Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(0.500000 - 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.449 |
Dual form | 1792.2.m.d.1345.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.89897 | − | 1.89897i | 1.09637 | − | 1.09637i | 0.101537 | − | 0.994832i | \(-0.467624\pi\) |
0.994832 | − | 0.101537i | \(-0.0323760\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.372364 | + | 0.372364i | 0.166526 | + | 0.166526i | 0.785451 | − | 0.618924i | \(-0.212431\pi\) |
−0.618924 | + | 0.785451i | \(0.712431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 4.21215i | − | 1.40405i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.158942 | + | 0.158942i | 0.0479227 | + | 0.0479227i | 0.730662 | − | 0.682739i | \(-0.239212\pi\) |
−0.682739 | + | 0.730662i | \(0.739212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.48475 | + | 1.48475i | −0.411796 | + | 0.411796i | −0.882364 | − | 0.470568i | \(-0.844049\pi\) |
0.470568 | + | 0.882364i | \(0.344049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79793 | 0.921134 | 0.460567 | − | 0.887625i | \(-0.347646\pi\) | ||||
0.460567 | + | 0.887625i | \(0.347646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94552 | − | 2.94552i | 0.675748 | − | 0.675748i | −0.283287 | − | 0.959035i | \(-0.591425\pi\) |
0.959035 | + | 0.283287i | \(0.0914248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.89897 | + | 1.89897i | 0.414388 | + | 0.414388i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.95687i | − | 0.408036i | −0.978967 | − | 0.204018i | \(-0.934600\pi\) | ||
0.978967 | − | 0.204018i | \(-0.0654002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.72269i | − | 0.944538i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.30182 | − | 2.30182i | −0.442986 | − | 0.442986i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0304945 | − | 0.0304945i | 0.00566268 | − | 0.00566268i | −0.704270 | − | 0.709932i | \(-0.748725\pi\) |
0.709932 | + | 0.704270i | \(0.248725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.16902 | 1.64680 | 0.823402 | − | 0.567458i | \(-0.192073\pi\) | ||||
0.823402 | + | 0.567458i | \(0.192073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.603650 | 0.105082 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.372364 | + | 0.372364i | −0.0629410 | + | 0.0629410i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.78530 | − | 5.78530i | −0.951098 | − | 0.951098i | 0.0477611 | − | 0.998859i | \(-0.484791\pi\) |
−0.998859 | + | 0.0477611i | \(0.984791\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.63899i | 0.902961i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.9442i | − | 1.70920i | −0.519284 | − | 0.854602i | \(-0.673801\pi\) | ||
0.519284 | − | 0.854602i | \(-0.326199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.62636 | + | 2.62636i | 0.400516 | + | 0.400516i | 0.878415 | − | 0.477899i | \(-0.158601\pi\) |
−0.477899 | + | 0.878415i | \(0.658601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.56845 | − | 1.56845i | 0.233811 | − | 0.233811i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.79793 | 1.13745 | 0.568723 | − | 0.822529i | \(-0.307438\pi\) | ||||
0.568723 | + | 0.822529i | \(0.307438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.21215 | − | 7.21215i | 1.00990 | − | 1.00990i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21215 | + | 2.21215i | 0.303862 | + | 0.303862i | 0.842523 | − | 0.538661i | \(-0.181070\pi\) |
−0.538661 | + | 0.842523i | \(0.681070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.118368i | 0.0159608i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 11.1869i | − | 1.48174i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.17030 | − | 9.17030i | −1.19387 | − | 1.19387i | −0.975971 | − | 0.217900i | \(-0.930079\pi\) |
−0.217900 | − | 0.975971i | \(-0.569921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.97601 | − | 4.97601i | 0.637113 | − | 0.637113i | −0.312729 | − | 0.949842i | \(-0.601243\pi\) |
0.949842 | + | 0.312729i | \(0.101243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.21215 | 0.530681 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.10574 | −0.137150 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.42429 | + | 4.42429i | −0.540513 | + | 0.540513i | −0.923679 | − | 0.383166i | \(-0.874834\pi\) |
0.383166 | + | 0.923679i | \(0.374834\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.71604 | − | 3.71604i | −0.447358 | − | 0.447358i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5174i | 1.72290i | 0.507844 | + | 0.861449i | \(0.330443\pi\) | ||||
−0.507844 | + | 0.861449i | \(0.669557\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0202i | 1.40685i | 0.710768 | + | 0.703427i | \(0.248348\pi\) | ||||
−0.710768 | + | 0.703427i | \(0.751652\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.96823 | − | 8.96823i | −1.03556 | − | 1.03556i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.158942 | + | 0.158942i | −0.0181131 | + | 0.0181131i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4165 | −1.28446 | −0.642229 | − | 0.766513i | \(-0.721990\pi\) | ||||
−0.642229 | + | 0.766513i | \(0.721990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.89426 | 0.432696 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.123744 | − | 0.123744i | 0.0135826 | − | 0.0135826i | −0.700283 | − | 0.713865i | \(-0.746943\pi\) |
0.713865 | + | 0.700283i | \(0.246943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | + | 1.41421i | 0.153393 | + | 0.153393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.115816i | − | 0.0124168i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.79956i | 0.720751i | 0.932807 | + | 0.360376i | \(0.117352\pi\) | ||||
−0.932807 | + | 0.360376i | \(0.882648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.48475 | − | 1.48475i | −0.155644 | − | 0.155644i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.4117 | − | 17.4117i | 1.80551 | − | 1.80551i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.19361 | 0.225060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.80572 | 0.894085 | 0.447043 | − | 0.894513i | \(-0.352477\pi\) | ||||
0.447043 | + | 0.894513i | \(0.352477\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.669485 | − | 0.669485i | 0.0672858 | − | 0.0672858i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.82372 | − | 4.82372i | −0.479978 | − | 0.479978i | 0.425146 | − | 0.905125i | \(-0.360223\pi\) |
−0.905125 | + | 0.425146i | \(0.860223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1158i | 1.19381i | 0.802313 | + | 0.596903i | \(0.203602\pi\) | ||||
−0.802313 | + | 0.596903i | \(0.796398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421i | 0.138013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4344 | + | 13.4344i | 1.29875 | + | 1.29875i | 0.929218 | + | 0.369531i | \(0.120482\pi\) |
0.369531 | + | 0.929218i | \(0.379518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0963303 | + | 0.0963303i | −0.00922677 | + | 0.00922677i | −0.711705 | − | 0.702478i | \(-0.752077\pi\) |
0.702478 | + | 0.711705i | \(0.252077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.9722 | −2.08551 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.89426 | −0.836702 | −0.418351 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418351 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.728670 | − | 0.728670i | 0.0679488 | − | 0.0679488i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.25400 | + | 6.25400i | 0.578182 | + | 0.578182i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.79793i | 0.348156i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.9495i | − | 0.995407i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.7827 | − | 20.7827i | −1.87392 | − | 1.87392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.62038 | − | 3.62038i | 0.323817 | − | 0.323817i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.61790 | −0.409773 | −0.204886 | − | 0.978786i | \(-0.565682\pi\) | ||||
−0.204886 | + | 0.978786i | \(0.565682\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.97474 | 0.878227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.6411 | + | 12.6411i | −1.10446 | + | 1.10446i | −0.110596 | + | 0.993865i | \(0.535276\pi\) |
−0.993865 | + | 0.110596i | \(0.964724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.94552 | + | 2.94552i | 0.255409 | + | 0.255409i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.71423i | − | 0.147538i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.6812i | 1.25430i | 0.778899 | + | 0.627149i | \(0.215778\pi\) | ||||
−0.778899 | + | 0.627149i | \(0.784222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.688625 | − | 0.688625i | −0.0584084 | − | 0.0584084i | 0.677299 | − | 0.735708i | \(-0.263150\pi\) |
−0.735708 | + | 0.677299i | \(0.763150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.8080 | − | 14.8080i | 1.24706 | − | 1.24706i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.471978 | −0.0394688 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0227101 | 0.00188597 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.89897 | + | 1.89897i | −0.156624 | + | 0.156624i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1133 | − | 15.1133i | −1.23813 | − | 1.23813i | −0.960766 | − | 0.277361i | \(-0.910540\pi\) |
−0.277361 | − | 0.960766i | \(-0.589460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.55274i | 0.777391i | 0.921366 | + | 0.388695i | \(0.127074\pi\) | ||||
−0.921366 | + | 0.388695i | \(0.872926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 15.9974i | − | 1.29332i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.41421 | + | 3.41421i | 0.274236 | + | 0.274236i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.77214 | + | 4.77214i | −0.380858 | + | 0.380858i | −0.871411 | − | 0.490553i | \(-0.836795\pi\) |
0.490553 | + | 0.871411i | \(0.336795\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.40158 | 0.666289 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.95687 | 0.154223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.33051 | − | 3.33051i | 0.260866 | − | 0.260866i | −0.564540 | − | 0.825406i | \(-0.690946\pi\) |
0.825406 | + | 0.564540i | \(0.190946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.224777 | + | 0.224777i | 0.0174989 | + | 0.0174989i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.202067i | − | 0.0156364i | −0.999969 | − | 0.00781822i | \(-0.997511\pi\) | ||
0.999969 | − | 0.00781822i | \(-0.00248864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.59102i | 0.660848i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4070 | − | 12.4070i | −0.948784 | − | 0.948784i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.48998 | + | 4.48998i | −0.341367 | + | 0.341367i | −0.856881 | − | 0.515514i | \(-0.827601\pi\) |
0.515514 | + | 0.856881i | \(0.327601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.72269 | 0.357002 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.8282 | −2.61785 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.10641 | + | 8.10641i | −0.605901 | + | 0.605901i | −0.941872 | − | 0.335971i | \(-0.890936\pi\) |
0.335971 | + | 0.941872i | \(0.390936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7889 | − | 15.7889i | −1.17358 | − | 1.17358i | −0.981350 | − | 0.192227i | \(-0.938429\pi\) |
−0.192227 | − | 0.981350i | \(-0.561571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.8986i | − | 1.39702i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.30848i | − | 0.316765i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.603650 | + | 0.603650i | 0.0441432 | + | 0.0441432i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.30182 | − | 2.30182i | 0.167433 | − | 0.167433i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.37470 | 0.388899 | 0.194450 | − | 0.980912i | \(-0.437708\pi\) | ||||
0.194450 | + | 0.980912i | \(0.437708\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.4194 | 1.18190 | 0.590949 | − | 0.806709i | \(-0.298754\pi\) | ||||
0.590949 | + | 0.806709i | \(0.298754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.09976 | + | 2.09976i | −0.150367 | + | 0.150367i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0685 | − | 12.0685i | −0.859846 | − | 0.859846i | 0.131474 | − | 0.991320i | \(-0.458029\pi\) |
−0.991320 | + | 0.131474i | \(0.958029\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00162i | 0.354556i | 0.984161 | + | 0.177278i | \(0.0567291\pi\) | ||||
−0.984161 | + | 0.177278i | \(0.943271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.8032i | 1.18520i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0304945 | + | 0.0304945i | 0.00214029 | + | 0.00214029i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.07524 | − | 4.07524i | 0.284627 | − | 0.284627i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.24264 | −0.572903 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.936331 | 0.0647674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.59587 | − | 7.59587i | 0.522921 | − | 0.522921i | −0.395531 | − | 0.918452i | \(-0.629440\pi\) |
0.918452 | + | 0.395531i | \(0.129440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27.5681 | + | 27.5681i | 1.88893 | + | 1.88893i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95592i | 0.133393i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.16902i | 0.622434i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.8259 | + | 22.8259i | 1.54243 | + | 1.54243i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.63899 | + | 5.63899i | −0.379320 | + | 0.379320i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.5995 | −1.31248 | −0.656239 | − | 0.754553i | \(-0.727854\pi\) | ||||
−0.656239 | + | 0.754553i | \(0.727854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.8927 | −1.32618 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2008 | + | 12.2008i | −0.809795 | + | 0.809795i | −0.984603 | − | 0.174808i | \(-0.944070\pi\) |
0.174808 | + | 0.984603i | \(0.444070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.97166 | + | 8.97166i | 0.592864 | + | 0.592864i | 0.938404 | − | 0.345540i | \(-0.112304\pi\) |
−0.345540 | + | 0.938404i | \(0.612304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.603650i | 0.0397172i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.7013i | − | 1.35619i | −0.734974 | − | 0.678095i | \(-0.762806\pi\) | ||
0.734974 | − | 0.678095i | \(-0.237194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.90367 | + | 2.90367i | 0.189415 | + | 0.189415i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.6796 | + | 21.6796i | −1.40824 | + | 1.40824i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.9926 | 1.16384 | 0.581922 | − | 0.813244i | \(-0.302301\pi\) | ||||
0.581922 | + | 0.813244i | \(0.302301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.45896 | 0.416058 | 0.208029 | − | 0.978123i | \(-0.433295\pi\) | ||||
0.208029 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3005 | − | 14.3005i | 0.917381 | − | 0.917381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.372364 | − | 0.372364i | −0.0237895 | − | 0.0237895i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.74674i | 0.556541i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.469970i | − | 0.0297832i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.50099 | − | 1.50099i | −0.0947419 | − | 0.0947419i | 0.658147 | − | 0.752889i | \(-0.271340\pi\) |
−0.752889 | + | 0.658147i | \(0.771340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.311029 | − | 0.311029i | 0.0195542 | − | 0.0195542i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.37109 | 0.336351 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0124 | 0.686933 | 0.343466 | − | 0.939165i | \(-0.388399\pi\) | ||||
0.343466 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.78530 | − | 5.78530i | 0.359481 | − | 0.359481i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.128447 | − | 0.128447i | −0.00795068 | − | 0.00795068i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.9018i | − | 1.72050i | −0.509874 | − | 0.860249i | \(-0.670308\pi\) | ||
0.509874 | − | 0.860249i | \(-0.329692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.64745i | 0.101202i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9121 | + | 12.9121i | 0.790209 | + | 0.790209i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1069 | + | 17.1069i | −1.04303 | + | 1.04303i | −0.0439967 | + | 0.999032i | \(0.514009\pi\) |
−0.999032 | + | 0.0439967i | \(0.985991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3660 | 1.29789 | 0.648946 | − | 0.760835i | \(-0.275210\pi\) | ||||
0.648946 | + | 0.760835i | \(0.275210\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.63899 | −0.341287 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.750632 | − | 0.750632i | 0.0452648 | − | 0.0452648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.57839 | + | 9.57839i | 0.575510 | + | 0.575510i | 0.933663 | − | 0.358153i | \(-0.116593\pi\) |
−0.358153 | + | 0.933663i | \(0.616593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 38.6213i | − | 2.31219i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.95365i | − | 0.534130i | −0.963679 | − | 0.267065i | \(-0.913946\pi\) | ||
0.963679 | − | 0.267065i | \(-0.0860538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.86685 | + | 5.86685i | 0.348748 | + | 0.348748i | 0.859643 | − | 0.510895i | \(-0.170686\pi\) |
−0.510895 | + | 0.859643i | \(0.670686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.16559 | − | 4.16559i | 0.246748 | − | 0.246748i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.9442 | 0.646018 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.57571 | −0.151512 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.7218 | − | 16.7218i | 0.980247 | − | 0.980247i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.63885 | − | 7.63885i | −0.446266 | − | 0.446266i | 0.447845 | − | 0.894111i | \(-0.352192\pi\) |
−0.894111 | + | 0.447845i | \(0.852192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.82938i | − | 0.397622i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.731712i | − | 0.0424582i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.90547 | + | 2.90547i | 0.168028 | + | 0.168028i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.62636 | + | 2.62636i | −0.151381 | + | 0.151381i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.3202 | −1.05247 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.70578 | 0.212192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.58271 | − | 6.58271i | 0.375695 | − | 0.375695i | −0.493851 | − | 0.869546i | \(-0.664411\pi\) |
0.869546 | + | 0.493851i | \(0.164411\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.0075 | + | 23.0075i | 1.30885 | + | 1.30885i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6229i | 1.33953i | 0.742573 | + | 0.669765i | \(0.233605\pi\) | ||||
−0.742573 | + | 0.669765i | \(0.766395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.51578i | 0.424817i | 0.977181 | + | 0.212408i | \(0.0681307\pi\) | ||||
−0.977181 | + | 0.212408i | \(0.931869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.56845 | + | 1.56845i | 0.0883722 | + | 0.0883722i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.661701 | + | 0.661701i | −0.0371648 | + | 0.0371648i | −0.725445 | − | 0.688280i | \(-0.758366\pi\) |
0.688280 | + | 0.725445i | \(0.258366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.00969368 | 0.000542742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 51.0228 | 2.84782 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1869 | − | 11.1869i | 0.622455 | − | 0.622455i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.01203 | + | 7.01203i | 0.388957 | + | 0.388957i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.365856i | 0.0202319i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.79793i | 0.429914i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5612 | + | 23.5612i | 1.29504 | + | 1.29504i | 0.931629 | + | 0.363412i | \(0.118388\pi\) |
0.363412 | + | 0.931629i | \(0.381612\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.3685 | + | 24.3685i | −1.33539 | + | 1.33539i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.29489 | −0.180019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8071 | 0.970014 | 0.485007 | − | 0.874510i | \(-0.338817\pi\) | ||||
0.485007 | + | 0.874510i | \(0.338817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.8899 | + | 16.8899i | −0.917334 | + | 0.917334i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.45734 | + | 1.45734i | 0.0789193 | + | 0.0789193i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.76744i | − | 0.148994i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.31265 | + | 1.31265i | 0.0704668 | + | 0.0704668i | 0.741462 | − | 0.670995i | \(-0.234133\pi\) |
−0.670995 | + | 0.741462i | \(0.734133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.9134 | + | 13.9134i | −0.744767 | + | 0.744767i | −0.973491 | − | 0.228724i | \(-0.926545\pi\) |
0.228724 | + | 0.973491i | \(0.426545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.83528 | 0.364840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8807 | −1.00492 | −0.502459 | − | 0.864601i | \(-0.667571\pi\) | ||||
−0.502459 | + | 0.864601i | \(0.667571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.40576 | + | 5.40576i | −0.286908 | + | 0.286908i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.21215 | + | 7.21215i | 0.381707 | + | 0.381707i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.8252i | − | 1.15189i | −0.817488 | − | 0.575945i | \(-0.804634\pi\) | ||
0.817488 | − | 0.575945i | \(-0.195366\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.64783i | 0.0867280i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.7927 | − | 20.7927i | −1.09133 | − | 1.09133i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.47587 | + | 4.47587i | −0.234278 | + | 0.234278i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.61788 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −46.0988 | −2.39981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.21215 | + | 2.21215i | −0.114849 | + | 0.114849i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7101 | + | 15.7101i | 0.813436 | + | 0.813436i | 0.985147 | − | 0.171711i | \(-0.0549296\pi\) |
−0.171711 | + | 0.985147i | \(0.554930\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 13.7500i | − | 0.710045i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0905535i | 0.00466374i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.8259 | + | 10.8259i | 0.556088 | + | 0.556088i | 0.928191 | − | 0.372103i | \(-0.121363\pi\) |
−0.372103 | + | 0.928191i | \(0.621363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.76924 | + | 8.76924i | −0.449262 | + | 0.449262i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.76582 | 0.192424 | 0.0962121 | − | 0.995361i | \(-0.469327\pi\) | ||||
0.0962121 | + | 0.995361i | \(0.469327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.118368 | −0.00603261 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0626 | − | 11.0626i | 0.562344 | − | 0.562344i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.0059 | − | 25.0059i | −1.26785 | − | 1.26785i | −0.947197 | − | 0.320653i | \(-0.896098\pi\) |
−0.320653 | − | 0.947197i | \(-0.603902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.43208i | − | 0.375856i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.0102i | 2.42179i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.25110 | − | 4.25110i | −0.213896 | − | 0.213896i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8246 | + | 11.8246i | −0.593460 | + | 0.593460i | −0.938564 | − | 0.345105i | \(-0.887843\pi\) |
0.345105 | + | 0.938564i | \(0.387843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.1869 | 0.560045 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.39511 | −0.269419 | −0.134710 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134710 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6137 | + | 13.6137i | −0.678148 | + | 0.678148i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.45008 | + | 1.45008i | 0.0720552 | + | 0.0720552i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.83905i | − | 0.0911584i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.95203i | − | 0.195415i | −0.995215 | − | 0.0977076i | \(-0.968849\pi\) | ||
0.995215 | − | 0.0977076i | \(-0.0311510\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.8791 | + | 27.8791i | 1.37517 | + | 1.37517i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.17030 | − | 9.17030i | 0.451241 | − | 0.451241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0921555 | 0.00452373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.61535 | −0.128074 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.2684 | + | 14.2684i | −0.697059 | + | 0.697059i | −0.963775 | − | 0.266717i | \(-0.914061\pi\) |
0.266717 | + | 0.963775i | \(0.414061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3092 | − | 23.3092i | −1.13602 | − | 1.13602i | −0.989157 | − | 0.146862i | \(-0.953083\pi\) |
−0.146862 | − | 0.989157i | \(-0.546917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 32.8460i | − | 1.59703i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 17.9365i | − | 0.870046i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.97601 | + | 4.97601i | 0.240806 | + | 0.240806i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.896271 | + | 0.896271i | −0.0432723 | + | 0.0432723i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1697 | 0.682530 | 0.341265 | − | 0.939967i | \(-0.389145\pi\) | ||||
0.341265 | + | 0.939967i | \(0.389145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.4860 | −0.503924 | −0.251962 | − | 0.967737i | \(-0.581076\pi\) | ||||
−0.251962 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0431257 | − | 0.0431257i | 0.00206772 | − | 0.00206772i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.76401 | − | 5.76401i | −0.275730 | − | 0.275730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.2381i | − | 0.488637i | −0.969695 | − | 0.244318i | \(-0.921436\pi\) | ||
0.969695 | − | 0.244318i | \(-0.0785642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.21215i | 0.200578i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.33536 | − | 1.33536i | −0.0634449 | − | 0.0634449i | 0.674672 | − | 0.738117i | \(-0.264285\pi\) |
−0.738117 | + | 0.674672i | \(0.764285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.53191 | + | 2.53191i | −0.120024 | + | 0.120024i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −57.3992 | −2.71489 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.7127 | −1.68539 | −0.842694 | − | 0.538393i | \(-0.819032\pi\) | ||||
−0.842694 | + | 0.538393i | \(0.819032\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.73950 | − | 1.73950i | 0.0819097 | − | 0.0819097i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.1403 | + | 18.1403i | 0.852307 | + | 0.852307i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.10574i | − | 0.0518378i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.3144i | 1.13738i | 0.822552 | + | 0.568689i | \(0.192549\pi\) | ||||
−0.822552 | + | 0.568689i | \(0.807451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.74218 | − | 8.74218i | −0.408050 | − | 0.408050i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.3124 | + | 30.3124i | −1.41179 | + | 1.41179i | −0.664522 | + | 0.747269i | \(0.731365\pi\) |
−0.747269 | + | 0.664522i | \(0.768635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.33480 | 0.201455 | 0.100728 | − | 0.994914i | \(-0.467883\pi\) | ||||
0.100728 | + | 0.994914i | \(0.467883\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9670 | 0.601328 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0292 | + | 19.0292i | −0.880567 | + | 0.880567i | −0.993592 | − | 0.113025i | \(-0.963946\pi\) |
0.113025 | + | 0.993592i | \(0.463946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.42429 | − | 4.42429i | −0.204295 | − | 0.204295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.1243i | 0.835122i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.834876i | 0.0383876i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.9108 | − | 13.9108i | −0.638270 | − | 0.638270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.31788 | − | 9.31788i | 0.426637 | − | 0.426637i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.69245 | 0.214404 | 0.107202 | − | 0.994237i | \(-0.465811\pi\) | ||||
0.107202 | + | 0.994237i | \(0.465811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1795 | 0.783317 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.71604 | − | 3.71604i | 0.169086 | − | 0.169086i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.27893 | + | 3.27893i | 0.148889 | + | 0.148889i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.300020i | − | 0.0135952i | −0.999977 | − | 0.00679760i | \(-0.997836\pi\) | ||
0.999977 | − | 0.00679760i | \(-0.00216376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.6491i | − | 0.572011i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00361 | + | 6.00361i | 0.270939 | + | 0.270939i | 0.829478 | − | 0.558539i | \(-0.188638\pi\) |
−0.558539 | + | 0.829478i | \(0.688638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.115816 | − | 0.115816i | 0.00521609 | − | 0.00521609i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.498585 | 0.0224097 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5174 | −0.651194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.25367 | + | 5.25367i | −0.235187 | + | 0.235187i | −0.814854 | − | 0.579667i | \(-0.803183\pi\) |
0.579667 | + | 0.814854i | \(0.303183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.383719 | − | 0.383719i | −0.0171433 | − | 0.0171433i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.645460i | 0.0287797i | 0.999896 | + | 0.0143898i | \(0.00458058\pi\) | ||||
−0.999896 | + | 0.0143898i | \(0.995419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.59236i | − | 0.159858i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.3141 | + | 16.3141i | 0.724533 | + | 0.724533i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9125 | − | 22.9125i | 1.01558 | − | 1.01558i | 0.0157007 | − | 0.999877i | \(-0.495002\pi\) |
0.999877 | − | 0.0157007i | \(-0.00499791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0202 | −0.531740 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.5601 | −0.598695 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.51149 | + | 4.51149i | −0.198800 | + | 0.198800i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.23942 | + | 1.23942i | 0.0545095 | + | 0.0545095i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.0527i | 0.748529i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.9433i | 1.57471i | 0.616503 | + | 0.787353i | \(0.288549\pi\) | ||||
−0.616503 | + | 0.787353i | \(0.711451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.198239 | − | 0.198239i | −0.00866838 | − | 0.00866838i | 0.702759 | − | 0.711428i | \(-0.251951\pi\) |
−0.711428 | + | 0.702759i | \(0.751951\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.96823 | − | 8.96823i | 0.391406 | − | 0.391406i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.8233 | 1.51693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1706 | 0.833506 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38.6266 | + | 38.6266i | −1.67625 | + | 1.67625i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.2495 | + | 16.2495i | 0.703844 | + | 0.703844i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0050i | 0.432552i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.7876i | 1.32858i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.158942 | − | 0.158942i | −0.00684610 | − | 0.00684610i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.4243 | − | 19.4243i | 0.835116 | − | 0.835116i | −0.153096 | − | 0.988211i | \(-0.548924\pi\) |
0.988211 | + | 0.153096i | \(0.0489243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −59.9651 | −2.57335 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0717399 | −0.00307300 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.42914 | + | 6.42914i | −0.274890 | + | 0.274890i | −0.831065 | − | 0.556175i | \(-0.812268\pi\) |
0.556175 | + | 0.831065i | \(0.312268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.9597 | − | 20.9597i | −0.894538 | − | 0.894538i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.179644i | − | 0.00765310i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.4165i | − | 0.485479i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.18165 | − | 8.18165i | −0.347292 | − | 0.347292i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3961 | − | 14.3961i | 0.609982 | − | 0.609982i | −0.332959 | − | 0.942941i | \(-0.608047\pi\) |
0.942941 | + | 0.332959i | \(0.108047\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.79899 | −0.329862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.29262 | 0.0967945 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5187 | − | 16.5187i | 0.696179 | − | 0.696179i | −0.267405 | − | 0.963584i | \(-0.586166\pi\) |
0.963584 | + | 0.267405i | \(0.0861662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.31190 | − | 3.31190i | −0.139333 | − | 0.139333i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.89426i | 0.163544i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.1860i | 1.43315i | 0.697510 | + | 0.716575i | \(0.254291\pi\) | ||||
−0.697510 | + | 0.716575i | \(0.745709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.70390 | + | 2.70390i | 0.113155 | + | 0.113155i | 0.761417 | − | 0.648262i | \(-0.224504\pi\) |
−0.648262 | + | 0.761417i | \(0.724504\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.2064 | − | 10.2064i | 0.426377 | − | 0.426377i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.24171 | −0.385406 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3564 | 0.514406 | 0.257203 | − | 0.966357i | \(-0.417199\pi\) | ||||
0.257203 | + | 0.966357i | \(0.417199\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.1800 | − | 31.1800i | 1.29580 | − | 1.29580i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.123744 | + | 0.123744i | 0.00513376 | + | 0.00513376i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.703204i | 0.0291237i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.65753i | 0.192565i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.74183 | − | 9.74183i | −0.402088 | − | 0.402088i | 0.476880 | − | 0.878968i | \(-0.341768\pi\) |
−0.878968 | + | 0.476880i | \(0.841768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.0075 | − | 27.0075i | 1.11283 | − | 1.11283i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −45.8354 | −1.88542 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.0335 | −1.31546 | −0.657728 | − | 0.753255i | \(-0.728482\pi\) | ||||
−0.657728 | + | 0.753255i | \(0.728482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.41421 | + | 1.41421i | −0.0579771 | + | 0.0579771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.49791 | + | 9.49791i | 0.388724 | + | 0.388724i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.42105i | − | 0.180639i | −0.995913 | − | 0.0903196i | \(-0.971211\pi\) | ||
0.995913 | − | 0.0903196i | \(-0.0287888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.7279i | 0.723138i | 0.932345 | + | 0.361569i | \(0.117759\pi\) | ||||
−0.932345 | + | 0.361569i | \(0.882241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.6358 | + | 18.6358i | 0.758907 | + | 0.758907i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.07719 | − | 4.07719i | 0.165761 | − | 0.165761i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.3546 | −1.31323 | −0.656616 | − | 0.754225i | \(-0.728013\pi\) | ||||
−0.656616 | + | 0.754225i | \(0.728013\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.115816 | 0.00469310 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.5780 | + | 11.5780i | −0.468396 | + | 0.468396i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7860 | + | 18.7860i | 0.758758 | + | 0.758758i | 0.976096 | − | 0.217338i | \(-0.0697374\pi\) |
−0.217338 | + | 0.976096i | \(0.569737\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 15.4775i | − | 0.624113i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.06491i | 0.284422i | 0.989836 | + | 0.142211i | \(0.0454212\pi\) | ||||
−0.989836 | + | 0.142211i | \(0.954579\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.3058 | − | 15.3058i | −0.615191 | − | 0.615191i | 0.329103 | − | 0.944294i | \(-0.393254\pi\) |
−0.944294 | + | 0.329103i | \(0.893254\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.50438 | + | 4.50438i | −0.180755 | + | 0.180755i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.79956 | −0.272418 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.9173 | −0.836690 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.77806 | − | 1.77806i | 0.0710089 | − | 0.0710089i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.9722 | − | 21.9722i | −0.876088 | − | 0.876088i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.3637i | 1.72628i | 0.504963 | + | 0.863141i | \(0.331506\pi\) | ||||
−0.504963 | + | 0.863141i | \(0.668494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 28.8486i | − | 1.14663i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.71954 | − | 1.71954i | −0.0682379 | − | 0.0682379i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.48475 | − | 1.48475i | 0.0588280 | − | 0.0588280i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 61.1494 | 2.41903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.9439 | 0.629745 | 0.314872 | − | 0.949134i | \(-0.398038\pi\) | ||||
0.314872 | + | 0.949134i | \(0.398038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.1476 | − | 15.1476i | 0.597363 | − | 0.597363i | −0.342247 | − | 0.939610i | \(-0.611188\pi\) |
0.939610 | + | 0.342247i | \(0.111188\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.71423 | + | 3.71423i | 0.146248 | + | 0.146248i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 41.6849i | − | 1.63880i | −0.573220 | − | 0.819402i | \(-0.694306\pi\) | ||
0.573220 | − | 0.819402i | \(-0.305694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.91508i | − | 0.114427i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.4117 | + | 17.4117i | 0.682417 | + | 0.682417i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.38694 | − | 4.38694i | 0.171674 | − | 0.171674i | −0.616040 | − | 0.787715i | \(-0.711264\pi\) |
0.787715 | + | 0.616040i | \(0.211264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.41421 | −0.367844 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 50.6307 | 1.97529 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.6974 | + | 33.6974i | −1.31267 | + | 1.31267i | −0.393222 | + | 0.919444i | \(0.628640\pi\) |
−0.919444 | + | 0.393222i | \(0.871360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0875 | − | 21.0875i | −0.820208 | − | 0.820208i | 0.165930 | − | 0.986138i | \(-0.446937\pi\) |
−0.986138 | + | 0.165930i | \(0.946937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.4165i | 0.831748i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.19361i | 0.0850646i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0596739 | − | 0.0596739i | −0.00231058 | − | 0.00231058i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.2187 | + | 37.2187i | −1.43896 | + | 1.43896i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.58179 | 0.0610644 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.6656 | −0.950790 | −0.475395 | − | 0.879773i | \(-0.657695\pi\) | ||||
−0.475395 | + | 0.879773i | \(0.657695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.8708 | + | 10.8708i | −0.418417 | + | 0.418417i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.1104 | − | 16.1104i | −0.619172 | − | 0.619172i | 0.326147 | − | 0.945319i | \(-0.394249\pi\) |
−0.945319 | + | 0.326147i | \(0.894249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.80572i | 0.337932i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 46.3378i | 1.77567i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3105 | − | 14.3105i | −0.547575 | − | 0.547575i | 0.378163 | − | 0.925739i | \(-0.376556\pi\) |
−0.925739 | + | 0.378163i | \(0.876556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.46675 | + | 5.46675i | −0.208874 | + | 0.208874i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.0737 | 1.29999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.56898 | −0.250258 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.0209 | − | 14.0209i | 0.533382 | − | 0.533382i | −0.388195 | − | 0.921577i | \(-0.626901\pi\) |
0.921577 | + | 0.388195i | \(0.126901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.669485 | + | 0.669485i | 0.0254317 | + | 0.0254317i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.512838i | − | 0.0194531i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 41.5655i | − | 1.57441i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.3112 | − | 39.3112i | −1.48688 | − | 1.48688i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.3024 | + | 26.3024i | −0.993430 | + | 0.993430i | −0.999979 | − | 0.00654904i | \(-0.997915\pi\) |
0.00654904 | + | 0.999979i | \(0.497915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.0814 | −1.28541 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0279 | 0.415336 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.82372 | − | 4.82372i | 0.181415 | − | 0.181415i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4665 | + | 18.4665i | 0.693524 | + | 0.693524i | 0.963005 | − | 0.269482i | \(-0.0868524\pi\) |
−0.269482 | + | 0.963005i | \(0.586852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.0880i | 1.80344i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.9426i | − | 0.671956i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.175748 | − | 0.175748i | −0.00657259 | − | 0.00657259i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.1673 | − | 34.1673i | 1.27600 | − | 1.27600i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0026 | 0.447620 | 0.223810 | − | 0.974633i | \(-0.428151\pi\) | ||||
0.223810 | + | 0.974633i | \(0.428151\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.1158 | −0.451217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.2654 | − | 12.2654i | 0.456153 | − | 0.456153i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.144016 | − | 0.144016i | −0.00534862 | − | 0.00534862i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8622i | 0.736647i | 0.929698 | + | 0.368323i | \(0.120068\pi\) | ||||
−0.929698 | + | 0.368323i | \(0.879932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 42.6297i | − | 1.57888i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.97474 | + | 9.97474i | 0.368929 | + | 0.368929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.1704 | − | 29.1704i | 1.07743 | − | 1.07743i | 0.0806954 | − | 0.996739i | \(-0.474286\pi\) |
0.996739 | − | 0.0806954i | \(-0.0257141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.41421 | −0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.40641 | −0.0518057 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4158 | + | 16.4158i | −0.603866 | + | 0.603866i | −0.941336 | − | 0.337470i | \(-0.890429\pi\) |
0.337470 | + | 0.941336i | \(0.390429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6098 | + | 16.6098i | 0.610175 | + | 0.610175i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.10225i | − | 0.223870i | −0.993716 | − | 0.111935i | \(-0.964295\pi\) | ||
0.993716 | − | 0.111935i | \(-0.0357048\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 11.2553i | − | 0.412361i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.521227 | − | 0.521227i | −0.0190707 | − | 0.0190707i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.4344 | + | 13.4344i | −0.490881 | + | 0.490881i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.6119 | 1.37248 | 0.686238 | − | 0.727377i | \(-0.259261\pi\) | ||||
0.686238 | + | 0.727377i | \(0.259261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.70067 | −0.207744 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.55710 | + | 3.55710i | −0.129456 | + | 0.129456i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5029 | + | 33.5029i | 1.21768 | + | 1.21768i | 0.968441 | + | 0.249242i | \(0.0801814\pi\) |
0.249242 | + | 0.968441i | \(0.419819\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.18127i | − | 0.0428773i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.2942i | − | 1.13442i | −0.823575 | − | 0.567208i | \(-0.808024\pi\) | ||
0.823575 | − | 0.567208i | \(-0.191976\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0963303 | − | 0.0963303i | −0.00348739 | − | 0.00348739i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.95687 | − | 5.95687i | 0.215371 | − | 0.215371i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.2312 | 0.983263 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.5011 | 0.595046 | 0.297523 | − | 0.954715i | \(-0.403839\pi\) | ||||
0.297523 | + | 0.954715i | \(0.403839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.9121 | − | 20.9121i | 0.753132 | − | 0.753132i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.1931 | − | 33.1931i | −1.19387 | − | 1.19387i | −0.975970 | − | 0.217904i | \(-0.930078\pi\) |
−0.217904 | − | 0.975970i | \(-0.569922\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 43.3024i | − | 1.55547i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 21.9722i | − | 0.788248i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.2365 | − | 32.2365i | −1.15499 | − | 1.15499i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.30742 | + | 2.30742i | −0.0825660 | + | 0.0825660i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.140386 | −0.00501698 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.55395 | −0.126846 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4484 | − | 37.4484i | 1.33489 | − | 1.33489i | 0.433959 | − | 0.900933i | \(-0.357116\pi\) |
0.900933 | − | 0.433959i | \(-0.142884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −52.9846 | − | 52.9846i | −1.88630 | − | 1.88630i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.89426i | − | 0.316244i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.7763i | 0.524722i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.12845 | + | 3.12845i | 0.110955 | + | 0.110955i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.2951 | + | 36.2951i | −1.28564 | + | 1.28564i | −0.348227 | + | 0.937410i | \(0.613216\pi\) |
−0.937410 | + | 0.348227i | \(0.886784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.6160 | 1.04774 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.6407 | 1.01197 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.91050 | + | 1.91050i | −0.0674202 | + | 0.0674202i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.728670 | + | 0.728670i | 0.0256822 | + | 0.0256822i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 64.9710i | 2.28709i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 53.8799i | − | 1.89432i | −0.320768 | − | 0.947158i | \(-0.603941\pi\) | ||
0.320768 | − | 0.947158i | \(-0.396059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.37216 | − | 3.37216i | −0.118413 | − | 0.118413i | 0.645417 | − | 0.763830i | \(-0.276683\pi\) |
−0.763830 | + | 0.645417i | \(0.776683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.5733 | − | 40.5733i | 1.42297 | − | 1.42297i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.48033 | 0.0868821 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.4720 | 0.541296 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.25400 | + | 6.25400i | −0.218532 | + | 0.218532i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9339 | + | 10.9339i | 0.381596 | + | 0.381596i | 0.871677 | − | 0.490081i | \(-0.163033\pi\) |
−0.490081 | + | 0.871677i | \(0.663033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.6379i | − | 1.79999i | −0.435905 | − | 0.899993i | \(-0.643572\pi\) | ||
0.435905 | − | 0.899993i | \(-0.356428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.85085i | − | 0.0992539i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.2096 | − | 31.2096i | −1.08526 | − | 1.08526i | −0.996009 | − | 0.0892551i | \(-0.971551\pi\) |
−0.0892551 | − | 0.996009i | \(-0.528449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.3646 | + | 15.3646i | −0.533634 | + | 0.533634i | −0.921652 | − | 0.388018i | \(-0.873160\pi\) |
0.388018 | + | 0.921652i | \(0.373160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.3781 | 1.26194 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.79793 | −0.131591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0752426 | − | 0.0752426i | 0.00260388 | − | 0.00260388i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.1055 | − | 21.1055i | −0.729512 | − | 0.729512i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.4882i | 1.22519i | 0.790397 | + | 0.612595i | \(0.209874\pi\) | ||||
−0.790397 | + | 0.612595i | \(0.790126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9981i | 0.999936i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.0027 | − | 17.0027i | −0.585603 | − | 0.585603i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.19899 | + | 3.19899i | −0.110048 | + | 0.110048i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9495 | 0.376228 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.2819 | 0.764713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.3211 | + | 11.3211i | −0.388083 | + | 0.388083i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.3684 | + | 35.3684i | 1.21099 | + | 1.21099i | 0.970701 | + | 0.240291i | \(0.0772428\pi\) |
0.240291 | + | 0.970701i | \(0.422757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 9.23981i | − | 0.315995i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 26.2359i | − | 0.896202i | −0.893983 | − | 0.448101i | \(-0.852100\pi\) | ||
0.893983 | − | 0.448101i | \(-0.147900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4164 | + | 14.4164i | 0.491880 | + | 0.491880i | 0.908898 | − | 0.417018i | \(-0.136925\pi\) |
−0.417018 | + | 0.908898i | \(0.636925\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.7827 | − | 20.7827i | 0.708274 | − | 0.708274i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.9719 | 1.46278 | 0.731390 | − | 0.681959i | \(-0.238872\pi\) | ||||
0.731390 | + | 0.681959i | \(0.238872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.34382 | −0.113693 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.89118 | + | 4.89118i | −0.166113 | + | 0.166113i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.81456 | − | 1.81456i | −0.0615547 | − | 0.0615547i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.1380i | − | 0.445163i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 37.0910i | − | 1.25534i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.62038 | + | 3.62038i | 0.122391 | + | 0.122391i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.33766 | + | 2.33766i | −0.0789370 | + | 0.0789370i | −0.745473 | − | 0.666536i | \(-0.767776\pi\) |
0.666536 | + | 0.745473i | \(0.267776\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.0118 | −0.978545 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.183946 | −0.00619731 | −0.00309865 | − | 0.999995i | \(-0.500986\pi\) | ||||
−0.00309865 | + | 0.999995i | \(0.500986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.7600 | − | 32.7600i | 1.10246 | − | 1.10246i | 0.108350 | − | 0.994113i | \(-0.465443\pi\) |
0.994113 | − | 0.108350i | \(-0.0345568\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.9688 | − | 12.9688i | −0.435940 | − | 0.435940i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8506i | 0.532210i | 0.963944 | + | 0.266105i | \(0.0857368\pi\) | ||||
−0.963944 | + | 0.266105i | \(0.914263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.61790i | − | 0.154880i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.618961 | + | 0.618961i | 0.0207360 | + | 0.0207360i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.9690 | − | 22.9690i | 0.768627 | − | 0.768627i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.03707 | −0.201797 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0348 | 0.368441 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.279604 | − | 0.279604i | 0.00932533 | − | 0.00932533i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.40158 | + | 8.40158i | 0.279897 | + | 0.279897i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.97474i | 0.331938i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 11.7584i | − | 0.390863i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.6027 | + | 23.6027i | 0.783715 | + | 0.783715i | 0.980456 | − | 0.196740i | \(-0.0630356\pi\) |
−0.196740 | + | 0.980456i | \(0.563036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.3182 | + | 20.3182i | −0.673913 | + | 0.673913i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3105 | 0.474127 | 0.237064 | − | 0.971494i | \(-0.423815\pi\) | ||||
0.237064 | + | 0.971494i | \(0.423815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0393361 | 0.00130183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.03715 | − | 7.03715i | 0.232641 | − | 0.232641i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.6411 | − | 12.6411i | −0.417447 | − | 0.417447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5848i | 0.349162i | 0.984643 | + | 0.174581i | \(0.0558570\pi\) | ||||
−0.984643 | + | 0.174581i | \(0.944143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 25.0007i | − | 0.823800i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.5547 | − | 21.5547i | −0.709483 | − | 0.709483i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.3222 | + | 27.3222i | −0.898348 | + | 0.898348i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 51.0336 | 1.67616 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.3891 | −1.22670 | −0.613348 | − | 0.789813i | \(-0.710178\pi\) | ||||
−0.613348 | + | 0.789813i | \(0.710178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.94552 | + | 2.94552i | −0.0965355 | + | 0.0965355i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.8590 | + | 44.8590i | 1.46862 | + | 1.46862i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.449555i | 0.0147020i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0986i | − | 0.623925i | −0.950094 | − | 0.311962i | \(-0.899014\pi\) | ||
0.950094 | − | 0.311962i | \(-0.100986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2722 | + | 14.2722i | 0.465756 | + | 0.465756i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.07900 | − | 8.07900i | 0.263368 | − | 0.263368i | −0.563053 | − | 0.826421i | \(-0.690373\pi\) |
0.826421 | + | 0.563053i | \(0.190373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.4165 | −0.697417 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.71423 | 0.0557640 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2015 | − | 30.2015i | 0.981418 | − | 0.981418i | −0.0184129 | − | 0.999830i | \(-0.505861\pi\) |
0.999830 | + | 0.0184129i | \(0.00586132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.8470 | − | 17.8470i | −0.579337 | − | 0.579337i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.51310i | 0.0814927i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.3192i | − | 0.593418i | −0.954968 | − | 0.296709i | \(-0.904111\pi\) | ||
0.954968 | − | 0.296709i | \(-0.0958891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.00134 | + | 2.00134i | 0.0647620 | + | 0.0647620i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0184080 | − | 0.0184080i | 0.000595045 | − | 0.000595045i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6812 | −0.474080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.0709 | 1.71197 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 56.5875 | − | 56.5875i | 1.82351 | − | 1.82351i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.11401 | + | 6.11401i | 0.196817 | + | 0.196817i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5495i | 0.628669i | 0.949312 | + | 0.314335i | \(0.101781\pi\) | ||||
−0.949312 | + | 0.314335i | \(0.898219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 42.4870i | − | 1.36488i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.1948 | + | 37.1948i | 1.19364 | + | 1.19364i | 0.976038 | + | 0.217598i | \(0.0698222\pi\) |
0.217598 | + | 0.976038i | \(0.430178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.688625 | − | 0.688625i | 0.0220763 | − | 0.0220763i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.6312 | 0.852881 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1324 | 0.580108 | 0.290054 | − | 0.957010i | \(-0.406327\pi\) | ||||
0.290054 | + | 0.957010i | \(0.406327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.08073 | + | 1.08073i | −0.0345404 | + | 0.0345404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.405757 | + | 0.405757i | 0.0129548 | + | 0.0129548i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.72823i | − | 0.0551220i | −0.999620 | − | 0.0275610i | \(-0.991226\pi\) | ||
0.999620 | − | 0.0275610i | \(-0.00877404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.98776i | − | 0.286374i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.8080 | + | 14.8080i | 0.471344 | + | 0.471344i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.13946 | − | 5.13946i | 0.163425 | − | 0.163425i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.5830 | −1.54329 | −0.771645 | − | 0.636054i | \(-0.780566\pi\) | ||||
−0.771645 | + | 0.636054i | \(0.780566\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 89.4838 | 2.83968 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.86242 | + | 1.86242i | −0.0590428 | + | 0.0590428i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1609 | + | 10.1609i | 0.321799 | + | 0.321799i | 0.849457 | − | 0.527658i | \(-0.176930\pi\) |
−0.527658 | + | 0.849457i | \(0.676930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.6335i | 0.842647i |
(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 | 1792.2.m.d.449.4 | yes | 8 | |
4.3 | odd | 2 | 1792.2.m.b.449.1 | yes | 8 | ||
8.3 | odd | 2 | 1792.2.m.c.449.4 | yes | 8 | ||
8.5 | even | 2 | 1792.2.m.a.449.1 | ✓ | 8 | ||
16.3 | odd | 4 | 1792.2.m.b.1345.1 | yes | 8 | ||
16.5 | even | 4 | 1792.2.m.a.1345.1 | yes | 8 | ||
16.11 | odd | 4 | 1792.2.m.c.1345.4 | yes | 8 | ||
16.13 | even | 4 | inner | 1792.2.m.d.1345.4 | yes | 8 | |
32.3 | odd | 8 | 7168.2.a.w.1.1 | 4 | |||
32.13 | even | 8 | 7168.2.a.t.1.1 | 4 | |||
32.19 | odd | 8 | 7168.2.a.s.1.4 | 4 | |||
32.29 | even | 8 | 7168.2.a.x.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.a.449.1 | ✓ | 8 | 8.5 | even | 2 | ||
1792.2.m.a.1345.1 | yes | 8 | 16.5 | even | 4 | ||
1792.2.m.b.449.1 | yes | 8 | 4.3 | odd | 2 | ||
1792.2.m.b.1345.1 | yes | 8 | 16.3 | odd | 4 | ||
1792.2.m.c.449.4 | yes | 8 | 8.3 | odd | 2 | ||
1792.2.m.c.1345.4 | yes | 8 | 16.11 | odd | 4 | ||
1792.2.m.d.449.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1792.2.m.d.1345.4 | yes | 8 | 16.13 | even | 4 | inner | |
7168.2.a.s.1.4 | 4 | 32.19 | odd | 8 | |||
7168.2.a.t.1.1 | 4 | 32.13 | even | 8 | |||
7168.2.a.w.1.1 | 4 | 32.3 | odd | 8 | |||
7168.2.a.x.1.4 | 4 | 32.29 | even | 8 |