Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.42864 | 1.67387 | 0.836934 | − | 0.547304i | \(-0.184346\pi\) | ||||
0.836934 | + | 0.547304i | \(0.184346\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.62222 | 0.790628 | 0.395314 | − | 0.918546i | \(-0.370636\pi\) | ||||
0.395314 | + | 0.918546i | \(0.370636\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.80642 | −1.61041 | −0.805206 | − | 0.592995i | \(-0.797945\pi\) | ||||
−0.805206 | + | 0.592995i | \(0.797945\pi\) | |||||||
\(14\) | −4.42864 | −1.18360 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.80642 | 0.923193 | 0.461597 | − | 0.887090i | \(-0.347277\pi\) | ||||
0.461597 | + | 0.887090i | \(0.347277\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.42864 | 0.966408 | ||||||||
\(22\) | −2.62222 | −0.559058 | ||||||||
\(23\) | 2.62222 | 0.546770 | 0.273385 | − | 0.961905i | \(-0.411857\pi\) | ||||
0.273385 | + | 0.961905i | \(0.411857\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.80642 | 1.13873 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.42864 | 0.836934 | ||||||||
\(29\) | 3.37778 | 0.627239 | 0.313619 | − | 0.949549i | \(-0.398458\pi\) | ||||
0.313619 | + | 0.949549i | \(0.398458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.42864 | −0.795407 | −0.397704 | − | 0.917514i | \(-0.630193\pi\) | ||||
−0.397704 | + | 0.917514i | \(0.630193\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.62222 | 0.456469 | ||||||||
\(34\) | −3.80642 | −0.652796 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.80642 | −0.954570 | −0.477285 | − | 0.878749i | \(-0.658379\pi\) | ||||
−0.477285 | + | 0.878749i | \(0.658379\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.80642 | −0.929772 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.67307 | 0.885985 | 0.442992 | − | 0.896525i | \(-0.353917\pi\) | ||||
0.442992 | + | 0.896525i | \(0.353917\pi\) | |||||||
\(42\) | −4.42864 | −0.683354 | ||||||||
\(43\) | 10.9906 | 1.67606 | 0.838028 | − | 0.545627i | \(-0.183709\pi\) | ||||
0.838028 | + | 0.545627i | \(0.183709\pi\) | |||||||
\(44\) | 2.62222 | 0.395314 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62222 | −0.386625 | ||||||||
\(47\) | −2.62222 | −0.382489 | −0.191245 | − | 0.981542i | \(-0.561252\pi\) | ||||
−0.191245 | + | 0.981542i | \(0.561252\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 12.6128 | 1.80184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.80642 | 0.533006 | ||||||||
\(52\) | −5.80642 | −0.805206 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.42864 | −0.591802 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −3.37778 | −0.443525 | ||||||||
\(59\) | −1.05086 | −0.136810 | −0.0684048 | − | 0.997658i | \(-0.521791\pi\) | ||||
−0.0684048 | + | 0.997658i | \(0.521791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.75557 | 0.608888 | 0.304444 | − | 0.952530i | \(-0.401529\pi\) | ||||
0.304444 | + | 0.952530i | \(0.401529\pi\) | |||||||
\(62\) | 4.42864 | 0.562438 | ||||||||
\(63\) | 4.42864 | 0.557956 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.62222 | −0.322772 | ||||||||
\(67\) | −15.6128 | −1.90741 | −0.953706 | − | 0.300739i | \(-0.902767\pi\) | ||||
−0.953706 | + | 0.300739i | \(0.902767\pi\) | |||||||
\(68\) | 3.80642 | 0.461597 | ||||||||
\(69\) | 2.62222 | 0.315678 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6128 | 1.85290 | 0.926452 | − | 0.376413i | \(-0.122843\pi\) | ||||
0.926452 | + | 0.376413i | \(0.122843\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.6128 | −1.35918 | −0.679591 | − | 0.733592i | \(-0.737843\pi\) | ||||
−0.679591 | + | 0.733592i | \(0.737843\pi\) | |||||||
\(74\) | 5.80642 | 0.674983 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 11.6128 | 1.32341 | ||||||||
\(78\) | 5.80642 | 0.657448 | ||||||||
\(79\) | 4.42864 | 0.498261 | 0.249130 | − | 0.968470i | \(-0.419855\pi\) | ||||
0.249130 | + | 0.968470i | \(0.419855\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.67307 | −0.626486 | ||||||||
\(83\) | −11.9081 | −1.30709 | −0.653544 | − | 0.756889i | \(-0.726718\pi\) | ||||
−0.653544 | + | 0.756889i | \(0.726718\pi\) | |||||||
\(84\) | 4.42864 | 0.483204 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.9906 | −1.18515 | ||||||||
\(87\) | 3.37778 | 0.362136 | ||||||||
\(88\) | −2.62222 | −0.279529 | ||||||||
\(89\) | 12.4286 | 1.31743 | 0.658717 | − | 0.752391i | \(-0.271100\pi\) | ||||
0.658717 | + | 0.752391i | \(0.271100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.7146 | −2.69562 | ||||||||
\(92\) | 2.62222 | 0.273385 | ||||||||
\(93\) | −4.42864 | −0.459229 | ||||||||
\(94\) | 2.62222 | 0.270461 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.37778 | −0.749101 | −0.374550 | − | 0.927207i | \(-0.622203\pi\) | ||||
−0.374550 | + | 0.927207i | \(0.622203\pi\) | |||||||
\(98\) | −12.6128 | −1.27409 | ||||||||
\(99\) | 2.62222 | 0.263543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6731 | 1.75854 | 0.879268 | − | 0.476327i | \(-0.158032\pi\) | ||||
0.879268 | + | 0.476327i | \(0.158032\pi\) | |||||||
\(102\) | −3.80642 | −0.376892 | ||||||||
\(103\) | 1.18421 | 0.116684 | 0.0583418 | − | 0.998297i | \(-0.481419\pi\) | ||||
0.0583418 | + | 0.998297i | \(0.481419\pi\) | |||||||
\(104\) | 5.80642 | 0.569367 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −4.85728 | −0.469571 | −0.234785 | − | 0.972047i | \(-0.575439\pi\) | ||||
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −6.04149 | −0.578670 | −0.289335 | − | 0.957228i | \(-0.593434\pi\) | ||||
−0.289335 | + | 0.957228i | \(0.593434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.80642 | −0.551121 | ||||||||
\(112\) | 4.42864 | 0.418467 | ||||||||
\(113\) | −9.34614 | −0.879211 | −0.439606 | − | 0.898191i | \(-0.644882\pi\) | ||||
−0.439606 | + | 0.898191i | \(0.644882\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.37778 | 0.313619 | ||||||||
\(117\) | −5.80642 | −0.536804 | ||||||||
\(118\) | 1.05086 | 0.0967391 | ||||||||
\(119\) | 16.8573 | 1.54530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.12399 | −0.374908 | ||||||||
\(122\) | −4.75557 | −0.430549 | ||||||||
\(123\) | 5.67307 | 0.511524 | ||||||||
\(124\) | −4.42864 | −0.397704 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.42864 | −0.394535 | ||||||||
\(127\) | −6.42864 | −0.570450 | −0.285225 | − | 0.958461i | \(-0.592068\pi\) | ||||
−0.285225 | + | 0.958461i | \(0.592068\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.9906 | 0.967671 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0923 | −1.31862 | −0.659312 | − | 0.751869i | \(-0.729152\pi\) | ||||
−0.659312 | + | 0.751869i | \(0.729152\pi\) | |||||||
\(132\) | 2.62222 | 0.228235 | ||||||||
\(133\) | 4.42864 | 0.384012 | ||||||||
\(134\) | 15.6128 | 1.34874 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.80642 | −0.326398 | ||||||||
\(137\) | 7.53972 | 0.644162 | 0.322081 | − | 0.946712i | \(-0.395618\pi\) | ||||
0.322081 | + | 0.946712i | \(0.395618\pi\) | |||||||
\(138\) | −2.62222 | −0.223218 | ||||||||
\(139\) | 0.387152 | 0.0328378 | 0.0164189 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164189 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.62222 | −0.220830 | ||||||||
\(142\) | −15.6128 | −1.31020 | ||||||||
\(143\) | −15.2257 | −1.27324 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.6128 | 0.961086 | ||||||||
\(147\) | 12.6128 | 1.04029 | ||||||||
\(148\) | −5.80642 | −0.477285 | ||||||||
\(149\) | −14.5303 | −1.19037 | −0.595186 | − | 0.803588i | \(-0.702922\pi\) | ||||
−0.595186 | + | 0.803588i | \(0.702922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.69535 | 0.382102 | 0.191051 | − | 0.981580i | \(-0.438810\pi\) | ||||
0.191051 | + | 0.981580i | \(0.438810\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 3.80642 | 0.307731 | ||||||||
\(154\) | −11.6128 | −0.935790 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.80642 | −0.464886 | ||||||||
\(157\) | 21.5210 | 1.71756 | 0.858781 | − | 0.512343i | \(-0.171222\pi\) | ||||
0.858781 | + | 0.512343i | \(0.171222\pi\) | |||||||
\(158\) | −4.42864 | −0.352324 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6128 | 0.915221 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 8.23506 | 0.645020 | 0.322510 | − | 0.946566i | \(-0.395473\pi\) | ||||
0.322510 | + | 0.946566i | \(0.395473\pi\) | |||||||
\(164\) | 5.67307 | 0.442992 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9081 | 0.924250 | ||||||||
\(167\) | −8.47013 | −0.655438 | −0.327719 | − | 0.944775i | \(-0.606280\pi\) | ||||
−0.327719 | + | 0.944775i | \(0.606280\pi\) | |||||||
\(168\) | −4.42864 | −0.341677 | ||||||||
\(169\) | 20.7146 | 1.59343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 10.9906 | 0.838028 | ||||||||
\(173\) | 22.4701 | 1.70837 | 0.854186 | − | 0.519967i | \(-0.174056\pi\) | ||||
0.854186 | + | 0.519967i | \(0.174056\pi\) | |||||||
\(174\) | −3.37778 | −0.256069 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.62222 | 0.197657 | ||||||||
\(177\) | −1.05086 | −0.0789871 | ||||||||
\(178\) | −12.4286 | −0.931566 | ||||||||
\(179\) | −2.94914 | −0.220429 | −0.110215 | − | 0.993908i | \(-0.535154\pi\) | ||||
−0.110215 | + | 0.993908i | \(0.535154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8988 | 1.70205 | 0.851026 | − | 0.525124i | \(-0.175981\pi\) | ||||
0.851026 | + | 0.525124i | \(0.175981\pi\) | |||||||
\(182\) | 25.7146 | 1.90609 | ||||||||
\(183\) | 4.75557 | 0.351542 | ||||||||
\(184\) | −2.62222 | −0.193312 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.42864 | 0.324724 | ||||||||
\(187\) | 9.98126 | 0.729902 | ||||||||
\(188\) | −2.62222 | −0.191245 | ||||||||
\(189\) | 4.42864 | 0.322136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.05086 | −0.654897 | −0.327448 | − | 0.944869i | \(-0.606189\pi\) | ||||
−0.327448 | + | 0.944869i | \(0.606189\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −18.7239 | −1.34778 | −0.673889 | − | 0.738833i | \(-0.735377\pi\) | ||||
−0.673889 | + | 0.738833i | \(0.735377\pi\) | |||||||
\(194\) | 7.37778 | 0.529694 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.6128 | 0.900918 | ||||||||
\(197\) | −0.888922 | −0.0633331 | −0.0316665 | − | 0.999498i | \(-0.510081\pi\) | ||||
−0.0316665 | + | 0.999498i | \(0.510081\pi\) | |||||||
\(198\) | −2.62222 | −0.186353 | ||||||||
\(199\) | 21.7146 | 1.53930 | 0.769652 | − | 0.638464i | \(-0.220430\pi\) | ||||
0.769652 | + | 0.638464i | \(0.220430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.6128 | −1.10125 | ||||||||
\(202\) | −17.6731 | −1.24347 | ||||||||
\(203\) | 14.9590 | 1.04992 | ||||||||
\(204\) | 3.80642 | 0.266503 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.18421 | −0.0825077 | ||||||||
\(207\) | 2.62222 | 0.182257 | ||||||||
\(208\) | −5.80642 | −0.402603 | ||||||||
\(209\) | 2.62222 | 0.181382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.61285 | −0.248719 | −0.124359 | − | 0.992237i | \(-0.539688\pi\) | ||||
−0.124359 | + | 0.992237i | \(0.539688\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 15.6128 | 1.06977 | ||||||||
\(214\) | 4.85728 | 0.332037 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −19.6128 | −1.33141 | ||||||||
\(218\) | 6.04149 | 0.409181 | ||||||||
\(219\) | −11.6128 | −0.784724 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1017 | −1.48672 | ||||||||
\(222\) | 5.80642 | 0.389702 | ||||||||
\(223\) | 21.3876 | 1.43222 | 0.716111 | − | 0.697987i | \(-0.245921\pi\) | ||||
0.716111 | + | 0.697987i | \(0.245921\pi\) | |||||||
\(224\) | −4.42864 | −0.295901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.34614 | 0.621696 | ||||||||
\(227\) | −8.47013 | −0.562182 | −0.281091 | − | 0.959681i | \(-0.590696\pi\) | ||||
−0.281091 | + | 0.959681i | \(0.590696\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −16.9590 | −1.12068 | −0.560341 | − | 0.828262i | \(-0.689330\pi\) | ||||
−0.560341 | + | 0.828262i | \(0.689330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.6128 | 0.764069 | ||||||||
\(232\) | −3.37778 | −0.221762 | ||||||||
\(233\) | 17.9081 | 1.17320 | 0.586600 | − | 0.809876i | \(-0.300466\pi\) | ||||
0.586600 | + | 0.809876i | \(0.300466\pi\) | |||||||
\(234\) | 5.80642 | 0.379578 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.05086 | −0.0684048 | ||||||||
\(237\) | 4.42864 | 0.287671 | ||||||||
\(238\) | −16.8573 | −1.09270 | ||||||||
\(239\) | −28.2766 | −1.82906 | −0.914529 | − | 0.404520i | \(-0.867438\pi\) | ||||
−0.914529 | + | 0.404520i | \(0.867438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5111 | −0.741498 | −0.370749 | − | 0.928733i | \(-0.620899\pi\) | ||||
−0.370749 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(242\) | 4.12399 | 0.265100 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.75557 | 0.304444 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.67307 | −0.361702 | ||||||||
\(247\) | −5.80642 | −0.369454 | ||||||||
\(248\) | 4.42864 | 0.281219 | ||||||||
\(249\) | −11.9081 | −0.754647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.74620 | −0.488936 | −0.244468 | − | 0.969657i | \(-0.578613\pi\) | ||||
−0.244468 | + | 0.969657i | \(0.578613\pi\) | |||||||
\(252\) | 4.42864 | 0.278978 | ||||||||
\(253\) | 6.87601 | 0.432291 | ||||||||
\(254\) | 6.42864 | 0.403369 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.8796 | 0.865783 | 0.432891 | − | 0.901446i | \(-0.357493\pi\) | ||||
0.432891 | + | 0.901446i | \(0.357493\pi\) | |||||||
\(258\) | −10.9906 | −0.684247 | ||||||||
\(259\) | −25.7146 | −1.59782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.37778 | 0.209080 | ||||||||
\(262\) | 15.0923 | 0.932408 | ||||||||
\(263\) | 18.6222 | 1.14830 | 0.574148 | − | 0.818752i | \(-0.305334\pi\) | ||||
0.574148 | + | 0.818752i | \(0.305334\pi\) | |||||||
\(264\) | −2.62222 | −0.161386 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.42864 | −0.271537 | ||||||||
\(267\) | 12.4286 | 0.760620 | ||||||||
\(268\) | −15.6128 | −0.953706 | ||||||||
\(269\) | 15.8479 | 0.966264 | 0.483132 | − | 0.875547i | \(-0.339499\pi\) | ||||
0.483132 | + | 0.875547i | \(0.339499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.51114 | 0.0917951 | 0.0458975 | − | 0.998946i | \(-0.485385\pi\) | ||||
0.0458975 | + | 0.998946i | \(0.485385\pi\) | |||||||
\(272\) | 3.80642 | 0.230798 | ||||||||
\(273\) | −25.7146 | −1.55632 | ||||||||
\(274\) | −7.53972 | −0.455491 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.62222 | 0.157839 | ||||||||
\(277\) | −1.05086 | −0.0631398 | −0.0315699 | − | 0.999502i | \(-0.510051\pi\) | ||||
−0.0315699 | + | 0.999502i | \(0.510051\pi\) | |||||||
\(278\) | −0.387152 | −0.0232199 | ||||||||
\(279\) | −4.42864 | −0.265136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.45091 | 0.205864 | 0.102932 | − | 0.994688i | \(-0.467178\pi\) | ||||
0.102932 | + | 0.994688i | \(0.467178\pi\) | |||||||
\(282\) | 2.62222 | 0.156151 | ||||||||
\(283\) | −15.5812 | −0.926206 | −0.463103 | − | 0.886304i | \(-0.653264\pi\) | ||||
−0.463103 | + | 0.886304i | \(0.653264\pi\) | |||||||
\(284\) | 15.6128 | 0.926452 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.2257 | 0.900314 | ||||||||
\(287\) | 25.1240 | 1.48302 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −2.51114 | −0.147714 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.37778 | −0.432493 | ||||||||
\(292\) | −11.6128 | −0.679591 | ||||||||
\(293\) | −7.12399 | −0.416188 | −0.208094 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208094 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(294\) | −12.6128 | −0.735596 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.80642 | 0.337492 | ||||||||
\(297\) | 2.62222 | 0.152156 | ||||||||
\(298\) | 14.5303 | 0.841721 | ||||||||
\(299\) | −15.2257 | −0.880525 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.6735 | 2.80550 | ||||||||
\(302\) | −4.69535 | −0.270187 | ||||||||
\(303\) | 17.6731 | 1.01529 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.80642 | −0.217599 | ||||||||
\(307\) | −1.12399 | −0.0641492 | −0.0320746 | − | 0.999485i | \(-0.510211\pi\) | ||||
−0.0320746 | + | 0.999485i | \(0.510211\pi\) | |||||||
\(308\) | 11.6128 | 0.661703 | ||||||||
\(309\) | 1.18421 | 0.0673673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9491 | 0.847688 | 0.423844 | − | 0.905735i | \(-0.360680\pi\) | ||||
0.423844 | + | 0.905735i | \(0.360680\pi\) | |||||||
\(312\) | 5.80642 | 0.328724 | ||||||||
\(313\) | −3.14272 | −0.177637 | −0.0888185 | − | 0.996048i | \(-0.528309\pi\) | ||||
−0.0888185 | + | 0.996048i | \(0.528309\pi\) | |||||||
\(314\) | −21.5210 | −1.21450 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.42864 | 0.249130 | ||||||||
\(317\) | −10.5906 | −0.594826 | −0.297413 | − | 0.954749i | \(-0.596124\pi\) | ||||
−0.297413 | + | 0.954749i | \(0.596124\pi\) | |||||||
\(318\) | −6.00000 | −0.336463 | ||||||||
\(319\) | 8.85728 | 0.495912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.85728 | −0.271107 | ||||||||
\(322\) | −11.6128 | −0.647159 | ||||||||
\(323\) | 3.80642 | 0.211795 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.23506 | −0.456098 | ||||||||
\(327\) | −6.04149 | −0.334095 | ||||||||
\(328\) | −5.67307 | −0.313243 | ||||||||
\(329\) | −11.6128 | −0.640237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.1427 | −0.832319 | −0.416160 | − | 0.909292i | \(-0.636624\pi\) | ||||
−0.416160 | + | 0.909292i | \(0.636624\pi\) | |||||||
\(332\) | −11.9081 | −0.653544 | ||||||||
\(333\) | −5.80642 | −0.318190 | ||||||||
\(334\) | 8.47013 | 0.463465 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.42864 | 0.241602 | ||||||||
\(337\) | −11.1111 | −0.605259 | −0.302629 | − | 0.953108i | \(-0.597864\pi\) | ||||
−0.302629 | + | 0.953108i | \(0.597864\pi\) | |||||||
\(338\) | −20.7146 | −1.12672 | ||||||||
\(339\) | −9.34614 | −0.507613 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6128 | −0.628871 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 24.8573 | 1.34217 | ||||||||
\(344\) | −10.9906 | −0.592575 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.4701 | −1.20800 | ||||||||
\(347\) | 14.1936 | 0.761951 | 0.380976 | − | 0.924585i | \(-0.375588\pi\) | ||||
0.380976 | + | 0.924585i | \(0.375588\pi\) | |||||||
\(348\) | 3.37778 | 0.181068 | ||||||||
\(349\) | 32.3684 | 1.73264 | 0.866321 | − | 0.499488i | \(-0.166479\pi\) | ||||
0.866321 | + | 0.499488i | \(0.166479\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.80642 | −0.309924 | ||||||||
\(352\) | −2.62222 | −0.139765 | ||||||||
\(353\) | 11.8064 | 0.628393 | 0.314196 | − | 0.949358i | \(-0.398265\pi\) | ||||
0.314196 | + | 0.949358i | \(0.398265\pi\) | |||||||
\(354\) | 1.05086 | 0.0558523 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.4286 | 0.658717 | ||||||||
\(357\) | 16.8573 | 0.892182 | ||||||||
\(358\) | 2.94914 | 0.155867 | ||||||||
\(359\) | −10.8287 | −0.571517 | −0.285758 | − | 0.958302i | \(-0.592245\pi\) | ||||
−0.285758 | + | 0.958302i | \(0.592245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −22.8988 | −1.20353 | ||||||||
\(363\) | −4.12399 | −0.216453 | ||||||||
\(364\) | −25.7146 | −1.34781 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.75557 | −0.248578 | ||||||||
\(367\) | 1.46965 | 0.0767151 | 0.0383576 | − | 0.999264i | \(-0.487787\pi\) | ||||
0.0383576 | + | 0.999264i | \(0.487787\pi\) | |||||||
\(368\) | 2.62222 | 0.136692 | ||||||||
\(369\) | 5.67307 | 0.295328 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.5718 | 1.37954 | ||||||||
\(372\) | −4.42864 | −0.229614 | ||||||||
\(373\) | −24.3783 | −1.26226 | −0.631129 | − | 0.775678i | \(-0.717408\pi\) | ||||
−0.631129 | + | 0.775678i | \(0.717408\pi\) | |||||||
\(374\) | −9.98126 | −0.516119 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.62222 | 0.135230 | ||||||||
\(377\) | −19.6128 | −1.01011 | ||||||||
\(378\) | −4.42864 | −0.227785 | ||||||||
\(379\) | 18.9590 | 0.973858 | 0.486929 | − | 0.873442i | \(-0.338117\pi\) | ||||
0.486929 | + | 0.873442i | \(0.338117\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.42864 | −0.329349 | ||||||||
\(382\) | 9.05086 | 0.463082 | ||||||||
\(383\) | 26.1017 | 1.33374 | 0.666868 | − | 0.745176i | \(-0.267635\pi\) | ||||
0.666868 | + | 0.745176i | \(0.267635\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.7239 | 0.953023 | ||||||||
\(387\) | 10.9906 | 0.558685 | ||||||||
\(388\) | −7.37778 | −0.374550 | ||||||||
\(389\) | −3.57136 | −0.181075 | −0.0905376 | − | 0.995893i | \(-0.528859\pi\) | ||||
−0.0905376 | + | 0.995893i | \(0.528859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.98126 | 0.504774 | ||||||||
\(392\) | −12.6128 | −0.637045 | ||||||||
\(393\) | −15.0923 | −0.761308 | ||||||||
\(394\) | 0.888922 | 0.0447832 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.62222 | 0.131771 | ||||||||
\(397\) | −31.4193 | −1.57689 | −0.788444 | − | 0.615107i | \(-0.789113\pi\) | ||||
−0.788444 | + | 0.615107i | \(0.789113\pi\) | |||||||
\(398\) | −21.7146 | −1.08845 | ||||||||
\(399\) | 4.42864 | 0.221709 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0415 | 0.601323 | 0.300662 | − | 0.953731i | \(-0.402793\pi\) | ||||
0.300662 | + | 0.953731i | \(0.402793\pi\) | |||||||
\(402\) | 15.6128 | 0.778698 | ||||||||
\(403\) | 25.7146 | 1.28093 | ||||||||
\(404\) | 17.6731 | 0.879268 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.9590 | −0.742402 | ||||||||
\(407\) | −15.2257 | −0.754710 | ||||||||
\(408\) | −3.80642 | −0.188446 | ||||||||
\(409\) | 26.4701 | 1.30886 | 0.654432 | − | 0.756121i | \(-0.272908\pi\) | ||||
0.654432 | + | 0.756121i | \(0.272908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.53972 | 0.371907 | ||||||||
\(412\) | 1.18421 | 0.0583418 | ||||||||
\(413\) | −4.65386 | −0.229001 | ||||||||
\(414\) | −2.62222 | −0.128875 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.80642 | 0.284683 | ||||||||
\(417\) | 0.387152 | 0.0189589 | ||||||||
\(418\) | −2.62222 | −0.128257 | ||||||||
\(419\) | −25.9684 | −1.26864 | −0.634319 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634319 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.2672 | −1.42640 | −0.713198 | − | 0.700963i | \(-0.752754\pi\) | ||||
−0.713198 | + | 0.700963i | \(0.752754\pi\) | |||||||
\(422\) | 3.61285 | 0.175871 | ||||||||
\(423\) | −2.62222 | −0.127496 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.6128 | −0.756445 | ||||||||
\(427\) | 21.0607 | 1.01920 | ||||||||
\(428\) | −4.85728 | −0.234785 | ||||||||
\(429\) | −15.2257 | −0.735104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8385 | 0.714747 | 0.357374 | − | 0.933961i | \(-0.383672\pi\) | ||||
0.357374 | + | 0.933961i | \(0.383672\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 5.27607 | 0.253552 | 0.126776 | − | 0.991931i | \(-0.459537\pi\) | ||||
0.126776 | + | 0.991931i | \(0.459537\pi\) | |||||||
\(434\) | 19.6128 | 0.941447 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.04149 | −0.289335 | ||||||||
\(437\) | 2.62222 | 0.125438 | ||||||||
\(438\) | 11.6128 | 0.554883 | ||||||||
\(439\) | 31.8578 | 1.52049 | 0.760244 | − | 0.649638i | \(-0.225079\pi\) | ||||
0.760244 | + | 0.649638i | \(0.225079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6128 | 0.600612 | ||||||||
\(442\) | 22.1017 | 1.05127 | ||||||||
\(443\) | 4.94914 | 0.235141 | 0.117570 | − | 0.993065i | \(-0.462489\pi\) | ||||
0.117570 | + | 0.993065i | \(0.462489\pi\) | |||||||
\(444\) | −5.80642 | −0.275561 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21.3876 | −1.01273 | ||||||||
\(447\) | −14.5303 | −0.687262 | ||||||||
\(448\) | 4.42864 | 0.209234 | ||||||||
\(449\) | 9.75605 | 0.460416 | 0.230208 | − | 0.973141i | \(-0.426059\pi\) | ||||
0.230208 | + | 0.973141i | \(0.426059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8760 | 0.700484 | ||||||||
\(452\) | −9.34614 | −0.439606 | ||||||||
\(453\) | 4.69535 | 0.220607 | ||||||||
\(454\) | 8.47013 | 0.397523 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −8.00000 | −0.374224 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(458\) | 16.9590 | 0.792442 | ||||||||
\(459\) | 3.80642 | 0.177669 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.1245 | −1.68248 | −0.841242 | − | 0.540659i | \(-0.818175\pi\) | ||||
−0.841242 | + | 0.540659i | \(0.818175\pi\) | |||||||
\(462\) | −11.6128 | −0.540279 | ||||||||
\(463\) | −35.1209 | −1.63221 | −0.816104 | − | 0.577905i | \(-0.803870\pi\) | ||||
−0.816104 | + | 0.577905i | \(0.803870\pi\) | |||||||
\(464\) | 3.37778 | 0.156810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9081 | −0.829578 | ||||||||
\(467\) | 4.56199 | 0.211104 | 0.105552 | − | 0.994414i | \(-0.466339\pi\) | ||||
0.105552 | + | 0.994414i | \(0.466339\pi\) | |||||||
\(468\) | −5.80642 | −0.268402 | ||||||||
\(469\) | −69.1437 | −3.19276 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.5210 | 0.991634 | ||||||||
\(472\) | 1.05086 | 0.0483695 | ||||||||
\(473\) | 28.8198 | 1.32514 | ||||||||
\(474\) | −4.42864 | −0.203414 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 16.8573 | 0.772652 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 28.2766 | 1.29334 | ||||||||
\(479\) | 37.4005 | 1.70887 | 0.854437 | − | 0.519555i | \(-0.173902\pi\) | ||||
0.854437 | + | 0.519555i | \(0.173902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.7146 | 1.53725 | ||||||||
\(482\) | 11.5111 | 0.524318 | ||||||||
\(483\) | 11.6128 | 0.528403 | ||||||||
\(484\) | −4.12399 | −0.187454 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 20.9175 | 0.947862 | 0.473931 | − | 0.880562i | \(-0.342835\pi\) | ||||
0.473931 | + | 0.880562i | \(0.342835\pi\) | |||||||
\(488\) | −4.75557 | −0.215274 | ||||||||
\(489\) | 8.23506 | 0.372402 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8666 | −0.716052 | −0.358026 | − | 0.933712i | \(-0.616550\pi\) | ||||
−0.358026 | + | 0.933712i | \(0.616550\pi\) | |||||||
\(492\) | 5.67307 | 0.255762 | ||||||||
\(493\) | 12.8573 | 0.579063 | ||||||||
\(494\) | 5.80642 | 0.261243 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.42864 | −0.198852 | ||||||||
\(497\) | 69.1437 | 3.10152 | ||||||||
\(498\) | 11.9081 | 0.533616 | ||||||||
\(499\) | 16.7368 | 0.749244 | 0.374622 | − | 0.927178i | \(-0.377773\pi\) | ||||
0.374622 | + | 0.927178i | \(0.377773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.47013 | −0.378417 | ||||||||
\(502\) | 7.74620 | 0.345730 | ||||||||
\(503\) | −21.9684 | −0.979521 | −0.489760 | − | 0.871857i | \(-0.662916\pi\) | ||||
−0.489760 | + | 0.871857i | \(0.662916\pi\) | |||||||
\(504\) | −4.42864 | −0.197267 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.87601 | −0.305676 | ||||||||
\(507\) | 20.7146 | 0.919966 | ||||||||
\(508\) | −6.42864 | −0.285225 | ||||||||
\(509\) | −15.2573 | −0.676270 | −0.338135 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338135 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51.4291 | −2.27509 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −13.8796 | −0.612201 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.9906 | 0.483836 | ||||||||
\(517\) | −6.87601 | −0.302407 | ||||||||
\(518\) | 25.7146 | 1.12983 | ||||||||
\(519\) | 22.4701 | 0.986329 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.3269 | −0.802917 | −0.401459 | − | 0.915877i | \(-0.631497\pi\) | ||||
−0.401459 | + | 0.915877i | \(0.631497\pi\) | |||||||
\(522\) | −3.37778 | −0.147842 | ||||||||
\(523\) | −24.8573 | −1.08693 | −0.543466 | − | 0.839431i | \(-0.682888\pi\) | ||||
−0.543466 | + | 0.839431i | \(0.682888\pi\) | |||||||
\(524\) | −15.0923 | −0.659312 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.6222 | −0.811967 | ||||||||
\(527\) | −16.8573 | −0.734315 | ||||||||
\(528\) | 2.62222 | 0.114117 | ||||||||
\(529\) | −16.1240 | −0.701043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.05086 | −0.0456032 | ||||||||
\(532\) | 4.42864 | 0.192006 | ||||||||
\(533\) | −32.9403 | −1.42680 | ||||||||
\(534\) | −12.4286 | −0.537840 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.6128 | 0.674372 | ||||||||
\(537\) | −2.94914 | −0.127265 | ||||||||
\(538\) | −15.8479 | −0.683252 | ||||||||
\(539\) | 33.0736 | 1.42458 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.34614 | −0.0578751 | −0.0289376 | − | 0.999581i | \(-0.509212\pi\) | ||||
−0.0289376 | + | 0.999581i | \(0.509212\pi\) | |||||||
\(542\) | −1.51114 | −0.0649089 | ||||||||
\(543\) | 22.8988 | 0.982680 | ||||||||
\(544\) | −3.80642 | −0.163199 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 25.7146 | 1.10048 | ||||||||
\(547\) | 8.59057 | 0.367306 | 0.183653 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183653 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(548\) | 7.53972 | 0.322081 | ||||||||
\(549\) | 4.75557 | 0.202963 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.37778 | 0.143898 | ||||||||
\(552\) | −2.62222 | −0.111609 | ||||||||
\(553\) | 19.6128 | 0.834023 | ||||||||
\(554\) | 1.05086 | 0.0446466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.387152 | 0.0164189 | ||||||||
\(557\) | 5.86665 | 0.248578 | 0.124289 | − | 0.992246i | \(-0.460335\pi\) | ||||
0.124289 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(558\) | 4.42864 | 0.187479 | ||||||||
\(559\) | −63.8163 | −2.69914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.98126 | 0.421409 | ||||||||
\(562\) | −3.45091 | −0.145568 | ||||||||
\(563\) | −31.4291 | −1.32458 | −0.662290 | − | 0.749248i | \(-0.730415\pi\) | ||||
−0.662290 | + | 0.749248i | \(0.730415\pi\) | |||||||
\(564\) | −2.62222 | −0.110415 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.5812 | 0.654927 | ||||||||
\(567\) | 4.42864 | 0.185985 | ||||||||
\(568\) | −15.6128 | −0.655101 | ||||||||
\(569\) | −7.95851 | −0.333638 | −0.166819 | − | 0.985988i | \(-0.553350\pi\) | ||||
−0.166819 | + | 0.985988i | \(0.553350\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.8385 | −1.29055 | −0.645276 | − | 0.763949i | \(-0.723258\pi\) | ||||
−0.645276 | + | 0.763949i | \(0.723258\pi\) | |||||||
\(572\) | −15.2257 | −0.636618 | ||||||||
\(573\) | −9.05086 | −0.378105 | ||||||||
\(574\) | −25.1240 | −1.04865 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −32.0000 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(578\) | 2.51114 | 0.104450 | ||||||||
\(579\) | −18.7239 | −0.778140 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −52.7368 | −2.18789 | ||||||||
\(582\) | 7.37778 | 0.305819 | ||||||||
\(583\) | 15.7333 | 0.651606 | ||||||||
\(584\) | 11.6128 | 0.480543 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.12399 | 0.294289 | ||||||||
\(587\) | −17.8064 | −0.734950 | −0.367475 | − | 0.930033i | \(-0.619778\pi\) | ||||
−0.367475 | + | 0.930033i | \(0.619778\pi\) | |||||||
\(588\) | 12.6128 | 0.520145 | ||||||||
\(589\) | −4.42864 | −0.182479 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.888922 | −0.0365654 | ||||||||
\(592\) | −5.80642 | −0.238643 | ||||||||
\(593\) | 13.3176 | 0.546887 | 0.273443 | − | 0.961888i | \(-0.411837\pi\) | ||||
0.273443 | + | 0.961888i | \(0.411837\pi\) | |||||||
\(594\) | −2.62222 | −0.107591 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14.5303 | −0.595186 | ||||||||
\(597\) | 21.7146 | 0.888718 | ||||||||
\(598\) | 15.2257 | 0.622625 | ||||||||
\(599\) | −43.8163 | −1.79028 | −0.895142 | − | 0.445781i | \(-0.852926\pi\) | ||||
−0.895142 | + | 0.445781i | \(0.852926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.73329 | −0.397029 | −0.198515 | − | 0.980098i | \(-0.563612\pi\) | ||||
−0.198515 | + | 0.980098i | \(0.563612\pi\) | |||||||
\(602\) | −48.6735 | −1.98379 | ||||||||
\(603\) | −15.6128 | −0.635804 | ||||||||
\(604\) | 4.69535 | 0.191051 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.6731 | −0.717919 | ||||||||
\(607\) | 31.9398 | 1.29640 | 0.648198 | − | 0.761472i | \(-0.275523\pi\) | ||||
0.648198 | + | 0.761472i | \(0.275523\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 14.9590 | 0.606169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.2257 | 0.615966 | ||||||||
\(612\) | 3.80642 | 0.153866 | ||||||||
\(613\) | −11.8064 | −0.476857 | −0.238428 | − | 0.971160i | \(-0.576632\pi\) | ||||
−0.238428 | + | 0.971160i | \(0.576632\pi\) | |||||||
\(614\) | 1.12399 | 0.0453603 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.6128 | −0.467895 | ||||||||
\(617\) | −26.5620 | −1.06935 | −0.534673 | − | 0.845059i | \(-0.679565\pi\) | ||||
−0.534673 | + | 0.845059i | \(0.679565\pi\) | |||||||
\(618\) | −1.18421 | −0.0476358 | ||||||||
\(619\) | 7.34614 | 0.295266 | 0.147633 | − | 0.989042i | \(-0.452834\pi\) | ||||
0.147633 | + | 0.989042i | \(0.452834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.62222 | 0.105226 | ||||||||
\(622\) | −14.9491 | −0.599406 | ||||||||
\(623\) | 55.0420 | 2.20521 | ||||||||
\(624\) | −5.80642 | −0.232443 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.14272 | 0.125608 | ||||||||
\(627\) | 2.62222 | 0.104721 | ||||||||
\(628\) | 21.5210 | 0.858781 | ||||||||
\(629\) | −22.1017 | −0.881253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7556 | −1.22436 | −0.612180 | − | 0.790718i | \(-0.709707\pi\) | ||||
−0.612180 | + | 0.790718i | \(0.709707\pi\) | |||||||
\(632\) | −4.42864 | −0.176162 | ||||||||
\(633\) | −3.61285 | −0.143598 | ||||||||
\(634\) | 10.5906 | 0.420605 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −73.2355 | −2.90170 | ||||||||
\(638\) | −8.85728 | −0.350663 | ||||||||
\(639\) | 15.6128 | 0.617635 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3876 | −1.55572 | −0.777859 | − | 0.628439i | \(-0.783694\pi\) | ||||
−0.777859 | + | 0.628439i | \(0.783694\pi\) | |||||||
\(642\) | 4.85728 | 0.191702 | ||||||||
\(643\) | −24.1146 | −0.950988 | −0.475494 | − | 0.879719i | \(-0.657731\pi\) | ||||
−0.475494 | + | 0.879719i | \(0.657731\pi\) | |||||||
\(644\) | 11.6128 | 0.457610 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.80642 | −0.149762 | ||||||||
\(647\) | 47.6829 | 1.87461 | 0.937304 | − | 0.348512i | \(-0.113313\pi\) | ||||
0.937304 | + | 0.348512i | \(0.113313\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.75557 | −0.108166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.6128 | −0.768688 | ||||||||
\(652\) | 8.23506 | 0.322510 | ||||||||
\(653\) | −21.7462 | −0.850995 | −0.425497 | − | 0.904960i | \(-0.639901\pi\) | ||||
−0.425497 | + | 0.904960i | \(0.639901\pi\) | |||||||
\(654\) | 6.04149 | 0.236241 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.67307 | 0.221496 | ||||||||
\(657\) | −11.6128 | −0.453060 | ||||||||
\(658\) | 11.6128 | 0.452716 | ||||||||
\(659\) | −16.1936 | −0.630812 | −0.315406 | − | 0.948957i | \(-0.602141\pi\) | ||||
−0.315406 | + | 0.948957i | \(0.602141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5116 | −0.875600 | −0.437800 | − | 0.899072i | \(-0.644242\pi\) | ||||
−0.437800 | + | 0.899072i | \(0.644242\pi\) | |||||||
\(662\) | 15.1427 | 0.588539 | ||||||||
\(663\) | −22.1017 | −0.858359 | ||||||||
\(664\) | 11.9081 | 0.462125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.80642 | 0.224994 | ||||||||
\(667\) | 8.85728 | 0.342955 | ||||||||
\(668\) | −8.47013 | −0.327719 | ||||||||
\(669\) | 21.3876 | 0.826893 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4701 | 0.481404 | ||||||||
\(672\) | −4.42864 | −0.170838 | ||||||||
\(673\) | −9.66323 | −0.372490 | −0.186245 | − | 0.982503i | \(-0.559632\pi\) | ||||
−0.186245 | + | 0.982503i | \(0.559632\pi\) | |||||||
\(674\) | 11.1111 | 0.427983 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.7146 | 0.796714 | ||||||||
\(677\) | 6.85728 | 0.263547 | 0.131773 | − | 0.991280i | \(-0.457933\pi\) | ||||
0.131773 | + | 0.991280i | \(0.457933\pi\) | |||||||
\(678\) | 9.34614 | 0.358936 | ||||||||
\(679\) | −32.6735 | −1.25390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.47013 | −0.324576 | ||||||||
\(682\) | 11.6128 | 0.444679 | ||||||||
\(683\) | −30.3051 | −1.15959 | −0.579797 | − | 0.814761i | \(-0.696868\pi\) | ||||
−0.579797 | + | 0.814761i | \(0.696868\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.8573 | −0.949055 | ||||||||
\(687\) | −16.9590 | −0.647026 | ||||||||
\(688\) | 10.9906 | 0.419014 | ||||||||
\(689\) | −34.8385 | −1.32724 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.61285 | 0.289606 | 0.144803 | − | 0.989460i | \(-0.453745\pi\) | ||||
0.144803 | + | 0.989460i | \(0.453745\pi\) | |||||||
\(692\) | 22.4701 | 0.854186 | ||||||||
\(693\) | 11.6128 | 0.441136 | ||||||||
\(694\) | −14.1936 | −0.538781 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.37778 | −0.128035 | ||||||||
\(697\) | 21.5941 | 0.817935 | ||||||||
\(698\) | −32.3684 | −1.22516 | ||||||||
\(699\) | 17.9081 | 0.677348 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3654 | −1.22242 | −0.611211 | − | 0.791467i | \(-0.709317\pi\) | ||||
−0.611211 | + | 0.791467i | \(0.709317\pi\) | |||||||
\(702\) | 5.80642 | 0.219149 | ||||||||
\(703\) | −5.80642 | −0.218993 | ||||||||
\(704\) | 2.62222 | 0.0988285 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8064 | −0.444341 | ||||||||
\(707\) | 78.2677 | 2.94356 | ||||||||
\(708\) | −1.05086 | −0.0394936 | ||||||||
\(709\) | −49.8992 | −1.87401 | −0.937003 | − | 0.349322i | \(-0.886412\pi\) | ||||
−0.937003 | + | 0.349322i | \(0.886412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.42864 | 0.166087 | ||||||||
\(712\) | −12.4286 | −0.465783 | ||||||||
\(713\) | −11.6128 | −0.434905 | ||||||||
\(714\) | −16.8573 | −0.630868 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.94914 | −0.110215 | ||||||||
\(717\) | −28.2766 | −1.05601 | ||||||||
\(718\) | 10.8287 | 0.404123 | ||||||||
\(719\) | −26.4415 | −0.986103 | −0.493052 | − | 0.870000i | \(-0.664119\pi\) | ||||
−0.493052 | + | 0.870000i | \(0.664119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.24443 | 0.195313 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −11.5111 | −0.428104 | ||||||||
\(724\) | 22.8988 | 0.851026 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.12399 | 0.153055 | ||||||||
\(727\) | −48.1245 | −1.78484 | −0.892419 | − | 0.451208i | \(-0.850993\pi\) | ||||
−0.892419 | + | 0.451208i | \(0.850993\pi\) | |||||||
\(728\) | 25.7146 | 0.953045 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.8350 | 1.54732 | ||||||||
\(732\) | 4.75557 | 0.175771 | ||||||||
\(733\) | 14.0286 | 0.518157 | 0.259079 | − | 0.965856i | \(-0.416581\pi\) | ||||
0.259079 | + | 0.965856i | \(0.416581\pi\) | |||||||
\(734\) | −1.46965 | −0.0542458 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.62222 | −0.0966562 | ||||||||
\(737\) | −40.9403 | −1.50805 | ||||||||
\(738\) | −5.67307 | −0.208829 | ||||||||
\(739\) | 10.1847 | 0.374650 | 0.187325 | − | 0.982298i | \(-0.440018\pi\) | ||||
0.187325 | + | 0.982298i | \(0.440018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.80642 | −0.213304 | ||||||||
\(742\) | −26.5718 | −0.975483 | ||||||||
\(743\) | 42.9590 | 1.57601 | 0.788006 | − | 0.615667i | \(-0.211113\pi\) | ||||
0.788006 | + | 0.615667i | \(0.211113\pi\) | |||||||
\(744\) | 4.42864 | 0.162362 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.3783 | 0.892552 | ||||||||
\(747\) | −11.9081 | −0.435696 | ||||||||
\(748\) | 9.98126 | 0.364951 | ||||||||
\(749\) | −21.5111 | −0.786000 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.18421 | −0.262155 | −0.131078 | − | 0.991372i | \(-0.541844\pi\) | ||||
−0.131078 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(752\) | −2.62222 | −0.0956224 | ||||||||
\(753\) | −7.74620 | −0.282287 | ||||||||
\(754\) | 19.6128 | 0.714258 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.42864 | 0.161068 | ||||||||
\(757\) | −41.2543 | −1.49941 | −0.749706 | − | 0.661771i | \(-0.769805\pi\) | ||||
−0.749706 | + | 0.661771i | \(0.769805\pi\) | |||||||
\(758\) | −18.9590 | −0.688621 | ||||||||
\(759\) | 6.87601 | 0.249584 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.3051 | 1.60606 | 0.803030 | − | 0.595939i | \(-0.203220\pi\) | ||||
0.803030 | + | 0.595939i | \(0.203220\pi\) | |||||||
\(762\) | 6.42864 | 0.232885 | ||||||||
\(763\) | −26.7556 | −0.968617 | ||||||||
\(764\) | −9.05086 | −0.327448 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.1017 | −0.943093 | ||||||||
\(767\) | 6.10171 | 0.220320 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −6.59057 | −0.237662 | −0.118831 | − | 0.992914i | \(-0.537915\pi\) | ||||
−0.118831 | + | 0.992914i | \(0.537915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.8796 | 0.499860 | ||||||||
\(772\) | −18.7239 | −0.673889 | ||||||||
\(773\) | 8.83854 | 0.317900 | 0.158950 | − | 0.987287i | \(-0.449189\pi\) | ||||
0.158950 | + | 0.987287i | \(0.449189\pi\) | |||||||
\(774\) | −10.9906 | −0.395050 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.37778 | 0.264847 | ||||||||
\(777\) | −25.7146 | −0.922505 | ||||||||
\(778\) | 3.57136 | 0.128039 | ||||||||
\(779\) | 5.67307 | 0.203259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.9403 | 1.46496 | ||||||||
\(782\) | −9.98126 | −0.356929 | ||||||||
\(783\) | 3.37778 | 0.120712 | ||||||||
\(784\) | 12.6128 | 0.450459 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.0923 | 0.538326 | ||||||||
\(787\) | 16.9403 | 0.603855 | 0.301927 | − | 0.953331i | \(-0.402370\pi\) | ||||
0.301927 | + | 0.953331i | \(0.402370\pi\) | |||||||
\(788\) | −0.888922 | −0.0316665 | ||||||||
\(789\) | 18.6222 | 0.662968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.3907 | −1.47168 | ||||||||
\(792\) | −2.62222 | −0.0931764 | ||||||||
\(793\) | −27.6128 | −0.980561 | ||||||||
\(794\) | 31.4193 | 1.11503 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.7146 | 0.769652 | ||||||||
\(797\) | 40.1847 | 1.42341 | 0.711707 | − | 0.702476i | \(-0.247922\pi\) | ||||
0.711707 | + | 0.702476i | \(0.247922\pi\) | |||||||
\(798\) | −4.42864 | −0.156772 | ||||||||
\(799\) | −9.98126 | −0.353112 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4286 | 0.439144 | ||||||||
\(802\) | −12.0415 | −0.425200 | ||||||||
\(803\) | −30.4514 | −1.07461 | ||||||||
\(804\) | −15.6128 | −0.550623 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.7146 | −0.905757 | ||||||||
\(807\) | 15.8479 | 0.557873 | ||||||||
\(808\) | −17.6731 | −0.621736 | ||||||||
\(809\) | 29.1052 | 1.02329 | 0.511643 | − | 0.859198i | \(-0.329037\pi\) | ||||
0.511643 | + | 0.859198i | \(0.329037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.7753 | 1.36158 | 0.680792 | − | 0.732477i | \(-0.261636\pi\) | ||||
0.680792 | + | 0.732477i | \(0.261636\pi\) | |||||||
\(812\) | 14.9590 | 0.524958 | ||||||||
\(813\) | 1.51114 | 0.0529979 | ||||||||
\(814\) | 15.2257 | 0.533660 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.80642 | 0.133251 | ||||||||
\(817\) | 10.9906 | 0.384514 | ||||||||
\(818\) | −26.4701 | −0.925506 | ||||||||
\(819\) | −25.7146 | −0.898539 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.53035 | 0.0883098 | 0.0441549 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441549 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(822\) | −7.53972 | −0.262978 | ||||||||
\(823\) | 24.0415 | 0.838034 | 0.419017 | − | 0.907978i | \(-0.362375\pi\) | ||||
0.419017 | + | 0.907978i | \(0.362375\pi\) | |||||||
\(824\) | −1.18421 | −0.0412538 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.65386 | 0.161928 | ||||||||
\(827\) | 6.57184 | 0.228525 | 0.114263 | − | 0.993451i | \(-0.463549\pi\) | ||||
0.114263 | + | 0.993451i | \(0.463549\pi\) | |||||||
\(828\) | 2.62222 | 0.0911283 | ||||||||
\(829\) | −28.7338 | −0.997965 | −0.498983 | − | 0.866612i | \(-0.666293\pi\) | ||||
−0.498983 | + | 0.866612i | \(0.666293\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.05086 | −0.0364538 | ||||||||
\(832\) | −5.80642 | −0.201302 | ||||||||
\(833\) | 48.0098 | 1.66344 | ||||||||
\(834\) | −0.387152 | −0.0134060 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.62222 | 0.0906912 | ||||||||
\(837\) | −4.42864 | −0.153076 | ||||||||
\(838\) | 25.9684 | 0.897062 | ||||||||
\(839\) | −50.5718 | −1.74593 | −0.872967 | − | 0.487780i | \(-0.837807\pi\) | ||||
−0.872967 | + | 0.487780i | \(0.837807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5906 | −0.606571 | ||||||||
\(842\) | 29.2672 | 1.00861 | ||||||||
\(843\) | 3.45091 | 0.118856 | ||||||||
\(844\) | −3.61285 | −0.124359 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.62222 | 0.0901536 | ||||||||
\(847\) | −18.2636 | −0.627546 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −15.5812 | −0.534746 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.2257 | −0.521930 | ||||||||
\(852\) | 15.6128 | 0.534887 | ||||||||
\(853\) | 31.2355 | 1.06948 | 0.534742 | − | 0.845015i | \(-0.320409\pi\) | ||||
0.534742 | + | 0.845015i | \(0.320409\pi\) | |||||||
\(854\) | −21.0607 | −0.720682 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.85728 | 0.166018 | ||||||||
\(857\) | −27.3274 | −0.933486 | −0.466743 | − | 0.884393i | \(-0.654573\pi\) | ||||
−0.466743 | + | 0.884393i | \(0.654573\pi\) | |||||||
\(858\) | 15.2257 | 0.519797 | ||||||||
\(859\) | −34.7753 | −1.18652 | −0.593258 | − | 0.805012i | \(-0.702159\pi\) | ||||
−0.593258 | + | 0.805012i | \(0.702159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.1240 | 0.856223 | ||||||||
\(862\) | −14.8385 | −0.505403 | ||||||||
\(863\) | −21.2444 | −0.723169 | −0.361584 | − | 0.932339i | \(-0.617764\pi\) | ||||
−0.361584 | + | 0.932339i | \(0.617764\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.27607 | −0.179288 | ||||||||
\(867\) | −2.51114 | −0.0852827 | ||||||||
\(868\) | −19.6128 | −0.665703 | ||||||||
\(869\) | 11.6128 | 0.393939 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 90.6548 | 3.07172 | ||||||||
\(872\) | 6.04149 | 0.204591 | ||||||||
\(873\) | −7.37778 | −0.249700 | ||||||||
\(874\) | −2.62222 | −0.0886978 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.6128 | −0.392362 | ||||||||
\(877\) | −22.3970 | −0.756293 | −0.378146 | − | 0.925746i | \(-0.623438\pi\) | ||||
−0.378146 | + | 0.925746i | \(0.623438\pi\) | |||||||
\(878\) | −31.8578 | −1.07515 | ||||||||
\(879\) | −7.12399 | −0.240286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3684 | −0.686229 | −0.343115 | − | 0.939294i | \(-0.611482\pi\) | ||||
−0.343115 | + | 0.939294i | \(0.611482\pi\) | |||||||
\(882\) | −12.6128 | −0.424697 | ||||||||
\(883\) | −21.6829 | −0.729688 | −0.364844 | − | 0.931069i | \(-0.618878\pi\) | ||||
−0.364844 | + | 0.931069i | \(0.618878\pi\) | |||||||
\(884\) | −22.1017 | −0.743361 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.94914 | −0.166270 | ||||||||
\(887\) | 7.14272 | 0.239829 | 0.119915 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119915 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(888\) | 5.80642 | 0.194851 | ||||||||
\(889\) | −28.4701 | −0.954857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.62222 | 0.0878475 | ||||||||
\(892\) | 21.3876 | 0.716111 | ||||||||
\(893\) | −2.62222 | −0.0877491 | ||||||||
\(894\) | 14.5303 | 0.485968 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.42864 | −0.147950 | ||||||||
\(897\) | −15.2257 | −0.508371 | ||||||||
\(898\) | −9.75605 | −0.325563 | ||||||||
\(899\) | −14.9590 | −0.498910 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.8385 | 0.760862 | ||||||||
\(902\) | −14.8760 | −0.495317 | ||||||||
\(903\) | 48.6735 | 1.61975 | ||||||||
\(904\) | 9.34614 | 0.310848 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.69535 | −0.155992 | ||||||||
\(907\) | −15.3461 | −0.509560 | −0.254780 | − | 0.966999i | \(-0.582003\pi\) | ||||
−0.254780 | + | 0.966999i | \(0.582003\pi\) | |||||||
\(908\) | −8.47013 | −0.281091 | ||||||||
\(909\) | 17.6731 | 0.586179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1204 | 0.401568 | 0.200784 | − | 0.979636i | \(-0.435651\pi\) | ||||
0.200784 | + | 0.979636i | \(0.435651\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −31.2257 | −1.03342 | ||||||||
\(914\) | 8.00000 | 0.264616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.9590 | −0.560341 | ||||||||
\(917\) | −66.8385 | −2.20720 | ||||||||
\(918\) | −3.80642 | −0.125631 | ||||||||
\(919\) | −12.2667 | −0.404641 | −0.202321 | − | 0.979319i | \(-0.564848\pi\) | ||||
−0.202321 | + | 0.979319i | \(0.564848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.12399 | −0.0370366 | ||||||||
\(922\) | 36.1245 | 1.18970 | ||||||||
\(923\) | −90.6548 | −2.98394 | ||||||||
\(924\) | 11.6128 | 0.382035 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.1209 | 1.15415 | ||||||||
\(927\) | 1.18421 | 0.0388945 | ||||||||
\(928\) | −3.37778 | −0.110881 | ||||||||
\(929\) | −40.1847 | −1.31842 | −0.659208 | − | 0.751960i | \(-0.729108\pi\) | ||||
−0.659208 | + | 0.751960i | \(0.729108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.6128 | 0.413369 | ||||||||
\(932\) | 17.9081 | 0.586600 | ||||||||
\(933\) | 14.9491 | 0.489413 | ||||||||
\(934\) | −4.56199 | −0.149273 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.80642 | 0.189789 | ||||||||
\(937\) | 24.7368 | 0.808117 | 0.404059 | − | 0.914733i | \(-0.367599\pi\) | ||||
0.404059 | + | 0.914733i | \(0.367599\pi\) | |||||||
\(938\) | 69.1437 | 2.25762 | ||||||||
\(939\) | −3.14272 | −0.102559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.66323 | −0.0542196 | −0.0271098 | − | 0.999632i | \(-0.508630\pi\) | ||||
−0.0271098 | + | 0.999632i | \(0.508630\pi\) | |||||||
\(942\) | −21.5210 | −0.701191 | ||||||||
\(943\) | 14.8760 | 0.484430 | ||||||||
\(944\) | −1.05086 | −0.0342024 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.8198 | −0.937013 | ||||||||
\(947\) | −14.8671 | −0.483117 | −0.241558 | − | 0.970386i | \(-0.577659\pi\) | ||||
−0.241558 | + | 0.970386i | \(0.577659\pi\) | |||||||
\(948\) | 4.42864 | 0.143836 | ||||||||
\(949\) | 67.4291 | 2.18884 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.5906 | −0.343423 | ||||||||
\(952\) | −16.8573 | −0.546348 | ||||||||
\(953\) | 8.83854 | 0.286308 | 0.143154 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143154 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.2766 | −0.914529 | ||||||||
\(957\) | 8.85728 | 0.286315 | ||||||||
\(958\) | −37.4005 | −1.20836 | ||||||||
\(959\) | 33.3907 | 1.07824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3872 | −0.367327 | ||||||||
\(962\) | −33.7146 | −1.08700 | ||||||||
\(963\) | −4.85728 | −0.156524 | ||||||||
\(964\) | −11.5111 | −0.370749 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.6128 | −0.373637 | ||||||||
\(967\) | −1.55262 | −0.0499290 | −0.0249645 | − | 0.999688i | \(-0.507947\pi\) | ||||
−0.0249645 | + | 0.999688i | \(0.507947\pi\) | |||||||
\(968\) | 4.12399 | 0.132550 | ||||||||
\(969\) | 3.80642 | 0.122280 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.5433 | 1.42946 | 0.714731 | − | 0.699400i | \(-0.246549\pi\) | ||||
0.714731 | + | 0.699400i | \(0.246549\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.71456 | 0.0549662 | ||||||||
\(974\) | −20.9175 | −0.670240 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.75557 | 0.152222 | ||||||||
\(977\) | −15.8350 | −0.506607 | −0.253303 | − | 0.967387i | \(-0.581517\pi\) | ||||
−0.253303 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(978\) | −8.23506 | −0.263328 | ||||||||
\(979\) | 32.5906 | 1.04160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.04149 | −0.192890 | ||||||||
\(982\) | 15.8666 | 0.506325 | ||||||||
\(983\) | −6.87601 | −0.219311 | −0.109655 | − | 0.993970i | \(-0.534975\pi\) | ||||
−0.109655 | + | 0.993970i | \(0.534975\pi\) | |||||||
\(984\) | −5.67307 | −0.180851 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.8573 | −0.409459 | ||||||||
\(987\) | −11.6128 | −0.369641 | ||||||||
\(988\) | −5.80642 | −0.184727 | ||||||||
\(989\) | 28.8198 | 0.916417 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.8765 | −0.949058 | −0.474529 | − | 0.880240i | \(-0.657382\pi\) | ||||
−0.474529 | + | 0.880240i | \(0.657382\pi\) | |||||||
\(992\) | 4.42864 | 0.140609 | ||||||||
\(993\) | −15.1427 | −0.480540 | ||||||||
\(994\) | −69.1437 | −2.19310 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.9081 | −0.377324 | ||||||||
\(997\) | −5.90813 | −0.187112 | −0.0935562 | − | 0.995614i | \(-0.529823\pi\) | ||||
−0.0935562 | + | 0.995614i | \(0.529823\pi\) | |||||||
\(998\) | −16.7368 | −0.529795 | ||||||||
\(999\) | −5.80642 | −0.183707 |
(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 | 2850.2.a.bl.1.3 | 3 | ||
3.2 | odd | 2 | 8550.2.a.cq.1.3 | 3 | |||
5.2 | odd | 4 | 570.2.d.c.229.3 | ✓ | 6 | ||
5.3 | odd | 4 | 570.2.d.c.229.6 | yes | 6 | ||
5.4 | even | 2 | 2850.2.a.bm.1.1 | 3 | |||
15.2 | even | 4 | 1710.2.d.f.1369.4 | 6 | |||
15.8 | even | 4 | 1710.2.d.f.1369.1 | 6 | |||
15.14 | odd | 2 | 8550.2.a.ce.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.c.229.3 | ✓ | 6 | 5.2 | odd | 4 | ||
570.2.d.c.229.6 | yes | 6 | 5.3 | odd | 4 | ||
1710.2.d.f.1369.1 | 6 | 15.8 | even | 4 | |||
1710.2.d.f.1369.4 | 6 | 15.2 | even | 4 | |||
2850.2.a.bl.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2850.2.a.bm.1.1 | 3 | 5.4 | even | 2 | |||
8550.2.a.ce.1.1 | 3 | 15.14 | odd | 2 | |||
8550.2.a.cq.1.3 | 3 | 3.2 | odd | 2 |