Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 170x^{16} + 6593x^{12} + 64168x^{8} + 95760x^{4} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.7 | ||
Root | \(-0.814454 - 0.814454i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.j.1217.14 |
$q$-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 \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.15181i | − 0.664999i | −0.943103 | − | 0.332500i | \(-0.892108\pi\) | ||||
0.943103 | − | 0.332500i | \(-0.107892\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.07587i | − 0.481146i | −0.970631 | − | 0.240573i | \(-0.922665\pi\) | ||||
0.970631 | − | 0.240573i | \(-0.0773353\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.238565 | 0.0901690 | 0.0450845 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450845 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.67333 | 0.557776 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.84249i | 0.857044i | 0.903531 | + | 0.428522i | \(0.140966\pi\) | ||||
−0.903531 | + | 0.428522i | \(0.859034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.31444i | − 0.364560i | −0.983247 | − | 0.182280i | \(-0.941652\pi\) | ||||
0.983247 | − | 0.182280i | \(-0.0583477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23921 | −0.319962 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47279 | −1.08481 | −0.542405 | − | 0.840117i | \(-0.682486\pi\) | ||||
−0.542405 | + | 0.840117i | \(0.682486\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.274782i | − 0.0599623i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94338 | 0.405222 | 0.202611 | − | 0.979259i | \(-0.435057\pi\) | ||||
0.202611 | + | 0.979259i | \(0.435057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.84249 | 0.768499 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.38280i | − 1.03592i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.83944i | − 1.64144i | −0.571329 | − | 0.820721i | \(-0.693572\pi\) | ||||
0.571329 | − | 0.820721i | \(-0.306428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.64877 | 1.19415 | 0.597077 | − | 0.802184i | \(-0.296329\pi\) | ||||
0.597077 | + | 0.802184i | \(0.296329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.27402 | 0.569933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.256666i | − 0.0433845i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.06763i | − 0.668715i | −0.942446 | − | 0.334357i | \(-0.891481\pi\) | ||||
0.942446 | − | 0.334357i | \(-0.108519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.51399 | −0.242432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.78211 | 0.434492 | 0.217246 | − | 0.976117i | \(-0.430293\pi\) | ||||
0.217246 | + | 0.976117i | \(0.430293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.21363i | 0.185077i | 0.995709 | + | 0.0925386i | \(0.0294982\pi\) | ||||
−0.995709 | + | 0.0925386i | \(0.970502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.80029i | − 0.268372i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2695 | 1.49796 | 0.748978 | − | 0.662595i | \(-0.230545\pi\) | ||||
0.748978 | + | 0.662595i | \(0.230545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94309 | −0.991870 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.15181i | 0.721398i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.36231i | − 1.14865i | −0.818627 | − | 0.574326i | \(-0.805264\pi\) | ||||
0.818627 | − | 0.574326i | \(-0.194736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.05817 | 0.412363 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.15181 | 0.152561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.25916i | − 1.20544i | −0.797953 | − | 0.602720i | \(-0.794084\pi\) | ||||
0.797953 | − | 0.602720i | \(-0.205916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.66035i | 0.596697i | 0.954457 | + | 0.298349i | \(0.0964358\pi\) | ||||
−0.954457 | + | 0.298349i | \(0.903564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.399197 | 0.0502941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.41417 | −0.175407 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31849i | 0.527587i | 0.964579 | + | 0.263794i | \(0.0849738\pi\) | ||||
−0.964579 | + | 0.263794i | \(0.915026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.23841i | − 0.269472i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.78069 | 0.330007 | 0.165003 | − | 0.986293i | \(-0.447236\pi\) | ||||
0.165003 | + | 0.986293i | \(0.447236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.134460 | 0.0157373 | 0.00786866 | − | 0.999969i | \(-0.497495\pi\) | ||||
0.00786866 | + | 0.999969i | \(0.497495\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 4.42583i | − 0.511051i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.678119i | 0.0772788i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7841 | −1.43832 | −0.719162 | − | 0.694843i | \(-0.755474\pi\) | ||||
−0.719162 | + | 0.694843i | \(0.755474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.17998 | −0.131109 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.4028i | 1.47115i | 0.677445 | + | 0.735573i | \(0.263087\pi\) | ||||
−0.677445 | + | 0.735573i | \(0.736913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.81216i | 0.521952i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.1814 | −1.09156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.20650 | −0.975887 | −0.487944 | − | 0.872875i | \(-0.662253\pi\) | ||||
−0.487944 | + | 0.872875i | \(0.662253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.313579i | − 0.0328720i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.65814i | − 0.794112i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.07587 | 0.110382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.247499 | −0.0251297 | −0.0125648 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125648 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.75643i | 0.478039i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 16.8026i | − 1.67193i | −0.548786 | − | 0.835963i | \(-0.684910\pi\) | ||||
0.548786 | − | 0.835963i | \(-0.315090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.40957 | 0.533020 | 0.266510 | − | 0.963832i | \(-0.414129\pi\) | ||||
0.266510 | + | 0.963832i | \(0.414129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.295631 | −0.0288506 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 6.39113i | − 0.617853i | −0.951086 | − | 0.308927i | \(-0.900030\pi\) | ||||
0.951086 | − | 0.308927i | \(-0.0999698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14.8779i | − 1.42505i | −0.701648 | − | 0.712524i | \(-0.747552\pi\) | ||||
0.701648 | − | 0.712524i | \(-0.252448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.68515 | −0.444695 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.59073 | 0.808148 | 0.404074 | − | 0.914726i | \(-0.367594\pi\) | ||||
0.404074 | + | 0.914726i | \(0.367594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.09083i | − 0.194971i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.19949i | − 0.203343i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.06705 | −0.0978163 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.92023 | 0.265476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.20446i | − 0.288937i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.51342i | − 0.850906i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.15983 | 0.102918 | 0.0514592 | − | 0.998675i | \(-0.483613\pi\) | ||||
0.0514592 | + | 0.998675i | \(0.483613\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.39788 | 0.123076 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.85559i | − 0.336864i | −0.985713 | − | 0.168432i | \(-0.946130\pi\) | ||||
0.985713 | − | 0.168432i | \(-0.0538704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.238565i | 0.0206862i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.79122 | −0.498428 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.42976 | 0.122152 | 0.0610761 | − | 0.998133i | \(-0.480547\pi\) | ||||
0.0610761 | + | 0.998133i | \(0.480547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.58190i | − 0.303813i | −0.988395 | − | 0.151907i | \(-0.951459\pi\) | ||||
0.988395 | − | 0.151907i | \(-0.0485413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 11.8285i | − 0.996139i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.73629 | 0.312444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.51013 | −0.789773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.99713i | 0.659592i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 16.2763i | − 1.33341i | −0.745322 | − | 0.666705i | \(-0.767704\pi\) | ||||
0.745322 | − | 0.666705i | \(-0.232296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3242 | −1.16569 | −0.582845 | − | 0.812583i | \(-0.698061\pi\) | ||||
−0.582845 | + | 0.812583i | \(0.698061\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.48445 | −0.605082 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 7.15325i | − 0.574563i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.73495i | 0.298081i | 0.988831 | + | 0.149041i | \(0.0476185\pi\) | ||||
−0.988831 | + | 0.149041i | \(0.952381\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.63181 | −0.763852 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.463621 | 0.0365385 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.98861i | − 0.312412i | −0.987724 | − | 0.156206i | \(-0.950074\pi\) | ||||
0.987724 | − | 0.156206i | \(-0.0499264\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 3.52243i | − 0.274221i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.17158 | 0.632336 | 0.316168 | − | 0.948703i | \(-0.397604\pi\) | ||||
0.316168 | + | 0.948703i | \(0.397604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.2722 | 0.867096 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.67333i | 0.127963i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.351356i | 0.0267131i | 0.999911 | + | 0.0133565i | \(0.00425164\pi\) | ||||
−0.999911 | + | 0.0133565i | \(0.995748\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.916684 | 0.0692948 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.6648 | −0.801616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.2740i | 1.14163i | 0.821077 | + | 0.570817i | \(0.193373\pi\) | ||||
−0.821077 | + | 0.570817i | \(0.806627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.94630i | − 0.664974i | −0.943108 | − | 0.332487i | \(-0.892112\pi\) | ||||
0.943108 | − | 0.332487i | \(-0.107888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.36785 | 0.396803 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.37626 | −0.321749 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.7139i | − 0.929730i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.28415i | − 0.0934079i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.3946 | −1.33098 | −0.665492 | − | 0.746405i | \(-0.731778\pi\) | ||||
−0.665492 | + | 0.746405i | \(0.731778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.09902 | −0.367035 | −0.183518 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183518 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.62886i | 0.116645i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2916i | 1.44572i | 0.690995 | + | 0.722860i | \(0.257173\pi\) | ||||
−0.690995 | + | 0.722860i | \(0.742827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.310999 | 0.0220461 | 0.0110231 | − | 0.999939i | \(-0.496491\pi\) | ||||
0.0110231 | + | 0.999939i | \(0.496491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.97408 | 0.350845 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.10878i | − 0.148007i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.99320i | − 0.209054i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.25191 | 0.226023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.84249 | −0.196619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3284i | 0.986406i | 0.869914 | + | 0.493203i | \(0.164174\pi\) | ||||
−0.869914 | + | 0.493203i | \(0.835826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.20283i | − 0.219454i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.30572 | 0.0890491 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.58616 | 0.107676 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 0.154872i | − 0.0104653i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.87921i | 0.395479i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8621 | 0.861312 | 0.430656 | − | 0.902516i | \(-0.358282\pi\) | ||||
0.430656 | + | 0.902516i | \(0.358282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.42976 | 0.428650 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.4491i | 1.22451i | 0.790659 | + | 0.612256i | \(0.209738\pi\) | ||||
−0.790659 | + | 0.612256i | \(0.790262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.73279i | 0.312751i | 0.987698 | + | 0.156376i | \(0.0499811\pi\) | ||||
−0.987698 | + | 0.156376i | \(0.950019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.781066 | 0.0513903 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.27809 | 0.280267 | 0.140133 | − | 0.990133i | \(-0.455247\pi\) | ||||
0.140133 | + | 0.990133i | \(0.455247\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 11.0487i | − 0.720735i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.7249i | 0.956483i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3905 | −1.31895 | −0.659474 | − | 0.751727i | \(-0.729221\pi\) | ||||
−0.659474 | + | 0.751727i | \(0.729221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5877 | 1.64825 | 0.824123 | − | 0.566410i | \(-0.191668\pi\) | ||||
0.824123 | + | 0.566410i | \(0.191668\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 14.7893i | − 0.948732i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.46989i | 0.477234i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.31444 | 0.0836358 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4375 | 0.978311 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 28.9847i | − 1.82950i | −0.404024 | − | 0.914749i | \(-0.632389\pi\) | ||||
0.404024 | − | 0.914749i | \(-0.367611\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.52404i | 0.347293i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.54270 | 0.347098 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.10203 | 0.318256 | 0.159128 | − | 0.987258i | \(-0.449132\pi\) | ||||
0.159128 | + | 0.987258i | \(0.449132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.970394i | − 0.0602974i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 14.7913i | − 0.915558i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6953 | 0.721160 | 0.360580 | − | 0.932728i | \(-0.382579\pi\) | ||||
0.360580 | + | 0.932728i | \(0.382579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.99680 | −0.552669 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.6042i | 0.648964i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.163433i | 0.00996466i | 0.999988 | + | 0.00498233i | \(0.00158593\pi\) | ||||
−0.999988 | + | 0.00498233i | \(0.998414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.01216 | −0.0614846 | −0.0307423 | − | 0.999527i | \(-0.509787\pi\) | ||||
−0.0307423 | + | 0.999527i | \(0.509787\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.361184 | −0.0218599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.9223i | 0.658637i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.14825i | 0.189160i | 0.995517 | + | 0.0945800i | \(0.0301508\pi\) | ||||
−0.995517 | + | 0.0945800i | \(0.969849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.1256 | 0.666071 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.6734 | −1.47189 | −0.735946 | − | 0.677040i | \(-0.763262\pi\) | ||||
−0.735946 | + | 0.677040i | \(0.763262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8095i | 0.820889i | 0.911886 | + | 0.410445i | \(0.134626\pi\) | ||||
−0.911886 | + | 0.410445i | \(0.865374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.23921i | − 0.0734042i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.663713 | 0.0391777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00584 | 0.176814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.285072i | 0.0167112i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.24682i | 0.481784i | 0.970552 | + | 0.240892i | \(0.0774400\pi\) | ||||
−0.970552 | + | 0.240892i | \(0.922560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.96169 | −0.579992 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.3006 | 0.887829 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.55445i | − 0.147728i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.289530i | 0.0166882i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.3535 | −1.11183 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.01396 | 0.287098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4540i | 0.996153i | 0.867133 | + | 0.498076i | \(0.165960\pi\) | ||||
−0.867133 | + | 0.498076i | \(0.834040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.23080i | − 0.354458i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5256 | 0.596851 | 0.298425 | − | 0.954433i | \(-0.403539\pi\) | ||||
0.298425 | + | 0.954433i | \(0.403539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3498 | −0.811098 | −0.405549 | − | 0.914073i | \(-0.632920\pi\) | ||||
−0.405549 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 0.429486i | − 0.0241988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 16.3470i | − 0.918138i | −0.888401 | − | 0.459069i | \(-0.848183\pi\) | ||||
0.888401 | − | 0.459069i | \(-0.151817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.1260 | 1.40679 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.36138 | −0.410872 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.47279i | − 0.248873i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.05073i | − 0.280164i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.1366 | −0.947656 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.44993 | 0.135069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0118i | 0.825123i | 0.910930 | + | 0.412562i | \(0.135366\pi\) | ||||
−0.910930 | + | 0.412562i | \(0.864634\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.80649i | − 0.372993i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.64615 | 0.253846 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.462187 | 0.0251769 | 0.0125885 | − | 0.999921i | \(-0.495993\pi\) | ||||
0.0125885 | + | 0.999921i | \(0.495993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 9.89491i | − 0.537418i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.8991i | 1.02344i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.32633 | −0.179605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.40824 | −0.129655 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 17.2669i | − 0.926935i | −0.886114 | − | 0.463468i | \(-0.846605\pi\) | ||||
0.886114 | − | 0.463468i | \(-0.153395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1466i | 1.39960i | 0.714341 | + | 0.699798i | \(0.246727\pi\) | ||||
−0.714341 | + | 0.699798i | \(0.753273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.07536 | −0.377655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.3930 | 0.659614 | 0.329807 | − | 0.944048i | \(-0.393016\pi\) | ||||
0.329807 | + | 0.944048i | \(0.393016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.99167i | − 0.158781i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.22904i | 0.0650478i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1664 | −0.747673 | −0.373837 | − | 0.927495i | \(-0.621958\pi\) | ||||
−0.373837 | + | 0.927495i | \(0.621958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.36356i | − 0.176541i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.144662i | − 0.00757195i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00328 | −0.156770 | −0.0783850 | − | 0.996923i | \(-0.524976\pi\) | ||||
−0.0783850 | + | 0.996923i | \(0.524976\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.65538 | 0.242349 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.99495i | − 0.103573i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.0432i | 1.96980i | 0.173119 | + | 0.984901i | \(0.444615\pi\) | ||||
−0.173119 | + | 0.984901i | \(0.555385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9577 | −0.565852 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.6189 | −0.598404 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 28.6291i | − 1.47058i | −0.677753 | − | 0.735290i | \(-0.737046\pi\) | ||||
0.677753 | − | 0.735290i | \(-0.262954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.33591i | − 0.0684407i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.1407 | 1.23353 | 0.616767 | − | 0.787146i | \(-0.288442\pi\) | ||||
0.616767 | + | 0.787146i | \(0.288442\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.729571 | 0.0371824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.03081i | 0.103232i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 16.2953i | − 0.826206i | −0.910684 | − | 0.413103i | \(-0.864445\pi\) | ||||
0.910684 | − | 0.413103i | \(-0.135555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.69231 | −0.439589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.44091 | −0.224014 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7541i | 0.692043i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.8139i | 1.84764i | 0.382829 | + | 0.923819i | \(0.374950\pi\) | ||||
−0.382829 | + | 0.923819i | \(0.625050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.274782 | 0.0137563 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.6899 | −1.18302 | −0.591508 | − | 0.806299i | \(-0.701467\pi\) | ||||
−0.591508 | + | 0.806299i | \(0.701467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.73941i | − 0.435341i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.26951i | 0.0630827i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5622 | 0.573118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.102363 | 0.00506154 | 0.00253077 | − | 0.999997i | \(-0.499194\pi\) | ||||
0.00253077 | + | 0.999997i | \(0.499194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.64681i | − 0.0812311i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.20891i | − 0.108693i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.4197 | 0.707836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.12568 | −0.202035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.7326i | 1.25712i | 0.777761 | + | 0.628560i | \(0.216355\pi\) | ||||
−0.777761 | + | 0.628560i | \(0.783645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0014i | 0.877334i | 0.898650 | + | 0.438667i | \(0.144549\pi\) | ||||
−0.898650 | + | 0.438667i | \(0.855451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.1842 | 0.835524 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.1867 | −0.833675 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.11180i | 0.0538036i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4.30350i | − 0.207775i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.6392 | 1.33133 | 0.665667 | − | 0.746249i | \(-0.268147\pi\) | ||||
0.665667 | + | 0.746249i | \(0.268147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5219 | 1.85124 | 0.925621 | − | 0.378451i | \(-0.123543\pi\) | ||||
0.925621 | + | 0.378451i | \(0.123543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.9539i | 0.525198i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.94338i | 0.0929643i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.1302 | 1.10394 | 0.551971 | − | 0.833863i | \(-0.313876\pi\) | ||||
0.551971 | + | 0.833863i | \(0.313876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6181 | −0.553241 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 19.2436i | − 0.914290i | −0.889392 | − | 0.457145i | \(-0.848872\pi\) | ||||
0.889392 | − | 0.457145i | \(-0.151128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.90505i | 0.469544i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.7473 | −0.886716 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0578 | 0.521851 | 0.260926 | − | 0.965359i | \(-0.415972\pi\) | ||||
0.260926 | + | 0.965359i | \(0.415972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.90812i | 0.372379i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.4988i | 0.775183i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.337372 | −0.0158162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.08310 | 0.190999 | 0.0954996 | − | 0.995429i | \(-0.469555\pi\) | ||||
0.0954996 | + | 0.995429i | \(0.469555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.0761i | 1.12378i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.59017i | 0.353509i | 0.984255 | + | 0.176755i | \(0.0565599\pi\) | ||||
−0.984255 | + | 0.176755i | \(0.943440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.2637 | 1.73179 | 0.865894 | − | 0.500227i | \(-0.166750\pi\) | ||||
0.865894 | + | 0.500227i | \(0.166750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.23920 | −0.382084 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.92480i | − 0.412991i | −0.978448 | − | 0.206495i | \(-0.933794\pi\) | ||||
0.978448 | − | 0.206495i | \(-0.0662058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.03024i | 0.0475720i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.30196 | 0.198224 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.44974 | −0.158619 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.84249i | 0.176306i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 13.9929i | − 0.640690i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6241 | −0.896650 | −0.448325 | − | 0.893871i | \(-0.647979\pi\) | ||||
−0.448325 | + | 0.893871i | \(0.647979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.34666 | −0.243787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 0.534005i | − 0.0242981i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.266277i | 0.0120910i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5448 | 0.613775 | 0.306887 | − | 0.951746i | \(-0.400712\pi\) | ||||
0.306887 | + | 0.951746i | \(0.400712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.59413 | −0.207754 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58255i | 0.432454i | 0.976343 | + | 0.216227i | \(0.0693752\pi\) | ||||
−0.976343 | + | 0.216227i | \(0.930625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.5369i | 1.78065i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.11732 | 0.230006 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.663374 | 0.0297564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.24834i | 0.324480i | 0.986751 | + | 0.162240i | \(0.0518719\pi\) | ||||
−0.986751 | + | 0.162240i | \(0.948128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 9.41213i | − 0.420503i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.19200 | −0.0977367 | −0.0488683 | − | 0.998805i | \(-0.515561\pi\) | ||||
−0.0488683 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0775 | −0.804440 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 12.9835i | − 0.576618i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5765i | 0.601766i | 0.953661 | + | 0.300883i | \(0.0972814\pi\) | ||||
−0.953661 | + | 0.300883i | \(0.902719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0320774 | 0.00141902 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.38280 | 0.237656 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.82002i | − 0.256461i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.1909i | 1.28381i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.404696 | 0.0177642 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.57594 | 0.288097 | 0.144049 | − | 0.989571i | \(-0.453988\pi\) | ||||
0.144049 | + | 0.989571i | \(0.453988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2161i | 0.971443i | 0.874114 | + | 0.485722i | \(0.161443\pi\) | ||||
−0.874114 | + | 0.485722i | \(0.838557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.05585i | − 0.0460810i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.7386 | −1.29543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2233 | −0.835795 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 15.4936i | − 0.672366i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.65691i | − 0.158398i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.87605 | −0.297278 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.5928 | 0.759185 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 19.7357i | − 0.850076i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5004i | 0.967368i | 0.875243 | + | 0.483684i | \(0.160702\pi\) | ||||
−0.875243 | + | 0.483684i | \(0.839298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.3045 | −0.442207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0068 | −0.685656 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 24.1551i | − 1.03280i | −0.856348 | − | 0.516399i | \(-0.827272\pi\) | ||||
0.856348 | − | 0.516399i | \(-0.172728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.79830i | 0.332823i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.83944 | 0.376573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.04984 | −0.129692 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.04063i | 0.213963i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 21.4469i | − 0.908734i | −0.890815 | − | 0.454367i | \(-0.849865\pi\) | ||||
0.890815 | − | 0.454367i | \(-0.150135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59525 | 0.0674717 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.6440 | −0.618270 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3594i | 0.647322i | 0.946173 | + | 0.323661i | \(0.104914\pi\) | ||||
−0.946173 | + | 0.323661i | \(0.895086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 9.24256i | − 0.388837i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.281503 | −0.0118220 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.05613 | −0.0861973 | −0.0430986 | − | 0.999071i | \(-0.513723\pi\) | ||||
−0.0430986 | + | 0.999071i | \(0.513723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 35.4718i | − 1.48445i | −0.670151 | − | 0.742225i | \(-0.733771\pi\) | ||||
0.670151 | − | 0.742225i | \(-0.266229\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.1871i | 0.885103i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.46741 | 0.311413 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6910 | 0.611595 | 0.305798 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305798 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.87311i | 0.244078i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.19743i | 0.132652i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7698 | 0.984445 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.36638 | −0.0978376 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.71339i | − 0.0707193i | −0.999375 | − | 0.0353596i | \(-0.988742\pi\) | ||||
0.999375 | − | 0.0353596i | \(-0.0112577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.64877i | 0.273958i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.3722 | 0.961402 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3947 | 0.837509 | 0.418754 | − | 0.908100i | \(-0.362467\pi\) | ||||
0.418754 | + | 0.908100i | \(0.362467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14801i | 0.0470639i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.358212i | − 0.0146607i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.9447 | −0.896637 | −0.448318 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448318 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.41894 | 0.139461 | 0.0697306 | − | 0.997566i | \(-0.477786\pi\) | ||||
0.0697306 | + | 0.997566i | \(0.477786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.22625i | 0.294276i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.14180i | − 0.127732i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1235 | −0.938555 | −0.469278 | − | 0.883051i | \(-0.655486\pi\) | ||||
−0.469278 | + | 0.883051i | \(0.655486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.42892 | −0.0984247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 13.4986i | − 0.546095i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.3763i | 1.87312i | 0.350504 | + | 0.936561i | \(0.386010\pi\) | ||||
−0.350504 | + | 0.936561i | \(0.613990\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.44760 | −0.139021 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.2123 | 1.01501 | 0.507504 | − | 0.861649i | \(-0.330568\pi\) | ||||
0.507504 | + | 0.861649i | \(0.330568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.2031i | 1.49532i | 0.664082 | + | 0.747660i | \(0.268822\pi\) | ||||
−0.664082 | + | 0.747660i | \(0.731178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 10.4608i | − 0.419778i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.19635 | −0.0879948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.97722 | 0.359089 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.27402i | 0.130752i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.1937i | 0.725429i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.8412 | −1.62586 | −0.812931 | − | 0.582360i | \(-0.802129\pi\) | ||||
−0.812931 | + | 0.582360i | \(0.802129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.5036 | 0.655959 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.24783i | − 0.0495188i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.12627i | 0.361596i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.65300 | 0.184070 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.87446 | 0.232027 | 0.116014 | − | 0.993248i | \(-0.462988\pi\) | ||||
0.116014 | + | 0.993248i | \(0.462988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 21.3344i | − 0.841347i | −0.907212 | − | 0.420673i | \(-0.861794\pi\) | ||||
0.907212 | − | 0.420673i | \(-0.138206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.50394i | − 0.0592176i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.1625 | −1.89346 | −0.946732 | − | 0.322024i | \(-0.895637\pi\) | ||||
−0.946732 | + | 0.322024i | \(0.895637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.3191 | 1.03311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.82696i | − 0.0716043i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3441i | 0.443929i | 0.975055 | + | 0.221965i | \(0.0712469\pi\) | ||||
−0.975055 | + | 0.221965i | \(0.928753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.14813 | −0.162081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.224995 | 0.00877791 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6320i | 0.959526i | 0.877398 | + | 0.479763i | \(0.159277\pi\) | ||||
−0.877398 | + | 0.479763i | \(0.840723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.3409i | 1.84135i | 0.390335 | + | 0.920673i | \(0.372359\pi\) | ||||
−0.390335 | + | 0.920673i | \(0.627641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.77175 | 0.262993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.256666 | 0.00995308 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 17.1784i | − 0.665149i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 14.8148i | − 0.572772i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.2470 | −0.511396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.1767 | −1.35596 | −0.677981 | − | 0.735079i | \(-0.737145\pi\) | ||||
−0.677981 | + | 0.735079i | \(0.737145\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 20.6834i | − 0.796103i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.71085i | − 0.104186i | −0.998642 | − | 0.0520932i | \(-0.983411\pi\) | ||||
0.998642 | − | 0.0520932i | \(-0.0165893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0590444 | −0.00226592 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.2499 | 0.814300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.4820i | 1.85511i | 0.373682 | + | 0.927557i | \(0.378095\pi\) | ||||
−0.373682 | + | 0.927557i | \(0.621905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.53824i | − 0.0587730i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.45128 | 0.207979 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.9917 | −0.418752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3295i | 1.57225i | 0.618068 | + | 0.786124i | \(0.287915\pi\) | ||||
−0.618068 | + | 0.786124i | \(0.712085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.13472i | 0.0431043i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.85368 | −0.146178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4438 | −0.471342 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.92755i | − 0.186377i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9692i | 0.603147i | 0.953443 | + | 0.301573i | \(0.0975118\pi\) | ||||
−0.953443 | + | 0.301573i | \(0.902488\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.06763 | 0.153414 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.7260 | −0.479288 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.00852i | − 0.150756i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.27532i | 0.0478957i | 0.999713 | + | 0.0239478i | \(0.00762356\pi\) | ||||
−0.999713 | + | 0.0239478i | \(0.992376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.3920 | −0.802263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9211 | 0.483898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4.01978i | − 0.150331i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.4860i | 0.877100i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.6245 | 1.44045 | 0.720225 | − | 0.693740i | \(-0.244038\pi\) | ||||
0.720225 | + | 0.693740i | \(0.244038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.29053 | 0.0480619 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 29.4722i | − 1.09608i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 33.9655i | − 1.26145i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.96945 | −0.147219 | −0.0736095 | − | 0.997287i | \(-0.523452\pi\) | ||||
−0.0736095 | + | 0.997287i | \(0.523452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.5744 | −0.762015 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.42832i | − 0.200774i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9821i | 0.885800i | 0.896571 | + | 0.442900i | \(0.146050\pi\) | ||||
−0.896571 | + | 0.442900i | \(0.853950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.60391 | 0.317360 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2753 | −0.452165 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 34.2553i | − 1.26010i | −0.776554 | − | 0.630051i | \(-0.783034\pi\) | ||||
0.776554 | − | 0.630051i | \(-0.216966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.51399i | − 0.0556177i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0058 | 1.13749 | 0.568746 | − | 0.822513i | \(-0.307429\pi\) | ||||
0.568746 | + | 0.822513i | \(0.307429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5113 | −0.641564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.4273i | 0.820571i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.52470i | − 0.0557112i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0417 | −1.31518 | −0.657590 | − | 0.753376i | \(-0.728424\pi\) | ||||
−0.657590 | + | 0.753376i | \(0.728424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.3849 | −1.21661 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4111i | 0.560867i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.6253i | − 0.967712i | −0.875148 | − | 0.483856i | \(-0.839236\pi\) | ||||
0.875148 | − | 0.483856i | \(-0.160764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.36265 | 0.230950 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.0064 | 1.45023 | 0.725115 | − | 0.688628i | \(-0.241787\pi\) | ||||
0.725115 | + | 0.688628i | \(0.241787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.54935i | − 0.128495i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.05233i | 0.291133i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.1706 | −0.439455 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1147 | 0.689295 | 0.344648 | − | 0.938732i | \(-0.387998\pi\) | ||||
0.344648 | + | 0.938732i | \(0.387998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 5.87658i | − 0.211640i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 42.2244i | − 1.51871i | −0.650679 | − | 0.759353i | \(-0.725516\pi\) | ||||
0.650679 | − | 0.759353i | \(-0.274484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.5479 | 0.917706 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.11771 | −0.0400977 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.78211i | 0.0996793i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.90408i | 0.282830i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −47.5809 | −1.70040 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.01833 | 0.143421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 43.6009i | − 1.55420i | −0.629375 | − | 0.777102i | \(-0.716689\pi\) | ||||
0.629375 | − | 0.777102i | \(-0.283311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 13.4707i | − 0.479571i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.04945 | 0.0728699 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.12575 | 0.217532 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.3626i | 0.367524i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.6901i | − 0.520351i | −0.965561 | − | 0.260176i | \(-0.916220\pi\) | ||||
0.965561 | − | 0.260176i | \(-0.0837805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.9332 | −1.62500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4055 | −0.544327 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.382201i | 0.0134876i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.498799i | − 0.0175803i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.188244 | 0.00662649 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.76004 | 0.167354 | 0.0836771 | − | 0.996493i | \(-0.473334\pi\) | ||||
0.0836771 | + | 0.996493i | \(0.473334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6172i | 0.513279i | 0.966507 | + | 0.256640i | \(0.0826154\pi\) | ||||
−0.966507 | + | 0.256640i | \(0.917385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.16582i | 0.0408872i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.29125 | −0.150316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.21363 | −0.0424596 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 0.524721i | − 0.0183352i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.3079i | 1.12755i | 0.825928 | + | 0.563776i | \(0.190652\pi\) | ||||
−0.825928 | + | 0.563776i | \(0.809348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.79982 | −0.341600 | −0.170800 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170800 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.5804 | 0.437993 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.2066i | 0.389691i | 0.980834 | + | 0.194845i | \(0.0624205\pi\) | ||||
−0.980834 | + | 0.194845i | \(0.937579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 45.4323i | − 1.57793i | −0.614438 | − | 0.788965i | \(-0.710617\pi\) | ||||
0.614438 | − | 0.788965i | \(-0.289383\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.62619 | 0.125791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.0550 | 1.07599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.79160i | − 0.304246i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 35.7890i | − 1.23705i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8997 | −0.583441 | −0.291721 | − | 0.956504i | \(-0.594228\pi\) | ||||
−0.291721 | + | 0.956504i | \(0.594228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −49.1356 | −1.69433 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.4191i | 0.978807i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 12.1275i | − 0.417200i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.696664 | 0.0239377 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.9059 | 0.545890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.90494i | − 0.270978i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7943i | 1.29405i | 0.762467 | + | 0.647027i | \(0.223988\pi\) | ||||
−0.762467 | + | 0.647027i | \(0.776012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.80029 | 0.0615687 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.8619 | 1.32750 | 0.663749 | − | 0.747956i | \(-0.268964\pi\) | ||||
0.663749 | + | 0.747956i | \(0.268964\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.1795i | 1.40503i | 0.711671 | + | 0.702513i | \(0.247939\pi\) | ||||
−0.711671 | + | 0.702513i | \(0.752061\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 0.764473i | − 0.0260532i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.5909 | 0.871125 | 0.435562 | − | 0.900159i | \(-0.356550\pi\) | ||||
0.435562 | + | 0.900159i | \(0.356550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.378015 | 0.0128529 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.46216i | − 0.117581i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 36.3387i | − 1.23271i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.67639 | 0.192337 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.414146 | −0.0140167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.26957i | − 0.0767253i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.4790i | 0.488920i | 0.969659 | + | 0.244460i | \(0.0786107\pi\) | ||||
−0.969659 | + | 0.244460i | \(0.921389\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.49879 | 0.320386 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.3407 | 1.62864 | 0.814320 | − | 0.580416i | \(-0.197110\pi\) | ||||
0.814320 | + | 0.580416i | \(0.197110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17.2669i | − 0.581077i | −0.956863 | − | 0.290539i | \(-0.906166\pi\) | ||||
0.956863 | − | 0.290539i | \(-0.0938344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.4740i | 0.385694i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.0650 | 1.71460 | 0.857298 | − | 0.514820i | \(-0.172141\pi\) | ||||
0.857298 | + | 0.514820i | \(0.172141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.276695 | 0.00928006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3.35410i | − 0.112366i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2695i | 0.343655i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4329 | 0.549292 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.94225 | −0.0982388 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 58.7714i | − 1.96014i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.4028i | 1.24607i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.333484 | 0.0110977 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.62510 | −0.319949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.0974i | 0.999367i | 0.866208 | + | 0.499684i | \(0.166550\pi\) | ||||
−0.866208 | + | 0.499684i | \(0.833450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 28.1164i | − 0.932561i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.15413 | 0.303290 | 0.151645 | − | 0.988435i | \(-0.451543\pi\) | ||||
0.151645 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.0973 | −1.26084 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 5.77514i | − 0.190920i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 0.919807i | − 0.0303747i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.49270 | −0.247161 | −0.123581 | − | 0.992335i | \(-0.539438\pi\) | ||||
−0.123581 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.1037 | 0.662440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.65505i | − 0.120307i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 15.6299i | − 0.513906i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.05198 | 0.297306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.0792 | −0.396306 | −0.198153 | − | 0.980171i | \(-0.563494\pi\) | ||||
−0.198153 | + | 0.980171i | \(0.563494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.94309i | − 0.227550i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 12.1235i | − 0.396905i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.6785 | −0.447336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.6732 | −0.544690 | −0.272345 | − | 0.962200i | \(-0.587799\pi\) | ||||
−0.272345 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.5283i | 0.539380i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 29.5263i | − 0.962529i | −0.876575 | − | 0.481265i | \(-0.840178\pi\) | ||||
0.876575 | − | 0.481265i | \(-0.159822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.40668 | 0.176066 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.38158 | −0.0449428 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2099i | 0.786717i | 0.919385 | + | 0.393358i | \(0.128687\pi\) | ||||
−0.919385 | + | 0.393358i | \(0.871313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 0.176739i | − 0.00573720i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.8287 | −0.610561 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5304 | −0.600258 | −0.300129 | − | 0.953899i | \(-0.597030\pi\) | ||||
−0.300129 | + | 0.953899i | \(0.597030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7903i | 0.640398i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 28.9405i | − 0.935513i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.341089 | 0.0110143 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2062 | 0.426005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10.6945i | − 0.344624i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.48590i | 0.176597i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2821 | 1.74559 | 0.872797 | − | 0.488084i | \(-0.162304\pi\) | ||||
0.872797 | + | 0.488084i | \(0.162304\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.15181 | −0.165500 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 7.69284i | − 0.246875i | −0.992352 | − | 0.123437i | \(-0.960608\pi\) | ||||
0.992352 | − | 0.123437i | \(-0.0393918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 0.854516i | − 0.0273945i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.81749 | −0.186309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.8587 | −1.05124 | −0.525621 | − | 0.850719i | \(-0.676167\pi\) | ||||
−0.525621 | + | 0.850719i | \(0.676167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 26.1694i | − 0.836378i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 24.8957i | − 0.794858i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4144 | −0.332169 | −0.166084 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166084 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8313 | 0.695602 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.82186i | − 0.0898209i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.35855i | 0.0749974i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.1164 | −1.97319 | −0.986596 | − | 0.163183i | \(-0.947824\pi\) | ||||
−0.986596 | + | 0.163183i | \(0.947824\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2908 | 0.548706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 0.334596i | − 0.0106074i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.60362i | − 0.177468i | −0.996055 | − | 0.0887341i | \(-0.971718\pi\) | ||||
0.996055 | − | 0.0887341i | \(-0.0282822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.8952 | −0.692735 |
(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 | 2432.2.c.j.1217.7 | ✓ | 20 | |
4.3 | odd | 2 | inner | 2432.2.c.j.1217.13 | yes | 20 | |
8.3 | odd | 2 | inner | 2432.2.c.j.1217.8 | yes | 20 | |
8.5 | even | 2 | inner | 2432.2.c.j.1217.14 | yes | 20 | |
16.3 | odd | 4 | 4864.2.a.bt.1.3 | 10 | |||
16.5 | even | 4 | 4864.2.a.bt.1.4 | 10 | |||
16.11 | odd | 4 | 4864.2.a.bs.1.8 | 10 | |||
16.13 | even | 4 | 4864.2.a.bs.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2432.2.c.j.1217.8 | yes | 20 | 8.3 | odd | 2 | inner | |
2432.2.c.j.1217.13 | yes | 20 | 4.3 | odd | 2 | inner | |
2432.2.c.j.1217.14 | yes | 20 | 8.5 | even | 2 | inner | |
4864.2.a.bs.1.7 | 10 | 16.13 | even | 4 | |||
4864.2.a.bs.1.8 | 10 | 16.11 | odd | 4 | |||
4864.2.a.bt.1.3 | 10 | 16.3 | odd | 4 | |||
4864.2.a.bt.1.4 | 10 | 16.5 | even | 4 |