Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(127,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.d (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.3 | ||
Root | \(-1.27733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.127 |
Dual form | 224.3.d.b.127.6 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.55467i | − 0.851556i | −0.904828 | − | 0.425778i | \(-0.860000\pi\) | ||||
0.904828 | − | 0.425778i | \(-0.140000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.86836 | 1.97367 | 0.986836 | − | 0.161727i | \(-0.0517064\pi\) | ||||
0.986836 | + | 0.161727i | \(0.0517064\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.64575i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47367 | 0.274852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.1537i | 1.19579i | 0.801574 | + | 0.597896i | \(0.203996\pi\) | ||||
−0.801574 | + | 0.597896i | \(0.796004\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.86836 | −0.451412 | −0.225706 | − | 0.974195i | \(-0.572469\pi\) | ||||
−0.225706 | + | 0.974195i | \(0.572469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 25.2104i | − 1.68069i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.570700 | −0.0335706 | −0.0167853 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167853 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 15.6640i | − 0.824421i | −0.911089 | − | 0.412211i | \(-0.864757\pi\) | ||||
0.911089 | − | 0.412211i | \(-0.135243\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.75902 | −0.321858 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.4817i | 0.716596i | 0.933607 | + | 0.358298i | \(0.116643\pi\) | ||||
−0.933607 | + | 0.358298i | \(0.883357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 72.3844 | 2.89538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 29.3114i | − 1.08561i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.7367 | −1.02540 | −0.512702 | − | 0.858567i | \(-0.671355\pi\) | ||||
−0.512702 | + | 0.858567i | \(0.671355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 54.8014i | − 1.76779i | −0.467687 | − | 0.883894i | \(-0.654913\pi\) | ||||
0.467687 | − | 0.883894i | \(-0.345087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 33.6034 | 1.01828 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 26.1092i | − 0.745978i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −42.0853 | −1.13744 | −0.568721 | − | 0.822531i | \(-0.692561\pi\) | ||||
−0.568721 | + | 0.822531i | \(0.692561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.9917i | 0.384403i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.773275 | 0.0188604 | 0.00943019 | − | 0.999956i | \(-0.496998\pi\) | ||||
0.00943019 | + | 0.999956i | \(0.496998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.7931i | 0.971933i | 0.873977 | + | 0.485967i | \(0.161532\pi\) | ||||
−0.873977 | + | 0.485967i | \(0.838468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.4110 | 0.542467 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.4528i | 1.24368i | 0.783145 | + | 0.621839i | \(0.213614\pi\) | ||||
−0.783145 | + | 0.621839i | \(0.786386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.45795i | 0.0285873i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65139 | 0.106630 | 0.0533150 | − | 0.998578i | \(-0.483021\pi\) | ||||
0.0533150 | + | 0.998578i | \(0.483021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 129.805i | 2.36010i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −40.0163 | −0.702041 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42.6434i | 0.722770i | 0.932417 | + | 0.361385i | \(0.117696\pi\) | ||||
−0.932417 | + | 0.361385i | \(0.882304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.9371 | −1.57274 | −0.786370 | − | 0.617756i | \(-0.788042\pi\) | ||||
−0.786370 | + | 0.617756i | \(0.788042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 6.54471i | − 0.103884i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −57.9110 | −0.890939 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.8503i | 1.04254i | 0.853391 | + | 0.521271i | \(0.174542\pi\) | ||||
−0.853391 | + | 0.521271i | \(0.825458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42.1053 | 0.610222 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 92.0882i | − 1.29702i | −0.761207 | − | 0.648509i | \(-0.775393\pi\) | ||||
0.761207 | − | 0.648509i | \(-0.224607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.97539 | 0.136649 | 0.0683246 | − | 0.997663i | \(-0.478235\pi\) | ||||
0.0683246 | + | 0.997663i | \(0.478235\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 184.918i | − 2.46558i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 34.8014 | 0.451967 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 20.1780i | − 0.255417i | −0.991812 | − | 0.127709i | \(-0.959238\pi\) | ||||
0.991812 | − | 0.127709i | \(-0.0407622\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −52.6180 | −0.649604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 151.307i | 1.82298i | 0.411321 | + | 0.911491i | \(0.365068\pi\) | ||||
−0.411321 | + | 0.911491i | \(0.634932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.63187 | −0.0662573 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 75.9674i | 0.873189i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.79743 | 0.0651396 | 0.0325698 | − | 0.999469i | \(-0.489631\pi\) | ||||
0.0325698 | + | 0.999469i | \(0.489631\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.5262i | 0.170618i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −140.000 | −1.50537 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 154.578i | − 1.62714i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 103.696 | 1.06903 | 0.534513 | − | 0.845160i | \(-0.320495\pi\) | ||||
0.534513 | + | 0.845160i | \(0.320495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 32.5379i | 0.328666i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 41.9176 | 0.415025 | 0.207513 | − | 0.978232i | \(-0.433463\pi\) | ||||
0.207513 | + | 0.978232i | \(0.433463\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.7378i | 0.181920i | 0.995855 | + | 0.0909602i | \(0.0289936\pi\) | ||||
−0.995855 | + | 0.0909602i | \(0.971006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −66.7004 | −0.635242 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 64.8549i | − 0.606121i | −0.952971 | − | 0.303060i | \(-0.901992\pi\) | ||||
0.952971 | − | 0.303060i | \(-0.0980084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −186.432 | −1.71039 | −0.855195 | − | 0.518307i | \(-0.826563\pi\) | ||||
−0.855195 | + | 0.518307i | \(0.826563\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 107.514i | 0.968595i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −84.7530 | −0.750027 | −0.375013 | − | 0.927019i | \(-0.622362\pi\) | ||||
−0.375013 | + | 0.927019i | \(0.622362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 162.647i | 1.41433i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.5164 | −0.124071 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50993i | 0.0126885i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.0200 | −0.429917 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.97546i | − 0.0160607i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 467.606 | 3.74085 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.3874i | 0.735334i | 0.929958 | + | 0.367667i | \(0.119843\pi\) | ||||
−0.929958 | + | 0.367667i | \(0.880157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 106.768 | 0.827656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 58.0857i | − 0.443403i | −0.975115 | − | 0.221701i | \(-0.928839\pi\) | ||||
0.975115 | − | 0.221701i | \(-0.0711610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −41.4431 | −0.311602 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 289.256i | − 2.14263i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 176.420 | 1.28774 | 0.643870 | − | 0.765135i | \(-0.277328\pi\) | ||||
0.643870 | + | 0.765135i | \(0.277328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.3041i | − 0.0885185i | −0.999020 | − | 0.0442592i | \(-0.985907\pi\) | ||||
0.999020 | − | 0.0442592i | \(-0.0140928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 149.328 | 1.05906 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 77.1906i | − 0.539795i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −293.452 | −2.02381 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.8827i | 0.121651i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 173.782 | 1.16632 | 0.583160 | − | 0.812358i | \(-0.301816\pi\) | ||||
0.583160 | + | 0.812358i | \(0.301816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 138.433i | 0.916776i | 0.888752 | + | 0.458388i | \(0.151573\pi\) | ||||
−0.888752 | + | 0.458388i | \(0.848427\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.41172 | −0.00922695 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 540.800i | − 3.48903i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 189.693 | 1.20824 | 0.604119 | − | 0.796894i | \(-0.293525\pi\) | ||||
0.604119 | + | 0.796894i | \(0.293525\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 14.4374i | − 0.0908014i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 43.6065 | 0.270848 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.7685i | − 0.109009i | −0.998514 | − | 0.0545047i | \(-0.982642\pi\) | ||||
0.998514 | − | 0.0545047i | \(-0.0173580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 331.610 | 2.00976 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.0890922i | 0 0.000533486i | 1.00000 | 0.000266743i | \(8.49069e-5\pi\) | |||||
−1.00000 | 0.000266743i | \(0.999915\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −134.562 | −0.796227 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 38.7475i | − 0.226594i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 43.2891 | 0.250226 | 0.125113 | − | 0.992143i | \(-0.460071\pi\) | ||||
0.125113 | + | 0.992143i | \(0.460071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 191.511i | − 1.09435i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 108.940 | 0.615479 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 190.838i | 1.06614i | 0.846072 | + | 0.533068i | \(0.178961\pi\) | ||||
−0.846072 | + | 0.533068i | \(0.821039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −207.153 | −1.14449 | −0.572246 | − | 0.820082i | \(-0.693928\pi\) | ||||
−0.572246 | + | 0.820082i | \(0.693928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 245.087i | 1.33928i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −415.313 | −2.24493 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 7.50683i | − 0.0401434i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −77.5507 | −0.410321 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 315.489i | − 1.65178i | −0.563833 | − | 0.825889i | \(-0.690674\pi\) | ||||
0.563833 | − | 0.825889i | \(-0.309326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −30.9403 | −0.160312 | −0.0801561 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801561 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 147.943i | 0.758684i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −264.248 | −1.34136 | −0.670681 | − | 0.741746i | \(-0.733998\pi\) | ||||
−0.670681 | + | 0.741746i | \(0.733998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 131.321i | 0.659903i | 0.943998 | + | 0.329951i | \(0.107032\pi\) | ||||
−0.943998 | + | 0.329951i | \(0.892968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 178.444 | 0.887783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78.6759i | 0.387566i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.63095 | 0.0372242 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 40.7703i | 0.196958i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 206.040 | 0.985836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 247.994i | − 1.17533i | −0.809105 | − | 0.587664i | \(-0.800048\pi\) | ||||
0.809105 | − | 0.587664i | \(-0.199952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −235.255 | −1.10448 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 412.430i | 1.91828i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −144.991 | −0.668161 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 25.4838i | − 0.116364i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.34907 | 0.0151542 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 56.7999i | − 0.254708i | −0.991857 | − | 0.127354i | \(-0.959352\pi\) | ||||
0.991857 | − | 0.127354i | \(-0.0406484\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 179.055 | 0.795800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 275.095i | − 1.21187i | −0.795513 | − | 0.605937i | \(-0.792798\pi\) | ||||
0.795513 | − | 0.605937i | \(-0.207202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.29210 | 0.0274764 | 0.0137382 | − | 0.999906i | \(-0.495627\pi\) | ||||
0.0137382 | + | 0.999906i | \(0.495627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 88.9061i | − 0.384875i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −142.049 | −0.609653 | −0.304827 | − | 0.952408i | \(-0.598599\pi\) | ||||
−0.304827 | + | 0.952408i | \(0.598599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 576.833i | 2.45461i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −51.5480 | −0.217502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 51.3954i | − 0.215043i | −0.994203 | − | 0.107522i | \(-0.965708\pi\) | ||||
0.994203 | − | 0.107522i | \(-0.0342915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 93.7048 | 0.388817 | 0.194408 | − | 0.980921i | \(-0.437721\pi\) | ||||
0.194408 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 129.381i | − 0.532433i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −69.0785 | −0.281953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 91.9220i | 0.372154i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 386.540 | 1.55237 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 12.4430i | − 0.0495737i | −0.999693 | − | 0.0247869i | \(-0.992109\pi\) | ||||
0.999693 | − | 0.0247869i | \(-0.00789071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −216.796 | −0.856900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.3876i | 0.0564219i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 169.884 | 0.661029 | 0.330514 | − | 0.943801i | \(-0.392778\pi\) | ||||
0.330514 | + | 0.943801i | \(0.392778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 111.347i | 0.429912i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −73.5587 | −0.281834 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 118.762i | 0.451565i | 0.974178 | + | 0.225782i | \(0.0724938\pi\) | ||||
−0.974178 | + | 0.225782i | \(0.927506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 55.7699 | 0.210452 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 14.8105i | − 0.0554700i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.37496 | −0.0348512 | −0.0174256 | − | 0.999848i | \(-0.505547\pi\) | ||||
−0.0174256 | + | 0.999848i | \(0.505547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 203.067i | − 0.749324i | −0.927161 | − | 0.374662i | \(-0.877759\pi\) | ||||
0.927161 | − | 0.374662i | \(-0.122241\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.6643 | 0.145291 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 952.124i | 3.46227i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 154.419 | 0.557471 | 0.278735 | − | 0.960368i | \(-0.410085\pi\) | ||||
0.278735 | + | 0.960368i | \(0.410085\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 135.561i | − 0.485880i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −217.495 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 431.849i | 1.52597i | 0.646418 | + | 0.762983i | \(0.276266\pi\) | ||||
−0.646418 | + | 0.762983i | \(0.723734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −394.896 | −1.38560 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.04589i | − 0.00712855i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.674 | −0.998873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 264.908i | − 0.910336i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −212.019 | −0.723616 | −0.361808 | − | 0.932253i | \(-0.617840\pi\) | ||||
−0.361808 | + | 0.932253i | \(0.617840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 420.820i | 1.42651i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 385.554 | 1.29816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 96.7206i | − 0.323480i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110.574 | 0.367356 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 107.086i | − 0.353418i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −946.741 | −3.10407 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 192.868i | − 0.628234i | −0.949384 | − | 0.314117i | \(-0.898292\pi\) | ||||
0.949384 | − | 0.314117i | \(-0.101708\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 47.8689 | 0.154915 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 269.814i | − 0.867569i | −0.901017 | − | 0.433785i | \(-0.857178\pi\) | ||||
0.901017 | − | 0.433785i | \(-0.142822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −236.490 | −0.755558 | −0.377779 | − | 0.925896i | \(-0.623312\pi\) | ||||
−0.377779 | + | 0.925896i | \(0.623312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 64.5855i | − 0.205033i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −249.012 | −0.785526 | −0.392763 | − | 0.919640i | \(-0.628481\pi\) | ||||
−0.392763 | + | 0.919640i | \(0.628481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 391.148i | − 1.22617i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −165.683 | −0.516146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.93945i | 0.0276763i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −424.778 | −1.30701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 476.273i | 1.45649i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 154.652 | 0.470066 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 465.343i | − 1.40587i | −0.711254 | − | 0.702935i | \(-0.751872\pi\) | ||||
0.711254 | − | 0.702935i | \(-0.248128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −104.105 | −0.312628 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 689.308i | 2.05763i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 626.243 | 1.85829 | 0.929144 | − | 0.369718i | \(-0.120546\pi\) | ||||
0.929144 | + | 0.369718i | \(0.120546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 216.516i | 0.638690i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 720.842 | 2.11391 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 415.510 | 1.20438 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 450.576i | − 1.29849i | −0.760580 | − | 0.649245i | \(-0.775085\pi\) | ||||
0.760580 | − | 0.649245i | \(-0.224915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −64.7762 | −0.185605 | −0.0928025 | − | 0.995685i | \(-0.529583\pi\) | ||||
−0.0928025 | + | 0.995685i | \(0.529583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 172.010i | 0.490057i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 589.179 | 1.66906 | 0.834532 | − | 0.550960i | \(-0.185738\pi\) | ||||
0.834532 | + | 0.550960i | \(0.185738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 908.760i | − 2.55989i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.85737 | 0.0108050 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 406.643i | − 1.13271i | −0.824161 | − | 0.566355i | \(-0.808353\pi\) | ||||
0.824161 | − | 0.566355i | \(-0.191647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 115.639 | 0.320329 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 132.894i | 0.366099i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 98.4407 | 0.269701 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 430.196i | − 1.17220i | −0.810240 | − | 0.586098i | \(-0.800663\pi\) | ||||
0.810240 | − | 0.586098i | \(-0.199337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.91283 | 0.00518381 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 14.9522i | − 0.0403023i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.60758 | 0.00699083 | 0.00349542 | − | 0.999994i | \(-0.498887\pi\) | ||||
0.00349542 | + | 0.999994i | \(0.498887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1194.58i | − 3.18555i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 174.506 | 0.462880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 359.118i | 0.947541i | 0.880648 | + | 0.473771i | \(0.157107\pi\) | ||||
−0.880648 | + | 0.473771i | \(0.842893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 238.574 | 0.626178 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 470.758i | 1.22913i | 0.788865 | + | 0.614567i | \(0.210669\pi\) | ||||
−0.788865 | + | 0.614567i | \(0.789331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 343.433 | 0.892034 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 103.382i | 0.267138i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −180.270 | −0.463418 | −0.231709 | − | 0.972785i | \(-0.574432\pi\) | ||||
−0.231709 | + | 0.972785i | \(0.574432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.40612i | − 0.0240566i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −148.390 | −0.377582 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 199.123i | − 0.504110i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −248.223 | −0.625248 | −0.312624 | − | 0.949877i | \(-0.601208\pi\) | ||||
−0.312624 | + | 0.949877i | \(0.601208\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 105.873i | 0.265347i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 369.502 | 0.921452 | 0.460726 | − | 0.887542i | \(-0.347589\pi\) | ||||
0.460726 | + | 0.887542i | \(0.347589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 321.594i | 0.798001i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −519.253 | −1.28211 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 553.578i | − 1.36014i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 479.494 | 1.17236 | 0.586179 | − | 0.810182i | \(-0.300632\pi\) | ||||
0.586179 | + | 0.810182i | \(0.300632\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 450.695i | − 1.09658i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 112.824 | 0.273181 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1493.16i | 3.59797i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.4328 | −0.0753785 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 564.644i | − 1.34760i | −0.738914 | − | 0.673800i | \(-0.764661\pi\) | ||||
0.738914 | − | 0.673800i | \(-0.235339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 544.282 | 1.29283 | 0.646415 | − | 0.762986i | \(-0.276267\pi\) | ||||
0.646415 | + | 0.762986i | \(0.276267\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 144.593i | 0.341827i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.3098 | −0.0971996 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 253.826i | 0.594440i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −197.196 | −0.459665 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 90.3539i | − 0.209638i | −0.994491 | − | 0.104819i | \(-0.966574\pi\) | ||||
0.994491 | − | 0.104819i | \(-0.0334263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −131.383 | −0.303425 | −0.151713 | − | 0.988425i | \(-0.548479\pi\) | ||||
−0.151713 | + | 0.988425i | \(0.548479\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 749.674i | 1.72339i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 258.170 | 0.590777 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 128.655i | 0.293064i | 0.989206 | + | 0.146532i | \(0.0468111\pi\) | ||||
−0.989206 | + | 0.146532i | \(0.953189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.3157 | −0.0392646 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 193.210i | 0.436139i | 0.975933 | + | 0.218070i | \(0.0699760\pi\) | ||||
−0.975933 | + | 0.218070i | \(0.930024\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57.2111 | 0.128564 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 443.954i | − 0.993186i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5046 | −0.0701661 | −0.0350830 | − | 0.999384i | \(-0.511170\pi\) | ||||
−0.0350830 | + | 0.999384i | \(0.511170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1714i | 0.0225531i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 353.651 | 0.780686 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 153.218i | 0.336743i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −426.401 | −0.933043 | −0.466521 | − | 0.884510i | \(-0.654493\pi\) | ||||
−0.466521 | + | 0.884510i | \(0.654493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.7280i | 0.0364445i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 430.182 | 0.933150 | 0.466575 | − | 0.884482i | \(-0.345488\pi\) | ||||
0.466575 | + | 0.884482i | \(0.345488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 183.454i | − 0.396230i | −0.980179 | − | 0.198115i | \(-0.936518\pi\) | ||||
0.980179 | − | 0.198115i | \(-0.0634819\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1381.56 | −2.97111 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 110.381i | − 0.236362i | −0.992992 | − | 0.118181i | \(-0.962294\pi\) | ||||
0.992992 | − | 0.118181i | \(-0.0377063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 184.807 | 0.394044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 484.604i | − 1.02888i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −549.735 | −1.16223 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1133.83i | − 2.38701i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.9797 | 0.0293075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 515.593i | − 1.07639i | −0.842819 | − | 0.538197i | \(-0.819106\pi\) | ||||
0.842819 | − | 0.538197i | \(-0.180894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 246.972 | 0.513455 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 111.400i | − 0.230642i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1023.30 | 2.10991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 59.2995i | 0.121765i | 0.998145 | + | 0.0608824i | \(0.0193915\pi\) | ||||
−0.998145 | + | 0.0608824i | \(0.980609\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.3927 | −0.0928276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 556.042i | 1.13247i | 0.824244 | + | 0.566234i | \(0.191600\pi\) | ||||
−0.824244 | + | 0.566234i | \(0.808400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.9708 | 0.0344234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 321.096i | 0.648678i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −243.643 | −0.490227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 150.429i | − 0.301461i | −0.988575 | − | 0.150730i | \(-0.951837\pi\) | ||||
0.988575 | − | 0.150730i | \(-0.0481626\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.227601 | 0.000454293 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 415.893i | − 0.826825i | −0.910544 | − | 0.413412i | \(-0.864337\pi\) | ||||
0.910544 | − | 0.413412i | \(-0.135663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 413.658 | 0.819124 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 343.762i | 0.678032i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 622.234 | 1.22246 | 0.611232 | − | 0.791452i | \(-0.290674\pi\) | ||||
0.611232 | + | 0.791452i | \(0.290674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 26.3924i | − 0.0516485i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −459.134 | −0.894999 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 184.911i | 0.359051i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −768.871 | −1.48718 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 110.589i | − 0.213081i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −644.142 | −1.23636 | −0.618179 | − | 0.786037i | \(-0.712129\pi\) | ||||
−0.618179 | + | 0.786037i | \(0.712129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 889.589i | 1.70093i | 0.526028 | + | 0.850467i | \(0.323681\pi\) | ||||
−0.526028 | + | 0.850467i | \(0.676319\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −489.248 | −0.931900 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.2752i | 0.0593457i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 257.353 | 0.486490 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.486i | 0.198655i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.53785 | −0.00851380 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 640.012i | − 1.19628i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 487.529 | 0.907875 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 92.0759i | − 0.170827i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 832.015 | 1.53792 | 0.768961 | − | 0.639296i | \(-0.220774\pi\) | ||||
0.768961 | + | 0.639296i | \(0.220774\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 529.207i | 0.974599i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1839.78 | −3.37575 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1014.85i | − 1.85531i | −0.373441 | − | 0.927654i | \(-0.621822\pi\) | ||||
0.373441 | − | 0.927654i | \(-0.378178\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −237.316 | −0.432270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 465.796i | 0.845365i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.3859 | −0.0965387 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1060.99i | 1.91169i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 473.280 | 0.849694 | 0.424847 | − | 0.905265i | \(-0.360328\pi\) | ||||
0.424847 | + | 0.905265i | \(0.360328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 245.257i | − 0.438742i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.1775 | −0.0341844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 102.364i | 0.181818i | 0.995859 | + | 0.0909092i | \(0.0289773\pi\) | ||||
−0.995859 | + | 0.0909092i | \(0.971023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −836.373 | −1.48031 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 139.214i | 0.245527i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −68.4059 | −0.120221 | −0.0601106 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601106 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 701.419i | 1.22841i | 0.789148 | + | 0.614203i | \(0.210522\pi\) | ||||
−0.789148 | + | 0.614203i | \(0.789478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −805.971 | −1.40658 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1193.02i | 2.07482i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.4710 | 0.0770727 | 0.0385364 | − | 0.999257i | \(-0.487730\pi\) | ||||
0.0385364 | + | 0.999257i | \(0.487730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 79.0421i | 0.136515i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 400.322 | 0.689022 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 74.3367i | 0.127507i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −143.253 | −0.244876 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 99.0239i | − 0.168695i | −0.996436 | − | 0.0843475i | \(-0.973119\pi\) | ||||
0.996436 | − | 0.0843475i | \(-0.0268806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −858.410 | −1.45740 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 675.066i | 1.14224i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −443.870 | −0.748516 | −0.374258 | − | 0.927325i | \(-0.622103\pi\) | ||||
−0.374258 | + | 0.927325i | \(0.622103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9005i | 0.0250429i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 335.481 | 0.561945 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 969.972i | 1.61932i | 0.586900 | + | 0.809659i | \(0.300348\pi\) | ||||
−0.586900 | + | 0.809659i | \(0.699652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −58.0231 | −0.0965443 | −0.0482722 | − | 0.998834i | \(-0.515371\pi\) | ||||
−0.0482722 | + | 0.998834i | \(0.515371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 172.786i | 0.286545i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −513.352 | −0.848515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 67.3822i | 0.111009i | 0.998458 | + | 0.0555043i | \(0.0176767\pi\) | ||||
−0.998458 | + | 0.0555043i | \(0.982323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 200.991 | 0.330034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 343.022i | − 0.561411i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −521.917 | −0.851415 | −0.425707 | − | 0.904861i | \(-0.639975\pi\) | ||||
−0.425707 | + | 0.904861i | \(0.639975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 19.4946i | − 0.0316985i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 165.257 | 0.267840 | 0.133920 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 205.392i | 0.331812i | 0.986142 | + | 0.165906i | \(0.0530549\pi\) | ||||
−0.986142 | + | 0.165906i | \(0.946945\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 483.103 | 0.777943 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 15.3385i | − 0.0246205i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2804.90 | 4.48783 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 526.363i | − 0.839495i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0181 | 0.0381846 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 631.682i | − 1.00108i | −0.865713 | − | 0.500540i | \(-0.833135\pi\) | ||||
0.865713 | − | 0.500540i | \(-0.166865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −633.543 | −1.00086 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 921.580i | 1.45131i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.0785 | 0.0644874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 227.796i | − 0.356488i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 817.936 | 1.27603 | 0.638016 | − | 0.770023i | \(-0.279755\pi\) | ||||
0.638016 | + | 0.770023i | \(0.279755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 607.082i | − 0.944140i | −0.881561 | − | 0.472070i | \(-0.843507\pi\) | ||||
0.881561 | − | 0.472070i | \(-0.156493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1053.62 | 1.63352 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 621.063i | 0.959911i | 0.877293 | + | 0.479956i | \(0.159347\pi\) | ||||
−0.877293 | + | 0.479956i | \(0.840653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −560.919 | −0.864282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 370.404i | 0.568977i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −850.083 | −1.30181 | −0.650906 | − | 0.759159i | \(-0.725611\pi\) | ||||
−0.650906 | + | 0.759159i | \(0.725611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 573.211i | − 0.875131i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.6758 | 0.0375583 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 331.172i | 0.502537i | 0.967917 | + | 0.251268i | \(0.0808477\pi\) | ||||
−0.967917 | + | 0.251268i | \(0.919152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 464.323 | 0.702456 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 8.55577i | − 0.0129046i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −408.975 | −0.615000 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 490.112i | − 0.734801i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −145.105 | −0.216898 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1261.93i | − 1.88067i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −844.655 | −1.25506 | −0.627529 | − | 0.778593i | \(-0.715934\pi\) | ||||
−0.627529 | + | 0.778593i | \(0.715934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2121.69i | − 3.14325i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −664.414 | −0.981410 | −0.490705 | − | 0.871326i | \(-0.663261\pi\) | ||||
−0.490705 | + | 0.871326i | \(0.663261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 274.353i | − 0.404054i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −702.778 | −1.03198 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 601.901i | − 0.881261i | −0.897689 | − | 0.440631i | \(-0.854755\pi\) | ||||
0.897689 | − | 0.440631i | \(-0.145245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1740.98 | 2.54157 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 16.0742i | − 0.0233977i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.1643 | −0.0481340 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 579.981i | 0.839336i | 0.907678 | + | 0.419668i | \(0.137854\pi\) | ||||
−0.907678 | + | 0.419668i | \(0.862146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 86.0872 | 0.124224 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 121.421i | − 0.174706i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.441308 | −0.000633154 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 362.889i | 0.519154i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 863.561 | 1.23190 | 0.615949 | − | 0.787786i | \(-0.288773\pi\) | ||||
0.615949 | + | 0.787786i | \(0.288773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 659.225i | 0.937731i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1473.62 | 2.09024 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 110.903i | − 0.156865i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −293.022 | −0.413290 | −0.206645 | − | 0.978416i | \(-0.566254\pi\) | ||||
−0.206645 | + | 0.978416i | \(0.566254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 49.9136i | − 0.0702019i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 903.222 | 1.26679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 761.744i | − 1.06538i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −131.298 | −0.183122 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 381.821i | − 0.531044i | −0.964105 | − | 0.265522i | \(-0.914456\pi\) | ||||
0.964105 | − | 0.265522i | \(-0.0855443\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.5756 | 0.0687594 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 239.385i | − 0.331099i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2152.48 | −2.96893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 387.165i | − 0.532552i | −0.963897 | − | 0.266276i | \(-0.914207\pi\) | ||||
0.963897 | − | 0.266276i | \(-0.0857932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −804.088 | −1.10300 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 23.8514i | − 0.0326284i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 59.1034 | 0.0806322 | 0.0403161 | − | 0.999187i | \(-0.487164\pi\) | ||||
0.0403161 | + | 0.999187i | \(0.487164\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 176.473i | 0.240099i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −918.790 | −1.24666 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1285.33i | − 1.73928i | −0.493687 | − | 0.869640i | \(-0.664351\pi\) | ||||
0.493687 | − | 0.869640i | \(-0.335649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 234.830 | 0.316910 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1450.21i | 1.95183i | 0.218141 | + | 0.975917i | \(0.430001\pi\) | ||||
−0.218141 | + | 0.975917i | \(0.569999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1714.94 | 2.30193 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 374.284i | 0.501050i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −171.590 | −0.229092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 190.150i | 0.253195i | 0.991954 | + | 0.126598i | \(0.0404057\pi\) | ||||
−0.991954 | + | 0.126598i | \(0.959594\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.7878 | −0.0422148 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1366.11i | 1.80941i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 441.225 | 0.582859 | 0.291430 | − | 0.956592i | \(-0.405869\pi\) | ||||
0.291430 | + | 0.956592i | \(0.405869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 553.841i | 0.729698i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1044.28 | −1.37225 | −0.686123 | − | 0.727486i | \(-0.740689\pi\) | ||||
−0.686123 | + | 0.727486i | \(0.740689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 493.254i | 0.646466i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.9314 | −0.0182110 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 250.247i | − 0.326267i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1141.60 | −1.48452 | −0.742262 | − | 0.670110i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670110i | \(0.766247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 433.998i | − 0.562903i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −211.566 | −0.273694 | −0.136847 | − | 0.990592i | \(-0.543697\pi\) | ||||
−0.136847 | + | 0.990592i | \(0.543697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 3966.77i | − 5.11841i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 284.455 | 0.366095 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 12.1126i | − 0.0155489i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1211.30 | 1.55096 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 871.625i | 1.11319i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1871.96 | 2.38466 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 523.213i | 0.664820i | 0.943135 | + | 0.332410i | \(0.107862\pi\) | ||||
−0.943135 | + | 0.332410i | \(0.892138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 303.396 | 0.384533 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.235i | 0.283483i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 562.993 | 0.709953 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 142.474i | − 0.179212i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −503.460 | −0.631693 | −0.315847 | − | 0.948810i | \(-0.602289\pi\) | ||||
−0.315847 | + | 0.948810i | \(0.602289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 33.3590i | − 0.0417510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3409 | 0.0179038 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 131.213i | 0.163404i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 430.325 | 0.534565 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.9499i | 0.0296777i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 100.517 | 0.124248 | 0.0621242 | − | 0.998068i | \(-0.480212\pi\) | ||||
0.0621242 | + | 0.998068i | \(0.480212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 759.830i | 0.936905i | 0.883489 | + | 0.468453i | \(0.155188\pi\) | ||||
−0.883489 | + | 0.468453i | \(0.844812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −518.768 | −0.638091 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 175.346i | − 0.215149i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 654.648 | 0.801283 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 38.4067i | 0.0468946i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −749.705 | −0.913160 | −0.456580 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456580 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 424.800i | 0.516160i | 0.966124 | + | 0.258080i | \(0.0830899\pi\) | ||||
−0.966124 | + | 0.258080i | \(0.916910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2432.36 | 2.94832 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 575.272i | − 0.695613i | −0.937566 | − | 0.347806i | \(-0.886927\pi\) | ||||
0.937566 | − | 0.347806i | \(-0.113073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 157.635 | 0.190151 | 0.0950756 | − | 0.995470i | \(-0.469691\pi\) | ||||
0.0950756 | + | 0.995470i | \(0.469691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 394.490i | − 0.474718i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.99490 | 0.00479580 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.879193i | 0.00105293i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1606.31 | −1.91913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 759.895i | − 0.905716i | −0.891583 | − | 0.452858i | \(-0.850405\pi\) | ||||
0.891583 | − | 0.452858i | \(-0.149595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.2720 | 0.0514530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 555.628i | 0.659108i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1327.91 | −1.57149 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 137.632i | 0.162493i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1103.23 | 1.29945 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 693.638i | − 0.815086i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 315.373 | 0.369722 | 0.184861 | − | 0.982765i | \(-0.440817\pi\) | ||||
0.184861 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 382.375i | − 0.447222i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1222.53 | 1.42652 | 0.713260 | − | 0.700900i | \(-0.247218\pi\) | ||||
0.713260 | + | 0.700900i | \(0.247218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1008.23i | − 1.17373i | −0.809687 | − | 0.586863i | \(-0.800363\pi\) | ||||
0.809687 | − | 0.586863i | \(-0.199637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.22658 | −0.00607036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1140.31i | − 1.32133i | −0.750679 | − | 0.660667i | \(-0.770274\pi\) | ||||
0.750679 | − | 0.660667i | \(-0.229726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 427.192 | 0.493864 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 737.467i | 0.850597i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 265.415 | 0.305426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 409.906i | − 0.470616i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 256.508 | 0.293824 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1237.17i | − 1.41391i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −306.788 | −0.349816 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 541.640i | 0.616200i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −248.968 | −0.282597 | −0.141299 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141299 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 458.136i | 0.518841i | 0.965765 | + | 0.259420i | \(0.0835315\pi\) | ||||
−0.965765 | + | 0.259420i | \(0.916469\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1075.06 | 1.21475 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 312.628i | 0.352456i | 0.984349 | + | 0.176228i | \(0.0563895\pi\) | ||||
−0.984349 | + | 0.176228i | \(0.943610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 247.080 | 0.277930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 692.121i | − 0.776791i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 915.605 | 1.02531 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1883.26i | 2.10420i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −247.089 | −0.275462 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1629.61i | 1.81270i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.22525 | −0.00357963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 282.481i | − 0.312825i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2044.26 | −2.25885 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 375.701i | 0.414224i | 0.978317 | + | 0.207112i | \(0.0664064\pi\) | ||||
−0.978317 | + | 0.207112i | \(0.933594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 103.690 | 0.114071 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.9614i | 0.0460608i | 0.999735 | + | 0.0230304i | \(0.00733145\pi\) | ||||
−0.999735 | + | 0.0230304i | \(0.992669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1990.25 | −2.17991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2418.61i | 2.64329i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −153.680 | −0.167590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1770.71i | 1.92678i | 0.268101 | + | 0.963391i | \(0.413604\pi\) | ||||
−0.268101 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −492.713 | −0.534976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 540.407i | 0.585489i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3046.32 | −3.29332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 46.3511i | 0.0500012i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1668.30 | 1.79581 | 0.897903 | − | 0.440193i | \(-0.145090\pi\) | ||||
0.897903 | + | 0.440193i | \(0.145090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 109.648i | 0.117774i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −689.285 | −0.738784 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 74.0800i | − 0.0792300i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −183.028 | −0.195334 | −0.0976668 | − | 0.995219i | \(-0.531138\pi\) | ||||
−0.0976668 | + | 0.995219i | \(0.531138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 604.152i | 0.643400i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 255.475 | 0.271493 | 0.135747 | − | 0.990744i | \(-0.456657\pi\) | ||||
0.135747 | + | 0.990744i | \(0.456657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.7449i | 0.0135153i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −765.298 | −0.809839 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 187.173i | − 0.197648i | −0.995105 | − | 0.0988242i | \(-0.968492\pi\) | ||||
0.995105 | − | 0.0988242i | \(-0.0315082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −58.5391 | −0.0616851 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 636.142i | 0.668920i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 362.350 | 0.380220 | 0.190110 | − | 0.981763i | \(-0.439115\pi\) | ||||
0.190110 | + | 0.981763i | \(0.439115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3113.36i | − 3.26007i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −999.253 | −1.04415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 466.764i | − 0.486720i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2042.20 | −2.12508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 160.430i | − 0.166594i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −305.330 | −0.316404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1473.76i | − 1.52406i | −0.647545 | − | 0.762028i | \(-0.724204\pi\) | ||||
0.647545 | − | 0.762028i | \(-0.275796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.8373 | 0.0235680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 223.833i | − 0.230518i | −0.993335 | − | 0.115259i | \(-0.963230\pi\) | ||||
0.993335 | − | 0.115259i | \(-0.0367698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.5535 | −0.0334568 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1085.17i | 1.11299i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 825.305 | 0.844734 | 0.422367 | − | 0.906425i | \(-0.361199\pi\) | ||||
0.422367 | + | 0.906425i | \(0.361199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 76.2576i | 0.0778934i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −461.172 | −0.470104 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 411.945i | 0.419069i | 0.977801 | + | 0.209535i | \(0.0671949\pi\) | ||||
−0.977801 | + | 0.209535i | \(0.932805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2607.69 | −2.64741 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 395.084i | − 0.400287i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −688.823 | −0.696484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1607.53i | 1.62213i | 0.584959 | + | 0.811063i | \(0.301111\pi\) | ||||
−0.584959 | + | 0.811063i | \(0.698889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1188.80 | −1.19718 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1295.92i | 1.30243i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 701.364 | 0.703474 | 0.351737 | − | 0.936099i | \(-0.385591\pi\) | ||||
0.351737 | + | 0.936099i | \(0.385591\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1233.58i | 1.23482i |
(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 | 224.3.d.b.127.3 | ✓ | 8 | |
3.2 | odd | 2 | 2016.3.m.c.127.1 | 8 | |||
4.3 | odd | 2 | inner | 224.3.d.b.127.6 | yes | 8 | |
7.6 | odd | 2 | 1568.3.d.n.1471.6 | 8 | |||
8.3 | odd | 2 | 448.3.d.e.127.3 | 8 | |||
8.5 | even | 2 | 448.3.d.e.127.6 | 8 | |||
12.11 | even | 2 | 2016.3.m.c.127.2 | 8 | |||
16.3 | odd | 4 | 1792.3.g.d.127.3 | 8 | |||
16.5 | even | 4 | 1792.3.g.d.127.4 | 8 | |||
16.11 | odd | 4 | 1792.3.g.f.127.6 | 8 | |||
16.13 | even | 4 | 1792.3.g.f.127.5 | 8 | |||
28.27 | even | 2 | 1568.3.d.n.1471.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.d.b.127.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
224.3.d.b.127.6 | yes | 8 | 4.3 | odd | 2 | inner | |
448.3.d.e.127.3 | 8 | 8.3 | odd | 2 | |||
448.3.d.e.127.6 | 8 | 8.5 | even | 2 | |||
1568.3.d.n.1471.3 | 8 | 28.27 | even | 2 | |||
1568.3.d.n.1471.6 | 8 | 7.6 | odd | 2 | |||
1792.3.g.d.127.3 | 8 | 16.3 | odd | 4 | |||
1792.3.g.d.127.4 | 8 | 16.5 | even | 4 | |||
1792.3.g.f.127.5 | 8 | 16.13 | even | 4 | |||
1792.3.g.f.127.6 | 8 | 16.11 | odd | 4 | |||
2016.3.m.c.127.1 | 8 | 3.2 | odd | 2 | |||
2016.3.m.c.127.2 | 8 | 12.11 | even | 2 |