Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(149,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.b (of order \(2\), degree \(1\), 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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.149 |
Dual form | 300.3.b.c.149.2 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.285714i | 0.989743 | + | 0.142857i | \(0.0456289\pi\) | ||||
−0.989743 | + | 0.142857i | \(0.954371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.4164i | 1.21967i | 0.792527 | + | 0.609837i | \(0.208765\pi\) | ||||
−0.792527 | + | 0.609837i | \(0.791235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 8.00000i | − | 0.615385i | −0.951486 | − | 0.307692i | \(-0.900443\pi\) | ||
0.951486 | − | 0.307692i | \(-0.0995567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.4164 | −0.789200 | −0.394600 | − | 0.918853i | \(-0.629117\pi\) | ||||
−0.394600 | + | 0.918853i | \(0.629117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.0000 | 1.78947 | 0.894737 | − | 0.446594i | \(-0.147363\pi\) | ||||
0.894737 | + | 0.446594i | \(0.147363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 4.47214i | 0.190476 | − | 0.212959i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.2492 | 1.74997 | 0.874983 | − | 0.484153i | \(-0.160872\pi\) | ||||
0.874983 | + | 0.484153i | \(0.160872\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.2492i | 1.38790i | 0.720021 | + | 0.693952i | \(0.244132\pi\) | ||||
−0.720021 | + | 0.693952i | \(0.755868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.0000 | 0.451613 | 0.225806 | − | 0.974172i | \(-0.427498\pi\) | ||||
0.225806 | + | 0.974172i | \(0.427498\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 26.8328 | − | 30.0000i | 0.813116 | − | 0.909091i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 56.0000i | 1.51351i | 0.653697 | + | 0.756757i | \(0.273217\pi\) | ||||
−0.653697 | + | 0.756757i | \(0.726783\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.0000 | + | 17.8885i | −0.410256 | + | 0.458681i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 26.8328i | − | 0.654459i | −0.944945 | − | 0.327229i | \(-0.893885\pi\) | ||
0.944945 | − | 0.327229i | \(-0.106115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 0.186047i | −0.995664 | − | 0.0930233i | \(-0.970347\pi\) | ||
0.995664 | − | 0.0930233i | \(-0.0296531\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.2492 | 0.856366 | 0.428183 | − | 0.903692i | \(-0.359154\pi\) | ||||
0.428183 | + | 0.903692i | \(0.359154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45.0000 | 0.918367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.0000 | + | 26.8328i | 0.588235 | + | 0.526134i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −40.2492 | −0.759419 | −0.379710 | − | 0.925106i | \(-0.623976\pi\) | ||||
−0.379710 | + | 0.925106i | \(0.623976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −76.0263 | − | 68.0000i | −1.33379 | − | 1.19298i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.4164i | − | 0.227397i | −0.993515 | − | 0.113698i | \(-0.963730\pi\) | ||
0.993515 | − | 0.113698i | \(-0.0362697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46.0000 | −0.754098 | −0.377049 | − | 0.926193i | \(-0.623061\pi\) | ||||
−0.377049 | + | 0.926193i | \(0.623061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −17.8885 | + | 2.00000i | −0.283945 | + | 0.0317460i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32.0000i | 0.477612i | 0.971067 | + | 0.238806i | \(0.0767560\pi\) | ||||
−0.971067 | + | 0.238806i | \(0.923244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −90.0000 | − | 80.4984i | −1.30435 | − | 1.16664i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.6656i | 0.755854i | 0.925835 | + | 0.377927i | \(0.123363\pi\) | ||||
−0.925835 | + | 0.377927i | \(0.876637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 106.000i | 1.45205i | 0.687666 | + | 0.726027i | \(0.258635\pi\) | ||||
−0.687666 | + | 0.726027i | \(0.741365\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26.8328 | −0.348478 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.0000 | 0.278481 | 0.139241 | − | 0.990259i | \(-0.455534\pi\) | ||||
0.139241 | + | 0.990259i | \(0.455534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −120.748 | −1.45479 | −0.727396 | − | 0.686218i | \(-0.759269\pi\) | ||||
−0.727396 | + | 0.686218i | \(0.759269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 80.4984 | − | 90.0000i | 0.925270 | − | 1.03448i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 107.331i | − | 1.20597i | −0.797753 | − | 0.602985i | \(-0.793978\pi\) | ||
0.797753 | − | 0.602985i | \(-0.206022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 0.175824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −31.3050 | − | 28.0000i | −0.336612 | − | 0.301075i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 122.000i | 1.25773i | 0.777514 | + | 0.628866i | \(0.216481\pi\) | ||||
−0.777514 | + | 0.628866i | \(0.783519\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −120.000 | + | 13.4164i | −1.21212 | + | 0.135519i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 174.413i | − | 1.72686i | −0.504465 | − | 0.863432i | \(-0.668310\pi\) | ||
0.504465 | − | 0.863432i | \(-0.331690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 46.0000i | 0.446602i | 0.974750 | + | 0.223301i | \(0.0716833\pi\) | ||||
−0.974750 | + | 0.223301i | \(0.928317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4164 | −0.125387 | −0.0626935 | − | 0.998033i | \(-0.519969\pi\) | ||||
−0.0626935 | + | 0.998033i | \(0.519969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86.0000 | −0.788991 | −0.394495 | − | 0.918898i | \(-0.629081\pi\) | ||||
−0.394495 | + | 0.918898i | \(0.629081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 112.000 | − | 125.220i | 1.00901 | − | 1.12811i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 93.9149 | 0.831105 | 0.415552 | − | 0.909569i | \(-0.363588\pi\) | ||||
0.415552 | + | 0.909569i | \(0.363588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 71.5542 | − | 8.00000i | 0.611574 | − | 0.0683761i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 26.8328i | − | 0.225486i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.0000 | −0.487603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −53.6656 | + | 60.0000i | −0.436306 | + | 0.487805i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 34.0000i | − | 0.267717i | −0.991000 | − | 0.133858i | \(-0.957263\pi\) | ||
0.991000 | − | 0.133858i | \(-0.0427367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.0000 | + | 17.8885i | −0.124031 | + | 0.138671i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 147.580i | 1.12657i | 0.826263 | + | 0.563284i | \(0.190462\pi\) | ||||
−0.826263 | + | 0.563284i | \(0.809538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 68.0000i | 0.511278i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 40.2492 | 0.293790 | 0.146895 | − | 0.989152i | \(-0.453072\pi\) | ||||
0.146895 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.0000 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −90.0000 | − | 80.4984i | −0.638298 | − | 0.570911i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 107.331 | 0.750568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −100.623 | − | 90.0000i | −0.684511 | − | 0.612245i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 147.580i | − | 0.990473i | −0.868758 | − | 0.495237i | \(-0.835081\pi\) | ||
0.868758 | − | 0.495237i | \(-0.164919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −46.0000 | −0.304636 | −0.152318 | − | 0.988332i | \(-0.548674\pi\) | ||||
−0.152318 | + | 0.988332i | \(0.548674\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.4164 | − | 120.000i | −0.0876889 | − | 0.784314i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 92.0000i | 0.585987i | 0.956114 | + | 0.292994i | \(0.0946515\pi\) | ||||
−0.956114 | + | 0.292994i | \(0.905349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 90.0000 | + | 80.4984i | 0.566038 | + | 0.506280i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 80.4984i | 0.499990i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 68.0000i | − | 0.417178i | −0.978003 | − | 0.208589i | \(-0.933113\pi\) | ||
0.978003 | − | 0.208589i | \(-0.0668871\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −67.0820 | −0.401689 | −0.200844 | − | 0.979623i | \(-0.564369\pi\) | ||||
−0.200844 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 105.000 | 0.621302 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 34.0000 | + | 304.105i | 0.198830 | + | 1.77839i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −120.748 | −0.697963 | −0.348982 | − | 0.937130i | \(-0.613472\pi\) | ||||
−0.348982 | + | 0.937130i | \(0.613472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.8328 | + | 30.0000i | −0.151598 | + | 0.169492i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 281.745i | 1.57399i | 0.616958 | + | 0.786996i | \(0.288365\pi\) | ||||
−0.616958 | + | 0.786996i | \(0.711635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 194.000 | 1.07182 | 0.535912 | − | 0.844274i | \(-0.319968\pi\) | ||||
0.535912 | + | 0.844274i | \(0.319968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 102.859 | + | 92.0000i | 0.562072 | + | 0.502732i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 180.000i | − | 0.962567i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 44.0000 | + | 31.3050i | 0.232804 | + | 0.165635i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 80.4984i | − | 0.421458i | −0.977545 | − | 0.210729i | \(-0.932416\pi\) | ||
0.977545 | − | 0.210729i | \(-0.0675837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 218.000i | − | 1.12953i | −0.825251 | − | 0.564767i | \(-0.808966\pi\) | ||
0.825251 | − | 0.564767i | \(-0.191034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −93.9149 | −0.476725 | −0.238363 | − | 0.971176i | \(-0.576611\pi\) | ||||
−0.238363 | + | 0.971176i | \(0.576611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 34.0000 | 0.170854 | 0.0854271 | − | 0.996344i | \(-0.472775\pi\) | ||||
0.0854271 | + | 0.996344i | \(0.472775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 64.0000 | − | 71.5542i | 0.318408 | − | 0.355991i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −80.4984 | −0.396544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 40.2492 | + | 360.000i | 0.194441 | + | 1.73913i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 456.158i | 2.18257i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −46.0000 | −0.218009 | −0.109005 | − | 0.994041i | \(-0.534766\pi\) | ||||
−0.109005 | + | 0.994041i | \(0.534766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 107.331 | − | 120.000i | 0.503903 | − | 0.563380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.0000i | 0.129032i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 212.000 | − | 237.023i | 0.968037 | − | 1.08230i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 107.331i | 0.485662i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 398.000i | − | 1.78475i | −0.451291 | − | 0.892377i | \(-0.649036\pi\) | ||
0.451291 | − | 0.892377i | \(-0.350964\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 335.410 | 1.47758 | 0.738789 | − | 0.673937i | \(-0.235398\pi\) | ||||
0.738789 | + | 0.673937i | \(0.235398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −86.0000 | −0.375546 | −0.187773 | − | 0.982212i | \(-0.560127\pi\) | ||||
−0.187773 | + | 0.982212i | \(0.560127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 60.0000 | + | 53.6656i | 0.259740 | + | 0.232319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 308.577 | 1.32437 | 0.662183 | − | 0.749342i | \(-0.269630\pi\) | ||||
0.662183 | + | 0.749342i | \(0.269630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −49.1935 | − | 44.0000i | −0.207567 | − | 0.185654i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.000 | 0.556017 | 0.278008 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278008 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 212.426 | + | 118.000i | 0.874183 | + | 0.485597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 272.000i | − | 1.10121i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 270.000 | + | 241.495i | 1.08434 | + | 0.969861i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 308.577i | − | 1.22939i | −0.788764 | − | 0.614696i | \(-0.789279\pi\) | ||
0.788764 | − | 0.614696i | \(-0.210721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 540.000i | 2.13439i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −174.413 | −0.678651 | −0.339325 | − | 0.940669i | \(-0.610199\pi\) | ||||
−0.339325 | + | 0.940669i | \(0.610199\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −112.000 | −0.432432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −360.000 | + | 40.2492i | −1.37931 | + | 0.154212i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 254.912 | 0.969246 | 0.484623 | − | 0.874723i | \(-0.338957\pi\) | ||||
0.484623 | + | 0.874723i | \(0.338957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −214.663 | + | 240.000i | −0.803979 | + | 0.898876i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 335.410i | − | 1.24688i | −0.781872 | − | 0.623439i | \(-0.785735\pi\) | ||
0.781872 | − | 0.623439i | \(-0.214265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.00738007 | 0.00369004 | − | 0.999993i | \(-0.498825\pi\) | ||||
0.00369004 | + | 0.999993i | \(0.498825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −35.7771 | − | 32.0000i | −0.131052 | − | 0.117216i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 448.000i | − | 1.61733i | −0.588270 | − | 0.808664i | \(-0.700191\pi\) | ||
0.588270 | − | 0.808664i | \(-0.299809\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.0000 | + | 125.220i | 0.0501792 | + | 0.448817i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 187.830i | 0.668433i | 0.942496 | + | 0.334217i | \(0.108472\pi\) | ||||
−0.942496 | + | 0.334217i | \(0.891528\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 248.000i | − | 0.876325i | −0.898896 | − | 0.438163i | \(-0.855629\pi\) | ||
0.898896 | − | 0.438163i | \(-0.144371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 53.6656 | 0.186988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −109.000 | −0.377163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 244.000 | − | 272.800i | 0.838488 | − | 0.937458i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −147.580 | −0.503688 | −0.251844 | − | 0.967768i | \(-0.581037\pi\) | ||||
−0.251844 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 295.161 | + | 210.000i | 0.993808 | + | 0.707071i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 321.994i | − | 1.07690i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | 0.0531561 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −348.827 | + | 390.000i | −1.15124 | + | 1.28713i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 272.000i | 0.885993i | 0.896523 | + | 0.442997i | \(0.146085\pi\) | ||||
−0.896523 | + | 0.442997i | \(0.853915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 92.0000 | − | 102.859i | 0.297735 | − | 0.332877i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 53.6656i | 0.172558i | 0.996271 | + | 0.0862792i | \(0.0274977\pi\) | ||||
−0.996271 | + | 0.0862792i | \(0.972502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 278.000i | − | 0.888179i | −0.895982 | − | 0.444089i | \(-0.853527\pi\) | ||
0.895982 | − | 0.444089i | \(-0.146473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −120.748 | −0.380907 | −0.190454 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190454 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −540.000 | −1.69279 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.0000 | + | 26.8328i | 0.0934579 | + | 0.0835913i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −456.158 | −1.41225 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 192.302 | + | 172.000i | 0.588079 | + | 0.525994i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 80.4984i | 0.244676i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −598.000 | −1.80665 | −0.903323 | − | 0.428960i | \(-0.858880\pi\) | ||||
−0.903323 | + | 0.428960i | \(0.858880\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −500.879 | + | 56.0000i | −1.50414 | + | 0.168168i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 358.000i | − | 1.06231i | −0.847273 | − | 0.531157i | \(-0.821757\pi\) | ||
0.847273 | − | 0.531157i | \(-0.178243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −210.000 | − | 187.830i | −0.619469 | − | 0.554070i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 187.830i | 0.550820i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 188.000i | 0.548105i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −254.912 | −0.734616 | −0.367308 | − | 0.930099i | \(-0.619720\pi\) | ||||
−0.367308 | + | 0.930099i | \(0.619720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −518.000 | −1.48424 | −0.742120 | − | 0.670267i | \(-0.766180\pi\) | ||||
−0.742120 | + | 0.670267i | \(0.766180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −176.000 | − | 125.220i | −0.501425 | − | 0.356752i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −281.745 | −0.798143 | −0.399072 | − | 0.916920i | \(-0.630668\pi\) | ||||
−0.399072 | + | 0.916920i | \(0.630668\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −53.6656 | + | 60.0000i | −0.150324 | + | 0.168067i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 348.827i | − | 0.971662i | −0.874053 | − | 0.485831i | \(-0.838517\pi\) | ||
0.874053 | − | 0.485831i | \(-0.161483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 795.000 | 2.20222 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 131.928 | + | 118.000i | 0.363438 | + | 0.325069i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 178.000i | − | 0.485014i | −0.970150 | − | 0.242507i | \(-0.922030\pi\) | ||
0.970150 | − | 0.242507i | \(-0.0779697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 240.000 | − | 26.8328i | 0.650407 | − | 0.0727177i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 80.4984i | − | 0.216977i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 532.000i | 1.42627i | 0.701025 | + | 0.713137i | \(0.252726\pi\) | ||||
−0.701025 | + | 0.713137i | \(0.747274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 321.994 | 0.854095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −86.0000 | −0.226913 | −0.113456 | − | 0.993543i | \(-0.536192\pi\) | ||||
−0.113456 | + | 0.993543i | \(0.536192\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −68.0000 | + | 76.0263i | −0.178478 | + | 0.199544i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −120.748 | −0.315268 | −0.157634 | − | 0.987498i | \(-0.550387\pi\) | ||||
−0.157634 | + | 0.987498i | \(0.550387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 71.5542 | − | 8.00000i | 0.184895 | − | 0.0206718i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 415.909i | − | 1.06917i | −0.845113 | − | 0.534587i | \(-0.820467\pi\) | ||
0.845113 | − | 0.534587i | \(-0.179533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −540.000 | −1.38107 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 295.161 | − | 330.000i | 0.751046 | − | 0.839695i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.0000i | − | 0.0705290i | −0.999378 | − | 0.0352645i | \(-0.988773\pi\) | ||
0.999378 | − | 0.0352645i | \(-0.0112274\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 136.000 | − | 152.053i | 0.340852 | − | 0.381084i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 268.328i | − | 0.669148i | −0.942370 | − | 0.334574i | \(-0.891408\pi\) | ||
0.942370 | − | 0.334574i | \(-0.108592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 112.000i | − | 0.277916i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −751.319 | −1.84599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 214.000 | 0.523227 | 0.261614 | − | 0.965173i | \(-0.415745\pi\) | ||||
0.261614 | + | 0.965173i | \(0.415745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −90.0000 | − | 80.4984i | −0.218978 | − | 0.195860i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.8328 | 0.0649705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −183.358 | − | 164.000i | −0.439706 | − | 0.393285i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 174.413i | 0.416261i | 0.978101 | + | 0.208130i | \(0.0667379\pi\) | ||||
−0.978101 | + | 0.208130i | \(0.933262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −238.000 | −0.565321 | −0.282660 | − | 0.959220i | \(-0.591217\pi\) | ||||
−0.282660 | + | 0.959220i | \(0.591217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.2492 | + | 360.000i | 0.0951518 | + | 0.851064i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 92.0000i | − | 0.215457i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −240.000 | − | 214.663i | −0.559441 | − | 0.500379i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 241.495i | − | 0.560314i | −0.959954 | − | 0.280157i | \(-0.909613\pi\) | ||
0.959954 | − | 0.280157i | \(-0.0903865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 382.000i | 0.882217i | 0.897454 | + | 0.441109i | \(0.145415\pi\) | ||||
−0.897454 | + | 0.441109i | \(0.854585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1368.47 | 3.13152 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 274.000 | 0.624146 | 0.312073 | − | 0.950058i | \(-0.398977\pi\) | ||||
0.312073 | + | 0.950058i | \(0.398977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 45.0000 | + | 402.492i | 0.102041 | + | 0.912681i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 764.735 | 1.72626 | 0.863132 | − | 0.504978i | \(-0.168499\pi\) | ||||
0.863132 | + | 0.504978i | \(0.168499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −295.161 | + | 330.000i | −0.660315 | + | 0.738255i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 778.152i | 1.73308i | 0.499110 | + | 0.866539i | \(0.333660\pi\) | ||||
−0.499110 | + | 0.866539i | \(0.666340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 360.000 | 0.798226 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 102.859 | + | 92.0000i | 0.227062 | + | 0.203091i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 446.000i | 0.975930i | 0.872863 | + | 0.487965i | \(0.162261\pi\) | ||||
−0.872863 | + | 0.487965i | \(0.837739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −210.000 | + | 295.161i | −0.457516 | + | 0.643052i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 93.9149i | − | 0.203720i | −0.994799 | − | 0.101860i | \(-0.967521\pi\) | ||
0.994799 | − | 0.101860i | \(-0.0324794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 854.000i | − | 1.84449i | −0.386603 | − | 0.922246i | \(-0.626352\pi\) | ||
0.386603 | − | 0.922246i | \(-0.373648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.4164 | −0.0287289 | −0.0143645 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143645 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.0000 | −0.136461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 184.000 | − | 205.718i | 0.390658 | − | 0.436769i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 107.331 | 0.226916 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.2492 | − | 360.000i | −0.0843799 | − | 0.754717i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 53.6656i | − | 0.112037i | −0.998430 | − | 0.0560184i | \(-0.982159\pi\) | ||
0.998430 | − | 0.0560184i | \(-0.0178406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 448.000 | 0.931393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 160.997 | − | 180.000i | 0.333327 | − | 0.372671i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000i | 0.00410678i | 0.999998 | + | 0.00205339i | \(0.000653614\pi\) | ||||
−0.999998 | + | 0.00205339i | \(0.999346\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −136.000 | + | 152.053i | −0.278119 | + | 0.310946i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 469.574i | − | 0.956363i | −0.878261 | − | 0.478182i | \(-0.841296\pi\) | ||
0.878261 | − | 0.478182i | \(-0.158704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 540.000i | − | 1.09533i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −107.331 | −0.215958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 514.000 | 1.03006 | 0.515030 | − | 0.857172i | \(-0.327781\pi\) | ||||
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 150.000 | + | 134.164i | 0.299401 | + | 0.267793i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −657.404 | −1.30697 | −0.653483 | − | 0.756941i | \(-0.726693\pi\) | ||||
−0.653483 | + | 0.756941i | \(0.726693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −234.787 | − | 210.000i | −0.463091 | − | 0.414201i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 308.577i | 0.606242i | 0.952952 | + | 0.303121i | \(0.0980287\pi\) | ||||
−0.952952 | + | 0.303121i | \(0.901971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −212.000 | −0.414873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 532.184 | − | 748.000i | 1.03740 | − | 1.45809i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 540.000i | 1.04449i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 270.000 | + | 241.495i | 0.520231 | + | 0.465309i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 670.820i | 1.28756i | 0.765209 | + | 0.643782i | \(0.222635\pi\) | ||||
−0.765209 | + | 0.643782i | \(0.777365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 832.000i | 1.59082i | 0.606070 | + | 0.795411i | \(0.292745\pi\) | ||||
−0.606070 | + | 0.795411i | \(0.707255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −187.830 | −0.356413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1091.00 | 2.06238 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 120.000 | − | 13.4164i | 0.225989 | − | 0.0252663i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −214.663 | −0.402744 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 563.489 | − | 630.000i | 1.04933 | − | 1.17318i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 603.738i | 1.12011i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 314.000 | 0.580407 | 0.290203 | − | 0.956965i | \(-0.406277\pi\) | ||||
0.290203 | + | 0.956965i | \(0.406277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −433.797 | − | 388.000i | −0.798890 | − | 0.714549i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 536.000i | 0.979890i | 0.871753 | + | 0.489945i | \(0.162983\pi\) | ||||
−0.871753 | + | 0.489945i | \(0.837017\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.0000 | − | 411.437i | −0.0837887 | − | 0.749429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1368.47i | 2.48362i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.0000i | 0.0795660i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −898.899 | −1.61382 | −0.806911 | − | 0.590672i | \(-0.798863\pi\) | ||||
−0.806911 | + | 0.590672i | \(0.798863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −64.0000 | −0.114490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −360.000 | + | 402.492i | −0.641711 | + | 0.717455i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 818.401 | 1.45364 | 0.726821 | − | 0.686827i | \(-0.240997\pi\) | ||||
0.726821 | + | 0.686827i | \(0.240997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.7771 | − | 158.000i | −0.0630989 | − | 0.278660i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −526.000 | −0.921191 | −0.460595 | − | 0.887610i | \(-0.652364\pi\) | ||||
−0.460595 | + | 0.887610i | \(0.652364\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −160.997 | + | 180.000i | −0.280972 | + | 0.314136i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 122.000i | 0.211438i | 0.994396 | + | 0.105719i | \(0.0337145\pi\) | ||||
−0.994396 | + | 0.105719i | \(0.966286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −436.000 | + | 487.463i | −0.753022 | + | 0.841905i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 241.495i | − | 0.415655i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 540.000i | − | 0.926244i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −228.079 | −0.388550 | −0.194275 | − | 0.980947i | \(-0.562235\pi\) | ||||
−0.194275 | + | 0.980947i | \(0.562235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 476.000 | 0.808149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 210.000 | + | 187.830i | 0.355330 | + | 0.317817i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 737.902 | 1.24435 | 0.622177 | − | 0.782876i | \(-0.286248\pi\) | ||||
0.622177 | + | 0.782876i | \(0.286248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −76.0263 | − | 68.0000i | −0.127347 | − | 0.113903i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 80.4984i | 0.134388i | 0.997740 | + | 0.0671940i | \(0.0214047\pi\) | ||||
−0.997740 | + | 0.0671940i | \(0.978595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −766.000 | −1.27454 | −0.637271 | − | 0.770640i | \(-0.719937\pi\) | ||||
−0.637271 | + | 0.770640i | \(0.719937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −286.217 | + | 32.0000i | −0.474655 | + | 0.0530680i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 206.000i | 0.339374i | 0.985498 | + | 0.169687i | \(0.0542757\pi\) | ||||
−0.985498 | + | 0.169687i | \(0.945724\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 180.000 | + | 160.997i | 0.295567 | + | 0.264363i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 321.994i | − | 0.526995i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 556.000i | 0.907015i | 0.891253 | + | 0.453507i | \(0.149827\pi\) | ||||
−0.891253 | + | 0.453507i | \(0.850173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −389.076 | −0.630593 | −0.315296 | − | 0.948993i | \(-0.602104\pi\) | ||||
−0.315296 | + | 0.948993i | \(0.602104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 514.000 | 0.830372 | 0.415186 | − | 0.909737i | \(-0.363717\pi\) | ||||
0.415186 | + | 0.909737i | \(0.363717\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 630.000 | − | 885.483i | 1.01449 | − | 1.42590i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 214.663 | 0.344563 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 912.316 | − | 1020.00i | 1.45505 | − | 1.62679i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 751.319i | − | 1.19447i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1094.00 | 1.73376 | 0.866878 | − | 0.498520i | \(-0.166123\pi\) | ||||
0.866878 | + | 0.498520i | \(0.166123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 102.859 | + | 92.0000i | 0.162495 | + | 0.145340i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 360.000i | − | 0.565149i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −480.000 | + | 53.6656i | −0.751174 | + | 0.0839838i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 160.997i | 0.251165i | 0.992083 | + | 0.125583i | \(0.0400800\pi\) | ||||
−0.992083 | + | 0.125583i | \(0.959920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 404.000i | − | 0.628305i | −0.949373 | − | 0.314152i | \(-0.898280\pi\) | ||
0.949373 | − | 0.314152i | \(-0.101720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1167.23 | 1.80406 | 0.902031 | − | 0.431672i | \(-0.142076\pi\) | ||||
0.902031 | + | 0.431672i | \(0.142076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 180.000 | 0.277350 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 56.0000 | − | 62.6099i | 0.0860215 | − | 0.0961750i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −764.735 | −1.17111 | −0.585555 | − | 0.810632i | \(-0.699124\pi\) | ||||
−0.585555 | + | 0.810632i | \(0.699124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −948.093 | + | 106.000i | −1.44306 | + | 0.161339i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 791.568i | − | 1.20117i | −0.799563 | − | 0.600583i | \(-0.794935\pi\) | ||
0.799563 | − | 0.600583i | \(-0.205065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −118.000 | −0.178517 | −0.0892587 | − | 0.996008i | \(-0.528450\pi\) | ||||
−0.0892587 | + | 0.996008i | \(0.528450\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 214.663 | − | 240.000i | 0.323775 | − | 0.361991i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1620.00i | 2.42879i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −796.000 | + | 889.955i | −1.18984 | + | 1.33028i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 617.155i | − | 0.919754i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 194.000i | − | 0.288262i | −0.989559 | − | 0.144131i | \(-0.953961\pi\) | ||
0.989559 | − | 0.144131i | \(-0.0460386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 415.909 | 0.614341 | 0.307170 | − | 0.951655i | \(-0.400618\pi\) | ||||
0.307170 | + | 0.951655i | \(0.400618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −244.000 | −0.359352 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −750.000 | − | 670.820i | −1.10132 | − | 0.985052i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 93.9149 | 0.137503 | 0.0687517 | − | 0.997634i | \(-0.478098\pi\) | ||||
0.0687517 | + | 0.997634i | \(0.478098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 192.302 | + | 172.000i | 0.279915 | + | 0.250364i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 321.994i | 0.467335i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 122.000 | 0.176556 | 0.0882779 | − | 0.996096i | \(-0.471864\pi\) | ||||
0.0882779 | + | 0.996096i | \(0.471864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.8328 | − | 240.000i | −0.0387198 | − | 0.346320i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 360.000i | 0.516499i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −690.000 | − | 617.155i | −0.987124 | − | 0.882911i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 576.906i | − | 0.822975i | −0.911415 | − | 0.411488i | \(-0.865009\pi\) | ||
0.911415 | − | 0.411488i | \(-0.134991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1904.00i | 2.70839i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 348.827 | 0.493390 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1166.00 | −1.64457 | −0.822285 | − | 0.569076i | \(-0.807301\pi\) | ||||
−0.822285 | + | 0.569076i | \(0.807301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.0000 | + | 196.774i | 0.0309423 | + | 0.276757i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 563.489 | 0.790307 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 214.663i | 0.298557i | 0.988795 | + | 0.149279i | \(0.0476951\pi\) | ||||
−0.988795 | + | 0.149279i | \(0.952305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −92.0000 | −0.127601 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −299.633 | − | 268.000i | −0.414430 | − | 0.370678i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1318.00i | − | 1.81293i | −0.422281 | − | 0.906465i | \(-0.638770\pi\) | ||
0.422281 | − | 0.906465i | \(-0.361230\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −239.000 | − | 688.709i | −0.327846 | − | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 107.331i | 0.146828i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 136.000i | 0.185539i | 0.995688 | + | 0.0927694i | \(0.0295720\pi\) | ||||
−0.995688 | + | 0.0927694i | \(0.970428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −429.325 | −0.582531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 682.000 | 0.922869 | 0.461434 | − | 0.887174i | \(-0.347335\pi\) | ||||
0.461434 | + | 0.887174i | \(0.347335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −544.000 | + | 608.210i | −0.734143 | + | 0.820797i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −872.067 | −1.17371 | −0.586855 | − | 0.809692i | \(-0.699634\pi\) | ||||
−0.586855 | + | 0.809692i | \(0.699634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −120.748 | − | 1080.00i | −0.161643 | − | 1.44578i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 26.8328i | − | 0.0358249i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −658.000 | −0.876165 | −0.438083 | − | 0.898935i | \(-0.644342\pi\) | ||||
−0.438083 | + | 0.898935i | \(0.644342\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −617.155 | + | 690.000i | −0.819595 | + | 0.916335i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1112.00i | 1.46896i | 0.678632 | + | 0.734478i | \(0.262573\pi\) | ||||
−0.678632 | + | 0.734478i | \(0.737427\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1080.00 | − | 1207.48i | 1.42292 | − | 1.59088i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 80.4984i | − | 0.105780i | −0.998600 | − | 0.0528899i | \(-0.983157\pi\) | ||
0.998600 | − | 0.0528899i | \(-0.0168432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 172.000i | − | 0.225426i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −107.331 | −0.139936 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −206.000 | −0.267880 | −0.133940 | − | 0.990989i | \(-0.542763\pi\) | ||||
−0.133940 | + | 0.990989i | \(0.542763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 390.000 | + | 348.827i | 0.505837 | + | 0.452434i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1086.73 | −1.40586 | −0.702930 | − | 0.711260i | \(-0.748125\pi\) | ||||
−0.702930 | + | 0.711260i | \(0.748125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 250.440 | + | 224.000i | 0.322316 | + | 0.288288i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 912.316i | − | 1.17114i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −720.000 | −0.921895 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 885.483 | + | 630.000i | 1.13088 | + | 0.804598i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1168.00i | − | 1.48412i | −0.670335 | − | 0.742058i | \(-0.733850\pi\) | ||
0.670335 | − | 0.742058i | \(-0.266150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −570.000 | − | 509.823i | −0.722433 | − | 0.646164i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 187.830i | 0.237459i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 368.000i | 0.464061i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1194.06 | −1.49819 | −0.749097 | − | 0.662461i | \(-0.769512\pi\) | ||||
−0.749097 | + | 0.662461i | \(0.769512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −540.000 | −0.675845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 960.000 | − | 107.331i | 1.19850 | − | 0.133997i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1422.14 | −1.77103 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −670.820 | + | 750.000i | −0.831252 | + | 0.929368i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 912.316i | − | 1.12771i | −0.825875 | − | 0.563854i | \(-0.809318\pi\) | ||
0.825875 | − | 0.563854i | \(-0.190682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 674.000 | 0.831073 | 0.415536 | − | 0.909577i | \(-0.363594\pi\) | ||||
0.415536 | + | 0.909577i | \(0.363594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.47214 | − | 4.00000i | −0.00550078 | − | 0.00492005i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 272.000i | − | 0.332925i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.0000 | + | 143.108i | 0.0195360 | + | 0.174735i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1355.06i | − | 1.65050i | −0.564771 | − | 0.825248i | \(-0.691035\pi\) | ||
0.564771 | − | 0.825248i | \(-0.308965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 98.0000i | − | 0.119077i | −0.998226 | − | 0.0595383i | \(-0.981037\pi\) | ||
0.998226 | − | 0.0595383i | \(-0.0189628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 818.401 | 0.989602 | 0.494801 | − | 0.869006i | \(-0.335241\pi\) | ||||
0.494801 | + | 0.869006i | \(0.335241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −398.000 | −0.480097 | −0.240048 | − | 0.970761i | \(-0.577163\pi\) | ||||
−0.240048 | + | 0.970761i | \(0.577163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −896.000 | + | 1001.76i | −1.07822 | + | 1.20549i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −603.738 | −0.724776 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 219.135 | − | 308.000i | 0.261810 | − | 0.367981i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 992.814i | 1.18333i | 0.806184 | + | 0.591665i | \(0.201529\pi\) | ||||
−0.806184 | + | 0.591665i | \(0.798471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −779.000 | −0.926278 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 375.659 | − | 420.000i | 0.445622 | − | 0.498221i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 118.000i | − | 0.139315i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −496.000 | + | 554.545i | −0.584217 | + | 0.653174i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2253.96i | 2.64860i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 668.000i | − | 0.783118i | −0.920153 | − | 0.391559i | \(-0.871936\pi\) | ||
0.920153 | − | 0.391559i | \(-0.128064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 308.577 | 0.360067 | 0.180033 | − | 0.983660i | \(-0.442379\pi\) | ||||
0.180033 | + | 0.983660i | \(0.442379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −278.000 | −0.323632 | −0.161816 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161816 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −120.000 | − | 107.331i | −0.139373 | − | 0.124659i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 362.243 | 0.419749 | 0.209874 | − | 0.977728i | \(-0.432695\pi\) | ||||
0.209874 | + | 0.977728i | \(0.432695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 243.731 | + | 218.000i | 0.281120 | + | 0.251442i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 295.161i | 0.339656i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 256.000 | 0.293915 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1091.20 | + | 122.000i | −1.24994 | + | 0.139748i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 572.000i | 0.652223i | 0.945331 | + | 0.326112i | \(0.105739\pi\) | ||||
−0.945331 | + | 0.326112i | \(0.894261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 330.000 | + | 295.161i | 0.375427 | + | 0.335792i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 804.984i | − | 0.913717i | −0.889539 | − | 0.456858i | \(-0.848975\pi\) | ||
0.889539 | − | 0.456858i | \(-0.151025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1132.00i | 1.28199i | 0.767544 | + | 0.640997i | \(0.221479\pi\) | ||||
−0.767544 | + | 0.640997i | \(0.778521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1220.89 | 1.37643 | 0.688215 | − | 0.725507i | \(-0.258395\pi\) | ||||
0.688215 | + | 0.725507i | \(0.258395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.0000 | 0.0764904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −240.000 | − | 1059.90i | −0.269360 | − | 1.18956i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1368.47 | 1.53245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −643.988 | + | 720.000i | −0.717935 | + | 0.802676i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 563.489i | 0.626795i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 540.000 | 0.599334 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.7771 | − | 32.0000i | −0.0396203 | − | 0.0354374i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 716.000i | 0.789416i | 0.918807 | + | 0.394708i | \(0.129154\pi\) | ||||
−0.918807 | + | 0.394708i | \(0.870846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1560.00 | − | 174.413i | 1.71617 | − | 0.191874i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1261.14i | − | 1.38435i | −0.721730 | − | 0.692175i | \(-0.756653\pi\) | ||
0.721730 | − | 0.692175i | \(-0.243347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1620.00i | − | 1.77437i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −295.161 | −0.321877 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −866.000 | −0.942329 | −0.471164 | − | 0.882045i | \(-0.656166\pi\) | ||||
−0.471164 | + | 0.882045i | \(0.656166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 544.000 | − | 608.210i | 0.590662 | − | 0.660381i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 429.325 | 0.465141 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −411.437 | + | 46.0000i | −0.443837 | + | 0.0496224i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 295.161i | − | 0.317719i | −0.987301 | − | 0.158860i | \(-0.949218\pi\) | ||
0.987301 | − | 0.158860i | \(-0.0507817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1530.00 | 1.64339 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 107.331 | − | 120.000i | 0.115039 | − | 0.128617i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1018.00i | − | 1.08645i | −0.839588 | − | 0.543223i | \(-0.817204\pi\) | ||
0.839588 | − | 0.543223i | \(-0.182796\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −556.000 | + | 621.627i | −0.592119 | + | 0.662009i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1194.06i | 1.26893i | 0.772953 | + | 0.634463i | \(0.218779\pi\) | ||||
−0.772953 | + | 0.634463i | \(0.781221\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1080.00i | − | 1.14528i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −737.902 | −0.779200 | −0.389600 | − | 0.920984i | \(-0.627387\pi\) | ||||
−0.389600 | + | 0.920984i | \(0.627387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 848.000 | 0.893572 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 270.000 | + | 241.495i | 0.283912 | + | 0.253938i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1542.89 | 1.61898 | 0.809489 | − | 0.587134i | \(-0.199744\pi\) | ||||
0.809489 | + | 0.587134i | \(0.199744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1207.48 | + | 1080.00i | 1.26173 | + | 1.12853i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 80.4984i | 0.0839400i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −765.000 | −0.796046 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4164 | − | 120.000i | −0.0139319 | − | 0.124611i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1414.00i | − | 1.46225i | −0.682241 | − | 0.731127i | \(-0.738995\pi\) | ||
0.682241 | − | 0.731127i | \(-0.261005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1020.00 | + | 912.316i | 1.05263 | + | 0.941502i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 335.410i | 0.345428i | 0.984972 | + | 0.172714i | \(0.0552536\pi\) | ||||
−0.984972 | + | 0.172714i | \(0.944746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 164.000i | 0.168551i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.2492 | 0.0411967 | 0.0205984 | − | 0.999788i | \(-0.493443\pi\) | ||||
0.0205984 | + | 0.999788i | \(0.493443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1440.00 | 1.47089 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −86.0000 | − | 769.207i | −0.0876656 | − | 0.784105i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 469.574 | 0.477695 | 0.238848 | − | 0.971057i | \(-0.423230\pi\) | ||||
0.238848 | + | 0.971057i | \(0.423230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 160.997 | − | 180.000i | 0.163117 | − | 0.182371i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 321.994i | − | 0.325575i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 914.000 | 0.922301 | 0.461150 | − | 0.887322i | \(-0.347437\pi\) | ||||
0.461150 | + | 0.887322i | \(0.347437\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1337.17 | + | 1196.00i | 1.34659 | + | 1.20443i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1264.00i | − | 1.26780i | −0.773414 | − | 0.633902i | \(-0.781452\pi\) | ||
0.773414 | − | 0.633902i | \(-0.218548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1232.00 | + | 876.539i | 1.23323 | + | 0.877416i |
(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 | 300.3.b.c.149.1 | 4 | ||
3.2 | odd | 2 | inner | 300.3.b.c.149.3 | 4 | ||
4.3 | odd | 2 | 1200.3.c.e.449.4 | 4 | |||
5.2 | odd | 4 | 300.3.g.d.101.2 | 2 | |||
5.3 | odd | 4 | 60.3.g.a.41.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 300.3.b.c.149.4 | 4 | ||
12.11 | even | 2 | 1200.3.c.e.449.2 | 4 | |||
15.2 | even | 4 | 300.3.g.d.101.1 | 2 | |||
15.8 | even | 4 | 60.3.g.a.41.2 | yes | 2 | ||
15.14 | odd | 2 | inner | 300.3.b.c.149.2 | 4 | ||
20.3 | even | 4 | 240.3.l.a.161.2 | 2 | |||
20.7 | even | 4 | 1200.3.l.r.401.1 | 2 | |||
20.19 | odd | 2 | 1200.3.c.e.449.1 | 4 | |||
40.3 | even | 4 | 960.3.l.d.641.1 | 2 | |||
40.13 | odd | 4 | 960.3.l.a.641.2 | 2 | |||
45.13 | odd | 12 | 1620.3.o.b.1241.1 | 4 | |||
45.23 | even | 12 | 1620.3.o.b.1241.2 | 4 | |||
45.38 | even | 12 | 1620.3.o.b.701.1 | 4 | |||
45.43 | odd | 12 | 1620.3.o.b.701.2 | 4 | |||
60.23 | odd | 4 | 240.3.l.a.161.1 | 2 | |||
60.47 | odd | 4 | 1200.3.l.r.401.2 | 2 | |||
60.59 | even | 2 | 1200.3.c.e.449.3 | 4 | |||
120.53 | even | 4 | 960.3.l.a.641.1 | 2 | |||
120.83 | odd | 4 | 960.3.l.d.641.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.g.a.41.1 | ✓ | 2 | 5.3 | odd | 4 | ||
60.3.g.a.41.2 | yes | 2 | 15.8 | even | 4 | ||
240.3.l.a.161.1 | 2 | 60.23 | odd | 4 | |||
240.3.l.a.161.2 | 2 | 20.3 | even | 4 | |||
300.3.b.c.149.1 | 4 | 1.1 | even | 1 | trivial | ||
300.3.b.c.149.2 | 4 | 15.14 | odd | 2 | inner | ||
300.3.b.c.149.3 | 4 | 3.2 | odd | 2 | inner | ||
300.3.b.c.149.4 | 4 | 5.4 | even | 2 | inner | ||
300.3.g.d.101.1 | 2 | 15.2 | even | 4 | |||
300.3.g.d.101.2 | 2 | 5.2 | odd | 4 | |||
960.3.l.a.641.1 | 2 | 120.53 | even | 4 | |||
960.3.l.a.641.2 | 2 | 40.13 | odd | 4 | |||
960.3.l.d.641.1 | 2 | 40.3 | even | 4 | |||
960.3.l.d.641.2 | 2 | 120.83 | odd | 4 | |||
1200.3.c.e.449.1 | 4 | 20.19 | odd | 2 | |||
1200.3.c.e.449.2 | 4 | 12.11 | even | 2 | |||
1200.3.c.e.449.3 | 4 | 60.59 | even | 2 | |||
1200.3.c.e.449.4 | 4 | 4.3 | odd | 2 | |||
1200.3.l.r.401.1 | 2 | 20.7 | even | 4 | |||
1200.3.l.r.401.2 | 2 | 60.47 | odd | 4 | |||
1620.3.o.b.701.1 | 4 | 45.38 | even | 12 | |||
1620.3.o.b.701.2 | 4 | 45.43 | odd | 12 | |||
1620.3.o.b.1241.1 | 4 | 45.13 | odd | 12 | |||
1620.3.o.b.1241.2 | 4 | 45.23 | even | 12 |