Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(7,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.f (of order \(3\), 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: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.7 |
Dual form | 342.2.f.c.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − | 1.73205i | − | 1.00000i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −2.50000 | + | 4.33013i | −0.753778 | + | 1.30558i | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 1.50000 | − | 2.59808i | 0.400892 | − | 0.694365i | ||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | −3.00000 | −0.707107 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | −4.50000 | − | 2.59808i | −0.981981 | − | 0.566947i | ||||
\(22\) | −2.50000 | + | 4.33013i | −0.533002 | + | 0.923186i | ||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | −1.50000 | − | 0.866025i | −0.273861 | − | 0.158114i | ||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | −1.50000 | − | 2.59808i | −0.253546 | − | 0.439155i | ||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | −4.00000 | − | 1.73205i | −0.648886 | − | 0.280976i | ||||
\(39\) | − | 3.46410i | − | 0.554700i | ||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −3.50000 | + | 6.06218i | −0.546608 | + | 0.946753i | 0.451896 | + | 0.892071i | \(0.350748\pi\) |
−0.998504 | + | 0.0546823i | \(0.982585\pi\) | |||||||
\(42\) | −4.50000 | − | 2.59808i | −0.694365 | − | 0.400892i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | − | 1.73205i | − | 0.250000i | ||||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −5.50000 | + | 9.52628i | −0.755483 | + | 1.30854i | 0.189651 | + | 0.981852i | \(0.439264\pi\) |
−0.945134 | + | 0.326683i | \(0.894069\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 2.50000 | + | 4.33013i | 0.337100 | + | 0.583874i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | −3.00000 | + | 6.92820i | −0.397360 | + | 0.917663i | ||||
\(58\) | 2.50000 | + | 4.33013i | 0.328266 | + | 0.568574i | ||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | −1.50000 | − | 0.866025i | −0.193649 | − | 0.111803i | ||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −3.50000 | − | 6.06218i | −0.444500 | − | 0.769897i | ||||
\(63\) | −4.50000 | + | 7.79423i | −0.566947 | + | 0.981981i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 7.50000 | + | 4.33013i | 0.923186 | + | 0.533002i | ||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | − | 13.8564i | − | 1.66812i | ||||||
\(70\) | −1.50000 | − | 2.59808i | −0.179284 | − | 0.310530i | ||||
\(71\) | 0.500000 | + | 0.866025i | 0.0593391 | + | 0.102778i | 0.894169 | − | 0.447730i | \(-0.147767\pi\) |
−0.834830 | + | 0.550508i | \(0.814434\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −1.50000 | − | 2.59808i | −0.175562 | − | 0.304082i | 0.764794 | − | 0.644275i | \(-0.222841\pi\) |
−0.940356 | + | 0.340193i | \(0.889507\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | 6.00000 | − | 3.46410i | 0.692820 | − | 0.400000i | ||||
\(76\) | −4.00000 | − | 1.73205i | −0.458831 | − | 0.198680i | ||||
\(77\) | 7.50000 | + | 12.9904i | 0.854704 | + | 1.48039i | ||||
\(78\) | − | 3.46410i | − | 0.392232i | ||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −3.50000 | + | 6.06218i | −0.386510 | + | 0.669456i | ||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | −4.50000 | − | 2.59808i | −0.490990 | − | 0.283473i | ||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 7.50000 | − | 4.33013i | 0.804084 | − | 0.464238i | ||||
\(88\) | −2.50000 | + | 4.33013i | −0.266501 | + | 0.461593i | ||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | −1.50000 | + | 2.59808i | −0.158114 | + | 0.273861i | ||||
\(91\) | 3.00000 | − | 5.19615i | 0.314485 | − | 0.544705i | ||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | −10.5000 | + | 6.06218i | −1.08880 | + | 0.628619i | ||||
\(94\) | 0.500000 | + | 0.866025i | 0.0515711 | + | 0.0893237i | ||||
\(95\) | −3.50000 | + | 2.59808i | −0.359092 | + | 0.266557i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | 7.50000 | − | 12.9904i | 0.753778 | − | 1.30558i | ||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | −5.50000 | − | 9.52628i | −0.547270 | − | 0.947900i | −0.998460 | − | 0.0554722i | \(-0.982334\pi\) |
0.451190 | − | 0.892428i | \(-0.351000\pi\) | |||||||
\(102\) | −4.50000 | + | 2.59808i | −0.445566 | + | 0.257248i | ||||
\(103\) | −7.50000 | − | 12.9904i | −0.738997 | − | 1.27998i | −0.952947 | − | 0.303136i | \(-0.901966\pi\) |
0.213950 | − | 0.976845i | \(-0.431367\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −4.50000 | + | 2.59808i | −0.439155 | + | 0.253546i | ||||
\(106\) | −5.50000 | + | 9.52628i | −0.534207 | + | 0.925274i | ||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | 4.50000 | + | 7.79423i | 0.431022 | + | 0.746552i | 0.996962 | − | 0.0778949i | \(-0.0248199\pi\) |
−0.565940 | + | 0.824447i | \(0.691487\pi\) | |||||||
\(110\) | 2.50000 | + | 4.33013i | 0.238366 | + | 0.412861i | ||||
\(111\) | − | 17.3205i | − | 1.64399i | ||||||
\(112\) | 1.50000 | − | 2.59808i | 0.141737 | − | 0.245495i | ||||
\(113\) | 0.500000 | + | 0.866025i | 0.0470360 | + | 0.0814688i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | −3.00000 | + | 6.92820i | −0.280976 | + | 0.648886i | ||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 2.50000 | + | 4.33013i | 0.232119 | + | 0.402042i | ||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | 1.50000 | − | 2.59808i | 0.138086 | − | 0.239172i | ||||
\(119\) | −9.00000 | −0.825029 | ||||||||
\(120\) | −1.50000 | − | 0.866025i | −0.136931 | − | 0.0790569i | ||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0.500000 | + | 0.866025i | 0.0452679 | + | 0.0784063i | ||||
\(123\) | 10.5000 | + | 6.06218i | 0.946753 | + | 0.546608i | ||||
\(124\) | −3.50000 | − | 6.06218i | −0.314309 | − | 0.544400i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −4.50000 | + | 7.79423i | −0.400892 | + | 0.694365i | ||||
\(127\) | 7.50000 | − | 12.9904i | 0.665517 | − | 1.15271i | −0.313627 | − | 0.949546i | \(-0.601544\pi\) |
0.979145 | − | 0.203164i | \(-0.0651224\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | 1.00000 | − | 1.73205i | 0.0877058 | − | 0.151911i | ||||
\(131\) | 7.50000 | − | 12.9904i | 0.655278 | − | 1.13497i | −0.326546 | − | 0.945181i | \(-0.605885\pi\) |
0.981824 | − | 0.189794i | \(-0.0607819\pi\) | |||||||
\(132\) | 7.50000 | + | 4.33013i | 0.652791 | + | 0.376889i | ||||
\(133\) | −10.5000 | + | 7.79423i | −0.910465 | + | 0.675845i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 4.50000 | + | 2.59808i | 0.387298 | + | 0.223607i | ||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | −9.50000 | − | 16.4545i | −0.811640 | − | 1.40580i | −0.911716 | − | 0.410822i | \(-0.865242\pi\) |
0.100076 | − | 0.994980i | \(-0.468091\pi\) | |||||||
\(138\) | − | 13.8564i | − | 1.17954i | ||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | −1.50000 | − | 2.59808i | −0.126773 | − | 0.219578i | ||||
\(141\) | 1.50000 | − | 0.866025i | 0.126323 | − | 0.0729325i | ||||
\(142\) | 0.500000 | + | 0.866025i | 0.0419591 | + | 0.0726752i | ||||
\(143\) | −5.00000 | + | 8.66025i | −0.418121 | + | 0.724207i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 5.00000 | 0.415227 | ||||||||
\(146\) | −1.50000 | − | 2.59808i | −0.124141 | − | 0.215018i | ||||
\(147\) | −3.00000 | + | 1.73205i | −0.247436 | + | 0.142857i | ||||
\(148\) | 10.0000 | 0.821995 | ||||||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | 6.00000 | − | 3.46410i | 0.489898 | − | 0.282843i | ||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | −4.00000 | − | 1.73205i | −0.324443 | − | 0.140488i | ||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | 7.50000 | + | 12.9904i | 0.604367 | + | 1.04679i | ||||
\(155\) | −7.00000 | −0.562254 | ||||||||
\(156\) | − | 3.46410i | − | 0.277350i | ||||||
\(157\) | 8.50000 | − | 14.7224i | 0.678374 | − | 1.17498i | −0.297097 | − | 0.954847i | \(-0.596018\pi\) |
0.975470 | − | 0.220131i | \(-0.0706483\pi\) | |||||||
\(158\) | −4.00000 | −0.318223 | ||||||||
\(159\) | 16.5000 | + | 9.52628i | 1.30854 | + | 0.755483i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 12.0000 | − | 20.7846i | 0.945732 | − | 1.63806i | ||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −3.50000 | + | 6.06218i | −0.273304 | + | 0.473377i | ||||
\(165\) | 7.50000 | − | 4.33013i | 0.583874 | − | 0.337100i | ||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | −4.50000 | − | 2.59808i | −0.347183 | − | 0.200446i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −3.00000 | −0.230089 | ||||||||
\(171\) | 12.0000 | + | 5.19615i | 0.917663 | + | 0.397360i | ||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 7.50000 | − | 4.33013i | 0.568574 | − | 0.328266i | ||||
\(175\) | 12.0000 | 0.907115 | ||||||||
\(176\) | −2.50000 | + | 4.33013i | −0.188445 | + | 0.326396i | ||||
\(177\) | −4.50000 | − | 2.59808i | −0.338241 | − | 0.195283i | ||||
\(178\) | −7.50000 | + | 12.9904i | −0.562149 | + | 0.973670i | ||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −1.50000 | + | 2.59808i | −0.111803 | + | 0.193649i | ||||
\(181\) | −9.50000 | + | 16.4545i | −0.706129 | + | 1.22305i | 0.260153 | + | 0.965567i | \(0.416227\pi\) |
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 3.00000 | − | 5.19615i | 0.222375 | − | 0.385164i | ||||
\(183\) | 1.50000 | − | 0.866025i | 0.110883 | − | 0.0640184i | ||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | 5.00000 | − | 8.66025i | 0.367607 | − | 0.636715i | ||||
\(186\) | −10.5000 | + | 6.06218i | −0.769897 | + | 0.444500i | ||||
\(187\) | 15.0000 | 1.09691 | ||||||||
\(188\) | 0.500000 | + | 0.866025i | 0.0364662 | + | 0.0631614i | ||||
\(189\) | 13.5000 | + | 7.79423i | 0.981981 | + | 0.566947i | ||||
\(190\) | −3.50000 | + | 2.59808i | −0.253917 | + | 0.188484i | ||||
\(191\) | −0.500000 | + | 0.866025i | −0.0361787 | + | 0.0626634i | −0.883548 | − | 0.468341i | \(-0.844852\pi\) |
0.847369 | + | 0.531004i | \(0.178185\pi\) | |||||||
\(192\) | − | 1.73205i | − | 0.125000i | ||||||
\(193\) | 4.50000 | − | 7.79423i | 0.323917 | − | 0.561041i | −0.657376 | − | 0.753563i | \(-0.728333\pi\) |
0.981293 | + | 0.192522i | \(0.0616668\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | −3.00000 | − | 1.73205i | −0.214834 | − | 0.124035i | ||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 7.50000 | − | 12.9904i | 0.533002 | − | 0.923186i | ||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | − | 20.7846i | − | 1.46603i | ||||||
\(202\) | −5.50000 | − | 9.52628i | −0.386979 | − | 0.670267i | ||||
\(203\) | 15.0000 | 1.05279 | ||||||||
\(204\) | −4.50000 | + | 2.59808i | −0.315063 | + | 0.181902i | ||||
\(205\) | 3.50000 | + | 6.06218i | 0.244451 | + | 0.423401i | ||||
\(206\) | −7.50000 | − | 12.9904i | −0.522550 | − | 0.905083i | ||||
\(207\) | −24.0000 | −1.66812 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 17.5000 | − | 12.9904i | 1.21050 | − | 0.898563i | ||||
\(210\) | −4.50000 | + | 2.59808i | −0.310530 | + | 0.179284i | ||||
\(211\) | −4.50000 | + | 7.79423i | −0.309793 | + | 0.536577i | −0.978317 | − | 0.207114i | \(-0.933593\pi\) |
0.668524 | + | 0.743690i | \(0.266926\pi\) | |||||||
\(212\) | −5.50000 | + | 9.52628i | −0.377742 | + | 0.654268i | ||||
\(213\) | 1.50000 | − | 0.866025i | 0.102778 | − | 0.0593391i | ||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | −4.00000 | + | 6.92820i | −0.272798 | + | 0.472500i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −21.0000 | −1.42557 | ||||||||
\(218\) | 4.50000 | + | 7.79423i | 0.304778 | + | 0.527892i | ||||
\(219\) | −4.50000 | + | 2.59808i | −0.304082 | + | 0.175562i | ||||
\(220\) | 2.50000 | + | 4.33013i | 0.168550 | + | 0.291937i | ||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | − | 17.3205i | − | 1.16248i | ||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | −6.00000 | − | 10.3923i | −0.400000 | − | 0.692820i | ||||
\(226\) | 0.500000 | + | 0.866025i | 0.0332595 | + | 0.0576072i | ||||
\(227\) | 5.50000 | − | 9.52628i | 0.365048 | − | 0.632281i | −0.623736 | − | 0.781635i | \(-0.714386\pi\) |
0.988784 | + | 0.149354i | \(0.0477193\pi\) | |||||||
\(228\) | −3.00000 | + | 6.92820i | −0.198680 | + | 0.458831i | ||||
\(229\) | 6.50000 | + | 11.2583i | 0.429532 | + | 0.743971i | 0.996832 | − | 0.0795401i | \(-0.0253452\pi\) |
−0.567300 | + | 0.823511i | \(0.692012\pi\) | |||||||
\(230\) | 4.00000 | − | 6.92820i | 0.263752 | − | 0.456832i | ||||
\(231\) | 22.5000 | − | 12.9904i | 1.48039 | − | 0.854704i | ||||
\(232\) | 2.50000 | + | 4.33013i | 0.164133 | + | 0.284287i | ||||
\(233\) | −7.50000 | − | 12.9904i | −0.491341 | − | 0.851028i | 0.508609 | − | 0.860998i | \(-0.330160\pi\) |
−0.999950 | + | 0.00996947i | \(0.996827\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 1.00000 | 0.0652328 | ||||||||
\(236\) | 1.50000 | − | 2.59808i | 0.0976417 | − | 0.169120i | ||||
\(237\) | 6.92820i | 0.450035i | ||||||||
\(238\) | −9.00000 | −0.583383 | ||||||||
\(239\) | −13.5000 | − | 23.3827i | −0.873242 | − | 1.51250i | −0.858623 | − | 0.512607i | \(-0.828680\pi\) |
−0.0146191 | − | 0.999893i | \(-0.504654\pi\) | |||||||
\(240\) | −1.50000 | − | 0.866025i | −0.0968246 | − | 0.0559017i | ||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | −7.00000 | − | 12.1244i | −0.449977 | − | 0.779383i | ||||
\(243\) | − | 15.5885i | − | 1.00000i | ||||||
\(244\) | 0.500000 | + | 0.866025i | 0.0320092 | + | 0.0554416i | ||||
\(245\) | −2.00000 | −0.127775 | ||||||||
\(246\) | 10.5000 | + | 6.06218i | 0.669456 | + | 0.386510i | ||||
\(247\) | −8.00000 | − | 3.46410i | −0.509028 | − | 0.220416i | ||||
\(248\) | −3.50000 | − | 6.06218i | −0.222250 | − | 0.384949i | ||||
\(249\) | 13.5000 | + | 7.79423i | 0.855528 | + | 0.493939i | ||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −2.50000 | + | 4.33013i | −0.157799 | + | 0.273315i | −0.934075 | − | 0.357078i | \(-0.883773\pi\) |
0.776276 | + | 0.630393i | \(0.217106\pi\) | |||||||
\(252\) | −4.50000 | + | 7.79423i | −0.283473 | + | 0.490990i | ||||
\(253\) | −20.0000 | + | 34.6410i | −1.25739 | + | 2.17786i | ||||
\(254\) | 7.50000 | − | 12.9904i | 0.470592 | − | 0.815089i | ||||
\(255\) | 5.19615i | 0.325396i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 13.8564i | 0.862662i | ||||||||
\(259\) | 15.0000 | − | 25.9808i | 0.932055 | − | 1.61437i | ||||
\(260\) | 1.00000 | − | 1.73205i | 0.0620174 | − | 0.107417i | ||||
\(261\) | −7.50000 | − | 12.9904i | −0.464238 | − | 0.804084i | ||||
\(262\) | 7.50000 | − | 12.9904i | 0.463352 | − | 0.802548i | ||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 7.50000 | + | 4.33013i | 0.461593 | + | 0.266501i | ||||
\(265\) | 5.50000 | + | 9.52628i | 0.337862 | + | 0.585195i | ||||
\(266\) | −10.5000 | + | 7.79423i | −0.643796 | + | 0.477895i | ||||
\(267\) | 22.5000 | + | 12.9904i | 1.37698 | + | 0.794998i | ||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −1.50000 | − | 2.59808i | −0.0914566 | − | 0.158408i | 0.816668 | − | 0.577108i | \(-0.195819\pi\) |
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(270\) | 4.50000 | + | 2.59808i | 0.273861 | + | 0.158114i | ||||
\(271\) | −3.50000 | − | 6.06218i | −0.212610 | − | 0.368251i | 0.739921 | − | 0.672694i | \(-0.234863\pi\) |
−0.952531 | + | 0.304443i | \(0.901530\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | −9.00000 | − | 5.19615i | −0.544705 | − | 0.314485i | ||||
\(274\) | −9.50000 | − | 16.4545i | −0.573916 | − | 0.994052i | ||||
\(275\) | −20.0000 | −1.20605 | ||||||||
\(276\) | − | 13.8564i | − | 0.834058i | ||||||
\(277\) | −9.50000 | + | 16.4545i | −0.570800 | + | 0.988654i | 0.425684 | + | 0.904872i | \(0.360033\pi\) |
−0.996484 | + | 0.0837823i | \(0.973300\pi\) | |||||||
\(278\) | −12.0000 | −0.719712 | ||||||||
\(279\) | 10.5000 | + | 18.1865i | 0.628619 | + | 1.08880i | ||||
\(280\) | −1.50000 | − | 2.59808i | −0.0896421 | − | 0.155265i | ||||
\(281\) | 2.50000 | + | 4.33013i | 0.149137 | + | 0.258314i | 0.930909 | − | 0.365251i | \(-0.119017\pi\) |
−0.781771 | + | 0.623565i | \(0.785684\pi\) | |||||||
\(282\) | 1.50000 | − | 0.866025i | 0.0893237 | − | 0.0515711i | ||||
\(283\) | 1.50000 | − | 2.59808i | 0.0891657 | − | 0.154440i | −0.817993 | − | 0.575228i | \(-0.804913\pi\) |
0.907159 | + | 0.420789i | \(0.138247\pi\) | |||||||
\(284\) | 0.500000 | + | 0.866025i | 0.0296695 | + | 0.0513892i | ||||
\(285\) | 4.50000 | + | 6.06218i | 0.266557 | + | 0.359092i | ||||
\(286\) | −5.00000 | + | 8.66025i | −0.295656 | + | 0.512092i | ||||
\(287\) | 10.5000 | + | 18.1865i | 0.619795 | + | 1.07352i | ||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 5.00000 | 0.293610 | ||||||||
\(291\) | 3.46410i | 0.203069i | ||||||||
\(292\) | −1.50000 | − | 2.59808i | −0.0877809 | − | 0.152041i | ||||
\(293\) | 4.50000 | + | 7.79423i | 0.262893 | + | 0.455344i | 0.967009 | − | 0.254741i | \(-0.0819901\pi\) |
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(294\) | −3.00000 | + | 1.73205i | −0.174964 | + | 0.101015i | ||||
\(295\) | −1.50000 | − | 2.59808i | −0.0873334 | − | 0.151266i | ||||
\(296\) | 10.0000 | 0.581238 | ||||||||
\(297\) | −22.5000 | − | 12.9904i | −1.30558 | − | 0.753778i | ||||
\(298\) | −1.50000 | + | 2.59808i | −0.0868927 | + | 0.150503i | ||||
\(299\) | 16.0000 | 0.925304 | ||||||||
\(300\) | 6.00000 | − | 3.46410i | 0.346410 | − | 0.200000i | ||||
\(301\) | −12.0000 | + | 20.7846i | −0.691669 | + | 1.19800i | ||||
\(302\) | −2.50000 | + | 4.33013i | −0.143859 | + | 0.249171i | ||||
\(303\) | −16.5000 | + | 9.52628i | −0.947900 | + | 0.547270i | ||||
\(304\) | −4.00000 | − | 1.73205i | −0.229416 | − | 0.0993399i | ||||
\(305\) | 1.00000 | 0.0572598 | ||||||||
\(306\) | 4.50000 | + | 7.79423i | 0.257248 | + | 0.445566i | ||||
\(307\) | 16.5000 | + | 28.5788i | 0.941705 | + | 1.63108i | 0.762218 | + | 0.647320i | \(0.224110\pi\) |
0.179486 | + | 0.983760i | \(0.442556\pi\) | |||||||
\(308\) | 7.50000 | + | 12.9904i | 0.427352 | + | 0.740196i | ||||
\(309\) | −22.5000 | + | 12.9904i | −1.27998 | + | 0.738997i | ||||
\(310\) | −7.00000 | −0.397573 | ||||||||
\(311\) | −3.50000 | − | 6.06218i | −0.198467 | − | 0.343755i | 0.749565 | − | 0.661931i | \(-0.230263\pi\) |
−0.948031 | + | 0.318177i | \(0.896930\pi\) | |||||||
\(312\) | − | 3.46410i | − | 0.196116i | ||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 8.50000 | − | 14.7224i | 0.479683 | − | 0.830835i | ||||
\(315\) | 4.50000 | + | 7.79423i | 0.253546 | + | 0.439155i | ||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | −1.50000 | − | 2.59808i | −0.0842484 | − | 0.145922i | 0.820822 | − | 0.571184i | \(-0.193516\pi\) |
−0.905071 | + | 0.425261i | \(0.860182\pi\) | |||||||
\(318\) | 16.5000 | + | 9.52628i | 0.925274 | + | 0.534207i | ||||
\(319\) | −25.0000 | −1.39973 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 6.92820i | 0.386695i | ||||||||
\(322\) | 12.0000 | − | 20.7846i | 0.668734 | − | 1.15828i | ||||
\(323\) | 1.50000 | + | 12.9904i | 0.0834622 | + | 0.722804i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 4.00000 | + | 6.92820i | 0.221880 | + | 0.384308i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 13.5000 | − | 7.79423i | 0.746552 | − | 0.431022i | ||||
\(328\) | −3.50000 | + | 6.06218i | −0.193255 | + | 0.334728i | ||||
\(329\) | 3.00000 | 0.165395 | ||||||||
\(330\) | 7.50000 | − | 4.33013i | 0.412861 | − | 0.238366i | ||||
\(331\) | −14.5000 | + | 25.1147i | −0.796992 | + | 1.38043i | 0.124574 | + | 0.992210i | \(0.460243\pi\) |
−0.921567 | + | 0.388221i | \(0.873090\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | −30.0000 | −1.64399 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 6.00000 | − | 10.3923i | 0.327815 | − | 0.567792i | ||||
\(336\) | −4.50000 | − | 2.59808i | −0.245495 | − | 0.141737i | ||||
\(337\) | 2.50000 | − | 4.33013i | 0.136184 | − | 0.235877i | −0.789865 | − | 0.613280i | \(-0.789850\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 1.50000 | − | 0.866025i | 0.0814688 | − | 0.0470360i | ||||
\(340\) | −3.00000 | −0.162698 | ||||||||
\(341\) | 35.0000 | 1.89536 | ||||||||
\(342\) | 12.0000 | + | 5.19615i | 0.648886 | + | 0.280976i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −12.0000 | − | 6.92820i | −0.646058 | − | 0.373002i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | 11.5000 | − | 19.9186i | 0.617352 | − | 1.06929i | −0.372615 | − | 0.927986i | \(-0.621539\pi\) |
0.989967 | − | 0.141299i | \(-0.0451280\pi\) | |||||||
\(348\) | 7.50000 | − | 4.33013i | 0.402042 | − | 0.232119i | ||||
\(349\) | 2.50000 | − | 4.33013i | 0.133822 | − | 0.231786i | −0.791325 | − | 0.611396i | \(-0.790608\pi\) |
0.925147 | + | 0.379610i | \(0.123942\pi\) | |||||||
\(350\) | 12.0000 | 0.641427 | ||||||||
\(351\) | 10.3923i | 0.554700i | ||||||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | −4.50000 | − | 2.59808i | −0.239172 | − | 0.138086i | ||||
\(355\) | 1.00000 | 0.0530745 | ||||||||
\(356\) | −7.50000 | + | 12.9904i | −0.397499 | + | 0.688489i | ||||
\(357\) | 15.5885i | 0.825029i | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −7.50000 | − | 12.9904i | −0.395835 | − | 0.685606i | 0.597372 | − | 0.801964i | \(-0.296211\pi\) |
−0.993207 | + | 0.116358i | \(0.962878\pi\) | |||||||
\(360\) | −1.50000 | + | 2.59808i | −0.0790569 | + | 0.136931i | ||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −9.50000 | + | 16.4545i | −0.499309 | + | 0.864828i | ||||
\(363\) | −21.0000 | + | 12.1244i | −1.10221 | + | 0.636364i | ||||
\(364\) | 3.00000 | − | 5.19615i | 0.157243 | − | 0.272352i | ||||
\(365\) | −3.00000 | −0.157027 | ||||||||
\(366\) | 1.50000 | − | 0.866025i | 0.0784063 | − | 0.0452679i | ||||
\(367\) | 8.50000 | + | 14.7224i | 0.443696 | + | 0.768505i | 0.997960 | − | 0.0638362i | \(-0.0203335\pi\) |
−0.554264 | + | 0.832341i | \(0.687000\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 10.5000 | − | 18.1865i | 0.546608 | − | 0.946753i | ||||
\(370\) | 5.00000 | − | 8.66025i | 0.259938 | − | 0.450225i | ||||
\(371\) | 16.5000 | + | 28.5788i | 0.856637 | + | 1.48374i | ||||
\(372\) | −10.5000 | + | 6.06218i | −0.544400 | + | 0.314309i | ||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 15.0000 | 0.775632 | ||||||||
\(375\) | − | 15.5885i | − | 0.804984i | ||||||
\(376\) | 0.500000 | + | 0.866025i | 0.0257855 | + | 0.0446619i | ||||
\(377\) | 5.00000 | + | 8.66025i | 0.257513 | + | 0.446026i | ||||
\(378\) | 13.5000 | + | 7.79423i | 0.694365 | + | 0.400892i | ||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | −3.50000 | + | 2.59808i | −0.179546 | + | 0.133278i | ||||
\(381\) | −22.5000 | − | 12.9904i | −1.15271 | − | 0.665517i | ||||
\(382\) | −0.500000 | + | 0.866025i | −0.0255822 | + | 0.0443097i | ||||
\(383\) | −6.50000 | + | 11.2583i | −0.332134 | + | 0.575274i | −0.982930 | − | 0.183979i | \(-0.941102\pi\) |
0.650796 | + | 0.759253i | \(0.274435\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 15.0000 | 0.764471 | ||||||||
\(386\) | 4.50000 | − | 7.79423i | 0.229044 | − | 0.396716i | ||||
\(387\) | 24.0000 | 1.21999 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 4.50000 | + | 7.79423i | 0.228159 | + | 0.395183i | 0.957263 | − | 0.289220i | \(-0.0933960\pi\) |
−0.729103 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(390\) | −3.00000 | − | 1.73205i | −0.151911 | − | 0.0877058i | ||||
\(391\) | −12.0000 | − | 20.7846i | −0.606866 | − | 1.05112i | ||||
\(392\) | −1.00000 | − | 1.73205i | −0.0505076 | − | 0.0874818i | ||||
\(393\) | −22.5000 | − | 12.9904i | −1.13497 | − | 0.655278i | ||||
\(394\) | 2.00000 | 0.100759 | ||||||||
\(395\) | −2.00000 | + | 3.46410i | −0.100631 | + | 0.174298i | ||||
\(396\) | 7.50000 | − | 12.9904i | 0.376889 | − | 0.652791i | ||||
\(397\) | −17.5000 | − | 30.3109i | −0.878300 | − | 1.52126i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
−0.0250943 | − | 0.999685i | \(-0.507989\pi\) | |||||||
\(398\) | 3.50000 | − | 6.06218i | 0.175439 | − | 0.303870i | ||||
\(399\) | 13.5000 | + | 18.1865i | 0.675845 | + | 0.910465i | ||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | −15.5000 | + | 26.8468i | −0.774033 | + | 1.34066i | 0.161303 | + | 0.986905i | \(0.448430\pi\) |
−0.935336 | + | 0.353760i | \(0.884903\pi\) | |||||||
\(402\) | − | 20.7846i | − | 1.03664i | ||||||
\(403\) | −7.00000 | − | 12.1244i | −0.348695 | − | 0.603957i | ||||
\(404\) | −5.50000 | − | 9.52628i | −0.273635 | − | 0.473950i | ||||
\(405\) | 4.50000 | − | 7.79423i | 0.223607 | − | 0.387298i | ||||
\(406\) | 15.0000 | 0.744438 | ||||||||
\(407\) | −25.0000 | + | 43.3013i | −1.23920 | + | 2.14636i | ||||
\(408\) | −4.50000 | + | 2.59808i | −0.222783 | + | 0.128624i | ||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 3.50000 | + | 6.06218i | 0.172853 | + | 0.299390i | ||||
\(411\) | −28.5000 | + | 16.4545i | −1.40580 | + | 0.811640i | ||||
\(412\) | −7.50000 | − | 12.9904i | −0.369498 | − | 0.639990i | ||||
\(413\) | −4.50000 | − | 7.79423i | −0.221431 | − | 0.383529i | ||||
\(414\) | −24.0000 | −1.17954 | ||||||||
\(415\) | 4.50000 | + | 7.79423i | 0.220896 | + | 0.382604i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 20.7846i | 1.01783i | ||||||||
\(418\) | 17.5000 | − | 12.9904i | 0.855953 | − | 0.635380i | ||||
\(419\) | 4.50000 | + | 7.79423i | 0.219839 | + | 0.380773i | 0.954759 | − | 0.297382i | \(-0.0961133\pi\) |
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(420\) | −4.50000 | + | 2.59808i | −0.219578 | + | 0.126773i | ||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | −4.50000 | + | 7.79423i | −0.219057 | + | 0.379417i | ||||
\(423\) | −1.50000 | − | 2.59808i | −0.0729325 | − | 0.126323i | ||||
\(424\) | −5.50000 | + | 9.52628i | −0.267104 | + | 0.462637i | ||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | 1.50000 | − | 0.866025i | 0.0726752 | − | 0.0419591i | ||||
\(427\) | 3.00000 | 0.145180 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 15.0000 | + | 8.66025i | 0.724207 | + | 0.418121i | ||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | 1.50000 | − | 2.59808i | 0.0722525 | − | 0.125145i | −0.827636 | − | 0.561266i | \(-0.810315\pi\) |
0.899888 | + | 0.436121i | \(0.143648\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | 18.5000 | − | 32.0429i | 0.889053 | − | 1.53989i | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) |
0.840996 | − | 0.541041i | \(-0.181970\pi\) | |||||||
\(434\) | −21.0000 | −1.00803 | ||||||||
\(435\) | − | 8.66025i | − | 0.415227i | ||||||
\(436\) | 4.50000 | + | 7.79423i | 0.215511 | + | 0.373276i | ||||
\(437\) | −32.0000 | − | 13.8564i | −1.53077 | − | 0.662842i | ||||
\(438\) | −4.50000 | + | 2.59808i | −0.215018 | + | 0.124141i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 2.50000 | + | 4.33013i | 0.119183 | + | 0.206431i | ||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | −3.00000 | − | 5.19615i | −0.142695 | − | 0.247156i | ||||
\(443\) | −15.5000 | − | 26.8468i | −0.736427 | − | 1.27553i | −0.954094 | − | 0.299506i | \(-0.903178\pi\) |
0.217667 | − | 0.976023i | \(-0.430155\pi\) | |||||||
\(444\) | − | 17.3205i | − | 0.821995i | ||||||
\(445\) | 7.50000 | + | 12.9904i | 0.355534 | + | 0.615803i | ||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | 4.50000 | + | 2.59808i | 0.212843 | + | 0.122885i | ||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | −6.00000 | − | 10.3923i | −0.282843 | − | 0.489898i | ||||
\(451\) | −17.5000 | − | 30.3109i | −0.824043 | − | 1.42728i | ||||
\(452\) | 0.500000 | + | 0.866025i | 0.0235180 | + | 0.0407344i | ||||
\(453\) | 7.50000 | + | 4.33013i | 0.352381 | + | 0.203447i | ||||
\(454\) | 5.50000 | − | 9.52628i | 0.258128 | − | 0.447090i | ||||
\(455\) | −3.00000 | − | 5.19615i | −0.140642 | − | 0.243599i | ||||
\(456\) | −3.00000 | + | 6.92820i | −0.140488 | + | 0.324443i | ||||
\(457\) | 6.50000 | − | 11.2583i | 0.304057 | − | 0.526642i | −0.672994 | − | 0.739648i | \(-0.734992\pi\) |
0.977051 | + | 0.213006i | \(0.0683253\pi\) | |||||||
\(458\) | 6.50000 | + | 11.2583i | 0.303725 | + | 0.526067i | ||||
\(459\) | 13.5000 | − | 7.79423i | 0.630126 | − | 0.363803i | ||||
\(460\) | 4.00000 | − | 6.92820i | 0.186501 | − | 0.323029i | ||||
\(461\) | 26.0000 | 1.21094 | 0.605470 | − | 0.795868i | \(-0.292985\pi\) | ||||
0.605470 | + | 0.795868i | \(0.292985\pi\) | |||||||
\(462\) | 22.5000 | − | 12.9904i | 1.04679 | − | 0.604367i | ||||
\(463\) | 14.5000 | + | 25.1147i | 0.673872 | + | 1.16718i | 0.976797 | + | 0.214166i | \(0.0687035\pi\) |
−0.302925 | + | 0.953014i | \(0.597963\pi\) | |||||||
\(464\) | 2.50000 | + | 4.33013i | 0.116060 | + | 0.201021i | ||||
\(465\) | 12.1244i | 0.562254i | ||||||||
\(466\) | −7.50000 | − | 12.9904i | −0.347431 | − | 0.601768i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | 18.0000 | − | 31.1769i | 0.831163 | − | 1.43962i | ||||
\(470\) | 1.00000 | 0.0461266 | ||||||||
\(471\) | −25.5000 | − | 14.7224i | −1.17498 | − | 0.678374i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | 20.0000 | − | 34.6410i | 0.919601 | − | 1.59280i | ||||
\(474\) | 6.92820i | 0.318223i | ||||||||
\(475\) | −2.00000 | − | 17.3205i | −0.0917663 | − | 0.794719i | ||||
\(476\) | −9.00000 | −0.412514 | ||||||||
\(477\) | 16.5000 | − | 28.5788i | 0.755483 | − | 1.30854i | ||||
\(478\) | −13.5000 | − | 23.3827i | −0.617476 | − | 1.06950i | ||||
\(479\) | 8.50000 | + | 14.7224i | 0.388375 | + | 0.672685i | 0.992231 | − | 0.124408i | \(-0.0397032\pi\) |
−0.603856 | + | 0.797093i | \(0.706370\pi\) | |||||||
\(480\) | −1.50000 | − | 0.866025i | −0.0684653 | − | 0.0395285i | ||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | 8.50000 | + | 14.7224i | 0.387164 | + | 0.670588i | ||||
\(483\) | −36.0000 | − | 20.7846i | −1.63806 | − | 0.945732i | ||||
\(484\) | −7.00000 | − | 12.1244i | −0.318182 | − | 0.551107i | ||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 40.0000 | 1.81257 | 0.906287 | − | 0.422664i | \(-0.138905\pi\) | ||||
0.906287 | + | 0.422664i | \(0.138905\pi\) | |||||||
\(488\) | 0.500000 | + | 0.866025i | 0.0226339 | + | 0.0392031i | ||||
\(489\) | 6.92820i | 0.313304i | ||||||||
\(490\) | −2.00000 | −0.0903508 | ||||||||
\(491\) | 9.50000 | − | 16.4545i | 0.428729 | − | 0.742580i | −0.568032 | − | 0.823007i | \(-0.692295\pi\) |
0.996761 | + | 0.0804264i | \(0.0256282\pi\) | |||||||
\(492\) | 10.5000 | + | 6.06218i | 0.473377 | + | 0.273304i | ||||
\(493\) | 7.50000 | − | 12.9904i | 0.337783 | − | 0.585057i | ||||
\(494\) | −8.00000 | − | 3.46410i | −0.359937 | − | 0.155857i | ||||
\(495\) | −7.50000 | − | 12.9904i | −0.337100 | − | 0.583874i | ||||
\(496\) | −3.50000 | − | 6.06218i | −0.157155 | − | 0.272200i | ||||
\(497\) | 3.00000 | 0.134568 | ||||||||
\(498\) | 13.5000 | + | 7.79423i | 0.604949 | + | 0.349268i | ||||
\(499\) | 5.50000 | − | 9.52628i | 0.246214 | − | 0.426455i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.962472 | + | 0.271380i | \(0.0874801\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | 20.7846i | 0.928588i | ||||||||
\(502\) | −2.50000 | + | 4.33013i | −0.111580 | + | 0.193263i | ||||
\(503\) | −16.5000 | + | 28.5788i | −0.735699 | + | 1.27427i | 0.218718 | + | 0.975788i | \(0.429813\pi\) |
−0.954416 | + | 0.298479i | \(0.903521\pi\) | |||||||
\(504\) | −4.50000 | + | 7.79423i | −0.200446 | + | 0.347183i | ||||
\(505\) | −11.0000 | −0.489494 | ||||||||
\(506\) | −20.0000 | + | 34.6410i | −0.889108 | + | 1.53998i | ||||
\(507\) | 15.5885i | 0.692308i | ||||||||
\(508\) | 7.50000 | − | 12.9904i | 0.332759 | − | 0.576355i | ||||
\(509\) | 42.0000 | 1.86162 | 0.930809 | − | 0.365507i | \(-0.119104\pi\) | ||||
0.930809 | + | 0.365507i | \(0.119104\pi\) | |||||||
\(510\) | 5.19615i | 0.230089i | ||||||||
\(511\) | −9.00000 | −0.398137 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.00000 | − | 20.7846i | 0.397360 | − | 0.917663i | ||||
\(514\) | 14.0000 | 0.617514 | ||||||||
\(515\) | −15.0000 | −0.660979 | ||||||||
\(516\) | 13.8564i | 0.609994i | ||||||||
\(517\) | −5.00000 | −0.219900 | ||||||||
\(518\) | 15.0000 | − | 25.9808i | 0.659062 | − | 1.14153i | ||||
\(519\) | 10.3923i | 0.456172i | ||||||||
\(520\) | 1.00000 | − | 1.73205i | 0.0438529 | − | 0.0759555i | ||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | −7.50000 | − | 12.9904i | −0.328266 | − | 0.568574i | ||||
\(523\) | −14.5000 | + | 25.1147i | −0.634041 | + | 1.09819i | 0.352677 | + | 0.935745i | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | 7.50000 | − | 12.9904i | 0.327639 | − | 0.567487i | ||||
\(525\) | − | 20.7846i | − | 0.907115i | ||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −10.5000 | + | 18.1865i | −0.457387 | + | 0.792218i | ||||
\(528\) | 7.50000 | + | 4.33013i | 0.326396 | + | 0.188445i | ||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 5.50000 | + | 9.52628i | 0.238905 | + | 0.413795i | ||||
\(531\) | −4.50000 | + | 7.79423i | −0.195283 | + | 0.338241i | ||||
\(532\) | −10.5000 | + | 7.79423i | −0.455233 | + | 0.337923i | ||||
\(533\) | −7.00000 | + | 12.1244i | −0.303204 | + | 0.525164i | ||||
\(534\) | 22.5000 | + | 12.9904i | 0.973670 | + | 0.562149i | ||||
\(535\) | −2.00000 | + | 3.46410i | −0.0864675 | + | 0.149766i | ||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | − | 20.7846i | − | 0.896922i | ||||||
\(538\) | −1.50000 | − | 2.59808i | −0.0646696 | − | 0.112011i | ||||
\(539\) | 10.0000 | 0.430730 | ||||||||
\(540\) | 4.50000 | + | 2.59808i | 0.193649 | + | 0.111803i | ||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | −3.50000 | − | 6.06218i | −0.150338 | − | 0.260393i | ||||
\(543\) | 28.5000 | + | 16.4545i | 1.22305 | + | 0.706129i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | −9.00000 | − | 5.19615i | −0.385164 | − | 0.222375i | ||||
\(547\) | 2.50000 | + | 4.33013i | 0.106892 | + | 0.185143i | 0.914510 | − | 0.404564i | \(-0.132577\pi\) |
−0.807617 | + | 0.589707i | \(0.799243\pi\) | |||||||
\(548\) | −9.50000 | − | 16.4545i | −0.405820 | − | 0.702901i | ||||
\(549\) | −1.50000 | − | 2.59808i | −0.0640184 | − | 0.110883i | ||||
\(550\) | −20.0000 | −0.852803 | ||||||||
\(551\) | −2.50000 | − | 21.6506i | −0.106504 | − | 0.922348i | ||||
\(552\) | − | 13.8564i | − | 0.589768i | ||||||
\(553\) | −6.00000 | + | 10.3923i | −0.255146 | + | 0.441926i | ||||
\(554\) | −9.50000 | + | 16.4545i | −0.403616 | + | 0.699084i | ||||
\(555\) | −15.0000 | − | 8.66025i | −0.636715 | − | 0.367607i | ||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | 8.50000 | − | 14.7224i | 0.360157 | − | 0.623809i | −0.627830 | − | 0.778351i | \(-0.716057\pi\) |
0.987986 | + | 0.154541i | \(0.0493899\pi\) | |||||||
\(558\) | 10.5000 | + | 18.1865i | 0.444500 | + | 0.769897i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | −1.50000 | − | 2.59808i | −0.0633866 | − | 0.109789i | ||||
\(561\) | − | 25.9808i | − | 1.09691i | ||||||
\(562\) | 2.50000 | + | 4.33013i | 0.105456 | + | 0.182655i | ||||
\(563\) | 10.5000 | + | 18.1865i | 0.442522 | + | 0.766471i | 0.997876 | − | 0.0651433i | \(-0.0207504\pi\) |
−0.555354 | + | 0.831614i | \(0.687417\pi\) | |||||||
\(564\) | 1.50000 | − | 0.866025i | 0.0631614 | − | 0.0364662i | ||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | 1.50000 | − | 2.59808i | 0.0630497 | − | 0.109205i | ||||
\(567\) | 13.5000 | − | 23.3827i | 0.566947 | − | 0.981981i | ||||
\(568\) | 0.500000 | + | 0.866025i | 0.0209795 | + | 0.0363376i | ||||
\(569\) | 20.5000 | − | 35.5070i | 0.859405 | − | 1.48853i | −0.0130929 | − | 0.999914i | \(-0.504168\pi\) |
0.872498 | − | 0.488618i | \(-0.162499\pi\) | |||||||
\(570\) | 4.50000 | + | 6.06218i | 0.188484 | + | 0.253917i | ||||
\(571\) | −5.50000 | − | 9.52628i | −0.230168 | − | 0.398662i | 0.727690 | − | 0.685907i | \(-0.240594\pi\) |
−0.957857 | + | 0.287244i | \(0.907261\pi\) | |||||||
\(572\) | −5.00000 | + | 8.66025i | −0.209061 | + | 0.362103i | ||||
\(573\) | 1.50000 | + | 0.866025i | 0.0626634 | + | 0.0361787i | ||||
\(574\) | 10.5000 | + | 18.1865i | 0.438262 | + | 0.759091i | ||||
\(575\) | 16.0000 | + | 27.7128i | 0.667246 | + | 1.15570i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | −13.5000 | − | 7.79423i | −0.561041 | − | 0.323917i | ||||
\(580\) | 5.00000 | 0.207614 | ||||||||
\(581\) | 13.5000 | + | 23.3827i | 0.560074 | + | 0.970077i | ||||
\(582\) | 3.46410i | 0.143592i | ||||||||
\(583\) | −27.5000 | − | 47.6314i | −1.13893 | − | 1.97269i | ||||
\(584\) | −1.50000 | − | 2.59808i | −0.0620704 | − | 0.107509i | ||||
\(585\) | −3.00000 | + | 5.19615i | −0.124035 | + | 0.214834i | ||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −3.00000 | + | 1.73205i | −0.123718 | + | 0.0714286i | ||||
\(589\) | 3.50000 | + | 30.3109i | 0.144215 | + | 1.24894i | ||||
\(590\) | −1.50000 | − | 2.59808i | −0.0617540 | − | 0.106961i | ||||
\(591\) | − | 3.46410i | − | 0.142494i | ||||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | 20.5000 | − | 35.5070i | 0.841834 | − | 1.45810i | −0.0465084 | − | 0.998918i | \(-0.514809\pi\) |
0.888342 | − | 0.459182i | \(-0.151857\pi\) | |||||||
\(594\) | −22.5000 | − | 12.9904i | −0.923186 | − | 0.533002i | ||||
\(595\) | −4.50000 | + | 7.79423i | −0.184482 | + | 0.319532i | ||||
\(596\) | −1.50000 | + | 2.59808i | −0.0614424 | + | 0.106421i | ||||
\(597\) | −10.5000 | − | 6.06218i | −0.429736 | − | 0.248108i | ||||
\(598\) | 16.0000 | 0.654289 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 6.00000 | − | 3.46410i | 0.244949 | − | 0.141421i | ||||
\(601\) | 2.50000 | − | 4.33013i | 0.101977 | − | 0.176630i | −0.810522 | − | 0.585708i | \(-0.800816\pi\) |
0.912499 | + | 0.409079i | \(0.134150\pi\) | |||||||
\(602\) | −12.0000 | + | 20.7846i | −0.489083 | + | 0.847117i | ||||
\(603\) | −36.0000 | −1.46603 | ||||||||
\(604\) | −2.50000 | + | 4.33013i | −0.101724 | + | 0.176190i | ||||
\(605\) | −14.0000 | −0.569181 | ||||||||
\(606\) | −16.5000 | + | 9.52628i | −0.670267 | + | 0.386979i | ||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | −4.00000 | − | 1.73205i | −0.162221 | − | 0.0702439i | ||||
\(609\) | − | 25.9808i | − | 1.05279i | ||||||
\(610\) | 1.00000 | 0.0404888 | ||||||||
\(611\) | 1.00000 | + | 1.73205i | 0.0404557 | + | 0.0700713i | ||||
\(612\) | 4.50000 | + | 7.79423i | 0.181902 | + | 0.315063i | ||||
\(613\) | −9.50000 | − | 16.4545i | −0.383701 | − | 0.664590i | 0.607887 | − | 0.794024i | \(-0.292017\pi\) |
−0.991588 | + | 0.129433i | \(0.958684\pi\) | |||||||
\(614\) | 16.5000 | + | 28.5788i | 0.665886 | + | 1.15335i | ||||
\(615\) | 10.5000 | − | 6.06218i | 0.423401 | − | 0.244451i | ||||
\(616\) | 7.50000 | + | 12.9904i | 0.302184 | + | 0.523397i | ||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | −22.5000 | + | 12.9904i | −0.905083 | + | 0.522550i | ||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | −7.00000 | −0.281127 | ||||||||
\(621\) | 41.5692i | 1.66812i | ||||||||
\(622\) | −3.50000 | − | 6.06218i | −0.140337 | − | 0.243071i | ||||
\(623\) | 22.5000 | + | 38.9711i | 0.901443 | + | 1.56135i | ||||
\(624\) | − | 3.46410i | − | 0.138675i | ||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0.500000 | + | 0.866025i | 0.0199840 | + | 0.0346133i | ||||
\(627\) | −22.5000 | − | 30.3109i | −0.898563 | − | 1.21050i | ||||
\(628\) | 8.50000 | − | 14.7224i | 0.339187 | − | 0.587489i | ||||
\(629\) | −15.0000 | − | 25.9808i | −0.598089 | − | 1.03592i | ||||
\(630\) | 4.50000 | + | 7.79423i | 0.179284 | + | 0.310530i | ||||
\(631\) | 21.5000 | − | 37.2391i | 0.855901 | − | 1.48246i | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) |
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 13.5000 | + | 7.79423i | 0.536577 | + | 0.309793i | ||||
\(634\) | −1.50000 | − | 2.59808i | −0.0595726 | − | 0.103183i | ||||
\(635\) | −7.50000 | − | 12.9904i | −0.297628 | − | 0.515508i | ||||
\(636\) | 16.5000 | + | 9.52628i | 0.654268 | + | 0.377742i | ||||
\(637\) | −2.00000 | − | 3.46410i | −0.0792429 | − | 0.137253i | ||||
\(638\) | −25.0000 | −0.989759 | ||||||||
\(639\) | −1.50000 | − | 2.59808i | −0.0593391 | − | 0.102778i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 6.92820i | 0.273434i | ||||||||
\(643\) | −24.5000 | + | 42.4352i | −0.966186 | + | 1.67348i | −0.259791 | + | 0.965665i | \(0.583654\pi\) |
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(644\) | 12.0000 | − | 20.7846i | 0.472866 | − | 0.819028i | ||||
\(645\) | 12.0000 | + | 6.92820i | 0.472500 | + | 0.272798i | ||||
\(646\) | 1.50000 | + | 12.9904i | 0.0590167 | + | 0.511100i | ||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 7.50000 | + | 12.9904i | 0.294401 | + | 0.509917i | ||||
\(650\) | 4.00000 | + | 6.92820i | 0.156893 | + | 0.271746i | ||||
\(651\) | 36.3731i | 1.42557i | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | 13.5000 | − | 7.79423i | 0.527892 | − | 0.304778i | ||||
\(655\) | −7.50000 | − | 12.9904i | −0.293049 | − | 0.507576i | ||||
\(656\) | −3.50000 | + | 6.06218i | −0.136652 | + | 0.236688i | ||||
\(657\) | 4.50000 | + | 7.79423i | 0.175562 | + | 0.304082i | ||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | −11.5000 | − | 19.9186i | −0.447976 | − | 0.775918i | 0.550278 | − | 0.834982i | \(-0.314522\pi\) |
−0.998254 | + | 0.0590638i | \(0.981188\pi\) | |||||||
\(660\) | 7.50000 | − | 4.33013i | 0.291937 | − | 0.168550i | ||||
\(661\) | 10.0000 | 0.388955 | 0.194477 | − | 0.980907i | \(-0.437699\pi\) | ||||
0.194477 | + | 0.980907i | \(0.437699\pi\) | |||||||
\(662\) | −14.5000 | + | 25.1147i | −0.563559 | + | 0.976112i | ||||
\(663\) | −9.00000 | + | 5.19615i | −0.349531 | + | 0.201802i | ||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | 1.50000 | + | 12.9904i | 0.0581675 | + | 0.503745i | ||||
\(666\) | −30.0000 | −1.16248 | ||||||||
\(667\) | 20.0000 | + | 34.6410i | 0.774403 | + | 1.34131i | ||||
\(668\) | −12.0000 | −0.464294 | ||||||||
\(669\) | 27.7128i | 1.07144i | ||||||||
\(670\) | 6.00000 | − | 10.3923i | 0.231800 | − | 0.401490i | ||||
\(671\) | −5.00000 | −0.193023 | ||||||||
\(672\) | −4.50000 | − | 2.59808i | −0.173591 | − | 0.100223i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | 2.50000 | − | 4.33013i | 0.0962964 | − | 0.166790i | ||||
\(675\) | −18.0000 | + | 10.3923i | −0.692820 | + | 0.400000i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −3.50000 | + | 6.06218i | −0.134516 | + | 0.232988i | −0.925412 | − | 0.378962i | \(-0.876281\pi\) |
0.790897 | + | 0.611950i | \(0.209615\pi\) | |||||||
\(678\) | 1.50000 | − | 0.866025i | 0.0576072 | − | 0.0332595i | ||||
\(679\) | −3.00000 | + | 5.19615i | −0.115129 | + | 0.199410i | ||||
\(680\) | −3.00000 | −0.115045 | ||||||||
\(681\) | −16.5000 | − | 9.52628i | −0.632281 | − | 0.365048i | ||||
\(682\) | 35.0000 | 1.34022 | ||||||||
\(683\) | −44.0000 | −1.68361 | −0.841807 | − | 0.539779i | \(-0.818508\pi\) | ||||
−0.841807 | + | 0.539779i | \(0.818508\pi\) | |||||||
\(684\) | 12.0000 | + | 5.19615i | 0.458831 | + | 0.198680i | ||||
\(685\) | −19.0000 | −0.725953 | ||||||||
\(686\) | 15.0000 | 0.572703 | ||||||||
\(687\) | 19.5000 | − | 11.2583i | 0.743971 | − | 0.429532i | ||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | −11.0000 | + | 19.0526i | −0.419067 | + | 0.725845i | ||||
\(690\) | −12.0000 | − | 6.92820i | −0.456832 | − | 0.263752i | ||||
\(691\) | −10.5000 | + | 18.1865i | −0.399439 | + | 0.691848i | −0.993657 | − | 0.112456i | \(-0.964128\pi\) |
0.594218 | + | 0.804304i | \(0.297462\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −22.5000 | − | 38.9711i | −0.854704 | − | 1.48039i | ||||
\(694\) | 11.5000 | − | 19.9186i | 0.436534 | − | 0.756099i | ||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | 7.50000 | − | 4.33013i | 0.284287 | − | 0.164133i | ||||
\(697\) | 21.0000 | 0.795432 | ||||||||
\(698\) | 2.50000 | − | 4.33013i | 0.0946264 | − | 0.163898i | ||||
\(699\) | −22.5000 | + | 12.9904i | −0.851028 | + | 0.491341i | ||||
\(700\) | 12.0000 | 0.453557 | ||||||||
\(701\) | 0.500000 | + | 0.866025i | 0.0188847 | + | 0.0327093i | 0.875313 | − | 0.483556i | \(-0.160655\pi\) |
−0.856429 | + | 0.516265i | \(0.827322\pi\) | |||||||
\(702\) | 10.3923i | 0.392232i | ||||||||
\(703\) | −40.0000 | − | 17.3205i | −1.50863 | − | 0.653255i | ||||
\(704\) | −2.50000 | + | 4.33013i | −0.0942223 | + | 0.163198i | ||||
\(705\) | − | 1.73205i | − | 0.0652328i | ||||||
\(706\) | −1.50000 | + | 2.59808i | −0.0564532 | + | 0.0977799i | ||||
\(707\) | −33.0000 | −1.24109 | ||||||||
\(708\) | −4.50000 | − | 2.59808i | −0.169120 | − | 0.0976417i | ||||
\(709\) | −1.50000 | − | 2.59808i | −0.0563337 | − | 0.0975728i | 0.836483 | − | 0.547992i | \(-0.184608\pi\) |
−0.892817 | + | 0.450420i | \(0.851274\pi\) | |||||||
\(710\) | 1.00000 | 0.0375293 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | −7.50000 | + | 12.9904i | −0.281074 | + | 0.486835i | ||||
\(713\) | −28.0000 | − | 48.4974i | −1.04861 | − | 1.81624i | ||||
\(714\) | 15.5885i | 0.583383i | ||||||||
\(715\) | 5.00000 | + | 8.66025i | 0.186989 | + | 0.323875i | ||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | −40.5000 | + | 23.3827i | −1.51250 | + | 0.873242i | ||||
\(718\) | −7.50000 | − | 12.9904i | −0.279898 | − | 0.484797i | ||||
\(719\) | −3.50000 | − | 6.06218i | −0.130528 | − | 0.226081i | 0.793352 | − | 0.608763i | \(-0.208334\pi\) |
−0.923880 | + | 0.382682i | \(0.875001\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | −45.0000 | −1.67589 | ||||||||
\(722\) | 13.0000 | + | 13.8564i | 0.483810 | + | 0.515682i | ||||
\(723\) | 25.5000 | − | 14.7224i | 0.948355 | − | 0.547533i | ||||
\(724\) | −9.50000 | + | 16.4545i | −0.353065 | + | 0.611526i | ||||
\(725\) | −10.0000 | + | 17.3205i | −0.371391 | + | 0.643268i | ||||
\(726\) | −21.0000 | + | 12.1244i | −0.779383 | + | 0.449977i | ||||
\(727\) | 40.0000 | 1.48352 | 0.741759 | − | 0.670667i | \(-0.233992\pi\) | ||||
0.741759 | + | 0.670667i | \(0.233992\pi\) | |||||||
\(728\) | 3.00000 | − | 5.19615i | 0.111187 | − | 0.192582i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −3.00000 | −0.111035 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 1.50000 | − | 0.866025i | 0.0554416 | − | 0.0320092i | ||||
\(733\) | −7.50000 | − | 12.9904i | −0.277019 | − | 0.479811i | 0.693624 | − | 0.720338i | \(-0.256013\pi\) |
−0.970642 | + | 0.240527i | \(0.922680\pi\) | |||||||
\(734\) | 8.50000 | + | 14.7224i | 0.313741 | + | 0.543415i | ||||
\(735\) | 3.46410i | 0.127775i | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | −30.0000 | + | 51.9615i | −1.10506 | + | 1.91403i | ||||
\(738\) | 10.5000 | − | 18.1865i | 0.386510 | − | 0.669456i | ||||
\(739\) | 18.5000 | + | 32.0429i | 0.680534 | + | 1.17872i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 5.00000 | − | 8.66025i | 0.183804 | − | 0.318357i | ||||
\(741\) | −6.00000 | + | 13.8564i | −0.220416 | + | 0.509028i | ||||
\(742\) | 16.5000 | + | 28.5788i | 0.605734 | + | 1.04916i | ||||
\(743\) | 9.50000 | − | 16.4545i | 0.348521 | − | 0.603656i | −0.637466 | − | 0.770479i | \(-0.720017\pi\) |
0.985987 | + | 0.166822i | \(0.0533506\pi\) | |||||||
\(744\) | −10.5000 | + | 6.06218i | −0.384949 | + | 0.222250i | ||||
\(745\) | 1.50000 | + | 2.59808i | 0.0549557 | + | 0.0951861i | ||||
\(746\) | 12.5000 | + | 21.6506i | 0.457658 | + | 0.792686i | ||||
\(747\) | 13.5000 | − | 23.3827i | 0.493939 | − | 0.855528i | ||||
\(748\) | 15.0000 | 0.548454 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | − | 15.5885i | − | 0.569210i | ||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | 0.500000 | + | 0.866025i | 0.0182331 | + | 0.0315807i | ||||
\(753\) | 7.50000 | + | 4.33013i | 0.273315 | + | 0.157799i | ||||
\(754\) | 5.00000 | + | 8.66025i | 0.182089 | + | 0.315388i | ||||
\(755\) | 2.50000 | + | 4.33013i | 0.0909843 | + | 0.157589i | ||||
\(756\) | 13.5000 | + | 7.79423i | 0.490990 | + | 0.283473i | ||||
\(757\) | 14.5000 | + | 25.1147i | 0.527011 | + | 0.912811i | 0.999505 | + | 0.0314762i | \(0.0100208\pi\) |
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | −12.0000 | −0.435860 | ||||||||
\(759\) | 60.0000 | + | 34.6410i | 2.17786 | + | 1.25739i | ||||
\(760\) | −3.50000 | + | 2.59808i | −0.126958 | + | 0.0942421i | ||||
\(761\) | −7.50000 | − | 12.9904i | −0.271875 | − | 0.470901i | 0.697467 | − | 0.716617i | \(-0.254310\pi\) |
−0.969342 | + | 0.245716i | \(0.920977\pi\) | |||||||
\(762\) | −22.5000 | − | 12.9904i | −0.815089 | − | 0.470592i | ||||
\(763\) | 27.0000 | 0.977466 | ||||||||
\(764\) | −0.500000 | + | 0.866025i | −0.0180894 | + | 0.0313317i | ||||
\(765\) | 9.00000 | 0.325396 | ||||||||
\(766\) | −6.50000 | + | 11.2583i | −0.234855 | + | 0.406780i | ||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | − | 1.73205i | − | 0.0625000i | ||||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 15.0000 | 0.540562 | ||||||||
\(771\) | − | 24.2487i | − | 0.873296i | ||||||
\(772\) | 4.50000 | − | 7.79423i | 0.161959 | − | 0.280520i | ||||
\(773\) | 10.5000 | − | 18.1865i | 0.377659 | − | 0.654124i | −0.613062 | − | 0.790034i | \(-0.710063\pi\) |
0.990721 | + | 0.135910i | \(0.0433959\pi\) | |||||||
\(774\) | 24.0000 | 0.862662 | ||||||||
\(775\) | 14.0000 | − | 24.2487i | 0.502895 | − | 0.871039i | ||||
\(776\) | −2.00000 | −0.0717958 | ||||||||
\(777\) | −45.0000 | − | 25.9808i | −1.61437 | − | 0.932055i | ||||
\(778\) | 4.50000 | + | 7.79423i | 0.161333 | + | 0.279437i | ||||
\(779\) | 24.5000 | − | 18.1865i | 0.877804 | − | 0.651600i | ||||
\(780\) | −3.00000 | − | 1.73205i | −0.107417 | − | 0.0620174i | ||||
\(781\) | −5.00000 | −0.178914 | ||||||||
\(782\) | −12.0000 | − | 20.7846i | −0.429119 | − | 0.743256i | ||||
\(783\) | −22.5000 | + | 12.9904i | −0.804084 | + | 0.464238i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | −8.50000 | − | 14.7224i | −0.303378 | − | 0.525466i | ||||
\(786\) | −22.5000 | − | 12.9904i | −0.802548 | − | 0.463352i | ||||
\(787\) | −3.50000 | − | 6.06218i | −0.124762 | − | 0.216093i | 0.796878 | − | 0.604140i | \(-0.206483\pi\) |
−0.921640 | + | 0.388047i | \(0.873150\pi\) | |||||||
\(788\) | 2.00000 | 0.0712470 | ||||||||
\(789\) | 41.5692i | 1.47990i | ||||||||
\(790\) | −2.00000 | + | 3.46410i | −0.0711568 | + | 0.123247i | ||||
\(791\) | 3.00000 | 0.106668 | ||||||||
\(792\) | 7.50000 | − | 12.9904i | 0.266501 | − | 0.461593i | ||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | −17.5000 | − | 30.3109i | −0.621052 | − | 1.07569i | ||||
\(795\) | 16.5000 | − | 9.52628i | 0.585195 | − | 0.337862i | ||||
\(796\) | 3.50000 | − | 6.06218i | 0.124054 | − | 0.214868i | ||||
\(797\) | 4.50000 | + | 7.79423i | 0.159398 | + | 0.276086i | 0.934652 | − | 0.355564i | \(-0.115711\pi\) |
−0.775254 | + | 0.631650i | \(0.782378\pi\) | |||||||
\(798\) | 13.5000 | + | 18.1865i | 0.477895 | + | 0.643796i | ||||
\(799\) | 1.50000 | − | 2.59808i | 0.0530662 | − | 0.0919133i | ||||
\(800\) | 2.00000 | + | 3.46410i | 0.0707107 | + | 0.122474i | ||||
\(801\) | 22.5000 | − | 38.9711i | 0.794998 | − | 1.37698i | ||||
\(802\) | −15.5000 | + | 26.8468i | −0.547324 | + | 0.947993i | ||||
\(803\) | 15.0000 | 0.529339 | ||||||||
\(804\) | − | 20.7846i | − | 0.733017i | ||||||
\(805\) | −12.0000 | − | 20.7846i | −0.422944 | − | 0.732561i | ||||
\(806\) | −7.00000 | − | 12.1244i | −0.246564 | − | 0.427062i | ||||
\(807\) | −4.50000 | + | 2.59808i | −0.158408 | + | 0.0914566i | ||||
\(808\) | −5.50000 | − | 9.52628i | −0.193489 | − | 0.335133i | ||||
\(809\) | 54.0000 | 1.89854 | 0.949269 | − | 0.314464i | \(-0.101825\pi\) | ||||
0.949269 | + | 0.314464i | \(0.101825\pi\) | |||||||
\(810\) | 4.50000 | − | 7.79423i | 0.158114 | − | 0.273861i | ||||
\(811\) | −16.5000 | + | 28.5788i | −0.579393 | + | 1.00354i | 0.416156 | + | 0.909293i | \(0.363377\pi\) |
−0.995549 | + | 0.0942453i | \(0.969956\pi\) | |||||||
\(812\) | 15.0000 | 0.526397 | ||||||||
\(813\) | −10.5000 | + | 6.06218i | −0.368251 | + | 0.212610i | ||||
\(814\) | −25.0000 | + | 43.3013i | −0.876250 | + | 1.51771i | ||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | −4.50000 | + | 2.59808i | −0.157532 | + | 0.0909509i | ||||
\(817\) | 32.0000 | + | 13.8564i | 1.11954 | + | 0.484774i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −9.00000 | + | 15.5885i | −0.314485 | + | 0.544705i | ||||
\(820\) | 3.50000 | + | 6.06218i | 0.122225 | + | 0.211700i | ||||
\(821\) | −1.50000 | − | 2.59808i | −0.0523504 | − | 0.0906735i | 0.838663 | − | 0.544651i | \(-0.183338\pi\) |
−0.891013 | + | 0.453978i | \(0.850005\pi\) | |||||||
\(822\) | −28.5000 | + | 16.4545i | −0.994052 | + | 0.573916i | ||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −7.50000 | − | 12.9904i | −0.261275 | − | 0.452541i | ||||
\(825\) | 34.6410i | 1.20605i | ||||||||
\(826\) | −4.50000 | − | 7.79423i | −0.156575 | − | 0.271196i | ||||
\(827\) | −20.5000 | + | 35.5070i | −0.712855 | + | 1.23470i | 0.250926 | + | 0.968006i | \(0.419265\pi\) |
−0.963781 | + | 0.266695i | \(0.914068\pi\) | |||||||
\(828\) | −24.0000 | −0.834058 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 4.50000 | + | 7.79423i | 0.156197 | + | 0.270542i | ||||
\(831\) | 28.5000 | + | 16.4545i | 0.988654 | + | 0.570800i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −3.00000 | + | 5.19615i | −0.103944 | + | 0.180036i | ||||
\(834\) | 20.7846i | 0.719712i | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | 17.5000 | − | 12.9904i | 0.605250 | − | 0.449282i | ||||
\(837\) | 31.5000 | − | 18.1865i | 1.08880 | − | 0.628619i | ||||
\(838\) | 4.50000 | + | 7.79423i | 0.155450 | + | 0.269247i | ||||
\(839\) | −16.0000 | −0.552381 | −0.276191 | − | 0.961103i | \(-0.589072\pi\) | ||||
−0.276191 | + | 0.961103i | \(0.589072\pi\) | |||||||
\(840\) | −4.50000 | + | 2.59808i | −0.155265 | + | 0.0896421i | ||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | −22.0000 | −0.758170 | ||||||||
\(843\) | 7.50000 | − | 4.33013i | 0.258314 | − | 0.149137i | ||||
\(844\) | −4.50000 | + | 7.79423i | −0.154896 | + | 0.268288i | ||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | −1.50000 | − | 2.59808i | −0.0515711 | − | 0.0893237i | ||||
\(847\) | −42.0000 | −1.44314 | ||||||||
\(848\) | −5.50000 | + | 9.52628i | −0.188871 | + | 0.327134i | ||||
\(849\) | −4.50000 | − | 2.59808i | −0.154440 | − | 0.0891657i | ||||
\(850\) | 6.00000 | − | 10.3923i | 0.205798 | − | 0.356453i | ||||
\(851\) | 80.0000 | 2.74236 | ||||||||
\(852\) | 1.50000 | − | 0.866025i | 0.0513892 | − | 0.0296695i | ||||
\(853\) | −30.0000 | −1.02718 | −0.513590 | − | 0.858036i | \(-0.671685\pi\) | ||||
−0.513590 | + | 0.858036i | \(0.671685\pi\) | |||||||
\(854\) | 3.00000 | 0.102658 | ||||||||
\(855\) | 10.5000 | − | 7.79423i | 0.359092 | − | 0.266557i | ||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | −42.0000 | −1.43469 | −0.717346 | − | 0.696717i | \(-0.754643\pi\) | ||||
−0.717346 | + | 0.696717i | \(0.754643\pi\) | |||||||
\(858\) | 15.0000 | + | 8.66025i | 0.512092 | + | 0.295656i | ||||
\(859\) | 28.0000 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(860\) | −4.00000 | + | 6.92820i | −0.136399 | + | 0.236250i | ||||
\(861\) | 31.5000 | − | 18.1865i | 1.07352 | − | 0.619795i | ||||
\(862\) | 1.50000 | − | 2.59808i | 0.0510902 | − | 0.0884908i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | −3.00000 | + | 5.19615i | −0.102003 | + | 0.176674i | ||||
\(866\) | 18.5000 | − | 32.0429i | 0.628656 | − | 1.08886i | ||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | −21.0000 | −0.712786 | ||||||||
\(869\) | 10.0000 | − | 17.3205i | 0.339227 | − | 0.587558i | ||||
\(870\) | − | 8.66025i | − | 0.293610i | ||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 4.50000 | + | 7.79423i | 0.152389 | + | 0.263946i | ||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | −32.0000 | − | 13.8564i | −1.08242 | − | 0.468700i | ||||
\(875\) | 13.5000 | − | 23.3827i | 0.456383 | − | 0.790479i | ||||
\(876\) | −4.50000 | + | 2.59808i | −0.152041 | + | 0.0877809i | ||||
\(877\) | 26.5000 | − | 45.8993i | 0.894841 | − | 1.54991i | 0.0608407 | − | 0.998147i | \(-0.480622\pi\) |
0.834001 | − | 0.551763i | \(-0.186045\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 13.5000 | − | 7.79423i | 0.455344 | − | 0.262893i | ||||
\(880\) | 2.50000 | + | 4.33013i | 0.0842750 | + | 0.145969i | ||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 3.00000 | + | 5.19615i | 0.101015 | + | 0.174964i | ||||
\(883\) | −6.50000 | + | 11.2583i | −0.218742 | + | 0.378873i | −0.954424 | − | 0.298455i | \(-0.903529\pi\) |
0.735681 | + | 0.677328i | \(0.236862\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | −4.50000 | + | 2.59808i | −0.151266 | + | 0.0873334i | ||||
\(886\) | −15.5000 | − | 26.8468i | −0.520733 | − | 0.901935i | ||||
\(887\) | −56.0000 | −1.88030 | −0.940148 | − | 0.340766i | \(-0.889313\pi\) | ||||
−0.940148 | + | 0.340766i | \(0.889313\pi\) | |||||||
\(888\) | − | 17.3205i | − | 0.581238i | ||||||
\(889\) | −22.5000 | − | 38.9711i | −0.754626 | − | 1.30705i | ||||
\(890\) | 7.50000 | + | 12.9904i | 0.251401 | + | 0.435439i | ||||
\(891\) | −22.5000 | + | 38.9711i | −0.753778 | + | 1.30558i | ||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | −0.500000 | − | 4.33013i | −0.0167319 | − | 0.144902i | ||||
\(894\) | 4.50000 | + | 2.59808i | 0.150503 | + | 0.0868927i | ||||
\(895\) | 6.00000 | − | 10.3923i | 0.200558 | − | 0.347376i | ||||
\(896\) | 1.50000 | − | 2.59808i | 0.0501115 | − | 0.0867956i | ||||
\(897\) | − | 27.7128i | − | 0.925304i | ||||||
\(898\) | −26.0000 | −0.867631 | ||||||||
\(899\) | 17.5000 | − | 30.3109i | 0.583658 | − | 1.01092i | ||||
\(900\) | −6.00000 | − | 10.3923i | −0.200000 | − | 0.346410i | ||||
\(901\) | 33.0000 | 1.09939 | ||||||||
\(902\) | −17.5000 | − | 30.3109i | −0.582686 | − | 1.00924i | ||||
\(903\) | 36.0000 | + | 20.7846i | 1.19800 | + | 0.691669i | ||||
\(904\) | 0.500000 | + | 0.866025i | 0.0166298 | + | 0.0288036i | ||||
\(905\) | 9.50000 | + | 16.4545i | 0.315791 | + | 0.546966i | ||||
\(906\) | 7.50000 | + | 4.33013i | 0.249171 | + | 0.143859i | ||||
\(907\) | 32.0000 | 1.06254 | 0.531271 | − | 0.847202i | \(-0.321714\pi\) | ||||
0.531271 | + | 0.847202i | \(0.321714\pi\) | |||||||
\(908\) | 5.50000 | − | 9.52628i | 0.182524 | − | 0.316141i | ||||
\(909\) | 16.5000 | + | 28.5788i | 0.547270 | + | 0.947900i | ||||
\(910\) | −3.00000 | − | 5.19615i | −0.0994490 | − | 0.172251i | ||||
\(911\) | 7.50000 | − | 12.9904i | 0.248486 | − | 0.430391i | −0.714620 | − | 0.699513i | \(-0.753400\pi\) |
0.963106 | + | 0.269122i | \(0.0867336\pi\) | |||||||
\(912\) | −3.00000 | + | 6.92820i | −0.0993399 | + | 0.229416i | ||||
\(913\) | −22.5000 | − | 38.9711i | −0.744641 | − | 1.28976i | ||||
\(914\) | 6.50000 | − | 11.2583i | 0.215001 | − | 0.372392i | ||||
\(915\) | − | 1.73205i | − | 0.0572598i | ||||||
\(916\) | 6.50000 | + | 11.2583i | 0.214766 | + | 0.371986i | ||||
\(917\) | −22.5000 | − | 38.9711i | −0.743015 | − | 1.28694i | ||||
\(918\) | 13.5000 | − | 7.79423i | 0.445566 | − | 0.257248i | ||||
\(919\) | −4.00000 | −0.131948 | −0.0659739 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659739 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(920\) | 4.00000 | − | 6.92820i | 0.131876 | − | 0.228416i | ||||
\(921\) | 49.5000 | − | 28.5788i | 1.63108 | − | 0.941705i | ||||
\(922\) | 26.0000 | 0.856264 | ||||||||
\(923\) | 1.00000 | + | 1.73205i | 0.0329154 | + | 0.0570111i | ||||
\(924\) | 22.5000 | − | 12.9904i | 0.740196 | − | 0.427352i | ||||
\(925\) | 20.0000 | + | 34.6410i | 0.657596 | + | 1.13899i | ||||
\(926\) | 14.5000 | + | 25.1147i | 0.476500 | + | 0.825321i | ||||
\(927\) | 22.5000 | + | 38.9711i | 0.738997 | + | 1.27998i | ||||
\(928\) | 2.50000 | + | 4.33013i | 0.0820665 | + | 0.142143i | ||||
\(929\) | 50.0000 | 1.64045 | 0.820223 | − | 0.572043i | \(-0.193849\pi\) | ||||
0.820223 | + | 0.572043i | \(0.193849\pi\) | |||||||
\(930\) | 12.1244i | 0.397573i | ||||||||
\(931\) | 1.00000 | + | 8.66025i | 0.0327737 | + | 0.283828i | ||||
\(932\) | −7.50000 | − | 12.9904i | −0.245671 | − | 0.425514i | ||||
\(933\) | −10.5000 | + | 6.06218i | −0.343755 | + | 0.198467i | ||||
\(934\) | −8.00000 | −0.261768 | ||||||||
\(935\) | 7.50000 | − | 12.9904i | 0.245276 | − | 0.424831i | ||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | −23.5000 | + | 40.7032i | −0.767712 | + | 1.32972i | 0.171089 | + | 0.985255i | \(0.445271\pi\) |
−0.938801 | + | 0.344460i | \(0.888062\pi\) | |||||||
\(938\) | 18.0000 | − | 31.1769i | 0.587721 | − | 1.01796i | ||||
\(939\) | 1.50000 | − | 0.866025i | 0.0489506 | − | 0.0282617i | ||||
\(940\) | 1.00000 | 0.0326164 | ||||||||
\(941\) | 10.0000 | 0.325991 | 0.162995 | − | 0.986627i | \(-0.447884\pi\) | ||||
0.162995 | + | 0.986627i | \(0.447884\pi\) | |||||||
\(942\) | −25.5000 | − | 14.7224i | −0.830835 | − | 0.479683i | ||||
\(943\) | −28.0000 | + | 48.4974i | −0.911805 | + | 1.57929i | ||||
\(944\) | 1.50000 | − | 2.59808i | 0.0488208 | − | 0.0845602i | ||||
\(945\) | 13.5000 | − | 7.79423i | 0.439155 | − | 0.253546i | ||||
\(946\) | 20.0000 | − | 34.6410i | 0.650256 | − | 1.12628i | ||||
\(947\) | −60.0000 | −1.94974 | −0.974869 | − | 0.222779i | \(-0.928487\pi\) | ||||
−0.974869 | + | 0.222779i | \(0.928487\pi\) | |||||||
\(948\) | 6.92820i | 0.225018i | ||||||||
\(949\) | −3.00000 | − | 5.19615i | −0.0973841 | − | 0.168674i | ||||
\(950\) | −2.00000 | − | 17.3205i | −0.0648886 | − | 0.561951i | ||||
\(951\) | −4.50000 | + | 2.59808i | −0.145922 | + | 0.0842484i | ||||
\(952\) | −9.00000 | −0.291692 | ||||||||
\(953\) | 0.500000 | + | 0.866025i | 0.0161966 | + | 0.0280533i | 0.874010 | − | 0.485908i | \(-0.161511\pi\) |
−0.857814 | + | 0.513961i | \(0.828178\pi\) | |||||||
\(954\) | 16.5000 | − | 28.5788i | 0.534207 | − | 0.925274i | ||||
\(955\) | 0.500000 | + | 0.866025i | 0.0161796 | + | 0.0280239i | ||||
\(956\) | −13.5000 | − | 23.3827i | −0.436621 | − | 0.756250i | ||||
\(957\) | 43.3013i | 1.39973i | ||||||||
\(958\) | 8.50000 | + | 14.7224i | 0.274623 | + | 0.475660i | ||||
\(959\) | −57.0000 | −1.84063 | ||||||||
\(960\) | −1.50000 | − | 0.866025i | −0.0484123 | − | 0.0279508i | ||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 20.0000 | 0.644826 | ||||||||
\(963\) | 12.0000 | 0.386695 | ||||||||
\(964\) | 8.50000 | + | 14.7224i | 0.273767 | + | 0.474178i | ||||
\(965\) | −4.50000 | − | 7.79423i | −0.144860 | − | 0.250905i | ||||
\(966\) | −36.0000 | − | 20.7846i | −1.15828 | − | 0.668734i | ||||
\(967\) | −4.50000 | + | 7.79423i | −0.144710 | + | 0.250645i | −0.929265 | − | 0.369414i | \(-0.879558\pi\) |
0.784555 | + | 0.620060i | \(0.212892\pi\) | |||||||
\(968\) | −7.00000 | − | 12.1244i | −0.224989 | − | 0.389692i | ||||
\(969\) | 22.5000 | − | 2.59808i | 0.722804 | − | 0.0834622i | ||||
\(970\) | −1.00000 | + | 1.73205i | −0.0321081 | + | 0.0556128i | ||||
\(971\) | −17.5000 | − | 30.3109i | −0.561602 | − | 0.972723i | −0.997357 | − | 0.0726575i | \(-0.976852\pi\) |
0.435755 | − | 0.900065i | \(-0.356481\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | −18.0000 | + | 31.1769i | −0.577054 | + | 0.999486i | ||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | 12.0000 | − | 6.92820i | 0.384308 | − | 0.221880i | ||||
\(976\) | 0.500000 | + | 0.866025i | 0.0160046 | + | 0.0277208i | ||||
\(977\) | −5.50000 | − | 9.52628i | −0.175961 | − | 0.304773i | 0.764533 | − | 0.644585i | \(-0.222970\pi\) |
−0.940493 | + | 0.339812i | \(0.889636\pi\) | |||||||
\(978\) | 6.92820i | 0.221540i | ||||||||
\(979\) | −37.5000 | − | 64.9519i | −1.19851 | − | 2.07587i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −13.5000 | − | 23.3827i | −0.431022 | − | 0.746552i | ||||
\(982\) | 9.50000 | − | 16.4545i | 0.303157 | − | 0.525084i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 10.5000 | + | 6.06218i | 0.334728 | + | 0.193255i | ||||
\(985\) | 1.00000 | − | 1.73205i | 0.0318626 | − | 0.0551877i | ||||
\(986\) | 7.50000 | − | 12.9904i | 0.238849 | − | 0.413698i | ||||
\(987\) | − | 5.19615i | − | 0.165395i | ||||||
\(988\) | −8.00000 | − | 3.46410i | −0.254514 | − | 0.110208i | ||||
\(989\) | −64.0000 | −2.03508 | ||||||||
\(990\) | −7.50000 | − | 12.9904i | −0.238366 | − | 0.412861i | ||||
\(991\) | −9.50000 | − | 16.4545i | −0.301777 | − | 0.522694i | 0.674761 | − | 0.738036i | \(-0.264247\pi\) |
−0.976539 | + | 0.215342i | \(0.930913\pi\) | |||||||
\(992\) | −3.50000 | − | 6.06218i | −0.111125 | − | 0.192474i | ||||
\(993\) | 43.5000 | + | 25.1147i | 1.38043 | + | 0.796992i | ||||
\(994\) | 3.00000 | 0.0951542 | ||||||||
\(995\) | −3.50000 | − | 6.06218i | −0.110957 | − | 0.192184i | ||||
\(996\) | 13.5000 | + | 7.79423i | 0.427764 | + | 0.246970i | ||||
\(997\) | 8.50000 | + | 14.7224i | 0.269198 | + | 0.466264i | 0.968655 | − | 0.248410i | \(-0.0799082\pi\) |
−0.699457 | + | 0.714675i | \(0.746575\pi\) | |||||||
\(998\) | 5.50000 | − | 9.52628i | 0.174099 | − | 0.301549i | ||||
\(999\) | 51.9615i | 1.64399i |
(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 | 342.2.f.c.7.1 | ✓ | 2 | |
3.2 | odd | 2 | 1026.2.f.a.235.1 | 2 | |||
9.4 | even | 3 | 342.2.h.a.121.1 | yes | 2 | ||
9.5 | odd | 6 | 1026.2.h.d.577.1 | 2 | |||
19.11 | even | 3 | 342.2.h.a.277.1 | yes | 2 | ||
57.11 | odd | 6 | 1026.2.h.d.505.1 | 2 | |||
171.49 | even | 3 | inner | 342.2.f.c.49.1 | yes | 2 | |
171.68 | odd | 6 | 1026.2.f.a.847.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.f.c.7.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
342.2.f.c.49.1 | yes | 2 | 171.49 | even | 3 | inner | |
342.2.h.a.121.1 | yes | 2 | 9.4 | even | 3 | ||
342.2.h.a.277.1 | yes | 2 | 19.11 | even | 3 | ||
1026.2.f.a.235.1 | 2 | 3.2 | odd | 2 | |||
1026.2.f.a.847.1 | 2 | 171.68 | odd | 6 | |||
1026.2.h.d.505.1 | 2 | 57.11 | odd | 6 | |||
1026.2.h.d.577.1 | 2 | 9.5 | odd | 6 |