Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,2,Mod(289,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1872.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.t (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: | \(14.9479952584\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 468) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1872.289 |
Dual form | 1872.2.t.o.1153.2 |
$q$-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 \(\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.64575 | 1.18322 | 0.591608 | − | 0.806226i | \(-0.298493\pi\) | ||||
0.591608 | + | 0.806226i | \(0.298493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64575 | + | 4.58258i | 0.797724 | + | 1.38170i | 0.921095 | + | 0.389338i | \(0.127296\pi\) |
−0.123371 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.96863 | + | 6.87386i | −0.962533 | + | 1.66716i | −0.246433 | + | 0.969160i | \(0.579258\pi\) |
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.64575 | − | 4.58258i | −0.551677 | − | 0.955533i | −0.998154 | − | 0.0607377i | \(-0.980655\pi\) |
0.446476 | − | 0.894795i | \(-0.352679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.32288 | − | 2.29129i | −0.245652 | − | 0.425481i | 0.716663 | − | 0.697420i | \(-0.245669\pi\) |
−0.962315 | + | 0.271938i | \(0.912335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64575 | + | 4.58258i | −0.447214 | + | 0.774597i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | + | 2.59808i | 0.246598 | + | 0.427121i | 0.962580 | − | 0.270998i | \(-0.0873538\pi\) |
−0.715981 | + | 0.698119i | \(0.754020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.96863 | − | 6.87386i | −0.619795 | − | 1.07352i | −0.989523 | − | 0.144377i | \(-0.953882\pi\) |
0.369727 | − | 0.929140i | \(-0.379451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.29150 | −0.771845 | −0.385922 | − | 0.922531i | \(-0.626117\pi\) | ||||
−0.385922 | + | 0.922531i | \(0.626117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.93725 | 1.09027 | 0.545133 | − | 0.838350i | \(-0.316479\pi\) | ||||
0.545133 | + | 0.838350i | \(0.316479\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.00000 | + | 12.1244i | 0.943880 | + | 1.63485i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.29150 | − | 9.16515i | 0.688895 | − | 1.19320i | −0.283301 | − | 0.959031i | \(-0.591429\pi\) |
0.972196 | − | 0.234170i | \(-0.0752372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.50000 | + | 11.2583i | −0.832240 | + | 1.44148i | 0.0640184 | + | 0.997949i | \(0.479608\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.26013 | − | 2.29129i | 1.14858 | − | 0.284199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.64575 | − | 4.58258i | 0.313993 | − | 0.543852i | −0.665230 | − | 0.746639i | \(-0.731667\pi\) |
0.979223 | + | 0.202787i | \(0.0649998\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.5830 | −1.20605 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8745 | 1.74245 | 0.871227 | − | 0.490881i | \(-0.163325\pi\) | ||||
0.871227 | + | 0.490881i | \(0.163325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.5000 | + | 18.1865i | −1.13888 | + | 1.97261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | + | 6.92820i | −0.209657 | + | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.93725 | + | 13.7477i | −0.814345 | + | 1.41049i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.32288 | + | 2.29129i | 0.131631 | + | 0.227992i | 0.924305 | − | 0.381654i | \(-0.124645\pi\) |
−0.792674 | + | 0.609645i | \(0.791312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.64575 | − | 4.58258i | −0.255774 | − | 0.443014i | 0.709331 | − | 0.704875i | \(-0.248997\pi\) |
−0.965106 | + | 0.261861i | \(0.915664\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.32288 | + | 2.29129i | −0.124446 | + | 0.215546i | −0.921516 | − | 0.388340i | \(-0.873049\pi\) |
0.797070 | + | 0.603886i | \(0.206382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.00000 | − | 12.1244i | −0.652753 | − | 1.13060i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.93725 | − | 13.7477i | −0.727607 | − | 1.26025i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.50000 | + | 14.7224i | −0.772727 | + | 1.33840i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | + | 13.8564i | 0.709885 | + | 1.22956i | 0.964899 | + | 0.262620i | \(0.0845865\pi\) |
−0.255014 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5830 | −0.924641 | −0.462321 | − | 0.886713i | \(-0.652983\pi\) | ||||
−0.462321 | + | 0.886713i | \(0.652983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 10.3923i | −0.520266 | − | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.96863 | − | 6.87386i | 0.339063 | − | 0.587274i | −0.645194 | − | 0.764019i | \(-0.723223\pi\) |
0.984257 | + | 0.176745i | \(0.0565568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | − | 13.8564i | 0.678551 | − | 1.17529i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2288 | + | 13.7477i | 1.10624 | + | 1.14964i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.50000 | − | 6.06218i | −0.290659 | − | 0.503436i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.96863 | − | 6.87386i | 0.325123 | − | 0.563129i | −0.656415 | − | 0.754400i | \(-0.727928\pi\) |
0.981537 | + | 0.191272i | \(0.0612611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0000 | 1.46482 | 0.732410 | − | 0.680864i | \(-0.238396\pi\) | ||||
0.732410 | + | 0.680864i | \(0.238396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5830 | −0.850047 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0000 | 1.35675 | 0.678374 | − | 0.734717i | \(-0.262685\pi\) | ||||
0.678374 | + | 0.734717i | \(0.262685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.5830 | 0.834058 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.29150 | + | 9.16515i | −0.402305 | + | 0.696814i | −0.994004 | − | 0.109346i | \(-0.965124\pi\) |
0.591698 | + | 0.806160i | \(0.298458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.93725 | + | 13.7477i | 0.593258 | + | 1.02755i | 0.993790 | + | 0.111271i | \(0.0354920\pi\) |
−0.400532 | + | 0.916283i | \(0.631175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | −0.668965 | −0.334482 | − | 0.942402i | \(-0.608561\pi\) | ||||
−0.334482 | + | 0.942402i | \(0.608561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.96863 | + | 6.87386i | 0.291779 | + | 0.505376i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.0000 | −3.07134 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5830 | − | 18.3303i | 0.765759 | − | 1.32633i | −0.174085 | − | 0.984731i | \(-0.555697\pi\) |
0.939844 | − | 0.341603i | \(-0.110970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5000 | + | 21.6506i | 0.899770 | + | 1.55845i | 0.827788 | + | 0.561041i | \(0.189599\pi\) |
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | + | 8.66025i | −0.354441 | + | 0.613909i | −0.987022 | − | 0.160585i | \(-0.948662\pi\) |
0.632581 | + | 0.774494i | \(0.281995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.29150 | 0.371391 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5000 | − | 18.1865i | −0.733352 | − | 1.27020i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.7490 | −2.19613 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | + | 6.92820i | 0.275371 | + | 0.476957i | 0.970229 | − | 0.242190i | \(-0.0778659\pi\) |
−0.694857 | + | 0.719148i | \(0.744533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.64575 | + | 4.58258i | −0.180439 | + | 0.312529i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | − | 6.92820i | 0.271538 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.93725 | + | 27.4955i | −0.533917 | + | 1.84954i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.93725 | + | 13.7477i | −0.526814 | + | 0.912469i | 0.472698 | + | 0.881225i | \(0.343280\pi\) |
−0.999512 | + | 0.0312441i | \(0.990053\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.1660 | 1.38663 | 0.693316 | − | 0.720634i | \(-0.256149\pi\) | ||||
0.693316 | + | 0.720634i | \(0.256149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0000 | −0.913259 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.8745 | −1.02684 | −0.513418 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513418 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | + | 18.1865i | −0.676364 | + | 1.17150i | 0.299704 | + | 0.954032i | \(0.403112\pi\) |
−0.976068 | + | 0.217465i | \(0.930221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.96863 | + | 6.87386i | 0.253546 | + | 0.439155i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | + | 20.7846i | −0.381771 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0000 | − | 24.2487i | 0.880172 | − | 1.52450i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.96863 | − | 6.87386i | −0.247556 | − | 0.428780i | 0.715291 | − | 0.698827i | \(-0.246294\pi\) |
−0.962847 | + | 0.270047i | \(0.912961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.93725 | + | 13.7477i | 0.489432 | + | 0.847721i | 0.999926 | − | 0.0121601i | \(-0.00387079\pi\) |
−0.510494 | + | 0.859881i | \(0.670537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0000 | 1.29002 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8745 | − | 27.4955i | 0.967886 | − | 1.67643i | 0.266233 | − | 0.963909i | \(-0.414221\pi\) |
0.701653 | − | 0.712519i | \(-0.252446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.29150 | + | 9.16515i | 0.319090 | + | 0.552679i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.50000 | − | 7.79423i | 0.270379 | − | 0.468310i | −0.698580 | − | 0.715532i | \(-0.746184\pi\) |
0.968959 | + | 0.247222i | \(0.0795177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2288 | 0.789161 | 0.394581 | − | 0.918861i | \(-0.370890\pi\) | ||||
0.394581 | + | 0.918861i | \(0.370890\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | − | 12.1244i | −0.416107 | − | 0.720718i | 0.579437 | − | 0.815017i | \(-0.303272\pi\) |
−0.995544 | + | 0.0942988i | \(0.969939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.8745 | 0.937043 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.0000 | − | 39.8372i | −1.35294 | − | 2.34336i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.26013 | − | 16.0390i | 0.540983 | − | 0.937009i | −0.457865 | − | 0.889022i | \(-0.651386\pi\) |
0.998848 | − | 0.0479877i | \(-0.0152808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0000 | − | 24.2487i | 0.815112 | − | 1.41181i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.2288 | − | 13.7477i | −0.765039 | − | 0.795052i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.1974 | + | 29.7867i | −0.984719 | + | 1.70558i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8745 | 0.900161 | 0.450080 | − | 0.892988i | \(-0.351395\pi\) | ||||
0.450080 | + | 0.892988i | \(0.351395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.93725 | 0.445801 | 0.222900 | − | 0.974841i | \(-0.428448\pi\) | ||||
0.222900 | + | 0.974841i | \(0.428448\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.00000 | − | 12.1244i | 0.391925 | − | 0.678834i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.8118 | − | 41.2432i | −1.32492 | − | 2.29483i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00000 | − | 1.73205i | 0.388290 | − | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.29150 | − | 9.16515i | 0.291730 | − | 0.505291i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.64575 | − | 4.58258i | −0.144553 | − | 0.250373i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5830 | − | 18.3303i | −0.573102 | − | 0.992642i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.93725 | − | 13.7477i | 0.426094 | − | 0.738017i | −0.570428 | − | 0.821348i | \(-0.693223\pi\) |
0.996522 | + | 0.0833311i | \(0.0265559\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | + | 1.73205i | 0.0535288 | + | 0.0927146i | 0.891548 | − | 0.452926i | \(-0.149620\pi\) |
−0.838019 | + | 0.545640i | \(0.816286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.61438 | − | 11.4564i | −0.352048 | − | 0.609765i | 0.634560 | − | 0.772873i | \(-0.281181\pi\) |
−0.986608 | + | 0.163109i | \(0.947848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.00000 | − | 12.1244i | 0.371521 | − | 0.643494i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8745 | 0.837824 | 0.418912 | − | 0.908027i | \(-0.362411\pi\) | ||||
0.418912 | + | 0.908027i | \(0.362411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.5203 | −0.969395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.93725 | + | 13.7477i | −0.412082 | + | 0.713746i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.50000 | + | 14.7224i | −0.440113 | + | 0.762299i | −0.997697 | − | 0.0678218i | \(-0.978395\pi\) |
0.557584 | + | 0.830120i | \(0.311728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.61438 | − | 6.87386i | −0.340658 | − | 0.354022i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | − | 17.3205i | −0.513665 | − | 0.889695i | −0.999874 | − | 0.0158521i | \(-0.994954\pi\) |
0.486209 | − | 0.873843i | \(-0.338379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.0000 | −1.42701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.93725 | −0.402435 | −0.201217 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201217 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.0000 | 2.12403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5830 | 0.532489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | + | 12.1244i | −0.351320 | + | 0.608504i | −0.986481 | − | 0.163876i | \(-0.947600\pi\) |
0.635161 | + | 0.772380i | \(0.280934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.9059 | − | 20.6216i | −0.594551 | − | 1.02979i | −0.993610 | − | 0.112868i | \(-0.963996\pi\) |
0.399059 | − | 0.916925i | \(-0.369337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | + | 3.46410i | −0.697390 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.93725 | + | 13.7477i | −0.393435 | + | 0.681450i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5000 | − | 30.3109i | 0.865319 | − | 1.49878i | −0.00141047 | − | 0.999999i | \(-0.500449\pi\) |
0.866730 | − | 0.498778i | \(-0.166218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5830 | + | 18.3303i | 0.520756 | + | 0.901975i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.0000 | 2.06170 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8745 | − | 27.4955i | −0.775520 | − | 1.34324i | −0.934501 | − | 0.355959i | \(-0.884154\pi\) |
0.158981 | − | 0.987282i | \(-0.449179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0000 | −1.41337 | −0.706687 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706687 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.93725 | + | 13.7477i | −0.385013 | + | 0.666863i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.0000 | − | 22.5167i | −0.629114 | − | 1.08966i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.93725 | − | 13.7477i | −0.382324 | − | 0.662205i | 0.609070 | − | 0.793117i | \(-0.291543\pi\) |
−0.991394 | + | 0.130912i | \(0.958210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.50000 | + | 16.4545i | −0.456541 | + | 0.790752i | −0.998775 | − | 0.0494752i | \(-0.984245\pi\) |
0.542234 | + | 0.840227i | \(0.317578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.7490 | 1.51876 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0000 | − | 19.0526i | −0.525001 | − | 0.909329i | −0.999576 | − | 0.0291138i | \(-0.990731\pi\) |
0.474575 | − | 0.880215i | \(-0.342602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7490 | −1.50844 | −0.754221 | − | 0.656621i | \(-0.771985\pi\) | ||||
−0.754221 | + | 0.656621i | \(0.771985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5830 | + | 18.3303i | −0.499443 | + | 0.865060i | −1.00000 | 0.000643168i | \(-0.999795\pi\) | |
0.500557 | + | 0.865704i | \(0.333129\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0000 | − | 36.3731i | 0.988851 | − | 1.71274i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.29150 | + | 18.3303i | −0.248069 | + | 0.859338i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | − | 21.6506i | −0.584725 | − | 1.01277i | −0.994910 | − | 0.100771i | \(-0.967869\pi\) |
0.410184 | − | 0.912003i | \(-0.365464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.9059 | − | 20.6216i | 0.554512 | − | 0.960443i | −0.443429 | − | 0.896309i | \(-0.646238\pi\) |
0.997941 | − | 0.0641338i | \(-0.0204284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.29150 | 0.244862 | 0.122431 | − | 0.992477i | \(-0.460931\pi\) | ||||
0.122431 | + | 0.992477i | \(0.460931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5830 | −0.486607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 10.3923i | −0.275299 | + | 0.476832i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.8745 | + | 27.4955i | 0.725325 | + | 1.25630i | 0.958840 | + | 0.283946i | \(0.0916437\pi\) |
−0.233515 | + | 0.972353i | \(0.575023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | + | 7.79423i | 0.341971 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.64575 | + | 4.58258i | −0.120137 | + | 0.208084i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | − | 1.73205i | 0.0453143 | − | 0.0784867i | −0.842479 | − | 0.538730i | \(-0.818904\pi\) |
0.887793 | + | 0.460243i | \(0.152238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5203 | + | 32.0780i | 0.835808 | + | 1.44766i | 0.893371 | + | 0.449319i | \(0.148333\pi\) |
−0.0575636 | + | 0.998342i | \(0.518333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.0000 | 0.945792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.29150 | + | 9.16515i | 0.237356 | + | 0.411113i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.2288 | + | 22.9129i | −0.589841 | + | 1.02163i | 0.404412 | + | 0.914577i | \(0.367476\pi\) |
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.50000 | + | 6.06218i | 0.155748 | + | 0.269763i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.1974 | + | 29.7867i | 0.762261 | + | 1.32027i | 0.941683 | + | 0.336502i | \(0.109244\pi\) |
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.00000 | − | 12.1244i | 0.309662 | − | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.0405 | 1.63220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.0000 | − | 24.2487i | −0.615719 | − | 1.06646i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.6863 | 1.73869 | 0.869344 | − | 0.494208i | \(-0.164542\pi\) | ||||
0.869344 | + | 0.494208i | \(0.164542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | − | 5.19615i | −0.131181 | − | 0.227212i | 0.792951 | − | 0.609285i | \(-0.208544\pi\) |
−0.924132 | + | 0.382073i | \(0.875210\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.8745 | − | 27.4955i | 0.691504 | − | 1.19772i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | + | 4.33013i | −0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.8431 | − | 20.6216i | −0.859502 | − | 0.893220i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.00000 | − | 12.1244i | −0.302636 | − | 0.524182i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.93725 | + | 13.7477i | −0.341882 | + | 0.592157i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0000 | −0.558914 | −0.279457 | − | 0.960158i | \(-0.590154\pi\) | ||||
−0.279457 | + | 0.960158i | \(0.590154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.4575 | 1.13332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.8745 | 0.676277 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | + | 6.92820i | −0.170097 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.96863 | − | 6.87386i | −0.168156 | − | 0.291255i | 0.769615 | − | 0.638508i | \(-0.220448\pi\) |
−0.937772 | + | 0.347253i | \(0.887115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | + | 6.92820i | −0.0845910 | + | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1660 | − | 36.6606i | 0.892041 | − | 1.54506i | 0.0546164 | − | 0.998507i | \(-0.482606\pi\) |
0.837425 | − | 0.546553i | \(-0.184060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.50000 | + | 6.06218i | −0.147246 | + | 0.255038i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.29150 | + | 9.16515i | 0.221831 | + | 0.384223i | 0.955364 | − | 0.295431i | \(-0.0954632\pi\) |
−0.733533 | + | 0.679654i | \(0.762130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.0000 | 1.25546 | 0.627730 | − | 0.778431i | \(-0.283984\pi\) | ||||
0.627730 | + | 0.778431i | \(0.283984\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.29150 | − | 9.16515i | −0.220671 | − | 0.382213i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | 0.124892 | 0.0624458 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624458 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.8745 | + | 27.4955i | −0.658586 | + | 1.14070i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.0000 | + | 36.3731i | 0.869731 | + | 1.50642i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.29150 | + | 9.16515i | 0.218404 | + | 0.378286i | 0.954320 | − | 0.298786i | \(-0.0965817\pi\) |
−0.735916 | + | 0.677072i | \(0.763248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | − | 20.7846i | 0.494451 | − | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.1033 | −1.19513 | −0.597564 | − | 0.801821i | \(-0.703865\pi\) | ||||
−0.597564 | + | 0.801821i | \(0.703865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.0000 | − | 36.3731i | −0.860916 | − | 1.49115i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.1660 | −0.864820 | −0.432410 | − | 0.901677i | \(-0.642337\pi\) | ||||
−0.432410 | + | 0.901677i | \(0.642337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.4889 | + | 38.9519i | −0.914303 | + | 1.58362i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0000 | + | 31.1769i | −0.730597 | + | 1.26543i | 0.226031 | + | 0.974120i | \(0.427425\pi\) |
−0.956628 | + | 0.291312i | \(0.905908\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.5203 | + | 4.58258i | −0.749249 | + | 0.185391i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.50000 | − | 4.33013i | −0.100974 | − | 0.174892i | 0.811112 | − | 0.584891i | \(-0.198863\pi\) |
−0.912086 | + | 0.409998i | \(0.865529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.32288 | − | 2.29129i | 0.0532570 | − | 0.0922438i | −0.838168 | − | 0.545412i | \(-0.816373\pi\) |
0.891425 | + | 0.453169i | \(0.149706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.8118 | −0.949437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | + | 6.92820i | −0.159237 | + | 0.275807i | −0.934594 | − | 0.355716i | \(-0.884237\pi\) |
0.775356 | + | 0.631524i | \(0.217570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.1660 | + | 36.6606i | 0.839948 | + | 1.45483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.50000 | + | 7.79423i | 0.297161 | + | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.26013 | − | 16.0390i | 0.365753 | − | 0.633503i | −0.623144 | − | 0.782107i | \(-0.714145\pi\) |
0.988897 | + | 0.148604i | \(0.0474781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0000 | + | 24.2487i | −0.552106 | + | 0.956276i | 0.446016 | + | 0.895025i | \(0.352842\pi\) |
−0.998122 | + | 0.0612510i | \(0.980491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.1660 | − | 36.6606i | −0.832122 | − | 1.44128i | −0.896353 | − | 0.443342i | \(-0.853793\pi\) |
0.0642308 | − | 0.997935i | \(-0.479541\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.0000 | 2.19819 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8745 | − | 27.4955i | −0.621217 | − | 1.07598i | −0.989259 | − | 0.146171i | \(-0.953305\pi\) |
0.368042 | − | 0.929809i | \(-0.380028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.0000 | −1.09405 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8745 | + | 27.4955i | −0.618383 | + | 1.07107i | 0.371398 | + | 0.928474i | \(0.378879\pi\) |
−0.989781 | + | 0.142597i | \(0.954455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5000 | + | 26.8468i | 0.602880 | + | 1.04422i | 0.992383 | + | 0.123194i | \(0.0393136\pi\) |
−0.389503 | + | 0.921025i | \(0.627353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.8745 | − | 27.4955i | −0.615587 | − | 1.06623i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.00000 | + | 12.1244i | −0.271041 | + | 0.469457i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −68.7895 | −2.65559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.50000 | − | 16.4545i | −0.366198 | − | 0.634274i | 0.622770 | − | 0.782405i | \(-0.286007\pi\) |
−0.988968 | + | 0.148132i | \(0.952674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7490 | 1.22021 | 0.610107 | − | 0.792319i | \(-0.291126\pi\) | ||||
0.610107 | + | 0.792319i | \(0.291126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.1660 | + | 36.6606i | −0.809895 | + | 1.40278i | 0.103041 | + | 0.994677i | \(0.467143\pi\) |
−0.912936 | + | 0.408102i | \(0.866191\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.5000 | − | 18.1865i | 0.401184 | − | 0.694872i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.7804 | − | 6.87386i | 1.05835 | − | 0.261873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.00000 | − | 12.1244i | −0.266293 | − | 0.461232i | 0.701609 | − | 0.712562i | \(-0.252465\pi\) |
−0.967901 | + | 0.251330i | \(0.919132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.1660 | − | 36.6606i | 0.802873 | − | 1.39062i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 63.0000 | 2.38630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.7490 | −1.19914 | −0.599572 | − | 0.800321i | \(-0.704662\pi\) | ||||
−0.599572 | + | 0.800321i | \(0.704662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | −0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.29150 | −0.199007 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.50000 | + | 9.52628i | −0.206557 | + | 0.357767i | −0.950628 | − | 0.310334i | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.5830 | + | 18.3303i | 0.396337 | + | 0.686475i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.0000 | + | 36.3731i | 1.30893 | + | 1.36028i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.29150 | − | 9.16515i | 0.197340 | − | 0.341802i | −0.750325 | − | 0.661069i | \(-0.770103\pi\) |
0.947665 | + | 0.319266i | \(0.103436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | + | 24.2487i | −0.521387 | + | 0.903069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.64575 | − | 4.58258i | −0.0982607 | − | 0.170193i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.93725 | − | 13.7477i | −0.293570 | − | 0.508478i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.00000 | −0.0369358 | −0.0184679 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184679 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.29150 | − | 9.16515i | 0.194915 | − | 0.337603i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.00000 | + | 10.3923i | 0.220714 | + | 0.382287i | 0.955025 | − | 0.296526i | \(-0.0958281\pi\) |
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5830 | + | 18.3303i | 0.388253 | + | 0.672474i | 0.992215 | − | 0.124540i | \(-0.0397454\pi\) |
−0.603962 | + | 0.797013i | \(0.706412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5000 | − | 18.1865i | 0.384690 | − | 0.666303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5830 | 0.386695 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.00000 | + | 15.5885i | 0.328415 | + | 0.568831i | 0.982197 | − | 0.187851i | \(-0.0601523\pi\) |
−0.653783 | + | 0.756682i | \(0.726819\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.6235 | 1.73320 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | + | 25.9808i | 0.545184 | + | 0.944287i | 0.998595 | + | 0.0529853i | \(0.0168737\pi\) |
−0.453411 | + | 0.891302i | \(0.649793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 17.3205i | −0.362024 | + | 0.627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5830 | − | 36.6606i | 0.382130 | − | 1.32374i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.0000 | − | 25.9808i | −0.540914 | − | 0.936890i | −0.998852 | − | 0.0479061i | \(-0.984745\pi\) |
0.457938 | − | 0.888984i | \(-0.348588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.29150 | + | 9.16515i | −0.190322 | + | 0.329648i | −0.945357 | − | 0.326037i | \(-0.894287\pi\) |
0.755035 | + | 0.655685i | \(0.227620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.6235 | 1.70629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0000 | 1.00192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.9778 | 1.60533 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.0000 | + | 45.0333i | −0.926800 | + | 1.60526i | −0.138159 | + | 0.990410i | \(0.544119\pi\) |
−0.788641 | + | 0.614855i | \(0.789215\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.64575 | − | 4.58258i | −0.0940721 | − | 0.162938i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0000 | + | 45.0333i | −0.461644 | + | 1.59918i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000 | − | 36.3731i | 0.742927 | − | 1.28679i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.5203 | − | 32.0780i | −0.653566 | − | 1.13201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.0000 | 0.986870 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.9059 | − | 20.6216i | −0.418588 | − | 0.725017i | 0.577209 | − | 0.816596i | \(-0.304142\pi\) |
−0.995798 | + | 0.0915798i | \(0.970808\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.29150 | + | 9.16515i | −0.185353 | + | 0.321041i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | − | 10.3923i | −0.209913 | − | 0.363581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.29150 | − | 9.16515i | −0.184675 | − | 0.319866i | 0.758792 | − | 0.651333i | \(-0.225790\pi\) |
−0.943467 | + | 0.331467i | \(0.892456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0000 | + | 20.7846i | −0.418294 | + | 0.724506i | −0.995768 | − | 0.0919029i | \(-0.970705\pi\) |
0.577474 | + | 0.816409i | \(0.304038\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.50000 | − | 6.06218i | −0.121560 | − | 0.210548i | 0.798823 | − | 0.601566i | \(-0.205456\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.8118 | −0.825029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.29150 | − | 9.16515i | 0.182683 | − | 0.316416i | −0.760110 | − | 0.649794i | \(-0.774855\pi\) |
0.942793 | + | 0.333378i | \(0.108188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | − | 19.0526i | 0.379310 | − | 0.656985i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.4261 | − | 16.0390i | 1.04669 | − | 0.551759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0000 | − | 29.4449i | −0.584127 | − | 1.01174i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.93725 | − | 13.7477i | 0.272086 | − | 0.471266i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.0000 | −1.60925 | −0.804625 | − | 0.593784i | \(-0.797633\pi\) | ||||
−0.804625 | + | 0.593784i | \(0.797633\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.3948 | −1.17490 | −0.587451 | − | 0.809259i | \(-0.699869\pi\) | ||||
−0.587451 | + | 0.809259i | \(0.699869\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | 0.750630 | 0.375315 | − | 0.926897i | \(-0.377534\pi\) | ||||
0.375315 | + | 0.926897i | \(0.377534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.29150 | −0.180125 | −0.0900624 | − | 0.995936i | \(-0.528707\pi\) | ||||
−0.0900624 | + | 0.995936i | \(0.528707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | + | 24.2487i | −0.476014 | + | 0.824481i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.5830 | + | 18.3303i | 0.359004 | + | 0.621813i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 5.19615i | −0.169419 | − | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.93725 | − | 13.7477i | 0.268328 | − | 0.464758i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5000 | − | 23.3827i | 0.455863 | − | 0.789577i | −0.542875 | − | 0.839814i | \(-0.682664\pi\) |
0.998737 | + | 0.0502365i | \(0.0159975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.96863 | + | 6.87386i | 0.133706 | + | 0.231586i | 0.925103 | − | 0.379717i | \(-0.123979\pi\) |
−0.791396 | + | 0.611304i | \(0.790645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.4575 | + | 45.8258i | 0.888356 | + | 1.53868i | 0.841818 | + | 0.539762i | \(0.181486\pi\) |
0.0465386 | + | 0.998916i | \(0.485181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.8745 | − | 27.4955i | 0.531220 | − | 0.920100i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0000 | + | 36.3731i | 0.701953 | + | 1.21582i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.29150 | + | 9.16515i | 0.176481 | + | 0.305675i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.5000 | + | 54.5596i | −1.04942 | + | 1.81764i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.8118 | −0.791530 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.7490 | 1.05189 | 0.525946 | − | 0.850518i | \(-0.323711\pi\) | ||||
0.525946 | + | 0.850518i | \(0.323711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.0000 | + | 72.7461i | 1.39000 | + | 2.40755i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5830 | − | 18.3303i | 0.349482 | − | 0.605320i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0000 | + | 20.7846i | −0.395843 | + | 0.685621i | −0.993208 | − | 0.116348i | \(-0.962881\pi\) |
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.29150 | − | 18.3303i | 0.174172 | − | 0.603349i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | + | 5.19615i | 0.0986394 | + | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96863 | − | 6.87386i | 0.130206 | − | 0.225524i | −0.793550 | − | 0.608506i | \(-0.791769\pi\) |
0.923756 | + | 0.382981i | \(0.125103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −111.122 | −3.63406 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.00000 | −0.294017 | −0.147009 | − | 0.989135i | \(-0.546964\pi\) | ||||
−0.147009 | + | 0.989135i | \(0.546964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5830 | −0.344996 | −0.172498 | − | 0.985010i | \(-0.555184\pi\) | ||||
−0.172498 | + | 0.985010i | \(0.555184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0000 | + | 36.3731i | −0.683854 | + | 1.18447i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.5000 | + | 6.06218i | −0.795304 | + | 0.196787i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.29150 | + | 9.16515i | −0.171409 | + | 0.296888i | −0.938913 | − | 0.344156i | \(-0.888165\pi\) |
0.767504 | + | 0.641044i | \(0.221498\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.0000 | − | 48.4974i | 0.906059 | − | 1.56934i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.93725 | + | 13.7477i | 0.256307 | + | 0.443937i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.0719 | + | 57.2822i | 1.06462 | + | 1.84398i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.8745 | − | 27.4955i | 0.509437 | − | 0.882371i | −0.490503 | − | 0.871439i | \(-0.663187\pi\) |
0.999940 | − | 0.0109316i | \(-0.00347972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | + | 27.7128i | 0.512936 | + | 0.888432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.8431 | + | 34.3693i | 0.634838 | + | 1.09957i | 0.986549 | + | 0.163463i | \(0.0522666\pi\) |
−0.351711 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.5830 | −0.337545 | −0.168773 | − | 0.985655i | \(-0.553980\pi\) | ||||
−0.168773 | + | 0.985655i | \(0.553980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.5830 | 0.336520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0000 | − | 46.7654i | −0.857683 | − | 1.48555i | −0.874133 | − | 0.485686i | \(-0.838570\pi\) |
0.0164499 | − | 0.999865i | \(-0.494764\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.2288 | + | 22.9129i | −0.419380 | + | 0.726387i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.50000 | − | 6.06218i | 0.110846 | − | 0.191991i | −0.805266 | − | 0.592914i | \(-0.797977\pi\) |
0.916112 | + | 0.400923i | \(0.131311\pi\) | |||||||
\(998\) | 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 | 1872.2.t.o.289.2 | 4 | ||
3.2 | odd | 2 | inner | 1872.2.t.o.289.1 | 4 | ||
4.3 | odd | 2 | 468.2.l.e.289.2 | yes | 4 | ||
12.11 | even | 2 | 468.2.l.e.289.1 | yes | 4 | ||
13.9 | even | 3 | inner | 1872.2.t.o.1153.2 | 4 | ||
39.35 | odd | 6 | inner | 1872.2.t.o.1153.1 | 4 | ||
52.3 | odd | 6 | 6084.2.a.q.1.2 | 2 | |||
52.11 | even | 12 | 6084.2.b.n.4393.4 | 4 | |||
52.15 | even | 12 | 6084.2.b.n.4393.1 | 4 | |||
52.23 | odd | 6 | 6084.2.a.w.1.1 | 2 | |||
52.35 | odd | 6 | 468.2.l.e.217.2 | yes | 4 | ||
156.11 | odd | 12 | 6084.2.b.n.4393.2 | 4 | |||
156.23 | even | 6 | 6084.2.a.w.1.2 | 2 | |||
156.35 | even | 6 | 468.2.l.e.217.1 | ✓ | 4 | ||
156.107 | even | 6 | 6084.2.a.q.1.1 | 2 | |||
156.119 | odd | 12 | 6084.2.b.n.4393.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
468.2.l.e.217.1 | ✓ | 4 | 156.35 | even | 6 | ||
468.2.l.e.217.2 | yes | 4 | 52.35 | odd | 6 | ||
468.2.l.e.289.1 | yes | 4 | 12.11 | even | 2 | ||
468.2.l.e.289.2 | yes | 4 | 4.3 | odd | 2 | ||
1872.2.t.o.289.1 | 4 | 3.2 | odd | 2 | inner | ||
1872.2.t.o.289.2 | 4 | 1.1 | even | 1 | trivial | ||
1872.2.t.o.1153.1 | 4 | 39.35 | odd | 6 | inner | ||
1872.2.t.o.1153.2 | 4 | 13.9 | even | 3 | inner | ||
6084.2.a.q.1.1 | 2 | 156.107 | even | 6 | |||
6084.2.a.q.1.2 | 2 | 52.3 | odd | 6 | |||
6084.2.a.w.1.1 | 2 | 52.23 | odd | 6 | |||
6084.2.a.w.1.2 | 2 | 156.23 | even | 6 | |||
6084.2.b.n.4393.1 | 4 | 52.15 | even | 12 | |||
6084.2.b.n.4393.2 | 4 | 156.11 | odd | 12 | |||
6084.2.b.n.4393.3 | 4 | 156.119 | odd | 12 | |||
6084.2.b.n.4393.4 | 4 | 52.11 | even | 12 |