Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2007,1,Mod(91,2007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2007, base_ring=CyclotomicField(74))
chi = DirichletCharacter(H, H._module([0, 45]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2007.91");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2007 = 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2007.v (of order \(74\), degree \(36\), 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: | \(1.00162348035\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Coefficient field: | \(\Q(\zeta_{74})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{36} - x^{35} + x^{34} - x^{33} + x^{32} - x^{31} + x^{30} - x^{29} + x^{28} - x^{27} + x^{26} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{74}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{74} - \cdots)\) |
Embedding invariants
Embedding label | 946.1 | ||
Root | \(-0.873014 + 0.487695i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2007.946 |
Dual form | 2007.1.v.a.541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2007\mathbb{Z}\right)^\times\).
\(n\) | \(226\) | \(893\) |
\(\chi(n)\) | \(e\left(\frac{61}{74}\right)\) | \(1\) |
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 | 0 | 0.927889 | − | 0.372856i | \(-0.121622\pi\) | ||||
−0.927889 | + | 0.372856i | \(0.878378\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.721956 | − | 0.691939i | 0.721956 | − | 0.691939i | ||||
\(5\) | 0 | 0 | 0.911228 | − | 0.411901i | \(-0.135135\pi\) | ||||
−0.911228 | + | 0.411901i | \(0.864865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0800337 | − | 0.0282777i | −0.0800337 | − | 0.0282777i | 0.292823 | − | 0.956167i | \(-0.405405\pi\) |
−0.372856 | + | 0.927889i | \(0.621622\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.594633 | − | 0.803997i | \(-0.297297\pi\) | ||||
−0.594633 | + | 0.803997i | \(0.702703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.701492 | − | 0.431926i | −0.701492 | − | 0.431926i | 0.127018 | − | 0.991900i | \(-0.459459\pi\) |
−0.828510 | + | 0.559975i | \(0.810811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0424412 | − | 0.999099i | 0.0424412 | − | 0.999099i | ||||
\(17\) | 0 | 0 | −0.803997 | − | 0.594633i | \(-0.797297\pi\) | ||||
0.803997 | + | 0.594633i | \(0.202703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.815860 | − | 0.658761i | 0.815860 | − | 0.658761i | −0.127018 | − | 0.991900i | \(-0.540541\pi\) |
0.942877 | + | 0.333140i | \(0.108108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.911228 | − | 0.411901i | \(-0.135135\pi\) | ||||
−0.911228 | + | 0.411901i | \(0.864865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.660675 | − | 0.750672i | 0.660675 | − | 0.750672i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0773473 | + | 0.0349632i | −0.0773473 | + | 0.0349632i | ||||
\(29\) | 0 | 0 | −0.999099 | − | 0.0424412i | \(-0.986486\pi\) | ||||
0.999099 | + | 0.0424412i | \(0.0135135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.123383 | − | 0.402889i | 0.123383 | − | 0.402889i | −0.873014 | − | 0.487695i | \(-0.837838\pi\) |
0.996397 | + | 0.0848059i | \(0.0270270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.348244 | + | 0.470857i | 0.348244 | + | 0.470857i | 0.942877 | − | 0.333140i | \(-0.108108\pi\) |
−0.594633 | + | 0.803997i | \(0.702703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.487695 | − | 0.873014i | \(-0.337838\pi\) | ||||
−0.487695 | + | 0.873014i | \(0.662162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.02806 | + | 1.16810i | 1.02806 | + | 1.16810i | 0.985616 | + | 0.169001i | \(0.0540541\pi\) |
0.0424412 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.628220 | − | 0.778036i | \(-0.283784\pi\) | ||||
−0.628220 | + | 0.778036i | \(0.716216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.772430 | − | 0.623694i | −0.772430 | − | 0.623694i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.805312 | + | 0.173558i | −0.805312 | + | 0.173558i | ||||
\(53\) | 0 | 0 | −0.169001 | − | 0.985616i | \(-0.554054\pi\) | ||||
0.169001 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.967733 | − | 0.251978i | \(-0.0810811\pi\) | ||||
−0.967733 | + | 0.251978i | \(0.918919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.567356 | − | 0.349335i | −0.567356 | − | 0.349335i | 0.210679 | − | 0.977555i | \(-0.432432\pi\) |
−0.778036 | + | 0.628220i | \(0.783784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.660675 | − | 0.750672i | −0.660675 | − | 0.750672i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.348707 | − | 0.363834i | −0.348707 | − | 0.363834i | 0.524307 | − | 0.851529i | \(-0.324324\pi\) |
−0.873014 | + | 0.487695i | \(0.837838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.967733 | − | 0.251978i | \(-0.0810811\pi\) | ||||
−0.967733 | + | 0.251978i | \(0.918919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.304202 | + | 1.41150i | 0.304202 | + | 1.41150i | 0.828510 | + | 0.559975i | \(0.189189\pi\) |
−0.524307 | + | 0.851529i | \(0.675676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.133193 | − | 1.04012i | 0.133193 | − | 1.04012i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.732198 | + | 1.31070i | −0.732198 | + | 1.31070i | 0.210679 | + | 0.977555i | \(0.432432\pi\) |
−0.942877 | + | 0.333140i | \(0.891892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.750672 | − | 0.660675i | \(-0.770270\pi\) | ||||
0.750672 | + | 0.660675i | \(0.229730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.411901 | − | 0.911228i | \(-0.364865\pi\) | ||||
−0.411901 | + | 0.911228i | \(0.635135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0439291 | + | 0.0544052i | 0.0439291 | + | 0.0544052i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.401764 | + | 0.888803i | −0.401764 | + | 0.888803i | 0.594633 | + | 0.803997i | \(0.297297\pi\) |
−0.996397 | + | 0.0848059i | \(0.972973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0424412 | − | 0.999099i | −0.0424412 | − | 0.999099i | ||||
\(101\) | 0 | 0 | 0.169001 | − | 0.985616i | \(-0.445946\pi\) | ||||
−0.169001 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.287818 | − | 0.177217i | 0.287818 | − | 0.177217i | −0.372856 | − | 0.927889i | \(-0.621622\pi\) |
0.660675 | + | 0.750672i | \(0.270270\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.660675 | − | 0.750672i | \(-0.729730\pi\) | ||||
0.660675 | + | 0.750672i | \(0.270270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0107816 | − | 0.253807i | −0.0107816 | − | 0.253807i | −0.996397 | − | 0.0848059i | \(-0.972973\pi\) |
0.985616 | − | 0.169001i | \(-0.0540541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0316490 | + | 0.0787615i | −0.0316490 | + | 0.0787615i | ||||
\(113\) | 0 | 0 | 0.985616 | − | 0.169001i | \(-0.0540541\pi\) | ||||
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.292823 | − | 0.956167i | −0.292823 | − | 0.956167i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.189697 | − | 0.376242i | −0.189697 | − | 0.376242i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.925292 | + | 0.747121i | 0.925292 | + | 0.747121i | 0.967733 | − | 0.251978i | \(-0.0810811\pi\) |
−0.0424412 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.927889 | − | 0.372856i | \(-0.878378\pi\) | ||||
0.927889 | + | 0.372856i | \(0.121622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0839245 | + | 0.0296524i | −0.0839245 | + | 0.0296524i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.450204 | − | 0.892926i | \(-0.351351\pi\) | ||||
−0.450204 | + | 0.892926i | \(0.648649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.745996 | + | 0.504205i | 0.745996 | + | 0.504205i | 0.873014 | − | 0.487695i | \(-0.162162\pi\) |
−0.127018 | + | 0.991900i | \(0.540541\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.577222 | + | 0.0989746i | 0.577222 | + | 0.0989746i | ||||
\(149\) | 0 | 0 | 0.524307 | − | 0.851529i | \(-0.324324\pi\) | ||||
−0.524307 | + | 0.851529i | \(0.675676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.703575 | + | 0.871361i | 0.703575 | + | 0.871361i | 0.996397 | − | 0.0848059i | \(-0.0270270\pi\) |
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.89684 | + | 0.580902i | −1.89684 | + | 0.580902i | −0.911228 | + | 0.411901i | \(0.864865\pi\) |
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.271752 | + | 1.58486i | 0.271752 | + | 1.58486i | 0.721956 | + | 0.691939i | \(0.243243\pi\) |
−0.450204 | + | 0.892926i | \(0.648649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.721956 | − | 0.691939i | \(-0.756757\pi\) | ||||
0.721956 | + | 0.691939i | \(0.243243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.144673 | − | 0.286941i | −0.144673 | − | 0.286941i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.55047 | + | 0.131964i | 1.55047 | + | 0.131964i | ||||
\(173\) | 0 | 0 | −0.942877 | − | 0.333140i | \(-0.891892\pi\) | ||||
0.942877 | + | 0.333140i | \(0.108108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0741035 | + | 0.0413967i | −0.0741035 | + | 0.0413967i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.991900 | − | 0.127018i | \(-0.0405405\pi\) | ||||
−0.991900 | + | 0.127018i | \(0.959459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.63318 | + | 1.10384i | −1.63318 | + | 1.10384i | −0.721956 | + | 0.691939i | \(0.756757\pi\) |
−0.911228 | + | 0.411901i | \(0.864865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.942877 | − | 0.333140i | \(-0.108108\pi\) | ||||
−0.942877 | + | 0.333140i | \(0.891892\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.35282 | + | 0.291554i | 1.35282 | + | 0.291554i | 0.828510 | − | 0.559975i | \(-0.189189\pi\) |
0.524307 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.989218 | + | 0.0841949i | −0.989218 | + | 0.0841949i | ||||
\(197\) | 0 | 0 | 0.169001 | − | 0.985616i | \(-0.445946\pi\) | ||||
−0.169001 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0947188 | − | 0.739673i | −0.0947188 | − | 0.739673i | −0.967733 | − | 0.251978i | \(-0.918919\pi\) |
0.873014 | − | 0.487695i | \(-0.162162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.461309 | + | 0.682528i | −0.461309 | + | 0.682528i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.721651 | + | 0.187903i | 0.721651 | + | 0.187903i | 0.594633 | − | 0.803997i | \(-0.297297\pi\) |
0.127018 | + | 0.991900i | \(0.459459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0212676 | + | 0.0287557i | −0.0212676 | + | 0.0287557i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.660675 | + | 0.750672i | −0.660675 | + | 0.750672i | ||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.691939 | − | 0.721956i | \(-0.743243\pi\) | ||||
0.691939 | + | 0.721956i | \(0.256757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29282 | − | 0.956167i | −1.29282 | − | 0.956167i | −0.292823 | − | 0.956167i | \(-0.594595\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.721956 | − | 0.691939i | \(-0.756757\pi\) | ||||
0.721956 | + | 0.691939i | \(0.243243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.999099 | − | 0.0424412i | \(-0.986486\pi\) | ||||
0.999099 | + | 0.0424412i | \(0.0135135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.87896 | + | 0.159923i | 1.87896 | + | 0.159923i | 0.967733 | − | 0.251978i | \(-0.0810811\pi\) |
0.911228 | + | 0.411901i | \(0.135135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.651325 | + | 0.140371i | −0.651325 | + | 0.140371i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.856854 | + | 0.109725i | −0.856854 | + | 0.109725i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.411901 | − | 0.911228i | \(-0.635135\pi\) | ||||
0.411901 | + | 0.911228i | \(0.364865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.996397 | − | 0.0848059i | −0.996397 | − | 0.0848059i | ||||
\(257\) | 0 | 0 | 0.251978 | − | 0.967733i | \(-0.418919\pi\) | ||||
−0.251978 | + | 0.967733i | \(0.581081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0145565 | − | 0.0475320i | −0.0145565 | − | 0.0475320i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.503502 | − | 0.0213885i | −0.503502 | − | 0.0213885i | ||||
\(269\) | 0 | 0 | −0.721956 | − | 0.691939i | \(-0.756757\pi\) | ||||
0.721956 | + | 0.691939i | \(0.243243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.674910 | + | 1.20814i | 0.674910 | + | 1.20814i | 0.967733 | + | 0.251978i | \(0.0810811\pi\) |
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.151451 | − | 0.0763599i | 0.151451 | − | 0.0763599i | −0.372856 | − | 0.927889i | \(-0.621622\pi\) |
0.524307 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.333140 | − | 0.942877i | \(-0.608108\pi\) | ||||
0.333140 | + | 0.942877i | \(0.391892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.63318 | + | 0.280038i | −1.63318 | + | 0.280038i | −0.911228 | − | 0.411901i | \(-0.864865\pi\) |
−0.721956 | + | 0.691939i | \(0.756757\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.292823 | + | 0.956167i | 0.292823 | + | 0.956167i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.19630 | + | 0.808554i | 1.19630 | + | 0.808554i | ||||
\(293\) | 0 | 0 | −0.450204 | − | 0.892926i | \(-0.648649\pi\) | ||||
0.450204 | + | 0.892926i | \(0.351351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0492480 | − | 0.122558i | −0.0492480 | − | 0.122558i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.623541 | − | 0.843083i | −0.623541 | − | 0.843083i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0949784 | − | 0.140525i | 0.0949784 | − | 0.140525i | −0.778036 | − | 0.628220i | \(-0.783784\pi\) |
0.873014 | + | 0.487695i | \(0.162162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.873014 | − | 0.487695i | \(-0.162162\pi\) | ||||
−0.873014 | + | 0.487695i | \(0.837838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.418570 | − | 1.18467i | −0.418570 | − | 1.18467i | −0.942877 | − | 0.333140i | \(-0.891892\pi\) |
0.524307 | − | 0.851529i | \(-0.324324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.378306 | + | 1.45290i | 0.378306 | + | 1.45290i | ||||
\(317\) | 0 | 0 | −0.956167 | − | 0.292823i | \(-0.905405\pi\) | ||||
0.956167 | + | 0.292823i | \(0.0945946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.787693 | + | 0.241228i | −0.787693 | + | 0.241228i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.943175 | + | 0.830098i | 0.943175 | + | 0.830098i | 0.985616 | − | 0.169001i | \(-0.0540541\pi\) |
−0.0424412 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.91061 | + | 0.0811617i | −1.91061 | + | 0.0811617i | −0.967733 | − | 0.251978i | \(-0.918919\pi\) |
−0.942877 | + | 0.333140i | \(0.891892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.0886883 | + | 0.144039i | 0.0886883 | + | 0.144039i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.892926 | − | 0.450204i | \(-0.148649\pi\) | ||||
−0.892926 | + | 0.450204i | \(0.851351\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.59103 | − | 0.719191i | −1.59103 | − | 0.719191i | −0.594633 | − | 0.803997i | \(-0.702703\pi\) |
−0.996397 | + | 0.0848059i | \(0.972973\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.251978 | − | 0.967733i | \(-0.581081\pi\) | ||||
0.251978 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.487695 | − | 0.873014i | \(-0.662162\pi\) | ||||
0.487695 | + | 0.873014i | \(0.337838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0209821 | − | 0.0973572i | 0.0209821 | − | 0.0973572i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0693600 | + | 0.00888189i | 0.0693600 | + | 0.00888189i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.03825 | + | 0.579999i | 1.03825 | + | 0.579999i | 0.911228 | − | 0.411901i | \(-0.135135\pi\) |
0.127018 | + | 0.991900i | \(0.459459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.330415 | + | 0.0712099i | −0.330415 | + | 0.0712099i | −0.372856 | − | 0.927889i | \(-0.621622\pi\) |
0.0424412 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.19630 | + | 1.14656i | −1.19630 | + | 1.14656i | −0.210679 | + | 0.977555i | \(0.567568\pi\) |
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.721956 | − | 0.691939i | \(-0.243243\pi\) | ||||
−0.721956 | + | 0.691939i | \(0.756757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.324941 | + | 0.919673i | 0.324941 | + | 0.919673i | ||||
\(389\) | 0 | 0 | 0.333140 | − | 0.942877i | \(-0.391892\pi\) | ||||
−0.333140 | + | 0.942877i | \(0.608108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.703575 | + | 0.871361i | −0.703575 | + | 0.871361i | −0.996397 | − | 0.0848059i | \(-0.972973\pi\) |
0.292823 | + | 0.956167i | \(0.405405\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.721956 | − | 0.691939i | −0.721956 | − | 0.691939i | ||||
\(401\) | 0 | 0 | −0.999099 | − | 0.0424412i | \(-0.986486\pi\) | ||||
0.999099 | + | 0.0424412i | \(0.0135135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.260571 | + | 0.229331i | −0.260571 | + | 0.229331i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.271752 | + | 0.200987i | −0.271752 | + | 0.200987i | −0.721956 | − | 0.691939i | \(-0.756757\pi\) |
0.450204 | + | 0.892926i | \(0.351351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.0851690 | − | 0.327095i | 0.0851690 | − | 0.327095i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.0848059 | − | 0.996397i | \(-0.527027\pi\) | ||||
0.0848059 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.732198 | + | 0.644415i | 0.732198 | + | 0.644415i | 0.942877 | − | 0.333140i | \(-0.108108\pi\) |
−0.210679 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0355292 | + | 0.0440021i | 0.0355292 | + | 0.0440021i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.828510 | − | 0.559975i | \(-0.810811\pi\) | ||||
0.828510 | + | 0.559975i | \(0.189189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.133193 | − | 0.216319i | 0.133193 | − | 0.216319i | −0.778036 | − | 0.628220i | \(-0.783784\pi\) |
0.911228 | + | 0.411901i | \(0.135135\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.183403 | − | 0.175777i | −0.183403 | − | 0.175777i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.618234 | − | 1.74977i | 0.618234 | − | 1.74977i | −0.0424412 | − | 0.999099i | \(-0.513514\pi\) |
0.660675 | − | 0.750672i | \(-0.270270\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.851529 | − | 0.524307i | \(-0.175676\pi\) | ||||
−0.851529 | + | 0.524307i | \(0.824324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0316490 | + | 0.0787615i | 0.0316490 | + | 0.0787615i | ||||
\(449\) | 0 | 0 | −0.524307 | − | 0.851529i | \(-0.675676\pi\) | ||||
0.524307 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.43582 | − | 1.06193i | −1.43582 | − | 1.06193i | −0.985616 | − | 0.169001i | \(-0.945946\pi\) |
−0.450204 | − | 0.892926i | \(-0.648649\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.559975 | − | 0.828510i | \(-0.310811\pi\) | ||||
−0.559975 | + | 0.828510i | \(0.689189\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.535412 | − | 0.723925i | 0.535412 | − | 0.723925i | −0.450204 | − | 0.892926i | \(-0.648649\pi\) |
0.985616 | + | 0.169001i | \(0.0540541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.210679 | − | 0.977555i | \(-0.567568\pi\) | ||||
0.210679 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0176199 | + | 0.0389796i | 0.0176199 | + | 0.0389796i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0445045 | − | 1.04767i | 0.0445045 | − | 1.04767i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.0848059 | − | 0.996397i | \(-0.472973\pi\) | ||||
−0.0848059 | + | 0.996397i | \(0.527027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0409151 | − | 0.480718i | −0.0409151 | − | 0.480718i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.873014 | − | 0.487695i | −0.873014 | − | 0.487695i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.72091 | + | 0.961360i | 1.72091 | + | 0.961360i | 0.942877 | + | 0.333140i | \(0.108108\pi\) |
0.778036 | + | 0.628220i | \(0.216216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.0424412 | − | 0.999099i | \(-0.486486\pi\) | ||||
−0.0424412 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.397289 | − | 0.140371i | −0.397289 | − | 0.140371i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.72091 | − | 0.295080i | 1.72091 | − | 0.295080i | 0.778036 | − | 0.628220i | \(-0.216216\pi\) |
0.942877 | + | 0.333140i | \(0.108108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.942877 | − | 0.333140i | \(-0.891892\pi\) | ||||
0.942877 | + | 0.333140i | \(0.108108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.18498 | − | 0.100857i | 1.18498 | − | 0.100857i | ||||
\(509\) | 0 | 0 | −0.691939 | − | 0.721956i | \(-0.743243\pi\) | ||||
0.691939 | + | 0.721956i | \(0.256757\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0155677 | − | 0.121570i | 0.0155677 | − | 0.121570i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.985616 | − | 0.169001i | \(-0.945946\pi\) | ||||
0.985616 | + | 0.169001i | \(0.0540541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.09481 | + | 1.61983i | 1.09481 | + | 1.61983i | 0.721956 | + | 0.691939i | \(0.243243\pi\) |
0.372856 | + | 0.927889i | \(0.378378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.660675 | − | 0.750672i | 0.660675 | − | 0.750672i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0400722 | + | 0.0794784i | −0.0400722 | + | 0.0794784i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.151451 | + | 0.0763599i | 0.151451 | + | 0.0763599i | 0.524307 | − | 0.851529i | \(-0.324324\pi\) |
−0.372856 | + | 0.927889i | \(0.621622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.734987 | − | 0.126026i | −0.734987 | − | 0.126026i | −0.210679 | − | 0.977555i | \(-0.567568\pi\) |
−0.524307 | + | 0.851529i | \(0.675676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0956640 | − | 0.0841949i | 0.0956640 | − | 0.0841949i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.887456 | − | 0.152170i | 0.887456 | − | 0.152170i | ||||
\(557\) | 0 | 0 | 0.372856 | − | 0.927889i | \(-0.378378\pi\) | ||||
−0.372856 | + | 0.927889i | \(0.621622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.216641 | − | 1.26346i | −0.216641 | − | 1.26346i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.524307 | − | 0.851529i | \(-0.675676\pi\) | ||||
0.524307 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.0424412 | − | 0.999099i | \(-0.513514\pi\) | ||||
0.0424412 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.932635 | + | 0.285616i | 0.932635 | + | 0.285616i | 0.721956 | − | 0.691939i | \(-0.243243\pi\) |
0.210679 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.721651 | − | 1.79590i | 0.721651 | − | 1.79590i | 0.127018 | − | 0.991900i | \(-0.459459\pi\) |
0.594633 | − | 0.803997i | \(-0.297297\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.127018 | − | 0.991900i | \(-0.459459\pi\) | ||||
−0.127018 | + | 0.991900i | \(0.540541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.164744 | − | 0.409981i | −0.164744 | − | 0.409981i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.485213 | − | 0.327947i | 0.485213 | − | 0.327947i | ||||
\(593\) | 0 | 0 | 0.127018 | − | 0.991900i | \(-0.459459\pi\) | ||||
−0.127018 | + | 0.991900i | \(0.540541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.892926 | − | 0.450204i | \(-0.148649\pi\) | ||||
−0.892926 | + | 0.450204i | \(0.851351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.499874 | − | 0.0640114i | 0.499874 | − | 0.0640114i | 0.127018 | − | 0.991900i | \(-0.459459\pi\) |
0.372856 | + | 0.927889i | \(0.378378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.11088 | + | 0.142254i | 1.11088 | + | 0.142254i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.106554 | − | 1.25191i | −0.106554 | − | 1.25191i | −0.828510 | − | 0.559975i | \(-0.810811\pi\) |
0.721956 | − | 0.691939i | \(-0.243243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.03884 | − | 1.08390i | 1.03884 | − | 1.08390i | 0.0424412 | − | 0.999099i | \(-0.486486\pi\) |
0.996397 | − | 0.0848059i | \(-0.0270270\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.977555 | − | 0.210679i | \(-0.0675676\pi\) | ||||
−0.977555 | + | 0.210679i | \(0.932432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.221964 | − | 0.628220i | 0.221964 | − | 0.628220i | −0.778036 | − | 0.628220i | \(-0.783784\pi\) |
1.00000 | \(0\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.127018 | − | 0.991900i | −0.127018 | − | 0.991900i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.967490 | + | 1.73189i | −0.967490 | + | 1.73189i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0827188 | + | 0.148074i | −0.0827188 | + | 0.148074i | −0.911228 | − | 0.411901i | \(-0.864865\pi\) |
0.828510 | + | 0.559975i | \(0.189189\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.272464 | + | 0.771148i | 0.272464 | + | 0.771148i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.911228 | − | 0.411901i | \(-0.135135\pi\) | ||||
−0.911228 | + | 0.411901i | \(0.864865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.85863 | − | 0.318694i | −1.85863 | − | 0.318694i | −0.873014 | − | 0.487695i | \(-0.837838\pi\) |
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.251978 | − | 0.967733i | \(-0.418919\pi\) | ||||
−0.251978 | + | 0.967733i | \(0.581081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.29282 | + | 0.956167i | 1.29282 | + | 0.956167i | ||||
\(653\) | 0 | 0 | 0.0424412 | − | 0.999099i | \(-0.486486\pi\) | ||||
−0.0424412 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.691939 | − | 0.721956i | \(-0.256757\pi\) | ||||
−0.691939 | + | 0.721956i | \(0.743243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.701492 | + | 1.55188i | −0.701492 | + | 1.55188i | 0.127018 | + | 0.991900i | \(0.459459\pi\) |
−0.828510 | + | 0.559975i | \(0.810811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26056 | − | 1.20814i | 1.26056 | − | 1.20814i | 0.292823 | − | 0.956167i | \(-0.405405\pi\) |
0.967733 | − | 0.251978i | \(-0.0810811\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.302993 | − | 0.107054i | −0.302993 | − | 0.107054i | ||||
\(677\) | 0 | 0 | 0.411901 | − | 0.911228i | \(-0.364865\pi\) | ||||
−0.411901 | + | 0.911228i | \(0.635135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0572880 | − | 0.0597732i | 0.0572880 | − | 0.0597732i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.999099 | − | 0.0424412i | \(-0.0135135\pi\) | ||||
−0.999099 | + | 0.0424412i | \(0.986486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.21068 | − | 0.977555i | 1.21068 | − | 0.977555i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.378306 | − | 1.45290i | 0.378306 | − | 1.45290i | −0.450204 | − | 0.892926i | \(-0.648649\pi\) |
0.828510 | − | 0.559975i | \(-0.189189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0248555 | + | 0.0811617i | −0.0248555 | + | 0.0811617i | ||||
\(701\) | 0 | 0 | −0.333140 | − | 0.942877i | \(-0.608108\pi\) | ||||
0.333140 | + | 0.942877i | \(0.391892\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.594301 | + | 0.154744i | 0.594301 | + | 0.154744i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.38388i | − | 1.38388i | −0.721956 | − | 0.691939i | \(-0.756757\pi\) | ||
0.721956 | − | 0.691939i | \(-0.243243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.333140 | − | 0.942877i | \(-0.391892\pi\) | ||||
−0.333140 | + | 0.942877i | \(0.608108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0280464 | + | 0.00604447i | −0.0280464 | + | 0.00604447i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.415298 | + | 1.92699i | −0.415298 | + | 1.92699i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.848974 | + | 0.299962i | −0.848974 | + | 0.299962i | −0.721956 | − | 0.691939i | \(-0.756757\pi\) |
−0.127018 | + | 0.991900i | \(0.540541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.492674 | + | 0.559786i | 0.492674 | + | 0.559786i | 0.942877 | − | 0.333140i | \(-0.108108\pi\) |
−0.450204 | + | 0.892926i | \(0.648649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70757 | − | 0.860940i | 1.70757 | − | 0.860940i | 0.721956 | − | 0.691939i | \(-0.243243\pi\) |
0.985616 | − | 0.169001i | \(-0.0540541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.851529 | − | 0.524307i | \(-0.824324\pi\) | ||||
0.851529 | + | 0.524307i | \(0.175676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.245839 | − | 1.91979i | 0.245839 | − | 1.91979i | −0.127018 | − | 0.991900i | \(-0.540541\pi\) |
0.372856 | − | 0.927889i | \(-0.378378\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.830573 | − | 1.48679i | −0.830573 | − | 1.48679i | −0.873014 | − | 0.487695i | \(-0.837838\pi\) |
0.0424412 | − | 0.999099i | \(-0.486486\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.372856 | − | 0.927889i | \(-0.378378\pi\) | ||||
−0.372856 | + | 0.927889i | \(0.621622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.00631418 | + | 0.0206180i | −0.00631418 | + | 0.0206180i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.0316490 | − | 0.745041i | −0.0316490 | − | 0.745041i | −0.942877 | − | 0.333140i | \(-0.891892\pi\) |
0.911228 | − | 0.411901i | \(-0.135135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.17841 | − | 0.725577i | 1.17841 | − | 0.725577i | ||||
\(773\) | 0 | 0 | 0.828510 | − | 0.559975i | \(-0.189189\pi\) | ||||
−0.828510 | + | 0.559975i | \(0.810811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.220921 | − | 0.358799i | −0.220921 | − | 0.358799i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.655915 | + | 0.745264i | −0.655915 | + | 0.745264i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.11263 | − | 0.822900i | 1.11263 | − | 0.822900i | 0.127018 | − | 0.991900i | \(-0.459459\pi\) |
0.985616 | + | 0.169001i | \(0.0540541\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.247109 | + | 0.490112i | 0.247109 | + | 0.490112i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.580191 | − | 0.468472i | −0.580191 | − | 0.468472i | ||||
\(797\) | 0 | 0 | −0.892926 | − | 0.450204i | \(-0.851351\pi\) | ||||
0.892926 | + | 0.450204i | \(0.148649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.660675 | − | 0.750672i | \(-0.270270\pi\) | ||||
−0.660675 | + | 0.750672i | \(0.729730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.36925 | + | 1.01269i | −1.36925 | + | 1.01269i | −0.372856 | + | 0.927889i | \(0.621622\pi\) |
−0.996397 | + | 0.0848059i | \(0.972973\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.60825 | + | 0.275762i | 1.60825 | + | 0.275762i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.251978 | − | 0.967733i | \(-0.581081\pi\) | ||||
0.251978 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.07086 | + | 1.58439i | −1.07086 | + | 1.58439i | −0.292823 | + | 0.956167i | \(0.594595\pi\) |
−0.778036 | + | 0.628220i | \(0.783784\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.127018 | − | 0.991900i | \(-0.459459\pi\) | ||||
−0.127018 | + | 0.991900i | \(0.540541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.35282 | − | 1.41150i | −1.35282 | − | 1.41150i | −0.828510 | − | 0.559975i | \(-0.810811\pi\) |
−0.524307 | − | 0.851529i | \(-0.675676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.139223 | + | 0.811953i | 0.139223 | + | 0.811953i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.985616 | − | 0.169001i | \(-0.0540541\pi\) | ||||
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.996397 | + | 0.0848059i | 0.996397 | + | 0.0848059i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.651018 | − | 0.363680i | 0.651018 | − | 0.363680i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.00360251 | + | 0.0848059i | −0.00360251 | + | 0.0848059i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.11995i | 1.11995i | 0.828510 | + | 0.559975i | \(0.189189\pi\) | ||||
−0.828510 | + | 0.559975i | \(0.810811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.0848059 | − | 0.996397i | \(-0.527027\pi\) | ||||
0.0848059 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.136367 | − | 1.60220i | 0.136367 | − | 1.60220i | −0.524307 | − | 0.851529i | \(-0.675676\pi\) |
0.660675 | − | 0.750672i | \(-0.270270\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.0424412 | − | 0.999099i | \(-0.486486\pi\) | ||||
−0.0424412 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.00454291 | + | 0.0354762i | 0.00454291 | + | 0.0354762i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0874657 | + | 0.405842i | 0.0874657 | + | 0.405842i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.282203 | − | 0.417533i | 0.282203 | − | 0.417533i | −0.660675 | − | 0.750672i | \(-0.729730\pi\) |
0.942877 | + | 0.333140i | \(0.108108\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.803997 | − | 0.594633i | \(-0.797297\pi\) | ||||
0.803997 | + | 0.594633i | \(0.202703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59463 | − | 0.803997i | −1.59463 | − | 0.803997i | −0.594633 | − | 0.803997i | \(-0.702703\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.411901 | − | 0.911228i | \(-0.635135\pi\) | ||||
0.411901 | + | 0.911228i | \(0.364865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0529277 | − | 0.0859600i | −0.0529277 | − | 0.0859600i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0424412 | + | 0.999099i | 0.0424412 | + | 0.999099i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.09475 | − | 0.739922i | −1.09475 | − | 0.739922i | −0.127018 | − | 0.991900i | \(-0.540541\pi\) |
−0.967733 | + | 0.251978i | \(0.918919\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.628220 | − | 0.778036i | \(-0.716216\pi\) | ||||
0.628220 | + | 0.778036i | \(0.283784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.59497 | + | 0.204244i | −1.59497 | + | 0.204244i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0286645 | − | 0.336784i | −0.0286645 | − | 0.336784i | −0.996397 | − | 0.0848059i | \(-0.972973\pi\) |
0.967733 | − | 0.251978i | \(-0.0810811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.583536 | + | 0.0496662i | 0.583536 | + | 0.0496662i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.803997 | − | 0.594633i | \(-0.202703\pi\) | ||||
−0.803997 | + | 0.594633i | \(0.797297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.04106 | −1.04106 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.974511 | − | 0.0413967i | −0.974511 | − | 0.0413967i | −0.450204 | − | 0.892926i | \(-0.648649\pi\) |
−0.524307 | + | 0.851529i | \(0.675676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.628220 | − | 0.778036i | \(-0.283784\pi\) | ||||
−0.628220 | + | 0.778036i | \(0.716216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.977555 | − | 0.210679i | \(-0.932432\pi\) | ||||
0.977555 | + | 0.210679i | \(0.0675676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.396269 | − | 1.12155i | 0.396269 | − | 1.12155i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.524307 | − | 0.851529i | \(-0.324324\pi\) | ||||
−0.524307 | + | 0.851529i | \(0.675676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.681414 | + | 0.460555i | 0.681414 | + | 0.460555i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.46718 | − | 1.18467i | 1.46718 | − | 1.18467i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.287818 | + | 1.67856i | −0.287818 | + | 1.67856i | 0.372856 | + | 0.927889i | \(0.378378\pi\) |
−0.660675 | + | 0.750672i | \(0.729730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.873014 | − | 0.487695i | \(-0.837838\pi\) | ||||
0.873014 | + | 0.487695i | \(0.162162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0454471 | − | 0.0614485i | −0.0454471 | − | 0.0614485i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.373100 | + | 0.552019i | −0.373100 | + | 0.552019i | ||||
\(977\) | 0 | 0 | 0.210679 | − | 0.977555i | \(-0.432432\pi\) | ||||
−0.210679 | + | 0.977555i | \(0.567568\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.778036 | − | 0.628220i | \(-0.216216\pi\) | ||||
−0.778036 | + | 0.628220i | \(0.783784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.542689 | + | 0.672107i | −0.542689 | + | 0.672107i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.77139 | − | 0.893115i | 1.77139 | − | 0.893115i | 0.828510 | − | 0.559975i | \(-0.189189\pi\) |
0.942877 | − | 0.333140i | \(-0.108108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.18498 | − | 1.60220i | −1.18498 | − | 1.60220i | −0.660675 | − | 0.750672i | \(-0.729730\pi\) |
−0.524307 | − | 0.851529i | \(-0.675676\pi\) | |||||||
\(998\) | 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 | 2007.1.v.a.946.1 | yes | 36 | |
3.2 | odd | 2 | CM | 2007.1.v.a.946.1 | yes | 36 | |
223.95 | odd | 74 | inner | 2007.1.v.a.541.1 | ✓ | 36 | |
669.95 | even | 74 | inner | 2007.1.v.a.541.1 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2007.1.v.a.541.1 | ✓ | 36 | 223.95 | odd | 74 | inner | |
2007.1.v.a.541.1 | ✓ | 36 | 669.95 | even | 74 | inner | |
2007.1.v.a.946.1 | yes | 36 | 1.1 | even | 1 | trivial | |
2007.1.v.a.946.1 | yes | 36 | 3.2 | odd | 2 | CM |