.290929i | ||||
\(320\) | 3.00000 | + | 1.73205i | 0.167705 | + | 0.0968246i | ||||
\(321\) | − | 20.7846i | − | 1.16008i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | + | 27.7128i | −0.667698 | + | 1.54198i | ||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | −21.0000 | − | 12.1244i | −1.16487 | − | 0.672538i | ||||
\(326\) | −8.50000 | + | 14.7224i | −0.470771 | + | 0.815400i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | − | 2.59808i | 0.0828236 | − | 0.143455i | ||||
\(329\) | 6.00000 | − | 3.46410i | 0.330791 | − | 0.190982i | ||||
\(330\) | −9.00000 | + | 5.19615i | −0.495434 | + | 0.286039i | ||||
\(331\) | − | 8.66025i | − | 0.476011i | −0.971264 | − | 0.238005i | \(-0.923506\pi\) | ||
0.971264 | − | 0.238005i | \(-0.0764936\pi\) | |||||||
\(332\) | −4.50000 | + | 2.59808i | −0.246970 | + | 0.142588i | ||||
\(333\) | 20.7846i | 1.13899i | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 18.0000 | 0.983445 | ||||||||
\(336\) | −3.00000 | − | 1.73205i | −0.163663 | − | 0.0944911i | ||||
\(337\) | −22.5000 | − | 12.9904i | −1.22565 | − | 0.707631i | −0.259536 | − | 0.965734i | \(-0.583569\pi\) |
−0.966118 | + | 0.258102i | \(0.916903\pi\) | |||||||
\(338\) | 0.500000 | + | 0.866025i | 0.0271964 | + | 0.0471056i | ||||
\(339\) | 25.9808i | 1.41108i | ||||||||
\(340\) | 12.0000 | − | 20.7846i | 0.650791 | − | 1.12720i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | −12.0000 | − | 5.19615i | −0.648886 | − | 0.280976i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 4.00000 | − | 6.92820i | 0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | − | 15.5885i | −0.483843 | − | 0.838041i | ||||
\(347\) | 7.50000 | + | 4.33013i | 0.402621 | + | 0.232453i | 0.687614 | − | 0.726076i | \(-0.258658\pi\) |
−0.284993 | + | 0.958530i | \(0.591991\pi\) | |||||||
\(348\) | 9.00000 | + | 5.19615i | 0.482451 | + | 0.278543i | ||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | −14.0000 | −0.748331 | ||||||||
\(351\) | −9.00000 | − | 15.5885i | −0.480384 | − | 0.832050i | ||||
\(352\) | 1.50000 | − | 0.866025i | 0.0799503 | − | 0.0461593i | ||||
\(353\) | 25.9808i | 1.38282i | 0.722464 | + | 0.691408i | \(0.243009\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(354\) | −4.50000 | + | 2.59808i | −0.239172 | + | 0.138086i | ||||
\(355\) | 18.0000 | − | 10.3923i | 0.955341 | − | 0.551566i | ||||
\(356\) | −3.00000 | + | 5.19615i | −0.159000 | + | 0.275396i | ||||
\(357\) | −12.0000 | + | 20.7846i | −0.635107 | + | 1.10004i | ||||
\(358\) | −1.50000 | + | 2.59808i | −0.0792775 | + | 0.137313i | ||||
\(359\) | −6.00000 | − | 3.46410i | −0.316668 | − | 0.182828i | 0.333238 | − | 0.942843i | \(-0.391859\pi\) |
−0.649906 | + | 0.760014i | \(0.725192\pi\) | |||||||
\(360\) | 9.00000 | + | 5.19615i | 0.474342 | + | 0.273861i | ||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | − | 6.92820i | − | 0.364138i | ||||||
\(363\) | − | 13.8564i | − | 0.727273i | ||||||
\(364\) | −6.00000 | − | 3.46410i | −0.314485 | − | 0.181568i | ||||
\(365\) | −15.0000 | + | 8.66025i | −0.785136 | + | 0.453298i | ||||
\(366\) | 17.3205i | 0.905357i | ||||||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | −12.0000 | − | 20.7846i | −0.623850 | − | 1.08054i | ||||
\(371\) | −6.00000 | − | 10.3923i | −0.311504 | − | 0.539542i | ||||
\(372\) | 6.00000 | + | 10.3923i | 0.311086 | + | 0.538816i | ||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | −6.00000 | − | 10.3923i | −0.310253 | − | 0.537373i | ||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | 3.00000 | − | 1.73205i | 0.154713 | − | 0.0893237i | ||||
\(377\) | 18.0000 | + | 10.3923i | 0.927047 | + | 0.535231i | ||||
\(378\) | −9.00000 | − | 5.19615i | −0.462910 | − | 0.267261i | ||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 15.0000 | − | 1.73205i | 0.769484 | − | 0.0888523i | ||||
\(381\) | 9.00000 | + | 15.5885i | 0.461084 | + | 0.798621i | ||||
\(382\) | 6.00000 | + | 3.46410i | 0.306987 | + | 0.177239i | ||||
\(383\) | −9.00000 | + | 15.5885i | −0.459879 | + | 0.796533i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) |
0.539076 | + | 0.842257i | \(0.318774\pi\) | |||||||
\(384\) | −1.50000 | − | 0.866025i | −0.0765466 | − | 0.0441942i | ||||
\(385\) | −6.00000 | + | 10.3923i | −0.305788 | + | 0.529641i | ||||
\(386\) | 18.0000 | − | 10.3923i | 0.916176 | − | 0.528954i | ||||
\(387\) | 12.0000 | − | 20.7846i | 0.609994 | − | 1.05654i | ||||
\(388\) | − | 8.66025i | − | 0.439658i | ||||||
\(389\) | 30.0000 | − | 17.3205i | 1.52106 | − | 0.878185i | 0.521369 | − | 0.853331i | \(-0.325421\pi\) |
0.999691 | − | 0.0248535i | \(-0.00791191\pi\) | |||||||
\(390\) | 18.0000 | + | 10.3923i | 0.911465 | + | 0.526235i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 16.5000 | − | 28.5788i | 0.832315 | − | 1.44161i | ||||
\(394\) | 18.0000 | + | 10.3923i | 0.906827 | + | 0.523557i | ||||
\(395\) | −24.0000 | − | 41.5692i | −1.20757 | − | 2.09157i | ||||
\(396\) | 4.50000 | − | 2.59808i | 0.226134 | − | 0.130558i | ||||
\(397\) | −10.0000 | + | 17.3205i | −0.501886 | + | 0.869291i | 0.498112 | + | 0.867113i | \(0.334027\pi\) |
−0.999998 | + | 0.00217869i | \(0.999307\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | −15.0000 | + | 1.73205i | −0.750939 | + | 0.0867110i | ||||
\(400\) | −7.00000 | −0.350000 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | −9.00000 | −0.448879 | ||||||||
\(403\) | 12.0000 | + | 20.7846i | 0.597763 | + | 1.03536i | ||||
\(404\) | −9.00000 | − | 5.19615i | −0.447767 | − | 0.258518i | ||||
\(405\) | 27.0000 | + | 15.5885i | 1.34164 | + | 0.774597i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | −6.00000 | + | 10.3923i | −0.297044 | + | 0.514496i | ||||
\(409\) | −16.5000 | + | 9.52628i | −0.815872 | + | 0.471044i | −0.848991 | − | 0.528407i | \(-0.822789\pi\) |
0.0331186 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(410\) | 10.3923i | 0.513239i | ||||||||
\(411\) | −1.50000 | − | 2.59808i | −0.0739895 | − | 0.128154i | ||||
\(412\) | 9.00000 | − | 5.19615i | 0.443398 | − | 0.255996i | ||||
\(413\) | −3.00000 | + | 5.19615i | −0.147620 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.00000 | − | 15.5885i | 0.441793 | − | 0.765207i | ||||
\(416\) | −3.00000 | − | 1.73205i | −0.147087 | − | 0.0849208i | ||||
\(417\) | −1.50000 | + | 0.866025i | −0.0734553 | + | 0.0424094i | ||||
\(418\) | 3.00000 | − | 6.92820i | 0.146735 | − | 0.338869i | ||||
\(419\) | 10.3923i | 0.507697i | 0.967244 | + | 0.253849i | \(0.0816965\pi\) | ||||
−0.967244 | + | 0.253849i | \(0.918303\pi\) | |||||||
\(420\) | 12.0000 | 0.585540 | ||||||||
\(421\) | −12.0000 | − | 6.92820i | −0.584844 | − | 0.337660i | 0.178212 | − | 0.983992i | \(-0.442969\pi\) |
−0.763056 | + | 0.646332i | \(0.776302\pi\) | |||||||
\(422\) | 9.00000 | − | 5.19615i | 0.438113 | − | 0.252945i | ||||
\(423\) | 9.00000 | − | 5.19615i | 0.437595 | − | 0.252646i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 48.4974i | 2.35247i | ||||||||
\(426\) | −9.00000 | + | 5.19615i | −0.436051 | + | 0.251754i | ||||
\(427\) | 10.0000 | + | 17.3205i | 0.483934 | + | 0.838198i | ||||
\(428\) | −6.00000 | − | 10.3923i | −0.290021 | − | 0.502331i | ||||
\(429\) | 9.00000 | − | 5.19615i | 0.434524 | − | 0.250873i | ||||
\(430\) | 27.7128i | 1.33643i | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −4.50000 | − | 2.59808i | −0.216506 | − | 0.125000i | ||||
\(433\) | −12.0000 | + | 6.92820i | −0.576683 | + | 0.332948i | −0.759814 | − | 0.650140i | \(-0.774710\pi\) |
0.183131 | + | 0.983089i | \(0.441377\pi\) | |||||||
\(434\) | 12.0000 | + | 6.92820i | 0.576018 | + | 0.332564i | ||||
\(435\) | −36.0000 | −1.72607 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 7.50000 | − | 4.33013i | 0.358364 | − | 0.206901i | ||||
\(439\) | −12.0000 | − | 6.92820i | −0.572729 | − | 0.330665i | 0.185510 | − | 0.982642i | \(-0.440606\pi\) |
−0.758238 | + | 0.651977i | \(0.773940\pi\) | |||||||
\(440\) | −3.00000 | + | 5.19615i | −0.143019 | + | 0.247717i | ||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | −12.0000 | + | 20.7846i | −0.570782 | + | 0.988623i | ||||
\(443\) | 10.5000 | − | 6.06218i | 0.498870 | − | 0.288023i | −0.229377 | − | 0.973338i | \(-0.573669\pi\) |
0.728247 | + | 0.685315i | \(0.240335\pi\) | |||||||
\(444\) | 6.00000 | + | 10.3923i | 0.284747 | + | 0.493197i | ||||
\(445\) | − | 20.7846i | − | 0.985285i | ||||||
\(446\) | 12.0000 | − | 6.92820i | 0.568216 | − | 0.328060i | ||||
\(447\) | 6.00000 | − | 10.3923i | 0.283790 | − | 0.491539i | ||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | −3.00000 | −0.141579 | −0.0707894 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707894 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(450\) | −21.0000 | −0.989949 | ||||||||
\(451\) | 4.50000 | + | 2.59808i | 0.211897 | + | 0.122339i | ||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | −10.5000 | + | 18.1865i | −0.492789 | + | 0.853536i | ||||
\(455\) | 24.0000 | 1.12514 | ||||||||
\(456\) | −7.50000 | + | 0.866025i | −0.351220 | + | 0.0405554i | ||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | 2.00000 | − | 3.46410i | 0.0934539 | − | 0.161867i | ||||
\(459\) | −18.0000 | + | 31.1769i | −0.840168 | + | 1.45521i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0000 | − | 12.1244i | −0.978068 | − | 0.564688i | −0.0763814 | − | 0.997079i | \(-0.524337\pi\) |
−0.901686 | + | 0.432391i | \(0.857670\pi\) | |||||||
\(462\) | 3.00000 | − | 5.19615i | 0.139573 | − | 0.241747i | ||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | −36.0000 | − | 20.7846i | −1.66946 | − | 0.963863i | ||||
\(466\) | 1.50000 | − | 0.866025i | 0.0694862 | − | 0.0401179i | ||||
\(467\) | − | 12.1244i | − | 0.561048i | −0.959847 | − | 0.280524i | \(-0.909492\pi\) | ||
0.959847 | − | 0.280524i | \(-0.0905083\pi\) | |||||||
\(468\) | −9.00000 | − | 5.19615i | −0.416025 | − | 0.240192i | ||||
\(469\) | −9.00000 | + | 5.19615i | −0.415581 | + | 0.239936i | ||||
\(470\) | −6.00000 | + | 10.3923i | −0.276759 | + | 0.479361i | ||||
\(471\) | −30.0000 | − | 17.3205i | −1.38233 | − | 0.798087i | ||||
\(472\) | −1.50000 | + | 2.59808i | −0.0690431 | + | 0.119586i | ||||
\(473\) | 12.0000 | + | 6.92820i | 0.551761 | + | 0.318559i | ||||
\(474\) | 12.0000 | + | 20.7846i | 0.551178 | + | 0.954669i | ||||
\(475\) | −24.5000 | + | 18.1865i | −1.12414 | + | 0.834455i | ||||
\(476\) | 13.8564i | 0.635107i | ||||||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | 6.00000 | + | 3.46410i | 0.274434 | + | 0.158444i | ||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 6.00000 | 0.273861 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | − | 5.19615i | − | 0.236678i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00000 | − | 6.92820i | −0.181818 | − | 0.314918i | ||||
\(485\) | 15.0000 | + | 25.9808i | 0.681115 | + | 1.17973i | ||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 6.92820i | 0.313947i | 0.987603 | + | 0.156973i | \(0.0501737\pi\) | ||||
−0.987603 | + | 0.156973i | \(0.949826\pi\) | |||||||
\(488\) | 5.00000 | + | 8.66025i | 0.226339 | + | 0.392031i | ||||
\(489\) | 29.4449i | 1.33154i | ||||||||
\(490\) | −9.00000 | + | 5.19615i | −0.406579 | + | 0.234738i | ||||
\(491\) | −27.0000 | − | 15.5885i | −1.21849 | − | 0.703497i | −0.253897 | − | 0.967231i | \(-0.581713\pi\) |
−0.964595 | + | 0.263734i | \(0.915046\pi\) | |||||||
\(492\) | − | 5.19615i | − | 0.234261i | ||||||
\(493\) | − | 41.5692i | − | 1.87218i | ||||||
\(494\) | −15.0000 | + | 1.73205i | −0.674882 | + | 0.0779287i | ||||
\(495\) | −9.00000 | + | 15.5885i | −0.404520 | + | 0.700649i | ||||
\(496\) | 6.00000 | + | 3.46410i | 0.269408 | + | 0.155543i | ||||
\(497\) | −6.00000 | + | 10.3923i | −0.269137 | + | 0.466159i | ||||
\(498\) | −4.50000 | + | 7.79423i | −0.201650 | + | 0.349268i | ||||
\(499\) | 20.5000 | − | 35.5070i | 0.917706 | − | 1.58951i | 0.114816 | − | 0.993387i | \(-0.463372\pi\) |
0.802890 | − | 0.596127i | \(-0.203294\pi\) | |||||||
\(500\) | 6.00000 | − | 3.46410i | 0.268328 | − | 0.154919i | ||||
\(501\) | 18.0000 | − | 10.3923i | 0.804181 | − | 0.464294i | ||||
\(502\) | − | 8.66025i | − | 0.386526i | ||||||
\(503\) | 18.0000 | − | 10.3923i | 0.802580 | − | 0.463370i | −0.0417923 | − | 0.999126i | \(-0.513307\pi\) |
0.844373 | + | 0.535756i | \(0.179973\pi\) | |||||||
\(504\) | −6.00000 | −0.267261 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.50000 | + | 0.866025i | 0.0666173 | + | 0.0384615i | ||||
\(508\) | 9.00000 | + | 5.19615i | 0.399310 | + | 0.230542i | ||||
\(509\) | −12.0000 | − | 20.7846i | −0.531891 | − | 0.921262i | −0.999307 | − | 0.0372243i | \(-0.988148\pi\) |
0.467416 | − | 0.884037i | \(-0.345185\pi\) | |||||||
\(510\) | − | 41.5692i | − | 1.84072i | ||||||
\(511\) | 5.00000 | − | 8.66025i | 0.221187 | − | 0.383107i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −22.5000 | + | 2.59808i | −0.993399 | + | 0.114708i | ||||
\(514\) | −15.0000 | −0.661622 | ||||||||
\(515\) | −18.0000 | + | 31.1769i | −0.793175 | + | 1.37382i | ||||
\(516\) | − | 13.8564i | − | 0.609994i | ||||||
\(517\) | 3.00000 | + | 5.19615i | 0.131940 | + | 0.228527i | ||||
\(518\) | 12.0000 | + | 6.92820i | 0.527250 | + | 0.304408i | ||||
\(519\) | −27.0000 | − | 15.5885i | −1.18517 | − | 0.684257i | ||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | 21.0000 | 0.920027 | 0.460013 | − | 0.887912i | \(-0.347845\pi\) | ||||
0.460013 | + | 0.887912i | \(0.347845\pi\) | |||||||
\(522\) | 18.0000 | 0.787839 | ||||||||
\(523\) | 15.0000 | − | 8.66025i | 0.655904 | − | 0.378686i | −0.134810 | − | 0.990871i | \(-0.543043\pi\) |
0.790715 | + | 0.612185i | \(0.209709\pi\) | |||||||
\(524\) | − | 19.0526i | − | 0.832315i | ||||||
\(525\) | −21.0000 | + | 12.1244i | −0.916515 | + | 0.529150i | ||||
\(526\) | −3.00000 | + | 1.73205i | −0.130806 | + | 0.0755210i | ||||
\(527\) | 24.0000 | − | 41.5692i | 1.04546 | − | 1.81078i | ||||
\(528\) | 1.50000 | − | 2.59808i | 0.0652791 | − | 0.113067i | ||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 18.0000 | + | 10.3923i | 0.781870 | + | 0.451413i | ||||
\(531\) | −4.50000 | + | 7.79423i | −0.195283 | + | 0.338241i | ||||
\(532\) | −7.00000 | + | 5.19615i | −0.303488 | + | 0.225282i | ||||
\(533\) | − | 10.3923i | − | 0.450141i | ||||||
\(534\) | 10.3923i | 0.449719i | ||||||||
\(535\) | 36.0000 | + | 20.7846i | 1.55642 | + | 0.898597i | ||||
\(536\) | −4.50000 | + | 2.59808i | −0.194370 | + | 0.112220i | ||||
\(537\) | 5.19615i | 0.224231i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.19615i | 0.223814i | ||||||||
\(540\) | 18.0000 | 0.774597 | ||||||||
\(541\) | −10.0000 | − | 17.3205i | −0.429934 | − | 0.744667i | 0.566933 | − | 0.823764i | \(-0.308130\pi\) |
−0.996867 | + | 0.0790969i | \(0.974796\pi\) | |||||||
\(542\) | 13.0000 | + | 22.5167i | 0.558398 | + | 0.967173i | ||||
\(543\) | −6.00000 | − | 10.3923i | −0.257485 | − | 0.445976i | ||||
\(544\) | 6.92820i | 0.297044i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.0000 | −0.513553 | ||||||||
\(547\) | −21.0000 | + | 12.1244i | −0.897895 | + | 0.518400i | −0.876517 | − | 0.481371i | \(-0.840139\pi\) |
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | −1.50000 | − | 0.866025i | −0.0640768 | − | 0.0369948i | ||||
\(549\) | 15.0000 | + | 25.9808i | 0.640184 | + | 1.10883i | ||||
\(550\) | − | 12.1244i | − | 0.516984i | ||||||
\(551\) | 21.0000 | − | 15.5885i | 0.894630 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | + | 13.8564i | 1.02058 | + | 0.589234i | ||||
\(554\) | −1.00000 | + | 1.73205i | −0.0424859 | + | 0.0735878i | ||||
\(555\) | −36.0000 | − | 20.7846i | −1.52811 | − | 0.882258i | ||||
\(556\) | −0.500000 | + | 0.866025i | −0.0212047 | + | 0.0367277i | ||||
\(557\) | −12.0000 | + | 6.92820i | −0.508456 | + | 0.293557i | −0.732199 | − | 0.681091i | \(-0.761506\pi\) |
0.223743 | + | 0.974648i | \(0.428173\pi\) | |||||||
\(558\) | 18.0000 | + | 10.3923i | 0.762001 | + | 0.439941i | ||||
\(559\) | − | 27.7128i | − | 1.17213i | ||||||
\(560\) | 6.00000 | − | 3.46410i | 0.253546 | − | 0.146385i | ||||
\(561\) | −18.0000 | − | 10.3923i | −0.759961 | − | 0.438763i | ||||
\(562\) | 15.0000 | 0.632737 | ||||||||
\(563\) | 21.0000 | 0.885044 | 0.442522 | − | 0.896758i | \(-0.354084\pi\) | ||||
0.442522 | + | 0.896758i | \(0.354084\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | −45.0000 | − | 25.9808i | −1.89316 | − | 1.09302i | ||||
\(566\) | −0.500000 | − | 0.866025i | −0.0210166 | − | 0.0364018i | ||||
\(567\) | −18.0000 | −0.755929 | ||||||||
\(568\) | −3.00000 | + | 5.19615i | −0.125877 | + | 0.218026i | ||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 21.0000 | − | 15.5885i | 0.879593 | − | 0.652929i | ||||
\(571\) | −43.0000 | −1.79949 | −0.899747 | − | 0.436412i | \(-0.856249\pi\) | ||||
−0.899747 | + | 0.436412i | \(0.856249\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −3.00000 | − | 5.19615i | −0.125218 | − | 0.216883i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −29.0000 | −1.20729 | −0.603643 | − | 0.797255i | \(-0.706285\pi\) | ||||
−0.603643 | + | 0.797255i | \(0.706285\pi\) | |||||||
\(578\) | 31.0000 | 1.28943 | ||||||||
\(579\) | 18.0000 | − | 31.1769i | 0.748054 | − | 1.29567i | ||||
\(580\) | −18.0000 | + | 10.3923i | −0.747409 | + | 0.431517i | ||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | −7.50000 | − | 12.9904i | −0.310885 | − | 0.538469i | ||||
\(583\) | 9.00000 | − | 5.19615i | 0.372742 | − | 0.215203i | ||||
\(584\) | 2.50000 | − | 4.33013i | 0.103451 | − | 0.179182i | ||||
\(585\) | 36.0000 | 1.48842 | ||||||||
\(586\) | 3.00000 | − | 5.19615i | 0.123929 | − | 0.214651i | ||||
\(587\) | 33.0000 | + | 19.0526i | 1.36206 | + | 0.786383i | 0.989897 | − | 0.141786i | \(-0.0452845\pi\) |
0.372158 | + | 0.928169i | \(0.378618\pi\) | |||||||
\(588\) | 4.50000 | − | 2.59808i | 0.185577 | − | 0.107143i | ||||
\(589\) | 30.0000 | − | 3.46410i | 1.23613 | − | 0.142736i | ||||
\(590\) | − | 10.3923i | − | 0.427844i | ||||||
\(591\) | 36.0000 | 1.48084 | ||||||||
\(592\) | 6.00000 | + | 3.46410i | 0.246598 | + | 0.142374i | ||||
\(593\) | −22.5000 | + | 12.9904i | −0.923964 | + | 0.533451i | −0.884898 | − | 0.465786i | \(-0.845772\pi\) |
−0.0390666 | + | 0.999237i | \(0.512438\pi\) | |||||||
\(594\) | 4.50000 | − | 7.79423i | 0.184637 | − | 0.319801i | ||||
\(595\) | −24.0000 | − | 41.5692i | −0.983904 | − | 1.70417i | ||||
\(596\) | − | 6.92820i | − | 0.283790i | ||||||
\(597\) | −21.0000 | + | 12.1244i | −0.859473 | + | 0.496217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0000 | − | 31.1769i | −0.735460 | − | 1.27385i | −0.954521 | − | 0.298143i | \(-0.903633\pi\) |
0.219061 | − | 0.975711i | \(-0.429701\pi\) | |||||||
\(600\) | −10.5000 | + | 6.06218i | −0.428661 | + | 0.247487i | ||||
\(601\) | − | 8.66025i | − | 0.353259i | −0.984277 | − | 0.176630i | \(-0.943481\pi\) | ||
0.984277 | − | 0.176630i | \(-0.0565195\pi\) | |||||||
\(602\) | −8.00000 | − | 13.8564i | −0.326056 | − | 0.564745i | ||||
\(603\) | −13.5000 | + | 7.79423i | −0.549762 | + | 0.317406i | ||||
\(604\) | 6.00000 | − | 3.46410i | 0.244137 | − | 0.140952i | ||||
\(605\) | 24.0000 | + | 13.8564i | 0.975739 | + | 0.563343i | ||||
\(606\) | −18.0000 | −0.731200 | ||||||||
\(607\) | 31.1769i | 1.26543i | 0.774384 | + | 0.632716i | \(0.218060\pi\) | ||||
−0.774384 | + | 0.632716i | \(0.781940\pi\) | |||||||
\(608\) | −3.50000 | + | 2.59808i | −0.141944 | + | 0.105366i | ||||
\(609\) | 18.0000 | − | 10.3923i | 0.729397 | − | 0.421117i | ||||
\(610\) | −30.0000 | − | 17.3205i | −1.21466 | − | 0.701287i | ||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | 20.7846i | 0.840168i | ||||||||
\(613\) | −17.0000 | + | 29.4449i | −0.686624 | + | 1.18927i | 0.286300 | + | 0.958140i | \(0.407575\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(614\) | −4.50000 | + | 2.59808i | −0.181605 | + | 0.104850i | ||||
\(615\) | 9.00000 | + | 15.5885i | 0.362915 | + | 0.628587i | ||||
\(616\) | − | 3.46410i | − | 0.139573i | ||||||
\(617\) | 1.50000 | − | 0.866025i | 0.0603877 | − | 0.0348649i | −0.469502 | − | 0.882931i | \(-0.655567\pi\) |
0.529890 | + | 0.848066i | \(0.322233\pi\) | |||||||
\(618\) | 9.00000 | − | 15.5885i | 0.362033 | − | 0.627060i | ||||
\(619\) | 40.0000 | 1.60774 | 0.803868 | − | 0.594808i | \(-0.202772\pi\) | ||||
0.803868 | + | 0.594808i | \(0.202772\pi\) | |||||||
\(620\) | −24.0000 | −0.963863 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | − | 6.92820i | −0.481156 | − | 0.277796i | ||||
\(623\) | 6.00000 | + | 10.3923i | 0.240385 | + | 0.416359i | ||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | −31.0000 | −1.23901 | ||||||||
\(627\) | −1.50000 | − | 12.9904i | −0.0599042 | − | 0.518786i | ||||
\(628\) | −20.0000 | −0.798087 | ||||||||
\(629\) | 24.0000 | − | 41.5692i | 0.956943 | − | 1.65747i | ||||
\(630\) | 18.0000 | − | 10.3923i | 0.717137 | − | 0.414039i | ||||
\(631\) | 1.00000 | + | 1.73205i | 0.0398094 | + | 0.0689519i | 0.885244 | − | 0.465128i | \(-0.153992\pi\) |
−0.845434 | + | 0.534080i | \(0.820658\pi\) | |||||||
\(632\) | 12.0000 | + | 6.92820i | 0.477334 | + | 0.275589i | ||||
\(633\) | 9.00000 | − | 15.5885i | 0.357718 | − | 0.619586i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | −36.0000 | −1.42862 | ||||||||
\(636\) | −9.00000 | − | 5.19615i | −0.356873 | − | 0.206041i | ||||
\(637\) | 9.00000 | − | 5.19615i | 0.356593 | − | 0.205879i | ||||
\(638\) | 10.3923i | 0.411435i | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 3.00000 | − | 1.73205i | 0.118585 | − | 0.0684653i | ||||
\(641\) | −22.5000 | + | 38.9711i | −0.888697 | + | 1.53927i | −0.0472793 | + | 0.998882i | \(0.515055\pi\) |
−0.841417 | + | 0.540386i | \(0.818278\pi\) | |||||||
\(642\) | −18.0000 | − | 10.3923i | −0.710403 | − | 0.410152i | ||||
\(643\) | 24.5000 | − | 42.4352i | 0.966186 | − | 1.67348i | 0.259791 | − | 0.965665i | \(-0.416346\pi\) |
0.706395 | − | 0.707818i | \(-0.250320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | + | 41.5692i | 0.944999 | + | 1.63679i | ||||
\(646\) | 18.0000 | + | 24.2487i | 0.708201 | + | 0.954053i | ||||
\(647\) | 24.2487i | 0.953315i | 0.879089 | + | 0.476658i | \(0.158152\pi\) | ||||
−0.879089 | + | 0.476658i | \(0.841848\pi\) | |||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | −4.50000 | − | 2.59808i | −0.176640 | − | 0.101983i | ||||
\(650\) | −21.0000 | + | 12.1244i | −0.823688 | + | 0.475556i | ||||
\(651\) | 24.0000 | 0.940634 | ||||||||
\(652\) | 8.50000 | + | 14.7224i | 0.332886 | + | 0.576575i | ||||
\(653\) | 6.92820i | 0.271122i | 0.990769 | + | 0.135561i | \(0.0432836\pi\) | ||||
−0.990769 | + | 0.135561i | \(0.956716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.0000 | + | 57.1577i | 1.28942 | + | 2.23334i | ||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 7.50000 | − | 12.9904i | 0.292603 | − | 0.506803i | ||||
\(658\) | − | 6.92820i | − | 0.270089i | ||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | 10.3923i | 0.404520i | ||||||||
\(661\) | −33.0000 | + | 19.0526i | −1.28355 | + | 0.741059i | −0.977496 | − | 0.210955i | \(-0.932343\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(662\) | −7.50000 | − | 4.33013i | −0.291496 | − | 0.168295i | ||||
\(663\) | 41.5692i | 1.61441i | ||||||||
\(664\) | 5.19615i | 0.201650i | ||||||||
\(665\) | 12.0000 | − | 27.7128i | 0.465340 | − | 1.07466i | ||||
\(666\) | 18.0000 | + | 10.3923i | 0.697486 | + | 0.402694i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 12.0000 | − | 20.7846i | 0.463947 | − | 0.803579i | ||||
\(670\) | 9.00000 | − | 15.5885i | 0.347700 | − | 0.602235i | ||||
\(671\) | −15.0000 | + | 8.66025i | −0.579069 | + | 0.334325i | ||||
\(672\) | −3.00000 | + | 1.73205i | −0.115728 | + | 0.0668153i | ||||
\(673\) | − | 20.7846i | − | 0.801188i | −0.916256 | − | 0.400594i | \(-0.868804\pi\) | ||
0.916256 | − | 0.400594i | \(-0.131196\pi\) | |||||||
\(674\) | −22.5000 | + | 12.9904i | −0.866668 | + | 0.500371i | ||||
\(675\) | −31.5000 | + | 18.1865i | −1.21244 | + | 0.700000i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 22.5000 | + | 12.9904i | 0.864107 | + | 0.498893i | ||||
\(679\) | −15.0000 | − | 8.66025i | −0.575647 | − | 0.332350i | ||||
\(680\) | −12.0000 | − | 20.7846i | −0.460179 | − | 0.797053i | ||||
\(681\) | 36.3731i | 1.39382i | ||||||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | −10.5000 | + | 7.79423i | −0.401478 | + | 0.298020i | ||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | − | 6.92820i | − | 0.264327i | ||||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | −18.0000 | − | 10.3923i | −0.685745 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | − | 10.3923i | − | 0.394771i | ||||||
\(694\) | 7.50000 | − | 4.33013i | 0.284696 | − | 0.164369i | ||||
\(695\) | − | 3.46410i | − | 0.131401i | ||||||
\(696\) | 9.00000 | − | 5.19615i | 0.341144 | − | 0.196960i | ||||
\(697\) | −18.0000 | + | 10.3923i | −0.681799 | + | 0.393637i | ||||
\(698\) | 4.00000 | − | 6.92820i | 0.151402 | − | 0.262236i | ||||
\(699\) | 1.50000 | − | 2.59808i | 0.0567352 | − | 0.0982683i | ||||
\(700\) | −7.00000 | + | 12.1244i | −0.264575 | + | 0.458258i | ||||
\(701\) | −9.00000 | − | 5.19615i | −0.339925 | − | 0.196256i | 0.320314 | − | 0.947312i | \(-0.396212\pi\) |
−0.660239 | + | 0.751056i | \(0.729545\pi\) | |||||||
\(702\) | −18.0000 | −0.679366 | ||||||||
\(703\) | 30.0000 | − | 3.46410i | 1.13147 | − | 0.130651i | ||||
\(704\) | − | 1.73205i | − | 0.0652791i | ||||||
\(705\) | 20.7846i | 0.782794i | ||||||||
\(706\) | 22.5000 | + | 12.9904i | 0.846799 | + | 0.488899i | ||||
\(707\) | −18.0000 | + | 10.3923i | −0.676960 | + | 0.390843i | ||||
\(708\) | 5.19615i | 0.195283i | ||||||||
\(709\) | −4.00000 | − | 6.92820i | −0.150223 | − | 0.260194i | 0.781086 | − | 0.624423i | \(-0.214666\pi\) |
−0.931309 | + | 0.364229i | \(0.881333\pi\) | |||||||
\(710\) | − | 20.7846i | − | 0.780033i | ||||||
\(711\) | 36.0000 | + | 20.7846i | 1.35011 | + | 0.779484i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.0000 | + | 20.7846i | 0.449089 | + | 0.777844i | ||||
\(715\) | 20.7846i | 0.777300i | ||||||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | 12.0000 | 0.448148 | ||||||||
\(718\) | −6.00000 | + | 3.46410i | −0.223918 | + | 0.129279i | ||||
\(719\) | −3.00000 | − | 1.73205i | −0.111881 | − | 0.0645946i | 0.443015 | − | 0.896514i | \(-0.353909\pi\) |
−0.554896 | + | 0.831919i | \(0.687242\pi\) | |||||||
\(720\) | 9.00000 | − | 5.19615i | 0.335410 | − | 0.193649i | ||||
\(721\) | − | 20.7846i | − | 0.774059i | ||||||
\(722\) | −5.50000 | + | 18.1865i | −0.204689 | + | 0.676833i | ||||
\(723\) | −4.50000 | − | 7.79423i | −0.167357 | − | 0.289870i | ||||
\(724\) | −6.00000 | − | 3.46410i | −0.222988 | − | 0.128742i | ||||
\(725\) | 21.0000 | − | 36.3731i | 0.779920 | − | 1.35086i | ||||
\(726\) | −12.0000 | − | 6.92820i | −0.445362 | − | 0.257130i | ||||
\(727\) | −4.00000 | + | 6.92820i | −0.148352 | + | 0.256953i | −0.930618 | − | 0.365991i | \(-0.880730\pi\) |
0.782267 | + | 0.622944i | \(0.214063\pi\) | |||||||
\(728\) | −6.00000 | + | 3.46410i | −0.222375 | + | 0.128388i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 17.3205i | 0.641061i | ||||||||
\(731\) | −48.0000 | + | 27.7128i | −1.77534 | + | 1.02500i | ||||
\(732\) | 15.0000 | + | 8.66025i | 0.554416 | + | 0.320092i | ||||
\(733\) | −4.00000 | −0.147743 | −0.0738717 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | −9.00000 | + | 15.5885i | −0.331970 | + | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | −4.50000 | − | 7.79423i | −0.165647 | − | 0.286910i | ||||
\(739\) | 5.50000 | − | 9.52628i | 0.202321 | − | 0.350430i | −0.746955 | − | 0.664875i | \(-0.768485\pi\) |
0.949276 | + | 0.314445i | \(0.101818\pi\) | |||||||
\(740\) | −24.0000 | −0.882258 | ||||||||
\(741\) | −21.0000 | + | 15.5885i | −0.771454 | + | 0.572656i | ||||
\(742\) | −12.0000 | −0.440534 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 12.0000 | 0.439941 | ||||||||
\(745\) | 12.0000 | + | 20.7846i | 0.439646 | + | 0.761489i | ||||
\(746\) | 6.00000 | + | 3.46410i | 0.219676 | + | 0.126830i | ||||
\(747\) | 15.5885i | 0.570352i | ||||||||
\(748\) | −12.0000 | −0.438763 | ||||||||
\(749\) | −24.0000 | −0.876941 | ||||||||
\(750\) | 6.00000 | − | 10.3923i | 0.219089 | − | 0.379473i | ||||
\(751\) | −33.0000 | + | 19.0526i | −1.20419 | + | 0.695238i | −0.961483 | − | 0.274863i | \(-0.911368\pi\) |
−0.242704 | + | 0.970100i | \(0.578034\pi\) | |||||||
\(752\) | − | 3.46410i | − | 0.126323i | ||||||
\(753\) | −7.50000 | − | 12.9904i | −0.273315 | − | 0.473396i | ||||
\(754\) | 18.0000 | − | 10.3923i | 0.655521 | − | 0.378465i | ||||
\(755\) | −12.0000 | + | 20.7846i | −0.436725 | + | 0.756429i | ||||
\(756\) | −9.00000 | + | 5.19615i | −0.327327 | + | 0.188982i | ||||
\(757\) | 19.0000 | − | 32.9090i | 0.690567 | − | 1.19610i | −0.281086 | − | 0.959683i | \(-0.590695\pi\) |
0.971652 | − | 0.236414i | \(-0.0759722\pi\) | |||||||
\(758\) | 9.00000 | + | 5.19615i | 0.326895 | + | 0.188733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | − | 13.8564i | 0.217643 | − | 0.502625i | ||||
\(761\) | 8.66025i | 0.313934i | 0.987604 | + | 0.156967i | \(0.0501716\pi\) | ||||
−0.987604 | + | 0.156967i | \(0.949828\pi\) | |||||||
\(762\) | 18.0000 | 0.652071 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.00000 | − | 3.46410i | 0.217072 | − | 0.125327i | ||||
\(765\) | −36.0000 | − | 62.3538i | −1.30158 | − | 2.25441i | ||||
\(766\) | 9.00000 | + | 15.5885i | 0.325183 | + | 0.563234i | ||||
\(767\) | 10.3923i | 0.375244i | ||||||||
\(768\) | −1.50000 | + | 0.866025i | −0.0541266 | + | 0.0312500i | ||||
\(769\) | 7.00000 | + | 12.1244i | 0.252426 | + | 0.437215i | 0.964193 | − | 0.265200i | \(-0.0854381\pi\) |
−0.711767 | + | 0.702416i | \(0.752105\pi\) | |||||||
\(770\) | 6.00000 | + | 10.3923i | 0.216225 | + | 0.374513i | ||||
\(771\) | −22.5000 | + | 12.9904i | −0.810318 | + | 0.467837i | ||||
\(772\) | − | 20.7846i | − | 0.748054i | ||||||
\(773\) | 3.00000 | + | 5.19615i | 0.107903 | + | 0.186893i | 0.914920 | − | 0.403634i | \(-0.132253\pi\) |
−0.807018 | + | 0.590527i | \(0.798920\pi\) | |||||||
\(774\) | −12.0000 | − | 20.7846i | −0.431331 | − | 0.747087i | ||||
\(775\) | 42.0000 | − | 24.2487i | 1.50868 | − | 0.871039i | ||||
\(776\) | −7.50000 | − | 4.33013i | −0.269234 | − | 0.155443i | ||||
\(777\) | 24.0000 | 0.860995 | ||||||||
\(778\) | − | 34.6410i | − | 1.24194i | ||||||
\(779\) | −12.0000 | − | 5.19615i | −0.429945 | − | 0.186171i | ||||
\(780\) | 18.0000 | − | 10.3923i | 0.644503 | − | 0.372104i | ||||
\(781\) | −9.00000 | − | 5.19615i | −0.322045 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.0000 | − | 15.5885i | 0.964901 | − | 0.557086i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 60.0000 | − | 34.6410i | 2.14149 | − | 1.23639i | ||||
\(786\) | −16.5000 | − | 28.5788i | −0.588536 | − | 1.01937i | ||||
\(787\) | 1.73205i | 0.0617409i | 0.999523 | + | 0.0308705i | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 18.0000 | − | 10.3923i | 0.641223 | − | 0.370211i | ||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | −48.0000 | −1.70776 | ||||||||
\(791\) | 30.0000 | 1.06668 | ||||||||
\(792\) | − | 5.19615i | − | 0.184637i | ||||||
\(793\) | 30.0000 | + | 17.3205i | 1.06533 | + | 0.615069i | ||||
\(794\) | 10.0000 | + | 17.3205i | 0.354887 | + | 0.614682i | ||||
\(795\) | 36.0000 | 1.27679 | ||||||||
\(796\) | −7.00000 | + | 12.1244i | −0.248108 | + | 0.429736i | ||||
\(797\) | 12.0000 | 0.425062 | 0.212531 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | −6.00000 | + | 13.8564i | −0.212398 | + | 0.490511i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −3.50000 | + | 6.06218i | −0.123744 | + | 0.214330i | ||||
\(801\) | 9.00000 | + | 15.5885i | 0.317999 | + | 0.550791i | ||||
\(802\) | 1.50000 | + | 2.59808i | 0.0529668 | + | 0.0917413i | ||||
\(803\) | 7.50000 | + | 4.33013i | 0.264669 | + | 0.152807i | ||||
\(804\) | −4.50000 | + | 7.79423i | −0.158703 | + | 0.274881i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.00000 | + | 5.19615i | −0.316619 | + | 0.182800i | ||||
\(809\) | − | 32.9090i | − | 1.15702i | −0.815676 | − | 0.578509i | \(-0.803635\pi\) | ||
0.815676 | − | 0.578509i | \(-0.196365\pi\) | |||||||
\(810\) | 27.0000 | − | 15.5885i | 0.948683 | − | 0.547723i | ||||
\(811\) | −27.0000 | + | 15.5885i | −0.948098 | + | 0.547385i | −0.892490 | − | 0.451068i | \(-0.851043\pi\) |
−0.0556086 | + | 0.998453i | \(0.517710\pi\) | |||||||
\(812\) | 6.00000 | − | 10.3923i | 0.210559 | − | 0.364698i | ||||
\(813\) | 39.0000 | + | 22.5167i | 1.36779 | + | 0.789694i | ||||
\(814\) | −6.00000 | + | 10.3923i | −0.210300 | + | 0.364250i | ||||
\(815\) | −51.0000 | − | 29.4449i | −1.78645 | − | 1.03141i | ||||
\(816\) | 6.00000 | + | 10.3923i | 0.210042 | + | 0.363803i | ||||
\(817\) | −32.0000 | − | 13.8564i | −1.11954 | − | 0.484774i | ||||
\(818\) | 19.0526i | 0.666157i | ||||||||
\(819\) | −18.0000 | + | 10.3923i | −0.628971 | + | 0.363137i | ||||
\(820\) | 9.00000 | + | 5.19615i | 0.314294 | + | 0.181458i | ||||
\(821\) | 33.0000 | − | 19.0526i | 1.15171 | − | 0.664939i | 0.202405 | − | 0.979302i | \(-0.435124\pi\) |
0.949303 | + | 0.314363i | \(0.101791\pi\) | |||||||
\(822\) | −3.00000 | −0.104637 | ||||||||
\(823\) | −11.0000 | − | 19.0526i | −0.383436 | − | 0.664130i | 0.608115 | − | 0.793849i | \(-0.291926\pi\) |
−0.991551 | + | 0.129719i | \(0.958593\pi\) | |||||||
\(824\) | − | 10.3923i | − | 0.362033i | ||||||
\(825\) | −10.5000 | − | 18.1865i | −0.365563 | − | 0.633174i | ||||
\(826\) | 3.00000 | + | 5.19615i | 0.104383 | + | 0.180797i | ||||
\(827\) | −4.50000 | − | 7.79423i | −0.156480 | − | 0.271032i | 0.777117 | − | 0.629356i | \(-0.216681\pi\) |
−0.933597 | + | 0.358325i | \(0.883348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7846i | 0.721879i | 0.932589 | + | 0.360940i | \(0.117544\pi\) | ||||
−0.932589 | + | 0.360940i | \(0.882456\pi\) | |||||||
\(830\) | −9.00000 | − | 15.5885i | −0.312395 | − | 0.541083i | ||||
\(831\) | 3.46410i | 0.120168i | ||||||||
\(832\) | −3.00000 | + | 1.73205i | −0.104006 | + | 0.0600481i | ||||
\(833\) | −18.0000 | − | 10.3923i | −0.623663 | − | 0.360072i | ||||
\(834\) | 1.73205i | 0.0599760i | ||||||||
\(835\) | 41.5692i | 1.43856i | ||||||||
\(836\) | −4.50000 | − | 6.06218i | −0.155636 | − | 0.209665i | ||||
\(837\) | 36.0000 | 1.24434 | ||||||||
\(838\) | 9.00000 | + | 5.19615i | 0.310900 | + | 0.179498i | ||||
\(839\) | −21.0000 | + | 36.3731i | −0.725001 | + | 1.25574i | 0.233973 | + | 0.972243i | \(0.424827\pi\) |
−0.958974 | + | 0.283495i | \(0.908506\pi\) | |||||||
\(840\) | 6.00000 | − | 10.3923i | 0.207020 | − | 0.358569i | ||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −12.0000 | + | 6.92820i | −0.413547 | + | 0.238762i | ||||
\(843\) | 22.5000 | − | 12.9904i | 0.774941 | − | 0.447412i | ||||
\(844\) | − | 10.3923i | − | 0.357718i | ||||||
\(845\) | −3.00000 | + | 1.73205i | −0.103203 | + | 0.0595844i | ||||
\(846\) | − | 10.3923i | − | 0.357295i | ||||||
\(847\) | −16.0000 | −0.549767 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −1.50000 | − | 0.866025i | −0.0514799 | − | 0.0297219i | ||||
\(850\) | 42.0000 | + | 24.2487i | 1.44059 | + | 0.831724i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 10.3923i | 0.356034i | ||||||||
\(853\) | 5.00000 | − | 8.66025i | 0.171197 | − | 0.296521i | −0.767642 | − | 0.640879i | \(-0.778570\pi\) |
0.938839 | + | 0.344358i | \(0.111903\pi\) | |||||||
\(854\) | 20.0000 | 0.684386 | ||||||||
\(855\) | 18.0000 | − | 41.5692i | 0.615587 | − | 1.42164i | ||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −10.5000 | + | 18.1865i | −0.358673 | + | 0.621240i | −0.987739 | − | 0.156112i | \(-0.950104\pi\) |
0.629066 | + | 0.777352i | \(0.283437\pi\) | |||||||
\(858\) | − | 10.3923i | − | 0.354787i | ||||||
\(859\) | −24.5000 | − | 42.4352i | −0.835929 | − | 1.44787i | −0.893272 | − | 0.449517i | \(-0.851596\pi\) |
0.0573424 | − | 0.998355i | \(-0.481737\pi\) | |||||||
\(860\) | 24.0000 | + | 13.8564i | 0.818393 | + | 0.472500i | ||||
\(861\) | −9.00000 | − | 5.19615i | −0.306719 | − | 0.177084i | ||||
\(862\) | −6.00000 | −0.204361 | ||||||||
\(863\) | 12.0000 | 0.408485 | 0.204242 | − | 0.978920i | \(-0.434527\pi\) | ||||
0.204242 | + | 0.978920i | \(0.434527\pi\) | |||||||
\(864\) | −4.50000 | + | 2.59808i | −0.153093 | + | 0.0883883i | ||||
\(865\) | 54.0000 | − | 31.1769i | 1.83606 | − | 1.06005i | ||||
\(866\) | 13.8564i | 0.470860i | ||||||||
\(867\) | 46.5000 | − | 26.8468i | 1.57922 | − | 0.911765i | ||||
\(868\) | 12.0000 | − | 6.92820i | 0.407307 | − | 0.235159i | ||||
\(869\) | −12.0000 | + | 20.7846i | −0.407072 | + | 0.705070i | ||||
\(870\) | −18.0000 | + | 31.1769i | −0.610257 | + | 1.05700i | ||||
\(871\) | −9.00000 | + | 15.5885i | −0.304953 | + | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.5000 | − | 12.9904i | −0.761510 | − | 0.439658i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 13.8564i | − | 0.468432i | ||||||
\(876\) | − | 8.66025i | − | 0.292603i | ||||||
\(877\) | −33.0000 | − | 19.0526i | −1.11433 | − | 0.643359i | −0.174383 | − | 0.984678i | \(-0.555793\pi\) |
−0.939948 | + | 0.341319i | \(0.889126\pi\) | |||||||
\(878\) | −12.0000 | + | 6.92820i | −0.404980 | + | 0.233816i | ||||
\(879\) | − | 10.3923i | − | 0.350524i | ||||||
\(880\) | 3.00000 | + | 5.19615i | 0.101130 | + | 0.175162i | ||||
\(881\) | − | 19.0526i | − | 0.641897i | −0.947097 | − | 0.320949i | \(-0.895998\pi\) | ||
0.947097 | − | 0.320949i | \(-0.104002\pi\) | |||||||
\(882\) | 4.50000 | − | 7.79423i | 0.151523 | − | 0.262445i | ||||
\(883\) | 5.50000 | + | 9.52628i | 0.185090 | + | 0.320585i | 0.943607 | − | 0.331068i | \(-0.107409\pi\) |
−0.758517 | + | 0.651653i | \(0.774076\pi\) | |||||||
\(884\) | 12.0000 | + | 20.7846i | 0.403604 | + | 0.699062i | ||||
\(885\) | −9.00000 | − | 15.5885i | −0.302532 | − | 0.524000i | ||||
\(886\) | − | 12.1244i | − | 0.407326i | ||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 12.0000 | 0.402694 | ||||||||
\(889\) | 18.0000 | − | 10.3923i | 0.603701 | − | 0.348547i | ||||
\(890\) | −18.0000 | − | 10.3923i | −0.603361 | − | 0.348351i | ||||
\(891\) | − | 15.5885i | − | 0.522233i | ||||||
\(892\) | − | 13.8564i | − | 0.463947i | ||||||
\(893\) | −9.00000 | − | 12.1244i | −0.301174 | − | 0.405726i | ||||
\(894\) | −6.00000 | − | 10.3923i | −0.200670 | − | 0.347571i | ||||
\(895\) | −9.00000 | − | 5.19615i | −0.300837 | − | 0.173688i | ||||
\(896\) | −1.00000 | + | 1.73205i | −0.0334077 | + | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.50000 | + | 2.59808i | −0.0500556 | + | 0.0866989i | ||||
\(899\) | −36.0000 | + | 20.7846i | −1.20067 | + | 0.693206i | ||||
\(900\) | −10.5000 | + | 18.1865i | −0.350000 | + | 0.606218i | ||||
\(901\) | 41.5692i | 1.38487i | ||||||||
\(902\) | 4.50000 | − | 2.59808i | 0.149834 | − | 0.0865065i | ||||
\(903\) | −24.0000 | − | 13.8564i | −0.798670 | − | 0.461112i | ||||
\(904\) | 15.0000 | 0.498893 | ||||||||
\(905\) | 24.0000 | 0.797787 | ||||||||
\(906\) | 6.00000 | − | 10.3923i | 0.199337 | − | 0.345261i | ||||
\(907\) | 1.50000 | + | 0.866025i | 0.0498067 | + | 0.0287559i | 0.524697 | − | 0.851289i | \(-0.324179\pi\) |
−0.474890 | + | 0.880045i | \(0.657512\pi\) | |||||||
\(908\) | 10.5000 | + | 18.1865i | 0.348455 | + | 0.603541i | ||||
\(909\) | −27.0000 | + | 15.5885i | −0.895533 | + | 0.517036i | ||||
\(910\) | 12.0000 | − | 20.7846i | 0.397796 | − | 0.689003i | ||||
\(911\) | 36.0000 | 1.19273 | 0.596367 | − | 0.802712i | \(-0.296610\pi\) | ||||
0.596367 | + | 0.802712i | \(0.296610\pi\) | |||||||
\(912\) | −3.00000 | + | 6.92820i | −0.0993399 | + | 0.229416i | ||||
\(913\) | −9.00000 | −0.297857 | ||||||||
\(914\) | 8.50000 | − | 14.7224i | 0.281155 | − | 0.486975i | ||||
\(915\) | −60.0000 | −1.98354 | ||||||||
\(916\) | −2.00000 | − | 3.46410i | −0.0660819 | − | 0.114457i | ||||
\(917\) | −33.0000 | − | 19.0526i | −1.08976 | − | 0.629171i | ||||
\(918\) | 18.0000 | + | 31.1769i | 0.594089 | + | 1.02899i | ||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.50000 | + | 7.79423i | −0.148280 | + | 0.256829i | ||||
\(922\) | −21.0000 | + | 12.1244i | −0.691598 | + | 0.399294i | ||||
\(923\) | 20.7846i | 0.684134i | ||||||||
\(924\) | −3.00000 | − | 5.19615i | −0.0986928 | − | 0.170941i | ||||
\(925\) | 42.0000 | − | 24.2487i | 1.38095 | − | 0.797293i | ||||
\(926\) | 7.00000 | − | 12.1244i | 0.230034 | − | 0.398431i | ||||
\(927\) | − | 31.1769i | − | 1.02398i | ||||||
\(928\) | 3.00000 | − | 5.19615i | 0.0984798 | − | 0.170572i | ||||
\(929\) | −31.5000 | − | 18.1865i | −1.03348 | − | 0.596681i | −0.115501 | − | 0.993307i | \(-0.536847\pi\) |
−0.917980 | + | 0.396627i | \(0.870181\pi\) | |||||||
\(930\) | −36.0000 | + | 20.7846i | −1.18049 | + | 0.681554i | ||||
\(931\) | −1.50000 | − | 12.9904i | −0.0491605 | − | 0.425743i | ||||
\(932\) | − | 1.73205i | − | 0.0567352i | ||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | −10.5000 | − | 6.06218i | −0.343570 | − | 0.198361i | ||||
\(935\) | 36.0000 | − | 20.7846i | 1.17733 | − | 0.679729i | ||||
\(936\) | −9.00000 | + | 5.19615i | −0.294174 | + | 0.169842i | ||||
\(937\) | 3.50000 | + | 6.06218i | 0.114340 | + | 0.198043i | 0.917516 | − | 0.397699i | \(-0.130191\pi\) |
−0.803176 | + | 0.595742i | \(0.796858\pi\) | |||||||
\(938\) | 10.3923i | 0.339321i | ||||||||
\(939\) | −46.5000 | + | 26.8468i | −1.51747 | + | 0.876112i | ||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | 27.0000 | + | 46.7654i | 0.880175 | + | 1.52451i | 0.851146 | + | 0.524929i | \(0.175908\pi\) |
0.0290288 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(942\) | −30.0000 | + | 17.3205i | −0.977453 | + | 0.564333i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.50000 | + | 2.59808i | 0.0488208 | + | 0.0845602i | ||||
\(945\) | 18.0000 | − | 31.1769i | 0.585540 | − | 1.01419i | ||||
\(946\) | 12.0000 | − | 6.92820i | 0.390154 | − | 0.225255i | ||||
\(947\) | 45.0000 | + | 25.9808i | 1.46230 | + | 0.844261i | 0.999118 | − | 0.0419998i | \(-0.0133729\pi\) |
0.463186 | + | 0.886261i | \(0.346706\pi\) | |||||||
\(948\) | 24.0000 | 0.779484 | ||||||||
\(949\) | − | 17.3205i | − | 0.562247i | ||||||
\(950\) | 3.50000 | + | 30.3109i | 0.113555 | + | 0.983415i | ||||
\(951\) | −9.00000 | + | 5.19615i | −0.291845 | + | 0.168497i | ||||
\(952\) | 12.0000 | + | 6.92820i | 0.388922 | + | 0.224544i | ||||
\(953\) | −25.5000 | + | 44.1673i | −0.826026 | + | 1.43072i | 0.0751066 | + | 0.997176i | \(0.476070\pi\) |
−0.901133 | + | 0.433544i | \(0.857263\pi\) | |||||||
\(954\) | −18.0000 | −0.582772 | ||||||||
\(955\) | −12.0000 | + | 20.7846i | −0.388311 | + | 0.672574i | ||||
\(956\) | 6.00000 | − | 3.46410i | 0.194054 | − | 0.112037i | ||||
\(957\) | 9.00000 | + | 15.5885i | 0.290929 | + | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00000 | + | 1.73205i | −0.0968751 | + | 0.0559308i | ||||
\(960\) | 3.00000 | − | 5.19615i | 0.0968246 | − | 0.167705i | ||||
\(961\) | −17.0000 | −0.548387 | ||||||||
\(962\) | 24.0000 | 0.773791 | ||||||||
\(963\) | −36.0000 | −1.16008 | ||||||||
\(964\) | −4.50000 | − | 2.59808i | −0.144935 | − | 0.0836784i | ||||
\(965\) | 36.0000 | + | 62.3538i | 1.15888 | + | 2.00724i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0000 | − | 43.3013i | 0.803946 | − | 1.39247i | −0.113055 | − | 0.993589i | \(-0.536064\pi\) |
0.917000 | − | 0.398886i | \(-0.130603\pi\) | |||||||
\(968\) | −8.00000 | −0.257130 | ||||||||
\(969\) | 48.0000 | + | 20.7846i | 1.54198 | + | 0.667698i | ||||
\(970\) | 30.0000 | 0.963242 | ||||||||
\(971\) | −4.50000 | + | 7.79423i | −0.144412 | + | 0.250129i | −0.929153 | − | 0.369694i | \(-0.879462\pi\) |
0.784741 | + | 0.619823i | \(0.212796\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | 1.00000 | + | 1.73205i | 0.0320585 | + | 0.0555270i | ||||
\(974\) | 6.00000 | + | 3.46410i | 0.192252 | + | 0.110997i | ||||
\(975\) | −21.0000 | + | 36.3731i | −0.672538 | + | 1.16487i | ||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 27.0000 | 0.863807 | 0.431903 | − | 0.901920i | \(-0.357842\pi\) | ||||
0.431903 | + | 0.901920i | \(0.357842\pi\) | |||||||
\(978\) | 25.5000 | + | 14.7224i | 0.815400 | + | 0.470771i | ||||
\(979\) | −9.00000 | + | 5.19615i | −0.287641 | + | 0.166070i | ||||
\(980\) | 10.3923i | 0.331970i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.0000 | + | 15.5885i | −0.861605 | + | 0.497448i | ||||
\(983\) | 18.0000 | − | 31.1769i | 0.574111 | − | 0.994389i | −0.422027 | − | 0.906583i | \(-0.638681\pi\) |
0.996138 | − | 0.0878058i | \(-0.0279855\pi\) | |||||||
\(984\) | −4.50000 | − | 2.59808i | −0.143455 | − | 0.0828236i | ||||
\(985\) | −36.0000 | + | 62.3538i | −1.14706 | + | 1.98676i | ||||
\(986\) | −36.0000 | − | 20.7846i | −1.14647 | − | 0.661917i | ||||
\(987\) | −6.00000 | − | 10.3923i | −0.190982 | − | 0.330791i | ||||
\(988\) | −6.00000 | + | 13.8564i | −0.190885 | + | 0.440831i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 9.00000 | + | 15.5885i | 0.286039 | + | 0.495434i | ||||
\(991\) | 6.00000 | + | 3.46410i | 0.190596 | + | 0.110041i | 0.592262 | − | 0.805746i | \(-0.298235\pi\) |
−0.401665 | + | 0.915786i | \(0.631569\pi\) | |||||||
\(992\) | 6.00000 | − | 3.46410i | 0.190500 | − | 0.109985i | ||||
\(993\) | −15.0000 | −0.476011 | ||||||||
\(994\) | 6.00000 | + | 10.3923i | 0.190308 | + | 0.329624i | ||||
\(995\) | − | 48.4974i | − | 1.53747i | ||||||
\(996\) | 4.50000 | + | 7.79423i | 0.142588 | + | 0.246970i | ||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | −20.5000 | − | 35.5070i | −0.648916 | − | 1.12396i | ||||
\(999\) | 36.0000 | 1.13899 |
(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 | 114.2.h.d.65.1 | yes | 2 | |
3.2 | odd | 2 | 114.2.h.a.65.1 | ✓ | 2 | ||
4.3 | odd | 2 | 912.2.bn.b.65.1 | 2 | |||
12.11 | even | 2 | 912.2.bn.d.65.1 | 2 | |||
19.12 | odd | 6 | 114.2.h.a.107.1 | yes | 2 | ||
57.50 | even | 6 | inner | 114.2.h.d.107.1 | yes | 2 | |
76.31 | even | 6 | 912.2.bn.d.449.1 | 2 | |||
228.107 | odd | 6 | 912.2.bn.b.449.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.a.65.1 | ✓ | 2 | 3.2 | odd | 2 | ||
114.2.h.a.107.1 | yes | 2 | 19.12 | odd | 6 | ||
114.2.h.d.65.1 | yes | 2 | 1.1 | even | 1 | trivial | |
114.2.h.d.107.1 | yes | 2 | 57.50 | even | 6 | inner | |
912.2.bn.b.65.1 | 2 | 4.3 | odd | 2 | |||
912.2.bn.b.449.1 | 2 | 228.107 | odd | 6 | |||
912.2.bn.d.65.1 | 2 | 12.11 | even | 2 | |||
912.2.bn.d.449.1 | 2 | 76.31 | even | 6 |