Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (of order \(2\), degree \(1\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.4 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.3.b.c.319.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.89898i | 1.77980i | 0.456160 | + | 0.889898i | \(0.349225\pi\) | ||||
−0.456160 | + | 0.889898i | \(0.650775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.82843i | − 0.404061i | −0.979379 | − | 0.202031i | \(-0.935246\pi\) | ||||
0.979379 | − | 0.202031i | \(-0.0647540\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.2419 | 1.65836 | 0.829178 | − | 0.558985i | \(-0.188809\pi\) | ||||
0.829178 | + | 0.558985i | \(0.188809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.79796i | 0.445997i | 0.974819 | + | 0.222998i | \(0.0715845\pi\) | ||||
−0.974819 | + | 0.222998i | \(0.928416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 15.4135i | − 1.02757i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.5959 | −1.27035 | −0.635174 | − | 0.772369i | \(-0.719072\pi\) | ||||
−0.635174 | + | 0.772369i | \(0.719072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.2419 | −0.960101 | −0.480050 | − | 0.877241i | \(-0.659382\pi\) | ||||
−0.480050 | + | 0.877241i | \(0.659382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.89898i | 0.233285i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.49490i | 0.154996i | 0.996992 | + | 0.0774982i | \(0.0246932\pi\) | ||||
−0.996992 | + | 0.0774982i | \(0.975307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 2.25697i | − 0.0728054i | −0.999337 | − | 0.0364027i | \(-0.988410\pi\) | ||||
0.999337 | − | 0.0364027i | \(-0.0115899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −31.5959 | −0.957452 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.1701 | 0.719146 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 43.1918i | 1.16735i | 0.811988 | + | 0.583673i | \(0.198385\pi\) | ||||
−0.811988 | + | 0.583673i | \(0.801615\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 10.0424i | − 0.257496i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.59592 | −0.0389248 | −0.0194624 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194624 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −63.4967 | −1.47667 | −0.738334 | − | 0.674435i | \(-0.764387\pi\) | ||||
−0.738334 | + | 0.674435i | \(0.764387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.6969i | 0.593265i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 72.3962i | − 1.54034i | −0.637836 | − | 0.770172i | \(-0.720170\pi\) | ||||
0.637836 | − | 0.770172i | \(-0.279830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.0000 | 0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 37.4052 | 0.733436 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 70.2929i | 1.32628i | 0.748495 | + | 0.663140i | \(0.230777\pi\) | ||||
−0.748495 | + | 0.663140i | \(0.769223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 162.334i | 2.95153i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 31.5959 | 0.554314 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.6410 | −0.587136 | −0.293568 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293568 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.5959i | 1.04256i | 0.853387 | + | 0.521278i | \(0.174545\pi\) | ||||
−0.853387 | + | 0.521278i | \(0.825455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 8.48528i | − 0.134687i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −51.5959 | −0.793783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.24259 | 0.0483968 | 0.0241984 | − | 0.999707i | \(-0.492297\pi\) | ||||
0.0241984 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 57.7980i | − 0.837652i | ||||||||
\(70\) | 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 | \(-0.521819\pi\) | ||||
−0.0684932 | + | 0.997652i | \(0.521819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 93.8630 | 1.25151 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 51.5959i | − 0.670077i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 35.0552i | − 0.443736i | −0.975077 | − | 0.221868i | \(-0.928785\pi\) | ||||
0.975077 | − | 0.221868i | \(-0.0712155\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −42.2691 | −0.509266 | −0.254633 | − | 0.967038i | \(-0.581955\pi\) | ||||
−0.254633 | + | 0.967038i | \(0.581955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 192.182i | − 2.26096i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 7.78539i | − 0.0894872i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19184 | 0.0583352 | 0.0291676 | − | 0.999575i | \(-0.490714\pi\) | ||||
0.0291676 | + | 0.999575i | \(0.490714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3991 | 0.180210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.90918i | 0.0420342i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 54.7257 | 0.552785 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 50.8786i | − 0.503748i | −0.967760 | − | 0.251874i | \(-0.918953\pi\) | ||||
0.967760 | − | 0.251874i | \(-0.0810469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 148.764i | 1.44431i | 0.691732 | + | 0.722154i | \(0.256848\pi\) | ||||
−0.691732 | + | 0.722154i | \(0.743152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −43.5959 | −0.415199 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 116.380 | 1.08766 | 0.543830 | − | 0.839195i | \(-0.316974\pi\) | ||||
0.543830 | + | 0.839195i | \(0.316974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 44.1816i | − 0.405336i | −0.979248 | − | 0.202668i | \(-0.935039\pi\) | ||||
0.979248 | − | 0.202668i | \(-0.0649612\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 74.8105i | − 0.673968i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 199.576 | 1.76615 | 0.883077 | − | 0.469227i | \(-0.155467\pi\) | ||||
0.883077 | + | 0.469227i | \(0.155467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −296.956 | −2.58223 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3939i | 0.148666i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 61.0825i | 0.513298i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 211.767 | 1.75014 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.76421 | 0.0224733 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 259.778i | − 2.07822i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.276i | 1.44312i | 0.692352 | + | 0.721560i | \(0.256575\pi\) | ||||
−0.692352 | + | 0.721560i | \(0.743425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 109.980 | 0.852555 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 176.891 | 1.35031 | 0.675155 | − | 0.737676i | \(-0.264077\pi\) | ||||
0.675155 | + | 0.737676i | \(0.264077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51.5959i | 0.387939i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 46.2405i | − 0.342522i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 147.980 | 1.08014 | 0.540071 | − | 0.841619i | \(-0.318397\pi\) | ||||
0.540071 | + | 0.841619i | \(0.318397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −114.980 | −0.827193 | −0.413597 | − | 0.910460i | \(-0.635728\pi\) | ||||
−0.413597 | + | 0.910460i | \(0.635728\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125.394i | 0.889318i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 105.766i | 0.739621i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.0000 | −0.275862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −71.0141 | −0.483089 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 229.303i | 1.53895i | 0.638679 | + | 0.769473i | \(0.279481\pi\) | ||||
−0.638679 | + | 0.769473i | \(0.720519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 225.674i | − 1.49453i | −0.664527 | − | 0.747264i | \(-0.731367\pi\) | ||||
0.664527 | − | 0.747264i | \(-0.268633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −64.7878 | −0.423449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0847 | 0.129579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.8082i | 0.234447i | 0.993106 | + | 0.117223i | \(0.0373994\pi\) | ||||
−0.993106 | + | 0.117223i | \(0.962601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 121.751i | − 0.765728i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 94.3837 | 0.586234 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 180.833 | 1.10941 | 0.554703 | − | 0.832048i | \(-0.312832\pi\) | ||||
0.554703 | + | 0.832048i | \(0.312832\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 281.171i | − 1.70407i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | −54.7257 | −0.320034 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 158.111i | − 0.913938i | −0.889483 | − | 0.456969i | \(-0.848935\pi\) | ||||
0.889483 | − | 0.456969i | \(-0.151065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 153.278i | 0.875872i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 60.0000 | 0.338983 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.6979 | 0.255295 | 0.127648 | − | 0.991820i | \(-0.459257\pi\) | ||||
0.127648 | + | 0.991820i | \(0.459257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 263.778i | − 1.45733i | −0.684868 | − | 0.728667i | \(-0.740140\pi\) | ||||
0.684868 | − | 0.728667i | \(-0.259860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 110.151i | − 0.601920i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −384.363 | −2.07764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −393.951 | −2.10669 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.6969i | 0.0777616i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 154.963i | 0.811325i | 0.914023 | + | 0.405663i | \(0.132959\pi\) | ||||
−0.914023 | + | 0.405663i | \(0.867041\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −182.767 | −0.946981 | −0.473491 | − | 0.880799i | \(-0.657006\pi\) | ||||
−0.473491 | + | 0.880799i | \(0.657006\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 89.3668 | 0.458291 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 178.697i | 0.907091i | 0.891233 | + | 0.453546i | \(0.149841\pi\) | ||||
−0.891233 | + | 0.453546i | \(0.850159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 37.9125i | 0.190515i | 0.995453 | + | 0.0952575i | \(0.0303674\pi\) | ||||
−0.995453 | + | 0.0952575i | \(0.969633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.61633 | −0.0279419 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.7135 | 0.0626280 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 14.2020i | − 0.0692782i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 100.109i | 0.483618i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −332.767 | −1.59219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.8986 | −0.0943060 | −0.0471530 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471530 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 118.565i | 0.556645i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 565.056i | − 2.62817i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.38367 | −0.0294178 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.3205 | 0.0790891 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 125.212i | − 0.566571i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 212.703i | − 0.953827i | −0.878950 | − | 0.476914i | \(-0.841755\pi\) | ||||
0.878950 | − | 0.476914i | \(-0.158245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −162.576 | −0.722558 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 104.180 | 0.458942 | 0.229471 | − | 0.973315i | \(-0.426300\pi\) | ||||
0.229471 | + | 0.973315i | \(0.426300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 316.545i | 1.38229i | 0.722715 | + | 0.691146i | \(0.242894\pi\) | ||||
−0.722715 | + | 0.691146i | \(0.757106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 89.3668i | 0.386869i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 120.424 | 0.516843 | 0.258422 | − | 0.966032i | \(-0.416798\pi\) | ||||
0.258422 | + | 0.966032i | \(0.416798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 644.252 | 2.74150 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 60.7173i | 0.256191i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 178.734i | 0.747839i | 0.927461 | + | 0.373919i | \(0.121986\pi\) | ||||
−0.927461 | + | 0.373919i | \(0.878014\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 46.8082 | 0.194225 | 0.0971124 | − | 0.995273i | \(-0.469039\pi\) | ||||
0.0971124 | + | 0.995273i | \(0.469039\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 364.858i | 1.48922i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 105.766i | − 0.428202i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 73.2122 | 0.294025 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −39.9833 | −0.159296 | −0.0796480 | − | 0.996823i | \(-0.525380\pi\) | ||||
−0.0796480 | + | 0.996823i | \(0.525380\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 608.727i | 2.40603i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 332.868i | 1.30537i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 290.000 | 1.12840 | 0.564202 | − | 0.825637i | \(-0.309184\pi\) | ||||
0.564202 | + | 0.825637i | \(0.309184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 122.165 | 0.471679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4847i | 0.0516655i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −8.99252 | −0.0336799 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 100.858i | 0.374937i | 0.982271 | + | 0.187469i | \(0.0600283\pi\) | ||||
−0.982271 | + | 0.187469i | \(0.939972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 222.817i | 0.822201i | 0.911590 | + | 0.411101i | \(0.134856\pi\) | ||||
−0.911590 | + | 0.411101i | \(0.865144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28.4041 | −0.104044 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −988.563 | −3.59477 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 194.202i | − 0.701090i | −0.936546 | − | 0.350545i | \(-0.885996\pi\) | ||||
0.936546 | − | 0.350545i | \(-0.114004\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 6.77091i | − 0.0242685i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202.767 | 0.721592 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 156.549 | 0.553177 | 0.276589 | − | 0.960988i | \(-0.410796\pi\) | ||||
0.276589 | + | 0.960988i | \(0.410796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 281.171i | 0.986566i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.51394i | 0.0157280i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 177.384 | 0.613784 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.4331 | 0.159564 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 116.677i | 0.398213i | 0.979978 | + | 0.199107i | \(0.0638040\pi\) | ||||
−0.979978 | + | 0.199107i | \(0.936196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 308.270i | − 1.04498i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −94.7878 | −0.319151 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −193.476 | −0.647077 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 179.596i | 0.596664i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 88.1243i | 0.290839i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −565.939 | −1.85554 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9850 | 0.0585832 | 0.0292916 | − | 0.999571i | \(-0.490675\pi\) | ||||
0.0292916 | + | 0.999571i | \(0.490675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 257.666i | − 0.833872i | ||||||||
\(310\) | 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 | \(-0.633844\pi\) | ||||
−0.408202 | + | 0.912891i | \(0.633844\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 75.5103 | 0.239715 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 93.4847i | − 0.294904i | −0.989069 | − | 0.147452i | \(-0.952893\pi\) | ||||
0.989069 | − | 0.147452i | \(-0.0471073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 81.9955i | 0.257039i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −201.576 | −0.627961 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 393.951 | 1.21966 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 314.202i | − 0.966776i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76.5248i | 0.234021i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −204.767 | −0.622393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 151.464 | 0.457594 | 0.228797 | − | 0.973474i | \(-0.426521\pi\) | ||||
0.228797 | + | 0.973474i | \(0.426521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 129.576i | 0.389116i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −345.675 | −1.01969 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 41.1714i | − 0.120737i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 254.558i | − 0.742153i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 514.343 | 1.49085 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −333.626 | −0.961458 | −0.480729 | − | 0.876869i | \(-0.659628\pi\) | ||||
−0.480729 | + | 0.876869i | \(0.659628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 553.939i | − 1.58722i | −0.608429 | − | 0.793609i | \(-0.708200\pi\) | ||||
0.608429 | − | 0.793609i | \(-0.291800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 30.1271i | − 0.0858321i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −398.727 | −1.12954 | −0.564768 | − | 0.825249i | \(-0.691035\pi\) | ||||
−0.564768 | + | 0.825249i | \(0.691035\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 609.168 | 1.71597 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 105.798i | − 0.296353i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | −366.792 | −1.01045 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 88.9898i | − 0.243808i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 372.181i | − 1.01412i | −0.861912 | − | 0.507058i | \(-0.830733\pi\) | ||||
0.861912 | − | 0.507058i | \(-0.169267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.78775 | −0.0129749 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 198.818 | 0.535898 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 277.980i | 0.745254i | 0.927981 | + | 0.372627i | \(0.121543\pi\) | ||||
−0.927981 | + | 0.372627i | \(0.878457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 449.948i | 1.19986i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.0612 | −0.0691279 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −320.797 | −0.846430 | −0.423215 | − | 0.906029i | \(-0.639099\pi\) | ||||
−0.423215 | + | 0.906029i | \(0.639099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 317.444i | − 0.833186i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 609.797i | 1.59216i | 0.605191 | + | 0.796080i | \(0.293097\pi\) | ||||
−0.605191 | + | 0.796080i | \(0.706903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 459.151 | 1.19260 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −190.490 | −0.492223 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 126.111i | 0.324193i | 0.986775 | + | 0.162097i | \(0.0518256\pi\) | ||||
−0.986775 | + | 0.162097i | \(0.948174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 720.649i | − 1.84309i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −306.384 | −0.779602 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 311.955 | 0.789760 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.36326i | − 0.0109906i | −0.999985 | − | 0.00549529i | \(-0.998251\pi\) | ||||
0.999985 | − | 0.00549529i | \(-0.00174921\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 89.3668i | − 0.223977i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 691.049 | 1.72331 | 0.861657 | − | 0.507491i | \(-0.169427\pi\) | ||||
0.861657 | + | 0.507491i | \(0.169427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0858 | 0.0324710 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 80.0908i | 0.197755i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 787.902i | 1.93588i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 485.959 | 1.18816 | 0.594082 | − | 0.804404i | \(-0.297515\pi\) | ||||
0.594082 | + | 0.804404i | \(0.297515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −256.308 | −0.623621 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 97.9796i | 0.237239i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 376.152i | − 0.906390i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 199.151 | 0.477580 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 499.531 | 1.19220 | 0.596098 | − | 0.802911i | \(-0.296717\pi\) | ||||
0.596098 | + | 0.802911i | \(0.296717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8796i | 0.0519705i | 0.999662 | + | 0.0259853i | \(0.00827230\pi\) | ||||
−0.999662 | + | 0.0259853i | \(0.991728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 217.189i | − 0.513448i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1170.32 | 2.75370 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 179.876 | 0.421256 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 183.192i | − 0.427021i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 513.631i | − 1.19172i | −0.803089 | − | 0.595859i | \(-0.796812\pi\) | ||||
0.803089 | − | 0.595859i | \(-0.203188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.3837 | −0.0378376 | −0.0189188 | − | 0.999821i | \(-0.506022\pi\) | ||||
−0.0189188 | + | 0.999821i | \(0.506022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 69.2820 | 0.159269 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 608.727i | − 1.39297i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 324.068i | 0.738197i | 0.929390 | + | 0.369098i | \(0.120333\pi\) | ||||
−0.929390 | + | 0.369098i | \(0.879667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 123.000 | 0.278912 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −221.003 | −0.498877 | −0.249439 | − | 0.968391i | \(-0.580246\pi\) | ||||
−0.249439 | + | 0.968391i | \(0.580246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 46.2020i | 0.103825i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 397.165i | − 0.888511i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 690.322 | 1.53747 | 0.768733 | − | 0.639570i | \(-0.220887\pi\) | ||||
0.768733 | + | 0.639570i | \(0.220887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.1126 | −0.0645512 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 390.879i | 0.862867i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 145.935i | 0.320737i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 397.878 | 0.870629 | 0.435315 | − | 0.900278i | \(-0.356637\pi\) | ||||
0.435315 | + | 0.900278i | \(0.356637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 112.216 | 0.244479 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 707.160i | − 1.53397i | −0.641665 | − | 0.766985i | \(-0.721756\pi\) | ||||
0.641665 | − | 0.766985i | \(-0.278244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 869.926i | − 1.87889i | −0.342700 | − | 0.939445i | \(-0.611341\pi\) | ||||
0.342700 | − | 0.939445i | \(-0.388659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −34.7878 | −0.0748124 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 75.4396 | 0.161541 | 0.0807705 | − | 0.996733i | \(-0.474262\pi\) | ||||
0.0807705 | + | 0.996733i | \(0.474262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.17143i | − 0.0195553i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 63.7536i | − 0.135358i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1158.30 | −2.44884 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 988.563 | 2.08118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 210.879i | 0.442093i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 90.5674i | 0.189076i | 0.995521 | + | 0.0945380i | \(0.0301374\pi\) | ||||
−0.995521 | + | 0.0945380i | \(0.969863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −250.424 | −0.520633 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −163.477 | −0.338462 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 238.565i | − 0.491887i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 137.392i | 0.282120i | 0.990001 | + | 0.141060i | \(0.0450510\pi\) | ||||
−0.990001 | + | 0.141060i | \(0.954949\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −313.212 | −0.640516 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −89.5529 | −0.182389 | −0.0911944 | − | 0.995833i | \(-0.529068\pi\) | ||||
−0.0911944 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 97.0714i | − 0.196899i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 487.003i | 0.983845i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −193.616 | −0.389570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −268.286 | −0.537648 | −0.268824 | − | 0.963189i | \(-0.586635\pi\) | ||||
−0.268824 | + | 0.963189i | \(0.586635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 302.747i | − 0.604285i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | −234.491 | −0.462508 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 168.272i | − 0.330594i | −0.986244 | − | 0.165297i | \(-0.947142\pi\) | ||||
0.986244 | − | 0.165297i | \(-0.0528583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2843i | 0.0553508i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 94.7878 | 0.184771 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1323.85 | −2.57057 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1320.64i | − 2.55444i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 273.857i | 0.527662i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 316.788 | 0.608038 | 0.304019 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304019 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −443.591 | −0.848167 | −0.424083 | − | 0.905623i | \(-0.639404\pi\) | ||||
−0.424083 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 265.485i | − 0.505685i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 48.7413i | 0.0924883i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −584.535 | −1.10498 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −103.923 | −0.195712 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.25307i | − 0.0173604i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1035.66i | 1.93581i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −79.1510 | −0.147395 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 747.918 | 1.38760 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 966.443i | − 1.78640i | −0.449659 | − | 0.893200i | \(-0.648454\pi\) | ||||
0.449659 | − | 0.893200i | \(-0.351546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 456.876i | 0.841392i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 393.171 | 0.721415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 578.470 | 1.05753 | 0.528766 | − | 0.848768i | \(-0.322655\pi\) | ||||
0.528766 | + | 0.848768i | \(0.322655\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 190.788i | 0.347519i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 81.9955i | − 0.148812i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −99.1510 | −0.179297 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 665.737 | 1.19953 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 590.293i | 1.05977i | 0.848069 | + | 0.529886i | \(0.177765\pi\) | ||||
−0.848069 | + | 0.529886i | \(0.822235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 368.152i | − 0.658589i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 682.343 | 1.21630 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −468.877 | −0.832818 | −0.416409 | − | 0.909177i | \(-0.636712\pi\) | ||||
−0.416409 | + | 0.909177i | \(0.636712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1776.02i | 3.14340i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 25.4558i | − 0.0448957i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −548.829 | −0.964549 | −0.482275 | − | 0.876020i | \(-0.660189\pi\) | ||||
−0.482275 | + | 0.876020i | \(0.660189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −133.036 | −0.232987 | −0.116494 | − | 0.993191i | \(-0.537165\pi\) | ||||
−0.116494 | + | 0.993191i | \(0.537165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 268.404i | − 0.468419i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 316.562 | 0.546740 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 119.555i | 0.205775i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1282.28i | 2.19944i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −154.788 | −0.264594 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −178.290 | −0.303732 | −0.151866 | − | 0.988401i | \(-0.548528\pi\) | ||||
−0.151866 | + | 0.988401i | \(0.548528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.1714i | 0.0699006i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 309.512i | − 0.523709i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −584.261 | −0.985263 | −0.492632 | − | 0.870238i | \(-0.663965\pi\) | ||||
−0.492632 | + | 0.870238i | \(0.663965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −543.572 | −0.913566 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 65.6663i | − 0.109994i | ||||||||
\(598\) | 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 | \(-0.326899\pi\) | ||||
0.517403 | + | 0.855742i | \(0.326899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.72777 | 0.0161323 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1884.51i | 3.11490i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 36.1404i | − 0.0595393i | −0.999557 | − | 0.0297697i | \(-0.990523\pi\) | ||||
0.999557 | − | 0.0297697i | \(-0.00947738\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.0204 | −0.0361583 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 419.750 | 0.686989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 385.857i | 0.629457i | 0.949182 | + | 0.314728i | \(0.101913\pi\) | ||||
−0.949182 | + | 0.314728i | \(0.898087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.5987i | 0.0399978i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 290.849 | 0.471392 | 0.235696 | − | 0.971827i | \(-0.424263\pi\) | ||||
0.235696 | + | 0.971827i | \(0.424263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −275.658 | −0.445327 | −0.222664 | − | 0.974895i | \(-0.571475\pi\) | ||||
−0.222664 | + | 0.974895i | \(0.571475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 173.394i | − 0.279217i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 14.6847i | − 0.0235710i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 956.959 | 1.53113 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 576.370 | 0.919250 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 932.767i | − 1.48294i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 940.608i | − 1.49066i | −0.666694 | − | 0.745331i | \(-0.732291\pi\) | ||||
0.666694 | − | 0.745331i | \(-0.267709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.4653 | 0.0544476 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1630.97 | −2.56846 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 237.716i | 0.373181i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 205.361i | − 0.321379i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.3633 | −0.0536088 | −0.0268044 | − | 0.999641i | \(-0.508533\pi\) | ||||
−0.0268044 | + | 0.999641i | \(0.508533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −308.340 | −0.479534 | −0.239767 | − | 0.970830i | \(-0.577071\pi\) | ||||
−0.239767 | + | 0.970830i | \(0.577071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 978.706i | 1.51737i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 11.0568 | 0.0169844 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1103.38i | 1.68971i | 0.534993 | + | 0.844857i | \(0.320314\pi\) | ||||
−0.534993 | + | 0.844857i | \(0.679686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1574.15i | 2.40328i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.0000 | −0.0456621 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 815.544 | 1.23755 | 0.618774 | − | 0.785569i | \(-0.287630\pi\) | ||||
0.618774 | + | 0.785569i | \(0.287630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 121.576i | 0.183927i | 0.995762 | + | 0.0919633i | \(0.0293143\pi\) | ||||
−0.995762 | + | 0.0919633i | \(0.970686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 216.874i | 0.327110i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −459.151 | −0.690453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −149.993 | −0.224877 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 368.413i | 0.550692i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 281.589 | 0.417169 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 657.526i | − 0.971234i | −0.874172 | − | 0.485617i | \(-0.838595\pi\) | ||||
0.874172 | − | 0.485617i | \(-0.161405\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 75.8249i | 0.111671i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −180.445 | −0.264970 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 772.318 | 1.13077 | 0.565386 | − | 0.824826i | \(-0.308727\pi\) | ||||
0.565386 | + | 0.824826i | \(0.308727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1316.87i | 1.92243i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 548.272i | − 0.798067i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −407.555 | −0.591517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1269.00 | 1.83647 | 0.918237 | − | 0.396030i | \(-0.129613\pi\) | ||||
0.918237 | + | 0.396030i | \(0.129613\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 154.788i | − 0.223359i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1023.20i | − 1.47224i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.4653 | 0.0494481 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −208.581 | −0.298400 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 535.383i | − 0.763741i | −0.924216 | − | 0.381871i | \(-0.875280\pi\) | ||||
0.924216 | − | 0.381871i | \(-0.124720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 787.902i | − 1.12077i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1115.88 | −1.58281 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −143.906 | −0.203545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 56.8673i | − 0.0802078i | −0.999196 | − | 0.0401039i | \(-0.987231\pi\) | ||||
0.999196 | − | 0.0401039i | \(-0.0127689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 105.166i | − 0.147912i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 75.3143 | 0.105630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −941.208 | −1.31638 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 309.576i | − 0.431765i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 980.922i | − 1.36429i | −0.731219 | − | 0.682143i | \(-0.761048\pi\) | ||||
0.731219 | − | 0.682143i | \(-0.238952\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 420.767 | 0.583589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −81.0741 | −0.112136 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 243.587i | − 0.335982i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 83.1673i | − 0.114398i | −0.998363 | − | 0.0571990i | \(-0.981783\pi\) | ||||
0.998363 | − | 0.0571990i | \(-0.0182169\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1371.27 | 1.87588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 345.476i | − 0.471317i | −0.971836 | − | 0.235659i | \(-0.924275\pi\) | ||||
0.971836 | − | 0.235659i | \(-0.0757247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 631.953i | − 0.859800i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59.1510 | 0.0802592 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1388.23 | −1.87852 | −0.939261 | − | 0.343203i | \(-0.888488\pi\) | ||||
−0.939261 | + | 0.343203i | \(0.888488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 183.192i | 0.247222i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | −126.807 | −0.169755 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 329.171i | − 0.439481i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1225.11i | 1.63130i | 0.578545 | + | 0.815651i | \(0.303621\pi\) | ||||
−0.578545 | + | 0.815651i | \(0.696379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 69.2531 | 0.0919695 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2008.27 | 2.65996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 86.9694i | 0.114887i | 0.998349 | + | 0.0574435i | \(0.0182949\pi\) | ||||
−0.998349 | + | 0.0574435i | \(0.981705\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 1054.35i | − 1.38912i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −764.020 | −1.00397 | −0.501985 | − | 0.864877i | \(-0.667397\pi\) | ||||
−0.501985 | + | 0.864877i | \(0.667397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −124.965 | −0.163781 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 576.545i | − 0.753653i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −502.295 | −0.651485 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1109.24i | 1.43498i | 0.696569 | + | 0.717490i | \(0.254709\pi\) | ||||
−0.696569 | + | 0.717490i | \(0.745291\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 122.309i | 0.157818i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −211.596 | −0.272324 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.1126 | 0.0373718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1248.73i | − 1.59888i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 23.3562i | − 0.0298291i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −327.555 | −0.417268 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1260.98 | −1.60226 | −0.801129 | − | 0.598491i | \(-0.795767\pi\) | ||||
−0.801129 | + | 0.598491i | \(0.795767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 432.000i | 0.547529i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 564.485i | − 0.713634i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −368.727 | −0.464977 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1083.46 | 1.36284 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 386.779i | 0.485293i | 0.970115 | + | 0.242647i | \(0.0780155\pi\) | ||||
−0.970115 | + | 0.242647i | \(0.921984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1563.46i | 1.95677i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5755 | 0.0194451 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −182.419 | −0.227172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 839.918i | 1.04338i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 174.691i | − 0.216470i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1139.98 | 1.40912 | 0.704561 | − | 0.709643i | \(-0.251144\pi\) | ||||
0.704561 | + | 0.709643i | \(0.251144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −959.450 | −1.18305 | −0.591523 | − | 0.806288i | \(-0.701473\pi\) | ||||
−0.591523 | + | 0.806288i | \(0.701473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 385.930i | − 0.474698i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1609.23i | 1.97452i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1158.30 | 1.41775 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 49.1973 | 0.0600700 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 918.674i | − 1.11897i | −0.828840 | − | 0.559485i | \(-0.810999\pi\) | ||||
0.828840 | − | 0.559485i | \(-0.189001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 678.107i | − 0.823945i | −0.911196 | − | 0.411972i | \(-0.864840\pi\) | ||||
0.911196 | − | 0.411972i | \(-0.135160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1712.24 | 2.07544 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1237.58 | 1.49647 | 0.748234 | − | 0.663434i | \(-0.230902\pi\) | ||||
0.748234 | + | 0.663434i | \(0.230902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 778.120i | 0.938625i | 0.883032 | + | 0.469313i | \(0.155498\pi\) | ||||
−0.883032 | + | 0.469313i | \(0.844502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 336.368i | 0.404775i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −885.433 | −1.06294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1555.46 | −1.86283 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.7276i | 0.0140114i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −351.203 | −0.416611 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1204.78i | 1.42577i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 598.968i | − 0.707165i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −271.151 | −0.319377 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1441.30 | −1.69365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1026.38i | 1.20326i | 0.798774 | + | 0.601632i | \(0.205482\pi\) | ||||
−0.798774 | + | 0.601632i | \(0.794518\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 487.003i | − 0.569594i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −296.061 | −0.345462 | −0.172731 | − | 0.984969i | \(-0.555259\pi\) | ||||
−0.172731 | + | 0.984969i | \(0.555259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 167.118 | 0.194550 | 0.0972748 | − | 0.995258i | \(-0.468987\pi\) | ||||
0.0972748 | + | 0.995258i | \(0.468987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 7.81837i | − 0.00908057i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.0553i | 0.0116516i | 0.999983 | + | 0.00582580i | \(0.00185442\pi\) | ||||
−0.999983 | + | 0.00582580i | \(0.998146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1407.03 | 1.62662 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −307.238 | −0.354369 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 639.473i | − 0.735873i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.8004i | 0.0215848i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −80.4245 | −0.0921243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −734.762 | −0.839728 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1154.58i | − 1.31651i | −0.752793 | − | 0.658257i | \(-0.771294\pi\) | ||||
0.752793 | − | 0.658257i | \(-0.228706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 202.090i | − 0.229909i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 160.220 | 0.181862 | 0.0909310 | − | 0.995857i | \(-0.471016\pi\) | ||||
0.0909310 | + | 0.995857i | \(0.471016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1311.46 | 1.48523 | 0.742616 | − | 0.669718i | \(-0.233585\pi\) | ||||
0.742616 | + | 0.669718i | \(0.233585\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 533.939i | 0.603321i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 164.177 | 0.184262 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1320.64i | 1.47889i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 406.664i | 0.454374i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 335.110 | 0.373590 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1448 | 0.0112846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1518.04i | − 1.68484i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 311.069i | − 0.344484i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2347.35 | 2.59376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1161.70 | 1.28081 | 0.640406 | − | 0.768036i | \(-0.278766\pi\) | ||||
0.640406 | + | 0.768036i | \(0.278766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 152.636i | − 0.167916i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1382.33i | 1.51737i | 0.651456 | + | 0.758687i | \(0.274159\pi\) | ||||
−0.651456 | + | 0.758687i | \(0.725841\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −771.069 | −0.844545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 980.235 | 1.07129 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 500.322i | − 0.545608i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1206.60i | 1.31294i | 0.754350 | + | 0.656472i | \(0.227952\pi\) | ||||
−0.754350 | + | 0.656472i | \(0.772048\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.1510 | −0.0338230 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 396.892 | 0.430002 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2340.64i | − 2.53043i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 446.291i | 0.481436i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1159.90 | 1.24854 | 0.624272 | − | 0.781207i | \(-0.285396\pi\) | ||||
0.624272 | + | 0.781207i | \(0.285396\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −747.918 | −0.803349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 502.665i | − 0.538762i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 3505.76i | − 3.74948i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 173.837 | 0.185525 | 0.0927624 | − | 0.995688i | \(-0.470430\pi\) | ||||
0.0927624 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 442.599 | 0.471352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 603.968i | − 0.641837i | −0.947107 | − | 0.320918i | \(-0.896008\pi\) | ||||
0.947107 | − | 0.320918i | \(-0.103992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 53.2553i | − 0.0564743i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −130.788 | −0.138400 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 951.077 | 1.00431 | 0.502153 | − | 0.864779i | \(-0.332542\pi\) | ||||
0.502153 | + | 0.864779i | \(0.332542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 57.9796i | − 0.0610955i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 161.920i | 0.170263i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1407.98 | −1.47742 | −0.738709 | − | 0.674024i | \(-0.764564\pi\) | ||||
−0.738709 | + | 0.674024i | \(0.764564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1379.01 | −1.44399 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 142.020i | − 0.148402i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 418.549i | − 0.436444i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 955.906 | 0.994699 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 349.139 | 0.362554 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1626.44i | − 1.68543i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 467.718i | 0.483679i | 0.970316 | + | 0.241840i | \(0.0777508\pi\) | ||||
−0.970316 | + | 0.241840i | \(0.922249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −682.343 | −0.704172 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1115.70 | −1.14902 | −0.574510 | − | 0.818498i | \(-0.694807\pi\) | ||||
−0.574510 | + | 0.818498i | \(0.694807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 325.212i | 0.334237i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 544.214i | 0.558168i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 494.363 | 0.506001 | 0.253001 | − | 0.967466i | \(-0.418583\pi\) | ||||
0.253001 | + | 0.967466i | \(0.418583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 94.7090 | 0.0967406 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 132.545i | − 0.135112i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 354.667 | 0.359339 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2118.87i | − 2.14243i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1895.81i | 1.91303i | 0.291681 | + | 0.956516i | \(0.405785\pi\) | ||||
−0.291681 | + | 0.956516i | \(0.594215\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −262.343 | −0.264192 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −337.382 | −0.339078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1317.98i | 1.32195i | 0.750410 | + | 0.660973i | \(0.229856\pi\) | ||||
−0.750410 | + | 0.660973i | \(0.770144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 224.431i | − 0.224656i |
(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 | 384.3.b.c.319.4 | yes | 8 | |
3.2 | odd | 2 | 1152.3.b.j.703.1 | 8 | |||
4.3 | odd | 2 | inner | 384.3.b.c.319.8 | yes | 8 | |
8.3 | odd | 2 | inner | 384.3.b.c.319.1 | ✓ | 8 | |
8.5 | even | 2 | inner | 384.3.b.c.319.5 | yes | 8 | |
12.11 | even | 2 | 1152.3.b.j.703.2 | 8 | |||
16.3 | odd | 4 | 768.3.g.g.511.4 | 4 | |||
16.5 | even | 4 | 768.3.g.c.511.3 | 4 | |||
16.11 | odd | 4 | 768.3.g.c.511.1 | 4 | |||
16.13 | even | 4 | 768.3.g.g.511.2 | 4 | |||
24.5 | odd | 2 | 1152.3.b.j.703.7 | 8 | |||
24.11 | even | 2 | 1152.3.b.j.703.8 | 8 | |||
48.5 | odd | 4 | 2304.3.g.x.1279.4 | 4 | |||
48.11 | even | 4 | 2304.3.g.x.1279.3 | 4 | |||
48.29 | odd | 4 | 2304.3.g.o.1279.2 | 4 | |||
48.35 | even | 4 | 2304.3.g.o.1279.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.b.c.319.1 | ✓ | 8 | 8.3 | odd | 2 | inner | |
384.3.b.c.319.4 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.b.c.319.5 | yes | 8 | 8.5 | even | 2 | inner | |
384.3.b.c.319.8 | yes | 8 | 4.3 | odd | 2 | inner | |
768.3.g.c.511.1 | 4 | 16.11 | odd | 4 | |||
768.3.g.c.511.3 | 4 | 16.5 | even | 4 | |||
768.3.g.g.511.2 | 4 | 16.13 | even | 4 | |||
768.3.g.g.511.4 | 4 | 16.3 | odd | 4 | |||
1152.3.b.j.703.1 | 8 | 3.2 | odd | 2 | |||
1152.3.b.j.703.2 | 8 | 12.11 | even | 2 | |||
1152.3.b.j.703.7 | 8 | 24.5 | odd | 2 | |||
1152.3.b.j.703.8 | 8 | 24.11 | even | 2 | |||
2304.3.g.o.1279.1 | 4 | 48.35 | even | 4 | |||
2304.3.g.o.1279.2 | 4 | 48.29 | odd | 4 | |||
2304.3.g.x.1279.3 | 4 | 48.11 | even | 4 | |||
2304.3.g.x.1279.4 | 4 | 48.5 | odd | 4 |