Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.u.177.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.41421 | + | 2.44949i | 0.632456 | + | 1.09545i | 0.987048 | + | 0.160424i | \(0.0512862\pi\) |
−0.354593 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | −1.41421 | + | 2.44949i | −0.447214 | + | 0.774597i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.41421 | + | 2.44949i | −0.342997 | + | 0.594089i | −0.984988 | − | 0.172624i | \(-0.944775\pi\) |
0.641991 | + | 0.766712i | \(0.278109\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | −4.24264 | − | 7.34847i | −0.973329 | − | 1.68585i | −0.685344 | − | 0.728219i | \(-0.740348\pi\) |
−0.287984 | − | 0.957635i | \(-0.592985\pi\) | |||||||
\(20\) | −2.82843 | −0.632456 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | 2.82843 | + | 4.89898i | 0.554700 | + | 0.960769i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24264 | − | 7.34847i | 0.762001 | − | 1.31982i | −0.179817 | − | 0.983700i | \(-0.557551\pi\) |
0.941818 | − | 0.336124i | \(-0.109116\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 3.00000 | + | 5.19615i | 0.493197 | + | 0.854242i | 0.999969 | − | 0.00783774i | \(-0.00249486\pi\) |
−0.506772 | + | 0.862080i | \(0.669162\pi\) | |||||||
\(38\) | 4.24264 | − | 7.34847i | 0.688247 | − | 1.19208i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.41421 | − | 2.44949i | −0.223607 | − | 0.387298i | ||||
\(41\) | −8.48528 | −1.32518 | −0.662589 | − | 0.748983i | \(-0.730542\pi\) | ||||
−0.662589 | + | 0.748983i | \(0.730542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | −4.24264 | + | 7.34847i | −0.632456 | + | 1.09545i | ||||
\(46\) | −4.00000 | + | 6.92820i | −0.589768 | + | 1.02151i | ||||
\(47\) | 1.41421 | + | 2.44949i | 0.206284 | + | 0.357295i | 0.950541 | − | 0.310599i | \(-0.100530\pi\) |
−0.744257 | + | 0.667893i | \(0.767196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.82843 | + | 4.89898i | −0.392232 | + | 0.679366i | ||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 2.82843 | − | 4.89898i | 0.368230 | − | 0.637793i | −0.621059 | − | 0.783764i | \(-0.713297\pi\) |
0.989289 | + | 0.145971i | \(0.0466306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82843 | + | 4.89898i | 0.362143 | + | 0.627250i | 0.988313 | − | 0.152436i | \(-0.0487119\pi\) |
−0.626170 | + | 0.779686i | \(0.715379\pi\) | |||||||
\(62\) | 8.48528 | 1.07763 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.00000 | + | 13.8564i | 0.992278 | + | 1.71868i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | −1.41421 | − | 2.44949i | −0.171499 | − | 0.297044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | 4.24264 | − | 7.34847i | 0.496564 | − | 0.860073i | −0.503429 | − | 0.864037i | \(-0.667928\pi\) |
0.999992 | + | 0.00396356i | \(0.00126164\pi\) | |||||||
\(74\) | −3.00000 | + | 5.19615i | −0.348743 | + | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.48528 | 0.973329 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 1.41421 | − | 2.44949i | 0.158114 | − | 0.273861i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −4.24264 | − | 7.34847i | −0.468521 | − | 0.811503i | ||||
\(83\) | −2.82843 | −0.310460 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −5.65685 | − | 9.79796i | −0.599625 | − | 1.03858i | −0.992876 | − | 0.119150i | \(-0.961983\pi\) |
0.393251 | − | 0.919431i | \(-0.371350\pi\) | |||||||
\(90\) | −8.48528 | −0.894427 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.41421 | + | 2.44949i | −0.145865 | + | 0.252646i | ||||
\(95\) | 12.0000 | − | 20.7846i | 1.23117 | − | 2.13246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3137 | 1.14873 | 0.574367 | − | 0.818598i | \(-0.305248\pi\) | ||||
0.574367 | + | 0.818598i | \(0.305248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −1.50000 | − | 2.59808i | −0.150000 | − | 0.259808i | ||||
\(101\) | −5.65685 | + | 9.79796i | −0.562878 | + | 0.974933i | 0.434366 | + | 0.900737i | \(0.356973\pi\) |
−0.997244 | + | 0.0741967i | \(0.976361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.07107 | + | 12.2474i | 0.696733 | + | 1.20678i | 0.969593 | + | 0.244723i | \(0.0786971\pi\) |
−0.272860 | + | 0.962054i | \(0.587970\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −2.00000 | − | 3.46410i | −0.193347 | − | 0.334887i | 0.753010 | − | 0.658009i | \(-0.228601\pi\) |
−0.946357 | + | 0.323122i | \(0.895268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | − | 12.1244i | 0.670478 | − | 1.16130i | −0.307290 | − | 0.951616i | \(-0.599422\pi\) |
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(110\) | −1.41421 | − | 2.44949i | −0.134840 | − | 0.233550i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.3137 | + | 19.5959i | −1.05501 | + | 1.82733i | ||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 8.48528 | + | 14.6969i | 0.784465 | + | 1.35873i | ||||
\(118\) | 5.65685 | 0.520756 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −2.82843 | + | 4.89898i | −0.256074 | + | 0.443533i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.24264 | + | 7.34847i | 0.381000 | + | 0.659912i | ||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.00000 | + | 13.8564i | −0.701646 | + | 1.21529i | ||||
\(131\) | −1.41421 | − | 2.44949i | −0.123560 | − | 0.214013i | 0.797609 | − | 0.603175i | \(-0.206098\pi\) |
−0.921169 | + | 0.389162i | \(0.872765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.41421 | − | 2.44949i | 0.121268 | − | 0.210042i | ||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.48528 | −0.719712 | −0.359856 | − | 0.933008i | \(-0.617174\pi\) | ||||
−0.359856 | + | 0.933008i | \(0.617174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.82843 | + | 4.89898i | −0.236525 | + | 0.409673i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | −8.48528 | − | 14.6969i | −0.704664 | − | 1.22051i | ||||
\(146\) | 8.48528 | 0.702247 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 4.24264 | + | 7.34847i | 0.344124 | + | 0.596040i | ||||
\(153\) | −8.48528 | −0.685994 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.0000 | 1.92773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.89949 | − | 17.1464i | 0.790066 | − | 1.36843i | −0.135860 | − | 0.990728i | \(-0.543380\pi\) |
0.925926 | − | 0.377706i | \(-0.123287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.82843 | 0.223607 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −6.00000 | − | 10.3923i | −0.469956 | − | 0.813988i | 0.529454 | − | 0.848339i | \(-0.322397\pi\) |
−0.999410 | + | 0.0343508i | \(0.989064\pi\) | |||||||
\(164\) | 4.24264 | − | 7.34847i | 0.331295 | − | 0.573819i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.41421 | − | 2.44949i | −0.109764 | − | 0.190117i | ||||
\(167\) | −5.65685 | −0.437741 | −0.218870 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | −4.00000 | − | 6.92820i | −0.306786 | − | 0.531369i | ||||
\(171\) | 12.7279 | − | 22.0454i | 0.973329 | − | 1.68585i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −2.82843 | − | 4.89898i | −0.215041 | − | 0.372463i | 0.738244 | − | 0.674534i | \(-0.235655\pi\) |
−0.953285 | + | 0.302071i | \(0.902322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.65685 | − | 9.79796i | 0.423999 | − | 0.734388i | ||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | −4.24264 | − | 7.34847i | −0.316228 | − | 0.547723i | ||||
\(181\) | 8.48528 | 0.630706 | 0.315353 | − | 0.948974i | \(-0.397877\pi\) | ||||
0.315353 | + | 0.948974i | \(0.397877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | − | 6.92820i | −0.294884 | − | 0.510754i | ||||
\(185\) | −8.48528 | + | 14.6969i | −0.623850 | + | 1.08054i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41421 | − | 2.44949i | −0.103418 | − | 0.179124i | ||||
\(188\) | −2.82843 | −0.206284 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.0000 | 1.74114 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 5.65685 | + | 9.79796i | 0.406138 | + | 0.703452i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | 7.07107 | − | 12.2474i | 0.501255 | − | 0.868199i | −0.498744 | − | 0.866749i | \(-0.666205\pi\) |
0.999999 | − | 0.00144942i | \(-0.000461364\pi\) | |||||||
\(200\) | 1.50000 | − | 2.59808i | 0.106066 | − | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.3137 | −0.796030 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | − | 20.7846i | −0.838116 | − | 1.45166i | ||||
\(206\) | −7.07107 | + | 12.2474i | −0.492665 | + | 0.853320i | ||||
\(207\) | −12.0000 | + | 20.7846i | −0.834058 | + | 1.44463i | ||||
\(208\) | −2.82843 | − | 4.89898i | −0.196116 | − | 0.339683i | ||||
\(209\) | 8.48528 | 0.586939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.0000 | 1.92760 | 0.963800 | − | 0.266627i | \(-0.0859092\pi\) | ||||
0.963800 | + | 0.266627i | \(0.0859092\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | − | 3.46410i | 0.136717 | − | 0.236801i | ||||
\(215\) | −5.65685 | − | 9.79796i | −0.385794 | − | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.41421 | − | 2.44949i | 0.0953463 | − | 0.165145i | ||||
\(221\) | −8.00000 | + | 13.8564i | −0.538138 | + | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82843 | 0.189405 | 0.0947027 | − | 0.995506i | \(-0.469810\pi\) | ||||
0.0947027 | + | 0.995506i | \(0.469810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | −3.00000 | − | 5.19615i | −0.199557 | − | 0.345643i | ||||
\(227\) | −1.41421 | + | 2.44949i | −0.0938647 | + | 0.162578i | −0.909134 | − | 0.416503i | \(-0.863255\pi\) |
0.815270 | + | 0.579082i | \(0.196589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.07107 | + | 12.2474i | 0.467269 | + | 0.809334i | 0.999301 | − | 0.0373904i | \(-0.0119045\pi\) |
−0.532031 | + | 0.846725i | \(0.678571\pi\) | |||||||
\(230\) | −22.6274 | −1.49201 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 13.0000 | + | 22.5167i | 0.851658 | + | 1.47512i | 0.879711 | + | 0.475509i | \(0.157736\pi\) |
−0.0280525 | + | 0.999606i | \(0.508931\pi\) | |||||||
\(234\) | −8.48528 | + | 14.6969i | −0.554700 | + | 0.960769i | ||||
\(235\) | −4.00000 | + | 6.92820i | −0.260931 | + | 0.451946i | ||||
\(236\) | 2.82843 | + | 4.89898i | 0.184115 | + | 0.318896i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.41421 | + | 2.44949i | −0.0910975 | + | 0.157786i | −0.907973 | − | 0.419028i | \(-0.862371\pi\) |
0.816876 | + | 0.576814i | \(0.195704\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.65685 | −0.362143 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | − | 41.5692i | −1.52708 | − | 2.64499i | ||||
\(248\) | −4.24264 | + | 7.34847i | −0.269408 | + | 0.466628i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.82843 | + | 4.89898i | 0.178885 | + | 0.309839i | ||||
\(251\) | −5.65685 | −0.357057 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 4.00000 | + | 6.92820i | 0.250982 | + | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.65685 | − | 9.79796i | −0.352865 | − | 0.611180i | 0.633885 | − | 0.773427i | \(-0.281459\pi\) |
−0.986750 | + | 0.162247i | \(0.948126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.0000 | −0.992278 | ||||||||
\(261\) | −9.00000 | − | 15.5885i | −0.557086 | − | 0.964901i | ||||
\(262\) | 1.41421 | − | 2.44949i | 0.0873704 | − | 0.151330i | ||||
\(263\) | 8.00000 | − | 13.8564i | 0.493301 | − | 0.854423i | −0.506669 | − | 0.862141i | \(-0.669123\pi\) |
0.999970 | + | 0.00771799i | \(0.00245674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9706 | −1.04249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | + | 3.46410i | 0.122169 | + | 0.211604i | ||||
\(269\) | 12.7279 | − | 22.0454i | 0.776035 | − | 1.34413i | −0.158176 | − | 0.987411i | \(-0.550561\pi\) |
0.934211 | − | 0.356721i | \(-0.116105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1421 | − | 24.4949i | −0.859074 | − | 1.48796i | −0.872814 | − | 0.488053i | \(-0.837707\pi\) |
0.0137402 | − | 0.999906i | \(-0.495626\pi\) | |||||||
\(272\) | 2.82843 | 0.171499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | −4.24264 | − | 7.34847i | −0.254457 | − | 0.440732i | ||||
\(279\) | 25.4558 | 1.52400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.07107 | + | 12.2474i | −0.420331 | + | 0.728035i | −0.995972 | − | 0.0896677i | \(-0.971419\pi\) |
0.575640 | + | 0.817703i | \(0.304753\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.65685 | −0.334497 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | 4.50000 | + | 7.79423i | 0.264706 | + | 0.458484i | ||||
\(290\) | 8.48528 | − | 14.6969i | 0.498273 | − | 0.863034i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.24264 | + | 7.34847i | 0.248282 | + | 0.430037i | ||||
\(293\) | 5.65685 | 0.330477 | 0.165238 | − | 0.986254i | \(-0.447161\pi\) | ||||
0.165238 | + | 0.986254i | \(0.447161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | −3.00000 | − | 5.19615i | −0.174371 | − | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.00000 | + | 8.66025i | −0.289642 | + | 0.501675i | ||||
\(299\) | 22.6274 | + | 39.1918i | 1.30858 | + | 2.26652i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.24264 | + | 7.34847i | −0.243332 | + | 0.421464i | ||||
\(305\) | −8.00000 | + | 13.8564i | −0.458079 | + | 0.793416i | ||||
\(306\) | −4.24264 | − | 7.34847i | −0.242536 | − | 0.420084i | ||||
\(307\) | 14.1421 | 0.807134 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0000 | + | 20.7846i | 0.681554 | + | 1.18049i | ||||
\(311\) | −7.07107 | + | 12.2474i | −0.400963 | + | 0.694489i | −0.993842 | − | 0.110802i | \(-0.964658\pi\) |
0.592879 | + | 0.805292i | \(0.297991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.48528 | + | 14.6969i | 0.479616 | + | 0.830720i | 0.999727 | − | 0.0233791i | \(-0.00744247\pi\) |
−0.520110 | + | 0.854099i | \(0.674109\pi\) | |||||||
\(314\) | 19.7990 | 1.11732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.00000 | + | 1.73205i | 0.0561656 | + | 0.0972817i | 0.892741 | − | 0.450570i | \(-0.148779\pi\) |
−0.836576 | + | 0.547852i | \(0.815446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | 1.41421 | + | 2.44949i | 0.0790569 | + | 0.136931i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | −8.48528 | + | 14.6969i | −0.470679 | + | 0.815239i | ||||
\(326\) | 6.00000 | − | 10.3923i | 0.332309 | − | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.48528 | 0.468521 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 1.41421 | − | 2.44949i | 0.0776151 | − | 0.134433i | ||||
\(333\) | −9.00000 | + | 15.5885i | −0.493197 | + | 0.854242i | ||||
\(334\) | −2.82843 | − | 4.89898i | −0.154765 | − | 0.268060i | ||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 9.50000 | + | 16.4545i | 0.516732 | + | 0.895006i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | − | 6.92820i | 0.216930 | − | 0.375735i | ||||
\(341\) | 4.24264 | + | 7.34847i | 0.229752 | + | 0.397942i | ||||
\(342\) | 25.4558 | 1.37649 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.82843 | − | 4.89898i | 0.152057 | − | 0.263371i | ||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.3137 | 0.599625 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −12.0000 | − | 20.7846i | −0.633336 | − | 1.09697i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.353529 | − | 0.935423i | \(-0.384981\pi\) | |||||||
\(360\) | 4.24264 | − | 7.34847i | 0.223607 | − | 0.387298i | ||||
\(361\) | −26.5000 | + | 45.8993i | −1.39474 | + | 2.41576i | ||||
\(362\) | 4.24264 | + | 7.34847i | 0.222988 | + | 0.386227i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0000 | 1.25622 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7279 | + | 22.0454i | −0.664392 | + | 1.15076i | 0.315058 | + | 0.949073i | \(0.397976\pi\) |
−0.979450 | + | 0.201688i | \(0.935357\pi\) | |||||||
\(368\) | 4.00000 | − | 6.92820i | 0.208514 | − | 0.361158i | ||||
\(369\) | −12.7279 | − | 22.0454i | −0.662589 | − | 1.14764i | ||||
\(370\) | −16.9706 | −0.882258 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | + | 1.73205i | 0.0517780 | + | 0.0896822i | 0.890753 | − | 0.454488i | \(-0.150178\pi\) |
−0.838975 | + | 0.544170i | \(0.816844\pi\) | |||||||
\(374\) | 1.41421 | − | 2.44949i | 0.0731272 | − | 0.126660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.41421 | − | 2.44949i | −0.0729325 | − | 0.126323i | ||||
\(377\) | −33.9411 | −1.74806 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 12.0000 | + | 20.7846i | 0.615587 | + | 1.06623i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | + | 6.92820i | −0.204658 | + | 0.354478i | ||||
\(383\) | −7.07107 | − | 12.2474i | −0.361315 | − | 0.625815i | 0.626863 | − | 0.779130i | \(-0.284339\pi\) |
−0.988177 | + | 0.153314i | \(0.951005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | −6.00000 | − | 10.3923i | −0.304997 | − | 0.528271i | ||||
\(388\) | −5.65685 | + | 9.79796i | −0.287183 | + | 0.497416i | ||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.6274 | −1.14432 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.50000 | − | 2.59808i | 0.0753778 | − | 0.130558i | ||||
\(397\) | 4.24264 | + | 7.34847i | 0.212932 | + | 0.368809i | 0.952631 | − | 0.304129i | \(-0.0983654\pi\) |
−0.739699 | + | 0.672938i | \(0.765032\pi\) | |||||||
\(398\) | 14.1421 | 0.708881 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 5.00000 | + | 8.66025i | 0.249688 | + | 0.432472i | 0.963439 | − | 0.267927i | \(-0.0863386\pi\) |
−0.713751 | + | 0.700399i | \(0.753005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.0000 | − | 41.5692i | 1.19553 | − | 2.07071i | ||||
\(404\) | −5.65685 | − | 9.79796i | −0.281439 | − | 0.487467i | ||||
\(405\) | −25.4558 | −1.26491 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.24264 | + | 7.34847i | −0.209785 | + | 0.363358i | −0.951647 | − | 0.307195i | \(-0.900610\pi\) |
0.741862 | + | 0.670553i | \(0.233943\pi\) | |||||||
\(410\) | 12.0000 | − | 20.7846i | 0.592638 | − | 1.02648i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.1421 | −0.696733 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −24.0000 | −1.17954 | ||||||||
\(415\) | −4.00000 | − | 6.92820i | −0.196352 | − | 0.340092i | ||||
\(416\) | 2.82843 | − | 4.89898i | 0.138675 | − | 0.240192i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.24264 | + | 7.34847i | 0.207514 | + | 0.359425i | ||||
\(419\) | 22.6274 | 1.10542 | 0.552711 | − | 0.833373i | \(-0.313593\pi\) | ||||
0.552711 | + | 0.833373i | \(0.313593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 14.0000 | + | 24.2487i | 0.681509 | + | 1.18041i | ||||
\(423\) | −4.24264 | + | 7.34847i | −0.206284 | + | 0.357295i | ||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | −4.24264 | − | 7.34847i | −0.205798 | − | 0.356453i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.65685 | − | 9.79796i | 0.272798 | − | 0.472500i | ||||
\(431\) | −8.00000 | + | 13.8564i | −0.385346 | + | 0.667440i | −0.991817 | − | 0.127666i | \(-0.959251\pi\) |
0.606471 | + | 0.795106i | \(0.292585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.9411 | −1.63111 | −0.815553 | − | 0.578682i | \(-0.803567\pi\) | ||||
−0.815553 | + | 0.578682i | \(0.803567\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.00000 | + | 12.1244i | 0.335239 | + | 0.580651i | ||||
\(437\) | 33.9411 | − | 58.7878i | 1.62362 | − | 2.81220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1421 | + | 24.4949i | 0.674967 | + | 1.16908i | 0.976478 | + | 0.215615i | \(0.0691756\pi\) |
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(440\) | 2.82843 | 0.134840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.0000 | −0.761042 | ||||||||
\(443\) | 10.0000 | + | 17.3205i | 0.475114 | + | 0.822922i | 0.999594 | − | 0.0285009i | \(-0.00907336\pi\) |
−0.524479 | + | 0.851423i | \(0.675740\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0000 | − | 27.7128i | 0.758473 | − | 1.31371i | ||||
\(446\) | 1.41421 | + | 2.44949i | 0.0669650 | + | 0.115987i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | −4.50000 | − | 7.79423i | −0.212132 | − | 0.367423i | ||||
\(451\) | 4.24264 | − | 7.34847i | 0.199778 | − | 0.346026i | ||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.82843 | −0.132745 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | − | 8.66025i | −0.233890 | − | 0.405110i | 0.725059 | − | 0.688686i | \(-0.241812\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | −7.07107 | + | 12.2474i | −0.330409 | + | 0.572286i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.3137 | − | 19.5959i | −0.527504 | − | 0.913664i | ||||
\(461\) | 11.3137 | 0.526932 | 0.263466 | − | 0.964669i | \(-0.415134\pi\) | ||||
0.263466 | + | 0.964669i | \(0.415134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0000 | + | 22.5167i | −0.602213 | + | 1.04306i | ||||
\(467\) | −16.9706 | − | 29.3939i | −0.785304 | − | 1.36019i | −0.928817 | − | 0.370538i | \(-0.879173\pi\) |
0.143513 | − | 0.989648i | \(-0.454160\pi\) | |||||||
\(468\) | −16.9706 | −0.784465 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.82843 | + | 4.89898i | −0.130189 | + | 0.225494i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.4558 | 1.16799 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0000 | −0.824163 | ||||||||
\(478\) | 12.0000 | + | 20.7846i | 0.548867 | + | 0.950666i | ||||
\(479\) | −5.65685 | + | 9.79796i | −0.258468 | + | 0.447680i | −0.965832 | − | 0.259170i | \(-0.916551\pi\) |
0.707364 | + | 0.706850i | \(0.249884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9706 | + | 29.3939i | 0.773791 | + | 1.34025i | ||||
\(482\) | −2.82843 | −0.128831 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 16.0000 | + | 27.7128i | 0.726523 | + | 1.25837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | + | 6.92820i | −0.181257 | + | 0.313947i | −0.942309 | − | 0.334744i | \(-0.891350\pi\) |
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(488\) | −2.82843 | − | 4.89898i | −0.128037 | − | 0.221766i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528 | − | 14.6969i | 0.382158 | − | 0.661917i | ||||
\(494\) | 24.0000 | − | 41.5692i | 1.07981 | − | 1.87029i | ||||
\(495\) | −4.24264 | − | 7.34847i | −0.190693 | − | 0.330289i | ||||
\(496\) | −8.48528 | −0.381000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0000 | − | 38.1051i | −0.984855 | − | 1.70582i | −0.642578 | − | 0.766220i | \(-0.722135\pi\) |
−0.342277 | − | 0.939599i | \(-0.611198\pi\) | |||||||
\(500\) | −2.82843 | + | 4.89898i | −0.126491 | + | 0.219089i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.82843 | − | 4.89898i | −0.126239 | − | 0.218652i | ||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | −1.42398 | ||||||||
\(506\) | −4.00000 | − | 6.92820i | −0.177822 | − | 0.307996i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | + | 6.92820i | −0.177471 | + | 0.307389i | ||||
\(509\) | −15.5563 | − | 26.9444i | −0.689523 | − | 1.19429i | −0.971992 | − | 0.235013i | \(-0.924487\pi\) |
0.282469 | − | 0.959276i | \(-0.408846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.65685 | − | 9.79796i | 0.249513 | − | 0.432169i | ||||
\(515\) | −20.0000 | + | 34.6410i | −0.881305 | + | 1.52647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.82843 | −0.124394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.00000 | − | 13.8564i | −0.350823 | − | 0.607644i | ||||
\(521\) | −5.65685 | + | 9.79796i | −0.247831 | + | 0.429256i | −0.962924 | − | 0.269773i | \(-0.913051\pi\) |
0.715093 | + | 0.699030i | \(0.246385\pi\) | |||||||
\(522\) | 9.00000 | − | 15.5885i | 0.393919 | − | 0.682288i | ||||
\(523\) | 15.5563 | + | 26.9444i | 0.680232 | + | 1.17820i | 0.974910 | + | 0.222599i | \(0.0714542\pi\) |
−0.294678 | + | 0.955596i | \(0.595213\pi\) | |||||||
\(524\) | 2.82843 | 0.123560 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | −8.48528 | − | 14.6969i | −0.368577 | − | 0.638394i | ||||
\(531\) | 16.9706 | 0.736460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −48.0000 | −2.07911 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.65685 | − | 9.79796i | 0.244567 | − | 0.423603i | ||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.4558 | 1.09748 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 14.1421 | − | 24.4949i | 0.607457 | − | 1.05215i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.41421 | + | 2.44949i | 0.0606339 | + | 0.105021i | ||||
\(545\) | 39.5980 | 1.69619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 9.00000 | + | 15.5885i | 0.384461 | + | 0.665906i | ||||
\(549\) | −8.48528 | + | 14.6969i | −0.362143 | + | 0.627250i | ||||
\(550\) | 1.50000 | − | 2.59808i | 0.0639602 | − | 0.110782i | ||||
\(551\) | 25.4558 | + | 44.0908i | 1.08446 | + | 1.87833i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.24264 | − | 7.34847i | 0.179928 | − | 0.311645i | ||||
\(557\) | 21.0000 | − | 36.3731i | 0.889799 | − | 1.54118i | 0.0496855 | − | 0.998765i | \(-0.484178\pi\) |
0.840113 | − | 0.542411i | \(-0.182489\pi\) | |||||||
\(558\) | 12.7279 | + | 22.0454i | 0.538816 | + | 0.933257i | ||||
\(559\) | −22.6274 | −0.957038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | + | 5.19615i | 0.126547 | + | 0.219186i | ||||
\(563\) | 9.89949 | − | 17.1464i | 0.417214 | − | 0.722636i | −0.578444 | − | 0.815722i | \(-0.696340\pi\) |
0.995658 | + | 0.0930862i | \(0.0296732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.48528 | − | 14.6969i | −0.356978 | − | 0.618305i | ||||
\(566\) | −14.1421 | −0.594438 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0000 | − | 19.0526i | −0.461144 | − | 0.798725i | 0.537874 | − | 0.843025i | \(-0.319228\pi\) |
−0.999018 | + | 0.0443003i | \(0.985894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | + | 10.3923i | −0.251092 | + | 0.434904i | −0.963827 | − | 0.266529i | \(-0.914123\pi\) |
0.712735 | + | 0.701434i | \(0.247456\pi\) | |||||||
\(572\) | −2.82843 | − | 4.89898i | −0.118262 | − | 0.204837i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.0000 | −1.00087 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −8.48528 | + | 14.6969i | −0.353247 | + | 0.611842i | −0.986816 | − | 0.161844i | \(-0.948256\pi\) |
0.633569 | + | 0.773686i | \(0.281589\pi\) | |||||||
\(578\) | −4.50000 | + | 7.79423i | −0.187175 | + | 0.324197i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.9706 | 0.704664 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | −4.24264 | + | 7.34847i | −0.175562 | + | 0.304082i | ||||
\(585\) | −24.0000 | + | 41.5692i | −0.992278 | + | 1.71868i | ||||
\(586\) | 2.82843 | + | 4.89898i | 0.116841 | + | 0.202375i | ||||
\(587\) | −39.5980 | −1.63438 | −0.817192 | − | 0.576366i | \(-0.804470\pi\) | ||||
−0.817192 | + | 0.576366i | \(0.804470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72.0000 | −2.96671 | ||||||||
\(590\) | 8.00000 | + | 13.8564i | 0.329355 | + | 0.570459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00000 | − | 5.19615i | 0.123299 | − | 0.213561i | ||||
\(593\) | −18.3848 | − | 31.8434i | −0.754972 | − | 1.30765i | −0.945388 | − | 0.325947i | \(-0.894317\pi\) |
0.190416 | − | 0.981704i | \(-0.439016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.6274 | + | 39.1918i | −0.925304 | + | 1.60267i | ||||
\(599\) | 8.00000 | − | 13.8564i | 0.326871 | − | 0.566157i | −0.655018 | − | 0.755613i | \(-0.727339\pi\) |
0.981889 | + | 0.189456i | \(0.0606724\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.7990 | 0.807618 | 0.403809 | − | 0.914843i | \(-0.367686\pi\) | ||||
0.403809 | + | 0.914843i | \(0.367686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | 1.41421 | − | 2.44949i | 0.0574960 | − | 0.0995859i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9706 | − | 29.3939i | −0.688814 | − | 1.19306i | −0.972222 | − | 0.234061i | \(-0.924798\pi\) |
0.283408 | − | 0.958999i | \(-0.408535\pi\) | |||||||
\(608\) | −8.48528 | −0.344124 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.0000 | −0.647821 | ||||||||
\(611\) | 8.00000 | + | 13.8564i | 0.323645 | + | 0.560570i | ||||
\(612\) | 4.24264 | − | 7.34847i | 0.171499 | − | 0.297044i | ||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 7.07107 | + | 12.2474i | 0.285365 | + | 0.494267i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0000 | 1.52982 | 0.764911 | − | 0.644136i | \(-0.222783\pi\) | ||||
0.764911 | + | 0.644136i | \(0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.65685 | + | 9.79796i | −0.227368 | + | 0.393813i | −0.957027 | − | 0.289998i | \(-0.906345\pi\) |
0.729659 | + | 0.683811i | \(0.239679\pi\) | |||||||
\(620\) | −12.0000 | + | 20.7846i | −0.481932 | + | 0.834730i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.1421 | −0.567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 26.8468i | 0.620000 | + | 1.07387i | ||||
\(626\) | −8.48528 | + | 14.6969i | −0.339140 | + | 0.587408i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.89949 | + | 17.1464i | 0.395033 | + | 0.684217i | ||||
\(629\) | −16.9706 | −0.676661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00000 | + | 1.73205i | −0.0397151 | + | 0.0687885i | ||||
\(635\) | 11.3137 | + | 19.5959i | 0.448971 | + | 0.777640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.41421 | + | 2.44949i | −0.0559017 | + | 0.0968246i | ||||
\(641\) | −23.0000 | + | 39.8372i | −0.908445 | + | 1.57347i | −0.0922210 | + | 0.995739i | \(0.529397\pi\) |
−0.816224 | + | 0.577735i | \(0.803937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.65685 | −0.223085 | −0.111542 | − | 0.993760i | \(-0.535579\pi\) | ||||
−0.111542 | + | 0.993760i | \(0.535579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | −18.3848 | + | 31.8434i | −0.722780 | + | 1.25189i | 0.237101 | + | 0.971485i | \(0.423803\pi\) |
−0.959881 | + | 0.280407i | \(0.909531\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 2.82843 | + | 4.89898i | 0.111025 | + | 0.192302i | ||||
\(650\) | −16.9706 | −0.665640 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0000 | 0.469956 | ||||||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | − | 6.92820i | 0.156293 | − | 0.270707i | ||||
\(656\) | 4.24264 | + | 7.34847i | 0.165647 | + | 0.286910i | ||||
\(657\) | 25.4558 | 0.993127 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.24264 | + | 7.34847i | −0.165020 | + | 0.285822i | −0.936662 | − | 0.350234i | \(-0.886102\pi\) |
0.771643 | + | 0.636056i | \(0.219435\pi\) | |||||||
\(662\) | −2.00000 | + | 3.46410i | −0.0777322 | + | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.82843 | 0.109764 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.0000 | −0.697486 | ||||||||
\(667\) | −24.0000 | − | 41.5692i | −0.929284 | − | 1.60957i | ||||
\(668\) | 2.82843 | − | 4.89898i | 0.109435 | − | 0.189547i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.65685 | + | 9.79796i | 0.218543 | + | 0.378528i | ||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | −9.00000 | − | 15.5885i | −0.346667 | − | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.50000 | + | 16.4545i | −0.365385 | + | 0.632865i | ||||
\(677\) | 14.1421 | + | 24.4949i | 0.543526 | + | 0.941415i | 0.998698 | + | 0.0510117i | \(0.0162446\pi\) |
−0.455172 | + | 0.890404i | \(0.650422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.24264 | + | 7.34847i | −0.162459 | + | 0.281387i | ||||
\(683\) | 10.0000 | − | 17.3205i | 0.382639 | − | 0.662751i | −0.608799 | − | 0.793324i | \(-0.708349\pi\) |
0.991439 | + | 0.130573i | \(0.0416818\pi\) | |||||||
\(684\) | 12.7279 | + | 22.0454i | 0.486664 | + | 0.842927i | ||||
\(685\) | 50.9117 | 1.94524 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −16.9706 | + | 29.3939i | −0.646527 | + | 1.11982i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4558 | − | 44.0908i | −0.968386 | − | 1.67729i | −0.700229 | − | 0.713918i | \(-0.746919\pi\) |
−0.268157 | − | 0.963375i | \(-0.586415\pi\) | |||||||
\(692\) | 5.65685 | 0.215041 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | −12.0000 | − | 20.7846i | −0.455186 | − | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0000 | − | 20.7846i | 0.454532 | − | 0.787273i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4558 | − | 44.0908i | 0.960085 | − | 1.66292i | ||||
\(704\) | −0.500000 | + | 0.866025i | −0.0188445 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | − | 8.66025i | −0.187779 | − | 0.325243i | 0.756730 | − | 0.653727i | \(-0.226796\pi\) |
−0.944509 | + | 0.328484i | \(0.893462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.65685 | + | 9.79796i | 0.212000 | + | 0.367194i | ||||
\(713\) | 67.8823 | 2.54221 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | −12.7279 | − | 22.0454i | −0.474671 | − | 0.822155i | 0.524908 | − | 0.851159i | \(-0.324100\pi\) |
−0.999579 | + | 0.0290041i | \(0.990766\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −53.0000 | −1.97246 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.24264 | + | 7.34847i | −0.157676 | + | 0.273104i | ||||
\(725\) | 9.00000 | − | 15.5885i | 0.334252 | − | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1421 | 0.524503 | 0.262251 | − | 0.965000i | \(-0.415535\pi\) | ||||
0.262251 | + | 0.965000i | \(0.415535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 12.0000 | + | 20.7846i | 0.444140 | + | 0.769273i | ||||
\(731\) | 5.65685 | − | 9.79796i | 0.209226 | − | 0.362391i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.48528 | − | 14.6969i | −0.313411 | − | 0.542844i | 0.665687 | − | 0.746231i | \(-0.268138\pi\) |
−0.979098 | + | 0.203387i | \(0.934805\pi\) | |||||||
\(734\) | −25.4558 | −0.939592 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 2.00000 | + | 3.46410i | 0.0736709 | + | 0.127602i | ||||
\(738\) | 12.7279 | − | 22.0454i | 0.468521 | − | 0.811503i | ||||
\(739\) | −18.0000 | + | 31.1769i | −0.662141 | + | 1.14686i | 0.317911 | + | 0.948120i | \(0.397019\pi\) |
−0.980052 | + | 0.198741i | \(0.936315\pi\) | |||||||
\(740\) | −8.48528 | − | 14.6969i | −0.311925 | − | 0.540270i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0000 | 0.586983 | 0.293492 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1421 | + | 24.4949i | −0.518128 | + | 0.897424i | ||||
\(746\) | −1.00000 | + | 1.73205i | −0.0366126 | + | 0.0634149i | ||||
\(747\) | −4.24264 | − | 7.34847i | −0.155230 | − | 0.268866i | ||||
\(748\) | 2.82843 | 0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 1.41421 | − | 2.44949i | 0.0515711 | − | 0.0893237i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.9706 | − | 29.3939i | −0.618031 | − | 1.07046i | ||||
\(755\) | −22.6274 | −0.823496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −14.0000 | − | 24.2487i | −0.508503 | − | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | + | 20.7846i | −0.435286 | + | 0.753937i | ||||
\(761\) | 1.41421 | + | 2.44949i | 0.0512652 | + | 0.0887939i | 0.890519 | − | 0.454946i | \(-0.150341\pi\) |
−0.839254 | + | 0.543740i | \(0.817008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | −12.0000 | − | 20.7846i | −0.433861 | − | 0.751469i | ||||
\(766\) | 7.07107 | − | 12.2474i | 0.255488 | − | 0.442518i | ||||
\(767\) | 16.0000 | − | 27.7128i | 0.577727 | − | 1.00065i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.7696 | −1.32594 | −0.662972 | − | 0.748644i | \(-0.730705\pi\) | ||||
−0.662972 | + | 0.748644i | \(0.730705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.00000 | + | 12.1244i | 0.251936 | + | 0.436365i | ||||
\(773\) | −1.41421 | + | 2.44949i | −0.0508657 | + | 0.0881020i | −0.890337 | − | 0.455302i | \(-0.849531\pi\) |
0.839471 | + | 0.543404i | \(0.182865\pi\) | |||||||
\(774\) | 6.00000 | − | 10.3923i | 0.215666 | − | 0.373544i | ||||
\(775\) | 12.7279 | + | 22.0454i | 0.457200 | + | 0.791894i | ||||
\(776\) | −11.3137 | −0.406138 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | 36.0000 | + | 62.3538i | 1.28983 | + | 2.23406i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −11.3137 | − | 19.5959i | −0.404577 | − | 0.700749i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.0000 | 1.99873 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7279 | − | 22.0454i | 0.453701 | − | 0.785834i | −0.544911 | − | 0.838494i | \(-0.683437\pi\) |
0.998613 | + | 0.0526599i | \(0.0167699\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | 16.0000 | + | 27.7128i | 0.568177 | + | 0.984111i | ||||
\(794\) | −4.24264 | + | 7.34847i | −0.150566 | + | 0.260787i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.07107 | + | 12.2474i | 0.250627 | + | 0.434099i | ||||
\(797\) | −19.7990 | −0.701316 | −0.350658 | − | 0.936504i | \(-0.614042\pi\) | ||||
−0.350658 | + | 0.936504i | \(0.614042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 1.50000 | + | 2.59808i | 0.0530330 | + | 0.0918559i | ||||
\(801\) | 16.9706 | − | 29.3939i | 0.599625 | − | 1.03858i | ||||
\(802\) | −5.00000 | + | 8.66025i | −0.176556 | + | 0.305804i | ||||
\(803\) | 4.24264 | + | 7.34847i | 0.149720 | + | 0.259322i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48.0000 | 1.69073 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.65685 | − | 9.79796i | 0.199007 | − | 0.344691i | ||||
\(809\) | −13.0000 | + | 22.5167i | −0.457056 | + | 0.791644i | −0.998804 | − | 0.0488972i | \(-0.984429\pi\) |
0.541748 | + | 0.840541i | \(0.317763\pi\) | |||||||
\(810\) | −12.7279 | − | 22.0454i | −0.447214 | − | 0.774597i | ||||
\(811\) | −8.48528 | −0.297959 | −0.148979 | − | 0.988840i | \(-0.547599\pi\) | ||||
−0.148979 | + | 0.988840i | \(0.547599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | − | 5.19615i | −0.105150 | − | 0.182125i | ||||
\(815\) | 16.9706 | − | 29.3939i | 0.594453 | − | 1.02962i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.9706 | + | 29.3939i | 0.593725 | + | 1.02836i | ||||
\(818\) | −8.48528 | −0.296681 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0000 | 0.838116 | ||||||||
\(821\) | −11.0000 | − | 19.0526i | −0.383903 | − | 0.664939i | 0.607714 | − | 0.794156i | \(-0.292087\pi\) |
−0.991616 | + | 0.129217i | \(0.958754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(824\) | −7.07107 | − | 12.2474i | −0.246332 | − | 0.426660i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | −12.0000 | − | 20.7846i | −0.417029 | − | 0.722315i | ||||
\(829\) | 12.7279 | − | 22.0454i | 0.442059 | − | 0.765669i | −0.555783 | − | 0.831327i | \(-0.687582\pi\) |
0.997842 | + | 0.0656587i | \(0.0209148\pi\) | |||||||
\(830\) | 4.00000 | − | 6.92820i | 0.138842 | − | 0.240481i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.65685 | 0.196116 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | − | 13.8564i | −0.276851 | − | 0.479521i | ||||
\(836\) | −4.24264 | + | 7.34847i | −0.146735 | + | 0.254152i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.3137 | + | 19.5959i | 0.390826 | + | 0.676930i | ||||
\(839\) | −53.7401 | −1.85531 | −0.927657 | − | 0.373432i | \(-0.878181\pi\) | ||||
−0.927657 | + | 0.373432i | \(0.878181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −13.0000 | − | 22.5167i | −0.448010 | − | 0.775975i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.0000 | + | 24.2487i | −0.481900 | + | 0.834675i | ||||
\(845\) | 26.8701 | + | 46.5403i | 0.924358 | + | 1.60104i | ||||
\(846\) | −8.48528 | −0.291730 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.24264 | − | 7.34847i | 0.145521 | − | 0.252050i | ||||
\(851\) | −24.0000 | + | 41.5692i | −0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.9117 | −1.74318 | −0.871592 | − | 0.490233i | \(-0.836912\pi\) | ||||
−0.871592 | + | 0.490233i | \(0.836912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72.0000 | 2.46235 | ||||||||
\(856\) | 2.00000 | + | 3.46410i | 0.0683586 | + | 0.118401i | ||||
\(857\) | 1.41421 | − | 2.44949i | 0.0483086 | − | 0.0836730i | −0.840860 | − | 0.541253i | \(-0.817950\pi\) |
0.889169 | + | 0.457580i | \(0.151284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7990 | − | 34.2929i | −0.675533 | − | 1.17006i | −0.976313 | − | 0.216364i | \(-0.930580\pi\) |
0.300780 | − | 0.953694i | \(-0.402753\pi\) | |||||||
\(860\) | 11.3137 | 0.385794 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | 12.0000 | + | 20.7846i | 0.408485 | + | 0.707516i | 0.994720 | − | 0.102624i | \(-0.0327240\pi\) |
−0.586235 | + | 0.810141i | \(0.699391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | − | 13.8564i | 0.272008 | − | 0.471132i | ||||
\(866\) | −16.9706 | − | 29.3939i | −0.576683 | − | 0.998845i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3137 | − | 19.5959i | 0.383350 | − | 0.663982i | ||||
\(872\) | −7.00000 | + | 12.1244i | −0.237050 | + | 0.410582i | ||||
\(873\) | 16.9706 | + | 29.3939i | 0.574367 | + | 0.994832i | ||||
\(874\) | 67.8823 | 2.29615 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.00000 | + | 12.1244i | 0.236373 | + | 0.409410i | 0.959671 | − | 0.281126i | \(-0.0907079\pi\) |
−0.723298 | + | 0.690536i | \(0.757375\pi\) | |||||||
\(878\) | −14.1421 | + | 24.4949i | −0.477274 | + | 0.826663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.41421 | + | 2.44949i | 0.0476731 | + | 0.0825723i | ||||
\(881\) | 5.65685 | 0.190584 | 0.0952921 | − | 0.995449i | \(-0.469621\pi\) | ||||
0.0952921 | + | 0.995449i | \(0.469621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | −8.00000 | − | 13.8564i | −0.269069 | − | 0.466041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.0000 | + | 17.3205i | −0.335957 | + | 0.581894i | ||||
\(887\) | 22.6274 | + | 39.1918i | 0.759754 | + | 1.31593i | 0.942976 | + | 0.332861i | \(0.108014\pi\) |
−0.183221 | + | 0.983072i | \(0.558653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.0000 | 1.07264 | ||||||||
\(891\) | −4.50000 | − | 7.79423i | −0.150756 | − | 0.261116i | ||||
\(892\) | −1.41421 | + | 2.44949i | −0.0473514 | + | 0.0820150i | ||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.9411 | 1.13453 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | −25.4558 | + | 44.0908i | −0.849000 | + | 1.47051i | ||||
\(900\) | 4.50000 | − | 7.79423i | 0.150000 | − | 0.259808i | ||||
\(901\) | −8.48528 | − | 14.6969i | −0.282686 | − | 0.489626i | ||||
\(902\) | 8.48528 | 0.282529 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 12.0000 | + | 20.7846i | 0.398893 | + | 0.690904i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | − | 10.3923i | 0.199227 | − | 0.345071i | −0.749051 | − | 0.662512i | \(-0.769490\pi\) |
0.948278 | + | 0.317441i | \(0.102824\pi\) | |||||||
\(908\) | −1.41421 | − | 2.44949i | −0.0469323 | − | 0.0812892i | ||||
\(909\) | −33.9411 | −1.12576 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0000 | 1.06021 | 0.530104 | − | 0.847933i | \(-0.322153\pi\) | ||||
0.530104 | + | 0.847933i | \(0.322153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.41421 | − | 2.44949i | 0.0468036 | − | 0.0810663i | ||||
\(914\) | 5.00000 | − | 8.66025i | 0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.1421 | −0.467269 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 11.3137 | − | 19.5959i | 0.373002 | − | 0.646058i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.65685 | + | 9.79796i | 0.186299 | + | 0.322679i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0000 | −0.591836 | ||||||||
\(926\) | −12.0000 | − | 20.7846i | −0.394344 | − | 0.683025i | ||||
\(927\) | −21.2132 | + | 36.7423i | −0.696733 | + | 1.20678i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | 5.65685 | + | 9.79796i | 0.185595 | + | 0.321461i | 0.943777 | − | 0.330583i | \(-0.107245\pi\) |
−0.758182 | + | 0.652043i | \(0.773912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26.0000 | −0.851658 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.9706 | − | 29.3939i | 0.555294 | − | 0.961797i | ||||
\(935\) | 4.00000 | − | 6.92820i | 0.130814 | − | 0.226576i | ||||
\(936\) | −8.48528 | − | 14.6969i | −0.277350 | − | 0.480384i | ||||
\(937\) | −19.7990 | −0.646805 | −0.323402 | − | 0.946262i | \(-0.604827\pi\) | ||||
−0.323402 | + | 0.946262i | \(0.604827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.00000 | − | 6.92820i | −0.130466 | − | 0.225973i | ||||
\(941\) | −25.4558 | + | 44.0908i | −0.829837 | + | 1.43732i | 0.0683291 | + | 0.997663i | \(0.478233\pi\) |
−0.898166 | + | 0.439657i | \(0.855100\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.9411 | − | 58.7878i | −1.10528 | − | 1.91439i | ||||
\(944\) | −5.65685 | −0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −26.0000 | − | 45.0333i | −0.844886 | − | 1.46339i | −0.885720 | − | 0.464220i | \(-0.846335\pi\) |
0.0408333 | − | 0.999166i | \(-0.486999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | − | 41.5692i | 0.779073 | − | 1.34939i | ||||
\(950\) | 12.7279 | + | 22.0454i | 0.412948 | + | 0.715247i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000 | 1.36051 | 0.680257 | − | 0.732974i | \(-0.261868\pi\) | ||||
0.680257 | + | 0.732974i | \(0.261868\pi\) | |||||||
\(954\) | −9.00000 | − | 15.5885i | −0.291386 | − | 0.504695i | ||||
\(955\) | −11.3137 | + | 19.5959i | −0.366103 | + | 0.634109i | ||||
\(956\) | −12.0000 | + | 20.7846i | −0.388108 | + | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.3137 | −0.365529 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5000 | − | 35.5070i | −0.661290 | − | 1.14539i | ||||
\(962\) | −16.9706 | + | 29.3939i | −0.547153 | + | 0.947697i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | −1.41421 | − | 2.44949i | −0.0455488 | − | 0.0788928i | ||||
\(965\) | 39.5980 | 1.27470 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0000 | −1.28631 | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.0000 | + | 27.7128i | −0.513729 | + | 0.889805i | ||||
\(971\) | −5.65685 | − | 9.79796i | −0.181537 | − | 0.314431i | 0.760867 | − | 0.648908i | \(-0.224774\pi\) |
−0.942404 | + | 0.334476i | \(0.891441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.82843 | − | 4.89898i | 0.0905357 | − | 0.156813i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3137 | 0.361588 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0000 | 1.34096 | ||||||||
\(982\) | −6.00000 | − | 10.3923i | −0.191468 | − | 0.331632i | ||||
\(983\) | 24.0416 | − | 41.6413i | 0.766809 | − | 1.32815i | −0.172476 | − | 0.985014i | \(-0.555177\pi\) |
0.939285 | − | 0.343138i | \(-0.111490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.4558 | − | 44.0908i | −0.811091 | − | 1.40485i | ||||
\(986\) | 16.9706 | 0.540453 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48.0000 | 1.52708 | ||||||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | 4.24264 | − | 7.34847i | 0.134840 | − | 0.233550i | ||||
\(991\) | −12.0000 | + | 20.7846i | −0.381193 | + | 0.660245i | −0.991233 | − | 0.132125i | \(-0.957820\pi\) |
0.610040 | + | 0.792370i | \(0.291153\pi\) | |||||||
\(992\) | −4.24264 | − | 7.34847i | −0.134704 | − | 0.233314i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.0000 | 1.26809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.65685 | + | 9.79796i | −0.179154 | + | 0.310304i | −0.941591 | − | 0.336758i | \(-0.890669\pi\) |
0.762437 | + | 0.647063i | \(0.224003\pi\) | |||||||
\(998\) | 22.0000 | − | 38.1051i | 0.696398 | − | 1.20620i | ||||
\(999\) | 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 | 1078.2.e.u.67.2 | 4 | ||
7.2 | even | 3 | inner | 1078.2.e.u.177.2 | 4 | ||
7.3 | odd | 6 | 1078.2.a.o.1.2 | yes | 2 | ||
7.4 | even | 3 | 1078.2.a.o.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 1078.2.e.u.177.1 | 4 | ||
7.6 | odd | 2 | inner | 1078.2.e.u.67.1 | 4 | ||
21.11 | odd | 6 | 9702.2.a.dk.1.2 | 2 | |||
21.17 | even | 6 | 9702.2.a.dk.1.1 | 2 | |||
28.3 | even | 6 | 8624.2.a.bo.1.2 | 2 | |||
28.11 | odd | 6 | 8624.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.a.o.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
1078.2.a.o.1.2 | yes | 2 | 7.3 | odd | 6 | ||
1078.2.e.u.67.1 | 4 | 7.6 | odd | 2 | inner | ||
1078.2.e.u.67.2 | 4 | 1.1 | even | 1 | trivial | ||
1078.2.e.u.177.1 | 4 | 7.5 | odd | 6 | inner | ||
1078.2.e.u.177.2 | 4 | 7.2 | even | 3 | inner | ||
8624.2.a.bo.1.1 | 2 | 28.11 | odd | 6 | |||
8624.2.a.bo.1.2 | 2 | 28.3 | even | 6 | |||
9702.2.a.dk.1.1 | 2 | 21.17 | even | 6 | |||
9702.2.a.dk.1.2 | 2 | 21.11 | odd | 6 |