Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(1279,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.g (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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.4 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1279 |
Dual form | 2304.3.g.x.1279.3 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.89898 | 1.77980 | 0.889898 | − | 0.456160i | \(-0.150775\pi\) | ||||
0.889898 | + | 0.456160i | \(0.150775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 0.404061i | 0.979379 | + | 0.202031i | \(0.0647540\pi\) | ||||
−0.979379 | + | 0.202031i | \(0.935246\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 18.2419i | − 1.65836i | −0.558985 | − | 0.829178i | \(-0.688809\pi\) | ||||
0.558985 | − | 0.829178i | \(-0.311191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.79796 | 0.445997 | 0.222998 | − | 0.974819i | \(-0.428416\pi\) | ||||
0.222998 | + | 0.974819i | \(0.428416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.5959 | 1.27035 | 0.635174 | − | 0.772369i | \(-0.280928\pi\) | ||||
0.635174 | + | 0.772369i | \(0.280928\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.2419i | 0.960101i | 0.877241 | + | 0.480050i | \(0.159382\pi\) | ||||
−0.877241 | + | 0.480050i | \(0.840618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.3697i | 1.45086i | 0.688299 | + | 0.725428i | \(0.258358\pi\) | ||||
−0.688299 | + | 0.725428i | \(0.741642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.1918 | 2.16767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.49490 | −0.154996 | −0.0774982 | − | 0.996992i | \(-0.524693\pi\) | ||||
−0.0774982 | + | 0.996992i | \(0.524693\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.25697i | − 0.0728054i | −0.999337 | − | 0.0364027i | \(-0.988410\pi\) | ||||
0.999337 | − | 0.0364027i | \(-0.0115899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.1701i | 0.719146i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −43.1918 | −1.16735 | −0.583673 | − | 0.811988i | \(-0.698385\pi\) | ||||
−0.583673 | + | 0.811988i | \(0.698385\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.59592 | −0.0389248 | −0.0194624 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194624 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 63.4967i | − 1.47667i | −0.674435 | − | 0.738334i | \(-0.735613\pi\) | ||||
0.674435 | − | 0.738334i | \(-0.264387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.3962i | 1.54034i | 0.637836 | + | 0.770172i | \(0.279830\pi\) | ||||
−0.637836 | + | 0.770172i | \(0.720170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.0000 | 0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 70.2929 | 1.32628 | 0.663140 | − | 0.748495i | \(-0.269223\pi\) | ||||
0.663140 | + | 0.748495i | \(0.269223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 162.334i | − 2.95153i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.6410i | 0.587136i | 0.955938 | + | 0.293568i | \(0.0948427\pi\) | ||||
−0.955938 | + | 0.293568i | \(0.905157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.5959 | 1.04256 | 0.521278 | − | 0.853387i | \(-0.325455\pi\) | ||||
0.521278 | + | 0.853387i | \(0.325455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 51.5959 | 0.793783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.24259i | − 0.0483968i | −0.999707 | − | 0.0241984i | \(-0.992297\pi\) | ||||
0.999707 | − | 0.0241984i | \(-0.00770335\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 68.4537i | − 0.964137i | −0.876134 | − | 0.482068i | \(-0.839886\pi\) | ||||
0.876134 | − | 0.482068i | \(-0.160114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 0.136986 | 0.0684932 | − | 0.997652i | \(-0.478181\pi\) | ||||
0.0684932 | + | 0.997652i | \(0.478181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.5959 | 0.670077 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 35.0552i | − 0.443736i | −0.975077 | − | 0.221868i | \(-0.928785\pi\) | ||||
0.975077 | − | 0.221868i | \(-0.0712155\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 42.2691i | − 0.509266i | −0.967038 | − | 0.254633i | \(-0.918045\pi\) | ||||
0.967038 | − | 0.254633i | \(-0.0819547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 192.182 | 2.26096 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19184 | 0.0583352 | 0.0291676 | − | 0.999575i | \(-0.490714\pi\) | ||||
0.0291676 | + | 0.999575i | \(0.490714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3991i | 0.180210i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 162.334i | 1.70878i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −26.8082 | −0.276373 | −0.138186 | − | 0.990406i | \(-0.544127\pi\) | ||||
−0.138186 | + | 0.990406i | \(0.544127\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.8786 | −0.503748 | −0.251874 | − | 0.967760i | \(-0.581047\pi\) | ||||
−0.251874 | + | 0.967760i | \(0.581047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 148.764i | − 1.44431i | −0.691732 | − | 0.722154i | \(-0.743152\pi\) | ||||
0.691732 | − | 0.722154i | \(-0.256848\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 116.380i | − 1.08766i | −0.839195 | − | 0.543830i | \(-0.816974\pi\) | ||||
0.839195 | − | 0.543830i | \(-0.183026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −44.1816 | −0.405336 | −0.202668 | − | 0.979248i | \(-0.564961\pi\) | ||||
−0.202668 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −199.576 | −1.76615 | −0.883077 | − | 0.469227i | \(-0.844533\pi\) | ||||
−0.883077 | + | 0.469227i | \(0.844533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 296.956i | 2.58223i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 61.0825i | 0.513298i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −211.767 | −1.75014 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 259.778 | 2.07822 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.276i | 1.44312i | 0.692352 | + | 0.721560i | \(0.256575\pi\) | ||||
−0.692352 | + | 0.721560i | \(0.743425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 176.891i | 1.35031i | 0.737676 | + | 0.675155i | \(0.235923\pi\) | ||||
−0.737676 | + | 0.675155i | \(0.764077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51.5959 | −0.387939 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 147.980 | 1.08014 | 0.540071 | − | 0.841619i | \(-0.318397\pi\) | ||||
0.540071 | + | 0.841619i | \(0.318397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 114.980i | − 0.827193i | −0.910460 | − | 0.413597i | \(-0.864272\pi\) | ||||
0.910460 | − | 0.413597i | \(-0.135728\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 105.766i | − 0.739621i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.0000 | −0.275862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 229.303 | 1.53895 | 0.769473 | − | 0.638679i | \(-0.220519\pi\) | ||||
0.769473 | + | 0.638679i | \(0.220519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 225.674i | 1.49453i | 0.664527 | + | 0.747264i | \(0.268633\pi\) | ||||
−0.664527 | + | 0.747264i | \(0.731367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 20.0847i | − 0.129579i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.8082 | 0.234447 | 0.117223 | − | 0.993106i | \(-0.462601\pi\) | ||||
0.117223 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −94.3837 | −0.586234 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 180.833i | − 1.10941i | −0.832048 | − | 0.554703i | \(-0.812832\pi\) | ||||
0.832048 | − | 0.554703i | \(-0.187168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 174.791i | 1.04665i | 0.852132 | + | 0.523326i | \(0.175309\pi\) | ||||
−0.852132 | + | 0.523326i | \(0.824691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −135.384 | −0.801087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 158.111 | 0.913938 | 0.456969 | − | 0.889483i | \(-0.348935\pi\) | ||||
0.456969 | + | 0.889483i | \(0.348935\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 153.278i | 0.875872i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.6979i | 0.255295i | 0.991820 | + | 0.127648i | \(0.0407427\pi\) | ||||
−0.991820 | + | 0.127648i | \(0.959257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 263.778 | 1.45733 | 0.728667 | − | 0.684868i | \(-0.240140\pi\) | ||||
0.728667 | + | 0.684868i | \(0.240140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −384.363 | −2.07764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 393.951i | − 2.10669i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 154.963i | − 0.811325i | −0.914023 | − | 0.405663i | \(-0.867041\pi\) | ||||
0.914023 | − | 0.405663i | \(-0.132959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −182.767 | −0.946981 | −0.473491 | − | 0.880799i | \(-0.657006\pi\) | ||||
−0.473491 | + | 0.880799i | \(0.657006\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 178.697 | 0.907091 | 0.453546 | − | 0.891233i | \(-0.350159\pi\) | ||||
0.453546 | + | 0.891233i | \(0.350159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 37.9125i | − 0.190515i | −0.995453 | − | 0.0952575i | \(-0.969633\pi\) | ||||
0.995453 | − | 0.0952575i | \(-0.0303674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 12.7135i | − 0.0626280i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.2020 | −0.0692782 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 332.767 | 1.59219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.8986i | 0.0943060i | 0.998888 | + | 0.0471530i | \(0.0150148\pi\) | ||||
−0.998888 | + | 0.0471530i | \(0.984985\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 565.056i | − 2.62817i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.38367 | 0.0294178 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 125.212 | 0.566571 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 212.703i | − 0.953827i | −0.878950 | − | 0.476914i | \(-0.841755\pi\) | ||||
0.878950 | − | 0.476914i | \(-0.158245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 104.180i | 0.458942i | 0.973315 | + | 0.229471i | \(0.0736997\pi\) | ||||
−0.973315 | + | 0.229471i | \(0.926300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −316.545 | −1.38229 | −0.691146 | − | 0.722715i | \(-0.742894\pi\) | ||||
−0.691146 | + | 0.722715i | \(0.742894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 120.424 | 0.516843 | 0.258422 | − | 0.966032i | \(-0.416798\pi\) | ||||
0.258422 | + | 0.966032i | \(0.416798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 644.252i | 2.74150i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 178.734i | − 0.747839i | −0.927461 | − | 0.373919i | \(-0.878014\pi\) | ||||
0.927461 | − | 0.373919i | \(-0.121986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 46.8082 | 0.194225 | 0.0971124 | − | 0.995273i | \(-0.469039\pi\) | ||||
0.0971124 | + | 0.995273i | \(0.469039\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 364.858 | 1.48922 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 105.766i | 0.428202i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 39.9833i | 0.159296i | 0.996823 | + | 0.0796480i | \(0.0253796\pi\) | ||||
−0.996823 | + | 0.0796480i | \(0.974620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 608.727 | 2.40603 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −290.000 | −1.12840 | −0.564202 | − | 0.825637i | \(-0.690816\pi\) | ||||
−0.564202 | + | 0.825637i | \(0.690816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 122.165i | − 0.471679i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 249.415i | − 0.948347i | −0.880431 | − | 0.474174i | \(-0.842747\pi\) | ||||
0.880431 | − | 0.474174i | \(-0.157253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 625.535 | 2.36051 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −100.858 | −0.374937 | −0.187469 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187469 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 222.817i | 0.822201i | 0.911590 | + | 0.411101i | \(0.134856\pi\) | ||||
−0.911590 | + | 0.411101i | \(0.865144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 988.563i | − 3.59477i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 194.202 | 0.701090 | 0.350545 | − | 0.936546i | \(-0.385996\pi\) | ||||
0.350545 | + | 0.936546i | \(0.385996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202.767 | 0.721592 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 156.549i | 0.553177i | 0.960988 | + | 0.276589i | \(0.0892039\pi\) | ||||
−0.960988 | + | 0.276589i | \(0.910796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4.51394i | − 0.0157280i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 177.384 | 0.613784 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 116.677 | 0.398213 | 0.199107 | − | 0.979978i | \(-0.436196\pi\) | ||||
0.199107 | + | 0.979978i | \(0.436196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 308.270i | 1.04498i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 193.476i | 0.647077i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 179.596 | 0.596664 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 565.939 | 1.85554 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 17.9850i | − 0.0585832i | −0.999571 | − | 0.0292916i | \(-0.990675\pi\) | ||||
0.999571 | − | 0.0292916i | \(-0.00932514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 290.214i | 0.933164i | 0.884478 | + | 0.466582i | \(0.154515\pi\) | ||||
−0.884478 | + | 0.466582i | \(0.845485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 255.535 | 0.816405 | 0.408202 | − | 0.912891i | \(-0.366156\pi\) | ||||
0.408202 | + | 0.912891i | \(0.366156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 93.4847 | 0.294904 | 0.147452 | − | 0.989069i | \(-0.452893\pi\) | ||||
0.147452 | + | 0.989069i | \(0.452893\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 81.9955i | 0.257039i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 393.951i | 1.21966i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 314.202 | 0.966776 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −204.767 | −0.622393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 151.464i | 0.457594i | 0.973474 | + | 0.228797i | \(0.0734793\pi\) | ||||
−0.973474 | + | 0.228797i | \(0.926521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 28.8557i | − 0.0861365i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 102.767 | 0.304948 | 0.152474 | − | 0.988308i | \(-0.451276\pi\) | ||||
0.152474 | + | 0.988308i | \(0.451276\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.1714 | −0.120737 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 254.558i | 0.742153i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 333.626i | 0.961458i | 0.876869 | + | 0.480729i | \(0.159628\pi\) | ||||
−0.876869 | + | 0.480729i | \(0.840372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −553.939 | −1.58722 | −0.793609 | − | 0.608429i | \(-0.791800\pi\) | ||||
−0.793609 | + | 0.608429i | \(0.791800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 398.727 | 1.12954 | 0.564768 | − | 0.825249i | \(-0.308965\pi\) | ||||
0.564768 | + | 0.825249i | \(0.308965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 609.168i | − 1.71597i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 110.280i | 0.307186i | 0.988134 | + | 0.153593i | \(0.0490845\pi\) | ||||
−0.988134 | + | 0.153593i | \(0.950916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.2327 | 0.0782068 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 88.9898 | 0.243808 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 372.181i | − 1.01412i | −0.861912 | − | 0.507058i | \(-0.830733\pi\) | ||||
0.861912 | − | 0.507058i | \(-0.169267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 198.818i | 0.535898i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −277.980 | −0.745254 | −0.372627 | − | 0.927981i | \(-0.621543\pi\) | ||||
−0.372627 | + | 0.927981i | \(0.621543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.0612 | −0.0691279 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 320.797i | − 0.846430i | −0.906029 | − | 0.423215i | \(-0.860901\pi\) | ||||
0.906029 | − | 0.423215i | \(-0.139099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 609.797i | − 1.59216i | −0.605191 | − | 0.796080i | \(-0.706903\pi\) | ||||
0.605191 | − | 0.796080i | \(-0.293097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 459.151 | 1.19260 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 126.111 | 0.324193 | 0.162097 | − | 0.986775i | \(-0.448174\pi\) | ||||
0.162097 | + | 0.986775i | \(0.448174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 720.649i | 1.84309i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 311.955i | − 0.789760i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.36326 | −0.0109906 | −0.00549529 | − | 0.999985i | \(-0.501749\pi\) | ||||
−0.00549529 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −691.049 | −1.72331 | −0.861657 | − | 0.507491i | \(-0.830573\pi\) | ||||
−0.861657 | + | 0.507491i | \(0.830573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 13.0858i | − 0.0324710i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 787.902i | 1.93588i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −485.959 | −1.18816 | −0.594082 | − | 0.804404i | \(-0.702485\pi\) | ||||
−0.594082 | + | 0.804404i | \(0.702485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −97.9796 | −0.237239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 376.152i | − 0.906390i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 499.531i | 1.19220i | 0.802911 | + | 0.596098i | \(0.203283\pi\) | ||||
−0.802911 | + | 0.596098i | \(0.796717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8796 | −0.0519705 | −0.0259853 | − | 0.999662i | \(-0.508272\pi\) | ||||
−0.0259853 | + | 0.999662i | \(0.508272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1170.32 | 2.75370 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 179.876i | 0.421256i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 513.631i | 1.19172i | 0.803089 | + | 0.595859i | \(0.203188\pi\) | ||||
−0.803089 | + | 0.595859i | \(0.796812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.3837 | −0.0378376 | −0.0189188 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189188 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −608.727 | −1.39297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 324.068i | − 0.738197i | −0.929390 | − | 0.369098i | \(-0.879667\pi\) | ||||
0.929390 | − | 0.369098i | \(-0.120333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 221.003i | 0.498877i | 0.968391 | + | 0.249439i | \(0.0802461\pi\) | ||||
−0.968391 | + | 0.249439i | \(0.919754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 46.2020 | 0.103825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −690.322 | −1.53747 | −0.768733 | − | 0.639570i | \(-0.779113\pi\) | ||||
−0.768733 | + | 0.639570i | \(0.779113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.1126i | 0.0645512i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 145.935i | 0.320737i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −397.878 | −0.870629 | −0.435315 | − | 0.900278i | \(-0.643363\pi\) | ||||
−0.435315 | + | 0.900278i | \(0.643363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 707.160 | 1.53397 | 0.766985 | − | 0.641665i | \(-0.221756\pi\) | ||||
0.766985 | + | 0.641665i | \(0.221756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 869.926i | − 1.87889i | −0.342700 | − | 0.939445i | \(-0.611341\pi\) | ||||
0.342700 | − | 0.939445i | \(-0.388659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 75.4396i | 0.161541i | 0.996733 | + | 0.0807705i | \(0.0257381\pi\) | ||||
−0.996733 | + | 0.0807705i | \(0.974262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.17143 | 0.0195553 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1158.30 | −2.44884 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 988.563i | 2.08118i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 90.5674i | − 0.189076i | −0.995521 | − | 0.0945380i | \(-0.969863\pi\) | ||||
0.995521 | − | 0.0945380i | \(-0.0301374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −250.424 | −0.520633 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −238.565 | −0.491887 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 137.392i | − 0.282120i | −0.990001 | − | 0.141060i | \(-0.954949\pi\) | ||||
0.990001 | − | 0.141060i | \(-0.0450510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 89.5529i | 0.182389i | 0.995833 | + | 0.0911944i | \(0.0290685\pi\) | ||||
−0.995833 | + | 0.0911944i | \(0.970932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −97.0714 | −0.196899 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 193.616 | 0.389570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 268.286i | 0.537648i | 0.963189 | + | 0.268824i | \(0.0866350\pi\) | ||||
−0.963189 | + | 0.268824i | \(0.913365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 93.2515i | 0.185391i | 0.995695 | + | 0.0926953i | \(0.0295483\pi\) | ||||
−0.995695 | + | 0.0926953i | \(0.970452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −452.767 | −0.896569 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 168.272 | 0.330594 | 0.165297 | − | 0.986244i | \(-0.447142\pi\) | ||||
0.165297 | + | 0.986244i | \(0.447142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2843i | 0.0553508i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1323.85i | − 2.57057i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1320.64 | 2.55444 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 316.788 | 0.608038 | 0.304019 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304019 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 443.591i | − 0.848167i | −0.905623 | − | 0.424083i | \(-0.860596\pi\) | ||||
0.905623 | − | 0.424083i | \(-0.139404\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 48.7413i | − 0.0924883i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −584.535 | −1.10498 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.25307 | −0.0173604 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1035.66i | − 1.93581i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 747.918i | − 1.38760i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −966.443 | −1.78640 | −0.893200 | − | 0.449659i | \(-0.851546\pi\) | ||||
−0.893200 | + | 0.449659i | \(0.851546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −393.171 | −0.721415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 578.470i | − 1.05753i | −0.848768 | − | 0.528766i | \(-0.822655\pi\) | ||||
0.848768 | − | 0.528766i | \(-0.177345\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 81.9955i | − 0.148812i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 99.1510 | 0.179297 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −590.293 | −1.05977 | −0.529886 | − | 0.848069i | \(-0.677765\pi\) | ||||
−0.529886 | + | 0.848069i | \(0.677765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 368.152i | − 0.658589i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 468.877i | − 0.832818i | −0.909177 | − | 0.416409i | \(-0.863288\pi\) | ||||
0.909177 | − | 0.416409i | \(-0.136712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1776.02 | −3.14340 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −548.829 | −0.964549 | −0.482275 | − | 0.876020i | \(-0.660189\pi\) | ||||
−0.482275 | + | 0.876020i | \(0.660189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 133.036i | − 0.232987i | −0.993191 | − | 0.116494i | \(-0.962835\pi\) | ||||
0.993191 | − | 0.116494i | \(-0.0371654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1808.36i | 3.14498i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −735.535 | −1.27476 | −0.637378 | − | 0.770551i | \(-0.719981\pi\) | ||||
−0.637378 | + | 0.770551i | \(0.719981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 119.555 | 0.205775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1282.28i | − 2.19944i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 178.290i | 0.303732i | 0.988401 | + | 0.151866i | \(0.0485282\pi\) | ||||
−0.988401 | + | 0.151866i | \(0.951472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.1714 | 0.0699006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 584.261 | 0.985263 | 0.492632 | − | 0.870238i | \(-0.336035\pi\) | ||||
0.492632 | + | 0.870238i | \(0.336035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 543.572i | 0.913566i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 134.050i | − 0.223790i | −0.993720 | − | 0.111895i | \(-0.964308\pi\) | ||||
0.993720 | − | 0.111895i | \(-0.0356920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −621.918 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1884.51 | −3.11490 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 36.1404i | − 0.0595393i | −0.999557 | − | 0.0297697i | \(-0.990523\pi\) | ||||
0.999557 | − | 0.0297697i | \(-0.00947738\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 419.750i | 0.686989i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −385.857 | −0.629457 | −0.314728 | − | 0.949182i | \(-0.601913\pi\) | ||||
−0.314728 | + | 0.949182i | \(0.601913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 290.849 | 0.471392 | 0.235696 | − | 0.971827i | \(-0.424263\pi\) | ||||
0.235696 | + | 0.971827i | \(0.424263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 275.658i | − 0.445327i | −0.974895 | − | 0.222664i | \(-0.928525\pi\) | ||||
0.974895 | − | 0.222664i | \(-0.0714752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6847i | 0.0235710i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 956.959 | 1.53113 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −932.767 | −1.48294 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 940.608i | 1.49066i | 0.666694 | + | 0.745331i | \(0.267709\pi\) | ||||
−0.666694 | + | 0.745331i | \(0.732291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1630.97i | 2.56846i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 237.716 | 0.373181 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.3633 | 0.0536088 | 0.0268044 | − | 0.999641i | \(-0.491467\pi\) | ||||
0.0268044 | + | 0.999641i | \(0.491467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 308.340i | 0.479534i | 0.970830 | + | 0.239767i | \(0.0770711\pi\) | ||||
−0.970830 | + | 0.239767i | \(0.922929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 190.503i | 0.294441i | 0.989104 | + | 0.147220i | \(0.0470327\pi\) | ||||
−0.989104 | + | 0.147220i | \(0.952967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 631.918 | 0.973680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1103.38 | −1.68971 | −0.844857 | − | 0.534993i | \(-0.820314\pi\) | ||||
−0.844857 | + | 0.534993i | \(0.820314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1574.15i | 2.40328i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 815.544i | 1.23755i | 0.785569 | + | 0.618774i | \(0.212370\pi\) | ||||
−0.785569 | + | 0.618774i | \(0.787630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −121.576 | −0.183927 | −0.0919633 | − | 0.995762i | \(-0.529314\pi\) | ||||
−0.0919633 | + | 0.995762i | \(0.529314\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −459.151 | −0.690453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 149.993i | − 0.224877i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1160.11i | − 1.72893i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1326.60 | −1.97118 | −0.985590 | − | 0.169152i | \(-0.945897\pi\) | ||||
−0.985590 | + | 0.169152i | \(0.945897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −657.526 | −0.971234 | −0.485617 | − | 0.874172i | \(-0.661405\pi\) | ||||
−0.485617 | + | 0.874172i | \(0.661405\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 75.8249i | − 0.111671i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 772.318i | − 1.13077i | −0.824826 | − | 0.565386i | \(-0.808727\pi\) | ||||
0.824826 | − | 0.565386i | \(-0.191273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1316.87 | 1.92243 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 407.555 | 0.591517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1269.00i | − 1.83647i | −0.396030 | − | 0.918237i | \(-0.629613\pi\) | ||||
0.396030 | − | 0.918237i | \(-0.370387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1023.20i | − 1.47224i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.4653 | −0.0494481 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 535.383 | 0.763741 | 0.381871 | − | 0.924216i | \(-0.375280\pi\) | ||||
0.381871 | + | 0.924216i | \(0.375280\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 787.902i | − 1.12077i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 143.906i | − 0.203545i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 56.8673 | 0.0802078 | 0.0401039 | − | 0.999196i | \(-0.487231\pi\) | ||||
0.0401039 | + | 0.999196i | \(0.487231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 75.3143 | 0.105630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 941.208i | − 1.31638i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 980.922i | 1.36429i | 0.731219 | + | 0.682143i | \(0.238952\pi\) | ||||
−0.731219 | + | 0.682143i | \(0.761048\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 420.767 | 0.583589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −243.587 | −0.335982 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 83.1673i | 0.114398i | 0.998363 | + | 0.0571990i | \(0.0182169\pi\) | ||||
−0.998363 | + | 0.0571990i | \(0.981783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1371.27i | − 1.87588i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −345.476 | −0.471317 | −0.235659 | − | 0.971836i | \(-0.575725\pi\) | ||||
−0.235659 | + | 0.971836i | \(0.575725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −59.1510 | −0.0802592 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1388.23i | 1.87852i | 0.343203 | + | 0.939261i | \(0.388488\pi\) | ||||
−0.343203 | + | 0.939261i | \(0.611512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 885.269i | 1.19148i | 0.803178 | + | 0.595739i | \(0.203141\pi\) | ||||
−0.803178 | + | 0.595739i | \(0.796859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2040.56 | 2.73901 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 329.171 | 0.439481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1225.11i | 1.63130i | 0.578545 | + | 0.815651i | \(0.303621\pi\) | ||||
−0.578545 | + | 0.815651i | \(0.696379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2008.27i | 2.65996i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −86.9694 | −0.114887 | −0.0574435 | − | 0.998349i | \(-0.518295\pi\) | ||||
−0.0574435 | + | 0.998349i | \(0.518295\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −764.020 | −1.00397 | −0.501985 | − | 0.864877i | \(-0.667397\pi\) | ||||
−0.501985 | + | 0.864877i | \(0.667397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 124.965i | − 0.163781i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 200.847i | 0.261861i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 269.918 | 0.350999 | 0.175500 | − | 0.984480i | \(-0.443846\pi\) | ||||
0.175500 | + | 0.984480i | \(0.443846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1109.24 | 1.43498 | 0.717490 | − | 0.696569i | \(-0.245291\pi\) | ||||
0.717490 | + | 0.696569i | \(0.245291\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 122.309i | − 0.157818i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 29.1126i | − 0.0373718i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1248.73 | −1.59888 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 327.555 | 0.417268 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1260.98i | 1.60226i | 0.598491 | + | 0.801129i | \(0.295767\pi\) | ||||
−0.598491 | + | 0.801129i | \(0.704233\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 564.485i | − 0.713634i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 368.727 | 0.464977 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −386.779 | −0.485293 | −0.242647 | − | 0.970115i | \(-0.578016\pi\) | ||||
−0.242647 | + | 0.970115i | \(0.578016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1563.46i | 1.95677i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 182.419i | − 0.227172i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −839.918 | −1.04338 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1139.98 | 1.40912 | 0.704561 | − | 0.709643i | \(-0.251144\pi\) | ||||
0.704561 | + | 0.709643i | \(0.251144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 959.450i | − 1.18305i | −0.806288 | − | 0.591523i | \(-0.798527\pi\) | ||||
0.806288 | − | 0.591523i | \(-0.201473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1609.23i | − 1.97452i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1158.30 | 1.41775 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −918.674 | −1.11897 | −0.559485 | − | 0.828840i | \(-0.689001\pi\) | ||||
−0.559485 | + | 0.828840i | \(0.689001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 678.107i | 0.823945i | 0.911196 | + | 0.411972i | \(0.135160\pi\) | ||||
−0.911196 | + | 0.411972i | \(0.864840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1237.58i | − 1.49647i | −0.663434 | − | 0.748234i | \(-0.730902\pi\) | ||||
0.663434 | − | 0.748234i | \(-0.269098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 778.120 | 0.938625 | 0.469313 | − | 0.883032i | \(-0.344502\pi\) | ||||
0.469313 | + | 0.883032i | \(0.344502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 885.433 | 1.06294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1555.46i | 1.86283i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 345.582i | 0.411897i | 0.978563 | + | 0.205949i | \(0.0660280\pi\) | ||||
−0.978563 | + | 0.205949i | \(0.933972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −820.796 | −0.975976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1204.78 | −1.42577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 598.968i | − 0.707165i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1441.30i | − 1.69365i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1026.38 | −1.20326 | −0.601632 | − | 0.798774i | \(-0.705482\pi\) | ||||
−0.601632 | + | 0.798774i | \(0.705482\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −296.061 | −0.345462 | −0.172731 | − | 0.984969i | \(-0.555259\pi\) | ||||
−0.172731 | + | 0.984969i | \(0.555259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 167.118i | 0.194550i | 0.995258 | + | 0.0972748i | \(0.0310126\pi\) | ||||
−0.995258 | + | 0.0972748i | \(0.968987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 10.0553i | − 0.0116516i | −0.999983 | − | 0.00582580i | \(-0.998146\pi\) | ||||
0.999983 | − | 0.00582580i | \(-0.00185442\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1407.03 | 1.62662 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −639.473 | −0.735873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 18.8004i | − 0.0215848i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 734.762i | 0.839728i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1154.58 | −1.31651 | −0.658257 | − | 0.752793i | \(-0.728706\pi\) | ||||
−0.658257 | + | 0.752793i | \(0.728706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −160.220 | −0.181862 | −0.0909310 | − | 0.995857i | \(-0.528984\pi\) | ||||
−0.0909310 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1311.46i | − 1.48523i | −0.669718 | − | 0.742616i | \(-0.733585\pi\) | ||||
0.669718 | − | 0.742616i | \(-0.266415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 234.673i | − 0.264569i | −0.991212 | − | 0.132285i | \(-0.957769\pi\) | ||||
0.991212 | − | 0.132285i | \(-0.0422313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −518.384 | −0.583109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1320.64 | −1.47889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 406.664i | 0.454374i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1448i | 0.0112846i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1518.04 | 1.68484 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2347.35 | 2.59376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1161.70i | 1.28081i | 0.768036 | + | 0.640406i | \(0.221234\pi\) | ||||
−0.768036 | + | 0.640406i | \(0.778766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1382.33i | − 1.51737i | −0.651456 | − | 0.758687i | \(-0.725841\pi\) | ||||
0.651456 | − | 0.758687i | \(-0.274159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −771.069 | −0.844545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −500.322 | −0.545608 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1206.60i | − 1.31294i | −0.754350 | − | 0.656472i | \(-0.772048\pi\) | ||||
0.754350 | − | 0.656472i | \(-0.227952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 396.892i | − 0.430002i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2340.64 | −2.53043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1159.90 | −1.24854 | −0.624272 | − | 0.781207i | \(-0.714604\pi\) | ||||
−0.624272 | + | 0.781207i | \(0.714604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 747.918i | 0.803349i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 3505.76i | − 3.74948i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −173.837 | −0.185525 | −0.0927624 | − | 0.995688i | \(-0.529570\pi\) | ||||
−0.0927624 | + | 0.995688i | \(0.529570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 603.968 | 0.641837 | 0.320918 | − | 0.947107i | \(-0.396008\pi\) | ||||
0.320918 | + | 0.947107i | \(0.396008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 53.2553i | − 0.0564743i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 951.077i | 1.00431i | 0.864779 | + | 0.502153i | \(0.167458\pi\) | ||||
−0.864779 | + | 0.502153i | \(0.832542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.9796 | 0.0610955 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1407.98 | −1.47742 | −0.738709 | − | 0.674024i | \(-0.764564\pi\) | ||||
−0.738709 | + | 0.674024i | \(0.764564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1379.01i | − 1.44399i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 418.549i | 0.436444i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 955.906 | 0.994699 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1626.44 | −1.68543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 467.718i | − 0.483679i | −0.970316 | − | 0.241840i | \(-0.922249\pi\) | ||||
0.970316 | − | 0.241840i | \(-0.0777508\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1115.70i | 1.14902i | 0.818498 | + | 0.574510i | \(0.194807\pi\) | ||||
−0.818498 | + | 0.574510i | \(0.805193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 325.212 | 0.334237 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −494.363 | −0.506001 | −0.253001 | − | 0.967466i | \(-0.581417\pi\) | ||||
−0.253001 | + | 0.967466i | \(0.581417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 94.7090i | − 0.0967406i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 188.391i | 0.191649i | 0.995398 | + | 0.0958243i | \(0.0305487\pi\) | ||||
−0.995398 | + | 0.0958243i | \(0.969451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1590.22 | 1.61444 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2118.87 | 2.14243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1895.81i | 1.91303i | 0.291681 | + | 0.956516i | \(0.405785\pi\) | ||||
−0.291681 | + | 0.956516i | \(0.594215\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 337.382i | − 0.339078i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1317.98 | −1.32195 | −0.660973 | − | 0.750410i | \(-0.729856\pi\) | ||||
−0.660973 | + | 0.750410i | \(0.729856\pi\) | |||||||
\(998\) | 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 | 2304.3.g.x.1279.4 | 4 | ||
3.2 | odd | 2 | 768.3.g.c.511.3 | 4 | |||
4.3 | odd | 2 | inner | 2304.3.g.x.1279.3 | 4 | ||
8.3 | odd | 2 | 2304.3.g.o.1279.1 | 4 | |||
8.5 | even | 2 | 2304.3.g.o.1279.2 | 4 | |||
12.11 | even | 2 | 768.3.g.c.511.1 | 4 | |||
16.3 | odd | 4 | 1152.3.b.j.703.2 | 8 | |||
16.5 | even | 4 | 1152.3.b.j.703.7 | 8 | |||
16.11 | odd | 4 | 1152.3.b.j.703.8 | 8 | |||
16.13 | even | 4 | 1152.3.b.j.703.1 | 8 | |||
24.5 | odd | 2 | 768.3.g.g.511.2 | 4 | |||
24.11 | even | 2 | 768.3.g.g.511.4 | 4 | |||
48.5 | odd | 4 | 384.3.b.c.319.5 | yes | 8 | ||
48.11 | even | 4 | 384.3.b.c.319.1 | ✓ | 8 | ||
48.29 | odd | 4 | 384.3.b.c.319.4 | yes | 8 | ||
48.35 | even | 4 | 384.3.b.c.319.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.b.c.319.1 | ✓ | 8 | 48.11 | even | 4 | ||
384.3.b.c.319.4 | yes | 8 | 48.29 | odd | 4 | ||
384.3.b.c.319.5 | yes | 8 | 48.5 | odd | 4 | ||
384.3.b.c.319.8 | yes | 8 | 48.35 | even | 4 | ||
768.3.g.c.511.1 | 4 | 12.11 | even | 2 | |||
768.3.g.c.511.3 | 4 | 3.2 | odd | 2 | |||
768.3.g.g.511.2 | 4 | 24.5 | odd | 2 | |||
768.3.g.g.511.4 | 4 | 24.11 | even | 2 | |||
1152.3.b.j.703.1 | 8 | 16.13 | even | 4 | |||
1152.3.b.j.703.2 | 8 | 16.3 | odd | 4 | |||
1152.3.b.j.703.7 | 8 | 16.5 | even | 4 | |||
1152.3.b.j.703.8 | 8 | 16.11 | odd | 4 | |||
2304.3.g.o.1279.1 | 4 | 8.3 | odd | 2 | |||
2304.3.g.o.1279.2 | 4 | 8.5 | even | 2 | |||
2304.3.g.x.1279.3 | 4 | 4.3 | odd | 2 | inner | ||
2304.3.g.x.1279.4 | 4 | 1.1 | even | 1 | trivial |