Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (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: | \(48.2935231425\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.a.2591.5 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − 1.19980i | − 0.536567i | −0.963340 | − | 0.268284i | \(-0.913544\pi\) | ||||
0.963340 | − | 0.268284i | \(-0.0864564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62863 | 0.491049 | 0.245525 | − | 0.969390i | \(-0.421040\pi\) | ||||
0.245525 | + | 0.969390i | \(0.421040\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.09638 | −0.581430 | −0.290715 | − | 0.956810i | \(-0.593893\pi\) | ||||
−0.290715 | + | 0.956810i | \(0.593893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.585786i | 0.142074i | 0.997474 | + | 0.0710370i | \(0.0226309\pi\) | ||||
−0.997474 | + | 0.0710370i | \(0.977369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.89898i | 1.35332i | 0.736296 | + | 0.676659i | \(0.236573\pi\) | ||||
−0.736296 | + | 0.676659i | \(0.763427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.09273 | −1.47894 | −0.739468 | − | 0.673192i | \(-0.764923\pi\) | ||||
−0.739468 | + | 0.673192i | \(0.764923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.56048 | 0.712096 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.08516i | − 1.31568i | −0.753157 | − | 0.657841i | \(-0.771470\pi\) | ||||
0.753157 | − | 0.657841i | \(-0.228530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.72741i | − 1.20828i | −0.796879 | − | 0.604139i | \(-0.793517\pi\) | ||||
0.796879 | − | 0.604139i | \(-0.206483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.19980 | 0.202803 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.17157 | 0.357004 | 0.178502 | − | 0.983940i | \(-0.442875\pi\) | ||||
0.178502 | + | 0.983940i | \(0.442875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.164525i | − 0.0256944i | −0.999917 | − | 0.0128472i | \(-0.995910\pi\) | ||||
0.999917 | − | 0.0128472i | \(-0.00408951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.75323i | − 0.877359i | −0.898643 | − | 0.438680i | \(-0.855446\pi\) | ||||
0.898643 | − | 0.438680i | \(-0.144554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.41421 | 0.498014 | 0.249007 | − | 0.968502i | \(-0.419896\pi\) | ||||
0.249007 | + | 0.968502i | \(0.419896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.29858i | − 0.453095i | −0.974000 | − | 0.226547i | \(-0.927256\pi\) | ||||
0.974000 | − | 0.226547i | \(-0.0727438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.95403i | − 0.263481i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.08641 | −0.271627 | −0.135814 | − | 0.990734i | \(-0.543365\pi\) | ||||
−0.135814 | + | 0.990734i | \(0.543365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.51523i | 0.311976i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4887i | 1.52574i | 0.646555 | + | 0.762868i | \(0.276209\pi\) | ||||
−0.646555 | + | 0.762868i | \(0.723791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2497 | 1.33509 | 0.667546 | − | 0.744568i | \(-0.267345\pi\) | ||||
0.667546 | + | 0.744568i | \(0.267345\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97418 | 0.465142 | 0.232571 | − | 0.972579i | \(-0.425286\pi\) | ||||
0.232571 | + | 0.972579i | \(0.425286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.62863i | 0.185599i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.702827i | 0.0790742i | 0.999218 | + | 0.0395371i | \(0.0125883\pi\) | ||||
−0.999218 | + | 0.0395371i | \(0.987412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.8831 | 1.85316 | 0.926582 | − | 0.376093i | \(-0.122733\pi\) | ||||
0.926582 | + | 0.376093i | \(0.122733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.702827 | 0.0762323 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 6.33485i | − 0.671493i | −0.941952 | − | 0.335747i | \(-0.891011\pi\) | ||||
0.941952 | − | 0.335747i | \(-0.108989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.09638i | − 0.219760i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.07760 | 0.726146 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.58506 | −0.668611 | −0.334306 | − | 0.942465i | \(-0.608502\pi\) | ||||
−0.334306 | + | 0.942465i | \(0.608502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.34366i | 0.929729i | 0.885382 | + | 0.464865i | \(0.153897\pi\) | ||||
−0.885382 | + | 0.464865i | \(0.846103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.586302i | 0.0577700i | 0.999583 | + | 0.0288850i | \(0.00919567\pi\) | ||||
−0.999583 | + | 0.0288850i | \(0.990804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.14162 | 0.303712 | 0.151856 | − | 0.988403i | \(-0.451475\pi\) | ||||
0.151856 | + | 0.988403i | \(0.451475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6522 | 1.11608 | 0.558040 | − | 0.829814i | \(-0.311554\pi\) | ||||
0.558040 | + | 0.829814i | \(0.311554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 19.5546i | − 1.83954i | −0.392457 | − | 0.919771i | \(-0.628375\pi\) | ||||
0.392457 | − | 0.919771i | \(-0.371625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.50986i | 0.793549i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.585786 | −0.0536990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.34758 | −0.758871 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10.2709i | − 0.918654i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.16693i | 0.369755i | 0.982762 | + | 0.184878i | \(0.0591889\pi\) | ||||
−0.982762 | + | 0.184878i | \(0.940811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6410 | 1.19182 | 0.595910 | − | 0.803051i | \(-0.296792\pi\) | ||||
0.595910 | + | 0.803051i | \(0.296792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.89898 | −0.511506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 8.15696i | − 0.696896i | −0.937328 | − | 0.348448i | \(-0.886709\pi\) | ||||
0.937328 | − | 0.348448i | \(-0.113291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.46410i | 0.802735i | 0.915917 | + | 0.401367i | \(0.131465\pi\) | ||||
−0.915917 | + | 0.401367i | \(0.868535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41421 | −0.285511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.50079 | −0.705952 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20.6848i | − 1.69457i | −0.531140 | − | 0.847284i | \(-0.678236\pi\) | ||||
0.531140 | − | 0.847284i | \(-0.321764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.07155 | −0.648322 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.246769 | 0.0196943 | 0.00984717 | − | 0.999952i | \(-0.496865\pi\) | ||||
0.00984717 | + | 0.999952i | \(0.496865\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.09273i | − 0.558985i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.89434i | − 0.618332i | −0.951008 | − | 0.309166i | \(-0.899950\pi\) | ||||
0.951008 | − | 0.309166i | \(-0.100050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.74150 | 0.134762 | 0.0673808 | − | 0.997727i | \(-0.478536\pi\) | ||||
0.0673808 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.60521 | −0.661939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.2709i | 0.780880i | 0.920628 | + | 0.390440i | \(0.127677\pi\) | ||||
−0.920628 | + | 0.390440i | \(0.872323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.56048i | 0.269147i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.81257 | 0.210221 | 0.105111 | − | 0.994461i | \(-0.466480\pi\) | ||||
0.105111 | + | 0.994461i | \(0.466480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.14110 | −0.605124 | −0.302562 | − | 0.953130i | \(-0.597842\pi\) | ||||
−0.302562 | + | 0.953130i | \(0.597842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.60545i | − 0.191557i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.954027i | 0.0697654i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0482 | 1.16120 | 0.580602 | − | 0.814187i | \(-0.302817\pi\) | ||||
0.580602 | + | 0.814187i | \(0.302817\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.87904 | −0.207238 | −0.103619 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103619 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8.09778i | − 0.576943i | −0.957488 | − | 0.288472i | \(-0.906853\pi\) | ||||
0.957488 | − | 0.288472i | \(-0.0931471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 21.9024i | − 1.55262i | −0.630352 | − | 0.776309i | \(-0.717090\pi\) | ||||
0.630352 | − | 0.776309i | \(-0.282910\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.08516 | 0.497281 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.197397 | −0.0137868 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.60723i | 0.664546i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.80725i | 0.262102i | 0.991376 | + | 0.131051i | \(0.0418351\pi\) | ||||
−0.991376 | + | 0.131051i | \(0.958165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.90273 | −0.470762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.72741 | 0.456686 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.22803i | − 0.0826062i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 27.4088i | − 1.83543i | −0.397237 | − | 0.917716i | \(-0.630031\pi\) | ||||
0.397237 | − | 0.917716i | \(-0.369969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.79920 | 0.318534 | 0.159267 | − | 0.987236i | \(-0.449087\pi\) | ||||
0.159267 | + | 0.987236i | \(0.449087\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9907 | 0.792369 | 0.396184 | − | 0.918171i | \(-0.370334\pi\) | ||||
0.396184 | + | 0.918171i | \(0.370334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 0.898979i | − 0.0588941i | −0.999566 | − | 0.0294471i | \(-0.990625\pi\) | ||||
0.999566 | − | 0.0294471i | \(-0.00937464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4.09638i | − 0.267218i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6702 | −1.01362 | −0.506811 | − | 0.862057i | \(-0.669176\pi\) | ||||
−0.506811 | + | 0.862057i | \(0.669176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1443 | 1.74852 | 0.874259 | − | 0.485460i | \(-0.161348\pi\) | ||||
0.874259 | + | 0.485460i | \(0.161348\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.19980i | 0.0766525i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 12.3665i | − 0.786860i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8977 | 1.38217 | 0.691086 | − | 0.722772i | \(-0.257132\pi\) | ||||
0.691086 | + | 0.722772i | \(0.257132\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5514 | −0.726230 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 2.89245i | − 0.180426i | −0.995923 | − | 0.0902129i | \(-0.971245\pi\) | ||||
0.995923 | − | 0.0902129i | \(-0.0287548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17157i | 0.134935i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.5901 | 1.57795 | 0.788977 | − | 0.614423i | \(-0.210611\pi\) | ||||
0.788977 | + | 0.614423i | \(0.210611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.95764 | −0.243116 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 25.6692i | − 1.56508i | −0.622600 | − | 0.782540i | \(-0.713924\pi\) | ||||
0.622600 | − | 0.782540i | \(-0.286076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 6.05845i | − 0.368024i | −0.982924 | − | 0.184012i | \(-0.941091\pi\) | ||||
0.982924 | − | 0.184012i | \(-0.0589086\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.79869 | 0.349674 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.8166 | −1.91168 | −0.955839 | − | 0.293892i | \(-0.905049\pi\) | ||||
−0.955839 | + | 0.293892i | \(0.905049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.80295i | 0.167210i | 0.996499 | + | 0.0836051i | \(0.0266434\pi\) | ||||
−0.996499 | + | 0.0836051i | \(0.973357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6367i | 0.632287i | 0.948711 | + | 0.316143i | \(0.102388\pi\) | ||||
−0.948711 | + | 0.316143i | \(0.897612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.164525 | 0.00971158 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6569 | 0.979815 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.702148i | 0.0410199i | 0.999790 | + | 0.0205100i | \(0.00652898\pi\) | ||||
−0.999790 | + | 0.0205100i | \(0.993471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.50327i | 0.145746i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8690 | 0.859898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.75323 | 0.331611 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 5.91286i | − 0.338570i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4122i | 1.22206i | 0.791607 | + | 0.611031i | \(0.209245\pi\) | ||||
−0.791607 | + | 0.611031i | \(0.790755\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3424 | 0.813284 | 0.406642 | − | 0.913588i | \(-0.366700\pi\) | ||||
0.406642 | + | 0.913588i | \(0.366700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.8238 | 1.00746 | 0.503730 | − | 0.863861i | \(-0.331961\pi\) | ||||
0.503730 | + | 0.863861i | \(0.331961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.7113i | 1.50026i | 0.661291 | + | 0.750129i | \(0.270009\pi\) | ||||
−0.661291 | + | 0.750129i | \(0.729991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 11.5391i | − 0.646065i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.45554 | −0.192272 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.46410 | −0.414034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.41421i | 0.188232i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.01086i | 0.165492i | 0.996571 | + | 0.0827459i | \(0.0263690\pi\) | ||||
−0.996571 | + | 0.0827459i | \(0.973631\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.9839 | 0.818660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1210 | −0.769217 | −0.384609 | − | 0.923080i | \(-0.625664\pi\) | ||||
−0.384609 | + | 0.923080i | \(0.625664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 10.9564i | − 0.593324i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.5835 | −0.621837 | −0.310919 | − | 0.950437i | \(-0.600637\pi\) | ||||
−0.310919 | + | 0.950437i | \(0.600637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7887 | 1.38044 | 0.690218 | − | 0.723602i | \(-0.257515\pi\) | ||||
0.690218 | + | 0.723602i | \(0.257515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 28.2326i | − 1.50267i | −0.659922 | − | 0.751335i | \(-0.729410\pi\) | ||||
0.659922 | − | 0.751335i | \(-0.270590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 13.4974i | − 0.716367i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.4976 | 0.870711 | 0.435355 | − | 0.900259i | \(-0.356623\pi\) | ||||
0.435355 | + | 0.900259i | \(0.356623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7980 | −0.831472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.76822i | − 0.249580i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.06818i | 0.368956i | 0.982837 | + | 0.184478i | \(0.0590595\pi\) | ||||
−0.982837 | + | 0.184478i | \(0.940941\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.29858 | 0.171254 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.88369 | 0.149312 | 0.0746559 | − | 0.997209i | \(-0.476214\pi\) | ||||
0.0746559 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.8532i | 0.764977i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.4076i | 1.51057i | 0.655398 | + | 0.755283i | \(0.272501\pi\) | ||||
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8977 | 0.710141 | 0.355071 | − | 0.934840i | \(-0.384457\pi\) | ||||
0.355071 | + | 0.934840i | \(0.384457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.95403 | 0.0995864 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 22.4263i | − 1.13706i | −0.822662 | − | 0.568530i | \(-0.807512\pi\) | ||||
0.822662 | − | 0.568530i | \(-0.192488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.15482i | − 0.210118i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.843253 | 0.0424286 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.3028 | −0.717839 | −0.358920 | − | 0.933368i | \(-0.616855\pi\) | ||||
−0.358920 | + | 0.933368i | \(0.616855\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 26.5964i | − 1.32816i | −0.747660 | − | 0.664081i | \(-0.768823\pi\) | ||||
0.747660 | − | 0.664081i | \(-0.231177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.1032i | 0.702529i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.53668 | 0.175307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2093 | −0.801498 | −0.400749 | − | 0.916188i | \(-0.631250\pi\) | ||||
−0.400749 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.08641i | − 0.102665i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 20.2564i | − 0.994347i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.5437 | −1.19904 | −0.599520 | − | 0.800360i | \(-0.704642\pi\) | ||||
−0.599520 | + | 0.800360i | \(0.704642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.373614 | −0.0182088 | −0.00910441 | − | 0.999959i | \(-0.502898\pi\) | ||||
−0.00910441 | + | 0.999959i | \(0.502898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.08568i | 0.101170i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.92820i | 0.238492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7801 | −0.856435 | −0.428217 | − | 0.903676i | \(-0.640858\pi\) | ||||
−0.428217 | + | 0.903676i | \(0.640858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.7613 | 0.517154 | 0.258577 | − | 0.965991i | \(-0.416746\pi\) | ||||
0.258577 | + | 0.965991i | \(0.416746\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 41.8399i | − 2.00147i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 18.5758i | − 0.886573i | −0.896380 | − | 0.443287i | \(-0.853812\pi\) | ||||
0.896380 | − | 0.443287i | \(-0.146188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.3699 | 1.44292 | 0.721459 | − | 0.692457i | \(-0.243472\pi\) | ||||
0.721459 | + | 0.692457i | \(0.243472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.60056 | −0.360301 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 31.4382i | − 1.48366i | −0.670587 | − | 0.741831i | \(-0.733958\pi\) | ||||
0.670587 | − | 0.741831i | \(-0.266042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 0.267949i | − 0.0126172i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.51523 | −0.117916 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.3629 | −1.42032 | −0.710158 | − | 0.704043i | \(-0.751376\pi\) | ||||
−0.710158 | + | 0.704043i | \(0.751376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.28745i | 0.106537i | 0.998580 | + | 0.0532687i | \(0.0169640\pi\) | ||||
−0.998580 | + | 0.0532687i | \(0.983036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.92140i | − 0.228717i | −0.993440 | − | 0.114359i | \(-0.963519\pi\) | ||||
0.993440 | − | 0.114359i | \(-0.0364813\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1860 | −0.795272 | −0.397636 | − | 0.917543i | \(-0.630169\pi\) | ||||
−0.397636 | + | 0.917543i | \(0.630169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4887 | −0.576674 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.36986i | − 0.430827i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.0032i | 0.963692i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.585057 | 0.0267320 | 0.0133660 | − | 0.999911i | \(-0.495745\pi\) | ||||
0.0133660 | + | 0.999911i | \(0.495745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.55243 | −0.207573 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.90076i | 0.358755i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 15.7318i | − 0.712878i | −0.934319 | − | 0.356439i | \(-0.883991\pi\) | ||||
0.934319 | − | 0.356439i | \(-0.116009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.7267 | −1.25129 | −0.625645 | − | 0.780108i | \(-0.715164\pi\) | ||||
−0.625645 | + | 0.780108i | \(0.715164\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.15039 | 0.186924 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.2497i | 0.504618i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.41688i | 0.0634285i | 0.999497 | + | 0.0317142i | \(0.0100966\pi\) | ||||
−0.999497 | + | 0.0317142i | \(0.989903\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.69870 | 0.209505 | 0.104752 | − | 0.994498i | \(-0.466595\pi\) | ||||
0.104752 | + | 0.994498i | \(0.466595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2105 | 0.498862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.82645i | 0.346901i | 0.984843 | + | 0.173451i | \(0.0554917\pi\) | ||||
−0.984843 | + | 0.173451i | \(0.944508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.97418i | 0.175807i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.703446 | 0.0309975 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.56048 | 0.244550 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 4.83496i | − 0.211823i | −0.994376 | − | 0.105912i | \(-0.966224\pi\) | ||||
0.994376 | − | 0.105912i | \(-0.0337761\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.46750i | 0.282804i | 0.989952 | + | 0.141402i | \(0.0451610\pi\) | ||||
−0.989952 | + | 0.141402i | \(0.954839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.94082 | 0.171665 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.3068 | 1.18725 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.344906i | 0.0149395i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 3.76932i | − 0.162962i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.62863 | −0.0701499 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0864 | 0.863583 | 0.431791 | − | 0.901973i | \(-0.357882\pi\) | ||||
0.431791 | + | 0.901973i | \(0.357882\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 13.9803i | − 0.598852i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2689i | 0.823877i | 0.911212 | + | 0.411938i | \(0.135148\pi\) | ||||
−0.911212 | + | 0.411938i | \(0.864852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.7952 | 1.78054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.702827 | −0.0298872 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.90346i | 0.123024i | 0.998106 | + | 0.0615118i | \(0.0195922\pi\) | ||||
−0.998106 | + | 0.0615118i | \(0.980408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0609i | 0.510123i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.18743 | 0.387204 | 0.193602 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193602 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.4616 | −0.987037 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 2.31694i | − 0.0971314i | −0.998820 | − | 0.0485657i | \(-0.984535\pi\) | ||||
0.998820 | − | 0.0485657i | \(-0.0154650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6770i | 0.781608i | 0.920474 | + | 0.390804i | \(0.127803\pi\) | ||||
−0.920474 | + | 0.390804i | \(0.872197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.2535 | −1.05314 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2011 | 1.63196 | 0.815982 | − | 0.578077i | \(-0.196197\pi\) | ||||
0.815982 | + | 0.578077i | \(0.196197\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8831i | 0.700430i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 5.37216i | − 0.222492i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.9839 | 0.742275 | 0.371138 | − | 0.928578i | \(-0.378968\pi\) | ||||
0.371138 | + | 0.928578i | \(0.378968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.6848 | 1.63519 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.6480i | 1.25856i | 0.777177 | + | 0.629282i | \(0.216651\pi\) | ||||
−0.777177 | + | 0.629282i | \(0.783349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.702827i | 0.0288131i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.8899 | −0.976116 | −0.488058 | − | 0.872811i | \(-0.662295\pi\) | ||||
−0.488058 | + | 0.872811i | \(0.662295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2161 | −0.498305 | −0.249152 | − | 0.968464i | \(-0.580152\pi\) | ||||
−0.249152 | + | 0.968464i | \(0.580152\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0154i | 0.407185i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.921404i | 0.0373986i | 0.999825 | + | 0.0186993i | \(0.00595252\pi\) | ||||
−0.999825 | + | 0.0186993i | \(0.994047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.15748 | −0.289561 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.7716 | −0.717788 | −0.358894 | − | 0.933378i | \(-0.616846\pi\) | ||||
−0.358894 | + | 0.933378i | \(0.616846\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 18.5702i | − 0.747609i | −0.927507 | − | 0.373805i | \(-0.878053\pi\) | ||||
0.927507 | − | 0.373805i | \(-0.121947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 28.9780i | − 1.16473i | −0.812929 | − | 0.582363i | \(-0.802128\pi\) | ||||
0.812929 | − | 0.582363i | \(-0.197872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.33485 | 0.253801 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.47939 | 0.219176 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.27208i | 0.0507211i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 32.3996i | − 1.28981i | −0.764265 | − | 0.644903i | \(-0.776898\pi\) | ||||
0.764265 | − | 0.644903i | \(-0.223102\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.99948 | 0.198398 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.09638 | 0.0830615 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.1701i | 1.62612i | 0.582179 | + | 0.813061i | \(0.302200\pi\) | ||||
−0.582179 | + | 0.813061i | \(0.697800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.52433i | 0.178422i | 0.996013 | + | 0.0892112i | \(0.0284346\pi\) | ||||
−0.996013 | + | 0.0892112i | \(0.971565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.4377 | −0.960746 | −0.480373 | − | 0.877064i | \(-0.659499\pi\) | ||||
−0.480373 | + | 0.877064i | \(0.659499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.39798 | −0.133382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.82564i | 0.110576i | 0.998470 | + | 0.0552878i | \(0.0176076\pi\) | ||||
−0.998470 | + | 0.0552878i | \(0.982392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 16.3665i | − 0.639491i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.8305 | 1.35680 | 0.678401 | − | 0.734692i | \(-0.262673\pi\) | ||||
0.678401 | + | 0.734692i | \(0.262673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.6230 | 1.26889 | 0.634444 | − | 0.772969i | \(-0.281229\pi\) | ||||
0.634444 | + | 0.772969i | \(0.281229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.07760i | 0.274458i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.2531i | 1.94581i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.02620 | 0.309848 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.6947i | 0.526330i | 0.964751 | + | 0.263165i | \(0.0847664\pi\) | ||||
−0.964751 | + | 0.263165i | \(0.915234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 6.58506i | − 0.252711i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.7975 | −1.21670 | −0.608349 | − | 0.793670i | \(-0.708168\pi\) | ||||
−0.608349 | + | 0.793670i | \(0.708168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.78673 | −0.373932 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.91507i | 0.263443i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.8496i | 1.13553i | 0.823190 | + | 0.567766i | \(0.192192\pi\) | ||||
−0.823190 | + | 0.567766i | \(0.807808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.3550 | 0.430721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0963763 | 0.00365051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 29.0711i | − 1.09800i | −0.835823 | − | 0.549000i | \(-0.815009\pi\) | ||||
0.835823 | − | 0.549000i | \(-0.184991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.8101i | 0.483141i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.34366 | −0.351405 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.4368 | 0.391963 | 0.195981 | − | 0.980608i | \(-0.437211\pi\) | ||||
0.195981 | + | 0.980608i | \(0.437211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 47.7157i | 1.78697i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.09638i | 0.153196i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.2268 | 1.61209 | 0.806044 | − | 0.591856i | \(-0.201605\pi\) | ||||
0.806044 | + | 0.591856i | \(0.201605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.586302 | −0.0218350 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 25.2266i | − 0.936891i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.31122i | 0.196982i | 0.995138 | + | 0.0984911i | \(0.0314016\pi\) | ||||
−0.995138 | + | 0.0984911i | \(0.968598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.37016 | 0.124650 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1057 | 0.594876 | 0.297438 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297438 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.3394i | 0.749211i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8673i | 0.620472i | 0.950660 | + | 0.310236i | \(0.100408\pi\) | ||||
−0.950660 | + | 0.310236i | \(0.899592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.2019 | −1.65830 | −0.829148 | − | 0.559029i | \(-0.811174\pi\) | ||||
−0.829148 | + | 0.559029i | \(0.811174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.8177 | −0.909249 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.14162i | 0.114792i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 0.479065i | − 0.0174813i | −0.999962 | − | 0.00874067i | \(-0.997218\pi\) | ||||
0.999962 | − | 0.00874067i | \(-0.00278228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.71530 | −0.135035 | −0.0675175 | − | 0.997718i | \(-0.521508\pi\) | ||||
−0.0675175 | + | 0.997718i | \(0.521508\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 22.2164i | − 0.805345i | −0.915344 | − | 0.402673i | \(-0.868081\pi\) | ||||
0.915344 | − | 0.402673i | \(-0.131919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6522i | 0.421838i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.37390 | 0.157932 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.1576 | −1.44812 | −0.724061 | − | 0.689736i | \(-0.757727\pi\) | ||||
−0.724061 | + | 0.689736i | \(0.757727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.25750i | 0.153132i | 0.997065 | + | 0.0765658i | \(0.0243955\pi\) | ||||
−0.997065 | + | 0.0765658i | \(0.975604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 23.9528i | − 0.860409i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.970528 | 0.0347728 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.3215 | 0.655596 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 0.296074i | − 0.0105673i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.70850i | − 0.203486i | −0.994811 | − | 0.101743i | \(-0.967558\pi\) | ||||
0.994811 | − | 0.101743i | \(-0.0324420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5546 | 0.695281 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3314 | −0.366878 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02499i | 0.0363071i | 0.999835 | + | 0.0181535i | \(0.00577877\pi\) | ||||
−0.999835 | + | 0.0181535i | \(0.994221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000i | 0.0707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.47245 | 0.228408 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.50986 | −0.299933 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 15.4989i | − 0.544911i | −0.962168 | − | 0.272455i | \(-0.912164\pi\) | ||||
0.962168 | − | 0.272455i | \(-0.0878358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 32.4913i | − 1.14092i | −0.821324 | − | 0.570462i | \(-0.806764\pi\) | ||||
0.821324 | − | 0.570462i | \(-0.193236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.47163 | −0.331777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.9382 | 1.18735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6559i | 1.41890i | 0.704755 | + | 0.709451i | \(0.251057\pi\) | ||||
−0.704755 | + | 0.709451i | \(0.748943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.07180i | − 0.107076i | −0.998566 | − | 0.0535381i | \(-0.982950\pi\) | ||||
0.998566 | − | 0.0535381i | \(-0.0170498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7665 | −0.965536 | −0.482768 | − | 0.875748i | \(-0.660369\pi\) | ||||
−0.482768 | + | 0.875748i | \(0.660369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.3673 | −1.92299 | −0.961493 | − | 0.274830i | \(-0.911378\pi\) | ||||
−0.961493 | + | 0.274830i | \(0.911378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.585786i | − 0.0202963i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.08946i | − 0.0723086i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.38698 | −0.185979 | −0.0929896 | − | 0.995667i | \(-0.529642\pi\) | ||||
−0.0929896 | + | 0.995667i | \(0.529642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1996 | −0.731019 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3245i | 0.355175i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 8.34758i | − 0.286826i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.4024 | −0.527987 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.9597 | −0.546450 | −0.273225 | − | 0.961950i | \(-0.588090\pi\) | ||||
−0.273225 | + | 0.961950i | \(0.588090\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.7050i | 1.15134i | 0.817682 | + | 0.575671i | \(0.195259\pi\) | ||||
−0.817682 | + | 0.575671i | \(0.804741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3739i | 0.695150i | 0.937652 | + | 0.347575i | \(0.112995\pi\) | ||||
−0.937652 | + | 0.347575i | \(0.887005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.986419 | −0.0335781 | −0.0167890 | − | 0.999859i | \(-0.505344\pi\) | ||||
−0.0167890 | + | 0.999859i | \(0.505344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3230 | 0.418994 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14464i | 0.0388293i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 26.1810i | − 0.887109i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2709 | 0.347219 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.0958 | 1.82669 | 0.913343 | − | 0.407191i | \(-0.133492\pi\) | ||||
0.913343 | + | 0.407191i | \(0.133492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 29.7649i | − 1.00281i | −0.865214 | − | 0.501403i | \(-0.832817\pi\) | ||||
0.865214 | − | 0.501403i | \(-0.167183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.48582i | − 0.0500019i | −0.999687 | − | 0.0250010i | \(-0.992041\pi\) | ||||
0.999687 | − | 0.0250010i | \(-0.00795888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.8854 | −0.466226 | −0.233113 | − | 0.972450i | \(-0.574891\pi\) | ||||
−0.233113 | + | 0.972450i | \(0.574891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.16693 | −0.139754 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.1404i | 0.673972i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.37452i | − 0.112798i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.6648 | −1.58971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.93226 | 0.0643731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.76770i | 0.324689i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.42580i | − 0.146956i | −0.997297 | − | 0.0734782i | \(-0.976590\pi\) | ||||
0.997297 | − | 0.0734782i | \(-0.0234099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.6657 | −0.982870 | −0.491435 | − | 0.870914i | \(-0.663527\pi\) | ||||
−0.491435 | + | 0.870914i | \(0.663527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.4963 | 0.909995 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6410i | 0.450465i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.4838i | 1.40141i | 0.713450 | + | 0.700706i | \(0.247132\pi\) | ||||
−0.713450 | + | 0.700706i | \(0.752868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.5836 | −0.776263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.73184 | 0.254221 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.3523i | 1.02864i | 0.857600 | + | 0.514318i | \(0.171955\pi\) | ||||
−0.857600 | + | 0.514318i | \(0.828045\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.89898i | − 0.193331i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.14464 | 0.0374338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0557 | 0.557186 | 0.278593 | − | 0.960409i | \(-0.410132\pi\) | ||||
0.278593 | + | 0.960409i | \(0.410132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 45.1949i | − 1.47331i | −0.676268 | − | 0.736656i | \(-0.736404\pi\) | ||||
0.676268 | − | 0.736656i | \(-0.263596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.16693i | 0.0380004i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.6571 | −1.02872 | −0.514359 | − | 0.857575i | \(-0.671970\pi\) | ||||
−0.514359 | + | 0.857575i | \(0.671970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.33137 | −0.270448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 39.1230i | − 1.26732i | −0.773612 | − | 0.633660i | \(-0.781552\pi\) | ||||
0.773612 | − | 0.633660i | \(-0.218448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19.2546i | − 0.623064i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.15696 | 0.263402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2580 | −0.459935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.45428i | 0.111197i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 50.8761i | − 1.63607i | −0.575171 | − | 0.818033i | \(-0.695065\pi\) | ||||
0.575171 | − | 0.818033i | \(-0.304935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.9782 | 1.47551 | 0.737755 | − | 0.675068i | \(-0.235886\pi\) | ||||
0.737755 | + | 0.675068i | \(0.235886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.46410 | −0.303405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1822i | 0.485722i | 0.970061 | + | 0.242861i | \(0.0780859\pi\) | ||||
−0.970061 | + | 0.242861i | \(0.921914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 10.3171i | − 0.329736i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.6625 | −1.36072 | −0.680361 | − | 0.732877i | \(-0.738177\pi\) | ||||
−0.680361 | + | 0.732877i | \(0.738177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.71573 | −0.309569 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.8061i | 1.29756i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.0072i | 1.20734i | 0.797234 | + | 0.603670i | \(0.206296\pi\) | ||||
−0.797234 | + | 0.603670i | \(0.793704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.2785 | −0.833084 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0560 | −0.761860 | −0.380930 | − | 0.924604i | \(-0.624396\pi\) | ||||
−0.380930 | + | 0.924604i | \(0.624396\pi\) | |||||||
\(998\) | 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 | 6048.2.h.a.2591.4 | ✓ | 8 | |
3.2 | odd | 2 | 6048.2.h.g.2591.5 | yes | 8 | ||
4.3 | odd | 2 | 6048.2.h.g.2591.4 | yes | 8 | ||
12.11 | even | 2 | inner | 6048.2.h.a.2591.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.a.2591.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.a.2591.5 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.g.2591.4 | yes | 8 | 4.3 | odd | 2 | ||
6048.2.h.g.2591.5 | yes | 8 | 3.2 | odd | 2 |