Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.6040479020157644046336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 \) |
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 | 218.5 | ||
Root | \(0.912166 + 1.47240i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.218 |
Dual form | 525.2.j.a.407.5 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.560232 | + | 0.560232i | 0.396143 | + | 0.396143i | 0.876870 | − | 0.480727i | \(-0.159627\pi\) |
−0.480727 | + | 0.876870i | \(0.659627\pi\) | |||||||
\(3\) | 0.0537601 | − | 1.73122i | 0.0310384 | − | 0.999518i | ||||
\(4\) | − | 1.37228i | − | 0.686141i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | − | 0.939764i | 0.408248 | − | 0.383657i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 1.88926 | − | 1.88926i | 0.667954 | − | 0.667954i | ||||
\(9\) | −2.99422 | − | 0.186141i | −0.998073 | − | 0.0620469i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.10891i | − | 1.23888i | −0.785043 | − | 0.619442i | \(-0.787359\pi\) | ||
0.785043 | − | 0.619442i | \(-0.212641\pi\) | |||||||
\(12\) | −2.37572 | − | 0.0737740i | −0.685810 | − | 0.0212967i | ||||
\(13\) | 1.67746 | + | 1.67746i | 0.465243 | + | 0.465243i | 0.900369 | − | 0.435127i | \(-0.143296\pi\) |
−0.435127 | + | 0.900369i | \(0.643296\pi\) | |||||||
\(14\) | −0.792287 | −0.211748 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.627719 | −0.156930 | ||||||||
\(17\) | −0.664513 | − | 0.664513i | −0.161168 | − | 0.161168i | 0.621916 | − | 0.783084i | \(-0.286355\pi\) |
−0.783084 | + | 0.621916i | \(0.786355\pi\) | |||||||
\(18\) | −1.57317 | − | 1.78174i | −0.370801 | − | 0.419960i | ||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18614 | + | 1.26217i | 0.258837 | + | 0.275428i | ||||
\(22\) | 2.30194 | − | 2.30194i | 0.490776 | − | 0.490776i | ||||
\(23\) | −2.44949 | + | 2.44949i | −0.510754 | + | 0.510754i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) |
0.404004 | + | 0.914757i | \(0.367618\pi\) | |||||||
\(24\) | −3.16915 | − | 3.37228i | −0.646900 | − | 0.688364i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.87953i | 0.368606i | ||||||||
\(27\) | −0.483219 | + | 5.17364i | −0.0929956 | + | 0.995667i | ||||
\(28\) | 0.970349 | + | 0.970349i | 0.183379 | + | 0.183379i | ||||
\(29\) | −5.98844 | −1.11203 | −0.556013 | − | 0.831174i | \(-0.687669\pi\) | ||||
−0.556013 | + | 0.831174i | \(0.687669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74456 | 0.852149 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(32\) | −4.13018 | − | 4.13018i | −0.730120 | − | 0.730120i | ||||
\(33\) | −7.11342 | − | 0.220895i | −1.23829 | − | 0.0384530i | ||||
\(34\) | − | 0.744563i | − | 0.127691i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.255437 | + | 4.10891i | −0.0425729 | + | 0.684819i | ||||
\(37\) | 3.35491 | − | 3.35491i | 0.551544 | − | 0.551544i | −0.375342 | − | 0.926886i | \(-0.622475\pi\) |
0.926886 | + | 0.375342i | \(0.122475\pi\) | |||||||
\(38\) | 2.24093 | − | 2.24093i | 0.363526 | − | 0.363526i | ||||
\(39\) | 2.99422 | − | 2.81386i | 0.479459 | − | 0.450578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.9769i | − | 1.87047i | −0.354022 | − | 0.935237i | \(-0.615186\pi\) | ||
0.354022 | − | 0.935237i | \(-0.384814\pi\) | |||||||
\(42\) | −0.0425934 | + | 1.37162i | −0.00657231 | + | 0.211646i | ||||
\(43\) | 5.65685 | + | 5.65685i | 0.862662 | + | 0.862662i | 0.991647 | − | 0.128984i | \(-0.0411717\pi\) |
−0.128984 | + | 0.991647i | \(0.541172\pi\) | |||||||
\(44\) | −5.63858 | −0.850048 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.74456 | −0.404664 | ||||||||
\(47\) | 3.11400 | + | 3.11400i | 0.454224 | + | 0.454224i | 0.896754 | − | 0.442530i | \(-0.145919\pi\) |
−0.442530 | + | 0.896754i | \(0.645919\pi\) | |||||||
\(48\) | −0.0337462 | + | 1.08672i | −0.00487085 | + | 0.156854i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18614 | + | 1.11469i | −0.166093 | + | 0.156088i | ||||
\(52\) | 2.30194 | − | 2.30194i | 0.319222 | − | 0.319222i | ||||
\(53\) | −8.46893 | + | 8.46893i | −1.16330 | + | 1.16330i | −0.179548 | + | 0.983749i | \(0.557464\pi\) |
−0.983749 | + | 0.179548i | \(0.942536\pi\) | |||||||
\(54\) | −3.16915 | + | 2.62772i | −0.431266 | + | 0.357587i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.67181i | 0.357036i | ||||||||
\(57\) | −6.92487 | − | 0.215040i | −0.917221 | − | 0.0284828i | ||||
\(58\) | −3.35491 | − | 3.35491i | −0.440522 | − | 0.440522i | ||||
\(59\) | 11.9769 | 1.55926 | 0.779628 | − | 0.626242i | \(-0.215408\pi\) | ||||
0.779628 | + | 0.626242i | \(0.215408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.74456 | 0.863553 | 0.431776 | − | 0.901981i | \(-0.357887\pi\) | ||||
0.431776 | + | 0.901981i | \(0.357887\pi\) | |||||||
\(62\) | 2.65805 | + | 2.65805i | 0.337573 | + | 0.337573i | ||||
\(63\) | 2.24885 | − | 1.98561i | 0.283329 | − | 0.250164i | ||||
\(64\) | − | 3.37228i | − | 0.421535i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.86141 | − | 4.10891i | −0.475306 | − | 0.505772i | ||||
\(67\) | 9.01177 | − | 9.01177i | 1.10096 | − | 1.10096i | 0.106668 | − | 0.994295i | \(-0.465982\pi\) |
0.994295 | − | 0.106668i | \(-0.0340181\pi\) | |||||||
\(68\) | −0.911899 | + | 0.911899i | −0.110584 | + | 0.110584i | ||||
\(69\) | 4.10891 | + | 4.37228i | 0.494655 | + | 0.526361i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.87953i | 0.223059i | 0.993761 | + | 0.111529i | \(0.0355749\pi\) | ||||
−0.993761 | + | 0.111529i | \(0.964425\pi\) | |||||||
\(72\) | −6.00852 | + | 5.30519i | −0.708111 | + | 0.625222i | ||||
\(73\) | 9.01177 | + | 9.01177i | 1.05475 | + | 1.05475i | 0.998412 | + | 0.0563356i | \(0.0179417\pi\) |
0.0563356 | + | 0.998412i | \(0.482058\pi\) | |||||||
\(74\) | 3.75906 | 0.436981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.48913 | −0.629646 | ||||||||
\(77\) | 2.90544 | + | 2.90544i | 0.331106 | + | 0.331106i | ||||
\(78\) | 3.25387 | + | 0.101044i | 0.368428 | + | 0.0114409i | ||||
\(79\) | 15.1168i | 1.70078i | 0.526155 | + | 0.850389i | \(0.323633\pi\) | ||||
−0.526155 | + | 0.850389i | \(0.676367\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.93070 | + | 1.11469i | 0.992300 | + | 0.123855i | ||||
\(82\) | 6.70982 | − | 6.70982i | 0.740976 | − | 0.740976i | ||||
\(83\) | 11.8303 | − | 11.8303i | 1.29855 | − | 1.29855i | 0.369194 | − | 0.929352i | \(-0.379634\pi\) |
0.929352 | − | 0.369194i | \(-0.120366\pi\) | |||||||
\(84\) | 1.73205 | − | 1.62772i | 0.188982 | − | 0.177599i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.33830i | 0.683476i | ||||||||
\(87\) | −0.321939 | + | 10.3673i | −0.0345155 | + | 1.11149i | ||||
\(88\) | −7.76280 | − | 7.76280i | −0.827517 | − | 0.827517i | ||||
\(89\) | 3.75906 | 0.398459 | 0.199230 | − | 0.979953i | \(-0.436156\pi\) | ||||
0.199230 | + | 0.979953i | \(0.436156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.37228 | −0.248683 | ||||||||
\(92\) | 3.36139 | + | 3.36139i | 0.350449 | + | 0.350449i | ||||
\(93\) | 0.255068 | − | 8.21386i | 0.0264493 | − | 0.851738i | ||||
\(94\) | 3.48913i | 0.359876i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.37228 | + | 6.92820i | −0.752430 | + | 0.707107i | ||||
\(97\) | −1.67746 | + | 1.67746i | −0.170320 | + | 0.170320i | −0.787120 | − | 0.616800i | \(-0.788429\pi\) |
0.616800 | + | 0.787120i | \(0.288429\pi\) | |||||||
\(98\) | 0.560232 | − | 0.560232i | 0.0565919 | − | 0.0565919i | ||||
\(99\) | −0.764836 | + | 12.3030i | −0.0768689 | + | 1.23650i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.75906i | 0.374040i | 0.982356 | + | 0.187020i | \(0.0598829\pi\) | ||||
−0.982356 | + | 0.187020i | \(0.940117\pi\) | |||||||
\(102\) | −1.28900 | − | 0.0400277i | −0.127630 | − | 0.00396334i | ||||
\(103\) | −5.03237 | − | 5.03237i | −0.495854 | − | 0.495854i | 0.414291 | − | 0.910145i | \(-0.364030\pi\) |
−0.910145 | + | 0.414291i | \(0.864030\pi\) | |||||||
\(104\) | 6.33830 | 0.621521 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.48913 | −0.921665 | ||||||||
\(107\) | −3.77852 | − | 3.77852i | −0.365283 | − | 0.365283i | 0.500471 | − | 0.865754i | \(-0.333160\pi\) |
−0.865754 | + | 0.500471i | \(0.833160\pi\) | |||||||
\(108\) | 7.09968 | + | 0.663113i | 0.683167 | + | 0.0638081i | ||||
\(109\) | 8.37228i | 0.801919i | 0.916096 | + | 0.400960i | \(0.131323\pi\) | ||||
−0.916096 | + | 0.400960i | \(0.868677\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.62772 | − | 5.98844i | −0.534159 | − | 0.568398i | ||||
\(112\) | 0.443864 | − | 0.443864i | 0.0419412 | − | 0.0419412i | ||||
\(113\) | 3.56995 | − | 3.56995i | 0.335833 | − | 0.335833i | −0.518963 | − | 0.854796i | \(-0.673682\pi\) |
0.854796 | + | 0.518963i | \(0.173682\pi\) | |||||||
\(114\) | −3.75906 | − | 4.00000i | −0.352068 | − | 0.374634i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.21782i | 0.763006i | ||||||||
\(117\) | −4.71043 | − | 5.33492i | −0.435479 | − | 0.493213i | ||||
\(118\) | 6.70982 | + | 6.70982i | 0.617689 | + | 0.617689i | ||||
\(119\) | 0.939764 | 0.0861480 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.88316 | −0.534832 | ||||||||
\(122\) | 3.77852 | + | 3.77852i | 0.342091 | + | 0.342091i | ||||
\(123\) | −20.7346 | − | 0.643878i | −1.86957 | − | 0.0580565i | ||||
\(124\) | − | 6.51087i | − | 0.584694i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.37228 | + | 0.147477i | 0.211340 | + | 0.0131383i | ||||
\(127\) | −2.30194 | + | 2.30194i | −0.204264 | + | 0.204264i | −0.801824 | − | 0.597560i | \(-0.796137\pi\) |
0.597560 | + | 0.801824i | \(0.296137\pi\) | |||||||
\(128\) | −6.37111 | + | 6.37111i | −0.563132 | + | 0.563132i | ||||
\(129\) | 10.0974 | − | 9.48913i | 0.889022 | − | 0.835471i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.21782i | 0.717995i | 0.933339 | + | 0.358997i | \(0.116881\pi\) | ||||
−0.933339 | + | 0.358997i | \(0.883119\pi\) | |||||||
\(132\) | −0.303131 | + | 9.76161i | −0.0263841 | + | 0.849639i | ||||
\(133\) | 2.82843 | + | 2.82843i | 0.245256 | + | 0.245256i | ||||
\(134\) | 10.0974 | 0.872278 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.51087 | −0.215306 | ||||||||
\(137\) | −12.0389 | − | 12.0389i | −1.02855 | − | 1.02855i | −0.999580 | − | 0.0289711i | \(-0.990777\pi\) |
−0.0289711 | − | 0.999580i | \(-0.509223\pi\) | |||||||
\(138\) | −0.147548 | + | 4.75143i | −0.0125601 | + | 0.404469i | ||||
\(139\) | 0.744563i | 0.0631530i | 0.999501 | + | 0.0315765i | \(0.0100528\pi\) | ||||
−0.999501 | + | 0.0315765i | \(0.989947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.55842 | − | 5.22360i | 0.468104 | − | 0.439907i | ||||
\(142\) | −1.05297 | + | 1.05297i | −0.0883633 | + | 0.0883633i | ||||
\(143\) | 6.89252 | − | 6.89252i | 0.576381 | − | 0.576381i | ||||
\(144\) | 1.87953 | + | 0.116844i | 0.156627 | + | 0.00973700i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0974i | 0.835663i | ||||||||
\(147\) | −1.73122 | − | 0.0537601i | −0.142788 | − | 0.00443406i | ||||
\(148\) | −4.60388 | − | 4.60388i | −0.378437 | − | 0.378437i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.11684 | −0.579161 | −0.289580 | − | 0.957154i | \(-0.593516\pi\) | ||||
−0.289580 | + | 0.957154i | \(0.593516\pi\) | |||||||
\(152\) | −7.55703 | − | 7.55703i | −0.612956 | − | 0.612956i | ||||
\(153\) | 1.86601 | + | 2.11339i | 0.150858 | + | 0.170858i | ||||
\(154\) | 3.25544i | 0.262331i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.86141 | − | 4.10891i | −0.309160 | − | 0.328976i | ||||
\(157\) | −9.01177 | + | 9.01177i | −0.719217 | + | 0.719217i | −0.968445 | − | 0.249228i | \(-0.919823\pi\) |
0.249228 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(158\) | −8.46893 | + | 8.46893i | −0.673752 | + | 0.673752i | ||||
\(159\) | 14.2063 | + | 15.1168i | 1.12663 | + | 1.19884i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.46410i | − | 0.273009i | ||||||
\(162\) | 4.37878 | + | 5.62775i | 0.344029 | + | 0.442158i | ||||
\(163\) | 9.01177 | + | 9.01177i | 0.705856 | + | 0.705856i | 0.965661 | − | 0.259805i | \(-0.0836583\pi\) |
−0.259805 | + | 0.965661i | \(0.583658\pi\) | |||||||
\(164\) | −16.4356 | −1.28341 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2554 | 1.02882 | ||||||||
\(167\) | −7.59586 | − | 7.59586i | −0.587785 | − | 0.587785i | 0.349246 | − | 0.937031i | \(-0.386438\pi\) |
−0.937031 | + | 0.349246i | \(0.886438\pi\) | |||||||
\(168\) | 4.62549 | + | 0.143637i | 0.356864 | + | 0.0110818i | ||||
\(169\) | − | 7.37228i | − | 0.567099i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.744563 | + | 11.9769i | −0.0569381 | + | 0.915895i | ||||
\(172\) | 7.76280 | − | 7.76280i | 0.591908 | − | 0.591908i | ||||
\(173\) | −11.3744 | + | 11.3744i | −0.864777 | + | 0.864777i | −0.991888 | − | 0.127111i | \(-0.959430\pi\) |
0.127111 | + | 0.991888i | \(0.459430\pi\) | |||||||
\(174\) | −5.98844 | + | 5.62772i | −0.453982 | + | 0.426636i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.57924i | 0.194418i | ||||||||
\(177\) | 0.643878 | − | 20.7346i | 0.0483968 | − | 1.55851i | ||||
\(178\) | 2.10594 | + | 2.10594i | 0.157847 | + | 0.157847i | ||||
\(179\) | −1.87953 | −0.140482 | −0.0702412 | − | 0.997530i | \(-0.522377\pi\) | ||||
−0.0702412 | + | 0.997530i | \(0.522377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | −1.32903 | − | 1.32903i | −0.0985140 | − | 0.0985140i | ||||
\(183\) | 0.362588 | − | 11.6763i | 0.0268033 | − | 0.863137i | ||||
\(184\) | 9.25544i | 0.682320i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.74456 | − | 4.45877i | 0.347888 | − | 0.326933i | ||||
\(187\) | −2.73043 | + | 2.73043i | −0.199669 | + | 0.199669i | ||||
\(188\) | 4.27329 | − | 4.27329i | 0.311662 | − | 0.311662i | ||||
\(189\) | −3.31662 | − | 4.00000i | −0.241249 | − | 0.290957i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.0858i | − | 1.16393i | −0.813215 | − | 0.581963i | \(-0.802285\pi\) | ||
0.813215 | − | 0.581963i | \(-0.197715\pi\) | |||||||
\(192\) | −5.83815 | − | 0.181294i | −0.421332 | − | 0.0130838i | ||||
\(193\) | −18.0235 | − | 18.0235i | −1.29736 | − | 1.29736i | −0.930129 | − | 0.367234i | \(-0.880305\pi\) |
−0.367234 | − | 0.930129i | \(-0.619695\pi\) | |||||||
\(194\) | −1.87953 | −0.134942 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.37228 | −0.0980201 | ||||||||
\(197\) | 15.6088 | + | 15.6088i | 1.11208 | + | 1.11208i | 0.992868 | + | 0.119215i | \(0.0380378\pi\) |
0.119215 | + | 0.992868i | \(0.461962\pi\) | |||||||
\(198\) | −7.32100 | + | 6.46403i | −0.520281 | + | 0.459379i | ||||
\(199\) | 12.7446i | 0.903438i | 0.892160 | + | 0.451719i | \(0.149189\pi\) | ||||
−0.892160 | + | 0.451719i | \(0.850811\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1168 | − | 16.0858i | −1.06626 | − | 1.13460i | ||||
\(202\) | −2.10594 | + | 2.10594i | −0.148174 | + | 0.148174i | ||||
\(203\) | 4.23447 | − | 4.23447i | 0.297201 | − | 0.297201i | ||||
\(204\) | 1.52967 | + | 1.62772i | 0.107098 | + | 0.113963i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 5.63858i | − | 0.392859i | ||||||
\(207\) | 7.79026 | − | 6.87836i | 0.541461 | − | 0.478079i | ||||
\(208\) | −1.05297 | − | 1.05297i | −0.0730104 | − | 0.0730104i | ||||
\(209\) | −16.4356 | −1.13688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.62772 | 0.662799 | 0.331400 | − | 0.943490i | \(-0.392479\pi\) | ||||
0.331400 | + | 0.943490i | \(0.392479\pi\) | |||||||
\(212\) | 11.6218 | + | 11.6218i | 0.798186 | + | 0.798186i | ||||
\(213\) | 3.25387 | + | 0.101044i | 0.222951 | + | 0.00692339i | ||||
\(214\) | − | 4.23369i | − | 0.289409i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.86141 | + | 10.6873i | 0.602942 | + | 0.727176i | ||||
\(217\) | −3.35491 | + | 3.35491i | −0.227746 | + | 0.227746i | ||||
\(218\) | −4.69042 | + | 4.69042i | −0.317675 | + | 0.317675i | ||||
\(219\) | 16.0858 | − | 15.1168i | 1.08698 | − | 1.02150i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.22938i | − | 0.149965i | ||||||
\(222\) | 0.202087 | − | 6.50774i | 0.0135632 | − | 0.436771i | ||||
\(223\) | 16.3461 | + | 16.3461i | 1.09461 | + | 1.09461i | 0.995029 | + | 0.0995853i | \(0.0317516\pi\) |
0.0995853 | + | 0.995029i | \(0.468248\pi\) | |||||||
\(224\) | 5.84096 | 0.390266 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | 9.34201 | + | 9.34201i | 0.620051 | + | 0.620051i | 0.945544 | − | 0.325493i | \(-0.105530\pi\) |
−0.325493 | + | 0.945544i | \(0.605530\pi\) | |||||||
\(228\) | −0.295096 | + | 9.50286i | −0.0195432 | + | 0.629342i | ||||
\(229\) | − | 28.9783i | − | 1.91494i | −0.288538 | − | 0.957468i | \(-0.593169\pi\) | ||
0.288538 | − | 0.957468i | \(-0.406831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.18614 | − | 4.87375i | 0.341223 | − | 0.320669i | ||||
\(232\) | −11.3137 | + | 11.3137i | −0.742781 | + | 0.742781i | ||||
\(233\) | 0.417127 | − | 0.417127i | 0.0273269 | − | 0.0273269i | −0.693311 | − | 0.720638i | \(-0.743849\pi\) |
0.720638 | + | 0.693311i | \(0.243849\pi\) | |||||||
\(234\) | 0.349857 | − | 5.62772i | 0.0228708 | − | 0.367895i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 16.4356i | − | 1.06987i | ||||||
\(237\) | 26.1705 | + | 0.812683i | 1.69996 | + | 0.0527894i | ||||
\(238\) | 0.526485 | + | 0.526485i | 0.0341270 | + | 0.0341270i | ||||
\(239\) | −7.86797 | −0.508936 | −0.254468 | − | 0.967081i | \(-0.581900\pi\) | ||||
−0.254468 | + | 0.967081i | \(0.581900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4891 | 0.740080 | 0.370040 | − | 0.929016i | \(-0.379344\pi\) | ||||
0.370040 | + | 0.929016i | \(0.379344\pi\) | |||||||
\(242\) | −3.29593 | − | 3.29593i | −0.211870 | − | 0.211870i | ||||
\(243\) | 2.40989 | − | 15.4011i | 0.154594 | − | 0.987978i | ||||
\(244\) | − | 9.25544i | − | 0.592519i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.2554 | − | 11.9769i | −0.717620 | − | 0.763618i | ||||
\(247\) | 6.70982 | − | 6.70982i | 0.426936 | − | 0.426936i | ||||
\(248\) | 8.96370 | − | 8.96370i | 0.569196 | − | 0.569196i | ||||
\(249\) | −19.8448 | − | 21.1168i | −1.25762 | − | 1.33823i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.4125i | 1.79338i | 0.442656 | + | 0.896691i | \(0.354036\pi\) | ||||
−0.442656 | + | 0.896691i | \(0.645964\pi\) | |||||||
\(252\) | −2.72482 | − | 3.08606i | −0.171647 | − | 0.194404i | ||||
\(253\) | 10.0647 | + | 10.0647i | 0.632765 | + | 0.632765i | ||||
\(254\) | −2.57924 | −0.161836 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | −4.89898 | − | 4.89898i | −0.305590 | − | 0.305590i | 0.537606 | − | 0.843196i | \(-0.319329\pi\) |
−0.843196 | + | 0.537606i | \(0.819329\pi\) | |||||||
\(258\) | 10.9730 | + | 0.340747i | 0.683147 | + | 0.0212140i | ||||
\(259\) | 4.74456i | 0.294813i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.9307 | + | 1.11469i | 1.10988 | + | 0.0689977i | ||||
\(262\) | −4.60388 | + | 4.60388i | −0.284429 | + | 0.284429i | ||||
\(263\) | −3.36139 | + | 3.36139i | −0.207272 | + | 0.207272i | −0.803107 | − | 0.595835i | \(-0.796821\pi\) |
0.595835 | + | 0.803107i | \(0.296821\pi\) | |||||||
\(264\) | −13.8564 | + | 13.0217i | −0.852803 | + | 0.801433i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.16915i | 0.194313i | ||||||||
\(267\) | 0.202087 | − | 6.50774i | 0.0123675 | − | 0.398267i | ||||
\(268\) | −12.3667 | − | 12.3667i | −0.755415 | − | 0.755415i | ||||
\(269\) | −11.9769 | −0.730243 | −0.365122 | − | 0.930960i | \(-0.618973\pi\) | ||||
−0.365122 | + | 0.930960i | \(0.618973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.48913 | 0.0904579 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(272\) | 0.417127 | + | 0.417127i | 0.0252921 | + | 0.0252921i | ||||
\(273\) | −0.127534 | + | 4.10693i | −0.00771871 | + | 0.248563i | ||||
\(274\) | − | 13.4891i | − | 0.814908i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | − | 5.63858i | 0.361158 | − | 0.339403i | ||||
\(277\) | −14.6686 | + | 14.6686i | −0.881352 | + | 0.881352i | −0.993672 | − | 0.112320i | \(-0.964172\pi\) |
0.112320 | + | 0.993672i | \(0.464172\pi\) | |||||||
\(278\) | −0.417127 | + | 0.417127i | −0.0250176 | + | 0.0250176i | ||||
\(279\) | −14.2063 | − | 0.883156i | −0.850507 | − | 0.0528732i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.4472i | − | 0.623228i | −0.950209 | − | 0.311614i | \(-0.899130\pi\) | ||
0.950209 | − | 0.311614i | \(-0.100870\pi\) | |||||||
\(282\) | 6.04043 | + | 0.187576i | 0.359702 | + | 0.0111700i | ||||
\(283\) | −8.38728 | − | 8.38728i | −0.498572 | − | 0.498572i | 0.412421 | − | 0.910993i | \(-0.364683\pi\) |
−0.910993 | + | 0.412421i | \(0.864683\pi\) | |||||||
\(284\) | 2.57924 | 0.153050 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.72281 | 0.456660 | ||||||||
\(287\) | 8.46893 | + | 8.46893i | 0.499905 | + | 0.499905i | ||||
\(288\) | 11.5979 | + | 13.1355i | 0.683412 | + | 0.774015i | ||||
\(289\) | − | 16.1168i | − | 0.948050i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.81386 | + | 2.99422i | 0.164951 | + | 0.175524i | ||||
\(292\) | 12.3667 | − | 12.3667i | 0.723705 | − | 0.723705i | ||||
\(293\) | 11.3744 | − | 11.3744i | 0.664498 | − | 0.664498i | −0.291939 | − | 0.956437i | \(-0.594300\pi\) |
0.956437 | + | 0.291939i | \(0.0943004\pi\) | |||||||
\(294\) | −0.939764 | − | 1.00000i | −0.0548081 | − | 0.0583212i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 12.6766i | − | 0.736812i | ||||||
\(297\) | 21.2580 | + | 1.98551i | 1.23351 | + | 0.115211i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.21782 | −0.475249 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | −3.98708 | − | 3.98708i | −0.229431 | − | 0.229431i | ||||
\(303\) | 6.50774 | + | 0.202087i | 0.373860 | + | 0.0116096i | ||||
\(304\) | 2.51087i | 0.144009i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.138593 | + | 2.22938i | −0.00792286 | + | 0.127445i | ||||
\(307\) | −9.63625 | + | 9.63625i | −0.549970 | + | 0.549970i | −0.926432 | − | 0.376462i | \(-0.877141\pi\) |
0.376462 | + | 0.926432i | \(0.377141\pi\) | |||||||
\(308\) | 3.98708 | − | 3.98708i | 0.227185 | − | 0.227185i | ||||
\(309\) | −8.98266 | + | 8.44158i | −0.511006 | + | 0.480225i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.75906i | 0.213156i | 0.994304 | + | 0.106578i | \(0.0339895\pi\) | ||||
−0.994304 | + | 0.106578i | \(0.966011\pi\) | |||||||
\(312\) | 0.340747 | − | 10.9730i | 0.0192910 | − | 0.621222i | ||||
\(313\) | −8.38728 | − | 8.38728i | −0.474077 | − | 0.474077i | 0.429154 | − | 0.903231i | \(-0.358812\pi\) |
−0.903231 | + | 0.429154i | \(0.858812\pi\) | |||||||
\(314\) | −10.0974 | −0.569826 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.7446 | 1.16697 | ||||||||
\(317\) | −4.48185 | − | 4.48185i | −0.251726 | − | 0.251726i | 0.569952 | − | 0.821678i | \(-0.306962\pi\) |
−0.821678 | + | 0.569952i | \(0.806962\pi\) | |||||||
\(318\) | −0.510136 | + | 16.4277i | −0.0286070 | + | 0.921221i | ||||
\(319\) | 24.6060i | 1.37767i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.74456 | + | 6.33830i | −0.376445 | + | 0.353769i | ||||
\(322\) | 1.94070 | − | 1.94070i | 0.108151 | − | 0.108151i | ||||
\(323\) | −2.65805 | + | 2.65805i | −0.147898 | + | 0.147898i | ||||
\(324\) | 1.52967 | − | 12.2554i | 0.0849817 | − | 0.680858i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.0974i | 0.559241i | ||||||||
\(327\) | 14.4942 | + | 0.450095i | 0.801533 | + | 0.0248903i | ||||
\(328\) | −22.6274 | − | 22.6274i | −1.24939 | − | 1.24939i | ||||
\(329\) | −4.40387 | −0.242793 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.9783 | −0.823279 | −0.411640 | − | 0.911347i | \(-0.635044\pi\) | ||||
−0.411640 | + | 0.911347i | \(0.635044\pi\) | |||||||
\(332\) | −16.2345 | − | 16.2345i | −0.890986 | − | 0.890986i | ||||
\(333\) | −10.6698 | + | 9.42086i | −0.584703 | + | 0.516260i | ||||
\(334\) | − | 8.51087i | − | 0.465694i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.744563 | − | 0.792287i | −0.0406192 | − | 0.0432228i | ||||
\(337\) | −3.35491 | + | 3.35491i | −0.182754 | + | 0.182754i | −0.792555 | − | 0.609801i | \(-0.791249\pi\) |
0.609801 | + | 0.792555i | \(0.291249\pi\) | |||||||
\(338\) | 4.13018 | − | 4.13018i | 0.224652 | − | 0.224652i | ||||
\(339\) | −5.98844 | − | 6.37228i | −0.325247 | − | 0.346095i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 19.4950i | − | 1.05571i | ||||||
\(342\) | −7.12695 | + | 6.29270i | −0.385381 | + | 0.340270i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 21.3745 | 1.15244 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.7446 | −0.685152 | ||||||||
\(347\) | 4.69042 | + | 4.69042i | 0.251795 | + | 0.251795i | 0.821706 | − | 0.569911i | \(-0.193022\pi\) |
−0.569911 | + | 0.821706i | \(0.693022\pi\) | |||||||
\(348\) | 14.2268 | + | 0.441791i | 0.762638 | + | 0.0236825i | ||||
\(349\) | − | 21.7228i | − | 1.16280i | −0.813619 | − | 0.581398i | \(-0.802506\pi\) | ||
0.813619 | − | 0.581398i | \(-0.197494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.48913 | + | 7.86797i | −0.506492 | + | 0.419961i | ||||
\(352\) | −16.9706 | + | 16.9706i | −0.904534 | + | 0.904534i | ||||
\(353\) | −7.80442 | + | 7.80442i | −0.415387 | + | 0.415387i | −0.883610 | − | 0.468223i | \(-0.844894\pi\) |
0.468223 | + | 0.883610i | \(0.344894\pi\) | |||||||
\(354\) | 11.9769 | − | 11.2554i | 0.636564 | − | 0.598220i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.15848i | − | 0.273399i | ||||||
\(357\) | 0.0505218 | − | 1.62693i | 0.00267390 | − | 0.0861065i | ||||
\(358\) | −1.05297 | − | 1.05297i | −0.0556512 | − | 0.0556512i | ||||
\(359\) | 29.5923 | 1.56182 | 0.780912 | − | 0.624641i | \(-0.214755\pi\) | ||||
0.780912 | + | 0.624641i | \(0.214755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 3.36139 | + | 3.36139i | 0.176671 | + | 0.176671i | ||||
\(363\) | −0.316279 | + | 10.1850i | −0.0166003 | + | 0.534575i | ||||
\(364\) | 3.25544i | 0.170631i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.74456 | − | 6.33830i | 0.352544 | − | 0.331308i | ||||
\(367\) | −5.03237 | + | 5.03237i | −0.262688 | + | 0.262688i | −0.826145 | − | 0.563458i | \(-0.809471\pi\) |
0.563458 | + | 0.826145i | \(0.309471\pi\) | |||||||
\(368\) | 1.53759 | − | 1.53759i | 0.0801524 | − | 0.0801524i | ||||
\(369\) | −2.22938 | + | 35.8614i | −0.116057 | + | 1.86687i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.9769i | − | 0.621809i | ||||||
\(372\) | −11.2717 | − | 0.350025i | −0.584412 | − | 0.0181480i | ||||
\(373\) | −11.3137 | − | 11.3137i | −0.585802 | − | 0.585802i | 0.350690 | − | 0.936492i | \(-0.385947\pi\) |
−0.936492 | + | 0.350690i | \(0.885947\pi\) | |||||||
\(374\) | −3.05934 | −0.158195 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7663 | 0.606801 | ||||||||
\(377\) | −10.0453 | − | 10.0453i | −0.517362 | − | 0.517362i | ||||
\(378\) | 0.382848 | − | 4.09900i | 0.0196916 | − | 0.210830i | ||||
\(379\) | − | 12.0000i | − | 0.616399i | −0.951322 | − | 0.308199i | \(-0.900274\pi\) | ||
0.951322 | − | 0.308199i | \(-0.0997264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.86141 | + | 4.10891i | 0.197826 | + | 0.210506i | ||||
\(382\) | 9.01177 | − | 9.01177i | 0.461082 | − | 0.461082i | ||||
\(383\) | −18.9702 | + | 18.9702i | −0.969333 | + | 0.969333i | −0.999544 | − | 0.0302103i | \(-0.990382\pi\) |
0.0302103 | + | 0.999544i | \(0.490382\pi\) | |||||||
\(384\) | 10.6873 | + | 11.3723i | 0.545382 | + | 0.580339i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 20.1947i | − | 1.02788i | ||||||
\(387\) | −15.8849 | − | 17.9908i | −0.807475 | − | 0.914526i | ||||
\(388\) | 2.30194 | + | 2.30194i | 0.116863 | + | 0.116863i | ||||
\(389\) | −26.1831 | −1.32754 | −0.663769 | − | 0.747938i | \(-0.731044\pi\) | ||||
−0.663769 | + | 0.747938i | \(0.731044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.25544 | 0.164635 | ||||||||
\(392\) | −1.88926 | − | 1.88926i | −0.0954220 | − | 0.0954220i | ||||
\(393\) | 14.2268 | + | 0.441791i | 0.717649 | + | 0.0222854i | ||||
\(394\) | 17.4891i | 0.881089i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.8832 | + | 1.04957i | 0.848411 | + | 0.0527429i | ||||
\(397\) | −20.9500 | + | 20.9500i | −1.05145 | + | 1.05145i | −0.0528457 | + | 0.998603i | \(0.516829\pi\) |
−0.998603 | + | 0.0528457i | \(0.983171\pi\) | |||||||
\(398\) | −7.13991 | + | 7.13991i | −0.357891 | + | 0.357891i | ||||
\(399\) | 5.04868 | − | 4.74456i | 0.252750 | − | 0.237525i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1831i | 1.30752i | 0.756700 | + | 0.653762i | \(0.226810\pi\) | ||||
−0.756700 | + | 0.653762i | \(0.773190\pi\) | |||||||
\(402\) | 0.542834 | − | 17.4807i | 0.0270741 | − | 0.871858i | ||||
\(403\) | 7.95880 | + | 7.95880i | 0.396456 | + | 0.396456i | ||||
\(404\) | 5.15848 | 0.256644 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.74456 | 0.235469 | ||||||||
\(407\) | −13.7850 | − | 13.7850i | −0.683299 | − | 0.683299i | ||||
\(408\) | −0.134985 | + | 4.34687i | −0.00668274 | + | 0.215202i | ||||
\(409\) | 17.2554i | 0.853226i | 0.904434 | + | 0.426613i | \(0.140293\pi\) | ||||
−0.904434 | + | 0.426613i | \(0.859707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.4891 | + | 20.1947i | −1.05998 | + | 0.996131i | ||||
\(412\) | −6.90583 | + | 6.90583i | −0.340226 | + | 0.340226i | ||||
\(413\) | −8.46893 | + | 8.46893i | −0.416729 | + | 0.416729i | ||||
\(414\) | 8.21782 | + | 0.510875i | 0.403884 | + | 0.0251081i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 13.8564i | − | 0.679366i | ||||||
\(417\) | 1.28900 | + | 0.0400277i | 0.0631226 | + | 0.00196017i | ||||
\(418\) | −9.20777 | − | 9.20777i | −0.450367 | − | 0.450367i | ||||
\(419\) | 28.4125 | 1.38804 | 0.694021 | − | 0.719954i | \(-0.255837\pi\) | ||||
0.694021 | + | 0.719954i | \(0.255837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.372281 | −0.0181439 | −0.00907194 | − | 0.999959i | \(-0.502888\pi\) | ||||
−0.00907194 | + | 0.999959i | \(0.502888\pi\) | |||||||
\(422\) | 5.39375 | + | 5.39375i | 0.262564 | + | 0.262564i | ||||
\(423\) | −8.74437 | − | 9.90365i | −0.425166 | − | 0.481532i | ||||
\(424\) | 32.0000i | 1.55406i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.76631 | + | 1.87953i | 0.0855781 | + | 0.0910634i | ||||
\(427\) | −4.76913 | + | 4.76913i | −0.230794 | + | 0.230794i | ||||
\(428\) | −5.18519 | + | 5.18519i | −0.250636 | + | 0.250636i | ||||
\(429\) | −11.5619 | − | 12.3030i | −0.558214 | − | 0.593994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.349857i | 0.0168520i | 0.999965 | + | 0.00842600i | \(0.00268211\pi\) | ||||
−0.999965 | + | 0.00842600i | \(0.997318\pi\) | |||||||
\(432\) | 0.303326 | − | 3.24759i | 0.0145938 | − | 0.156250i | ||||
\(433\) | 2.30194 | + | 2.30194i | 0.110624 | + | 0.110624i | 0.760252 | − | 0.649628i | \(-0.225075\pi\) |
−0.649628 | + | 0.760252i | \(0.725075\pi\) | |||||||
\(434\) | −3.75906 | −0.180440 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.4891 | 0.550229 | ||||||||
\(437\) | 9.79796 | + | 9.79796i | 0.468700 | + | 0.468700i | ||||
\(438\) | 17.4807 | + | 0.542834i | 0.835260 | + | 0.0259376i | ||||
\(439\) | − | 19.2554i | − | 0.919012i | −0.888175 | − | 0.459506i | \(-0.848026\pi\) | ||
0.888175 | − | 0.459506i | \(-0.151974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.186141 | + | 2.99422i | −0.00886384 | + | 0.142582i | ||||
\(442\) | 1.24897 | − | 1.24897i | 0.0594075 | − | 0.0594075i | ||||
\(443\) | 1.12046 | − | 1.12046i | 0.0532348 | − | 0.0532348i | −0.679988 | − | 0.733223i | \(-0.738015\pi\) |
0.733223 | + | 0.679988i | \(0.238015\pi\) | |||||||
\(444\) | −8.21782 | + | 7.72281i | −0.390001 | + | 0.366508i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.3152i | 0.867249i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.38456 | + | 2.38456i | 0.112660 | + | 0.112660i | ||||
\(449\) | −1.52967 | −0.0721896 | −0.0360948 | − | 0.999348i | \(-0.511492\pi\) | ||||
−0.0360948 | + | 0.999348i | \(0.511492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −49.2119 | −2.31730 | ||||||||
\(452\) | −4.89898 | − | 4.89898i | −0.230429 | − | 0.230429i | ||||
\(453\) | −0.382602 | + | 12.3208i | −0.0179762 | + | 0.578882i | ||||
\(454\) | 10.4674i | 0.491258i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4891 | + | 12.6766i | −0.631686 | + | 0.593636i | ||||
\(457\) | −1.24897 | + | 1.24897i | −0.0584244 | + | 0.0584244i | −0.735715 | − | 0.677291i | \(-0.763154\pi\) |
0.677291 | + | 0.735715i | \(0.263154\pi\) | |||||||
\(458\) | 16.2345 | − | 16.2345i | 0.758590 | − | 0.758590i | ||||
\(459\) | 3.75906 | − | 3.11684i | 0.175458 | − | 0.145482i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 20.1947i | − | 0.940561i | −0.882517 | − | 0.470281i | \(-0.844153\pi\) | ||
0.882517 | − | 0.470281i | \(-0.155847\pi\) | |||||||
\(462\) | 5.63587 | + | 0.175013i | 0.262204 | + | 0.00814232i | ||||
\(463\) | −19.0765 | − | 19.0765i | −0.886560 | − | 0.886560i | 0.107631 | − | 0.994191i | \(-0.465674\pi\) |
−0.994191 | + | 0.107631i | \(0.965674\pi\) | |||||||
\(464\) | 3.75906 | 0.174510 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.467376 | 0.0216508 | ||||||||
\(467\) | 15.6477 | + | 15.6477i | 0.724087 | + | 0.724087i | 0.969435 | − | 0.245348i | \(-0.0789022\pi\) |
−0.245348 | + | 0.969435i | \(0.578902\pi\) | |||||||
\(468\) | −7.32100 | + | 6.46403i | −0.338414 | + | 0.298800i | ||||
\(469\) | 12.7446i | 0.588489i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1168 | + | 16.0858i | 0.696547 | + | 0.741194i | ||||
\(472\) | 22.6274 | − | 22.6274i | 1.04151 | − | 1.04151i | ||||
\(473\) | 23.2435 | − | 23.2435i | 1.06874 | − | 1.06874i | ||||
\(474\) | 14.2063 | + | 15.1168i | 0.652515 | + | 0.694340i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1.28962i | − | 0.0591097i | ||||||
\(477\) | 26.9343 | − | 23.7814i | 1.23323 | − | 1.08888i | ||||
\(478\) | −4.40788 | − | 4.40788i | −0.201612 | − | 0.201612i | ||||
\(479\) | 24.6535 | 1.12645 | 0.563223 | − | 0.826305i | \(-0.309561\pi\) | ||||
0.563223 | + | 0.826305i | \(0.309561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2554 | 0.513204 | ||||||||
\(482\) | 6.43657 | + | 6.43657i | 0.293178 | + | 0.293178i | ||||
\(483\) | −5.99711 | − | 0.186230i | −0.272878 | − | 0.00847378i | ||||
\(484\) | 8.07335i | 0.366970i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.97825 | − | 7.27806i | 0.452623 | − | 0.330139i | ||||
\(487\) | −11.1177 | + | 11.1177i | −0.503791 | + | 0.503791i | −0.912614 | − | 0.408822i | \(-0.865940\pi\) |
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(488\) | 12.7422 | − | 12.7422i | 0.576813 | − | 0.576813i | ||||
\(489\) | 16.0858 | − | 15.1168i | 0.727425 | − | 0.683607i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.5808i | 1.60574i | 0.596155 | + | 0.802869i | \(0.296694\pi\) | ||||
−0.596155 | + | 0.802869i | \(0.703306\pi\) | |||||||
\(492\) | −0.883582 | + | 28.4537i | −0.0398349 | + | 1.28279i | ||||
\(493\) | 3.97940 | + | 3.97940i | 0.179223 | + | 0.179223i | ||||
\(494\) | 7.51811 | 0.338256 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.97825 | −0.133727 | ||||||||
\(497\) | −1.32903 | − | 1.32903i | −0.0596150 | − | 0.0596150i | ||||
\(498\) | 0.712613 | − | 22.9480i | 0.0319330 | − | 1.02833i | ||||
\(499\) | 1.62772i | 0.0728667i | 0.999336 | + | 0.0364333i | \(0.0115997\pi\) | ||||
−0.999336 | + | 0.0364333i | \(0.988400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5584 | + | 12.7417i | −0.605746 | + | 0.569258i | ||||
\(502\) | −15.9176 | + | 15.9176i | −0.710437 | + | 0.710437i | ||||
\(503\) | −3.53113 | + | 3.53113i | −0.157445 | + | 0.157445i | −0.781434 | − | 0.623988i | \(-0.785511\pi\) |
0.623988 | + | 0.781434i | \(0.285511\pi\) | |||||||
\(504\) | 0.497333 | − | 8.00000i | 0.0221530 | − | 0.356348i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.2772i | 0.501331i | ||||||||
\(507\) | −12.7630 | − | 0.396334i | −0.566825 | − | 0.0176018i | ||||
\(508\) | 3.15891 | + | 3.15891i | 0.140154 | + | 0.140154i | ||||
\(509\) | 8.21782 | 0.364249 | 0.182124 | − | 0.983276i | \(-0.441703\pi\) | ||||
0.182124 | + | 0.983276i | \(0.441703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7446 | −0.563786 | ||||||||
\(512\) | 4.96444 | + | 4.96444i | 0.219399 | + | 0.219399i | ||||
\(513\) | 20.6945 | + | 1.93288i | 0.913686 | + | 0.0853386i | ||||
\(514\) | − | 5.48913i | − | 0.242115i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.0217 | − | 13.8564i | −0.573251 | − | 0.609994i | ||||
\(517\) | 12.7952 | − | 12.7952i | 0.562731 | − | 0.562731i | ||||
\(518\) | −2.65805 | + | 2.65805i | −0.116788 | + | 0.116788i | ||||
\(519\) | 19.0800 | + | 20.3030i | 0.837519 | + | 0.891202i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1947i | 0.884746i | 0.896831 | + | 0.442373i | \(0.145863\pi\) | ||||
−0.896831 | + | 0.442373i | \(0.854137\pi\) | |||||||
\(522\) | 9.42086 | + | 10.6698i | 0.412340 | + | 0.467006i | ||||
\(523\) | 25.7863 | + | 25.7863i | 1.12756 | + | 1.12756i | 0.990573 | + | 0.136984i | \(0.0437410\pi\) |
0.136984 | + | 0.990573i | \(0.456259\pi\) | |||||||
\(524\) | 11.2772 | 0.492645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.76631 | −0.164219 | ||||||||
\(527\) | −3.15283 | − | 3.15283i | −0.137339 | − | 0.137339i | ||||
\(528\) | 4.46522 | + | 0.138660i | 0.194324 | + | 0.00603441i | ||||
\(529\) | 11.0000i | 0.478261i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.8614 | − | 2.22938i | −1.55625 | − | 0.0967470i | ||||
\(532\) | 3.88140 | − | 3.88140i | 0.168280 | − | 0.168280i | ||||
\(533\) | 20.0907 | − | 20.0907i | 0.870224 | − | 0.870224i | ||||
\(534\) | 3.75906 | − | 3.53262i | 0.162670 | − | 0.152872i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 34.0511i | − | 1.47078i | ||||||
\(537\) | −0.101044 | + | 3.25387i | −0.00436035 | + | 0.140415i | ||||
\(538\) | −6.70982 | − | 6.70982i | −0.289281 | − | 0.289281i | ||||
\(539\) | −4.10891 | −0.176983 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.3723 | −1.04785 | −0.523923 | − | 0.851766i | \(-0.675532\pi\) | ||||
−0.523923 | + | 0.851766i | \(0.675532\pi\) | |||||||
\(542\) | 0.834255 | + | 0.834255i | 0.0358343 | + | 0.0358343i | ||||
\(543\) | 0.322560 | − | 10.3873i | 0.0138424 | − | 0.445762i | ||||
\(544\) | 5.48913i | 0.235344i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.37228 | + | 2.22938i | −0.101524 | + | 0.0954088i | ||||
\(547\) | 23.6804 | − | 23.6804i | 1.01250 | − | 1.01250i | 0.0125794 | − | 0.999921i | \(-0.495996\pi\) |
0.999921 | − | 0.0125794i | \(-0.00400425\pi\) | |||||||
\(548\) | −16.5207 | + | 16.5207i | −0.705731 | + | 0.705731i | ||||
\(549\) | −20.1947 | − | 1.25544i | −0.861889 | − | 0.0535808i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.9538i | 1.02046i | ||||||||
\(552\) | 16.0232 | + | 0.497573i | 0.681991 | + | 0.0211781i | ||||
\(553\) | −10.6892 | − | 10.6892i | −0.454552 | − | 0.454552i | ||||
\(554\) | −16.4356 | −0.698284 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.02175 | 0.0433318 | ||||||||
\(557\) | 16.9379 | + | 16.9379i | 0.717680 | + | 0.717680i | 0.968130 | − | 0.250449i | \(-0.0805784\pi\) |
−0.250449 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(558\) | −7.46402 | − | 8.45357i | −0.315977 | − | 0.357868i | ||||
\(559\) | 18.9783i | 0.802694i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.58017 | + | 4.87375i | 0.193375 | + | 0.205770i | ||||
\(562\) | 5.85285 | − | 5.85285i | 0.246888 | − | 0.246888i | ||||
\(563\) | −26.1101 | + | 26.1101i | −1.10041 | + | 1.10041i | −0.106050 | + | 0.994361i | \(0.533820\pi\) |
−0.994361 | + | 0.106050i | \(0.966180\pi\) | |||||||
\(564\) | −7.16825 | − | 7.62772i | −0.301838 | − | 0.321185i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 9.39764i | − | 0.395012i | ||||||
\(567\) | −7.10317 | + | 5.52675i | −0.298305 | + | 0.232102i | ||||
\(568\) | 3.55091 | + | 3.55091i | 0.148993 | + | 0.148993i | ||||
\(569\) | −3.75906 | −0.157588 | −0.0787939 | − | 0.996891i | \(-0.525107\pi\) | ||||
−0.0787939 | + | 0.996891i | \(0.525107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9783 | −0.626820 | −0.313410 | − | 0.949618i | \(-0.601471\pi\) | ||||
−0.313410 | + | 0.949618i | \(0.601471\pi\) | |||||||
\(572\) | −9.45848 | − | 9.45848i | −0.395479 | − | 0.395479i | ||||
\(573\) | −27.8480 | − | 0.864773i | −1.16337 | − | 0.0361264i | ||||
\(574\) | 9.48913i | 0.396068i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.627719 | + | 10.0974i | −0.0261549 | + | 0.420723i | ||||
\(577\) | −21.8069 | + | 21.8069i | −0.907834 | + | 0.907834i | −0.996097 | − | 0.0882628i | \(-0.971868\pi\) |
0.0882628 | + | 0.996097i | \(0.471868\pi\) | |||||||
\(578\) | 9.02916 | − | 9.02916i | 0.375564 | − | 0.375564i | ||||
\(579\) | −32.1716 | + | 30.2337i | −1.33701 | + | 1.25647i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.7306i | 0.694102i | ||||||||
\(582\) | −0.101044 | + | 3.25387i | −0.00418839 | + | 0.134877i | ||||
\(583\) | 34.7981 | + | 34.7981i | 1.44119 | + | 1.44119i | ||||
\(584\) | 34.0511 | 1.40904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.7446 | 0.526473 | ||||||||
\(587\) | −10.0065 | − | 10.0065i | −0.413013 | − | 0.413013i | 0.469774 | − | 0.882787i | \(-0.344336\pi\) |
−0.882787 | + | 0.469774i | \(0.844336\pi\) | |||||||
\(588\) | −0.0737740 | + | 2.37572i | −0.00304239 | + | 0.0979729i | ||||
\(589\) | − | 18.9783i | − | 0.781985i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.8614 | − | 26.1831i | 1.14607 | − | 1.07703i | ||||
\(592\) | −2.10594 | + | 2.10594i | −0.0865536 | + | 0.0865536i | ||||
\(593\) | 18.9314 | − | 18.9314i | 0.777420 | − | 0.777420i | −0.201972 | − | 0.979391i | \(-0.564735\pi\) |
0.979391 | + | 0.201972i | \(0.0647349\pi\) | |||||||
\(594\) | 10.7971 | + | 13.0217i | 0.443009 | + | 0.534289i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.0636 | + | 0.685149i | 0.903003 | + | 0.0280413i | ||||
\(598\) | −4.60388 | − | 4.60388i | −0.188267 | − | 0.188267i | ||||
\(599\) | 32.5214 | 1.32879 | 0.664395 | − | 0.747382i | \(-0.268689\pi\) | ||||
0.664395 | + | 0.747382i | \(0.268689\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.2337 | 0.988513 | 0.494256 | − | 0.869316i | \(-0.335440\pi\) | ||||
0.494256 | + | 0.869316i | \(0.335440\pi\) | |||||||
\(602\) | −4.48185 | − | 4.48185i | −0.182667 | − | 0.182667i | ||||
\(603\) | −28.6607 | + | 25.3058i | −1.16715 | + | 1.03053i | ||||
\(604\) | 9.76631i | 0.397386i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.53262 | + | 3.75906i | 0.143503 | + | 0.152701i | ||||
\(607\) | 6.28134 | − | 6.28134i | 0.254952 | − | 0.254952i | −0.568045 | − | 0.822997i | \(-0.692300\pi\) |
0.822997 | + | 0.568045i | \(0.192300\pi\) | |||||||
\(608\) | −16.5207 | + | 16.5207i | −0.670004 | + | 0.670004i | ||||
\(609\) | −7.10313 | − | 7.55842i | −0.287833 | − | 0.306283i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4472i | 0.422649i | ||||||||
\(612\) | 2.90017 | − | 2.56069i | 0.117232 | − | 0.103510i | ||||
\(613\) | 22.6274 | + | 22.6274i | 0.913913 | + | 0.913913i | 0.996577 | − | 0.0826647i | \(-0.0263430\pi\) |
−0.0826647 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(614\) | −10.7971 | −0.435734 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9783 | 0.442326 | ||||||||
\(617\) | −6.22801 | − | 6.22801i | −0.250730 | − | 0.250730i | 0.570540 | − | 0.821270i | \(-0.306734\pi\) |
−0.821270 | + | 0.570540i | \(0.806734\pi\) | |||||||
\(618\) | −9.76161 | − | 0.303131i | −0.392669 | − | 0.0121937i | ||||
\(619\) | 15.2554i | 0.613168i | 0.951844 | + | 0.306584i | \(0.0991860\pi\) | ||||
−0.951844 | + | 0.306584i | \(0.900814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4891 | − | 13.8564i | −0.461043 | − | 0.556038i | ||||
\(622\) | −2.10594 | + | 2.10594i | −0.0844405 | + | 0.0844405i | ||||
\(623\) | −2.65805 | + | 2.65805i | −0.106493 | + | 0.106493i | ||||
\(624\) | −1.87953 | + | 1.76631i | −0.0752413 | + | 0.0707091i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 9.39764i | − | 0.375605i | ||||||
\(627\) | −0.883582 | + | 28.4537i | −0.0352869 | + | 1.13633i | ||||
\(628\) | 12.3667 | + | 12.3667i | 0.493484 | + | 0.493484i | ||||
\(629\) | −4.45877 | −0.177783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0951 | 0.720354 | 0.360177 | − | 0.932884i | \(-0.382716\pi\) | ||||
0.360177 | + | 0.932884i | \(0.382716\pi\) | |||||||
\(632\) | 28.5596 | + | 28.5596i | 1.13604 | + | 1.13604i | ||||
\(633\) | 0.517587 | − | 16.6677i | 0.0205722 | − | 0.662480i | ||||
\(634\) | − | 5.02175i | − | 0.199439i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 20.7446 | − | 19.4950i | 0.822575 | − | 0.773027i | ||||
\(637\) | 1.67746 | − | 1.67746i | 0.0664632 | − | 0.0664632i | ||||
\(638\) | −13.7850 | + | 13.7850i | −0.545755 | + | 0.545755i | ||||
\(639\) | 0.349857 | − | 5.62772i | 0.0138401 | − | 0.222629i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.75906i | 0.148474i | 0.997241 | + | 0.0742369i | \(0.0236521\pi\) | ||||
−0.997241 | + | 0.0742369i | \(0.976348\pi\) | |||||||
\(642\) | −7.32943 | − | 0.227603i | −0.289270 | − | 0.00898279i | ||||
\(643\) | −12.9912 | − | 12.9912i | −0.512322 | − | 0.512322i | 0.402916 | − | 0.915237i | \(-0.367997\pi\) |
−0.915237 | + | 0.402916i | \(0.867997\pi\) | |||||||
\(644\) | −4.75372 | −0.187323 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.97825 | −0.117178 | ||||||||
\(647\) | −31.4262 | − | 31.4262i | −1.23549 | − | 1.23549i | −0.961824 | − | 0.273669i | \(-0.911763\pi\) |
−0.273669 | − | 0.961824i | \(-0.588237\pi\) | |||||||
\(648\) | 18.9783 | − | 14.7665i | 0.745540 | − | 0.580081i | ||||
\(649\) | − | 49.2119i | − | 1.93174i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.62772 | + | 5.98844i | 0.220568 | + | 0.234705i | ||||
\(652\) | 12.3667 | − | 12.3667i | 0.484317 | − | 0.484317i | ||||
\(653\) | 11.6218 | − | 11.6218i | 0.454795 | − | 0.454795i | −0.442148 | − | 0.896942i | \(-0.645783\pi\) |
0.896942 | + | 0.442148i | \(0.145783\pi\) | |||||||
\(654\) | 7.86797 | + | 8.37228i | 0.307662 | + | 0.327382i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.51811i | 0.293533i | ||||||||
\(657\) | −25.3058 | − | 28.6607i | −0.987271 | − | 1.11816i | ||||
\(658\) | −2.46718 | − | 2.46718i | −0.0961809 | − | 0.0961809i | ||||
\(659\) | −28.0627 | −1.09317 | −0.546583 | − | 0.837405i | \(-0.684072\pi\) | ||||
−0.546583 | + | 0.837405i | \(0.684072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.76631 | 0.302075 | 0.151037 | − | 0.988528i | \(-0.451739\pi\) | ||||
0.151037 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(662\) | −8.39129 | − | 8.39129i | −0.326137 | − | 0.326137i | ||||
\(663\) | −3.85955 | − | 0.119852i | −0.149892 | − | 0.00465466i | ||||
\(664\) | − | 44.7011i | − | 1.73474i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.2554 | − | 0.699713i | −0.436139 | − | 0.0271133i | ||||
\(667\) | 14.6686 | − | 14.6686i | 0.567971 | − | 0.567971i | ||||
\(668\) | −10.4237 | + | 10.4237i | −0.403303 | + | 0.403303i | ||||
\(669\) | 29.1774 | − | 27.4198i | 1.12806 | − | 1.06011i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 27.7128i | − | 1.06984i | ||||||
\(672\) | 0.314011 | − | 10.1120i | 0.0121132 | − | 0.390078i | ||||
\(673\) | 13.4196 | + | 13.4196i | 0.517289 | + | 0.517289i | 0.916750 | − | 0.399461i | \(-0.130803\pi\) |
−0.399461 | + | 0.916750i | \(0.630803\pi\) | |||||||
\(674\) | −3.75906 | −0.144793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1168 | −0.389109 | ||||||||
\(677\) | 19.8433 | + | 19.8433i | 0.762640 | + | 0.762640i | 0.976799 | − | 0.214159i | \(-0.0687010\pi\) |
−0.214159 | + | 0.976799i | \(0.568701\pi\) | |||||||
\(678\) | 0.215040 | − | 6.92487i | 0.00825857 | − | 0.265948i | ||||
\(679\) | − | 2.37228i | − | 0.0910398i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.6753 | − | 15.6708i | 0.638998 | − | 0.600507i | ||||
\(682\) | 10.9217 | − | 10.9217i | 0.418214 | − | 0.418214i | ||||
\(683\) | −4.19564 | + | 4.19564i | −0.160542 | + | 0.160542i | −0.782807 | − | 0.622265i | \(-0.786213\pi\) |
0.622265 | + | 0.782807i | \(0.286213\pi\) | |||||||
\(684\) | 16.4356 | + | 1.02175i | 0.628433 | + | 0.0390676i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.792287i | 0.0302497i | ||||||||
\(687\) | −50.1676 | − | 1.55787i | −1.91401 | − | 0.0594366i | ||||
\(688\) | −3.55091 | − | 3.55091i | −0.135377 | − | 0.135377i | ||||
\(689\) | −28.4125 | −1.08243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | −0.152167 | −0.0760836 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760836 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(692\) | 15.6088 | + | 15.6088i | 0.593359 | + | 0.593359i | ||||
\(693\) | −8.15870 | − | 9.24034i | −0.309924 | − | 0.351012i | ||||
\(694\) | 5.25544i | 0.199494i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 18.9783 | + | 20.1947i | 0.719369 | + | 0.765478i | ||||
\(697\) | −7.95880 | + | 7.95880i | −0.301461 | + | 0.301461i | ||||
\(698\) | 12.1698 | − | 12.1698i | 0.460634 | − | 0.460634i | ||||
\(699\) | −0.699713 | − | 0.744563i | −0.0264656 | − | 0.0281619i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.68815i | 0.252608i | 0.991992 | + | 0.126304i | \(0.0403115\pi\) | ||||
−0.991992 | + | 0.126304i | \(0.959689\pi\) | |||||||
\(702\) | −9.72399 | − | 0.908224i | −0.367008 | − | 0.0342787i | ||||
\(703\) | −13.4196 | − | 13.4196i | −0.506132 | − | 0.506132i | ||||
\(704\) | −13.8564 | −0.522233 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.74456 | −0.329106 | ||||||||
\(707\) | −2.65805 | − | 2.65805i | −0.0999664 | − | 0.0999664i | ||||
\(708\) | −28.4537 | − | 0.883582i | −1.06935 | − | 0.0332070i | ||||
\(709\) | 19.3505i | 0.726724i | 0.931648 | + | 0.363362i | \(0.118371\pi\) | ||||
−0.931648 | + | 0.363362i | \(0.881629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.81386 | − | 45.2632i | 0.105528 | − | 1.69750i | ||||
\(712\) | 7.10183 | − | 7.10183i | 0.266152 | − | 0.266152i | ||||
\(713\) | −11.6218 | + | 11.6218i | −0.435238 | + | 0.435238i | ||||
\(714\) | 0.939764 | − | 0.883156i | 0.0351698 | − | 0.0330513i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.57924i | 0.0963907i | ||||||||
\(717\) | −0.422983 | + | 13.6212i | −0.0157966 | + | 0.508691i | ||||
\(718\) | 16.5786 | + | 16.5786i | 0.618706 | + | 0.618706i | ||||
\(719\) | −11.9769 | −0.446662 | −0.223331 | − | 0.974743i | \(-0.571693\pi\) | ||||
−0.223331 | + | 0.974743i | \(0.571693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.11684 | 0.265045 | ||||||||
\(722\) | 1.68069 | + | 1.68069i | 0.0625490 | + | 0.0625490i | ||||
\(723\) | 0.617656 | − | 19.8902i | 0.0229709 | − | 0.739723i | ||||
\(724\) | − | 8.23369i | − | 0.306003i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.88316 | + | 5.52878i | −0.218344 | + | 0.205192i | ||||
\(727\) | 34.9941 | − | 34.9941i | 1.29786 | − | 1.29786i | 0.368055 | − | 0.929804i | \(-0.380024\pi\) |
0.929804 | − | 0.368055i | \(-0.119976\pi\) | |||||||
\(728\) | −4.48185 | + | 4.48185i | −0.166108 | + | 0.166108i | ||||
\(729\) | −26.5330 | − | 5.00000i | −0.982704 | − | 0.185185i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.51811i | − | 0.278067i | ||||||
\(732\) | −16.0232 | − | 0.497573i | −0.592233 | − | 0.0183908i | ||||
\(733\) | −15.0971 | − | 15.0971i | −0.557624 | − | 0.557624i | 0.371006 | − | 0.928630i | \(-0.379013\pi\) |
−0.928630 | + | 0.371006i | \(0.879013\pi\) | |||||||
\(734\) | −5.63858 | −0.208124 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.2337 | 0.745824 | ||||||||
\(737\) | −37.0286 | − | 37.0286i | −1.36396 | − | 1.36396i | ||||
\(738\) | −21.3397 | + | 18.8417i | −0.785524 | + | 0.693573i | ||||
\(739\) | 9.62772i | 0.354161i | 0.984196 | + | 0.177081i | \(0.0566654\pi\) | ||||
−0.984196 | + | 0.177081i | \(0.943335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.2554 | − | 11.9769i | −0.413479 | − | 0.439982i | ||||
\(742\) | 6.70982 | − | 6.70982i | 0.246325 | − | 0.246325i | ||||
\(743\) | −23.4521 | + | 23.4521i | −0.860373 | + | 0.860373i | −0.991381 | − | 0.131008i | \(-0.958179\pi\) |
0.131008 | + | 0.991381i | \(0.458179\pi\) | |||||||
\(744\) | −15.0362 | − | 16.0000i | −0.551255 | − | 0.586588i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 12.6766i | − | 0.464123i | ||||||
\(747\) | −37.6247 | + | 33.2205i | −1.37662 | + | 1.21547i | ||||
\(748\) | 3.74691 | + | 3.74691i | 0.137001 | + | 0.137001i | ||||
\(749\) | 5.34363 | 0.195252 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6277 | −0.497283 | −0.248641 | − | 0.968596i | \(-0.579984\pi\) | ||||
−0.248641 | + | 0.968596i | \(0.579984\pi\) | |||||||
\(752\) | −1.95472 | − | 1.95472i | −0.0712812 | − | 0.0712812i | ||||
\(753\) | 49.1882 | + | 1.52746i | 1.79252 | + | 0.0556637i | ||||
\(754\) | − | 11.2554i | − | 0.409899i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.48913 | + | 4.55134i | −0.199638 | + | 0.165531i | ||||
\(757\) | −22.6274 | + | 22.6274i | −0.822407 | + | 0.822407i | −0.986453 | − | 0.164045i | \(-0.947546\pi\) |
0.164045 | + | 0.986453i | \(0.447546\pi\) | |||||||
\(758\) | 6.72278 | − | 6.72278i | 0.244182 | − | 0.244182i | ||||
\(759\) | 17.9653 | − | 16.8832i | 0.652100 | − | 0.612820i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.1716i | − | 1.16622i | −0.812394 | − | 0.583109i | \(-0.801836\pi\) | ||
0.812394 | − | 0.583109i | \(-0.198164\pi\) | |||||||
\(762\) | −0.138660 | + | 4.46522i | −0.00502313 | + | 0.161758i | ||||
\(763\) | −5.92010 | − | 5.92010i | −0.214322 | − | 0.214322i | ||||
\(764\) | −22.0742 | −0.798618 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.2554 | −0.767990 | ||||||||
\(767\) | 20.0907 | + | 20.0907i | 0.725433 | + | 0.725433i | ||||
\(768\) | −0.746360 | + | 24.0347i | −0.0269319 | + | 0.867279i | ||||
\(769\) | 16.2337i | 0.585402i | 0.956204 | + | 0.292701i | \(0.0945540\pi\) | ||||
−0.956204 | + | 0.292701i | \(0.905446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.74456 | + | 8.21782i | −0.314928 | + | 0.295958i | ||||
\(772\) | −24.7334 | + | 24.7334i | −0.890173 | + | 0.890173i | ||||
\(773\) | −19.0090 | + | 19.0090i | −0.683708 | + | 0.683708i | −0.960834 | − | 0.277126i | \(-0.910618\pi\) |
0.277126 | + | 0.960834i | \(0.410618\pi\) | |||||||
\(774\) | 1.17981 | − | 18.9783i | 0.0424076 | − | 0.682159i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.33830i | 0.227532i | ||||||||
\(777\) | 8.21386 | + | 0.255068i | 0.294671 | + | 0.00915052i | ||||
\(778\) | −14.6686 | − | 14.6686i | −0.525896 | − | 0.525896i | ||||
\(779\) | −47.9075 | −1.71646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.72281 | 0.276344 | ||||||||
\(782\) | 1.82380 | + | 1.82380i | 0.0652189 | + | 0.0652189i | ||||
\(783\) | 2.89373 | − | 30.9820i | 0.103413 | − | 1.10721i | ||||
\(784\) | 0.627719i | 0.0224185i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.72281 | + | 8.21782i | 0.275464 | + | 0.293120i | ||||
\(787\) | 23.0559 | − | 23.0559i | 0.821854 | − | 0.821854i | −0.164520 | − | 0.986374i | \(-0.552607\pi\) |
0.986374 | + | 0.164520i | \(0.0526074\pi\) | |||||||
\(788\) | 21.4197 | − | 21.4197i | 0.763046 | − | 0.763046i | ||||
\(789\) | 5.63858 | + | 6.00000i | 0.200739 | + | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.04868i | 0.179510i | ||||||||
\(792\) | 21.7985 | + | 24.6885i | 0.774578 | + | 0.877267i | ||||
\(793\) | 11.3137 | + | 11.3137i | 0.401762 | + | 0.401762i | ||||
\(794\) | −23.4737 | −0.833049 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4891 | 0.619886 | ||||||||
\(797\) | −15.3615 | − | 15.3615i | −0.544131 | − | 0.544131i | 0.380607 | − | 0.924737i | \(-0.375715\pi\) |
−0.924737 | + | 0.380607i | \(0.875715\pi\) | |||||||
\(798\) | 5.48648 | + | 0.170374i | 0.194219 | + | 0.00603116i | ||||
\(799\) | − | 4.13859i | − | 0.146413i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.2554 | − | 0.699713i | −0.397691 | − | 0.0247231i | ||||
\(802\) | −14.6686 | + | 14.6686i | −0.517967 | + | 0.517967i | ||||
\(803\) | 37.0286 | − | 37.0286i | 1.30671 | − | 1.30671i | ||||
\(804\) | −22.0742 | + | 20.7446i | −0.778498 | + | 0.731604i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.91754i | 0.314107i | ||||||||
\(807\) | −0.643878 | + | 20.7346i | −0.0226656 | + | 0.729891i | ||||
\(808\) | 7.10183 | + | 7.10183i | 0.249841 | + | 0.249841i | ||||
\(809\) | −14.2063 | −0.499466 | −0.249733 | − | 0.968315i | \(-0.580343\pi\) | ||||
−0.249733 | + | 0.968315i | \(0.580343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7446 | 1.14982 | 0.574909 | − | 0.818218i | \(-0.305038\pi\) | ||||
0.574909 | + | 0.818218i | \(0.305038\pi\) | |||||||
\(812\) | −5.81088 | − | 5.81088i | −0.203922 | − | 0.203922i | ||||
\(813\) | 0.0800555 | − | 2.57800i | 0.00280767 | − | 0.0904143i | ||||
\(814\) | − | 15.4456i | − | 0.541369i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.744563 | − | 0.699713i | 0.0260649 | − | 0.0244949i | ||||
\(817\) | 22.6274 | − | 22.6274i | 0.791633 | − | 0.791633i | ||||
\(818\) | −9.66704 | + | 9.66704i | −0.338000 | + | 0.338000i | ||||
\(819\) | 7.10313 | + | 0.441578i | 0.248204 | + | 0.0154300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.22938i | 0.0778060i | 0.999243 | + | 0.0389030i | \(0.0123863\pi\) | ||||
−0.999243 | + | 0.0389030i | \(0.987614\pi\) | |||||||
\(822\) | −23.3526 | − | 0.725176i | −0.814515 | − | 0.0252934i | ||||
\(823\) | 15.7216 | + | 15.7216i | 0.548020 | + | 0.548020i | 0.925868 | − | 0.377848i | \(-0.123336\pi\) |
−0.377848 | + | 0.925868i | \(0.623336\pi\) | |||||||
\(824\) | −19.0149 | −0.662415 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.48913 | −0.330169 | ||||||||
\(827\) | 0.625691 | + | 0.625691i | 0.0217574 | + | 0.0217574i | 0.717902 | − | 0.696144i | \(-0.245103\pi\) |
−0.696144 | + | 0.717902i | \(0.745103\pi\) | |||||||
\(828\) | −9.43905 | − | 10.6904i | −0.328030 | − | 0.371518i | ||||
\(829\) | − | 46.0000i | − | 1.59765i | −0.601566 | − | 0.798823i | \(-0.705456\pi\) | ||
0.601566 | − | 0.798823i | \(-0.294544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.6060 | + | 26.1831i | 0.853572 | + | 0.908283i | ||||
\(832\) | 5.65685 | − | 5.65685i | 0.196116 | − | 0.196116i | ||||
\(833\) | −0.664513 | + | 0.664513i | −0.0230240 | + | 0.0230240i | ||||
\(834\) | 0.699713 | + | 0.744563i | 0.0242291 | + | 0.0257821i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 22.5543i | 0.780058i | ||||||||
\(837\) | −2.29266 | + | 24.5466i | −0.0792461 | + | 0.848456i | ||||
\(838\) | 15.9176 | + | 15.9176i | 0.549864 | + | 0.549864i | ||||
\(839\) | 0.699713 | 0.0241568 | 0.0120784 | − | 0.999927i | \(-0.496155\pi\) | ||||
0.0120784 | + | 0.999927i | \(0.496155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.86141 | 0.236600 | ||||||||
\(842\) | −0.208564 | − | 0.208564i | −0.00718758 | − | 0.00718758i | ||||
\(843\) | −18.0864 | − | 0.561643i | −0.622928 | − | 0.0193440i | ||||
\(844\) | − | 13.2119i | − | 0.454774i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.649468 | − | 10.4472i | 0.0223292 | − | 0.359182i | ||||
\(847\) | 4.16002 | − | 4.16002i | 0.142940 | − | 0.142940i | ||||
\(848\) | 5.31611 | − | 5.31611i | 0.182556 | − | 0.182556i | ||||
\(849\) | −14.9711 | + | 14.0693i | −0.513807 | + | 0.482857i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.4356i | 0.563407i | ||||||||
\(852\) | 0.138660 | − | 4.46522i | 0.00475042 | − | 0.152976i | ||||
\(853\) | −13.6157 | − | 13.6157i | −0.466191 | − | 0.466191i | 0.434487 | − | 0.900678i | \(-0.356930\pi\) |
−0.900678 | + | 0.434487i | \(0.856930\pi\) | |||||||
\(854\) | −5.34363 | −0.182855 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.2772 | −0.487984 | ||||||||
\(857\) | 14.6969 | + | 14.6969i | 0.502038 | + | 0.502038i | 0.912071 | − | 0.410033i | \(-0.134483\pi\) |
−0.410033 | + | 0.912071i | \(0.634483\pi\) | |||||||
\(858\) | 0.415179 | − | 13.3699i | 0.0141740 | − | 0.456439i | ||||
\(859\) | − | 28.0000i | − | 0.955348i | −0.878537 | − | 0.477674i | \(-0.841480\pi\) | ||
0.878537 | − | 0.477674i | \(-0.158520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.1168 | − | 14.2063i | 0.515181 | − | 0.484148i | ||||
\(862\) | −0.196001 | + | 0.196001i | −0.00667581 | + | 0.00667581i | ||||
\(863\) | 29.1853 | − | 29.1853i | 0.993480 | − | 0.993480i | −0.00649926 | − | 0.999979i | \(-0.502069\pi\) |
0.999979 | + | 0.00649926i | \(0.00206879\pi\) | |||||||
\(864\) | 23.3639 | − | 19.3723i | 0.794854 | − | 0.659058i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.57924i | 0.0876462i | ||||||||
\(867\) | −27.9017 | − | 0.866443i | −0.947593 | − | 0.0294259i | ||||
\(868\) | 4.60388 | + | 4.60388i | 0.156266 | + | 0.156266i | ||||
\(869\) | 62.1138 | 2.10707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.2337 | 1.02443 | ||||||||
\(872\) | 15.8174 | + | 15.8174i | 0.535645 | + | 0.535645i | ||||
\(873\) | 5.33492 | − | 4.71043i | 0.180560 | − | 0.159424i | ||||
\(874\) | 10.9783i | 0.371345i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.7446 | − | 22.0742i | −0.700894 | − | 0.745819i | ||||
\(877\) | 20.1295 | − | 20.1295i | 0.679724 | − | 0.679724i | −0.280214 | − | 0.959938i | \(-0.590405\pi\) |
0.959938 | + | 0.280214i | \(0.0904053\pi\) | |||||||
\(878\) | 10.7875 | − | 10.7875i | 0.364061 | − | 0.364061i | ||||
\(879\) | −19.0800 | − | 20.3030i | −0.643553 | − | 0.684803i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −1.78174 | + | 1.57317i | −0.0599942 | + | 0.0529715i | ||||
\(883\) | −7.76280 | − | 7.76280i | −0.261239 | − | 0.261239i | 0.564318 | − | 0.825557i | \(-0.309139\pi\) |
−0.825557 | + | 0.564318i | \(0.809139\pi\) | |||||||
\(884\) | −3.05934 | −0.102897 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.25544 | 0.0421772 | ||||||||
\(887\) | 5.52467 | + | 5.52467i | 0.185500 | + | 0.185500i | 0.793748 | − | 0.608247i | \(-0.208127\pi\) |
−0.608247 | + | 0.793748i | \(0.708127\pi\) | |||||||
\(888\) | −21.9459 | − | 0.681495i | −0.736457 | − | 0.0228695i | ||||
\(889\) | − | 3.25544i | − | 0.109184i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.58017 | − | 36.6955i | 0.153442 | − | 1.22934i | ||||
\(892\) | 22.4314 | − | 22.4314i | 0.751059 | − | 0.751059i | ||||
\(893\) | 12.4560 | − | 12.4560i | 0.416825 | − | 0.416825i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 9.01011i | − | 0.301007i | ||||||
\(897\) | −0.441791 | + | 14.2268i | −0.0147510 | + | 0.475020i | ||||
\(898\) | −0.856970 | − | 0.856970i | −0.0285975 | − | 0.0285975i | ||||
\(899\) | −28.4125 | −0.947611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2554 | 0.374973 | ||||||||
\(902\) | −27.5701 | − | 27.5701i | −0.917983 | − | 0.917983i | ||||
\(903\) | −0.430081 | + | 13.8497i | −0.0143122 | + | 0.460890i | ||||
\(904\) | − | 13.4891i | − | 0.448642i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.11684 | + | 6.68815i | −0.236441 | + | 0.222199i | ||||
\(907\) | 2.30194 | − | 2.30194i | 0.0764347 | − | 0.0764347i | −0.667856 | − | 0.744291i | \(-0.732788\pi\) |
0.744291 | + | 0.667856i | \(0.232788\pi\) | |||||||
\(908\) | 12.8199 | − | 12.8199i | 0.425442 | − | 0.425442i | ||||
\(909\) | 0.699713 | − | 11.2554i | 0.0232080 | − | 0.373319i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.3152i | − | 0.606809i | −0.952862 | − | 0.303404i | \(-0.901877\pi\) | ||
0.952862 | − | 0.303404i | \(-0.0981233\pi\) | |||||||
\(912\) | 4.34687 | + | 0.134985i | 0.143939 | + | 0.00446979i | ||||
\(913\) | −48.6097 | − | 48.6097i | −1.60875 | − | 1.60875i | ||||
\(914\) | −1.39943 | −0.0462889 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −39.7663 | −1.31392 | ||||||||
\(917\) | −5.81088 | − | 5.81088i | −0.191892 | − | 0.191892i | ||||
\(918\) | 3.85210 | + | 0.359787i | 0.127138 | + | 0.0118747i | ||||
\(919\) | 23.1168i | 0.762554i | 0.924461 | + | 0.381277i | \(0.124516\pi\) | ||||
−0.924461 | + | 0.381277i | \(0.875484\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.1644 | + | 17.2005i | 0.532635 | + | 0.566775i | ||||
\(922\) | 11.3137 | − | 11.3137i | 0.372597 | − | 0.372597i | ||||
\(923\) | −3.15283 | + | 3.15283i | −0.103777 | + | 0.103777i | ||||
\(924\) | −6.68815 | − | 7.11684i | −0.220024 | − | 0.234127i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 21.3745i | − | 0.702410i | ||||||
\(927\) | 14.1313 | + | 16.0047i | 0.464132 | + | 0.525665i | ||||
\(928\) | 24.7334 | + | 24.7334i | 0.811912 | + | 0.811912i | ||||
\(929\) | 44.8482 | 1.47142 | 0.735710 | − | 0.677296i | \(-0.236848\pi\) | ||||
0.735710 | + | 0.677296i | \(0.236848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.00000 | −0.131095 | ||||||||
\(932\) | −0.572416 | − | 0.572416i | −0.0187501 | − | 0.0187501i | ||||
\(933\) | 6.50774 | + | 0.202087i | 0.213054 | + | 0.00661604i | ||||
\(934\) | 17.5326i | 0.573685i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.9783 | − | 1.17981i | −0.620324 | − | 0.0385634i | ||||
\(937\) | 5.03237 | − | 5.03237i | 0.164400 | − | 0.164400i | −0.620113 | − | 0.784513i | \(-0.712913\pi\) |
0.784513 | + | 0.620113i | \(0.212913\pi\) | |||||||
\(938\) | −7.13991 | + | 7.13991i | −0.233126 | + | 0.233126i | ||||
\(939\) | −14.9711 | + | 14.0693i | −0.488563 | + | 0.459134i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 36.6303i | − | 1.19412i | −0.802198 | − | 0.597058i | \(-0.796336\pi\) | ||
0.802198 | − | 0.597058i | \(-0.203664\pi\) | |||||||
\(942\) | −0.542834 | + | 17.4807i | −0.0176865 | + | 0.569552i | ||||
\(943\) | 29.3372 | + | 29.3372i | 0.955352 | + | 0.955352i | ||||
\(944\) | −7.51811 | −0.244694 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.0435 | 0.846747 | ||||||||
\(947\) | −11.4132 | − | 11.4132i | −0.370879 | − | 0.370879i | 0.496918 | − | 0.867797i | \(-0.334465\pi\) |
−0.867797 | + | 0.496918i | \(0.834465\pi\) | |||||||
\(948\) | 1.11523 | − | 35.9133i | 0.0362210 | − | 1.16641i | ||||
\(949\) | 30.2337i | 0.981427i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.00000 | + | 7.51811i | −0.259418 | + | 0.243791i | ||||
\(952\) | 1.77546 | − | 1.77546i | 0.0575429 | − | 0.0575429i | ||||
\(953\) | 12.5337 | − | 12.5337i | 0.406005 | − | 0.406005i | −0.474338 | − | 0.880343i | \(-0.657312\pi\) |
0.880343 | + | 0.474338i | \(0.157312\pi\) | |||||||
\(954\) | 28.4125 | + | 1.76631i | 0.919889 | + | 0.0571865i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.7971i | 0.349202i | ||||||||
\(957\) | 42.5983 | + | 1.32282i | 1.37701 | + | 0.0427607i | ||||
\(958\) | 13.8117 | + | 13.8117i | 0.446234 | + | 0.446234i | ||||
\(959\) | 17.0256 | 0.549784 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 6.30565 | + | 6.30565i | 0.203302 | + | 0.203302i | ||||
\(963\) | 10.6104 | + | 12.0170i | 0.341914 | + | 0.387244i | ||||
\(964\) | − | 15.7663i | − | 0.507799i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.25544 | − | 3.46410i | −0.104742 | − | 0.111456i | ||||
\(967\) | 25.7863 | − | 25.7863i | 0.829232 | − | 0.829232i | −0.158178 | − | 0.987411i | \(-0.550562\pi\) |
0.987411 | + | 0.158178i | \(0.0505620\pi\) | |||||||
\(968\) | −11.1148 | + | 11.1148i | −0.357243 | + | 0.357243i | ||||
\(969\) | 4.45877 | + | 4.74456i | 0.143236 | + | 0.152417i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2540i | 0.746258i | 0.927780 | + | 0.373129i | \(0.121715\pi\) | ||||
−0.927780 | + | 0.373129i | \(0.878285\pi\) | |||||||
\(972\) | −21.1346 | − | 3.30704i | −0.677892 | − | 0.106074i | ||||
\(973\) | −0.526485 | − | 0.526485i | −0.0168783 | − | 0.0168783i | ||||
\(974\) | −12.4570 | −0.399147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.23369 | −0.135517 | ||||||||
\(977\) | 40.5985 | + | 40.5985i | 1.29886 | + | 1.29886i | 0.929144 | + | 0.369717i | \(0.120545\pi\) |
0.369717 | + | 0.929144i | \(0.379455\pi\) | |||||||
\(978\) | 17.4807 | + | 0.542834i | 0.558971 | + | 0.0173579i | ||||
\(979\) | − | 15.4456i | − | 0.493644i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.55842 | − | 25.0684i | 0.0497566 | − | 0.800374i | ||||
\(982\) | −19.9335 | + | 19.9335i | −0.636103 | + | 0.636103i | ||||
\(983\) | −38.3964 | + | 38.3964i | −1.22466 | + | 1.22466i | −0.258696 | + | 0.965959i | \(0.583293\pi\) |
−0.965959 | + | 0.258696i | \(0.916707\pi\) | |||||||
\(984\) | −40.3894 | + | 37.9565i | −1.28757 | + | 1.21001i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.45877i | 0.141996i | ||||||||
\(987\) | −0.236752 | + | 7.62404i | −0.00753590 | + | 0.242676i | ||||
\(988\) | −9.20777 | − | 9.20777i | −0.292938 | − | 0.292938i | ||||
\(989\) | −27.7128 | −0.881216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9783 | 1.61938 | 0.809689 | − | 0.586860i | \(-0.199636\pi\) | ||||
0.809689 | + | 0.586860i | \(0.199636\pi\) | |||||||
\(992\) | −19.5959 | − | 19.5959i | −0.622171 | − | 0.622171i | ||||
\(993\) | −0.805232 | + | 25.9306i | −0.0255533 | + | 0.822882i | ||||
\(994\) | − | 1.48913i | − | 0.0472322i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.9783 | + | 27.2327i | −0.918211 | + | 0.862901i | ||||
\(997\) | 5.03237 | − | 5.03237i | 0.159377 | − | 0.159377i | −0.622914 | − | 0.782290i | \(-0.714051\pi\) |
0.782290 | + | 0.622914i | \(0.214051\pi\) | |||||||
\(998\) | −0.911899 | + | 0.911899i | −0.0288657 | + | 0.0288657i | ||||
\(999\) | 15.7359 | + | 18.9783i | 0.497863 | + | 0.600445i |
(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 | 525.2.j.a.218.5 | yes | 16 | |
3.2 | odd | 2 | inner | 525.2.j.a.218.3 | ✓ | 16 | |
5.2 | odd | 4 | inner | 525.2.j.a.407.3 | yes | 16 | |
5.3 | odd | 4 | inner | 525.2.j.a.407.6 | yes | 16 | |
5.4 | even | 2 | inner | 525.2.j.a.218.4 | yes | 16 | |
15.2 | even | 4 | inner | 525.2.j.a.407.5 | yes | 16 | |
15.8 | even | 4 | inner | 525.2.j.a.407.4 | yes | 16 | |
15.14 | odd | 2 | inner | 525.2.j.a.218.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.j.a.218.3 | ✓ | 16 | 3.2 | odd | 2 | inner | |
525.2.j.a.218.4 | yes | 16 | 5.4 | even | 2 | inner | |
525.2.j.a.218.5 | yes | 16 | 1.1 | even | 1 | trivial | |
525.2.j.a.218.6 | yes | 16 | 15.14 | odd | 2 | inner | |
525.2.j.a.407.3 | yes | 16 | 5.2 | odd | 4 | inner | |
525.2.j.a.407.4 | yes | 16 | 15.8 | even | 4 | inner | |
525.2.j.a.407.5 | yes | 16 | 15.2 | even | 4 | inner | |
525.2.j.a.407.6 | yes | 16 | 5.3 | odd | 4 | inner |