Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(82,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.c (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: | \(1.94036476912\) |
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: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.163 |
Dual form | 243.2.c.c.82.1 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 2.12132i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −1.00000 | − | 1.73205i | ||||
\(5\) | 1.22474 | + | 2.12132i | 0.547723 | + | 0.948683i | 0.998430 | + | 0.0560116i | \(0.0178384\pi\) |
−0.450708 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | 4.89898 | 1.73205 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.00000 | −1.89737 | ||||||||
\(11\) | −1.22474 | + | 2.12132i | −0.369274 | + | 0.639602i | −0.989452 | − | 0.144859i | \(-0.953727\pi\) |
0.620178 | + | 0.784461i | \(0.287060\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | −2.44949 | − | 4.24264i | −0.654654 | − | 1.13389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −7.34847 | −1.78227 | −0.891133 | − | 0.453743i | \(-0.850089\pi\) | ||||
−0.891133 | + | 0.453743i | \(0.850089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 4.89898 | − | 8.48528i | 1.09545 | − | 1.89737i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | − | 5.19615i | −0.639602 | − | 1.10782i | ||||
\(23\) | 1.22474 | + | 2.12132i | 0.255377 | + | 0.442326i | 0.964998 | − | 0.262258i | \(-0.0844671\pi\) |
−0.709621 | + | 0.704584i | \(0.751134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.00000 | 1.51186 | ||||||||
\(29\) | 2.44949 | − | 4.24264i | 0.454859 | − | 0.787839i | −0.543821 | − | 0.839201i | \(-0.683023\pi\) |
0.998680 | + | 0.0513625i | \(0.0163564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.00000 | − | 15.5885i | 1.54349 | − | 2.67340i | ||||
\(35\) | −4.89898 | −0.828079 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 1.22474 | − | 2.12132i | 0.198680 | − | 0.344124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.00000 | + | 10.3923i | 0.948683 | + | 1.64317i | ||||
\(41\) | −2.44949 | − | 4.24264i | −0.382546 | − | 0.662589i | 0.608879 | − | 0.793263i | \(-0.291619\pi\) |
−0.991425 | + | 0.130674i | \(0.958286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | + | 9.52628i | −0.838742 | + | 1.45274i | 0.0522047 | + | 0.998636i | \(0.483375\pi\) |
−0.890947 | + | 0.454108i | \(0.849958\pi\) | |||||||
\(44\) | 9.79796 | 1.47710 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −4.89898 | + | 8.48528i | −0.714590 | + | 1.23771i | 0.248528 | + | 0.968625i | \(0.420053\pi\) |
−0.963118 | + | 0.269081i | \(0.913280\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −1.22474 | − | 2.12132i | −0.173205 | − | 0.300000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | − | 3.46410i | 0.277350 | − | 0.480384i | ||||
\(53\) | 7.34847 | 1.00939 | 0.504695 | − | 0.863298i | \(-0.331605\pi\) | ||||
0.504695 | + | 0.863298i | \(0.331605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | −4.89898 | + | 8.48528i | −0.654654 | + | 1.13389i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000 | + | 10.3923i | 0.787839 | + | 1.36458i | ||||
\(59\) | 1.22474 | + | 2.12132i | 0.159448 | + | 0.276172i | 0.934670 | − | 0.355517i | \(-0.115695\pi\) |
−0.775222 | + | 0.631689i | \(0.782362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | −2.44949 | −0.311086 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −1.22474 | + | 2.12132i | −0.151911 | + | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 14.6969 | + | 25.4558i | 1.78227 | + | 3.08697i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | − | 10.3923i | 0.717137 | − | 1.24212i | ||||
\(71\) | 7.34847 | 0.872103 | 0.436051 | − | 0.899922i | \(-0.356377\pi\) | ||||
0.436051 | + | 0.899922i | \(0.356377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | −9.79796 | + | 16.9706i | −1.13899 | + | 1.97279i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | −2.44949 | − | 4.24264i | −0.279145 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50000 | − | 6.06218i | 0.393781 | − | 0.682048i | −0.599164 | − | 0.800626i | \(-0.704500\pi\) |
0.992945 | + | 0.118578i | \(0.0378336\pi\) | |||||||
\(80\) | −9.79796 | −1.09545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0000 | 1.32518 | ||||||||
\(83\) | 6.12372 | − | 10.6066i | 0.672166 | − | 1.16423i | −0.305123 | − | 0.952313i | \(-0.598697\pi\) |
0.977289 | − | 0.211913i | \(-0.0679692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | − | 15.5885i | −0.976187 | − | 1.69081i | ||||
\(86\) | −13.4722 | − | 23.3345i | −1.45274 | − | 2.51623i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | + | 10.3923i | −0.639602 | + | 1.10782i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 4.89898 | − | 8.48528i | 0.510754 | − | 0.884652i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0000 | − | 20.7846i | −1.23771 | − | 2.14377i | ||||
\(95\) | −1.22474 | − | 2.12132i | −0.125656 | − | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.50000 | − | 6.06218i | 0.355371 | − | 0.615521i | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | −7.34847 | −0.742307 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 2.44949 | − | 4.24264i | 0.243733 | − | 0.422159i | −0.718041 | − | 0.696000i | \(-0.754961\pi\) |
0.961775 | + | 0.273842i | \(0.0882945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | + | 6.06218i | 0.344865 | + | 0.597324i | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 2.44949 | + | 4.24264i | 0.240192 | + | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | + | 15.5885i | −0.874157 | + | 1.51408i | ||||
\(107\) | 14.6969 | 1.42081 | 0.710403 | − | 0.703795i | \(-0.248513\pi\) | ||||
0.710403 | + | 0.703795i | \(0.248513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 7.34847 | − | 12.7279i | 0.700649 | − | 1.21356i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | − | 6.92820i | −0.377964 | − | 0.654654i | ||||
\(113\) | 4.89898 | + | 8.48528i | 0.460857 | + | 0.798228i | 0.999004 | − | 0.0446231i | \(-0.0142087\pi\) |
−0.538147 | + | 0.842851i | \(0.680875\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 5.19615i | −0.279751 | + | 0.484544i | ||||
\(116\) | −19.5959 | −1.81944 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 7.34847 | − | 12.7279i | 0.673633 | − | 1.16677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.50000 | + | 4.33013i | 0.227273 | + | 0.393648i | ||||
\(122\) | −6.12372 | − | 10.6066i | −0.554416 | − | 0.960277i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 9.79796 | − | 16.9706i | 0.866025 | − | 1.50000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | −6.12372 | − | 10.6066i | −0.535032 | − | 0.926703i | −0.999162 | − | 0.0409357i | \(-0.986966\pi\) |
0.464130 | − | 0.885767i | \(-0.346367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | −17.1464 | −1.48123 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.0000 | −3.08697 | ||||||||
\(137\) | −4.89898 | + | 8.48528i | −0.418548 | + | 0.724947i | −0.995794 | − | 0.0916241i | \(-0.970794\pi\) |
0.577246 | + | 0.816571i | \(0.304128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | + | 8.66025i | 0.424094 | + | 0.734553i | 0.996335 | − | 0.0855324i | \(-0.0272591\pi\) |
−0.572241 | + | 0.820086i | \(0.693926\pi\) | |||||||
\(140\) | 9.79796 | + | 16.9706i | 0.828079 | + | 1.43427i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.00000 | + | 15.5885i | −0.755263 | + | 1.30815i | ||||
\(143\) | −2.44949 | −0.204837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | −13.4722 | + | 23.3345i | −1.11497 | + | 1.93118i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.0000 | − | 27.7128i | −1.31519 | − | 2.27798i | ||||
\(149\) | −6.12372 | − | 10.6066i | −0.501675 | − | 0.868927i | −0.999998 | − | 0.00193526i | \(-0.999384\pi\) |
0.498323 | − | 0.866991i | \(-0.333949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | −4.89898 | −0.397360 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | −1.22474 | + | 2.12132i | −0.0983739 | + | 0.170389i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.50000 | − | 14.7224i | −0.678374 | − | 1.17498i | −0.975470 | − | 0.220131i | \(-0.929352\pi\) |
0.297097 | − | 0.954847i | \(-0.403982\pi\) | |||||||
\(158\) | 8.57321 | + | 14.8492i | 0.682048 | + | 1.18134i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.89898 | −0.386094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | −9.79796 | + | 16.9706i | −0.765092 | + | 1.32518i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0000 | + | 25.9808i | 1.16423 | + | 2.01650i | ||||
\(167\) | −2.44949 | − | 4.24264i | −0.189547 | − | 0.328305i | 0.755552 | − | 0.655089i | \(-0.227369\pi\) |
−0.945099 | + | 0.326783i | \(0.894035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 44.0908 | 3.38161 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 44.0000 | 3.35497 | ||||||||
\(173\) | −4.89898 | + | 8.48528i | −0.372463 | + | 0.645124i | −0.989944 | − | 0.141462i | \(-0.954820\pi\) |
0.617481 | + | 0.786586i | \(0.288153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | −4.89898 | − | 8.48528i | −0.369274 | − | 0.639602i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.6969 | −1.09850 | −0.549250 | − | 0.835658i | \(-0.685087\pi\) | ||||
−0.549250 | + | 0.835658i | \(0.685087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 2.44949 | − | 4.24264i | 0.181568 | − | 0.314485i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | + | 10.3923i | 0.442326 | + | 0.766131i | ||||
\(185\) | 9.79796 | + | 16.9706i | 0.720360 | + | 1.24770i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 15.5885i | 0.658145 | − | 1.13994i | ||||
\(188\) | 39.1918 | 2.85836 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −4.89898 | + | 8.48528i | −0.354478 | + | 0.613973i | −0.987028 | − | 0.160546i | \(-0.948675\pi\) |
0.632551 | + | 0.774519i | \(0.282008\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | − | 9.52628i | −0.395899 | − | 0.685717i | 0.597317 | − | 0.802005i | \(-0.296234\pi\) |
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(194\) | 8.57321 | + | 14.8492i | 0.615521 | + | 1.06611i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000 | − | 10.3923i | 0.428571 | − | 0.742307i | ||||
\(197\) | 14.6969 | 1.04711 | 0.523557 | − | 0.851991i | \(-0.324605\pi\) | ||||
0.523557 | + | 0.851991i | \(0.324605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00000 | −0.0708881 | −0.0354441 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354441 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(200\) | −2.44949 | + | 4.24264i | −0.173205 | + | 0.300000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.00000 | + | 10.3923i | 0.422159 | + | 0.731200i | ||||
\(203\) | 4.89898 | + | 8.48528i | 0.343841 | + | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | −17.1464 | −1.19465 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 1.22474 | − | 2.12132i | 0.0847174 | − | 0.146735i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | + | 0.866025i | 0.0344214 | + | 0.0596196i | 0.882723 | − | 0.469894i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(212\) | −14.6969 | − | 25.4558i | −1.00939 | − | 1.74831i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | + | 31.1769i | −1.23045 | + | 2.13121i | ||||
\(215\) | −26.9444 | −1.83759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 1.22474 | − | 2.12132i | 0.0829502 | − | 0.143674i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.0000 | + | 20.7846i | 0.809040 | + | 1.40130i | ||||
\(221\) | −3.67423 | − | 6.36396i | −0.247156 | − | 0.428086i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.50000 | − | 6.06218i | 0.234377 | − | 0.405953i | −0.724714 | − | 0.689050i | \(-0.758028\pi\) |
0.959092 | + | 0.283096i | \(0.0913615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.0000 | −1.59646 | ||||||||
\(227\) | −4.89898 | + | 8.48528i | −0.325157 | + | 0.563188i | −0.981544 | − | 0.191236i | \(-0.938750\pi\) |
0.656387 | + | 0.754424i | \(0.272084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | −7.34847 | − | 12.7279i | −0.484544 | − | 0.839254i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000 | − | 20.7846i | 0.787839 | − | 1.36458i | ||||
\(233\) | −7.34847 | −0.481414 | −0.240707 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240707 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | 4.89898 | − | 8.48528i | 0.318896 | − | 0.552345i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.0000 | + | 31.1769i | 1.16677 | + | 2.02090i | ||||
\(239\) | 1.22474 | + | 2.12132i | 0.0792222 | + | 0.137217i | 0.902915 | − | 0.429820i | \(-0.141423\pi\) |
−0.823692 | + | 0.567037i | \(0.808090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | − | 13.8564i | 0.515325 | − | 0.892570i | −0.484516 | − | 0.874782i | \(-0.661004\pi\) |
0.999842 | − | 0.0177875i | \(-0.00566223\pi\) | |||||||
\(242\) | −12.2474 | −0.787296 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.0000 | 1.28037 | ||||||||
\(245\) | −3.67423 | + | 6.36396i | −0.234738 | + | 0.406579i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.500000 | − | 0.866025i | −0.0318142 | − | 0.0551039i | ||||
\(248\) | 2.44949 | + | 4.24264i | 0.155543 | + | 0.269408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | + | 20.7846i | −0.758947 | + | 1.31453i | ||||
\(251\) | −7.34847 | −0.463831 | −0.231916 | − | 0.972736i | \(-0.574499\pi\) | ||||
−0.231916 | + | 0.972736i | \(0.574499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 23.2702 | − | 40.3051i | 1.46010 | − | 2.52897i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | + | 27.7128i | 1.00000 | + | 1.73205i | ||||
\(257\) | 8.57321 | + | 14.8492i | 0.534782 | + | 0.926270i | 0.999174 | + | 0.0406402i | \(0.0129398\pi\) |
−0.464391 | + | 0.885630i | \(0.653727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | + | 13.8564i | −0.497096 | + | 0.860995i | ||||
\(260\) | 9.79796 | 0.607644 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.0000 | 1.85341 | ||||||||
\(263\) | 13.4722 | − | 23.3345i | 0.830731 | − | 1.43887i | −0.0667283 | − | 0.997771i | \(-0.521256\pi\) |
0.897459 | − | 0.441097i | \(-0.145411\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | + | 15.5885i | 0.552866 | + | 0.957591i | ||||
\(266\) | 2.44949 | + | 4.24264i | 0.150188 | + | 0.260133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0000 | − | 24.2487i | 0.855186 | − | 1.48123i | ||||
\(269\) | −22.0454 | −1.34413 | −0.672066 | − | 0.740491i | \(-0.734593\pi\) | ||||
−0.672066 | + | 0.740491i | \(0.734593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | 14.6969 | − | 25.4558i | 0.891133 | − | 1.54349i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | − | 20.7846i | −0.724947 | − | 1.25564i | ||||
\(275\) | −1.22474 | − | 2.12132i | −0.0738549 | − | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50000 | + | 9.52628i | −0.330463 | + | 0.572379i | −0.982603 | − | 0.185720i | \(-0.940538\pi\) |
0.652140 | + | 0.758099i | \(0.273872\pi\) | |||||||
\(278\) | −24.4949 | −1.46911 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −24.0000 | −1.43427 | ||||||||
\(281\) | 6.12372 | − | 10.6066i | 0.365311 | − | 0.632737i | −0.623515 | − | 0.781811i | \(-0.714296\pi\) |
0.988826 | + | 0.149074i | \(0.0476294\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.50000 | − | 14.7224i | −0.505273 | − | 0.875158i | −0.999981 | − | 0.00609896i | \(-0.998059\pi\) |
0.494709 | − | 0.869059i | \(-0.335275\pi\) | |||||||
\(284\) | −14.6969 | − | 25.4558i | −0.872103 | − | 1.51053i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | − | 5.19615i | 0.177394 | − | 0.307255i | ||||
\(287\) | 9.79796 | 0.578355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.0000 | 2.17647 | ||||||||
\(290\) | −14.6969 | + | 25.4558i | −0.863034 | + | 1.49482i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.0000 | − | 38.1051i | −1.28745 | − | 2.22993i | ||||
\(293\) | −2.44949 | − | 4.24264i | −0.143101 | − | 0.247858i | 0.785562 | − | 0.618783i | \(-0.212374\pi\) |
−0.928663 | + | 0.370925i | \(0.879041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00000 | + | 5.19615i | −0.174667 | + | 0.302532i | ||||
\(296\) | 39.1918 | 2.27798 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.0000 | 1.73785 | ||||||||
\(299\) | −1.22474 | + | 2.12132i | −0.0708288 | + | 0.122679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0000 | − | 19.0526i | −0.634029 | − | 1.09817i | ||||
\(302\) | −6.12372 | − | 10.6066i | −0.352381 | − | 0.610341i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | −12.2474 | −0.701287 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −9.79796 | + | 16.9706i | −0.558291 | + | 0.966988i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.00000 | − | 5.19615i | −0.170389 | − | 0.295122i | ||||
\(311\) | 12.2474 | + | 21.2132i | 0.694489 | + | 1.20289i | 0.970353 | + | 0.241694i | \(0.0777029\pi\) |
−0.275864 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000 | − | 13.8564i | 0.452187 | − | 0.783210i | −0.546335 | − | 0.837567i | \(-0.683977\pi\) |
0.998522 | + | 0.0543564i | \(0.0173107\pi\) | |||||||
\(314\) | 41.6413 | 2.34996 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.0000 | −1.57512 | ||||||||
\(317\) | −4.89898 | + | 8.48528i | −0.275154 | + | 0.476581i | −0.970174 | − | 0.242410i | \(-0.922062\pi\) |
0.695020 | + | 0.718991i | \(0.255396\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | −9.79796 | − | 16.9706i | −0.547723 | − | 0.948683i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.00000 | − | 10.3923i | 0.334367 | − | 0.579141i | ||||
\(323\) | 7.34847 | 0.408880 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 12.2474 | − | 21.2132i | 0.678323 | − | 1.17489i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.0000 | − | 20.7846i | −0.662589 | − | 1.14764i | ||||
\(329\) | −9.79796 | − | 16.9706i | −0.540179 | − | 0.935617i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | − | 6.06218i | 0.192377 | − | 0.333207i | −0.753660 | − | 0.657264i | \(-0.771714\pi\) |
0.946038 | + | 0.324057i | \(0.105047\pi\) | |||||||
\(332\) | −48.9898 | −2.68866 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −8.57321 | + | 14.8492i | −0.468405 | + | 0.811301i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | + | 24.2487i | 0.762629 | + | 1.32091i | 0.941491 | + | 0.337037i | \(0.109425\pi\) |
−0.178863 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(338\) | 14.6969 | + | 25.4558i | 0.799408 | + | 1.38462i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −36.0000 | + | 62.3538i | −1.95237 | + | 3.38161i | ||||
\(341\) | −2.44949 | −0.132647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −26.9444 | + | 46.6690i | −1.45274 | + | 2.51623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | − | 20.7846i | −0.645124 | − | 1.11739i | ||||
\(347\) | 12.2474 | + | 21.2132i | 0.657477 | + | 1.13878i | 0.981267 | + | 0.192655i | \(0.0617099\pi\) |
−0.323789 | + | 0.946129i | \(0.604957\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | + | 17.3205i | −0.535288 | + | 0.927146i | 0.463862 | + | 0.885908i | \(0.346463\pi\) |
−0.999149 | + | 0.0412379i | \(0.986870\pi\) | |||||||
\(350\) | 4.89898 | 0.261861 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.22474 | + | 2.12132i | −0.0651866 | + | 0.112906i | −0.896777 | − | 0.442483i | \(-0.854098\pi\) |
0.831590 | + | 0.555390i | \(0.187431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | + | 15.5885i | 0.477670 | + | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.0000 | − | 31.1769i | 0.951330 | − | 1.64775i | ||||
\(359\) | 29.3939 | 1.55135 | 0.775675 | − | 0.631133i | \(-0.217410\pi\) | ||||
0.775675 | + | 0.631133i | \(0.217410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −9.79796 | + | 16.9706i | −0.514969 | + | 0.891953i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | + | 6.92820i | 0.209657 | + | 0.363137i | ||||
\(365\) | 13.4722 | + | 23.3345i | 0.705167 | + | 1.22138i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50000 | + | 4.33013i | −0.130499 | + | 0.226031i | −0.923869 | − | 0.382709i | \(-0.874991\pi\) |
0.793370 | + | 0.608740i | \(0.208325\pi\) | |||||||
\(368\) | −9.79796 | −0.510754 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −48.0000 | −2.49540 | ||||||||
\(371\) | −7.34847 | + | 12.7279i | −0.381514 | + | 0.660801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5000 | − | 30.3109i | −0.906116 | − | 1.56944i | −0.819413 | − | 0.573204i | \(-0.805700\pi\) |
−0.0867031 | − | 0.996234i | \(-0.527633\pi\) | |||||||
\(374\) | 22.0454 | + | 38.1838i | 1.13994 | + | 1.97444i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | + | 41.5692i | −1.23771 | + | 2.14377i | ||||
\(377\) | 4.89898 | 0.252310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | −4.89898 | + | 8.48528i | −0.251312 | + | 0.435286i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | − | 20.7846i | −0.613973 | − | 1.06343i | ||||
\(383\) | −17.1464 | − | 29.6985i | −0.876142 | − | 1.51752i | −0.855542 | − | 0.517734i | \(-0.826776\pi\) |
−0.0205998 | − | 0.999788i | \(-0.506558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 10.3923i | 0.305788 | − | 0.529641i | ||||
\(386\) | 26.9444 | 1.37143 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.0000 | −1.42148 | ||||||||
\(389\) | 13.4722 | − | 23.3345i | 0.683067 | − | 1.18311i | −0.290973 | − | 0.956731i | \(-0.593979\pi\) |
0.974040 | − | 0.226376i | \(-0.0726878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | 7.34847 | + | 12.7279i | 0.371154 | + | 0.642857i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0000 | + | 31.1769i | −0.906827 | + | 1.57067i | ||||
\(395\) | 17.1464 | 0.862730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | −0.0501886 | −0.0250943 | − | 0.999685i | \(-0.507989\pi\) | ||||
−0.0250943 | + | 0.999685i | \(0.507989\pi\) | |||||||
\(398\) | 1.22474 | − | 2.12132i | 0.0613909 | − | 0.106332i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −17.1464 | − | 29.6985i | −0.856252 | − | 1.48307i | −0.875479 | − | 0.483256i | \(-0.839454\pi\) |
0.0192271 | − | 0.999815i | \(-0.493879\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.500000 | + | 0.866025i | −0.0249068 | + | 0.0431398i | ||||
\(404\) | −19.5959 | −0.974933 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | −9.79796 | + | 16.9706i | −0.485667 | + | 0.841200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | + | 24.2487i | 0.692255 | + | 1.19902i | 0.971097 | + | 0.238685i | \(0.0767162\pi\) |
−0.278842 | + | 0.960337i | \(0.589950\pi\) | |||||||
\(410\) | 14.6969 | + | 25.4558i | 0.725830 | + | 1.25717i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0000 | − | 24.2487i | 0.689730 | − | 1.19465i | ||||
\(413\) | −4.89898 | −0.241063 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.0000 | 1.47264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.00000 | + | 5.19615i | 0.146735 | + | 0.254152i | ||||
\(419\) | −17.1464 | − | 29.6985i | −0.837658 | − | 1.45087i | −0.891848 | − | 0.452335i | \(-0.850591\pi\) |
0.0541901 | − | 0.998531i | \(-0.482742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | + | 1.73205i | −0.0487370 | + | 0.0844150i | −0.889365 | − | 0.457198i | \(-0.848853\pi\) |
0.840628 | + | 0.541613i | \(0.182186\pi\) | |||||||
\(422\) | −2.44949 | −0.119239 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 36.0000 | 1.74831 | ||||||||
\(425\) | 3.67423 | − | 6.36396i | 0.178227 | − | 0.308697i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.00000 | − | 8.66025i | −0.241967 | − | 0.419099i | ||||
\(428\) | −29.3939 | − | 50.9117i | −1.42081 | − | 2.46091i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.0000 | − | 57.1577i | 1.59140 | − | 2.75639i | ||||
\(431\) | −7.34847 | −0.353963 | −0.176982 | − | 0.984214i | \(-0.556633\pi\) | ||||
−0.176982 | + | 0.984214i | \(0.556633\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | 2.44949 | − | 4.24264i | 0.117579 | − | 0.203653i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −1.22474 | − | 2.12132i | −0.0585875 | − | 0.101477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.00000 | + | 12.1244i | −0.334092 | + | 0.578664i | −0.983310 | − | 0.181938i | \(-0.941763\pi\) |
0.649218 | + | 0.760602i | \(0.275096\pi\) | |||||||
\(440\) | −29.3939 | −1.40130 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.0000 | 0.856173 | ||||||||
\(443\) | 6.12372 | − | 10.6066i | 0.290947 | − | 0.503935i | −0.683087 | − | 0.730337i | \(-0.739363\pi\) |
0.974034 | + | 0.226402i | \(0.0726964\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.57321 | + | 14.8492i | 0.405953 | + | 0.703132i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | − | 13.8564i | 0.377964 | − | 0.654654i | ||||
\(449\) | 22.0454 | 1.04039 | 0.520194 | − | 0.854048i | \(-0.325860\pi\) | ||||
0.520194 | + | 0.854048i | \(0.325860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 19.5959 | − | 33.9411i | 0.921714 | − | 1.59646i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.0000 | − | 20.7846i | −0.563188 | − | 0.975470i | ||||
\(455\) | −2.44949 | − | 4.24264i | −0.114834 | − | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5000 | + | 25.1147i | −0.678281 | + | 1.17482i | 0.297217 | + | 0.954810i | \(0.403942\pi\) |
−0.975498 | + | 0.220008i | \(0.929392\pi\) | |||||||
\(458\) | −2.44949 | −0.114457 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.0000 | 1.11901 | ||||||||
\(461\) | 13.4722 | − | 23.3345i | 0.627463 | − | 1.08680i | −0.360597 | − | 0.932722i | \(-0.617427\pi\) |
0.988059 | − | 0.154075i | \(-0.0492398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.50000 | + | 16.4545i | 0.441502 | + | 0.764705i | 0.997801 | − | 0.0662777i | \(-0.0211123\pi\) |
−0.556299 | + | 0.830982i | \(0.687779\pi\) | |||||||
\(464\) | 9.79796 | + | 16.9706i | 0.454859 | + | 0.787839i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.00000 | − | 15.5885i | 0.416917 | − | 0.722121i | ||||
\(467\) | 14.6969 | 0.680093 | 0.340047 | − | 0.940409i | \(-0.389557\pi\) | ||||
0.340047 | + | 0.940409i | \(0.389557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 29.3939 | − | 50.9117i | 1.35584 | − | 2.34838i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | −13.4722 | − | 23.3345i | −0.619452 | − | 1.07292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | − | 0.866025i | 0.0229416 | − | 0.0397360i | ||||
\(476\) | −58.7878 | −2.69453 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.00000 | −0.274434 | ||||||||
\(479\) | 13.4722 | − | 23.3345i | 0.615560 | − | 1.06618i | −0.374726 | − | 0.927136i | \(-0.622263\pi\) |
0.990286 | − | 0.139046i | \(-0.0444036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 19.5959 | + | 33.9411i | 0.892570 | + | 1.54598i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0000 | − | 17.3205i | 0.454545 | − | 0.787296i | ||||
\(485\) | 17.1464 | 0.778579 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0000 | 1.58600 | 0.793001 | − | 0.609221i | \(-0.208518\pi\) | ||||
0.793001 | + | 0.609221i | \(0.208518\pi\) | |||||||
\(488\) | −12.2474 | + | 21.2132i | −0.554416 | + | 0.960277i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.00000 | − | 15.5885i | −0.406579 | − | 0.704215i | ||||
\(491\) | 19.5959 | + | 33.9411i | 0.884351 | + | 1.53174i | 0.846455 | + | 0.532460i | \(0.178732\pi\) |
0.0378961 | + | 0.999282i | \(0.487934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | + | 31.1769i | −0.810679 | + | 1.40414i | ||||
\(494\) | 2.44949 | 0.110208 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −7.34847 | + | 12.7279i | −0.329624 | + | 0.570925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.00000 | − | 1.73205i | −0.0447661 | − | 0.0775372i | 0.842774 | − | 0.538267i | \(-0.180921\pi\) |
−0.887540 | + | 0.460730i | \(0.847588\pi\) | |||||||
\(500\) | −19.5959 | − | 33.9411i | −0.876356 | − | 1.51789i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | − | 15.5885i | 0.401690 | − | 0.695747i | ||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 7.34847 | − | 12.7279i | 0.326679 | − | 0.565825i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.0000 | + | 65.8179i | 1.68598 | + | 2.92020i | ||||
\(509\) | 4.89898 | + | 8.48528i | 0.217143 | + | 0.376103i | 0.953934 | − | 0.300018i | \(-0.0969927\pi\) |
−0.736790 | + | 0.676122i | \(0.763659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0000 | + | 19.0526i | −0.486611 | + | 0.842836i | ||||
\(512\) | −39.1918 | −1.73205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −42.0000 | −1.85254 | ||||||||
\(515\) | −8.57321 | + | 14.8492i | −0.377781 | + | 0.654336i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | −19.5959 | − | 33.9411i | −0.860995 | − | 1.49129i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | + | 10.3923i | −0.263117 | + | 0.455733i | ||||
\(521\) | 22.0454 | 0.965827 | 0.482913 | − | 0.875668i | \(-0.339579\pi\) | ||||
0.482913 | + | 0.875668i | \(0.339579\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0000 | −1.09317 | −0.546587 | − | 0.837402i | \(-0.684073\pi\) | ||||
−0.546587 | + | 0.837402i | \(0.684073\pi\) | |||||||
\(524\) | −24.4949 | + | 42.4264i | −1.07006 | + | 1.85341i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.0000 | + | 57.1577i | 1.43887 | + | 2.49219i | ||||
\(527\) | −3.67423 | − | 6.36396i | −0.160052 | − | 0.277218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.50000 | − | 14.7224i | 0.369565 | − | 0.640106i | ||||
\(530\) | −44.0908 | −1.91518 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 2.44949 | − | 4.24264i | 0.106099 | − | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | + | 31.1769i | 0.778208 | + | 1.34790i | ||||
\(536\) | 17.1464 | + | 29.6985i | 0.740613 | + | 1.28278i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.0000 | − | 46.7654i | 1.16405 | − | 2.01620i | ||||
\(539\) | −7.34847 | −0.316521 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.0000 | −1.20381 | −0.601907 | − | 0.798566i | \(-0.705592\pi\) | ||||
−0.601907 | + | 0.798566i | \(0.705592\pi\) | |||||||
\(542\) | 8.57321 | − | 14.8492i | 0.368251 | − | 0.637830i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.22474 | − | 2.12132i | −0.0524623 | − | 0.0908674i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.50000 | − | 11.2583i | 0.277920 | − | 0.481371i | −0.692948 | − | 0.720988i | \(-0.743688\pi\) |
0.970868 | + | 0.239616i | \(0.0770217\pi\) | |||||||
\(548\) | 39.1918 | 1.67419 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | −2.44949 | + | 4.24264i | −0.104352 | + | 0.180743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.00000 | + | 12.1244i | 0.297670 | + | 0.515580i | ||||
\(554\) | −13.4722 | − | 23.3345i | −0.572379 | − | 0.991389i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.0000 | − | 34.6410i | 0.848189 | − | 1.46911i | ||||
\(557\) | 7.34847 | 0.311365 | 0.155682 | − | 0.987807i | \(-0.450242\pi\) | ||||
0.155682 | + | 0.987807i | \(0.450242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0000 | −0.465250 | ||||||||
\(560\) | 9.79796 | − | 16.9706i | 0.414039 | − | 0.717137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.0000 | + | 25.9808i | 0.632737 | + | 1.09593i | ||||
\(563\) | −6.12372 | − | 10.6066i | −0.258084 | − | 0.447015i | 0.707644 | − | 0.706569i | \(-0.249758\pi\) |
−0.965729 | + | 0.259554i | \(0.916425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | + | 20.7846i | −0.504844 | + | 0.874415i | ||||
\(566\) | 41.6413 | 1.75032 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.0000 | 1.51053 | ||||||||
\(569\) | 6.12372 | − | 10.6066i | 0.256720 | − | 0.444652i | −0.708641 | − | 0.705569i | \(-0.750692\pi\) |
0.965361 | + | 0.260917i | \(0.0840249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000 | + | 8.66025i | 0.209243 | + | 0.362420i | 0.951476 | − | 0.307722i | \(-0.0995665\pi\) |
−0.742233 | + | 0.670142i | \(0.766233\pi\) | |||||||
\(572\) | 4.89898 | + | 8.48528i | 0.204837 | + | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | + | 20.7846i | −0.500870 | + | 0.867533i | ||||
\(575\) | −2.44949 | −0.102151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.0000 | −1.04076 | −0.520382 | − | 0.853934i | \(-0.674210\pi\) | ||||
−0.520382 | + | 0.853934i | \(0.674210\pi\) | |||||||
\(578\) | −45.3156 | + | 78.4889i | −1.88488 | + | 3.26471i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.0000 | − | 41.5692i | −0.996546 | − | 1.72607i | ||||
\(581\) | 12.2474 | + | 21.2132i | 0.508110 | + | 0.880072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | + | 15.5885i | −0.372742 | + | 0.645608i | ||||
\(584\) | 53.8888 | 2.22993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −1.22474 | + | 2.12132i | −0.0505506 | + | 0.0875563i | −0.890194 | − | 0.455583i | \(-0.849431\pi\) |
0.839643 | + | 0.543139i | \(0.182764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.500000 | − | 0.866025i | −0.0206021 | − | 0.0356840i | ||||
\(590\) | −7.34847 | − | 12.7279i | −0.302532 | − | 0.524000i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0000 | + | 27.7128i | −0.657596 | + | 1.13899i | ||||
\(593\) | 7.34847 | 0.301765 | 0.150883 | − | 0.988552i | \(-0.451788\pi\) | ||||
0.150883 | + | 0.988552i | \(0.451788\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.0000 | 1.47586 | ||||||||
\(596\) | −24.4949 | + | 42.4264i | −1.00335 | + | 1.73785i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | 19.5959 | + | 33.9411i | 0.800668 | + | 1.38680i | 0.919177 | + | 0.393844i | \(0.128855\pi\) |
−0.118510 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | − | 6.06218i | 0.142768 | − | 0.247281i | −0.785770 | − | 0.618519i | \(-0.787733\pi\) |
0.928538 | + | 0.371237i | \(0.121066\pi\) | |||||||
\(602\) | 53.8888 | 2.19634 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | −6.12372 | + | 10.6066i | −0.248965 | + | 0.431220i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0000 | − | 38.1051i | −0.892952 | − | 1.54664i | −0.836318 | − | 0.548244i | \(-0.815297\pi\) |
−0.0566340 | − | 0.998395i | \(-0.518037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0000 | − | 25.9808i | 0.607332 | − | 1.05193i | ||||
\(611\) | −9.79796 | −0.396383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | 0.444286 | 0.222143 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222143 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(614\) | −2.44949 | + | 4.24264i | −0.0988534 | + | 0.171219i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 20.7846i | −0.483494 | − | 0.837436i | ||||
\(617\) | 12.2474 | + | 21.2132i | 0.493064 | + | 0.854011i | 0.999968 | − | 0.00799089i | \(-0.00254361\pi\) |
−0.506904 | + | 0.862002i | \(0.669210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5000 | − | 42.4352i | 0.984738 | − | 1.70562i | 0.341644 | − | 0.939829i | \(-0.389016\pi\) |
0.643094 | − | 0.765787i | \(-0.277650\pi\) | |||||||
\(620\) | 9.79796 | 0.393496 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −60.0000 | −2.40578 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 19.5959 | + | 33.9411i | 0.783210 | + | 1.35656i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.0000 | + | 58.8897i | −1.35675 | + | 2.34996i | ||||
\(629\) | −58.7878 | −2.34402 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.0000 | 1.75161 | 0.875806 | − | 0.482663i | \(-0.160330\pi\) | ||||
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | 17.1464 | − | 29.6985i | 0.682048 | − | 1.18134i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.0000 | − | 20.7846i | −0.476581 | − | 0.825462i | ||||
\(635\) | −23.2702 | − | 40.3051i | −0.923448 | − | 1.59946i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50000 | + | 2.59808i | −0.0594322 | + | 0.102940i | ||||
\(638\) | −29.3939 | −1.16371 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.0000 | 1.89737 | ||||||||
\(641\) | −8.57321 | + | 14.8492i | −0.338622 | + | 0.586510i | −0.984174 | − | 0.177206i | \(-0.943294\pi\) |
0.645552 | + | 0.763716i | \(0.276627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0000 | − | 32.9090i | −0.749287 | − | 1.29780i | −0.948165 | − | 0.317779i | \(-0.897063\pi\) |
0.198878 | − | 0.980024i | \(-0.436270\pi\) | |||||||
\(644\) | 9.79796 | + | 16.9706i | 0.386094 | + | 0.668734i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.00000 | + | 15.5885i | −0.354100 | + | 0.613320i | ||||
\(647\) | 36.7423 | 1.44449 | 0.722245 | − | 0.691637i | \(-0.243110\pi\) | ||||
0.722245 | + | 0.691637i | \(0.243110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 1.22474 | − | 2.12132i | 0.0480384 | − | 0.0832050i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0000 | + | 34.6410i | 0.783260 | + | 1.35665i | ||||
\(653\) | 4.89898 | + | 8.48528i | 0.191712 | + | 0.332055i | 0.945818 | − | 0.324698i | \(-0.105263\pi\) |
−0.754106 | + | 0.656753i | \(0.771929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0000 | − | 25.9808i | 0.586098 | − | 1.01515i | ||||
\(656\) | 19.5959 | 0.765092 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 48.0000 | 1.87123 | ||||||||
\(659\) | 9.79796 | − | 16.9706i | 0.381674 | − | 0.661079i | −0.609627 | − | 0.792688i | \(-0.708681\pi\) |
0.991302 | + | 0.131609i | \(0.0420143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | − | 9.52628i | −0.213925 | − | 0.370529i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 8.57321 | + | 14.8492i | 0.333207 | + | 0.577132i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30.0000 | − | 51.9615i | 1.16423 | − | 2.01650i | ||||
\(665\) | 4.89898 | 0.189974 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | −9.79796 | + | 16.9706i | −0.379094 | + | 0.656611i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.0000 | − | 36.3731i | −0.811301 | − | 1.40521i | ||||
\(671\) | −6.12372 | − | 10.6066i | −0.236404 | − | 0.409463i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5000 | + | 25.1147i | −0.558934 | + | 0.968102i | 0.438652 | + | 0.898657i | \(0.355456\pi\) |
−0.997586 | + | 0.0694449i | \(0.977877\pi\) | |||||||
\(674\) | −68.5857 | −2.64182 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.0000 | −1.84615 | ||||||||
\(677\) | −23.2702 | + | 40.3051i | −0.894345 | + | 1.54905i | −0.0597310 | + | 0.998215i | \(0.519024\pi\) |
−0.834614 | + | 0.550836i | \(0.814309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | + | 12.1244i | 0.268635 | + | 0.465290i | ||||
\(680\) | −44.0908 | − | 76.3675i | −1.69081 | − | 2.92856i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | −22.0454 | −0.843544 | −0.421772 | − | 0.906702i | \(-0.638592\pi\) | ||||
−0.421772 | + | 0.906702i | \(0.638592\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0000 | −0.916993 | ||||||||
\(686\) | 24.4949 | − | 42.4264i | 0.935220 | − | 1.61985i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22.0000 | − | 38.1051i | −0.838742 | − | 1.45274i | ||||
\(689\) | 3.67423 | + | 6.36396i | 0.139977 | + | 0.242448i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5000 | + | 40.7032i | −0.893982 | + | 1.54842i | −0.0589228 | + | 0.998263i | \(0.518767\pi\) |
−0.835059 | + | 0.550160i | \(0.814567\pi\) | |||||||
\(692\) | 39.1918 | 1.48985 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −60.0000 | −2.27757 | ||||||||
\(695\) | −12.2474 | + | 21.2132i | −0.464572 | + | 0.804663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | −24.4949 | − | 42.4264i | −0.927146 | − | 1.60586i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.00000 | + | 6.92820i | −0.151186 | + | 0.261861i | ||||
\(701\) | −14.6969 | −0.555096 | −0.277548 | − | 0.960712i | \(-0.589522\pi\) | ||||
−0.277548 | + | 0.960712i | \(0.589522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 9.79796 | − | 16.9706i | 0.369274 | − | 0.639602i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.00000 | − | 5.19615i | −0.112906 | − | 0.195560i | ||||
\(707\) | 4.89898 | + | 8.48528i | 0.184245 | + | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.50000 | − | 6.06218i | 0.131445 | − | 0.227670i | −0.792789 | − | 0.609497i | \(-0.791372\pi\) |
0.924234 | + | 0.381827i | \(0.124705\pi\) | |||||||
\(710\) | −44.0908 | −1.65470 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.22474 | + | 2.12132i | −0.0458671 | + | 0.0794441i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | − | 5.19615i | −0.112194 | − | 0.194325i | ||||
\(716\) | 29.3939 | + | 50.9117i | 1.09850 | + | 1.90266i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.0000 | + | 62.3538i | −1.34351 | + | 2.32702i | ||||
\(719\) | −36.7423 | −1.37026 | −0.685129 | − | 0.728422i | \(-0.740254\pi\) | ||||
−0.685129 | + | 0.728422i | \(0.740254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 22.0454 | − | 38.1838i | 0.820445 | − | 1.42105i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.0000 | − | 27.7128i | −0.594635 | − | 1.02994i | ||||
\(725\) | 2.44949 | + | 4.24264i | 0.0909718 | + | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00000 | + | 12.1244i | −0.259616 | + | 0.449667i | −0.966139 | − | 0.258022i | \(-0.916929\pi\) |
0.706523 | + | 0.707690i | \(0.250263\pi\) | |||||||
\(728\) | −9.79796 | −0.363137 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −66.0000 | −2.44277 | ||||||||
\(731\) | 40.4166 | − | 70.0036i | 1.49486 | − | 2.58918i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.50000 | − | 14.7224i | −0.313955 | − | 0.543785i | 0.665260 | − | 0.746612i | \(-0.268321\pi\) |
−0.979215 | + | 0.202826i | \(0.934987\pi\) | |||||||
\(734\) | −6.12372 | − | 10.6066i | −0.226031 | − | 0.391497i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.1464 | −0.631597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00000 | −0.0367856 | −0.0183928 | − | 0.999831i | \(-0.505855\pi\) | ||||
−0.0183928 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(740\) | 39.1918 | − | 67.8823i | 1.44072 | − | 2.49540i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.0000 | − | 31.1769i | −0.660801 | − | 1.14454i | ||||
\(743\) | 15.9217 | + | 27.5772i | 0.584110 | + | 1.01171i | 0.994986 | + | 0.100017i | \(0.0318896\pi\) |
−0.410876 | + | 0.911691i | \(0.634777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0000 | − | 25.9808i | 0.549557 | − | 0.951861i | ||||
\(746\) | 85.7321 | 3.13888 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −72.0000 | −2.63258 | ||||||||
\(749\) | −14.6969 | + | 25.4558i | −0.537014 | + | 0.930136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | − | 22.5167i | −0.474377 | − | 0.821645i | 0.525193 | − | 0.850983i | \(-0.323993\pi\) |
−0.999570 | + | 0.0293387i | \(0.990660\pi\) | |||||||
\(752\) | −19.5959 | − | 33.9411i | −0.714590 | − | 1.23771i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | −12.2474 | −0.445730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.00000 | −0.254419 | −0.127210 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127210 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(758\) | −9.79796 | + | 16.9706i | −0.355878 | + | 0.616399i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | − | 10.3923i | −0.217643 | − | 0.376969i | ||||
\(761\) | 1.22474 | + | 2.12132i | 0.0443970 | + | 0.0768978i | 0.887370 | − | 0.461058i | \(-0.152530\pi\) |
−0.842973 | + | 0.537956i | \(0.819197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | − | 1.73205i | 0.0362024 | − | 0.0627044i | ||||
\(764\) | 39.1918 | 1.41791 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 84.0000 | 3.03504 | ||||||||
\(767\) | −1.22474 | + | 2.12132i | −0.0442230 | + | 0.0765964i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5000 | + | 32.0429i | 0.667127 | + | 1.15550i | 0.978704 | + | 0.205277i | \(0.0658095\pi\) |
−0.311577 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(770\) | 14.6969 | + | 25.4558i | 0.529641 | + | 0.917365i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.0000 | + | 38.1051i | −0.791797 | + | 1.37143i | ||||
\(773\) | −44.0908 | −1.58584 | −0.792918 | − | 0.609328i | \(-0.791439\pi\) | ||||
−0.792918 | + | 0.609328i | \(0.791439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 17.1464 | − | 29.6985i | 0.615521 | − | 1.06611i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.0000 | + | 57.1577i | 1.18311 | + | 2.04920i | ||||
\(779\) | 2.44949 | + | 4.24264i | 0.0877621 | + | 0.152008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | + | 15.5885i | −0.322045 | + | 0.557799i | ||||
\(782\) | 44.0908 | 1.57668 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 20.8207 | − | 36.0624i | 0.743121 | − | 1.28712i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.5000 | + | 21.6506i | 0.445577 | + | 0.771762i | 0.998092 | − | 0.0617409i | \(-0.0196653\pi\) |
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | −29.3939 | − | 50.9117i | −1.04711 | − | 1.81365i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.0000 | + | 36.3731i | −0.747146 | + | 1.29410i | ||||
\(791\) | −19.5959 | −0.696751 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | −0.177555 | ||||||||
\(794\) | 1.22474 | − | 2.12132i | 0.0434646 | − | 0.0752828i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −20.8207 | − | 36.0624i | −0.737506 | − | 1.27740i | −0.953615 | − | 0.301028i | \(-0.902670\pi\) |
0.216110 | − | 0.976369i | \(-0.430663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | − | 62.3538i | 1.27359 | − | 2.20592i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 84.0000 | 2.96614 | ||||||||
\(803\) | −13.4722 | + | 23.3345i | −0.475423 | + | 0.823457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | − | 10.3923i | −0.211472 | − | 0.366281i | ||||
\(806\) | −1.22474 | − | 2.12132i | −0.0431398 | − | 0.0747203i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0000 | − | 20.7846i | 0.422159 | − | 0.731200i | ||||
\(809\) | 22.0454 | 0.775075 | 0.387538 | − | 0.921854i | \(-0.373326\pi\) | ||||
0.387538 | + | 0.921854i | \(0.373326\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | 19.5959 | − | 33.9411i | 0.687682 | − | 1.19110i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.0000 | − | 41.5692i | −0.841200 | − | 1.45700i | ||||
\(815\) | −12.2474 | − | 21.2132i | −0.429009 | − | 0.743066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.50000 | − | 9.52628i | 0.192421 | − | 0.333282i | ||||
\(818\) | −68.5857 | −2.39804 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.0000 | −1.67623 | ||||||||
\(821\) | −19.5959 | + | 33.9411i | −0.683902 | + | 1.18455i | 0.289878 | + | 0.957064i | \(0.406385\pi\) |
−0.973780 | + | 0.227490i | \(0.926948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5000 | − | 30.3109i | −0.610012 | − | 1.05657i | −0.991238 | − | 0.132089i | \(-0.957831\pi\) |
0.381226 | − | 0.924482i | \(-0.375502\pi\) | |||||||
\(824\) | 17.1464 | + | 29.6985i | 0.597324 | + | 1.03460i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | − | 10.3923i | 0.208767 | − | 0.361595i | ||||
\(827\) | −22.0454 | −0.766594 | −0.383297 | − | 0.923625i | \(-0.625211\pi\) | ||||
−0.383297 | + | 0.923625i | \(0.625211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.0000 | −1.28506 | −0.642532 | − | 0.766259i | \(-0.722116\pi\) | ||||
−0.642532 | + | 0.766259i | \(0.722116\pi\) | |||||||
\(830\) | −36.7423 | + | 63.6396i | −1.27535 | + | 2.20896i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 6.92820i | −0.138675 | − | 0.240192i | ||||
\(833\) | −11.0227 | − | 19.0919i | −0.381914 | − | 0.661495i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | −9.79796 | −0.338869 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 84.0000 | 2.90173 | ||||||||
\(839\) | 2.44949 | − | 4.24264i | 0.0845658 | − | 0.146472i | −0.820640 | − | 0.571445i | \(-0.806383\pi\) |
0.905206 | + | 0.424973i | \(0.139716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.50000 | + | 4.33013i | 0.0862069 | + | 0.149315i | ||||
\(842\) | −2.44949 | − | 4.24264i | −0.0844150 | − | 0.146211i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | 29.3939 | 1.01118 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0000 | −0.343604 | ||||||||
\(848\) | −14.6969 | + | 25.4558i | −0.504695 | + | 0.874157i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.00000 | + | 15.5885i | 0.308697 | + | 0.534680i | ||||
\(851\) | 9.79796 | + | 16.9706i | 0.335870 | + | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.50000 | − | 11.2583i | 0.222556 | − | 0.385478i | −0.733028 | − | 0.680199i | \(-0.761893\pi\) |
0.955583 | + | 0.294721i | \(0.0952267\pi\) | |||||||
\(854\) | 24.4949 | 0.838198 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 72.0000 | 2.46091 | ||||||||
\(857\) | −12.2474 | + | 21.2132i | −0.418365 | + | 0.724629i | −0.995775 | − | 0.0918249i | \(-0.970730\pi\) |
0.577410 | + | 0.816454i | \(0.304063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0000 | − | 22.5167i | −0.443554 | − | 0.768259i | 0.554396 | − | 0.832253i | \(-0.312949\pi\) |
−0.997950 | + | 0.0639945i | \(0.979616\pi\) | |||||||
\(860\) | 53.8888 | + | 93.3381i | 1.83759 | + | 3.18280i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.00000 | − | 15.5885i | 0.306541 | − | 0.530945i | ||||
\(863\) | −7.34847 | −0.250145 | −0.125072 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125072 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0000 | −0.816024 | ||||||||
\(866\) | −20.8207 | + | 36.0624i | −0.707515 | + | 1.22545i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.00000 | + | 6.92820i | 0.135769 | + | 0.235159i | ||||
\(869\) | 8.57321 | + | 14.8492i | 0.290826 | + | 0.503726i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.50000 | + | 6.06218i | −0.118593 | + | 0.205409i | ||||
\(872\) | −4.89898 | −0.165900 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | −9.79796 | + | 16.9706i | −0.331231 | + | 0.573710i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.00000 | − | 6.92820i | −0.135070 | − | 0.233949i | 0.790554 | − | 0.612392i | \(-0.209793\pi\) |
−0.925624 | + | 0.378444i | \(0.876459\pi\) | |||||||
\(878\) | −17.1464 | − | 29.6985i | −0.578664 | − | 1.00228i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.0000 | − | 20.7846i | 0.404520 | − | 0.700649i | ||||
\(881\) | 36.7423 | 1.23788 | 0.618941 | − | 0.785438i | \(-0.287562\pi\) | ||||
0.618941 | + | 0.785438i | \(0.287562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0000 | 0.572096 | 0.286048 | − | 0.958215i | \(-0.407658\pi\) | ||||
0.286048 | + | 0.958215i | \(0.407658\pi\) | |||||||
\(884\) | −14.6969 | + | 25.4558i | −0.494312 | + | 0.856173i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0000 | + | 25.9808i | 0.503935 | + | 0.872841i | ||||
\(887\) | 8.57321 | + | 14.8492i | 0.287860 | + | 0.498589i | 0.973299 | − | 0.229542i | \(-0.0737228\pi\) |
−0.685438 | + | 0.728131i | \(0.740389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0000 | − | 32.9090i | 0.637240 | − | 1.10373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | 4.89898 | − | 8.48528i | 0.163938 | − | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0000 | − | 31.1769i | −0.601674 | − | 1.04213i | ||||
\(896\) | 19.5959 | + | 33.9411i | 0.654654 | + | 1.13389i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.0000 | + | 46.7654i | −0.901002 | + | 1.56058i | ||||
\(899\) | 4.89898 | 0.163390 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.0000 | −1.79900 | ||||||||
\(902\) | −14.6969 | + | 25.4558i | −0.489355 | + | 0.847587i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.0000 | + | 41.5692i | 0.798228 | + | 1.38257i | ||||
\(905\) | 9.79796 | + | 16.9706i | 0.325695 | + | 0.564121i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.50000 | − | 6.06218i | 0.116216 | − | 0.201291i | −0.802049 | − | 0.597258i | \(-0.796257\pi\) |
0.918265 | + | 0.395966i | \(0.129590\pi\) | |||||||
\(908\) | 39.1918 | 1.30063 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | 0.397796 | ||||||||
\(911\) | 6.12372 | − | 10.6066i | 0.202888 | − | 0.351412i | −0.746570 | − | 0.665307i | \(-0.768301\pi\) |
0.949458 | + | 0.313895i | \(0.101634\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0000 | + | 25.9808i | 0.496428 | + | 0.859838i | ||||
\(914\) | −35.5176 | − | 61.5183i | −1.17482 | − | 2.03484i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | − | 3.46410i | 0.0660819 | − | 0.114457i | ||||
\(917\) | 24.4949 | 0.808893 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | −14.6969 | + | 25.4558i | −0.484544 | + | 0.839254i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.0000 | + | 57.1577i | 1.08680 | + | 1.88239i | ||||
\(923\) | 3.67423 | + | 6.36396i | 0.120939 | + | 0.209472i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | −46.5403 | −1.52941 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4722 | − | 23.3345i | 0.442008 | − | 0.765581i | −0.555830 | − | 0.831296i | \(-0.687599\pi\) |
0.997838 | + | 0.0657150i | \(0.0209328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50000 | − | 2.59808i | −0.0491605 | − | 0.0851485i | ||||
\(932\) | 14.6969 | + | 25.4558i | 0.481414 | + | 0.833834i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.0000 | + | 31.1769i | −0.588978 | + | 1.02014i | ||||
\(935\) | 44.0908 | 1.44192 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.00000 | 0.261349 | 0.130674 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130674 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(938\) | 17.1464 | − | 29.6985i | 0.559851 | − | 0.969690i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48.0000 | + | 83.1384i | 1.56559 | + | 2.71168i | ||||
\(941\) | 4.89898 | + | 8.48528i | 0.159702 | + | 0.276612i | 0.934761 | − | 0.355276i | \(-0.115613\pi\) |
−0.775059 | + | 0.631889i | \(0.782280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | − | 10.3923i | 0.195387 | − | 0.338420i | ||||
\(944\) | −9.79796 | −0.318896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 66.0000 | 2.14585 | ||||||||
\(947\) | −12.2474 | + | 21.2132i | −0.397989 | + | 0.689336i | −0.993478 | − | 0.114027i | \(-0.963625\pi\) |
0.595489 | + | 0.803363i | \(0.296958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | + | 9.52628i | 0.178538 | + | 0.309236i | ||||
\(950\) | 1.22474 | + | 2.12132i | 0.0397360 | + | 0.0688247i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36.0000 | − | 62.3538i | 1.16677 | − | 2.02090i | ||||
\(953\) | 29.3939 | 0.952161 | 0.476081 | − | 0.879402i | \(-0.342057\pi\) | ||||
0.476081 | + | 0.879402i | \(0.342057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | −0.776622 | ||||||||
\(956\) | 4.89898 | − | 8.48528i | 0.158444 | − | 0.274434i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.0000 | + | 57.1577i | 1.06618 | + | 1.84668i | ||||
\(959\) | −9.79796 | − | 16.9706i | −0.316393 | − | 0.548008i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | −19.5959 | −0.631798 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −64.0000 | −2.06130 | ||||||||
\(965\) | 13.4722 | − | 23.3345i | 0.433685 | − | 0.751165i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.50000 | + | 6.06218i | 0.112552 | + | 0.194946i | 0.916799 | − | 0.399350i | \(-0.130764\pi\) |
−0.804246 | + | 0.594296i | \(0.797431\pi\) | |||||||
\(968\) | 12.2474 | + | 21.2132i | 0.393648 | + | 0.681818i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.0000 | + | 36.3731i | −0.674269 | + | 1.16787i | ||||
\(971\) | 29.3939 | 0.943294 | 0.471647 | − | 0.881787i | \(-0.343660\pi\) | ||||
0.471647 | + | 0.881787i | \(0.343660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | −0.641171 | ||||||||
\(974\) | −42.8661 | + | 74.2462i | −1.37352 | + | 2.37900i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | − | 17.3205i | −0.320092 | − | 0.554416i | ||||
\(977\) | 12.2474 | + | 21.2132i | 0.391831 | + | 0.678671i | 0.992691 | − | 0.120683i | \(-0.0385086\pi\) |
−0.600860 | + | 0.799354i | \(0.705175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 29.3939 | 0.938953 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −96.0000 | −3.06348 | ||||||||
\(983\) | 2.44949 | − | 4.24264i | 0.0781266 | − | 0.135319i | −0.824315 | − | 0.566131i | \(-0.808439\pi\) |
0.902442 | + | 0.430812i | \(0.141773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000 | + | 31.1769i | 0.573528 | + | 0.993379i | ||||
\(986\) | −44.0908 | − | 76.3675i | −1.40414 | − | 2.43204i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | + | 3.46410i | −0.0636285 | + | 0.110208i | ||||
\(989\) | −26.9444 | −0.856782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.00000 | −0.222362 | −0.111181 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111181 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.0000 | − | 31.1769i | −0.570925 | − | 0.988872i | ||||
\(995\) | −1.22474 | − | 2.12132i | −0.0388270 | − | 0.0672504i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.0000 | + | 43.3013i | −0.791758 | + | 1.37136i | 0.133120 | + | 0.991100i | \(0.457501\pi\) |
−0.924878 | + | 0.380265i | \(0.875833\pi\) | |||||||
\(998\) | 4.89898 | 0.155074 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 243.2.c.c.163.1 | 4 | ||
3.2 | odd | 2 | inner | 243.2.c.c.163.2 | 4 | ||
9.2 | odd | 6 | 243.2.a.d.1.1 | ✓ | 2 | ||
9.4 | even | 3 | inner | 243.2.c.c.82.1 | 4 | ||
9.5 | odd | 6 | inner | 243.2.c.c.82.2 | 4 | ||
9.7 | even | 3 | 243.2.a.d.1.2 | yes | 2 | ||
27.2 | odd | 18 | 729.2.e.p.325.1 | 12 | |||
27.4 | even | 9 | 729.2.e.p.163.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.p.406.1 | 12 | |||
27.7 | even | 9 | 729.2.e.p.82.2 | 12 | |||
27.11 | odd | 18 | 729.2.e.p.568.2 | 12 | |||
27.13 | even | 9 | 729.2.e.p.649.2 | 12 | |||
27.14 | odd | 18 | 729.2.e.p.649.1 | 12 | |||
27.16 | even | 9 | 729.2.e.p.568.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.p.82.1 | 12 | |||
27.22 | even | 9 | 729.2.e.p.406.2 | 12 | |||
27.23 | odd | 18 | 729.2.e.p.163.2 | 12 | |||
27.25 | even | 9 | 729.2.e.p.325.2 | 12 | |||
36.7 | odd | 6 | 3888.2.a.z.1.1 | 2 | |||
36.11 | even | 6 | 3888.2.a.z.1.2 | 2 | |||
45.29 | odd | 6 | 6075.2.a.bn.1.2 | 2 | |||
45.34 | even | 6 | 6075.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
243.2.a.d.1.1 | ✓ | 2 | 9.2 | odd | 6 | ||
243.2.a.d.1.2 | yes | 2 | 9.7 | even | 3 | ||
243.2.c.c.82.1 | 4 | 9.4 | even | 3 | inner | ||
243.2.c.c.82.2 | 4 | 9.5 | odd | 6 | inner | ||
243.2.c.c.163.1 | 4 | 1.1 | even | 1 | trivial | ||
243.2.c.c.163.2 | 4 | 3.2 | odd | 2 | inner | ||
729.2.e.p.82.1 | 12 | 27.20 | odd | 18 | |||
729.2.e.p.82.2 | 12 | 27.7 | even | 9 | |||
729.2.e.p.163.1 | 12 | 27.4 | even | 9 | |||
729.2.e.p.163.2 | 12 | 27.23 | odd | 18 | |||
729.2.e.p.325.1 | 12 | 27.2 | odd | 18 | |||
729.2.e.p.325.2 | 12 | 27.25 | even | 9 | |||
729.2.e.p.406.1 | 12 | 27.5 | odd | 18 | |||
729.2.e.p.406.2 | 12 | 27.22 | even | 9 | |||
729.2.e.p.568.1 | 12 | 27.16 | even | 9 | |||
729.2.e.p.568.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.p.649.1 | 12 | 27.14 | odd | 18 | |||
729.2.e.p.649.2 | 12 | 27.13 | even | 9 | |||
3888.2.a.z.1.1 | 2 | 36.7 | odd | 6 | |||
3888.2.a.z.1.2 | 2 | 36.11 | even | 6 | |||
6075.2.a.bn.1.1 | 2 | 45.34 | even | 6 | |||
6075.2.a.bn.1.2 | 2 | 45.29 | odd | 6 |