Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(601,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.601");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.bg (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.2 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.841 |
Dual form | 1560.2.bg.g.601.2 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.13746 | − | 3.70219i | 0.644468 | − | 1.11625i | −0.339956 | − | 0.940441i | \(-0.610412\pi\) |
0.984424 | − | 0.175810i | \(-0.0562545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 2.59808i | 0.693375 | − | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13746 | + | 1.97014i | 0.260951 | + | 0.451980i | 0.966495 | − | 0.256686i | \(-0.0826306\pi\) |
−0.705544 | + | 0.708666i | \(0.749297\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.27492 | + | 5.67232i | −0.682867 | + | 1.18276i | 0.291234 | + | 0.956652i | \(0.405934\pi\) |
−0.974102 | + | 0.226109i | \(0.927399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.27492 | − | 9.13642i | 0.979528 | − | 1.69659i | 0.315424 | − | 0.948951i | \(-0.397853\pi\) |
0.664104 | − | 0.747641i | \(-0.268813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.27492 | −1.30661 | −0.653307 | − | 0.757093i | \(-0.726619\pi\) | ||||
−0.653307 | + | 0.757093i | \(0.726619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.13746 | − | 3.70219i | −0.372084 | − | 0.644468i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.500000 | − | 0.866025i | −0.0845154 | − | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.137459 | + | 0.238085i | −0.0225981 | + | 0.0391410i | −0.877103 | − | 0.480302i | \(-0.840527\pi\) |
0.854505 | + | 0.519443i | \(0.173860\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | − | 3.46410i | −0.160128 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.27492 | + | 7.40437i | −0.667630 | + | 1.15637i | 0.310935 | + | 0.950431i | \(0.399358\pi\) |
−0.978565 | + | 0.205938i | \(0.933976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.63746 | − | 6.30026i | −0.554707 | − | 0.960781i | −0.997926 | − | 0.0643678i | \(-0.979497\pi\) |
0.443219 | − | 0.896413i | \(-0.353836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.27492 | 0.623561 | 0.311780 | − | 0.950154i | \(-0.399075\pi\) | ||||
0.311780 | + | 0.950154i | \(0.399075\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.72508 | 0.236958 | 0.118479 | − | 0.992957i | \(-0.462198\pi\) | ||||
0.118479 | + | 0.992957i | \(0.462198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13746 | − | 3.70219i | 0.288215 | − | 0.499203i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.27492 | 0.301320 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.27492 | − | 12.6005i | −0.947114 | − | 1.64045i | −0.751463 | − | 0.659775i | \(-0.770652\pi\) |
−0.195650 | − | 0.980674i | \(-0.562682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.63746 | + | 2.83616i | 0.209655 | + | 0.363133i | 0.951606 | − | 0.307321i | \(-0.0994326\pi\) |
−0.741951 | + | 0.670454i | \(0.766099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | + | 0.866025i | −0.0629941 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.50000 | − | 2.59808i | 0.310087 | − | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.63746 | − | 4.56821i | 0.322217 | − | 0.558096i | −0.658728 | − | 0.752381i | \(-0.728905\pi\) |
0.980945 | + | 0.194285i | \(0.0622386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.27492 | + | 5.67232i | 0.394254 | + | 0.682867i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | + | 1.73205i | 0.118678 | + | 0.205557i | 0.919244 | − | 0.393688i | \(-0.128801\pi\) |
−0.800566 | + | 0.599245i | \(0.795468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8248 | 1.38398 | 0.691991 | − | 0.721906i | \(-0.256734\pi\) | ||||
0.691991 | + | 0.721906i | \(0.256734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.27492 | −0.487172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.725083 | −0.0815782 | −0.0407891 | − | 0.999168i | \(-0.512987\pi\) | ||||
−0.0407891 | + | 0.999168i | \(0.512987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.0997 | 1.87693 | 0.938466 | − | 0.345371i | \(-0.112247\pi\) | ||||
0.938466 | + | 0.345371i | \(0.112247\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.27492 | − | 9.13642i | −0.565530 | − | 0.979528i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.86254 | − | 4.95807i | 0.303429 | − | 0.525554i | −0.673481 | − | 0.739204i | \(-0.735202\pi\) |
0.976910 | + | 0.213650i | \(0.0685352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50000 | − | 0.866025i | −0.366900 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.63746 | + | 6.30026i | −0.377187 | + | 0.653307i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.13746 | + | 1.97014i | 0.116701 | + | 0.202132i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.91238 | − | 6.77643i | −0.397242 | − | 0.688043i | 0.596143 | − | 0.802878i | \(-0.296699\pi\) |
−0.993384 | + | 0.114836i | \(0.963366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.27492 | −0.429645 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.27492 | − | 5.67232i | 0.325866 | − | 0.564417i | −0.655821 | − | 0.754917i | \(-0.727677\pi\) |
0.981687 | + | 0.190499i | \(0.0610107\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5498 | −1.53217 | −0.766085 | − | 0.642739i | \(-0.777798\pi\) | ||||
−0.766085 | + | 0.642739i | \(0.777798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.54983 | + | 13.0767i | −0.729870 | + | 1.26417i | 0.227068 | + | 0.973879i | \(0.427086\pi\) |
−0.956938 | + | 0.290293i | \(0.906247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8248 | −1.32417 | −0.662086 | − | 0.749428i | \(-0.730328\pi\) | ||||
−0.662086 | + | 0.749428i | \(0.730328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.137459 | + | 0.238085i | 0.0130470 | + | 0.0225981i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.72508 | + | 4.71998i | 0.256354 | + | 0.444019i | 0.965262 | − | 0.261282i | \(-0.0841453\pi\) |
−0.708908 | + | 0.705301i | \(0.750812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.27492 | + | 5.67232i | −0.305388 | + | 0.528947i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.50000 | − | 0.866025i | −0.323575 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.63746 | − | 6.30026i | −0.330678 | − | 0.572751i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.27492 | + | 7.40437i | 0.385456 | + | 0.667630i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.500000 | + | 0.866025i | −0.0443678 | + | 0.0768473i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) |
0.842989 | + | 0.537931i | \(0.180794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.27492 | −0.640521 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.72508 | 0.325462 | 0.162731 | − | 0.986670i | \(-0.447970\pi\) | ||||
0.162731 | + | 0.986670i | \(0.447970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.13746 | − | 1.97014i | 0.0986302 | − | 0.170832i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5498 | + | 18.2728i | 0.901333 | + | 1.56115i | 0.825765 | + | 0.564014i | \(0.190744\pi\) |
0.0755681 | + | 0.997141i | \(0.475923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.50000 | − | 9.52628i | −0.466504 | − | 0.808008i | 0.532764 | − | 0.846264i | \(-0.321153\pi\) |
−0.999268 | + | 0.0382553i | \(0.987820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.13746 | − | 3.70219i | 0.180006 | − | 0.311780i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.27492 | − | 14.8087i | −0.357487 | − | 1.23837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.27492 | − | 9.13642i | 0.438058 | − | 0.758739i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | − | 5.19615i | −0.247436 | − | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.27492 | + | 14.3326i | 0.677908 | + | 1.17417i | 0.975610 | + | 0.219512i | \(0.0704464\pi\) |
−0.297702 | + | 0.954659i | \(0.596220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.45017 | −0.280770 | −0.140385 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140385 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.27492 | −0.584335 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.5498 | 0.921777 | 0.460889 | − | 0.887458i | \(-0.347531\pi\) | ||||
0.460889 | + | 0.887458i | \(0.347531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.862541 | − | 1.49397i | 0.0684040 | − | 0.118479i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.54983 | 0.516199 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.36254 | − | 2.35999i | −0.106722 | − | 0.184849i | 0.807718 | − | 0.589569i | \(-0.200702\pi\) |
−0.914441 | + | 0.404720i | \(0.867369\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.13746 | − | 3.70219i | −0.166401 | − | 0.288215i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.13746 | − | 8.89834i | 0.397548 | − | 0.688574i | −0.595874 | − | 0.803078i | \(-0.703194\pi\) |
0.993423 | + | 0.114503i | \(0.0365277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 12.9904i | −0.0384615 | − | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.13746 | − | 1.97014i | 0.0869836 | − | 0.150660i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.86254 | + | 13.6183i | 0.597778 | + | 1.03538i | 0.993148 | + | 0.116860i | \(0.0372829\pi\) |
−0.395370 | + | 0.918522i | \(0.629384\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.5498 | −1.09363 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.27492 | 0.242089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.137459 | + | 0.238085i | −0.0101062 | + | 0.0175044i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.500000 | + | 0.866025i | 0.0363696 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.18729 | + | 12.4488i | −0.517353 | + | 0.896081i | 0.482444 | + | 0.875927i | \(0.339749\pi\) |
−0.999797 | + | 0.0201544i | \(0.993584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | − | 3.46410i | −0.0716115 | − | 0.248069i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.41238 | − | 2.44631i | 0.100628 | − | 0.174292i | −0.811316 | − | 0.584608i | \(-0.801248\pi\) |
0.911943 | + | 0.410316i | \(0.134582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.36254 | − | 4.09204i | −0.167476 | − | 0.290077i | 0.770056 | − | 0.637977i | \(-0.220228\pi\) |
−0.937532 | + | 0.347899i | \(0.886895\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.63746 | − | 4.56821i | −0.186032 | − | 0.322217i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.5498 | −0.740453 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.27492 | + | 7.40437i | −0.298573 | + | 0.517144i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.54983 | 0.455245 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.72508 | 0.672698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.50000 | + | 4.33013i | −0.172107 | + | 0.298098i | −0.939156 | − | 0.343490i | \(-0.888391\pi\) |
0.767049 | + | 0.641588i | \(0.221724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.63746 | − | 6.30026i | −0.248073 | − | 0.429674i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.63746 | + | 6.30026i | 0.246927 | + | 0.427690i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.91238 | − | 10.2405i | 0.399521 | − | 0.691991i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4124 | + | 23.2309i | −0.898159 | + | 1.55566i | −0.0683137 | + | 0.997664i | \(0.521762\pi\) |
−0.829845 | + | 0.557993i | \(0.811571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.54983 | − | 7.88054i | −0.301983 | − | 0.523050i | 0.674602 | − | 0.738182i | \(-0.264315\pi\) |
−0.976585 | + | 0.215132i | \(0.930982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.13746 | + | 3.70219i | −0.140634 | + | 0.243586i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.0997 | 1.51331 | 0.756655 | − | 0.653815i | \(-0.226832\pi\) | ||||
0.756655 | + | 0.653815i | \(0.226832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.27492 | 0.278865 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.362541 | + | 0.627940i | −0.0235496 | + | 0.0407891i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.54983 | −0.294304 | −0.147152 | − | 0.989114i | \(-0.547011\pi\) | ||||
−0.147152 | + | 0.989114i | \(0.547011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.13746 | − | 7.16629i | −0.266517 | − | 0.461621i | 0.701443 | − | 0.712726i | \(-0.252540\pi\) |
−0.967960 | + | 0.251104i | \(0.919206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | − | 5.19615i | 0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.96221 | + | 1.97014i | 0.506623 | + | 0.125357i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.54983 | − | 14.8087i | 0.541824 | − | 0.938466i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1375 | + | 22.7547i | 0.829229 | + | 1.43627i | 0.898644 | + | 0.438679i | \(0.144553\pi\) |
−0.0694148 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0000 | + | 24.2487i | 0.880172 | + | 1.52450i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.00000 | + | 6.92820i | −0.249513 | + | 0.432169i | −0.963391 | − | 0.268101i | \(-0.913604\pi\) |
0.713878 | + | 0.700270i | \(0.246937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.274917 | 0.0170825 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.5498 | −0.653018 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.13746 | − | 1.97014i | 0.0701387 | − | 0.121484i | −0.828823 | − | 0.559511i | \(-0.810989\pi\) |
0.898962 | + | 0.438027i | \(0.144322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.72508 | 0.105971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.86254 | − | 4.95807i | −0.175185 | − | 0.303429i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6375 | + | 21.8887i | −0.767671 | + | 1.32965i | 0.171152 | + | 0.985245i | \(0.445251\pi\) |
−0.938823 | + | 0.344400i | \(0.888082\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.50000 | + | 2.59808i | −0.151307 | + | 0.157243i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.13746 | − | 3.70219i | 0.128894 | − | 0.223250i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4124 | + | 24.9630i | 0.865956 | + | 1.49988i | 0.866095 | + | 0.499879i | \(0.166622\pi\) |
−0.000139316 | 1.00000i | \(0.500044\pi\) | ||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.63746 | + | 6.30026i | 0.217769 | + | 0.377187i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0997 | −1.61663 | −0.808315 | − | 0.588750i | \(-0.799620\pi\) | ||||
−0.808315 | + | 0.588750i | \(0.799620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4622 | − | 19.8531i | 0.681358 | − | 1.18015i | −0.293209 | − | 0.956048i | \(-0.594723\pi\) |
0.974567 | − | 0.224098i | \(-0.0719435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.27492 | 0.134754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.54983 | 0.504681 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.82475 | −0.458695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1375 | + | 24.4868i | 0.825919 | + | 1.43053i | 0.901215 | + | 0.433373i | \(0.142677\pi\) |
−0.0752957 | + | 0.997161i | \(0.523990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.27492 | − | 12.6005i | −0.423562 | − | 0.733631i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.13746 | + | 3.70219i | −0.124028 | + | 0.214823i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.54983 | + | 22.6893i | 0.378787 | + | 1.31216i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.63746 | + | 6.30026i | −0.209660 | + | 0.363141i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.27492 | − | 5.67232i | −0.188139 | − | 0.325866i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.63746 | + | 2.83616i | 0.0937606 | + | 0.162398i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9244 | −1.30837 | −0.654183 | − | 0.756336i | \(-0.726987\pi\) | ||||
−0.654183 | + | 0.756336i | \(0.726987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.77492 | + | 13.4666i | −0.442300 | + | 0.766085i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.72508 | 0.267077 | 0.133539 | − | 0.991044i | \(-0.457366\pi\) | ||||
0.133539 | + | 0.991044i | \(0.457366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.500000 | + | 0.866025i | −0.0281718 | + | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.3746 | −1.08819 | −0.544093 | − | 0.839025i | \(-0.683126\pi\) | ||||
−0.544093 | + | 0.839025i | \(0.683126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5498 | − | 39.0575i | −1.26255 | − | 2.18680i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.54983 | + | 13.0767i | 0.421391 | + | 0.729870i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.50000 | − | 2.59808i | 0.138675 | − | 0.144115i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.91238 | + | 11.9726i | −0.382255 | + | 0.662086i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.13746 | − | 3.70219i | −0.117842 | − | 0.204108i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.36254 | + | 16.2164i | 0.514612 | + | 0.891334i | 0.999856 | + | 0.0169553i | \(0.00539729\pi\) |
−0.485244 | + | 0.874379i | \(0.661269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.274917 | 0.0150654 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.63746 | − | 4.56821i | 0.144100 | − | 0.249588i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.2749 | 1.04997 | 0.524986 | − | 0.851111i | \(-0.324071\pi\) | ||||
0.524986 | + | 0.851111i | \(0.324071\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.45017 | 0.296012 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.5498 | + | 26.9331i | −0.842071 | + | 1.45851i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.27492 | + | 5.67232i | 0.176316 | + | 0.305388i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.54983 | + | 14.8087i | 0.458979 | + | 0.794975i | 0.998907 | − | 0.0467359i | \(-0.0148819\pi\) |
−0.539928 | + | 0.841711i | \(0.681549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4622 | − | 18.1211i | 0.560029 | − | 0.969999i | −0.437464 | − | 0.899236i | \(-0.644123\pi\) |
0.997493 | − | 0.0707632i | \(-0.0225435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | + | 2.59808i | −0.133440 | + | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2749 | + | 26.4569i | −0.813002 | + | 1.40816i | 0.0977520 | + | 0.995211i | \(0.468835\pi\) |
−0.910754 | + | 0.412950i | \(0.864499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.5498 | 1.50680 | 0.753401 | − | 0.657561i | \(-0.228412\pi\) | ||||
0.753401 | + | 0.657561i | \(0.228412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.91238 | − | 11.9726i | 0.363809 | − | 0.630136i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.27492 | −0.381834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.8248 | 0.618936 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.63746 | + | 14.9605i | −0.450872 | + | 0.780933i | −0.998440 | − | 0.0558281i | \(-0.982220\pi\) |
0.547569 | + | 0.836761i | \(0.315553\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.54983 | 0.445087 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.862541 | − | 1.49397i | −0.0447809 | − | 0.0775628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.63746 | + | 13.2285i | 0.395453 | + | 0.684944i | 0.993159 | − | 0.116771i | \(-0.0372544\pi\) |
−0.597706 | + | 0.801715i | \(0.703921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.5498 | − | 36.5457i | −0.543344 | − | 1.88220i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7749 | + | 18.6627i | −0.553470 | + | 0.958639i | 0.444550 | + | 0.895754i | \(0.353363\pi\) |
−0.998021 | + | 0.0628849i | \(0.979970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.500000 | + | 0.866025i | 0.0256158 | + | 0.0443678i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5498 | + | 21.7370i | 0.641267 | + | 1.11071i | 0.985150 | + | 0.171694i | \(0.0549241\pi\) |
−0.343884 | + | 0.939012i | \(0.611743\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.27492 | −0.217870 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.63746 | + | 6.30026i | −0.184902 | + | 0.320260i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.00000 | −0.405616 | −0.202808 | − | 0.979219i | \(-0.565007\pi\) | ||||
−0.202808 | + | 0.979219i | \(0.565007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.86254 | − | 3.22602i | 0.0939528 | − | 0.162731i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.725083 | −0.0364829 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.04983 | − | 3.55042i | −0.102878 | − | 0.178190i | 0.809991 | − | 0.586442i | \(-0.199472\pi\) |
−0.912869 | + | 0.408252i | \(0.866139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.13746 | − | 1.97014i | −0.0569442 | − | 0.0986302i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9622 | − | 34.5756i | 0.996865 | − | 1.72662i | 0.429914 | − | 0.902870i | \(-0.358544\pi\) |
0.566951 | − | 0.823751i | \(-0.308123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.1873 | + | 18.9008i | −0.905974 | + | 0.941515i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.587624 | + | 1.01779i | 0.0291274 | + | 0.0504502i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.95017 | − | 3.37779i | −0.0964295 | − | 0.167021i | 0.813775 | − | 0.581180i | \(-0.197409\pi\) |
−0.910204 | + | 0.414160i | \(0.864076\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0997 | 1.04077 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.27492 | + | 12.6005i | −0.357975 | + | 0.620031i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.0997 | 0.839390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0000 | −0.538672 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0997 | − | 26.1534i | 0.737667 | − | 1.27768i | −0.215876 | − | 0.976421i | \(-0.569261\pi\) |
0.953543 | − | 0.301256i | \(-0.0974059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8248 | 0.771251 | 0.385626 | − | 0.922655i | \(-0.373986\pi\) | ||||
0.385626 | + | 0.922655i | \(0.373986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.13746 | − | 3.70219i | −0.103927 | − | 0.180006i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.63746 | − | 2.83616i | 0.0792422 | − | 0.137251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.9622 | − | 3.70219i | −0.722382 | − | 0.178743i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.18729 | − | 12.4488i | −0.345399 | − | 0.598249i | 0.640027 | − | 0.768352i | \(-0.278923\pi\) |
−0.985426 | + | 0.170103i | \(0.945590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.27492 | − | 9.13642i | −0.252913 | − | 0.438058i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.9003 | −0.712780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3625 | − | 21.4125i | 0.590032 | − | 1.02197i | −0.404196 | − | 0.914673i | \(-0.632448\pi\) |
0.994227 | − | 0.107293i | \(-0.0342182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6495 | −0.838553 | −0.419277 | − | 0.907859i | \(-0.637716\pi\) | ||||
−0.419277 | + | 0.907859i | \(0.637716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.86254 | − | 4.95807i | 0.135697 | − | 0.235035i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.5498 | 0.782780 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.86254 | − | 13.6183i | −0.371056 | − | 0.642688i | 0.618672 | − | 0.785649i | \(-0.287671\pi\) |
−0.989728 | + | 0.142961i | \(0.954338\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2749 | + | 31.6531i | 0.860532 | + | 1.49049i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.72508 | + | 2.98793i | −0.0810515 | + | 0.140385i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.50000 | − | 0.866025i | −0.164083 | − | 0.0405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.1873 | + | 24.5731i | −0.663654 | + | 1.14948i | 0.315995 | + | 0.948761i | \(0.397662\pi\) |
−0.979648 | + | 0.200721i | \(0.935672\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | + | 10.3923i | 0.279448 | + | 0.484018i | 0.971248 | − | 0.238071i | \(-0.0765153\pi\) |
−0.691800 | + | 0.722089i | \(0.743182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.7251 | −1.42792 | −0.713958 | − | 0.700189i | \(-0.753099\pi\) | ||||
−0.713958 | + | 0.700189i | \(0.753099\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.63746 | + | 6.30026i | −0.168683 | + | 0.292168i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.5498 | 0.673286 | 0.336643 | − | 0.941632i | \(-0.390708\pi\) | ||||
0.336643 | + | 0.941632i | \(0.390708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.27492 | −0.243573 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.77492 | − | 10.0025i | 0.266094 | − | 0.460889i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.0997 | −1.42996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.13746 | + | 1.97014i | 0.0521902 | + | 0.0903960i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.862541 | − | 1.49397i | −0.0394931 | − | 0.0684040i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5498 | + | 25.2011i | −0.664799 | + | 1.15147i | 0.314541 | + | 0.949244i | \(0.398149\pi\) |
−0.979340 | + | 0.202222i | \(0.935184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.274917 | + | 0.952341i | 0.0125351 | + | 0.0434230i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.27492 | − | 5.67232i | 0.149014 | − | 0.258100i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.91238 | − | 6.77643i | −0.177652 | − | 0.307702i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1375 | + | 29.6829i | 0.776572 | + | 1.34506i | 0.933906 | + | 0.357517i | \(0.116377\pi\) |
−0.157334 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.72508 | −0.123233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.58762 | − | 6.21395i | 0.161907 | − | 0.280432i | −0.773645 | − | 0.633619i | \(-0.781569\pi\) |
0.935553 | + | 0.353187i | \(0.114902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.27492 | −0.192143 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.00000 | − | 1.73205i | 0.0448561 | − | 0.0776931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0997 | 0.765486 | 0.382743 | − | 0.923855i | \(-0.374979\pi\) | ||||
0.382743 | + | 0.923855i | \(0.374979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.13746 | − | 8.89834i | −0.229525 | − | 0.397548i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4124 | + | 21.4989i | 0.553440 | + | 0.958587i | 0.998023 | + | 0.0628492i | \(0.0200187\pi\) |
−0.444583 | + | 0.895738i | \(0.646648\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.27492 | − | 5.67232i | 0.145732 | − | 0.252415i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5000 | − | 6.06218i | −0.510733 | − | 0.269231i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.5498 | + | 20.0049i | −0.511937 | + | 0.886702i | 0.487967 | + | 0.872862i | \(0.337739\pi\) |
−0.999904 | + | 0.0138394i | \(0.995595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.91238 | − | 10.2405i | −0.261548 | − | 0.453015i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.13746 | − | 1.97014i | −0.0502200 | − | 0.0869836i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.5498 | −0.685208 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.13746 | − | 15.8265i | 0.401865 | − | 0.696051i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.7251 | 0.690255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.7251 | −0.601307 | −0.300653 | − | 0.953733i | \(-0.597205\pi\) | ||||
−0.300653 | + | 0.953733i | \(0.597205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2749 | + | 28.1890i | −0.711652 | + | 1.23262i | 0.252584 | + | 0.967575i | \(0.418720\pi\) |
−0.964237 | + | 0.265043i | \(0.914614\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.95017 | − | 17.2342i | −0.432616 | − | 0.749313i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.27492 | + | 12.6005i | −0.315705 | + | 0.546816i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.54983 | + | 29.6175i | 0.370334 | + | 1.28288i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.54983 | + | 13.0767i | −0.326408 | + | 0.565355i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.8248 | − | 22.2131i | −0.552401 | − | 0.956787i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.8248 | −1.28227 | −0.641133 | − | 0.767430i | \(-0.721535\pi\) | ||||
−0.641133 | + | 0.767430i | \(0.721535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.8248 | −0.592187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.8248 | 1.27521 | 0.637607 | − | 0.770362i | \(-0.279924\pi\) | ||||
0.637607 | + | 0.770362i | \(0.279924\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.63746 | − | 2.83616i | 0.0698850 | − | 0.121044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.362541 | + | 0.627940i | 0.0154168 | + | 0.0267027i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.137459 | + | 0.238085i | 0.00583479 | + | 0.0101062i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.31271 | − | 4.00573i | 0.0979925 | − | 0.169728i | −0.812861 | − | 0.582458i | \(-0.802091\pi\) |
0.910854 | + | 0.412730i | \(0.135425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.4622 | − | 6.30026i | −1.07694 | − | 0.266473i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.27492 | + | 16.0646i | 0.390891 | + | 0.677043i | 0.992567 | − | 0.121697i | \(-0.0388335\pi\) |
−0.601676 | + | 0.798740i | \(0.705500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.72508 | + | 4.71998i | 0.114645 | + | 0.198571i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6873 | − | 35.8314i | 0.867256 | − | 1.50213i | 0.00246734 | − | 0.999997i | \(-0.499215\pi\) |
0.864789 | − | 0.502135i | \(-0.167452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.62541 | 0.193568 | 0.0967838 | − | 0.995305i | \(-0.469144\pi\) | ||||
0.0967838 | + | 0.995305i | \(0.469144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.27492 | + | 5.67232i | −0.136573 | + | 0.236552i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.0997 | 1.29470 | 0.647348 | − | 0.762195i | \(-0.275878\pi\) | ||||
0.647348 | + | 0.762195i | \(0.275878\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.18729 | + | 12.4488i | 0.298694 | + | 0.517353i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.54983 | − | 14.8087i | −0.354707 | − | 0.614370i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.68729 | − | 6.38658i | 0.152712 | − | 0.264505i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.50000 | − | 0.866025i | −0.144707 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.0997 | − | 17.4931i | 0.416858 | − | 0.722019i | −0.578764 | − | 0.815495i | \(-0.696465\pi\) |
0.995622 | + | 0.0934763i | \(0.0297979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.27492 | − | 14.3326i | −0.340962 | − | 0.590564i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.41238 | − | 2.44631i | −0.0580974 | − | 0.100628i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.4502 | −0.716592 | −0.358296 | − | 0.933608i | \(-0.616642\pi\) | ||||
−0.358296 | + | 0.933608i | \(0.616642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.72508 | −0.193385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.90033 | 0.200222 | 0.100111 | − | 0.994976i | \(-0.468080\pi\) | ||||
0.100111 | + | 0.994976i | \(0.468080\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1375 | − | 31.4150i | 0.739842 | − | 1.28144i | −0.212724 | − | 0.977112i | \(-0.568233\pi\) |
0.952566 | − | 0.304332i | \(-0.0984333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.27492 | −0.214811 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.63746 | − | 6.30026i | −0.147884 | − | 0.256142i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.68729 | − | 13.3148i | −0.312018 | − | 0.540430i | 0.666781 | − | 0.745253i | \(-0.267671\pi\) |
−0.978799 | + | 0.204823i | \(0.934338\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.27492 | + | 9.13642i | −0.213750 | + | 0.370227i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.6873 | − | 11.1066i | 0.432362 | − | 0.449323i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.59967 | − | 16.6271i | 0.387727 | − | 0.671563i | −0.604416 | − | 0.796669i | \(-0.706594\pi\) |
0.992143 | + | 0.125106i | \(0.0399270\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.27492 | + | 7.40437i | 0.172381 | + | 0.298573i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.45017 | − | 4.24381i | −0.0986400 | − | 0.170849i | 0.812482 | − | 0.582986i | \(-0.198116\pi\) |
−0.911122 | + | 0.412137i | \(0.864783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.54983 | 0.303453 | 0.151727 | − | 0.988422i | \(-0.451517\pi\) | ||||
0.151727 | + | 0.988422i | \(0.451517\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.27492 | − | 5.67232i | 0.131418 | − | 0.227622i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.72508 | −0.229371 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.86254 | − | 8.42217i | 0.194191 | − | 0.336349i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.36254 | − | 2.35999i | −0.0542419 | − | 0.0939498i | 0.837630 | − | 0.546239i | \(-0.183941\pi\) |
−0.891871 | + | 0.452289i | \(0.850608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.50000 | + | 4.33013i | 0.0993661 | + | 0.172107i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.500000 | + | 0.866025i | −0.0198419 | + | 0.0343672i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | − | 20.7846i | −0.237729 | − | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9622 | + | 29.3794i | 0.669967 | + | 1.16042i | 0.977913 | + | 0.209013i | \(0.0670251\pi\) |
−0.307946 | + | 0.951404i | \(0.599642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.36254 | − | 2.35999i | −0.0537334 | − | 0.0930690i | 0.837908 | − | 0.545812i | \(-0.183779\pi\) |
−0.891641 | + | 0.452743i | \(0.850445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.27492 | −0.286450 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.58762 | − | 13.1422i | 0.298300 | − | 0.516671i | −0.677447 | − | 0.735572i | \(-0.736914\pi\) |
0.975747 | + | 0.218900i | \(0.0702470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −62.1993 | −2.44154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.27492 | 0.285126 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.58762 | + | 4.48190i | −0.101262 | + | 0.175390i | −0.912205 | − | 0.409735i | \(-0.865621\pi\) |
0.810943 | + | 0.585125i | \(0.198955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.72508 | 0.145551 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.91238 | − | 10.2405i | −0.230664 | − | 0.399521i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | − | 10.3923i | −0.233727 | − | 0.404827i | 0.725175 | − | 0.688565i | \(-0.241759\pi\) |
−0.958902 | + | 0.283738i | \(0.908425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4622 | + | 19.8531i | −0.445828 | + | 0.772197i | −0.998110 | − | 0.0614606i | \(-0.980424\pi\) |
0.552281 | + | 0.833658i | \(0.313757\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.13746 | − | 1.97014i | 0.0441088 | − | 0.0763986i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.5498 | + | 59.8421i | 1.33777 | + | 2.31709i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4124 | + | 23.2309i | 0.518552 | + | 0.898159i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0000 | 0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.81271 | − | 8.33585i | 0.185516 | − | 0.321324i | −0.758234 | − | 0.651982i | \(-0.773938\pi\) |
0.943750 | + | 0.330659i | \(0.107271\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.45017 | −0.286333 | −0.143167 | − | 0.989699i | \(-0.545728\pi\) | ||||
−0.143167 | + | 0.989699i | \(0.545728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.91238 | + | 6.77643i | −0.150143 | + | 0.260056i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.09967 | −0.348700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0000 | − | 25.9808i | −0.573959 | − | 0.994126i | −0.996154 | − | 0.0876211i | \(-0.972074\pi\) |
0.422195 | − | 0.906505i | \(-0.361260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.5498 | + | 18.2728i | 0.403088 | + | 0.698170i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.00000 | + | 8.66025i | −0.190762 | + | 0.330409i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.31271 | − | 4.48190i | 0.164301 | − | 0.170747i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3248 | − | 30.0074i | 0.659065 | − | 1.14153i | −0.321794 | − | 0.946810i | \(-0.604286\pi\) |
0.980858 | − | 0.194724i | \(-0.0623810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.13746 | + | 3.70219i | 0.0811953 | + | 0.140634i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.50000 | − | 9.52628i | −0.208627 | − | 0.361352i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5498 | − | 20.0049i | 0.436855 | − | 0.756655i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.0000 | −1.05755 | −0.528773 | − | 0.848763i | \(-0.677348\pi\) | ||||
−0.528773 | + | 0.848763i | \(0.677348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.625414 | −0.0235879 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.13746 | − | 3.70219i | 0.0805013 | − | 0.139432i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.54983 | −0.246332 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.36254 | − | 9.28819i | −0.201394 | − | 0.348825i | 0.747583 | − | 0.664168i | \(-0.231214\pi\) |
−0.948978 | + | 0.315342i | \(0.897881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.362541 | + | 0.627940i | 0.0135964 | + | 0.0235496i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.8248 | − | 41.2657i | 0.892244 | − | 1.54541i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.27492 | − | 14.8087i | −0.159873 | − | 0.553816i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.27492 | + | 3.94027i | −0.0849583 | + | 0.147152i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2749 | + | 19.5287i | 0.420483 | + | 0.728299i | 0.995987 | − | 0.0895007i | \(-0.0285271\pi\) |
−0.575503 | + | 0.817799i | \(0.695194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.77492 | + | 13.4666i | 0.289553 | + | 0.501521i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.27492 | −0.307747 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.27492 | − | 9.13642i | 0.195906 | − | 0.339318i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4502 | 1.05516 | 0.527579 | − | 0.849506i | \(-0.323100\pi\) | ||||
0.527579 | + | 0.849506i | \(0.323100\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6495 | 0.984322 | 0.492161 | − | 0.870504i | \(-0.336207\pi\) | ||||
0.492161 | + | 0.870504i | \(0.336207\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | − | 5.19615i | −0.110657 | − | 0.191663i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.2749 | − | 19.5287i | −0.415317 | − | 0.719350i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.86254 | + | 4.95807i | −0.105300 | + | 0.182385i | −0.913861 | − | 0.406028i | \(-0.866914\pi\) |
0.808561 | + | 0.588413i | \(0.200247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.68729 | − | 5.91041i | 0.208928 | − | 0.217124i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.8248 | − | 20.4811i | 0.433808 | − | 0.751378i | −0.563389 | − | 0.826191i | \(-0.690503\pi\) |
0.997198 | + | 0.0748138i | \(0.0238363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.27492 | + | 14.3326i | 0.303170 | + | 0.525105i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.54983 | − | 14.8087i | −0.312822 | − | 0.541824i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.0997 | 0.551730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.45017 | − | 5.97586i | 0.125898 | − | 0.218062i | −0.796185 | − | 0.605053i | \(-0.793152\pi\) |
0.922084 | + | 0.386990i | \(0.126485\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.2749 | 0.957511 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.45017 | −0.125564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.68729 | + | 11.5827i | −0.243054 | + | 0.420982i | −0.961583 | − | 0.274516i | \(-0.911482\pi\) |
0.718529 | + | 0.695497i | \(0.244816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.0000 | 1.01634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6873 | − | 44.4917i | −0.931164 | − | 1.61282i | −0.781336 | − | 0.624111i | \(-0.785461\pi\) |
−0.149828 | − | 0.988712i | \(-0.547872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.91238 | + | 11.9726i | 0.250245 | + | 0.433437i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.9244 | − | 12.6005i | −1.83877 | − | 0.454979i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.00000 | + | 6.92820i | 0.144056 | + | 0.249513i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2371 | − | 33.3197i | −0.691911 | − | 1.19843i | −0.971211 | − | 0.238222i | \(-0.923436\pi\) |
0.279299 | − | 0.960204i | \(-0.409898\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.27492 | −0.261323 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.137459 | − | 0.238085i | 0.00493130 | − | 0.00854126i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.4502 | −0.696875 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.54983 | 0.305937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.27492 | + | 9.13642i | −0.188510 | + | 0.326509i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5498 | 0.412231 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1873 | + | 19.3770i | 0.398784 | + | 0.690714i | 0.993576 | − | 0.113165i | \(-0.0360990\pi\) |
−0.594792 | + | 0.803879i | \(0.702766\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.13746 | − | 1.97014i | −0.0404946 | − | 0.0701387i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.72508 | − | 4.71998i | 0.0968928 | − | 0.167823i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4622 | + | 2.83616i | 0.407035 | + | 0.100715i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.862541 | − | 1.49397i | 0.0305912 | − | 0.0529855i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.274917 | + | 0.476171i | 0.00973807 | + | 0.0168668i | 0.870853 | − | 0.491543i | \(-0.163567\pi\) |
−0.861115 | + | 0.508410i | \(0.830234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.72508 | −0.202286 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.2749 | − | 43.7774i | 0.891932 | − | 1.54487i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.54983 | 0.230851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.0000 | 0.422420 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.7251 | − | 27.2366i | 0.552864 | − | 0.957589i | −0.445202 | − | 0.895430i | \(-0.646868\pi\) |
0.998066 | − | 0.0621591i | \(-0.0197986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5498 | 0.546029 | 0.273014 | − | 0.962010i | \(-0.411979\pi\) | ||||
0.273014 | + | 0.962010i | \(0.411979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6375 | + | 21.8887i | 0.443215 | + | 0.767671i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.36254 | − | 2.35999i | −0.0477277 | − | 0.0826669i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.27492 | − | 14.3326i | 0.289503 | − | 0.501433i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.00000 | + | 3.46410i | 0.0349428 | + | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.31271 | − | 7.46983i | −0.150332 | − | 0.260382i | 0.781018 | − | 0.624509i | \(-0.214701\pi\) |
−0.931349 | + | 0.364127i | \(0.881367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.13746 | − | 3.70219i | −0.0744168 | − | 0.128894i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.5498 | −0.575494 | −0.287747 | − | 0.957706i | \(-0.592906\pi\) | ||||
−0.287747 | + | 0.957706i | \(0.592906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9124 | + | 20.6328i | −0.413734 | + | 0.716608i | −0.995295 | − | 0.0968948i | \(-0.969109\pi\) |
0.581561 | + | 0.813503i | \(0.302442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.8248 | 0.999920 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.13746 | − | 8.89834i | 0.177789 | − | 0.307940i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.27492 | 0.251458 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.54983 | + | 2.68439i | 0.0535062 | + | 0.0926755i | 0.891538 | − | 0.452946i | \(-0.149627\pi\) |
−0.838032 | + | 0.545622i | \(0.816294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −41.1495 | − | 71.2730i | −1.41895 | − | 2.45769i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.5498 | + | 23.4690i | −0.466681 | + | 0.808315i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.500000 | − | 12.9904i | −0.0172005 | − | 0.446883i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.63746 | + | 6.30026i | −0.124985 | + | 0.216480i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.4622 | − | 19.8531i | −0.393382 | − | 0.681358i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.900331 | − | 1.55942i | −0.0308630 | − | 0.0534562i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.5739 | −1.86858 | −0.934288 | − | 0.356520i | \(-0.883963\pi\) | ||||
−0.934288 | + | 0.356520i | \(0.883963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.13746 | − | 1.97014i | 0.0389003 | − | 0.0673772i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6495 | −0.568074 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.27492 | − | 7.40437i | 0.145689 | − | 0.252340i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.350497 | 0.0119310 | 0.00596552 | − | 0.999982i | \(-0.498101\pi\) | ||||
0.00596552 | + | 0.999982i | \(0.498101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.86254 | + | 13.6183i | 0.267334 | + | 0.463037i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.50000 | − | 14.7224i | −0.288675 | − | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.54983 | + | 2.68439i | −0.0525745 | + | 0.0910618i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.27492 | − | 18.2728i | −0.178734 | − | 0.619152i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.91238 | + | 6.77643i | −0.132414 | + | 0.229348i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.45017 | + | 4.24381i | 0.0827362 | + | 0.143303i | 0.904424 | − | 0.426634i | \(-0.140301\pi\) |
−0.821688 | + | 0.569937i | \(0.806967\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.2749 | 0.953689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2371 | + | 21.1953i | −0.412279 | + | 0.714089i | −0.995139 | − | 0.0984844i | \(-0.968601\pi\) |
0.582859 | + | 0.812573i | \(0.301934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.37459 | −0.147217 | −0.0736083 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736083 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.5498 | −0.489087 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9622 | − | 29.3794i | 0.569535 | − | 0.986464i | −0.427077 | − | 0.904215i | \(-0.640457\pi\) |
0.996612 | − | 0.0822486i | \(-0.0262101\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.13746 | + | 3.70219i | 0.0716076 | + | 0.124028i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.86254 | + | 8.42217i | 0.162719 | + | 0.281837i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | − | 10.3923i | 0.200558 | − | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.9244 | + | 5.67232i | 0.765424 | + | 0.189393i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3746 | + | 66.4667i | −1.27986 | + | 2.21679i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.63746 | + | 6.30026i | 0.121047 | + | 0.209660i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.00000 | −0.0664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2749 | − | 21.2608i | 0.407582 | − | 0.705953i | −0.587036 | − | 0.809561i | \(-0.699705\pi\) |
0.994618 | + | 0.103608i | \(0.0330387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.54983 | −0.217244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.09967 | 0.301485 | 0.150743 | − | 0.988573i | \(-0.451833\pi\) | ||||
0.150743 | + | 0.988573i | \(0.451833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.5498 | − | 63.3062i | 1.20962 | − | 2.09513i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.27492 | 0.108265 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.86254 | − | 3.22602i | −0.0615065 | − | 0.106532i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.27492 | − | 10.8685i | −0.206990 | − | 0.358518i | 0.743775 | − | 0.668430i | \(-0.233034\pi\) |
−0.950765 | + | 0.309913i | \(0.899700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4622 | + | 19.8531i | −0.377693 | + | 0.654183i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.00000 | + | 1.73205i | 0.230408 | + | 0.0570111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.137459 | + | 0.238085i | −0.00451961 | + | 0.00782820i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.77492 | + | 13.4666i | 0.255362 | + | 0.442300i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.8248 | − | 36.0695i | −0.683238 | − | 1.18340i | −0.973987 | − | 0.226604i | \(-0.927238\pi\) |
0.290749 | − | 0.956799i | \(-0.406095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6495 | 0.447344 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.00000 | − | 10.3923i | 0.196431 | − | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.36254 | − | 4.09204i | 0.0770986 | − | 0.133539i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.350497 | −0.0114259 | −0.00571293 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571293 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0000 | − | 48.4974i | −0.911805 | − | 1.57929i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.500000 | + | 0.866025i | 0.0162650 | + | 0.0281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.17525 | − | 5.49969i | 0.103182 | − | 0.178716i | −0.809812 | − | 0.586689i | \(-0.800431\pi\) |
0.912994 | + | 0.407973i | \(0.133764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.5619 | − | 30.7216i | 0.959619 | − | 0.997266i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.68729 | + | 16.7789i | −0.314132 | + | 0.544093i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.0997 | + | 17.4931i | 0.327160 | + | 0.566658i | 0.981947 | − | 0.189155i | \(-0.0605749\pi\) |
−0.654787 | + | 0.755814i | \(0.727242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.0997 | −1.45787 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5498 | − | 18.2728i | 0.340672 | − | 0.590061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9244 | 0.707239 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0997 | 0.486580 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.18729 | + | 12.4488i | −0.231367 | + | 0.400740i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.6254 | 0.406006 | 0.203003 | − | 0.979178i | \(-0.434930\pi\) | ||||
0.203003 | + | 0.979178i | \(0.434930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5120 | − | 32.0638i | −0.594080 | − | 1.02898i | −0.993676 | − | 0.112285i | \(-0.964183\pi\) |
0.399596 | − | 0.916691i | \(-0.369150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.50000 | + | 9.52628i | −0.176322 | + | 0.305398i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | − | 3.46410i | −0.0320256 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0000 | + | 27.7128i | −0.511885 | + | 0.886611i | 0.488020 | + | 0.872833i | \(0.337719\pi\) |
−0.999905 | + | 0.0137788i | \(0.995614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2371 | − | 21.1953i | −0.391100 | − | 0.677406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.91238 | + | 11.9726i | 0.220695 | + | 0.382255i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.3746 | −1.19206 | −0.596032 | − | 0.802961i | \(-0.703257\pi\) | ||||
−0.596032 | + | 0.802961i | \(0.703257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.41238 | − | 2.44631i | 0.0450020 | − | 0.0779458i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.27492 | −0.136072 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.6495 | 1.51517 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.72508 | + | 9.91613i | −0.181863 | + | 0.314996i | −0.942515 | − | 0.334164i | \(-0.891546\pi\) |
0.760652 | + | 0.649160i | \(0.224879\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7251 | 0.594223 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.36254 | − | 4.09204i | −0.0748976 | − | 0.129726i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8746 | − | 46.5481i | −0.851127 | − | 1.47419i | −0.880192 | − | 0.474617i | \(-0.842587\pi\) |
0.0290657 | − | 0.999578i | \(-0.490747\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.137459 | − | 0.238085i | 0.00434900 | − | 0.00753269i |
(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 | 1560.2.bg.g.841.2 | yes | 4 | |
13.3 | even | 3 | inner | 1560.2.bg.g.601.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.bg.g.601.2 | ✓ | 4 | 13.3 | even | 3 | inner | |
1560.2.bg.g.841.2 | yes | 4 | 1.1 | even | 1 | trivial |