Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(251,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.251 |
Dual form | 525.2.b.j.251.8 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.73205i | − | 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 1.41421 | − | 1.00000i | 0.816497 | − | 0.577350i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.73205 | − | 2.44949i | −0.707107 | − | 1.00000i | ||||
\(7\) | −2.44949 | − | 1.00000i | −0.925820 | − | 0.377964i | ||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | −1.41421 | + | 1.00000i | −0.408248 | + | 0.288675i | ||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −1.73205 | + | 4.24264i | −0.462910 | + | 1.13389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | −4.89898 | − | 1.73205i | −1.15470 | − | 0.408248i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.46410 | + | 1.03528i | −0.974147 | + | 0.225916i | ||||
\(22\) | 4.89898 | 1.04447 | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | −1.73205 | − | 2.44949i | −0.353553 | − | 0.500000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.92820 | −1.35873 | ||||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | 2.44949 | + | 1.00000i | 0.462910 | + | 0.188982i | ||||
\(29\) | 5.65685i | 1.05045i | 0.850963 | + | 0.525226i | \(0.176019\pi\) | ||||
−0.850963 | + | 0.525226i | \(0.823981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.79796i | − | 1.75977i | −0.475191 | − | 0.879883i | \(-0.657621\pi\) | ||
0.475191 | − | 0.879883i | \(-0.342379\pi\) | |||||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | 2.82843 | + | 4.00000i | 0.492366 | + | 0.696311i | ||||
\(34\) | − | 4.89898i | − | 0.840168i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.00000 | − | 5.65685i | −0.640513 | − | 0.905822i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 1.79315 | + | 7.73205i | 0.276689 | + | 1.19308i | ||||
\(43\) | 4.89898 | 0.747087 | 0.373544 | − | 0.927613i | \(-0.378143\pi\) | ||||
0.373544 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.426401i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | −7.07107 | + | 5.00000i | −1.02062 | + | 0.721688i | ||||
\(49\) | 5.00000 | + | 4.89898i | 0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | − | 2.82843i | 0.560112 | − | 0.396059i | ||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −8.66025 | + | 2.44949i | −1.17851 | + | 0.333333i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73205 | + | 4.24264i | −0.231455 | + | 0.566947i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.79796 | 1.28654 | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.79796i | 1.25450i | 0.778818 | + | 0.627250i | \(0.215820\pi\) | ||||
−0.778818 | + | 0.627250i | \(0.784180\pi\) | |||||||
\(62\) | −16.9706 | −2.15526 | ||||||||
\(63\) | −5.27792 | + | 5.92820i | −0.664955 | + | 0.746883i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.92820 | − | 4.89898i | 0.852803 | − | 0.603023i | ||||
\(67\) | 4.89898 | 0.598506 | 0.299253 | − | 0.954174i | \(-0.403263\pi\) | ||||
0.299253 | + | 0.954174i | \(0.403263\pi\) | |||||||
\(68\) | −2.82843 | −0.342997 | ||||||||
\(69\) | 3.46410 | + | 4.89898i | 0.417029 | + | 0.589768i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | −4.89898 | − | 1.73205i | −0.577350 | − | 0.204124i | ||||
\(73\) | 8.00000i | 0.936329i | 0.883641 | + | 0.468165i | \(0.155085\pi\) | ||||
−0.883641 | + | 0.468165i | \(0.844915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82843 | − | 6.92820i | 0.322329 | − | 0.789542i | ||||
\(78\) | −9.79796 | + | 6.92820i | −1.10940 | + | 0.784465i | ||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | − | 6.00000i | − | 0.662589i | ||||||
\(83\) | −2.82843 | −0.310460 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | 4.46410 | − | 1.03528i | 0.487073 | − | 0.112958i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.48528i | − | 0.914991i | ||||||
\(87\) | 5.65685 | + | 8.00000i | 0.606478 | + | 0.857690i | ||||
\(88\) | 4.89898 | 0.522233 | ||||||||
\(89\) | 10.3923 | 1.10158 | 0.550791 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550791 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 9.79796i | −0.419314 | + | 1.02711i | ||||
\(92\) | − | 3.46410i | − | 0.361158i | ||||||
\(93\) | −9.79796 | − | 13.8564i | −1.01600 | − | 1.43684i | ||||
\(94\) | − | 4.89898i | − | 0.505291i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.19615 | + | 7.34847i | 0.530330 | + | 0.750000i | ||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 8.48528 | − | 8.66025i | 0.857143 | − | 0.874818i | ||||
\(99\) | 8.00000 | + | 2.82843i | 0.804030 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3205 | 1.72345 | 0.861727 | − | 0.507371i | \(-0.169383\pi\) | ||||
0.861727 | + | 0.507371i | \(0.169383\pi\) | |||||||
\(102\) | −4.89898 | − | 6.92820i | −0.485071 | − | 0.685994i | ||||
\(103\) | − | 10.0000i | − | 0.985329i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||
0.870219 | − | 0.492665i | \(-0.163977\pi\) | |||||||
\(104\) | −6.92820 | −0.679366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 1.41421 | + | 5.00000i | 0.136083 | + | 0.481125i | ||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.2474 | + | 5.00000i | 1.15728 | + | 0.472456i | ||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 5.65685i | − | 0.525226i | ||||||
\(117\) | −11.3137 | − | 4.00000i | −1.04595 | − | 0.369800i | ||||
\(118\) | − | 12.0000i | − | 1.10469i | ||||||
\(119\) | −6.92820 | − | 2.82843i | −0.635107 | − | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 16.9706 | 1.53644 | ||||||||
\(123\) | 4.89898 | − | 3.46410i | 0.441726 | − | 0.312348i | ||||
\(124\) | 9.79796i | 0.879883i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.2679 | + | 9.14162i | 0.914742 | + | 0.814400i | ||||
\(127\) | −14.6969 | −1.30414 | −0.652071 | − | 0.758158i | \(-0.726100\pi\) | ||||
−0.652071 | + | 0.758158i | \(0.726100\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | 6.92820 | − | 4.89898i | 0.609994 | − | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92820 | −0.605320 | −0.302660 | − | 0.953099i | \(-0.597875\pi\) | ||||
−0.302660 | + | 0.953099i | \(0.597875\pi\) | |||||||
\(132\) | −2.82843 | − | 4.00000i | −0.246183 | − | 0.348155i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.48528i | − | 0.733017i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 4.89898i | − | 0.420084i | ||||||
\(137\) | − | 6.92820i | − | 0.591916i | −0.955201 | − | 0.295958i | \(-0.904361\pi\) | ||
0.955201 | − | 0.295958i | \(-0.0956389\pi\) | |||||||
\(138\) | 8.48528 | − | 6.00000i | 0.722315 | − | 0.510754i | ||||
\(139\) | 9.79796i | 0.831052i | 0.909581 | + | 0.415526i | \(0.136402\pi\) | ||||
−0.909581 | + | 0.415526i | \(0.863598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | − | 2.82843i | 0.336861 | − | 0.238197i | ||||
\(142\) | 4.89898 | 0.411113 | ||||||||
\(143\) | 11.3137 | 0.946100 | ||||||||
\(144\) | −5.00000 | + | 14.1421i | −0.416667 | + | 1.17851i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.8564 | 1.14676 | ||||||||
\(147\) | 11.9700 | + | 1.92820i | 0.987273 | + | 0.159036i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.3137i | − | 0.926855i | −0.886135 | − | 0.463428i | \(-0.846619\pi\) | ||
0.886135 | − | 0.463428i | \(-0.153381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | − | 8.00000i | 0.228665 | − | 0.646762i | ||||
\(154\) | −12.0000 | − | 4.89898i | −0.966988 | − | 0.394771i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.00000 | + | 5.65685i | 0.320256 | + | 0.452911i | ||||
\(157\) | 4.00000i | 0.319235i | 0.987179 | + | 0.159617i | \(0.0510260\pi\) | ||||
−0.987179 | + | 0.159617i | \(0.948974\pi\) | |||||||
\(158\) | 13.8564i | 1.10236i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | − | 8.48528i | 0.273009 | − | 0.668734i | ||||
\(162\) | −9.79796 | + | 12.1244i | −0.769800 | + | 0.952579i | ||||
\(163\) | −14.6969 | −1.15115 | −0.575577 | − | 0.817748i | \(-0.695222\pi\) | ||||
−0.575577 | + | 0.817748i | \(0.695222\pi\) | |||||||
\(164\) | −3.46410 | −0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.89898i | 0.380235i | ||||||||
\(167\) | −14.1421 | −1.09435 | −0.547176 | − | 0.837018i | \(-0.684297\pi\) | ||||
−0.547176 | + | 0.837018i | \(0.684297\pi\) | |||||||
\(168\) | 1.79315 | + | 7.73205i | 0.138345 | + | 0.596541i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.89898 | −0.373544 | ||||||||
\(173\) | −19.7990 | −1.50529 | −0.752645 | − | 0.658427i | \(-0.771222\pi\) | ||||
−0.752645 | + | 0.658427i | \(0.771222\pi\) | |||||||
\(174\) | 13.8564 | − | 9.79796i | 1.05045 | − | 0.742781i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 14.1421i | − | 1.06600i | ||||||
\(177\) | 9.79796 | − | 6.92820i | 0.736460 | − | 0.520756i | ||||
\(178\) | − | 18.0000i | − | 1.34916i | ||||||
\(179\) | − | 2.82843i | − | 0.211407i | −0.994398 | − | 0.105703i | \(-0.966291\pi\) | ||
0.994398 | − | 0.105703i | \(-0.0337094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 16.9706 | + | 6.92820i | 1.25794 | + | 0.513553i | ||||
\(183\) | 9.79796 | + | 13.8564i | 0.724286 | + | 1.02430i | ||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −24.0000 | + | 16.9706i | −1.75977 | + | 1.24434i | ||||
\(187\) | 8.00000i | 0.585018i | ||||||||
\(188\) | −2.82843 | −0.206284 | ||||||||
\(189\) | −1.53590 | + | 13.6617i | −0.111720 | + | 0.993740i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7990i | 1.43260i | 0.697790 | + | 0.716302i | \(0.254167\pi\) | ||||
−0.697790 | + | 0.716302i | \(0.745833\pi\) | |||||||
\(192\) | −1.41421 | + | 1.00000i | −0.102062 | + | 0.0721688i | ||||
\(193\) | 9.79796 | 0.705273 | 0.352636 | − | 0.935760i | \(-0.385285\pi\) | ||||
0.352636 | + | 0.935760i | \(0.385285\pi\) | |||||||
\(194\) | −13.8564 | −0.994832 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | − | 4.89898i | −0.357143 | − | 0.349927i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 4.89898 | − | 13.8564i | 0.348155 | − | 0.984732i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.92820 | − | 4.89898i | 0.488678 | − | 0.345547i | ||||
\(202\) | − | 30.0000i | − | 2.11079i | ||||||
\(203\) | 5.65685 | − | 13.8564i | 0.397033 | − | 0.972529i | ||||
\(204\) | −4.00000 | + | 2.82843i | −0.280056 | + | 0.198030i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −17.3205 | −1.20678 | ||||||||
\(207\) | 9.79796 | + | 3.46410i | 0.681005 | + | 0.240772i | ||||
\(208\) | 20.0000i | 1.38675i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.82843 | + | 4.00000i | 0.193801 | + | 0.274075i | ||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.66025 | + | 2.44949i | −0.589256 | + | 0.166667i | ||||
\(217\) | −9.79796 | + | 24.0000i | −0.665129 | + | 1.62923i | ||||
\(218\) | − | 17.3205i | − | 1.17309i | ||||||
\(219\) | 8.00000 | + | 11.3137i | 0.540590 | + | 0.764510i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.3137i | − | 0.761042i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.0000i | 1.74109i | 0.492090 | + | 0.870544i | \(0.336233\pi\) | ||||
−0.492090 | + | 0.870544i | \(0.663767\pi\) | |||||||
\(224\) | 5.19615 | − | 12.7279i | 0.347183 | − | 0.850420i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | 2.82843 | 0.187729 | 0.0938647 | − | 0.995585i | \(-0.470078\pi\) | ||||
0.0938647 | + | 0.995585i | \(0.470078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.5959i | − | 1.29493i | −0.762093 | − | 0.647467i | \(-0.775828\pi\) | ||
0.762093 | − | 0.647467i | \(-0.224172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92820 | − | 12.6264i | −0.192662 | − | 0.830755i | ||||
\(232\) | 9.79796 | 0.643268 | ||||||||
\(233\) | 20.7846i | 1.36165i | 0.732448 | + | 0.680823i | \(0.238378\pi\) | ||||
−0.732448 | + | 0.680823i | \(0.761622\pi\) | |||||||
\(234\) | −6.92820 | + | 19.5959i | −0.452911 | + | 1.28103i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.92820 | −0.450988 | ||||||||
\(237\) | −11.3137 | + | 8.00000i | −0.734904 | + | 0.519656i | ||||
\(238\) | −4.89898 | + | 12.0000i | −0.317554 | + | 0.777844i | ||||
\(239\) | − | 2.82843i | − | 0.182956i | −0.995807 | − | 0.0914779i | \(-0.970841\pi\) | ||
0.995807 | − | 0.0914779i | \(-0.0291591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.79796i | 0.631142i | 0.948902 | + | 0.315571i | \(0.102196\pi\) | ||||
−0.948902 | + | 0.315571i | \(0.897804\pi\) | |||||||
\(242\) | − | 5.19615i | − | 0.334021i | ||||||
\(243\) | −15.5563 | − | 1.00000i | −0.997940 | − | 0.0641500i | ||||
\(244\) | − | 9.79796i | − | 0.627250i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | − | 8.48528i | −0.382546 | − | 0.541002i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.9706 | −1.07763 | ||||||||
\(249\) | −4.00000 | + | 2.82843i | −0.253490 | + | 0.179244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.7846 | −1.31191 | −0.655956 | − | 0.754799i | \(-0.727735\pi\) | ||||
−0.655956 | + | 0.754799i | \(0.727735\pi\) | |||||||
\(252\) | 5.27792 | − | 5.92820i | 0.332478 | − | 0.373442i | ||||
\(253\) | −9.79796 | −0.615992 | ||||||||
\(254\) | 25.4558i | 1.59724i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −14.1421 | −0.882162 | −0.441081 | − | 0.897467i | \(-0.645405\pi\) | ||||
−0.441081 | + | 0.897467i | \(0.645405\pi\) | |||||||
\(258\) | −8.48528 | − | 12.0000i | −0.528271 | − | 0.747087i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.0000 | + | 5.65685i | 0.990375 | + | 0.350150i | ||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | − | 3.46410i | − | 0.213606i | −0.994280 | − | 0.106803i | \(-0.965939\pi\) | ||
0.994280 | − | 0.106803i | \(-0.0340614\pi\) | |||||||
\(264\) | 6.92820 | − | 4.89898i | 0.426401 | − | 0.301511i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6969 | − | 10.3923i | 0.899438 | − | 0.635999i | ||||
\(268\) | −4.89898 | −0.299253 | ||||||||
\(269\) | −10.3923 | −0.633630 | −0.316815 | − | 0.948487i | \(-0.602613\pi\) | ||||
−0.316815 | + | 0.948487i | \(0.602613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.3939i | − | 1.78555i | −0.450502 | − | 0.892775i | \(-0.648755\pi\) | ||
0.450502 | − | 0.892775i | \(-0.351245\pi\) | |||||||
\(272\) | −14.1421 | −0.857493 | ||||||||
\(273\) | 4.14110 | + | 17.8564i | 0.250631 | + | 1.08072i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.46410 | − | 4.89898i | −0.208514 | − | 0.294884i | ||||
\(277\) | −19.5959 | −1.17740 | −0.588702 | − | 0.808350i | \(-0.700361\pi\) | ||||
−0.588702 | + | 0.808350i | \(0.700361\pi\) | |||||||
\(278\) | 16.9706 | 1.01783 | ||||||||
\(279\) | −27.7128 | − | 9.79796i | −1.65912 | − | 0.586588i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.2843i | 1.68730i | 0.536895 | + | 0.843649i | \(0.319597\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | −4.89898 | − | 6.92820i | −0.291730 | − | 0.412568i | ||||
\(283\) | 14.0000i | 0.832214i | 0.909316 | + | 0.416107i | \(0.136606\pi\) | ||||
−0.909316 | + | 0.416107i | \(0.863394\pi\) | |||||||
\(284\) | − | 2.82843i | − | 0.167836i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 19.5959i | − | 1.15873i | ||||||
\(287\) | −8.48528 | − | 3.46410i | −0.500870 | − | 0.204479i | ||||
\(288\) | 14.6969 | + | 5.19615i | 0.866025 | + | 0.306186i | ||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00000 | − | 11.3137i | −0.468968 | − | 0.663221i | ||||
\(292\) | − | 8.00000i | − | 0.468165i | ||||||
\(293\) | −2.82843 | −0.165238 | −0.0826192 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826192 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(294\) | 3.33975 | − | 20.7327i | 0.194778 | − | 1.20916i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.1421 | − | 4.00000i | 0.820610 | − | 0.232104i | ||||
\(298\) | −19.5959 | −1.13516 | ||||||||
\(299\) | 13.8564 | 0.801337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | − | 4.89898i | −0.691669 | − | 0.282372i | ||||
\(302\) | − | 13.8564i | − | 0.797347i | ||||||
\(303\) | 24.4949 | − | 17.3205i | 1.40720 | − | 0.995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.8564 | − | 4.89898i | −0.792118 | − | 0.280056i | ||||
\(307\) | 10.0000i | 0.570730i | 0.958419 | + | 0.285365i | \(0.0921148\pi\) | ||||
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(308\) | −2.82843 | + | 6.92820i | −0.161165 | + | 0.394771i | ||||
\(309\) | −10.0000 | − | 14.1421i | −0.568880 | − | 0.804518i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.7128 | −1.57145 | −0.785725 | − | 0.618576i | \(-0.787710\pi\) | ||||
−0.785725 | + | 0.618576i | \(0.787710\pi\) | |||||||
\(312\) | −9.79796 | + | 6.92820i | −0.554700 | + | 0.392232i | ||||
\(313\) | − | 16.0000i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(314\) | 6.92820 | 0.390981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 13.8564i | 0.778253i | 0.921184 | + | 0.389127i | \(0.127223\pi\) | ||||
−0.921184 | + | 0.389127i | \(0.872777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0000 | −0.895828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3923 | + | 14.6969i | 0.580042 | + | 0.820303i | ||||
\(322\) | −14.6969 | − | 6.00000i | −0.819028 | − | 0.334367i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.00000 | + | 5.65685i | 0.388889 | + | 0.314270i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.4558i | 1.40987i | ||||||||
\(327\) | 14.1421 | − | 10.0000i | 0.782062 | − | 0.553001i | ||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | −6.92820 | − | 2.82843i | −0.381964 | − | 0.155936i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 2.82843 | 0.155230 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.4949i | 1.34030i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.3205 | − | 5.17638i | 1.21768 | − | 0.282395i | ||||
\(337\) | 19.5959 | 1.06746 | 0.533729 | − | 0.845656i | \(-0.320790\pi\) | ||||
0.533729 | + | 0.845656i | \(0.320790\pi\) | |||||||
\(338\) | 5.19615i | 0.282633i | ||||||||
\(339\) | −6.92820 | − | 9.79796i | −0.376288 | − | 0.532152i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7128 | 1.50073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | − | 17.0000i | −0.396780 | − | 0.917914i | ||||
\(344\) | − | 8.48528i | − | 0.457496i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.2929i | 1.84360i | ||||||||
\(347\) | 17.3205i | 0.929814i | 0.885360 | + | 0.464907i | \(0.153912\pi\) | ||||
−0.885360 | + | 0.464907i | \(0.846088\pi\) | |||||||
\(348\) | −5.65685 | − | 8.00000i | −0.303239 | − | 0.428845i | ||||
\(349\) | 19.5959i | 1.04895i | 0.851427 | + | 0.524473i | \(0.175738\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0000 | + | 5.65685i | −1.06752 | + | 0.301941i | ||||
\(352\) | −14.6969 | −0.783349 | ||||||||
\(353\) | 31.1127 | 1.65596 | 0.827981 | − | 0.560756i | \(-0.189490\pi\) | ||||
0.827981 | + | 0.560756i | \(0.189490\pi\) | |||||||
\(354\) | −12.0000 | − | 16.9706i | −0.637793 | − | 0.901975i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.3923 | −0.550791 | ||||||||
\(357\) | −12.6264 | + | 2.92820i | −0.668259 | + | 0.154977i | ||||
\(358\) | −4.89898 | −0.258919 | ||||||||
\(359\) | 31.1127i | 1.64207i | 0.570881 | + | 0.821033i | \(0.306602\pi\) | ||||
−0.570881 | + | 0.821033i | \(0.693398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.24264 | − | 3.00000i | 0.222681 | − | 0.157459i | ||||
\(364\) | 4.00000 | − | 9.79796i | 0.209657 | − | 0.513553i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.0000 | − | 16.9706i | 1.25450 | − | 0.887066i | ||||
\(367\) | 10.0000i | 0.521996i | 0.965339 | + | 0.260998i | \(0.0840516\pi\) | ||||
−0.965339 | + | 0.260998i | \(0.915948\pi\) | |||||||
\(368\) | − | 17.3205i | − | 0.902894i | ||||||
\(369\) | 3.46410 | − | 9.79796i | 0.180334 | − | 0.510061i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.79796 | + | 13.8564i | 0.508001 | + | 0.718421i | ||||
\(373\) | 9.79796 | 0.507319 | 0.253660 | − | 0.967294i | \(-0.418366\pi\) | ||||
0.253660 | + | 0.967294i | \(0.418366\pi\) | |||||||
\(374\) | 13.8564 | 0.716498 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 4.89898i | − | 0.252646i | ||||||
\(377\) | 22.6274 | 1.16537 | ||||||||
\(378\) | 23.6627 | + | 2.66025i | 1.21708 | + | 0.136829i | ||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.7846 | + | 14.6969i | −1.06483 | + | 0.752947i | ||||
\(382\) | 34.2929 | 1.75458 | ||||||||
\(383\) | 14.1421 | 0.722629 | 0.361315 | − | 0.932444i | \(-0.382328\pi\) | ||||
0.361315 | + | 0.932444i | \(0.382328\pi\) | |||||||
\(384\) | 12.1244 | + | 17.1464i | 0.618718 | + | 0.875000i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.9706i | − | 0.863779i | ||||||
\(387\) | 4.89898 | − | 13.8564i | 0.249029 | − | 0.704361i | ||||
\(388\) | 8.00000i | 0.406138i | ||||||||
\(389\) | 22.6274i | 1.14726i | 0.819116 | + | 0.573628i | \(0.194464\pi\) | ||||
−0.819116 | + | 0.573628i | \(0.805536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796i | 0.495504i | ||||||||
\(392\) | 8.48528 | − | 8.66025i | 0.428571 | − | 0.437409i | ||||
\(393\) | −9.79796 | + | 6.92820i | −0.494242 | + | 0.349482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.00000 | − | 2.82843i | −0.402015 | − | 0.142134i | ||||
\(397\) | − | 20.0000i | − | 1.00377i | −0.864934 | − | 0.501886i | \(-0.832640\pi\) | ||
0.864934 | − | 0.501886i | \(-0.167360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.6274i | − | 1.12996i | −0.825105 | − | 0.564980i | \(-0.808884\pi\) | ||
0.825105 | − | 0.564980i | \(-0.191116\pi\) | |||||||
\(402\) | −8.48528 | − | 12.0000i | −0.423207 | − | 0.598506i | ||||
\(403\) | −39.1918 | −1.95228 | ||||||||
\(404\) | −17.3205 | −0.861727 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | − | 9.79796i | −1.19110 | − | 0.486265i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.89898 | − | 6.92820i | −0.242536 | − | 0.342997i | ||||
\(409\) | 9.79796i | 0.484478i | 0.970217 | + | 0.242239i | \(0.0778818\pi\) | ||||
−0.970217 | + | 0.242239i | \(0.922118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.92820 | − | 9.79796i | −0.341743 | − | 0.483298i | ||||
\(412\) | 10.0000i | 0.492665i | ||||||||
\(413\) | −16.9706 | − | 6.92820i | −0.835067 | − | 0.340915i | ||||
\(414\) | 6.00000 | − | 16.9706i | 0.294884 | − | 0.834058i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.7846 | 1.01905 | ||||||||
\(417\) | 9.79796 | + | 13.8564i | 0.479808 | + | 0.678551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.92820 | 0.338465 | 0.169232 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169232 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 6.92820i | 0.337260i | ||||||||
\(423\) | 2.82843 | − | 8.00000i | 0.137523 | − | 0.388973i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.92820 | − | 4.89898i | 0.335673 | − | 0.237356i | ||||
\(427\) | 9.79796 | − | 24.0000i | 0.474156 | − | 1.16144i | ||||
\(428\) | − | 10.3923i | − | 0.502331i | ||||||
\(429\) | 16.0000 | − | 11.3137i | 0.772487 | − | 0.546231i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.82843i | 0.136241i | 0.997677 | + | 0.0681203i | \(0.0217002\pi\) | ||||
−0.997677 | + | 0.0681203i | \(0.978300\pi\) | |||||||
\(432\) | 7.07107 | + | 25.0000i | 0.340207 | + | 1.20281i | ||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | 41.5692 | + | 16.9706i | 1.99539 | + | 0.814613i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 19.5959 | − | 13.8564i | 0.936329 | − | 0.662085i | ||||
\(439\) | − | 39.1918i | − | 1.87052i | −0.353956 | − | 0.935262i | \(-0.615164\pi\) | ||
0.353956 | − | 0.935262i | \(-0.384836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.8564 | − | 9.24316i | 0.897924 | − | 0.440150i | ||||
\(442\) | −19.5959 | −0.932083 | ||||||||
\(443\) | 17.3205i | 0.822922i | 0.911427 | + | 0.411461i | \(0.134981\pi\) | ||||
−0.911427 | + | 0.411461i | \(0.865019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 45.0333 | 2.13239 | ||||||||
\(447\) | −11.3137 | − | 16.0000i | −0.535120 | − | 0.756774i | ||||
\(448\) | 2.44949 | + | 1.00000i | 0.115728 | + | 0.0472456i | ||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.79796i | 0.461368i | ||||||||
\(452\) | 6.92820i | 0.325875i | ||||||||
\(453\) | 11.3137 | − | 8.00000i | 0.531564 | − | 0.375873i | ||||
\(454\) | − | 4.89898i | − | 0.229920i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.5959 | −0.916658 | −0.458329 | − | 0.888783i | \(-0.651552\pi\) | ||||
−0.458329 | + | 0.888783i | \(0.651552\pi\) | |||||||
\(458\) | −33.9411 | −1.58596 | ||||||||
\(459\) | −4.00000 | − | 14.1421i | −0.186704 | − | 0.660098i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.46410 | −0.161339 | −0.0806696 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806696 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(462\) | −21.8695 | + | 5.07180i | −1.01746 | + | 0.235961i | ||||
\(463\) | −4.89898 | −0.227675 | −0.113837 | − | 0.993499i | \(-0.536314\pi\) | ||||
−0.113837 | + | 0.993499i | \(0.536314\pi\) | |||||||
\(464\) | − | 28.2843i | − | 1.31306i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.0000 | 1.66767 | ||||||||
\(467\) | 2.82843 | 0.130884 | 0.0654420 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654420 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(468\) | 11.3137 | + | 4.00000i | 0.522976 | + | 0.184900i | ||||
\(469\) | −12.0000 | − | 4.89898i | −0.554109 | − | 0.226214i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.00000 | + | 5.65685i | 0.184310 | + | 0.260654i | ||||
\(472\) | − | 12.0000i | − | 0.552345i | ||||||
\(473\) | 13.8564i | 0.637118i | ||||||||
\(474\) | 13.8564 | + | 19.5959i | 0.636446 | + | 0.900070i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.92820 | + | 2.82843i | 0.317554 | + | 0.129641i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.89898 | −0.224074 | ||||||||
\(479\) | −27.7128 | −1.26623 | −0.633115 | − | 0.774057i | \(-0.718224\pi\) | ||||
−0.633115 | + | 0.774057i | \(0.718224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 16.9706 | 0.772988 | ||||||||
\(483\) | −3.58630 | − | 15.4641i | −0.163182 | − | 0.703641i | ||||
\(484\) | −3.00000 | −0.136364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.73205 | + | 26.9444i | −0.0785674 | + | 1.22222i | ||||
\(487\) | −14.6969 | −0.665982 | −0.332991 | − | 0.942930i | \(-0.608058\pi\) | ||||
−0.332991 | + | 0.942930i | \(0.608058\pi\) | |||||||
\(488\) | 16.9706 | 0.768221 | ||||||||
\(489\) | −20.7846 | + | 14.6969i | −0.939913 | + | 0.664619i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | −4.89898 | + | 3.46410i | −0.220863 | + | 0.156174i | ||||
\(493\) | 16.0000i | 0.720604i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 48.9898i | 2.19971i | ||||||||
\(497\) | 2.82843 | − | 6.92820i | 0.126872 | − | 0.310772i | ||||
\(498\) | 4.89898 | + | 6.92820i | 0.219529 | + | 0.310460i | ||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0000 | + | 14.1421i | −0.893534 | + | 0.631824i | ||||
\(502\) | 36.0000i | 1.60676i | ||||||||
\(503\) | −19.7990 | −0.882793 | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(504\) | 10.2679 | + | 9.14162i | 0.457371 | + | 0.407200i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.9706i | 0.754434i | ||||||||
\(507\) | −4.24264 | + | 3.00000i | −0.188422 | + | 0.133235i | ||||
\(508\) | 14.6969 | 0.652071 | ||||||||
\(509\) | −3.46410 | −0.153544 | −0.0767718 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767718 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | − | 19.5959i | 0.353899 | − | 0.866872i | ||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.4949i | 1.08042i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.92820 | + | 4.89898i | −0.304997 | + | 0.215666i | ||||
\(517\) | 8.00000i | 0.351840i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.0000 | + | 19.7990i | −1.22906 | + | 0.869079i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 9.79796 | − | 27.7128i | 0.428845 | − | 1.21296i | ||||
\(523\) | 26.0000i | 1.13690i | 0.822718 | + | 0.568450i | \(0.192457\pi\) | ||||
−0.822718 | + | 0.568450i | \(0.807543\pi\) | |||||||
\(524\) | 6.92820 | 0.302660 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | −14.1421 | − | 20.0000i | −0.615457 | − | 0.870388i | ||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.92820 | − | 19.5959i | 0.300658 | − | 0.850390i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.8564i | − | 0.600188i | ||||||
\(534\) | −18.0000 | − | 25.4558i | −0.778936 | − | 1.10158i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.48528i | − | 0.366508i | ||||||
\(537\) | −2.82843 | − | 4.00000i | −0.122056 | − | 0.172613i | ||||
\(538\) | 18.0000i | 0.776035i | ||||||||
\(539\) | −13.8564 | + | 14.1421i | −0.596838 | + | 0.609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −50.9117 | −2.18684 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.6969i | 0.630126i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.9282 | − | 7.17260i | 1.32360 | − | 0.306959i | ||||
\(547\) | −34.2929 | −1.46626 | −0.733128 | − | 0.680090i | \(-0.761941\pi\) | ||||
−0.733128 | + | 0.680090i | \(0.761941\pi\) | |||||||
\(548\) | 6.92820i | 0.295958i | ||||||||
\(549\) | 27.7128 | + | 9.79796i | 1.18275 | + | 0.418167i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.48528 | − | 6.00000i | 0.361158 | − | 0.255377i | ||||
\(553\) | 19.5959 | + | 8.00000i | 0.833303 | + | 0.340195i | ||||
\(554\) | 33.9411i | 1.44202i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.79796i | − | 0.415526i | ||||||
\(557\) | − | 41.5692i | − | 1.76134i | −0.473726 | − | 0.880672i | \(-0.657091\pi\) | ||
0.473726 | − | 0.880672i | \(-0.342909\pi\) | |||||||
\(558\) | −16.9706 | + | 48.0000i | −0.718421 | + | 2.03200i | ||||
\(559\) | − | 19.5959i | − | 0.828819i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | + | 11.3137i | 0.337760 | + | 0.477665i | ||||
\(562\) | 48.9898 | 2.06651 | ||||||||
\(563\) | 14.1421 | 0.596020 | 0.298010 | − | 0.954563i | \(-0.403677\pi\) | ||||
0.298010 | + | 0.954563i | \(0.403677\pi\) | |||||||
\(564\) | −4.00000 | + | 2.82843i | −0.168430 | + | 0.119098i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.2487 | 1.01925 | ||||||||
\(567\) | 11.4896 | + | 20.8564i | 0.482517 | + | 0.875887i | ||||
\(568\) | 4.89898 | 0.205557 | ||||||||
\(569\) | − | 28.2843i | − | 1.18574i | −0.805299 | − | 0.592869i | \(-0.797995\pi\) | ||
0.805299 | − | 0.592869i | \(-0.202005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | −11.3137 | −0.473050 | ||||||||
\(573\) | 19.7990 | + | 28.0000i | 0.827115 | + | 1.16972i | ||||
\(574\) | −6.00000 | + | 14.6969i | −0.250435 | + | 0.613438i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | + | 2.82843i | −0.0416667 | + | 0.117851i | ||||
\(577\) | − | 8.00000i | − | 0.333044i | −0.986038 | − | 0.166522i | \(-0.946746\pi\) | ||
0.986038 | − | 0.166522i | \(-0.0532537\pi\) | |||||||
\(578\) | 15.5885i | 0.648394i | ||||||||
\(579\) | 13.8564 | − | 9.79796i | 0.575853 | − | 0.407189i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92820 | + | 2.82843i | 0.287430 | + | 0.117343i | ||||
\(582\) | −19.5959 | + | 13.8564i | −0.812277 | + | 0.574367i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.8564 | 0.573382 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.89898i | 0.202375i | ||||||||
\(587\) | 19.7990 | 0.817192 | 0.408596 | − | 0.912715i | \(-0.366019\pi\) | ||||
0.408596 | + | 0.912715i | \(0.366019\pi\) | |||||||
\(588\) | −11.9700 | − | 1.92820i | −0.493636 | − | 0.0795178i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.7990 | −0.813047 | −0.406524 | − | 0.913640i | \(-0.633259\pi\) | ||||
−0.406524 | + | 0.913640i | \(0.633259\pi\) | |||||||
\(594\) | −6.92820 | − | 24.4949i | −0.284268 | − | 1.00504i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.3137i | 0.463428i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 24.0000i | − | 0.981433i | ||||||
\(599\) | − | 36.7696i | − | 1.50236i | −0.660096 | − | 0.751182i | \(-0.729484\pi\) | ||
0.660096 | − | 0.751182i | \(-0.270516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.79796i | 0.399667i | 0.979830 | + | 0.199834i | \(0.0640401\pi\) | ||||
−0.979830 | + | 0.199834i | \(0.935960\pi\) | |||||||
\(602\) | −8.48528 | + | 20.7846i | −0.345834 | + | 0.847117i | ||||
\(603\) | 4.89898 | − | 13.8564i | 0.199502 | − | 0.564276i | ||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.0000 | − | 42.4264i | −1.21867 | − | 1.72345i | ||||
\(607\) | 10.0000i | 0.405887i | 0.979190 | + | 0.202944i | \(0.0650509\pi\) | ||||
−0.979190 | + | 0.202944i | \(0.934949\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.85641 | − | 25.2528i | −0.237314 | − | 1.02329i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.3137i | − | 0.457704i | ||||||
\(612\) | −2.82843 | + | 8.00000i | −0.114332 | + | 0.323381i | ||||
\(613\) | 29.3939 | 1.18721 | 0.593604 | − | 0.804757i | \(-0.297705\pi\) | ||||
0.593604 | + | 0.804757i | \(0.297705\pi\) | |||||||
\(614\) | 17.3205 | 0.698999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 4.89898i | −0.483494 | − | 0.197386i | ||||
\(617\) | 48.4974i | 1.95243i | 0.216799 | + | 0.976216i | \(0.430439\pi\) | ||||
−0.216799 | + | 0.976216i | \(0.569561\pi\) | |||||||
\(618\) | −24.4949 | + | 17.3205i | −0.985329 | + | 0.696733i | ||||
\(619\) | − | 9.79796i | − | 0.393813i | −0.980422 | − | 0.196907i | \(-0.936910\pi\) | ||
0.980422 | − | 0.196907i | \(-0.0630896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.3205 | − | 4.89898i | 0.695048 | − | 0.196589i | ||||
\(622\) | 48.0000i | 1.92462i | ||||||||
\(623\) | −25.4558 | − | 10.3923i | −1.01987 | − | 0.416359i | ||||
\(624\) | 20.0000 | + | 28.2843i | 0.800641 | + | 1.13228i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.7128 | −1.10763 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4.00000i | − | 0.159617i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 13.8564i | 0.551178i | ||||||||
\(633\) | −5.65685 | + | 4.00000i | −0.224840 | + | 0.158986i | ||||
\(634\) | 24.0000 | 0.953162 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.5959 | − | 20.0000i | 0.776419 | − | 0.792429i | ||||
\(638\) | 27.7128i | 1.09716i | ||||||||
\(639\) | 8.00000 | + | 2.82843i | 0.316475 | + | 0.111891i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.65685i | − | 0.223432i | −0.993740 | − | 0.111716i | \(-0.964365\pi\) | ||
0.993740 | − | 0.111716i | \(-0.0356347\pi\) | |||||||
\(642\) | 25.4558 | − | 18.0000i | 1.00466 | − | 0.710403i | ||||
\(643\) | − | 22.0000i | − | 0.867595i | −0.901010 | − | 0.433798i | \(-0.857173\pi\) | ||
0.901010 | − | 0.433798i | \(-0.142827\pi\) | |||||||
\(644\) | −3.46410 | + | 8.48528i | −0.136505 | + | 0.334367i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7990 | 0.778379 | 0.389189 | − | 0.921158i | \(-0.372755\pi\) | ||||
0.389189 | + | 0.921158i | \(0.372755\pi\) | |||||||
\(648\) | −9.79796 | + | 12.1244i | −0.384900 | + | 0.476290i | ||||
\(649\) | 19.5959i | 0.769207i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.1436 | + | 43.7391i | 0.397559 | + | 1.71427i | ||||
\(652\) | 14.6969 | 0.575577 | ||||||||
\(653\) | − | 27.7128i | − | 1.08449i | −0.840222 | − | 0.542243i | \(-0.817575\pi\) | ||
0.840222 | − | 0.542243i | \(-0.182425\pi\) | |||||||
\(654\) | −17.3205 | − | 24.4949i | −0.677285 | − | 0.957826i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.3205 | −0.676252 | ||||||||
\(657\) | 22.6274 | + | 8.00000i | 0.882780 | + | 0.312110i | ||||
\(658\) | −4.89898 | + | 12.0000i | −0.190982 | + | 0.467809i | ||||
\(659\) | − | 2.82843i | − | 0.110180i | −0.998481 | − | 0.0550899i | \(-0.982455\pi\) | ||
0.998481 | − | 0.0550899i | \(-0.0175446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.79796i | − | 0.381096i | −0.981678 | − | 0.190548i | \(-0.938973\pi\) | ||
0.981678 | − | 0.190548i | \(-0.0610266\pi\) | |||||||
\(662\) | 48.4974i | 1.88491i | ||||||||
\(663\) | −11.3137 | − | 16.0000i | −0.439388 | − | 0.621389i | ||||
\(664\) | 4.89898i | 0.190117i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5959 | −0.758757 | ||||||||
\(668\) | 14.1421 | 0.547176 | ||||||||
\(669\) | 26.0000 | + | 36.7696i | 1.00522 | + | 1.42159i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.7128 | −1.06984 | ||||||||
\(672\) | −5.37945 | − | 23.1962i | −0.207517 | − | 0.894811i | ||||
\(673\) | −9.79796 | −0.377684 | −0.188842 | − | 0.982008i | \(-0.560473\pi\) | ||||
−0.188842 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(674\) | − | 33.9411i | − | 1.30736i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 2.82843 | 0.108705 | 0.0543526 | − | 0.998522i | \(-0.482690\pi\) | ||||
0.0543526 | + | 0.998522i | \(0.482690\pi\) | |||||||
\(678\) | −16.9706 | + | 12.0000i | −0.651751 | + | 0.460857i | ||||
\(679\) | −8.00000 | + | 19.5959i | −0.307012 | + | 0.752022i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | − | 2.82843i | 0.153280 | − | 0.108386i | ||||
\(682\) | − | 48.0000i | − | 1.83801i | ||||||
\(683\) | − | 10.3923i | − | 0.397650i | −0.980035 | − | 0.198825i | \(-0.936287\pi\) | ||
0.980035 | − | 0.198825i | \(-0.0637126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −29.4449 | + | 12.7279i | −1.12421 | + | 0.485954i | ||||
\(687\) | −19.5959 | − | 27.7128i | −0.747631 | − | 1.05731i | ||||
\(688\) | −24.4949 | −0.933859 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.79796i | 0.372732i | 0.982480 | + | 0.186366i | \(0.0596710\pi\) | ||||
−0.982480 | + | 0.186366i | \(0.940329\pi\) | |||||||
\(692\) | 19.7990 | 0.752645 | ||||||||
\(693\) | −16.7675 | − | 14.9282i | −0.636944 | − | 0.567076i | ||||
\(694\) | 30.0000 | 1.13878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.8564 | − | 9.79796i | 0.525226 | − | 0.371391i | ||||
\(697\) | 9.79796 | 0.371124 | ||||||||
\(698\) | 33.9411 | 1.28469 | ||||||||
\(699\) | 20.7846 | + | 29.3939i | 0.786146 | + | 1.11178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.6274i | − | 0.854626i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) | ||
0.904104 | − | 0.427313i | \(-0.140540\pi\) | |||||||
\(702\) | 9.79796 | + | 34.6410i | 0.369800 | + | 1.30744i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 2.82843i | − | 0.106600i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 53.8888i | − | 2.02813i | ||||||
\(707\) | −42.4264 | − | 17.3205i | −1.59561 | − | 0.651405i | ||||
\(708\) | −9.79796 | + | 6.92820i | −0.368230 | + | 0.260378i | ||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | + | 22.6274i | −0.300023 | + | 0.848594i | ||||
\(712\) | − | 18.0000i | − | 0.674579i | ||||||
\(713\) | 33.9411 | 1.27111 | ||||||||
\(714\) | 5.07180 | + | 21.8695i | 0.189807 | + | 0.818447i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.82843i | 0.105703i | ||||||||
\(717\) | −2.82843 | − | 4.00000i | −0.105630 | − | 0.149383i | ||||
\(718\) | 53.8888 | 2.01111 | ||||||||
\(719\) | −41.5692 | −1.55027 | −0.775135 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775135 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | + | 24.4949i | −0.372419 | + | 0.912238i | ||||
\(722\) | − | 32.9090i | − | 1.22474i | ||||||
\(723\) | 9.79796 | + | 13.8564i | 0.364390 | + | 0.515325i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.19615 | − | 7.34847i | −0.192847 | − | 0.272727i | ||||
\(727\) | 10.0000i | 0.370879i | 0.982656 | + | 0.185440i | \(0.0593710\pi\) | ||||
−0.982656 | + | 0.185440i | \(0.940629\pi\) | |||||||
\(728\) | 16.9706 | + | 6.92820i | 0.628971 | + | 0.256776i | ||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8564 | 0.512498 | ||||||||
\(732\) | −9.79796 | − | 13.8564i | −0.362143 | − | 0.512148i | ||||
\(733\) | − | 28.0000i | − | 1.03420i | −0.855924 | − | 0.517102i | \(-0.827011\pi\) | ||
0.855924 | − | 0.517102i | \(-0.172989\pi\) | |||||||
\(734\) | 17.3205 | 0.639312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.0000 | −0.663489 | ||||||||
\(737\) | 13.8564i | 0.510407i | ||||||||
\(738\) | −16.9706 | − | 6.00000i | −0.624695 | − | 0.220863i | ||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2487i | 0.889599i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(744\) | −24.0000 | + | 16.9706i | −0.879883 | + | 0.622171i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 16.9706i | − | 0.621336i | ||||||
\(747\) | −2.82843 | + | 8.00000i | −0.103487 | + | 0.292705i | ||||
\(748\) | − | 8.00000i | − | 0.292509i | ||||||
\(749\) | 10.3923 | − | 25.4558i | 0.379727 | − | 0.930136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | −14.1421 | −0.515711 | ||||||||
\(753\) | −29.3939 | + | 20.7846i | −1.07117 | + | 0.757433i | ||||
\(754\) | − | 39.1918i | − | 1.42728i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.53590 | − | 13.6617i | 0.0558601 | − | 0.496870i | ||||
\(757\) | 29.3939 | 1.06834 | 0.534169 | − | 0.845378i | \(-0.320624\pi\) | ||||
0.534169 | + | 0.845378i | \(0.320624\pi\) | |||||||
\(758\) | − | 48.4974i | − | 1.76151i | ||||||
\(759\) | −13.8564 | + | 9.79796i | −0.502956 | + | 0.355643i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.1051 | −1.38131 | −0.690655 | − | 0.723185i | \(-0.742678\pi\) | ||||
−0.690655 | + | 0.723185i | \(0.742678\pi\) | |||||||
\(762\) | 25.4558 | + | 36.0000i | 0.922168 | + | 1.30414i | ||||
\(763\) | −24.4949 | − | 10.0000i | −0.886775 | − | 0.362024i | ||||
\(764\) | − | 19.7990i | − | 0.716302i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 24.4949i | − | 0.885037i | ||||||
\(767\) | − | 27.7128i | − | 1.00065i | ||||||
\(768\) | 26.8701 | − | 19.0000i | 0.969590 | − | 0.685603i | ||||
\(769\) | − | 19.5959i | − | 0.706647i | −0.935501 | − | 0.353323i | \(-0.885052\pi\) | ||
0.935501 | − | 0.353323i | \(-0.114948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0000 | + | 14.1421i | −0.720282 | + | 0.509317i | ||||
\(772\) | −9.79796 | −0.352636 | ||||||||
\(773\) | −2.82843 | −0.101731 | −0.0508657 | − | 0.998706i | \(-0.516198\pi\) | ||||
−0.0508657 | + | 0.998706i | \(0.516198\pi\) | |||||||
\(774\) | −24.0000 | − | 8.48528i | −0.862662 | − | 0.304997i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.8564 | −0.497416 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.1918 | 1.40510 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 16.9706 | 0.606866 | ||||||||
\(783\) | 28.2843 | − | 8.00000i | 1.01080 | − | 0.285897i | ||||
\(784\) | −25.0000 | − | 24.4949i | −0.892857 | − | 0.874818i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.0000 | + | 16.9706i | 0.428026 | + | 0.605320i | ||||
\(787\) | − | 14.0000i | − | 0.499046i | −0.968369 | − | 0.249523i | \(-0.919726\pi\) | ||
0.968369 | − | 0.249523i | \(-0.0802738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.46410 | − | 4.89898i | −0.123325 | − | 0.174408i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.92820 | + | 16.9706i | −0.246339 | + | 0.603404i | ||||
\(792\) | 4.89898 | − | 13.8564i | 0.174078 | − | 0.492366i | ||||
\(793\) | 39.1918 | 1.39174 | ||||||||
\(794\) | −34.6410 | −1.22936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7696 | 1.30244 | 0.651222 | − | 0.758887i | \(-0.274257\pi\) | ||||
0.651222 | + | 0.758887i | \(0.274257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3923 | − | 29.3939i | 0.367194 | − | 1.03858i | ||||
\(802\) | −39.1918 | −1.38391 | ||||||||
\(803\) | −22.6274 | −0.798504 | ||||||||
\(804\) | −6.92820 | + | 4.89898i | −0.244339 | + | 0.172774i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 67.8823i | 2.39105i | ||||||||
\(807\) | −14.6969 | + | 10.3923i | −0.517357 | + | 0.365826i | ||||
\(808\) | − | 30.0000i | − | 1.05540i | ||||||
\(809\) | 22.6274i | 0.795538i | 0.917486 | + | 0.397769i | \(0.130215\pi\) | ||||
−0.917486 | + | 0.397769i | \(0.869785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.3939i | − | 1.03216i | −0.856541 | − | 0.516079i | \(-0.827391\pi\) | ||
0.856541 | − | 0.516079i | \(-0.172609\pi\) | |||||||
\(812\) | −5.65685 | + | 13.8564i | −0.198517 | + | 0.486265i | ||||
\(813\) | −29.3939 | − | 41.5692i | −1.03089 | − | 1.45790i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.0000 | + | 14.1421i | −0.700140 | + | 0.495074i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.9706 | 0.593362 | ||||||||
\(819\) | 23.7128 | + | 21.1117i | 0.828593 | + | 0.737701i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.6274i | − | 0.789702i | −0.918745 | − | 0.394851i | \(-0.870796\pi\) | ||
0.918745 | − | 0.394851i | \(-0.129204\pi\) | |||||||
\(822\) | −16.9706 | + | 12.0000i | −0.591916 | + | 0.418548i | ||||
\(823\) | −4.89898 | −0.170768 | −0.0853838 | − | 0.996348i | \(-0.527212\pi\) | ||||
−0.0853838 | + | 0.996348i | \(0.527212\pi\) | |||||||
\(824\) | −17.3205 | −0.603388 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | + | 29.3939i | −0.417533 | + | 1.02274i | ||||
\(827\) | 10.3923i | 0.361376i | 0.983540 | + | 0.180688i | \(0.0578324\pi\) | ||||
−0.983540 | + | 0.180688i | \(0.942168\pi\) | |||||||
\(828\) | −9.79796 | − | 3.46410i | −0.340503 | − | 0.120386i | ||||
\(829\) | − | 29.3939i | − | 1.02089i | −0.859910 | − | 0.510446i | \(-0.829480\pi\) | ||
0.859910 | − | 0.510446i | \(-0.170520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.7128 | + | 19.5959i | −0.961347 | + | 0.679775i | ||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | 14.1421 | + | 13.8564i | 0.489996 | + | 0.480096i | ||||
\(834\) | 24.0000 | − | 16.9706i | 0.831052 | − | 0.587643i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −48.9898 | + | 13.8564i | −1.69334 | + | 0.478947i | ||||
\(838\) | − | 12.0000i | − | 0.414533i | ||||||
\(839\) | −27.7128 | −0.956753 | −0.478376 | − | 0.878155i | \(-0.658774\pi\) | ||||
−0.478376 | + | 0.878155i | \(0.658774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | − | 45.0333i | − | 1.55195i | ||||||
\(843\) | 28.2843 | + | 40.0000i | 0.974162 | + | 1.37767i | ||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.8564 | − | 4.89898i | −0.476393 | − | 0.168430i | ||||
\(847\) | −7.34847 | − | 3.00000i | −0.252496 | − | 0.103081i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.0000 | + | 19.7990i | 0.480479 | + | 0.679500i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.82843 | − | 4.00000i | −0.0969003 | − | 0.137038i | ||||
\(853\) | 20.0000i | 0.684787i | 0.939557 | + | 0.342393i | \(0.111238\pi\) | ||||
−0.939557 | + | 0.342393i | \(0.888762\pi\) | |||||||
\(854\) | −41.5692 | − | 16.9706i | −1.42247 | − | 0.580721i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | −48.0833 | −1.64249 | −0.821246 | − | 0.570574i | \(-0.806721\pi\) | ||||
−0.821246 | + | 0.570574i | \(0.806721\pi\) | |||||||
\(858\) | −19.5959 | − | 27.7128i | −0.668994 | − | 0.946100i | ||||
\(859\) | 39.1918i | 1.33721i | 0.743619 | + | 0.668604i | \(0.233108\pi\) | ||||
−0.743619 | + | 0.668604i | \(0.766892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.4641 | + | 3.58630i | −0.527015 | + | 0.122221i | ||||
\(862\) | 4.89898 | 0.166860 | ||||||||
\(863\) | − | 10.3923i | − | 0.353758i | −0.984233 | − | 0.176879i | \(-0.943400\pi\) | ||
0.984233 | − | 0.176879i | \(-0.0566002\pi\) | |||||||
\(864\) | 25.9808 | − | 7.34847i | 0.883883 | − | 0.250000i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27.7128 | −0.941720 | ||||||||
\(867\) | −12.7279 | + | 9.00000i | −0.432263 | + | 0.305656i | ||||
\(868\) | 9.79796 | − | 24.0000i | 0.332564 | − | 0.814613i | ||||
\(869\) | − | 22.6274i | − | 0.767583i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 19.5959i | − | 0.663982i | ||||||
\(872\) | − | 17.3205i | − | 0.586546i | ||||||
\(873\) | −22.6274 | − | 8.00000i | −0.765822 | − | 0.270759i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.00000 | − | 11.3137i | −0.270295 | − | 0.382255i | ||||
\(877\) | 48.9898 | 1.65427 | 0.827134 | − | 0.562005i | \(-0.189970\pi\) | ||||
0.827134 | + | 0.562005i | \(0.189970\pi\) | |||||||
\(878\) | −67.8823 | −2.29092 | ||||||||
\(879\) | −4.00000 | + | 2.82843i | −0.134917 | + | 0.0954005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3923 | 0.350126 | 0.175063 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175063 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(882\) | −16.0096 | − | 32.6603i | −0.539072 | − | 1.09973i | ||||
\(883\) | 14.6969 | 0.494591 | 0.247296 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247296 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(884\) | 11.3137i | 0.380521i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.0000 | 1.00787 | ||||||||
\(887\) | 2.82843 | 0.0949693 | 0.0474846 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474846 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000 | + | 14.6969i | 1.20740 | + | 0.492919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0000 | − | 19.7990i | 0.536020 | − | 0.663291i | ||||
\(892\) | − | 26.0000i | − | 0.870544i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −27.7128 | + | 19.5959i | −0.926855 | + | 0.655386i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.1244 | − | 29.6985i | 0.405046 | − | 0.992157i | ||||
\(897\) | 19.5959 | − | 13.8564i | 0.654289 | − | 0.462652i | ||||
\(898\) | 9.79796 | 0.326962 | ||||||||
\(899\) | 55.4256 | 1.84855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 16.9706 | 0.565058 | ||||||||
\(903\) | −21.8695 | + | 5.07180i | −0.727773 | + | 0.168779i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.8564 | − | 19.5959i | −0.460348 | − | 0.651031i | ||||
\(907\) | 24.4949 | 0.813340 | 0.406670 | − | 0.913575i | \(-0.366690\pi\) | ||||
0.406670 | + | 0.913575i | \(0.366690\pi\) | |||||||
\(908\) | −2.82843 | −0.0938647 | ||||||||
\(909\) | 17.3205 | − | 48.9898i | 0.574485 | − | 1.62489i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.0833i | − | 1.59307i | −0.604593 | − | 0.796535i | \(-0.706664\pi\) | ||
0.604593 | − | 0.796535i | \(-0.293336\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.00000i | − | 0.264761i | ||||||
\(914\) | 33.9411i | 1.12267i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5959i | 0.647467i | ||||||||
\(917\) | 16.9706 | + | 6.92820i | 0.560417 | + | 0.228789i | ||||
\(918\) | −24.4949 | + | 6.92820i | −0.808452 | + | 0.228665i | ||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 14.1421i | 0.329511 | + | 0.465999i | ||||
\(922\) | 6.00000i | 0.197599i | ||||||||
\(923\) | 11.3137 | 0.372395 | ||||||||
\(924\) | 2.92820 | + | 12.6264i | 0.0963308 | + | 0.415378i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.48528i | 0.278844i | ||||||||
\(927\) | −28.2843 | − | 10.0000i | −0.928977 | − | 0.328443i | ||||
\(928\) | −29.3939 | −0.964901 | ||||||||
\(929\) | 45.0333 | 1.47750 | 0.738748 | − | 0.673982i | \(-0.235418\pi\) | ||||
0.738748 | + | 0.673982i | \(0.235418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 20.7846i | − | 0.680823i | ||||||
\(933\) | −39.1918 | + | 27.7128i | −1.28308 | + | 0.907277i | ||||
\(934\) | − | 4.89898i | − | 0.160300i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.92820 | + | 19.5959i | −0.226455 | + | 0.640513i | ||||
\(937\) | − | 8.00000i | − | 0.261349i | −0.991425 | − | 0.130674i | \(-0.958286\pi\) | ||
0.991425 | − | 0.130674i | \(-0.0417142\pi\) | |||||||
\(938\) | −8.48528 | + | 20.7846i | −0.277054 | + | 0.678642i | ||||
\(939\) | −16.0000 | − | 22.6274i | −0.522140 | − | 0.738418i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2487 | 0.790485 | 0.395243 | − | 0.918577i | \(-0.370660\pi\) | ||||
0.395243 | + | 0.918577i | \(0.370660\pi\) | |||||||
\(942\) | 9.79796 | − | 6.92820i | 0.319235 | − | 0.225733i | ||||
\(943\) | 12.0000i | 0.390774i | ||||||||
\(944\) | −34.6410 | −1.12747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0000 | 0.780307 | ||||||||
\(947\) | 3.46410i | 0.112568i | 0.998415 | + | 0.0562841i | \(0.0179253\pi\) | ||||
−0.998415 | + | 0.0562841i | \(0.982075\pi\) | |||||||
\(948\) | 11.3137 | − | 8.00000i | 0.367452 | − | 0.259828i | ||||
\(949\) | 32.0000 | 1.03876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.8564 | + | 19.5959i | 0.449325 | + | 0.635441i | ||||
\(952\) | −4.89898 | + | 12.0000i | −0.158777 | + | 0.388922i | ||||
\(953\) | 20.7846i | 0.673280i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.82843i | 0.0914779i | ||||||||
\(957\) | −22.6274 | + | 16.0000i | −0.731441 | + | 0.517207i | ||||
\(958\) | 48.0000i | 1.55081i | ||||||||
\(959\) | −6.92820 | + | 16.9706i | −0.223723 | + | 0.548008i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.0000 | −2.09677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.3939 | + | 10.3923i | 0.947204 | + | 0.334887i | ||||
\(964\) | − | 9.79796i | − | 0.315571i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −26.7846 | + | 6.21166i | −0.861781 | + | 0.199857i | ||||
\(967\) | 34.2929 | 1.10278 | 0.551392 | − | 0.834246i | \(-0.314097\pi\) | ||||
0.551392 | + | 0.834246i | \(0.314097\pi\) | |||||||
\(968\) | − | 5.19615i | − | 0.167011i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.7846 | 0.667010 | 0.333505 | − | 0.942748i | \(-0.391769\pi\) | ||||
0.333505 | + | 0.942748i | \(0.391769\pi\) | |||||||
\(972\) | 15.5563 | + | 1.00000i | 0.498970 | + | 0.0320750i | ||||
\(973\) | 9.79796 | − | 24.0000i | 0.314108 | − | 0.769405i | ||||
\(974\) | 25.4558i | 0.815658i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 48.9898i | − | 1.56813i | ||||||
\(977\) | 48.4974i | 1.55157i | 0.630997 | + | 0.775785i | \(0.282646\pi\) | ||||
−0.630997 | + | 0.775785i | \(0.717354\pi\) | |||||||
\(978\) | 25.4558 | + | 36.0000i | 0.813988 | + | 1.15115i | ||||
\(979\) | 29.3939i | 0.939432i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | − | 28.2843i | 0.319275 | − | 0.903047i | ||||
\(982\) | −24.4949 | −0.781664 | ||||||||
\(983\) | −2.82843 | −0.0902128 | −0.0451064 | − | 0.998982i | \(-0.514363\pi\) | ||||
−0.0451064 | + | 0.998982i | \(0.514363\pi\) | |||||||
\(984\) | −6.00000 | − | 8.48528i | −0.191273 | − | 0.270501i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 27.7128 | 0.882556 | ||||||||
\(987\) | −12.6264 | + | 2.92820i | −0.401902 | + | 0.0932057i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706i | 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | 50.9117 | 1.61645 | ||||||||
\(993\) | −39.5980 | + | 28.0000i | −1.25660 | + | 0.888553i | ||||
\(994\) | −12.0000 | − | 4.89898i | −0.380617 | − | 0.155386i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.00000 | − | 2.82843i | 0.126745 | − | 0.0896221i | ||||
\(997\) | 52.0000i | 1.64686i | 0.567420 | + | 0.823428i | \(0.307941\pi\) | ||||
−0.567420 | + | 0.823428i | \(0.692059\pi\) | |||||||
\(998\) | − | 6.92820i | − | 0.219308i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))