Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, 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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.61803 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 2.61803 | 0.827895 | ||||||||
\(11\) | −4.85410 | −1.46357 | −0.731783 | − | 0.681537i | \(-0.761312\pi\) | ||||
−0.731783 | + | 0.681537i | \(0.761312\pi\) | |||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −4.23607 | −1.09375 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | 0.381966 | 0.0900303 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.61803 | −0.585410 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 4.85410 | 1.03490 | ||||||||
\(23\) | 8.94427 | 1.86501 | 0.932505 | − | 0.361158i | \(-0.117618\pi\) | ||||
0.932505 | + | 0.361158i | \(0.117618\pi\) | |||||||
\(24\) | −1.61803 | −0.330280 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 4.47214 | 0.877058 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.145898 | 0.0270926 | 0.0135463 | − | 0.999908i | \(-0.495688\pi\) | ||||
0.0135463 | + | 0.999908i | \(0.495688\pi\) | |||||||
\(30\) | 4.23607 | 0.773397 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.85410 | −1.36722 | ||||||||
\(34\) | −0.763932 | −0.131013 | ||||||||
\(35\) | −2.61803 | −0.442529 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | 7.85410 | 1.29121 | 0.645603 | − | 0.763673i | \(-0.276606\pi\) | ||||
0.645603 | + | 0.763673i | \(0.276606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.23607 | −1.15870 | ||||||||
\(40\) | 2.61803 | 0.413948 | ||||||||
\(41\) | −9.56231 | −1.49338 | −0.746691 | − | 0.665171i | \(-0.768358\pi\) | ||||
−0.746691 | + | 0.665171i | \(0.768358\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | 3.85410 | 0.587745 | 0.293873 | − | 0.955845i | \(-0.405056\pi\) | ||||
0.293873 | + | 0.955845i | \(0.405056\pi\) | |||||||
\(44\) | −4.85410 | −0.731783 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −8.94427 | −1.31876 | ||||||||
\(47\) | −10.8541 | −1.58323 | −0.791617 | − | 0.611018i | \(-0.790760\pi\) | ||||
−0.791617 | + | 0.611018i | \(0.790760\pi\) | |||||||
\(48\) | 1.61803 | 0.233543 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.85410 | −0.262210 | ||||||||
\(51\) | 1.23607 | 0.173084 | ||||||||
\(52\) | −4.47214 | −0.620174 | ||||||||
\(53\) | −5.14590 | −0.706843 | −0.353422 | − | 0.935464i | \(-0.614982\pi\) | ||||
−0.353422 | + | 0.935464i | \(0.614982\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 12.7082 | 1.71357 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.145898 | −0.0191574 | ||||||||
\(59\) | −11.5623 | −1.50528 | −0.752642 | − | 0.658430i | \(-0.771221\pi\) | ||||
−0.752642 | + | 0.658430i | \(0.771221\pi\) | |||||||
\(60\) | −4.23607 | −0.546874 | ||||||||
\(61\) | −8.56231 | −1.09629 | −0.548145 | − | 0.836383i | \(-0.684666\pi\) | ||||
−0.548145 | + | 0.836383i | \(0.684666\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | −0.381966 | −0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.7082 | 1.45222 | ||||||||
\(66\) | 7.85410 | 0.966773 | ||||||||
\(67\) | 5.23607 | 0.639688 | 0.319844 | − | 0.947470i | \(-0.396370\pi\) | ||||
0.319844 | + | 0.947470i | \(0.396370\pi\) | |||||||
\(68\) | 0.763932 | 0.0926404 | ||||||||
\(69\) | 14.4721 | 1.74224 | ||||||||
\(70\) | 2.61803 | 0.312915 | ||||||||
\(71\) | 8.56231 | 1.01616 | 0.508079 | − | 0.861310i | \(-0.330356\pi\) | ||||
0.508079 | + | 0.861310i | \(0.330356\pi\) | |||||||
\(72\) | 0.381966 | 0.0450151 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −7.85410 | −0.913021 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | 7.23607 | 0.819323 | ||||||||
\(79\) | 0.326238 | 0.0367046 | 0.0183523 | − | 0.999832i | \(-0.494158\pi\) | ||||
0.0183523 | + | 0.999832i | \(0.494158\pi\) | |||||||
\(80\) | −2.61803 | −0.292705 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 9.56231 | 1.05598 | ||||||||
\(83\) | 11.2361 | 1.23332 | 0.616659 | − | 0.787230i | \(-0.288486\pi\) | ||||
0.616659 | + | 0.787230i | \(0.288486\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | −3.85410 | −0.415599 | ||||||||
\(87\) | 0.236068 | 0.0253091 | ||||||||
\(88\) | 4.85410 | 0.517449 | ||||||||
\(89\) | −3.14590 | −0.333465 | −0.166732 | − | 0.986002i | \(-0.553322\pi\) | ||||
−0.166732 | + | 0.986002i | \(0.553322\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 8.94427 | 0.932505 | ||||||||
\(93\) | 9.70820 | 1.00669 | ||||||||
\(94\) | 10.8541 | 1.11952 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.61803 | −0.165140 | ||||||||
\(97\) | 7.14590 | 0.725556 | 0.362778 | − | 0.931876i | \(-0.381828\pi\) | ||||
0.362778 | + | 0.931876i | \(0.381828\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.85410 | 0.186344 | ||||||||
\(100\) | 1.85410 | 0.185410 | ||||||||
\(101\) | 2.94427 | 0.292966 | 0.146483 | − | 0.989213i | \(-0.453205\pi\) | ||||
0.146483 | + | 0.989213i | \(0.453205\pi\) | |||||||
\(102\) | −1.23607 | −0.122389 | ||||||||
\(103\) | 8.94427 | 0.881305 | 0.440653 | − | 0.897678i | \(-0.354747\pi\) | ||||
0.440653 | + | 0.897678i | \(0.354747\pi\) | |||||||
\(104\) | 4.47214 | 0.438529 | ||||||||
\(105\) | −4.23607 | −0.413398 | ||||||||
\(106\) | 5.14590 | 0.499814 | ||||||||
\(107\) | 19.7082 | 1.90526 | 0.952632 | − | 0.304125i | \(-0.0983642\pi\) | ||||
0.952632 | + | 0.304125i | \(0.0983642\pi\) | |||||||
\(108\) | −5.47214 | −0.526557 | ||||||||
\(109\) | 10.8541 | 1.03963 | 0.519817 | − | 0.854278i | \(-0.326000\pi\) | ||||
0.519817 | + | 0.854278i | \(0.326000\pi\) | |||||||
\(110\) | −12.7082 | −1.21168 | ||||||||
\(111\) | 12.7082 | 1.20621 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.4164 | −2.18359 | ||||||||
\(116\) | 0.145898 | 0.0135463 | ||||||||
\(117\) | 1.70820 | 0.157924 | ||||||||
\(118\) | 11.5623 | 1.06440 | ||||||||
\(119\) | 0.763932 | 0.0700295 | ||||||||
\(120\) | 4.23607 | 0.386698 | ||||||||
\(121\) | 12.5623 | 1.14203 | ||||||||
\(122\) | 8.56231 | 0.775195 | ||||||||
\(123\) | −15.4721 | −1.39508 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 8.23607 | 0.736656 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | 22.0902 | 1.96019 | 0.980093 | − | 0.198540i | \(-0.0636199\pi\) | ||||
0.980093 | + | 0.198540i | \(0.0636199\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.23607 | 0.549055 | ||||||||
\(130\) | −11.7082 | −1.02688 | ||||||||
\(131\) | −4.47214 | −0.390732 | −0.195366 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195366 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(132\) | −7.85410 | −0.683612 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.23607 | −0.452327 | ||||||||
\(135\) | 14.3262 | 1.23301 | ||||||||
\(136\) | −0.763932 | −0.0655066 | ||||||||
\(137\) | 3.38197 | 0.288941 | 0.144470 | − | 0.989509i | \(-0.453852\pi\) | ||||
0.144470 | + | 0.989509i | \(0.453852\pi\) | |||||||
\(138\) | −14.4721 | −1.23195 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | −2.61803 | −0.221264 | ||||||||
\(141\) | −17.5623 | −1.47901 | ||||||||
\(142\) | −8.56231 | −0.718533 | ||||||||
\(143\) | 21.7082 | 1.81533 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | −0.381966 | −0.0317206 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.61803 | 0.133453 | ||||||||
\(148\) | 7.85410 | 0.645603 | ||||||||
\(149\) | −17.2361 | −1.41203 | −0.706017 | − | 0.708195i | \(-0.749510\pi\) | ||||
−0.706017 | + | 0.708195i | \(0.749510\pi\) | |||||||
\(150\) | −3.00000 | −0.244949 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.291796 | −0.0235903 | ||||||||
\(154\) | 4.85410 | 0.391155 | ||||||||
\(155\) | −15.7082 | −1.26171 | ||||||||
\(156\) | −7.23607 | −0.579349 | ||||||||
\(157\) | 2.85410 | 0.227782 | 0.113891 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113891 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(158\) | −0.326238 | −0.0259541 | ||||||||
\(159\) | −8.32624 | −0.660314 | ||||||||
\(160\) | 2.61803 | 0.206974 | ||||||||
\(161\) | 8.94427 | 0.704907 | ||||||||
\(162\) | 7.70820 | 0.605614 | ||||||||
\(163\) | −20.2705 | −1.58771 | −0.793854 | − | 0.608108i | \(-0.791929\pi\) | ||||
−0.793854 | + | 0.608108i | \(0.791929\pi\) | |||||||
\(164\) | −9.56231 | −0.746691 | ||||||||
\(165\) | 20.5623 | 1.60077 | ||||||||
\(166\) | −11.2361 | −0.872088 | ||||||||
\(167\) | −10.0000 | −0.773823 | −0.386912 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386912 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(168\) | −1.61803 | −0.124834 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.85410 | 0.293873 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | −0.236068 | −0.0178963 | ||||||||
\(175\) | 1.85410 | 0.140157 | ||||||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | −18.7082 | −1.40619 | ||||||||
\(178\) | 3.14590 | 0.235795 | ||||||||
\(179\) | 17.7082 | 1.32357 | 0.661787 | − | 0.749692i | \(-0.269798\pi\) | ||||
0.661787 | + | 0.749692i | \(0.269798\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −7.41641 | −0.551257 | −0.275629 | − | 0.961264i | \(-0.588886\pi\) | ||||
−0.275629 | + | 0.961264i | \(0.588886\pi\) | |||||||
\(182\) | 4.47214 | 0.331497 | ||||||||
\(183\) | −13.8541 | −1.02412 | ||||||||
\(184\) | −8.94427 | −0.659380 | ||||||||
\(185\) | −20.5623 | −1.51177 | ||||||||
\(186\) | −9.70820 | −0.711840 | ||||||||
\(187\) | −3.70820 | −0.271171 | ||||||||
\(188\) | −10.8541 | −0.791617 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9443 | 1.08133 | 0.540665 | − | 0.841238i | \(-0.318173\pi\) | ||||
0.540665 | + | 0.841238i | \(0.318173\pi\) | |||||||
\(192\) | 1.61803 | 0.116772 | ||||||||
\(193\) | −20.9443 | −1.50760 | −0.753801 | − | 0.657103i | \(-0.771782\pi\) | ||||
−0.753801 | + | 0.657103i | \(0.771782\pi\) | |||||||
\(194\) | −7.14590 | −0.513046 | ||||||||
\(195\) | 18.9443 | 1.35663 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −5.23607 | −0.373054 | −0.186527 | − | 0.982450i | \(-0.559723\pi\) | ||||
−0.186527 | + | 0.982450i | \(0.559723\pi\) | |||||||
\(198\) | −1.85410 | −0.131765 | ||||||||
\(199\) | 1.56231 | 0.110749 | 0.0553745 | − | 0.998466i | \(-0.482365\pi\) | ||||
0.0553745 | + | 0.998466i | \(0.482365\pi\) | |||||||
\(200\) | −1.85410 | −0.131105 | ||||||||
\(201\) | 8.47214 | 0.597578 | ||||||||
\(202\) | −2.94427 | −0.207158 | ||||||||
\(203\) | 0.145898 | 0.0102400 | ||||||||
\(204\) | 1.23607 | 0.0865421 | ||||||||
\(205\) | 25.0344 | 1.74848 | ||||||||
\(206\) | −8.94427 | −0.623177 | ||||||||
\(207\) | −3.41641 | −0.237457 | ||||||||
\(208\) | −4.47214 | −0.310087 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.23607 | 0.292316 | ||||||||
\(211\) | 17.2361 | 1.18658 | 0.593290 | − | 0.804989i | \(-0.297829\pi\) | ||||
0.593290 | + | 0.804989i | \(0.297829\pi\) | |||||||
\(212\) | −5.14590 | −0.353422 | ||||||||
\(213\) | 13.8541 | 0.949267 | ||||||||
\(214\) | −19.7082 | −1.34723 | ||||||||
\(215\) | −10.0902 | −0.688144 | ||||||||
\(216\) | 5.47214 | 0.372332 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −10.8541 | −0.735133 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.7082 | 0.856787 | ||||||||
\(221\) | −3.41641 | −0.229812 | ||||||||
\(222\) | −12.7082 | −0.852919 | ||||||||
\(223\) | −5.23607 | −0.350633 | −0.175317 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175317 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.708204 | −0.0472136 | ||||||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | 19.4164 | 1.28871 | 0.644356 | − | 0.764726i | \(-0.277125\pi\) | ||||
0.644356 | + | 0.764726i | \(0.277125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8541 | 1.57632 | 0.788162 | − | 0.615468i | \(-0.211033\pi\) | ||||
0.788162 | + | 0.615468i | \(0.211033\pi\) | |||||||
\(230\) | 23.4164 | 1.54403 | ||||||||
\(231\) | −7.85410 | −0.516762 | ||||||||
\(232\) | −0.145898 | −0.00957868 | ||||||||
\(233\) | 4.09017 | 0.267956 | 0.133978 | − | 0.990984i | \(-0.457225\pi\) | ||||
0.133978 | + | 0.990984i | \(0.457225\pi\) | |||||||
\(234\) | −1.70820 | −0.111669 | ||||||||
\(235\) | 28.4164 | 1.85368 | ||||||||
\(236\) | −11.5623 | −0.752642 | ||||||||
\(237\) | 0.527864 | 0.0342885 | ||||||||
\(238\) | −0.763932 | −0.0495184 | ||||||||
\(239\) | 14.1803 | 0.917250 | 0.458625 | − | 0.888630i | \(-0.348342\pi\) | ||||
0.458625 | + | 0.888630i | \(0.348342\pi\) | |||||||
\(240\) | −4.23607 | −0.273437 | ||||||||
\(241\) | 17.5623 | 1.13129 | 0.565644 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565644 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(242\) | −12.5623 | −0.807536 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | −8.56231 | −0.548145 | ||||||||
\(245\) | −2.61803 | −0.167260 | ||||||||
\(246\) | 15.4721 | 0.986467 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 18.1803 | 1.15213 | ||||||||
\(250\) | −8.23607 | −0.520895 | ||||||||
\(251\) | 9.05573 | 0.571592 | 0.285796 | − | 0.958290i | \(-0.407742\pi\) | ||||
0.285796 | + | 0.958290i | \(0.407742\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | −43.4164 | −2.72957 | ||||||||
\(254\) | −22.0902 | −1.38606 | ||||||||
\(255\) | −3.23607 | −0.202650 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.85410 | 0.614682 | 0.307341 | − | 0.951599i | \(-0.400561\pi\) | ||||
0.307341 | + | 0.951599i | \(0.400561\pi\) | |||||||
\(258\) | −6.23607 | −0.388241 | ||||||||
\(259\) | 7.85410 | 0.488030 | ||||||||
\(260\) | 11.7082 | 0.726112 | ||||||||
\(261\) | −0.0557281 | −0.00344948 | ||||||||
\(262\) | 4.47214 | 0.276289 | ||||||||
\(263\) | 12.6525 | 0.780185 | 0.390093 | − | 0.920776i | \(-0.372443\pi\) | ||||
0.390093 | + | 0.920776i | \(0.372443\pi\) | |||||||
\(264\) | 7.85410 | 0.483387 | ||||||||
\(265\) | 13.4721 | 0.827587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.09017 | −0.311513 | ||||||||
\(268\) | 5.23607 | 0.319844 | ||||||||
\(269\) | −4.58359 | −0.279467 | −0.139733 | − | 0.990189i | \(-0.544625\pi\) | ||||
−0.139733 | + | 0.990189i | \(0.544625\pi\) | |||||||
\(270\) | −14.3262 | −0.871867 | ||||||||
\(271\) | 2.43769 | 0.148079 | 0.0740397 | − | 0.997255i | \(-0.476411\pi\) | ||||
0.0740397 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(272\) | 0.763932 | 0.0463202 | ||||||||
\(273\) | −7.23607 | −0.437947 | ||||||||
\(274\) | −3.38197 | −0.204312 | ||||||||
\(275\) | −9.00000 | −0.542720 | ||||||||
\(276\) | 14.4721 | 0.871120 | ||||||||
\(277\) | −25.4164 | −1.52712 | −0.763562 | − | 0.645735i | \(-0.776551\pi\) | ||||
−0.763562 | + | 0.645735i | \(0.776551\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | −2.29180 | −0.137206 | ||||||||
\(280\) | 2.61803 | 0.156457 | ||||||||
\(281\) | −23.4164 | −1.39691 | −0.698453 | − | 0.715656i | \(-0.746128\pi\) | ||||
−0.698453 | + | 0.715656i | \(0.746128\pi\) | |||||||
\(282\) | 17.5623 | 1.04582 | ||||||||
\(283\) | 8.00000 | 0.475551 | 0.237775 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237775 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(284\) | 8.56231 | 0.508079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.7082 | −1.28363 | ||||||||
\(287\) | −9.56231 | −0.564445 | ||||||||
\(288\) | 0.381966 | 0.0225076 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0.381966 | 0.0224298 | ||||||||
\(291\) | 11.5623 | 0.677794 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.4164 | 1.83537 | 0.917683 | − | 0.397313i | \(-0.130057\pi\) | ||||
0.917683 | + | 0.397313i | \(0.130057\pi\) | |||||||
\(294\) | −1.61803 | −0.0943657 | ||||||||
\(295\) | 30.2705 | 1.76242 | ||||||||
\(296\) | −7.85410 | −0.456510 | ||||||||
\(297\) | 26.5623 | 1.54130 | ||||||||
\(298\) | 17.2361 | 0.998459 | ||||||||
\(299\) | −40.0000 | −2.31326 | ||||||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | 3.85410 | 0.222147 | ||||||||
\(302\) | −3.05573 | −0.175837 | ||||||||
\(303\) | 4.76393 | 0.273681 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.4164 | 1.28356 | ||||||||
\(306\) | 0.291796 | 0.0166809 | ||||||||
\(307\) | 18.9787 | 1.08317 | 0.541586 | − | 0.840645i | \(-0.317824\pi\) | ||||
0.541586 | + | 0.840645i | \(0.317824\pi\) | |||||||
\(308\) | −4.85410 | −0.276588 | ||||||||
\(309\) | 14.4721 | 0.823291 | ||||||||
\(310\) | 15.7082 | 0.892166 | ||||||||
\(311\) | −21.3262 | −1.20930 | −0.604650 | − | 0.796491i | \(-0.706687\pi\) | ||||
−0.604650 | + | 0.796491i | \(0.706687\pi\) | |||||||
\(312\) | 7.23607 | 0.409662 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | −2.85410 | −0.161066 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0.326238 | 0.0183523 | ||||||||
\(317\) | −25.6869 | −1.44272 | −0.721361 | − | 0.692560i | \(-0.756483\pi\) | ||||
−0.721361 | + | 0.692560i | \(0.756483\pi\) | |||||||
\(318\) | 8.32624 | 0.466912 | ||||||||
\(319\) | −0.708204 | −0.0396518 | ||||||||
\(320\) | −2.61803 | −0.146353 | ||||||||
\(321\) | 31.8885 | 1.77984 | ||||||||
\(322\) | −8.94427 | −0.498445 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | −8.29180 | −0.459946 | ||||||||
\(326\) | 20.2705 | 1.12268 | ||||||||
\(327\) | 17.5623 | 0.971198 | ||||||||
\(328\) | 9.56231 | 0.527990 | ||||||||
\(329\) | −10.8541 | −0.598406 | ||||||||
\(330\) | −20.5623 | −1.13192 | ||||||||
\(331\) | −3.70820 | −0.203821 | −0.101911 | − | 0.994794i | \(-0.532496\pi\) | ||||
−0.101911 | + | 0.994794i | \(0.532496\pi\) | |||||||
\(332\) | 11.2361 | 0.616659 | ||||||||
\(333\) | −3.00000 | −0.164399 | ||||||||
\(334\) | 10.0000 | 0.547176 | ||||||||
\(335\) | −13.7082 | −0.748959 | ||||||||
\(336\) | 1.61803 | 0.0882710 | ||||||||
\(337\) | 9.70820 | 0.528840 | 0.264420 | − | 0.964408i | \(-0.414820\pi\) | ||||
0.264420 | + | 0.964408i | \(0.414820\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | 16.1803 | 0.878795 | ||||||||
\(340\) | −2.00000 | −0.108465 | ||||||||
\(341\) | −29.1246 | −1.57719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.85410 | −0.207799 | ||||||||
\(345\) | −37.8885 | −2.03985 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | 8.94427 | 0.480154 | 0.240077 | − | 0.970754i | \(-0.422827\pi\) | ||||
0.240077 | + | 0.970754i | \(0.422827\pi\) | |||||||
\(348\) | 0.236068 | 0.0126546 | ||||||||
\(349\) | −16.8328 | −0.901040 | −0.450520 | − | 0.892766i | \(-0.648761\pi\) | ||||
−0.450520 | + | 0.892766i | \(0.648761\pi\) | |||||||
\(350\) | −1.85410 | −0.0991059 | ||||||||
\(351\) | 24.4721 | 1.30623 | ||||||||
\(352\) | 4.85410 | 0.258725 | ||||||||
\(353\) | 13.4164 | 0.714083 | 0.357042 | − | 0.934088i | \(-0.383785\pi\) | ||||
0.357042 | + | 0.934088i | \(0.383785\pi\) | |||||||
\(354\) | 18.7082 | 0.994330 | ||||||||
\(355\) | −22.4164 | −1.18974 | ||||||||
\(356\) | −3.14590 | −0.166732 | ||||||||
\(357\) | 1.23607 | 0.0654197 | ||||||||
\(358\) | −17.7082 | −0.935908 | ||||||||
\(359\) | 2.29180 | 0.120956 | 0.0604782 | − | 0.998170i | \(-0.480737\pi\) | ||||
0.0604782 | + | 0.998170i | \(0.480737\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 7.41641 | 0.389798 | ||||||||
\(363\) | 20.3262 | 1.06685 | ||||||||
\(364\) | −4.47214 | −0.234404 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.8541 | 0.724166 | ||||||||
\(367\) | −6.27051 | −0.327318 | −0.163659 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163659 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(368\) | 8.94427 | 0.466252 | ||||||||
\(369\) | 3.65248 | 0.190140 | ||||||||
\(370\) | 20.5623 | 1.06898 | ||||||||
\(371\) | −5.14590 | −0.267162 | ||||||||
\(372\) | 9.70820 | 0.503347 | ||||||||
\(373\) | 14.6180 | 0.756893 | 0.378447 | − | 0.925623i | \(-0.376458\pi\) | ||||
0.378447 | + | 0.925623i | \(0.376458\pi\) | |||||||
\(374\) | 3.70820 | 0.191747 | ||||||||
\(375\) | 13.3262 | 0.688164 | ||||||||
\(376\) | 10.8541 | 0.559758 | ||||||||
\(377\) | −0.652476 | −0.0336042 | ||||||||
\(378\) | 5.47214 | 0.281456 | ||||||||
\(379\) | 32.1803 | 1.65299 | 0.826497 | − | 0.562942i | \(-0.190331\pi\) | ||||
0.826497 | + | 0.562942i | \(0.190331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.7426 | 1.83115 | ||||||||
\(382\) | −14.9443 | −0.764615 | ||||||||
\(383\) | −13.1246 | −0.670636 | −0.335318 | − | 0.942105i | \(-0.608844\pi\) | ||||
−0.335318 | + | 0.942105i | \(0.608844\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | 12.7082 | 0.647670 | ||||||||
\(386\) | 20.9443 | 1.06604 | ||||||||
\(387\) | −1.47214 | −0.0748329 | ||||||||
\(388\) | 7.14590 | 0.362778 | ||||||||
\(389\) | −37.3050 | −1.89144 | −0.945718 | − | 0.324988i | \(-0.894640\pi\) | ||||
−0.945718 | + | 0.324988i | \(0.894640\pi\) | |||||||
\(390\) | −18.9443 | −0.959280 | ||||||||
\(391\) | 6.83282 | 0.345550 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −7.23607 | −0.365011 | ||||||||
\(394\) | 5.23607 | 0.263789 | ||||||||
\(395\) | −0.854102 | −0.0429745 | ||||||||
\(396\) | 1.85410 | 0.0931721 | ||||||||
\(397\) | −28.5623 | −1.43350 | −0.716751 | − | 0.697330i | \(-0.754371\pi\) | ||||
−0.716751 | + | 0.697330i | \(0.754371\pi\) | |||||||
\(398\) | −1.56231 | −0.0783113 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.85410 | 0.0927051 | ||||||||
\(401\) | −25.4164 | −1.26923 | −0.634617 | − | 0.772826i | \(-0.718842\pi\) | ||||
−0.634617 | + | 0.772826i | \(0.718842\pi\) | |||||||
\(402\) | −8.47214 | −0.422552 | ||||||||
\(403\) | −26.8328 | −1.33664 | ||||||||
\(404\) | 2.94427 | 0.146483 | ||||||||
\(405\) | 20.1803 | 1.00277 | ||||||||
\(406\) | −0.145898 | −0.00724080 | ||||||||
\(407\) | −38.1246 | −1.88977 | ||||||||
\(408\) | −1.23607 | −0.0611945 | ||||||||
\(409\) | −1.79837 | −0.0889239 | −0.0444619 | − | 0.999011i | \(-0.514157\pi\) | ||||
−0.0444619 | + | 0.999011i | \(0.514157\pi\) | |||||||
\(410\) | −25.0344 | −1.23636 | ||||||||
\(411\) | 5.47214 | 0.269921 | ||||||||
\(412\) | 8.94427 | 0.440653 | ||||||||
\(413\) | −11.5623 | −0.568944 | ||||||||
\(414\) | 3.41641 | 0.167907 | ||||||||
\(415\) | −29.4164 | −1.44399 | ||||||||
\(416\) | 4.47214 | 0.219265 | ||||||||
\(417\) | 9.70820 | 0.475413 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6525 | −0.618114 | −0.309057 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309057 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(420\) | −4.23607 | −0.206699 | ||||||||
\(421\) | 19.5279 | 0.951730 | 0.475865 | − | 0.879518i | \(-0.342135\pi\) | ||||
0.475865 | + | 0.879518i | \(0.342135\pi\) | |||||||
\(422\) | −17.2361 | −0.839039 | ||||||||
\(423\) | 4.14590 | 0.201580 | ||||||||
\(424\) | 5.14590 | 0.249907 | ||||||||
\(425\) | 1.41641 | 0.0687059 | ||||||||
\(426\) | −13.8541 | −0.671233 | ||||||||
\(427\) | −8.56231 | −0.414359 | ||||||||
\(428\) | 19.7082 | 0.952632 | ||||||||
\(429\) | 35.1246 | 1.69583 | ||||||||
\(430\) | 10.0902 | 0.486591 | ||||||||
\(431\) | 22.8541 | 1.10084 | 0.550422 | − | 0.834887i | \(-0.314467\pi\) | ||||
0.550422 | + | 0.834887i | \(0.314467\pi\) | |||||||
\(432\) | −5.47214 | −0.263278 | ||||||||
\(433\) | −3.38197 | −0.162527 | −0.0812635 | − | 0.996693i | \(-0.525896\pi\) | ||||
−0.0812635 | + | 0.996693i | \(0.525896\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | −0.618034 | −0.0296325 | ||||||||
\(436\) | 10.8541 | 0.519817 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.18034 | −0.104062 | −0.0520310 | − | 0.998645i | \(-0.516569\pi\) | ||||
−0.0520310 | + | 0.998645i | \(0.516569\pi\) | |||||||
\(440\) | −12.7082 | −0.605840 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 3.41641 | 0.162502 | ||||||||
\(443\) | 1.09017 | 0.0517955 | 0.0258978 | − | 0.999665i | \(-0.491756\pi\) | ||||
0.0258978 | + | 0.999665i | \(0.491756\pi\) | |||||||
\(444\) | 12.7082 | 0.603105 | ||||||||
\(445\) | 8.23607 | 0.390427 | ||||||||
\(446\) | 5.23607 | 0.247935 | ||||||||
\(447\) | −27.8885 | −1.31908 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −0.291796 | −0.0137707 | −0.00688535 | − | 0.999976i | \(-0.502192\pi\) | ||||
−0.00688535 | + | 0.999976i | \(0.502192\pi\) | |||||||
\(450\) | 0.708204 | 0.0333851 | ||||||||
\(451\) | 46.4164 | 2.18566 | ||||||||
\(452\) | 10.0000 | 0.470360 | ||||||||
\(453\) | 4.94427 | 0.232302 | ||||||||
\(454\) | −19.4164 | −0.911257 | ||||||||
\(455\) | 11.7082 | 0.548889 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.1459 | 1.45694 | 0.728472 | − | 0.685076i | \(-0.240231\pi\) | ||||
0.728472 | + | 0.685076i | \(0.240231\pi\) | |||||||
\(458\) | −23.8541 | −1.11463 | ||||||||
\(459\) | −4.18034 | −0.195122 | ||||||||
\(460\) | −23.4164 | −1.09180 | ||||||||
\(461\) | −41.5066 | −1.93315 | −0.966577 | − | 0.256376i | \(-0.917471\pi\) | ||||
−0.966577 | + | 0.256376i | \(0.917471\pi\) | |||||||
\(462\) | 7.85410 | 0.365406 | ||||||||
\(463\) | −12.0000 | −0.557687 | −0.278844 | − | 0.960337i | \(-0.589951\pi\) | ||||
−0.278844 | + | 0.960337i | \(0.589951\pi\) | |||||||
\(464\) | 0.145898 | 0.00677315 | ||||||||
\(465\) | −25.4164 | −1.17866 | ||||||||
\(466\) | −4.09017 | −0.189473 | ||||||||
\(467\) | −40.3607 | −1.86767 | −0.933835 | − | 0.357705i | \(-0.883559\pi\) | ||||
−0.933835 | + | 0.357705i | \(0.883559\pi\) | |||||||
\(468\) | 1.70820 | 0.0789618 | ||||||||
\(469\) | 5.23607 | 0.241779 | ||||||||
\(470\) | −28.4164 | −1.31075 | ||||||||
\(471\) | 4.61803 | 0.212788 | ||||||||
\(472\) | 11.5623 | 0.532198 | ||||||||
\(473\) | −18.7082 | −0.860204 | ||||||||
\(474\) | −0.527864 | −0.0242456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.763932 | 0.0350148 | ||||||||
\(477\) | 1.96556 | 0.0899967 | ||||||||
\(478\) | −14.1803 | −0.648594 | ||||||||
\(479\) | 36.3262 | 1.65979 | 0.829894 | − | 0.557921i | \(-0.188401\pi\) | ||||
0.829894 | + | 0.557921i | \(0.188401\pi\) | |||||||
\(480\) | 4.23607 | 0.193349 | ||||||||
\(481\) | −35.1246 | −1.60154 | ||||||||
\(482\) | −17.5623 | −0.799941 | ||||||||
\(483\) | 14.4721 | 0.658505 | ||||||||
\(484\) | 12.5623 | 0.571014 | ||||||||
\(485\) | −18.7082 | −0.849496 | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 16.9098 | 0.766258 | 0.383129 | − | 0.923695i | \(-0.374847\pi\) | ||||
0.383129 | + | 0.923695i | \(0.374847\pi\) | |||||||
\(488\) | 8.56231 | 0.387597 | ||||||||
\(489\) | −32.7984 | −1.48319 | ||||||||
\(490\) | 2.61803 | 0.118271 | ||||||||
\(491\) | −40.3607 | −1.82145 | −0.910726 | − | 0.413011i | \(-0.864477\pi\) | ||||
−0.910726 | + | 0.413011i | \(0.864477\pi\) | |||||||
\(492\) | −15.4721 | −0.697538 | ||||||||
\(493\) | 0.111456 | 0.00501973 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.85410 | −0.218176 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 8.56231 | 0.384072 | ||||||||
\(498\) | −18.1803 | −0.814681 | ||||||||
\(499\) | −18.6869 | −0.836541 | −0.418271 | − | 0.908322i | \(-0.637364\pi\) | ||||
−0.418271 | + | 0.908322i | \(0.637364\pi\) | |||||||
\(500\) | 8.23607 | 0.368328 | ||||||||
\(501\) | −16.1803 | −0.722884 | ||||||||
\(502\) | −9.05573 | −0.404177 | ||||||||
\(503\) | 30.2148 | 1.34721 | 0.673605 | − | 0.739091i | \(-0.264745\pi\) | ||||
0.673605 | + | 0.739091i | \(0.264745\pi\) | |||||||
\(504\) | 0.381966 | 0.0170141 | ||||||||
\(505\) | −7.70820 | −0.343011 | ||||||||
\(506\) | 43.4164 | 1.93009 | ||||||||
\(507\) | 11.3262 | 0.503016 | ||||||||
\(508\) | 22.0902 | 0.980093 | ||||||||
\(509\) | −35.1246 | −1.55687 | −0.778436 | − | 0.627725i | \(-0.783986\pi\) | ||||
−0.778436 | + | 0.627725i | \(0.783986\pi\) | |||||||
\(510\) | 3.23607 | 0.143295 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.85410 | −0.434646 | ||||||||
\(515\) | −23.4164 | −1.03185 | ||||||||
\(516\) | 6.23607 | 0.274528 | ||||||||
\(517\) | 52.6869 | 2.31717 | ||||||||
\(518\) | −7.85410 | −0.345089 | ||||||||
\(519\) | 29.1246 | 1.27843 | ||||||||
\(520\) | −11.7082 | −0.513439 | ||||||||
\(521\) | −21.4164 | −0.938270 | −0.469135 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469135 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(522\) | 0.0557281 | 0.00243915 | ||||||||
\(523\) | 24.0000 | 1.04945 | 0.524723 | − | 0.851273i | \(-0.324169\pi\) | ||||
0.524723 | + | 0.851273i | \(0.324169\pi\) | |||||||
\(524\) | −4.47214 | −0.195366 | ||||||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | −12.6525 | −0.551674 | ||||||||
\(527\) | 4.58359 | 0.199664 | ||||||||
\(528\) | −7.85410 | −0.341806 | ||||||||
\(529\) | 57.0000 | 2.47826 | ||||||||
\(530\) | −13.4721 | −0.585192 | ||||||||
\(531\) | 4.41641 | 0.191656 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.7639 | 1.85231 | ||||||||
\(534\) | 5.09017 | 0.220273 | ||||||||
\(535\) | −51.5967 | −2.23072 | ||||||||
\(536\) | −5.23607 | −0.226164 | ||||||||
\(537\) | 28.6525 | 1.23645 | ||||||||
\(538\) | 4.58359 | 0.197613 | ||||||||
\(539\) | −4.85410 | −0.209081 | ||||||||
\(540\) | 14.3262 | 0.616503 | ||||||||
\(541\) | 19.1246 | 0.822231 | 0.411116 | − | 0.911583i | \(-0.365139\pi\) | ||||
0.411116 | + | 0.911583i | \(0.365139\pi\) | |||||||
\(542\) | −2.43769 | −0.104708 | ||||||||
\(543\) | −12.0000 | −0.514969 | ||||||||
\(544\) | −0.763932 | −0.0327533 | ||||||||
\(545\) | −28.4164 | −1.21723 | ||||||||
\(546\) | 7.23607 | 0.309675 | ||||||||
\(547\) | 12.6525 | 0.540981 | 0.270490 | − | 0.962723i | \(-0.412814\pi\) | ||||
0.270490 | + | 0.962723i | \(0.412814\pi\) | |||||||
\(548\) | 3.38197 | 0.144470 | ||||||||
\(549\) | 3.27051 | 0.139582 | ||||||||
\(550\) | 9.00000 | 0.383761 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −14.4721 | −0.615975 | ||||||||
\(553\) | 0.326238 | 0.0138730 | ||||||||
\(554\) | 25.4164 | 1.07984 | ||||||||
\(555\) | −33.2705 | −1.41225 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | −32.0689 | −1.35880 | −0.679401 | − | 0.733767i | \(-0.737760\pi\) | ||||
−0.679401 | + | 0.733767i | \(0.737760\pi\) | |||||||
\(558\) | 2.29180 | 0.0970195 | ||||||||
\(559\) | −17.2361 | −0.729008 | ||||||||
\(560\) | −2.61803 | −0.110632 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 23.4164 | 0.987762 | ||||||||
\(563\) | −6.56231 | −0.276568 | −0.138284 | − | 0.990393i | \(-0.544159\pi\) | ||||
−0.138284 | + | 0.990393i | \(0.544159\pi\) | |||||||
\(564\) | −17.5623 | −0.739506 | ||||||||
\(565\) | −26.1803 | −1.10142 | ||||||||
\(566\) | −8.00000 | −0.336265 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −8.56231 | −0.359266 | ||||||||
\(569\) | −25.7082 | −1.07774 | −0.538872 | − | 0.842388i | \(-0.681149\pi\) | ||||
−0.538872 | + | 0.842388i | \(0.681149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6869 | 0.656477 | 0.328239 | − | 0.944595i | \(-0.393545\pi\) | ||||
0.328239 | + | 0.944595i | \(0.393545\pi\) | |||||||
\(572\) | 21.7082 | 0.907666 | ||||||||
\(573\) | 24.1803 | 1.01015 | ||||||||
\(574\) | 9.56231 | 0.399123 | ||||||||
\(575\) | 16.5836 | 0.691584 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | −13.1246 | −0.546385 | −0.273192 | − | 0.961959i | \(-0.588080\pi\) | ||||
−0.273192 | + | 0.961959i | \(0.588080\pi\) | |||||||
\(578\) | 16.4164 | 0.682833 | ||||||||
\(579\) | −33.8885 | −1.40836 | ||||||||
\(580\) | −0.381966 | −0.0158603 | ||||||||
\(581\) | 11.2361 | 0.466151 | ||||||||
\(582\) | −11.5623 | −0.479273 | ||||||||
\(583\) | 24.9787 | 1.03451 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | −31.4164 | −1.29780 | ||||||||
\(587\) | 19.5279 | 0.806001 | 0.403001 | − | 0.915200i | \(-0.367967\pi\) | ||||
0.403001 | + | 0.915200i | \(0.367967\pi\) | |||||||
\(588\) | 1.61803 | 0.0667266 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −30.2705 | −1.24622 | ||||||||
\(591\) | −8.47214 | −0.348497 | ||||||||
\(592\) | 7.85410 | 0.322802 | ||||||||
\(593\) | 16.4721 | 0.676430 | 0.338215 | − | 0.941069i | \(-0.390177\pi\) | ||||
0.338215 | + | 0.941069i | \(0.390177\pi\) | |||||||
\(594\) | −26.5623 | −1.08986 | ||||||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | −17.2361 | −0.706017 | ||||||||
\(597\) | 2.52786 | 0.103459 | ||||||||
\(598\) | 40.0000 | 1.63572 | ||||||||
\(599\) | 11.9787 | 0.489437 | 0.244718 | − | 0.969594i | \(-0.421304\pi\) | ||||
0.244718 | + | 0.969594i | \(0.421304\pi\) | |||||||
\(600\) | −3.00000 | −0.122474 | ||||||||
\(601\) | 10.3607 | 0.422621 | 0.211310 | − | 0.977419i | \(-0.432227\pi\) | ||||
0.211310 | + | 0.977419i | \(0.432227\pi\) | |||||||
\(602\) | −3.85410 | −0.157081 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 3.05573 | 0.124336 | ||||||||
\(605\) | −32.8885 | −1.33711 | ||||||||
\(606\) | −4.76393 | −0.193522 | ||||||||
\(607\) | 16.3607 | 0.664060 | 0.332030 | − | 0.943269i | \(-0.392267\pi\) | ||||
0.332030 | + | 0.943269i | \(0.392267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.236068 | 0.00956596 | ||||||||
\(610\) | −22.4164 | −0.907614 | ||||||||
\(611\) | 48.5410 | 1.96376 | ||||||||
\(612\) | −0.291796 | −0.0117952 | ||||||||
\(613\) | 12.2918 | 0.496461 | 0.248230 | − | 0.968701i | \(-0.420151\pi\) | ||||
0.248230 | + | 0.968701i | \(0.420151\pi\) | |||||||
\(614\) | −18.9787 | −0.765919 | ||||||||
\(615\) | 40.5066 | 1.63338 | ||||||||
\(616\) | 4.85410 | 0.195577 | ||||||||
\(617\) | 33.9230 | 1.36569 | 0.682844 | − | 0.730564i | \(-0.260743\pi\) | ||||
0.682844 | + | 0.730564i | \(0.260743\pi\) | |||||||
\(618\) | −14.4721 | −0.582155 | ||||||||
\(619\) | −35.4164 | −1.42351 | −0.711753 | − | 0.702430i | \(-0.752098\pi\) | ||||
−0.711753 | + | 0.702430i | \(0.752098\pi\) | |||||||
\(620\) | −15.7082 | −0.630857 | ||||||||
\(621\) | −48.9443 | −1.96407 | ||||||||
\(622\) | 21.3262 | 0.855104 | ||||||||
\(623\) | −3.14590 | −0.126038 | ||||||||
\(624\) | −7.23607 | −0.289675 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.85410 | 0.113891 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | 22.8328 | 0.908960 | 0.454480 | − | 0.890757i | \(-0.349825\pi\) | ||||
0.454480 | + | 0.890757i | \(0.349825\pi\) | |||||||
\(632\) | −0.326238 | −0.0129770 | ||||||||
\(633\) | 27.8885 | 1.10847 | ||||||||
\(634\) | 25.6869 | 1.02016 | ||||||||
\(635\) | −57.8328 | −2.29503 | ||||||||
\(636\) | −8.32624 | −0.330157 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0.708204 | 0.0280381 | ||||||||
\(639\) | −3.27051 | −0.129379 | ||||||||
\(640\) | 2.61803 | 0.103487 | ||||||||
\(641\) | −7.41641 | −0.292930 | −0.146465 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146465 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(642\) | −31.8885 | −1.25854 | ||||||||
\(643\) | 21.4164 | 0.844581 | 0.422290 | − | 0.906461i | \(-0.361226\pi\) | ||||
0.422290 | + | 0.906461i | \(0.361226\pi\) | |||||||
\(644\) | 8.94427 | 0.352454 | ||||||||
\(645\) | −16.3262 | −0.642845 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.326238 | −0.0128257 | −0.00641287 | − | 0.999979i | \(-0.502041\pi\) | ||||
−0.00641287 | + | 0.999979i | \(0.502041\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | 56.1246 | 2.20308 | ||||||||
\(650\) | 8.29180 | 0.325231 | ||||||||
\(651\) | 9.70820 | 0.380495 | ||||||||
\(652\) | −20.2705 | −0.793854 | ||||||||
\(653\) | −13.5279 | −0.529386 | −0.264693 | − | 0.964333i | \(-0.585271\pi\) | ||||
−0.264693 | + | 0.964333i | \(0.585271\pi\) | |||||||
\(654\) | −17.5623 | −0.686741 | ||||||||
\(655\) | 11.7082 | 0.457477 | ||||||||
\(656\) | −9.56231 | −0.373345 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.8541 | 0.423137 | ||||||||
\(659\) | −0.875388 | −0.0341003 | −0.0170501 | − | 0.999855i | \(-0.505427\pi\) | ||||
−0.0170501 | + | 0.999855i | \(0.505427\pi\) | |||||||
\(660\) | 20.5623 | 0.800387 | ||||||||
\(661\) | −26.8328 | −1.04368 | −0.521838 | − | 0.853045i | \(-0.674753\pi\) | ||||
−0.521838 | + | 0.853045i | \(0.674753\pi\) | |||||||
\(662\) | 3.70820 | 0.144123 | ||||||||
\(663\) | −5.52786 | −0.214684 | ||||||||
\(664\) | −11.2361 | −0.436044 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.00000 | 0.116248 | ||||||||
\(667\) | 1.30495 | 0.0505279 | ||||||||
\(668\) | −10.0000 | −0.386912 | ||||||||
\(669\) | −8.47214 | −0.327552 | ||||||||
\(670\) | 13.7082 | 0.529594 | ||||||||
\(671\) | 41.5623 | 1.60450 | ||||||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | −3.05573 | −0.117790 | −0.0588948 | − | 0.998264i | \(-0.518758\pi\) | ||||
−0.0588948 | + | 0.998264i | \(0.518758\pi\) | |||||||
\(674\) | −9.70820 | −0.373946 | ||||||||
\(675\) | −10.1459 | −0.390516 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | −41.7082 | −1.60298 | −0.801488 | − | 0.598011i | \(-0.795958\pi\) | ||||
−0.801488 | + | 0.598011i | \(0.795958\pi\) | |||||||
\(678\) | −16.1803 | −0.621402 | ||||||||
\(679\) | 7.14590 | 0.274234 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 31.4164 | 1.20388 | ||||||||
\(682\) | 29.1246 | 1.11524 | ||||||||
\(683\) | −2.29180 | −0.0876931 | −0.0438466 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438466 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.85410 | −0.338298 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 38.5967 | 1.47256 | ||||||||
\(688\) | 3.85410 | 0.146936 | ||||||||
\(689\) | 23.0132 | 0.876731 | ||||||||
\(690\) | 37.8885 | 1.44239 | ||||||||
\(691\) | 20.5410 | 0.781417 | 0.390709 | − | 0.920514i | \(-0.372230\pi\) | ||||
0.390709 | + | 0.920514i | \(0.372230\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | 1.85410 | 0.0704315 | ||||||||
\(694\) | −8.94427 | −0.339520 | ||||||||
\(695\) | −15.7082 | −0.595846 | ||||||||
\(696\) | −0.236068 | −0.00894813 | ||||||||
\(697\) | −7.30495 | −0.276695 | ||||||||
\(698\) | 16.8328 | 0.637131 | ||||||||
\(699\) | 6.61803 | 0.250317 | ||||||||
\(700\) | 1.85410 | 0.0700785 | ||||||||
\(701\) | −5.23607 | −0.197764 | −0.0988818 | − | 0.995099i | \(-0.531527\pi\) | ||||
−0.0988818 | + | 0.995099i | \(0.531527\pi\) | |||||||
\(702\) | −24.4721 | −0.923641 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.85410 | −0.182946 | ||||||||
\(705\) | 45.9787 | 1.73166 | ||||||||
\(706\) | −13.4164 | −0.504933 | ||||||||
\(707\) | 2.94427 | 0.110731 | ||||||||
\(708\) | −18.7082 | −0.703097 | ||||||||
\(709\) | 9.12461 | 0.342682 | 0.171341 | − | 0.985212i | \(-0.445190\pi\) | ||||
0.171341 | + | 0.985212i | \(0.445190\pi\) | |||||||
\(710\) | 22.4164 | 0.841273 | ||||||||
\(711\) | −0.124612 | −0.00467331 | ||||||||
\(712\) | 3.14590 | 0.117898 | ||||||||
\(713\) | 53.6656 | 2.00979 | ||||||||
\(714\) | −1.23607 | −0.0462587 | ||||||||
\(715\) | −56.8328 | −2.12543 | ||||||||
\(716\) | 17.7082 | 0.661787 | ||||||||
\(717\) | 22.9443 | 0.856870 | ||||||||
\(718\) | −2.29180 | −0.0855291 | ||||||||
\(719\) | 16.3607 | 0.610150 | 0.305075 | − | 0.952328i | \(-0.401318\pi\) | ||||
0.305075 | + | 0.952328i | \(0.401318\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 8.94427 | 0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.4164 | 1.05682 | ||||||||
\(724\) | −7.41641 | −0.275629 | ||||||||
\(725\) | 0.270510 | 0.0100465 | ||||||||
\(726\) | −20.3262 | −0.754377 | ||||||||
\(727\) | 28.5623 | 1.05932 | 0.529659 | − | 0.848211i | \(-0.322320\pi\) | ||||
0.529659 | + | 0.848211i | \(0.322320\pi\) | |||||||
\(728\) | 4.47214 | 0.165748 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.94427 | 0.108898 | ||||||||
\(732\) | −13.8541 | −0.512062 | ||||||||
\(733\) | −19.5623 | −0.722550 | −0.361275 | − | 0.932459i | \(-0.617658\pi\) | ||||
−0.361275 | + | 0.932459i | \(0.617658\pi\) | |||||||
\(734\) | 6.27051 | 0.231449 | ||||||||
\(735\) | −4.23607 | −0.156250 | ||||||||
\(736\) | −8.94427 | −0.329690 | ||||||||
\(737\) | −25.4164 | −0.936225 | ||||||||
\(738\) | −3.65248 | −0.134449 | ||||||||
\(739\) | 35.2705 | 1.29745 | 0.648723 | − | 0.761024i | \(-0.275303\pi\) | ||||
0.648723 | + | 0.761024i | \(0.275303\pi\) | |||||||
\(740\) | −20.5623 | −0.755885 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.14590 | 0.188912 | ||||||||
\(743\) | 24.9787 | 0.916380 | 0.458190 | − | 0.888854i | \(-0.348498\pi\) | ||||
0.458190 | + | 0.888854i | \(0.348498\pi\) | |||||||
\(744\) | −9.70820 | −0.355920 | ||||||||
\(745\) | 45.1246 | 1.65324 | ||||||||
\(746\) | −14.6180 | −0.535204 | ||||||||
\(747\) | −4.29180 | −0.157029 | ||||||||
\(748\) | −3.70820 | −0.135585 | ||||||||
\(749\) | 19.7082 | 0.720122 | ||||||||
\(750\) | −13.3262 | −0.486605 | ||||||||
\(751\) | −0.326238 | −0.0119046 | −0.00595230 | − | 0.999982i | \(-0.501895\pi\) | ||||
−0.00595230 | + | 0.999982i | \(0.501895\pi\) | |||||||
\(752\) | −10.8541 | −0.395808 | ||||||||
\(753\) | 14.6525 | 0.533966 | ||||||||
\(754\) | 0.652476 | 0.0237618 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | −5.47214 | −0.199020 | ||||||||
\(757\) | 46.2492 | 1.68096 | 0.840478 | − | 0.541845i | \(-0.182274\pi\) | ||||
0.840478 | + | 0.541845i | \(0.182274\pi\) | |||||||
\(758\) | −32.1803 | −1.16884 | ||||||||
\(759\) | −70.2492 | −2.54989 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7771 | −0.644419 | −0.322209 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322209 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(762\) | −35.7426 | −1.29482 | ||||||||
\(763\) | 10.8541 | 0.392945 | ||||||||
\(764\) | 14.9443 | 0.540665 | ||||||||
\(765\) | 0.763932 | 0.0276200 | ||||||||
\(766\) | 13.1246 | 0.474212 | ||||||||
\(767\) | 51.7082 | 1.86708 | ||||||||
\(768\) | 1.61803 | 0.0583858 | ||||||||
\(769\) | 12.2918 | 0.443254 | 0.221627 | − | 0.975132i | \(-0.428863\pi\) | ||||
0.221627 | + | 0.975132i | \(0.428863\pi\) | |||||||
\(770\) | −12.7082 | −0.457972 | ||||||||
\(771\) | 15.9443 | 0.574219 | ||||||||
\(772\) | −20.9443 | −0.753801 | ||||||||
\(773\) | 1.70820 | 0.0614398 | 0.0307199 | − | 0.999528i | \(-0.490220\pi\) | ||||
0.0307199 | + | 0.999528i | \(0.490220\pi\) | |||||||
\(774\) | 1.47214 | 0.0529148 | ||||||||
\(775\) | 11.1246 | 0.399608 | ||||||||
\(776\) | −7.14590 | −0.256523 | ||||||||
\(777\) | 12.7082 | 0.455904 | ||||||||
\(778\) | 37.3050 | 1.33745 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 18.9443 | 0.678314 | ||||||||
\(781\) | −41.5623 | −1.48722 | ||||||||
\(782\) | −6.83282 | −0.244341 | ||||||||
\(783\) | −0.798374 | −0.0285316 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −7.47214 | −0.266692 | ||||||||
\(786\) | 7.23607 | 0.258102 | ||||||||
\(787\) | −27.2705 | −0.972089 | −0.486044 | − | 0.873934i | \(-0.661561\pi\) | ||||
−0.486044 | + | 0.873934i | \(0.661561\pi\) | |||||||
\(788\) | −5.23607 | −0.186527 | ||||||||
\(789\) | 20.4721 | 0.728827 | ||||||||
\(790\) | 0.854102 | 0.0303876 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | −1.85410 | −0.0658826 | ||||||||
\(793\) | 38.2918 | 1.35978 | ||||||||
\(794\) | 28.5623 | 1.01364 | ||||||||
\(795\) | 21.7984 | 0.773109 | ||||||||
\(796\) | 1.56231 | 0.0553745 | ||||||||
\(797\) | −44.8328 | −1.58806 | −0.794030 | − | 0.607879i | \(-0.792021\pi\) | ||||
−0.794030 | + | 0.607879i | \(0.792021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.29180 | −0.293343 | ||||||||
\(800\) | −1.85410 | −0.0655524 | ||||||||
\(801\) | 1.20163 | 0.0424574 | ||||||||
\(802\) | 25.4164 | 0.897485 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.47214 | 0.298789 | ||||||||
\(805\) | −23.4164 | −0.825320 | ||||||||
\(806\) | 26.8328 | 0.945146 | ||||||||
\(807\) | −7.41641 | −0.261070 | ||||||||
\(808\) | −2.94427 | −0.103579 | ||||||||
\(809\) | −16.0344 | −0.563741 | −0.281870 | − | 0.959452i | \(-0.590955\pi\) | ||||
−0.281870 | + | 0.959452i | \(0.590955\pi\) | |||||||
\(810\) | −20.1803 | −0.709065 | ||||||||
\(811\) | 2.02129 | 0.0709770 | 0.0354885 | − | 0.999370i | \(-0.488701\pi\) | ||||
0.0354885 | + | 0.999370i | \(0.488701\pi\) | |||||||
\(812\) | 0.145898 | 0.00512002 | ||||||||
\(813\) | 3.94427 | 0.138332 | ||||||||
\(814\) | 38.1246 | 1.33627 | ||||||||
\(815\) | 53.0689 | 1.85892 | ||||||||
\(816\) | 1.23607 | 0.0432710 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.79837 | 0.0628787 | ||||||||
\(819\) | 1.70820 | 0.0596895 | ||||||||
\(820\) | 25.0344 | 0.874241 | ||||||||
\(821\) | 6.87539 | 0.239953 | 0.119976 | − | 0.992777i | \(-0.461718\pi\) | ||||
0.119976 | + | 0.992777i | \(0.461718\pi\) | |||||||
\(822\) | −5.47214 | −0.190863 | ||||||||
\(823\) | −2.29180 | −0.0798870 | −0.0399435 | − | 0.999202i | \(-0.512718\pi\) | ||||
−0.0399435 | + | 0.999202i | \(0.512718\pi\) | |||||||
\(824\) | −8.94427 | −0.311588 | ||||||||
\(825\) | −14.5623 | −0.506994 | ||||||||
\(826\) | 11.5623 | 0.402304 | ||||||||
\(827\) | −43.9574 | −1.52855 | −0.764275 | − | 0.644891i | \(-0.776903\pi\) | ||||
−0.764275 | + | 0.644891i | \(0.776903\pi\) | |||||||
\(828\) | −3.41641 | −0.118728 | ||||||||
\(829\) | −35.1246 | −1.21993 | −0.609964 | − | 0.792429i | \(-0.708816\pi\) | ||||
−0.609964 | + | 0.792429i | \(0.708816\pi\) | |||||||
\(830\) | 29.4164 | 1.02106 | ||||||||
\(831\) | −41.1246 | −1.42660 | ||||||||
\(832\) | −4.47214 | −0.155043 | ||||||||
\(833\) | 0.763932 | 0.0264687 | ||||||||
\(834\) | −9.70820 | −0.336168 | ||||||||
\(835\) | 26.1803 | 0.906008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.8328 | −1.13487 | ||||||||
\(838\) | 12.6525 | 0.437073 | ||||||||
\(839\) | −4.83282 | −0.166847 | −0.0834237 | − | 0.996514i | \(-0.526585\pi\) | ||||
−0.0834237 | + | 0.996514i | \(0.526585\pi\) | |||||||
\(840\) | 4.23607 | 0.146158 | ||||||||
\(841\) | −28.9787 | −0.999266 | ||||||||
\(842\) | −19.5279 | −0.672975 | ||||||||
\(843\) | −37.8885 | −1.30495 | ||||||||
\(844\) | 17.2361 | 0.593290 | ||||||||
\(845\) | −18.3262 | −0.630442 | ||||||||
\(846\) | −4.14590 | −0.142539 | ||||||||
\(847\) | 12.5623 | 0.431646 | ||||||||
\(848\) | −5.14590 | −0.176711 | ||||||||
\(849\) | 12.9443 | 0.444246 | ||||||||
\(850\) | −1.41641 | −0.0485824 | ||||||||
\(851\) | 70.2492 | 2.40811 | ||||||||
\(852\) | 13.8541 | 0.474634 | ||||||||
\(853\) | −23.2705 | −0.796767 | −0.398384 | − | 0.917219i | \(-0.630429\pi\) | ||||
−0.398384 | + | 0.917219i | \(0.630429\pi\) | |||||||
\(854\) | 8.56231 | 0.292996 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.7082 | −0.673613 | ||||||||
\(857\) | 32.2492 | 1.10161 | 0.550806 | − | 0.834633i | \(-0.314320\pi\) | ||||
0.550806 | + | 0.834633i | \(0.314320\pi\) | |||||||
\(858\) | −35.1246 | −1.19913 | ||||||||
\(859\) | −34.0000 | −1.16007 | −0.580033 | − | 0.814593i | \(-0.696960\pi\) | ||||
−0.580033 | + | 0.814593i | \(0.696960\pi\) | |||||||
\(860\) | −10.0902 | −0.344072 | ||||||||
\(861\) | −15.4721 | −0.527289 | ||||||||
\(862\) | −22.8541 | −0.778414 | ||||||||
\(863\) | 48.9787 | 1.66725 | 0.833627 | − | 0.552327i | \(-0.186260\pi\) | ||||
0.833627 | + | 0.552327i | \(0.186260\pi\) | |||||||
\(864\) | 5.47214 | 0.186166 | ||||||||
\(865\) | −47.1246 | −1.60228 | ||||||||
\(866\) | 3.38197 | 0.114924 | ||||||||
\(867\) | −26.5623 | −0.902103 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | −1.58359 | −0.0537197 | ||||||||
\(870\) | 0.618034 | 0.0209533 | ||||||||
\(871\) | −23.4164 | −0.793435 | ||||||||
\(872\) | −10.8541 | −0.367566 | ||||||||
\(873\) | −2.72949 | −0.0923792 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.23607 | 0.278430 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.3951 | −1.60042 | −0.800210 | − | 0.599720i | \(-0.795279\pi\) | ||||
−0.800210 | + | 0.599720i | \(0.795279\pi\) | |||||||
\(878\) | 2.18034 | 0.0735829 | ||||||||
\(879\) | 50.8328 | 1.71455 | ||||||||
\(880\) | 12.7082 | 0.428393 | ||||||||
\(881\) | 9.81966 | 0.330833 | 0.165416 | − | 0.986224i | \(-0.447103\pi\) | ||||
0.165416 | + | 0.986224i | \(0.447103\pi\) | |||||||
\(882\) | 0.381966 | 0.0128615 | ||||||||
\(883\) | −27.6869 | −0.931739 | −0.465869 | − | 0.884853i | \(-0.654258\pi\) | ||||
−0.465869 | + | 0.884853i | \(0.654258\pi\) | |||||||
\(884\) | −3.41641 | −0.114906 | ||||||||
\(885\) | 48.9787 | 1.64640 | ||||||||
\(886\) | −1.09017 | −0.0366250 | ||||||||
\(887\) | 2.83282 | 0.0951166 | 0.0475583 | − | 0.998868i | \(-0.484856\pi\) | ||||
0.0475583 | + | 0.998868i | \(0.484856\pi\) | |||||||
\(888\) | −12.7082 | −0.426459 | ||||||||
\(889\) | 22.0902 | 0.740881 | ||||||||
\(890\) | −8.23607 | −0.276074 | ||||||||
\(891\) | 37.4164 | 1.25350 | ||||||||
\(892\) | −5.23607 | −0.175317 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 27.8885 | 0.932732 | ||||||||
\(895\) | −46.3607 | −1.54967 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −64.7214 | −2.16098 | ||||||||
\(898\) | 0.291796 | 0.00973736 | ||||||||
\(899\) | 0.875388 | 0.0291958 | ||||||||
\(900\) | −0.708204 | −0.0236068 | ||||||||
\(901\) | −3.93112 | −0.130964 | ||||||||
\(902\) | −46.4164 | −1.54550 | ||||||||
\(903\) | 6.23607 | 0.207523 | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | 19.4164 | 0.645423 | ||||||||
\(906\) | −4.94427 | −0.164262 | ||||||||
\(907\) | 48.0000 | 1.59381 | 0.796907 | − | 0.604102i | \(-0.206468\pi\) | ||||
0.796907 | + | 0.604102i | \(0.206468\pi\) | |||||||
\(908\) | 19.4164 | 0.644356 | ||||||||
\(909\) | −1.12461 | −0.0373010 | ||||||||
\(910\) | −11.7082 | −0.388123 | ||||||||
\(911\) | −49.8541 | −1.65174 | −0.825870 | − | 0.563861i | \(-0.809316\pi\) | ||||
−0.825870 | + | 0.563861i | \(0.809316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.5410 | −1.80504 | ||||||||
\(914\) | −31.1459 | −1.03021 | ||||||||
\(915\) | 36.2705 | 1.19907 | ||||||||
\(916\) | 23.8541 | 0.788162 | ||||||||
\(917\) | −4.47214 | −0.147683 | ||||||||
\(918\) | 4.18034 | 0.137972 | ||||||||
\(919\) | −12.2918 | −0.405469 | −0.202734 | − | 0.979234i | \(-0.564983\pi\) | ||||
−0.202734 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(920\) | 23.4164 | 0.772016 | ||||||||
\(921\) | 30.7082 | 1.01187 | ||||||||
\(922\) | 41.5066 | 1.36695 | ||||||||
\(923\) | −38.2918 | −1.26039 | ||||||||
\(924\) | −7.85410 | −0.258381 | ||||||||
\(925\) | 14.5623 | 0.478806 | ||||||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | −3.41641 | −0.112210 | ||||||||
\(928\) | −0.145898 | −0.00478934 | ||||||||
\(929\) | 42.7639 | 1.40304 | 0.701520 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701520 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(930\) | 25.4164 | 0.833437 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.09017 | 0.133978 | ||||||||
\(933\) | −34.5066 | −1.12969 | ||||||||
\(934\) | 40.3607 | 1.32064 | ||||||||
\(935\) | 9.70820 | 0.317492 | ||||||||
\(936\) | −1.70820 | −0.0558344 | ||||||||
\(937\) | 13.7082 | 0.447828 | 0.223914 | − | 0.974609i | \(-0.428117\pi\) | ||||
0.223914 | + | 0.974609i | \(0.428117\pi\) | |||||||
\(938\) | −5.23607 | −0.170964 | ||||||||
\(939\) | 16.1803 | 0.528025 | ||||||||
\(940\) | 28.4164 | 0.926841 | ||||||||
\(941\) | −33.7082 | −1.09886 | −0.549428 | − | 0.835541i | \(-0.685154\pi\) | ||||
−0.549428 | + | 0.835541i | \(0.685154\pi\) | |||||||
\(942\) | −4.61803 | −0.150464 | ||||||||
\(943\) | −85.5279 | −2.78517 | ||||||||
\(944\) | −11.5623 | −0.376321 | ||||||||
\(945\) | 14.3262 | 0.466033 | ||||||||
\(946\) | 18.7082 | 0.608256 | ||||||||
\(947\) | −43.1459 | −1.40205 | −0.701027 | − | 0.713135i | \(-0.747275\pi\) | ||||
−0.701027 | + | 0.713135i | \(0.747275\pi\) | |||||||
\(948\) | 0.527864 | 0.0171442 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.5623 | −1.34775 | ||||||||
\(952\) | −0.763932 | −0.0247592 | ||||||||
\(953\) | 2.29180 | 0.0742386 | 0.0371193 | − | 0.999311i | \(-0.488182\pi\) | ||||
0.0371193 | + | 0.999311i | \(0.488182\pi\) | |||||||
\(954\) | −1.96556 | −0.0636373 | ||||||||
\(955\) | −39.1246 | −1.26604 | ||||||||
\(956\) | 14.1803 | 0.458625 | ||||||||
\(957\) | −1.14590 | −0.0370416 | ||||||||
\(958\) | −36.3262 | −1.17365 | ||||||||
\(959\) | 3.38197 | 0.109209 | ||||||||
\(960\) | −4.23607 | −0.136719 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 35.1246 | 1.13246 | ||||||||
\(963\) | −7.52786 | −0.242582 | ||||||||
\(964\) | 17.5623 | 0.565644 | ||||||||
\(965\) | 54.8328 | 1.76513 | ||||||||
\(966\) | −14.4721 | −0.465633 | ||||||||
\(967\) | 54.2492 | 1.74454 | 0.872269 | − | 0.489027i | \(-0.162648\pi\) | ||||
0.872269 | + | 0.489027i | \(0.162648\pi\) | |||||||
\(968\) | −12.5623 | −0.403768 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18.7082 | 0.600684 | ||||||||
\(971\) | 11.7295 | 0.376417 | 0.188209 | − | 0.982129i | \(-0.439732\pi\) | ||||
0.188209 | + | 0.982129i | \(0.439732\pi\) | |||||||
\(972\) | 3.94427 | 0.126513 | ||||||||
\(973\) | 6.00000 | 0.192351 | ||||||||
\(974\) | −16.9098 | −0.541826 | ||||||||
\(975\) | −13.4164 | −0.429669 | ||||||||
\(976\) | −8.56231 | −0.274073 | ||||||||
\(977\) | 35.7082 | 1.14241 | 0.571203 | − | 0.820809i | \(-0.306477\pi\) | ||||
0.571203 | + | 0.820809i | \(0.306477\pi\) | |||||||
\(978\) | 32.7984 | 1.04878 | ||||||||
\(979\) | 15.2705 | 0.488048 | ||||||||
\(980\) | −2.61803 | −0.0836300 | ||||||||
\(981\) | −4.14590 | −0.132368 | ||||||||
\(982\) | 40.3607 | 1.28796 | ||||||||
\(983\) | 19.1246 | 0.609980 | 0.304990 | − | 0.952355i | \(-0.401347\pi\) | ||||
0.304990 | + | 0.952355i | \(0.401347\pi\) | |||||||
\(984\) | 15.4721 | 0.493234 | ||||||||
\(985\) | 13.7082 | 0.436780 | ||||||||
\(986\) | −0.111456 | −0.00354949 | ||||||||
\(987\) | −17.5623 | −0.559014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.4721 | 1.09615 | ||||||||
\(990\) | 4.85410 | 0.154273 | ||||||||
\(991\) | 47.3951 | 1.50556 | 0.752778 | − | 0.658275i | \(-0.228713\pi\) | ||||
0.752778 | + | 0.658275i | \(0.228713\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | −6.00000 | −0.190404 | ||||||||
\(994\) | −8.56231 | −0.271580 | ||||||||
\(995\) | −4.09017 | −0.129667 | ||||||||
\(996\) | 18.1803 | 0.576066 | ||||||||
\(997\) | −51.8541 | −1.64224 | −0.821118 | − | 0.570759i | \(-0.806649\pi\) | ||||
−0.821118 | + | 0.570759i | \(0.806649\pi\) | |||||||
\(998\) | 18.6869 | 0.591524 | ||||||||
\(999\) | −42.9787 | −1.35979 |
(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 | 5054.2.a.g.1.2 | ✓ | 2 | |
19.18 | odd | 2 | 5054.2.a.l.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.g.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5054.2.a.l.1.1 | yes | 2 | 19.18 | odd | 2 |