Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
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: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 2.61803 | 1.51152 | 0.755761 | − | 0.654847i | \(-0.227267\pi\) | ||||
0.755761 | + | 0.654847i | \(0.227267\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.61803 | 1.06881 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.61803 | 0.755761 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.61803 | −0.675973 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.61803 | −0.392431 | −0.196215 | − | 0.980561i | \(-0.562865\pi\) | ||||
−0.196215 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(18\) | 3.85410 | 0.908421 | ||||||||
\(19\) | 6.85410 | 1.57244 | 0.786219 | − | 0.617947i | \(-0.212036\pi\) | ||||
0.786219 | + | 0.617947i | \(0.212036\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.61803 | 0.571302 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 2.61803 | 0.534404 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.23607 | 0.600923 | 0.300461 | − | 0.953794i | \(-0.402859\pi\) | ||||
0.300461 | + | 0.953794i | \(0.402859\pi\) | |||||||
\(30\) | −2.61803 | −0.477985 | ||||||||
\(31\) | −1.23607 | −0.222004 | −0.111002 | − | 0.993820i | \(-0.535406\pi\) | ||||
−0.111002 | + | 0.993820i | \(0.535406\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.61803 | −0.277491 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.85410 | 0.642350 | ||||||||
\(37\) | −6.47214 | −1.06401 | −0.532006 | − | 0.846740i | \(-0.678562\pi\) | ||||
−0.532006 | + | 0.846740i | \(0.678562\pi\) | |||||||
\(38\) | 6.85410 | 1.11188 | ||||||||
\(39\) | 5.23607 | 0.838442 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.3262 | −1.61269 | −0.806344 | − | 0.591447i | \(-0.798557\pi\) | ||||
−0.806344 | + | 0.591447i | \(0.798557\pi\) | |||||||
\(42\) | 2.61803 | 0.403971 | ||||||||
\(43\) | 1.85410 | 0.282748 | 0.141374 | − | 0.989956i | \(-0.454848\pi\) | ||||
0.141374 | + | 0.989956i | \(0.454848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.85410 | −0.574536 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 9.23607 | 1.34722 | 0.673609 | − | 0.739087i | \(-0.264743\pi\) | ||||
0.673609 | + | 0.739087i | \(0.264743\pi\) | |||||||
\(48\) | 2.61803 | 0.377881 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.23607 | −0.593168 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 1.23607 | 0.169787 | 0.0848935 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848935 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(54\) | 2.23607 | 0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 17.9443 | 2.37678 | ||||||||
\(58\) | 3.23607 | 0.424917 | ||||||||
\(59\) | −7.61803 | −0.991784 | −0.495892 | − | 0.868384i | \(-0.665159\pi\) | ||||
−0.495892 | + | 0.868384i | \(0.665159\pi\) | |||||||
\(60\) | −2.61803 | −0.337987 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | −1.23607 | −0.156981 | ||||||||
\(63\) | 3.85410 | 0.485571 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09017 | 0.744033 | 0.372016 | − | 0.928226i | \(-0.378667\pi\) | ||||
0.372016 | + | 0.928226i | \(0.378667\pi\) | |||||||
\(68\) | −1.61803 | −0.196215 | ||||||||
\(69\) | 15.7082 | 1.89105 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −9.70820 | −1.15215 | −0.576076 | − | 0.817396i | \(-0.695417\pi\) | ||||
−0.576076 | + | 0.817396i | \(0.695417\pi\) | |||||||
\(72\) | 3.85410 | 0.454210 | ||||||||
\(73\) | 13.8541 | 1.62150 | 0.810750 | − | 0.585393i | \(-0.199060\pi\) | ||||
0.810750 | + | 0.585393i | \(0.199060\pi\) | |||||||
\(74\) | −6.47214 | −0.752371 | ||||||||
\(75\) | 2.61803 | 0.302305 | ||||||||
\(76\) | 6.85410 | 0.786219 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.23607 | 0.592868 | ||||||||
\(79\) | −8.47214 | −0.953190 | −0.476595 | − | 0.879123i | \(-0.658129\pi\) | ||||
−0.476595 | + | 0.879123i | \(0.658129\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −10.3262 | −1.14034 | ||||||||
\(83\) | 10.3262 | 1.13345 | 0.566726 | − | 0.823906i | \(-0.308210\pi\) | ||||
0.566726 | + | 0.823906i | \(0.308210\pi\) | |||||||
\(84\) | 2.61803 | 0.285651 | ||||||||
\(85\) | 1.61803 | 0.175500 | ||||||||
\(86\) | 1.85410 | 0.199933 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0902 | 1.38756 | 0.693778 | − | 0.720189i | \(-0.255945\pi\) | ||||
0.693778 | + | 0.720189i | \(0.255945\pi\) | |||||||
\(90\) | −3.85410 | −0.406258 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −3.23607 | −0.335565 | ||||||||
\(94\) | 9.23607 | 0.952628 | ||||||||
\(95\) | −6.85410 | −0.703216 | ||||||||
\(96\) | 2.61803 | 0.267202 | ||||||||
\(97\) | −9.56231 | −0.970905 | −0.485453 | − | 0.874263i | \(-0.661345\pi\) | ||||
−0.485453 | + | 0.874263i | \(0.661345\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.94427 | 0.889988 | 0.444994 | − | 0.895533i | \(-0.353206\pi\) | ||||
0.444994 | + | 0.895533i | \(0.353206\pi\) | |||||||
\(102\) | −4.23607 | −0.419433 | ||||||||
\(103\) | −16.9443 | −1.66957 | −0.834784 | − | 0.550577i | \(-0.814408\pi\) | ||||
−0.834784 | + | 0.550577i | \(0.814408\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −2.61803 | −0.255494 | ||||||||
\(106\) | 1.23607 | 0.120058 | ||||||||
\(107\) | 15.3820 | 1.48703 | 0.743515 | − | 0.668719i | \(-0.233157\pi\) | ||||
0.743515 | + | 0.668719i | \(0.233157\pi\) | |||||||
\(108\) | 2.23607 | 0.215166 | ||||||||
\(109\) | −0.472136 | −0.0452224 | −0.0226112 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226112 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.9443 | −1.60828 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −9.32624 | −0.877339 | −0.438669 | − | 0.898649i | \(-0.644550\pi\) | ||||
−0.438669 | + | 0.898649i | \(0.644550\pi\) | |||||||
\(114\) | 17.9443 | 1.68064 | ||||||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | 3.23607 | 0.300461 | ||||||||
\(117\) | 7.70820 | 0.712624 | ||||||||
\(118\) | −7.61803 | −0.701297 | ||||||||
\(119\) | −1.61803 | −0.148325 | ||||||||
\(120\) | −2.61803 | −0.238993 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.52786 | −0.319398 | ||||||||
\(123\) | −27.0344 | −2.43761 | ||||||||
\(124\) | −1.23607 | −0.111002 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.85410 | 0.343351 | ||||||||
\(127\) | −11.4164 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.85410 | 0.427380 | ||||||||
\(130\) | −2.00000 | −0.175412 | ||||||||
\(131\) | −7.79837 | −0.681347 | −0.340674 | − | 0.940182i | \(-0.610655\pi\) | ||||
−0.340674 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.85410 | 0.594326 | ||||||||
\(134\) | 6.09017 | 0.526111 | ||||||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | −1.61803 | −0.138745 | ||||||||
\(137\) | −1.09017 | −0.0931395 | −0.0465698 | − | 0.998915i | \(-0.514829\pi\) | ||||
−0.0465698 | + | 0.998915i | \(0.514829\pi\) | |||||||
\(138\) | 15.7082 | 1.33717 | ||||||||
\(139\) | 18.4721 | 1.56679 | 0.783393 | − | 0.621527i | \(-0.213487\pi\) | ||||
0.783393 | + | 0.621527i | \(0.213487\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 24.1803 | 2.03635 | ||||||||
\(142\) | −9.70820 | −0.814694 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.85410 | 0.321175 | ||||||||
\(145\) | −3.23607 | −0.268741 | ||||||||
\(146\) | 13.8541 | 1.14657 | ||||||||
\(147\) | 2.61803 | 0.215932 | ||||||||
\(148\) | −6.47214 | −0.532006 | ||||||||
\(149\) | 24.1803 | 1.98093 | 0.990465 | − | 0.137762i | \(-0.0439910\pi\) | ||||
0.990465 | + | 0.137762i | \(0.0439910\pi\) | |||||||
\(150\) | 2.61803 | 0.213762 | ||||||||
\(151\) | 2.29180 | 0.186504 | 0.0932519 | − | 0.995643i | \(-0.470274\pi\) | ||||
0.0932519 | + | 0.995643i | \(0.470274\pi\) | |||||||
\(152\) | 6.85410 | 0.555941 | ||||||||
\(153\) | −6.23607 | −0.504156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.23607 | 0.0992834 | ||||||||
\(156\) | 5.23607 | 0.419221 | ||||||||
\(157\) | 0.291796 | 0.0232879 | 0.0116439 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116439 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(158\) | −8.47214 | −0.674007 | ||||||||
\(159\) | 3.23607 | 0.256637 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | −5.70820 | −0.448479 | ||||||||
\(163\) | 2.85410 | 0.223551 | 0.111775 | − | 0.993734i | \(-0.464346\pi\) | ||||
0.111775 | + | 0.993734i | \(0.464346\pi\) | |||||||
\(164\) | −10.3262 | −0.806344 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3262 | 0.801471 | ||||||||
\(167\) | 6.47214 | 0.500829 | 0.250414 | − | 0.968139i | \(-0.419433\pi\) | ||||
0.250414 | + | 0.968139i | \(0.419433\pi\) | |||||||
\(168\) | 2.61803 | 0.201986 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 1.61803 | 0.124098 | ||||||||
\(171\) | 26.4164 | 2.02011 | ||||||||
\(172\) | 1.85410 | 0.141374 | ||||||||
\(173\) | 12.0000 | 0.912343 | 0.456172 | − | 0.889892i | \(-0.349220\pi\) | ||||
0.456172 | + | 0.889892i | \(0.349220\pi\) | |||||||
\(174\) | 8.47214 | 0.642271 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.9443 | −1.49910 | ||||||||
\(178\) | 13.0902 | 0.981150 | ||||||||
\(179\) | −6.38197 | −0.477011 | −0.238505 | − | 0.971141i | \(-0.576657\pi\) | ||||
−0.238505 | + | 0.971141i | \(0.576657\pi\) | |||||||
\(180\) | −3.85410 | −0.287268 | ||||||||
\(181\) | 3.52786 | 0.262224 | 0.131112 | − | 0.991368i | \(-0.458145\pi\) | ||||
0.131112 | + | 0.991368i | \(0.458145\pi\) | |||||||
\(182\) | 2.00000 | 0.148250 | ||||||||
\(183\) | −9.23607 | −0.682750 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 6.47214 | 0.475841 | ||||||||
\(186\) | −3.23607 | −0.237280 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.23607 | 0.673609 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | −6.85410 | −0.497249 | ||||||||
\(191\) | −1.52786 | −0.110552 | −0.0552762 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552762 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(192\) | 2.61803 | 0.188940 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −9.56231 | −0.686534 | ||||||||
\(195\) | −5.23607 | −0.374963 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4164 | −1.37639 | −0.688196 | − | 0.725525i | \(-0.741597\pi\) | ||||
−0.688196 | + | 0.725525i | \(0.741597\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.9443 | 1.12462 | ||||||||
\(202\) | 8.94427 | 0.629317 | ||||||||
\(203\) | 3.23607 | 0.227127 | ||||||||
\(204\) | −4.23607 | −0.296584 | ||||||||
\(205\) | 10.3262 | 0.721216 | ||||||||
\(206\) | −16.9443 | −1.18056 | ||||||||
\(207\) | 23.1246 | 1.60727 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.61803 | −0.180662 | ||||||||
\(211\) | 11.2705 | 0.775894 | 0.387947 | − | 0.921682i | \(-0.373184\pi\) | ||||
0.387947 | + | 0.921682i | \(0.373184\pi\) | |||||||
\(212\) | 1.23607 | 0.0848935 | ||||||||
\(213\) | −25.4164 | −1.74150 | ||||||||
\(214\) | 15.3820 | 1.05149 | ||||||||
\(215\) | −1.85410 | −0.126449 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −1.23607 | −0.0839098 | ||||||||
\(218\) | −0.472136 | −0.0319771 | ||||||||
\(219\) | 36.2705 | 2.45093 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.23607 | −0.217681 | ||||||||
\(222\) | −16.9443 | −1.13723 | ||||||||
\(223\) | 6.29180 | 0.421330 | 0.210665 | − | 0.977558i | \(-0.432437\pi\) | ||||
0.210665 | + | 0.977558i | \(0.432437\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 3.85410 | 0.256940 | ||||||||
\(226\) | −9.32624 | −0.620372 | ||||||||
\(227\) | −24.2705 | −1.61089 | −0.805445 | − | 0.592670i | \(-0.798074\pi\) | ||||
−0.805445 | + | 0.592670i | \(0.798074\pi\) | |||||||
\(228\) | 17.9443 | 1.18839 | ||||||||
\(229\) | 11.1246 | 0.735135 | 0.367568 | − | 0.929997i | \(-0.380191\pi\) | ||||
0.367568 | + | 0.929997i | \(0.380191\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23607 | 0.212458 | ||||||||
\(233\) | 10.9098 | 0.714727 | 0.357363 | − | 0.933965i | \(-0.383676\pi\) | ||||
0.357363 | + | 0.933965i | \(0.383676\pi\) | |||||||
\(234\) | 7.70820 | 0.503901 | ||||||||
\(235\) | −9.23607 | −0.602495 | ||||||||
\(236\) | −7.61803 | −0.495892 | ||||||||
\(237\) | −22.1803 | −1.44077 | ||||||||
\(238\) | −1.61803 | −0.104882 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −2.61803 | −0.168993 | ||||||||
\(241\) | −6.27051 | −0.403919 | −0.201960 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201960 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6525 | −1.38901 | ||||||||
\(244\) | −3.52786 | −0.225848 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −27.0344 | −1.72365 | ||||||||
\(247\) | 13.7082 | 0.872232 | ||||||||
\(248\) | −1.23607 | −0.0784904 | ||||||||
\(249\) | 27.0344 | 1.71324 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 26.8328 | 1.69367 | 0.846836 | − | 0.531854i | \(-0.178504\pi\) | ||||
0.846836 | + | 0.531854i | \(0.178504\pi\) | |||||||
\(252\) | 3.85410 | 0.242786 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.4164 | −0.716329 | ||||||||
\(255\) | 4.23607 | 0.265273 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.5623 | 1.84405 | 0.922023 | − | 0.387135i | \(-0.126535\pi\) | ||||
0.922023 | + | 0.387135i | \(0.126535\pi\) | |||||||
\(258\) | 4.85410 | 0.302203 | ||||||||
\(259\) | −6.47214 | −0.402159 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 12.4721 | 0.772006 | ||||||||
\(262\) | −7.79837 | −0.481785 | ||||||||
\(263\) | 20.1803 | 1.24437 | 0.622187 | − | 0.782869i | \(-0.286245\pi\) | ||||
0.622187 | + | 0.782869i | \(0.286245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.23607 | −0.0759311 | ||||||||
\(266\) | 6.85410 | 0.420252 | ||||||||
\(267\) | 34.2705 | 2.09732 | ||||||||
\(268\) | 6.09017 | 0.372016 | ||||||||
\(269\) | −12.1803 | −0.742648 | −0.371324 | − | 0.928503i | \(-0.621096\pi\) | ||||
−0.371324 | + | 0.928503i | \(0.621096\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | −9.41641 | −0.572006 | −0.286003 | − | 0.958229i | \(-0.592327\pi\) | ||||
−0.286003 | + | 0.958229i | \(0.592327\pi\) | |||||||
\(272\) | −1.61803 | −0.0981077 | ||||||||
\(273\) | 5.23607 | 0.316901 | ||||||||
\(274\) | −1.09017 | −0.0658596 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.7082 | 0.945523 | ||||||||
\(277\) | 6.29180 | 0.378037 | 0.189019 | − | 0.981973i | \(-0.439469\pi\) | ||||
0.189019 | + | 0.981973i | \(0.439469\pi\) | |||||||
\(278\) | 18.4721 | 1.10789 | ||||||||
\(279\) | −4.76393 | −0.285209 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −24.0344 | −1.43377 | −0.716887 | − | 0.697189i | \(-0.754434\pi\) | ||||
−0.716887 | + | 0.697189i | \(0.754434\pi\) | |||||||
\(282\) | 24.1803 | 1.43992 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | −9.70820 | −0.576076 | ||||||||
\(285\) | −17.9443 | −1.06293 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3262 | −0.609539 | ||||||||
\(288\) | 3.85410 | 0.227105 | ||||||||
\(289\) | −14.3820 | −0.845998 | ||||||||
\(290\) | −3.23607 | −0.190028 | ||||||||
\(291\) | −25.0344 | −1.46754 | ||||||||
\(292\) | 13.8541 | 0.810750 | ||||||||
\(293\) | 16.4721 | 0.962312 | 0.481156 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481156 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(294\) | 2.61803 | 0.152687 | ||||||||
\(295\) | 7.61803 | 0.443539 | ||||||||
\(296\) | −6.47214 | −0.376185 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.1803 | 1.40073 | ||||||||
\(299\) | 12.0000 | 0.693978 | ||||||||
\(300\) | 2.61803 | 0.151152 | ||||||||
\(301\) | 1.85410 | 0.106869 | ||||||||
\(302\) | 2.29180 | 0.131878 | ||||||||
\(303\) | 23.4164 | 1.34524 | ||||||||
\(304\) | 6.85410 | 0.393110 | ||||||||
\(305\) | 3.52786 | 0.202005 | ||||||||
\(306\) | −6.23607 | −0.356492 | ||||||||
\(307\) | −27.5623 | −1.57306 | −0.786532 | − | 0.617550i | \(-0.788125\pi\) | ||||
−0.786532 | + | 0.617550i | \(0.788125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −44.3607 | −2.52359 | ||||||||
\(310\) | 1.23607 | 0.0702039 | ||||||||
\(311\) | −29.1246 | −1.65151 | −0.825753 | − | 0.564032i | \(-0.809249\pi\) | ||||
−0.825753 | + | 0.564032i | \(0.809249\pi\) | |||||||
\(312\) | 5.23607 | 0.296434 | ||||||||
\(313\) | −0.854102 | −0.0482767 | −0.0241383 | − | 0.999709i | \(-0.507684\pi\) | ||||
−0.0241383 | + | 0.999709i | \(0.507684\pi\) | |||||||
\(314\) | 0.291796 | 0.0164670 | ||||||||
\(315\) | −3.85410 | −0.217154 | ||||||||
\(316\) | −8.47214 | −0.476595 | ||||||||
\(317\) | −20.7639 | −1.16622 | −0.583109 | − | 0.812394i | \(-0.698164\pi\) | ||||
−0.583109 | + | 0.812394i | \(0.698164\pi\) | |||||||
\(318\) | 3.23607 | 0.181470 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 40.2705 | 2.24768 | ||||||||
\(322\) | 6.00000 | 0.334367 | ||||||||
\(323\) | −11.0902 | −0.617074 | ||||||||
\(324\) | −5.70820 | −0.317122 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 2.85410 | 0.158074 | ||||||||
\(327\) | −1.23607 | −0.0683547 | ||||||||
\(328\) | −10.3262 | −0.570171 | ||||||||
\(329\) | 9.23607 | 0.509201 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.03444 | 0.331683 | 0.165841 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165841 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(332\) | 10.3262 | 0.566726 | ||||||||
\(333\) | −24.9443 | −1.36694 | ||||||||
\(334\) | 6.47214 | 0.354140 | ||||||||
\(335\) | −6.09017 | −0.332742 | ||||||||
\(336\) | 2.61803 | 0.142825 | ||||||||
\(337\) | −15.6180 | −0.850769 | −0.425384 | − | 0.905013i | \(-0.639861\pi\) | ||||
−0.425384 | + | 0.905013i | \(0.639861\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | −24.4164 | −1.32612 | ||||||||
\(340\) | 1.61803 | 0.0877502 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 26.4164 | 1.42844 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.85410 | 0.0999665 | ||||||||
\(345\) | −15.7082 | −0.845701 | ||||||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | 5.32624 | 0.285927 | 0.142964 | − | 0.989728i | \(-0.454337\pi\) | ||||
0.142964 | + | 0.989728i | \(0.454337\pi\) | |||||||
\(348\) | 8.47214 | 0.454154 | ||||||||
\(349\) | 5.52786 | 0.295900 | 0.147950 | − | 0.988995i | \(-0.452733\pi\) | ||||
0.147950 | + | 0.988995i | \(0.452733\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.4508 | −1.51429 | −0.757143 | − | 0.653249i | \(-0.773405\pi\) | ||||
−0.757143 | + | 0.653249i | \(0.773405\pi\) | |||||||
\(354\) | −19.9443 | −1.06003 | ||||||||
\(355\) | 9.70820 | 0.515258 | ||||||||
\(356\) | 13.0902 | 0.693778 | ||||||||
\(357\) | −4.23607 | −0.224196 | ||||||||
\(358\) | −6.38197 | −0.337297 | ||||||||
\(359\) | 18.6525 | 0.984440 | 0.492220 | − | 0.870471i | \(-0.336186\pi\) | ||||
0.492220 | + | 0.870471i | \(0.336186\pi\) | |||||||
\(360\) | −3.85410 | −0.203129 | ||||||||
\(361\) | 27.9787 | 1.47256 | ||||||||
\(362\) | 3.52786 | 0.185420 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −13.8541 | −0.725157 | ||||||||
\(366\) | −9.23607 | −0.482777 | ||||||||
\(367\) | 28.1803 | 1.47100 | 0.735501 | − | 0.677524i | \(-0.236947\pi\) | ||||
0.735501 | + | 0.677524i | \(0.236947\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | −39.7984 | −2.07182 | ||||||||
\(370\) | 6.47214 | 0.336470 | ||||||||
\(371\) | 1.23607 | 0.0641735 | ||||||||
\(372\) | −3.23607 | −0.167782 | ||||||||
\(373\) | −24.4721 | −1.26712 | −0.633560 | − | 0.773694i | \(-0.718407\pi\) | ||||
−0.633560 | + | 0.773694i | \(0.718407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.61803 | −0.135195 | ||||||||
\(376\) | 9.23607 | 0.476314 | ||||||||
\(377\) | 6.47214 | 0.333332 | ||||||||
\(378\) | 2.23607 | 0.115011 | ||||||||
\(379\) | −27.8541 | −1.43077 | −0.715385 | − | 0.698731i | \(-0.753748\pi\) | ||||
−0.715385 | + | 0.698731i | \(0.753748\pi\) | |||||||
\(380\) | −6.85410 | −0.351608 | ||||||||
\(381\) | −29.8885 | −1.53124 | ||||||||
\(382\) | −1.52786 | −0.0781723 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 2.61803 | 0.133601 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 7.14590 | 0.363246 | ||||||||
\(388\) | −9.56231 | −0.485453 | ||||||||
\(389\) | −32.8328 | −1.66469 | −0.832345 | − | 0.554258i | \(-0.813002\pi\) | ||||
−0.832345 | + | 0.554258i | \(0.813002\pi\) | |||||||
\(390\) | −5.23607 | −0.265139 | ||||||||
\(391\) | −9.70820 | −0.490965 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −20.4164 | −1.02987 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 8.47214 | 0.426279 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9443 | −0.850409 | −0.425204 | − | 0.905097i | \(-0.639798\pi\) | ||||
−0.425204 | + | 0.905097i | \(0.639798\pi\) | |||||||
\(398\) | −19.4164 | −0.973257 | ||||||||
\(399\) | 17.9443 | 0.898337 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −26.5066 | −1.32368 | −0.661838 | − | 0.749647i | \(-0.730223\pi\) | ||||
−0.661838 | + | 0.749647i | \(0.730223\pi\) | |||||||
\(402\) | 15.9443 | 0.795228 | ||||||||
\(403\) | −2.47214 | −0.123146 | ||||||||
\(404\) | 8.94427 | 0.444994 | ||||||||
\(405\) | 5.70820 | 0.283643 | ||||||||
\(406\) | 3.23607 | 0.160603 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.23607 | −0.209717 | ||||||||
\(409\) | 27.8885 | 1.37900 | 0.689500 | − | 0.724286i | \(-0.257830\pi\) | ||||
0.689500 | + | 0.724286i | \(0.257830\pi\) | |||||||
\(410\) | 10.3262 | 0.509977 | ||||||||
\(411\) | −2.85410 | −0.140782 | ||||||||
\(412\) | −16.9443 | −0.834784 | ||||||||
\(413\) | −7.61803 | −0.374859 | ||||||||
\(414\) | 23.1246 | 1.13651 | ||||||||
\(415\) | −10.3262 | −0.506895 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 48.3607 | 2.36823 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.3262 | 0.602176 | 0.301088 | − | 0.953596i | \(-0.402650\pi\) | ||||
0.301088 | + | 0.953596i | \(0.402650\pi\) | |||||||
\(420\) | −2.61803 | −0.127747 | ||||||||
\(421\) | −6.36068 | −0.310001 | −0.155000 | − | 0.987914i | \(-0.549538\pi\) | ||||
−0.155000 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(422\) | 11.2705 | 0.548640 | ||||||||
\(423\) | 35.5967 | 1.73077 | ||||||||
\(424\) | 1.23607 | 0.0600288 | ||||||||
\(425\) | −1.61803 | −0.0784862 | ||||||||
\(426\) | −25.4164 | −1.23143 | ||||||||
\(427\) | −3.52786 | −0.170725 | ||||||||
\(428\) | 15.3820 | 0.743515 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.85410 | −0.0894127 | ||||||||
\(431\) | 31.2361 | 1.50459 | 0.752294 | − | 0.658827i | \(-0.228947\pi\) | ||||
0.752294 | + | 0.658827i | \(0.228947\pi\) | |||||||
\(432\) | 2.23607 | 0.107583 | ||||||||
\(433\) | 16.4508 | 0.790577 | 0.395289 | − | 0.918557i | \(-0.370645\pi\) | ||||
0.395289 | + | 0.918557i | \(0.370645\pi\) | |||||||
\(434\) | −1.23607 | −0.0593332 | ||||||||
\(435\) | −8.47214 | −0.406208 | ||||||||
\(436\) | −0.472136 | −0.0226112 | ||||||||
\(437\) | 41.1246 | 1.96726 | ||||||||
\(438\) | 36.2705 | 1.73307 | ||||||||
\(439\) | −28.6525 | −1.36751 | −0.683754 | − | 0.729713i | \(-0.739654\pi\) | ||||
−0.683754 | + | 0.729713i | \(0.739654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.85410 | 0.183529 | ||||||||
\(442\) | −3.23607 | −0.153924 | ||||||||
\(443\) | 28.0344 | 1.33196 | 0.665978 | − | 0.745971i | \(-0.268014\pi\) | ||||
0.665978 | + | 0.745971i | \(0.268014\pi\) | |||||||
\(444\) | −16.9443 | −0.804140 | ||||||||
\(445\) | −13.0902 | −0.620534 | ||||||||
\(446\) | 6.29180 | 0.297925 | ||||||||
\(447\) | 63.3050 | 2.99422 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 24.4508 | 1.15391 | 0.576953 | − | 0.816777i | \(-0.304241\pi\) | ||||
0.576953 | + | 0.816777i | \(0.304241\pi\) | |||||||
\(450\) | 3.85410 | 0.181684 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.32624 | −0.438669 | ||||||||
\(453\) | 6.00000 | 0.281905 | ||||||||
\(454\) | −24.2705 | −1.13907 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 17.9443 | 0.840318 | ||||||||
\(457\) | −31.2705 | −1.46277 | −0.731386 | − | 0.681963i | \(-0.761126\pi\) | ||||
−0.731386 | + | 0.681963i | \(0.761126\pi\) | |||||||
\(458\) | 11.1246 | 0.519819 | ||||||||
\(459\) | −3.61803 | −0.168875 | ||||||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | 6.94427 | 0.323427 | 0.161713 | − | 0.986838i | \(-0.448298\pi\) | ||||
0.161713 | + | 0.986838i | \(0.448298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.41641 | −0.344670 | −0.172335 | − | 0.985038i | \(-0.555131\pi\) | ||||
−0.172335 | + | 0.985038i | \(0.555131\pi\) | |||||||
\(464\) | 3.23607 | 0.150231 | ||||||||
\(465\) | 3.23607 | 0.150069 | ||||||||
\(466\) | 10.9098 | 0.505388 | ||||||||
\(467\) | −17.8885 | −0.827783 | −0.413892 | − | 0.910326i | \(-0.635831\pi\) | ||||
−0.413892 | + | 0.910326i | \(0.635831\pi\) | |||||||
\(468\) | 7.70820 | 0.356312 | ||||||||
\(469\) | 6.09017 | 0.281218 | ||||||||
\(470\) | −9.23607 | −0.426028 | ||||||||
\(471\) | 0.763932 | 0.0352001 | ||||||||
\(472\) | −7.61803 | −0.350648 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −22.1803 | −1.01878 | ||||||||
\(475\) | 6.85410 | 0.314488 | ||||||||
\(476\) | −1.61803 | −0.0741625 | ||||||||
\(477\) | 4.76393 | 0.218125 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.8885 | −1.73117 | −0.865586 | − | 0.500761i | \(-0.833054\pi\) | ||||
−0.865586 | + | 0.500761i | \(0.833054\pi\) | |||||||
\(480\) | −2.61803 | −0.119496 | ||||||||
\(481\) | −12.9443 | −0.590208 | ||||||||
\(482\) | −6.27051 | −0.285614 | ||||||||
\(483\) | 15.7082 | 0.714748 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.56231 | 0.434202 | ||||||||
\(486\) | −21.6525 | −0.982176 | ||||||||
\(487\) | −26.8328 | −1.21591 | −0.607955 | − | 0.793971i | \(-0.708010\pi\) | ||||
−0.607955 | + | 0.793971i | \(0.708010\pi\) | |||||||
\(488\) | −3.52786 | −0.159699 | ||||||||
\(489\) | 7.47214 | 0.337902 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −32.5066 | −1.46700 | −0.733501 | − | 0.679689i | \(-0.762115\pi\) | ||||
−0.733501 | + | 0.679689i | \(0.762115\pi\) | |||||||
\(492\) | −27.0344 | −1.21881 | ||||||||
\(493\) | −5.23607 | −0.235821 | ||||||||
\(494\) | 13.7082 | 0.616761 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.23607 | −0.0555011 | ||||||||
\(497\) | −9.70820 | −0.435472 | ||||||||
\(498\) | 27.0344 | 1.21144 | ||||||||
\(499\) | −15.2016 | −0.680518 | −0.340259 | − | 0.940332i | \(-0.610515\pi\) | ||||
−0.340259 | + | 0.940332i | \(0.610515\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 16.9443 | 0.757014 | ||||||||
\(502\) | 26.8328 | 1.19761 | ||||||||
\(503\) | −17.1246 | −0.763549 | −0.381774 | − | 0.924256i | \(-0.624687\pi\) | ||||
−0.381774 | + | 0.924256i | \(0.624687\pi\) | |||||||
\(504\) | 3.85410 | 0.171675 | ||||||||
\(505\) | −8.94427 | −0.398015 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.5623 | −1.04644 | ||||||||
\(508\) | −11.4164 | −0.506521 | ||||||||
\(509\) | −25.5279 | −1.13150 | −0.565751 | − | 0.824576i | \(-0.691414\pi\) | ||||
−0.565751 | + | 0.824576i | \(0.691414\pi\) | |||||||
\(510\) | 4.23607 | 0.187576 | ||||||||
\(511\) | 13.8541 | 0.612869 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.3262 | 0.676670 | ||||||||
\(514\) | 29.5623 | 1.30394 | ||||||||
\(515\) | 16.9443 | 0.746654 | ||||||||
\(516\) | 4.85410 | 0.213690 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.47214 | −0.284369 | ||||||||
\(519\) | 31.4164 | 1.37903 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 35.7984 | 1.56836 | 0.784178 | − | 0.620536i | \(-0.213085\pi\) | ||||
0.784178 | + | 0.620536i | \(0.213085\pi\) | |||||||
\(522\) | 12.4721 | 0.545891 | ||||||||
\(523\) | 5.97871 | 0.261431 | 0.130715 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130715 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(524\) | −7.79837 | −0.340674 | ||||||||
\(525\) | 2.61803 | 0.114260 | ||||||||
\(526\) | 20.1803 | 0.879905 | ||||||||
\(527\) | 2.00000 | 0.0871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −1.23607 | −0.0536914 | ||||||||
\(531\) | −29.3607 | −1.27414 | ||||||||
\(532\) | 6.85410 | 0.297163 | ||||||||
\(533\) | −20.6525 | −0.894558 | ||||||||
\(534\) | 34.2705 | 1.48303 | ||||||||
\(535\) | −15.3820 | −0.665020 | ||||||||
\(536\) | 6.09017 | 0.263055 | ||||||||
\(537\) | −16.7082 | −0.721012 | ||||||||
\(538\) | −12.1803 | −0.525132 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.23607 | −0.0962250 | ||||||||
\(541\) | 14.8328 | 0.637713 | 0.318856 | − | 0.947803i | \(-0.396701\pi\) | ||||
0.318856 | + | 0.947803i | \(0.396701\pi\) | |||||||
\(542\) | −9.41641 | −0.404469 | ||||||||
\(543\) | 9.23607 | 0.396358 | ||||||||
\(544\) | −1.61803 | −0.0693726 | ||||||||
\(545\) | 0.472136 | 0.0202241 | ||||||||
\(546\) | 5.23607 | 0.224083 | ||||||||
\(547\) | −17.9098 | −0.765769 | −0.382885 | − | 0.923796i | \(-0.625069\pi\) | ||||
−0.382885 | + | 0.923796i | \(0.625069\pi\) | |||||||
\(548\) | −1.09017 | −0.0465698 | ||||||||
\(549\) | −13.5967 | −0.580295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.1803 | 0.944914 | ||||||||
\(552\) | 15.7082 | 0.668586 | ||||||||
\(553\) | −8.47214 | −0.360272 | ||||||||
\(554\) | 6.29180 | 0.267313 | ||||||||
\(555\) | 16.9443 | 0.719244 | ||||||||
\(556\) | 18.4721 | 0.783393 | ||||||||
\(557\) | 38.1803 | 1.61775 | 0.808876 | − | 0.587979i | \(-0.200076\pi\) | ||||
0.808876 | + | 0.587979i | \(0.200076\pi\) | |||||||
\(558\) | −4.76393 | −0.201673 | ||||||||
\(559\) | 3.70820 | 0.156840 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.0344 | −1.01383 | ||||||||
\(563\) | 3.49342 | 0.147230 | 0.0736151 | − | 0.997287i | \(-0.476546\pi\) | ||||
0.0736151 | + | 0.997287i | \(0.476546\pi\) | |||||||
\(564\) | 24.1803 | 1.01818 | ||||||||
\(565\) | 9.32624 | 0.392358 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | −9.70820 | −0.407347 | ||||||||
\(569\) | −8.09017 | −0.339158 | −0.169579 | − | 0.985517i | \(-0.554241\pi\) | ||||
−0.169579 | + | 0.985517i | \(0.554241\pi\) | |||||||
\(570\) | −17.9443 | −0.751603 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | −10.3262 | −0.431009 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 3.85410 | 0.160588 | ||||||||
\(577\) | 25.2148 | 1.04971 | 0.524853 | − | 0.851193i | \(-0.324120\pi\) | ||||
0.524853 | + | 0.851193i | \(0.324120\pi\) | |||||||
\(578\) | −14.3820 | −0.598211 | ||||||||
\(579\) | −5.23607 | −0.217604 | ||||||||
\(580\) | −3.23607 | −0.134370 | ||||||||
\(581\) | 10.3262 | 0.428405 | ||||||||
\(582\) | −25.0344 | −1.03771 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.8541 | 0.573287 | ||||||||
\(585\) | −7.70820 | −0.318695 | ||||||||
\(586\) | 16.4721 | 0.680458 | ||||||||
\(587\) | 2.74265 | 0.113201 | 0.0566006 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0566006 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(588\) | 2.61803 | 0.107966 | ||||||||
\(589\) | −8.47214 | −0.349088 | ||||||||
\(590\) | 7.61803 | 0.313629 | ||||||||
\(591\) | 15.7082 | 0.646149 | ||||||||
\(592\) | −6.47214 | −0.266003 | ||||||||
\(593\) | 12.0902 | 0.496484 | 0.248242 | − | 0.968698i | \(-0.420147\pi\) | ||||
0.248242 | + | 0.968698i | \(0.420147\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.61803 | 0.0663329 | ||||||||
\(596\) | 24.1803 | 0.990465 | ||||||||
\(597\) | −50.8328 | −2.08045 | ||||||||
\(598\) | 12.0000 | 0.490716 | ||||||||
\(599\) | −25.2361 | −1.03112 | −0.515559 | − | 0.856854i | \(-0.672416\pi\) | ||||
−0.515559 | + | 0.856854i | \(0.672416\pi\) | |||||||
\(600\) | 2.61803 | 0.106881 | ||||||||
\(601\) | −29.0902 | −1.18661 | −0.593306 | − | 0.804977i | \(-0.702178\pi\) | ||||
−0.593306 | + | 0.804977i | \(0.702178\pi\) | |||||||
\(602\) | 1.85410 | 0.0755676 | ||||||||
\(603\) | 23.4721 | 0.955859 | ||||||||
\(604\) | 2.29180 | 0.0932519 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23.4164 | 0.951227 | ||||||||
\(607\) | −29.5967 | −1.20129 | −0.600647 | − | 0.799514i | \(-0.705090\pi\) | ||||
−0.600647 | + | 0.799514i | \(0.705090\pi\) | |||||||
\(608\) | 6.85410 | 0.277971 | ||||||||
\(609\) | 8.47214 | 0.343308 | ||||||||
\(610\) | 3.52786 | 0.142839 | ||||||||
\(611\) | 18.4721 | 0.747303 | ||||||||
\(612\) | −6.23607 | −0.252078 | ||||||||
\(613\) | −37.4164 | −1.51123 | −0.755617 | − | 0.655013i | \(-0.772663\pi\) | ||||
−0.755617 | + | 0.655013i | \(0.772663\pi\) | |||||||
\(614\) | −27.5623 | −1.11232 | ||||||||
\(615\) | 27.0344 | 1.09013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0344 | 0.927332 | 0.463666 | − | 0.886010i | \(-0.346534\pi\) | ||||
0.463666 | + | 0.886010i | \(0.346534\pi\) | |||||||
\(618\) | −44.3607 | −1.78445 | ||||||||
\(619\) | 18.6738 | 0.750562 | 0.375281 | − | 0.926911i | \(-0.377546\pi\) | ||||
0.375281 | + | 0.926911i | \(0.377546\pi\) | |||||||
\(620\) | 1.23607 | 0.0496417 | ||||||||
\(621\) | 13.4164 | 0.538382 | ||||||||
\(622\) | −29.1246 | −1.16779 | ||||||||
\(623\) | 13.0902 | 0.524447 | ||||||||
\(624\) | 5.23607 | 0.209610 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.854102 | −0.0341368 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.291796 | 0.0116439 | ||||||||
\(629\) | 10.4721 | 0.417551 | ||||||||
\(630\) | −3.85410 | −0.153551 | ||||||||
\(631\) | −23.7082 | −0.943809 | −0.471904 | − | 0.881650i | \(-0.656433\pi\) | ||||
−0.471904 | + | 0.881650i | \(0.656433\pi\) | |||||||
\(632\) | −8.47214 | −0.337003 | ||||||||
\(633\) | 29.5066 | 1.17278 | ||||||||
\(634\) | −20.7639 | −0.824641 | ||||||||
\(635\) | 11.4164 | 0.453046 | ||||||||
\(636\) | 3.23607 | 0.128318 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −37.4164 | −1.48017 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 40.3262 | 1.59279 | 0.796395 | − | 0.604776i | \(-0.206738\pi\) | ||||
0.796395 | + | 0.604776i | \(0.206738\pi\) | |||||||
\(642\) | 40.2705 | 1.58935 | ||||||||
\(643\) | −14.9787 | −0.590703 | −0.295351 | − | 0.955389i | \(-0.595437\pi\) | ||||
−0.295351 | + | 0.955389i | \(0.595437\pi\) | |||||||
\(644\) | 6.00000 | 0.236433 | ||||||||
\(645\) | −4.85410 | −0.191130 | ||||||||
\(646\) | −11.0902 | −0.436337 | ||||||||
\(647\) | 0.180340 | 0.00708989 | 0.00354495 | − | 0.999994i | \(-0.498872\pi\) | ||||
0.00354495 | + | 0.999994i | \(0.498872\pi\) | |||||||
\(648\) | −5.70820 | −0.224239 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | −3.23607 | −0.126832 | ||||||||
\(652\) | 2.85410 | 0.111775 | ||||||||
\(653\) | 26.8328 | 1.05005 | 0.525025 | − | 0.851087i | \(-0.324056\pi\) | ||||
0.525025 | + | 0.851087i | \(0.324056\pi\) | |||||||
\(654\) | −1.23607 | −0.0483341 | ||||||||
\(655\) | 7.79837 | 0.304708 | ||||||||
\(656\) | −10.3262 | −0.403172 | ||||||||
\(657\) | 53.3951 | 2.08314 | ||||||||
\(658\) | 9.23607 | 0.360059 | ||||||||
\(659\) | 4.09017 | 0.159330 | 0.0796652 | − | 0.996822i | \(-0.474615\pi\) | ||||
0.0796652 | + | 0.996822i | \(0.474615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.8885 | −1.78486 | −0.892429 | − | 0.451188i | \(-0.851000\pi\) | ||||
−0.892429 | + | 0.451188i | \(0.851000\pi\) | |||||||
\(662\) | 6.03444 | 0.234535 | ||||||||
\(663\) | −8.47214 | −0.329030 | ||||||||
\(664\) | 10.3262 | 0.400736 | ||||||||
\(665\) | −6.85410 | −0.265791 | ||||||||
\(666\) | −24.9443 | −0.966571 | ||||||||
\(667\) | 19.4164 | 0.751806 | ||||||||
\(668\) | 6.47214 | 0.250414 | ||||||||
\(669\) | 16.4721 | 0.636850 | ||||||||
\(670\) | −6.09017 | −0.235284 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.61803 | 0.100993 | ||||||||
\(673\) | −38.8541 | −1.49772 | −0.748858 | − | 0.662731i | \(-0.769397\pi\) | ||||
−0.748858 | + | 0.662731i | \(0.769397\pi\) | |||||||
\(674\) | −15.6180 | −0.601584 | ||||||||
\(675\) | 2.23607 | 0.0860663 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −13.5967 | −0.522565 | −0.261283 | − | 0.965262i | \(-0.584145\pi\) | ||||
−0.261283 | + | 0.965262i | \(0.584145\pi\) | |||||||
\(678\) | −24.4164 | −0.937706 | ||||||||
\(679\) | −9.56231 | −0.366968 | ||||||||
\(680\) | 1.61803 | 0.0620488 | ||||||||
\(681\) | −63.5410 | −2.43490 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.0557 | −1.18831 | −0.594157 | − | 0.804349i | \(-0.702514\pi\) | ||||
−0.594157 | + | 0.804349i | \(0.702514\pi\) | |||||||
\(684\) | 26.4164 | 1.01006 | ||||||||
\(685\) | 1.09017 | 0.0416533 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 29.1246 | 1.11117 | ||||||||
\(688\) | 1.85410 | 0.0706870 | ||||||||
\(689\) | 2.47214 | 0.0941809 | ||||||||
\(690\) | −15.7082 | −0.598001 | ||||||||
\(691\) | 21.1459 | 0.804428 | 0.402214 | − | 0.915546i | \(-0.368241\pi\) | ||||
0.402214 | + | 0.915546i | \(0.368241\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.32624 | 0.202181 | ||||||||
\(695\) | −18.4721 | −0.700688 | ||||||||
\(696\) | 8.47214 | 0.321135 | ||||||||
\(697\) | 16.7082 | 0.632868 | ||||||||
\(698\) | 5.52786 | 0.209233 | ||||||||
\(699\) | 28.5623 | 1.08033 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −12.1803 | −0.460045 | −0.230023 | − | 0.973185i | \(-0.573880\pi\) | ||||
−0.230023 | + | 0.973185i | \(0.573880\pi\) | |||||||
\(702\) | 4.47214 | 0.168790 | ||||||||
\(703\) | −44.3607 | −1.67309 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.1803 | −0.910684 | ||||||||
\(706\) | −28.4508 | −1.07076 | ||||||||
\(707\) | 8.94427 | 0.336384 | ||||||||
\(708\) | −19.9443 | −0.749552 | ||||||||
\(709\) | −24.9443 | −0.936802 | −0.468401 | − | 0.883516i | \(-0.655170\pi\) | ||||
−0.468401 | + | 0.883516i | \(0.655170\pi\) | |||||||
\(710\) | 9.70820 | 0.364342 | ||||||||
\(711\) | −32.6525 | −1.22456 | ||||||||
\(712\) | 13.0902 | 0.490575 | ||||||||
\(713\) | −7.41641 | −0.277747 | ||||||||
\(714\) | −4.23607 | −0.158531 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.38197 | −0.238505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.6525 | 0.696104 | ||||||||
\(719\) | 32.3607 | 1.20685 | 0.603425 | − | 0.797420i | \(-0.293802\pi\) | ||||
0.603425 | + | 0.797420i | \(0.293802\pi\) | |||||||
\(720\) | −3.85410 | −0.143634 | ||||||||
\(721\) | −16.9443 | −0.631038 | ||||||||
\(722\) | 27.9787 | 1.04126 | ||||||||
\(723\) | −16.4164 | −0.610533 | ||||||||
\(724\) | 3.52786 | 0.131112 | ||||||||
\(725\) | 3.23607 | 0.120185 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.8328 | 1.44023 | 0.720115 | − | 0.693855i | \(-0.244089\pi\) | ||||
0.720115 | + | 0.693855i | \(0.244089\pi\) | |||||||
\(728\) | 2.00000 | 0.0741249 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −13.8541 | −0.512763 | ||||||||
\(731\) | −3.00000 | −0.110959 | ||||||||
\(732\) | −9.23607 | −0.341375 | ||||||||
\(733\) | −13.2361 | −0.488885 | −0.244443 | − | 0.969664i | \(-0.578605\pi\) | ||||
−0.244443 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(734\) | 28.1803 | 1.04016 | ||||||||
\(735\) | −2.61803 | −0.0965676 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −39.7984 | −1.46500 | ||||||||
\(739\) | −24.6738 | −0.907639 | −0.453820 | − | 0.891094i | \(-0.649939\pi\) | ||||
−0.453820 | + | 0.891094i | \(0.649939\pi\) | |||||||
\(740\) | 6.47214 | 0.237920 | ||||||||
\(741\) | 35.8885 | 1.31840 | ||||||||
\(742\) | 1.23607 | 0.0453775 | ||||||||
\(743\) | −12.1115 | −0.444326 | −0.222163 | − | 0.975010i | \(-0.571312\pi\) | ||||
−0.222163 | + | 0.975010i | \(0.571312\pi\) | |||||||
\(744\) | −3.23607 | −0.118640 | ||||||||
\(745\) | −24.1803 | −0.885899 | ||||||||
\(746\) | −24.4721 | −0.895989 | ||||||||
\(747\) | 39.7984 | 1.45615 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.3820 | 0.562045 | ||||||||
\(750\) | −2.61803 | −0.0955971 | ||||||||
\(751\) | −32.6525 | −1.19151 | −0.595753 | − | 0.803168i | \(-0.703146\pi\) | ||||
−0.595753 | + | 0.803168i | \(0.703146\pi\) | |||||||
\(752\) | 9.23607 | 0.336805 | ||||||||
\(753\) | 70.2492 | 2.56002 | ||||||||
\(754\) | 6.47214 | 0.235701 | ||||||||
\(755\) | −2.29180 | −0.0834070 | ||||||||
\(756\) | 2.23607 | 0.0813250 | ||||||||
\(757\) | 19.8885 | 0.722861 | 0.361431 | − | 0.932399i | \(-0.382288\pi\) | ||||
0.361431 | + | 0.932399i | \(0.382288\pi\) | |||||||
\(758\) | −27.8541 | −1.01171 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.85410 | −0.248624 | ||||||||
\(761\) | −31.7984 | −1.15269 | −0.576345 | − | 0.817206i | \(-0.695522\pi\) | ||||
−0.576345 | + | 0.817206i | \(0.695522\pi\) | |||||||
\(762\) | −29.8885 | −1.08275 | ||||||||
\(763\) | −0.472136 | −0.0170925 | ||||||||
\(764\) | −1.52786 | −0.0552762 | ||||||||
\(765\) | 6.23607 | 0.225466 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | −15.2361 | −0.550143 | ||||||||
\(768\) | 2.61803 | 0.0944702 | ||||||||
\(769\) | −7.88854 | −0.284468 | −0.142234 | − | 0.989833i | \(-0.545429\pi\) | ||||
−0.142234 | + | 0.989833i | \(0.545429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 77.3951 | 2.78732 | ||||||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | −24.6525 | −0.886688 | −0.443344 | − | 0.896352i | \(-0.646208\pi\) | ||||
−0.443344 | + | 0.896352i | \(0.646208\pi\) | |||||||
\(774\) | 7.14590 | 0.256854 | ||||||||
\(775\) | −1.23607 | −0.0444009 | ||||||||
\(776\) | −9.56231 | −0.343267 | ||||||||
\(777\) | −16.9443 | −0.607872 | ||||||||
\(778\) | −32.8328 | −1.17711 | ||||||||
\(779\) | −70.7771 | −2.53585 | ||||||||
\(780\) | −5.23607 | −0.187481 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.70820 | −0.347165 | ||||||||
\(783\) | 7.23607 | 0.258596 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −0.291796 | −0.0104146 | ||||||||
\(786\) | −20.4164 | −0.728229 | ||||||||
\(787\) | 51.1033 | 1.82164 | 0.910818 | − | 0.412807i | \(-0.135452\pi\) | ||||
0.910818 | + | 0.412807i | \(0.135452\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 52.8328 | 1.88090 | ||||||||
\(790\) | 8.47214 | 0.301425 | ||||||||
\(791\) | −9.32624 | −0.331603 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.05573 | −0.250556 | ||||||||
\(794\) | −16.9443 | −0.601330 | ||||||||
\(795\) | −3.23607 | −0.114772 | ||||||||
\(796\) | −19.4164 | −0.688196 | ||||||||
\(797\) | −6.36068 | −0.225307 | −0.112653 | − | 0.993634i | \(-0.535935\pi\) | ||||
−0.112653 | + | 0.993634i | \(0.535935\pi\) | |||||||
\(798\) | 17.9443 | 0.635220 | ||||||||
\(799\) | −14.9443 | −0.528690 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 50.4508 | 1.78259 | ||||||||
\(802\) | −26.5066 | −0.935980 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.9443 | 0.562311 | ||||||||
\(805\) | −6.00000 | −0.211472 | ||||||||
\(806\) | −2.47214 | −0.0870773 | ||||||||
\(807\) | −31.8885 | −1.12253 | ||||||||
\(808\) | 8.94427 | 0.314658 | ||||||||
\(809\) | −48.8115 | −1.71612 | −0.858061 | − | 0.513548i | \(-0.828331\pi\) | ||||
−0.858061 | + | 0.513548i | \(0.828331\pi\) | |||||||
\(810\) | 5.70820 | 0.200566 | ||||||||
\(811\) | −29.9230 | −1.05074 | −0.525369 | − | 0.850874i | \(-0.676073\pi\) | ||||
−0.525369 | + | 0.850874i | \(0.676073\pi\) | |||||||
\(812\) | 3.23607 | 0.113564 | ||||||||
\(813\) | −24.6525 | −0.864600 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.85410 | −0.0999748 | ||||||||
\(816\) | −4.23607 | −0.148292 | ||||||||
\(817\) | 12.7082 | 0.444604 | ||||||||
\(818\) | 27.8885 | 0.975100 | ||||||||
\(819\) | 7.70820 | 0.269346 | ||||||||
\(820\) | 10.3262 | 0.360608 | ||||||||
\(821\) | 31.0557 | 1.08385 | 0.541926 | − | 0.840426i | \(-0.317695\pi\) | ||||
0.541926 | + | 0.840426i | \(0.317695\pi\) | |||||||
\(822\) | −2.85410 | −0.0995482 | ||||||||
\(823\) | −2.83282 | −0.0987457 | −0.0493729 | − | 0.998780i | \(-0.515722\pi\) | ||||
−0.0493729 | + | 0.998780i | \(0.515722\pi\) | |||||||
\(824\) | −16.9443 | −0.590282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.61803 | −0.265065 | ||||||||
\(827\) | −40.7426 | −1.41676 | −0.708380 | − | 0.705831i | \(-0.750574\pi\) | ||||
−0.708380 | + | 0.705831i | \(0.750574\pi\) | |||||||
\(828\) | 23.1246 | 0.803636 | ||||||||
\(829\) | 34.1803 | 1.18713 | 0.593566 | − | 0.804785i | \(-0.297720\pi\) | ||||
0.593566 | + | 0.804785i | \(0.297720\pi\) | |||||||
\(830\) | −10.3262 | −0.358429 | ||||||||
\(831\) | 16.4721 | 0.571412 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −1.61803 | −0.0560616 | ||||||||
\(834\) | 48.3607 | 1.67459 | ||||||||
\(835\) | −6.47214 | −0.223978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.76393 | −0.0955355 | ||||||||
\(838\) | 12.3262 | 0.425803 | ||||||||
\(839\) | 4.47214 | 0.154395 | 0.0771976 | − | 0.997016i | \(-0.475403\pi\) | ||||
0.0771976 | + | 0.997016i | \(0.475403\pi\) | |||||||
\(840\) | −2.61803 | −0.0903308 | ||||||||
\(841\) | −18.5279 | −0.638892 | ||||||||
\(842\) | −6.36068 | −0.219204 | ||||||||
\(843\) | −62.9230 | −2.16718 | ||||||||
\(844\) | 11.2705 | 0.387947 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 35.5967 | 1.22384 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.23607 | 0.0424467 | ||||||||
\(849\) | −31.4164 | −1.07821 | ||||||||
\(850\) | −1.61803 | −0.0554981 | ||||||||
\(851\) | −38.8328 | −1.33117 | ||||||||
\(852\) | −25.4164 | −0.870752 | ||||||||
\(853\) | −4.29180 | −0.146948 | −0.0734741 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734741 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(854\) | −3.52786 | −0.120721 | ||||||||
\(855\) | −26.4164 | −0.903422 | ||||||||
\(856\) | 15.3820 | 0.525745 | ||||||||
\(857\) | −9.27051 | −0.316675 | −0.158337 | − | 0.987385i | \(-0.550613\pi\) | ||||
−0.158337 | + | 0.987385i | \(0.550613\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.43769 | −0.253771 | −0.126885 | − | 0.991917i | \(-0.540498\pi\) | ||||
−0.126885 | + | 0.991917i | \(0.540498\pi\) | |||||||
\(860\) | −1.85410 | −0.0632244 | ||||||||
\(861\) | −27.0344 | −0.921331 | ||||||||
\(862\) | 31.2361 | 1.06390 | ||||||||
\(863\) | 6.76393 | 0.230247 | 0.115123 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115123 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(864\) | 2.23607 | 0.0760726 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 16.4508 | 0.559023 | ||||||||
\(867\) | −37.6525 | −1.27875 | ||||||||
\(868\) | −1.23607 | −0.0419549 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −8.47214 | −0.287232 | ||||||||
\(871\) | 12.1803 | 0.412715 | ||||||||
\(872\) | −0.472136 | −0.0159885 | ||||||||
\(873\) | −36.8541 | −1.24732 | ||||||||
\(874\) | 41.1246 | 1.39106 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 36.2705 | 1.22547 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | −28.6525 | −0.966974 | ||||||||
\(879\) | 43.1246 | 1.45456 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.14590 | 0.139679 | 0.0698394 | − | 0.997558i | \(-0.477751\pi\) | ||||
0.0698394 | + | 0.997558i | \(0.477751\pi\) | |||||||
\(882\) | 3.85410 | 0.129774 | ||||||||
\(883\) | 2.43769 | 0.0820349 | 0.0410175 | − | 0.999158i | \(-0.486940\pi\) | ||||
0.0410175 | + | 0.999158i | \(0.486940\pi\) | |||||||
\(884\) | −3.23607 | −0.108841 | ||||||||
\(885\) | 19.9443 | 0.670419 | ||||||||
\(886\) | 28.0344 | 0.941835 | ||||||||
\(887\) | −4.36068 | −0.146417 | −0.0732086 | − | 0.997317i | \(-0.523324\pi\) | ||||
−0.0732086 | + | 0.997317i | \(0.523324\pi\) | |||||||
\(888\) | −16.9443 | −0.568613 | ||||||||
\(889\) | −11.4164 | −0.382894 | ||||||||
\(890\) | −13.0902 | −0.438783 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.29180 | 0.210665 | ||||||||
\(893\) | 63.3050 | 2.11842 | ||||||||
\(894\) | 63.3050 | 2.11723 | ||||||||
\(895\) | 6.38197 | 0.213326 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 31.4164 | 1.04896 | ||||||||
\(898\) | 24.4508 | 0.815935 | ||||||||
\(899\) | −4.00000 | −0.133407 | ||||||||
\(900\) | 3.85410 | 0.128470 | ||||||||
\(901\) | −2.00000 | −0.0666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.85410 | 0.161534 | ||||||||
\(904\) | −9.32624 | −0.310186 | ||||||||
\(905\) | −3.52786 | −0.117270 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | 22.2705 | 0.739480 | 0.369740 | − | 0.929135i | \(-0.379447\pi\) | ||||
0.369740 | + | 0.929135i | \(0.379447\pi\) | |||||||
\(908\) | −24.2705 | −0.805445 | ||||||||
\(909\) | 34.4721 | 1.14337 | ||||||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | −51.5967 | −1.70948 | −0.854738 | − | 0.519059i | \(-0.826282\pi\) | ||||
−0.854738 | + | 0.519059i | \(0.826282\pi\) | |||||||
\(912\) | 17.9443 | 0.594194 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −31.2705 | −1.03434 | ||||||||
\(915\) | 9.23607 | 0.305335 | ||||||||
\(916\) | 11.1246 | 0.367568 | ||||||||
\(917\) | −7.79837 | −0.257525 | ||||||||
\(918\) | −3.61803 | −0.119413 | ||||||||
\(919\) | −8.83282 | −0.291368 | −0.145684 | − | 0.989331i | \(-0.546538\pi\) | ||||
−0.145684 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(920\) | −6.00000 | −0.197814 | ||||||||
\(921\) | −72.1591 | −2.37772 | ||||||||
\(922\) | 6.94427 | 0.228697 | ||||||||
\(923\) | −19.4164 | −0.639099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.47214 | −0.212803 | ||||||||
\(926\) | −7.41641 | −0.243718 | ||||||||
\(927\) | −65.3050 | −2.14490 | ||||||||
\(928\) | 3.23607 | 0.106229 | ||||||||
\(929\) | −3.25735 | −0.106870 | −0.0534352 | − | 0.998571i | \(-0.517017\pi\) | ||||
−0.0534352 | + | 0.998571i | \(0.517017\pi\) | |||||||
\(930\) | 3.23607 | 0.106115 | ||||||||
\(931\) | 6.85410 | 0.224634 | ||||||||
\(932\) | 10.9098 | 0.357363 | ||||||||
\(933\) | −76.2492 | −2.49629 | ||||||||
\(934\) | −17.8885 | −0.585331 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.70820 | 0.251951 | ||||||||
\(937\) | 33.3951 | 1.09097 | 0.545486 | − | 0.838120i | \(-0.316345\pi\) | ||||
0.545486 | + | 0.838120i | \(0.316345\pi\) | |||||||
\(938\) | 6.09017 | 0.198851 | ||||||||
\(939\) | −2.23607 | −0.0729713 | ||||||||
\(940\) | −9.23607 | −0.301247 | ||||||||
\(941\) | 34.1803 | 1.11425 | 0.557124 | − | 0.830430i | \(-0.311905\pi\) | ||||
0.557124 | + | 0.830430i | \(0.311905\pi\) | |||||||
\(942\) | 0.763932 | 0.0248903 | ||||||||
\(943\) | −61.9574 | −2.01761 | ||||||||
\(944\) | −7.61803 | −0.247946 | ||||||||
\(945\) | −2.23607 | −0.0727393 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.9098 | −1.36189 | −0.680943 | − | 0.732336i | \(-0.738430\pi\) | ||||
−0.680943 | + | 0.732336i | \(0.738430\pi\) | |||||||
\(948\) | −22.1803 | −0.720384 | ||||||||
\(949\) | 27.7082 | 0.899446 | ||||||||
\(950\) | 6.85410 | 0.222376 | ||||||||
\(951\) | −54.3607 | −1.76277 | ||||||||
\(952\) | −1.61803 | −0.0524408 | ||||||||
\(953\) | 29.4508 | 0.954007 | 0.477003 | − | 0.878902i | \(-0.341723\pi\) | ||||
0.477003 | + | 0.878902i | \(0.341723\pi\) | |||||||
\(954\) | 4.76393 | 0.154238 | ||||||||
\(955\) | 1.52786 | 0.0494405 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.8885 | −1.22412 | ||||||||
\(959\) | −1.09017 | −0.0352034 | ||||||||
\(960\) | −2.61803 | −0.0844967 | ||||||||
\(961\) | −29.4721 | −0.950714 | ||||||||
\(962\) | −12.9443 | −0.417340 | ||||||||
\(963\) | 59.2837 | 1.91039 | ||||||||
\(964\) | −6.27051 | −0.201960 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 15.7082 | 0.505403 | ||||||||
\(967\) | 27.0132 | 0.868685 | 0.434342 | − | 0.900748i | \(-0.356981\pi\) | ||||
0.434342 | + | 0.900748i | \(0.356981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.0344 | −0.932721 | ||||||||
\(970\) | 9.56231 | 0.307027 | ||||||||
\(971\) | −26.8328 | −0.861106 | −0.430553 | − | 0.902565i | \(-0.641681\pi\) | ||||
−0.430553 | + | 0.902565i | \(0.641681\pi\) | |||||||
\(972\) | −21.6525 | −0.694503 | ||||||||
\(973\) | 18.4721 | 0.592189 | ||||||||
\(974\) | −26.8328 | −0.859779 | ||||||||
\(975\) | 5.23607 | 0.167688 | ||||||||
\(976\) | −3.52786 | −0.112924 | ||||||||
\(977\) | 43.3050 | 1.38545 | 0.692724 | − | 0.721203i | \(-0.256410\pi\) | ||||
0.692724 | + | 0.721203i | \(0.256410\pi\) | |||||||
\(978\) | 7.47214 | 0.238933 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −1.81966 | −0.0580973 | ||||||||
\(982\) | −32.5066 | −1.03733 | ||||||||
\(983\) | −14.6525 | −0.467341 | −0.233671 | − | 0.972316i | \(-0.575074\pi\) | ||||
−0.233671 | + | 0.972316i | \(0.575074\pi\) | |||||||
\(984\) | −27.0344 | −0.861827 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | −5.23607 | −0.166750 | ||||||||
\(987\) | 24.1803 | 0.769669 | ||||||||
\(988\) | 13.7082 | 0.436116 | ||||||||
\(989\) | 11.1246 | 0.353742 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.6525 | 0.656048 | 0.328024 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328024 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(992\) | −1.23607 | −0.0392452 | ||||||||
\(993\) | 15.7984 | 0.501346 | ||||||||
\(994\) | −9.70820 | −0.307926 | ||||||||
\(995\) | 19.4164 | 0.615542 | ||||||||
\(996\) | 27.0344 | 0.856619 | ||||||||
\(997\) | −23.1246 | −0.732364 | −0.366182 | − | 0.930543i | \(-0.619335\pi\) | ||||
−0.366182 | + | 0.930543i | \(0.619335\pi\) | |||||||
\(998\) | −15.2016 | −0.481199 | ||||||||
\(999\) | −14.4721 | −0.457878 |
(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 | 8470.2.a.cf.1.2 | 2 | ||
11.7 | odd | 10 | 770.2.n.b.71.1 | ✓ | 4 | ||
11.8 | odd | 10 | 770.2.n.b.141.1 | yes | 4 | ||
11.10 | odd | 2 | 8470.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.b.71.1 | ✓ | 4 | 11.7 | odd | 10 | ||
770.2.n.b.141.1 | yes | 4 | 11.8 | odd | 10 | ||
8470.2.a.bt.1.2 | 2 | 11.10 | odd | 2 | |||
8470.2.a.cf.1.2 | 2 | 1.1 | even | 1 | trivial |