Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.8 | ||
Root | \(-1.41701 - 1.41701i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.127 |
Dual form | 1638.2.bj.i.1135.5 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.18381i | 1.42384i | 0.702258 | + | 0.711922i | \(0.252175\pi\) | ||||
−0.702258 | + | 0.711922i | \(0.747825\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.59191 | + | 2.75726i | 0.503405 | + | 0.871923i | ||||
\(11\) | 3.49326 | − | 2.01684i | 1.05326 | − | 0.608099i | 0.129698 | − | 0.991553i | \(-0.458599\pi\) |
0.923560 | + | 0.383455i | \(0.125266\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.333648 | − | 3.59008i | −0.0925372 | − | 0.995709i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.23249 | − | 2.13473i | 0.298922 | − | 0.517748i | −0.676968 | − | 0.736013i | \(-0.736706\pi\) |
0.975890 | + | 0.218265i | \(0.0700397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.595420 | + | 0.343766i | 0.136599 | + | 0.0788653i | 0.566742 | − | 0.823895i | \(-0.308204\pi\) |
−0.430143 | + | 0.902761i | \(0.641537\pi\) | |||||||
\(20\) | 2.75726 | + | 1.59191i | 0.616543 | + | 0.355961i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.01684 | − | 3.49326i | 0.429991 | − | 0.744766i | ||||
\(23\) | 2.89543 | + | 5.01503i | 0.603739 | + | 1.04571i | 0.992249 | + | 0.124262i | \(0.0396564\pi\) |
−0.388510 | + | 0.921444i | \(0.627010\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.13667 | −1.02733 | ||||||||
\(26\) | −2.08399 | − | 2.94228i | −0.408704 | − | 0.577028i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866025 | − | 0.500000i | 0.163663 | − | 0.0944911i | ||||
\(29\) | 0.940078 | + | 1.62826i | 0.174568 | + | 0.302361i | 0.940012 | − | 0.341142i | \(-0.110814\pi\) |
−0.765444 | + | 0.643503i | \(0.777480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17543i | 0.749929i | 0.927039 | + | 0.374964i | \(0.122345\pi\) | ||||
−0.927039 | + | 0.374964i | \(0.877655\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.46497i | − | 0.422739i | ||||||
\(35\) | −1.59191 | + | 2.75726i | −0.269081 | + | 0.466063i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.322768 | + | 0.186350i | −0.0530628 | + | 0.0306358i | −0.526297 | − | 0.850301i | \(-0.676420\pi\) |
0.473234 | + | 0.880937i | \(0.343087\pi\) | |||||||
\(38\) | 0.687532 | 0.111532 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.18381 | 0.503405 | ||||||||
\(41\) | 6.83868 | − | 3.94832i | 1.06802 | − | 0.616623i | 0.140382 | − | 0.990097i | \(-0.455167\pi\) |
0.927641 | + | 0.373474i | \(0.121834\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.48320 | − | 4.30103i | 0.378684 | − | 0.655900i | −0.612187 | − | 0.790713i | \(-0.709710\pi\) |
0.990871 | + | 0.134813i | \(0.0430433\pi\) | |||||||
\(44\) | − | 4.03367i | − | 0.608099i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.01503 | + | 2.89543i | 0.739426 | + | 0.426908i | ||||
\(47\) | 11.8723i | 1.73176i | 0.500254 | + | 0.865879i | \(0.333240\pi\) | ||||
−0.500254 | + | 0.865879i | \(0.666760\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −4.44848 | + | 2.56833i | −0.629111 | + | 0.363217i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.27592 | − | 1.50609i | −0.454289 | − | 0.208858i | ||||
\(53\) | 9.59637 | 1.31816 | 0.659081 | − | 0.752072i | \(-0.270945\pi\) | ||||
0.659081 | + | 0.752072i | \(0.270945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.42123 | + | 11.1219i | 0.865838 | + | 1.49968i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.62826 | + | 0.940078i | 0.213801 | + | 0.123438i | ||||
\(59\) | 2.23154 | + | 1.28838i | 0.290522 | + | 0.167733i | 0.638177 | − | 0.769889i | \(-0.279689\pi\) |
−0.347655 | + | 0.937623i | \(0.613022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.79497 | + | 11.7692i | −0.870006 | + | 1.50690i | −0.00801784 | + | 0.999968i | \(0.502552\pi\) |
−0.861989 | + | 0.506928i | \(0.830781\pi\) | |||||||
\(62\) | 2.08771 | + | 3.61603i | 0.265140 | + | 0.459236i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 11.4301 | − | 1.06227i | 1.41774 | − | 0.131759i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.46491 | − | 4.30987i | 0.911984 | − | 0.526534i | 0.0309151 | − | 0.999522i | \(-0.490158\pi\) |
0.881069 | + | 0.472988i | \(0.156825\pi\) | |||||||
\(68\) | −1.23249 | − | 2.13473i | −0.149461 | − | 0.258874i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.18381i | 0.380538i | ||||||||
\(71\) | −9.08320 | − | 5.24419i | −1.07798 | − | 0.622371i | −0.147627 | − | 0.989043i | \(-0.547164\pi\) |
−0.930350 | + | 0.366672i | \(0.880497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5347i | 1.93524i | 0.252406 | + | 0.967621i | \(0.418778\pi\) | ||||
−0.252406 | + | 0.967621i | \(0.581222\pi\) | |||||||
\(74\) | −0.186350 | + | 0.322768i | −0.0216628 | + | 0.0375211i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.595420 | − | 0.343766i | 0.0682993 | − | 0.0394326i | ||||
\(77\) | 4.03367 | 0.459680 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.2874 | −1.49495 | −0.747477 | − | 0.664288i | \(-0.768735\pi\) | ||||
−0.747477 | + | 0.664288i | \(0.768735\pi\) | |||||||
\(80\) | 2.75726 | − | 1.59191i | 0.308271 | − | 0.177981i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.94832 | − | 6.83868i | 0.436019 | − | 0.755206i | ||||
\(83\) | − | 9.39302i | − | 1.03102i | −0.856884 | − | 0.515509i | \(-0.827603\pi\) | ||
0.856884 | − | 0.515509i | \(-0.172397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.79658 | + | 3.92401i | 0.737192 | + | 0.425618i | ||||
\(86\) | − | 4.96640i | − | 0.535540i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.01684 | − | 3.49326i | −0.214995 | − | 0.372383i | ||||
\(89\) | 7.55214 | − | 4.36023i | 0.800525 | − | 0.462183i | −0.0431297 | − | 0.999069i | \(-0.513733\pi\) |
0.843655 | + | 0.536886i | \(0.180400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50609 | − | 3.27592i | 0.157881 | − | 0.343410i | ||||
\(92\) | 5.79086 | 0.603739 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.93616 | + | 10.2817i | 0.612269 | + | 1.06048i | ||||
\(95\) | −1.09449 | + | 1.89571i | −0.112292 | + | 0.194495i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.32679 | − | 3.07542i | −0.540854 | − | 0.312262i | 0.204571 | − | 0.978852i | \(-0.434420\pi\) |
−0.745425 | + | 0.666590i | \(0.767753\pi\) | |||||||
\(98\) | 0.866025 | + | 0.500000i | 0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.56833 | + | 4.44848i | −0.256833 | + | 0.444848i | ||||
\(101\) | 3.54879 | + | 6.14668i | 0.353117 | + | 0.611617i | 0.986794 | − | 0.161981i | \(-0.0517883\pi\) |
−0.633677 | + | 0.773598i | \(0.718455\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.44343 | −0.831956 | −0.415978 | − | 0.909375i | \(-0.636561\pi\) | ||||
−0.415978 | + | 0.909375i | \(0.636561\pi\) | |||||||
\(104\) | −3.59008 | + | 0.333648i | −0.352036 | + | 0.0327168i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.31070 | − | 4.79818i | 0.807206 | − | 0.466041i | ||||
\(107\) | −5.42496 | − | 9.39631i | −0.524451 | − | 0.908376i | −0.999595 | − | 0.0284677i | \(-0.990937\pi\) |
0.475144 | − | 0.879908i | \(-0.342396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9645i | − | 1.43334i | −0.697414 | − | 0.716669i | \(-0.745666\pi\) | ||
0.697414 | − | 0.716669i | \(-0.254334\pi\) | |||||||
\(110\) | 11.1219 | + | 6.42123i | 1.06043 | + | 0.612240i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 4.75100 | − | 8.22897i | 0.446936 | − | 0.774117i | −0.551248 | − | 0.834341i | \(-0.685848\pi\) |
0.998185 | + | 0.0602246i | \(0.0191817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.9669 | + | 9.21851i | −1.48892 | + | 0.859630i | ||||
\(116\) | 1.88016 | 0.174568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.57677 | 0.237211 | ||||||||
\(119\) | 2.13473 | − | 1.23249i | 0.195690 | − | 0.112982i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.63525 | − | 4.56440i | 0.239569 | − | 0.414945i | ||||
\(122\) | 13.5899i | 1.23037i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.61603 | + | 2.08771i | 0.324729 | + | 0.187482i | ||||
\(125\) | − | 0.435119i | − | 0.0389182i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.28578 | − | 7.42319i | −0.380302 | − | 0.658702i | 0.610803 | − | 0.791782i | \(-0.290847\pi\) |
−0.991105 | + | 0.133080i | \(0.957513\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.36766 | − | 6.63503i | 0.821598 | − | 0.581930i | ||||
\(131\) | 9.45294 | 0.825907 | 0.412953 | − | 0.910752i | \(-0.364497\pi\) | ||||
0.412953 | + | 0.910752i | \(0.364497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.343766 | + | 0.595420i | 0.0298083 | + | 0.0516295i | ||||
\(134\) | 4.30987 | − | 7.46491i | 0.372316 | − | 0.644870i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.13473 | − | 1.23249i | −0.183051 | − | 0.105685i | ||||
\(137\) | −6.77434 | − | 3.91117i | −0.578771 | − | 0.334153i | 0.181874 | − | 0.983322i | \(-0.441784\pi\) |
−0.760645 | + | 0.649168i | \(0.775117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.33554 | − | 2.31322i | 0.113279 | − | 0.196205i | −0.803812 | − | 0.594884i | \(-0.797198\pi\) |
0.917090 | + | 0.398679i | \(0.130531\pi\) | |||||||
\(140\) | 1.59191 | + | 2.75726i | 0.134541 | + | 0.233031i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4884 | −0.880165 | ||||||||
\(143\) | −8.40612 | − | 11.8682i | −0.702955 | − | 0.992467i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.18408 | + | 2.99303i | −0.430515 | + | 0.248558i | ||||
\(146\) | 8.26736 | + | 14.3195i | 0.684212 | + | 1.18509i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.372701i | 0.0306358i | ||||||||
\(149\) | 3.71910 | + | 2.14722i | 0.304680 | + | 0.175907i | 0.644543 | − | 0.764568i | \(-0.277047\pi\) |
−0.339863 | + | 0.940475i | \(0.610381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.9425i | − | 1.94841i | −0.225656 | − | 0.974207i | \(-0.572452\pi\) | ||
0.225656 | − | 0.974207i | \(-0.427548\pi\) | |||||||
\(152\) | 0.343766 | − | 0.595420i | 0.0278831 | − | 0.0482949i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.49326 | − | 2.01684i | 0.281495 | − | 0.162521i | ||||
\(155\) | −13.2938 | −1.06778 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1640 | −1.68907 | −0.844535 | − | 0.535501i | \(-0.820123\pi\) | ||||
−0.844535 | + | 0.535501i | \(0.820123\pi\) | |||||||
\(158\) | −11.5073 | + | 6.64372i | −0.915469 | + | 0.528546i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.59191 | − | 2.75726i | 0.125851 | − | 0.217981i | ||||
\(161\) | 5.79086i | 0.456384i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.97609 | + | 1.71825i | 0.233105 | + | 0.134583i | 0.612004 | − | 0.790855i | \(-0.290364\pi\) |
−0.378898 | + | 0.925438i | \(0.623697\pi\) | |||||||
\(164\) | − | 7.89663i | − | 0.616623i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.69651 | − | 8.13460i | −0.364520 | − | 0.631367i | ||||
\(167\) | 1.29715 | − | 0.748912i | 0.100377 | − | 0.0579526i | −0.448971 | − | 0.893546i | \(-0.648209\pi\) |
0.549348 | + | 0.835594i | \(0.314876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7774 | + | 2.39564i | −0.982874 | + | 0.184280i | ||||
\(170\) | 7.84801 | 0.601915 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.48320 | − | 4.30103i | −0.189342 | − | 0.327950i | ||||
\(173\) | −4.11216 | + | 7.12246i | −0.312641 | + | 0.541511i | −0.978933 | − | 0.204180i | \(-0.934547\pi\) |
0.666292 | + | 0.745691i | \(0.267880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.44848 | − | 2.56833i | −0.336274 | − | 0.194148i | ||||
\(176\) | −3.49326 | − | 2.01684i | −0.263315 | − | 0.152025i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.36023 | − | 7.55214i | 0.326813 | − | 0.566057i | ||||
\(179\) | 4.56957 | + | 7.91473i | 0.341546 | + | 0.591575i | 0.984720 | − | 0.174145i | \(-0.0557162\pi\) |
−0.643174 | + | 0.765720i | \(0.722383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.97003 | 0.295090 | 0.147545 | − | 0.989055i | \(-0.452863\pi\) | ||||
0.147545 | + | 0.989055i | \(0.452863\pi\) | |||||||
\(182\) | −0.333648 | − | 3.59008i | −0.0247316 | − | 0.266114i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.01503 | − | 2.89543i | 0.369713 | − | 0.213454i | ||||
\(185\) | −0.593305 | − | 1.02763i | −0.0436206 | − | 0.0755532i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.94289i | − | 0.727096i | ||||||
\(188\) | 10.2817 | + | 5.93616i | 0.749873 | + | 0.432939i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.18897i | 0.158805i | ||||||||
\(191\) | −7.22054 | + | 12.5063i | −0.522460 | + | 0.904927i | 0.477198 | + | 0.878796i | \(0.341652\pi\) |
−0.999659 | + | 0.0261318i | \(0.991681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.55466 | + | 2.05228i | −0.255870 | + | 0.147727i | −0.622449 | − | 0.782660i | \(-0.713862\pi\) |
0.366579 | + | 0.930387i | \(0.380529\pi\) | |||||||
\(194\) | −6.15085 | −0.441605 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −15.8433 | + | 9.14716i | −1.12879 | + | 0.651708i | −0.943631 | − | 0.331000i | \(-0.892614\pi\) |
−0.185161 | + | 0.982708i | \(0.559281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.69290 | − | 15.0566i | 0.616224 | − | 1.06733i | −0.373945 | − | 0.927451i | \(-0.621995\pi\) |
0.990169 | − | 0.139880i | \(-0.0446716\pi\) | |||||||
\(200\) | 5.13667i | 0.363217i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.14668 | + | 3.54879i | 0.432479 | + | 0.249692i | ||||
\(203\) | 1.88016i | 0.131961i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5707 | + | 21.7731i | 0.877976 | + | 1.52070i | ||||
\(206\) | −7.31223 | + | 4.22172i | −0.509467 | + | 0.294141i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.94228 | + | 2.08399i | −0.204010 | + | 0.144499i | ||||
\(209\) | 2.77328 | 0.191832 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.51818 | + | 4.36161i | 0.173359 | + | 0.300266i | 0.939592 | − | 0.342297i | \(-0.111205\pi\) |
−0.766233 | + | 0.642562i | \(0.777871\pi\) | |||||||
\(212\) | 4.79818 | − | 8.31070i | 0.329541 | − | 0.570781i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.39631 | − | 5.42496i | −0.642319 | − | 0.370843i | ||||
\(215\) | 13.6937 | + | 7.90604i | 0.933900 | + | 0.539187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.08771 | + | 3.61603i | −0.141723 | + | 0.245472i | ||||
\(218\) | −7.48224 | − | 12.9596i | −0.506761 | − | 0.877736i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.8425 | 0.865838 | ||||||||
\(221\) | −8.07506 | − | 3.71248i | −0.543188 | − | 0.249728i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.39565 | − | 2.53783i | 0.294355 | − | 0.169946i | −0.345549 | − | 0.938401i | \(-0.612307\pi\) |
0.639904 | + | 0.768455i | \(0.278974\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 9.50200i | − | 0.632064i | ||||||
\(227\) | −23.7848 | − | 13.7322i | −1.57865 | − | 0.911436i | −0.995048 | − | 0.0993983i | \(-0.968308\pi\) |
−0.583605 | − | 0.812037i | \(-0.698358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.6832i | − | 1.82936i | −0.404181 | − | 0.914679i | \(-0.632443\pi\) | ||
0.404181 | − | 0.914679i | \(-0.367557\pi\) | |||||||
\(230\) | −9.21851 | + | 15.9669i | −0.607850 | + | 1.05283i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.62826 | − | 0.940078i | 0.106901 | − | 0.0617191i | ||||
\(233\) | 27.1843 | 1.78090 | 0.890451 | − | 0.455078i | \(-0.150389\pi\) | ||||
0.890451 | + | 0.455078i | \(0.150389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.7993 | −2.46575 | ||||||||
\(236\) | 2.23154 | − | 1.28838i | 0.145261 | − | 0.0838666i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.23249 | − | 2.13473i | 0.0798902 | − | 0.138374i | ||||
\(239\) | − | 3.65168i | − | 0.236207i | −0.993001 | − | 0.118104i | \(-0.962318\pi\) | ||
0.993001 | − | 0.118104i | \(-0.0376815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.107048 | − | 0.0618044i | −0.00689559 | − | 0.00398117i | 0.496548 | − | 0.868009i | \(-0.334601\pi\) |
−0.503444 | + | 0.864028i | \(0.667934\pi\) | |||||||
\(242\) | − | 5.27051i | − | 0.338801i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.79497 | + | 11.7692i | 0.435003 | + | 0.753448i | ||||
\(245\) | −2.75726 | + | 1.59191i | −0.176155 | + | 0.101703i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03549 | − | 2.25230i | 0.0658864 | − | 0.143311i | ||||
\(248\) | 4.17543 | 0.265140 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.217559 | − | 0.376824i | −0.0137597 | − | 0.0238324i | ||||
\(251\) | 7.54462 | − | 13.0677i | 0.476212 | − | 0.824824i | −0.523416 | − | 0.852077i | \(-0.675343\pi\) |
0.999629 | + | 0.0272533i | \(0.00867608\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.2290 | + | 11.6792i | 1.27179 | + | 0.734266i | ||||
\(254\) | −7.42319 | − | 4.28578i | −0.465773 | − | 0.268914i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.94509 | + | 6.83309i | 0.246088 | + | 0.426237i | 0.962437 | − | 0.271506i | \(-0.0875215\pi\) |
−0.716349 | + | 0.697742i | \(0.754188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.372701 | −0.0231585 | ||||||||
\(260\) | 4.79512 | − | 10.4299i | 0.297381 | − | 0.646837i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.18648 | − | 4.72647i | 0.505763 | − | 0.292002i | ||||
\(263\) | −4.45634 | − | 7.71861i | −0.274790 | − | 0.475950i | 0.695292 | − | 0.718727i | \(-0.255275\pi\) |
−0.970082 | + | 0.242777i | \(0.921942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.5530i | 1.87686i | ||||||||
\(266\) | 0.595420 | + | 0.343766i | 0.0365075 | + | 0.0210776i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 8.61974i | − | 0.526534i | ||||||
\(269\) | −7.21199 | + | 12.4915i | −0.439723 | + | 0.761622i | −0.997668 | − | 0.0682557i | \(-0.978257\pi\) |
0.557945 | + | 0.829878i | \(0.311590\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2356 | + | 9.37361i | −0.986240 | + | 0.569406i | −0.904148 | − | 0.427219i | \(-0.859493\pi\) |
−0.0820919 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(272\) | −2.46497 | −0.149461 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.82233 | −0.472564 | ||||||||
\(275\) | −17.9437 | + | 10.3598i | −1.08205 | + | 0.624720i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.70728 | + | 16.8135i | −0.583254 | + | 1.01023i | 0.411836 | + | 0.911258i | \(0.364887\pi\) |
−0.995091 | + | 0.0989680i | \(0.968446\pi\) | |||||||
\(278\) | − | 2.67107i | − | 0.160200i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.75726 | + | 1.59191i | 0.164778 | + | 0.0951346i | ||||
\(281\) | − | 19.4085i | − | 1.15781i | −0.815394 | − | 0.578906i | \(-0.803480\pi\) | ||
0.815394 | − | 0.578906i | \(-0.196520\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.70552 | + | 11.6143i | 0.398602 | + | 0.690398i | 0.993554 | − | 0.113363i | \(-0.0361622\pi\) |
−0.594952 | + | 0.803761i | \(0.702829\pi\) | |||||||
\(284\) | −9.08320 | + | 5.24419i | −0.538989 | + | 0.311185i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.2140 | − | 6.07509i | −0.781361 | − | 0.359227i | ||||
\(287\) | 7.89663 | 0.466123 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.46196 | + | 9.46039i | 0.321292 | + | 0.556493i | ||||
\(290\) | −2.99303 | + | 5.18408i | −0.175757 | + | 0.304420i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.3195 | + | 8.26736i | 0.837985 | + | 0.483811i | ||||
\(293\) | 2.01398 | + | 1.16277i | 0.117658 | + | 0.0679299i | 0.557674 | − | 0.830060i | \(-0.311694\pi\) |
−0.440016 | + | 0.897990i | \(0.645027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.10197 | + | 7.10482i | −0.238826 | + | 0.413659i | ||||
\(296\) | 0.186350 | + | 0.322768i | 0.0108314 | + | 0.0187605i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.29444 | 0.248770 | ||||||||
\(299\) | 17.0383 | − | 12.0681i | 0.985351 | − | 0.697915i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.30103 | − | 2.48320i | 0.247907 | − | 0.143129i | ||||
\(302\) | −11.9713 | − | 20.7348i | −0.688868 | − | 1.19316i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.687532i | − | 0.0394326i | ||||||
\(305\) | −37.4710 | − | 21.6339i | −2.14558 | − | 1.23875i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.09575i | 0.404976i | 0.979285 | + | 0.202488i | \(0.0649027\pi\) | ||||
−0.979285 | + | 0.202488i | \(0.935097\pi\) | |||||||
\(308\) | 2.01684 | − | 3.49326i | 0.114920 | − | 0.199047i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.5128 | + | 6.64689i | −0.653880 | + | 0.377518i | ||||
\(311\) | −12.0586 | −0.683780 | −0.341890 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341890 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4098 | −0.644921 | −0.322461 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322461 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(314\) | −18.3285 | + | 10.5820i | −1.03434 | + | 0.597176i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.64372 | + | 11.5073i | −0.373739 | + | 0.647334i | ||||
\(317\) | 6.67694i | 0.375014i | 0.982263 | + | 0.187507i | \(0.0600408\pi\) | ||||
−0.982263 | + | 0.187507i | \(0.939959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.56788 | + | 3.79197i | 0.367731 | + | 0.212309i | ||||
\(320\) | − | 3.18381i | − | 0.177981i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.89543 | + | 5.01503i | 0.161356 | + | 0.279477i | ||||
\(323\) | 1.46769 | − | 0.847373i | 0.0816646 | − | 0.0471491i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.71384 | + | 18.4410i | 0.0950665 | + | 1.02293i | ||||
\(326\) | 3.43649 | 0.190330 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.94832 | − | 6.83868i | −0.218009 | − | 0.377603i | ||||
\(329\) | −5.93616 | + | 10.2817i | −0.327271 | + | 0.566851i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10741 | − | 0.639361i | −0.0608685 | − | 0.0351424i | 0.469257 | − | 0.883062i | \(-0.344522\pi\) |
−0.530125 | + | 0.847919i | \(0.677855\pi\) | |||||||
\(332\) | −8.13460 | − | 4.69651i | −0.446444 | − | 0.257755i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.748912 | − | 1.29715i | 0.0409787 | − | 0.0709771i | ||||
\(335\) | 13.7218 | + | 23.7669i | 0.749703 | + | 1.29852i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9634 | −0.597214 | −0.298607 | − | 0.954376i | \(-0.596522\pi\) | ||||
−0.298607 | + | 0.954376i | \(0.596522\pi\) | |||||||
\(338\) | −9.86770 | + | 8.46337i | −0.536732 | + | 0.460347i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.79658 | − | 3.92401i | 0.368596 | − | 0.212809i | ||||
\(341\) | 8.42115 | + | 14.5859i | 0.456031 | + | 0.789869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −4.30103 | − | 2.48320i | −0.231896 | − | 0.133885i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.22431i | 0.442142i | ||||||||
\(347\) | −12.1257 | + | 21.0023i | −0.650942 | + | 1.12746i | 0.331953 | + | 0.943296i | \(0.392293\pi\) |
−0.982895 | + | 0.184169i | \(0.941041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.792668 | + | 0.457647i | −0.0424305 | + | 0.0244973i | −0.521065 | − | 0.853517i | \(-0.674465\pi\) |
0.478635 | + | 0.878014i | \(0.341132\pi\) | |||||||
\(350\) | −5.13667 | −0.274566 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.03367 | −0.214995 | ||||||||
\(353\) | −10.2702 | + | 5.92948i | −0.546625 | + | 0.315594i | −0.747760 | − | 0.663969i | \(-0.768871\pi\) |
0.201134 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6965 | − | 28.9192i | 0.886159 | − | 1.53487i | ||||
\(356\) | − | 8.72046i | − | 0.462183i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.91473 | + | 4.56957i | 0.418306 | + | 0.241509i | ||||
\(359\) | 6.14816i | 0.324488i | 0.986751 | + | 0.162244i | \(0.0518731\pi\) | ||||
−0.986751 | + | 0.162244i | \(0.948127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.26365 | − | 16.0451i | −0.487561 | − | 0.844480i | ||||
\(362\) | 3.43815 | − | 1.98502i | 0.180705 | − | 0.104330i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.08399 | − | 2.94228i | −0.109231 | − | 0.154217i | ||||
\(365\) | −52.6435 | −2.75549 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.27627 | − | 16.0670i | −0.484217 | − | 0.838689i | 0.515618 | − | 0.856818i | \(-0.327562\pi\) |
−0.999836 | + | 0.0181296i | \(0.994229\pi\) | |||||||
\(368\) | 2.89543 | − | 5.01503i | 0.150935 | − | 0.261427i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.02763 | − | 0.593305i | −0.0534242 | − | 0.0308445i | ||||
\(371\) | 8.31070 | + | 4.79818i | 0.431470 | + | 0.249109i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0745 | − | 20.9137i | 0.625195 | − | 1.08287i | −0.363308 | − | 0.931669i | \(-0.618353\pi\) |
0.988503 | − | 0.151201i | \(-0.0483140\pi\) | |||||||
\(374\) | −4.97144 | − | 8.61079i | −0.257067 | − | 0.445254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.8723 | 0.612269 | ||||||||
\(377\) | 5.53194 | − | 3.91822i | 0.284909 | − | 0.201799i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4253 | − | 7.75109i | 0.689610 | − | 0.398147i | −0.113856 | − | 0.993497i | \(-0.536320\pi\) |
0.803466 | + | 0.595351i | \(0.202987\pi\) | |||||||
\(380\) | 1.09449 | + | 1.89571i | 0.0561460 | + | 0.0972477i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.4411i | 0.738870i | ||||||||
\(383\) | −4.10975 | − | 2.37277i | −0.209998 | − | 0.121243i | 0.391312 | − | 0.920258i | \(-0.372021\pi\) |
−0.601311 | + | 0.799015i | \(0.705355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.8425i | 0.654512i | ||||||||
\(386\) | −2.05228 | + | 3.55466i | −0.104459 | + | 0.180927i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.32679 | + | 3.07542i | −0.270427 | + | 0.156131i | ||||
\(389\) | 0.255450 | 0.0129519 | 0.00647593 | − | 0.999979i | \(-0.497939\pi\) | ||||
0.00647593 | + | 0.999979i | \(0.497939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.2743 | 0.721883 | ||||||||
\(392\) | 0.866025 | − | 0.500000i | 0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.14716 | + | 15.8433i | −0.460827 | + | 0.798176i | ||||
\(395\) | − | 42.3047i | − | 2.12858i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.10155 | + | 2.94538i | 0.256040 | + | 0.147825i | 0.622527 | − | 0.782599i | \(-0.286106\pi\) |
−0.366487 | + | 0.930423i | \(0.619440\pi\) | |||||||
\(398\) | − | 17.3858i | − | 0.871472i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.56833 | + | 4.44848i | 0.128417 | + | 0.222424i | ||||
\(401\) | −9.14301 | + | 5.27872i | −0.456580 | + | 0.263607i | −0.710605 | − | 0.703591i | \(-0.751579\pi\) |
0.254025 | + | 0.967198i | \(0.418245\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.9901 | − | 1.39312i | 0.746711 | − | 0.0693963i | ||||
\(404\) | 7.09757 | 0.353117 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.940078 | + | 1.62826i | 0.0466553 | + | 0.0808093i | ||||
\(407\) | −0.751677 | + | 1.30194i | −0.0372592 | + | 0.0645349i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.15730 | + | 1.24552i | 0.106672 | + | 0.0615869i | 0.552387 | − | 0.833588i | \(-0.313717\pi\) |
−0.445715 | + | 0.895175i | \(0.647051\pi\) | |||||||
\(410\) | 21.7731 | + | 12.5707i | 1.07530 | + | 0.620823i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.22172 | + | 7.31223i | −0.207989 | + | 0.360248i | ||||
\(413\) | 1.28838 | + | 2.23154i | 0.0633972 | + | 0.109807i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.9056 | 1.46801 | ||||||||
\(416\) | −1.50609 | + | 3.27592i | −0.0738423 | + | 0.160615i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.40173 | − | 1.38664i | 0.117472 | − | 0.0678227i | ||||
\(419\) | 8.30873 | + | 14.3911i | 0.405908 | + | 0.703053i | 0.994427 | − | 0.105430i | \(-0.0336220\pi\) |
−0.588519 | + | 0.808484i | \(0.700289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.3927i | 1.87114i | 0.353137 | + | 0.935572i | \(0.385115\pi\) | ||||
−0.353137 | + | 0.935572i | \(0.614885\pi\) | |||||||
\(422\) | 4.36161 | + | 2.51818i | 0.212320 | + | 0.122583i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 9.59637i | − | 0.466041i | ||||||
\(425\) | −6.33087 | + | 10.9654i | −0.307092 | + | 0.531899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.7692 | + | 6.79497i | −0.569553 | + | 0.328832i | ||||
\(428\) | −10.8499 | −0.524451 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.8121 | 0.762526 | ||||||||
\(431\) | 21.5077 | − | 12.4175i | 1.03599 | − | 0.598130i | 0.117296 | − | 0.993097i | \(-0.462577\pi\) |
0.918695 | + | 0.394967i | \(0.129244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5166 | − | 19.9473i | 0.553450 | − | 0.958604i | −0.444572 | − | 0.895743i | \(-0.646644\pi\) |
0.998022 | − | 0.0628608i | \(-0.0200224\pi\) | |||||||
\(434\) | 4.17543i | 0.200427i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.9596 | − | 7.48224i | −0.620653 | − | 0.358334i | ||||
\(437\) | 3.98140i | 0.190456i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.05272 | + | 1.82337i | 0.0502437 | + | 0.0870247i | 0.890053 | − | 0.455856i | \(-0.150667\pi\) |
−0.839810 | + | 0.542881i | \(0.817334\pi\) | |||||||
\(440\) | 11.1219 | − | 6.42123i | 0.530216 | − | 0.306120i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.84945 | + | 0.822432i | −0.420925 | + | 0.0391191i | ||||
\(443\) | −36.8615 | −1.75134 | −0.875670 | − | 0.482910i | \(-0.839580\pi\) | ||||
−0.875670 | + | 0.482910i | \(0.839580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8822 | + | 24.0446i | 0.658077 | + | 1.13982i | ||||
\(446\) | 2.53783 | − | 4.39565i | 0.120170 | − | 0.208140i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.866025 | − | 0.500000i | −0.0409159 | − | 0.0236228i | ||||
\(449\) | −27.0644 | − | 15.6257i | −1.27725 | − | 0.737421i | −0.300908 | − | 0.953653i | \(-0.597290\pi\) |
−0.976342 | + | 0.216232i | \(0.930623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.9262 | − | 27.5850i | 0.749936 | − | 1.29893i | ||||
\(452\) | −4.75100 | − | 8.22897i | −0.223468 | − | 0.387058i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.4643 | −1.28896 | ||||||||
\(455\) | 10.4299 | + | 4.79512i | 0.488963 | + | 0.224799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.93318 | − | 5.73492i | 0.464654 | − | 0.268268i | −0.249345 | − | 0.968415i | \(-0.580215\pi\) |
0.713999 | + | 0.700146i | \(0.246882\pi\) | |||||||
\(458\) | −13.8416 | − | 23.9744i | −0.646776 | − | 1.12025i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.4370i | 0.859630i | ||||||||
\(461\) | −13.6364 | − | 7.87297i | −0.635110 | − | 0.366681i | 0.147619 | − | 0.989044i | \(-0.452839\pi\) |
−0.782728 | + | 0.622364i | \(0.786173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.5070i | − | 0.860093i | −0.902807 | − | 0.430046i | \(-0.858497\pi\) | ||
0.902807 | − | 0.430046i | \(-0.141503\pi\) | |||||||
\(464\) | 0.940078 | − | 1.62826i | 0.0436420 | − | 0.0755902i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.5423 | − | 13.5922i | 1.09058 | − | 0.629644i | ||||
\(467\) | −11.7992 | −0.546001 | −0.273000 | − | 0.962014i | \(-0.588016\pi\) | ||||
−0.273000 | + | 0.962014i | \(0.588016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.61974 | 0.398023 | ||||||||
\(470\) | −32.7351 | + | 18.8996i | −1.50996 | + | 0.871775i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.28838 | − | 2.23154i | 0.0593026 | − | 0.102715i | ||||
\(473\) | − | 20.0328i | − | 0.921110i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.05847 | − | 1.76581i | −0.140332 | − | 0.0810209i | ||||
\(476\) | − | 2.46497i | − | 0.112982i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.82584 | − | 3.16245i | −0.0835120 | − | 0.144647i | ||||
\(479\) | 7.04158 | − | 4.06546i | 0.321738 | − | 0.185755i | −0.330429 | − | 0.943831i | \(-0.607193\pi\) |
0.652167 | + | 0.758075i | \(0.273860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.776704 | + | 1.09659i | 0.0354147 | + | 0.0500002i | ||||
\(482\) | −0.123609 | −0.00563022 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.63525 | − | 4.56440i | −0.119784 | − | 0.207473i | ||||
\(485\) | 9.79157 | − | 16.9595i | 0.444612 | − | 0.770091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.1884 | − | 16.2746i | −1.27734 | − | 0.737473i | −0.300982 | − | 0.953630i | \(-0.597314\pi\) |
−0.976359 | + | 0.216157i | \(0.930648\pi\) | |||||||
\(488\) | 11.7692 | + | 6.79497i | 0.532768 | + | 0.307594i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.59191 | + | 2.75726i | −0.0719150 | + | 0.124560i | ||||
\(491\) | 10.6268 | + | 18.4062i | 0.479583 | + | 0.830661i | 0.999726 | − | 0.0234177i | \(-0.00745477\pi\) |
−0.520143 | + | 0.854079i | \(0.674121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.63453 | 0.208729 | ||||||||
\(494\) | −0.229393 | − | 2.46829i | −0.0103209 | − | 0.111054i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.61603 | − | 2.08771i | 0.162364 | − | 0.0937411i | ||||
\(497\) | −5.24419 | − | 9.08320i | −0.235234 | − | 0.407437i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.0619i | − | 1.52482i | −0.647095 | − | 0.762409i | \(-0.724016\pi\) | ||
0.647095 | − | 0.762409i | \(-0.275984\pi\) | |||||||
\(500\) | −0.376824 | − | 0.217559i | −0.0168521 | − | 0.00972955i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 15.0892i | − | 0.673466i | ||||||
\(503\) | 2.96436 | − | 5.13442i | 0.132174 | − | 0.228933i | −0.792340 | − | 0.610080i | \(-0.791137\pi\) |
0.924514 | + | 0.381147i | \(0.124471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.5699 | + | 11.2987i | −0.870848 | + | 0.502784i | ||||
\(506\) | 23.3584 | 1.03841 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.57157 | −0.380302 | ||||||||
\(509\) | −32.6711 | + | 18.8626i | −1.44812 | + | 0.836072i | −0.998369 | − | 0.0570827i | \(-0.981820\pi\) |
−0.449750 | + | 0.893155i | \(0.648487\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.26736 | + | 14.3195i | −0.365727 | + | 0.633457i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.83309 | + | 3.94509i | 0.301395 | + | 0.174010i | ||||
\(515\) | − | 26.8823i | − | 1.18458i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9445 | + | 41.4732i | 1.05308 | + | 1.82399i | ||||
\(518\) | −0.322768 | + | 0.186350i | −0.0141816 | + | 0.00818777i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.06227 | − | 11.4301i | −0.0465837 | − | 0.501245i | ||||
\(521\) | 16.7098 | 0.732070 | 0.366035 | − | 0.930601i | \(-0.380715\pi\) | ||||
0.366035 | + | 0.930601i | \(0.380715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.3349 | − | 24.8287i | −0.626821 | − | 1.08569i | −0.988186 | − | 0.153261i | \(-0.951023\pi\) |
0.361365 | − | 0.932424i | \(-0.382311\pi\) | |||||||
\(524\) | 4.72647 | − | 8.18648i | 0.206477 | − | 0.357628i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.71861 | − | 4.45634i | −0.336547 | − | 0.194306i | ||||
\(527\) | 8.91340 | + | 5.14616i | 0.388274 | + | 0.224170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.26703 | + | 9.12277i | −0.229001 | + | 0.396642i | ||||
\(530\) | 15.2765 | + | 26.4597i | 0.663570 | + | 1.14934i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.687532 | 0.0298083 | ||||||||
\(533\) | −16.4565 | − | 23.2341i | −0.712809 | − | 1.00638i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.9161 | − | 17.2721i | 1.29339 | − | 0.746737i | ||||
\(536\) | −4.30987 | − | 7.46491i | −0.186158 | − | 0.322435i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.4240i | 0.621862i | ||||||||
\(539\) | 3.49326 | + | 2.01684i | 0.150465 | + | 0.0868713i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.03625i | − | 0.345505i | −0.984965 | − | 0.172753i | \(-0.944734\pi\) | ||
0.984965 | − | 0.172753i | \(-0.0552661\pi\) | |||||||
\(542\) | −9.37361 | + | 16.2356i | −0.402631 | + | 0.697377i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.13473 | + | 1.23249i | −0.0915257 | + | 0.0528424i | ||||
\(545\) | 47.6441 | 2.04085 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.2164 | 1.07817 | 0.539087 | − | 0.842250i | \(-0.318769\pi\) | ||||
0.539087 | + | 0.842250i | \(0.318769\pi\) | |||||||
\(548\) | −6.77434 | + | 3.91117i | −0.289385 | + | 0.167077i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.3598 | + | 17.9437i | −0.441744 | + | 0.765123i | ||||
\(551\) | 1.29267i | 0.0550695i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5073 | − | 6.64372i | −0.489339 | − | 0.282520i | ||||
\(554\) | 19.4146i | 0.824846i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.33554 | − | 2.31322i | −0.0566394 | − | 0.0981023i | ||||
\(557\) | −18.8958 | + | 10.9095i | −0.800639 | + | 0.462249i | −0.843695 | − | 0.536824i | \(-0.819624\pi\) |
0.0430556 | + | 0.999073i | \(0.486291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.2695 | − | 7.47986i | −0.688128 | − | 0.316364i | ||||
\(560\) | 3.18381 | 0.134541 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.70424 | − | 16.8082i | −0.409349 | − | 0.709013i | ||||
\(563\) | −10.7185 | + | 18.5650i | −0.451732 | + | 0.782422i | −0.998494 | − | 0.0548657i | \(-0.982527\pi\) |
0.546762 | + | 0.837288i | \(0.315860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.1995 | + | 15.1263i | 1.10222 | + | 0.636368i | ||||
\(566\) | 11.6143 | + | 6.70552i | 0.488185 | + | 0.281854i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.24419 | + | 9.08320i | −0.220041 | + | 0.381123i | ||||
\(569\) | 19.9983 | + | 34.6381i | 0.838373 | + | 1.45210i | 0.891254 | + | 0.453504i | \(0.149826\pi\) |
−0.0528815 | + | 0.998601i | \(0.516841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.1693 | 1.01145 | 0.505726 | − | 0.862694i | \(-0.331225\pi\) | ||||
0.505726 | + | 0.862694i | \(0.331225\pi\) | |||||||
\(572\) | −14.4812 | + | 1.34583i | −0.605490 | + | 0.0562718i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.83868 | − | 3.94832i | 0.285441 | − | 0.164800i | ||||
\(575\) | −14.8729 | − | 25.7605i | −0.620241 | − | 1.07429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23.0573i | − | 0.959887i | −0.877300 | − | 0.479943i | \(-0.840657\pi\) | ||
0.877300 | − | 0.479943i | \(-0.159343\pi\) | |||||||
\(578\) | 9.46039 | + | 5.46196i | 0.393500 | + | 0.227187i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.98606i | 0.248558i | ||||||||
\(581\) | 4.69651 | − | 8.13460i | 0.194844 | − | 0.337480i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.5226 | − | 19.3543i | 1.38837 | − | 0.801573i | ||||
\(584\) | 16.5347 | 0.684212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.32554 | 0.0960674 | ||||||||
\(587\) | −31.2097 | + | 18.0189i | −1.28816 | + | 0.743720i | −0.978326 | − | 0.207070i | \(-0.933607\pi\) |
−0.309835 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.43537 | + | 2.48613i | −0.0591434 | + | 0.102439i | ||||
\(590\) | 8.20394i | 0.337751i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.322768 | + | 0.186350i | 0.0132657 | + | 0.00765896i | ||||
\(593\) | − | 16.5198i | − | 0.678386i | −0.940717 | − | 0.339193i | \(-0.889846\pi\) | ||
0.940717 | − | 0.339193i | \(-0.110154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.92401 | + | 6.79658i | 0.160869 | + | 0.278632i | ||||
\(596\) | 3.71910 | − | 2.14722i | 0.152340 | − | 0.0879536i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.72157 | − | 18.9704i | 0.356652 | − | 0.775758i | ||||
\(599\) | −5.57909 | −0.227956 | −0.113978 | − | 0.993483i | \(-0.536359\pi\) | ||||
−0.113978 | + | 0.993483i | \(0.536359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7171 | − | 32.4190i | −0.763486 | − | 1.32240i | −0.941043 | − | 0.338286i | \(-0.890153\pi\) |
0.177557 | − | 0.984111i | \(-0.443181\pi\) | |||||||
\(602\) | 2.48320 | − | 4.30103i | 0.101208 | − | 0.175297i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.7348 | − | 11.9713i | −0.843688 | − | 0.487104i | ||||
\(605\) | 14.5322 | + | 8.39016i | 0.590817 | + | 0.341108i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.72160 | + | 2.98191i | −0.0698778 | + | 0.121032i | −0.898847 | − | 0.438262i | \(-0.855594\pi\) |
0.828970 | + | 0.559294i | \(0.188928\pi\) | |||||||
\(608\) | −0.343766 | − | 0.595420i | −0.0139415 | − | 0.0241475i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.2678 | −1.75186 | ||||||||
\(611\) | 42.6226 | − | 3.96117i | 1.72433 | − | 0.160252i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3407 | + | 19.8266i | −1.38701 | + | 0.800790i | −0.992977 | − | 0.118307i | \(-0.962253\pi\) |
−0.394032 | + | 0.919097i | \(0.628920\pi\) | |||||||
\(614\) | 3.54788 | + | 6.14510i | 0.143181 | + | 0.247996i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.03367i | − | 0.162521i | ||||||
\(617\) | −15.6609 | − | 9.04183i | −0.630485 | − | 0.364010i | 0.150455 | − | 0.988617i | \(-0.451926\pi\) |
−0.780940 | + | 0.624606i | \(0.785259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.5906i | 0.948187i | 0.880475 | + | 0.474093i | \(0.157224\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(620\) | −6.64689 | + | 11.5128i | −0.266946 | + | 0.462363i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.4430 | + | 6.02929i | −0.418728 | + | 0.241753i | ||||
\(623\) | 8.72046 | 0.349378 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2980 | −0.971920 | ||||||||
\(626\) | −9.88120 | + | 5.70491i | −0.394932 | + | 0.228014i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.5820 | + | 18.3285i | −0.422267 | + | 0.731388i | ||||
\(629\) | 0.918697i | 0.0366309i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3081 | − | 24.4266i | −1.68426 | − | 0.972406i | −0.958775 | − | 0.284166i | \(-0.908283\pi\) |
−0.725482 | − | 0.688241i | \(-0.758383\pi\) | |||||||
\(632\) | 13.2874i | 0.528546i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.33847 | + | 5.78240i | 0.132588 | + | 0.229648i | ||||
\(635\) | 23.6341 | − | 13.6451i | 0.937889 | − | 0.541491i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.94228 | − | 2.08399i | 0.116577 | − | 0.0825706i | ||||
\(638\) | 7.58393 | 0.300251 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.59191 | − | 2.75726i | −0.0629256 | − | 0.108990i | ||||
\(641\) | 3.62675 | − | 6.28172i | 0.143248 | − | 0.248113i | −0.785470 | − | 0.618900i | \(-0.787579\pi\) |
0.928718 | + | 0.370787i | \(0.120912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.0001 | + | 19.0526i | 1.30140 | + | 0.751361i | 0.980644 | − | 0.195802i | \(-0.0627308\pi\) |
0.320753 | + | 0.947163i | \(0.396064\pi\) | |||||||
\(644\) | 5.01503 | + | 2.89543i | 0.197620 | + | 0.114096i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.847373 | − | 1.46769i | 0.0333395 | − | 0.0577456i | ||||
\(647\) | −16.2780 | − | 28.1943i | −0.639953 | − | 1.10843i | −0.985443 | − | 0.170009i | \(-0.945620\pi\) |
0.345489 | − | 0.938423i | \(-0.387713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3938 | 0.407993 | ||||||||
\(650\) | 10.7047 | + | 15.1135i | 0.419875 | + | 0.592800i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.97609 | − | 1.71825i | 0.116553 | − | 0.0672917i | ||||
\(653\) | 14.0997 | + | 24.4214i | 0.551763 | + | 0.955682i | 0.998148 | + | 0.0608403i | \(0.0193780\pi\) |
−0.446384 | + | 0.894841i | \(0.647289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.0964i | 1.17596i | ||||||||
\(656\) | −6.83868 | − | 3.94832i | −0.267006 | − | 0.154156i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.8723i | 0.462832i | ||||||||
\(659\) | −12.5440 | + | 21.7268i | −0.488644 | + | 0.846356i | −0.999915 | − | 0.0130635i | \(-0.995842\pi\) |
0.511271 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.853782 | + | 0.492931i | −0.0332083 | + | 0.0191728i | −0.516512 | − | 0.856280i | \(-0.672770\pi\) |
0.483304 | + | 0.875453i | \(0.339437\pi\) | |||||||
\(662\) | −1.27872 | −0.0496989 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.39302 | −0.364520 | ||||||||
\(665\) | −1.89571 | + | 1.09449i | −0.0735123 | + | 0.0424424i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44386 | + | 9.42904i | −0.210787 | + | 0.365094i | ||||
\(668\) | − | 1.49782i | − | 0.0579526i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.7669 | + | 13.7218i | 0.918195 | + | 0.530120i | ||||
\(671\) | 54.8173i | 2.11620i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9713 | + | 36.3233i | 0.808383 | + | 1.40016i | 0.913984 | + | 0.405751i | \(0.132990\pi\) |
−0.105601 | + | 0.994409i | \(0.533677\pi\) | |||||||
\(674\) | −9.49457 | + | 5.48170i | −0.365717 | + | 0.211147i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.31399 | + | 12.2633i | −0.165923 | + | 0.471667i | ||||
\(677\) | 25.0312 | 0.962027 | 0.481013 | − | 0.876713i | \(-0.340269\pi\) | ||||
0.481013 | + | 0.876713i | \(0.340269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.07542 | − | 5.32679i | −0.118024 | − | 0.204423i | ||||
\(680\) | 3.92401 | − | 6.79658i | 0.150479 | − | 0.260637i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.5859 | + | 8.42115i | 0.558522 | + | 0.322463i | ||||
\(683\) | 18.2859 | + | 10.5573i | 0.699689 | + | 0.403966i | 0.807232 | − | 0.590235i | \(-0.200965\pi\) |
−0.107542 | + | 0.994200i | \(0.534298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4524 | − | 21.5682i | 0.475782 | − | 0.824079i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.96640 | −0.189342 | ||||||||
\(689\) | −3.20181 | − | 34.4517i | −0.121979 | − | 1.31251i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.7299 | + | 24.6701i | −1.62552 | + | 0.938495i | −0.640114 | + | 0.768280i | \(0.721113\pi\) |
−0.985407 | + | 0.170216i | \(0.945554\pi\) | |||||||
\(692\) | 4.11216 | + | 7.12246i | 0.156321 | + | 0.270755i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.2514i | 0.920571i | ||||||||
\(695\) | 7.36485 | + | 4.25210i | 0.279365 | + | 0.161291i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.4650i | − | 0.737289i | ||||||
\(698\) | −0.457647 | + | 0.792668i | −0.0173222 | + | 0.0300029i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.44848 | + | 2.56833i | −0.168137 | + | 0.0970739i | ||||
\(701\) | 26.1837 | 0.988946 | 0.494473 | − | 0.869193i | \(-0.335361\pi\) | ||||
0.494473 | + | 0.869193i | \(0.335361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.256244 | −0.00966441 | ||||||||
\(704\) | −3.49326 | + | 2.01684i | −0.131657 | + | 0.0760124i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.92948 | + | 10.2702i | −0.223159 | + | 0.386523i | ||||
\(707\) | 7.09757i | 0.266932i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3232 | + | 11.1562i | 0.725697 | + | 0.418981i | 0.816846 | − | 0.576856i | \(-0.195721\pi\) |
−0.0911490 | + | 0.995837i | \(0.529054\pi\) | |||||||
\(710\) | − | 33.3930i | − | 1.25322i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.36023 | − | 7.55214i | −0.163406 | − | 0.283028i | ||||
\(713\) | −20.9399 | + | 12.0897i | −0.784206 | + | 0.452761i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.7861 | − | 26.7635i | 1.41312 | − | 1.00090i | ||||
\(716\) | 9.13914 | 0.341546 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.07408 | + | 5.32446i | 0.114724 | + | 0.198707i | ||||
\(719\) | −1.77486 | + | 3.07415i | −0.0661912 | + | 0.114647i | −0.897222 | − | 0.441580i | \(-0.854418\pi\) |
0.831031 | + | 0.556227i | \(0.187751\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.31223 | − | 4.22172i | −0.272322 | − | 0.157225i | ||||
\(722\) | −16.0451 | − | 9.26365i | −0.597137 | − | 0.344757i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.98502 | − | 3.43815i | 0.0737726 | − | 0.127778i | ||||
\(725\) | −4.82887 | − | 8.36384i | −0.179340 | − | 0.310625i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.112332 | −0.00416615 | −0.00208307 | − | 0.999998i | \(-0.500663\pi\) | ||||
−0.00208307 | + | 0.999998i | \(0.500663\pi\) | |||||||
\(728\) | −3.27592 | − | 1.50609i | −0.121414 | − | 0.0558195i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −45.5906 | + | 26.3217i | −1.68738 | + | 0.974211i | ||||
\(731\) | −6.12102 | − | 10.6019i | −0.226394 | − | 0.392126i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.6154i | 1.35242i | 0.736708 | + | 0.676211i | \(0.236379\pi\) | ||||
−0.736708 | + | 0.676211i | \(0.763621\pi\) | |||||||
\(734\) | −16.0670 | − | 9.27627i | −0.593042 | − | 0.342393i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.79086i | − | 0.213454i | ||||||
\(737\) | 17.3846 | − | 30.1110i | 0.640370 | − | 1.10915i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.4611 | − | 22.7829i | 1.45160 | − | 0.838081i | 0.453026 | − | 0.891497i | \(-0.350344\pi\) |
0.998572 | + | 0.0534162i | \(0.0170110\pi\) | |||||||
\(740\) | −1.18661 | −0.0436206 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.59637 | 0.352294 | ||||||||
\(743\) | −0.246449 | + | 0.142287i | −0.00904132 | + | 0.00522001i | −0.504514 | − | 0.863404i | \(-0.668328\pi\) |
0.495473 | + | 0.868624i | \(0.334995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.83635 | + | 11.8409i | −0.250464 | + | 0.433817i | ||||
\(746\) | − | 24.1491i | − | 0.884160i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.61079 | − | 4.97144i | −0.314842 | − | 0.181774i | ||||
\(749\) | − | 10.8499i | − | 0.396448i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0384437 | + | 0.0665865i | 0.00140283 | + | 0.00242977i | 0.866726 | − | 0.498785i | \(-0.166220\pi\) |
−0.865323 | + | 0.501214i | \(0.832887\pi\) | |||||||
\(752\) | 10.2817 | − | 5.93616i | 0.374936 | − | 0.216470i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.83169 | − | 6.15925i | 0.103124 | − | 0.224307i | ||||
\(755\) | 76.2285 | 2.77424 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1791 | − | 21.0948i | −0.442656 | − | 0.766702i | 0.555230 | − | 0.831697i | \(-0.312630\pi\) |
−0.997886 | + | 0.0649946i | \(0.979297\pi\) | |||||||
\(758\) | 7.75109 | − | 13.4253i | 0.281532 | − | 0.487628i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.89571 | + | 1.09449i | 0.0687645 | + | 0.0397012i | ||||
\(761\) | 27.6551 | + | 15.9667i | 1.00249 | + | 0.578791i | 0.908986 | − | 0.416828i | \(-0.136858\pi\) |
0.0935094 | + | 0.995618i | \(0.470191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.48224 | − | 12.9596i | 0.270875 | − | 0.469170i | ||||
\(764\) | 7.22054 | + | 12.5063i | 0.261230 | + | 0.452464i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.74553 | −0.171463 | ||||||||
\(767\) | 3.88085 | − | 8.44129i | 0.140129 | − | 0.304797i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0798 | + | 8.12896i | −0.507730 | + | 0.293138i | −0.731900 | − | 0.681412i | \(-0.761366\pi\) |
0.224170 | + | 0.974550i | \(0.428033\pi\) | |||||||
\(770\) | 6.42123 | + | 11.1219i | 0.231405 | + | 0.400805i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.10457i | 0.147727i | ||||||||
\(773\) | 11.0350 | + | 6.37105i | 0.396900 | + | 0.229151i | 0.685146 | − | 0.728406i | \(-0.259739\pi\) |
−0.288245 | + | 0.957557i | \(0.593072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 21.4478i | − | 0.770427i | ||||||
\(776\) | −3.07542 | + | 5.32679i | −0.110401 | + | 0.191221i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.221227 | − | 0.127725i | 0.00793136 | − | 0.00457917i | ||||
\(779\) | 5.42918 | 0.194521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.3067 | −1.51385 | ||||||||
\(782\) | 12.3619 | − | 7.13715i | 0.442061 | − | 0.255224i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | − | 67.3821i | − | 2.40497i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.7761 | − | 14.3045i | −0.883173 | − | 0.509900i | −0.0114696 | − | 0.999934i | \(-0.503651\pi\) |
−0.871703 | + | 0.490034i | \(0.836984\pi\) | |||||||
\(788\) | 18.2943i | 0.651708i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.1524 | − | 36.6370i | −0.752568 | − | 1.30349i | ||||
\(791\) | 8.22897 | − | 4.75100i | 0.292589 | − | 0.168926i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.5196 | + | 20.4677i | 1.58094 | + | 0.726830i | ||||
\(794\) | 5.89077 | 0.209055 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.69290 | − | 15.0566i | −0.308112 | − | 0.533665i | ||||
\(797\) | −4.14067 | + | 7.17185i | −0.146670 | + | 0.254040i | −0.929995 | − | 0.367573i | \(-0.880189\pi\) |
0.783325 | + | 0.621613i | \(0.213522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3442 | + | 14.6325i | 0.896613 | + | 0.517660i | ||||
\(800\) | 4.44848 | + | 2.56833i | 0.157278 | + | 0.0908043i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.27872 | + | 9.14301i | −0.186398 | + | 0.322851i | ||||
\(803\) | 33.3478 | + | 57.7601i | 1.17682 | + | 2.03831i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.4370 | −0.649819 | ||||||||
\(806\) | 12.2853 | − | 8.70154i | 0.432730 | − | 0.306499i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.14668 | − | 3.54879i | 0.216239 | − | 0.124846i | ||||
\(809\) | 10.3018 | + | 17.8433i | 0.362193 | + | 0.627337i | 0.988321 | − | 0.152383i | \(-0.0486948\pi\) |
−0.626129 | + | 0.779720i | \(0.715361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.1892i | − | 0.673826i | −0.941536 | − | 0.336913i | \(-0.890617\pi\) | ||
0.941536 | − | 0.336913i | \(-0.109383\pi\) | |||||||
\(812\) | 1.62826 | + | 0.940078i | 0.0571408 | + | 0.0329903i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.50335i | 0.0526925i | ||||||||
\(815\) | −5.47057 | + | 9.47531i | −0.191626 | + | 0.331906i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.95709 | − | 1.70728i | 0.103456 | − | 0.0597301i | ||||
\(818\) | 2.49104 | 0.0870971 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.1414 | 0.877976 | ||||||||
\(821\) | −19.1914 | + | 11.0801i | −0.669783 | + | 0.386699i | −0.795994 | − | 0.605304i | \(-0.793052\pi\) |
0.126211 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.40969 | − | 7.63781i | 0.153712 | − | 0.266237i | −0.778877 | − | 0.627176i | \(-0.784210\pi\) |
0.932589 | + | 0.360939i | \(0.117544\pi\) | |||||||
\(824\) | 8.44343i | 0.294141i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.23154 | + | 1.28838i | 0.0776454 | + | 0.0448286i | ||||
\(827\) | − | 48.9775i | − | 1.70312i | −0.524260 | − | 0.851558i | \(-0.675658\pi\) | ||
0.524260 | − | 0.851558i | \(-0.324342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10592 | − | 5.37962i | −0.107873 | − | 0.186842i | 0.807035 | − | 0.590503i | \(-0.201071\pi\) |
−0.914908 | + | 0.403661i | \(0.867737\pi\) | |||||||
\(830\) | 25.8990 | − | 14.9528i | 0.898969 | − | 0.519020i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.333648 | + | 3.59008i | 0.0115672 | + | 0.124464i | ||||
\(833\) | 2.46497 | 0.0854062 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.38440 | + | 4.12990i | 0.0825154 | + | 0.142921i | ||||
\(836\) | 1.38664 | − | 2.40173i | 0.0479579 | − | 0.0830655i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.3911 | + | 8.30873i | 0.497134 | + | 0.287020i | ||||
\(839\) | 1.46160 | + | 0.843857i | 0.0504601 | + | 0.0291332i | 0.525018 | − | 0.851091i | \(-0.324059\pi\) |
−0.474558 | + | 0.880224i | \(0.657392\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7325 | − | 22.0533i | 0.439052 | − | 0.760460i | ||||
\(842\) | 19.1963 | + | 33.2490i | 0.661549 | + | 1.14584i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.03636 | 0.173359 | ||||||||
\(845\) | −7.62728 | − | 40.6807i | −0.262386 | − | 1.39946i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.56440 | − | 2.63525i | 0.156834 | − | 0.0905484i | ||||
\(848\) | −4.79818 | − | 8.31070i | −0.164770 | − | 0.285391i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.6617i | 0.434294i | ||||||||
\(851\) | −1.86911 | − | 1.07913i | −0.0640722 | − | 0.0369921i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.1066i | 0.756914i | 0.925619 | + | 0.378457i | \(0.123545\pi\) | ||||
−0.925619 | + | 0.378457i | \(0.876455\pi\) | |||||||
\(854\) | −6.79497 | + | 11.7692i | −0.232519 | + | 0.402735i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.39631 | + | 5.42496i | −0.321159 | + | 0.185421i | ||||
\(857\) | 5.43662 | 0.185711 | 0.0928556 | − | 0.995680i | \(-0.470400\pi\) | ||||
0.0928556 | + | 0.995680i | \(0.470400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.9329 | −1.84017 | −0.920083 | − | 0.391724i | \(-0.871879\pi\) | ||||
−0.920083 | + | 0.391724i | \(0.871879\pi\) | |||||||
\(860\) | 13.6937 | − | 7.90604i | 0.466950 | − | 0.269594i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.4175 | − | 21.5077i | 0.422942 | − | 0.732557i | ||||
\(863\) | − | 26.9278i | − | 0.916633i | −0.888789 | − | 0.458316i | \(-0.848453\pi\) | ||
0.888789 | − | 0.458316i | \(-0.151547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.6766 | − | 13.0923i | −0.771027 | − | 0.445153i | ||||
\(866\) | − | 23.0331i | − | 0.782697i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.08771 | + | 3.61603i | 0.0708616 | + | 0.122736i | ||||
\(869\) | −46.4165 | + | 26.7986i | −1.57457 | + | 0.909080i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.9634 | − | 25.3617i | −0.608668 | − | 0.859347i | ||||
\(872\) | −14.9645 | −0.506761 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.99070 | + | 3.44799i | 0.0673364 | + | 0.116630i | ||||
\(875\) | 0.217559 | − | 0.376824i | 0.00735485 | − | 0.0127390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.6890 | + | 24.6465i | 1.44150 | + | 0.832253i | 0.997950 | − | 0.0639940i | \(-0.0203839\pi\) |
0.443555 | + | 0.896247i | \(0.353717\pi\) | |||||||
\(878\) | 1.82337 | + | 1.05272i | 0.0615357 | + | 0.0355277i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.42123 | − | 11.1219i | 0.216460 | − | 0.374919i | ||||
\(881\) | 8.61337 | + | 14.9188i | 0.290192 | + | 0.502627i | 0.973855 | − | 0.227171i | \(-0.0729475\pi\) |
−0.683663 | + | 0.729798i | \(0.739614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2874 | −0.817335 | −0.408667 | − | 0.912683i | \(-0.634006\pi\) | ||||
−0.408667 | + | 0.912683i | \(0.634006\pi\) | |||||||
\(884\) | −7.25263 | + | 5.13697i | −0.243932 | + | 0.172775i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.9230 | + | 18.4307i | −1.07247 | + | 0.619192i | ||||
\(887\) | −19.9927 | − | 34.6283i | −0.671289 | − | 1.16271i | −0.977539 | − | 0.210755i | \(-0.932408\pi\) |
0.306250 | − | 0.951951i | \(-0.400926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.57157i | − | 0.287481i | ||||||
\(890\) | 24.0446 | + | 13.8822i | 0.805977 | + | 0.465331i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 5.07566i | − | 0.169946i | ||||||
\(893\) | −4.08130 | + | 7.06902i | −0.136576 | + | 0.236556i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.1990 | + | 14.5487i | −0.842310 | + | 0.486308i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.2513 | −1.04287 | ||||||||
\(899\) | −6.79869 | + | 3.92523i | −0.226749 | + | 0.130914i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.8274 | − | 20.4856i | 0.394027 | − | 0.682476i | ||||
\(902\) | − | 31.8524i | − | 1.06057i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.22897 | − | 4.75100i | −0.273692 | − | 0.158016i | ||||
\(905\) | 12.6398i | 0.420163i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.0476 | − | 26.0632i | −0.499648 | − | 0.865416i | 0.500352 | − | 0.865822i | \(-0.333204\pi\) |
−1.00000 | 0.000406499i | \(0.999871\pi\) | ||||||||
\(908\) | −23.7848 | + | 13.7322i | −0.789327 | + | 0.455718i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.4301 | − | 1.06227i | 0.378906 | − | 0.0352140i | ||||
\(911\) | 20.2884 | 0.672184 | 0.336092 | − | 0.941829i | \(-0.390895\pi\) | ||||
0.336092 | + | 0.941829i | \(0.390895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.9442 | − | 32.8123i | −0.626961 | − | 1.08593i | ||||
\(914\) | 5.73492 | − | 9.93318i | 0.189694 | − | 0.328560i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.9744 | − | 13.8416i | −0.792135 | − | 0.457339i | ||||
\(917\) | 8.18648 | + | 4.72647i | 0.270341 | + | 0.156082i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.47940 | − | 16.4188i | 0.312697 | − | 0.541606i | −0.666249 | − | 0.745730i | \(-0.732101\pi\) |
0.978945 | + | 0.204123i | \(0.0654344\pi\) | |||||||
\(920\) | 9.21851 | + | 15.9669i | 0.303925 | + | 0.526414i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.7459 | −0.518565 | ||||||||
\(923\) | −15.7965 | + | 34.3591i | −0.519947 | + | 1.13094i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.65795 | − | 0.957220i | 0.0545132 | − | 0.0314732i | ||||
\(926\) | −9.25349 | − | 16.0275i | −0.304089 | − | 0.526697i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 1.88016i | − | 0.0617191i | ||||||
\(929\) | 38.9321 | + | 22.4774i | 1.27732 | + | 0.737461i | 0.976355 | − | 0.216174i | \(-0.0693580\pi\) |
0.300965 | + | 0.953635i | \(0.402691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.687532i | 0.0225329i | ||||||||
\(932\) | 13.5922 | − | 23.5423i | 0.445226 | − | 0.771154i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.2184 | + | 5.89959i | −0.334356 | + | 0.193040i | ||||
\(935\) | 31.6563 | 1.03527 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.2773 | 1.64249 | 0.821244 | − | 0.570577i | \(-0.193280\pi\) | ||||
0.821244 | + | 0.570577i | \(0.193280\pi\) | |||||||
\(938\) | 7.46491 | − | 4.30987i | 0.243738 | − | 0.140722i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.8996 | + | 32.7351i | −0.616438 | + | 1.06770i | ||||
\(941\) | 26.1622i | 0.852862i | 0.904520 | + | 0.426431i | \(0.140229\pi\) | ||||
−0.904520 | + | 0.426431i | \(0.859771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.6019 | + | 22.8641i | 1.28961 | + | 0.744559i | ||||
\(944\) | − | 2.57677i | − | 0.0838666i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0164 | − | 17.3489i | −0.325662 | − | 0.564062i | ||||
\(947\) | −29.4303 | + | 16.9916i | −0.956358 | + | 0.552153i | −0.895050 | − | 0.445966i | \(-0.852860\pi\) |
−0.0613076 | + | 0.998119i | \(0.519527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.3610 | − | 5.51677i | 1.92694 | − | 0.179082i | ||||
\(950\) | −3.53162 | −0.114581 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.23249 | − | 2.13473i | −0.0399451 | − | 0.0691869i | ||||
\(953\) | 9.86552 | − | 17.0876i | 0.319576 | − | 0.553521i | −0.660824 | − | 0.750541i | \(-0.729793\pi\) |
0.980400 | + | 0.197020i | \(0.0631263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.8179 | − | 22.9889i | −1.28848 | − | 0.743902i | ||||
\(956\) | −3.16245 | − | 1.82584i | −0.102281 | − | 0.0590519i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.06546 | − | 7.04158i | 0.131349 | − | 0.227503i | ||||
\(959\) | −3.91117 | − | 6.77434i | −0.126298 | − | 0.218755i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5658 | 0.437607 | ||||||||
\(962\) | 1.22094 | + | 0.561322i | 0.0393647 | + | 0.0180978i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.107048 | + | 0.0618044i | −0.00344779 | + | 0.00199058i | ||||
\(965\) | −6.53409 | − | 11.3174i | −0.210340 | − | 0.364319i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0777i | − | 1.28881i | −0.764683 | − | 0.644406i | \(-0.777105\pi\) | ||
0.764683 | − | 0.644406i | \(-0.222895\pi\) | |||||||
\(968\) | −4.56440 | − | 2.63525i | −0.146705 | − | 0.0847003i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 19.5831i | − | 0.628777i | ||||||
\(971\) | 20.4682 | − | 35.4519i | 0.656855 | − | 1.13771i | −0.324570 | − | 0.945862i | \(-0.605220\pi\) |
0.981425 | − | 0.191845i | \(-0.0614470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.31322 | − | 1.33554i | 0.0741583 | − | 0.0428153i | ||||
\(974\) | −32.5492 | −1.04294 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.5899 | 0.435003 | ||||||||
\(977\) | −51.3639 | + | 29.6549i | −1.64328 | + | 0.948746i | −0.663618 | + | 0.748072i | \(0.730980\pi\) |
−0.979658 | + | 0.200674i | \(0.935687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5877 | − | 30.4628i | 0.562106 | − | 0.973597i | ||||
\(980\) | 3.18381i | 0.101703i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.4062 | + | 10.6268i | 0.587366 | + | 0.339116i | ||||
\(983\) | 26.5688i | 0.847412i | 0.905800 | + | 0.423706i | \(0.139271\pi\) | ||||
−0.905800 | + | 0.423706i | \(0.860729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.1228 | − | 50.4422i | −0.927931 | − | 1.60722i | ||||
\(986\) | 4.01362 | − | 2.31727i | 0.127820 | − | 0.0737968i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.43281 | − | 2.02291i | −0.0455837 | − | 0.0643573i | ||||
\(989\) | 28.7597 | 0.914506 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.0282 | + | 29.4937i | 0.540918 | + | 0.936898i | 0.998852 | + | 0.0479116i | \(0.0152566\pi\) |
−0.457933 | + | 0.888987i | \(0.651410\pi\) | |||||||
\(992\) | 2.08771 | − | 3.61603i | 0.0662850 | − | 0.114809i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.08320 | − | 5.24419i | −0.288102 | − | 0.166336i | ||||
\(995\) | 47.9372 | + | 27.6766i | 1.51971 | + | 0.877407i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.03595 | − | 10.4546i | 0.191160 | − | 0.331100i | −0.754475 | − | 0.656329i | \(-0.772108\pi\) |
0.945635 | + | 0.325230i | \(0.105442\pi\) | |||||||
\(998\) | −17.0309 | − | 29.4984i | −0.539105 | − | 0.933757i | ||||
\(999\) | 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 | 1638.2.bj.i.127.8 | yes | 16 | |
3.2 | odd | 2 | 1638.2.bj.h.127.1 | ✓ | 16 | ||
13.4 | even | 6 | inner | 1638.2.bj.i.1135.5 | yes | 16 | |
39.17 | odd | 6 | 1638.2.bj.h.1135.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.bj.h.127.1 | ✓ | 16 | 3.2 | odd | 2 | ||
1638.2.bj.h.1135.4 | yes | 16 | 39.17 | odd | 6 | ||
1638.2.bj.i.127.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1638.2.bj.i.1135.5 | yes | 16 | 13.4 | even | 6 | inner |