Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bl (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 431.8 | ||
Character | \(\chi\) | \(=\) | 2880.431 |
Dual form | 2880.2.bl.b.1871.8 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.13654 | 1.56347 | 0.781733 | − | 0.623613i | \(-0.214336\pi\) | ||||
0.781733 | + | 0.623613i | \(0.214336\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.99565 | + | 1.99565i | −0.601712 | + | 0.601712i | −0.940767 | − | 0.339055i | \(-0.889893\pi\) |
0.339055 | + | 0.940767i | \(0.389893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.516505 | + | 0.516505i | 0.143253 | + | 0.143253i | 0.775096 | − | 0.631843i | \(-0.217701\pi\) |
−0.631843 | + | 0.775096i | \(0.717701\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.26086i | − | 0.790874i | −0.918493 | − | 0.395437i | \(-0.870593\pi\) | ||
0.918493 | − | 0.395437i | \(-0.129407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.73322 | − | 3.73322i | 0.856460 | − | 0.856460i | −0.134459 | − | 0.990919i | \(-0.542930\pi\) |
0.990919 | + | 0.134459i | \(0.0429297\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.20935i | 1.50325i | 0.659589 | + | 0.751627i | \(0.270731\pi\) | ||||
−0.659589 | + | 0.751627i | \(0.729269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.21770 | + | 1.21770i | −0.226120 | + | 0.226120i | −0.811070 | − | 0.584949i | \(-0.801114\pi\) |
0.584949 | + | 0.811070i | \(0.301114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.55357i | 1.71587i | 0.513757 | + | 0.857936i | \(0.328253\pi\) | ||||
−0.513757 | + | 0.857936i | \(0.671747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.92498 | + | 2.92498i | 0.494412 | + | 0.494412i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.37513 | − | 6.37513i | 1.04807 | − | 1.04807i | 0.0492801 | − | 0.998785i | \(-0.484307\pi\) |
0.998785 | − | 0.0492801i | \(-0.0156927\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.26417 | 1.13447 | 0.567236 | − | 0.823555i | \(-0.308013\pi\) | ||||
0.567236 | + | 0.823555i | \(0.308013\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.127818 | − | 0.127818i | −0.0194921 | − | 0.0194921i | 0.697294 | − | 0.716786i | \(-0.254387\pi\) |
−0.716786 | + | 0.697294i | \(0.754387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.87784 | 1.29497 | 0.647483 | − | 0.762080i | \(-0.275822\pi\) | ||||
0.647483 | + | 0.762080i | \(0.275822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.1110 | 1.44443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.72788 | − | 9.72788i | −1.33623 | − | 1.33623i | −0.899683 | − | 0.436544i | \(-0.856202\pi\) |
−0.436544 | − | 0.899683i | \(-0.643798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82228 | −0.380556 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.86405 | + | 2.86405i | −0.372868 | + | 0.372868i | −0.868521 | − | 0.495653i | \(-0.834929\pi\) |
0.495653 | + | 0.868521i | \(0.334929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.64789 | − | 4.64789i | −0.595102 | − | 0.595102i | 0.343903 | − | 0.939005i | \(-0.388251\pi\) |
−0.939005 | + | 0.343903i | \(0.888251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.730448i | 0.0906009i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.264363 | + | 0.264363i | −0.0322970 | + | 0.0322970i | −0.723071 | − | 0.690774i | \(-0.757270\pi\) |
0.690774 | + | 0.723071i | \(0.257270\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.88076i | 0.223206i | 0.993753 | + | 0.111603i | \(0.0355984\pi\) | ||||
−0.993753 | + | 0.111603i | \(0.964402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.96795i | 0.347372i | 0.984801 | + | 0.173686i | \(0.0555678\pi\) | ||||
−0.984801 | + | 0.173686i | \(0.944432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.25510 | + | 8.25510i | −0.940756 | + | 0.940756i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.08712i | 0.684855i | 0.939544 | + | 0.342427i | \(0.111249\pi\) | ||||
−0.939544 | + | 0.342427i | \(0.888751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.98155 | + | 4.98155i | 0.546797 | + | 0.546797i | 0.925513 | − | 0.378716i | \(-0.123634\pi\) |
−0.378716 | + | 0.925513i | \(0.623634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.30577 | − | 2.30577i | 0.250096 | − | 0.250096i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.90265 | −0.731679 | −0.365840 | − | 0.930678i | \(-0.619218\pi\) | ||||
−0.365840 | + | 0.930678i | \(0.619218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.13654 | + | 2.13654i | 0.223971 | + | 0.223971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.27957 | 0.541673 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.2393 | −1.03964 | −0.519822 | − | 0.854275i | \(-0.674002\pi\) | ||||
−0.519822 | + | 0.854275i | \(0.674002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.82574 | + | 7.82574i | 0.778690 | + | 0.778690i | 0.979608 | − | 0.200918i | \(-0.0643925\pi\) |
−0.200918 | + | 0.979608i | \(0.564393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1803 | 1.00309 | 0.501546 | − | 0.865131i | \(-0.332765\pi\) | ||||
0.501546 | + | 0.865131i | \(0.332765\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.52289 | + | 9.52289i | −0.920613 | + | 0.920613i | −0.997073 | − | 0.0764598i | \(-0.975638\pi\) |
0.0764598 | + | 0.997073i | \(0.475638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.83148 | + | 8.83148i | 0.845903 | + | 0.845903i | 0.989619 | − | 0.143716i | \(-0.0459052\pi\) |
−0.143716 | + | 0.989619i | \(0.545905\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.46386i | 0.325853i | 0.986638 | + | 0.162926i | \(0.0520933\pi\) | ||||
−0.986638 | + | 0.162926i | \(0.947907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.09778 | + | 5.09778i | −0.475371 | + | 0.475371i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 13.4887i | − | 1.23650i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.03475i | 0.275886i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.3548i | − | 1.89493i | −0.319856 | − | 0.947466i | \(-0.603634\pi\) | ||
0.319856 | − | 0.947466i | \(-0.396366\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.26817 | + | 3.26817i | 0.285541 | + | 0.285541i | 0.835314 | − | 0.549773i | \(-0.185286\pi\) |
−0.549773 | + | 0.835314i | \(0.685286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.4426 | − | 15.4426i | 1.33905 | − | 1.33905i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.20493 | 0.615559 | 0.307779 | − | 0.951458i | \(-0.400414\pi\) | ||||
0.307779 | + | 0.951458i | \(0.400414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1704 | − | 13.1704i | −1.11710 | − | 1.11710i | −0.992165 | − | 0.124932i | \(-0.960129\pi\) |
−0.124932 | − | 0.992165i | \(-0.539871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.06153 | −0.172394 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72208 | −0.143011 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.9496 | − | 15.9496i | −1.30664 | − | 1.30664i | −0.923824 | − | 0.382817i | \(-0.874954\pi\) |
−0.382817 | − | 0.923824i | \(-0.625046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6263 | 0.946132 | 0.473066 | − | 0.881027i | \(-0.343147\pi\) | ||||
0.473066 | + | 0.881027i | \(0.343147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.75539 | + | 6.75539i | −0.542606 | + | 0.542606i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4861 | + | 13.4861i | 1.07631 | + | 1.07631i | 0.996837 | + | 0.0794735i | \(0.0253239\pi\) |
0.0794735 | + | 0.996837i | \(0.474676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.8218i | 2.35029i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.19882 | + | 1.19882i | −0.0938991 | + | 0.0938991i | −0.752496 | − | 0.658597i | \(-0.771150\pi\) |
0.658597 | + | 0.752496i | \(0.271150\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.51068i | − | 0.503811i | −0.967752 | − | 0.251906i | \(-0.918943\pi\) | ||
0.967752 | − | 0.251906i | \(-0.0810573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.4664i | − | 0.958957i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.24028 | − | 7.24028i | 0.550468 | − | 0.550468i | −0.376108 | − | 0.926576i | \(-0.622738\pi\) |
0.926576 | + | 0.376108i | \(0.122738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.13654i | 0.312693i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.11091 | + | 4.11091i | 0.307264 | + | 0.307264i | 0.843847 | − | 0.536583i | \(-0.180285\pi\) |
−0.536583 | + | 0.843847i | \(0.680285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7469 | − | 11.7469i | 0.873142 | − | 0.873142i | −0.119672 | − | 0.992814i | \(-0.538184\pi\) |
0.992814 | + | 0.119672i | \(0.0381842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.01580 | 0.662855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.50753 | + | 6.50753i | 0.475878 | + | 0.475878i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.86217 | −0.424171 | −0.212086 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212086 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.4308 | 1.68659 | 0.843293 | − | 0.537453i | \(-0.180614\pi\) | ||||
0.843293 | + | 0.537453i | \(0.180614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.18092 | + | 3.18092i | 0.226631 | + | 0.226631i | 0.811284 | − | 0.584653i | \(-0.198769\pi\) |
−0.584653 | + | 0.811284i | \(0.698769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5758 | 1.52947 | 0.764736 | − | 0.644344i | \(-0.222870\pi\) | ||||
0.764736 | + | 0.644344i | \(0.222870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.03705 | + | 5.03705i | −0.353532 | + | 0.353532i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.13654 | + | 5.13654i | 0.358752 | + | 0.358752i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9004i | 1.03068i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.30351 | + | 4.30351i | −0.296266 | + | 0.296266i | −0.839549 | − | 0.543283i | \(-0.817181\pi\) |
0.543283 | + | 0.839549i | \(0.317181\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.180762i | − | 0.0123279i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 39.5188i | 2.68271i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.68425 | − | 1.68425i | 0.113295 | − | 0.113295i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9977i | 0.736460i | 0.929735 | + | 0.368230i | \(0.120036\pi\) | ||||
−0.929735 | + | 0.368230i | \(0.879964\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9364 | + | 10.9364i | 0.725876 | + | 0.725876i | 0.969796 | − | 0.243919i | \(-0.0784332\pi\) |
−0.243919 | + | 0.969796i | \(0.578433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.16994 | + | 5.16994i | −0.341639 | + | 0.341639i | −0.856983 | − | 0.515344i | \(-0.827664\pi\) |
0.515344 | + | 0.856983i | \(0.327664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.98003 | −0.326252 | −0.163126 | − | 0.986605i | \(-0.552158\pi\) | ||||
−0.163126 | + | 0.986605i | \(0.552158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.27758 | + | 6.27758i | 0.409504 | + | 0.409504i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5353 | −0.746156 | −0.373078 | − | 0.927800i | \(-0.621698\pi\) | ||||
−0.373078 | + | 0.927800i | \(0.621698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.58992 | −0.424494 | −0.212247 | − | 0.977216i | \(-0.568078\pi\) | ||||
−0.212247 | + | 0.977216i | \(0.568078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.14956 | + | 7.14956i | 0.456768 | + | 0.456768i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.85645 | 0.245380 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.76507 | + | 6.76507i | −0.427007 | + | 0.427007i | −0.887608 | − | 0.460600i | \(-0.847634\pi\) |
0.460600 | + | 0.887608i | \(0.347634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.3874 | − | 14.3874i | −0.904525 | − | 0.904525i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.6146i | 1.59780i | 0.601466 | + | 0.798899i | \(0.294584\pi\) | ||||
−0.601466 | + | 0.798899i | \(0.705416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.3710 | − | 26.3710i | 1.63862 | − | 1.63862i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.56169i | − | 0.281286i | −0.990060 | − | 0.140643i | \(-0.955083\pi\) | ||
0.990060 | − | 0.140643i | \(-0.0449169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.7573i | − | 0.845104i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.80272 | + | 9.80272i | −0.597682 | + | 0.597682i | −0.939695 | − | 0.342013i | \(-0.888891\pi\) |
0.342013 | + | 0.939695i | \(0.388891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.97033i | − | 0.180435i | −0.995922 | − | 0.0902174i | \(-0.971244\pi\) | ||
0.995922 | − | 0.0902174i | \(-0.0287562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.99565 | − | 1.99565i | −0.120342 | − | 0.120342i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6705 | + | 12.6705i | −0.761297 | + | 0.761297i | −0.976557 | − | 0.215260i | \(-0.930940\pi\) |
0.215260 | + | 0.976557i | \(0.430940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7093 | 1.35472 | 0.677362 | − | 0.735650i | \(-0.263123\pi\) | ||||
0.677362 | + | 0.735650i | \(0.263123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.6922 | − | 15.6922i | −0.932804 | − | 0.932804i | 0.0650764 | − | 0.997880i | \(-0.479271\pi\) |
−0.997880 | + | 0.0650764i | \(0.979271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.0486 | 1.77371 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.36682 | 0.374519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.60395 | − | 4.60395i | −0.268965 | − | 0.268965i | 0.559718 | − | 0.828683i | \(-0.310910\pi\) |
−0.828683 | + | 0.559718i | \(0.810910\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.05038 | −0.235822 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.72366 | + | 3.72366i | −0.215345 | + | 0.215345i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.528725 | − | 0.528725i | −0.0304752 | − | 0.0304752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.57312i | − | 0.376376i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.49416 | + | 6.49416i | −0.370641 | + | 0.370641i | −0.867711 | − | 0.497069i | \(-0.834409\pi\) |
0.497069 | + | 0.867711i | \(0.334409\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.5023i | − | 1.50280i | −0.659844 | − | 0.751402i | \(-0.729378\pi\) | ||
0.659844 | − | 0.751402i | \(-0.270622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2292i | 0.917327i | 0.888610 | + | 0.458664i | \(0.151672\pi\) | ||||
−0.888610 | + | 0.458664i | \(0.848328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.45683 | − | 3.45683i | 0.194155 | − | 0.194155i | −0.603334 | − | 0.797489i | \(-0.706161\pi\) |
0.797489 | + | 0.603334i | \(0.206161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.86019i | − | 0.272119i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1735 | − | 12.1735i | −0.677352 | − | 0.677352i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.516505 | + | 0.516505i | −0.0286505 | + | 0.0286505i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.7236 | 2.02464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.270581 | + | 0.270581i | 0.0148725 | + | 0.0148725i | 0.714504 | − | 0.699631i | \(-0.246652\pi\) |
−0.699631 | + | 0.714504i | \(0.746652\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.373865 | −0.0204264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.5747 | −1.88340 | −0.941702 | − | 0.336447i | \(-0.890775\pi\) | ||||
−0.941702 | + | 0.336447i | \(0.890775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.0656 | − | 19.0656i | −1.03246 | − | 1.03246i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.8688 | 0.694850 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.32453 | − | 2.32453i | 0.124787 | − | 0.124787i | −0.641955 | − | 0.766742i | \(-0.721876\pi\) |
0.766742 | + | 0.641955i | \(0.221876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1089 | − | 17.1089i | −0.915819 | − | 0.915819i | 0.0809032 | − | 0.996722i | \(-0.474220\pi\) |
−0.996722 | + | 0.0809032i | \(0.974220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 0.666944i | − | 0.0354978i | −0.999842 | − | 0.0177489i | \(-0.994350\pi\) | ||
0.999842 | − | 0.0177489i | \(-0.00564995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.32990 | + | 1.32990i | −0.0705838 | + | 0.0705838i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 29.8378i | − | 1.57478i | −0.616456 | − | 0.787389i | \(-0.711432\pi\) | ||
0.616456 | − | 0.787389i | \(-0.288568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 8.87391i | − | 0.467048i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.09866 | + | 2.09866i | −0.109849 | + | 0.109849i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.9584i | 1.14622i | 0.819478 | + | 0.573111i | \(0.194263\pi\) | ||||
−0.819478 | + | 0.573111i | \(0.805737\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.2398 | − | 40.2398i | −2.08915 | − | 2.08915i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.34820 | + | 8.34820i | −0.432253 | + | 0.432253i | −0.889394 | − | 0.457141i | \(-0.848873\pi\) |
0.457141 | + | 0.889394i | \(0.348873\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.25789 | −0.0647847 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5127 | + | 14.5127i | 0.745469 | + | 0.745469i | 0.973625 | − | 0.228156i | \(-0.0732696\pi\) |
−0.228156 | + | 0.973625i | \(0.573270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6064 | 1.10404 | 0.552019 | − | 0.833832i | \(-0.313858\pi\) | ||||
0.552019 | + | 0.833832i | \(0.313858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.6745 | −0.594986 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3468 | − | 23.3468i | −1.18373 | − | 1.18373i | −0.978771 | − | 0.204958i | \(-0.934294\pi\) |
−0.204958 | − | 0.978771i | \(-0.565706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.5086 | 1.18888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.30424 | + | 4.30424i | −0.216570 | + | 0.216570i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1620 | − | 12.1620i | −0.610394 | − | 0.610394i | 0.332655 | − | 0.943049i | \(-0.392056\pi\) |
−0.943049 | + | 0.332655i | \(0.892056\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 35.4000i | − | 1.76779i | −0.467683 | − | 0.883896i | \(-0.654911\pi\) | ||
0.467683 | − | 0.883896i | \(-0.345089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.93446 | + | 4.93446i | −0.245803 | + | 0.245803i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4451i | 1.26127i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.10272i | − | 0.252313i | −0.992010 | − | 0.126157i | \(-0.959736\pi\) | ||
0.992010 | − | 0.126157i | \(-0.0402642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.8473 | + | 11.8473i | −0.582967 | + | 0.582967i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.04498i | 0.345825i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.52922 | + | 5.52922i | 0.270120 | + | 0.270120i | 0.829148 | − | 0.559028i | \(-0.188826\pi\) |
−0.559028 | + | 0.829148i | \(0.688826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8492 | − | 14.8492i | 0.723708 | − | 0.723708i | −0.245651 | − | 0.969358i | \(-0.579002\pi\) |
0.969358 | + | 0.245651i | \(0.0790016\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.26086 | 0.158175 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.2262 | − | 19.2262i | −0.930422 | − | 0.930422i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0747 | −0.870626 | −0.435313 | − | 0.900279i | \(-0.643362\pi\) | ||||
−0.435313 | + | 0.900279i | \(0.643362\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6052 | −0.990223 | −0.495112 | − | 0.868829i | \(-0.664873\pi\) | ||||
−0.495112 | + | 0.868829i | \(0.664873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.9141 | + | 26.9141i | 1.28748 | + | 1.28748i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.9204 | −1.66666 | −0.833330 | − | 0.552776i | \(-0.813568\pi\) | ||||
−0.833330 | + | 0.552776i | \(0.813568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.35145 | + | 3.35145i | −0.159232 | + | 0.159232i | −0.782226 | − | 0.622994i | \(-0.785916\pi\) |
0.622994 | + | 0.782226i | \(0.285916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.88091 | − | 4.88091i | −0.231377 | − | 0.231377i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 35.4234i | − | 1.67173i | −0.548931 | − | 0.835867i | \(-0.684965\pi\) | ||
0.548931 | − | 0.835867i | \(-0.315035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.4968 | + | 14.4968i | −0.682625 | + | 0.682625i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.02153i | 0.141652i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3448i | 0.858135i | 0.903272 | + | 0.429067i | \(0.141158\pi\) | ||||
−0.903272 | + | 0.429067i | \(0.858842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.16968 | − | 6.16968i | 0.287351 | − | 0.287351i | −0.548681 | − | 0.836032i | \(-0.684870\pi\) |
0.836032 | + | 0.548681i | \(0.184870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.5392i | − | 0.768641i | −0.923200 | − | 0.384320i | \(-0.874436\pi\) | ||
0.923200 | − | 0.384320i | \(-0.125564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.7412 | + | 17.7412i | 0.820964 | + | 0.820964i | 0.986246 | − | 0.165282i | \(-0.0528534\pi\) |
−0.165282 | + | 0.986246i | \(0.552853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.09355 | + | 1.09355i | −0.0504953 | + | 0.0504953i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.510161 | 0.0234572 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.73322 | + | 3.73322i | 0.171292 | + | 0.171292i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.04478 | −0.276193 | −0.138096 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138096 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.58557 | 0.300276 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.24028 | − | 7.24028i | −0.328764 | − | 0.328764i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.1826 | −1.23176 | −0.615882 | − | 0.787839i | \(-0.711200\pi\) | ||||
−0.615882 | + | 0.787839i | \(0.711200\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.92201 | + | 3.92201i | −0.176998 | + | 0.176998i | −0.790046 | − | 0.613048i | \(-0.789943\pi\) |
0.613048 | + | 0.790046i | \(0.289943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.97073 | + | 3.97073i | 0.178833 | + | 0.178833i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.77987i | 0.348975i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8663 | − | 16.8663i | 0.755039 | − | 0.755039i | −0.220376 | − | 0.975415i | \(-0.570729\pi\) |
0.975415 | + | 0.220376i | \(0.0707285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 19.7695i | − | 0.881480i | −0.897635 | − | 0.440740i | \(-0.854716\pi\) | ||
0.897635 | − | 0.440740i | \(-0.145284\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0673i | 0.492487i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.29061 | − | 5.29061i | 0.234502 | − | 0.234502i | −0.580067 | − | 0.814569i | \(-0.696974\pi\) |
0.814569 | + | 0.580067i | \(0.196974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2771i | 0.543105i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.19855 | + | 7.19855i | 0.317206 | + | 0.317206i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.7171 | + | 17.7171i | −0.779196 | + | 0.779196i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0355 | −1.22826 | −0.614129 | − | 0.789206i | \(-0.710493\pi\) | ||||
−0.614129 | + | 0.789206i | \(0.710493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.8808 | − | 30.8808i | −1.35032 | − | 1.35032i | −0.885298 | − | 0.465024i | \(-0.846046\pi\) |
−0.465024 | − | 0.885298i | \(-0.653954\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.1528 | 1.35704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.9747 | −1.25977 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.75198 | + | 3.75198i | 0.162516 | + | 0.162516i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.4674 | −0.582247 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.1780 | + | 20.1780i | −0.869129 | + | 0.869129i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.3056 | − | 26.3056i | −1.13096 | − | 1.13096i | −0.990017 | − | 0.140948i | \(-0.954985\pi\) |
−0.140948 | − | 0.990017i | \(-0.545015\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4896i | 0.534996i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3884 | + | 10.3884i | −0.444178 | + | 0.444178i | −0.893413 | − | 0.449236i | \(-0.851696\pi\) |
0.449236 | + | 0.893413i | \(0.351696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.09186i | 0.387326i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.1796i | 1.07075i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.76163 | + | 6.76163i | −0.286499 | + | 0.286499i | −0.835694 | − | 0.549195i | \(-0.814934\pi\) |
0.549195 | + | 0.835694i | \(0.314934\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.132037i | − | 0.00558458i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.6530 | − | 18.6530i | −0.786132 | − | 0.786132i | 0.194726 | − | 0.980858i | \(-0.437618\pi\) |
−0.980858 | + | 0.194726i | \(0.937618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.44932 | + | 2.44932i | −0.103044 | + | 0.103044i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.7176 | −0.616995 | −0.308497 | − | 0.951225i | \(-0.599826\pi\) | ||||
−0.308497 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1005 | − | 15.1005i | −0.631935 | − | 0.631935i | 0.316618 | − | 0.948553i | \(-0.397453\pi\) |
−0.948553 | + | 0.316618i | \(0.897453\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.20935 | −0.300651 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5374 | 0.730092 | 0.365046 | − | 0.930989i | \(-0.381053\pi\) | ||||
0.365046 | + | 0.930989i | \(0.381053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.6064 | + | 20.6064i | 0.854898 | + | 0.854898i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.8269 | 1.60805 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.2367 | − | 14.2367i | 0.587611 | − | 0.587611i | −0.349373 | − | 0.936984i | \(-0.613605\pi\) |
0.936984 | + | 0.349373i | \(0.113605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6656 | + | 35.6656i | 1.46958 | + | 1.46958i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.18442i | 0.130769i | 0.997860 | + | 0.0653843i | \(0.0208273\pi\) | ||||
−0.997860 | + | 0.0653843i | \(0.979173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.53793 | − | 9.53793i | 0.391017 | − | 0.391017i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 15.3081i | − | 0.625471i | −0.949840 | − | 0.312736i | \(-0.898755\pi\) | ||
0.949840 | − | 0.312736i | \(-0.101245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18.5232i | − | 0.755575i | −0.925892 | − | 0.377788i | \(-0.876685\pi\) | ||
0.925892 | − | 0.377788i | \(-0.123315\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.14589 | + | 2.14589i | −0.0872429 | + | 0.0872429i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7857i | 0.681312i | 0.940188 | + | 0.340656i | \(0.110649\pi\) | ||||
−0.940188 | + | 0.340656i | \(0.889351\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.58545 | + | 4.58545i | 0.185507 | + | 0.185507i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.4664 | − | 16.4664i | 0.665071 | − | 0.665071i | −0.291500 | − | 0.956571i | \(-0.594154\pi\) |
0.956571 | + | 0.291500i | \(0.0941544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.4236 | 1.74817 | 0.874084 | − | 0.485775i | \(-0.161463\pi\) | ||||
0.874084 | + | 0.485775i | \(0.161463\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4967 | + | 10.4967i | 0.421900 | + | 0.421900i | 0.885857 | − | 0.463958i | \(-0.153571\pi\) |
−0.463958 | + | 0.885857i | \(0.653571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.5531 | −1.14396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.7884 | − | 20.7884i | −0.828887 | − | 0.828887i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8165 | −1.10736 | −0.553679 | − | 0.832730i | \(-0.686777\pi\) | ||||
−0.553679 | + | 0.832730i | \(0.686777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.1001 | − | 15.1001i | 0.599230 | − | 0.599230i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.22238 | + | 5.22238i | 0.206918 | + | 0.206918i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.37454i | − | 0.330774i | −0.986229 | − | 0.165387i | \(-0.947113\pi\) | ||
0.986229 | − | 0.165387i | \(-0.0528874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.42530 | + | 8.42530i | −0.332261 | + | 0.332261i | −0.853445 | − | 0.521183i | \(-0.825491\pi\) |
0.521183 | + | 0.853445i | \(0.325491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.1494i | 1.02804i | 0.857778 | + | 0.514020i | \(0.171844\pi\) | ||||
−0.857778 | + | 0.514020i | \(0.828156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4313i | − | 0.448718i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.2934 | − | 21.2934i | 0.833275 | − | 0.833275i | −0.154689 | − | 0.987963i | \(-0.549437\pi\) |
0.987963 | + | 0.154689i | \(0.0494375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.62189i | 0.180592i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8901 | − | 15.8901i | −0.618991 | − | 0.618991i | 0.326282 | − | 0.945273i | \(-0.394204\pi\) |
−0.945273 | + | 0.326282i | \(0.894204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1989 | − | 15.1989i | 0.591169 | − | 0.591169i | −0.346778 | − | 0.937947i | \(-0.612724\pi\) |
0.937947 | + | 0.346778i | \(0.112724\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.8392 | 0.846888 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.77880 | − | 8.77880i | −0.339916 | − | 0.339916i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5512 | 0.716159 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.85084 | −0.109892 | −0.0549460 | − | 0.998489i | \(-0.517499\pi\) | ||||
−0.0549460 | + | 0.998489i | \(0.517499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.5131 | − | 21.5131i | −0.826814 | − | 0.826814i | 0.160261 | − | 0.987075i | \(-0.448766\pi\) |
−0.987075 | + | 0.160261i | \(0.948766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.3553 | −1.62545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.3993 | − | 33.3993i | 1.27799 | − | 1.27799i | 0.336198 | − | 0.941791i | \(-0.390859\pi\) |
0.941791 | − | 0.336198i | \(-0.109141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.09465 | + | 5.09465i | 0.194657 | + | 0.194657i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 10.0490i | − | 0.382836i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3790 | + | 26.3790i | −1.00351 | + | 1.00351i | −0.00351149 | + | 0.999994i | \(0.501118\pi\) |
−0.999994 | + | 0.00351149i | \(0.998882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 18.6257i | − | 0.706515i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 23.6874i | − | 0.897225i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.58696 | − | 5.58696i | 0.211016 | − | 0.211016i | −0.593683 | − | 0.804699i | \(-0.702327\pi\) |
0.804699 | + | 0.593683i | \(0.202327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 47.5996i | − | 1.79525i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.3715 | + | 32.3715i | 1.21746 | + | 1.21746i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9208 | − | 14.9208i | 0.560362 | − | 0.560362i | −0.369048 | − | 0.929410i | \(-0.620316\pi\) |
0.929410 | + | 0.369048i | \(0.120316\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −68.8750 | −2.57939 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.45772 | − | 1.45772i | −0.0545156 | − | 0.0545156i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0373 | −0.747265 | −0.373633 | − | 0.927577i | \(-0.621888\pi\) | ||||
−0.373633 | + | 0.927577i | \(0.621888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.1112 | 1.56830 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.21770 | − | 1.21770i | −0.0452241 | − | 0.0452241i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3409 | −0.717313 | −0.358656 | − | 0.933470i | \(-0.616765\pi\) | ||||
−0.358656 | + | 0.933470i | \(0.616765\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.416796 | + | 0.416796i | −0.0154158 | + | 0.0154158i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.24076 | − | 8.24076i | −0.304379 | − | 0.304379i | 0.538345 | − | 0.842724i | \(-0.319050\pi\) |
−0.842724 | + | 0.538345i | \(0.819050\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.05515i | − | 0.0388670i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2855 | + | 12.2855i | −0.451930 | + | 0.451930i | −0.895995 | − | 0.444065i | \(-0.853536\pi\) |
0.444065 | + | 0.895995i | \(0.353536\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.2633i | 0.596644i | 0.954465 | + | 0.298322i | \(0.0964269\pi\) | ||||
−0.954465 | + | 0.298322i | \(0.903573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 22.5561i | − | 0.826392i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39.3919 | + | 39.3919i | −1.43935 | + | 1.43935i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.6548i | 0.899667i | 0.893113 | + | 0.449833i | \(0.148517\pi\) | ||||
−0.893113 | + | 0.449833i | \(0.851483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.22101 | + | 8.22101i | 0.299193 | + | 0.299193i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1769 | + | 25.1769i | −0.915072 | + | 0.915072i | −0.996666 | − | 0.0815940i | \(-0.973999\pi\) |
0.0815940 | + | 0.996666i | \(0.473999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.1018 | −1.23619 | −0.618095 | − | 0.786103i | \(-0.712095\pi\) | ||||
−0.618095 | + | 0.786103i | \(0.712095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.5318 | + | 36.5318i | 1.32254 | + | 1.32254i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.95859 | −0.106829 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.1599 | −1.19578 | −0.597888 | − | 0.801580i | \(-0.703993\pi\) | ||||
−0.597888 | + | 0.801580i | \(0.703993\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.69057 | + | 5.69057i | 0.204676 | + | 0.204676i | 0.802000 | − | 0.597324i | \(-0.203769\pi\) |
−0.597324 | + | 0.802000i | \(0.703769\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.55357 | −0.343174 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.1188 | − | 27.1188i | 0.971631 | − | 0.971631i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.75335 | − | 3.75335i | −0.134305 | − | 0.134305i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.0723i | 0.680719i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6712 | + | 24.6712i | −0.879434 | + | 0.879434i | −0.993476 | − | 0.114042i | \(-0.963620\pi\) |
0.114042 | + | 0.993476i | \(0.463620\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.3284i | 0.509460i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.80132i | − | 0.170500i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.3362 | − | 37.3362i | 1.32251 | − | 1.32251i | 0.410780 | − | 0.911734i | \(-0.365256\pi\) |
0.911734 | − | 0.410780i | \(-0.134744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 28.9494i | − | 1.02415i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.92299 | − | 5.92299i | −0.209018 | − | 0.209018i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.0872 | + | 21.0872i | −0.743226 | + | 0.743226i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.9038 | −0.629465 | −0.314732 | − | 0.949180i | \(-0.601915\pi\) | ||||
−0.314732 | + | 0.949180i | \(0.601915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.6377 | − | 11.6377i | −0.408656 | − | 0.408656i | 0.472614 | − | 0.881270i | \(-0.343311\pi\) |
−0.881270 | + | 0.472614i | \(0.843311\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.69539 | −0.0593870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.954347 | −0.0333884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3168 | − | 29.3168i | −1.02316 | − | 1.02316i | −0.999725 | − | 0.0234386i | \(-0.992539\pi\) |
−0.0234386 | − | 0.999725i | \(-0.507461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.89629 | −0.344963 | −0.172481 | − | 0.985013i | \(-0.555178\pi\) | ||||
−0.172481 | + | 0.985013i | \(0.555178\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.195254 | − | 0.195254i | 0.00678966 | − | 0.00678966i | −0.703704 | − | 0.710493i | \(-0.748472\pi\) |
0.710493 | + | 0.703704i | \(0.248472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.9291 | + | 38.9291i | 1.35206 | + | 1.35206i | 0.883351 | + | 0.468712i | \(0.155282\pi\) |
0.468712 | + | 0.883351i | \(0.344718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 32.9705i | − | 1.14236i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.60374 | − | 4.60374i | 0.159319 | − | 0.159319i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26.1042i | − | 0.901217i | −0.892722 | − | 0.450609i | \(-0.851207\pi\) | ||
0.892722 | − | 0.450609i | \(-0.148793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0344i | 0.897739i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.81511 | − | 8.81511i | 0.303249 | − | 0.303249i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5534i | 0.431339i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.9606 | + | 45.9606i | 1.57551 | + | 1.57551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.88268 | − | 3.88268i | 0.132940 | − | 0.132940i | −0.637505 | − | 0.770446i | \(-0.720034\pi\) |
0.770446 | + | 0.637505i | \(0.220034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.0296 | −0.957472 | −0.478736 | − | 0.877959i | \(-0.658905\pi\) | ||||
−0.478736 | + | 0.877959i | \(0.658905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.91482 | + | 9.91482i | 0.338289 | + | 0.338289i | 0.855723 | − | 0.517434i | \(-0.173113\pi\) |
−0.517434 | + | 0.855723i | \(0.673113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.8640 | −0.437895 | −0.218948 | − | 0.975737i | \(-0.570262\pi\) | ||||
−0.218948 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2393 | 0.348147 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.1478 | − | 12.1478i | −0.412085 | − | 0.412085i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.273089 | −0.00925327 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.92498 | + | 2.92498i | −0.0988823 | + | 0.0988823i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2843 | − | 28.2843i | −0.955091 | − | 0.955091i | 0.0439427 | − | 0.999034i | \(-0.486008\pi\) |
−0.999034 | + | 0.0439427i | \(0.986008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.3589i | − | 0.517456i | −0.965950 | − | 0.258728i | \(-0.916697\pi\) | ||
0.965950 | − | 0.258728i | \(-0.0833033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.6553 | + | 33.6553i | −1.13259 | + | 1.13259i | −0.142847 | + | 0.989745i | \(0.545626\pi\) |
−0.989745 | + | 0.142847i | \(0.954374\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22.1187i | − | 0.742675i | −0.928498 | − | 0.371337i | \(-0.878899\pi\) | ||
0.928498 | − | 0.371337i | \(-0.121101\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 88.3351i | − | 2.96266i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.1430 | − | 33.1430i | 1.10909 | − | 1.10909i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.81371i | 0.194331i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.6333 | − | 11.6333i | −0.387994 | − | 0.387994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7212 | + | 31.7212i | −1.05679 | + | 1.05679i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.6127 | 0.552223 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.5189 | − | 36.5189i | −1.21259 | − | 1.21259i | −0.970171 | − | 0.242420i | \(-0.922059\pi\) |
−0.242420 | − | 0.970171i | \(-0.577941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.60406 | 0.218802 | 0.109401 | − | 0.993998i | \(-0.465107\pi\) | ||||
0.109401 | + | 0.993998i | \(0.465107\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.8829 | −0.658028 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.5189 | + | 13.5189i | 0.446434 | + | 0.446434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3917 | −0.507727 | −0.253863 | − | 0.967240i | \(-0.581701\pi\) | ||||
−0.253863 | + | 0.967240i | \(0.581701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.971424 | + | 0.971424i | −0.0319748 | + | 0.0319748i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.37513 | + | 6.37513i | 0.209613 | + | 0.209613i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 55.9587i | − | 1.83594i | −0.396645 | − | 0.917972i | \(-0.629826\pi\) | ||
0.396645 | − | 0.917972i | \(-0.370174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.7466 | − | 37.7466i | 1.23710 | − | 1.23710i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.20304i | 0.300972i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.1509i | 0.494959i | 0.968893 | + | 0.247480i | \(0.0796023\pi\) | ||||
−0.968893 | + | 0.247480i | \(0.920398\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.6844 | − | 41.6844i | 1.35887 | − | 1.35887i | 0.483564 | − | 0.875309i | \(-0.339342\pi\) |
0.875309 | − | 0.483564i | \(-0.160658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.3700i | 1.70540i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.30064 | − | 6.30064i | −0.204743 | − | 0.204743i | 0.597285 | − | 0.802029i | \(-0.296246\pi\) |
−0.802029 | + | 0.597285i | \(0.796246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.53296 | + | 1.53296i | −0.0497620 | + | 0.0497620i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.87663 | −0.319935 | −0.159968 | − | 0.987122i | \(-0.551139\pi\) | ||||
−0.159968 | + | 0.987122i | \(0.551139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.14518 | − | 4.14518i | −0.134135 | − | 0.134135i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.8035 | 0.962406 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −60.2706 | −1.94421 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5681 | + | 16.5681i | 0.533346 | + | 0.533346i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.1357 | 1.03342 | 0.516708 | − | 0.856162i | \(-0.327157\pi\) | ||||
0.516708 | + | 0.856162i | \(0.327157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.4159 | − | 17.4159i | 0.558902 | − | 0.558902i | −0.370093 | − | 0.928995i | \(-0.620674\pi\) |
0.928995 | + | 0.370093i | \(0.120674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.4799 | − | 54.4799i | −1.74654 | − | 1.74654i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.9741i | 0.639027i | 0.947582 | + | 0.319513i | \(0.103519\pi\) | ||||
−0.947582 | + | 0.319513i | \(0.896481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.7753 | − | 13.7753i | 0.440260 | − | 0.440260i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.23440i | 0.0712662i | 0.999365 | + | 0.0356331i | \(0.0113448\pi\) | ||||
−0.999365 | + | 0.0356331i | \(0.988655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.49850i | 0.143334i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.921486 | − | 0.921486i | 0.0293015 | − | 0.0293015i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 45.3220i | − | 1.43970i | −0.694129 | − | 0.719851i | \(-0.744210\pi\) | ||
0.694129 | − | 0.719851i | \(-0.255790\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2564 | + | 15.2564i | 0.483661 | + | 0.483661i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.4556 | + | 10.4556i | −0.331132 | + | 0.331132i | −0.853016 | − | 0.521884i | \(-0.825229\pi\) |
0.521884 | + | 0.853016i | \(0.325229\pi\) | |||||||
\(998\) | 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 | 2880.2.bl.b.431.8 | 24 | ||
3.2 | odd | 2 | inner | 2880.2.bl.b.431.6 | 24 | ||
4.3 | odd | 2 | 720.2.bl.b.611.2 | yes | 24 | ||
12.11 | even | 2 | 720.2.bl.b.611.11 | yes | 24 | ||
16.5 | even | 4 | 720.2.bl.b.251.11 | yes | 24 | ||
16.11 | odd | 4 | inner | 2880.2.bl.b.1871.6 | 24 | ||
48.5 | odd | 4 | 720.2.bl.b.251.2 | ✓ | 24 | ||
48.11 | even | 4 | inner | 2880.2.bl.b.1871.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bl.b.251.2 | ✓ | 24 | 48.5 | odd | 4 | ||
720.2.bl.b.251.11 | yes | 24 | 16.5 | even | 4 | ||
720.2.bl.b.611.2 | yes | 24 | 4.3 | odd | 2 | ||
720.2.bl.b.611.11 | yes | 24 | 12.11 | even | 2 | ||
2880.2.bl.b.431.6 | 24 | 3.2 | odd | 2 | inner | ||
2880.2.bl.b.431.8 | 24 | 1.1 | even | 1 | trivial | ||
2880.2.bl.b.1871.6 | 24 | 16.11 | odd | 4 | inner | ||
2880.2.bl.b.1871.8 | 24 | 48.11 | even | 4 | inner |