Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.65 |
Dual form | 912.2.bn.l.449.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 1.65831i | 0.288675 | − | 0.957427i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.68614 | + | 2.12819i | 1.64849 | + | 0.951757i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37228 | 0.896638 | 0.448319 | − | 0.893874i | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50000 | − | 1.65831i | −0.833333 | − | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.58457i | − | 0.477767i | −0.971048 | − | 0.238884i | \(-0.923219\pi\) | ||
0.971048 | − | 0.238884i | \(-0.0767814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50000 | − | 0.866025i | 0.416025 | − | 0.240192i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.37228 | − | 5.04868i | 1.38712 | − | 1.30356i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.31386 | − | 1.33591i | −0.561193 | − | 0.324005i | 0.192431 | − | 0.981311i | \(-0.438363\pi\) |
−0.753624 | + | 0.657305i | \(0.771696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18614 | − | 3.93398i | 0.258837 | − | 0.858466i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.68614 | − | 2.12819i | 0.768613 | − | 0.443759i | −0.0637663 | − | 0.997965i | \(-0.520311\pi\) |
0.832380 | + | 0.554206i | \(0.186978\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.55842 | + | 11.3595i | 1.31168 | + | 2.27190i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.31386 | + | 4.00772i | 0.429673 | + | 0.744215i | 0.996844 | − | 0.0793847i | \(-0.0252955\pi\) |
−0.567171 | + | 0.823600i | \(0.691962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.57301i | 1.36015i | 0.733141 | + | 0.680077i | \(0.238054\pi\) | ||||
−0.733141 | + | 0.680077i | \(0.761946\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.62772 | − | 0.792287i | −0.457427 | − | 0.137919i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.74456 | + | 5.04868i | 1.47810 | + | 0.853382i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.10891i | − | 0.675501i | −0.941236 | − | 0.337750i | \(-0.890334\pi\) | ||
0.941236 | − | 0.337750i | \(-0.109666\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.686141 | − | 2.92048i | −0.109870 | − | 0.467651i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.05842 | − | 8.76144i | 0.789993 | − | 1.36831i | −0.135978 | − | 0.990712i | \(-0.543418\pi\) |
0.925971 | − | 0.377596i | \(-0.123249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.87228 | + | 8.43904i | −0.743016 | + | 1.28694i | 0.208100 | + | 0.978108i | \(0.433272\pi\) |
−0.951116 | + | 0.308834i | \(0.900061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.68614 | − | 11.4333i | −0.847640 | − | 1.70437i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.31386 | + | 1.33591i | −0.337511 | + | 0.194862i | −0.659171 | − | 0.751993i | \(-0.729093\pi\) |
0.321660 | + | 0.946855i | \(0.395759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.37228 | + | 3.16915i | −0.472214 | + | 0.443769i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.68614 | − | 6.38458i | −0.506330 | − | 0.876990i | −0.999973 | − | 0.00732516i | \(-0.997668\pi\) |
0.493643 | − | 0.869665i | \(-0.335665\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37228 | − | 5.84096i | 0.454718 | − | 0.787595i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.87228 | + | 5.76722i | −0.645349 | + | 0.763888i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.68614 | − | 6.38458i | 0.479895 | − | 0.831202i | −0.519839 | − | 0.854264i | \(-0.674008\pi\) |
0.999734 | + | 0.0230621i | \(0.00734155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.87228 | + | 8.43904i | 0.623832 | + | 1.08051i | 0.988766 | + | 0.149475i | \(0.0477583\pi\) |
−0.364934 | + | 0.931033i | \(0.618908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.93070 | − | 3.93398i | −0.747198 | − | 0.495635i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.37228 | 0.914419 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | − | 0.866025i | 0.183254 | − | 0.105802i | −0.405567 | − | 0.914066i | \(-0.632926\pi\) |
0.588821 | + | 0.808264i | \(0.299592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.68614 | − | 7.17687i | −0.202987 | − | 0.863994i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.05842 | + | 8.76144i | −0.600324 | + | 1.03979i | 0.392448 | + | 0.919774i | \(0.371628\pi\) |
−0.992772 | + | 0.120018i | \(0.961705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.12772 | + | 1.95327i | −0.131989 | + | 0.228612i | −0.924443 | − | 0.381319i | \(-0.875470\pi\) |
0.792454 | + | 0.609932i | \(0.208803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.1168 | − | 5.19615i | 2.55383 | − | 0.600000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.75906i | − | 0.428384i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.61684 | − | 4.97494i | −0.969471 | − | 0.559724i | −0.0703959 | − | 0.997519i | \(-0.522426\pi\) |
−0.899075 | + | 0.437795i | \(0.855760\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.51278i | − | 0.934399i | −0.884152 | − | 0.467199i | \(-0.845263\pi\) | ||
0.884152 | − | 0.467199i | \(-0.154737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.68614 | − | 9.84868i | −0.616749 | − | 1.06824i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.80298 | − | 1.83324i | 0.836568 | − | 0.196544i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.68614 | − | 6.38458i | −0.390730 | − | 0.676764i | 0.601816 | − | 0.798635i | \(-0.294444\pi\) |
−0.992546 | + | 0.121870i | \(0.961111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.55842 | − | 2.05446i | 0.373024 | − | 0.215365i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.5584 | + | 3.78651i | 1.30225 | + | 0.392642i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.0584 | − | 14.8974i | −1.13457 | − | 1.52844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1753 | − | 8.76144i | −1.54081 | − | 0.889590i | −0.998788 | − | 0.0492290i | \(-0.984324\pi\) |
−0.542027 | − | 0.840361i | \(-0.682343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.62772 | + | 3.96143i | −0.264096 | + | 0.398139i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.430703 | − | 0.248667i | 0.0428566 | − | 0.0247433i | −0.478419 | − | 0.878132i | \(-0.658790\pi\) |
0.521275 | + | 0.853389i | \(0.325457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.28339i | 0.619121i | 0.950880 | + | 0.309561i | \(0.100182\pi\) | ||||
−0.950880 | + | 0.309561i | \(0.899818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.7446 | − | 11.9769i | 1.24374 | − | 1.16882i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.48913 | 0.530654 | 0.265327 | − | 0.964159i | \(-0.414520\pi\) | ||||
0.265327 | + | 0.964159i | \(0.414520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0584 | + | 6.38458i | 1.05920 | + | 0.611532i | 0.925212 | − | 0.379450i | \(-0.123887\pi\) |
0.133993 | + | 0.990982i | \(0.457220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.81386 | − | 2.05446i | −0.646743 | − | 0.195000i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.74456 | −0.258187 | −0.129093 | − | 0.991632i | \(-0.541207\pi\) | ||||
−0.129093 | + | 0.991632i | \(0.541207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.1168 | 1.68940 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.18614 | − | 0.322405i | −0.479459 | − | 0.0298064i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.48913 | − | 3.16915i | −0.503187 | − | 0.290515i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.48913 | 0.771739 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.0000 | − | 12.7692i | −1.08200 | − | 1.15136i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 34.5484i | 3.09011i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.05842 | + | 1.18843i | −0.182655 | + | 0.105456i | −0.588540 | − | 0.808468i | \(-0.700297\pi\) |
0.405884 | + | 0.913924i | \(0.366964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5584 | + | 12.2993i | 1.01766 | + | 1.08289i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.31386 | + | 1.33591i | 0.202163 | + | 0.116719i | 0.597664 | − | 0.801747i | \(-0.296096\pi\) |
−0.395501 | + | 0.918466i | \(0.629429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.48913 | − | 4.10891i | −0.822812 | − | 0.356288i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.8030 | + | 3.71277i | −1.87650 | + | 0.319544i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8030 | + | 11.4333i | −1.69188 | + | 0.976809i | −0.738886 | + | 0.673831i | \(0.764648\pi\) |
−0.952997 | + | 0.302978i | \(0.902019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.50000 | + | 14.7224i | 0.720961 | + | 1.24874i | 0.960615 | + | 0.277882i | \(0.0896325\pi\) |
−0.239655 | + | 0.970858i | \(0.577034\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.05842 | + | 4.50506i | 0.0891352 | + | 0.379394i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.37228 | − | 2.37686i | −0.114756 | − | 0.198763i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.6974i | 1.63578i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.686141 | + | 2.27567i | −0.0565919 | + | 0.187694i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5475 | − | 9.55373i | −1.35563 | − | 0.782672i | −0.366597 | − | 0.930380i | \(-0.619477\pi\) |
−0.989031 | + | 0.147708i | \(0.952810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.56930 | + | 7.17687i | 0.288561 | + | 0.580216i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.1168 | + | 27.9152i | −1.29454 | + | 2.24220i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.61684 | + | 11.4607i | −0.528082 | + | 0.914664i | 0.471382 | + | 0.881929i | \(0.343755\pi\) |
−0.999464 | + | 0.0327353i | \(0.989578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4307 | + | 2.92048i | −0.985819 | + | 0.231609i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.74456 | − | 5.04868i | 0.689168 | − | 0.397891i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.1168 | 0.870738 | 0.435369 | − | 0.900252i | \(-0.356618\pi\) | ||||
0.435369 | + | 0.900252i | \(0.356618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | − | 8.51278i | −0.622799 | − | 0.662719i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.43070 | − | 11.1383i | −0.497623 | − | 0.861908i | 0.502373 | − | 0.864651i | \(-0.332460\pi\) |
−0.999996 | + | 0.00274283i | \(0.999127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.12772 | + | 10.9634i | 0.545070 | + | 0.838390i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.31386 | − | 4.00772i | 0.175919 | − | 0.304701i | −0.764560 | − | 0.644553i | \(-0.777044\pi\) |
0.940479 | + | 0.339852i | \(0.110377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5584 | + | 26.9480i | 1.17611 | + | 2.03708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.74456 | − | 9.30506i | −0.657282 | − | 0.699411i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.941578 | + | 0.543620i | −0.0699869 | + | 0.0404070i | −0.534585 | − | 0.845115i | \(-0.679532\pi\) |
0.464598 | + | 0.885522i | \(0.346199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.4307 | − | 3.86025i | 1.21459 | − | 0.285358i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.74456 | − | 15.1460i | 0.642913 | − | 1.11356i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.11684 | + | 3.66648i | −0.154799 | + | 0.268120i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.48913 | + | 7.86797i | −0.690232 | + | 0.572310i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.92287i | 0.573279i | 0.958039 | + | 0.286639i | \(0.0925381\pi\) | ||||
−0.958039 | + | 0.286639i | \(0.907462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5000 | − | 6.06218i | −0.755807 | − | 0.436365i | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.68614 | − | 12.2255i | 0.263970 | − | 0.875489i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.75906i | 0.267822i | 0.990993 | + | 0.133911i | \(0.0427536\pi\) | ||||
−0.990993 | + | 0.133911i | \(0.957246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.87228 | − | 3.24289i | −0.132723 | − | 0.229882i | 0.792003 | − | 0.610518i | \(-0.209039\pi\) |
−0.924725 | + | 0.380636i | \(0.875705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.686141 | − | 2.92048i | −0.0483966 | − | 0.205995i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.48913 | + | 9.50744i | 0.385261 | + | 0.667292i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37.2921 | − | 21.5306i | 2.60459 | − | 1.50376i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7446 | − | 0.792287i | −0.885808 | − | 0.0550678i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.74456 | + | 6.33830i | −0.189845 | + | 0.438429i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.73369 | − | 5.61975i | −0.670095 | − | 0.386879i | 0.126018 | − | 0.992028i | \(-0.459780\pi\) |
−0.796113 | + | 0.605149i | \(0.793114\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | + | 12.7692i | 0.822226 | + | 0.874929i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −35.9198 | + | 20.7383i | −2.44971 | + | 1.41434i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.9653i | 1.21957i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.67527 | + | 2.84674i | 0.180778 | + | 0.192365i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.62772 | −0.311294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6168 | − | 8.43904i | −0.978816 | − | 0.565120i | −0.0769037 | − | 0.997039i | \(-0.524503\pi\) |
−0.901913 | + | 0.431919i | \(0.857837\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.44158 | − | 39.2747i | 0.162772 | − | 2.61831i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.9783 | 1.52512 | 0.762560 | − | 0.646917i | \(-0.223942\pi\) | ||||
0.762560 | + | 0.646917i | \(0.223942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.37228 | −0.553256 | −0.276628 | − | 0.960977i | \(-0.589217\pi\) | ||||
−0.276628 | + | 0.960977i | \(0.589217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.23369 | − | 1.87953i | −0.410147 | − | 0.123664i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.68614 | + | 5.59230i | 0.634560 | + | 0.366363i | 0.782516 | − | 0.622630i | \(-0.213936\pi\) |
−0.147956 | + | 0.988994i | \(0.547269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3723 | −0.741846 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.5584 | + | 11.8020i | −0.815757 | + | 0.766619i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.58457i | − | 0.102498i | −0.998686 | − | 0.0512488i | \(-0.983680\pi\) | ||
0.998686 | − | 0.0512488i | \(-0.0163201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6168 | + | 6.70699i | −0.748307 | + | 0.432035i | −0.825082 | − | 0.565013i | \(-0.808871\pi\) |
0.0767751 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5000 | − | 1.65831i | 0.994325 | − | 0.106381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.05842 | − | 2.92048i | −0.323171 | − | 0.186583i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.50000 | + | 0.866025i | −0.477214 | + | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.1168 | − | 4.25639i | −0.894619 | − | 0.269738i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3139 | + | 8.26411i | −0.903483 | + | 0.521626i | −0.878329 | − | 0.478058i | \(-0.841341\pi\) |
−0.0251543 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.37228 | − | 5.84096i | −0.212014 | − | 0.367218i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.1753 | + | 4.50506i | −1.20080 | + | 0.282118i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.941578 | − | 1.63086i | −0.0587340 | − | 0.101730i | 0.835163 | − | 0.550002i | \(-0.185373\pi\) |
−0.893897 | + | 0.448272i | \(0.852040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.74749i | − | 0.605680i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.861407 | − | 13.8564i | 0.0533197 | − | 0.857690i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3139 | + | 8.26411i | 0.882630 | + | 0.509587i | 0.871525 | − | 0.490351i | \(-0.163132\pi\) |
0.0111056 | + | 0.999938i | \(0.496465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 31.3793i | − | 1.92761i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4307 | + | 2.92048i | −0.760747 | + | 0.178731i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.68614 | + | 6.38458i | −0.224748 | + | 0.389275i | −0.956244 | − | 0.292571i | \(-0.905489\pi\) |
0.731496 | + | 0.681846i | \(0.238823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.05842 | − | 5.29734i | 0.185786 | − | 0.321791i | −0.758055 | − | 0.652190i | \(-0.773850\pi\) |
0.943841 | + | 0.330400i | \(0.107184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.62772 | − | 6.92820i | −0.0985140 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0000 | − | 10.3923i | 1.08544 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.51087 | 0.511369 | 0.255684 | − | 0.966760i | \(-0.417699\pi\) | ||||
0.255684 | + | 0.966760i | \(0.417699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.5584 | − | 18.9325i | 0.751853 | − | 1.13346i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.43070 | − | 11.1383i | −0.383624 | − | 0.664456i | 0.607954 | − | 0.793973i | \(-0.291991\pi\) |
−0.991577 | + | 0.129517i | \(0.958657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.68614 | + | 9.84868i | −0.338006 | + | 0.585444i | −0.984058 | − | 0.177850i | \(-0.943086\pi\) |
0.646052 | + | 0.763294i | \(0.276419\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −30.2337 | + | 10.8896i | −1.79089 | + | 0.645046i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | − | 20.7846i | 0.708338 | − | 1.22688i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.93070 | − | 8.54023i | −0.290041 | − | 0.502366i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.1168 | + | 20.7846i | −1.29651 | + | 1.21842i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.2337 | 1.18206 | 0.591032 | − | 0.806648i | \(-0.298721\pi\) | ||||
0.591032 | + | 0.806648i | \(0.298721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.1753 | − | 15.6896i | 1.58221 | − | 0.913487i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.25544 | + | 6.33830i | 0.304951 | + | 0.367785i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.68614 | − | 6.38458i | 0.213175 | − | 0.369230i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5584 | + | 20.0198i | −0.666216 | + | 1.15392i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.197015 | − | 0.838574i | −0.0113182 | − | 0.0481748i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.4766i | 2.37495i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.94158 | − | 5.73977i | −0.567396 | − | 0.327586i | 0.188713 | − | 0.982032i | \(-0.439568\pi\) |
−0.756109 | + | 0.654446i | \(0.772902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4198 | + | 3.14170i | 0.592763 | + | 0.178725i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.2718i | 0.695872i | 0.937518 | + | 0.347936i | \(0.113117\pi\) | ||||
−0.937518 | + | 0.347936i | \(0.886883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.94158 | − | 3.36291i | −0.109744 | − | 0.190083i | 0.805922 | − | 0.592021i | \(-0.201670\pi\) |
−0.915667 | + | 0.401938i | \(0.868337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.4891 | − | 27.1229i | −0.760026 | − | 1.52820i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.941578 | − | 1.63086i | −0.0528843 | − | 0.0915983i | 0.838371 | − | 0.545099i | \(-0.183508\pi\) |
−0.891256 | + | 0.453501i | \(0.850175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.35053 | − | 3.66648i | 0.355562 | − | 0.205284i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.74456 | − | 9.10268i | 0.153187 | − | 0.508062i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.94158 | + | 9.35135i | 0.386240 | + | 0.520323i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.6753 | + | 11.3595i | 1.09139 | + | 0.630113i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.1168 | − | 15.1460i | 0.891264 | − | 0.837577i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.48913 | + | 3.16915i | −0.302625 | + | 0.174721i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.5012i | − | 0.797059i | −0.917156 | − | 0.398529i | \(-0.869521\pi\) | ||
0.917156 | − | 0.398529i | \(-0.130479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.81386 | + | 10.2723i | −0.373397 | + | 0.562917i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.37228 | 0.402791 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.50000 | + | 4.33013i | 0.408551 | + | 0.235877i | 0.690167 | − | 0.723650i | \(-0.257537\pi\) |
−0.281616 | + | 0.959527i | \(0.590870\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.37228 | + | 4.55134i | −0.0745321 | + | 0.247195i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8614 | −1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.05842 | − | 30.0434i | 0.487689 | − | 1.61748i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.68614 | − | 2.12819i | −0.197882 | − | 0.114247i | 0.397785 | − | 0.917479i | \(-0.369779\pi\) |
−0.595667 | + | 0.803231i | \(0.703112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.86141 | −0.0996388 | −0.0498194 | − | 0.998758i | \(-0.515865\pi\) | ||||
−0.0498194 | + | 0.998758i | \(0.515865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.12772 | + | 8.43904i | −0.166945 | + | 0.450443i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2665i | 0.706105i | 0.935604 | + | 0.353052i | \(0.114856\pi\) | ||||
−0.935604 | + | 0.353052i | \(0.885144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.2921 | + | 21.5306i | −1.97926 | + | 1.14273i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | + | 7.51811i | −0.423405 | + | 0.397901i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.6861 | − | 12.5205i | −1.14455 | − | 0.660807i | −0.196997 | − | 0.980404i | \(-0.563119\pi\) |
−0.947553 | + | 0.319597i | \(0.896452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.24456 | − | 14.0776i | 0.222782 | − | 0.738884i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.31386 | + | 4.80001i | −0.435167 | + | 0.251244i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.50000 | − | 6.06218i | −0.182699 | − | 0.316443i | 0.760100 | − | 0.649806i | \(-0.225150\pi\) |
−0.942799 | + | 0.333363i | \(0.891817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.1753 | + | 13.5152i | −1.41469 | + | 0.703571i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.74456 | − | 15.1460i | −0.453995 | − | 0.786343i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 20.7846i | − | 1.07619i | −0.842885 | − | 0.538093i | \(-0.819145\pi\) | ||
0.842885 | − | 0.538093i | \(-0.180855\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 57.2921 | + | 17.2742i | 2.95855 | + | 0.892037i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.94158 | + | 4.00772i | 0.357509 | + | 0.206408i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7908i | 0.811121i | 0.914068 | + | 0.405560i | \(0.132924\pi\) | ||||
−0.914068 | + | 0.405560i | \(0.867076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.941578 | + | 4.00772i | 0.0482385 | + | 0.205322i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.68614 | − | 6.38458i | 0.188353 | − | 0.326237i | −0.756348 | − | 0.654169i | \(-0.773018\pi\) |
0.944701 | + | 0.327932i | \(0.106352\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00000 | − | 13.8564i | 0.407718 | − | 0.706188i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.1753 | − | 13.0178i | 1.33056 | − | 0.661734i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4307 | − | 10.6410i | 0.934474 | − | 0.539519i | 0.0462501 | − | 0.998930i | \(-0.485273\pi\) |
0.888224 | + | 0.459411i | \(0.151940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3723 | −0.575121 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.37228 | − | 3.16915i | 0.170109 | − | 0.159862i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.1753 | − | 36.6766i | −1.06544 | − | 1.84540i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.500000 | − | 0.866025i | 0.0250943 | − | 0.0434646i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.5584 | + | 13.6815i | −0.578645 | + | 0.684931i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.8030 | − | 23.9075i | 0.689288 | − | 1.19388i | −0.282780 | − | 0.959185i | \(-0.591257\pi\) |
0.972068 | − | 0.234697i | \(-0.0754099\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.55842 | + | 11.3595i | 0.326698 | + | 0.565858i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.74456 | + | 38.0125i | −0.235759 | + | 1.88886i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.51087 | −0.322732 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9416 | + | 10.9359i | −0.936601 | + | 0.540747i | −0.888893 | − | 0.458115i | \(-0.848525\pi\) |
−0.0477076 | + | 0.998861i | \(0.515192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.05842 | + | 38.5562i | 0.446819 | + | 1.90184i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.74456 | − | 15.1460i | 0.430292 | − | 0.745287i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.1168 | − | 31.3793i | 0.889321 | − | 1.54035i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.6644 | − | 6.73444i | 1.40370 | − | 0.329787i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2718i | 0.599518i | 0.954015 | + | 0.299759i | \(0.0969063\pi\) | ||||
−0.954015 | + | 0.299759i | \(0.903094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2921 | + | 18.0665i | 1.52508 | + | 0.880508i | 0.999558 | + | 0.0297303i | \(0.00946484\pi\) |
0.525526 | + | 0.850777i | \(0.323868\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000 | + | 0.497333i | 0.388973 | + | 0.0241812i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 35.0458i | − | 1.69997i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.5584 | + | 20.0198i | 0.559351 | + | 0.968825i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.62772 | + | 1.08724i | −0.223428 | + | 0.0524925i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.0584 | + | 29.5461i | 0.821675 | + | 1.42318i | 0.904434 | + | 0.426614i | \(0.140294\pi\) |
−0.0827587 | + | 0.996570i | \(0.526373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7337 | + | 14.2800i | −1.18863 | + | 0.686253i | −0.957994 | − | 0.286788i | \(-0.907412\pi\) |
−0.230631 | + | 0.973041i | \(0.574079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.6644 | + | 9.84868i | 1.56614 | + | 0.472208i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.4307 | + | 2.12819i | −0.881660 | + | 0.101805i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.61684 | + | 3.24289i | 0.268077 | + | 0.154775i | 0.628014 | − | 0.778202i | \(-0.283868\pi\) |
−0.359936 | + | 0.932977i | \(0.617202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.43070 | + | 2.27567i | 0.163367 | + | 0.108365i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.6861 | − | 12.5205i | 1.03034 | − | 0.594867i | 0.113258 | − | 0.993566i | \(-0.463871\pi\) |
0.917082 | + | 0.398699i | \(0.130538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 31.3793i | − | 1.48752i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.1168 | + | 22.6641i | −1.14069 | + | 1.07198i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.25544 | −0.436791 | −0.218396 | − | 0.975860i | \(-0.570082\pi\) | ||||
−0.218396 | + | 0.975860i | \(0.570082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8832 | − | 8.01544i | −0.653732 | − | 0.377433i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.74456 | − | 1.73205i | −0.269903 | − | 0.0813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.4891 | 0.819903 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.3505 | 1.09229 | 0.546146 | − | 0.837690i | \(-0.316094\pi\) | ||||
0.546146 | + | 0.837690i | \(0.316094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6861 | − | 2.33057i | 0.638814 | − | 0.108782i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.9198 | + | 13.8101i | 1.11406 | + | 0.643201i | 0.939877 | − | 0.341512i | \(-0.110939\pi\) |
0.174180 | + | 0.984714i | \(0.444272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3723 | 0.667937 | 0.333968 | − | 0.942584i | \(-0.391612\pi\) | ||||
0.333968 | + | 0.942584i | \(0.391612\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.2337 | + | 40.6844i | 1.77304 | + | 1.88669i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.8511i | 0.687226i | 0.939111 | + | 0.343613i | \(0.111651\pi\) | ||||
−0.939111 | + | 0.343613i | \(0.888349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.55842 | − | 2.05446i | 0.164313 | − | 0.0948660i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.6970 | + | 16.7031i | 0.723280 | + | 0.769640i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.3723 | + | 7.72049i | 0.614858 | + | 0.354989i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.55842 | − | 56.7976i | −0.300921 | − | 2.60605i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.37228 | + | 22.0742i | −0.0628324 | + | 1.01071i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.3139 | + | 8.26411i | −0.654017 | + | 0.377597i | −0.789994 | − | 0.613115i | \(-0.789916\pi\) |
0.135977 | + | 0.990712i | \(0.456583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.55842 | − | 6.16337i | −0.162250 | − | 0.281025i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | − | 17.0256i | −0.182006 | − | 0.774690i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.2921 | − | 64.5918i | −1.69335 | − | 2.93296i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.884861i | − | 0.0400969i | −0.999799 | − | 0.0200484i | \(-0.993618\pi\) | ||
0.999799 | − | 0.0200484i | \(-0.00638204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.55842 | − | 18.4352i | 0.251361 | − | 0.833669i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.6861 | − | 12.5205i | −0.978682 | − | 0.565042i | −0.0768099 | − | 0.997046i | \(-0.524473\pi\) |
−0.901872 | + | 0.432004i | \(0.857807\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.3644i | − | 0.556865i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.1168 | + | 9.01011i | −0.814292 | + | 0.404974i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.0000 | + | 20.7846i | −0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.87228 | + | 8.43904i | −0.218113 | + | 0.377783i | −0.954231 | − | 0.299070i | \(-0.903324\pi\) |
0.736118 | + | 0.676853i | \(0.236657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.6861 | + | 5.09496i | −0.968865 | + | 0.227626i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.9198 | − | 17.2742i | 1.33406 | − | 0.770219i | 0.348140 | − | 0.937443i | \(-0.386813\pi\) |
0.985919 | + | 0.167223i | \(0.0534800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.11684 | 0.0941983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.8614 | + | 12.6217i | 0.526784 | + | 0.560549i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.1753 | − | 26.2843i | −0.672632 | − | 1.16503i | −0.977155 | − | 0.212528i | \(-0.931830\pi\) |
0.304523 | − | 0.952505i | \(-0.401503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.67527 | + | 4.63370i | −0.118347 | + | 0.204983i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.7446 | − | 6.33830i | 0.960046 | − | 0.279843i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.3723 | + | 23.1615i | −0.589253 | + | 1.02062i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.11684 | + | 3.66648i | 0.0930987 | + | 0.161252i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.48913 | − | 5.84096i | −0.240946 | − | 0.256390i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2554 | −0.931218 | −0.465609 | − | 0.884991i | \(-0.654165\pi\) | ||||
−0.465609 | + | 0.884991i | \(0.654165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5000 | − | 7.79423i | 0.590314 | − | 0.340818i | −0.174908 | − | 0.984585i | \(-0.555963\pi\) |
0.765222 | + | 0.643767i | \(0.222629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 52.4674 | − | 12.3267i | 2.28986 | − | 0.537983i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.1168 | − | 17.5229i | 0.440697 | − | 0.763309i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.44158 | + | 4.22894i | −0.106156 | + | 0.183867i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.8030 | + | 9.84868i | −0.859376 | + | 0.427397i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 17.5229i | − | 0.759001i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.2337 | + | 11.6819i | 0.874779 | + | 0.505054i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | − | 19.8997i | 0.258919 | − | 0.858738i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.17448i | 0.0936615i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.6168 | − | 32.2453i | −0.800401 | − | 1.38633i | −0.919353 | − | 0.393435i | \(-0.871287\pi\) |
0.118952 | − | 0.992900i | \(-0.462047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.430703 | + | 1.83324i | 0.0184832 | + | 0.0786719i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.1753 | + | 47.0689i | 1.16406 | + | 2.01621i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.61684 | − | 1.51084i | 0.111888 | − | 0.0645987i | −0.443012 | − | 0.896516i | \(-0.646090\pi\) |
0.554900 | + | 0.831917i | \(0.312757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.81386 | − | 29.1774i | 0.0774136 | − | 1.24526i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.31386 | − | 20.0386i | −0.0985737 | − | 0.853673i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4416 | − | 11.8020i | −0.869264 | − | 0.501870i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.7446 | − | 22.0742i | −0.880558 | − | 0.936999i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.19702 | − | 2.42315i | 0.177833 | − | 0.102672i | −0.408441 | − | 0.912785i | \(-0.633927\pi\) |
0.586274 | + | 0.810113i | \(0.300594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.8781i | 0.713867i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.02175 | + | 5.34363i | 0.212018 | + | 0.225608i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.48913 | 0.231339 | 0.115670 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115670 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1168 | − | 5.84096i | −0.425619 | − | 0.245731i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.30298 | + | 19.6699i | 0.348693 | + | 0.826059i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.2554 | −1.39414 | −0.697070 | − | 0.717003i | \(-0.745513\pi\) | ||||
−0.697070 | + | 0.717003i | \(0.745513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1168 | 0.465225 | 0.232613 | − | 0.972569i | \(-0.425273\pi\) | ||||
0.232613 | + | 0.972569i | \(0.425273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.1386 | + | 3.96143i | 0.548873 | + | 0.165491i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.3505 | + | 27.9152i | 2.01636 | + | 1.16414i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.9783 | 1.03986 | 0.519929 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519929 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.3030 | + | 14.3812i | −0.635970 | + | 0.597662i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.1947i | − | 0.837817i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1168 | + | 5.84096i | −0.418997 | + | 0.241908i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.4307 | − | 12.2255i | −0.762016 | − | 0.505464i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9198 | − | 6.88192i | −0.491984 | − | 0.284047i | 0.233413 | − | 0.972378i | \(-0.425011\pi\) |
−0.725397 | + | 0.688331i | \(0.758344\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.1168 | − | 30.2921i | 0.540470 | − | 1.24816i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.23369 | + | 1.87953i | 0.256420 | + | 0.0773134i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.4307 | − | 10.6410i | 0.756858 | − | 0.436972i | −0.0713083 | − | 0.997454i | \(-0.522717\pi\) |
0.828167 | + | 0.560482i | \(0.189384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4891 | − | 23.3639i | −0.553000 | − | 0.957824i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.31386 | + | 1.48338i | −0.258409 | + | 0.0607109i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.6861 | − | 27.1692i | −0.640918 | − | 1.11010i | −0.985228 | − | 0.171247i | \(-0.945220\pi\) |
0.344310 | − | 0.938856i | \(-0.388113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2549i | 0.785425i | 0.919661 | + | 0.392713i | \(0.128463\pi\) | ||||
−0.919661 | + | 0.392713i | \(0.871537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.18614 | − | 0.322405i | −0.211196 | − | 0.0131293i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.2921 | + | 18.0665i | 1.27221 | + | 0.734508i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.644810i | 0.0261720i | 0.999914 | + | 0.0130860i | \(0.00416553\pi\) | ||||
−0.999914 | + | 0.0130860i | \(0.995834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.5109 | − | 4.34896i | 0.750098 | − | 0.176229i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.31386 | + | 4.00772i | −0.0936087 | + | 0.162135i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3139 | − | 23.0603i | 0.537742 | − | 0.931396i | −0.461284 | − | 0.887253i | \(-0.652611\pi\) |
0.999025 | − | 0.0441432i | \(-0.0140558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.0584 | − | 72.6073i | −0.687862 | − | 2.92781i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.4307 | − | 17.5692i | 1.22509 | − | 0.707308i | 0.259094 | − | 0.965852i | \(-0.416576\pi\) |
0.966000 | + | 0.258544i | \(0.0832426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8832 | 0.839365 | 0.419682 | − | 0.907671i | \(-0.362141\pi\) | ||||
0.419682 | + | 0.907671i | \(0.362141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.68614 | + | 20.7383i | −0.308434 | + | 0.832200i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.74456 | − | 15.1460i | −0.350344 | − | 0.606813i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −40.7337 | + | 70.5528i | −1.62935 | + | 2.82211i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.13859 | + | 7.72049i | 0.364960 | + | 0.308327i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.48913 | + | 9.50744i | −0.218866 | + | 0.379087i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.98913 | − | 15.5696i | −0.357851 | − | 0.619817i | 0.629750 | − | 0.776798i | \(-0.283157\pi\) |
−0.987602 | + | 0.156981i | \(0.949824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.1861 | + | 13.3316i | −0.563848 | + | 0.529884i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1168 | −0.401475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.05842 | + | 1.18843i | −0.0815576 | + | 0.0470873i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.1753 | − | 13.5152i | 1.07504 | − | 0.534652i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.1753 | + | 26.2843i | −0.599387 | + | 1.03817i | 0.393525 | + | 0.919314i | \(0.371256\pi\) |
−0.992912 | + | 0.118855i | \(0.962078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.24456 | − | 3.88770i | 0.0885169 | − | 0.153316i | −0.818368 | − | 0.574695i | \(-0.805121\pi\) |
0.906884 | + | 0.421379i | \(0.138454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.4307 | + | 69.9355i | 0.646958 | + | 2.75371i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 22.3692i | − | 0.879423i | −0.898139 | − | 0.439712i | \(-0.855081\pi\) | ||
0.898139 | − | 0.439712i | \(-0.144919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1168 | − | 5.84096i | −0.397121 | − | 0.229278i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.7921 | + | 8.98266i | 1.16764 | + | 0.352058i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.33830i | 0.248037i | 0.992280 | + | 0.124018i | \(0.0395782\pi\) | ||||
−0.992280 | + | 0.124018i | \(0.960422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.68614 | + | 9.84868i | 0.222176 | + | 0.384820i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.05842 | − | 3.01306i | 0.236362 | − | 0.117550i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.1753 | − | 36.6766i | −0.824871 | − | 1.42872i | −0.902018 | − | 0.431699i | \(-0.857914\pi\) |
0.0771464 | − | 0.997020i | \(-0.475419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2921 | − | 11.1383i | 0.750376 | − | 0.433230i | −0.0754537 | − | 0.997149i | \(-0.524041\pi\) |
0.825830 | + | 0.563919i | \(0.190707\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.31386 | + | 7.67420i | −0.0898629 | + | 0.298041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.2337 | − | 35.3407i | −1.01730 | − | 1.37045i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.0584 | + | 9.84868i | 0.660505 | + | 0.381343i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.3030 | + | 20.0198i | −0.823621 | + | 0.774009i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.3723 | − | 7.72049i | 0.516231 | − | 0.298046i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.0371i | − | 0.425450i | −0.977112 | − | 0.212725i | \(-0.931766\pi\) | ||
0.977112 | − | 0.212725i | \(-0.0682338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −63.9090 | − | 23.6863i | −2.45986 | − | 0.911684i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.2337 | 1.70004 | 0.850019 | − | 0.526751i | \(-0.176590\pi\) | ||||
0.850019 | + | 0.526751i | \(0.176590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0000 | − | 20.7846i | −1.38155 | − | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.4891 | − | 38.1051i | 0.440264 | − | 1.46019i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.4674 | −1.08927 | −0.544637 | − | 0.838672i | \(-0.683333\pi\) | ||||
−0.544637 | + | 0.838672i | \(0.683333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −97.3288 | −3.71874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.18614 | + | 13.8839i | −0.159711 | + | 0.529702i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0584 | − | 6.38458i | −0.421292 | − | 0.243233i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4674 | 1.23512 | 0.617559 | − | 0.786525i | \(-0.288122\pi\) | ||||
0.617559 | + | 0.786525i | \(0.288122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.23369 | + | 9.39764i | −0.236798 | + | 0.356987i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 72.3586i | 2.74472i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.4090 | + | 13.5152i | −0.886677 | + | 0.511923i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.1168 | − | 13.2665i | 0.533948 | − | 0.501785i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9198 | + | 6.88192i | 0.450206 | + | 0.259926i | 0.707917 | − | 0.706296i | \(-0.249635\pi\) |
−0.257711 | + | 0.966222i | \(0.582968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.11684 | + | 16.4356i | −0.268417 | + | 0.619882i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.68614 | + | 18.8588i | −0.214152 | + | 0.710263i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02175 | − | 0.589907i | 0.0384268 | − | 0.0221857i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6168 | − | 21.8530i | −0.473836 | − | 0.820707i | 0.525716 | − | 0.850660i | \(-0.323798\pi\) |
−0.999551 | + | 0.0299531i | \(0.990464\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.2921 | + | 26.7268i | 0.498493 | + | 1.00233i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1168 | + | 27.9152i | 0.603581 | + | 1.04543i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 11.6819i | − | 0.436879i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.62772 | − | 0.792287i | −0.0981340 | − | 0.0295885i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.9198 | − | 6.88192i | −0.444535 | − | 0.256652i | 0.260985 | − | 0.965343i | \(-0.415953\pi\) |
−0.705519 | + | 0.708691i | \(0.749286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9060i | 0.555128i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.31386 | + | 22.6179i | 0.197625 | + | 0.841167i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.3505 | + | 52.5687i | −1.12719 | + | 1.95235i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.5000 | − | 19.9186i | 0.426511 | − | 0.738739i | −0.570049 | − | 0.821611i | \(-0.693076\pi\) |
0.996560 | + | 0.0828714i | \(0.0264091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.5475 | − | 13.0178i | 0.833951 | − | 0.481482i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.00000 | 0.0738717 | 0.0369358 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369358 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.37228 | + | 6.92820i | −0.271931 | + | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.37228 | − | 2.37686i | −0.0505486 | − | 0.0875528i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.50000 | + | 11.2583i | −0.239106 | + | 0.414144i | −0.960458 | − | 0.278425i | \(-0.910188\pi\) |
0.721352 | + | 0.692569i | \(0.243521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.31386 | + | 12.8704i | −0.0850017 | + | 0.472804i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.0584 | + | 39.9384i | −0.845931 | + | 1.46520i | 0.0388784 | + | 0.999244i | \(0.487622\pi\) |
−0.884810 | + | 0.465952i | \(0.845712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.6644 | − | 70.4328i | −1.48983 | − | 2.58046i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1168 | + | 21.2819i | −0.516508 | + | 0.778666i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.0217 | 0.475804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8505 | + | 11.4607i | −0.724356 | + | 0.418207i | −0.816354 | − | 0.577552i | \(-0.804008\pi\) |
0.0919977 | + | 0.995759i | \(0.470675\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.54755 | + | 27.8689i | 0.238606 | + | 1.01560i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.37228 | − | 12.7692i | 0.268305 | − | 0.464718i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5000 | + | 19.9186i | −0.417975 | + | 0.723953i | −0.995736 | − | 0.0922527i | \(-0.970593\pi\) |
0.577761 | + | 0.816206i | \(0.303927\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.3723 | + | 2.67181i | −0.412788 | + | 0.0969807i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.2665i | 0.480910i | 0.970660 | + | 0.240455i | \(0.0772967\pi\) | ||||
−0.970660 | + | 0.240455i | \(0.922703\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.2337 | + | 15.1460i | 0.949723 | + | 0.548323i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.11684 | + | 34.0511i | −0.0765347 | + | 1.23112i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.7692i | − | 0.461068i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.3614 | + | 28.3388i | 0.590007 | + | 1.02192i | 0.994231 | + | 0.107262i | \(0.0342085\pi\) |
−0.404223 | + | 0.914660i | \(0.632458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.17527 | + | 0.746000i | −0.114354 | + | 0.0268665i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.430703 | − | 0.746000i | −0.0154913 | − | 0.0268318i | 0.858176 | − | 0.513356i | \(-0.171598\pi\) |
−0.873667 | + | 0.486524i | \(0.838265\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −86.0258 | + | 49.6670i | −3.09014 | + | 1.78409i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.1644 | − | 4.87375i | −0.579894 | − | 0.174845i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.4090 | + | 26.2843i | −1.26866 | + | 0.941734i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8832 | + | 8.01544i | 0.496778 | + | 0.286815i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.5475 | − | 8.35668i | −0.805784 | − | 0.298644i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.7812 | + | 28.1639i | −1.74108 | + | 1.00521i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22.7190i | − | 0.809846i | −0.914351 | − | 0.404923i | \(-0.867298\pi\) | ||
0.914351 | − | 0.404923i | \(-0.132702\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.8614 | − | 19.6048i | 0.742686 | − | 0.697949i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.51087 | −0.231500 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.6168 | + | 8.43904i | 0.519059 | + | 0.299679i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −52.0367 | − | 15.6896i | −1.84555 | − | 0.556454i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.76631 | −0.133410 | −0.0667048 | − | 0.997773i | \(-0.521249\pi\) | ||||
−0.0667048 | + | 0.997773i | \(0.521249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.13859 | 0.252545 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37228 | + | 22.0742i | −0.0484872 | + | 0.779955i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.09509 | + | 1.78695i | 0.109224 | + | 0.0630602i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 42.9783 | 1.51478 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.74456 | + | 9.30506i | 0.307823 | + | 0.327554i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.74839i | − | 0.202103i | −0.994881 | − | 0.101051i | \(-0.967779\pi\) | ||
0.994881 | − | 0.101051i | \(-0.0322206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.4090 | − | 22.1754i | 1.34872 | − | 0.778684i | 0.360652 | − | 0.932700i | \(-0.382554\pi\) |
0.988068 | + | 0.154016i | \(0.0492207\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.25544 | − | 7.72049i | −0.254459 | − | 0.270769i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.9783 | + | 23.6588i | 1.43541 | + | 0.828732i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1060 | − | 25.3171i | 1.19322 | − | 0.885734i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.3030 | − | 0.764836i | −0.429901 | − | 0.0267255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4307 | − | 7.17687i | 0.433835 | − | 0.250474i | −0.267144 | − | 0.963657i | \(-0.586080\pi\) |
0.700979 | + | 0.713182i | \(0.252747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.05842 | − | 12.2255i | −0.246041 | − | 0.426156i | 0.716383 | − | 0.697708i | \(-0.245796\pi\) |
−0.962424 | + | 0.271552i | \(0.912463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.23369 | − | 35.0458i | −0.286660 | − | 1.22014i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.8030 | + | 34.2998i | 0.688617 | + | 1.19272i | 0.972285 | + | 0.233798i | \(0.0751153\pi\) |
−0.283668 | + | 0.958923i | \(0.591551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.39853i | 0.187499i | 0.995596 | + | 0.0937494i | \(0.0298852\pi\) | ||||
−0.995596 | + | 0.0937494i | \(0.970115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.25544 | − | 14.1137i | 0.147619 | − | 0.489598i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.17527 | + | 1.83324i | 0.110016 | + | 0.0635180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 54.7431i | − | 1.89446i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.1168 | − | 30.2921i | −0.868165 | − | 1.04705i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.9416 | − | 22.4155i | 0.446793 | − | 0.773868i | −0.551382 | − | 0.834253i | \(-0.685899\pi\) |
0.998175 | + | 0.0603847i | \(0.0192328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.79211 | − | 6.56813i | 0.130762 | − | 0.226487i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.6861 | + | 5.09496i | −0.746910 | + | 0.175480i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.8614 | + | 21.2819i | −1.26807 | + | 0.732121i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1386 | 0.691970 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.4891 | + | 14.3537i | 0.462946 | + | 0.492619i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.74456 | − | 15.1460i | −0.299760 | − | 0.519199i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7337 | − | 46.3041i | 0.915344 | − | 1.58542i | 0.108947 | − | 0.994048i | \(-0.465252\pi\) |
0.806397 | − | 0.591375i | \(-0.201415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.94158 | + | 55.5817i | 0.100600 | + | 1.90085i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.80298 | − | 13.5152i | 0.266545 | − | 0.461669i | −0.701422 | − | 0.712746i | \(-0.747451\pi\) |
0.967967 | + | 0.251077i | \(0.0807846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1060 | − | 38.2887i | −0.754246 | − | 1.30639i | −0.945748 | − | 0.324900i | \(-0.894669\pi\) |
0.191502 | − | 0.981492i | \(-0.438664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.4674 | − | 30.2921i | −0.970166 | − | 1.03235i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.4674 | 1.37753 | 0.688763 | − | 0.724987i | \(-0.258154\pi\) | ||||
0.688763 | + | 0.724987i | \(0.258154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.0584 | − | 9.84868i | 0.580004 | − | 0.334865i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.6277 | + | 3.90653i | −0.564707 | + | 0.132673i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.88316 | + | 13.6540i | −0.267418 | + | 0.463181i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50000 | − | 2.59808i | 0.0508256 | − | 0.0880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.4090 | + | 47.0689i | 0.792273 | + | 1.59304i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 81.9586i | 2.77071i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.26631 | + | 3.04051i | 0.177831 | + | 0.102671i | 0.586273 | − | 0.810114i | \(-0.300595\pi\) |
−0.408442 | + | 0.912784i | \(0.633928\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1168 | − | 33.5538i | 0.341233 | − | 1.13174i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.589907i | − | 0.0198745i | −0.999951 | − | 0.00993724i | \(-0.996837\pi\) | ||
0.999951 | − | 0.00993724i | \(-0.00316317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8723 | + | 32.6878i | 0.635103 | + | 1.10003i | 0.986493 | + | 0.163801i | \(0.0523756\pi\) |
−0.351391 | + | 0.936229i | \(0.614291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.4307 | − | 52.9099i | −0.417854 | − | 1.77855i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0584 | + | 39.9384i | 0.774226 | + | 1.34100i | 0.935228 | + | 0.354045i | \(0.115194\pi\) |
−0.161002 | + | 0.986954i | \(0.551473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.88316 | + | 2.81929i | −0.163776 | + | 0.0945560i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1386 | − | 5.54601i | 0.440159 | − | 0.185798i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.5693 | − | 1.33591i | 0.387152 | − | 0.0447044i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.2337 | + | 25.5383i | 1.47857 | + | 0.853652i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.74456 | − | 9.30506i | −0.291972 | − | 0.310687i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.3505 | + | 17.5229i | −1.01225 | + | 0.584421i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.6974i | 0.656215i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4198 | + | 29.1774i | 0.912475 | + | 0.970962i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.62772 | −0.153831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.1753 | − | 20.8858i | −1.20118 | − | 0.693502i | −0.240362 | − | 0.970683i | \(-0.577266\pi\) |
−0.960818 | + | 0.277182i | \(0.910600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.48913 | − | 0.0925740i | −0.0493912 | − | 0.00307048i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4891 | −0.446425 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 68.7812 | + | 20.7383i | 2.27384 | + | 0.685588i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.48913 | + | 3.16915i | 0.181267 | + | 0.104654i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.883156 | −0.0291326 | −0.0145663 | − | 0.999894i | \(-0.504637\pi\) | ||||
−0.0145663 | + | 0.999894i | \(0.504637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.4891 | + | 13.6164i | −0.477433 | + | 0.448674i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.5229i | 0.576773i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.6753 | − | 26.9480i | 1.53467 | − | 0.886044i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.4198 | − | 15.7085i | 0.342232 | − | 0.515934i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.7812 | − | 28.1639i | −1.60046 | − | 0.924026i | −0.991395 | − | 0.130906i | \(-0.958211\pi\) |
−0.609066 | − | 0.793120i | \(-0.708455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.48913 | + | 2.37686i | 0.179899 | + | 0.0778985i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.3505 | + | 6.13592i | 0.666247 | + | 0.200881i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.6060 | + | 9.01011i | −0.510370 | + | 0.294662i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7337 | − | 23.7874i | −0.448660 | − | 0.777102i | 0.549639 | − | 0.835402i | \(-0.314765\pi\) |
−0.998299 | + | 0.0583003i | \(0.981432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.54755 | + | 1.53829i | −0.213671 | + | 0.0502001i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.5693 | + | 20.0386i | 0.377148 | + | 0.653240i | 0.990646 | − | 0.136456i | \(-0.0435714\pi\) |
−0.613498 | + | 0.789696i | \(0.710238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43.0612i | − | 1.40227i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −51.7228 | + | 8.80773i | −1.68254 | + | 0.286516i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.9198 | − | 17.2742i | −0.972264 | − | 0.561337i | −0.0723382 | − | 0.997380i | \(-0.523046\pi\) |
−0.899926 | + | 0.436043i | \(0.856379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.90653i | 0.126811i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.17527 | + | 0.746000i | −0.102965 | + | 0.0241907i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.56930 | − | 9.64630i | 0.180407 | − | 0.312474i | −0.761612 | − | 0.648033i | \(-0.775592\pi\) |
0.942019 | + | 0.335559i | \(0.108925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.8614 | + | 29.2048i | −0.545622 | + | 0.945046i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.90491 | − | 12.3644i | −0.0939023 | − | 0.399684i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.9783 | + | 27.1229i | −1.51701 | + | 0.875844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3505 | −0.850017 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.7228 | − | 9.10268i | −0.442211 | − | 0.293330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.8030 | − | 44.6921i | −0.830627 | − | 1.43869i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.7337 | − | 34.1798i | 0.634593 | − | 1.09915i | −0.352009 | − | 0.935997i | \(-0.614501\pi\) |
0.986601 | − | 0.163150i | \(-0.0521654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9783 | − | 6.83563i | 0.609669 | − | 0.219592i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4307 | − | 42.3152i | 0.784019 | − | 1.35796i | −0.145565 | − | 0.989349i | \(-0.546500\pi\) |
0.929584 | − | 0.368611i | \(-0.120167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.1644 | + | 34.9258i | 0.646441 | + | 1.11967i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.6753 | − | 26.9480i | 0.918343 | − | 0.863026i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.7446 | 1.23955 | 0.619774 | − | 0.784780i | \(-0.287224\pi\) | ||||
0.619774 | + | 0.784780i | \(0.287224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1168 | + | 5.84096i | −0.323336 | + | 0.186678i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0584 | − | 34.2998i | −0.544633 | − | 1.09511i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6644 | − | 46.1841i | 0.850462 | − | 1.47304i | −0.0303300 | − | 0.999540i | \(-0.509656\pi\) |
0.880792 | − | 0.473503i | \(-0.157011\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | + | 13.8564i | −0.254901 | + | 0.441502i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.51087 | + | 10.6873i | 0.0799220 | + | 0.340179i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.4766i | 1.31888i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.7337 | − | 29.8685i | −1.64337 | − | 0.948803i | −0.979622 | − | 0.200851i | \(-0.935629\pi\) |
−0.663753 | − | 0.747952i | \(-0.731037\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0475 | − | 7.25061i | −0.763126 | − | 0.230091i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 15.9383i | − | 0.505279i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.61684 | + | 2.80046i | 0.0512060 | + | 0.0886913i | 0.890492 | − | 0.454998i | \(-0.150360\pi\) |
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.6277 | + | 16.4356i | 0.431162 | + | 0.520001i |
(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 | 912.2.bn.l.65.1 | 4 | ||
3.2 | odd | 2 | 912.2.bn.k.65.1 | 4 | |||
4.3 | odd | 2 | 228.2.p.c.65.2 | ✓ | 4 | ||
12.11 | even | 2 | 228.2.p.d.65.2 | yes | 4 | ||
19.12 | odd | 6 | 912.2.bn.k.449.1 | 4 | |||
57.50 | even | 6 | inner | 912.2.bn.l.449.2 | 4 | ||
76.31 | even | 6 | 228.2.p.d.221.2 | yes | 4 | ||
228.107 | odd | 6 | 228.2.p.c.221.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.p.c.65.2 | ✓ | 4 | 4.3 | odd | 2 | ||
228.2.p.c.221.1 | yes | 4 | 228.107 | odd | 6 | ||
228.2.p.d.65.2 | yes | 4 | 12.11 | even | 2 | ||
228.2.p.d.221.2 | yes | 4 | 76.31 | even | 6 | ||
912.2.bn.k.65.1 | 4 | 3.2 | odd | 2 | |||
912.2.bn.k.449.1 | 4 | 19.12 | odd | 6 | |||
912.2.bn.l.65.1 | 4 | 1.1 | even | 1 | trivial | ||
912.2.bn.l.449.2 | 4 | 57.50 | even | 6 | inner |