Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5700,2,Mod(3649,5700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5700.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5700.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(45.5147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.3 | ||
Root | \(-1.33641 + 1.33641i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5700.3649 |
Dual form | 5700.2.f.q.3649.4 |
$q$-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 \(\left(\mathbb{Z}/5700\mathbb{Z}\right)^\times\).
\(n\) | \(1901\) | \(2851\) | \(3877\) | \(4201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67282i | 1.76616i | 0.469221 | + | 0.883081i | \(0.344535\pi\) | ||||
−0.469221 | + | 0.883081i | \(0.655465\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.81681 | 1.75383 | 0.876917 | − | 0.480642i | \(-0.159596\pi\) | ||||
0.876917 | + | 0.480642i | \(0.159596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67282i | 0.741308i | 0.928771 | + | 0.370654i | \(0.120866\pi\) | ||||
−0.928771 | + | 0.370654i | \(0.879134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.48963i | − 1.57397i | −0.616974 | − | 0.786984i | \(-0.711642\pi\) | ||||
0.616974 | − | 0.786984i | \(-0.288358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.67282 | 1.01969 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.20166i | − 1.71016i | −0.518492 | − | 0.855082i | \(-0.673507\pi\) | ||||
0.518492 | − | 0.855082i | \(-0.326493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.81681 | 0.708764 | 0.354382 | − | 0.935101i | \(-0.384691\pi\) | ||||
0.354382 | + | 0.935101i | \(0.384691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.20166 | −1.11385 | −0.556926 | − | 0.830562i | \(-0.688019\pi\) | ||||
−0.556926 | + | 0.830562i | \(0.688019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.81681i | − 1.01258i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 12.0185i | − 1.97582i | −0.155014 | − | 0.987912i | \(-0.549542\pi\) | ||||
0.155014 | − | 0.987912i | \(-0.450458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.67282 | 0.427994 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.183190 | 0.0286094 | 0.0143047 | − | 0.999898i | \(-0.495447\pi\) | ||||
0.0143047 | + | 0.999898i | \(0.495447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.96080i | 1.06151i | 0.847525 | + | 0.530756i | \(0.178092\pi\) | ||||
−0.847525 | + | 0.530756i | \(0.821908\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.20166i | − 0.612875i | −0.951891 | − | 0.306438i | \(-0.900863\pi\) | ||||
0.951891 | − | 0.306438i | \(-0.0991371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.8353 | −2.11933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.48963 | −0.908731 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.7776i | − 1.48042i | −0.672377 | − | 0.740209i | \(-0.734727\pi\) | ||||
0.672377 | − | 0.740209i | \(-0.265273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.05767 | 0.918831 | 0.459415 | − | 0.888221i | \(-0.348059\pi\) | ||||
0.459415 | + | 0.888221i | \(0.348059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.14399 | 0.658620 | 0.329310 | − | 0.944222i | \(-0.393184\pi\) | ||||
0.329310 | + | 0.944222i | \(0.393184\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.67282i | − 0.588720i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6913i | 1.30615i | 0.757293 | + | 0.653075i | \(0.226521\pi\) | ||||
−0.757293 | + | 0.653075i | \(0.773479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.20166 | −0.987364 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0577 | 1.31230 | 0.656152 | − | 0.754629i | \(-0.272183\pi\) | ||||
0.656152 | + | 0.754629i | \(0.272183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.28797i | 0.501869i | 0.968004 | + | 0.250935i | \(0.0807379\pi\) | ||||
−0.968004 | + | 0.250935i | \(0.919262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.1809i | 3.09755i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.28797 | 0.707452 | 0.353726 | − | 0.935349i | \(-0.384914\pi\) | ||||
0.353726 | + | 0.935349i | \(0.384914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.14399i | − 0.125569i | −0.998027 | − | 0.0627844i | \(-0.980002\pi\) | ||||
0.998027 | − | 0.0627844i | \(-0.0199981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3.81681i | − 0.409205i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.81681 | 0.404581 | 0.202291 | − | 0.979326i | \(-0.435161\pi\) | ||||
0.202291 | + | 0.979326i | \(0.435161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4896 | −1.30927 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.20166i | 0.643082i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.67282i | − 0.677523i | −0.940872 | − | 0.338761i | \(-0.889992\pi\) | ||||
0.940872 | − | 0.338761i | \(-0.110008\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.81681 | −0.584611 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.654353 | 0.0651105 | 0.0325553 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325553 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.71203i | 0.168691i | 0.996437 | + | 0.0843455i | \(0.0268799\pi\) | ||||
−0.996437 | + | 0.0843455i | \(0.973120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.05767 | 0.867568 | 0.433784 | − | 0.901017i | \(-0.357178\pi\) | ||||
0.433784 | + | 0.901017i | \(0.357178\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0185 | −1.14074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.5473i | − 1.08628i | −0.839642 | − | 0.543140i | \(-0.817235\pi\) | ||||
0.839642 | − | 0.543140i | \(-0.182765\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.67282i | − 0.247103i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.3249 | 2.77988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.8353 | 2.07593 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.183190i | − 0.0165177i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.00000i | − 0.354943i | −0.984126 | − | 0.177471i | \(-0.943208\pi\) | ||||
0.984126 | − | 0.177471i | \(-0.0567917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.96080 | 0.612864 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.18319 | 0.190746 | 0.0953731 | − | 0.995442i | \(-0.469596\pi\) | ||||
0.0953731 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.67282i | 0.405185i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000i | 0.170872i | 0.996344 | + | 0.0854358i | \(0.0272282\pi\) | ||||
−0.996344 | + | 0.0854358i | \(0.972772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.36638 | 0.370351 | 0.185176 | − | 0.982705i | \(-0.440715\pi\) | ||||
0.185176 | + | 0.982705i | \(0.440715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.20166 | −0.353844 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5473i | 1.30013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.8353i | 1.22359i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.28797 | −0.351284 | −0.175642 | − | 0.984454i | \(-0.556200\pi\) | ||||
−0.175642 | + | 0.984454i | \(0.556200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8930 | 1.37473 | 0.687365 | − | 0.726313i | \(-0.258767\pi\) | ||||
0.687365 | + | 0.726313i | \(0.258767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.48963i | 0.524656i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3249i | 1.30287i | 0.758704 | + | 0.651435i | \(0.225833\pi\) | ||||
−0.758704 | + | 0.651435i | \(0.774167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7776 | −0.854720 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.3249 | 3.02043 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0185i | 1.41132i | 0.708553 | + | 0.705658i | \(0.249348\pi\) | ||||
−0.708553 | + | 0.705658i | \(0.750652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.14399i | − 0.552818i | −0.961040 | − | 0.276409i | \(-0.910856\pi\) | ||||
0.961040 | − | 0.276409i | \(-0.0891445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.85601 | 0.450463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4112i | 1.70389i | 0.523628 | + | 0.851947i | \(0.324578\pi\) | ||||
−0.523628 | + | 0.851947i | \(0.675422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 7.05767i | − 0.530487i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0369 | −1.19866 | −0.599329 | − | 0.800503i | \(-0.704566\pi\) | ||||
−0.599329 | + | 0.800503i | \(0.704566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9216 | −0.886125 | −0.443063 | − | 0.896491i | \(-0.646108\pi\) | ||||
−0.443063 | + | 0.896491i | \(0.646108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 5.14399i | − 0.380254i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 37.7490i | − 2.76048i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.67282 | −0.339898 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.47116 | 0.612952 | 0.306476 | − | 0.951878i | \(-0.400850\pi\) | ||||
0.306476 | + | 0.951878i | \(0.400850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7305i | 0.988343i | 0.869364 | + | 0.494171i | \(0.164528\pi\) | ||||
−0.869364 | + | 0.494171i | \(0.835472\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 19.4689i | − 1.38710i | −0.720408 | − | 0.693551i | \(-0.756045\pi\) | ||||
0.720408 | − | 0.693551i | \(-0.243955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.942326 | 0.0667997 | 0.0333998 | − | 0.999442i | \(-0.489367\pi\) | ||||
0.0333998 | + | 0.999442i | \(0.489367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6913 | 0.754106 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.8353i | 1.25179i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.20166i | 0.570055i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.81681 | 0.402357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.71203 | −0.393232 | −0.196616 | − | 0.980481i | \(-0.562995\pi\) | ||||
−0.196616 | + | 0.980481i | \(0.562995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 11.0577i | − 0.757659i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 28.9793i | − 1.96724i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.28797 | 0.289754 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3456 | 1.16679 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.71203i | 0.114646i | 0.998356 | + | 0.0573229i | \(0.0182565\pi\) | ||||
−0.998356 | + | 0.0573229i | \(0.981744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 0.452692i | − 0.0300462i | −0.999887 | − | 0.0150231i | \(-0.995218\pi\) | ||||
0.999887 | − | 0.0150231i | \(-0.00478218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1233 | 0.933291 | 0.466645 | − | 0.884444i | \(-0.345462\pi\) | ||||
0.466645 | + | 0.884444i | \(0.345462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.1809 | 1.78837 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7120i | 0.767280i | 0.923483 | + | 0.383640i | \(0.125330\pi\) | ||||
−0.923483 | + | 0.383640i | \(0.874670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6.28797i | − 0.408448i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4874 | −1.64864 | −0.824321 | − | 0.566123i | \(-0.808443\pi\) | ||||
−0.824321 | + | 0.566123i | \(0.808443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.67282i | 0.170068i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.14399 | −0.0724972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.12552 | 0.197281 | 0.0986404 | − | 0.995123i | \(-0.468551\pi\) | ||||
0.0986404 | + | 0.995123i | \(0.468551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 47.7075i | − 2.99935i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 14.5680i | − 0.908729i | −0.890816 | − | 0.454365i | \(-0.849866\pi\) | ||||
0.890816 | − | 0.454365i | \(-0.150134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 56.1602 | 3.48962 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.81681 | −0.236255 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5.54731i | − 0.342062i | −0.985266 | − | 0.171031i | \(-0.945290\pi\) | ||||
0.985266 | − | 0.171031i | \(-0.0547098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.81681i | − 0.233585i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.1625 | −1.77807 | −0.889033 | − | 0.457843i | \(-0.848622\pi\) | ||||
−0.889033 | + | 0.457843i | \(0.848622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.92159 | 0.116728 | 0.0583642 | − | 0.998295i | \(-0.481412\pi\) | ||||
0.0583642 | + | 0.998295i | \(0.481412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.4896i | 0.755907i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 26.9793i | − 1.62103i | −0.585720 | − | 0.810514i | \(-0.699188\pi\) | ||||
0.585720 | − | 0.810514i | \(-0.300812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.20166 | 0.371284 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.39276 | 0.262050 | 0.131025 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131025 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.8824i | 1.47910i | 0.673099 | + | 0.739552i | \(0.264963\pi\) | ||||
−0.673099 | + | 0.739552i | \(0.735037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.856013i | 0.0505289i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.1153 | −1.47737 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.67282 | −0.391168 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.83528i | − 0.107218i | −0.998562 | − | 0.0536091i | \(-0.982927\pi\) | ||||
0.998562 | − | 0.0536091i | \(-0.0170725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.81681i | 0.337526i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.9216 | 1.26776 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.5266 | −1.87480 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 0.654353i | − 0.0375916i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 12.3664i | − 0.705787i | −0.935664 | − | 0.352893i | \(-0.885198\pi\) | ||||
0.935664 | − | 0.352893i | \(-0.114802\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.71203 | 0.0973938 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.79608 | −0.385370 | −0.192685 | − | 0.981261i | \(-0.561720\pi\) | ||||
−0.192685 | + | 0.981261i | \(0.561720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5.23030i | − 0.295634i | −0.989015 | − | 0.147817i | \(-0.952775\pi\) | ||||
0.989015 | − | 0.147817i | \(-0.0472247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.7569i | 1.78364i | 0.452387 | + | 0.891822i | \(0.350573\pi\) | ||||
−0.452387 | + | 0.891822i | \(0.649427\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.2017 | 1.24305 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.48963i | − 0.361093i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 9.05767i | − 0.500891i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.6336 | 1.08244 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8930 | 0.708661 | 0.354330 | − | 0.935120i | \(-0.384709\pi\) | ||||
0.354330 | + | 0.935120i | \(0.384709\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0185i | 0.658608i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 24.2280i | − 1.31979i | −0.751360 | − | 0.659893i | \(-0.770602\pi\) | ||||
0.751360 | − | 0.659893i | \(-0.229398\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.5473 | −0.627164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.0739 | −1.95351 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 36.6129i | − 1.97691i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.45269i | − 0.346399i | −0.984887 | − | 0.173199i | \(-0.944590\pi\) | ||||
0.984887 | − | 0.173199i | \(-0.0554105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3087 | −0.605341 | −0.302671 | − | 0.953095i | \(-0.597878\pi\) | ||||
−0.302671 | + | 0.953095i | \(0.597878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.67282 | −0.142665 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.6913i | 1.73998i | 0.493068 | + | 0.869991i | \(0.335876\pi\) | ||||
−0.493068 | + | 0.869991i | \(0.664124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 30.3249i | − 1.60496i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.04711 | −0.266376 | −0.133188 | − | 0.991091i | \(-0.542521\pi\) | ||||
−0.133188 | + | 0.991091i | \(0.542521\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 22.8353i | − 1.19854i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 34.2280i | − 1.78669i | −0.449372 | − | 0.893345i | \(-0.648352\pi\) | ||||
0.449372 | − | 0.893345i | \(-0.351648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.183190 | −0.00953648 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 50.3619 | 2.61466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 26.3064i | − 1.36210i | −0.732239 | − | 0.681048i | \(-0.761524\pi\) | ||||
0.732239 | − | 0.681048i | \(-0.238476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2017i | 0.525412i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.6050 | 1.98300 | 0.991502 | − | 0.130089i | \(-0.0415262\pi\) | ||||
0.991502 | + | 0.130089i | \(0.0415262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 8.40332i | − 0.429390i | −0.976681 | − | 0.214695i | \(-0.931124\pi\) | ||||
0.976681 | − | 0.214695i | \(-0.0688757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6.96080i | − 0.353837i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2880 | −0.623025 | −0.311512 | − | 0.950242i | \(-0.600836\pi\) | ||||
−0.311512 | + | 0.950242i | \(0.600836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.2258 | −2.69174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 2.18319i | − 0.110127i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.6498i | 1.73903i | 0.493911 | + | 0.869513i | \(0.335567\pi\) | ||||
−0.493911 | + | 0.869513i | \(0.664433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.67282 | 0.233934 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.73840 | −0.286562 | −0.143281 | − | 0.989682i | \(-0.545765\pi\) | ||||
−0.143281 | + | 0.989682i | \(0.545765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16.5759i | − 0.825707i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 69.9092i | − 3.46527i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.9009 | −1.42906 | −0.714528 | − | 0.699607i | \(-0.753358\pi\) | ||||
−0.714528 | + | 0.699607i | \(0.753358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.9793i | 1.62280i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 4.36638i | − 0.213823i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.87448 | 0.238134 | 0.119067 | − | 0.992886i | \(-0.462010\pi\) | ||||
0.119067 | + | 0.992886i | \(0.462010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.20166i | 0.204292i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0369i | 1.16323i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.5473 | 0.750631 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6544 | 0.513202 | 0.256601 | − | 0.966517i | \(-0.417397\pi\) | ||||
0.256601 | + | 0.966517i | \(0.417397\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.88239i | 0.330747i | 0.986231 | + | 0.165373i | \(0.0528829\pi\) | ||||
−0.986231 | + | 0.165373i | \(0.947117\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.20166i | − 0.392339i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.0739 | −1.91262 | −0.956311 | − | 0.292351i | \(-0.905562\pi\) | ||||
−0.956311 | + | 0.292351i | \(0.905562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8353 | 0.706442 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8930i | 1.46777i | 0.679274 | + | 0.733884i | \(0.262295\pi\) | ||||
−0.679274 | + | 0.733884i | \(0.737705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.28797i | 0.202814i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7961 | 0.603884 | 0.301942 | − | 0.953326i | \(-0.402365\pi\) | ||||
0.301942 | + | 0.953326i | \(0.402365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06558 | 0.0501762 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 16.8930i | − 0.793700i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.3249i | 1.32498i | 0.749069 | + | 0.662492i | \(0.230501\pi\) | ||||
−0.749069 | + | 0.662492i | \(0.769499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.48963 | 0.302910 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.42405 | 0.0663248 | 0.0331624 | − | 0.999450i | \(-0.489442\pi\) | ||||
0.0331624 | + | 0.999450i | \(0.489442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 31.7305i | − 1.47464i | −0.675543 | − | 0.737321i | \(-0.736091\pi\) | ||||
0.675543 | − | 0.737321i | \(-0.263909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 14.4896i | − 0.670500i | −0.942129 | − | 0.335250i | \(-0.891179\pi\) | ||||
0.942129 | − | 0.335250i | \(-0.108821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.9585 | −2.30687 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.3249 | 0.752212 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.4896i | 1.86172i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7776i | 0.493473i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.1994 | 1.42554 | 0.712768 | − | 0.701399i | \(-0.247441\pi\) | ||||
0.712768 | + | 0.701399i | \(0.247441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.1233 | 1.46469 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 38.3249i | − 1.74384i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.3249i | 1.73667i | 0.495980 | + | 0.868334i | \(0.334809\pi\) | ||||
−0.495980 | + | 0.868334i | \(0.665191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0185 | 0.814823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1625 | 0.684272 | 0.342136 | − | 0.939650i | \(-0.388850\pi\) | ||||
0.342136 | + | 0.939650i | \(0.388850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 24.7697i | − 1.11557i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 51.6706i | 2.31774i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.9009 | 1.20425 | 0.602124 | − | 0.798403i | \(-0.294321\pi\) | ||||
0.602124 | + | 0.798403i | \(0.294321\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.14399 | −0.319170 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 34.8560i | − 1.55415i | −0.629406 | − | 0.777076i | \(-0.716702\pi\) | ||||
0.629406 | − | 0.777076i | \(-0.283298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 5.85601i | − 0.260075i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7591 | 0.565539 | 0.282769 | − | 0.959188i | \(-0.408747\pi\) | ||||
0.282769 | + | 0.959188i | \(0.408747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0369 | −0.886382 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 24.4403i | − 1.07488i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.4112 | 0.983744 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.52884 | 0.242223 | 0.121111 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121111 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 11.0577i | − 0.483518i | −0.970336 | − | 0.241759i | \(-0.922276\pi\) | ||||
0.970336 | − | 0.241759i | \(-0.0777244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.2465i | 1.75317i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.2672 | −1.92466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.05767 | −0.306277 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.489634i | 0.0212084i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.0369i | 0.692045i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −86.2940 | −3.71695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9585 | −1.03006 | −0.515029 | − | 0.857173i | \(-0.672219\pi\) | ||||
−0.515029 | + | 0.857173i | \(0.672219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.9216i | 0.511605i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.209567i | 0.00896042i | 0.999990 | + | 0.00448021i | \(0.00142610\pi\) | ||||
−0.999990 | + | 0.00448021i | \(0.998574\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.14399 | −0.219540 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.81681 | 0.162602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.3826i | 1.24947i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 14.9793i | − 0.634692i | −0.948310 | − | 0.317346i | \(-0.897208\pi\) | ||||
0.948310 | − | 0.317346i | \(-0.102792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.6050 | −0.786907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.7490 | −1.59376 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 16.6992i | − 0.703787i | −0.936040 | − | 0.351894i | \(-0.885538\pi\) | ||||
0.936040 | − | 0.351894i | \(-0.114462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.67282i | 0.196240i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.5450 | −1.44820 | −0.724102 | − | 0.689693i | \(-0.757745\pi\) | ||||
−0.724102 | + | 0.689693i | \(0.757745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.92159 | −0.247811 | −0.123905 | − | 0.992294i | \(-0.539542\pi\) | ||||
−0.123905 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 8.47116i | − 0.353888i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.6544i | 1.02637i | 0.858277 | + | 0.513187i | \(0.171535\pi\) | ||||
−0.858277 | + | 0.513187i | \(0.828465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.7305 | 0.570620 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.34565 | 0.221775 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 62.6913i | − 2.59641i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2017i | 0.503616i | 0.967777 | + | 0.251808i | \(0.0810252\pi\) | ||||
−0.967777 | + | 0.251808i | \(0.918975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.20166 | −0.255535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.4689 | −0.800844 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.02073i | 0.0419164i | 0.999780 | + | 0.0209582i | \(0.00667170\pi\) | ||||
−0.999780 | + | 0.0209582i | \(0.993328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.942326i | − 0.0385668i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.42405 | −0.303339 | −0.151669 | − | 0.988431i | \(-0.548465\pi\) | ||||
−0.151669 | + | 0.988431i | \(0.548465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3456 | 0.789125 | 0.394563 | − | 0.918869i | \(-0.370896\pi\) | ||||
0.394563 | + | 0.918869i | \(0.370896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10.6913i | − 0.435383i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.0369i | − 0.650919i | −0.945556 | − | 0.325460i | \(-0.894481\pi\) | ||||
0.945556 | − | 0.325460i | \(-0.105519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.8353 | 0.722722 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.2303 | 0.454329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1523i | 1.46018i | 0.683352 | + | 0.730089i | \(0.260521\pi\) | ||||
−0.683352 | + | 0.730089i | \(0.739479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 40.4482i | − 1.62838i | −0.580597 | − | 0.814191i | \(-0.697181\pi\) | ||||
0.580597 | − | 0.814191i | \(-0.302819\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.19376 | 0.168561 | 0.0842806 | − | 0.996442i | \(-0.473141\pi\) | ||||
0.0842806 | + | 0.996442i | \(0.473141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.20166 | 0.329121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.8353i | 0.714555i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5.81681i | − 0.232301i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −77.9955 | −3.10988 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.30871 | 0.211336 | 0.105668 | − | 0.994401i | \(-0.466302\pi\) | ||||
0.105668 | + | 0.994401i | \(0.466302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.71203i | 0.227033i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 39.6521i | − 1.57107i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0577 | −0.437435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.24086 | −0.285997 | −0.142998 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142998 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.38485i | − 0.0940493i | −0.998894 | − | 0.0470247i | \(-0.985026\pi\) | ||||
0.998894 | − | 0.0470247i | \(-0.0149739\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.47342i | 0.0579263i | 0.999580 | + | 0.0289631i | \(0.00922054\pi\) | ||||
−0.999580 | + | 0.0289631i | \(0.990779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.0532 | 1.61148 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.9793 | −1.13579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9137i | 1.01408i | 0.861922 | + | 0.507040i | \(0.169261\pi\) | ||||
−0.861922 | + | 0.507040i | \(0.830739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 4.28797i | − 0.167290i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.9793 | 0.973054 | 0.486527 | − | 0.873666i | \(-0.338264\pi\) | ||||
0.486527 | + | 0.873666i | \(0.338264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.4195 | 1.53324 | 0.766621 | − | 0.642100i | \(-0.221937\pi\) | ||||
0.766621 | + | 0.642100i | \(0.221937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 17.3456i | − 0.673649i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 31.3042i | − 1.21210i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.71203 | 0.0661908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.9216 | 1.15511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 12.0185i | − 0.463278i | −0.972802 | − | 0.231639i | \(-0.925591\pi\) | ||||
0.972802 | − | 0.231639i | \(-0.0744088\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.2017i | 0.853279i | 0.904422 | + | 0.426640i | \(0.140303\pi\) | ||||
−0.904422 | + | 0.426640i | \(0.859697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.1809 | 1.19661 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.452692 | −0.0173472 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0739i | 1.22727i | 0.789589 | + | 0.613637i | \(0.210294\pi\) | ||||
−0.789589 | + | 0.613637i | \(0.789706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 14.1233i | − 0.538836i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.8066 | 1.09745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0369 | 1.67524 | 0.837622 | − | 0.546250i | \(-0.183945\pi\) | ||||
0.837622 | + | 0.546250i | \(0.183945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 27.1809i | − 1.03252i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.18883i | − 0.0450303i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.7120 | 0.442990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.9793 | −0.716837 | −0.358419 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358419 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 12.0185i | − 0.453285i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.05767i | 0.114996i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.12325 | 0.0797405 | 0.0398702 | − | 0.999205i | \(-0.487306\pi\) | ||||
0.0398702 | + | 0.999205i | \(0.487306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.28797 | −0.235817 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.8639i | 1.90487i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.4874i | 0.951843i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5658 | 0.431331 | 0.215665 | − | 0.976467i | \(-0.430808\pi\) | ||||
0.215665 | + | 0.976467i | \(0.430808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 14.0000i | − 0.520666i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3064i | 1.19818i | 0.800682 | + | 0.599090i | \(0.204471\pi\) | ||||
−0.800682 | + | 0.599090i | \(0.795529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.1730 | 1.67078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18.4033i | − 0.679742i | −0.940472 | − | 0.339871i | \(-0.889617\pi\) | ||||
0.940472 | − | 0.339871i | \(-0.110383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 62.1892i | 2.29077i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.67282 | 0.0981886 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 33.5552i | − 1.23102i | −0.788129 | − | 0.615511i | \(-0.788950\pi\) | ||||
0.788129 | − | 0.615511i | \(-0.211050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.14399i | 0.0418563i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.06558 | 0.330808 | 0.165404 | − | 0.986226i | \(-0.447107\pi\) | ||||
0.165404 | + | 0.986226i | \(0.447107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 3.12552i | − 0.113900i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.1316i | 1.78572i | 0.450337 | + | 0.892858i | \(0.351304\pi\) | ||||
−0.450337 | + | 0.892858i | \(0.648696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −47.7075 | −1.73167 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4033 | −0.957120 | −0.478560 | − | 0.878055i | \(-0.658841\pi\) | ||||
−0.478560 | + | 0.878055i | \(0.658841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.3249i | 1.53226i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.8639i | 0.681137i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.6913 | −0.601903 | −0.300952 | − | 0.953639i | \(-0.597304\pi\) | ||||
−0.300952 | + | 0.953639i | \(0.597304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.5680 | −0.524655 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 37.8722i | − 1.36217i | −0.732205 | − | 0.681085i | \(-0.761509\pi\) | ||||
0.732205 | − | 0.681085i | \(-0.238491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 56.1602i | − 2.01474i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.183190 | 0.00656345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.3204 | 2.30156 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.81681i | 0.136402i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14.4817i | − 0.516218i | −0.966116 | − | 0.258109i | \(-0.916901\pi\) | ||||
0.966116 | − | 0.258109i | \(-0.0830993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.54731 | −0.197489 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.9585 | 1.91854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.7490i | 0.488240i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 42.6419i | − 1.51045i | −0.655463 | − | 0.755227i | \(-0.727527\pi\) | ||||
0.655463 | − | 0.755227i | \(-0.272473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2672 | −0.964646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.81681 | −0.134860 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.9423i | 0.880196i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.1625i | 1.02657i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.6706 | 1.46506 | 0.732529 | − | 0.680735i | \(-0.238340\pi\) | ||||
0.732529 | + | 0.680735i | \(0.238340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.9585 | 1.89474 | 0.947370 | − | 0.320140i | \(-0.103730\pi\) | ||||
0.947370 | + | 0.320140i | \(0.103730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.92159i | − 0.0673932i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.96080i | 0.243527i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.4896 | 0.436423 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.74897 | 0.270441 | 0.135220 | − | 0.990816i | \(-0.456826\pi\) | ||||
0.135220 | + | 0.990816i | \(0.456826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.0554i | 1.32653i | 0.748385 | + | 0.663264i | \(0.230829\pi\) | ||||
−0.748385 | + | 0.663264i | \(0.769171\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 48.9299i | − 1.70146i | −0.525604 | − | 0.850730i | \(-0.676160\pi\) | ||||
0.525604 | − | 0.850730i | \(-0.323840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0369 | 0.626449 | 0.313224 | − | 0.949679i | \(-0.398591\pi\) | ||||
0.313224 | + | 0.949679i | \(0.398591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9793 | −0.935900 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 96.2755i | 3.33575i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.20166i | − 0.214361i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0577 | −0.934135 | −0.467067 | − | 0.884222i | \(-0.654689\pi\) | ||||
−0.467067 | + | 0.884222i | \(0.654689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4320 | −0.497654 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4.39276i | − 0.151295i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 106.705i | 3.66644i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.8824 | 0.853961 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −98.5714 | −3.37898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.6336i | 1.42551i | 0.701414 | + | 0.712754i | \(0.252552\pi\) | ||||
−0.701414 | + | 0.712754i | \(0.747448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.8722i | 1.56697i | 0.621414 | + | 0.783483i | \(0.286559\pi\) | ||||
−0.621414 | + | 0.783483i | \(0.713441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.5187 | −1.04128 | −0.520642 | − | 0.853775i | \(-0.674307\pi\) | ||||
−0.520642 | + | 0.853775i | \(0.674307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.856013 | 0.0291729 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 7.42405i | − 0.252718i | −0.991985 | − | 0.126359i | \(-0.959671\pi\) | ||||
0.991985 | − | 0.126359i | \(-0.0403291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.1153i | 0.852962i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.5759 | 1.24075 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.5759 | −0.968259 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.67282i | 0.225841i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 24.0554i | − 0.812294i | −0.913808 | − | 0.406147i | \(-0.866872\pi\) | ||||
0.913808 | − | 0.406147i | \(-0.133128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.83528 | −0.0619025 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.481728 | −0.0162298 | −0.00811492 | − | 0.999967i | \(-0.502583\pi\) | ||||
−0.00811492 | + | 0.999967i | \(0.502583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 25.4056i | − 0.854966i | −0.904023 | − | 0.427483i | \(-0.859400\pi\) | ||||
0.904023 | − | 0.427483i | \(-0.140600\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.2307i | 0.947894i | 0.880553 | + | 0.473947i | \(0.157171\pi\) | ||||
−0.880553 | + | 0.473947i | \(0.842829\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6913 | 0.626886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.81681 | 0.194870 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.20166i | − 0.140603i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 21.9216i | − 0.731941i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.6706 | −0.789457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.9427 | −2.33013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.5266i | 1.08242i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 37.1888i | − 1.23483i | −0.786636 | − | 0.617417i | \(-0.788179\pi\) | ||||
0.786636 | − | 0.617417i | \(-0.211821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.654353 | −0.0217035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.5187 | 0.613551 | 0.306775 | − | 0.951782i | \(-0.400750\pi\) | ||||
0.306775 | + | 0.951782i | \(0.400750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6.65435i | − 0.220227i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2017i | 0.336889i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.3294 | −0.406711 | −0.203355 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203355 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.3664 | −0.407486 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5552i | 0.972822i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.71203i | − 0.0562303i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.67508 | 0.251811 | 0.125906 | − | 0.992042i | \(-0.459816\pi\) | ||||
0.125906 | + | 0.992042i | \(0.459816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.8353 | −0.486207 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.79608i | 0.222494i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 9.05767i | − 0.295901i | −0.988995 | − | 0.147951i | \(-0.952732\pi\) | ||||
0.988995 | − | 0.147951i | \(-0.0472677\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.23030 | −0.170684 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.2201 | −1.83272 | −0.916362 | − | 0.400351i | \(-0.868888\pi\) | ||||
−0.916362 | + | 0.400351i | \(0.868888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.50246i | − 0.0489268i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 33.2179i | − 1.07944i | −0.841846 | − | 0.539718i | \(-0.818531\pi\) | ||||
0.841846 | − | 0.539718i | \(-0.181469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4610 | −0.372040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.7569 | 1.02979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 6.81455i | − 0.220745i | −0.993890 | − | 0.110372i | \(-0.964796\pi\) | ||||
0.993890 | − | 0.110372i | \(-0.0352044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 22.2017i | − 0.717678i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.34565 | −0.301787 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.46060 | 0.240664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2857i | 1.45629i | 0.685423 | + | 0.728145i | \(0.259617\pi\) | ||||
−0.685423 | + | 0.728145i | \(0.740383\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.48963 | −0.208477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0207 | 0.482038 | 0.241019 | − | 0.970520i | \(-0.422518\pi\) | ||||
0.241019 | + | 0.970520i | \(0.422518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4033i | 0.654100i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.77761i | 0.216835i | 0.994105 | + | 0.108417i | \(0.0345783\pi\) | ||||
−0.994105 | + | 0.108417i | \(0.965422\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2017 | 0.709568 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.05767 | −0.289189 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 33.1025i | − 1.05581i | −0.849305 | − | 0.527903i | \(-0.822978\pi\) | ||||
0.849305 | − | 0.527903i | \(-0.177022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 19.6336i | − 0.624945i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.0901 | 1.81536 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2672 | −1.50149 | −0.750747 | − | 0.660590i | \(-0.770306\pi\) | ||||
−0.750747 | + | 0.660590i | \(0.770306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 12.8930i | − 0.409146i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.09422i | 0.129665i | 0.997896 | + | 0.0648326i | \(0.0206513\pi\) | ||||
−0.997896 | + | 0.0648326i | \(0.979349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0185 | 0.380248 |
(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 | 5700.2.f.q.3649.3 | 6 | ||
5.2 | odd | 4 | 5700.2.a.w.1.1 | 3 | |||
5.3 | odd | 4 | 1140.2.a.g.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 5700.2.f.q.3649.4 | 6 | ||
15.8 | even | 4 | 3420.2.a.m.1.3 | 3 | |||
20.3 | even | 4 | 4560.2.a.br.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.g.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
3420.2.a.m.1.3 | 3 | 15.8 | even | 4 | |||
4560.2.a.br.1.1 | 3 | 20.3 | even | 4 | |||
5700.2.a.w.1.1 | 3 | 5.2 | odd | 4 | |||
5700.2.f.q.3649.3 | 6 | 1.1 | even | 1 | trivial | ||
5700.2.f.q.3649.4 | 6 | 5.4 | even | 2 | inner |