Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.73205 | −0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.46410 | −1.51547 | −0.757735 | − | 0.652563i | \(-0.773694\pi\) | ||||
−0.757735 | + | 0.652563i | \(0.773694\pi\) | |||||||
\(14\) | −3.46410 | −0.925820 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 1.73205 | 0.408248 | ||||||||
\(19\) | −5.46410 | −1.25355 | −0.626775 | − | 0.779200i | \(-0.715626\pi\) | ||||
−0.626775 | + | 0.779200i | \(0.715626\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.92820 | 1.44463 | 0.722315 | − | 0.691564i | \(-0.243078\pi\) | ||||
0.722315 | + | 0.691564i | \(0.243078\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.46410 | −1.85606 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 3.46410 | 0.643268 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | −10.9282 | −1.96276 | −0.981382 | − | 0.192068i | \(-0.938481\pi\) | ||||
−0.981382 | + | 0.192068i | \(0.938481\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.92820 | −0.810192 | −0.405096 | − | 0.914274i | \(-0.632762\pi\) | ||||
−0.405096 | + | 0.914274i | \(0.632762\pi\) | |||||||
\(38\) | −9.46410 | −1.53528 | ||||||||
\(39\) | −5.46410 | −0.874957 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | −3.46410 | −0.534522 | ||||||||
\(43\) | 4.92820 | 0.751544 | 0.375772 | − | 0.926712i | \(-0.377378\pi\) | ||||
0.375772 | + | 0.926712i | \(0.377378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 12.0000 | 1.76930 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | −5.00000 | −0.721688 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 1.73205 | 0.244949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.46410 | −0.757735 | ||||||||
\(53\) | 0.928203 | 0.127499 | 0.0637493 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637493 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(54\) | 1.73205 | 0.235702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | −5.46410 | −0.723738 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −18.9282 | −2.40388 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.46410 | 0.677738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820 | 0.834058 | ||||||||
\(70\) | 3.46410 | 0.414039 | ||||||||
\(71\) | 13.8564 | 1.64445 | 0.822226 | − | 0.569160i | \(-0.192732\pi\) | ||||
0.822226 | + | 0.569160i | \(0.192732\pi\) | |||||||
\(72\) | −1.73205 | −0.204124 | ||||||||
\(73\) | 8.39230 | 0.982245 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(74\) | −8.53590 | −0.992278 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −5.46410 | −0.626775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.46410 | −1.07160 | ||||||||
\(79\) | 6.53590 | 0.735346 | 0.367673 | − | 0.929955i | \(-0.380155\pi\) | ||||
0.367673 | + | 0.929955i | \(0.380155\pi\) | |||||||
\(80\) | 5.00000 | 0.559017 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | −8.53590 | −0.936937 | −0.468468 | − | 0.883480i | \(-0.655194\pi\) | ||||
−0.468468 | + | 0.883480i | \(0.655194\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.53590 | 0.920450 | ||||||||
\(87\) | 3.46410 | 0.371391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.928203 | 0.0983893 | 0.0491947 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491947 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(90\) | −1.73205 | −0.182574 | ||||||||
\(91\) | 10.9282 | 1.14559 | ||||||||
\(92\) | 6.92820 | 0.722315 | ||||||||
\(93\) | −10.9282 | −1.13320 | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | 5.46410 | 0.560605 | ||||||||
\(96\) | −5.19615 | −0.530330 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −5.19615 | −0.524891 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 9.46410 | 0.928032 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 1.60770 | 0.156153 | ||||||||
\(107\) | −8.53590 | −0.825196 | −0.412598 | − | 0.910913i | \(-0.635379\pi\) | ||||
−0.412598 | + | 0.910913i | \(0.635379\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 10.0000 | 0.944911 | ||||||||
\(113\) | −12.9282 | −1.21618 | −0.608092 | − | 0.793867i | \(-0.708065\pi\) | ||||
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(114\) | −9.46410 | −0.886394 | ||||||||
\(115\) | −6.92820 | −0.646058 | ||||||||
\(116\) | 3.46410 | 0.321634 | ||||||||
\(117\) | −5.46410 | −0.505156 | ||||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.73205 | 0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.46410 | −0.313625 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | −10.9282 | −0.981382 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.46410 | −0.308607 | ||||||||
\(127\) | −8.92820 | −0.792250 | −0.396125 | − | 0.918197i | \(-0.629645\pi\) | ||||
−0.396125 | + | 0.918197i | \(0.629645\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | 4.92820 | 0.433904 | ||||||||
\(130\) | 9.46410 | 0.830057 | ||||||||
\(131\) | −18.9282 | −1.65376 | −0.826882 | − | 0.562375i | \(-0.809888\pi\) | ||||
−0.826882 | + | 0.562375i | \(0.809888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9282 | 0.947595 | ||||||||
\(134\) | 13.8564 | 1.19701 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | −12.3923 | −1.05110 | −0.525551 | − | 0.850762i | \(-0.676141\pi\) | ||||
−0.525551 | + | 0.850762i | \(0.676141\pi\) | |||||||
\(140\) | 2.00000 | 0.169031 | ||||||||
\(141\) | −6.92820 | −0.583460 | ||||||||
\(142\) | 24.0000 | 2.01404 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | −3.46410 | −0.287678 | ||||||||
\(146\) | 14.5359 | 1.20300 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | −4.92820 | −0.405096 | ||||||||
\(149\) | 15.4641 | 1.26687 | 0.633434 | − | 0.773796i | \(-0.281645\pi\) | ||||
0.633434 | + | 0.773796i | \(0.281645\pi\) | |||||||
\(150\) | 1.73205 | 0.141421 | ||||||||
\(151\) | 20.3923 | 1.65950 | 0.829751 | − | 0.558134i | \(-0.188482\pi\) | ||||
0.829751 | + | 0.558134i | \(0.188482\pi\) | |||||||
\(152\) | 9.46410 | 0.767640 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.9282 | 0.877774 | ||||||||
\(156\) | −5.46410 | −0.437478 | ||||||||
\(157\) | −3.07180 | −0.245156 | −0.122578 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122578 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(158\) | 11.3205 | 0.900611 | ||||||||
\(159\) | 0.928203 | 0.0736113 | ||||||||
\(160\) | 5.19615 | 0.410792 | ||||||||
\(161\) | −13.8564 | −1.09204 | ||||||||
\(162\) | 1.73205 | 0.136083 | ||||||||
\(163\) | 9.85641 | 0.772013 | 0.386007 | − | 0.922496i | \(-0.373854\pi\) | ||||
0.386007 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(164\) | −3.46410 | −0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.7846 | −1.14751 | ||||||||
\(167\) | 10.3923 | 0.804181 | 0.402090 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402090 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(168\) | 3.46410 | 0.267261 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.46410 | −0.417850 | ||||||||
\(172\) | 4.92820 | 0.375772 | ||||||||
\(173\) | 12.0000 | 0.912343 | 0.456172 | − | 0.889892i | \(-0.349220\pi\) | ||||
0.456172 | + | 0.889892i | \(0.349220\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.92820 | −0.520756 | ||||||||
\(178\) | 1.60770 | 0.120502 | ||||||||
\(179\) | 6.92820 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 15.8564 | 1.17860 | 0.589299 | − | 0.807915i | \(-0.299404\pi\) | ||||
0.589299 | + | 0.807915i | \(0.299404\pi\) | |||||||
\(182\) | 18.9282 | 1.40305 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −12.0000 | −0.884652 | ||||||||
\(185\) | 4.92820 | 0.362329 | ||||||||
\(186\) | −18.9282 | −1.38788 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.92820 | −0.505291 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 9.46410 | 0.686598 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −24.3923 | −1.75580 | −0.877898 | − | 0.478847i | \(-0.841055\pi\) | ||||
−0.877898 | + | 0.478847i | \(0.841055\pi\) | |||||||
\(194\) | −17.3205 | −1.24354 | ||||||||
\(195\) | 5.46410 | 0.391292 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.7846 | −1.75693 | −0.878467 | − | 0.477803i | \(-0.841433\pi\) | ||||
−0.878467 | + | 0.477803i | \(0.841433\pi\) | |||||||
\(200\) | −1.73205 | −0.122474 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 18.0000 | 1.26648 | ||||||||
\(203\) | −6.92820 | −0.486265 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | 13.8564 | 0.965422 | ||||||||
\(207\) | 6.92820 | 0.481543 | ||||||||
\(208\) | 27.3205 | 1.89434 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.46410 | 0.239046 | ||||||||
\(211\) | 8.39230 | 0.577750 | 0.288875 | − | 0.957367i | \(-0.406719\pi\) | ||||
0.288875 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(212\) | 0.928203 | 0.0637493 | ||||||||
\(213\) | 13.8564 | 0.949425 | ||||||||
\(214\) | −14.7846 | −1.01066 | ||||||||
\(215\) | −4.92820 | −0.336101 | ||||||||
\(216\) | −1.73205 | −0.117851 | ||||||||
\(217\) | 21.8564 | 1.48371 | ||||||||
\(218\) | 17.3205 | 1.17309 | ||||||||
\(219\) | 8.39230 | 0.567099 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.53590 | −0.572892 | ||||||||
\(223\) | 9.85641 | 0.660034 | 0.330017 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(224\) | 10.3923 | 0.694365 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −22.3923 | −1.48951 | ||||||||
\(227\) | −15.4641 | −1.02639 | −0.513194 | − | 0.858272i | \(-0.671538\pi\) | ||||
−0.513194 | + | 0.858272i | \(0.671538\pi\) | |||||||
\(228\) | −5.46410 | −0.361869 | ||||||||
\(229\) | −23.8564 | −1.57648 | −0.788238 | − | 0.615371i | \(-0.789006\pi\) | ||||
−0.788238 | + | 0.615371i | \(0.789006\pi\) | |||||||
\(230\) | −12.0000 | −0.791257 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −12.0000 | −0.786146 | −0.393073 | − | 0.919507i | \(-0.628588\pi\) | ||||
−0.393073 | + | 0.919507i | \(0.628588\pi\) | |||||||
\(234\) | −9.46410 | −0.618688 | ||||||||
\(235\) | 6.92820 | 0.451946 | ||||||||
\(236\) | −6.92820 | −0.450988 | ||||||||
\(237\) | 6.53590 | 0.424552 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 5.00000 | 0.322749 | ||||||||
\(241\) | −0.143594 | −0.00924967 | −0.00462484 | − | 0.999989i | \(-0.501472\pi\) | ||||
−0.00462484 | + | 0.999989i | \(0.501472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 29.8564 | 1.89972 | ||||||||
\(248\) | 18.9282 | 1.20194 | ||||||||
\(249\) | −8.53590 | −0.540941 | ||||||||
\(250\) | −1.73205 | −0.109545 | ||||||||
\(251\) | −1.85641 | −0.117175 | −0.0585877 | − | 0.998282i | \(-0.518660\pi\) | ||||
−0.0585877 | + | 0.998282i | \(0.518660\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −15.4641 | −0.970304 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −19.8564 | −1.23861 | −0.619304 | − | 0.785151i | \(-0.712585\pi\) | ||||
−0.619304 | + | 0.785151i | \(0.712585\pi\) | |||||||
\(258\) | 8.53590 | 0.531422 | ||||||||
\(259\) | 9.85641 | 0.612447 | ||||||||
\(260\) | 5.46410 | 0.338869 | ||||||||
\(261\) | 3.46410 | 0.214423 | ||||||||
\(262\) | −32.7846 | −2.02544 | ||||||||
\(263\) | −20.5359 | −1.26630 | −0.633149 | − | 0.774030i | \(-0.718238\pi\) | ||||
−0.633149 | + | 0.774030i | \(0.718238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.928203 | −0.0570191 | ||||||||
\(266\) | 18.9282 | 1.16056 | ||||||||
\(267\) | 0.928203 | 0.0568051 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | 19.8564 | 1.21067 | 0.605333 | − | 0.795972i | \(-0.293040\pi\) | ||||
0.605333 | + | 0.795972i | \(0.293040\pi\) | |||||||
\(270\) | −1.73205 | −0.105409 | ||||||||
\(271\) | 11.6077 | 0.705117 | 0.352559 | − | 0.935790i | \(-0.385312\pi\) | ||||
0.352559 | + | 0.935790i | \(0.385312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9282 | 0.661405 | ||||||||
\(274\) | −31.1769 | −1.88347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.92820 | 0.417029 | ||||||||
\(277\) | −29.4641 | −1.77033 | −0.885163 | − | 0.465281i | \(-0.845953\pi\) | ||||
−0.885163 | + | 0.465281i | \(0.845953\pi\) | |||||||
\(278\) | −21.4641 | −1.28733 | ||||||||
\(279\) | −10.9282 | −0.654254 | ||||||||
\(280\) | −3.46410 | −0.207020 | ||||||||
\(281\) | −3.46410 | −0.206651 | −0.103325 | − | 0.994648i | \(-0.532948\pi\) | ||||
−0.103325 | + | 0.994648i | \(0.532948\pi\) | |||||||
\(282\) | −12.0000 | −0.714590 | ||||||||
\(283\) | 4.92820 | 0.292951 | 0.146476 | − | 0.989214i | \(-0.453207\pi\) | ||||
0.146476 | + | 0.989214i | \(0.453207\pi\) | |||||||
\(284\) | 13.8564 | 0.822226 | ||||||||
\(285\) | 5.46410 | 0.323665 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | 0.408959 | ||||||||
\(288\) | −5.19615 | −0.306186 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −6.00000 | −0.352332 | ||||||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 8.39230 | 0.491122 | ||||||||
\(293\) | 13.8564 | 0.809500 | 0.404750 | − | 0.914427i | \(-0.367359\pi\) | ||||
0.404750 | + | 0.914427i | \(0.367359\pi\) | |||||||
\(294\) | −5.19615 | −0.303046 | ||||||||
\(295\) | 6.92820 | 0.403376 | ||||||||
\(296\) | 8.53590 | 0.496139 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.7846 | 1.55159 | ||||||||
\(299\) | −37.8564 | −2.18929 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −9.85641 | −0.568114 | ||||||||
\(302\) | 35.3205 | 2.03247 | ||||||||
\(303\) | 10.3923 | 0.597022 | ||||||||
\(304\) | 27.3205 | 1.56694 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0000 | −0.799022 | −0.399511 | − | 0.916728i | \(-0.630820\pi\) | ||||
−0.399511 | + | 0.916728i | \(0.630820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 18.9282 | 1.07505 | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | 9.46410 | 0.535799 | ||||||||
\(313\) | 20.9282 | 1.18293 | 0.591466 | − | 0.806330i | \(-0.298549\pi\) | ||||
0.591466 | + | 0.806330i | \(0.298549\pi\) | |||||||
\(314\) | −5.32051 | −0.300254 | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 6.53590 | 0.367673 | ||||||||
\(317\) | −24.9282 | −1.40011 | −0.700054 | − | 0.714090i | \(-0.746841\pi\) | ||||
−0.700054 | + | 0.714090i | \(0.746841\pi\) | |||||||
\(318\) | 1.60770 | 0.0901551 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −8.53590 | −0.476427 | ||||||||
\(322\) | −24.0000 | −1.33747 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.46410 | −0.303094 | ||||||||
\(326\) | 17.0718 | 0.945519 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 13.8564 | 0.763928 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.85641 | 0.541757 | 0.270879 | − | 0.962614i | \(-0.412686\pi\) | ||||
0.270879 | + | 0.962614i | \(0.412686\pi\) | |||||||
\(332\) | −8.53590 | −0.468468 | ||||||||
\(333\) | −4.92820 | −0.270064 | ||||||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 10.0000 | 0.545545 | ||||||||
\(337\) | −33.1769 | −1.80726 | −0.903631 | − | 0.428312i | \(-0.859108\pi\) | ||||
−0.903631 | + | 0.428312i | \(0.859108\pi\) | |||||||
\(338\) | 29.1962 | 1.58806 | ||||||||
\(339\) | −12.9282 | −0.702164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.46410 | −0.511760 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −8.53590 | −0.460225 | ||||||||
\(345\) | −6.92820 | −0.373002 | ||||||||
\(346\) | 20.7846 | 1.11739 | ||||||||
\(347\) | −22.3923 | −1.20208 | −0.601041 | − | 0.799218i | \(-0.705247\pi\) | ||||
−0.601041 | + | 0.799218i | \(0.705247\pi\) | |||||||
\(348\) | 3.46410 | 0.185695 | ||||||||
\(349\) | 8.14359 | 0.435917 | 0.217958 | − | 0.975958i | \(-0.430060\pi\) | ||||
0.217958 | + | 0.975958i | \(0.430060\pi\) | |||||||
\(350\) | −3.46410 | −0.185164 | ||||||||
\(351\) | −5.46410 | −0.291652 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | −13.8564 | −0.735422 | ||||||||
\(356\) | 0.928203 | 0.0491947 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 20.7846 | 1.09697 | 0.548485 | − | 0.836160i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(360\) | 1.73205 | 0.0912871 | ||||||||
\(361\) | 10.8564 | 0.571390 | ||||||||
\(362\) | 27.4641 | 1.44348 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.9282 | 0.572793 | ||||||||
\(365\) | −8.39230 | −0.439273 | ||||||||
\(366\) | −3.46410 | −0.181071 | ||||||||
\(367\) | 20.0000 | 1.04399 | 0.521996 | − | 0.852948i | \(-0.325188\pi\) | ||||
0.521996 | + | 0.852948i | \(0.325188\pi\) | |||||||
\(368\) | −34.6410 | −1.80579 | ||||||||
\(369\) | −3.46410 | −0.180334 | ||||||||
\(370\) | 8.53590 | 0.443760 | ||||||||
\(371\) | −1.85641 | −0.0963798 | ||||||||
\(372\) | −10.9282 | −0.566601 | ||||||||
\(373\) | 20.3923 | 1.05587 | 0.527937 | − | 0.849284i | \(-0.322966\pi\) | ||||
0.527937 | + | 0.849284i | \(0.322966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 12.0000 | 0.618853 | ||||||||
\(377\) | −18.9282 | −0.974852 | ||||||||
\(378\) | −3.46410 | −0.178174 | ||||||||
\(379\) | −17.8564 | −0.917222 | −0.458611 | − | 0.888637i | \(-0.651653\pi\) | ||||
−0.458611 | + | 0.888637i | \(0.651653\pi\) | |||||||
\(380\) | 5.46410 | 0.280302 | ||||||||
\(381\) | −8.92820 | −0.457406 | ||||||||
\(382\) | −32.7846 | −1.67741 | ||||||||
\(383\) | −13.8564 | −0.708029 | −0.354015 | − | 0.935240i | \(-0.615184\pi\) | ||||
−0.354015 | + | 0.935240i | \(0.615184\pi\) | |||||||
\(384\) | 12.1244 | 0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −42.2487 | −2.15040 | ||||||||
\(387\) | 4.92820 | 0.250515 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 11.0718 | 0.561362 | 0.280681 | − | 0.959801i | \(-0.409440\pi\) | ||||
0.280681 | + | 0.959801i | \(0.409440\pi\) | |||||||
\(390\) | 9.46410 | 0.479233 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.19615 | 0.262445 | ||||||||
\(393\) | −18.9282 | −0.954802 | ||||||||
\(394\) | 20.7846 | 1.04711 | ||||||||
\(395\) | −6.53590 | −0.328857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | −42.9282 | −2.15180 | ||||||||
\(399\) | 10.9282 | 0.547094 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −7.85641 | −0.392330 | −0.196165 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196165 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(402\) | 13.8564 | 0.691095 | ||||||||
\(403\) | 59.7128 | 2.97451 | ||||||||
\(404\) | 10.3923 | 0.517036 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.78461 | 0.335477 | 0.167739 | − | 0.985831i | \(-0.446354\pi\) | ||||
0.167739 | + | 0.985831i | \(0.446354\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 13.8564 | 0.681829 | ||||||||
\(414\) | 12.0000 | 0.589768 | ||||||||
\(415\) | 8.53590 | 0.419011 | ||||||||
\(416\) | 28.3923 | 1.39205 | ||||||||
\(417\) | −12.3923 | −0.606854 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9282 | 1.51094 | 0.755471 | − | 0.655182i | \(-0.227408\pi\) | ||||
0.755471 | + | 0.655182i | \(0.227408\pi\) | |||||||
\(420\) | 2.00000 | 0.0975900 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 14.5359 | 0.707596 | ||||||||
\(423\) | −6.92820 | −0.336861 | ||||||||
\(424\) | −1.60770 | −0.0780766 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 24.0000 | 1.16280 | ||||||||
\(427\) | 4.00000 | 0.193574 | ||||||||
\(428\) | −8.53590 | −0.412598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.53590 | −0.411638 | ||||||||
\(431\) | −8.78461 | −0.423140 | −0.211570 | − | 0.977363i | \(-0.567858\pi\) | ||||
−0.211570 | + | 0.977363i | \(0.567858\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | 0.143594 | 0.00690067 | 0.00345033 | − | 0.999994i | \(-0.498902\pi\) | ||||
0.00345033 | + | 0.999994i | \(0.498902\pi\) | |||||||
\(434\) | 37.8564 | 1.81717 | ||||||||
\(435\) | −3.46410 | −0.166091 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | −37.8564 | −1.81092 | ||||||||
\(438\) | 14.5359 | 0.694552 | ||||||||
\(439\) | −33.1769 | −1.58345 | −0.791724 | − | 0.610879i | \(-0.790816\pi\) | ||||
−0.791724 | + | 0.610879i | \(0.790816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | 0.570137 | 0.285069 | − | 0.958507i | \(-0.407984\pi\) | ||||
0.285069 | + | 0.958507i | \(0.407984\pi\) | |||||||
\(444\) | −4.92820 | −0.233882 | ||||||||
\(445\) | −0.928203 | −0.0440011 | ||||||||
\(446\) | 17.0718 | 0.808373 | ||||||||
\(447\) | 15.4641 | 0.731427 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | −26.7846 | −1.26404 | −0.632022 | − | 0.774950i | \(-0.717775\pi\) | ||||
−0.632022 | + | 0.774950i | \(0.717775\pi\) | |||||||
\(450\) | 1.73205 | 0.0816497 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.9282 | −0.608092 | ||||||||
\(453\) | 20.3923 | 0.958114 | ||||||||
\(454\) | −26.7846 | −1.25706 | ||||||||
\(455\) | −10.9282 | −0.512322 | ||||||||
\(456\) | 9.46410 | 0.443197 | ||||||||
\(457\) | −12.3923 | −0.579688 | −0.289844 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289844 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(458\) | −41.3205 | −1.93078 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.92820 | −0.323029 | ||||||||
\(461\) | −36.2487 | −1.68827 | −0.844135 | − | 0.536130i | \(-0.819886\pi\) | ||||
−0.844135 | + | 0.536130i | \(0.819886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0000 | −1.30127 | −0.650635 | − | 0.759390i | \(-0.725497\pi\) | ||||
−0.650635 | + | 0.759390i | \(0.725497\pi\) | |||||||
\(464\) | −17.3205 | −0.804084 | ||||||||
\(465\) | 10.9282 | 0.506783 | ||||||||
\(466\) | −20.7846 | −0.962828 | ||||||||
\(467\) | 5.07180 | 0.234695 | 0.117347 | − | 0.993091i | \(-0.462561\pi\) | ||||
0.117347 | + | 0.993091i | \(0.462561\pi\) | |||||||
\(468\) | −5.46410 | −0.252578 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 12.0000 | 0.553519 | ||||||||
\(471\) | −3.07180 | −0.141541 | ||||||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 11.3205 | 0.519968 | ||||||||
\(475\) | −5.46410 | −0.250710 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.928203 | 0.0424995 | ||||||||
\(478\) | 20.7846 | 0.950666 | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 5.19615 | 0.237171 | ||||||||
\(481\) | 26.9282 | 1.22782 | ||||||||
\(482\) | −0.248711 | −0.0113285 | ||||||||
\(483\) | −13.8564 | −0.630488 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 1.73205 | 0.0785674 | ||||||||
\(487\) | −31.7128 | −1.43704 | −0.718522 | − | 0.695504i | \(-0.755181\pi\) | ||||
−0.718522 | + | 0.695504i | \(0.755181\pi\) | |||||||
\(488\) | 3.46410 | 0.156813 | ||||||||
\(489\) | 9.85641 | 0.445722 | ||||||||
\(490\) | 5.19615 | 0.234738 | ||||||||
\(491\) | 30.9282 | 1.39577 | 0.697885 | − | 0.716210i | \(-0.254125\pi\) | ||||
0.697885 | + | 0.716210i | \(0.254125\pi\) | |||||||
\(492\) | −3.46410 | −0.156174 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 51.7128 | 2.32667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 54.6410 | 2.45345 | ||||||||
\(497\) | −27.7128 | −1.24309 | ||||||||
\(498\) | −14.7846 | −0.662514 | ||||||||
\(499\) | 28.7846 | 1.28858 | 0.644288 | − | 0.764783i | \(-0.277154\pi\) | ||||
0.644288 | + | 0.764783i | \(0.277154\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 10.3923 | 0.464294 | ||||||||
\(502\) | −3.21539 | −0.143510 | ||||||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | 3.46410 | 0.154303 | ||||||||
\(505\) | −10.3923 | −0.462451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.8564 | 0.748619 | ||||||||
\(508\) | −8.92820 | −0.396125 | ||||||||
\(509\) | 19.8564 | 0.880120 | 0.440060 | − | 0.897968i | \(-0.354957\pi\) | ||||
0.440060 | + | 0.897968i | \(0.354957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.7846 | −0.742507 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | −5.46410 | −0.241246 | ||||||||
\(514\) | −34.3923 | −1.51698 | ||||||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 4.92820 | 0.216952 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 17.0718 | 0.750092 | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | −9.46410 | −0.415028 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 6.00000 | 0.262613 | ||||||||
\(523\) | 22.0000 | 0.961993 | 0.480996 | − | 0.876723i | \(-0.340275\pi\) | ||||
0.480996 | + | 0.876723i | \(0.340275\pi\) | |||||||
\(524\) | −18.9282 | −0.826882 | ||||||||
\(525\) | −2.00000 | −0.0872872 | ||||||||
\(526\) | −35.5692 | −1.55089 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | −1.60770 | −0.0698338 | ||||||||
\(531\) | −6.92820 | −0.300658 | ||||||||
\(532\) | 10.9282 | 0.473798 | ||||||||
\(533\) | 18.9282 | 0.819871 | ||||||||
\(534\) | 1.60770 | 0.0695718 | ||||||||
\(535\) | 8.53590 | 0.369039 | ||||||||
\(536\) | −13.8564 | −0.598506 | ||||||||
\(537\) | 6.92820 | 0.298974 | ||||||||
\(538\) | 34.3923 | 1.48276 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −27.8564 | −1.19764 | −0.598820 | − | 0.800883i | \(-0.704364\pi\) | ||||
−0.598820 | + | 0.800883i | \(0.704364\pi\) | |||||||
\(542\) | 20.1051 | 0.863589 | ||||||||
\(543\) | 15.8564 | 0.680464 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 18.9282 | 0.810052 | ||||||||
\(547\) | −2.00000 | −0.0855138 | −0.0427569 | − | 0.999086i | \(-0.513614\pi\) | ||||
−0.0427569 | + | 0.999086i | \(0.513614\pi\) | |||||||
\(548\) | −18.0000 | −0.768922 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9282 | −0.806369 | ||||||||
\(552\) | −12.0000 | −0.510754 | ||||||||
\(553\) | −13.0718 | −0.555869 | ||||||||
\(554\) | −51.0333 | −2.16820 | ||||||||
\(555\) | 4.92820 | 0.209191 | ||||||||
\(556\) | −12.3923 | −0.525551 | ||||||||
\(557\) | −3.21539 | −0.136240 | −0.0681202 | − | 0.997677i | \(-0.521700\pi\) | ||||
−0.0681202 | + | 0.997677i | \(0.521700\pi\) | |||||||
\(558\) | −18.9282 | −0.801295 | ||||||||
\(559\) | −26.9282 | −1.13894 | ||||||||
\(560\) | −10.0000 | −0.422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | −0.253095 | ||||||||
\(563\) | −10.3923 | −0.437983 | −0.218992 | − | 0.975727i | \(-0.570277\pi\) | ||||
−0.218992 | + | 0.975727i | \(0.570277\pi\) | |||||||
\(564\) | −6.92820 | −0.291730 | ||||||||
\(565\) | 12.9282 | 0.543894 | ||||||||
\(566\) | 8.53590 | 0.358791 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | −24.0000 | −1.00702 | ||||||||
\(569\) | −5.32051 | −0.223047 | −0.111524 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111524 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(570\) | 9.46410 | 0.396408 | ||||||||
\(571\) | −3.60770 | −0.150977 | −0.0754887 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754887 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.9282 | −0.790737 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 6.92820 | 0.288926 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.7846 | −0.782014 | −0.391007 | − | 0.920388i | \(-0.627873\pi\) | ||||
−0.391007 | + | 0.920388i | \(0.627873\pi\) | |||||||
\(578\) | −29.4449 | −1.22474 | ||||||||
\(579\) | −24.3923 | −1.01371 | ||||||||
\(580\) | −3.46410 | −0.143839 | ||||||||
\(581\) | 17.0718 | 0.708257 | ||||||||
\(582\) | −17.3205 | −0.717958 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.5359 | −0.601500 | ||||||||
\(585\) | 5.46410 | 0.225913 | ||||||||
\(586\) | 24.0000 | 0.991431 | ||||||||
\(587\) | −18.9282 | −0.781251 | −0.390625 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390625 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | 59.7128 | 2.46042 | ||||||||
\(590\) | 12.0000 | 0.494032 | ||||||||
\(591\) | 12.0000 | 0.493614 | ||||||||
\(592\) | 24.6410 | 1.01274 | ||||||||
\(593\) | −8.78461 | −0.360741 | −0.180370 | − | 0.983599i | \(-0.557730\pi\) | ||||
−0.180370 | + | 0.983599i | \(0.557730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.4641 | 0.633434 | ||||||||
\(597\) | −24.7846 | −1.01437 | ||||||||
\(598\) | −65.5692 | −2.68132 | ||||||||
\(599\) | −37.8564 | −1.54677 | −0.773385 | − | 0.633936i | \(-0.781438\pi\) | ||||
−0.773385 | + | 0.633936i | \(0.781438\pi\) | |||||||
\(600\) | −1.73205 | −0.0707107 | ||||||||
\(601\) | 32.6410 | 1.33145 | 0.665727 | − | 0.746195i | \(-0.268121\pi\) | ||||
0.665727 | + | 0.746195i | \(0.268121\pi\) | |||||||
\(602\) | −17.0718 | −0.695794 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 20.3923 | 0.829751 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 18.7846 | 0.762444 | 0.381222 | − | 0.924484i | \(-0.375503\pi\) | ||||
0.381222 | + | 0.924484i | \(0.375503\pi\) | |||||||
\(608\) | 28.3923 | 1.15146 | ||||||||
\(609\) | −6.92820 | −0.280745 | ||||||||
\(610\) | 3.46410 | 0.140257 | ||||||||
\(611\) | 37.8564 | 1.53151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.3923 | 0.823637 | 0.411819 | − | 0.911266i | \(-0.364894\pi\) | ||||
0.411819 | + | 0.911266i | \(0.364894\pi\) | |||||||
\(614\) | −24.2487 | −0.978598 | ||||||||
\(615\) | 3.46410 | 0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.9282 | −1.48667 | −0.743337 | − | 0.668917i | \(-0.766758\pi\) | ||||
−0.743337 | + | 0.668917i | \(0.766758\pi\) | |||||||
\(618\) | 13.8564 | 0.557386 | ||||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 10.9282 | 0.438887 | ||||||||
\(621\) | 6.92820 | 0.278019 | ||||||||
\(622\) | 8.78461 | 0.352231 | ||||||||
\(623\) | −1.85641 | −0.0743754 | ||||||||
\(624\) | 27.3205 | 1.09370 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 36.2487 | 1.44879 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.07180 | −0.122578 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.46410 | 0.138013 | ||||||||
\(631\) | −21.0718 | −0.838855 | −0.419427 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419427 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(632\) | −11.3205 | −0.450306 | ||||||||
\(633\) | 8.39230 | 0.333564 | ||||||||
\(634\) | −43.1769 | −1.71477 | ||||||||
\(635\) | 8.92820 | 0.354305 | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | 16.3923 | 0.649487 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.8564 | 0.548151 | ||||||||
\(640\) | −12.1244 | −0.479257 | ||||||||
\(641\) | −12.9282 | −0.510633 | −0.255317 | − | 0.966857i | \(-0.582180\pi\) | ||||
−0.255317 | + | 0.966857i | \(0.582180\pi\) | |||||||
\(642\) | −14.7846 | −0.583502 | ||||||||
\(643\) | 37.5692 | 1.48159 | 0.740793 | − | 0.671734i | \(-0.234450\pi\) | ||||
0.740793 | + | 0.671734i | \(0.234450\pi\) | |||||||
\(644\) | −13.8564 | −0.546019 | ||||||||
\(645\) | −4.92820 | −0.194048 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.7128 | 1.08950 | 0.544752 | − | 0.838597i | \(-0.316624\pi\) | ||||
0.544752 | + | 0.838597i | \(0.316624\pi\) | |||||||
\(648\) | −1.73205 | −0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −9.46410 | −0.371213 | ||||||||
\(651\) | 21.8564 | 0.856620 | ||||||||
\(652\) | 9.85641 | 0.386007 | ||||||||
\(653\) | 19.8564 | 0.777041 | 0.388521 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388521 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(654\) | 17.3205 | 0.677285 | ||||||||
\(655\) | 18.9282 | 0.739586 | ||||||||
\(656\) | 17.3205 | 0.676252 | ||||||||
\(657\) | 8.39230 | 0.327415 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | 15.7128 | 0.612084 | 0.306042 | − | 0.952018i | \(-0.400995\pi\) | ||||
0.306042 | + | 0.952018i | \(0.400995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 17.0718 | 0.663514 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.7846 | 0.573754 | ||||||||
\(665\) | −10.9282 | −0.423778 | ||||||||
\(666\) | −8.53590 | −0.330759 | ||||||||
\(667\) | 24.0000 | 0.929284 | ||||||||
\(668\) | 10.3923 | 0.402090 | ||||||||
\(669\) | 9.85641 | 0.381071 | ||||||||
\(670\) | −13.8564 | −0.535320 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.3923 | 0.400892 | ||||||||
\(673\) | 3.32051 | 0.127996 | 0.0639981 | − | 0.997950i | \(-0.479615\pi\) | ||||
0.0639981 | + | 0.997950i | \(0.479615\pi\) | |||||||
\(674\) | −57.4641 | −2.21343 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | −8.78461 | −0.337620 | −0.168810 | − | 0.985649i | \(-0.553992\pi\) | ||||
−0.168810 | + | 0.985649i | \(0.553992\pi\) | |||||||
\(678\) | −22.3923 | −0.859971 | ||||||||
\(679\) | 20.0000 | 0.767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.4641 | −0.592586 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7846 | −1.25447 | −0.627234 | − | 0.778831i | \(-0.715813\pi\) | ||||
−0.627234 | + | 0.778831i | \(0.715813\pi\) | |||||||
\(684\) | −5.46410 | −0.208925 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | −23.8564 | −0.910179 | ||||||||
\(688\) | −24.6410 | −0.939430 | ||||||||
\(689\) | −5.07180 | −0.193220 | ||||||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | 47.7128 | 1.81508 | 0.907540 | − | 0.419965i | \(-0.137958\pi\) | ||||
0.907540 | + | 0.419965i | \(0.137958\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.7846 | −1.47224 | ||||||||
\(695\) | 12.3923 | 0.470067 | ||||||||
\(696\) | −6.00000 | −0.227429 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 14.1051 | 0.533887 | ||||||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | −2.00000 | −0.0755929 | ||||||||
\(701\) | −39.4641 | −1.49054 | −0.745269 | − | 0.666764i | \(-0.767679\pi\) | ||||
−0.745269 | + | 0.666764i | \(0.767679\pi\) | |||||||
\(702\) | −9.46410 | −0.357199 | ||||||||
\(703\) | 26.9282 | 1.01562 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.92820 | 0.260931 | ||||||||
\(706\) | 22.3923 | 0.842746 | ||||||||
\(707\) | −20.7846 | −0.781686 | ||||||||
\(708\) | −6.92820 | −0.260378 | ||||||||
\(709\) | −11.8564 | −0.445277 | −0.222638 | − | 0.974901i | \(-0.571467\pi\) | ||||
−0.222638 | + | 0.974901i | \(0.571467\pi\) | |||||||
\(710\) | −24.0000 | −0.900704 | ||||||||
\(711\) | 6.53590 | 0.245115 | ||||||||
\(712\) | −1.60770 | −0.0602509 | ||||||||
\(713\) | −75.7128 | −2.83547 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.92820 | 0.258919 | ||||||||
\(717\) | 12.0000 | 0.448148 | ||||||||
\(718\) | 36.0000 | 1.34351 | ||||||||
\(719\) | −5.07180 | −0.189146 | −0.0945731 | − | 0.995518i | \(-0.530149\pi\) | ||||
−0.0945731 | + | 0.995518i | \(0.530149\pi\) | |||||||
\(720\) | 5.00000 | 0.186339 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | 18.8038 | 0.699807 | ||||||||
\(723\) | −0.143594 | −0.00534030 | ||||||||
\(724\) | 15.8564 | 0.589299 | ||||||||
\(725\) | 3.46410 | 0.128654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | −18.9282 | −0.701526 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.5359 | −0.537998 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | −53.9615 | −1.99311 | −0.996557 | − | 0.0829082i | \(-0.973579\pi\) | ||||
−0.996557 | + | 0.0829082i | \(0.973579\pi\) | |||||||
\(734\) | 34.6410 | 1.27862 | ||||||||
\(735\) | 3.00000 | 0.110657 | ||||||||
\(736\) | −36.0000 | −1.32698 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | −17.4641 | −0.642427 | −0.321214 | − | 0.947007i | \(-0.604091\pi\) | ||||
−0.321214 | + | 0.947007i | \(0.604091\pi\) | |||||||
\(740\) | 4.92820 | 0.181164 | ||||||||
\(741\) | 29.8564 | 1.09680 | ||||||||
\(742\) | −3.21539 | −0.118041 | ||||||||
\(743\) | −25.6077 | −0.939455 | −0.469728 | − | 0.882811i | \(-0.655648\pi\) | ||||
−0.469728 | + | 0.882811i | \(0.655648\pi\) | |||||||
\(744\) | 18.9282 | 0.693942 | ||||||||
\(745\) | −15.4641 | −0.566561 | ||||||||
\(746\) | 35.3205 | 1.29318 | ||||||||
\(747\) | −8.53590 | −0.312312 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0718 | 0.623790 | ||||||||
\(750\) | −1.73205 | −0.0632456 | ||||||||
\(751\) | 26.9282 | 0.982624 | 0.491312 | − | 0.870984i | \(-0.336517\pi\) | ||||
0.491312 | + | 0.870984i | \(0.336517\pi\) | |||||||
\(752\) | 34.6410 | 1.26323 | ||||||||
\(753\) | −1.85641 | −0.0676512 | ||||||||
\(754\) | −32.7846 | −1.19395 | ||||||||
\(755\) | −20.3923 | −0.742152 | ||||||||
\(756\) | −2.00000 | −0.0727393 | ||||||||
\(757\) | 34.7846 | 1.26427 | 0.632134 | − | 0.774859i | \(-0.282179\pi\) | ||||
0.632134 | + | 0.774859i | \(0.282179\pi\) | |||||||
\(758\) | −30.9282 | −1.12336 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.46410 | −0.343299 | ||||||||
\(761\) | 32.5359 | 1.17943 | 0.589713 | − | 0.807613i | \(-0.299241\pi\) | ||||
0.589713 | + | 0.807613i | \(0.299241\pi\) | |||||||
\(762\) | −15.4641 | −0.560205 | ||||||||
\(763\) | −20.0000 | −0.724049 | ||||||||
\(764\) | −18.9282 | −0.684798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 37.8564 | 1.36692 | ||||||||
\(768\) | 19.0000 | 0.685603 | ||||||||
\(769\) | −50.4974 | −1.82098 | −0.910492 | − | 0.413527i | \(-0.864297\pi\) | ||||
−0.910492 | + | 0.413527i | \(0.864297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.8564 | −0.715111 | ||||||||
\(772\) | −24.3923 | −0.877898 | ||||||||
\(773\) | −4.14359 | −0.149035 | −0.0745174 | − | 0.997220i | \(-0.523742\pi\) | ||||
−0.0745174 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(774\) | 8.53590 | 0.306817 | ||||||||
\(775\) | −10.9282 | −0.392553 | ||||||||
\(776\) | 17.3205 | 0.621770 | ||||||||
\(777\) | 9.85641 | 0.353597 | ||||||||
\(778\) | 19.1769 | 0.687526 | ||||||||
\(779\) | 18.9282 | 0.678173 | ||||||||
\(780\) | 5.46410 | 0.195646 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.46410 | 0.123797 | ||||||||
\(784\) | 15.0000 | 0.535714 | ||||||||
\(785\) | 3.07180 | 0.109637 | ||||||||
\(786\) | −32.7846 | −1.16939 | ||||||||
\(787\) | −22.7846 | −0.812184 | −0.406092 | − | 0.913832i | \(-0.633109\pi\) | ||||
−0.406092 | + | 0.913832i | \(0.633109\pi\) | |||||||
\(788\) | 12.0000 | 0.427482 | ||||||||
\(789\) | −20.5359 | −0.731097 | ||||||||
\(790\) | −11.3205 | −0.402766 | ||||||||
\(791\) | 25.8564 | 0.919348 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9282 | 0.388072 | ||||||||
\(794\) | 3.46410 | 0.122936 | ||||||||
\(795\) | −0.928203 | −0.0329200 | ||||||||
\(796\) | −24.7846 | −0.878467 | ||||||||
\(797\) | −52.6410 | −1.86464 | −0.932320 | − | 0.361634i | \(-0.882219\pi\) | ||||
−0.932320 | + | 0.361634i | \(0.882219\pi\) | |||||||
\(798\) | 18.9282 | 0.670051 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.19615 | −0.183712 | ||||||||
\(801\) | 0.928203 | 0.0327964 | ||||||||
\(802\) | −13.6077 | −0.480504 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 13.8564 | 0.488374 | ||||||||
\(806\) | 103.426 | 3.64301 | ||||||||
\(807\) | 19.8564 | 0.698979 | ||||||||
\(808\) | −18.0000 | −0.633238 | ||||||||
\(809\) | 15.4641 | 0.543689 | 0.271844 | − | 0.962341i | \(-0.412366\pi\) | ||||
0.271844 | + | 0.962341i | \(0.412366\pi\) | |||||||
\(810\) | −1.73205 | −0.0608581 | ||||||||
\(811\) | −12.3923 | −0.435153 | −0.217576 | − | 0.976043i | \(-0.569815\pi\) | ||||
−0.217576 | + | 0.976043i | \(0.569815\pi\) | |||||||
\(812\) | −6.92820 | −0.243132 | ||||||||
\(813\) | 11.6077 | 0.407100 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.85641 | −0.345255 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9282 | −0.942099 | ||||||||
\(818\) | 11.7513 | 0.410874 | ||||||||
\(819\) | 10.9282 | 0.381862 | ||||||||
\(820\) | 3.46410 | 0.120972 | ||||||||
\(821\) | −20.5359 | −0.716708 | −0.358354 | − | 0.933586i | \(-0.616662\pi\) | ||||
−0.358354 | + | 0.933586i | \(0.616662\pi\) | |||||||
\(822\) | −31.1769 | −1.08742 | ||||||||
\(823\) | −33.5692 | −1.17015 | −0.585075 | − | 0.810979i | \(-0.698935\pi\) | ||||
−0.585075 | + | 0.810979i | \(0.698935\pi\) | |||||||
\(824\) | −13.8564 | −0.482711 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | 0.835067 | ||||||||
\(827\) | −22.3923 | −0.778657 | −0.389328 | − | 0.921099i | \(-0.627293\pi\) | ||||
−0.389328 | + | 0.921099i | \(0.627293\pi\) | |||||||
\(828\) | 6.92820 | 0.240772 | ||||||||
\(829\) | 29.7128 | 1.03197 | 0.515984 | − | 0.856598i | \(-0.327426\pi\) | ||||
0.515984 | + | 0.856598i | \(0.327426\pi\) | |||||||
\(830\) | 14.7846 | 0.513181 | ||||||||
\(831\) | −29.4641 | −1.02210 | ||||||||
\(832\) | −5.46410 | −0.189434 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.4641 | −0.743241 | ||||||||
\(835\) | −10.3923 | −0.359641 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.9282 | −0.377734 | ||||||||
\(838\) | 53.5692 | 1.85052 | ||||||||
\(839\) | 56.7846 | 1.96042 | 0.980211 | − | 0.197954i | \(-0.0634298\pi\) | ||||
0.980211 | + | 0.197954i | \(0.0634298\pi\) | |||||||
\(840\) | −3.46410 | −0.119523 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 3.46410 | 0.119381 | ||||||||
\(843\) | −3.46410 | −0.119310 | ||||||||
\(844\) | 8.39230 | 0.288875 | ||||||||
\(845\) | −16.8564 | −0.579878 | ||||||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.64102 | −0.159373 | ||||||||
\(849\) | 4.92820 | 0.169135 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.1436 | −1.17043 | ||||||||
\(852\) | 13.8564 | 0.474713 | ||||||||
\(853\) | −3.60770 | −0.123525 | −0.0617626 | − | 0.998091i | \(-0.519672\pi\) | ||||
−0.0617626 | + | 0.998091i | \(0.519672\pi\) | |||||||
\(854\) | 6.92820 | 0.237078 | ||||||||
\(855\) | 5.46410 | 0.186868 | ||||||||
\(856\) | 14.7846 | 0.505328 | ||||||||
\(857\) | 37.8564 | 1.29315 | 0.646575 | − | 0.762850i | \(-0.276201\pi\) | ||||
0.646575 | + | 0.762850i | \(0.276201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.71281 | −0.263158 | −0.131579 | − | 0.991306i | \(-0.542005\pi\) | ||||
−0.131579 | + | 0.991306i | \(0.542005\pi\) | |||||||
\(860\) | −4.92820 | −0.168050 | ||||||||
\(861\) | 6.92820 | 0.236113 | ||||||||
\(862\) | −15.2154 | −0.518238 | ||||||||
\(863\) | −37.8564 | −1.28865 | −0.644324 | − | 0.764753i | \(-0.722861\pi\) | ||||
−0.644324 | + | 0.764753i | \(0.722861\pi\) | |||||||
\(864\) | −5.19615 | −0.176777 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 0.248711 | 0.00845155 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 21.8564 | 0.741855 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.00000 | −0.203419 | ||||||||
\(871\) | −43.7128 | −1.48115 | ||||||||
\(872\) | −17.3205 | −0.586546 | ||||||||
\(873\) | −10.0000 | −0.338449 | ||||||||
\(874\) | −65.5692 | −2.21791 | ||||||||
\(875\) | 2.00000 | 0.0676123 | ||||||||
\(876\) | 8.39230 | 0.283550 | ||||||||
\(877\) | 34.2487 | 1.15650 | 0.578248 | − | 0.815861i | \(-0.303736\pi\) | ||||
0.578248 | + | 0.815861i | \(0.303736\pi\) | |||||||
\(878\) | −57.4641 | −1.93932 | ||||||||
\(879\) | 13.8564 | 0.467365 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.928203 | −0.0312720 | −0.0156360 | − | 0.999878i | \(-0.504977\pi\) | ||||
−0.0156360 | + | 0.999878i | \(0.504977\pi\) | |||||||
\(882\) | −5.19615 | −0.174964 | ||||||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.92820 | 0.232889 | ||||||||
\(886\) | 20.7846 | 0.698273 | ||||||||
\(887\) | −12.2487 | −0.411271 | −0.205636 | − | 0.978629i | \(-0.565926\pi\) | ||||
−0.205636 | + | 0.978629i | \(0.565926\pi\) | |||||||
\(888\) | 8.53590 | 0.286446 | ||||||||
\(889\) | 17.8564 | 0.598885 | ||||||||
\(890\) | −1.60770 | −0.0538901 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.85641 | 0.330017 | ||||||||
\(893\) | 37.8564 | 1.26682 | ||||||||
\(894\) | 26.7846 | 0.895811 | ||||||||
\(895\) | −6.92820 | −0.231584 | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | −37.8564 | −1.26399 | ||||||||
\(898\) | −46.3923 | −1.54813 | ||||||||
\(899\) | −37.8564 | −1.26258 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.85641 | −0.328001 | ||||||||
\(904\) | 22.3923 | 0.744757 | ||||||||
\(905\) | −15.8564 | −0.527085 | ||||||||
\(906\) | 35.3205 | 1.17345 | ||||||||
\(907\) | 18.1436 | 0.602448 | 0.301224 | − | 0.953553i | \(-0.402605\pi\) | ||||
0.301224 | + | 0.953553i | \(0.402605\pi\) | |||||||
\(908\) | −15.4641 | −0.513194 | ||||||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | −18.9282 | −0.627464 | ||||||||
\(911\) | 18.9282 | 0.627119 | 0.313560 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313560 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(912\) | 27.3205 | 0.904672 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −21.4641 | −0.709969 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | −23.8564 | −0.788238 | ||||||||
\(917\) | 37.8564 | 1.25013 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.3923 | 1.06852 | 0.534262 | − | 0.845319i | \(-0.320590\pi\) | ||||
0.534262 | + | 0.845319i | \(0.320590\pi\) | |||||||
\(920\) | 12.0000 | 0.395628 | ||||||||
\(921\) | −14.0000 | −0.461316 | ||||||||
\(922\) | −62.7846 | −2.06770 | ||||||||
\(923\) | −75.7128 | −2.49212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92820 | −0.162038 | ||||||||
\(926\) | −48.4974 | −1.59372 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | −18.0000 | −0.590879 | ||||||||
\(929\) | 2.78461 | 0.0913601 | 0.0456800 | − | 0.998956i | \(-0.485455\pi\) | ||||
0.0456800 | + | 0.998956i | \(0.485455\pi\) | |||||||
\(930\) | 18.9282 | 0.620680 | ||||||||
\(931\) | 16.3923 | 0.537236 | ||||||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | 5.07180 | 0.166043 | ||||||||
\(934\) | 8.78461 | 0.287441 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.46410 | 0.309344 | ||||||||
\(937\) | 20.3923 | 0.666188 | 0.333094 | − | 0.942894i | \(-0.391907\pi\) | ||||
0.333094 | + | 0.942894i | \(0.391907\pi\) | |||||||
\(938\) | −27.7128 | −0.904855 | ||||||||
\(939\) | 20.9282 | 0.682966 | ||||||||
\(940\) | 6.92820 | 0.225973 | ||||||||
\(941\) | −27.4641 | −0.895304 | −0.447652 | − | 0.894208i | \(-0.647740\pi\) | ||||
−0.447652 | + | 0.894208i | \(0.647740\pi\) | |||||||
\(942\) | −5.32051 | −0.173352 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | 34.6410 | 1.12747 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.9282 | −0.615084 | −0.307542 | − | 0.951535i | \(-0.599506\pi\) | ||||
−0.307542 | + | 0.951535i | \(0.599506\pi\) | |||||||
\(948\) | 6.53590 | 0.212276 | ||||||||
\(949\) | −45.8564 | −1.48856 | ||||||||
\(950\) | −9.46410 | −0.307056 | ||||||||
\(951\) | −24.9282 | −0.808352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.21539 | 0.104157 | 0.0520784 | − | 0.998643i | \(-0.483415\pi\) | ||||
0.0520784 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(954\) | 1.60770 | 0.0520511 | ||||||||
\(955\) | 18.9282 | 0.612502 | ||||||||
\(956\) | 12.0000 | 0.388108 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.7846 | −0.671520 | ||||||||
\(959\) | 36.0000 | 1.16250 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | 46.6410 | 1.50377 | ||||||||
\(963\) | −8.53590 | −0.275065 | ||||||||
\(964\) | −0.143594 | −0.00462484 | ||||||||
\(965\) | 24.3923 | 0.785216 | ||||||||
\(966\) | −24.0000 | −0.772187 | ||||||||
\(967\) | −22.7846 | −0.732704 | −0.366352 | − | 0.930476i | \(-0.619393\pi\) | ||||
−0.366352 | + | 0.930476i | \(0.619393\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.3205 | 0.556128 | ||||||||
\(971\) | 25.8564 | 0.829772 | 0.414886 | − | 0.909873i | \(-0.363822\pi\) | ||||
0.414886 | + | 0.909873i | \(0.363822\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 24.7846 | 0.794558 | ||||||||
\(974\) | −54.9282 | −1.76001 | ||||||||
\(975\) | −5.46410 | −0.174991 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 47.5692 | 1.52187 | 0.760937 | − | 0.648826i | \(-0.224740\pi\) | ||||
0.760937 | + | 0.648826i | \(0.224740\pi\) | |||||||
\(978\) | 17.0718 | 0.545896 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 53.5692 | 1.70946 | ||||||||
\(983\) | 24.0000 | 0.765481 | 0.382741 | − | 0.923856i | \(-0.374980\pi\) | ||||
0.382741 | + | 0.923856i | \(0.374980\pi\) | |||||||
\(984\) | 6.00000 | 0.191273 | ||||||||
\(985\) | −12.0000 | −0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8564 | 0.441054 | ||||||||
\(988\) | 29.8564 | 0.949859 | ||||||||
\(989\) | 34.1436 | 1.08570 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.21539 | −0.229204 | −0.114602 | − | 0.993411i | \(-0.536559\pi\) | ||||
−0.114602 | + | 0.993411i | \(0.536559\pi\) | |||||||
\(992\) | 56.7846 | 1.80291 | ||||||||
\(993\) | 9.85641 | 0.312784 | ||||||||
\(994\) | −48.0000 | −1.52247 | ||||||||
\(995\) | 24.7846 | 0.785725 | ||||||||
\(996\) | −8.53590 | −0.270470 | ||||||||
\(997\) | −27.6077 | −0.874344 | −0.437172 | − | 0.899378i | \(-0.644020\pi\) | ||||
−0.437172 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(998\) | 49.8564 | 1.57818 | ||||||||
\(999\) | −4.92820 | −0.155921 |
(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 | 1815.2.a.i.1.2 | 2 | ||
3.2 | odd | 2 | 5445.2.a.s.1.1 | 2 | |||
5.4 | even | 2 | 9075.2.a.bh.1.1 | 2 | |||
11.10 | odd | 2 | 165.2.a.b.1.1 | ✓ | 2 | ||
33.32 | even | 2 | 495.2.a.c.1.2 | 2 | |||
44.43 | even | 2 | 2640.2.a.x.1.2 | 2 | |||
55.32 | even | 4 | 825.2.c.c.199.1 | 4 | |||
55.43 | even | 4 | 825.2.c.c.199.4 | 4 | |||
55.54 | odd | 2 | 825.2.a.e.1.2 | 2 | |||
77.76 | even | 2 | 8085.2.a.bd.1.1 | 2 | |||
132.131 | odd | 2 | 7920.2.a.bz.1.2 | 2 | |||
165.32 | odd | 4 | 2475.2.c.n.199.4 | 4 | |||
165.98 | odd | 4 | 2475.2.c.n.199.1 | 4 | |||
165.164 | even | 2 | 2475.2.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.b.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
495.2.a.c.1.2 | 2 | 33.32 | even | 2 | |||
825.2.a.e.1.2 | 2 | 55.54 | odd | 2 | |||
825.2.c.c.199.1 | 4 | 55.32 | even | 4 | |||
825.2.c.c.199.4 | 4 | 55.43 | even | 4 | |||
1815.2.a.i.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2475.2.a.r.1.1 | 2 | 165.164 | even | 2 | |||
2475.2.c.n.199.1 | 4 | 165.98 | odd | 4 | |||
2475.2.c.n.199.4 | 4 | 165.32 | odd | 4 | |||
2640.2.a.x.1.2 | 2 | 44.43 | even | 2 | |||
5445.2.a.s.1.1 | 2 | 3.2 | odd | 2 | |||
7920.2.a.bz.1.2 | 2 | 132.131 | odd | 2 | |||
8085.2.a.bd.1.1 | 2 | 77.76 | even | 2 | |||
9075.2.a.bh.1.1 | 2 | 5.4 | even | 2 |