Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.361 |
Dual form | 1170.2.bs.e.901.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 1.00000i | −0.654654 | − | 0.377964i | 0.135583 | − | 0.990766i | \(-0.456709\pi\) |
−0.790237 | + | 0.612801i | \(0.790043\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −5.59808 | + | 3.23205i | −1.68788 | + | 0.974500i | −0.731748 | + | 0.681575i | \(0.761295\pi\) |
−0.956136 | + | 0.292925i | \(0.905371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 3.46410i | 0.277350 | + | 0.960769i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.46410 | + | 3.73205i | 1.48297 | + | 0.856191i | 0.999813 | − | 0.0193444i | \(-0.00615788\pi\) |
0.483154 | + | 0.875536i | \(0.339491\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.23205 | + | 5.59808i | −0.689076 | + | 1.19351i | ||||
\(23\) | 1.86603 | + | 3.23205i | 0.389093 | + | 0.673929i | 0.992328 | − | 0.123635i | \(-0.0394551\pi\) |
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.59808 | + | 2.50000i | 0.509525 | + | 0.490290i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.73205 | + | 1.00000i | −0.327327 | + | 0.188982i | ||||
\(29\) | 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 | \(0.950287\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.96410 | − | 4.59808i | 1.30929 | − | 0.755919i | 0.327313 | − | 0.944916i | \(-0.393857\pi\) |
0.981978 | + | 0.188997i | \(0.0605237\pi\) | |||||||
\(38\) | 7.46410 | 1.21084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.73205 | + | 1.00000i | −0.270501 | + | 0.156174i | −0.629115 | − | 0.777312i | \(-0.716583\pi\) |
0.358614 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.96410 | + | 10.3301i | −0.909517 | + | 1.57533i | −0.0947805 | + | 0.995498i | \(0.530215\pi\) |
−0.814736 | + | 0.579831i | \(0.803118\pi\) | |||||||
\(44\) | 6.46410i | 0.974500i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.23205 | + | 1.86603i | 0.476540 | + | 0.275130i | ||||
\(47\) | − | 3.53590i | − | 0.515764i | −0.966176 | − | 0.257882i | \(-0.916975\pi\) | ||
0.966176 | − | 0.257882i | \(-0.0830245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | + | 0.866025i | 0.485363 | + | 0.120096i | ||||
\(53\) | −0.928203 | −0.127499 | −0.0637493 | − | 0.997966i | \(-0.520306\pi\) | ||||
−0.0637493 | + | 0.997966i | \(0.520306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.23205 | − | 5.59808i | −0.435810 | − | 0.754844i | ||||
\(56\) | −1.00000 | + | 1.73205i | −0.133631 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.232051 | + | 0.133975i | 0.0304698 | + | 0.0175917i | ||||
\(59\) | −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 | \(-0.0650293\pi\) | |||||||
\(62\) | 0.866025 | + | 1.50000i | 0.109985 | + | 0.190500i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.46410 | + | 1.00000i | −0.429669 | + | 0.124035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.92820 | + | 5.73205i | −1.21292 | + | 0.700281i | −0.963395 | − | 0.268086i | \(-0.913609\pi\) |
−0.249528 | + | 0.968368i | \(0.580276\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 2.00000i | − | 0.239046i | ||||||
\(71\) | 10.7321 | + | 6.19615i | 1.27366 | + | 0.735348i | 0.975675 | − | 0.219222i | \(-0.0703521\pi\) |
0.297985 | + | 0.954570i | \(0.403685\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.00000i | − | 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 4.59808 | − | 7.96410i | 0.534516 | − | 0.925808i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.46410 | − | 3.73205i | 0.741483 | − | 0.428096i | ||||
\(77\) | 12.9282 | 1.47331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9282 | −1.56705 | −0.783523 | − | 0.621363i | \(-0.786579\pi\) | ||||
−0.783523 | + | 0.621363i | \(0.786579\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | 8.92820i | 0.979998i | 0.871723 | + | 0.489999i | \(0.163003\pi\) | ||||
−0.871723 | + | 0.489999i | \(0.836997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | − | 2.00000i | −0.375735 | − | 0.216930i | ||||
\(86\) | 11.9282i | 1.28625i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.23205 | + | 5.59808i | 0.344538 | + | 0.596757i | ||||
\(89\) | 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 | ||||
\(92\) | 3.73205 | 0.389093 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.76795 | − | 3.06218i | −0.182350 | − | 0.315840i | ||||
\(95\) | −3.73205 | + | 6.46410i | −0.382900 | + | 0.663203i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.464102 | + | 0.267949i | 0.0471224 | + | 0.0272061i | 0.523376 | − | 0.852102i | \(-0.324672\pi\) |
−0.476254 | + | 0.879308i | \(0.658006\pi\) | |||||||
\(98\) | −2.59808 | − | 1.50000i | −0.262445 | − | 0.151523i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.46410 | + | 2.53590i | 0.145684 | + | 0.252331i | 0.929628 | − | 0.368500i | \(-0.120129\pi\) |
−0.783944 | + | 0.620831i | \(0.786795\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8564 | −1.16825 | −0.584123 | − | 0.811665i | \(-0.698562\pi\) | ||||
−0.584123 | + | 0.811665i | \(0.698562\pi\) | |||||||
\(104\) | 3.46410 | − | 1.00000i | 0.339683 | − | 0.0980581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.803848 | + | 0.464102i | −0.0780766 | + | 0.0450775i | ||||
\(107\) | −3.92820 | − | 6.80385i | −0.379754 | − | 0.657753i | 0.611273 | − | 0.791420i | \(-0.290658\pi\) |
−0.991026 | + | 0.133667i | \(0.957325\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8564i | 1.51877i | 0.650643 | + | 0.759384i | \(0.274500\pi\) | ||||
−0.650643 | + | 0.759384i | \(0.725500\pi\) | |||||||
\(110\) | −5.59808 | − | 3.23205i | −0.533756 | − | 0.308164i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 0.401924 | − | 0.696152i | 0.0378098 | − | 0.0654885i | −0.846501 | − | 0.532387i | \(-0.821295\pi\) |
0.884311 | + | 0.466898i | \(0.154629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.23205 | + | 1.86603i | −0.301390 | + | 0.174008i | ||||
\(116\) | 0.267949 | 0.0248785 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.46410 | −0.779184 | ||||||||
\(119\) | 6.92820 | − | 4.00000i | 0.635107 | − | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3923 | − | 26.6603i | 1.39930 | − | 2.42366i | ||||
\(122\) | − | 10.3923i | − | 0.940875i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | + | 0.866025i | 0.134704 | + | 0.0777714i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.46410 | + | 4.26795i | 0.218654 | + | 0.378719i | 0.954397 | − | 0.298542i | \(-0.0965002\pi\) |
−0.735743 | + | 0.677261i | \(0.763167\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.50000 | + | 2.59808i | −0.219265 | + | 0.227866i | ||||
\(131\) | 18.6603 | 1.63035 | 0.815177 | − | 0.579212i | \(-0.196640\pi\) | ||||
0.815177 | + | 0.579212i | \(0.196640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.46410 | − | 12.9282i | −0.647220 | − | 1.12102i | ||||
\(134\) | −5.73205 | + | 9.92820i | −0.495174 | + | 0.857666i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | 2.13397 | + | 1.23205i | 0.182318 | + | 0.105261i | 0.588381 | − | 0.808584i | \(-0.299765\pi\) |
−0.406063 | + | 0.913845i | \(0.633099\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.46410 | − | 11.1962i | 0.548278 | − | 0.949645i | −0.450115 | − | 0.892971i | \(-0.648617\pi\) |
0.998393 | − | 0.0566745i | \(-0.0180497\pi\) | |||||||
\(140\) | −1.00000 | − | 1.73205i | −0.0845154 | − | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.3923 | 1.03994 | ||||||||
\(143\) | −16.7942 | − | 16.1603i | −1.40440 | − | 1.35139i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.232051 | + | 0.133975i | −0.0192708 | + | 0.0111260i | ||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.19615i | − | 0.755919i | ||||||
\(149\) | 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 | \(0.861027\pi\) | |||||||
\(152\) | 3.73205 | − | 6.46410i | 0.302709 | − | 0.524308i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.1962 | − | 6.46410i | 0.902212 | − | 0.520892i | ||||
\(155\) | −1.73205 | −0.139122 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | −0.399043 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(158\) | −12.0622 | + | 6.96410i | −0.959615 | + | 0.554034i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | − | 7.46410i | − | 0.588254i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0359 | + | 7.52628i | 1.02105 | + | 0.589504i | 0.914408 | − | 0.404794i | \(-0.132657\pi\) |
0.106642 | + | 0.994297i | \(0.465990\pi\) | |||||||
\(164\) | 2.00000i | 0.156174i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.46410 | + | 7.73205i | 0.346481 | + | 0.600124i | ||||
\(167\) | −14.1340 | + | 8.16025i | −1.09372 | + | 0.631459i | −0.934564 | − | 0.355794i | \(-0.884210\pi\) |
−0.159155 | + | 0.987254i | \(0.550877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.96410 | + | 10.3301i | 0.454758 | + | 0.787665i | ||||
\(173\) | 5.46410 | − | 9.46410i | 0.415428 | − | 0.719542i | −0.580045 | − | 0.814584i | \(-0.696965\pi\) |
0.995473 | + | 0.0950419i | \(0.0302985\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | + | 1.00000i | 0.130931 | + | 0.0755929i | ||||
\(176\) | 5.59808 | + | 3.23205i | 0.421971 | + | 0.243625i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.267949 | − | 0.464102i | 0.0200836 | − | 0.0347859i | ||||
\(179\) | −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 | \(0.534709\pi\) | |||||||
\(182\) | −2.00000 | − | 6.92820i | −0.148250 | − | 0.513553i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.23205 | − | 1.86603i | 0.238270 | − | 0.137565i | ||||
\(185\) | 4.59808 | + | 7.96410i | 0.338057 | + | 0.585532i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 25.8564i | − | 1.89081i | ||||||
\(188\) | −3.06218 | − | 1.76795i | −0.223332 | − | 0.128941i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.46410i | 0.541503i | ||||||||
\(191\) | 10.7321 | − | 18.5885i | 0.776544 | − | 1.34501i | −0.157379 | − | 0.987538i | \(-0.550304\pi\) |
0.933923 | − | 0.357475i | \(-0.116362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.80385 | − | 5.66025i | 0.705696 | − | 0.407434i | −0.103769 | − | 0.994601i | \(-0.533090\pi\) |
0.809466 | + | 0.587167i | \(0.199757\pi\) | |||||||
\(194\) | 0.535898 | 0.0384753 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −3.80385 | + | 2.19615i | −0.271013 | + | 0.156469i | −0.629348 | − | 0.777124i | \(-0.716678\pi\) |
0.358335 | + | 0.933593i | \(0.383345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.53590 | − | 4.39230i | 0.179765 | − | 0.311362i | −0.762035 | − | 0.647536i | \(-0.775800\pi\) |
0.941800 | + | 0.336174i | \(0.109133\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.53590 | + | 1.46410i | 0.178425 | + | 0.103014i | ||||
\(203\) | − | 0.535898i | − | 0.0376127i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | −10.2679 | + | 5.92820i | −0.715402 | + | 0.413037i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.50000 | − | 2.59808i | 0.173344 | − | 0.180144i | ||||
\(209\) | −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 | \(0.705923\pi\) | |||||||
\(212\) | −0.464102 | + | 0.803848i | −0.0318746 | + | 0.0552085i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.80385 | − | 3.92820i | −0.465101 | − | 0.268526i | ||||
\(215\) | −10.3301 | − | 5.96410i | −0.704509 | − | 0.406748i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73205 | − | 3.00000i | 0.117579 | − | 0.203653i | ||||
\(218\) | 7.92820 | + | 13.7321i | 0.536966 | + | 0.930052i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.46410 | −0.435810 | ||||||||
\(221\) | −14.0000 | − | 3.46410i | −0.941742 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7846 | + | 10.2679i | −1.19095 | + | 0.687593i | −0.958521 | − | 0.285022i | \(-0.907999\pi\) |
−0.232424 | + | 0.972614i | \(0.574666\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 0.803848i | − | 0.0534711i | ||||||
\(227\) | 14.1962 | + | 8.19615i | 0.942232 | + | 0.543998i | 0.890659 | − | 0.454672i | \(-0.150243\pi\) |
0.0515725 | + | 0.998669i | \(0.483577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.85641i | 0.519166i | 0.965721 | + | 0.259583i | \(0.0835851\pi\) | ||||
−0.965721 | + | 0.259583i | \(0.916415\pi\) | |||||||
\(230\) | −1.86603 | + | 3.23205i | −0.123042 | + | 0.213115i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.232051 | − | 0.133975i | 0.0152349 | − | 0.00879586i | ||||
\(233\) | −6.12436 | −0.401220 | −0.200610 | − | 0.979671i | \(-0.564292\pi\) | ||||
−0.200610 | + | 0.979671i | \(0.564292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53590 | 0.230657 | ||||||||
\(236\) | −7.33013 | + | 4.23205i | −0.477151 | + | 0.275483i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | − | 6.92820i | 0.259281 | − | 0.449089i | ||||
\(239\) | − | 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 | \(0.473179\pi\) | |||||||
\(242\) | − | 30.7846i | − | 1.97891i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.19615 | − | 9.00000i | −0.332650 | − | 0.576166i | ||||
\(245\) | 2.59808 | − | 1.50000i | 0.165985 | − | 0.0958315i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.46410 | + | 26.1244i | −0.411301 | + | 1.66225i | ||||
\(248\) | 1.73205 | 0.109985 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 7.86603 | − | 13.6244i | 0.496499 | − | 0.859962i | −0.503493 | − | 0.863999i | \(-0.667952\pi\) |
0.999992 | + | 0.00403776i | \(0.00128526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.8923 | − | 12.0622i | −1.31349 | − | 0.758343i | ||||
\(254\) | 4.26795 | + | 2.46410i | 0.267795 | + | 0.154611i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.66987 | − | 4.62436i | −0.166542 | − | 0.288459i | 0.770660 | − | 0.637247i | \(-0.219927\pi\) |
−0.937202 | + | 0.348787i | \(0.886593\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.3923 | −1.14284 | ||||||||
\(260\) | −0.866025 | + | 3.50000i | −0.0537086 | + | 0.217061i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.1603 | − | 9.33013i | 0.998384 | − | 0.576417i | ||||
\(263\) | 3.06218 | + | 5.30385i | 0.188822 | + | 0.327049i | 0.944858 | − | 0.327481i | \(-0.106200\pi\) |
−0.756036 | + | 0.654530i | \(0.772866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.928203i | − | 0.0570191i | ||||||
\(266\) | −12.9282 | − | 7.46410i | −0.792679 | − | 0.457653i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.4641i | 0.700281i | ||||||||
\(269\) | 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 | \(0.321766\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.46410 | 0.148862 | ||||||||
\(275\) | 5.59808 | − | 3.23205i | 0.337577 | − | 0.194900i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96410 | − | 3.40192i | 0.118011 | − | 0.204402i | −0.800968 | − | 0.598707i | \(-0.795681\pi\) |
0.918980 | + | 0.394305i | \(0.129015\pi\) | |||||||
\(278\) | − | 12.9282i | − | 0.775382i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.73205 | − | 1.00000i | −0.103510 | − | 0.0597614i | ||||
\(281\) | − | 8.92820i | − | 0.532612i | −0.963889 | − | 0.266306i | \(-0.914197\pi\) | ||
0.963889 | − | 0.266306i | \(-0.0858032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.96410 | + | 8.59808i | 0.295085 | + | 0.511103i | 0.975005 | − | 0.222184i | \(-0.0713186\pi\) |
−0.679920 | + | 0.733287i | \(0.737985\pi\) | |||||||
\(284\) | 10.7321 | − | 6.19615i | 0.636830 | − | 0.367674i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.6244 | − | 5.59808i | −1.33781 | − | 0.331021i | ||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | −0.133975 | + | 0.232051i | −0.00786726 | + | 0.0136265i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.73205 | − | 1.00000i | −0.101361 | − | 0.0585206i | ||||
\(293\) | 27.5885 | + | 15.9282i | 1.61173 | + | 0.930536i | 0.988968 | + | 0.148128i | \(0.0473247\pi\) |
0.622767 | + | 0.782408i | \(0.286009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.23205 | − | 7.33013i | 0.246400 | − | 0.426776i | ||||
\(296\) | −4.59808 | − | 7.96410i | −0.267258 | − | 0.462904i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.5359 | 0.784114 | ||||||||
\(299\) | −9.33013 | + | 9.69615i | −0.539575 | + | 0.560743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.6603 | − | 11.9282i | 1.19084 | − | 0.687530i | ||||
\(302\) | 5.19615 | + | 9.00000i | 0.299005 | + | 0.517892i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 7.46410i | − | 0.428096i | ||||||
\(305\) | 9.00000 | + | 5.19615i | 0.515339 | + | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.4641i | − | 1.11087i | −0.831558 | − | 0.555437i | \(-0.812551\pi\) | ||
0.831558 | − | 0.555437i | \(-0.187449\pi\) | |||||||
\(308\) | 6.46410 | − | 11.1962i | 0.368326 | − | 0.637960i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.50000 | + | 0.866025i | −0.0851943 | + | 0.0491869i | ||||
\(311\) | 28.3923 | 1.60998 | 0.804990 | − | 0.593288i | \(-0.202171\pi\) | ||||
0.804990 | + | 0.593288i | \(0.202171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0000 | −1.58265 | −0.791327 | − | 0.611393i | \(-0.790609\pi\) | ||||
−0.791327 | + | 0.611393i | \(0.790609\pi\) | |||||||
\(314\) | −4.33013 | + | 2.50000i | −0.244363 | + | 0.141083i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.96410 | + | 12.0622i | −0.391761 | + | 0.678551i | ||||
\(317\) | 14.5359i | 0.816417i | 0.912889 | + | 0.408209i | \(0.133846\pi\) | ||||
−0.912889 | + | 0.408209i | \(0.866154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.50000 | − | 0.866025i | −0.0839839 | − | 0.0484881i | ||||
\(320\) | − | 1.00000i | − | 0.0559017i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.73205 | − | 6.46410i | −0.207979 | − | 0.360230i | ||||
\(323\) | −25.8564 | + | 14.9282i | −1.43869 | + | 0.830627i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | − | 3.46410i | −0.0554700 | − | 0.192154i | ||||
\(326\) | 15.0526 | 0.833684 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.00000 | + | 1.73205i | 0.0552158 | + | 0.0956365i | ||||
\(329\) | −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 | \(0.819277\pi\) | |||||||
\(332\) | 7.73205 | + | 4.46410i | 0.424351 | + | 0.244999i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.16025 | + | 14.1340i | −0.446509 | + | 0.773377i | ||||
\(335\) | −5.73205 | − | 9.92820i | −0.313175 | − | 0.542436i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.32051 | 0.507720 | 0.253860 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(338\) | −6.06218 | + | 11.5000i | −0.329739 | + | 0.625518i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46410 | + | 2.00000i | −0.187867 | + | 0.108465i | ||||
\(341\) | −5.59808 | − | 9.69615i | −0.303153 | − | 0.525076i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 10.3301 | + | 5.96410i | 0.556963 | + | 0.321563i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 10.9282i | − | 0.587504i | ||||||
\(347\) | 0.803848 | − | 1.39230i | 0.0431528 | − | 0.0747428i | −0.843642 | − | 0.536906i | \(-0.819593\pi\) |
0.886795 | + | 0.462163i | \(0.152926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.5885 | − | 10.7321i | 0.995017 | − | 0.574474i | 0.0882471 | − | 0.996099i | \(-0.471873\pi\) |
0.906770 | + | 0.421625i | \(0.138540\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.46410 | 0.344538 | ||||||||
\(353\) | −1.73205 | + | 1.00000i | −0.0921878 | + | 0.0532246i | −0.545385 | − | 0.838186i | \(-0.683617\pi\) |
0.453197 | + | 0.891410i | \(0.350283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.19615 | + | 10.7321i | −0.328858 | + | 0.569598i | ||||
\(356\) | − | 0.535898i | − | 0.0284026i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.0885 | − | 9.86603i | −0.903153 | − | 0.521436i | ||||
\(359\) | 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 | ||||
\(362\) | −2.53590 | + | 1.46410i | −0.133284 | + | 0.0769515i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.19615 | − | 5.00000i | −0.272352 | − | 0.262071i | ||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.80385 | − | 13.5167i | −0.407358 | − | 0.705564i | 0.587235 | − | 0.809416i | \(-0.300216\pi\) |
−0.994593 | + | 0.103852i | \(0.966883\pi\) | |||||||
\(368\) | 1.86603 | − | 3.23205i | 0.0972733 | − | 0.168482i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.96410 | + | 4.59808i | 0.414034 | + | 0.239043i | ||||
\(371\) | 1.60770 | + | 0.928203i | 0.0834674 | + | 0.0481899i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.89230 | − | 13.6699i | 0.408648 | − | 0.707799i | −0.586090 | − | 0.810246i | \(-0.699334\pi\) |
0.994739 | + | 0.102446i | \(0.0326670\pi\) | |||||||
\(374\) | −12.9282 | − | 22.3923i | −0.668501 | − | 1.15788i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.53590 | −0.182350 | ||||||||
\(377\) | −0.669873 | + | 0.696152i | −0.0345002 | + | 0.0358537i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1244 | − | 13.9282i | 1.23918 | − | 0.715444i | 0.270257 | − | 0.962788i | \(-0.412891\pi\) |
0.968928 | + | 0.247344i | \(0.0795579\pi\) | |||||||
\(380\) | 3.73205 | + | 6.46410i | 0.191450 | + | 0.331601i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 21.4641i | − | 1.09820i | ||||||
\(383\) | −21.9904 | − | 12.6962i | −1.12366 | − | 0.648743i | −0.181324 | − | 0.983423i | \(-0.558038\pi\) |
−0.942332 | + | 0.334680i | \(0.891372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9282i | 0.658882i | ||||||||
\(386\) | 5.66025 | − | 9.80385i | 0.288099 | − | 0.499003i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.464102 | − | 0.267949i | 0.0235612 | − | 0.0136031i | ||||
\(389\) | 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 | ||||||||
\(392\) | −2.59808 | + | 1.50000i | −0.131223 | + | 0.0757614i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.19615 | + | 3.80385i | −0.110641 | + | 0.191635i | ||||
\(395\) | − | 13.9282i | − | 0.700804i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5000 | + | 6.06218i | 0.526980 | + | 0.304252i | 0.739786 | − | 0.672843i | \(-0.234927\pi\) |
−0.212806 | + | 0.977095i | \(0.568260\pi\) | |||||||
\(398\) | − | 5.07180i | − | 0.254226i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 27.7128 | − | 16.0000i | 1.38391 | − | 0.799002i | 0.391292 | − | 0.920267i | \(-0.372028\pi\) |
0.992620 | + | 0.121265i | \(0.0386950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | + | 1.73205i | −0.298881 | + | 0.0862796i | ||||
\(404\) | 2.92820 | 0.145684 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.267949 | − | 0.464102i | −0.0132981 | − | 0.0230330i | ||||
\(407\) | −29.7224 | + | 51.4808i | −1.47329 | + | 2.55181i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.46410 | + | 2.00000i | 0.171289 | + | 0.0988936i | 0.583193 | − | 0.812333i | \(-0.301803\pi\) |
−0.411905 | + | 0.911227i | \(0.635136\pi\) | |||||||
\(410\) | −1.73205 | − | 1.00000i | −0.0855399 | − | 0.0493865i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.92820 | + | 10.2679i | −0.292062 | + | 0.505866i | ||||
\(413\) | 8.46410 | + | 14.6603i | 0.416491 | + | 0.721384i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.92820 | −0.438268 | ||||||||
\(416\) | 0.866025 | − | 3.50000i | 0.0424604 | − | 0.171602i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −41.7846 | + | 24.1244i | −2.04375 | + | 1.17996i | ||||
\(419\) | 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 | \(-0.0341353\pi\) | |||||||
\(422\) | 9.80385 | + | 5.66025i | 0.477244 | + | 0.275537i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.928203i | 0.0450775i | ||||||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.0000 | + | 10.3923i | −0.871081 | + | 0.502919i | ||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.9282 | −0.575229 | ||||||||
\(431\) | −24.5885 | + | 14.1962i | −1.18438 | + | 0.683805i | −0.957025 | − | 0.290006i | \(-0.906343\pi\) |
−0.227360 | + | 0.973811i | \(0.573009\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.66025 | + | 16.7321i | −0.464242 | + | 0.804091i | −0.999167 | − | 0.0408086i | \(-0.987007\pi\) |
0.534925 | + | 0.844900i | \(0.320340\pi\) | |||||||
\(434\) | − | 3.46410i | − | 0.166282i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.7321 | + | 7.92820i | 0.657646 | + | 0.379692i | ||||
\(437\) | 27.8564i | 1.33255i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.92820 | + | 15.4641i | 0.426120 | + | 0.738061i | 0.996524 | − | 0.0833027i | \(-0.0265468\pi\) |
−0.570404 | + | 0.821364i | \(0.693214\pi\) | |||||||
\(440\) | −5.59808 | + | 3.23205i | −0.266878 | + | 0.154082i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.8564 | + | 4.00000i | −0.659082 | + | 0.190261i | ||||
\(443\) | −16.3923 | −0.778822 | −0.389411 | − | 0.921064i | \(-0.627321\pi\) | ||||
−0.389411 | + | 0.921064i | \(0.627321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.267949 | + | 0.464102i | 0.0127020 | + | 0.0220005i | ||||
\(446\) | −10.2679 | + | 17.7846i | −0.486201 | + | 0.842126i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.73205 | + | 1.00000i | 0.0818317 | + | 0.0472456i | ||||
\(449\) | 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 | ||||
\(452\) | −0.401924 | − | 0.696152i | −0.0189049 | − | 0.0327443i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.3923 | 0.769329 | ||||||||
\(455\) | 7.00000 | + | 1.73205i | 0.328165 | + | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2487 | − | 12.2679i | 0.993973 | − | 0.573870i | 0.0875134 | − | 0.996163i | \(-0.472108\pi\) |
0.906459 | + | 0.422293i | \(0.138775\pi\) | |||||||
\(458\) | 3.92820 | + | 6.80385i | 0.183553 | + | 0.317923i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.73205i | 0.174008i | ||||||||
\(461\) | −0.401924 | − | 0.232051i | −0.0187195 | − | 0.0108077i | 0.490611 | − | 0.871379i | \(-0.336774\pi\) |
−0.509331 | + | 0.860571i | \(0.670107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.07180i | − | 0.328654i | −0.986406 | − | 0.164327i | \(-0.947455\pi\) | ||
0.986406 | − | 0.164327i | \(-0.0525453\pi\) | |||||||
\(464\) | 0.133975 | − | 0.232051i | 0.00621961 | − | 0.0107727i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.30385 | + | 3.06218i | −0.245696 | + | 0.141853i | ||||
\(467\) | 15.8564 | 0.733747 | 0.366873 | − | 0.930271i | \(-0.380428\pi\) | ||||
0.366873 | + | 0.930271i | \(0.380428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.9282 | 1.05873 | ||||||||
\(470\) | 3.06218 | − | 1.76795i | 0.141248 | − | 0.0815494i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.23205 | + | 7.33013i | −0.194796 | + | 0.337396i | ||||
\(473\) | − | 77.1051i | − | 3.54530i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.46410 | − | 3.73205i | −0.296593 | − | 0.171238i | ||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.19615 | − | 14.1962i | −0.374883 | − | 0.649317i | ||||
\(479\) | −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 | ||||
\(482\) | 17.7321 | 0.807673 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.3923 | − | 26.6603i | −0.699650 | − | 1.21183i | ||||
\(485\) | −0.267949 | + | 0.464102i | −0.0121669 | + | 0.0210738i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0718 | + | 11.5885i | 0.909540 | + | 0.525123i | 0.880283 | − | 0.474449i | \(-0.157353\pi\) |
0.0292568 | + | 0.999572i | \(0.490686\pi\) | |||||||
\(488\) | −9.00000 | − | 5.19615i | −0.407411 | − | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.50000 | − | 2.59808i | 0.0677631 | − | 0.117369i | ||||
\(491\) | −8.66025 | − | 15.0000i | −0.390832 | − | 0.676941i | 0.601728 | − | 0.798701i | \(-0.294479\pi\) |
−0.992559 | + | 0.121761i | \(0.961146\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.07180 | −0.0482713 | ||||||||
\(494\) | 7.46410 | + | 25.8564i | 0.335826 | + | 1.16333i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | − | 0.866025i | 0.0673520 | − | 0.0388857i | ||||
\(497\) | −12.3923 | − | 21.4641i | −0.555871 | − | 0.962797i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.53590i | − | 0.292587i | −0.989241 | − | 0.146293i | \(-0.953266\pi\) | ||
0.989241 | − | 0.146293i | \(-0.0467344\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 15.7321i | − | 0.702156i | ||||||
\(503\) | −15.5885 | + | 27.0000i | −0.695055 | + | 1.20387i | 0.275107 | + | 0.961414i | \(0.411287\pi\) |
−0.970162 | + | 0.242457i | \(0.922047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53590 | + | 1.46410i | −0.112846 | + | 0.0651517i | ||||
\(506\) | −24.1244 | −1.07246 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.92820 | 0.218654 | ||||||||
\(509\) | −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 | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.62436 | − | 2.66987i | −0.203972 | − | 0.117763i | ||||
\(515\) | − | 11.8564i | − | 0.522456i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4282 | + | 19.7942i | 0.502612 | + | 0.870549i | ||||
\(518\) | −15.9282 | + | 9.19615i | −0.699845 | + | 0.404056i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | + | 3.46410i | 0.0438529 | + | 0.151911i | ||||
\(521\) | 17.3205 | 0.758825 | 0.379413 | − | 0.925228i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925228i | \(0.376126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.89230 | − | 10.2058i | −0.257653 | − | 0.446267i | 0.707960 | − | 0.706252i | \(-0.249616\pi\) |
−0.965613 | + | 0.259985i | \(0.916282\pi\) | |||||||
\(524\) | 9.33013 | − | 16.1603i | 0.407588 | − | 0.705964i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.30385 | + | 3.06218i | 0.231259 | + | 0.133517i | ||||
\(527\) | −6.00000 | − | 3.46410i | −0.261364 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.53590 | − | 7.85641i | 0.197213 | − | 0.341583i | ||||
\(530\) | −0.464102 | − | 0.803848i | −0.0201593 | − | 0.0349169i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9282 | −0.647220 | ||||||||
\(533\) | −5.19615 | − | 5.00000i | −0.225070 | − | 0.216574i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.80385 | − | 3.92820i | 0.294156 | − | 0.169831i | ||||
\(536\) | 5.73205 | + | 9.92820i | 0.247587 | + | 0.428833i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 12.0000i | − | 0.517357i | ||||||
\(539\) | 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 | \(-0.196505\pi\) | |||||||
\(542\) | 0.598076 | − | 1.03590i | 0.0256896 | − | 0.0444956i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | −15.8564 | −0.679214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9282 | 0.980339 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(548\) | 2.13397 | − | 1.23205i | 0.0911589 | − | 0.0526306i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.23205 | − | 5.59808i | 0.137815 | − | 0.238703i | ||||
\(551\) | 2.00000i | 0.0852029i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.1244 | + | 13.9282i | 1.02587 | + | 0.592287i | ||||
\(554\) | − | 3.92820i | − | 0.166893i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.46410 | − | 11.1962i | −0.274139 | − | 0.474823i | ||||
\(557\) | −15.3397 | + | 8.85641i | −0.649966 | + | 0.375258i | −0.788443 | − | 0.615108i | \(-0.789113\pi\) |
0.138477 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.7487 | − | 10.3301i | −1.76578 | − | 0.436918i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.46410 | − | 7.73205i | −0.188307 | − | 0.326157i | ||||
\(563\) | −2.33975 | + | 4.05256i | −0.0986085 | + | 0.170795i | −0.911109 | − | 0.412166i | \(-0.864772\pi\) |
0.812500 | + | 0.582961i | \(0.198106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.696152 | + | 0.401924i | 0.0292874 | + | 0.0169091i | ||||
\(566\) | 8.59808 | + | 4.96410i | 0.361404 | + | 0.208657i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.19615 | − | 10.7321i | 0.259985 | − | 0.450307i | ||||
\(569\) | 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 | \(0.617024\pi\) | |||||||
\(572\) | −22.3923 | + | 6.46410i | −0.936269 | + | 0.270278i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.46410 | − | 2.00000i | 0.144589 | − | 0.0834784i | ||||
\(575\) | −1.86603 | − | 3.23205i | −0.0778186 | − | 0.134786i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0000i | 0.416305i | 0.978096 | + | 0.208153i | \(0.0667451\pi\) | ||||
−0.978096 | + | 0.208153i | \(0.933255\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.267949i | 0.0111260i | ||||||||
\(581\) | 8.92820 | − | 15.4641i | 0.370404 | − | 0.641559i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.19615 | − | 3.00000i | 0.215203 | − | 0.124247i | ||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8564 | 1.31598 | ||||||||
\(587\) | 2.07180 | − | 1.19615i | 0.0855122 | − | 0.0493705i | −0.456634 | − | 0.889655i | \(-0.650945\pi\) |
0.542146 | + | 0.840284i | \(0.317612\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.46410 | + | 11.1962i | −0.266349 | + | 0.461329i | ||||
\(590\) | − | 8.46410i | − | 0.348462i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.96410 | − | 4.59808i | −0.327323 | − | 0.188980i | ||||
\(593\) | 45.1051i | 1.85225i | 0.377223 | + | 0.926123i | \(0.376879\pi\) | ||||
−0.377223 | + | 0.926123i | \(0.623121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | + | 6.92820i | 0.163984 | + | 0.284029i | ||||
\(596\) | 11.7224 | − | 6.76795i | 0.480170 | − | 0.277226i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.23205 | + | 13.0622i | −0.132168 | + | 0.534152i | ||||
\(599\) | 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 | \(0.701121\pi\) | |||||||
\(602\) | 11.9282 | − | 20.6603i | 0.486157 | − | 0.842049i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.00000 | + | 5.19615i | 0.366205 | + | 0.211428i | ||||
\(605\) | 26.6603 | + | 15.3923i | 1.08389 | + | 0.625786i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.58846 | − | 16.6077i | 0.389183 | − | 0.674086i | −0.603156 | − | 0.797623i | \(-0.706091\pi\) |
0.992340 | + | 0.123537i | \(0.0394239\pi\) | |||||||
\(608\) | −3.73205 | − | 6.46410i | −0.151355 | − | 0.262154i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.3923 | 0.420772 | ||||||||
\(611\) | 12.2487 | − | 3.53590i | 0.495530 | − | 0.143047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.8205 | + | 19.5263i | −1.36600 | + | 0.788659i | −0.990414 | − | 0.138130i | \(-0.955891\pi\) |
−0.375583 | + | 0.926789i | \(0.622558\pi\) | |||||||
\(614\) | −9.73205 | − | 16.8564i | −0.392754 | − | 0.680269i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 12.9282i | − | 0.520892i | ||||||
\(617\) | 19.4545 | + | 11.2321i | 0.783208 | + | 0.452185i | 0.837566 | − | 0.546336i | \(-0.183978\pi\) |
−0.0543580 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.2487i | 0.974638i | 0.873224 | + | 0.487319i | \(0.162025\pi\) | ||||
−0.873224 | + | 0.487319i | \(0.837975\pi\) | |||||||
\(620\) | −0.866025 | + | 1.50000i | −0.0347804 | + | 0.0602414i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.5885 | − | 14.1962i | 0.985907 | − | 0.569214i | ||||
\(623\) | −1.07180 | −0.0429406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.2487 | + | 14.0000i | −0.969173 | + | 0.559553i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.50000 | + | 4.33013i | −0.0997609 | + | 0.172791i | ||||
\(629\) | 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 | \(0.451242\pi\) | |||||||
\(632\) | 13.9282i | 0.554034i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.26795 | + | 12.5885i | 0.288647 | + | 0.499952i | ||||
\(635\) | −4.26795 | + | 2.46410i | −0.169368 | + | 0.0977849i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.50000 | − | 7.79423i | 0.297161 | − | 0.308819i | ||||
\(638\) | −1.73205 | −0.0685725 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 0.0717968 | − | 0.124356i | 0.00283580 | − | 0.00491175i | −0.864604 | − | 0.502454i | \(-0.832431\pi\) |
0.867440 | + | 0.497542i | \(0.165764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7846 | − | 10.2679i | −0.701357 | − | 0.404928i | 0.106496 | − | 0.994313i | \(-0.466037\pi\) |
−0.807852 | + | 0.589385i | \(0.799370\pi\) | |||||||
\(644\) | −6.46410 | − | 3.73205i | −0.254721 | − | 0.147063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9282 | + | 25.8564i | −0.587342 | + | 1.01731i | ||||
\(647\) | −6.66025 | − | 11.5359i | −0.261842 | − | 0.453523i | 0.704890 | − | 0.709317i | \(-0.250996\pi\) |
−0.966731 | + | 0.255794i | \(0.917663\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.7128 | 2.14767 | ||||||||
\(650\) | −2.59808 | − | 2.50000i | −0.101905 | − | 0.0980581i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0359 | − | 7.52628i | 0.510525 | − | 0.294752i | ||||
\(653\) | 2.12436 | + | 3.67949i | 0.0831325 | + | 0.143990i | 0.904594 | − | 0.426274i | \(-0.140174\pi\) |
−0.821461 | + | 0.570264i | \(0.806841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.6603i | 0.729116i | ||||||||
\(656\) | 1.73205 | + | 1.00000i | 0.0676252 | + | 0.0390434i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.07180i | 0.275687i | ||||||||
\(659\) | −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 | \(0.387321\pi\) | |||||||
\(662\) | −16.7846 | −0.652352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.92820 | 0.346481 | ||||||||
\(665\) | 12.9282 | − | 7.46410i | 0.501334 | − | 0.289445i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.500000 | + | 0.866025i | −0.0193601 | + | 0.0335326i | ||||
\(668\) | 16.3205i | 0.631459i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.92820 | − | 5.73205i | −0.383560 | − | 0.221448i | ||||
\(671\) | 67.1769i | 2.59334i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | − | 27.7128i | −0.616755 | − | 1.06825i | −0.990074 | − | 0.140548i | \(-0.955114\pi\) |
0.373319 | − | 0.927703i | \(-0.378220\pi\) | |||||||
\(674\) | 8.07180 | − | 4.66025i | 0.310914 | − | 0.179506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 12.9904i | 0.0192308 | + | 0.499630i | ||||
\(677\) | −32.3923 | −1.24494 | −0.622469 | − | 0.782645i | \(-0.713870\pi\) | ||||
−0.622469 | + | 0.782645i | \(0.713870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.535898 | − | 0.928203i | −0.0205659 | − | 0.0356212i | ||||
\(680\) | −2.00000 | + | 3.46410i | −0.0766965 | + | 0.132842i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.69615 | − | 5.59808i | −0.371285 | − | 0.214361i | ||||
\(683\) | 35.3205 | + | 20.3923i | 1.35150 | + | 0.780290i | 0.988460 | − | 0.151483i | \(-0.0484049\pi\) |
0.363042 | + | 0.931773i | \(0.381738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.23205 | + | 2.13397i | −0.0470742 | + | 0.0815350i | ||||
\(686\) | 10.0000 | + | 17.3205i | 0.381802 | + | 0.661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.9282 | 0.454758 | ||||||||
\(689\) | −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 | \(0.506258\pi\) | |||||||
\(692\) | −5.46410 | − | 9.46410i | −0.207714 | − | 0.359771i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.60770i | − | 0.0610273i | ||||||
\(695\) | 11.1962 | + | 6.46410i | 0.424694 | + | 0.245197i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.00000i | − | 0.303022i | ||||||
\(698\) | 10.7321 | − | 18.5885i | 0.406214 | − | 0.703583i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.73205 | − | 1.00000i | 0.0654654 | − | 0.0377964i | ||||
\(701\) | 0.267949 | 0.0101203 | 0.00506015 | − | 0.999987i | \(-0.498389\pi\) | ||||
0.00506015 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6410 | 2.58884 | ||||||||
\(704\) | 5.59808 | − | 3.23205i | 0.210985 | − | 0.121812i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.00000 | + | 1.73205i | −0.0376355 | + | 0.0651866i | ||||
\(707\) | − | 5.85641i | − | 0.220253i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8564 | − | 11.4641i | −0.745723 | − | 0.430543i | 0.0784234 | − | 0.996920i | \(-0.475011\pi\) |
−0.824146 | + | 0.566377i | \(0.808345\pi\) | |||||||
\(710\) | 12.3923i | 0.465075i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.267949 | − | 0.464102i | −0.0100418 | − | 0.0173929i | ||||
\(713\) | −5.59808 | + | 3.23205i | −0.209650 | + | 0.121041i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1603 | − | 16.7942i | 0.604359 | − | 0.628069i | ||||
\(716\) | −19.7321 | −0.737421 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.53590 | + | 4.39230i | 0.0946389 | + | 0.163919i | ||||
\(719\) | −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 | ||||
\(722\) | 31.7942 | + | 18.3564i | 1.18326 | + | 0.683155i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.46410 | + | 2.53590i | −0.0544129 | + | 0.0942459i | ||||
\(725\) | −0.133975 | − | 0.232051i | −0.00497569 | − | 0.00861815i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7128 | −1.17616 | −0.588082 | − | 0.808802i | \(-0.700117\pi\) | ||||
−0.588082 | + | 0.808802i | \(0.700117\pi\) | |||||||
\(728\) | −7.00000 | − | 1.73205i | −0.259437 | − | 0.0641941i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.73205 | − | 1.00000i | 0.0641061 | − | 0.0370117i | ||||
\(731\) | −23.8564 | − | 41.3205i | −0.882361 | − | 1.52829i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.9282i | 1.88108i | 0.339688 | + | 0.940538i | \(0.389678\pi\) | ||||
−0.339688 | + | 0.940538i | \(0.610322\pi\) | |||||||
\(734\) | −13.5167 | − | 7.80385i | −0.498909 | − | 0.288045i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.73205i | − | 0.137565i | ||||||
\(737\) | 37.0526 | − | 64.1769i | 1.36485 | − | 2.36399i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7321 | + | 9.66025i | −0.615498 | + | 0.355358i | −0.775114 | − | 0.631821i | \(-0.782308\pi\) |
0.159616 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(740\) | 9.19615 | 0.338057 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85641 | 0.0681508 | ||||||||
\(743\) | 35.0429 | − | 20.2321i | 1.28560 | − | 0.742242i | 0.307734 | − | 0.951472i | \(-0.400429\pi\) |
0.977866 | + | 0.209230i | \(0.0670958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.76795 | + | 11.7224i | −0.247958 | + | 0.429477i | ||||
\(746\) | − | 15.7846i | − | 0.577916i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.3923 | − | 12.9282i | −0.818744 | − | 0.472702i | ||||
\(749\) | 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 | \(0.915983\pi\) | |||||||
\(752\) | −3.06218 | + | 1.76795i | −0.111666 | + | 0.0644705i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.232051 | + | 0.937822i | −0.00845079 | + | 0.0341535i | ||||
\(755\) | −10.3923 | −0.378215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | + | 15.5885i | 0.327111 | + | 0.566572i | 0.981937 | − | 0.189207i | \(-0.0605917\pi\) |
−0.654827 | + | 0.755779i | \(0.727258\pi\) | |||||||
\(758\) | 13.9282 | − | 24.1244i | 0.505895 | − | 0.876236i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.46410 | + | 3.73205i | 0.234478 | + | 0.135376i | ||||
\(761\) | −4.39230 | − | 2.53590i | −0.159221 | − | 0.0919262i | 0.418272 | − | 0.908322i | \(-0.362636\pi\) |
−0.577493 | + | 0.816395i | \(0.695969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.8564 | − | 27.4641i | 0.574040 | − | 0.994267i | ||||
\(764\) | −10.7321 | − | 18.5885i | −0.388272 | − | 0.672507i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.3923 | −0.917461 | ||||||||
\(767\) | 7.33013 | − | 29.6244i | 0.264676 | − | 1.06967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0359 | + | 5.79423i | −0.361904 | + | 0.208945i | −0.669916 | − | 0.742437i | \(-0.733670\pi\) |
0.308012 | + | 0.951383i | \(0.400336\pi\) | |||||||
\(770\) | 6.46410 | + | 11.1962i | 0.232950 | + | 0.403481i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 11.3205i | − | 0.407434i | ||||||
\(773\) | −24.0000 | − | 13.8564i | −0.863220 | − | 0.498380i | 0.00186926 | − | 0.999998i | \(-0.499405\pi\) |
−0.865089 | + | 0.501618i | \(0.832738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.73205i | − | 0.0622171i | ||||||
\(776\) | 0.267949 | − | 0.464102i | 0.00961882 | − | 0.0166603i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.5526 | − | 11.8660i | 0.736845 | − | 0.425418i | ||||
\(779\) | −14.9282 | −0.534858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −80.1051 | −2.86639 | ||||||||
\(782\) | −12.9282 | + | 7.46410i | −0.462312 | + | 0.266916i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | − | 5.00000i | − | 0.178458i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | + | 0.866025i | 0.0534692 | + | 0.0308705i | 0.526496 | − | 0.850177i | \(-0.323505\pi\) |
−0.473027 | + | 0.881048i | \(0.656839\pi\) | |||||||
\(788\) | 4.39230i | 0.156469i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.96410 | − | 12.0622i | −0.247772 | − | 0.429153i | ||||
\(791\) | −1.39230 | + | 0.803848i | −0.0495047 | + | 0.0285815i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.3731 | + | 9.00000i | 1.29165 | + | 0.319599i | ||||
\(794\) | 12.1244 | 0.430277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.53590 | − | 4.39230i | −0.0898825 | − | 0.155681i | ||||
\(797\) | −5.07180 | + | 8.78461i | −0.179652 | + | 0.311167i | −0.941761 | − | 0.336282i | \(-0.890831\pi\) |
0.762109 | + | 0.647449i | \(0.224164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2487 | + | 7.07180i | 0.433328 | + | 0.250182i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0000 | − | 27.7128i | 0.564980 | − | 0.978573i | ||||
\(803\) | 6.46410 | + | 11.1962i | 0.228113 | + | 0.395104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.46410 | 0.263075 | ||||||||
\(806\) | −4.33013 | + | 4.50000i | −0.152522 | + | 0.158506i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.53590 | − | 1.46410i | 0.0892126 | − | 0.0515069i | ||||
\(809\) | −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 | \(-0.254061\pi\) | |||||||
\(812\) | −0.464102 | − | 0.267949i | −0.0162868 | − | 0.00940317i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 59.4449i | 2.08354i | ||||||||
\(815\) | −7.52628 | + | 13.0359i | −0.263634 | + | 0.456628i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −77.1051 | + | 44.5167i | −2.69757 | + | 1.55744i | ||||
\(818\) | 4.00000 | 0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | −12.6506 | + | 7.30385i | −0.441510 | + | 0.254906i | −0.704238 | − | 0.709964i | \(-0.748711\pi\) |
0.262728 | + | 0.964870i | \(0.415378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.5885 | + | 33.9282i | −0.682811 | + | 1.18266i | 0.291309 | + | 0.956629i | \(0.405909\pi\) |
−0.974119 | + | 0.226034i | \(0.927424\pi\) | |||||||
\(824\) | 11.8564i | 0.413037i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.6603 | + | 8.46410i | 0.510095 | + | 0.294504i | ||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.26795 | − | 14.3205i | −0.287158 | − | 0.497372i | 0.685972 | − | 0.727628i | \(-0.259377\pi\) |
−0.973130 | + | 0.230256i | \(0.926044\pi\) | |||||||
\(830\) | −7.73205 | + | 4.46410i | −0.268383 | + | 0.154951i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | − | 3.46410i | −0.0346688 | − | 0.120096i | ||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.16025 | − | 14.1340i | −0.282397 | − | 0.489126i | ||||
\(836\) | −24.1244 | + | 41.7846i | −0.834358 | + | 1.44515i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.3923 | + | 11.1962i | 0.669896 | + | 0.386765i | ||||
\(839\) | 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 | ||||
\(842\) | −2.19615 | − | 3.80385i | −0.0756844 | − | 0.131089i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.3205 | 0.389668 | ||||||||
\(845\) | −6.92820 | − | 11.0000i | −0.238337 | − | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.3205 | + | 30.7846i | −1.83211 | + | 1.05777i | ||||
\(848\) | 0.464102 | + | 0.803848i | 0.0159373 | + | 0.0276042i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 4.00000i | − | 0.137199i | ||||||
\(851\) | 29.7224 | + | 17.1603i | 1.01887 | + | 0.588246i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.8372i | − | 1.50096i | −0.660895 | − | 0.750478i | \(-0.729823\pi\) | ||
0.660895 | − | 0.750478i | \(-0.270177\pi\) | |||||||
\(854\) | −10.3923 | + | 18.0000i | −0.355617 | + | 0.615947i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.80385 | + | 3.92820i | −0.232551 | + | 0.134263i | ||||
\(857\) | −24.5167 | −0.837473 | −0.418737 | − | 0.908108i | \(-0.637527\pi\) | ||||
−0.418737 | + | 0.908108i | \(0.637527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.1769 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(860\) | −10.3301 | + | 5.96410i | −0.352254 | + | 0.203374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.1962 | + | 24.5885i | −0.483523 | + | 0.837486i | ||||
\(863\) | 35.5359i | 1.20966i | 0.796356 | + | 0.604828i | \(0.206758\pi\) | ||||
−0.796356 | + | 0.604828i | \(0.793242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.46410 | + | 5.46410i | 0.321789 | + | 0.185785i | ||||
\(866\) | 19.3205i | 0.656538i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.73205 | − | 3.00000i | −0.0587896 | − | 0.101827i | ||||
\(869\) | 77.9711 | − | 45.0167i | 2.64499 | − | 1.52709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.7846 | − | 28.6603i | −1.00921 | − | 0.971116i | ||||
\(872\) | 15.8564 | 0.536966 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.9282 | + | 24.1244i | 0.471129 | + | 0.816019i | ||||
\(875\) | −1.00000 | + | 1.73205i | −0.0338062 | + | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.35641 | − | 1.93782i | −0.113338 | − | 0.0654356i | 0.442260 | − | 0.896887i | \(-0.354177\pi\) |
−0.555597 | + | 0.831452i | \(0.687510\pi\) | |||||||
\(878\) | 15.4641 | + | 8.92820i | 0.521888 | + | 0.301312i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.23205 | + | 5.59808i | −0.108952 | + | 0.188711i | ||||
\(881\) | −7.00000 | − | 12.1244i | −0.235836 | − | 0.408480i | 0.723679 | − | 0.690136i | \(-0.242449\pi\) |
−0.959515 | + | 0.281656i | \(0.909116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9282 | 1.00716 | 0.503582 | − | 0.863947i | \(-0.332015\pi\) | ||||
0.503582 | + | 0.863947i | \(0.332015\pi\) | |||||||
\(884\) | −10.0000 | + | 10.3923i | −0.336336 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.1962 | + | 8.19615i | −0.476929 | + | 0.275355i | ||||
\(887\) | 7.06218 | + | 12.2321i | 0.237125 | + | 0.410712i | 0.959888 | − | 0.280384i | \(-0.0904617\pi\) |
−0.722763 | + | 0.691096i | \(0.757128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.85641i | − | 0.330573i | ||||||
\(890\) | 0.464102 | + | 0.267949i | 0.0155567 | + | 0.00898168i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.5359i | 0.687593i | ||||||||
\(893\) | 13.1962 | − | 22.8564i | 0.441592 | − | 0.764860i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0885 | − | 9.86603i | 0.571204 | − | 0.329785i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.7128 | 0.524343 | ||||||||
\(899\) | −0.401924 | + | 0.232051i | −0.0134049 | + | 0.00773933i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.85641 | − | 3.21539i | 0.0618459 | − | 0.107120i | ||||
\(902\) | − | 12.9282i | − | 0.430462i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.696152 | − | 0.401924i | −0.0231537 | − | 0.0133678i | ||||
\(905\) | − | 2.92820i | − | 0.0973368i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4282 | + | 18.0622i | 0.346263 | + | 0.599745i | 0.985582 | − | 0.169196i | \(-0.0541172\pi\) |
−0.639320 | + | 0.768941i | \(0.720784\pi\) | |||||||
\(908\) | 14.1962 | − | 8.19615i | 0.471116 | − | 0.271999i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.92820 | − | 2.00000i | 0.229668 | − | 0.0662994i | ||||
\(911\) | −24.2487 | −0.803396 | −0.401698 | − | 0.915772i | \(-0.631580\pi\) | ||||
−0.401698 | + | 0.915772i | \(0.631580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8564 | − | 49.9808i | −0.955008 | − | 1.65412i | ||||
\(914\) | 12.2679 | − | 21.2487i | 0.405788 | − | 0.702845i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.80385 | + | 3.92820i | 0.224805 | + | 0.129791i | ||||
\(917\) | −32.3205 | − | 18.6603i | −1.06732 | − | 0.616216i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.32051 | + | 12.6795i | −0.241481 | + | 0.418258i | −0.961136 | − | 0.276074i | \(-0.910967\pi\) |
0.719655 | + | 0.694332i | \(0.244300\pi\) | |||||||
\(920\) | 1.86603 | + | 3.23205i | 0.0615210 | + | 0.106558i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.464102 | −0.0152844 | ||||||||
\(923\) | −10.7321 | + | 43.3731i | −0.353250 | + | 1.42764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.96410 | + | 4.59808i | −0.261858 | + | 0.151184i | ||||
\(926\) | −3.53590 | − | 6.12436i | −0.116197 | − | 0.201259i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 0.267949i | − | 0.00879586i | ||||||
\(929\) | 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 | ||||||
\(932\) | −3.06218 | + | 5.30385i | −0.100305 | + | 0.173733i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.7321 | − | 7.92820i | 0.449326 | − | 0.259419i | ||||
\(935\) | 25.8564 | 0.845595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6410 | −0.804987 | −0.402493 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402493 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(938\) | 19.8564 | − | 11.4641i | 0.648335 | − | 0.374316i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.76795 | − | 3.06218i | 0.0576641 | − | 0.0998772i | ||||
\(941\) | − | 14.7846i | − | 0.481965i | −0.970530 | − | 0.240982i | \(-0.922530\pi\) | ||
0.970530 | − | 0.240982i | \(-0.0774696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.46410 | − | 3.73205i | −0.210500 | − | 0.121532i | ||||
\(944\) | 8.46410i | 0.275483i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.5526 | − | 66.7750i | −1.25345 | − | 2.17104i | ||||
\(947\) | −8.19615 | + | 4.73205i | −0.266339 | + | 0.153771i | −0.627223 | − | 0.778840i | \(-0.715808\pi\) |
0.360884 | + | 0.932611i | \(0.382475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.92820 | − | 2.00000i | 0.224899 | − | 0.0649227i | ||||
\(950\) | −7.46410 | −0.242167 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.00000 | − | 6.92820i | −0.129641 | − | 0.224544i | ||||
\(953\) | −6.13397 | + | 10.6244i | −0.198699 | + | 0.344157i | −0.948107 | − | 0.317952i | \(-0.897005\pi\) |
0.749408 | + | 0.662109i | \(0.230338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.5885 | + | 10.7321i | 0.601508 | + | 0.347281i | ||||
\(956\) | −14.1962 | − | 8.19615i | −0.459136 | − | 0.265083i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.73205 | + | 4.73205i | −0.0882686 | + | 0.152886i | ||||
\(959\) | −2.46410 | − | 4.26795i | −0.0795700 | − | 0.137819i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 32.1865 | + | 7.96410i | 1.03774 | + | 0.256773i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.3564 | − | 8.86603i | 0.494597 | − | 0.285555i | ||||
\(965\) | 5.66025 | + | 9.80385i | 0.182210 | + | 0.315597i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.4641i | 1.33340i | 0.745328 | + | 0.666698i | \(0.232293\pi\) | ||||
−0.745328 | + | 0.666698i | \(0.767707\pi\) | |||||||
\(968\) | −26.6603 | − | 15.3923i | −0.856893 | − | 0.494727i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.535898i | 0.0172067i | ||||||||
\(971\) | 2.26795 | − | 3.92820i | 0.0727820 | − | 0.126062i | −0.827338 | − | 0.561705i | \(-0.810146\pi\) |
0.900120 | + | 0.435643i | \(0.143479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.3923 | + | 12.9282i | −0.717864 | + | 0.414459i | ||||
\(974\) | 23.1769 | 0.742636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3923 | −0.332650 | ||||||||
\(977\) | −10.9186 | + | 6.30385i | −0.349316 | + | 0.201678i | −0.664384 | − | 0.747391i | \(-0.731306\pi\) |
0.315068 | + | 0.949069i | \(0.397973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.73205 | + | 3.00000i | −0.0553566 | + | 0.0958804i | ||||
\(980\) | − | 3.00000i | − | 0.0958315i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.0000 | − | 8.66025i | −0.478669 | − | 0.276360i | ||||
\(983\) | − | 36.6077i | − | 1.16760i | −0.811896 | − | 0.583802i | \(-0.801564\pi\) | ||
0.811896 | − | 0.583802i | \(-0.198436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.19615 | − | 3.80385i | −0.0699752 | − | 0.121201i | ||||
\(986\) | −0.928203 | + | 0.535898i | −0.0295600 | + | 0.0170665i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.3923 | + | 18.6603i | 0.616951 | + | 0.593662i | ||||
\(989\) | −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 | \(0.516170\pi\) | |||||||
\(992\) | 0.866025 | − | 1.50000i | 0.0274963 | − | 0.0476250i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.4641 | − | 12.3923i | −0.680800 | − | 0.393060i | ||||
\(995\) | 4.39230 | + | 2.53590i | 0.139245 | + | 0.0803934i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7846 | + | 30.8038i | −0.563244 | + | 0.975568i | 0.433966 | + | 0.900929i | \(0.357114\pi\) |
−0.997211 | + | 0.0746386i | \(0.976220\pi\) | |||||||
\(998\) | −3.26795 | − | 5.66025i | −0.103445 | − | 0.179172i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.bs.e.361.2 | 4 | ||
3.2 | odd | 2 | 390.2.bb.b.361.1 | yes | 4 | ||
13.4 | even | 6 | inner | 1170.2.bs.e.901.2 | 4 | ||
15.2 | even | 4 | 1950.2.y.c.49.2 | 4 | |||
15.8 | even | 4 | 1950.2.y.f.49.1 | 4 | |||
15.14 | odd | 2 | 1950.2.bc.b.751.2 | 4 | |||
39.2 | even | 12 | 5070.2.a.y.1.1 | 2 | |||
39.11 | even | 12 | 5070.2.a.bg.1.2 | 2 | |||
39.17 | odd | 6 | 390.2.bb.b.121.1 | ✓ | 4 | ||
39.23 | odd | 6 | 5070.2.b.o.1351.3 | 4 | |||
39.29 | odd | 6 | 5070.2.b.o.1351.2 | 4 | |||
195.17 | even | 12 | 1950.2.y.f.199.1 | 4 | |||
195.134 | odd | 6 | 1950.2.bc.b.901.2 | 4 | |||
195.173 | even | 12 | 1950.2.y.c.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.1 | ✓ | 4 | 39.17 | odd | 6 | ||
390.2.bb.b.361.1 | yes | 4 | 3.2 | odd | 2 | ||
1170.2.bs.e.361.2 | 4 | 1.1 | even | 1 | trivial | ||
1170.2.bs.e.901.2 | 4 | 13.4 | even | 6 | inner | ||
1950.2.y.c.49.2 | 4 | 15.2 | even | 4 | |||
1950.2.y.c.199.2 | 4 | 195.173 | even | 12 | |||
1950.2.y.f.49.1 | 4 | 15.8 | even | 4 | |||
1950.2.y.f.199.1 | 4 | 195.17 | even | 12 | |||
1950.2.bc.b.751.2 | 4 | 15.14 | odd | 2 | |||
1950.2.bc.b.901.2 | 4 | 195.134 | odd | 6 | |||
5070.2.a.y.1.1 | 2 | 39.2 | even | 12 | |||
5070.2.a.bg.1.2 | 2 | 39.11 | even | 12 | |||
5070.2.b.o.1351.2 | 4 | 39.29 | odd | 6 | |||
5070.2.b.o.1351.3 | 4 | 39.23 | odd | 6 |