Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13955077.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 14x^{3} - x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.31091\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.31091 | −0.756856 | −0.378428 | − | 0.925631i | \(-0.623535\pi\) | ||||
−0.378428 | + | 0.925631i | \(0.623535\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.66212 | −1.76211 | −0.881057 | − | 0.473010i | \(-0.843168\pi\) | ||||
−0.881057 | + | 0.473010i | \(0.843168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.28151 | −0.427169 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23020 | 0.672430 | 0.336215 | − | 0.941785i | \(-0.390853\pi\) | ||||
0.336215 | + | 0.941785i | \(0.390853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.80072 | −0.776779 | −0.388389 | − | 0.921495i | \(-0.626968\pi\) | ||||
−0.388389 | + | 0.921495i | \(0.626968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.31091 | 0.338476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.63271 | 1.85120 | 0.925602 | − | 0.378498i | \(-0.123559\pi\) | ||||
0.925602 | + | 0.378498i | \(0.123559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.36222 | −0.312515 | −0.156258 | − | 0.987716i | \(-0.549943\pi\) | ||||
−0.156258 | + | 0.987716i | \(0.549943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.11163 | 1.33367 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61268 | 1.08016 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.94362 | 1.66079 | 0.830395 | − | 0.557176i | \(-0.188115\pi\) | ||||
0.830395 | + | 0.557176i | \(0.188115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.58140 | −0.284028 | −0.142014 | − | 0.989865i | \(-0.545358\pi\) | ||||
−0.142014 | + | 0.989865i | \(0.545358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.92360 | −0.508933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.66212 | 0.788042 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.40251 | −0.230572 | −0.115286 | − | 0.993332i | \(-0.536778\pi\) | ||||
−0.115286 | + | 0.993332i | \(0.536778\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.67149 | 0.587909 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7134 | 1.67316 | 0.836578 | − | 0.547848i | \(-0.184553\pi\) | ||||
0.836578 | + | 0.547848i | \(0.184553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.28151 | 0.191036 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.26391 | −1.05955 | −0.529775 | − | 0.848138i | \(-0.677724\pi\) | ||||
−0.529775 | + | 0.848138i | \(0.677724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.7353 | 2.10505 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0058 | −1.40109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.38212 | −1.15137 | −0.575686 | − | 0.817671i | \(-0.695265\pi\) | ||||
−0.575686 | + | 0.817671i | \(0.695265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.23020 | −0.300720 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.78575 | 0.236529 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.88331 | −0.635752 | −0.317876 | − | 0.948132i | \(-0.602970\pi\) | ||||
−0.317876 | + | 0.948132i | \(0.602970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.33282 | 0.554760 | 0.277380 | − | 0.960760i | \(-0.410534\pi\) | ||||
0.277380 | + | 0.960760i | \(0.410534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.97454 | 0.752721 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.80072 | 0.347386 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.54355 | 1.04376 | 0.521880 | − | 0.853019i | \(-0.325231\pi\) | ||||
0.521880 | + | 0.853019i | \(0.325231\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.31091 | 0.157815 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.81604 | 1.04627 | 0.523136 | − | 0.852249i | \(-0.324762\pi\) | ||||
0.523136 | + | 0.852249i | \(0.324762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.26391 | −0.616095 | −0.308047 | − | 0.951371i | \(-0.599675\pi\) | ||||
−0.308047 | + | 0.951371i | \(0.599675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.31091 | −0.151371 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.3974 | −1.18490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.08222 | 0.796812 | 0.398406 | − | 0.917209i | \(-0.369563\pi\) | ||||
0.398406 | + | 0.917209i | \(0.369563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.51322 | −0.390357 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.59749 | −0.504640 | −0.252320 | − | 0.967644i | \(-0.581194\pi\) | ||||
−0.252320 | + | 0.967644i | \(0.581194\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.63271 | −0.827884 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.7243 | −1.25698 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.70241 | −0.498454 | −0.249227 | − | 0.968445i | \(-0.580177\pi\) | ||||
−0.249227 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.0573 | 1.36877 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07308 | 0.214968 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36222 | 0.139761 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5160 | 1.67695 | 0.838474 | − | 0.544942i | \(-0.183448\pi\) | ||||
0.838474 | + | 0.544942i | \(0.183448\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.85802 | −0.287241 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7267 | 1.06735 | 0.533676 | − | 0.845689i | \(-0.320810\pi\) | ||||
0.533676 | + | 0.845689i | \(0.320810\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.95300 | 0.192435 | 0.0962175 | − | 0.995360i | \(-0.469326\pi\) | ||||
0.0962175 | + | 0.995360i | \(0.469326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.11163 | −0.596434 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.97566 | −0.190994 | −0.0954972 | − | 0.995430i | \(-0.530444\pi\) | ||||
−0.0954972 | + | 0.995430i | \(0.530444\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.92360 | −0.854725 | −0.427363 | − | 0.904080i | \(-0.640557\pi\) | ||||
−0.427363 | + | 0.904080i | \(0.640557\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.83857 | 0.174510 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3486 | 1.63202 | 0.816008 | − | 0.578040i | \(-0.196182\pi\) | ||||
0.816008 | + | 0.578040i | \(0.196182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.58914 | 0.331816 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −35.5846 | −3.26203 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.02621 | −0.547838 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0444 | −1.26634 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.4872 | 1.72921 | 0.864603 | − | 0.502455i | \(-0.167570\pi\) | ||||
0.864603 | + | 0.502455i | \(0.167570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.68050 | 0.496308 | 0.248154 | − | 0.968721i | \(-0.420176\pi\) | ||||
0.248154 | + | 0.968721i | \(0.420176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.35084 | 0.550687 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.61268 | −0.483063 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.68645 | −0.742134 | −0.371067 | − | 0.928606i | \(-0.621008\pi\) | ||||
−0.371067 | + | 0.928606i | \(0.621008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.22569 | −0.782513 | −0.391256 | − | 0.920282i | \(-0.627959\pi\) | ||||
−0.391256 | + | 0.920282i | \(0.627959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.52236 | 0.801927 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.24615 | −0.522329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.94362 | −0.742728 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.3167 | −1.59322 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.6056 | 1.52423 | 0.762115 | − | 0.647441i | \(-0.224161\pi\) | ||||
0.762115 | + | 0.647441i | \(0.224161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4316 | 1.41856 | 0.709280 | − | 0.704927i | \(-0.249020\pi\) | ||||
0.709280 | + | 0.704927i | \(0.249020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.78138 | −0.790778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.58140 | 0.127021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.839497 | 0.0669992 | 0.0334996 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334996 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.9882 | 0.871423 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.66212 | 0.367426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.5673 | −1.14100 | −0.570500 | − | 0.821297i | \(-0.693251\pi\) | ||||
−0.570500 | + | 0.821297i | \(0.693251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.92360 | 0.227602 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.03842 | −0.389884 | −0.194942 | − | 0.980815i | \(-0.562452\pi\) | ||||
−0.194942 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.15599 | −0.396615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.74570 | 0.133497 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3124 | −0.860067 | −0.430034 | − | 0.902813i | \(-0.641498\pi\) | ||||
−0.430034 | + | 0.902813i | \(0.641498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.66212 | −0.352423 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.40159 | 0.481173 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.3053 | −1.81667 | −0.908333 | − | 0.418247i | \(-0.862645\pi\) | ||||
−0.908333 | + | 0.418247i | \(0.862645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4829 | −1.44815 | −0.724075 | − | 0.689721i | \(-0.757733\pi\) | ||||
−0.724075 | + | 0.689721i | \(0.757733\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.67994 | −0.419874 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.40251 | 0.103115 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.0225 | 1.24481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −26.1670 | −1.90337 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.62183 | 0.189709 | 0.0948543 | − | 0.995491i | \(-0.469761\pi\) | ||||
0.0948543 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4332 | 1.25487 | 0.627436 | − | 0.778668i | \(-0.284105\pi\) | ||||
0.627436 | + | 0.778668i | \(0.284105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.67149 | −0.262921 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.4402 | −1.67004 | −0.835022 | − | 0.550217i | \(-0.814545\pi\) | ||||
−0.835022 | + | 0.550217i | \(0.814545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.29759 | −0.0919839 | −0.0459920 | − | 0.998942i | \(-0.514645\pi\) | ||||
−0.0459920 | + | 0.998942i | \(0.514645\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1998 | −0.789976 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −41.6962 | −2.92650 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7134 | −0.748258 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.28151 | 0.0890709 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.03803 | −0.210145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7619 | 1.01625 | 0.508127 | − | 0.861282i | \(-0.330338\pi\) | ||||
0.508127 | + | 0.861282i | \(0.330338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.5571 | −0.791877 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.37268 | 0.500490 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.90053 | 0.466295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.3771 | −1.43798 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8434 | 0.793095 | 0.396548 | − | 0.918014i | \(-0.370208\pi\) | ||||
0.396548 | + | 0.918014i | \(0.370208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.28151 | −0.0854338 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.27556 | −0.350151 | −0.175075 | − | 0.984555i | \(-0.556017\pi\) | ||||
−0.175075 | + | 0.984555i | \(0.556017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.23878 | −0.0818611 | −0.0409305 | − | 0.999162i | \(-0.513032\pi\) | ||||
−0.0409305 | + | 0.999162i | \(0.513032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.6301 | 0.896798 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.66412 | 0.174533 | 0.0872663 | − | 0.996185i | \(-0.472187\pi\) | ||||
0.0872663 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.26391 | 0.473845 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.28418 | −0.603072 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.2577 | 1.69847 | 0.849235 | − | 0.528014i | \(-0.177063\pi\) | ||||
0.849235 | + | 0.528014i | \(0.177063\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.22326 | −0.143213 | −0.0716063 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716063 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.2325 | −0.784717 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7353 | −0.941406 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.81520 | 0.242755 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.02690 | 0.381940 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4829 | 0.851031 | 0.425515 | − | 0.904951i | \(-0.360093\pi\) | ||||
0.425515 | + | 0.904951i | \(0.360093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23020 | −0.140211 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.0058 | 0.626589 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0281 | 1.37408 | 0.687039 | − | 0.726620i | \(-0.258910\pi\) | ||||
0.687039 | + | 0.726620i | \(0.258910\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.53868 | 0.406294 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4613 | −0.709438 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.3164 | 1.37609 | 0.688043 | − | 0.725670i | \(-0.258470\pi\) | ||||
0.688043 | + | 0.725670i | \(0.258470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.38212 | 0.514909 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.16445 | 0.377258 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5050 | 0.640501 | 0.320251 | − | 0.947333i | \(-0.396233\pi\) | ||||
0.320251 | + | 0.947333i | \(0.396233\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.84696 | −0.233686 | −0.116843 | − | 0.993150i | \(-0.537277\pi\) | ||||
−0.116843 | + | 0.993150i | \(0.537277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.1169 | −1.03596 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.23020 | 0.134486 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8653 | 0.893172 | 0.446586 | − | 0.894741i | \(-0.352640\pi\) | ||||
0.446586 | + | 0.894741i | \(0.352640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.02658 | 0.121328 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.41659 | 0.263472 | 0.131736 | − | 0.991285i | \(-0.457945\pi\) | ||||
0.131736 | + | 0.991285i | \(0.457945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.88495 | 0.230936 | 0.115468 | − | 0.993311i | \(-0.463163\pi\) | ||||
0.115468 | + | 0.993311i | \(0.463163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.78575 | −0.105779 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −49.9472 | −2.94829 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.2583 | 2.42696 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.6511 | −1.26921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.0257 | −1.46202 | −0.731009 | − | 0.682368i | \(-0.760950\pi\) | ||||
−0.731009 | + | 0.682368i | \(0.760950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.88331 | 0.284317 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.5174 | 0.726333 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80072 | 0.161970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.0618 | −0.807831 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.33282 | −0.248096 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0197 | 1.25673 | 0.628365 | − | 0.777918i | \(-0.283724\pi\) | ||||
0.628365 | + | 0.777918i | \(0.283724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.56021 | −0.145645 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6217 | 1.11264 | 0.556322 | − | 0.830967i | \(-0.312212\pi\) | ||||
0.556322 | + | 0.830967i | \(0.312212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9496 | −1.01457 | −0.507285 | − | 0.861778i | \(-0.669351\pi\) | ||||
−0.507285 | + | 0.861778i | \(0.669351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.97454 | −0.336627 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.3185 | 1.92752 | 0.963761 | − | 0.266768i | \(-0.0859559\pi\) | ||||
0.963761 | + | 0.266768i | \(0.0859559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.9461 | 1.11676 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.58992 | 0.144555 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3974 | −0.578529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.80072 | −0.155356 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.6981 | 0.646904 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.8652 | 1.86705 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.299762 | −0.0164764 | −0.00823821 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823821 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.79733 | 0.0984931 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.54355 | −0.466784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2965 | −1.21457 | −0.607284 | − | 0.794485i | \(-0.707741\pi\) | ||||
−0.607284 | + | 0.794485i | \(0.707741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.7425 | −1.23520 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.52684 | −0.190989 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −36.0630 | −1.94722 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.31091 | −0.0705772 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.1240 | 1.77819 | 0.889094 | − | 0.457725i | \(-0.151336\pi\) | ||||
0.889094 | + | 0.457725i | \(0.151336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0041 | −1.17785 | −0.588926 | − | 0.808187i | \(-0.700449\pi\) | ||||
−0.588926 | + | 0.808187i | \(0.700449\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7195 | −0.839046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.6085 | −0.830759 | −0.415379 | − | 0.909648i | \(-0.636351\pi\) | ||||
−0.415379 | + | 0.909648i | \(0.636351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.81604 | −0.467907 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 46.6483 | 2.46889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.263781 | 0.0139218 | 0.00696092 | − | 0.999976i | \(-0.497784\pi\) | ||||
0.00696092 | + | 0.999976i | \(0.497784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1444 | −0.902334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.89984 | 0.414634 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.26391 | 0.275526 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8615 | 0.566967 | 0.283484 | − | 0.958977i | \(-0.408510\pi\) | ||||
0.283484 | + | 0.958977i | \(0.408510\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.7293 | −0.714721 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.0784 | 2.02885 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.8889 | 1.39225 | 0.696127 | − | 0.717919i | \(-0.254905\pi\) | ||||
0.696127 | + | 0.717919i | \(0.254905\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.31091 | 0.0676952 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.0485 | −1.29007 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.15824 | −0.110861 | −0.0554306 | − | 0.998463i | \(-0.517653\pi\) | ||||
−0.0554306 | + | 0.998463i | \(0.517653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.5460 | −1.30876 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.62814 | −0.236487 | −0.118244 | − | 0.992985i | \(-0.537726\pi\) | ||||
−0.118244 | + | 0.992985i | \(0.537726\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3974 | 0.529903 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4988 | −0.937929 | −0.468964 | − | 0.883217i | \(-0.655373\pi\) | ||||
−0.468964 | + | 0.883217i | \(0.655373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.63271 | −0.386003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.44664 | −0.375634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.08222 | −0.356345 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2685 | −0.515360 | −0.257680 | − | 0.966230i | \(-0.582958\pi\) | ||||
−0.257680 | + | 0.966230i | \(0.582958\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.32539 | −0.416791 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.885607 | −0.0442251 | −0.0221125 | − | 0.999755i | \(-0.507039\pi\) | ||||
−0.0221125 | + | 0.999755i | \(0.507039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.42906 | 0.220627 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.51322 | 0.174573 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.12788 | −0.155043 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3497 | 1.20401 | 0.602006 | − | 0.798491i | \(-0.294368\pi\) | ||||
0.602006 | + | 0.798491i | \(0.294368\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3872 | 0.561688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.7665 | 1.12027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.59749 | 0.225682 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0941 | 0.592249 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4535 | 1.24348 | 0.621742 | − | 0.783222i | \(-0.286425\pi\) | ||||
0.621742 | + | 0.783222i | \(0.286425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2376 | 0.742634 | 0.371317 | − | 0.928506i | \(-0.378906\pi\) | ||||
0.371317 | + | 0.928506i | \(0.378906\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.30876 | 0.452607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.63271 | 0.370241 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.2001 | −0.977551 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.18816 | 0.395328 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.6166 | −1.66742 | −0.833711 | − | 0.552202i | \(-0.813788\pi\) | ||||
−0.833711 | + | 0.552202i | \(0.813788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4774 | 1.36854 | 0.684268 | − | 0.729230i | \(-0.260122\pi\) | ||||
0.684268 | + | 0.729230i | \(0.260122\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.7243 | 0.562138 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.36222 | 0.0651639 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.6009 | 1.03095 | 0.515477 | − | 0.856904i | \(-0.327615\pi\) | ||||
0.515477 | + | 0.856904i | \(0.327615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8834 | −0.899211 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.3700 | 1.91804 | 0.959018 | − | 0.283346i | \(-0.0914445\pi\) | ||||
0.959018 | + | 0.283346i | \(0.0914445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.70241 | 0.222915 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.3903 | −1.15362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.95484 | 0.281026 | 0.140513 | − | 0.990079i | \(-0.455125\pi\) | ||||
0.140513 | + | 0.990079i | \(0.455125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.8931 | 1.12508 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.8512 | −1.07365 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.0573 | −0.612134 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.66169 | −0.264843 | −0.132421 | − | 0.991194i | \(-0.542275\pi\) | ||||
−0.132421 | + | 0.991194i | \(0.542275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 42.8400 | 1.99960 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.26391 | −0.431463 | −0.215732 | − | 0.976453i | \(-0.569214\pi\) | ||||
−0.215732 | + | 0.976453i | \(0.569214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.9899 | 1.76554 | 0.882769 | − | 0.469807i | \(-0.155676\pi\) | ||||
0.882769 | + | 0.469807i | \(0.155676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.07308 | −0.0961368 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.2865 | −1.21640 | −0.608198 | − | 0.793785i | \(-0.708107\pi\) | ||||
−0.608198 | + | 0.793785i | \(0.708107\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.8310 | −1.83922 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.10051 | −0.0507087 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.36222 | −0.0625030 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7417 | 0.491831 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.0770 | −1.41994 | −0.709971 | − | 0.704231i | \(-0.751292\pi\) | ||||
−0.709971 | + | 0.704231i | \(0.751292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.92804 | 0.179103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.11163 | −0.278089 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5160 | −0.749954 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9591 | 0.677860 | 0.338930 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338930 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0965 | 0.863573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.1333 | 1.08912 | 0.544561 | − | 0.838721i | \(-0.316696\pi\) | ||||
0.544561 | + | 0.838721i | \(0.316696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 68.2641 | 3.07446 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.85802 | 0.128458 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41.1014 | −1.84365 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7266 | −0.793552 | −0.396776 | − | 0.917915i | \(-0.629871\pi\) | ||||
−0.396776 | + | 0.917915i | \(0.629871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.60492 | 0.295086 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.69566 | −0.343133 | −0.171566 | − | 0.985173i | \(-0.554883\pi\) | ||||
−0.171566 | + | 0.985173i | \(0.554883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7267 | −0.477334 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.75906 | 0.300180 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.0564 | −1.46520 | −0.732600 | − | 0.680659i | \(-0.761693\pi\) | ||||
−0.732600 | + | 0.680659i | \(0.761693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.5410 | 1.08563 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.64572 | −0.337567 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.95300 | −0.0860595 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2000 | −0.712474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.8296 | 0.650947 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.6047 | 0.464598 | 0.232299 | − | 0.972644i | \(-0.425375\pi\) | ||||
0.232299 | + | 0.972644i | \(0.425375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.5128 | −1.50914 | −0.754570 | − | 0.656219i | \(-0.772155\pi\) | ||||
−0.754570 | + | 0.656219i | \(0.772155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.11163 | 0.266733 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0704 | −0.525794 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.25799 | 0.271574 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.0053 | −1.29967 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.97566 | 0.0854153 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.8622 | 1.37495 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.8627 | 1.41550 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3344 | −1.17520 | −0.587598 | − | 0.809153i | \(-0.699926\pi\) | ||||
−0.587598 | + | 0.809153i | \(0.699926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.5403 | 1.09604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.92360 | 0.382245 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6190 | 1.48020 | 0.740101 | − | 0.672496i | \(-0.234778\pi\) | ||||
0.740101 | + | 0.672496i | \(0.234778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.55254 | −0.236977 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.1832 | −0.519022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.0181 | −1.40407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.83857 | −0.0780430 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.2490 | 1.06983 | 0.534917 | − | 0.844905i | \(-0.320343\pi\) | ||||
0.534917 | + | 0.844905i | \(0.320343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.3150 | −0.942139 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.0793 | 1.73128 | 0.865642 | − | 0.500663i | \(-0.166910\pi\) | ||||
0.865642 | + | 0.500663i | \(0.166910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.3486 | −0.729860 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.3790 | 0.687854 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.4230 | −1.19155 | −0.595776 | − | 0.803150i | \(-0.703156\pi\) | ||||
−0.595776 | + | 0.803150i | \(0.703156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.4690 | 0.563659 | 0.281830 | − | 0.959464i | \(-0.409059\pi\) | ||||
0.281830 | + | 0.959464i | \(0.409059\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.43698 | −0.143582 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.69392 | 0.153780 | 0.0768899 | − | 0.997040i | \(-0.475501\pi\) | ||||
0.0768899 | + | 0.997040i | \(0.475501\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.8534 | −0.949757 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.4340 | 0.889233 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.6938 | −0.774218 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.58914 | −0.148393 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.1042 | 0.788513 | 0.394257 | − | 0.919000i | \(-0.371002\pi\) | ||||
0.394257 | + | 0.919000i | \(0.371002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.15422 | 0.0887631 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.7280 | 1.26398 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.9194 | 0.571602 | 0.285801 | − | 0.958289i | \(-0.407740\pi\) | ||||
0.285801 | + | 0.958289i | \(0.407740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.5846 | 1.45883 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.70103 | 0.0696186 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.9498 | 0.447396 | 0.223698 | − | 0.974659i | \(-0.428187\pi\) | ||||
0.223698 | + | 0.974659i | \(0.428187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.7034 | 1.17084 | 0.585418 | − | 0.810731i | \(-0.300930\pi\) | ||||
0.585418 | + | 0.810731i | \(0.300930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9486 | −0.445862 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.02621 | 0.245000 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.7745 | −1.77675 | −0.888376 | − | 0.459117i | \(-0.848166\pi\) | ||||
−0.888376 | + | 0.459117i | \(0.848166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 54.6601 | 2.21494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.3442 | 0.823036 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.59492 | 0.266366 | 0.133183 | − | 0.991091i | \(-0.457480\pi\) | ||||
0.133183 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.0444 | 0.566324 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.3939 | 0.821029 | 0.410514 | − | 0.911854i | \(-0.365349\pi\) | ||||
0.410514 | + | 0.911854i | \(0.365349\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.513389 | 0.0206348 | 0.0103174 | − | 0.999947i | \(-0.496716\pi\) | ||||
0.0103174 | + | 0.999947i | \(0.496716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.61268 | −0.225229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.9232 | 0.878333 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.98259 | 0.159049 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.7050 | −0.426835 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3428 | 0.650596 | 0.325298 | − | 0.945612i | \(-0.394535\pi\) | ||||
0.325298 | + | 0.945612i | \(0.394535\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.3516 | −0.769157 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.4872 | −0.773325 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.2695 | −1.63516 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.2978 | −0.446935 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7798 | −1.33422 | −0.667110 | − | 0.744959i | \(-0.732469\pi\) | ||||
−0.667110 | + | 0.744959i | \(0.732469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.18090 | −0.0860062 | −0.0430031 | − | 0.999075i | \(-0.513693\pi\) | ||||
−0.0430031 | + | 0.999075i | \(0.513693\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.7346 | −1.36556 | −0.682778 | − | 0.730625i | \(-0.739229\pi\) | ||||
−0.682778 | + | 0.730625i | \(0.739229\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8907 | −0.427499 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.66494 | −0.378799 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.68309 | −0.261530 | −0.130765 | − | 0.991413i | \(-0.541743\pi\) | ||||
−0.130765 | + | 0.991413i | \(0.541743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.68050 | −0.221956 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.74575 | 0.263177 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.8903 | −1.78763 | −0.893815 | − | 0.448435i | \(-0.851982\pi\) | ||||
−0.893815 | + | 0.448435i | \(0.851982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6251 | 0.529957 | 0.264978 | − | 0.964254i | \(-0.414635\pi\) | ||||
0.264978 | + | 0.964254i | \(0.414635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.0234 | 1.08834 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.35084 | −0.246275 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.94362 | −0.346299 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.5257 | −0.600259 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.66304 | 0.373038 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.3475 | −0.977075 | −0.488537 | − | 0.872543i | \(-0.662469\pi\) | ||||
−0.488537 | + | 0.872543i | \(0.662469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.61268 | 0.216032 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2279 | −0.662123 | −0.331062 | − | 0.943609i | \(-0.607407\pi\) | ||||
−0.331062 | + | 0.943609i | \(0.607407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −76.9996 | −2.95497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.91579 | 0.265014 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.5454 | 1.51316 | 0.756582 | − | 0.653899i | \(-0.226868\pi\) | ||||
0.756582 | + | 0.653899i | \(0.226868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.68645 | 0.331892 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.62394 | 0.0619570 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.4759 | 0.894361 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.0501 | −1.10512 | −0.552558 | − | 0.833474i | \(-0.686348\pi\) | ||||
−0.552558 | + | 0.833474i | \(0.686348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.3244 | 0.506152 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.22569 | 0.349950 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 81.7725 | 3.09735 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.49244 | −0.132096 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7735 | −0.671298 | −0.335649 | − | 0.941987i | \(-0.608956\pi\) | ||||
−0.335649 | + | 0.941987i | \(0.608956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.91053 | 0.0720571 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.52236 | −0.358633 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.0093 | −1.88079 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.8606 | −0.558103 | −0.279052 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279052 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.07592 | −0.340374 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.58140 | 0.0592240 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.24615 | 0.233593 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.4216 | −1.28550 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.4365 | 1.02321 | 0.511604 | − | 0.859221i | \(-0.329051\pi\) | ||||
0.511604 | + | 0.859221i | \(0.329051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.10512 | −0.339092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.91449 | 0.108391 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.94362 | 0.332158 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.3674 | −0.866649 | −0.433325 | − | 0.901238i | \(-0.642660\pi\) | ||||
−0.433325 | + | 0.901238i | \(0.642660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5754 | 0.984275 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.53381 | −0.0935884 | −0.0467942 | − | 0.998905i | \(-0.514900\pi\) | ||||
−0.0467942 | + | 0.998905i | \(0.514900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.3167 | 0.712508 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.0538 | 0.701856 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9318 | 0.953918 | 0.476959 | − | 0.878925i | \(-0.341739\pi\) | ||||
0.476959 | + | 0.878925i | \(0.341739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.00139 | −0.183731 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.11370 | −0.0775442 | −0.0387721 | − | 0.999248i | \(-0.512345\pi\) | ||||
−0.0387721 | + | 0.999248i | \(0.512345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.6056 | −0.681657 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.89172 | 0.215567 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.21077 | 0.336554 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.54986 | 0.0930459 | 0.0465229 | − | 0.998917i | \(-0.485186\pi\) | ||||
0.0465229 | + | 0.998917i | \(0.485186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.6749 | −0.644107 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.4316 | −0.634399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.6897 | 1.11544 | 0.557718 | − | 0.830030i | \(-0.311677\pi\) | ||||
0.557718 | + | 0.830030i | \(0.311677\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.92360 | 0.106120 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3112 | 0.700032 | 0.350016 | − | 0.936744i | \(-0.386176\pi\) | ||||
0.350016 | + | 0.936744i | \(0.386176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.6028 | 1.50612 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.78138 | 0.353646 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.6767 | 0.493839 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.52624 | −0.307464 | −0.153732 | − | 0.988113i | \(-0.549129\pi\) | ||||
−0.153732 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.8770 | −1.03998 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.5107 | 1.06143 | 0.530713 | − | 0.847551i | \(-0.321924\pi\) | ||||
0.530713 | + | 0.847551i | \(0.321924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.58140 | −0.0568056 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.57164 | −0.307506 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.5941 | −0.522887 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.6615 | 0.703545 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.1977 | 1.79392 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.839497 | −0.0299629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1733 | −1.32508 | −0.662542 | − | 0.749025i | \(-0.730522\pi\) | ||||
−0.662542 | + | 0.749025i | \(0.730522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.2548 | −1.04150 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −80.8811 | −2.87580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.1350 | −0.430926 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.9882 | −0.389712 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.9954 | 0.602008 | 0.301004 | − | 0.953623i | \(-0.402678\pi\) | ||||
0.301004 | + | 0.953623i | \(0.402678\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.4434 | −1.96144 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.02617 | 0.212924 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.7396 | −0.414281 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.66212 | −0.164318 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.7711 | −0.484767 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.8409 | 0.592095 | 0.296047 | − | 0.955173i | \(-0.404331\pi\) | ||||
0.296047 | + | 0.955173i | \(0.404331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.44804 | 0.156192 | 0.0780959 | − | 0.996946i | \(-0.475116\pi\) | ||||
0.0780959 | + | 0.996946i | \(0.475116\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.04303 | 0.176867 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.5673 | 0.510271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.7330 | −0.584698 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.7361 | −0.584093 | −0.292047 | − | 0.956404i | \(-0.594336\pi\) | ||||
−0.292047 | + | 0.956404i | \(0.594336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.6605 | −1.52191 | −0.760955 | − | 0.648805i | \(-0.775269\pi\) | ||||
−0.760955 | + | 0.648805i | \(0.775269\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.92360 | −0.101787 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.9750 | −1.32052 | −0.660260 | − | 0.751037i | \(-0.729554\pi\) | ||||
−0.660260 | + | 0.751037i | \(0.729554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9046 | 0.621851 | 0.310925 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310925 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4872 | −0.676002 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 112.471 | 3.89687 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.03842 | 0.174362 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.87591 | −0.306796 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4503 | −1.46555 | −0.732773 | − | 0.680473i | \(-0.761774\pi\) | ||||
−0.732773 | + | 0.680473i | \(0.761774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.9884 | 1.75822 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.78976 | −0.199410 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.15599 | 0.177372 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0949 | 0.965353 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.09283 | −0.174785 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.40251 | 0.0480775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.9952 | −0.787339 | −0.393670 | − | 0.919252i | \(-0.628795\pi\) | ||||
−0.393670 | + | 0.919252i | \(0.628795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.74570 | −0.0597016 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.46053 | −0.323166 | −0.161583 | − | 0.986859i | \(-0.551660\pi\) | ||||
−0.161583 | + | 0.986859i | \(0.551660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.20043 | −0.211556 | −0.105778 | − | 0.994390i | \(-0.533733\pi\) | ||||
−0.105778 | + | 0.994390i | \(0.533733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 65.4765 | 2.23143 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.68754 | −0.329768 | −0.164884 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164884 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.3124 | 0.384634 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −54.0860 | −1.83686 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.7948 | 0.535801 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9280 | −0.810771 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.1654 | −0.716340 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.66212 | 0.157608 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.5663 | 1.74127 | 0.870636 | − | 0.491928i | \(-0.163708\pi\) | ||||
0.870636 | + | 0.491928i | \(0.163708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.8065 | 1.10654 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.5969 | −1.13191 | −0.565954 | − | 0.824437i | \(-0.691492\pi\) | ||||
−0.565954 | + | 0.824437i | \(0.691492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.7914 | 0.396814 | 0.198407 | − | 0.980120i | \(-0.436423\pi\) | ||||
0.198407 | + | 0.980120i | \(0.436423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.40159 | −0.215187 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.9578 | −1.84530 | −0.922652 | − | 0.385634i | \(-0.873983\pi\) | ||||
−0.922652 | + | 0.385634i | \(0.873983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −90.8515 | −3.04706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.83517 | −0.262488 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.89506 | 0.331126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.3053 | 0.812438 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.67149 | −0.122588 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.1435 | −0.471711 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63.9783 | −2.13143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.4829 | 0.647632 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.41429 | 0.279392 | 0.139696 | − | 0.990194i | \(-0.455387\pi\) | ||||
0.139696 | + | 0.990194i | \(0.455387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7464 | −0.455940 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.4143 | −0.875146 | −0.437573 | − | 0.899183i | \(-0.644162\pi\) | ||||
−0.437573 | + | 0.899183i | \(0.644162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2533 | −0.339335 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.67994 | 0.187773 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.4832 | −0.874551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.2734 | 1.95525 | 0.977624 | − | 0.210359i | \(-0.0674633\pi\) | ||||
0.977624 | + | 0.210359i | \(0.0674633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.8659 | −0.951164 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.6912 | −0.812722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.40251 | −0.0461143 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.50279 | −0.0822023 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.2475 | −0.565871 | −0.282935 | − | 0.959139i | \(-0.591308\pi\) | ||||
−0.282935 | + | 0.959139i | \(0.591308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0728 | −0.657859 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.7223 | −0.842111 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.0225 | −0.556694 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.6918 | −0.708642 | −0.354321 | − | 0.935124i | \(-0.615288\pi\) | ||||
−0.354321 | + | 0.935124i | \(0.615288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.5303 | 0.767883 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.1158 | −0.362365 | −0.181182 | − | 0.983449i | \(-0.557992\pi\) | ||||
−0.181182 | + | 0.983449i | \(0.557992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7134 | −0.348877 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 26.1670 | 0.851212 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.8093 | −1.32613 | −0.663063 | − | 0.748564i | \(-0.730744\pi\) | ||||
−0.663063 | + | 0.748564i | \(0.730744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7427 | 0.478569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.9886 | −1.45886 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.8237 | 0.383009 | 0.191504 | − | 0.981492i | \(-0.438663\pi\) | ||||
0.191504 | + | 0.981492i | \(0.438663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.62183 | −0.0848403 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26.1475 | −0.845230 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.4973 | 1.30772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4992 | −0.919328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.53183 | 0.0815869 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.4332 | −0.561195 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.8536 | 0.895710 | 0.447855 | − | 0.894106i | \(-0.352188\pi\) | ||||
0.447855 | + | 0.894106i | \(0.352188\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.6301 | 0.437863 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5249 | −0.530309 | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||||
−0.265155 | + | 0.964206i | \(0.585423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.0112 | 1.37888 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.67149 | 0.117582 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.0059 | −1.59983 | −0.799915 | − | 0.600114i | \(-0.795122\pi\) | ||||
−0.799915 | + | 0.600114i | \(0.795122\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.4873 | −0.335176 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4357 | 0.365112 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7894 | 0.726869 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.4402 | 0.746866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.3943 | −1.41309 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.9822 | 1.07948 | 0.539740 | − | 0.841832i | \(-0.318522\pi\) | ||||
0.539740 | + | 0.841832i | \(0.318522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.392962 | 0.0124703 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.29759 | 0.0411365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7258 | −0.561382 | −0.280691 | − | 0.959798i | \(-0.590564\pi\) | ||||
−0.280691 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.87186 | −0.249055 |
(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 | 920.2.a.j.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 8280.2.a.bs.1.1 | 5 | |||
4.3 | odd | 2 | 1840.2.a.v.1.4 | 5 | |||
5.2 | odd | 4 | 4600.2.e.u.4049.7 | 10 | |||
5.3 | odd | 4 | 4600.2.e.u.4049.4 | 10 | |||
5.4 | even | 2 | 4600.2.a.be.1.4 | 5 | |||
8.3 | odd | 2 | 7360.2.a.cp.1.2 | 5 | |||
8.5 | even | 2 | 7360.2.a.co.1.4 | 5 | |||
20.19 | odd | 2 | 9200.2.a.cu.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.j.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1840.2.a.v.1.4 | 5 | 4.3 | odd | 2 | |||
4600.2.a.be.1.4 | 5 | 5.4 | even | 2 | |||
4600.2.e.u.4049.4 | 10 | 5.3 | odd | 4 | |||
4600.2.e.u.4049.7 | 10 | 5.2 | odd | 4 | |||
7360.2.a.co.1.4 | 5 | 8.5 | even | 2 | |||
7360.2.a.cp.1.2 | 5 | 8.3 | odd | 2 | |||
8280.2.a.bs.1.1 | 5 | 3.2 | odd | 2 | |||
9200.2.a.cu.1.2 | 5 | 20.19 | odd | 2 |