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 | 199.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.199 |
Dual form | 1950.2.y.c.49.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 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 | 0.956136 | + | 0.292925i | \(0.0946285\pi\) |
0.731748 | + | 0.681575i | \(0.238705\pi\) | |||||||
\(12\) | − | 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 | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.46410 | + | 3.73205i | −1.48297 | + | 0.856191i | −0.999813 | − | 0.0193444i | \(-0.993842\pi\) |
−0.483154 | + | 0.875536i | \(0.660509\pi\) | |||||||
\(20\) | 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 | \(-0.460545\pi\) |
−0.797564 | + | 0.603235i | \(0.793878\pi\) | |||||||
\(24\) | 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 | −0.853318 | − | 0.521391i | \(-0.825413\pi\) |
0.878197 | + | 0.478300i | \(0.158747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | −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 | −0.188997 | − | 0.981978i | \(-0.560524\pi\) |
0.944916 | − | 0.327313i | \(-0.106143\pi\) | |||||||
\(38\) | − | 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 | 0.629115 | − | 0.777312i | \(-0.283417\pi\) |
−0.358614 | + | 0.933486i | \(0.616751\pi\) | |||||||
\(42\) | −1.73205 | − | 1.00000i | −0.267261 | − | 0.154303i | ||||
\(43\) | 10.3301 | − | 5.96410i | 1.57533 | − | 0.909517i | 0.579831 | − | 0.814736i | \(-0.303118\pi\) |
0.995498 | − | 0.0947805i | \(-0.0302149\pi\) | |||||||
\(44\) | − | 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 | \(-0.583025\pi\) | ||||
−0.257882 | + | 0.966176i | \(0.583025\pi\) | |||||||
\(48\) | −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 | −0.894414 | − | 0.447239i | \(-0.852407\pi\) |
−0.0598868 | + | 0.998205i | \(0.519074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19615 | + | 9.00000i | 0.665299 | + | 1.15233i | 0.979204 | + | 0.202878i | \(0.0650293\pi\) |
−0.313905 | + | 0.949454i | \(0.601637\pi\) | |||||||
\(62\) | 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 | 0.268086 | + | 0.963395i | \(0.413609\pi\) |
−0.968368 | + | 0.249528i | \(0.919724\pi\) | |||||||
\(68\) | −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 | −0.975675 | − | 0.219222i | \(-0.929648\pi\) |
−0.297985 | + | 0.954570i | \(0.596315\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 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 | \(-0.663003\pi\) | ||||
−0.489999 | + | 0.871723i | \(0.663003\pi\) | |||||||
\(84\) | 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 | 0.524396 | − | 0.851475i | \(-0.324291\pi\) |
−0.475201 | + | 0.879877i | \(0.657625\pi\) | |||||||
\(90\) | 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 | \(-0.175328\pi\) |
−0.879308 | + | 0.476254i | \(0.841994\pi\) | |||||||
\(98\) | 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 | −0.929628 | − | 0.368500i | \(-0.879871\pi\) |
0.783944 | + | 0.620831i | \(0.213205\pi\) | |||||||
\(102\) | −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 | \(-0.457325\pi\) |
−0.791420 | + | 0.611273i | \(0.790658\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 15.8564i | 1.51877i | 0.650643 | + | 0.759384i | \(0.274500\pi\) | ||||
−0.650643 | + | 0.759384i | \(0.725500\pi\) | |||||||
\(110\) | 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 | \(-0.654629\pi\) |
0.532387 | + | 0.846501i | \(0.321295\pi\) | |||||||
\(114\) | 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 | \(-0.403500\pi\) |
−0.677261 | + | 0.735743i | \(0.736833\pi\) | |||||||
\(128\) | −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 | \(-0.133099\pi\) |
−0.808584 | + | 0.588381i | \(0.799765\pi\) | |||||||
\(138\) | 3.73205 | 0.317693 | ||||||||
\(139\) | −6.46410 | − | 11.1962i | −0.548278 | − | 0.949645i | −0.998393 | − | 0.0566745i | \(-0.981950\pi\) |
0.450115 | − | 0.892971i | \(-0.351383\pi\) | |||||||
\(140\) | 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 | 0.0640617 | − | 0.997946i | \(-0.479595\pi\) |
0.896277 | + | 0.443494i | \(0.146261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.3923i | − | 0.845714i | −0.906196 | − | 0.422857i | \(-0.861027\pi\) | ||
0.906196 | − | 0.422857i | \(-0.138973\pi\) | |||||||
\(152\) | −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 | 0.994297 | + | 0.106642i | \(0.0340100\pi\) |
−0.404794 | + | 0.914408i | \(0.632657\pi\) | |||||||
\(164\) | − | 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 | −0.355794 | − | 0.934564i | \(-0.615790\pi\) |
0.987254 | − | 0.159155i | \(-0.0508771\pi\) | |||||||
\(168\) | 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 | \(-0.530299\pi\) |
0.814584 | + | 0.580045i | \(0.196965\pi\) | |||||||
\(174\) | 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 | 0.216231 | + | 0.976342i | \(0.430623\pi\) |
−0.953653 | + | 0.300909i | \(0.902710\pi\) | |||||||
\(180\) | 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 | −0.933923 | − | 0.357475i | \(-0.883638\pi\) |
0.157379 | − | 0.987538i | \(-0.449696\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −5.66025 | + | 9.80385i | −0.407434 | + | 0.705696i | −0.994601 | − | 0.103769i | \(-0.966910\pi\) |
0.587167 | + | 0.809466i | \(0.300243\pi\) | |||||||
\(194\) | 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 | \(-0.783322\pi\) |
0.933593 | + | 0.358335i | \(0.116655\pi\) | |||||||
\(198\) | −5.59808 | − | 3.23205i | −0.397838 | − | 0.229692i | ||||
\(199\) | −2.53590 | − | 4.39230i | −0.179765 | − | 0.311362i | 0.762035 | − | 0.647536i | \(-0.224200\pi\) |
−0.941800 | + | 0.336174i | \(0.890867\pi\) | |||||||
\(200\) | 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 | −0.602737 | − | 0.797940i | \(-0.705923\pi\) |
0.992405 | + | 0.123015i | \(0.0392564\pi\) | |||||||
\(212\) | 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 | −0.285022 | − | 0.958521i | \(-0.592001\pi\) |
0.972614 | − | 0.232424i | \(-0.0746659\pi\) | |||||||
\(224\) | 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 | 0.998669 | + | 0.0515725i | \(0.0164233\pi\) |
−0.454672 | + | 0.890659i | \(0.650243\pi\) | |||||||
\(228\) | 3.73205 | + | 6.46410i | 0.247161 | + | 0.428096i | ||||
\(229\) | 7.85641i | 0.519166i | 0.965721 | + | 0.259583i | \(0.0835851\pi\) | ||||
−0.965721 | + | 0.259583i | \(0.916415\pi\) | |||||||
\(230\) | 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 | \(0.177870\pi\) | ||||
−0.847894 | + | 0.530165i | \(0.822130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3564 | − | 8.86603i | 0.989193 | − | 0.571111i | 0.0841601 | − | 0.996452i | \(-0.473179\pi\) |
0.905033 | + | 0.425341i | \(0.139846\pi\) | |||||||
\(242\) | −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 | 0.503493 | − | 0.863999i | \(-0.332048\pi\) |
−0.999992 | + | 0.00403776i | \(0.998715\pi\) | |||||||
\(252\) | 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 | \(-0.386593\pi\) |
−0.637247 | + | 0.770660i | \(0.719927\pi\) | |||||||
\(258\) | −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 | \(-0.393800\pi\) |
−0.654530 | + | 0.756036i | \(0.727134\pi\) | |||||||
\(264\) | 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 | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03590 | + | 0.598076i | 0.0629263 | + | 0.0363305i | 0.531133 | − | 0.847288i | \(-0.321766\pi\) |
−0.468207 | + | 0.883619i | \(0.655100\pi\) | |||||||
\(272\) | 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 | \(-0.629015\pi\) |
0.598707 | + | 0.800968i | \(0.295681\pi\) | |||||||
\(278\) | 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 | \(-0.914197\pi\) | ||
0.963889 | − | 0.266306i | \(-0.0858032\pi\) | |||||||
\(282\) | 3.06218 | − | 1.76795i | 0.182350 | − | 0.105280i | ||||
\(283\) | 8.59808 | + | 4.96410i | 0.511103 | + | 0.295085i | 0.733287 | − | 0.679920i | \(-0.237985\pi\) |
−0.222184 | + | 0.975005i | \(0.571319\pi\) | |||||||
\(284\) | 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 | −0.782408 | − | 0.622767i | \(-0.786009\pi\) |
−0.148128 | − | 0.988968i | \(-0.547325\pi\) | |||||||
\(294\) | 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 | \(-0.312551\pi\) | ||||
0.555437 | + | 0.831558i | \(0.312551\pi\) | |||||||
\(308\) | 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 | \(-0.366154\pi\) | ||||
0.408209 | + | 0.912889i | \(0.366154\pi\) | |||||||
\(318\) | −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 | −0.843109 | − | 0.537742i | \(-0.819277\pi\) |
0.0441440 | + | 0.999025i | \(0.485944\pi\) | |||||||
\(332\) | 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 | \(-0.680407\pi\) |
0.462163 | + | 0.886795i | \(0.347074\pi\) | |||||||
\(348\) | −0.232051 | − | 0.133975i | −0.0124392 | − | 0.00718179i | ||||
\(349\) | −18.5885 | − | 10.7321i | −0.995017 | − | 0.574474i | −0.0882471 | − | 0.996099i | \(-0.528127\pi\) |
−0.906770 | + | 0.421625i | \(0.861460\pi\) | |||||||
\(350\) | 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 | \(-0.850283\pi\) |
0.838186 | + | 0.545385i | \(0.183617\pi\) | |||||||
\(354\) | 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 | \(-0.957269\pi\) | ||
0.991003 | − | 0.133840i | \(-0.0427307\pi\) | |||||||
\(360\) | 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 | \(-0.199784\pi\) |
−0.103852 | + | 0.994593i | \(0.533117\pi\) | |||||||
\(368\) | 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 | \(-0.800666\pi\) |
0.102446 | + | 0.994739i | \(0.467333\pi\) | |||||||
\(374\) | −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 | −0.270257 | − | 0.962788i | \(-0.587109\pi\) |
−0.968928 | + | 0.247344i | \(0.920442\pi\) | |||||||
\(380\) | 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 | 0.983423 | + | 0.181324i | \(0.0580383\pi\) |
−0.334680 | + | 0.942332i | \(0.608628\pi\) | |||||||
\(384\) | −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 | \(-0.265073\pi\) |
−0.977095 | + | 0.212806i | \(0.931740\pi\) | |||||||
\(398\) | 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 | −0.391292 | − | 0.920267i | \(-0.627972\pi\) |
−0.992620 | + | 0.121265i | \(0.961305\pi\) | |||||||
\(402\) | − | 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 | −0.583193 | − | 0.812333i | \(-0.698197\pi\) |
0.411905 | + | 0.911227i | \(0.364864\pi\) | |||||||
\(410\) | 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 | −0.451512 | − | 0.892265i | \(-0.649115\pi\) |
0.998480 | − | 0.0551112i | \(-0.0175513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.39230i | 0.214068i | 0.994255 | + | 0.107034i | \(0.0341353\pi\) | ||||
−0.994255 | + | 0.107034i | \(0.965865\pi\) | |||||||
\(422\) | 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 | 0.957025 | − | 0.290006i | \(-0.0936574\pi\) |
0.227360 | + | 0.973811i | \(0.426991\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 16.7321 | − | 9.66025i | 0.804091 | − | 0.464242i | −0.0408086 | − | 0.999167i | \(-0.512993\pi\) |
0.844900 | + | 0.534925i | \(0.179660\pi\) | |||||||
\(434\) | 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 | −0.996524 | − | 0.0833027i | \(-0.973453\pi\) |
0.570404 | + | 0.821364i | \(0.306786\pi\) | |||||||
\(440\) | 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 | −0.143270 | − | 0.989684i | \(-0.545762\pi\) |
0.785456 | + | 0.618917i | \(0.212428\pi\) | |||||||
\(450\) | 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 | −0.422293 | − | 0.906459i | \(-0.638775\pi\) |
0.996163 | − | 0.0875134i | \(-0.0278920\pi\) | |||||||
\(458\) | −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 | −0.490611 | − | 0.871379i | \(-0.663226\pi\) |
0.509331 | + | 0.860571i | \(0.329893\pi\) | |||||||
\(462\) | −6.46410 | − | 11.1962i | −0.300737 | − | 0.520892i | ||||
\(463\) | −7.07180 | −0.328654 | −0.164327 | − | 0.986406i | \(-0.552545\pi\) | ||||
−0.164327 | + | 0.986406i | \(0.552545\pi\) | |||||||
\(464\) | 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 | 0.387983 | − | 0.921667i | \(-0.373172\pi\) |
−0.604195 | + | 0.796836i | \(0.706505\pi\) | |||||||
\(480\) | 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 | −0.999572 | − | 0.0292568i | \(-0.990686\pi\) |
0.474449 | − | 0.880283i | \(-0.342647\pi\) | |||||||
\(488\) | 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 | −0.601728 | − | 0.798701i | \(-0.705521\pi\) |
0.992559 | + | 0.121761i | \(0.0388541\pi\) | |||||||
\(492\) | 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 | \(-0.953266\pi\) | ||
0.989241 | − | 0.146293i | \(-0.0467344\pi\) | |||||||
\(500\) | 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 | \(-0.911287\pi\) |
−0.242457 | + | 0.970162i | \(0.577953\pi\) | |||||||
\(504\) | −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 | 0.473039 | − | 0.881041i | \(-0.343157\pi\) |
−0.526484 | + | 0.850185i | \(0.676490\pi\) | |||||||
\(510\) | 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 | \(-0.416282\pi\) |
−0.706252 | + | 0.707960i | \(0.749616\pi\) | |||||||
\(524\) | 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 | \(0.196505\pi\) | ||||
−0.815422 | + | 0.578867i | \(0.803495\pi\) | |||||||
\(542\) | −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 | \(-0.710887\pi\) |
0.990366 | + | 0.138477i | \(0.0442208\pi\) | |||||||
\(558\) | 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 | \(-0.698106\pi\) |
0.412166 | + | 0.911109i | \(0.364772\pi\) | |||||||
\(564\) | 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 | −0.375867 | − | 0.926674i | \(-0.622655\pi\) |
0.990456 | − | 0.137827i | \(-0.0440118\pi\) | |||||||
\(570\) | 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 | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | −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 | \(-0.849055\pi\) |
0.840284 | + | 0.542146i | \(0.182388\pi\) | |||||||
\(588\) | −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 | \(-0.876879\pi\) | ||||
−0.926123 | + | 0.377223i | \(0.876879\pi\) | |||||||
\(594\) | −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 | −0.590632 | − | 0.806941i | \(-0.701121\pi\) |
0.994147 | + | 0.108032i | \(0.0344548\pi\) | |||||||
\(602\) | −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 | \(-0.539424\pi\) |
0.797623 | + | 0.603156i | \(0.206091\pi\) | |||||||
\(608\) | 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 | −0.138130 | − | 0.990414i | \(-0.544109\pi\) |
0.926789 | − | 0.375583i | \(-0.122558\pi\) | |||||||
\(614\) | −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 | \(-0.0173112\pi\) |
−0.546336 | + | 0.837566i | \(0.683978\pi\) | |||||||
\(618\) | 5.92820 | + | 10.2679i | 0.238467 | + | 0.413037i | ||||
\(619\) | 24.2487i | 0.974638i | 0.873224 | + | 0.487319i | \(0.162025\pi\) | ||||
−0.873224 | + | 0.487319i | \(0.837975\pi\) | |||||||
\(620\) | 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 | 0.152579 | − | 0.988291i | \(-0.451242\pi\) |
0.932175 | + | 0.362008i | \(0.117909\pi\) | |||||||
\(632\) | 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 | 0.864604 | − | 0.502454i | \(-0.167569\pi\) |
−0.867440 | + | 0.497542i | \(0.834236\pi\) | |||||||
\(642\) | 7.85641 | 0.310068 | ||||||||
\(643\) | −10.2679 | − | 17.7846i | −0.404928 | − | 0.701357i | 0.589385 | − | 0.807852i | \(-0.299370\pi\) |
−0.994313 | + | 0.106496i | \(0.966037\pi\) | |||||||
\(644\) | −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 | \(-0.417663\pi\) |
−0.709317 | + | 0.704890i | \(0.750996\pi\) | |||||||
\(648\) | −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 | \(-0.359826\pi\) |
−0.570264 | + | 0.821461i | \(0.693159\pi\) | |||||||
\(654\) | −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 | 0.863404 | − | 0.504513i | \(-0.168328\pi\) |
−0.868623 | + | 0.495473i | \(0.834995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.51666 | − | 4.33975i | −0.292364 | − | 0.168797i | 0.346643 | − | 0.937997i | \(-0.387321\pi\) |
−0.639008 | + | 0.769200i | \(0.720655\pi\) | |||||||
\(662\) | − | 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 | \(-0.544886\pi\) |
−0.927703 | + | 0.373319i | \(0.878220\pi\) | |||||||
\(674\) | 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 | −0.931773 | − | 0.363042i | \(-0.881738\pi\) |
0.151483 | − | 0.988460i | \(-0.451595\pi\) | |||||||
\(684\) | 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 | −0.0196598 | − | 0.999807i | \(-0.506258\pi\) |
−0.875688 | + | 0.482877i | \(0.839592\pi\) | |||||||
\(692\) | −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 | −0.0784234 | − | 0.996920i | \(-0.524989\pi\) |
0.824146 | + | 0.566377i | \(0.191655\pi\) | |||||||
\(710\) | 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 | −0.984082 | − | 0.177714i | \(-0.943130\pi\) |
0.338136 | − | 0.941097i | \(-0.390204\pi\) | |||||||
\(720\) | 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 | \(-0.110322\pi\) | ||||
0.940538 | + | 0.339688i | \(0.110322\pi\) | |||||||
\(734\) | −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 | 0.775114 | − | 0.631821i | \(-0.217692\pi\) |
−0.159616 | + | 0.987179i | \(0.551026\pi\) | |||||||
\(740\) | 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 | −0.209230 | − | 0.977866i | \(-0.567096\pi\) |
0.951472 | − | 0.307734i | \(-0.0995708\pi\) | |||||||
\(744\) | 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 | −0.965368 | − | 0.260893i | \(-0.915983\pi\) |
0.708624 | + | 0.705586i | \(0.249316\pi\) | |||||||
\(752\) | 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 | \(-0.439408\pi\) |
−0.755779 | + | 0.654827i | \(0.772742\pi\) | |||||||
\(758\) | 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 | −0.418272 | − | 0.908322i | \(-0.637364\pi\) |
0.577493 | + | 0.816395i | \(0.304031\pi\) | |||||||
\(762\) | 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 | 0.669916 | − | 0.742437i | \(-0.266330\pi\) |
−0.308012 | + | 0.951383i | \(0.599664\pi\) | |||||||
\(770\) | 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 | \(-0.000595004\pi\) |
−0.501618 | + | 0.865089i | \(0.667262\pi\) | |||||||
\(774\) | −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 | \(-0.176495\pi\) |
−0.881048 | + | 0.473027i | \(0.843161\pi\) | |||||||
\(788\) | −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 | \(-0.609169\pi\) |
0.647449 | + | 0.762109i | \(0.275836\pi\) | |||||||
\(798\) | 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 | 0.194683 | + | 0.980866i | \(0.437632\pi\) |
−0.946797 | + | 0.321832i | \(0.895701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7846i | 1.43214i | 0.698028 | + | 0.716071i | \(0.254061\pi\) | ||||
−0.698028 | + | 0.716071i | \(0.745939\pi\) | |||||||
\(812\) | −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 | 0.704238 | − | 0.709964i | \(-0.251289\pi\) |
−0.262728 | + | 0.964870i | \(0.584622\pi\) | |||||||
\(822\) | −2.13397 | − | 1.23205i | −0.0744309 | − | 0.0429727i | ||||
\(823\) | 33.9282 | − | 19.5885i | 1.18266 | − | 0.682811i | 0.226034 | − | 0.974119i | \(-0.427424\pi\) |
0.956629 | + | 0.291309i | \(0.0940907\pi\) | |||||||
\(824\) | − | 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 | \(-0.402631\pi\) | ||||
0.301147 | + | 0.953578i | \(0.402631\pi\) | |||||||
\(828\) | −3.23205 | + | 1.86603i | −0.112322 | + | 0.0648489i | ||||
\(829\) | 8.26795 | − | 14.3205i | 0.287158 | − | 0.497372i | −0.685972 | − | 0.727628i | \(-0.740623\pi\) |
0.973130 | + | 0.230256i | \(0.0739563\pi\) | |||||||
\(830\) | 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 | 0.321796 | − | 0.946809i | \(-0.395713\pi\) |
0.980859 | + | 0.194721i | \(0.0623800\pi\) | |||||||
\(840\) | 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 | \(-0.770177\pi\) | ||||
−0.750478 | + | 0.660895i | \(0.770177\pi\) | |||||||
\(854\) | −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 | \(-0.706758\pi\) | ||||
−0.604828 | + | 0.796356i | \(0.706758\pi\) | |||||||
\(864\) | 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 | \(-0.145823\pi\) |
−0.831452 | + | 0.555597i | \(0.812490\pi\) | |||||||
\(878\) | −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 | −0.723679 | − | 0.690136i | \(-0.757551\pi\) |
0.959515 | + | 0.281656i | \(0.0908839\pi\) | |||||||
\(882\) | −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 | \(-0.257128\pi\) |
−0.280384 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(888\) | 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 | \(-0.445883\pi\) |
−0.768941 | + | 0.639320i | \(0.779216\pi\) | |||||||
\(908\) | 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 | 0.961136 | − | 0.276074i | \(-0.0890334\pi\) |
−0.719655 | + | 0.694332i | \(0.755700\pi\) | |||||||
\(920\) | 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 | −0.410174 | − | 0.912007i | \(-0.634532\pi\) |
0.584734 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(930\) | 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 | \(-0.922530\pi\) | ||
0.970530 | − | 0.240982i | \(-0.0774696\pi\) | |||||||
\(942\) | −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 | \(-0.784192\pi\) |
0.932611 | + | 0.360884i | \(0.117525\pi\) | |||||||
\(948\) | − | 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 | \(-0.730338\pi\) |
0.317952 | + | 0.948107i | \(0.397005\pi\) | |||||||
\(954\) | − | 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 | \(-0.732293\pi\) | ||||
−0.666698 | + | 0.745328i | \(0.732293\pi\) | |||||||
\(968\) | 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 | 0.827338 | − | 0.561705i | \(-0.189854\pi\) |
−0.900120 | + | 0.435643i | \(0.856521\pi\) | |||||||
\(972\) | 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 | \(-0.768694\pi\) |
0.949069 | + | 0.315068i | \(0.102027\pi\) | |||||||
\(978\) | −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 | \(-0.301564\pi\) | ||||
0.583802 | + | 0.811896i | \(0.301564\pi\) | |||||||
\(984\) | 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 | −0.0507774 | − | 0.998710i | \(-0.516170\pi\) |
0.890297 | − | 0.455381i | \(-0.150497\pi\) | |||||||
\(992\) | −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 | \(-0.857114\pi\) |
−0.0746386 | + | 0.997211i | \(0.523780\pi\) | |||||||
\(998\) | 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.c.199.2 | 4 | ||
5.2 | odd | 4 | 390.2.bb.b.121.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1950.2.bc.b.901.2 | 4 | |||
5.4 | even | 2 | 1950.2.y.f.199.1 | 4 | |||
13.10 | even | 6 | 1950.2.y.f.49.1 | 4 | |||
15.2 | even | 4 | 1170.2.bs.e.901.2 | 4 | |||
65.7 | even | 12 | 5070.2.a.y.1.1 | 2 | |||
65.17 | odd | 12 | 5070.2.b.o.1351.2 | 4 | |||
65.22 | odd | 12 | 5070.2.b.o.1351.3 | 4 | |||
65.23 | odd | 12 | 1950.2.bc.b.751.2 | 4 | |||
65.32 | even | 12 | 5070.2.a.bg.1.2 | 2 | |||
65.49 | even | 6 | inner | 1950.2.y.c.49.2 | 4 | ||
65.62 | odd | 12 | 390.2.bb.b.361.1 | yes | 4 | ||
195.62 | even | 12 | 1170.2.bs.e.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.1 | ✓ | 4 | 5.2 | odd | 4 | ||
390.2.bb.b.361.1 | yes | 4 | 65.62 | odd | 12 | ||
1170.2.bs.e.361.2 | 4 | 195.62 | even | 12 | |||
1170.2.bs.e.901.2 | 4 | 15.2 | even | 4 | |||
1950.2.y.c.49.2 | 4 | 65.49 | even | 6 | inner | ||
1950.2.y.c.199.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.y.f.49.1 | 4 | 13.10 | even | 6 | |||
1950.2.y.f.199.1 | 4 | 5.4 | even | 2 | |||
1950.2.bc.b.751.2 | 4 | 65.23 | odd | 12 | |||
1950.2.bc.b.901.2 | 4 | 5.3 | odd | 4 | |||
5070.2.a.y.1.1 | 2 | 65.7 | even | 12 | |||
5070.2.a.bg.1.2 | 2 | 65.32 | even | 12 | |||
5070.2.b.o.1351.2 | 4 | 65.17 | odd | 12 | |||
5070.2.b.o.1351.3 | 4 | 65.22 | odd | 12 |