Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,2,Mod(2351,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3920.2351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3013575923\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2351.7 | ||
Root | \(0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.2351 |
Dual form | 3920.2.k.a.2351.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3920\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1471\) | \(3041\) | \(3137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.26197 | 1.30595 | 0.652975 | − | 0.757379i | \(-0.273521\pi\) | ||||
0.652975 | + | 0.757379i | \(0.273521\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.11652 | 0.705507 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.28130i | 0.386328i | 0.981166 | + | 0.193164i | \(0.0618749\pi\) | ||||
−0.981166 | + | 0.193164i | \(0.938125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.26197i | 0.627358i | 0.949529 | + | 0.313679i | \(0.101562\pi\) | ||||
−0.949529 | + | 0.313679i | \(0.898438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2.26197i | − 0.584039i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 0.0698487i | − 0.0169408i | −0.999964 | − | 0.00847040i | \(-0.997304\pi\) | ||||
0.999964 | − | 0.00847040i | \(-0.00269625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44834 | 0.561688 | 0.280844 | − | 0.959753i | \(-0.409386\pi\) | ||||
0.280844 | + | 0.959753i | \(0.409386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.21824i | 0.462536i | 0.972890 | + | 0.231268i | \(0.0742874\pi\) | ||||
−0.972890 | + | 0.231268i | \(0.925713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.99841 | −0.384594 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.98361 | 0.368347 | 0.184174 | − | 0.982894i | \(-0.441039\pi\) | ||||
0.184174 | + | 0.982894i | \(0.441039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.31703 | 1.13457 | 0.567286 | − | 0.823521i | \(-0.307994\pi\) | ||||
0.567286 | + | 0.823521i | \(0.307994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.89828i | 0.504525i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48822 | 1.39546 | 0.697728 | − | 0.716363i | \(-0.254195\pi\) | ||||
0.697728 | + | 0.716363i | \(0.254195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.11652i | 0.819299i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.20692i | 0.657011i | 0.944502 | + | 0.328505i | \(0.106545\pi\) | ||||
−0.944502 | + | 0.328505i | \(0.893455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.01095i | − 0.764163i | −0.924129 | − | 0.382081i | \(-0.875207\pi\) | ||||
0.924129 | − | 0.382081i | \(-0.124793\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.11652i | − 0.315512i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.6211 | 1.54925 | 0.774626 | − | 0.632420i | \(-0.217938\pi\) | ||||
0.774626 | + | 0.632420i | \(0.217938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.157996i | − 0.0221239i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.01480 | 0.551475 | 0.275737 | − | 0.961233i | \(-0.411078\pi\) | ||||
0.275737 | + | 0.961233i | \(0.411078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.28130 | 0.172771 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.53808 | 0.733537 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.89149 | 0.897195 | 0.448598 | − | 0.893734i | \(-0.351924\pi\) | ||||
0.448598 | + | 0.893734i | \(0.351924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.73925i | 0.862872i | 0.902144 | + | 0.431436i | \(0.141993\pi\) | ||||
−0.902144 | + | 0.431436i | \(0.858007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26197 | 0.280563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1519i | 1.36242i | 0.732089 | + | 0.681209i | \(0.238545\pi\) | ||||
−0.732089 | + | 0.681209i | \(0.761455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.01761i | 0.604049i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 14.5335i | − 1.72481i | −0.506215 | − | 0.862407i | \(-0.668956\pi\) | ||||
0.506215 | − | 0.862407i | \(-0.331044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11.8490i | − 1.38682i | −0.720544 | − | 0.693409i | \(-0.756108\pi\) | ||||
0.720544 | − | 0.693409i | \(-0.243892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.26197 | −0.261190 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.86709i | 0.660099i | 0.943964 | + | 0.330050i | \(0.107065\pi\) | ||||
−0.943964 | + | 0.330050i | \(0.892935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8699 | −1.20777 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.79655 | −0.636254 | −0.318127 | − | 0.948048i | \(-0.603054\pi\) | ||||
−0.318127 | + | 0.948048i | \(0.603054\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0698487 | −0.00757616 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.48687 | 0.481043 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.5854i | 1.86405i | 0.362394 | + | 0.932025i | \(0.381959\pi\) | ||||
−0.362394 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.2889 | 1.48169 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 2.44834i | − 0.251195i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 7.06081i | − 0.716916i | −0.933546 | − | 0.358458i | \(-0.883303\pi\) | ||||
0.933546 | − | 0.358458i | \(-0.116697\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.71191i | 0.272557i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.98226i | − 0.595257i | −0.954682 | − | 0.297629i | \(-0.903804\pi\) | ||||
0.954682 | − | 0.297629i | \(-0.0961957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.29610 | 0.915972 | 0.457986 | − | 0.888959i | \(-0.348571\pi\) | ||||
0.457986 | + | 0.888959i | \(0.348571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.50981i | − 0.339306i | −0.985504 | − | 0.169653i | \(-0.945735\pi\) | ||||
0.985504 | − | 0.169653i | \(-0.0542647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.28772 | 0.698037 | 0.349018 | − | 0.937116i | \(-0.386515\pi\) | ||||
0.349018 | + | 0.937116i | \(0.386515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.2001 | 1.82240 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.14771 | −0.107967 | −0.0539835 | − | 0.998542i | \(-0.517192\pi\) | ||||
−0.0539835 | + | 0.998542i | \(0.517192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.21824 | 0.206852 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.78751i | 0.442606i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.35826 | 0.850751 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.51594i | 0.858023i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9398i | 1.32569i | 0.748757 | + | 0.662844i | \(0.230651\pi\) | ||||
−0.748757 | + | 0.662844i | \(0.769349\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 11.3346i | − 0.997959i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9275 | −1.56634 | −0.783168 | − | 0.621811i | \(-0.786397\pi\) | ||||
−0.783168 | + | 0.621811i | \(0.786397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.99841i | 0.171996i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6382 | −1.07976 | −0.539878 | − | 0.841743i | \(-0.681530\pi\) | ||||
−0.539878 | + | 0.841743i | \(0.681530\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3894 | −1.05086 | −0.525429 | − | 0.850837i | \(-0.676095\pi\) | ||||
−0.525429 | + | 0.850837i | \(0.676095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.0247 | 2.02325 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.89828 | −0.242366 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 1.98361i | − 0.164730i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.40424 | 0.524656 | 0.262328 | − | 0.964979i | \(-0.415510\pi\) | ||||
0.262328 | + | 0.964979i | \(0.415510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 23.6469i | − 1.92436i | −0.272422 | − | 0.962178i | \(-0.587825\pi\) | ||||
0.272422 | − | 0.962178i | \(-0.412175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 0.147836i | − 0.0119519i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.31703i | − 0.507396i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2.34315i | − 0.187003i | −0.995619 | − | 0.0935017i | \(-0.970194\pi\) | ||||
0.995619 | − | 0.0935017i | \(-0.0298061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.08136 | 0.720199 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.918827i | 0.0719681i | 0.999352 | + | 0.0359840i | \(0.0114565\pi\) | ||||
−0.999352 | + | 0.0359840i | \(0.988543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.89828 | 0.225630 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6234 | −1.05421 | −0.527106 | − | 0.849800i | \(-0.676723\pi\) | ||||
−0.527106 | + | 0.849800i | \(0.676723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.88348 | 0.606422 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.18196 | 0.396275 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.92790i | − 0.298633i | −0.988789 | − | 0.149316i | \(-0.952293\pi\) | ||||
0.988789 | − | 0.149316i | \(-0.0477073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.5884 | 1.17169 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.999626i | 0.0747156i | 0.999302 | + | 0.0373578i | \(0.0118941\pi\) | ||||
−0.999302 | + | 0.0373578i | \(0.988106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1.09666i | − 0.0815141i | −0.999169 | − | 0.0407570i | \(-0.987023\pi\) | ||||
0.999169 | − | 0.0407570i | \(-0.0129770\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.2440i | 1.12687i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 8.48822i | − 0.624067i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0894975 | 0.00654471 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.36558i | 0.388239i | 0.980978 | + | 0.194120i | \(0.0621850\pi\) | ||||
−0.980978 | + | 0.194120i | \(0.937815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2036 | 0.950416 | 0.475208 | − | 0.879873i | \(-0.342373\pi\) | ||||
0.475208 | + | 0.879873i | \(0.342373\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.11652 | 0.366402 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.1264 | 1.64769 | 0.823845 | − | 0.566815i | \(-0.191825\pi\) | ||||
0.823845 | + | 0.566815i | \(0.191825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9597 | −1.48580 | −0.742898 | − | 0.669404i | \(-0.766549\pi\) | ||||
−0.742898 | + | 0.669404i | \(0.766549\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.2252i | 1.77925i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.20692 | 0.293824 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.69496i | 0.326322i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.13707i | 0.216996i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 24.9864i | − 1.72014i | −0.510179 | − | 0.860068i | \(-0.670421\pi\) | ||||
0.510179 | − | 0.860068i | \(-0.329579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 32.8745i | − 2.25252i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.01095 | −0.341744 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 26.8021i | − 1.81112i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.157996 | 0.0106280 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0721013 | 0.00482826 | 0.00241413 | − | 0.999997i | \(-0.499232\pi\) | ||||
0.00241413 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.11652 | −0.141101 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.9302 | −1.45556 | −0.727778 | − | 0.685813i | \(-0.759447\pi\) | ||||
−0.727778 | + | 0.685813i | \(0.759447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.73259i | − 0.312738i | −0.987699 | − | 0.156369i | \(-0.950021\pi\) | ||||
0.987699 | − | 0.156369i | \(-0.0499790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.33145 | 0.349275 | 0.174637 | − | 0.984633i | \(-0.444125\pi\) | ||||
0.174637 | + | 0.984633i | \(0.444125\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 10.6211i | − 0.692846i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.2712i | 0.862057i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.4393i | 1.19274i | 0.802710 | + | 0.596370i | \(0.203391\pi\) | ||||
−0.802710 | + | 0.596370i | \(0.796609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.6021i | 1.26268i | 0.775505 | + | 0.631342i | \(0.217495\pi\) | ||||
−0.775505 | + | 0.631342i | \(0.782505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.5922 | −1.19269 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.53808i | 0.352380i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1116 | −0.830917 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4391 | 0.974505 | 0.487252 | − | 0.873261i | \(-0.337999\pi\) | ||||
0.487252 | + | 0.873261i | \(0.337999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.84225 | −0.178691 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.157996 | −0.00989409 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.8216i | 0.986927i | 0.869767 | + | 0.493463i | \(0.164269\pi\) | ||||
−0.869767 | + | 0.493463i | \(0.835731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.19835 | 0.259872 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 21.5945i | − 1.33157i | −0.746142 | − | 0.665786i | \(-0.768096\pi\) | ||||
0.746142 | − | 0.665786i | \(-0.231904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 4.01480i | − 0.246627i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.7777i | 2.43436i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 0.710688i | − 0.0433314i | −0.999765 | − | 0.0216657i | \(-0.993103\pi\) | ||||
0.999765 | − | 0.0216657i | \(-0.00689695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5687 | −1.06722 | −0.533610 | − | 0.845731i | \(-0.679165\pi\) | ||||
−0.533610 | + | 0.845731i | \(0.679165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.28130i | − 0.0772656i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.92471 | 0.295897 | 0.147949 | − | 0.988995i | \(-0.452733\pi\) | ||||
0.147949 | + | 0.988995i | \(0.452733\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.3701 | 0.800448 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.87707 | 0.290941 | 0.145471 | − | 0.989363i | \(-0.453530\pi\) | ||||
0.145471 | + | 0.989363i | \(0.453530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.8838 | −1.06308 | −0.531541 | − | 0.847033i | \(-0.678387\pi\) | ||||
−0.531541 | + | 0.847033i | \(0.678387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 5.53808i | − 0.328048i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9951 | 0.999713 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 15.9714i | − 0.936257i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0836i | 1.40698i | 0.710705 | + | 0.703490i | \(0.248376\pi\) | ||||
−0.710705 | + | 0.703490i | \(0.751624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.89149i | − 0.401238i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.56057i | − 0.148579i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.01761 | −0.290176 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 13.5317i | − 0.777376i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.73925 | 0.385888 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.1042 | −1.66106 | −0.830531 | − | 0.556972i | \(-0.811963\pi\) | ||||
−0.830531 | + | 0.556972i | \(0.811963\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.0275 | 1.19621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3693 | −0.701398 | −0.350699 | − | 0.936488i | \(-0.614056\pi\) | ||||
−0.350699 | + | 0.936488i | \(0.614056\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.08027i | − 0.174107i | −0.996204 | − | 0.0870536i | \(-0.972255\pi\) | ||||
0.996204 | − | 0.0870536i | \(-0.0277451\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.9983 | −1.01088 | −0.505442 | − | 0.862861i | \(-0.668671\pi\) | ||||
−0.505442 | + | 0.862861i | \(0.668671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.54161i | 0.142303i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 7.93909i | − 0.443117i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.171014i | − 0.00951545i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.26197i | − 0.125472i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.4846 | 0.911602 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.09011i | − 0.114883i | −0.998349 | − | 0.0574415i | \(-0.981706\pi\) | ||||
0.998349 | − | 0.0574415i | \(-0.0182943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.9655 | 0.984503 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1519 | 0.609292 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.22975 | −0.448303 | −0.224152 | − | 0.974554i | \(-0.571961\pi\) | ||||
−0.224152 | + | 0.974554i | \(0.571961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.59608 | −0.141000 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.09403i | 0.438316i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.01761 | 0.270139 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.8760i | 0.583854i | 0.956441 | + | 0.291927i | \(0.0942965\pi\) | ||||
−0.956441 | + | 0.291927i | \(0.905704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.39422i | − 0.395804i | −0.980222 | − | 0.197902i | \(-0.936587\pi\) | ||||
0.980222 | − | 0.197902i | \(-0.0634127\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 4.52034i | − 0.241278i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 29.6796i | − 1.57969i | −0.613309 | − | 0.789843i | \(-0.710162\pi\) | ||||
0.613309 | − | 0.789843i | \(-0.289838\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.5335 | −0.771361 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3548i | 1.44373i | 0.692033 | + | 0.721866i | \(0.256715\pi\) | ||||
−0.692033 | + | 0.721866i | \(0.743285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0056 | −0.684507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.1681 | 1.11104 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.8490 | −0.620204 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.7326 | −0.716835 | −0.358418 | − | 0.933561i | \(-0.616684\pi\) | ||||
−0.358418 | + | 0.933561i | \(0.616684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.90403i | 0.463525i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.3020 | 1.36187 | 0.680933 | − | 0.732345i | \(-0.261574\pi\) | ||||
0.680933 | + | 0.732345i | \(0.261574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.26197i | 0.116808i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.48687i | 0.231086i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0292i | 0.874732i | 0.899284 | + | 0.437366i | \(0.144089\pi\) | ||||
−0.899284 | + | 0.437366i | \(0.855911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.7933i | 1.73128i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.58770 | 0.438811 | 0.219405 | − | 0.975634i | \(-0.429588\pi\) | ||||
0.219405 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 10.6058i | − 0.539122i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.3201 | −1.03027 | −0.515136 | − | 0.857109i | \(-0.672258\pi\) | ||||
−0.515136 | + | 0.857109i | \(0.672258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.154942 | 0.00783573 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40.5516 | −2.04556 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.86709 | 0.295205 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2011i | 0.913487i | 0.889598 | + | 0.456744i | \(0.150984\pi\) | ||||
−0.889598 | + | 0.456744i | \(0.849016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.91270 | −0.0955156 | −0.0477578 | − | 0.998859i | \(-0.515208\pi\) | ||||
−0.0477578 | + | 0.998859i | \(0.515208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.2889i | 0.711783i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.8699i | 0.540130i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8760i | 0.539103i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.51299i | 0.371494i | 0.982598 | + | 0.185747i | \(0.0594704\pi\) | ||||
−0.982598 | + | 0.185747i | \(0.940530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.5873 | −1.41011 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.79655i | 0.284542i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.0246 | −1.37237 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.5844 | −1.64070 | −0.820352 | − | 0.571859i | \(-0.806223\pi\) | ||||
−0.820352 | + | 0.571859i | \(0.806223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7594 | 1.25544 | 0.627719 | − | 0.778440i | \(-0.283989\pi\) | ||||
0.627719 | + | 0.778440i | \(0.283989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.4798 | 1.09301 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0698487i | 0.00338816i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.55582 | −0.316518 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 23.7343i | − 1.14324i | −0.820518 | − | 0.571621i | \(-0.806315\pi\) | ||||
0.820518 | − | 0.571621i | \(-0.193685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 33.1945i | − 1.59523i | −0.603169 | − | 0.797614i | \(-0.706095\pi\) | ||||
0.603169 | − | 0.797614i | \(-0.293905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 4.48687i | − 0.215129i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.43102i | 0.259801i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.628450 | 0.0299943 | 0.0149972 | − | 0.999888i | \(-0.495226\pi\) | ||||
0.0149972 | + | 0.999888i | \(0.495226\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 0.315992i | − 0.0150132i | −0.999972 | − | 0.00750661i | \(-0.997611\pi\) | ||||
0.999972 | − | 0.00750661i | \(-0.00238945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.5854 | 0.833629 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.4862 | 0.685174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.7179 | −1.35528 | −0.677642 | − | 0.735392i | \(-0.736998\pi\) | ||||
−0.677642 | + | 0.735392i | \(0.736998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.39035 | −0.253821 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 53.4886i | − 2.51311i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.67975 | 0.0785752 | 0.0392876 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392876 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.139586i | 0.00651533i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.34502i | 0.248943i | 0.992223 | + | 0.124471i | \(0.0397235\pi\) | ||||
−0.992223 | + | 0.124471i | \(0.960277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.161599i | 0.00751013i | 0.999993 | + | 0.00375507i | \(0.00119528\pi\) | ||||
−0.999993 | + | 0.00375507i | \(0.998805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 14.2889i | − 0.662634i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5406 | 0.857958 | 0.428979 | − | 0.903315i | \(-0.358874\pi\) | ||||
0.428979 | + | 0.903315i | \(0.358874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 5.30013i | − 0.244217i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.42055 | 0.295217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.44834 | −0.112338 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.49740 | 0.389069 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.41716 | −0.247516 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.2001i | 0.875451i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.06081 | −0.320615 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.19297i | 0.325945i | 0.986631 | + | 0.162972i | \(0.0521081\pi\) | ||||
−0.986631 | + | 0.162972i | \(0.947892\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.07836i | 0.0939867i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 32.6329i | − 1.47270i | −0.676599 | − | 0.736352i | \(-0.736547\pi\) | ||||
0.676599 | − | 0.736352i | \(-0.263453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.138553i | − 0.00624010i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.71191 | 0.121891 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.96951i | 0.356764i | 0.983961 | + | 0.178382i | \(0.0570863\pi\) | ||||
−0.983961 | + | 0.178382i | \(0.942914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.8158 | −1.37675 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.7556 | −1.19297 | −0.596486 | − | 0.802623i | \(-0.703437\pi\) | ||||
−0.596486 | + | 0.802623i | \(0.703437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.98226 | −0.266207 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8322 | 0.791956 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 26.4518i | − 1.17246i | −0.810146 | − | 0.586228i | \(-0.800612\pi\) | ||||
0.810146 | − | 0.586228i | \(-0.199388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.89278 | −0.216022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 9.29610i | − 0.409635i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6089i | 0.598519i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 8.88480i | − 0.389999i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6460i | 0.860706i | 0.902661 | + | 0.430353i | \(0.141611\pi\) | ||||
−0.902661 | + | 0.430353i | \(0.858389\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7807 | 0.471407 | 0.235703 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235703 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 0.441236i | − 0.0192206i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.0794 | 0.786061 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.5860 | 0.632977 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.51594 | −0.412181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.50981 | −0.151742 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.26113i | 0.0975748i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.74203 | −0.418842 | −0.209421 | − | 0.977826i | \(-0.567158\pi\) | ||||
−0.209421 | + | 0.977826i | \(0.567158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 2.48061i | − 0.106453i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 7.28772i | − 0.312172i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.0170i | − 0.855865i | −0.903811 | − | 0.427932i | \(-0.859242\pi\) | ||||
0.903811 | − | 0.427932i | \(-0.140758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.2638i | 0.608762i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.85656 | 0.206896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 19.2001i | − 0.815000i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.6069 | 1.04263 | 0.521314 | − | 0.853365i | \(-0.325442\pi\) | ||||
0.521314 | + | 0.853365i | \(0.325442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3346 | 0.479404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.202441 | 0.00854706 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.48345 | −0.231100 | −0.115550 | − | 0.993302i | \(-0.536863\pi\) | ||||
−0.115550 | + | 0.993302i | \(0.536863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.14771i | 0.0482843i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.6101 | −0.864021 | −0.432011 | − | 0.901868i | \(-0.642196\pi\) | ||||
−0.432011 | + | 0.901868i | \(0.642196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2191i | 0.804294i | 0.915575 | + | 0.402147i | \(0.131736\pi\) | ||||
−0.915575 | + | 0.402147i | \(0.868264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.1368i | 0.507021i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.21824i | − 0.0925072i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.9735i | 1.99716i | 0.0532429 | + | 0.998582i | \(0.483044\pi\) | ||||
−0.0532429 | + | 0.998582i | \(0.516956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.8662 | 1.24120 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.14418i | 0.213050i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.78751 | 0.197939 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.534337 | −0.0220544 | −0.0110272 | − | 0.999939i | \(-0.503510\pi\) | ||||
−0.0110272 | + | 0.999939i | \(0.503510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.4662 | 0.637275 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.3114 | 2.15180 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.7714i | − 1.22257i | −0.791412 | − | 0.611283i | \(-0.790654\pi\) | ||||
0.791412 | − | 0.611283i | \(-0.209346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47.4104 | −1.94038 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0758i | 1.18800i | 0.804463 | + | 0.594002i | \(0.202453\pi\) | ||||
−0.804463 | + | 0.594002i | \(0.797547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 23.6224i | − 0.963576i | −0.876288 | − | 0.481788i | \(-0.839988\pi\) | ||||
0.876288 | − | 0.481788i | \(-0.160012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.6032i | 0.961195i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 9.35826i | − 0.380467i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.8327 | 0.520864 | 0.260432 | − | 0.965492i | \(-0.416135\pi\) | ||||
0.260432 | + | 0.965492i | \(0.416135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0247i | 0.971936i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4044 | 1.47036 | 0.735180 | − | 0.677871i | \(-0.237097\pi\) | ||||
0.735180 | + | 0.677871i | \(0.237097\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.51594 | 0.383720 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.80275 | −0.354386 | −0.177193 | − | 0.984176i | \(-0.556702\pi\) | ||||
−0.177193 | + | 0.984176i | \(0.556702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.8467 | 1.68196 | 0.840980 | − | 0.541066i | \(-0.181979\pi\) | ||||
0.840980 | + | 0.541066i | \(0.181979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 4.43296i | − 0.177888i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.09597i | 0.283386i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 0.592892i | − 0.0236401i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 28.7721i | − 1.14540i | −0.819765 | − | 0.572700i | \(-0.805896\pi\) | ||||
0.819765 | − | 0.572700i | \(-0.194104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 56.5186i | − 2.24641i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9398 | 0.592866 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 30.7605i | − 1.21687i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.3384 | −1.11930 | −0.559650 | − | 0.828729i | \(-0.689064\pi\) | ||||
−0.559650 | + | 0.828729i | \(0.689064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.69981 | 0.0670340 | 0.0335170 | − | 0.999438i | \(-0.489329\pi\) | ||||
0.0335170 | + | 0.999438i | \(0.489329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.3346 | −0.446301 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.36235 | 0.171502 | 0.0857508 | − | 0.996317i | \(-0.472671\pi\) | ||||
0.0857508 | + | 0.996317i | \(0.472671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.83009i | 0.346612i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.2849 | −0.402481 | −0.201240 | − | 0.979542i | \(-0.564497\pi\) | ||||
−0.201240 | + | 0.979542i | \(0.564497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.9275i | 0.700486i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 25.0786i | − 0.978409i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 19.5800i | − 0.762729i | −0.924425 | − | 0.381364i | \(-0.875454\pi\) | ||||
0.924425 | − | 0.381364i | \(-0.124546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.3927i | 1.60999i | 0.593281 | + | 0.804995i | \(0.297832\pi\) | ||||
−0.593281 | + | 0.804995i | \(0.702168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.357382 | 0.0138796 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.40013i | 0.170374i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.163091 | 0.00630547 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.63503 | −0.333352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.6784 | −1.83787 | −0.918934 | − | 0.394412i | \(-0.870948\pi\) | ||||
−0.918934 | + | 0.394412i | \(0.870948\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.99841 | 0.0769187 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.60650i | 0.177042i | 0.996074 | + | 0.0885211i | \(0.0282141\pi\) | ||||
−0.996074 | + | 0.0885211i | \(0.971786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.6054 | −1.90088 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.3757i | 1.58320i | 0.611041 | + | 0.791599i | \(0.290751\pi\) | ||||
−0.611041 | + | 0.791599i | \(0.709249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6382i | 0.482881i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 10.7050i | − 0.408421i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.08136i | 0.345972i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1121 | 0.993353 | 0.496676 | − | 0.867936i | \(-0.334554\pi\) | ||||
0.496676 | + | 0.867936i | \(0.334554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.3894i | 0.469958i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.293848 | 0.0111303 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0596 | 0.456136 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8190 | 1.39063 | 0.695317 | − | 0.718703i | \(-0.255264\pi\) | ||||
0.695317 | + | 0.718703i | \(0.255264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7821 | 0.783811 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 24.0247i | − 0.904823i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.0518671 | −0.00194791 | −0.000973955 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000973955 | 1.00000i | \(0.500310\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4178i | 0.465705i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.0127i | 0.524780i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.89828i | 0.108389i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.7092i | 1.55766i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2869 | −0.570104 | −0.285052 | − | 0.958512i | \(-0.592011\pi\) | ||||
−0.285052 | + | 0.958512i | \(0.592011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.3395i | 1.64900i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.98361 | −0.0736695 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4261 | −1.01718 | −0.508588 | − | 0.861010i | \(-0.669832\pi\) | ||||
−0.508588 | + | 0.861010i | \(0.669832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.44534 | −0.349827 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.350009 | −0.0129455 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 29.6566i | − 1.09539i | −0.836677 | − | 0.547697i | \(-0.815505\pi\) | ||||
0.836677 | − | 0.547697i | \(-0.184495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2889 | −0.526340 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 38.0930i | − 1.40127i | −0.713519 | − | 0.700636i | \(-0.752900\pi\) | ||||
0.713519 | − | 0.700636i | \(-0.247100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.5270i | 0.460190i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 35.6723i | − 1.30869i | −0.756197 | − | 0.654345i | \(-0.772945\pi\) | ||||
0.756197 | − | 0.654345i | \(-0.227055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 6.40424i | − 0.234633i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2685 | −0.448882 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.970408i | 0.0354107i | 0.999843 | + | 0.0177053i | \(0.00563608\pi\) | ||||
−0.999843 | + | 0.0177053i | \(0.994364\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.9227 | 1.27265 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.6469 | −0.860598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0405 | 0.546658 | 0.273329 | − | 0.961921i | \(-0.411875\pi\) | ||||
0.273329 | + | 0.961921i | \(0.411875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.42908 | −0.233361 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.2355i | 0.371035i | 0.982641 | + | 0.185517i | \(0.0593961\pi\) | ||||
−0.982641 | + | 0.185517i | \(0.940604\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.147836 | −0.00534503 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5884i | 0.562863i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 40.4890i | − 1.46007i | −0.683409 | − | 0.730036i | \(-0.739503\pi\) | ||||
0.683409 | − | 0.730036i | \(-0.260497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.7881i | 1.28888i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 16.3932i | − 0.589624i | −0.955555 | − | 0.294812i | \(-0.904743\pi\) | ||||
0.955555 | − | 0.294812i | \(-0.0952570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.31703 | −0.226914 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3000i | 0.369035i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.6219 | 0.666344 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.96406 | −0.141664 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.34315 | −0.0836305 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.18768 | 0.256213 | 0.128106 | − | 0.991760i | \(-0.459110\pi\) | ||||
0.128106 | + | 0.991760i | \(0.459110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 48.8461i | − 1.73897i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2440 | −0.541330 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 9.08136i | − 0.322083i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 16.4615i | − 0.583096i | −0.956556 | − | 0.291548i | \(-0.905830\pi\) | ||||
0.956556 | − | 0.291548i | \(-0.0941703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 0.741873i | − 0.0262456i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.2199i | 1.31510i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1821 | 0.535766 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.60756i | − 0.0565887i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2638 | −0.888228 | −0.444114 | − | 0.895970i | \(-0.646481\pi\) | ||||
−0.444114 | + | 0.895970i | \(0.646481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4145 | 0.541275 | 0.270637 | − | 0.962681i | \(-0.412766\pi\) | ||||
0.270637 | + | 0.962681i | \(0.412766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.7398 | −1.39374 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.918827 | 0.0321851 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 12.2685i | − 0.429221i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.3340 | −1.79157 | −0.895784 | − | 0.444490i | \(-0.853385\pi\) | ||||
−0.895784 | + | 0.444490i | \(0.853385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 23.2020i | − 0.808772i | −0.914588 | − | 0.404386i | \(-0.867485\pi\) | ||||
0.914588 | − | 0.404386i | \(-0.132515\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 2.89828i | − 0.100905i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 13.0659i | − 0.454345i | −0.973855 | − | 0.227172i | \(-0.927052\pi\) | ||||
0.973855 | − | 0.227172i | \(-0.0729481\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.5361i | 1.40788i | 0.710261 | + | 0.703938i | \(0.248577\pi\) | ||||
−0.710261 | + | 0.703938i | \(0.751423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.1396 | 0.386427 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.6234i | 0.471458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.6240 | −0.436349 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.80249 | −0.0622290 | −0.0311145 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311145 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0653 | −0.864320 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.0318 | 0.379955 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.88348i | − 0.271200i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.4527 | −1.38833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.8290i | 0.645448i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 20.3256i | − 0.695937i | −0.937506 | − | 0.347968i | \(-0.886872\pi\) | ||||
0.937506 | − | 0.347968i | \(-0.113128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 5.18196i | − 0.177219i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.3433i | − 0.729073i | −0.931189 | − | 0.364537i | \(-0.881227\pi\) | ||||
0.931189 | − | 0.364537i | \(-0.118773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.152184 | −0.00519245 | −0.00259623 | − | 0.999997i | \(-0.500826\pi\) | ||||
−0.00259623 | + | 0.999997i | \(0.500826\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 52.9477i | − 1.80236i | −0.433445 | − | 0.901180i | \(-0.642702\pi\) | ||||
0.433445 | − | 0.901180i | \(-0.357298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.92790 | −0.133553 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.4425 | 1.30558 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.51753 | −0.255015 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.2252 | −0.854724 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 14.9443i | − 0.505789i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7875 | 0.465572 | 0.232786 | − | 0.972528i | \(-0.425216\pi\) | ||||
0.232786 | + | 0.972528i | \(0.425216\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.4765i | 1.83745i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6991i | 0.427844i | 0.976851 | + | 0.213922i | \(0.0686239\pi\) | ||||
−0.976851 | + | 0.213922i | \(0.931376\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 41.9953i | − 1.41326i | −0.707586 | − | 0.706628i | \(-0.750216\pi\) | ||||
0.707586 | − | 0.706628i | \(-0.249784\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 15.5884i | − 0.523997i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.5309 | −0.924398 | −0.462199 | − | 0.886776i | \(-0.652939\pi\) | ||||
−0.462199 | + | 0.886776i | \(0.652939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 13.9277i | − 0.466594i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.0042 | 0.870196 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.999626 | 0.0334138 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3497 | −0.378955 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5305 | 0.417916 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.280428i | − 0.00934243i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.09666 | −0.0364542 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 28.2562i | − 0.938233i | −0.883136 | − | 0.469117i | \(-0.844572\pi\) | ||||
0.883136 | − | 0.469117i | \(-0.155428\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 12.6616i | − 0.419958i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.4861i | 1.57328i | 0.617410 | + | 0.786642i | \(0.288182\pi\) | ||||
−0.617410 | + | 0.786642i | \(0.711818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 7.42715i | − 0.245803i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.2440 | 0.503951 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9408i | 1.44947i | 0.689027 | + | 0.724736i | \(0.258038\pi\) | ||||
−0.689027 | + | 0.724736i | \(0.741962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −65.8328 | −2.16927 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.8745 | 1.08208 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.48822 | −0.279091 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.6754 | 0.646224 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0003i | 0.984277i | 0.870517 | + | 0.492139i | \(0.163785\pi\) | ||||
−0.870517 | + | 0.492139i | \(0.836215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.9790 | −0.915991 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 0.0894975i | − 0.00292688i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 42.7802i | − 1.39757i | −0.715332 | − | 0.698784i | \(-0.753725\pi\) | ||||
0.715332 | − | 0.698784i | \(-0.246275\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 6.96749i | − 0.227375i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.7822i | 1.29686i | 0.761273 | + | 0.648432i | \(0.224575\pi\) | ||||
−0.761273 | + | 0.648432i | \(0.775425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.33198 | −0.303891 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.7788i | 1.09766i | 0.835933 | + | 0.548832i | \(0.184927\pi\) | ||||
−0.835933 | + | 0.548832i | \(0.815073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.8021 | 0.870032 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.7116 | −1.32016 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.3496 | −1.30705 | −0.653526 | − | 0.756904i | \(-0.726711\pi\) | ||||
−0.653526 | + | 0.756904i | \(0.726711\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.36558 | 0.173626 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.74905i | 0.185840i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.90481 | 0.287252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 7.42858i | − 0.239383i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 13.2036i | − 0.425039i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 14.3062i | − 0.460057i | −0.973184 | − | 0.230028i | \(-0.926118\pi\) | ||||
0.973184 | − | 0.230028i | \(-0.0738819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 0.386828i | − 0.0124267i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.9837 | 1.44360 | 0.721798 | − | 0.692103i | \(-0.243316\pi\) | ||||
0.721798 | + | 0.692103i | \(0.243316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 5.11652i | − 0.163860i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.8058 | −1.43346 | −0.716732 | − | 0.697349i | \(-0.754363\pi\) | ||||
−0.716732 | + | 0.697349i | \(0.754363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.5323 | −0.720134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.4246 | 0.492470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9903 | −0.892751 | −0.446375 | − | 0.894846i | \(-0.647285\pi\) | ||||
−0.446375 | + | 0.894846i | \(0.647285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 23.1264i | − 0.736870i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.1155 | 0.353453 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2555i | 0.452840i | 0.974030 | + | 0.226420i | \(0.0727022\pi\) | ||||
−0.974030 | + | 0.226420i | \(0.927298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 4.72778i | − 0.150032i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.9597i | 0.664469i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.5810i | 1.69693i | 0.529254 | + | 0.848464i | \(0.322472\pi\) | ||||
−0.529254 | + | 0.848464i | \(0.677528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.9629 | −0.536683 |
(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 | 3920.2.k.a.2351.7 | ✓ | 8 | |
4.3 | odd | 2 | 3920.2.k.c.2351.1 | yes | 8 | ||
7.6 | odd | 2 | 3920.2.k.c.2351.2 | yes | 8 | ||
28.27 | even | 2 | inner | 3920.2.k.a.2351.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3920.2.k.a.2351.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3920.2.k.a.2351.8 | yes | 8 | 28.27 | even | 2 | inner | |
3920.2.k.c.2351.1 | yes | 8 | 4.3 | odd | 2 | ||
3920.2.k.c.2351.2 | yes | 8 | 7.6 | odd | 2 |