Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(107,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.be (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.107 |
Dual form | 756.2.be.a.431.2 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.866025 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 2.44949 | + | 1.41421i | 1.09545 | + | 0.632456i | 0.935021 | − | 0.354593i | \(-0.115380\pi\) |
0.160424 | + | 0.987048i | \(0.448714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 3.46410i | 0.632456 | + | 1.09545i | ||||
\(11\) | 1.22474 | + | 2.12132i | 0.369274 | + | 0.639602i | 0.989452 | − | 0.144859i | \(-0.0462729\pi\) |
−0.620178 | + | 0.784461i | \(0.712940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −1.22474 | − | 3.53553i | −0.327327 | − | 0.944911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 1.22474 | − | 0.707107i | 0.297044 | − | 0.171499i | −0.344070 | − | 0.938944i | \(-0.611806\pi\) |
0.641114 | + | 0.767445i | \(0.278472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | + | 3.46410i | 1.37649 | + | 0.794719i | 0.991736 | − | 0.128298i | \(-0.0409513\pi\) |
0.384759 | + | 0.923017i | \(0.374285\pi\) | |||||||
\(20\) | 5.65685i | 1.26491i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.46410i | 0.738549i | ||||||||
\(23\) | −1.22474 | + | 2.12132i | −0.255377 | + | 0.442326i | −0.964998 | − | 0.262258i | \(-0.915533\pi\) |
0.709621 | + | 0.704584i | \(0.248866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | + | 2.59808i | 0.300000 | + | 0.519615i | ||||
\(26\) | −1.22474 | − | 0.707107i | −0.240192 | − | 0.138675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 5.19615i | 0.188982 | − | 0.981981i | ||||
\(29\) | − | 7.07107i | − | 1.31306i | −0.754298 | − | 0.656532i | \(-0.772023\pi\) | ||
0.754298 | − | 0.656532i | \(-0.227977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | + | 2.59808i | −0.808224 | + | 0.466628i | −0.846339 | − | 0.532645i | \(-0.821198\pi\) |
0.0381148 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.866025 | + | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −2.44949 | − | 7.07107i | −0.414039 | − | 1.19523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50000 | + | 4.33013i | −0.410997 | + | 0.711868i | −0.994999 | − | 0.0998840i | \(-0.968153\pi\) |
0.584002 | + | 0.811752i | \(0.301486\pi\) | |||||||
\(38\) | 4.89898 | + | 8.48528i | 0.794719 | + | 1.37649i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.00000 | + | 6.92820i | −0.632456 | + | 1.09545i | ||||
\(41\) | − | 7.07107i | − | 1.10432i | −0.833740 | − | 0.552158i | \(-0.813805\pi\) | ||
0.833740 | − | 0.552158i | \(-0.186195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.66025i | − | 1.32068i | −0.750968 | − | 0.660338i | \(-0.770413\pi\) | ||
0.750968 | − | 0.660338i | \(-0.229587\pi\) | |||||||
\(44\) | −2.44949 | + | 4.24264i | −0.369274 | + | 0.639602i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 1.73205i | −0.442326 | + | 0.255377i | ||||
\(47\) | 3.67423 | − | 6.36396i | 0.535942 | − | 0.928279i | −0.463175 | − | 0.886267i | \(-0.653290\pi\) |
0.999117 | − | 0.0420122i | \(-0.0133768\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 4.24264i | 0.600000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 8.57321 | − | 4.94975i | 1.17762 | − | 0.679900i | 0.222158 | − | 0.975011i | \(-0.428690\pi\) |
0.955463 | + | 0.295110i | \(0.0953565\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820i | 0.934199i | ||||||||
\(56\) | 4.89898 | − | 5.65685i | 0.654654 | − | 0.755929i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.00000 | − | 8.66025i | 0.656532 | − | 1.13715i | ||||
\(59\) | 3.67423 | + | 6.36396i | 0.478345 | + | 0.828517i | 0.999692 | − | 0.0248275i | \(-0.00790366\pi\) |
−0.521347 | + | 0.853345i | \(0.674570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | −7.34847 | −0.933257 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.44949 | − | 1.41421i | −0.303822 | − | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50000 | − | 2.59808i | 0.549762 | − | 0.317406i | −0.199264 | − | 0.979946i | \(-0.563855\pi\) |
0.749026 | + | 0.662540i | \(0.230522\pi\) | |||||||
\(68\) | 2.44949 | + | 1.41421i | 0.297044 | + | 0.171499i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | − | 10.3923i | 0.239046 | − | 1.24212i | ||||
\(71\) | −14.6969 | −1.74421 | −0.872103 | − | 0.489323i | \(-0.837244\pi\) | ||||
−0.872103 | + | 0.489323i | \(0.837244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | −6.12372 | + | 3.53553i | −0.711868 | + | 0.410997i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.8564i | 1.58944i | ||||||||
\(77\) | 1.22474 | − | 6.36396i | 0.139573 | − | 0.725241i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5000 | − | 7.79423i | −1.51887 | − | 0.876919i | −0.999753 | − | 0.0222151i | \(-0.992928\pi\) |
−0.519115 | − | 0.854704i | \(-0.673739\pi\) | |||||||
\(80\) | −9.79796 | + | 5.65685i | −1.09545 | + | 0.632456i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.00000 | − | 8.66025i | 0.552158 | − | 0.956365i | ||||
\(83\) | 2.44949 | 0.268866 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 6.12372 | − | 10.6066i | 0.660338 | − | 1.14374i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | + | 3.46410i | −0.639602 | + | 0.369274i | ||||
\(89\) | −12.2474 | − | 7.07107i | −1.29823 | − | 0.749532i | −0.318129 | − | 0.948047i | \(-0.603055\pi\) |
−0.980098 | + | 0.198516i | \(0.936388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | −4.89898 | −0.510754 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000 | − | 5.19615i | 0.928279 | − | 0.535942i | ||||
\(95\) | 9.79796 | + | 16.9706i | 1.00525 | + | 1.74114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −3.67423 | + | 9.19239i | −0.371154 | + | 0.928571i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | + | 5.19615i | −0.300000 | + | 0.519615i | ||||
\(101\) | 12.2474 | − | 7.07107i | 1.21867 | − | 0.703598i | 0.254034 | − | 0.967195i | \(-0.418242\pi\) |
0.964633 | + | 0.263598i | \(0.0849092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5000 | + | 9.52628i | 1.62579 | + | 0.938652i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | − | 2.82843i | − | 0.277350i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0000 | 1.35980 | ||||||||
\(107\) | 8.57321 | − | 14.8492i | 0.828804 | − | 1.43553i | −0.0701732 | − | 0.997535i | \(-0.522355\pi\) |
0.898977 | − | 0.437996i | \(-0.144311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | −4.89898 | + | 8.48528i | −0.467099 | + | 0.809040i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0000 | − | 3.46410i | 0.944911 | − | 0.327327i | ||||
\(113\) | − | 2.82843i | − | 0.266076i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) | ||
0.991111 | − | 0.133038i | \(-0.0424732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | + | 3.46410i | −0.559503 | + | 0.323029i | ||||
\(116\) | 12.2474 | − | 7.07107i | 1.13715 | − | 0.656532i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3923i | 0.956689i | ||||||||
\(119\) | −3.67423 | − | 0.707107i | −0.336817 | − | 0.0648204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.50000 | − | 4.33013i | 0.227273 | − | 0.393648i | ||||
\(122\) | −6.12372 | + | 3.53553i | −0.554416 | + | 0.320092i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | − | 5.19615i | −0.808224 | − | 0.466628i | ||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.19615i | − | 0.461084i | −0.973062 | − | 0.230542i | \(-0.925950\pi\) | ||
0.973062 | − | 0.230542i | \(-0.0740499\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | − | 3.46410i | −0.175412 | − | 0.303822i | ||||
\(131\) | −4.89898 | + | 8.48528i | −0.428026 | + | 0.741362i | −0.996698 | − | 0.0812020i | \(-0.974124\pi\) |
0.568672 | + | 0.822564i | \(0.307457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 17.3205i | −0.520266 | − | 1.50188i | ||||
\(134\) | 7.34847 | 0.634811 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | −6.12372 | + | 3.53553i | −0.523185 | + | 0.302061i | −0.738237 | − | 0.674542i | \(-0.764341\pi\) |
0.215052 | + | 0.976603i | \(0.431008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.66025i | 0.734553i | 0.930112 | + | 0.367277i | \(0.119710\pi\) | ||||
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(140\) | 9.79796 | − | 11.3137i | 0.828079 | − | 0.956183i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.0000 | − | 10.3923i | −1.51053 | − | 0.872103i | ||||
\(143\) | −1.22474 | − | 2.12132i | −0.102418 | − | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | − | 17.3205i | 0.830455 | − | 1.43839i | ||||
\(146\) | 5.65685i | 0.468165i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | 2.44949 | + | 1.41421i | 0.200670 | + | 0.115857i | 0.596968 | − | 0.802265i | \(-0.296372\pi\) |
−0.396298 | + | 0.918122i | \(0.629705\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.50000 | − | 4.33013i | 0.610341 | − | 0.352381i | −0.162758 | − | 0.986666i | \(-0.552039\pi\) |
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | −9.79796 | + | 16.9706i | −0.794719 | + | 1.37649i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | − | 6.92820i | 0.483494 | − | 0.558291i | ||||
\(155\) | −14.6969 | −1.18049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | − | 17.3205i | −0.798087 | − | 1.38233i | −0.920860 | − | 0.389892i | \(-0.872512\pi\) |
0.122774 | − | 0.992435i | \(-0.460821\pi\) | |||||||
\(158\) | −11.0227 | − | 19.0919i | −0.876919 | − | 1.51887i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0000 | −1.26491 | ||||||||
\(161\) | 6.12372 | − | 2.12132i | 0.482617 | − | 0.167183i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.5000 | − | 9.52628i | −1.29238 | − | 0.746156i | −0.313304 | − | 0.949653i | \(-0.601436\pi\) |
−0.979076 | + | 0.203497i | \(0.934769\pi\) | |||||||
\(164\) | 12.2474 | − | 7.07107i | 0.956365 | − | 0.552158i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 1.73205i | 0.232845 | + | 0.134433i | ||||
\(167\) | 12.2474 | 0.947736 | 0.473868 | − | 0.880596i | \(-0.342857\pi\) | ||||
0.473868 | + | 0.880596i | \(0.342857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 4.89898 | + | 2.82843i | 0.375735 | + | 0.216930i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.0000 | − | 8.66025i | 1.14374 | − | 0.660338i | ||||
\(173\) | 9.79796 | + | 5.65685i | 0.744925 | + | 0.430083i | 0.823857 | − | 0.566797i | \(-0.191818\pi\) |
−0.0789322 | + | 0.996880i | \(0.525151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.50000 | − | 7.79423i | 0.113389 | − | 0.589188i | ||||
\(176\) | −9.79796 | −0.738549 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0000 | − | 17.3205i | −0.749532 | − | 1.29823i | ||||
\(179\) | 2.44949 | + | 4.24264i | 0.183083 | + | 0.317110i | 0.942929 | − | 0.332994i | \(-0.108059\pi\) |
−0.759846 | + | 0.650104i | \(0.774725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 1.22474 | + | 3.53553i | 0.0907841 | + | 0.262071i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | − | 3.46410i | −0.442326 | − | 0.255377i | ||||
\(185\) | −12.2474 | + | 7.07107i | −0.900450 | + | 0.519875i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 1.73205i | 0.219382 | + | 0.126660i | ||||
\(188\) | 14.6969 | 1.07188 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.7128i | 2.01050i | ||||||||
\(191\) | 7.34847 | − | 12.7279i | 0.531717 | − | 0.920960i | −0.467598 | − | 0.883941i | \(-0.654880\pi\) |
0.999315 | − | 0.0370189i | \(-0.0117862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | − | 9.52628i | −0.395899 | − | 0.685717i | 0.597317 | − | 0.802005i | \(-0.296234\pi\) |
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(194\) | 6.12372 | + | 3.53553i | 0.439658 | + | 0.253837i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.0000 | + | 8.66025i | −0.785714 | + | 0.618590i | ||||
\(197\) | 22.6274i | 1.61214i | 0.591822 | + | 0.806068i | \(0.298409\pi\) | ||||
−0.591822 | + | 0.806068i | \(0.701591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | + | 4.33013i | −0.531661 | + | 0.306955i | −0.741693 | − | 0.670740i | \(-0.765977\pi\) |
0.210032 | + | 0.977695i | \(0.432643\pi\) | |||||||
\(200\) | −7.34847 | + | 4.24264i | −0.519615 | + | 0.300000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0000 | 1.40720 | ||||||||
\(203\) | −12.2474 | + | 14.1421i | −0.859602 | + | 0.992583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | − | 17.3205i | 0.698430 | − | 1.20972i | ||||
\(206\) | 13.4722 | + | 23.3345i | 0.938652 | + | 1.62579i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 16.9706i | 1.17388i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.66025i | 0.596196i | 0.954535 | + | 0.298098i | \(0.0963523\pi\) | ||||
−0.954535 | + | 0.298098i | \(0.903648\pi\) | |||||||
\(212\) | 17.1464 | + | 9.89949i | 1.17762 | + | 0.679900i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.0000 | − | 12.1244i | 1.43553 | − | 0.828804i | ||||
\(215\) | 12.2474 | − | 21.2132i | 0.835269 | − | 1.44673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5000 | + | 2.59808i | 0.916440 | + | 0.176369i | ||||
\(218\) | − | 7.07107i | − | 0.478913i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0000 | + | 6.92820i | −0.809040 | + | 0.467099i | ||||
\(221\) | −1.22474 | + | 0.707107i | −0.0823853 | + | 0.0475651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820i | 0.463947i | 0.972722 | + | 0.231973i | \(0.0745182\pi\) | ||||
−0.972722 | + | 0.231973i | \(0.925482\pi\) | |||||||
\(224\) | 14.6969 | + | 2.82843i | 0.981981 | + | 0.188982i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | − | 3.46410i | 0.133038 | − | 0.230429i | ||||
\(227\) | −6.12372 | − | 10.6066i | −0.406446 | − | 0.703985i | 0.588043 | − | 0.808830i | \(-0.299899\pi\) |
−0.994489 | + | 0.104845i | \(0.966565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.50000 | + | 14.7224i | −0.561696 | + | 0.972886i | 0.435653 | + | 0.900115i | \(0.356518\pi\) |
−0.997349 | + | 0.0727709i | \(0.976816\pi\) | |||||||
\(230\) | −9.79796 | −0.646058 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.0000 | 1.31306 | ||||||||
\(233\) | 9.79796 | + | 5.65685i | 0.641886 | + | 0.370593i | 0.785341 | − | 0.619064i | \(-0.212488\pi\) |
−0.143455 | + | 0.989657i | \(0.545821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | − | 10.3923i | 1.17419 | − | 0.677919i | ||||
\(236\) | −7.34847 | + | 12.7279i | −0.478345 | + | 0.828517i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.00000 | − | 3.46410i | −0.259281 | − | 0.224544i | ||||
\(239\) | −24.4949 | −1.58444 | −0.792222 | − | 0.610234i | \(-0.791076\pi\) | ||||
−0.792222 | + | 0.610234i | \(0.791076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | + | 21.6506i | 0.805196 | + | 1.39464i | 0.916159 | + | 0.400815i | \(0.131273\pi\) |
−0.110963 | + | 0.993825i | \(0.535394\pi\) | |||||||
\(242\) | 6.12372 | − | 3.53553i | 0.393648 | − | 0.227273i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | −7.34847 | + | 18.3848i | −0.469476 | + | 1.17456i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 3.46410i | −0.381771 | − | 0.220416i | ||||
\(248\) | −7.34847 | − | 12.7279i | −0.466628 | − | 0.808224i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.00000 | − | 6.92820i | 0.252982 | − | 0.438178i | ||||
\(251\) | 22.0454 | 1.39149 | 0.695747 | − | 0.718287i | \(-0.255074\pi\) | ||||
0.695747 | + | 0.718287i | \(0.255074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 3.67423 | − | 6.36396i | 0.230542 | − | 0.399310i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 13.4722 | + | 7.77817i | 0.840372 | + | 0.485189i | 0.857391 | − | 0.514666i | \(-0.172084\pi\) |
−0.0170184 | + | 0.999855i | \(0.505417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5000 | − | 4.33013i | 0.776712 | − | 0.269061i | ||||
\(260\) | − | 5.65685i | − | 0.350823i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0000 | + | 6.92820i | −0.741362 | + | 0.428026i | ||||
\(263\) | 1.22474 | + | 2.12132i | 0.0755210 | + | 0.130806i | 0.901313 | − | 0.433169i | \(-0.142605\pi\) |
−0.825792 | + | 0.563975i | \(0.809271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.0000 | 1.72003 | ||||||||
\(266\) | 4.89898 | − | 25.4558i | 0.300376 | − | 1.56080i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | + | 5.19615i | 0.549762 | + | 0.317406i | ||||
\(269\) | −9.79796 | + | 5.65685i | −0.597392 | + | 0.344904i | −0.768015 | − | 0.640432i | \(-0.778755\pi\) |
0.170623 | + | 0.985336i | \(0.445422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.50000 | − | 4.33013i | −0.455593 | − | 0.263036i | 0.254597 | − | 0.967047i | \(-0.418057\pi\) |
−0.710189 | + | 0.704011i | \(0.751391\pi\) | |||||||
\(272\) | 5.65685i | 0.342997i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | −3.67423 | + | 6.36396i | −0.221565 | + | 0.383761i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.50000 | + | 11.2583i | 0.390547 | + | 0.676448i | 0.992522 | − | 0.122068i | \(-0.0389525\pi\) |
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(278\) | −6.12372 | + | 10.6066i | −0.367277 | + | 0.636142i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20.0000 | − | 6.92820i | 1.19523 | − | 0.414039i | ||||
\(281\) | − | 19.7990i | − | 1.18111i | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5000 | + | 7.79423i | −0.802492 | + | 0.463319i | −0.844342 | − | 0.535805i | \(-0.820008\pi\) |
0.0418500 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(284\) | −14.6969 | − | 25.4558i | −0.872103 | − | 1.51053i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 3.46410i | − | 0.204837i | ||||||
\(287\) | −12.2474 | + | 14.1421i | −0.722944 | + | 0.834784i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.50000 | + | 12.9904i | −0.441176 | + | 0.764140i | ||||
\(290\) | 24.4949 | − | 14.1421i | 1.43839 | − | 0.830455i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00000 | + | 6.92820i | −0.234082 | + | 0.405442i | ||||
\(293\) | 9.89949i | 0.578335i | 0.957279 | + | 0.289167i | \(0.0933784\pi\) | ||||
−0.957279 | + | 0.289167i | \(0.906622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7846i | 1.21013i | ||||||||
\(296\) | −12.2474 | − | 7.07107i | −0.711868 | − | 0.410997i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | + | 3.46410i | 0.115857 | + | 0.200670i | ||||
\(299\) | 1.22474 | − | 2.12132i | 0.0708288 | − | 0.122679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0000 | + | 17.3205i | −0.864586 | + | 0.998337i | ||||
\(302\) | 12.2474 | 0.704761 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.0000 | + | 13.8564i | −1.37649 | + | 0.794719i | ||||
\(305\) | −12.2474 | + | 7.07107i | −0.701287 | + | 0.404888i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.19615i | 0.296560i | 0.988945 | + | 0.148280i | \(0.0473737\pi\) | ||||
−0.988945 | + | 0.148280i | \(0.952626\pi\) | |||||||
\(308\) | 12.2474 | − | 4.24264i | 0.697863 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.0000 | − | 10.3923i | −1.02233 | − | 0.590243i | ||||
\(311\) | 7.34847 | + | 12.7279i | 0.416693 | + | 0.721734i | 0.995605 | − | 0.0936564i | \(-0.0298555\pi\) |
−0.578911 | + | 0.815391i | \(0.696522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | − | 28.2843i | − | 1.59617i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 31.1769i | − | 1.75384i | ||||||
\(317\) | −23.2702 | − | 13.4350i | −1.30698 | − | 0.754586i | −0.325391 | − | 0.945580i | \(-0.605496\pi\) |
−0.981591 | + | 0.190993i | \(0.938829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0000 | − | 8.66025i | 0.839839 | − | 0.484881i | ||||
\(320\) | −19.5959 | − | 11.3137i | −1.09545 | − | 0.632456i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.00000 | + | 1.73205i | 0.501550 | + | 0.0965234i | ||||
\(323\) | 9.79796 | 0.545173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50000 | − | 2.59808i | −0.0832050 | − | 0.144115i | ||||
\(326\) | −13.4722 | − | 23.3345i | −0.746156 | − | 1.29238i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.0000 | 1.10432 | ||||||||
\(329\) | −18.3712 | + | 6.36396i | −1.01284 | + | 0.350857i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | 2.44949 | + | 4.24264i | 0.134433 | + | 0.232845i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.0000 | + | 8.66025i | 0.820763 | + | 0.473868i | ||||
\(335\) | 14.6969 | 0.802980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | −14.6969 | − | 8.48528i | −0.799408 | − | 0.461538i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 6.92820i | 0.216930 | + | 0.375735i | ||||
\(341\) | −11.0227 | − | 6.36396i | −0.596913 | − | 0.344628i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 24.4949 | 1.32068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | + | 13.8564i | 0.430083 | + | 0.744925i | ||||
\(347\) | 14.6969 | + | 25.4558i | 0.788973 | + | 1.36654i | 0.926597 | + | 0.376057i | \(0.122720\pi\) |
−0.137624 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | −0.695874 | −0.347937 | − | 0.937518i | \(-0.613118\pi\) | ||||
−0.347937 | + | 0.937518i | \(0.613118\pi\) | |||||||
\(350\) | 7.34847 | − | 8.48528i | 0.392792 | − | 0.453557i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.0000 | − | 6.92820i | −0.639602 | − | 0.369274i | ||||
\(353\) | −9.79796 | + | 5.65685i | −0.521493 | + | 0.301084i | −0.737545 | − | 0.675298i | \(-0.764015\pi\) |
0.216052 | + | 0.976382i | \(0.430682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.0000 | − | 20.7846i | −1.91068 | − | 1.10313i | ||||
\(356\) | − | 28.2843i | − | 1.49906i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.92820i | 0.366167i | ||||||||
\(359\) | −6.12372 | + | 10.6066i | −0.323198 | + | 0.559795i | −0.981146 | − | 0.193268i | \(-0.938091\pi\) |
0.657948 | + | 0.753063i | \(0.271425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5000 | + | 25.1147i | 0.763158 | + | 1.32183i | ||||
\(362\) | −19.5959 | − | 11.3137i | −1.02994 | − | 0.594635i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | + | 5.19615i | −0.0524142 | + | 0.272352i | ||||
\(365\) | 11.3137i | 0.592187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00000 | − | 1.73205i | 0.156599 | − | 0.0904123i | −0.419653 | − | 0.907685i | \(-0.637848\pi\) |
0.576252 | + | 0.817272i | \(0.304515\pi\) | |||||||
\(368\) | −4.89898 | − | 8.48528i | −0.255377 | − | 0.442326i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.0000 | −1.03975 | ||||||||
\(371\) | −25.7196 | − | 4.94975i | −1.33530 | − | 0.256978i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | + | 17.3205i | −0.517780 | + | 0.896822i | 0.482006 | + | 0.876168i | \(0.339908\pi\) |
−0.999787 | + | 0.0206542i | \(0.993425\pi\) | |||||||
\(374\) | 2.44949 | + | 4.24264i | 0.126660 | + | 0.219382i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.0000 | + | 10.3923i | 0.928279 | + | 0.535942i | ||||
\(377\) | 7.07107i | 0.364179i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.9808i | 1.33454i | 0.744815 | + | 0.667271i | \(0.232538\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | −19.5959 | + | 33.9411i | −1.00525 | + | 1.74114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.0000 | − | 10.3923i | 0.920960 | − | 0.531717i | ||||
\(383\) | 13.4722 | − | 23.3345i | 0.688397 | − | 1.19234i | −0.283959 | − | 0.958836i | \(-0.591648\pi\) |
0.972356 | − | 0.233502i | \(-0.0750186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | − | 13.8564i | 0.611577 | − | 0.706188i | ||||
\(386\) | − | 15.5563i | − | 0.791797i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | −9.79796 | + | 5.65685i | −0.496776 | + | 0.286814i | −0.727381 | − | 0.686234i | \(-0.759263\pi\) |
0.230605 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.46410i | 0.175187i | ||||||||
\(392\) | −19.5959 | + | 2.82843i | −0.989743 | + | 0.142857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.0000 | + | 27.7128i | −0.806068 | + | 1.39615i | ||||
\(395\) | −22.0454 | − | 38.1838i | −1.10922 | − | 1.92123i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | −12.2474 | −0.613909 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | 13.4722 | + | 7.77817i | 0.672769 | + | 0.388424i | 0.797125 | − | 0.603814i | \(-0.206353\pi\) |
−0.124356 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50000 | − | 2.59808i | 0.224161 | − | 0.129419i | ||||
\(404\) | 24.4949 | + | 14.1421i | 1.21867 | + | 0.703598i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.0000 | + | 8.66025i | −1.24073 | + | 0.429801i | ||||
\(407\) | −12.2474 | −0.607083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 24.4949 | − | 14.1421i | 1.20972 | − | 0.698430i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.1051i | 1.87730i | ||||||||
\(413\) | 3.67423 | − | 19.0919i | 0.180797 | − | 0.939450i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | + | 3.46410i | 0.294528 | + | 0.170046i | ||||
\(416\) | 4.89898 | − | 2.82843i | 0.240192 | − | 0.138675i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.0000 | + | 20.7846i | −0.586939 | + | 1.01661i | ||||
\(419\) | 4.89898 | 0.239331 | 0.119665 | − | 0.992814i | \(-0.461818\pi\) | ||||
0.119665 | + | 0.992814i | \(0.461818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | −6.12372 | + | 10.6066i | −0.298098 | + | 0.516321i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.0000 | + | 24.2487i | 0.679900 | + | 1.17762i | ||||
\(425\) | 3.67423 | + | 2.12132i | 0.178227 | + | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5000 | − | 4.33013i | 0.604917 | − | 0.209550i | ||||
\(428\) | 34.2929 | 1.65761 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 30.0000 | − | 17.3205i | 1.44673 | − | 0.835269i | ||||
\(431\) | 6.12372 | + | 10.6066i | 0.294969 | + | 0.510902i | 0.974978 | − | 0.222302i | \(-0.0713572\pi\) |
−0.680008 | + | 0.733204i | \(0.738024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 14.6969 | + | 12.7279i | 0.705476 | + | 0.610960i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −14.6969 | + | 8.48528i | −0.703050 | + | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | −19.5959 | −0.934199 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.00000 | −0.0951303 | ||||||||
\(443\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0000 | − | 34.6410i | −0.948091 | − | 1.64214i | ||||
\(446\) | −4.89898 | + | 8.48528i | −0.231973 | + | 0.401790i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000 | + | 13.8564i | 0.755929 | + | 0.654654i | ||||
\(449\) | 31.1127i | 1.46830i | 0.678988 | + | 0.734150i | \(0.262419\pi\) | ||||
−0.678988 | + | 0.734150i | \(0.737581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | − | 8.66025i | 0.706322 | − | 0.407795i | ||||
\(452\) | 4.89898 | − | 2.82843i | 0.230429 | − | 0.133038i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 17.3205i | − | 0.812892i | ||||||
\(455\) | 2.44949 | + | 7.07107i | 0.114834 | + | 0.331497i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | + | 4.33013i | −0.116945 | + | 0.202555i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) |
0.801611 | + | 0.597847i | \(0.203977\pi\) | |||||||
\(458\) | −20.8207 | + | 12.0208i | −0.972886 | + | 0.561696i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | − | 6.92820i | −0.559503 | − | 0.323029i | ||||
\(461\) | 1.41421i | 0.0658665i | 0.999458 | + | 0.0329332i | \(0.0104849\pi\) | ||||
−0.999458 | + | 0.0329332i | \(0.989515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.92820i | − | 0.321981i | −0.986956 | − | 0.160990i | \(-0.948531\pi\) | ||
0.986956 | − | 0.160990i | \(-0.0514688\pi\) | |||||||
\(464\) | 24.4949 | + | 14.1421i | 1.13715 | + | 0.656532i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.00000 | + | 13.8564i | 0.370593 | + | 0.641886i | ||||
\(467\) | 12.2474 | − | 21.2132i | 0.566744 | − | 0.981630i | −0.430141 | − | 0.902762i | \(-0.641536\pi\) |
0.996885 | − | 0.0788681i | \(-0.0251306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5000 | − | 2.59808i | −0.623372 | − | 0.119968i | ||||
\(470\) | 29.3939 | 1.35584 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.0000 | + | 10.3923i | −0.828517 | + | 0.478345i | ||||
\(473\) | 18.3712 | − | 10.6066i | 0.844707 | − | 0.487692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.7846i | 0.953663i | ||||||||
\(476\) | −2.44949 | − | 7.07107i | −0.112272 | − | 0.324102i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0000 | − | 17.3205i | −1.37217 | − | 0.792222i | ||||
\(479\) | −2.44949 | − | 4.24264i | −0.111920 | − | 0.193851i | 0.804624 | − | 0.593784i | \(-0.202367\pi\) |
−0.916544 | + | 0.399933i | \(0.869033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 35.3553i | 1.61039i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | 12.2474 | + | 7.07107i | 0.556128 | + | 0.321081i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.0000 | + | 17.3205i | −1.35943 | + | 0.784867i | −0.989547 | − | 0.144211i | \(-0.953936\pi\) |
−0.369883 | + | 0.929078i | \(0.620602\pi\) | |||||||
\(488\) | −12.2474 | − | 7.07107i | −0.554416 | − | 0.320092i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22.0000 | + | 17.3205i | −0.993859 | + | 0.782461i | ||||
\(491\) | 12.2474 | 0.552720 | 0.276360 | − | 0.961054i | \(-0.410872\pi\) | ||||
0.276360 | + | 0.961054i | \(0.410872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.00000 | − | 8.66025i | −0.225189 | − | 0.390038i | ||||
\(494\) | −4.89898 | − | 8.48528i | −0.220416 | − | 0.381771i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.7846i | − | 0.933257i | ||||||
\(497\) | 29.3939 | + | 25.4558i | 1.31850 | + | 1.14185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5000 | − | 16.4545i | −1.27584 | − | 0.736604i | −0.299755 | − | 0.954016i | \(-0.596905\pi\) |
−0.976080 | + | 0.217412i | \(0.930238\pi\) | |||||||
\(500\) | 9.79796 | − | 5.65685i | 0.438178 | − | 0.252982i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.0000 | + | 15.5885i | 1.20507 | + | 0.695747i | ||||
\(503\) | −36.7423 | −1.63826 | −0.819130 | − | 0.573608i | \(-0.805543\pi\) | ||||
−0.819130 | + | 0.573608i | \(0.805543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0000 | 1.77998 | ||||||||
\(506\) | −7.34847 | − | 4.24264i | −0.326679 | − | 0.188608i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.00000 | − | 5.19615i | 0.399310 | − | 0.230542i | ||||
\(509\) | −15.9217 | − | 9.19239i | −0.705716 | − | 0.407445i | 0.103757 | − | 0.994603i | \(-0.466914\pi\) |
−0.809473 | + | 0.587157i | \(0.800247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 10.3923i | 0.0884748 | − | 0.459728i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.0000 | + | 19.0526i | 0.485189 | + | 0.840372i | ||||
\(515\) | 26.9444 | + | 46.6690i | 1.18731 | + | 2.05648i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 18.3712 | + | 3.53553i | 0.807183 | + | 0.155342i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 6.92820i | 0.175412 | − | 0.303822i | ||||
\(521\) | 30.6186 | − | 17.6777i | 1.34143 | − | 0.774473i | 0.354409 | − | 0.935090i | \(-0.384682\pi\) |
0.987017 | + | 0.160618i | \(0.0513486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.50000 | + | 0.866025i | 0.0655904 | + | 0.0378686i | 0.532437 | − | 0.846470i | \(-0.321276\pi\) |
−0.466846 | + | 0.884339i | \(0.654610\pi\) | |||||||
\(524\) | −19.5959 | −0.856052 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.46410i | 0.151042i | ||||||||
\(527\) | −3.67423 | + | 6.36396i | −0.160052 | + | 0.277218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.50000 | + | 14.7224i | 0.369565 | + | 0.640106i | ||||
\(530\) | 34.2929 | + | 19.7990i | 1.48959 | + | 0.860013i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.0000 | − | 27.7128i | 1.04053 | − | 1.20150i | ||||
\(533\) | 7.07107i | 0.306282i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 42.0000 | − | 24.2487i | 1.81582 | − | 1.04836i | ||||
\(536\) | 7.34847 | + | 12.7279i | 0.317406 | + | 0.549762i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.0000 | −0.689809 | ||||||||
\(539\) | −13.4722 | + | 10.6066i | −0.580288 | + | 0.456859i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | − | 3.46410i | 0.0859867 | − | 0.148933i | −0.819825 | − | 0.572615i | \(-0.805929\pi\) |
0.905811 | + | 0.423681i | \(0.139262\pi\) | |||||||
\(542\) | −6.12372 | − | 10.6066i | −0.263036 | − | 0.455593i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | + | 6.92820i | −0.171499 | + | 0.297044i | ||||
\(545\) | − | 14.1421i | − | 0.605783i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1244i | 0.518400i | 0.965824 | + | 0.259200i | \(0.0834589\pi\) | ||||
−0.965824 | + | 0.259200i | \(0.916541\pi\) | |||||||
\(548\) | −12.2474 | − | 7.07107i | −0.523185 | − | 0.302061i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.00000 | + | 5.19615i | −0.383761 | + | 0.221565i | ||||
\(551\) | 24.4949 | − | 42.4264i | 1.04352 | − | 1.80743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5000 | + | 38.9711i | 0.574078 | + | 1.65722i | ||||
\(554\) | 18.3848i | 0.781094i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0000 | + | 8.66025i | −0.636142 | + | 0.367277i | ||||
\(557\) | −31.8434 | + | 18.3848i | −1.34925 | + | 0.778988i | −0.988143 | − | 0.153538i | \(-0.950933\pi\) |
−0.361104 | + | 0.932526i | \(0.617600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.66025i | 0.366290i | ||||||||
\(560\) | 29.3939 | + | 5.65685i | 1.24212 | + | 0.239046i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0000 | − | 24.2487i | 0.590554 | − | 1.02287i | ||||
\(563\) | −18.3712 | − | 31.8198i | −0.774253 | − | 1.34104i | −0.935214 | − | 0.354084i | \(-0.884793\pi\) |
0.160961 | − | 0.986961i | \(-0.448541\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | −22.0454 | −0.926638 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 41.5692i | − | 1.74421i | ||||||
\(569\) | −12.2474 | − | 7.07107i | −0.513440 | − | 0.296435i | 0.220807 | − | 0.975318i | \(-0.429131\pi\) |
−0.734246 | + | 0.678883i | \(0.762464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.0000 | + | 15.5885i | −1.12991 | + | 0.652357i | −0.943913 | − | 0.330193i | \(-0.892886\pi\) |
−0.186001 | + | 0.982549i | \(0.559553\pi\) | |||||||
\(572\) | 2.44949 | − | 4.24264i | 0.102418 | − | 0.177394i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25.0000 | + | 8.66025i | −1.04348 | + | 0.361472i | ||||
\(575\) | −7.34847 | −0.306452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.50000 | − | 4.33013i | −0.104076 | − | 0.180266i | 0.809284 | − | 0.587417i | \(-0.199855\pi\) |
−0.913360 | + | 0.407152i | \(0.866522\pi\) | |||||||
\(578\) | −18.3712 | + | 10.6066i | −0.764140 | + | 0.441176i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 40.0000 | 1.66091 | ||||||||
\(581\) | −4.89898 | − | 4.24264i | −0.203244 | − | 0.176014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.0000 | + | 12.1244i | 0.869731 | + | 0.502140i | ||||
\(584\) | −9.79796 | + | 5.65685i | −0.405442 | + | 0.234082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.00000 | + | 12.1244i | −0.289167 | + | 0.500853i | ||||
\(587\) | −4.89898 | −0.202203 | −0.101101 | − | 0.994876i | \(-0.532237\pi\) | ||||
−0.101101 | + | 0.994876i | \(0.532237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | −14.6969 | + | 25.4558i | −0.605063 | + | 1.04800i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.0000 | − | 17.3205i | −0.410997 | − | 0.711868i | ||||
\(593\) | −12.2474 | − | 7.07107i | −0.502942 | − | 0.290374i | 0.226985 | − | 0.973898i | \(-0.427113\pi\) |
−0.729928 | + | 0.683524i | \(0.760446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.00000 | − | 6.92820i | −0.327968 | − | 0.284029i | ||||
\(596\) | 5.65685i | 0.231714i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.00000 | − | 1.73205i | 0.122679 | − | 0.0708288i | ||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | 0.448699 | 0.224350 | − | 0.974509i | \(-0.427974\pi\) | ||||
0.224350 | + | 0.974509i | \(0.427974\pi\) | |||||||
\(602\) | −30.6186 | + | 10.6066i | −1.24792 | + | 0.432293i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.0000 | + | 8.66025i | 0.610341 | + | 0.352381i | ||||
\(605\) | 12.2474 | − | 7.07107i | 0.497930 | − | 0.287480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | + | 6.92820i | 0.487065 | + | 0.281207i | 0.723356 | − | 0.690475i | \(-0.242599\pi\) |
−0.236291 | + | 0.971682i | \(0.575932\pi\) | |||||||
\(608\) | −39.1918 | −1.58944 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | −0.809776 | ||||||||
\(611\) | −3.67423 | + | 6.36396i | −0.148644 | + | 0.257458i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.500000 | + | 0.866025i | 0.0201948 | + | 0.0349784i | 0.875946 | − | 0.482409i | \(-0.160238\pi\) |
−0.855751 | + | 0.517387i | \(0.826905\pi\) | |||||||
\(614\) | −3.67423 | + | 6.36396i | −0.148280 | + | 0.256829i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.0000 | + | 3.46410i | 0.725241 | + | 0.139573i | ||||
\(617\) | − | 15.5563i | − | 0.626275i | −0.949708 | − | 0.313138i | \(-0.898620\pi\) | ||
0.949708 | − | 0.313138i | \(-0.101380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.50000 | − | 4.33013i | 0.301450 | − | 0.174042i | −0.341644 | − | 0.939829i | \(-0.610984\pi\) |
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | −14.6969 | − | 25.4558i | −0.590243 | − | 1.02233i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.7846i | 0.833387i | ||||||||
\(623\) | 12.2474 | + | 35.3553i | 0.490684 | + | 1.41648i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | −17.1464 | + | 9.89949i | −0.685309 | + | 0.395663i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | − | 34.6410i | 0.798087 | − | 1.38233i | ||||
\(629\) | 7.07107i | 0.281942i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.9808i | − | 1.03428i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) | ||
0.855901 | − | 0.517139i | \(-0.173003\pi\) | |||||||
\(632\) | 22.0454 | − | 38.1838i | 0.876919 | − | 1.51887i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.0000 | − | 32.9090i | −0.754586 | − | 1.30698i | ||||
\(635\) | 7.34847 | − | 12.7279i | 0.291615 | − | 0.505092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | − | 6.92820i | −0.0396214 | − | 0.274505i | ||||
\(638\) | 24.4949 | 0.969762 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0000 | − | 27.7128i | −0.632456 | − | 1.09545i | ||||
\(641\) | 37.9671 | − | 21.9203i | 1.49961 | − | 0.865800i | 0.499610 | − | 0.866250i | \(-0.333477\pi\) |
1.00000 | 0.000450234i | \(0.000143314\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.1244i | − | 0.478138i | −0.971003 | − | 0.239069i | \(-0.923158\pi\) | ||
0.971003 | − | 0.239069i | \(-0.0768422\pi\) | |||||||
\(644\) | 9.79796 | + | 8.48528i | 0.386094 | + | 0.334367i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 6.92820i | 0.472134 | + | 0.272587i | ||||
\(647\) | 9.79796 | + | 16.9706i | 0.385198 | + | 0.667182i | 0.991797 | − | 0.127826i | \(-0.0408000\pi\) |
−0.606599 | + | 0.795008i | \(0.707467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | + | 15.5885i | −0.353281 | + | 0.611900i | ||||
\(650\) | − | 4.24264i | − | 0.166410i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 38.1051i | − | 1.49231i | ||||||
\(653\) | 6.12372 | + | 3.53553i | 0.239640 | + | 0.138356i | 0.615011 | − | 0.788518i | \(-0.289151\pi\) |
−0.375371 | + | 0.926875i | \(0.622485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.0000 | + | 13.8564i | −0.937758 | + | 0.541415i | ||||
\(656\) | 24.4949 | + | 14.1421i | 0.956365 | + | 0.552158i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.0000 | − | 5.19615i | −1.05257 | − | 0.202567i | ||||
\(659\) | 24.4949 | 0.954186 | 0.477093 | − | 0.878853i | \(-0.341691\pi\) | ||||
0.477093 | + | 0.878853i | \(0.341691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | − | 17.3205i | −0.388955 | − | 0.673690i | 0.603354 | − | 0.797473i | \(-0.293830\pi\) |
−0.992309 | + | 0.123784i | \(0.960497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.92820i | 0.268866i | ||||||||
\(665\) | 9.79796 | − | 50.9117i | 0.379949 | − | 1.97427i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000 | + | 8.66025i | 0.580802 | + | 0.335326i | ||||
\(668\) | 12.2474 | + | 21.2132i | 0.473868 | + | 0.820763i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.0000 | + | 10.3923i | 0.695401 | + | 0.401490i | ||||
\(671\) | −12.2474 | −0.472808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 24.4949 | + | 14.1421i | 0.943508 | + | 0.544735i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | − | 20.7846i | −0.461538 | − | 0.799408i | ||||
\(677\) | 24.4949 | + | 14.1421i | 0.941415 | + | 0.543526i | 0.890404 | − | 0.455172i | \(-0.150422\pi\) |
0.0510117 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | − | 8.66025i | −0.383765 | − | 0.332350i | ||||
\(680\) | 11.3137i | 0.433861i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.00000 | − | 15.5885i | −0.344628 | − | 0.596913i | ||||
\(683\) | 17.1464 | + | 29.6985i | 0.656090 | + | 1.13638i | 0.981619 | + | 0.190849i | \(0.0611241\pi\) |
−0.325530 | + | 0.945532i | \(0.605543\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0000 | −0.764161 | ||||||||
\(686\) | 23.2702 | − | 12.0208i | 0.888459 | − | 0.458957i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.0000 | + | 17.3205i | 1.14374 | + | 0.660338i | ||||
\(689\) | −8.57321 | + | 4.94975i | −0.326613 | + | 0.188570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.50000 | + | 2.59808i | 0.171188 | + | 0.0988355i | 0.583146 | − | 0.812367i | \(-0.301822\pi\) |
−0.411958 | + | 0.911203i | \(0.635155\pi\) | |||||||
\(692\) | 22.6274i | 0.860165i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.5692i | 1.57795i | ||||||||
\(695\) | −12.2474 | + | 21.2132i | −0.464572 | + | 0.804663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | − | 8.66025i | −0.189389 | − | 0.328031i | ||||
\(698\) | −15.9217 | − | 9.19239i | −0.602645 | − | 0.347937i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.0000 | − | 5.19615i | 0.566947 | − | 0.196396i | ||||
\(701\) | − | 28.2843i | − | 1.06828i | −0.845395 | − | 0.534141i | \(-0.820635\pi\) | ||
0.845395 | − | 0.534141i | \(-0.179365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.0000 | + | 17.3205i | −1.13147 | + | 0.653255i | ||||
\(704\) | −9.79796 | − | 16.9706i | −0.369274 | − | 0.639602i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0000 | −0.602168 | ||||||||
\(707\) | −36.7423 | − | 7.07107i | −1.38184 | − | 0.265935i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5000 | + | 19.9186i | −0.431892 | + | 0.748058i | −0.997036 | − | 0.0769337i | \(-0.975487\pi\) |
0.565145 | + | 0.824992i | \(0.308820\pi\) | |||||||
\(710\) | −29.3939 | − | 50.9117i | −1.10313 | − | 1.91068i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.0000 | − | 34.6410i | 0.749532 | − | 1.29823i | ||||
\(713\) | − | 12.7279i | − | 0.476664i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.92820i | − | 0.259100i | ||||||
\(716\) | −4.89898 | + | 8.48528i | −0.183083 | + | 0.317110i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.0000 | + | 8.66025i | −0.559795 | + | 0.323198i | ||||
\(719\) | −2.44949 | + | 4.24264i | −0.0913506 | + | 0.158224i | −0.908080 | − | 0.418797i | \(-0.862452\pi\) |
0.816729 | + | 0.577021i | \(0.195785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5000 | − | 47.6314i | −0.614492 | − | 1.77389i | ||||
\(722\) | 41.0122i | 1.52632i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.0000 | − | 27.7128i | −0.594635 | − | 1.02994i | ||||
\(725\) | 18.3712 | − | 10.6066i | 0.682288 | − | 0.393919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.66025i | − | 0.321191i | −0.987020 | − | 0.160596i | \(-0.948659\pi\) | ||
0.987020 | − | 0.160596i | \(-0.0513415\pi\) | |||||||
\(728\) | −4.89898 | + | 5.65685i | −0.181568 | + | 0.209657i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.00000 | + | 13.8564i | −0.296093 | + | 0.512849i | ||||
\(731\) | −6.12372 | − | 10.6066i | −0.226494 | − | 0.392299i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50000 | + | 9.52628i | −0.203147 | + | 0.351861i | −0.949541 | − | 0.313644i | \(-0.898450\pi\) |
0.746394 | + | 0.665505i | \(0.231784\pi\) | |||||||
\(734\) | 4.89898 | 0.180825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 13.8564i | − | 0.510754i | ||||||
\(737\) | 11.0227 | + | 6.36396i | 0.406027 | + | 0.234420i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.5000 | − | 16.4545i | 1.04839 | − | 0.605288i | 0.126191 | − | 0.992006i | \(-0.459725\pi\) |
0.922198 | + | 0.386718i | \(0.126391\pi\) | |||||||
\(740\) | −24.4949 | − | 14.1421i | −0.900450 | − | 0.519875i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.0000 | − | 24.2487i | −1.02791 | − | 0.890198i | ||||
\(743\) | 12.2474 | 0.449315 | 0.224658 | − | 0.974438i | \(-0.427874\pi\) | ||||
0.224658 | + | 0.974438i | \(0.427874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | + | 6.92820i | 0.146549 | + | 0.253830i | ||||
\(746\) | −24.4949 | + | 14.1421i | −0.896822 | + | 0.517780i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.92820i | 0.253320i | ||||||||
\(749\) | −42.8661 | + | 14.8492i | −1.56629 | + | 0.542580i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0000 | + | 17.3205i | 1.09472 | + | 0.632034i | 0.934828 | − | 0.355101i | \(-0.115553\pi\) |
0.159888 | + | 0.987135i | \(0.448887\pi\) | |||||||
\(752\) | 14.6969 | + | 25.4558i | 0.535942 | + | 0.928279i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.00000 | + | 8.66025i | −0.182089 | + | 0.315388i | ||||
\(755\) | 24.4949 | 0.891461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | −0.254419 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(758\) | −18.3712 | + | 31.8198i | −0.667271 | + | 1.15575i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −48.0000 | + | 27.7128i | −1.74114 | + | 1.00525i | ||||
\(761\) | 24.4949 | + | 14.1421i | 0.887939 | + | 0.512652i | 0.873268 | − | 0.487240i | \(-0.161996\pi\) |
0.0146714 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | + | 12.9904i | −0.0905061 | + | 0.470283i | ||||
\(764\) | 29.3939 | 1.06343 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.0000 | − | 19.0526i | 1.19234 | − | 0.688397i | ||||
\(767\) | −3.67423 | − | 6.36396i | −0.132669 | − | 0.229789i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 24.4949 | − | 8.48528i | 0.882735 | − | 0.305788i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0000 | − | 19.0526i | 0.395899 | − | 0.685717i | ||||
\(773\) | 34.2929 | − | 19.7990i | 1.23343 | − | 0.712120i | 0.265685 | − | 0.964060i | \(-0.414402\pi\) |
0.967743 | + | 0.251940i | \(0.0810684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.5000 | − | 7.79423i | −0.484934 | − | 0.279977i | ||||
\(776\) | 14.1421i | 0.507673i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.0000 | −0.573628 | ||||||||
\(779\) | 24.4949 | − | 42.4264i | 0.877621 | − | 1.52008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | −2.44949 | + | 4.24264i | −0.0875936 | + | 0.151717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.0000 | − | 10.3923i | −0.928571 | − | 0.371154i | ||||
\(785\) | − | 56.5685i | − | 2.01902i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5000 | + | 12.9904i | −0.802038 | + | 0.463057i | −0.844183 | − | 0.536054i | \(-0.819914\pi\) |
0.0421450 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(788\) | −39.1918 | + | 22.6274i | −1.39615 | + | 0.806068i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 62.3538i | − | 2.21845i | ||||||
\(791\) | −4.89898 | + | 5.65685i | −0.174188 | + | 0.201135i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50000 | − | 4.33013i | 0.0887776 | − | 0.153767i | ||||
\(794\) | 15.9217 | − | 9.19239i | 0.565039 | − | 0.326226i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.0000 | − | 8.66025i | −0.531661 | − | 0.306955i | ||||
\(797\) | − | 41.0122i | − | 1.45273i | −0.687311 | − | 0.726363i | \(-0.741209\pi\) | ||
0.687311 | − | 0.726363i | \(-0.258791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.3923i | − | 0.367653i | ||||||
\(800\) | −14.6969 | − | 8.48528i | −0.519615 | − | 0.300000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.0000 | + | 19.0526i | 0.388424 | + | 0.672769i | ||||
\(803\) | −4.89898 | + | 8.48528i | −0.172881 | + | 0.299439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | + | 3.46410i | 0.634417 | + | 0.122094i | ||||
\(806\) | 7.34847 | 0.258839 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.0000 | + | 34.6410i | 0.703598 | + | 1.21867i | ||||
\(809\) | −20.8207 | + | 12.0208i | −0.732016 | + | 0.422629i | −0.819159 | − | 0.573566i | \(-0.805559\pi\) |
0.0871435 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.9615i | − | 1.82462i | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||
0.409505 | − | 0.912308i | \(-0.365701\pi\) | |||||||
\(812\) | −36.7423 | − | 7.07107i | −1.28940 | − | 0.248146i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.0000 | − | 8.66025i | −0.525750 | − | 0.303542i | ||||
\(815\) | −26.9444 | − | 46.6690i | −0.943821 | − | 1.63475i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | − | 51.9615i | 1.04957 | − | 1.81790i | ||||
\(818\) | 9.89949i | 0.346128i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.0000 | 1.39686 | ||||||||
\(821\) | −23.2702 | − | 13.4350i | −0.812134 | − | 0.468886i | 0.0355625 | − | 0.999367i | \(-0.488678\pi\) |
−0.847696 | + | 0.530482i | \(0.822011\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.5000 | + | 12.9904i | −0.784301 | + | 0.452816i | −0.837952 | − | 0.545743i | \(-0.816247\pi\) |
0.0536516 | + | 0.998560i | \(0.482914\pi\) | |||||||
\(824\) | −26.9444 | + | 46.6690i | −0.938652 | + | 1.62579i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | − | 20.7846i | 0.626300 | − | 0.723189i | ||||
\(827\) | −29.3939 | −1.02213 | −0.511063 | − | 0.859543i | \(-0.670748\pi\) | ||||
−0.511063 | + | 0.859543i | \(0.670748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.00000 | − | 6.92820i | −0.138926 | − | 0.240626i | 0.788165 | − | 0.615465i | \(-0.211032\pi\) |
−0.927090 | + | 0.374838i | \(0.877698\pi\) | |||||||
\(830\) | 4.89898 | + | 8.48528i | 0.170046 | + | 0.294528i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 6.12372 | + | 7.77817i | 0.212174 | + | 0.269498i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0000 | + | 17.3205i | 1.03819 | + | 0.599401i | ||||
\(836\) | −29.3939 | + | 16.9706i | −1.01661 | + | 0.586939i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.00000 | + | 3.46410i | 0.207267 | + | 0.119665i | ||||
\(839\) | 2.44949 | 0.0845658 | 0.0422829 | − | 0.999106i | \(-0.486537\pi\) | ||||
0.0422829 | + | 0.999106i | \(0.486537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | −19.5959 | − | 11.3137i | −0.675320 | − | 0.389896i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0000 | + | 8.66025i | −0.516321 | + | 0.298098i | ||||
\(845\) | −29.3939 | − | 16.9706i | −1.01118 | − | 0.583805i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.5000 | + | 4.33013i | −0.429505 | + | 0.148785i | ||||
\(848\) | 39.5980i | 1.35980i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.00000 | + | 5.19615i | 0.102899 | + | 0.178227i | ||||
\(851\) | −6.12372 | − | 10.6066i | −0.209919 | − | 0.363590i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.0000 | −1.36957 | −0.684787 | − | 0.728743i | \(-0.740105\pi\) | ||||
−0.684787 | + | 0.728743i | \(0.740105\pi\) | |||||||
\(854\) | 18.3712 | + | 3.53553i | 0.628649 | + | 0.120983i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.0000 | + | 24.2487i | 1.43553 | + | 0.828804i | ||||
\(857\) | −17.1464 | + | 9.89949i | −0.585711 | + | 0.338160i | −0.763400 | − | 0.645926i | \(-0.776471\pi\) |
0.177689 | + | 0.984087i | \(0.443138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.50000 | + | 4.33013i | 0.255897 | + | 0.147742i | 0.622461 | − | 0.782651i | \(-0.286133\pi\) |
−0.366565 | + | 0.930393i | \(0.619466\pi\) | |||||||
\(860\) | 48.9898 | 1.67054 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.3205i | 0.589939i | ||||||||
\(863\) | 4.89898 | − | 8.48528i | 0.166763 | − | 0.288842i | −0.770517 | − | 0.637420i | \(-0.780002\pi\) |
0.937280 | + | 0.348577i | \(0.113335\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0000 | + | 27.7128i | 0.544016 | + | 0.942264i | ||||
\(866\) | −23.2702 | − | 13.4350i | −0.790752 | − | 0.456541i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.00000 | + | 25.9808i | 0.305480 | + | 0.881845i | ||||
\(869\) | − | 38.1838i | − | 1.29530i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.50000 | + | 2.59808i | −0.152477 | + | 0.0880325i | ||||
\(872\) | 12.2474 | − | 7.07107i | 0.414751 | − | 0.239457i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | −9.79796 | + | 11.3137i | −0.331231 | + | 0.382473i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5000 | − | 47.6314i | 0.928609 | − | 1.60840i | 0.142957 | − | 0.989729i | \(-0.454339\pi\) |
0.785652 | − | 0.618669i | \(-0.212328\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24.0000 | − | 13.8564i | −0.809040 | − | 0.467099i | ||||
\(881\) | − | 7.07107i | − | 0.238230i | −0.992880 | − | 0.119115i | \(-0.961994\pi\) | ||
0.992880 | − | 0.119115i | \(-0.0380058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3923i | 0.349729i | 0.984593 | + | 0.174864i | \(0.0559487\pi\) | ||||
−0.984593 | + | 0.174864i | \(0.944051\pi\) | |||||||
\(884\) | −2.44949 | − | 1.41421i | −0.0823853 | − | 0.0475651i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8207 | − | 36.0624i | 0.699089 | − | 1.21086i | −0.269693 | − | 0.962946i | \(-0.586922\pi\) |
0.968783 | − | 0.247912i | \(-0.0797444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.00000 | + | 10.3923i | −0.301850 | + | 0.348547i | ||||
\(890\) | − | 56.5685i | − | 1.89618i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.0000 | + | 6.92820i | −0.401790 | + | 0.231973i | ||||
\(893\) | 44.0908 | − | 25.4558i | 1.47544 | − | 0.851847i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8564i | 0.463169i | ||||||||
\(896\) | 9.79796 | + | 28.2843i | 0.327327 | + | 0.944911i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0000 | + | 38.1051i | −0.734150 | + | 1.27158i | ||||
\(899\) | 18.3712 | + | 31.8198i | 0.612713 | + | 1.06125i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.00000 | − | 12.1244i | 0.233204 | − | 0.403921i | ||||
\(902\) | 24.4949 | 0.815591 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | 0.266076 | ||||||||
\(905\) | −39.1918 | − | 22.6274i | −1.30278 | − | 0.752161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5000 | − | 14.7224i | 0.846714 | − | 0.488850i | −0.0128270 | − | 0.999918i | \(-0.504083\pi\) |
0.859541 | + | 0.511067i | \(0.170750\pi\) | |||||||
\(908\) | 12.2474 | − | 21.2132i | 0.406446 | − | 0.703985i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.00000 | + | 10.3923i | −0.0662994 | + | 0.344502i | ||||
\(911\) | −26.9444 | −0.892707 | −0.446354 | − | 0.894857i | \(-0.647278\pi\) | ||||
−0.446354 | + | 0.894857i | \(0.647278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.00000 | + | 5.19615i | 0.0992855 | + | 0.171968i | ||||
\(914\) | −6.12372 | + | 3.53553i | −0.202555 | + | 0.116945i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.0000 | −1.12339 | ||||||||
\(917\) | 24.4949 | − | 8.48528i | 0.808893 | − | 0.280209i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.50000 | − | 4.33013i | −0.247402 | − | 0.142838i | 0.371172 | − | 0.928564i | \(-0.378956\pi\) |
−0.618574 | + | 0.785726i | \(0.712289\pi\) | |||||||
\(920\) | −9.79796 | − | 16.9706i | −0.323029 | − | 0.559503i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.00000 | + | 1.73205i | −0.0329332 | + | 0.0570421i | ||||
\(923\) | 14.6969 | 0.483756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0000 | −0.493197 | ||||||||
\(926\) | 4.89898 | − | 8.48528i | 0.160990 | − | 0.278844i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.0000 | + | 34.6410i | 0.656532 | + | 1.13715i | ||||
\(929\) | −12.2474 | − | 7.07107i | −0.401826 | − | 0.231994i | 0.285446 | − | 0.958395i | \(-0.407858\pi\) |
−0.687271 | + | 0.726401i | \(0.741192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | + | 45.0333i | −0.589926 | + | 1.47591i | ||||
\(932\) | 22.6274i | 0.741186i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0000 | − | 17.3205i | 0.981630 | − | 0.566744i | ||||
\(935\) | 4.89898 | + | 8.48528i | 0.160214 | + | 0.277498i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | −14.6969 | − | 12.7279i | −0.479872 | − | 0.415581i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 36.0000 | + | 20.7846i | 1.17419 | + | 0.677919i | ||||
\(941\) | −6.12372 | + | 3.53553i | −0.199628 | + | 0.115255i | −0.596482 | − | 0.802627i | \(-0.703435\pi\) |
0.396854 | + | 0.917882i | \(0.370102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0000 | + | 8.66025i | 0.488467 | + | 0.282017i | ||||
\(944\) | −29.3939 | −0.956689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −3.67423 | + | 6.36396i | −0.119397 | + | 0.206801i | −0.919529 | − | 0.393023i | \(-0.871429\pi\) |
0.800132 | + | 0.599824i | \(0.204763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | −14.6969 | + | 25.4558i | −0.476832 | + | 0.825897i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.00000 | − | 10.3923i | 0.0648204 | − | 0.336817i | ||||
\(953\) | 35.3553i | 1.14527i | 0.819810 | + | 0.572636i | \(0.194079\pi\) | ||||
−0.819810 | + | 0.572636i | \(0.805921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0000 | − | 20.7846i | 1.16493 | − | 0.672574i | ||||
\(956\) | −24.4949 | − | 42.4264i | −0.792222 | − | 1.37217i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.92820i | − | 0.223840i | ||||||
\(959\) | 18.3712 | + | 3.53553i | 0.593236 | + | 0.114168i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | + | 3.46410i | −0.0645161 | + | 0.111745i | ||||
\(962\) | 6.12372 | − | 3.53553i | 0.197437 | − | 0.113990i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.0000 | + | 43.3013i | −0.805196 | + | 1.39464i | ||||
\(965\) | − | 31.1127i | − | 1.00155i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.5167i | − | 0.724087i | −0.932161 | − | 0.362043i | \(-0.882079\pi\) | ||
0.932161 | − | 0.362043i | \(-0.117921\pi\) | |||||||
\(968\) | 12.2474 | + | 7.07107i | 0.393648 | + | 0.227273i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | + | 17.3205i | 0.321081 | + | 0.556128i | ||||
\(971\) | −24.4949 | + | 42.4264i | −0.786079 | + | 1.36153i | 0.142274 | + | 0.989827i | \(0.454559\pi\) |
−0.928353 | + | 0.371701i | \(0.878775\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0000 | − | 17.3205i | 0.480878 | − | 0.555270i | ||||
\(974\) | −48.9898 | −1.56973 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | − | 17.3205i | −0.320092 | − | 0.554416i | ||||
\(977\) | 1.22474 | − | 0.707107i | 0.0391831 | − | 0.0226224i | −0.480281 | − | 0.877115i | \(-0.659465\pi\) |
0.519464 | + | 0.854493i | \(0.326132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 34.6410i | − | 1.10713i | ||||||
\(980\) | −39.1918 | + | 5.65685i | −1.25194 | + | 0.180702i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.0000 | + | 8.66025i | 0.478669 | + | 0.276360i | ||||
\(983\) | 12.2474 | + | 21.2132i | 0.390633 | + | 0.676596i | 0.992533 | − | 0.121975i | \(-0.0389228\pi\) |
−0.601900 | + | 0.798571i | \(0.705590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.0000 | + | 55.4256i | −1.01960 | + | 1.76601i | ||||
\(986\) | − | 14.1421i | − | 0.450377i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 13.8564i | − | 0.440831i | ||||||
\(989\) | 18.3712 | + | 10.6066i | 0.584169 | + | 0.337270i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.5000 | + | 19.9186i | −1.09593 | + | 0.632735i | −0.935149 | − | 0.354256i | \(-0.884734\pi\) |
−0.160780 | + | 0.986990i | \(0.551401\pi\) | |||||||
\(992\) | 14.6969 | − | 25.4558i | 0.466628 | − | 0.808224i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.0000 | + | 51.9615i | 0.570925 | + | 1.64812i | ||||
\(995\) | −24.4949 | −0.776540 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5000 | + | 21.6506i | 0.395879 | + | 0.685682i | 0.993213 | − | 0.116310i | \(-0.0371066\pi\) |
−0.597334 | + | 0.801993i | \(0.703773\pi\) | |||||||
\(998\) | −23.2702 | − | 40.3051i | −0.736604 | − | 1.27584i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.be.a.107.2 | yes | 4 | |
3.2 | odd | 2 | inner | 756.2.be.a.107.1 | ✓ | 4 | |
4.3 | odd | 2 | 756.2.be.b.107.2 | yes | 4 | ||
7.4 | even | 3 | 756.2.be.b.431.1 | yes | 4 | ||
12.11 | even | 2 | 756.2.be.b.107.1 | yes | 4 | ||
21.11 | odd | 6 | 756.2.be.b.431.2 | yes | 4 | ||
28.11 | odd | 6 | inner | 756.2.be.a.431.1 | yes | 4 | |
84.11 | even | 6 | inner | 756.2.be.a.431.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.be.a.107.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
756.2.be.a.107.2 | yes | 4 | 1.1 | even | 1 | trivial | |
756.2.be.a.431.1 | yes | 4 | 28.11 | odd | 6 | inner | |
756.2.be.a.431.2 | yes | 4 | 84.11 | even | 6 | inner | |
756.2.be.b.107.1 | yes | 4 | 12.11 | even | 2 | ||
756.2.be.b.107.2 | yes | 4 | 4.3 | odd | 2 | ||
756.2.be.b.431.1 | yes | 4 | 7.4 | even | 3 | ||
756.2.be.b.431.2 | yes | 4 | 21.11 | odd | 6 |