Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(-0.642116 - 1.60863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.d.881.13 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.24045 | − | 1.20883i | 0.716175 | − | 0.697920i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.20883 | − | 1.24045i | −0.493504 | − | 0.506412i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.0774422 | − | 2.99900i | 0.0258141 | − | 0.999667i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | − | 0.388831i | − | 0.117237i | −0.998280 | − | 0.0586184i | \(-0.981330\pi\) | ||
0.998280 | − | 0.0586184i | \(-0.0186695\pi\) | |||||||
\(12\) | −1.24045 | + | 1.20883i | −0.358088 | + | 0.348960i | ||||
\(13\) | − | 0.436189i | − | 0.120977i | −0.998169 | − | 0.0604885i | \(-0.980734\pi\) | ||
0.998169 | − | 0.0604885i | \(-0.0192659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.24045 | − | 1.20883i | 0.320283 | − | 0.312120i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.581546 | 0.141046 | 0.0705228 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705228 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(18\) | −2.99900 | − | 0.0774422i | −0.706871 | − | 0.0182533i | ||||
\(19\) | − | 0.597750i | − | 0.137133i | −0.997647 | − | 0.0685666i | \(-0.978157\pi\) | ||
0.997647 | − | 0.0685666i | \(-0.0218426\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.388831 | −0.0828989 | ||||||||
\(23\) | − | 7.83308i | − | 1.63331i | −0.577126 | − | 0.816655i | \(-0.695826\pi\) | ||
0.577126 | − | 0.816655i | \(-0.304174\pi\) | |||||||
\(24\) | 1.20883 | + | 1.24045i | 0.246752 | + | 0.253206i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.436189 | −0.0855437 | ||||||||
\(27\) | −3.52923 | − | 3.81373i | −0.679200 | − | 0.733953i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39564i | 0.444859i | 0.974949 | + | 0.222429i | \(0.0713987\pi\) | ||||
−0.974949 | + | 0.222429i | \(0.928601\pi\) | |||||||
\(30\) | −1.20883 | − | 1.24045i | −0.220702 | − | 0.226475i | ||||
\(31\) | − | 8.53890i | − | 1.53363i | −0.641868 | − | 0.766815i | \(-0.721840\pi\) | ||
0.641868 | − | 0.766815i | \(-0.278160\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.470031 | − | 0.482326i | −0.0818220 | − | 0.0839621i | ||||
\(34\) | − | 0.581546i | − | 0.0997343i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0774422 | + | 2.99900i | −0.0129070 | + | 0.499833i | ||||
\(37\) | 6.55608 | 1.07781 | 0.538907 | − | 0.842366i | \(-0.318838\pi\) | ||||
0.538907 | + | 0.842366i | \(0.318838\pi\) | |||||||
\(38\) | −0.597750 | −0.0969678 | ||||||||
\(39\) | −0.527280 | − | 0.541071i | −0.0844324 | − | 0.0866408i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −2.65306 | −0.414338 | −0.207169 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207169 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1640 | −1.70250 | −0.851250 | − | 0.524760i | \(-0.824155\pi\) | ||||
−0.851250 | + | 0.524760i | \(0.824155\pi\) | |||||||
\(44\) | 0.388831i | 0.0586184i | ||||||||
\(45\) | 0.0774422 | − | 2.99900i | 0.0115444 | − | 0.447065i | ||||
\(46\) | −7.83308 | −1.15492 | ||||||||
\(47\) | 5.35068 | 0.780477 | 0.390238 | − | 0.920714i | \(-0.372393\pi\) | ||||
0.390238 | + | 0.920714i | \(0.372393\pi\) | |||||||
\(48\) | 1.24045 | − | 1.20883i | 0.179044 | − | 0.174480i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0.721380 | − | 0.702992i | 0.101013 | − | 0.0984386i | ||||
\(52\) | 0.436189i | 0.0604885i | ||||||||
\(53\) | 7.66134i | 1.05237i | 0.850372 | + | 0.526183i | \(0.176377\pi\) | ||||
−0.850372 | + | 0.526183i | \(0.823623\pi\) | |||||||
\(54\) | −3.81373 | + | 3.52923i | −0.518983 | + | 0.480267i | ||||
\(55\) | − | 0.388831i | − | 0.0524299i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.722580 | − | 0.741480i | −0.0957081 | − | 0.0982114i | ||||
\(58\) | 2.39564 | 0.314563 | ||||||||
\(59\) | −5.33043 | −0.693963 | −0.346982 | − | 0.937872i | \(-0.612793\pi\) | ||||
−0.346982 | + | 0.937872i | \(0.612793\pi\) | |||||||
\(60\) | −1.24045 | + | 1.20883i | −0.160142 | + | 0.156060i | ||||
\(61\) | − | 14.8030i | − | 1.89532i | −0.319276 | − | 0.947662i | \(-0.603440\pi\) | ||
0.319276 | − | 0.947662i | \(-0.396560\pi\) | |||||||
\(62\) | −8.53890 | −1.08444 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 0.436189i | − | 0.0541026i | ||||||
\(66\) | −0.482326 | + | 0.470031i | −0.0593702 | + | 0.0578569i | ||||
\(67\) | 11.8218 | 1.44426 | 0.722130 | − | 0.691757i | \(-0.243163\pi\) | ||||
0.722130 | + | 0.691757i | \(0.243163\pi\) | |||||||
\(68\) | −0.581546 | −0.0705228 | ||||||||
\(69\) | −9.46889 | − | 9.71656i | −1.13992 | − | 1.16974i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5318i | 1.72461i | 0.506387 | + | 0.862306i | \(0.330981\pi\) | ||||
−0.506387 | + | 0.862306i | \(0.669019\pi\) | |||||||
\(72\) | 2.99900 | + | 0.0774422i | 0.353436 | + | 0.00912665i | ||||
\(73\) | − | 7.51730i | − | 0.879834i | −0.898038 | − | 0.439917i | \(-0.855008\pi\) | ||
0.898038 | − | 0.439917i | \(-0.144992\pi\) | |||||||
\(74\) | − | 6.55608i | − | 0.762129i | ||||||
\(75\) | 1.24045 | − | 1.20883i | 0.143235 | − | 0.139584i | ||||
\(76\) | 0.597750i | 0.0685666i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.541071 | + | 0.527280i | −0.0612643 | + | 0.0597027i | ||||
\(79\) | 4.78108 | 0.537913 | 0.268957 | − | 0.963152i | \(-0.413321\pi\) | ||||
0.268957 | + | 0.963152i | \(0.413321\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −8.98801 | − | 0.464498i | −0.998667 | − | 0.0516109i | ||||
\(82\) | 2.65306i | 0.292981i | ||||||||
\(83\) | 0.157211 | 0.0172562 | 0.00862808 | − | 0.999963i | \(-0.497254\pi\) | ||||
0.00862808 | + | 0.999963i | \(0.497254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.581546 | 0.0630775 | ||||||||
\(86\) | 11.1640i | 1.20385i | ||||||||
\(87\) | 2.89593 | + | 2.97167i | 0.310476 | + | 0.318597i | ||||
\(88\) | 0.388831 | 0.0414495 | ||||||||
\(89\) | 11.1040 | 1.17703 | 0.588513 | − | 0.808487i | \(-0.299713\pi\) | ||||
0.588513 | + | 0.808487i | \(0.299713\pi\) | |||||||
\(90\) | −2.99900 | − | 0.0774422i | −0.316122 | − | 0.00816312i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.83308i | 0.816655i | ||||||||
\(93\) | −10.3221 | − | 10.5921i | −1.07035 | − | 1.09835i | ||||
\(94\) | − | 5.35068i | − | 0.551880i | ||||||
\(95\) | − | 0.597750i | − | 0.0613278i | ||||||
\(96\) | −1.20883 | − | 1.24045i | −0.123376 | − | 0.126603i | ||||
\(97\) | − | 1.08768i | − | 0.110437i | −0.998474 | − | 0.0552186i | \(-0.982414\pi\) | ||
0.998474 | − | 0.0552186i | \(-0.0175856\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.16610 | − | 0.0301119i | −0.117198 | − | 0.00302636i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −16.5092 | −1.64272 | −0.821362 | − | 0.570408i | \(-0.806785\pi\) | ||||
−0.821362 | + | 0.570408i | \(0.806785\pi\) | |||||||
\(102\) | −0.702992 | − | 0.721380i | −0.0696066 | − | 0.0714273i | ||||
\(103\) | 2.68965i | 0.265019i | 0.991182 | + | 0.132510i | \(0.0423035\pi\) | ||||
−0.991182 | + | 0.132510i | \(0.957696\pi\) | |||||||
\(104\) | 0.436189 | 0.0427718 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.66134 | 0.744135 | ||||||||
\(107\) | 10.1568i | 0.981895i | 0.871189 | + | 0.490947i | \(0.163349\pi\) | ||||
−0.871189 | + | 0.490947i | \(0.836651\pi\) | |||||||
\(108\) | 3.52923 | + | 3.81373i | 0.339600 | + | 0.366976i | ||||
\(109\) | 9.81570 | 0.940174 | 0.470087 | − | 0.882620i | \(-0.344223\pi\) | ||||
0.470087 | + | 0.882620i | \(0.344223\pi\) | |||||||
\(110\) | −0.388831 | −0.0370735 | ||||||||
\(111\) | 8.13250 | − | 7.92521i | 0.771903 | − | 0.752228i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.68271i | 0.816801i | 0.912803 | + | 0.408400i | \(0.133913\pi\) | ||||
−0.912803 | + | 0.408400i | \(0.866087\pi\) | |||||||
\(114\) | −0.741480 | + | 0.722580i | −0.0694460 | + | 0.0676758i | ||||
\(115\) | − | 7.83308i | − | 0.730439i | ||||||
\(116\) | − | 2.39564i | − | 0.222429i | ||||||
\(117\) | −1.30813 | − | 0.0337794i | −0.120937 | − | 0.00312291i | ||||
\(118\) | 5.33043i | 0.490706i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.20883 | + | 1.24045i | 0.110351 | + | 0.113237i | ||||
\(121\) | 10.8488 | 0.986256 | ||||||||
\(122\) | −14.8030 | −1.34020 | ||||||||
\(123\) | −3.29099 | + | 3.20710i | −0.296739 | + | 0.289175i | ||||
\(124\) | 8.53890i | 0.766815i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1119 | −1.60717 | −0.803585 | − | 0.595190i | \(-0.797077\pi\) | ||||
−0.803585 | + | 0.595190i | \(0.797077\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −13.8485 | + | 13.4955i | −1.21929 | + | 1.18821i | ||||
\(130\) | −0.436189 | −0.0382563 | ||||||||
\(131\) | 2.03892 | 0.178141 | 0.0890707 | − | 0.996025i | \(-0.471610\pi\) | ||||
0.0890707 | + | 0.996025i | \(0.471610\pi\) | |||||||
\(132\) | 0.470031 | + | 0.482326i | 0.0409110 | + | 0.0419811i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 11.8218i | − | 1.02125i | ||||||
\(135\) | −3.52923 | − | 3.81373i | −0.303748 | − | 0.328234i | ||||
\(136\) | 0.581546i | 0.0498672i | ||||||||
\(137\) | 16.1364i | 1.37863i | 0.724462 | + | 0.689315i | \(0.242088\pi\) | ||||
−0.724462 | + | 0.689315i | \(0.757912\pi\) | |||||||
\(138\) | −9.71656 | + | 9.46889i | −0.827129 | + | 0.806046i | ||||
\(139\) | − | 12.3487i | − | 1.04741i | −0.851901 | − | 0.523703i | \(-0.824550\pi\) | ||
0.851901 | − | 0.523703i | \(-0.175450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.63726 | − | 6.46808i | 0.558958 | − | 0.544711i | ||||
\(142\) | 14.5318 | 1.21949 | ||||||||
\(143\) | −0.169604 | −0.0141830 | ||||||||
\(144\) | 0.0774422 | − | 2.99900i | 0.00645352 | − | 0.249917i | ||||
\(145\) | 2.39564i | 0.198947i | ||||||||
\(146\) | −7.51730 | −0.622137 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.55608 | −0.538907 | ||||||||
\(149\) | 2.95913i | 0.242421i | 0.992627 | + | 0.121211i | \(0.0386776\pi\) | ||||
−0.992627 | + | 0.121211i | \(0.961322\pi\) | |||||||
\(150\) | −1.20883 | − | 1.24045i | −0.0987009 | − | 0.101282i | ||||
\(151\) | 8.33959 | 0.678666 | 0.339333 | − | 0.940666i | \(-0.389799\pi\) | ||||
0.339333 | + | 0.940666i | \(0.389799\pi\) | |||||||
\(152\) | 0.597750 | 0.0484839 | ||||||||
\(153\) | 0.0450362 | − | 1.74406i | 0.00364096 | − | 0.140999i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.53890i | − | 0.685861i | ||||||
\(156\) | 0.527280 | + | 0.541071i | 0.0422162 | + | 0.0433204i | ||||
\(157\) | 22.4692i | 1.79324i | 0.442805 | + | 0.896618i | \(0.353983\pi\) | ||||
−0.442805 | + | 0.896618i | \(0.646017\pi\) | |||||||
\(158\) | − | 4.78108i | − | 0.380362i | ||||||
\(159\) | 9.26128 | + | 9.50352i | 0.734467 | + | 0.753678i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.464498 | + | 8.98801i | −0.0364944 | + | 0.706164i | ||||
\(163\) | −13.6027 | −1.06545 | −0.532724 | − | 0.846289i | \(-0.678831\pi\) | ||||
−0.532724 | + | 0.846289i | \(0.678831\pi\) | |||||||
\(164\) | 2.65306 | 0.207169 | ||||||||
\(165\) | −0.470031 | − | 0.482326i | −0.0365919 | − | 0.0375490i | ||||
\(166\) | − | 0.157211i | − | 0.0122020i | ||||||
\(167\) | 20.4857 | 1.58523 | 0.792615 | − | 0.609723i | \(-0.208719\pi\) | ||||
0.792615 | + | 0.609723i | \(0.208719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8097 | 0.985365 | ||||||||
\(170\) | − | 0.581546i | − | 0.0446025i | ||||||
\(171\) | −1.79265 | − | 0.0462911i | −0.137088 | − | 0.00353997i | ||||
\(172\) | 11.1640 | 0.851250 | ||||||||
\(173\) | −15.3753 | −1.16896 | −0.584480 | − | 0.811408i | \(-0.698701\pi\) | ||||
−0.584480 | + | 0.811408i | \(0.698701\pi\) | |||||||
\(174\) | 2.97167 | − | 2.89593i | 0.225282 | − | 0.219540i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.388831i | − | 0.0293092i | ||||||
\(177\) | −6.61215 | + | 6.44361i | −0.496999 | + | 0.484331i | ||||
\(178\) | − | 11.1040i | − | 0.832284i | ||||||
\(179\) | − | 1.13504i | − | 0.0848367i | −0.999100 | − | 0.0424183i | \(-0.986494\pi\) | ||
0.999100 | − | 0.0424183i | \(-0.0135062\pi\) | |||||||
\(180\) | −0.0774422 | + | 2.99900i | −0.00577220 | + | 0.223532i | ||||
\(181\) | 11.1559i | 0.829211i | 0.910001 | + | 0.414605i | \(0.136080\pi\) | ||||
−0.910001 | + | 0.414605i | \(0.863920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.8943 | − | 18.3623i | −1.32279 | − | 1.35738i | ||||
\(184\) | 7.83308 | 0.577462 | ||||||||
\(185\) | 6.55608 | 0.482013 | ||||||||
\(186\) | −10.5921 | + | 10.3221i | −0.776650 | + | 0.756853i | ||||
\(187\) | − | 0.226123i | − | 0.0165357i | ||||||
\(188\) | −5.35068 | −0.390238 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.597750 | −0.0433653 | ||||||||
\(191\) | 5.87467i | 0.425076i | 0.977153 | + | 0.212538i | \(0.0681730\pi\) | ||||
−0.977153 | + | 0.212538i | \(0.931827\pi\) | |||||||
\(192\) | −1.24045 | + | 1.20883i | −0.0895219 | + | 0.0872401i | ||||
\(193\) | 2.60022 | 0.187168 | 0.0935839 | − | 0.995611i | \(-0.470168\pi\) | ||||
0.0935839 | + | 0.995611i | \(0.470168\pi\) | |||||||
\(194\) | −1.08768 | −0.0780909 | ||||||||
\(195\) | −0.527280 | − | 0.541071i | −0.0377593 | − | 0.0387469i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.23018i | 0.301388i | 0.988580 | + | 0.150694i | \(0.0481508\pi\) | ||||
−0.988580 | + | 0.150694i | \(0.951849\pi\) | |||||||
\(198\) | −0.0301119 | + | 1.16610i | −0.00213996 | + | 0.0828713i | ||||
\(199\) | − | 4.74835i | − | 0.336602i | −0.985736 | − | 0.168301i | \(-0.946172\pi\) | ||
0.985736 | − | 0.168301i | \(-0.0538280\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 14.6644 | − | 14.2906i | 1.03434 | − | 1.00798i | ||||
\(202\) | 16.5092i | 1.16158i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.721380 | + | 0.702992i | −0.0505067 | + | 0.0492193i | ||||
\(205\) | −2.65306 | −0.185298 | ||||||||
\(206\) | 2.68965 | 0.187397 | ||||||||
\(207\) | −23.4914 | − | 0.606611i | −1.63277 | − | 0.0421624i | ||||
\(208\) | − | 0.436189i | − | 0.0302443i | ||||||
\(209\) | −0.232423 | −0.0160771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3905 | 0.990682 | 0.495341 | − | 0.868699i | \(-0.335043\pi\) | ||||
0.495341 | + | 0.868699i | \(0.335043\pi\) | |||||||
\(212\) | − | 7.66134i | − | 0.526183i | ||||||
\(213\) | 17.5666 | + | 18.0261i | 1.20364 | + | 1.23513i | ||||
\(214\) | 10.1568 | 0.694304 | ||||||||
\(215\) | −11.1640 | −0.761381 | ||||||||
\(216\) | 3.81373 | − | 3.52923i | 0.259491 | − | 0.240134i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 9.81570i | − | 0.664803i | ||||||
\(219\) | −9.08717 | − | 9.32486i | −0.614054 | − | 0.630115i | ||||
\(220\) | 0.388831i | 0.0262149i | ||||||||
\(221\) | − | 0.253664i | − | 0.0170633i | ||||||
\(222\) | −7.92521 | − | 8.13250i | −0.531905 | − | 0.545818i | ||||
\(223\) | 17.3485i | 1.16174i | 0.813996 | + | 0.580870i | \(0.197288\pi\) | ||||
−0.813996 | + | 0.580870i | \(0.802712\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0774422 | − | 2.99900i | 0.00516281 | − | 0.199933i | ||||
\(226\) | 8.68271 | 0.577565 | ||||||||
\(227\) | 12.2684 | 0.814280 | 0.407140 | − | 0.913366i | \(-0.366526\pi\) | ||||
0.407140 | + | 0.913366i | \(0.366526\pi\) | |||||||
\(228\) | 0.722580 | + | 0.741480i | 0.0478540 | + | 0.0491057i | ||||
\(229\) | 1.44031i | 0.0951784i | 0.998867 | + | 0.0475892i | \(0.0151538\pi\) | ||||
−0.998867 | + | 0.0475892i | \(0.984846\pi\) | |||||||
\(230\) | −7.83308 | −0.516498 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.39564 | −0.157281 | ||||||||
\(233\) | − | 27.2147i | − | 1.78289i | −0.453128 | − | 0.891446i | \(-0.649692\pi\) | ||
0.453128 | − | 0.891446i | \(-0.350308\pi\) | |||||||
\(234\) | −0.0337794 | + | 1.30813i | −0.00220823 | + | 0.0855152i | ||||
\(235\) | 5.35068 | 0.349040 | ||||||||
\(236\) | 5.33043 | 0.346982 | ||||||||
\(237\) | 5.93070 | − | 5.77953i | 0.385240 | − | 0.375421i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.6627i | − | 1.33656i | −0.743911 | − | 0.668278i | \(-0.767032\pi\) | ||
0.743911 | − | 0.668278i | \(-0.232968\pi\) | |||||||
\(240\) | 1.24045 | − | 1.20883i | 0.0800708 | − | 0.0780299i | ||||
\(241\) | 11.8237i | 0.761633i | 0.924651 | + | 0.380816i | \(0.124357\pi\) | ||||
−0.924651 | + | 0.380816i | \(0.875643\pi\) | |||||||
\(242\) | − | 10.8488i | − | 0.697388i | ||||||
\(243\) | −11.7107 | + | 10.2888i | −0.751241 | + | 0.660028i | ||||
\(244\) | 14.8030i | 0.947662i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.20710 | + | 3.29099i | 0.204478 | + | 0.209826i | ||||
\(247\) | −0.260732 | −0.0165900 | ||||||||
\(248\) | 8.53890 | 0.542220 | ||||||||
\(249\) | 0.195013 | − | 0.190042i | 0.0123584 | − | 0.0120434i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 26.0569 | 1.64470 | 0.822349 | − | 0.568983i | \(-0.192663\pi\) | ||||
0.822349 | + | 0.568983i | \(0.192663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.04574 | −0.191484 | ||||||||
\(254\) | 18.1119i | 1.13644i | ||||||||
\(255\) | 0.721380 | − | 0.702992i | 0.0451746 | − | 0.0440231i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.94372 | 0.433137 | 0.216569 | − | 0.976267i | \(-0.430514\pi\) | ||||
0.216569 | + | 0.976267i | \(0.430514\pi\) | |||||||
\(258\) | 13.4955 | + | 13.8485i | 0.840191 | + | 0.862167i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.436189i | 0.0270513i | ||||||||
\(261\) | 7.18452 | + | 0.185523i | 0.444711 | + | 0.0114836i | ||||
\(262\) | − | 2.03892i | − | 0.125965i | ||||||
\(263\) | 11.4248i | 0.704484i | 0.935909 | + | 0.352242i | \(0.114581\pi\) | ||||
−0.935909 | + | 0.352242i | \(0.885419\pi\) | |||||||
\(264\) | 0.482326 | − | 0.470031i | 0.0296851 | − | 0.0289284i | ||||
\(265\) | 7.66134i | 0.470632i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.7740 | − | 13.4229i | 0.842957 | − | 0.821471i | ||||
\(268\) | −11.8218 | −0.722130 | ||||||||
\(269\) | 11.2718 | 0.687257 | 0.343628 | − | 0.939106i | \(-0.388344\pi\) | ||||
0.343628 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(270\) | −3.81373 | + | 3.52923i | −0.232096 | + | 0.214782i | ||||
\(271\) | − | 20.4663i | − | 1.24324i | −0.783318 | − | 0.621621i | \(-0.786474\pi\) | ||
0.783318 | − | 0.621621i | \(-0.213526\pi\) | |||||||
\(272\) | 0.581546 | 0.0352614 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.1364 | 0.974838 | ||||||||
\(275\) | − | 0.388831i | − | 0.0234474i | ||||||
\(276\) | 9.46889 | + | 9.71656i | 0.569960 | + | 0.584868i | ||||
\(277\) | 7.48525 | 0.449745 | 0.224873 | − | 0.974388i | \(-0.427803\pi\) | ||||
0.224873 | + | 0.974388i | \(0.427803\pi\) | |||||||
\(278\) | −12.3487 | −0.740628 | ||||||||
\(279\) | −25.6082 | − | 0.661271i | −1.53312 | − | 0.0395892i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.1139i | 0.662998i | 0.943456 | + | 0.331499i | \(0.107554\pi\) | ||||
−0.943456 | + | 0.331499i | \(0.892446\pi\) | |||||||
\(282\) | −6.46808 | − | 6.63726i | −0.385169 | − | 0.395243i | ||||
\(283\) | − | 27.8744i | − | 1.65696i | −0.560016 | − | 0.828481i | \(-0.689205\pi\) | ||
0.560016 | − | 0.828481i | \(-0.310795\pi\) | |||||||
\(284\) | − | 14.5318i | − | 0.862306i | ||||||
\(285\) | −0.722580 | − | 0.741480i | −0.0428020 | − | 0.0439215i | ||||
\(286\) | 0.169604i | 0.0100289i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.99900 | − | 0.0774422i | −0.176718 | − | 0.00456332i | ||||
\(289\) | −16.6618 | −0.980106 | ||||||||
\(290\) | 2.39564 | 0.140677 | ||||||||
\(291\) | −1.31482 | − | 1.34922i | −0.0770764 | − | 0.0790924i | ||||
\(292\) | 7.51730i | 0.439917i | ||||||||
\(293\) | −19.7545 | −1.15407 | −0.577034 | − | 0.816720i | \(-0.695790\pi\) | ||||
−0.577034 | + | 0.816720i | \(0.695790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.33043 | −0.310350 | ||||||||
\(296\) | 6.55608i | 0.381065i | ||||||||
\(297\) | −1.48289 | + | 1.37227i | −0.0860463 | + | 0.0796273i | ||||
\(298\) | 2.95913 | 0.171418 | ||||||||
\(299\) | −3.41670 | −0.197593 | ||||||||
\(300\) | −1.24045 | + | 1.20883i | −0.0716175 | + | 0.0697920i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 8.33959i | − | 0.479889i | ||||||
\(303\) | −20.4788 | + | 19.9568i | −1.17648 | + | 1.14649i | ||||
\(304\) | − | 0.597750i | − | 0.0342833i | ||||||
\(305\) | − | 14.8030i | − | 0.847614i | ||||||
\(306\) | −1.74406 | − | 0.0450362i | −0.0997011 | − | 0.00257455i | ||||
\(307\) | − | 8.92019i | − | 0.509102i | −0.967059 | − | 0.254551i | \(-0.918072\pi\) | ||
0.967059 | − | 0.254551i | \(-0.0819277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.25134 | + | 3.33638i | 0.184962 | + | 0.189800i | ||||
\(310\) | −8.53890 | −0.484977 | ||||||||
\(311\) | 0.960152 | 0.0544452 | 0.0272226 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272226 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(312\) | 0.541071 | − | 0.527280i | 0.0306321 | − | 0.0298513i | ||||
\(313\) | 4.56673i | 0.258127i | 0.991636 | + | 0.129063i | \(0.0411971\pi\) | ||||
−0.991636 | + | 0.129063i | \(0.958803\pi\) | |||||||
\(314\) | 22.4692 | 1.26801 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.78108 | −0.268957 | ||||||||
\(317\) | 12.2121i | 0.685900i | 0.939354 | + | 0.342950i | \(0.111426\pi\) | ||||
−0.939354 | + | 0.342950i | \(0.888574\pi\) | |||||||
\(318\) | 9.50352 | − | 9.26128i | 0.532931 | − | 0.519347i | ||||
\(319\) | 0.931497 | 0.0521538 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 12.2779 | + | 12.5990i | 0.685284 | + | 0.703209i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.347619i | − | 0.0193420i | ||||||
\(324\) | 8.98801 | + | 0.464498i | 0.499334 | + | 0.0258055i | ||||
\(325\) | − | 0.436189i | − | 0.0241954i | ||||||
\(326\) | 13.6027i | 0.753385i | ||||||||
\(327\) | 12.1759 | − | 11.8655i | 0.673329 | − | 0.656166i | ||||
\(328\) | − | 2.65306i | − | 0.146491i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.482326 | + | 0.470031i | −0.0265511 | + | 0.0258744i | ||||
\(331\) | 19.3496 | 1.06355 | 0.531775 | − | 0.846886i | \(-0.321525\pi\) | ||||
0.531775 | + | 0.846886i | \(0.321525\pi\) | |||||||
\(332\) | −0.157211 | −0.00862808 | ||||||||
\(333\) | 0.507717 | − | 19.6617i | 0.0278227 | − | 1.07745i | ||||
\(334\) | − | 20.4857i | − | 1.12093i | ||||||
\(335\) | 11.8218 | 0.645893 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.9183 | 1.79317 | 0.896587 | − | 0.442867i | \(-0.146039\pi\) | ||||
0.896587 | + | 0.442867i | \(0.146039\pi\) | |||||||
\(338\) | − | 12.8097i | − | 0.696758i | ||||||
\(339\) | 10.4960 | + | 10.7705i | 0.570062 | + | 0.584972i | ||||
\(340\) | −0.581546 | −0.0315388 | ||||||||
\(341\) | −3.32018 | −0.179798 | ||||||||
\(342\) | −0.0462911 | + | 1.79265i | −0.00250313 | + | 0.0969355i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 11.1640i | − | 0.601925i | ||||||
\(345\) | −9.46889 | − | 9.71656i | −0.509788 | − | 0.523122i | ||||
\(346\) | 15.3753i | 0.826579i | ||||||||
\(347\) | − | 6.94260i | − | 0.372698i | −0.982484 | − | 0.186349i | \(-0.940334\pi\) | ||
0.982484 | − | 0.186349i | \(-0.0596655\pi\) | |||||||
\(348\) | −2.89593 | − | 2.97167i | −0.155238 | − | 0.159298i | ||||
\(349\) | 22.3154i | 1.19451i | 0.802050 | + | 0.597257i | \(0.203743\pi\) | ||||
−0.802050 | + | 0.597257i | \(0.796257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.66351 | + | 1.53941i | −0.0887914 | + | 0.0821677i | ||||
\(352\) | −0.388831 | −0.0207247 | ||||||||
\(353\) | 27.3114 | 1.45364 | 0.726820 | − | 0.686828i | \(-0.240997\pi\) | ||||
0.726820 | + | 0.686828i | \(0.240997\pi\) | |||||||
\(354\) | 6.44361 | + | 6.61215i | 0.342474 | + | 0.351432i | ||||
\(355\) | 14.5318i | 0.771270i | ||||||||
\(356\) | −11.1040 | −0.588513 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.13504 | −0.0599886 | ||||||||
\(359\) | 10.2004i | 0.538357i | 0.963090 | + | 0.269178i | \(0.0867521\pi\) | ||||
−0.963090 | + | 0.269178i | \(0.913248\pi\) | |||||||
\(360\) | 2.99900 | + | 0.0774422i | 0.158061 | + | 0.00408156i | ||||
\(361\) | 18.6427 | 0.981194 | ||||||||
\(362\) | 11.1559 | 0.586341 | ||||||||
\(363\) | 13.4574 | − | 13.1144i | 0.706332 | − | 0.688328i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 7.51730i | − | 0.393474i | ||||||
\(366\) | −18.3623 | + | 17.8943i | −0.959815 | + | 0.935350i | ||||
\(367\) | 9.33458i | 0.487261i | 0.969868 | + | 0.243631i | \(0.0783385\pi\) | ||||
−0.969868 | + | 0.243631i | \(0.921662\pi\) | |||||||
\(368\) | − | 7.83308i | − | 0.408328i | ||||||
\(369\) | −0.205459 | + | 7.95652i | −0.0106957 | + | 0.414200i | ||||
\(370\) | − | 6.55608i | − | 0.340834i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.3221 | + | 10.5921i | 0.535176 | + | 0.549174i | ||||
\(373\) | −7.34793 | −0.380461 | −0.190231 | − | 0.981739i | \(-0.560924\pi\) | ||||
−0.190231 | + | 0.981739i | \(0.560924\pi\) | |||||||
\(374\) | −0.226123 | −0.0116925 | ||||||||
\(375\) | 1.24045 | − | 1.20883i | 0.0640567 | − | 0.0624239i | ||||
\(376\) | 5.35068i | 0.275940i | ||||||||
\(377\) | 1.04495 | 0.0538177 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2225 | 0.576462 | 0.288231 | − | 0.957561i | \(-0.406933\pi\) | ||||
0.288231 | + | 0.957561i | \(0.406933\pi\) | |||||||
\(380\) | 0.597750i | 0.0306639i | ||||||||
\(381\) | −22.4669 | + | 21.8943i | −1.15102 | + | 1.12168i | ||||
\(382\) | 5.87467 | 0.300574 | ||||||||
\(383\) | −22.5133 | −1.15038 | −0.575188 | − | 0.818021i | \(-0.695071\pi\) | ||||
−0.575188 | + | 0.818021i | \(0.695071\pi\) | |||||||
\(384\) | 1.20883 | + | 1.24045i | 0.0616880 | + | 0.0633015i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.60022i | − | 0.132348i | ||||||
\(387\) | −0.864568 | + | 33.4810i | −0.0439484 | + | 1.70193i | ||||
\(388\) | 1.08768i | 0.0552186i | ||||||||
\(389\) | 20.8569i | 1.05749i | 0.848782 | + | 0.528743i | \(0.177336\pi\) | ||||
−0.848782 | + | 0.528743i | \(0.822664\pi\) | |||||||
\(390\) | −0.541071 | + | 0.527280i | −0.0273982 | + | 0.0266999i | ||||
\(391\) | − | 4.55530i | − | 0.230371i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.52918 | − | 2.46472i | 0.127580 | − | 0.124329i | ||||
\(394\) | 4.23018 | 0.213113 | ||||||||
\(395\) | 4.78108 | 0.240562 | ||||||||
\(396\) | 1.16610 | + | 0.0301119i | 0.0585989 | + | 0.00151318i | ||||
\(397\) | − | 5.80599i | − | 0.291394i | −0.989329 | − | 0.145697i | \(-0.953457\pi\) | ||
0.989329 | − | 0.145697i | \(-0.0465425\pi\) | |||||||
\(398\) | −4.74835 | −0.238013 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.60821i | 0.379936i | 0.981790 | + | 0.189968i | \(0.0608384\pi\) | ||||
−0.981790 | + | 0.189968i | \(0.939162\pi\) | |||||||
\(402\) | −14.2906 | − | 14.6644i | −0.712749 | − | 0.731392i | ||||
\(403\) | −3.72457 | −0.185534 | ||||||||
\(404\) | 16.5092 | 0.821362 | ||||||||
\(405\) | −8.98801 | − | 0.464498i | −0.446618 | − | 0.0230811i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.54920i | − | 0.126359i | ||||||
\(408\) | 0.702992 | + | 0.721380i | 0.0348033 | + | 0.0357136i | ||||
\(409\) | − | 25.4555i | − | 1.25869i | −0.777124 | − | 0.629347i | \(-0.783322\pi\) | ||
0.777124 | − | 0.629347i | \(-0.216678\pi\) | |||||||
\(410\) | 2.65306i | 0.131025i | ||||||||
\(411\) | 19.5063 | + | 20.0165i | 0.962174 | + | 0.987341i | ||||
\(412\) | − | 2.68965i | − | 0.132510i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.606611 | + | 23.4914i | −0.0298133 | + | 1.15454i | ||||
\(415\) | 0.157211 | 0.00771719 | ||||||||
\(416\) | −0.436189 | −0.0213859 | ||||||||
\(417\) | −14.9276 | − | 15.3180i | −0.731006 | − | 0.750126i | ||||
\(418\) | 0.232423i | 0.0113682i | ||||||||
\(419\) | 32.2860 | 1.57727 | 0.788636 | − | 0.614860i | \(-0.210787\pi\) | ||||
0.788636 | + | 0.614860i | \(0.210787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.83642 | 0.138239 | 0.0691194 | − | 0.997608i | \(-0.477981\pi\) | ||||
0.0691194 | + | 0.997608i | \(0.477981\pi\) | |||||||
\(422\) | − | 14.3905i | − | 0.700518i | ||||||
\(423\) | 0.414368 | − | 16.0467i | 0.0201473 | − | 0.780217i | ||||
\(424\) | −7.66134 | −0.372067 | ||||||||
\(425\) | 0.581546 | 0.0282091 | ||||||||
\(426\) | 18.0261 | − | 17.5666i | 0.873365 | − | 0.851104i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 10.1568i | − | 0.490947i | ||||||
\(429\) | −0.210385 | + | 0.205023i | −0.0101575 | + | 0.00989858i | ||||
\(430\) | 11.1640i | 0.538378i | ||||||||
\(431\) | − | 33.8559i | − | 1.63078i | −0.578911 | − | 0.815391i | \(-0.696522\pi\) | ||
0.578911 | − | 0.815391i | \(-0.303478\pi\) | |||||||
\(432\) | −3.52923 | − | 3.81373i | −0.169800 | − | 0.183488i | ||||
\(433\) | 36.2694i | 1.74300i | 0.490398 | + | 0.871499i | \(0.336851\pi\) | ||||
−0.490398 | + | 0.871499i | \(0.663149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.89593 | + | 2.97167i | 0.138849 | + | 0.142481i | ||||
\(436\) | −9.81570 | −0.470087 | ||||||||
\(437\) | −4.68222 | −0.223981 | ||||||||
\(438\) | −9.32486 | + | 9.08717i | −0.445559 | + | 0.434202i | ||||
\(439\) | − | 27.1425i | − | 1.29544i | −0.761878 | − | 0.647721i | \(-0.775722\pi\) | ||
0.761878 | − | 0.647721i | \(-0.224278\pi\) | |||||||
\(440\) | 0.388831 | 0.0185368 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.253664 | −0.0120656 | ||||||||
\(443\) | − | 11.7451i | − | 0.558025i | −0.960287 | − | 0.279012i | \(-0.909993\pi\) | ||
0.960287 | − | 0.279012i | \(-0.0900071\pi\) | |||||||
\(444\) | −8.13250 | + | 7.92521i | −0.385952 | + | 0.376114i | ||||
\(445\) | 11.1040 | 0.526382 | ||||||||
\(446\) | 17.3485 | 0.821474 | ||||||||
\(447\) | 3.57709 | + | 3.67066i | 0.169191 | + | 0.173616i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.2663i | 0.909235i | 0.890687 | + | 0.454618i | \(0.150224\pi\) | ||||
−0.890687 | + | 0.454618i | \(0.849776\pi\) | |||||||
\(450\) | −2.99900 | − | 0.0774422i | −0.141374 | − | 0.00365066i | ||||
\(451\) | 1.03159i | 0.0485756i | ||||||||
\(452\) | − | 8.68271i | − | 0.408400i | ||||||
\(453\) | 10.3449 | − | 10.0812i | 0.486044 | − | 0.473655i | ||||
\(454\) | − | 12.2684i | − | 0.575783i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.741480 | − | 0.722580i | 0.0347230 | − | 0.0338379i | ||||
\(457\) | −9.32357 | −0.436138 | −0.218069 | − | 0.975933i | \(-0.569976\pi\) | ||||
−0.218069 | + | 0.975933i | \(0.569976\pi\) | |||||||
\(458\) | 1.44031 | 0.0673013 | ||||||||
\(459\) | −2.05241 | − | 2.21786i | −0.0957983 | − | 0.103521i | ||||
\(460\) | 7.83308i | 0.365219i | ||||||||
\(461\) | −6.36590 | −0.296490 | −0.148245 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148245 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.83216 | −0.0851475 | −0.0425737 | − | 0.999093i | \(-0.513556\pi\) | ||||
−0.0425737 | + | 0.999093i | \(0.513556\pi\) | |||||||
\(464\) | 2.39564i | 0.111215i | ||||||||
\(465\) | −10.3221 | − | 10.5921i | −0.478676 | − | 0.491196i | ||||
\(466\) | −27.2147 | −1.26069 | ||||||||
\(467\) | 2.25893 | 0.104531 | 0.0522653 | − | 0.998633i | \(-0.483356\pi\) | ||||
0.0522653 | + | 0.998633i | \(0.483356\pi\) | |||||||
\(468\) | 1.30813 | + | 0.0337794i | 0.0604684 | + | 0.00156145i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 5.35068i | − | 0.246808i | ||||||
\(471\) | 27.1615 | + | 27.8719i | 1.25154 | + | 1.28427i | ||||
\(472\) | − | 5.33043i | − | 0.245353i | ||||||
\(473\) | 4.34092i | 0.199596i | ||||||||
\(474\) | −5.77953 | − | 5.93070i | −0.265463 | − | 0.272406i | ||||
\(475\) | − | 0.597750i | − | 0.0274266i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.9763 | + | 0.593311i | 1.05201 | + | 0.0271658i | ||||
\(478\) | −20.6627 | −0.945088 | ||||||||
\(479\) | 37.0085 | 1.69096 | 0.845480 | − | 0.534007i | \(-0.179315\pi\) | ||||
0.845480 | + | 0.534007i | \(0.179315\pi\) | |||||||
\(480\) | −1.20883 | − | 1.24045i | −0.0551755 | − | 0.0566186i | ||||
\(481\) | − | 2.85969i | − | 0.130391i | ||||||
\(482\) | 11.8237 | 0.538556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8488 | −0.493128 | ||||||||
\(485\) | − | 1.08768i | − | 0.0493890i | ||||||
\(486\) | 10.2888 | + | 11.7107i | 0.466710 | + | 0.531208i | ||||
\(487\) | −40.3476 | −1.82832 | −0.914162 | − | 0.405349i | \(-0.867150\pi\) | ||||
−0.914162 | + | 0.405349i | \(0.867150\pi\) | |||||||
\(488\) | 14.8030 | 0.670098 | ||||||||
\(489\) | −16.8735 | + | 16.4434i | −0.763047 | + | 0.743598i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8602i | 1.25731i | 0.777684 | + | 0.628656i | \(0.216395\pi\) | ||||
−0.777684 | + | 0.628656i | \(0.783605\pi\) | |||||||
\(492\) | 3.29099 | − | 3.20710i | 0.148369 | − | 0.144587i | ||||
\(493\) | 1.39317i | 0.0627454i | ||||||||
\(494\) | 0.260732i | 0.0117309i | ||||||||
\(495\) | −1.16610 | − | 0.0301119i | −0.0524124 | − | 0.00135343i | ||||
\(496\) | − | 8.53890i | − | 0.383408i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.190042 | − | 0.195013i | −0.00851599 | − | 0.00873874i | ||||
\(499\) | 14.0739 | 0.630034 | 0.315017 | − | 0.949086i | \(-0.397990\pi\) | ||||
0.315017 | + | 0.949086i | \(0.397990\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 25.4115 | − | 24.7638i | 1.13530 | − | 1.10636i | ||||
\(502\) | − | 26.0569i | − | 1.16298i | ||||||
\(503\) | −5.77708 | −0.257587 | −0.128794 | − | 0.991671i | \(-0.541110\pi\) | ||||
−0.128794 | + | 0.991671i | \(0.541110\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.5092 | −0.734648 | ||||||||
\(506\) | 3.04574i | 0.135400i | ||||||||
\(507\) | 15.8899 | − | 15.4848i | 0.705694 | − | 0.687706i | ||||
\(508\) | 18.1119 | 0.803585 | ||||||||
\(509\) | −13.8369 | −0.613308 | −0.306654 | − | 0.951821i | \(-0.599209\pi\) | ||||
−0.306654 | + | 0.951821i | \(0.599209\pi\) | |||||||
\(510\) | −0.702992 | − | 0.721380i | −0.0311290 | − | 0.0319432i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −2.27966 | + | 2.10960i | −0.100649 | + | 0.0931410i | ||||
\(514\) | − | 6.94372i | − | 0.306274i | ||||||
\(515\) | 2.68965i | 0.118520i | ||||||||
\(516\) | 13.8485 | − | 13.4955i | 0.609644 | − | 0.594105i | ||||
\(517\) | − | 2.08051i | − | 0.0915006i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.0723 | + | 18.5861i | −0.837180 | + | 0.815841i | ||||
\(520\) | 0.436189 | 0.0191282 | ||||||||
\(521\) | −31.9328 | −1.39900 | −0.699501 | − | 0.714632i | \(-0.746594\pi\) | ||||
−0.699501 | + | 0.714632i | \(0.746594\pi\) | |||||||
\(522\) | 0.185523 | − | 7.18452i | 0.00812014 | − | 0.314458i | ||||
\(523\) | 28.6600i | 1.25322i | 0.779335 | + | 0.626608i | \(0.215557\pi\) | ||||
−0.779335 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(524\) | −2.03892 | −0.0890707 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.4248 | 0.498146 | ||||||||
\(527\) | − | 4.96576i | − | 0.216312i | ||||||
\(528\) | −0.470031 | − | 0.482326i | −0.0204555 | − | 0.0209905i | ||||
\(529\) | −38.3572 | −1.66770 | ||||||||
\(530\) | 7.66134 | 0.332787 | ||||||||
\(531\) | −0.412800 | + | 15.9860i | −0.0179140 | + | 0.693732i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.15723i | 0.0501254i | ||||||||
\(534\) | −13.4229 | − | 13.7740i | −0.580868 | − | 0.596061i | ||||
\(535\) | 10.1568i | 0.439117i | ||||||||
\(536\) | 11.8218i | 0.510623i | ||||||||
\(537\) | −1.37207 | − | 1.40796i | −0.0592092 | − | 0.0607579i | ||||
\(538\) | − | 11.2718i | − | 0.485964i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.52923 | + | 3.81373i | 0.151874 | + | 0.164117i | ||||
\(541\) | 23.0782 | 0.992211 | 0.496106 | − | 0.868262i | \(-0.334763\pi\) | ||||
0.496106 | + | 0.868262i | \(0.334763\pi\) | |||||||
\(542\) | −20.4663 | −0.879105 | ||||||||
\(543\) | 13.4856 | + | 13.8383i | 0.578723 | + | 0.593860i | ||||
\(544\) | − | 0.581546i | − | 0.0249336i | ||||||
\(545\) | 9.81570 | 0.420458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.41240 | −0.316931 | −0.158466 | − | 0.987365i | \(-0.550655\pi\) | ||||
−0.158466 | + | 0.987365i | \(0.550655\pi\) | |||||||
\(548\) | − | 16.1364i | − | 0.689315i | ||||||
\(549\) | −44.3941 | − | 1.14637i | −1.89469 | − | 0.0489260i | ||||
\(550\) | −0.388831 | −0.0165798 | ||||||||
\(551\) | 1.43199 | 0.0610049 | ||||||||
\(552\) | 9.71656 | − | 9.46889i | 0.413564 | − | 0.403023i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 7.48525i | − | 0.318018i | ||||||
\(555\) | 8.13250 | − | 7.92521i | 0.345206 | − | 0.336407i | ||||
\(556\) | 12.3487i | 0.523703i | ||||||||
\(557\) | 26.7659i | 1.13411i | 0.823681 | + | 0.567054i | \(0.191917\pi\) | ||||
−0.823681 | + | 0.567054i | \(0.808083\pi\) | |||||||
\(558\) | −0.661271 | + | 25.6082i | −0.0279938 | + | 1.08408i | ||||
\(559\) | 4.86963i | 0.205963i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.273345 | − | 0.280495i | −0.0115406 | − | 0.0118425i | ||||
\(562\) | 11.1139 | 0.468810 | ||||||||
\(563\) | −23.0597 | −0.971851 | −0.485926 | − | 0.874000i | \(-0.661517\pi\) | ||||
−0.485926 | + | 0.874000i | \(0.661517\pi\) | |||||||
\(564\) | −6.63726 | + | 6.46808i | −0.279479 | + | 0.272355i | ||||
\(565\) | 8.68271i | 0.365284i | ||||||||
\(566\) | −27.8744 | −1.17165 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.5318 | −0.609743 | ||||||||
\(569\) | 25.8069i | 1.08188i | 0.841061 | + | 0.540940i | \(0.181931\pi\) | ||||
−0.841061 | + | 0.540940i | \(0.818069\pi\) | |||||||
\(570\) | −0.741480 | + | 0.722580i | −0.0310572 | + | 0.0302656i | ||||
\(571\) | 31.4767 | 1.31726 | 0.658629 | − | 0.752468i | \(-0.271137\pi\) | ||||
0.658629 | + | 0.752468i | \(0.271137\pi\) | |||||||
\(572\) | 0.169604 | 0.00709148 | ||||||||
\(573\) | 7.10150 | + | 7.28725i | 0.296670 | + | 0.304429i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.83308i | − | 0.326662i | ||||||
\(576\) | −0.0774422 | + | 2.99900i | −0.00322676 | + | 0.124958i | ||||
\(577\) | 2.04044i | 0.0849445i | 0.999098 | + | 0.0424722i | \(0.0135234\pi\) | ||||
−0.999098 | + | 0.0424722i | \(0.986477\pi\) | |||||||
\(578\) | 16.6618i | 0.693040i | ||||||||
\(579\) | 3.22545 | − | 3.14323i | 0.134045 | − | 0.130628i | ||||
\(580\) | − | 2.39564i | − | 0.0994735i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.34922 | + | 1.31482i | −0.0559268 | + | 0.0545012i | ||||
\(583\) | 2.97896 | 0.123376 | ||||||||
\(584\) | 7.51730 | 0.311068 | ||||||||
\(585\) | −1.30813 | − | 0.0337794i | −0.0540846 | − | 0.00139661i | ||||
\(586\) | 19.7545i | 0.816049i | ||||||||
\(587\) | −31.1133 | −1.28418 | −0.642092 | − | 0.766627i | \(-0.721933\pi\) | ||||
−0.642092 | + | 0.766627i | \(0.721933\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.10412 | −0.210312 | ||||||||
\(590\) | 5.33043i | 0.219450i | ||||||||
\(591\) | 5.11358 | + | 5.24733i | 0.210345 | + | 0.215846i | ||||
\(592\) | 6.55608 | 0.269453 | ||||||||
\(593\) | 14.5622 | 0.597997 | 0.298999 | − | 0.954254i | \(-0.403347\pi\) | ||||
0.298999 | + | 0.954254i | \(0.403347\pi\) | |||||||
\(594\) | 1.37227 | + | 1.48289i | 0.0563050 | + | 0.0608439i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.95913i | − | 0.121211i | ||||||
\(597\) | −5.73997 | − | 5.89010i | −0.234921 | − | 0.241066i | ||||
\(598\) | 3.41670i | 0.139719i | ||||||||
\(599\) | − | 1.64056i | − | 0.0670316i | −0.999438 | − | 0.0335158i | \(-0.989330\pi\) | ||
0.999438 | − | 0.0335158i | \(-0.0106704\pi\) | |||||||
\(600\) | 1.20883 | + | 1.24045i | 0.0493504 | + | 0.0506412i | ||||
\(601\) | 9.87727i | 0.402902i | 0.979499 | + | 0.201451i | \(0.0645658\pi\) | ||||
−0.979499 | + | 0.201451i | \(0.935434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.915505 | − | 35.4535i | 0.0372822 | − | 1.44378i | ||||
\(604\) | −8.33959 | −0.339333 | ||||||||
\(605\) | 10.8488 | 0.441067 | ||||||||
\(606\) | 19.9568 | + | 20.4788i | 0.810691 | + | 0.831895i | ||||
\(607\) | 13.7514i | 0.558153i | 0.960269 | + | 0.279076i | \(0.0900283\pi\) | ||||
−0.960269 | + | 0.279076i | \(0.909972\pi\) | |||||||
\(608\) | −0.597750 | −0.0242420 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.8030 | −0.599354 | ||||||||
\(611\) | − | 2.33391i | − | 0.0944198i | ||||||
\(612\) | −0.0450362 | + | 1.74406i | −0.00182048 | + | 0.0704993i | ||||
\(613\) | −19.7544 | −0.797872 | −0.398936 | − | 0.916979i | \(-0.630620\pi\) | ||||
−0.398936 | + | 0.916979i | \(0.630620\pi\) | |||||||
\(614\) | −8.92019 | −0.359990 | ||||||||
\(615\) | −3.29099 | + | 3.20710i | −0.132706 | + | 0.129323i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3699i | 0.578509i | 0.957252 | + | 0.289255i | \(0.0934074\pi\) | ||||
−0.957252 | + | 0.289255i | \(0.906593\pi\) | |||||||
\(618\) | 3.33638 | − | 3.25134i | 0.134209 | − | 0.130788i | ||||
\(619\) | 5.11190i | 0.205465i | 0.994709 | + | 0.102732i | \(0.0327585\pi\) | ||||
−0.994709 | + | 0.102732i | \(0.967242\pi\) | |||||||
\(620\) | 8.53890i | 0.342930i | ||||||||
\(621\) | −29.8733 | + | 27.6447i | −1.19877 | + | 1.10935i | ||||
\(622\) | − | 0.960152i | − | 0.0384986i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.527280 | − | 0.541071i | −0.0211081 | − | 0.0216602i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.56673 | 0.182523 | ||||||||
\(627\) | −0.288310 | + | 0.280961i | −0.0115140 | + | 0.0112205i | ||||
\(628\) | − | 22.4692i | − | 0.896618i | ||||||
\(629\) | 3.81266 | 0.152021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.6945 | −1.54040 | −0.770202 | − | 0.637800i | \(-0.779845\pi\) | ||||
−0.770202 | + | 0.637800i | \(0.779845\pi\) | |||||||
\(632\) | 4.78108i | 0.190181i | ||||||||
\(633\) | 17.8507 | − | 17.3957i | 0.709502 | − | 0.691417i | ||||
\(634\) | 12.2121 | 0.485004 | ||||||||
\(635\) | −18.1119 | −0.718749 | ||||||||
\(636\) | −9.26128 | − | 9.50352i | −0.367234 | − | 0.376839i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 0.931497i | − | 0.0368783i | ||||||
\(639\) | 43.5810 | + | 1.12538i | 1.72404 | + | 0.0445193i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 20.7823i | 0.820851i | 0.911894 | + | 0.410426i | \(0.134620\pi\) | ||||
−0.911894 | + | 0.410426i | \(0.865380\pi\) | |||||||
\(642\) | 12.5990 | − | 12.2779i | 0.497244 | − | 0.484569i | ||||
\(643\) | − | 36.2631i | − | 1.43008i | −0.699084 | − | 0.715039i | \(-0.746409\pi\) | ||
0.699084 | − | 0.715039i | \(-0.253591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.8485 | + | 13.4955i | −0.545282 | + | 0.531383i | ||||
\(646\) | −0.347619 | −0.0136769 | ||||||||
\(647\) | −2.34138 | −0.0920492 | −0.0460246 | − | 0.998940i | \(-0.514655\pi\) | ||||
−0.0460246 | + | 0.998940i | \(0.514655\pi\) | |||||||
\(648\) | 0.464498 | − | 8.98801i | 0.0182472 | − | 0.353082i | ||||
\(649\) | 2.07263i | 0.0813580i | ||||||||
\(650\) | −0.436189 | −0.0171087 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6027 | 0.532724 | ||||||||
\(653\) | − | 44.9330i | − | 1.75836i | −0.476487 | − | 0.879182i | \(-0.658090\pi\) | ||
0.476487 | − | 0.879182i | \(-0.341910\pi\) | |||||||
\(654\) | −11.8655 | − | 12.1759i | −0.463980 | − | 0.476116i | ||||
\(655\) | 2.03892 | 0.0796672 | ||||||||
\(656\) | −2.65306 | −0.103584 | ||||||||
\(657\) | −22.5444 | − | 0.582157i | −0.879541 | − | 0.0227121i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 21.9425i | − | 0.854759i | −0.904072 | − | 0.427380i | \(-0.859437\pi\) | ||
0.904072 | − | 0.427380i | \(-0.140563\pi\) | |||||||
\(660\) | 0.470031 | + | 0.482326i | 0.0182959 | + | 0.0187745i | ||||
\(661\) | 10.3004i | 0.400639i | 0.979731 | + | 0.200319i | \(0.0641980\pi\) | ||||
−0.979731 | + | 0.200319i | \(0.935802\pi\) | |||||||
\(662\) | − | 19.3496i | − | 0.752044i | ||||||
\(663\) | −0.306638 | − | 0.314658i | −0.0119088 | − | 0.0122203i | ||||
\(664\) | 0.157211i | 0.00610098i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.6617 | − | 0.507717i | −0.761875 | − | 0.0196736i | ||||
\(667\) | 18.7652 | 0.726592 | ||||||||
\(668\) | −20.4857 | −0.792615 | ||||||||
\(669\) | 20.9714 | + | 21.5200i | 0.810802 | + | 0.832010i | ||||
\(670\) | − | 11.8218i | − | 0.456715i | ||||||
\(671\) | −5.75584 | −0.222202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4103 | 0.632569 | 0.316284 | − | 0.948664i | \(-0.397565\pi\) | ||||
0.316284 | + | 0.948664i | \(0.397565\pi\) | |||||||
\(674\) | − | 32.9183i | − | 1.26797i | ||||||
\(675\) | −3.52923 | − | 3.81373i | −0.135840 | − | 0.146791i | ||||
\(676\) | −12.8097 | −0.492682 | ||||||||
\(677\) | −34.8088 | −1.33781 | −0.668906 | − | 0.743347i | \(-0.733237\pi\) | ||||
−0.668906 | + | 0.743347i | \(0.733237\pi\) | |||||||
\(678\) | 10.7705 | − | 10.4960i | 0.413638 | − | 0.403095i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.581546i | 0.0223013i | ||||||||
\(681\) | 15.2183 | − | 14.8304i | 0.583167 | − | 0.568302i | ||||
\(682\) | 3.32018i | 0.127136i | ||||||||
\(683\) | 8.67671i | 0.332005i | 0.986125 | + | 0.166002i | \(0.0530860\pi\) | ||||
−0.986125 | + | 0.166002i | \(0.946914\pi\) | |||||||
\(684\) | 1.79265 | + | 0.0462911i | 0.0685438 | + | 0.00176998i | ||||
\(685\) | 16.1364i | 0.616542i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.74110 | + | 1.78664i | 0.0664270 | + | 0.0681644i | ||||
\(688\) | −11.1640 | −0.425625 | ||||||||
\(689\) | 3.34179 | 0.127312 | ||||||||
\(690\) | −9.71656 | + | 9.46889i | −0.369903 | + | 0.360475i | ||||
\(691\) | 8.45771i | 0.321746i | 0.986975 | + | 0.160873i | \(0.0514310\pi\) | ||||
−0.986975 | + | 0.160873i | \(0.948569\pi\) | |||||||
\(692\) | 15.3753 | 0.584480 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.94260 | −0.263537 | ||||||||
\(695\) | − | 12.3487i | − | 0.468414i | ||||||
\(696\) | −2.97167 | + | 2.89593i | −0.112641 | + | 0.109770i | ||||
\(697\) | −1.54287 | −0.0584405 | ||||||||
\(698\) | 22.3154 | 0.844649 | ||||||||
\(699\) | −32.8980 | − | 33.7585i | −1.24432 | − | 1.27686i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.82591i | − | 0.333350i | −0.986012 | − | 0.166675i | \(-0.946697\pi\) | ||
0.986012 | − | 0.166675i | \(-0.0533031\pi\) | |||||||
\(702\) | 1.53941 | + | 1.66351i | 0.0581013 | + | 0.0627850i | ||||
\(703\) | − | 3.91890i | − | 0.147804i | ||||||
\(704\) | 0.388831i | 0.0146546i | ||||||||
\(705\) | 6.63726 | − | 6.46808i | 0.249974 | − | 0.243602i | ||||
\(706\) | − | 27.3114i | − | 1.02788i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.61215 | − | 6.44361i | 0.248500 | − | 0.242166i | ||||
\(709\) | −12.1827 | −0.457533 | −0.228766 | − | 0.973481i | \(-0.573469\pi\) | ||||
−0.228766 | + | 0.973481i | \(0.573469\pi\) | |||||||
\(710\) | 14.5318 | 0.545370 | ||||||||
\(711\) | 0.370257 | − | 14.3385i | 0.0138857 | − | 0.537734i | ||||
\(712\) | 11.1040i | 0.416142i | ||||||||
\(713\) | −66.8859 | −2.50490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.169604 | −0.00634281 | ||||||||
\(716\) | 1.13504i | 0.0424183i | ||||||||
\(717\) | −24.9777 | − | 25.6310i | −0.932810 | − | 0.957209i | ||||
\(718\) | 10.2004 | 0.380676 | ||||||||
\(719\) | −40.6750 | −1.51692 | −0.758460 | − | 0.651719i | \(-0.774048\pi\) | ||||
−0.758460 | + | 0.651719i | \(0.774048\pi\) | |||||||
\(720\) | 0.0774422 | − | 2.99900i | 0.00288610 | − | 0.111766i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.6427i | − | 0.693809i | ||||||
\(723\) | 14.2929 | + | 14.6668i | 0.531559 | + | 0.545462i | ||||
\(724\) | − | 11.1559i | − | 0.414605i | ||||||
\(725\) | 2.39564i | 0.0889718i | ||||||||
\(726\) | −13.1144 | − | 13.4574i | −0.486721 | − | 0.499452i | ||||
\(727\) | − | 36.8741i | − | 1.36758i | −0.729677 | − | 0.683792i | \(-0.760329\pi\) | ||
0.729677 | − | 0.683792i | \(-0.239671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.08908 | + | 26.9191i | −0.0773734 | + | 0.997002i | ||||
\(730\) | −7.51730 | −0.278228 | ||||||||
\(731\) | −6.49240 | −0.240130 | ||||||||
\(732\) | 17.8943 | + | 18.3623i | 0.661393 | + | 0.678692i | ||||
\(733\) | 39.5252i | 1.45990i | 0.683503 | + | 0.729948i | \(0.260456\pi\) | ||||
−0.683503 | + | 0.729948i | \(0.739544\pi\) | |||||||
\(734\) | 9.33458 | 0.344546 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.83308 | −0.288731 | ||||||||
\(737\) | − | 4.59667i | − | 0.169321i | ||||||
\(738\) | 7.95652 | + | 0.205459i | 0.292883 | + | 0.00756303i | ||||
\(739\) | −41.5566 | −1.52868 | −0.764341 | − | 0.644812i | \(-0.776936\pi\) | ||||
−0.764341 | + | 0.644812i | \(0.776936\pi\) | |||||||
\(740\) | −6.55608 | −0.241006 | ||||||||
\(741\) | −0.323425 | + | 0.315181i | −0.0118813 | + | 0.0115785i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.833494i | 0.0305779i | 0.999883 | + | 0.0152890i | \(0.00486682\pi\) | ||||
−0.999883 | + | 0.0152890i | \(0.995133\pi\) | |||||||
\(744\) | 10.5921 | − | 10.3221i | 0.388325 | − | 0.378427i | ||||
\(745\) | 2.95913i | 0.108414i | ||||||||
\(746\) | 7.34793i | 0.269027i | ||||||||
\(747\) | 0.0121748 | − | 0.471476i | 0.000445452 | − | 0.0172504i | ||||
\(748\) | 0.226123i | 0.00826787i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.20883 | − | 1.24045i | −0.0441404 | − | 0.0452949i | ||||
\(751\) | 12.7670 | 0.465874 | 0.232937 | − | 0.972492i | \(-0.425166\pi\) | ||||
0.232937 | + | 0.972492i | \(0.425166\pi\) | |||||||
\(752\) | 5.35068 | 0.195119 | ||||||||
\(753\) | 32.3224 | − | 31.4985i | 1.17789 | − | 1.14787i | ||||
\(754\) | − | 1.04495i | − | 0.0380549i | ||||||
\(755\) | 8.33959 | 0.303509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3506 | −1.28484 | −0.642420 | − | 0.766353i | \(-0.722070\pi\) | ||||
−0.642420 | + | 0.766353i | \(0.722070\pi\) | |||||||
\(758\) | − | 11.2225i | − | 0.407620i | ||||||
\(759\) | −3.77810 | + | 3.68179i | −0.137136 | + | 0.133641i | ||||
\(760\) | 0.597750 | 0.0216827 | ||||||||
\(761\) | −38.2309 | −1.38587 | −0.692935 | − | 0.721000i | \(-0.743683\pi\) | ||||
−0.692935 | + | 0.721000i | \(0.743683\pi\) | |||||||
\(762\) | 21.8943 | + | 22.4669i | 0.793146 | + | 0.813891i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 5.87467i | − | 0.212538i | ||||||
\(765\) | 0.0450362 | − | 1.74406i | 0.00162829 | − | 0.0630565i | ||||
\(766\) | 22.5133i | 0.813438i | ||||||||
\(767\) | 2.32508i | 0.0839536i | ||||||||
\(768\) | 1.24045 | − | 1.20883i | 0.0447610 | − | 0.0436200i | ||||
\(769\) | − | 35.5109i | − | 1.28056i | −0.768143 | − | 0.640279i | \(-0.778819\pi\) | ||
0.768143 | − | 0.640279i | \(-0.221181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.61335 | − | 8.39380i | 0.310202 | − | 0.302295i | ||||
\(772\) | −2.60022 | −0.0935839 | ||||||||
\(773\) | −13.4235 | −0.482811 | −0.241406 | − | 0.970424i | \(-0.577608\pi\) | ||||
−0.241406 | + | 0.970424i | \(0.577608\pi\) | |||||||
\(774\) | 33.4810 | + | 0.864568i | 1.20345 | + | 0.0310762i | ||||
\(775\) | − | 8.53890i | − | 0.306726i | ||||||
\(776\) | 1.08768 | 0.0390455 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8569 | 0.747755 | ||||||||
\(779\) | 1.58586i | 0.0568195i | ||||||||
\(780\) | 0.527280 | + | 0.541071i | 0.0188796 | + | 0.0193735i | ||||
\(781\) | 5.65042 | 0.202188 | ||||||||
\(782\) | −4.55530 | −0.162897 | ||||||||
\(783\) | 9.13632 | − | 8.45476i | 0.326505 | − | 0.302148i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.4692i | 0.801959i | ||||||||
\(786\) | −2.46472 | − | 2.52918i | −0.0879135 | − | 0.0902130i | ||||
\(787\) | 4.82661i | 0.172050i | 0.996293 | + | 0.0860251i | \(0.0274165\pi\) | ||||
−0.996293 | + | 0.0860251i | \(0.972583\pi\) | |||||||
\(788\) | − | 4.23018i | − | 0.150694i | ||||||
\(789\) | 13.8107 | + | 14.1719i | 0.491674 | + | 0.504534i | ||||
\(790\) | − | 4.78108i | − | 0.170103i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.0301119 | − | 1.16610i | 0.00106998 | − | 0.0414357i | ||||
\(793\) | −6.45688 | −0.229291 | ||||||||
\(794\) | −5.80599 | −0.206047 | ||||||||
\(795\) | 9.26128 | + | 9.50352i | 0.328464 | + | 0.337055i | ||||
\(796\) | 4.74835i | 0.168301i | ||||||||
\(797\) | −43.5755 | −1.54352 | −0.771762 | − | 0.635912i | \(-0.780624\pi\) | ||||
−0.771762 | + | 0.635912i | \(0.780624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.11167 | 0.110083 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 0.859922 | − | 33.3010i | 0.0303838 | − | 1.17663i | ||||
\(802\) | 7.60821 | 0.268655 | ||||||||
\(803\) | −2.92296 | −0.103149 | ||||||||
\(804\) | −14.6644 | + | 14.2906i | −0.517172 | + | 0.503990i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.72457i | 0.131192i | ||||||||
\(807\) | 13.9822 | − | 13.6258i | 0.492196 | − | 0.479650i | ||||
\(808\) | − | 16.5092i | − | 0.580790i | ||||||
\(809\) | − | 27.0518i | − | 0.951091i | −0.879691 | − | 0.475546i | \(-0.842251\pi\) | ||
0.879691 | − | 0.475546i | \(-0.157749\pi\) | |||||||
\(810\) | −0.464498 | + | 8.98801i | −0.0163208 | + | 0.315806i | ||||
\(811\) | − | 36.2283i | − | 1.27215i | −0.771628 | − | 0.636074i | \(-0.780557\pi\) | ||
0.771628 | − | 0.636074i | \(-0.219443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.7404 | − | 25.3875i | −0.867684 | − | 0.890379i | ||||
\(814\) | −2.54920 | −0.0893496 | ||||||||
\(815\) | −13.6027 | −0.476483 | ||||||||
\(816\) | 0.721380 | − | 0.702992i | 0.0252533 | − | 0.0246097i | ||||
\(817\) | 6.67330i | 0.233469i | ||||||||
\(818\) | −25.4555 | −0.890032 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.65306 | 0.0926488 | ||||||||
\(821\) | − | 35.5633i | − | 1.24117i | −0.784140 | − | 0.620583i | \(-0.786896\pi\) | ||
0.784140 | − | 0.620583i | \(-0.213104\pi\) | |||||||
\(822\) | 20.0165 | − | 19.5063i | 0.698155 | − | 0.680360i | ||||
\(823\) | −31.5533 | −1.09988 | −0.549940 | − | 0.835204i | \(-0.685349\pi\) | ||||
−0.549940 | + | 0.835204i | \(0.685349\pi\) | |||||||
\(824\) | −2.68965 | −0.0936984 | ||||||||
\(825\) | −0.470031 | − | 0.482326i | −0.0163644 | − | 0.0167924i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.3366i | 1.19400i | 0.802241 | + | 0.597000i | \(0.203641\pi\) | ||||
−0.802241 | + | 0.597000i | \(0.796359\pi\) | |||||||
\(828\) | 23.4914 | + | 0.606611i | 0.816383 | + | 0.0210812i | ||||
\(829\) | 14.9753i | 0.520115i | 0.965593 | + | 0.260057i | \(0.0837415\pi\) | ||||
−0.965593 | + | 0.260057i | \(0.916258\pi\) | |||||||
\(830\) | − | 0.157211i | − | 0.00545688i | ||||||
\(831\) | 9.28509 | − | 9.04842i | 0.322096 | − | 0.313886i | ||||
\(832\) | 0.436189i | 0.0151221i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.3180 | + | 14.9276i | −0.530419 | + | 0.516899i | ||||
\(835\) | 20.4857 | 0.708936 | ||||||||
\(836\) | 0.232423 | 0.00803853 | ||||||||
\(837\) | −32.5650 | + | 30.1357i | −1.12561 | + | 1.04164i | ||||
\(838\) | − | 32.2860i | − | 1.11530i | ||||||
\(839\) | 36.5386 | 1.26145 | 0.630727 | − | 0.776005i | \(-0.282757\pi\) | ||||
0.630727 | + | 0.776005i | \(0.282757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2609 | 0.802101 | ||||||||
\(842\) | − | 2.83642i | − | 0.0977496i | ||||||
\(843\) | 13.4348 | + | 13.7862i | 0.462720 | + | 0.474822i | ||||
\(844\) | −14.3905 | −0.495341 | ||||||||
\(845\) | 12.8097 | 0.440668 | ||||||||
\(846\) | −16.0467 | − | 0.414368i | −0.551697 | − | 0.0142463i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.66134i | 0.263091i | ||||||||
\(849\) | −33.6956 | − | 34.5769i | −1.15643 | − | 1.18668i | ||||
\(850\) | − | 0.581546i | − | 0.0199469i | ||||||
\(851\) | − | 51.3543i | − | 1.76040i | ||||||
\(852\) | −17.5666 | − | 18.0261i | −0.601821 | − | 0.617563i | ||||
\(853\) | − | 28.9097i | − | 0.989848i | −0.868936 | − | 0.494924i | \(-0.835196\pi\) | ||
0.868936 | − | 0.494924i | \(-0.164804\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.79265 | − | 0.0462911i | −0.0613074 | − | 0.00158312i | ||||
\(856\) | −10.1568 | −0.347152 | ||||||||
\(857\) | 8.54473 | 0.291882 | 0.145941 | − | 0.989293i | \(-0.453379\pi\) | ||||
0.145941 | + | 0.989293i | \(0.453379\pi\) | |||||||
\(858\) | 0.205023 | + | 0.210385i | 0.00699935 | + | 0.00718243i | ||||
\(859\) | − | 2.49789i | − | 0.0852268i | −0.999092 | − | 0.0426134i | \(-0.986432\pi\) | ||
0.999092 | − | 0.0426134i | \(-0.0135684\pi\) | |||||||
\(860\) | 11.1640 | 0.380691 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.8559 | −1.15314 | ||||||||
\(863\) | 20.9966i | 0.714734i | 0.933964 | + | 0.357367i | \(0.116325\pi\) | ||||
−0.933964 | + | 0.357367i | \(0.883675\pi\) | |||||||
\(864\) | −3.81373 | + | 3.52923i | −0.129746 | + | 0.120067i | ||||
\(865\) | −15.3753 | −0.522774 | ||||||||
\(866\) | 36.2694 | 1.23249 | ||||||||
\(867\) | −20.6682 | + | 20.1414i | −0.701928 | + | 0.684036i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.85903i | − | 0.0630633i | ||||||
\(870\) | 2.97167 | − | 2.89593i | 0.100749 | − | 0.0981812i | ||||
\(871\) | − | 5.15653i | − | 0.174722i | ||||||
\(872\) | 9.81570i | 0.332402i | ||||||||
\(873\) | −3.26195 | − | 0.0842324i | −0.110400 | − | 0.00285083i | ||||
\(874\) | 4.68222i | 0.158379i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.08717 | + | 9.32486i | 0.307027 | + | 0.315058i | ||||
\(877\) | −29.8881 | −1.00925 | −0.504625 | − | 0.863339i | \(-0.668369\pi\) | ||||
−0.504625 | + | 0.863339i | \(0.668369\pi\) | |||||||
\(878\) | −27.1425 | −0.916015 | ||||||||
\(879\) | −24.5045 | + | 23.8799i | −0.826515 | + | 0.805447i | ||||
\(880\) | − | 0.388831i | − | 0.0131075i | ||||||
\(881\) | −34.6874 | −1.16865 | −0.584324 | − | 0.811521i | \(-0.698640\pi\) | ||||
−0.584324 | + | 0.811521i | \(0.698640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8034 | 0.363564 | 0.181782 | − | 0.983339i | \(-0.441813\pi\) | ||||
0.181782 | + | 0.983339i | \(0.441813\pi\) | |||||||
\(884\) | 0.253664i | 0.00853164i | ||||||||
\(885\) | −6.61215 | + | 6.44361i | −0.222265 | + | 0.216599i | ||||
\(886\) | −11.7451 | −0.394583 | ||||||||
\(887\) | 16.6529 | 0.559150 | 0.279575 | − | 0.960124i | \(-0.409806\pi\) | ||||
0.279575 | + | 0.960124i | \(0.409806\pi\) | |||||||
\(888\) | 7.92521 | + | 8.13250i | 0.265953 | + | 0.272909i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 11.1040i | − | 0.372209i | ||||||
\(891\) | −0.180611 | + | 3.49481i | −0.00605070 | + | 0.117081i | ||||
\(892\) | − | 17.3485i | − | 0.580870i | ||||||
\(893\) | − | 3.19837i | − | 0.107029i | ||||||
\(894\) | 3.67066 | − | 3.57709i | 0.122765 | − | 0.119636i | ||||
\(895\) | − | 1.13504i | − | 0.0379401i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.23826 | + | 4.13023i | −0.141511 | + | 0.137904i | ||||
\(898\) | 19.2663 | 0.642926 | ||||||||
\(899\) | 20.4561 | 0.682249 | ||||||||
\(900\) | −0.0774422 | + | 2.99900i | −0.00258141 | + | 0.0999667i | ||||
\(901\) | 4.45542i | 0.148432i | ||||||||
\(902\) | 1.03159 | 0.0343482 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.68271 | −0.288783 | ||||||||
\(905\) | 11.1559i | 0.370834i | ||||||||
\(906\) | −10.0812 | − | 10.3449i | −0.334925 | − | 0.343685i | ||||
\(907\) | 0.100841 | 0.00334836 | 0.00167418 | − | 0.999999i | \(-0.499467\pi\) | ||||
0.00167418 | + | 0.999999i | \(0.499467\pi\) | |||||||
\(908\) | −12.2684 | −0.407140 | ||||||||
\(909\) | −1.27851 | + | 49.5110i | −0.0424054 | + | 1.64218i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.686016i | 0.0227287i | 0.999935 | + | 0.0113644i | \(0.00361747\pi\) | ||||
−0.999935 | + | 0.0113644i | \(0.996383\pi\) | |||||||
\(912\) | −0.722580 | − | 0.741480i | −0.0239270 | − | 0.0245529i | ||||
\(913\) | − | 0.0611285i | − | 0.00202306i | ||||||
\(914\) | 9.32357i | 0.308396i | ||||||||
\(915\) | −17.8943 | − | 18.3623i | −0.591567 | − | 0.607041i | ||||
\(916\) | − | 1.44031i | − | 0.0475892i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.21786 | + | 2.05241i | −0.0732003 | + | 0.0677396i | ||||
\(919\) | 2.42356 | 0.0799459 | 0.0399729 | − | 0.999201i | \(-0.487273\pi\) | ||||
0.0399729 | + | 0.999201i | \(0.487273\pi\) | |||||||
\(920\) | 7.83308 | 0.258249 | ||||||||
\(921\) | −10.7830 | − | 11.0651i | −0.355313 | − | 0.364606i | ||||
\(922\) | 6.36590i | 0.209650i | ||||||||
\(923\) | 6.33863 | 0.208639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.55608 | 0.215563 | ||||||||
\(926\) | 1.83216i | 0.0602083i | ||||||||
\(927\) | 8.06627 | + | 0.208292i | 0.264931 | + | 0.00684122i | ||||
\(928\) | 2.39564 | 0.0786407 | ||||||||
\(929\) | 22.4384 | 0.736179 | 0.368090 | − | 0.929790i | \(-0.380012\pi\) | ||||
0.368090 | + | 0.929790i | \(0.380012\pi\) | |||||||
\(930\) | −10.5921 | + | 10.3221i | −0.347328 | + | 0.338475i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.2147i | 0.891446i | ||||||||
\(933\) | 1.19102 | − | 1.16066i | 0.0389923 | − | 0.0379984i | ||||
\(934\) | − | 2.25893i | − | 0.0739143i | ||||||
\(935\) | − | 0.226123i | − | 0.00739501i | ||||||
\(936\) | 0.0337794 | − | 1.30813i | 0.00110412 | − | 0.0427576i | ||||
\(937\) | 8.08505i | 0.264127i | 0.991241 | + | 0.132063i | \(0.0421603\pi\) | ||||
−0.991241 | + | 0.132063i | \(0.957840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.52042 | + | 5.66481i | 0.180152 | + | 0.184864i | ||||
\(940\) | −5.35068 | −0.174520 | ||||||||
\(941\) | −29.7880 | −0.971062 | −0.485531 | − | 0.874219i | \(-0.661374\pi\) | ||||
−0.485531 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(942\) | 27.8719 | − | 27.1615i | 0.908117 | − | 0.884970i | ||||
\(943\) | 20.7816i | 0.676742i | ||||||||
\(944\) | −5.33043 | −0.173491 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.34092 | 0.141135 | ||||||||
\(947\) | 28.2621i | 0.918395i | 0.888334 | + | 0.459198i | \(0.151863\pi\) | ||||
−0.888334 | + | 0.459198i | \(0.848137\pi\) | |||||||
\(948\) | −5.93070 | + | 5.77953i | −0.192620 | + | 0.187710i | ||||
\(949\) | −3.27897 | −0.106440 | ||||||||
\(950\) | −0.597750 | −0.0193936 | ||||||||
\(951\) | 14.7624 | + | 15.1485i | 0.478703 | + | 0.491224i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.9316i | 0.904794i | 0.891817 | + | 0.452397i | \(0.149431\pi\) | ||||
−0.891817 | + | 0.452397i | \(0.850569\pi\) | |||||||
\(954\) | 0.593311 | − | 22.9763i | 0.0192091 | − | 0.743887i | ||||
\(955\) | 5.87467i | 0.190100i | ||||||||
\(956\) | 20.6627i | 0.668278i | ||||||||
\(957\) | 1.15548 | − | 1.12603i | 0.0373513 | − | 0.0363992i | ||||
\(958\) | − | 37.0085i | − | 1.19569i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.24045 | + | 1.20883i | −0.0400354 | + | 0.0390149i | ||||
\(961\) | −41.9127 | −1.35202 | ||||||||
\(962\) | −2.85969 | −0.0922001 | ||||||||
\(963\) | 30.4602 | + | 0.786565i | 0.981568 | + | 0.0253467i | ||||
\(964\) | − | 11.8237i | − | 0.380816i | ||||||
\(965\) | 2.60022 | 0.0837040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.70893 | 0.151429 | 0.0757144 | − | 0.997130i | \(-0.475876\pi\) | ||||
0.0757144 | + | 0.997130i | \(0.475876\pi\) | |||||||
\(968\) | 10.8488i | 0.348694i | ||||||||
\(969\) | −0.420214 | − | 0.431205i | −0.0134992 | − | 0.0138523i | ||||
\(970\) | −1.08768 | −0.0349233 | ||||||||
\(971\) | 29.4048 | 0.943646 | 0.471823 | − | 0.881693i | \(-0.343596\pi\) | ||||
0.471823 | + | 0.881693i | \(0.343596\pi\) | |||||||
\(972\) | 11.7107 | − | 10.2888i | 0.375621 | − | 0.330014i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 40.3476i | 1.29282i | ||||||||
\(975\) | −0.527280 | − | 0.541071i | −0.0168865 | − | 0.0173282i | ||||
\(976\) | − | 14.8030i | − | 0.473831i | ||||||
\(977\) | 22.8318i | 0.730455i | 0.930918 | + | 0.365228i | \(0.119009\pi\) | ||||
−0.930918 | + | 0.365228i | \(0.880991\pi\) | |||||||
\(978\) | 16.4434 | + | 16.8735i | 0.525803 | + | 0.539556i | ||||
\(979\) | − | 4.31759i | − | 0.137991i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.760149 | − | 29.4373i | 0.0242697 | − | 0.939860i | ||||
\(982\) | 27.8602 | 0.889054 | ||||||||
\(983\) | −51.8878 | −1.65496 | −0.827482 | − | 0.561493i | \(-0.810227\pi\) | ||||
−0.827482 | + | 0.561493i | \(0.810227\pi\) | |||||||
\(984\) | −3.20710 | − | 3.29099i | −0.102239 | − | 0.104913i | ||||
\(985\) | 4.23018i | 0.134785i | ||||||||
\(986\) | 1.39317 | 0.0443677 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.260732 | 0.00829499 | ||||||||
\(989\) | 87.4488i | 2.78071i | ||||||||
\(990\) | −0.0301119 | + | 1.16610i | −0.000957019 | + | 0.0370612i | ||||
\(991\) | −25.7580 | −0.818231 | −0.409115 | − | 0.912483i | \(-0.634163\pi\) | ||||
−0.409115 | + | 0.912483i | \(0.634163\pi\) | |||||||
\(992\) | −8.53890 | −0.271110 | ||||||||
\(993\) | 24.0023 | − | 23.3904i | 0.761688 | − | 0.742273i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.74835i | − | 0.150533i | ||||||
\(996\) | −0.195013 | + | 0.190042i | −0.00617922 | + | 0.00602171i | ||||
\(997\) | 49.2249i | 1.55897i | 0.626423 | + | 0.779484i | \(0.284518\pi\) | ||||
−0.626423 | + | 0.779484i | \(0.715482\pi\) | |||||||
\(998\) | − | 14.0739i | − | 0.445501i | ||||||
\(999\) | −23.1379 | − | 25.0031i | −0.732051 | − | 0.791064i |
(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 | 1470.2.b.d.881.5 | yes | 16 | |
3.2 | odd | 2 | 1470.2.b.c.881.12 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.b.c.881.4 | ✓ | 16 | ||
21.20 | even | 2 | inner | 1470.2.b.d.881.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.b.c.881.4 | ✓ | 16 | 7.6 | odd | 2 | ||
1470.2.b.c.881.12 | yes | 16 | 3.2 | odd | 2 | ||
1470.2.b.d.881.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1470.2.b.d.881.13 | yes | 16 | 21.20 | even | 2 | inner |