Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.f.199.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.59808 | − | 3.23205i | 1.68788 | − | 0.974500i | 0.731748 | − | 0.681575i | \(-0.238705\pi\) |
0.956136 | − | 0.292925i | \(-0.0946285\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −3.46410 | + | 1.00000i | −0.960769 | + | 0.277350i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.46410 | − | 3.73205i | −1.48297 | − | 0.856191i | −0.483154 | − | 0.875536i | \(-0.660509\pi\) |
−0.999813 | + | 0.0193444i | \(0.993842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | 5.59808 | + | 3.23205i | 1.19351 | + | 0.689076i | ||||
\(23\) | 3.23205 | − | 1.86603i | 0.673929 | − | 0.389093i | −0.123635 | − | 0.992328i | \(-0.539455\pi\) |
0.797564 | + | 0.603235i | \(0.206122\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.59808 | − | 2.50000i | −0.509525 | − | 0.490290i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.00000 | − | 1.73205i | −0.188982 | − | 0.327327i | ||||
\(29\) | 0.133975 | + | 0.232051i | 0.0248785 | + | 0.0430908i | 0.878197 | − | 0.478300i | \(-0.158747\pi\) |
−0.853318 | + | 0.521391i | \(0.825413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73205i | 0.311086i | 0.987829 | + | 0.155543i | \(0.0497126\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.23205 | + | 5.59808i | −0.562628 | + | 0.974500i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −4.59808 | − | 7.96410i | −0.755919 | − | 1.30929i | −0.944916 | − | 0.327313i | \(-0.893857\pi\) |
0.188997 | − | 0.981978i | \(-0.439476\pi\) | |||||||
\(38\) | − | 7.46410i | − | 1.21084i | ||||||
\(39\) | 2.50000 | − | 2.59808i | 0.400320 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.73205 | − | 1.00000i | 0.270501 | − | 0.156174i | −0.358614 | − | 0.933486i | \(-0.616751\pi\) |
0.629115 | + | 0.777312i | \(0.283417\pi\) | |||||||
\(42\) | 1.73205 | − | 1.00000i | 0.267261 | − | 0.154303i | ||||
\(43\) | −10.3301 | − | 5.96410i | −1.57533 | − | 0.909517i | −0.995498 | − | 0.0947805i | \(-0.969785\pi\) |
−0.579831 | − | 0.814736i | \(-0.696882\pi\) | |||||||
\(44\) | 6.46410i | 0.974500i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.23205 | + | 1.86603i | 0.476540 | + | 0.275130i | ||||
\(47\) | 3.53590 | 0.515764 | 0.257882 | − | 0.966176i | \(-0.416975\pi\) | ||||
0.257882 | + | 0.966176i | \(0.416975\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0.866025 | − | 3.50000i | 0.120096 | − | 0.485363i | ||||
\(53\) | 0.928203i | 0.127499i | 0.997966 | + | 0.0637493i | \(0.0203058\pi\) | ||||
−0.997966 | + | 0.0637493i | \(0.979694\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 7.46410 | 0.988644 | ||||||||
\(58\) | −0.133975 | + | 0.232051i | −0.0175917 | + | 0.0304698i | ||||
\(59\) | −7.33013 | − | 4.23205i | −0.954301 | − | 0.550966i | −0.0598868 | − | 0.998205i | \(-0.519074\pi\) |
−0.894414 | + | 0.447239i | \(0.852407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19615 | − | 9.00000i | 0.665299 | − | 1.15233i | −0.313905 | − | 0.949454i | \(-0.601637\pi\) |
0.979204 | − | 0.202878i | \(-0.0650293\pi\) | |||||||
\(62\) | −1.50000 | + | 0.866025i | −0.190500 | + | 0.109985i | ||||
\(63\) | 1.00000 | + | 1.73205i | 0.125988 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.46410 | −0.795676 | ||||||||
\(67\) | 5.73205 | + | 9.92820i | 0.700281 | + | 1.21292i | 0.968368 | + | 0.249528i | \(0.0802755\pi\) |
−0.268086 | + | 0.963395i | \(0.586391\pi\) | |||||||
\(68\) | 3.46410 | − | 2.00000i | 0.420084 | − | 0.242536i | ||||
\(69\) | −1.86603 | + | 3.23205i | −0.224643 | + | 0.389093i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7321 | − | 6.19615i | −1.27366 | − | 0.735348i | −0.297985 | − | 0.954570i | \(-0.596315\pi\) |
−0.975675 | + | 0.219222i | \(0.929648\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 4.59808 | − | 7.96410i | 0.534516 | − | 0.925808i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.46410 | − | 3.73205i | 0.741483 | − | 0.428096i | ||||
\(77\) | 12.9282i | 1.47331i | ||||||||
\(78\) | 3.50000 | + | 0.866025i | 0.396297 | + | 0.0980581i | ||||
\(79\) | 13.9282 | 1.56705 | 0.783523 | − | 0.621363i | \(-0.213421\pi\) | ||||
0.783523 | + | 0.621363i | \(0.213421\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.73205 | + | 1.00000i | 0.191273 | + | 0.110432i | ||||
\(83\) | 8.92820 | 0.979998 | 0.489999 | − | 0.871723i | \(-0.336997\pi\) | ||||
0.489999 | + | 0.871723i | \(0.336997\pi\) | |||||||
\(84\) | 1.73205 | + | 1.00000i | 0.188982 | + | 0.109109i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 11.9282i | − | 1.28625i | ||||||
\(87\) | −0.232051 | − | 0.133975i | −0.0248785 | − | 0.0143636i | ||||
\(88\) | −5.59808 | + | 3.23205i | −0.596757 | + | 0.344538i | ||||
\(89\) | 0.464102 | − | 0.267949i | 0.0491947 | − | 0.0284026i | −0.475201 | − | 0.879877i | \(-0.657625\pi\) |
0.524396 | + | 0.851475i | \(0.324291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.73205 | − | 7.00000i | 0.181568 | − | 0.733799i | ||||
\(92\) | 3.73205i | 0.389093i | ||||||||
\(93\) | −0.866025 | − | 1.50000i | −0.0898027 | − | 0.155543i | ||||
\(94\) | 1.76795 | + | 3.06218i | 0.182350 | + | 0.315840i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 0.267949 | − | 0.464102i | 0.0272061 | − | 0.0471224i | −0.852102 | − | 0.523376i | \(-0.824672\pi\) |
0.879308 | + | 0.476254i | \(0.158006\pi\) | |||||||
\(98\) | −1.50000 | + | 2.59808i | −0.151523 | + | 0.262445i | ||||
\(99\) | − | 6.46410i | − | 0.649667i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.46410 | − | 2.53590i | −0.145684 | − | 0.252331i | 0.783944 | − | 0.620831i | \(-0.213205\pi\) |
−0.929628 | + | 0.368500i | \(0.879871\pi\) | |||||||
\(102\) | 2.00000 | + | 3.46410i | 0.198030 | + | 0.342997i | ||||
\(103\) | − | 11.8564i | − | 1.16825i | −0.811665 | − | 0.584123i | \(-0.801438\pi\) | ||
0.811665 | − | 0.584123i | \(-0.198562\pi\) | |||||||
\(104\) | 3.46410 | − | 1.00000i | 0.339683 | − | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.803848 | + | 0.464102i | −0.0780766 | + | 0.0450775i | ||||
\(107\) | 6.80385 | − | 3.92820i | 0.657753 | − | 0.379754i | −0.133667 | − | 0.991026i | \(-0.542675\pi\) |
0.791420 | + | 0.611273i | \(0.209342\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | − | 15.8564i | − | 1.51877i | −0.650643 | − | 0.759384i | \(-0.725500\pi\) | ||
0.650643 | − | 0.759384i | \(-0.274500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.96410 | + | 4.59808i | 0.755919 | + | 0.436430i | ||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −0.696152 | − | 0.401924i | −0.0654885 | − | 0.0378098i | 0.466898 | − | 0.884311i | \(-0.345371\pi\) |
−0.532387 | + | 0.846501i | \(0.678705\pi\) | |||||||
\(114\) | 3.73205 | + | 6.46410i | 0.349539 | + | 0.605419i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.267949 | −0.0248785 | ||||||||
\(117\) | −0.866025 | + | 3.50000i | −0.0800641 | + | 0.323575i | ||||
\(118\) | − | 8.46410i | − | 0.779184i | ||||||
\(119\) | 6.92820 | − | 4.00000i | 0.635107 | − | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3923 | − | 26.6603i | 1.39930 | − | 2.42366i | ||||
\(122\) | 10.3923 | 0.940875 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | −1.50000 | − | 0.866025i | −0.134704 | − | 0.0777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.00000 | + | 1.73205i | −0.0890871 | + | 0.154303i | ||||
\(127\) | 4.26795 | − | 2.46410i | 0.378719 | − | 0.218654i | −0.298542 | − | 0.954397i | \(-0.596500\pi\) |
0.677261 | + | 0.735743i | \(0.263167\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 11.9282 | 1.05022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6603 | −1.63035 | −0.815177 | − | 0.579212i | \(-0.803360\pi\) | ||||
−0.815177 | + | 0.579212i | \(0.803360\pi\) | |||||||
\(132\) | −3.23205 | − | 5.59808i | −0.281314 | − | 0.487250i | ||||
\(133\) | 12.9282 | − | 7.46410i | 1.12102 | − | 0.647220i | ||||
\(134\) | −5.73205 | + | 9.92820i | −0.495174 | + | 0.857666i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | −1.23205 | + | 2.13397i | −0.105261 | + | 0.182318i | −0.913845 | − | 0.406063i | \(-0.866901\pi\) |
0.808584 | + | 0.588381i | \(0.200235\pi\) | |||||||
\(138\) | −3.73205 | −0.317693 | ||||||||
\(139\) | −6.46410 | + | 11.1962i | −0.548278 | + | 0.949645i | 0.450115 | + | 0.892971i | \(0.351383\pi\) |
−0.998393 | + | 0.0566745i | \(0.981950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06218 | + | 1.76795i | −0.257882 | + | 0.148888i | ||||
\(142\) | − | 12.3923i | − | 1.03994i | ||||||
\(143\) | −16.1603 | + | 16.7942i | −1.35139 | + | 1.40440i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.00000 | + | 1.73205i | 0.0827606 | + | 0.143346i | ||||
\(147\) | −2.59808 | − | 1.50000i | −0.214286 | − | 0.123718i | ||||
\(148\) | 9.19615 | 0.755919 | ||||||||
\(149\) | 11.7224 | + | 6.76795i | 0.960339 | + | 0.554452i | 0.896277 | − | 0.443494i | \(-0.146261\pi\) |
0.0640617 | + | 0.997946i | \(0.479595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3923i | 0.845714i | 0.906196 | + | 0.422857i | \(0.138973\pi\) | ||||
−0.906196 | + | 0.422857i | \(0.861027\pi\) | |||||||
\(152\) | 6.46410 | + | 3.73205i | 0.524308 | + | 0.302709i | ||||
\(153\) | −3.46410 | + | 2.00000i | −0.280056 | + | 0.161690i | ||||
\(154\) | −11.1962 | + | 6.46410i | −0.902212 | + | 0.520892i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | + | 3.46410i | 0.0800641 | + | 0.277350i | ||||
\(157\) | 5.00000i | 0.399043i | 0.979893 | + | 0.199522i | \(0.0639388\pi\) | ||||
−0.979893 | + | 0.199522i | \(0.936061\pi\) | |||||||
\(158\) | 6.96410 | + | 12.0622i | 0.554034 | + | 0.959615i | ||||
\(159\) | −0.464102 | − | 0.803848i | −0.0368057 | − | 0.0637493i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.46410i | 0.588254i | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −7.52628 | + | 13.0359i | −0.589504 | + | 1.02105i | 0.404794 | + | 0.914408i | \(0.367343\pi\) |
−0.994297 | + | 0.106642i | \(0.965990\pi\) | |||||||
\(164\) | 2.00000i | 0.156174i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.46410 | + | 7.73205i | 0.346481 | + | 0.600124i | ||||
\(167\) | −8.16025 | − | 14.1340i | −0.631459 | − | 1.09372i | −0.987254 | − | 0.159155i | \(-0.949123\pi\) |
0.355794 | − | 0.934564i | \(-0.384210\pi\) | |||||||
\(168\) | 2.00000i | 0.154303i | ||||||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.46410 | + | 3.73205i | −0.494322 | + | 0.285397i | ||||
\(172\) | 10.3301 | − | 5.96410i | 0.787665 | − | 0.454758i | ||||
\(173\) | −9.46410 | − | 5.46410i | −0.719542 | − | 0.415428i | 0.0950419 | − | 0.995473i | \(-0.469701\pi\) |
−0.814584 | + | 0.580045i | \(0.803035\pi\) | |||||||
\(174\) | − | 0.267949i | − | 0.0203132i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.59808 | − | 3.23205i | −0.421971 | − | 0.243625i | ||||
\(177\) | 8.46410 | 0.636201 | ||||||||
\(178\) | 0.464102 | + | 0.267949i | 0.0347859 | + | 0.0200836i | ||||
\(179\) | −9.86603 | − | 17.0885i | −0.737421 | − | 1.27725i | −0.953653 | − | 0.300909i | \(-0.902710\pi\) |
0.216231 | − | 0.976342i | \(-0.430623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.92820 | −0.217652 | −0.108826 | − | 0.994061i | \(-0.534709\pi\) | ||||
−0.108826 | + | 0.994061i | \(0.534709\pi\) | |||||||
\(182\) | 6.92820 | − | 2.00000i | 0.513553 | − | 0.148250i | ||||
\(183\) | 10.3923i | 0.768221i | ||||||||
\(184\) | −3.23205 | + | 1.86603i | −0.238270 | + | 0.137565i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.866025 | − | 1.50000i | 0.0635001 | − | 0.109985i | ||||
\(187\) | −25.8564 | −1.89081 | ||||||||
\(188\) | −1.76795 | + | 3.06218i | −0.128941 | + | 0.223332i | ||||
\(189\) | −1.73205 | − | 1.00000i | −0.125988 | − | 0.0727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.7321 | + | 18.5885i | −0.776544 | + | 1.34501i | 0.157379 | + | 0.987538i | \(0.449696\pi\) |
−0.933923 | + | 0.357475i | \(0.883638\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 5.66025 | + | 9.80385i | 0.407434 | + | 0.705696i | 0.994601 | − | 0.103769i | \(-0.0330903\pi\) |
−0.587167 | + | 0.809466i | \(0.699757\pi\) | |||||||
\(194\) | 0.535898 | 0.0384753 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −2.19615 | − | 3.80385i | −0.156469 | − | 0.271013i | 0.777124 | − | 0.629348i | \(-0.216678\pi\) |
−0.933593 | + | 0.358335i | \(0.883345\pi\) | |||||||
\(198\) | 5.59808 | − | 3.23205i | 0.397838 | − | 0.229692i | ||||
\(199\) | −2.53590 | + | 4.39230i | −0.179765 | + | 0.311362i | −0.941800 | − | 0.336174i | \(-0.890867\pi\) |
0.762035 | + | 0.647536i | \(0.224200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.92820 | − | 5.73205i | −0.700281 | − | 0.404308i | ||||
\(202\) | 1.46410 | − | 2.53590i | 0.103014 | − | 0.178425i | ||||
\(203\) | −0.535898 | −0.0376127 | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.2679 | − | 5.92820i | 0.715402 | − | 0.413037i | ||||
\(207\) | − | 3.73205i | − | 0.259395i | ||||||
\(208\) | 2.59808 | + | 2.50000i | 0.180144 | + | 0.173344i | ||||
\(209\) | −48.2487 | −3.33743 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.66025 | + | 9.80385i | 0.389668 | + | 0.674925i | 0.992405 | − | 0.123015i | \(-0.0392564\pi\) |
−0.602737 | + | 0.797940i | \(0.705923\pi\) | |||||||
\(212\) | −0.803848 | − | 0.464102i | −0.0552085 | − | 0.0318746i | ||||
\(213\) | 12.3923 | 0.849107 | ||||||||
\(214\) | 6.80385 | + | 3.92820i | 0.465101 | + | 0.268526i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −3.00000 | − | 1.73205i | −0.203653 | − | 0.117579i | ||||
\(218\) | 13.7321 | − | 7.92820i | 0.930052 | − | 0.536966i | ||||
\(219\) | −1.73205 | + | 1.00000i | −0.117041 | + | 0.0675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0000 | + | 3.46410i | 0.941742 | + | 0.233021i | ||||
\(222\) | 9.19615i | 0.617205i | ||||||||
\(223\) | −10.2679 | − | 17.7846i | −0.687593 | − | 1.19095i | −0.972614 | − | 0.232424i | \(-0.925334\pi\) |
0.285022 | − | 0.958521i | \(-0.407999\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 0.803848i | − | 0.0534711i | ||||||
\(227\) | −8.19615 | + | 14.1962i | −0.543998 | + | 0.942232i | 0.454672 | + | 0.890659i | \(0.349757\pi\) |
−0.998669 | + | 0.0515725i | \(0.983577\pi\) | |||||||
\(228\) | −3.73205 | + | 6.46410i | −0.247161 | + | 0.428096i | ||||
\(229\) | − | 7.85641i | − | 0.519166i | −0.965721 | − | 0.259583i | \(-0.916415\pi\) | ||
0.965721 | − | 0.259583i | \(-0.0835851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.46410 | − | 11.1962i | −0.425307 | − | 0.736653i | ||||
\(232\) | −0.133975 | − | 0.232051i | −0.00879586 | − | 0.0152349i | ||||
\(233\) | 6.12436i | 0.401220i | 0.979671 | + | 0.200610i | \(0.0642924\pi\) | ||||
−0.979671 | + | 0.200610i | \(0.935708\pi\) | |||||||
\(234\) | −3.46410 | + | 1.00000i | −0.226455 | + | 0.0653720i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.33013 | − | 4.23205i | 0.477151 | − | 0.275483i | ||||
\(237\) | −12.0622 | + | 6.96410i | −0.783523 | + | 0.452367i | ||||
\(238\) | 6.92820 | + | 4.00000i | 0.449089 | + | 0.259281i | ||||
\(239\) | − | 16.3923i | − | 1.06033i | −0.847894 | − | 0.530165i | \(-0.822130\pi\) | ||
0.847894 | − | 0.530165i | \(-0.177870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3564 | + | 8.86603i | 0.989193 | + | 0.571111i | 0.905033 | − | 0.425341i | \(-0.139846\pi\) |
0.0841601 | + | 0.996452i | \(0.473179\pi\) | |||||||
\(242\) | 30.7846 | 1.97891 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 5.19615 | + | 9.00000i | 0.332650 | + | 0.576166i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 26.1244 | + | 6.46410i | 1.66225 | + | 0.411301i | ||||
\(248\) | − | 1.73205i | − | 0.109985i | ||||||
\(249\) | −7.73205 | + | 4.46410i | −0.489999 | + | 0.282901i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.86603 | + | 13.6244i | −0.496499 | + | 0.859962i | −0.999992 | − | 0.00403776i | \(-0.998715\pi\) |
0.503493 | + | 0.863999i | \(0.332048\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 12.0622 | − | 20.8923i | 0.758343 | − | 1.31349i | ||||
\(254\) | 4.26795 | + | 2.46410i | 0.267795 | + | 0.154611i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.62436 | − | 2.66987i | 0.288459 | − | 0.166542i | −0.348787 | − | 0.937202i | \(-0.613407\pi\) |
0.637247 | + | 0.770660i | \(0.280073\pi\) | |||||||
\(258\) | 5.96410 | + | 10.3301i | 0.371309 | + | 0.643126i | ||||
\(259\) | 18.3923 | 1.14284 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.267949 | 0.0165856 | ||||||||
\(262\) | −9.33013 | − | 16.1603i | −0.576417 | − | 0.998384i | ||||
\(263\) | 5.30385 | − | 3.06218i | 0.327049 | − | 0.188822i | −0.327481 | − | 0.944858i | \(-0.606200\pi\) |
0.654530 | + | 0.756036i | \(0.272866\pi\) | |||||||
\(264\) | 3.23205 | − | 5.59808i | 0.198919 | − | 0.344538i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.9282 | + | 7.46410i | 0.792679 | + | 0.457653i | ||||
\(267\) | −0.267949 | + | 0.464102i | −0.0163982 | + | 0.0284026i | ||||
\(268\) | −11.4641 | −0.700281 | ||||||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03590 | − | 0.598076i | 0.0629263 | − | 0.0363305i | −0.468207 | − | 0.883619i | \(-0.655100\pi\) |
0.531133 | + | 0.847288i | \(0.321766\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 2.00000 | + | 6.92820i | 0.121046 | + | 0.419314i | ||||
\(274\) | −2.46410 | −0.148862 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.86603 | − | 3.23205i | −0.112322 | − | 0.194547i | ||||
\(277\) | −3.40192 | − | 1.96410i | −0.204402 | − | 0.118011i | 0.394305 | − | 0.918980i | \(-0.370985\pi\) |
−0.598707 | + | 0.800968i | \(0.704319\pi\) | |||||||
\(278\) | −12.9282 | −0.775382 | ||||||||
\(279\) | 1.50000 | + | 0.866025i | 0.0898027 | + | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.92820i | 0.532612i | 0.963889 | + | 0.266306i | \(0.0858032\pi\) | ||||
−0.963889 | + | 0.266306i | \(0.914197\pi\) | |||||||
\(282\) | −3.06218 | − | 1.76795i | −0.182350 | − | 0.105280i | ||||
\(283\) | −8.59808 | + | 4.96410i | −0.511103 | + | 0.295085i | −0.733287 | − | 0.679920i | \(-0.762015\pi\) |
0.222184 | + | 0.975005i | \(0.428681\pi\) | |||||||
\(284\) | 10.7321 | − | 6.19615i | 0.636830 | − | 0.367674i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.6244 | − | 5.59808i | −1.33781 | − | 0.331021i | ||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.535898i | 0.0314149i | ||||||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | 15.9282 | − | 27.5885i | 0.930536 | − | 1.61173i | 0.148128 | − | 0.988968i | \(-0.452675\pi\) |
0.782408 | − | 0.622767i | \(-0.213991\pi\) | |||||||
\(294\) | − | 3.00000i | − | 0.174964i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.59808 | + | 7.96410i | 0.267258 | + | 0.462904i | ||||
\(297\) | 3.23205 | + | 5.59808i | 0.187543 | + | 0.324833i | ||||
\(298\) | 13.5359i | 0.784114i | ||||||||
\(299\) | −9.33013 | + | 9.69615i | −0.539575 | + | 0.560743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.6603 | − | 11.9282i | 1.19084 | − | 0.687530i | ||||
\(302\) | −9.00000 | + | 5.19615i | −0.517892 | + | 0.299005i | ||||
\(303\) | 2.53590 | + | 1.46410i | 0.145684 | + | 0.0841104i | ||||
\(304\) | 7.46410i | 0.428096i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.46410 | − | 2.00000i | −0.198030 | − | 0.114332i | ||||
\(307\) | −19.4641 | −1.11087 | −0.555437 | − | 0.831558i | \(-0.687449\pi\) | ||||
−0.555437 | + | 0.831558i | \(0.687449\pi\) | |||||||
\(308\) | −11.1962 | − | 6.46410i | −0.637960 | − | 0.368326i | ||||
\(309\) | 5.92820 | + | 10.2679i | 0.337244 | + | 0.584123i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3923 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(312\) | −2.50000 | + | 2.59808i | −0.141535 | + | 0.147087i | ||||
\(313\) | − | 28.0000i | − | 1.58265i | −0.611393 | − | 0.791327i | \(-0.709391\pi\) | ||
0.611393 | − | 0.791327i | \(-0.290609\pi\) | |||||||
\(314\) | −4.33013 | + | 2.50000i | −0.244363 | + | 0.141083i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.96410 | + | 12.0622i | −0.391761 | + | 0.678551i | ||||
\(317\) | −14.5359 | −0.816417 | −0.408209 | − | 0.912889i | \(-0.633846\pi\) | ||||
−0.408209 | + | 0.912889i | \(0.633846\pi\) | |||||||
\(318\) | 0.464102 | − | 0.803848i | 0.0260255 | − | 0.0450775i | ||||
\(319\) | 1.50000 | + | 0.866025i | 0.0839839 | + | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.92820 | + | 6.80385i | −0.219251 | + | 0.379754i | ||||
\(322\) | −6.46410 | + | 3.73205i | −0.360230 | + | 0.207979i | ||||
\(323\) | 14.9282 | + | 25.8564i | 0.830627 | + | 1.43869i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0526 | −0.833684 | ||||||||
\(327\) | 7.92820 | + | 13.7321i | 0.438431 | + | 0.759384i | ||||
\(328\) | −1.73205 | + | 1.00000i | −0.0956365 | + | 0.0552158i | ||||
\(329\) | −3.53590 | + | 6.12436i | −0.194940 | + | 0.337647i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5359 | − | 8.39230i | −0.798965 | − | 0.461283i | 0.0441440 | − | 0.999025i | \(-0.485944\pi\) |
−0.843109 | + | 0.537742i | \(0.819277\pi\) | |||||||
\(332\) | −4.46410 | + | 7.73205i | −0.244999 | + | 0.424351i | ||||
\(333\) | −9.19615 | −0.503946 | ||||||||
\(334\) | 8.16025 | − | 14.1340i | 0.446509 | − | 0.773377i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.73205 | + | 1.00000i | −0.0944911 | + | 0.0545545i | ||||
\(337\) | − | 9.32051i | − | 0.507720i | −0.967241 | − | 0.253860i | \(-0.918300\pi\) | ||
0.967241 | − | 0.253860i | \(-0.0817003\pi\) | |||||||
\(338\) | 11.5000 | + | 6.06218i | 0.625518 | + | 0.329739i | ||||
\(339\) | 0.803848 | 0.0436590 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.59808 | + | 9.69615i | 0.303153 | + | 0.525076i | ||||
\(342\) | −6.46410 | − | 3.73205i | −0.349539 | − | 0.201806i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 10.3301 | + | 5.96410i | 0.556963 | + | 0.321563i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 10.9282i | − | 0.587504i | ||||||
\(347\) | 1.39230 | + | 0.803848i | 0.0747428 | + | 0.0431528i | 0.536906 | − | 0.843642i | \(-0.319593\pi\) |
−0.462163 | + | 0.886795i | \(0.652926\pi\) | |||||||
\(348\) | 0.232051 | − | 0.133975i | 0.0124392 | − | 0.00718179i | ||||
\(349\) | −18.5885 | + | 10.7321i | −0.995017 | + | 0.574474i | −0.906770 | − | 0.421625i | \(-0.861460\pi\) |
−0.0882471 | + | 0.996099i | \(0.528127\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | − | 3.46410i | −0.0533761 | − | 0.184900i | ||||
\(352\) | − | 6.46410i | − | 0.344538i | ||||||
\(353\) | 1.00000 | + | 1.73205i | 0.0532246 | + | 0.0921878i | 0.891410 | − | 0.453197i | \(-0.149717\pi\) |
−0.838186 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(354\) | 4.23205 | + | 7.33013i | 0.224931 | + | 0.389592i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.535898i | 0.0284026i | ||||||||
\(357\) | −4.00000 | + | 6.92820i | −0.211702 | + | 0.366679i | ||||
\(358\) | 9.86603 | − | 17.0885i | 0.521436 | − | 0.903153i | ||||
\(359\) | 5.07180i | 0.267679i | 0.991003 | + | 0.133840i | \(0.0427307\pi\) | ||||
−0.991003 | + | 0.133840i | \(0.957269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3564 | + | 31.7942i | 0.966127 | + | 1.67338i | ||||
\(362\) | −1.46410 | − | 2.53590i | −0.0769515 | − | 0.133284i | ||||
\(363\) | 30.7846i | 1.61577i | ||||||||
\(364\) | 5.19615 | + | 5.00000i | 0.272352 | + | 0.262071i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.00000 | + | 5.19615i | −0.470438 | + | 0.271607i | ||||
\(367\) | −13.5167 | + | 7.80385i | −0.705564 | + | 0.407358i | −0.809416 | − | 0.587235i | \(-0.800216\pi\) |
0.103852 | + | 0.994593i | \(0.466883\pi\) | |||||||
\(368\) | −3.23205 | − | 1.86603i | −0.168482 | − | 0.0972733i | ||||
\(369\) | − | 2.00000i | − | 0.104116i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.60770 | − | 0.928203i | −0.0834674 | − | 0.0481899i | ||||
\(372\) | 1.73205 | 0.0898027 | ||||||||
\(373\) | 13.6699 | + | 7.89230i | 0.707799 | + | 0.408648i | 0.810246 | − | 0.586090i | \(-0.199334\pi\) |
−0.102446 | + | 0.994739i | \(0.532667\pi\) | |||||||
\(374\) | −12.9282 | − | 22.3923i | −0.668501 | − | 1.15788i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.53590 | −0.182350 | ||||||||
\(377\) | −0.696152 | − | 0.669873i | −0.0358537 | − | 0.0345002i | ||||
\(378\) | − | 2.00000i | − | 0.102869i | ||||||
\(379\) | −24.1244 | + | 13.9282i | −1.23918 | + | 0.715444i | −0.968928 | − | 0.247344i | \(-0.920442\pi\) |
−0.270257 | + | 0.962788i | \(0.587109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.46410 | + | 4.26795i | −0.126240 | + | 0.218654i | ||||
\(382\) | −21.4641 | −1.09820 | ||||||||
\(383\) | −12.6962 | + | 21.9904i | −0.648743 | + | 1.12366i | 0.334680 | + | 0.942332i | \(0.391372\pi\) |
−0.983423 | + | 0.181324i | \(0.941962\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.66025 | + | 9.80385i | −0.288099 | + | 0.499003i | ||||
\(387\) | −10.3301 | + | 5.96410i | −0.525110 | + | 0.303172i | ||||
\(388\) | 0.267949 | + | 0.464102i | 0.0136031 | + | 0.0235612i | ||||
\(389\) | 23.7321 | 1.20326 | 0.601631 | − | 0.798774i | \(-0.294518\pi\) | ||||
0.601631 | + | 0.798774i | \(0.294518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9282 | −0.754952 | ||||||||
\(392\) | −1.50000 | − | 2.59808i | −0.0757614 | − | 0.131223i | ||||
\(393\) | 16.1603 | − | 9.33013i | 0.815177 | − | 0.470643i | ||||
\(394\) | 2.19615 | − | 3.80385i | 0.110641 | − | 0.191635i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.59808 | + | 3.23205i | 0.281314 | + | 0.162417i | ||||
\(397\) | 6.06218 | − | 10.5000i | 0.304252 | − | 0.526980i | −0.672843 | − | 0.739786i | \(-0.734927\pi\) |
0.977095 | + | 0.212806i | \(0.0682602\pi\) | |||||||
\(398\) | −5.07180 | −0.254226 | ||||||||
\(399\) | −7.46410 | + | 12.9282i | −0.373672 | + | 0.647220i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.7128 | + | 16.0000i | −1.38391 | + | 0.799002i | −0.992620 | − | 0.121265i | \(-0.961305\pi\) |
−0.391292 | + | 0.920267i | \(0.627972\pi\) | |||||||
\(402\) | − | 11.4641i | − | 0.571777i | ||||||
\(403\) | −1.73205 | − | 6.00000i | −0.0862796 | − | 0.298881i | ||||
\(404\) | 2.92820 | 0.145684 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.267949 | − | 0.464102i | −0.0132981 | − | 0.0230330i | ||||
\(407\) | −51.4808 | − | 29.7224i | −2.55181 | − | 1.47329i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | −3.46410 | − | 2.00000i | −0.171289 | − | 0.0988936i | 0.411905 | − | 0.911227i | \(-0.364864\pi\) |
−0.583193 | + | 0.812333i | \(0.698197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.46410i | − | 0.121545i | ||||||
\(412\) | 10.2679 | + | 5.92820i | 0.505866 | + | 0.292062i | ||||
\(413\) | 14.6603 | − | 8.46410i | 0.721384 | − | 0.416491i | ||||
\(414\) | 3.23205 | − | 1.86603i | 0.158847 | − | 0.0917101i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.866025 | + | 3.50000i | −0.0424604 | + | 0.171602i | ||||
\(417\) | − | 12.9282i | − | 0.633097i | ||||||
\(418\) | −24.1244 | − | 41.7846i | −1.17996 | − | 2.04375i | ||||
\(419\) | 11.1962 | + | 19.3923i | 0.546968 | + | 0.947376i | 0.998480 | + | 0.0551112i | \(0.0175513\pi\) |
−0.451512 | + | 0.892265i | \(0.649115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.39230i | − | 0.214068i | −0.994255 | − | 0.107034i | \(-0.965865\pi\) | ||
0.994255 | − | 0.107034i | \(-0.0341353\pi\) | |||||||
\(422\) | −5.66025 | + | 9.80385i | −0.275537 | + | 0.477244i | ||||
\(423\) | 1.76795 | − | 3.06218i | 0.0859606 | − | 0.148888i | ||||
\(424\) | − | 0.928203i | − | 0.0450775i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.19615 | + | 10.7321i | 0.300205 | + | 0.519970i | ||||
\(427\) | 10.3923 | + | 18.0000i | 0.502919 | + | 0.871081i | ||||
\(428\) | 7.85641i | 0.379754i | ||||||||
\(429\) | 5.59808 | − | 22.6244i | 0.270278 | − | 1.09231i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.5885 | − | 14.1962i | 1.18438 | − | 0.683805i | 0.227360 | − | 0.973811i | \(-0.426991\pi\) |
0.957025 | + | 0.290006i | \(0.0936574\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | −16.7321 | − | 9.66025i | −0.804091 | − | 0.464242i | 0.0408086 | − | 0.999167i | \(-0.487007\pi\) |
−0.844900 | + | 0.534925i | \(0.820340\pi\) | |||||||
\(434\) | − | 3.46410i | − | 0.166282i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.7321 | + | 7.92820i | 0.657646 | + | 0.379692i | ||||
\(437\) | −27.8564 | −1.33255 | ||||||||
\(438\) | −1.73205 | − | 1.00000i | −0.0827606 | − | 0.0477818i | ||||
\(439\) | −8.92820 | − | 15.4641i | −0.426120 | − | 0.738061i | 0.570404 | − | 0.821364i | \(-0.306786\pi\) |
−0.996524 | + | 0.0833027i | \(0.973453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 4.00000 | + | 13.8564i | 0.190261 | + | 0.659082i | ||||
\(443\) | 16.3923i | 0.778822i | 0.921064 | + | 0.389411i | \(0.127321\pi\) | ||||
−0.921064 | + | 0.389411i | \(0.872679\pi\) | |||||||
\(444\) | −7.96410 | + | 4.59808i | −0.377960 | + | 0.218215i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.2679 | − | 17.7846i | 0.486201 | − | 0.842126i | ||||
\(447\) | −13.5359 | −0.640226 | ||||||||
\(448\) | −1.00000 | + | 1.73205i | −0.0472456 | + | 0.0818317i | ||||
\(449\) | 13.6077 | + | 7.85641i | 0.642187 | + | 0.370767i | 0.785456 | − | 0.618917i | \(-0.212428\pi\) |
−0.143270 | + | 0.989684i | \(0.545762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.46410 | − | 11.1962i | 0.304383 | − | 0.527206i | ||||
\(452\) | 0.696152 | − | 0.401924i | 0.0327443 | − | 0.0189049i | ||||
\(453\) | −5.19615 | − | 9.00000i | −0.244137 | − | 0.422857i | ||||
\(454\) | −16.3923 | −0.769329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.46410 | −0.349539 | ||||||||
\(457\) | −12.2679 | − | 21.2487i | −0.573870 | − | 0.993973i | −0.996163 | − | 0.0875134i | \(-0.972108\pi\) |
0.422293 | − | 0.906459i | \(-0.361225\pi\) | |||||||
\(458\) | 6.80385 | − | 3.92820i | 0.317923 | − | 0.183553i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.401924 | + | 0.232051i | 0.0187195 | + | 0.0108077i | 0.509331 | − | 0.860571i | \(-0.329893\pi\) |
−0.490611 | + | 0.871379i | \(0.663226\pi\) | |||||||
\(462\) | 6.46410 | − | 11.1962i | 0.300737 | − | 0.520892i | ||||
\(463\) | 7.07180 | 0.328654 | 0.164327 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164327 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(464\) | 0.133975 | − | 0.232051i | 0.00621961 | − | 0.0107727i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.30385 | + | 3.06218i | −0.245696 | + | 0.141853i | ||||
\(467\) | 15.8564i | 0.733747i | 0.930271 | + | 0.366873i | \(0.119572\pi\) | ||||
−0.930271 | + | 0.366873i | \(0.880428\pi\) | |||||||
\(468\) | −2.59808 | − | 2.50000i | −0.120096 | − | 0.115563i | ||||
\(469\) | −22.9282 | −1.05873 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.50000 | − | 4.33013i | −0.115194 | − | 0.199522i | ||||
\(472\) | 7.33013 | + | 4.23205i | 0.337396 | + | 0.194796i | ||||
\(473\) | −77.1051 | −3.54530 | ||||||||
\(474\) | −12.0622 | − | 6.96410i | −0.554034 | − | 0.319872i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.00000i | 0.366679i | ||||||||
\(477\) | 0.803848 | + | 0.464102i | 0.0368057 | + | 0.0212498i | ||||
\(478\) | 14.1962 | − | 8.19615i | 0.649317 | − | 0.374883i | ||||
\(479\) | −4.73205 | + | 2.73205i | −0.216213 | + | 0.124831i | −0.604195 | − | 0.796836i | \(-0.706505\pi\) |
0.387983 | + | 0.921667i | \(0.373172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.8923 | + | 22.9904i | 1.08940 | + | 1.04827i | ||||
\(482\) | 17.7321i | 0.807673i | ||||||||
\(483\) | −3.73205 | − | 6.46410i | −0.169814 | − | 0.294127i | ||||
\(484\) | 15.3923 | + | 26.6603i | 0.699650 | + | 1.21183i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 11.5885 | − | 20.0718i | 0.525123 | − | 0.909540i | −0.474449 | − | 0.880283i | \(-0.657353\pi\) |
0.999572 | − | 0.0292568i | \(-0.00931407\pi\) | |||||||
\(488\) | −5.19615 | + | 9.00000i | −0.235219 | + | 0.407411i | ||||
\(489\) | − | 15.0526i | − | 0.680700i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.66025 | + | 15.0000i | 0.390832 | + | 0.676941i | 0.992559 | − | 0.121761i | \(-0.0388541\pi\) |
−0.601728 | + | 0.798701i | \(0.705521\pi\) | |||||||
\(492\) | −1.00000 | − | 1.73205i | −0.0450835 | − | 0.0780869i | ||||
\(493\) | − | 1.07180i | − | 0.0482713i | ||||||
\(494\) | 7.46410 | + | 25.8564i | 0.335826 | + | 1.16333i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | − | 0.866025i | 0.0673520 | − | 0.0388857i | ||||
\(497\) | 21.4641 | − | 12.3923i | 0.962797 | − | 0.555871i | ||||
\(498\) | −7.73205 | − | 4.46410i | −0.346481 | − | 0.200041i | ||||
\(499\) | 6.53590i | 0.292587i | 0.989241 | + | 0.146293i | \(0.0467344\pi\) | ||||
−0.989241 | + | 0.146293i | \(0.953266\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.1340 | + | 8.16025i | 0.631459 | + | 0.364573i | ||||
\(502\) | −15.7321 | −0.702156 | ||||||||
\(503\) | 27.0000 | + | 15.5885i | 1.20387 | + | 0.695055i | 0.961414 | − | 0.275107i | \(-0.0887134\pi\) |
0.242457 | + | 0.970162i | \(0.422047\pi\) | |||||||
\(504\) | −1.00000 | − | 1.73205i | −0.0445435 | − | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.1244 | 1.07246 | ||||||||
\(507\) | −6.06218 | + | 11.5000i | −0.269231 | + | 0.510733i | ||||
\(508\) | 4.92820i | 0.218654i | ||||||||
\(509\) | −1.20577 | + | 0.696152i | −0.0534449 | + | 0.0308564i | −0.526484 | − | 0.850185i | \(-0.676490\pi\) |
0.473039 | + | 0.881041i | \(0.343157\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.73205 | − | 6.46410i | 0.164774 | − | 0.285397i | ||||
\(514\) | 4.62436 | + | 2.66987i | 0.203972 | + | 0.117763i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.96410 | + | 10.3301i | −0.262555 | + | 0.454758i | ||||
\(517\) | 19.7942 | − | 11.4282i | 0.870549 | − | 0.502612i | ||||
\(518\) | 9.19615 | + | 15.9282i | 0.404056 | + | 0.699845i | ||||
\(519\) | 10.9282 | 0.479695 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3205 | −0.758825 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(522\) | 0.133975 | + | 0.232051i | 0.00586391 | + | 0.0101566i | ||||
\(523\) | 10.2058 | − | 5.89230i | 0.446267 | − | 0.257653i | −0.259985 | − | 0.965613i | \(-0.583718\pi\) |
0.706252 | + | 0.707960i | \(0.250384\pi\) | |||||||
\(524\) | 9.33013 | − | 16.1603i | 0.407588 | − | 0.705964i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.30385 | + | 3.06218i | 0.231259 | + | 0.133517i | ||||
\(527\) | 3.46410 | − | 6.00000i | 0.150899 | − | 0.261364i | ||||
\(528\) | 6.46410 | 0.281314 | ||||||||
\(529\) | −4.53590 | + | 7.85641i | −0.197213 | + | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.33013 | + | 4.23205i | −0.318100 | + | 0.183655i | ||||
\(532\) | 14.9282i | 0.647220i | ||||||||
\(533\) | −5.00000 | + | 5.19615i | −0.216574 | + | 0.225070i | ||||
\(534\) | −0.535898 | −0.0231906 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.73205 | − | 9.92820i | −0.247587 | − | 0.428833i | ||||
\(537\) | 17.0885 | + | 9.86603i | 0.737421 | + | 0.425750i | ||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 16.7942 | + | 9.69615i | 0.723379 | + | 0.417643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 26.9282i | − | 1.15773i | −0.815422 | − | 0.578867i | \(-0.803495\pi\) | ||
0.815422 | − | 0.578867i | \(-0.196505\pi\) | |||||||
\(542\) | 1.03590 | + | 0.598076i | 0.0444956 | + | 0.0256896i | ||||
\(543\) | 2.53590 | − | 1.46410i | 0.108826 | − | 0.0628306i | ||||
\(544\) | −3.46410 | + | 2.00000i | −0.148522 | + | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.00000 | + | 5.19615i | −0.213980 | + | 0.222375i | ||||
\(547\) | − | 22.9282i | − | 0.980339i | −0.871627 | − | 0.490170i | \(-0.836935\pi\) | ||
0.871627 | − | 0.490170i | \(-0.163065\pi\) | |||||||
\(548\) | −1.23205 | − | 2.13397i | −0.0526306 | − | 0.0911589i | ||||
\(549\) | −5.19615 | − | 9.00000i | −0.221766 | − | 0.384111i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.00000i | − | 0.0852029i | ||||||
\(552\) | 1.86603 | − | 3.23205i | 0.0794233 | − | 0.137565i | ||||
\(553\) | −13.9282 | + | 24.1244i | −0.592287 | + | 1.02587i | ||||
\(554\) | − | 3.92820i | − | 0.166893i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.46410 | − | 11.1962i | −0.274139 | − | 0.474823i | ||||
\(557\) | −8.85641 | − | 15.3397i | −0.375258 | − | 0.649966i | 0.615108 | − | 0.788443i | \(-0.289113\pi\) |
−0.990366 | + | 0.138477i | \(0.955779\pi\) | |||||||
\(558\) | 1.73205i | 0.0733236i | ||||||||
\(559\) | 41.7487 | + | 10.3301i | 1.76578 | + | 0.436918i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.3923 | − | 12.9282i | 0.945404 | − | 0.545829i | ||||
\(562\) | −7.73205 | + | 4.46410i | −0.326157 | + | 0.188307i | ||||
\(563\) | 4.05256 | + | 2.33975i | 0.170795 | + | 0.0986085i | 0.582961 | − | 0.812500i | \(-0.301894\pi\) |
−0.412166 | + | 0.911109i | \(0.635228\pi\) | |||||||
\(564\) | − | 3.53590i | − | 0.148888i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.59808 | − | 4.96410i | −0.361404 | − | 0.208657i | ||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | 10.7321 | + | 6.19615i | 0.450307 | + | 0.259985i | ||||
\(569\) | 14.6603 | + | 25.3923i | 0.614590 | + | 1.06450i | 0.990456 | + | 0.137827i | \(0.0440118\pi\) |
−0.375867 | + | 0.926674i | \(0.622655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1769 | −0.718832 | −0.359416 | − | 0.933178i | \(-0.617024\pi\) | ||||
−0.359416 | + | 0.933178i | \(0.617024\pi\) | |||||||
\(572\) | −6.46410 | − | 22.3923i | −0.270278 | − | 0.936269i | ||||
\(573\) | − | 21.4641i | − | 0.896676i | ||||||
\(574\) | −3.46410 | + | 2.00000i | −0.144589 | + | 0.0834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | −9.80385 | − | 5.66025i | −0.407434 | − | 0.235232i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.92820 | + | 15.4641i | −0.370404 | + | 0.641559i | ||||
\(582\) | −0.464102 | + | 0.267949i | −0.0192376 | + | 0.0111069i | ||||
\(583\) | 3.00000 | + | 5.19615i | 0.124247 | + | 0.215203i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8564 | 1.31598 | ||||||||
\(587\) | 1.19615 | + | 2.07180i | 0.0493705 | + | 0.0855122i | 0.889655 | − | 0.456634i | \(-0.150945\pi\) |
−0.840284 | + | 0.542146i | \(0.817612\pi\) | |||||||
\(588\) | 2.59808 | − | 1.50000i | 0.107143 | − | 0.0618590i | ||||
\(589\) | 6.46410 | − | 11.1962i | 0.266349 | − | 0.461329i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.80385 | + | 2.19615i | 0.156469 | + | 0.0903376i | ||||
\(592\) | −4.59808 | + | 7.96410i | −0.188980 | + | 0.327323i | ||||
\(593\) | 45.1051 | 1.85225 | 0.926123 | − | 0.377223i | \(-0.123121\pi\) | ||||
0.926123 | + | 0.377223i | \(0.123121\pi\) | |||||||
\(594\) | −3.23205 | + | 5.59808i | −0.132613 | + | 0.229692i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.7224 | + | 6.76795i | −0.480170 | + | 0.277226i | ||||
\(597\) | − | 5.07180i | − | 0.207575i | ||||||
\(598\) | −13.0622 | − | 3.23205i | −0.534152 | − | 0.132168i | ||||
\(599\) | 10.3923 | 0.424618 | 0.212309 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212309 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.89230 | + | 17.1340i | 0.403516 | + | 0.698909i | 0.994147 | − | 0.108032i | \(-0.0344548\pi\) |
−0.590632 | + | 0.806941i | \(0.701121\pi\) | |||||||
\(602\) | 20.6603 | + | 11.9282i | 0.842049 | + | 0.486157i | ||||
\(603\) | 11.4641 | 0.466854 | ||||||||
\(604\) | −9.00000 | − | 5.19615i | −0.366205 | − | 0.211428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.92820i | 0.118950i | ||||||||
\(607\) | −16.6077 | − | 9.58846i | −0.674086 | − | 0.389183i | 0.123537 | − | 0.992340i | \(-0.460576\pi\) |
−0.797623 | + | 0.603156i | \(0.793909\pi\) | |||||||
\(608\) | −6.46410 | + | 3.73205i | −0.262154 | + | 0.151355i | ||||
\(609\) | 0.464102 | − | 0.267949i | 0.0188063 | − | 0.0108578i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2487 | + | 3.53590i | −0.495530 | + | 0.143047i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | −19.5263 | − | 33.8205i | −0.788659 | − | 1.36600i | −0.926789 | − | 0.375583i | \(-0.877442\pi\) |
0.138130 | − | 0.990414i | \(-0.455891\pi\) | |||||||
\(614\) | −9.73205 | − | 16.8564i | −0.392754 | − | 0.680269i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 12.9282i | − | 0.520892i | ||||||
\(617\) | −11.2321 | + | 19.4545i | −0.452185 | + | 0.783208i | −0.998522 | − | 0.0543580i | \(-0.982689\pi\) |
0.546336 | + | 0.837566i | \(0.316022\pi\) | |||||||
\(618\) | −5.92820 | + | 10.2679i | −0.238467 | + | 0.413037i | ||||
\(619\) | − | 24.2487i | − | 0.974638i | −0.873224 | − | 0.487319i | \(-0.837975\pi\) | ||
0.873224 | − | 0.487319i | \(-0.162025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.86603 | + | 3.23205i | 0.0748810 | + | 0.129698i | ||||
\(622\) | −14.1962 | − | 24.5885i | −0.569214 | − | 0.985907i | ||||
\(623\) | 1.07180i | 0.0429406i | ||||||||
\(624\) | −3.50000 | − | 0.866025i | −0.140112 | − | 0.0346688i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.2487 | − | 14.0000i | 0.969173 | − | 0.559553i | ||||
\(627\) | 41.7846 | − | 24.1244i | 1.66872 | − | 0.963434i | ||||
\(628\) | −4.33013 | − | 2.50000i | −0.172791 | − | 0.0997609i | ||||
\(629\) | 36.7846i | 1.46670i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.2487 | + | 15.7321i | 1.08475 | + | 0.626283i | 0.932175 | − | 0.362008i | \(-0.117909\pi\) |
0.152579 | + | 0.988291i | \(0.451242\pi\) | |||||||
\(632\) | −13.9282 | −0.554034 | ||||||||
\(633\) | −9.80385 | − | 5.66025i | −0.389668 | − | 0.224975i | ||||
\(634\) | −7.26795 | − | 12.5885i | −0.288647 | − | 0.499952i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | −7.79423 | − | 7.50000i | −0.308819 | − | 0.297161i | ||||
\(638\) | 1.73205i | 0.0685725i | ||||||||
\(639\) | −10.7321 | + | 6.19615i | −0.424553 | + | 0.245116i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0717968 | + | 0.124356i | −0.00283580 | + | 0.00491175i | −0.867440 | − | 0.497542i | \(-0.834236\pi\) |
0.864604 | + | 0.502454i | \(0.167569\pi\) | |||||||
\(642\) | −7.85641 | −0.310068 | ||||||||
\(643\) | 10.2679 | − | 17.7846i | 0.404928 | − | 0.701357i | −0.589385 | − | 0.807852i | \(-0.700630\pi\) |
0.994313 | + | 0.106496i | \(0.0339631\pi\) | |||||||
\(644\) | −6.46410 | − | 3.73205i | −0.254721 | − | 0.147063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9282 | + | 25.8564i | −0.587342 | + | 1.01731i | ||||
\(647\) | 11.5359 | − | 6.66025i | 0.453523 | − | 0.261842i | −0.255794 | − | 0.966731i | \(-0.582337\pi\) |
0.709317 | + | 0.704890i | \(0.249004\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −54.7128 | −2.14767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.46410 | 0.135769 | ||||||||
\(652\) | −7.52628 | − | 13.0359i | −0.294752 | − | 0.510525i | ||||
\(653\) | 3.67949 | − | 2.12436i | 0.143990 | − | 0.0831325i | −0.426274 | − | 0.904594i | \(-0.640174\pi\) |
0.570264 | + | 0.821461i | \(0.306841\pi\) | |||||||
\(654\) | −7.92820 | + | 13.7321i | −0.310017 | + | 0.536966i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.73205 | − | 1.00000i | −0.0676252 | − | 0.0390434i | ||||
\(657\) | 1.00000 | − | 1.73205i | 0.0390137 | − | 0.0675737i | ||||
\(658\) | −7.07180 | −0.275687 | ||||||||
\(659\) | −0.133975 | + | 0.232051i | −0.00521891 | + | 0.00903942i | −0.868623 | − | 0.495473i | \(-0.834995\pi\) |
0.863404 | + | 0.504513i | \(0.168328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.51666 | + | 4.33975i | −0.292364 | + | 0.168797i | −0.639008 | − | 0.769200i | \(-0.720655\pi\) |
0.346643 | + | 0.937997i | \(0.387321\pi\) | |||||||
\(662\) | − | 16.7846i | − | 0.652352i | ||||||
\(663\) | −13.8564 | + | 4.00000i | −0.538138 | + | 0.155347i | ||||
\(664\) | −8.92820 | −0.346481 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.59808 | − | 7.96410i | −0.178172 | − | 0.308603i | ||||
\(667\) | 0.866025 | + | 0.500000i | 0.0335326 | + | 0.0193601i | ||||
\(668\) | 16.3205 | 0.631459 | ||||||||
\(669\) | 17.7846 | + | 10.2679i | 0.687593 | + | 0.396982i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 67.1769i | − | 2.59334i | ||||||
\(672\) | −1.73205 | − | 1.00000i | −0.0668153 | − | 0.0385758i | ||||
\(673\) | 27.7128 | − | 16.0000i | 1.06825 | − | 0.616755i | 0.140548 | − | 0.990074i | \(-0.455114\pi\) |
0.927703 | + | 0.373319i | \(0.121780\pi\) | |||||||
\(674\) | 8.07180 | − | 4.66025i | 0.310914 | − | 0.179506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 12.9904i | 0.0192308 | + | 0.499630i | ||||
\(677\) | − | 32.3923i | − | 1.24494i | −0.782645 | − | 0.622469i | \(-0.786130\pi\) | ||
0.782645 | − | 0.622469i | \(-0.213870\pi\) | |||||||
\(678\) | 0.401924 | + | 0.696152i | 0.0154358 | + | 0.0267356i | ||||
\(679\) | 0.535898 | + | 0.928203i | 0.0205659 | + | 0.0356212i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 16.3923i | − | 0.628154i | ||||||
\(682\) | −5.59808 | + | 9.69615i | −0.214361 | + | 0.371285i | ||||
\(683\) | 20.3923 | − | 35.3205i | 0.780290 | − | 1.35150i | −0.151483 | − | 0.988460i | \(-0.548405\pi\) |
0.931773 | − | 0.363042i | \(-0.118262\pi\) | |||||||
\(684\) | − | 7.46410i | − | 0.285397i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 3.92820 | + | 6.80385i | 0.149870 | + | 0.259583i | ||||
\(688\) | 11.9282i | 0.454758i | ||||||||
\(689\) | −0.928203 | − | 3.21539i | −0.0353617 | − | 0.122497i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5359 | + | 13.5885i | −0.895348 | + | 0.516929i | −0.875688 | − | 0.482877i | \(-0.839592\pi\) |
−0.0196598 | + | 0.999807i | \(0.506258\pi\) | |||||||
\(692\) | 9.46410 | − | 5.46410i | 0.359771 | − | 0.207714i | ||||
\(693\) | 11.1962 | + | 6.46410i | 0.425307 | + | 0.245551i | ||||
\(694\) | 1.60770i | 0.0610273i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.232051 | + | 0.133975i | 0.00879586 | + | 0.00507829i | ||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | −18.5885 | − | 10.7321i | −0.703583 | − | 0.406214i | ||||
\(699\) | −3.06218 | − | 5.30385i | −0.115822 | − | 0.200610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.267949 | −0.0101203 | −0.00506015 | − | 0.999987i | \(-0.501611\pi\) | ||||
−0.00506015 | + | 0.999987i | \(0.501611\pi\) | |||||||
\(702\) | 2.50000 | − | 2.59808i | 0.0943564 | − | 0.0980581i | ||||
\(703\) | 68.6410i | 2.58884i | ||||||||
\(704\) | 5.59808 | − | 3.23205i | 0.210985 | − | 0.121812i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00000 | + | 1.73205i | −0.0376355 | + | 0.0651866i | ||||
\(707\) | 5.85641 | 0.220253 | ||||||||
\(708\) | −4.23205 | + | 7.33013i | −0.159050 | + | 0.275483i | ||||
\(709\) | 19.8564 | + | 11.4641i | 0.745723 | + | 0.430543i | 0.824146 | − | 0.566377i | \(-0.191655\pi\) |
−0.0784234 | + | 0.996920i | \(0.524989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.96410 | − | 12.0622i | 0.261174 | − | 0.452367i | ||||
\(712\) | −0.464102 | + | 0.267949i | −0.0173929 | + | 0.0100418i | ||||
\(713\) | 3.23205 | + | 5.59808i | 0.121041 | + | 0.209650i | ||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7321 | 0.737421 | ||||||||
\(717\) | 8.19615 | + | 14.1962i | 0.306091 | + | 0.530165i | ||||
\(718\) | −4.39230 | + | 2.53590i | −0.163919 | + | 0.0946389i | ||||
\(719\) | −17.3205 | + | 30.0000i | −0.645946 | + | 1.11881i | 0.338136 | + | 0.941097i | \(0.390204\pi\) |
−0.984082 | + | 0.177714i | \(0.943130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5359 | + | 11.8564i | 0.764797 | + | 0.441556i | ||||
\(722\) | −18.3564 | + | 31.7942i | −0.683155 | + | 1.18326i | ||||
\(723\) | −17.7321 | −0.659462 | ||||||||
\(724\) | 1.46410 | − | 2.53590i | 0.0544129 | − | 0.0942459i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.6603 | + | 15.3923i | −0.989455 | + | 0.571262i | ||||
\(727\) | 31.7128i | 1.17616i | 0.808802 | + | 0.588082i | \(0.200117\pi\) | ||||
−0.808802 | + | 0.588082i | \(0.799883\pi\) | |||||||
\(728\) | −1.73205 | + | 7.00000i | −0.0641941 | + | 0.259437i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8564 | + | 41.3205i | 0.882361 | + | 1.52829i | ||||
\(732\) | −9.00000 | − | 5.19615i | −0.332650 | − | 0.192055i | ||||
\(733\) | −50.9282 | −1.88108 | −0.940538 | − | 0.339688i | \(-0.889678\pi\) | ||||
−0.940538 | + | 0.339688i | \(0.889678\pi\) | |||||||
\(734\) | −13.5167 | − | 7.80385i | −0.498909 | − | 0.288045i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.73205i | − | 0.137565i | ||||||
\(737\) | 64.1769 | + | 37.0526i | 2.36399 | + | 1.36485i | ||||
\(738\) | 1.73205 | − | 1.00000i | 0.0637577 | − | 0.0368105i | ||||
\(739\) | 16.7321 | − | 9.66025i | 0.615498 | − | 0.355358i | −0.159616 | − | 0.987179i | \(-0.551026\pi\) |
0.775114 | + | 0.631821i | \(0.217692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.8564 | + | 7.46410i | −0.949859 | + | 0.274201i | ||||
\(742\) | − | 1.85641i | − | 0.0681508i | ||||||
\(743\) | −20.2321 | − | 35.0429i | −0.742242 | − | 1.28560i | −0.951472 | − | 0.307734i | \(-0.900429\pi\) |
0.209230 | − | 0.977866i | \(-0.432904\pi\) | |||||||
\(744\) | 0.866025 | + | 1.50000i | 0.0317500 | + | 0.0549927i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.7846i | 0.577916i | ||||||||
\(747\) | 4.46410 | − | 7.73205i | 0.163333 | − | 0.282901i | ||||
\(748\) | 12.9282 | − | 22.3923i | 0.472702 | − | 0.818744i | ||||
\(749\) | 15.7128i | 0.574134i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.03590 | − | 12.1865i | −0.256744 | − | 0.444693i | 0.708624 | − | 0.705586i | \(-0.249316\pi\) |
−0.965368 | + | 0.260893i | \(0.915983\pi\) | |||||||
\(752\) | −1.76795 | − | 3.06218i | −0.0644705 | − | 0.111666i | ||||
\(753\) | − | 15.7321i | − | 0.573308i | ||||||
\(754\) | 0.232051 | − | 0.937822i | 0.00845079 | − | 0.0341535i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.73205 | − | 1.00000i | 0.0629941 | − | 0.0363696i | ||||
\(757\) | 15.5885 | − | 9.00000i | 0.566572 | − | 0.327111i | −0.189207 | − | 0.981937i | \(-0.560592\pi\) |
0.755779 | + | 0.654827i | \(0.227258\pi\) | |||||||
\(758\) | −24.1244 | − | 13.9282i | −0.876236 | − | 0.505895i | ||||
\(759\) | 24.1244i | 0.875659i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.39230 | + | 2.53590i | 0.159221 | + | 0.0919262i | 0.577493 | − | 0.816395i | \(-0.304031\pi\) |
−0.418272 | + | 0.908322i | \(0.637364\pi\) | |||||||
\(762\) | −4.92820 | −0.178530 | ||||||||
\(763\) | 27.4641 | + | 15.8564i | 0.994267 | + | 0.574040i | ||||
\(764\) | −10.7321 | − | 18.5885i | −0.388272 | − | 0.672507i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.3923 | −0.917461 | ||||||||
\(767\) | 29.6244 | + | 7.33013i | 1.06967 | + | 0.264676i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 10.0359 | − | 5.79423i | 0.361904 | − | 0.208945i | −0.308012 | − | 0.951383i | \(-0.599664\pi\) |
0.669916 | + | 0.742437i | \(0.266330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.66987 | + | 4.62436i | −0.0961531 | + | 0.166542i | ||||
\(772\) | −11.3205 | −0.407434 | ||||||||
\(773\) | −13.8564 | + | 24.0000i | −0.498380 | + | 0.863220i | −0.999998 | − | 0.00186926i | \(-0.999405\pi\) |
0.501618 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(774\) | −10.3301 | − | 5.96410i | −0.371309 | − | 0.214375i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.267949 | + | 0.464102i | −0.00961882 | + | 0.0166603i | ||||
\(777\) | −15.9282 | + | 9.19615i | −0.571421 | + | 0.329910i | ||||
\(778\) | 11.8660 | + | 20.5526i | 0.425418 | + | 0.736845i | ||||
\(779\) | −14.9282 | −0.534858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −80.1051 | −2.86639 | ||||||||
\(782\) | −7.46410 | − | 12.9282i | −0.266916 | − | 0.462312i | ||||
\(783\) | −0.232051 | + | 0.133975i | −0.00829282 | + | 0.00478786i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 16.1603 | + | 9.33013i | 0.576417 | + | 0.332795i | ||||
\(787\) | 0.866025 | − | 1.50000i | 0.0308705 | − | 0.0534692i | −0.850177 | − | 0.526496i | \(-0.823505\pi\) |
0.881048 | + | 0.473027i | \(0.156839\pi\) | |||||||
\(788\) | 4.39230 | 0.156469 | ||||||||
\(789\) | −3.06218 | + | 5.30385i | −0.109016 | + | 0.188822i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.39230 | − | 0.803848i | 0.0495047 | − | 0.0285815i | ||||
\(792\) | 6.46410i | 0.229692i | ||||||||
\(793\) | −9.00000 | + | 36.3731i | −0.319599 | + | 1.29165i | ||||
\(794\) | 12.1244 | 0.430277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.53590 | − | 4.39230i | −0.0898825 | − | 0.155681i | ||||
\(797\) | −8.78461 | − | 5.07180i | −0.311167 | − | 0.179652i | 0.336282 | − | 0.941761i | \(-0.390831\pi\) |
−0.647449 | + | 0.762109i | \(0.724164\pi\) | |||||||
\(798\) | −14.9282 | −0.528453 | ||||||||
\(799\) | −12.2487 | − | 7.07180i | −0.433328 | − | 0.250182i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.535898i | − | 0.0189350i | ||||||
\(802\) | −27.7128 | − | 16.0000i | −0.978573 | − | 0.564980i | ||||
\(803\) | 11.1962 | − | 6.46410i | 0.395104 | − | 0.228113i | ||||
\(804\) | 9.92820 | − | 5.73205i | 0.350141 | − | 0.202154i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.33013 | − | 4.50000i | 0.152522 | − | 0.158506i | ||||
\(807\) | 12.0000i | 0.422420i | ||||||||
\(808\) | 1.46410 | + | 2.53590i | 0.0515069 | + | 0.0892126i | ||||
\(809\) | −21.3923 | − | 37.0526i | −0.752113 | − | 1.30270i | −0.946797 | − | 0.321832i | \(-0.895701\pi\) |
0.194683 | − | 0.980866i | \(-0.437632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40.7846i | − | 1.43214i | −0.698028 | − | 0.716071i | \(-0.745939\pi\) | ||
0.698028 | − | 0.716071i | \(-0.254061\pi\) | |||||||
\(812\) | 0.267949 | − | 0.464102i | 0.00940317 | − | 0.0162868i | ||||
\(813\) | −0.598076 | + | 1.03590i | −0.0209754 | + | 0.0363305i | ||||
\(814\) | − | 59.4449i | − | 2.08354i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 3.46410i | −0.0700140 | − | 0.121268i | ||||
\(817\) | 44.5167 | + | 77.1051i | 1.55744 | + | 2.69757i | ||||
\(818\) | − | 4.00000i | − | 0.139857i | ||||||
\(819\) | −5.19615 | − | 5.00000i | −0.181568 | − | 0.174714i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.6506 | − | 7.30385i | 0.441510 | − | 0.254906i | −0.262728 | − | 0.964870i | \(-0.584622\pi\) |
0.704238 | + | 0.709964i | \(0.251289\pi\) | |||||||
\(822\) | 2.13397 | − | 1.23205i | 0.0744309 | − | 0.0429727i | ||||
\(823\) | −33.9282 | − | 19.5885i | −1.18266 | − | 0.682811i | −0.226034 | − | 0.974119i | \(-0.572576\pi\) |
−0.956629 | + | 0.291309i | \(0.905909\pi\) | |||||||
\(824\) | 11.8564i | 0.413037i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.6603 | + | 8.46410i | 0.510095 | + | 0.294504i | ||||
\(827\) | −17.3205 | −0.602293 | −0.301147 | − | 0.953578i | \(-0.597369\pi\) | ||||
−0.301147 | + | 0.953578i | \(0.597369\pi\) | |||||||
\(828\) | 3.23205 | + | 1.86603i | 0.112322 | + | 0.0648489i | ||||
\(829\) | 8.26795 | + | 14.3205i | 0.287158 | + | 0.497372i | 0.973130 | − | 0.230256i | \(-0.0739563\pi\) |
−0.685972 | + | 0.727628i | \(0.740623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.92820 | 0.136268 | ||||||||
\(832\) | −3.46410 | + | 1.00000i | −0.120096 | + | 0.0346688i | ||||
\(833\) | − | 12.0000i | − | 0.415775i | ||||||
\(834\) | 11.1962 | − | 6.46410i | 0.387691 | − | 0.223834i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.1244 | − | 41.7846i | 0.834358 | − | 1.44515i | ||||
\(837\) | −1.73205 | −0.0598684 | ||||||||
\(838\) | −11.1962 | + | 19.3923i | −0.386765 | + | 0.669896i | ||||
\(839\) | 37.7321 | + | 21.7846i | 1.30266 | + | 0.752088i | 0.980859 | − | 0.194721i | \(-0.0623800\pi\) |
0.321796 | + | 0.946809i | \(0.395713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4641 | − | 25.0526i | 0.498762 | − | 0.863881i | ||||
\(842\) | 3.80385 | − | 2.19615i | 0.131089 | − | 0.0756844i | ||||
\(843\) | −4.46410 | − | 7.73205i | −0.153752 | − | 0.266306i | ||||
\(844\) | −11.3205 | −0.389668 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.53590 | 0.121567 | ||||||||
\(847\) | 30.7846 | + | 53.3205i | 1.05777 | + | 1.83211i | ||||
\(848\) | 0.803848 | − | 0.464102i | 0.0276042 | − | 0.0159373i | ||||
\(849\) | 4.96410 | − | 8.59808i | 0.170368 | − | 0.295085i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.7224 | − | 17.1603i | −1.01887 | − | 0.588246i | ||||
\(852\) | −6.19615 | + | 10.7321i | −0.212277 | + | 0.367674i | ||||
\(853\) | 43.8372 | 1.50096 | 0.750478 | − | 0.660895i | \(-0.229823\pi\) | ||||
0.750478 | + | 0.660895i | \(0.229823\pi\) | |||||||
\(854\) | −10.3923 | + | 18.0000i | −0.355617 | + | 0.615947i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.80385 | + | 3.92820i | −0.232551 | + | 0.134263i | ||||
\(857\) | − | 24.5167i | − | 0.837473i | −0.908108 | − | 0.418737i | \(-0.862473\pi\) | ||
0.908108 | − | 0.418737i | \(-0.137527\pi\) | |||||||
\(858\) | 22.3923 | − | 6.46410i | 0.764461 | − | 0.220681i | ||||
\(859\) | 35.1769 | 1.20022 | 0.600110 | − | 0.799917i | \(-0.295123\pi\) | ||||
0.600110 | + | 0.799917i | \(0.295123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | − | 3.46410i | −0.0681598 | − | 0.118056i | ||||
\(862\) | 24.5885 | + | 14.1962i | 0.837486 | + | 0.483523i | ||||
\(863\) | 35.5359 | 1.20966 | 0.604828 | − | 0.796356i | \(-0.293242\pi\) | ||||
0.604828 | + | 0.796356i | \(0.293242\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 19.3205i | − | 0.656538i | ||||||
\(867\) | 0.866025 | + | 0.500000i | 0.0294118 | + | 0.0169809i | ||||
\(868\) | 3.00000 | − | 1.73205i | 0.101827 | − | 0.0587896i | ||||
\(869\) | 77.9711 | − | 45.0167i | 2.64499 | − | 1.52709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7846 | − | 28.6603i | −1.00921 | − | 0.971116i | ||||
\(872\) | 15.8564i | 0.536966i | ||||||||
\(873\) | −0.267949 | − | 0.464102i | −0.00906871 | − | 0.0157075i | ||||
\(874\) | −13.9282 | − | 24.1244i | −0.471129 | − | 0.816019i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.00000i | − | 0.0675737i | ||||||
\(877\) | −1.93782 | + | 3.35641i | −0.0654356 | + | 0.113338i | −0.896887 | − | 0.442260i | \(-0.854177\pi\) |
0.831452 | + | 0.555597i | \(0.187510\pi\) | |||||||
\(878\) | 8.92820 | − | 15.4641i | 0.301312 | − | 0.521888i | ||||
\(879\) | 31.8564i | 1.07449i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.00000 | + | 12.1244i | 0.235836 | + | 0.408480i | 0.959515 | − | 0.281656i | \(-0.0908839\pi\) |
−0.723679 | + | 0.690136i | \(0.757551\pi\) | |||||||
\(882\) | 1.50000 | + | 2.59808i | 0.0505076 | + | 0.0874818i | ||||
\(883\) | 29.9282i | 1.00716i | 0.863947 | + | 0.503582i | \(0.167985\pi\) | ||||
−0.863947 | + | 0.503582i | \(0.832015\pi\) | |||||||
\(884\) | −10.0000 | + | 10.3923i | −0.336336 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.1962 | + | 8.19615i | −0.476929 | + | 0.275355i | ||||
\(887\) | −12.2321 | + | 7.06218i | −0.410712 | + | 0.237125i | −0.691096 | − | 0.722763i | \(-0.742872\pi\) |
0.280384 | + | 0.959888i | \(0.409538\pi\) | |||||||
\(888\) | −7.96410 | − | 4.59808i | −0.267258 | − | 0.154301i | ||||
\(889\) | 9.85641i | 0.330573i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.59808 | − | 3.23205i | −0.187543 | − | 0.108278i | ||||
\(892\) | 20.5359 | 0.687593 | ||||||||
\(893\) | −22.8564 | − | 13.1962i | −0.764860 | − | 0.441592i | ||||
\(894\) | −6.76795 | − | 11.7224i | −0.226354 | − | 0.392057i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 3.23205 | − | 13.0622i | 0.107915 | − | 0.436133i | ||||
\(898\) | 15.7128i | 0.524343i | ||||||||
\(899\) | −0.401924 | + | 0.232051i | −0.0134049 | + | 0.00773933i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.85641 | − | 3.21539i | 0.0618459 | − | 0.107120i | ||||
\(902\) | 12.9282 | 0.430462 | ||||||||
\(903\) | −11.9282 | + | 20.6603i | −0.396946 | + | 0.687530i | ||||
\(904\) | 0.696152 | + | 0.401924i | 0.0231537 | + | 0.0133678i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.19615 | − | 9.00000i | 0.172631 | − | 0.299005i | ||||
\(907\) | 18.0622 | − | 10.4282i | 0.599745 | − | 0.346263i | −0.169196 | − | 0.985582i | \(-0.554117\pi\) |
0.768941 | + | 0.639320i | \(0.220784\pi\) | |||||||
\(908\) | −8.19615 | − | 14.1962i | −0.271999 | − | 0.471116i | ||||
\(909\) | −2.92820 | −0.0971224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2487 | 0.803396 | 0.401698 | − | 0.915772i | \(-0.368420\pi\) | ||||
0.401698 | + | 0.915772i | \(0.368420\pi\) | |||||||
\(912\) | −3.73205 | − | 6.46410i | −0.123581 | − | 0.214048i | ||||
\(913\) | 49.9808 | − | 28.8564i | 1.65412 | − | 0.955008i | ||||
\(914\) | 12.2679 | − | 21.2487i | 0.405788 | − | 0.702845i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.80385 | + | 3.92820i | 0.224805 | + | 0.129791i | ||||
\(917\) | 18.6603 | − | 32.3205i | 0.616216 | − | 1.06732i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 7.32051 | − | 12.6795i | 0.241481 | − | 0.418258i | −0.719655 | − | 0.694332i | \(-0.755700\pi\) |
0.961136 | + | 0.276074i | \(0.0890334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.8564 | − | 9.73205i | 0.555437 | − | 0.320682i | ||||
\(922\) | 0.464102i | 0.0152844i | ||||||||
\(923\) | 43.3731 | + | 10.7321i | 1.42764 | + | 0.353250i | ||||
\(924\) | 12.9282 | 0.425307 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.53590 | + | 6.12436i | 0.116197 | + | 0.201259i | ||||
\(927\) | −10.2679 | − | 5.92820i | −0.337244 | − | 0.194708i | ||||
\(928\) | 0.267949 | 0.00879586 | ||||||||
\(929\) | 5.32051 | + | 3.07180i | 0.174560 | + | 0.100782i | 0.584734 | − | 0.811225i | \(-0.301199\pi\) |
−0.410174 | + | 0.912007i | \(0.634532\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 22.3923i | − | 0.733878i | ||||||
\(932\) | −5.30385 | − | 3.06218i | −0.173733 | − | 0.100305i | ||||
\(933\) | 24.5885 | − | 14.1962i | 0.804990 | − | 0.464761i | ||||
\(934\) | −13.7321 | + | 7.92820i | −0.449326 | + | 0.259419i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.866025 | − | 3.50000i | 0.0283069 | − | 0.114401i | ||||
\(937\) | 24.6410i | 0.804987i | 0.915423 | + | 0.402493i | \(0.131856\pi\) | ||||
−0.915423 | + | 0.402493i | \(0.868144\pi\) | |||||||
\(938\) | −11.4641 | − | 19.8564i | −0.374316 | − | 0.648335i | ||||
\(939\) | 14.0000 | + | 24.2487i | 0.456873 | + | 0.791327i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7846i | 0.481965i | 0.970530 | + | 0.240982i | \(0.0774696\pi\) | ||||
−0.970530 | + | 0.240982i | \(0.922530\pi\) | |||||||
\(942\) | 2.50000 | − | 4.33013i | 0.0814544 | − | 0.141083i | ||||
\(943\) | 3.73205 | − | 6.46410i | 0.121532 | − | 0.210500i | ||||
\(944\) | 8.46410i | 0.275483i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.5526 | − | 66.7750i | −1.25345 | − | 2.17104i | ||||
\(947\) | −4.73205 | − | 8.19615i | −0.153771 | − | 0.266339i | 0.778840 | − | 0.627223i | \(-0.215808\pi\) |
−0.932611 | + | 0.360884i | \(0.882475\pi\) | |||||||
\(948\) | − | 13.9282i | − | 0.452367i | ||||||
\(949\) | −6.92820 | + | 2.00000i | −0.224899 | + | 0.0649227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5885 | − | 7.26795i | 0.408209 | − | 0.235679i | ||||
\(952\) | −6.92820 | + | 4.00000i | −0.224544 | + | 0.129641i | ||||
\(953\) | 10.6244 | + | 6.13397i | 0.344157 | + | 0.198699i | 0.662109 | − | 0.749408i | \(-0.269662\pi\) |
−0.317952 | + | 0.948107i | \(0.602995\pi\) | |||||||
\(954\) | 0.928203i | 0.0300517i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.1962 | + | 8.19615i | 0.459136 | + | 0.265083i | ||||
\(957\) | −1.73205 | −0.0559893 | ||||||||
\(958\) | −4.73205 | − | 2.73205i | −0.152886 | − | 0.0882686i | ||||
\(959\) | −2.46410 | − | 4.26795i | −0.0795700 | − | 0.137819i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | −7.96410 | + | 32.1865i | −0.256773 | + | 1.03774i | ||||
\(963\) | − | 7.85641i | − | 0.253169i | ||||||
\(964\) | −15.3564 | + | 8.86603i | −0.494597 | + | 0.285555i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.73205 | − | 6.46410i | 0.120077 | − | 0.207979i | ||||
\(967\) | 41.4641 | 1.33340 | 0.666698 | − | 0.745328i | \(-0.267707\pi\) | ||||
0.666698 | + | 0.745328i | \(0.267707\pi\) | |||||||
\(968\) | −15.3923 | + | 26.6603i | −0.494727 | + | 0.856893i | ||||
\(969\) | −25.8564 | − | 14.9282i | −0.830627 | − | 0.479563i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.26795 | + | 3.92820i | −0.0727820 | + | 0.126062i | −0.900120 | − | 0.435643i | \(-0.856521\pi\) |
0.827338 | + | 0.561705i | \(0.189854\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | −12.9282 | − | 22.3923i | −0.414459 | − | 0.717864i | ||||
\(974\) | 23.1769 | 0.742636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3923 | −0.332650 | ||||||||
\(977\) | −6.30385 | − | 10.9186i | −0.201678 | − | 0.349316i | 0.747391 | − | 0.664384i | \(-0.231306\pi\) |
−0.949069 | + | 0.315068i | \(0.897973\pi\) | |||||||
\(978\) | 13.0359 | − | 7.52628i | 0.416842 | − | 0.240664i | ||||
\(979\) | 1.73205 | − | 3.00000i | 0.0553566 | − | 0.0958804i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7321 | − | 7.92820i | −0.438431 | − | 0.253128i | ||||
\(982\) | −8.66025 | + | 15.0000i | −0.276360 | + | 0.478669i | ||||
\(983\) | −36.6077 | −1.16760 | −0.583802 | − | 0.811896i | \(-0.698436\pi\) | ||||
−0.583802 | + | 0.811896i | \(0.698436\pi\) | |||||||
\(984\) | 1.00000 | − | 1.73205i | 0.0318788 | − | 0.0552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.928203 | − | 0.535898i | 0.0295600 | − | 0.0170665i | ||||
\(987\) | − | 7.07180i | − | 0.225098i | ||||||
\(988\) | −18.6603 | + | 19.3923i | −0.593662 | + | 0.616951i | ||||
\(989\) | −44.5167 | −1.41555 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4282 | + | 45.7750i | 0.839520 | + | 1.45409i | 0.890297 | + | 0.455381i | \(0.150497\pi\) |
−0.0507774 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(992\) | 1.50000 | + | 0.866025i | 0.0476250 | + | 0.0274963i | ||||
\(993\) | 16.7846 | 0.532643 | ||||||||
\(994\) | 21.4641 | + | 12.3923i | 0.680800 | + | 0.393060i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 8.92820i | − | 0.282901i | ||||||
\(997\) | 30.8038 | + | 17.7846i | 0.975568 | + | 0.563244i | 0.900929 | − | 0.433966i | \(-0.142886\pi\) |
0.0746386 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(998\) | −5.66025 | + | 3.26795i | −0.179172 | + | 0.103445i | ||||
\(999\) | 7.96410 | − | 4.59808i | 0.251973 | − | 0.145477i |
(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 | 1950.2.y.f.49.1 | 4 | ||
5.2 | odd | 4 | 390.2.bb.b.361.1 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.bc.b.751.2 | 4 | |||
5.4 | even | 2 | 1950.2.y.c.49.2 | 4 | |||
13.4 | even | 6 | 1950.2.y.c.199.2 | 4 | |||
15.2 | even | 4 | 1170.2.bs.e.361.2 | 4 | |||
65.2 | even | 12 | 5070.2.a.y.1.1 | 2 | |||
65.4 | even | 6 | inner | 1950.2.y.f.199.1 | 4 | ||
65.17 | odd | 12 | 390.2.bb.b.121.1 | ✓ | 4 | ||
65.37 | even | 12 | 5070.2.a.bg.1.2 | 2 | |||
65.42 | odd | 12 | 5070.2.b.o.1351.2 | 4 | |||
65.43 | odd | 12 | 1950.2.bc.b.901.2 | 4 | |||
65.62 | odd | 12 | 5070.2.b.o.1351.3 | 4 | |||
195.17 | even | 12 | 1170.2.bs.e.901.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.1 | ✓ | 4 | 65.17 | odd | 12 | ||
390.2.bb.b.361.1 | yes | 4 | 5.2 | odd | 4 | ||
1170.2.bs.e.361.2 | 4 | 15.2 | even | 4 | |||
1170.2.bs.e.901.2 | 4 | 195.17 | even | 12 | |||
1950.2.y.c.49.2 | 4 | 5.4 | even | 2 | |||
1950.2.y.c.199.2 | 4 | 13.4 | even | 6 | |||
1950.2.y.f.49.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.y.f.199.1 | 4 | 65.4 | even | 6 | inner | ||
1950.2.bc.b.751.2 | 4 | 5.3 | odd | 4 | |||
1950.2.bc.b.901.2 | 4 | 65.43 | odd | 12 | |||
5070.2.a.y.1.1 | 2 | 65.2 | even | 12 | |||
5070.2.a.bg.1.2 | 2 | 65.37 | even | 12 | |||
5070.2.b.o.1351.2 | 4 | 65.42 | odd | 12 | |||
5070.2.b.o.1351.3 | 4 | 65.62 | odd | 12 |