Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,2,Mod(123,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.123");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.990144985064\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 123.3 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.123 |
Dual form | 124.2.d.a.123.1 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | −2.44949 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 2.44949 | − | 2.44949i | 1.00000 | − | 1.00000i | ||||
\(7\) | − | 3.00000i | − | 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | −1.00000 | + | 1.00000i | −0.316228 | + | 0.316228i | ||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 4.89898i | 1.41421i | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | 3.00000 | + | 3.00000i | 0.801784 | + | 0.801784i | ||||
\(15\) | −2.44949 | −0.632456 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − | 7.34847i | − | 1.78227i | −0.453743 | − | 0.891133i | \(-0.649911\pi\) | ||
0.453743 | − | 0.891133i | \(-0.350089\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.707107 | + | 0.707107i | ||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | − | 2.00000i | − | 0.447214i | ||||||
\(21\) | 7.34847i | 1.60357i | ||||||||
\(22\) | −4.89898 | + | 4.89898i | −1.04447 | + | 1.04447i | ||||
\(23\) | −2.44949 | −0.510754 | −0.255377 | − | 0.966842i | \(-0.582200\pi\) | ||||
−0.255377 | + | 0.966842i | \(0.582200\pi\) | |||||||
\(24\) | −4.89898 | − | 4.89898i | −1.00000 | − | 1.00000i | ||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 2.44949 | + | 2.44949i | 0.480384 | + | 0.480384i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.00000 | −1.13389 | ||||||||
\(29\) | 2.44949i | 0.454859i | 0.973795 | + | 0.227429i | \(0.0730321\pi\) | ||||
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(30\) | 2.44949 | − | 2.44949i | 0.447214 | − | 0.447214i | ||||
\(31\) | 2.44949 | − | 5.00000i | 0.439941 | − | 0.898027i | ||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | −12.0000 | −2.08893 | ||||||||
\(34\) | 7.34847 | + | 7.34847i | 1.26025 | + | 1.26025i | ||||
\(35\) | − | 3.00000i | − | 0.507093i | ||||||
\(36\) | − | 6.00000i | − | 1.00000i | ||||||
\(37\) | 4.89898i | 0.805387i | 0.915335 | + | 0.402694i | \(0.131926\pi\) | ||||
−0.915335 | + | 0.402694i | \(0.868074\pi\) | |||||||
\(38\) | −1.00000 | − | 1.00000i | −0.162221 | − | 0.162221i | ||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 2.00000 | + | 2.00000i | 0.316228 | + | 0.316228i | ||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | −7.34847 | − | 7.34847i | −1.13389 | − | 1.13389i | ||||
\(43\) | −2.44949 | −0.373544 | −0.186772 | − | 0.982403i | \(-0.559803\pi\) | ||||
−0.186772 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(44\) | − | 9.79796i | − | 1.47710i | ||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 2.44949 | − | 2.44949i | 0.361158 | − | 0.361158i | ||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | 9.79796 | 1.41421 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 4.00000 | − | 4.00000i | 0.565685 | − | 0.565685i | ||||
\(51\) | 18.0000i | 2.52050i | ||||||||
\(52\) | −4.89898 | −0.679366 | ||||||||
\(53\) | 9.79796i | 1.34585i | 0.739709 | + | 0.672927i | \(0.234963\pi\) | ||||
−0.739709 | + | 0.672927i | \(0.765037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898 | 0.660578 | ||||||||
\(56\) | 6.00000 | − | 6.00000i | 0.801784 | − | 0.801784i | ||||
\(57\) | − | 2.44949i | − | 0.324443i | ||||||
\(58\) | −2.44949 | − | 2.44949i | −0.321634 | − | 0.321634i | ||||
\(59\) | 11.0000i | 1.43208i | 0.698060 | + | 0.716039i | \(0.254047\pi\) | ||||
−0.698060 | + | 0.716039i | \(0.745953\pi\) | |||||||
\(60\) | 4.89898i | 0.632456i | ||||||||
\(61\) | − | 12.2474i | − | 1.56813i | −0.620682 | − | 0.784063i | \(-0.713144\pi\) | ||
0.620682 | − | 0.784063i | \(-0.286856\pi\) | |||||||
\(62\) | 2.55051 | + | 7.44949i | 0.323915 | + | 0.946086i | ||||
\(63\) | − | 9.00000i | − | 1.13389i | ||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | − | 2.44949i | − | 0.303822i | ||||||
\(66\) | 12.0000 | − | 12.0000i | 1.47710 | − | 1.47710i | ||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | −14.6969 | −1.78227 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 3.00000 | + | 3.00000i | 0.358569 | + | 0.358569i | ||||
\(71\) | − | 5.00000i | − | 0.593391i | −0.954972 | − | 0.296695i | \(-0.904115\pi\) | ||
0.954972 | − | 0.296695i | \(-0.0958846\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.707107 | + | 0.707107i | ||||
\(73\) | 9.79796i | 1.14676i | 0.819288 | + | 0.573382i | \(0.194369\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | −4.89898 | − | 4.89898i | −0.569495 | − | 0.569495i | ||||
\(75\) | 9.79796 | 1.13137 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | − | 14.6969i | − | 1.67487i | ||||||
\(78\) | −6.00000 | − | 6.00000i | −0.679366 | − | 0.679366i | ||||
\(79\) | −12.2474 | −1.37795 | −0.688973 | − | 0.724787i | \(-0.741938\pi\) | ||||
−0.688973 | + | 0.724787i | \(0.741938\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −7.00000 | + | 7.00000i | −0.773021 | + | 0.773021i | ||||
\(83\) | 9.79796 | 1.07547 | 0.537733 | − | 0.843115i | \(-0.319281\pi\) | ||||
0.537733 | + | 0.843115i | \(0.319281\pi\) | |||||||
\(84\) | 14.6969 | 1.60357 | ||||||||
\(85\) | − | 7.34847i | − | 0.797053i | ||||||
\(86\) | 2.44949 | − | 2.44949i | 0.264135 | − | 0.264135i | ||||
\(87\) | − | 6.00000i | − | 0.643268i | ||||||
\(88\) | 9.79796 | + | 9.79796i | 1.04447 | + | 1.04447i | ||||
\(89\) | 2.44949i | 0.259645i | 0.991537 | + | 0.129823i | \(0.0414408\pi\) | ||||
−0.991537 | + | 0.129823i | \(0.958559\pi\) | |||||||
\(90\) | −3.00000 | + | 3.00000i | −0.316228 | + | 0.316228i | ||||
\(91\) | −7.34847 | −0.770329 | ||||||||
\(92\) | 4.89898i | 0.510754i | ||||||||
\(93\) | −6.00000 | + | 12.2474i | −0.622171 | + | 1.27000i | ||||
\(94\) | −2.00000 | − | 2.00000i | −0.206284 | − | 0.206284i | ||||
\(95\) | 1.00000i | 0.102598i | ||||||||
\(96\) | −9.79796 | + | 9.79796i | −1.00000 | + | 1.00000i | ||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | 2.00000 | − | 2.00000i | 0.202031 | − | 0.202031i | ||||
\(99\) | 14.6969 | 1.47710 | ||||||||
\(100\) | 8.00000i | 0.800000i | ||||||||
\(101\) | −13.0000 | −1.29355 | −0.646774 | − | 0.762682i | \(-0.723882\pi\) | ||||
−0.646774 | + | 0.762682i | \(0.723882\pi\) | |||||||
\(102\) | −18.0000 | − | 18.0000i | −1.78227 | − | 1.78227i | ||||
\(103\) | − | 1.00000i | − | 0.0985329i | −0.998786 | − | 0.0492665i | \(-0.984312\pi\) | ||
0.998786 | − | 0.0492665i | \(-0.0156884\pi\) | |||||||
\(104\) | 4.89898 | − | 4.89898i | 0.480384 | − | 0.480384i | ||||
\(105\) | 7.34847i | 0.717137i | ||||||||
\(106\) | −9.79796 | − | 9.79796i | −0.951662 | − | 0.951662i | ||||
\(107\) | 7.00000i | 0.676716i | 0.941018 | + | 0.338358i | \(0.109871\pi\) | ||||
−0.941018 | + | 0.338358i | \(0.890129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | −4.89898 | + | 4.89898i | −0.467099 | + | 0.467099i | ||||
\(111\) | − | 12.0000i | − | 1.13899i | ||||||
\(112\) | 12.0000i | 1.13389i | ||||||||
\(113\) | −1.00000 | −0.0940721 | −0.0470360 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470360 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(114\) | 2.44949 | + | 2.44949i | 0.229416 | + | 0.229416i | ||||
\(115\) | −2.44949 | −0.228416 | ||||||||
\(116\) | 4.89898 | 0.454859 | ||||||||
\(117\) | − | 7.34847i | − | 0.679366i | ||||||
\(118\) | −11.0000 | − | 11.0000i | −1.01263 | − | 1.01263i | ||||
\(119\) | −22.0454 | −2.02090 | ||||||||
\(120\) | −4.89898 | − | 4.89898i | −0.447214 | − | 0.447214i | ||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 12.2474 | + | 12.2474i | 1.10883 | + | 1.10883i | ||||
\(123\) | −17.1464 | −1.54604 | ||||||||
\(124\) | −10.0000 | − | 4.89898i | −0.898027 | − | 0.439941i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 9.00000 | + | 9.00000i | 0.801784 | + | 0.801784i | ||||
\(127\) | −4.89898 | −0.434714 | −0.217357 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217357 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 2.44949 | + | 2.44949i | 0.214834 | + | 0.214834i | ||||
\(131\) | 10.0000i | 0.873704i | 0.899533 | + | 0.436852i | \(0.143907\pi\) | ||||
−0.899533 | + | 0.436852i | \(0.856093\pi\) | |||||||
\(132\) | 24.0000i | 2.08893i | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | 8.00000 | + | 8.00000i | 0.691095 | + | 0.691095i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.6969 | − | 14.6969i | 1.26025 | − | 1.26025i | ||||
\(137\) | 17.1464i | 1.46492i | 0.680811 | + | 0.732459i | \(0.261627\pi\) | ||||
−0.680811 | + | 0.732459i | \(0.738373\pi\) | |||||||
\(138\) | −6.00000 | + | 6.00000i | −0.510754 | + | 0.510754i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | − | 4.89898i | − | 0.412568i | ||||||
\(142\) | 5.00000 | + | 5.00000i | 0.419591 | + | 0.419591i | ||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 2.44949i | 0.203419i | ||||||||
\(146\) | −9.79796 | − | 9.79796i | −0.810885 | − | 0.810885i | ||||
\(147\) | 4.89898 | 0.404061 | ||||||||
\(148\) | 9.79796 | 0.805387 | ||||||||
\(149\) | 20.0000 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(150\) | −9.79796 | + | 9.79796i | −0.800000 | + | 0.800000i | ||||
\(151\) | 17.1464 | 1.39536 | 0.697678 | − | 0.716411i | \(-0.254217\pi\) | ||||
0.697678 | + | 0.716411i | \(0.254217\pi\) | |||||||
\(152\) | −2.00000 | + | 2.00000i | −0.162221 | + | 0.162221i | ||||
\(153\) | − | 22.0454i | − | 1.78227i | ||||||
\(154\) | 14.6969 | + | 14.6969i | 1.18431 | + | 1.18431i | ||||
\(155\) | 2.44949 | − | 5.00000i | 0.196748 | − | 0.401610i | ||||
\(156\) | 12.0000 | 0.960769 | ||||||||
\(157\) | 3.00000 | 0.239426 | 0.119713 | − | 0.992809i | \(-0.461803\pi\) | ||||
0.119713 | + | 0.992809i | \(0.461803\pi\) | |||||||
\(158\) | 12.2474 | − | 12.2474i | 0.974355 | − | 0.974355i | ||||
\(159\) | − | 24.0000i | − | 1.90332i | ||||||
\(160\) | 4.00000 | − | 4.00000i | 0.316228 | − | 0.316228i | ||||
\(161\) | 7.34847i | 0.579141i | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.707107 | − | 0.707107i | ||||
\(163\) | 9.00000i | 0.704934i | 0.935824 | + | 0.352467i | \(0.114657\pi\) | ||||
−0.935824 | + | 0.352467i | \(0.885343\pi\) | |||||||
\(164\) | − | 14.0000i | − | 1.09322i | ||||||
\(165\) | −12.0000 | −0.934199 | ||||||||
\(166\) | −9.79796 | + | 9.79796i | −0.760469 | + | 0.760469i | ||||
\(167\) | 19.5959 | 1.51638 | 0.758189 | − | 0.652035i | \(-0.226085\pi\) | ||||
0.758189 | + | 0.652035i | \(0.226085\pi\) | |||||||
\(168\) | −14.6969 | + | 14.6969i | −1.13389 | + | 1.13389i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 7.34847 | + | 7.34847i | 0.563602 | + | 0.563602i | ||||
\(171\) | 3.00000i | 0.229416i | ||||||||
\(172\) | 4.89898i | 0.373544i | ||||||||
\(173\) | −16.0000 | −1.21646 | −0.608229 | − | 0.793762i | \(-0.708120\pi\) | ||||
−0.608229 | + | 0.793762i | \(0.708120\pi\) | |||||||
\(174\) | 6.00000 | + | 6.00000i | 0.454859 | + | 0.454859i | ||||
\(175\) | 12.0000i | 0.907115i | ||||||||
\(176\) | −19.5959 | −1.47710 | ||||||||
\(177\) | − | 26.9444i | − | 2.02526i | ||||||
\(178\) | −2.44949 | − | 2.44949i | −0.183597 | − | 0.183597i | ||||
\(179\) | −12.2474 | −0.915417 | −0.457709 | − | 0.889102i | \(-0.651330\pi\) | ||||
−0.457709 | + | 0.889102i | \(0.651330\pi\) | |||||||
\(180\) | − | 6.00000i | − | 0.447214i | ||||||
\(181\) | − | 12.2474i | − | 0.910346i | −0.890403 | − | 0.455173i | \(-0.849577\pi\) | ||
0.890403 | − | 0.455173i | \(-0.150423\pi\) | |||||||
\(182\) | 7.34847 | − | 7.34847i | 0.544705 | − | 0.544705i | ||||
\(183\) | 30.0000i | 2.21766i | ||||||||
\(184\) | −4.89898 | − | 4.89898i | −0.361158 | − | 0.361158i | ||||
\(185\) | 4.89898i | 0.360180i | ||||||||
\(186\) | −6.24745 | − | 18.2474i | −0.458085 | − | 1.33797i | ||||
\(187\) | − | 36.0000i | − | 2.63258i | ||||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000 | − | 1.00000i | −0.0725476 | − | 0.0725476i | ||||
\(191\) | − | 5.00000i | − | 0.361787i | −0.983503 | − | 0.180894i | \(-0.942101\pi\) | ||
0.983503 | − | 0.180894i | \(-0.0578990\pi\) | |||||||
\(192\) | − | 19.5959i | − | 1.41421i | ||||||
\(193\) | 9.00000 | 0.647834 | 0.323917 | − | 0.946085i | \(-0.395000\pi\) | ||||
0.323917 | + | 0.946085i | \(0.395000\pi\) | |||||||
\(194\) | −13.0000 | + | 13.0000i | −0.933346 | + | 0.933346i | ||||
\(195\) | 6.00000i | 0.429669i | ||||||||
\(196\) | 4.00000i | 0.285714i | ||||||||
\(197\) | 4.89898i | 0.349038i | 0.984654 | + | 0.174519i | \(0.0558370\pi\) | ||||
−0.984654 | + | 0.174519i | \(0.944163\pi\) | |||||||
\(198\) | −14.6969 | + | 14.6969i | −1.04447 | + | 1.04447i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −8.00000 | − | 8.00000i | −0.565685 | − | 0.565685i | ||||
\(201\) | 19.5959i | 1.38219i | ||||||||
\(202\) | 13.0000 | − | 13.0000i | 0.914677 | − | 0.914677i | ||||
\(203\) | 7.34847 | 0.515761 | ||||||||
\(204\) | 36.0000 | 2.52050 | ||||||||
\(205\) | 7.00000 | 0.488901 | ||||||||
\(206\) | 1.00000 | + | 1.00000i | 0.0696733 | + | 0.0696733i | ||||
\(207\) | −7.34847 | −0.510754 | ||||||||
\(208\) | 9.79796i | 0.679366i | ||||||||
\(209\) | 4.89898i | 0.338869i | ||||||||
\(210\) | −7.34847 | − | 7.34847i | −0.507093 | − | 0.507093i | ||||
\(211\) | 15.0000i | 1.03264i | 0.856395 | + | 0.516321i | \(0.172699\pi\) | ||||
−0.856395 | + | 0.516321i | \(0.827301\pi\) | |||||||
\(212\) | 19.5959 | 1.34585 | ||||||||
\(213\) | 12.2474i | 0.839181i | ||||||||
\(214\) | −7.00000 | − | 7.00000i | −0.478510 | − | 0.478510i | ||||
\(215\) | −2.44949 | −0.167054 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.0000 | − | 7.34847i | −1.01827 | − | 0.498847i | ||||
\(218\) | −5.00000 | + | 5.00000i | −0.338643 | + | 0.338643i | ||||
\(219\) | − | 24.0000i | − | 1.62177i | ||||||
\(220\) | − | 9.79796i | − | 0.660578i | ||||||
\(221\) | −18.0000 | −1.21081 | ||||||||
\(222\) | 12.0000 | + | 12.0000i | 0.805387 | + | 0.805387i | ||||
\(223\) | −14.6969 | −0.984180 | −0.492090 | − | 0.870544i | \(-0.663767\pi\) | ||||
−0.492090 | + | 0.870544i | \(0.663767\pi\) | |||||||
\(224\) | −12.0000 | − | 12.0000i | −0.801784 | − | 0.801784i | ||||
\(225\) | −12.0000 | −0.800000 | ||||||||
\(226\) | 1.00000 | − | 1.00000i | 0.0665190 | − | 0.0665190i | ||||
\(227\) | 22.0000i | 1.46019i | 0.683345 | + | 0.730096i | \(0.260525\pi\) | ||||
−0.683345 | + | 0.730096i | \(0.739475\pi\) | |||||||
\(228\) | −4.89898 | −0.324443 | ||||||||
\(229\) | − | 9.79796i | − | 0.647467i | −0.946148 | − | 0.323734i | \(-0.895062\pi\) | ||
0.946148 | − | 0.323734i | \(-0.104938\pi\) | |||||||
\(230\) | 2.44949 | − | 2.44949i | 0.161515 | − | 0.161515i | ||||
\(231\) | 36.0000i | 2.36863i | ||||||||
\(232\) | −4.89898 | + | 4.89898i | −0.321634 | + | 0.321634i | ||||
\(233\) | −1.00000 | −0.0655122 | −0.0327561 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327561 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(234\) | 7.34847 | + | 7.34847i | 0.480384 | + | 0.480384i | ||||
\(235\) | 2.00000i | 0.130466i | ||||||||
\(236\) | 22.0000 | 1.43208 | ||||||||
\(237\) | 30.0000 | 1.94871 | ||||||||
\(238\) | 22.0454 | − | 22.0454i | 1.42899 | − | 1.42899i | ||||
\(239\) | 12.2474 | 0.792222 | 0.396111 | − | 0.918203i | \(-0.370360\pi\) | ||||
0.396111 | + | 0.918203i | \(0.370360\pi\) | |||||||
\(240\) | 9.79796 | 0.632456 | ||||||||
\(241\) | 24.4949i | 1.57786i | 0.614486 | + | 0.788928i | \(0.289363\pi\) | ||||
−0.614486 | + | 0.788928i | \(0.710637\pi\) | |||||||
\(242\) | −13.0000 | + | 13.0000i | −0.835672 | + | 0.835672i | ||||
\(243\) | 22.0454 | 1.41421 | ||||||||
\(244\) | −24.4949 | −1.56813 | ||||||||
\(245\) | −2.00000 | −0.127775 | ||||||||
\(246\) | 17.1464 | − | 17.1464i | 1.09322 | − | 1.09322i | ||||
\(247\) | 2.44949 | 0.155857 | ||||||||
\(248\) | 14.8990 | − | 5.10102i | 0.946086 | − | 0.323915i | ||||
\(249\) | −24.0000 | −1.52094 | ||||||||
\(250\) | 9.00000 | − | 9.00000i | 0.569210 | − | 0.569210i | ||||
\(251\) | −7.34847 | −0.463831 | −0.231916 | − | 0.972736i | \(-0.574499\pi\) | ||||
−0.231916 | + | 0.972736i | \(0.574499\pi\) | |||||||
\(252\) | −18.0000 | −1.13389 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 4.89898 | − | 4.89898i | 0.307389 | − | 0.307389i | ||||
\(255\) | 18.0000i | 1.12720i | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 13.0000 | 0.810918 | 0.405459 | − | 0.914113i | \(-0.367112\pi\) | ||||
0.405459 | + | 0.914113i | \(0.367112\pi\) | |||||||
\(258\) | −6.00000 | + | 6.00000i | −0.373544 | + | 0.373544i | ||||
\(259\) | 14.6969 | 0.913223 | ||||||||
\(260\) | −4.89898 | −0.303822 | ||||||||
\(261\) | 7.34847i | 0.454859i | ||||||||
\(262\) | −10.0000 | − | 10.0000i | −0.617802 | − | 0.617802i | ||||
\(263\) | −2.44949 | −0.151042 | −0.0755210 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755210 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(264\) | −24.0000 | − | 24.0000i | −1.47710 | − | 1.47710i | ||||
\(265\) | 9.79796i | 0.601884i | ||||||||
\(266\) | −3.00000 | + | 3.00000i | −0.183942 | + | 0.183942i | ||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | −16.0000 | −0.977356 | ||||||||
\(269\) | − | 9.79796i | − | 0.597392i | −0.954348 | − | 0.298696i | \(-0.903448\pi\) | ||
0.954348 | − | 0.298696i | \(-0.0965517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.34847 | −0.446388 | −0.223194 | − | 0.974774i | \(-0.571648\pi\) | ||||
−0.223194 | + | 0.974774i | \(0.571648\pi\) | |||||||
\(272\) | 29.3939i | 1.78227i | ||||||||
\(273\) | 18.0000 | 1.08941 | ||||||||
\(274\) | −17.1464 | − | 17.1464i | −1.03585 | − | 1.03585i | ||||
\(275\) | −19.5959 | −1.18168 | ||||||||
\(276\) | − | 12.0000i | − | 0.722315i | ||||||
\(277\) | 17.1464i | 1.03023i | 0.857121 | + | 0.515115i | \(0.172251\pi\) | ||||
−0.857121 | + | 0.515115i | \(0.827749\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.34847 | − | 15.0000i | 0.439941 | − | 0.898027i | ||||
\(280\) | 6.00000 | − | 6.00000i | 0.358569 | − | 0.358569i | ||||
\(281\) | −13.0000 | −0.775515 | −0.387757 | − | 0.921761i | \(-0.626750\pi\) | ||||
−0.387757 | + | 0.921761i | \(0.626750\pi\) | |||||||
\(282\) | 4.89898 | + | 4.89898i | 0.291730 | + | 0.291730i | ||||
\(283\) | − | 6.00000i | − | 0.356663i | −0.983970 | − | 0.178331i | \(-0.942930\pi\) | ||
0.983970 | − | 0.178331i | \(-0.0570699\pi\) | |||||||
\(284\) | −10.0000 | −0.593391 | ||||||||
\(285\) | − | 2.44949i | − | 0.145095i | ||||||
\(286\) | 12.0000 | + | 12.0000i | 0.709575 | + | 0.709575i | ||||
\(287\) | − | 21.0000i | − | 1.23959i | ||||||
\(288\) | 12.0000 | − | 12.0000i | 0.707107 | − | 0.707107i | ||||
\(289\) | −37.0000 | −2.17647 | ||||||||
\(290\) | −2.44949 | − | 2.44949i | −0.143839 | − | 0.143839i | ||||
\(291\) | −31.8434 | −1.86669 | ||||||||
\(292\) | 19.5959 | 1.14676 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | −4.89898 | + | 4.89898i | −0.285714 | + | 0.285714i | ||||
\(295\) | 11.0000i | 0.640445i | ||||||||
\(296\) | −9.79796 | + | 9.79796i | −0.569495 | + | 0.569495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0000 | + | 20.0000i | −1.15857 | + | 1.15857i | ||||
\(299\) | 6.00000i | 0.346989i | ||||||||
\(300\) | − | 19.5959i | − | 1.13137i | ||||||
\(301\) | 7.34847i | 0.423559i | ||||||||
\(302\) | −17.1464 | + | 17.1464i | −0.986666 | + | 0.986666i | ||||
\(303\) | 31.8434 | 1.82935 | ||||||||
\(304\) | − | 4.00000i | − | 0.229416i | ||||||
\(305\) | − | 12.2474i | − | 0.701287i | ||||||
\(306\) | 22.0454 | + | 22.0454i | 1.26025 | + | 1.26025i | ||||
\(307\) | − | 13.0000i | − | 0.741949i | −0.928643 | − | 0.370975i | \(-0.879024\pi\) | ||
0.928643 | − | 0.370975i | \(-0.120976\pi\) | |||||||
\(308\) | −29.3939 | −1.67487 | ||||||||
\(309\) | 2.44949i | 0.139347i | ||||||||
\(310\) | 2.55051 | + | 7.44949i | 0.144859 | + | 0.423103i | ||||
\(311\) | 5.00000i | 0.283524i | 0.989901 | + | 0.141762i | \(0.0452768\pi\) | ||||
−0.989901 | + | 0.141762i | \(0.954723\pi\) | |||||||
\(312\) | −12.0000 | + | 12.0000i | −0.679366 | + | 0.679366i | ||||
\(313\) | − | 26.9444i | − | 1.52299i | −0.648173 | − | 0.761493i | \(-0.724466\pi\) | ||
0.648173 | − | 0.761493i | \(-0.275534\pi\) | |||||||
\(314\) | −3.00000 | + | 3.00000i | −0.169300 | + | 0.169300i | ||||
\(315\) | − | 9.00000i | − | 0.507093i | ||||||
\(316\) | 24.4949i | 1.37795i | ||||||||
\(317\) | −17.0000 | −0.954815 | −0.477408 | − | 0.878682i | \(-0.658423\pi\) | ||||
−0.477408 | + | 0.878682i | \(0.658423\pi\) | |||||||
\(318\) | 24.0000 | + | 24.0000i | 1.34585 | + | 1.34585i | ||||
\(319\) | 12.0000i | 0.671871i | ||||||||
\(320\) | 8.00000i | 0.447214i | ||||||||
\(321\) | − | 17.1464i | − | 0.957020i | ||||||
\(322\) | −7.34847 | − | 7.34847i | −0.409514 | − | 0.409514i | ||||
\(323\) | 7.34847 | 0.408880 | ||||||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 9.79796i | 0.543493i | ||||||||
\(326\) | −9.00000 | − | 9.00000i | −0.498464 | − | 0.498464i | ||||
\(327\) | −12.2474 | −0.677285 | ||||||||
\(328\) | 14.0000 | + | 14.0000i | 0.773021 | + | 0.773021i | ||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | 12.0000 | − | 12.0000i | 0.660578 | − | 0.660578i | ||||
\(331\) | 4.89898 | 0.269272 | 0.134636 | − | 0.990895i | \(-0.457013\pi\) | ||||
0.134636 | + | 0.990895i | \(0.457013\pi\) | |||||||
\(332\) | − | 19.5959i | − | 1.07547i | ||||||
\(333\) | 14.6969i | 0.805387i | ||||||||
\(334\) | −19.5959 | + | 19.5959i | −1.07224 | + | 1.07224i | ||||
\(335\) | − | 8.00000i | − | 0.437087i | ||||||
\(336\) | − | 29.3939i | − | 1.60357i | ||||||
\(337\) | − | 7.34847i | − | 0.400297i | −0.979766 | − | 0.200148i | \(-0.935858\pi\) | ||
0.979766 | − | 0.200148i | \(-0.0641424\pi\) | |||||||
\(338\) | −7.00000 | + | 7.00000i | −0.380750 | + | 0.380750i | ||||
\(339\) | 2.44949 | 0.133038 | ||||||||
\(340\) | −14.6969 | −0.797053 | ||||||||
\(341\) | 12.0000 | − | 24.4949i | 0.649836 | − | 1.32647i | ||||
\(342\) | −3.00000 | − | 3.00000i | −0.162221 | − | 0.162221i | ||||
\(343\) | − | 15.0000i | − | 0.809924i | ||||||
\(344\) | −4.89898 | − | 4.89898i | −0.264135 | − | 0.264135i | ||||
\(345\) | 6.00000 | 0.323029 | ||||||||
\(346\) | 16.0000 | − | 16.0000i | 0.860165 | − | 0.860165i | ||||
\(347\) | 7.34847 | 0.394486 | 0.197243 | − | 0.980355i | \(-0.436801\pi\) | ||||
0.197243 | + | 0.980355i | \(0.436801\pi\) | |||||||
\(348\) | −12.0000 | −0.643268 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −12.0000 | − | 12.0000i | −0.641427 | − | 0.641427i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.5959 | − | 19.5959i | 1.04447 | − | 1.04447i | ||||
\(353\) | − | 14.6969i | − | 0.782239i | −0.920340 | − | 0.391120i | \(-0.872088\pi\) | ||
0.920340 | − | 0.391120i | \(-0.127912\pi\) | |||||||
\(354\) | 26.9444 | + | 26.9444i | 1.43208 | + | 1.43208i | ||||
\(355\) | − | 5.00000i | − | 0.265372i | ||||||
\(356\) | 4.89898 | 0.259645 | ||||||||
\(357\) | 54.0000 | 2.85798 | ||||||||
\(358\) | 12.2474 | − | 12.2474i | 0.647298 | − | 0.647298i | ||||
\(359\) | − | 29.0000i | − | 1.53056i | −0.643697 | − | 0.765281i | \(-0.722600\pi\) | ||
0.643697 | − | 0.765281i | \(-0.277400\pi\) | |||||||
\(360\) | 6.00000 | + | 6.00000i | 0.316228 | + | 0.316228i | ||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 12.2474 | + | 12.2474i | 0.643712 | + | 0.643712i | ||||
\(363\) | −31.8434 | −1.67134 | ||||||||
\(364\) | 14.6969i | 0.770329i | ||||||||
\(365\) | 9.79796i | 0.512849i | ||||||||
\(366\) | −30.0000 | − | 30.0000i | −1.56813 | − | 1.56813i | ||||
\(367\) | −4.89898 | −0.255725 | −0.127862 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127862 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(368\) | 9.79796 | 0.510754 | ||||||||
\(369\) | 21.0000 | 1.09322 | ||||||||
\(370\) | −4.89898 | − | 4.89898i | −0.254686 | − | 0.254686i | ||||
\(371\) | 29.3939 | 1.52605 | ||||||||
\(372\) | 24.4949 | + | 12.0000i | 1.27000 | + | 0.622171i | ||||
\(373\) | 19.0000 | 0.983783 | 0.491891 | − | 0.870657i | \(-0.336306\pi\) | ||||
0.491891 | + | 0.870657i | \(0.336306\pi\) | |||||||
\(374\) | 36.0000 | + | 36.0000i | 1.86152 | + | 1.86152i | ||||
\(375\) | 22.0454 | 1.13842 | ||||||||
\(376\) | −4.00000 | + | 4.00000i | −0.206284 | + | 0.206284i | ||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.00000i | 0.308199i | 0.988055 | + | 0.154100i | \(0.0492477\pi\) | ||||
−0.988055 | + | 0.154100i | \(0.950752\pi\) | |||||||
\(380\) | 2.00000 | 0.102598 | ||||||||
\(381\) | 12.0000 | 0.614779 | ||||||||
\(382\) | 5.00000 | + | 5.00000i | 0.255822 | + | 0.255822i | ||||
\(383\) | −14.6969 | −0.750978 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(384\) | 19.5959 | + | 19.5959i | 1.00000 | + | 1.00000i | ||||
\(385\) | − | 14.6969i | − | 0.749025i | ||||||
\(386\) | −9.00000 | + | 9.00000i | −0.458088 | + | 0.458088i | ||||
\(387\) | −7.34847 | −0.373544 | ||||||||
\(388\) | − | 26.0000i | − | 1.31995i | ||||||
\(389\) | 14.6969i | 0.745164i | 0.927999 | + | 0.372582i | \(0.121528\pi\) | ||||
−0.927999 | + | 0.372582i | \(0.878472\pi\) | |||||||
\(390\) | −6.00000 | − | 6.00000i | −0.303822 | − | 0.303822i | ||||
\(391\) | 18.0000i | 0.910299i | ||||||||
\(392\) | −4.00000 | − | 4.00000i | −0.202031 | − | 0.202031i | ||||
\(393\) | − | 24.4949i | − | 1.23560i | ||||||
\(394\) | −4.89898 | − | 4.89898i | −0.246807 | − | 0.246807i | ||||
\(395\) | −12.2474 | −0.616236 | ||||||||
\(396\) | − | 29.3939i | − | 1.47710i | ||||||
\(397\) | −17.0000 | −0.853206 | −0.426603 | − | 0.904439i | \(-0.640290\pi\) | ||||
−0.426603 | + | 0.904439i | \(0.640290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.34847 | −0.367884 | ||||||||
\(400\) | 16.0000 | 0.800000 | ||||||||
\(401\) | 12.2474i | 0.611608i | 0.952094 | + | 0.305804i | \(0.0989253\pi\) | ||||
−0.952094 | + | 0.305804i | \(0.901075\pi\) | |||||||
\(402\) | −19.5959 | − | 19.5959i | −0.977356 | − | 0.977356i | ||||
\(403\) | −12.2474 | − | 6.00000i | −0.610089 | − | 0.298881i | ||||
\(404\) | 26.0000i | 1.29355i | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | −7.34847 | + | 7.34847i | −0.364698 | + | 0.364698i | ||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | −36.0000 | + | 36.0000i | −1.78227 | + | 1.78227i | ||||
\(409\) | − | 22.0454i | − | 1.09008i | −0.838412 | − | 0.545038i | \(-0.816515\pi\) | ||
0.838412 | − | 0.545038i | \(-0.183485\pi\) | |||||||
\(410\) | −7.00000 | + | 7.00000i | −0.345705 | + | 0.345705i | ||||
\(411\) | − | 42.0000i | − | 2.07171i | ||||||
\(412\) | −2.00000 | −0.0985329 | ||||||||
\(413\) | 33.0000 | 1.62382 | ||||||||
\(414\) | 7.34847 | − | 7.34847i | 0.361158 | − | 0.361158i | ||||
\(415\) | 9.79796 | 0.480963 | ||||||||
\(416\) | −9.79796 | − | 9.79796i | −0.480384 | − | 0.480384i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.89898 | − | 4.89898i | −0.239617 | − | 0.239617i | ||||
\(419\) | 1.00000i | 0.0488532i | 0.999702 | + | 0.0244266i | \(0.00777600\pi\) | ||||
−0.999702 | + | 0.0244266i | \(0.992224\pi\) | |||||||
\(420\) | 14.6969 | 0.717137 | ||||||||
\(421\) | −33.0000 | −1.60832 | −0.804161 | − | 0.594412i | \(-0.797385\pi\) | ||||
−0.804161 | + | 0.594412i | \(0.797385\pi\) | |||||||
\(422\) | −15.0000 | − | 15.0000i | −0.730189 | − | 0.730189i | ||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | −19.5959 | + | 19.5959i | −0.951662 | + | 0.951662i | ||||
\(425\) | 29.3939i | 1.42581i | ||||||||
\(426\) | −12.2474 | − | 12.2474i | −0.593391 | − | 0.593391i | ||||
\(427\) | −36.7423 | −1.77809 | ||||||||
\(428\) | 14.0000 | 0.676716 | ||||||||
\(429\) | 29.3939i | 1.41915i | ||||||||
\(430\) | 2.44949 | − | 2.44949i | 0.118125 | − | 0.118125i | ||||
\(431\) | 20.0000i | 0.963366i | 0.876346 | + | 0.481683i | \(0.159974\pi\) | ||||
−0.876346 | + | 0.481683i | \(0.840026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.0454i | 1.05943i | 0.848174 | + | 0.529717i | \(0.177702\pi\) | ||||
−0.848174 | + | 0.529717i | \(0.822298\pi\) | |||||||
\(434\) | 22.3485 | − | 7.65153i | 1.07276 | − | 0.367285i | ||||
\(435\) | − | 6.00000i | − | 0.287678i | ||||||
\(436\) | − | 10.0000i | − | 0.478913i | ||||||
\(437\) | − | 2.44949i | − | 0.117175i | ||||||
\(438\) | 24.0000 | + | 24.0000i | 1.14676 | + | 1.14676i | ||||
\(439\) | 31.0000i | 1.47955i | 0.672855 | + | 0.739775i | \(0.265068\pi\) | ||||
−0.672855 | + | 0.739775i | \(0.734932\pi\) | |||||||
\(440\) | 9.79796 | + | 9.79796i | 0.467099 | + | 0.467099i | ||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 18.0000 | − | 18.0000i | 0.856173 | − | 0.856173i | ||||
\(443\) | − | 11.0000i | − | 0.522626i | −0.965254 | − | 0.261313i | \(-0.915845\pi\) | ||
0.965254 | − | 0.261313i | \(-0.0841554\pi\) | |||||||
\(444\) | −24.0000 | −1.13899 | ||||||||
\(445\) | 2.44949i | 0.116117i | ||||||||
\(446\) | 14.6969 | − | 14.6969i | 0.695920 | − | 0.695920i | ||||
\(447\) | −48.9898 | −2.31714 | ||||||||
\(448\) | 24.0000 | 1.13389 | ||||||||
\(449\) | − | 9.79796i | − | 0.462394i | −0.972907 | − | 0.231197i | \(-0.925736\pi\) | ||
0.972907 | − | 0.231197i | \(-0.0742642\pi\) | |||||||
\(450\) | 12.0000 | − | 12.0000i | 0.565685 | − | 0.565685i | ||||
\(451\) | 34.2929 | 1.61479 | ||||||||
\(452\) | 2.00000i | 0.0940721i | ||||||||
\(453\) | −42.0000 | −1.97333 | ||||||||
\(454\) | −22.0000 | − | 22.0000i | −1.03251 | − | 1.03251i | ||||
\(455\) | −7.34847 | −0.344502 | ||||||||
\(456\) | 4.89898 | − | 4.89898i | 0.229416 | − | 0.229416i | ||||
\(457\) | 4.89898i | 0.229165i | 0.993414 | + | 0.114582i | \(0.0365530\pi\) | ||||
−0.993414 | + | 0.114582i | \(0.963447\pi\) | |||||||
\(458\) | 9.79796 | + | 9.79796i | 0.457829 | + | 0.457829i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.89898i | 0.228416i | ||||||||
\(461\) | − | 24.4949i | − | 1.14084i | −0.821353 | − | 0.570421i | \(-0.806780\pi\) | ||
0.821353 | − | 0.570421i | \(-0.193220\pi\) | |||||||
\(462\) | −36.0000 | − | 36.0000i | −1.67487 | − | 1.67487i | ||||
\(463\) | 34.2929 | 1.59372 | 0.796862 | − | 0.604161i | \(-0.206492\pi\) | ||||
0.796862 | + | 0.604161i | \(0.206492\pi\) | |||||||
\(464\) | − | 9.79796i | − | 0.454859i | ||||||
\(465\) | −6.00000 | + | 12.2474i | −0.278243 | + | 0.567962i | ||||
\(466\) | 1.00000 | − | 1.00000i | 0.0463241 | − | 0.0463241i | ||||
\(467\) | − | 13.0000i | − | 0.601568i | −0.953692 | − | 0.300784i | \(-0.902752\pi\) | ||
0.953692 | − | 0.300784i | \(-0.0972484\pi\) | |||||||
\(468\) | −14.6969 | −0.679366 | ||||||||
\(469\) | −24.0000 | −1.10822 | ||||||||
\(470\) | −2.00000 | − | 2.00000i | −0.0922531 | − | 0.0922531i | ||||
\(471\) | −7.34847 | −0.338600 | ||||||||
\(472\) | −22.0000 | + | 22.0000i | −1.01263 | + | 1.01263i | ||||
\(473\) | −12.0000 | −0.551761 | ||||||||
\(474\) | −30.0000 | + | 30.0000i | −1.37795 | + | 1.37795i | ||||
\(475\) | − | 4.00000i | − | 0.183533i | ||||||
\(476\) | 44.0908i | 2.02090i | ||||||||
\(477\) | 29.3939i | 1.34585i | ||||||||
\(478\) | −12.2474 | + | 12.2474i | −0.560185 | + | 0.560185i | ||||
\(479\) | 11.0000i | 0.502603i | 0.967909 | + | 0.251301i | \(0.0808585\pi\) | ||||
−0.967909 | + | 0.251301i | \(0.919141\pi\) | |||||||
\(480\) | −9.79796 | + | 9.79796i | −0.447214 | + | 0.447214i | ||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | −24.4949 | − | 24.4949i | −1.11571 | − | 1.11571i | ||||
\(483\) | − | 18.0000i | − | 0.819028i | ||||||
\(484\) | − | 26.0000i | − | 1.18182i | ||||||
\(485\) | 13.0000 | 0.590300 | ||||||||
\(486\) | −22.0454 | + | 22.0454i | −1.00000 | + | 1.00000i | ||||
\(487\) | 31.8434 | 1.44296 | 0.721480 | − | 0.692435i | \(-0.243462\pi\) | ||||
0.721480 | + | 0.692435i | \(0.243462\pi\) | |||||||
\(488\) | 24.4949 | − | 24.4949i | 1.10883 | − | 1.10883i | ||||
\(489\) | − | 22.0454i | − | 0.996928i | ||||||
\(490\) | 2.00000 | − | 2.00000i | 0.0903508 | − | 0.0903508i | ||||
\(491\) | 29.3939 | 1.32653 | 0.663264 | − | 0.748386i | \(-0.269171\pi\) | ||||
0.663264 | + | 0.748386i | \(0.269171\pi\) | |||||||
\(492\) | 34.2929i | 1.54604i | ||||||||
\(493\) | 18.0000 | 0.810679 | ||||||||
\(494\) | −2.44949 | + | 2.44949i | −0.110208 | + | 0.110208i | ||||
\(495\) | 14.6969 | 0.660578 | ||||||||
\(496\) | −9.79796 | + | 20.0000i | −0.439941 | + | 0.898027i | ||||
\(497\) | −15.0000 | −0.672842 | ||||||||
\(498\) | 24.0000 | − | 24.0000i | 1.07547 | − | 1.07547i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 18.0000i | 0.804984i | ||||||||
\(501\) | −48.0000 | −2.14448 | ||||||||
\(502\) | 7.34847 | − | 7.34847i | 0.327978 | − | 0.327978i | ||||
\(503\) | − | 11.0000i | − | 0.490466i | −0.969464 | − | 0.245233i | \(-0.921136\pi\) | ||
0.969464 | − | 0.245233i | \(-0.0788644\pi\) | |||||||
\(504\) | 18.0000 | − | 18.0000i | 0.801784 | − | 0.801784i | ||||
\(505\) | −13.0000 | −0.578492 | ||||||||
\(506\) | 12.0000 | − | 12.0000i | 0.533465 | − | 0.533465i | ||||
\(507\) | −17.1464 | −0.761500 | ||||||||
\(508\) | 9.79796i | 0.434714i | ||||||||
\(509\) | − | 22.0454i | − | 0.977146i | −0.872523 | − | 0.488573i | \(-0.837518\pi\) | ||
0.872523 | − | 0.488573i | \(-0.162482\pi\) | |||||||
\(510\) | −18.0000 | − | 18.0000i | −0.797053 | − | 0.797053i | ||||
\(511\) | 29.3939 | 1.30031 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.0000 | + | 13.0000i | −0.573405 | + | 0.573405i | ||||
\(515\) | − | 1.00000i | − | 0.0440653i | ||||||
\(516\) | − | 12.0000i | − | 0.528271i | ||||||
\(517\) | 9.79796i | 0.430914i | ||||||||
\(518\) | −14.6969 | + | 14.6969i | −0.645746 | + | 0.645746i | ||||
\(519\) | 39.1918 | 1.72033 | ||||||||
\(520\) | 4.89898 | − | 4.89898i | 0.214834 | − | 0.214834i | ||||
\(521\) | −8.00000 | −0.350486 | −0.175243 | − | 0.984525i | \(-0.556071\pi\) | ||||
−0.175243 | + | 0.984525i | \(0.556071\pi\) | |||||||
\(522\) | −7.34847 | − | 7.34847i | −0.321634 | − | 0.321634i | ||||
\(523\) | −2.44949 | −0.107109 | −0.0535544 | − | 0.998565i | \(-0.517055\pi\) | ||||
−0.0535544 | + | 0.998565i | \(0.517055\pi\) | |||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | − | 29.3939i | − | 1.28285i | ||||||
\(526\) | 2.44949 | − | 2.44949i | 0.106803 | − | 0.106803i | ||||
\(527\) | −36.7423 | − | 18.0000i | −1.60052 | − | 0.784092i | ||||
\(528\) | 48.0000 | 2.08893 | ||||||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | −9.79796 | − | 9.79796i | −0.425596 | − | 0.425596i | ||||
\(531\) | 33.0000i | 1.43208i | ||||||||
\(532\) | − | 6.00000i | − | 0.260133i | ||||||
\(533\) | − | 17.1464i | − | 0.742694i | ||||||
\(534\) | 6.00000 | + | 6.00000i | 0.259645 | + | 0.259645i | ||||
\(535\) | 7.00000i | 0.302636i | ||||||||
\(536\) | 16.0000 | − | 16.0000i | 0.691095 | − | 0.691095i | ||||
\(537\) | 30.0000 | 1.29460 | ||||||||
\(538\) | 9.79796 | + | 9.79796i | 0.422420 | + | 0.422420i | ||||
\(539\) | −9.79796 | −0.422028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | −0.128980 | −0.0644900 | − | 0.997918i | \(-0.520542\pi\) | ||||
−0.0644900 | + | 0.997918i | \(0.520542\pi\) | |||||||
\(542\) | 7.34847 | − | 7.34847i | 0.315644 | − | 0.315644i | ||||
\(543\) | 30.0000i | 1.28742i | ||||||||
\(544\) | −29.3939 | − | 29.3939i | −1.26025 | − | 1.26025i | ||||
\(545\) | 5.00000 | 0.214176 | ||||||||
\(546\) | −18.0000 | + | 18.0000i | −0.770329 | + | 0.770329i | ||||
\(547\) | 37.0000i | 1.58201i | 0.611812 | + | 0.791003i | \(0.290441\pi\) | ||||
−0.611812 | + | 0.791003i | \(0.709559\pi\) | |||||||
\(548\) | 34.2929 | 1.46492 | ||||||||
\(549\) | − | 36.7423i | − | 1.56813i | ||||||
\(550\) | 19.5959 | − | 19.5959i | 0.835573 | − | 0.835573i | ||||
\(551\) | −2.44949 | −0.104352 | ||||||||
\(552\) | 12.0000 | + | 12.0000i | 0.510754 | + | 0.510754i | ||||
\(553\) | 36.7423i | 1.56244i | ||||||||
\(554\) | −17.1464 | − | 17.1464i | −0.728482 | − | 0.728482i | ||||
\(555\) | − | 12.0000i | − | 0.509372i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3939i | 1.24546i | 0.782437 | + | 0.622729i | \(0.213976\pi\) | ||||
−0.782437 | + | 0.622729i | \(0.786024\pi\) | |||||||
\(558\) | 7.65153 | + | 22.3485i | 0.323915 | + | 0.946086i | ||||
\(559\) | 6.00000i | 0.253773i | ||||||||
\(560\) | 12.0000i | 0.507093i | ||||||||
\(561\) | 88.1816i | 3.72303i | ||||||||
\(562\) | 13.0000 | − | 13.0000i | 0.548372 | − | 0.548372i | ||||
\(563\) | − | 11.0000i | − | 0.463595i | −0.972764 | − | 0.231797i | \(-0.925539\pi\) | ||
0.972764 | − | 0.231797i | \(-0.0744606\pi\) | |||||||
\(564\) | −9.79796 | −0.412568 | ||||||||
\(565\) | −1.00000 | −0.0420703 | ||||||||
\(566\) | 6.00000 | + | 6.00000i | 0.252199 | + | 0.252199i | ||||
\(567\) | 27.0000i | 1.13389i | ||||||||
\(568\) | 10.0000 | − | 10.0000i | 0.419591 | − | 0.419591i | ||||
\(569\) | − | 9.79796i | − | 0.410752i | −0.978683 | − | 0.205376i | \(-0.934158\pi\) | ||
0.978683 | − | 0.205376i | \(-0.0658417\pi\) | |||||||
\(570\) | 2.44949 | + | 2.44949i | 0.102598 | + | 0.102598i | ||||
\(571\) | 17.1464 | 0.717556 | 0.358778 | − | 0.933423i | \(-0.383194\pi\) | ||||
0.358778 | + | 0.933423i | \(0.383194\pi\) | |||||||
\(572\) | −24.0000 | −1.00349 | ||||||||
\(573\) | 12.2474i | 0.511645i | ||||||||
\(574\) | 21.0000 | + | 21.0000i | 0.876523 | + | 0.876523i | ||||
\(575\) | 9.79796 | 0.408603 | ||||||||
\(576\) | 24.0000i | 1.00000i | ||||||||
\(577\) | −12.0000 | −0.499567 | −0.249783 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249783 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(578\) | 37.0000 | − | 37.0000i | 1.53900 | − | 1.53900i | ||||
\(579\) | −22.0454 | −0.916176 | ||||||||
\(580\) | 4.89898 | 0.203419 | ||||||||
\(581\) | − | 29.3939i | − | 1.21946i | ||||||
\(582\) | 31.8434 | − | 31.8434i | 1.31995 | − | 1.31995i | ||||
\(583\) | 48.0000i | 1.98796i | ||||||||
\(584\) | −19.5959 | + | 19.5959i | −0.810885 | + | 0.810885i | ||||
\(585\) | − | 7.34847i | − | 0.303822i | ||||||
\(586\) | −4.00000 | + | 4.00000i | −0.165238 | + | 0.165238i | ||||
\(587\) | −4.89898 | −0.202203 | −0.101101 | − | 0.994876i | \(-0.532237\pi\) | ||||
−0.101101 | + | 0.994876i | \(0.532237\pi\) | |||||||
\(588\) | − | 9.79796i | − | 0.404061i | ||||||
\(589\) | 5.00000 | + | 2.44949i | 0.206021 | + | 0.100929i | ||||
\(590\) | −11.0000 | − | 11.0000i | −0.452863 | − | 0.452863i | ||||
\(591\) | − | 12.0000i | − | 0.493614i | ||||||
\(592\) | − | 19.5959i | − | 0.805387i | ||||||
\(593\) | 29.0000 | 1.19089 | 0.595444 | − | 0.803397i | \(-0.296976\pi\) | ||||
0.595444 | + | 0.803397i | \(0.296976\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.0454 | −0.903774 | ||||||||
\(596\) | − | 40.0000i | − | 1.63846i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | − | 6.00000i | −0.245358 | − | 0.245358i | ||||
\(599\) | − | 19.0000i | − | 0.776319i | −0.921592 | − | 0.388159i | \(-0.873111\pi\) | ||
0.921592 | − | 0.388159i | \(-0.126889\pi\) | |||||||
\(600\) | 19.5959 | + | 19.5959i | 0.800000 | + | 0.800000i | ||||
\(601\) | − | 12.2474i | − | 0.499584i | −0.968300 | − | 0.249792i | \(-0.919638\pi\) | ||
0.968300 | − | 0.249792i | \(-0.0803622\pi\) | |||||||
\(602\) | −7.34847 | − | 7.34847i | −0.299501 | − | 0.299501i | ||||
\(603\) | − | 24.0000i | − | 0.977356i | ||||||
\(604\) | − | 34.2929i | − | 1.39536i | ||||||
\(605\) | 13.0000 | 0.528525 | ||||||||
\(606\) | −31.8434 | + | 31.8434i | −1.29355 | + | 1.29355i | ||||
\(607\) | 2.00000i | 0.0811775i | 0.999176 | + | 0.0405887i | \(0.0129233\pi\) | ||||
−0.999176 | + | 0.0405887i | \(0.987077\pi\) | |||||||
\(608\) | 4.00000 | + | 4.00000i | 0.162221 | + | 0.162221i | ||||
\(609\) | −18.0000 | −0.729397 | ||||||||
\(610\) | 12.2474 | + | 12.2474i | 0.495885 | + | 0.495885i | ||||
\(611\) | 4.89898 | 0.198191 | ||||||||
\(612\) | −44.0908 | −1.78227 | ||||||||
\(613\) | − | 39.1918i | − | 1.58294i | −0.611206 | − | 0.791472i | \(-0.709315\pi\) | ||
0.611206 | − | 0.791472i | \(-0.290685\pi\) | |||||||
\(614\) | 13.0000 | + | 13.0000i | 0.524637 | + | 0.524637i | ||||
\(615\) | −17.1464 | −0.691411 | ||||||||
\(616\) | 29.3939 | − | 29.3939i | 1.18431 | − | 1.18431i | ||||
\(617\) | 8.00000 | 0.322068 | 0.161034 | − | 0.986949i | \(-0.448517\pi\) | ||||
0.161034 | + | 0.986949i | \(0.448517\pi\) | |||||||
\(618\) | −2.44949 | − | 2.44949i | −0.0985329 | − | 0.0985329i | ||||
\(619\) | −12.2474 | −0.492267 | −0.246133 | − | 0.969236i | \(-0.579160\pi\) | ||||
−0.246133 | + | 0.969236i | \(0.579160\pi\) | |||||||
\(620\) | −10.0000 | − | 4.89898i | −0.401610 | − | 0.196748i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.00000 | − | 5.00000i | −0.200482 | − | 0.200482i | ||||
\(623\) | 7.34847 | 0.294410 | ||||||||
\(624\) | − | 24.0000i | − | 0.960769i | ||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 26.9444 | + | 26.9444i | 1.07691 | + | 1.07691i | ||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | − | 6.00000i | − | 0.239426i | ||||||
\(629\) | 36.0000 | 1.43541 | ||||||||
\(630\) | 9.00000 | + | 9.00000i | 0.358569 | + | 0.358569i | ||||
\(631\) | −44.0908 | −1.75523 | −0.877614 | − | 0.479368i | \(-0.840866\pi\) | ||||
−0.877614 | + | 0.479368i | \(0.840866\pi\) | |||||||
\(632\) | −24.4949 | − | 24.4949i | −0.974355 | − | 0.974355i | ||||
\(633\) | − | 36.7423i | − | 1.46038i | ||||||
\(634\) | 17.0000 | − | 17.0000i | 0.675156 | − | 0.675156i | ||||
\(635\) | −4.89898 | −0.194410 | ||||||||
\(636\) | −48.0000 | −1.90332 | ||||||||
\(637\) | 4.89898i | 0.194105i | ||||||||
\(638\) | −12.0000 | − | 12.0000i | −0.475085 | − | 0.475085i | ||||
\(639\) | − | 15.0000i | − | 0.593391i | ||||||
\(640\) | −8.00000 | − | 8.00000i | −0.316228 | − | 0.316228i | ||||
\(641\) | 24.4949i | 0.967490i | 0.875209 | + | 0.483745i | \(0.160724\pi\) | ||||
−0.875209 | + | 0.483745i | \(0.839276\pi\) | |||||||
\(642\) | 17.1464 | + | 17.1464i | 0.676716 | + | 0.676716i | ||||
\(643\) | −14.6969 | −0.579591 | −0.289795 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289795 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(644\) | 14.6969 | 0.579141 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | −7.34847 | + | 7.34847i | −0.289122 | + | 0.289122i | ||||
\(647\) | 19.5959 | 0.770395 | 0.385198 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385198 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.707107 | − | 0.707107i | ||||
\(649\) | 53.8888i | 2.11532i | ||||||||
\(650\) | −9.79796 | − | 9.79796i | −0.384308 | − | 0.384308i | ||||
\(651\) | 36.7423 | + | 18.0000i | 1.44005 | + | 0.705476i | ||||
\(652\) | 18.0000 | 0.704934 | ||||||||
\(653\) | 4.00000 | 0.156532 | 0.0782660 | − | 0.996933i | \(-0.475062\pi\) | ||||
0.0782660 | + | 0.996933i | \(0.475062\pi\) | |||||||
\(654\) | 12.2474 | − | 12.2474i | 0.478913 | − | 0.478913i | ||||
\(655\) | 10.0000i | 0.390732i | ||||||||
\(656\) | −28.0000 | −1.09322 | ||||||||
\(657\) | 29.3939i | 1.14676i | ||||||||
\(658\) | −6.00000 | + | 6.00000i | −0.233904 | + | 0.233904i | ||||
\(659\) | − | 19.0000i | − | 0.740135i | −0.929005 | − | 0.370067i | \(-0.879335\pi\) | ||
0.929005 | − | 0.370067i | \(-0.120665\pi\) | |||||||
\(660\) | 24.0000i | 0.934199i | ||||||||
\(661\) | −43.0000 | −1.67251 | −0.836253 | − | 0.548344i | \(-0.815259\pi\) | ||||
−0.836253 | + | 0.548344i | \(0.815259\pi\) | |||||||
\(662\) | −4.89898 | + | 4.89898i | −0.190404 | + | 0.190404i | ||||
\(663\) | 44.0908 | 1.71235 | ||||||||
\(664\) | 19.5959 | + | 19.5959i | 0.760469 | + | 0.760469i | ||||
\(665\) | 3.00000 | 0.116335 | ||||||||
\(666\) | −14.6969 | − | 14.6969i | −0.569495 | − | 0.569495i | ||||
\(667\) | − | 6.00000i | − | 0.232321i | ||||||
\(668\) | − | 39.1918i | − | 1.51638i | ||||||
\(669\) | 36.0000 | 1.39184 | ||||||||
\(670\) | 8.00000 | + | 8.00000i | 0.309067 | + | 0.309067i | ||||
\(671\) | − | 60.0000i | − | 2.31627i | ||||||
\(672\) | 29.3939 | + | 29.3939i | 1.13389 | + | 1.13389i | ||||
\(673\) | 22.0454i | 0.849788i | 0.905243 | + | 0.424894i | \(0.139689\pi\) | ||||
−0.905243 | + | 0.424894i | \(0.860311\pi\) | |||||||
\(674\) | 7.34847 | + | 7.34847i | 0.283052 | + | 0.283052i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 14.0000i | − | 0.538462i | ||||||
\(677\) | 4.89898i | 0.188283i | 0.995559 | + | 0.0941415i | \(0.0300106\pi\) | ||||
−0.995559 | + | 0.0941415i | \(0.969989\pi\) | |||||||
\(678\) | −2.44949 | + | 2.44949i | −0.0940721 | + | 0.0940721i | ||||
\(679\) | − | 39.0000i | − | 1.49668i | ||||||
\(680\) | 14.6969 | − | 14.6969i | 0.563602 | − | 0.563602i | ||||
\(681\) | − | 53.8888i | − | 2.06502i | ||||||
\(682\) | 12.4949 | + | 36.4949i | 0.478454 | + | 1.39746i | ||||
\(683\) | 29.0000i | 1.10965i | 0.831966 | + | 0.554827i | \(0.187216\pi\) | ||||
−0.831966 | + | 0.554827i | \(0.812784\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | 17.1464i | 0.655131i | ||||||||
\(686\) | 15.0000 | + | 15.0000i | 0.572703 | + | 0.572703i | ||||
\(687\) | 24.0000i | 0.915657i | ||||||||
\(688\) | 9.79796 | 0.373544 | ||||||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | −6.00000 | + | 6.00000i | −0.228416 | + | 0.228416i | ||||
\(691\) | 15.0000i | 0.570627i | 0.958434 | + | 0.285313i | \(0.0920977\pi\) | ||||
−0.958434 | + | 0.285313i | \(0.907902\pi\) | |||||||
\(692\) | 32.0000i | 1.21646i | ||||||||
\(693\) | − | 44.0908i | − | 1.67487i | ||||||
\(694\) | −7.34847 | + | 7.34847i | −0.278944 | + | 0.278944i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.0000 | − | 12.0000i | 0.454859 | − | 0.454859i | ||||
\(697\) | − | 51.4393i | − | 1.94840i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.44949 | 0.0926482 | ||||||||
\(700\) | 24.0000 | 0.907115 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 39.1918i | 1.47710i | ||||||||
\(705\) | − | 4.89898i | − | 0.184506i | ||||||
\(706\) | 14.6969 | + | 14.6969i | 0.553127 | + | 0.553127i | ||||
\(707\) | 39.0000i | 1.46675i | ||||||||
\(708\) | −53.8888 | −2.02526 | ||||||||
\(709\) | 14.6969i | 0.551955i | 0.961164 | + | 0.275978i | \(0.0890015\pi\) | ||||
−0.961164 | + | 0.275978i | \(0.910998\pi\) | |||||||
\(710\) | 5.00000 | + | 5.00000i | 0.187647 | + | 0.187647i | ||||
\(711\) | −36.7423 | −1.37795 | ||||||||
\(712\) | −4.89898 | + | 4.89898i | −0.183597 | + | 0.183597i | ||||
\(713\) | −6.00000 | + | 12.2474i | −0.224702 | + | 0.458671i | ||||
\(714\) | −54.0000 | + | 54.0000i | −2.02090 | + | 2.02090i | ||||
\(715\) | − | 12.0000i | − | 0.448775i | ||||||
\(716\) | 24.4949i | 0.915417i | ||||||||
\(717\) | −30.0000 | −1.12037 | ||||||||
\(718\) | 29.0000 | + | 29.0000i | 1.08227 | + | 1.08227i | ||||
\(719\) | −36.7423 | −1.37026 | −0.685129 | − | 0.728422i | \(-0.740254\pi\) | ||||
−0.685129 | + | 0.728422i | \(0.740254\pi\) | |||||||
\(720\) | −12.0000 | −0.447214 | ||||||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | −18.0000 | + | 18.0000i | −0.669891 | + | 0.669891i | ||||
\(723\) | − | 60.0000i | − | 2.23142i | ||||||
\(724\) | −24.4949 | −0.910346 | ||||||||
\(725\) | − | 9.79796i | − | 0.363887i | ||||||
\(726\) | 31.8434 | − | 31.8434i | 1.18182 | − | 1.18182i | ||||
\(727\) | − | 33.0000i | − | 1.22390i | −0.790896 | − | 0.611951i | \(-0.790385\pi\) | ||
0.790896 | − | 0.611951i | \(-0.209615\pi\) | |||||||
\(728\) | −14.6969 | − | 14.6969i | −0.544705 | − | 0.544705i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −9.79796 | − | 9.79796i | −0.362639 | − | 0.362639i | ||||
\(731\) | 18.0000i | 0.665754i | ||||||||
\(732\) | 60.0000 | 2.21766 | ||||||||
\(733\) | 9.00000 | 0.332423 | 0.166211 | − | 0.986090i | \(-0.446847\pi\) | ||||
0.166211 | + | 0.986090i | \(0.446847\pi\) | |||||||
\(734\) | 4.89898 | − | 4.89898i | 0.180825 | − | 0.180825i | ||||
\(735\) | 4.89898 | 0.180702 | ||||||||
\(736\) | −9.79796 | + | 9.79796i | −0.361158 | + | 0.361158i | ||||
\(737\) | − | 39.1918i | − | 1.44365i | ||||||
\(738\) | −21.0000 | + | 21.0000i | −0.773021 | + | 0.773021i | ||||
\(739\) | 36.7423 | 1.35159 | 0.675795 | − | 0.737090i | \(-0.263801\pi\) | ||||
0.675795 | + | 0.737090i | \(0.263801\pi\) | |||||||
\(740\) | 9.79796 | 0.360180 | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | −29.3939 | + | 29.3939i | −1.07908 | + | 1.07908i | ||||
\(743\) | −51.4393 | −1.88712 | −0.943562 | − | 0.331195i | \(-0.892548\pi\) | ||||
−0.943562 | + | 0.331195i | \(0.892548\pi\) | |||||||
\(744\) | −36.4949 | + | 12.4949i | −1.33797 | + | 0.458085i | ||||
\(745\) | 20.0000 | 0.732743 | ||||||||
\(746\) | −19.0000 | + | 19.0000i | −0.695639 | + | 0.695639i | ||||
\(747\) | 29.3939 | 1.07547 | ||||||||
\(748\) | −72.0000 | −2.63258 | ||||||||
\(749\) | 21.0000 | 0.767323 | ||||||||
\(750\) | −22.0454 | + | 22.0454i | −0.804984 | + | 0.804984i | ||||
\(751\) | − | 25.0000i | − | 0.912263i | −0.889912 | − | 0.456131i | \(-0.849235\pi\) | ||
0.889912 | − | 0.456131i | \(-0.150765\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | −6.00000 | + | 6.00000i | −0.218507 | + | 0.218507i | ||||
\(755\) | 17.1464 | 0.624022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.1464i | 0.623198i | 0.950214 | + | 0.311599i | \(0.100864\pi\) | ||||
−0.950214 | + | 0.311599i | \(0.899136\pi\) | |||||||
\(758\) | −6.00000 | − | 6.00000i | −0.217930 | − | 0.217930i | ||||
\(759\) | 29.3939 | 1.06693 | ||||||||
\(760\) | −2.00000 | + | 2.00000i | −0.0725476 | + | 0.0725476i | ||||
\(761\) | 24.4949i | 0.887939i | 0.896042 | + | 0.443970i | \(0.146430\pi\) | ||||
−0.896042 | + | 0.443970i | \(0.853570\pi\) | |||||||
\(762\) | −12.0000 | + | 12.0000i | −0.434714 | + | 0.434714i | ||||
\(763\) | − | 15.0000i | − | 0.543036i | ||||||
\(764\) | −10.0000 | −0.361787 | ||||||||
\(765\) | − | 22.0454i | − | 0.797053i | ||||||
\(766\) | 14.6969 | − | 14.6969i | 0.531022 | − | 0.531022i | ||||
\(767\) | 26.9444 | 0.972905 | ||||||||
\(768\) | −39.1918 | −1.41421 | ||||||||
\(769\) | 15.0000 | 0.540914 | 0.270457 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270457 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(770\) | 14.6969 | + | 14.6969i | 0.529641 | + | 0.529641i | ||||
\(771\) | −31.8434 | −1.14681 | ||||||||
\(772\) | − | 18.0000i | − | 0.647834i | ||||||
\(773\) | 22.0454i | 0.792918i | 0.918052 | + | 0.396459i | \(0.129761\pi\) | ||||
−0.918052 | + | 0.396459i | \(0.870239\pi\) | |||||||
\(774\) | 7.34847 | − | 7.34847i | 0.264135 | − | 0.264135i | ||||
\(775\) | −9.79796 | + | 20.0000i | −0.351953 | + | 0.718421i | ||||
\(776\) | 26.0000 | + | 26.0000i | 0.933346 | + | 0.933346i | ||||
\(777\) | −36.0000 | −1.29149 | ||||||||
\(778\) | −14.6969 | − | 14.6969i | −0.526911 | − | 0.526911i | ||||
\(779\) | 7.00000i | 0.250801i | ||||||||
\(780\) | 12.0000 | 0.429669 | ||||||||
\(781\) | − | 24.4949i | − | 0.876496i | ||||||
\(782\) | −18.0000 | − | 18.0000i | −0.643679 | − | 0.643679i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.00000 | 0.285714 | ||||||||
\(785\) | 3.00000 | 0.107075 | ||||||||
\(786\) | 24.4949 | + | 24.4949i | 0.873704 | + | 0.873704i | ||||
\(787\) | −17.1464 | −0.611204 | −0.305602 | − | 0.952159i | \(-0.598858\pi\) | ||||
−0.305602 | + | 0.952159i | \(0.598858\pi\) | |||||||
\(788\) | 9.79796 | 0.349038 | ||||||||
\(789\) | 6.00000 | 0.213606 | ||||||||
\(790\) | 12.2474 | − | 12.2474i | 0.435745 | − | 0.435745i | ||||
\(791\) | 3.00000i | 0.106668i | ||||||||
\(792\) | 29.3939 | + | 29.3939i | 1.04447 | + | 1.04447i | ||||
\(793\) | −30.0000 | −1.06533 | ||||||||
\(794\) | 17.0000 | − | 17.0000i | 0.603307 | − | 0.603307i | ||||
\(795\) | − | 24.0000i | − | 0.851192i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.89898i | 0.173531i | 0.996229 | + | 0.0867654i | \(0.0276530\pi\) | ||||
−0.996229 | + | 0.0867654i | \(0.972347\pi\) | |||||||
\(798\) | 7.34847 | − | 7.34847i | 0.260133 | − | 0.260133i | ||||
\(799\) | 14.6969 | 0.519940 | ||||||||
\(800\) | −16.0000 | + | 16.0000i | −0.565685 | + | 0.565685i | ||||
\(801\) | 7.34847i | 0.259645i | ||||||||
\(802\) | −12.2474 | − | 12.2474i | −0.432472 | − | 0.432472i | ||||
\(803\) | 48.0000i | 1.69388i | ||||||||
\(804\) | 39.1918 | 1.38219 | ||||||||
\(805\) | 7.34847i | 0.259000i | ||||||||
\(806\) | 18.2474 | − | 6.24745i | 0.642739 | − | 0.220057i | ||||
\(807\) | 24.0000i | 0.844840i | ||||||||
\(808\) | −26.0000 | − | 26.0000i | −0.914677 | − | 0.914677i | ||||
\(809\) | − | 34.2929i | − | 1.20567i | −0.797865 | − | 0.602836i | \(-0.794037\pi\) | ||
0.797865 | − | 0.602836i | \(-0.205963\pi\) | |||||||
\(810\) | 9.00000 | − | 9.00000i | 0.316228 | − | 0.316228i | ||||
\(811\) | − | 10.0000i | − | 0.351147i | −0.984466 | − | 0.175574i | \(-0.943822\pi\) | ||
0.984466 | − | 0.175574i | \(-0.0561780\pi\) | |||||||
\(812\) | − | 14.6969i | − | 0.515761i | ||||||
\(813\) | 18.0000 | 0.631288 | ||||||||
\(814\) | −24.0000 | − | 24.0000i | −0.841200 | − | 0.841200i | ||||
\(815\) | 9.00000i | 0.315256i | ||||||||
\(816\) | − | 72.0000i | − | 2.52050i | ||||||
\(817\) | − | 2.44949i | − | 0.0856968i | ||||||
\(818\) | 22.0454 | + | 22.0454i | 0.770800 | + | 0.770800i | ||||
\(819\) | −22.0454 | −0.770329 | ||||||||
\(820\) | − | 14.0000i | − | 0.488901i | ||||||
\(821\) | 36.7423i | 1.28232i | 0.767409 | + | 0.641158i | \(0.221546\pi\) | ||||
−0.767409 | + | 0.641158i | \(0.778454\pi\) | |||||||
\(822\) | 42.0000 | + | 42.0000i | 1.46492 | + | 1.46492i | ||||
\(823\) | −2.44949 | −0.0853838 | −0.0426919 | − | 0.999088i | \(-0.513593\pi\) | ||||
−0.0426919 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(824\) | 2.00000 | − | 2.00000i | 0.0696733 | − | 0.0696733i | ||||
\(825\) | 48.0000 | 1.67115 | ||||||||
\(826\) | −33.0000 | + | 33.0000i | −1.14822 | + | 1.14822i | ||||
\(827\) | −17.1464 | −0.596240 | −0.298120 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298120 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(828\) | 14.6969i | 0.510754i | ||||||||
\(829\) | 14.6969i | 0.510446i | 0.966882 | + | 0.255223i | \(0.0821488\pi\) | ||||
−0.966882 | + | 0.255223i | \(0.917851\pi\) | |||||||
\(830\) | −9.79796 | + | 9.79796i | −0.340092 | + | 0.340092i | ||||
\(831\) | − | 42.0000i | − | 1.45696i | ||||||
\(832\) | 19.5959 | 0.679366 | ||||||||
\(833\) | 14.6969i | 0.509219i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5959 | 0.678145 | ||||||||
\(836\) | 9.79796 | 0.338869 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.00000 | − | 1.00000i | −0.0345444 | − | 0.0345444i | ||||
\(839\) | 46.0000i | 1.58810i | 0.607855 | + | 0.794048i | \(0.292030\pi\) | ||||
−0.607855 | + | 0.794048i | \(0.707970\pi\) | |||||||
\(840\) | −14.6969 | + | 14.6969i | −0.507093 | + | 0.507093i | ||||
\(841\) | 23.0000 | 0.793103 | ||||||||
\(842\) | 33.0000 | − | 33.0000i | 1.13726 | − | 1.13726i | ||||
\(843\) | 31.8434 | 1.09674 | ||||||||
\(844\) | 30.0000 | 1.03264 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | −6.00000 | − | 6.00000i | −0.206284 | − | 0.206284i | ||||
\(847\) | − | 39.0000i | − | 1.34006i | ||||||
\(848\) | − | 39.1918i | − | 1.34585i | ||||||
\(849\) | 14.6969i | 0.504398i | ||||||||
\(850\) | −29.3939 | − | 29.3939i | −1.00820 | − | 1.00820i | ||||
\(851\) | − | 12.0000i | − | 0.411355i | ||||||
\(852\) | 24.4949 | 0.839181 | ||||||||
\(853\) | −36.0000 | −1.23262 | −0.616308 | − | 0.787505i | \(-0.711372\pi\) | ||||
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(854\) | 36.7423 | − | 36.7423i | 1.25730 | − | 1.25730i | ||||
\(855\) | 3.00000i | 0.102598i | ||||||||
\(856\) | −14.0000 | + | 14.0000i | −0.478510 | + | 0.478510i | ||||
\(857\) | −32.0000 | −1.09310 | −0.546550 | − | 0.837427i | \(-0.684059\pi\) | ||||
−0.546550 | + | 0.837427i | \(0.684059\pi\) | |||||||
\(858\) | −29.3939 | − | 29.3939i | −1.00349 | − | 1.00349i | ||||
\(859\) | −48.9898 | −1.67151 | −0.835755 | − | 0.549102i | \(-0.814970\pi\) | ||||
−0.835755 | + | 0.549102i | \(0.814970\pi\) | |||||||
\(860\) | 4.89898i | 0.167054i | ||||||||
\(861\) | 51.4393i | 1.75305i | ||||||||
\(862\) | −20.0000 | − | 20.0000i | −0.681203 | − | 0.681203i | ||||
\(863\) | −2.44949 | −0.0833816 | −0.0416908 | − | 0.999131i | \(-0.513274\pi\) | ||||
−0.0416908 | + | 0.999131i | \(0.513274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0000 | −0.544016 | ||||||||
\(866\) | −22.0454 | − | 22.0454i | −0.749133 | − | 0.749133i | ||||
\(867\) | 90.6311 | 3.07799 | ||||||||
\(868\) | −14.6969 | + | 30.0000i | −0.498847 | + | 1.01827i | ||||
\(869\) | −60.0000 | −2.03536 | ||||||||
\(870\) | 6.00000 | + | 6.00000i | 0.203419 | + | 0.203419i | ||||
\(871\) | −19.5959 | −0.663982 | ||||||||
\(872\) | 10.0000 | + | 10.0000i | 0.338643 | + | 0.338643i | ||||
\(873\) | 39.0000 | 1.31995 | ||||||||
\(874\) | 2.44949 | + | 2.44949i | 0.0828552 | + | 0.0828552i | ||||
\(875\) | 27.0000i | 0.912767i | ||||||||
\(876\) | −48.0000 | −1.62177 | ||||||||
\(877\) | −27.0000 | −0.911725 | −0.455863 | − | 0.890050i | \(-0.650669\pi\) | ||||
−0.455863 | + | 0.890050i | \(0.650669\pi\) | |||||||
\(878\) | −31.0000 | − | 31.0000i | −1.04620 | − | 1.04620i | ||||
\(879\) | −9.79796 | −0.330477 | ||||||||
\(880\) | −19.5959 | −0.660578 | ||||||||
\(881\) | − | 24.4949i | − | 0.825254i | −0.910900 | − | 0.412627i | \(-0.864611\pi\) | ||
0.910900 | − | 0.412627i | \(-0.135389\pi\) | |||||||
\(882\) | 6.00000 | − | 6.00000i | 0.202031 | − | 0.202031i | ||||
\(883\) | −39.1918 | −1.31891 | −0.659455 | − | 0.751744i | \(-0.729213\pi\) | ||||
−0.659455 | + | 0.751744i | \(0.729213\pi\) | |||||||
\(884\) | 36.0000i | 1.21081i | ||||||||
\(885\) | − | 26.9444i | − | 0.905726i | ||||||
\(886\) | 11.0000 | + | 11.0000i | 0.369552 | + | 0.369552i | ||||
\(887\) | − | 43.0000i | − | 1.44380i | −0.691998 | − | 0.721899i | \(-0.743269\pi\) | ||
0.691998 | − | 0.721899i | \(-0.256731\pi\) | |||||||
\(888\) | 24.0000 | − | 24.0000i | 0.805387 | − | 0.805387i | ||||
\(889\) | 14.6969i | 0.492919i | ||||||||
\(890\) | −2.44949 | − | 2.44949i | −0.0821071 | − | 0.0821071i | ||||
\(891\) | −44.0908 | −1.47710 | ||||||||
\(892\) | 29.3939i | 0.984180i | ||||||||
\(893\) | −2.00000 | −0.0669274 | ||||||||
\(894\) | 48.9898 | − | 48.9898i | 1.63846 | − | 1.63846i | ||||
\(895\) | −12.2474 | −0.409387 | ||||||||
\(896\) | −24.0000 | + | 24.0000i | −0.801784 | + | 0.801784i | ||||
\(897\) | − | 14.6969i | − | 0.490716i | ||||||
\(898\) | 9.79796 | + | 9.79796i | 0.326962 | + | 0.326962i | ||||
\(899\) | 12.2474 | + | 6.00000i | 0.408475 | + | 0.200111i | ||||
\(900\) | 24.0000i | 0.800000i | ||||||||
\(901\) | 72.0000 | 2.39867 | ||||||||
\(902\) | −34.2929 | + | 34.2929i | −1.14183 | + | 1.14183i | ||||
\(903\) | − | 18.0000i | − | 0.599002i | ||||||
\(904\) | −2.00000 | − | 2.00000i | −0.0665190 | − | 0.0665190i | ||||
\(905\) | − | 12.2474i | − | 0.407119i | ||||||
\(906\) | 42.0000 | − | 42.0000i | 1.39536 | − | 1.39536i | ||||
\(907\) | 7.00000i | 0.232431i | 0.993224 | + | 0.116216i | \(0.0370764\pi\) | ||||
−0.993224 | + | 0.116216i | \(0.962924\pi\) | |||||||
\(908\) | 44.0000 | 1.46019 | ||||||||
\(909\) | −39.0000 | −1.29355 | ||||||||
\(910\) | 7.34847 | − | 7.34847i | 0.243599 | − | 0.243599i | ||||
\(911\) | −31.8434 | −1.05502 | −0.527509 | − | 0.849550i | \(-0.676874\pi\) | ||||
−0.527509 | + | 0.849550i | \(0.676874\pi\) | |||||||
\(912\) | 9.79796i | 0.324443i | ||||||||
\(913\) | 48.0000 | 1.58857 | ||||||||
\(914\) | −4.89898 | − | 4.89898i | −0.162044 | − | 0.162044i | ||||
\(915\) | 30.0000i | 0.991769i | ||||||||
\(916\) | −19.5959 | −0.647467 | ||||||||
\(917\) | 30.0000 | 0.990687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0000i | 1.51740i | 0.651440 | + | 0.758700i | \(0.274165\pi\) | ||||
−0.651440 | + | 0.758700i | \(0.725835\pi\) | |||||||
\(920\) | −4.89898 | − | 4.89898i | −0.161515 | − | 0.161515i | ||||
\(921\) | 31.8434i | 1.04927i | ||||||||
\(922\) | 24.4949 | + | 24.4949i | 0.806696 | + | 0.806696i | ||||
\(923\) | −12.2474 | −0.403130 | ||||||||
\(924\) | 72.0000 | 2.36863 | ||||||||
\(925\) | − | 19.5959i | − | 0.644310i | ||||||
\(926\) | −34.2929 | + | 34.2929i | −1.12693 | + | 1.12693i | ||||
\(927\) | − | 3.00000i | − | 0.0985329i | ||||||
\(928\) | 9.79796 | + | 9.79796i | 0.321634 | + | 0.321634i | ||||
\(929\) | − | 9.79796i | − | 0.321461i | −0.986998 | − | 0.160730i | \(-0.948615\pi\) | ||
0.986998 | − | 0.160730i | \(-0.0513849\pi\) | |||||||
\(930\) | −6.24745 | − | 18.2474i | −0.204862 | − | 0.598357i | ||||
\(931\) | − | 2.00000i | − | 0.0655474i | ||||||
\(932\) | 2.00000i | 0.0655122i | ||||||||
\(933\) | − | 12.2474i | − | 0.400963i | ||||||
\(934\) | 13.0000 | + | 13.0000i | 0.425373 | + | 0.425373i | ||||
\(935\) | − | 36.0000i | − | 1.17733i | ||||||
\(936\) | 14.6969 | − | 14.6969i | 0.480384 | − | 0.480384i | ||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | 24.0000 | − | 24.0000i | 0.783628 | − | 0.783628i | ||||
\(939\) | 66.0000i | 2.15383i | ||||||||
\(940\) | 4.00000 | 0.130466 | ||||||||
\(941\) | 48.9898i | 1.59702i | 0.601980 | + | 0.798511i | \(0.294379\pi\) | ||||
−0.601980 | + | 0.798511i | \(0.705621\pi\) | |||||||
\(942\) | 7.34847 | − | 7.34847i | 0.239426 | − | 0.239426i | ||||
\(943\) | −17.1464 | −0.558365 | ||||||||
\(944\) | − | 44.0000i | − | 1.43208i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | − | 12.0000i | 0.390154 | − | 0.390154i | ||||
\(947\) | 19.5959 | 0.636782 | 0.318391 | − | 0.947960i | \(-0.396858\pi\) | ||||
0.318391 | + | 0.947960i | \(0.396858\pi\) | |||||||
\(948\) | − | 60.0000i | − | 1.94871i | ||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 4.00000 | + | 4.00000i | 0.129777 | + | 0.129777i | ||||
\(951\) | 41.6413 | 1.35031 | ||||||||
\(952\) | −44.0908 | − | 44.0908i | −1.42899 | − | 1.42899i | ||||
\(953\) | − | 2.44949i | − | 0.0793468i | −0.999213 | − | 0.0396734i | \(-0.987368\pi\) | ||
0.999213 | − | 0.0396734i | \(-0.0126317\pi\) | |||||||
\(954\) | −29.3939 | − | 29.3939i | −0.951662 | − | 0.951662i | ||||
\(955\) | − | 5.00000i | − | 0.161796i | ||||||
\(956\) | − | 24.4949i | − | 0.792222i | ||||||
\(957\) | − | 29.3939i | − | 0.950169i | ||||||
\(958\) | −11.0000 | − | 11.0000i | −0.355394 | − | 0.355394i | ||||
\(959\) | 51.4393 | 1.66106 | ||||||||
\(960\) | − | 19.5959i | − | 0.632456i | ||||||
\(961\) | −19.0000 | − | 24.4949i | −0.612903 | − | 0.790158i | ||||
\(962\) | −12.0000 | + | 12.0000i | −0.386896 | + | 0.386896i | ||||
\(963\) | 21.0000i | 0.676716i | ||||||||
\(964\) | 48.9898 | 1.57786 | ||||||||
\(965\) | 9.00000 | 0.289720 | ||||||||
\(966\) | 18.0000 | + | 18.0000i | 0.579141 | + | 0.579141i | ||||
\(967\) | 44.0908 | 1.41787 | 0.708933 | − | 0.705276i | \(-0.249177\pi\) | ||||
0.708933 | + | 0.705276i | \(0.249177\pi\) | |||||||
\(968\) | 26.0000 | + | 26.0000i | 0.835672 | + | 0.835672i | ||||
\(969\) | −18.0000 | −0.578243 | ||||||||
\(970\) | −13.0000 | + | 13.0000i | −0.417405 | + | 0.417405i | ||||
\(971\) | 50.0000i | 1.60458i | 0.596937 | + | 0.802288i | \(0.296384\pi\) | ||||
−0.596937 | + | 0.802288i | \(0.703616\pi\) | |||||||
\(972\) | − | 44.0908i | − | 1.41421i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.8434 | + | 31.8434i | −1.02033 | + | 1.02033i | ||||
\(975\) | − | 24.0000i | − | 0.768615i | ||||||
\(976\) | 48.9898i | 1.56813i | ||||||||
\(977\) | −47.0000 | −1.50366 | −0.751832 | − | 0.659355i | \(-0.770829\pi\) | ||||
−0.751832 | + | 0.659355i | \(0.770829\pi\) | |||||||
\(978\) | 22.0454 | + | 22.0454i | 0.704934 | + | 0.704934i | ||||
\(979\) | 12.0000i | 0.383522i | ||||||||
\(980\) | 4.00000i | 0.127775i | ||||||||
\(981\) | 15.0000 | 0.478913 | ||||||||
\(982\) | −29.3939 | + | 29.3939i | −0.937996 | + | 0.937996i | ||||
\(983\) | 9.79796 | 0.312506 | 0.156253 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156253 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(984\) | −34.2929 | − | 34.2929i | −1.09322 | − | 1.09322i | ||||
\(985\) | 4.89898i | 0.156094i | ||||||||
\(986\) | −18.0000 | + | 18.0000i | −0.573237 | + | 0.573237i | ||||
\(987\) | −14.6969 | −0.467809 | ||||||||
\(988\) | − | 4.89898i | − | 0.155857i | ||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | −14.6969 | + | 14.6969i | −0.467099 | + | 0.467099i | ||||
\(991\) | −7.34847 | −0.233432 | −0.116716 | − | 0.993165i | \(-0.537237\pi\) | ||||
−0.116716 | + | 0.993165i | \(0.537237\pi\) | |||||||
\(992\) | −10.2020 | − | 29.7980i | −0.323915 | − | 0.946086i | ||||
\(993\) | −12.0000 | −0.380808 | ||||||||
\(994\) | 15.0000 | − | 15.0000i | 0.475771 | − | 0.475771i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 48.0000i | 1.52094i | ||||||||
\(997\) | 23.0000 | 0.728417 | 0.364209 | − | 0.931317i | \(-0.381339\pi\) | ||||
0.364209 | + | 0.931317i | \(0.381339\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 124.2.d.a.123.3 | yes | 4 | |
3.2 | odd | 2 | 1116.2.g.d.991.1 | 4 | |||
4.3 | odd | 2 | inner | 124.2.d.a.123.2 | yes | 4 | |
8.3 | odd | 2 | 1984.2.h.d.1983.2 | 4 | |||
8.5 | even | 2 | 1984.2.h.d.1983.3 | 4 | |||
12.11 | even | 2 | 1116.2.g.d.991.4 | 4 | |||
31.30 | odd | 2 | inner | 124.2.d.a.123.4 | yes | 4 | |
93.92 | even | 2 | 1116.2.g.d.991.2 | 4 | |||
124.123 | even | 2 | inner | 124.2.d.a.123.1 | ✓ | 4 | |
248.61 | odd | 2 | 1984.2.h.d.1983.1 | 4 | |||
248.123 | even | 2 | 1984.2.h.d.1983.4 | 4 | |||
372.371 | odd | 2 | 1116.2.g.d.991.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.2.d.a.123.1 | ✓ | 4 | 124.123 | even | 2 | inner | |
124.2.d.a.123.2 | yes | 4 | 4.3 | odd | 2 | inner | |
124.2.d.a.123.3 | yes | 4 | 1.1 | even | 1 | trivial | |
124.2.d.a.123.4 | yes | 4 | 31.30 | odd | 2 | inner | |
1116.2.g.d.991.1 | 4 | 3.2 | odd | 2 | |||
1116.2.g.d.991.2 | 4 | 93.92 | even | 2 | |||
1116.2.g.d.991.3 | 4 | 372.371 | odd | 2 | |||
1116.2.g.d.991.4 | 4 | 12.11 | even | 2 | |||
1984.2.h.d.1983.1 | 4 | 248.61 | odd | 2 | |||
1984.2.h.d.1983.2 | 4 | 8.3 | odd | 2 | |||
1984.2.h.d.1983.3 | 4 | 8.5 | even | 2 | |||
1984.2.h.d.1983.4 | 4 | 248.123 | even | 2 |