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 | 241.6 | ||
Root | \(0.500000 - 1.56688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.241 |
Dual form | 462.2.p.b.439.6 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | −0.629542 | − | 0.776966i | \(-0.716758\pi\) |
0.358101 | + | 0.933683i | \(0.383424\pi\) | |||||||
\(6\) | 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 | −0.826133 | − | 0.563475i | \(-0.809464\pi\) |
0.901050 | + | 0.433714i | \(0.142797\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | −0.391696 | − | 0.678438i | −0.0898613 | − | 0.155644i | 0.817591 | − | 0.575799i | \(-0.195309\pi\) |
−0.907452 | + | 0.420155i | \(0.861976\pi\) | |||||||
\(20\) | 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 | 0.998300 | + | 0.0582859i | \(0.0185635\pi\) |
−0.448673 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(24\) | 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 | \(-0.937784\pi\) | ||
0.980959 | − | 0.194215i | \(-0.0622161\pi\) | |||||||
\(30\) | −0.606961 | + | 0.350429i | −0.110815 | + | 0.0639793i | ||||
\(31\) | −5.35024 | − | 3.08896i | −0.960932 | − | 0.554794i | −0.0644719 | − | 0.997920i | \(-0.520536\pi\) |
−0.896460 | + | 0.443125i | \(0.853870\pi\) | |||||||
\(32\) | −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 | 0.982179 | − | 0.187950i | \(-0.0601842\pi\) |
−0.653859 | + | 0.756617i | \(0.726851\pi\) | |||||||
\(38\) | −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 | \(0.0891277\pi\) | ||||
−0.961055 | + | 0.276359i | \(0.910872\pi\) | |||||||
\(44\) | −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 | −0.641017 | − | 0.767527i | \(-0.721487\pi\) |
0.344189 | + | 0.938900i | \(0.388154\pi\) | |||||||
\(48\) | − | 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 | 0.456082 | + | 0.889938i | \(0.349252\pi\) |
−0.998750 | + | 0.0499906i | \(0.984081\pi\) | |||||||
\(54\) | 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 | 0.272578 | − | 0.962134i | \(-0.412124\pi\) |
−0.696943 | + | 0.717127i | \(0.745457\pi\) | |||||||
\(60\) | −0.350429 | + | 0.606961i | −0.0452402 | + | 0.0783583i | ||||
\(61\) | −4.18286 | − | 7.24493i | −0.535560 | − | 0.927618i | −0.999136 | − | 0.0415604i | \(-0.986767\pi\) |
0.463576 | − | 0.886057i | \(-0.346566\pi\) | |||||||
\(62\) | −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 | −0.923974 | − | 0.382456i | \(-0.875078\pi\) |
0.793203 | + | 0.608957i | \(0.208412\pi\) | |||||||
\(68\) | −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 | −0.978262 | − | 0.207373i | \(-0.933508\pi\) |
0.668722 | + | 0.743513i | \(0.266842\pi\) | |||||||
\(74\) | 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 | −0.696287 | − | 0.717764i | \(-0.745166\pi\) |
0.273458 | + | 0.961884i | \(0.411832\pi\) | |||||||
\(80\) | 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 | 0.488281 | − | 0.872687i | \(-0.337624\pi\) |
0.999909 | + | 0.0134796i | \(0.00429082\pi\) | |||||||
\(90\) | −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 | \(0.178815\pi\) | ||||
−0.846317 | + | 0.532680i | \(0.821185\pi\) | |||||||
\(98\) | −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 | 0.203702 | + | 0.979033i | \(0.434703\pi\) |
−0.949718 | + | 0.313105i | \(0.898631\pi\) | |||||||
\(102\) | 0.308893 | − | 0.535018i | 0.0305849 | − | 0.0529746i | ||||
\(103\) | 12.4289 | − | 7.17585i | 1.22466 | − | 0.707057i | 0.258752 | − | 0.965944i | \(-0.416689\pi\) |
0.965908 | + | 0.258887i | \(0.0833556\pi\) | |||||||
\(104\) | − | 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 | −0.896188 | − | 0.443675i | \(-0.853674\pi\) |
−0.0638601 | + | 0.997959i | \(0.520341\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | 1.25820 | + | 0.726424i | 0.120514 | + | 0.0695788i | 0.559045 | − | 0.829137i | \(-0.311168\pi\) |
−0.438531 | + | 0.898716i | \(0.644501\pi\) | |||||||
\(110\) | 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 | \(0.0486568\pi\) | ||||
−0.988340 | + | 0.152265i | \(0.951343\pi\) | |||||||
\(128\) | −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 | −0.985859 | − | 0.167578i | \(-0.946406\pi\) |
0.347803 | − | 0.937568i | \(-0.386928\pi\) | |||||||
\(132\) | −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 | 0.249240 | + | 0.968442i | \(0.419819\pi\) |
−0.963315 | + | 0.268373i | \(0.913514\pi\) | |||||||
\(138\) | 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 | −0.803695 | − | 0.595041i | \(-0.797136\pi\) |
0.113474 | + | 0.993541i | \(0.463802\pi\) | |||||||
\(150\) | −2.25440 | + | 3.90473i | −0.184071 | + | 0.318820i | ||||
\(151\) | −17.1367 | − | 9.89387i | −1.39456 | − | 0.805151i | −0.400747 | − | 0.916189i | \(-0.631249\pi\) |
−0.993816 | + | 0.111037i | \(0.964583\pi\) | |||||||
\(152\) | −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 | 0.853893 | − | 0.520448i | \(-0.174235\pi\) |
−0.0237745 | + | 0.999717i | \(0.507568\pi\) | |||||||
\(158\) | −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 | −0.854515 | − | 0.519426i | \(-0.826146\pi\) |
−0.0225784 | − | 0.999745i | \(-0.507188\pi\) | |||||||
\(164\) | −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 | 0.873128 | − | 0.487491i | \(-0.162088\pi\) |
−0.858744 | + | 0.512405i | \(0.828755\pi\) | |||||||
\(174\) | − | 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 | −0.774159 | − | 0.632991i | \(-0.781827\pi\) |
0.935266 | + | 0.353946i | \(0.115160\pi\) | |||||||
\(180\) | −0.606961 | + | 0.350429i | −0.0452402 | + | 0.0261194i | ||||
\(181\) | 6.96276i | 0.517538i | 0.965939 | + | 0.258769i | \(0.0833169\pi\) | ||||
−0.965939 | + | 0.258769i | \(0.916683\pi\) | |||||||
\(182\) | 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 | 0.977496 | + | 0.210955i | \(0.0676574\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 15.1738 | + | 8.76059i | 1.09223 | + | 0.630601i | 0.934170 | − | 0.356828i | \(-0.116142\pi\) |
0.158063 | + | 0.987429i | \(0.449475\pi\) | |||||||
\(194\) | 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 | \(-0.765399\pi\) | ||
0.740474 | − | 0.672086i | \(-0.234601\pi\) | |||||||
\(198\) | −1.80865 | − | 2.78007i | −0.128535 | − | 0.197571i | ||||
\(199\) | −11.7194 | − | 6.76618i | −0.830764 | − | 0.479642i | 0.0233504 | − | 0.999727i | \(-0.492567\pi\) |
−0.854114 | + | 0.520086i | \(0.825900\pi\) | |||||||
\(200\) | 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 | \(0.0544312\pi\) | ||||
−0.985415 | + | 0.170168i | \(0.945569\pi\) | |||||||
\(212\) | 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 | \(-0.721550\pi\) | ||
0.641169 | − | 0.767400i | \(-0.278450\pi\) | |||||||
\(224\) | −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 | −0.112894 | − | 0.993607i | \(-0.536012\pi\) |
0.916936 | − | 0.399034i | \(-0.130655\pi\) | |||||||
\(228\) | −0.678438 | − | 0.391696i | −0.0449307 | − | 0.0259407i | ||||
\(229\) | −11.5855 | + | 6.68891i | −0.765594 | + | 0.442016i | −0.831300 | − | 0.555823i | \(-0.812403\pi\) |
0.0657068 | + | 0.997839i | \(0.479070\pi\) | |||||||
\(230\) | −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 | 0.588805 | − | 0.808275i | \(-0.299599\pi\) |
0.994389 | − | 0.105782i | \(-0.0337346\pi\) | |||||||
\(234\) | 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 | \(0.0969798\pi\) | ||||
−0.953946 | + | 0.299979i | \(0.903020\pi\) | |||||||
\(240\) | 0.350429 | + | 0.606961i | 0.0226201 | + | 0.0391791i | ||||
\(241\) | 9.54851 | − | 16.5385i | 0.615074 | − | 1.06534i | −0.375298 | − | 0.926904i | \(-0.622460\pi\) |
0.990372 | − | 0.138434i | \(-0.0442070\pi\) | |||||||
\(242\) | 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 | \(-0.874922\pi\) | ||
0.923786 | − | 0.382909i | \(-0.125078\pi\) | |||||||
\(252\) | 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 | 0.147327 | − | 0.989088i | \(-0.452933\pi\) |
0.930239 | + | 0.366955i | \(0.119600\pi\) | |||||||
\(258\) | 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 | 0.876041 | − | 0.482236i | \(-0.160175\pi\) |
0.0203919 | + | 0.999792i | \(0.493509\pi\) | |||||||
\(264\) | −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 | −0.112589 | − | 0.993642i | \(-0.535914\pi\) |
−0.916813 | + | 0.399316i | \(0.869248\pi\) | |||||||
\(270\) | −0.606961 | − | 0.350429i | −0.0369384 | − | 0.0213264i | ||||
\(271\) | −5.34130 | − | 9.25140i | −0.324461 | − | 0.561983i | 0.656942 | − | 0.753941i | \(-0.271850\pi\) |
−0.981403 | + | 0.191958i | \(0.938516\pi\) | |||||||
\(272\) | −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 | −0.991080 | − | 0.133268i | \(-0.957453\pi\) |
−0.610954 | − | 0.791666i | \(-0.709214\pi\) | |||||||
\(278\) | 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 | \(-0.780397\pi\) | ||
0.771308 | − | 0.636462i | \(-0.219603\pi\) | |||||||
\(282\) | −2.03495 | + | 1.17488i | −0.121179 | + | 0.0699630i | ||||
\(283\) | −1.26154 | + | 2.18504i | −0.0749905 | + | 0.129887i | −0.901082 | − | 0.433648i | \(-0.857226\pi\) |
0.826092 | + | 0.563536i | \(0.190559\pi\) | |||||||
\(284\) | −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 | 0.308069 | − | 0.951364i | \(-0.400317\pi\) |
−0.669871 | + | 0.742477i | \(0.733651\pi\) | |||||||
\(312\) | 3.51781 | − | 6.09302i | 0.199157 | − | 0.344950i | ||||
\(313\) | −6.36871 | + | 3.67697i | −0.359981 | + | 0.207835i | −0.669072 | − | 0.743197i | \(-0.733308\pi\) |
0.309092 | + | 0.951032i | \(0.399975\pi\) | |||||||
\(314\) | 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 | 0.995437 | − | 0.0954222i | \(-0.0304201\pi\) |
−0.580356 | + | 0.814363i | \(0.697087\pi\) | |||||||
\(318\) | −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 | −0.947826 | − | 0.318787i | \(-0.896725\pi\) |
0.197836 | − | 0.980235i | \(-0.436609\pi\) | |||||||
\(332\) | −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 | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356607i | \(0.883933\pi\) | |||||||
\(338\) | 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 | 0.212471 | − | 0.977167i | \(-0.431849\pi\) |
−0.740016 | + | 0.672589i | \(0.765182\pi\) | |||||||
\(348\) | −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 | 0.648958 | − | 0.760824i | \(-0.275205\pi\) |
−0.334414 | + | 0.942426i | \(0.608538\pi\) | |||||||
\(354\) | −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 | −0.888031 | − | 0.459783i | \(-0.847927\pi\) |
−0.0458314 | + | 0.998949i | \(0.514594\pi\) | |||||||
\(360\) | −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 | 0.880821 | − | 0.473450i | \(-0.156991\pi\) |
0.0303908 | + | 0.999538i | \(0.490325\pi\) | |||||||
\(368\) | 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 | −0.675165 | − | 0.737667i | \(-0.735928\pi\) |
0.301256 | + | 0.953543i | \(0.402594\pi\) | |||||||
\(374\) | −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 | −0.0268936 | − | 0.999638i | \(-0.508562\pi\) |
0.852265 | + | 0.523110i | \(0.175228\pi\) | |||||||
\(384\) | −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 | −0.719856 | − | 0.694123i | \(-0.755792\pi\) |
0.961057 | + | 0.276352i | \(0.0891255\pi\) | |||||||
\(390\) | −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 | −0.999764 | − | 0.0217370i | \(-0.993080\pi\) |
−0.481057 | + | 0.876689i | \(0.659747\pi\) | |||||||
\(398\) | −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 | 0.952508 | + | 0.304512i | \(0.0984934\pi\) |
−0.212539 | + | 0.977153i | \(0.568173\pi\) | |||||||
\(402\) | −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 | 0.300613 | + | 0.953746i | \(0.402809\pi\) |
−0.976275 | + | 0.216534i | \(0.930525\pi\) | |||||||
\(410\) | 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 | \(0.216002\pi\) | ||||
−0.778459 | + | 0.627696i | \(0.783998\pi\) | |||||||
\(420\) | 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 | 0.0174831 | − | 0.999847i | \(-0.494435\pi\) |
−0.857152 | + | 0.515064i | \(0.827768\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 38.1992i | 1.83574i | 0.396884 | + | 0.917869i | \(0.370092\pi\) | ||||
−0.396884 | + | 0.917869i | \(0.629908\pi\) | |||||||
\(434\) | −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 | 0.765338 | − | 0.643628i | \(-0.222572\pi\) |
−0.940068 | + | 0.340988i | \(0.889238\pi\) | |||||||
\(440\) | −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 | 0.929281 | + | 0.369373i | \(0.120428\pi\) |
−0.144754 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(444\) | 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 | −0.987386 | − | 0.158334i | \(-0.949388\pi\) |
−0.356572 | + | 0.934268i | \(0.616054\pi\) | |||||||
\(458\) | −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 | −0.207500 | − | 0.978235i | \(-0.566533\pi\) |
0.743427 | + | 0.668817i | \(0.233199\pi\) | |||||||
\(468\) | 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 | −0.708244 | − | 0.705968i | \(-0.750512\pi\) |
0.965508 | + | 0.260374i | \(0.0838457\pi\) | |||||||
\(480\) | 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 | −0.894683 | − | 0.446702i | \(-0.852598\pi\) |
0.834197 | + | 0.551467i | \(0.185932\pi\) | |||||||
\(488\) | −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 | \(-0.917884\pi\) | ||
0.966909 | − | 0.255123i | \(-0.0821158\pi\) | |||||||
\(492\) | −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 | 0.519840 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230633i | \(0.992658\pi\) | |||||||
\(500\) | −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 | −0.218416 | − | 0.975856i | \(-0.570089\pi\) |
0.735908 | + | 0.677082i | \(0.236756\pi\) | |||||||
\(510\) | 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 | 0.273839 | − | 0.961776i | \(-0.411707\pi\) |
−0.696003 | + | 0.718039i | \(0.745040\pi\) | |||||||
\(522\) | 1.04588 | − | 1.81152i | 0.0457770 | − | 0.0792881i | ||||
\(523\) | −7.45440 | − | 12.9114i | −0.325958 | − | 0.564576i | 0.655748 | − | 0.754980i | \(-0.272354\pi\) |
−0.981706 | + | 0.190404i | \(0.939020\pi\) | |||||||
\(524\) | −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 | 0.0845270 | − | 0.996421i | \(-0.473062\pi\) |
0.905190 | + | 0.425008i | \(0.139729\pi\) | |||||||
\(542\) | −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 | \(0.127420\pi\) | ||||
−0.920943 | + | 0.389696i | \(0.872580\pi\) | |||||||
\(548\) | 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 | 0.950178 | − | 0.311707i | \(-0.100901\pi\) |
0.205143 | + | 0.978732i | \(0.434234\pi\) | |||||||
\(558\) | −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 | −0.536742 | − | 0.843746i | \(-0.680345\pi\) |
0.999077 | + | 0.0429591i | \(0.0136785\pi\) | |||||||
\(564\) | −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 | −0.943356 | − | 0.331781i | \(-0.892350\pi\) |
−0.184347 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(570\) | 0.475489 | + | 0.274523i | 0.0199160 | + | 0.0114985i | ||||
\(571\) | 8.45951 | + | 4.88410i | 0.354020 | + | 0.204393i | 0.666454 | − | 0.745546i | \(-0.267811\pi\) |
−0.312435 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(572\) | −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 | 0.806985 | − | 0.590571i | \(-0.201098\pi\) |
−0.107957 | + | 0.994156i | \(0.534431\pi\) | |||||||
\(578\) | 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 | \(-0.906275\pi\) | ||
0.956963 | − | 0.290210i | \(-0.0937253\pi\) | |||||||
\(588\) | −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 | −0.930493 | − | 0.366310i | \(-0.880621\pi\) |
0.148013 | − | 0.988985i | \(-0.452712\pi\) | |||||||
\(594\) | −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 | −0.498817 | − | 0.866708i | \(-0.666232\pi\) |
0.999999 | − | 0.00136605i | \(-0.000434826\pi\) | |||||||
\(600\) | 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 | 0.900105 | + | 0.435673i | \(0.143490\pi\) |
−0.0727485 | + | 0.997350i | \(0.523177\pi\) | |||||||
\(608\) | 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 | 0.648373 | − | 0.761322i | \(-0.275450\pi\) |
−0.335138 | + | 0.942169i | \(0.608783\pi\) | |||||||
\(614\) | 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 | 0.557518 | − | 0.830165i | \(-0.311754\pi\) |
−0.440185 | + | 0.897907i | \(0.645087\pi\) | |||||||
\(620\) | 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 | −0.294242 | − | 0.955731i | \(-0.595067\pi\) |
0.974808 | − | 0.223045i | \(-0.0715995\pi\) | |||||||
\(642\) | −9.93081 | + | 5.73356i | −0.391938 | + | 0.226285i | ||||
\(643\) | − | 2.69205i | − | 0.106164i | −0.998590 | − | 0.0530821i | \(-0.983095\pi\) | ||
0.998590 | − | 0.0530821i | \(-0.0169045\pi\) | |||||||
\(644\) | 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 | 0.993414 | + | 0.114577i | \(0.0365514\pi\) |
0.595934 | + | 0.803033i | \(0.296782\pi\) | |||||||
\(648\) | 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 | −0.930550 | − | 0.366165i | \(-0.880671\pi\) |
0.148167 | − | 0.988962i | \(-0.452663\pi\) | |||||||
\(654\) | 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 | \(0.161834\pi\) | ||||
−0.873516 | + | 0.486795i | \(0.838166\pi\) | |||||||
\(660\) | 1.94843 | − | 1.26761i | 0.0758427 | − | 0.0493415i | ||||
\(661\) | 12.7267 | + | 7.34774i | 0.495010 | + | 0.285794i | 0.726650 | − | 0.687007i | \(-0.241076\pi\) |
−0.231641 | + | 0.972801i | \(0.574409\pi\) | |||||||
\(662\) | −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 | \(-0.523635\pi\) | ||
0.0741830 | − | 0.997245i | \(-0.476365\pi\) | |||||||
\(674\) | 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 | −0.961111 | − | 0.276161i | \(-0.910938\pi\) |
0.241393 | − | 0.970427i | \(-0.422396\pi\) | |||||||
\(678\) | 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 | −0.113223 | − | 0.993570i | \(-0.536117\pi\) |
0.917068 | − | 0.398731i | \(-0.130549\pi\) | |||||||
\(684\) | −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 | −0.880735 | − | 0.473610i | \(-0.842951\pi\) |
−0.0302096 | + | 0.999544i | \(0.509617\pi\) | |||||||
\(692\) | 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 | \(-0.947234\pi\) | ||
0.986292 | − | 0.165011i | \(-0.0527659\pi\) | |||||||
\(702\) | 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 | 0.988349 | + | 0.152208i | \(0.0486382\pi\) |
−0.362359 | + | 0.932039i | \(0.618028\pi\) | |||||||
\(710\) | 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 | −0.659711 | − | 0.751520i | \(-0.729321\pi\) |
0.320980 | + | 0.947086i | \(0.395988\pi\) | |||||||
\(720\) | 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 | \(-0.942248\pi\) | ||
0.983586 | − | 0.180440i | \(-0.0577523\pi\) | |||||||
\(728\) | −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 | 0.880430 | − | 0.474176i | \(-0.157254\pi\) |
−0.850863 | + | 0.525387i | \(0.823920\pi\) | |||||||
\(734\) | 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 | −0.00326478 | − | 0.999995i | \(-0.501039\pi\) |
−0.867653 | + | 0.497170i | \(0.834373\pi\) | |||||||
\(740\) | −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 | \(0.366203\pi\) | ||||
−0.408067 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(744\) | −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 | 0.996018 | − | 0.0891499i | \(-0.0284150\pi\) |
−0.575215 | + | 0.818002i | \(0.695082\pi\) | |||||||
\(752\) | 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 | 0.680071 | − | 0.733146i | \(-0.261949\pi\) |
−0.974959 | + | 0.222385i | \(0.928616\pi\) | |||||||
\(762\) | 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 | 0.220107 | − | 0.975476i | \(-0.429359\pi\) |
−0.734733 | + | 0.678356i | \(0.762693\pi\) | |||||||
\(774\) | −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 | −0.992920 | − | 0.118786i | \(-0.962100\pi\) |
0.599331 | + | 0.800501i | \(0.295433\pi\) | |||||||
\(788\) | −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 | \(-0.849358\pi\) | ||
0.890090 | − | 0.455785i | \(-0.150642\pi\) | |||||||
\(798\) | −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 | 0.871410 | − | 0.490556i | \(-0.163206\pi\) |
0.0108712 | + | 0.999941i | \(0.496540\pi\) | |||||||
\(810\) | −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 | −0.581168 | − | 0.813784i | \(-0.697404\pi\) |
0.414173 | + | 0.910198i | \(0.364071\pi\) | |||||||
\(822\) | −8.35804 | + | 14.4765i | −0.291520 | + | 0.504928i | ||||
\(823\) | 8.11088 | − | 14.0485i | 0.282728 | − | 0.489699i | −0.689328 | − | 0.724449i | \(-0.742094\pi\) |
0.972056 | + | 0.234751i | \(0.0754274\pi\) | |||||||
\(824\) | −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 | \(-0.967501\pi\) | ||
0.994793 | − | 0.101920i | \(-0.0324986\pi\) | |||||||
\(828\) | 2.63592 | + | 4.56555i | 0.0916045 | + | 0.158664i | ||||
\(829\) | −16.8080 | − | 9.70409i | −0.583765 | − | 0.337037i | 0.178863 | − | 0.983874i | \(-0.442758\pi\) |
−0.762628 | + | 0.646837i | \(0.776091\pi\) | |||||||
\(830\) | 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 | \(-0.900413\pi\) | ||
0.951457 | − | 0.307783i | \(-0.0995870\pi\) | |||||||
\(840\) | 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 | −0.692226 | − | 0.721681i | \(-0.743370\pi\) |
0.971107 | + | 0.238644i | \(0.0767030\pi\) | |||||||
\(858\) | −20.7999 | − | 10.5766i | −0.710097 | − | 0.361078i | ||||
\(859\) | −22.3768 | + | 12.9193i | −0.763487 | + | 0.440799i | −0.830546 | − | 0.556950i | \(-0.811972\pi\) |
0.0670596 | + | 0.997749i | \(0.478638\pi\) | |||||||
\(860\) | −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 | 0.673918 | − | 0.738806i | \(-0.264610\pi\) |
−0.976784 | + | 0.214227i | \(0.931277\pi\) | |||||||
\(864\) | 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 | −0.522058 | − | 0.852910i | \(-0.674836\pi\) |
0.477612 | + | 0.878571i | \(0.341502\pi\) | |||||||
\(878\) | −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 | \(-0.985971\pi\) | ||
0.999029 | − | 0.0440605i | \(-0.0140294\pi\) | |||||||
\(882\) | 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 | 0.602601 | − | 0.798043i | \(-0.294131\pi\) |
−0.992426 | + | 0.122846i | \(0.960798\pi\) | |||||||
\(888\) | 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 | −0.715055 | − | 0.699068i | \(-0.753598\pi\) |
0.962938 | + | 0.269722i | \(0.0869317\pi\) | |||||||
\(908\) | −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 | −0.833368 | − | 0.552718i | \(-0.813591\pi\) |
0.0619837 | + | 0.998077i | \(0.480257\pi\) | |||||||
\(920\) | −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 | 0.143983 | − | 0.989580i | \(-0.454009\pi\) |
0.928993 | + | 0.370097i | \(0.120676\pi\) | |||||||
\(930\) | 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 | −0.997564 | − | 0.0697641i | \(-0.977775\pi\) |
0.559199 | + | 0.829033i | \(0.311109\pi\) | |||||||
\(942\) | 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 | 0.989447 | − | 0.144897i | \(-0.0462852\pi\) |
−0.620208 | + | 0.784437i | \(0.712952\pi\) | |||||||
\(948\) | −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 | \(0.0824298\pi\) | ||||
−0.966657 | + | 0.256076i | \(0.917570\pi\) | |||||||
\(954\) | −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 | \(0.298337\pi\) | ||||
−0.592005 | + | 0.805934i | \(0.701663\pi\) | |||||||
\(968\) | 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 | −0.886080 | − | 0.463532i | \(-0.846582\pi\) |
−0.0416095 | + | 0.999134i | \(0.513249\pi\) | |||||||
\(972\) | 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 | −0.506985 | − | 0.861955i | \(-0.669240\pi\) |
0.999967 | + | 0.00808403i | \(0.00257325\pi\) | |||||||
\(978\) | −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 | −0.0369470 | − | 0.999317i | \(-0.511763\pi\) |
−0.883908 | + | 0.467662i | \(0.845097\pi\) | |||||||
\(984\) | −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 | 0.126461 | − | 0.991972i | \(-0.459638\pi\) |
0.795842 | − | 0.605504i | \(-0.207029\pi\) | |||||||
\(992\) | 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 | 0.415106 | + | 0.909773i | \(0.363745\pi\) |
−0.995440 | + | 0.0953943i | \(0.969589\pi\) | |||||||
\(998\) | −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.241.6 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.b.703.3 | 16 | |||
7.3 | odd | 6 | 3234.2.e.a.2155.12 | 16 | |||
7.4 | even | 3 | 3234.2.e.b.2155.13 | 16 | |||
7.5 | odd | 6 | 462.2.p.a.439.2 | yes | 16 | ||
11.10 | odd | 2 | 462.2.p.a.241.2 | ✓ | 16 | ||
21.5 | even | 6 | 1386.2.bk.a.901.7 | 16 | |||
33.32 | even | 2 | 1386.2.bk.a.703.7 | 16 | |||
77.10 | even | 6 | 3234.2.e.b.2155.4 | 16 | |||
77.32 | odd | 6 | 3234.2.e.a.2155.5 | 16 | |||
77.54 | even | 6 | inner | 462.2.p.b.439.6 | yes | 16 | |
231.131 | odd | 6 | 1386.2.bk.b.901.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.2 | ✓ | 16 | 11.10 | odd | 2 | ||
462.2.p.a.439.2 | yes | 16 | 7.5 | odd | 6 | ||
462.2.p.b.241.6 | yes | 16 | 1.1 | even | 1 | trivial | |
462.2.p.b.439.6 | yes | 16 | 77.54 | even | 6 | inner | |
1386.2.bk.a.703.7 | 16 | 33.32 | even | 2 | |||
1386.2.bk.a.901.7 | 16 | 21.5 | even | 6 | |||
1386.2.bk.b.703.3 | 16 | 3.2 | odd | 2 | |||
1386.2.bk.b.901.3 | 16 | 231.131 | odd | 6 | |||
3234.2.e.a.2155.5 | 16 | 77.32 | odd | 6 | |||
3234.2.e.a.2155.12 | 16 | 7.3 | odd | 6 | |||
3234.2.e.b.2155.4 | 16 | 77.10 | even | 6 | |||
3234.2.e.b.2155.13 | 16 | 7.4 | even | 3 |