Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (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: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.27 |
Dual form | 74.2.e.b.11.2 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −1.36603 | − | 2.36603i | −0.788675 | − | 1.36603i | −0.926779 | − | 0.375608i | \(-0.877434\pi\) |
0.138104 | − | 0.990418i | \(-0.455899\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | − | 2.73205i | − | 1.11536i | ||||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.23205 | + | 3.86603i | −0.744017 | + | 1.28868i | ||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 1.36603 | − | 2.36603i | 0.394338 | − | 0.683013i | ||||
\(13\) | −3.00000 | + | 1.73205i | −0.832050 | + | 0.480384i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
0.0225039 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(14\) | 2.00000i | 0.534522i | ||||||||
\(15\) | −4.09808 | − | 2.36603i | −1.05812 | − | 0.610905i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.69615 | + | 3.86603i | 1.62406 | + | 0.937649i | 0.985820 | + | 0.167808i | \(0.0536689\pi\) |
0.638236 | + | 0.769841i | \(0.279664\pi\) | |||||||
\(18\) | −3.86603 | + | 2.23205i | −0.911231 | + | 0.526099i | ||||
\(19\) | 1.09808 | − | 0.633975i | 0.251916 | − | 0.145444i | −0.368725 | − | 0.929538i | \(-0.620206\pi\) |
0.620641 | + | 0.784095i | \(0.286872\pi\) | |||||||
\(20\) | 1.50000 | + | 0.866025i | 0.335410 | + | 0.193649i | ||||
\(21\) | 2.73205 | − | 4.73205i | 0.596182 | − | 1.03262i | ||||
\(22\) | −4.09808 | − | 2.36603i | −0.873713 | − | 0.504438i | ||||
\(23\) | − | 4.73205i | − | 0.986701i | −0.869831 | − | 0.493350i | \(-0.835772\pi\) | ||
0.869831 | − | 0.493350i | \(-0.164228\pi\) | |||||||
\(24\) | 2.36603 | − | 1.36603i | 0.482963 | − | 0.278839i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | −3.46410 | −0.679366 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.00000 | + | 1.73205i | −0.188982 | + | 0.327327i | ||||
\(29\) | − | 8.66025i | − | 1.60817i | −0.594515 | − | 0.804084i | \(-0.702656\pi\) | ||
0.594515 | − | 0.804084i | \(-0.297344\pi\) | |||||||
\(30\) | −2.36603 | − | 4.09808i | −0.431975 | − | 0.748203i | ||||
\(31\) | 1.26795i | 0.227730i | 0.993496 | + | 0.113865i | \(0.0363232\pi\) | ||||
−0.993496 | + | 0.113865i | \(0.963677\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 6.46410 | + | 11.1962i | 1.12526 | + | 1.94900i | ||||
\(34\) | 3.86603 | + | 6.69615i | 0.663018 | + | 1.14838i | ||||
\(35\) | 3.00000 | + | 1.73205i | 0.507093 | + | 0.292770i | ||||
\(36\) | −4.46410 | −0.744017 | ||||||||
\(37\) | −5.69615 | + | 2.13397i | −0.936442 | + | 0.350823i | ||||
\(38\) | 1.26795 | 0.205689 | ||||||||
\(39\) | 8.19615 | + | 4.73205i | 1.31243 | + | 0.757735i | ||||
\(40\) | 0.866025 | + | 1.50000i | 0.136931 | + | 0.237171i | ||||
\(41\) | −4.96410 | − | 8.59808i | −0.775262 | − | 1.34279i | −0.934647 | − | 0.355577i | \(-0.884284\pi\) |
0.159384 | − | 0.987217i | \(-0.449049\pi\) | |||||||
\(42\) | 4.73205 | − | 2.73205i | 0.730171 | − | 0.421565i | ||||
\(43\) | 0.928203i | 0.141550i | 0.997492 | + | 0.0707748i | \(0.0225472\pi\) | ||||
−0.997492 | + | 0.0707748i | \(0.977453\pi\) | |||||||
\(44\) | −2.36603 | − | 4.09808i | −0.356692 | − | 0.617808i | ||||
\(45\) | 7.73205i | 1.15263i | ||||||||
\(46\) | 2.36603 | − | 4.09808i | 0.348851 | − | 0.604228i | ||||
\(47\) | 4.73205 | 0.690241 | 0.345120 | − | 0.938558i | \(-0.387838\pi\) | ||||
0.345120 | + | 0.938558i | \(0.387838\pi\) | |||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −1.73205 | + | 1.00000i | −0.244949 | + | 0.141421i | ||||
\(51\) | − | 21.1244i | − | 2.95800i | ||||||
\(52\) | −3.00000 | − | 1.73205i | −0.416025 | − | 0.240192i | ||||
\(53\) | −1.26795 | + | 2.19615i | −0.174166 | + | 0.301665i | −0.939872 | − | 0.341526i | \(-0.889056\pi\) |
0.765706 | + | 0.643191i | \(0.222390\pi\) | |||||||
\(54\) | 3.46410 | + | 2.00000i | 0.471405 | + | 0.272166i | ||||
\(55\) | −7.09808 | + | 4.09808i | −0.957104 | + | 0.552584i | ||||
\(56\) | −1.73205 | + | 1.00000i | −0.231455 | + | 0.133631i | ||||
\(57\) | −3.00000 | − | 1.73205i | −0.397360 | − | 0.229416i | ||||
\(58\) | 4.33013 | − | 7.50000i | 0.568574 | − | 0.984798i | ||||
\(59\) | 2.19615 | + | 1.26795i | 0.285915 | + | 0.165073i | 0.636098 | − | 0.771608i | \(-0.280547\pi\) |
−0.350183 | + | 0.936681i | \(0.613881\pi\) | |||||||
\(60\) | − | 4.73205i | − | 0.610905i | ||||||
\(61\) | 1.50000 | − | 0.866025i | 0.192055 | − | 0.110883i | −0.400889 | − | 0.916127i | \(-0.631299\pi\) |
0.592944 | + | 0.805243i | \(0.297965\pi\) | |||||||
\(62\) | −0.633975 | + | 1.09808i | −0.0805149 | + | 0.139456i | ||||
\(63\) | −8.92820 | −1.12485 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 12.9282i | 1.59135i | ||||||||
\(67\) | 5.09808 | + | 8.83013i | 0.622829 | + | 1.07877i | 0.988956 | + | 0.148207i | \(0.0473502\pi\) |
−0.366127 | + | 0.930565i | \(0.619317\pi\) | |||||||
\(68\) | 7.73205i | 0.937649i | ||||||||
\(69\) | −11.1962 | + | 6.46410i | −1.34786 | + | 0.778186i | ||||
\(70\) | 1.73205 | + | 3.00000i | 0.207020 | + | 0.358569i | ||||
\(71\) | −1.73205 | − | 3.00000i | −0.205557 | − | 0.356034i | 0.744753 | − | 0.667340i | \(-0.232567\pi\) |
−0.950310 | + | 0.311305i | \(0.899234\pi\) | |||||||
\(72\) | −3.86603 | − | 2.23205i | −0.455615 | − | 0.263050i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −6.00000 | − | 1.00000i | −0.697486 | − | 0.116248i | ||||
\(75\) | 5.46410 | 0.630940 | ||||||||
\(76\) | 1.09808 | + | 0.633975i | 0.125958 | + | 0.0727219i | ||||
\(77\) | −4.73205 | − | 8.19615i | −0.539267 | − | 0.934038i | ||||
\(78\) | 4.73205 | + | 8.19615i | 0.535799 | + | 0.928032i | ||||
\(79\) | −11.4904 | + | 6.63397i | −1.29277 | + | 0.746380i | −0.979144 | − | 0.203167i | \(-0.934877\pi\) |
−0.313625 | + | 0.949547i | \(0.601543\pi\) | |||||||
\(80\) | 1.73205i | 0.193649i | ||||||||
\(81\) | 1.23205 | + | 2.13397i | 0.136895 | + | 0.237108i | ||||
\(82\) | − | 9.92820i | − | 1.09639i | ||||||
\(83\) | 2.83013 | − | 4.90192i | 0.310647 | − | 0.538056i | −0.667856 | − | 0.744291i | \(-0.732788\pi\) |
0.978503 | + | 0.206235i | \(0.0661210\pi\) | |||||||
\(84\) | 5.46410 | 0.596182 | ||||||||
\(85\) | 13.3923 | 1.45260 | ||||||||
\(86\) | −0.464102 | + | 0.803848i | −0.0500454 | + | 0.0866811i | ||||
\(87\) | −20.4904 | + | 11.8301i | −2.19680 | + | 1.26832i | ||||
\(88\) | − | 4.73205i | − | 0.504438i | ||||||
\(89\) | −5.89230 | − | 3.40192i | −0.624583 | − | 0.360603i | 0.154068 | − | 0.988060i | \(-0.450762\pi\) |
−0.778651 | + | 0.627457i | \(0.784096\pi\) | |||||||
\(90\) | −3.86603 | + | 6.69615i | −0.407515 | + | 0.705836i | ||||
\(91\) | −6.00000 | − | 3.46410i | −0.628971 | − | 0.363137i | ||||
\(92\) | 4.09808 | − | 2.36603i | 0.427254 | − | 0.246675i | ||||
\(93\) | 3.00000 | − | 1.73205i | 0.311086 | − | 0.179605i | ||||
\(94\) | 4.09808 | + | 2.36603i | 0.422684 | + | 0.244037i | ||||
\(95\) | 1.09808 | − | 1.90192i | 0.112660 | − | 0.195133i | ||||
\(96\) | 2.36603 | + | 1.36603i | 0.241481 | + | 0.139419i | ||||
\(97\) | − | 7.73205i | − | 0.785071i | −0.919737 | − | 0.392535i | \(-0.871598\pi\) | ||
0.919737 | − | 0.392535i | \(-0.128402\pi\) | |||||||
\(98\) | 2.59808 | − | 1.50000i | 0.262445 | − | 0.151523i | ||||
\(99\) | 10.5622 | − | 18.2942i | 1.06154 | − | 1.83864i | ||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 12.4641 | 1.24022 | 0.620112 | − | 0.784513i | \(-0.287087\pi\) | ||||
0.620112 | + | 0.784513i | \(0.287087\pi\) | |||||||
\(102\) | 10.5622 | − | 18.2942i | 1.04581 | − | 1.81140i | ||||
\(103\) | 8.53590i | 0.841067i | 0.907277 | + | 0.420534i | \(0.138157\pi\) | ||||
−0.907277 | + | 0.420534i | \(0.861843\pi\) | |||||||
\(104\) | −1.73205 | − | 3.00000i | −0.169842 | − | 0.294174i | ||||
\(105\) | − | 9.46410i | − | 0.923602i | ||||||
\(106\) | −2.19615 | + | 1.26795i | −0.213309 | + | 0.123154i | ||||
\(107\) | 5.19615 | + | 9.00000i | 0.502331 | + | 0.870063i | 0.999996 | + | 0.00269372i | \(0.000857438\pi\) |
−0.497665 | + | 0.867369i | \(0.665809\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | 2.30385 | + | 1.33013i | 0.220669 | + | 0.127403i | 0.606260 | − | 0.795267i | \(-0.292669\pi\) |
−0.385591 | + | 0.922670i | \(0.626002\pi\) | |||||||
\(110\) | −8.19615 | −0.781472 | ||||||||
\(111\) | 12.8301 | + | 10.5622i | 1.21778 | + | 1.00252i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | −3.00000 | − | 1.73205i | −0.282216 | − | 0.162938i | 0.352210 | − | 0.935921i | \(-0.385430\pi\) |
−0.634426 | + | 0.772983i | \(0.718764\pi\) | |||||||
\(114\) | −1.73205 | − | 3.00000i | −0.162221 | − | 0.280976i | ||||
\(115\) | −4.09808 | − | 7.09808i | −0.382148 | − | 0.661899i | ||||
\(116\) | 7.50000 | − | 4.33013i | 0.696358 | − | 0.402042i | ||||
\(117\) | − | 15.4641i | − | 1.42966i | ||||||
\(118\) | 1.26795 | + | 2.19615i | 0.116724 | + | 0.202172i | ||||
\(119\) | 15.4641i | 1.41759i | ||||||||
\(120\) | 2.36603 | − | 4.09808i | 0.215988 | − | 0.374101i | ||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 1.73205 | 0.156813 | ||||||||
\(123\) | −13.5622 | + | 23.4904i | −1.22286 | + | 2.11806i | ||||
\(124\) | −1.09808 | + | 0.633975i | −0.0986102 | + | 0.0569326i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −7.73205 | − | 4.46410i | −0.688826 | − | 0.397694i | ||||
\(127\) | 3.90192 | − | 6.75833i | 0.346240 | − | 0.599705i | −0.639338 | − | 0.768925i | \(-0.720792\pi\) |
0.985578 | + | 0.169221i | \(0.0541250\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.19615 | − | 1.26795i | 0.193360 | − | 0.111637i | ||||
\(130\) | −5.19615 | + | 3.00000i | −0.455733 | + | 0.263117i | ||||
\(131\) | 8.49038 | + | 4.90192i | 0.741808 | + | 0.428283i | 0.822726 | − | 0.568438i | \(-0.192452\pi\) |
−0.0809183 | + | 0.996721i | \(0.525785\pi\) | |||||||
\(132\) | −6.46410 | + | 11.1962i | −0.562628 | + | 0.974500i | ||||
\(133\) | 2.19615 | + | 1.26795i | 0.190431 | + | 0.109945i | ||||
\(134\) | 10.1962i | 0.880813i | ||||||||
\(135\) | 6.00000 | − | 3.46410i | 0.516398 | − | 0.298142i | ||||
\(136\) | −3.86603 | + | 6.69615i | −0.331509 | + | 0.574190i | ||||
\(137\) | −1.39230 | −0.118953 | −0.0594763 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594763 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(138\) | −12.9282 | −1.10052 | ||||||||
\(139\) | 10.2942 | − | 17.8301i | 0.873145 | − | 1.51233i | 0.0144194 | − | 0.999896i | \(-0.495410\pi\) |
0.858726 | − | 0.512436i | \(-0.171257\pi\) | |||||||
\(140\) | 3.46410i | 0.292770i | ||||||||
\(141\) | −6.46410 | − | 11.1962i | −0.544376 | − | 0.942886i | ||||
\(142\) | − | 3.46410i | − | 0.290701i | ||||||
\(143\) | 14.1962 | − | 8.19615i | 1.18714 | − | 0.685397i | ||||
\(144\) | −2.23205 | − | 3.86603i | −0.186004 | − | 0.322169i | ||||
\(145\) | −7.50000 | − | 12.9904i | −0.622841 | − | 1.07879i | ||||
\(146\) | 3.46410 | + | 2.00000i | 0.286691 | + | 0.165521i | ||||
\(147\) | −8.19615 | −0.676007 | ||||||||
\(148\) | −4.69615 | − | 3.86603i | −0.386021 | − | 0.317785i | ||||
\(149\) | −15.9282 | −1.30489 | −0.652445 | − | 0.757836i | \(-0.726257\pi\) | ||||
−0.652445 | + | 0.757836i | \(0.726257\pi\) | |||||||
\(150\) | 4.73205 | + | 2.73205i | 0.386370 | + | 0.223071i | ||||
\(151\) | −2.09808 | − | 3.63397i | −0.170739 | − | 0.295729i | 0.767939 | − | 0.640522i | \(-0.221282\pi\) |
−0.938678 | + | 0.344794i | \(0.887949\pi\) | |||||||
\(152\) | 0.633975 | + | 1.09808i | 0.0514221 | + | 0.0890657i | ||||
\(153\) | −29.8923 | + | 17.2583i | −2.41665 | + | 1.39525i | ||||
\(154\) | − | 9.46410i | − | 0.762639i | ||||||
\(155\) | 1.09808 | + | 1.90192i | 0.0881996 | + | 0.152766i | ||||
\(156\) | 9.46410i | 0.757735i | ||||||||
\(157\) | −0.500000 | + | 0.866025i | −0.0399043 | + | 0.0691164i | −0.885288 | − | 0.465044i | \(-0.846039\pi\) |
0.845383 | + | 0.534160i | \(0.179372\pi\) | |||||||
\(158\) | −13.2679 | −1.05554 | ||||||||
\(159\) | 6.92820 | 0.549442 | ||||||||
\(160\) | −0.866025 | + | 1.50000i | −0.0684653 | + | 0.118585i | ||||
\(161\) | 8.19615 | − | 4.73205i | 0.645947 | − | 0.372938i | ||||
\(162\) | 2.46410i | 0.193598i | ||||||||
\(163\) | 11.1962 | + | 6.46410i | 0.876950 | + | 0.506308i | 0.869652 | − | 0.493666i | \(-0.164343\pi\) |
0.00729867 | + | 0.999973i | \(0.497677\pi\) | |||||||
\(164\) | 4.96410 | − | 8.59808i | 0.387631 | − | 0.671397i | ||||
\(165\) | 19.3923 | + | 11.1962i | 1.50969 | + | 0.871619i | ||||
\(166\) | 4.90192 | − | 2.83013i | 0.380463 | − | 0.219660i | ||||
\(167\) | −12.0000 | + | 6.92820i | −0.928588 | + | 0.536120i | −0.886365 | − | 0.462988i | \(-0.846777\pi\) |
−0.0422232 | + | 0.999108i | \(0.513444\pi\) | |||||||
\(168\) | 4.73205 | + | 2.73205i | 0.365086 | + | 0.210782i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 11.5981 | + | 6.69615i | 0.889532 | + | 0.513571i | ||||
\(171\) | 5.66025i | 0.432850i | ||||||||
\(172\) | −0.803848 | + | 0.464102i | −0.0612928 | + | 0.0353874i | ||||
\(173\) | −2.76795 | + | 4.79423i | −0.210443 | + | 0.364498i | −0.951853 | − | 0.306554i | \(-0.900824\pi\) |
0.741410 | + | 0.671052i | \(0.234157\pi\) | |||||||
\(174\) | −23.6603 | −1.79368 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 2.36603 | − | 4.09808i | 0.178346 | − | 0.308904i | ||||
\(177\) | − | 6.92820i | − | 0.520756i | ||||||
\(178\) | −3.40192 | − | 5.89230i | −0.254985 | − | 0.441647i | ||||
\(179\) | 9.46410i | 0.707380i | 0.935363 | + | 0.353690i | \(0.115073\pi\) | ||||
−0.935363 | + | 0.353690i | \(0.884927\pi\) | |||||||
\(180\) | −6.69615 | + | 3.86603i | −0.499102 | + | 0.288157i | ||||
\(181\) | 4.69615 | + | 8.13397i | 0.349062 | + | 0.604594i | 0.986083 | − | 0.166253i | \(-0.0531668\pi\) |
−0.637021 | + | 0.770847i | \(0.719834\pi\) | |||||||
\(182\) | −3.46410 | − | 6.00000i | −0.256776 | − | 0.444750i | ||||
\(183\) | −4.09808 | − | 2.36603i | −0.302939 | − | 0.174902i | ||||
\(184\) | 4.73205 | 0.348851 | ||||||||
\(185\) | −6.69615 | + | 8.13397i | −0.492311 | + | 0.598022i | ||||
\(186\) | 3.46410 | 0.254000 | ||||||||
\(187\) | −31.6865 | − | 18.2942i | −2.31715 | − | 1.33781i | ||||
\(188\) | 2.36603 | + | 4.09808i | 0.172560 | + | 0.298883i | ||||
\(189\) | 4.00000 | + | 6.92820i | 0.290957 | + | 0.503953i | ||||
\(190\) | 1.90192 | − | 1.09808i | 0.137980 | − | 0.0796628i | ||||
\(191\) | − | 2.19615i | − | 0.158908i | −0.996839 | − | 0.0794540i | \(-0.974682\pi\) | ||
0.996839 | − | 0.0794540i | \(-0.0253177\pi\) | |||||||
\(192\) | 1.36603 | + | 2.36603i | 0.0985844 | + | 0.170753i | ||||
\(193\) | − | 11.1962i | − | 0.805917i | −0.915218 | − | 0.402958i | \(-0.867982\pi\) | ||
0.915218 | − | 0.402958i | \(-0.132018\pi\) | |||||||
\(194\) | 3.86603 | − | 6.69615i | 0.277564 | − | 0.480756i | ||||
\(195\) | 16.3923 | 1.17388 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −3.23205 | + | 5.59808i | −0.230274 | + | 0.398846i | −0.957889 | − | 0.287140i | \(-0.907296\pi\) |
0.727615 | + | 0.685986i | \(0.240629\pi\) | |||||||
\(198\) | 18.2942 | − | 10.5622i | 1.30011 | − | 0.750621i | ||||
\(199\) | 10.3923i | 0.736691i | 0.929689 | + | 0.368345i | \(0.120076\pi\) | ||||
−0.929689 | + | 0.368345i | \(0.879924\pi\) | |||||||
\(200\) | −1.73205 | − | 1.00000i | −0.122474 | − | 0.0707107i | ||||
\(201\) | 13.9282 | − | 24.1244i | 0.982420 | − | 1.70160i | ||||
\(202\) | 10.7942 | + | 6.23205i | 0.759479 | + | 0.438486i | ||||
\(203\) | 15.0000 | − | 8.66025i | 1.05279 | − | 0.607831i | ||||
\(204\) | 18.2942 | − | 10.5622i | 1.28085 | − | 0.739500i | ||||
\(205\) | −14.8923 | − | 8.59808i | −1.04012 | − | 0.600516i | ||||
\(206\) | −4.26795 | + | 7.39230i | −0.297362 | + | 0.515046i | ||||
\(207\) | 18.2942 | + | 10.5622i | 1.27154 | + | 0.734122i | ||||
\(208\) | − | 3.46410i | − | 0.240192i | ||||||
\(209\) | −5.19615 | + | 3.00000i | −0.359425 | + | 0.207514i | ||||
\(210\) | 4.73205 | − | 8.19615i | 0.326543 | − | 0.565588i | ||||
\(211\) | −2.39230 | −0.164693 | −0.0823465 | − | 0.996604i | \(-0.526241\pi\) | ||||
−0.0823465 | + | 0.996604i | \(0.526241\pi\) | |||||||
\(212\) | −2.53590 | −0.174166 | ||||||||
\(213\) | −4.73205 | + | 8.19615i | −0.324235 | + | 0.561591i | ||||
\(214\) | 10.3923i | 0.710403i | ||||||||
\(215\) | 0.803848 | + | 1.39230i | 0.0548219 | + | 0.0949544i | ||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | −2.19615 | + | 1.26795i | −0.149085 | + | 0.0860740i | ||||
\(218\) | 1.33013 | + | 2.30385i | 0.0900876 | + | 0.156036i | ||||
\(219\) | −5.46410 | − | 9.46410i | −0.369230 | − | 0.639525i | ||||
\(220\) | −7.09808 | − | 4.09808i | −0.478552 | − | 0.276292i | ||||
\(221\) | −26.7846 | −1.80173 | ||||||||
\(222\) | 5.83013 | + | 15.5622i | 0.391293 | + | 1.04446i | ||||
\(223\) | 16.1962 | 1.08457 | 0.542287 | − | 0.840193i | \(-0.317558\pi\) | ||||
0.542287 | + | 0.840193i | \(0.317558\pi\) | |||||||
\(224\) | −1.73205 | − | 1.00000i | −0.115728 | − | 0.0668153i | ||||
\(225\) | −4.46410 | − | 7.73205i | −0.297607 | − | 0.515470i | ||||
\(226\) | −1.73205 | − | 3.00000i | −0.115214 | − | 0.199557i | ||||
\(227\) | 1.09808 | − | 0.633975i | 0.0728819 | − | 0.0420784i | −0.463116 | − | 0.886298i | \(-0.653269\pi\) |
0.535998 | + | 0.844219i | \(0.319935\pi\) | |||||||
\(228\) | − | 3.46410i | − | 0.229416i | ||||||
\(229\) | −13.6962 | − | 23.7224i | −0.905067 | − | 1.56762i | −0.820827 | − | 0.571177i | \(-0.806487\pi\) |
−0.0842403 | − | 0.996445i | \(-0.526846\pi\) | |||||||
\(230\) | − | 8.19615i | − | 0.540438i | ||||||
\(231\) | −12.9282 | + | 22.3923i | −0.850613 | + | 1.47331i | ||||
\(232\) | 8.66025 | 0.568574 | ||||||||
\(233\) | 15.0000 | 0.982683 | 0.491341 | − | 0.870967i | \(-0.336507\pi\) | ||||
0.491341 | + | 0.870967i | \(0.336507\pi\) | |||||||
\(234\) | 7.73205 | − | 13.3923i | 0.505460 | − | 0.875482i | ||||
\(235\) | 7.09808 | − | 4.09808i | 0.463027 | − | 0.267329i | ||||
\(236\) | 2.53590i | 0.165073i | ||||||||
\(237\) | 31.3923 | + | 18.1244i | 2.03915 | + | 1.17730i | ||||
\(238\) | −7.73205 | + | 13.3923i | −0.501194 | + | 0.868094i | ||||
\(239\) | −15.0000 | − | 8.66025i | −0.970269 | − | 0.560185i | −0.0709510 | − | 0.997480i | \(-0.522603\pi\) |
−0.899318 | + | 0.437295i | \(0.855937\pi\) | |||||||
\(240\) | 4.09808 | − | 2.36603i | 0.264530 | − | 0.152726i | ||||
\(241\) | 13.3923 | − | 7.73205i | 0.862674 | − | 0.498065i | −0.00223270 | − | 0.999998i | \(-0.500711\pi\) |
0.864907 | + | 0.501932i | \(0.167377\pi\) | |||||||
\(242\) | 9.86603 | + | 5.69615i | 0.634212 | + | 0.366163i | ||||
\(243\) | 9.36603 | − | 16.2224i | 0.600831 | − | 1.04067i | ||||
\(244\) | 1.50000 | + | 0.866025i | 0.0960277 | + | 0.0554416i | ||||
\(245\) | − | 5.19615i | − | 0.331970i | ||||||
\(246\) | −23.4904 | + | 13.5622i | −1.49769 | + | 0.864693i | ||||
\(247\) | −2.19615 | + | 3.80385i | −0.139738 | + | 0.242033i | ||||
\(248\) | −1.26795 | −0.0805149 | ||||||||
\(249\) | −15.4641 | −0.979998 | ||||||||
\(250\) | −6.06218 | + | 10.5000i | −0.383406 | + | 0.664078i | ||||
\(251\) | 17.3205i | 1.09326i | 0.837374 | + | 0.546630i | \(0.184090\pi\) | ||||
−0.837374 | + | 0.546630i | \(0.815910\pi\) | |||||||
\(252\) | −4.46410 | − | 7.73205i | −0.281212 | − | 0.487073i | ||||
\(253\) | 22.3923i | 1.40779i | ||||||||
\(254\) | 6.75833 | − | 3.90192i | 0.424055 | − | 0.244828i | ||||
\(255\) | −18.2942 | − | 31.6865i | −1.14563 | − | 1.98429i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.89230 | + | 3.40192i | 0.367552 | + | 0.212206i | 0.672388 | − | 0.740199i | \(-0.265268\pi\) |
−0.304837 | + | 0.952405i | \(0.598602\pi\) | |||||||
\(258\) | 2.53590 | 0.157878 | ||||||||
\(259\) | −9.39230 | − | 7.73205i | −0.583609 | − | 0.480446i | ||||
\(260\) | −6.00000 | −0.372104 | ||||||||
\(261\) | 33.4808 | + | 19.3301i | 2.07241 | + | 1.19650i | ||||
\(262\) | 4.90192 | + | 8.49038i | 0.302842 | + | 0.524537i | ||||
\(263\) | −10.7321 | − | 18.5885i | −0.661767 | − | 1.14621i | −0.980151 | − | 0.198252i | \(-0.936474\pi\) |
0.318385 | − | 0.947962i | \(-0.396860\pi\) | |||||||
\(264\) | −11.1962 | + | 6.46410i | −0.689076 | + | 0.397838i | ||||
\(265\) | 4.39230i | 0.269817i | ||||||||
\(266\) | 1.26795 | + | 2.19615i | 0.0777430 | + | 0.134655i | ||||
\(267\) | 18.5885i | 1.13760i | ||||||||
\(268\) | −5.09808 | + | 8.83013i | −0.311415 | + | 0.539386i | ||||
\(269\) | −4.39230 | −0.267804 | −0.133902 | − | 0.990995i | \(-0.542751\pi\) | ||||
−0.133902 | + | 0.990995i | \(0.542751\pi\) | |||||||
\(270\) | 6.92820 | 0.421637 | ||||||||
\(271\) | 1.29423 | − | 2.24167i | 0.0786188 | − | 0.136172i | −0.824035 | − | 0.566538i | \(-0.808282\pi\) |
0.902654 | + | 0.430367i | \(0.141616\pi\) | |||||||
\(272\) | −6.69615 | + | 3.86603i | −0.406014 | + | 0.234412i | ||||
\(273\) | 18.9282i | 1.14559i | ||||||||
\(274\) | −1.20577 | − | 0.696152i | −0.0728433 | − | 0.0420561i | ||||
\(275\) | 4.73205 | − | 8.19615i | 0.285353 | − | 0.494247i | ||||
\(276\) | −11.1962 | − | 6.46410i | −0.673929 | − | 0.389093i | ||||
\(277\) | 9.69615 | − | 5.59808i | 0.582585 | − | 0.336356i | −0.179575 | − | 0.983744i | \(-0.557472\pi\) |
0.762160 | + | 0.647389i | \(0.224139\pi\) | |||||||
\(278\) | 17.8301 | − | 10.2942i | 1.06938 | − | 0.617407i | ||||
\(279\) | −4.90192 | − | 2.83013i | −0.293471 | − | 0.169435i | ||||
\(280\) | −1.73205 | + | 3.00000i | −0.103510 | + | 0.179284i | ||||
\(281\) | −23.8923 | − | 13.7942i | −1.42530 | − | 0.822895i | −0.428551 | − | 0.903518i | \(-0.640976\pi\) |
−0.996745 | + | 0.0806230i | \(0.974309\pi\) | |||||||
\(282\) | − | 12.9282i | − | 0.769863i | ||||||
\(283\) | −6.80385 | + | 3.92820i | −0.404447 | + | 0.233507i | −0.688401 | − | 0.725330i | \(-0.741687\pi\) |
0.283954 | + | 0.958838i | \(0.408354\pi\) | |||||||
\(284\) | 1.73205 | − | 3.00000i | 0.102778 | − | 0.178017i | ||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 16.3923 | 0.969297 | ||||||||
\(287\) | 9.92820 | − | 17.1962i | 0.586043 | − | 1.01506i | ||||
\(288\) | − | 4.46410i | − | 0.263050i | ||||||
\(289\) | 21.3923 | + | 37.0526i | 1.25837 | + | 2.17956i | ||||
\(290\) | − | 15.0000i | − | 0.880830i | ||||||
\(291\) | −18.2942 | + | 10.5622i | −1.07243 | + | 0.619166i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | 0.696152 | + | 1.20577i | 0.0406697 | + | 0.0704419i | 0.885644 | − | 0.464365i | \(-0.153718\pi\) |
−0.844974 | + | 0.534807i | \(0.820384\pi\) | |||||||
\(294\) | −7.09808 | − | 4.09808i | −0.413968 | − | 0.239005i | ||||
\(295\) | 4.39230 | 0.255730 | ||||||||
\(296\) | −2.13397 | − | 5.69615i | −0.124035 | − | 0.331082i | ||||
\(297\) | −18.9282 | −1.09833 | ||||||||
\(298\) | −13.7942 | − | 7.96410i | −0.799078 | − | 0.461348i | ||||
\(299\) | 8.19615 | + | 14.1962i | 0.473996 | + | 0.820985i | ||||
\(300\) | 2.73205 | + | 4.73205i | 0.157735 | + | 0.273205i | ||||
\(301\) | −1.60770 | + | 0.928203i | −0.0926660 | + | 0.0535007i | ||||
\(302\) | − | 4.19615i | − | 0.241461i | ||||||
\(303\) | −17.0263 | − | 29.4904i | −0.978134 | − | 1.69418i | ||||
\(304\) | 1.26795i | 0.0727219i | ||||||||
\(305\) | 1.50000 | − | 2.59808i | 0.0858898 | − | 0.148765i | ||||
\(306\) | −34.5167 | −1.97319 | ||||||||
\(307\) | −22.0000 | −1.25561 | −0.627803 | − | 0.778372i | \(-0.716046\pi\) | ||||
−0.627803 | + | 0.778372i | \(0.716046\pi\) | |||||||
\(308\) | 4.73205 | − | 8.19615i | 0.269634 | − | 0.467019i | ||||
\(309\) | 20.1962 | − | 11.6603i | 1.14892 | − | 0.663329i | ||||
\(310\) | 2.19615i | 0.124733i | ||||||||
\(311\) | −15.5885 | − | 9.00000i | −0.883940 | − | 0.510343i | −0.0119847 | − | 0.999928i | \(-0.503815\pi\) |
−0.871956 | + | 0.489585i | \(0.837148\pi\) | |||||||
\(312\) | −4.73205 | + | 8.19615i | −0.267900 | + | 0.464016i | ||||
\(313\) | 20.8923 | + | 12.0622i | 1.18090 | + | 0.681795i | 0.956223 | − | 0.292638i | \(-0.0945331\pi\) |
0.224680 | + | 0.974433i | \(0.427866\pi\) | |||||||
\(314\) | −0.866025 | + | 0.500000i | −0.0488726 | + | 0.0282166i | ||||
\(315\) | −13.3923 | + | 7.73205i | −0.754571 | + | 0.435652i | ||||
\(316\) | −11.4904 | − | 6.63397i | −0.646384 | − | 0.373190i | ||||
\(317\) | −3.69615 | + | 6.40192i | −0.207597 | + | 0.359568i | −0.950957 | − | 0.309323i | \(-0.899897\pi\) |
0.743360 | + | 0.668891i | \(0.233231\pi\) | |||||||
\(318\) | 6.00000 | + | 3.46410i | 0.336463 | + | 0.194257i | ||||
\(319\) | 40.9808i | 2.29448i | ||||||||
\(320\) | −1.50000 | + | 0.866025i | −0.0838525 | + | 0.0484123i | ||||
\(321\) | 14.1962 | − | 24.5885i | 0.792352 | − | 1.37239i | ||||
\(322\) | 9.46410 | 0.527414 | ||||||||
\(323\) | 9.80385 | 0.545501 | ||||||||
\(324\) | −1.23205 | + | 2.13397i | −0.0684473 | + | 0.118554i | ||||
\(325\) | − | 6.92820i | − | 0.384308i | ||||||
\(326\) | 6.46410 | + | 11.1962i | 0.358013 | + | 0.620098i | ||||
\(327\) | − | 7.26795i | − | 0.401919i | ||||||
\(328\) | 8.59808 | − | 4.96410i | 0.474749 | − | 0.274097i | ||||
\(329\) | 4.73205 | + | 8.19615i | 0.260886 | + | 0.451869i | ||||
\(330\) | 11.1962 | + | 19.3923i | 0.616328 | + | 1.06751i | ||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 5.66025 | 0.310647 | ||||||||
\(333\) | 4.46410 | − | 26.7846i | 0.244631 | − | 1.46779i | ||||
\(334\) | −13.8564 | −0.758189 | ||||||||
\(335\) | 15.2942 | + | 8.83013i | 0.835613 | + | 0.482441i | ||||
\(336\) | 2.73205 | + | 4.73205i | 0.149046 | + | 0.258155i | ||||
\(337\) | 16.0885 | + | 27.8660i | 0.876394 | + | 1.51796i | 0.855270 | + | 0.518182i | \(0.173391\pi\) |
0.0211239 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(338\) | −0.866025 | + | 0.500000i | −0.0471056 | + | 0.0271964i | ||||
\(339\) | 9.46410i | 0.514019i | ||||||||
\(340\) | 6.69615 | + | 11.5981i | 0.363150 | + | 0.628994i | ||||
\(341\) | − | 6.00000i | − | 0.324918i | ||||||
\(342\) | −2.83013 | + | 4.90192i | −0.153036 | + | 0.265066i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −0.928203 | −0.0500454 | ||||||||
\(345\) | −11.1962 | + | 19.3923i | −0.602781 | + | 1.04405i | ||||
\(346\) | −4.79423 | + | 2.76795i | −0.257739 | + | 0.148806i | ||||
\(347\) | − | 9.12436i | − | 0.489821i | −0.969546 | − | 0.244911i | \(-0.921241\pi\) | ||
0.969546 | − | 0.244911i | \(-0.0787586\pi\) | |||||||
\(348\) | −20.4904 | − | 11.8301i | −1.09840 | − | 0.634161i | ||||
\(349\) | −5.69615 | + | 9.86603i | −0.304908 | + | 0.528116i | −0.977241 | − | 0.212133i | \(-0.931959\pi\) |
0.672333 | + | 0.740249i | \(0.265292\pi\) | |||||||
\(350\) | −3.46410 | − | 2.00000i | −0.185164 | − | 0.106904i | ||||
\(351\) | −12.0000 | + | 6.92820i | −0.640513 | + | 0.369800i | ||||
\(352\) | 4.09808 | − | 2.36603i | 0.218428 | − | 0.126110i | ||||
\(353\) | −17.0885 | − | 9.86603i | −0.909527 | − | 0.525116i | −0.0292479 | − | 0.999572i | \(-0.509311\pi\) |
−0.880279 | + | 0.474457i | \(0.842645\pi\) | |||||||
\(354\) | 3.46410 | − | 6.00000i | 0.184115 | − | 0.318896i | ||||
\(355\) | −5.19615 | − | 3.00000i | −0.275783 | − | 0.159223i | ||||
\(356\) | − | 6.80385i | − | 0.360603i | ||||||
\(357\) | 36.5885 | − | 21.1244i | 1.93647 | − | 1.11802i | ||||
\(358\) | −4.73205 | + | 8.19615i | −0.250097 | + | 0.433180i | ||||
\(359\) | 35.3205 | 1.86415 | 0.932073 | − | 0.362272i | \(-0.117999\pi\) | ||||
0.932073 | + | 0.362272i | \(0.117999\pi\) | |||||||
\(360\) | −7.73205 | −0.407515 | ||||||||
\(361\) | −8.69615 | + | 15.0622i | −0.457692 | + | 0.792746i | ||||
\(362\) | 9.39230i | 0.493649i | ||||||||
\(363\) | −15.5622 | − | 26.9545i | −0.816803 | − | 1.41474i | ||||
\(364\) | − | 6.92820i | − | 0.363137i | ||||||
\(365\) | 6.00000 | − | 3.46410i | 0.314054 | − | 0.181319i | ||||
\(366\) | −2.36603 | − | 4.09808i | −0.123674 | − | 0.214210i | ||||
\(367\) | −6.19615 | − | 10.7321i | −0.323437 | − | 0.560208i | 0.657758 | − | 0.753229i | \(-0.271505\pi\) |
−0.981195 | + | 0.193021i | \(0.938172\pi\) | |||||||
\(368\) | 4.09808 | + | 2.36603i | 0.213627 | + | 0.123338i | ||||
\(369\) | 44.3205 | 2.30723 | ||||||||
\(370\) | −9.86603 | + | 3.69615i | −0.512910 | + | 0.192154i | ||||
\(371\) | −5.07180 | −0.263315 | ||||||||
\(372\) | 3.00000 | + | 1.73205i | 0.155543 | + | 0.0898027i | ||||
\(373\) | −3.50000 | − | 6.06218i | −0.181223 | − | 0.313888i | 0.761074 | − | 0.648665i | \(-0.224672\pi\) |
−0.942297 | + | 0.334777i | \(0.891339\pi\) | |||||||
\(374\) | −18.2942 | − | 31.6865i | −0.945972 | − | 1.63847i | ||||
\(375\) | 28.6865 | − | 16.5622i | 1.48137 | − | 0.855267i | ||||
\(376\) | 4.73205i | 0.244037i | ||||||||
\(377\) | 15.0000 | + | 25.9808i | 0.772539 | + | 1.33808i | ||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | 17.3923 | − | 30.1244i | 0.893383 | − | 1.54738i | 0.0575891 | − | 0.998340i | \(-0.481659\pi\) |
0.835794 | − | 0.549044i | \(-0.185008\pi\) | |||||||
\(380\) | 2.19615 | 0.112660 | ||||||||
\(381\) | −21.3205 | −1.09228 | ||||||||
\(382\) | 1.09808 | − | 1.90192i | 0.0561825 | − | 0.0973109i | ||||
\(383\) | −3.00000 | + | 1.73205i | −0.153293 | + | 0.0885037i | −0.574684 | − | 0.818375i | \(-0.694875\pi\) |
0.421392 | + | 0.906879i | \(0.361542\pi\) | |||||||
\(384\) | 2.73205i | 0.139419i | ||||||||
\(385\) | −14.1962 | − | 8.19615i | −0.723503 | − | 0.417715i | ||||
\(386\) | 5.59808 | − | 9.69615i | 0.284935 | − | 0.493521i | ||||
\(387\) | −3.58846 | − | 2.07180i | −0.182412 | − | 0.105315i | ||||
\(388\) | 6.69615 | − | 3.86603i | 0.339946 | − | 0.196268i | ||||
\(389\) | −22.5000 | + | 12.9904i | −1.14080 | + | 0.658638i | −0.946627 | − | 0.322330i | \(-0.895534\pi\) |
−0.194168 | + | 0.980968i | \(0.562201\pi\) | |||||||
\(390\) | 14.1962 | + | 8.19615i | 0.718850 | + | 0.415028i | ||||
\(391\) | 18.2942 | − | 31.6865i | 0.925179 | − | 1.60246i | ||||
\(392\) | 2.59808 | + | 1.50000i | 0.131223 | + | 0.0757614i | ||||
\(393\) | − | 26.7846i | − | 1.35110i | ||||||
\(394\) | −5.59808 | + | 3.23205i | −0.282027 | + | 0.162828i | ||||
\(395\) | −11.4904 | + | 19.9019i | −0.578144 | + | 1.00137i | ||||
\(396\) | 21.1244 | 1.06154 | ||||||||
\(397\) | −23.0000 | −1.15434 | −0.577168 | − | 0.816625i | \(-0.695842\pi\) | ||||
−0.577168 | + | 0.816625i | \(0.695842\pi\) | |||||||
\(398\) | −5.19615 | + | 9.00000i | −0.260460 | + | 0.451129i | ||||
\(399\) | − | 6.92820i | − | 0.346844i | ||||||
\(400\) | −1.00000 | − | 1.73205i | −0.0500000 | − | 0.0866025i | ||||
\(401\) | 10.3923i | 0.518967i | 0.965748 | + | 0.259483i | \(0.0835523\pi\) | ||||
−0.965748 | + | 0.259483i | \(0.916448\pi\) | |||||||
\(402\) | 24.1244 | − | 13.9282i | 1.20321 | − | 0.694676i | ||||
\(403\) | −2.19615 | − | 3.80385i | −0.109398 | − | 0.189483i | ||||
\(404\) | 6.23205 | + | 10.7942i | 0.310056 | + | 0.537033i | ||||
\(405\) | 3.69615 | + | 2.13397i | 0.183663 | + | 0.106038i | ||||
\(406\) | 17.3205 | 0.859602 | ||||||||
\(407\) | 26.9545 | − | 10.0981i | 1.33608 | − | 0.500543i | ||||
\(408\) | 21.1244 | 1.04581 | ||||||||
\(409\) | 9.10770 | + | 5.25833i | 0.450347 | + | 0.260008i | 0.707977 | − | 0.706236i | \(-0.249608\pi\) |
−0.257630 | + | 0.966244i | \(0.582942\pi\) | |||||||
\(410\) | −8.59808 | − | 14.8923i | −0.424629 | − | 0.735479i | ||||
\(411\) | 1.90192 | + | 3.29423i | 0.0938150 | + | 0.162492i | ||||
\(412\) | −7.39230 | + | 4.26795i | −0.364193 | + | 0.210267i | ||||
\(413\) | 5.07180i | 0.249567i | ||||||||
\(414\) | 10.5622 | + | 18.2942i | 0.519103 | + | 0.899112i | ||||
\(415\) | − | 9.80385i | − | 0.481252i | ||||||
\(416\) | 1.73205 | − | 3.00000i | 0.0849208 | − | 0.147087i | ||||
\(417\) | −56.2487 | −2.75451 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | 2.07180 | − | 3.58846i | 0.101214 | − | 0.175308i | −0.810971 | − | 0.585086i | \(-0.801061\pi\) |
0.912185 | + | 0.409779i | \(0.134394\pi\) | |||||||
\(420\) | 8.19615 | − | 4.73205i | 0.399931 | − | 0.230900i | ||||
\(421\) | 12.1244i | 0.590905i | 0.955357 | + | 0.295452i | \(0.0954704\pi\) | ||||
−0.955357 | + | 0.295452i | \(0.904530\pi\) | |||||||
\(422\) | −2.07180 | − | 1.19615i | −0.100853 | − | 0.0582278i | ||||
\(423\) | −10.5622 | + | 18.2942i | −0.513551 | + | 0.889496i | ||||
\(424\) | −2.19615 | − | 1.26795i | −0.106655 | − | 0.0615771i | ||||
\(425\) | −13.3923 | + | 7.73205i | −0.649622 | + | 0.375060i | ||||
\(426\) | −8.19615 | + | 4.73205i | −0.397105 | + | 0.229269i | ||||
\(427\) | 3.00000 | + | 1.73205i | 0.145180 | + | 0.0838198i | ||||
\(428\) | −5.19615 | + | 9.00000i | −0.251166 | + | 0.435031i | ||||
\(429\) | −38.7846 | − | 22.3923i | −1.87254 | − | 1.08111i | ||||
\(430\) | 1.60770i | 0.0775299i | ||||||||
\(431\) | −15.2942 | + | 8.83013i | −0.736697 | + | 0.425332i | −0.820867 | − | 0.571119i | \(-0.806509\pi\) |
0.0841701 | + | 0.996451i | \(0.473176\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | 15.7846 | 0.758560 | 0.379280 | − | 0.925282i | \(-0.376172\pi\) | ||||
0.379280 | + | 0.925282i | \(0.376172\pi\) | |||||||
\(434\) | −2.53590 | −0.121727 | ||||||||
\(435\) | −20.4904 | + | 35.4904i | −0.982439 | + | 1.70163i | ||||
\(436\) | 2.66025i | 0.127403i | ||||||||
\(437\) | −3.00000 | − | 5.19615i | −0.143509 | − | 0.248566i | ||||
\(438\) | − | 10.9282i | − | 0.522170i | ||||||
\(439\) | −15.8038 | + | 9.12436i | −0.754276 | + | 0.435482i | −0.827237 | − | 0.561853i | \(-0.810089\pi\) |
0.0729605 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(440\) | −4.09808 | − | 7.09808i | −0.195368 | − | 0.338388i | ||||
\(441\) | 6.69615 | + | 11.5981i | 0.318864 | + | 0.552289i | ||||
\(442\) | −23.1962 | − | 13.3923i | −1.10333 | − | 0.637007i | ||||
\(443\) | −14.5359 | −0.690621 | −0.345311 | − | 0.938488i | \(-0.612226\pi\) | ||||
−0.345311 | + | 0.938488i | \(0.612226\pi\) | |||||||
\(444\) | −2.73205 | + | 16.3923i | −0.129657 | + | 0.777944i | ||||
\(445\) | −11.7846 | −0.558644 | ||||||||
\(446\) | 14.0263 | + | 8.09808i | 0.664164 | + | 0.383455i | ||||
\(447\) | 21.7583 | + | 37.6865i | 1.02913 | + | 1.78251i | ||||
\(448\) | −1.00000 | − | 1.73205i | −0.0472456 | − | 0.0818317i | ||||
\(449\) | 17.7846 | − | 10.2679i | 0.839308 | − | 0.484574i | −0.0177212 | − | 0.999843i | \(-0.505641\pi\) |
0.857029 | + | 0.515268i | \(0.172308\pi\) | |||||||
\(450\) | − | 8.92820i | − | 0.420880i | ||||||
\(451\) | 23.4904 | + | 40.6865i | 1.10612 | + | 1.91585i | ||||
\(452\) | − | 3.46410i | − | 0.162938i | ||||||
\(453\) | −5.73205 | + | 9.92820i | −0.269315 | + | 0.466468i | ||||
\(454\) | 1.26795 | 0.0595078 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 1.73205 | − | 3.00000i | 0.0811107 | − | 0.140488i | ||||
\(457\) | −32.8923 | + | 18.9904i | −1.53864 | + | 0.888333i | −0.539718 | + | 0.841846i | \(0.681469\pi\) |
−0.998919 | + | 0.0464868i | \(0.985197\pi\) | |||||||
\(458\) | − | 27.3923i | − | 1.27996i | ||||||
\(459\) | 26.7846 | + | 15.4641i | 1.25020 | + | 0.721802i | ||||
\(460\) | 4.09808 | − | 7.09808i | 0.191074 | − | 0.330950i | ||||
\(461\) | −34.1769 | − | 19.7321i | −1.59178 | − | 0.919013i | −0.993002 | − | 0.118096i | \(-0.962321\pi\) |
−0.598775 | − | 0.800917i | \(-0.704346\pi\) | |||||||
\(462\) | −22.3923 | + | 12.9282i | −1.04178 | + | 0.601474i | ||||
\(463\) | −25.9808 | + | 15.0000i | −1.20743 | + | 0.697109i | −0.962197 | − | 0.272355i | \(-0.912197\pi\) |
−0.245232 | + | 0.969465i | \(0.578864\pi\) | |||||||
\(464\) | 7.50000 | + | 4.33013i | 0.348179 | + | 0.201021i | ||||
\(465\) | 3.00000 | − | 5.19615i | 0.139122 | − | 0.240966i | ||||
\(466\) | 12.9904 | + | 7.50000i | 0.601768 | + | 0.347431i | ||||
\(467\) | 2.53590i | 0.117347i | 0.998277 | + | 0.0586737i | \(0.0186871\pi\) | ||||
−0.998277 | + | 0.0586737i | \(0.981313\pi\) | |||||||
\(468\) | 13.3923 | − | 7.73205i | 0.619060 | − | 0.357414i | ||||
\(469\) | −10.1962 | + | 17.6603i | −0.470815 | + | 0.815475i | ||||
\(470\) | 8.19615 | 0.378060 | ||||||||
\(471\) | 2.73205 | 0.125886 | ||||||||
\(472\) | −1.26795 | + | 2.19615i | −0.0583621 | + | 0.101086i | ||||
\(473\) | − | 4.39230i | − | 0.201958i | ||||||
\(474\) | 18.1244 | + | 31.3923i | 0.832479 | + | 1.44190i | ||||
\(475\) | 2.53590i | 0.116355i | ||||||||
\(476\) | −13.3923 | + | 7.73205i | −0.613835 | + | 0.354398i | ||||
\(477\) | −5.66025 | − | 9.80385i | −0.259165 | − | 0.448887i | ||||
\(478\) | −8.66025 | − | 15.0000i | −0.396111 | − | 0.686084i | ||||
\(479\) | 8.19615 | + | 4.73205i | 0.374492 | + | 0.216213i | 0.675419 | − | 0.737434i | \(-0.263963\pi\) |
−0.300927 | + | 0.953647i | \(0.597296\pi\) | |||||||
\(480\) | 4.73205 | 0.215988 | ||||||||
\(481\) | 13.3923 | − | 16.2679i | 0.610637 | − | 0.741755i | ||||
\(482\) | 15.4641 | 0.704371 | ||||||||
\(483\) | −22.3923 | − | 12.9282i | −1.01889 | − | 0.588254i | ||||
\(484\) | 5.69615 | + | 9.86603i | 0.258916 | + | 0.448456i | ||||
\(485\) | −6.69615 | − | 11.5981i | −0.304057 | − | 0.526642i | ||||
\(486\) | 16.2224 | − | 9.36603i | 0.735864 | − | 0.424852i | ||||
\(487\) | − | 16.0526i | − | 0.727411i | −0.931514 | − | 0.363705i | \(-0.881511\pi\) | ||
0.931514 | − | 0.363705i | \(-0.118489\pi\) | |||||||
\(488\) | 0.866025 | + | 1.50000i | 0.0392031 | + | 0.0679018i | ||||
\(489\) | − | 35.3205i | − | 1.59725i | ||||||
\(490\) | 2.59808 | − | 4.50000i | 0.117369 | − | 0.203289i | ||||
\(491\) | 26.1962 | 1.18222 | 0.591108 | − | 0.806592i | \(-0.298691\pi\) | ||||
0.591108 | + | 0.806592i | \(0.298691\pi\) | |||||||
\(492\) | −27.1244 | −1.22286 | ||||||||
\(493\) | 33.4808 | − | 57.9904i | 1.50790 | − | 2.61176i | ||||
\(494\) | −3.80385 | + | 2.19615i | −0.171143 | + | 0.0988096i | ||||
\(495\) | − | 36.5885i | − | 1.64453i | ||||||
\(496\) | −1.09808 | − | 0.633975i | −0.0493051 | − | 0.0284663i | ||||
\(497\) | 3.46410 | − | 6.00000i | 0.155386 | − | 0.269137i | ||||
\(498\) | −13.3923 | − | 7.73205i | −0.600124 | − | 0.346481i | ||||
\(499\) | −17.4904 | + | 10.0981i | −0.782977 | + | 0.452052i | −0.837484 | − | 0.546461i | \(-0.815975\pi\) |
0.0545073 | + | 0.998513i | \(0.482641\pi\) | |||||||
\(500\) | −10.5000 | + | 6.06218i | −0.469574 | + | 0.271109i | ||||
\(501\) | 32.7846 | + | 18.9282i | 1.46471 | + | 0.845650i | ||||
\(502\) | −8.66025 | + | 15.0000i | −0.386526 | + | 0.669483i | ||||
\(503\) | −17.4904 | − | 10.0981i | −0.779858 | − | 0.450251i | 0.0565223 | − | 0.998401i | \(-0.481999\pi\) |
−0.836380 | + | 0.548150i | \(0.815332\pi\) | |||||||
\(504\) | − | 8.92820i | − | 0.397694i | ||||||
\(505\) | 18.6962 | − | 10.7942i | 0.831968 | − | 0.480337i | ||||
\(506\) | −11.1962 | + | 19.3923i | −0.497730 | + | 0.862093i | ||||
\(507\) | 2.73205 | 0.121335 | ||||||||
\(508\) | 7.80385 | 0.346240 | ||||||||
\(509\) | 3.23205 | − | 5.59808i | 0.143258 | − | 0.248130i | −0.785464 | − | 0.618908i | \(-0.787575\pi\) |
0.928722 | + | 0.370777i | \(0.120909\pi\) | |||||||
\(510\) | − | 36.5885i | − | 1.62016i | ||||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.39230 | − | 2.53590i | 0.193925 | − | 0.111963i | ||||
\(514\) | 3.40192 | + | 5.89230i | 0.150052 | + | 0.259898i | ||||
\(515\) | 7.39230 | + | 12.8038i | 0.325744 | + | 0.564205i | ||||
\(516\) | 2.19615 | + | 1.26795i | 0.0966802 | + | 0.0558184i | ||||
\(517\) | −22.3923 | −0.984812 | ||||||||
\(518\) | −4.26795 | − | 11.3923i | −0.187523 | − | 0.500549i | ||||
\(519\) | 15.1244 | 0.663886 | ||||||||
\(520\) | −5.19615 | − | 3.00000i | −0.227866 | − | 0.131559i | ||||
\(521\) | −2.53590 | − | 4.39230i | −0.111100 | − | 0.192430i | 0.805114 | − | 0.593120i | \(-0.202104\pi\) |
−0.916214 | + | 0.400689i | \(0.868771\pi\) | |||||||
\(522\) | 19.3301 | + | 33.4808i | 0.846057 | + | 1.46541i | ||||
\(523\) | 17.7058 | − | 10.2224i | 0.774219 | − | 0.446996i | −0.0601584 | − | 0.998189i | \(-0.519161\pi\) |
0.834378 | + | 0.551193i | \(0.185827\pi\) | |||||||
\(524\) | 9.80385i | 0.428283i | ||||||||
\(525\) | 5.46410 | + | 9.46410i | 0.238473 | + | 0.413047i | ||||
\(526\) | − | 21.4641i | − | 0.935879i | ||||||
\(527\) | −4.90192 | + | 8.49038i | −0.213531 | + | 0.369847i | ||||
\(528\) | −12.9282 | −0.562628 | ||||||||
\(529\) | 0.607695 | 0.0264215 | ||||||||
\(530\) | −2.19615 | + | 3.80385i | −0.0953948 | + | 0.165229i | ||||
\(531\) | −9.80385 | + | 5.66025i | −0.425451 | + | 0.245634i | ||||
\(532\) | 2.53590i | 0.109945i | ||||||||
\(533\) | 29.7846 | + | 17.1962i | 1.29011 | + | 0.744848i | ||||
\(534\) | −9.29423 | + | 16.0981i | −0.402201 | + | 0.696632i | ||||
\(535\) | 15.5885 | + | 9.00000i | 0.673948 | + | 0.389104i | ||||
\(536\) | −8.83013 | + | 5.09808i | −0.381403 | + | 0.220203i | ||||
\(537\) | 22.3923 | − | 12.9282i | 0.966299 | − | 0.557893i | ||||
\(538\) | −3.80385 | − | 2.19615i | −0.163996 | − | 0.0946829i | ||||
\(539\) | −7.09808 | + | 12.2942i | −0.305736 | + | 0.529550i | ||||
\(540\) | 6.00000 | + | 3.46410i | 0.258199 | + | 0.149071i | ||||
\(541\) | − | 19.0526i | − | 0.819133i | −0.912280 | − | 0.409567i | \(-0.865680\pi\) | ||
0.912280 | − | 0.409567i | \(-0.134320\pi\) | |||||||
\(542\) | 2.24167 | − | 1.29423i | 0.0962880 | − | 0.0555919i | ||||
\(543\) | 12.8301 | − | 22.2224i | 0.550593 | − | 0.953656i | ||||
\(544\) | −7.73205 | −0.331509 | ||||||||
\(545\) | 4.60770 | 0.197372 | ||||||||
\(546\) | −9.46410 | + | 16.3923i | −0.405026 | + | 0.701526i | ||||
\(547\) | − | 41.6603i | − | 1.78126i | −0.454725 | − | 0.890632i | \(-0.650262\pi\) | ||
0.454725 | − | 0.890632i | \(-0.349738\pi\) | |||||||
\(548\) | −0.696152 | − | 1.20577i | −0.0297382 | − | 0.0515080i | ||||
\(549\) | 7.73205i | 0.329996i | ||||||||
\(550\) | 8.19615 | − | 4.73205i | 0.349485 | − | 0.201775i | ||||
\(551\) | −5.49038 | − | 9.50962i | −0.233898 | − | 0.405123i | ||||
\(552\) | −6.46410 | − | 11.1962i | −0.275130 | − | 0.476540i | ||||
\(553\) | −22.9808 | − | 13.2679i | −0.977241 | − | 0.564211i | ||||
\(554\) | 11.1962 | 0.475679 | ||||||||
\(555\) | 28.3923 | + | 4.73205i | 1.20519 | + | 0.200864i | ||||
\(556\) | 20.5885 | 0.873145 | ||||||||
\(557\) | 20.3038 | + | 11.7224i | 0.860302 | + | 0.496695i | 0.864113 | − | 0.503297i | \(-0.167880\pi\) |
−0.00381165 | + | 0.999993i | \(0.501213\pi\) | |||||||
\(558\) | −2.83013 | − | 4.90192i | −0.119809 | − | 0.207515i | ||||
\(559\) | −1.60770 | − | 2.78461i | −0.0679983 | − | 0.117776i | ||||
\(560\) | −3.00000 | + | 1.73205i | −0.126773 | + | 0.0731925i | ||||
\(561\) | 99.9615i | 4.22038i | ||||||||
\(562\) | −13.7942 | − | 23.8923i | −0.581874 | − | 1.00784i | ||||
\(563\) | 18.5885i | 0.783410i | 0.920091 | + | 0.391705i | \(0.128115\pi\) | ||||
−0.920091 | + | 0.391705i | \(0.871885\pi\) | |||||||
\(564\) | 6.46410 | − | 11.1962i | 0.272188 | − | 0.471443i | ||||
\(565\) | −6.00000 | −0.252422 | ||||||||
\(566\) | −7.85641 | −0.330229 | ||||||||
\(567\) | −2.46410 | + | 4.26795i | −0.103483 | + | 0.179237i | ||||
\(568\) | 3.00000 | − | 1.73205i | 0.125877 | − | 0.0726752i | ||||
\(569\) | 5.87564i | 0.246320i | 0.992387 | + | 0.123160i | \(0.0393028\pi\) | ||||
−0.992387 | + | 0.123160i | \(0.960697\pi\) | |||||||
\(570\) | −5.19615 | − | 3.00000i | −0.217643 | − | 0.125656i | ||||
\(571\) | −18.6865 | + | 32.3660i | −0.782007 | + | 1.35448i | 0.148764 | + | 0.988873i | \(0.452471\pi\) |
−0.930771 | + | 0.365603i | \(0.880863\pi\) | |||||||
\(572\) | 14.1962 | + | 8.19615i | 0.593571 | + | 0.342698i | ||||
\(573\) | −5.19615 | + | 3.00000i | −0.217072 | + | 0.125327i | ||||
\(574\) | 17.1962 | − | 9.92820i | 0.717754 | − | 0.414395i | ||||
\(575\) | 8.19615 | + | 4.73205i | 0.341803 | + | 0.197340i | ||||
\(576\) | 2.23205 | − | 3.86603i | 0.0930021 | − | 0.161084i | ||||
\(577\) | −0.803848 | − | 0.464102i | −0.0334646 | − | 0.0193208i | 0.483174 | − | 0.875524i | \(-0.339484\pi\) |
−0.516639 | + | 0.856203i | \(0.672817\pi\) | |||||||
\(578\) | 42.7846i | 1.77961i | ||||||||
\(579\) | −26.4904 | + | 15.2942i | −1.10090 | + | 0.635606i | ||||
\(580\) | 7.50000 | − | 12.9904i | 0.311421 | − | 0.539396i | ||||
\(581\) | 11.3205 | 0.469654 | ||||||||
\(582\) | −21.1244 | −0.875633 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 4.00000i | 0.165521i | ||||||||
\(585\) | −13.3923 | − | 23.1962i | −0.553704 | − | 0.959043i | ||||
\(586\) | 1.39230i | 0.0575156i | ||||||||
\(587\) | 28.6865 | − | 16.5622i | 1.18402 | − | 0.683594i | 0.227079 | − | 0.973876i | \(-0.427082\pi\) |
0.956941 | + | 0.290282i | \(0.0937492\pi\) | |||||||
\(588\) | −4.09808 | − | 7.09808i | −0.169002 | − | 0.292720i | ||||
\(589\) | 0.803848 | + | 1.39230i | 0.0331220 | + | 0.0573689i | ||||
\(590\) | 3.80385 | + | 2.19615i | 0.156602 | + | 0.0904142i | ||||
\(591\) | 17.6603 | 0.726446 | ||||||||
\(592\) | 1.00000 | − | 6.00000i | 0.0410997 | − | 0.246598i | ||||
\(593\) | 43.6410 | 1.79212 | 0.896061 | − | 0.443931i | \(-0.146417\pi\) | ||||
0.896061 | + | 0.443931i | \(0.146417\pi\) | |||||||
\(594\) | −16.3923 | − | 9.46410i | −0.672584 | − | 0.388317i | ||||
\(595\) | 13.3923 | + | 23.1962i | 0.549031 | + | 0.950950i | ||||
\(596\) | −7.96410 | − | 13.7942i | −0.326222 | − | 0.565034i | ||||
\(597\) | 24.5885 | − | 14.1962i | 1.00634 | − | 0.581010i | ||||
\(598\) | 16.3923i | 0.670331i | ||||||||
\(599\) | −23.8301 | − | 41.2750i | −0.973673 | − | 1.68645i | −0.684248 | − | 0.729250i | \(-0.739869\pi\) |
−0.289425 | − | 0.957201i | \(-0.593464\pi\) | |||||||
\(600\) | 5.46410i | 0.223071i | ||||||||
\(601\) | 6.30385 | − | 10.9186i | 0.257139 | − | 0.445378i | −0.708335 | − | 0.705876i | \(-0.750553\pi\) |
0.965474 | + | 0.260498i | \(0.0838867\pi\) | |||||||
\(602\) | −1.85641 | −0.0756615 | ||||||||
\(603\) | −45.5167 | −1.85358 | ||||||||
\(604\) | 2.09808 | − | 3.63397i | 0.0853695 | − | 0.147864i | ||||
\(605\) | 17.0885 | − | 9.86603i | 0.694745 | − | 0.401111i | ||||
\(606\) | − | 34.0526i | − | 1.38329i | ||||||
\(607\) | −20.7058 | − | 11.9545i | −0.840421 | − | 0.485217i | 0.0169861 | − | 0.999856i | \(-0.494593\pi\) |
−0.857407 | + | 0.514638i | \(0.827926\pi\) | |||||||
\(608\) | −0.633975 | + | 1.09808i | −0.0257111 | + | 0.0445329i | ||||
\(609\) | −40.9808 | − | 23.6603i | −1.66062 | − | 0.958762i | ||||
\(610\) | 2.59808 | − | 1.50000i | 0.105193 | − | 0.0607332i | ||||
\(611\) | −14.1962 | + | 8.19615i | −0.574315 | + | 0.331581i | ||||
\(612\) | −29.8923 | − | 17.2583i | −1.20832 | − | 0.697627i | ||||
\(613\) | −3.89230 | + | 6.74167i | −0.157209 | + | 0.272293i | −0.933861 | − | 0.357636i | \(-0.883583\pi\) |
0.776652 | + | 0.629929i | \(0.216916\pi\) | |||||||
\(614\) | −19.0526 | − | 11.0000i | −0.768899 | − | 0.443924i | ||||
\(615\) | 46.9808i | 1.89445i | ||||||||
\(616\) | 8.19615 | − | 4.73205i | 0.330232 | − | 0.190660i | ||||
\(617\) | −6.33975 | + | 10.9808i | −0.255229 | + | 0.442069i | −0.964958 | − | 0.262406i | \(-0.915484\pi\) |
0.709729 | + | 0.704475i | \(0.248817\pi\) | |||||||
\(618\) | 23.3205 | 0.938088 | ||||||||
\(619\) | 30.3923 | 1.22157 | 0.610785 | − | 0.791797i | \(-0.290854\pi\) | ||||
0.610785 | + | 0.791797i | \(0.290854\pi\) | |||||||
\(620\) | −1.09808 | + | 1.90192i | −0.0440998 | + | 0.0763831i | ||||
\(621\) | − | 18.9282i | − | 0.759563i | ||||||
\(622\) | −9.00000 | − | 15.5885i | −0.360867 | − | 0.625040i | ||||
\(623\) | − | 13.6077i | − | 0.545181i | ||||||
\(624\) | −8.19615 | + | 4.73205i | −0.328109 | + | 0.189434i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 12.0622 | + | 20.8923i | 0.482102 | + | 0.835024i | ||||
\(627\) | 14.1962 | + | 8.19615i | 0.566940 | + | 0.327323i | ||||
\(628\) | −1.00000 | −0.0399043 | ||||||||
\(629\) | −46.3923 | − | 7.73205i | −1.84978 | − | 0.308297i | ||||
\(630\) | −15.4641 | −0.616105 | ||||||||
\(631\) | −30.2942 | − | 17.4904i | −1.20599 | − | 0.696281i | −0.244112 | − | 0.969747i | \(-0.578497\pi\) |
−0.961882 | + | 0.273466i | \(0.911830\pi\) | |||||||
\(632\) | −6.63397 | − | 11.4904i | −0.263885 | − | 0.457063i | ||||
\(633\) | 3.26795 | + | 5.66025i | 0.129889 | + | 0.224975i | ||||
\(634\) | −6.40192 | + | 3.69615i | −0.254253 | + | 0.146793i | ||||
\(635\) | − | 13.5167i | − | 0.536392i | ||||||
\(636\) | 3.46410 | + | 6.00000i | 0.137361 | + | 0.237915i | ||||
\(637\) | 10.3923i | 0.411758i | ||||||||
\(638\) | −20.4904 | + | 35.4904i | −0.811222 | + | 1.40508i | ||||
\(639\) | 15.4641 | 0.611750 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | −0.571797 | + | 0.990381i | −0.0225846 | + | 0.0391177i | −0.877097 | − | 0.480314i | \(-0.840523\pi\) |
0.854512 | + | 0.519431i | \(0.173856\pi\) | |||||||
\(642\) | 24.5885 | − | 14.1962i | 0.970429 | − | 0.560277i | ||||
\(643\) | 13.2679i | 0.523237i | 0.965171 | + | 0.261618i | \(0.0842562\pi\) | ||||
−0.965171 | + | 0.261618i | \(0.915744\pi\) | |||||||
\(644\) | 8.19615 | + | 4.73205i | 0.322974 | + | 0.186469i | ||||
\(645\) | 2.19615 | − | 3.80385i | 0.0864734 | − | 0.149776i | ||||
\(646\) | 8.49038 | + | 4.90192i | 0.334050 | + | 0.192864i | ||||
\(647\) | 19.9808 | − | 11.5359i | 0.785525 | − | 0.453523i | −0.0528599 | − | 0.998602i | \(-0.516834\pi\) |
0.838385 | + | 0.545079i | \(0.183500\pi\) | |||||||
\(648\) | −2.13397 | + | 1.23205i | −0.0838304 | + | 0.0483995i | ||||
\(649\) | −10.3923 | − | 6.00000i | −0.407934 | − | 0.235521i | ||||
\(650\) | 3.46410 | − | 6.00000i | 0.135873 | − | 0.235339i | ||||
\(651\) | 6.00000 | + | 3.46410i | 0.235159 | + | 0.135769i | ||||
\(652\) | 12.9282i | 0.506308i | ||||||||
\(653\) | −38.0885 | + | 21.9904i | −1.49052 | + | 0.860550i | −0.999941 | − | 0.0108487i | \(-0.996547\pi\) |
−0.490575 | + | 0.871399i | \(0.663213\pi\) | |||||||
\(654\) | 3.63397 | − | 6.29423i | 0.142100 | − | 0.246124i | ||||
\(655\) | 16.9808 | 0.663493 | ||||||||
\(656\) | 9.92820 | 0.387631 | ||||||||
\(657\) | −8.92820 | + | 15.4641i | −0.348322 | + | 0.603312i | ||||
\(658\) | 9.46410i | 0.368949i | ||||||||
\(659\) | 4.73205 | + | 8.19615i | 0.184335 | + | 0.319277i | 0.943352 | − | 0.331793i | \(-0.107654\pi\) |
−0.759018 | + | 0.651070i | \(0.774320\pi\) | |||||||
\(660\) | 22.3923i | 0.871619i | ||||||||
\(661\) | 1.50000 | − | 0.866025i | 0.0583432 | − | 0.0336845i | −0.470545 | − | 0.882376i | \(-0.655943\pi\) |
0.528888 | + | 0.848692i | \(0.322609\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.5885 | + | 63.3731i | 1.42098 | + | 2.46121i | ||||
\(664\) | 4.90192 | + | 2.83013i | 0.190232 | + | 0.109830i | ||||
\(665\) | 4.39230 | 0.170326 | ||||||||
\(666\) | 17.2583 | − | 20.9641i | 0.668747 | − | 0.812342i | ||||
\(667\) | −40.9808 | −1.58678 | ||||||||
\(668\) | −12.0000 | − | 6.92820i | −0.464294 | − | 0.268060i | ||||
\(669\) | −22.1244 | − | 38.3205i | −0.855377 | − | 1.48156i | ||||
\(670\) | 8.83013 | + | 15.2942i | 0.341138 | + | 0.590868i | ||||
\(671\) | −7.09808 | + | 4.09808i | −0.274018 | + | 0.158204i | ||||
\(672\) | 5.46410i | 0.210782i | ||||||||
\(673\) | −8.00000 | − | 13.8564i | −0.308377 | − | 0.534125i | 0.669630 | − | 0.742695i | \(-0.266453\pi\) |
−0.978008 | + | 0.208569i | \(0.933119\pi\) | |||||||
\(674\) | 32.1769i | 1.23941i | ||||||||
\(675\) | −4.00000 | + | 6.92820i | −0.153960 | + | 0.266667i | ||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 33.9282 | 1.30397 | 0.651983 | − | 0.758233i | \(-0.273937\pi\) | ||||
0.651983 | + | 0.758233i | \(0.273937\pi\) | |||||||
\(678\) | −4.73205 | + | 8.19615i | −0.181733 | + | 0.314771i | ||||
\(679\) | 13.3923 | − | 7.73205i | 0.513949 | − | 0.296729i | ||||
\(680\) | 13.3923i | 0.513571i | ||||||||
\(681\) | −3.00000 | − | 1.73205i | −0.114960 | − | 0.0663723i | ||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | −17.7846 | − | 10.2679i | −0.680509 | − | 0.392892i | 0.119538 | − | 0.992830i | \(-0.461859\pi\) |
−0.800047 | + | 0.599938i | \(0.795192\pi\) | |||||||
\(684\) | −4.90192 | + | 2.83013i | −0.187430 | + | 0.108213i | ||||
\(685\) | −2.08846 | + | 1.20577i | −0.0797959 | + | 0.0460702i | ||||
\(686\) | 17.3205 | + | 10.0000i | 0.661300 | + | 0.381802i | ||||
\(687\) | −37.4186 | + | 64.8109i | −1.42761 | + | 2.47269i | ||||
\(688\) | −0.803848 | − | 0.464102i | −0.0306464 | − | 0.0176937i | ||||
\(689\) | − | 8.78461i | − | 0.334667i | ||||||
\(690\) | −19.3923 | + | 11.1962i | −0.738252 | + | 0.426230i | ||||
\(691\) | −13.4904 | + | 23.3660i | −0.513198 | + | 0.888885i | 0.486685 | + | 0.873578i | \(0.338206\pi\) |
−0.999883 | + | 0.0153077i | \(0.995127\pi\) | |||||||
\(692\) | −5.53590 | −0.210443 | ||||||||
\(693\) | 42.2487 | 1.60490 | ||||||||
\(694\) | 4.56218 | − | 7.90192i | 0.173178 | − | 0.299953i | ||||
\(695\) | − | 35.6603i | − | 1.35267i | ||||||
\(696\) | −11.8301 | − | 20.4904i | −0.448420 | − | 0.776686i | ||||
\(697\) | − | 76.7654i | − | 2.90770i | ||||||
\(698\) | −9.86603 | + | 5.69615i | −0.373435 | + | 0.215603i | ||||
\(699\) | −20.4904 | − | 35.4904i | −0.775017 | − | 1.34237i | ||||
\(700\) | −2.00000 | − | 3.46410i | −0.0755929 | − | 0.130931i | ||||
\(701\) | 16.3923 | + | 9.46410i | 0.619129 | + | 0.357454i | 0.776530 | − | 0.630081i | \(-0.216978\pi\) |
−0.157401 | + | 0.987535i | \(0.550311\pi\) | |||||||
\(702\) | −13.8564 | −0.522976 | ||||||||
\(703\) | −4.90192 | + | 5.95448i | −0.184880 | + | 0.224578i | ||||
\(704\) | 4.73205 | 0.178346 | ||||||||
\(705\) | −19.3923 | − | 11.1962i | −0.730356 | − | 0.421671i | ||||
\(706\) | −9.86603 | − | 17.0885i | −0.371313 | − | 0.643133i | ||||
\(707\) | 12.4641 | + | 21.5885i | 0.468761 | + | 0.811917i | ||||
\(708\) | 6.00000 | − | 3.46410i | 0.225494 | − | 0.130189i | ||||
\(709\) | 9.71281i | 0.364772i | 0.983227 | + | 0.182386i | \(0.0583821\pi\) | ||||
−0.983227 | + | 0.182386i | \(0.941618\pi\) | |||||||
\(710\) | −3.00000 | − | 5.19615i | −0.112588 | − | 0.195008i | ||||
\(711\) | − | 59.2295i | − | 2.22128i | ||||||
\(712\) | 3.40192 | − | 5.89230i | 0.127492 | − | 0.220823i | ||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 42.2487 | 1.58112 | ||||||||
\(715\) | 14.1962 | − | 24.5885i | 0.530906 | − | 0.919556i | ||||
\(716\) | −8.19615 | + | 4.73205i | −0.306305 | + | 0.176845i | ||||
\(717\) | 47.3205i | 1.76722i | ||||||||
\(718\) | 30.5885 | + | 17.6603i | 1.14155 | + | 0.659075i | ||||
\(719\) | −18.6340 | + | 32.2750i | −0.694930 | + | 1.20365i | 0.275274 | + | 0.961366i | \(0.411231\pi\) |
−0.970204 | + | 0.242288i | \(0.922102\pi\) | |||||||
\(720\) | −6.69615 | − | 3.86603i | −0.249551 | − | 0.144078i | ||||
\(721\) | −14.7846 | + | 8.53590i | −0.550608 | + | 0.317893i | ||||
\(722\) | −15.0622 | + | 8.69615i | −0.560556 | + | 0.323637i | ||||
\(723\) | −36.5885 | − | 21.1244i | −1.36074 | − | 0.785623i | ||||
\(724\) | −4.69615 | + | 8.13397i | −0.174531 | + | 0.302297i | ||||
\(725\) | 15.0000 | + | 8.66025i | 0.557086 | + | 0.321634i | ||||
\(726\) | − | 31.1244i | − | 1.15513i | ||||||
\(727\) | 34.3923 | − | 19.8564i | 1.27554 | − | 0.736433i | 0.299515 | − | 0.954092i | \(-0.403175\pi\) |
0.976025 | + | 0.217658i | \(0.0698418\pi\) | |||||||
\(728\) | 3.46410 | − | 6.00000i | 0.128388 | − | 0.222375i | ||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 6.92820 | 0.256424 | ||||||||
\(731\) | −3.58846 | + | 6.21539i | −0.132724 | + | 0.229885i | ||||
\(732\) | − | 4.73205i | − | 0.174902i | ||||||
\(733\) | 16.7846 | + | 29.0718i | 0.619954 | + | 1.07379i | 0.989494 | + | 0.144576i | \(0.0461820\pi\) |
−0.369540 | + | 0.929215i | \(0.620485\pi\) | |||||||
\(734\) | − | 12.3923i | − | 0.457408i | ||||||
\(735\) | −12.2942 | + | 7.09808i | −0.453479 | + | 0.261816i | ||||
\(736\) | 2.36603 | + | 4.09808i | 0.0872129 | + | 0.151057i | ||||
\(737\) | −24.1244 | − | 41.7846i | −0.888632 | − | 1.53916i | ||||
\(738\) | 38.3827 | + | 22.1603i | 1.41289 | + | 0.815730i | ||||
\(739\) | 32.5885 | 1.19879 | 0.599393 | − | 0.800455i | \(-0.295409\pi\) | ||||
0.599393 | + | 0.800455i | \(0.295409\pi\) | |||||||
\(740\) | −10.3923 | − | 1.73205i | −0.382029 | − | 0.0636715i | ||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | −4.39230 | − | 2.53590i | −0.161247 | − | 0.0930958i | ||||
\(743\) | −0.758330 | − | 1.31347i | −0.0278204 | − | 0.0481864i | 0.851780 | − | 0.523900i | \(-0.175523\pi\) |
−0.879600 | + | 0.475713i | \(0.842190\pi\) | |||||||
\(744\) | 1.73205 | + | 3.00000i | 0.0635001 | + | 0.109985i | ||||
\(745\) | −23.8923 | + | 13.7942i | −0.875346 | + | 0.505381i | ||||
\(746\) | − | 7.00000i | − | 0.256288i | ||||||
\(747\) | 12.6340 | + | 21.8827i | 0.462253 | + | 0.800646i | ||||
\(748\) | − | 36.5885i | − | 1.33781i | ||||||
\(749\) | −10.3923 | + | 18.0000i | −0.379727 | + | 0.657706i | ||||
\(750\) | 33.1244 | 1.20953 | ||||||||
\(751\) | 29.6077 | 1.08040 | 0.540200 | − | 0.841537i | \(-0.318349\pi\) | ||||
0.540200 | + | 0.841537i | \(0.318349\pi\) | |||||||
\(752\) | −2.36603 | + | 4.09808i | −0.0862801 | + | 0.149441i | ||||
\(753\) | 40.9808 | − | 23.6603i | 1.49342 | − | 0.862228i | ||||
\(754\) | 30.0000i | 1.09254i | ||||||||
\(755\) | −6.29423 | − | 3.63397i | −0.229070 | − | 0.132254i | ||||
\(756\) | −4.00000 | + | 6.92820i | −0.145479 | + | 0.251976i | ||||
\(757\) | 14.8923 | + | 8.59808i | 0.541270 | + | 0.312502i | 0.745593 | − | 0.666401i | \(-0.232166\pi\) |
−0.204323 | + | 0.978903i | \(0.565499\pi\) | |||||||
\(758\) | 30.1244 | − | 17.3923i | 1.09417 | − | 0.631717i | ||||
\(759\) | 52.9808 | − | 30.5885i | 1.92308 | − | 1.11029i | ||||
\(760\) | 1.90192 | + | 1.09808i | 0.0689900 | + | 0.0398314i | ||||
\(761\) | 1.16025 | − | 2.00962i | 0.0420592 | − | 0.0728486i | −0.844229 | − | 0.535982i | \(-0.819942\pi\) |
0.886289 | + | 0.463133i | \(0.153275\pi\) | |||||||
\(762\) | −18.4641 | − | 10.6603i | −0.668884 | − | 0.386180i | ||||
\(763\) | 5.32051i | 0.192615i | ||||||||
\(764\) | 1.90192 | − | 1.09808i | 0.0688092 | − | 0.0397270i | ||||
\(765\) | −29.8923 | + | 51.7750i | −1.08076 | + | 1.87193i | ||||
\(766\) | −3.46410 | −0.125163 | ||||||||
\(767\) | −8.78461 | −0.317194 | ||||||||
\(768\) | −1.36603 | + | 2.36603i | −0.0492922 | + | 0.0853766i | ||||
\(769\) | − | 13.6077i | − | 0.490706i | −0.969434 | − | 0.245353i | \(-0.921096\pi\) | ||
0.969434 | − | 0.245353i | \(-0.0789039\pi\) | |||||||
\(770\) | −8.19615 | − | 14.1962i | −0.295369 | − | 0.511594i | ||||
\(771\) | − | 18.5885i | − | 0.669447i | ||||||
\(772\) | 9.69615 | − | 5.59808i | 0.348972 | − | 0.201479i | ||||
\(773\) | −16.9641 | − | 29.3827i | −0.610156 | − | 1.05682i | −0.991214 | − | 0.132270i | \(-0.957773\pi\) |
0.381057 | − | 0.924551i | \(-0.375560\pi\) | |||||||
\(774\) | −2.07180 | − | 3.58846i | −0.0744692 | − | 0.128984i | ||||
\(775\) | −2.19615 | − | 1.26795i | −0.0788881 | − | 0.0455461i | ||||
\(776\) | 7.73205 | 0.277564 | ||||||||
\(777\) | −5.46410 | + | 32.7846i | −0.196024 | + | 1.17614i | ||||
\(778\) | −25.9808 | −0.931455 | ||||||||
\(779\) | −10.9019 | − | 6.29423i | −0.390602 | − | 0.225514i | ||||
\(780\) | 8.19615 | + | 14.1962i | 0.293469 | + | 0.508304i | ||||
\(781\) | 8.19615 | + | 14.1962i | 0.293281 | + | 0.507978i | ||||
\(782\) | 31.6865 | − | 18.2942i | 1.13311 | − | 0.654200i | ||||
\(783\) | − | 34.6410i | − | 1.23797i | ||||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | 1.73205i | 0.0618195i | ||||||||
\(786\) | 13.3923 | − | 23.1962i | 0.477688 | − | 0.827379i | ||||
\(787\) | −41.1769 | −1.46780 | −0.733899 | − | 0.679258i | \(-0.762302\pi\) | ||||
−0.733899 | + | 0.679258i | \(0.762302\pi\) | |||||||
\(788\) | −6.46410 | −0.230274 | ||||||||
\(789\) | −29.3205 | + | 50.7846i | −1.04384 | + | 1.80798i | ||||
\(790\) | −19.9019 | + | 11.4904i | −0.708079 | + | 0.408809i | ||||
\(791\) | − | 6.92820i | − | 0.246339i | ||||||
\(792\) | 18.2942 | + | 10.5622i | 0.650057 | + | 0.375311i | ||||
\(793\) | −3.00000 | + | 5.19615i | −0.106533 | + | 0.184521i | ||||
\(794\) | −19.9186 | − | 11.5000i | −0.706884 | − | 0.408120i | ||||
\(795\) | 10.3923 | − | 6.00000i | 0.368577 | − | 0.212798i | ||||
\(796\) | −9.00000 | + | 5.19615i | −0.318997 | + | 0.184173i | ||||
\(797\) | 7.60770 | + | 4.39230i | 0.269478 | + | 0.155583i | 0.628651 | − | 0.777688i | \(-0.283608\pi\) |
−0.359172 | + | 0.933271i | \(0.616941\pi\) | |||||||
\(798\) | 3.46410 | − | 6.00000i | 0.122628 | − | 0.212398i | ||||
\(799\) | 31.6865 | + | 18.2942i | 1.12099 | + | 0.647203i | ||||
\(800\) | − | 2.00000i | − | 0.0707107i | ||||||
\(801\) | 26.3038 | − | 15.1865i | 0.929401 | − | 0.536590i | ||||
\(802\) | −5.19615 | + | 9.00000i | −0.183483 | + | 0.317801i | ||||
\(803\) | −18.9282 | −0.667962 | ||||||||
\(804\) | 27.8564 | 0.982420 | ||||||||
\(805\) | 8.19615 | − | 14.1962i | 0.288876 | − | 0.500349i | ||||
\(806\) | − | 4.39230i | − | 0.154712i | ||||||
\(807\) | 6.00000 | + | 10.3923i | 0.211210 | + | 0.365826i | ||||
\(808\) | 12.4641i | 0.438486i | ||||||||
\(809\) | 13.6077 | − | 7.85641i | 0.478421 | − | 0.276217i | −0.241337 | − | 0.970441i | \(-0.577586\pi\) |
0.719758 | + | 0.694225i | \(0.244253\pi\) | |||||||
\(810\) | 2.13397 | + | 3.69615i | 0.0749802 | + | 0.129870i | ||||
\(811\) | −10.1962 | − | 17.6603i | −0.358035 | − | 0.620135i | 0.629597 | − | 0.776922i | \(-0.283220\pi\) |
−0.987633 | + | 0.156786i | \(0.949887\pi\) | |||||||
\(812\) | 15.0000 | + | 8.66025i | 0.526397 | + | 0.303915i | ||||
\(813\) | −7.07180 | −0.248019 | ||||||||
\(814\) | 28.3923 | + | 4.73205i | 0.995150 | + | 0.165858i | ||||
\(815\) | 22.3923 | 0.784368 | ||||||||
\(816\) | 18.2942 | + | 10.5622i | 0.640426 | + | 0.369750i | ||||
\(817\) | 0.588457 | + | 1.01924i | 0.0205875 | + | 0.0356586i | ||||
\(818\) | 5.25833 | + | 9.10770i | 0.183853 | + | 0.318443i | ||||
\(819\) | 26.7846 | − | 15.4641i | 0.935930 | − | 0.540359i | ||||
\(820\) | − | 17.1962i | − | 0.600516i | ||||||
\(821\) | −1.26795 | − | 2.19615i | −0.0442517 | − | 0.0766462i | 0.843051 | − | 0.537833i | \(-0.180757\pi\) |
−0.887303 | + | 0.461187i | \(0.847424\pi\) | |||||||
\(822\) | 3.80385i | 0.132674i | ||||||||
\(823\) | −11.9019 | + | 20.6147i | −0.414875 | + | 0.718585i | −0.995415 | − | 0.0956469i | \(-0.969508\pi\) |
0.580540 | + | 0.814231i | \(0.302841\pi\) | |||||||
\(824\) | −8.53590 | −0.297362 | ||||||||
\(825\) | −25.8564 | −0.900205 | ||||||||
\(826\) | −2.53590 | + | 4.39230i | −0.0882352 | + | 0.152828i | ||||
\(827\) | −1.60770 | + | 0.928203i | −0.0559050 | + | 0.0322768i | −0.527692 | − | 0.849436i | \(-0.676942\pi\) |
0.471787 | + | 0.881713i | \(0.343609\pi\) | |||||||
\(828\) | 21.1244i | 0.734122i | ||||||||
\(829\) | 9.00000 | + | 5.19615i | 0.312583 | + | 0.180470i | 0.648082 | − | 0.761571i | \(-0.275572\pi\) |
−0.335499 | + | 0.942041i | \(0.608905\pi\) | |||||||
\(830\) | 4.90192 | − | 8.49038i | 0.170148 | − | 0.294705i | ||||
\(831\) | −26.4904 | − | 15.2942i | −0.918941 | − | 0.530551i | ||||
\(832\) | 3.00000 | − | 1.73205i | 0.104006 | − | 0.0600481i | ||||
\(833\) | 20.0885 | − | 11.5981i | 0.696024 | − | 0.401850i | ||||
\(834\) | −48.7128 | − | 28.1244i | −1.68679 | − | 0.973867i | ||||
\(835\) | −12.0000 | + | 20.7846i | −0.415277 | + | 0.719281i | ||||
\(836\) | −5.19615 | − | 3.00000i | −0.179713 | − | 0.103757i | ||||
\(837\) | 5.07180i | 0.175307i | ||||||||
\(838\) | 3.58846 | − | 2.07180i | 0.123961 | − | 0.0715690i | ||||
\(839\) | 26.4904 | − | 45.8827i | 0.914550 | − | 1.58405i | 0.106990 | − | 0.994260i | \(-0.465879\pi\) |
0.807559 | − | 0.589786i | \(-0.200788\pi\) | |||||||
\(840\) | 9.46410 | 0.326543 | ||||||||
\(841\) | −46.0000 | −1.58621 | ||||||||
\(842\) | −6.06218 | + | 10.5000i | −0.208916 | + | 0.361854i | ||||
\(843\) | 75.3731i | 2.59599i | ||||||||
\(844\) | −1.19615 | − | 2.07180i | −0.0411733 | − | 0.0713142i | ||||
\(845\) | 1.73205i | 0.0595844i | ||||||||
\(846\) | −18.2942 | + | 10.5622i | −0.628969 | + | 0.363135i | ||||
\(847\) | 11.3923 | + | 19.7321i | 0.391444 | + | 0.678001i | ||||
\(848\) | −1.26795 | − | 2.19615i | −0.0435416 | − | 0.0754162i | ||||
\(849\) | 18.5885 | + | 10.7321i | 0.637954 | + | 0.368323i | ||||
\(850\) | −15.4641 | −0.530414 | ||||||||
\(851\) | 10.0981 | + | 26.9545i | 0.346158 | + | 0.923988i | ||||
\(852\) | −9.46410 | −0.324235 | ||||||||
\(853\) | −8.89230 | − | 5.13397i | −0.304467 | − | 0.175784i | 0.339981 | − | 0.940432i | \(-0.389579\pi\) |
−0.644448 | + | 0.764648i | \(0.722913\pi\) | |||||||
\(854\) | 1.73205 | + | 3.00000i | 0.0592696 | + | 0.102658i | ||||
\(855\) | 4.90192 | + | 8.49038i | 0.167642 | + | 0.290365i | ||||
\(856\) | −9.00000 | + | 5.19615i | −0.307614 | + | 0.177601i | ||||
\(857\) | − | 2.66025i | − | 0.0908725i | −0.998967 | − | 0.0454363i | \(-0.985532\pi\) | ||
0.998967 | − | 0.0454363i | \(-0.0144678\pi\) | |||||||
\(858\) | −22.3923 | − | 38.7846i | −0.764461 | − | 1.32408i | ||||
\(859\) | − | 30.0000i | − | 1.02359i | −0.859109 | − | 0.511793i | \(-0.828981\pi\) | ||
0.859109 | − | 0.511793i | \(-0.171019\pi\) | |||||||
\(860\) | −0.803848 | + | 1.39230i | −0.0274110 | + | 0.0474772i | ||||
\(861\) | −54.2487 | −1.84879 | ||||||||
\(862\) | −17.6603 | −0.601511 | ||||||||
\(863\) | −2.19615 | + | 3.80385i | −0.0747579 | + | 0.129484i | −0.900981 | − | 0.433859i | \(-0.857152\pi\) |
0.826223 | + | 0.563343i | \(0.190485\pi\) | |||||||
\(864\) | −3.46410 | + | 2.00000i | −0.117851 | + | 0.0680414i | ||||
\(865\) | 9.58846i | 0.326017i | ||||||||
\(866\) | 13.6699 | + | 7.89230i | 0.464521 | + | 0.268191i | ||||
\(867\) | 58.4449 | − | 101.229i | 1.98489 | − | 3.43793i | ||||
\(868\) | −2.19615 | − | 1.26795i | −0.0745423 | − | 0.0430370i | ||||
\(869\) | 54.3731 | − | 31.3923i | 1.84448 | − | 1.06491i | ||||
\(870\) | −35.4904 | + | 20.4904i | −1.20324 | + | 0.694689i | ||||
\(871\) | −30.5885 | − | 17.6603i | −1.03645 | − | 0.598395i | ||||
\(872\) | −1.33013 | + | 2.30385i | −0.0450438 | + | 0.0780181i | ||||
\(873\) | 29.8923 | + | 17.2583i | 1.01170 | + | 0.584106i | ||||
\(874\) | − | 6.00000i | − | 0.202953i | ||||||
\(875\) | −21.0000 | + | 12.1244i | −0.709930 | + | 0.409878i | ||||
\(876\) | 5.46410 | − | 9.46410i | 0.184615 | − | 0.319762i | ||||
\(877\) | 38.1769 | 1.28914 | 0.644571 | − | 0.764544i | \(-0.277036\pi\) | ||||
0.644571 | + | 0.764544i | \(0.277036\pi\) | |||||||
\(878\) | −18.2487 | −0.615864 | ||||||||
\(879\) | 1.90192 | − | 3.29423i | 0.0641503 | − | 0.111112i | ||||
\(880\) | − | 8.19615i | − | 0.276292i | ||||||
\(881\) | −14.3038 | − | 24.7750i | −0.481909 | − | 0.834691i | 0.517876 | − | 0.855456i | \(-0.326723\pi\) |
−0.999784 | + | 0.0207653i | \(0.993390\pi\) | |||||||
\(882\) | 13.3923i | 0.450942i | ||||||||
\(883\) | −13.9019 | + | 8.02628i | −0.467837 | + | 0.270106i | −0.715334 | − | 0.698783i | \(-0.753725\pi\) |
0.247497 | + | 0.968889i | \(0.420392\pi\) | |||||||
\(884\) | −13.3923 | − | 23.1962i | −0.450432 | − | 0.780171i | ||||
\(885\) | −6.00000 | − | 10.3923i | −0.201688 | − | 0.349334i | ||||
\(886\) | −12.5885 | − | 7.26795i | −0.422917 | − | 0.244172i | ||||
\(887\) | −46.0526 | −1.54629 | −0.773147 | − | 0.634227i | \(-0.781318\pi\) | ||||
−0.773147 | + | 0.634227i | \(0.781318\pi\) | |||||||
\(888\) | −10.5622 | + | 12.8301i | −0.354443 | + | 0.430551i | ||||
\(889\) | 15.6077 | 0.523465 | ||||||||
\(890\) | −10.2058 | − | 5.89230i | −0.342098 | − | 0.197511i | ||||
\(891\) | −5.83013 | − | 10.0981i | −0.195317 | − | 0.338298i | ||||
\(892\) | 8.09808 | + | 14.0263i | 0.271144 | + | 0.469635i | ||||
\(893\) | 5.19615 | − | 3.00000i | 0.173883 | − | 0.100391i | ||||
\(894\) | 43.5167i | 1.45541i | ||||||||
\(895\) | 8.19615 | + | 14.1962i | 0.273967 | + | 0.474525i | ||||
\(896\) | − | 2.00000i | − | 0.0668153i | ||||||
\(897\) | 22.3923 | − | 38.7846i | 0.747657 | − | 1.29498i | ||||
\(898\) | 20.5359 | 0.685292 | ||||||||
\(899\) | 10.9808 | 0.366229 | ||||||||
\(900\) | 4.46410 | − | 7.73205i | 0.148803 | − | 0.257735i | ||||
\(901\) | −16.9808 | + | 9.80385i | −0.565711 | + | 0.326614i | ||||
\(902\) | 46.9808i | 1.56429i | ||||||||
\(903\) | 4.39230 | + | 2.53590i | 0.146167 | + | 0.0843894i | ||||
\(904\) | 1.73205 | − | 3.00000i | 0.0576072 | − | 0.0997785i | ||||
\(905\) | 14.0885 | + | 8.13397i | 0.468316 | + | 0.270382i | ||||
\(906\) | −9.92820 | + | 5.73205i | −0.329842 | + | 0.190435i | ||||
\(907\) | 9.88269 | − | 5.70577i | 0.328149 | − | 0.189457i | −0.326870 | − | 0.945069i | \(-0.605994\pi\) |
0.655019 | + | 0.755612i | \(0.272661\pi\) | |||||||
\(908\) | 1.09808 | + | 0.633975i | 0.0364409 | + | 0.0210392i | ||||
\(909\) | −27.8205 | + | 48.1865i | −0.922748 | + | 1.59825i | ||||
\(910\) | −10.3923 | − | 6.00000i | −0.344502 | − | 0.198898i | ||||
\(911\) | − | 35.6603i | − | 1.18148i | −0.806863 | − | 0.590738i | \(-0.798837\pi\) | ||
0.806863 | − | 0.590738i | \(-0.201163\pi\) | |||||||
\(912\) | 3.00000 | − | 1.73205i | 0.0993399 | − | 0.0573539i | ||||
\(913\) | −13.3923 | + | 23.1962i | −0.443221 | + | 0.767681i | ||||
\(914\) | −37.9808 | −1.25629 | ||||||||
\(915\) | −8.19615 | −0.270956 | ||||||||
\(916\) | 13.6962 | − | 23.7224i | 0.452534 | − | 0.783811i | ||||
\(917\) | 19.6077i | 0.647503i | ||||||||
\(918\) | 15.4641 | + | 26.7846i | 0.510391 | + | 0.884024i | ||||
\(919\) | 21.1244i | 0.696828i | 0.937341 | + | 0.348414i | \(0.113280\pi\) | ||||
−0.937341 | + | 0.348414i | \(0.886720\pi\) | |||||||
\(920\) | 7.09808 | − | 4.09808i | 0.234017 | − | 0.135110i | ||||
\(921\) | 30.0526 | + | 52.0526i | 0.990265 | + | 1.71519i | ||||
\(922\) | −19.7321 | − | 34.1769i | −0.649840 | − | 1.12556i | ||||
\(923\) | 10.3923 | + | 6.00000i | 0.342067 | + | 0.197492i | ||||
\(924\) | −25.8564 | −0.850613 | ||||||||
\(925\) | 2.00000 | − | 12.0000i | 0.0657596 | − | 0.394558i | ||||
\(926\) | −30.0000 | −0.985861 | ||||||||
\(927\) | −33.0000 | − | 19.0526i | −1.08386 | − | 0.625768i | ||||
\(928\) | 4.33013 | + | 7.50000i | 0.142143 | + | 0.246200i | ||||
\(929\) | 12.6962 | + | 21.9904i | 0.416547 | + | 0.721481i | 0.995590 | − | 0.0938165i | \(-0.0299067\pi\) |
−0.579042 | + | 0.815298i | \(0.696573\pi\) | |||||||
\(930\) | 5.19615 | − | 3.00000i | 0.170389 | − | 0.0983739i | ||||
\(931\) | − | 3.80385i | − | 0.124666i | ||||||
\(932\) | 7.50000 | + | 12.9904i | 0.245671 | + | 0.425514i | ||||
\(933\) | 49.1769i | 1.60998i | ||||||||
\(934\) | −1.26795 | + | 2.19615i | −0.0414886 | + | 0.0718603i | ||||
\(935\) | −63.3731 | −2.07252 | ||||||||
\(936\) | 15.4641 | 0.505460 | ||||||||
\(937\) | −13.6962 | + | 23.7224i | −0.447434 | + | 0.774978i | −0.998218 | − | 0.0596695i | \(-0.980995\pi\) |
0.550784 | + | 0.834648i | \(0.314329\pi\) | |||||||
\(938\) | −17.6603 | + | 10.1962i | −0.576628 | + | 0.332916i | ||||
\(939\) | − | 65.9090i | − | 2.15086i | ||||||
\(940\) | 7.09808 | + | 4.09808i | 0.231514 | + | 0.133665i | ||||
\(941\) | −14.8923 | + | 25.7942i | −0.485475 | + | 0.840868i | −0.999861 | − | 0.0166913i | \(-0.994687\pi\) |
0.514385 | + | 0.857559i | \(0.328020\pi\) | |||||||
\(942\) | 2.36603 | + | 1.36603i | 0.0770893 | + | 0.0445075i | ||||
\(943\) | −40.6865 | + | 23.4904i | −1.32494 | + | 0.764952i | ||||
\(944\) | −2.19615 | + | 1.26795i | −0.0714787 | + | 0.0412682i | ||||
\(945\) | 12.0000 | + | 6.92820i | 0.390360 | + | 0.225374i | ||||
\(946\) | 2.19615 | − | 3.80385i | 0.0714031 | − | 0.123674i | ||||
\(947\) | 32.1962 | + | 18.5885i | 1.04623 | + | 0.604044i | 0.921593 | − | 0.388158i | \(-0.126889\pi\) |
0.124642 | + | 0.992202i | \(0.460222\pi\) | |||||||
\(948\) | 36.2487i | 1.17730i | ||||||||
\(949\) | −12.0000 | + | 6.92820i | −0.389536 | + | 0.224899i | ||||
\(950\) | −1.26795 | + | 2.19615i | −0.0411377 | + | 0.0712526i | ||||
\(951\) | 20.1962 | 0.654905 | ||||||||
\(952\) | −15.4641 | −0.501194 | ||||||||
\(953\) | −9.92820 | + | 17.1962i | −0.321606 | + | 0.557038i | −0.980820 | − | 0.194918i | \(-0.937556\pi\) |
0.659214 | + | 0.751956i | \(0.270889\pi\) | |||||||
\(954\) | − | 11.3205i | − | 0.366515i | ||||||
\(955\) | −1.90192 | − | 3.29423i | −0.0615448 | − | 0.106599i | ||||
\(956\) | − | 17.3205i | − | 0.560185i | ||||||
\(957\) | 96.9615 | − | 55.9808i | 3.13432 | − | 1.80960i | ||||
\(958\) | 4.73205 | + | 8.19615i | 0.152886 | + | 0.264806i | ||||
\(959\) | −1.39230 | − | 2.41154i | −0.0449599 | − | 0.0778728i | ||||
\(960\) | 4.09808 | + | 2.36603i | 0.132265 | + | 0.0763631i | ||||
\(961\) | 29.3923 | 0.948139 | ||||||||
\(962\) | 19.7321 | − | 7.39230i | 0.636187 | − | 0.238337i | ||||
\(963\) | −46.3923 | −1.49497 | ||||||||
\(964\) | 13.3923 | + | 7.73205i | 0.431337 | + | 0.249033i | ||||
\(965\) | −9.69615 | − | 16.7942i | −0.312130 | − | 0.540625i | ||||
\(966\) | −12.9282 | − | 22.3923i | −0.415958 | − | 0.720461i | ||||
\(967\) | −41.5692 | + | 24.0000i | −1.33678 | + | 0.771788i | −0.986328 | − | 0.164794i | \(-0.947304\pi\) |
−0.350448 | + | 0.936582i | \(0.613971\pi\) | |||||||
\(968\) | 11.3923i | 0.366163i | ||||||||
\(969\) | −13.3923 | − | 23.1962i | −0.430223 | − | 0.745168i | ||||
\(970\) | − | 13.3923i | − | 0.430001i | ||||||
\(971\) | 3.50962 | − | 6.07884i | 0.112629 | − | 0.195079i | −0.804200 | − | 0.594358i | \(-0.797406\pi\) |
0.916829 | + | 0.399279i | \(0.130739\pi\) | |||||||
\(972\) | 18.7321 | 0.600831 | ||||||||
\(973\) | 41.1769 | 1.32007 | ||||||||
\(974\) | 8.02628 | − | 13.9019i | 0.257179 | − | 0.445446i | ||||
\(975\) | −16.3923 | + | 9.46410i | −0.524974 | + | 0.303094i | ||||
\(976\) | 1.73205i | 0.0554416i | ||||||||
\(977\) | −3.00000 | − | 1.73205i | −0.0959785 | − | 0.0554132i | 0.451243 | − | 0.892401i | \(-0.350981\pi\) |
−0.547221 | + | 0.836988i | \(0.684314\pi\) | |||||||
\(978\) | 17.6603 | − | 30.5885i | 0.564713 | − | 0.978111i | ||||
\(979\) | 27.8827 | + | 16.0981i | 0.891135 | + | 0.514497i | ||||
\(980\) | 4.50000 | − | 2.59808i | 0.143747 | − | 0.0829925i | ||||
\(981\) | −10.2846 | + | 5.93782i | −0.328362 | + | 0.189580i | ||||
\(982\) | 22.6865 | + | 13.0981i | 0.723956 | + | 0.417976i | ||||
\(983\) | −22.5622 | + | 39.0788i | −0.719622 | + | 1.24642i | 0.241528 | + | 0.970394i | \(0.422351\pi\) |
−0.961150 | + | 0.276028i | \(0.910982\pi\) | |||||||
\(984\) | −23.4904 | − | 13.5622i | −0.748846 | − | 0.432346i | ||||
\(985\) | 11.1962i | 0.356739i | ||||||||
\(986\) | 57.9904 | − | 33.4808i | 1.84679 | − | 1.06624i | ||||
\(987\) | 12.9282 | − | 22.3923i | 0.411509 | − | 0.712755i | ||||
\(988\) | −4.39230 | −0.139738 | ||||||||
\(989\) | 4.39230 | 0.139667 | ||||||||
\(990\) | 18.2942 | − | 31.6865i | 0.581429 | − | 1.00706i | ||||
\(991\) | 16.6410i | 0.528619i | 0.964438 | + | 0.264310i | \(0.0851441\pi\) | ||||
−0.964438 | + | 0.264310i | \(0.914856\pi\) | |||||||
\(992\) | −0.633975 | − | 1.09808i | −0.0201287 | − | 0.0348640i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | − | 3.46410i | 0.190308 | − | 0.109875i | ||||
\(995\) | 9.00000 | + | 15.5885i | 0.285319 | + | 0.494187i | ||||
\(996\) | −7.73205 | − | 13.3923i | −0.244999 | − | 0.424351i | ||||
\(997\) | −9.00000 | − | 5.19615i | −0.285033 | − | 0.164564i | 0.350667 | − | 0.936500i | \(-0.385955\pi\) |
−0.635700 | + | 0.771936i | \(0.719288\pi\) | |||||||
\(998\) | −20.1962 | −0.639298 | ||||||||
\(999\) | −22.7846 | + | 8.53590i | −0.720873 | + | 0.270064i |
(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 | 74.2.e.b.27.2 | yes | 4 | |
3.2 | odd | 2 | 666.2.s.a.397.1 | 4 | |||
4.3 | odd | 2 | 592.2.w.e.545.2 | 4 | |||
37.11 | even | 6 | inner | 74.2.e.b.11.2 | ✓ | 4 | |
37.14 | odd | 12 | 2738.2.a.i.1.1 | 2 | |||
37.23 | odd | 12 | 2738.2.a.e.1.1 | 2 | |||
111.11 | odd | 6 | 666.2.s.a.307.1 | 4 | |||
148.11 | odd | 6 | 592.2.w.e.529.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.e.b.11.2 | ✓ | 4 | 37.11 | even | 6 | inner | |
74.2.e.b.27.2 | yes | 4 | 1.1 | even | 1 | trivial | |
592.2.w.e.529.2 | 4 | 148.11 | odd | 6 | |||
592.2.w.e.545.2 | 4 | 4.3 | odd | 2 | |||
666.2.s.a.307.1 | 4 | 111.11 | odd | 6 | |||
666.2.s.a.397.1 | 4 | 3.2 | odd | 2 | |||
2738.2.a.e.1.1 | 2 | 37.23 | odd | 12 | |||
2738.2.a.i.1.1 | 2 | 37.14 | odd | 12 |