Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,2,Mod(361,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3528.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.s (of order \(3\), 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: | \(28.1712218331\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 392) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3313.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.3313 |
Dual form | 3528.2.s.be.361.2 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | − | 2.44949i | 0.632456 | − | 1.09545i | −0.354593 | − | 0.935021i | \(-0.615380\pi\) |
0.987048 | − | 0.160424i | \(-0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | − | 3.46410i | −0.603023 | − | 1.04447i | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | − | 4.89898i | −0.685994 | − | 1.18818i | −0.973123 | − | 0.230285i | \(-0.926034\pi\) |
0.287129 | − | 0.957892i | \(-0.407299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | − | 2.44949i | 0.324443 | − | 0.561951i | −0.656957 | − | 0.753928i | \(-0.728157\pi\) |
0.981399 | + | 0.191977i | \(0.0614899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | + | 4.89898i | 0.508001 | + | 0.879883i | 0.999957 | + | 0.00926296i | \(0.00294853\pi\) |
−0.491957 | + | 0.870620i | \(0.663718\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | + | 8.66025i | −0.821995 | + | 1.42374i | 0.0821995 | + | 0.996616i | \(0.473806\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.65685 | −0.883452 | −0.441726 | − | 0.897150i | \(-0.645634\pi\) | ||||
−0.441726 | + | 0.897150i | \(0.645634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | − | 4.89898i | 0.412568 | − | 0.714590i | −0.582601 | − | 0.812758i | \(-0.697965\pi\) |
0.995170 | + | 0.0981685i | \(0.0312984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.3137 | −1.52554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | − | 2.44949i | −0.184115 | − | 0.318896i | 0.759163 | − | 0.650901i | \(-0.225609\pi\) |
−0.943278 | + | 0.332004i | \(0.892275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07107 | + | 12.2474i | −0.905357 | + | 1.56813i | −0.0849208 | + | 0.996388i | \(0.527064\pi\) |
−0.820437 | + | 0.571737i | \(0.806270\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.00000 | + | 6.92820i | −0.496139 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1421 | 1.55230 | 0.776151 | − | 0.630548i | \(-0.217170\pi\) | ||||
0.776151 | + | 0.630548i | \(0.217170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | −1.73544 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | − | 6.92820i | −0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.65685 | 0.574367 | 0.287183 | − | 0.957876i | \(-0.407281\pi\) | ||||
0.287183 | + | 0.957876i | \(0.407281\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24264 | − | 7.34847i | −0.422159 | − | 0.731200i | 0.573992 | − | 0.818861i | \(-0.305394\pi\) |
−0.996150 | + | 0.0876610i | \(0.972061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.48528 | − | 14.6969i | 0.836080 | − | 1.44813i | −0.0570688 | − | 0.998370i | \(-0.518175\pi\) |
0.893148 | − | 0.449762i | \(-0.148491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.07107 | + | 12.2474i | −0.617802 | + | 1.07006i | 0.372084 | + | 0.928199i | \(0.378643\pi\) |
−0.989886 | + | 0.141865i | \(0.954690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | − | 8.66025i | −0.427179 | − | 0.739895i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
−0.996621 | + | 0.0821359i | \(0.973826\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1421 | 1.19952 | 0.599760 | − | 0.800180i | \(-0.295263\pi\) | ||||
0.599760 | + | 0.800180i | \(0.295263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | + | 9.79796i | 0.473050 | + | 0.819346i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.82843 | + | 4.89898i | −0.234888 | + | 0.406838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | − | 13.8564i | −0.651031 | − | 1.12762i | −0.982873 | − | 0.184284i | \(-0.941004\pi\) |
0.331842 | − | 0.943335i | \(-0.392330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.07107 | + | 12.2474i | 0.564333 | + | 0.977453i | 0.997111 | + | 0.0759527i | \(0.0241998\pi\) |
−0.432779 | + | 0.901500i | \(0.642467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.41421 | + | 2.44949i | −0.107521 | + | 0.186231i | −0.914765 | − | 0.403986i | \(-0.867625\pi\) |
0.807245 | + | 0.590217i | \(0.200958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | − | 17.3205i | −0.747435 | − | 1.29460i | −0.949048 | − | 0.315130i | \(-0.897952\pi\) |
0.201613 | − | 0.979465i | \(-0.435382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528 | 0.630706 | 0.315353 | − | 0.948974i | \(-0.397877\pi\) | ||||
0.315353 | + | 0.948974i | \(0.397877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.1421 | + | 24.4949i | 1.03975 | + | 1.80090i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3137 | + | 19.5959i | −0.827340 | + | 1.43300i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | − | 20.7846i | 0.868290 | − | 1.50392i | 0.00454614 | − | 0.999990i | \(-0.498553\pi\) |
0.863743 | − | 0.503932i | \(-0.168114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | − | 8.66025i | −0.359908 | − | 0.623379i | 0.628037 | − | 0.778183i | \(-0.283859\pi\) |
−0.987945 | + | 0.154805i | \(0.950525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.48528 | − | 14.6969i | −0.601506 | − | 1.04184i | −0.992593 | − | 0.121485i | \(-0.961234\pi\) |
0.391088 | − | 0.920353i | \(-0.372099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 13.8564i | −0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | + | 9.79796i | −0.385794 | + | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | + | 13.8564i | 0.538138 | + | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3137 | −0.757622 | −0.378811 | − | 0.925474i | \(-0.623667\pi\) | ||||
−0.378811 | + | 0.925474i | \(0.623667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.24264 | + | 7.34847i | 0.281594 | + | 0.487735i | 0.971778 | − | 0.235899i | \(-0.0758036\pi\) |
−0.690184 | + | 0.723634i | \(0.742470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7279 | − | 22.0454i | 0.841085 | − | 1.45680i | −0.0478936 | − | 0.998852i | \(-0.515251\pi\) |
0.888978 | − | 0.457949i | \(-0.151416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.00000 | + | 8.66025i | −0.327561 | + | 0.567352i | −0.982027 | − | 0.188739i | \(-0.939560\pi\) |
0.654466 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | − | 13.8564i | −0.521862 | − | 0.903892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1421 | − | 24.4949i | −0.910975 | − | 1.57786i | −0.812690 | − | 0.582697i | \(-0.801998\pi\) |
−0.0982854 | − | 0.995158i | \(-0.531336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | + | 6.92820i | −0.254514 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1421 | −0.892644 | −0.446322 | − | 0.894873i | \(-0.647266\pi\) | ||||
−0.446322 | + | 0.894873i | \(0.647266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | − | 13.8564i | −0.493301 | − | 0.854423i | 0.506669 | − | 0.862141i | \(-0.330877\pi\) |
−0.999970 | + | 0.00771799i | \(0.997543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.9706 | 1.04249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.07107 | − | 12.2474i | −0.431131 | − | 0.746740i | 0.565840 | − | 0.824515i | \(-0.308552\pi\) |
−0.996971 | + | 0.0777747i | \(0.975219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.00000 | + | 10.3923i | −0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.41421 | + | 2.44949i | 0.0840663 | + | 0.145607i | 0.904993 | − | 0.425427i | \(-0.139876\pi\) |
−0.820927 | + | 0.571034i | \(0.806543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.50000 | + | 12.9904i | −0.441176 | + | 0.764140i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.82843 | −0.165238 | −0.0826192 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826192 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.0000 | + | 34.6410i | 1.14520 | + | 1.98354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.48528 | 0.484281 | 0.242140 | − | 0.970241i | \(-0.422151\pi\) | ||||
0.242140 | + | 0.970241i | \(0.422151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | − | 19.5959i | −0.641542 | − | 1.11118i | −0.985089 | − | 0.172047i | \(-0.944962\pi\) |
0.343547 | − | 0.939135i | \(-0.388371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.48528 | − | 14.6969i | 0.479616 | − | 0.830720i | −0.520110 | − | 0.854099i | \(-0.674109\pi\) |
0.999727 | + | 0.0233791i | \(0.00744247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.24264 | + | 7.34847i | 0.235339 | + | 0.407620i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.9411 | −1.85440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137 | − | 19.5959i | 0.612672 | − | 1.06118i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0000 | − | 17.3205i | −0.536828 | − | 0.929814i | −0.999072 | − | 0.0430610i | \(-0.986289\pi\) |
0.462244 | − | 0.886753i | \(-0.347044\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4558 | −1.36262 | −0.681310 | − | 0.731995i | \(-0.738589\pi\) | ||||
−0.681310 | + | 0.731995i | \(0.738589\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.65685 | + | 9.79796i | 0.301084 | + | 0.521493i | 0.976382 | − | 0.216052i | \(-0.0693182\pi\) |
−0.675298 | + | 0.737545i | \(0.735985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9706 | − | 29.3939i | −0.885856 | − | 1.53435i | −0.844729 | − | 0.535194i | \(-0.820239\pi\) |
−0.0411270 | − | 0.999154i | \(-0.513095\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.65685 | 0.291343 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.1421 | − | 24.4949i | 0.722629 | − | 1.25163i | −0.237313 | − | 0.971433i | \(-0.576267\pi\) |
0.959942 | − | 0.280198i | \(-0.0904000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.0000 | − | 19.0526i | −0.557722 | − | 0.966003i | −0.997686 | − | 0.0679877i | \(-0.978342\pi\) |
0.439964 | − | 0.898015i | \(-0.354991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3137 | + | 19.5959i | 0.569254 | + | 0.985978i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.24264 | + | 7.34847i | −0.212932 | + | 0.368809i | −0.952631 | − | 0.304129i | \(-0.901635\pi\) |
0.739699 | + | 0.672938i | \(0.234968\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | − | 13.8564i | −0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0000 | 1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.48528 | + | 14.6969i | 0.419570 | + | 0.726717i | 0.995896 | − | 0.0905030i | \(-0.0288475\pi\) |
−0.576326 | + | 0.817220i | \(0.695514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0000 | − | 34.6410i | 0.981761 | − | 1.70046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.82843 | −0.138178 | −0.0690889 | − | 0.997611i | \(-0.522009\pi\) | ||||
−0.0690889 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.48528 | + | 14.6969i | −0.411597 | + | 0.712906i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | + | 20.7846i | 0.578020 | + | 1.00116i | 0.995706 | + | 0.0925683i | \(0.0295076\pi\) |
−0.417687 | + | 0.908591i | \(0.637159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.65685 | 0.271851 | 0.135926 | − | 0.990719i | \(-0.456599\pi\) | ||||
0.135926 | + | 0.990719i | \(0.456599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.00000 | − | 3.46410i | 0.0950229 | − | 0.164584i | −0.814595 | − | 0.580030i | \(-0.803041\pi\) |
0.909618 | + | 0.415445i | \(0.136374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3137 | + | 19.5959i | 0.532742 | + | 0.922736i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00000 | + | 15.5885i | −0.421002 | + | 0.729197i | −0.996038 | − | 0.0889312i | \(-0.971655\pi\) |
0.575036 | + | 0.818128i | \(0.304988\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1421 | 0.658665 | 0.329332 | − | 0.944214i | \(-0.393176\pi\) | ||||
0.329332 | + | 0.944214i | \(0.393176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0000 | 1.85896 | 0.929479 | − | 0.368875i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368875i | \(0.120257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.24264 | − | 7.34847i | 0.196326 | − | 0.340047i | −0.751008 | − | 0.660293i | \(-0.770432\pi\) |
0.947334 | + | 0.320246i | \(0.103766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.48528 | −0.389331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.1421 | − | 24.4949i | −0.646171 | − | 1.11920i | −0.984030 | − | 0.178004i | \(-0.943036\pi\) |
0.337859 | − | 0.941197i | \(-0.390297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.1421 | − | 24.4949i | 0.644826 | − | 1.11687i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.00000 | − | 13.8564i | 0.363261 | − | 0.629187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.00000 | −0.180517 | −0.0902587 | − | 0.995918i | \(-0.528769\pi\) | ||||
−0.0902587 | + | 0.995918i | \(0.528769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685 | + | 9.79796i | 0.254772 | + | 0.441278i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.3137 | −0.504453 | −0.252227 | − | 0.967668i | \(-0.581163\pi\) | ||||
−0.252227 | + | 0.967668i | \(0.581163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.07107 | + | 12.2474i | −0.313420 | + | 0.542859i | −0.979100 | − | 0.203378i | \(-0.934808\pi\) |
0.665681 | + | 0.746237i | \(0.268141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | − | 41.5692i | −1.05757 | − | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.6274 | −0.995153 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.82843 | − | 4.89898i | −0.123916 | − | 0.214628i | 0.797393 | − | 0.603460i | \(-0.206212\pi\) |
−0.921309 | + | 0.388832i | \(0.872879\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.89949 | + | 17.1464i | −0.432875 | + | 0.749761i | −0.997119 | − | 0.0758466i | \(-0.975834\pi\) |
0.564245 | + | 0.825608i | \(0.309167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000 | − | 27.7128i | 0.696971 | − | 1.20719i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0000 | 0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.9706 | + | 29.3939i | 0.733701 | + | 1.27081i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | − | 29.4449i | 0.730887 | − | 1.26593i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.956504 | − | 0.291718i | \(-0.0942267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.65685 | −0.242313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.82843 | + | 4.89898i | −0.120495 | + | 0.208704i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0000 | + | 25.9808i | 0.635570 | + | 1.10084i | 0.986394 | + | 0.164399i | \(0.0525683\pi\) |
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3137 | 0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.2132 | − | 36.7423i | −0.894030 | − | 1.54851i | −0.835001 | − | 0.550249i | \(-0.814533\pi\) |
−0.0590293 | − | 0.998256i | \(-0.518801\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.1421 | + | 24.4949i | −0.594964 | + | 1.03051i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0000 | − | 25.9808i | 0.628833 | − | 1.08917i | −0.358954 | − | 0.933355i | \(-0.616866\pi\) |
0.987786 | − | 0.155815i | \(-0.0498003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | + | 17.3205i | 0.418487 | + | 0.724841i | 0.995788 | − | 0.0916910i | \(-0.0292272\pi\) |
−0.577301 | + | 0.816532i | \(0.695894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9706 | − | 29.3939i | −0.706494 | − | 1.22368i | −0.966150 | − | 0.257982i | \(-0.916942\pi\) |
0.259656 | − | 0.965701i | \(-0.416391\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | − | 20.7846i | 0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.4264 | 1.75113 | 0.875563 | − | 0.483105i | \(-0.160491\pi\) | ||||
0.875563 | + | 0.483105i | \(0.160491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.65685 | + | 9.79796i | −0.232299 | + | 0.402354i | −0.958484 | − | 0.285145i | \(-0.907958\pi\) |
0.726185 | + | 0.687499i | \(0.241292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000 | + | 27.7128i | 0.653742 | + | 1.13231i | 0.982208 | + | 0.187799i | \(0.0601353\pi\) |
−0.328465 | + | 0.944516i | \(0.606531\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6274 | −0.922992 | −0.461496 | − | 0.887142i | \(-0.652687\pi\) | ||||
−0.461496 | + | 0.887142i | \(0.652687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.07107 | + | 12.2474i | 0.287480 | + | 0.497930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3137 | + | 19.5959i | −0.459209 | + | 0.795374i | −0.998919 | − | 0.0464772i | \(-0.985201\pi\) |
0.539710 | + | 0.841851i | \(0.318534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | + | 13.8564i | −0.323645 | + | 0.560570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | + | 5.19615i | 0.121169 | + | 0.209871i | 0.920229 | − | 0.391381i | \(-0.128002\pi\) |
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.07107 | + | 12.2474i | 0.284210 | + | 0.492267i | 0.972417 | − | 0.233248i | \(-0.0749353\pi\) |
−0.688207 | + | 0.725514i | \(0.741602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.5685 | 2.25554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.3137 | − | 19.5959i | 0.448971 | − | 0.777640i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.00000 | − | 8.66025i | −0.197488 | − | 0.342059i | 0.750225 | − | 0.661182i | \(-0.229945\pi\) |
−0.947713 | + | 0.319123i | \(0.896612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.4558 | 1.00388 | 0.501940 | − | 0.864902i | \(-0.332620\pi\) | ||||
0.501940 | + | 0.864902i | \(0.332620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.48528 | + | 14.6969i | 0.333591 | + | 0.577796i | 0.983213 | − | 0.182461i | \(-0.0584063\pi\) |
−0.649622 | + | 0.760257i | \(0.725073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.65685 | + | 9.79796i | −0.222051 | + | 0.384604i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | + | 34.6410i | 0.781465 | + | 1.35354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.07107 | − | 12.2474i | −0.275033 | − | 0.476371i | 0.695111 | − | 0.718903i | \(-0.255355\pi\) |
−0.970143 | + | 0.242532i | \(0.922022\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.5685 | 2.18380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.24264 | − | 7.34847i | 0.163058 | − | 0.282425i | −0.772906 | − | 0.634521i | \(-0.781198\pi\) |
0.935964 | + | 0.352096i | \(0.114531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.0000 | + | 17.3205i | 0.382639 | + | 0.662751i | 0.991439 | − | 0.130573i | \(-0.0416818\pi\) |
−0.608799 | + | 0.793324i | \(0.708349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.2843 | −1.08069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.48528 | − | 14.6969i | −0.323263 | − | 0.559909i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.07107 | − | 12.2474i | 0.268996 | − | 0.465915i | −0.699607 | − | 0.714528i | \(-0.746641\pi\) |
0.968603 | + | 0.248613i | \(0.0799748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.0000 | − | 34.6410i | 0.758643 | − | 1.31401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | + | 27.7128i | 0.606043 | + | 1.04970i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1421 | + | 24.4949i | 0.533381 | + | 0.923843i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0000 | − | 19.0526i | 0.413114 | − | 0.715534i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.995228 | + | 0.0975728i | \(0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | 1.19673 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.1421 | + | 24.4949i | −0.527413 | + | 0.913506i | 0.472077 | + | 0.881557i | \(0.343504\pi\) |
−0.999490 | + | 0.0319481i | \(0.989829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2843 | 1.04901 | 0.524503 | − | 0.851409i | \(-0.324251\pi\) | ||||
0.524503 | + | 0.851409i | \(0.324251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3137 | + | 19.5959i | 0.418453 | + | 0.724781i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.7279 | + | 22.0454i | −0.470117 | + | 0.814266i | −0.999416 | − | 0.0341693i | \(-0.989121\pi\) |
0.529300 | + | 0.848435i | \(0.322455\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.0000 | + | 41.5692i | −0.884051 | + | 1.53122i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.00000 | + | 10.3923i | 0.220714 | + | 0.382287i | 0.955025 | − | 0.296526i | \(-0.0958281\pi\) |
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0000 | 0.586983 | 0.293492 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1421 | + | 24.4949i | 0.518128 | + | 0.897424i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | − | 20.7846i | 0.437886 | − | 0.758441i | −0.559640 | − | 0.828736i | \(-0.689061\pi\) |
0.997526 | + | 0.0702946i | \(0.0223939\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.2548 | −1.64699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1421 | + | 24.4949i | −0.512652 | + | 0.887939i | 0.487240 | + | 0.873268i | \(0.338004\pi\) |
−0.999892 | + | 0.0146714i | \(0.995330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | + | 6.92820i | 0.144432 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9706 | 0.611974 | 0.305987 | − | 0.952036i | \(-0.401014\pi\) | ||||
0.305987 | + | 0.952036i | \(0.401014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.8701 | − | 46.5403i | −0.966449 | − | 1.67394i | −0.705671 | − | 0.708540i | \(-0.749354\pi\) |
−0.260778 | − | 0.965399i | \(-0.583979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.48528 | − | 14.6969i | 0.304800 | − | 0.527930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | + | 13.8564i | −0.286630 | + | 0.496457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.0000 | 1.42766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.24264 | − | 7.34847i | −0.151234 | − | 0.261945i | 0.780447 | − | 0.625221i | \(-0.214991\pi\) |
−0.931681 | + | 0.363277i | \(0.881658\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0000 | − | 34.6410i | 0.710221 | − | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.48528 | −0.300564 | −0.150282 | − | 0.988643i | \(-0.548018\pi\) | ||||
−0.150282 | + | 0.988643i | \(0.548018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.00000 | + | 15.5885i | 0.316423 | + | 0.548061i | 0.979739 | − | 0.200279i | \(-0.0641847\pi\) |
−0.663316 | + | 0.748340i | \(0.730851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1421 | −0.496598 | −0.248299 | − | 0.968683i | \(-0.579871\pi\) | ||||
−0.248299 | + | 0.968683i | \(0.579871\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.2843 | + | 48.9898i | 0.990755 | + | 1.71604i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.65685 | + | 9.79796i | −0.197908 | + | 0.342787i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.0000 | − | 46.7654i | 0.942306 | − | 1.63212i | 0.181250 | − | 0.983437i | \(-0.441986\pi\) |
0.761056 | − | 0.648686i | \(-0.224681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | + | 13.8564i | 0.278862 | + | 0.483004i | 0.971102 | − | 0.238664i | \(-0.0767093\pi\) |
−0.692240 | + | 0.721668i | \(0.743376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0000 | −0.695468 | −0.347734 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347734 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.5563 | + | 26.9444i | 0.540294 | + | 0.935817i | 0.998887 | + | 0.0471706i | \(0.0150204\pi\) |
−0.458593 | + | 0.888647i | \(0.651646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | − | 13.8564i | 0.276851 | − | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.2843 | −0.976481 | −0.488241 | − | 0.872709i | \(-0.662361\pi\) | ||||
−0.488241 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.07107 | + | 12.2474i | −0.243252 | + | 0.421325i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4264 | 1.45265 | 0.726326 | − | 0.687350i | \(-0.241226\pi\) | ||||
0.726326 | + | 0.687350i | \(0.241226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.1421 | + | 24.4949i | 0.483086 | + | 0.836730i | 0.999811 | − | 0.0194215i | \(-0.00618245\pi\) |
−0.516725 | + | 0.856151i | \(0.672849\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2132 | − | 36.7423i | 0.723785 | − | 1.25363i | −0.235687 | − | 0.971829i | \(-0.575734\pi\) |
0.959472 | − | 0.281804i | \(-0.0909327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0000 | − | 20.7846i | 0.408485 | − | 0.707516i | −0.586235 | − | 0.810141i | \(-0.699391\pi\) |
0.994720 | + | 0.102624i | \(0.0327240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00000 | + | 6.92820i | 0.136004 | + | 0.235566i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706 | + | 29.3939i | 0.575026 | + | 0.995974i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.1421 | − | 24.4949i | 0.474846 | − | 0.822458i | −0.524739 | − | 0.851263i | \(-0.675837\pi\) |
0.999585 | + | 0.0288053i | \(0.00917026\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.00000 | − | 13.8564i | −0.267710 | − | 0.463687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.5685 | −1.89088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.65685 | − | 9.79796i | −0.188667 | − | 0.326780i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.9706 | − | 29.3939i | 0.565371 | − | 0.979252i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.0000 | − | 20.7846i | 0.398893 | − | 0.690904i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | − | 17.3205i | −0.332045 | − | 0.575118i | 0.650868 | − | 0.759191i | \(-0.274405\pi\) |
−0.982913 | + | 0.184073i | \(0.941072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2843 | − | 48.9898i | −0.936073 | − | 1.62133i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | − | 27.7128i | 0.527791 | − | 0.914161i | −0.471684 | − | 0.881768i | \(-0.656354\pi\) |
0.999475 | − | 0.0323936i | \(-0.0103130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | 0.986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.7990 | − | 34.2929i | 0.649584 | − | 1.12511i | −0.333639 | − | 0.942701i | \(-0.608277\pi\) |
0.983222 | − | 0.182411i | \(-0.0583902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.0000 | + | 55.4256i | 1.04651 | + | 1.81261i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6274 | −0.739205 | −0.369603 | − | 0.929190i | \(-0.620506\pi\) | ||||
−0.369603 | + | 0.929190i | \(0.620506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.07107 | + | 12.2474i | 0.230510 | + | 0.399255i | 0.957958 | − | 0.286907i | \(-0.0926272\pi\) |
−0.727448 | + | 0.686163i | \(0.759294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.00000 | + | 10.3923i | −0.194974 | + | 0.337705i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.751918 | + | 0.659256i | \(0.229129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.9411 | − | 58.7878i | −1.09831 | − | 1.90233i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | + | 0.866025i | −0.0161290 | + | 0.0279363i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.2843 | −0.910503 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.89949 | − | 17.1464i | 0.317690 | − | 0.550255i | −0.662316 | − | 0.749225i | \(-0.730426\pi\) |
0.980006 | + | 0.198970i | \(0.0637596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.7990 | − | 34.2929i | −0.631490 | − | 1.09377i | −0.987247 | − | 0.159194i | \(-0.949110\pi\) |
0.355758 | − | 0.934578i | \(-0.384223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.1127 | + | 53.8888i | −0.991333 | + | 1.71704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.0000 | −1.52170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3848 | − | 31.8434i | −0.582252 | − | 1.00849i | −0.995212 | − | 0.0977405i | \(-0.968838\pi\) |
0.412960 | − | 0.910749i | \(-0.364495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3528.2.s.be.3313.2 | 4 | ||
3.2 | odd | 2 | 392.2.i.g.177.1 | 4 | |||
7.2 | even | 3 | 3528.2.a.bj.1.1 | 2 | |||
7.3 | odd | 6 | inner | 3528.2.s.be.361.1 | 4 | ||
7.4 | even | 3 | inner | 3528.2.s.be.361.2 | 4 | ||
7.5 | odd | 6 | 3528.2.a.bj.1.2 | 2 | |||
7.6 | odd | 2 | inner | 3528.2.s.be.3313.1 | 4 | ||
12.11 | even | 2 | 784.2.i.k.177.2 | 4 | |||
21.2 | odd | 6 | 392.2.a.h.1.2 | yes | 2 | ||
21.5 | even | 6 | 392.2.a.h.1.1 | ✓ | 2 | ||
21.11 | odd | 6 | 392.2.i.g.361.1 | 4 | |||
21.17 | even | 6 | 392.2.i.g.361.2 | 4 | |||
21.20 | even | 2 | 392.2.i.g.177.2 | 4 | |||
28.19 | even | 6 | 7056.2.a.cj.1.2 | 2 | |||
28.23 | odd | 6 | 7056.2.a.cj.1.1 | 2 | |||
84.11 | even | 6 | 784.2.i.k.753.2 | 4 | |||
84.23 | even | 6 | 784.2.a.n.1.1 | 2 | |||
84.47 | odd | 6 | 784.2.a.n.1.2 | 2 | |||
84.59 | odd | 6 | 784.2.i.k.753.1 | 4 | |||
84.83 | odd | 2 | 784.2.i.k.177.1 | 4 | |||
105.44 | odd | 6 | 9800.2.a.bw.1.1 | 2 | |||
105.89 | even | 6 | 9800.2.a.bw.1.2 | 2 | |||
168.5 | even | 6 | 3136.2.a.bt.1.2 | 2 | |||
168.107 | even | 6 | 3136.2.a.bq.1.2 | 2 | |||
168.131 | odd | 6 | 3136.2.a.bq.1.1 | 2 | |||
168.149 | odd | 6 | 3136.2.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.2.a.h.1.1 | ✓ | 2 | 21.5 | even | 6 | ||
392.2.a.h.1.2 | yes | 2 | 21.2 | odd | 6 | ||
392.2.i.g.177.1 | 4 | 3.2 | odd | 2 | |||
392.2.i.g.177.2 | 4 | 21.20 | even | 2 | |||
392.2.i.g.361.1 | 4 | 21.11 | odd | 6 | |||
392.2.i.g.361.2 | 4 | 21.17 | even | 6 | |||
784.2.a.n.1.1 | 2 | 84.23 | even | 6 | |||
784.2.a.n.1.2 | 2 | 84.47 | odd | 6 | |||
784.2.i.k.177.1 | 4 | 84.83 | odd | 2 | |||
784.2.i.k.177.2 | 4 | 12.11 | even | 2 | |||
784.2.i.k.753.1 | 4 | 84.59 | odd | 6 | |||
784.2.i.k.753.2 | 4 | 84.11 | even | 6 | |||
3136.2.a.bq.1.1 | 2 | 168.131 | odd | 6 | |||
3136.2.a.bq.1.2 | 2 | 168.107 | even | 6 | |||
3136.2.a.bt.1.1 | 2 | 168.149 | odd | 6 | |||
3136.2.a.bt.1.2 | 2 | 168.5 | even | 6 | |||
3528.2.a.bj.1.1 | 2 | 7.2 | even | 3 | |||
3528.2.a.bj.1.2 | 2 | 7.5 | odd | 6 | |||
3528.2.s.be.361.1 | 4 | 7.3 | odd | 6 | inner | ||
3528.2.s.be.361.2 | 4 | 7.4 | even | 3 | inner | ||
3528.2.s.be.3313.1 | 4 | 7.6 | odd | 2 | inner | ||
3528.2.s.be.3313.2 | 4 | 1.1 | even | 1 | trivial | ||
7056.2.a.cj.1.1 | 2 | 28.23 | odd | 6 | |||
7056.2.a.cj.1.2 | 2 | 28.19 | even | 6 | |||
9800.2.a.bw.1.1 | 2 | 105.44 | odd | 6 | |||
9800.2.a.bw.1.2 | 2 | 105.89 | even | 6 |