Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6625,2,Mod(1,6625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6625 = 5^{3} \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6625.a (trivial) |
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: | yes |
Analytic conductor: | \(52.9008913391\) |
Analytic rank: | \(2\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
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: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.23607 | −0.356822 | ||||||||
\(13\) | −4.61803 | −1.28081 | −0.640406 | − | 0.768036i | \(-0.721234\pi\) | ||||
−0.640406 | + | 0.768036i | \(0.721234\pi\) | |||||||
\(14\) | −4.85410 | −1.29731 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −7.47214 | −1.81226 | −0.906130 | − | 0.423000i | \(-0.860977\pi\) | ||||
−0.906130 | + | 0.423000i | \(0.860977\pi\) | |||||||
\(18\) | 1.61803 | 0.381374 | ||||||||
\(19\) | −1.76393 | −0.404674 | −0.202337 | − | 0.979316i | \(-0.564854\pi\) | ||||
−0.202337 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | 1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.61803 | −1.17144 | −0.585721 | − | 0.810513i | \(-0.699188\pi\) | ||||
−0.585721 | + | 0.810513i | \(0.699188\pi\) | |||||||
\(24\) | 4.47214 | 0.912871 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.47214 | −1.46541 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.85410 | −0.350392 | ||||||||
\(29\) | −10.4721 | −1.94463 | −0.972313 | − | 0.233681i | \(-0.924923\pi\) | ||||
−0.972313 | + | 0.233681i | \(0.924923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.236068 | −0.0423991 | −0.0211995 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0211995 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.0902 | −2.07345 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 2.70820 | 0.445226 | 0.222613 | − | 0.974907i | \(-0.428541\pi\) | ||||
0.222613 | + | 0.974907i | \(0.428541\pi\) | |||||||
\(38\) | −2.85410 | −0.462996 | ||||||||
\(39\) | 9.23607 | 1.47895 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0902 | 1.57582 | 0.787910 | − | 0.615791i | \(-0.211163\pi\) | ||||
0.787910 | + | 0.615791i | \(0.211163\pi\) | |||||||
\(42\) | 9.70820 | 1.49801 | ||||||||
\(43\) | −4.23607 | −0.645994 | −0.322997 | − | 0.946400i | \(-0.604690\pi\) | ||||
−0.322997 | + | 0.946400i | \(0.604690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.09017 | −1.34027 | ||||||||
\(47\) | −6.76393 | −0.986621 | −0.493310 | − | 0.869853i | \(-0.664213\pi\) | ||||
−0.493310 | + | 0.869853i | \(0.664213\pi\) | |||||||
\(48\) | 9.70820 | 1.40126 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.9443 | 2.09262 | ||||||||
\(52\) | −2.85410 | −0.395793 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 6.47214 | 0.880746 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.70820 | 0.896421 | ||||||||
\(57\) | 3.52786 | 0.467277 | ||||||||
\(58\) | −16.9443 | −2.22489 | ||||||||
\(59\) | −1.09017 | −0.141928 | −0.0709640 | − | 0.997479i | \(-0.522608\pi\) | ||||
−0.0709640 | + | 0.997479i | \(0.522608\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8541 | 1.64580 | 0.822900 | − | 0.568187i | \(-0.192355\pi\) | ||||
0.822900 | + | 0.568187i | \(0.192355\pi\) | |||||||
\(62\) | −0.381966 | −0.0485097 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.85410 | −0.837362 | −0.418681 | − | 0.908133i | \(-0.637507\pi\) | ||||
−0.418681 | + | 0.908133i | \(0.637507\pi\) | |||||||
\(68\) | −4.61803 | −0.560019 | ||||||||
\(69\) | 11.2361 | 1.35266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.61803 | −0.785416 | −0.392708 | − | 0.919663i | \(-0.628462\pi\) | ||||
−0.392708 | + | 0.919663i | \(0.628462\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | −10.7639 | −1.25982 | −0.629911 | − | 0.776667i | \(-0.716909\pi\) | ||||
−0.629911 | + | 0.776667i | \(0.716909\pi\) | |||||||
\(74\) | 4.38197 | 0.509393 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.09017 | −0.125051 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 14.9443 | 1.69211 | ||||||||
\(79\) | −2.52786 | −0.284407 | −0.142203 | − | 0.989837i | \(-0.545419\pi\) | ||||
−0.142203 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 16.3262 | 1.80293 | ||||||||
\(83\) | 7.94427 | 0.871997 | 0.435999 | − | 0.899947i | \(-0.356395\pi\) | ||||
0.435999 | + | 0.899947i | \(0.356395\pi\) | |||||||
\(84\) | 3.70820 | 0.404598 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.85410 | −0.739097 | ||||||||
\(87\) | 20.9443 | 2.24546 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.61803 | −0.171511 | −0.0857556 | − | 0.996316i | \(-0.527330\pi\) | ||||
−0.0857556 | + | 0.996316i | \(0.527330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8541 | 1.45230 | ||||||||
\(92\) | −3.47214 | −0.361995 | ||||||||
\(93\) | 0.472136 | 0.0489582 | ||||||||
\(94\) | −10.9443 | −1.12882 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.76393 | 0.690341 | ||||||||
\(97\) | 4.56231 | 0.463232 | 0.231616 | − | 0.972807i | \(-0.425599\pi\) | ||||
0.231616 | + | 0.972807i | \(0.425599\pi\) | |||||||
\(98\) | 3.23607 | 0.326892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.618034 | 0.0614967 | 0.0307483 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307483 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(102\) | 24.1803 | 2.39421 | ||||||||
\(103\) | 0.618034 | 0.0608967 | 0.0304483 | − | 0.999536i | \(-0.490306\pi\) | ||||
0.0304483 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(104\) | 10.3262 | 1.01257 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.61803 | −0.157157 | ||||||||
\(107\) | 8.94427 | 0.864675 | 0.432338 | − | 0.901712i | \(-0.357689\pi\) | ||||
0.432338 | + | 0.901712i | \(0.357689\pi\) | |||||||
\(108\) | 2.47214 | 0.237881 | ||||||||
\(109\) | −13.7639 | −1.31835 | −0.659173 | − | 0.751992i | \(-0.729093\pi\) | ||||
−0.659173 | + | 0.751992i | \(0.729093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.41641 | −0.514103 | ||||||||
\(112\) | 14.5623 | 1.37601 | ||||||||
\(113\) | −14.6180 | −1.37515 | −0.687574 | − | 0.726114i | \(-0.741325\pi\) | ||||
−0.687574 | + | 0.726114i | \(0.741325\pi\) | |||||||
\(114\) | 5.70820 | 0.534622 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.47214 | −0.600923 | ||||||||
\(117\) | −4.61803 | −0.426937 | ||||||||
\(118\) | −1.76393 | −0.162383 | ||||||||
\(119\) | 22.4164 | 2.05491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 20.7984 | 1.88300 | ||||||||
\(123\) | −20.1803 | −1.81960 | ||||||||
\(124\) | −0.145898 | −0.0131020 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.85410 | −0.432438 | ||||||||
\(127\) | −21.2705 | −1.88745 | −0.943726 | − | 0.330728i | \(-0.892706\pi\) | ||||
−0.943726 | + | 0.330728i | \(0.892706\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 8.47214 | 0.745930 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8541 | −1.21044 | −0.605219 | − | 0.796059i | \(-0.706915\pi\) | ||||
−0.605219 | + | 0.796059i | \(0.706915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29180 | 0.458857 | ||||||||
\(134\) | −11.0902 | −0.958045 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.7082 | 1.43272 | ||||||||
\(137\) | −1.38197 | −0.118069 | −0.0590347 | − | 0.998256i | \(-0.518802\pi\) | ||||
−0.0590347 | + | 0.998256i | \(0.518802\pi\) | |||||||
\(138\) | 18.1803 | 1.54761 | ||||||||
\(139\) | −7.41641 | −0.629052 | −0.314526 | − | 0.949249i | \(-0.601845\pi\) | ||||
−0.314526 | + | 0.949249i | \(0.601845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.5279 | 1.13925 | ||||||||
\(142\) | −10.7082 | −0.898613 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.4164 | −1.44139 | ||||||||
\(147\) | −4.00000 | −0.329914 | ||||||||
\(148\) | 1.67376 | 0.137582 | ||||||||
\(149\) | 10.1803 | 0.834006 | 0.417003 | − | 0.908905i | \(-0.363080\pi\) | ||||
0.417003 | + | 0.908905i | \(0.363080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.00000 | 0.732410 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(152\) | 3.94427 | 0.319923 | ||||||||
\(153\) | −7.47214 | −0.604086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.70820 | 0.457022 | ||||||||
\(157\) | 15.1803 | 1.21152 | 0.605762 | − | 0.795646i | \(-0.292869\pi\) | ||||
0.605762 | + | 0.795646i | \(0.292869\pi\) | |||||||
\(158\) | −4.09017 | −0.325396 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.8541 | 1.32829 | ||||||||
\(162\) | −17.7984 | −1.39837 | ||||||||
\(163\) | 2.29180 | 0.179507 | 0.0897537 | − | 0.995964i | \(-0.471392\pi\) | ||||
0.0897537 | + | 0.995964i | \(0.471392\pi\) | |||||||
\(164\) | 6.23607 | 0.486955 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8541 | 0.997672 | ||||||||
\(167\) | 8.18034 | 0.633014 | 0.316507 | − | 0.948590i | \(-0.397490\pi\) | ||||
0.316507 | + | 0.948590i | \(0.397490\pi\) | |||||||
\(168\) | −13.4164 | −1.03510 | ||||||||
\(169\) | 8.32624 | 0.640480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.76393 | −0.134891 | ||||||||
\(172\) | −2.61803 | −0.199623 | ||||||||
\(173\) | −19.6180 | −1.49153 | −0.745766 | − | 0.666208i | \(-0.767916\pi\) | ||||
−0.745766 | + | 0.666208i | \(0.767916\pi\) | |||||||
\(174\) | 33.8885 | 2.56908 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.18034 | 0.163884 | ||||||||
\(178\) | −2.61803 | −0.196230 | ||||||||
\(179\) | 10.8885 | 0.813848 | 0.406924 | − | 0.913462i | \(-0.366601\pi\) | ||||
0.406924 | + | 0.913462i | \(0.366601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4721 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(182\) | 22.4164 | 1.66161 | ||||||||
\(183\) | −25.7082 | −1.90041 | ||||||||
\(184\) | 12.5623 | 0.926105 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.763932 | 0.0560142 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.18034 | −0.304883 | ||||||||
\(189\) | −12.0000 | −0.872872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.18034 | −0.519551 | −0.259776 | − | 0.965669i | \(-0.583649\pi\) | ||||
−0.259776 | + | 0.965669i | \(0.583649\pi\) | |||||||
\(192\) | −8.47214 | −0.611424 | ||||||||
\(193\) | 15.5623 | 1.12020 | 0.560100 | − | 0.828425i | \(-0.310763\pi\) | ||||
0.560100 | + | 0.828425i | \(0.310763\pi\) | |||||||
\(194\) | 7.38197 | 0.529994 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23607 | 0.0882906 | ||||||||
\(197\) | 23.4721 | 1.67232 | 0.836160 | − | 0.548485i | \(-0.184795\pi\) | ||||
0.836160 | + | 0.548485i | \(0.184795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.38197 | 0.168853 | 0.0844265 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844265 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.7082 | 0.966902 | ||||||||
\(202\) | 1.00000 | 0.0703598 | ||||||||
\(203\) | 31.4164 | 2.20500 | ||||||||
\(204\) | 9.23607 | 0.646654 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −5.61803 | −0.390480 | ||||||||
\(208\) | 22.4164 | 1.55430 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.41641 | −0.579409 | −0.289705 | − | 0.957116i | \(-0.593557\pi\) | ||||
−0.289705 | + | 0.957116i | \(0.593557\pi\) | |||||||
\(212\) | −0.618034 | −0.0424467 | ||||||||
\(213\) | 13.2361 | 0.906920 | ||||||||
\(214\) | 14.4721 | 0.989295 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.94427 | −0.608581 | ||||||||
\(217\) | 0.708204 | 0.0480760 | ||||||||
\(218\) | −22.2705 | −1.50835 | ||||||||
\(219\) | 21.5279 | 1.45472 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.5066 | 2.32116 | ||||||||
\(222\) | −8.76393 | −0.588197 | ||||||||
\(223\) | −2.05573 | −0.137662 | −0.0688309 | − | 0.997628i | \(-0.521927\pi\) | ||||
−0.0688309 | + | 0.997628i | \(0.521927\pi\) | |||||||
\(224\) | 10.1459 | 0.677901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.6525 | −1.57334 | ||||||||
\(227\) | 7.94427 | 0.527280 | 0.263640 | − | 0.964621i | \(-0.415077\pi\) | ||||
0.263640 | + | 0.964621i | \(0.415077\pi\) | |||||||
\(228\) | 2.18034 | 0.144397 | ||||||||
\(229\) | 11.8541 | 0.783341 | 0.391671 | − | 0.920106i | \(-0.371897\pi\) | ||||
0.391671 | + | 0.920106i | \(0.371897\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.4164 | 1.53736 | ||||||||
\(233\) | 4.23607 | 0.277514 | 0.138757 | − | 0.990326i | \(-0.455689\pi\) | ||||
0.138757 | + | 0.990326i | \(0.455689\pi\) | |||||||
\(234\) | −7.47214 | −0.488469 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.673762 | −0.0438582 | ||||||||
\(237\) | 5.05573 | 0.328405 | ||||||||
\(238\) | 36.2705 | 2.35107 | ||||||||
\(239\) | 28.0689 | 1.81563 | 0.907813 | − | 0.419376i | \(-0.137751\pi\) | ||||
0.907813 | + | 0.419376i | \(0.137751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.2705 | −1.69223 | −0.846116 | − | 0.532999i | \(-0.821065\pi\) | ||||
−0.846116 | + | 0.532999i | \(0.821065\pi\) | |||||||
\(242\) | −17.7984 | −1.14412 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 7.94427 | 0.508580 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −32.6525 | −2.08185 | ||||||||
\(247\) | 8.14590 | 0.518311 | ||||||||
\(248\) | 0.527864 | 0.0335194 | ||||||||
\(249\) | −15.8885 | −1.00690 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4721 | 0.787234 | 0.393617 | − | 0.919274i | \(-0.371224\pi\) | ||||
0.393617 | + | 0.919274i | \(0.371224\pi\) | |||||||
\(252\) | −1.85410 | −0.116797 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −34.4164 | −2.15948 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −18.3820 | −1.14664 | −0.573318 | − | 0.819333i | \(-0.694344\pi\) | ||||
−0.573318 | + | 0.819333i | \(0.694344\pi\) | |||||||
\(258\) | 13.7082 | 0.853435 | ||||||||
\(259\) | −8.12461 | −0.504839 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.4721 | −0.648209 | ||||||||
\(262\) | −22.4164 | −1.38489 | ||||||||
\(263\) | −8.56231 | −0.527974 | −0.263987 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263987 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.56231 | 0.524989 | ||||||||
\(267\) | 3.23607 | 0.198044 | ||||||||
\(268\) | −4.23607 | −0.258759 | ||||||||
\(269\) | −24.2705 | −1.47980 | −0.739900 | − | 0.672717i | \(-0.765127\pi\) | ||||
−0.739900 | + | 0.672717i | \(0.765127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.70820 | −0.528986 | −0.264493 | − | 0.964388i | \(-0.585205\pi\) | ||||
−0.264493 | + | 0.964388i | \(0.585205\pi\) | |||||||
\(272\) | 36.2705 | 2.19922 | ||||||||
\(273\) | −27.7082 | −1.67698 | ||||||||
\(274\) | −2.23607 | −0.135086 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.94427 | 0.417996 | ||||||||
\(277\) | 14.4164 | 0.866198 | 0.433099 | − | 0.901346i | \(-0.357420\pi\) | ||||
0.433099 | + | 0.901346i | \(0.357420\pi\) | |||||||
\(278\) | −12.0000 | −0.719712 | ||||||||
\(279\) | −0.236068 | −0.0141330 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2361 | 0.670288 | 0.335144 | − | 0.942167i | \(-0.391215\pi\) | ||||
0.335144 | + | 0.942167i | \(0.391215\pi\) | |||||||
\(282\) | 21.8885 | 1.30344 | ||||||||
\(283\) | −19.1803 | −1.14015 | −0.570076 | − | 0.821592i | \(-0.693086\pi\) | ||||
−0.570076 | + | 0.821592i | \(0.693086\pi\) | |||||||
\(284\) | −4.09017 | −0.242707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.2705 | −1.78681 | ||||||||
\(288\) | −3.38197 | −0.199284 | ||||||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.12461 | −0.534894 | ||||||||
\(292\) | −6.65248 | −0.389307 | ||||||||
\(293\) | −27.7082 | −1.61873 | −0.809365 | − | 0.587306i | \(-0.800189\pi\) | ||||
−0.809365 | + | 0.587306i | \(0.800189\pi\) | |||||||
\(294\) | −6.47214 | −0.377463 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.05573 | −0.351982 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.4721 | 0.954205 | ||||||||
\(299\) | 25.9443 | 1.50040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7082 | 0.732489 | ||||||||
\(302\) | 14.5623 | 0.837967 | ||||||||
\(303\) | −1.23607 | −0.0710102 | ||||||||
\(304\) | 8.56231 | 0.491082 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.0902 | −0.691149 | ||||||||
\(307\) | 2.14590 | 0.122473 | 0.0612364 | − | 0.998123i | \(-0.480496\pi\) | ||||
0.0612364 | + | 0.998123i | \(0.480496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.23607 | −0.0703175 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.52786 | 0.0866372 | 0.0433186 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433186 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(312\) | −20.6525 | −1.16922 | ||||||||
\(313\) | −20.1246 | −1.13751 | −0.568755 | − | 0.822507i | \(-0.692575\pi\) | ||||
−0.568755 | + | 0.822507i | \(0.692575\pi\) | |||||||
\(314\) | 24.5623 | 1.38613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.56231 | −0.0878866 | ||||||||
\(317\) | −23.1803 | −1.30194 | −0.650969 | − | 0.759104i | \(-0.725637\pi\) | ||||
−0.650969 | + | 0.759104i | \(0.725637\pi\) | |||||||
\(318\) | 3.23607 | 0.181470 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8885 | −0.998441 | ||||||||
\(322\) | 27.2705 | 1.51973 | ||||||||
\(323\) | 13.1803 | 0.733374 | ||||||||
\(324\) | −6.79837 | −0.377687 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.70820 | 0.205378 | ||||||||
\(327\) | 27.5279 | 1.52229 | ||||||||
\(328\) | −22.5623 | −1.24579 | ||||||||
\(329\) | 20.2918 | 1.11872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8541 | 0.926385 | 0.463193 | − | 0.886258i | \(-0.346704\pi\) | ||||
0.463193 | + | 0.886258i | \(0.346704\pi\) | |||||||
\(332\) | 4.90983 | 0.269462 | ||||||||
\(333\) | 2.70820 | 0.148409 | ||||||||
\(334\) | 13.2361 | 0.724245 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −29.1246 | −1.58888 | ||||||||
\(337\) | −14.4164 | −0.785312 | −0.392656 | − | 0.919685i | \(-0.628444\pi\) | ||||
−0.392656 | + | 0.919685i | \(0.628444\pi\) | |||||||
\(338\) | 13.4721 | 0.732788 | ||||||||
\(339\) | 29.2361 | 1.58789 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.85410 | −0.154332 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 9.47214 | 0.510703 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −31.7426 | −1.70650 | ||||||||
\(347\) | 27.2148 | 1.46097 | 0.730483 | − | 0.682931i | \(-0.239295\pi\) | ||||
0.730483 | + | 0.682931i | \(0.239295\pi\) | |||||||
\(348\) | 12.9443 | 0.693886 | ||||||||
\(349\) | −22.4164 | −1.19992 | −0.599961 | − | 0.800029i | \(-0.704817\pi\) | ||||
−0.599961 | + | 0.800029i | \(0.704817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4721 | −0.985970 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.2705 | −0.972441 | −0.486221 | − | 0.873836i | \(-0.661625\pi\) | ||||
−0.486221 | + | 0.873836i | \(0.661625\pi\) | |||||||
\(354\) | 3.52786 | 0.187504 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | −44.8328 | −2.37280 | ||||||||
\(358\) | 17.6180 | 0.931142 | ||||||||
\(359\) | 20.2361 | 1.06802 | 0.534009 | − | 0.845479i | \(-0.320685\pi\) | ||||
0.534009 | + | 0.845479i | \(0.320685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8885 | −0.836239 | ||||||||
\(362\) | −33.1246 | −1.74099 | ||||||||
\(363\) | 22.0000 | 1.15470 | ||||||||
\(364\) | 8.56231 | 0.448787 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −41.5967 | −2.17430 | ||||||||
\(367\) | 18.6738 | 0.974762 | 0.487381 | − | 0.873189i | \(-0.337952\pi\) | ||||
0.487381 | + | 0.873189i | \(0.337952\pi\) | |||||||
\(368\) | 27.2705 | 1.42157 | ||||||||
\(369\) | 10.0902 | 0.525273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | 0.155752 | ||||||||
\(372\) | 0.291796 | 0.0151289 | ||||||||
\(373\) | 9.14590 | 0.473557 | 0.236778 | − | 0.971564i | \(-0.423908\pi\) | ||||
0.236778 | + | 0.971564i | \(0.423908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.1246 | 0.779992 | ||||||||
\(377\) | 48.3607 | 2.49070 | ||||||||
\(378\) | −19.4164 | −0.998672 | ||||||||
\(379\) | −26.5279 | −1.36264 | −0.681322 | − | 0.731983i | \(-0.738595\pi\) | ||||
−0.681322 | + | 0.731983i | \(0.738595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.5410 | 2.17944 | ||||||||
\(382\) | −11.6180 | −0.594430 | ||||||||
\(383\) | −21.0000 | −1.07305 | −0.536525 | − | 0.843884i | \(-0.680263\pi\) | ||||
−0.536525 | + | 0.843884i | \(0.680263\pi\) | |||||||
\(384\) | −27.2361 | −1.38988 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1803 | 1.28165 | ||||||||
\(387\) | −4.23607 | −0.215331 | ||||||||
\(388\) | 2.81966 | 0.143147 | ||||||||
\(389\) | −9.90983 | −0.502448 | −0.251224 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251224 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.9787 | 2.12295 | ||||||||
\(392\) | −4.47214 | −0.225877 | ||||||||
\(393\) | 27.7082 | 1.39769 | ||||||||
\(394\) | 37.9787 | 1.91334 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1246 | −0.909648 | −0.454824 | − | 0.890581i | \(-0.650298\pi\) | ||||
−0.454824 | + | 0.890581i | \(0.650298\pi\) | |||||||
\(398\) | 3.85410 | 0.193189 | ||||||||
\(399\) | −10.5836 | −0.529842 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3262 | −0.715418 | −0.357709 | − | 0.933833i | \(-0.616442\pi\) | ||||
−0.357709 | + | 0.933833i | \(0.616442\pi\) | |||||||
\(402\) | 22.1803 | 1.10625 | ||||||||
\(403\) | 1.09017 | 0.0543052 | ||||||||
\(404\) | 0.381966 | 0.0190035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 50.8328 | 2.52279 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −33.4164 | −1.65436 | ||||||||
\(409\) | −31.9787 | −1.58125 | −0.790623 | − | 0.612303i | \(-0.790243\pi\) | ||||
−0.790623 | + | 0.612303i | \(0.790243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.76393 | 0.136335 | ||||||||
\(412\) | 0.381966 | 0.0188181 | ||||||||
\(413\) | 3.27051 | 0.160931 | ||||||||
\(414\) | −9.09017 | −0.446757 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.6180 | 0.765737 | ||||||||
\(417\) | 14.8328 | 0.726366 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.96556 | 0.340290 | 0.170145 | − | 0.985419i | \(-0.445576\pi\) | ||||
0.170145 | + | 0.985419i | \(0.445576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | −13.6180 | −0.662916 | ||||||||
\(423\) | −6.76393 | −0.328874 | ||||||||
\(424\) | 2.23607 | 0.108593 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 21.4164 | 1.03763 | ||||||||
\(427\) | −38.5623 | −1.86616 | ||||||||
\(428\) | 5.52786 | 0.267199 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.4721 | 0.841603 | 0.420802 | − | 0.907153i | \(-0.361749\pi\) | ||||
0.420802 | + | 0.907153i | \(0.361749\pi\) | |||||||
\(432\) | −19.4164 | −0.934172 | ||||||||
\(433\) | 19.9787 | 0.960116 | 0.480058 | − | 0.877237i | \(-0.340616\pi\) | ||||
0.480058 | + | 0.877237i | \(0.340616\pi\) | |||||||
\(434\) | 1.14590 | 0.0550049 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.50658 | −0.407391 | ||||||||
\(437\) | 9.90983 | 0.474051 | ||||||||
\(438\) | 34.8328 | 1.66438 | ||||||||
\(439\) | 5.29180 | 0.252564 | 0.126282 | − | 0.991994i | \(-0.459696\pi\) | ||||
0.126282 | + | 0.991994i | \(0.459696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 55.8328 | 2.65570 | ||||||||
\(443\) | −10.5836 | −0.502842 | −0.251421 | − | 0.967878i | \(-0.580898\pi\) | ||||
−0.251421 | + | 0.967878i | \(0.580898\pi\) | |||||||
\(444\) | −3.34752 | −0.158866 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.32624 | −0.157502 | ||||||||
\(447\) | −20.3607 | −0.963027 | ||||||||
\(448\) | −12.7082 | −0.600406 | ||||||||
\(449\) | 9.09017 | 0.428992 | 0.214496 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214496 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.03444 | −0.424944 | ||||||||
\(453\) | −18.0000 | −0.845714 | ||||||||
\(454\) | 12.8541 | 0.603273 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.88854 | −0.369415 | ||||||||
\(457\) | 20.7984 | 0.972907 | 0.486453 | − | 0.873706i | \(-0.338290\pi\) | ||||
0.486453 | + | 0.873706i | \(0.338290\pi\) | |||||||
\(458\) | 19.1803 | 0.896238 | ||||||||
\(459\) | −29.8885 | −1.39508 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0344 | 0.933097 | 0.466548 | − | 0.884496i | \(-0.345497\pi\) | ||||
0.466548 | + | 0.884496i | \(0.345497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.5623 | 1.79214 | 0.896071 | − | 0.443910i | \(-0.146409\pi\) | ||||
0.896071 | + | 0.443910i | \(0.146409\pi\) | |||||||
\(464\) | 50.8328 | 2.35985 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.85410 | 0.317510 | ||||||||
\(467\) | −41.6525 | −1.92745 | −0.963723 | − | 0.266903i | \(-0.914000\pi\) | ||||
−0.963723 | + | 0.266903i | \(0.914000\pi\) | |||||||
\(468\) | −2.85410 | −0.131931 | ||||||||
\(469\) | 20.5623 | 0.949479 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.3607 | −1.39895 | ||||||||
\(472\) | 2.43769 | 0.112204 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.18034 | 0.375735 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.8541 | 0.635002 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 45.4164 | 2.07730 | ||||||||
\(479\) | −42.8885 | −1.95963 | −0.979814 | − | 0.199912i | \(-0.935934\pi\) | ||||
−0.979814 | + | 0.199912i | \(0.935934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5066 | −0.570251 | ||||||||
\(482\) | −42.5066 | −1.93612 | ||||||||
\(483\) | −33.7082 | −1.53378 | ||||||||
\(484\) | −6.79837 | −0.309017 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16.1803 | 0.733955 | ||||||||
\(487\) | −34.5410 | −1.56520 | −0.782602 | − | 0.622523i | \(-0.786108\pi\) | ||||
−0.782602 | + | 0.622523i | \(0.786108\pi\) | |||||||
\(488\) | −28.7426 | −1.30112 | ||||||||
\(489\) | −4.58359 | −0.207277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3607 | 0.693218 | 0.346609 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346609 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(492\) | −12.4721 | −0.562287 | ||||||||
\(493\) | 78.2492 | 3.52417 | ||||||||
\(494\) | 13.1803 | 0.593012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.14590 | 0.0514523 | ||||||||
\(497\) | 19.8541 | 0.890578 | ||||||||
\(498\) | −25.7082 | −1.15201 | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.3607 | −0.730941 | ||||||||
\(502\) | 20.1803 | 0.900693 | ||||||||
\(503\) | 16.4164 | 0.731971 | 0.365986 | − | 0.930620i | \(-0.380732\pi\) | ||||
0.365986 | + | 0.930620i | \(0.380732\pi\) | |||||||
\(504\) | 6.70820 | 0.298807 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6525 | −0.739562 | ||||||||
\(508\) | −13.1459 | −0.583255 | ||||||||
\(509\) | −5.12461 | −0.227144 | −0.113572 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113572 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.2918 | 1.42850 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | −7.05573 | −0.311518 | ||||||||
\(514\) | −29.7426 | −1.31189 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.23607 | 0.230505 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.1459 | −0.577598 | ||||||||
\(519\) | 39.2361 | 1.72227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5967 | 0.551874 | 0.275937 | − | 0.961176i | \(-0.411012\pi\) | ||||
0.275937 | + | 0.961176i | \(0.411012\pi\) | |||||||
\(522\) | −16.9443 | −0.741631 | ||||||||
\(523\) | 16.2705 | 0.711460 | 0.355730 | − | 0.934589i | \(-0.384232\pi\) | ||||
0.355730 | + | 0.934589i | \(0.384232\pi\) | |||||||
\(524\) | −8.56231 | −0.374046 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8541 | −0.604068 | ||||||||
\(527\) | 1.76393 | 0.0768381 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.56231 | 0.372274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.09017 | −0.0473093 | ||||||||
\(532\) | 3.27051 | 0.141795 | ||||||||
\(533\) | −46.5967 | −2.01833 | ||||||||
\(534\) | 5.23607 | 0.226587 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.3262 | 0.661993 | ||||||||
\(537\) | −21.7771 | −0.939751 | ||||||||
\(538\) | −39.2705 | −1.69307 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.29180 | −0.0555387 | −0.0277693 | − | 0.999614i | \(-0.508840\pi\) | ||||
−0.0277693 | + | 0.999614i | \(0.508840\pi\) | |||||||
\(542\) | −14.0902 | −0.605225 | ||||||||
\(543\) | 40.9443 | 1.75709 | ||||||||
\(544\) | 25.2705 | 1.08346 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −44.8328 | −1.91867 | ||||||||
\(547\) | −27.5623 | −1.17848 | −0.589240 | − | 0.807958i | \(-0.700573\pi\) | ||||
−0.589240 | + | 0.807958i | \(0.700573\pi\) | |||||||
\(548\) | −0.854102 | −0.0364854 | ||||||||
\(549\) | 12.8541 | 0.548600 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.4721 | 0.786939 | ||||||||
\(552\) | −25.1246 | −1.06937 | ||||||||
\(553\) | 7.58359 | 0.322487 | ||||||||
\(554\) | 23.3262 | 0.991037 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.58359 | −0.194388 | ||||||||
\(557\) | −13.4508 | −0.569931 | −0.284965 | − | 0.958538i | \(-0.591982\pi\) | ||||
−0.284965 | + | 0.958538i | \(0.591982\pi\) | |||||||
\(558\) | −0.381966 | −0.0161699 | ||||||||
\(559\) | 19.5623 | 0.827397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.1803 | 0.766891 | ||||||||
\(563\) | −32.5066 | −1.36999 | −0.684994 | − | 0.728548i | \(-0.740195\pi\) | ||||
−0.684994 | + | 0.728548i | \(0.740195\pi\) | |||||||
\(564\) | 8.36068 | 0.352048 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31.0344 | −1.30447 | ||||||||
\(567\) | 33.0000 | 1.38587 | ||||||||
\(568\) | 14.7984 | 0.620926 | ||||||||
\(569\) | 3.43769 | 0.144116 | 0.0720578 | − | 0.997400i | \(-0.477043\pi\) | ||||
0.0720578 | + | 0.997400i | \(0.477043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.79837 | 0.368200 | 0.184100 | − | 0.982907i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982907i | \(0.441063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.3607 | 0.599926 | ||||||||
\(574\) | −48.9787 | −2.04433 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −28.1803 | −1.17316 | −0.586581 | − | 0.809890i | \(-0.699527\pi\) | ||||
−0.586581 | + | 0.809890i | \(0.699527\pi\) | |||||||
\(578\) | 62.8328 | 2.61350 | ||||||||
\(579\) | −31.1246 | −1.29349 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.8328 | −0.988752 | ||||||||
\(582\) | −14.7639 | −0.611985 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 24.0689 | 0.995977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −44.8328 | −1.85203 | ||||||||
\(587\) | −11.3607 | −0.468905 | −0.234453 | − | 0.972128i | \(-0.575330\pi\) | ||||
−0.234453 | + | 0.972128i | \(0.575330\pi\) | |||||||
\(588\) | −2.47214 | −0.101949 | ||||||||
\(589\) | 0.416408 | 0.0171578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.9443 | −1.93103 | ||||||||
\(592\) | −13.1459 | −0.540293 | ||||||||
\(593\) | −9.97871 | −0.409777 | −0.204888 | − | 0.978785i | \(-0.565683\pi\) | ||||
−0.204888 | + | 0.978785i | \(0.565683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.29180 | 0.257722 | ||||||||
\(597\) | −4.76393 | −0.194975 | ||||||||
\(598\) | 41.9787 | 1.71664 | ||||||||
\(599\) | −28.7426 | −1.17439 | −0.587196 | − | 0.809445i | \(-0.699768\pi\) | ||||
−0.587196 | + | 0.809445i | \(0.699768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.29180 | 0.338229 | 0.169115 | − | 0.985596i | \(-0.445909\pi\) | ||||
0.169115 | + | 0.985596i | \(0.445909\pi\) | |||||||
\(602\) | 20.5623 | 0.838057 | ||||||||
\(603\) | −6.85410 | −0.279121 | ||||||||
\(604\) | 5.56231 | 0.226327 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | −29.5623 | −1.19990 | −0.599948 | − | 0.800039i | \(-0.704812\pi\) | ||||
−0.599948 | + | 0.800039i | \(0.704812\pi\) | |||||||
\(608\) | 5.96556 | 0.241935 | ||||||||
\(609\) | −62.8328 | −2.54611 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.2361 | 1.26368 | ||||||||
\(612\) | −4.61803 | −0.186673 | ||||||||
\(613\) | 46.1246 | 1.86296 | 0.931478 | − | 0.363798i | \(-0.118520\pi\) | ||||
0.931478 | + | 0.363798i | \(0.118520\pi\) | |||||||
\(614\) | 3.47214 | 0.140124 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.3607 | −0.859949 | −0.429974 | − | 0.902841i | \(-0.641477\pi\) | ||||
−0.429974 | + | 0.902841i | \(0.641477\pi\) | |||||||
\(618\) | −2.00000 | −0.0804518 | ||||||||
\(619\) | −5.49342 | −0.220799 | −0.110400 | − | 0.993887i | \(-0.535213\pi\) | ||||
−0.110400 | + | 0.993887i | \(0.535213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.4721 | −0.901776 | ||||||||
\(622\) | 2.47214 | 0.0991236 | ||||||||
\(623\) | 4.85410 | 0.194475 | ||||||||
\(624\) | −44.8328 | −1.79475 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5623 | −1.30145 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.38197 | 0.374381 | ||||||||
\(629\) | −20.2361 | −0.806865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.0557 | −1.15669 | −0.578345 | − | 0.815792i | \(-0.696301\pi\) | ||||
−0.578345 | + | 0.815792i | \(0.696301\pi\) | |||||||
\(632\) | 5.65248 | 0.224843 | ||||||||
\(633\) | 16.8328 | 0.669044 | ||||||||
\(634\) | −37.5066 | −1.48958 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.23607 | 0.0490133 | ||||||||
\(637\) | −9.23607 | −0.365946 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.61803 | −0.261805 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.81966 | 0.269360 | 0.134680 | − | 0.990889i | \(-0.456999\pi\) | ||||
0.134680 | + | 0.990889i | \(0.456999\pi\) | |||||||
\(642\) | −28.9443 | −1.14234 | ||||||||
\(643\) | −40.7771 | −1.60809 | −0.804046 | − | 0.594568i | \(-0.797323\pi\) | ||||
−0.804046 | + | 0.594568i | \(0.797323\pi\) | |||||||
\(644\) | 10.4164 | 0.410464 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.3262 | 0.839070 | ||||||||
\(647\) | −17.5066 | −0.688255 | −0.344127 | − | 0.938923i | \(-0.611825\pi\) | ||||
−0.344127 | + | 0.938923i | \(0.611825\pi\) | |||||||
\(648\) | 24.5967 | 0.966252 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.41641 | −0.0555134 | ||||||||
\(652\) | 1.41641 | 0.0554708 | ||||||||
\(653\) | −20.9443 | −0.819613 | −0.409806 | − | 0.912173i | \(-0.634404\pi\) | ||||
−0.409806 | + | 0.912173i | \(0.634404\pi\) | |||||||
\(654\) | 44.5410 | 1.74169 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −48.9787 | −1.91230 | ||||||||
\(657\) | −10.7639 | −0.419941 | ||||||||
\(658\) | 32.8328 | 1.27996 | ||||||||
\(659\) | −36.6312 | −1.42695 | −0.713474 | − | 0.700681i | \(-0.752879\pi\) | ||||
−0.713474 | + | 0.700681i | \(0.752879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.854102 | 0.0332207 | 0.0166104 | − | 0.999862i | \(-0.494713\pi\) | ||||
0.0166104 | + | 0.999862i | \(0.494713\pi\) | |||||||
\(662\) | 27.2705 | 1.05990 | ||||||||
\(663\) | −69.0132 | −2.68025 | ||||||||
\(664\) | −17.7639 | −0.689374 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.38197 | 0.169798 | ||||||||
\(667\) | 58.8328 | 2.27802 | ||||||||
\(668\) | 5.05573 | 0.195612 | ||||||||
\(669\) | 4.11146 | 0.158958 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −20.2918 | −0.782773 | ||||||||
\(673\) | −11.0000 | −0.424019 | −0.212009 | − | 0.977268i | \(-0.568001\pi\) | ||||
−0.212009 | + | 0.977268i | \(0.568001\pi\) | |||||||
\(674\) | −23.3262 | −0.898493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.14590 | 0.197919 | ||||||||
\(677\) | 2.18034 | 0.0837973 | 0.0418986 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0418986 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(678\) | 47.3050 | 1.81674 | ||||||||
\(679\) | −13.6869 | −0.525256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.8885 | −0.608850 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.8885 | 1.18192 | 0.590959 | − | 0.806702i | \(-0.298750\pi\) | ||||
0.590959 | + | 0.806702i | \(0.298750\pi\) | |||||||
\(684\) | −1.09017 | −0.0416837 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 24.2705 | 0.926652 | ||||||||
\(687\) | −23.7082 | −0.904524 | ||||||||
\(688\) | 20.5623 | 0.783931 | ||||||||
\(689\) | 4.61803 | 0.175933 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.124612 | 0.00474046 | 0.00237023 | − | 0.999997i | \(-0.499246\pi\) | ||||
0.00237023 | + | 0.999997i | \(0.499246\pi\) | |||||||
\(692\) | −12.1246 | −0.460909 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.0344 | 1.67152 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −46.8328 | −1.77519 | ||||||||
\(697\) | −75.3951 | −2.85579 | ||||||||
\(698\) | −36.2705 | −1.37286 | ||||||||
\(699\) | −8.47214 | −0.320446 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.67376 | −0.214295 | −0.107148 | − | 0.994243i | \(-0.534172\pi\) | ||||
−0.107148 | + | 0.994243i | \(0.534172\pi\) | |||||||
\(702\) | −29.8885 | −1.12807 | ||||||||
\(703\) | −4.77709 | −0.180171 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.5623 | −1.11259 | ||||||||
\(707\) | −1.85410 | −0.0697307 | ||||||||
\(708\) | 1.34752 | 0.0506431 | ||||||||
\(709\) | −12.8541 | −0.482746 | −0.241373 | − | 0.970432i | \(-0.577598\pi\) | ||||
−0.241373 | + | 0.970432i | \(0.577598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.52786 | −0.0948023 | ||||||||
\(712\) | 3.61803 | 0.135592 | ||||||||
\(713\) | 1.32624 | 0.0496680 | ||||||||
\(714\) | −72.5410 | −2.71478 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.72949 | 0.251493 | ||||||||
\(717\) | −56.1378 | −2.09650 | ||||||||
\(718\) | 32.7426 | 1.22194 | ||||||||
\(719\) | −10.0902 | −0.376300 | −0.188150 | − | 0.982140i | \(-0.560249\pi\) | ||||
−0.188150 | + | 0.982140i | \(0.560249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.85410 | −0.0690504 | ||||||||
\(722\) | −25.7082 | −0.956760 | ||||||||
\(723\) | 52.5410 | 1.95402 | ||||||||
\(724\) | −12.6525 | −0.470226 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 35.5967 | 1.32112 | ||||||||
\(727\) | 18.1459 | 0.672994 | 0.336497 | − | 0.941685i | \(-0.390758\pi\) | ||||
0.336497 | + | 0.941685i | \(0.390758\pi\) | |||||||
\(728\) | −30.9787 | −1.14815 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.6525 | 1.17071 | ||||||||
\(732\) | −15.8885 | −0.587257 | ||||||||
\(733\) | −11.4721 | −0.423733 | −0.211867 | − | 0.977299i | \(-0.567954\pi\) | ||||
−0.211867 | + | 0.977299i | \(0.567954\pi\) | |||||||
\(734\) | 30.2148 | 1.11525 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.0000 | 0.700349 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.3262 | 0.600977 | ||||||||
\(739\) | −51.6312 | −1.89928 | −0.949642 | − | 0.313337i | \(-0.898553\pi\) | ||||
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2918 | −0.598494 | ||||||||
\(742\) | 4.85410 | 0.178200 | ||||||||
\(743\) | −21.3607 | −0.783647 | −0.391824 | − | 0.920040i | \(-0.628156\pi\) | ||||
−0.391824 | + | 0.920040i | \(0.628156\pi\) | |||||||
\(744\) | −1.05573 | −0.0387049 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.7984 | 0.541807 | ||||||||
\(747\) | 7.94427 | 0.290666 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.8328 | −0.980450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.3951 | 1.91193 | 0.955963 | − | 0.293489i | \(-0.0948163\pi\) | ||||
0.955963 | + | 0.293489i | \(0.0948163\pi\) | |||||||
\(752\) | 32.8328 | 1.19729 | ||||||||
\(753\) | −24.9443 | −0.909020 | ||||||||
\(754\) | 78.2492 | 2.84967 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.41641 | −0.269732 | ||||||||
\(757\) | 20.1246 | 0.731441 | 0.365721 | − | 0.930725i | \(-0.380823\pi\) | ||||
0.365721 | + | 0.930725i | \(0.380823\pi\) | |||||||
\(758\) | −42.9230 | −1.55903 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.8541 | −1.37221 | −0.686105 | − | 0.727502i | \(-0.740681\pi\) | ||||
−0.686105 | + | 0.727502i | \(0.740681\pi\) | |||||||
\(762\) | 68.8328 | 2.49355 | ||||||||
\(763\) | 41.2918 | 1.49486 | ||||||||
\(764\) | −4.43769 | −0.160550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.9787 | −1.22770 | ||||||||
\(767\) | 5.03444 | 0.181783 | ||||||||
\(768\) | −27.1246 | −0.978775 | ||||||||
\(769\) | −12.2918 | −0.443254 | −0.221627 | − | 0.975132i | \(-0.571137\pi\) | ||||
−0.221627 | + | 0.975132i | \(0.571137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.7639 | 1.32402 | ||||||||
\(772\) | 9.61803 | 0.346161 | ||||||||
\(773\) | −31.4508 | −1.13121 | −0.565604 | − | 0.824677i | \(-0.691357\pi\) | ||||
−0.565604 | + | 0.824677i | \(0.691357\pi\) | |||||||
\(774\) | −6.85410 | −0.246366 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.2016 | −0.366217 | ||||||||
\(777\) | 16.2492 | 0.582938 | ||||||||
\(778\) | −16.0344 | −0.574863 | ||||||||
\(779\) | −17.7984 | −0.637693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 67.9230 | 2.42892 | ||||||||
\(783\) | −41.8885 | −1.49697 | ||||||||
\(784\) | −9.70820 | −0.346722 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 44.8328 | 1.59913 | ||||||||
\(787\) | −11.4934 | −0.409696 | −0.204848 | − | 0.978794i | \(-0.565670\pi\) | ||||
−0.204848 | + | 0.978794i | \(0.565670\pi\) | |||||||
\(788\) | 14.5066 | 0.516775 | ||||||||
\(789\) | 17.1246 | 0.609652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.8541 | 1.55927 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.3607 | −2.10796 | ||||||||
\(794\) | −29.3262 | −1.04075 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.47214 | 0.0521785 | ||||||||
\(797\) | 34.0344 | 1.20556 | 0.602781 | − | 0.797907i | \(-0.294059\pi\) | ||||
0.602781 | + | 0.797907i | \(0.294059\pi\) | |||||||
\(798\) | −17.1246 | −0.606205 | ||||||||
\(799\) | 50.5410 | 1.78801 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.61803 | −0.0571704 | ||||||||
\(802\) | −23.1803 | −0.818526 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.47214 | 0.298789 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.76393 | 0.0621319 | ||||||||
\(807\) | 48.5410 | 1.70872 | ||||||||
\(808\) | −1.38197 | −0.0486174 | ||||||||
\(809\) | −20.2361 | −0.711462 | −0.355731 | − | 0.934588i | \(-0.615768\pi\) | ||||
−0.355731 | + | 0.934588i | \(0.615768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0132 | 0.983675 | 0.491837 | − | 0.870687i | \(-0.336325\pi\) | ||||
0.491837 | + | 0.870687i | \(0.336325\pi\) | |||||||
\(812\) | 19.4164 | 0.681382 | ||||||||
\(813\) | 17.4164 | 0.610820 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −72.5410 | −2.53944 | ||||||||
\(817\) | 7.47214 | 0.261417 | ||||||||
\(818\) | −51.7426 | −1.80914 | ||||||||
\(819\) | 13.8541 | 0.484102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4508 | 0.888241 | 0.444120 | − | 0.895967i | \(-0.353516\pi\) | ||||
0.444120 | + | 0.895967i | \(0.353516\pi\) | |||||||
\(822\) | 4.47214 | 0.155984 | ||||||||
\(823\) | −10.8328 | −0.377608 | −0.188804 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188804 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(824\) | −1.38197 | −0.0481431 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.29180 | 0.184125 | ||||||||
\(827\) | −29.5066 | −1.02604 | −0.513022 | − | 0.858375i | \(-0.671474\pi\) | ||||
−0.513022 | + | 0.858375i | \(0.671474\pi\) | |||||||
\(828\) | −3.47214 | −0.120665 | ||||||||
\(829\) | −12.2705 | −0.426172 | −0.213086 | − | 0.977033i | \(-0.568352\pi\) | ||||
−0.213086 | + | 0.977033i | \(0.568352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.8328 | −1.00020 | ||||||||
\(832\) | −19.5623 | −0.678201 | ||||||||
\(833\) | −14.9443 | −0.517788 | ||||||||
\(834\) | 24.0000 | 0.831052 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.944272 | −0.0326388 | ||||||||
\(838\) | 11.2705 | 0.389333 | ||||||||
\(839\) | 27.4721 | 0.948443 | 0.474222 | − | 0.880405i | \(-0.342730\pi\) | ||||
0.474222 | + | 0.880405i | \(0.342730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 80.6656 | 2.78157 | ||||||||
\(842\) | 3.23607 | 0.111522 | ||||||||
\(843\) | −22.4721 | −0.773981 | ||||||||
\(844\) | −5.20163 | −0.179047 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.9443 | −0.376272 | ||||||||
\(847\) | 33.0000 | 1.13389 | ||||||||
\(848\) | 4.85410 | 0.166691 | ||||||||
\(849\) | 38.3607 | 1.31654 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.2148 | −0.521556 | ||||||||
\(852\) | 8.18034 | 0.280254 | ||||||||
\(853\) | 6.56231 | 0.224689 | 0.112345 | − | 0.993669i | \(-0.464164\pi\) | ||||
0.112345 | + | 0.993669i | \(0.464164\pi\) | |||||||
\(854\) | −62.3951 | −2.13512 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.0000 | −0.683586 | ||||||||
\(857\) | −17.2016 | −0.587596 | −0.293798 | − | 0.955867i | \(-0.594919\pi\) | ||||
−0.293798 | + | 0.955867i | \(0.594919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.8328 | 0.608448 | 0.304224 | − | 0.952601i | \(-0.401603\pi\) | ||||
0.304224 | + | 0.952601i | \(0.401603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.5410 | 2.06323 | ||||||||
\(862\) | 28.2705 | 0.962897 | ||||||||
\(863\) | 13.9098 | 0.473496 | 0.236748 | − | 0.971571i | \(-0.423918\pi\) | ||||
0.236748 | + | 0.971571i | \(0.423918\pi\) | |||||||
\(864\) | −13.5279 | −0.460227 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.3262 | 1.09849 | ||||||||
\(867\) | −77.6656 | −2.63766 | ||||||||
\(868\) | 0.437694 | 0.0148563 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6525 | 1.07250 | ||||||||
\(872\) | 30.7771 | 1.04224 | ||||||||
\(873\) | 4.56231 | 0.154411 | ||||||||
\(874\) | 16.0344 | 0.542373 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.3050 | 0.449533 | ||||||||
\(877\) | 39.0689 | 1.31926 | 0.659631 | − | 0.751589i | \(-0.270712\pi\) | ||||
0.659631 | + | 0.751589i | \(0.270712\pi\) | |||||||
\(878\) | 8.56231 | 0.288964 | ||||||||
\(879\) | 55.4164 | 1.86915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3820 | −1.15836 | −0.579179 | − | 0.815200i | \(-0.696627\pi\) | ||||
−0.579179 | + | 0.815200i | \(0.696627\pi\) | |||||||
\(882\) | 3.23607 | 0.108964 | ||||||||
\(883\) | 36.0000 | 1.21150 | 0.605748 | − | 0.795656i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795656i | \(0.292874\pi\) | |||||||
\(884\) | 21.3262 | 0.717279 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.1246 | −0.575313 | ||||||||
\(887\) | 54.4853 | 1.82944 | 0.914719 | − | 0.404092i | \(-0.132412\pi\) | ||||
0.914719 | + | 0.404092i | \(0.132412\pi\) | |||||||
\(888\) | 12.1115 | 0.406434 | ||||||||
\(889\) | 63.8115 | 2.14017 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.27051 | −0.0425398 | ||||||||
\(893\) | 11.9311 | 0.399260 | ||||||||
\(894\) | −32.9443 | −1.10182 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −40.8541 | −1.36484 | ||||||||
\(897\) | −51.8885 | −1.73251 | ||||||||
\(898\) | 14.7082 | 0.490819 | ||||||||
\(899\) | 2.47214 | 0.0824504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.47214 | 0.248933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.4164 | −0.845805 | ||||||||
\(904\) | 32.6869 | 1.08715 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −29.1246 | −0.967600 | ||||||||
\(907\) | 2.70820 | 0.0899244 | 0.0449622 | − | 0.998989i | \(-0.485683\pi\) | ||||
0.0449622 | + | 0.998989i | \(0.485683\pi\) | |||||||
\(908\) | 4.90983 | 0.162938 | ||||||||
\(909\) | 0.618034 | 0.0204989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3050 | 1.03718 | 0.518590 | − | 0.855023i | \(-0.326457\pi\) | ||||
0.518590 | + | 0.855023i | \(0.326457\pi\) | |||||||
\(912\) | −17.1246 | −0.567053 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 33.6525 | 1.11312 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.32624 | 0.242066 | ||||||||
\(917\) | 41.5623 | 1.37251 | ||||||||
\(918\) | −48.3607 | −1.59614 | ||||||||
\(919\) | 23.4721 | 0.774274 | 0.387137 | − | 0.922022i | \(-0.373464\pi\) | ||||
0.387137 | + | 0.922022i | \(0.373464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.29180 | −0.141419 | ||||||||
\(922\) | 32.4164 | 1.06758 | ||||||||
\(923\) | 30.5623 | 1.00597 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 62.3951 | 2.05043 | ||||||||
\(927\) | 0.618034 | 0.0202989 | ||||||||
\(928\) | 35.4164 | 1.16260 | ||||||||
\(929\) | 9.76393 | 0.320344 | 0.160172 | − | 0.987089i | \(-0.448795\pi\) | ||||
0.160172 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.52786 | −0.115621 | ||||||||
\(932\) | 2.61803 | 0.0857566 | ||||||||
\(933\) | −3.05573 | −0.100040 | ||||||||
\(934\) | −67.3951 | −2.20524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3262 | 0.337524 | ||||||||
\(937\) | −50.7639 | −1.65839 | −0.829193 | − | 0.558963i | \(-0.811199\pi\) | ||||
−0.829193 | + | 0.558963i | \(0.811199\pi\) | |||||||
\(938\) | 33.2705 | 1.08632 | ||||||||
\(939\) | 40.2492 | 1.31348 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0000 | −0.488986 | −0.244493 | − | 0.969651i | \(-0.578622\pi\) | ||||
−0.244493 | + | 0.969651i | \(0.578622\pi\) | |||||||
\(942\) | −49.1246 | −1.60057 | ||||||||
\(943\) | −56.6869 | −1.84598 | ||||||||
\(944\) | 5.29180 | 0.172233 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.7639 | 1.32465 | 0.662325 | − | 0.749217i | \(-0.269570\pi\) | ||||
0.662325 | + | 0.749217i | \(0.269570\pi\) | |||||||
\(948\) | 3.12461 | 0.101483 | ||||||||
\(949\) | 49.7082 | 1.61360 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 46.3607 | 1.50335 | ||||||||
\(952\) | −50.1246 | −1.62455 | ||||||||
\(953\) | −26.9443 | −0.872811 | −0.436405 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436405 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(954\) | −1.61803 | −0.0523858 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.3475 | 0.561059 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −69.3951 | −2.24205 | ||||||||
\(959\) | 4.14590 | 0.133878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9443 | −0.998202 | ||||||||
\(962\) | −20.2361 | −0.652437 | ||||||||
\(963\) | 8.94427 | 0.288225 | ||||||||
\(964\) | −16.2361 | −0.522929 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −54.5410 | −1.75483 | ||||||||
\(967\) | 3.70820 | 0.119248 | 0.0596239 | − | 0.998221i | \(-0.481010\pi\) | ||||
0.0596239 | + | 0.998221i | \(0.481010\pi\) | |||||||
\(968\) | 24.5967 | 0.790569 | ||||||||
\(969\) | −26.3607 | −0.846827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.0557 | −1.02872 | −0.514359 | − | 0.857575i | \(-0.671970\pi\) | ||||
−0.514359 | + | 0.857575i | \(0.671970\pi\) | |||||||
\(972\) | 6.18034 | 0.198234 | ||||||||
\(973\) | 22.2492 | 0.713277 | ||||||||
\(974\) | −55.8885 | −1.79078 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −62.3951 | −1.99722 | ||||||||
\(977\) | −47.7426 | −1.52742 | −0.763711 | − | 0.645558i | \(-0.776625\pi\) | ||||
−0.763711 | + | 0.645558i | \(0.776625\pi\) | |||||||
\(978\) | −7.41641 | −0.237151 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7639 | −0.439449 | ||||||||
\(982\) | 24.8541 | 0.793126 | ||||||||
\(983\) | −54.8115 | −1.74822 | −0.874108 | − | 0.485731i | \(-0.838553\pi\) | ||||
−0.874108 | + | 0.485731i | \(0.838553\pi\) | |||||||
\(984\) | 45.1246 | 1.43852 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 126.610 | 4.03208 | ||||||||
\(987\) | −40.5836 | −1.29179 | ||||||||
\(988\) | 5.03444 | 0.160167 | ||||||||
\(989\) | 23.7984 | 0.756744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8328 | −0.471180 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(992\) | 0.798374 | 0.0253484 | ||||||||
\(993\) | −33.7082 | −1.06970 | ||||||||
\(994\) | 32.1246 | 1.01893 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.81966 | −0.311148 | ||||||||
\(997\) | −55.2492 | −1.74976 | −0.874880 | − | 0.484339i | \(-0.839060\pi\) | ||||
−0.874880 | + | 0.484339i | \(0.839060\pi\) | |||||||
\(998\) | 9.70820 | 0.307308 | ||||||||
\(999\) | 10.8328 | 0.342735 |
(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 | 6625.2.a.c.1.2 | yes | 2 | |
5.4 | even | 2 | 6625.2.a.b.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6625.2.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
6625.2.a.c.1.2 | yes | 2 | 1.1 | even | 1 | trivial |