Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5775,2,Mod(1,5775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5775, 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("5775.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5775.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: | \(46.1136071673\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5775.1 |
$q$-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 | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 5.47214 | 1.51770 | 0.758849 | − | 0.651267i | \(-0.225762\pi\) | ||||
0.758849 | + | 0.651267i | \(0.225762\pi\) | |||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | 6.70820 | 1.53897 | 0.769484 | − | 0.638666i | \(-0.220514\pi\) | ||||
0.769484 | + | 0.638666i | \(0.220514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.61803 | −0.344966 | ||||||||
\(23\) | 7.70820 | 1.60727 | 0.803636 | − | 0.595121i | \(-0.202896\pi\) | ||||
0.803636 | + | 0.595121i | \(0.202896\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.85410 | −1.73643 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.618034 | −0.116797 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.763932 | −0.137206 | −0.0686031 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686031 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 1.23607 | 0.211984 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | −10.8541 | −1.76077 | ||||||||
\(39\) | −5.47214 | −0.876243 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.47214 | 1.01078 | 0.505389 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505389 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | 0.618034 | 0.0931721 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.4721 | −1.83892 | ||||||||
\(47\) | 4.23607 | 0.617894 | 0.308947 | − | 0.951079i | \(-0.400023\pi\) | ||||
0.308947 | + | 0.951079i | \(0.400023\pi\) | |||||||
\(48\) | 4.85410 | 0.700629 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.763932 | 0.106972 | ||||||||
\(52\) | 3.38197 | 0.468994 | ||||||||
\(53\) | −10.1803 | −1.39838 | −0.699189 | − | 0.714937i | \(-0.746455\pi\) | ||||
−0.699189 | + | 0.714937i | \(0.746455\pi\) | |||||||
\(54\) | 1.61803 | 0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | −6.70820 | −0.888523 | ||||||||
\(58\) | −8.09017 | −1.06229 | ||||||||
\(59\) | 11.1803 | 1.45556 | 0.727778 | − | 0.685813i | \(-0.240553\pi\) | ||||
0.727778 | + | 0.685813i | \(0.240553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 1.23607 | 0.156981 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.61803 | 0.199166 | ||||||||
\(67\) | 14.2361 | 1.73921 | 0.869606 | − | 0.493746i | \(-0.164373\pi\) | ||||
0.869606 | + | 0.493746i | \(0.164373\pi\) | |||||||
\(68\) | −0.472136 | −0.0572549 | ||||||||
\(69\) | −7.70820 | −0.927959 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47214 | 0.768101 | 0.384051 | − | 0.923312i | \(-0.374529\pi\) | ||||
0.384051 | + | 0.923312i | \(0.374529\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | −13.4721 | −1.57679 | −0.788397 | − | 0.615167i | \(-0.789089\pi\) | ||||
−0.788397 | + | 0.615167i | \(0.789089\pi\) | |||||||
\(74\) | −11.3262 | −1.31665 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.14590 | 0.475567 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 8.85410 | 1.00253 | ||||||||
\(79\) | −5.52786 | −0.621933 | −0.310967 | − | 0.950421i | \(-0.600653\pi\) | ||||
−0.310967 | + | 0.950421i | \(0.600653\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.4721 | −1.15645 | ||||||||
\(83\) | −11.2361 | −1.23332 | −0.616659 | − | 0.787230i | \(-0.711514\pi\) | ||||
−0.616659 | + | 0.787230i | \(0.711514\pi\) | |||||||
\(84\) | 0.618034 | 0.0674330 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.4721 | −1.34491 | ||||||||
\(87\) | −5.00000 | −0.536056 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | 4.47214 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.47214 | −0.573636 | ||||||||
\(92\) | 4.76393 | 0.496674 | ||||||||
\(93\) | 0.763932 | 0.0792161 | ||||||||
\(94\) | −6.85410 | −0.706947 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.38197 | −0.345170 | ||||||||
\(97\) | 3.70820 | 0.376511 | 0.188256 | − | 0.982120i | \(-0.439717\pi\) | ||||
0.188256 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(98\) | −1.61803 | −0.163446 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.18034 | −0.415959 | −0.207980 | − | 0.978133i | \(-0.566689\pi\) | ||||
−0.207980 | + | 0.978133i | \(0.566689\pi\) | |||||||
\(102\) | −1.23607 | −0.122389 | ||||||||
\(103\) | 9.41641 | 0.927826 | 0.463913 | − | 0.885881i | \(-0.346445\pi\) | ||||
0.463913 | + | 0.885881i | \(0.346445\pi\) | |||||||
\(104\) | 12.2361 | 1.19985 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.4721 | 1.59992 | ||||||||
\(107\) | −0.236068 | −0.0228216 | −0.0114108 | − | 0.999935i | \(-0.503632\pi\) | ||||
−0.0114108 | + | 0.999935i | \(0.503632\pi\) | |||||||
\(108\) | −0.618034 | −0.0594703 | ||||||||
\(109\) | 7.23607 | 0.693090 | 0.346545 | − | 0.938033i | \(-0.387355\pi\) | ||||
0.346545 | + | 0.938033i | \(0.387355\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | 4.85410 | 0.458670 | ||||||||
\(113\) | −8.47214 | −0.796992 | −0.398496 | − | 0.917170i | \(-0.630468\pi\) | ||||
−0.398496 | + | 0.917170i | \(0.630468\pi\) | |||||||
\(114\) | 10.8541 | 1.01658 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.09017 | 0.286915 | ||||||||
\(117\) | 5.47214 | 0.505899 | ||||||||
\(118\) | −18.0902 | −1.66534 | ||||||||
\(119\) | 0.763932 | 0.0700295 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.23607 | −0.292980 | ||||||||
\(123\) | −6.47214 | −0.583573 | ||||||||
\(124\) | −0.472136 | −0.0423991 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.61803 | 0.144146 | ||||||||
\(127\) | −18.6525 | −1.65514 | −0.827570 | − | 0.561363i | \(-0.810277\pi\) | ||||
−0.827570 | + | 0.561363i | \(0.810277\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | −7.70820 | −0.678670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9443 | −1.48043 | −0.740214 | − | 0.672371i | \(-0.765276\pi\) | ||||
−0.740214 | + | 0.672371i | \(0.765276\pi\) | |||||||
\(132\) | −0.618034 | −0.0537930 | ||||||||
\(133\) | −6.70820 | −0.581675 | ||||||||
\(134\) | −23.0344 | −1.98987 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.70820 | −0.146477 | ||||||||
\(137\) | −6.29180 | −0.537544 | −0.268772 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268772 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(138\) | 12.4721 | 1.06170 | ||||||||
\(139\) | 5.52786 | 0.468867 | 0.234434 | − | 0.972132i | \(-0.424676\pi\) | ||||
0.234434 | + | 0.972132i | \(0.424676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.23607 | −0.356741 | ||||||||
\(142\) | −10.4721 | −0.878802 | ||||||||
\(143\) | 5.47214 | 0.457603 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.7984 | 1.80405 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 4.32624 | 0.355615 | ||||||||
\(149\) | 5.00000 | 0.409616 | 0.204808 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204808 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.18034 | 0.665707 | 0.332853 | − | 0.942979i | \(-0.391989\pi\) | ||||
0.332853 | + | 0.942979i | \(0.391989\pi\) | |||||||
\(152\) | 15.0000 | 1.21666 | ||||||||
\(153\) | −0.763932 | −0.0617602 | ||||||||
\(154\) | 1.61803 | 0.130385 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.38197 | −0.270774 | ||||||||
\(157\) | −11.4164 | −0.911129 | −0.455564 | − | 0.890203i | \(-0.650562\pi\) | ||||
−0.455564 | + | 0.890203i | \(0.650562\pi\) | |||||||
\(158\) | 8.94427 | 0.711568 | ||||||||
\(159\) | 10.1803 | 0.807353 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.70820 | −0.607492 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | 9.29180 | 0.727790 | 0.363895 | − | 0.931440i | \(-0.381447\pi\) | ||||
0.363895 | + | 0.931440i | \(0.381447\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.1803 | 1.41107 | ||||||||
\(167\) | −8.65248 | −0.669549 | −0.334774 | − | 0.942298i | \(-0.608660\pi\) | ||||
−0.334774 | + | 0.942298i | \(0.608660\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | 16.9443 | 1.30341 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.70820 | 0.512989 | ||||||||
\(172\) | 4.76393 | 0.363246 | ||||||||
\(173\) | 10.4721 | 0.796182 | 0.398091 | − | 0.917346i | \(-0.369673\pi\) | ||||
0.398091 | + | 0.917346i | \(0.369673\pi\) | |||||||
\(174\) | 8.09017 | 0.613314 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | −11.1803 | −0.840366 | ||||||||
\(178\) | −7.23607 | −0.542366 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.23607 | −0.389194 | −0.194597 | − | 0.980883i | \(-0.562340\pi\) | ||||
−0.194597 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(182\) | 8.85410 | 0.656310 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 17.2361 | 1.27066 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.23607 | −0.0906329 | ||||||||
\(187\) | −0.763932 | −0.0558642 | ||||||||
\(188\) | 2.61803 | 0.190940 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2361 | −1.10244 | −0.551222 | − | 0.834359i | \(-0.685838\pi\) | ||||
−0.551222 | + | 0.834359i | \(0.685838\pi\) | |||||||
\(192\) | −4.23607 | −0.305712 | ||||||||
\(193\) | 16.6525 | 1.19867 | 0.599336 | − | 0.800498i | \(-0.295431\pi\) | ||||
0.599336 | + | 0.800498i | \(0.295431\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 7.52786 | 0.536338 | 0.268169 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268169 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(198\) | −1.61803 | −0.114989 | ||||||||
\(199\) | −26.1803 | −1.85588 | −0.927938 | − | 0.372736i | \(-0.878420\pi\) | ||||
−0.927938 | + | 0.372736i | \(0.878420\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.2361 | −1.00413 | ||||||||
\(202\) | 6.76393 | 0.475909 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0.472136 | 0.0330561 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.2361 | −1.06155 | ||||||||
\(207\) | 7.70820 | 0.535757 | ||||||||
\(208\) | −26.5623 | −1.84176 | ||||||||
\(209\) | 6.70820 | 0.464016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4164 | −1.47437 | −0.737183 | − | 0.675693i | \(-0.763845\pi\) | ||||
−0.737183 | + | 0.675693i | \(0.763845\pi\) | |||||||
\(212\) | −6.29180 | −0.432122 | ||||||||
\(213\) | −6.47214 | −0.443463 | ||||||||
\(214\) | 0.381966 | 0.0261107 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 0.763932 | 0.0518591 | ||||||||
\(218\) | −11.7082 | −0.792980 | ||||||||
\(219\) | 13.4721 | 0.910363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.18034 | −0.281200 | ||||||||
\(222\) | 11.3262 | 0.760167 | ||||||||
\(223\) | 6.00000 | 0.401790 | 0.200895 | − | 0.979613i | \(-0.435615\pi\) | ||||
0.200895 | + | 0.979613i | \(0.435615\pi\) | |||||||
\(224\) | −3.38197 | −0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.7082 | 0.911856 | ||||||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | −4.14590 | −0.274569 | ||||||||
\(229\) | 2.76393 | 0.182646 | 0.0913229 | − | 0.995821i | \(-0.470890\pi\) | ||||
0.0913229 | + | 0.995821i | \(0.470890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 11.1803 | 0.734025 | ||||||||
\(233\) | −2.94427 | −0.192886 | −0.0964428 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964428 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(234\) | −8.85410 | −0.578811 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.90983 | 0.449792 | ||||||||
\(237\) | 5.52786 | 0.359073 | ||||||||
\(238\) | −1.23607 | −0.0801224 | ||||||||
\(239\) | −30.1246 | −1.94860 | −0.974300 | − | 0.225256i | \(-0.927678\pi\) | ||||
−0.974300 | + | 0.225256i | \(0.927678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.05573 | 0.518915 | 0.259458 | − | 0.965755i | \(-0.416456\pi\) | ||||
0.259458 | + | 0.965755i | \(0.416456\pi\) | |||||||
\(242\) | −1.61803 | −0.104011 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.23607 | 0.0791311 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4721 | 0.667679 | ||||||||
\(247\) | 36.7082 | 2.33569 | ||||||||
\(248\) | −1.70820 | −0.108471 | ||||||||
\(249\) | 11.2361 | 0.712057 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.1246 | −1.77521 | −0.887605 | − | 0.460606i | \(-0.847632\pi\) | ||||
−0.887605 | + | 0.460606i | \(0.847632\pi\) | |||||||
\(252\) | −0.618034 | −0.0389325 | ||||||||
\(253\) | 7.70820 | 0.484611 | ||||||||
\(254\) | 30.1803 | 1.89368 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 7.00000 | 0.436648 | 0.218324 | − | 0.975876i | \(-0.429941\pi\) | ||||
0.218324 | + | 0.975876i | \(0.429941\pi\) | |||||||
\(258\) | 12.4721 | 0.776481 | ||||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 27.4164 | 1.69379 | ||||||||
\(263\) | −14.1246 | −0.870961 | −0.435480 | − | 0.900198i | \(-0.643421\pi\) | ||||
−0.435480 | + | 0.900198i | \(0.643421\pi\) | |||||||
\(264\) | −2.23607 | −0.137620 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.8541 | 0.665508 | ||||||||
\(267\) | −4.47214 | −0.273690 | ||||||||
\(268\) | 8.79837 | 0.537446 | ||||||||
\(269\) | 18.9443 | 1.15505 | 0.577526 | − | 0.816372i | \(-0.304018\pi\) | ||||
0.577526 | + | 0.816372i | \(0.304018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7082 | 1.13644 | 0.568221 | − | 0.822876i | \(-0.307632\pi\) | ||||
0.568221 | + | 0.822876i | \(0.307632\pi\) | |||||||
\(272\) | 3.70820 | 0.224843 | ||||||||
\(273\) | 5.47214 | 0.331189 | ||||||||
\(274\) | 10.1803 | 0.615017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.76393 | −0.286755 | ||||||||
\(277\) | −2.47214 | −0.148536 | −0.0742681 | − | 0.997238i | \(-0.523662\pi\) | ||||
−0.0742681 | + | 0.997238i | \(0.523662\pi\) | |||||||
\(278\) | −8.94427 | −0.536442 | ||||||||
\(279\) | −0.763932 | −0.0457354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.52786 | 0.150800 | 0.0753999 | − | 0.997153i | \(-0.475977\pi\) | ||||
0.0753999 | + | 0.997153i | \(0.475977\pi\) | |||||||
\(282\) | 6.85410 | 0.408156 | ||||||||
\(283\) | 18.2361 | 1.08402 | 0.542011 | − | 0.840371i | \(-0.317663\pi\) | ||||
0.542011 | + | 0.840371i | \(0.317663\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.85410 | −0.523554 | ||||||||
\(287\) | −6.47214 | −0.382038 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.70820 | −0.217379 | ||||||||
\(292\) | −8.32624 | −0.487256 | ||||||||
\(293\) | 16.0000 | 0.934730 | 0.467365 | − | 0.884064i | \(-0.345203\pi\) | ||||
0.467365 | + | 0.884064i | \(0.345203\pi\) | |||||||
\(294\) | 1.61803 | 0.0943657 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.6525 | 0.909782 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −8.09017 | −0.468651 | ||||||||
\(299\) | 42.1803 | 2.43935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.70820 | −0.444293 | ||||||||
\(302\) | −13.2361 | −0.761650 | ||||||||
\(303\) | 4.18034 | 0.240154 | ||||||||
\(304\) | −32.5623 | −1.86758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.23607 | 0.0706613 | ||||||||
\(307\) | 3.05573 | 0.174400 | 0.0871998 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0871998 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(308\) | −0.618034 | −0.0352158 | ||||||||
\(309\) | −9.41641 | −0.535681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.8885 | −1.46800 | −0.734002 | − | 0.679147i | \(-0.762350\pi\) | ||||
−0.734002 | + | 0.679147i | \(0.762350\pi\) | |||||||
\(312\) | −12.2361 | −0.692731 | ||||||||
\(313\) | 6.65248 | 0.376020 | 0.188010 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188010 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(314\) | 18.4721 | 1.04244 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.41641 | −0.192188 | ||||||||
\(317\) | −1.81966 | −0.102202 | −0.0511011 | − | 0.998693i | \(-0.516273\pi\) | ||||
−0.0511011 | + | 0.998693i | \(0.516273\pi\) | |||||||
\(318\) | −16.4721 | −0.923712 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.236068 | 0.0131760 | ||||||||
\(322\) | 12.4721 | 0.695045 | ||||||||
\(323\) | −5.12461 | −0.285141 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0344 | −0.832681 | ||||||||
\(327\) | −7.23607 | −0.400155 | ||||||||
\(328\) | 14.4721 | 0.799090 | ||||||||
\(329\) | −4.23607 | −0.233542 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4164 | 0.847362 | 0.423681 | − | 0.905811i | \(-0.360738\pi\) | ||||
0.423681 | + | 0.905811i | \(0.360738\pi\) | |||||||
\(332\) | −6.94427 | −0.381116 | ||||||||
\(333\) | 7.00000 | 0.383598 | ||||||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.85410 | −0.264813 | ||||||||
\(337\) | −14.1803 | −0.772452 | −0.386226 | − | 0.922404i | \(-0.626222\pi\) | ||||
−0.386226 | + | 0.922404i | \(0.626222\pi\) | |||||||
\(338\) | −27.4164 | −1.49126 | ||||||||
\(339\) | 8.47214 | 0.460143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.763932 | −0.0413692 | ||||||||
\(342\) | −10.8541 | −0.586923 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 17.2361 | 0.929307 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.9443 | −0.910930 | ||||||||
\(347\) | −28.0000 | −1.50312 | −0.751559 | − | 0.659665i | \(-0.770698\pi\) | ||||
−0.751559 | + | 0.659665i | \(0.770698\pi\) | |||||||
\(348\) | −3.09017 | −0.165650 | ||||||||
\(349\) | 28.4164 | 1.52110 | 0.760548 | − | 0.649282i | \(-0.224931\pi\) | ||||
0.760548 | + | 0.649282i | \(0.224931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.47214 | −0.292081 | ||||||||
\(352\) | 3.38197 | 0.180259 | ||||||||
\(353\) | −33.4721 | −1.78154 | −0.890771 | − | 0.454452i | \(-0.849835\pi\) | ||||
−0.890771 | + | 0.454452i | \(0.849835\pi\) | |||||||
\(354\) | 18.0902 | 0.961482 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.76393 | 0.146488 | ||||||||
\(357\) | −0.763932 | −0.0404316 | ||||||||
\(358\) | 14.4721 | 0.764876 | ||||||||
\(359\) | −3.41641 | −0.180311 | −0.0901556 | − | 0.995928i | \(-0.528736\pi\) | ||||
−0.0901556 | + | 0.995928i | \(0.528736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 8.47214 | 0.445286 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −3.38197 | −0.177263 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.23607 | 0.169152 | ||||||||
\(367\) | −15.8885 | −0.829375 | −0.414688 | − | 0.909964i | \(-0.636109\pi\) | ||||
−0.414688 | + | 0.909964i | \(0.636109\pi\) | |||||||
\(368\) | −37.4164 | −1.95047 | ||||||||
\(369\) | 6.47214 | 0.336926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1803 | 0.528537 | ||||||||
\(372\) | 0.472136 | 0.0244791 | ||||||||
\(373\) | 26.6525 | 1.38001 | 0.690006 | − | 0.723803i | \(-0.257608\pi\) | ||||
0.690006 | + | 0.723803i | \(0.257608\pi\) | |||||||
\(374\) | 1.23607 | 0.0639156 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.47214 | 0.488488 | ||||||||
\(377\) | 27.3607 | 1.40915 | ||||||||
\(378\) | −1.61803 | −0.0832227 | ||||||||
\(379\) | −8.81966 | −0.453036 | −0.226518 | − | 0.974007i | \(-0.572734\pi\) | ||||
−0.226518 | + | 0.974007i | \(0.572734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6525 | 0.955595 | ||||||||
\(382\) | 24.6525 | 1.26133 | ||||||||
\(383\) | −15.0557 | −0.769312 | −0.384656 | − | 0.923060i | \(-0.625680\pi\) | ||||
−0.384656 | + | 0.923060i | \(0.625680\pi\) | |||||||
\(384\) | 13.6180 | 0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.9443 | −1.37143 | ||||||||
\(387\) | 7.70820 | 0.391830 | ||||||||
\(388\) | 2.29180 | 0.116348 | ||||||||
\(389\) | 28.9443 | 1.46753 | 0.733766 | − | 0.679402i | \(-0.237761\pi\) | ||||
0.733766 | + | 0.679402i | \(0.237761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.88854 | −0.297796 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 16.9443 | 0.854725 | ||||||||
\(394\) | −12.1803 | −0.613637 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.618034 | 0.0310574 | ||||||||
\(397\) | 17.1246 | 0.859460 | 0.429730 | − | 0.902958i | \(-0.358609\pi\) | ||||
0.429730 | + | 0.902958i | \(0.358609\pi\) | |||||||
\(398\) | 42.3607 | 2.12335 | ||||||||
\(399\) | 6.70820 | 0.335830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.2918 | −0.813573 | −0.406787 | − | 0.913523i | \(-0.633351\pi\) | ||||
−0.406787 | + | 0.913523i | \(0.633351\pi\) | |||||||
\(402\) | 23.0344 | 1.14885 | ||||||||
\(403\) | −4.18034 | −0.208238 | ||||||||
\(404\) | −2.58359 | −0.128539 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.09017 | 0.401508 | ||||||||
\(407\) | 7.00000 | 0.346977 | ||||||||
\(408\) | 1.70820 | 0.0845687 | ||||||||
\(409\) | 38.9443 | 1.92567 | 0.962835 | − | 0.270090i | \(-0.0870534\pi\) | ||||
0.962835 | + | 0.270090i | \(0.0870534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.29180 | 0.310351 | ||||||||
\(412\) | 5.81966 | 0.286714 | ||||||||
\(413\) | −11.1803 | −0.550149 | ||||||||
\(414\) | −12.4721 | −0.612972 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 18.5066 | 0.907360 | ||||||||
\(417\) | −5.52786 | −0.270701 | ||||||||
\(418\) | −10.8541 | −0.530891 | ||||||||
\(419\) | 21.1803 | 1.03473 | 0.517364 | − | 0.855766i | \(-0.326913\pi\) | ||||
0.517364 | + | 0.855766i | \(0.326913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | 34.6525 | 1.68686 | ||||||||
\(423\) | 4.23607 | 0.205965 | ||||||||
\(424\) | −22.7639 | −1.10551 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.4721 | 0.507377 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | −0.145898 | −0.00705225 | ||||||||
\(429\) | −5.47214 | −0.264197 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.70820 | −0.226786 | −0.113393 | − | 0.993550i | \(-0.536172\pi\) | ||||
−0.113393 | + | 0.993550i | \(0.536172\pi\) | |||||||
\(432\) | 4.85410 | 0.233543 | ||||||||
\(433\) | 1.52786 | 0.0734245 | 0.0367122 | − | 0.999326i | \(-0.488312\pi\) | ||||
0.0367122 | + | 0.999326i | \(0.488312\pi\) | |||||||
\(434\) | −1.23607 | −0.0593332 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.47214 | 0.214176 | ||||||||
\(437\) | 51.7082 | 2.47354 | ||||||||
\(438\) | −21.7984 | −1.04157 | ||||||||
\(439\) | −11.1803 | −0.533609 | −0.266804 | − | 0.963751i | \(-0.585968\pi\) | ||||
−0.266804 | + | 0.963751i | \(0.585968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 6.76393 | 0.321727 | ||||||||
\(443\) | −9.52786 | −0.452682 | −0.226341 | − | 0.974048i | \(-0.572676\pi\) | ||||
−0.226341 | + | 0.974048i | \(0.572676\pi\) | |||||||
\(444\) | −4.32624 | −0.205314 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.70820 | −0.459697 | ||||||||
\(447\) | −5.00000 | −0.236492 | ||||||||
\(448\) | −4.23607 | −0.200135 | ||||||||
\(449\) | 20.0000 | 0.943858 | 0.471929 | − | 0.881636i | \(-0.343558\pi\) | ||||
0.471929 | + | 0.881636i | \(0.343558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.47214 | 0.304761 | ||||||||
\(452\) | −5.23607 | −0.246284 | ||||||||
\(453\) | −8.18034 | −0.384346 | ||||||||
\(454\) | −3.23607 | −0.151876 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.0000 | −0.702439 | ||||||||
\(457\) | −10.7639 | −0.503516 | −0.251758 | − | 0.967790i | \(-0.581009\pi\) | ||||
−0.251758 | + | 0.967790i | \(0.581009\pi\) | |||||||
\(458\) | −4.47214 | −0.208969 | ||||||||
\(459\) | 0.763932 | 0.0356573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | −1.61803 | −0.0752778 | ||||||||
\(463\) | 27.1803 | 1.26318 | 0.631589 | − | 0.775304i | \(-0.282403\pi\) | ||||
0.631589 | + | 0.775304i | \(0.282403\pi\) | |||||||
\(464\) | −24.2705 | −1.12673 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.76393 | 0.220685 | ||||||||
\(467\) | −6.81966 | −0.315576 | −0.157788 | − | 0.987473i | \(-0.550436\pi\) | ||||
−0.157788 | + | 0.987473i | \(0.550436\pi\) | |||||||
\(468\) | 3.38197 | 0.156331 | ||||||||
\(469\) | −14.2361 | −0.657361 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4164 | 0.526040 | ||||||||
\(472\) | 25.0000 | 1.15072 | ||||||||
\(473\) | 7.70820 | 0.354424 | ||||||||
\(474\) | −8.94427 | −0.410824 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.472136 | 0.0216403 | ||||||||
\(477\) | −10.1803 | −0.466126 | ||||||||
\(478\) | 48.7426 | 2.22944 | ||||||||
\(479\) | −1.70820 | −0.0780498 | −0.0390249 | − | 0.999238i | \(-0.512425\pi\) | ||||
−0.0390249 | + | 0.999238i | \(0.512425\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.3050 | 1.74656 | ||||||||
\(482\) | −13.0344 | −0.593703 | ||||||||
\(483\) | 7.70820 | 0.350735 | ||||||||
\(484\) | 0.618034 | 0.0280925 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.61803 | 0.0733955 | ||||||||
\(487\) | 0.944272 | 0.0427890 | 0.0213945 | − | 0.999771i | \(-0.493189\pi\) | ||||
0.0213945 | + | 0.999771i | \(0.493189\pi\) | |||||||
\(488\) | 4.47214 | 0.202444 | ||||||||
\(489\) | −9.29180 | −0.420190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1246 | 0.998470 | 0.499235 | − | 0.866467i | \(-0.333614\pi\) | ||||
0.499235 | + | 0.866467i | \(0.333614\pi\) | |||||||
\(492\) | −4.00000 | −0.180334 | ||||||||
\(493\) | −3.81966 | −0.172029 | ||||||||
\(494\) | −59.3951 | −2.67231 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.70820 | 0.166503 | ||||||||
\(497\) | −6.47214 | −0.290315 | ||||||||
\(498\) | −18.1803 | −0.814681 | ||||||||
\(499\) | 2.23607 | 0.100100 | 0.0500501 | − | 0.998747i | \(-0.484062\pi\) | ||||
0.0500501 | + | 0.998747i | \(0.484062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.65248 | 0.386564 | ||||||||
\(502\) | 45.5066 | 2.03106 | ||||||||
\(503\) | −15.7082 | −0.700394 | −0.350197 | − | 0.936676i | \(-0.613885\pi\) | ||||
−0.350197 | + | 0.936676i | \(0.613885\pi\) | |||||||
\(504\) | −2.23607 | −0.0996024 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.4721 | −0.554454 | ||||||||
\(507\) | −16.9443 | −0.752522 | ||||||||
\(508\) | −11.5279 | −0.511466 | ||||||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4721 | 0.595972 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | −6.70820 | −0.296174 | ||||||||
\(514\) | −11.3262 | −0.499579 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.76393 | −0.209720 | ||||||||
\(517\) | 4.23607 | 0.186302 | ||||||||
\(518\) | 11.3262 | 0.497646 | ||||||||
\(519\) | −10.4721 | −0.459676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.3050 | −1.06482 | −0.532410 | − | 0.846487i | \(-0.678713\pi\) | ||||
−0.532410 | + | 0.846487i | \(0.678713\pi\) | |||||||
\(522\) | −8.09017 | −0.354097 | ||||||||
\(523\) | −9.65248 | −0.422073 | −0.211037 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211037 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(524\) | −10.4721 | −0.457477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.8541 | 0.996486 | ||||||||
\(527\) | 0.583592 | 0.0254217 | ||||||||
\(528\) | 4.85410 | 0.211248 | ||||||||
\(529\) | 36.4164 | 1.58332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1803 | 0.485185 | ||||||||
\(532\) | −4.14590 | −0.179747 | ||||||||
\(533\) | 35.4164 | 1.53405 | ||||||||
\(534\) | 7.23607 | 0.313135 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 31.8328 | 1.37497 | ||||||||
\(537\) | 8.94427 | 0.385974 | ||||||||
\(538\) | −30.6525 | −1.32152 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0557 | −0.819270 | −0.409635 | − | 0.912250i | \(-0.634344\pi\) | ||||
−0.409635 | + | 0.912250i | \(0.634344\pi\) | |||||||
\(542\) | −30.2705 | −1.30023 | ||||||||
\(543\) | 5.23607 | 0.224701 | ||||||||
\(544\) | −2.58359 | −0.110771 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.85410 | −0.378921 | ||||||||
\(547\) | 38.8328 | 1.66037 | 0.830186 | − | 0.557487i | \(-0.188234\pi\) | ||||
0.830186 | + | 0.557487i | \(0.188234\pi\) | |||||||
\(548\) | −3.88854 | −0.166110 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.5410 | 1.42890 | ||||||||
\(552\) | −17.2361 | −0.733616 | ||||||||
\(553\) | 5.52786 | 0.235069 | ||||||||
\(554\) | 4.00000 | 0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.41641 | 0.144888 | ||||||||
\(557\) | 21.4721 | 0.909804 | 0.454902 | − | 0.890542i | \(-0.349674\pi\) | ||||
0.454902 | + | 0.890542i | \(0.349674\pi\) | |||||||
\(558\) | 1.23607 | 0.0523269 | ||||||||
\(559\) | 42.1803 | 1.78404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.763932 | 0.0322532 | ||||||||
\(562\) | −4.09017 | −0.172533 | ||||||||
\(563\) | −3.34752 | −0.141081 | −0.0705407 | − | 0.997509i | \(-0.522472\pi\) | ||||
−0.0705407 | + | 0.997509i | \(0.522472\pi\) | |||||||
\(564\) | −2.61803 | −0.110239 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.5066 | −1.24025 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 14.4721 | 0.607237 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4721 | 1.10782 | 0.553912 | − | 0.832575i | \(-0.313134\pi\) | ||||
0.553912 | + | 0.832575i | \(0.313134\pi\) | |||||||
\(572\) | 3.38197 | 0.141407 | ||||||||
\(573\) | 15.2361 | 0.636496 | ||||||||
\(574\) | 10.4721 | 0.437099 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −38.6525 | −1.60912 | −0.804562 | − | 0.593869i | \(-0.797600\pi\) | ||||
−0.804562 | + | 0.593869i | \(0.797600\pi\) | |||||||
\(578\) | 26.5623 | 1.10485 | ||||||||
\(579\) | −16.6525 | −0.692053 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2361 | 0.466151 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | −10.1803 | −0.421627 | ||||||||
\(584\) | −30.1246 | −1.24657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.8885 | −1.06945 | ||||||||
\(587\) | 30.0132 | 1.23878 | 0.619388 | − | 0.785085i | \(-0.287381\pi\) | ||||
0.619388 | + | 0.785085i | \(0.287381\pi\) | |||||||
\(588\) | −0.618034 | −0.0254873 | ||||||||
\(589\) | −5.12461 | −0.211156 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.52786 | −0.309655 | ||||||||
\(592\) | −33.9787 | −1.39652 | ||||||||
\(593\) | −30.8328 | −1.26615 | −0.633076 | − | 0.774090i | \(-0.718208\pi\) | ||||
−0.633076 | + | 0.774090i | \(0.718208\pi\) | |||||||
\(594\) | 1.61803 | 0.0663887 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.09017 | 0.126578 | ||||||||
\(597\) | 26.1803 | 1.07149 | ||||||||
\(598\) | −68.2492 | −2.79092 | ||||||||
\(599\) | −34.4721 | −1.40849 | −0.704247 | − | 0.709955i | \(-0.748715\pi\) | ||||
−0.704247 | + | 0.709955i | \(0.748715\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.0000 | 1.10135 | 0.550676 | − | 0.834719i | \(-0.314370\pi\) | ||||
0.550676 | + | 0.834719i | \(0.314370\pi\) | |||||||
\(602\) | 12.4721 | 0.508326 | ||||||||
\(603\) | 14.2361 | 0.579738 | ||||||||
\(604\) | 5.05573 | 0.205715 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.76393 | −0.274766 | ||||||||
\(607\) | −29.1803 | −1.18439 | −0.592197 | − | 0.805793i | \(-0.701739\pi\) | ||||
−0.592197 | + | 0.805793i | \(0.701739\pi\) | |||||||
\(608\) | 22.6869 | 0.920076 | ||||||||
\(609\) | 5.00000 | 0.202610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.1803 | 0.937776 | ||||||||
\(612\) | −0.472136 | −0.0190850 | ||||||||
\(613\) | 35.5967 | 1.43774 | 0.718870 | − | 0.695145i | \(-0.244660\pi\) | ||||
0.718870 | + | 0.695145i | \(0.244660\pi\) | |||||||
\(614\) | −4.94427 | −0.199535 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.23607 | −0.0900937 | ||||||||
\(617\) | −23.5279 | −0.947196 | −0.473598 | − | 0.880741i | \(-0.657045\pi\) | ||||
−0.473598 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(618\) | 15.2361 | 0.612885 | ||||||||
\(619\) | 14.0689 | 0.565476 | 0.282738 | − | 0.959197i | \(-0.408757\pi\) | ||||
0.282738 | + | 0.959197i | \(0.408757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.70820 | −0.309320 | ||||||||
\(622\) | 41.8885 | 1.67958 | ||||||||
\(623\) | −4.47214 | −0.179172 | ||||||||
\(624\) | 26.5623 | 1.06334 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.7639 | −0.430213 | ||||||||
\(627\) | −6.70820 | −0.267900 | ||||||||
\(628\) | −7.05573 | −0.281554 | ||||||||
\(629\) | −5.34752 | −0.213220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.360680 | −0.0143584 | −0.00717922 | − | 0.999974i | \(-0.502285\pi\) | ||||
−0.00717922 | + | 0.999974i | \(0.502285\pi\) | |||||||
\(632\) | −12.3607 | −0.491681 | ||||||||
\(633\) | 21.4164 | 0.851226 | ||||||||
\(634\) | 2.94427 | 0.116932 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.29180 | 0.249486 | ||||||||
\(637\) | 5.47214 | 0.216814 | ||||||||
\(638\) | −8.09017 | −0.320293 | ||||||||
\(639\) | 6.47214 | 0.256034 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5410 | 0.811321 | 0.405661 | − | 0.914024i | \(-0.367041\pi\) | ||||
0.405661 | + | 0.914024i | \(0.367041\pi\) | |||||||
\(642\) | −0.381966 | −0.0150750 | ||||||||
\(643\) | −45.9574 | −1.81238 | −0.906192 | − | 0.422866i | \(-0.861024\pi\) | ||||
−0.906192 | + | 0.422866i | \(0.861024\pi\) | |||||||
\(644\) | −4.76393 | −0.187725 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.29180 | 0.326236 | ||||||||
\(647\) | −43.6525 | −1.71616 | −0.858078 | − | 0.513519i | \(-0.828341\pi\) | ||||
−0.858078 | + | 0.513519i | \(0.828341\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 11.1803 | 0.438867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.763932 | −0.0299409 | ||||||||
\(652\) | 5.74265 | 0.224899 | ||||||||
\(653\) | 27.0557 | 1.05877 | 0.529386 | − | 0.848381i | \(-0.322422\pi\) | ||||
0.529386 | + | 0.848381i | \(0.322422\pi\) | |||||||
\(654\) | 11.7082 | 0.457827 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −31.4164 | −1.22660 | ||||||||
\(657\) | −13.4721 | −0.525598 | ||||||||
\(658\) | 6.85410 | 0.267201 | ||||||||
\(659\) | −43.5410 | −1.69612 | −0.848059 | − | 0.529902i | \(-0.822229\pi\) | ||||
−0.848059 | + | 0.529902i | \(0.822229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5410 | −1.03233 | −0.516163 | − | 0.856490i | \(-0.672640\pi\) | ||||
−0.516163 | + | 0.856490i | \(0.672640\pi\) | |||||||
\(662\) | −24.9443 | −0.969487 | ||||||||
\(663\) | 4.18034 | 0.162351 | ||||||||
\(664\) | −25.1246 | −0.975024 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.3262 | −0.438883 | ||||||||
\(667\) | 38.5410 | 1.49231 | ||||||||
\(668\) | −5.34752 | −0.206902 | ||||||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 3.38197 | 0.130462 | ||||||||
\(673\) | 45.5967 | 1.75763 | 0.878813 | − | 0.477167i | \(-0.158336\pi\) | ||||
0.878813 | + | 0.477167i | \(0.158336\pi\) | |||||||
\(674\) | 22.9443 | 0.883780 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4721 | 0.402774 | ||||||||
\(677\) | 43.3050 | 1.66434 | 0.832172 | − | 0.554517i | \(-0.187097\pi\) | ||||
0.832172 | + | 0.554517i | \(0.187097\pi\) | |||||||
\(678\) | −13.7082 | −0.526460 | ||||||||
\(679\) | −3.70820 | −0.142308 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | −0.0766402 | ||||||||
\(682\) | 1.23607 | 0.0473315 | ||||||||
\(683\) | 39.0132 | 1.49280 | 0.746398 | − | 0.665499i | \(-0.231781\pi\) | ||||
0.746398 | + | 0.665499i | \(0.231781\pi\) | |||||||
\(684\) | 4.14590 | 0.158522 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.61803 | 0.0617768 | ||||||||
\(687\) | −2.76393 | −0.105451 | ||||||||
\(688\) | −37.4164 | −1.42649 | ||||||||
\(689\) | −55.7082 | −2.12231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | 0.0760836 | 0.0380418 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380418 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(692\) | 6.47214 | 0.246034 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 45.3050 | 1.71975 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11.1803 | −0.423790 | ||||||||
\(697\) | −4.94427 | −0.187278 | ||||||||
\(698\) | −45.9787 | −1.74032 | ||||||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.8885 | 1.50657 | 0.753285 | − | 0.657695i | \(-0.228468\pi\) | ||||
0.753285 | + | 0.657695i | \(0.228468\pi\) | |||||||
\(702\) | 8.85410 | 0.334177 | ||||||||
\(703\) | 46.9574 | 1.77103 | ||||||||
\(704\) | 4.23607 | 0.159653 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.1591 | 2.03830 | ||||||||
\(707\) | 4.18034 | 0.157218 | ||||||||
\(708\) | −6.90983 | −0.259687 | ||||||||
\(709\) | 39.7214 | 1.49177 | 0.745883 | − | 0.666076i | \(-0.232028\pi\) | ||||
0.745883 | + | 0.666076i | \(0.232028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.52786 | −0.207311 | ||||||||
\(712\) | 10.0000 | 0.374766 | ||||||||
\(713\) | −5.88854 | −0.220528 | ||||||||
\(714\) | 1.23607 | 0.0462587 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.52786 | −0.206586 | ||||||||
\(717\) | 30.1246 | 1.12502 | ||||||||
\(718\) | 5.52786 | 0.206298 | ||||||||
\(719\) | 12.2361 | 0.456328 | 0.228164 | − | 0.973623i | \(-0.426728\pi\) | ||||
0.228164 | + | 0.973623i | \(0.426728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.41641 | −0.350685 | ||||||||
\(722\) | −42.0689 | −1.56564 | ||||||||
\(723\) | −8.05573 | −0.299596 | ||||||||
\(724\) | −3.23607 | −0.120268 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.61803 | 0.0600509 | ||||||||
\(727\) | −1.81966 | −0.0674875 | −0.0337437 | − | 0.999431i | \(-0.510743\pi\) | ||||
−0.0337437 | + | 0.999431i | \(0.510743\pi\) | |||||||
\(728\) | −12.2361 | −0.453499 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.88854 | −0.217796 | ||||||||
\(732\) | −1.23607 | −0.0456864 | ||||||||
\(733\) | 43.8885 | 1.62106 | 0.810530 | − | 0.585697i | \(-0.199179\pi\) | ||||
0.810530 | + | 0.585697i | \(0.199179\pi\) | |||||||
\(734\) | 25.7082 | 0.948907 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.0689 | 0.960912 | ||||||||
\(737\) | 14.2361 | 0.524392 | ||||||||
\(738\) | −10.4721 | −0.385485 | ||||||||
\(739\) | −24.0689 | −0.885388 | −0.442694 | − | 0.896673i | \(-0.645977\pi\) | ||||
−0.442694 | + | 0.896673i | \(0.645977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.7082 | −1.34851 | ||||||||
\(742\) | −16.4721 | −0.604711 | ||||||||
\(743\) | −25.1803 | −0.923777 | −0.461889 | − | 0.886938i | \(-0.652828\pi\) | ||||
−0.461889 | + | 0.886938i | \(0.652828\pi\) | |||||||
\(744\) | 1.70820 | 0.0626258 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −43.1246 | −1.57890 | ||||||||
\(747\) | −11.2361 | −0.411106 | ||||||||
\(748\) | −0.472136 | −0.0172630 | ||||||||
\(749\) | 0.236068 | 0.00862574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.2361 | 1.61420 | 0.807099 | − | 0.590417i | \(-0.201037\pi\) | ||||
0.807099 | + | 0.590417i | \(0.201037\pi\) | |||||||
\(752\) | −20.5623 | −0.749830 | ||||||||
\(753\) | 28.1246 | 1.02492 | ||||||||
\(754\) | −44.2705 | −1.61224 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.618034 | 0.0224777 | ||||||||
\(757\) | −37.7214 | −1.37101 | −0.685503 | − | 0.728070i | \(-0.740418\pi\) | ||||
−0.685503 | + | 0.728070i | \(0.740418\pi\) | |||||||
\(758\) | 14.2705 | 0.518328 | ||||||||
\(759\) | −7.70820 | −0.279790 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.7771 | −1.58692 | −0.793459 | − | 0.608624i | \(-0.791722\pi\) | ||||
−0.793459 | + | 0.608624i | \(0.791722\pi\) | |||||||
\(762\) | −30.1803 | −1.09332 | ||||||||
\(763\) | −7.23607 | −0.261963 | ||||||||
\(764\) | −9.41641 | −0.340674 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.3607 | 0.880187 | ||||||||
\(767\) | 61.1803 | 2.20909 | ||||||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −3.94427 | −0.142234 | −0.0711170 | − | 0.997468i | \(-0.522656\pi\) | ||||
−0.0711170 | + | 0.997468i | \(0.522656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.00000 | −0.252099 | ||||||||
\(772\) | 10.2918 | 0.370410 | ||||||||
\(773\) | −3.47214 | −0.124884 | −0.0624420 | − | 0.998049i | \(-0.519889\pi\) | ||||
−0.0624420 | + | 0.998049i | \(0.519889\pi\) | |||||||
\(774\) | −12.4721 | −0.448302 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.29180 | 0.297658 | ||||||||
\(777\) | 7.00000 | 0.251124 | ||||||||
\(778\) | −46.8328 | −1.67904 | ||||||||
\(779\) | 43.4164 | 1.55555 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.47214 | 0.231591 | ||||||||
\(782\) | 9.52786 | 0.340716 | ||||||||
\(783\) | −5.00000 | −0.178685 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −27.4164 | −0.977911 | ||||||||
\(787\) | 27.6525 | 0.985704 | 0.492852 | − | 0.870113i | \(-0.335954\pi\) | ||||
0.492852 | + | 0.870113i | \(0.335954\pi\) | |||||||
\(788\) | 4.65248 | 0.165738 | ||||||||
\(789\) | 14.1246 | 0.502849 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.47214 | 0.301234 | ||||||||
\(792\) | 2.23607 | 0.0794552 | ||||||||
\(793\) | 10.9443 | 0.388642 | ||||||||
\(794\) | −27.7082 | −0.983327 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.1803 | −0.573497 | ||||||||
\(797\) | 11.4721 | 0.406364 | 0.203182 | − | 0.979141i | \(-0.434872\pi\) | ||||
0.203182 | + | 0.979141i | \(0.434872\pi\) | |||||||
\(798\) | −10.8541 | −0.384231 | ||||||||
\(799\) | −3.23607 | −0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.47214 | 0.158015 | ||||||||
\(802\) | 26.3607 | 0.930828 | ||||||||
\(803\) | −13.4721 | −0.475421 | ||||||||
\(804\) | −8.79837 | −0.310295 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.76393 | 0.238249 | ||||||||
\(807\) | −18.9443 | −0.666870 | ||||||||
\(808\) | −9.34752 | −0.328845 | ||||||||
\(809\) | 6.30495 | 0.221670 | 0.110835 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110835 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.7082 | 1.00808 | 0.504041 | − | 0.863680i | \(-0.331846\pi\) | ||||
0.504041 | + | 0.863680i | \(0.331846\pi\) | |||||||
\(812\) | −3.09017 | −0.108444 | ||||||||
\(813\) | −18.7082 | −0.656125 | ||||||||
\(814\) | −11.3262 | −0.396984 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.70820 | −0.129813 | ||||||||
\(817\) | 51.7082 | 1.80904 | ||||||||
\(818\) | −63.0132 | −2.20320 | ||||||||
\(819\) | −5.47214 | −0.191212 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.47214 | 0.0513779 | 0.0256889 | − | 0.999670i | \(-0.491822\pi\) | ||||
0.0256889 | + | 0.999670i | \(0.491822\pi\) | |||||||
\(822\) | −10.1803 | −0.355080 | ||||||||
\(823\) | −5.18034 | −0.180575 | −0.0902876 | − | 0.995916i | \(-0.528779\pi\) | ||||
−0.0902876 | + | 0.995916i | \(0.528779\pi\) | |||||||
\(824\) | 21.0557 | 0.733511 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0902 | 0.629438 | ||||||||
\(827\) | −43.6525 | −1.51795 | −0.758973 | − | 0.651122i | \(-0.774298\pi\) | ||||
−0.758973 | + | 0.651122i | \(0.774298\pi\) | |||||||
\(828\) | 4.76393 | 0.165558 | ||||||||
\(829\) | −35.7771 | −1.24259 | −0.621295 | − | 0.783577i | \(-0.713393\pi\) | ||||
−0.621295 | + | 0.783577i | \(0.713393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.47214 | 0.0857574 | ||||||||
\(832\) | 23.1803 | 0.803634 | ||||||||
\(833\) | −0.763932 | −0.0264687 | ||||||||
\(834\) | 8.94427 | 0.309715 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.14590 | 0.143389 | ||||||||
\(837\) | 0.763932 | 0.0264054 | ||||||||
\(838\) | −34.2705 | −1.18386 | ||||||||
\(839\) | 43.5410 | 1.50320 | 0.751601 | − | 0.659617i | \(-0.229282\pi\) | ||||
0.751601 | + | 0.659617i | \(0.229282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 21.0344 | 0.724895 | ||||||||
\(843\) | −2.52786 | −0.0870643 | ||||||||
\(844\) | −13.2361 | −0.455604 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.85410 | −0.235649 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 49.4164 | 1.69697 | ||||||||
\(849\) | −18.2361 | −0.625860 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.9574 | 1.84964 | ||||||||
\(852\) | −4.00000 | −0.137038 | ||||||||
\(853\) | 2.58359 | 0.0884605 | 0.0442303 | − | 0.999021i | \(-0.485916\pi\) | ||||
0.0442303 | + | 0.999021i | \(0.485916\pi\) | |||||||
\(854\) | 3.23607 | 0.110736 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.527864 | −0.0180420 | ||||||||
\(857\) | −35.8885 | −1.22593 | −0.612965 | − | 0.790110i | \(-0.710023\pi\) | ||||
−0.612965 | + | 0.790110i | \(0.710023\pi\) | |||||||
\(858\) | 8.85410 | 0.302274 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.47214 | 0.220570 | ||||||||
\(862\) | 7.61803 | 0.259471 | ||||||||
\(863\) | 38.7639 | 1.31954 | 0.659770 | − | 0.751468i | \(-0.270654\pi\) | ||||
0.659770 | + | 0.751468i | \(0.270654\pi\) | |||||||
\(864\) | −3.38197 | −0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.47214 | −0.0840066 | ||||||||
\(867\) | 16.4164 | 0.557530 | ||||||||
\(868\) | 0.472136 | 0.0160253 | ||||||||
\(869\) | −5.52786 | −0.187520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77.9017 | 2.63960 | ||||||||
\(872\) | 16.1803 | 0.547935 | ||||||||
\(873\) | 3.70820 | 0.125504 | ||||||||
\(874\) | −83.6656 | −2.83003 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.32624 | 0.281318 | ||||||||
\(877\) | −31.4164 | −1.06086 | −0.530428 | − | 0.847730i | \(-0.677969\pi\) | ||||
−0.530428 | + | 0.847730i | \(0.677969\pi\) | |||||||
\(878\) | 18.0902 | 0.610514 | ||||||||
\(879\) | −16.0000 | −0.539667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1115 | 0.643881 | 0.321941 | − | 0.946760i | \(-0.395665\pi\) | ||||
0.321941 | + | 0.946760i | \(0.395665\pi\) | |||||||
\(882\) | −1.61803 | −0.0544820 | ||||||||
\(883\) | 37.1803 | 1.25122 | 0.625609 | − | 0.780137i | \(-0.284851\pi\) | ||||
0.625609 | + | 0.780137i | \(0.284851\pi\) | |||||||
\(884\) | −2.58359 | −0.0868956 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.4164 | 0.517924 | ||||||||
\(887\) | −15.2361 | −0.511577 | −0.255789 | − | 0.966733i | \(-0.582335\pi\) | ||||
−0.255789 | + | 0.966733i | \(0.582335\pi\) | |||||||
\(888\) | −15.6525 | −0.525263 | ||||||||
\(889\) | 18.6525 | 0.625584 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 3.70820 | 0.124160 | ||||||||
\(893\) | 28.4164 | 0.950919 | ||||||||
\(894\) | 8.09017 | 0.270576 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.6180 | 0.454947 | ||||||||
\(897\) | −42.1803 | −1.40836 | ||||||||
\(898\) | −32.3607 | −1.07989 | ||||||||
\(899\) | −3.81966 | −0.127393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.77709 | 0.259092 | ||||||||
\(902\) | −10.4721 | −0.348684 | ||||||||
\(903\) | 7.70820 | 0.256513 | ||||||||
\(904\) | −18.9443 | −0.630077 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.2361 | 0.439739 | ||||||||
\(907\) | −28.0000 | −0.929725 | −0.464862 | − | 0.885383i | \(-0.653896\pi\) | ||||
−0.464862 | + | 0.885383i | \(0.653896\pi\) | |||||||
\(908\) | 1.23607 | 0.0410204 | ||||||||
\(909\) | −4.18034 | −0.138653 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.4164 | −1.37219 | −0.686093 | − | 0.727513i | \(-0.740676\pi\) | ||||
−0.686093 | + | 0.727513i | \(0.740676\pi\) | |||||||
\(912\) | 32.5623 | 1.07825 | ||||||||
\(913\) | −11.2361 | −0.371860 | ||||||||
\(914\) | 17.4164 | 0.576084 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.70820 | 0.0564406 | ||||||||
\(917\) | 16.9443 | 0.559549 | ||||||||
\(918\) | −1.23607 | −0.0407963 | ||||||||
\(919\) | −9.59675 | −0.316567 | −0.158284 | − | 0.987394i | \(-0.550596\pi\) | ||||
−0.158284 | + | 0.987394i | \(0.550596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.05573 | −0.100690 | ||||||||
\(922\) | 45.3050 | 1.49204 | ||||||||
\(923\) | 35.4164 | 1.16575 | ||||||||
\(924\) | 0.618034 | 0.0203318 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −43.9787 | −1.44523 | ||||||||
\(927\) | 9.41641 | 0.309275 | ||||||||
\(928\) | 16.9098 | 0.555092 | ||||||||
\(929\) | −22.8885 | −0.750949 | −0.375474 | − | 0.926833i | \(-0.622520\pi\) | ||||
−0.375474 | + | 0.926833i | \(0.622520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.70820 | 0.219853 | ||||||||
\(932\) | −1.81966 | −0.0596049 | ||||||||
\(933\) | 25.8885 | 0.847553 | ||||||||
\(934\) | 11.0344 | 0.361058 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.2361 | 0.399948 | ||||||||
\(937\) | 4.11146 | 0.134315 | 0.0671577 | − | 0.997742i | \(-0.478607\pi\) | ||||
0.0671577 | + | 0.997742i | \(0.478607\pi\) | |||||||
\(938\) | 23.0344 | 0.752101 | ||||||||
\(939\) | −6.65248 | −0.217095 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.6393 | −0.509827 | −0.254914 | − | 0.966964i | \(-0.582047\pi\) | ||||
−0.254914 | + | 0.966964i | \(0.582047\pi\) | |||||||
\(942\) | −18.4721 | −0.601855 | ||||||||
\(943\) | 49.8885 | 1.62459 | ||||||||
\(944\) | −54.2705 | −1.76635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4721 | −0.405504 | ||||||||
\(947\) | −21.4164 | −0.695940 | −0.347970 | − | 0.937506i | \(-0.613129\pi\) | ||||
−0.347970 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(948\) | 3.41641 | 0.110960 | ||||||||
\(949\) | −73.7214 | −2.39310 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.81966 | 0.0590065 | ||||||||
\(952\) | 1.70820 | 0.0553632 | ||||||||
\(953\) | 26.7771 | 0.867395 | 0.433697 | − | 0.901059i | \(-0.357209\pi\) | ||||
0.433697 | + | 0.901059i | \(0.357209\pi\) | |||||||
\(954\) | 16.4721 | 0.533305 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.6180 | −0.602150 | ||||||||
\(957\) | −5.00000 | −0.161627 | ||||||||
\(958\) | 2.76393 | 0.0892986 | ||||||||
\(959\) | 6.29180 | 0.203173 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4164 | −0.981174 | ||||||||
\(962\) | −61.9787 | −1.99827 | ||||||||
\(963\) | −0.236068 | −0.00760718 | ||||||||
\(964\) | 4.97871 | 0.160354 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.4721 | −0.401284 | ||||||||
\(967\) | −37.1935 | −1.19606 | −0.598031 | − | 0.801473i | \(-0.704050\pi\) | ||||
−0.598031 | + | 0.801473i | \(0.704050\pi\) | |||||||
\(968\) | 2.23607 | 0.0718699 | ||||||||
\(969\) | 5.12461 | 0.164626 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.12461 | −0.260731 | −0.130366 | − | 0.991466i | \(-0.541615\pi\) | ||||
−0.130366 | + | 0.991466i | \(0.541615\pi\) | |||||||
\(972\) | −0.618034 | −0.0198234 | ||||||||
\(973\) | −5.52786 | −0.177215 | ||||||||
\(974\) | −1.52786 | −0.0489559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.70820 | −0.310752 | ||||||||
\(977\) | 18.1803 | 0.581641 | 0.290820 | − | 0.956778i | \(-0.406072\pi\) | ||||
0.290820 | + | 0.956778i | \(0.406072\pi\) | |||||||
\(978\) | 15.0344 | 0.480748 | ||||||||
\(979\) | 4.47214 | 0.142930 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.23607 | 0.231030 | ||||||||
\(982\) | −35.7984 | −1.14237 | ||||||||
\(983\) | −0.583592 | −0.0186137 | −0.00930685 | − | 0.999957i | \(-0.502963\pi\) | ||||
−0.00930685 | + | 0.999957i | \(0.502963\pi\) | |||||||
\(984\) | −14.4721 | −0.461355 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.18034 | 0.196822 | ||||||||
\(987\) | 4.23607 | 0.134836 | ||||||||
\(988\) | 22.6869 | 0.721767 | ||||||||
\(989\) | 59.4164 | 1.88933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.81966 | −0.216634 | −0.108317 | − | 0.994116i | \(-0.534546\pi\) | ||||
−0.108317 | + | 0.994116i | \(0.534546\pi\) | |||||||
\(992\) | −2.58359 | −0.0820291 | ||||||||
\(993\) | −15.4164 | −0.489225 | ||||||||
\(994\) | 10.4721 | 0.332156 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.94427 | 0.220038 | ||||||||
\(997\) | −9.05573 | −0.286798 | −0.143399 | − | 0.989665i | \(-0.545803\pi\) | ||||
−0.143399 | + | 0.989665i | \(0.545803\pi\) | |||||||
\(998\) | −3.61803 | −0.114527 | ||||||||
\(999\) | −7.00000 | −0.221470 |
(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 | 5775.2.a.be.1.1 | 2 | ||
5.4 | even | 2 | 231.2.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 693.2.a.f.1.1 | 2 | |||
20.19 | odd | 2 | 3696.2.a.be.1.1 | 2 | |||
35.34 | odd | 2 | 1617.2.a.p.1.2 | 2 | |||
55.54 | odd | 2 | 2541.2.a.t.1.1 | 2 | |||
105.104 | even | 2 | 4851.2.a.w.1.1 | 2 | |||
165.164 | even | 2 | 7623.2.a.bm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
693.2.a.f.1.1 | 2 | 15.14 | odd | 2 | |||
1617.2.a.p.1.2 | 2 | 35.34 | odd | 2 | |||
2541.2.a.t.1.1 | 2 | 55.54 | odd | 2 | |||
3696.2.a.be.1.1 | 2 | 20.19 | odd | 2 | |||
4851.2.a.w.1.1 | 2 | 105.104 | even | 2 | |||
5775.2.a.be.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.bm.1.2 | 2 | 165.164 | even | 2 |