Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,2,Mod(53,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.958204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 77.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.77 |
Dual form | 120.2.w.b.53.1 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | ||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −2.22474 | − | 0.224745i | −0.994936 | − | 0.100509i | ||||
\(6\) | −2.44949 | −1.00000 | ||||||||
\(7\) | 1.44949 | + | 1.44949i | 0.547856 | + | 0.547856i | 0.925820 | − | 0.377964i | \(-0.123376\pi\) |
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | −2.00000 | − | 2.44949i | −0.632456 | − | 0.774597i | ||||
\(11\) | 6.44949 | 1.94459 | 0.972297 | − | 0.233748i | \(-0.0750991\pi\) | ||||
0.972297 | + | 0.233748i | \(0.0750991\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.707107 | − | 0.707107i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 2.89898i | 0.774785i | ||||||||
\(15\) | 3.00000 | − | 2.44949i | 0.774597 | − | 0.632456i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.707107 | − | 0.707107i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0.449490 | − | 4.44949i | 0.100509 | − | 0.994936i | ||||
\(21\) | −3.55051 | −0.774785 | ||||||||
\(22\) | 6.44949 | + | 6.44949i | 1.37504 | + | 1.37504i | ||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | − | 4.89898i | − | 1.00000i | ||||||
\(25\) | 4.89898 | + | 1.00000i | 0.979796 | + | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | −2.89898 | + | 2.89898i | −0.547856 | + | 0.547856i | ||||
\(29\) | − | 9.34847i | − | 1.73597i | −0.496593 | − | 0.867984i | \(-0.665416\pi\) | ||
0.496593 | − | 0.867984i | \(-0.334584\pi\) | |||||||
\(30\) | 5.44949 | + | 0.550510i | 0.994936 | + | 0.100509i | ||||
\(31\) | −4.89898 | −0.879883 | −0.439941 | − | 0.898027i | \(-0.645001\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | −7.89898 | + | 7.89898i | −1.37504 | + | 1.37504i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.89898 | − | 3.55051i | −0.490017 | − | 0.600146i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.89898 | − | 4.00000i | 0.774597 | − | 0.632456i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | −3.55051 | − | 3.55051i | −0.547856 | − | 0.547856i | ||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 12.8990i | 1.94459i | ||||||||
\(45\) | −0.674235 | + | 6.67423i | −0.100509 | + | 0.994936i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.707107 | − | 0.707107i | ||||
\(49\) | − | 2.79796i | − | 0.399708i | ||||||
\(50\) | 3.89898 | + | 5.89898i | 0.551399 | + | 0.834242i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | + | 2.44949i | −0.336463 | + | 0.336463i | −0.855034 | − | 0.518571i | \(-0.826464\pi\) |
0.518571 | + | 0.855034i | \(0.326464\pi\) | |||||||
\(54\) | 7.34847i | 1.00000i | ||||||||
\(55\) | −14.3485 | − | 1.44949i | −1.93475 | − | 0.195449i | ||||
\(56\) | −5.79796 | −0.774785 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.34847 | − | 9.34847i | 1.22751 | − | 1.22751i | ||||
\(59\) | 0.651531i | 0.0848221i | 0.999100 | + | 0.0424110i | \(0.0135039\pi\) | ||||
−0.999100 | + | 0.0424110i | \(0.986496\pi\) | |||||||
\(60\) | 4.89898 | + | 6.00000i | 0.632456 | + | 0.774597i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −4.89898 | − | 4.89898i | −0.622171 | − | 0.622171i | ||||
\(63\) | 4.34847 | − | 4.34847i | 0.547856 | − | 0.547856i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −15.7980 | −1.94459 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.651531 | − | 6.44949i | 0.0778728 | − | 0.770861i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 6.00000 | + | 6.00000i | 0.707107 | + | 0.707107i | ||||
\(73\) | 2.10102 | − | 2.10102i | 0.245906 | − | 0.245906i | −0.573382 | − | 0.819288i | \(-0.694369\pi\) |
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.22474 | + | 4.77526i | −0.834242 | + | 0.551399i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.34847 | + | 9.34847i | 1.06536 | + | 1.06536i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6969i | 1.65353i | 0.562544 | + | 0.826767i | \(0.309823\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 8.89898 | + | 0.898979i | 0.994936 | + | 0.100509i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | + | 4.00000i | −0.439057 | + | 0.439057i | −0.891695 | − | 0.452638i | \(-0.850483\pi\) |
0.452638 | + | 0.891695i | \(0.350483\pi\) | |||||||
\(84\) | − | 7.10102i | − | 0.774785i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.4495 | + | 11.4495i | 1.22751 | + | 1.22751i | ||||
\(88\) | −12.8990 | + | 12.8990i | −1.37504 | + | 1.37504i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −7.34847 | + | 6.00000i | −0.774597 | + | 0.632456i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | − | 6.00000i | 0.622171 | − | 0.622171i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | 1.00000 | ||||||||
\(97\) | −10.7980 | − | 10.7980i | −1.09637 | − | 1.09637i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) |
−0.101535 | − | 0.994832i | \(-0.532375\pi\) | |||||||
\(98\) | 2.79796 | − | 2.79796i | 0.282637 | − | 0.282637i | ||||
\(99\) | − | 19.3485i | − | 1.94459i | ||||||
\(100\) | −2.00000 | + | 9.79796i | −0.200000 | + | 0.979796i | ||||
\(101\) | 16.4495 | 1.63679 | 0.818393 | − | 0.574659i | \(-0.194865\pi\) | ||||
0.818393 | + | 0.574659i | \(0.194865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3485 | − | 14.3485i | 1.41380 | − | 1.41380i | 0.689730 | − | 0.724066i | \(-0.257729\pi\) |
0.724066 | − | 0.689730i | \(-0.242271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.89898 | + | 0.797959i | 0.770861 | + | 0.0778728i | ||||
\(106\) | −4.89898 | −0.475831 | ||||||||
\(107\) | −8.00000 | − | 8.00000i | −0.773389 | − | 0.773389i | 0.205308 | − | 0.978697i | \(-0.434180\pi\) |
−0.978697 | + | 0.205308i | \(0.934180\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.707107 | + | 0.707107i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −12.8990 | − | 15.7980i | −1.22987 | − | 1.50628i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.79796 | − | 5.79796i | −0.547856 | − | 0.547856i | ||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.6969 | 1.73597 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.651531 | + | 0.651531i | −0.0599783 | + | 0.0599783i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.10102 | + | 10.8990i | −0.100509 | + | 0.994936i | ||||
\(121\) | 30.5959 | 2.78145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 9.79796i | − | 0.879883i | ||||||
\(125\) | −10.6742 | − | 3.32577i | −0.954733 | − | 0.297465i | ||||
\(126\) | 8.69694 | 0.774785 | ||||||||
\(127\) | −8.55051 | − | 8.55051i | −0.758735 | − | 0.758735i | 0.217357 | − | 0.976092i | \(-0.430256\pi\) |
−0.976092 | + | 0.217357i | \(0.930256\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5505 | −1.18391 | −0.591957 | − | 0.805970i | \(-0.701644\pi\) | ||||
−0.591957 | + | 0.805970i | \(0.701644\pi\) | |||||||
\(132\) | −15.7980 | − | 15.7980i | −1.37504 | − | 1.37504i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.34847 | − | 9.00000i | −0.632456 | − | 0.774597i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 7.10102 | − | 5.79796i | 0.600146 | − | 0.490017i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | −2.10102 | + | 20.7980i | −0.174480 | + | 1.72718i | ||||
\(146\) | 4.20204 | 0.347763 | ||||||||
\(147\) | 3.42679 | + | 3.42679i | 0.282637 | + | 0.282637i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.1464i | 1.24084i | 0.784268 | + | 0.620422i | \(0.213039\pi\) | ||||
−0.784268 | + | 0.620422i | \(0.786961\pi\) | |||||||
\(150\) | −12.0000 | − | 2.44949i | −0.979796 | − | 0.200000i | ||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 18.6969i | 1.50664i | ||||||||
\(155\) | 10.8990 | + | 1.10102i | 0.875427 | + | 0.0884361i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | −14.6969 | + | 14.6969i | −1.16923 | + | 1.16923i | ||||
\(159\) | − | 6.00000i | − | 0.475831i | ||||||
\(160\) | 8.00000 | + | 9.79796i | 0.632456 | + | 0.774597i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.707107 | − | 0.707107i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.3485 | − | 15.7980i | 1.50628 | − | 1.22987i | ||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 7.10102 | − | 7.10102i | 0.547856 | − | 0.547856i | ||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.0000 | + | 14.0000i | −1.06440 | + | 1.06440i | −0.0666220 | + | 0.997778i | \(0.521222\pi\) |
−0.997778 | + | 0.0666220i | \(0.978778\pi\) | |||||||
\(174\) | 22.8990i | 1.73597i | ||||||||
\(175\) | 5.65153 | + | 8.55051i | 0.427216 | + | 0.646358i | ||||
\(176\) | −25.7980 | −1.94459 | ||||||||
\(177\) | −0.797959 | − | 0.797959i | −0.0599783 | − | 0.0599783i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.1464i | 1.87953i | 0.341818 | + | 0.939766i | \(0.388957\pi\) | ||||
−0.341818 | + | 0.939766i | \(0.611043\pi\) | |||||||
\(180\) | −13.3485 | − | 1.34847i | −0.994936 | − | 0.100509i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.0000 | 0.879883 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.6515i | 0.774785i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 9.79796 | + | 9.79796i | 0.707107 | + | 0.707107i | ||||
\(193\) | −17.8990 | + | 17.8990i | −1.28840 | + | 1.28840i | −0.352636 | + | 0.935760i | \(0.614715\pi\) |
−0.935760 | + | 0.352636i | \(0.885285\pi\) | |||||||
\(194\) | − | 21.5959i | − | 1.55050i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.59592 | 0.399708 | ||||||||
\(197\) | −17.1464 | − | 17.1464i | −1.22163 | − | 1.22163i | −0.967051 | − | 0.254581i | \(-0.918062\pi\) |
−0.254581 | − | 0.967051i | \(-0.581938\pi\) | |||||||
\(198\) | 19.3485 | − | 19.3485i | 1.37504 | − | 1.37504i | ||||
\(199\) | 14.0000i | 0.992434i | 0.868199 | + | 0.496217i | \(0.165278\pi\) | ||||
−0.868199 | + | 0.496217i | \(0.834722\pi\) | |||||||
\(200\) | −11.7980 | + | 7.79796i | −0.834242 | + | 0.551399i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.4495 | + | 16.4495i | 1.15738 | + | 1.15738i | ||||
\(203\) | 13.5505 | − | 13.5505i | 0.951059 | − | 0.951059i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.6969 | 1.99941 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 7.10102 | + | 8.69694i | 0.490017 | + | 0.600146i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | −4.89898 | − | 4.89898i | −0.336463 | − | 0.336463i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 16.0000i | − | 1.09374i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −1.00000 | ||||||||
\(217\) | −7.10102 | − | 7.10102i | −0.482049 | − | 0.482049i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.14643i | 0.347763i | ||||||||
\(220\) | 2.89898 | − | 28.6969i | 0.195449 | − | 1.93475i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.65153 | + | 5.65153i | −0.378454 | + | 0.378454i | −0.870544 | − | 0.492090i | \(-0.836233\pi\) |
0.492090 | + | 0.870544i | \(0.336233\pi\) | |||||||
\(224\) | − | 11.5959i | − | 0.774785i | ||||||
\(225\) | 3.00000 | − | 14.6969i | 0.200000 | − | 0.979796i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.34847 | + | 7.34847i | 0.487735 | + | 0.487735i | 0.907591 | − | 0.419856i | \(-0.137919\pi\) |
−0.419856 | + | 0.907591i | \(0.637919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.8990 | −1.50664 | ||||||||
\(232\) | 18.6969 | + | 18.6969i | 1.22751 | + | 1.22751i | ||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.30306 | −0.0848221 | ||||||||
\(237\) | −18.0000 | − | 18.0000i | −1.16923 | − | 1.16923i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −12.0000 | + | 9.79796i | −0.774597 | + | 0.632456i | ||||
\(241\) | −29.3939 | −1.89343 | −0.946713 | − | 0.322078i | \(-0.895619\pi\) | ||||
−0.946713 | + | 0.322078i | \(0.895619\pi\) | |||||||
\(242\) | 30.5959 | + | 30.5959i | 1.96678 | + | 1.96678i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.707107 | − | 0.707107i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.628827 | + | 6.22474i | −0.0401743 | + | 0.397684i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.79796 | − | 9.79796i | 0.622171 | − | 0.622171i | ||||
\(249\) | − | 9.79796i | − | 0.620920i | ||||||
\(250\) | −7.34847 | − | 14.0000i | −0.464758 | − | 0.885438i | ||||
\(251\) | −18.0454 | −1.13902 | −0.569508 | − | 0.821986i | \(-0.692866\pi\) | ||||
−0.569508 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(252\) | 8.69694 | + | 8.69694i | 0.547856 | + | 0.547856i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 17.1010i | − | 1.07301i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.0454 | −1.73597 | ||||||||
\(262\) | −13.5505 | − | 13.5505i | −0.837153 | − | 0.837153i | ||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | − | 31.5959i | − | 1.94459i | ||||||
\(265\) | 6.00000 | − | 4.89898i | 0.368577 | − | 0.300942i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 29.3485i | − | 1.78941i | −0.446660 | − | 0.894704i | \(-0.647387\pi\) | ||
0.446660 | − | 0.894704i | \(-0.352613\pi\) | |||||||
\(270\) | 1.65153 | − | 16.3485i | 0.100509 | − | 0.994936i | ||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 31.5959 | + | 6.44949i | 1.90531 | + | 0.388919i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.6969i | 0.879883i | ||||||||
\(280\) | 12.8990 | + | 1.30306i | 0.770861 | + | 0.0778728i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.0000 | + | 12.0000i | −0.707107 | + | 0.707107i | ||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | −22.8990 | + | 18.6969i | −1.34467 | + | 1.09792i | ||||
\(291\) | 26.4495 | 1.55050 | ||||||||
\(292\) | 4.20204 | + | 4.20204i | 0.245906 | + | 0.245906i | ||||
\(293\) | 22.0454 | − | 22.0454i | 1.28791 | − | 1.28791i | 0.351850 | − | 0.936056i | \(-0.385553\pi\) |
0.936056 | − | 0.351850i | \(-0.114447\pi\) | |||||||
\(294\) | 6.85357i | 0.399708i | ||||||||
\(295\) | 0.146428 | − | 1.44949i | 0.00852538 | − | 0.0843926i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.6969 | + | 23.6969i | 1.37504 | + | 1.37504i | ||||
\(298\) | −15.1464 | + | 15.1464i | −0.877409 | + | 0.877409i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.55051 | − | 14.4495i | −0.551399 | − | 0.834242i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.00000 | + | 2.00000i | 0.115087 | + | 0.115087i | ||||
\(303\) | −20.1464 | + | 20.1464i | −1.15738 | + | 1.15738i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | −18.6969 | + | 18.6969i | −1.06536 | + | 1.06536i | ||||
\(309\) | 35.1464i | 1.99941i | ||||||||
\(310\) | 9.79796 | + | 12.0000i | 0.556487 | + | 0.681554i | ||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1010 | − | 12.1010i | 0.683990 | − | 0.683990i | −0.276907 | − | 0.960897i | \(-0.589309\pi\) |
0.960897 | + | 0.276907i | \(0.0893093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.6515 | + | 8.69694i | −0.600146 | + | 0.490017i | ||||
\(316\) | −29.3939 | −1.65353 | ||||||||
\(317\) | 22.0000 | + | 22.0000i | 1.23564 | + | 1.23564i | 0.961764 | + | 0.273879i | \(0.0883068\pi\) |
0.273879 | + | 0.961764i | \(0.411693\pi\) | |||||||
\(318\) | 6.00000 | − | 6.00000i | 0.336463 | − | 0.336463i | ||||
\(319\) | − | 60.2929i | − | 3.37575i | ||||||
\(320\) | −1.79796 | + | 17.7980i | −0.100509 | + | 0.994936i | ||||
\(321\) | 19.5959 | 1.09374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 35.1464 | + | 3.55051i | 1.93475 | + | 0.195449i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | −8.00000 | − | 8.00000i | −0.439057 | − | 0.439057i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.2020 | 0.774785 | ||||||||
\(337\) | 3.69694 | + | 3.69694i | 0.201385 | + | 0.201385i | 0.800593 | − | 0.599208i | \(-0.204518\pi\) |
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 13.0000 | − | 13.0000i | 0.707107 | − | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.5959 | −1.71101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2020 | − | 14.2020i | 0.766838 | − | 0.766838i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.0000 | −1.50529 | ||||||||
\(347\) | −17.1464 | − | 17.1464i | −0.920468 | − | 0.920468i | 0.0765939 | − | 0.997062i | \(-0.475596\pi\) |
−0.997062 | + | 0.0765939i | \(0.975596\pi\) | |||||||
\(348\) | −22.8990 | + | 22.8990i | −1.22751 | + | 1.22751i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | −2.89898 | + | 14.2020i | −0.154957 | + | 0.759131i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.7980 | − | 25.7980i | −1.37504 | − | 1.37504i | ||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | − | 1.59592i | − | 0.0848221i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.1464 | + | 25.1464i | −1.32903 | + | 1.32903i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −12.0000 | − | 14.6969i | −0.632456 | − | 0.774597i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −37.4722 | + | 37.4722i | −1.96678 | + | 1.96678i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.14643 | + | 4.20204i | −0.269376 | + | 0.219945i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.4495 | + | 21.4495i | 1.11965 | + | 1.11965i | 0.991792 | + | 0.127862i | \(0.0408116\pi\) |
0.127862 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.10102 | −0.368667 | ||||||||
\(372\) | 12.0000 | + | 12.0000i | 0.622171 | + | 0.622171i | ||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.1464 | − | 9.00000i | 0.885438 | − | 0.464758i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −10.6515 | + | 10.6515i | −0.547856 | + | 0.547856i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.9444 | 1.07301 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 19.5959i | 1.00000i | ||||||||
\(385\) | −18.6969 | − | 22.8990i | −0.952884 | − | 1.16704i | ||||
\(386\) | −35.7980 | −1.82207 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.5959 | − | 21.5959i | 1.09637 | − | 1.09637i | ||||
\(389\) | − | 4.85357i | − | 0.246086i | −0.992401 | − | 0.123043i | \(-0.960735\pi\) | ||
0.992401 | − | 0.123043i | \(-0.0392653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.59592 | + | 5.59592i | 0.282637 | + | 0.282637i | ||||
\(393\) | 16.5959 | − | 16.5959i | 0.837153 | − | 0.837153i | ||||
\(394\) | − | 34.2929i | − | 1.72765i | ||||||
\(395\) | 3.30306 | − | 32.6969i | 0.166195 | − | 1.64516i | ||||
\(396\) | 38.6969 | 1.94459 | ||||||||
\(397\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(398\) | −14.0000 | + | 14.0000i | −0.701757 | + | 0.701757i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.5959 | − | 4.00000i | −0.979796 | − | 0.200000i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 32.8990i | 1.63679i | ||||||||
\(405\) | 20.0227 | + | 2.02270i | 0.994936 | + | 0.100509i | ||||
\(406\) | 27.1010 | 1.34500 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.1918i | 1.93791i | 0.247234 | + | 0.968956i | \(0.420478\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.6969 | + | 28.6969i | 1.41380 | + | 1.41380i | ||||
\(413\) | −0.944387 | + | 0.944387i | −0.0464703 | + | 0.0464703i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.79796 | − | 8.00000i | 0.480963 | − | 0.392705i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.6515i | 1.00889i | 0.863443 | + | 0.504447i | \(0.168303\pi\) | ||||
−0.863443 | + | 0.504447i | \(0.831697\pi\) | |||||||
\(420\) | −1.59592 | + | 15.7980i | −0.0778728 | + | 0.770861i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 9.79796i | − | 0.475831i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0000 | − | 16.0000i | 0.773389 | − | 0.773389i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −14.6969 | − | 14.6969i | −0.707107 | − | 0.707107i | ||||
\(433\) | 26.5959 | − | 26.5959i | 1.27812 | − | 1.27812i | 0.336399 | − | 0.941720i | \(-0.390791\pi\) |
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | − | 14.2020i | − | 0.681720i | ||||||
\(435\) | −22.8990 | − | 28.0454i | −1.09792 | − | 1.34467i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.14643 | + | 5.14643i | −0.245906 | + | 0.245906i | ||||
\(439\) | 34.0000i | 1.62273i | 0.584539 | + | 0.811366i | \(0.301275\pi\) | ||||
−0.584539 | + | 0.811366i | \(0.698725\pi\) | |||||||
\(440\) | 31.5959 | − | 25.7980i | 1.50628 | − | 1.22987i | ||||
\(441\) | −8.39388 | −0.399708 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0454 | − | 22.0454i | 1.04741 | − | 1.04741i | 0.0485901 | − | 0.998819i | \(-0.484527\pi\) |
0.998819 | − | 0.0485901i | \(-0.0154728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.3031 | −0.535215 | ||||||||
\(447\) | −18.5505 | − | 18.5505i | −0.877409 | − | 0.877409i | ||||
\(448\) | 11.5959 | − | 11.5959i | 0.547856 | − | 0.547856i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 17.6969 | − | 11.6969i | 0.834242 | − | 0.551399i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.44949 | + | 2.44949i | −0.115087 | + | 0.115087i | ||||
\(454\) | 14.6969i | 0.689761i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.20204 | + | 9.20204i | 0.430453 | + | 0.430453i | 0.888783 | − | 0.458329i | \(-0.151552\pi\) |
−0.458329 | + | 0.888783i | \(0.651552\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.9444 | 1.90697 | 0.953485 | − | 0.301440i | \(-0.0974673\pi\) | ||||
0.953485 | + | 0.301440i | \(0.0974673\pi\) | |||||||
\(462\) | −22.8990 | − | 22.8990i | −1.06536 | − | 1.06536i | ||||
\(463\) | −30.1464 | + | 30.1464i | −1.40102 | + | 1.40102i | −0.604161 | + | 0.796862i | \(0.706492\pi\) |
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(464\) | 37.3939i | 1.73597i | ||||||||
\(465\) | −14.6969 | + | 12.0000i | −0.681554 | + | 0.556487i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.0000 | − | 28.0000i | −1.29569 | − | 1.29569i | −0.931215 | − | 0.364471i | \(-0.881250\pi\) |
−0.364471 | − | 0.931215i | \(-0.618750\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.30306 | − | 1.30306i | −0.0599783 | − | 0.0599783i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 36.0000i | − | 1.65353i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.34847 | + | 7.34847i | 0.336463 | + | 0.336463i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −21.7980 | − | 2.20204i | −0.994936 | − | 0.100509i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −29.3939 | − | 29.3939i | −1.33885 | − | 1.33885i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 61.1918i | 2.78145i | ||||||||
\(485\) | 21.5959 | + | 26.4495i | 0.980620 | + | 1.20101i | ||||
\(486\) | 22.0454 | 1.00000 | ||||||||
\(487\) | −23.0454 | − | 23.0454i | −1.04429 | − | 1.04429i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) |
−0.0453143 | − | 0.998973i | \(-0.514429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.85357 | + | 5.59592i | −0.309613 | + | 0.252798i | ||||
\(491\) | 10.9444 | 0.493913 | 0.246957 | − | 0.969027i | \(-0.420569\pi\) | ||||
0.246957 | + | 0.969027i | \(0.420569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.34847 | + | 43.0454i | −0.195449 | + | 1.93475i | ||||
\(496\) | 19.5959 | 0.879883 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.79796 | − | 9.79796i | 0.439057 | − | 0.439057i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 6.65153 | − | 21.3485i | 0.297465 | − | 0.954733i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.0454 | − | 18.0454i | −0.805406 | − | 0.805406i | ||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 17.3939i | 0.774785i | ||||||||
\(505\) | −36.5959 | − | 3.69694i | −1.62850 | − | 0.164512i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.9217 | + | 15.9217i | 0.707107 | + | 0.707107i | ||||
\(508\) | 17.1010 | − | 17.1010i | 0.758735 | − | 0.758735i | ||||
\(509\) | − | 33.8434i | − | 1.50008i | −0.661392 | − | 0.750040i | \(-0.730034\pi\) | ||
0.661392 | − | 0.750040i | \(-0.269966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.09082 | 0.269442 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −35.1464 | + | 28.6969i | −1.54874 | + | 1.26454i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 34.2929i | − | 1.50529i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | −28.0454 | − | 28.0454i | −1.22751 | − | 1.22751i | ||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | − | 27.1010i | − | 1.18391i | ||||||
\(525\) | −17.3939 | − | 3.55051i | −0.759131 | − | 0.154957i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 31.5959 | − | 31.5959i | 1.37504 | − | 1.37504i | ||||
\(529\) | − | 23.0000i | − | 1.00000i | ||||||
\(530\) | 10.8990 | + | 1.10102i | 0.473421 | + | 0.0478253i | ||||
\(531\) | 1.95459 | 0.0848221 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000 | + | 19.5959i | 0.691740 | + | 0.847205i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.7980 | − | 30.7980i | −1.32903 | − | 1.32903i | ||||
\(538\) | 29.3485 | − | 29.3485i | 1.26530 | − | 1.26530i | ||||
\(539\) | − | 18.0454i | − | 0.777271i | ||||||
\(540\) | 18.0000 | − | 14.6969i | 0.774597 | − | 0.632456i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 22.0000 | + | 22.0000i | 0.944981 | + | 0.944981i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.1464 | + | 38.0454i | 1.07225 | + | 1.62226i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.3031 | + | 21.3031i | −0.905898 | + | 0.905898i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8434 | + | 31.8434i | 1.34925 | + | 1.34925i | 0.886480 | + | 0.462767i | \(0.153143\pi\) |
0.462767 | + | 0.886480i | \(0.346857\pi\) | |||||||
\(558\) | −14.6969 | + | 14.6969i | −0.622171 | + | 0.622171i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 11.5959 | + | 14.2020i | 0.490017 | + | 0.600146i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.9444 | + | 26.9444i | −1.13557 | + | 1.13557i | −0.146336 | + | 0.989235i | \(0.546748\pi\) |
−0.989235 | + | 0.146336i | \(0.953252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.0454 | − | 13.0454i | −0.547856 | − | 0.547856i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −1.00000 | ||||||||
\(577\) | 33.6969 | + | 33.6969i | 1.40282 | + | 1.40282i | 0.790980 | + | 0.611842i | \(0.209571\pi\) |
0.611842 | + | 0.790980i | \(0.290429\pi\) | |||||||
\(578\) | −17.0000 | + | 17.0000i | −0.707107 | + | 0.707107i | ||||
\(579\) | − | 43.8434i | − | 1.82207i | ||||||
\(580\) | −41.5959 | − | 4.20204i | −1.72718 | − | 0.174480i | ||||
\(581\) | −11.5959 | −0.481080 | ||||||||
\(582\) | 26.4495 | + | 26.4495i | 1.09637 | + | 1.09637i | ||||
\(583\) | −15.7980 | + | 15.7980i | −0.654285 | + | 0.654285i | ||||
\(584\) | 8.40408i | 0.347763i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 44.0908 | 1.82137 | ||||||||
\(587\) | 32.0000 | + | 32.0000i | 1.32078 | + | 1.32078i | 0.913144 | + | 0.407638i | \(0.133647\pi\) |
0.407638 | + | 0.913144i | \(0.366353\pi\) | |||||||
\(588\) | −6.85357 | + | 6.85357i | −0.282637 | + | 0.282637i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.59592 | − | 1.30306i | 0.0657029 | − | 0.0536462i | ||||
\(591\) | 42.0000 | 1.72765 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 47.3939i | 1.94459i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.2929 | −1.24084 | ||||||||
\(597\) | −17.1464 | − | 17.1464i | −0.701757 | − | 0.701757i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 4.89898 | − | 24.0000i | 0.200000 | − | 0.979796i | ||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000i | 0.162758i | ||||||||
\(605\) | −68.0681 | − | 6.87628i | −2.76736 | − | 0.279560i | ||||
\(606\) | −40.2929 | −1.63679 | ||||||||
\(607\) | −33.0454 | − | 33.0454i | −1.34127 | − | 1.34127i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
−0.446476 | − | 0.894795i | \(-0.647321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.1918i | 1.34500i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −37.3939 | −1.50664 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | −35.1464 | + | 35.1464i | −1.41380 | + | 1.41380i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | −2.20204 | + | 21.7980i | −0.0884361 | + | 0.875427i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 24.2020 | 0.967308 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −19.3485 | − | 1.95459i | −0.770861 | − | 0.0778728i | ||||
\(631\) | −4.89898 | −0.195025 | −0.0975126 | − | 0.995234i | \(-0.531089\pi\) | ||||
−0.0975126 | + | 0.995234i | \(0.531089\pi\) | |||||||
\(632\) | −29.3939 | − | 29.3939i | −1.16923 | − | 1.16923i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 44.0000i | 1.74746i | ||||||||
\(635\) | 17.1010 | + | 20.9444i | 0.678633 | + | 0.831153i | ||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 60.2929 | − | 60.2929i | 2.38702 | − | 2.38702i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.5959 | + | 16.0000i | −0.774597 | + | 0.632456i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 19.5959 | + | 19.5959i | 0.773389 | + | 0.773389i | ||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.707107 | − | 0.707107i | ||||
\(649\) | 4.20204i | 0.164945i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3939 | 0.681720 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.0000 | + | 34.0000i | −1.33052 | + | 1.33052i | −0.425622 | + | 0.904901i | \(0.639945\pi\) |
−0.904901 | + | 0.425622i | \(0.860055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.1464 | + | 3.04541i | 1.17792 | + | 0.118994i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.30306 | − | 6.30306i | −0.245906 | − | 0.245906i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 14.8536i | − | 0.578613i | −0.957237 | − | 0.289307i | \(-0.906575\pi\) | ||
0.957237 | − | 0.289307i | \(-0.0934247\pi\) | |||||||
\(660\) | 31.5959 | + | 38.6969i | 1.22987 | + | 1.50628i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 16.0000i | − | 0.620920i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 13.8434i | − | 0.535215i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 14.2020 | + | 14.2020i | 0.547856 | + | 0.547856i | ||||
\(673\) | 36.5959 | − | 36.5959i | 1.41067 | − | 1.41067i | 0.655302 | − | 0.755367i | \(-0.272541\pi\) |
0.755367 | − | 0.655302i | \(-0.227459\pi\) | |||||||
\(674\) | 7.39388i | 0.284801i | ||||||||
\(675\) | 14.3258 | + | 21.6742i | 0.551399 | + | 0.834242i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 2.00000 | + | 2.00000i | 0.0768662 | + | 0.0768662i | 0.744495 | − | 0.667628i | \(-0.232690\pi\) |
−0.667628 | + | 0.744495i | \(0.732690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 31.3031i | − | 1.20130i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | −31.5959 | − | 31.5959i | −1.20987 | − | 1.20987i | ||||
\(683\) | −4.00000 | + | 4.00000i | −0.153056 | + | 0.153056i | −0.779481 | − | 0.626426i | \(-0.784517\pi\) |
0.626426 | + | 0.779481i | \(0.284517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28.4041 | 1.08447 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | −28.0000 | − | 28.0000i | −1.06440 | − | 1.06440i | ||||
\(693\) | 28.0454 | − | 28.0454i | 1.06536 | − | 1.06536i | ||||
\(694\) | − | 34.2929i | − | 1.30174i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −45.7980 | −1.73597 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.1010 | + | 11.3031i | −0.646358 | + | 0.427216i | ||||
\(701\) | 0.944387 | 0.0356690 | 0.0178345 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178345 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 51.5959i | − | 1.94459i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.8434 | + | 23.8434i | 0.896722 | + | 0.896722i | ||||
\(708\) | 1.59592 | − | 1.59592i | 0.0599783 | − | 0.0599783i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.0908 | 1.65353 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −50.2929 | −1.87953 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 2.69694 | − | 26.6969i | 0.100509 | − | 0.994936i | ||||
\(721\) | 41.5959 | 1.54911 | ||||||||
\(722\) | −19.0000 | − | 19.0000i | −0.707107 | − | 0.707107i | ||||
\(723\) | 36.0000 | − | 36.0000i | 1.33885 | − | 1.33885i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.34847 | − | 45.7980i | 0.347193 | − | 1.70089i | ||||
\(726\) | −74.9444 | −2.78145 | ||||||||
\(727\) | 25.9444 | + | 25.9444i | 0.962224 | + | 0.962224i | 0.999312 | − | 0.0370879i | \(-0.0118082\pi\) |
−0.0370879 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | −9.34847 | − | 0.944387i | −0.346002 | − | 0.0349533i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 42.8990i | 1.58343i | ||||||||
\(735\) | −6.85357 | − | 8.39388i | −0.252798 | − | 0.309613i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.10102 | − | 7.10102i | −0.260687 | − | 0.260687i | ||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 24.0000i | 0.879883i | ||||||||
\(745\) | 3.40408 | − | 33.6969i | 0.124716 | − | 1.23456i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 12.0000i | 0.439057 | + | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 23.1918i | − | 0.847411i | ||||||
\(750\) | 26.1464 | + | 8.14643i | 0.954733 | + | 0.297465i | ||||
\(751\) | −53.8888 | −1.96643 | −0.983215 | − | 0.182453i | \(-0.941596\pi\) | ||||
−0.983215 | + | 0.182453i | \(0.941596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.1010 | − | 22.1010i | 0.805406 | − | 0.805406i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.44949 | − | 0.449490i | −0.161934 | − | 0.0163586i | ||||
\(756\) | −21.3031 | −0.774785 | ||||||||
\(757\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 20.9444 | + | 20.9444i | 0.758735 | + | 0.758735i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −19.5959 | + | 19.5959i | −0.707107 | + | 0.707107i | ||||
\(769\) | − | 26.0000i | − | 0.937584i | −0.883309 | − | 0.468792i | \(-0.844689\pi\) | ||
0.883309 | − | 0.468792i | \(-0.155311\pi\) | |||||||
\(770\) | 4.20204 | − | 41.5959i | 0.151431 | − | 1.49901i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −35.7980 | − | 35.7980i | −1.28840 | − | 1.28840i | ||||
\(773\) | −14.0000 | + | 14.0000i | −0.503545 | + | 0.503545i | −0.912538 | − | 0.408993i | \(-0.865880\pi\) |
0.408993 | + | 0.912538i | \(0.365880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.0000 | − | 4.89898i | −0.862105 | − | 0.175977i | ||||
\(776\) | 43.1918 | 1.55050 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.85357 | − | 4.85357i | 0.174009 | − | 0.174009i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.3485 | − | 34.3485i | 1.22751 | − | 1.22751i | ||||
\(784\) | 11.1918i | 0.399708i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 33.1918 | 1.18391 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | 34.2929 | − | 34.2929i | 1.22163 | − | 1.22163i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 36.0000 | − | 29.3939i | 1.28082 | − | 1.04579i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 38.6969 | + | 38.6969i | 1.37504 | + | 1.37504i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.34847 | + | 13.3485i | −0.0478253 | + | 0.473421i | ||||
\(796\) | −28.0000 | −0.992434 | ||||||||
\(797\) | −38.0000 | − | 38.0000i | −1.34603 | − | 1.34603i | −0.889928 | − | 0.456101i | \(-0.849246\pi\) |
−0.456101 | − | 0.889928i | \(-0.650754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −15.5959 | − | 23.5959i | −0.551399 | − | 0.834242i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5505 | − | 13.5505i | 0.478187 | − | 0.478187i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.9444 | + | 35.9444i | 1.26530 | + | 1.26530i | ||||
\(808\) | −32.8990 | + | 32.8990i | −1.15738 | + | 1.15738i | ||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 18.0000 | + | 22.0454i | 0.632456 | + | 0.774597i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 27.1010 | + | 27.1010i | 0.951059 | + | 0.951059i | ||||
\(813\) | −26.9444 | + | 26.9444i | −0.944981 | + | 0.944981i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −39.1918 | + | 39.1918i | −1.37031 | + | 1.37031i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.9546 | 0.417218 | 0.208609 | − | 0.977999i | \(-0.433106\pi\) | ||||
0.208609 | + | 0.977999i | \(0.433106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.1464 | + | 40.1464i | −1.39942 | + | 1.39942i | −0.597687 | + | 0.801730i | \(0.703913\pi\) |
−0.801730 | + | 0.597687i | \(0.796087\pi\) | |||||||
\(824\) | 57.3939i | 1.99941i | ||||||||
\(825\) | −46.5959 | + | 30.7980i | −1.62226 | + | 1.07225i | ||||
\(826\) | −1.88877 | −0.0657189 | ||||||||
\(827\) | 7.34847 | + | 7.34847i | 0.255531 | + | 0.255531i | 0.823234 | − | 0.567702i | \(-0.192168\pi\) |
−0.567702 | + | 0.823234i | \(0.692168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 17.7980 | + | 1.79796i | 0.617776 | + | 0.0624081i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.0000 | − | 18.0000i | −0.622171 | − | 0.622171i | ||||
\(838\) | −20.6515 | + | 20.6515i | −0.713395 | + | 0.713395i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −17.3939 | + | 14.2020i | −0.600146 | + | 0.490017i | ||||
\(841\) | −58.3939 | −2.01358 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.92168 | + | 28.9217i | −0.100509 | + | 0.994936i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.3485 | + | 44.3485i | 1.52383 | + | 1.52383i | ||||
\(848\) | 9.79796 | − | 9.79796i | 0.336463 | − | 0.336463i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.0000 | 1.09374 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | − | 29.3939i | − | 1.00000i | ||||||
\(865\) | 34.2929 | − | 28.0000i | 1.16599 | − | 0.952029i | ||||
\(866\) | 53.1918 | 1.80753 | ||||||||
\(867\) | −20.8207 | − | 20.8207i | −0.707107 | − | 0.707107i | ||||
\(868\) | 14.2020 | − | 14.2020i | 0.482049 | − | 0.482049i | ||||
\(869\) | 94.7878i | 3.21545i | ||||||||
\(870\) | 5.14643 | − | 50.9444i | 0.174480 | − | 1.72718i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.3939 | + | 32.3939i | −1.09637 | + | 1.09637i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.6515 | − | 20.2929i | −0.360087 | − | 0.686024i | ||||
\(876\) | −10.2929 | −0.347763 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | −34.0000 | + | 34.0000i | −1.14744 | + | 1.14744i | ||||
\(879\) | 54.0000i | 1.82137i | ||||||||
\(880\) | 57.3939 | + | 5.79796i | 1.93475 | + | 0.195449i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −8.39388 | − | 8.39388i | −0.282637 | − | 0.282637i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.59592 | + | 1.95459i | 0.0536462 | + | 0.0657029i | ||||
\(886\) | 44.0908 | 1.48126 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.7878i | − | 0.831355i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −58.0454 | −1.94459 | ||||||||
\(892\) | −11.3031 | − | 11.3031i | −0.378454 | − | 0.378454i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 37.1010i | − | 1.24084i | ||||||
\(895\) | 5.65153 | − | 55.9444i | 0.188910 | − | 1.87001i | ||||
\(896\) | 23.1918 | 0.774785 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.7980i | 1.52745i | ||||||||
\(900\) | 29.3939 | + | 6.00000i | 0.979796 | + | 0.200000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.89898 | −0.162758 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | −14.6969 | + | 14.6969i | −0.487735 | + | 0.487735i | ||||
\(909\) | − | 49.3485i | − | 1.63679i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7980 | + | 25.7980i | −0.853788 | + | 0.853788i | ||||
\(914\) | 18.4041i | 0.608753i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.6413 | − | 19.6413i | −0.648614 | − | 0.648614i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.2929i | − | 1.13122i | −0.824674 | − | 0.565608i | \(-0.808641\pi\) | ||
0.824674 | − | 0.565608i | \(-0.191359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.9444 | + | 40.9444i | 1.34843 | + | 1.34843i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | − | 45.7980i | − | 1.50664i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −60.2929 | −1.98135 | ||||||||
\(927\) | −43.0454 | − | 43.0454i | −1.41380 | − | 1.41380i | ||||
\(928\) | −37.3939 | + | 37.3939i | −1.22751 | + | 1.22751i | ||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | −26.6969 | − | 2.69694i | −0.875427 | − | 0.0884361i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 56.0000i | − | 1.83238i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2020 | + | 19.2020i | 0.627303 | + | 0.627303i | 0.947389 | − | 0.320085i | \(-0.103712\pi\) |
−0.320085 | + | 0.947389i | \(0.603712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.6413i | 0.967308i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.9444 | 1.98673 | 0.993365 | − | 0.115003i | \(-0.0366878\pi\) | ||||
0.993365 | + | 0.115003i | \(0.0366878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 2.60612i | − | 0.0848221i | ||||||
\(945\) | 2.39388 | − | 23.6969i | 0.0778728 | − | 0.770861i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.1464 | − | 17.1464i | −0.557184 | − | 0.557184i | 0.371321 | − | 0.928505i | \(-0.378905\pi\) |
−0.928505 | + | 0.371321i | \(0.878905\pi\) | |||||||
\(948\) | 36.0000 | − | 36.0000i | 1.16923 | − | 1.16923i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.8888 | −1.74746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 14.6969i | 0.475831i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 73.8434 | + | 73.8434i | 2.38702 | + | 2.38702i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −19.5959 | − | 24.0000i | −0.632456 | − | 0.774597i | ||||
\(961\) | −7.00000 | −0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0000 | + | 24.0000i | −0.773389 | + | 0.773389i | ||||
\(964\) | − | 58.7878i | − | 1.89343i | ||||||
\(965\) | 43.8434 | − | 35.7980i | 1.41137 | − | 1.15238i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.5505 | − | 28.5505i | −0.918123 | − | 0.918123i | 0.0787703 | − | 0.996893i | \(-0.474901\pi\) |
−0.996893 | + | 0.0787703i | \(0.974901\pi\) | |||||||
\(968\) | −61.1918 | + | 61.1918i | −1.96678 | + | 1.96678i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.85357 | + | 48.0454i | −0.155839 | + | 1.54265i | ||||
\(971\) | 46.4495 | 1.49064 | 0.745318 | − | 0.666710i | \(-0.232298\pi\) | ||||
0.745318 | + | 0.666710i | \(0.232298\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.707107 | + | 0.707107i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 46.0908i | − | 1.47684i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −12.4495 | − | 1.25765i | −0.397684 | − | 0.0401743i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.9444 | + | 10.9444i | 0.349249 | + | 0.349249i | ||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.2929 | + | 42.0000i | 1.09266 | + | 1.33823i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −47.3939 | + | 38.6969i | −1.50628 | + | 1.22987i | ||||
\(991\) | −58.0000 | −1.84243 | −0.921215 | − | 0.389053i | \(-0.872802\pi\) | ||||
−0.921215 | + | 0.389053i | \(0.872802\pi\) | |||||||
\(992\) | 19.5959 | + | 19.5959i | 0.622171 | + | 0.622171i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.14643 | − | 31.1464i | 0.0997485 | − | 0.987408i | ||||
\(996\) | 19.5959 | 0.620920 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | 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 | 120.2.w.b.77.1 | yes | 4 | |
3.2 | odd | 2 | 120.2.w.a.77.2 | yes | 4 | ||
4.3 | odd | 2 | 480.2.bi.a.17.2 | 4 | |||
5.2 | odd | 4 | 600.2.w.b.293.2 | 4 | |||
5.3 | odd | 4 | inner | 120.2.w.b.53.1 | yes | 4 | |
5.4 | even | 2 | 600.2.w.b.557.2 | 4 | |||
8.3 | odd | 2 | 480.2.bi.b.17.1 | 4 | |||
8.5 | even | 2 | 120.2.w.a.77.2 | yes | 4 | ||
12.11 | even | 2 | 480.2.bi.b.17.1 | 4 | |||
15.2 | even | 4 | 600.2.w.h.293.1 | 4 | |||
15.8 | even | 4 | 120.2.w.a.53.2 | ✓ | 4 | ||
15.14 | odd | 2 | 600.2.w.h.557.1 | 4 | |||
20.3 | even | 4 | 480.2.bi.a.113.2 | 4 | |||
24.5 | odd | 2 | CM | 120.2.w.b.77.1 | yes | 4 | |
24.11 | even | 2 | 480.2.bi.a.17.2 | 4 | |||
40.3 | even | 4 | 480.2.bi.b.113.1 | 4 | |||
40.13 | odd | 4 | 120.2.w.a.53.2 | ✓ | 4 | ||
40.29 | even | 2 | 600.2.w.h.557.1 | 4 | |||
40.37 | odd | 4 | 600.2.w.h.293.1 | 4 | |||
60.23 | odd | 4 | 480.2.bi.b.113.1 | 4 | |||
120.29 | odd | 2 | 600.2.w.b.557.2 | 4 | |||
120.53 | even | 4 | inner | 120.2.w.b.53.1 | yes | 4 | |
120.77 | even | 4 | 600.2.w.b.293.2 | 4 | |||
120.83 | odd | 4 | 480.2.bi.a.113.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.w.a.53.2 | ✓ | 4 | 15.8 | even | 4 | ||
120.2.w.a.53.2 | ✓ | 4 | 40.13 | odd | 4 | ||
120.2.w.a.77.2 | yes | 4 | 3.2 | odd | 2 | ||
120.2.w.a.77.2 | yes | 4 | 8.5 | even | 2 | ||
120.2.w.b.53.1 | yes | 4 | 5.3 | odd | 4 | inner | |
120.2.w.b.53.1 | yes | 4 | 120.53 | even | 4 | inner | |
120.2.w.b.77.1 | yes | 4 | 1.1 | even | 1 | trivial | |
120.2.w.b.77.1 | yes | 4 | 24.5 | odd | 2 | CM | |
480.2.bi.a.17.2 | 4 | 4.3 | odd | 2 | |||
480.2.bi.a.17.2 | 4 | 24.11 | even | 2 | |||
480.2.bi.a.113.2 | 4 | 20.3 | even | 4 | |||
480.2.bi.a.113.2 | 4 | 120.83 | odd | 4 | |||
480.2.bi.b.17.1 | 4 | 8.3 | odd | 2 | |||
480.2.bi.b.17.1 | 4 | 12.11 | even | 2 | |||
480.2.bi.b.113.1 | 4 | 40.3 | even | 4 | |||
480.2.bi.b.113.1 | 4 | 60.23 | odd | 4 | |||
600.2.w.b.293.2 | 4 | 5.2 | odd | 4 | |||
600.2.w.b.293.2 | 4 | 120.77 | even | 4 | |||
600.2.w.b.557.2 | 4 | 5.4 | even | 2 | |||
600.2.w.b.557.2 | 4 | 120.29 | odd | 2 | |||
600.2.w.h.293.1 | 4 | 15.2 | even | 4 | |||
600.2.w.h.293.1 | 4 | 40.37 | odd | 4 | |||
600.2.w.h.557.1 | 4 | 15.14 | odd | 2 | |||
600.2.w.h.557.1 | 4 | 40.29 | even | 2 |