Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 106.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.106 |
Dual form | 315.2.i.b.211.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 3.00000 | + | 1.73205i | 0.866025 | + | 0.500000i | ||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.00000 | + | 1.73205i | −0.223607 | + | 0.387298i | ||||
\(21\) | 1.73205i | 0.377964i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | + | 0.866025i | 0.240192 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 3.46410i | 0.304997 | − | 0.528271i | −0.672264 | − | 0.740312i | \(-0.734678\pi\) |
0.977261 | + | 0.212041i | \(0.0680112\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 6.92820i | 1.00000i | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | − | 1.73205i | 0.397360 | − | 0.229416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | − | 5.19615i | −0.390567 | − | 0.676481i | 0.601958 | − | 0.798528i | \(-0.294388\pi\) |
−0.992524 | + | 0.122047i | \(0.961054\pi\) | |||||||
\(60\) | 3.46410i | 0.447214i | ||||||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.50000 | + | 2.59808i | 0.188982 | + | 0.327327i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −0.500000 | + | 0.866025i | −0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | −9.00000 | − | 5.19615i | −1.08347 | − | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | −3.00000 | + | 1.73205i | −0.327327 | + | 0.188982i | ||||
\(85\) | −1.50000 | − | 2.59808i | −0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 15.5885i | − | 1.67126i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 6.00000 | − | 10.3923i | 0.625543 | − | 1.08347i | ||||
\(93\) | 6.00000 | + | 3.46410i | 0.622171 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | + | 1.73205i | 0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.50000 | − | 9.52628i | −0.541931 | − | 0.938652i | −0.998793 | − | 0.0491146i | \(-0.984360\pi\) |
0.456862 | − | 0.889538i | \(-0.348973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.50000 | + | 0.866025i | −0.146385 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 3.46410i | −0.569495 | + | 0.328798i | ||||
\(112\) | −2.00000 | − | 3.46410i | −0.188982 | − | 0.327327i | ||||
\(113\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | − | 5.19615i | 0.279751 | − | 0.484544i | ||||
\(116\) | 18.0000 | 1.67126 | ||||||||
\(117\) | 3.00000 | 0.277350 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | − | 2.59808i | 0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.92820i | − | 0.609994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | + | 1.73205i | −0.0867110 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.50000 | − | 2.59808i | 0.387298 | − | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | − | 6.92820i | −0.339276 | − | 0.587643i | 0.645021 | − | 0.764165i | \(-0.276849\pi\) |
−0.984297 | + | 0.176522i | \(0.943515\pi\) | |||||||
\(140\) | −1.00000 | − | 1.73205i | −0.0845154 | − | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(145\) | 9.00000 | 0.747409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.50000 | − | 0.866025i | −0.123718 | − | 0.0714286i | ||||
\(148\) | −4.00000 | − | 6.92820i | −0.328798 | − | 0.569495i | ||||
\(149\) | 10.5000 | + | 18.1865i | 0.860194 | + | 1.48990i | 0.871742 | + | 0.489966i | \(0.162991\pi\) |
−0.0115483 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50000 | + | 7.79423i | −0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | + | 3.46410i | −0.160644 | + | 0.278243i | ||||
\(156\) | 3.46410i | 0.277350i | ||||||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | + | 5.19615i | −0.713746 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.50000 | + | 12.9904i | 0.580367 | + | 1.00523i | 0.995436 | + | 0.0954356i | \(0.0304244\pi\) |
−0.415068 | + | 0.909790i | \(0.636242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −10.5000 | + | 18.1865i | −0.798300 | + | 1.38270i | 0.122422 | + | 0.992478i | \(0.460934\pi\) |
−0.920722 | + | 0.390218i | \(0.872399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00000 | − | 5.19615i | −0.676481 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | 3.00000 | + | 5.19615i | 0.223607 | + | 0.387298i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.2487i | 1.79252i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.866025 | + | 0.500000i | ||||
\(193\) | −13.0000 | − | 22.5167i | −0.935760 | − | 1.62078i | −0.773272 | − | 0.634074i | \(-0.781381\pi\) |
−0.162488 | − | 0.986710i | \(-0.551952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.73205i | 0.124035i | ||||||||
\(196\) | 1.00000 | − | 1.73205i | 0.0714286 | − | 0.123718i | ||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0000 | 1.84309 | 0.921546 | − | 0.388270i | \(-0.126927\pi\) | ||||
0.921546 | + | 0.388270i | \(0.126927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.0000 | − | 12.1244i | −1.48123 | − | 0.855186i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.50000 | + | 7.79423i | 0.315838 | + | 0.547048i | ||||
\(204\) | −9.00000 | − | 5.19615i | −0.630126 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.0000 | −1.25109 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | − | 17.3205i | −0.688428 | − | 1.19239i | −0.972346 | − | 0.233544i | \(-0.924968\pi\) |
0.283918 | − | 0.958849i | \(-0.408366\pi\) | |||||||
\(212\) | −6.00000 | − | 10.3923i | −0.412082 | − | 0.713746i | ||||
\(213\) | 13.5000 | − | 7.79423i | 0.925005 | − | 0.534052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | 0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5000 | − | 9.52628i | 1.11497 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.50000 | − | 2.59808i | −0.100901 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 6.00000 | + | 3.46410i | 0.397360 | + | 0.229416i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | − | 10.3923i | 0.390567 | − | 0.676481i | ||||
\(237\) | 13.8564i | 0.900070i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.50000 | + | 7.79423i | 0.291081 | + | 0.504167i | 0.974066 | − | 0.226266i | \(-0.0726518\pi\) |
−0.682985 | + | 0.730433i | \(0.739318\pi\) | |||||||
\(240\) | −6.00000 | + | 3.46410i | −0.387298 | + | 0.223607i | ||||
\(241\) | −10.0000 | + | 17.3205i | −0.644157 | + | 1.11571i | 0.340339 | + | 0.940303i | \(0.389458\pi\) |
−0.984496 | + | 0.175409i | \(0.943875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | −28.0000 | −1.79252 | ||||||||
\(245\) | 0.500000 | − | 0.866025i | 0.0319438 | − | 0.0553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | + | 1.73205i | 0.0636285 | + | 0.110208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5885i | 0.987878i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | −3.00000 | + | 5.19615i | −0.188982 | + | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.50000 | − | 2.59808i | −0.281801 | − | 0.162698i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | − | 3.46410i | 0.124274 | − | 0.215249i | ||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | −13.5000 | − | 23.3827i | −0.835629 | − | 1.44735i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | + | 10.3923i | −1.10158 | + | 0.635999i | ||||
\(268\) | 14.0000 | − | 24.2487i | 0.855186 | − | 1.48123i | ||||
\(269\) | −24.0000 | −1.46331 | −0.731653 | − | 0.681677i | \(-0.761251\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | 6.00000 | − | 10.3923i | 0.363803 | − | 0.630126i | ||||
\(273\) | −1.50000 | + | 0.866025i | −0.0907841 | + | 0.0524142i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 20.7846i | − | 1.25109i | ||||||
\(277\) | −13.0000 | + | 22.5167i | −0.781094 | + | 1.35290i | 0.150210 | + | 0.988654i | \(0.452005\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.0000 | 0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | + | 5.19615i | −0.178965 | + | 0.309976i | −0.941526 | − | 0.336939i | \(-0.890608\pi\) |
0.762561 | + | 0.646916i | \(0.223942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 9.00000 | + | 15.5885i | 0.534052 | + | 0.925005i | ||||
\(285\) | 3.00000 | + | 1.73205i | 0.177705 | + | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.46410i | 0.203069i | ||||||||
\(292\) | 11.0000 | + | 19.0526i | 0.643726 | + | 1.11497i | ||||
\(293\) | −10.5000 | − | 18.1865i | −0.613417 | − | 1.06247i | −0.990660 | − | 0.136355i | \(-0.956461\pi\) |
0.377244 | − | 0.926114i | \(-0.376872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | −3.00000 | + | 1.73205i | −0.173205 | + | 0.100000i | ||||
\(301\) | 2.00000 | + | 3.46410i | 0.115278 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.7846i | 1.19404i | ||||||||
\(304\) | −4.00000 | + | 6.92820i | −0.229416 | + | 0.397360i | ||||
\(305\) | −14.0000 | −0.801638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.5000 | − | 9.52628i | −0.938652 | − | 0.541931i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | + | 5.19615i | 0.170114 | + | 0.294647i | 0.938460 | − | 0.345389i | \(-0.112253\pi\) |
−0.768345 | + | 0.640036i | \(0.778920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50000 | + | 2.59808i | −0.0845154 | + | 0.146385i | ||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | −12.0000 | + | 20.7846i | −0.673987 | + | 1.16738i | 0.302777 | + | 0.953062i | \(0.402086\pi\) |
−0.976764 | + | 0.214318i | \(0.931247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.00000 | − | 6.92820i | −0.223607 | − | 0.387298i | ||||
\(321\) | −9.00000 | + | 5.19615i | −0.502331 | + | 0.290021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 9.00000 | − | 15.5885i | 0.500000 | − | 0.866025i | ||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.0000 | − | 12.1244i | 1.16130 | − | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | − | 16.4545i | 0.522167 | − | 0.904420i | −0.477500 | − | 0.878632i | \(-0.658457\pi\) |
0.999667 | − | 0.0257885i | \(-0.00820965\pi\) | |||||||
\(332\) | −18.0000 | −0.987878 | ||||||||
\(333\) | −6.00000 | + | 10.3923i | −0.328798 | + | 0.569495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.00000 | − | 12.1244i | 0.382451 | − | 0.662424i | ||||
\(336\) | −6.00000 | − | 3.46410i | −0.327327 | − | 0.188982i | ||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 10.3923i | − | 0.559503i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 27.0000 | − | 15.5885i | 1.44735 | − | 0.835629i | ||||
\(349\) | 2.00000 | − | 3.46410i | 0.107058 | − | 0.185429i | −0.807519 | − | 0.589841i | \(-0.799190\pi\) |
0.914577 | + | 0.404412i | \(0.132524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.50000 | − | 2.59808i | 0.240192 | − | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5000 | + | 28.5788i | −0.878206 | + | 1.52110i | −0.0248989 | + | 0.999690i | \(0.507926\pi\) |
−0.853307 | + | 0.521408i | \(0.825407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50000 | + | 7.79423i | 0.238835 | + | 0.413675i | ||||
\(356\) | −12.0000 | − | 20.7846i | −0.635999 | − | 1.10158i | ||||
\(357\) | − | 5.19615i | − | 0.275010i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5000 | + | 9.52628i | 0.866025 | + | 0.500000i | ||||
\(364\) | −1.00000 | − | 1.73205i | −0.0524142 | − | 0.0907841i | ||||
\(365\) | 5.50000 | + | 9.52628i | 0.287883 | + | 0.498628i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | \(-0.979666\pi\) |
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(368\) | 24.0000 | 1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | − | 5.19615i | 0.155752 | − | 0.269771i | ||||
\(372\) | 13.8564i | 0.718421i | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | + | 0.866025i | −0.0774597 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | −2.00000 | + | 3.46410i | −0.102598 | + | 0.177705i | ||||
\(381\) | 12.0000 | − | 6.92820i | 0.614779 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.50000 | − | 12.9904i | −0.383232 | − | 0.663777i | 0.608290 | − | 0.793715i | \(-0.291856\pi\) |
−0.991522 | + | 0.129937i | \(0.958522\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.00000 | − | 10.3923i | −0.304997 | − | 0.528271i | ||||
\(388\) | −4.00000 | −0.203069 | ||||||||
\(389\) | 9.00000 | − | 15.5885i | 0.456318 | − | 0.790366i | −0.542445 | − | 0.840091i | \(-0.682501\pi\) |
0.998763 | + | 0.0497253i | \(0.0158346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | + | 15.5885i | 0.455150 | + | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.0000 | 1.45547 | 0.727734 | − | 0.685859i | \(-0.240573\pi\) | ||||
0.727734 | + | 0.685859i | \(0.240573\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.46410i | 0.173422i | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −16.5000 | − | 28.5788i | −0.823971 | − | 1.42716i | −0.902703 | − | 0.430263i | \(-0.858421\pi\) |
0.0787327 | − | 0.996896i | \(-0.474913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | −24.0000 | −1.19404 | ||||||||
\(405\) | 4.50000 | − | 7.79423i | 0.223607 | − | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0000 | + | 29.4449i | 0.840596 | + | 1.45595i | 0.889392 | + | 0.457146i | \(0.151128\pi\) |
−0.0487958 | + | 0.998809i | \(0.515538\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 10.3923i | − | 0.512615i | ||||||
\(412\) | 11.0000 | − | 19.0526i | 0.541931 | − | 0.938652i | ||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | − | 6.92820i | −0.587643 | − | 0.339276i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | −3.00000 | − | 1.73205i | −0.146385 | − | 0.0845154i | ||||
\(421\) | 5.00000 | − | 8.66025i | 0.243685 | − | 0.422075i | −0.718076 | − | 0.695965i | \(-0.754977\pi\) |
0.961761 | + | 0.273890i | \(0.0883103\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50000 | − | 2.59808i | 0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 12.1244i | −0.338754 | − | 0.586739i | ||||
\(428\) | −6.00000 | − | 10.3923i | −0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | −0.433515 | −0.216757 | − | 0.976226i | \(-0.569548\pi\) | ||||
−0.216757 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.866025 | + | 0.500000i | ||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.5000 | − | 7.79423i | 0.647275 | − | 0.373705i | ||||
\(436\) | 14.0000 | + | 24.2487i | 0.670478 | + | 1.16130i | ||||
\(437\) | −6.00000 | − | 10.3923i | −0.287019 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.00000 | + | 5.19615i | −0.142534 | + | 0.246877i | −0.928450 | − | 0.371457i | \(-0.878858\pi\) |
0.785916 | + | 0.618333i | \(0.212192\pi\) | |||||||
\(444\) | −12.0000 | − | 6.92820i | −0.569495 | − | 0.328798i | ||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.5000 | + | 18.1865i | 1.48990 | + | 0.860194i | ||||
\(448\) | 4.00000 | − | 6.92820i | 0.188982 | − | 0.327327i | ||||
\(449\) | −21.0000 | −0.991051 | −0.495526 | − | 0.868593i | \(-0.665025\pi\) | ||||
−0.495526 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.66025i | 0.406894i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.500000 | − | 0.866025i | −0.0234404 | − | 0.0405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | 12.0000 | 0.559503 | ||||||||
\(461\) | 12.0000 | − | 20.7846i | 0.558896 | − | 0.968036i | −0.438693 | − | 0.898637i | \(-0.644559\pi\) |
0.997589 | − | 0.0693989i | \(-0.0221081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | + | 3.46410i | 0.0929479 | + | 0.160990i | 0.908750 | − | 0.417340i | \(-0.137038\pi\) |
−0.815802 | + | 0.578331i | \(0.803704\pi\) | |||||||
\(464\) | 18.0000 | + | 31.1769i | 0.835629 | + | 1.44735i | ||||
\(465\) | 6.92820i | 0.321288i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.0000 | 1.66588 | 0.832941 | − | 0.553362i | \(-0.186655\pi\) | ||||
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(468\) | 3.00000 | + | 5.19615i | 0.138675 | + | 0.240192i | ||||
\(469\) | 14.0000 | 0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5000 | + | 11.2583i | 0.898513 | + | 0.518756i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | + | 1.73205i | −0.0458831 | + | 0.0794719i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −9.00000 | + | 15.5885i | −0.412082 | + | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | − | 15.5885i | 0.411220 | − | 0.712255i | −0.583803 | − | 0.811895i | \(-0.698436\pi\) |
0.995023 | + | 0.0996406i | \(0.0317693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.00000 | − | 5.19615i | 0.409514 | − | 0.236433i | ||||
\(484\) | −11.0000 | + | 19.0526i | −0.500000 | + | 0.866025i | ||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.0000 | − | 12.1244i | 0.949653 | − | 0.548282i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.5000 | + | 23.3827i | 0.609246 | + | 1.05525i | 0.991365 | + | 0.131132i | \(0.0418613\pi\) |
−0.382118 | + | 0.924113i | \(0.624805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5000 | + | 23.3827i | −0.608009 | + | 1.05310i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | −4.50000 | + | 7.79423i | −0.201853 | + | 0.349619i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | 22.5000 | + | 12.9904i | 1.00523 | + | 0.580367i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 20.7846i | − | 0.923077i | ||||||
\(508\) | 8.00000 | + | 13.8564i | 0.354943 | + | 0.614779i | ||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.50000 | + | 9.52628i | −0.243306 | + | 0.421418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 10.3923i | − | 0.458831i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.50000 | − | 9.52628i | 0.242359 | − | 0.419778i | ||||
\(516\) | 12.0000 | − | 6.92820i | 0.528271 | − | 0.304997i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.3731i | 1.59660i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0000 | −0.568450 | −0.284225 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284225 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.50000 | − | 0.866025i | −0.0654654 | − | 0.0377964i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.5000 | − | 12.9904i | 0.970947 | − | 0.560576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.00000 | + | 5.19615i | 0.387298 | + | 0.223607i | ||||
\(541\) | 11.0000 | 0.472927 | 0.236463 | − | 0.971640i | \(-0.424012\pi\) | ||||
0.236463 | + | 0.971640i | \(0.424012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.00000 | − | 1.73205i | 0.128742 | − | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00000 | + | 12.1244i | 0.299847 | + | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | + | 1.73205i | −0.0427569 | + | 0.0740571i | −0.886612 | − | 0.462514i | \(-0.846947\pi\) |
0.843855 | + | 0.536571i | \(0.180281\pi\) | |||||||
\(548\) | 12.0000 | 0.512615 | ||||||||
\(549\) | 21.0000 | + | 36.3731i | 0.896258 | + | 1.55236i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | − | 6.92820i | −0.170097 | − | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | − | 3.46410i | −0.254686 | − | 0.147043i | ||||
\(556\) | 8.00000 | − | 13.8564i | 0.339276 | − | 0.587643i | ||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 2.00000 | − | 3.46410i | 0.0845154 | − | 0.146385i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5000 | − | 18.1865i | −0.442522 | − | 0.766471i | 0.555354 | − | 0.831614i | \(-0.312583\pi\) |
−0.997876 | + | 0.0651433i | \(0.979250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000 | 0.377964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.50000 | − | 12.9904i | 0.314416 | − | 0.544585i | −0.664897 | − | 0.746935i | \(-0.731525\pi\) |
0.979313 | + | 0.202350i | \(0.0648579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.19615i | − | 0.217072i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | −12.0000 | + | 20.7846i | −0.500000 | + | 0.866025i | ||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.0000 | − | 22.5167i | −1.62078 | − | 0.935760i | ||||
\(580\) | 9.00000 | + | 15.5885i | 0.373705 | + | 0.647275i | ||||
\(581\) | −4.50000 | − | 7.79423i | −0.186691 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.50000 | + | 2.59808i | 0.0620174 | + | 0.107417i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.00000 | + | 10.3923i | −0.247647 | + | 0.428936i | −0.962872 | − | 0.269957i | \(-0.912990\pi\) |
0.715226 | + | 0.698893i | \(0.246324\pi\) | |||||||
\(588\) | − | 3.46410i | − | 0.142857i | ||||||
\(589\) | 4.00000 | + | 6.92820i | 0.164817 | + | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.0000 | − | 20.7846i | 1.48084 | − | 0.854965i | ||||
\(592\) | 8.00000 | − | 13.8564i | 0.328798 | − | 0.569495i | ||||
\(593\) | 3.00000 | 0.123195 | 0.0615976 | − | 0.998101i | \(-0.480380\pi\) | ||||
0.0615976 | + | 0.998101i | \(0.480380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | 0.122988 | ||||||||
\(596\) | −21.0000 | + | 36.3731i | −0.860194 | + | 1.48990i | ||||
\(597\) | 39.0000 | − | 22.5167i | 1.59616 | − | 0.921546i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.5000 | − | 23.3827i | −0.551595 | − | 0.955391i | −0.998160 | − | 0.0606393i | \(-0.980686\pi\) |
0.446565 | − | 0.894751i | \(-0.352647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | + | 1.73205i | −0.0407909 | + | 0.0706518i | −0.885700 | − | 0.464258i | \(-0.846321\pi\) |
0.844909 | + | 0.534910i | \(0.179654\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.0000 | −1.71037 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | −5.50000 | + | 9.52628i | −0.223607 | + | 0.387298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5000 | − | 35.5070i | −0.832069 | − | 1.44119i | −0.896394 | − | 0.443257i | \(-0.853823\pi\) |
0.0643251 | − | 0.997929i | \(-0.479511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.5000 | + | 7.79423i | 0.547048 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | − | 15.5885i | −0.362326 | − | 0.627568i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.988343 | + | 0.152242i | \(0.951351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | − | 13.8564i | 0.321547 | − | 0.556936i | −0.659260 | − | 0.751915i | \(-0.729130\pi\) |
0.980807 | + | 0.194979i | \(0.0624638\pi\) | |||||||
\(620\) | −8.00000 | −0.321288 | ||||||||
\(621\) | −27.0000 | + | 15.5885i | −1.08347 | + | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | − | 10.3923i | 0.240385 | − | 0.416359i | ||||
\(624\) | −6.00000 | + | 3.46410i | −0.240192 | + | 0.138675i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.0000 | + | 22.5167i | −0.518756 | + | 0.898513i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.0000 | − | 17.3205i | −1.19239 | − | 0.688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | + | 6.92820i | 0.158735 | + | 0.274937i | ||||
\(636\) | −18.0000 | − | 10.3923i | −0.713746 | − | 0.412082i | ||||
\(637\) | 0.500000 | − | 0.866025i | 0.0198107 | − | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.5000 | − | 23.3827i | 0.534052 | − | 0.925005i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000 | + | 3.46410i | 0.0788723 | + | 0.136611i | 0.902764 | − | 0.430137i | \(-0.141535\pi\) |
−0.823891 | + | 0.566748i | \(0.808201\pi\) | |||||||
\(644\) | 6.00000 | + | 10.3923i | 0.236433 | + | 0.409514i | ||||
\(645\) | 6.00000 | − | 3.46410i | 0.236250 | − | 0.136399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | + | 3.46410i | −0.235159 | + | 0.135769i | ||||
\(652\) | 14.0000 | + | 24.2487i | 0.548282 | + | 0.949653i | ||||
\(653\) | −15.0000 | − | 25.9808i | −0.586995 | − | 1.01671i | −0.994623 | − | 0.103558i | \(-0.966977\pi\) |
0.407628 | − | 0.913148i | \(-0.366356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5000 | − | 28.5788i | 0.643726 | − | 1.11497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5000 | − | 38.9711i | 0.876476 | − | 1.51810i | 0.0212930 | − | 0.999773i | \(-0.493222\pi\) |
0.855183 | − | 0.518327i | \(-0.173445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.50000 | − | 2.59808i | −0.174766 | − | 0.100901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | −0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.0000 | −2.09089 | ||||||||
\(668\) | −15.0000 | + | 25.9808i | −0.580367 | + | 1.00523i | ||||
\(669\) | − | 32.9090i | − | 1.27233i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 24.0000 | 0.923077 | ||||||||
\(677\) | −19.5000 | + | 33.7750i | −0.749446 | + | 1.29808i | 0.198643 | + | 0.980072i | \(0.436347\pi\) |
−0.948089 | + | 0.318006i | \(0.896987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 5.19615i | − | 0.199117i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 12.0000 | 0.458831 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.0000 | − | 12.1244i | −0.801200 | − | 0.462573i | ||||
\(688\) | 8.00000 | + | 13.8564i | 0.304997 | + | 0.528271i | ||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00000 | + | 1.73205i | −0.0380418 | + | 0.0658903i | −0.884419 | − | 0.466693i | \(-0.845445\pi\) |
0.846378 | + | 0.532583i | \(0.178779\pi\) | |||||||
\(692\) | −42.0000 | −1.59660 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | − | 6.92820i | 0.151729 | − | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.0000 | + | 20.7846i | −1.36165 | + | 0.786146i | ||||
\(700\) | 1.00000 | − | 1.73205i | 0.0377964 | − | 0.0654654i | ||||
\(701\) | −33.0000 | −1.24639 | −0.623196 | − | 0.782065i | \(-0.714166\pi\) | ||||
−0.623196 | + | 0.782065i | \(0.714166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | − | 10.3923i | −0.225653 | − | 0.390843i | ||||
\(708\) | − | 20.7846i | − | 0.781133i | ||||||
\(709\) | 12.5000 | − | 21.6506i | 0.469447 | − | 0.813107i | −0.529943 | − | 0.848034i | \(-0.677787\pi\) |
0.999390 | + | 0.0349269i | \(0.0111198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | + | 20.7846i | 0.450035 | + | 0.779484i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0000 | − | 20.7846i | 0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.0000 | + | 25.9808i | 0.560576 | + | 0.970947i | ||||
\(717\) | 13.5000 | + | 7.79423i | 0.504167 | + | 0.291081i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | −6.00000 | + | 10.3923i | −0.223607 | + | 0.387298i | ||||
\(721\) | 11.0000 | 0.409661 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.6410i | 1.28831i | ||||||||
\(724\) | 2.00000 | + | 3.46410i | 0.0743294 | + | 0.128742i | ||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.50000 | − | 11.2583i | 0.241072 | − | 0.417548i | −0.719948 | − | 0.694028i | \(-0.755834\pi\) |
0.961020 | + | 0.276479i | \(0.0891678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | −42.0000 | + | 24.2487i | −1.55236 | + | 0.896258i | ||||
\(733\) | −5.50000 | − | 9.52628i | −0.203147 | − | 0.351861i | 0.746394 | − | 0.665505i | \(-0.231784\pi\) |
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.73205i | − | 0.0638877i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0000 | 0.625355 | 0.312678 | − | 0.949859i | \(-0.398774\pi\) | ||||
0.312678 | + | 0.949859i | \(0.398774\pi\) | |||||||
\(740\) | 4.00000 | − | 6.92820i | 0.147043 | − | 0.254686i | ||||
\(741\) | 3.00000 | + | 1.73205i | 0.110208 | + | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5000 | + | 18.1865i | −0.384690 | + | 0.666303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5000 | + | 23.3827i | 0.493939 | + | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.00000 | − | 5.19615i | 0.109618 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | + | 11.2583i | 0.237188 | + | 0.410822i | 0.959906 | − | 0.280321i | \(-0.0904408\pi\) |
−0.722718 | + | 0.691143i | \(0.757107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.0000 | − | 20.7846i | 1.31191 | − | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | 10.3923i | 0.377964i | ||||||||
\(757\) | 8.00000 | 0.290765 | 0.145382 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145382 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.00000 | + | 12.1244i | −0.253417 | + | 0.438931i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | −9.00000 | −0.325396 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.866025 | − | 0.500000i | ||||
\(769\) | −7.00000 | − | 12.1244i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.5000 | + | 23.3827i | 1.45857 | + | 0.842107i | ||||
\(772\) | 26.0000 | − | 45.0333i | 0.935760 | − | 1.62078i | ||||
\(773\) | 42.0000 | 1.51064 | 0.755318 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755318 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.92820i | − | 0.248548i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −3.00000 | + | 1.73205i | −0.107417 | + | 0.0620174i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.5000 | − | 23.3827i | −1.44735 | − | 0.835629i | ||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | −6.50000 | + | 11.2583i | −0.231995 | + | 0.401827i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.5000 | − | 25.1147i | −0.516869 | − | 0.895244i | −0.999808 | − | 0.0195896i | \(-0.993764\pi\) |
0.482939 | − | 0.875654i | \(-0.339569\pi\) | |||||||
\(788\) | 24.0000 | + | 41.5692i | 0.854965 | + | 1.48084i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0000 | −0.497155 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.00000 | − | 5.19615i | −0.319197 | − | 0.184289i | ||||
\(796\) | 26.0000 | + | 45.0333i | 0.921546 | + | 1.59616i | ||||
\(797\) | 19.5000 | + | 33.7750i | 0.690725 | + | 1.19637i | 0.971601 | + | 0.236627i | \(0.0760420\pi\) |
−0.280875 | + | 0.959744i | \(0.590625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | + | 31.1769i | −0.635999 | + | 1.10158i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 48.4974i | − | 1.71037i | ||||||
\(805\) | 3.00000 | + | 5.19615i | 0.105736 | + | 0.183140i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.0000 | + | 20.7846i | −1.26726 | + | 0.731653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | −0.527372 | −0.263686 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263686 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | −9.00000 | + | 15.5885i | −0.315838 | + | 0.547048i | ||||
\(813\) | 21.0000 | − | 12.1244i | 0.736502 | − | 0.425220i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.00000 | + | 12.1244i | 0.245199 | + | 0.424698i | ||||
\(816\) | − | 20.7846i | − | 0.727607i | ||||||
\(817\) | 4.00000 | − | 6.92820i | 0.139942 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.50000 | + | 2.59808i | −0.0524142 | + | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5000 | − | 44.1673i | 0.889956 | − | 1.54145i | 0.0500305 | − | 0.998748i | \(-0.484068\pi\) |
0.839926 | − | 0.542702i | \(-0.182599\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0000 | + | 29.4449i | 0.592583 | + | 1.02638i | 0.993883 | + | 0.110437i | \(0.0352250\pi\) |
−0.401300 | + | 0.915947i | \(0.631442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0000 | 1.66912 | 0.834562 | − | 0.550914i | \(-0.185721\pi\) | ||||
0.834562 | + | 0.550914i | \(0.185721\pi\) | |||||||
\(828\) | −18.0000 | − | 31.1769i | −0.625543 | − | 1.08347i | ||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.0333i | 1.56219i | ||||||||
\(832\) | −4.00000 | − | 6.92820i | −0.138675 | − | 0.240192i | ||||
\(833\) | 1.50000 | + | 2.59808i | 0.0519719 | + | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.50000 | + | 12.9904i | −0.259548 | + | 0.449551i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0000 | − | 10.3923i | 0.622171 | − | 0.359211i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | + | 41.5692i | −0.828572 | + | 1.43513i | 0.0705865 | + | 0.997506i | \(0.477513\pi\) |
−0.899158 | + | 0.437623i | \(0.855820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3923i | 0.357930i | ||||||||
\(844\) | 20.0000 | − | 34.6410i | 0.688428 | − | 1.19239i | ||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0000 | −0.377964 | ||||||||
\(848\) | 12.0000 | − | 20.7846i | 0.412082 | − | 0.713746i | ||||
\(849\) | 6.00000 | + | 3.46410i | 0.205919 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | + | 20.7846i | 0.411355 | + | 0.712487i | ||||
\(852\) | 27.0000 | + | 15.5885i | 0.925005 | + | 0.534052i | ||||
\(853\) | 5.00000 | − | 8.66025i | 0.171197 | − | 0.296521i | −0.767642 | − | 0.640879i | \(-0.778570\pi\) |
0.938839 | + | 0.344358i | \(0.111903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5000 | − | 28.5788i | 0.563629 | − | 0.976235i | −0.433546 | − | 0.901131i | \(-0.642738\pi\) |
0.997176 | − | 0.0751033i | \(-0.0239287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0000 | − | 48.4974i | −0.955348 | − | 1.65471i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
−0.221777 | − | 0.975097i | \(-0.571186\pi\) | |||||||
\(860\) | 4.00000 | + | 6.92820i | 0.136399 | + | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.0000 | 1.83818 | 0.919091 | − | 0.394046i | \(-0.128925\pi\) | ||||
0.919091 | + | 0.394046i | \(0.128925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | − | 12.1244i | 0.237186 | − | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | + | 5.19615i | 0.101535 | + | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.500000 | − | 0.866025i | 0.0169031 | − | 0.0292770i | ||||
\(876\) | 33.0000 | + | 19.0526i | 1.11497 | + | 0.643726i | ||||
\(877\) | −7.00000 | − | 12.1244i | −0.236373 | − | 0.409410i | 0.723298 | − | 0.690536i | \(-0.242625\pi\) |
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.5000 | − | 18.1865i | −1.06247 | − | 0.613417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | − | 10.3923i | − | 0.349334i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | + | 6.92820i | −0.134156 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.0000 | 1.27233 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.50000 | + | 12.9904i | 0.250697 | + | 0.434221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 10.3923i | − | 0.346989i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.0000 | 1.20067 | ||||||||
\(900\) | −3.00000 | + | 5.19615i | −0.100000 | + | 0.173205i | ||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00000 | + | 3.46410i | 0.199667 | + | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.00000 | + | 1.73205i | 0.0332411 | + | 0.0575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 6.00000 | 0.199117 | ||||||||
\(909\) | 18.0000 | + | 31.1769i | 0.597022 | + | 1.03407i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.5000 | + | 44.1673i | −0.844853 | + | 1.46333i | 0.0408964 | + | 0.999163i | \(0.486979\pi\) |
−0.885749 | + | 0.464164i | \(0.846355\pi\) | |||||||
\(912\) | 13.8564i | 0.458831i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.0000 | + | 12.1244i | −0.694239 | + | 0.400819i | ||||
\(916\) | 14.0000 | − | 24.2487i | 0.462573 | − | 0.801200i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.0000 | −1.61636 | −0.808180 | − | 0.588935i | \(-0.799547\pi\) | ||||
−0.808180 | + | 0.588935i | \(0.799547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.5000 | + | 11.2583i | −0.642547 | + | 0.370975i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.50000 | + | 7.79423i | 0.148119 | + | 0.256550i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.0000 | −1.08386 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | − | 1.73205i | −0.0327737 | − | 0.0567657i | ||||
\(932\) | −24.0000 | − | 41.5692i | −0.786146 | − | 1.36165i | ||||
\(933\) | 9.00000 | + | 5.19615i | 0.294647 | + | 0.170114i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.00000 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.73205i | − | 0.0565233i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0000 | + | 46.7654i | 0.880175 | + | 1.52451i | 0.851146 | + | 0.524929i | \(0.175908\pi\) |
0.0290288 | + | 0.999579i | \(0.490759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 24.0000 | 0.781133 | ||||||||
\(945\) | 5.19615i | 0.169031i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | + | 20.7846i | −0.389948 | + | 0.675409i | −0.992442 | − | 0.122714i | \(-0.960840\pi\) |
0.602494 | + | 0.798123i | \(0.294174\pi\) | |||||||
\(948\) | −24.0000 | + | 13.8564i | −0.779484 | + | 0.450035i | ||||
\(949\) | 5.50000 | + | 9.52628i | 0.178538 | + | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.5692i | 1.34797i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | 0.0970777 | ||||||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | + | 5.19615i | 0.0968751 | + | 0.167793i | ||||
\(960\) | −12.0000 | − | 6.92820i | −0.387298 | − | 0.223607i | ||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.00000 | + | 15.5885i | −0.290021 | + | 0.502331i | ||||
\(964\) | −40.0000 | −1.28831 | ||||||||
\(965\) | 13.0000 | − | 22.5167i | 0.418485 | − | 0.724837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0000 | + | 29.4449i | 0.546683 | + | 0.946883i | 0.998499 | + | 0.0547717i | \(0.0174431\pi\) |
−0.451816 | + | 0.892111i | \(0.649224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.00000 | + | 5.19615i | −0.289122 | + | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | − | 31.1769i | − | 1.00000i | ||||||
\(973\) | 8.00000 | 0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.50000 | + | 0.866025i | −0.0480384 | + | 0.0277350i | ||||
\(976\) | −28.0000 | − | 48.4974i | −0.896258 | − | 1.55236i | ||||
\(977\) | −6.00000 | − | 10.3923i | −0.191957 | − | 0.332479i | 0.753942 | − | 0.656941i | \(-0.228150\pi\) |
−0.945899 | + | 0.324462i | \(0.894817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | 21.0000 | − | 36.3731i | 0.670478 | − | 1.16130i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000 | − | 41.5692i | 0.765481 | − | 1.32585i | −0.174511 | − | 0.984655i | \(-0.555834\pi\) |
0.939992 | − | 0.341197i | \(-0.110832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | + | 20.7846i | 0.382352 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | + | 3.46410i | −0.0636285 | + | 0.110208i | ||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.9090i | − | 1.04433i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0000 | + | 22.5167i | 0.412128 | + | 0.713826i | ||||
\(996\) | −27.0000 | + | 15.5885i | −0.855528 | + | 0.493939i | ||||
\(997\) | −8.50000 | + | 14.7224i | −0.269198 | + | 0.466264i | −0.968655 | − | 0.248410i | \(-0.920092\pi\) |
0.699457 | + | 0.714675i | \(0.253425\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.7846i | 0.657596i |
(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 | 315.2.i.b.106.1 | ✓ | 2 | |
3.2 | odd | 2 | 945.2.i.a.316.1 | 2 | |||
9.2 | odd | 6 | 2835.2.a.f.1.1 | 1 | |||
9.4 | even | 3 | inner | 315.2.i.b.211.1 | yes | 2 | |
9.5 | odd | 6 | 945.2.i.a.631.1 | 2 | |||
9.7 | even | 3 | 2835.2.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.b.106.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.2.i.b.211.1 | yes | 2 | 9.4 | even | 3 | inner | |
945.2.i.a.316.1 | 2 | 3.2 | odd | 2 | |||
945.2.i.a.631.1 | 2 | 9.5 | odd | 6 | |||
2835.2.a.c.1.1 | 1 | 9.7 | even | 3 | |||
2835.2.a.f.1.1 | 1 | 9.2 | odd | 6 |