Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(241,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.p (of order \(6\), degree \(2\), 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: | \(3.68908857338\) |
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: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.6 | ||
Root | \(0.500000 + 1.56688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.439 |
Dual form | 462.2.p.b.241.6 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||
\(5\) | −0.606961 | − | 0.350429i | −0.271441 | − | 0.156717i | 0.358101 | − | 0.933683i | \(-0.383424\pi\) |
−0.629542 | + | 0.776966i | \(0.716758\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.82993 | + | 1.91085i | 0.691650 | + | 0.722233i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.350429 | − | 0.606961i | −0.110815 | − | 0.191938i | ||||
\(11\) | −2.95637 | + | 1.50329i | −0.891379 | + | 0.453258i | ||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 7.03562 | 1.95133 | 0.975665 | − | 0.219267i | \(-0.0703667\pi\) | ||||
0.975665 | + | 0.219267i | \(0.0703667\pi\) | |||||||
\(14\) | 0.629345 | + | 2.56981i | 0.168199 | + | 0.686811i | ||||
\(15\) | −0.700858 | −0.180961 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.308893 | + | 0.535018i | 0.0749175 | + | 0.129761i | 0.901050 | − | 0.433714i | \(-0.142797\pi\) |
−0.826133 | + | 0.563475i | \(0.809464\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −0.391696 | + | 0.678438i | −0.0898613 | + | 0.155644i | −0.907452 | − | 0.420155i | \(-0.861976\pi\) |
0.817591 | + | 0.575799i | \(0.195309\pi\) | |||||||
\(20\) | − | 0.700858i | − | 0.156717i | ||||||
\(21\) | 2.54019 | + | 0.739877i | 0.554316 | + | 0.161454i | ||||
\(22\) | −3.31194 | − | 0.176300i | −0.706107 | − | 0.0375874i | ||||
\(23\) | 2.63592 | − | 4.56555i | 0.549627 | − | 0.951982i | −0.448673 | − | 0.893696i | \(-0.648103\pi\) |
0.998300 | − | 0.0582859i | \(-0.0185635\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −2.25440 | − | 3.90473i | −0.450880 | − | 0.780947i | ||||
\(26\) | 6.09302 | + | 3.51781i | 1.19494 | + | 0.689899i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.739877 | + | 2.54019i | −0.139824 | + | 0.480051i | ||||
\(29\) | 2.09176i | 0.388431i | 0.980959 | + | 0.194215i | \(0.0622161\pi\) | ||||
−0.980959 | + | 0.194215i | \(0.937784\pi\) | |||||||
\(30\) | −0.606961 | − | 0.350429i | −0.110815 | − | 0.0639793i | ||||
\(31\) | −5.35024 | + | 3.08896i | −0.960932 | + | 0.554794i | −0.896460 | − | 0.443125i | \(-0.853870\pi\) |
−0.0644719 | + | 0.997920i | \(0.520536\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −1.80865 | + | 2.78007i | −0.314845 | + | 0.483948i | ||||
\(34\) | 0.617785i | 0.105949i | ||||||||
\(35\) | −0.441081 | − | 1.80107i | −0.0745563 | − | 0.304437i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.99709 | − | 3.45907i | 0.328320 | − | 0.568667i | −0.653859 | − | 0.756617i | \(-0.726851\pi\) |
0.982179 | + | 0.187950i | \(0.0601842\pi\) | |||||||
\(38\) | −0.678438 | + | 0.391696i | −0.110057 | + | 0.0635416i | ||||
\(39\) | 6.09302 | − | 3.51781i | 0.975665 | − | 0.563300i | ||||
\(40\) | 0.350429 | − | 0.606961i | 0.0554077 | − | 0.0959689i | ||||
\(41\) | −5.85343 | −0.914152 | −0.457076 | − | 0.889428i | \(-0.651103\pi\) | ||||
−0.457076 | + | 0.889428i | \(0.651103\pi\) | |||||||
\(42\) | 1.82993 | + | 1.91085i | 0.282365 | + | 0.294850i | ||||
\(43\) | − | 3.62441i | − | 0.552717i | −0.961055 | − | 0.276359i | \(-0.910872\pi\) | ||
0.961055 | − | 0.276359i | \(-0.0891277\pi\) | |||||||
\(44\) | −2.78007 | − | 1.80865i | −0.419111 | − | 0.272664i | ||||
\(45\) | −0.606961 | + | 0.350429i | −0.0904803 | + | 0.0522389i | ||||
\(46\) | 4.56555 | − | 2.63592i | 0.673153 | − | 0.388645i | ||||
\(47\) | −2.03495 | − | 1.17488i | −0.296828 | − | 0.171374i | 0.344189 | − | 0.938900i | \(-0.388154\pi\) |
−0.641017 | + | 0.767527i | \(0.721487\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −0.302687 | + | 6.99345i | −0.0432409 | + | 0.999065i | ||||
\(50\) | − | 4.50880i | − | 0.637640i | ||||||
\(51\) | 0.535018 | + | 0.308893i | 0.0749175 | + | 0.0432536i | ||||
\(52\) | 3.51781 | + | 6.09302i | 0.487832 | + | 0.844951i | ||||
\(53\) | −3.95068 | − | 6.84278i | −0.542668 | − | 0.939928i | −0.998750 | − | 0.0499906i | \(-0.984081\pi\) |
0.456082 | − | 0.889938i | \(-0.349252\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 2.32120 | + | 0.123562i | 0.312990 | + | 0.0166610i | ||||
\(56\) | −1.91085 | + | 1.82993i | −0.255348 | + | 0.244535i | ||||
\(57\) | 0.783393i | 0.103763i | ||||||||
\(58\) | −1.04588 | + | 1.81152i | −0.137331 | + | 0.237864i | ||||
\(59\) | −3.25961 | + | 1.88193i | −0.424365 | + | 0.245007i | −0.696943 | − | 0.717127i | \(-0.745457\pi\) |
0.272578 | + | 0.962134i | \(0.412124\pi\) | |||||||
\(60\) | −0.350429 | − | 0.606961i | −0.0452402 | − | 0.0783583i | ||||
\(61\) | −4.18286 | + | 7.24493i | −0.535560 | + | 0.927618i | 0.463576 | + | 0.886057i | \(0.346566\pi\) |
−0.999136 | + | 0.0415604i | \(0.986767\pi\) | |||||||
\(62\) | −6.17793 | −0.784597 | ||||||||
\(63\) | 2.56981 | − | 0.629345i | 0.323766 | − | 0.0792900i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.27034 | − | 2.46548i | −0.529671 | − | 0.305806i | ||||
\(66\) | −2.95637 | + | 1.50329i | −0.363904 | + | 0.185042i | ||||
\(67\) | −1.07040 | − | 1.85399i | −0.130771 | − | 0.226501i | 0.793203 | − | 0.608957i | \(-0.208412\pi\) |
−0.923974 | + | 0.382456i | \(0.875078\pi\) | |||||||
\(68\) | −0.308893 | + | 0.535018i | −0.0374587 | + | 0.0648804i | ||||
\(69\) | − | 5.27184i | − | 0.634655i | ||||||
\(70\) | 0.518548 | − | 1.78031i | 0.0619784 | − | 0.212788i | ||||
\(71\) | −4.48503 | −0.532275 | −0.266138 | − | 0.963935i | \(-0.585748\pi\) | ||||
−0.266138 | + | 0.963935i | \(0.585748\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −2.64471 | − | 4.58078i | −0.309540 | − | 0.536139i | 0.668722 | − | 0.743513i | \(-0.266842\pi\) |
−0.978262 | + | 0.207373i | \(0.933508\pi\) | |||||||
\(74\) | 3.45907 | − | 1.99709i | 0.402108 | − | 0.232157i | ||||
\(75\) | −3.90473 | − | 2.25440i | −0.450880 | − | 0.260316i | ||||
\(76\) | −0.783393 | −0.0898613 | ||||||||
\(77\) | −8.28252 | − | 2.89826i | −0.943880 | − | 0.330288i | ||||
\(78\) | 7.03562 | 0.796627 | ||||||||
\(79\) | −3.75818 | − | 2.16979i | −0.422828 | − | 0.244120i | 0.273458 | − | 0.961884i | \(-0.411832\pi\) |
−0.696287 | + | 0.717764i | \(0.745166\pi\) | |||||||
\(80\) | 0.606961 | − | 0.350429i | 0.0678603 | − | 0.0391791i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −5.06922 | − | 2.92671i | −0.559801 | − | 0.323202i | ||||
\(83\) | −4.03988 | −0.443435 | −0.221717 | − | 0.975111i | \(-0.571166\pi\) | ||||
−0.221717 | + | 0.975111i | \(0.571166\pi\) | |||||||
\(84\) | 0.629345 | + | 2.56981i | 0.0686671 | + | 0.280389i | ||||
\(85\) | − | 0.432980i | − | 0.0469632i | ||||||
\(86\) | 1.81220 | − | 3.13883i | 0.195415 | − | 0.338469i | ||||
\(87\) | 1.04588 | + | 1.81152i | 0.112130 | + | 0.194215i | ||||
\(88\) | −1.50329 | − | 2.95637i | −0.160251 | − | 0.315150i | ||||
\(89\) | 14.0396 | + | 8.10574i | 1.48819 | + | 0.859207i | 0.999909 | − | 0.0134796i | \(-0.00429082\pi\) |
0.488281 | + | 0.872687i | \(0.337624\pi\) | |||||||
\(90\) | −0.700858 | −0.0738769 | ||||||||
\(91\) | 12.8747 | + | 13.4440i | 1.34964 | + | 1.40931i | ||||
\(92\) | 5.27184 | 0.549627 | ||||||||
\(93\) | −3.08896 | + | 5.35024i | −0.320311 | + | 0.554794i | ||||
\(94\) | −1.17488 | − | 2.03495i | −0.121179 | − | 0.209889i | ||||
\(95\) | 0.475489 | − | 0.274523i | 0.0487841 | − | 0.0281655i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 10.4926i | − | 1.06536i | −0.846317 | − | 0.532680i | \(-0.821185\pi\) | ||
0.846317 | − | 0.532680i | \(-0.178815\pi\) | |||||||
\(98\) | −3.75886 | + | 5.90516i | −0.379702 | + | 0.596512i | ||||
\(99\) | −0.176300 | + | 3.31194i | −0.0177189 | + | 0.332862i | ||||
\(100\) | 2.25440 | − | 3.90473i | 0.225440 | − | 0.390473i | ||||
\(101\) | −7.49737 | − | 12.9858i | −0.746016 | − | 1.29214i | −0.949718 | − | 0.313105i | \(-0.898631\pi\) |
0.203702 | − | 0.979033i | \(-0.434703\pi\) | |||||||
\(102\) | 0.308893 | + | 0.535018i | 0.0305849 | + | 0.0529746i | ||||
\(103\) | 12.4289 | + | 7.17585i | 1.22466 | + | 0.707057i | 0.965908 | − | 0.258887i | \(-0.0833556\pi\) |
0.258752 | + | 0.965944i | \(0.416689\pi\) | |||||||
\(104\) | 7.03562i | 0.689899i | ||||||||
\(105\) | −1.28252 | − | 1.33923i | −0.125161 | − | 0.130696i | ||||
\(106\) | − | 7.90136i | − | 0.767448i | ||||||
\(107\) | −9.93081 | − | 5.73356i | −0.960048 | − | 0.554284i | −0.0638601 | − | 0.997959i | \(-0.520341\pi\) |
−0.896188 | + | 0.443675i | \(0.853674\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 1.25820 | − | 0.726424i | 0.120514 | − | 0.0695788i | −0.438531 | − | 0.898716i | \(-0.644501\pi\) |
0.559045 | + | 0.829137i | \(0.311168\pi\) | |||||||
\(110\) | 1.94843 | + | 1.26761i | 0.185776 | + | 0.120861i | ||||
\(111\) | − | 3.99419i | − | 0.379111i | ||||||
\(112\) | −2.56981 | + | 0.629345i | −0.242824 | + | 0.0594675i | ||||
\(113\) | 12.0074 | 1.12956 | 0.564781 | − | 0.825241i | \(-0.308961\pi\) | ||||
0.564781 | + | 0.825241i | \(0.308961\pi\) | |||||||
\(114\) | −0.391696 | + | 0.678438i | −0.0366857 | + | 0.0635416i | ||||
\(115\) | −3.19980 | + | 1.84740i | −0.298383 | + | 0.172271i | ||||
\(116\) | −1.81152 | + | 1.04588i | −0.168195 | + | 0.0971077i | ||||
\(117\) | 3.51781 | − | 6.09302i | 0.325222 | − | 0.563300i | ||||
\(118\) | −3.76387 | −0.346492 | ||||||||
\(119\) | −0.457085 | + | 1.56929i | −0.0419009 | + | 0.143857i | ||||
\(120\) | − | 0.700858i | − | 0.0639793i | ||||||
\(121\) | 6.48026 | − | 8.88855i | 0.589114 | − | 0.808050i | ||||
\(122\) | −7.24493 | + | 4.18286i | −0.655925 | + | 0.378698i | ||||
\(123\) | −5.06922 | + | 2.92671i | −0.457076 | + | 0.263893i | ||||
\(124\) | −5.35024 | − | 3.08896i | −0.480466 | − | 0.277397i | ||||
\(125\) | 6.66432i | 0.596074i | ||||||||
\(126\) | 2.54019 | + | 0.739877i | 0.226298 | + | 0.0659135i | ||||
\(127\) | − | 3.43188i | − | 0.304530i | −0.988340 | − | 0.152265i | \(-0.951343\pi\) | ||
0.988340 | − | 0.152265i | \(-0.0486568\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.81220 | − | 3.13883i | −0.159556 | − | 0.276359i | ||||
\(130\) | −2.46548 | − | 4.27034i | −0.216237 | − | 0.374534i | ||||
\(131\) | −7.30288 | + | 12.6490i | −0.638056 | + | 1.10515i | 0.347803 | + | 0.937568i | \(0.386928\pi\) |
−0.985859 | + | 0.167578i | \(0.946406\pi\) | |||||||
\(132\) | −3.31194 | − | 0.176300i | −0.288267 | − | 0.0153450i | ||||
\(133\) | −2.01317 | + | 0.493024i | −0.174564 | + | 0.0427506i | ||||
\(134\) | − | 2.14081i | − | 0.184938i | ||||||
\(135\) | −0.350429 | + | 0.606961i | −0.0301601 | + | 0.0522389i | ||||
\(136\) | −0.535018 | + | 0.308893i | −0.0458774 | + | 0.0264873i | ||||
\(137\) | −8.35804 | − | 14.4765i | −0.714075 | − | 1.23681i | −0.963315 | − | 0.268373i | \(-0.913514\pi\) |
0.249240 | − | 0.968442i | \(-0.419819\pi\) | |||||||
\(138\) | 2.63592 | − | 4.56555i | 0.224384 | − | 0.388645i | ||||
\(139\) | 12.9399 | 1.09755 | 0.548775 | − | 0.835970i | \(-0.315094\pi\) | ||||
0.548775 | + | 0.835970i | \(0.315094\pi\) | |||||||
\(140\) | 1.33923 | − | 1.28252i | 0.113186 | − | 0.108393i | ||||
\(141\) | −2.34976 | −0.197885 | ||||||||
\(142\) | −3.88415 | − | 2.24252i | −0.325951 | − | 0.188188i | ||||
\(143\) | −20.7999 | + | 10.5766i | −1.73937 | + | 0.884456i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0.733014 | − | 1.26962i | 0.0608735 | − | 0.105436i | ||||
\(146\) | − | 5.28943i | − | 0.437756i | ||||||
\(147\) | 3.23459 | + | 6.20785i | 0.266785 | + | 0.512015i | ||||
\(148\) | 3.99419 | 0.328320 | ||||||||
\(149\) | −8.42523 | − | 4.86431i | −0.690221 | − | 0.398500i | 0.113474 | − | 0.993541i | \(-0.463802\pi\) |
−0.803695 | + | 0.595041i | \(0.797136\pi\) | |||||||
\(150\) | −2.25440 | − | 3.90473i | −0.184071 | − | 0.318820i | ||||
\(151\) | −17.1367 | + | 9.89387i | −1.39456 | + | 0.805151i | −0.993816 | − | 0.111037i | \(-0.964583\pi\) |
−0.400747 | + | 0.916189i | \(0.631249\pi\) | |||||||
\(152\) | −0.678438 | − | 0.391696i | −0.0550286 | − | 0.0317708i | ||||
\(153\) | 0.617785 | 0.0499450 | ||||||||
\(154\) | −5.72374 | − | 6.65123i | −0.461232 | − | 0.535971i | ||||
\(155\) | 4.32985 | 0.347782 | ||||||||
\(156\) | 6.09302 | + | 3.51781i | 0.487832 | + | 0.281650i | ||||
\(157\) | 10.4014 | − | 6.00523i | 0.830119 | − | 0.479269i | −0.0237745 | − | 0.999717i | \(-0.507568\pi\) |
0.853893 | + | 0.520448i | \(0.174235\pi\) | |||||||
\(158\) | −2.16979 | − | 3.75818i | −0.172619 | − | 0.298985i | ||||
\(159\) | −6.84278 | − | 3.95068i | −0.542668 | − | 0.313309i | ||||
\(160\) | 0.700858 | 0.0554077 | ||||||||
\(161\) | 13.5476 | − | 3.31780i | 1.06770 | − | 0.261479i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −11.1980 | + | 19.3955i | −0.877094 | + | 1.51917i | −0.0225784 | + | 0.999745i | \(0.507188\pi\) |
−0.854515 | + | 0.519426i | \(0.826146\pi\) | |||||||
\(164\) | −2.92671 | − | 5.06922i | −0.228538 | − | 0.395839i | ||||
\(165\) | 2.07200 | − | 1.05359i | 0.161305 | − | 0.0820219i | ||||
\(166\) | −3.49864 | − | 2.01994i | −0.271547 | − | 0.156778i | ||||
\(167\) | 17.9924 | 1.39229 | 0.696145 | − | 0.717901i | \(-0.254897\pi\) | ||||
0.696145 | + | 0.717901i | \(0.254897\pi\) | |||||||
\(168\) | −0.739877 | + | 2.54019i | −0.0570827 | + | 0.195980i | ||||
\(169\) | 36.4999 | 2.80769 | ||||||||
\(170\) | 0.216490 | − | 0.374971i | 0.0166040 | − | 0.0287590i | ||||
\(171\) | 0.391696 | + | 0.678438i | 0.0299538 | + | 0.0518815i | ||||
\(172\) | 3.13883 | − | 1.81220i | 0.239334 | − | 0.138179i | ||||
\(173\) | 0.189191 | − | 0.327689i | 0.0143839 | − | 0.0249137i | −0.858744 | − | 0.512405i | \(-0.828755\pi\) |
0.873128 | + | 0.487491i | \(0.162088\pi\) | |||||||
\(174\) | 2.09176i | 0.158576i | ||||||||
\(175\) | 3.33596 | − | 11.4532i | 0.252175 | − | 0.865782i | ||||
\(176\) | 0.176300 | − | 3.31194i | 0.0132891 | − | 0.249647i | ||||
\(177\) | −1.88193 | + | 3.25961i | −0.141455 | + | 0.245007i | ||||
\(178\) | 8.10574 | + | 14.0396i | 0.607551 | + | 1.05231i | ||||
\(179\) | 2.15547 | + | 3.73338i | 0.161107 | + | 0.279046i | 0.935266 | − | 0.353946i | \(-0.115160\pi\) |
−0.774159 | + | 0.632991i | \(0.781827\pi\) | |||||||
\(180\) | −0.606961 | − | 0.350429i | −0.0452402 | − | 0.0261194i | ||||
\(181\) | − | 6.96276i | − | 0.517538i | −0.965939 | − | 0.258769i | \(-0.916683\pi\) | ||
0.965939 | − | 0.258769i | \(-0.0833169\pi\) | |||||||
\(182\) | 4.42783 | + | 18.0802i | 0.328212 | + | 1.34019i | ||||
\(183\) | 8.36572i | 0.618412i | ||||||||
\(184\) | 4.56555 | + | 2.63592i | 0.336576 | + | 0.194323i | ||||
\(185\) | −2.42431 | + | 1.39968i | −0.178239 | + | 0.102906i | ||||
\(186\) | −5.35024 | + | 3.08896i | −0.392299 | + | 0.226494i | ||||
\(187\) | −1.71749 | − | 1.11736i | −0.125595 | − | 0.0817092i | ||||
\(188\) | − | 2.34976i | − | 0.171374i | ||||||
\(189\) | 1.91085 | − | 1.82993i | 0.138994 | − | 0.133108i | ||||
\(190\) | 0.549047 | 0.0398321 | ||||||||
\(191\) | 9.27949 | − | 16.0725i | 0.671440 | − | 1.16297i | −0.306055 | − | 0.952014i | \(-0.599009\pi\) |
0.977496 | − | 0.210955i | \(-0.0676574\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 15.1738 | − | 8.76059i | 1.09223 | − | 0.630601i | 0.158063 | − | 0.987429i | \(-0.449475\pi\) |
0.934170 | + | 0.356828i | \(0.116142\pi\) | |||||||
\(194\) | 5.24629 | − | 9.08684i | 0.376662 | − | 0.652397i | ||||
\(195\) | −4.93097 | −0.353114 | ||||||||
\(196\) | −6.20785 | + | 3.23459i | −0.443418 | + | 0.231042i | ||||
\(197\) | 18.8663i | 1.34417i | 0.740474 | + | 0.672086i | \(0.234601\pi\) | ||||
−0.740474 | + | 0.672086i | \(0.765399\pi\) | |||||||
\(198\) | −1.80865 | + | 2.78007i | −0.128535 | + | 0.197571i | ||||
\(199\) | −11.7194 | + | 6.76618i | −0.830764 | + | 0.479642i | −0.854114 | − | 0.520086i | \(-0.825900\pi\) |
0.0233504 | + | 0.999727i | \(0.492567\pi\) | |||||||
\(200\) | 3.90473 | − | 2.25440i | 0.276106 | − | 0.159410i | ||||
\(201\) | −1.85399 | − | 1.07040i | −0.130771 | − | 0.0755004i | ||||
\(202\) | − | 14.9947i | − | 1.05503i | ||||||
\(203\) | −3.99704 | + | 3.82779i | −0.280537 | + | 0.268658i | ||||
\(204\) | 0.617785i | 0.0432536i | ||||||||
\(205\) | 3.55280 | + | 2.05121i | 0.248138 | + | 0.143263i | ||||
\(206\) | 7.17585 | + | 12.4289i | 0.499965 | + | 0.865965i | ||||
\(207\) | −2.63592 | − | 4.56555i | −0.183209 | − | 0.317327i | ||||
\(208\) | −3.51781 | + | 6.09302i | −0.243916 | + | 0.422475i | ||||
\(209\) | 0.138113 | − | 2.59455i | 0.00955344 | − | 0.179469i | ||||
\(210\) | −0.441081 | − | 1.80107i | −0.0304375 | − | 0.124286i | ||||
\(211\) | − | 4.94368i | − | 0.340337i | −0.985415 | − | 0.170168i | \(-0.945569\pi\) | ||
0.985415 | − | 0.170168i | \(-0.0544312\pi\) | |||||||
\(212\) | 3.95068 | − | 6.84278i | 0.271334 | − | 0.469964i | ||||
\(213\) | −3.88415 | + | 2.24252i | −0.266138 | + | 0.153655i | ||||
\(214\) | −5.73356 | − | 9.93081i | −0.391938 | − | 0.678856i | ||||
\(215\) | −1.27010 | + | 2.19987i | −0.0866199 | + | 0.150030i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −15.6931 | − | 4.57090i | −1.06532 | − | 0.310293i | ||||
\(218\) | 1.45285 | 0.0983993 | ||||||||
\(219\) | −4.58078 | − | 2.64471i | −0.309540 | − | 0.178713i | ||||
\(220\) | 1.05359 | + | 2.07200i | 0.0710331 | + | 0.139694i | ||||
\(221\) | 2.17325 | + | 3.76418i | 0.146189 | + | 0.253206i | ||||
\(222\) | 1.99709 | − | 3.45907i | 0.134036 | − | 0.232157i | ||||
\(223\) | 22.9194i | 1.53480i | 0.641169 | + | 0.767400i | \(0.278450\pi\) | ||||
−0.641169 | + | 0.767400i | \(0.721550\pi\) | |||||||
\(224\) | −2.54019 | − | 0.739877i | −0.169724 | − | 0.0494351i | ||||
\(225\) | −4.50880 | −0.300587 | ||||||||
\(226\) | 10.3987 | + | 6.00371i | 0.691713 | + | 0.399361i | ||||
\(227\) | 12.1141 | + | 20.9823i | 0.804042 | + | 1.39264i | 0.916936 | + | 0.399034i | \(0.130655\pi\) |
−0.112894 | + | 0.993607i | \(0.536012\pi\) | |||||||
\(228\) | −0.678438 | + | 0.391696i | −0.0449307 | + | 0.0259407i | ||||
\(229\) | −11.5855 | − | 6.68891i | −0.765594 | − | 0.442016i | 0.0657068 | − | 0.997839i | \(-0.479070\pi\) |
−0.831300 | + | 0.555823i | \(0.812403\pi\) | |||||||
\(230\) | −3.69481 | −0.243628 | ||||||||
\(231\) | −8.62200 | + | 1.63129i | −0.567286 | + | 0.107331i | ||||
\(232\) | −2.09176 | −0.137331 | ||||||||
\(233\) | 24.1664 | + | 13.9525i | 1.58319 | + | 0.914057i | 0.994389 | + | 0.105782i | \(0.0337346\pi\) |
0.588805 | + | 0.808275i | \(0.299599\pi\) | |||||||
\(234\) | 6.09302 | − | 3.51781i | 0.398313 | − | 0.229966i | ||||
\(235\) | 0.823423 | + | 1.42621i | 0.0537142 | + | 0.0930357i | ||||
\(236\) | −3.25961 | − | 1.88193i | −0.212182 | − | 0.122503i | ||||
\(237\) | −4.33957 | −0.281886 | ||||||||
\(238\) | −1.18049 | + | 1.13051i | −0.0765201 | + | 0.0732798i | ||||
\(239\) | − | 9.27514i | − | 0.599959i | −0.953946 | − | 0.299979i | \(-0.903020\pi\) | ||
0.953946 | − | 0.299979i | \(-0.0969798\pi\) | |||||||
\(240\) | 0.350429 | − | 0.606961i | 0.0226201 | − | 0.0391791i | ||||
\(241\) | 9.54851 | + | 16.5385i | 0.615074 | + | 1.06534i | 0.990372 | + | 0.138434i | \(0.0442070\pi\) |
−0.375298 | + | 0.926904i | \(0.622460\pi\) | |||||||
\(242\) | 10.0563 | − | 4.45758i | 0.646446 | − | 0.286544i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −8.36572 | −0.535560 | ||||||||
\(245\) | 2.63443 | − | 4.13868i | 0.168307 | − | 0.264411i | ||||
\(246\) | −5.85343 | −0.373201 | ||||||||
\(247\) | −2.75583 | + | 4.77323i | −0.175349 | + | 0.303713i | ||||
\(248\) | −3.08896 | − | 5.35024i | −0.196149 | − | 0.339741i | ||||
\(249\) | −3.49864 | + | 2.01994i | −0.221717 | + | 0.128009i | ||||
\(250\) | −3.33216 | + | 5.77147i | −0.210744 | + | 0.365020i | ||||
\(251\) | 12.1328i | 0.765818i | 0.923786 | + | 0.382909i | \(0.125078\pi\) | ||||
−0.923786 | + | 0.382909i | \(0.874922\pi\) | |||||||
\(252\) | 1.82993 | + | 1.91085i | 0.115275 | + | 0.120372i | ||||
\(253\) | −0.929428 | + | 17.4600i | −0.0584326 | + | 1.09770i | ||||
\(254\) | 1.71594 | − | 2.97210i | 0.107668 | − | 0.186486i | ||||
\(255\) | −0.216490 | − | 0.374971i | −0.0135571 | − | 0.0234816i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 17.2747 | + | 9.97355i | 1.07757 | + | 0.622133i | 0.930239 | − | 0.366955i | \(-0.119600\pi\) |
0.147327 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(258\) | − | 3.62441i | − | 0.225646i | ||||||
\(259\) | 10.2643 | − | 2.51372i | 0.637793 | − | 0.156195i | ||||
\(260\) | − | 4.93097i | − | 0.305806i | ||||||
\(261\) | 1.81152 | + | 1.04588i | 0.112130 | + | 0.0647385i | ||||
\(262\) | −12.6490 | + | 7.30288i | −0.781456 | + | 0.451174i | ||||
\(263\) | 14.5377 | − | 8.39335i | 0.896433 | − | 0.517556i | 0.0203919 | − | 0.999792i | \(-0.493509\pi\) |
0.876041 | + | 0.482236i | \(0.160175\pi\) | |||||||
\(264\) | −2.78007 | − | 1.80865i | −0.171101 | − | 0.111315i | ||||
\(265\) | 5.53773i | 0.340180i | ||||||||
\(266\) | −1.98997 | − | 0.579614i | −0.122013 | − | 0.0355384i | ||||
\(267\) | 16.2115 | 0.992127 | ||||||||
\(268\) | 1.07040 | − | 1.85399i | 0.0653853 | − | 0.113251i | ||||
\(269\) | −16.8835 | + | 9.74767i | −1.02940 | + | 0.594326i | −0.916813 | − | 0.399316i | \(-0.869248\pi\) |
−0.112589 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(270\) | −0.606961 | + | 0.350429i | −0.0369384 | + | 0.0213264i | ||||
\(271\) | −5.34130 | + | 9.25140i | −0.324461 | + | 0.561983i | −0.981403 | − | 0.191958i | \(-0.938516\pi\) |
0.656942 | + | 0.753941i | \(0.271850\pi\) | |||||||
\(272\) | −0.617785 | −0.0374587 | ||||||||
\(273\) | 17.8718 | + | 5.20549i | 1.08165 | + | 0.315051i | ||||
\(274\) | − | 16.7161i | − | 1.00986i | ||||||
\(275\) | 12.5348 | + | 8.15483i | 0.755875 | + | 0.491755i | ||||
\(276\) | 4.56555 | − | 2.63592i | 0.274814 | − | 0.158664i | ||||
\(277\) | −26.6632 | + | 15.3940i | −1.60203 | + | 0.924934i | −0.610954 | + | 0.791666i | \(0.709214\pi\) |
−0.991080 | + | 0.133268i | \(0.957453\pi\) | |||||||
\(278\) | 11.2063 | + | 6.46997i | 0.672110 | + | 0.388043i | ||||
\(279\) | 6.17793i | 0.369863i | ||||||||
\(280\) | 1.80107 | − | 0.441081i | 0.107635 | − | 0.0263596i | ||||
\(281\) | 21.3381i | 1.27292i | 0.771308 | + | 0.636462i | \(0.219603\pi\) | ||||
−0.771308 | + | 0.636462i | \(0.780397\pi\) | |||||||
\(282\) | −2.03495 | − | 1.17488i | −0.121179 | − | 0.0699630i | ||||
\(283\) | −1.26154 | − | 2.18504i | −0.0749905 | − | 0.129887i | 0.826092 | − | 0.563536i | \(-0.190559\pi\) |
−0.901082 | + | 0.433648i | \(0.857226\pi\) | |||||||
\(284\) | −2.24252 | − | 3.88415i | −0.133069 | − | 0.230482i | ||||
\(285\) | 0.274523 | − | 0.475489i | 0.0162614 | − | 0.0281655i | ||||
\(286\) | −23.3015 | − | 1.24038i | −1.37785 | − | 0.0733454i | ||||
\(287\) | −10.7114 | − | 11.1850i | −0.632273 | − | 0.660231i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 8.30917 | − | 14.3919i | 0.488775 | − | 0.846583i | ||||
\(290\) | 1.26962 | − | 0.733014i | 0.0745545 | − | 0.0430441i | ||||
\(291\) | −5.24629 | − | 9.08684i | −0.307543 | − | 0.532680i | ||||
\(292\) | 2.64471 | − | 4.58078i | 0.154770 | − | 0.268070i | ||||
\(293\) | 5.71831 | 0.334067 | 0.167034 | − | 0.985951i | \(-0.446581\pi\) | ||||
0.167034 | + | 0.985951i | \(0.446581\pi\) | |||||||
\(294\) | −0.302687 | + | 6.99345i | −0.0176530 | + | 0.407866i | ||||
\(295\) | 2.63794 | 0.153587 | ||||||||
\(296\) | 3.45907 | + | 1.99709i | 0.201054 | + | 0.116079i | ||||
\(297\) | 1.50329 | + | 2.95637i | 0.0872296 | + | 0.171546i | ||||
\(298\) | −4.86431 | − | 8.42523i | −0.281782 | − | 0.488060i | ||||
\(299\) | 18.5453 | − | 32.1214i | 1.07250 | − | 1.85763i | ||||
\(300\) | − | 4.50880i | − | 0.260316i | ||||||
\(301\) | 6.92570 | − | 6.63243i | 0.399191 | − | 0.382287i | ||||
\(302\) | −19.7877 | −1.13866 | ||||||||
\(303\) | −12.9858 | − | 7.49737i | −0.746016 | − | 0.430713i | ||||
\(304\) | −0.391696 | − | 0.678438i | −0.0224653 | − | 0.0389111i | ||||
\(305\) | 5.07766 | − | 2.93159i | 0.290746 | − | 0.167862i | ||||
\(306\) | 0.535018 | + | 0.308893i | 0.0305849 | + | 0.0176582i | ||||
\(307\) | 20.7839 | 1.18620 | 0.593099 | − | 0.805130i | \(-0.297904\pi\) | ||||
0.593099 | + | 0.805130i | \(0.297904\pi\) | |||||||
\(308\) | −1.63129 | − | 8.62200i | −0.0929514 | − | 0.491284i | ||||
\(309\) | 14.3517 | 0.816439 | ||||||||
\(310\) | 3.74976 | + | 2.16492i | 0.212972 | + | 0.122959i | ||||
\(311\) | −6.38045 | + | 3.68376i | −0.361802 | + | 0.208887i | −0.669871 | − | 0.742477i | \(-0.733651\pi\) |
0.308069 | + | 0.951364i | \(0.400317\pi\) | |||||||
\(312\) | 3.51781 | + | 6.09302i | 0.199157 | + | 0.344950i | ||||
\(313\) | −6.36871 | − | 3.67697i | −0.359981 | − | 0.207835i | 0.309092 | − | 0.951032i | \(-0.399975\pi\) |
−0.669072 | + | 0.743197i | \(0.733308\pi\) | |||||||
\(314\) | 12.0105 | 0.677789 | ||||||||
\(315\) | −1.78031 | − | 0.518548i | −0.100309 | − | 0.0292169i | ||||
\(316\) | − | 4.33957i | − | 0.244120i | ||||||
\(317\) | 7.39030 | − | 12.8004i | 0.415080 | − | 0.718940i | −0.580356 | − | 0.814363i | \(-0.697087\pi\) |
0.995437 | + | 0.0954222i | \(0.0304201\pi\) | |||||||
\(318\) | −3.95068 | − | 6.84278i | −0.221543 | − | 0.383724i | ||||
\(319\) | −3.14452 | − | 6.18403i | −0.176059 | − | 0.346239i | ||||
\(320\) | 0.606961 | + | 0.350429i | 0.0339301 | + | 0.0195896i | ||||
\(321\) | −11.4671 | −0.640032 | ||||||||
\(322\) | 13.3915 | + | 3.90051i | 0.746278 | + | 0.217367i | ||||
\(323\) | −0.483969 | −0.0269287 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −15.8611 | − | 27.4722i | −0.879815 | − | 1.52388i | ||||
\(326\) | −19.3955 | + | 11.1980i | −1.07422 | + | 0.620199i | ||||
\(327\) | 0.726424 | − | 1.25820i | 0.0401714 | − | 0.0695788i | ||||
\(328\) | − | 5.85343i | − | 0.323202i | ||||||
\(329\) | −1.47881 | − | 6.03843i | −0.0815292 | − | 0.332909i | ||||
\(330\) | 2.32120 | + | 0.123562i | 0.127778 | + | 0.00680184i | ||||
\(331\) | −13.6449 | + | 23.6336i | −0.749991 | + | 1.29902i | 0.197836 | + | 0.980235i | \(0.436609\pi\) |
−0.947826 | + | 0.318787i | \(0.896725\pi\) | |||||||
\(332\) | −2.01994 | − | 3.49864i | −0.110859 | − | 0.192013i | ||||
\(333\) | −1.99709 | − | 3.45907i | −0.109440 | − | 0.189556i | ||||
\(334\) | 15.5818 | + | 8.99618i | 0.852600 | + | 0.492249i | ||||
\(335\) | 1.50040i | 0.0819757i | ||||||||
\(336\) | −1.91085 | + | 1.82993i | −0.104245 | + | 0.0998311i | ||||
\(337\) | − | 13.0929i | − | 0.713215i | −0.934254 | − | 0.356607i | \(-0.883933\pi\) | ||
0.934254 | − | 0.356607i | \(-0.116067\pi\) | |||||||
\(338\) | 31.6099 | + | 18.2500i | 1.71935 | + | 0.992667i | ||||
\(339\) | 10.3987 | − | 6.00371i | 0.564781 | − | 0.326077i | ||||
\(340\) | 0.374971 | − | 0.216490i | 0.0203357 | − | 0.0117408i | ||||
\(341\) | 11.1737 | − | 17.1751i | 0.605090 | − | 0.930082i | ||||
\(342\) | 0.783393i | 0.0423610i | ||||||||
\(343\) | −13.9173 | + | 12.2192i | −0.751465 | + | 0.659773i | ||||
\(344\) | 3.62441 | 0.195415 | ||||||||
\(345\) | −1.84740 | + | 3.19980i | −0.0994609 | + | 0.172271i | ||||
\(346\) | 0.327689 | − | 0.189191i | 0.0176167 | − | 0.0101710i | ||||
\(347\) | −9.82708 | + | 5.67367i | −0.527545 | + | 0.304578i | −0.740016 | − | 0.672589i | \(-0.765182\pi\) |
0.212471 | + | 0.977167i | \(0.431849\pi\) | |||||||
\(348\) | −1.04588 | + | 1.81152i | −0.0560651 | + | 0.0971077i | ||||
\(349\) | 12.4060 | 0.664076 | 0.332038 | − | 0.943266i | \(-0.392264\pi\) | ||||
0.332038 | + | 0.943266i | \(0.392264\pi\) | |||||||
\(350\) | 8.61563 | − | 8.25080i | 0.460525 | − | 0.441024i | ||||
\(351\) | − | 7.03562i | − | 0.375534i | ||||||
\(352\) | 1.80865 | − | 2.78007i | 0.0964013 | − | 0.148178i | ||||
\(353\) | 5.90974 | − | 3.41199i | 0.314544 | − | 0.181602i | −0.334414 | − | 0.942426i | \(-0.608538\pi\) |
0.648958 | + | 0.760824i | \(0.275205\pi\) | |||||||
\(354\) | −3.25961 | + | 1.88193i | −0.173246 | + | 0.100024i | ||||
\(355\) | 2.72224 | + | 1.57168i | 0.144481 | + | 0.0834163i | ||||
\(356\) | 16.2115i | 0.859207i | ||||||||
\(357\) | 0.388800 | + | 1.58759i | 0.0205775 | + | 0.0840242i | ||||
\(358\) | 4.31093i | 0.227840i | ||||||||
\(359\) | −17.6942 | − | 10.2157i | −0.933862 | − | 0.539166i | −0.0458314 | − | 0.998949i | \(-0.514594\pi\) |
−0.888031 | + | 0.459783i | \(0.847927\pi\) | |||||||
\(360\) | −0.350429 | − | 0.606961i | −0.0184692 | − | 0.0319896i | ||||
\(361\) | 9.19315 | + | 15.9230i | 0.483850 | + | 0.838053i | ||||
\(362\) | 3.48138 | − | 6.02993i | 0.182977 | − | 0.316926i | ||||
\(363\) | 1.16779 | − | 10.9378i | 0.0612932 | − | 0.574088i | ||||
\(364\) | −5.20549 | + | 17.8718i | −0.272842 | + | 0.936739i | ||||
\(365\) | 3.70714i | 0.194040i | ||||||||
\(366\) | −4.18286 | + | 7.24493i | −0.218642 | + | 0.378698i | ||||
\(367\) | 17.4563 | − | 10.0784i | 0.911212 | − | 0.526088i | 0.0303908 | − | 0.999538i | \(-0.490325\pi\) |
0.880821 | + | 0.473450i | \(0.156991\pi\) | |||||||
\(368\) | 2.63592 | + | 4.56555i | 0.137407 | + | 0.237995i | ||||
\(369\) | −2.92671 | + | 5.06922i | −0.152359 | + | 0.263893i | ||||
\(370\) | −2.79936 | −0.145532 | ||||||||
\(371\) | 5.84604 | − | 20.0710i | 0.303511 | − | 1.04203i | ||||
\(372\) | −6.17793 | −0.320311 | ||||||||
\(373\) | −7.22139 | − | 4.16927i | −0.373909 | − | 0.215877i | 0.301256 | − | 0.953543i | \(-0.402594\pi\) |
−0.675165 | + | 0.737667i | \(0.735928\pi\) | |||||||
\(374\) | −0.928709 | − | 1.82640i | −0.0480224 | − | 0.0944410i | ||||
\(375\) | 3.33216 | + | 5.77147i | 0.172072 | + | 0.298037i | ||||
\(376\) | 1.17488 | − | 2.03495i | 0.0605897 | − | 0.104944i | ||||
\(377\) | 14.7169i | 0.757956i | ||||||||
\(378\) | 2.56981 | − | 0.629345i | 0.132177 | − | 0.0323700i | ||||
\(379\) | −12.2093 | −0.627151 | −0.313575 | − | 0.949563i | \(-0.601527\pi\) | ||||
−0.313575 | + | 0.949563i | \(0.601527\pi\) | |||||||
\(380\) | 0.475489 | + | 0.274523i | 0.0243921 | + | 0.0140828i | ||||
\(381\) | −1.71594 | − | 2.97210i | −0.0879103 | − | 0.152265i | ||||
\(382\) | 16.0725 | − | 9.27949i | 0.822343 | − | 0.474780i | ||||
\(383\) | 16.1528 | + | 9.32585i | 0.825372 | + | 0.476529i | 0.852265 | − | 0.523110i | \(-0.175228\pi\) |
−0.0268936 | + | 0.999638i | \(0.508562\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 4.01153 | + | 4.66156i | 0.204446 | + | 0.237575i | ||||
\(386\) | 17.5212 | 0.891805 | ||||||||
\(387\) | −3.13883 | − | 1.81220i | −0.159556 | − | 0.0921195i | ||||
\(388\) | 9.08684 | − | 5.24629i | 0.461314 | − | 0.266340i | ||||
\(389\) | 4.75722 | + | 8.23974i | 0.241201 | + | 0.417772i | 0.961057 | − | 0.276352i | \(-0.0891255\pi\) |
−0.719856 | + | 0.694123i | \(0.755792\pi\) | |||||||
\(390\) | −4.27034 | − | 2.46548i | −0.216237 | − | 0.124845i | ||||
\(391\) | 3.25686 | 0.164707 | ||||||||
\(392\) | −6.99345 | − | 0.302687i | −0.353223 | − | 0.0152880i | ||||
\(393\) | 14.6058i | 0.736764i | ||||||||
\(394\) | −9.43317 | + | 16.3387i | −0.475236 | + | 0.823133i | ||||
\(395\) | 1.52071 | + | 2.63395i | 0.0765153 | + | 0.132528i | ||||
\(396\) | −2.95637 | + | 1.50329i | −0.148563 | + | 0.0755430i | ||||
\(397\) | −29.5051 | − | 17.0348i | −1.48082 | − | 0.854952i | −0.481057 | − | 0.876689i | \(-0.659747\pi\) |
−0.999764 | + | 0.0217370i | \(0.993080\pi\) | |||||||
\(398\) | −13.5324 | −0.678316 | ||||||||
\(399\) | −1.49695 | + | 1.43356i | −0.0749410 | + | 0.0717676i | ||||
\(400\) | 4.50880 | 0.225440 | ||||||||
\(401\) | 14.8179 | − | 25.6653i | 0.739969 | − | 1.28166i | −0.212539 | − | 0.977153i | \(-0.568173\pi\) |
0.952508 | − | 0.304512i | \(-0.0984934\pi\) | |||||||
\(402\) | −1.07040 | − | 1.85399i | −0.0533869 | − | 0.0924688i | ||||
\(403\) | −37.6423 | + | 21.7328i | −1.87509 | + | 1.08259i | ||||
\(404\) | 7.49737 | − | 12.9858i | 0.373008 | − | 0.646069i | ||||
\(405\) | 0.700858i | 0.0348259i | ||||||||
\(406\) | −5.37544 | + | 1.31644i | −0.266778 | + | 0.0653338i | ||||
\(407\) | −0.704177 | + | 13.2285i | −0.0349048 | + | 0.655712i | ||||
\(408\) | −0.308893 | + | 0.535018i | −0.0152925 | + | 0.0264873i | ||||
\(409\) | −13.6644 | − | 23.6675i | −0.675662 | − | 1.17028i | −0.976275 | − | 0.216534i | \(-0.930525\pi\) |
0.300613 | − | 0.953746i | \(-0.402809\pi\) | |||||||
\(410\) | 2.05121 | + | 3.55280i | 0.101302 | + | 0.175460i | ||||
\(411\) | −14.4765 | − | 8.35804i | −0.714075 | − | 0.412272i | ||||
\(412\) | 14.3517i | 0.707057i | ||||||||
\(413\) | −9.56095 | − | 2.78480i | −0.470464 | − | 0.137031i | ||||
\(414\) | − | 5.27184i | − | 0.259097i | ||||||
\(415\) | 2.45205 | + | 1.41569i | 0.120366 | + | 0.0694936i | ||||
\(416\) | −6.09302 | + | 3.51781i | −0.298735 | + | 0.172475i | ||||
\(417\) | 11.2063 | − | 6.46997i | 0.548775 | − | 0.316836i | ||||
\(418\) | 1.41688 | − | 2.17789i | 0.0693020 | − | 0.106524i | ||||
\(419\) | − | 25.6972i | − | 1.25539i | −0.778459 | − | 0.627696i | \(-0.783998\pi\) | ||
0.778459 | − | 0.627696i | \(-0.216002\pi\) | |||||||
\(420\) | 0.518548 | − | 1.78031i | 0.0253026 | − | 0.0868704i | ||||
\(421\) | −36.9246 | −1.79959 | −0.899797 | − | 0.436309i | \(-0.856285\pi\) | ||||
−0.899797 | + | 0.436309i | \(0.856285\pi\) | |||||||
\(422\) | 2.47184 | − | 4.28135i | 0.120327 | − | 0.208413i | ||||
\(423\) | −2.03495 | + | 1.17488i | −0.0989426 | + | 0.0571245i | ||||
\(424\) | 6.84278 | − | 3.95068i | 0.332315 | − | 0.191862i | ||||
\(425\) | 1.39273 | − | 2.41229i | 0.0675575 | − | 0.117013i | ||||
\(426\) | −4.48503 | −0.217300 | ||||||||
\(427\) | −21.4983 | + | 5.26492i | −1.04038 | + | 0.254787i | ||||
\(428\) | − | 11.4671i | − | 0.554284i | ||||||
\(429\) | −12.7250 | + | 19.5595i | −0.614367 | + | 0.944342i | ||||
\(430\) | −2.19987 | + | 1.27010i | −0.106087 | + | 0.0612495i | ||||
\(431\) | −17.4320 | + | 10.0644i | −0.839668 | + | 0.484783i | −0.857152 | − | 0.515064i | \(-0.827768\pi\) |
0.0174831 | + | 0.999847i | \(0.494435\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 38.1992i | − | 1.83574i | −0.396884 | − | 0.917869i | \(-0.629908\pi\) | ||
0.396884 | − | 0.917869i | \(-0.370092\pi\) | |||||||
\(434\) | −11.3052 | − | 11.8051i | −0.542667 | − | 0.566662i | ||||
\(435\) | − | 1.46603i | − | 0.0702907i | ||||||
\(436\) | 1.25820 | + | 0.726424i | 0.0602570 | + | 0.0347894i | ||||
\(437\) | 2.06496 | + | 3.57662i | 0.0987804 | + | 0.171093i | ||||
\(438\) | −2.64471 | − | 4.58078i | −0.126369 | − | 0.218878i | ||||
\(439\) | −3.66099 | + | 6.34102i | −0.174729 | + | 0.302640i | −0.940068 | − | 0.340988i | \(-0.889238\pi\) |
0.765338 | + | 0.643628i | \(0.222572\pi\) | |||||||
\(440\) | −0.123562 | + | 2.32120i | −0.00589057 | + | 0.110659i | ||||
\(441\) | 5.90516 | + | 3.75886i | 0.281198 | + | 0.178993i | ||||
\(442\) | 4.34650i | 0.206742i | ||||||||
\(443\) | 16.5124 | − | 28.6003i | 0.784527 | − | 1.35884i | −0.144754 | − | 0.989468i | \(-0.546239\pi\) |
0.929281 | − | 0.369373i | \(-0.120428\pi\) | |||||||
\(444\) | 3.45907 | − | 1.99709i | 0.164160 | − | 0.0947778i | ||||
\(445\) | −5.68097 | − | 9.83973i | −0.269304 | − | 0.466448i | ||||
\(446\) | −11.4597 | + | 19.8488i | −0.542633 | + | 0.939869i | ||||
\(447\) | −9.72861 | −0.460148 | ||||||||
\(448\) | −1.82993 | − | 1.91085i | −0.0864562 | − | 0.0902791i | ||||
\(449\) | −22.5285 | −1.06319 | −0.531594 | − | 0.846999i | \(-0.678407\pi\) | ||||
−0.531594 | + | 0.846999i | \(0.678407\pi\) | |||||||
\(450\) | −3.90473 | − | 2.25440i | −0.184071 | − | 0.106273i | ||||
\(451\) | 17.3049 | − | 8.79938i | 0.814856 | − | 0.414347i | ||||
\(452\) | 6.00371 | + | 10.3987i | 0.282391 | + | 0.489115i | ||||
\(453\) | −9.89387 | + | 17.1367i | −0.464854 | + | 0.805151i | ||||
\(454\) | 24.2282i | 1.13709i | ||||||||
\(455\) | −3.10328 | − | 12.6717i | −0.145484 | − | 0.594056i | ||||
\(456\) | −0.783393 | −0.0366857 | ||||||||
\(457\) | −28.7305 | − | 16.5876i | −1.34396 | − | 0.775934i | −0.356572 | − | 0.934268i | \(-0.616054\pi\) |
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(458\) | −6.68891 | − | 11.5855i | −0.312552 | − | 0.541356i | ||||
\(459\) | 0.535018 | − | 0.308893i | 0.0249725 | − | 0.0144179i | ||||
\(460\) | −3.19980 | − | 1.84740i | −0.149191 | − | 0.0861357i | ||||
\(461\) | 7.42955 | 0.346029 | 0.173014 | − | 0.984919i | \(-0.444649\pi\) | ||||
0.173014 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(462\) | −8.28252 | − | 2.89826i | −0.385338 | − | 0.134839i | ||||
\(463\) | −15.7504 | −0.731984 | −0.365992 | − | 0.930618i | \(-0.619270\pi\) | ||||
−0.365992 | + | 0.930618i | \(0.619270\pi\) | |||||||
\(464\) | −1.81152 | − | 1.04588i | −0.0840977 | − | 0.0485538i | ||||
\(465\) | 3.74976 | − | 2.16492i | 0.173891 | − | 0.100396i | ||||
\(466\) | 13.9525 | + | 24.1664i | 0.646336 | + | 1.11949i | ||||
\(467\) | 11.5815 | + | 6.68657i | 0.535927 | + | 0.309418i | 0.743427 | − | 0.668817i | \(-0.233199\pi\) |
−0.207500 | + | 0.978235i | \(0.566533\pi\) | |||||||
\(468\) | 7.03562 | 0.325222 | ||||||||
\(469\) | 1.58393 | − | 5.43806i | 0.0731392 | − | 0.251106i | ||||
\(470\) | 1.64685i | 0.0759633i | ||||||||
\(471\) | 6.00523 | − | 10.4014i | 0.276706 | − | 0.479269i | ||||
\(472\) | −1.88193 | − | 3.25961i | −0.0866231 | − | 0.150036i | ||||
\(473\) | 5.44853 | + | 10.7151i | 0.250524 | + | 0.492681i | ||||
\(474\) | −3.75818 | − | 2.16979i | −0.172619 | − | 0.0996616i | ||||
\(475\) | 3.53216 | 0.162067 | ||||||||
\(476\) | −1.58759 | + | 0.388800i | −0.0727671 | + | 0.0178206i | ||||
\(477\) | −7.90136 | −0.361779 | ||||||||
\(478\) | 4.63757 | − | 8.03251i | 0.212117 | − | 0.367398i | ||||
\(479\) | 5.63050 | + | 9.75230i | 0.257264 | + | 0.445594i | 0.965508 | − | 0.260374i | \(-0.0838457\pi\) |
−0.708244 | + | 0.705968i | \(0.750512\pi\) | |||||||
\(480\) | 0.606961 | − | 0.350429i | 0.0277038 | − | 0.0159948i | ||||
\(481\) | 14.0508 | − | 24.3367i | 0.640661 | − | 1.10966i | ||||
\(482\) | 19.0970i | 0.869845i | ||||||||
\(483\) | 10.0737 | − | 9.64711i | 0.458369 | − | 0.438959i | ||||
\(484\) | 10.9378 | + | 1.16779i | 0.497174 | + | 0.0530814i | ||||
\(485\) | −3.67690 | + | 6.36858i | −0.166960 | + | 0.289182i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −1.33482 | − | 2.31197i | −0.0604862 | − | 0.104765i | 0.834197 | − | 0.551467i | \(-0.185932\pi\) |
−0.894683 | + | 0.446702i | \(0.852598\pi\) | |||||||
\(488\) | −7.24493 | − | 4.18286i | −0.327962 | − | 0.189349i | ||||
\(489\) | 22.3960i | 1.01278i | ||||||||
\(490\) | 4.35082 | − | 2.26699i | 0.196550 | − | 0.102412i | ||||
\(491\) | 11.3063i | 0.510245i | 0.966909 | + | 0.255123i | \(0.0821158\pi\) | ||||
−0.966909 | + | 0.255123i | \(0.917884\pi\) | |||||||
\(492\) | −5.06922 | − | 2.92671i | −0.228538 | − | 0.131946i | ||||
\(493\) | −1.11913 | + | 0.646130i | −0.0504031 | + | 0.0291002i | ||||
\(494\) | −4.77323 | + | 2.75583i | −0.214758 | + | 0.123991i | ||||
\(495\) | 1.26761 | − | 1.94843i | 0.0569746 | − | 0.0875756i | ||||
\(496\) | − | 6.17793i | − | 0.277397i | ||||||
\(497\) | −8.20731 | − | 8.57022i | −0.368148 | − | 0.384427i | ||||
\(498\) | −4.03988 | −0.181032 | ||||||||
\(499\) | −10.7200 | + | 18.5676i | −0.479894 | + | 0.831200i | −0.999734 | − | 0.0230633i | \(-0.992658\pi\) |
0.519840 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(500\) | −5.77147 | + | 3.33216i | −0.258108 | + | 0.149019i | ||||
\(501\) | 15.5818 | − | 8.99618i | 0.696145 | − | 0.401920i | ||||
\(502\) | −6.06642 | + | 10.5073i | −0.270757 | + | 0.468966i | ||||
\(503\) | −30.0822 | −1.34130 | −0.670649 | − | 0.741775i | \(-0.733984\pi\) | ||||
−0.670649 | + | 0.741775i | \(0.733984\pi\) | |||||||
\(504\) | 0.629345 | + | 2.56981i | 0.0280332 | + | 0.114468i | ||||
\(505\) | 10.5092i | 0.467652i | ||||||||
\(506\) | −9.53490 | + | 14.6561i | −0.423878 | + | 0.651542i | ||||
\(507\) | 31.6099 | − | 18.2500i | 1.40384 | − | 0.810509i | ||||
\(508\) | 2.97210 | − | 1.71594i | 0.131866 | − | 0.0761326i | ||||
\(509\) | 11.6751 | + | 6.74064i | 0.517491 | + | 0.298774i | 0.735908 | − | 0.677082i | \(-0.236756\pi\) |
−0.218416 | + | 0.975856i | \(0.570089\pi\) | |||||||
\(510\) | − | 0.432980i | − | 0.0191727i | ||||||
\(511\) | 3.91352 | − | 13.4362i | 0.173124 | − | 0.594381i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0.678438 | + | 0.391696i | 0.0299538 | + | 0.0172938i | ||||
\(514\) | 9.97355 | + | 17.2747i | 0.439914 | + | 0.761954i | ||||
\(515\) | −5.02925 | − | 8.71091i | −0.221615 | − | 0.383849i | ||||
\(516\) | 1.81220 | − | 3.13883i | 0.0797779 | − | 0.138179i | ||||
\(517\) | 7.78224 | + | 0.414263i | 0.342263 | + | 0.0182193i | ||||
\(518\) | 10.1460 | + | 2.95521i | 0.445790 | + | 0.129844i | ||||
\(519\) | − | 0.378382i | − | 0.0166091i | ||||||
\(520\) | 2.46548 | − | 4.27034i | 0.108119 | − | 0.187267i | ||||
\(521\) | −9.63608 | + | 5.56339i | −0.422164 | + | 0.243737i | −0.696003 | − | 0.718039i | \(-0.745040\pi\) |
0.273839 | + | 0.961776i | \(0.411707\pi\) | |||||||
\(522\) | 1.04588 | + | 1.81152i | 0.0457770 | + | 0.0792881i | ||||
\(523\) | −7.45440 | + | 12.9114i | −0.325958 | + | 0.564576i | −0.981706 | − | 0.190404i | \(-0.939020\pi\) |
0.655748 | + | 0.754980i | \(0.272354\pi\) | |||||||
\(524\) | −14.6058 | −0.638056 | ||||||||
\(525\) | −2.83759 | − | 11.5868i | −0.123842 | − | 0.505688i | ||||
\(526\) | 16.7867 | 0.731935 | ||||||||
\(527\) | −3.30530 | − | 1.90832i | −0.143981 | − | 0.0831275i | ||||
\(528\) | −1.50329 | − | 2.95637i | −0.0654222 | − | 0.128660i | ||||
\(529\) | −2.39614 | − | 4.15023i | −0.104180 | − | 0.180445i | ||||
\(530\) | −2.76887 | + | 4.79582i | −0.120272 | + | 0.208317i | ||||
\(531\) | 3.76387i | 0.163338i | ||||||||
\(532\) | −1.43356 | − | 1.49695i | −0.0621526 | − | 0.0649008i | ||||
\(533\) | −41.1825 | −1.78381 | ||||||||
\(534\) | 14.0396 | + | 8.10574i | 0.607551 | + | 0.350770i | ||||
\(535\) | 4.01841 | + | 6.96009i | 0.173731 | + | 0.300911i | ||||
\(536\) | 1.85399 | − | 1.07040i | 0.0800803 | − | 0.0462344i | ||||
\(537\) | 3.73338 | + | 2.15547i | 0.161107 | + | 0.0930152i | ||||
\(538\) | −19.4953 | −0.840504 | ||||||||
\(539\) | −9.61831 | − | 21.1303i | −0.414290 | − | 0.910145i | ||||
\(540\) | −0.700858 | −0.0301601 | ||||||||
\(541\) | 23.0202 | + | 13.2907i | 0.989717 | + | 0.571413i | 0.905190 | − | 0.425008i | \(-0.139729\pi\) |
0.0845270 | + | 0.996421i | \(0.473062\pi\) | |||||||
\(542\) | −9.25140 | + | 5.34130i | −0.397382 | + | 0.229428i | ||||
\(543\) | −3.48138 | − | 6.02993i | −0.149400 | − | 0.258769i | ||||
\(544\) | −0.535018 | − | 0.308893i | −0.0229387 | − | 0.0132437i | ||||
\(545\) | −1.01824 | −0.0436166 | ||||||||
\(546\) | 12.8747 | + | 13.4440i | 0.550987 | + | 0.575350i | ||||
\(547\) | − | 18.2285i | − | 0.779393i | −0.920943 | − | 0.389696i | \(-0.872580\pi\) | ||
0.920943 | − | 0.389696i | \(-0.127420\pi\) | |||||||
\(548\) | 8.35804 | − | 14.4765i | 0.357038 | − | 0.618407i | ||||
\(549\) | 4.18286 | + | 7.24493i | 0.178520 | + | 0.309206i | ||||
\(550\) | 6.77802 | + | 13.3297i | 0.289016 | + | 0.568379i | ||||
\(551\) | −1.41913 | − | 0.819336i | −0.0604571 | − | 0.0349049i | ||||
\(552\) | 5.27184 | 0.224384 | ||||||||
\(553\) | −2.73109 | − | 11.1519i | −0.116138 | − | 0.474226i | ||||
\(554\) | −30.7880 | −1.30805 | ||||||||
\(555\) | −1.39968 | + | 2.42431i | −0.0594130 | + | 0.102906i | ||||
\(556\) | 6.46997 | + | 11.2063i | 0.274388 | + | 0.475253i | ||||
\(557\) | 27.2666 | − | 15.7424i | 1.15532 | − | 0.667025i | 0.205143 | − | 0.978732i | \(-0.434234\pi\) |
0.950178 | + | 0.311707i | \(0.100901\pi\) | |||||||
\(558\) | −3.08896 | + | 5.35024i | −0.130766 | + | 0.226494i | ||||
\(559\) | − | 25.5000i | − | 1.07853i | ||||||
\(560\) | 1.78031 | + | 0.518548i | 0.0752320 | + | 0.0219127i | ||||
\(561\) | −2.04606 | − | 0.108916i | −0.0863849 | − | 0.00459843i | ||||
\(562\) | −10.6691 | + | 18.4793i | −0.450047 | + | 0.779504i | ||||
\(563\) | 10.9701 | + | 19.0008i | 0.462335 | + | 0.800787i | 0.999077 | − | 0.0429591i | \(-0.0136785\pi\) |
−0.536742 | + | 0.843746i | \(0.680345\pi\) | |||||||
\(564\) | −1.17488 | − | 2.03495i | −0.0494713 | − | 0.0856868i | ||||
\(565\) | −7.28803 | − | 4.20774i | −0.306610 | − | 0.177021i | ||||
\(566\) | − | 2.52307i | − | 0.106053i | ||||||
\(567\) | 0.739877 | − | 2.54019i | 0.0310719 | − | 0.106678i | ||||
\(568\) | − | 4.48503i | − | 0.188188i | ||||||
\(569\) | −26.8999 | − | 15.5307i | −1.12770 | − | 0.651080i | −0.184347 | − | 0.982861i | \(-0.559017\pi\) |
−0.943356 | + | 0.331781i | \(0.892350\pi\) | |||||||
\(570\) | 0.475489 | − | 0.274523i | 0.0199160 | − | 0.0114985i | ||||
\(571\) | 8.45951 | − | 4.88410i | 0.354020 | − | 0.204393i | −0.312435 | − | 0.949939i | \(-0.601145\pi\) |
0.666454 | + | 0.745546i | \(0.267811\pi\) | |||||||
\(572\) | −19.5595 | − | 12.7250i | −0.817824 | − | 0.532057i | ||||
\(573\) | − | 18.5590i | − | 0.775313i | ||||||
\(574\) | −3.68382 | − | 15.0422i | −0.153760 | − | 0.627849i | ||||
\(575\) | −23.7697 | −0.991263 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 16.7912 | − | 9.69442i | 0.699028 | − | 0.403584i | −0.107957 | − | 0.994156i | \(-0.534431\pi\) |
0.806985 | + | 0.590571i | \(0.201098\pi\) | |||||||
\(578\) | 14.3919 | − | 8.30917i | 0.598624 | − | 0.345616i | ||||
\(579\) | 8.76059 | − | 15.1738i | 0.364078 | − | 0.630601i | ||||
\(580\) | 1.46603 | 0.0608735 | ||||||||
\(581\) | −7.39272 | − | 7.71961i | −0.306702 | − | 0.320263i | ||||
\(582\) | − | 10.4926i | − | 0.434931i | ||||||
\(583\) | 21.9663 | + | 14.2908i | 0.909753 | + | 0.591864i | ||||
\(584\) | 4.58078 | − | 2.64471i | 0.189554 | − | 0.109439i | ||||
\(585\) | −4.27034 | + | 2.46548i | −0.176557 | + | 0.101935i | ||||
\(586\) | 4.95220 | + | 2.85916i | 0.204574 | + | 0.118111i | ||||
\(587\) | 14.0625i | 0.580421i | 0.956963 | + | 0.290210i | \(0.0937253\pi\) | ||||
−0.956963 | + | 0.290210i | \(0.906275\pi\) | |||||||
\(588\) | −3.75886 | + | 5.90516i | −0.155013 | + | 0.243525i | ||||
\(589\) | − | 4.83974i | − | 0.199418i | ||||||
\(590\) | 2.28452 | + | 1.31897i | 0.0940522 | + | 0.0543011i | ||||
\(591\) | 9.43317 | + | 16.3387i | 0.388029 | + | 0.672086i | ||||
\(592\) | 1.99709 | + | 3.45907i | 0.0820800 | + | 0.142167i | ||||
\(593\) | −19.0546 | + | 33.0036i | −0.782480 | + | 1.35530i | 0.148013 | + | 0.988985i | \(0.452712\pi\) |
−0.930493 | + | 0.366310i | \(0.880621\pi\) | |||||||
\(594\) | −0.176300 | + | 3.31194i | −0.00723370 | + | 0.135890i | ||||
\(595\) | 0.827358 | − | 0.792324i | 0.0339184 | − | 0.0324821i | ||||
\(596\) | − | 9.72861i | − | 0.398500i | ||||||
\(597\) | −6.76618 | + | 11.7194i | −0.276921 | + | 0.479642i | ||||
\(598\) | 32.1214 | − | 18.5453i | 1.31354 | − | 0.758375i | ||||
\(599\) | 12.2662 | + | 21.2456i | 0.501183 | + | 0.868074i | 0.999999 | + | 0.00136605i | \(0.000434826\pi\) |
−0.498817 | + | 0.866708i | \(0.666232\pi\) | |||||||
\(600\) | 2.25440 | − | 3.90473i | 0.0920355 | − | 0.159410i | ||||
\(601\) | 3.08091 | 0.125673 | 0.0628365 | − | 0.998024i | \(-0.479985\pi\) | ||||
0.0628365 | + | 0.998024i | \(0.479985\pi\) | |||||||
\(602\) | 9.31404 | − | 2.28100i | 0.379612 | − | 0.0929667i | ||||
\(603\) | −2.14081 | −0.0871804 | ||||||||
\(604\) | −17.1367 | − | 9.89387i | −0.697282 | − | 0.402576i | ||||
\(605\) | −7.04806 | + | 3.12413i | −0.286545 | + | 0.127014i | ||||
\(606\) | −7.49737 | − | 12.9858i | −0.304560 | − | 0.527513i | ||||
\(607\) | 20.3839 | − | 35.3059i | 0.827356 | − | 1.43302i | −0.0727485 | − | 0.997350i | \(-0.523177\pi\) |
0.900105 | − | 0.435673i | \(-0.143490\pi\) | |||||||
\(608\) | − | 0.783393i | − | 0.0317708i | ||||||
\(609\) | −1.54765 | + | 5.31348i | −0.0627138 | + | 0.215313i | ||||
\(610\) | 5.86318 | 0.237393 | ||||||||
\(611\) | −14.3171 | − | 8.26600i | −0.579209 | − | 0.334406i | ||||
\(612\) | 0.308893 | + | 0.535018i | 0.0124862 | + | 0.0216268i | ||||
\(613\) | 7.75535 | − | 4.47755i | 0.313236 | − | 0.180847i | −0.335138 | − | 0.942169i | \(-0.608783\pi\) |
0.648373 | + | 0.761322i | \(0.275450\pi\) | |||||||
\(614\) | 17.9993 | + | 10.3919i | 0.726394 | + | 0.419384i | ||||
\(615\) | 4.10242 | 0.165426 | ||||||||
\(616\) | 2.89826 | − | 8.28252i | 0.116774 | − | 0.333712i | ||||
\(617\) | 19.1914 | 0.772618 | 0.386309 | − | 0.922369i | \(-0.373750\pi\) | ||||
0.386309 | + | 0.922369i | \(0.373750\pi\) | |||||||
\(618\) | 12.4289 | + | 7.17585i | 0.499965 | + | 0.288655i | ||||
\(619\) | 2.91921 | − | 1.68541i | 0.117333 | − | 0.0677422i | −0.440185 | − | 0.897907i | \(-0.645087\pi\) |
0.557518 | + | 0.830165i | \(0.311754\pi\) | |||||||
\(620\) | 2.16492 | + | 3.74976i | 0.0869454 | + | 0.150594i | ||||
\(621\) | −4.56555 | − | 2.63592i | −0.183209 | − | 0.105776i | ||||
\(622\) | −7.36751 | −0.295410 | ||||||||
\(623\) | 10.2026 | + | 41.6604i | 0.408759 | + | 1.66909i | ||||
\(624\) | 7.03562i | 0.281650i | ||||||||
\(625\) | −8.93663 | + | 15.4787i | −0.357465 | + | 0.619148i | ||||
\(626\) | −3.67697 | − | 6.36871i | −0.146961 | − | 0.254545i | ||||
\(627\) | −1.17766 | − | 2.31600i | −0.0470314 | − | 0.0924921i | ||||
\(628\) | 10.4014 | + | 6.00523i | 0.415059 | + | 0.239635i | ||||
\(629\) | 2.46755 | 0.0983876 | ||||||||
\(630\) | −1.28252 | − | 1.33923i | −0.0510969 | − | 0.0533563i | ||||
\(631\) | 33.1910 | 1.32131 | 0.660657 | − | 0.750688i | \(-0.270278\pi\) | ||||
0.660657 | + | 0.750688i | \(0.270278\pi\) | |||||||
\(632\) | 2.16979 | − | 3.75818i | 0.0863095 | − | 0.149492i | ||||
\(633\) | −2.47184 | − | 4.28135i | −0.0982468 | − | 0.170168i | ||||
\(634\) | 12.8004 | − | 7.39030i | 0.508368 | − | 0.293506i | ||||
\(635\) | −1.20263 | + | 2.08302i | −0.0477250 | + | 0.0826620i | ||||
\(636\) | − | 7.90136i | − | 0.313309i | ||||||
\(637\) | −2.12959 | + | 49.2033i | −0.0843773 | + | 1.94950i | ||||
\(638\) | 0.368779 | − | 6.92779i | 0.0146001 | − | 0.274274i | ||||
\(639\) | −2.24252 | + | 3.88415i | −0.0887125 | + | 0.153655i | ||||
\(640\) | 0.350429 | + | 0.606961i | 0.0138519 | + | 0.0239922i | ||||
\(641\) | 17.2306 | + | 29.8442i | 0.680566 | + | 1.17878i | 0.974808 | + | 0.223045i | \(0.0715995\pi\) |
−0.294242 | + | 0.955731i | \(0.595067\pi\) | |||||||
\(642\) | −9.93081 | − | 5.73356i | −0.391938 | − | 0.226285i | ||||
\(643\) | 2.69205i | 0.106164i | 0.998590 | + | 0.0530821i | \(0.0169045\pi\) | ||||
−0.998590 | + | 0.0530821i | \(0.983095\pi\) | |||||||
\(644\) | 9.64711 | + | 10.0737i | 0.380149 | + | 0.396959i | ||||
\(645\) | 2.54020i | 0.100020i | ||||||||
\(646\) | −0.419129 | − | 0.241984i | −0.0164904 | − | 0.00952074i | ||||
\(647\) | 40.4270 | − | 23.3405i | 1.58935 | − | 0.917611i | 0.595934 | − | 0.803033i | \(-0.296782\pi\) |
0.993414 | − | 0.114577i | \(-0.0365514\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 6.80752 | − | 10.4638i | 0.267218 | − | 0.410741i | ||||
\(650\) | − | 31.7222i | − | 1.24425i | ||||||
\(651\) | −15.8761 | + | 3.88804i | −0.622233 | + | 0.152384i | ||||
\(652\) | −22.3960 | −0.877094 | ||||||||
\(653\) | −19.9929 | + | 34.6287i | −0.782383 | + | 1.35513i | 0.148167 | + | 0.988962i | \(0.452663\pi\) |
−0.930550 | + | 0.366165i | \(0.880671\pi\) | |||||||
\(654\) | 1.25820 | − | 0.726424i | 0.0491997 | − | 0.0284054i | ||||
\(655\) | 8.86513 | − | 5.11828i | 0.346389 | − | 0.199988i | ||||
\(656\) | 2.92671 | − | 5.06922i | 0.114269 | − | 0.197920i | ||||
\(657\) | −5.28943 | −0.206360 | ||||||||
\(658\) | 1.73853 | − | 5.96884i | 0.0677750 | − | 0.232689i | ||||
\(659\) | − | 24.9930i | − | 0.973590i | −0.873516 | − | 0.486795i | \(-0.838166\pi\) | ||
0.873516 | − | 0.486795i | \(-0.161834\pi\) | |||||||
\(660\) | 1.94843 | + | 1.26761i | 0.0758427 | + | 0.0493415i | ||||
\(661\) | 12.7267 | − | 7.34774i | 0.495010 | − | 0.285794i | −0.231641 | − | 0.972801i | \(-0.574409\pi\) |
0.726650 | + | 0.687007i | \(0.241076\pi\) | |||||||
\(662\) | −23.6336 | + | 13.6449i | −0.918547 | + | 0.530323i | ||||
\(663\) | 3.76418 | + | 2.17325i | 0.146189 | + | 0.0844021i | ||||
\(664\) | − | 4.03988i | − | 0.156778i | ||||||
\(665\) | 1.39469 | + | 0.406227i | 0.0540836 | + | 0.0157528i | ||||
\(666\) | − | 3.99419i | − | 0.154772i | ||||||
\(667\) | 9.55004 | + | 5.51372i | 0.369779 | + | 0.213492i | ||||
\(668\) | 8.99618 | + | 15.5818i | 0.348073 | + | 0.602879i | ||||
\(669\) | 11.4597 | + | 19.8488i | 0.443058 | + | 0.767400i | ||||
\(670\) | −0.750200 | + | 1.29939i | −0.0289828 | + | 0.0501996i | ||||
\(671\) | 1.47488 | − | 27.7067i | 0.0569371 | − | 1.06961i | ||||
\(672\) | −2.56981 | + | 0.629345i | −0.0991326 | + | 0.0242775i | ||||
\(673\) | 51.7415i | 1.99449i | 0.0741830 | + | 0.997245i | \(0.476365\pi\) | ||||
−0.0741830 | + | 0.997245i | \(0.523635\pi\) | |||||||
\(674\) | 6.54644 | − | 11.3388i | 0.252159 | − | 0.436753i | ||||
\(675\) | −3.90473 | + | 2.25440i | −0.150293 | + | 0.0867719i | ||||
\(676\) | 18.2500 | + | 31.6099i | 0.701922 | + | 1.21576i | ||||
\(677\) | −18.7265 | + | 32.4353i | −0.719718 | + | 1.24659i | 0.241393 | + | 0.970427i | \(0.422396\pi\) |
−0.961111 | + | 0.276161i | \(0.910938\pi\) | |||||||
\(678\) | 12.0074 | 0.461142 | ||||||||
\(679\) | 20.0497 | − | 19.2007i | 0.769438 | − | 0.736856i | ||||
\(680\) | 0.432980 | 0.0166040 | ||||||||
\(681\) | 20.9823 | + | 12.1141i | 0.804042 | + | 0.464214i | ||||
\(682\) | 18.2642 | − | 9.28720i | 0.699374 | − | 0.355625i | ||||
\(683\) | 21.0079 | + | 36.3868i | 0.803845 | + | 1.39230i | 0.917068 | + | 0.398731i | \(0.130549\pi\) |
−0.113223 | + | 0.993570i | \(0.536117\pi\) | |||||||
\(684\) | −0.391696 | + | 0.678438i | −0.0149769 | + | 0.0259407i | ||||
\(685\) | 11.7156i | 0.447630i | ||||||||
\(686\) | −18.1623 | + | 3.62344i | −0.693441 | + | 0.138344i | ||||
\(687\) | −13.3778 | −0.510396 | ||||||||
\(688\) | 3.13883 | + | 1.81220i | 0.119667 | + | 0.0690896i | ||||
\(689\) | −27.7955 | − | 48.1432i | −1.05892 | − | 1.83411i | ||||
\(690\) | −3.19980 | + | 1.84740i | −0.121814 | + | 0.0703295i | ||||
\(691\) | −23.9459 | − | 13.8252i | −0.910945 | − | 0.525934i | −0.0302096 | − | 0.999544i | \(-0.509617\pi\) |
−0.880735 | + | 0.473610i | \(0.842951\pi\) | |||||||
\(692\) | 0.378382 | 0.0143839 | ||||||||
\(693\) | −6.65123 | + | 5.72374i | −0.252659 | + | 0.217427i | ||||
\(694\) | −11.3473 | −0.430739 | ||||||||
\(695\) | −7.85403 | − | 4.53453i | −0.297920 | − | 0.172004i | ||||
\(696\) | −1.81152 | + | 1.04588i | −0.0686655 | + | 0.0396440i | ||||
\(697\) | −1.80808 | − | 3.13169i | −0.0684859 | − | 0.118621i | ||||
\(698\) | 10.7439 | + | 6.20298i | 0.406662 | + | 0.234786i | ||||
\(699\) | 27.9050 | 1.05546 | ||||||||
\(700\) | 11.5868 | − | 2.83759i | 0.437938 | − | 0.107251i | ||||
\(701\) | 8.73779i | 0.330022i | 0.986292 | + | 0.165011i | \(0.0527659\pi\) | ||||
−0.986292 | + | 0.165011i | \(0.947234\pi\) | |||||||
\(702\) | 3.51781 | − | 6.09302i | 0.132771 | − | 0.229966i | ||||
\(703\) | 1.56451 | + | 2.70981i | 0.0590065 | + | 0.102202i | ||||
\(704\) | 2.95637 | − | 1.50329i | 0.111422 | − | 0.0566573i | ||||
\(705\) | 1.42621 | + | 0.823423i | 0.0537142 | + | 0.0310119i | ||||
\(706\) | 6.82398 | 0.256824 | ||||||||
\(707\) | 11.0943 | − | 38.0895i | 0.417243 | − | 1.43250i | ||||
\(708\) | −3.76387 | −0.141455 | ||||||||
\(709\) | 16.6683 | − | 28.8703i | 0.625990 | − | 1.08425i | −0.362359 | − | 0.932039i | \(-0.618028\pi\) |
0.988349 | − | 0.152208i | \(-0.0486382\pi\) | |||||||
\(710\) | 1.57168 | + | 2.72224i | 0.0589843 | + | 0.102164i | ||||
\(711\) | −3.75818 | + | 2.16979i | −0.140943 | + | 0.0813734i | ||||
\(712\) | −8.10574 | + | 14.0396i | −0.303776 | + | 0.526155i | ||||
\(713\) | 32.5690i | 1.21972i | ||||||||
\(714\) | −0.457085 | + | 1.56929i | −0.0171060 | + | 0.0587293i | ||||
\(715\) | 16.3310 | + | 0.869332i | 0.610747 | + | 0.0325112i | ||||
\(716\) | −2.15547 | + | 3.73338i | −0.0805536 | + | 0.139523i | ||||
\(717\) | −4.63757 | − | 8.03251i | −0.173193 | − | 0.299979i | ||||
\(718\) | −10.2157 | − | 17.6942i | −0.381248 | − | 0.660340i | ||||
\(719\) | −9.08278 | − | 5.24394i | −0.338730 | − | 0.195566i | 0.320980 | − | 0.947086i | \(-0.395988\pi\) |
−0.659711 | + | 0.751520i | \(0.729321\pi\) | |||||||
\(720\) | − | 0.700858i | − | 0.0261194i | ||||||
\(721\) | 9.03216 | + | 36.8811i | 0.336375 | + | 1.37353i | ||||
\(722\) | 18.3863i | 0.684267i | ||||||||
\(723\) | 16.5385 | + | 9.54851i | 0.615074 | + | 0.355113i | ||||
\(724\) | 6.02993 | − | 3.48138i | 0.224101 | − | 0.129385i | ||||
\(725\) | 8.16778 | − | 4.71567i | 0.303344 | − | 0.175136i | ||||
\(726\) | 6.48026 | − | 8.88855i | 0.240505 | − | 0.329885i | ||||
\(727\) | 9.73041i | 0.360881i | 0.983586 | + | 0.180440i | \(0.0577523\pi\) | ||||
−0.983586 | + | 0.180440i | \(0.942248\pi\) | |||||||
\(728\) | −13.4440 | + | 12.8747i | −0.498268 | + | 0.477169i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.85357 | + | 3.21047i | −0.0686036 | + | 0.118825i | ||||
\(731\) | 1.93912 | − | 1.11955i | 0.0717210 | − | 0.0414082i | ||||
\(732\) | −7.24493 | + | 4.18286i | −0.267780 | + | 0.154603i | ||||
\(733\) | 0.800499 | − | 1.38650i | 0.0295671 | − | 0.0512117i | −0.850863 | − | 0.525387i | \(-0.823920\pi\) |
0.880430 | + | 0.474176i | \(0.157254\pi\) | |||||||
\(734\) | 20.1568 | 0.744001 | ||||||||
\(735\) | 0.212140 | − | 4.90142i | 0.00782491 | − | 0.180791i | ||||
\(736\) | 5.27184i | 0.194323i | ||||||||
\(737\) | 5.95159 | + | 3.87197i | 0.219230 | + | 0.142626i | ||||
\(738\) | −5.06922 | + | 2.92671i | −0.186600 | + | 0.107734i | ||||
\(739\) | −23.6755 | + | 13.6691i | −0.870918 | + | 0.502825i | −0.867653 | − | 0.497170i | \(-0.834373\pi\) |
−0.00326478 | + | 0.999995i | \(0.501039\pi\) | |||||||
\(740\) | −2.42431 | − | 1.39968i | −0.0891195 | − | 0.0514532i | ||||
\(741\) | 5.51165i | 0.202476i | ||||||||
\(742\) | 15.0983 | − | 14.4590i | 0.554277 | − | 0.530806i | ||||
\(743\) | − | 49.7705i | − | 1.82590i | −0.408067 | − | 0.912952i | \(-0.633797\pi\) | ||
0.408067 | − | 0.912952i | \(-0.366203\pi\) | |||||||
\(744\) | −5.35024 | − | 3.08896i | −0.196149 | − | 0.113247i | ||||
\(745\) | 3.40919 | + | 5.90489i | 0.124903 | + | 0.216338i | ||||
\(746\) | −4.16927 | − | 7.22139i | −0.152648 | − | 0.264394i | ||||
\(747\) | −2.01994 | + | 3.49864i | −0.0739058 | + | 0.128009i | ||||
\(748\) | 0.108916 | − | 2.04606i | 0.00398236 | − | 0.0748115i | ||||
\(749\) | −7.21677 | − | 29.4683i | −0.263695 | − | 1.07675i | ||||
\(750\) | 6.66432i | 0.243346i | ||||||||
\(751\) | 11.5318 | − | 19.9737i | 0.420803 | − | 0.728852i | −0.575215 | − | 0.818002i | \(-0.695082\pi\) |
0.996018 | + | 0.0891499i | \(0.0284150\pi\) | |||||||
\(752\) | 2.03495 | − | 1.17488i | 0.0742070 | − | 0.0428434i | ||||
\(753\) | 6.06642 | + | 10.5073i | 0.221073 | + | 0.382909i | ||||
\(754\) | −7.35843 | + | 12.7452i | −0.267978 | + | 0.464152i | ||||
\(755\) | 13.8684 | 0.504722 | ||||||||
\(756\) | 2.54019 | + | 0.739877i | 0.0923859 | + | 0.0269091i | ||||
\(757\) | −35.4691 | −1.28915 | −0.644574 | − | 0.764542i | \(-0.722965\pi\) | ||||
−0.644574 | + | 0.764542i | \(0.722965\pi\) | |||||||
\(758\) | −10.5736 | − | 6.10466i | −0.384050 | − | 0.221731i | ||||
\(759\) | 7.92509 | + | 15.5855i | 0.287662 | + | 0.565718i | ||||
\(760\) | 0.274523 | + | 0.475489i | 0.00995801 | + | 0.0172478i | ||||
\(761\) | −8.13485 | + | 14.0900i | −0.294888 | + | 0.510761i | −0.974959 | − | 0.222385i | \(-0.928616\pi\) |
0.680071 | + | 0.733146i | \(0.261949\pi\) | |||||||
\(762\) | − | 3.43188i | − | 0.124324i | ||||||
\(763\) | 3.69052 | + | 1.07493i | 0.133606 | + | 0.0389151i | ||||
\(764\) | 18.5590 | 0.671440 | ||||||||
\(765\) | −0.374971 | − | 0.216490i | −0.0135571 | − | 0.00782720i | ||||
\(766\) | 9.32585 | + | 16.1528i | 0.336957 | + | 0.583626i | ||||
\(767\) | −22.9333 | + | 13.2406i | −0.828075 | + | 0.478089i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 31.2492 | 1.12687 | 0.563437 | − | 0.826159i | \(-0.309479\pi\) | ||||
0.563437 | + | 0.826159i | \(0.309479\pi\) | |||||||
\(770\) | 1.14330 | + | 6.04280i | 0.0412017 | + | 0.217767i | ||||
\(771\) | 19.9471 | 0.718377 | ||||||||
\(772\) | 15.1738 | + | 8.76059i | 0.546117 | + | 0.315301i | ||||
\(773\) | −14.3081 | + | 8.26079i | −0.514627 | + | 0.297120i | −0.734733 | − | 0.678356i | \(-0.762693\pi\) |
0.220107 | + | 0.975476i | \(0.429359\pi\) | |||||||
\(774\) | −1.81220 | − | 3.13883i | −0.0651383 | − | 0.112823i | ||||
\(775\) | 24.1232 | + | 13.9275i | 0.866529 | + | 0.500291i | ||||
\(776\) | 10.4926 | 0.376662 | ||||||||
\(777\) | 7.63228 | − | 7.30909i | 0.273807 | − | 0.262212i | ||||
\(778\) | 9.51444i | 0.341109i | ||||||||
\(779\) | 2.29277 | − | 3.97119i | 0.0821469 | − | 0.142283i | ||||
\(780\) | −2.46548 | − | 4.27034i | −0.0882785 | − | 0.152903i | ||||
\(781\) | 13.2594 | − | 6.74229i | 0.474459 | − | 0.241258i | ||||
\(782\) | 2.82053 | + | 1.62843i | 0.100862 | + | 0.0582326i | ||||
\(783\) | 2.09176 | 0.0747535 | ||||||||
\(784\) | −5.90516 | − | 3.75886i | −0.210899 | − | 0.134245i | ||||
\(785\) | −8.41762 | −0.300438 | ||||||||
\(786\) | −7.30288 | + | 12.6490i | −0.260485 | + | 0.451174i | ||||
\(787\) | −11.0415 | − | 19.1245i | −0.393589 | − | 0.681715i | 0.599331 | − | 0.800501i | \(-0.295433\pi\) |
−0.992920 | + | 0.118786i | \(0.962100\pi\) | |||||||
\(788\) | −16.3387 | + | 9.43317i | −0.582043 | + | 0.336043i | ||||
\(789\) | 8.39335 | − | 14.5377i | 0.298811 | − | 0.517556i | ||||
\(790\) | 3.04142i | 0.108209i | ||||||||
\(791\) | 21.9728 | + | 22.9443i | 0.781262 | + | 0.815807i | ||||
\(792\) | −3.31194 | − | 0.176300i | −0.117685 | − | 0.00626457i | ||||
\(793\) | −29.4290 | + | 50.9725i | −1.04505 | + | 1.81009i | ||||
\(794\) | −17.0348 | − | 29.5051i | −0.604543 | − | 1.04710i | ||||
\(795\) | 2.76887 | + | 4.79582i | 0.0982016 | + | 0.170090i | ||||
\(796\) | −11.7194 | − | 6.76618i | −0.415382 | − | 0.239821i | ||||
\(797\) | 25.7347i | 0.911571i | 0.890090 | + | 0.455785i | \(0.150642\pi\) | ||||
−0.890090 | + | 0.455785i | \(0.849358\pi\) | |||||||
\(798\) | −2.01317 | + | 0.493024i | −0.0712655 | + | 0.0174529i | ||||
\(799\) | − | 1.45165i | − | 0.0513555i | ||||||
\(800\) | 3.90473 | + | 2.25440i | 0.138053 | + | 0.0797050i | ||||
\(801\) | 14.0396 | − | 8.10574i | 0.496063 | − | 0.286402i | ||||
\(802\) | 25.6653 | − | 14.8179i | 0.906274 | − | 0.523237i | ||||
\(803\) | 14.7050 | + | 9.56671i | 0.518927 | + | 0.337602i | ||||
\(804\) | − | 2.14081i | − | 0.0755004i | ||||||
\(805\) | −9.38553 | − | 2.73370i | −0.330796 | − | 0.0963504i | ||||
\(806\) | −43.4655 | −1.53101 | ||||||||
\(807\) | −9.74767 | + | 16.8835i | −0.343134 | + | 0.594326i | ||||
\(808\) | 12.9858 | − | 7.49737i | 0.456840 | − | 0.263757i | ||||
\(809\) | 25.0947 | − | 14.4884i | 0.882281 | − | 0.509385i | 0.0108712 | − | 0.999941i | \(-0.496540\pi\) |
0.871410 | + | 0.490556i | \(0.163206\pi\) | |||||||
\(810\) | −0.350429 | + | 0.606961i | −0.0123128 | + | 0.0213264i | ||||
\(811\) | −1.48290 | −0.0520715 | −0.0260358 | − | 0.999661i | \(-0.508288\pi\) | ||||
−0.0260358 | + | 0.999661i | \(0.508288\pi\) | |||||||
\(812\) | −5.31348 | − | 1.54765i | −0.186467 | − | 0.0543118i | ||||
\(813\) | 10.6826i | 0.374655i | ||||||||
\(814\) | −7.22408 | + | 11.1041i | −0.253204 | + | 0.389199i | ||||
\(815\) | 13.5935 | − | 7.84819i | 0.476159 | − | 0.274910i | ||||
\(816\) | −0.535018 | + | 0.308893i | −0.0187294 | + | 0.0108134i | ||||
\(817\) | 2.45894 | + | 1.41967i | 0.0860273 | + | 0.0496679i | ||||
\(818\) | − | 27.3288i | − | 0.955530i | ||||||
\(819\) | 18.0802 | − | 4.42783i | 0.631774 | − | 0.154721i | ||||
\(820\) | 4.10242i | 0.143263i | ||||||||
\(821\) | −4.78490 | − | 2.76257i | −0.166994 | − | 0.0964142i | 0.414173 | − | 0.910198i | \(-0.364071\pi\) |
−0.581168 | + | 0.813784i | \(0.697404\pi\) | |||||||
\(822\) | −8.35804 | − | 14.4765i | −0.291520 | − | 0.504928i | ||||
\(823\) | 8.11088 | + | 14.0485i | 0.282728 | + | 0.489699i | 0.972056 | − | 0.234751i | \(-0.0754274\pi\) |
−0.689328 | + | 0.724449i | \(0.742094\pi\) | |||||||
\(824\) | −7.17585 | + | 12.4289i | −0.249983 | + | 0.432982i | ||||
\(825\) | 14.9329 | + | 0.794903i | 0.519895 | + | 0.0276750i | ||||
\(826\) | −6.88763 | − | 7.19218i | −0.239651 | − | 0.250248i | ||||
\(827\) | 5.86195i | 0.203840i | 0.994793 | + | 0.101920i | \(0.0324986\pi\) | ||||
−0.994793 | + | 0.101920i | \(0.967501\pi\) | |||||||
\(828\) | 2.63592 | − | 4.56555i | 0.0916045 | − | 0.158664i | ||||
\(829\) | −16.8080 | + | 9.70409i | −0.583765 | + | 0.337037i | −0.762628 | − | 0.646837i | \(-0.776091\pi\) |
0.178863 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(830\) | 1.41569 | + | 2.45205i | 0.0491394 | + | 0.0851119i | ||||
\(831\) | −15.3940 | + | 26.6632i | −0.534011 | + | 0.924934i | ||||
\(832\) | −7.03562 | −0.243916 | ||||||||
\(833\) | −3.83512 | + | 1.99828i | −0.132879 | + | 0.0692364i | ||||
\(834\) | 12.9399 | 0.448073 | ||||||||
\(835\) | −10.9207 | − | 6.30504i | −0.377925 | − | 0.218195i | ||||
\(836\) | 2.31600 | − | 1.17766i | 0.0801005 | − | 0.0407304i | ||||
\(837\) | 3.08896 | + | 5.35024i | 0.106770 | + | 0.184931i | ||||
\(838\) | 12.8486 | − | 22.2545i | 0.443848 | − | 0.768767i | ||||
\(839\) | 17.8302i | 0.615565i | 0.951457 | + | 0.307783i | \(0.0995870\pi\) | ||||
−0.951457 | + | 0.307783i | \(0.900413\pi\) | |||||||
\(840\) | 1.33923 | − | 1.28252i | 0.0462079 | − | 0.0442513i | ||||
\(841\) | 24.6245 | 0.849122 | ||||||||
\(842\) | −31.9776 | − | 18.4623i | −1.10202 | − | 0.636252i | ||||
\(843\) | 10.6691 | + | 18.4793i | 0.367462 | + | 0.636462i | ||||
\(844\) | 4.28135 | − | 2.47184i | 0.147370 | − | 0.0850842i | ||||
\(845\) | −22.1540 | − | 12.7906i | −0.762122 | − | 0.440011i | ||||
\(846\) | −2.34976 | −0.0807863 | ||||||||
\(847\) | 28.8431 | − | 3.88266i | 0.991061 | − | 0.133410i | ||||
\(848\) | 7.90136 | 0.271334 | ||||||||
\(849\) | −2.18504 | − | 1.26154i | −0.0749905 | − | 0.0432958i | ||||
\(850\) | 2.41229 | − | 1.39273i | 0.0827408 | − | 0.0477704i | ||||
\(851\) | −10.5283 | − | 18.2356i | −0.360907 | − | 0.625109i | ||||
\(852\) | −3.88415 | − | 2.24252i | −0.133069 | − | 0.0768273i | ||||
\(853\) | 2.57158 | 0.0880491 | 0.0440246 | − | 0.999030i | \(-0.485982\pi\) | ||||
0.0440246 | + | 0.999030i | \(0.485982\pi\) | |||||||
\(854\) | −21.2505 | − | 6.18960i | −0.727179 | − | 0.211804i | ||||
\(855\) | − | 0.549047i | − | 0.0187770i | ||||||
\(856\) | 5.73356 | − | 9.93081i | 0.195969 | − | 0.339428i | ||||
\(857\) | 8.16413 | + | 14.1407i | 0.278881 | + | 0.483037i | 0.971107 | − | 0.238644i | \(-0.0767030\pi\) |
−0.692226 | + | 0.721681i | \(0.743370\pi\) | |||||||
\(858\) | −20.7999 | + | 10.5766i | −0.710097 | + | 0.361078i | ||||
\(859\) | −22.3768 | − | 12.9193i | −0.763487 | − | 0.440799i | 0.0670596 | − | 0.997749i | \(-0.478638\pi\) |
−0.830546 | + | 0.556950i | \(0.811972\pi\) | |||||||
\(860\) | −2.54020 | −0.0866199 | ||||||||
\(861\) | −14.8688 | − | 4.33082i | −0.506729 | − | 0.147594i | ||||
\(862\) | −20.1287 | −0.685586 | ||||||||
\(863\) | −8.89726 | + | 15.4105i | −0.302866 | + | 0.524580i | −0.976784 | − | 0.214227i | \(-0.931277\pi\) |
0.673918 | + | 0.738806i | \(0.264610\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −0.229663 | + | 0.132596i | −0.00780878 | + | 0.00450840i | ||||
\(866\) | 19.0996 | − | 33.0815i | 0.649031 | − | 1.12416i | ||||
\(867\) | − | 16.6183i | − | 0.564388i | ||||||
\(868\) | −3.88804 | − | 15.8761i | −0.131969 | − | 0.538870i | ||||
\(869\) | 14.3724 | + | 0.765069i | 0.487550 | + | 0.0259532i | ||||
\(870\) | 0.733014 | − | 1.26962i | 0.0248515 | − | 0.0430441i | ||||
\(871\) | −7.53095 | − | 13.0440i | −0.255176 | − | 0.441979i | ||||
\(872\) | 0.726424 | + | 1.25820i | 0.0245998 | + | 0.0426082i | ||||
\(873\) | −9.08684 | − | 5.24629i | −0.307543 | − | 0.177560i | ||||
\(874\) | 4.12992i | 0.139697i | ||||||||
\(875\) | −12.7345 | + | 12.1953i | −0.430505 | + | 0.412275i | ||||
\(876\) | − | 5.28943i | − | 0.178713i | ||||||
\(877\) | −1.31624 | − | 0.759931i | −0.0444463 | − | 0.0256611i | 0.477612 | − | 0.878571i | \(-0.341502\pi\) |
−0.522058 | + | 0.852910i | \(0.674836\pi\) | |||||||
\(878\) | −6.34102 | + | 3.66099i | −0.213999 | + | 0.123552i | ||||
\(879\) | 4.95220 | − | 2.85916i | 0.167034 | − | 0.0964370i | ||||
\(880\) | −1.26761 | + | 1.94843i | −0.0427310 | + | 0.0656817i | ||||
\(881\) | 2.61558i | 0.0881210i | 0.999029 | + | 0.0440605i | \(0.0140294\pi\) | ||||
−0.999029 | + | 0.0440605i | \(0.985971\pi\) | |||||||
\(882\) | 3.23459 | + | 6.20785i | 0.108914 | + | 0.209029i | ||||
\(883\) | −32.7433 | −1.10190 | −0.550950 | − | 0.834538i | \(-0.685735\pi\) | ||||
−0.550950 | + | 0.834538i | \(0.685735\pi\) | |||||||
\(884\) | −2.17325 | + | 3.76418i | −0.0730943 | + | 0.126603i | ||||
\(885\) | 2.28452 | − | 1.31897i | 0.0767933 | − | 0.0443366i | ||||
\(886\) | 28.6003 | − | 16.5124i | 0.960846 | − | 0.554745i | ||||
\(887\) | −11.6100 | + | 20.1091i | −0.389825 | + | 0.675197i | −0.992426 | − | 0.122846i | \(-0.960798\pi\) |
0.602601 | + | 0.798043i | \(0.294131\pi\) | |||||||
\(888\) | 3.99419 | 0.134036 | ||||||||
\(889\) | 6.55781 | − | 6.28012i | 0.219942 | − | 0.210628i | ||||
\(890\) | − | 11.3619i | − | 0.380853i | ||||||
\(891\) | 2.78007 | + | 1.80865i | 0.0931359 | + | 0.0605920i | ||||
\(892\) | −19.8488 | + | 11.4597i | −0.664588 | + | 0.383700i | ||||
\(893\) | 1.59416 | − | 0.920391i | 0.0533467 | − | 0.0307997i | ||||
\(894\) | −8.42523 | − | 4.86431i | −0.281782 | − | 0.162687i | ||||
\(895\) | − | 3.02135i | − | 0.100993i | ||||||
\(896\) | −0.629345 | − | 2.56981i | −0.0210249 | − | 0.0858513i | ||||
\(897\) | − | 37.0906i | − | 1.23842i | ||||||
\(898\) | −19.5103 | − | 11.2643i | −0.651067 | − | 0.375894i | ||||
\(899\) | −6.46138 | − | 11.1914i | −0.215499 | − | 0.373255i | ||||
\(900\) | −2.25440 | − | 3.90473i | −0.0751466 | − | 0.130158i | ||||
\(901\) | 2.44067 | − | 4.22737i | 0.0813106 | − | 0.140834i | ||||
\(902\) | 19.3862 | + | 1.03196i | 0.645489 | + | 0.0343606i | ||||
\(903\) | 2.68162 | − | 9.20670i | 0.0892386 | − | 0.306380i | ||||
\(904\) | 12.0074i | 0.399361i | ||||||||
\(905\) | −2.43995 | + | 4.22612i | −0.0811068 | + | 0.140481i | ||||
\(906\) | −17.1367 | + | 9.89387i | −0.569328 | + | 0.328702i | ||||
\(907\) | 7.46536 | + | 12.9304i | 0.247883 | + | 0.429346i | 0.962938 | − | 0.269722i | \(-0.0869317\pi\) |
−0.715055 | + | 0.699068i | \(0.753598\pi\) | |||||||
\(908\) | −12.1141 | + | 20.9823i | −0.402021 | + | 0.696321i | ||||
\(909\) | −14.9947 | −0.497344 | ||||||||
\(910\) | 3.64831 | − | 12.5256i | 0.120940 | − | 0.415220i | ||||
\(911\) | 33.6372 | 1.11445 | 0.557225 | − | 0.830362i | \(-0.311866\pi\) | ||||
0.557225 | + | 0.830362i | \(0.311866\pi\) | |||||||
\(912\) | −0.678438 | − | 0.391696i | −0.0224653 | − | 0.0129704i | ||||
\(913\) | 11.9434 | − | 6.07311i | 0.395269 | − | 0.200990i | ||||
\(914\) | −16.5876 | − | 28.7305i | −0.548668 | − | 0.950321i | ||||
\(915\) | 2.93159 | − | 5.07766i | 0.0969154 | − | 0.167862i | ||||
\(916\) | − | 13.3778i | − | 0.442016i | ||||||
\(917\) | −37.5341 | + | 9.19206i | −1.23948 | + | 0.303549i | ||||
\(918\) | 0.617785 | 0.0203899 | ||||||||
\(919\) | −23.3845 | − | 13.5011i | −0.771385 | − | 0.445359i | 0.0619837 | − | 0.998077i | \(-0.480257\pi\) |
−0.833368 | + | 0.552718i | \(0.813591\pi\) | |||||||
\(920\) | −1.84740 | − | 3.19980i | −0.0609071 | − | 0.105494i | ||||
\(921\) | 17.9993 | − | 10.3919i | 0.593099 | − | 0.342426i | ||||
\(922\) | 6.43418 | + | 3.71478i | 0.211899 | + | 0.122340i | ||||
\(923\) | −31.5550 | −1.03864 | ||||||||
\(924\) | −5.72374 | − | 6.65123i | −0.188297 | − | 0.218809i | ||||
\(925\) | −18.0090 | −0.592131 | ||||||||
\(926\) | −13.6403 | − | 7.87521i | −0.448247 | − | 0.258795i | ||||
\(927\) | 12.4289 | − | 7.17585i | 0.408220 | − | 0.235686i | ||||
\(928\) | −1.04588 | − | 1.81152i | −0.0343328 | − | 0.0594661i | ||||
\(929\) | 32.7038 | + | 18.8815i | 1.07298 | + | 0.619483i | 0.928993 | − | 0.370097i | \(-0.120676\pi\) |
0.143983 | + | 0.989580i | \(0.454009\pi\) | |||||||
\(930\) | 4.32985 | 0.141981 | ||||||||
\(931\) | −4.62606 | − | 2.94466i | −0.151613 | − | 0.0965075i | ||||
\(932\) | 27.9050i | 0.914057i | ||||||||
\(933\) | −3.68376 | + | 6.38045i | −0.120601 | + | 0.208887i | ||||
\(934\) | 6.68657 | + | 11.5815i | 0.218791 | + | 0.378958i | ||||
\(935\) | 0.650893 | + | 1.28005i | 0.0212865 | + | 0.0418620i | ||||
\(936\) | 6.09302 | + | 3.51781i | 0.199157 | + | 0.114983i | ||||
\(937\) | −33.9310 | −1.10848 | −0.554239 | − | 0.832357i | \(-0.686991\pi\) | ||||
−0.554239 | + | 0.832357i | \(0.686991\pi\) | |||||||
\(938\) | 4.09076 | − | 3.91753i | 0.133568 | − | 0.127912i | ||||
\(939\) | −7.35395 | −0.239987 | ||||||||
\(940\) | −0.823423 | + | 1.42621i | −0.0268571 | + | 0.0465178i | ||||
\(941\) | −13.4471 | − | 23.2911i | −0.438364 | − | 0.759269i | 0.559199 | − | 0.829033i | \(-0.311109\pi\) |
−0.997564 | + | 0.0697641i | \(0.977775\pi\) | |||||||
\(942\) | 10.4014 | − | 6.00523i | 0.338895 | − | 0.195661i | ||||
\(943\) | −15.4292 | + | 26.7241i | −0.502443 | + | 0.870256i | ||||
\(944\) | − | 3.76387i | − | 0.122503i | ||||||
\(945\) | −1.80107 | + | 0.441081i | −0.0585889 | + | 0.0143484i | ||||
\(946\) | −0.638985 | + | 12.0038i | −0.0207752 | + | 0.390278i | ||||
\(947\) | 11.3627 | − | 19.6808i | 0.369239 | − | 0.639540i | −0.620208 | − | 0.784437i | \(-0.712952\pi\) |
0.989447 | + | 0.144897i | \(0.0462852\pi\) | |||||||
\(948\) | −2.16979 | − | 3.75818i | −0.0704714 | − | 0.122060i | ||||
\(949\) | −18.6072 | − | 32.2286i | −0.604015 | − | 1.04618i | ||||
\(950\) | 3.05894 | + | 1.76608i | 0.0992451 | + | 0.0572992i | ||||
\(951\) | − | 14.7806i | − | 0.479294i | ||||||
\(952\) | −1.56929 | − | 0.457085i | −0.0508611 | − | 0.0148142i | ||||
\(953\) | − | 15.8105i | − | 0.512152i | −0.966657 | − | 0.256076i | \(-0.917570\pi\) | ||
0.966657 | − | 0.256076i | \(-0.0824298\pi\) | |||||||
\(954\) | −6.84278 | − | 3.95068i | −0.221543 | − | 0.127908i | ||||
\(955\) | −11.2646 | + | 6.50360i | −0.364513 | + | 0.210452i | ||||
\(956\) | 8.03251 | − | 4.63757i | 0.259790 | − | 0.149990i | ||||
\(957\) | −5.81525 | − | 3.78327i | −0.187980 | − | 0.122296i | ||||
\(958\) | 11.2610i | 0.363826i | ||||||||
\(959\) | 12.3678 | − | 42.4621i | 0.399378 | − | 1.37117i | ||||
\(960\) | 0.700858 | 0.0226201 | ||||||||
\(961\) | 3.58338 | − | 6.20660i | 0.115593 | − | 0.200213i | ||||
\(962\) | 24.3367 | − | 14.0508i | 0.784646 | − | 0.453015i | ||||
\(963\) | −9.93081 | + | 5.73356i | −0.320016 | + | 0.184761i | ||||
\(964\) | −9.54851 | + | 16.5385i | −0.307537 | + | 0.532669i | ||||
\(965\) | −12.2799 | −0.395303 | ||||||||
\(966\) | 13.5476 | − | 3.31780i | 0.435888 | − | 0.106749i | ||||
\(967\) | − | 50.1237i | − | 1.61187i | −0.592005 | − | 0.805934i | \(-0.701663\pi\) | ||
0.592005 | − | 0.805934i | \(-0.298337\pi\) | |||||||
\(968\) | 8.88855 | + | 6.48026i | 0.285689 | + | 0.208283i | ||||
\(969\) | −0.419129 | + | 0.241984i | −0.0134644 | + | 0.00777365i | ||||
\(970\) | −6.36858 | + | 3.67690i | −0.204483 | + | 0.118058i | ||||
\(971\) | −28.9076 | − | 16.6898i | −0.927690 | − | 0.535602i | −0.0416095 | − | 0.999134i | \(-0.513249\pi\) |
−0.886080 | + | 0.463532i | \(0.846582\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 23.6792 | + | 24.7263i | 0.759121 | + | 0.792687i | ||||
\(974\) | − | 2.66963i | − | 0.0855405i | ||||||
\(975\) | −27.4722 | − | 15.8611i | −0.879815 | − | 0.507962i | ||||
\(976\) | −4.18286 | − | 7.24493i | −0.133890 | − | 0.231904i | ||||
\(977\) | 15.4092 | + | 26.6894i | 0.492983 | + | 0.853871i | 0.999967 | − | 0.00808403i | \(-0.00257325\pi\) |
−0.506985 | + | 0.861955i | \(0.669240\pi\) | |||||||
\(978\) | −11.1980 | + | 19.3955i | −0.358072 | + | 0.620199i | ||||
\(979\) | −53.6914 | − | 2.85809i | −1.71598 | − | 0.0913450i | ||||
\(980\) | 4.90142 | + | 0.212140i | 0.156570 | + | 0.00677657i | ||||
\(981\) | − | 1.45285i | − | 0.0463859i | ||||||
\(982\) | −5.65314 | + | 9.79152i | −0.180399 | + | 0.312460i | ||||
\(983\) | −28.8714 | + | 16.6689i | −0.920855 | + | 0.531656i | −0.883908 | − | 0.467662i | \(-0.845097\pi\) |
−0.0369470 | + | 0.999317i | \(0.511763\pi\) | |||||||
\(984\) | −2.92671 | − | 5.06922i | −0.0933002 | − | 0.161601i | ||||
\(985\) | 6.61131 | − | 11.4511i | 0.210654 | − | 0.364863i | ||||
\(986\) | −1.29226 | −0.0411540 | ||||||||
\(987\) | −4.29990 | − | 4.49003i | −0.136867 | − | 0.142919i | ||||
\(988\) | −5.51165 | −0.175349 | ||||||||
\(989\) | −16.5474 | − | 9.55365i | −0.526177 | − | 0.303788i | ||||
\(990\) | 2.07200 | − | 1.05359i | 0.0658523 | − | 0.0334853i | ||||
\(991\) | 29.0342 | + | 50.2888i | 0.922303 | + | 1.59748i | 0.795842 | + | 0.605504i | \(0.207029\pi\) |
0.126461 | + | 0.991972i | \(0.459638\pi\) | |||||||
\(992\) | 3.08896 | − | 5.35024i | 0.0980747 | − | 0.169870i | ||||
\(993\) | 27.2898i | 0.866015i | ||||||||
\(994\) | −2.82263 | − | 11.5257i | −0.0895284 | − | 0.365572i | ||||
\(995\) | 9.48426 | 0.300671 | ||||||||
\(996\) | −3.49864 | − | 2.01994i | −0.110859 | − | 0.0640043i | ||||
\(997\) | −18.3242 | − | 31.7385i | −0.580334 | − | 1.00517i | −0.995440 | − | 0.0953943i | \(-0.969589\pi\) |
0.415106 | − | 0.909773i | \(-0.363745\pi\) | |||||||
\(998\) | −18.5676 | + | 10.7200i | −0.587747 | + | 0.339336i | ||||
\(999\) | −3.45907 | − | 1.99709i | −0.109440 | − | 0.0631852i |
(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 | 462.2.p.b.439.6 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.b.901.3 | 16 | |||
7.2 | even | 3 | 3234.2.e.b.2155.4 | 16 | |||
7.3 | odd | 6 | 462.2.p.a.241.2 | ✓ | 16 | ||
7.5 | odd | 6 | 3234.2.e.a.2155.5 | 16 | |||
11.10 | odd | 2 | 462.2.p.a.439.2 | yes | 16 | ||
21.17 | even | 6 | 1386.2.bk.a.703.7 | 16 | |||
33.32 | even | 2 | 1386.2.bk.a.901.7 | 16 | |||
77.10 | even | 6 | inner | 462.2.p.b.241.6 | yes | 16 | |
77.54 | even | 6 | 3234.2.e.b.2155.13 | 16 | |||
77.65 | odd | 6 | 3234.2.e.a.2155.12 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.b.703.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.2 | ✓ | 16 | 7.3 | odd | 6 | ||
462.2.p.a.439.2 | yes | 16 | 11.10 | odd | 2 | ||
462.2.p.b.241.6 | yes | 16 | 77.10 | even | 6 | inner | |
462.2.p.b.439.6 | yes | 16 | 1.1 | even | 1 | trivial | |
1386.2.bk.a.703.7 | 16 | 21.17 | even | 6 | |||
1386.2.bk.a.901.7 | 16 | 33.32 | even | 2 | |||
1386.2.bk.b.703.3 | 16 | 231.164 | odd | 6 | |||
1386.2.bk.b.901.3 | 16 | 3.2 | odd | 2 | |||
3234.2.e.a.2155.5 | 16 | 7.5 | odd | 6 | |||
3234.2.e.a.2155.12 | 16 | 77.65 | odd | 6 | |||
3234.2.e.b.2155.4 | 16 | 7.2 | even | 3 | |||
3234.2.e.b.2155.13 | 16 | 77.54 | even | 6 |