Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 4x^{2} - 5x + 25 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.2 | ||
Root | \(2.13746 - 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.j.295.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 4.27492 | 1.91180 | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) | ||||
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −2.13746 | − | 3.70219i | −0.675924 | − | 1.17073i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.13746 | − | 3.70219i | −0.551889 | − | 0.955901i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.27492 | + | 5.67232i | −0.751318 | + | 1.30132i | 0.195867 | + | 0.980631i | \(0.437248\pi\) |
−0.947184 | + | 0.320690i | \(0.896085\pi\) | |||||||
\(20\) | −2.13746 | + | 3.70219i | −0.477950 | + | 0.827834i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 2.00000 | − | 3.46410i | 0.426401 | − | 0.738549i | ||||
\(23\) | 2.63746 | + | 4.56821i | 0.549948 | + | 0.952538i | 0.998277 | + | 0.0586697i | \(0.0186859\pi\) |
−0.448329 | + | 0.893868i | \(0.647981\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 13.2749 | 2.65498 | ||||||||
\(26\) | −2.50000 | − | 2.59808i | −0.490290 | − | 0.509525i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −4.13746 | − | 7.16629i | −0.768307 | − | 1.33075i | −0.938480 | − | 0.345332i | \(-0.887766\pi\) |
0.170174 | − | 0.985414i | \(-0.445567\pi\) | |||||||
\(30\) | −2.13746 | + | 3.70219i | −0.390245 | + | 0.675924i | ||||
\(31\) | −1.27492 | −0.228982 | −0.114491 | − | 0.993424i | \(-0.536524\pi\) | ||||
−0.114491 | + | 0.993424i | \(0.536524\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | −2.13746 | + | 3.70219i | −0.361296 | + | 0.625784i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −0.137459 | − | 0.238085i | −0.0225981 | − | 0.0391410i | 0.854505 | − | 0.519443i | \(-0.173860\pi\) |
−0.877103 | + | 0.480302i | \(0.840527\pi\) | |||||||
\(38\) | 6.54983 | 1.06252 | ||||||||
\(39\) | −2.50000 | − | 2.59808i | −0.400320 | − | 0.416025i | ||||
\(40\) | 4.27492 | 0.675924 | ||||||||
\(41\) | −4.13746 | − | 7.16629i | −0.646162 | − | 1.11919i | −0.984032 | − | 0.177993i | \(-0.943040\pi\) |
0.337869 | − | 0.941193i | \(-0.390294\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | 5.91238 | − | 10.2405i | 0.901629 | − | 1.56167i | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) |
0.825380 | − | 0.564578i | \(-0.190961\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | −2.13746 | + | 3.70219i | −0.318634 | + | 0.551889i | ||||
\(46\) | 2.63746 | − | 4.56821i | 0.388872 | − | 0.673546i | ||||
\(47\) | −6.54983 | −0.955392 | −0.477696 | − | 0.878525i | \(-0.658528\pi\) | ||||
−0.477696 | + | 0.878525i | \(0.658528\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −6.63746 | − | 11.4964i | −0.938678 | − | 1.62584i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | −1.00000 | + | 3.46410i | −0.138675 | + | 0.480384i | ||||
\(53\) | −3.54983 | −0.487607 | −0.243804 | − | 0.969825i | \(-0.578395\pi\) | ||||
−0.243804 | + | 0.969825i | \(0.578395\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 8.54983 | + | 14.8087i | 1.15286 | + | 1.99681i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 6.54983 | 0.867547 | ||||||||
\(58\) | −4.13746 | + | 7.16629i | −0.543275 | + | 0.940980i | ||||
\(59\) | 5.91238 | − | 10.2405i | 0.769726 | − | 1.33320i | −0.167986 | − | 0.985789i | \(-0.553726\pi\) |
0.937712 | − | 0.347415i | \(-0.112940\pi\) | |||||||
\(60\) | 4.27492 | 0.551889 | ||||||||
\(61\) | 4.50000 | − | 7.79423i | 0.576166 | − | 0.997949i | −0.419748 | − | 0.907641i | \(-0.637882\pi\) |
0.995914 | − | 0.0903080i | \(-0.0287851\pi\) | |||||||
\(62\) | 0.637459 | + | 1.10411i | 0.0809573 | + | 0.140222i | ||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.9622 | − | 3.70219i | 1.85583 | − | 0.459200i | ||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 1.36254 | + | 2.35999i | 0.166461 | + | 0.288319i | 0.937173 | − | 0.348865i | \(-0.113433\pi\) |
−0.770712 | + | 0.637183i | \(0.780099\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | 2.63746 | − | 4.56821i | 0.317513 | − | 0.549948i | ||||
\(70\) | 4.27492 | 0.510950 | ||||||||
\(71\) | −2.63746 | + | 4.56821i | −0.313009 | + | 0.542147i | −0.979012 | − | 0.203802i | \(-0.934670\pi\) |
0.666003 | + | 0.745949i | \(0.268004\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 5.72508 | 0.670070 | 0.335035 | − | 0.942206i | \(-0.391252\pi\) | ||||
0.335035 | + | 0.942206i | \(0.391252\pi\) | |||||||
\(74\) | −0.137459 | + | 0.238085i | −0.0159792 | + | 0.0276769i | ||||
\(75\) | −6.63746 | − | 11.4964i | −0.766428 | − | 1.32749i | ||||
\(76\) | −3.27492 | − | 5.67232i | −0.375659 | − | 0.650660i | ||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | −1.00000 | + | 3.46410i | −0.113228 | + | 0.392232i | ||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | −2.13746 | − | 3.70219i | −0.238975 | − | 0.413917i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.13746 | + | 7.16629i | −0.456906 | + | 0.791384i | ||||
\(83\) | −11.8248 | −1.29794 | −0.648968 | − | 0.760816i | \(-0.724799\pi\) | ||||
−0.648968 | + | 0.760816i | \(0.724799\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | −6.41238 | + | 11.1066i | −0.695520 | + | 1.20468i | ||||
\(86\) | −11.8248 | −1.27510 | ||||||||
\(87\) | −4.13746 | + | 7.16629i | −0.443582 | + | 0.768307i | ||||
\(88\) | 2.00000 | + | 3.46410i | 0.213201 | + | 0.369274i | ||||
\(89\) | −0.362541 | − | 0.627940i | −0.0384293 | − | 0.0665615i | 0.846171 | − | 0.532911i | \(-0.178902\pi\) |
−0.884600 | + | 0.466350i | \(0.845569\pi\) | |||||||
\(90\) | 4.27492 | 0.450616 | ||||||||
\(91\) | −1.00000 | + | 3.46410i | −0.104828 | + | 0.363137i | ||||
\(92\) | −5.27492 | −0.549948 | ||||||||
\(93\) | 0.637459 | + | 1.10411i | 0.0661014 | + | 0.114491i | ||||
\(94\) | 3.27492 | + | 5.67232i | 0.337782 | + | 0.585055i | ||||
\(95\) | −14.0000 | + | 24.2487i | −1.43637 | + | 2.48787i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 0.274917 | − | 0.476171i | 0.0279136 | − | 0.0483478i | −0.851731 | − | 0.523979i | \(-0.824447\pi\) |
0.879645 | + | 0.475631i | \(0.157780\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | −6.63746 | + | 11.4964i | −0.663746 | + | 1.14964i | ||||
\(101\) | −0.862541 | − | 1.49397i | −0.0858261 | − | 0.148655i | 0.819917 | − | 0.572483i | \(-0.194020\pi\) |
−0.905743 | + | 0.423828i | \(0.860686\pi\) | |||||||
\(102\) | −1.50000 | − | 2.59808i | −0.148522 | − | 0.257248i | ||||
\(103\) | 5.27492 | 0.519753 | 0.259877 | − | 0.965642i | \(-0.416318\pi\) | ||||
0.259877 | + | 0.965642i | \(0.416318\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | 4.27492 | 0.417189 | ||||||||
\(106\) | 1.77492 | + | 3.07425i | 0.172395 | + | 0.298597i | ||||
\(107\) | −1.27492 | − | 2.20822i | −0.123251 | − | 0.213477i | 0.797797 | − | 0.602926i | \(-0.205999\pi\) |
−0.921048 | + | 0.389449i | \(0.872665\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −4.54983 | −0.435795 | −0.217898 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217898 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(110\) | 8.54983 | − | 14.8087i | 0.815195 | − | 1.41196i | ||||
\(111\) | −0.137459 | + | 0.238085i | −0.0130470 | + | 0.0225981i | ||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −7.41238 | + | 12.8386i | −0.697298 | + | 1.20775i | 0.272102 | + | 0.962268i | \(0.412281\pi\) |
−0.969400 | + | 0.245487i | \(0.921052\pi\) | |||||||
\(114\) | −3.27492 | − | 5.67232i | −0.306724 | − | 0.531262i | ||||
\(115\) | 11.2749 | + | 19.5287i | 1.05139 | + | 1.82106i | ||||
\(116\) | 8.27492 | 0.768307 | ||||||||
\(117\) | −1.00000 | + | 3.46410i | −0.0924500 | + | 0.320256i | ||||
\(118\) | −11.8248 | −1.08856 | ||||||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | −2.13746 | − | 3.70219i | −0.195122 | − | 0.337962i | ||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −9.00000 | −0.814822 | ||||||||
\(123\) | −4.13746 | + | 7.16629i | −0.373062 | + | 0.646162i | ||||
\(124\) | 0.637459 | − | 1.10411i | 0.0572455 | − | 0.0991521i | ||||
\(125\) | 35.3746 | 3.16400 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | −4.00000 | − | 6.92820i | −0.354943 | − | 0.614779i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −11.8248 | −1.04111 | ||||||||
\(130\) | −10.6873 | − | 11.1066i | −0.937338 | − | 0.974110i | ||||
\(131\) | −2.72508 | −0.238092 | −0.119046 | − | 0.992889i | \(-0.537984\pi\) | ||||
−0.119046 | + | 0.992889i | \(0.537984\pi\) | |||||||
\(132\) | 2.00000 | + | 3.46410i | 0.174078 | + | 0.301511i | ||||
\(133\) | −3.27492 | − | 5.67232i | −0.283971 | − | 0.491853i | ||||
\(134\) | 1.36254 | − | 2.35999i | 0.117706 | − | 0.203872i | ||||
\(135\) | 4.27492 | 0.367926 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | −11.4124 | + | 19.7668i | −0.975025 | + | 1.68879i | −0.295173 | + | 0.955444i | \(0.595377\pi\) |
−0.679852 | + | 0.733349i | \(0.737956\pi\) | |||||||
\(138\) | −5.27492 | −0.449031 | ||||||||
\(139\) | 4.54983 | − | 7.88054i | 0.385912 | − | 0.668419i | −0.605983 | − | 0.795477i | \(-0.707220\pi\) |
0.991895 | + | 0.127058i | \(0.0405535\pi\) | |||||||
\(140\) | −2.13746 | − | 3.70219i | −0.180648 | − | 0.312892i | ||||
\(141\) | 3.27492 | + | 5.67232i | 0.275798 | + | 0.477696i | ||||
\(142\) | 5.27492 | 0.442661 | ||||||||
\(143\) | 10.0000 | + | 10.3923i | 0.836242 | + | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −17.6873 | − | 30.6353i | −1.46885 | − | 2.54412i | ||||
\(146\) | −2.86254 | − | 4.95807i | −0.236906 | − | 0.410333i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | 0.274917 | 0.0225981 | ||||||||
\(149\) | 0.500000 | − | 0.866025i | 0.0409616 | − | 0.0709476i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) |
0.885779 | + | 0.464107i | \(0.153625\pi\) | |||||||
\(150\) | −6.63746 | + | 11.4964i | −0.541946 | + | 0.938678i | ||||
\(151\) | 13.0997 | 1.06604 | 0.533018 | − | 0.846104i | \(-0.321058\pi\) | ||||
0.533018 | + | 0.846104i | \(0.321058\pi\) | |||||||
\(152\) | −3.27492 | + | 5.67232i | −0.265631 | + | 0.460086i | ||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | 2.00000 | + | 3.46410i | 0.161165 | + | 0.279145i | ||||
\(155\) | −5.45017 | −0.437768 | ||||||||
\(156\) | 3.50000 | − | 0.866025i | 0.280224 | − | 0.0693375i | ||||
\(157\) | −3.72508 | −0.297294 | −0.148647 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148647 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(158\) | 4.00000 | + | 6.92820i | 0.318223 | + | 0.551178i | ||||
\(159\) | 1.77492 | + | 3.07425i | 0.140760 | + | 0.243804i | ||||
\(160\) | −2.13746 | + | 3.70219i | −0.168981 | + | 0.292684i | ||||
\(161\) | −5.27492 | −0.415722 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 6.63746 | − | 11.4964i | 0.519886 | − | 0.900469i | −0.479847 | − | 0.877352i | \(-0.659308\pi\) |
0.999733 | − | 0.0231165i | \(-0.00735887\pi\) | |||||||
\(164\) | 8.27492 | 0.646162 | ||||||||
\(165\) | 8.54983 | − | 14.8087i | 0.665604 | − | 1.15286i | ||||
\(166\) | 5.91238 | + | 10.2405i | 0.458889 | + | 0.794820i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | 12.8248 | 0.983614 | ||||||||
\(171\) | −3.27492 | − | 5.67232i | −0.250439 | − | 0.433773i | ||||
\(172\) | 5.91238 | + | 10.2405i | 0.450814 | + | 0.780833i | ||||
\(173\) | 2.27492 | − | 3.94027i | 0.172959 | − | 0.299573i | −0.766494 | − | 0.642251i | \(-0.778001\pi\) |
0.939453 | + | 0.342678i | \(0.111334\pi\) | |||||||
\(174\) | 8.27492 | 0.627320 | ||||||||
\(175\) | −6.63746 | + | 11.4964i | −0.501745 | + | 0.869047i | ||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | −11.8248 | −0.888803 | ||||||||
\(178\) | −0.362541 | + | 0.627940i | −0.0271736 | + | 0.0470661i | ||||
\(179\) | −0.725083 | − | 1.25588i | −0.0541952 | − | 0.0938689i | 0.837655 | − | 0.546200i | \(-0.183926\pi\) |
−0.891850 | + | 0.452331i | \(0.850593\pi\) | |||||||
\(180\) | −2.13746 | − | 3.70219i | −0.159317 | − | 0.275945i | ||||
\(181\) | −16.8248 | −1.25057 | −0.625287 | − | 0.780395i | \(-0.715018\pi\) | ||||
−0.625287 | + | 0.780395i | \(0.715018\pi\) | |||||||
\(182\) | 3.50000 | − | 0.866025i | 0.259437 | − | 0.0641941i | ||||
\(183\) | −9.00000 | −0.665299 | ||||||||
\(184\) | 2.63746 | + | 4.56821i | 0.194436 | + | 0.336773i | ||||
\(185\) | −0.587624 | − | 1.01779i | −0.0432030 | − | 0.0748298i | ||||
\(186\) | 0.637459 | − | 1.10411i | 0.0467407 | − | 0.0809573i | ||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 3.27492 | − | 5.67232i | 0.238848 | − | 0.413697i | ||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | 28.0000 | 2.03133 | ||||||||
\(191\) | −3.36254 | + | 5.82409i | −0.243305 | + | 0.421417i | −0.961654 | − | 0.274267i | \(-0.911565\pi\) |
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 12.4124 | + | 21.4989i | 0.893462 | + | 1.54752i | 0.835696 | + | 0.549192i | \(0.185064\pi\) |
0.0577662 | + | 0.998330i | \(0.481602\pi\) | |||||||
\(194\) | −0.549834 | −0.0394758 | ||||||||
\(195\) | −10.6873 | − | 11.1066i | −0.765333 | − | 0.795357i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.9124 | + | 18.9008i | 0.777475 | + | 1.34663i | 0.933393 | + | 0.358856i | \(0.116833\pi\) |
−0.155919 | + | 0.987770i | \(0.549834\pi\) | |||||||
\(198\) | 2.00000 | + | 3.46410i | 0.142134 | + | 0.246183i | ||||
\(199\) | −5.91238 | + | 10.2405i | −0.419117 | + | 0.725932i | −0.995851 | − | 0.0909999i | \(-0.970994\pi\) |
0.576734 | + | 0.816932i | \(0.304327\pi\) | |||||||
\(200\) | 13.2749 | 0.938678 | ||||||||
\(201\) | 1.36254 | − | 2.35999i | 0.0961063 | − | 0.166461i | ||||
\(202\) | −0.862541 | + | 1.49397i | −0.0606882 | + | 0.105115i | ||||
\(203\) | 8.27492 | 0.580785 | ||||||||
\(204\) | −1.50000 | + | 2.59808i | −0.105021 | + | 0.181902i | ||||
\(205\) | −17.6873 | − | 30.6353i | −1.23533 | − | 2.13966i | ||||
\(206\) | −2.63746 | − | 4.56821i | −0.183760 | − | 0.318282i | ||||
\(207\) | −5.27492 | −0.366632 | ||||||||
\(208\) | −2.50000 | − | 2.59808i | −0.173344 | − | 0.180144i | ||||
\(209\) | −26.1993 | −1.81225 | ||||||||
\(210\) | −2.13746 | − | 3.70219i | −0.147499 | − | 0.255475i | ||||
\(211\) | −10.5498 | − | 18.2728i | −0.726281 | − | 1.25795i | −0.958445 | − | 0.285278i | \(-0.907914\pi\) |
0.232164 | − | 0.972677i | \(-0.425419\pi\) | |||||||
\(212\) | 1.77492 | − | 3.07425i | 0.121902 | − | 0.211140i | ||||
\(213\) | 5.27492 | 0.361431 | ||||||||
\(214\) | −1.27492 | + | 2.20822i | −0.0871515 | + | 0.150951i | ||||
\(215\) | 25.2749 | − | 43.7774i | 1.72374 | − | 2.98560i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.637459 | − | 1.10411i | 0.0432735 | − | 0.0749519i | ||||
\(218\) | 2.27492 | + | 3.94027i | 0.154077 | + | 0.266869i | ||||
\(219\) | −2.86254 | − | 4.95807i | −0.193433 | − | 0.335035i | ||||
\(220\) | −17.0997 | −1.15286 | ||||||||
\(221\) | −3.00000 | + | 10.3923i | −0.201802 | + | 0.699062i | ||||
\(222\) | 0.274917 | 0.0184512 | ||||||||
\(223\) | −5.36254 | − | 9.28819i | −0.359102 | − | 0.621983i | 0.628709 | − | 0.777641i | \(-0.283584\pi\) |
−0.987811 | + | 0.155657i | \(0.950250\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | −6.63746 | + | 11.4964i | −0.442497 | + | 0.766428i | ||||
\(226\) | 14.8248 | 0.986128 | ||||||||
\(227\) | 10.5498 | − | 18.2728i | 0.700217 | − | 1.21281i | −0.268173 | − | 0.963371i | \(-0.586420\pi\) |
0.968390 | − | 0.249441i | \(-0.0802468\pi\) | |||||||
\(228\) | −3.27492 | + | 5.67232i | −0.216887 | + | 0.375659i | ||||
\(229\) | 12.7251 | 0.840897 | 0.420449 | − | 0.907316i | \(-0.361873\pi\) | ||||
0.420449 | + | 0.907316i | \(0.361873\pi\) | |||||||
\(230\) | 11.2749 | − | 19.5287i | 0.743446 | − | 1.28769i | ||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | −4.13746 | − | 7.16629i | −0.271637 | − | 0.470490i | ||||
\(233\) | 7.45017 | 0.488077 | 0.244038 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244038 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(234\) | 3.50000 | − | 0.866025i | 0.228802 | − | 0.0566139i | ||||
\(235\) | −28.0000 | −1.82652 | ||||||||
\(236\) | 5.91238 | + | 10.2405i | 0.384863 | + | 0.666602i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | −1.50000 | + | 2.59808i | −0.0972306 | + | 0.168408i | ||||
\(239\) | −5.27492 | −0.341206 | −0.170603 | − | 0.985340i | \(-0.554572\pi\) | ||||
−0.170603 | + | 0.985340i | \(0.554572\pi\) | |||||||
\(240\) | −2.13746 | + | 3.70219i | −0.137972 | + | 0.238975i | ||||
\(241\) | 7.86254 | − | 13.6183i | 0.506471 | − | 0.877233i | −0.493501 | − | 0.869745i | \(-0.664283\pi\) |
0.999972 | − | 0.00748804i | \(-0.00238354\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 4.50000 | + | 7.79423i | 0.288083 | + | 0.498974i | ||||
\(245\) | −2.13746 | − | 3.70219i | −0.136557 | − | 0.236524i | ||||
\(246\) | 8.27492 | 0.527589 | ||||||||
\(247\) | −6.54983 | + | 22.6893i | −0.416756 | + | 1.44369i | ||||
\(248\) | −1.27492 | −0.0809573 | ||||||||
\(249\) | 5.91238 | + | 10.2405i | 0.374682 | + | 0.648968i | ||||
\(250\) | −17.6873 | − | 30.6353i | −1.11864 | − | 1.93755i | ||||
\(251\) | −6.63746 | + | 11.4964i | −0.418953 | + | 0.725647i | −0.995834 | − | 0.0911804i | \(-0.970936\pi\) |
0.576882 | + | 0.816828i | \(0.304269\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −10.5498 | + | 18.2728i | −0.663262 | + | 1.14880i | ||||
\(254\) | −4.00000 | + | 6.92820i | −0.250982 | + | 0.434714i | ||||
\(255\) | 12.8248 | 0.803117 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | 5.91238 | + | 10.2405i | 0.368088 | + | 0.637548i | ||||
\(259\) | 0.274917 | 0.0170825 | ||||||||
\(260\) | −4.27492 | + | 14.8087i | −0.265119 | + | 0.918400i | ||||
\(261\) | 8.27492 | 0.512205 | ||||||||
\(262\) | 1.36254 | + | 2.35999i | 0.0841781 | + | 0.145801i | ||||
\(263\) | −10.5498 | − | 18.2728i | −0.650531 | − | 1.12675i | −0.982994 | − | 0.183636i | \(-0.941213\pi\) |
0.332464 | − | 0.943116i | \(-0.392120\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | −15.1752 | −0.932208 | ||||||||
\(266\) | −3.27492 | + | 5.67232i | −0.200798 | + | 0.347792i | ||||
\(267\) | −0.362541 | + | 0.627940i | −0.0221872 | + | 0.0384293i | ||||
\(268\) | −2.72508 | −0.166461 | ||||||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | −2.13746 | − | 3.70219i | −0.130082 | − | 0.225308i | ||||
\(271\) | −12.6375 | − | 21.8887i | −0.767671 | − | 1.32965i | −0.938823 | − | 0.344400i | \(-0.888082\pi\) |
0.171152 | − | 0.985245i | \(-0.445251\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 3.50000 | − | 0.866025i | 0.211830 | − | 0.0524142i | ||||
\(274\) | 22.8248 | 1.37889 | ||||||||
\(275\) | 26.5498 | + | 45.9857i | 1.60102 | + | 2.77304i | ||||
\(276\) | 2.63746 | + | 4.56821i | 0.158756 | + | 0.274974i | ||||
\(277\) | −7.41238 | + | 12.8386i | −0.445366 | + | 0.771397i | −0.998078 | − | 0.0619755i | \(-0.980260\pi\) |
0.552711 | + | 0.833373i | \(0.313593\pi\) | |||||||
\(278\) | −9.09967 | −0.545762 | ||||||||
\(279\) | 0.637459 | − | 1.10411i | 0.0381636 | − | 0.0661014i | ||||
\(280\) | −2.13746 | + | 3.70219i | −0.127738 | + | 0.221248i | ||||
\(281\) | −20.8248 | −1.24230 | −0.621150 | − | 0.783691i | \(-0.713334\pi\) | ||||
−0.621150 | + | 0.783691i | \(0.713334\pi\) | |||||||
\(282\) | 3.27492 | − | 5.67232i | 0.195018 | − | 0.337782i | ||||
\(283\) | 4.72508 | + | 8.18408i | 0.280877 | + | 0.486493i | 0.971601 | − | 0.236625i | \(-0.0760414\pi\) |
−0.690724 | + | 0.723119i | \(0.742708\pi\) | |||||||
\(284\) | −2.63746 | − | 4.56821i | −0.156504 | − | 0.271074i | ||||
\(285\) | 28.0000 | 1.65858 | ||||||||
\(286\) | 4.00000 | − | 13.8564i | 0.236525 | − | 0.819346i | ||||
\(287\) | 8.27492 | 0.488453 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −17.6873 | + | 30.6353i | −1.03863 | + | 1.79897i | ||||
\(291\) | −0.549834 | −0.0322319 | ||||||||
\(292\) | −2.86254 | + | 4.95807i | −0.167518 | + | 0.290149i | ||||
\(293\) | 9.13746 | − | 15.8265i | 0.533816 | − | 0.924596i | −0.465404 | − | 0.885099i | \(-0.654091\pi\) |
0.999220 | − | 0.0394979i | \(-0.0125759\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 25.2749 | − | 43.7774i | 1.47156 | − | 2.54882i | ||||
\(296\) | −0.137459 | − | 0.238085i | −0.00798962 | − | 0.0138384i | ||||
\(297\) | 2.00000 | + | 3.46410i | 0.116052 | + | 0.201008i | ||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 13.1873 | + | 13.7046i | 0.762641 | + | 0.792560i | ||||
\(300\) | 13.2749 | 0.766428 | ||||||||
\(301\) | 5.91238 | + | 10.2405i | 0.340784 | + | 0.590255i | ||||
\(302\) | −6.54983 | − | 11.3446i | −0.376901 | − | 0.652811i | ||||
\(303\) | −0.862541 | + | 1.49397i | −0.0495517 | + | 0.0858261i | ||||
\(304\) | 6.54983 | 0.375659 | ||||||||
\(305\) | 19.2371 | − | 33.3197i | 1.10151 | − | 1.90788i | ||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | −1.45017 | −0.0827653 | −0.0413827 | − | 0.999143i | \(-0.513176\pi\) | ||||
−0.0413827 | + | 0.999143i | \(0.513176\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | −2.63746 | − | 4.56821i | −0.150040 | − | 0.259877i | ||||
\(310\) | 2.72508 | + | 4.71998i | 0.154774 | + | 0.268077i | ||||
\(311\) | −2.54983 | −0.144588 | −0.0722939 | − | 0.997383i | \(-0.523032\pi\) | ||||
−0.0722939 | + | 0.997383i | \(0.523032\pi\) | |||||||
\(312\) | −2.50000 | − | 2.59808i | −0.141535 | − | 0.147087i | ||||
\(313\) | 17.6495 | 0.997609 | 0.498804 | − | 0.866715i | \(-0.333773\pi\) | ||||
0.498804 | + | 0.866715i | \(0.333773\pi\) | |||||||
\(314\) | 1.86254 | + | 3.22602i | 0.105109 | + | 0.182055i | ||||
\(315\) | −2.13746 | − | 3.70219i | −0.120432 | − | 0.208595i | ||||
\(316\) | 4.00000 | − | 6.92820i | 0.225018 | − | 0.389742i | ||||
\(317\) | −7.54983 | −0.424041 | −0.212020 | − | 0.977265i | \(-0.568004\pi\) | ||||
−0.212020 | + | 0.977265i | \(0.568004\pi\) | |||||||
\(318\) | 1.77492 | − | 3.07425i | 0.0995324 | − | 0.172395i | ||||
\(319\) | 16.5498 | − | 28.6652i | 0.926613 | − | 1.60494i | ||||
\(320\) | 4.27492 | 0.238975 | ||||||||
\(321\) | −1.27492 | + | 2.20822i | −0.0711589 | + | 0.123251i | ||||
\(322\) | 2.63746 | + | 4.56821i | 0.146980 | + | 0.254577i | ||||
\(323\) | −9.82475 | − | 17.0170i | −0.546664 | − | 0.946849i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 46.4622 | − | 11.4964i | 2.57726 | − | 0.637706i | ||||
\(326\) | −13.2749 | −0.735230 | ||||||||
\(327\) | 2.27492 | + | 3.94027i | 0.125803 | + | 0.217898i | ||||
\(328\) | −4.13746 | − | 7.16629i | −0.228453 | − | 0.395692i | ||||
\(329\) | 3.27492 | − | 5.67232i | 0.180552 | − | 0.312725i | ||||
\(330\) | −17.0997 | −0.941306 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 5.91238 | − | 10.2405i | 0.324484 | − | 0.562022i | ||||
\(333\) | 0.274917 | 0.0150654 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.82475 | + | 10.0888i | 0.318240 | + | 0.551208i | ||||
\(336\) | −0.500000 | − | 0.866025i | −0.0272772 | − | 0.0472456i | ||||
\(337\) | 0.274917 | 0.0149757 | 0.00748785 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748785 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(338\) | −11.0000 | − | 6.92820i | −0.598321 | − | 0.376845i | ||||
\(339\) | 14.8248 | 0.805170 | ||||||||
\(340\) | −6.41238 | − | 11.1066i | −0.347760 | − | 0.602338i | ||||
\(341\) | −2.54983 | − | 4.41644i | −0.138081 | − | 0.239164i | ||||
\(342\) | −3.27492 | + | 5.67232i | −0.177087 | + | 0.306724i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.91238 | − | 10.2405i | 0.318774 | − | 0.552133i | ||||
\(345\) | 11.2749 | − | 19.5287i | 0.607021 | − | 1.05139i | ||||
\(346\) | −4.54983 | −0.244601 | ||||||||
\(347\) | −15.2749 | + | 26.4569i | −0.820001 | + | 1.42028i | 0.0856804 | + | 0.996323i | \(0.472694\pi\) |
−0.905681 | + | 0.423960i | \(0.860640\pi\) | |||||||
\(348\) | −4.13746 | − | 7.16629i | −0.221791 | − | 0.384153i | ||||
\(349\) | 17.4622 | + | 30.2454i | 0.934731 | + | 1.61900i | 0.775113 | + | 0.631822i | \(0.217693\pi\) |
0.159617 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(350\) | 13.2749 | 0.709574 | ||||||||
\(351\) | 3.50000 | − | 0.866025i | 0.186816 | − | 0.0462250i | ||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | 9.77492 | + | 16.9307i | 0.520266 | + | 0.901128i | 0.999722 | + | 0.0235618i | \(0.00750066\pi\) |
−0.479456 | + | 0.877566i | \(0.659166\pi\) | |||||||
\(354\) | 5.91238 | + | 10.2405i | 0.314239 | + | 0.544278i | ||||
\(355\) | −11.2749 | + | 19.5287i | −0.598410 | + | 1.03648i | ||||
\(356\) | 0.725083 | 0.0384293 | ||||||||
\(357\) | −1.50000 | + | 2.59808i | −0.0793884 | + | 0.137505i | ||||
\(358\) | −0.725083 | + | 1.25588i | −0.0383218 | + | 0.0663753i | ||||
\(359\) | −1.09967 | −0.0580383 | −0.0290192 | − | 0.999579i | \(-0.509238\pi\) | ||||
−0.0290192 | + | 0.999579i | \(0.509238\pi\) | |||||||
\(360\) | −2.13746 | + | 3.70219i | −0.112654 | + | 0.195122i | ||||
\(361\) | −11.9502 | − | 20.6983i | −0.628956 | − | 1.08938i | ||||
\(362\) | 8.41238 | + | 14.5707i | 0.442145 | + | 0.765817i | ||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | −2.50000 | − | 2.59808i | −0.131036 | − | 0.136176i | ||||
\(365\) | 24.4743 | 1.28104 | ||||||||
\(366\) | 4.50000 | + | 7.79423i | 0.235219 | + | 0.407411i | ||||
\(367\) | −6.63746 | − | 11.4964i | −0.346473 | − | 0.600108i | 0.639148 | − | 0.769084i | \(-0.279287\pi\) |
−0.985620 | + | 0.168976i | \(0.945954\pi\) | |||||||
\(368\) | 2.63746 | − | 4.56821i | 0.137487 | − | 0.238135i | ||||
\(369\) | 8.27492 | 0.430775 | ||||||||
\(370\) | −0.587624 | + | 1.01779i | −0.0305491 | + | 0.0529126i | ||||
\(371\) | 1.77492 | − | 3.07425i | 0.0921491 | − | 0.159607i | ||||
\(372\) | −1.27492 | −0.0661014 | ||||||||
\(373\) | −13.4124 | + | 23.2309i | −0.694466 | + | 1.20285i | 0.275894 | + | 0.961188i | \(0.411026\pi\) |
−0.970360 | + | 0.241663i | \(0.922307\pi\) | |||||||
\(374\) | 6.00000 | + | 10.3923i | 0.310253 | + | 0.537373i | ||||
\(375\) | −17.6873 | − | 30.6353i | −0.913368 | − | 1.58200i | ||||
\(376\) | −6.54983 | −0.337782 | ||||||||
\(377\) | −20.6873 | − | 21.4989i | −1.06545 | − | 1.10725i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 10.0000 | + | 17.3205i | 0.513665 | + | 0.889695i | 0.999874 | + | 0.0158521i | \(0.00504609\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(380\) | −14.0000 | − | 24.2487i | −0.718185 | − | 1.24393i | ||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | 6.72508 | 0.344085 | ||||||||
\(383\) | −11.0997 | + | 19.2252i | −0.567167 | + | 0.982361i | 0.429678 | + | 0.902982i | \(0.358627\pi\) |
−0.996844 | + | 0.0793791i | \(0.974706\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −17.0997 | −0.871480 | ||||||||
\(386\) | 12.4124 | − | 21.4989i | 0.631773 | − | 1.09426i | ||||
\(387\) | 5.91238 | + | 10.2405i | 0.300543 | + | 0.520556i | ||||
\(388\) | 0.274917 | + | 0.476171i | 0.0139568 | + | 0.0241739i | ||||
\(389\) | −24.6495 | −1.24978 | −0.624890 | − | 0.780713i | \(-0.714856\pi\) | ||||
−0.624890 | + | 0.780713i | \(0.714856\pi\) | |||||||
\(390\) | −4.27492 | + | 14.8087i | −0.216469 | + | 0.749870i | ||||
\(391\) | −15.8248 | −0.800292 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | 1.36254 | + | 2.35999i | 0.0687311 | + | 0.119046i | ||||
\(394\) | 10.9124 | − | 18.9008i | 0.549758 | − | 0.952208i | ||||
\(395\) | −34.1993 | −1.72076 | ||||||||
\(396\) | 2.00000 | − | 3.46410i | 0.100504 | − | 0.174078i | ||||
\(397\) | −11.6375 | + | 20.1567i | −0.584067 | + | 1.01163i | 0.410924 | + | 0.911670i | \(0.365206\pi\) |
−0.994991 | + | 0.0999645i | \(0.968127\pi\) | |||||||
\(398\) | 11.8248 | 0.592721 | ||||||||
\(399\) | −3.27492 | + | 5.67232i | −0.163951 | + | 0.283971i | ||||
\(400\) | −6.63746 | − | 11.4964i | −0.331873 | − | 0.574821i | ||||
\(401\) | 1.13746 | + | 1.97014i | 0.0568020 | + | 0.0983839i | 0.893028 | − | 0.450001i | \(-0.148576\pi\) |
−0.836226 | + | 0.548385i | \(0.815243\pi\) | |||||||
\(402\) | −2.72508 | −0.135915 | ||||||||
\(403\) | −4.46221 | + | 1.10411i | −0.222279 | + | 0.0549997i | ||||
\(404\) | 1.72508 | 0.0858261 | ||||||||
\(405\) | −2.13746 | − | 3.70219i | −0.106211 | − | 0.183963i | ||||
\(406\) | −4.13746 | − | 7.16629i | −0.205339 | − | 0.355657i | ||||
\(407\) | 0.549834 | − | 0.952341i | 0.0272543 | − | 0.0472058i | ||||
\(408\) | 3.00000 | 0.148522 | ||||||||
\(409\) | 14.9622 | − | 25.9153i | 0.739834 | − | 1.28143i | −0.212736 | − | 0.977110i | \(-0.568238\pi\) |
0.952570 | − | 0.304320i | \(-0.0984292\pi\) | |||||||
\(410\) | −17.6873 | + | 30.6353i | −0.873513 | + | 1.51297i | ||||
\(411\) | 22.8248 | 1.12586 | ||||||||
\(412\) | −2.63746 | + | 4.56821i | −0.129938 | + | 0.225060i | ||||
\(413\) | 5.91238 | + | 10.2405i | 0.290929 | + | 0.503904i | ||||
\(414\) | 2.63746 | + | 4.56821i | 0.129624 | + | 0.224515i | ||||
\(415\) | −50.5498 | −2.48139 | ||||||||
\(416\) | −1.00000 | + | 3.46410i | −0.0490290 | + | 0.169842i | ||||
\(417\) | −9.09967 | −0.445613 | ||||||||
\(418\) | 13.0997 | + | 22.6893i | 0.640726 | + | 1.10977i | ||||
\(419\) | 11.1873 | + | 19.3770i | 0.546535 | + | 0.946626i | 0.998509 | + | 0.0545951i | \(0.0173868\pi\) |
−0.451974 | + | 0.892031i | \(0.649280\pi\) | |||||||
\(420\) | −2.13746 | + | 3.70219i | −0.104297 | + | 0.180648i | ||||
\(421\) | 8.27492 | 0.403295 | 0.201647 | − | 0.979458i | \(-0.435370\pi\) | ||||
0.201647 | + | 0.979458i | \(0.435370\pi\) | |||||||
\(422\) | −10.5498 | + | 18.2728i | −0.513558 | + | 0.889508i | ||||
\(423\) | 3.27492 | − | 5.67232i | 0.159232 | − | 0.275798i | ||||
\(424\) | −3.54983 | −0.172395 | ||||||||
\(425\) | −19.9124 | + | 34.4892i | −0.965892 | + | 1.67297i | ||||
\(426\) | −2.63746 | − | 4.56821i | −0.127785 | − | 0.221331i | ||||
\(427\) | 4.50000 | + | 7.79423i | 0.217770 | + | 0.377189i | ||||
\(428\) | 2.54983 | 0.123251 | ||||||||
\(429\) | 4.00000 | − | 13.8564i | 0.193122 | − | 0.668994i | ||||
\(430\) | −50.5498 | −2.43773 | ||||||||
\(431\) | 6.63746 | + | 11.4964i | 0.319715 | + | 0.553763i | 0.980429 | − | 0.196875i | \(-0.0630795\pi\) |
−0.660713 | + | 0.750638i | \(0.729746\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 5.13746 | − | 8.89834i | 0.246891 | − | 0.427627i | −0.715771 | − | 0.698335i | \(-0.753925\pi\) |
0.962661 | + | 0.270708i | \(0.0872579\pi\) | |||||||
\(434\) | −1.27492 | −0.0611980 | ||||||||
\(435\) | −17.6873 | + | 30.6353i | −0.848041 | + | 1.46885i | ||||
\(436\) | 2.27492 | − | 3.94027i | 0.108949 | − | 0.188705i | ||||
\(437\) | −34.5498 | −1.65274 | ||||||||
\(438\) | −2.86254 | + | 4.95807i | −0.136778 | + | 0.236906i | ||||
\(439\) | −6.54983 | − | 11.3446i | −0.312607 | − | 0.541450i | 0.666319 | − | 0.745667i | \(-0.267869\pi\) |
−0.978926 | + | 0.204216i | \(0.934535\pi\) | |||||||
\(440\) | 8.54983 | + | 14.8087i | 0.407597 | + | 0.705979i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 10.5000 | − | 2.59808i | 0.499434 | − | 0.123578i | ||||
\(443\) | 34.5498 | 1.64151 | 0.820756 | − | 0.571279i | \(-0.193552\pi\) | ||||
0.820756 | + | 0.571279i | \(0.193552\pi\) | |||||||
\(444\) | −0.137459 | − | 0.238085i | −0.00652350 | − | 0.0112990i | ||||
\(445\) | −1.54983 | − | 2.68439i | −0.0734692 | − | 0.127252i | ||||
\(446\) | −5.36254 | + | 9.28819i | −0.253924 | + | 0.439809i | ||||
\(447\) | −1.00000 | −0.0472984 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | 9.54983 | − | 16.5408i | 0.450685 | − | 0.780609i | −0.547744 | − | 0.836646i | \(-0.684513\pi\) |
0.998429 | + | 0.0560374i | \(0.0178466\pi\) | |||||||
\(450\) | 13.2749 | 0.625786 | ||||||||
\(451\) | 16.5498 | − | 28.6652i | 0.779301 | − | 1.34979i | ||||
\(452\) | −7.41238 | − | 12.8386i | −0.348649 | − | 0.603877i | ||||
\(453\) | −6.54983 | − | 11.3446i | −0.307738 | − | 0.533018i | ||||
\(454\) | −21.0997 | −0.990257 | ||||||||
\(455\) | −4.27492 | + | 14.8087i | −0.200411 | + | 0.694245i | ||||
\(456\) | 6.54983 | 0.306724 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | −6.36254 | − | 11.0202i | −0.297302 | − | 0.514942i | ||||
\(459\) | −1.50000 | + | 2.59808i | −0.0700140 | + | 0.121268i | ||||
\(460\) | −22.5498 | −1.05139 | ||||||||
\(461\) | 9.68729 | − | 16.7789i | 0.451182 | − | 0.781471i | −0.547278 | − | 0.836951i | \(-0.684336\pi\) |
0.998460 | + | 0.0554807i | \(0.0176691\pi\) | |||||||
\(462\) | 2.00000 | − | 3.46410i | 0.0930484 | − | 0.161165i | ||||
\(463\) | −10.5498 | −0.490292 | −0.245146 | − | 0.969486i | \(-0.578836\pi\) | ||||
−0.245146 | + | 0.969486i | \(0.578836\pi\) | |||||||
\(464\) | −4.13746 | + | 7.16629i | −0.192077 | + | 0.332687i | ||||
\(465\) | 2.72508 | + | 4.71998i | 0.126373 | + | 0.218884i | ||||
\(466\) | −3.72508 | − | 6.45203i | −0.172561 | − | 0.298885i | ||||
\(467\) | −8.17525 | −0.378305 | −0.189153 | − | 0.981948i | \(-0.560574\pi\) | ||||
−0.189153 | + | 0.981948i | \(0.560574\pi\) | |||||||
\(468\) | −2.50000 | − | 2.59808i | −0.115563 | − | 0.120096i | ||||
\(469\) | −2.72508 | −0.125833 | ||||||||
\(470\) | 14.0000 | + | 24.2487i | 0.645772 | + | 1.11851i | ||||
\(471\) | 1.86254 | + | 3.22602i | 0.0858214 | + | 0.148647i | ||||
\(472\) | 5.91238 | − | 10.2405i | 0.272139 | − | 0.471359i | ||||
\(473\) | 47.2990 | 2.17481 | ||||||||
\(474\) | 4.00000 | − | 6.92820i | 0.183726 | − | 0.318223i | ||||
\(475\) | −43.4743 | + | 75.2996i | −1.99474 | + | 3.45498i | ||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | 1.77492 | − | 3.07425i | 0.0812679 | − | 0.140760i | ||||
\(478\) | 2.63746 | + | 4.56821i | 0.120635 | + | 0.208945i | ||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | 4.27492 | 0.195122 | ||||||||
\(481\) | −0.687293 | − | 0.714256i | −0.0313379 | − | 0.0325673i | ||||
\(482\) | −15.7251 | −0.716258 | ||||||||
\(483\) | 2.63746 | + | 4.56821i | 0.120009 | + | 0.207861i | ||||
\(484\) | −2.50000 | − | 4.33013i | −0.113636 | − | 0.196824i | ||||
\(485\) | 1.17525 | − | 2.03559i | 0.0533653 | − | 0.0924314i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 0.549834 | − | 0.952341i | 0.0249154 | − | 0.0431547i | −0.853299 | − | 0.521422i | \(-0.825402\pi\) |
0.878214 | + | 0.478267i | \(0.158735\pi\) | |||||||
\(488\) | 4.50000 | − | 7.79423i | 0.203705 | − | 0.352828i | ||||
\(489\) | −13.2749 | −0.600313 | ||||||||
\(490\) | −2.13746 | + | 3.70219i | −0.0965605 | + | 0.167248i | ||||
\(491\) | −12.5498 | − | 21.7370i | −0.566366 | − | 0.980975i | −0.996921 | − | 0.0784105i | \(-0.975016\pi\) |
0.430555 | − | 0.902564i | \(-0.358318\pi\) | |||||||
\(492\) | −4.13746 | − | 7.16629i | −0.186531 | − | 0.323081i | ||||
\(493\) | 24.8248 | 1.11805 | ||||||||
\(494\) | 22.9244 | − | 5.67232i | 1.03142 | − | 0.255210i | ||||
\(495\) | −17.0997 | −0.768573 | ||||||||
\(496\) | 0.637459 | + | 1.10411i | 0.0286227 | + | 0.0495760i | ||||
\(497\) | −2.63746 | − | 4.56821i | −0.118306 | − | 0.204912i | ||||
\(498\) | 5.91238 | − | 10.2405i | 0.264940 | − | 0.458889i | ||||
\(499\) | −31.8248 | −1.42467 | −0.712336 | − | 0.701839i | \(-0.752363\pi\) | ||||
−0.712336 | + | 0.701839i | \(0.752363\pi\) | |||||||
\(500\) | −17.6873 | + | 30.6353i | −0.791000 | + | 1.37005i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.2749 | 0.592489 | ||||||||
\(503\) | 10.5498 | − | 18.2728i | 0.470394 | − | 0.814746i | −0.529033 | − | 0.848601i | \(-0.677445\pi\) |
0.999427 | + | 0.0338552i | \(0.0107785\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | −3.68729 | − | 6.38658i | −0.164082 | − | 0.284199i | ||||
\(506\) | 21.0997 | 0.937995 | ||||||||
\(507\) | −11.0000 | − | 6.92820i | −0.488527 | − | 0.307692i | ||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | 6.58762 | + | 11.4101i | 0.291991 | + | 0.505744i | 0.974281 | − | 0.225339i | \(-0.0723488\pi\) |
−0.682289 | + | 0.731082i | \(0.739015\pi\) | |||||||
\(510\) | −6.41238 | − | 11.1066i | −0.283945 | − | 0.491807i | ||||
\(511\) | −2.86254 | + | 4.95807i | −0.126631 | + | 0.219332i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.27492 | + | 5.67232i | −0.144591 | + | 0.250439i | ||||
\(514\) | −7.50000 | + | 12.9904i | −0.330811 | + | 0.572981i | ||||
\(515\) | 22.5498 | 0.993664 | ||||||||
\(516\) | 5.91238 | − | 10.2405i | 0.260278 | − | 0.450814i | ||||
\(517\) | −13.0997 | − | 22.6893i | −0.576123 | − | 0.997874i | ||||
\(518\) | −0.137459 | − | 0.238085i | −0.00603958 | − | 0.0104609i | ||||
\(519\) | −4.54983 | −0.199716 | ||||||||
\(520\) | 14.9622 | − | 3.70219i | 0.656136 | − | 0.162352i | ||||
\(521\) | −20.8248 | −0.912349 | −0.456174 | − | 0.889890i | \(-0.650781\pi\) | ||||
−0.456174 | + | 0.889890i | \(0.650781\pi\) | |||||||
\(522\) | −4.13746 | − | 7.16629i | −0.181092 | − | 0.313660i | ||||
\(523\) | 13.0997 | + | 22.6893i | 0.572809 | + | 0.992133i | 0.996276 | + | 0.0862221i | \(0.0274795\pi\) |
−0.423467 | + | 0.905911i | \(0.639187\pi\) | |||||||
\(524\) | 1.36254 | − | 2.35999i | 0.0595229 | − | 0.103097i | ||||
\(525\) | 13.2749 | 0.579365 | ||||||||
\(526\) | −10.5498 | + | 18.2728i | −0.459995 | + | 0.796734i | ||||
\(527\) | 1.91238 | − | 3.31233i | 0.0833044 | − | 0.144287i | ||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | −2.41238 | + | 4.17836i | −0.104886 | + | 0.181668i | ||||
\(530\) | 7.58762 | + | 13.1422i | 0.329585 | + | 0.570859i | ||||
\(531\) | 5.91238 | + | 10.2405i | 0.256575 | + | 0.444401i | ||||
\(532\) | 6.54983 | 0.283971 | ||||||||
\(533\) | −20.6873 | − | 21.4989i | −0.896066 | − | 0.931219i | ||||
\(534\) | 0.725083 | 0.0313774 | ||||||||
\(535\) | −5.45017 | − | 9.43996i | −0.235631 | − | 0.408125i | ||||
\(536\) | 1.36254 | + | 2.35999i | 0.0588528 | + | 0.101936i | ||||
\(537\) | −0.725083 | + | 1.25588i | −0.0312896 | + | 0.0541952i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 2.00000 | − | 3.46410i | 0.0861461 | − | 0.149209i | ||||
\(540\) | −2.13746 | + | 3.70219i | −0.0919816 | + | 0.159317i | ||||
\(541\) | 25.3746 | 1.09094 | 0.545469 | − | 0.838131i | \(-0.316351\pi\) | ||||
0.545469 | + | 0.838131i | \(0.316351\pi\) | |||||||
\(542\) | −12.6375 | + | 21.8887i | −0.542825 | + | 0.940201i | ||||
\(543\) | 8.41238 | + | 14.5707i | 0.361010 | + | 0.625287i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | −19.4502 | −0.833154 | ||||||||
\(546\) | −2.50000 | − | 2.59808i | −0.106990 | − | 0.111187i | ||||
\(547\) | 2.90033 | 0.124009 | 0.0620046 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620046 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(548\) | −11.4124 | − | 19.7668i | −0.487513 | − | 0.844396i | ||||
\(549\) | 4.50000 | + | 7.79423i | 0.192055 | + | 0.332650i | ||||
\(550\) | 26.5498 | − | 45.9857i | 1.13209 | − | 1.96084i | ||||
\(551\) | 54.1993 | 2.30897 | ||||||||
\(552\) | 2.63746 | − | 4.56821i | 0.112258 | − | 0.194436i | ||||
\(553\) | 4.00000 | − | 6.92820i | 0.170097 | − | 0.294617i | ||||
\(554\) | 14.8248 | 0.629843 | ||||||||
\(555\) | −0.587624 | + | 1.01779i | −0.0249433 | + | 0.0432030i | ||||
\(556\) | 4.54983 | + | 7.88054i | 0.192956 | + | 0.334210i | ||||
\(557\) | 17.5997 | + | 30.4835i | 0.745722 | + | 1.29163i | 0.949857 | + | 0.312685i | \(0.101229\pi\) |
−0.204135 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(558\) | −1.27492 | −0.0539715 | ||||||||
\(559\) | 11.8248 | − | 40.9621i | 0.500134 | − | 1.73251i | ||||
\(560\) | 4.27492 | 0.180648 | ||||||||
\(561\) | 6.00000 | + | 10.3923i | 0.253320 | + | 0.438763i | ||||
\(562\) | 10.4124 | + | 18.0348i | 0.439220 | + | 0.760751i | ||||
\(563\) | −12.0000 | + | 20.7846i | −0.505740 | + | 0.875967i | 0.494238 | + | 0.869326i | \(0.335447\pi\) |
−0.999978 | + | 0.00664037i | \(0.997886\pi\) | |||||||
\(564\) | −6.54983 | −0.275798 | ||||||||
\(565\) | −31.6873 | + | 54.8840i | −1.33309 | + | 2.30899i | ||||
\(566\) | 4.72508 | − | 8.18408i | 0.198610 | − | 0.344003i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −2.63746 | + | 4.56821i | −0.110665 | + | 0.191678i | ||||
\(569\) | −2.45017 | − | 4.24381i | −0.102716 | − | 0.177910i | 0.810087 | − | 0.586310i | \(-0.199420\pi\) |
−0.912803 | + | 0.408400i | \(0.866087\pi\) | |||||||
\(570\) | −14.0000 | − | 24.2487i | −0.586395 | − | 1.01567i | ||||
\(571\) | −14.7251 | −0.616226 | −0.308113 | − | 0.951350i | \(-0.599697\pi\) | ||||
−0.308113 | + | 0.951350i | \(0.599697\pi\) | |||||||
\(572\) | −14.0000 | + | 3.46410i | −0.585369 | + | 0.144841i | ||||
\(573\) | 6.72508 | 0.280944 | ||||||||
\(574\) | −4.13746 | − | 7.16629i | −0.172694 | − | 0.299115i | ||||
\(575\) | 35.0120 | + | 60.6426i | 1.46010 | + | 2.52897i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 9.37459 | 0.390269 | 0.195135 | − | 0.980776i | \(-0.437486\pi\) | ||||
0.195135 | + | 0.980776i | \(0.437486\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 12.4124 | − | 21.4989i | 0.515841 | − | 0.893462i | ||||
\(580\) | 35.3746 | 1.46885 | ||||||||
\(581\) | 5.91238 | − | 10.2405i | 0.245287 | − | 0.424849i | ||||
\(582\) | 0.274917 | + | 0.476171i | 0.0113957 | + | 0.0197379i | ||||
\(583\) | −7.09967 | − | 12.2970i | −0.294038 | − | 0.509289i | ||||
\(584\) | 5.72508 | 0.236906 | ||||||||
\(585\) | −4.27492 | + | 14.8087i | −0.176746 | + | 0.612266i | ||||
\(586\) | −18.2749 | −0.754930 | ||||||||
\(587\) | −4.46221 | − | 7.72877i | −0.184175 | − | 0.319001i | 0.759123 | − | 0.650947i | \(-0.225628\pi\) |
−0.943298 | + | 0.331946i | \(0.892295\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | 4.17525 | − | 7.23174i | 0.172038 | − | 0.297979i | ||||
\(590\) | −50.5498 | −2.08110 | ||||||||
\(591\) | 10.9124 | − | 18.9008i | 0.448875 | − | 0.777475i | ||||
\(592\) | −0.137459 | + | 0.238085i | −0.00564951 | + | 0.00978525i | ||||
\(593\) | 4.45017 | 0.182746 | 0.0913732 | − | 0.995817i | \(-0.470874\pi\) | ||||
0.0913732 | + | 0.995817i | \(0.470874\pi\) | |||||||
\(594\) | 2.00000 | − | 3.46410i | 0.0820610 | − | 0.142134i | ||||
\(595\) | −6.41238 | − | 11.1066i | −0.262882 | − | 0.455325i | ||||
\(596\) | 0.500000 | + | 0.866025i | 0.0204808 | + | 0.0354738i | ||||
\(597\) | 11.8248 | 0.483955 | ||||||||
\(598\) | 5.27492 | − | 18.2728i | 0.215707 | − | 0.747232i | ||||
\(599\) | −10.7251 | −0.438215 | −0.219108 | − | 0.975701i | \(-0.570315\pi\) | ||||
−0.219108 | + | 0.975701i | \(0.570315\pi\) | |||||||
\(600\) | −6.63746 | − | 11.4964i | −0.270973 | − | 0.469339i | ||||
\(601\) | 3.86254 | + | 6.69012i | 0.157556 | + | 0.272896i | 0.933987 | − | 0.357307i | \(-0.116305\pi\) |
−0.776431 | + | 0.630203i | \(0.782972\pi\) | |||||||
\(602\) | 5.91238 | − | 10.2405i | 0.240970 | − | 0.417373i | ||||
\(603\) | −2.72508 | −0.110974 | ||||||||
\(604\) | −6.54983 | + | 11.3446i | −0.266509 | + | 0.461607i | ||||
\(605\) | −10.6873 | + | 18.5109i | −0.434500 | + | 0.752577i | ||||
\(606\) | 1.72508 | 0.0700767 | ||||||||
\(607\) | −7.36254 | + | 12.7523i | −0.298836 | + | 0.517600i | −0.975870 | − | 0.218352i | \(-0.929932\pi\) |
0.677034 | + | 0.735952i | \(0.263265\pi\) | |||||||
\(608\) | −3.27492 | − | 5.67232i | −0.132815 | − | 0.230043i | ||||
\(609\) | −4.13746 | − | 7.16629i | −0.167658 | − | 0.290393i | ||||
\(610\) | −38.4743 | −1.55778 | ||||||||
\(611\) | −22.9244 | + | 5.67232i | −0.927423 | + | 0.229478i | ||||
\(612\) | 3.00000 | 0.121268 | ||||||||
\(613\) | −14.6873 | − | 25.4391i | −0.593214 | − | 1.02748i | −0.993796 | − | 0.111216i | \(-0.964525\pi\) |
0.400582 | − | 0.916261i | \(-0.368808\pi\) | |||||||
\(614\) | 0.725083 | + | 1.25588i | 0.0292620 | + | 0.0506832i | ||||
\(615\) | −17.6873 | + | 30.6353i | −0.713220 | + | 1.23533i | ||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −19.9622 | + | 34.5756i | −0.803648 | + | 1.39196i | 0.113551 | + | 0.993532i | \(0.463777\pi\) |
−0.917200 | + | 0.398428i | \(0.869556\pi\) | |||||||
\(618\) | −2.63746 | + | 4.56821i | −0.106094 | + | 0.183760i | ||||
\(619\) | −15.6495 | −0.629007 | −0.314503 | − | 0.949256i | \(-0.601838\pi\) | ||||
−0.314503 | + | 0.949256i | \(0.601838\pi\) | |||||||
\(620\) | 2.72508 | − | 4.71998i | 0.109442 | − | 0.189559i | ||||
\(621\) | 2.63746 | + | 4.56821i | 0.105838 | + | 0.183316i | ||||
\(622\) | 1.27492 | + | 2.20822i | 0.0511195 | + | 0.0885416i | ||||
\(623\) | 0.725083 | 0.0290498 | ||||||||
\(624\) | −1.00000 | + | 3.46410i | −0.0400320 | + | 0.138675i | ||||
\(625\) | 84.8488 | 3.39395 | ||||||||
\(626\) | −8.82475 | − | 15.2849i | −0.352708 | − | 0.610908i | ||||
\(627\) | 13.0997 | + | 22.6893i | 0.523150 | + | 0.906123i | ||||
\(628\) | 1.86254 | − | 3.22602i | 0.0743235 | − | 0.128732i | ||||
\(629\) | 0.824752 | 0.0328850 | ||||||||
\(630\) | −2.13746 | + | 3.70219i | −0.0851584 | + | 0.147499i | ||||
\(631\) | 14.5498 | − | 25.2011i | 0.579220 | − | 1.00324i | −0.416349 | − | 0.909205i | \(-0.636691\pi\) |
0.995569 | − | 0.0940333i | \(-0.0299760\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | −10.5498 | + | 18.2728i | −0.419318 | + | 0.726281i | ||||
\(634\) | 3.77492 | + | 6.53835i | 0.149921 | + | 0.259671i | ||||
\(635\) | −17.0997 | − | 29.6175i | −0.678580 | − | 1.17533i | ||||
\(636\) | −3.54983 | −0.140760 | ||||||||
\(637\) | −2.50000 | − | 2.59808i | −0.0990536 | − | 0.102940i | ||||
\(638\) | −33.0997 | −1.31043 | ||||||||
\(639\) | −2.63746 | − | 4.56821i | −0.104336 | − | 0.180716i | ||||
\(640\) | −2.13746 | − | 3.70219i | −0.0844905 | − | 0.146342i | ||||
\(641\) | −9.41238 | + | 16.3027i | −0.371766 | + | 0.643918i | −0.989837 | − | 0.142204i | \(-0.954581\pi\) |
0.618071 | + | 0.786122i | \(0.287914\pi\) | |||||||
\(642\) | 2.54983 | 0.100634 | ||||||||
\(643\) | 16.3746 | − | 28.3616i | 0.645751 | − | 1.11847i | −0.338377 | − | 0.941011i | \(-0.609878\pi\) |
0.984128 | − | 0.177462i | \(-0.0567888\pi\) | |||||||
\(644\) | 2.63746 | − | 4.56821i | 0.103930 | − | 0.180013i | ||||
\(645\) | −50.5498 | −1.99040 | ||||||||
\(646\) | −9.82475 | + | 17.0170i | −0.386550 | + | 0.669524i | ||||
\(647\) | −4.72508 | − | 8.18408i | −0.185762 | − | 0.321750i | 0.758071 | − | 0.652172i | \(-0.226142\pi\) |
−0.943833 | + | 0.330423i | \(0.892809\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 47.2990 | 1.85665 | ||||||||
\(650\) | −33.1873 | − | 34.4892i | −1.30171 | − | 1.35278i | ||||
\(651\) | −1.27492 | −0.0499679 | ||||||||
\(652\) | 6.63746 | + | 11.4964i | 0.259943 | + | 0.450234i | ||||
\(653\) | −16.7371 | − | 28.9896i | −0.654974 | − | 1.13445i | −0.981900 | − | 0.189399i | \(-0.939346\pi\) |
0.326926 | − | 0.945050i | \(-0.393987\pi\) | |||||||
\(654\) | 2.27492 | − | 3.94027i | 0.0889563 | − | 0.154077i | ||||
\(655\) | −11.6495 | −0.455184 | ||||||||
\(656\) | −4.13746 | + | 7.16629i | −0.161541 | + | 0.279797i | ||||
\(657\) | −2.86254 | + | 4.95807i | −0.111678 | + | 0.193433i | ||||
\(658\) | −6.54983 | −0.255339 | ||||||||
\(659\) | 6.72508 | − | 11.6482i | 0.261972 | − | 0.453749i | −0.704794 | − | 0.709412i | \(-0.748961\pi\) |
0.966766 | + | 0.255663i | \(0.0822938\pi\) | |||||||
\(660\) | 8.54983 | + | 14.8087i | 0.332802 | + | 0.576430i | ||||
\(661\) | −4.95017 | − | 8.57394i | −0.192539 | − | 0.333488i | 0.753552 | − | 0.657388i | \(-0.228339\pi\) |
−0.946091 | + | 0.323901i | \(0.895006\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 10.5000 | − | 2.59808i | 0.407786 | − | 0.100901i | ||||
\(664\) | −11.8248 | −0.458889 | ||||||||
\(665\) | −14.0000 | − | 24.2487i | −0.542897 | − | 0.940325i | ||||
\(666\) | −0.137459 | − | 0.238085i | −0.00532641 | − | 0.00922562i | ||||
\(667\) | 21.8248 | − | 37.8016i | 0.845058 | − | 1.46368i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.36254 | + | 9.28819i | −0.207328 | + | 0.359102i | ||||
\(670\) | 5.82475 | − | 10.0888i | 0.225030 | − | 0.389763i | ||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | 9.04983 | + | 15.6748i | 0.348845 | + | 0.604218i | 0.986045 | − | 0.166481i | \(-0.0532405\pi\) |
−0.637199 | + | 0.770699i | \(0.719907\pi\) | |||||||
\(674\) | −0.137459 | − | 0.238085i | −0.00529471 | − | 0.00917070i | ||||
\(675\) | 13.2749 | 0.510952 | ||||||||
\(676\) | −0.500000 | + | 12.9904i | −0.0192308 | + | 0.499630i | ||||
\(677\) | −33.6495 | −1.29326 | −0.646628 | − | 0.762806i | \(-0.723821\pi\) | ||||
−0.646628 | + | 0.762806i | \(0.723821\pi\) | |||||||
\(678\) | −7.41238 | − | 12.8386i | −0.284671 | − | 0.493064i | ||||
\(679\) | 0.274917 | + | 0.476171i | 0.0105504 | + | 0.0182738i | ||||
\(680\) | −6.41238 | + | 11.1066i | −0.245903 | + | 0.425917i | ||||
\(681\) | −21.0997 | −0.808541 | ||||||||
\(682\) | −2.54983 | + | 4.41644i | −0.0976382 | + | 0.169114i | ||||
\(683\) | 2.17525 | − | 3.76764i | 0.0832336 | − | 0.144165i | −0.821404 | − | 0.570347i | \(-0.806809\pi\) |
0.904637 | + | 0.426183i | \(0.140142\pi\) | |||||||
\(684\) | 6.54983 | 0.250439 | ||||||||
\(685\) | −48.7870 | + | 84.5015i | −1.86405 | + | 3.22864i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −6.36254 | − | 11.0202i | −0.242746 | − | 0.420449i | ||||
\(688\) | −11.8248 | −0.450814 | ||||||||
\(689\) | −12.4244 | + | 3.07425i | −0.473333 | + | 0.117119i | ||||
\(690\) | −22.5498 | −0.858458 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 2.27492 | + | 3.94027i | 0.0864794 | + | 0.149787i | ||||
\(693\) | 2.00000 | − | 3.46410i | 0.0759737 | − | 0.131590i | ||||
\(694\) | 30.5498 | 1.15966 | ||||||||
\(695\) | 19.4502 | − | 33.6887i | 0.737787 | − | 1.27788i | ||||
\(696\) | −4.13746 | + | 7.16629i | −0.156830 | + | 0.271637i | ||||
\(697\) | 24.8248 | 0.940305 | ||||||||
\(698\) | 17.4622 | − | 30.2454i | 0.660954 | − | 1.14481i | ||||
\(699\) | −3.72508 | − | 6.45203i | −0.140896 | − | 0.244038i | ||||
\(700\) | −6.63746 | − | 11.4964i | −0.250872 | − | 0.434524i | ||||
\(701\) | 14.9244 | 0.563688 | 0.281844 | − | 0.959460i | \(-0.409054\pi\) | ||||
0.281844 | + | 0.959460i | \(0.409054\pi\) | |||||||
\(702\) | −2.50000 | − | 2.59808i | −0.0943564 | − | 0.0980581i | ||||
\(703\) | 1.80066 | 0.0679133 | ||||||||
\(704\) | 2.00000 | + | 3.46410i | 0.0753778 | + | 0.130558i | ||||
\(705\) | 14.0000 | + | 24.2487i | 0.527271 | + | 0.913259i | ||||
\(706\) | 9.77492 | − | 16.9307i | 0.367884 | − | 0.637194i | ||||
\(707\) | 1.72508 | 0.0648784 | ||||||||
\(708\) | 5.91238 | − | 10.2405i | 0.222201 | − | 0.384863i | ||||
\(709\) | 23.6873 | − | 41.0276i | 0.889595 | − | 1.54082i | 0.0492402 | − | 0.998787i | \(-0.484320\pi\) |
0.840355 | − | 0.542037i | \(-0.182347\pi\) | |||||||
\(710\) | 22.5498 | 0.846280 | ||||||||
\(711\) | 4.00000 | − | 6.92820i | 0.150012 | − | 0.259828i | ||||
\(712\) | −0.362541 | − | 0.627940i | −0.0135868 | − | 0.0235331i | ||||
\(713\) | −3.36254 | − | 5.82409i | −0.125928 | − | 0.218114i | ||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | 42.7492 | + | 44.4262i | 1.59873 | + | 1.66145i | ||||
\(716\) | 1.45017 | 0.0541952 | ||||||||
\(717\) | 2.63746 | + | 4.56821i | 0.0984977 | + | 0.170603i | ||||
\(718\) | 0.549834 | + | 0.952341i | 0.0205196 | + | 0.0355411i | ||||
\(719\) | 4.00000 | − | 6.92820i | 0.149175 | − | 0.258378i | −0.781748 | − | 0.623595i | \(-0.785672\pi\) |
0.930923 | + | 0.365216i | \(0.119005\pi\) | |||||||
\(720\) | 4.27492 | 0.159317 | ||||||||
\(721\) | −2.63746 | + | 4.56821i | −0.0982241 | + | 0.170129i | ||||
\(722\) | −11.9502 | + | 20.6983i | −0.444739 | + | 0.770311i | ||||
\(723\) | −15.7251 | −0.584822 | ||||||||
\(724\) | 8.41238 | − | 14.5707i | 0.312643 | − | 0.541514i | ||||
\(725\) | −54.9244 | − | 95.1319i | −2.03984 | − | 3.53311i | ||||
\(726\) | −2.50000 | − | 4.33013i | −0.0927837 | − | 0.160706i | ||||
\(727\) | 19.8248 | 0.735259 | 0.367630 | − | 0.929972i | \(-0.380169\pi\) | ||||
0.367630 | + | 0.929972i | \(0.380169\pi\) | |||||||
\(728\) | −1.00000 | + | 3.46410i | −0.0370625 | + | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.2371 | − | 21.1953i | −0.452916 | − | 0.784474i | ||||
\(731\) | 17.7371 | + | 30.7216i | 0.656031 | + | 1.13628i | ||||
\(732\) | 4.50000 | − | 7.79423i | 0.166325 | − | 0.288083i | ||||
\(733\) | −32.6495 | −1.20594 | −0.602968 | − | 0.797765i | \(-0.706016\pi\) | ||||
−0.602968 | + | 0.797765i | \(0.706016\pi\) | |||||||
\(734\) | −6.63746 | + | 11.4964i | −0.244993 | + | 0.424340i | ||||
\(735\) | −2.13746 | + | 3.70219i | −0.0788413 | + | 0.136557i | ||||
\(736\) | −5.27492 | −0.194436 | ||||||||
\(737\) | −5.45017 | + | 9.43996i | −0.200759 | + | 0.347726i | ||||
\(738\) | −4.13746 | − | 7.16629i | −0.152302 | − | 0.263795i | ||||
\(739\) | 24.6375 | + | 42.6733i | 0.906304 | + | 1.56976i | 0.819158 | + | 0.573568i | \(0.194441\pi\) |
0.0871458 | + | 0.996196i | \(0.472225\pi\) | |||||||
\(740\) | 1.17525 | 0.0432030 | ||||||||
\(741\) | 22.9244 | − | 5.67232i | 0.842150 | − | 0.208378i | ||||
\(742\) | −3.54983 | −0.130319 | ||||||||
\(743\) | 2.08762 | + | 3.61587i | 0.0765875 | + | 0.132653i | 0.901776 | − | 0.432205i | \(-0.142264\pi\) |
−0.825188 | + | 0.564858i | \(0.808931\pi\) | |||||||
\(744\) | 0.637459 | + | 1.10411i | 0.0233704 | + | 0.0404787i | ||||
\(745\) | 2.13746 | − | 3.70219i | 0.0783104 | − | 0.135638i | ||||
\(746\) | 26.8248 | 0.982124 | ||||||||
\(747\) | 5.91238 | − | 10.2405i | 0.216323 | − | 0.374682i | ||||
\(748\) | 6.00000 | − | 10.3923i | 0.219382 | − | 0.379980i | ||||
\(749\) | 2.54983 | 0.0931689 | ||||||||
\(750\) | −17.6873 | + | 30.6353i | −0.645849 | + | 1.11864i | ||||
\(751\) | 9.27492 | + | 16.0646i | 0.338447 | + | 0.586207i | 0.984141 | − | 0.177390i | \(-0.0567652\pi\) |
−0.645694 | + | 0.763596i | \(0.723432\pi\) | |||||||
\(752\) | 3.27492 | + | 5.67232i | 0.119424 | + | 0.206848i | ||||
\(753\) | 13.2749 | 0.483765 | ||||||||
\(754\) | −8.27492 | + | 28.6652i | −0.301355 | + | 1.04392i | ||||
\(755\) | 56.0000 | 2.03805 | ||||||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | 13.0000 | + | 22.5167i | 0.472493 | + | 0.818382i | 0.999505 | − | 0.0314762i | \(-0.0100208\pi\) |
−0.527011 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | 21.0997 | 0.765869 | ||||||||
\(760\) | −14.0000 | + | 24.2487i | −0.507833 | + | 0.879593i | ||||
\(761\) | −10.0997 | + | 17.4931i | −0.366113 | + | 0.634126i | −0.988954 | − | 0.148222i | \(-0.952645\pi\) |
0.622841 | + | 0.782348i | \(0.285978\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | 2.27492 | − | 3.94027i | 0.0823575 | − | 0.142647i | ||||
\(764\) | −3.36254 | − | 5.82409i | −0.121652 | − | 0.210708i | ||||
\(765\) | −6.41238 | − | 11.1066i | −0.231840 | − | 0.401559i | ||||
\(766\) | 22.1993 | 0.802095 | ||||||||
\(767\) | 11.8248 | − | 40.9621i | 0.426967 | − | 1.47906i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −20.8248 | − | 36.0695i | −0.750960 | − | 1.30070i | −0.947358 | − | 0.320176i | \(-0.896258\pi\) |
0.196398 | − | 0.980524i | \(-0.437075\pi\) | |||||||
\(770\) | 8.54983 | + | 14.8087i | 0.308115 | + | 0.533670i | ||||
\(771\) | −7.50000 | + | 12.9904i | −0.270106 | + | 0.467837i | ||||
\(772\) | −24.8248 | −0.893462 | ||||||||
\(773\) | 10.4502 | − | 18.1002i | 0.375866 | − | 0.651020i | −0.614590 | − | 0.788847i | \(-0.710679\pi\) |
0.990456 | + | 0.137827i | \(0.0440118\pi\) | |||||||
\(774\) | 5.91238 | − | 10.2405i | 0.212516 | − | 0.368088i | ||||
\(775\) | −16.9244 | −0.607943 | ||||||||
\(776\) | 0.274917 | − | 0.476171i | 0.00986895 | − | 0.0170935i | ||||
\(777\) | −0.137459 | − | 0.238085i | −0.00493130 | − | 0.00854126i | ||||
\(778\) | 12.3248 | + | 21.3471i | 0.441864 | + | 0.765330i | ||||
\(779\) | 54.1993 | 1.94189 | ||||||||
\(780\) | 14.9622 | − | 3.70219i | 0.535733 | − | 0.132560i | ||||
\(781\) | −21.0997 | −0.755006 | ||||||||
\(782\) | 7.91238 | + | 13.7046i | 0.282946 | + | 0.490077i | ||||
\(783\) | −4.13746 | − | 7.16629i | −0.147861 | − | 0.256102i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | −15.9244 | −0.568367 | ||||||||
\(786\) | 1.36254 | − | 2.35999i | 0.0486002 | − | 0.0841781i | ||||
\(787\) | −10.5498 | + | 18.2728i | −0.376061 | + | 0.651357i | −0.990485 | − | 0.137619i | \(-0.956055\pi\) |
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(788\) | −21.8248 | −0.777475 | ||||||||
\(789\) | −10.5498 | + | 18.2728i | −0.375584 | + | 0.650531i | ||||
\(790\) | 17.0997 | + | 29.6175i | 0.608379 | + | 1.05374i | ||||
\(791\) | −7.41238 | − | 12.8386i | −0.263554 | − | 0.456488i | ||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 9.00000 | − | 31.1769i | 0.319599 | − | 1.10712i | ||||
\(794\) | 23.2749 | 0.825996 | ||||||||
\(795\) | 7.58762 | + | 13.1422i | 0.269105 | + | 0.466104i | ||||
\(796\) | −5.91238 | − | 10.2405i | −0.209559 | − | 0.362966i | ||||
\(797\) | −8.27492 | + | 14.3326i | −0.293113 | + | 0.507686i | −0.974544 | − | 0.224196i | \(-0.928024\pi\) |
0.681431 | + | 0.731882i | \(0.261358\pi\) | |||||||
\(798\) | 6.54983 | 0.231862 | ||||||||
\(799\) | 9.82475 | − | 17.0170i | 0.347575 | − | 0.602017i | ||||
\(800\) | −6.63746 | + | 11.4964i | −0.234670 | + | 0.406460i | ||||
\(801\) | 0.725083 | 0.0256195 | ||||||||
\(802\) | 1.13746 | − | 1.97014i | 0.0401651 | − | 0.0695679i | ||||
\(803\) | 11.4502 | + | 19.8323i | 0.404068 | + | 0.699866i | ||||
\(804\) | 1.36254 | + | 2.35999i | 0.0480531 | + | 0.0832305i | ||||
\(805\) | −22.5498 | −0.794777 | ||||||||
\(806\) | 3.18729 | + | 3.31233i | 0.112268 | + | 0.116672i | ||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | −0.862541 | − | 1.49397i | −0.0303441 | − | 0.0525575i | ||||
\(809\) | −4.86254 | − | 8.42217i | −0.170958 | − | 0.296108i | 0.767797 | − | 0.640693i | \(-0.221353\pi\) |
−0.938755 | + | 0.344585i | \(0.888020\pi\) | |||||||
\(810\) | −2.13746 | + | 3.70219i | −0.0751026 | + | 0.130082i | ||||
\(811\) | 5.09967 | 0.179074 | 0.0895368 | − | 0.995984i | \(-0.471461\pi\) | ||||
0.0895368 | + | 0.995984i | \(0.471461\pi\) | |||||||
\(812\) | −4.13746 | + | 7.16629i | −0.145196 | + | 0.251487i | ||||
\(813\) | −12.6375 | + | 21.8887i | −0.443215 | + | 0.767671i | ||||
\(814\) | −1.09967 | −0.0385434 | ||||||||
\(815\) | 28.3746 | − | 49.1462i | 0.993918 | − | 1.72152i | ||||
\(816\) | −1.50000 | − | 2.59808i | −0.0525105 | − | 0.0909509i | ||||
\(817\) | 38.7251 | + | 67.0738i | 1.35482 | + | 2.34662i | ||||
\(818\) | −29.9244 | −1.04628 | ||||||||
\(819\) | −2.50000 | − | 2.59808i | −0.0873571 | − | 0.0907841i | ||||
\(820\) | 35.3746 | 1.23533 | ||||||||
\(821\) | −7.63746 | − | 13.2285i | −0.266549 | − | 0.461677i | 0.701419 | − | 0.712749i | \(-0.252550\pi\) |
−0.967968 | + | 0.251072i | \(0.919217\pi\) | |||||||
\(822\) | −11.4124 | − | 19.7668i | −0.398052 | − | 0.689447i | ||||
\(823\) | 3.45017 | − | 5.97586i | 0.120265 | − | 0.208305i | −0.799607 | − | 0.600524i | \(-0.794959\pi\) |
0.919872 | + | 0.392218i | \(0.128292\pi\) | |||||||
\(824\) | 5.27492 | 0.183760 | ||||||||
\(825\) | 26.5498 | − | 45.9857i | 0.924347 | − | 1.60102i | ||||
\(826\) | 5.91238 | − | 10.2405i | 0.205718 | − | 0.356314i | ||||
\(827\) | 5.09967 | 0.177333 | 0.0886664 | − | 0.996061i | \(-0.471739\pi\) | ||||
0.0886664 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(828\) | 2.63746 | − | 4.56821i | 0.0916580 | − | 0.158756i | ||||
\(829\) | 22.4124 | + | 38.8194i | 0.778414 | + | 1.34825i | 0.932856 | + | 0.360251i | \(0.117309\pi\) |
−0.154442 | + | 0.988002i | \(0.549358\pi\) | |||||||
\(830\) | 25.2749 | + | 43.7774i | 0.877305 | + | 1.51954i | ||||
\(831\) | 14.8248 | 0.514265 | ||||||||
\(832\) | 3.50000 | − | 0.866025i | 0.121341 | − | 0.0300240i | ||||
\(833\) | 3.00000 | 0.103944 | ||||||||
\(834\) | 4.54983 | + | 7.88054i | 0.157548 | + | 0.272881i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.0997 | − | 22.6893i | 0.453062 | − | 0.784726i | ||||
\(837\) | −1.27492 | −0.0440676 | ||||||||
\(838\) | 11.1873 | − | 19.3770i | 0.386459 | − | 0.669366i | ||||
\(839\) | 10.3746 | − | 17.9693i | 0.358170 | − | 0.620369i | −0.629485 | − | 0.777013i | \(-0.716734\pi\) |
0.987655 | + | 0.156643i | \(0.0500673\pi\) | |||||||
\(840\) | 4.27492 | 0.147499 | ||||||||
\(841\) | −19.7371 | + | 34.1857i | −0.680591 | + | 1.17882i | ||||
\(842\) | −4.13746 | − | 7.16629i | −0.142586 | − | 0.246967i | ||||
\(843\) | 10.4124 | + | 18.0348i | 0.358621 | + | 0.621150i | ||||
\(844\) | 21.0997 | 0.726281 | ||||||||
\(845\) | 49.1615 | − | 25.9153i | 1.69121 | − | 0.891514i | ||||
\(846\) | −6.54983 | −0.225188 | ||||||||
\(847\) | −2.50000 | − | 4.33013i | −0.0859010 | − | 0.148785i | ||||
\(848\) | 1.77492 | + | 3.07425i | 0.0609509 | + | 0.105570i | ||||
\(849\) | 4.72508 | − | 8.18408i | 0.162164 | − | 0.280877i | ||||
\(850\) | 39.8248 | 1.36598 | ||||||||
\(851\) | 0.725083 | − | 1.25588i | 0.0248555 | − | 0.0430510i | ||||
\(852\) | −2.63746 | + | 4.56821i | −0.0903578 | + | 0.156504i | ||||
\(853\) | −14.4502 | −0.494764 | −0.247382 | − | 0.968918i | \(-0.579570\pi\) | ||||
−0.247382 | + | 0.968918i | \(0.579570\pi\) | |||||||
\(854\) | 4.50000 | − | 7.79423i | 0.153987 | − | 0.266713i | ||||
\(855\) | −14.0000 | − | 24.2487i | −0.478790 | − | 0.829288i | ||||
\(856\) | −1.27492 | − | 2.20822i | −0.0435758 | − | 0.0754755i | ||||
\(857\) | −36.8248 | −1.25791 | −0.628955 | − | 0.777442i | \(-0.716517\pi\) | ||||
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(858\) | −14.0000 | + | 3.46410i | −0.477952 | + | 0.118262i | ||||
\(859\) | −27.6495 | −0.943389 | −0.471694 | − | 0.881762i | \(-0.656357\pi\) | ||||
−0.471694 | + | 0.881762i | \(0.656357\pi\) | |||||||
\(860\) | 25.2749 | + | 43.7774i | 0.861868 | + | 1.49280i | ||||
\(861\) | −4.13746 | − | 7.16629i | −0.141004 | − | 0.244226i | ||||
\(862\) | 6.63746 | − | 11.4964i | 0.226073 | − | 0.391569i | ||||
\(863\) | 35.2990 | 1.20159 | 0.600796 | − | 0.799402i | \(-0.294850\pi\) | ||||
0.600796 | + | 0.799402i | \(0.294850\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 9.72508 | − | 16.8443i | 0.330663 | − | 0.572725i | ||||
\(866\) | −10.2749 | −0.349156 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 0.637459 | + | 1.10411i | 0.0216368 | + | 0.0374760i | ||||
\(869\) | −16.0000 | − | 27.7128i | −0.542763 | − | 0.940093i | ||||
\(870\) | 35.3746 | 1.19931 | ||||||||
\(871\) | 6.81271 | + | 7.07997i | 0.230840 | + | 0.239896i | ||||
\(872\) | −4.54983 | −0.154077 | ||||||||
\(873\) | 0.274917 | + | 0.476171i | 0.00930454 | + | 0.0161159i | ||||
\(874\) | 17.2749 | + | 29.9210i | 0.584333 | + | 1.01209i | ||||
\(875\) | −17.6873 | + | 30.6353i | −0.597940 | + | 1.03566i | ||||
\(876\) | 5.72508 | 0.193433 | ||||||||
\(877\) | 1.86254 | − | 3.22602i | 0.0628936 | − | 0.108935i | −0.832864 | − | 0.553478i | \(-0.813300\pi\) |
0.895758 | + | 0.444543i | \(0.146634\pi\) | |||||||
\(878\) | −6.54983 | + | 11.3446i | −0.221046 | + | 0.382863i | ||||
\(879\) | −18.2749 | −0.616398 | ||||||||
\(880\) | 8.54983 | − | 14.8087i | 0.288215 | − | 0.499203i | ||||
\(881\) | −0.774917 | − | 1.34220i | −0.0261076 | − | 0.0452197i | 0.852676 | − | 0.522439i | \(-0.174978\pi\) |
−0.878784 | + | 0.477220i | \(0.841645\pi\) | |||||||
\(882\) | −0.500000 | − | 0.866025i | −0.0168359 | − | 0.0291606i | ||||
\(883\) | 58.0241 | 1.95267 | 0.976333 | − | 0.216273i | \(-0.0693900\pi\) | ||||
0.976333 | + | 0.216273i | \(0.0693900\pi\) | |||||||
\(884\) | −7.50000 | − | 7.79423i | −0.252252 | − | 0.262148i | ||||
\(885\) | −50.5498 | −1.69921 | ||||||||
\(886\) | −17.2749 | − | 29.9210i | −0.580362 | − | 1.00522i | ||||
\(887\) | −23.2749 | − | 40.3133i | −0.781495 | − | 1.35359i | −0.931071 | − | 0.364839i | \(-0.881124\pi\) |
0.149575 | − | 0.988750i | \(-0.452209\pi\) | |||||||
\(888\) | −0.137459 | + | 0.238085i | −0.00461281 | + | 0.00798962i | ||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | −1.54983 | + | 2.68439i | −0.0519506 | + | 0.0899810i | ||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | 10.7251 | 0.359102 | ||||||||
\(893\) | 21.4502 | − | 37.1528i | 0.717802 | − | 1.24327i | ||||
\(894\) | 0.500000 | + | 0.866025i | 0.0167225 | + | 0.0289642i | ||||
\(895\) | −3.09967 | − | 5.36878i | −0.103611 | − | 0.179459i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 5.27492 | − | 18.2728i | 0.176124 | − | 0.610113i | ||||
\(898\) | −19.0997 | −0.637364 | ||||||||
\(899\) | 5.27492 | + | 9.13642i | 0.175928 | + | 0.304717i | ||||
\(900\) | −6.63746 | − | 11.4964i | −0.221249 | − | 0.383214i | ||||
\(901\) | 5.32475 | − | 9.22274i | 0.177393 | − | 0.307254i | ||||
\(902\) | −33.0997 | −1.10210 | ||||||||
\(903\) | 5.91238 | − | 10.2405i | 0.196752 | − | 0.340784i | ||||
\(904\) | −7.41238 | + | 12.8386i | −0.246532 | + | 0.427006i | ||||
\(905\) | −71.9244 | −2.39085 | ||||||||
\(906\) | −6.54983 | + | 11.3446i | −0.217604 | + | 0.376901i | ||||
\(907\) | 19.9124 | + | 34.4892i | 0.661180 | + | 1.14520i | 0.980306 | + | 0.197484i | \(0.0632772\pi\) |
−0.319126 | + | 0.947712i | \(0.603389\pi\) | |||||||
\(908\) | 10.5498 | + | 18.2728i | 0.350109 | + | 0.606406i | ||||
\(909\) | 1.72508 | 0.0572174 | ||||||||
\(910\) | 14.9622 | − | 3.70219i | 0.495992 | − | 0.122726i | ||||
\(911\) | −25.0997 | −0.831589 | −0.415795 | − | 0.909459i | \(-0.636496\pi\) | ||||
−0.415795 | + | 0.909459i | \(0.636496\pi\) | |||||||
\(912\) | −3.27492 | − | 5.67232i | −0.108443 | − | 0.187829i | ||||
\(913\) | −23.6495 | − | 40.9621i | −0.782684 | − | 1.35565i | ||||
\(914\) | 8.50000 | − | 14.7224i | 0.281155 | − | 0.486975i | ||||
\(915\) | −38.4743 | −1.27192 | ||||||||
\(916\) | −6.36254 | + | 11.0202i | −0.210224 | + | 0.364119i | ||||
\(917\) | 1.36254 | − | 2.35999i | 0.0449951 | − | 0.0779338i | ||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | −19.8248 | + | 34.3375i | −0.653958 | + | 1.13269i | 0.328196 | + | 0.944610i | \(0.393559\pi\) |
−0.982154 | + | 0.188079i | \(0.939774\pi\) | |||||||
\(920\) | 11.2749 | + | 19.5287i | 0.371723 | + | 0.643843i | ||||
\(921\) | 0.725083 | + | 1.25588i | 0.0238923 | + | 0.0413827i | ||||
\(922\) | −19.3746 | −0.638068 | ||||||||
\(923\) | −5.27492 | + | 18.2728i | −0.173626 | + | 0.601458i | ||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | −1.82475 | − | 3.16056i | −0.0599975 | − | 0.103919i | ||||
\(926\) | 5.27492 | + | 9.13642i | 0.173345 | + | 0.300242i | ||||
\(927\) | −2.63746 | + | 4.56821i | −0.0866255 | + | 0.150040i | ||||
\(928\) | 8.27492 | 0.271637 | ||||||||
\(929\) | −26.7749 | + | 46.3755i | −0.878457 | + | 1.52153i | −0.0254221 | + | 0.999677i | \(0.508093\pi\) |
−0.853034 | + | 0.521855i | \(0.825240\pi\) | |||||||
\(930\) | 2.72508 | − | 4.71998i | 0.0893590 | − | 0.154774i | ||||
\(931\) | 6.54983 | 0.214662 | ||||||||
\(932\) | −3.72508 | + | 6.45203i | −0.122019 | + | 0.211343i | ||||
\(933\) | 1.27492 | + | 2.20822i | 0.0417389 | + | 0.0722939i | ||||
\(934\) | 4.08762 | + | 7.07997i | 0.133751 | + | 0.231664i | ||||
\(935\) | −51.2990 | −1.67766 | ||||||||
\(936\) | −1.00000 | + | 3.46410i | −0.0326860 | + | 0.113228i | ||||
\(937\) | 19.1752 | 0.626428 | 0.313214 | − | 0.949683i | \(-0.398594\pi\) | ||||
0.313214 | + | 0.949683i | \(0.398594\pi\) | |||||||
\(938\) | 1.36254 | + | 2.35999i | 0.0444886 | + | 0.0770564i | ||||
\(939\) | −8.82475 | − | 15.2849i | −0.287985 | − | 0.498804i | ||||
\(940\) | 14.0000 | − | 24.2487i | 0.456630 | − | 0.790906i | ||||
\(941\) | 37.6495 | 1.22734 | 0.613669 | − | 0.789563i | \(-0.289693\pi\) | ||||
0.613669 | + | 0.789563i | \(0.289693\pi\) | |||||||
\(942\) | 1.86254 | − | 3.22602i | 0.0606849 | − | 0.105109i | ||||
\(943\) | 21.8248 | − | 37.8016i | 0.710712 | − | 1.23099i | ||||
\(944\) | −11.8248 | −0.384863 | ||||||||
\(945\) | −2.13746 | + | 3.70219i | −0.0695315 | + | 0.120432i | ||||
\(946\) | −23.6495 | − | 40.9621i | −0.768912 | − | 1.33179i | ||||
\(947\) | 4.54983 | + | 7.88054i | 0.147850 | + | 0.256083i | 0.930433 | − | 0.366463i | \(-0.119431\pi\) |
−0.782583 | + | 0.622547i | \(0.786098\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 20.0378 | − | 4.95807i | 0.650454 | − | 0.160946i | ||||
\(950\) | 86.9485 | 2.82098 | ||||||||
\(951\) | 3.77492 | + | 6.53835i | 0.122410 | + | 0.212020i | ||||
\(952\) | −1.50000 | − | 2.59808i | −0.0486153 | − | 0.0842041i | ||||
\(953\) | 5.54983 | − | 9.61260i | 0.179777 | − | 0.311383i | −0.762027 | − | 0.647545i | \(-0.775796\pi\) |
0.941804 | + | 0.336162i | \(0.109129\pi\) | |||||||
\(954\) | −3.54983 | −0.114930 | ||||||||
\(955\) | −14.3746 | + | 24.8975i | −0.465151 | + | 0.805665i | ||||
\(956\) | 2.63746 | − | 4.56821i | 0.0853015 | − | 0.147747i | ||||
\(957\) | −33.0997 | −1.06996 | ||||||||
\(958\) | −10.0000 | + | 17.3205i | −0.323085 | + | 0.559600i | ||||
\(959\) | −11.4124 | − | 19.7668i | −0.368525 | − | 0.638304i | ||||
\(960\) | −2.13746 | − | 3.70219i | −0.0689862 | − | 0.119488i | ||||
\(961\) | −29.3746 | −0.947567 | ||||||||
\(962\) | −0.274917 | + | 0.952341i | −0.00886369 | + | 0.0307047i | ||||
\(963\) | 2.54983 | 0.0821673 | ||||||||
\(964\) | 7.86254 | + | 13.6183i | 0.253235 | + | 0.438617i | ||||
\(965\) | 53.0619 | + | 91.9059i | 1.70812 | + | 2.95855i | ||||
\(966\) | 2.63746 | − | 4.56821i | 0.0848588 | − | 0.146980i | ||||
\(967\) | −18.5498 | −0.596522 | −0.298261 | − | 0.954484i | \(-0.596407\pi\) | ||||
−0.298261 | + | 0.954484i | \(0.596407\pi\) | |||||||
\(968\) | −2.50000 | + | 4.33013i | −0.0803530 | + | 0.139176i | ||||
\(969\) | −9.82475 | + | 17.0170i | −0.315616 | + | 0.546664i | ||||
\(970\) | −2.35050 | −0.0754699 | ||||||||
\(971\) | −24.2870 | + | 42.0663i | −0.779406 | + | 1.34997i | 0.152879 | + | 0.988245i | \(0.451146\pi\) |
−0.932285 | + | 0.361725i | \(0.882188\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 4.54983 | + | 7.88054i | 0.145861 | + | 0.252639i | ||||
\(974\) | −1.09967 | −0.0352357 | ||||||||
\(975\) | −33.1873 | − | 34.4892i | −1.06284 | − | 1.10454i | ||||
\(976\) | −9.00000 | −0.288083 | ||||||||
\(977\) | −12.3127 | − | 21.3262i | −0.393918 | − | 0.682287i | 0.599044 | − | 0.800716i | \(-0.295547\pi\) |
−0.992962 | + | 0.118429i | \(0.962214\pi\) | |||||||
\(978\) | 6.63746 | + | 11.4964i | 0.212243 | + | 0.367615i | ||||
\(979\) | 1.45017 | − | 2.51176i | 0.0463475 | − | 0.0802762i | ||||
\(980\) | 4.27492 | 0.136557 | ||||||||
\(981\) | 2.27492 | − | 3.94027i | 0.0726325 | − | 0.125803i | ||||
\(982\) | −12.5498 | + | 21.7370i | −0.400481 | + | 0.693654i | ||||
\(983\) | 53.8488 | 1.71751 | 0.858756 | − | 0.512385i | \(-0.171238\pi\) | ||||
0.858756 | + | 0.512385i | \(0.171238\pi\) | |||||||
\(984\) | −4.13746 | + | 7.16629i | −0.131897 | + | 0.228453i | ||||
\(985\) | 46.6495 | + | 80.7993i | 1.48638 | + | 2.57448i | ||||
\(986\) | −12.4124 | − | 21.4989i | −0.395291 | − | 0.684663i | ||||
\(987\) | −6.54983 | −0.208484 | ||||||||
\(988\) | −16.3746 | − | 17.0170i | −0.520945 | − | 0.541382i | ||||
\(989\) | 62.3746 | 1.98340 | ||||||||
\(990\) | 8.54983 | + | 14.8087i | 0.271732 | + | 0.470653i | ||||
\(991\) | 18.3746 | + | 31.8257i | 0.583688 | + | 1.01098i | 0.995038 | + | 0.0994996i | \(0.0317242\pi\) |
−0.411350 | + | 0.911478i | \(0.634942\pi\) | |||||||
\(992\) | 0.637459 | − | 1.10411i | 0.0202393 | − | 0.0350555i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | −2.63746 | + | 4.56821i | −0.0836551 | + | 0.144895i | ||||
\(995\) | −25.2749 | + | 43.7774i | −0.801269 | + | 1.38784i | ||||
\(996\) | −11.8248 | −0.374682 | ||||||||
\(997\) | 1.95017 | − | 3.37779i | 0.0617624 | − | 0.106976i | −0.833491 | − | 0.552533i | \(-0.813661\pi\) |
0.895253 | + | 0.445558i | \(0.146995\pi\) | |||||||
\(998\) | 15.9124 | + | 27.5610i | 0.503697 | + | 0.872430i | ||||
\(999\) | −0.137459 | − | 0.238085i | −0.00434900 | − | 0.00753269i |
(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 | 546.2.l.j.211.2 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.r.x.757.1 | 4 | |||
13.3 | even | 3 | 7098.2.a.ca.1.2 | 2 | |||
13.9 | even | 3 | inner | 546.2.l.j.295.2 | yes | 4 | |
13.10 | even | 6 | 7098.2.a.bm.1.1 | 2 | |||
39.35 | odd | 6 | 1638.2.r.x.1387.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.j.211.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.l.j.295.2 | yes | 4 | 13.9 | even | 3 | inner | |
1638.2.r.x.757.1 | 4 | 3.2 | odd | 2 | |||
1638.2.r.x.1387.1 | 4 | 39.35 | odd | 6 | |||
7098.2.a.bm.1.1 | 2 | 13.10 | even | 6 | |||
7098.2.a.ca.1.2 | 2 | 13.3 | even | 3 |