Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(1,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.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: | \(5.98878015160\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.618034 | 0.233595 | 0.116797 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116797 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61803 | −0.487856 | −0.243928 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243928 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.85410 | −1.34629 | −0.673143 | − | 0.739512i | \(-0.735056\pi\) | ||||
−0.673143 | + | 0.739512i | \(0.735056\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.85410 | 1.34302 | 0.671512 | − | 0.740994i | \(-0.265645\pi\) | ||||
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 1.61803 | 0.344966 | ||||||||
\(23\) | −4.85410 | −1.01215 | −0.506075 | − | 0.862489i | \(-0.668904\pi\) | ||||
−0.506075 | + | 0.862489i | \(0.668904\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.85410 | 0.951968 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.618034 | 0.116797 | ||||||||
\(29\) | −2.76393 | −0.513249 | −0.256625 | − | 0.966511i | \(-0.582610\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.61803 | 0.281664 | ||||||||
\(34\) | 0.763932 | 0.131013 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.56231 | 1.57203 | 0.786017 | − | 0.618205i | \(-0.212140\pi\) | ||||
0.786017 | + | 0.618205i | \(0.212140\pi\) | |||||||
\(38\) | −5.85410 | −0.949661 | ||||||||
\(39\) | 4.85410 | 0.777278 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.38197 | −1.46522 | −0.732608 | − | 0.680650i | \(-0.761697\pi\) | ||||
−0.732608 | + | 0.680650i | \(0.761697\pi\) | |||||||
\(42\) | 0.618034 | 0.0953647 | ||||||||
\(43\) | −5.70820 | −0.870493 | −0.435246 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435246 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(44\) | −1.61803 | −0.243928 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.85410 | 0.715698 | ||||||||
\(47\) | −1.61803 | −0.236015 | −0.118007 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118007 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.763932 | 0.106972 | ||||||||
\(52\) | −4.85410 | −0.673143 | ||||||||
\(53\) | −5.38197 | −0.739270 | −0.369635 | − | 0.929177i | \(-0.620517\pi\) | ||||
−0.369635 | + | 0.929177i | \(0.620517\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.618034 | −0.0825883 | ||||||||
\(57\) | −5.85410 | −0.775395 | ||||||||
\(58\) | 2.76393 | 0.362922 | ||||||||
\(59\) | −13.0902 | −1.70419 | −0.852097 | − | 0.523383i | \(-0.824670\pi\) | ||||
−0.852097 | + | 0.523383i | \(0.824670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.70820 | −1.24301 | −0.621504 | − | 0.783411i | \(-0.713478\pi\) | ||||
−0.621504 | + | 0.783411i | \(0.713478\pi\) | |||||||
\(62\) | 2.47214 | 0.313962 | ||||||||
\(63\) | 0.618034 | 0.0778650 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.61803 | −0.199166 | ||||||||
\(67\) | 3.70820 | 0.453029 | 0.226515 | − | 0.974008i | \(-0.427267\pi\) | ||||
0.226515 | + | 0.974008i | \(0.427267\pi\) | |||||||
\(68\) | −0.763932 | −0.0926404 | ||||||||
\(69\) | 4.85410 | 0.584365 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.52786 | −0.418680 | −0.209340 | − | 0.977843i | \(-0.567132\pi\) | ||||
−0.209340 | + | 0.977843i | \(0.567132\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.9443 | −1.51501 | −0.757506 | − | 0.652828i | \(-0.773582\pi\) | ||||
−0.757506 | + | 0.652828i | \(0.773582\pi\) | |||||||
\(74\) | −9.56231 | −1.11160 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.85410 | 0.671512 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −4.85410 | −0.549619 | ||||||||
\(79\) | 13.4164 | 1.50946 | 0.754732 | − | 0.656033i | \(-0.227767\pi\) | ||||
0.754732 | + | 0.656033i | \(0.227767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.38197 | 1.03606 | ||||||||
\(83\) | 14.9443 | 1.64035 | 0.820173 | − | 0.572115i | \(-0.193877\pi\) | ||||
0.820173 | + | 0.572115i | \(0.193877\pi\) | |||||||
\(84\) | −0.618034 | −0.0674330 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.70820 | 0.615531 | ||||||||
\(87\) | 2.76393 | 0.296325 | ||||||||
\(88\) | 1.61803 | 0.172483 | ||||||||
\(89\) | −18.0902 | −1.91755 | −0.958777 | − | 0.284159i | \(-0.908286\pi\) | ||||
−0.958777 | + | 0.284159i | \(0.908286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | −0.314485 | ||||||||
\(92\) | −4.85410 | −0.506075 | ||||||||
\(93\) | 2.47214 | 0.256349 | ||||||||
\(94\) | 1.61803 | 0.166887 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −9.70820 | −0.985719 | −0.492859 | − | 0.870109i | \(-0.664048\pi\) | ||||
−0.492859 | + | 0.870109i | \(0.664048\pi\) | |||||||
\(98\) | 6.61803 | 0.668522 | ||||||||
\(99\) | −1.61803 | −0.162619 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.6525 | 1.25897 | 0.629484 | − | 0.777013i | \(-0.283266\pi\) | ||||
0.629484 | + | 0.777013i | \(0.283266\pi\) | |||||||
\(102\) | −0.763932 | −0.0756405 | ||||||||
\(103\) | 8.56231 | 0.843669 | 0.421835 | − | 0.906673i | \(-0.361386\pi\) | ||||
0.421835 | + | 0.906673i | \(0.361386\pi\) | |||||||
\(104\) | 4.85410 | 0.475984 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.38197 | 0.522743 | ||||||||
\(107\) | −6.94427 | −0.671328 | −0.335664 | − | 0.941982i | \(-0.608961\pi\) | ||||
−0.335664 | + | 0.941982i | \(0.608961\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.18034 | −0.591969 | −0.295985 | − | 0.955193i | \(-0.595648\pi\) | ||||
−0.295985 | + | 0.955193i | \(0.595648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.56231 | −0.907614 | ||||||||
\(112\) | 0.618034 | 0.0583987 | ||||||||
\(113\) | 3.23607 | 0.304424 | 0.152212 | − | 0.988348i | \(-0.451360\pi\) | ||||
0.152212 | + | 0.988348i | \(0.451360\pi\) | |||||||
\(114\) | 5.85410 | 0.548287 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.76393 | −0.256625 | ||||||||
\(117\) | −4.85410 | −0.448762 | ||||||||
\(118\) | 13.0902 | 1.20505 | ||||||||
\(119\) | −0.472136 | −0.0432806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.38197 | −0.761997 | ||||||||
\(122\) | 9.70820 | 0.878939 | ||||||||
\(123\) | 9.38197 | 0.845943 | ||||||||
\(124\) | −2.47214 | −0.222004 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.618034 | −0.0550588 | ||||||||
\(127\) | −11.4164 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.70820 | 0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.90983 | 0.341603 | 0.170802 | − | 0.985305i | \(-0.445364\pi\) | ||||
0.170802 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(132\) | 1.61803 | 0.140832 | ||||||||
\(133\) | 3.61803 | 0.313723 | ||||||||
\(134\) | −3.70820 | −0.320340 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.763932 | 0.0655066 | ||||||||
\(137\) | 3.05573 | 0.261068 | 0.130534 | − | 0.991444i | \(-0.458331\pi\) | ||||
0.130534 | + | 0.991444i | \(0.458331\pi\) | |||||||
\(138\) | −4.85410 | −0.413209 | ||||||||
\(139\) | 12.5623 | 1.06552 | 0.532760 | − | 0.846266i | \(-0.321155\pi\) | ||||
0.532760 | + | 0.846266i | \(0.321155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.61803 | 0.136263 | ||||||||
\(142\) | 3.52786 | 0.296052 | ||||||||
\(143\) | 7.85410 | 0.656793 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.9443 | 1.07128 | ||||||||
\(147\) | 6.61803 | 0.545846 | ||||||||
\(148\) | 9.56231 | 0.786017 | ||||||||
\(149\) | −13.4164 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685204\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2918 | 0.837534 | 0.418767 | − | 0.908094i | \(-0.362462\pi\) | ||||
0.418767 | + | 0.908094i | \(0.362462\pi\) | |||||||
\(152\) | −5.85410 | −0.474830 | ||||||||
\(153\) | −0.763932 | −0.0617602 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.85410 | 0.388639 | ||||||||
\(157\) | 10.9443 | 0.873448 | 0.436724 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436724 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(158\) | −13.4164 | −1.06735 | ||||||||
\(159\) | 5.38197 | 0.426818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 4.94427 | 0.387265 | 0.193633 | − | 0.981074i | \(-0.437973\pi\) | ||||
0.193633 | + | 0.981074i | \(0.437973\pi\) | |||||||
\(164\) | −9.38197 | −0.732608 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9443 | −1.15990 | ||||||||
\(167\) | 7.85410 | 0.607769 | 0.303884 | − | 0.952709i | \(-0.401716\pi\) | ||||
0.303884 | + | 0.952709i | \(0.401716\pi\) | |||||||
\(168\) | 0.618034 | 0.0476824 | ||||||||
\(169\) | 10.5623 | 0.812485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.85410 | 0.447674 | ||||||||
\(172\) | −5.70820 | −0.435246 | ||||||||
\(173\) | 14.6180 | 1.11139 | 0.555694 | − | 0.831387i | \(-0.312453\pi\) | ||||
0.555694 | + | 0.831387i | \(0.312453\pi\) | |||||||
\(174\) | −2.76393 | −0.209533 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.61803 | −0.121964 | ||||||||
\(177\) | 13.0902 | 0.983917 | ||||||||
\(178\) | 18.0902 | 1.35592 | ||||||||
\(179\) | 22.0344 | 1.64693 | 0.823466 | − | 0.567366i | \(-0.192038\pi\) | ||||
0.823466 | + | 0.567366i | \(0.192038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.4164 | 1.88919 | 0.944593 | − | 0.328243i | \(-0.106456\pi\) | ||||
0.944593 | + | 0.328243i | \(0.106456\pi\) | |||||||
\(182\) | 3.00000 | 0.222375 | ||||||||
\(183\) | 9.70820 | 0.717651 | ||||||||
\(184\) | 4.85410 | 0.357849 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.47214 | −0.181266 | ||||||||
\(187\) | 1.23607 | 0.0903902 | ||||||||
\(188\) | −1.61803 | −0.118007 | ||||||||
\(189\) | −0.618034 | −0.0449554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9443 | −1.22604 | −0.613022 | − | 0.790066i | \(-0.710046\pi\) | ||||
−0.613022 | + | 0.790066i | \(0.710046\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.29180 | 0.308930 | 0.154465 | − | 0.987998i | \(-0.450635\pi\) | ||||
0.154465 | + | 0.987998i | \(0.450635\pi\) | |||||||
\(194\) | 9.70820 | 0.697008 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61803 | −0.472717 | ||||||||
\(197\) | −6.94427 | −0.494759 | −0.247379 | − | 0.968919i | \(-0.579569\pi\) | ||||
−0.247379 | + | 0.968919i | \(0.579569\pi\) | |||||||
\(198\) | 1.61803 | 0.114989 | ||||||||
\(199\) | −6.18034 | −0.438113 | −0.219056 | − | 0.975712i | \(-0.570298\pi\) | ||||
−0.219056 | + | 0.975712i | \(0.570298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | −12.6525 | −0.890225 | ||||||||
\(203\) | −1.70820 | −0.119892 | ||||||||
\(204\) | 0.763932 | 0.0534859 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.56231 | −0.596564 | ||||||||
\(207\) | −4.85410 | −0.337383 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | −9.47214 | −0.655201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2705 | −1.18895 | −0.594475 | − | 0.804114i | \(-0.702640\pi\) | ||||
−0.594475 | + | 0.804114i | \(0.702640\pi\) | |||||||
\(212\) | −5.38197 | −0.369635 | ||||||||
\(213\) | 3.52786 | 0.241725 | ||||||||
\(214\) | 6.94427 | 0.474701 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.52786 | −0.103718 | ||||||||
\(218\) | 6.18034 | 0.418585 | ||||||||
\(219\) | 12.9443 | 0.874693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.70820 | 0.249441 | ||||||||
\(222\) | 9.56231 | 0.641780 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | −0.618034 | −0.0412941 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.23607 | −0.215260 | ||||||||
\(227\) | 28.1803 | 1.87039 | 0.935197 | − | 0.354127i | \(-0.115222\pi\) | ||||
0.935197 | + | 0.354127i | \(0.115222\pi\) | |||||||
\(228\) | −5.85410 | −0.387697 | ||||||||
\(229\) | 1.70820 | 0.112881 | 0.0564406 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564406 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 2.76393 | 0.181461 | ||||||||
\(233\) | 19.4164 | 1.27201 | 0.636006 | − | 0.771684i | \(-0.280586\pi\) | ||||
0.636006 | + | 0.771684i | \(0.280586\pi\) | |||||||
\(234\) | 4.85410 | 0.317323 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.0902 | −0.852097 | ||||||||
\(237\) | −13.4164 | −0.871489 | ||||||||
\(238\) | 0.472136 | 0.0306040 | ||||||||
\(239\) | 8.94427 | 0.578557 | 0.289278 | − | 0.957245i | \(-0.406585\pi\) | ||||
0.289278 | + | 0.957245i | \(0.406585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.14590 | −0.460308 | −0.230154 | − | 0.973154i | \(-0.573923\pi\) | ||||
−0.230154 | + | 0.973154i | \(0.573923\pi\) | |||||||
\(242\) | 8.38197 | 0.538813 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.70820 | −0.621504 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.38197 | −0.598172 | ||||||||
\(247\) | −28.4164 | −1.80809 | ||||||||
\(248\) | 2.47214 | 0.156981 | ||||||||
\(249\) | −14.9443 | −0.947055 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9443 | 1.32199 | 0.660995 | − | 0.750390i | \(-0.270134\pi\) | ||||
0.660995 | + | 0.750390i | \(0.270134\pi\) | |||||||
\(252\) | 0.618034 | 0.0389325 | ||||||||
\(253\) | 7.85410 | 0.493783 | ||||||||
\(254\) | 11.4164 | 0.716329 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.5279 | −0.843845 | −0.421922 | − | 0.906632i | \(-0.638645\pi\) | ||||
−0.421922 | + | 0.906632i | \(0.638645\pi\) | |||||||
\(258\) | −5.70820 | −0.355377 | ||||||||
\(259\) | 5.90983 | 0.367219 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.76393 | −0.171083 | ||||||||
\(262\) | −3.90983 | −0.241550 | ||||||||
\(263\) | 14.6180 | 0.901387 | 0.450693 | − | 0.892679i | \(-0.351177\pi\) | ||||
0.450693 | + | 0.892679i | \(0.351177\pi\) | |||||||
\(264\) | −1.61803 | −0.0995831 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.61803 | −0.221836 | ||||||||
\(267\) | 18.0902 | 1.10710 | ||||||||
\(268\) | 3.70820 | 0.226515 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4164 | 1.54394 | 0.771968 | − | 0.635661i | \(-0.219272\pi\) | ||||
0.771968 | + | 0.635661i | \(0.219272\pi\) | |||||||
\(272\) | −0.763932 | −0.0463202 | ||||||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | −3.05573 | −0.184603 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.85410 | 0.292183 | ||||||||
\(277\) | 12.8541 | 0.772328 | 0.386164 | − | 0.922430i | \(-0.373800\pi\) | ||||
0.386164 | + | 0.922430i | \(0.373800\pi\) | |||||||
\(278\) | −12.5623 | −0.753437 | ||||||||
\(279\) | −2.47214 | −0.148003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.09017 | −0.363309 | −0.181655 | − | 0.983362i | \(-0.558145\pi\) | ||||
−0.181655 | + | 0.983362i | \(0.558145\pi\) | |||||||
\(282\) | −1.61803 | −0.0963525 | ||||||||
\(283\) | −30.1803 | −1.79403 | −0.897017 | − | 0.441995i | \(-0.854271\pi\) | ||||
−0.897017 | + | 0.441995i | \(0.854271\pi\) | |||||||
\(284\) | −3.52786 | −0.209340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.85410 | −0.464423 | ||||||||
\(287\) | −5.79837 | −0.342267 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.70820 | 0.569105 | ||||||||
\(292\) | −12.9443 | −0.757506 | ||||||||
\(293\) | −22.0902 | −1.29052 | −0.645261 | − | 0.763962i | \(-0.723251\pi\) | ||||
−0.645261 | + | 0.763962i | \(0.723251\pi\) | |||||||
\(294\) | −6.61803 | −0.385972 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.56231 | −0.555798 | ||||||||
\(297\) | 1.61803 | 0.0938879 | ||||||||
\(298\) | 13.4164 | 0.777192 | ||||||||
\(299\) | 23.5623 | 1.36264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.52786 | −0.203343 | ||||||||
\(302\) | −10.2918 | −0.592226 | ||||||||
\(303\) | −12.6525 | −0.726866 | ||||||||
\(304\) | 5.85410 | 0.335756 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.763932 | 0.0436711 | ||||||||
\(307\) | −20.7639 | −1.18506 | −0.592530 | − | 0.805548i | \(-0.701871\pi\) | ||||
−0.592530 | + | 0.805548i | \(0.701871\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | −8.56231 | −0.487093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | −4.85410 | −0.274809 | ||||||||
\(313\) | −2.29180 | −0.129540 | −0.0647700 | − | 0.997900i | \(-0.520631\pi\) | ||||
−0.0647700 | + | 0.997900i | \(0.520631\pi\) | |||||||
\(314\) | −10.9443 | −0.617621 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4164 | 0.754732 | ||||||||
\(317\) | 1.14590 | 0.0643600 | 0.0321800 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321800 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(318\) | −5.38197 | −0.301806 | ||||||||
\(319\) | 4.47214 | 0.250392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.94427 | 0.387591 | ||||||||
\(322\) | 3.00000 | 0.167183 | ||||||||
\(323\) | −4.47214 | −0.248836 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.94427 | −0.273838 | ||||||||
\(327\) | 6.18034 | 0.341774 | ||||||||
\(328\) | 9.38197 | 0.518032 | ||||||||
\(329\) | −1.00000 | −0.0551318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.47214 | −0.135881 | −0.0679404 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679404 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(332\) | 14.9443 | 0.820173 | ||||||||
\(333\) | 9.56231 | 0.524011 | ||||||||
\(334\) | −7.85410 | −0.429757 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.618034 | −0.0337165 | ||||||||
\(337\) | 19.8885 | 1.08340 | 0.541699 | − | 0.840573i | \(-0.317781\pi\) | ||||
0.541699 | + | 0.840573i | \(0.317781\pi\) | |||||||
\(338\) | −10.5623 | −0.574514 | ||||||||
\(339\) | −3.23607 | −0.175759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | −5.85410 | −0.316554 | ||||||||
\(343\) | −8.41641 | −0.454443 | ||||||||
\(344\) | 5.70820 | 0.307766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.6180 | −0.785870 | ||||||||
\(347\) | 26.0689 | 1.39945 | 0.699726 | − | 0.714412i | \(-0.253306\pi\) | ||||
0.699726 | + | 0.714412i | \(0.253306\pi\) | |||||||
\(348\) | 2.76393 | 0.148162 | ||||||||
\(349\) | −26.8328 | −1.43633 | −0.718164 | − | 0.695874i | \(-0.755017\pi\) | ||||
−0.718164 | + | 0.695874i | \(0.755017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.85410 | 0.259093 | ||||||||
\(352\) | 1.61803 | 0.0862415 | ||||||||
\(353\) | −15.7082 | −0.836063 | −0.418032 | − | 0.908432i | \(-0.637280\pi\) | ||||
−0.418032 | + | 0.908432i | \(0.637280\pi\) | |||||||
\(354\) | −13.0902 | −0.695735 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.0902 | −0.958777 | ||||||||
\(357\) | 0.472136 | 0.0249881 | ||||||||
\(358\) | −22.0344 | −1.16456 | ||||||||
\(359\) | 4.47214 | 0.236030 | 0.118015 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118015 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | −25.4164 | −1.33586 | ||||||||
\(363\) | 8.38197 | 0.439939 | ||||||||
\(364\) | −3.00000 | −0.157243 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.70820 | −0.507456 | ||||||||
\(367\) | −4.58359 | −0.239262 | −0.119631 | − | 0.992818i | \(-0.538171\pi\) | ||||
−0.119631 | + | 0.992818i | \(0.538171\pi\) | |||||||
\(368\) | −4.85410 | −0.253038 | ||||||||
\(369\) | −9.38197 | −0.488406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.32624 | −0.172690 | ||||||||
\(372\) | 2.47214 | 0.128174 | ||||||||
\(373\) | −30.5066 | −1.57957 | −0.789785 | − | 0.613383i | \(-0.789808\pi\) | ||||
−0.789785 | + | 0.613383i | \(0.789808\pi\) | |||||||
\(374\) | −1.23607 | −0.0639156 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.61803 | 0.0834437 | ||||||||
\(377\) | 13.4164 | 0.690980 | ||||||||
\(378\) | 0.618034 | 0.0317882 | ||||||||
\(379\) | −15.9787 | −0.820771 | −0.410386 | − | 0.911912i | \(-0.634606\pi\) | ||||
−0.410386 | + | 0.911912i | \(0.634606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4164 | 0.584880 | ||||||||
\(382\) | 16.9443 | 0.866944 | ||||||||
\(383\) | −37.0902 | −1.89522 | −0.947610 | − | 0.319431i | \(-0.896508\pi\) | ||||
−0.947610 | + | 0.319431i | \(0.896508\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.29180 | −0.218447 | ||||||||
\(387\) | −5.70820 | −0.290164 | ||||||||
\(388\) | −9.70820 | −0.492859 | ||||||||
\(389\) | 12.7639 | 0.647157 | 0.323579 | − | 0.946201i | \(-0.395114\pi\) | ||||
0.323579 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70820 | 0.187532 | ||||||||
\(392\) | 6.61803 | 0.334261 | ||||||||
\(393\) | −3.90983 | −0.197225 | ||||||||
\(394\) | 6.94427 | 0.349847 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.61803 | −0.0813093 | ||||||||
\(397\) | −17.2705 | −0.866782 | −0.433391 | − | 0.901206i | \(-0.642683\pi\) | ||||
−0.433391 | + | 0.901206i | \(0.642683\pi\) | |||||||
\(398\) | 6.18034 | 0.309792 | ||||||||
\(399\) | −3.61803 | −0.181128 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.32624 | 0.116167 | 0.0580834 | − | 0.998312i | \(-0.481501\pi\) | ||||
0.0580834 | + | 0.998312i | \(0.481501\pi\) | |||||||
\(402\) | 3.70820 | 0.184948 | ||||||||
\(403\) | 12.0000 | 0.597763 | ||||||||
\(404\) | 12.6525 | 0.629484 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.70820 | 0.0847767 | ||||||||
\(407\) | −15.4721 | −0.766925 | ||||||||
\(408\) | −0.763932 | −0.0378203 | ||||||||
\(409\) | −14.1459 | −0.699470 | −0.349735 | − | 0.936849i | \(-0.613728\pi\) | ||||
−0.349735 | + | 0.936849i | \(0.613728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.05573 | −0.150728 | ||||||||
\(412\) | 8.56231 | 0.421835 | ||||||||
\(413\) | −8.09017 | −0.398091 | ||||||||
\(414\) | 4.85410 | 0.238566 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.85410 | 0.237992 | ||||||||
\(417\) | −12.5623 | −0.615179 | ||||||||
\(418\) | 9.47214 | 0.463297 | ||||||||
\(419\) | 11.0557 | 0.540108 | 0.270054 | − | 0.962845i | \(-0.412958\pi\) | ||||
0.270054 | + | 0.962845i | \(0.412958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1803 | 0.886056 | 0.443028 | − | 0.896508i | \(-0.353904\pi\) | ||||
0.443028 | + | 0.896508i | \(0.353904\pi\) | |||||||
\(422\) | 17.2705 | 0.840715 | ||||||||
\(423\) | −1.61803 | −0.0786715 | ||||||||
\(424\) | 5.38197 | 0.261371 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.52786 | −0.170926 | ||||||||
\(427\) | −6.00000 | −0.290360 | ||||||||
\(428\) | −6.94427 | −0.335664 | ||||||||
\(429\) | −7.85410 | −0.379200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8197 | 0.762006 | 0.381003 | − | 0.924574i | \(-0.375579\pi\) | ||||
0.381003 | + | 0.924574i | \(0.375579\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −17.4164 | −0.836979 | −0.418490 | − | 0.908222i | \(-0.637440\pi\) | ||||
−0.418490 | + | 0.908222i | \(0.637440\pi\) | |||||||
\(434\) | 1.52786 | 0.0733398 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.18034 | −0.295985 | ||||||||
\(437\) | −28.4164 | −1.35934 | ||||||||
\(438\) | −12.9443 | −0.618501 | ||||||||
\(439\) | 1.70820 | 0.0815281 | 0.0407641 | − | 0.999169i | \(-0.487021\pi\) | ||||
0.0407641 | + | 0.999169i | \(0.487021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.61803 | −0.315144 | ||||||||
\(442\) | −3.70820 | −0.176381 | ||||||||
\(443\) | −13.5967 | −0.646001 | −0.323000 | − | 0.946399i | \(-0.604692\pi\) | ||||
−0.323000 | + | 0.946399i | \(0.604692\pi\) | |||||||
\(444\) | −9.56231 | −0.453807 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.0000 | 1.13643 | ||||||||
\(447\) | 13.4164 | 0.634574 | ||||||||
\(448\) | 0.618034 | 0.0291994 | ||||||||
\(449\) | 28.2148 | 1.33154 | 0.665769 | − | 0.746158i | \(-0.268104\pi\) | ||||
0.665769 | + | 0.746158i | \(0.268104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.1803 | 0.714814 | ||||||||
\(452\) | 3.23607 | 0.152212 | ||||||||
\(453\) | −10.2918 | −0.483551 | ||||||||
\(454\) | −28.1803 | −1.32257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.85410 | 0.274143 | ||||||||
\(457\) | 38.8328 | 1.81652 | 0.908261 | − | 0.418404i | \(-0.137410\pi\) | ||||
0.908261 | + | 0.418404i | \(0.137410\pi\) | |||||||
\(458\) | −1.70820 | −0.0798191 | ||||||||
\(459\) | 0.763932 | 0.0356573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1803 | 1.77824 | 0.889118 | − | 0.457678i | \(-0.151319\pi\) | ||||
0.889118 | + | 0.457678i | \(0.151319\pi\) | |||||||
\(462\) | −1.00000 | −0.0465242 | ||||||||
\(463\) | 31.7771 | 1.47681 | 0.738403 | − | 0.674359i | \(-0.235580\pi\) | ||||
0.738403 | + | 0.674359i | \(0.235580\pi\) | |||||||
\(464\) | −2.76393 | −0.128312 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.4164 | −0.899448 | ||||||||
\(467\) | −15.2361 | −0.705041 | −0.352521 | − | 0.935804i | \(-0.614675\pi\) | ||||
−0.352521 | + | 0.935804i | \(0.614675\pi\) | |||||||
\(468\) | −4.85410 | −0.224381 | ||||||||
\(469\) | 2.29180 | 0.105825 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9443 | −0.504285 | ||||||||
\(472\) | 13.0902 | 0.602524 | ||||||||
\(473\) | 9.23607 | 0.424675 | ||||||||
\(474\) | 13.4164 | 0.616236 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.472136 | −0.0216403 | ||||||||
\(477\) | −5.38197 | −0.246423 | ||||||||
\(478\) | −8.94427 | −0.409101 | ||||||||
\(479\) | 8.29180 | 0.378862 | 0.189431 | − | 0.981894i | \(-0.439336\pi\) | ||||
0.189431 | + | 0.981894i | \(0.439336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.4164 | −2.11641 | ||||||||
\(482\) | 7.14590 | 0.325487 | ||||||||
\(483\) | 3.00000 | 0.136505 | ||||||||
\(484\) | −8.38197 | −0.380998 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 17.3262 | 0.785127 | 0.392563 | − | 0.919725i | \(-0.371588\pi\) | ||||
0.392563 | + | 0.919725i | \(0.371588\pi\) | |||||||
\(488\) | 9.70820 | 0.439470 | ||||||||
\(489\) | −4.94427 | −0.223588 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9787 | −0.856497 | −0.428249 | − | 0.903661i | \(-0.640869\pi\) | ||||
−0.428249 | + | 0.903661i | \(0.640869\pi\) | |||||||
\(492\) | 9.38197 | 0.422972 | ||||||||
\(493\) | 2.11146 | 0.0950952 | ||||||||
\(494\) | 28.4164 | 1.27851 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.47214 | −0.111002 | ||||||||
\(497\) | −2.18034 | −0.0978016 | ||||||||
\(498\) | 14.9443 | 0.669669 | ||||||||
\(499\) | −5.72949 | −0.256487 | −0.128244 | − | 0.991743i | \(-0.540934\pi\) | ||||
−0.128244 | + | 0.991743i | \(0.540934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.85410 | −0.350895 | ||||||||
\(502\) | −20.9443 | −0.934789 | ||||||||
\(503\) | 13.0344 | 0.581177 | 0.290589 | − | 0.956848i | \(-0.406149\pi\) | ||||
0.290589 | + | 0.956848i | \(0.406149\pi\) | |||||||
\(504\) | −0.618034 | −0.0275294 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.85410 | −0.349157 | ||||||||
\(507\) | −10.5623 | −0.469088 | ||||||||
\(508\) | −11.4164 | −0.506521 | ||||||||
\(509\) | 30.6525 | 1.35865 | 0.679324 | − | 0.733839i | \(-0.262273\pi\) | ||||
0.679324 | + | 0.733839i | \(0.262273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.85410 | −0.258465 | ||||||||
\(514\) | 13.5279 | 0.596689 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.70820 | 0.251290 | ||||||||
\(517\) | 2.61803 | 0.115141 | ||||||||
\(518\) | −5.90983 | −0.259663 | ||||||||
\(519\) | −14.6180 | −0.641660 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.4508 | −1.68456 | −0.842281 | − | 0.539038i | \(-0.818788\pi\) | ||||
−0.842281 | + | 0.539038i | \(0.818788\pi\) | |||||||
\(522\) | 2.76393 | 0.120974 | ||||||||
\(523\) | −29.5279 | −1.29116 | −0.645582 | − | 0.763691i | \(-0.723385\pi\) | ||||
−0.645582 | + | 0.763691i | \(0.723385\pi\) | |||||||
\(524\) | 3.90983 | 0.170802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.6180 | −0.637377 | ||||||||
\(527\) | 1.88854 | 0.0822663 | ||||||||
\(528\) | 1.61803 | 0.0704159 | ||||||||
\(529\) | 0.562306 | 0.0244481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.0902 | −0.568065 | ||||||||
\(532\) | 3.61803 | 0.156862 | ||||||||
\(533\) | 45.5410 | 1.97260 | ||||||||
\(534\) | −18.0902 | −0.782838 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.70820 | −0.160170 | ||||||||
\(537\) | −22.0344 | −0.950856 | ||||||||
\(538\) | 13.4164 | 0.578422 | ||||||||
\(539\) | 10.7082 | 0.461235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.4164 | 1.95260 | 0.976302 | − | 0.216413i | \(-0.0694357\pi\) | ||||
0.976302 | + | 0.216413i | \(0.0694357\pi\) | |||||||
\(542\) | −25.4164 | −1.09173 | ||||||||
\(543\) | −25.4164 | −1.09072 | ||||||||
\(544\) | 0.763932 | 0.0327533 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.00000 | −0.128388 | ||||||||
\(547\) | −23.1246 | −0.988737 | −0.494369 | − | 0.869252i | \(-0.664601\pi\) | ||||
−0.494369 | + | 0.869252i | \(0.664601\pi\) | |||||||
\(548\) | 3.05573 | 0.130534 | ||||||||
\(549\) | −9.70820 | −0.414336 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1803 | −0.689306 | ||||||||
\(552\) | −4.85410 | −0.206604 | ||||||||
\(553\) | 8.29180 | 0.352603 | ||||||||
\(554\) | −12.8541 | −0.546118 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.5623 | 0.532760 | ||||||||
\(557\) | −11.6180 | −0.492272 | −0.246136 | − | 0.969235i | \(-0.579161\pi\) | ||||
−0.246136 | + | 0.969235i | \(0.579161\pi\) | |||||||
\(558\) | 2.47214 | 0.104654 | ||||||||
\(559\) | 27.7082 | 1.17193 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23607 | −0.0521868 | ||||||||
\(562\) | 6.09017 | 0.256898 | ||||||||
\(563\) | −2.94427 | −0.124086 | −0.0620431 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620431 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(564\) | 1.61803 | 0.0681315 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.1803 | 1.26857 | ||||||||
\(567\) | 0.618034 | 0.0259550 | ||||||||
\(568\) | 3.52786 | 0.148026 | ||||||||
\(569\) | −14.6738 | −0.615156 | −0.307578 | − | 0.951523i | \(-0.599519\pi\) | ||||
−0.307578 | + | 0.951523i | \(0.599519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.2148 | −1.09705 | −0.548527 | − | 0.836133i | \(-0.684811\pi\) | ||||
−0.548527 | + | 0.836133i | \(0.684811\pi\) | |||||||
\(572\) | 7.85410 | 0.328397 | ||||||||
\(573\) | 16.9443 | 0.707857 | ||||||||
\(574\) | 5.79837 | 0.242019 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 33.7082 | 1.40329 | 0.701645 | − | 0.712526i | \(-0.252449\pi\) | ||||
0.701645 | + | 0.712526i | \(0.252449\pi\) | |||||||
\(578\) | 16.4164 | 0.682833 | ||||||||
\(579\) | −4.29180 | −0.178361 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.23607 | 0.383177 | ||||||||
\(582\) | −9.70820 | −0.402418 | ||||||||
\(583\) | 8.70820 | 0.360657 | ||||||||
\(584\) | 12.9443 | 0.535638 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0902 | 0.912537 | ||||||||
\(587\) | 15.8197 | 0.652947 | 0.326474 | − | 0.945206i | \(-0.394140\pi\) | ||||
0.326474 | + | 0.945206i | \(0.394140\pi\) | |||||||
\(588\) | 6.61803 | 0.272923 | ||||||||
\(589\) | −14.4721 | −0.596314 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.94427 | 0.285649 | ||||||||
\(592\) | 9.56231 | 0.393008 | ||||||||
\(593\) | −1.63932 | −0.0673188 | −0.0336594 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336594 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(594\) | −1.61803 | −0.0663887 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.4164 | −0.549557 | ||||||||
\(597\) | 6.18034 | 0.252944 | ||||||||
\(598\) | −23.5623 | −0.963534 | ||||||||
\(599\) | 48.5410 | 1.98333 | 0.991666 | − | 0.128834i | \(-0.0411235\pi\) | ||||
0.991666 | + | 0.128834i | \(0.0411235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.2705 | −1.31634 | −0.658171 | − | 0.752869i | \(-0.728670\pi\) | ||||
−0.658171 | + | 0.752869i | \(0.728670\pi\) | |||||||
\(602\) | 3.52786 | 0.143785 | ||||||||
\(603\) | 3.70820 | 0.151010 | ||||||||
\(604\) | 10.2918 | 0.418767 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.6525 | 0.513972 | ||||||||
\(607\) | −20.6869 | −0.839656 | −0.419828 | − | 0.907604i | \(-0.637910\pi\) | ||||
−0.419828 | + | 0.907604i | \(0.637910\pi\) | |||||||
\(608\) | −5.85410 | −0.237415 | ||||||||
\(609\) | 1.70820 | 0.0692199 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.85410 | 0.317743 | ||||||||
\(612\) | −0.763932 | −0.0308801 | ||||||||
\(613\) | 22.3820 | 0.903999 | 0.452000 | − | 0.892018i | \(-0.350711\pi\) | ||||
0.452000 | + | 0.892018i | \(0.350711\pi\) | |||||||
\(614\) | 20.7639 | 0.837964 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −29.3050 | −1.17977 | −0.589886 | − | 0.807486i | \(-0.700828\pi\) | ||||
−0.589886 | + | 0.807486i | \(0.700828\pi\) | |||||||
\(618\) | 8.56231 | 0.344426 | ||||||||
\(619\) | −18.0902 | −0.727105 | −0.363553 | − | 0.931574i | \(-0.618436\pi\) | ||||
−0.363553 | + | 0.931574i | \(0.618436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.85410 | 0.194788 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | −11.1803 | −0.447931 | ||||||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.29180 | 0.0915986 | ||||||||
\(627\) | 9.47214 | 0.378281 | ||||||||
\(628\) | 10.9443 | 0.436724 | ||||||||
\(629\) | −7.30495 | −0.291267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.81966 | −0.0724395 | −0.0362198 | − | 0.999344i | \(-0.511532\pi\) | ||||
−0.0362198 | + | 0.999344i | \(0.511532\pi\) | |||||||
\(632\) | −13.4164 | −0.533676 | ||||||||
\(633\) | 17.2705 | 0.686441 | ||||||||
\(634\) | −1.14590 | −0.0455094 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.38197 | 0.213409 | ||||||||
\(637\) | 32.1246 | 1.27282 | ||||||||
\(638\) | −4.47214 | −0.177054 | ||||||||
\(639\) | −3.52786 | −0.139560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.74265 | −0.0688304 | −0.0344152 | − | 0.999408i | \(-0.510957\pi\) | ||||
−0.0344152 | + | 0.999408i | \(0.510957\pi\) | |||||||
\(642\) | −6.94427 | −0.274069 | ||||||||
\(643\) | 7.05573 | 0.278251 | 0.139125 | − | 0.990275i | \(-0.455571\pi\) | ||||
0.139125 | + | 0.990275i | \(0.455571\pi\) | |||||||
\(644\) | −3.00000 | −0.118217 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.47214 | 0.175954 | ||||||||
\(647\) | 5.09017 | 0.200115 | 0.100058 | − | 0.994982i | \(-0.468097\pi\) | ||||
0.100058 | + | 0.994982i | \(0.468097\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 21.1803 | 0.831401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.52786 | 0.0598817 | ||||||||
\(652\) | 4.94427 | 0.193633 | ||||||||
\(653\) | −13.1459 | −0.514439 | −0.257219 | − | 0.966353i | \(-0.582806\pi\) | ||||
−0.257219 | + | 0.966353i | \(0.582806\pi\) | |||||||
\(654\) | −6.18034 | −0.241670 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.38197 | −0.366304 | ||||||||
\(657\) | −12.9443 | −0.505004 | ||||||||
\(658\) | 1.00000 | 0.0389841 | ||||||||
\(659\) | −1.25735 | −0.0489796 | −0.0244898 | − | 0.999700i | \(-0.507796\pi\) | ||||
−0.0244898 | + | 0.999700i | \(0.507796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.65248 | 0.103169 | 0.0515847 | − | 0.998669i | \(-0.483573\pi\) | ||||
0.0515847 | + | 0.998669i | \(0.483573\pi\) | |||||||
\(662\) | 2.47214 | 0.0960823 | ||||||||
\(663\) | −3.70820 | −0.144015 | ||||||||
\(664\) | −14.9443 | −0.579950 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.56231 | −0.370532 | ||||||||
\(667\) | 13.4164 | 0.519485 | ||||||||
\(668\) | 7.85410 | 0.303884 | ||||||||
\(669\) | 24.0000 | 0.927894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.7082 | 0.606408 | ||||||||
\(672\) | 0.618034 | 0.0238412 | ||||||||
\(673\) | 21.5279 | 0.829838 | 0.414919 | − | 0.909858i | \(-0.363810\pi\) | ||||
0.414919 | + | 0.909858i | \(0.363810\pi\) | |||||||
\(674\) | −19.8885 | −0.766078 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5623 | 0.406243 | ||||||||
\(677\) | 7.85410 | 0.301858 | 0.150929 | − | 0.988545i | \(-0.451774\pi\) | ||||
0.150929 | + | 0.988545i | \(0.451774\pi\) | |||||||
\(678\) | 3.23607 | 0.124280 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.1803 | −1.07987 | ||||||||
\(682\) | −4.00000 | −0.153168 | ||||||||
\(683\) | 24.9443 | 0.954466 | 0.477233 | − | 0.878777i | \(-0.341640\pi\) | ||||
0.477233 | + | 0.878777i | \(0.341640\pi\) | |||||||
\(684\) | 5.85410 | 0.223837 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.41641 | 0.321340 | ||||||||
\(687\) | −1.70820 | −0.0651720 | ||||||||
\(688\) | −5.70820 | −0.217623 | ||||||||
\(689\) | 26.1246 | 0.995268 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 14.6180 | 0.555694 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | −26.0689 | −0.989561 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.76393 | −0.104767 | ||||||||
\(697\) | 7.16718 | 0.271476 | ||||||||
\(698\) | 26.8328 | 1.01564 | ||||||||
\(699\) | −19.4164 | −0.734396 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2361 | −0.953153 | −0.476577 | − | 0.879133i | \(-0.658122\pi\) | ||||
−0.476577 | + | 0.879133i | \(0.658122\pi\) | |||||||
\(702\) | −4.85410 | −0.183206 | ||||||||
\(703\) | 55.9787 | 2.11128 | ||||||||
\(704\) | −1.61803 | −0.0609820 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.7082 | 0.591186 | ||||||||
\(707\) | 7.81966 | 0.294089 | ||||||||
\(708\) | 13.0902 | 0.491959 | ||||||||
\(709\) | −2.76393 | −0.103802 | −0.0519008 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0519008 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4164 | 0.503155 | ||||||||
\(712\) | 18.0902 | 0.677958 | ||||||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | −0.472136 | −0.0176692 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.0344 | 0.823466 | ||||||||
\(717\) | −8.94427 | −0.334030 | ||||||||
\(718\) | −4.47214 | −0.166899 | ||||||||
\(719\) | −27.8885 | −1.04007 | −0.520034 | − | 0.854146i | \(-0.674081\pi\) | ||||
−0.520034 | + | 0.854146i | \(0.674081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.29180 | 0.197077 | ||||||||
\(722\) | −15.2705 | −0.568310 | ||||||||
\(723\) | 7.14590 | 0.265759 | ||||||||
\(724\) | 25.4164 | 0.944593 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.38197 | −0.311084 | ||||||||
\(727\) | −44.1033 | −1.63570 | −0.817851 | − | 0.575430i | \(-0.804835\pi\) | ||||
−0.817851 | + | 0.575430i | \(0.804835\pi\) | |||||||
\(728\) | 3.00000 | 0.111187 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.36068 | 0.161286 | ||||||||
\(732\) | 9.70820 | 0.358826 | ||||||||
\(733\) | 31.3262 | 1.15706 | 0.578530 | − | 0.815661i | \(-0.303626\pi\) | ||||
0.578530 | + | 0.815661i | \(0.303626\pi\) | |||||||
\(734\) | 4.58359 | 0.169183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.85410 | 0.178925 | ||||||||
\(737\) | −6.00000 | −0.221013 | ||||||||
\(738\) | 9.38197 | 0.345355 | ||||||||
\(739\) | 10.7295 | 0.394691 | 0.197345 | − | 0.980334i | \(-0.436768\pi\) | ||||
0.197345 | + | 0.980334i | \(0.436768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.4164 | 1.04390 | ||||||||
\(742\) | 3.32624 | 0.122110 | ||||||||
\(743\) | −4.85410 | −0.178080 | −0.0890399 | − | 0.996028i | \(-0.528380\pi\) | ||||
−0.0890399 | + | 0.996028i | \(0.528380\pi\) | |||||||
\(744\) | −2.47214 | −0.0906329 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.5066 | 1.11693 | ||||||||
\(747\) | 14.9443 | 0.546782 | ||||||||
\(748\) | 1.23607 | 0.0451951 | ||||||||
\(749\) | −4.29180 | −0.156819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.5967 | −1.73683 | −0.868415 | − | 0.495838i | \(-0.834861\pi\) | ||||
−0.868415 | + | 0.495838i | \(0.834861\pi\) | |||||||
\(752\) | −1.61803 | −0.0590036 | ||||||||
\(753\) | −20.9443 | −0.763252 | ||||||||
\(754\) | −13.4164 | −0.488597 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.618034 | −0.0224777 | ||||||||
\(757\) | 21.7984 | 0.792275 | 0.396138 | − | 0.918191i | \(-0.370350\pi\) | ||||
0.396138 | + | 0.918191i | \(0.370350\pi\) | |||||||
\(758\) | 15.9787 | 0.580373 | ||||||||
\(759\) | −7.85410 | −0.285086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0344 | −0.363748 | −0.181874 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181874 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(762\) | −11.4164 | −0.413573 | ||||||||
\(763\) | −3.81966 | −0.138281 | ||||||||
\(764\) | −16.9443 | −0.613022 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.0902 | 1.34012 | ||||||||
\(767\) | 63.5410 | 2.29433 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −15.7295 | −0.567220 | −0.283610 | − | 0.958940i | \(-0.591532\pi\) | ||||
−0.283610 | + | 0.958940i | \(0.591532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.5279 | 0.487194 | ||||||||
\(772\) | 4.29180 | 0.154465 | ||||||||
\(773\) | −2.94427 | −0.105898 | −0.0529491 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529491 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(774\) | 5.70820 | 0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.70820 | 0.348504 | ||||||||
\(777\) | −5.90983 | −0.212014 | ||||||||
\(778\) | −12.7639 | −0.457609 | ||||||||
\(779\) | −54.9230 | −1.96782 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.70820 | 0.204256 | ||||||||
\(782\) | −3.70820 | −0.132605 | ||||||||
\(783\) | 2.76393 | 0.0987749 | ||||||||
\(784\) | −6.61803 | −0.236358 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.90983 | 0.139459 | ||||||||
\(787\) | 25.4164 | 0.905997 | 0.452999 | − | 0.891511i | \(-0.350354\pi\) | ||||
0.452999 | + | 0.891511i | \(0.350354\pi\) | |||||||
\(788\) | −6.94427 | −0.247379 | ||||||||
\(789\) | −14.6180 | −0.520416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 1.61803 | 0.0574943 | ||||||||
\(793\) | 47.1246 | 1.67344 | ||||||||
\(794\) | 17.2705 | 0.612907 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.18034 | −0.219056 | ||||||||
\(797\) | 5.09017 | 0.180303 | 0.0901515 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901515 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(798\) | 3.61803 | 0.128077 | ||||||||
\(799\) | 1.23607 | 0.0437289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0902 | −0.639185 | ||||||||
\(802\) | −2.32624 | −0.0821423 | ||||||||
\(803\) | 20.9443 | 0.739107 | ||||||||
\(804\) | −3.70820 | −0.130778 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | 13.4164 | 0.472280 | ||||||||
\(808\) | −12.6525 | −0.445113 | ||||||||
\(809\) | 15.9787 | 0.561782 | 0.280891 | − | 0.959740i | \(-0.409370\pi\) | ||||
0.280891 | + | 0.959740i | \(0.409370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.1033 | 1.86471 | 0.932355 | − | 0.361544i | \(-0.117750\pi\) | ||||
0.932355 | + | 0.361544i | \(0.117750\pi\) | |||||||
\(812\) | −1.70820 | −0.0599462 | ||||||||
\(813\) | −25.4164 | −0.891392 | ||||||||
\(814\) | 15.4721 | 0.542298 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.763932 | 0.0267430 | ||||||||
\(817\) | −33.4164 | −1.16909 | ||||||||
\(818\) | 14.1459 | 0.494600 | ||||||||
\(819\) | −3.00000 | −0.104828 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.9443 | −0.591359 | −0.295680 | − | 0.955287i | \(-0.595546\pi\) | ||||
−0.295680 | + | 0.955287i | \(0.595546\pi\) | |||||||
\(822\) | 3.05573 | 0.106581 | ||||||||
\(823\) | 8.03444 | 0.280063 | 0.140032 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140032 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(824\) | −8.56231 | −0.298282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.09017 | 0.281493 | ||||||||
\(827\) | −36.5410 | −1.27066 | −0.635328 | − | 0.772243i | \(-0.719135\pi\) | ||||
−0.635328 | + | 0.772243i | \(0.719135\pi\) | |||||||
\(828\) | −4.85410 | −0.168692 | ||||||||
\(829\) | −40.2492 | −1.39791 | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.8541 | −0.445904 | ||||||||
\(832\) | −4.85410 | −0.168286 | ||||||||
\(833\) | 5.05573 | 0.175171 | ||||||||
\(834\) | 12.5623 | 0.434997 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.47214 | −0.327601 | ||||||||
\(837\) | 2.47214 | 0.0854495 | ||||||||
\(838\) | −11.0557 | −0.381914 | ||||||||
\(839\) | −16.1803 | −0.558607 | −0.279304 | − | 0.960203i | \(-0.590104\pi\) | ||||
−0.279304 | + | 0.960203i | \(0.590104\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | −18.1803 | −0.626536 | ||||||||
\(843\) | 6.09017 | 0.209757 | ||||||||
\(844\) | −17.2705 | −0.594475 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.61803 | 0.0556292 | ||||||||
\(847\) | −5.18034 | −0.177999 | ||||||||
\(848\) | −5.38197 | −0.184817 | ||||||||
\(849\) | 30.1803 | 1.03579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.4164 | −1.59113 | ||||||||
\(852\) | 3.52786 | 0.120863 | ||||||||
\(853\) | −6.43769 | −0.220422 | −0.110211 | − | 0.993908i | \(-0.535153\pi\) | ||||
−0.110211 | + | 0.993908i | \(0.535153\pi\) | |||||||
\(854\) | 6.00000 | 0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.94427 | 0.237350 | ||||||||
\(857\) | 8.18034 | 0.279435 | 0.139718 | − | 0.990191i | \(-0.455381\pi\) | ||||
0.139718 | + | 0.990191i | \(0.455381\pi\) | |||||||
\(858\) | 7.85410 | 0.268135 | ||||||||
\(859\) | 0.978714 | 0.0333933 | 0.0166966 | − | 0.999861i | \(-0.494685\pi\) | ||||
0.0166966 | + | 0.999861i | \(0.494685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.79837 | 0.197608 | ||||||||
\(862\) | −15.8197 | −0.538820 | ||||||||
\(863\) | 2.90983 | 0.0990518 | 0.0495259 | − | 0.998773i | \(-0.484229\pi\) | ||||
0.0495259 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.4164 | 0.591834 | ||||||||
\(867\) | 16.4164 | 0.557530 | ||||||||
\(868\) | −1.52786 | −0.0518591 | ||||||||
\(869\) | −21.7082 | −0.736400 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0000 | −0.609907 | ||||||||
\(872\) | 6.18034 | 0.209293 | ||||||||
\(873\) | −9.70820 | −0.328573 | ||||||||
\(874\) | 28.4164 | 0.961199 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.9443 | 0.437346 | ||||||||
\(877\) | 7.72949 | 0.261006 | 0.130503 | − | 0.991448i | \(-0.458341\pi\) | ||||
0.130503 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(878\) | −1.70820 | −0.0576491 | ||||||||
\(879\) | 22.0902 | 0.745083 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.72949 | −0.294104 | −0.147052 | − | 0.989129i | \(-0.546978\pi\) | ||||
−0.147052 | + | 0.989129i | \(0.546978\pi\) | |||||||
\(882\) | 6.61803 | 0.222841 | ||||||||
\(883\) | −38.4721 | −1.29469 | −0.647345 | − | 0.762197i | \(-0.724121\pi\) | ||||
−0.647345 | + | 0.762197i | \(0.724121\pi\) | |||||||
\(884\) | 3.70820 | 0.124720 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5967 | 0.456792 | ||||||||
\(887\) | −34.9098 | −1.17216 | −0.586079 | − | 0.810254i | \(-0.699329\pi\) | ||||
−0.586079 | + | 0.810254i | \(0.699329\pi\) | |||||||
\(888\) | 9.56231 | 0.320890 | ||||||||
\(889\) | −7.05573 | −0.236642 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61803 | −0.0542062 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | −9.47214 | −0.316973 | ||||||||
\(894\) | −13.4164 | −0.448712 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.618034 | −0.0206471 | ||||||||
\(897\) | −23.5623 | −0.786722 | ||||||||
\(898\) | −28.2148 | −0.941539 | ||||||||
\(899\) | 6.83282 | 0.227887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.11146 | 0.136972 | ||||||||
\(902\) | −15.1803 | −0.505450 | ||||||||
\(903\) | 3.52786 | 0.117400 | ||||||||
\(904\) | −3.23607 | −0.107630 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.2918 | 0.341922 | ||||||||
\(907\) | −13.1246 | −0.435796 | −0.217898 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217898 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(908\) | 28.1803 | 0.935197 | ||||||||
\(909\) | 12.6525 | 0.419656 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.8885 | −1.18904 | −0.594520 | − | 0.804081i | \(-0.702658\pi\) | ||||
−0.594520 | + | 0.804081i | \(0.702658\pi\) | |||||||
\(912\) | −5.85410 | −0.193849 | ||||||||
\(913\) | −24.1803 | −0.800252 | ||||||||
\(914\) | −38.8328 | −1.28448 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.70820 | 0.0564406 | ||||||||
\(917\) | 2.41641 | 0.0797968 | ||||||||
\(918\) | −0.763932 | −0.0252135 | ||||||||
\(919\) | −29.5967 | −0.976307 | −0.488153 | − | 0.872758i | \(-0.662329\pi\) | ||||
−0.488153 | + | 0.872758i | \(0.662329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7639 | 0.684195 | ||||||||
\(922\) | −38.1803 | −1.25740 | ||||||||
\(923\) | 17.1246 | 0.563663 | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.7771 | −1.04426 | ||||||||
\(927\) | 8.56231 | 0.281223 | ||||||||
\(928\) | 2.76393 | 0.0907305 | ||||||||
\(929\) | −30.4508 | −0.999060 | −0.499530 | − | 0.866297i | \(-0.666494\pi\) | ||||
−0.499530 | + | 0.866297i | \(0.666494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.7426 | −1.26974 | ||||||||
\(932\) | 19.4164 | 0.636006 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 15.2361 | 0.498539 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.85410 | 0.158661 | ||||||||
\(937\) | 27.1246 | 0.886122 | 0.443061 | − | 0.896491i | \(-0.353892\pi\) | ||||
0.443061 | + | 0.896491i | \(0.353892\pi\) | |||||||
\(938\) | −2.29180 | −0.0748298 | ||||||||
\(939\) | 2.29180 | 0.0747899 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.1246 | 0.558246 | 0.279123 | − | 0.960255i | \(-0.409956\pi\) | ||||
0.279123 | + | 0.960255i | \(0.409956\pi\) | |||||||
\(942\) | 10.9443 | 0.356584 | ||||||||
\(943\) | 45.5410 | 1.48302 | ||||||||
\(944\) | −13.0902 | −0.426049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.23607 | −0.300290 | ||||||||
\(947\) | 29.8885 | 0.971247 | 0.485624 | − | 0.874168i | \(-0.338593\pi\) | ||||
0.485624 | + | 0.874168i | \(0.338593\pi\) | |||||||
\(948\) | −13.4164 | −0.435745 | ||||||||
\(949\) | 62.8328 | 2.03964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.14590 | −0.0371583 | ||||||||
\(952\) | 0.472136 | 0.0153020 | ||||||||
\(953\) | −60.1803 | −1.94943 | −0.974716 | − | 0.223446i | \(-0.928269\pi\) | ||||
−0.974716 | + | 0.223446i | \(0.928269\pi\) | |||||||
\(954\) | 5.38197 | 0.174248 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.94427 | 0.289278 | ||||||||
\(957\) | −4.47214 | −0.144564 | ||||||||
\(958\) | −8.29180 | −0.267896 | ||||||||
\(959\) | 1.88854 | 0.0609843 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 46.4164 | 1.49653 | ||||||||
\(963\) | −6.94427 | −0.223776 | ||||||||
\(964\) | −7.14590 | −0.230154 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.00000 | −0.0965234 | ||||||||
\(967\) | −13.3262 | −0.428543 | −0.214271 | − | 0.976774i | \(-0.568738\pi\) | ||||
−0.214271 | + | 0.976774i | \(0.568738\pi\) | |||||||
\(968\) | 8.38197 | 0.269407 | ||||||||
\(969\) | 4.47214 | 0.143666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.02129 | −0.0648662 | −0.0324331 | − | 0.999474i | \(-0.510326\pi\) | ||||
−0.0324331 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 7.76393 | 0.248900 | ||||||||
\(974\) | −17.3262 | −0.555168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.70820 | −0.310752 | ||||||||
\(977\) | −4.58359 | −0.146642 | −0.0733211 | − | 0.997308i | \(-0.523360\pi\) | ||||
−0.0733211 | + | 0.997308i | \(0.523360\pi\) | |||||||
\(978\) | 4.94427 | 0.158100 | ||||||||
\(979\) | 29.2705 | 0.935490 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.18034 | −0.197323 | ||||||||
\(982\) | 18.9787 | 0.605635 | ||||||||
\(983\) | −24.4508 | −0.779861 | −0.389930 | − | 0.920844i | \(-0.627501\pi\) | ||||
−0.389930 | + | 0.920844i | \(0.627501\pi\) | |||||||
\(984\) | −9.38197 | −0.299086 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.11146 | −0.0672425 | ||||||||
\(987\) | 1.00000 | 0.0318304 | ||||||||
\(988\) | −28.4164 | −0.904046 | ||||||||
\(989\) | 27.7082 | 0.881070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.0000 | 1.33417 | 0.667087 | − | 0.744980i | \(-0.267541\pi\) | ||||
0.667087 | + | 0.744980i | \(0.267541\pi\) | |||||||
\(992\) | 2.47214 | 0.0784904 | ||||||||
\(993\) | 2.47214 | 0.0784509 | ||||||||
\(994\) | 2.18034 | 0.0691562 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.9443 | −0.473527 | ||||||||
\(997\) | −22.1459 | −0.701368 | −0.350684 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(998\) | 5.72949 | 0.181364 | ||||||||
\(999\) | −9.56231 | −0.302538 |
(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 | 750.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2250.2.a.l.1.2 | 2 | |||
4.3 | odd | 2 | 6000.2.a.w.1.1 | 2 | |||
5.2 | odd | 4 | 750.2.c.d.499.2 | 4 | |||
5.3 | odd | 4 | 750.2.c.d.499.3 | 4 | |||
5.4 | even | 2 | 750.2.a.g.1.1 | yes | 2 | ||
15.2 | even | 4 | 2250.2.c.d.1999.4 | 4 | |||
15.8 | even | 4 | 2250.2.c.d.1999.1 | 4 | |||
15.14 | odd | 2 | 2250.2.a.e.1.1 | 2 | |||
20.3 | even | 4 | 6000.2.f.h.1249.4 | 4 | |||
20.7 | even | 4 | 6000.2.f.h.1249.1 | 4 | |||
20.19 | odd | 2 | 6000.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
750.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
750.2.a.g.1.1 | yes | 2 | 5.4 | even | 2 | ||
750.2.c.d.499.2 | 4 | 5.2 | odd | 4 | |||
750.2.c.d.499.3 | 4 | 5.3 | odd | 4 | |||
2250.2.a.e.1.1 | 2 | 15.14 | odd | 2 | |||
2250.2.a.l.1.2 | 2 | 3.2 | odd | 2 | |||
2250.2.c.d.1999.1 | 4 | 15.8 | even | 4 | |||
2250.2.c.d.1999.4 | 4 | 15.2 | even | 4 | |||
6000.2.a.f.1.2 | 2 | 20.19 | odd | 2 | |||
6000.2.a.w.1.1 | 2 | 4.3 | odd | 2 | |||
6000.2.f.h.1249.1 | 4 | 20.7 | even | 4 | |||
6000.2.f.h.1249.4 | 4 | 20.3 | even | 4 |