Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(99,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.99");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.g (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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.99 |
Dual form | 392.3.g.d.99.2 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(3\) | −1.00000 | −0.333333 | −0.166667 | − | 0.986013i | \(-0.553300\pi\) | ||||
−0.166667 | + | 0.986013i | \(0.553300\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | 5.19615i | 1.03923i | 0.854400 | + | 0.519615i | \(0.173925\pi\) | ||||
−0.854400 | + | 0.519615i | \(0.826075\pi\) | |||||||
\(6\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | −8.00000 | −0.888889 | ||||||||
\(10\) | 9.00000 | + | 5.19615i | 0.900000 | + | 0.519615i | ||||
\(11\) | 17.0000 | 1.54545 | 0.772727 | − | 0.634738i | \(-0.218892\pi\) | ||||
0.772727 | + | 0.634738i | \(0.218892\pi\) | |||||||
\(12\) | 2.00000 | + | 3.46410i | 0.166667 | + | 0.288675i | ||||
\(13\) | 13.8564i | 1.06588i | 0.846154 | + | 0.532939i | \(0.178912\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.19615i | − | 0.346410i | ||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | 25.0000 | 1.47059 | 0.735294 | − | 0.677748i | \(-0.237044\pi\) | ||||
0.735294 | + | 0.677748i | \(0.237044\pi\) | |||||||
\(18\) | −8.00000 | + | 13.8564i | −0.444444 | + | 0.769800i | ||||
\(19\) | 7.00000 | 0.368421 | 0.184211 | − | 0.982887i | \(-0.441027\pi\) | ||||
0.184211 | + | 0.982887i | \(0.441027\pi\) | |||||||
\(20\) | 18.0000 | − | 10.3923i | 0.900000 | − | 0.519615i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 17.0000 | − | 29.4449i | 0.772727 | − | 1.33840i | ||||
\(23\) | 5.19615i | 0.225920i | 0.993600 | + | 0.112960i | \(0.0360331\pi\) | ||||
−0.993600 | + | 0.112960i | \(0.963967\pi\) | |||||||
\(24\) | 8.00000 | 0.333333 | ||||||||
\(25\) | −2.00000 | −0.0800000 | ||||||||
\(26\) | 24.0000 | + | 13.8564i | 0.923077 | + | 0.532939i | ||||
\(27\) | 17.0000 | 0.629630 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.8564i | 0.477807i | 0.971043 | + | 0.238904i | \(0.0767880\pi\) | ||||
−0.971043 | + | 0.238904i | \(0.923212\pi\) | |||||||
\(30\) | −9.00000 | − | 5.19615i | −0.300000 | − | 0.173205i | ||||
\(31\) | 32.9090i | 1.06158i | 0.847504 | + | 0.530790i | \(0.178105\pi\) | ||||
−0.847504 | + | 0.530790i | \(0.821895\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.500000 | + | 0.866025i | ||||
\(33\) | −17.0000 | −0.515152 | ||||||||
\(34\) | 25.0000 | − | 43.3013i | 0.735294 | − | 1.27357i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.0000 | + | 27.7128i | 0.444444 | + | 0.769800i | ||||
\(37\) | 8.66025i | 0.234061i | 0.993128 | + | 0.117030i | \(0.0373375\pi\) | ||||
−0.993128 | + | 0.117030i | \(0.962662\pi\) | |||||||
\(38\) | 7.00000 | − | 12.1244i | 0.184211 | − | 0.319062i | ||||
\(39\) | − | 13.8564i | − | 0.355292i | ||||||
\(40\) | − | 41.5692i | − | 1.03923i | ||||||
\(41\) | −26.0000 | −0.634146 | −0.317073 | − | 0.948401i | \(-0.602700\pi\) | ||||
−0.317073 | + | 0.948401i | \(0.602700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14.0000 | 0.325581 | 0.162791 | − | 0.986661i | \(-0.447950\pi\) | ||||
0.162791 | + | 0.986661i | \(0.447950\pi\) | |||||||
\(44\) | −34.0000 | − | 58.8897i | −0.772727 | − | 1.33840i | ||||
\(45\) | − | 41.5692i | − | 0.923760i | ||||||
\(46\) | 9.00000 | + | 5.19615i | 0.195652 | + | 0.112960i | ||||
\(47\) | 50.2295i | 1.06871i | 0.845259 | + | 0.534356i | \(0.179446\pi\) | ||||
−0.845259 | + | 0.534356i | \(0.820554\pi\) | |||||||
\(48\) | 8.00000 | − | 13.8564i | 0.166667 | − | 0.288675i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 3.46410i | −0.0400000 | + | 0.0692820i | ||||
\(51\) | −25.0000 | −0.490196 | ||||||||
\(52\) | 48.0000 | − | 27.7128i | 0.923077 | − | 0.532939i | ||||
\(53\) | − | 91.7987i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(54\) | 17.0000 | − | 29.4449i | 0.314815 | − | 0.545275i | ||||
\(55\) | 88.3346i | 1.60608i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.122807 | ||||||||
\(58\) | 24.0000 | + | 13.8564i | 0.413793 | + | 0.238904i | ||||
\(59\) | 55.0000 | 0.932203 | 0.466102 | − | 0.884731i | \(-0.345658\pi\) | ||||
0.466102 | + | 0.884731i | \(0.345658\pi\) | |||||||
\(60\) | −18.0000 | + | 10.3923i | −0.300000 | + | 0.173205i | ||||
\(61\) | − | 22.5167i | − | 0.369126i | −0.982821 | − | 0.184563i | \(-0.940913\pi\) | ||
0.982821 | − | 0.184563i | \(-0.0590869\pi\) | |||||||
\(62\) | 57.0000 | + | 32.9090i | 0.919355 | + | 0.530790i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −72.0000 | −1.10769 | ||||||||
\(66\) | −17.0000 | + | 29.4449i | −0.257576 | + | 0.446134i | ||||
\(67\) | 17.0000 | 0.253731 | 0.126866 | − | 0.991920i | \(-0.459508\pi\) | ||||
0.126866 | + | 0.991920i | \(0.459508\pi\) | |||||||
\(68\) | −50.0000 | − | 86.6025i | −0.735294 | − | 1.27357i | ||||
\(69\) | − | 5.19615i | − | 0.0753066i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 64.0000 | 0.888889 | ||||||||
\(73\) | −119.000 | −1.63014 | −0.815068 | − | 0.579365i | \(-0.803301\pi\) | ||||
−0.815068 | + | 0.579365i | \(0.803301\pi\) | |||||||
\(74\) | 15.0000 | + | 8.66025i | 0.202703 | + | 0.117030i | ||||
\(75\) | 2.00000 | 0.0266667 | ||||||||
\(76\) | −14.0000 | − | 24.2487i | −0.184211 | − | 0.319062i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −24.0000 | − | 13.8564i | −0.307692 | − | 0.177646i | ||||
\(79\) | 74.4782i | 0.942762i | 0.881930 | + | 0.471381i | \(0.156244\pi\) | ||||
−0.881930 | + | 0.471381i | \(0.843756\pi\) | |||||||
\(80\) | −72.0000 | − | 41.5692i | −0.900000 | − | 0.519615i | ||||
\(81\) | 55.0000 | 0.679012 | ||||||||
\(82\) | −26.0000 | + | 45.0333i | −0.317073 | + | 0.549187i | ||||
\(83\) | −110.000 | −1.32530 | −0.662651 | − | 0.748929i | \(-0.730569\pi\) | ||||
−0.662651 | + | 0.748929i | \(0.730569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 129.904i | 1.52828i | ||||||||
\(86\) | 14.0000 | − | 24.2487i | 0.162791 | − | 0.281962i | ||||
\(87\) | − | 13.8564i | − | 0.159269i | ||||||
\(88\) | −136.000 | −1.54545 | ||||||||
\(89\) | −71.0000 | −0.797753 | −0.398876 | − | 0.917005i | \(-0.630600\pi\) | ||||
−0.398876 | + | 0.917005i | \(0.630600\pi\) | |||||||
\(90\) | −72.0000 | − | 41.5692i | −0.800000 | − | 0.461880i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.0000 | − | 10.3923i | 0.195652 | − | 0.112960i | ||||
\(93\) | − | 32.9090i | − | 0.353860i | ||||||
\(94\) | 87.0000 | + | 50.2295i | 0.925532 | + | 0.534356i | ||||
\(95\) | 36.3731i | 0.382874i | ||||||||
\(96\) | −16.0000 | − | 27.7128i | −0.166667 | − | 0.288675i | ||||
\(97\) | 22.0000 | 0.226804 | 0.113402 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113402 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −136.000 | −1.37374 | ||||||||
\(100\) | 4.00000 | + | 6.92820i | 0.0400000 | + | 0.0692820i | ||||
\(101\) | 77.9423i | 0.771706i | 0.922560 | + | 0.385853i | \(0.126093\pi\) | ||||
−0.922560 | + | 0.385853i | \(0.873907\pi\) | |||||||
\(102\) | −25.0000 | + | 43.3013i | −0.245098 | + | 0.424522i | ||||
\(103\) | 161.081i | 1.56389i | 0.623347 | + | 0.781945i | \(0.285772\pi\) | ||||
−0.623347 | + | 0.781945i | \(0.714228\pi\) | |||||||
\(104\) | − | 110.851i | − | 1.06588i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −159.000 | − | 91.7987i | −1.50000 | − | 0.866025i | ||||
\(107\) | 65.0000 | 0.607477 | 0.303738 | − | 0.952755i | \(-0.401765\pi\) | ||||
0.303738 | + | 0.952755i | \(0.401765\pi\) | |||||||
\(108\) | −34.0000 | − | 58.8897i | −0.314815 | − | 0.545275i | ||||
\(109\) | − | 8.66025i | − | 0.0794519i | −0.999211 | − | 0.0397259i | \(-0.987352\pi\) | ||
0.999211 | − | 0.0397259i | \(-0.0126485\pi\) | |||||||
\(110\) | 153.000 | + | 88.3346i | 1.39091 | + | 0.803042i | ||||
\(111\) | − | 8.66025i | − | 0.0780203i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122.000 | 1.07965 | 0.539823 | − | 0.841779i | \(-0.318491\pi\) | ||||
0.539823 | + | 0.841779i | \(0.318491\pi\) | |||||||
\(114\) | −7.00000 | + | 12.1244i | −0.0614035 | + | 0.106354i | ||||
\(115\) | −27.0000 | −0.234783 | ||||||||
\(116\) | 48.0000 | − | 27.7128i | 0.413793 | − | 0.238904i | ||||
\(117\) | − | 110.851i | − | 0.947447i | ||||||
\(118\) | 55.0000 | − | 95.2628i | 0.466102 | − | 0.807312i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 41.5692i | 0.346410i | ||||||||
\(121\) | 168.000 | 1.38843 | ||||||||
\(122\) | −39.0000 | − | 22.5167i | −0.319672 | − | 0.184563i | ||||
\(123\) | 26.0000 | 0.211382 | ||||||||
\(124\) | 114.000 | − | 65.8179i | 0.919355 | − | 0.530790i | ||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 166.277i | − | 1.30927i | −0.755947 | − | 0.654633i | \(-0.772823\pi\) | ||
0.755947 | − | 0.654633i | \(-0.227177\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.500000 | − | 0.866025i | ||||
\(129\) | −14.0000 | −0.108527 | ||||||||
\(130\) | −72.0000 | + | 124.708i | −0.553846 | + | 0.959290i | ||||
\(131\) | −17.0000 | −0.129771 | −0.0648855 | − | 0.997893i | \(-0.520668\pi\) | ||||
−0.0648855 | + | 0.997893i | \(0.520668\pi\) | |||||||
\(132\) | 34.0000 | + | 58.8897i | 0.257576 | + | 0.446134i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.0000 | − | 29.4449i | 0.126866 | − | 0.219738i | ||||
\(135\) | 88.3346i | 0.654330i | ||||||||
\(136\) | −200.000 | −1.47059 | ||||||||
\(137\) | −145.000 | −1.05839 | −0.529197 | − | 0.848499i | \(-0.677507\pi\) | ||||
−0.529197 | + | 0.848499i | \(0.677507\pi\) | |||||||
\(138\) | −9.00000 | − | 5.19615i | −0.0652174 | − | 0.0376533i | ||||
\(139\) | 82.0000 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 50.2295i | − | 0.356237i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 235.559i | 1.64727i | ||||||||
\(144\) | 64.0000 | − | 110.851i | 0.444444 | − | 0.769800i | ||||
\(145\) | −72.0000 | −0.496552 | ||||||||
\(146\) | −119.000 | + | 206.114i | −0.815068 | + | 1.41174i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 30.0000 | − | 17.3205i | 0.202703 | − | 0.117030i | ||||
\(149\) | − | 5.19615i | − | 0.0348735i | −0.999848 | − | 0.0174368i | \(-0.994449\pi\) | ||
0.999848 | − | 0.0174368i | \(-0.00555057\pi\) | |||||||
\(150\) | 2.00000 | − | 3.46410i | 0.0133333 | − | 0.0230940i | ||||
\(151\) | 36.3731i | 0.240881i | 0.992721 | + | 0.120441i | \(0.0384307\pi\) | ||||
−0.992721 | + | 0.120441i | \(0.961569\pi\) | |||||||
\(152\) | −56.0000 | −0.368421 | ||||||||
\(153\) | −200.000 | −1.30719 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −171.000 | −1.10323 | ||||||||
\(156\) | −48.0000 | + | 27.7128i | −0.307692 | + | 0.177646i | ||||
\(157\) | − | 310.037i | − | 1.97476i | −0.158373 | − | 0.987379i | \(-0.550625\pi\) | ||
0.158373 | − | 0.987379i | \(-0.449375\pi\) | |||||||
\(158\) | 129.000 | + | 74.4782i | 0.816456 | + | 0.471381i | ||||
\(159\) | 91.7987i | 0.577350i | ||||||||
\(160\) | −144.000 | + | 83.1384i | −0.900000 | + | 0.519615i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 55.0000 | − | 95.2628i | 0.339506 | − | 0.588042i | ||||
\(163\) | 17.0000 | 0.104294 | 0.0521472 | − | 0.998639i | \(-0.483393\pi\) | ||||
0.0521472 | + | 0.998639i | \(0.483393\pi\) | |||||||
\(164\) | 52.0000 | + | 90.0666i | 0.317073 | + | 0.549187i | ||||
\(165\) | − | 88.3346i | − | 0.535361i | ||||||
\(166\) | −110.000 | + | 190.526i | −0.662651 | + | 1.14774i | ||||
\(167\) | 13.8564i | 0.0829725i | 0.999139 | + | 0.0414862i | \(0.0132093\pi\) | ||||
−0.999139 | + | 0.0414862i | \(0.986791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 225.000 | + | 129.904i | 1.32353 | + | 0.764140i | ||||
\(171\) | −56.0000 | −0.327485 | ||||||||
\(172\) | −28.0000 | − | 48.4974i | −0.162791 | − | 0.281962i | ||||
\(173\) | − | 105.655i | − | 0.610723i | −0.952236 | − | 0.305362i | \(-0.901223\pi\) | ||
0.952236 | − | 0.305362i | \(-0.0987773\pi\) | |||||||
\(174\) | −24.0000 | − | 13.8564i | −0.137931 | − | 0.0796345i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −136.000 | + | 235.559i | −0.772727 | + | 1.33840i | ||||
\(177\) | −55.0000 | −0.310734 | ||||||||
\(178\) | −71.0000 | + | 122.976i | −0.398876 | + | 0.690874i | ||||
\(179\) | 89.0000 | 0.497207 | 0.248603 | − | 0.968605i | \(-0.420028\pi\) | ||||
0.248603 | + | 0.968605i | \(0.420028\pi\) | |||||||
\(180\) | −144.000 | + | 83.1384i | −0.800000 | + | 0.461880i | ||||
\(181\) | − | 249.415i | − | 1.37799i | −0.724768 | − | 0.688993i | \(-0.758053\pi\) | ||
0.724768 | − | 0.688993i | \(-0.241947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.5167i | 0.123042i | ||||||||
\(184\) | − | 41.5692i | − | 0.225920i | ||||||
\(185\) | −45.0000 | −0.243243 | ||||||||
\(186\) | −57.0000 | − | 32.9090i | −0.306452 | − | 0.176930i | ||||
\(187\) | 425.000 | 2.27273 | ||||||||
\(188\) | 174.000 | − | 100.459i | 0.925532 | − | 0.534356i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 63.0000 | + | 36.3731i | 0.331579 | + | 0.191437i | ||||
\(191\) | − | 216.506i | − | 1.13354i | −0.823876 | − | 0.566771i | \(-0.808193\pi\) | ||
0.823876 | − | 0.566771i | \(-0.191807\pi\) | |||||||
\(192\) | −64.0000 | −0.333333 | ||||||||
\(193\) | −73.0000 | −0.378238 | −0.189119 | − | 0.981954i | \(-0.560563\pi\) | ||||
−0.189119 | + | 0.981954i | \(0.560563\pi\) | |||||||
\(194\) | 22.0000 | − | 38.1051i | 0.113402 | − | 0.196418i | ||||
\(195\) | 72.0000 | 0.369231 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 207.846i | 1.05506i | 0.849538 | + | 0.527528i | \(0.176881\pi\) | ||||
−0.849538 | + | 0.527528i | \(0.823119\pi\) | |||||||
\(198\) | −136.000 | + | 235.559i | −0.686869 | + | 1.18969i | ||||
\(199\) | − | 64.0859i | − | 0.322040i | −0.986951 | − | 0.161020i | \(-0.948522\pi\) | ||
0.986951 | − | 0.161020i | \(-0.0514783\pi\) | |||||||
\(200\) | 16.0000 | 0.0800000 | ||||||||
\(201\) | −17.0000 | −0.0845771 | ||||||||
\(202\) | 135.000 | + | 77.9423i | 0.668317 | + | 0.385853i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 50.0000 | + | 86.6025i | 0.245098 | + | 0.424522i | ||||
\(205\) | − | 135.100i | − | 0.659024i | ||||||
\(206\) | 279.000 | + | 161.081i | 1.35437 | + | 0.781945i | ||||
\(207\) | − | 41.5692i | − | 0.200817i | ||||||
\(208\) | −192.000 | − | 110.851i | −0.923077 | − | 0.532939i | ||||
\(209\) | 119.000 | 0.569378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 302.000 | 1.43128 | 0.715640 | − | 0.698470i | \(-0.246135\pi\) | ||||
0.715640 | + | 0.698470i | \(0.246135\pi\) | |||||||
\(212\) | −318.000 | + | 183.597i | −1.50000 | + | 0.866025i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 65.0000 | − | 112.583i | 0.303738 | − | 0.526090i | ||||
\(215\) | 72.7461i | 0.338354i | ||||||||
\(216\) | −136.000 | −0.629630 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.0000 | − | 8.66025i | −0.0688073 | − | 0.0397259i | ||||
\(219\) | 119.000 | 0.543379 | ||||||||
\(220\) | 306.000 | − | 176.669i | 1.39091 | − | 0.803042i | ||||
\(221\) | 346.410i | 1.56747i | ||||||||
\(222\) | −15.0000 | − | 8.66025i | −0.0675676 | − | 0.0390102i | ||||
\(223\) | − | 138.564i | − | 0.621364i | −0.950514 | − | 0.310682i | \(-0.899443\pi\) | ||
0.950514 | − | 0.310682i | \(-0.100557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.0000 | 0.0711111 | ||||||||
\(226\) | 122.000 | − | 211.310i | 0.539823 | − | 0.935001i | ||||
\(227\) | 55.0000 | 0.242291 | 0.121145 | − | 0.992635i | \(-0.461343\pi\) | ||||
0.121145 | + | 0.992635i | \(0.461343\pi\) | |||||||
\(228\) | 14.0000 | + | 24.2487i | 0.0614035 | + | 0.106354i | ||||
\(229\) | − | 327.358i | − | 1.42951i | −0.699375 | − | 0.714755i | \(-0.746538\pi\) | ||
0.699375 | − | 0.714755i | \(-0.253462\pi\) | |||||||
\(230\) | −27.0000 | + | 46.7654i | −0.117391 | + | 0.203328i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 110.851i | − | 0.477807i | ||||||
\(233\) | −385.000 | −1.65236 | −0.826180 | − | 0.563406i | \(-0.809491\pi\) | ||||
−0.826180 | + | 0.563406i | \(0.809491\pi\) | |||||||
\(234\) | −192.000 | − | 110.851i | −0.820513 | − | 0.473723i | ||||
\(235\) | −261.000 | −1.11064 | ||||||||
\(236\) | −110.000 | − | 190.526i | −0.466102 | − | 0.807312i | ||||
\(237\) | − | 74.4782i | − | 0.314254i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 429.549i | − | 1.79727i | −0.438693 | − | 0.898637i | \(-0.644558\pi\) | ||
0.438693 | − | 0.898637i | \(-0.355442\pi\) | |||||||
\(240\) | 72.0000 | + | 41.5692i | 0.300000 | + | 0.173205i | ||||
\(241\) | 145.000 | 0.601660 | 0.300830 | − | 0.953678i | \(-0.402736\pi\) | ||||
0.300830 | + | 0.953678i | \(0.402736\pi\) | |||||||
\(242\) | 168.000 | − | 290.985i | 0.694215 | − | 1.20242i | ||||
\(243\) | −208.000 | −0.855967 | ||||||||
\(244\) | −78.0000 | + | 45.0333i | −0.319672 | + | 0.184563i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 26.0000 | − | 45.0333i | 0.105691 | − | 0.183062i | ||||
\(247\) | 96.9948i | 0.392692i | ||||||||
\(248\) | − | 263.272i | − | 1.06158i | ||||||
\(249\) | 110.000 | 0.441767 | ||||||||
\(250\) | 207.000 | + | 119.512i | 0.828000 | + | 0.478046i | ||||
\(251\) | 58.0000 | 0.231076 | 0.115538 | − | 0.993303i | \(-0.463141\pi\) | ||||
0.115538 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 88.3346i | 0.349149i | ||||||||
\(254\) | −288.000 | − | 166.277i | −1.13386 | − | 0.654633i | ||||
\(255\) | − | 129.904i | − | 0.509427i | ||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | −119.000 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(258\) | −14.0000 | + | 24.2487i | −0.0542636 | + | 0.0939873i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 144.000 | + | 249.415i | 0.553846 | + | 0.959290i | ||||
\(261\) | − | 110.851i | − | 0.424717i | ||||||
\(262\) | −17.0000 | + | 29.4449i | −0.0648855 | + | 0.112385i | ||||
\(263\) | 327.358i | 1.24471i | 0.782737 | + | 0.622353i | \(0.213823\pi\) | ||||
−0.782737 | + | 0.622353i | \(0.786177\pi\) | |||||||
\(264\) | 136.000 | 0.515152 | ||||||||
\(265\) | 477.000 | 1.80000 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 71.0000 | 0.265918 | ||||||||
\(268\) | −34.0000 | − | 58.8897i | −0.126866 | − | 0.219738i | ||||
\(269\) | 133.368i | 0.495791i | 0.968787 | + | 0.247896i | \(0.0797390\pi\) | ||||
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(270\) | 153.000 | + | 88.3346i | 0.566667 | + | 0.327165i | ||||
\(271\) | − | 434.745i | − | 1.60422i | −0.597174 | − | 0.802112i | \(-0.703710\pi\) | ||
0.597174 | − | 0.802112i | \(-0.296290\pi\) | |||||||
\(272\) | −200.000 | + | 346.410i | −0.735294 | + | 1.27357i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −145.000 | + | 251.147i | −0.529197 | + | 0.916596i | ||||
\(275\) | −34.0000 | −0.123636 | ||||||||
\(276\) | −18.0000 | + | 10.3923i | −0.0652174 | + | 0.0376533i | ||||
\(277\) | − | 202.650i | − | 0.731588i | −0.930696 | − | 0.365794i | \(-0.880797\pi\) | ||
0.930696 | − | 0.365794i | \(-0.119203\pi\) | |||||||
\(278\) | 82.0000 | − | 142.028i | 0.294964 | − | 0.510893i | ||||
\(279\) | − | 263.272i | − | 0.943626i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74.0000 | 0.263345 | 0.131673 | − | 0.991293i | \(-0.457965\pi\) | ||||
0.131673 | + | 0.991293i | \(0.457965\pi\) | |||||||
\(282\) | −87.0000 | − | 50.2295i | −0.308511 | − | 0.178119i | ||||
\(283\) | 463.000 | 1.63604 | 0.818021 | − | 0.575188i | \(-0.195071\pi\) | ||||
0.818021 | + | 0.575188i | \(0.195071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 36.3731i | − | 0.127625i | ||||||
\(286\) | 408.000 | + | 235.559i | 1.42657 | + | 0.823633i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −128.000 | − | 221.703i | −0.444444 | − | 0.769800i | ||||
\(289\) | 336.000 | 1.16263 | ||||||||
\(290\) | −72.0000 | + | 124.708i | −0.248276 | + | 0.430026i | ||||
\(291\) | −22.0000 | −0.0756014 | ||||||||
\(292\) | 238.000 | + | 412.228i | 0.815068 | + | 1.41174i | ||||
\(293\) | − | 110.851i | − | 0.378332i | −0.981945 | − | 0.189166i | \(-0.939422\pi\) | ||
0.981945 | − | 0.189166i | \(-0.0605784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 285.788i | 0.968774i | ||||||||
\(296\) | − | 69.2820i | − | 0.234061i | ||||||
\(297\) | 289.000 | 0.973064 | ||||||||
\(298\) | −9.00000 | − | 5.19615i | −0.0302013 | − | 0.0174368i | ||||
\(299\) | −72.0000 | −0.240803 | ||||||||
\(300\) | −4.00000 | − | 6.92820i | −0.0133333 | − | 0.0230940i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 63.0000 | + | 36.3731i | 0.208609 | + | 0.120441i | ||||
\(303\) | − | 77.9423i | − | 0.257235i | ||||||
\(304\) | −56.0000 | + | 96.9948i | −0.184211 | + | 0.319062i | ||||
\(305\) | 117.000 | 0.383607 | ||||||||
\(306\) | −200.000 | + | 346.410i | −0.653595 | + | 1.13206i | ||||
\(307\) | 274.000 | 0.892508 | 0.446254 | − | 0.894906i | \(-0.352758\pi\) | ||||
0.446254 | + | 0.894906i | \(0.352758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 161.081i | − | 0.521297i | ||||||
\(310\) | −171.000 | + | 296.181i | −0.551613 | + | 0.955422i | ||||
\(311\) | − | 50.2295i | − | 0.161510i | −0.996734 | − | 0.0807548i | \(-0.974267\pi\) | ||
0.996734 | − | 0.0807548i | \(-0.0257331\pi\) | |||||||
\(312\) | 110.851i | 0.355292i | ||||||||
\(313\) | 409.000 | 1.30671 | 0.653355 | − | 0.757052i | \(-0.273361\pi\) | ||||
0.653355 | + | 0.757052i | \(0.273361\pi\) | |||||||
\(314\) | −537.000 | − | 310.037i | −1.71019 | − | 0.987379i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 258.000 | − | 148.956i | 0.816456 | − | 0.471381i | ||||
\(317\) | 188.794i | 0.595563i | 0.954634 | + | 0.297782i | \(0.0962467\pi\) | ||||
−0.954634 | + | 0.297782i | \(0.903753\pi\) | |||||||
\(318\) | 159.000 | + | 91.7987i | 0.500000 | + | 0.288675i | ||||
\(319\) | 235.559i | 0.738429i | ||||||||
\(320\) | 332.554i | 1.03923i | ||||||||
\(321\) | −65.0000 | −0.202492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 175.000 | 0.541796 | ||||||||
\(324\) | −110.000 | − | 190.526i | −0.339506 | − | 0.588042i | ||||
\(325\) | − | 27.7128i | − | 0.0852702i | ||||||
\(326\) | 17.0000 | − | 29.4449i | 0.0521472 | − | 0.0903217i | ||||
\(327\) | 8.66025i | 0.0264840i | ||||||||
\(328\) | 208.000 | 0.634146 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −153.000 | − | 88.3346i | −0.463636 | − | 0.267681i | ||||
\(331\) | −295.000 | −0.891239 | −0.445619 | − | 0.895223i | \(-0.647017\pi\) | ||||
−0.445619 | + | 0.895223i | \(0.647017\pi\) | |||||||
\(332\) | 220.000 | + | 381.051i | 0.662651 | + | 1.14774i | ||||
\(333\) | − | 69.2820i | − | 0.208054i | ||||||
\(334\) | 24.0000 | + | 13.8564i | 0.0718563 | + | 0.0414862i | ||||
\(335\) | 88.3346i | 0.263685i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 0.0771513 | 0.0385757 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385757 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(338\) | −23.0000 | + | 39.8372i | −0.0680473 | + | 0.117861i | ||||
\(339\) | −122.000 | −0.359882 | ||||||||
\(340\) | 450.000 | − | 259.808i | 1.32353 | − | 0.764140i | ||||
\(341\) | 559.452i | 1.64062i | ||||||||
\(342\) | −56.0000 | + | 96.9948i | −0.163743 | + | 0.283611i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −112.000 | −0.325581 | ||||||||
\(345\) | 27.0000 | 0.0782609 | ||||||||
\(346\) | −183.000 | − | 105.655i | −0.528902 | − | 0.305362i | ||||
\(347\) | 377.000 | 1.08646 | 0.543228 | − | 0.839585i | \(-0.317202\pi\) | ||||
0.543228 | + | 0.839585i | \(0.317202\pi\) | |||||||
\(348\) | −48.0000 | + | 27.7128i | −0.137931 | + | 0.0796345i | ||||
\(349\) | − | 96.9948i | − | 0.277922i | −0.990298 | − | 0.138961i | \(-0.955624\pi\) | ||
0.990298 | − | 0.138961i | \(-0.0443763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 235.559i | 0.671108i | ||||||||
\(352\) | 272.000 | + | 471.118i | 0.772727 | + | 1.33840i | ||||
\(353\) | −503.000 | −1.42493 | −0.712465 | − | 0.701708i | \(-0.752421\pi\) | ||||
−0.712465 | + | 0.701708i | \(0.752421\pi\) | |||||||
\(354\) | −55.0000 | + | 95.2628i | −0.155367 | + | 0.269104i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 142.000 | + | 245.951i | 0.398876 | + | 0.690874i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 89.0000 | − | 154.153i | 0.248603 | − | 0.430594i | ||||
\(359\) | 185.329i | 0.516238i | 0.966113 | + | 0.258119i | \(0.0831027\pi\) | ||||
−0.966113 | + | 0.258119i | \(0.916897\pi\) | |||||||
\(360\) | 332.554i | 0.923760i | ||||||||
\(361\) | −312.000 | −0.864266 | ||||||||
\(362\) | −432.000 | − | 249.415i | −1.19337 | − | 0.688993i | ||||
\(363\) | −168.000 | −0.462810 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 618.342i | − | 1.69409i | ||||||
\(366\) | 39.0000 | + | 22.5167i | 0.106557 | + | 0.0615209i | ||||
\(367\) | 296.181i | 0.807032i | 0.914973 | + | 0.403516i | \(0.132212\pi\) | ||||
−0.914973 | + | 0.403516i | \(0.867788\pi\) | |||||||
\(368\) | −72.0000 | − | 41.5692i | −0.195652 | − | 0.112960i | ||||
\(369\) | 208.000 | 0.563686 | ||||||||
\(370\) | −45.0000 | + | 77.9423i | −0.121622 | + | 0.210655i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −114.000 | + | 65.8179i | −0.306452 | + | 0.176930i | ||||
\(373\) | 119.512i | 0.320406i | 0.987084 | + | 0.160203i | \(0.0512149\pi\) | ||||
−0.987084 | + | 0.160203i | \(0.948785\pi\) | |||||||
\(374\) | 425.000 | − | 736.122i | 1.13636 | − | 1.96824i | ||||
\(375\) | − | 119.512i | − | 0.318697i | ||||||
\(376\) | − | 401.836i | − | 1.06871i | ||||||
\(377\) | −192.000 | −0.509284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −634.000 | −1.67282 | −0.836412 | − | 0.548102i | \(-0.815351\pi\) | ||||
−0.836412 | + | 0.548102i | \(0.815351\pi\) | |||||||
\(380\) | 126.000 | − | 72.7461i | 0.331579 | − | 0.191437i | ||||
\(381\) | 166.277i | 0.436422i | ||||||||
\(382\) | −375.000 | − | 216.506i | −0.981675 | − | 0.566771i | ||||
\(383\) | 244.219i | 0.637648i | 0.947814 | + | 0.318824i | \(0.103288\pi\) | ||||
−0.947814 | + | 0.318824i | \(0.896712\pi\) | |||||||
\(384\) | −64.0000 | + | 110.851i | −0.166667 | + | 0.288675i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −73.0000 | + | 126.440i | −0.189119 | + | 0.327564i | ||||
\(387\) | −112.000 | −0.289406 | ||||||||
\(388\) | −44.0000 | − | 76.2102i | −0.113402 | − | 0.196418i | ||||
\(389\) | 587.165i | 1.50942i | 0.656057 | + | 0.754711i | \(0.272223\pi\) | ||||
−0.656057 | + | 0.754711i | \(0.727777\pi\) | |||||||
\(390\) | 72.0000 | − | 124.708i | 0.184615 | − | 0.319763i | ||||
\(391\) | 129.904i | 0.332235i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0000 | 0.0432570 | ||||||||
\(394\) | 360.000 | + | 207.846i | 0.913706 | + | 0.527528i | ||||
\(395\) | −387.000 | −0.979747 | ||||||||
\(396\) | 272.000 | + | 471.118i | 0.686869 | + | 1.18969i | ||||
\(397\) | 240.755i | 0.606436i | 0.952921 | + | 0.303218i | \(0.0980610\pi\) | ||||
−0.952921 | + | 0.303218i | \(0.901939\pi\) | |||||||
\(398\) | −111.000 | − | 64.0859i | −0.278894 | − | 0.161020i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0000 | − | 27.7128i | 0.0400000 | − | 0.0692820i | ||||
\(401\) | 119.000 | 0.296758 | 0.148379 | − | 0.988931i | \(-0.452594\pi\) | ||||
0.148379 | + | 0.988931i | \(0.452594\pi\) | |||||||
\(402\) | −17.0000 | + | 29.4449i | −0.0422886 | + | 0.0732459i | ||||
\(403\) | −456.000 | −1.13151 | ||||||||
\(404\) | 270.000 | − | 155.885i | 0.668317 | − | 0.385853i | ||||
\(405\) | 285.788i | 0.705650i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 147.224i | 0.361731i | ||||||||
\(408\) | 200.000 | 0.490196 | ||||||||
\(409\) | 145.000 | 0.354523 | 0.177262 | − | 0.984164i | \(-0.443276\pi\) | ||||
0.177262 | + | 0.984164i | \(0.443276\pi\) | |||||||
\(410\) | −234.000 | − | 135.100i | −0.570732 | − | 0.329512i | ||||
\(411\) | 145.000 | 0.352798 | ||||||||
\(412\) | 558.000 | − | 322.161i | 1.35437 | − | 0.781945i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −72.0000 | − | 41.5692i | −0.173913 | − | 0.100409i | ||||
\(415\) | − | 571.577i | − | 1.37729i | ||||||
\(416\) | −384.000 | + | 221.703i | −0.923077 | + | 0.532939i | ||||
\(417\) | −82.0000 | −0.196643 | ||||||||
\(418\) | 119.000 | − | 206.114i | 0.284689 | − | 0.493096i | ||||
\(419\) | −302.000 | −0.720764 | −0.360382 | − | 0.932805i | \(-0.617354\pi\) | ||||
−0.360382 | + | 0.932805i | \(0.617354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 401.836i | − | 0.954479i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) | ||
0.878773 | − | 0.477240i | \(-0.158363\pi\) | |||||||
\(422\) | 302.000 | − | 523.079i | 0.715640 | − | 1.23952i | ||||
\(423\) | − | 401.836i | − | 0.949966i | ||||||
\(424\) | 734.390i | 1.73205i | ||||||||
\(425\) | −50.0000 | −0.117647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −130.000 | − | 225.167i | −0.303738 | − | 0.526090i | ||||
\(429\) | − | 235.559i | − | 0.549088i | ||||||
\(430\) | 126.000 | + | 72.7461i | 0.293023 | + | 0.169177i | ||||
\(431\) | − | 808.868i | − | 1.87672i | −0.345655 | − | 0.938362i | \(-0.612343\pi\) | ||
0.345655 | − | 0.938362i | \(-0.387657\pi\) | |||||||
\(432\) | −136.000 | + | 235.559i | −0.314815 | + | 0.545275i | ||||
\(433\) | −410.000 | −0.946882 | −0.473441 | − | 0.880825i | \(-0.656988\pi\) | ||||
−0.473441 | + | 0.880825i | \(0.656988\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 72.0000 | 0.165517 | ||||||||
\(436\) | −30.0000 | + | 17.3205i | −0.0688073 | + | 0.0397259i | ||||
\(437\) | 36.3731i | 0.0832336i | ||||||||
\(438\) | 119.000 | − | 206.114i | 0.271689 | − | 0.470580i | ||||
\(439\) | − | 490.170i | − | 1.11656i | −0.829652 | − | 0.558281i | \(-0.811461\pi\) | ||
0.829652 | − | 0.558281i | \(-0.188539\pi\) | |||||||
\(440\) | − | 706.677i | − | 1.60608i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 600.000 | + | 346.410i | 1.35747 | + | 0.783733i | ||||
\(443\) | 401.000 | 0.905192 | 0.452596 | − | 0.891716i | \(-0.350498\pi\) | ||||
0.452596 | + | 0.891716i | \(0.350498\pi\) | |||||||
\(444\) | −30.0000 | + | 17.3205i | −0.0675676 | + | 0.0390102i | ||||
\(445\) | − | 368.927i | − | 0.829049i | ||||||
\(446\) | −240.000 | − | 138.564i | −0.538117 | − | 0.310682i | ||||
\(447\) | 5.19615i | 0.0116245i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −310.000 | −0.690423 | −0.345212 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(450\) | 16.0000 | − | 27.7128i | 0.0355556 | − | 0.0615840i | ||||
\(451\) | −442.000 | −0.980044 | ||||||||
\(452\) | −244.000 | − | 422.620i | −0.539823 | − | 0.935001i | ||||
\(453\) | − | 36.3731i | − | 0.0802937i | ||||||
\(454\) | 55.0000 | − | 95.2628i | 0.121145 | − | 0.209830i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 56.0000 | 0.122807 | ||||||||
\(457\) | 167.000 | 0.365427 | 0.182713 | − | 0.983166i | \(-0.441512\pi\) | ||||
0.182713 | + | 0.983166i | \(0.441512\pi\) | |||||||
\(458\) | −567.000 | − | 327.358i | −1.23799 | − | 0.714755i | ||||
\(459\) | 425.000 | 0.925926 | ||||||||
\(460\) | 54.0000 | + | 93.5307i | 0.117391 | + | 0.203328i | ||||
\(461\) | − | 13.8564i | − | 0.0300573i | −0.999887 | − | 0.0150286i | \(-0.995216\pi\) | ||
0.999887 | − | 0.0150286i | \(-0.00478394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 609.682i | 1.31681i | 0.752665 | + | 0.658404i | \(0.228768\pi\) | ||||
−0.752665 | + | 0.658404i | \(0.771232\pi\) | |||||||
\(464\) | −192.000 | − | 110.851i | −0.413793 | − | 0.238904i | ||||
\(465\) | 171.000 | 0.367742 | ||||||||
\(466\) | −385.000 | + | 666.840i | −0.826180 | + | 1.43099i | ||||
\(467\) | −785.000 | −1.68094 | −0.840471 | − | 0.541856i | \(-0.817722\pi\) | ||||
−0.840471 | + | 0.541856i | \(0.817722\pi\) | |||||||
\(468\) | −384.000 | + | 221.703i | −0.820513 | + | 0.473723i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −261.000 | + | 452.065i | −0.555319 | + | 0.961841i | ||||
\(471\) | 310.037i | 0.658253i | ||||||||
\(472\) | −440.000 | −0.932203 | ||||||||
\(473\) | 238.000 | 0.503171 | ||||||||
\(474\) | −129.000 | − | 74.4782i | −0.272152 | − | 0.157127i | ||||
\(475\) | −14.0000 | −0.0294737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 734.390i | 1.53960i | ||||||||
\(478\) | −744.000 | − | 429.549i | −1.55649 | − | 0.898637i | ||||
\(479\) | − | 618.342i | − | 1.29090i | −0.763802 | − | 0.645451i | \(-0.776669\pi\) | ||
0.763802 | − | 0.645451i | \(-0.223331\pi\) | |||||||
\(480\) | 144.000 | − | 83.1384i | 0.300000 | − | 0.173205i | ||||
\(481\) | −120.000 | −0.249480 | ||||||||
\(482\) | 145.000 | − | 251.147i | 0.300830 | − | 0.521053i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −336.000 | − | 581.969i | −0.694215 | − | 1.20242i | ||||
\(485\) | 114.315i | 0.235702i | ||||||||
\(486\) | −208.000 | + | 360.267i | −0.427984 | + | 0.741289i | ||||
\(487\) | − | 393.176i | − | 0.807342i | −0.914904 | − | 0.403671i | \(-0.867734\pi\) | ||
0.914904 | − | 0.403671i | \(-0.132266\pi\) | |||||||
\(488\) | 180.133i | 0.369126i | ||||||||
\(489\) | −17.0000 | −0.0347648 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 422.000 | 0.859470 | 0.429735 | − | 0.902955i | \(-0.358607\pi\) | ||||
0.429735 | + | 0.902955i | \(0.358607\pi\) | |||||||
\(492\) | −52.0000 | − | 90.0666i | −0.105691 | − | 0.183062i | ||||
\(493\) | 346.410i | 0.702658i | ||||||||
\(494\) | 168.000 | + | 96.9948i | 0.340081 | + | 0.196346i | ||||
\(495\) | − | 706.677i | − | 1.42763i | ||||||
\(496\) | −456.000 | − | 263.272i | −0.919355 | − | 0.530790i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 110.000 | − | 190.526i | 0.220884 | − | 0.382582i | ||||
\(499\) | 65.0000 | 0.130261 | 0.0651303 | − | 0.997877i | \(-0.479254\pi\) | ||||
0.0651303 | + | 0.997877i | \(0.479254\pi\) | |||||||
\(500\) | 414.000 | − | 239.023i | 0.828000 | − | 0.478046i | ||||
\(501\) | − | 13.8564i | − | 0.0276575i | ||||||
\(502\) | 58.0000 | − | 100.459i | 0.115538 | − | 0.200117i | ||||
\(503\) | 249.415i | 0.495855i | 0.968779 | + | 0.247928i | \(0.0797496\pi\) | ||||
−0.968779 | + | 0.247928i | \(0.920250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −405.000 | −0.801980 | ||||||||
\(506\) | 153.000 | + | 88.3346i | 0.302372 | + | 0.174574i | ||||
\(507\) | 23.0000 | 0.0453649 | ||||||||
\(508\) | −576.000 | + | 332.554i | −1.13386 | + | 0.654633i | ||||
\(509\) | 545.596i | 1.07190i | 0.844250 | + | 0.535949i | \(0.180046\pi\) | ||||
−0.844250 | + | 0.535949i | \(0.819954\pi\) | |||||||
\(510\) | −225.000 | − | 129.904i | −0.441176 | − | 0.254713i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 119.000 | 0.231969 | ||||||||
\(514\) | −119.000 | + | 206.114i | −0.231518 | + | 0.401000i | ||||
\(515\) | −837.000 | −1.62524 | ||||||||
\(516\) | 28.0000 | + | 48.4974i | 0.0542636 | + | 0.0939873i | ||||
\(517\) | 853.901i | 1.65165i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 105.655i | 0.203574i | ||||||||
\(520\) | 576.000 | 1.10769 | ||||||||
\(521\) | 25.0000 | 0.0479846 | 0.0239923 | − | 0.999712i | \(-0.492362\pi\) | ||||
0.0239923 | + | 0.999712i | \(0.492362\pi\) | |||||||
\(522\) | −192.000 | − | 110.851i | −0.367816 | − | 0.212359i | ||||
\(523\) | −593.000 | −1.13384 | −0.566922 | − | 0.823772i | \(-0.691866\pi\) | ||||
−0.566922 | + | 0.823772i | \(0.691866\pi\) | |||||||
\(524\) | 34.0000 | + | 58.8897i | 0.0648855 | + | 0.112385i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 567.000 | + | 327.358i | 1.07795 | + | 0.622353i | ||||
\(527\) | 822.724i | 1.56115i | ||||||||
\(528\) | 136.000 | − | 235.559i | 0.257576 | − | 0.446134i | ||||
\(529\) | 502.000 | 0.948960 | ||||||||
\(530\) | 477.000 | − | 826.188i | 0.900000 | − | 1.55885i | ||||
\(531\) | −440.000 | −0.828625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 360.267i | − | 0.675922i | ||||||
\(534\) | 71.0000 | − | 122.976i | 0.132959 | − | 0.230291i | ||||
\(535\) | 337.750i | 0.631308i | ||||||||
\(536\) | −136.000 | −0.253731 | ||||||||
\(537\) | −89.0000 | −0.165736 | ||||||||
\(538\) | 231.000 | + | 133.368i | 0.429368 | + | 0.247896i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 306.000 | − | 176.669i | 0.566667 | − | 0.327165i | ||||
\(541\) | 756.906i | 1.39909i | 0.714590 | + | 0.699544i | \(0.246613\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753387\pi\) | |||||||
\(542\) | −753.000 | − | 434.745i | −1.38930 | − | 0.802112i | ||||
\(543\) | 249.415i | 0.459328i | ||||||||
\(544\) | 400.000 | + | 692.820i | 0.735294 | + | 1.27357i | ||||
\(545\) | 45.0000 | 0.0825688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 662.000 | 1.21024 | 0.605119 | − | 0.796135i | \(-0.293126\pi\) | ||||
0.605119 | + | 0.796135i | \(0.293126\pi\) | |||||||
\(548\) | 290.000 | + | 502.295i | 0.529197 | + | 0.916596i | ||||
\(549\) | 180.133i | 0.328112i | ||||||||
\(550\) | −34.0000 | + | 58.8897i | −0.0618182 | + | 0.107072i | ||||
\(551\) | 96.9948i | 0.176034i | ||||||||
\(552\) | 41.5692i | 0.0753066i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −351.000 | − | 202.650i | −0.633574 | − | 0.365794i | ||||
\(555\) | 45.0000 | 0.0810811 | ||||||||
\(556\) | −164.000 | − | 284.056i | −0.294964 | − | 0.510893i | ||||
\(557\) | − | 590.629i | − | 1.06038i | −0.847880 | − | 0.530188i | \(-0.822121\pi\) | ||
0.847880 | − | 0.530188i | \(-0.177879\pi\) | |||||||
\(558\) | −456.000 | − | 263.272i | −0.817204 | − | 0.471813i | ||||
\(559\) | 193.990i | 0.347030i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −425.000 | −0.757576 | ||||||||
\(562\) | 74.0000 | − | 128.172i | 0.131673 | − | 0.228064i | ||||
\(563\) | −737.000 | −1.30906 | −0.654529 | − | 0.756037i | \(-0.727133\pi\) | ||||
−0.654529 | + | 0.756037i | \(0.727133\pi\) | |||||||
\(564\) | −174.000 | + | 100.459i | −0.308511 | + | 0.178119i | ||||
\(565\) | 633.931i | 1.12200i | ||||||||
\(566\) | 463.000 | − | 801.940i | 0.818021 | − | 1.41685i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −121.000 | −0.212654 | −0.106327 | − | 0.994331i | \(-0.533909\pi\) | ||||
−0.106327 | + | 0.994331i | \(0.533909\pi\) | |||||||
\(570\) | −63.0000 | − | 36.3731i | −0.110526 | − | 0.0638124i | ||||
\(571\) | 737.000 | 1.29072 | 0.645359 | − | 0.763879i | \(-0.276708\pi\) | ||||
0.645359 | + | 0.763879i | \(0.276708\pi\) | |||||||
\(572\) | 816.000 | − | 471.118i | 1.42657 | − | 0.823633i | ||||
\(573\) | 216.506i | 0.377847i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.3923i | − | 0.0180736i | ||||||
\(576\) | −512.000 | −0.888889 | ||||||||
\(577\) | −47.0000 | −0.0814558 | −0.0407279 | − | 0.999170i | \(-0.512968\pi\) | ||||
−0.0407279 | + | 0.999170i | \(0.512968\pi\) | |||||||
\(578\) | 336.000 | − | 581.969i | 0.581315 | − | 1.00687i | ||||
\(579\) | 73.0000 | 0.126079 | ||||||||
\(580\) | 144.000 | + | 249.415i | 0.248276 | + | 0.430026i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.0000 | + | 38.1051i | −0.0378007 | + | 0.0654727i | ||||
\(583\) | − | 1560.58i | − | 2.67681i | ||||||
\(584\) | 952.000 | 1.63014 | ||||||||
\(585\) | 576.000 | 0.984615 | ||||||||
\(586\) | −192.000 | − | 110.851i | −0.327645 | − | 0.189166i | ||||
\(587\) | −446.000 | −0.759796 | −0.379898 | − | 0.925028i | \(-0.624041\pi\) | ||||
−0.379898 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 230.363i | 0.391108i | ||||||||
\(590\) | 495.000 | + | 285.788i | 0.838983 | + | 0.484387i | ||||
\(591\) | − | 207.846i | − | 0.351685i | ||||||
\(592\) | −120.000 | − | 69.2820i | −0.202703 | − | 0.117030i | ||||
\(593\) | −215.000 | −0.362563 | −0.181282 | − | 0.983431i | \(-0.558025\pi\) | ||||
−0.181282 | + | 0.983431i | \(0.558025\pi\) | |||||||
\(594\) | 289.000 | − | 500.563i | 0.486532 | − | 0.842698i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | + | 10.3923i | −0.0302013 | + | 0.0174368i | ||||
\(597\) | 64.0859i | 0.107347i | ||||||||
\(598\) | −72.0000 | + | 124.708i | −0.120401 | + | 0.208541i | ||||
\(599\) | − | 282.324i | − | 0.471326i | −0.971835 | − | 0.235663i | \(-0.924274\pi\) | ||
0.971835 | − | 0.235663i | \(-0.0757262\pi\) | |||||||
\(600\) | −16.0000 | −0.0266667 | ||||||||
\(601\) | −266.000 | −0.442596 | −0.221298 | − | 0.975206i | \(-0.571029\pi\) | ||||
−0.221298 | + | 0.975206i | \(0.571029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −136.000 | −0.225539 | ||||||||
\(604\) | 126.000 | − | 72.7461i | 0.208609 | − | 0.120441i | ||||
\(605\) | 872.954i | 1.44290i | ||||||||
\(606\) | −135.000 | − | 77.9423i | −0.222772 | − | 0.128618i | ||||
\(607\) | 659.911i | 1.08717i | 0.839355 | + | 0.543584i | \(0.182933\pi\) | ||||
−0.839355 | + | 0.543584i | \(0.817067\pi\) | |||||||
\(608\) | 112.000 | + | 193.990i | 0.184211 | + | 0.319062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 117.000 | − | 202.650i | 0.191803 | − | 0.332213i | ||||
\(611\) | −696.000 | −1.13912 | ||||||||
\(612\) | 400.000 | + | 692.820i | 0.653595 | + | 1.13206i | ||||
\(613\) | 698.016i | 1.13869i | 0.822099 | + | 0.569345i | \(0.192803\pi\) | ||||
−0.822099 | + | 0.569345i | \(0.807197\pi\) | |||||||
\(614\) | 274.000 | − | 474.582i | 0.446254 | − | 0.772935i | ||||
\(615\) | 135.100i | 0.219675i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −118.000 | −0.191248 | −0.0956240 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956240 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(618\) | −279.000 | − | 161.081i | −0.451456 | − | 0.260648i | ||||
\(619\) | 919.000 | 1.48465 | 0.742326 | − | 0.670039i | \(-0.233722\pi\) | ||||
0.742326 | + | 0.670039i | \(0.233722\pi\) | |||||||
\(620\) | 342.000 | + | 592.361i | 0.551613 | + | 0.955422i | ||||
\(621\) | 88.3346i | 0.142246i | ||||||||
\(622\) | −87.0000 | − | 50.2295i | −0.139871 | − | 0.0807548i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 192.000 | + | 110.851i | 0.307692 | + | 0.177646i | ||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | 409.000 | − | 708.409i | 0.653355 | − | 1.13164i | ||||
\(627\) | −119.000 | −0.189793 | ||||||||
\(628\) | −1074.00 | + | 620.074i | −1.71019 | + | 0.987379i | ||||
\(629\) | 216.506i | 0.344207i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 166.277i | − | 0.263513i | −0.991282 | − | 0.131757i | \(-0.957938\pi\) | ||
0.991282 | − | 0.131757i | \(-0.0420617\pi\) | |||||||
\(632\) | − | 595.825i | − | 0.942762i | ||||||
\(633\) | −302.000 | −0.477093 | ||||||||
\(634\) | 327.000 | + | 188.794i | 0.515773 | + | 0.297782i | ||||
\(635\) | 864.000 | 1.36063 | ||||||||
\(636\) | 318.000 | − | 183.597i | 0.500000 | − | 0.288675i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 408.000 | + | 235.559i | 0.639498 | + | 0.369215i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 576.000 | + | 332.554i | 0.900000 | + | 0.519615i | ||||
\(641\) | −1.00000 | −0.00156006 | −0.000780031 | − | 1.00000i | \(-0.500248\pi\) | ||||
−0.000780031 | 1.00000i | \(0.500248\pi\) | ||||||||
\(642\) | −65.0000 | + | 112.583i | −0.101246 | + | 0.175363i | ||||
\(643\) | 514.000 | 0.799378 | 0.399689 | − | 0.916651i | \(-0.369118\pi\) | ||||
0.399689 | + | 0.916651i | \(0.369118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 72.7461i | − | 0.112785i | ||||||
\(646\) | 175.000 | − | 303.109i | 0.270898 | − | 0.469209i | ||||
\(647\) | 60.6218i | 0.0936967i | 0.998902 | + | 0.0468484i | \(0.0149178\pi\) | ||||
−0.998902 | + | 0.0468484i | \(0.985082\pi\) | |||||||
\(648\) | −440.000 | −0.679012 | ||||||||
\(649\) | 935.000 | 1.44068 | ||||||||
\(650\) | −48.0000 | − | 27.7128i | −0.0738462 | − | 0.0426351i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −34.0000 | − | 58.8897i | −0.0521472 | − | 0.0903217i | ||||
\(653\) | 327.358i | 0.501313i | 0.968076 | + | 0.250657i | \(0.0806465\pi\) | ||||
−0.968076 | + | 0.250657i | \(0.919353\pi\) | |||||||
\(654\) | 15.0000 | + | 8.66025i | 0.0229358 | + | 0.0132420i | ||||
\(655\) | − | 88.3346i | − | 0.134862i | ||||||
\(656\) | 208.000 | − | 360.267i | 0.317073 | − | 0.549187i | ||||
\(657\) | 952.000 | 1.44901 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 542.000 | 0.822458 | 0.411229 | − | 0.911532i | \(-0.365100\pi\) | ||||
0.411229 | + | 0.911532i | \(0.365100\pi\) | |||||||
\(660\) | −306.000 | + | 176.669i | −0.463636 | + | 0.267681i | ||||
\(661\) | − | 1182.99i | − | 1.78970i | −0.446368 | − | 0.894849i | \(-0.647283\pi\) | ||
0.446368 | − | 0.894849i | \(-0.352717\pi\) | |||||||
\(662\) | −295.000 | + | 510.955i | −0.445619 | + | 0.771835i | ||||
\(663\) | − | 346.410i | − | 0.522489i | ||||||
\(664\) | 880.000 | 1.32530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −120.000 | − | 69.2820i | −0.180180 | − | 0.104027i | ||||
\(667\) | −72.0000 | −0.107946 | ||||||||
\(668\) | 48.0000 | − | 27.7128i | 0.0718563 | − | 0.0414862i | ||||
\(669\) | 138.564i | 0.207121i | ||||||||
\(670\) | 153.000 | + | 88.3346i | 0.228358 | + | 0.131843i | ||||
\(671\) | − | 382.783i | − | 0.570467i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 218.000 | 0.323923 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(674\) | 26.0000 | − | 45.0333i | 0.0385757 | − | 0.0668150i | ||||
\(675\) | −34.0000 | −0.0503704 | ||||||||
\(676\) | 46.0000 | + | 79.6743i | 0.0680473 | + | 0.117861i | ||||
\(677\) | 642.591i | 0.949174i | 0.880209 | + | 0.474587i | \(0.157403\pi\) | ||||
−0.880209 | + | 0.474587i | \(0.842597\pi\) | |||||||
\(678\) | −122.000 | + | 211.310i | −0.179941 | + | 0.311667i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 1039.23i | − | 1.52828i | ||||||
\(681\) | −55.0000 | −0.0807636 | ||||||||
\(682\) | 969.000 | + | 559.452i | 1.42082 | + | 0.820311i | ||||
\(683\) | −367.000 | −0.537335 | −0.268668 | − | 0.963233i | \(-0.586583\pi\) | ||||
−0.268668 | + | 0.963233i | \(0.586583\pi\) | |||||||
\(684\) | 112.000 | + | 193.990i | 0.163743 | + | 0.283611i | ||||
\(685\) | − | 753.442i | − | 1.09992i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 327.358i | 0.476503i | ||||||||
\(688\) | −112.000 | + | 193.990i | −0.162791 | + | 0.281962i | ||||
\(689\) | 1272.00 | 1.84615 | ||||||||
\(690\) | 27.0000 | − | 46.7654i | 0.0391304 | − | 0.0677759i | ||||
\(691\) | −497.000 | −0.719247 | −0.359624 | − | 0.933097i | \(-0.617095\pi\) | ||||
−0.359624 | + | 0.933097i | \(0.617095\pi\) | |||||||
\(692\) | −366.000 | + | 211.310i | −0.528902 | + | 0.305362i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 377.000 | − | 652.983i | 0.543228 | − | 0.940898i | ||||
\(695\) | 426.084i | 0.613071i | ||||||||
\(696\) | 110.851i | 0.159269i | ||||||||
\(697\) | −650.000 | −0.932568 | ||||||||
\(698\) | −168.000 | − | 96.9948i | −0.240688 | − | 0.138961i | ||||
\(699\) | 385.000 | 0.550787 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 332.554i | − | 0.474399i | −0.971461 | − | 0.237200i | \(-0.923770\pi\) | ||
0.971461 | − | 0.237200i | \(-0.0762295\pi\) | |||||||
\(702\) | 408.000 | + | 235.559i | 0.581197 | + | 0.335554i | ||||
\(703\) | 60.6218i | 0.0862330i | ||||||||
\(704\) | 1088.00 | 1.54545 | ||||||||
\(705\) | 261.000 | 0.370213 | ||||||||
\(706\) | −503.000 | + | 871.222i | −0.712465 | + | 1.23402i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 110.000 | + | 190.526i | 0.155367 | + | 0.269104i | ||||
\(709\) | 396.640i | 0.559435i | 0.960082 | + | 0.279718i | \(0.0902409\pi\) | ||||
−0.960082 | + | 0.279718i | \(0.909759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 595.825i | − | 0.838011i | ||||||
\(712\) | 568.000 | 0.797753 | ||||||||
\(713\) | −171.000 | −0.239832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1224.00 | −1.71189 | ||||||||
\(716\) | −178.000 | − | 308.305i | −0.248603 | − | 0.430594i | ||||
\(717\) | 429.549i | 0.599091i | ||||||||
\(718\) | 321.000 | + | 185.329i | 0.447075 | + | 0.258119i | ||||
\(719\) | 64.0859i | 0.0891320i | 0.999006 | + | 0.0445660i | \(0.0141905\pi\) | ||||
−0.999006 | + | 0.0445660i | \(0.985810\pi\) | |||||||
\(720\) | 576.000 | + | 332.554i | 0.800000 | + | 0.461880i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −312.000 | + | 540.400i | −0.432133 | + | 0.748476i | ||||
\(723\) | −145.000 | −0.200553 | ||||||||
\(724\) | −864.000 | + | 498.831i | −1.19337 | + | 0.688993i | ||||
\(725\) | − | 27.7128i | − | 0.0382246i | ||||||
\(726\) | −168.000 | + | 290.985i | −0.231405 | + | 0.400805i | ||||
\(727\) | − | 55.4256i | − | 0.0762388i | −0.999273 | − | 0.0381194i | \(-0.987863\pi\) | ||
0.999273 | − | 0.0381194i | \(-0.0121367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −287.000 | −0.393690 | ||||||||
\(730\) | −1071.00 | − | 618.342i | −1.46712 | − | 0.847044i | ||||
\(731\) | 350.000 | 0.478796 | ||||||||
\(732\) | 78.0000 | − | 45.0333i | 0.106557 | − | 0.0615209i | ||||
\(733\) | − | 826.188i | − | 1.12713i | −0.826071 | − | 0.563566i | \(-0.809429\pi\) | ||
0.826071 | − | 0.563566i | \(-0.190571\pi\) | |||||||
\(734\) | 513.000 | + | 296.181i | 0.698910 | + | 0.403516i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −144.000 | + | 83.1384i | −0.195652 | + | 0.112960i | ||||
\(737\) | 289.000 | 0.392130 | ||||||||
\(738\) | 208.000 | − | 360.267i | 0.281843 | − | 0.488166i | ||||
\(739\) | 713.000 | 0.964817 | 0.482409 | − | 0.875946i | \(-0.339762\pi\) | ||||
0.482409 | + | 0.875946i | \(0.339762\pi\) | |||||||
\(740\) | 90.0000 | + | 155.885i | 0.121622 | + | 0.210655i | ||||
\(741\) | − | 96.9948i | − | 0.130897i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 637.395i | − | 0.857866i | −0.903336 | − | 0.428933i | \(-0.858890\pi\) | ||
0.903336 | − | 0.428933i | \(-0.141110\pi\) | |||||||
\(744\) | 263.272i | 0.353860i | ||||||||
\(745\) | 27.0000 | 0.0362416 | ||||||||
\(746\) | 207.000 | + | 119.512i | 0.277480 | + | 0.160203i | ||||
\(747\) | 880.000 | 1.17805 | ||||||||
\(748\) | −850.000 | − | 1472.24i | −1.13636 | − | 1.96824i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −207.000 | − | 119.512i | −0.276000 | − | 0.159349i | ||||
\(751\) | 1169.13i | 1.55677i | 0.627787 | + | 0.778385i | \(0.283961\pi\) | ||||
−0.627787 | + | 0.778385i | \(0.716039\pi\) | |||||||
\(752\) | −696.000 | − | 401.836i | −0.925532 | − | 0.534356i | ||||
\(753\) | −58.0000 | −0.0770252 | ||||||||
\(754\) | −192.000 | + | 332.554i | −0.254642 | + | 0.441053i | ||||
\(755\) | −189.000 | −0.250331 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1039.23i | − | 1.37283i | −0.727211 | − | 0.686414i | \(-0.759184\pi\) | ||
0.727211 | − | 0.686414i | \(-0.240816\pi\) | |||||||
\(758\) | −634.000 | + | 1098.12i | −0.836412 | + | 1.44871i | ||||
\(759\) | − | 88.3346i | − | 0.116383i | ||||||
\(760\) | − | 290.985i | − | 0.382874i | ||||||
\(761\) | −863.000 | −1.13403 | −0.567017 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567017 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(762\) | 288.000 | + | 166.277i | 0.377953 | + | 0.218211i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −750.000 | + | 433.013i | −0.981675 | + | 0.566771i | ||||
\(765\) | − | 1039.23i | − | 1.35847i | ||||||
\(766\) | 423.000 | + | 244.219i | 0.552219 | + | 0.318824i | ||||
\(767\) | 762.102i | 0.993615i | ||||||||
\(768\) | 128.000 | + | 221.703i | 0.166667 | + | 0.288675i | ||||
\(769\) | −410.000 | −0.533160 | −0.266580 | − | 0.963813i | \(-0.585894\pi\) | ||||
−0.266580 | + | 0.963813i | \(0.585894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 119.000 | 0.154345 | ||||||||
\(772\) | 146.000 | + | 252.879i | 0.189119 | + | 0.327564i | ||||
\(773\) | 798.475i | 1.03296i | 0.856300 | + | 0.516478i | \(0.172757\pi\) | ||||
−0.856300 | + | 0.516478i | \(0.827243\pi\) | |||||||
\(774\) | −112.000 | + | 193.990i | −0.144703 | + | 0.250633i | ||||
\(775\) | − | 65.8179i | − | 0.0849264i | ||||||
\(776\) | −176.000 | −0.226804 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1017.00 | + | 587.165i | 1.30720 | + | 0.754711i | ||||
\(779\) | −182.000 | −0.233633 | ||||||||
\(780\) | −144.000 | − | 249.415i | −0.184615 | − | 0.319763i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 225.000 | + | 129.904i | 0.287724 | + | 0.166117i | ||||
\(783\) | 235.559i | 0.300842i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1611.00 | 2.05223 | ||||||||
\(786\) | 17.0000 | − | 29.4449i | 0.0216285 | − | 0.0374617i | ||||
\(787\) | 31.0000 | 0.0393901 | 0.0196950 | − | 0.999806i | \(-0.493730\pi\) | ||||
0.0196950 | + | 0.999806i | \(0.493730\pi\) | |||||||
\(788\) | 720.000 | − | 415.692i | 0.913706 | − | 0.527528i | ||||
\(789\) | − | 327.358i | − | 0.414902i | ||||||
\(790\) | −387.000 | + | 670.304i | −0.489873 | + | 0.848486i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1088.00 | 1.37374 | ||||||||
\(793\) | 312.000 | 0.393443 | ||||||||
\(794\) | 417.000 | + | 240.755i | 0.525189 | + | 0.303218i | ||||
\(795\) | −477.000 | −0.600000 | ||||||||
\(796\) | −222.000 | + | 128.172i | −0.278894 | + | 0.161020i | ||||
\(797\) | 595.825i | 0.747585i | 0.927512 | + | 0.373793i | \(0.121943\pi\) | ||||
−0.927512 | + | 0.373793i | \(0.878057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1255.74i | 1.57164i | ||||||||
\(800\) | −32.0000 | − | 55.4256i | −0.0400000 | − | 0.0692820i | ||||
\(801\) | 568.000 | 0.709114 | ||||||||
\(802\) | 119.000 | − | 206.114i | 0.148379 | − | 0.257000i | ||||
\(803\) | −2023.00 | −2.51930 | ||||||||
\(804\) | 34.0000 | + | 58.8897i | 0.0422886 | + | 0.0732459i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −456.000 | + | 789.815i | −0.565757 | + | 0.979920i | ||||
\(807\) | − | 133.368i | − | 0.165264i | ||||||
\(808\) | − | 623.538i | − | 0.771706i | ||||||
\(809\) | −313.000 | −0.386897 | −0.193449 | − | 0.981110i | \(-0.561967\pi\) | ||||
−0.193449 | + | 0.981110i | \(0.561967\pi\) | |||||||
\(810\) | 495.000 | + | 285.788i | 0.611111 | + | 0.352825i | ||||
\(811\) | 1138.00 | 1.40321 | 0.701603 | − | 0.712568i | \(-0.252468\pi\) | ||||
0.701603 | + | 0.712568i | \(0.252468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 434.745i | 0.534741i | ||||||||
\(814\) | 255.000 | + | 147.224i | 0.313268 | + | 0.180865i | ||||
\(815\) | 88.3346i | 0.108386i | ||||||||
\(816\) | 200.000 | − | 346.410i | 0.245098 | − | 0.424522i | ||||
\(817\) | 98.0000 | 0.119951 | ||||||||
\(818\) | 145.000 | − | 251.147i | 0.177262 | − | 0.307026i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −468.000 | + | 270.200i | −0.570732 | + | 0.329512i | ||||
\(821\) | − | 1224.56i | − | 1.49155i | −0.666200 | − | 0.745773i | \(-0.732080\pi\) | ||
0.666200 | − | 0.745773i | \(-0.267920\pi\) | |||||||
\(822\) | 145.000 | − | 251.147i | 0.176399 | − | 0.305532i | ||||
\(823\) | − | 116.047i | − | 0.141005i | −0.997512 | − | 0.0705027i | \(-0.977540\pi\) | ||
0.997512 | − | 0.0705027i | \(-0.0224603\pi\) | |||||||
\(824\) | − | 1288.65i | − | 1.56389i | ||||||
\(825\) | 34.0000 | 0.0412121 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −754.000 | −0.911729 | −0.455865 | − | 0.890049i | \(-0.650670\pi\) | ||||
−0.455865 | + | 0.890049i | \(0.650670\pi\) | |||||||
\(828\) | −144.000 | + | 83.1384i | −0.173913 | + | 0.100409i | ||||
\(829\) | − | 905.863i | − | 1.09272i | −0.837551 | − | 0.546359i | \(-0.816014\pi\) | ||
0.837551 | − | 0.546359i | \(-0.183986\pi\) | |||||||
\(830\) | −990.000 | − | 571.577i | −1.19277 | − | 0.688647i | ||||
\(831\) | 202.650i | 0.243863i | ||||||||
\(832\) | 886.810i | 1.06588i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −82.0000 | + | 142.028i | −0.0983213 | + | 0.170298i | ||||
\(835\) | −72.0000 | −0.0862275 | ||||||||
\(836\) | −238.000 | − | 412.228i | −0.284689 | − | 0.493096i | ||||
\(837\) | 559.452i | 0.668402i | ||||||||
\(838\) | −302.000 | + | 523.079i | −0.360382 | + | 0.624200i | ||||
\(839\) | − | 1053.09i | − | 1.25517i | −0.778548 | − | 0.627585i | \(-0.784044\pi\) | ||
0.778548 | − | 0.627585i | \(-0.215956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 649.000 | 0.771700 | ||||||||
\(842\) | −696.000 | − | 401.836i | −0.826603 | − | 0.477240i | ||||
\(843\) | −74.0000 | −0.0877817 | ||||||||
\(844\) | −604.000 | − | 1046.16i | −0.715640 | − | 1.23952i | ||||
\(845\) | − | 119.512i | − | 0.141434i | ||||||
\(846\) | −696.000 | − | 401.836i | −0.822695 | − | 0.474983i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1272.00 | + | 734.390i | 1.50000 | + | 0.866025i | ||||
\(849\) | −463.000 | −0.545347 | ||||||||
\(850\) | −50.0000 | + | 86.6025i | −0.0588235 | + | 0.101885i | ||||
\(851\) | −45.0000 | −0.0528790 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 845.241i | − | 0.990904i | −0.868635 | − | 0.495452i | \(-0.835003\pi\) | ||
0.868635 | − | 0.495452i | \(-0.164997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 290.985i | − | 0.340333i | ||||||
\(856\) | −520.000 | −0.607477 | ||||||||
\(857\) | −887.000 | −1.03501 | −0.517503 | − | 0.855681i | \(-0.673138\pi\) | ||||
−0.517503 | + | 0.855681i | \(0.673138\pi\) | |||||||
\(858\) | −408.000 | − | 235.559i | −0.475524 | − | 0.274544i | ||||
\(859\) | 1663.00 | 1.93597 | 0.967986 | − | 0.251004i | \(-0.0807608\pi\) | ||||
0.967986 | + | 0.251004i | \(0.0807608\pi\) | |||||||
\(860\) | 252.000 | − | 145.492i | 0.293023 | − | 0.169177i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1401.00 | − | 808.868i | −1.62529 | − | 0.938362i | ||||
\(863\) | − | 562.917i | − | 0.652279i | −0.945322 | − | 0.326139i | \(-0.894252\pi\) | ||
0.945322 | − | 0.326139i | \(-0.105748\pi\) | |||||||
\(864\) | 272.000 | + | 471.118i | 0.314815 | + | 0.545275i | ||||
\(865\) | 549.000 | 0.634682 | ||||||||
\(866\) | −410.000 | + | 710.141i | −0.473441 | + | 0.820024i | ||||
\(867\) | −336.000 | −0.387543 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1266.13i | 1.45700i | ||||||||
\(870\) | 72.0000 | − | 124.708i | 0.0827586 | − | 0.143342i | ||||
\(871\) | 235.559i | 0.270447i | ||||||||
\(872\) | 69.2820i | 0.0794519i | ||||||||
\(873\) | −176.000 | −0.201604 | ||||||||
\(874\) | 63.0000 | + | 36.3731i | 0.0720824 | + | 0.0416168i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −238.000 | − | 412.228i | −0.271689 | − | 0.470580i | ||||
\(877\) | 119.512i | 0.136273i | 0.997676 | + | 0.0681365i | \(0.0217054\pi\) | ||||
−0.997676 | + | 0.0681365i | \(0.978295\pi\) | |||||||
\(878\) | −849.000 | − | 490.170i | −0.966970 | − | 0.558281i | ||||
\(879\) | 110.851i | 0.126111i | ||||||||
\(880\) | −1224.00 | − | 706.677i | −1.39091 | − | 0.803042i | ||||
\(881\) | 574.000 | 0.651532 | 0.325766 | − | 0.945450i | \(-0.394378\pi\) | ||||
0.325766 | + | 0.945450i | \(0.394378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1166.00 | 1.32050 | 0.660249 | − | 0.751047i | \(-0.270451\pi\) | ||||
0.660249 | + | 0.751047i | \(0.270451\pi\) | |||||||
\(884\) | 1200.00 | − | 692.820i | 1.35747 | − | 0.783733i | ||||
\(885\) | − | 285.788i | − | 0.322925i | ||||||
\(886\) | 401.000 | − | 694.552i | 0.452596 | − | 0.783919i | ||||
\(887\) | − | 545.596i | − | 0.615103i | −0.951532 | − | 0.307551i | \(-0.900490\pi\) | ||
0.951532 | − | 0.307551i | \(-0.0995096\pi\) | |||||||
\(888\) | 69.2820i | 0.0780203i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −639.000 | − | 368.927i | −0.717978 | − | 0.414525i | ||||
\(891\) | 935.000 | 1.04938 | ||||||||
\(892\) | −480.000 | + | 277.128i | −0.538117 | + | 0.310682i | ||||
\(893\) | 351.606i | 0.393736i | ||||||||
\(894\) | 9.00000 | + | 5.19615i | 0.0100671 | + | 0.00581225i | ||||
\(895\) | 462.458i | 0.516712i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 72.0000 | 0.0802676 | ||||||||
\(898\) | −310.000 | + | 536.936i | −0.345212 | + | 0.597924i | ||||
\(899\) | −456.000 | −0.507230 | ||||||||
\(900\) | −32.0000 | − | 55.4256i | −0.0355556 | − | 0.0615840i | ||||
\(901\) | − | 2294.97i | − | 2.54713i | ||||||
\(902\) | −442.000 | + | 765.566i | −0.490022 | + | 0.848743i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −976.000 | −1.07965 | ||||||||
\(905\) | 1296.00 | 1.43204 | ||||||||
\(906\) | −63.0000 | − | 36.3731i | −0.0695364 | − | 0.0401469i | ||||
\(907\) | 521.000 | 0.574421 | 0.287211 | − | 0.957867i | \(-0.407272\pi\) | ||||
0.287211 | + | 0.957867i | \(0.407272\pi\) | |||||||
\(908\) | −110.000 | − | 190.526i | −0.121145 | − | 0.209830i | ||||
\(909\) | − | 623.538i | − | 0.685961i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1191.65i | − | 1.30807i | −0.756465 | − | 0.654035i | \(-0.773075\pi\) | ||
0.756465 | − | 0.654035i | \(-0.226925\pi\) | |||||||
\(912\) | 56.0000 | − | 96.9948i | 0.0614035 | − | 0.106354i | ||||
\(913\) | −1870.00 | −2.04819 | ||||||||
\(914\) | 167.000 | − | 289.252i | 0.182713 | − | 0.316469i | ||||
\(915\) | −117.000 | −0.127869 | ||||||||
\(916\) | −1134.00 | + | 654.715i | −1.23799 | + | 0.714755i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 425.000 | − | 736.122i | 0.462963 | − | 0.801875i | ||||
\(919\) | − | 1394.30i | − | 1.51719i | −0.651560 | − | 0.758597i | \(-0.725885\pi\) | ||
0.651560 | − | 0.758597i | \(-0.274115\pi\) | |||||||
\(920\) | 216.000 | 0.234783 | ||||||||
\(921\) | −274.000 | −0.297503 | ||||||||
\(922\) | −24.0000 | − | 13.8564i | −0.0260304 | − | 0.0150286i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 17.3205i | − | 0.0187249i | ||||||
\(926\) | 1056.00 | + | 609.682i | 1.14039 | + | 0.658404i | ||||
\(927\) | − | 1288.65i | − | 1.39012i | ||||||
\(928\) | −384.000 | + | 221.703i | −0.413793 | + | 0.238904i | ||||
\(929\) | 961.000 | 1.03445 | 0.517223 | − | 0.855851i | \(-0.326966\pi\) | ||||
0.517223 | + | 0.855851i | \(0.326966\pi\) | |||||||
\(930\) | 171.000 | − | 296.181i | 0.183871 | − | 0.318474i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 770.000 | + | 1333.68i | 0.826180 | + | 1.43099i | ||||
\(933\) | 50.2295i | 0.0538365i | ||||||||
\(934\) | −785.000 | + | 1359.66i | −0.840471 | + | 1.45574i | ||||
\(935\) | 2208.36i | 2.36189i | ||||||||
\(936\) | 886.810i | 0.947447i | ||||||||
\(937\) | 142.000 | 0.151547 | 0.0757737 | − | 0.997125i | \(-0.475857\pi\) | ||||
0.0757737 | + | 0.997125i | \(0.475857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −409.000 | −0.435570 | ||||||||
\(940\) | 522.000 | + | 904.131i | 0.555319 | + | 0.961841i | ||||
\(941\) | − | 1224.56i | − | 1.30134i | −0.759361 | − | 0.650669i | \(-0.774488\pi\) | ||
0.759361 | − | 0.650669i | \(-0.225512\pi\) | |||||||
\(942\) | 537.000 | + | 310.037i | 0.570064 | + | 0.329126i | ||||
\(943\) | − | 135.100i | − | 0.143266i | ||||||
\(944\) | −440.000 | + | 762.102i | −0.466102 | + | 0.807312i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 238.000 | − | 412.228i | 0.251586 | − | 0.435759i | ||||
\(947\) | −175.000 | −0.184794 | −0.0923970 | − | 0.995722i | \(-0.529453\pi\) | ||||
−0.0923970 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(948\) | −258.000 | + | 148.956i | −0.272152 | + | 0.157127i | ||||
\(949\) | − | 1648.91i | − | 1.73753i | ||||||
\(950\) | −14.0000 | + | 24.2487i | −0.0147368 | + | 0.0255250i | ||||
\(951\) | − | 188.794i | − | 0.198521i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −454.000 | −0.476390 | −0.238195 | − | 0.971217i | \(-0.576556\pi\) | ||||
−0.238195 | + | 0.971217i | \(0.576556\pi\) | |||||||
\(954\) | 1272.00 | + | 734.390i | 1.33333 | + | 0.769800i | ||||
\(955\) | 1125.00 | 1.17801 | ||||||||
\(956\) | −1488.00 | + | 859.097i | −1.55649 | + | 0.898637i | ||||
\(957\) | − | 235.559i | − | 0.246143i | ||||||
\(958\) | −1071.00 | − | 618.342i | −1.11795 | − | 0.645451i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 332.554i | − | 0.346410i | ||||||
\(961\) | −122.000 | −0.126951 | ||||||||
\(962\) | −120.000 | + | 207.846i | −0.124740 | + | 0.216056i | ||||
\(963\) | −520.000 | −0.539979 | ||||||||
\(964\) | −290.000 | − | 502.295i | −0.300830 | − | 0.521053i | ||||
\(965\) | − | 379.319i | − | 0.393077i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 720.533i | − | 0.745122i | −0.928008 | − | 0.372561i | \(-0.878480\pi\) | ||
0.928008 | − | 0.372561i | \(-0.121520\pi\) | |||||||
\(968\) | −1344.00 | −1.38843 | ||||||||
\(969\) | −175.000 | −0.180599 | ||||||||
\(970\) | 198.000 | + | 114.315i | 0.204124 | + | 0.117851i | ||||
\(971\) | 1639.00 | 1.68795 | 0.843975 | − | 0.536382i | \(-0.180209\pi\) | ||||
0.843975 | + | 0.536382i | \(0.180209\pi\) | |||||||
\(972\) | 416.000 | + | 720.533i | 0.427984 | + | 0.741289i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −681.000 | − | 393.176i | −0.699179 | − | 0.403671i | ||||
\(975\) | 27.7128i | 0.0284234i | ||||||||
\(976\) | 312.000 | + | 180.133i | 0.319672 | + | 0.184563i | ||||
\(977\) | −793.000 | −0.811668 | −0.405834 | − | 0.913947i | \(-0.633019\pi\) | ||||
−0.405834 | + | 0.913947i | \(0.633019\pi\) | |||||||
\(978\) | −17.0000 | + | 29.4449i | −0.0173824 | + | 0.0301072i | ||||
\(979\) | −1207.00 | −1.23289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 69.2820i | 0.0706239i | ||||||||
\(982\) | 422.000 | − | 730.925i | 0.429735 | − | 0.744323i | ||||
\(983\) | 1543.26i | 1.56995i | 0.619530 | + | 0.784973i | \(0.287323\pi\) | ||||
−0.619530 | + | 0.784973i | \(0.712677\pi\) | |||||||
\(984\) | −208.000 | −0.211382 | ||||||||
\(985\) | −1080.00 | −1.09645 | ||||||||
\(986\) | 600.000 | + | 346.410i | 0.608519 | + | 0.351329i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 336.000 | − | 193.990i | 0.340081 | − | 0.196346i | ||||
\(989\) | 72.7461i | 0.0735552i | ||||||||
\(990\) | −1224.00 | − | 706.677i | −1.23636 | − | 0.713815i | ||||
\(991\) | 895.470i | 0.903603i | 0.892119 | + | 0.451801i | \(0.149218\pi\) | ||||
−0.892119 | + | 0.451801i | \(0.850782\pi\) | |||||||
\(992\) | −912.000 | + | 526.543i | −0.919355 | + | 0.530790i | ||||
\(993\) | 295.000 | 0.297080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 333.000 | 0.334673 | ||||||||
\(996\) | −220.000 | − | 381.051i | −0.220884 | − | 0.382582i | ||||
\(997\) | − | 795.011i | − | 0.797404i | −0.917081 | − | 0.398702i | \(-0.869461\pi\) | ||
0.917081 | − | 0.398702i | \(-0.130539\pi\) | |||||||
\(998\) | 65.0000 | − | 112.583i | 0.0651303 | − | 0.112809i | ||||
\(999\) | 147.224i | 0.147372i |
(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 | 392.3.g.d.99.1 | 2 | ||
4.3 | odd | 2 | 1568.3.g.f.687.2 | 2 | |||
7.2 | even | 3 | 392.3.k.a.67.1 | 2 | |||
7.3 | odd | 6 | 56.3.k.b.51.1 | yes | 2 | ||
7.4 | even | 3 | 392.3.k.c.275.1 | 2 | |||
7.5 | odd | 6 | 56.3.k.a.11.1 | ✓ | 2 | ||
7.6 | odd | 2 | 392.3.g.e.99.1 | 2 | |||
8.3 | odd | 2 | inner | 392.3.g.d.99.2 | 2 | ||
8.5 | even | 2 | 1568.3.g.f.687.1 | 2 | |||
28.3 | even | 6 | 224.3.o.b.79.1 | 2 | |||
28.19 | even | 6 | 224.3.o.a.207.1 | 2 | |||
28.27 | even | 2 | 1568.3.g.c.687.1 | 2 | |||
56.3 | even | 6 | 56.3.k.a.51.1 | yes | 2 | ||
56.5 | odd | 6 | 224.3.o.b.207.1 | 2 | |||
56.11 | odd | 6 | 392.3.k.a.275.1 | 2 | |||
56.13 | odd | 2 | 1568.3.g.c.687.2 | 2 | |||
56.19 | even | 6 | 56.3.k.b.11.1 | yes | 2 | ||
56.27 | even | 2 | 392.3.g.e.99.2 | 2 | |||
56.45 | odd | 6 | 224.3.o.a.79.1 | 2 | |||
56.51 | odd | 6 | 392.3.k.c.67.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.a.11.1 | ✓ | 2 | 7.5 | odd | 6 | ||
56.3.k.a.51.1 | yes | 2 | 56.3 | even | 6 | ||
56.3.k.b.11.1 | yes | 2 | 56.19 | even | 6 | ||
56.3.k.b.51.1 | yes | 2 | 7.3 | odd | 6 | ||
224.3.o.a.79.1 | 2 | 56.45 | odd | 6 | |||
224.3.o.a.207.1 | 2 | 28.19 | even | 6 | |||
224.3.o.b.79.1 | 2 | 28.3 | even | 6 | |||
224.3.o.b.207.1 | 2 | 56.5 | odd | 6 | |||
392.3.g.d.99.1 | 2 | 1.1 | even | 1 | trivial | ||
392.3.g.d.99.2 | 2 | 8.3 | odd | 2 | inner | ||
392.3.g.e.99.1 | 2 | 7.6 | odd | 2 | |||
392.3.g.e.99.2 | 2 | 56.27 | even | 2 | |||
392.3.k.a.67.1 | 2 | 7.2 | even | 3 | |||
392.3.k.a.275.1 | 2 | 56.11 | odd | 6 | |||
392.3.k.c.67.1 | 2 | 56.51 | odd | 6 | |||
392.3.k.c.275.1 | 2 | 7.4 | even | 3 | |||
1568.3.g.c.687.1 | 2 | 28.27 | even | 2 | |||
1568.3.g.c.687.2 | 2 | 56.13 | odd | 2 | |||
1568.3.g.f.687.1 | 2 | 8.5 | even | 2 | |||
1568.3.g.f.687.2 | 2 | 4.3 | odd | 2 |