Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.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: | \(5.76519902594\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.23607 | 1.86834 | 0.934172 | − | 0.356822i | \(-0.116140\pi\) | ||||
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.38197 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | 1.23607 | 0.467190 | 0.233595 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233595 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 1.38197 | 0.437016 | ||||||||
\(11\) | 1.23607 | 0.372689 | 0.186344 | − | 0.982485i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(12\) | 3.23607 | 0.934172 | ||||||||
\(13\) | 3.61803 | 1.00346 | 0.501731 | − | 0.865024i | \(-0.332697\pi\) | ||||
0.501731 | + | 0.865024i | \(0.332697\pi\) | |||||||
\(14\) | −1.23607 | −0.330353 | ||||||||
\(15\) | −4.47214 | −1.15470 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.61803 | −1.36257 | −0.681287 | − | 0.732017i | \(-0.738579\pi\) | ||||
−0.681287 | + | 0.732017i | \(0.738579\pi\) | |||||||
\(18\) | −7.47214 | −1.76120 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.38197 | −0.309017 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | −1.23607 | −0.263531 | ||||||||
\(23\) | 0.763932 | 0.159291 | 0.0796454 | − | 0.996823i | \(-0.474621\pi\) | ||||
0.0796454 | + | 0.996823i | \(0.474621\pi\) | |||||||
\(24\) | −3.23607 | −0.660560 | ||||||||
\(25\) | −3.09017 | −0.618034 | ||||||||
\(26\) | −3.61803 | −0.709555 | ||||||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | 1.23607 | 0.233595 | ||||||||
\(29\) | 2.09017 | 0.388135 | 0.194067 | − | 0.980988i | \(-0.437832\pi\) | ||||
0.194067 | + | 0.980988i | \(0.437832\pi\) | |||||||
\(30\) | 4.47214 | 0.816497 | ||||||||
\(31\) | 3.23607 | 0.581215 | 0.290607 | − | 0.956842i | \(-0.406143\pi\) | ||||
0.290607 | + | 0.956842i | \(0.406143\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 5.61803 | 0.963485 | ||||||||
\(35\) | −1.70820 | −0.288739 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | 10.6180 | 1.74559 | 0.872797 | − | 0.488083i | \(-0.162304\pi\) | ||||
0.872797 | + | 0.488083i | \(0.162304\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.7082 | 1.87481 | ||||||||
\(40\) | 1.38197 | 0.218508 | ||||||||
\(41\) | −5.85410 | −0.914257 | −0.457129 | − | 0.889401i | \(-0.651122\pi\) | ||||
−0.457129 | + | 0.889401i | \(0.651122\pi\) | |||||||
\(42\) | −4.00000 | −0.617213 | ||||||||
\(43\) | −4.76393 | −0.726493 | −0.363246 | − | 0.931693i | \(-0.618332\pi\) | ||||
−0.363246 | + | 0.931693i | \(0.618332\pi\) | |||||||
\(44\) | 1.23607 | 0.186344 | ||||||||
\(45\) | −10.3262 | −1.53934 | ||||||||
\(46\) | −0.763932 | −0.112636 | ||||||||
\(47\) | −4.47214 | −0.652328 | −0.326164 | − | 0.945313i | \(-0.605756\pi\) | ||||
−0.326164 | + | 0.945313i | \(0.605756\pi\) | |||||||
\(48\) | 3.23607 | 0.467086 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 3.09017 | 0.437016 | ||||||||
\(51\) | −18.1803 | −2.54576 | ||||||||
\(52\) | 3.61803 | 0.501731 | ||||||||
\(53\) | 5.09017 | 0.699189 | 0.349594 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349594 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(54\) | −14.4721 | −1.96941 | ||||||||
\(55\) | −1.70820 | −0.230334 | ||||||||
\(56\) | −1.23607 | −0.165177 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.09017 | −0.274453 | ||||||||
\(59\) | 8.47214 | 1.10298 | 0.551489 | − | 0.834182i | \(-0.314060\pi\) | ||||
0.551489 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(60\) | −4.47214 | −0.577350 | ||||||||
\(61\) | 3.61803 | 0.463242 | 0.231621 | − | 0.972806i | \(-0.425597\pi\) | ||||
0.231621 | + | 0.972806i | \(0.425597\pi\) | |||||||
\(62\) | −3.23607 | −0.410981 | ||||||||
\(63\) | 9.23607 | 1.16364 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.00000 | −0.620174 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | −1.70820 | −0.208690 | −0.104345 | − | 0.994541i | \(-0.533275\pi\) | ||||
−0.104345 | + | 0.994541i | \(0.533275\pi\) | |||||||
\(68\) | −5.61803 | −0.681287 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 1.70820 | 0.204169 | ||||||||
\(71\) | −14.9443 | −1.77356 | −0.886779 | − | 0.462193i | \(-0.847063\pi\) | ||||
−0.886779 | + | 0.462193i | \(0.847063\pi\) | |||||||
\(72\) | −7.47214 | −0.880600 | ||||||||
\(73\) | −3.38197 | −0.395829 | −0.197915 | − | 0.980219i | \(-0.563417\pi\) | ||||
−0.197915 | + | 0.980219i | \(0.563417\pi\) | |||||||
\(74\) | −10.6180 | −1.23432 | ||||||||
\(75\) | −10.0000 | −1.15470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.52786 | 0.174116 | ||||||||
\(78\) | −11.7082 | −1.32569 | ||||||||
\(79\) | −7.23607 | −0.814121 | −0.407061 | − | 0.913401i | \(-0.633446\pi\) | ||||
−0.407061 | + | 0.913401i | \(0.633446\pi\) | |||||||
\(80\) | −1.38197 | −0.154508 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 5.85410 | 0.646477 | ||||||||
\(83\) | 8.47214 | 0.929938 | 0.464969 | − | 0.885327i | \(-0.346066\pi\) | ||||
0.464969 | + | 0.885327i | \(0.346066\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 7.76393 | 0.842117 | ||||||||
\(86\) | 4.76393 | 0.513708 | ||||||||
\(87\) | 6.76393 | 0.725170 | ||||||||
\(88\) | −1.23607 | −0.131765 | ||||||||
\(89\) | 2.14590 | 0.227465 | 0.113732 | − | 0.993511i | \(-0.463719\pi\) | ||||
0.113732 | + | 0.993511i | \(0.463719\pi\) | |||||||
\(90\) | 10.3262 | 1.08848 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0.763932 | 0.0796454 | ||||||||
\(93\) | 10.4721 | 1.08591 | ||||||||
\(94\) | 4.47214 | 0.461266 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.23607 | −0.330280 | ||||||||
\(97\) | 6.38197 | 0.647990 | 0.323995 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323995 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(98\) | 5.47214 | 0.552769 | ||||||||
\(99\) | 9.23607 | 0.928260 | ||||||||
\(100\) | −3.09017 | −0.309017 | ||||||||
\(101\) | −13.3820 | −1.33156 | −0.665778 | − | 0.746150i | \(-0.731900\pi\) | ||||
−0.665778 | + | 0.746150i | \(0.731900\pi\) | |||||||
\(102\) | 18.1803 | 1.80012 | ||||||||
\(103\) | −16.6525 | −1.64082 | −0.820409 | − | 0.571778i | \(-0.806254\pi\) | ||||
−0.820409 | + | 0.571778i | \(0.806254\pi\) | |||||||
\(104\) | −3.61803 | −0.354777 | ||||||||
\(105\) | −5.52786 | −0.539464 | ||||||||
\(106\) | −5.09017 | −0.494401 | ||||||||
\(107\) | −17.4164 | −1.68371 | −0.841854 | − | 0.539706i | \(-0.818536\pi\) | ||||
−0.841854 | + | 0.539706i | \(0.818536\pi\) | |||||||
\(108\) | 14.4721 | 1.39258 | ||||||||
\(109\) | 18.0344 | 1.72739 | 0.863693 | − | 0.504018i | \(-0.168145\pi\) | ||||
0.863693 | + | 0.504018i | \(0.168145\pi\) | |||||||
\(110\) | 1.70820 | 0.162871 | ||||||||
\(111\) | 34.3607 | 3.26137 | ||||||||
\(112\) | 1.23607 | 0.116797 | ||||||||
\(113\) | −3.14590 | −0.295941 | −0.147971 | − | 0.988992i | \(-0.547274\pi\) | ||||
−0.147971 | + | 0.988992i | \(0.547274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.05573 | −0.0984472 | ||||||||
\(116\) | 2.09017 | 0.194067 | ||||||||
\(117\) | 27.0344 | 2.49934 | ||||||||
\(118\) | −8.47214 | −0.779923 | ||||||||
\(119\) | −6.94427 | −0.636580 | ||||||||
\(120\) | 4.47214 | 0.408248 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | −3.61803 | −0.327561 | ||||||||
\(123\) | −18.9443 | −1.70815 | ||||||||
\(124\) | 3.23607 | 0.290607 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | −9.23607 | −0.822814 | ||||||||
\(127\) | 15.4164 | 1.36798 | 0.683992 | − | 0.729489i | \(-0.260242\pi\) | ||||
0.683992 | + | 0.729489i | \(0.260242\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −15.4164 | −1.35734 | ||||||||
\(130\) | 5.00000 | 0.438529 | ||||||||
\(131\) | −4.47214 | −0.390732 | −0.195366 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195366 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.70820 | 0.147566 | ||||||||
\(135\) | −20.0000 | −1.72133 | ||||||||
\(136\) | 5.61803 | 0.481742 | ||||||||
\(137\) | 4.61803 | 0.394545 | 0.197273 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197273 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(138\) | −2.47214 | −0.210442 | ||||||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | −1.70820 | −0.144370 | ||||||||
\(141\) | −14.4721 | −1.21877 | ||||||||
\(142\) | 14.9443 | 1.25410 | ||||||||
\(143\) | 4.47214 | 0.373979 | ||||||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | −2.88854 | −0.239881 | ||||||||
\(146\) | 3.38197 | 0.279893 | ||||||||
\(147\) | −17.7082 | −1.46055 | ||||||||
\(148\) | 10.6180 | 0.872797 | ||||||||
\(149\) | −1.90983 | −0.156459 | −0.0782297 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782297 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(150\) | 10.0000 | 0.816497 | ||||||||
\(151\) | 5.52786 | 0.449851 | 0.224926 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224926 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −41.9787 | −3.39378 | ||||||||
\(154\) | −1.52786 | −0.123119 | ||||||||
\(155\) | −4.47214 | −0.359211 | ||||||||
\(156\) | 11.7082 | 0.937407 | ||||||||
\(157\) | 11.6180 | 0.927220 | 0.463610 | − | 0.886039i | \(-0.346554\pi\) | ||||
0.463610 | + | 0.886039i | \(0.346554\pi\) | |||||||
\(158\) | 7.23607 | 0.575671 | ||||||||
\(159\) | 16.4721 | 1.30633 | ||||||||
\(160\) | 1.38197 | 0.109254 | ||||||||
\(161\) | 0.944272 | 0.0744191 | ||||||||
\(162\) | −24.4164 | −1.91833 | ||||||||
\(163\) | −20.6525 | −1.61763 | −0.808813 | − | 0.588065i | \(-0.799890\pi\) | ||||
−0.808813 | + | 0.588065i | \(0.799890\pi\) | |||||||
\(164\) | −5.85410 | −0.457129 | ||||||||
\(165\) | −5.52786 | −0.430344 | ||||||||
\(166\) | −8.47214 | −0.657565 | ||||||||
\(167\) | −3.52786 | −0.272994 | −0.136497 | − | 0.990640i | \(-0.543584\pi\) | ||||
−0.136497 | + | 0.990640i | \(0.543584\pi\) | |||||||
\(168\) | −4.00000 | −0.308607 | ||||||||
\(169\) | 0.0901699 | 0.00693615 | ||||||||
\(170\) | −7.76393 | −0.595466 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.76393 | −0.363246 | ||||||||
\(173\) | −14.3262 | −1.08920 | −0.544602 | − | 0.838695i | \(-0.683319\pi\) | ||||
−0.544602 | + | 0.838695i | \(0.683319\pi\) | |||||||
\(174\) | −6.76393 | −0.512772 | ||||||||
\(175\) | −3.81966 | −0.288739 | ||||||||
\(176\) | 1.23607 | 0.0931721 | ||||||||
\(177\) | 27.4164 | 2.06074 | ||||||||
\(178\) | −2.14590 | −0.160842 | ||||||||
\(179\) | 3.41641 | 0.255354 | 0.127677 | − | 0.991816i | \(-0.459248\pi\) | ||||
0.127677 | + | 0.991816i | \(0.459248\pi\) | |||||||
\(180\) | −10.3262 | −0.769672 | ||||||||
\(181\) | −21.4164 | −1.59187 | −0.795935 | − | 0.605383i | \(-0.793020\pi\) | ||||
−0.795935 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(182\) | −4.47214 | −0.331497 | ||||||||
\(183\) | 11.7082 | 0.865495 | ||||||||
\(184\) | −0.763932 | −0.0563178 | ||||||||
\(185\) | −14.6738 | −1.07884 | ||||||||
\(186\) | −10.4721 | −0.767854 | ||||||||
\(187\) | −6.94427 | −0.507815 | ||||||||
\(188\) | −4.47214 | −0.326164 | ||||||||
\(189\) | 17.8885 | 1.30120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4721 | 0.902452 | 0.451226 | − | 0.892410i | \(-0.350987\pi\) | ||||
0.451226 | + | 0.892410i | \(0.350987\pi\) | |||||||
\(192\) | 3.23607 | 0.233543 | ||||||||
\(193\) | −20.4721 | −1.47362 | −0.736808 | − | 0.676102i | \(-0.763668\pi\) | ||||
−0.736808 | + | 0.676102i | \(0.763668\pi\) | |||||||
\(194\) | −6.38197 | −0.458198 | ||||||||
\(195\) | −16.1803 | −1.15870 | ||||||||
\(196\) | −5.47214 | −0.390867 | ||||||||
\(197\) | −10.8541 | −0.773323 | −0.386661 | − | 0.922222i | \(-0.626372\pi\) | ||||
−0.386661 | + | 0.922222i | \(0.626372\pi\) | |||||||
\(198\) | −9.23607 | −0.656379 | ||||||||
\(199\) | 1.52786 | 0.108307 | 0.0541537 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541537 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(200\) | 3.09017 | 0.218508 | ||||||||
\(201\) | −5.52786 | −0.389905 | ||||||||
\(202\) | 13.3820 | 0.941552 | ||||||||
\(203\) | 2.58359 | 0.181333 | ||||||||
\(204\) | −18.1803 | −1.27288 | ||||||||
\(205\) | 8.09017 | 0.565042 | ||||||||
\(206\) | 16.6525 | 1.16023 | ||||||||
\(207\) | 5.70820 | 0.396748 | ||||||||
\(208\) | 3.61803 | 0.250866 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5.52786 | 0.381459 | ||||||||
\(211\) | −2.76393 | −0.190277 | −0.0951385 | − | 0.995464i | \(-0.530329\pi\) | ||||
−0.0951385 | + | 0.995464i | \(0.530329\pi\) | |||||||
\(212\) | 5.09017 | 0.349594 | ||||||||
\(213\) | −48.3607 | −3.31362 | ||||||||
\(214\) | 17.4164 | 1.19056 | ||||||||
\(215\) | 6.58359 | 0.448997 | ||||||||
\(216\) | −14.4721 | −0.984704 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | −18.0344 | −1.22145 | ||||||||
\(219\) | −10.9443 | −0.739545 | ||||||||
\(220\) | −1.70820 | −0.115167 | ||||||||
\(221\) | −20.3262 | −1.36729 | ||||||||
\(222\) | −34.3607 | −2.30614 | ||||||||
\(223\) | 14.2918 | 0.957049 | 0.478525 | − | 0.878074i | \(-0.341172\pi\) | ||||
0.478525 | + | 0.878074i | \(0.341172\pi\) | |||||||
\(224\) | −1.23607 | −0.0825883 | ||||||||
\(225\) | −23.0902 | −1.53934 | ||||||||
\(226\) | 3.14590 | 0.209262 | ||||||||
\(227\) | 8.94427 | 0.593652 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.61803 | 0.437332 | 0.218666 | − | 0.975800i | \(-0.429829\pi\) | ||||
0.218666 | + | 0.975800i | \(0.429829\pi\) | |||||||
\(230\) | 1.05573 | 0.0696126 | ||||||||
\(231\) | 4.94427 | 0.325309 | ||||||||
\(232\) | −2.09017 | −0.137226 | ||||||||
\(233\) | −18.5623 | −1.21606 | −0.608029 | − | 0.793915i | \(-0.708039\pi\) | ||||
−0.608029 | + | 0.793915i | \(0.708039\pi\) | |||||||
\(234\) | −27.0344 | −1.76730 | ||||||||
\(235\) | 6.18034 | 0.403161 | ||||||||
\(236\) | 8.47214 | 0.551489 | ||||||||
\(237\) | −23.4164 | −1.52106 | ||||||||
\(238\) | 6.94427 | 0.450130 | ||||||||
\(239\) | 7.81966 | 0.505812 | 0.252906 | − | 0.967491i | \(-0.418614\pi\) | ||||
0.252906 | + | 0.967491i | \(0.418614\pi\) | |||||||
\(240\) | −4.47214 | −0.288675 | ||||||||
\(241\) | 1.41641 | 0.0912389 | 0.0456194 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456194 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(242\) | 9.47214 | 0.608892 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | 3.61803 | 0.231621 | ||||||||
\(245\) | 7.56231 | 0.483138 | ||||||||
\(246\) | 18.9443 | 1.20784 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.23607 | −0.205491 | ||||||||
\(249\) | 27.4164 | 1.73744 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | −15.7082 | −0.991493 | −0.495747 | − | 0.868467i | \(-0.665105\pi\) | ||||
−0.495747 | + | 0.868467i | \(0.665105\pi\) | |||||||
\(252\) | 9.23607 | 0.581818 | ||||||||
\(253\) | 0.944272 | 0.0593659 | ||||||||
\(254\) | −15.4164 | −0.967311 | ||||||||
\(255\) | 25.1246 | 1.57336 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6180 | 1.28612 | 0.643059 | − | 0.765817i | \(-0.277665\pi\) | ||||
0.643059 | + | 0.765817i | \(0.277665\pi\) | |||||||
\(258\) | 15.4164 | 0.959784 | ||||||||
\(259\) | 13.1246 | 0.815524 | ||||||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 15.6180 | 0.966732 | ||||||||
\(262\) | 4.47214 | 0.276289 | ||||||||
\(263\) | −14.9443 | −0.921503 | −0.460752 | − | 0.887529i | \(-0.652420\pi\) | ||||
−0.460752 | + | 0.887529i | \(0.652420\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | −7.03444 | −0.432122 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.94427 | 0.424983 | ||||||||
\(268\) | −1.70820 | −0.104345 | ||||||||
\(269\) | −1.32624 | −0.0808622 | −0.0404311 | − | 0.999182i | \(-0.512873\pi\) | ||||
−0.0404311 | + | 0.999182i | \(0.512873\pi\) | |||||||
\(270\) | 20.0000 | 1.21716 | ||||||||
\(271\) | 26.0000 | 1.57939 | 0.789694 | − | 0.613501i | \(-0.210239\pi\) | ||||
0.789694 | + | 0.613501i | \(0.210239\pi\) | |||||||
\(272\) | −5.61803 | −0.340643 | ||||||||
\(273\) | 14.4721 | 0.875894 | ||||||||
\(274\) | −4.61803 | −0.278986 | ||||||||
\(275\) | −3.81966 | −0.230334 | ||||||||
\(276\) | 2.47214 | 0.148805 | ||||||||
\(277\) | 1.09017 | 0.0655020 | 0.0327510 | − | 0.999464i | \(-0.489573\pi\) | ||||
0.0327510 | + | 0.999464i | \(0.489573\pi\) | |||||||
\(278\) | 14.0000 | 0.839664 | ||||||||
\(279\) | 24.1803 | 1.44764 | ||||||||
\(280\) | 1.70820 | 0.102085 | ||||||||
\(281\) | −25.9787 | −1.54976 | −0.774880 | − | 0.632108i | \(-0.782190\pi\) | ||||
−0.774880 | + | 0.632108i | \(0.782190\pi\) | |||||||
\(282\) | 14.4721 | 0.861803 | ||||||||
\(283\) | 13.5279 | 0.804148 | 0.402074 | − | 0.915607i | \(-0.368289\pi\) | ||||
0.402074 | + | 0.915607i | \(0.368289\pi\) | |||||||
\(284\) | −14.9443 | −0.886779 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.47214 | −0.264443 | ||||||||
\(287\) | −7.23607 | −0.427132 | ||||||||
\(288\) | −7.47214 | −0.440300 | ||||||||
\(289\) | 14.5623 | 0.856606 | ||||||||
\(290\) | 2.88854 | 0.169621 | ||||||||
\(291\) | 20.6525 | 1.21067 | ||||||||
\(292\) | −3.38197 | −0.197915 | ||||||||
\(293\) | 5.05573 | 0.295359 | 0.147679 | − | 0.989035i | \(-0.452820\pi\) | ||||
0.147679 | + | 0.989035i | \(0.452820\pi\) | |||||||
\(294\) | 17.7082 | 1.03276 | ||||||||
\(295\) | −11.7082 | −0.681678 | ||||||||
\(296\) | −10.6180 | −0.617161 | ||||||||
\(297\) | 17.8885 | 1.03800 | ||||||||
\(298\) | 1.90983 | 0.110633 | ||||||||
\(299\) | 2.76393 | 0.159842 | ||||||||
\(300\) | −10.0000 | −0.577350 | ||||||||
\(301\) | −5.88854 | −0.339410 | ||||||||
\(302\) | −5.52786 | −0.318093 | ||||||||
\(303\) | −43.3050 | −2.48780 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.00000 | −0.286299 | ||||||||
\(306\) | 41.9787 | 2.39976 | ||||||||
\(307\) | −1.70820 | −0.0974923 | −0.0487462 | − | 0.998811i | \(-0.515523\pi\) | ||||
−0.0487462 | + | 0.998811i | \(0.515523\pi\) | |||||||
\(308\) | 1.52786 | 0.0870581 | ||||||||
\(309\) | −53.8885 | −3.06561 | ||||||||
\(310\) | 4.47214 | 0.254000 | ||||||||
\(311\) | 26.7639 | 1.51764 | 0.758822 | − | 0.651298i | \(-0.225775\pi\) | ||||
0.758822 | + | 0.651298i | \(0.225775\pi\) | |||||||
\(312\) | −11.7082 | −0.662847 | ||||||||
\(313\) | 22.5066 | 1.27215 | 0.636073 | − | 0.771628i | \(-0.280558\pi\) | ||||
0.636073 | + | 0.771628i | \(0.280558\pi\) | |||||||
\(314\) | −11.6180 | −0.655644 | ||||||||
\(315\) | −12.7639 | −0.719166 | ||||||||
\(316\) | −7.23607 | −0.407061 | ||||||||
\(317\) | −14.3262 | −0.804642 | −0.402321 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402321 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(318\) | −16.4721 | −0.923712 | ||||||||
\(319\) | 2.58359 | 0.144653 | ||||||||
\(320\) | −1.38197 | −0.0772542 | ||||||||
\(321\) | −56.3607 | −3.14575 | ||||||||
\(322\) | −0.944272 | −0.0526222 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 24.4164 | 1.35647 | ||||||||
\(325\) | −11.1803 | −0.620174 | ||||||||
\(326\) | 20.6525 | 1.14383 | ||||||||
\(327\) | 58.3607 | 3.22735 | ||||||||
\(328\) | 5.85410 | 0.323239 | ||||||||
\(329\) | −5.52786 | −0.304761 | ||||||||
\(330\) | 5.52786 | 0.304299 | ||||||||
\(331\) | 12.2918 | 0.675618 | 0.337809 | − | 0.941215i | \(-0.390314\pi\) | ||||
0.337809 | + | 0.941215i | \(0.390314\pi\) | |||||||
\(332\) | 8.47214 | 0.464969 | ||||||||
\(333\) | 79.3394 | 4.34777 | ||||||||
\(334\) | 3.52786 | 0.193036 | ||||||||
\(335\) | 2.36068 | 0.128978 | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | 4.61803 | 0.251560 | 0.125780 | − | 0.992058i | \(-0.459857\pi\) | ||||
0.125780 | + | 0.992058i | \(0.459857\pi\) | |||||||
\(338\) | −0.0901699 | −0.00490460 | ||||||||
\(339\) | −10.1803 | −0.552920 | ||||||||
\(340\) | 7.76393 | 0.421058 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4164 | −0.832408 | ||||||||
\(344\) | 4.76393 | 0.256854 | ||||||||
\(345\) | −3.41641 | −0.183933 | ||||||||
\(346\) | 14.3262 | 0.770183 | ||||||||
\(347\) | 28.6525 | 1.53815 | 0.769073 | − | 0.639161i | \(-0.220718\pi\) | ||||
0.769073 | + | 0.639161i | \(0.220718\pi\) | |||||||
\(348\) | 6.76393 | 0.362585 | ||||||||
\(349\) | −21.9098 | −1.17281 | −0.586403 | − | 0.810019i | \(-0.699457\pi\) | ||||
−0.586403 | + | 0.810019i | \(0.699457\pi\) | |||||||
\(350\) | 3.81966 | 0.204169 | ||||||||
\(351\) | 52.3607 | 2.79481 | ||||||||
\(352\) | −1.23607 | −0.0658826 | ||||||||
\(353\) | 18.7426 | 0.997570 | 0.498785 | − | 0.866726i | \(-0.333780\pi\) | ||||
0.498785 | + | 0.866726i | \(0.333780\pi\) | |||||||
\(354\) | −27.4164 | −1.45717 | ||||||||
\(355\) | 20.6525 | 1.09612 | ||||||||
\(356\) | 2.14590 | 0.113732 | ||||||||
\(357\) | −22.4721 | −1.18935 | ||||||||
\(358\) | −3.41641 | −0.180563 | ||||||||
\(359\) | 20.4721 | 1.08048 | 0.540239 | − | 0.841512i | \(-0.318334\pi\) | ||||
0.540239 | + | 0.841512i | \(0.318334\pi\) | |||||||
\(360\) | 10.3262 | 0.544241 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 21.4164 | 1.12562 | ||||||||
\(363\) | −30.6525 | −1.60884 | ||||||||
\(364\) | 4.47214 | 0.234404 | ||||||||
\(365\) | 4.67376 | 0.244636 | ||||||||
\(366\) | −11.7082 | −0.611998 | ||||||||
\(367\) | −34.8328 | −1.81826 | −0.909129 | − | 0.416514i | \(-0.863252\pi\) | ||||
−0.909129 | + | 0.416514i | \(0.863252\pi\) | |||||||
\(368\) | 0.763932 | 0.0398227 | ||||||||
\(369\) | −43.7426 | −2.27715 | ||||||||
\(370\) | 14.6738 | 0.762853 | ||||||||
\(371\) | 6.29180 | 0.326654 | ||||||||
\(372\) | 10.4721 | 0.542955 | ||||||||
\(373\) | 2.67376 | 0.138442 | 0.0692211 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692211 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(374\) | 6.94427 | 0.359080 | ||||||||
\(375\) | 36.1803 | 1.86834 | ||||||||
\(376\) | 4.47214 | 0.230633 | ||||||||
\(377\) | 7.56231 | 0.389479 | ||||||||
\(378\) | −17.8885 | −0.920087 | ||||||||
\(379\) | −8.58359 | −0.440910 | −0.220455 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.8885 | 2.55587 | ||||||||
\(382\) | −12.4721 | −0.638130 | ||||||||
\(383\) | 25.2361 | 1.28950 | 0.644751 | − | 0.764392i | \(-0.276961\pi\) | ||||
0.644751 | + | 0.764392i | \(0.276961\pi\) | |||||||
\(384\) | −3.23607 | −0.165140 | ||||||||
\(385\) | −2.11146 | −0.107610 | ||||||||
\(386\) | 20.4721 | 1.04200 | ||||||||
\(387\) | −35.5967 | −1.80948 | ||||||||
\(388\) | 6.38197 | 0.323995 | ||||||||
\(389\) | −11.7984 | −0.598201 | −0.299101 | − | 0.954222i | \(-0.596687\pi\) | ||||
−0.299101 | + | 0.954222i | \(0.596687\pi\) | |||||||
\(390\) | 16.1803 | 0.819323 | ||||||||
\(391\) | −4.29180 | −0.217045 | ||||||||
\(392\) | 5.47214 | 0.276385 | ||||||||
\(393\) | −14.4721 | −0.730023 | ||||||||
\(394\) | 10.8541 | 0.546822 | ||||||||
\(395\) | 10.0000 | 0.503155 | ||||||||
\(396\) | 9.23607 | 0.464130 | ||||||||
\(397\) | 22.3607 | 1.12225 | 0.561125 | − | 0.827731i | \(-0.310369\pi\) | ||||
0.561125 | + | 0.827731i | \(0.310369\pi\) | |||||||
\(398\) | −1.52786 | −0.0765849 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.09017 | −0.154508 | ||||||||
\(401\) | 1.05573 | 0.0527205 | 0.0263603 | − | 0.999653i | \(-0.491608\pi\) | ||||
0.0263603 | + | 0.999653i | \(0.491608\pi\) | |||||||
\(402\) | 5.52786 | 0.275705 | ||||||||
\(403\) | 11.7082 | 0.583227 | ||||||||
\(404\) | −13.3820 | −0.665778 | ||||||||
\(405\) | −33.7426 | −1.67669 | ||||||||
\(406\) | −2.58359 | −0.128222 | ||||||||
\(407\) | 13.1246 | 0.650563 | ||||||||
\(408\) | 18.1803 | 0.900061 | ||||||||
\(409\) | −17.2705 | −0.853972 | −0.426986 | − | 0.904258i | \(-0.640425\pi\) | ||||
−0.426986 | + | 0.904258i | \(0.640425\pi\) | |||||||
\(410\) | −8.09017 | −0.399545 | ||||||||
\(411\) | 14.9443 | 0.737147 | ||||||||
\(412\) | −16.6525 | −0.820409 | ||||||||
\(413\) | 10.4721 | 0.515300 | ||||||||
\(414\) | −5.70820 | −0.280543 | ||||||||
\(415\) | −11.7082 | −0.574733 | ||||||||
\(416\) | −3.61803 | −0.177389 | ||||||||
\(417\) | −45.3050 | −2.21859 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.47214 | 0.120772 | 0.0603859 | − | 0.998175i | \(-0.480767\pi\) | ||||
0.0603859 | + | 0.998175i | \(0.480767\pi\) | |||||||
\(420\) | −5.52786 | −0.269732 | ||||||||
\(421\) | 25.0902 | 1.22282 | 0.611410 | − | 0.791314i | \(-0.290603\pi\) | ||||
0.611410 | + | 0.791314i | \(0.290603\pi\) | |||||||
\(422\) | 2.76393 | 0.134546 | ||||||||
\(423\) | −33.4164 | −1.62476 | ||||||||
\(424\) | −5.09017 | −0.247201 | ||||||||
\(425\) | 17.3607 | 0.842117 | ||||||||
\(426\) | 48.3607 | 2.34308 | ||||||||
\(427\) | 4.47214 | 0.216422 | ||||||||
\(428\) | −17.4164 | −0.841854 | ||||||||
\(429\) | 14.4721 | 0.698721 | ||||||||
\(430\) | −6.58359 | −0.317489 | ||||||||
\(431\) | −24.6525 | −1.18747 | −0.593734 | − | 0.804661i | \(-0.702347\pi\) | ||||
−0.593734 | + | 0.804661i | \(0.702347\pi\) | |||||||
\(432\) | 14.4721 | 0.696291 | ||||||||
\(433\) | 4.03444 | 0.193883 | 0.0969415 | − | 0.995290i | \(-0.469094\pi\) | ||||
0.0969415 | + | 0.995290i | \(0.469094\pi\) | |||||||
\(434\) | −4.00000 | −0.192006 | ||||||||
\(435\) | −9.34752 | −0.448179 | ||||||||
\(436\) | 18.0344 | 0.863693 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 10.9443 | 0.522938 | ||||||||
\(439\) | 24.7639 | 1.18192 | 0.590959 | − | 0.806702i | \(-0.298749\pi\) | ||||
0.590959 | + | 0.806702i | \(0.298749\pi\) | |||||||
\(440\) | 1.70820 | 0.0814354 | ||||||||
\(441\) | −40.8885 | −1.94707 | ||||||||
\(442\) | 20.3262 | 0.966821 | ||||||||
\(443\) | 4.76393 | 0.226341 | 0.113171 | − | 0.993576i | \(-0.463899\pi\) | ||||
0.113171 | + | 0.993576i | \(0.463899\pi\) | |||||||
\(444\) | 34.3607 | 1.63069 | ||||||||
\(445\) | −2.96556 | −0.140581 | ||||||||
\(446\) | −14.2918 | −0.676736 | ||||||||
\(447\) | −6.18034 | −0.292320 | ||||||||
\(448\) | 1.23607 | 0.0583987 | ||||||||
\(449\) | 1.79837 | 0.0848705 | 0.0424353 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424353 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(450\) | 23.0902 | 1.08848 | ||||||||
\(451\) | −7.23607 | −0.340733 | ||||||||
\(452\) | −3.14590 | −0.147971 | ||||||||
\(453\) | 17.8885 | 0.840477 | ||||||||
\(454\) | −8.94427 | −0.419775 | ||||||||
\(455\) | −6.18034 | −0.289739 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2148 | −1.22628 | −0.613138 | − | 0.789976i | \(-0.710093\pi\) | ||||
−0.613138 | + | 0.789976i | \(0.710093\pi\) | |||||||
\(458\) | −6.61803 | −0.309240 | ||||||||
\(459\) | −81.3050 | −3.79499 | ||||||||
\(460\) | −1.05573 | −0.0492236 | ||||||||
\(461\) | −5.41641 | −0.252267 | −0.126134 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126134 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(462\) | −4.94427 | −0.230028 | ||||||||
\(463\) | −22.9443 | −1.06631 | −0.533155 | − | 0.846017i | \(-0.678994\pi\) | ||||
−0.533155 | + | 0.846017i | \(0.678994\pi\) | |||||||
\(464\) | 2.09017 | 0.0970337 | ||||||||
\(465\) | −14.4721 | −0.671129 | ||||||||
\(466\) | 18.5623 | 0.859882 | ||||||||
\(467\) | 29.3050 | 1.35607 | 0.678036 | − | 0.735029i | \(-0.262831\pi\) | ||||
0.678036 | + | 0.735029i | \(0.262831\pi\) | |||||||
\(468\) | 27.0344 | 1.24967 | ||||||||
\(469\) | −2.11146 | −0.0974980 | ||||||||
\(470\) | −6.18034 | −0.285078 | ||||||||
\(471\) | 37.5967 | 1.73237 | ||||||||
\(472\) | −8.47214 | −0.389962 | ||||||||
\(473\) | −5.88854 | −0.270756 | ||||||||
\(474\) | 23.4164 | 1.07555 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.94427 | −0.318290 | ||||||||
\(477\) | 38.0344 | 1.74148 | ||||||||
\(478\) | −7.81966 | −0.357663 | ||||||||
\(479\) | −5.70820 | −0.260814 | −0.130407 | − | 0.991461i | \(-0.541628\pi\) | ||||
−0.130407 | + | 0.991461i | \(0.541628\pi\) | |||||||
\(480\) | 4.47214 | 0.204124 | ||||||||
\(481\) | 38.4164 | 1.75164 | ||||||||
\(482\) | −1.41641 | −0.0645156 | ||||||||
\(483\) | 3.05573 | 0.139040 | ||||||||
\(484\) | −9.47214 | −0.430552 | ||||||||
\(485\) | −8.81966 | −0.400480 | ||||||||
\(486\) | −35.5967 | −1.61470 | ||||||||
\(487\) | 14.7639 | 0.669018 | 0.334509 | − | 0.942393i | \(-0.391430\pi\) | ||||
0.334509 | + | 0.942393i | \(0.391430\pi\) | |||||||
\(488\) | −3.61803 | −0.163781 | ||||||||
\(489\) | −66.8328 | −3.02228 | ||||||||
\(490\) | −7.56231 | −0.341630 | ||||||||
\(491\) | −10.4721 | −0.472601 | −0.236300 | − | 0.971680i | \(-0.575935\pi\) | ||||
−0.236300 | + | 0.971680i | \(0.575935\pi\) | |||||||
\(492\) | −18.9443 | −0.854074 | ||||||||
\(493\) | −11.7426 | −0.528862 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7639 | −0.573696 | ||||||||
\(496\) | 3.23607 | 0.145304 | ||||||||
\(497\) | −18.4721 | −0.828589 | ||||||||
\(498\) | −27.4164 | −1.22856 | ||||||||
\(499\) | 27.3050 | 1.22234 | 0.611169 | − | 0.791500i | \(-0.290700\pi\) | ||||
0.611169 | + | 0.791500i | \(0.290700\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | −11.4164 | −0.510047 | ||||||||
\(502\) | 15.7082 | 0.701091 | ||||||||
\(503\) | 11.2361 | 0.500992 | 0.250496 | − | 0.968118i | \(-0.419406\pi\) | ||||
0.250496 | + | 0.968118i | \(0.419406\pi\) | |||||||
\(504\) | −9.23607 | −0.411407 | ||||||||
\(505\) | 18.4934 | 0.822946 | ||||||||
\(506\) | −0.944272 | −0.0419780 | ||||||||
\(507\) | 0.291796 | 0.0129591 | ||||||||
\(508\) | 15.4164 | 0.683992 | ||||||||
\(509\) | −17.6869 | −0.783959 | −0.391979 | − | 0.919974i | \(-0.628210\pi\) | ||||
−0.391979 | + | 0.919974i | \(0.628210\pi\) | |||||||
\(510\) | −25.1246 | −1.11254 | ||||||||
\(511\) | −4.18034 | −0.184927 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.6180 | −0.909422 | ||||||||
\(515\) | 23.0132 | 1.01408 | ||||||||
\(516\) | −15.4164 | −0.678670 | ||||||||
\(517\) | −5.52786 | −0.243115 | ||||||||
\(518\) | −13.1246 | −0.576662 | ||||||||
\(519\) | −46.3607 | −2.03501 | ||||||||
\(520\) | 5.00000 | 0.219265 | ||||||||
\(521\) | 28.2705 | 1.23855 | 0.619277 | − | 0.785173i | \(-0.287426\pi\) | ||||
0.619277 | + | 0.785173i | \(0.287426\pi\) | |||||||
\(522\) | −15.6180 | −0.683583 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | −4.47214 | −0.195366 | ||||||||
\(525\) | −12.3607 | −0.539464 | ||||||||
\(526\) | 14.9443 | 0.651601 | ||||||||
\(527\) | −18.1803 | −0.791948 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | −22.4164 | −0.974626 | ||||||||
\(530\) | 7.03444 | 0.305557 | ||||||||
\(531\) | 63.3050 | 2.74720 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.1803 | −0.917422 | ||||||||
\(534\) | −6.94427 | −0.300508 | ||||||||
\(535\) | 24.0689 | 1.04059 | ||||||||
\(536\) | 1.70820 | 0.0737832 | ||||||||
\(537\) | 11.0557 | 0.477090 | ||||||||
\(538\) | 1.32624 | 0.0571782 | ||||||||
\(539\) | −6.76393 | −0.291343 | ||||||||
\(540\) | −20.0000 | −0.860663 | ||||||||
\(541\) | −24.3820 | −1.04826 | −0.524131 | − | 0.851637i | \(-0.675610\pi\) | ||||
−0.524131 | + | 0.851637i | \(0.675610\pi\) | |||||||
\(542\) | −26.0000 | −1.11680 | ||||||||
\(543\) | −69.3050 | −2.97416 | ||||||||
\(544\) | 5.61803 | 0.240871 | ||||||||
\(545\) | −24.9230 | −1.06758 | ||||||||
\(546\) | −14.4721 | −0.619350 | ||||||||
\(547\) | 22.9443 | 0.981026 | 0.490513 | − | 0.871434i | \(-0.336809\pi\) | ||||
0.490513 | + | 0.871434i | \(0.336809\pi\) | |||||||
\(548\) | 4.61803 | 0.197273 | ||||||||
\(549\) | 27.0344 | 1.15380 | ||||||||
\(550\) | 3.81966 | 0.162871 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.47214 | −0.105221 | ||||||||
\(553\) | −8.94427 | −0.380349 | ||||||||
\(554\) | −1.09017 | −0.0463169 | ||||||||
\(555\) | −47.4853 | −2.01564 | ||||||||
\(556\) | −14.0000 | −0.593732 | ||||||||
\(557\) | 22.9443 | 0.972180 | 0.486090 | − | 0.873909i | \(-0.338423\pi\) | ||||
0.486090 | + | 0.873909i | \(0.338423\pi\) | |||||||
\(558\) | −24.1803 | −1.02364 | ||||||||
\(559\) | −17.2361 | −0.729008 | ||||||||
\(560\) | −1.70820 | −0.0721848 | ||||||||
\(561\) | −22.4721 | −0.948774 | ||||||||
\(562\) | 25.9787 | 1.09585 | ||||||||
\(563\) | 39.7082 | 1.67350 | 0.836751 | − | 0.547584i | \(-0.184452\pi\) | ||||
0.836751 | + | 0.547584i | \(0.184452\pi\) | |||||||
\(564\) | −14.4721 | −0.609387 | ||||||||
\(565\) | 4.34752 | 0.182902 | ||||||||
\(566\) | −13.5279 | −0.568619 | ||||||||
\(567\) | 30.1803 | 1.26746 | ||||||||
\(568\) | 14.9443 | 0.627048 | ||||||||
\(569\) | 19.0902 | 0.800302 | 0.400151 | − | 0.916449i | \(-0.368958\pi\) | ||||
0.400151 | + | 0.916449i | \(0.368958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5410 | 1.44550 | 0.722748 | − | 0.691111i | \(-0.242879\pi\) | ||||
0.722748 | + | 0.691111i | \(0.242879\pi\) | |||||||
\(572\) | 4.47214 | 0.186989 | ||||||||
\(573\) | 40.3607 | 1.68609 | ||||||||
\(574\) | 7.23607 | 0.302028 | ||||||||
\(575\) | −2.36068 | −0.0984472 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | −18.9230 | −0.787774 | −0.393887 | − | 0.919159i | \(-0.628870\pi\) | ||||
−0.393887 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(578\) | −14.5623 | −0.605712 | ||||||||
\(579\) | −66.2492 | −2.75322 | ||||||||
\(580\) | −2.88854 | −0.119940 | ||||||||
\(581\) | 10.4721 | 0.434457 | ||||||||
\(582\) | −20.6525 | −0.856073 | ||||||||
\(583\) | 6.29180 | 0.260580 | ||||||||
\(584\) | 3.38197 | 0.139947 | ||||||||
\(585\) | −37.3607 | −1.54467 | ||||||||
\(586\) | −5.05573 | −0.208850 | ||||||||
\(587\) | 43.1246 | 1.77994 | 0.889972 | − | 0.456016i | \(-0.150724\pi\) | ||||
0.889972 | + | 0.456016i | \(0.150724\pi\) | |||||||
\(588\) | −17.7082 | −0.730274 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.7082 | 0.482019 | ||||||||
\(591\) | −35.1246 | −1.44483 | ||||||||
\(592\) | 10.6180 | 0.436399 | ||||||||
\(593\) | 29.9230 | 1.22879 | 0.614395 | − | 0.788999i | \(-0.289400\pi\) | ||||
0.614395 | + | 0.788999i | \(0.289400\pi\) | |||||||
\(594\) | −17.8885 | −0.733976 | ||||||||
\(595\) | 9.59675 | 0.393428 | ||||||||
\(596\) | −1.90983 | −0.0782297 | ||||||||
\(597\) | 4.94427 | 0.202356 | ||||||||
\(598\) | −2.76393 | −0.113026 | ||||||||
\(599\) | 1.12461 | 0.0459504 | 0.0229752 | − | 0.999736i | \(-0.492686\pi\) | ||||
0.0229752 | + | 0.999736i | \(0.492686\pi\) | |||||||
\(600\) | 10.0000 | 0.408248 | ||||||||
\(601\) | 7.52786 | 0.307068 | 0.153534 | − | 0.988143i | \(-0.450935\pi\) | ||||
0.153534 | + | 0.988143i | \(0.450935\pi\) | |||||||
\(602\) | 5.88854 | 0.239999 | ||||||||
\(603\) | −12.7639 | −0.519787 | ||||||||
\(604\) | 5.52786 | 0.224926 | ||||||||
\(605\) | 13.0902 | 0.532191 | ||||||||
\(606\) | 43.3050 | 1.75914 | ||||||||
\(607\) | 23.7771 | 0.965082 | 0.482541 | − | 0.875873i | \(-0.339714\pi\) | ||||
0.482541 | + | 0.875873i | \(0.339714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.36068 | 0.338792 | ||||||||
\(610\) | 5.00000 | 0.202444 | ||||||||
\(611\) | −16.1803 | −0.654586 | ||||||||
\(612\) | −41.9787 | −1.69689 | ||||||||
\(613\) | 10.6180 | 0.428858 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(614\) | 1.70820 | 0.0689375 | ||||||||
\(615\) | 26.1803 | 1.05569 | ||||||||
\(616\) | −1.52786 | −0.0615594 | ||||||||
\(617\) | 25.0557 | 1.00871 | 0.504353 | − | 0.863498i | \(-0.331731\pi\) | ||||
0.504353 | + | 0.863498i | \(0.331731\pi\) | |||||||
\(618\) | 53.8885 | 2.16772 | ||||||||
\(619\) | −22.3607 | −0.898752 | −0.449376 | − | 0.893343i | \(-0.648354\pi\) | ||||
−0.449376 | + | 0.893343i | \(0.648354\pi\) | |||||||
\(620\) | −4.47214 | −0.179605 | ||||||||
\(621\) | 11.0557 | 0.443651 | ||||||||
\(622\) | −26.7639 | −1.07314 | ||||||||
\(623\) | 2.65248 | 0.106269 | ||||||||
\(624\) | 11.7082 | 0.468703 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.5066 | −0.899544 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.6180 | 0.463610 | ||||||||
\(629\) | −59.6525 | −2.37850 | ||||||||
\(630\) | 12.7639 | 0.508527 | ||||||||
\(631\) | 9.12461 | 0.363245 | 0.181623 | − | 0.983368i | \(-0.441865\pi\) | ||||
0.181623 | + | 0.983368i | \(0.441865\pi\) | |||||||
\(632\) | 7.23607 | 0.287835 | ||||||||
\(633\) | −8.94427 | −0.355503 | ||||||||
\(634\) | 14.3262 | 0.568968 | ||||||||
\(635\) | −21.3050 | −0.845461 | ||||||||
\(636\) | 16.4721 | 0.653163 | ||||||||
\(637\) | −19.7984 | −0.784440 | ||||||||
\(638\) | −2.58359 | −0.102285 | ||||||||
\(639\) | −111.666 | −4.41742 | ||||||||
\(640\) | 1.38197 | 0.0546270 | ||||||||
\(641\) | 20.2705 | 0.800637 | 0.400319 | − | 0.916376i | \(-0.368899\pi\) | ||||
0.400319 | + | 0.916376i | \(0.368899\pi\) | |||||||
\(642\) | 56.3607 | 2.22438 | ||||||||
\(643\) | 14.8328 | 0.584949 | 0.292475 | − | 0.956273i | \(-0.405521\pi\) | ||||
0.292475 | + | 0.956273i | \(0.405521\pi\) | |||||||
\(644\) | 0.944272 | 0.0372095 | ||||||||
\(645\) | 21.3050 | 0.838882 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0689 | −1.26076 | −0.630379 | − | 0.776288i | \(-0.717100\pi\) | ||||
−0.630379 | + | 0.776288i | \(0.717100\pi\) | |||||||
\(648\) | −24.4164 | −0.959167 | ||||||||
\(649\) | 10.4721 | 0.411067 | ||||||||
\(650\) | 11.1803 | 0.438529 | ||||||||
\(651\) | 12.9443 | 0.507326 | ||||||||
\(652\) | −20.6525 | −0.808813 | ||||||||
\(653\) | 38.3951 | 1.50252 | 0.751259 | − | 0.660008i | \(-0.229447\pi\) | ||||
0.751259 | + | 0.660008i | \(0.229447\pi\) | |||||||
\(654\) | −58.3607 | −2.28208 | ||||||||
\(655\) | 6.18034 | 0.241486 | ||||||||
\(656\) | −5.85410 | −0.228564 | ||||||||
\(657\) | −25.2705 | −0.985896 | ||||||||
\(658\) | 5.52786 | 0.215499 | ||||||||
\(659\) | 18.5410 | 0.722256 | 0.361128 | − | 0.932516i | \(-0.382392\pi\) | ||||
0.361128 | + | 0.932516i | \(0.382392\pi\) | |||||||
\(660\) | −5.52786 | −0.215172 | ||||||||
\(661\) | 5.41641 | 0.210674 | 0.105337 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105337 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(662\) | −12.2918 | −0.477734 | ||||||||
\(663\) | −65.7771 | −2.55457 | ||||||||
\(664\) | −8.47214 | −0.328783 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −79.3394 | −3.07434 | ||||||||
\(667\) | 1.59675 | 0.0618263 | ||||||||
\(668\) | −3.52786 | −0.136497 | ||||||||
\(669\) | 46.2492 | 1.78810 | ||||||||
\(670\) | −2.36068 | −0.0912010 | ||||||||
\(671\) | 4.47214 | 0.172645 | ||||||||
\(672\) | −4.00000 | −0.154303 | ||||||||
\(673\) | 32.6180 | 1.25733 | 0.628666 | − | 0.777675i | \(-0.283601\pi\) | ||||
0.628666 | + | 0.777675i | \(0.283601\pi\) | |||||||
\(674\) | −4.61803 | −0.177880 | ||||||||
\(675\) | −44.7214 | −1.72133 | ||||||||
\(676\) | 0.0901699 | 0.00346807 | ||||||||
\(677\) | −4.38197 | −0.168413 | −0.0842063 | − | 0.996448i | \(-0.526835\pi\) | ||||
−0.0842063 | + | 0.996448i | \(0.526835\pi\) | |||||||
\(678\) | 10.1803 | 0.390974 | ||||||||
\(679\) | 7.88854 | 0.302735 | ||||||||
\(680\) | −7.76393 | −0.297733 | ||||||||
\(681\) | 28.9443 | 1.10915 | ||||||||
\(682\) | −4.00000 | −0.153168 | ||||||||
\(683\) | 2.18034 | 0.0834284 | 0.0417142 | − | 0.999130i | \(-0.486718\pi\) | ||||
0.0417142 | + | 0.999130i | \(0.486718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.38197 | −0.243842 | ||||||||
\(686\) | 15.4164 | 0.588601 | ||||||||
\(687\) | 21.4164 | 0.817087 | ||||||||
\(688\) | −4.76393 | −0.181623 | ||||||||
\(689\) | 18.4164 | 0.701609 | ||||||||
\(690\) | 3.41641 | 0.130060 | ||||||||
\(691\) | 22.3607 | 0.850640 | 0.425320 | − | 0.905043i | \(-0.360161\pi\) | ||||
0.425320 | + | 0.905043i | \(0.360161\pi\) | |||||||
\(692\) | −14.3262 | −0.544602 | ||||||||
\(693\) | 11.4164 | 0.433673 | ||||||||
\(694\) | −28.6525 | −1.08763 | ||||||||
\(695\) | 19.3475 | 0.733893 | ||||||||
\(696\) | −6.76393 | −0.256386 | ||||||||
\(697\) | 32.8885 | 1.24574 | ||||||||
\(698\) | 21.9098 | 0.829299 | ||||||||
\(699\) | −60.0689 | −2.27201 | ||||||||
\(700\) | −3.81966 | −0.144370 | ||||||||
\(701\) | −39.6312 | −1.49685 | −0.748425 | − | 0.663220i | \(-0.769189\pi\) | ||||
−0.748425 | + | 0.663220i | \(0.769189\pi\) | |||||||
\(702\) | −52.3607 | −1.97623 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.23607 | 0.0465861 | ||||||||
\(705\) | 20.0000 | 0.753244 | ||||||||
\(706\) | −18.7426 | −0.705389 | ||||||||
\(707\) | −16.5410 | −0.622089 | ||||||||
\(708\) | 27.4164 | 1.03037 | ||||||||
\(709\) | 18.0902 | 0.679391 | 0.339695 | − | 0.940536i | \(-0.389676\pi\) | ||||
0.339695 | + | 0.940536i | \(0.389676\pi\) | |||||||
\(710\) | −20.6525 | −0.775074 | ||||||||
\(711\) | −54.0689 | −2.02774 | ||||||||
\(712\) | −2.14590 | −0.0804209 | ||||||||
\(713\) | 2.47214 | 0.0925822 | ||||||||
\(714\) | 22.4721 | 0.840999 | ||||||||
\(715\) | −6.18034 | −0.231132 | ||||||||
\(716\) | 3.41641 | 0.127677 | ||||||||
\(717\) | 25.3050 | 0.945031 | ||||||||
\(718\) | −20.4721 | −0.764013 | ||||||||
\(719\) | 25.7082 | 0.958754 | 0.479377 | − | 0.877609i | \(-0.340863\pi\) | ||||
0.479377 | + | 0.877609i | \(0.340863\pi\) | |||||||
\(720\) | −10.3262 | −0.384836 | ||||||||
\(721\) | −20.5836 | −0.766573 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.58359 | 0.170466 | ||||||||
\(724\) | −21.4164 | −0.795935 | ||||||||
\(725\) | −6.45898 | −0.239881 | ||||||||
\(726\) | 30.6525 | 1.13762 | ||||||||
\(727\) | −13.0557 | −0.484210 | −0.242105 | − | 0.970250i | \(-0.577838\pi\) | ||||
−0.242105 | + | 0.970250i | \(0.577838\pi\) | |||||||
\(728\) | −4.47214 | −0.165748 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | −4.67376 | −0.172984 | ||||||||
\(731\) | 26.7639 | 0.989900 | ||||||||
\(732\) | 11.7082 | 0.432748 | ||||||||
\(733\) | 10.0902 | 0.372689 | 0.186344 | − | 0.982484i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982484i | \(0.440336\pi\) | |||||||
\(734\) | 34.8328 | 1.28570 | ||||||||
\(735\) | 24.4721 | 0.902668 | ||||||||
\(736\) | −0.763932 | −0.0281589 | ||||||||
\(737\) | −2.11146 | −0.0777765 | ||||||||
\(738\) | 43.7426 | 1.61019 | ||||||||
\(739\) | −31.1246 | −1.14494 | −0.572469 | − | 0.819927i | \(-0.694014\pi\) | ||||
−0.572469 | + | 0.819927i | \(0.694014\pi\) | |||||||
\(740\) | −14.6738 | −0.539418 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.29180 | −0.230979 | ||||||||
\(743\) | 41.8885 | 1.53674 | 0.768371 | − | 0.640005i | \(-0.221068\pi\) | ||||
0.768371 | + | 0.640005i | \(0.221068\pi\) | |||||||
\(744\) | −10.4721 | −0.383927 | ||||||||
\(745\) | 2.63932 | 0.0966972 | ||||||||
\(746\) | −2.67376 | −0.0978934 | ||||||||
\(747\) | 63.3050 | 2.31621 | ||||||||
\(748\) | −6.94427 | −0.253908 | ||||||||
\(749\) | −21.5279 | −0.786611 | ||||||||
\(750\) | −36.1803 | −1.32112 | ||||||||
\(751\) | 34.0689 | 1.24319 | 0.621596 | − | 0.783338i | \(-0.286485\pi\) | ||||
0.621596 | + | 0.783338i | \(0.286485\pi\) | |||||||
\(752\) | −4.47214 | −0.163082 | ||||||||
\(753\) | −50.8328 | −1.85245 | ||||||||
\(754\) | −7.56231 | −0.275403 | ||||||||
\(755\) | −7.63932 | −0.278023 | ||||||||
\(756\) | 17.8885 | 0.650600 | ||||||||
\(757\) | 24.5623 | 0.892732 | 0.446366 | − | 0.894850i | \(-0.352718\pi\) | ||||
0.446366 | + | 0.894850i | \(0.352718\pi\) | |||||||
\(758\) | 8.58359 | 0.311770 | ||||||||
\(759\) | 3.05573 | 0.110916 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3607 | −0.665574 | −0.332787 | − | 0.943002i | \(-0.607989\pi\) | ||||
−0.332787 | + | 0.943002i | \(0.607989\pi\) | |||||||
\(762\) | −49.8885 | −1.80727 | ||||||||
\(763\) | 22.2918 | 0.807017 | ||||||||
\(764\) | 12.4721 | 0.451226 | ||||||||
\(765\) | 58.0132 | 2.09747 | ||||||||
\(766\) | −25.2361 | −0.911816 | ||||||||
\(767\) | 30.6525 | 1.10680 | ||||||||
\(768\) | 3.23607 | 0.116772 | ||||||||
\(769\) | −3.74265 | −0.134963 | −0.0674816 | − | 0.997721i | \(-0.521496\pi\) | ||||
−0.0674816 | + | 0.997721i | \(0.521496\pi\) | |||||||
\(770\) | 2.11146 | 0.0760916 | ||||||||
\(771\) | 66.7214 | 2.40291 | ||||||||
\(772\) | −20.4721 | −0.736808 | ||||||||
\(773\) | −14.8541 | −0.534265 | −0.267132 | − | 0.963660i | \(-0.586076\pi\) | ||||
−0.267132 | + | 0.963660i | \(0.586076\pi\) | |||||||
\(774\) | 35.5967 | 1.27950 | ||||||||
\(775\) | −10.0000 | −0.359211 | ||||||||
\(776\) | −6.38197 | −0.229099 | ||||||||
\(777\) | 42.4721 | 1.52368 | ||||||||
\(778\) | 11.7984 | 0.422992 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −16.1803 | −0.579349 | ||||||||
\(781\) | −18.4721 | −0.660985 | ||||||||
\(782\) | 4.29180 | 0.153474 | ||||||||
\(783\) | 30.2492 | 1.08102 | ||||||||
\(784\) | −5.47214 | −0.195433 | ||||||||
\(785\) | −16.0557 | −0.573054 | ||||||||
\(786\) | 14.4721 | 0.516204 | ||||||||
\(787\) | 19.5279 | 0.696093 | 0.348047 | − | 0.937477i | \(-0.386845\pi\) | ||||
0.348047 | + | 0.937477i | \(0.386845\pi\) | |||||||
\(788\) | −10.8541 | −0.386661 | ||||||||
\(789\) | −48.3607 | −1.72169 | ||||||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | −3.88854 | −0.138261 | ||||||||
\(792\) | −9.23607 | −0.328189 | ||||||||
\(793\) | 13.0902 | 0.464846 | ||||||||
\(794\) | −22.3607 | −0.793551 | ||||||||
\(795\) | −22.7639 | −0.807353 | ||||||||
\(796\) | 1.52786 | 0.0541537 | ||||||||
\(797\) | 48.5623 | 1.72017 | 0.860083 | − | 0.510155i | \(-0.170412\pi\) | ||||
0.860083 | + | 0.510155i | \(0.170412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1246 | 0.888845 | ||||||||
\(800\) | 3.09017 | 0.109254 | ||||||||
\(801\) | 16.0344 | 0.566549 | ||||||||
\(802\) | −1.05573 | −0.0372791 | ||||||||
\(803\) | −4.18034 | −0.147521 | ||||||||
\(804\) | −5.52786 | −0.194953 | ||||||||
\(805\) | −1.30495 | −0.0459935 | ||||||||
\(806\) | −11.7082 | −0.412404 | ||||||||
\(807\) | −4.29180 | −0.151078 | ||||||||
\(808\) | 13.3820 | 0.470776 | ||||||||
\(809\) | −39.7426 | −1.39728 | −0.698639 | − | 0.715475i | \(-0.746210\pi\) | ||||
−0.698639 | + | 0.715475i | \(0.746210\pi\) | |||||||
\(810\) | 33.7426 | 1.18560 | ||||||||
\(811\) | −43.5967 | −1.53089 | −0.765444 | − | 0.643502i | \(-0.777481\pi\) | ||||
−0.765444 | + | 0.643502i | \(0.777481\pi\) | |||||||
\(812\) | 2.58359 | 0.0906663 | ||||||||
\(813\) | 84.1378 | 2.95084 | ||||||||
\(814\) | −13.1246 | −0.460017 | ||||||||
\(815\) | 28.5410 | 0.999748 | ||||||||
\(816\) | −18.1803 | −0.636439 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.2705 | 0.603849 | ||||||||
\(819\) | 33.4164 | 1.16766 | ||||||||
\(820\) | 8.09017 | 0.282521 | ||||||||
\(821\) | −14.2705 | −0.498044 | −0.249022 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249022 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(822\) | −14.9443 | −0.521241 | ||||||||
\(823\) | 32.8328 | 1.14448 | 0.572240 | − | 0.820086i | \(-0.306075\pi\) | ||||
0.572240 | + | 0.820086i | \(0.306075\pi\) | |||||||
\(824\) | 16.6525 | 0.580116 | ||||||||
\(825\) | −12.3607 | −0.430344 | ||||||||
\(826\) | −10.4721 | −0.364372 | ||||||||
\(827\) | 36.5410 | 1.27066 | 0.635328 | − | 0.772243i | \(-0.280865\pi\) | ||||
0.635328 | + | 0.772243i | \(0.280865\pi\) | |||||||
\(828\) | 5.70820 | 0.198374 | ||||||||
\(829\) | −43.2705 | −1.50285 | −0.751423 | − | 0.659820i | \(-0.770632\pi\) | ||||
−0.751423 | + | 0.659820i | \(0.770632\pi\) | |||||||
\(830\) | 11.7082 | 0.406398 | ||||||||
\(831\) | 3.52786 | 0.122380 | ||||||||
\(832\) | 3.61803 | 0.125433 | ||||||||
\(833\) | 30.7426 | 1.06517 | ||||||||
\(834\) | 45.3050 | 1.56878 | ||||||||
\(835\) | 4.87539 | 0.168720 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.8328 | 1.61878 | ||||||||
\(838\) | −2.47214 | −0.0853985 | ||||||||
\(839\) | 22.0000 | 0.759524 | 0.379762 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379762 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(840\) | 5.52786 | 0.190729 | ||||||||
\(841\) | −24.6312 | −0.849351 | ||||||||
\(842\) | −25.0902 | −0.864664 | ||||||||
\(843\) | −84.0689 | −2.89549 | ||||||||
\(844\) | −2.76393 | −0.0951385 | ||||||||
\(845\) | −0.124612 | −0.00428678 | ||||||||
\(846\) | 33.4164 | 1.14888 | ||||||||
\(847\) | −11.7082 | −0.402299 | ||||||||
\(848\) | 5.09017 | 0.174797 | ||||||||
\(849\) | 43.7771 | 1.50243 | ||||||||
\(850\) | −17.3607 | −0.595466 | ||||||||
\(851\) | 8.11146 | 0.278057 | ||||||||
\(852\) | −48.3607 | −1.65681 | ||||||||
\(853\) | −17.9098 | −0.613221 | −0.306610 | − | 0.951835i | \(-0.599195\pi\) | ||||
−0.306610 | + | 0.951835i | \(0.599195\pi\) | |||||||
\(854\) | −4.47214 | −0.153033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.4164 | 0.595281 | ||||||||
\(857\) | −14.5623 | −0.497439 | −0.248719 | − | 0.968576i | \(-0.580010\pi\) | ||||
−0.248719 | + | 0.968576i | \(0.580010\pi\) | |||||||
\(858\) | −14.4721 | −0.494071 | ||||||||
\(859\) | −30.0689 | −1.02594 | −0.512969 | − | 0.858407i | \(-0.671454\pi\) | ||||
−0.512969 | + | 0.858407i | \(0.671454\pi\) | |||||||
\(860\) | 6.58359 | 0.224499 | ||||||||
\(861\) | −23.4164 | −0.798029 | ||||||||
\(862\) | 24.6525 | 0.839667 | ||||||||
\(863\) | 9.88854 | 0.336610 | 0.168305 | − | 0.985735i | \(-0.446171\pi\) | ||||
0.168305 | + | 0.985735i | \(0.446171\pi\) | |||||||
\(864\) | −14.4721 | −0.492352 | ||||||||
\(865\) | 19.7984 | 0.673165 | ||||||||
\(866\) | −4.03444 | −0.137096 | ||||||||
\(867\) | 47.1246 | 1.60044 | ||||||||
\(868\) | 4.00000 | 0.135769 | ||||||||
\(869\) | −8.94427 | −0.303414 | ||||||||
\(870\) | 9.34752 | 0.316911 | ||||||||
\(871\) | −6.18034 | −0.209413 | ||||||||
\(872\) | −18.0344 | −0.610723 | ||||||||
\(873\) | 47.6869 | 1.61396 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.8197 | 0.467190 | ||||||||
\(876\) | −10.9443 | −0.369773 | ||||||||
\(877\) | −40.7426 | −1.37578 | −0.687891 | − | 0.725814i | \(-0.741463\pi\) | ||||
−0.687891 | + | 0.725814i | \(0.741463\pi\) | |||||||
\(878\) | −24.7639 | −0.835742 | ||||||||
\(879\) | 16.3607 | 0.551832 | ||||||||
\(880\) | −1.70820 | −0.0575835 | ||||||||
\(881\) | −46.2148 | −1.55702 | −0.778508 | − | 0.627635i | \(-0.784023\pi\) | ||||
−0.778508 | + | 0.627635i | \(0.784023\pi\) | |||||||
\(882\) | 40.8885 | 1.37679 | ||||||||
\(883\) | −40.1803 | −1.35218 | −0.676088 | − | 0.736821i | \(-0.736326\pi\) | ||||
−0.676088 | + | 0.736821i | \(0.736326\pi\) | |||||||
\(884\) | −20.3262 | −0.683645 | ||||||||
\(885\) | −37.8885 | −1.27361 | ||||||||
\(886\) | −4.76393 | −0.160047 | ||||||||
\(887\) | −10.9443 | −0.367473 | −0.183736 | − | 0.982976i | \(-0.558819\pi\) | ||||
−0.183736 | + | 0.982976i | \(0.558819\pi\) | |||||||
\(888\) | −34.3607 | −1.15307 | ||||||||
\(889\) | 19.0557 | 0.639109 | ||||||||
\(890\) | 2.96556 | 0.0994057 | ||||||||
\(891\) | 30.1803 | 1.01108 | ||||||||
\(892\) | 14.2918 | 0.478525 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.18034 | 0.206701 | ||||||||
\(895\) | −4.72136 | −0.157818 | ||||||||
\(896\) | −1.23607 | −0.0412941 | ||||||||
\(897\) | 8.94427 | 0.298641 | ||||||||
\(898\) | −1.79837 | −0.0600125 | ||||||||
\(899\) | 6.76393 | 0.225590 | ||||||||
\(900\) | −23.0902 | −0.769672 | ||||||||
\(901\) | −28.5967 | −0.952696 | ||||||||
\(902\) | 7.23607 | 0.240935 | ||||||||
\(903\) | −19.0557 | −0.634135 | ||||||||
\(904\) | 3.14590 | 0.104631 | ||||||||
\(905\) | 29.5967 | 0.983829 | ||||||||
\(906\) | −17.8885 | −0.594307 | ||||||||
\(907\) | −13.7082 | −0.455173 | −0.227587 | − | 0.973758i | \(-0.573084\pi\) | ||||
−0.227587 | + | 0.973758i | \(0.573084\pi\) | |||||||
\(908\) | 8.94427 | 0.296826 | ||||||||
\(909\) | −99.9919 | −3.31652 | ||||||||
\(910\) | 6.18034 | 0.204876 | ||||||||
\(911\) | −46.0689 | −1.52633 | −0.763165 | − | 0.646204i | \(-0.776356\pi\) | ||||
−0.763165 | + | 0.646204i | \(0.776356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4721 | 0.346577 | ||||||||
\(914\) | 26.2148 | 0.867108 | ||||||||
\(915\) | −16.1803 | −0.534906 | ||||||||
\(916\) | 6.61803 | 0.218666 | ||||||||
\(917\) | −5.52786 | −0.182546 | ||||||||
\(918\) | 81.3050 | 2.68346 | ||||||||
\(919\) | 10.1115 | 0.333546 | 0.166773 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166773 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(920\) | 1.05573 | 0.0348063 | ||||||||
\(921\) | −5.52786 | −0.182149 | ||||||||
\(922\) | 5.41641 | 0.178380 | ||||||||
\(923\) | −54.0689 | −1.77970 | ||||||||
\(924\) | 4.94427 | 0.162655 | ||||||||
\(925\) | −32.8115 | −1.07884 | ||||||||
\(926\) | 22.9443 | 0.753996 | ||||||||
\(927\) | −124.430 | −4.08680 | ||||||||
\(928\) | −2.09017 | −0.0686132 | ||||||||
\(929\) | 10.1591 | 0.333308 | 0.166654 | − | 0.986015i | \(-0.446704\pi\) | ||||
0.166654 | + | 0.986015i | \(0.446704\pi\) | |||||||
\(930\) | 14.4721 | 0.474560 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.5623 | −0.608029 | ||||||||
\(933\) | 86.6099 | 2.83548 | ||||||||
\(934\) | −29.3050 | −0.958887 | ||||||||
\(935\) | 9.59675 | 0.313847 | ||||||||
\(936\) | −27.0344 | −0.883648 | ||||||||
\(937\) | −19.8885 | −0.649730 | −0.324865 | − | 0.945760i | \(-0.605319\pi\) | ||||
−0.324865 | + | 0.945760i | \(0.605319\pi\) | |||||||
\(938\) | 2.11146 | 0.0689415 | ||||||||
\(939\) | 72.8328 | 2.37681 | ||||||||
\(940\) | 6.18034 | 0.201580 | ||||||||
\(941\) | 26.0000 | 0.847576 | 0.423788 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423788 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(942\) | −37.5967 | −1.22497 | ||||||||
\(943\) | −4.47214 | −0.145633 | ||||||||
\(944\) | 8.47214 | 0.275745 | ||||||||
\(945\) | −24.7214 | −0.804186 | ||||||||
\(946\) | 5.88854 | 0.191453 | ||||||||
\(947\) | −14.1803 | −0.460799 | −0.230400 | − | 0.973096i | \(-0.574003\pi\) | ||||
−0.230400 | + | 0.973096i | \(0.574003\pi\) | |||||||
\(948\) | −23.4164 | −0.760530 | ||||||||
\(949\) | −12.2361 | −0.397200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −46.3607 | −1.50335 | ||||||||
\(952\) | 6.94427 | 0.225065 | ||||||||
\(953\) | −52.8115 | −1.71073 | −0.855367 | − | 0.518023i | \(-0.826668\pi\) | ||||
−0.855367 | + | 0.518023i | \(0.826668\pi\) | |||||||
\(954\) | −38.0344 | −1.23141 | ||||||||
\(955\) | −17.2361 | −0.557746 | ||||||||
\(956\) | 7.81966 | 0.252906 | ||||||||
\(957\) | 8.36068 | 0.270262 | ||||||||
\(958\) | 5.70820 | 0.184424 | ||||||||
\(959\) | 5.70820 | 0.184328 | ||||||||
\(960\) | −4.47214 | −0.144338 | ||||||||
\(961\) | −20.5279 | −0.662189 | ||||||||
\(962\) | −38.4164 | −1.23859 | ||||||||
\(963\) | −130.138 | −4.19363 | ||||||||
\(964\) | 1.41641 | 0.0456194 | ||||||||
\(965\) | 28.2918 | 0.910745 | ||||||||
\(966\) | −3.05573 | −0.0983164 | ||||||||
\(967\) | −44.8328 | −1.44173 | −0.720863 | − | 0.693077i | \(-0.756254\pi\) | ||||
−0.720863 | + | 0.693077i | \(0.756254\pi\) | |||||||
\(968\) | 9.47214 | 0.304446 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.81966 | 0.283182 | ||||||||
\(971\) | −6.54102 | −0.209911 | −0.104956 | − | 0.994477i | \(-0.533470\pi\) | ||||
−0.104956 | + | 0.994477i | \(0.533470\pi\) | |||||||
\(972\) | 35.5967 | 1.14177 | ||||||||
\(973\) | −17.3050 | −0.554771 | ||||||||
\(974\) | −14.7639 | −0.473067 | ||||||||
\(975\) | −36.1803 | −1.15870 | ||||||||
\(976\) | 3.61803 | 0.115810 | ||||||||
\(977\) | 20.0344 | 0.640959 | 0.320479 | − | 0.947256i | \(-0.396156\pi\) | ||||
0.320479 | + | 0.947256i | \(0.396156\pi\) | |||||||
\(978\) | 66.8328 | 2.13708 | ||||||||
\(979\) | 2.65248 | 0.0847735 | ||||||||
\(980\) | 7.56231 | 0.241569 | ||||||||
\(981\) | 134.756 | 4.30242 | ||||||||
\(982\) | 10.4721 | 0.334179 | ||||||||
\(983\) | −29.5967 | −0.943990 | −0.471995 | − | 0.881601i | \(-0.656466\pi\) | ||||
−0.471995 | + | 0.881601i | \(0.656466\pi\) | |||||||
\(984\) | 18.9443 | 0.603921 | ||||||||
\(985\) | 15.0000 | 0.477940 | ||||||||
\(986\) | 11.7426 | 0.373962 | ||||||||
\(987\) | −17.8885 | −0.569399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.63932 | −0.115724 | ||||||||
\(990\) | 12.7639 | 0.405664 | ||||||||
\(991\) | 0.652476 | 0.0207266 | 0.0103633 | − | 0.999946i | \(-0.496701\pi\) | ||||
0.0103633 | + | 0.999946i | \(0.496701\pi\) | |||||||
\(992\) | −3.23607 | −0.102745 | ||||||||
\(993\) | 39.7771 | 1.26229 | ||||||||
\(994\) | 18.4721 | 0.585901 | ||||||||
\(995\) | −2.11146 | −0.0669377 | ||||||||
\(996\) | 27.4164 | 0.868722 | ||||||||
\(997\) | 24.5066 | 0.776131 | 0.388066 | − | 0.921632i | \(-0.373143\pi\) | ||||
0.388066 | + | 0.921632i | \(0.373143\pi\) | |||||||
\(998\) | −27.3050 | −0.864323 | ||||||||
\(999\) | 153.666 | 4.86177 |
(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 | 722.2.a.h.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6498.2.a.bk.1.1 | 2 | |||
4.3 | odd | 2 | 5776.2.a.t.1.1 | 2 | |||
19.2 | odd | 18 | 722.2.e.p.99.1 | 12 | |||
19.3 | odd | 18 | 722.2.e.p.389.1 | 12 | |||
19.4 | even | 9 | 722.2.e.q.415.1 | 12 | |||
19.5 | even | 9 | 722.2.e.q.595.1 | 12 | |||
19.6 | even | 9 | 722.2.e.q.245.2 | 12 | |||
19.7 | even | 3 | 722.2.c.i.429.1 | 4 | |||
19.8 | odd | 6 | 722.2.c.h.653.2 | 4 | |||
19.9 | even | 9 | 722.2.e.q.423.2 | 12 | |||
19.10 | odd | 18 | 722.2.e.p.423.1 | 12 | |||
19.11 | even | 3 | 722.2.c.i.653.1 | 4 | |||
19.12 | odd | 6 | 722.2.c.h.429.2 | 4 | |||
19.13 | odd | 18 | 722.2.e.p.245.1 | 12 | |||
19.14 | odd | 18 | 722.2.e.p.595.2 | 12 | |||
19.15 | odd | 18 | 722.2.e.p.415.2 | 12 | |||
19.16 | even | 9 | 722.2.e.q.389.2 | 12 | |||
19.17 | even | 9 | 722.2.e.q.99.2 | 12 | |||
19.18 | odd | 2 | 722.2.a.i.1.1 | yes | 2 | ||
57.56 | even | 2 | 6498.2.a.be.1.1 | 2 | |||
76.75 | even | 2 | 5776.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.h.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
722.2.a.i.1.1 | yes | 2 | 19.18 | odd | 2 | ||
722.2.c.h.429.2 | 4 | 19.12 | odd | 6 | |||
722.2.c.h.653.2 | 4 | 19.8 | odd | 6 | |||
722.2.c.i.429.1 | 4 | 19.7 | even | 3 | |||
722.2.c.i.653.1 | 4 | 19.11 | even | 3 | |||
722.2.e.p.99.1 | 12 | 19.2 | odd | 18 | |||
722.2.e.p.245.1 | 12 | 19.13 | odd | 18 | |||
722.2.e.p.389.1 | 12 | 19.3 | odd | 18 | |||
722.2.e.p.415.2 | 12 | 19.15 | odd | 18 | |||
722.2.e.p.423.1 | 12 | 19.10 | odd | 18 | |||
722.2.e.p.595.2 | 12 | 19.14 | odd | 18 | |||
722.2.e.q.99.2 | 12 | 19.17 | even | 9 | |||
722.2.e.q.245.2 | 12 | 19.6 | even | 9 | |||
722.2.e.q.389.2 | 12 | 19.16 | even | 9 | |||
722.2.e.q.415.1 | 12 | 19.4 | even | 9 | |||
722.2.e.q.423.2 | 12 | 19.9 | even | 9 | |||
722.2.e.q.595.1 | 12 | 19.5 | even | 9 | |||
5776.2.a.t.1.1 | 2 | 4.3 | odd | 2 | |||
5776.2.a.be.1.2 | 2 | 76.75 | even | 2 | |||
6498.2.a.be.1.1 | 2 | 57.56 | even | 2 | |||
6498.2.a.bk.1.1 | 2 | 3.2 | odd | 2 |