Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(139,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.11416567883\) |
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 | 139.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.139 |
Dual form | 390.2.y.b.289.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −2.23205 | − | 0.133975i | −0.998203 | − | 0.0599153i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −2.36603 | + | 1.36603i | −0.894274 | + | 0.516309i | −0.875338 | − | 0.483512i | \(-0.839361\pi\) |
−0.0189356 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −1.86603 | − | 1.23205i | −0.590089 | − | 0.389609i | ||||
\(11\) | −0.366025 | + | 0.633975i | −0.110361 | + | 0.191151i | −0.915916 | − | 0.401371i | \(-0.868534\pi\) |
0.805555 | + | 0.592521i | \(0.201867\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −3.59808 | + | 0.232051i | −0.997927 | + | 0.0643593i | ||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | 1.86603 | + | 1.23205i | 0.481806 | + | 0.318114i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.86603 | + | 2.23205i | −0.937649 | + | 0.541352i | −0.889223 | − | 0.457475i | \(-0.848754\pi\) |
−0.0484264 | + | 0.998827i | \(0.515421\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.633975 | + | 1.09808i | 0.145444 | + | 0.251916i | 0.929538 | − | 0.368725i | \(-0.120206\pi\) |
−0.784095 | + | 0.620641i | \(0.786872\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 2.73205 | 0.596182 | ||||||||
\(22\) | −0.633975 | + | 0.366025i | −0.135164 | + | 0.0780369i | ||||
\(23\) | −5.36603 | − | 3.09808i | −1.11889 | − | 0.645994i | −0.177775 | − | 0.984071i | \(-0.556890\pi\) |
−0.941118 | + | 0.338078i | \(0.890223\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 4.96410 | + | 0.598076i | 0.992820 | + | 0.119615i | ||||
\(26\) | −3.23205 | − | 1.59808i | −0.633857 | − | 0.313409i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −2.36603 | − | 1.36603i | −0.447137 | − | 0.258155i | ||||
\(29\) | −3.23205 | + | 5.59808i | −0.600177 | + | 1.03954i | 0.392617 | + | 0.919702i | \(0.371570\pi\) |
−0.992794 | + | 0.119835i | \(0.961764\pi\) | |||||||
\(30\) | 1.00000 | + | 2.00000i | 0.182574 | + | 0.365148i | ||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0.633975 | − | 0.366025i | 0.110361 | − | 0.0637168i | ||||
\(34\) | −4.46410 | −0.765587 | ||||||||
\(35\) | 5.46410 | − | 2.73205i | 0.923602 | − | 0.461801i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 6.86603 | + | 3.96410i | 1.12877 | + | 0.651694i | 0.943625 | − | 0.331017i | \(-0.107392\pi\) |
0.185143 | + | 0.982712i | \(0.440725\pi\) | |||||||
\(38\) | 1.26795i | 0.205689i | ||||||||
\(39\) | 3.23205 | + | 1.59808i | 0.517542 | + | 0.255897i | ||||
\(40\) | 0.133975 | − | 2.23205i | 0.0211832 | − | 0.352918i | ||||
\(41\) | 4.59808 | − | 7.96410i | 0.718099 | − | 1.24378i | −0.243653 | − | 0.969862i | \(-0.578346\pi\) |
0.961752 | − | 0.273921i | \(-0.0883208\pi\) | |||||||
\(42\) | 2.36603 | + | 1.36603i | 0.365086 | + | 0.210782i | ||||
\(43\) | −2.83013 | + | 1.63397i | −0.431590 | + | 0.249179i | −0.700024 | − | 0.714119i | \(-0.746827\pi\) |
0.268434 | + | 0.963298i | \(0.413494\pi\) | |||||||
\(44\) | −0.732051 | −0.110361 | ||||||||
\(45\) | −1.00000 | − | 2.00000i | −0.149071 | − | 0.298142i | ||||
\(46\) | −3.09808 | − | 5.36603i | −0.456786 | − | 0.791177i | ||||
\(47\) | − | 7.66025i | − | 1.11736i | −0.829382 | − | 0.558681i | \(-0.811307\pi\) | ||
0.829382 | − | 0.558681i | \(-0.188693\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 0.232051 | − | 0.401924i | 0.0331501 | − | 0.0574177i | ||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 4.46410 | 0.625099 | ||||||||
\(52\) | −2.00000 | − | 3.00000i | −0.277350 | − | 0.416025i | ||||
\(53\) | 7.73205i | 1.06208i | 0.847347 | + | 0.531039i | \(0.178198\pi\) | ||||
−0.847347 | + | 0.531039i | \(0.821802\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0.901924 | − | 1.36603i | 0.121615 | − | 0.184195i | ||||
\(56\) | −1.36603 | − | 2.36603i | −0.182543 | − | 0.316173i | ||||
\(57\) | − | 1.26795i | − | 0.167944i | ||||||
\(58\) | −5.59808 | + | 3.23205i | −0.735063 | + | 0.424389i | ||||
\(59\) | −6.19615 | − | 10.7321i | −0.806670 | − | 1.39719i | −0.915158 | − | 0.403096i | \(-0.867934\pi\) |
0.108487 | − | 0.994098i | \(-0.465399\pi\) | |||||||
\(60\) | −0.133975 | + | 2.23205i | −0.0172960 | + | 0.288157i | ||||
\(61\) | 5.06218 | + | 8.76795i | 0.648145 | + | 1.12262i | 0.983565 | + | 0.180552i | \(0.0577885\pi\) |
−0.335420 | + | 0.942069i | \(0.608878\pi\) | |||||||
\(62\) | 3.46410 | + | 2.00000i | 0.439941 | + | 0.254000i | ||||
\(63\) | −2.36603 | − | 1.36603i | −0.298091 | − | 0.172103i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.06218 | − | 0.0358984i | 0.999990 | − | 0.00445265i | ||||
\(66\) | 0.732051 | 0.0901092 | ||||||||
\(67\) | 6.63397 | + | 3.83013i | 0.810469 | + | 0.467924i | 0.847119 | − | 0.531404i | \(-0.178335\pi\) |
−0.0366497 | + | 0.999328i | \(0.511669\pi\) | |||||||
\(68\) | −3.86603 | − | 2.23205i | −0.468824 | − | 0.270676i | ||||
\(69\) | 3.09808 | + | 5.36603i | 0.372965 | + | 0.645994i | ||||
\(70\) | 6.09808 | + | 0.366025i | 0.728860 | + | 0.0437484i | ||||
\(71\) | −0.633975 | − | 1.09808i | −0.0752389 | − | 0.130318i | 0.825951 | − | 0.563742i | \(-0.190639\pi\) |
−0.901190 | + | 0.433424i | \(0.857305\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 4.66025i | − | 0.545441i | −0.962093 | − | 0.272721i | \(-0.912076\pi\) | ||
0.962093 | − | 0.272721i | \(-0.0879235\pi\) | |||||||
\(74\) | 3.96410 | + | 6.86603i | 0.460817 | + | 0.798159i | ||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | −0.633975 | + | 1.09808i | −0.0727219 | + | 0.125958i | ||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | 2.00000 | + | 3.00000i | 0.226455 | + | 0.339683i | ||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 1.23205 | − | 1.86603i | 0.137747 | − | 0.208628i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 7.96410 | − | 4.59808i | 0.879488 | − | 0.507773i | ||||
\(83\) | 5.26795i | 0.578233i | 0.957294 | + | 0.289116i | \(0.0933614\pi\) | ||||
−0.957294 | + | 0.289116i | \(0.906639\pi\) | |||||||
\(84\) | 1.36603 | + | 2.36603i | 0.149046 | + | 0.258155i | ||||
\(85\) | 8.92820 | − | 4.46410i | 0.968400 | − | 0.484200i | ||||
\(86\) | −3.26795 | −0.352392 | ||||||||
\(87\) | 5.59808 | − | 3.23205i | 0.600177 | − | 0.346512i | ||||
\(88\) | −0.633975 | − | 0.366025i | −0.0675819 | − | 0.0390184i | ||||
\(89\) | −2.46410 | + | 4.26795i | −0.261194 | + | 0.452402i | −0.966560 | − | 0.256442i | \(-0.917450\pi\) |
0.705365 | + | 0.708844i | \(0.250783\pi\) | |||||||
\(90\) | 0.133975 | − | 2.23205i | 0.0141222 | − | 0.235279i | ||||
\(91\) | 8.19615 | − | 5.46410i | 0.859190 | − | 0.572793i | ||||
\(92\) | − | 6.19615i | − | 0.645994i | ||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | 3.83013 | − | 6.63397i | 0.395047 | − | 0.684242i | ||||
\(95\) | −1.26795 | − | 2.53590i | −0.130089 | − | 0.260178i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | 0.401924 | − | 0.232051i | 0.0406004 | − | 0.0234407i | ||||
\(99\) | −0.732051 | −0.0735739 | ||||||||
\(100\) | 1.96410 | + | 4.59808i | 0.196410 | + | 0.459808i | ||||
\(101\) | −6.96410 | + | 12.0622i | −0.692954 | + | 1.20023i | 0.277912 | + | 0.960607i | \(0.410358\pi\) |
−0.970866 | + | 0.239625i | \(0.922976\pi\) | |||||||
\(102\) | 3.86603 | + | 2.23205i | 0.382794 | + | 0.221006i | ||||
\(103\) | 9.26795i | 0.913198i | 0.889673 | + | 0.456599i | \(0.150933\pi\) | ||||
−0.889673 | + | 0.456599i | \(0.849067\pi\) | |||||||
\(104\) | −0.232051 | − | 3.59808i | −0.0227545 | − | 0.352820i | ||||
\(105\) | −6.09808 | − | 0.366025i | −0.595111 | − | 0.0357204i | ||||
\(106\) | −3.86603 | + | 6.69615i | −0.375502 | + | 0.650388i | ||||
\(107\) | 1.09808 | + | 0.633975i | 0.106155 | + | 0.0612886i | 0.552138 | − | 0.833753i | \(-0.313812\pi\) |
−0.445983 | + | 0.895042i | \(0.647146\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 1.46410 | − | 0.732051i | 0.139597 | − | 0.0697983i | ||||
\(111\) | −3.96410 | − | 6.86603i | −0.376256 | − | 0.651694i | ||||
\(112\) | − | 2.73205i | − | 0.258155i | ||||||
\(113\) | 7.79423 | − | 4.50000i | 0.733219 | − | 0.423324i | −0.0863794 | − | 0.996262i | \(-0.527530\pi\) |
0.819599 | + | 0.572938i | \(0.194196\pi\) | |||||||
\(114\) | 0.633975 | − | 1.09808i | 0.0593772 | − | 0.102844i | ||||
\(115\) | 11.5622 | + | 7.63397i | 1.07818 | + | 0.711872i | ||||
\(116\) | −6.46410 | −0.600177 | ||||||||
\(117\) | −2.00000 | − | 3.00000i | −0.184900 | − | 0.277350i | ||||
\(118\) | − | 12.3923i | − | 1.14080i | ||||||
\(119\) | 6.09808 | − | 10.5622i | 0.559010 | − | 0.968233i | ||||
\(120\) | −1.23205 | + | 1.86603i | −0.112470 | + | 0.170344i | ||||
\(121\) | 5.23205 | + | 9.06218i | 0.475641 | + | 0.823834i | ||||
\(122\) | 10.1244i | 0.916616i | ||||||||
\(123\) | −7.96410 | + | 4.59808i | −0.718099 | + | 0.414595i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | −1.36603 | − | 2.36603i | −0.121695 | − | 0.210782i | ||||
\(127\) | 3.46410 | + | 2.00000i | 0.307389 | + | 0.177471i | 0.645758 | − | 0.763542i | \(-0.276542\pi\) |
−0.338368 | + | 0.941014i | \(0.609875\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 3.26795 | 0.287727 | ||||||||
\(130\) | 7.00000 | + | 4.00000i | 0.613941 | + | 0.350823i | ||||
\(131\) | −13.8564 | −1.21064 | −0.605320 | − | 0.795982i | \(-0.706955\pi\) | ||||
−0.605320 | + | 0.795982i | \(0.706955\pi\) | |||||||
\(132\) | 0.633975 | + | 0.366025i | 0.0551804 | + | 0.0318584i | ||||
\(133\) | −3.00000 | − | 1.73205i | −0.260133 | − | 0.150188i | ||||
\(134\) | 3.83013 | + | 6.63397i | 0.330873 | + | 0.573088i | ||||
\(135\) | −0.133975 | + | 2.23205i | −0.0115307 | + | 0.192104i | ||||
\(136\) | −2.23205 | − | 3.86603i | −0.191397 | − | 0.331509i | ||||
\(137\) | −15.9904 | + | 9.23205i | −1.36615 | + | 0.788747i | −0.990434 | − | 0.137987i | \(-0.955937\pi\) |
−0.375716 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(138\) | 6.19615i | 0.527452i | ||||||||
\(139\) | −0.535898 | − | 0.928203i | −0.0454543 | − | 0.0787292i | 0.842403 | − | 0.538848i | \(-0.181140\pi\) |
−0.887857 | + | 0.460119i | \(0.847807\pi\) | |||||||
\(140\) | 5.09808 | + | 3.36603i | 0.430866 | + | 0.284481i | ||||
\(141\) | −3.83013 | + | 6.63397i | −0.322555 | + | 0.558681i | ||||
\(142\) | − | 1.26795i | − | 0.106404i | ||||||
\(143\) | 1.16987 | − | 2.36603i | 0.0978297 | − | 0.197857i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 7.96410 | − | 12.0622i | 0.661383 | − | 1.00171i | ||||
\(146\) | 2.33013 | − | 4.03590i | 0.192843 | − | 0.334013i | ||||
\(147\) | −0.401924 | + | 0.232051i | −0.0331501 | + | 0.0191392i | ||||
\(148\) | 7.92820i | 0.651694i | ||||||||
\(149\) | 9.96410 | + | 17.2583i | 0.816291 | + | 1.41386i | 0.908397 | + | 0.418108i | \(0.137307\pi\) |
−0.0921062 | + | 0.995749i | \(0.529360\pi\) | |||||||
\(150\) | −1.96410 | − | 4.59808i | −0.160368 | − | 0.375431i | ||||
\(151\) | −5.12436 | −0.417014 | −0.208507 | − | 0.978021i | \(-0.566860\pi\) | ||||
−0.208507 | + | 0.978021i | \(0.566860\pi\) | |||||||
\(152\) | −1.09808 | + | 0.633975i | −0.0890657 | + | 0.0514221i | ||||
\(153\) | −3.86603 | − | 2.23205i | −0.312550 | − | 0.180451i | ||||
\(154\) | 1.00000 | − | 1.73205i | 0.0805823 | − | 0.139573i | ||||
\(155\) | −8.92820 | − | 0.535898i | −0.717131 | − | 0.0430444i | ||||
\(156\) | 0.232051 | + | 3.59808i | 0.0185789 | + | 0.288077i | ||||
\(157\) | − | 9.39230i | − | 0.749588i | −0.927108 | − | 0.374794i | \(-0.877714\pi\) | ||
0.927108 | − | 0.374794i | \(-0.122286\pi\) | |||||||
\(158\) | −10.3923 | − | 6.00000i | −0.826767 | − | 0.477334i | ||||
\(159\) | 3.86603 | − | 6.69615i | 0.306596 | − | 0.531039i | ||||
\(160\) | 2.00000 | − | 1.00000i | 0.158114 | − | 0.0790569i | ||||
\(161\) | 16.9282 | 1.33413 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −11.6603 | + | 6.73205i | −0.913302 | + | 0.527295i | −0.881492 | − | 0.472199i | \(-0.843460\pi\) |
−0.0318096 | + | 0.999494i | \(0.510127\pi\) | |||||||
\(164\) | 9.19615 | 0.718099 | ||||||||
\(165\) | −1.46410 | + | 0.732051i | −0.113980 | + | 0.0569901i | ||||
\(166\) | −2.63397 | + | 4.56218i | −0.204436 | + | 0.354094i | ||||
\(167\) | −12.0000 | − | 6.92820i | −0.928588 | − | 0.536120i | −0.0422232 | − | 0.999108i | \(-0.513444\pi\) |
−0.886365 | + | 0.462988i | \(0.846777\pi\) | |||||||
\(168\) | 2.73205i | 0.210782i | ||||||||
\(169\) | 12.8923 | − | 1.66987i | 0.991716 | − | 0.128452i | ||||
\(170\) | 9.96410 | + | 0.598076i | 0.764212 | + | 0.0458704i | ||||
\(171\) | −0.633975 | + | 1.09808i | −0.0484812 | + | 0.0839720i | ||||
\(172\) | −2.83013 | − | 1.63397i | −0.215795 | − | 0.124589i | ||||
\(173\) | −16.2679 | + | 9.39230i | −1.23683 | + | 0.714084i | −0.968445 | − | 0.249228i | \(-0.919823\pi\) |
−0.268384 | + | 0.963312i | \(0.586490\pi\) | |||||||
\(174\) | 6.46410 | 0.490042 | ||||||||
\(175\) | −12.5622 | + | 5.36603i | −0.949611 | + | 0.405633i | ||||
\(176\) | −0.366025 | − | 0.633975i | −0.0275902 | − | 0.0477876i | ||||
\(177\) | 12.3923i | 0.931463i | ||||||||
\(178\) | −4.26795 | + | 2.46410i | −0.319896 | + | 0.184692i | ||||
\(179\) | 9.09808 | − | 15.7583i | 0.680022 | − | 1.17783i | −0.294951 | − | 0.955512i | \(-0.595303\pi\) |
0.974974 | − | 0.222321i | \(-0.0713632\pi\) | |||||||
\(180\) | 1.23205 | − | 1.86603i | 0.0918316 | − | 0.139085i | ||||
\(181\) | −16.1244 | −1.19851 | −0.599257 | − | 0.800557i | \(-0.704537\pi\) | ||||
−0.599257 | + | 0.800557i | \(0.704537\pi\) | |||||||
\(182\) | 9.83013 | − | 0.633975i | 0.728657 | − | 0.0469933i | ||||
\(183\) | − | 10.1244i | − | 0.748414i | ||||||
\(184\) | 3.09808 | − | 5.36603i | 0.228393 | − | 0.395589i | ||||
\(185\) | −14.7942 | − | 9.76795i | −1.08769 | − | 0.718154i | ||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | − | 3.26795i | − | 0.238976i | ||||||
\(188\) | 6.63397 | − | 3.83013i | 0.483832 | − | 0.279341i | ||||
\(189\) | 1.36603 | + | 2.36603i | 0.0993637 | + | 0.172103i | ||||
\(190\) | 0.169873 | − | 2.83013i | 0.0123239 | − | 0.205319i | ||||
\(191\) | 4.73205 | + | 8.19615i | 0.342399 | + | 0.593053i | 0.984878 | − | 0.173251i | \(-0.0554272\pi\) |
−0.642479 | + | 0.766304i | \(0.722094\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 9.23205 | + | 5.33013i | 0.664538 | + | 0.383671i | 0.794004 | − | 0.607913i | \(-0.207993\pi\) |
−0.129466 | + | 0.991584i | \(0.541326\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | −7.00000 | − | 4.00000i | −0.501280 | − | 0.286446i | ||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | 8.53590 | + | 4.92820i | 0.608158 | + | 0.351120i | 0.772244 | − | 0.635326i | \(-0.219134\pi\) |
−0.164086 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(198\) | −0.633975 | − | 0.366025i | −0.0450546 | − | 0.0260123i | ||||
\(199\) | −14.0263 | − | 24.2942i | −0.994297 | − | 1.72217i | −0.589510 | − | 0.807761i | \(-0.700679\pi\) |
−0.404786 | − | 0.914411i | \(-0.632654\pi\) | |||||||
\(200\) | −0.598076 | + | 4.96410i | −0.0422904 | + | 0.351015i | ||||
\(201\) | −3.83013 | − | 6.63397i | −0.270156 | − | 0.467924i | ||||
\(202\) | −12.0622 | + | 6.96410i | −0.848692 | + | 0.489992i | ||||
\(203\) | − | 17.6603i | − | 1.23951i | ||||||
\(204\) | 2.23205 | + | 3.86603i | 0.156275 | + | 0.270676i | ||||
\(205\) | −11.3301 | + | 17.1603i | −0.791330 | + | 1.19852i | ||||
\(206\) | −4.63397 | + | 8.02628i | −0.322864 | + | 0.559217i | ||||
\(207\) | − | 6.19615i | − | 0.430662i | ||||||
\(208\) | 1.59808 | − | 3.23205i | 0.110807 | − | 0.224102i | ||||
\(209\) | −0.928203 | −0.0642052 | ||||||||
\(210\) | −5.09808 | − | 3.36603i | −0.351801 | − | 0.232278i | ||||
\(211\) | 10.7321 | − | 18.5885i | 0.738825 | − | 1.27968i | −0.214200 | − | 0.976790i | \(-0.568714\pi\) |
0.953025 | − | 0.302892i | \(-0.0979523\pi\) | |||||||
\(212\) | −6.69615 | + | 3.86603i | −0.459894 | + | 0.265520i | ||||
\(213\) | 1.26795i | 0.0868784i | ||||||||
\(214\) | 0.633975 | + | 1.09808i | 0.0433376 | + | 0.0750629i | ||||
\(215\) | 6.53590 | − | 3.26795i | 0.445745 | − | 0.222872i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.46410 | + | 5.46410i | −0.642465 | + | 0.370927i | ||||
\(218\) | −8.66025 | − | 5.00000i | −0.586546 | − | 0.338643i | ||||
\(219\) | −2.33013 | + | 4.03590i | −0.157455 | + | 0.272721i | ||||
\(220\) | 1.63397 | + | 0.0980762i | 0.110163 | + | 0.00661230i | ||||
\(221\) | 13.3923 | − | 8.92820i | 0.900864 | − | 0.600576i | ||||
\(222\) | − | 7.92820i | − | 0.532106i | ||||||
\(223\) | 0.339746 | + | 0.196152i | 0.0227511 | + | 0.0131353i | 0.511332 | − | 0.859383i | \(-0.329152\pi\) |
−0.488581 | + | 0.872518i | \(0.662485\pi\) | |||||||
\(224\) | 1.36603 | − | 2.36603i | 0.0912714 | − | 0.158087i | ||||
\(225\) | 1.96410 | + | 4.59808i | 0.130940 | + | 0.306538i | ||||
\(226\) | 9.00000 | 0.598671 | ||||||||
\(227\) | 3.63397 | − | 2.09808i | 0.241195 | − | 0.139254i | −0.374531 | − | 0.927215i | \(-0.622196\pi\) |
0.615726 | + | 0.787960i | \(0.288863\pi\) | |||||||
\(228\) | 1.09808 | − | 0.633975i | 0.0727219 | − | 0.0419860i | ||||
\(229\) | −28.7846 | −1.90214 | −0.951070 | − | 0.308975i | \(-0.900014\pi\) | ||||
−0.951070 | + | 0.308975i | \(0.900014\pi\) | |||||||
\(230\) | 6.19615 | + | 12.3923i | 0.408562 | + | 0.817124i | ||||
\(231\) | −1.00000 | + | 1.73205i | −0.0657952 | + | 0.113961i | ||||
\(232\) | −5.59808 | − | 3.23205i | −0.367532 | − | 0.212195i | ||||
\(233\) | 12.3923i | 0.811847i | 0.913907 | + | 0.405923i | \(0.133050\pi\) | ||||
−0.913907 | + | 0.405923i | \(0.866950\pi\) | |||||||
\(234\) | −0.232051 | − | 3.59808i | −0.0151696 | − | 0.235214i | ||||
\(235\) | −1.02628 | + | 17.0981i | −0.0669471 | + | 1.11536i | ||||
\(236\) | 6.19615 | − | 10.7321i | 0.403335 | − | 0.698597i | ||||
\(237\) | 10.3923 | + | 6.00000i | 0.675053 | + | 0.389742i | ||||
\(238\) | 10.5622 | − | 6.09808i | 0.684644 | − | 0.395280i | ||||
\(239\) | 4.58846 | 0.296803 | 0.148401 | − | 0.988927i | \(-0.452587\pi\) | ||||
0.148401 | + | 0.988927i | \(0.452587\pi\) | |||||||
\(240\) | −2.00000 | + | 1.00000i | −0.129099 | + | 0.0645497i | ||||
\(241\) | 4.69615 | + | 8.13397i | 0.302506 | + | 0.523955i | 0.976703 | − | 0.214596i | \(-0.0688435\pi\) |
−0.674197 | + | 0.738551i | \(0.735510\pi\) | |||||||
\(242\) | 10.4641i | 0.672658i | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −5.06218 | + | 8.76795i | −0.324073 | + | 0.561310i | ||||
\(245\) | −0.571797 | + | 0.866025i | −0.0365308 | + | 0.0553283i | ||||
\(246\) | −9.19615 | −0.586325 | ||||||||
\(247\) | −2.53590 | − | 3.80385i | −0.161355 | − | 0.242033i | ||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 2.63397 | − | 4.56218i | 0.166921 | − | 0.289116i | ||||
\(250\) | −8.52628 | − | 7.23205i | −0.539249 | − | 0.457395i | ||||
\(251\) | 10.7321 | + | 18.5885i | 0.677401 | + | 1.17329i | 0.975761 | + | 0.218840i | \(0.0702271\pi\) |
−0.298360 | + | 0.954453i | \(0.596440\pi\) | |||||||
\(252\) | − | 2.73205i | − | 0.172103i | ||||||
\(253\) | 3.92820 | − | 2.26795i | 0.246964 | − | 0.142585i | ||||
\(254\) | 2.00000 | + | 3.46410i | 0.125491 | + | 0.217357i | ||||
\(255\) | −9.96410 | − | 0.598076i | −0.623976 | − | 0.0374530i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.59808 | − | 1.50000i | −0.162064 | − | 0.0935674i | 0.416775 | − | 0.909010i | \(-0.363160\pi\) |
−0.578838 | + | 0.815442i | \(0.696494\pi\) | |||||||
\(258\) | 2.83013 | + | 1.63397i | 0.176196 | + | 0.101727i | ||||
\(259\) | −21.6603 | −1.34590 | ||||||||
\(260\) | 4.06218 | + | 6.96410i | 0.251926 | + | 0.431895i | ||||
\(261\) | −6.46410 | −0.400118 | ||||||||
\(262\) | −12.0000 | − | 6.92820i | −0.741362 | − | 0.428026i | ||||
\(263\) | 14.8301 | + | 8.56218i | 0.914465 | + | 0.527967i | 0.881865 | − | 0.471502i | \(-0.156288\pi\) |
0.0325998 | + | 0.999468i | \(0.489621\pi\) | |||||||
\(264\) | 0.366025 | + | 0.633975i | 0.0225273 | + | 0.0390184i | ||||
\(265\) | 1.03590 | − | 17.2583i | 0.0636347 | − | 1.06017i | ||||
\(266\) | −1.73205 | − | 3.00000i | −0.106199 | − | 0.183942i | ||||
\(267\) | 4.26795 | − | 2.46410i | 0.261194 | − | 0.150801i | ||||
\(268\) | 7.66025i | 0.467924i | ||||||||
\(269\) | 2.19615 | + | 3.80385i | 0.133902 | + | 0.231925i | 0.925177 | − | 0.379535i | \(-0.123916\pi\) |
−0.791276 | + | 0.611460i | \(0.790583\pi\) | |||||||
\(270\) | −1.23205 | + | 1.86603i | −0.0749802 | + | 0.113563i | ||||
\(271\) | −2.92820 | + | 5.07180i | −0.177876 | + | 0.308090i | −0.941153 | − | 0.337982i | \(-0.890256\pi\) |
0.763277 | + | 0.646071i | \(0.223589\pi\) | |||||||
\(272\) | − | 4.46410i | − | 0.270676i | ||||||
\(273\) | −9.83013 | + | 0.633975i | −0.594946 | + | 0.0383699i | ||||
\(274\) | −18.4641 | −1.11546 | ||||||||
\(275\) | −2.19615 | + | 2.92820i | −0.132433 | + | 0.176577i | ||||
\(276\) | −3.09808 | + | 5.36603i | −0.186482 | + | 0.322997i | ||||
\(277\) | −10.6699 | + | 6.16025i | −0.641091 | + | 0.370134i | −0.785034 | − | 0.619452i | \(-0.787355\pi\) |
0.143944 | + | 0.989586i | \(0.454021\pi\) | |||||||
\(278\) | − | 1.07180i | − | 0.0642821i | ||||||
\(279\) | 2.00000 | + | 3.46410i | 0.119737 | + | 0.207390i | ||||
\(280\) | 2.73205 | + | 5.46410i | 0.163271 | + | 0.326543i | ||||
\(281\) | 1.73205 | 0.103325 | 0.0516627 | − | 0.998665i | \(-0.483548\pi\) | ||||
0.0516627 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(282\) | −6.63397 | + | 3.83013i | −0.395047 | + | 0.228081i | ||||
\(283\) | −6.63397 | − | 3.83013i | −0.394349 | − | 0.227677i | 0.289694 | − | 0.957119i | \(-0.406447\pi\) |
−0.684043 | + | 0.729442i | \(0.739780\pi\) | |||||||
\(284\) | 0.633975 | − | 1.09808i | 0.0376195 | − | 0.0651588i | ||||
\(285\) | −0.169873 | + | 2.83013i | −0.0100624 | + | 0.167642i | ||||
\(286\) | 2.19615 | − | 1.46410i | 0.129861 | − | 0.0865741i | ||||
\(287\) | 25.1244i | 1.48304i | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 1.46410 | − | 2.53590i | 0.0861236 | − | 0.149170i | ||||
\(290\) | 12.9282 | − | 6.46410i | 0.759170 | − | 0.379585i | ||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 4.03590 | − | 2.33013i | 0.236183 | − | 0.136360i | ||||
\(293\) | 11.8923 | − | 6.86603i | 0.694756 | − | 0.401117i | −0.110635 | − | 0.993861i | \(-0.535289\pi\) |
0.805391 | + | 0.592744i | \(0.201955\pi\) | |||||||
\(294\) | −0.464102 | −0.0270670 | ||||||||
\(295\) | 12.3923 | + | 24.7846i | 0.721508 | + | 1.44302i | ||||
\(296\) | −3.96410 | + | 6.86603i | −0.230409 | + | 0.399080i | ||||
\(297\) | 0.633975 | + | 0.366025i | 0.0367869 | + | 0.0212389i | ||||
\(298\) | 19.9282i | 1.15441i | ||||||||
\(299\) | 20.0263 | + | 9.90192i | 1.15815 | + | 0.572643i | ||||
\(300\) | 0.598076 | − | 4.96410i | 0.0345299 | − | 0.286603i | ||||
\(301\) | 4.46410 | − | 7.73205i | 0.257307 | − | 0.445668i | ||||
\(302\) | −4.43782 | − | 2.56218i | −0.255368 | − | 0.147437i | ||||
\(303\) | 12.0622 | − | 6.96410i | 0.692954 | − | 0.400077i | ||||
\(304\) | −1.26795 | −0.0727219 | ||||||||
\(305\) | −10.1244 | − | 20.2487i | −0.579719 | − | 1.15944i | ||||
\(306\) | −2.23205 | − | 3.86603i | −0.127598 | − | 0.221006i | ||||
\(307\) | 19.2679i | 1.09968i | 0.835270 | + | 0.549840i | \(0.185311\pi\) | ||||
−0.835270 | + | 0.549840i | \(0.814689\pi\) | |||||||
\(308\) | 1.73205 | − | 1.00000i | 0.0986928 | − | 0.0569803i | ||||
\(309\) | 4.63397 | − | 8.02628i | 0.263618 | − | 0.456599i | ||||
\(310\) | −7.46410 | − | 4.92820i | −0.423932 | − | 0.279903i | ||||
\(311\) | 3.12436 | 0.177166 | 0.0885830 | − | 0.996069i | \(-0.471766\pi\) | ||||
0.0885830 | + | 0.996069i | \(0.471766\pi\) | |||||||
\(312\) | −1.59808 | + | 3.23205i | −0.0904732 | + | 0.182979i | ||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | 4.69615 | − | 8.13397i | 0.265019 | − | 0.459027i | ||||
\(315\) | 5.09808 | + | 3.36603i | 0.287244 | + | 0.189654i | ||||
\(316\) | −6.00000 | − | 10.3923i | −0.337526 | − | 0.584613i | ||||
\(317\) | − | 29.7321i | − | 1.66992i | −0.550312 | − | 0.834959i | \(-0.685491\pi\) | ||
0.550312 | − | 0.834959i | \(-0.314509\pi\) | |||||||
\(318\) | 6.69615 | − | 3.86603i | 0.375502 | − | 0.216796i | ||||
\(319\) | −2.36603 | − | 4.09808i | −0.132472 | − | 0.229448i | ||||
\(320\) | 2.23205 | + | 0.133975i | 0.124775 | + | 0.00748941i | ||||
\(321\) | −0.633975 | − | 1.09808i | −0.0353850 | − | 0.0612886i | ||||
\(322\) | 14.6603 | + | 8.46410i | 0.816984 | + | 0.471686i | ||||
\(323\) | −4.90192 | − | 2.83013i | −0.272750 | − | 0.157472i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −18.0000 | − | 1.00000i | −0.998460 | − | 0.0554700i | ||||
\(326\) | −13.4641 | −0.745708 | ||||||||
\(327\) | 8.66025 | + | 5.00000i | 0.478913 | + | 0.276501i | ||||
\(328\) | 7.96410 | + | 4.59808i | 0.439744 | + | 0.253886i | ||||
\(329\) | 10.4641 | + | 18.1244i | 0.576905 | + | 0.999228i | ||||
\(330\) | −1.63397 | − | 0.0980762i | −0.0899473 | − | 0.00539892i | ||||
\(331\) | 14.3923 | + | 24.9282i | 0.791073 | + | 1.37018i | 0.925303 | + | 0.379228i | \(0.123810\pi\) |
−0.134231 | + | 0.990950i | \(0.542856\pi\) | |||||||
\(332\) | −4.56218 | + | 2.63397i | −0.250382 | + | 0.144558i | ||||
\(333\) | 7.92820i | 0.434463i | ||||||||
\(334\) | −6.92820 | − | 12.0000i | −0.379094 | − | 0.656611i | ||||
\(335\) | −14.2942 | − | 9.43782i | −0.780977 | − | 0.515643i | ||||
\(336\) | −1.36603 | + | 2.36603i | −0.0745228 | + | 0.129077i | ||||
\(337\) | − | 11.0526i | − | 0.602071i | −0.953613 | − | 0.301036i | \(-0.902668\pi\) | ||
0.953613 | − | 0.301036i | \(-0.0973323\pi\) | |||||||
\(338\) | 12.0000 | + | 5.00000i | 0.652714 | + | 0.271964i | ||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 8.33013 | + | 5.50000i | 0.451765 | + | 0.298279i | ||||
\(341\) | −1.46410 | + | 2.53590i | −0.0792855 | + | 0.137327i | ||||
\(342\) | −1.09808 | + | 0.633975i | −0.0593772 | + | 0.0342814i | ||||
\(343\) | − | 17.8564i | − | 0.964155i | ||||||
\(344\) | −1.63397 | − | 2.83013i | −0.0880980 | − | 0.152590i | ||||
\(345\) | −6.19615 | − | 12.3923i | −0.333590 | − | 0.667179i | ||||
\(346\) | −18.7846 | −1.00987 | ||||||||
\(347\) | 4.90192 | − | 2.83013i | 0.263149 | − | 0.151929i | −0.362621 | − | 0.931937i | \(-0.618118\pi\) |
0.625770 | + | 0.780007i | \(0.284785\pi\) | |||||||
\(348\) | 5.59808 | + | 3.23205i | 0.300088 | + | 0.173256i | ||||
\(349\) | −9.53590 | + | 16.5167i | −0.510445 | + | 0.884117i | 0.489482 | + | 0.872014i | \(0.337186\pi\) |
−0.999927 | + | 0.0121031i | \(0.996147\pi\) | |||||||
\(350\) | −13.5622 | − | 1.63397i | −0.724929 | − | 0.0873396i | ||||
\(351\) | 0.232051 | + | 3.59808i | 0.0123860 | + | 0.192051i | ||||
\(352\) | − | 0.732051i | − | 0.0390184i | ||||||
\(353\) | 21.8660 | + | 12.6244i | 1.16381 | + | 0.671927i | 0.952214 | − | 0.305430i | \(-0.0988003\pi\) |
0.211597 | + | 0.977357i | \(0.432134\pi\) | |||||||
\(354\) | −6.19615 | + | 10.7321i | −0.329322 | + | 0.570402i | ||||
\(355\) | 1.26795 | + | 2.53590i | 0.0672958 | + | 0.134592i | ||||
\(356\) | −4.92820 | −0.261194 | ||||||||
\(357\) | −10.5622 | + | 6.09808i | −0.559010 | + | 0.322744i | ||||
\(358\) | 15.7583 | − | 9.09808i | 0.832854 | − | 0.480848i | ||||
\(359\) | −8.87564 | −0.468439 | −0.234219 | − | 0.972184i | \(-0.575253\pi\) | ||||
−0.234219 | + | 0.972184i | \(0.575253\pi\) | |||||||
\(360\) | 2.00000 | − | 1.00000i | 0.105409 | − | 0.0527046i | ||||
\(361\) | 8.69615 | − | 15.0622i | 0.457692 | − | 0.792746i | ||||
\(362\) | −13.9641 | − | 8.06218i | −0.733937 | − | 0.423739i | ||||
\(363\) | − | 10.4641i | − | 0.549223i | ||||||
\(364\) | 8.83013 | + | 4.36603i | 0.462824 | + | 0.228842i | ||||
\(365\) | −0.624356 | + | 10.4019i | −0.0326803 | + | 0.544462i | ||||
\(366\) | 5.06218 | − | 8.76795i | 0.264604 | − | 0.458308i | ||||
\(367\) | 28.5622 | + | 16.4904i | 1.49093 | + | 0.860791i | 0.999946 | − | 0.0103758i | \(-0.00330278\pi\) |
0.490987 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(368\) | 5.36603 | − | 3.09808i | 0.279723 | − | 0.161498i | ||||
\(369\) | 9.19615 | 0.478733 | ||||||||
\(370\) | −7.92820 | − | 15.8564i | −0.412168 | − | 0.824335i | ||||
\(371\) | −10.5622 | − | 18.2942i | −0.548361 | − | 0.949789i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 20.3827 | − | 11.7679i | 1.05538 | − | 0.609321i | 0.131226 | − | 0.991352i | \(-0.458109\pi\) |
0.924149 | + | 0.382031i | \(0.124775\pi\) | |||||||
\(374\) | 1.63397 | − | 2.83013i | 0.0844908 | − | 0.146342i | ||||
\(375\) | 8.52628 | + | 7.23205i | 0.440295 | + | 0.373461i | ||||
\(376\) | 7.66025 | 0.395047 | ||||||||
\(377\) | 10.3301 | − | 20.8923i | 0.532029 | − | 1.07601i | ||||
\(378\) | 2.73205i | 0.140522i | ||||||||
\(379\) | 13.1244 | − | 22.7321i | 0.674153 | − | 1.16767i | −0.302563 | − | 0.953129i | \(-0.597842\pi\) |
0.976716 | − | 0.214538i | \(-0.0688244\pi\) | |||||||
\(380\) | 1.56218 | − | 2.36603i | 0.0801380 | − | 0.121375i | ||||
\(381\) | −2.00000 | − | 3.46410i | −0.102463 | − | 0.177471i | ||||
\(382\) | 9.46410i | 0.484226i | ||||||||
\(383\) | 23.3205 | − | 13.4641i | 1.19162 | − | 0.687983i | 0.232948 | − | 0.972489i | \(-0.425163\pi\) |
0.958674 | + | 0.284506i | \(0.0918295\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −0.267949 | + | 4.46410i | −0.0136560 | + | 0.227512i | ||||
\(386\) | 5.33013 | + | 9.23205i | 0.271296 | + | 0.469899i | ||||
\(387\) | −2.83013 | − | 1.63397i | −0.143863 | − | 0.0830596i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | 24.0718 | 1.22049 | 0.610244 | − | 0.792213i | \(-0.291071\pi\) | ||||
0.610244 | + | 0.792213i | \(0.291071\pi\) | |||||||
\(390\) | −4.06218 | − | 6.96410i | −0.205696 | − | 0.352641i | ||||
\(391\) | 27.6603 | 1.39884 | ||||||||
\(392\) | 0.401924 | + | 0.232051i | 0.0203002 | + | 0.0117203i | ||||
\(393\) | 12.0000 | + | 6.92820i | 0.605320 | + | 0.349482i | ||||
\(394\) | 4.92820 | + | 8.53590i | 0.248279 | + | 0.430032i | ||||
\(395\) | 26.7846 | + | 1.60770i | 1.34768 | + | 0.0808919i | ||||
\(396\) | −0.366025 | − | 0.633975i | −0.0183935 | − | 0.0318584i | ||||
\(397\) | 16.7321 | − | 9.66025i | 0.839758 | − | 0.484834i | −0.0174242 | − | 0.999848i | \(-0.505547\pi\) |
0.857182 | + | 0.515014i | \(0.172213\pi\) | |||||||
\(398\) | − | 28.0526i | − | 1.40615i | ||||||
\(399\) | 1.73205 | + | 3.00000i | 0.0867110 | + | 0.150188i | ||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 4.52628 | − | 7.83975i | 0.226032 | − | 0.391498i | −0.730597 | − | 0.682809i | \(-0.760758\pi\) |
0.956628 | + | 0.291311i | \(0.0940914\pi\) | |||||||
\(402\) | − | 7.66025i | − | 0.382059i | ||||||
\(403\) | −14.3923 | + | 0.928203i | −0.716932 | + | 0.0462371i | ||||
\(404\) | −13.9282 | −0.692954 | ||||||||
\(405\) | 1.23205 | − | 1.86603i | 0.0612211 | − | 0.0927235i | ||||
\(406\) | 8.83013 | − | 15.2942i | 0.438232 | − | 0.759040i | ||||
\(407\) | −5.02628 | + | 2.90192i | −0.249143 | + | 0.143843i | ||||
\(408\) | 4.46410i | 0.221006i | ||||||||
\(409\) | 8.03590 | + | 13.9186i | 0.397350 | + | 0.688230i | 0.993398 | − | 0.114719i | \(-0.0365967\pi\) |
−0.596048 | + | 0.802949i | \(0.703263\pi\) | |||||||
\(410\) | −18.3923 | + | 9.19615i | −0.908331 | + | 0.454166i | ||||
\(411\) | 18.4641 | 0.910767 | ||||||||
\(412\) | −8.02628 | + | 4.63397i | −0.395426 | + | 0.228300i | ||||
\(413\) | 29.3205 | + | 16.9282i | 1.44277 | + | 0.832982i | ||||
\(414\) | 3.09808 | − | 5.36603i | 0.152262 | − | 0.263726i | ||||
\(415\) | 0.705771 | − | 11.7583i | 0.0346450 | − | 0.577194i | ||||
\(416\) | 3.00000 | − | 2.00000i | 0.147087 | − | 0.0980581i | ||||
\(417\) | 1.07180i | 0.0524861i | ||||||||
\(418\) | −0.803848 | − | 0.464102i | −0.0393175 | − | 0.0227000i | ||||
\(419\) | −3.26795 | + | 5.66025i | −0.159650 | + | 0.276522i | −0.934742 | − | 0.355326i | \(-0.884370\pi\) |
0.775093 | + | 0.631848i | \(0.217703\pi\) | |||||||
\(420\) | −2.73205 | − | 5.46410i | −0.133310 | − | 0.266621i | ||||
\(421\) | 17.0526 | 0.831091 | 0.415545 | − | 0.909572i | \(-0.363591\pi\) | ||||
0.415545 | + | 0.909572i | \(0.363591\pi\) | |||||||
\(422\) | 18.5885 | − | 10.7321i | 0.904872 | − | 0.522428i | ||||
\(423\) | 6.63397 | − | 3.83013i | 0.322555 | − | 0.186227i | ||||
\(424\) | −7.73205 | −0.375502 | ||||||||
\(425\) | −20.5263 | + | 8.76795i | −0.995671 | + | 0.425308i | ||||
\(426\) | −0.633975 | + | 1.09808i | −0.0307162 | + | 0.0532020i | ||||
\(427\) | −23.9545 | − | 13.8301i | −1.15924 | − | 0.669287i | ||||
\(428\) | 1.26795i | 0.0612886i | ||||||||
\(429\) | −2.19615 | + | 1.46410i | −0.106031 | + | 0.0706875i | ||||
\(430\) | 7.29423 | + | 0.437822i | 0.351759 | + | 0.0211137i | ||||
\(431\) | 3.90192 | − | 6.75833i | 0.187949 | − | 0.325537i | −0.756617 | − | 0.653858i | \(-0.773149\pi\) |
0.944566 | + | 0.328321i | \(0.106483\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −12.8205 | + | 7.40192i | −0.616114 | + | 0.355714i | −0.775355 | − | 0.631526i | \(-0.782429\pi\) |
0.159240 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(434\) | −10.9282 | −0.524571 | ||||||||
\(435\) | −12.9282 | + | 6.46410i | −0.619860 | + | 0.309930i | ||||
\(436\) | −5.00000 | − | 8.66025i | −0.239457 | − | 0.414751i | ||||
\(437\) | − | 7.85641i | − | 0.375823i | ||||||
\(438\) | −4.03590 | + | 2.33013i | −0.192843 | + | 0.111338i | ||||
\(439\) | 4.90192 | − | 8.49038i | 0.233956 | − | 0.405224i | −0.725013 | − | 0.688735i | \(-0.758166\pi\) |
0.958969 | + | 0.283512i | \(0.0914995\pi\) | |||||||
\(440\) | 1.36603 | + | 0.901924i | 0.0651227 | + | 0.0429975i | ||||
\(441\) | 0.464102 | 0.0221001 | ||||||||
\(442\) | 16.0622 | − | 1.03590i | 0.764000 | − | 0.0492727i | ||||
\(443\) | 34.6410i | 1.64584i | 0.568154 | + | 0.822922i | \(0.307658\pi\) | ||||
−0.568154 | + | 0.822922i | \(0.692342\pi\) | |||||||
\(444\) | 3.96410 | − | 6.86603i | 0.188128 | − | 0.325847i | ||||
\(445\) | 6.07180 | − | 9.19615i | 0.287831 | − | 0.435939i | ||||
\(446\) | 0.196152 | + | 0.339746i | 0.00928809 | + | 0.0160874i | ||||
\(447\) | − | 19.9282i | − | 0.942572i | ||||||
\(448\) | 2.36603 | − | 1.36603i | 0.111784 | − | 0.0645386i | ||||
\(449\) | −3.92820 | − | 6.80385i | −0.185383 | − | 0.321093i | 0.758322 | − | 0.651880i | \(-0.226019\pi\) |
−0.943706 | + | 0.330786i | \(0.892686\pi\) | |||||||
\(450\) | −0.598076 | + | 4.96410i | −0.0281936 | + | 0.234010i | ||||
\(451\) | 3.36603 | + | 5.83013i | 0.158500 | + | 0.274530i | ||||
\(452\) | 7.79423 | + | 4.50000i | 0.366610 | + | 0.211662i | ||||
\(453\) | 4.43782 | + | 2.56218i | 0.208507 | + | 0.120382i | ||||
\(454\) | 4.19615 | 0.196935 | ||||||||
\(455\) | −19.0263 | + | 11.0981i | −0.891966 | + | 0.520286i | ||||
\(456\) | 1.26795 | 0.0593772 | ||||||||
\(457\) | −7.62436 | − | 4.40192i | −0.356652 | − | 0.205913i | 0.310959 | − | 0.950423i | \(-0.399350\pi\) |
−0.667611 | + | 0.744510i | \(0.732683\pi\) | |||||||
\(458\) | −24.9282 | − | 14.3923i | −1.16482 | − | 0.672508i | ||||
\(459\) | 2.23205 | + | 3.86603i | 0.104183 | + | 0.180451i | ||||
\(460\) | −0.830127 | + | 13.8301i | −0.0387049 | + | 0.644833i | ||||
\(461\) | −13.0359 | − | 22.5788i | −0.607142 | − | 1.05160i | −0.991709 | − | 0.128504i | \(-0.958982\pi\) |
0.384567 | − | 0.923097i | \(-0.374351\pi\) | |||||||
\(462\) | −1.73205 | + | 1.00000i | −0.0805823 | + | 0.0465242i | ||||
\(463\) | − | 6.33975i | − | 0.294633i | −0.989089 | − | 0.147316i | \(-0.952936\pi\) | ||
0.989089 | − | 0.147316i | \(-0.0470636\pi\) | |||||||
\(464\) | −3.23205 | − | 5.59808i | −0.150044 | − | 0.259884i | ||||
\(465\) | 7.46410 | + | 4.92820i | 0.346139 | + | 0.228540i | ||||
\(466\) | −6.19615 | + | 10.7321i | −0.287031 | + | 0.497153i | ||||
\(467\) | 22.0526i | 1.02047i | 0.860035 | + | 0.510235i | \(0.170442\pi\) | ||||
−0.860035 | + | 0.510235i | \(0.829558\pi\) | |||||||
\(468\) | 1.59808 | − | 3.23205i | 0.0738711 | − | 0.149402i | ||||
\(469\) | −20.9282 | −0.966375 | ||||||||
\(470\) | −9.43782 | + | 14.2942i | −0.435334 | + | 0.659344i | ||||
\(471\) | −4.69615 | + | 8.13397i | −0.216387 | + | 0.374794i | ||||
\(472\) | 10.7321 | − | 6.19615i | 0.493983 | − | 0.285201i | ||||
\(473\) | − | 2.39230i | − | 0.109998i | ||||||
\(474\) | 6.00000 | + | 10.3923i | 0.275589 | + | 0.477334i | ||||
\(475\) | 2.49038 | + | 5.83013i | 0.114267 | + | 0.267505i | ||||
\(476\) | 12.1962 | 0.559010 | ||||||||
\(477\) | −6.69615 | + | 3.86603i | −0.306596 | + | 0.177013i | ||||
\(478\) | 3.97372 | + | 2.29423i | 0.181754 | + | 0.104936i | ||||
\(479\) | −8.00000 | + | 13.8564i | −0.365529 | + | 0.633115i | −0.988861 | − | 0.148842i | \(-0.952445\pi\) |
0.623332 | + | 0.781958i | \(0.285779\pi\) | |||||||
\(480\) | −2.23205 | − | 0.133975i | −0.101879 | − | 0.00611508i | ||||
\(481\) | −25.6244 | − | 12.6699i | −1.16837 | − | 0.577696i | ||||
\(482\) | 9.39230i | 0.427808i | ||||||||
\(483\) | −14.6603 | − | 8.46410i | −0.667065 | − | 0.385130i | ||||
\(484\) | −5.23205 | + | 9.06218i | −0.237820 | + | 0.411917i | ||||
\(485\) | −20.0000 | + | 10.0000i | −0.908153 | + | 0.454077i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −33.2942 | + | 19.2224i | −1.50871 | + | 0.871052i | −0.508757 | + | 0.860910i | \(0.669895\pi\) |
−0.999949 | + | 0.0101413i | \(0.996772\pi\) | |||||||
\(488\) | −8.76795 | + | 5.06218i | −0.396906 | + | 0.229154i | ||||
\(489\) | 13.4641 | 0.608868 | ||||||||
\(490\) | −0.928203 | + | 0.464102i | −0.0419319 | + | 0.0209660i | ||||
\(491\) | −10.9019 | + | 18.8827i | −0.491997 | + | 0.852164i | −0.999958 | − | 0.00921662i | \(-0.997066\pi\) |
0.507961 | + | 0.861380i | \(0.330400\pi\) | |||||||
\(492\) | −7.96410 | − | 4.59808i | −0.359049 | − | 0.207297i | ||||
\(493\) | − | 28.8564i | − | 1.29963i | ||||||
\(494\) | −0.294229 | − | 4.56218i | −0.0132380 | − | 0.205262i | ||||
\(495\) | 1.63397 | + | 0.0980762i | 0.0734417 | + | 0.00440820i | ||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | 3.00000 | + | 1.73205i | 0.134568 | + | 0.0776931i | ||||
\(498\) | 4.56218 | − | 2.63397i | 0.204436 | − | 0.118031i | ||||
\(499\) | −40.3923 | −1.80821 | −0.904104 | − | 0.427313i | \(-0.859460\pi\) | ||||
−0.904104 | + | 0.427313i | \(0.859460\pi\) | |||||||
\(500\) | −3.76795 | − | 10.5263i | −0.168508 | − | 0.470750i | ||||
\(501\) | 6.92820 | + | 12.0000i | 0.309529 | + | 0.536120i | ||||
\(502\) | 21.4641i | 0.957990i | ||||||||
\(503\) | 18.8827 | − | 10.9019i | 0.841937 | − | 0.486093i | −0.0159849 | − | 0.999872i | \(-0.505088\pi\) |
0.857922 | + | 0.513779i | \(0.171755\pi\) | |||||||
\(504\) | 1.36603 | − | 2.36603i | 0.0608476 | − | 0.105391i | ||||
\(505\) | 17.1603 | − | 25.9904i | 0.763621 | − | 1.15656i | ||||
\(506\) | 4.53590 | 0.201645 | ||||||||
\(507\) | −12.0000 | − | 5.00000i | −0.532939 | − | 0.222058i | ||||
\(508\) | 4.00000i | 0.177471i | ||||||||
\(509\) | −15.3564 | + | 26.5981i | −0.680661 | + | 1.17894i | 0.294119 | + | 0.955769i | \(0.404974\pi\) |
−0.974780 | + | 0.223170i | \(0.928359\pi\) | |||||||
\(510\) | −8.33013 | − | 5.50000i | −0.368864 | − | 0.243544i | ||||
\(511\) | 6.36603 | + | 11.0263i | 0.281616 | + | 0.487774i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.09808 | − | 0.633975i | 0.0484812 | − | 0.0279907i | ||||
\(514\) | −1.50000 | − | 2.59808i | −0.0661622 | − | 0.114596i | ||||
\(515\) | 1.24167 | − | 20.6865i | 0.0547145 | − | 0.911558i | ||||
\(516\) | 1.63397 | + | 2.83013i | 0.0719317 | + | 0.124589i | ||||
\(517\) | 4.85641 | + | 2.80385i | 0.213585 | + | 0.123313i | ||||
\(518\) | −18.7583 | − | 10.8301i | −0.824194 | − | 0.475848i | ||||
\(519\) | 18.7846 | 0.824553 | ||||||||
\(520\) | 0.0358984 | + | 8.06218i | 0.00157425 | + | 0.353550i | ||||
\(521\) | −19.4449 | −0.851895 | −0.425947 | − | 0.904748i | \(-0.640059\pi\) | ||||
−0.425947 | + | 0.904748i | \(0.640059\pi\) | |||||||
\(522\) | −5.59808 | − | 3.23205i | −0.245021 | − | 0.141463i | ||||
\(523\) | 31.5622 | + | 18.2224i | 1.38012 | + | 0.796811i | 0.992173 | − | 0.124871i | \(-0.0398518\pi\) |
0.387945 | + | 0.921683i | \(0.373185\pi\) | |||||||
\(524\) | −6.92820 | − | 12.0000i | −0.302660 | − | 0.524222i | ||||
\(525\) | 13.5622 | + | 1.63397i | 0.591902 | + | 0.0713125i | ||||
\(526\) | 8.56218 | + | 14.8301i | 0.373329 | + | 0.646624i | ||||
\(527\) | −15.4641 | + | 8.92820i | −0.673627 | + | 0.388919i | ||||
\(528\) | 0.732051i | 0.0318584i | ||||||||
\(529\) | 7.69615 | + | 13.3301i | 0.334615 | + | 0.579571i | ||||
\(530\) | 9.52628 | − | 14.4282i | 0.413795 | − | 0.626721i | ||||
\(531\) | 6.19615 | − | 10.7321i | 0.268890 | − | 0.465731i | ||||
\(532\) | − | 3.46410i | − | 0.150188i | ||||||
\(533\) | −14.6962 | + | 29.7224i | −0.636561 | + | 1.28742i | ||||
\(534\) | 4.92820 | 0.213264 | ||||||||
\(535\) | −2.36603 | − | 1.56218i | −0.102292 | − | 0.0675388i | ||||
\(536\) | −3.83013 | + | 6.63397i | −0.165436 | + | 0.286544i | ||||
\(537\) | −15.7583 | + | 9.09808i | −0.680022 | + | 0.392611i | ||||
\(538\) | 4.39230i | 0.189366i | ||||||||
\(539\) | 0.169873 | + | 0.294229i | 0.00731695 | + | 0.0126733i | ||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | −1.19615 | −0.0514266 | −0.0257133 | − | 0.999669i | \(-0.508186\pi\) | ||||
−0.0257133 | + | 0.999669i | \(0.508186\pi\) | |||||||
\(542\) | −5.07180 | + | 2.92820i | −0.217852 | + | 0.125777i | ||||
\(543\) | 13.9641 | + | 8.06218i | 0.599257 | + | 0.345981i | ||||
\(544\) | 2.23205 | − | 3.86603i | 0.0956984 | − | 0.165754i | ||||
\(545\) | 22.3205 | + | 1.33975i | 0.956106 | + | 0.0573884i | ||||
\(546\) | −8.83013 | − | 4.36603i | −0.377895 | − | 0.186849i | ||||
\(547\) | − | 25.8038i | − | 1.10329i | −0.834078 | − | 0.551646i | \(-0.814000\pi\) | ||
0.834078 | − | 0.551646i | \(-0.186000\pi\) | |||||||
\(548\) | −15.9904 | − | 9.23205i | −0.683075 | − | 0.394374i | ||||
\(549\) | −5.06218 | + | 8.76795i | −0.216048 | + | 0.374207i | ||||
\(550\) | −3.36603 | + | 1.43782i | −0.143528 | + | 0.0613089i | ||||
\(551\) | −8.19615 | −0.349168 | ||||||||
\(552\) | −5.36603 | + | 3.09808i | −0.228393 | + | 0.131863i | ||||
\(553\) | 28.3923 | − | 16.3923i | 1.20736 | − | 0.697072i | ||||
\(554\) | −12.3205 | −0.523448 | ||||||||
\(555\) | 7.92820 | + | 15.8564i | 0.336533 | + | 0.673067i | ||||
\(556\) | 0.535898 | − | 0.928203i | 0.0227272 | − | 0.0393646i | ||||
\(557\) | −12.6962 | − | 7.33013i | −0.537953 | − | 0.310587i | 0.206296 | − | 0.978490i | \(-0.433859\pi\) |
−0.744249 | + | 0.667902i | \(0.767192\pi\) | |||||||
\(558\) | 4.00000i | 0.169334i | ||||||||
\(559\) | 9.80385 | − | 6.53590i | 0.414659 | − | 0.276439i | ||||
\(560\) | −0.366025 | + | 6.09808i | −0.0154674 | + | 0.257691i | ||||
\(561\) | −1.63397 | + | 2.83013i | −0.0689865 | + | 0.119488i | ||||
\(562\) | 1.50000 | + | 0.866025i | 0.0632737 | + | 0.0365311i | ||||
\(563\) | 6.92820 | − | 4.00000i | 0.291989 | − | 0.168580i | −0.346850 | − | 0.937921i | \(-0.612749\pi\) |
0.638838 | + | 0.769341i | \(0.279415\pi\) | |||||||
\(564\) | −7.66025 | −0.322555 | ||||||||
\(565\) | −18.0000 | + | 9.00000i | −0.757266 | + | 0.378633i | ||||
\(566\) | −3.83013 | − | 6.63397i | −0.160992 | − | 0.278847i | ||||
\(567\) | − | 2.73205i | − | 0.114735i | ||||||
\(568\) | 1.09808 | − | 0.633975i | 0.0460743 | − | 0.0266010i | ||||
\(569\) | 9.07180 | − | 15.7128i | 0.380310 | − | 0.658715i | −0.610797 | − | 0.791787i | \(-0.709151\pi\) |
0.991106 | + | 0.133072i | \(0.0424841\pi\) | |||||||
\(570\) | −1.56218 | + | 2.36603i | −0.0654324 | + | 0.0991019i | ||||
\(571\) | −25.6603 | −1.07385 | −0.536924 | − | 0.843631i | \(-0.680414\pi\) | ||||
−0.536924 | + | 0.843631i | \(0.680414\pi\) | |||||||
\(572\) | 2.63397 | − | 0.169873i | 0.110132 | − | 0.00710275i | ||||
\(573\) | − | 9.46410i | − | 0.395369i | ||||||
\(574\) | −12.5622 | + | 21.7583i | −0.524335 | + | 0.908175i | ||||
\(575\) | −24.7846 | − | 18.5885i | −1.03359 | − | 0.775192i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 23.9808i | − | 0.998332i | −0.866506 | − | 0.499166i | \(-0.833640\pi\) | ||
0.866506 | − | 0.499166i | \(-0.166360\pi\) | |||||||
\(578\) | 2.53590 | − | 1.46410i | 0.105479 | − | 0.0608986i | ||||
\(579\) | −5.33013 | − | 9.23205i | −0.221513 | − | 0.383671i | ||||
\(580\) | 14.4282 | + | 0.866025i | 0.599099 | + | 0.0359597i | ||||
\(581\) | −7.19615 | − | 12.4641i | −0.298547 | − | 0.517098i | ||||
\(582\) | −8.66025 | − | 5.00000i | −0.358979 | − | 0.207257i | ||||
\(583\) | −4.90192 | − | 2.83013i | −0.203017 | − | 0.117212i | ||||
\(584\) | 4.66025 | 0.192843 | ||||||||
\(585\) | 4.06218 | + | 6.96410i | 0.167950 | + | 0.287930i | ||||
\(586\) | 13.7321 | 0.567266 | ||||||||
\(587\) | 8.78461 | + | 5.07180i | 0.362580 | + | 0.209335i | 0.670212 | − | 0.742170i | \(-0.266203\pi\) |
−0.307632 | + | 0.951505i | \(0.599537\pi\) | |||||||
\(588\) | −0.401924 | − | 0.232051i | −0.0165751 | − | 0.00956961i | ||||
\(589\) | 2.53590 | + | 4.39230i | 0.104490 | + | 0.180982i | ||||
\(590\) | −1.66025 | + | 27.6603i | −0.0683516 | + | 1.13875i | ||||
\(591\) | −4.92820 | − | 8.53590i | −0.202719 | − | 0.351120i | ||||
\(592\) | −6.86603 | + | 3.96410i | −0.282192 | + | 0.162924i | ||||
\(593\) | 19.3923i | 0.796347i | 0.917310 | + | 0.398173i | \(0.130356\pi\) | ||||
−0.917310 | + | 0.398173i | \(0.869644\pi\) | |||||||
\(594\) | 0.366025 | + | 0.633975i | 0.0150182 | + | 0.0260123i | ||||
\(595\) | −15.0263 | + | 22.7583i | −0.616017 | + | 0.933001i | ||||
\(596\) | −9.96410 | + | 17.2583i | −0.408146 | + | 0.706929i | ||||
\(597\) | 28.0526i | 1.14811i | ||||||||
\(598\) | 12.3923 | + | 18.5885i | 0.506759 | + | 0.760139i | ||||
\(599\) | −8.78461 | −0.358929 | −0.179465 | − | 0.983764i | \(-0.557437\pi\) | ||||
−0.179465 | + | 0.983764i | \(0.557437\pi\) | |||||||
\(600\) | 3.00000 | − | 4.00000i | 0.122474 | − | 0.163299i | ||||
\(601\) | −8.50000 | + | 14.7224i | −0.346722 | + | 0.600541i | −0.985665 | − | 0.168714i | \(-0.946039\pi\) |
0.638943 | + | 0.769254i | \(0.279372\pi\) | |||||||
\(602\) | 7.73205 | − | 4.46410i | 0.315135 | − | 0.181943i | ||||
\(603\) | 7.66025i | 0.311950i | ||||||||
\(604\) | −2.56218 | − | 4.43782i | −0.104254 | − | 0.180572i | ||||
\(605\) | −10.4641 | − | 20.9282i | −0.425426 | − | 0.850852i | ||||
\(606\) | 13.9282 | 0.565795 | ||||||||
\(607\) | −41.9090 | + | 24.1962i | −1.70103 | + | 0.982092i | −0.756314 | + | 0.654209i | \(0.773002\pi\) |
−0.944718 | + | 0.327883i | \(0.893665\pi\) | |||||||
\(608\) | −1.09808 | − | 0.633975i | −0.0445329 | − | 0.0257111i | ||||
\(609\) | −8.83013 | + | 15.2942i | −0.357815 | + | 0.619753i | ||||
\(610\) | 1.35641 | − | 22.5981i | 0.0549193 | − | 0.914969i | ||||
\(611\) | 1.77757 | + | 27.5622i | 0.0719127 | + | 1.11505i | ||||
\(612\) | − | 4.46410i | − | 0.180451i | ||||||
\(613\) | −18.8660 | − | 10.8923i | −0.761992 | − | 0.439936i | 0.0680188 | − | 0.997684i | \(-0.478332\pi\) |
−0.830010 | + | 0.557748i | \(0.811666\pi\) | |||||||
\(614\) | −9.63397 | + | 16.6865i | −0.388796 | + | 0.673414i | ||||
\(615\) | 18.3923 | − | 9.19615i | 0.741649 | − | 0.370825i | ||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | 28.3301 | − | 16.3564i | 1.14053 | − | 0.658484i | 0.193967 | − | 0.981008i | \(-0.437865\pi\) |
0.946561 | + | 0.322524i | \(0.104531\pi\) | |||||||
\(618\) | 8.02628 | − | 4.63397i | 0.322864 | − | 0.186406i | ||||
\(619\) | 36.1051 | 1.45119 | 0.725594 | − | 0.688123i | \(-0.241565\pi\) | ||||
0.725594 | + | 0.688123i | \(0.241565\pi\) | |||||||
\(620\) | −4.00000 | − | 8.00000i | −0.160644 | − | 0.321288i | ||||
\(621\) | −3.09808 | + | 5.36603i | −0.124322 | + | 0.215331i | ||||
\(622\) | 2.70577 | + | 1.56218i | 0.108492 | + | 0.0626376i | ||||
\(623\) | − | 13.4641i | − | 0.539428i | ||||||
\(624\) | −3.00000 | + | 2.00000i | −0.120096 | + | 0.0800641i | ||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 7.00000 | − | 12.1244i | 0.279776 | − | 0.484587i | ||||
\(627\) | 0.803848 | + | 0.464102i | 0.0321026 | + | 0.0185344i | ||||
\(628\) | 8.13397 | − | 4.69615i | 0.324581 | − | 0.187397i | ||||
\(629\) | −35.3923 | −1.41118 | ||||||||
\(630\) | 2.73205 | + | 5.46410i | 0.108848 | + | 0.217695i | ||||
\(631\) | −4.92820 | − | 8.53590i | −0.196189 | − | 0.339809i | 0.751101 | − | 0.660187i | \(-0.229523\pi\) |
−0.947290 | + | 0.320379i | \(0.896190\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | −18.5885 | + | 10.7321i | −0.738825 | + | 0.426561i | ||||
\(634\) | 14.8660 | − | 25.7487i | 0.590405 | − | 1.02261i | ||||
\(635\) | −7.46410 | − | 4.92820i | −0.296204 | − | 0.195570i | ||||
\(636\) | 7.73205 | 0.306596 | ||||||||
\(637\) | −0.741670 | + | 1.50000i | −0.0293860 | + | 0.0594322i | ||||
\(638\) | − | 4.73205i | − | 0.187344i | ||||||
\(639\) | 0.633975 | − | 1.09808i | 0.0250796 | − | 0.0434392i | ||||
\(640\) | 1.86603 | + | 1.23205i | 0.0737611 | + | 0.0487011i | ||||
\(641\) | −4.52628 | − | 7.83975i | −0.178777 | − | 0.309651i | 0.762685 | − | 0.646770i | \(-0.223881\pi\) |
−0.941462 | + | 0.337119i | \(0.890547\pi\) | |||||||
\(642\) | − | 1.26795i | − | 0.0500420i | ||||||
\(643\) | −7.60770 | + | 4.39230i | −0.300018 | + | 0.173216i | −0.642451 | − | 0.766327i | \(-0.722082\pi\) |
0.342433 | + | 0.939542i | \(0.388749\pi\) | |||||||
\(644\) | 8.46410 | + | 14.6603i | 0.333532 | + | 0.577695i | ||||
\(645\) | −7.29423 | − | 0.437822i | −0.287210 | − | 0.0172392i | ||||
\(646\) | −2.83013 | − | 4.90192i | −0.111350 | − | 0.192864i | ||||
\(647\) | −20.1962 | − | 11.6603i | −0.793993 | − | 0.458412i | 0.0473736 | − | 0.998877i | \(-0.484915\pi\) |
−0.841366 | + | 0.540465i | \(0.818248\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 9.07180 | 0.356099 | ||||||||
\(650\) | −15.0885 | − | 9.86603i | −0.591818 | − | 0.386977i | ||||
\(651\) | 10.9282 | 0.428310 | ||||||||
\(652\) | −11.6603 | − | 6.73205i | −0.456651 | − | 0.263647i | ||||
\(653\) | −28.2679 | − | 16.3205i | −1.10621 | − | 0.638671i | −0.168365 | − | 0.985725i | \(-0.553849\pi\) |
−0.937845 | + | 0.347054i | \(0.887182\pi\) | |||||||
\(654\) | 5.00000 | + | 8.66025i | 0.195515 | + | 0.338643i | ||||
\(655\) | 30.9282 | + | 1.85641i | 1.20846 | + | 0.0725358i | ||||
\(656\) | 4.59808 | + | 7.96410i | 0.179525 | + | 0.310946i | ||||
\(657\) | 4.03590 | − | 2.33013i | 0.157455 | − | 0.0909069i | ||||
\(658\) | 20.9282i | 0.815866i | ||||||||
\(659\) | −20.7321 | − | 35.9090i | −0.807606 | − | 1.39881i | −0.914518 | − | 0.404546i | \(-0.867430\pi\) |
0.106912 | − | 0.994269i | \(-0.465904\pi\) | |||||||
\(660\) | −1.36603 | − | 0.901924i | −0.0531725 | − | 0.0351073i | ||||
\(661\) | 19.2583 | − | 33.3564i | 0.749062 | − | 1.29741i | −0.199210 | − | 0.979957i | \(-0.563838\pi\) |
0.948273 | − | 0.317457i | \(-0.102829\pi\) | |||||||
\(662\) | 28.7846i | 1.11875i | ||||||||
\(663\) | −16.0622 | + | 1.03590i | −0.623803 | + | 0.0402310i | ||||
\(664\) | −5.26795 | −0.204436 | ||||||||
\(665\) | 6.46410 | + | 4.26795i | 0.250667 | + | 0.165504i | ||||
\(666\) | −3.96410 | + | 6.86603i | −0.153606 | + | 0.266053i | ||||
\(667\) | 34.6865 | − | 20.0263i | 1.34307 | − | 0.775421i | ||||
\(668\) | − | 13.8564i | − | 0.536120i | ||||||
\(669\) | −0.196152 | − | 0.339746i | −0.00758369 | − | 0.0131353i | ||||
\(670\) | −7.66025 | − | 15.3205i | −0.295941 | − | 0.591883i | ||||
\(671\) | −7.41154 | −0.286119 | ||||||||
\(672\) | −2.36603 | + | 1.36603i | −0.0912714 | + | 0.0526956i | ||||
\(673\) | −8.89230 | − | 5.13397i | −0.342773 | − | 0.197900i | 0.318725 | − | 0.947847i | \(-0.396746\pi\) |
−0.661498 | + | 0.749947i | \(0.730079\pi\) | |||||||
\(674\) | 5.52628 | − | 9.57180i | 0.212864 | − | 0.368692i | ||||
\(675\) | 0.598076 | − | 4.96410i | 0.0230200 | − | 0.191068i | ||||
\(676\) | 7.89230 | + | 10.3301i | 0.303550 | + | 0.397313i | ||||
\(677\) | 48.6410i | 1.86943i | 0.355403 | + | 0.934713i | \(0.384344\pi\) | ||||
−0.355403 | + | 0.934713i | \(0.615656\pi\) | |||||||
\(678\) | −7.79423 | − | 4.50000i | −0.299336 | − | 0.172821i | ||||
\(679\) | −13.6603 | + | 23.6603i | −0.524232 | + | 0.907997i | ||||
\(680\) | 4.46410 | + | 8.92820i | 0.171190 | + | 0.342381i | ||||
\(681\) | −4.19615 | −0.160797 | ||||||||
\(682\) | −2.53590 | + | 1.46410i | −0.0971046 | + | 0.0560633i | ||||
\(683\) | −23.3205 | + | 13.4641i | −0.892334 | + | 0.515190i | −0.874705 | − | 0.484655i | \(-0.838945\pi\) |
−0.0176291 | + | 0.999845i | \(0.505612\pi\) | |||||||
\(684\) | −1.26795 | −0.0484812 | ||||||||
\(685\) | 36.9282 | − | 18.4641i | 1.41095 | − | 0.705477i | ||||
\(686\) | 8.92820 | − | 15.4641i | 0.340880 | − | 0.590422i | ||||
\(687\) | 24.9282 | + | 14.3923i | 0.951070 | + | 0.549101i | ||||
\(688\) | − | 3.26795i | − | 0.124589i | ||||||
\(689\) | −1.79423 | − | 27.8205i | −0.0683547 | − | 1.05988i | ||||
\(690\) | 0.830127 | − | 13.8301i | 0.0316024 | − | 0.526504i | ||||
\(691\) | −20.2942 | + | 35.1506i | −0.772029 | + | 1.33719i | 0.164420 | + | 0.986390i | \(0.447425\pi\) |
−0.936449 | + | 0.350803i | \(0.885909\pi\) | |||||||
\(692\) | −16.2679 | − | 9.39230i | −0.618415 | − | 0.357042i | ||||
\(693\) | 1.73205 | − | 1.00000i | 0.0657952 | − | 0.0379869i | ||||
\(694\) | 5.66025 | 0.214860 | ||||||||
\(695\) | 1.07180 | + | 2.14359i | 0.0406556 | + | 0.0813111i | ||||
\(696\) | 3.23205 | + | 5.59808i | 0.122511 | + | 0.212195i | ||||
\(697\) | 41.0526i | 1.55498i | ||||||||
\(698\) | −16.5167 | + | 9.53590i | −0.625165 | + | 0.360939i | ||||
\(699\) | 6.19615 | − | 10.7321i | 0.234360 | − | 0.405923i | ||||
\(700\) | −10.9282 | − | 8.19615i | −0.413047 | − | 0.309785i | ||||
\(701\) | −13.4641 | −0.508532 | −0.254266 | − | 0.967134i | \(-0.581834\pi\) | ||||
−0.254266 | + | 0.967134i | \(0.581834\pi\) | |||||||
\(702\) | −1.59808 | + | 3.23205i | −0.0603155 | + | 0.121986i | ||||
\(703\) | 10.0526i | 0.379139i | ||||||||
\(704\) | 0.366025 | − | 0.633975i | 0.0137951 | − | 0.0238938i | ||||
\(705\) | 9.43782 | − | 14.2942i | 0.355449 | − | 0.538352i | ||||
\(706\) | 12.6244 | + | 21.8660i | 0.475124 | + | 0.822939i | ||||
\(707\) | − | 38.0526i | − | 1.43111i | ||||||
\(708\) | −10.7321 | + | 6.19615i | −0.403335 | + | 0.232866i | ||||
\(709\) | 18.5263 | + | 32.0885i | 0.695769 | + | 1.20511i | 0.969921 | + | 0.243421i | \(0.0782696\pi\) |
−0.274152 | + | 0.961686i | \(0.588397\pi\) | |||||||
\(710\) | −0.169873 | + | 2.83013i | −0.00637522 | + | 0.106213i | ||||
\(711\) | −6.00000 | − | 10.3923i | −0.225018 | − | 0.389742i | ||||
\(712\) | −4.26795 | − | 2.46410i | −0.159948 | − | 0.0923461i | ||||
\(713\) | −21.4641 | − | 12.3923i | −0.803837 | − | 0.464095i | ||||
\(714\) | −12.1962 | −0.456430 | ||||||||
\(715\) | −2.92820 | + | 5.12436i | −0.109509 | + | 0.191640i | ||||
\(716\) | 18.1962 | 0.680022 | ||||||||
\(717\) | −3.97372 | − | 2.29423i | −0.148401 | − | 0.0856795i | ||||
\(718\) | −7.68653 | − | 4.43782i | −0.286859 | − | 0.165618i | ||||
\(719\) | −16.1962 | − | 28.0526i | −0.604015 | − | 1.04618i | −0.992206 | − | 0.124605i | \(-0.960234\pi\) |
0.388192 | − | 0.921579i | \(-0.373100\pi\) | |||||||
\(720\) | 2.23205 | + | 0.133975i | 0.0831836 | + | 0.00499294i | ||||
\(721\) | −12.6603 | − | 21.9282i | −0.471492 | − | 0.816649i | ||||
\(722\) | 15.0622 | − | 8.69615i | 0.560556 | − | 0.323637i | ||||
\(723\) | − | 9.39230i | − | 0.349304i | ||||||
\(724\) | −8.06218 | − | 13.9641i | −0.299628 | − | 0.518972i | ||||
\(725\) | −19.3923 | + | 25.8564i | −0.720212 | + | 0.960283i | ||||
\(726\) | 5.23205 | − | 9.06218i | 0.194180 | − | 0.336329i | ||||
\(727\) | 13.2679i | 0.492081i | 0.969260 | + | 0.246040i | \(0.0791296\pi\) | ||||
−0.969260 | + | 0.246040i | \(0.920870\pi\) | |||||||
\(728\) | 5.46410 | + | 8.19615i | 0.202513 | + | 0.303770i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −5.74167 | + | 8.69615i | −0.212509 | + | 0.321859i | ||||
\(731\) | 7.29423 | − | 12.6340i | 0.269787 | − | 0.467284i | ||||
\(732\) | 8.76795 | − | 5.06218i | 0.324073 | − | 0.187103i | ||||
\(733\) | 45.3923i | 1.67660i | 0.545207 | + | 0.838302i | \(0.316451\pi\) | ||||
−0.545207 | + | 0.838302i | \(0.683549\pi\) | |||||||
\(734\) | 16.4904 | + | 28.5622i | 0.608671 | + | 1.05425i | ||||
\(735\) | 0.928203 | − | 0.464102i | 0.0342373 | − | 0.0171186i | ||||
\(736\) | 6.19615 | 0.228393 | ||||||||
\(737\) | −4.85641 | + | 2.80385i | −0.178888 | + | 0.103281i | ||||
\(738\) | 7.96410 | + | 4.59808i | 0.293163 | + | 0.169258i | ||||
\(739\) | 1.07180 | − | 1.85641i | 0.0394267 | − | 0.0682890i | −0.845639 | − | 0.533756i | \(-0.820780\pi\) |
0.885065 | + | 0.465467i | \(0.154114\pi\) | |||||||
\(740\) | 1.06218 | − | 17.6962i | 0.0390464 | − | 0.650524i | ||||
\(741\) | 0.294229 | + | 4.56218i | 0.0108088 | + | 0.167596i | ||||
\(742\) | − | 21.1244i | − | 0.775499i | ||||||
\(743\) | 18.5885 | + | 10.7321i | 0.681944 | + | 0.393721i | 0.800587 | − | 0.599216i | \(-0.204521\pi\) |
−0.118643 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −19.9282 | − | 39.8564i | −0.730113 | − | 1.46023i | ||||
\(746\) | 23.5359 | 0.861710 | ||||||||
\(747\) | −4.56218 | + | 2.63397i | −0.166921 | + | 0.0963721i | ||||
\(748\) | 2.83013 | − | 1.63397i | 0.103480 | − | 0.0597440i | ||||
\(749\) | −3.46410 | −0.126576 | ||||||||
\(750\) | 3.76795 | + | 10.5263i | 0.137586 | + | 0.384365i | ||||
\(751\) | −18.0263 | + | 31.2224i | −0.657788 | + | 1.13932i | 0.323399 | + | 0.946263i | \(0.395175\pi\) |
−0.981187 | + | 0.193060i | \(0.938159\pi\) | |||||||
\(752\) | 6.63397 | + | 3.83013i | 0.241916 | + | 0.139670i | ||||
\(753\) | − | 21.4641i | − | 0.782195i | ||||||
\(754\) | 19.3923 | − | 12.9282i | 0.706226 | − | 0.470817i | ||||
\(755\) | 11.4378 | + | 0.686533i | 0.416265 | + | 0.0249855i | ||||
\(756\) | −1.36603 | + | 2.36603i | −0.0496819 | + | 0.0860515i | ||||
\(757\) | −34.7321 | − | 20.0526i | −1.26236 | − | 0.728823i | −0.288828 | − | 0.957381i | \(-0.593265\pi\) |
−0.973530 | + | 0.228558i | \(0.926599\pi\) | |||||||
\(758\) | 22.7321 | − | 13.1244i | 0.825665 | − | 0.476698i | ||||
\(759\) | −4.53590 | −0.164643 | ||||||||
\(760\) | 2.53590 | − | 1.26795i | 0.0919867 | − | 0.0459934i | ||||
\(761\) | −11.5359 | − | 19.9808i | −0.418176 | − | 0.724302i | 0.577580 | − | 0.816334i | \(-0.303997\pi\) |
−0.995756 | + | 0.0920320i | \(0.970664\pi\) | |||||||
\(762\) | − | 4.00000i | − | 0.144905i | ||||||
\(763\) | 23.6603 | − | 13.6603i | 0.856559 | − | 0.494534i | ||||
\(764\) | −4.73205 | + | 8.19615i | −0.171200 | + | 0.296526i | ||||
\(765\) | 8.33013 | + | 5.50000i | 0.301176 | + | 0.198853i | ||||
\(766\) | 26.9282 | 0.972956 | ||||||||
\(767\) | 24.7846 | + | 37.1769i | 0.894920 | + | 1.34238i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 22.7321 | − | 39.3731i | 0.819739 | − | 1.41983i | −0.0861360 | − | 0.996283i | \(-0.527452\pi\) |
0.905875 | − | 0.423546i | \(-0.139215\pi\) | |||||||
\(770\) | −2.46410 | + | 3.73205i | −0.0888001 | + | 0.134494i | ||||
\(771\) | 1.50000 | + | 2.59808i | 0.0540212 | + | 0.0935674i | ||||
\(772\) | 10.6603i | 0.383671i | ||||||||
\(773\) | 35.1962 | − | 20.3205i | 1.26592 | − | 0.730878i | 0.291705 | − | 0.956508i | \(-0.405778\pi\) |
0.974213 | + | 0.225631i | \(0.0724442\pi\) | |||||||
\(774\) | −1.63397 | − | 2.83013i | −0.0587320 | − | 0.101727i | ||||
\(775\) | 19.8564 | + | 2.39230i | 0.713263 | + | 0.0859341i | ||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 18.7583 | + | 10.8301i | 0.672951 | + | 0.388529i | ||||
\(778\) | 20.8468 | + | 12.0359i | 0.747394 | + | 0.431508i | ||||
\(779\) | 11.6603 | 0.417772 | ||||||||
\(780\) | −0.0358984 | − | 8.06218i | −0.00128537 | − | 0.288672i | ||||
\(781\) | 0.928203 | 0.0332137 | ||||||||
\(782\) | 23.9545 | + | 13.8301i | 0.856611 | + | 0.494564i | ||||
\(783\) | 5.59808 | + | 3.23205i | 0.200059 | + | 0.115504i | ||||
\(784\) | 0.232051 | + | 0.401924i | 0.00828753 | + | 0.0143544i | ||||
\(785\) | −1.25833 | + | 20.9641i | −0.0449117 | + | 0.748241i | ||||
\(786\) | 6.92820 | + | 12.0000i | 0.247121 | + | 0.428026i | ||||
\(787\) | 16.7321 | − | 9.66025i | 0.596433 | − | 0.344351i | −0.171204 | − | 0.985236i | \(-0.554766\pi\) |
0.767637 | + | 0.640885i | \(0.221432\pi\) | |||||||
\(788\) | 9.85641i | 0.351120i | ||||||||
\(789\) | −8.56218 | − | 14.8301i | −0.304822 | − | 0.527967i | ||||
\(790\) | 22.3923 | + | 14.7846i | 0.796682 | + | 0.526013i | ||||
\(791\) | −12.2942 | + | 21.2942i | −0.437132 | + | 0.757136i | ||||
\(792\) | − | 0.732051i | − | 0.0260123i | ||||||
\(793\) | −20.2487 | − | 30.3731i | −0.719053 | − | 1.07858i | ||||
\(794\) | 19.3205 | 0.685659 | ||||||||
\(795\) | −9.52628 | + | 14.4282i | −0.337862 | + | 0.511716i | ||||
\(796\) | 14.0263 | − | 24.2942i | 0.497148 | − | 0.861086i | ||||
\(797\) | 0.928203 | − | 0.535898i | 0.0328786 | − | 0.0189825i | −0.483471 | − | 0.875361i | \(-0.660624\pi\) |
0.516349 | + | 0.856378i | \(0.327291\pi\) | |||||||
\(798\) | 3.46410i | 0.122628i | ||||||||
\(799\) | 17.0981 | + | 29.6147i | 0.604886 | + | 1.04769i | ||||
\(800\) | −4.59808 | + | 1.96410i | −0.162567 | + | 0.0694415i | ||||
\(801\) | −4.92820 | −0.174129 | ||||||||
\(802\) | 7.83975 | − | 4.52628i | 0.276831 | − | 0.159828i | ||||
\(803\) | 2.95448 | + | 1.70577i | 0.104261 | + | 0.0601954i | ||||
\(804\) | 3.83013 | − | 6.63397i | 0.135078 | − | 0.233962i | ||||
\(805\) | −37.7846 | − | 2.26795i | −1.33173 | − | 0.0799347i | ||||
\(806\) | −12.9282 | − | 6.39230i | −0.455377 | − | 0.225159i | ||||
\(807\) | − | 4.39230i | − | 0.154616i | ||||||
\(808\) | −12.0622 | − | 6.96410i | −0.424346 | − | 0.244996i | ||||
\(809\) | 0.990381 | − | 1.71539i | 0.0348199 | − | 0.0603099i | −0.848090 | − | 0.529852i | \(-0.822248\pi\) |
0.882910 | + | 0.469542i | \(0.155581\pi\) | |||||||
\(810\) | 2.00000 | − | 1.00000i | 0.0702728 | − | 0.0351364i | ||||
\(811\) | −33.8564 | −1.18886 | −0.594430 | − | 0.804148i | \(-0.702622\pi\) | ||||
−0.594430 | + | 0.804148i | \(0.702622\pi\) | |||||||
\(812\) | 15.2942 | − | 8.83013i | 0.536722 | − | 0.309877i | ||||
\(813\) | 5.07180 | − | 2.92820i | 0.177876 | − | 0.102697i | ||||
\(814\) | −5.80385 | −0.203425 | ||||||||
\(815\) | 26.9282 | − | 13.4641i | 0.943254 | − | 0.471627i | ||||
\(816\) | −2.23205 | + | 3.86603i | −0.0781374 | + | 0.135338i | ||||
\(817\) | −3.58846 | − | 2.07180i | −0.125544 | − | 0.0724830i | ||||
\(818\) | 16.0718i | 0.561937i | ||||||||
\(819\) | 8.83013 | + | 4.36603i | 0.308550 | + | 0.152561i | ||||
\(820\) | −20.5263 | − | 1.23205i | −0.716809 | − | 0.0430251i | ||||
\(821\) | −5.12436 | + | 8.87564i | −0.178841 | + | 0.309762i | −0.941484 | − | 0.337058i | \(-0.890568\pi\) |
0.762643 | + | 0.646820i | \(0.223902\pi\) | |||||||
\(822\) | 15.9904 | + | 9.23205i | 0.557729 | + | 0.322005i | ||||
\(823\) | −34.9808 | + | 20.1962i | −1.21935 | + | 0.703994i | −0.964780 | − | 0.263060i | \(-0.915268\pi\) |
−0.254573 | + | 0.967054i | \(0.581935\pi\) | |||||||
\(824\) | −9.26795 | −0.322864 | ||||||||
\(825\) | 3.36603 | − | 1.43782i | 0.117190 | − | 0.0500585i | ||||
\(826\) | 16.9282 | + | 29.3205i | 0.589008 | + | 1.02019i | ||||
\(827\) | − | 48.7846i | − | 1.69641i | −0.529670 | − | 0.848204i | \(-0.677684\pi\) | ||
0.529670 | − | 0.848204i | \(-0.322316\pi\) | |||||||
\(828\) | 5.36603 | − | 3.09808i | 0.186482 | − | 0.107666i | ||||
\(829\) | 8.93782 | − | 15.4808i | 0.310423 | − | 0.537669i | −0.668031 | − | 0.744134i | \(-0.732863\pi\) |
0.978454 | + | 0.206465i | \(0.0661958\pi\) | |||||||
\(830\) | 6.49038 | − | 9.83013i | 0.225284 | − | 0.341209i | ||||
\(831\) | 12.3205 | 0.427394 | ||||||||
\(832\) | 3.59808 | − | 0.232051i | 0.124741 | − | 0.00804491i | ||||
\(833\) | 2.07180i | 0.0717835i | ||||||||
\(834\) | −0.535898 | + | 0.928203i | −0.0185566 | + | 0.0321410i | ||||
\(835\) | 25.8564 | + | 17.0718i | 0.894798 | + | 0.590794i | ||||
\(836\) | −0.464102 | − | 0.803848i | −0.0160513 | − | 0.0278016i | ||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | −5.66025 | + | 3.26795i | −0.195530 | + | 0.112889i | ||||
\(839\) | 24.0526 | + | 41.6603i | 0.830387 | + | 1.43827i | 0.897732 | + | 0.440542i | \(0.145214\pi\) |
−0.0673455 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(840\) | 0.366025 | − | 6.09808i | 0.0126291 | − | 0.210404i | ||||
\(841\) | −6.39230 | − | 11.0718i | −0.220424 | − | 0.381786i | ||||
\(842\) | 14.7679 | + | 8.52628i | 0.508937 | + | 0.293835i | ||||
\(843\) | −1.50000 | − | 0.866025i | −0.0516627 | − | 0.0298275i | ||||
\(844\) | 21.4641 | 0.738825 | ||||||||
\(845\) | −29.0000 | + | 2.00000i | −0.997630 | + | 0.0688021i | ||||
\(846\) | 7.66025 | 0.263365 | ||||||||
\(847\) | −24.7583 | − | 14.2942i | −0.850706 | − | 0.491156i | ||||
\(848\) | −6.69615 | − | 3.86603i | −0.229947 | − | 0.132760i | ||||
\(849\) | 3.83013 | + | 6.63397i | 0.131450 | + | 0.227677i | ||||
\(850\) | −22.1603 | − | 2.66987i | −0.760090 | − | 0.0915759i | ||||
\(851\) | −24.5622 | − | 42.5429i | −0.841981 | − | 1.45835i | ||||
\(852\) | −1.09808 | + | 0.633975i | −0.0376195 | + | 0.0217196i | ||||
\(853\) | − | 12.0718i | − | 0.413330i | −0.978412 | − | 0.206665i | \(-0.933739\pi\) | ||
0.978412 | − | 0.206665i | \(-0.0662611\pi\) | |||||||
\(854\) | −13.8301 | − | 23.9545i | −0.473257 | − | 0.819706i | ||||
\(855\) | 1.56218 | − | 2.36603i | 0.0534254 | − | 0.0809164i | ||||
\(856\) | −0.633975 | + | 1.09808i | −0.0216688 | + | 0.0375315i | ||||
\(857\) | − | 3.92820i | − | 0.134185i | −0.997747 | − | 0.0670924i | \(-0.978628\pi\) | ||
0.997747 | − | 0.0670924i | \(-0.0213722\pi\) | |||||||
\(858\) | −2.63397 | + | 0.169873i | −0.0899224 | + | 0.00579937i | ||||
\(859\) | 44.3013 | 1.51154 | 0.755770 | − | 0.654837i | \(-0.227263\pi\) | ||||
0.755770 | + | 0.654837i | \(0.227263\pi\) | |||||||
\(860\) | 6.09808 | + | 4.02628i | 0.207943 | + | 0.137295i | ||||
\(861\) | 12.5622 | − | 21.7583i | 0.428118 | − | 0.741522i | ||||
\(862\) | 6.75833 | − | 3.90192i | 0.230190 | − | 0.132900i | ||||
\(863\) | 21.1244i | 0.719081i | 0.933129 | + | 0.359541i | \(0.117067\pi\) | ||||
−0.933129 | + | 0.359541i | \(0.882933\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 37.5692 | − | 18.7846i | 1.27739 | − | 0.638696i | ||||
\(866\) | −14.8038 | −0.503055 | ||||||||
\(867\) | −2.53590 | + | 1.46410i | −0.0861236 | + | 0.0497235i | ||||
\(868\) | −9.46410 | − | 5.46410i | −0.321233 | − | 0.185464i | ||||
\(869\) | 4.39230 | − | 7.60770i | 0.148999 | − | 0.258073i | ||||
\(870\) | −14.4282 | − | 0.866025i | −0.489162 | − | 0.0293610i | ||||
\(871\) | −24.7583 | − | 12.2417i | −0.838904 | − | 0.414793i | ||||
\(872\) | − | 10.0000i | − | 0.338643i | ||||||
\(873\) | 8.66025 | + | 5.00000i | 0.293105 | + | 0.169224i | ||||
\(874\) | 3.92820 | − | 6.80385i | 0.132873 | − | 0.230144i | ||||
\(875\) | 28.7583 | − | 10.2942i | 0.972209 | − | 0.348008i | ||||
\(876\) | −4.66025 | −0.157455 | ||||||||
\(877\) | 8.25833 | − | 4.76795i | 0.278864 | − | 0.161002i | −0.354045 | − | 0.935228i | \(-0.615194\pi\) |
0.632909 | + | 0.774226i | \(0.281861\pi\) | |||||||
\(878\) | 8.49038 | − | 4.90192i | 0.286536 | − | 0.165432i | ||||
\(879\) | −13.7321 | −0.463171 | ||||||||
\(880\) | 0.732051 | + | 1.46410i | 0.0246774 | + | 0.0493549i | ||||
\(881\) | −8.93782 | + | 15.4808i | −0.301123 | + | 0.521560i | −0.976391 | − | 0.216013i | \(-0.930695\pi\) |
0.675268 | + | 0.737573i | \(0.264028\pi\) | |||||||
\(882\) | 0.401924 | + | 0.232051i | 0.0135335 | + | 0.00781356i | ||||
\(883\) | − | 18.2487i | − | 0.614118i | −0.951690 | − | 0.307059i | \(-0.900655\pi\) | ||
0.951690 | − | 0.307059i | \(-0.0993449\pi\) | |||||||
\(884\) | 14.4282 | + | 7.13397i | 0.485273 | + | 0.239942i | ||||
\(885\) | 1.66025 | − | 27.6603i | 0.0558088 | − | 0.929789i | ||||
\(886\) | −17.3205 | + | 30.0000i | −0.581894 | + | 1.00787i | ||||
\(887\) | 25.1769 | + | 14.5359i | 0.845358 | + | 0.488068i | 0.859082 | − | 0.511838i | \(-0.171035\pi\) |
−0.0137239 | + | 0.999906i | \(0.504369\pi\) | |||||||
\(888\) | 6.86603 | − | 3.96410i | 0.230409 | − | 0.133027i | ||||
\(889\) | −10.9282 | −0.366520 | ||||||||
\(890\) | 9.85641 | − | 4.92820i | 0.330387 | − | 0.165194i | ||||
\(891\) | −0.366025 | − | 0.633975i | −0.0122623 | − | 0.0212389i | ||||
\(892\) | 0.392305i | 0.0131353i | ||||||||
\(893\) | 8.41154 | − | 4.85641i | 0.281482 | − | 0.162513i | ||||
\(894\) | 9.96410 | − | 17.2583i | 0.333249 | − | 0.577205i | ||||
\(895\) | −22.4186 | + | 33.9545i | −0.749371 | + | 1.13497i | ||||
\(896\) | 2.73205 | 0.0912714 | ||||||||
\(897\) | −12.3923 | − | 18.5885i | −0.413767 | − | 0.620651i | ||||
\(898\) | − | 7.85641i | − | 0.262172i | ||||||
\(899\) | −12.9282 | + | 22.3923i | −0.431180 | + | 0.746825i | ||||
\(900\) | −3.00000 | + | 4.00000i | −0.100000 | + | 0.133333i | ||||
\(901\) | −17.2583 | − | 29.8923i | −0.574958 | − | 0.995857i | ||||
\(902\) | 6.73205i | 0.224153i | ||||||||
\(903\) | −7.73205 | + | 4.46410i | −0.257307 | + | 0.148556i | ||||
\(904\) | 4.50000 | + | 7.79423i | 0.149668 | + | 0.259232i | ||||
\(905\) | 35.9904 | + | 2.16025i | 1.19636 | + | 0.0718093i | ||||
\(906\) | 2.56218 | + | 4.43782i | 0.0851227 | + | 0.147437i | ||||
\(907\) | 6.00000 | + | 3.46410i | 0.199227 | + | 0.115024i | 0.596295 | − | 0.802766i | \(-0.296639\pi\) |
−0.397068 | + | 0.917789i | \(0.629972\pi\) | |||||||
\(908\) | 3.63397 | + | 2.09808i | 0.120598 | + | 0.0696271i | ||||
\(909\) | −13.9282 | −0.461969 | ||||||||
\(910\) | −22.0263 | + | 0.0980762i | −0.730164 | + | 0.00325119i | ||||
\(911\) | 44.1051 | 1.46127 | 0.730634 | − | 0.682769i | \(-0.239225\pi\) | ||||
0.730634 | + | 0.682769i | \(0.239225\pi\) | |||||||
\(912\) | 1.09808 | + | 0.633975i | 0.0363609 | + | 0.0209930i | ||||
\(913\) | −3.33975 | − | 1.92820i | −0.110529 | − | 0.0638142i | ||||
\(914\) | −4.40192 | − | 7.62436i | −0.145603 | − | 0.252191i | ||||
\(915\) | −1.35641 | + | 22.5981i | −0.0448414 | + | 0.747069i | ||||
\(916\) | −14.3923 | − | 24.9282i | −0.475535 | − | 0.823651i | ||||
\(917\) | 32.7846 | − | 18.9282i | 1.08264 | − | 0.625064i | ||||
\(918\) | 4.46410i | 0.147337i | ||||||||
\(919\) | −28.7321 | − | 49.7654i | −0.947783 | − | 1.64161i | −0.750081 | − | 0.661346i | \(-0.769986\pi\) |
−0.197702 | − | 0.980262i | \(-0.563348\pi\) | |||||||
\(920\) | −7.63397 | + | 11.5622i | −0.251685 | + | 0.381194i | ||||
\(921\) | 9.63397 | − | 16.6865i | 0.317450 | − | 0.549840i | ||||
\(922\) | − | 26.0718i | − | 0.858629i | ||||||
\(923\) | 2.53590 | + | 3.80385i | 0.0834701 | + | 0.125205i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 31.7128 | + | 23.7846i | 1.04271 | + | 0.782033i | ||||
\(926\) | 3.16987 | − | 5.49038i | 0.104168 | − | 0.180425i | ||||
\(927\) | −8.02628 | + | 4.63397i | −0.263618 | + | 0.152200i | ||||
\(928\) | − | 6.46410i | − | 0.212195i | ||||||
\(929\) | 19.7942 | + | 34.2846i | 0.649428 | + | 1.12484i | 0.983260 | + | 0.182209i | \(0.0583248\pi\) |
−0.333832 | + | 0.942633i | \(0.608342\pi\) | |||||||
\(930\) | 4.00000 | + | 8.00000i | 0.131165 | + | 0.262330i | ||||
\(931\) | 0.588457 | 0.0192859 | ||||||||
\(932\) | −10.7321 | + | 6.19615i | −0.351540 | + | 0.202962i | ||||
\(933\) | −2.70577 | − | 1.56218i | −0.0885830 | − | 0.0511434i | ||||
\(934\) | −11.0263 | + | 19.0981i | −0.360791 | + | 0.624908i | ||||
\(935\) | −0.437822 | + | 7.29423i | −0.0143183 | + | 0.238547i | ||||
\(936\) | 3.00000 | − | 2.00000i | 0.0980581 | − | 0.0653720i | ||||
\(937\) | 17.0526i | 0.557083i | 0.960424 | + | 0.278541i | \(0.0898509\pi\) | ||||
−0.960424 | + | 0.278541i | \(0.910149\pi\) | |||||||
\(938\) | −18.1244 | − | 10.4641i | −0.591781 | − | 0.341665i | ||||
\(939\) | −7.00000 | + | 12.1244i | −0.228436 | + | 0.395663i | ||||
\(940\) | −15.3205 | + | 7.66025i | −0.499700 | + | 0.249850i | ||||
\(941\) | 12.3923 | 0.403978 | 0.201989 | − | 0.979388i | \(-0.435260\pi\) | ||||
0.201989 | + | 0.979388i | \(0.435260\pi\) | |||||||
\(942\) | −8.13397 | + | 4.69615i | −0.265019 | + | 0.153009i | ||||
\(943\) | −49.3468 | + | 28.4904i | −1.60695 | + | 0.927774i | ||||
\(944\) | 12.3923 | 0.403335 | ||||||||
\(945\) | −2.73205 | − | 5.46410i | −0.0888736 | − | 0.177747i | ||||
\(946\) | 1.19615 | − | 2.07180i | 0.0388903 | − | 0.0673599i | ||||
\(947\) | 24.0000 | + | 13.8564i | 0.779895 | + | 0.450273i | 0.836393 | − | 0.548130i | \(-0.184660\pi\) |
−0.0564979 | + | 0.998403i | \(0.517993\pi\) | |||||||
\(948\) | 12.0000i | 0.389742i | ||||||||
\(949\) | 1.08142 | + | 16.7679i | 0.0351042 | + | 0.544311i | ||||
\(950\) | −0.758330 | + | 6.29423i | −0.0246035 | + | 0.204212i | ||||
\(951\) | −14.8660 | + | 25.7487i | −0.482064 | + | 0.834959i | ||||
\(952\) | 10.5622 | + | 6.09808i | 0.342322 | + | 0.197640i | ||||
\(953\) | −32.6603 | + | 18.8564i | −1.05797 | + | 0.610819i | −0.924870 | − | 0.380284i | \(-0.875826\pi\) |
−0.133100 | + | 0.991103i | \(0.542493\pi\) | |||||||
\(954\) | −7.73205 | −0.250334 | ||||||||
\(955\) | −9.46410 | − | 18.9282i | −0.306251 | − | 0.612502i | ||||
\(956\) | 2.29423 | + | 3.97372i | 0.0742007 | + | 0.128519i | ||||
\(957\) | 4.73205i | 0.152965i | ||||||||
\(958\) | −13.8564 | + | 8.00000i | −0.447680 | + | 0.258468i | ||||
\(959\) | 25.2224 | − | 43.6865i | 0.814475 | − | 1.41071i | ||||
\(960\) | −1.86603 | − | 1.23205i | −0.0602257 | − | 0.0397643i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −15.8564 | − | 23.7846i | −0.511231 | − | 0.766847i | ||||
\(963\) | 1.26795i | 0.0408591i | ||||||||
\(964\) | −4.69615 | + | 8.13397i | −0.151253 | + | 0.261978i | ||||
\(965\) | −19.8923 | − | 13.1340i | −0.640356 | − | 0.422798i | ||||
\(966\) | −8.46410 | − | 14.6603i | −0.272328 | − | 0.471686i | ||||
\(967\) | 16.5885i | 0.533449i | 0.963773 | + | 0.266724i | \(0.0859413\pi\) | ||||
−0.963773 | + | 0.266724i | \(0.914059\pi\) | |||||||
\(968\) | −9.06218 | + | 5.23205i | −0.291269 | + | 0.168164i | ||||
\(969\) | 2.83013 | + | 4.90192i | 0.0909168 | + | 0.157472i | ||||
\(970\) | −22.3205 | − | 1.33975i | −0.716668 | − | 0.0430167i | ||||
\(971\) | 27.4641 | + | 47.5692i | 0.881365 | + | 1.52657i | 0.849824 | + | 0.527066i | \(0.176708\pi\) |
0.0315409 | + | 0.999502i | \(0.489959\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | 2.53590 | + | 1.46410i | 0.0812972 | + | 0.0469369i | ||||
\(974\) | −38.4449 | −1.23185 | ||||||||
\(975\) | 15.0885 | + | 9.86603i | 0.483217 | + | 0.315966i | ||||
\(976\) | −10.1244 | −0.324073 | ||||||||
\(977\) | 18.4019 | + | 10.6244i | 0.588730 | + | 0.339903i | 0.764595 | − | 0.644511i | \(-0.222939\pi\) |
−0.175865 | + | 0.984414i | \(0.556272\pi\) | |||||||
\(978\) | 11.6603 | + | 6.73205i | 0.372854 | + | 0.215267i | ||||
\(979\) | −1.80385 | − | 3.12436i | −0.0576512 | − | 0.0998548i | ||||
\(980\) | −1.03590 | − | 0.0621778i | −0.0330906 | − | 0.00198620i | ||||
\(981\) | −5.00000 | − | 8.66025i | −0.159638 | − | 0.276501i | ||||
\(982\) | −18.8827 | + | 10.9019i | −0.602571 | + | 0.347894i | ||||
\(983\) | − | 31.7128i | − | 1.01148i | −0.862685 | − | 0.505741i | \(-0.831219\pi\) | ||
0.862685 | − | 0.505741i | \(-0.168781\pi\) | |||||||
\(984\) | −4.59808 | − | 7.96410i | −0.146581 | − | 0.253886i | ||||
\(985\) | −18.3923 | − | 12.1436i | −0.586028 | − | 0.386927i | ||||
\(986\) | 14.4282 | − | 24.9904i | 0.459488 | − | 0.795856i | ||||
\(987\) | − | 20.9282i | − | 0.666152i | ||||||
\(988\) | 2.02628 | − | 4.09808i | 0.0644645 | − | 0.130377i | ||||
\(989\) | 20.2487 | 0.643872 | ||||||||
\(990\) | 1.36603 | + | 0.901924i | 0.0434151 | + | 0.0286650i | ||||
\(991\) | −4.02628 | + | 6.97372i | −0.127899 | + | 0.221528i | −0.922862 | − | 0.385130i | \(-0.874157\pi\) |
0.794963 | + | 0.606657i | \(0.207490\pi\) | |||||||
\(992\) | −3.46410 | + | 2.00000i | −0.109985 | + | 0.0635001i | ||||
\(993\) | − | 28.7846i | − | 0.913452i | ||||||
\(994\) | 1.73205 | + | 3.00000i | 0.0549373 | + | 0.0951542i | ||||
\(995\) | 28.0526 | + | 56.1051i | 0.889326 | + | 1.77865i | ||||
\(996\) | 5.26795 | 0.166921 | ||||||||
\(997\) | 13.7942 | − | 7.96410i | 0.436868 | − | 0.252226i | −0.265400 | − | 0.964138i | \(-0.585504\pi\) |
0.702268 | + | 0.711913i | \(0.252171\pi\) | |||||||
\(998\) | −34.9808 | − | 20.1962i | −1.10730 | − | 0.639298i | ||||
\(999\) | 3.96410 | − | 6.86603i | 0.125419 | − | 0.217231i |
(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 | 390.2.y.b.139.2 | ✓ | 4 | |
3.2 | odd | 2 | 1170.2.bp.d.919.1 | 4 | |||
5.2 | odd | 4 | 1950.2.i.y.451.1 | 4 | |||
5.3 | odd | 4 | 1950.2.i.bh.451.2 | 4 | |||
5.4 | even | 2 | 390.2.y.c.139.1 | yes | 4 | ||
13.3 | even | 3 | 390.2.y.c.289.1 | yes | 4 | ||
15.14 | odd | 2 | 1170.2.bp.e.919.2 | 4 | |||
39.29 | odd | 6 | 1170.2.bp.e.289.2 | 4 | |||
65.3 | odd | 12 | 1950.2.i.bh.601.2 | 4 | |||
65.29 | even | 6 | inner | 390.2.y.b.289.2 | yes | 4 | |
65.42 | odd | 12 | 1950.2.i.y.601.1 | 4 | |||
195.29 | odd | 6 | 1170.2.bp.d.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.y.b.139.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
390.2.y.b.289.2 | yes | 4 | 65.29 | even | 6 | inner | |
390.2.y.c.139.1 | yes | 4 | 5.4 | even | 2 | ||
390.2.y.c.289.1 | yes | 4 | 13.3 | even | 3 | ||
1170.2.bp.d.289.1 | 4 | 195.29 | odd | 6 | |||
1170.2.bp.d.919.1 | 4 | 3.2 | odd | 2 | |||
1170.2.bp.e.289.2 | 4 | 39.29 | odd | 6 | |||
1170.2.bp.e.919.2 | 4 | 15.14 | odd | 2 | |||
1950.2.i.y.451.1 | 4 | 5.2 | odd | 4 | |||
1950.2.i.y.601.1 | 4 | 65.42 | odd | 12 | |||
1950.2.i.bh.451.2 | 4 | 5.3 | odd | 4 | |||
1950.2.i.bh.601.2 | 4 | 65.3 | odd | 12 |