Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.o.177.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.41421 | + | 2.44949i | −0.816497 | + | 1.41421i | 0.0917517 | + | 0.995782i | \(0.470753\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 2.82843 | 1.15470 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.50000 | − | 4.33013i | −0.833333 | − | 1.44338i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.41421 | − | 2.44949i | −0.408248 | − | 0.707107i | ||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.41421 | − | 2.44949i | 0.342997 | − | 0.594089i | −0.641991 | − | 0.766712i | \(-0.721891\pi\) |
0.984988 | + | 0.172624i | \(0.0552245\pi\) | |||||||
\(18\) | −2.50000 | + | 4.33013i | −0.589256 | + | 1.02062i | ||||
\(19\) | 2.12132 | + | 3.67423i | 0.486664 | + | 0.842927i | 0.999882 | − | 0.0153309i | \(-0.00488018\pi\) |
−0.513218 | + | 0.858258i | \(0.671547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | −1.41421 | + | 2.44949i | −0.288675 | + | 0.500000i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −2.12132 | − | 3.67423i | −0.416025 | − | 0.720577i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.53553 | − | 6.12372i | 0.635001 | − | 1.09985i | −0.351514 | − | 0.936182i | \(-0.614333\pi\) |
0.986515 | − | 0.163671i | \(-0.0523335\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.41421 | + | 2.44949i | 0.246183 | + | 0.426401i | ||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.00000 | 0.833333 | ||||||||
\(37\) | −1.00000 | − | 1.73205i | −0.164399 | − | 0.284747i | 0.772043 | − | 0.635571i | \(-0.219235\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 2.12132 | − | 3.67423i | 0.344124 | − | 0.596040i | ||||
\(39\) | −6.00000 | + | 10.3923i | −0.960769 | + | 1.66410i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 6.36396 | + | 11.0227i | 0.928279 | + | 1.60783i | 0.786201 | + | 0.617971i | \(0.212045\pi\) |
0.142078 | + | 0.989855i | \(0.454621\pi\) | |||||||
\(48\) | 2.82843 | 0.408248 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | 4.00000 | + | 6.92820i | 0.560112 | + | 0.970143i | ||||
\(52\) | −2.12132 | + | 3.67423i | −0.294174 | + | 0.509525i | ||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | −2.82843 | − | 4.89898i | −0.384900 | − | 0.666667i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | 2.00000 | + | 3.46410i | 0.262613 | + | 0.454859i | ||||
\(59\) | −5.65685 | + | 9.79796i | −0.736460 | + | 1.27559i | 0.217620 | + | 0.976034i | \(0.430171\pi\) |
−0.954080 | + | 0.299552i | \(0.903163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.94975 | + | 8.57321i | 0.633750 | + | 1.09769i | 0.986778 | + | 0.162075i | \(0.0518186\pi\) |
−0.353028 | + | 0.935613i | \(0.614848\pi\) | |||||||
\(62\) | −7.07107 | −0.898027 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.41421 | − | 2.44949i | 0.174078 | − | 0.301511i | ||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 1.41421 | + | 2.44949i | 0.171499 | + | 0.297044i | ||||
\(69\) | 16.9706 | 2.04302 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | −2.50000 | − | 4.33013i | −0.294628 | − | 0.510310i | ||||
\(73\) | 4.24264 | − | 7.34847i | 0.496564 | − | 0.860073i | −0.503429 | − | 0.864037i | \(-0.667928\pi\) |
0.999992 | + | 0.00396356i | \(0.00126164\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 7.07107 | + | 12.2474i | 0.816497 | + | 1.41421i | ||||
\(76\) | −4.24264 | −0.486664 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0000 | 1.35873 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.41421 | − | 2.44949i | −0.156174 | − | 0.270501i | ||||
\(83\) | −12.7279 | −1.39707 | −0.698535 | − | 0.715575i | \(-0.746165\pi\) | ||||
−0.698535 | + | 0.715575i | \(0.746165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.00000 | − | 8.66025i | −0.539164 | − | 0.933859i | ||||
\(87\) | 5.65685 | − | 9.79796i | 0.606478 | − | 1.05045i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −3.53553 | − | 6.12372i | −0.374766 | − | 0.649113i | 0.615526 | − | 0.788116i | \(-0.288944\pi\) |
−0.990292 | + | 0.139003i | \(0.955610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 10.0000 | + | 17.3205i | 1.03695 | + | 1.79605i | ||||
\(94\) | 6.36396 | − | 11.0227i | 0.656392 | − | 1.13691i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.41421 | − | 2.44949i | −0.144338 | − | 0.250000i | ||||
\(97\) | −7.07107 | −0.717958 | −0.358979 | − | 0.933346i | \(-0.616875\pi\) | ||||
−0.358979 | + | 0.933346i | \(0.616875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | 0.707107 | − | 1.22474i | 0.0703598 | − | 0.121867i | −0.828699 | − | 0.559694i | \(-0.810919\pi\) |
0.899059 | + | 0.437828i | \(0.144252\pi\) | |||||||
\(102\) | 4.00000 | − | 6.92820i | 0.396059 | − | 0.685994i | ||||
\(103\) | 0.707107 | + | 1.22474i | 0.0696733 | + | 0.120678i | 0.898757 | − | 0.438446i | \(-0.144471\pi\) |
−0.829084 | + | 0.559124i | \(0.811138\pi\) | |||||||
\(104\) | 4.24264 | 0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 7.00000 | + | 12.1244i | 0.676716 | + | 1.17211i | 0.975964 | + | 0.217931i | \(0.0699306\pi\) |
−0.299249 | + | 0.954175i | \(0.596736\pi\) | |||||||
\(108\) | −2.82843 | + | 4.89898i | −0.272166 | + | 0.471405i | ||||
\(109\) | 7.00000 | − | 12.1244i | 0.670478 | − | 1.16130i | −0.307290 | − | 0.951616i | \(-0.599422\pi\) |
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65685 | 0.536925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000 | 1.50515 | 0.752577 | − | 0.658505i | \(-0.228811\pi\) | ||||
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 6.00000 | + | 10.3923i | 0.561951 | + | 0.973329i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.00000 | − | 3.46410i | 0.185695 | − | 0.321634i | ||||
\(117\) | −10.6066 | − | 18.3712i | −0.980581 | − | 1.69842i | ||||
\(118\) | 11.3137 | 1.04151 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 4.94975 | − | 8.57321i | 0.448129 | − | 0.776182i | ||||
\(123\) | −4.00000 | + | 6.92820i | −0.360668 | + | 0.624695i | ||||
\(124\) | 3.53553 | + | 6.12372i | 0.317500 | + | 0.549927i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −14.1421 | + | 24.4949i | −1.24515 | + | 2.15666i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.53553 | − | 6.12372i | −0.308901 | − | 0.535032i | 0.669221 | − | 0.743063i | \(-0.266628\pi\) |
−0.978122 | + | 0.208031i | \(0.933295\pi\) | |||||||
\(132\) | −2.82843 | −0.246183 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.41421 | − | 2.44949i | 0.121268 | − | 0.210042i | ||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | −8.48528 | − | 14.6969i | −0.722315 | − | 1.25109i | ||||
\(139\) | 18.3848 | 1.55938 | 0.779688 | − | 0.626168i | \(-0.215378\pi\) | ||||
0.779688 | + | 0.626168i | \(0.215378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −36.0000 | −3.03175 | ||||||||
\(142\) | −8.00000 | − | 13.8564i | −0.671345 | − | 1.16280i | ||||
\(143\) | 2.12132 | − | 3.67423i | 0.177394 | − | 0.307255i | ||||
\(144\) | −2.50000 | + | 4.33013i | −0.208333 | + | 0.360844i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.48528 | −0.702247 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −4.00000 | − | 6.92820i | −0.327693 | − | 0.567581i | 0.654361 | − | 0.756182i | \(-0.272938\pi\) |
−0.982054 | + | 0.188602i | \(0.939604\pi\) | |||||||
\(150\) | 7.07107 | − | 12.2474i | 0.577350 | − | 1.00000i | ||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 2.12132 | + | 3.67423i | 0.172062 | + | 0.298020i | ||||
\(153\) | −14.1421 | −1.14332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | − | 10.3923i | −0.480384 | − | 0.832050i | ||||
\(157\) | −4.24264 | + | 7.34847i | −0.338600 | + | 0.586472i | −0.984170 | − | 0.177229i | \(-0.943287\pi\) |
0.645570 | + | 0.763701i | \(0.276620\pi\) | |||||||
\(158\) | 4.00000 | − | 6.92820i | 0.318223 | − | 0.551178i | ||||
\(159\) | −2.82843 | − | 4.89898i | −0.224309 | − | 0.388514i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.00000 | + | 3.46410i | 0.156652 | + | 0.271329i | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | −1.41421 | + | 2.44949i | −0.110432 | + | 0.191273i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.36396 | + | 11.0227i | 0.493939 | + | 0.855528i | ||||
\(167\) | −14.1421 | −1.09435 | −0.547176 | − | 0.837018i | \(-0.684297\pi\) | ||||
−0.547176 | + | 0.837018i | \(0.684297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.6066 | − | 18.3712i | 0.811107 | − | 1.40488i | ||||
\(172\) | −5.00000 | + | 8.66025i | −0.381246 | + | 0.660338i | ||||
\(173\) | −3.53553 | − | 6.12372i | −0.268802 | − | 0.465578i | 0.699751 | − | 0.714387i | \(-0.253294\pi\) |
−0.968553 | + | 0.248809i | \(0.919961\pi\) | |||||||
\(174\) | −11.3137 | −0.857690 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −16.0000 | − | 27.7128i | −1.20263 | − | 2.08302i | ||||
\(178\) | −3.53553 | + | 6.12372i | −0.264999 | + | 0.458993i | ||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3137 | 0.840941 | 0.420471 | − | 0.907306i | \(-0.361865\pi\) | ||||
0.420471 | + | 0.907306i | \(0.361865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.0000 | −2.06982 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0000 | − | 17.3205i | 0.733236 | − | 1.27000i | ||||
\(187\) | −1.41421 | − | 2.44949i | −0.103418 | − | 0.179124i | ||||
\(188\) | −12.7279 | −0.928279 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.00000 | − | 8.66025i | −0.361787 | − | 0.626634i | 0.626468 | − | 0.779447i | \(-0.284500\pi\) |
−0.988255 | + | 0.152813i | \(0.951167\pi\) | |||||||
\(192\) | −1.41421 | + | 2.44949i | −0.102062 | + | 0.176777i | ||||
\(193\) | −3.00000 | + | 5.19615i | −0.215945 | + | 0.374027i | −0.953564 | − | 0.301189i | \(-0.902616\pi\) |
0.737620 | + | 0.675216i | \(0.235950\pi\) | |||||||
\(194\) | 3.53553 | + | 6.12372i | 0.253837 | + | 0.439658i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 2.50000 | + | 4.33013i | 0.177667 | + | 0.307729i | ||||
\(199\) | −4.94975 | + | 8.57321i | −0.350878 | + | 0.607739i | −0.986404 | − | 0.164341i | \(-0.947450\pi\) |
0.635525 | + | 0.772080i | \(0.280784\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | −11.3137 | − | 19.5959i | −0.798007 | − | 1.38219i | ||||
\(202\) | −1.41421 | −0.0995037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.00000 | −0.560112 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.707107 | − | 1.22474i | 0.0492665 | − | 0.0853320i | ||||
\(207\) | −15.0000 | + | 25.9808i | −1.04257 | + | 1.80579i | ||||
\(208\) | −2.12132 | − | 3.67423i | −0.147087 | − | 0.254762i | ||||
\(209\) | 4.24264 | 0.293470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | −1.00000 | − | 1.73205i | −0.0686803 | − | 0.118958i | ||||
\(213\) | −22.6274 | + | 39.1918i | −1.55041 | + | 2.68538i | ||||
\(214\) | 7.00000 | − | 12.1244i | 0.478510 | − | 0.828804i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.65685 | 0.384900 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | 12.0000 | + | 20.7846i | 0.810885 | + | 1.40449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | −2.82843 | − | 4.89898i | −0.189832 | − | 0.328798i | ||||
\(223\) | 21.2132 | 1.42054 | 0.710271 | − | 0.703929i | \(-0.248573\pi\) | ||||
0.710271 | + | 0.703929i | \(0.248573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.0000 | −1.66667 | ||||||||
\(226\) | −8.00000 | − | 13.8564i | −0.532152 | − | 0.921714i | ||||
\(227\) | 3.53553 | − | 6.12372i | 0.234662 | − | 0.406446i | −0.724513 | − | 0.689261i | \(-0.757935\pi\) |
0.959174 | + | 0.282816i | \(0.0912685\pi\) | |||||||
\(228\) | 6.00000 | − | 10.3923i | 0.397360 | − | 0.688247i | ||||
\(229\) | 11.3137 | + | 19.5959i | 0.747631 | + | 1.29493i | 0.948955 | + | 0.315410i | \(0.102142\pi\) |
−0.201325 | + | 0.979525i | \(0.564525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | −13.0000 | − | 22.5167i | −0.851658 | − | 1.47512i | −0.879711 | − | 0.475509i | \(-0.842264\pi\) |
0.0280525 | − | 0.999606i | \(-0.491069\pi\) | |||||||
\(234\) | −10.6066 | + | 18.3712i | −0.693375 | + | 1.20096i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.65685 | − | 9.79796i | −0.368230 | − | 0.637793i | ||||
\(237\) | −22.6274 | −1.46981 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24264 | − | 7.34847i | 0.273293 | − | 0.473357i | −0.696410 | − | 0.717644i | \(-0.745221\pi\) |
0.969703 | + | 0.244287i | \(0.0785540\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 7.07107 | + | 12.2474i | 0.453609 | + | 0.785674i | ||||
\(244\) | −9.89949 | −0.633750 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.00000 | 0.510061 | ||||||||
\(247\) | 9.00000 | + | 15.5885i | 0.572656 | + | 0.991870i | ||||
\(248\) | 3.53553 | − | 6.12372i | 0.224507 | − | 0.388857i | ||||
\(249\) | 18.0000 | − | 31.1769i | 1.14070 | − | 1.97576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65685 | −0.357057 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 10.0000 | + | 17.3205i | 0.627456 | + | 1.08679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.53553 | − | 6.12372i | −0.220541 | − | 0.381987i | 0.734432 | − | 0.678683i | \(-0.237449\pi\) |
−0.954972 | + | 0.296695i | \(0.904115\pi\) | |||||||
\(258\) | 28.2843 | 1.76090 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | + | 17.3205i | 0.618984 | + | 1.07211i | ||||
\(262\) | −3.53553 | + | 6.12372i | −0.218426 | + | 0.378325i | ||||
\(263\) | −2.00000 | + | 3.46410i | −0.123325 | + | 0.213606i | −0.921077 | − | 0.389380i | \(-0.872689\pi\) |
0.797752 | + | 0.602986i | \(0.206023\pi\) | |||||||
\(264\) | 1.41421 | + | 2.44949i | 0.0870388 | + | 0.150756i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.0000 | 1.22398 | ||||||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | −5.65685 | + | 9.79796i | −0.344904 | + | 0.597392i | −0.985336 | − | 0.170623i | \(-0.945422\pi\) |
0.640432 | + | 0.768015i | \(0.278755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.24264 | − | 7.34847i | −0.257722 | − | 0.446388i | 0.707909 | − | 0.706303i | \(-0.249639\pi\) |
−0.965631 | + | 0.259916i | \(0.916305\pi\) | |||||||
\(272\) | −2.82843 | −0.171499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | −8.48528 | + | 14.6969i | −0.510754 | + | 0.884652i | ||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | −9.19239 | − | 15.9217i | −0.551323 | − | 0.954919i | ||||
\(279\) | −35.3553 | −2.11667 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 18.0000 | + | 31.1769i | 1.07188 | + | 1.85656i | ||||
\(283\) | −3.53553 | + | 6.12372i | −0.210166 | + | 0.364018i | −0.951766 | − | 0.306824i | \(-0.900734\pi\) |
0.741601 | + | 0.670842i | \(0.234067\pi\) | |||||||
\(284\) | −8.00000 | + | 13.8564i | −0.474713 | + | 0.822226i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.24264 | −0.250873 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | 4.50000 | + | 7.79423i | 0.264706 | + | 0.458484i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0000 | − | 17.3205i | 0.586210 | − | 1.01535i | ||||
\(292\) | 4.24264 | + | 7.34847i | 0.248282 | + | 0.430037i | ||||
\(293\) | −21.2132 | −1.23929 | −0.619644 | − | 0.784883i | \(-0.712723\pi\) | ||||
−0.619644 | + | 0.784883i | \(0.712723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | 2.82843 | − | 4.89898i | 0.164122 | − | 0.284268i | ||||
\(298\) | −4.00000 | + | 6.92820i | −0.231714 | + | 0.401340i | ||||
\(299\) | −12.7279 | − | 22.0454i | −0.736075 | − | 1.27492i | ||||
\(300\) | −14.1421 | −0.816497 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | 2.00000 | + | 3.46410i | 0.114897 | + | 0.199007i | ||||
\(304\) | 2.12132 | − | 3.67423i | 0.121666 | − | 0.210732i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.07107 | + | 12.2474i | 0.404226 | + | 0.700140i | ||||
\(307\) | 21.2132 | 1.21070 | 0.605351 | − | 0.795959i | \(-0.293033\pi\) | ||||
0.605351 | + | 0.795959i | \(0.293033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.707107 | − | 1.22474i | 0.0400963 | − | 0.0694489i | −0.845281 | − | 0.534322i | \(-0.820567\pi\) |
0.885377 | + | 0.464873i | \(0.153900\pi\) | |||||||
\(312\) | −6.00000 | + | 10.3923i | −0.339683 | + | 0.588348i | ||||
\(313\) | 14.8492 | + | 25.7196i | 0.839329 | + | 1.45376i | 0.890457 | + | 0.455068i | \(0.150385\pi\) |
−0.0511279 | + | 0.998692i | \(0.516282\pi\) | |||||||
\(314\) | 8.48528 | 0.478852 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | −2.82843 | + | 4.89898i | −0.158610 | + | 0.274721i | ||||
\(319\) | −2.00000 | + | 3.46410i | −0.111979 | + | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.5980 | −2.21014 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 10.6066 | − | 18.3712i | 0.588348 | − | 1.01905i | ||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | 19.7990 | + | 34.2929i | 1.09489 | + | 1.89640i | ||||
\(328\) | 2.82843 | 0.156174 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 6.36396 | − | 11.0227i | 0.349268 | − | 0.604949i | ||||
\(333\) | −5.00000 | + | 8.66025i | −0.273998 | + | 0.474579i | ||||
\(334\) | 7.07107 | + | 12.2474i | 0.386912 | + | 0.670151i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | −2.50000 | − | 4.33013i | −0.135982 | − | 0.235528i | ||||
\(339\) | −22.6274 | + | 39.1918i | −1.22895 | + | 2.12861i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.53553 | − | 6.12372i | −0.191460 | − | 0.331618i | ||||
\(342\) | −21.2132 | −1.14708 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.53553 | + | 6.12372i | −0.190071 | + | 0.329213i | ||||
\(347\) | −13.0000 | + | 22.5167i | −0.697877 | + | 1.20876i | 0.271325 | + | 0.962488i | \(0.412538\pi\) |
−0.969201 | + | 0.246270i | \(0.920795\pi\) | |||||||
\(348\) | 5.65685 | + | 9.79796i | 0.303239 | + | 0.525226i | ||||
\(349\) | −26.8701 | −1.43832 | −0.719161 | − | 0.694844i | \(-0.755473\pi\) | ||||
−0.719161 | + | 0.694844i | \(0.755473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0000 | 1.28103 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −7.77817 | + | 13.4722i | −0.413990 | + | 0.717053i | −0.995322 | − | 0.0966144i | \(-0.969199\pi\) |
0.581331 | + | 0.813667i | \(0.302532\pi\) | |||||||
\(354\) | −16.0000 | + | 27.7128i | −0.850390 | + | 1.47292i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.07107 | 0.374766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −6.00000 | − | 10.3923i | −0.316668 | − | 0.548485i | 0.663123 | − | 0.748511i | \(-0.269231\pi\) |
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.500000 | − | 0.866025i | 0.0263158 | − | 0.0455803i | ||||
\(362\) | −5.65685 | − | 9.79796i | −0.297318 | − | 0.514969i | ||||
\(363\) | 2.82843 | 0.148454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0000 | + | 24.2487i | 0.731792 | + | 1.26750i | ||||
\(367\) | 10.6066 | − | 18.3712i | 0.553660 | − | 0.958967i | −0.444346 | − | 0.895855i | \(-0.646564\pi\) |
0.998006 | − | 0.0631123i | \(-0.0201026\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | −7.07107 | − | 12.2474i | −0.368105 | − | 0.637577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −20.0000 | −1.03695 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | −1.41421 | + | 2.44949i | −0.0731272 | + | 0.126660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.36396 | + | 11.0227i | 0.328196 | + | 0.568453i | ||||
\(377\) | −16.9706 | −0.874028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.2843 | − | 48.9898i | 1.44905 | − | 2.50982i | ||||
\(382\) | −5.00000 | + | 8.66025i | −0.255822 | + | 0.443097i | ||||
\(383\) | 7.77817 | + | 13.4722i | 0.397446 | + | 0.688397i | 0.993410 | − | 0.114614i | \(-0.0365632\pi\) |
−0.595964 | + | 0.803011i | \(0.703230\pi\) | |||||||
\(384\) | 2.82843 | 0.144338 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | −25.0000 | − | 43.3013i | −1.27082 | − | 2.20113i | ||||
\(388\) | 3.53553 | − | 6.12372i | 0.179490 | − | 0.310885i | ||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9706 | −0.858238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | 1.00000 | + | 1.73205i | 0.0503793 | + | 0.0872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | − | 4.33013i | 0.125630 | − | 0.217597i | ||||
\(397\) | −12.7279 | − | 22.0454i | −0.638796 | − | 1.10643i | −0.985697 | − | 0.168526i | \(-0.946099\pi\) |
0.346901 | − | 0.937902i | \(-0.387234\pi\) | |||||||
\(398\) | 9.89949 | 0.496217 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 15.0000 | + | 25.9808i | 0.749064 | + | 1.29742i | 0.948272 | + | 0.317460i | \(0.102830\pi\) |
−0.199207 | + | 0.979957i | \(0.563837\pi\) | |||||||
\(402\) | −11.3137 | + | 19.5959i | −0.564276 | + | 0.977356i | ||||
\(403\) | 15.0000 | − | 25.9808i | 0.747203 | − | 1.29419i | ||||
\(404\) | 0.707107 | + | 1.22474i | 0.0351799 | + | 0.0609333i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 4.00000 | + | 6.92820i | 0.198030 | + | 0.342997i | ||||
\(409\) | −14.1421 | + | 24.4949i | −0.699284 | + | 1.21119i | 0.269432 | + | 0.963020i | \(0.413164\pi\) |
−0.968715 | + | 0.248175i | \(0.920169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.48528 | + | 14.6969i | 0.418548 | + | 0.724947i | ||||
\(412\) | −1.41421 | −0.0696733 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 30.0000 | 1.47442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.12132 | + | 3.67423i | −0.104006 | + | 0.180144i | ||||
\(417\) | −26.0000 | + | 45.0333i | −1.27323 | + | 2.20529i | ||||
\(418\) | −2.12132 | − | 3.67423i | −0.103757 | − | 0.179713i | ||||
\(419\) | 14.1421 | 0.690889 | 0.345444 | − | 0.938439i | \(-0.387728\pi\) | ||||
0.345444 | + | 0.938439i | \(0.387728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | −13.0000 | − | 22.5167i | −0.632830 | − | 1.09609i | ||||
\(423\) | 31.8198 | − | 55.1135i | 1.54713 | − | 2.67971i | ||||
\(424\) | −1.00000 | + | 1.73205i | −0.0485643 | + | 0.0841158i | ||||
\(425\) | −7.07107 | − | 12.2474i | −0.342997 | − | 0.594089i | ||||
\(426\) | 45.2548 | 2.19260 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.0000 | −0.676716 | ||||||||
\(429\) | 6.00000 | + | 10.3923i | 0.289683 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.00000 | + | 6.92820i | −0.192673 | + | 0.333720i | −0.946135 | − | 0.323772i | \(-0.895049\pi\) |
0.753462 | + | 0.657491i | \(0.228382\pi\) | |||||||
\(432\) | −2.82843 | − | 4.89898i | −0.136083 | − | 0.235702i | ||||
\(433\) | 29.6985 | 1.42722 | 0.713609 | − | 0.700544i | \(-0.247059\pi\) | ||||
0.713609 | + | 0.700544i | \(0.247059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.00000 | + | 12.1244i | 0.335239 | + | 0.580651i | ||||
\(437\) | 12.7279 | − | 22.0454i | 0.608859 | − | 1.05457i | ||||
\(438\) | 12.0000 | − | 20.7846i | 0.573382 | − | 0.993127i | ||||
\(439\) | −12.7279 | − | 22.0454i | −0.607471 | − | 1.05217i | −0.991656 | − | 0.128914i | \(-0.958851\pi\) |
0.384185 | − | 0.923256i | \(-0.374482\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | −2.82843 | + | 4.89898i | −0.134231 | + | 0.232495i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.6066 | − | 18.3712i | −0.502237 | − | 0.869900i | ||||
\(447\) | 22.6274 | 1.07024 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | 12.5000 | + | 21.6506i | 0.589256 | + | 1.02062i | ||||
\(451\) | 1.41421 | − | 2.44949i | 0.0665927 | − | 0.115342i | ||||
\(452\) | −8.00000 | + | 13.8564i | −0.376288 | + | 0.651751i | ||||
\(453\) | 11.3137 | + | 19.5959i | 0.531564 | + | 0.920697i | ||||
\(454\) | −7.07107 | −0.331862 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | 11.0000 | + | 19.0526i | 0.514558 | + | 0.891241i | 0.999857 | + | 0.0168929i | \(0.00537742\pi\) |
−0.485299 | + | 0.874348i | \(0.661289\pi\) | |||||||
\(458\) | 11.3137 | − | 19.5959i | 0.528655 | − | 0.915657i | ||||
\(459\) | 8.00000 | − | 13.8564i | 0.373408 | − | 0.646762i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41421 | 0.0658665 | 0.0329332 | − | 0.999458i | \(-0.489515\pi\) | ||||
0.0329332 | + | 0.999458i | \(0.489515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 2.00000 | + | 3.46410i | 0.0928477 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0000 | + | 22.5167i | −0.602213 | + | 1.04306i | ||||
\(467\) | −12.7279 | − | 22.0454i | −0.588978 | − | 1.02014i | −0.994367 | − | 0.105995i | \(-0.966197\pi\) |
0.405389 | − | 0.914144i | \(-0.367136\pi\) | |||||||
\(468\) | 21.2132 | 0.980581 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0000 | − | 20.7846i | −0.552931 | − | 0.957704i | ||||
\(472\) | −5.65685 | + | 9.79796i | −0.260378 | + | 0.450988i | ||||
\(473\) | 5.00000 | − | 8.66025i | 0.229900 | − | 0.398199i | ||||
\(474\) | 11.3137 | + | 19.5959i | 0.519656 | + | 0.900070i | ||||
\(475\) | 21.2132 | 0.973329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1421 | − | 24.4949i | 0.646171 | − | 1.11920i | −0.337859 | − | 0.941197i | \(-0.609703\pi\) |
0.984030 | − | 0.178004i | \(-0.0569639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.24264 | − | 7.34847i | −0.193448 | − | 0.335061i | ||||
\(482\) | −8.48528 | −0.386494 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.07107 | − | 12.2474i | 0.320750 | − | 0.555556i | ||||
\(487\) | −19.0000 | + | 32.9090i | −0.860972 | + | 1.49125i | 0.0100195 | + | 0.999950i | \(0.496811\pi\) |
−0.870992 | + | 0.491298i | \(0.836523\pi\) | |||||||
\(488\) | 4.94975 | + | 8.57321i | 0.224065 | + | 0.388091i | ||||
\(489\) | −11.3137 | −0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −4.00000 | − | 6.92820i | −0.180334 | − | 0.312348i | ||||
\(493\) | −5.65685 | + | 9.79796i | −0.254772 | + | 0.441278i | ||||
\(494\) | 9.00000 | − | 15.5885i | 0.404929 | − | 0.701358i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.07107 | −0.317500 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −36.0000 | −1.61320 | ||||||||
\(499\) | −18.0000 | − | 31.1769i | −0.805791 | − | 1.39567i | −0.915756 | − | 0.401735i | \(-0.868407\pi\) |
0.109965 | − | 0.993935i | \(-0.464926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0000 | − | 34.6410i | 0.893534 | − | 1.54765i | ||||
\(502\) | 2.82843 | + | 4.89898i | 0.126239 | + | 0.218652i | ||||
\(503\) | 19.7990 | 0.882793 | 0.441397 | − | 0.897312i | \(-0.354483\pi\) | ||||
0.441397 | + | 0.897312i | \(0.354483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −7.07107 | + | 12.2474i | −0.314037 | + | 0.543928i | ||||
\(508\) | 10.0000 | − | 17.3205i | 0.443678 | − | 0.768473i | ||||
\(509\) | −8.48528 | − | 14.6969i | −0.376103 | − | 0.651430i | 0.614388 | − | 0.789004i | \(-0.289403\pi\) |
−0.990492 | + | 0.137574i | \(0.956070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.0000 | + | 20.7846i | 0.529813 | + | 0.917663i | ||||
\(514\) | −3.53553 | + | 6.12372i | −0.155946 | + | 0.270106i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.1421 | − | 24.4949i | −0.622573 | − | 1.07833i | ||||
\(517\) | 12.7279 | 0.559773 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.0000 | 0.877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.707107 | − | 1.22474i | 0.0309789 | − | 0.0536570i | −0.850120 | − | 0.526589i | \(-0.823471\pi\) |
0.881099 | + | 0.472931i | \(0.156804\pi\) | |||||||
\(522\) | 10.0000 | − | 17.3205i | 0.437688 | − | 0.758098i | ||||
\(523\) | −2.12132 | − | 3.67423i | −0.0927589 | − | 0.160663i | 0.815912 | − | 0.578176i | \(-0.196235\pi\) |
−0.908671 | + | 0.417513i | \(0.862902\pi\) | |||||||
\(524\) | 7.07107 | 0.308901 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.00000 | 0.174408 | ||||||||
\(527\) | −10.0000 | − | 17.3205i | −0.435607 | − | 0.754493i | ||||
\(528\) | 1.41421 | − | 2.44949i | 0.0615457 | − | 0.106600i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 56.5685 | 2.45487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | −10.0000 | − | 17.3205i | −0.432742 | − | 0.749532i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | + | 6.92820i | −0.172774 | + | 0.299253i | ||||
\(537\) | 16.9706 | + | 29.3939i | 0.732334 | + | 1.26844i | ||||
\(538\) | 11.3137 | 0.487769 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | + | 25.9808i | 0.644900 | + | 1.11700i | 0.984325 | + | 0.176367i | \(0.0564345\pi\) |
−0.339424 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(542\) | −4.24264 | + | 7.34847i | −0.182237 | + | 0.315644i | ||||
\(543\) | −16.0000 | + | 27.7128i | −0.686626 | + | 1.18927i | ||||
\(544\) | 1.41421 | + | 2.44949i | 0.0606339 | + | 0.105021i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | 24.7487 | − | 42.8661i | 1.05625 | − | 1.82948i | ||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | −8.48528 | − | 14.6969i | −0.361485 | − | 0.626111i | ||||
\(552\) | 16.9706 | 0.722315 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.19239 | + | 15.9217i | −0.389844 | + | 0.675230i | ||||
\(557\) | 3.00000 | − | 5.19615i | 0.127114 | − | 0.220168i | −0.795443 | − | 0.606028i | \(-0.792762\pi\) |
0.922557 | + | 0.385860i | \(0.126095\pi\) | |||||||
\(558\) | 17.6777 | + | 30.6186i | 0.748355 | + | 1.29619i | ||||
\(559\) | 42.4264 | 1.79445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | −11.0000 | − | 19.0526i | −0.464007 | − | 0.803684i | ||||
\(563\) | −20.5061 | + | 35.5176i | −0.864229 | + | 1.49689i | 0.00358183 | + | 0.999994i | \(0.498860\pi\) |
−0.867811 | + | 0.496895i | \(0.834473\pi\) | |||||||
\(564\) | 18.0000 | − | 31.1769i | 0.757937 | − | 1.31278i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.07107 | 0.297219 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0000 | 0.671345 | ||||||||
\(569\) | −21.0000 | − | 36.3731i | −0.880366 | − | 1.52484i | −0.850935 | − | 0.525271i | \(-0.823964\pi\) |
−0.0294311 | − | 0.999567i | \(-0.509370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 2.12132 | + | 3.67423i | 0.0886969 | + | 0.153627i | ||||
\(573\) | 28.2843 | 1.18159 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.0000 | −1.25109 | ||||||||
\(576\) | −2.50000 | − | 4.33013i | −0.104167 | − | 0.180422i | ||||
\(577\) | 4.94975 | − | 8.57321i | 0.206061 | − | 0.356908i | −0.744409 | − | 0.667723i | \(-0.767269\pi\) |
0.950470 | + | 0.310816i | \(0.100602\pi\) | |||||||
\(578\) | 4.50000 | − | 7.79423i | 0.187175 | − | 0.324197i | ||||
\(579\) | −8.48528 | − | 14.6969i | −0.352636 | − | 0.610784i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −20.0000 | −0.829027 | ||||||||
\(583\) | 1.00000 | + | 1.73205i | 0.0414158 | + | 0.0717342i | ||||
\(584\) | 4.24264 | − | 7.34847i | 0.175562 | − | 0.304082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6066 | + | 18.3712i | 0.438155 | + | 0.758906i | ||||
\(587\) | 5.65685 | 0.233483 | 0.116742 | − | 0.993162i | \(-0.462755\pi\) | ||||
0.116742 | + | 0.993162i | \(0.462755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.0000 | 1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.82843 | − | 4.89898i | 0.116346 | − | 0.201517i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | −4.24264 | − | 7.34847i | −0.174224 | − | 0.301765i | 0.765668 | − | 0.643236i | \(-0.222408\pi\) |
−0.939893 | + | 0.341470i | \(0.889075\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.00000 | 0.327693 | ||||||||
\(597\) | −14.0000 | − | 24.2487i | −0.572982 | − | 0.992434i | ||||
\(598\) | −12.7279 | + | 22.0454i | −0.520483 | + | 0.901504i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 7.07107 | + | 12.2474i | 0.288675 | + | 0.500000i | ||||
\(601\) | 11.3137 | 0.461496 | 0.230748 | − | 0.973014i | \(-0.425883\pi\) | ||||
0.230748 | + | 0.973014i | \(0.425883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.0000 | 1.62893 | ||||||||
\(604\) | 4.00000 | + | 6.92820i | 0.162758 | + | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.00000 | − | 3.46410i | 0.0812444 | − | 0.140720i | ||||
\(607\) | 8.48528 | + | 14.6969i | 0.344407 | + | 0.596530i | 0.985246 | − | 0.171145i | \(-0.0547467\pi\) |
−0.640839 | + | 0.767675i | \(0.721413\pi\) | |||||||
\(608\) | −4.24264 | −0.172062 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.0000 | + | 46.7654i | 1.09230 | + | 1.89192i | ||||
\(612\) | 7.07107 | − | 12.2474i | 0.285831 | − | 0.495074i | ||||
\(613\) | 8.00000 | − | 13.8564i | 0.323117 | − | 0.559655i | −0.658012 | − | 0.753007i | \(-0.728603\pi\) |
0.981129 | + | 0.193352i | \(0.0619359\pi\) | |||||||
\(614\) | −10.6066 | − | 18.3712i | −0.428048 | − | 0.741400i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.0000 | 1.12724 | 0.563619 | − | 0.826035i | \(-0.309409\pi\) | ||||
0.563619 | + | 0.826035i | \(0.309409\pi\) | |||||||
\(618\) | 2.00000 | + | 3.46410i | 0.0804518 | + | 0.139347i | ||||
\(619\) | 7.07107 | − | 12.2474i | 0.284210 | − | 0.492267i | −0.688207 | − | 0.725514i | \(-0.741602\pi\) |
0.972417 | + | 0.233248i | \(0.0749353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.9706 | − | 29.3939i | −0.681005 | − | 1.17954i | ||||
\(622\) | −1.41421 | −0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 12.0000 | 0.480384 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 14.8492 | − | 25.7196i | 0.593495 | − | 1.02796i | ||||
\(627\) | −6.00000 | + | 10.3923i | −0.239617 | + | 0.415029i | ||||
\(628\) | −4.24264 | − | 7.34847i | −0.169300 | − | 0.293236i | ||||
\(629\) | −5.65685 | −0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0000 | −1.19428 | −0.597141 | − | 0.802137i | \(-0.703697\pi\) | ||||
−0.597141 | + | 0.802137i | \(0.703697\pi\) | |||||||
\(632\) | 4.00000 | + | 6.92820i | 0.159111 | + | 0.275589i | ||||
\(633\) | −36.7696 | + | 63.6867i | −1.46146 | + | 2.53132i | ||||
\(634\) | −9.00000 | + | 15.5885i | −0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.65685 | 0.224309 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.00000 | 0.158362 | ||||||||
\(639\) | −40.0000 | − | 69.2820i | −1.58238 | − | 2.74075i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.0000 | + | 38.1051i | −0.868948 | + | 1.50506i | −0.00587459 | + | 0.999983i | \(0.501870\pi\) |
−0.863073 | + | 0.505079i | \(0.831463\pi\) | |||||||
\(642\) | 19.7990 | + | 34.2929i | 0.781404 | + | 1.35343i | ||||
\(643\) | −33.9411 | −1.33851 | −0.669254 | − | 0.743034i | \(-0.733386\pi\) | ||||
−0.669254 | + | 0.743034i | \(0.733386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | −16.2635 | + | 28.1691i | −0.639382 | + | 1.10744i | 0.346186 | + | 0.938166i | \(0.387477\pi\) |
−0.985569 | + | 0.169277i | \(0.945857\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 5.65685 | + | 9.79796i | 0.222051 | + | 0.384604i | ||||
\(650\) | −21.2132 | −0.832050 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | 19.7990 | − | 34.2929i | 0.774202 | − | 1.34096i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.41421 | − | 2.44949i | −0.0552158 | − | 0.0956365i | ||||
\(657\) | −42.4264 | −1.65521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.0000 | 1.16863 | 0.584317 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584317 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.48528 | − | 14.6969i | 0.330039 | − | 0.571645i | −0.652480 | − | 0.757806i | \(-0.726271\pi\) |
0.982519 | + | 0.186161i | \(0.0596047\pi\) | |||||||
\(662\) | −4.00000 | + | 6.92820i | −0.155464 | + | 0.269272i | ||||
\(663\) | 16.9706 | + | 29.3939i | 0.659082 | + | 1.14156i | ||||
\(664\) | −12.7279 | −0.493939 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.0000 | 0.387492 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 7.07107 | − | 12.2474i | 0.273588 | − | 0.473868i | ||||
\(669\) | −30.0000 | + | 51.9615i | −1.15987 | + | 2.00895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.89949 | 0.382166 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0000 | −1.77317 | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | 11.0000 | + | 19.0526i | 0.423704 | + | 0.733877i | ||||
\(675\) | 14.1421 | − | 24.4949i | 0.544331 | − | 0.942809i | ||||
\(676\) | −2.50000 | + | 4.33013i | −0.0961538 | + | 0.166543i | ||||
\(677\) | −4.94975 | − | 8.57321i | −0.190234 | − | 0.329495i | 0.755094 | − | 0.655617i | \(-0.227591\pi\) |
−0.945328 | + | 0.326122i | \(0.894258\pi\) | |||||||
\(678\) | 45.2548 | 1.73800 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | + | 17.3205i | 0.383201 | + | 0.663723i | ||||
\(682\) | −3.53553 | + | 6.12372i | −0.135383 | + | 0.234490i | ||||
\(683\) | −16.0000 | + | 27.7128i | −0.612223 | + | 1.06040i | 0.378642 | + | 0.925543i | \(0.376391\pi\) |
−0.990865 | + | 0.134858i | \(0.956942\pi\) | |||||||
\(684\) | 10.6066 | + | 18.3712i | 0.405554 | + | 0.702439i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −64.0000 | −2.44175 | ||||||||
\(688\) | −5.00000 | − | 8.66025i | −0.190623 | − | 0.330169i | ||||
\(689\) | −4.24264 | + | 7.34847i | −0.161632 | + | 0.279954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7990 | − | 34.2929i | −0.753189 | − | 1.30456i | −0.946270 | − | 0.323379i | \(-0.895181\pi\) |
0.193081 | − | 0.981183i | \(-0.438152\pi\) | |||||||
\(692\) | 7.07107 | 0.268802 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.0000 | 0.986947 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.65685 | − | 9.79796i | 0.214423 | − | 0.371391i | ||||
\(697\) | 4.00000 | − | 6.92820i | 0.151511 | − | 0.262424i | ||||
\(698\) | 13.4350 | + | 23.2702i | 0.508523 | + | 0.880788i | ||||
\(699\) | 73.5391 | 2.78150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | −12.0000 | − | 20.7846i | −0.452911 | − | 0.784465i | ||||
\(703\) | 4.24264 | − | 7.34847i | 0.160014 | − | 0.277153i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.5563 | 0.585471 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 32.0000 | 1.20263 | ||||||||
\(709\) | 19.0000 | + | 32.9090i | 0.713560 | + | 1.23592i | 0.963512 | + | 0.267664i | \(0.0862517\pi\) |
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.0000 | − | 34.6410i | 0.750059 | − | 1.29914i | ||||
\(712\) | −3.53553 | − | 6.12372i | −0.132500 | − | 0.229496i | ||||
\(713\) | −42.4264 | −1.58888 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | −16.2635 | − | 28.1691i | −0.606525 | − | 1.05053i | −0.991809 | − | 0.127733i | \(-0.959230\pi\) |
0.385284 | − | 0.922798i | \(-0.374103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 12.0000 | + | 20.7846i | 0.446285 | + | 0.772988i | ||||
\(724\) | −5.65685 | + | 9.79796i | −0.210235 | + | 0.364138i | ||||
\(725\) | −10.0000 | + | 17.3205i | −0.371391 | + | 0.643268i | ||||
\(726\) | −1.41421 | − | 2.44949i | −0.0524864 | − | 0.0909091i | ||||
\(727\) | −46.6690 | −1.73086 | −0.865430 | − | 0.501031i | \(-0.832954\pi\) | ||||
−0.865430 | + | 0.501031i | \(0.832954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1421 | − | 24.4949i | 0.523066 | − | 0.905977i | ||||
\(732\) | 14.0000 | − | 24.2487i | 0.517455 | − | 0.896258i | ||||
\(733\) | −3.53553 | − | 6.12372i | −0.130588 | − | 0.226185i | 0.793315 | − | 0.608811i | \(-0.208353\pi\) |
−0.923903 | + | 0.382626i | \(0.875020\pi\) | |||||||
\(734\) | −21.2132 | −0.782994 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 4.00000 | + | 6.92820i | 0.147342 | + | 0.255204i | ||||
\(738\) | −7.07107 | + | 12.2474i | −0.260290 | + | 0.450835i | ||||
\(739\) | 6.00000 | − | 10.3923i | 0.220714 | − | 0.382287i | −0.734311 | − | 0.678813i | \(-0.762495\pi\) |
0.955025 | + | 0.296526i | \(0.0958281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.9117 | −1.87029 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.00000 | −0.293492 | −0.146746 | − | 0.989174i | \(-0.546880\pi\) | ||||
−0.146746 | + | 0.989174i | \(0.546880\pi\) | |||||||
\(744\) | 10.0000 | + | 17.3205i | 0.366618 | + | 0.635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.00000 | − | 8.66025i | 0.183063 | − | 0.317074i | ||||
\(747\) | 31.8198 | + | 55.1135i | 1.16423 | + | 2.01650i | ||||
\(748\) | 2.82843 | 0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | + | 1.73205i | 0.0364905 | + | 0.0632034i | 0.883694 | − | 0.468065i | \(-0.155049\pi\) |
−0.847203 | + | 0.531269i | \(0.821715\pi\) | |||||||
\(752\) | 6.36396 | − | 11.0227i | 0.232070 | − | 0.401957i | ||||
\(753\) | 8.00000 | − | 13.8564i | 0.291536 | − | 0.504956i | ||||
\(754\) | 8.48528 | + | 14.6969i | 0.309016 | + | 0.535231i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.0000 | 1.67190 | 0.835949 | − | 0.548807i | \(-0.184918\pi\) | ||||
0.835949 | + | 0.548807i | \(0.184918\pi\) | |||||||
\(758\) | −12.0000 | − | 20.7846i | −0.435860 | − | 0.754931i | ||||
\(759\) | 8.48528 | − | 14.6969i | 0.307996 | − | 0.533465i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9706 | + | 29.3939i | 0.615182 | + | 1.06553i | 0.990352 | + | 0.138571i | \(0.0442510\pi\) |
−0.375170 | + | 0.926956i | \(0.622416\pi\) | |||||||
\(762\) | −56.5685 | −2.04926 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.0000 | 0.361787 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.77817 | − | 13.4722i | 0.281037 | − | 0.486770i | ||||
\(767\) | −24.0000 | + | 41.5692i | −0.866590 | + | 1.50098i | ||||
\(768\) | −1.41421 | − | 2.44949i | −0.0510310 | − | 0.0883883i | ||||
\(769\) | 5.65685 | 0.203991 | 0.101996 | − | 0.994785i | \(-0.467477\pi\) | ||||
0.101996 | + | 0.994785i | \(0.467477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | 0.720282 | ||||||||
\(772\) | −3.00000 | − | 5.19615i | −0.107972 | − | 0.187014i | ||||
\(773\) | 24.0416 | − | 41.6413i | 0.864717 | − | 1.49773i | −0.00261021 | − | 0.999997i | \(-0.500831\pi\) |
0.867328 | − | 0.497738i | \(-0.165836\pi\) | |||||||
\(774\) | −25.0000 | + | 43.3013i | −0.898606 | + | 1.55643i | ||||
\(775\) | −17.6777 | − | 30.6186i | −0.635001 | − | 1.09985i | ||||
\(776\) | −7.07107 | −0.253837 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | − | 13.8564i | 0.286263 | − | 0.495821i | ||||
\(782\) | 8.48528 | + | 14.6969i | 0.303433 | + | 0.525561i | ||||
\(783\) | −22.6274 |