Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.a (trivial) |
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: | yes |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.940.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 7x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.29240\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.83991 | −1.82931 | −0.914657 | − | 0.404232i | \(-0.867539\pi\) | ||||
−0.914657 | + | 0.404232i | \(0.867539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.25511 | 0.679940 | 0.339970 | − | 0.940436i | \(-0.389583\pi\) | ||||
0.339970 | + | 0.940436i | \(0.389583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.32970 | 1.53518 | 0.767589 | − | 0.640943i | \(-0.221456\pi\) | ||||
0.767589 | + | 0.640943i | \(0.221456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.58480 | −0.592995 | −0.296497 | − | 0.955034i | \(-0.595819\pi\) | ||||
−0.296497 | + | 0.955034i | \(0.595819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.83991 | −1.05615 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.83991 | 1.00919 | 0.504595 | − | 0.863356i | \(-0.331642\pi\) | ||||
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.09501 | 1.68890 | 0.844451 | − | 0.535633i | \(-0.179927\pi\) | ||||
0.844451 | + | 0.535633i | \(0.179927\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.510210 | −0.0916364 | −0.0458182 | − | 0.998950i | \(-0.514589\pi\) | ||||
−0.0458182 | + | 0.998950i | \(0.514589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.25511 | 0.392563 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.83991 | −0.818094 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.25511 | 0.699535 | 0.349767 | − | 0.936837i | \(-0.386261\pi\) | ||||
0.349767 | + | 0.936837i | \(0.386261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.255105 | 0.0398407 | 0.0199204 | − | 0.999802i | \(-0.493659\pi\) | ||||
0.0199204 | + | 0.999802i | \(0.493659\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.16961 | 1.39835 | 0.699176 | − | 0.714950i | \(-0.253550\pi\) | ||||
0.699176 | + | 0.714950i | \(0.253550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.51021 | −0.657882 | −0.328941 | − | 0.944351i | \(-0.606692\pi\) | ||||
−0.328941 | + | 0.944351i | \(0.606692\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4247 | 2.34639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.32970 | 0.886335 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.93492 | −1.36467 | −0.682333 | − | 0.731041i | \(-0.739035\pi\) | ||||
−0.682333 | + | 0.731041i | \(0.739035\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.25511 | 0.304078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.58480 | −0.342366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1900 | 1.84738 | 0.923692 | − | 0.383136i | \(-0.125156\pi\) | ||||
0.923692 | + | 0.383136i | \(0.125156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.93492 | 1.27204 | 0.636018 | − | 0.771674i | \(-0.280580\pi\) | ||||
0.636018 | + | 0.771674i | \(0.280580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.83991 | −0.609771 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.1696 | −1.60892 | −0.804462 | − | 0.594004i | \(-0.797546\pi\) | ||||
−0.804462 | + | 0.594004i | \(0.797546\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.83991 | 0.582656 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.74489 | −0.681794 | −0.340897 | − | 0.940101i | \(-0.610731\pi\) | ||||
−0.340897 | + | 0.940101i | \(0.610731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.90499 | 0.340003 | 0.170001 | − | 0.985444i | \(-0.445623\pi\) | ||||
0.170001 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.9145 | −1.24382 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.74489 | 0.646351 | 0.323176 | − | 0.946339i | \(-0.395250\pi\) | ||||
0.323176 | + | 0.946339i | \(0.395250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1900 | 1.11850 | 0.559250 | − | 0.828999i | \(-0.311089\pi\) | ||||
0.559250 | + | 0.828999i | \(0.311089\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.32970 | 0.686552 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.09501 | 0.975088 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.74489 | 0.396958 | 0.198479 | − | 0.980105i | \(-0.436400\pi\) | ||||
0.198479 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.83991 | 0.507360 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.510210 | −0.0529063 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.58480 | −0.265195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5197 | −1.27119 | −0.635593 | − | 0.772025i | \(-0.719244\pi\) | ||||
−0.635593 | + | 0.772025i | \(0.719244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.25511 | 0.226647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.6052 | −1.75179 | −0.875893 | − | 0.482506i | \(-0.839727\pi\) | ||||
−0.875893 | + | 0.482506i | \(0.839727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1696 | −1.69177 | −0.845886 | − | 0.533364i | \(-0.820928\pi\) | ||||
−0.845886 | + | 0.533364i | \(0.820928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.83991 | −0.472327 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.91450 | 0.668450 | 0.334225 | − | 0.942493i | \(-0.391525\pi\) | ||||
0.334225 | + | 0.942493i | \(0.391525\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.41520 | 0.327117 | 0.163558 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163558 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.25511 | 0.403877 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.09501 | 0.479299 | 0.239649 | − | 0.970860i | \(-0.422968\pi\) | ||||
0.239649 | + | 0.970860i | \(0.422968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.83991 | 0.451324 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −30.6352 | −2.80832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.91450 | −0.537682 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.255105 | 0.0230020 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6594 | −1.12334 | −0.561670 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561670 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.16961 | 0.807339 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.7748 | −1.46562 | −0.732812 | − | 0.680431i | \(-0.761792\pi\) | ||||
−0.732812 | + | 0.680431i | \(0.761792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5102 | 1.08477 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.23468 | 0.444000 | 0.222000 | − | 0.975047i | \(-0.428741\pi\) | ||||
0.222000 | + | 0.975047i | \(0.428741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.51021 | −0.379828 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.25511 | −0.188581 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.09501 | 0.755300 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.4247 | 1.35469 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.74489 | 0.306794 | 0.153397 | − | 0.988165i | \(-0.450979\pi\) | ||||
0.153397 | + | 0.988165i | \(0.450979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3596 | 1.24995 | 0.624975 | − | 0.780645i | \(-0.285109\pi\) | ||||
0.624975 | + | 0.780645i | \(0.285109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.32970 | 0.511726 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.510210 | −0.0409811 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.979580 | 0.0781790 | 0.0390895 | − | 0.999236i | \(-0.487554\pi\) | ||||
0.0390895 | + | 0.999236i | \(0.487554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.93492 | −0.787891 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.4247 | −1.84613 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.42471 | 0.581548 | 0.290774 | − | 0.956792i | \(-0.406087\pi\) | ||||
0.290774 | + | 0.956792i | \(0.406087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.25511 | 0.175560 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.1696 | −1.63815 | −0.819077 | − | 0.573684i | \(-0.805514\pi\) | ||||
−0.819077 | + | 0.573684i | \(0.805514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.58480 | −0.197665 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.83991 | −0.365863 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.1900 | 1.06659 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.77483 | 0.655862 | 0.327931 | − | 0.944702i | \(-0.393649\pi\) | ||||
0.327931 | + | 0.944702i | \(0.393649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.1045 | 1.71735 | 0.858673 | − | 0.512524i | \(-0.171289\pi\) | ||||
0.858673 | + | 0.512524i | \(0.171289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.93492 | 0.734411 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.25511 | 0.312842 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2741 | 1.04383 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.83991 | −0.352052 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3596 | 1.40081 | 0.700407 | − | 0.713744i | \(-0.253002\pi\) | ||||
0.700407 | + | 0.713744i | \(0.253002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.18051 | 0.444883 | 0.222441 | − | 0.974946i | \(-0.428597\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8698 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.83039 | 0.200641 | 0.100321 | − | 0.994955i | \(-0.468013\pi\) | ||||
0.100321 | + | 0.994955i | \(0.468013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1696 | −0.928912 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −44.0190 | −3.08953 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.255105 | 0.0178173 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.83991 | 0.336397 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.82900 | −0.403201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.3392 | −1.53789 | −0.768947 | − | 0.639312i | \(-0.779219\pi\) | ||||
−0.768947 | + | 0.639312i | \(0.779219\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.74489 | −0.393634 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.16961 | 0.625362 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.46937 | 0.167632 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.90499 | 0.196301 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.32970 | −0.425782 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0950 | −1.54656 | −0.773278 | − | 0.634067i | \(-0.781384\pi\) | ||||
−0.773278 | + | 0.634067i | \(0.781384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.510210 | −0.0338638 | −0.0169319 | − | 0.999857i | \(-0.505390\pi\) | ||||
−0.0169319 | + | 0.999857i | \(0.505390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.09501 | −0.0723605 | −0.0361803 | − | 0.999345i | \(-0.511519\pi\) | ||||
−0.0361803 | + | 0.999345i | \(0.511519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9145 | −0.718121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.81949 | 0.119199 | 0.0595993 | − | 0.998222i | \(-0.481018\pi\) | ||||
0.0595993 | + | 0.998222i | \(0.481018\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.51021 | −0.294214 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.74489 | 0.373171 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.44513 | 0.546270 | 0.273135 | − | 0.961976i | \(-0.411939\pi\) | ||||
0.273135 | + | 0.961976i | \(0.411939\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3392 | 1.31016 | 0.655082 | − | 0.755558i | \(-0.272634\pi\) | ||||
0.655082 | + | 0.755558i | \(0.272634\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.4247 | 1.04934 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.58480 | 0.164467 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.1900 | 0.645767 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4342 | −1.10044 | −0.550219 | − | 0.835020i | \(-0.685456\pi\) | ||||
−0.550219 | + | 0.835020i | \(0.685456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9145 | 0.686189 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.32970 | 0.396381 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4342 | 0.962761 | 0.481380 | − | 0.876512i | \(-0.340136\pi\) | ||||
0.481380 | + | 0.876512i | \(0.340136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.5943 | −1.27967 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.09501 | 0.562967 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.90499 | −0.549105 | −0.274553 | − | 0.961572i | \(-0.588530\pi\) | ||||
−0.274553 | + | 0.961572i | \(0.588530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.93492 | −0.610297 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.74489 | 0.229184 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.5848 | −1.01119 | −0.505597 | − | 0.862770i | \(-0.668728\pi\) | ||||
−0.505597 | + | 0.862770i | \(0.668728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8290 | 1.08303 | 0.541517 | − | 0.840690i | \(-0.317850\pi\) | ||||
0.541517 | + | 0.840690i | \(0.317850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.83991 | 0.292925 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.25511 | 0.135988 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3801 | 1.34469 | 0.672344 | − | 0.740239i | \(-0.265288\pi\) | ||||
0.672344 | + | 0.740239i | \(0.265288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.510210 | −0.0305455 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1900 | −1.44306 | −0.721528 | − | 0.692385i | \(-0.756560\pi\) | ||||
−0.721528 | + | 0.692385i | \(0.756560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1900 | −1.55684 | −0.778418 | − | 0.627747i | \(-0.783977\pi\) | ||||
−0.778418 | + | 0.627747i | \(0.783977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.58480 | −0.153111 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.23468 | −0.0728811 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.0651 | 1.35677 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5197 | −0.733919 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.48979 | −0.320717 | −0.160358 | − | 0.987059i | \(-0.551265\pi\) | ||||
−0.160358 | + | 0.987059i | \(0.551265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1900 | 0.826175 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.25511 | 0.130854 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.83991 | −0.279899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −44.3801 | −2.55802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.6052 | −1.01139 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.93492 | 0.568872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.76532 | −0.386117 | −0.193058 | − | 0.981187i | \(-0.561841\pi\) | ||||
−0.193058 | + | 0.981187i | \(0.561841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.1696 | −0.976745 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.0204 | −0.965139 | −0.482570 | − | 0.875858i | \(-0.660297\pi\) | ||||
−0.482570 | + | 0.875858i | \(0.660297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8304 | 0.725217 | 0.362608 | − | 0.931942i | \(-0.381886\pi\) | ||||
0.362608 | + | 0.931942i | \(0.381886\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.83991 | −0.272698 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.4898 | −0.757662 | −0.378831 | − | 0.925466i | \(-0.623674\pi\) | ||||
−0.378831 | + | 0.925466i | \(0.623674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.5102 | 1.14835 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.91450 | 0.385930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.3610 | −0.910352 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.41520 | 0.188861 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.8290 | 1.20347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0746 | −0.773610 | −0.386805 | − | 0.922162i | \(-0.626421\pi\) | ||||
−0.386805 | + | 0.922162i | \(0.626421\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.25511 | 0.233178 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.1696 | −0.719532 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.6594 | −1.23434 | −0.617168 | − | 0.786831i | \(-0.711720\pi\) | ||||
−0.617168 | + | 0.786831i | \(0.711720\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.09501 | 0.276723 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.15058 | −0.0623073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.6147 | −2.46296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.83991 | 0.260572 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.59432 | −0.461367 | −0.230684 | − | 0.973029i | \(-0.574096\pi\) | ||||
−0.230684 | + | 0.973029i | \(0.574096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.9444 | −1.28172 | −0.640858 | − | 0.767659i | \(-0.721421\pi\) | ||||
−0.640858 | + | 0.767659i | \(0.721421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.74489 | −0.304907 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.6352 | −1.62138 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.80997 | −0.0955268 | −0.0477634 | − | 0.998859i | \(-0.515209\pi\) | ||||
−0.0477634 | + | 0.998859i | \(0.515209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3188 | −0.648358 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.91450 | −0.310431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.90499 | 0.152054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.16961 | 0.478650 | 0.239325 | − | 0.970940i | \(-0.423074\pi\) | ||||
0.239325 | + | 0.970940i | \(0.423074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.255105 | 0.0132802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.0841 | 2.49640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.8494 | −1.49377 | −0.746883 | − | 0.664955i | \(-0.768451\pi\) | ||||
−0.746883 | + | 0.664955i | \(0.768451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.09501 | −0.468417 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9444 | 1.12721 | 0.563605 | − | 0.826044i | \(-0.309414\pi\) | ||||
0.563605 | + | 0.826044i | \(0.309414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6594 | −0.648561 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.32018 | −0.322946 | −0.161473 | − | 0.986877i | \(-0.551625\pi\) | ||||
−0.161473 | + | 0.986877i | \(0.551625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9145 | −0.556254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.16961 | 0.466117 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6052 | −0.892620 | −0.446310 | − | 0.894878i | \(-0.647262\pi\) | ||||
−0.446310 | + | 0.894878i | \(0.647262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6352 | 1.54929 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.7748 | −0.846178 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.74489 | 0.289057 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0841 | −1.50988 | −0.754939 | − | 0.655795i | \(-0.772334\pi\) | ||||
−0.754939 | + | 0.655795i | \(0.772334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5102 | 0.626294 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5292 | 1.12506 | 0.562528 | − | 0.826778i | \(-0.309829\pi\) | ||||
0.562528 | + | 0.826778i | \(0.309829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.510210 | 0.0254154 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.59571 | 0.475642 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.1696 | 1.14566 | 0.572832 | − | 0.819673i | \(-0.305845\pi\) | ||||
0.572832 | + | 0.819673i | \(0.305845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −68.6784 | −3.37944 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1900 | 0.500209 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.23468 | 0.256344 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.56438 | 0.467251 | 0.233625 | − | 0.972327i | \(-0.424941\pi\) | ||||
0.233625 | + | 0.972327i | \(0.424941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.7952 | −1.74455 | −0.872277 | − | 0.489012i | \(-0.837357\pi\) | ||||
−0.872277 | + | 0.489012i | \(0.837357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.51021 | −0.219294 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.32970 | 0.307035 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.0841 | −2.32695 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.25511 | −0.108877 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3801 | 1.36702 | 0.683510 | − | 0.729942i | \(-0.260453\pi\) | ||||
0.683510 | + | 0.729942i | \(0.260453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6798 | 0.945752 | 0.472876 | − | 0.881129i | \(-0.343216\pi\) | ||||
0.472876 | + | 0.881129i | \(0.343216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.09501 | 0.436073 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.5102 | −0.598445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.7639 | 1.61146 | 0.805732 | − | 0.592280i | \(-0.201772\pi\) | ||||
0.805732 | + | 0.592280i | \(0.201772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.4247 | 0.782129 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1045 | 1.38280 | 0.691399 | − | 0.722473i | \(-0.256995\pi\) | ||||
0.691399 | + | 0.722473i | \(0.256995\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.74489 | 0.177525 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.74489 | 0.177127 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4642 | −1.06015 | −0.530075 | − | 0.847951i | \(-0.677836\pi\) | ||||
−0.530075 | + | 0.847951i | \(0.677836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.575289 | 0.0270893 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.3596 | 0.721659 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.83991 | 0.226898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.4993 | −0.537915 | −0.268957 | − | 0.963152i | \(-0.586679\pi\) | ||||
−0.268957 | + | 0.963152i | \(0.586679\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.32970 | 0.295445 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.7843 | 0.781725 | 0.390862 | − | 0.920449i | \(-0.372177\pi\) | ||||
0.390862 | + | 0.920449i | \(0.372177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6893 | 0.915041 | 0.457520 | − | 0.889199i | \(-0.348738\pi\) | ||||
0.457520 | + | 0.889199i | \(0.348738\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.510210 | −0.0236604 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.38387 | −0.0640379 | −0.0320190 | − | 0.999487i | \(-0.510194\pi\) | ||||
−0.0320190 | + | 0.999487i | \(0.510194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.7397 | 2.94323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.979580 | 0.0451367 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.6784 | 0.950795 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.58480 | −0.118599 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.93492 | −0.454889 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.9553 | 1.32300 | 0.661502 | − | 0.749944i | \(-0.269919\pi\) | ||||
0.661502 | + | 0.749944i | \(0.269919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.25511 | −0.194016 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.4247 | −1.06586 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.5197 | −0.568491 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.3705 | −1.19496 | −0.597482 | − | 0.801883i | \(-0.703832\pi\) | ||||
−0.597482 | + | 0.801883i | \(0.703832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.42471 | 0.335757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.05417 | 0.228092 | 0.114046 | − | 0.993475i | \(-0.463619\pi\) | ||||
0.114046 | + | 0.993475i | \(0.463619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 57.5687 | 2.59276 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.25511 | 0.101359 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.8048 | 1.24721 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7544 | −0.705264 | −0.352632 | − | 0.935762i | \(-0.614713\pi\) | ||||
−0.352632 | + | 0.935762i | \(0.614713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1696 | −0.945788 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.92541 | −0.442552 | −0.221276 | − | 0.975211i | \(-0.571022\pi\) | ||||
−0.221276 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6052 | −0.783422 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.4247 | −1.12693 | −0.563465 | − | 0.826140i | \(-0.690532\pi\) | ||||
−0.563465 | + | 0.826140i | \(0.690532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0599 | −0.621972 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.58480 | −0.114122 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.1696 | −0.756583 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1710 | −0.447320 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.5292 | −0.636538 | −0.318269 | − | 0.948001i | \(-0.603101\pi\) | ||||
−0.318269 | + | 0.948001i | \(0.603101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.83991 | −0.211231 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.22948 | −0.140678 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.424711 | 0.0184657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.1900 | 0.615795 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.255105 | −0.0110498 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.91450 | 0.298940 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.77483 | 0.378662 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.0394 | 1.59540 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.11543 | 0.262923 | 0.131462 | − | 0.991321i | \(-0.458033\pi\) | ||||
0.131462 | + | 0.991321i | \(0.458033\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.1045 | 0.991510 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.41520 | 0.146291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3596 | 0.656730 | 0.328365 | − | 0.944551i | \(-0.393502\pi\) | ||||
0.328365 | + | 0.944551i | \(0.393502\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.93492 | 0.424012 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.5088 | −1.00151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.8048 | −1.18238 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.25511 | 0.180619 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.3801 | −0.948273 | −0.474137 | − | 0.880451i | \(-0.657240\pi\) | ||||
−0.474137 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.16961 | −0.387833 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.2741 | 0.602654 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7449 | 0.747858 | 0.373929 | − | 0.927457i | \(-0.378010\pi\) | ||||
0.373929 | + | 0.927457i | \(0.378010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.09501 | 0.214349 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.83991 | −0.203257 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.0190 | −0.420020 | −0.210010 | − | 0.977699i | \(-0.567350\pi\) | ||||
−0.210010 | + | 0.977699i | \(0.567350\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6147 | −0.737154 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.3596 | 0.808760 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.83991 | 0.201838 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.3501 | −0.639034 | −0.319517 | − | 0.947581i | \(-0.603521\pi\) | ||||
−0.319517 | + | 0.947581i | \(0.603521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.18051 | 0.256853 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.3188 | −2.04609 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.4043 | −0.927891 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.4898 | 0.969527 | 0.484764 | − | 0.874645i | \(-0.338906\pi\) | ||||
0.484764 | + | 0.874645i | \(0.338906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31879 | 0.0543399 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.8698 | 0.899605 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.63898 | −0.231565 | −0.115782 | − | 0.993275i | \(-0.536938\pi\) | ||||
−0.115782 | + | 0.993275i | \(0.536938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.6352 | −1.25592 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.83039 | 0.115840 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0408 | −0.410258 | −0.205129 | − | 0.978735i | \(-0.565761\pi\) | ||||
−0.205129 | + | 0.978735i | \(0.565761\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.04466 | 0.205776 | 0.102888 | − | 0.994693i | \(-0.467192\pi\) | ||||
0.102888 | + | 0.994693i | \(0.467192\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.1696 | −0.536308 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.91450 | −0.240459 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.19003 | −0.0888904 | −0.0444452 | − | 0.999012i | \(-0.514152\pi\) | ||||
−0.0444452 | + | 0.999012i | \(0.514152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −44.0190 | −1.78374 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.51021 | 0.182464 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.4437 | 1.83546 | 0.917728 | − | 0.397210i | \(-0.130022\pi\) | ||||
0.917728 | + | 0.397210i | \(0.130022\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.255105 | 0.0102868 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.31879 | −0.294643 | −0.147322 | − | 0.989089i | \(-0.547065\pi\) | ||||
−0.147322 | + | 0.989089i | \(0.547065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6256 | 0.829015 | 0.414507 | − | 0.910046i | \(-0.363954\pi\) | ||||
0.414507 | + | 0.910046i | \(0.363954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.83991 | 0.194219 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.1249 | −0.726161 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.82900 | −0.232788 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.9335 | 1.07391 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.8304 | 0.590389 | 0.295194 | − | 0.955437i | \(-0.404616\pi\) | ||||
0.295194 | + | 0.955437i | \(0.404616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3392 | −0.887904 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.6594 | −0.502373 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.4247 | −0.650771 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.74489 | −0.227265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8494 | −1.13948 | −0.569742 | − | 0.821824i | \(-0.692957\pi\) | ||||
−0.569742 | + | 0.821824i | \(0.692957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.7449 | −1.17302 | −0.586512 | − | 0.809940i | \(-0.699499\pi\) | ||||
−0.586512 | + | 0.809940i | \(0.699499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.16961 | 0.361053 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.13967 | 0.0841192 | 0.0420596 | − | 0.999115i | \(-0.486608\pi\) | ||||
0.0420596 | + | 0.999115i | \(0.486608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000 | 1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.46937 | 0.0967822 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2104 | −0.516965 | −0.258482 | − | 0.966016i | \(-0.583222\pi\) | ||||
−0.258482 | + | 0.966016i | \(0.583222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.7748 | −0.655447 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.90499 | 0.113334 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −48.6447 | −1.89493 | −0.947464 | − | 0.319863i | \(-0.896363\pi\) | ||||
−0.947464 | + | 0.319863i | \(0.896363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7340 | −0.962041 | −0.481020 | − | 0.876709i | \(-0.659734\pi\) | ||||
−0.481020 | + | 0.876709i | \(0.659734\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.32970 | −0.245825 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.5102 | 0.485125 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.0190 | 1.70442 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.0950 | −0.892905 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4043 | 0.864908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6988 | 1.53028 | 0.765139 | − | 0.643865i | \(-0.222670\pi\) | ||||
0.765139 | + | 0.643865i | \(0.222670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5535 | 1.09740 | 0.548700 | − | 0.836020i | \(-0.315123\pi\) | ||||
0.548700 | + | 0.836020i | \(0.315123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 60.5943 | 2.32540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.510210 | −0.0195513 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.8508 | 0.606515 | 0.303257 | − | 0.952909i | \(-0.401926\pi\) | ||||
0.303257 | + | 0.952909i | \(0.401926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.09501 | −0.0417774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.93492 | 0.378490 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.6256 | −1.08897 | −0.544485 | − | 0.838770i | \(-0.683275\pi\) | ||||
−0.544485 | + | 0.838770i | \(0.683275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.9145 | −0.414608 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.23468 | 0.198563 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.61474 | 0.0611626 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.81949 | 0.0688194 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.58480 | −0.324244 | −0.162122 | − | 0.986771i | \(-0.551834\pi\) | ||||
−0.162122 | + | 0.986771i | \(0.551834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9986 | −0.414820 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.51021 | −0.169864 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 85.2077 | 3.20456 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.56438 | −0.133863 | −0.0669316 | − | 0.997758i | \(-0.521321\pi\) | ||||
−0.0669316 | + | 0.997758i | \(0.521321\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.74489 | 0.215450 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.46937 | −0.0924786 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.25511 | −0.0843361 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.44513 | 0.315389 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.1900 | 0.827548 | 0.413774 | − | 0.910380i | \(-0.364210\pi\) | ||||
0.413774 | + | 0.910380i | \(0.364210\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 83.0993 | 3.09478 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.3392 | 0.756423 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.09501 | 0.337780 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.82900 | 0.364538 | 0.182269 | − | 0.983249i | \(-0.441656\pi\) | ||||
0.182269 | + | 0.983249i | \(0.441656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.0408 | 2.14672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.0637 | −1.07349 | −0.536746 | − | 0.843744i | \(-0.680347\pi\) | ||||
−0.536746 | + | 0.843744i | \(0.680347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.4247 | 0.605835 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.6988 | −1.09397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.9240 | 1.06399 | 0.531994 | − | 0.846748i | \(-0.321443\pi\) | ||||
0.531994 | + | 0.846748i | \(0.321443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.58480 | 0.0949551 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.0190 | −0.734427 | −0.367213 | − | 0.930137i | \(-0.619688\pi\) | ||||
−0.367213 | + | 0.930137i | \(0.619688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.74489 | 0.137202 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.1900 | 0.372834 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.4656 | −1.22280 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2741 | −0.812795 | −0.406397 | − | 0.913696i | \(-0.633215\pi\) | ||||
−0.406397 | + | 0.913696i | \(0.633215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.4342 | −0.635339 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.3596 | 0.558994 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.1886 | −0.842805 | −0.421403 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421403 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9145 | 0.396171 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.5497 | 1.72367 | 0.861837 | − | 0.507186i | \(-0.169314\pi\) | ||||
0.861837 | + | 0.507186i | \(0.169314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.5292 | −0.598399 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.32970 | 0.228851 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.1900 | −0.512372 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8698 | −0.788647 | −0.394323 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394323 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.4342 | 0.555850 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.84942 | −0.318292 | −0.159146 | − | 0.987255i | \(-0.550874\pi\) | ||||
−0.159146 | + | 0.987255i | \(0.550874\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.510210 | −0.0183273 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.5943 | −0.738817 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.659396 | −0.0236253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9553 | −0.463579 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.09501 | 0.325029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.979580 | 0.0349627 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.02042 | 0.321543 | 0.160772 | − | 0.986992i | \(-0.448602\pi\) | ||||
0.160772 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.90499 | −0.317026 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.6594 | −0.876787 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.93492 | −0.352799 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.93492 | −0.352355 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.55487 | 0.338451 | 0.169225 | − | 0.985577i | \(-0.445873\pi\) | ||||
0.169225 | + | 0.985577i | \(0.445873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.5483 | −1.00997 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.74489 | 0.132319 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.55105 | 0.231182 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.4247 | −0.825613 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5848 | −0.583813 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.3596 | 1.87602 | 0.938012 | − | 0.346602i | \(-0.112664\pi\) | ||||
0.938012 | + | 0.346602i | \(0.112664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.9458 | 0.384360 | 0.192180 | − | 0.981360i | \(-0.438444\pi\) | ||||
0.192180 | + | 0.981360i | \(0.438444\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.8290 | 0.625290 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.42471 | 0.260076 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.7016 | −0.829215 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.83991 | 0.169120 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.6147 | 1.24296 | 0.621481 | − | 0.783429i | \(-0.286531\pi\) | ||||
0.621481 | + | 0.783429i | \(0.286531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1900 | 0.355202 | 0.177601 | − | 0.984103i | \(-0.443166\pi\) | ||||
0.177601 | + | 0.984103i | \(0.443166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.25511 | 0.0785127 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.0394 | −0.870707 | −0.435353 | − | 0.900260i | \(-0.643377\pi\) | ||||
−0.435353 | + | 0.900260i | \(0.643377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.3392 | −1.26211 | −0.631057 | − | 0.775737i | \(-0.717378\pi\) | ||||
−0.631057 | + | 0.775737i | \(0.717378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.3801 | 0.776355 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 103.963 | 3.60212 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1696 | −0.732604 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.510210 | −0.0176354 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.4043 | 1.32586 | 0.662932 | − | 0.748680i | \(-0.269312\pi\) | ||||
0.662932 | + | 0.748680i | \(0.269312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.7193 | 1.85239 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.1900 | −0.833149 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.6256 | 0.983589 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.1900 | −0.898839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.5943 | 0.705964 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7245 | 0.778071 | 0.389036 | − | 0.921223i | \(-0.372808\pi\) | ||||
0.389036 | + | 0.921223i | \(0.372808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.58480 | −0.0883984 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.3297 | −0.352856 | −0.176428 | − | 0.984314i | \(-0.556454\pi\) | ||||
−0.176428 | + | 0.984314i | \(0.556454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.40429 | 0.0820334 | 0.0410167 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410167 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.23468 | −0.0420779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.6798 | 0.601828 | 0.300914 | − | 0.953651i | \(-0.402708\pi\) | ||||
0.300914 | + | 0.953651i | \(0.402708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.0651 | 0.783331 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9553 | 0.439480 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1696 | 0.446235 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.5197 | −0.423728 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.83991 | −0.163619 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.7601 | 1.71405 | 0.857023 | − | 0.515277i | \(-0.172311\pi\) | ||||
0.857023 | + | 0.515277i | \(0.172311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.48979 | −0.185166 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.5905 | −1.67075 | −0.835373 | − | 0.549683i | \(-0.814748\pi\) | ||||
−0.835373 | + | 0.549683i | \(0.814748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3188 | 0.717434 | 0.358717 | − | 0.933446i | \(-0.383214\pi\) | ||||
0.358717 | + | 0.933446i | \(0.383214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1900 | 0.476993 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9891 | −0.570438 | −0.285219 | − | 0.958462i | \(-0.592066\pi\) | ||||
−0.285219 | + | 0.958462i | \(0.592066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 61.2703 | 2.05494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.25511 | 0.0755489 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.6580 | 0.390120 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.77483 | 0.293310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.83991 | −0.161600 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.64037 | −0.154765 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −62.8851 | −2.09500 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −44.3801 | −1.47688 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.1045 | 0.768020 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.6594 | −1.21726 | −0.608628 | − | 0.793456i | \(-0.708280\pi\) | ||||
−0.608628 | + | 0.793456i | \(0.708280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.6052 | −0.583928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.1900 | 0.735188 | 0.367594 | − | 0.929986i | \(-0.380182\pi\) | ||||
0.367594 | + | 0.929986i | \(0.380182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.9796 | 0.760513 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.93492 | 0.328438 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 81.1886 | 2.68108 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.5957 | 0.844325 | 0.422162 | − | 0.906520i | \(-0.361271\pi\) | ||||
0.422162 | + | 0.906520i | \(0.361271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76532 | −0.222925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.74489 | 0.189096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.25511 | 0.139907 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1696 | −0.563924 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.40568 | 0.308590 | 0.154295 | − | 0.988025i | \(-0.450689\pi\) | ||||
0.154295 | + | 0.988025i | \(0.450689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.4546 | −1.39139 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.0204 | −0.557224 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2741 | 0.466814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.7601 | 1.65826 | 0.829130 | − | 0.559056i | \(-0.188836\pi\) | ||||
0.829130 | + | 0.559056i | \(0.188836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.8304 | 0.418704 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.5943 | −0.997346 | −0.498673 | − | 0.866790i | \(-0.666179\pi\) | ||||
−0.498673 | + | 0.866790i | \(0.666179\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.23468 | 0.0402069 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.83991 | −0.157442 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.12877 | 0.231654 | 0.115827 | − | 0.993269i | \(-0.463048\pi\) | ||||
0.115827 | + | 0.993269i | \(0.463048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.90499 | −0.0942999 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.4898 | −0.437436 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.99049 | 0.129265 | 0.0646323 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646323 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3596 | 0.626463 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5102 | 0.663001 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.67982 | −0.312578 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7397 | −0.991603 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.91450 | 0.222817 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.18051 | 0.198958 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.4751 | 0.883539 | 0.441769 | − | 0.897129i | \(-0.354351\pi\) | ||||
0.441769 | + | 0.897129i | \(0.354351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.3610 | −0.525592 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5834 | 0.949377 | 0.474688 | − | 0.880154i | \(-0.342561\pi\) | ||||
0.474688 | + | 0.880154i | \(0.342561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.3354 | −0.812215 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.72066 | −0.0550487 | −0.0275243 | − | 0.999621i | \(-0.508762\pi\) | ||||
−0.0275243 | + | 0.999621i | \(0.508762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.44513 | 0.269908 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.41520 | 0.109039 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.8889 | 0.889517 | 0.444758 | − | 0.895651i | \(-0.353290\pi\) | ||||
0.444758 | + | 0.895651i | \(0.353290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8698 | 0.696831 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.8290 | 0.694825 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.3801 | 1.41120 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.6147 | 1.44900 | 0.724500 | − | 0.689275i | \(-0.242071\pi\) | ||||
0.724500 | + | 0.689275i | \(0.242071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.0746 | −0.446644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.83039 | 0.0897295 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.8290 | −0.627991 | −0.313995 | − | 0.949425i | \(-0.601668\pi\) | ||||
−0.313995 | + | 0.949425i | \(0.601668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.25511 | 0.134626 |
(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 | 1560.2.a.q.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 4680.2.a.bh.1.1 | 3 | |||
4.3 | odd | 2 | 3120.2.a.bi.1.3 | 3 | |||
5.4 | even | 2 | 7800.2.a.bi.1.3 | 3 | |||
12.11 | even | 2 | 9360.2.a.cy.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.q.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3120.2.a.bi.1.3 | 3 | 4.3 | odd | 2 | |||
4680.2.a.bh.1.1 | 3 | 3.2 | odd | 2 | |||
7800.2.a.bi.1.3 | 3 | 5.4 | even | 2 | |||
9360.2.a.cy.1.3 | 3 | 12.11 | even | 2 |