Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Root | \(2.73710 + 1.58027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.79 |
Dual form | 1470.2.n.k.949.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.506647 | + | 2.17791i | 0.226580 | + | 0.973993i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0.650187 | − | 2.13945i | 0.205607 | − | 0.676554i | ||||
\(11\) | −2.23483 | − | 3.87084i | −0.673828 | − | 1.16710i | −0.976810 | − | 0.214107i | \(-0.931316\pi\) |
0.302983 | − | 0.952996i | \(-0.402018\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 5.88388i | 1.63189i | 0.578126 | + | 0.815947i | \(0.303784\pi\) | ||||
−0.578126 | + | 0.815947i | \(0.696216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52773 | − | 1.63280i | −0.394457 | − | 0.421588i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.69895 | − | 3.86764i | 1.62473 | − | 0.938040i | 0.639103 | − | 0.769121i | \(-0.279306\pi\) |
0.985630 | − | 0.168919i | \(-0.0540276\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 3.30913 | − | 5.73159i | 0.759168 | − | 1.31492i | −0.184108 | − | 0.982906i | \(-0.558940\pi\) |
0.943276 | − | 0.332011i | \(-0.107727\pi\) | |||||||
\(20\) | −1.63280 | + | 1.52773i | −0.365106 | + | 0.341610i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.46967i | 0.952936i | ||||||||
\(23\) | −2.26749 | − | 1.30913i | −0.472804 | − | 0.272974i | 0.244609 | − | 0.969622i | \(-0.421340\pi\) |
−0.717413 | + | 0.696648i | \(0.754674\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −4.48662 | + | 2.20687i | −0.897323 | + | 0.441374i | ||||
\(26\) | 2.94194 | − | 5.09559i | 0.576962 | − | 0.999327i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.17246 | 1.51759 | 0.758794 | − | 0.651331i | \(-0.225789\pi\) | ||||
0.758794 | + | 0.651331i | \(0.225789\pi\) | |||||||
\(30\) | 0.506647 | + | 2.17791i | 0.0925007 | + | 0.397631i | ||||
\(31\) | −4.23483 | − | 7.33495i | −0.760598 | − | 1.31740i | −0.942542 | − | 0.334086i | \(-0.891572\pi\) |
0.181944 | − | 0.983309i | \(-0.441761\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 3.87084 | + | 2.23483i | 0.673828 | + | 0.389035i | ||||
\(34\) | −7.73528 | −1.32659 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.76019 | + | 1.59359i | 0.453772 | + | 0.261985i | 0.709422 | − | 0.704784i | \(-0.248956\pi\) |
−0.255650 | + | 0.966769i | \(0.582289\pi\) | |||||||
\(38\) | −5.73159 | + | 3.30913i | −0.929787 | + | 0.536813i | ||||
\(39\) | −2.94194 | − | 5.09559i | −0.471087 | − | 0.815947i | ||||
\(40\) | 2.17791 | − | 0.506647i | 0.344358 | − | 0.0801080i | ||||
\(41\) | 3.56282 | 0.556419 | 0.278209 | − | 0.960520i | \(-0.410259\pi\) | ||||
0.278209 | + | 0.960520i | \(0.410259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43108i | 0.218238i | 0.994029 | + | 0.109119i | \(0.0348029\pi\) | ||||
−0.994029 | + | 0.109119i | \(0.965197\pi\) | |||||||
\(44\) | 2.23483 | − | 3.87084i | 0.336914 | − | 0.583552i | ||||
\(45\) | 2.13945 | + | 0.650187i | 0.318931 | + | 0.0969242i | ||||
\(46\) | 1.30913 | + | 2.26749i | 0.193021 | + | 0.334323i | ||||
\(47\) | 5.88094 | + | 3.39536i | 0.857824 | + | 0.495265i | 0.863283 | − | 0.504720i | \(-0.168404\pi\) |
−0.00545912 | + | 0.999985i | \(0.501738\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.98896 | + | 0.332104i | 0.705545 | + | 0.0469666i | ||||
\(51\) | −3.86764 | + | 6.69895i | −0.541578 | + | 0.938040i | ||||
\(52\) | −5.09559 | + | 2.94194i | −0.706631 | + | 0.407974i | ||||
\(53\) | −1.19661 | + | 0.690865i | −0.164367 | + | 0.0948976i | −0.579927 | − | 0.814668i | \(-0.696919\pi\) |
0.415560 | + | 0.909566i | \(0.363586\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 7.29809 | − | 6.82843i | 0.984075 | − | 0.920745i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.61827i | 0.876611i | ||||||||
\(58\) | −7.07756 | − | 4.08623i | −0.929329 | − | 0.536548i | ||||
\(59\) | 2.33210 | + | 4.03932i | 0.303614 | + | 0.525875i | 0.976952 | − | 0.213460i | \(-0.0684733\pi\) |
−0.673338 | + | 0.739335i | \(0.735140\pi\) | |||||||
\(60\) | 0.650187 | − | 2.13945i | 0.0839388 | − | 0.276202i | ||||
\(61\) | −4.89841 | + | 8.48430i | −0.627178 | + | 1.08630i | 0.360938 | + | 0.932590i | \(0.382457\pi\) |
−0.988115 | + | 0.153714i | \(0.950877\pi\) | |||||||
\(62\) | 8.46967i | 1.07565i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −12.8146 | + | 2.98105i | −1.58945 | + | 0.369754i | ||||
\(66\) | −2.23483 | − | 3.87084i | −0.275089 | − | 0.476468i | ||||
\(67\) | −1.60336 | + | 0.925698i | −0.195881 | + | 0.113092i | −0.594733 | − | 0.803923i | \(-0.702742\pi\) |
0.398852 | + | 0.917015i | \(0.369409\pi\) | |||||||
\(68\) | 6.69895 | + | 3.86764i | 0.812366 | + | 0.469020i | ||||
\(69\) | 2.61827 | 0.315203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02386 | 0.240187 | 0.120094 | − | 0.992763i | \(-0.461680\pi\) | ||||
0.120094 | + | 0.992763i | \(0.461680\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 3.47871 | − | 2.00843i | 0.407152 | − | 0.235069i | −0.282413 | − | 0.959293i | \(-0.591135\pi\) |
0.689565 | + | 0.724223i | \(0.257802\pi\) | |||||||
\(74\) | −1.59359 | − | 2.76019i | −0.185252 | − | 0.320865i | ||||
\(75\) | 2.78209 | − | 4.15451i | 0.321248 | − | 0.479722i | ||||
\(76\) | 6.61827 | 0.759168 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.88388i | 0.666218i | ||||||||
\(79\) | −3.49264 | + | 6.04942i | −0.392952 | + | 0.680613i | −0.992837 | − | 0.119473i | \(-0.961880\pi\) |
0.599885 | + | 0.800086i | \(0.295213\pi\) | |||||||
\(80\) | −2.13945 | − | 0.650187i | −0.239198 | − | 0.0726932i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.08549 | − | 1.78141i | −0.340735 | − | 0.196724i | ||||
\(83\) | 5.35965i | 0.588298i | 0.955760 | + | 0.294149i | \(0.0950361\pi\) | ||||
−0.955760 | + | 0.294149i | \(0.904964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8174 | + | 12.6302i | 1.28178 | + | 1.36994i | ||||
\(86\) | 0.715541 | − | 1.23935i | 0.0771588 | − | 0.133643i | ||||
\(87\) | −7.07756 | + | 4.08623i | −0.758794 | + | 0.438090i | ||||
\(88\) | −3.87084 | + | 2.23483i | −0.412633 | + | 0.238234i | ||||
\(89\) | 7.19562 | − | 12.4632i | 0.762734 | − | 1.32109i | −0.178702 | − | 0.983903i | \(-0.557190\pi\) |
0.941436 | − | 0.337191i | \(-0.109477\pi\) | |||||||
\(90\) | −1.52773 | − | 1.63280i | −0.161036 | − | 0.172113i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2.61827i | − | 0.272974i | ||||||
\(93\) | 7.33495 | + | 4.23483i | 0.760598 | + | 0.439132i | ||||
\(94\) | −3.39536 | − | 5.88094i | −0.350205 | − | 0.606573i | ||||
\(95\) | 14.1595 | + | 4.30312i | 1.45273 | + | 0.441490i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 7.71966i | 0.783813i | 0.920005 | + | 0.391906i | \(0.128184\pi\) | ||||
−0.920005 | + | 0.391906i | \(0.871816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.46967 | −0.449218 | ||||||||
\(100\) | −4.15451 | − | 2.78209i | −0.415451 | − | 0.278209i | ||||
\(101\) | 6.67722 | + | 11.5653i | 0.664408 | + | 1.15079i | 0.979446 | + | 0.201709i | \(0.0646495\pi\) |
−0.315038 | + | 0.949079i | \(0.602017\pi\) | |||||||
\(102\) | 6.69895 | − | 3.86764i | 0.663294 | − | 0.382953i | ||||
\(103\) | 8.10569 | + | 4.67982i | 0.798678 | + | 0.461117i | 0.843009 | − | 0.537900i | \(-0.180782\pi\) |
−0.0443310 | + | 0.999017i | \(0.514116\pi\) | |||||||
\(104\) | 5.88388 | 0.576962 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.38173 | 0.134205 | ||||||||
\(107\) | 9.54057 | + | 5.50825i | 0.922322 | + | 0.532503i | 0.884375 | − | 0.466777i | \(-0.154585\pi\) |
0.0379467 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −2.34772 | − | 4.06637i | −0.224871 | − | 0.389488i | 0.731410 | − | 0.681938i | \(-0.238863\pi\) |
−0.956281 | + | 0.292451i | \(0.905529\pi\) | |||||||
\(110\) | −9.73455 | + | 2.26454i | −0.928153 | + | 0.215916i | ||||
\(111\) | −3.18719 | −0.302514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.5723i | − | 1.18271i | −0.806413 | − | 0.591353i | \(-0.798594\pi\) | ||
0.806413 | − | 0.591353i | \(-0.201406\pi\) | |||||||
\(114\) | 3.30913 | − | 5.73159i | 0.309929 | − | 0.536813i | ||||
\(115\) | 1.70237 | − | 5.60166i | 0.158746 | − | 0.522358i | ||||
\(116\) | 4.08623 | + | 7.07756i | 0.379397 | + | 0.657135i | ||||
\(117\) | 5.09559 | + | 2.94194i | 0.471087 | + | 0.271982i | ||||
\(118\) | − | 4.66421i | − | 0.429375i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.63280 | + | 1.52773i | −0.149054 | + | 0.139462i | ||||
\(121\) | −4.48896 | + | 7.77510i | −0.408087 | + | 0.706828i | ||||
\(122\) | 8.48430 | − | 4.89841i | 0.768133 | − | 0.443482i | ||||
\(123\) | −3.08549 | + | 1.78141i | −0.278209 | + | 0.160624i | ||||
\(124\) | 4.23483 | − | 7.33495i | 0.380299 | − | 0.658698i | ||||
\(125\) | −7.07950 | − | 8.65336i | −0.633210 | − | 0.773980i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.59619i | 0.585317i | 0.956217 | + | 0.292658i | \(0.0945399\pi\) | ||||
−0.956217 | + | 0.292658i | \(0.905460\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −0.715541 | − | 1.23935i | −0.0629999 | − | 0.109119i | ||||
\(130\) | 12.5883 | + | 3.82562i | 1.10407 | + | 0.335529i | ||||
\(131\) | 1.16053 | − | 2.01010i | 0.101396 | − | 0.175623i | −0.810864 | − | 0.585235i | \(-0.801002\pi\) |
0.912260 | + | 0.409611i | \(0.134336\pi\) | |||||||
\(132\) | 4.46967i | 0.389035i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.85140 | 0.159936 | ||||||||
\(135\) | −2.17791 | + | 0.506647i | −0.187445 | + | 0.0436053i | ||||
\(136\) | −3.86764 | − | 6.69895i | −0.331647 | − | 0.574430i | ||||
\(137\) | 12.3626 | − | 7.13756i | 1.05621 | − | 0.609803i | 0.131828 | − | 0.991273i | \(-0.457915\pi\) |
0.924381 | + | 0.381469i | \(0.124582\pi\) | |||||||
\(138\) | −2.26749 | − | 1.30913i | −0.193021 | − | 0.111441i | ||||
\(139\) | 14.9632 | 1.26916 | 0.634581 | − | 0.772857i | \(-0.281173\pi\) | ||||
0.634581 | + | 0.772857i | \(0.281173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.79073 | −0.571883 | ||||||||
\(142\) | −1.75271 | − | 1.01193i | −0.147084 | − | 0.0849191i | ||||
\(143\) | 22.7756 | − | 13.1495i | 1.90459 | − | 1.09962i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.14055 | + | 17.7989i | 0.343854 | + | 1.47812i | ||||
\(146\) | −4.01687 | −0.332438 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.18719i | 0.261985i | ||||||||
\(149\) | 5.58255 | − | 9.66926i | 0.457341 | − | 0.792137i | −0.541479 | − | 0.840714i | \(-0.682135\pi\) |
0.998819 | + | 0.0485773i | \(0.0154687\pi\) | |||||||
\(150\) | −4.48662 | + | 2.20687i | −0.366331 | + | 0.180190i | ||||
\(151\) | −0.332104 | − | 0.575221i | −0.0270263 | − | 0.0468109i | 0.852196 | − | 0.523223i | \(-0.175270\pi\) |
−0.879222 | + | 0.476412i | \(0.841937\pi\) | |||||||
\(152\) | −5.73159 | − | 3.30913i | −0.464893 | − | 0.268406i | ||||
\(153\) | − | 7.73528i | − | 0.625360i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8293 | − | 12.9393i | 1.11080 | − | 1.03931i | ||||
\(156\) | 2.94194 | − | 5.09559i | 0.235544 | − | 0.407974i | ||||
\(157\) | 6.99907 | − | 4.04092i | 0.558587 | − | 0.322500i | −0.193991 | − | 0.981003i | \(-0.562143\pi\) |
0.752578 | + | 0.658503i | \(0.228810\pi\) | |||||||
\(158\) | 6.04942 | − | 3.49264i | 0.481266 | − | 0.277859i | ||||
\(159\) | 0.690865 | − | 1.19661i | 0.0547892 | − | 0.0948976i | ||||
\(160\) | 1.52773 | + | 1.63280i | 0.120777 | + | 0.129085i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 0.724575 | + | 0.418334i | 0.0567531 | + | 0.0327664i | 0.528108 | − | 0.849177i | \(-0.322902\pi\) |
−0.471355 | + | 0.881944i | \(0.656235\pi\) | |||||||
\(164\) | 1.78141 | + | 3.08549i | 0.139105 | + | 0.240936i | ||||
\(165\) | −2.90612 | + | 9.56264i | −0.226241 | + | 0.744450i | ||||
\(166\) | 2.67982 | − | 4.64159i | 0.207995 | − | 0.360257i | ||||
\(167\) | − | 2.66762i | − | 0.206427i | −0.994659 | − | 0.103213i | \(-0.967088\pi\) | ||
0.994659 | − | 0.103213i | \(-0.0329125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.6200 | −1.66308 | ||||||||
\(170\) | −3.91906 | − | 16.8468i | −0.300578 | − | 1.29209i | ||||
\(171\) | −3.30913 | − | 5.73159i | −0.253056 | − | 0.438306i | ||||
\(172\) | −1.23935 | + | 0.715541i | −0.0944998 | + | 0.0545595i | ||||
\(173\) | −0.560613 | − | 0.323670i | −0.0426226 | − | 0.0246082i | 0.478537 | − | 0.878067i | \(-0.341167\pi\) |
−0.521160 | + | 0.853459i | \(0.674500\pi\) | |||||||
\(174\) | 8.17246 | 0.619553 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.46967 | 0.336914 | ||||||||
\(177\) | −4.03932 | − | 2.33210i | −0.303614 | − | 0.175292i | ||||
\(178\) | −12.4632 | + | 7.19562i | −0.934155 | + | 0.539335i | ||||
\(179\) | −12.8687 | − | 22.2893i | −0.961853 | − | 1.66598i | −0.717842 | − | 0.696206i | \(-0.754870\pi\) |
−0.244011 | − | 0.969772i | \(-0.578463\pi\) | |||||||
\(180\) | 0.506647 | + | 2.17791i | 0.0377633 | + | 0.162332i | ||||
\(181\) | 7.42245 | 0.551707 | 0.275853 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275853 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.79683i | − | 0.724203i | ||||||
\(184\) | −1.30913 | + | 2.26749i | −0.0965107 | + | 0.167161i | ||||
\(185\) | −2.07227 | + | 6.81884i | −0.152356 | + | 0.501331i | ||||
\(186\) | −4.23483 | − | 7.33495i | −0.310513 | − | 0.537824i | ||||
\(187\) | −29.9421 | − | 17.2871i | −2.18958 | − | 1.26415i | ||||
\(188\) | 6.79073i | 0.495265i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.1109 | − | 10.8063i | −0.733522 | − | 0.783975i | ||||
\(191\) | 0.542261 | − | 0.939224i | 0.0392367 | − | 0.0679599i | −0.845740 | − | 0.533595i | \(-0.820841\pi\) |
0.884977 | + | 0.465635i | \(0.154174\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −7.74169 | + | 4.46967i | −0.557259 | + | 0.321734i | −0.752045 | − | 0.659112i | \(-0.770932\pi\) |
0.194786 | + | 0.980846i | \(0.437599\pi\) | |||||||
\(194\) | 3.85983 | − | 6.68542i | 0.277120 | − | 0.479985i | ||||
\(195\) | 9.60723 | − | 8.98896i | 0.687988 | − | 0.643713i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.45890i | 0.531425i | 0.964052 | + | 0.265712i | \(0.0856071\pi\) | ||||
−0.964052 | + | 0.265712i | \(0.914393\pi\) | |||||||
\(198\) | 3.87084 | + | 2.23483i | 0.275089 | + | 0.158823i | ||||
\(199\) | 12.9147 | + | 22.3688i | 0.915496 | + | 1.58569i | 0.806174 | + | 0.591679i | \(0.201535\pi\) |
0.109322 | + | 0.994006i | \(0.465132\pi\) | |||||||
\(200\) | 2.20687 | + | 4.48662i | 0.156049 | + | 0.317252i | ||||
\(201\) | 0.925698 | − | 1.60336i | 0.0652937 | − | 0.113092i | ||||
\(202\) | − | 13.3544i | − | 0.939615i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.73528 | −0.541578 | ||||||||
\(205\) | 1.80509 | + | 7.75951i | 0.126073 | + | 0.541948i | ||||
\(206\) | −4.67982 | − | 8.10569i | −0.326059 | − | 0.564750i | ||||
\(207\) | −2.26749 | + | 1.30913i | −0.157601 | + | 0.0909912i | ||||
\(208\) | −5.09559 | − | 2.94194i | −0.353316 | − | 0.203987i | ||||
\(209\) | −29.5815 | −2.04619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.53375 | 0.380959 | 0.190479 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190479 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(212\) | −1.19661 | − | 0.690865i | −0.0821837 | − | 0.0474488i | ||||
\(213\) | −1.75271 | + | 1.01193i | −0.120094 | + | 0.0693361i | ||||
\(214\) | −5.50825 | − | 9.54057i | −0.376536 | − | 0.652180i | ||||
\(215\) | −3.11677 | + | 0.725054i | −0.212562 | + | 0.0494483i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.69544i | 0.318015i | ||||||||
\(219\) | −2.00843 | + | 3.47871i | −0.135717 | + | 0.235069i | ||||
\(220\) | 9.56264 | + | 2.90612i | 0.644713 | + | 0.195931i | ||||
\(221\) | 22.7567 | + | 39.4158i | 1.53078 | + | 2.65139i | ||||
\(222\) | 2.76019 | + | 1.59359i | 0.185252 | + | 0.106955i | ||||
\(223\) | − | 3.28248i | − | 0.219811i | −0.993942 | − | 0.109906i | \(-0.964945\pi\) | ||
0.993942 | − | 0.109906i | \(-0.0350548\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.332104 | + | 4.98896i | −0.0221403 | + | 0.332597i | ||||
\(226\) | −6.28617 | + | 10.8880i | −0.418150 | + | 0.724256i | ||||
\(227\) | 3.82810 | − | 2.21016i | 0.254080 | − | 0.146693i | −0.367551 | − | 0.930003i | \(-0.619804\pi\) |
0.621631 | + | 0.783310i | \(0.286470\pi\) | |||||||
\(228\) | −5.73159 | + | 3.30913i | −0.379584 | + | 0.219153i | ||||
\(229\) | −3.98635 | + | 6.90456i | −0.263426 | + | 0.456266i | −0.967150 | − | 0.254207i | \(-0.918186\pi\) |
0.703724 | + | 0.710473i | \(0.251519\pi\) | |||||||
\(230\) | −4.27512 | + | 4.00000i | −0.281893 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.17246i | − | 0.536548i | ||||||
\(233\) | −15.5502 | − | 8.97792i | −1.01873 | − | 0.588163i | −0.104993 | − | 0.994473i | \(-0.533482\pi\) |
−0.913735 | + | 0.406310i | \(0.866815\pi\) | |||||||
\(234\) | −2.94194 | − | 5.09559i | −0.192321 | − | 0.333109i | ||||
\(235\) | −4.41525 | + | 14.5284i | −0.288019 | + | 0.947731i | ||||
\(236\) | −2.33210 | + | 4.03932i | −0.151807 | + | 0.262938i | ||||
\(237\) | − | 6.98527i | − | 0.453742i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.41296 | −0.350135 | −0.175068 | − | 0.984556i | \(-0.556014\pi\) | ||||
−0.175068 | + | 0.984556i | \(0.556014\pi\) | |||||||
\(240\) | 2.17791 | − | 0.506647i | 0.140584 | − | 0.0327039i | ||||
\(241\) | 2.34835 | + | 4.06745i | 0.151270 | + | 0.262008i | 0.931695 | − | 0.363242i | \(-0.118330\pi\) |
−0.780424 | + | 0.625250i | \(0.784997\pi\) | |||||||
\(242\) | 7.77510 | − | 4.48896i | 0.499803 | − | 0.288561i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −9.79683 | −0.627178 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.56282 | 0.227157 | ||||||||
\(247\) | 33.7240 | + | 19.4706i | 2.14581 | + | 1.23888i | ||||
\(248\) | −7.33495 | + | 4.23483i | −0.465770 | + | 0.268912i | ||||
\(249\) | −2.67982 | − | 4.64159i | −0.169827 | − | 0.294149i | ||||
\(250\) | 1.80435 | + | 11.0338i | 0.114117 | + | 0.697838i | ||||
\(251\) | 7.73402 | 0.488167 | 0.244084 | − | 0.969754i | \(-0.421513\pi\) | ||||
0.244084 | + | 0.969754i | \(0.421513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7028i | 0.735748i | ||||||||
\(254\) | 3.29809 | − | 5.71247i | 0.206941 | − | 0.358432i | ||||
\(255\) | −16.5493 | − | 5.02938i | −1.03635 | − | 0.314952i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.16430 | + | 0.672210i | 0.0726271 | + | 0.0419313i | 0.535874 | − | 0.844298i | \(-0.319982\pi\) |
−0.463247 | + | 0.886229i | \(0.653316\pi\) | |||||||
\(258\) | 1.43108i | 0.0890953i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.98896 | − | 9.60723i | −0.557472 | − | 0.595815i | ||||
\(261\) | 4.08623 | − | 7.07756i | 0.252931 | − | 0.438090i | ||||
\(262\) | −2.01010 | + | 1.16053i | −0.124184 | + | 0.0716979i | ||||
\(263\) | −3.78193 | + | 2.18350i | −0.233204 | + | 0.134640i | −0.612049 | − | 0.790820i | \(-0.709655\pi\) |
0.378845 | + | 0.925460i | \(0.376321\pi\) | |||||||
\(264\) | 2.23483 | − | 3.87084i | 0.137544 | − | 0.238234i | ||||
\(265\) | −2.11091 | − | 2.25610i | −0.129672 | − | 0.138591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3912i | 0.880730i | ||||||||
\(268\) | −1.60336 | − | 0.925698i | −0.0979406 | − | 0.0565460i | ||||
\(269\) | 11.5336 | + | 19.9767i | 0.703213 | + | 1.21800i | 0.967333 | + | 0.253511i | \(0.0815854\pi\) |
−0.264119 | + | 0.964490i | \(0.585081\pi\) | |||||||
\(270\) | 2.13945 | + | 0.650187i | 0.130203 | + | 0.0395691i | ||||
\(271\) | −7.36047 | + | 12.7487i | −0.447117 | + | 0.774429i | −0.998197 | − | 0.0600236i | \(-0.980882\pi\) |
0.551080 | + | 0.834452i | \(0.314216\pi\) | |||||||
\(272\) | 7.73528i | 0.469020i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.2751 | −0.862392 | ||||||||
\(275\) | 18.5693 | + | 12.4350i | 1.11977 | + | 0.749860i | ||||
\(276\) | 1.30913 | + | 2.26749i | 0.0788007 | + | 0.136487i | ||||
\(277\) | 2.78085 | − | 1.60552i | 0.167085 | − | 0.0964665i | −0.414126 | − | 0.910220i | \(-0.635913\pi\) |
0.581211 | + | 0.813753i | \(0.302579\pi\) | |||||||
\(278\) | −12.9585 | − | 7.48159i | −0.777199 | − | 0.448716i | ||||
\(279\) | −8.46967 | −0.507066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.72488 | −0.460827 | −0.230414 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230414 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(282\) | 5.88094 | + | 3.39536i | 0.350205 | + | 0.202191i | ||||
\(283\) | −25.5992 | + | 14.7797i | −1.52171 | + | 0.878561i | −0.522041 | + | 0.852920i | \(0.674829\pi\) |
−0.999671 | + | 0.0256411i | \(0.991837\pi\) | |||||||
\(284\) | 1.01193 | + | 1.75271i | 0.0600469 | + | 0.104004i | ||||
\(285\) | −14.4140 | + | 3.35313i | −0.853813 | + | 0.198622i | ||||
\(286\) | −26.2990 | −1.55509 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 21.4172 | − | 37.0958i | 1.25984 | − | 2.18210i | ||||
\(290\) | 5.31363 | − | 17.4846i | 0.312027 | − | 1.02673i | ||||
\(291\) | −3.85983 | − | 6.68542i | −0.226267 | − | 0.391906i | ||||
\(292\) | 3.47871 | + | 2.00843i | 0.203576 | + | 0.117535i | ||||
\(293\) | 1.17679i | 0.0687487i | 0.999409 | + | 0.0343743i | \(0.0109438\pi\) | ||||
−0.999409 | + | 0.0343743i | \(0.989056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.61574 | + | 7.12563i | −0.443406 | + | 0.414870i | ||||
\(296\) | 1.59359 | − | 2.76019i | 0.0926258 | − | 0.160433i | ||||
\(297\) | 3.87084 | − | 2.23483i | 0.224609 | − | 0.129678i | ||||
\(298\) | −9.66926 | + | 5.58255i | −0.560125 | + | 0.323389i | ||||
\(299\) | 7.70279 | − | 13.3416i | 0.445464 | − | 0.771566i | ||||
\(300\) | 4.98896 | + | 0.332104i | 0.288038 | + | 0.0191740i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.664208i | 0.0382209i | ||||||||
\(303\) | −11.5653 | − | 6.67722i | −0.664408 | − | 0.383596i | ||||
\(304\) | 3.30913 | + | 5.73159i | 0.189792 | + | 0.328729i | ||||
\(305\) | −20.9599 | − | 6.36978i | −1.20016 | − | 0.364732i | ||||
\(306\) | −3.86764 | + | 6.69895i | −0.221098 | + | 0.382953i | ||||
\(307\) | − | 20.3761i | − | 1.16293i | −0.813572 | − | 0.581464i | \(-0.802480\pi\) | ||
0.813572 | − | 0.581464i | \(-0.197520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.35965 | −0.532452 | ||||||||
\(310\) | −18.4462 | + | 4.29113i | −1.04767 | + | 0.243720i | ||||
\(311\) | 9.44670 | + | 16.3622i | 0.535673 | + | 0.927813i | 0.999130 | + | 0.0416937i | \(0.0132754\pi\) |
−0.463457 | + | 0.886119i | \(0.653391\pi\) | |||||||
\(312\) | −5.09559 | + | 2.94194i | −0.288481 | + | 0.166555i | ||||
\(313\) | −14.2763 | − | 8.24245i | −0.806946 | − | 0.465891i | 0.0389480 | − | 0.999241i | \(-0.487599\pi\) |
−0.845894 | + | 0.533351i | \(0.820933\pi\) | |||||||
\(314\) | −8.08184 | −0.456084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.98527 | −0.392952 | ||||||||
\(317\) | −8.93830 | − | 5.16053i | −0.502025 | − | 0.289844i | 0.227524 | − | 0.973772i | \(-0.426937\pi\) |
−0.729549 | + | 0.683928i | \(0.760270\pi\) | |||||||
\(318\) | −1.19661 | + | 0.690865i | −0.0671027 | + | 0.0387418i | ||||
\(319\) | −18.2641 | − | 31.6343i | −1.02259 | − | 1.77118i | ||||
\(320\) | −0.506647 | − | 2.17791i | −0.0283224 | − | 0.121749i | ||||
\(321\) | −11.0165 | −0.614881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 51.1941i | − | 2.84852i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −12.9849 | − | 26.3987i | −0.720275 | − | 1.46434i | ||||
\(326\) | −0.418334 | − | 0.724575i | −0.0231694 | − | 0.0401305i | ||||
\(327\) | 4.06637 | + | 2.34772i | 0.224871 | + | 0.129829i | ||||
\(328\) | − | 3.56282i | − | 0.196724i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.29809 | − | 6.82843i | 0.401747 | − | 0.375893i | ||||
\(331\) | 9.59530 | − | 16.6195i | 0.527405 | − | 0.913493i | −0.472084 | − | 0.881553i | \(-0.656498\pi\) |
0.999490 | − | 0.0319396i | \(-0.0101684\pi\) | |||||||
\(332\) | −4.64159 | + | 2.67982i | −0.254740 | + | 0.147074i | ||||
\(333\) | 2.76019 | − | 1.59359i | 0.151257 | − | 0.0873284i | ||||
\(334\) | −1.33381 | + | 2.31023i | −0.0729829 | + | 0.126410i | ||||
\(335\) | −2.82843 | − | 3.02297i | −0.154533 | − | 0.165162i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.6035i | − | 1.50366i | −0.659357 | − | 0.751830i | \(-0.729171\pi\) | ||
0.659357 | − | 0.751830i | \(-0.270829\pi\) | |||||||
\(338\) | 18.7235 | + | 10.8100i | 1.01842 | + | 0.587988i | ||||
\(339\) | 6.28617 | + | 10.8880i | 0.341418 | + | 0.591353i | ||||
\(340\) | −5.02938 | + | 16.5493i | −0.272756 | + | 0.897509i | ||||
\(341\) | −18.9283 | + | 32.7848i | −1.02502 | + | 1.77539i | ||||
\(342\) | 6.61827i | 0.357875i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.43108 | 0.0771588 | ||||||||
\(345\) | 1.32654 | + | 5.70237i | 0.0714185 | + | 0.307005i | ||||
\(346\) | 0.323670 | + | 0.560613i | 0.0174006 | + | 0.0301387i | ||||
\(347\) | −17.6463 | + | 10.1881i | −0.947301 | + | 0.546924i | −0.892241 | − | 0.451559i | \(-0.850868\pi\) |
−0.0550595 | + | 0.998483i | \(0.517535\pi\) | |||||||
\(348\) | −7.07756 | − | 4.08623i | −0.379397 | − | 0.219045i | ||||
\(349\) | 17.8281 | 0.954314 | 0.477157 | − | 0.878818i | \(-0.341667\pi\) | ||||
0.477157 | + | 0.878818i | \(0.341667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.88388 | −0.314058 | ||||||||
\(352\) | −3.87084 | − | 2.23483i | −0.206317 | − | 0.119117i | ||||
\(353\) | 3.04275 | − | 1.75673i | 0.161949 | − | 0.0935014i | −0.416835 | − | 0.908982i | \(-0.636861\pi\) |
0.578784 | + | 0.815481i | \(0.303527\pi\) | |||||||
\(354\) | 2.33210 | + | 4.03932i | 0.123950 | + | 0.214688i | ||||
\(355\) | 1.02538 | + | 4.40778i | 0.0544216 | + | 0.233941i | ||||
\(356\) | 14.3912 | 0.762734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.7374i | 1.36027i | ||||||||
\(359\) | −1.09898 | + | 1.90349i | −0.0580018 | + | 0.100462i | −0.893568 | − | 0.448927i | \(-0.851806\pi\) |
0.835567 | + | 0.549389i | \(0.185140\pi\) | |||||||
\(360\) | 0.650187 | − | 2.13945i | 0.0342679 | − | 0.112759i | ||||
\(361\) | −12.4007 | − | 21.4787i | −0.652671 | − | 1.13046i | ||||
\(362\) | −6.42803 | − | 3.71123i | −0.337850 | − | 0.195058i | ||||
\(363\) | − | 8.97792i | − | 0.471218i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.13668 | + | 6.55876i | 0.321208 | + | 0.343301i | ||||
\(366\) | −4.89841 | + | 8.48430i | −0.256044 | + | 0.443482i | ||||
\(367\) | −24.9173 | + | 14.3860i | −1.30067 | + | 0.750945i | −0.980520 | − | 0.196421i | \(-0.937068\pi\) |
−0.320155 | + | 0.947365i | \(0.603735\pi\) | |||||||
\(368\) | 2.26749 | − | 1.30913i | 0.118201 | − | 0.0682434i | ||||
\(369\) | 1.78141 | − | 3.08549i | 0.0927364 | − | 0.160624i | ||||
\(370\) | 5.20406 | − | 4.86915i | 0.270546 | − | 0.253135i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.46967i | 0.439132i | ||||||||
\(373\) | −12.6171 | − | 7.28446i | −0.653286 | − | 0.377175i | 0.136428 | − | 0.990650i | \(-0.456438\pi\) |
−0.789714 | + | 0.613475i | \(0.789771\pi\) | |||||||
\(374\) | 17.2871 | + | 29.9421i | 0.893892 | + | 1.54827i | ||||
\(375\) | 10.4577 | + | 3.95428i | 0.540034 | + | 0.204198i | ||||
\(376\) | 3.39536 | − | 5.88094i | 0.175103 | − | 0.303287i | ||||
\(377\) | 48.0858i | 2.47654i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.7868 | 1.58141 | 0.790705 | − | 0.612197i | \(-0.209714\pi\) | ||||
0.790705 | + | 0.612197i | \(0.209714\pi\) | |||||||
\(380\) | 3.35313 | + | 14.4140i | 0.172012 | + | 0.739424i | ||||
\(381\) | −3.29809 | − | 5.71247i | −0.168966 | − | 0.292658i | ||||
\(382\) | −0.939224 | + | 0.542261i | −0.0480549 | + | 0.0277445i | ||||
\(383\) | −20.2139 | − | 11.6705i | −1.03288 | − | 0.596334i | −0.115072 | − | 0.993357i | \(-0.536710\pi\) |
−0.917809 | + | 0.397023i | \(0.870043\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.93933 | 0.455000 | ||||||||
\(387\) | 1.23935 | + | 0.715541i | 0.0629999 | + | 0.0363730i | ||||
\(388\) | −6.68542 | + | 3.85983i | −0.339401 | + | 0.195953i | ||||
\(389\) | −0.609209 | − | 1.05518i | −0.0308881 | − | 0.0534998i | 0.850168 | − | 0.526511i | \(-0.176500\pi\) |
−0.881056 | + | 0.473012i | \(0.843167\pi\) | |||||||
\(390\) | −12.8146 | + | 2.98105i | −0.648892 | + | 0.150951i | ||||
\(391\) | −20.2530 | −1.02424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.32106i | 0.117082i | ||||||||
\(394\) | 3.72945 | − | 6.45960i | 0.187887 | − | 0.325430i | ||||
\(395\) | −14.9447 | − | 4.54174i | −0.751947 | − | 0.228520i | ||||
\(396\) | −2.23483 | − | 3.87084i | −0.112305 | − | 0.194517i | ||||
\(397\) | 7.27977 | + | 4.20298i | 0.365361 | + | 0.210941i | 0.671430 | − | 0.741068i | \(-0.265680\pi\) |
−0.306069 | + | 0.952009i | \(0.599014\pi\) | |||||||
\(398\) | − | 25.8293i | − | 1.29471i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | 0.332104 | − | 0.575221i | 0.0165845 | − | 0.0287252i | −0.857614 | − | 0.514294i | \(-0.828054\pi\) |
0.874199 | + | 0.485569i | \(0.161387\pi\) | |||||||
\(402\) | −1.60336 | + | 0.925698i | −0.0799681 | + | 0.0461696i | ||||
\(403\) | 43.1579 | − | 24.9172i | 2.14985 | − | 1.24122i | ||||
\(404\) | −6.67722 | + | 11.5653i | −0.332204 | + | 0.575394i | ||||
\(405\) | 1.63280 | − | 1.52773i | 0.0811347 | − | 0.0759133i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.2457i | − | 0.706131i | ||||||
\(408\) | 6.69895 | + | 3.86764i | 0.331647 | + | 0.191477i | ||||
\(409\) | −3.69238 | − | 6.39539i | −0.182576 | − | 0.316231i | 0.760181 | − | 0.649712i | \(-0.225110\pi\) |
−0.942757 | + | 0.333480i | \(0.891777\pi\) | |||||||
\(410\) | 2.31650 | − | 7.62248i | 0.114404 | − | 0.376447i | ||||
\(411\) | −7.13756 | + | 12.3626i | −0.352070 | + | 0.609803i | ||||
\(412\) | 9.35965i | 0.461117i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.61827 | 0.128681 | ||||||||
\(415\) | −11.6728 | + | 2.71545i | −0.572998 | + | 0.133296i | ||||
\(416\) | 2.94194 | + | 5.09559i | 0.144240 | + | 0.249832i | ||||
\(417\) | −12.9585 | + | 7.48159i | −0.634581 | + | 0.366375i | ||||
\(418\) | 25.6183 | + | 14.7907i | 1.25303 | + | 0.723438i | ||||
\(419\) | −18.6274 | −0.910009 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5043 | −0.658159 | −0.329079 | − | 0.944302i | \(-0.606738\pi\) | ||||
−0.329079 | + | 0.944302i | \(0.606738\pi\) | |||||||
\(422\) | −4.79237 | − | 2.76687i | −0.233289 | − | 0.134689i | ||||
\(423\) | 5.88094 | − | 3.39536i | 0.285941 | − | 0.165088i | ||||
\(424\) | 0.690865 | + | 1.19661i | 0.0335514 | + | 0.0581127i | ||||
\(425\) | −21.5202 | + | 32.1363i | −1.04388 | + | 1.55884i | ||||
\(426\) | 2.02386 | 0.0980561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0165i | 0.532503i | ||||||||
\(429\) | −13.1495 | + | 22.7756i | −0.634863 | + | 1.09962i | ||||
\(430\) | 3.06173 | + | 0.930471i | 0.147650 | + | 0.0448713i | ||||
\(431\) | 15.8404 | + | 27.4363i | 0.763003 | + | 1.32156i | 0.941296 | + | 0.337583i | \(0.109609\pi\) |
−0.178293 | + | 0.983977i | \(0.557057\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 25.3184i | 1.21672i | 0.793660 | + | 0.608362i | \(0.208173\pi\) | ||||
−0.793660 | + | 0.608362i | \(0.791827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.4853 | − | 13.3440i | −0.598623 | − | 0.639797i | ||||
\(436\) | 2.34772 | − | 4.06637i | 0.112435 | − | 0.194744i | ||||
\(437\) | −15.0068 | + | 8.66421i | −0.717875 | + | 0.414465i | ||||
\(438\) | 3.47871 | − | 2.00843i | 0.166219 | − | 0.0959667i | ||||
\(439\) | 16.4073 | − | 28.4183i | 0.783077 | − | 1.35633i | −0.147064 | − | 0.989127i | \(-0.546982\pi\) |
0.930141 | − | 0.367203i | \(-0.119684\pi\) | |||||||
\(440\) | −6.82843 | − | 7.29809i | −0.325532 | − | 0.347923i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 45.5134i | − | 2.16485i | ||||||
\(443\) | 14.4125 | + | 8.32106i | 0.684759 | + | 0.395346i | 0.801646 | − | 0.597800i | \(-0.203958\pi\) |
−0.116887 | + | 0.993145i | \(0.537291\pi\) | |||||||
\(444\) | −1.59359 | − | 2.76019i | −0.0756286 | − | 0.130993i | ||||
\(445\) | 30.7894 | + | 9.35701i | 1.45956 | + | 0.443565i | ||||
\(446\) | −1.64124 | + | 2.84271i | −0.0777149 | + | 0.134606i | ||||
\(447\) | 11.1651i | 0.528091i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.1759 | −0.952158 | −0.476079 | − | 0.879402i | \(-0.657942\pi\) | ||||
−0.476079 | + | 0.879402i | \(0.657942\pi\) | |||||||
\(450\) | 2.78209 | − | 4.15451i | 0.131149 | − | 0.195846i | ||||
\(451\) | −7.96230 | − | 13.7911i | −0.374930 | − | 0.649398i | ||||
\(452\) | 10.8880 | − | 6.28617i | 0.512126 | − | 0.295676i | ||||
\(453\) | 0.575221 | + | 0.332104i | 0.0270263 | + | 0.0156036i | ||||
\(454\) | −4.42031 | −0.207456 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.61827 | 0.309929 | ||||||||
\(457\) | 30.6680 | + | 17.7062i | 1.43459 | + | 0.828261i | 0.997466 | − | 0.0711396i | \(-0.0226636\pi\) |
0.437124 | + | 0.899401i | \(0.355997\pi\) | |||||||
\(458\) | 6.90456 | − | 3.98635i | 0.322629 | − | 0.186270i | ||||
\(459\) | 3.86764 | + | 6.69895i | 0.180526 | + | 0.312680i | ||||
\(460\) | 5.70237 | − | 1.32654i | 0.265874 | − | 0.0618502i | ||||
\(461\) | −12.5940 | −0.586562 | −0.293281 | − | 0.956026i | \(-0.594747\pi\) | ||||
−0.293281 | + | 0.956026i | \(0.594747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.5061i | − | 1.51069i | −0.655330 | − | 0.755343i | \(-0.727470\pi\) | ||
0.655330 | − | 0.755343i | \(-0.272530\pi\) | |||||||
\(464\) | −4.08623 | + | 7.07756i | −0.189698 | + | 0.328567i | ||||
\(465\) | −5.50687 | + | 18.1204i | −0.255375 | + | 0.840316i | ||||
\(466\) | 8.97792 | + | 15.5502i | 0.415894 | + | 0.720349i | ||||
\(467\) | −7.97203 | − | 4.60265i | −0.368902 | − | 0.212985i | 0.304077 | − | 0.952648i | \(-0.401652\pi\) |
−0.672979 | + | 0.739662i | \(0.734985\pi\) | |||||||
\(468\) | 5.88388i | 0.271982i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.0879 | − | 10.3744i | 0.511448 | − | 0.478534i | ||||
\(471\) | −4.04092 | + | 6.99907i | −0.186196 | + | 0.322500i | ||||
\(472\) | 4.03932 | − | 2.33210i | 0.185925 | − | 0.107344i | ||||
\(473\) | 5.53950 | − | 3.19823i | 0.254706 | − | 0.147055i | ||||
\(474\) | −3.49264 | + | 6.04942i | −0.160422 | + | 0.277859i | ||||
\(475\) | −2.19796 | + | 33.0183i | −0.100849 | + | 1.51498i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.38173i | 0.0632651i | ||||||||
\(478\) | 4.68776 | + | 2.70648i | 0.214413 | + | 0.123792i | ||||
\(479\) | −19.7457 | − | 34.2005i | −0.902203 | − | 1.56266i | −0.824628 | − | 0.565675i | \(-0.808616\pi\) |
−0.0775746 | − | 0.996987i | \(-0.524718\pi\) | |||||||
\(480\) | −2.13945 | − | 0.650187i | −0.0976522 | − | 0.0296769i | ||||
\(481\) | −9.37652 | + | 16.2406i | −0.427532 | + | 0.740508i | ||||
\(482\) | − | 4.69669i | − | 0.213928i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.97792 | −0.408087 | ||||||||
\(485\) | −16.8128 | + | 3.91115i | −0.763428 | + | 0.177596i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −25.3466 | + | 14.6339i | −1.14857 | + | 0.663125i | −0.948537 | − | 0.316666i | \(-0.897437\pi\) |
−0.200028 | + | 0.979790i | \(0.564103\pi\) | |||||||
\(488\) | 8.48430 | + | 4.89841i | 0.384066 | + | 0.221741i | ||||
\(489\) | −0.836668 | −0.0378354 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3631 | 0.693325 | 0.346663 | − | 0.937990i | \(-0.387315\pi\) | ||||
0.346663 | + | 0.937990i | \(0.387315\pi\) | |||||||
\(492\) | −3.08549 | − | 1.78141i | −0.139105 | − | 0.0803121i | ||||
\(493\) | 54.7469 | − | 31.6081i | 2.46567 | − | 1.42356i | ||||
\(494\) | −19.4706 | − | 33.7240i | −0.876022 | − | 1.51731i | ||||
\(495\) | −2.26454 | − | 9.73455i | −0.101784 | − | 0.437535i | ||||
\(496\) | 8.46967 | 0.380299 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.35965i | 0.240172i | ||||||||
\(499\) | 10.2751 | − | 17.7970i | 0.459978 | − | 0.796705i | −0.538981 | − | 0.842318i | \(-0.681191\pi\) |
0.998959 | + | 0.0456128i | \(0.0145241\pi\) | |||||||
\(500\) | 3.95428 | − | 10.4577i | 0.176841 | − | 0.467683i | ||||
\(501\) | 1.33381 | + | 2.31023i | 0.0595903 | + | 0.103213i | ||||
\(502\) | −6.69786 | − | 3.86701i | −0.298940 | − | 0.172593i | ||||
\(503\) | − | 20.4788i | − | 0.913105i | −0.889696 | − | 0.456553i | \(-0.849084\pi\) | ||
0.889696 | − | 0.456553i | \(-0.150916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.8052 | + | 20.4019i | −0.970318 | + | 0.907873i | ||||
\(506\) | 5.85140 | − | 10.1349i | 0.260126 | − | 0.450552i | ||||
\(507\) | 18.7235 | − | 10.8100i | 0.831540 | − | 0.480090i | ||||
\(508\) | −5.71247 | + | 3.29809i | −0.253450 | + | 0.146329i | ||||
\(509\) | 6.03509 | − | 10.4531i | 0.267501 | − | 0.463325i | −0.700715 | − | 0.713441i | \(-0.747136\pi\) |
0.968216 | + | 0.250116i | \(0.0804689\pi\) | |||||||
\(510\) | 11.8174 | + | 12.6302i | 0.523283 | + | 0.559275i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.73159 | + | 3.30913i | 0.253056 | + | 0.146102i | ||||
\(514\) | −0.672210 | − | 1.16430i | −0.0296499 | − | 0.0513551i | ||||
\(515\) | −6.08552 | + | 20.0245i | −0.268160 | + | 0.882386i | ||||
\(516\) | 0.715541 | − | 1.23935i | 0.0314999 | − | 0.0545595i | ||||
\(517\) | − | 30.3523i | − | 1.33489i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.647340 | 0.0284151 | ||||||||
\(520\) | 2.98105 | + | 12.8146i | 0.130728 | + | 0.561957i | ||||
\(521\) | −7.35247 | − | 12.7348i | −0.322117 | − | 0.557924i | 0.658807 | − | 0.752312i | \(-0.271061\pi\) |
−0.980925 | + | 0.194388i | \(0.937728\pi\) | |||||||
\(522\) | −7.07756 | + | 4.08623i | −0.309776 | + | 0.178849i | ||||
\(523\) | 5.58081 | + | 3.22208i | 0.244032 | + | 0.140892i | 0.617028 | − | 0.786941i | \(-0.288336\pi\) |
−0.372996 | + | 0.927833i | \(0.621670\pi\) | |||||||
\(524\) | 2.32106 | 0.101396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.36700 | 0.190410 | ||||||||
\(527\) | −56.7378 | − | 32.7576i | −2.47154 | − | 1.42694i | ||||
\(528\) | −3.87084 | + | 2.23483i | −0.168457 | + | 0.0972586i | ||||
\(529\) | −8.07233 | − | 13.9817i | −0.350971 | − | 0.607899i | ||||
\(530\) | 0.700050 | + | 3.00929i | 0.0304082 | + | 0.130715i | ||||
\(531\) | 4.66421 | 0.202409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.9632i | 0.908016i | ||||||||
\(534\) | 7.19562 | − | 12.4632i | 0.311385 | − | 0.539335i | ||||
\(535\) | −7.16279 | + | 23.5693i | −0.309674 | + | 1.01899i | ||||
\(536\) | 0.925698 | + | 1.60336i | 0.0399841 | + | 0.0692544i | ||||
\(537\) | 22.2893 | + | 12.8687i | 0.961853 | + | 0.555326i | ||||
\(538\) | − | 23.0671i | − | 0.994494i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.52773 | − | 1.63280i | −0.0657429 | − | 0.0702647i | ||||
\(541\) | 5.79073 | − | 10.0298i | 0.248963 | − | 0.431216i | −0.714275 | − | 0.699865i | \(-0.753244\pi\) |
0.963238 | + | 0.268648i | \(0.0865769\pi\) | |||||||
\(542\) | 12.7487 | − | 7.36047i | 0.547604 | − | 0.316159i | ||||
\(543\) | −6.42803 | + | 3.71123i | −0.275853 | + | 0.159264i | ||||
\(544\) | 3.86764 | − | 6.69895i | 0.165824 | − | 0.287215i | ||||
\(545\) | 7.66674 | − | 7.17335i | 0.328407 | − | 0.307272i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2656i | 0.823737i | 0.911243 | + | 0.411868i | \(0.135124\pi\) | ||||
−0.911243 | + | 0.411868i | \(0.864876\pi\) | |||||||
\(548\) | 12.3626 | + | 7.13756i | 0.528105 | + | 0.304902i | ||||
\(549\) | 4.89841 | + | 8.48430i | 0.209059 | + | 0.362101i | ||||
\(550\) | −9.86397 | − | 20.0537i | −0.420601 | − | 0.855092i | ||||
\(551\) | 27.0438 | − | 46.8412i | 1.15210 | − | 1.99550i | ||||
\(552\) | − | 2.61827i | − | 0.111441i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.21104 | −0.136424 | ||||||||
\(555\) | −1.61478 | − | 6.94142i | −0.0685436 | − | 0.294647i | ||||
\(556\) | 7.48159 | + | 12.9585i | 0.317290 | + | 0.549563i | ||||
\(557\) | 18.2215 | − | 10.5202i | 0.772069 | − | 0.445754i | −0.0615432 | − | 0.998104i | \(-0.519602\pi\) |
0.833612 | + | 0.552350i | \(0.186269\pi\) | |||||||
\(558\) | 7.33495 | + | 4.23483i | 0.310513 | + | 0.179275i | ||||
\(559\) | −8.42031 | −0.356141 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.5741 | 1.45972 | ||||||||
\(562\) | 6.68994 | + | 3.86244i | 0.282198 | + | 0.162927i | ||||
\(563\) | −3.12714 | + | 1.80546i | −0.131793 | + | 0.0760910i | −0.564447 | − | 0.825469i | \(-0.690911\pi\) |
0.432654 | + | 0.901560i | \(0.357577\pi\) | |||||||
\(564\) | −3.39536 | − | 5.88094i | −0.142971 | − | 0.247632i | ||||
\(565\) | 27.3815 | − | 6.36974i | 1.15195 | − | 0.267977i | ||||
\(566\) | 29.5594 | 1.24247 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.02386i | − | 0.0849191i | ||||||
\(569\) | 16.6072 | − | 28.7646i | 0.696211 | − | 1.20587i | −0.273559 | − | 0.961855i | \(-0.588201\pi\) |
0.969771 | − | 0.244018i | \(-0.0784656\pi\) | |||||||
\(570\) | 14.1595 | + | 4.30312i | 0.593075 | + | 0.180238i | ||||
\(571\) | 16.0888 | + | 27.8667i | 0.673296 | + | 1.16618i | 0.976964 | + | 0.213405i | \(0.0684555\pi\) |
−0.303667 | + | 0.952778i | \(0.598211\pi\) | |||||||
\(572\) | 22.7756 | + | 13.1495i | 0.952295 | + | 0.549808i | ||||
\(573\) | 1.08452i | 0.0453066i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.0624 | + | 0.869539i | 0.544741 | + | 0.0362623i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −29.6096 | + | 17.0951i | −1.23266 | + | 0.711679i | −0.967585 | − | 0.252547i | \(-0.918732\pi\) |
−0.265080 | + | 0.964226i | \(0.585398\pi\) | |||||||
\(578\) | −37.0958 | + | 21.4172i | −1.54298 | + | 0.890840i | ||||
\(579\) | 4.46967 | − | 7.74169i | 0.185753 | − | 0.321734i | ||||
\(580\) | −13.3440 | + | 12.4853i | −0.554081 | + | 0.518423i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.71966i | 0.319990i | ||||||||
\(583\) | 5.34846 | + | 3.08794i | 0.221511 | + | 0.127889i | ||||
\(584\) | −2.00843 | − | 3.47871i | −0.0831096 | − | 0.143950i | ||||
\(585\) | −3.82562 | + | 12.5883i | −0.158170 | + | 0.520461i | ||||
\(586\) | 0.588394 | − | 1.01913i | 0.0243063 | − | 0.0420998i | ||||
\(587\) | − | 34.5962i | − | 1.42794i | −0.700178 | − | 0.713969i | \(-0.746896\pi\) | ||
0.700178 | − | 0.713969i | \(-0.253104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.0545 | −2.30969 | ||||||||
\(590\) | 10.1582 | − | 2.36311i | 0.418208 | − | 0.0972877i | ||||
\(591\) | −3.72945 | − | 6.45960i | −0.153409 | − | 0.265712i | ||||
\(592\) | −2.76019 | + | 1.59359i | −0.113443 | + | 0.0654963i | ||||
\(593\) | 28.6520 | + | 16.5422i | 1.17660 | + | 0.679309i | 0.955225 | − | 0.295881i | \(-0.0956131\pi\) |
0.221372 | + | 0.975189i | \(0.428946\pi\) | |||||||
\(594\) | −4.46967 | −0.183393 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1651 | 0.457341 | ||||||||
\(597\) | −22.3688 | − | 12.9147i | −0.915496 | − | 0.528562i | ||||
\(598\) | −13.3416 | + | 7.70279i | −0.545580 | + | 0.314991i | ||||
\(599\) | 3.03742 | + | 5.26097i | 0.124106 | + | 0.214958i | 0.921383 | − | 0.388656i | \(-0.127060\pi\) |
−0.797277 | + | 0.603613i | \(0.793727\pi\) | |||||||
\(600\) | −4.15451 | − | 2.78209i | −0.169607 | − | 0.113578i | ||||
\(601\) | −11.7469 | −0.479167 | −0.239584 | − | 0.970876i | \(-0.577011\pi\) | ||||
−0.239584 | + | 0.970876i | \(0.577011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85140i | 0.0753947i | ||||||||
\(604\) | 0.332104 | − | 0.575221i | 0.0135131 | − | 0.0234054i | ||||
\(605\) | −19.2078 | − | 5.83733i | −0.780909 | − | 0.237321i | ||||
\(606\) | 6.67722 | + | 11.5653i | 0.271243 | + | 0.469807i | ||||
\(607\) | −39.6796 | − | 22.9090i | −1.61054 | − | 0.929848i | −0.989244 | − | 0.146275i | \(-0.953271\pi\) |
−0.621300 | − | 0.783573i | \(-0.713395\pi\) | |||||||
\(608\) | − | 6.61827i | − | 0.268406i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.9669 | + | 15.9963i | 0.605991 | + | 0.647672i | ||||
\(611\) | −19.9779 | + | 34.6028i | −0.808220 | + | 1.39988i | ||||
\(612\) | 6.69895 | − | 3.86764i | 0.270789 | − | 0.156340i | ||||
\(613\) | 29.6626 | − | 17.1257i | 1.19806 | − | 0.691701i | 0.237938 | − | 0.971280i | \(-0.423528\pi\) |
0.960122 | + | 0.279580i | \(0.0901952\pi\) | |||||||
\(614\) | −10.1881 | + | 17.6463i | −0.411157 | + | 0.712145i | ||||
\(615\) | −5.44301 | − | 5.81739i | −0.219483 | − | 0.234580i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.8106i | 1.56246i | 0.624245 | + | 0.781228i | \(0.285407\pi\) | ||||
−0.624245 | + | 0.781228i | \(0.714593\pi\) | |||||||
\(618\) | 8.10569 | + | 4.67982i | 0.326059 | + | 0.188250i | ||||
\(619\) | −2.13756 | − | 3.70237i | −0.0859159 | − | 0.148811i | 0.819865 | − | 0.572557i | \(-0.194048\pi\) |
−0.905781 | + | 0.423746i | \(0.860715\pi\) | |||||||
\(620\) | 18.1204 | + | 5.50687i | 0.727735 | + | 0.221161i | ||||
\(621\) | 1.30913 | − | 2.26749i | 0.0525338 | − | 0.0909912i | ||||
\(622\) | − | 18.8934i | − | 0.757556i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.88388 | 0.235544 | ||||||||
\(625\) | 15.2595 | − | 19.8027i | 0.610379 | − | 0.792110i | ||||
\(626\) | 8.24245 | + | 14.2763i | 0.329434 | + | 0.570597i | ||||
\(627\) | 25.6183 | − | 14.7907i | 1.02310 | − | 0.590685i | ||||
\(628\) | 6.99907 | + | 4.04092i | 0.279293 | + | 0.161250i | ||||
\(629\) | 24.6538 | 0.983011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8419 | 1.46665 | 0.733326 | − | 0.679878i | \(-0.237967\pi\) | ||||
0.733326 | + | 0.679878i | \(0.237967\pi\) | |||||||
\(632\) | 6.04942 | + | 3.49264i | 0.240633 | + | 0.138930i | ||||
\(633\) | −4.79237 | + | 2.76687i | −0.190479 | + | 0.109973i | ||||
\(634\) | 5.16053 | + | 8.93830i | 0.204951 | + | 0.354985i | ||||
\(635\) | −14.3659 | + | 3.34194i | −0.570094 | + | 0.132621i | ||||
\(636\) | 1.38173 | 0.0547892 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.5282i | 1.44616i | ||||||||
\(639\) | 1.01193 | − | 1.75271i | 0.0400312 | − | 0.0693361i | ||||
\(640\) | −0.650187 | + | 2.13945i | −0.0257009 | + | 0.0845693i | ||||
\(641\) | −24.9521 | − | 43.2184i | −0.985551 | − | 1.70702i | −0.639464 | − | 0.768821i | \(-0.720844\pi\) |
−0.346086 | − | 0.938203i | \(-0.612490\pi\) | |||||||
\(642\) | 9.54057 | + | 5.50825i | 0.376536 | + | 0.217393i | ||||
\(643\) | 29.0091i | 1.14401i | 0.820251 | + | 0.572004i | \(0.193834\pi\) | ||||
−0.820251 | + | 0.572004i | \(0.806166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.33668 | − | 2.18630i | 0.0920066 | − | 0.0860855i | ||||
\(646\) | −25.5971 | + | 44.3354i | −1.00710 | + | 1.74435i | ||||
\(647\) | −4.28102 | + | 2.47165i | −0.168304 | + | 0.0971705i | −0.581786 | − | 0.813342i | \(-0.697646\pi\) |
0.413482 | + | 0.910512i | \(0.364313\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 10.4237 | − | 18.0544i | 0.409167 | − | 0.708698i | ||||
\(650\) | −1.95406 | + | 29.3544i | −0.0766446 | + | 1.15138i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.836668i | 0.0327664i | ||||||||
\(653\) | −8.14548 | − | 4.70279i | −0.318757 | − | 0.184035i | 0.332081 | − | 0.943251i | \(-0.392249\pi\) |
−0.650838 | + | 0.759216i | \(0.725582\pi\) | |||||||
\(654\) | −2.34772 | − | 4.06637i | −0.0918031 | − | 0.159008i | ||||
\(655\) | 4.96580 | + | 1.50913i | 0.194030 | + | 0.0589664i | ||||
\(656\) | −1.78141 | + | 3.08549i | −0.0695523 | + | 0.120468i | ||||
\(657\) | − | 4.01687i | − | 0.156713i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4090 | −0.522340 | −0.261170 | − | 0.965293i | \(-0.584108\pi\) | ||||
−0.261170 | + | 0.965293i | \(0.584108\pi\) | |||||||
\(660\) | −9.73455 | + | 2.26454i | −0.378917 | + | 0.0881473i | ||||
\(661\) | −6.62545 | − | 11.4756i | −0.257700 | − | 0.446350i | 0.707925 | − | 0.706287i | \(-0.249631\pi\) |
−0.965625 | + | 0.259938i | \(0.916298\pi\) | |||||||
\(662\) | −16.6195 | + | 9.59530i | −0.645937 | + | 0.372932i | ||||
\(663\) | −39.4158 | − | 22.7567i | −1.53078 | − | 0.883798i | ||||
\(664\) | 5.35965 | 0.207995 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.18719 | −0.123501 | ||||||||
\(667\) | −18.5310 | − | 10.6989i | −0.717521 | − | 0.414261i | ||||
\(668\) | 2.31023 | − | 1.33381i | 0.0893854 | − | 0.0516067i | ||||
\(669\) | 1.64124 | + | 2.84271i | 0.0634540 | + | 0.109906i | ||||
\(670\) | 0.938005 | + | 4.03218i | 0.0362383 | + | 0.155777i | ||||
\(671\) | 43.7886 | 1.69044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8236i | 0.841237i | 0.907238 | + | 0.420619i | \(0.138187\pi\) | ||||
−0.907238 | + | 0.420619i | \(0.861813\pi\) | |||||||
\(674\) | −13.8018 | + | 23.9054i | −0.531624 | + | 0.920800i | ||||
\(675\) | −2.20687 | − | 4.48662i | −0.0849424 | − | 0.172690i | ||||
\(676\) | −10.8100 | − | 18.7235i | −0.415770 | − | 0.720135i | ||||
\(677\) | 35.5566 | + | 20.5286i | 1.36655 | + | 0.788979i | 0.990486 | − | 0.137614i | \(-0.0439435\pi\) |
0.376065 | + | 0.926593i | \(0.377277\pi\) | |||||||
\(678\) | − | 12.5723i | − | 0.482837i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.6302 | − | 11.8174i | 0.484346 | − | 0.453176i | ||||
\(681\) | −2.21016 | + | 3.82810i | −0.0846934 | + | 0.146693i | ||||
\(682\) | 32.7848 | − | 18.9283i | 1.25539 | − | 0.724802i | ||||
\(683\) | 26.9024 | − | 15.5321i | 1.02939 | − | 0.594320i | 0.112581 | − | 0.993643i | \(-0.464088\pi\) |
0.916810 | + | 0.399323i | \(0.130755\pi\) | |||||||
\(684\) | 3.30913 | − | 5.73159i | 0.126528 | − | 0.219153i | ||||
\(685\) | 21.8085 | + | 23.3085i | 0.833259 | + | 0.890572i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.97270i | − | 0.304178i | ||||||
\(688\) | −1.23935 | − | 0.715541i | −0.0472499 | − | 0.0272797i | ||||
\(689\) | −4.06497 | − | 7.04073i | −0.154863 | − | 0.268230i | ||||
\(690\) | 1.70237 | − | 5.60166i | 0.0648080 | − | 0.213252i | ||||
\(691\) | 16.0006 | − | 27.7139i | 0.608692 | − | 1.05429i | −0.382764 | − | 0.923846i | \(-0.625028\pi\) |
0.991456 | − | 0.130439i | \(-0.0416388\pi\) | |||||||
\(692\) | − | 0.647340i | − | 0.0246082i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.3761 | 0.773468 | ||||||||
\(695\) | 7.58106 | + | 32.5885i | 0.287566 | + | 1.23615i | ||||
\(696\) | 4.08623 | + | 7.07756i | 0.154888 | + | 0.268274i | ||||
\(697\) | 23.8671 | − | 13.7797i | 0.904032 | − | 0.521943i | ||||
\(698\) | −15.4396 | − | 8.91403i | −0.584396 | − | 0.337401i | ||||
\(699\) | 17.9558 | 0.679152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.4635 | −1.71713 | −0.858567 | − | 0.512701i | \(-0.828645\pi\) | ||||
−0.858567 | + | 0.512701i | \(0.828645\pi\) | |||||||
\(702\) | 5.09559 | + | 2.94194i | 0.192321 | + | 0.111036i | ||||
\(703\) | 18.2677 | − | 10.5468i | 0.688978 | − | 0.397781i | ||||
\(704\) | 2.23483 | + | 3.87084i | 0.0842284 | + | 0.145888i | ||||
\(705\) | −3.44050 | − | 14.7896i | −0.129577 | − | 0.557009i | ||||
\(706\) | −3.51347 | −0.132231 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 4.66421i | − | 0.175292i | ||||||
\(709\) | −23.8798 | + | 41.3611i | −0.896826 | + | 1.55335i | −0.0652969 | + | 0.997866i | \(0.520799\pi\) |
−0.831529 | + | 0.555482i | \(0.812534\pi\) | |||||||
\(710\) | 1.31589 | − | 4.32994i | 0.0493843 | − | 0.162500i | ||||
\(711\) | 3.49264 | + | 6.04942i | 0.130984 | + | 0.226871i | ||||
\(712\) | −12.4632 | − | 7.19562i | −0.467078 | − | 0.269667i | ||||
\(713\) | 22.1759i | 0.830493i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.1776 | + | 42.9411i | 1.50256 | + | 1.60591i | ||||
\(716\) | 12.8687 | − | 22.2893i | 0.480927 | − | 0.832989i | ||||
\(717\) | 4.68776 | − | 2.70648i | 0.175068 | − | 0.101075i | ||||
\(718\) | 1.90349 | − | 1.09898i | 0.0710374 | − | 0.0410135i | ||||
\(719\) | 6.58057 | − | 11.3979i | 0.245414 | − | 0.425069i | −0.716834 | − | 0.697244i | \(-0.754409\pi\) |
0.962248 | + | 0.272175i | \(0.0877428\pi\) | |||||||
\(720\) | −1.63280 | + | 1.52773i | −0.0608510 | + | 0.0569350i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.8015i | 0.923016i | ||||||||
\(723\) | −4.06745 | − | 2.34835i | −0.151270 | − | 0.0873359i | ||||
\(724\) | 3.71123 | + | 6.42803i | 0.137927 | + | 0.238896i | ||||
\(725\) | −36.6667 | + | 18.0355i | −1.36177 | + | 0.669823i | ||||
\(726\) | −4.48896 | + | 7.77510i | −0.166601 | + | 0.288561i | ||||
\(727\) | 8.17082i | 0.303039i | 0.988454 | + | 0.151519i | \(0.0484166\pi\) | ||||
−0.988454 | + | 0.151519i | \(0.951583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −2.03514 | − | 8.74839i | −0.0753238 | − | 0.323793i | ||||
\(731\) | 5.53491 | + | 9.58674i | 0.204716 | + | 0.354578i | ||||
\(732\) | 8.48430 | − | 4.89841i | 0.313589 | − | 0.181051i | ||||
\(733\) | −1.74512 | − | 1.00755i | −0.0644576 | − | 0.0372146i | 0.467425 | − | 0.884033i | \(-0.345182\pi\) |
−0.531882 | + | 0.846818i | \(0.678515\pi\) | |||||||
\(734\) | 28.7721 | 1.06200 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.61827 | −0.0965107 | ||||||||
\(737\) | 7.16647 | + | 4.13756i | 0.263980 | + | 0.152409i | ||||
\(738\) | −3.08549 | + | 1.78141i | −0.113578 | + | 0.0655746i | ||||
\(739\) | −1.91295 | − | 3.31333i | −0.0703690 | − | 0.121883i | 0.828694 | − | 0.559702i | \(-0.189084\pi\) |
−0.899063 | + | 0.437819i | \(0.855751\pi\) | |||||||
\(740\) | −6.94142 | + | 1.61478i | −0.255172 | + | 0.0593605i | ||||
\(741\) | −38.9411 | −1.43054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.6654i | 1.34512i | 0.740041 | + | 0.672562i | \(0.234806\pi\) | ||||
−0.740041 | + | 0.672562i | \(0.765194\pi\) | |||||||
\(744\) | 4.23483 | − | 7.33495i | 0.155257 | − | 0.268912i | ||||
\(745\) | 23.8872 | + | 7.25941i | 0.875160 | + | 0.265964i | ||||
\(746\) | 7.28446 | + | 12.6171i | 0.266703 | + | 0.461943i | ||||
\(747\) | 4.64159 | + | 2.67982i | 0.169827 | + | 0.0980496i | ||||
\(748\) | − | 34.5741i | − | 1.26415i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.07950 | − | 8.65336i | −0.258507 | − | 0.315976i | ||||
\(751\) | 10.2329 | − | 17.7238i | 0.373402 | − | 0.646751i | −0.616684 | − | 0.787210i | \(-0.711525\pi\) |
0.990086 | + | 0.140459i | \(0.0448579\pi\) | |||||||
\(752\) | −5.88094 | + | 3.39536i | −0.214456 | + | 0.123816i | ||||
\(753\) | −6.69786 | + | 3.86701i | −0.244084 | + | 0.140922i | ||||
\(754\) | 24.0429 | − | 41.6435i | 0.875590 | − | 1.51657i | ||||
\(755\) | 1.08452 | − | 1.01473i | 0.0394698 | − | 0.0369298i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.9575i | − | 1.37959i | −0.724006 | − | 0.689794i | \(-0.757701\pi\) | ||
0.724006 | − | 0.689794i | \(-0.242299\pi\) | |||||||
\(758\) | −26.6621 | − | 15.3934i | −0.968412 | − | 0.559113i | ||||
\(759\) | −5.85140 | − | 10.1349i | −0.212392 | − | 0.367874i | ||||
\(760\) | 4.30312 | − | 14.1595i | 0.156090 | − | 0.513618i | ||||
\(761\) | 17.3065 | − | 29.9758i | 0.627361 | − | 1.08662i | −0.360718 | − | 0.932675i | \(-0.617468\pi\) |
0.988079 | − | 0.153946i | \(-0.0491983\pi\) | |||||||
\(762\) | 6.59619i | 0.238955i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.08452 | 0.0392367 | ||||||||
\(765\) | 16.8468 | − | 3.91906i | 0.609096 | − | 0.141694i | ||||
\(766\) | 11.6705 | + | 20.2139i | 0.421672 | + | 0.730357i | ||||
\(767\) | −23.7669 | + | 13.7218i | −0.858173 | + | 0.495466i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 1.48961 | 0.0537167 | 0.0268584 | − | 0.999639i | \(-0.491450\pi\) | ||||
0.0268584 | + | 0.999639i | \(0.491450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.34442 | −0.0484181 | ||||||||
\(772\) | −7.74169 | − | 4.46967i | −0.278629 | − | 0.160867i | ||||
\(773\) | −0.859321 | + | 0.496129i | −0.0309076 | + | 0.0178445i | −0.515374 | − | 0.856965i | \(-0.672347\pi\) |
0.484467 | + | 0.874810i | \(0.339014\pi\) | |||||||
\(774\) | −0.715541 | − | 1.23935i | −0.0257196 | − | 0.0445476i | ||||
\(775\) | 35.1873 | + | 23.5634i | 1.26397 | + | 0.846421i | ||||
\(776\) | 7.71966 | 0.277120 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21842i | 0.0436824i | ||||||||
\(779\) | 11.7898 | − | 20.4206i | 0.422415 | − | 0.731644i | ||||
\(780\) | 12.5883 | + | 3.82562i | 0.450733 | + | 0.136979i | ||||
\(781\) | −4.52298 | − | 7.83403i | −0.161845 | − | 0.280324i | ||||
\(782\) | 17.5396 | + | 10.1265i | 0.627217 | + | 0.362124i | ||||
\(783\) | 8.17246i | 0.292060i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3468 | + | 13.1961i | 0.440677 | + | 0.470988i | ||||
\(786\) | 1.16053 | − | 2.01010i | 0.0413948 | − | 0.0716979i | ||||
\(787\) | −8.87786 | + | 5.12563i | −0.316461 | + | 0.182709i | −0.649814 | − | 0.760093i | \(-0.725153\pi\) |
0.333353 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(788\) | −6.45960 | + | 3.72945i | −0.230114 | + | 0.132856i | ||||
\(789\) | 2.18350 | − | 3.78193i | 0.0777347 | − | 0.134640i | ||||
\(790\) | 10.6716 | + | 11.4056i | 0.379678 | + | 0.405793i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.46967i | 0.158823i | ||||||||
\(793\) | −49.9206 | − | 28.8217i | −1.77273 | − | 1.02349i | ||||
\(794\) | −4.20298 | − | 7.27977i | −0.149158 | − | 0.258349i | ||||
\(795\) | 2.95615 | + | 0.898384i | 0.104844 | + | 0.0318624i | ||||
\(796\) | −12.9147 | + | 22.3688i | −0.457748 | + | 0.792843i | ||||
\(797\) | − | 32.6811i | − | 1.15762i | −0.815461 | − | 0.578812i | \(-0.803517\pi\) | ||
0.815461 | − | 0.578812i | \(-0.196483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.5282 | 1.85831 | ||||||||
\(800\) | −2.78209 | + | 4.15451i | −0.0983617 | + | 0.146884i | ||||
\(801\) | −7.19562 | − | 12.4632i | −0.254245 | − | 0.440365i | ||||
\(802\) | −0.575221 | + | 0.332104i | −0.0203118 | + | 0.0117270i | ||||
\(803\) | −15.5487 | − | 8.97703i | −0.548701 | − | 0.316793i | ||||
\(804\) | 1.85140 | 0.0652937 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −49.8345 | −1.75535 | ||||||||
\(807\) | −19.9767 | − | 11.5336i | −0.703213 | − | 0.406000i | ||||
\(808\) | 11.5653 | − | 6.67722i | 0.406865 | − | 0.234904i | ||||
\(809\) | 11.2258 | + | 19.4436i | 0.394677 | + | 0.683601i | 0.993060 | − | 0.117610i | \(-0.0375231\pi\) |
−0.598383 | + | 0.801210i | \(0.704190\pi\) | |||||||
\(810\) | −2.17791 | + | 0.506647i | −0.0765241 | + | 0.0178018i | ||||
\(811\) | 37.6581 | 1.32235 | 0.661177 | − | 0.750230i | \(-0.270057\pi\) | ||||
0.661177 | + | 0.750230i | \(0.270057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 14.7209i | − | 0.516286i | ||||||
\(814\) | −7.12283 | + | 12.3371i | −0.249655 | + | 0.432415i | ||||
\(815\) | −0.543991 | + | 1.79001i | −0.0190552 | + | 0.0627013i | ||||
\(816\) | −3.86764 | − | 6.69895i | −0.135394 | − | 0.234510i | ||||
\(817\) | 8.20237 | + | 4.73564i | 0.286965 | + | 0.165679i | ||||
\(818\) | 7.38476i | 0.258202i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.81739 | + | 5.44301i | −0.203152 | + | 0.190078i | ||||
\(821\) | 10.7419 | − | 18.6056i | 0.374896 | − | 0.649338i | −0.615416 | − | 0.788203i | \(-0.711012\pi\) |
0.990311 | + | 0.138864i | \(0.0443452\pi\) | |||||||
\(822\) | 12.3626 | − | 7.13756i | 0.431196 | − | 0.248951i | ||||
\(823\) | −16.1190 | + | 9.30633i | −0.561875 | + | 0.324398i | −0.753898 | − | 0.656992i | \(-0.771829\pi\) |
0.192023 | + | 0.981390i | \(0.438495\pi\) | |||||||
\(824\) | 4.67982 | − | 8.10569i | 0.163029 | − | 0.282375i | ||||
\(825\) | −22.2990 | − | 1.48440i | −0.776351 | − | 0.0516800i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4254i | 0.640713i | 0.947297 | + | 0.320356i | \(0.103803\pi\) | ||||
−0.947297 | + | 0.320356i | \(0.896197\pi\) | |||||||
\(828\) | −2.26749 | − | 1.30913i | −0.0788007 | − | 0.0454956i | ||||
\(829\) | 16.0188 | + | 27.7454i | 0.556357 | + | 0.963639i | 0.997797 | + | 0.0663478i | \(0.0211347\pi\) |
−0.441439 | + | 0.897291i | \(0.645532\pi\) | |||||||
\(830\) | 11.4667 | + | 3.48478i | 0.398015 | + | 0.120958i | ||||
\(831\) | −1.60552 | + | 2.78085i | −0.0556949 | + | 0.0964665i | ||||
\(832\) | − | 5.88388i | − | 0.203987i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.9632 | 0.518133 | ||||||||
\(835\) | 5.80985 | − | 1.35154i | 0.201058 | − | 0.0467721i | ||||
\(836\) | −14.7907 | − | 25.6183i | −0.511548 | − | 0.886027i | ||||
\(837\) | 7.33495 | − | 4.23483i | 0.253533 | − | 0.146377i | ||||
\(838\) | 16.1318 | + | 9.31371i | 0.557264 | + | 0.321737i | ||||
\(839\) | −8.45154 | −0.291780 | −0.145890 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145890 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7891 | 1.30307 | ||||||||
\(842\) | 11.6951 | + | 6.75214i | 0.403038 | + | 0.232694i | ||||
\(843\) | 6.68994 | − | 3.86244i | 0.230414 | − | 0.133029i | ||||
\(844\) | 2.76687 | + | 4.79237i | 0.0952397 | + | 0.164960i | ||||
\(845\) | −10.9537 | − | 47.0866i | −0.376820 | − | 1.61983i | ||||
\(846\) | −6.79073 | −0.233470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1.38173i | − | 0.0474488i | ||||||
\(849\) | 14.7797 | − | 25.5992i | 0.507238 | − | 0.878561i | ||||
\(850\) | 34.7052 | − | 17.0707i | 1.19038 | − | 0.585521i | ||||
\(851\) | −4.17246 | − | 7.22691i | −0.143030 | − | 0.247735i | ||||
\(852\) | −1.75271 | − | 1.01193i | −0.0600469 | − | 0.0346681i | ||||
\(853\) | 50.6270i | 1.73344i | 0.498798 | + | 0.866718i | \(0.333775\pi\) | ||||
−0.498798 | + | 0.866718i | \(0.666225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8063 | − | 10.1109i | 0.369569 | − | 0.345786i | ||||
\(856\) | 5.50825 | − | 9.54057i | 0.188268 | − | 0.326090i | ||||
\(857\) | −10.3934 | + | 6.00063i | −0.355031 | + | 0.204978i | −0.666899 | − | 0.745148i | \(-0.732379\pi\) |
0.311868 | + | 0.950126i | \(0.399045\pi\) | |||||||
\(858\) | 22.7756 | − | 13.1495i | 0.777546 | − | 0.448916i | ||||
\(859\) | −17.8560 | + | 30.9274i | −0.609238 | + | 1.05523i | 0.382128 | + | 0.924109i | \(0.375191\pi\) |
−0.991366 | + | 0.131122i | \(0.958142\pi\) | |||||||
\(860\) | −2.18630 | − | 2.33668i | −0.0745523 | − | 0.0796801i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 31.6807i | − | 1.07905i | ||||||
\(863\) | −1.11219 | − | 0.642125i | −0.0378595 | − | 0.0218582i | 0.480951 | − | 0.876748i | \(-0.340292\pi\) |
−0.518810 | + | 0.854889i | \(0.673625\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0.420892 | − | 1.38495i | 0.0143108 | − | 0.0470898i | ||||
\(866\) | 12.6592 | − | 21.9264i | 0.430177 | − | 0.745088i | ||||
\(867\) | 42.8345i | 1.45474i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2218 | 1.05913 | ||||||||
\(870\) | 4.14055 | + | 17.7989i | 0.140378 | + | 0.603440i | ||||
\(871\) | −5.44670 | − | 9.43396i | −0.184554 | − | 0.319657i | ||||
\(872\) | −4.06637 | + | 2.34772i | −0.137705 | + | 0.0795038i | ||||
\(873\) | 6.68542 | + | 3.85983i | 0.226267 | + | 0.130635i | ||||
\(874\) | 17.3284 | 0.586142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.01687 | −0.135717 | ||||||||
\(877\) | −33.2122 | − | 19.1751i | −1.12150 | − | 0.647496i | −0.179713 | − | 0.983719i | \(-0.557517\pi\) |
−0.941782 | + | 0.336224i | \(0.890850\pi\) | |||||||
\(878\) | −28.4183 | + | 16.4073i | −0.959070 | + | 0.553719i | ||||
\(879\) | −0.588394 | − | 1.01913i | −0.0198460 | − | 0.0343743i | ||||
\(880\) | 2.26454 | + | 9.73455i | 0.0763378 | + | 0.328152i | ||||
\(881\) | 0.389472 | 0.0131216 | 0.00656082 | − | 0.999978i | \(-0.497912\pi\) | ||||
0.00656082 | + | 0.999978i | \(0.497912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5412i | 0.623962i | 0.950088 | + | 0.311981i | \(0.100993\pi\) | ||||
−0.950088 | + | 0.311981i | \(0.899007\pi\) | |||||||
\(884\) | −22.7567 | + | 39.4158i | −0.765391 | + | 1.32570i | ||||
\(885\) | 3.03261 | − | 9.97885i | 0.101940 | − | 0.335435i | ||||
\(886\) | −8.32106 | − | 14.4125i | −0.279552 | − | 0.484198i | ||||
\(887\) | 36.7893 | + | 21.2403i | 1.23526 | + | 0.713179i | 0.968122 | − | 0.250478i | \(-0.0805879\pi\) |
0.267140 | + | 0.963658i | \(0.413921\pi\) | |||||||
\(888\) | 3.18719i | 0.106955i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −21.9859 | − | 23.4981i | −0.736968 | − | 0.787658i | ||||
\(891\) | −2.23483 | + | 3.87084i | −0.0748697 | + | 0.129678i | ||||
\(892\) | 2.84271 | − | 1.64124i | 0.0951810 | − | 0.0549528i | ||||
\(893\) | 38.9217 | − | 22.4714i | 1.30246 | − | 0.751978i | ||||
\(894\) | 5.58255 | − | 9.66926i | 0.186708 | − | 0.323389i | ||||
\(895\) | 42.0242 | − | 39.3198i | 1.40471 | − | 1.31431i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4056i | 0.514378i | ||||||||
\(898\) | 17.4728 | + | 10.0879i | 0.583075 | + | 0.336639i | ||||
\(899\) | −34.6090 | − | 59.9445i | −1.15427 | − | 1.99926i | ||||
\(900\) | −4.48662 | + | 2.20687i | −0.149554 | + | 0.0735623i | ||||
\(901\) | −5.34403 | + | 9.25613i | −0.178036 | + | 0.308367i | ||||
\(902\) | 15.9246i | 0.530231i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5723 | −0.418150 | ||||||||
\(905\) | 3.76057 | + | 16.1655i | 0.125005 | + | 0.537358i | ||||
\(906\) | −0.332104 | − | 0.575221i | −0.0110334 | − | 0.0191105i | ||||
\(907\) | −35.6531 | + | 20.5843i | −1.18384 | + | 0.683491i | −0.956900 | − | 0.290417i | \(-0.906206\pi\) |
−0.226941 | + | 0.973908i | \(0.572873\pi\) | |||||||
\(908\) | 3.82810 | + | 2.21016i | 0.127040 | + | 0.0733466i | ||||
\(909\) | 13.3544 | 0.442939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1703 | −0.833929 | −0.416964 | − | 0.908923i | \(-0.636906\pi\) | ||||
−0.416964 | + | 0.908923i | \(0.636906\pi\) | |||||||
\(912\) | −5.73159 | − | 3.30913i | −0.189792 | − | 0.109576i | ||||
\(913\) | 20.7464 | − | 11.9779i | 0.686604 | − | 0.396411i | ||||
\(914\) | −17.7062 | − | 30.6680i | −0.585669 | − | 1.01441i | ||||
\(915\) | 21.3367 | − | 4.96354i | 0.705368 | − | 0.164090i | ||||
\(916\) | −7.97270 | −0.263426 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 7.73528i | − | 0.255302i | ||||||
\(919\) | −2.51841 | + | 4.36201i | −0.0830745 | + | 0.143889i | −0.904569 | − | 0.426327i | \(-0.859807\pi\) |
0.821495 | + | 0.570216i | \(0.193141\pi\) | |||||||
\(920\) | −5.60166 | − | 1.70237i | −0.184681 | − | 0.0561253i | ||||
\(921\) | 10.1881 | + | 17.6463i | 0.335708 | + | 0.581464i | ||||
\(922\) | 10.9067 | + | 6.29701i | 0.359195 | + | 0.207381i | ||||
\(923\) | 11.9081i | 0.391961i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9007 | − | 1.05848i | −0.522813 | − | 0.0348026i | ||||
\(926\) | −16.2530 | + | 28.1511i | −0.534108 | + | 0.925102i | ||||
\(927\) | 8.10569 | − | 4.67982i | 0.266226 | − | 0.153706i | ||||
\(928\) | 7.07756 | − | 4.08623i | 0.232332 | − | 0.134137i | ||||
\(929\) | −7.14231 | + | 12.3708i | −0.234332 | + | 0.405874i | −0.959078 | − | 0.283141i | \(-0.908623\pi\) |
0.724747 | + | 0.689015i | \(0.241957\pi\) | |||||||
\(930\) | 13.8293 | − | 12.9393i | 0.453481 | − | 0.424297i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 17.9558i | − | 0.588163i | ||||||
\(933\) | −16.3622 | − | 9.44670i | −0.535673 | − | 0.309271i | ||||
\(934\) | 4.60265 | + | 7.97203i | 0.150603 | + | 0.260853i | ||||
\(935\) | 22.4796 | − | 73.9696i | 0.735163 | − | 2.41907i | ||||
\(936\) | 2.94194 | − | 5.09559i | 0.0961603 | − | 0.166555i | ||||
\(937\) | − | 19.8403i | − | 0.648153i | −0.946031 | − | 0.324077i | \(-0.894946\pi\) | ||
0.946031 | − | 0.324077i | \(-0.105054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.4849 | 0.537964 | ||||||||
\(940\) | −14.7896 | + | 3.44050i | −0.482384 | + | 0.112217i | ||||
\(941\) | −7.95271 | − | 13.7745i | −0.259251 | − | 0.449036i | 0.706791 | − | 0.707423i | \(-0.250142\pi\) |
−0.966041 | + | 0.258387i | \(0.916809\pi\) | |||||||
\(942\) | 6.99907 | − | 4.04092i | 0.228042 | − | 0.131660i | ||||
\(943\) | −8.07865 | − | 4.66421i | −0.263077 | − | 0.151888i | ||||
\(944\) | −4.66421 | −0.151807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39646 | −0.207967 | ||||||||
\(947\) | −8.27760 | − | 4.77908i | −0.268986 | − | 0.155299i | 0.359441 | − | 0.933168i | \(-0.382967\pi\) |
−0.628427 | + | 0.777869i | \(0.716301\pi\) | |||||||
\(948\) | 6.04942 | − | 3.49264i | 0.196476 | − | 0.113436i | ||||
\(949\) | 11.8174 | + | 20.4683i | 0.383609 | + | 0.664430i | ||||
\(950\) | 18.4126 | − | 27.4957i | 0.597384 | − | 0.892078i | ||||
\(951\) | 10.3211 | 0.334683 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.7505i | − | 0.769354i | −0.923051 | − | 0.384677i | \(-0.874313\pi\) | ||
0.923051 | − | 0.384677i | \(-0.125687\pi\) | |||||||
\(954\) | 0.690865 | − | 1.19661i | 0.0223676 | − | 0.0387418i | ||||
\(955\) | 2.32029 | + | 0.705143i | 0.0750827 | + | 0.0228179i | ||||
\(956\) | −2.70648 | − | 4.68776i | −0.0875338 | − | 0.151613i | ||||
\(957\) | 31.6343 | + | 18.2641i | 1.02259 | + | 0.590394i | ||||
\(958\) | 39.4914i | 1.27591i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.52773 | + | 1.63280i | 0.0493072 | + | 0.0526986i | ||||
\(961\) | −20.3676 | + | 35.2778i | −0.657020 | + | 1.13799i | ||||
\(962\) | 16.2406 | − | 9.37652i | 0.523618 | − | 0.302311i | ||||
\(963\) | 9.54057 | − | 5.50825i | 0.307441 | − | 0.177501i | ||||
\(964\) | −2.34835 | + | 4.06745i | −0.0756351 | + | 0.131004i | ||||
\(965\) | −13.6569 | − | 14.5962i | −0.439630 | − | 0.469868i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 56.9706i | − | 1.83205i | −0.401121 | − | 0.916025i | \(-0.631379\pi\) | ||
0.401121 | − | 0.916025i | \(-0.368621\pi\) | |||||||
\(968\) | 7.77510 | + | 4.48896i | 0.249901 | + | 0.144281i | ||||
\(969\) | 25.5971 | + | 44.3354i | 0.822296 | + | 1.42426i | ||||
\(970\) | 16.5158 | + | 5.01923i | 0.530292 | + | 0.161158i | ||||
\(971\) | −16.5429 | + | 28.6531i | −0.530886 | + | 0.919522i | 0.468464 | + | 0.883482i | \(0.344807\pi\) |
−0.999350 | + | 0.0360392i | \(0.988526\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29.2678 | 0.937800 | ||||||||
\(975\) | 24.4447 | + | 16.3695i | 0.782855 | + | 0.524243i | ||||
\(976\) | −4.89841 | − | 8.48430i | −0.156794 | − | 0.271576i | ||||
\(977\) | −21.3152 | + | 12.3063i | −0.681934 | + | 0.393715i | −0.800583 | − | 0.599222i | \(-0.795477\pi\) |
0.118650 | + | 0.992936i | \(0.462143\pi\) | |||||||
\(978\) | 0.724575 | + | 0.418334i | 0.0231694 | + | 0.0133768i | ||||
\(979\) | −64.3241 | −2.05581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.69544 | −0.149914 | ||||||||
\(982\) | −13.3048 | − | 7.68153i | −0.424573 | − | 0.245127i | ||||
\(983\) | −36.7893 | + | 21.2403i | −1.17340 | + | 0.677460i | −0.954477 | − | 0.298283i | \(-0.903586\pi\) |
−0.218918 | + | 0.975743i | \(0.570253\pi\) | |||||||
\(984\) | 1.78141 | + | 3.08549i | 0.0567892 | + | 0.0983618i | ||||
\(985\) | −16.2448 | + | 3.77903i | −0.517604 | + | 0.120410i | ||||
\(986\) | −63.2162 | −2.01321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.9411i | 1.23888i | ||||||||
\(989\) | 1.87348 | − | 3.24496i | 0.0595732 | − | 0.103184i | ||||
\(990\) | −2.90612 | + | 9.56264i | −0.0923626 | + | 0.303921i | ||||
\(991\) | 0.419154 | + | 0.725996i | 0.0133149 | + | 0.0230620i | 0.872606 | − | 0.488425i | \(-0.162428\pi\) |
−0.859291 | + | 0.511487i | \(0.829095\pi\) | |||||||
\(992\) | −7.33495 | − | 4.23483i | −0.232885 | − | 0.134456i | ||||
\(993\) | 19.1906i | 0.608995i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.1742 | + | 39.4601i | −1.33701 | + | 1.25097i | ||||
\(996\) | 2.67982 | − | 4.64159i | 0.0849135 | − | 0.147074i | ||||
\(997\) | −27.3612 | + | 15.7970i | −0.866539 | + | 0.500297i | −0.866197 | − | 0.499703i | \(-0.833442\pi\) |
−0.000342701 | 1.00000i | \(0.500109\pi\) | ||||||||
\(998\) | −17.7970 | + | 10.2751i | −0.563355 | + | 0.325253i | ||||
\(999\) | −1.59359 | + | 2.76019i | −0.0504191 | + | 0.0873284i |
(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 | 1470.2.n.k.79.3 | 16 | ||
5.4 | even | 2 | inner | 1470.2.n.k.79.5 | 16 | ||
7.2 | even | 3 | 1470.2.g.k.589.7 | yes | 8 | ||
7.3 | odd | 6 | 1470.2.n.l.949.8 | 16 | |||
7.4 | even | 3 | inner | 1470.2.n.k.949.5 | 16 | ||
7.5 | odd | 6 | 1470.2.g.j.589.6 | yes | 8 | ||
7.6 | odd | 2 | 1470.2.n.l.79.2 | 16 | |||
35.2 | odd | 12 | 7350.2.a.dr.1.4 | 4 | |||
35.4 | even | 6 | inner | 1470.2.n.k.949.3 | 16 | ||
35.9 | even | 6 | 1470.2.g.k.589.3 | yes | 8 | ||
35.12 | even | 12 | 7350.2.a.ds.1.4 | 4 | |||
35.19 | odd | 6 | 1470.2.g.j.589.2 | ✓ | 8 | ||
35.23 | odd | 12 | 7350.2.a.du.1.4 | 4 | |||
35.24 | odd | 6 | 1470.2.n.l.949.2 | 16 | |||
35.33 | even | 12 | 7350.2.a.dt.1.4 | 4 | |||
35.34 | odd | 2 | 1470.2.n.l.79.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.2 | ✓ | 8 | 35.19 | odd | 6 | ||
1470.2.g.j.589.6 | yes | 8 | 7.5 | odd | 6 | ||
1470.2.g.k.589.3 | yes | 8 | 35.9 | even | 6 | ||
1470.2.g.k.589.7 | yes | 8 | 7.2 | even | 3 | ||
1470.2.n.k.79.3 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.n.k.79.5 | 16 | 5.4 | even | 2 | inner | ||
1470.2.n.k.949.3 | 16 | 35.4 | even | 6 | inner | ||
1470.2.n.k.949.5 | 16 | 7.4 | even | 3 | inner | ||
1470.2.n.l.79.2 | 16 | 7.6 | odd | 2 | |||
1470.2.n.l.79.8 | 16 | 35.34 | odd | 2 | |||
1470.2.n.l.949.2 | 16 | 35.24 | odd | 6 | |||
1470.2.n.l.949.8 | 16 | 7.3 | odd | 6 | |||
7350.2.a.dr.1.4 | 4 | 35.2 | odd | 12 | |||
7350.2.a.ds.1.4 | 4 | 35.12 | even | 12 | |||
7350.2.a.dt.1.4 | 4 | 35.33 | even | 12 | |||
7350.2.a.du.1.4 | 4 | 35.23 | odd | 12 |