Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8670,2,Mod(1,8670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8670, 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("8670.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8670.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: | \(69.2302985525\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 510) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8670.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.82843 | 1.82497 | 0.912487 | − | 0.409106i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409106i | \(0.134159\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.41421 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(14\) | −4.82843 | −1.29045 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −4.82843 | −1.05365 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −2.24264 | −0.467623 | −0.233811 | − | 0.972282i | \(-0.575120\pi\) | ||||
−0.233811 | + | 0.972282i | \(0.575120\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.41421 | 0.669582 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.82843 | 0.912487 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.24264 | −1.12121 | −0.560606 | − | 0.828083i | \(-0.689432\pi\) | ||||
−0.560606 | + | 0.828083i | \(0.689432\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.82843 | −0.816153 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 3.41421 | 0.546712 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −6.82843 | −1.06642 | −0.533211 | − | 0.845983i | \(-0.679015\pi\) | ||||
−0.533211 | + | 0.845983i | \(0.679015\pi\) | |||||||
\(42\) | 4.82843 | 0.745042 | ||||||||
\(43\) | 8.24264 | 1.25699 | 0.628495 | − | 0.777813i | \(-0.283671\pi\) | ||||
0.628495 | + | 0.777813i | \(0.283671\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 2.24264 | 0.330659 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.41421 | −0.473466 | ||||||||
\(53\) | −7.65685 | −1.05175 | −0.525875 | − | 0.850562i | \(-0.676262\pi\) | ||||
−0.525875 | + | 0.850562i | \(0.676262\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −4.82843 | −0.645226 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 1.17157 | 0.153835 | ||||||||
\(59\) | −12.2426 | −1.59386 | −0.796928 | − | 0.604074i | \(-0.793543\pi\) | ||||
−0.796928 | + | 0.604074i | \(0.793543\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 6.24264 | 0.792816 | ||||||||
\(63\) | 4.82843 | 0.608325 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.41421 | 0.423481 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | −15.0711 | −1.84122 | −0.920612 | − | 0.390479i | \(-0.872310\pi\) | ||||
−0.920612 | + | 0.390479i | \(0.872310\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.24264 | 0.269982 | ||||||||
\(70\) | 4.82843 | 0.577107 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.3137 | −1.79233 | −0.896167 | − | 0.443717i | \(-0.853660\pi\) | ||||
−0.896167 | + | 0.443717i | \(0.853660\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.82843 | 0.324443 | ||||||||
\(77\) | 9.65685 | 1.10050 | ||||||||
\(78\) | −3.41421 | −0.386584 | ||||||||
\(79\) | −10.2426 | −1.15239 | −0.576194 | − | 0.817313i | \(-0.695463\pi\) | ||||
−0.576194 | + | 0.817313i | \(0.695463\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.82843 | 0.754074 | ||||||||
\(83\) | 2.34315 | 0.257194 | 0.128597 | − | 0.991697i | \(-0.458953\pi\) | ||||
0.128597 | + | 0.991697i | \(0.458953\pi\) | |||||||
\(84\) | −4.82843 | −0.526825 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.24264 | −0.888827 | ||||||||
\(87\) | 1.17157 | 0.125606 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | −10.4853 | −1.11144 | −0.555719 | − | 0.831370i | \(-0.687557\pi\) | ||||
−0.555719 | + | 0.831370i | \(0.687557\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −16.4853 | −1.72813 | ||||||||
\(92\) | −2.24264 | −0.233811 | ||||||||
\(93\) | 6.24264 | 0.647332 | ||||||||
\(94\) | −5.65685 | −0.583460 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.6569 | 1.38664 | 0.693322 | − | 0.720628i | \(-0.256146\pi\) | ||||
0.693322 | + | 0.720628i | \(0.256146\pi\) | |||||||
\(98\) | −16.3137 | −1.64793 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −15.4142 | −1.53377 | −0.766886 | − | 0.641784i | \(-0.778195\pi\) | ||||
−0.766886 | + | 0.641784i | \(0.778195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.82843 | 0.278693 | 0.139347 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139347 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(104\) | 3.41421 | 0.334791 | ||||||||
\(105\) | 4.82843 | 0.471206 | ||||||||
\(106\) | 7.65685 | 0.743699 | ||||||||
\(107\) | 6.82843 | 0.660129 | 0.330064 | − | 0.943958i | \(-0.392930\pi\) | ||||
0.330064 | + | 0.943958i | \(0.392930\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.31371 | −0.892091 | −0.446046 | − | 0.895010i | \(-0.647168\pi\) | ||||
−0.446046 | + | 0.895010i | \(0.647168\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 4.82843 | 0.456243 | ||||||||
\(113\) | 7.75736 | 0.729751 | 0.364875 | − | 0.931056i | \(-0.381112\pi\) | ||||
0.364875 | + | 0.931056i | \(0.381112\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | 2.24264 | 0.209127 | ||||||||
\(116\) | −1.17157 | −0.108778 | ||||||||
\(117\) | −3.41421 | −0.315644 | ||||||||
\(118\) | 12.2426 | 1.12703 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 6.82843 | 0.615699 | ||||||||
\(124\) | −6.24264 | −0.560606 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.82843 | −0.430150 | ||||||||
\(127\) | −18.8284 | −1.67075 | −0.835376 | − | 0.549678i | \(-0.814750\pi\) | ||||
−0.835376 | + | 0.549678i | \(0.814750\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.24264 | −0.725724 | ||||||||
\(130\) | −3.41421 | −0.299446 | ||||||||
\(131\) | −2.34315 | −0.204722 | −0.102361 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102361 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | 13.6569 | 1.18420 | ||||||||
\(134\) | 15.0711 | 1.30194 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | −2.24264 | −0.190906 | ||||||||
\(139\) | 10.8284 | 0.918455 | 0.459228 | − | 0.888319i | \(-0.348126\pi\) | ||||
0.459228 | + | 0.888319i | \(0.348126\pi\) | |||||||
\(140\) | −4.82843 | −0.408077 | ||||||||
\(141\) | −5.65685 | −0.476393 | ||||||||
\(142\) | 10.0000 | 0.839181 | ||||||||
\(143\) | −6.82843 | −0.571022 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.17157 | 0.0972938 | ||||||||
\(146\) | 15.3137 | 1.26737 | ||||||||
\(147\) | −16.3137 | −1.34553 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 23.2132 | 1.90170 | 0.950850 | − | 0.309652i | \(-0.100213\pi\) | ||||
0.950850 | + | 0.309652i | \(0.100213\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −2.48528 | −0.202249 | −0.101125 | − | 0.994874i | \(-0.532244\pi\) | ||||
−0.101125 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.65685 | −0.778171 | ||||||||
\(155\) | 6.24264 | 0.501421 | ||||||||
\(156\) | 3.41421 | 0.273356 | ||||||||
\(157\) | −1.07107 | −0.0854805 | −0.0427403 | − | 0.999086i | \(-0.513609\pi\) | ||||
−0.0427403 | + | 0.999086i | \(0.513609\pi\) | |||||||
\(158\) | 10.2426 | 0.814861 | ||||||||
\(159\) | 7.65685 | 0.607228 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −10.8284 | −0.853400 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −6.82843 | −0.533211 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | −2.34315 | −0.181863 | ||||||||
\(167\) | 7.41421 | 0.573729 | 0.286865 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(168\) | 4.82843 | 0.372521 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 8.24264 | 0.628495 | ||||||||
\(173\) | −10.4853 | −0.797181 | −0.398591 | − | 0.917129i | \(-0.630501\pi\) | ||||
−0.398591 | + | 0.917129i | \(0.630501\pi\) | |||||||
\(174\) | −1.17157 | −0.0888167 | ||||||||
\(175\) | 4.82843 | 0.364995 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 12.2426 | 0.920213 | ||||||||
\(178\) | 10.4853 | 0.785905 | ||||||||
\(179\) | −5.41421 | −0.404677 | −0.202339 | − | 0.979316i | \(-0.564854\pi\) | ||||
−0.202339 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 18.4853 | 1.37400 | 0.687000 | − | 0.726657i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726657i | \(0.258927\pi\) | |||||||
\(182\) | 16.4853 | 1.22197 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 2.24264 | 0.165330 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | −6.24264 | −0.457733 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.65685 | 0.412568 | ||||||||
\(189\) | −4.82843 | −0.351216 | ||||||||
\(190\) | 2.82843 | 0.205196 | ||||||||
\(191\) | −10.1421 | −0.733859 | −0.366930 | − | 0.930249i | \(-0.619591\pi\) | ||||
−0.366930 | + | 0.930249i | \(0.619591\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 21.6569 | 1.55889 | 0.779447 | − | 0.626468i | \(-0.215500\pi\) | ||||
0.779447 | + | 0.626468i | \(0.215500\pi\) | |||||||
\(194\) | −13.6569 | −0.980505 | ||||||||
\(195\) | −3.41421 | −0.244497 | ||||||||
\(196\) | 16.3137 | 1.16526 | ||||||||
\(197\) | −6.97056 | −0.496632 | −0.248316 | − | 0.968679i | \(-0.579877\pi\) | ||||
−0.248316 | + | 0.968679i | \(0.579877\pi\) | |||||||
\(198\) | −2.00000 | −0.142134 | ||||||||
\(199\) | 17.5563 | 1.24454 | 0.622268 | − | 0.782804i | \(-0.286211\pi\) | ||||
0.622268 | + | 0.782804i | \(0.286211\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 15.0711 | 1.06303 | ||||||||
\(202\) | 15.4142 | 1.08454 | ||||||||
\(203\) | −5.65685 | −0.397033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.82843 | 0.476918 | ||||||||
\(206\) | −2.82843 | −0.197066 | ||||||||
\(207\) | −2.24264 | −0.155874 | ||||||||
\(208\) | −3.41421 | −0.236733 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | −4.82843 | −0.333193 | ||||||||
\(211\) | −6.14214 | −0.422842 | −0.211421 | − | 0.977395i | \(-0.567809\pi\) | ||||
−0.211421 | + | 0.977395i | \(0.567809\pi\) | |||||||
\(212\) | −7.65685 | −0.525875 | ||||||||
\(213\) | 10.0000 | 0.685189 | ||||||||
\(214\) | −6.82843 | −0.466782 | ||||||||
\(215\) | −8.24264 | −0.562143 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −30.1421 | −2.04618 | ||||||||
\(218\) | 9.31371 | 0.630804 | ||||||||
\(219\) | 15.3137 | 1.03480 | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | −22.1421 | −1.48275 | −0.741374 | − | 0.671093i | \(-0.765825\pi\) | ||||
−0.741374 | + | 0.671093i | \(0.765825\pi\) | |||||||
\(224\) | −4.82843 | −0.322613 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.75736 | −0.516012 | ||||||||
\(227\) | 4.97056 | 0.329908 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(228\) | −2.82843 | −0.187317 | ||||||||
\(229\) | 25.3137 | 1.67278 | 0.836388 | − | 0.548137i | \(-0.184663\pi\) | ||||
0.836388 | + | 0.548137i | \(0.184663\pi\) | |||||||
\(230\) | −2.24264 | −0.147875 | ||||||||
\(231\) | −9.65685 | −0.635374 | ||||||||
\(232\) | 1.17157 | 0.0769175 | ||||||||
\(233\) | 6.38478 | 0.418281 | 0.209140 | − | 0.977886i | \(-0.432933\pi\) | ||||
0.209140 | + | 0.977886i | \(0.432933\pi\) | |||||||
\(234\) | 3.41421 | 0.223194 | ||||||||
\(235\) | −5.65685 | −0.369012 | ||||||||
\(236\) | −12.2426 | −0.796928 | ||||||||
\(237\) | 10.2426 | 0.665331 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 2.58579 | 0.166565 | 0.0832826 | − | 0.996526i | \(-0.473460\pi\) | ||||
0.0832826 | + | 0.996526i | \(0.473460\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −16.3137 | −1.04224 | ||||||||
\(246\) | −6.82843 | −0.435365 | ||||||||
\(247\) | −9.65685 | −0.614451 | ||||||||
\(248\) | 6.24264 | 0.396408 | ||||||||
\(249\) | −2.34315 | −0.148491 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −27.0711 | −1.70871 | −0.854355 | − | 0.519689i | \(-0.826048\pi\) | ||||
−0.854355 | + | 0.519689i | \(0.826048\pi\) | |||||||
\(252\) | 4.82843 | 0.304162 | ||||||||
\(253\) | −4.48528 | −0.281987 | ||||||||
\(254\) | 18.8284 | 1.18140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.65685 | 0.103352 | 0.0516759 | − | 0.998664i | \(-0.483544\pi\) | ||||
0.0516759 | + | 0.998664i | \(0.483544\pi\) | |||||||
\(258\) | 8.24264 | 0.513164 | ||||||||
\(259\) | 9.65685 | 0.600048 | ||||||||
\(260\) | 3.41421 | 0.211741 | ||||||||
\(261\) | −1.17157 | −0.0725185 | ||||||||
\(262\) | 2.34315 | 0.144760 | ||||||||
\(263\) | −18.4853 | −1.13985 | −0.569926 | − | 0.821696i | \(-0.693028\pi\) | ||||
−0.569926 | + | 0.821696i | \(0.693028\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 7.65685 | 0.470357 | ||||||||
\(266\) | −13.6569 | −0.837355 | ||||||||
\(267\) | 10.4853 | 0.641689 | ||||||||
\(268\) | −15.0711 | −0.920612 | ||||||||
\(269\) | 11.6569 | 0.710731 | 0.355365 | − | 0.934727i | \(-0.384356\pi\) | ||||
0.355365 | + | 0.934727i | \(0.384356\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −1.51472 | −0.0920126 | −0.0460063 | − | 0.998941i | \(-0.514649\pi\) | ||||
−0.0460063 | + | 0.998941i | \(0.514649\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.4853 | 0.997735 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 2.24264 | 0.134991 | ||||||||
\(277\) | 11.5147 | 0.691852 | 0.345926 | − | 0.938262i | \(-0.387565\pi\) | ||||
0.345926 | + | 0.938262i | \(0.387565\pi\) | |||||||
\(278\) | −10.8284 | −0.649446 | ||||||||
\(279\) | −6.24264 | −0.373737 | ||||||||
\(280\) | 4.82843 | 0.288554 | ||||||||
\(281\) | −11.1716 | −0.666440 | −0.333220 | − | 0.942849i | \(-0.608135\pi\) | ||||
−0.333220 | + | 0.942849i | \(0.608135\pi\) | |||||||
\(282\) | 5.65685 | 0.336861 | ||||||||
\(283\) | 15.6569 | 0.930703 | 0.465352 | − | 0.885126i | \(-0.345928\pi\) | ||||
0.465352 | + | 0.885126i | \(0.345928\pi\) | |||||||
\(284\) | −10.0000 | −0.593391 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 6.82843 | 0.403773 | ||||||||
\(287\) | −32.9706 | −1.94619 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.17157 | −0.0687971 | ||||||||
\(291\) | −13.6569 | −0.800579 | ||||||||
\(292\) | −15.3137 | −0.896167 | ||||||||
\(293\) | 20.6274 | 1.20507 | 0.602533 | − | 0.798094i | \(-0.294158\pi\) | ||||
0.602533 | + | 0.798094i | \(0.294158\pi\) | |||||||
\(294\) | 16.3137 | 0.951435 | ||||||||
\(295\) | 12.2426 | 0.712794 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | −23.2132 | −1.34470 | ||||||||
\(299\) | 7.65685 | 0.442807 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 39.7990 | 2.29398 | ||||||||
\(302\) | 2.48528 | 0.143012 | ||||||||
\(303\) | 15.4142 | 0.885523 | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.75736 | 0.442736 | 0.221368 | − | 0.975190i | \(-0.428948\pi\) | ||||
0.221368 | + | 0.975190i | \(0.428948\pi\) | |||||||
\(308\) | 9.65685 | 0.550250 | ||||||||
\(309\) | −2.82843 | −0.160904 | ||||||||
\(310\) | −6.24264 | −0.354558 | ||||||||
\(311\) | −23.6569 | −1.34146 | −0.670729 | − | 0.741703i | \(-0.734018\pi\) | ||||
−0.670729 | + | 0.741703i | \(0.734018\pi\) | |||||||
\(312\) | −3.41421 | −0.193292 | ||||||||
\(313\) | −1.65685 | −0.0936509 | −0.0468255 | − | 0.998903i | \(-0.514910\pi\) | ||||
−0.0468255 | + | 0.998903i | \(0.514910\pi\) | |||||||
\(314\) | 1.07107 | 0.0604439 | ||||||||
\(315\) | −4.82843 | −0.272051 | ||||||||
\(316\) | −10.2426 | −0.576194 | ||||||||
\(317\) | 13.3137 | 0.747772 | 0.373886 | − | 0.927475i | \(-0.378025\pi\) | ||||
0.373886 | + | 0.927475i | \(0.378025\pi\) | |||||||
\(318\) | −7.65685 | −0.429375 | ||||||||
\(319\) | −2.34315 | −0.131191 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.82843 | −0.381126 | ||||||||
\(322\) | 10.8284 | 0.603445 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.41421 | −0.189386 | ||||||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 9.31371 | 0.515049 | ||||||||
\(328\) | 6.82843 | 0.377037 | ||||||||
\(329\) | 27.3137 | 1.50585 | ||||||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | −13.1716 | −0.723975 | −0.361988 | − | 0.932183i | \(-0.617902\pi\) | ||||
−0.361988 | + | 0.932183i | \(0.617902\pi\) | |||||||
\(332\) | 2.34315 | 0.128597 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | −7.41421 | −0.405688 | ||||||||
\(335\) | 15.0711 | 0.823420 | ||||||||
\(336\) | −4.82843 | −0.263412 | ||||||||
\(337\) | 3.31371 | 0.180509 | 0.0902546 | − | 0.995919i | \(-0.471232\pi\) | ||||
0.0902546 | + | 0.995919i | \(0.471232\pi\) | |||||||
\(338\) | 1.34315 | 0.0730575 | ||||||||
\(339\) | −7.75736 | −0.421322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4853 | −0.676116 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | 44.9706 | 2.42818 | ||||||||
\(344\) | −8.24264 | −0.444413 | ||||||||
\(345\) | −2.24264 | −0.120740 | ||||||||
\(346\) | 10.4853 | 0.563692 | ||||||||
\(347\) | −19.3137 | −1.03681 | −0.518407 | − | 0.855134i | \(-0.673475\pi\) | ||||
−0.518407 | + | 0.855134i | \(0.673475\pi\) | |||||||
\(348\) | 1.17157 | 0.0628029 | ||||||||
\(349\) | −7.65685 | −0.409862 | −0.204931 | − | 0.978776i | \(-0.565697\pi\) | ||||
−0.204931 | + | 0.978776i | \(0.565697\pi\) | |||||||
\(350\) | −4.82843 | −0.258090 | ||||||||
\(351\) | 3.41421 | 0.182237 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −30.9706 | −1.64840 | −0.824198 | − | 0.566301i | \(-0.808374\pi\) | ||||
−0.824198 | + | 0.566301i | \(0.808374\pi\) | |||||||
\(354\) | −12.2426 | −0.650689 | ||||||||
\(355\) | 10.0000 | 0.530745 | ||||||||
\(356\) | −10.4853 | −0.555719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.41421 | 0.286150 | ||||||||
\(359\) | 21.1716 | 1.11739 | 0.558696 | − | 0.829372i | \(-0.311302\pi\) | ||||
0.558696 | + | 0.829372i | \(0.311302\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −18.4853 | −0.971565 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | −16.4853 | −0.864064 | ||||||||
\(365\) | 15.3137 | 0.801556 | ||||||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | 4.82843 | 0.252042 | 0.126021 | − | 0.992028i | \(-0.459779\pi\) | ||||
0.126021 | + | 0.992028i | \(0.459779\pi\) | |||||||
\(368\) | −2.24264 | −0.116906 | ||||||||
\(369\) | −6.82843 | −0.355474 | ||||||||
\(370\) | 2.00000 | 0.103975 | ||||||||
\(371\) | −36.9706 | −1.91942 | ||||||||
\(372\) | 6.24264 | 0.323666 | ||||||||
\(373\) | 9.55635 | 0.494809 | 0.247405 | − | 0.968912i | \(-0.420422\pi\) | ||||
0.247405 | + | 0.968912i | \(0.420422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −5.65685 | −0.291730 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | 4.82843 | 0.248347 | ||||||||
\(379\) | 14.3431 | 0.736758 | 0.368379 | − | 0.929676i | \(-0.379913\pi\) | ||||
0.368379 | + | 0.929676i | \(0.379913\pi\) | |||||||
\(380\) | −2.82843 | −0.145095 | ||||||||
\(381\) | 18.8284 | 0.964610 | ||||||||
\(382\) | 10.1421 | 0.518917 | ||||||||
\(383\) | 24.1421 | 1.23361 | 0.616803 | − | 0.787118i | \(-0.288428\pi\) | ||||
0.616803 | + | 0.787118i | \(0.288428\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −9.65685 | −0.492159 | ||||||||
\(386\) | −21.6569 | −1.10230 | ||||||||
\(387\) | 8.24264 | 0.418997 | ||||||||
\(388\) | 13.6569 | 0.693322 | ||||||||
\(389\) | 26.7279 | 1.35516 | 0.677580 | − | 0.735449i | \(-0.263029\pi\) | ||||
0.677580 | + | 0.735449i | \(0.263029\pi\) | |||||||
\(390\) | 3.41421 | 0.172885 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −16.3137 | −0.823967 | ||||||||
\(393\) | 2.34315 | 0.118196 | ||||||||
\(394\) | 6.97056 | 0.351172 | ||||||||
\(395\) | 10.2426 | 0.515363 | ||||||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 7.79899 | 0.391420 | 0.195710 | − | 0.980662i | \(-0.437299\pi\) | ||||
0.195710 | + | 0.980662i | \(0.437299\pi\) | |||||||
\(398\) | −17.5563 | −0.880020 | ||||||||
\(399\) | −13.6569 | −0.683698 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 4.97056 | 0.248218 | 0.124109 | − | 0.992269i | \(-0.460393\pi\) | ||||
0.124109 | + | 0.992269i | \(0.460393\pi\) | |||||||
\(402\) | −15.0711 | −0.751677 | ||||||||
\(403\) | 21.3137 | 1.06171 | ||||||||
\(404\) | −15.4142 | −0.766886 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 5.65685 | 0.280745 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6274 | −1.21775 | −0.608874 | − | 0.793267i | \(-0.708378\pi\) | ||||
−0.608874 | + | 0.793267i | \(0.708378\pi\) | |||||||
\(410\) | −6.82843 | −0.337232 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 2.82843 | 0.139347 | ||||||||
\(413\) | −59.1127 | −2.90875 | ||||||||
\(414\) | 2.24264 | 0.110220 | ||||||||
\(415\) | −2.34315 | −0.115021 | ||||||||
\(416\) | 3.41421 | 0.167396 | ||||||||
\(417\) | −10.8284 | −0.530270 | ||||||||
\(418\) | −5.65685 | −0.276686 | ||||||||
\(419\) | −22.9706 | −1.12219 | −0.561093 | − | 0.827753i | \(-0.689619\pi\) | ||||
−0.561093 | + | 0.827753i | \(0.689619\pi\) | |||||||
\(420\) | 4.82843 | 0.235603 | ||||||||
\(421\) | −12.1421 | −0.591771 | −0.295886 | − | 0.955223i | \(-0.595615\pi\) | ||||
−0.295886 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(422\) | 6.14214 | 0.298994 | ||||||||
\(423\) | 5.65685 | 0.275046 | ||||||||
\(424\) | 7.65685 | 0.371850 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.0000 | −0.484502 | ||||||||
\(427\) | 28.9706 | 1.40198 | ||||||||
\(428\) | 6.82843 | 0.330064 | ||||||||
\(429\) | 6.82843 | 0.329680 | ||||||||
\(430\) | 8.24264 | 0.397495 | ||||||||
\(431\) | −20.3431 | −0.979895 | −0.489947 | − | 0.871752i | \(-0.662984\pi\) | ||||
−0.489947 | + | 0.871752i | \(0.662984\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −20.3431 | −0.977629 | −0.488815 | − | 0.872388i | \(-0.662571\pi\) | ||||
−0.488815 | + | 0.872388i | \(0.662571\pi\) | |||||||
\(434\) | 30.1421 | 1.44687 | ||||||||
\(435\) | −1.17157 | −0.0561726 | ||||||||
\(436\) | −9.31371 | −0.446046 | ||||||||
\(437\) | −6.34315 | −0.303434 | ||||||||
\(438\) | −15.3137 | −0.731717 | ||||||||
\(439\) | −38.7279 | −1.84838 | −0.924191 | − | 0.381930i | \(-0.875260\pi\) | ||||
−0.924191 | + | 0.381930i | \(0.875260\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.4558 | 1.58954 | 0.794768 | − | 0.606914i | \(-0.207593\pi\) | ||||
0.794768 | + | 0.606914i | \(0.207593\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 10.4853 | 0.497050 | ||||||||
\(446\) | 22.1421 | 1.04846 | ||||||||
\(447\) | −23.2132 | −1.09795 | ||||||||
\(448\) | 4.82843 | 0.228122 | ||||||||
\(449\) | 6.62742 | 0.312767 | 0.156384 | − | 0.987696i | \(-0.450016\pi\) | ||||
0.156384 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −13.6569 | −0.643076 | ||||||||
\(452\) | 7.75736 | 0.364875 | ||||||||
\(453\) | 2.48528 | 0.116769 | ||||||||
\(454\) | −4.97056 | −0.233280 | ||||||||
\(455\) | 16.4853 | 0.772842 | ||||||||
\(456\) | 2.82843 | 0.132453 | ||||||||
\(457\) | 29.3137 | 1.37124 | 0.685619 | − | 0.727961i | \(-0.259532\pi\) | ||||
0.685619 | + | 0.727961i | \(0.259532\pi\) | |||||||
\(458\) | −25.3137 | −1.18283 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.24264 | 0.104564 | ||||||||
\(461\) | 10.0416 | 0.467685 | 0.233843 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233843 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(462\) | 9.65685 | 0.449278 | ||||||||
\(463\) | 23.7990 | 1.10603 | 0.553016 | − | 0.833170i | \(-0.313477\pi\) | ||||
0.553016 | + | 0.833170i | \(0.313477\pi\) | |||||||
\(464\) | −1.17157 | −0.0543889 | ||||||||
\(465\) | −6.24264 | −0.289496 | ||||||||
\(466\) | −6.38478 | −0.295769 | ||||||||
\(467\) | −24.9706 | −1.15550 | −0.577750 | − | 0.816214i | \(-0.696069\pi\) | ||||
−0.577750 | + | 0.816214i | \(0.696069\pi\) | |||||||
\(468\) | −3.41421 | −0.157822 | ||||||||
\(469\) | −72.7696 | −3.36019 | ||||||||
\(470\) | 5.65685 | 0.260931 | ||||||||
\(471\) | 1.07107 | 0.0493522 | ||||||||
\(472\) | 12.2426 | 0.563513 | ||||||||
\(473\) | 16.4853 | 0.757994 | ||||||||
\(474\) | −10.2426 | −0.470460 | ||||||||
\(475\) | 2.82843 | 0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.65685 | −0.350583 | ||||||||
\(478\) | 4.00000 | 0.182956 | ||||||||
\(479\) | −38.0000 | −1.73626 | −0.868132 | − | 0.496333i | \(-0.834679\pi\) | ||||
−0.868132 | + | 0.496333i | \(0.834679\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −6.82843 | −0.311349 | ||||||||
\(482\) | −2.58579 | −0.117779 | ||||||||
\(483\) | 10.8284 | 0.492710 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −13.6569 | −0.620126 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 26.0000 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 16.3137 | 0.736978 | ||||||||
\(491\) | 32.2426 | 1.45509 | 0.727545 | − | 0.686060i | \(-0.240661\pi\) | ||||
0.727545 | + | 0.686060i | \(0.240661\pi\) | |||||||
\(492\) | 6.82843 | 0.307849 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 9.65685 | 0.434482 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −6.24264 | −0.280303 | ||||||||
\(497\) | −48.2843 | −2.16585 | ||||||||
\(498\) | 2.34315 | 0.104999 | ||||||||
\(499\) | −17.1716 | −0.768705 | −0.384353 | − | 0.923186i | \(-0.625575\pi\) | ||||
−0.384353 | + | 0.923186i | \(0.625575\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −7.41421 | −0.331243 | ||||||||
\(502\) | 27.0711 | 1.20824 | ||||||||
\(503\) | −4.38478 | −0.195508 | −0.0977538 | − | 0.995211i | \(-0.531166\pi\) | ||||
−0.0977538 | + | 0.995211i | \(0.531166\pi\) | |||||||
\(504\) | −4.82843 | −0.215075 | ||||||||
\(505\) | 15.4142 | 0.685924 | ||||||||
\(506\) | 4.48528 | 0.199395 | ||||||||
\(507\) | 1.34315 | 0.0596512 | ||||||||
\(508\) | −18.8284 | −0.835376 | ||||||||
\(509\) | −21.0711 | −0.933959 | −0.466979 | − | 0.884268i | \(-0.654658\pi\) | ||||
−0.466979 | + | 0.884268i | \(0.654658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −73.9411 | −3.27096 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | −1.65685 | −0.0730807 | ||||||||
\(515\) | −2.82843 | −0.124635 | ||||||||
\(516\) | −8.24264 | −0.362862 | ||||||||
\(517\) | 11.3137 | 0.497576 | ||||||||
\(518\) | −9.65685 | −0.424298 | ||||||||
\(519\) | 10.4853 | 0.460253 | ||||||||
\(520\) | −3.41421 | −0.149723 | ||||||||
\(521\) | 21.6569 | 0.948804 | 0.474402 | − | 0.880308i | \(-0.342664\pi\) | ||||
0.474402 | + | 0.880308i | \(0.342664\pi\) | |||||||
\(522\) | 1.17157 | 0.0512784 | ||||||||
\(523\) | −24.5269 | −1.07249 | −0.536243 | − | 0.844063i | \(-0.680157\pi\) | ||||
−0.536243 | + | 0.844063i | \(0.680157\pi\) | |||||||
\(524\) | −2.34315 | −0.102361 | ||||||||
\(525\) | −4.82843 | −0.210730 | ||||||||
\(526\) | 18.4853 | 0.805997 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.00000 | −0.0870388 | ||||||||
\(529\) | −17.9706 | −0.781329 | ||||||||
\(530\) | −7.65685 | −0.332592 | ||||||||
\(531\) | −12.2426 | −0.531285 | ||||||||
\(532\) | 13.6569 | 0.592100 | ||||||||
\(533\) | 23.3137 | 1.00983 | ||||||||
\(534\) | −10.4853 | −0.453743 | ||||||||
\(535\) | −6.82843 | −0.295219 | ||||||||
\(536\) | 15.0711 | 0.650971 | ||||||||
\(537\) | 5.41421 | 0.233641 | ||||||||
\(538\) | −11.6569 | −0.502563 | ||||||||
\(539\) | 32.6274 | 1.40536 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −25.3137 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(542\) | 1.51472 | 0.0650627 | ||||||||
\(543\) | −18.4853 | −0.793279 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.31371 | 0.398955 | ||||||||
\(546\) | −16.4853 | −0.705505 | ||||||||
\(547\) | −36.6274 | −1.56608 | −0.783038 | − | 0.621974i | \(-0.786331\pi\) | ||||
−0.783038 | + | 0.621974i | \(0.786331\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | −3.31371 | −0.141169 | ||||||||
\(552\) | −2.24264 | −0.0954531 | ||||||||
\(553\) | −49.4558 | −2.10308 | ||||||||
\(554\) | −11.5147 | −0.489214 | ||||||||
\(555\) | 2.00000 | 0.0848953 | ||||||||
\(556\) | 10.8284 | 0.459228 | ||||||||
\(557\) | 19.6569 | 0.832888 | 0.416444 | − | 0.909161i | \(-0.363276\pi\) | ||||
0.416444 | + | 0.909161i | \(0.363276\pi\) | |||||||
\(558\) | 6.24264 | 0.264272 | ||||||||
\(559\) | −28.1421 | −1.19029 | ||||||||
\(560\) | −4.82843 | −0.204038 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1716 | 0.471244 | ||||||||
\(563\) | 30.6274 | 1.29079 | 0.645396 | − | 0.763848i | \(-0.276692\pi\) | ||||
0.645396 | + | 0.763848i | \(0.276692\pi\) | |||||||
\(564\) | −5.65685 | −0.238197 | ||||||||
\(565\) | −7.75736 | −0.326355 | ||||||||
\(566\) | −15.6569 | −0.658107 | ||||||||
\(567\) | 4.82843 | 0.202775 | ||||||||
\(568\) | 10.0000 | 0.419591 | ||||||||
\(569\) | −25.5147 | −1.06963 | −0.534816 | − | 0.844968i | \(-0.679619\pi\) | ||||
−0.534816 | + | 0.844968i | \(0.679619\pi\) | |||||||
\(570\) | −2.82843 | −0.118470 | ||||||||
\(571\) | −5.65685 | −0.236732 | −0.118366 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118366 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(572\) | −6.82843 | −0.285511 | ||||||||
\(573\) | 10.1421 | 0.423694 | ||||||||
\(574\) | 32.9706 | 1.37616 | ||||||||
\(575\) | −2.24264 | −0.0935246 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −30.9706 | −1.28932 | −0.644661 | − | 0.764469i | \(-0.723001\pi\) | ||||
−0.644661 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.6569 | −0.900028 | ||||||||
\(580\) | 1.17157 | 0.0486469 | ||||||||
\(581\) | 11.3137 | 0.469372 | ||||||||
\(582\) | 13.6569 | 0.566095 | ||||||||
\(583\) | −15.3137 | −0.634229 | ||||||||
\(584\) | 15.3137 | 0.633686 | ||||||||
\(585\) | 3.41421 | 0.141160 | ||||||||
\(586\) | −20.6274 | −0.852111 | ||||||||
\(587\) | 3.79899 | 0.156801 | 0.0784005 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0784005 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(588\) | −16.3137 | −0.672766 | ||||||||
\(589\) | −17.6569 | −0.727538 | ||||||||
\(590\) | −12.2426 | −0.504022 | ||||||||
\(591\) | 6.97056 | 0.286731 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −32.6274 | −1.33985 | −0.669924 | − | 0.742430i | \(-0.733673\pi\) | ||||
−0.669924 | + | 0.742430i | \(0.733673\pi\) | |||||||
\(594\) | 2.00000 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.2132 | 0.950850 | ||||||||
\(597\) | −17.5563 | −0.718534 | ||||||||
\(598\) | −7.65685 | −0.313112 | ||||||||
\(599\) | −42.4264 | −1.73350 | −0.866748 | − | 0.498746i | \(-0.833794\pi\) | ||||
−0.866748 | + | 0.498746i | \(0.833794\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −1.41421 | −0.0576870 | −0.0288435 | − | 0.999584i | \(-0.509182\pi\) | ||||
−0.0288435 | + | 0.999584i | \(0.509182\pi\) | |||||||
\(602\) | −39.7990 | −1.62209 | ||||||||
\(603\) | −15.0711 | −0.613741 | ||||||||
\(604\) | −2.48528 | −0.101125 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | −15.4142 | −0.626160 | ||||||||
\(607\) | −10.0000 | −0.405887 | −0.202944 | − | 0.979190i | \(-0.565051\pi\) | ||||
−0.202944 | + | 0.979190i | \(0.565051\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | 5.65685 | 0.229227 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −19.3137 | −0.781349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.7279 | −1.40265 | −0.701324 | − | 0.712843i | \(-0.747407\pi\) | ||||
−0.701324 | + | 0.712843i | \(0.747407\pi\) | |||||||
\(614\) | −7.75736 | −0.313062 | ||||||||
\(615\) | −6.82843 | −0.275349 | ||||||||
\(616\) | −9.65685 | −0.389086 | ||||||||
\(617\) | −32.2426 | −1.29804 | −0.649020 | − | 0.760771i | \(-0.724821\pi\) | ||||
−0.649020 | + | 0.760771i | \(0.724821\pi\) | |||||||
\(618\) | 2.82843 | 0.113776 | ||||||||
\(619\) | −10.3431 | −0.415726 | −0.207863 | − | 0.978158i | \(-0.566651\pi\) | ||||
−0.207863 | + | 0.978158i | \(0.566651\pi\) | |||||||
\(620\) | 6.24264 | 0.250710 | ||||||||
\(621\) | 2.24264 | 0.0899941 | ||||||||
\(622\) | 23.6569 | 0.948553 | ||||||||
\(623\) | −50.6274 | −2.02834 | ||||||||
\(624\) | 3.41421 | 0.136678 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.65685 | 0.0662212 | ||||||||
\(627\) | −5.65685 | −0.225913 | ||||||||
\(628\) | −1.07107 | −0.0427403 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.82843 | 0.192369 | ||||||||
\(631\) | 41.1127 | 1.63667 | 0.818335 | − | 0.574741i | \(-0.194897\pi\) | ||||
0.818335 | + | 0.574741i | \(0.194897\pi\) | |||||||
\(632\) | 10.2426 | 0.407430 | ||||||||
\(633\) | 6.14214 | 0.244128 | ||||||||
\(634\) | −13.3137 | −0.528755 | ||||||||
\(635\) | 18.8284 | 0.747183 | ||||||||
\(636\) | 7.65685 | 0.303614 | ||||||||
\(637\) | −55.6985 | −2.20685 | ||||||||
\(638\) | 2.34315 | 0.0927660 | ||||||||
\(639\) | −10.0000 | −0.395594 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −25.6569 | −1.01338 | −0.506692 | − | 0.862127i | \(-0.669132\pi\) | ||||
−0.506692 | + | 0.862127i | \(0.669132\pi\) | |||||||
\(642\) | 6.82843 | 0.269497 | ||||||||
\(643\) | −16.6274 | −0.655721 | −0.327861 | − | 0.944726i | \(-0.606328\pi\) | ||||
−0.327861 | + | 0.944726i | \(0.606328\pi\) | |||||||
\(644\) | −10.8284 | −0.426700 | ||||||||
\(645\) | 8.24264 | 0.324554 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.1127 | 1.14454 | 0.572269 | − | 0.820066i | \(-0.306063\pi\) | ||||
0.572269 | + | 0.820066i | \(0.306063\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −24.4853 | −0.961131 | ||||||||
\(650\) | 3.41421 | 0.133916 | ||||||||
\(651\) | 30.1421 | 1.18136 | ||||||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | 22.2843 | 0.872051 | 0.436025 | − | 0.899934i | \(-0.356386\pi\) | ||||
0.436025 | + | 0.899934i | \(0.356386\pi\) | |||||||
\(654\) | −9.31371 | −0.364195 | ||||||||
\(655\) | 2.34315 | 0.0915543 | ||||||||
\(656\) | −6.82843 | −0.266605 | ||||||||
\(657\) | −15.3137 | −0.597445 | ||||||||
\(658\) | −27.3137 | −1.06480 | ||||||||
\(659\) | 25.4142 | 0.989997 | 0.494999 | − | 0.868894i | \(-0.335169\pi\) | ||||
0.494999 | + | 0.868894i | \(0.335169\pi\) | |||||||
\(660\) | 2.00000 | 0.0778499 | ||||||||
\(661\) | 26.2843 | 1.02234 | 0.511170 | − | 0.859480i | \(-0.329212\pi\) | ||||
0.511170 | + | 0.859480i | \(0.329212\pi\) | |||||||
\(662\) | 13.1716 | 0.511928 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.34315 | −0.0909317 | ||||||||
\(665\) | −13.6569 | −0.529590 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | 2.62742 | 0.101734 | ||||||||
\(668\) | 7.41421 | 0.286865 | ||||||||
\(669\) | 22.1421 | 0.856064 | ||||||||
\(670\) | −15.0711 | −0.582246 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 4.82843 | 0.186261 | ||||||||
\(673\) | 38.6274 | 1.48898 | 0.744489 | − | 0.667635i | \(-0.232693\pi\) | ||||
0.744489 | + | 0.667635i | \(0.232693\pi\) | |||||||
\(674\) | −3.31371 | −0.127639 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −1.34315 | −0.0516595 | ||||||||
\(677\) | −42.9706 | −1.65149 | −0.825746 | − | 0.564041i | \(-0.809246\pi\) | ||||
−0.825746 | + | 0.564041i | \(0.809246\pi\) | |||||||
\(678\) | 7.75736 | 0.297920 | ||||||||
\(679\) | 65.9411 | 2.53059 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.97056 | −0.190472 | ||||||||
\(682\) | 12.4853 | 0.478086 | ||||||||
\(683\) | 6.34315 | 0.242714 | 0.121357 | − | 0.992609i | \(-0.461275\pi\) | ||||
0.121357 | + | 0.992609i | \(0.461275\pi\) | |||||||
\(684\) | 2.82843 | 0.108148 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −44.9706 | −1.71698 | ||||||||
\(687\) | −25.3137 | −0.965778 | ||||||||
\(688\) | 8.24264 | 0.314248 | ||||||||
\(689\) | 26.1421 | 0.995936 | ||||||||
\(690\) | 2.24264 | 0.0853759 | ||||||||
\(691\) | −14.1421 | −0.537992 | −0.268996 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268996 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(692\) | −10.4853 | −0.398591 | ||||||||
\(693\) | 9.65685 | 0.366834 | ||||||||
\(694\) | 19.3137 | 0.733138 | ||||||||
\(695\) | −10.8284 | −0.410746 | ||||||||
\(696\) | −1.17157 | −0.0444084 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.65685 | 0.289816 | ||||||||
\(699\) | −6.38478 | −0.241494 | ||||||||
\(700\) | 4.82843 | 0.182497 | ||||||||
\(701\) | −42.0416 | −1.58789 | −0.793945 | − | 0.607989i | \(-0.791976\pi\) | ||||
−0.793945 | + | 0.607989i | \(0.791976\pi\) | |||||||
\(702\) | −3.41421 | −0.128861 | ||||||||
\(703\) | 5.65685 | 0.213352 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 5.65685 | 0.213049 | ||||||||
\(706\) | 30.9706 | 1.16559 | ||||||||
\(707\) | −74.4264 | −2.79909 | ||||||||
\(708\) | 12.2426 | 0.460107 | ||||||||
\(709\) | 35.4558 | 1.33157 | 0.665786 | − | 0.746143i | \(-0.268096\pi\) | ||||
0.665786 | + | 0.746143i | \(0.268096\pi\) | |||||||
\(710\) | −10.0000 | −0.375293 | ||||||||
\(711\) | −10.2426 | −0.384129 | ||||||||
\(712\) | 10.4853 | 0.392953 | ||||||||
\(713\) | 14.0000 | 0.524304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.82843 | 0.255369 | ||||||||
\(716\) | −5.41421 | −0.202339 | ||||||||
\(717\) | 4.00000 | 0.149383 | ||||||||
\(718\) | −21.1716 | −0.790116 | ||||||||
\(719\) | −14.9706 | −0.558308 | −0.279154 | − | 0.960246i | \(-0.590054\pi\) | ||||
−0.279154 | + | 0.960246i | \(0.590054\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 13.6569 | 0.508608 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | −2.58579 | −0.0961664 | ||||||||
\(724\) | 18.4853 | 0.687000 | ||||||||
\(725\) | −1.17157 | −0.0435111 | ||||||||
\(726\) | −7.00000 | −0.259794 | ||||||||
\(727\) | 44.0833 | 1.63496 | 0.817479 | − | 0.575959i | \(-0.195371\pi\) | ||||
0.817479 | + | 0.575959i | \(0.195371\pi\) | |||||||
\(728\) | 16.4853 | 0.610985 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.3137 | −0.566786 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | 7.21320 | 0.266426 | 0.133213 | − | 0.991087i | \(-0.457471\pi\) | ||||
0.133213 | + | 0.991087i | \(0.457471\pi\) | |||||||
\(734\) | −4.82843 | −0.178220 | ||||||||
\(735\) | 16.3137 | 0.601740 | ||||||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | −30.1421 | −1.11030 | ||||||||
\(738\) | 6.82843 | 0.251358 | ||||||||
\(739\) | 14.3431 | 0.527621 | 0.263811 | − | 0.964575i | \(-0.415021\pi\) | ||||
0.263811 | + | 0.964575i | \(0.415021\pi\) | |||||||
\(740\) | −2.00000 | −0.0735215 | ||||||||
\(741\) | 9.65685 | 0.354753 | ||||||||
\(742\) | 36.9706 | 1.35723 | ||||||||
\(743\) | 10.7279 | 0.393569 | 0.196785 | − | 0.980447i | \(-0.436950\pi\) | ||||
0.196785 | + | 0.980447i | \(0.436950\pi\) | |||||||
\(744\) | −6.24264 | −0.228866 | ||||||||
\(745\) | −23.2132 | −0.850466 | ||||||||
\(746\) | −9.55635 | −0.349883 | ||||||||
\(747\) | 2.34315 | 0.0857312 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.9706 | 1.20472 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 38.5269 | 1.40587 | 0.702933 | − | 0.711256i | \(-0.251873\pi\) | ||||
0.702933 | + | 0.711256i | \(0.251873\pi\) | |||||||
\(752\) | 5.65685 | 0.206284 | ||||||||
\(753\) | 27.0711 | 0.986525 | ||||||||
\(754\) | −4.00000 | −0.145671 | ||||||||
\(755\) | 2.48528 | 0.0904487 | ||||||||
\(756\) | −4.82843 | −0.175608 | ||||||||
\(757\) | −5.75736 | −0.209255 | −0.104627 | − | 0.994511i | \(-0.533365\pi\) | ||||
−0.104627 | + | 0.994511i | \(0.533365\pi\) | |||||||
\(758\) | −14.3431 | −0.520967 | ||||||||
\(759\) | 4.48528 | 0.162805 | ||||||||
\(760\) | 2.82843 | 0.102598 | ||||||||
\(761\) | −28.8284 | −1.04503 | −0.522515 | − | 0.852630i | \(-0.675006\pi\) | ||||
−0.522515 | + | 0.852630i | \(0.675006\pi\) | |||||||
\(762\) | −18.8284 | −0.682082 | ||||||||
\(763\) | −44.9706 | −1.62804 | ||||||||
\(764\) | −10.1421 | −0.366930 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.1421 | −0.872291 | ||||||||
\(767\) | 41.7990 | 1.50927 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 9.65685 | 0.348009 | ||||||||
\(771\) | −1.65685 | −0.0596701 | ||||||||
\(772\) | 21.6569 | 0.779447 | ||||||||
\(773\) | 41.1127 | 1.47872 | 0.739360 | − | 0.673310i | \(-0.235128\pi\) | ||||
0.739360 | + | 0.673310i | \(0.235128\pi\) | |||||||
\(774\) | −8.24264 | −0.296276 | ||||||||
\(775\) | −6.24264 | −0.224242 | ||||||||
\(776\) | −13.6569 | −0.490252 | ||||||||
\(777\) | −9.65685 | −0.346438 | ||||||||
\(778\) | −26.7279 | −0.958242 | ||||||||
\(779\) | −19.3137 | −0.691985 | ||||||||
\(780\) | −3.41421 | −0.122248 | ||||||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.17157 | 0.0418686 | ||||||||
\(784\) | 16.3137 | 0.582632 | ||||||||
\(785\) | 1.07107 | 0.0382280 | ||||||||
\(786\) | −2.34315 | −0.0835772 | ||||||||
\(787\) | 16.9706 | 0.604935 | 0.302468 | − | 0.953160i | \(-0.402190\pi\) | ||||
0.302468 | + | 0.953160i | \(0.402190\pi\) | |||||||
\(788\) | −6.97056 | −0.248316 | ||||||||
\(789\) | 18.4853 | 0.658093 | ||||||||
\(790\) | −10.2426 | −0.364417 | ||||||||
\(791\) | 37.4558 | 1.33178 | ||||||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | −20.4853 | −0.727454 | ||||||||
\(794\) | −7.79899 | −0.276776 | ||||||||
\(795\) | −7.65685 | −0.271561 | ||||||||
\(796\) | 17.5563 | 0.622268 | ||||||||
\(797\) | −12.8284 | −0.454406 | −0.227203 | − | 0.973847i | \(-0.572958\pi\) | ||||
−0.227203 | + | 0.973847i | \(0.572958\pi\) | |||||||
\(798\) | 13.6569 | 0.483447 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −10.4853 | −0.370479 | ||||||||
\(802\) | −4.97056 | −0.175517 | ||||||||
\(803\) | −30.6274 | −1.08082 | ||||||||
\(804\) | 15.0711 | 0.531516 | ||||||||
\(805\) | 10.8284 | 0.381652 | ||||||||
\(806\) | −21.3137 | −0.750743 | ||||||||
\(807\) | −11.6569 | −0.410341 | ||||||||
\(808\) | 15.4142 | 0.542270 | ||||||||
\(809\) | 27.1127 | 0.953232 | 0.476616 | − | 0.879112i | \(-0.341863\pi\) | ||||
0.476616 | + | 0.879112i | \(0.341863\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −24.9706 | −0.876835 | −0.438418 | − | 0.898771i | \(-0.644461\pi\) | ||||
−0.438418 | + | 0.898771i | \(0.644461\pi\) | |||||||
\(812\) | −5.65685 | −0.198517 | ||||||||
\(813\) | 1.51472 | 0.0531235 | ||||||||
\(814\) | −4.00000 | −0.140200 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.3137 | 0.815643 | ||||||||
\(818\) | 24.6274 | 0.861077 | ||||||||
\(819\) | −16.4853 | −0.576042 | ||||||||
\(820\) | 6.82843 | 0.238459 | ||||||||
\(821\) | −2.82843 | −0.0987128 | −0.0493564 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493564 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(822\) | −12.0000 | −0.418548 | ||||||||
\(823\) | 5.51472 | 0.192231 | 0.0961155 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961155 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(824\) | −2.82843 | −0.0985329 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 59.1127 | 2.05679 | ||||||||
\(827\) | 18.8284 | 0.654729 | 0.327364 | − | 0.944898i | \(-0.393840\pi\) | ||||
0.327364 | + | 0.944898i | \(0.393840\pi\) | |||||||
\(828\) | −2.24264 | −0.0779372 | ||||||||
\(829\) | −30.4853 | −1.05880 | −0.529399 | − | 0.848373i | \(-0.677582\pi\) | ||||
−0.529399 | + | 0.848373i | \(0.677582\pi\) | |||||||
\(830\) | 2.34315 | 0.0813318 | ||||||||
\(831\) | −11.5147 | −0.399441 | ||||||||
\(832\) | −3.41421 | −0.118367 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.8284 | 0.374958 | ||||||||
\(835\) | −7.41421 | −0.256579 | ||||||||
\(836\) | 5.65685 | 0.195646 | ||||||||
\(837\) | 6.24264 | 0.215777 | ||||||||
\(838\) | 22.9706 | 0.793505 | ||||||||
\(839\) | −23.8579 | −0.823665 | −0.411832 | − | 0.911260i | \(-0.635111\pi\) | ||||
−0.411832 | + | 0.911260i | \(0.635111\pi\) | |||||||
\(840\) | −4.82843 | −0.166597 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 12.1421 | 0.418446 | ||||||||
\(843\) | 11.1716 | 0.384769 | ||||||||
\(844\) | −6.14214 | −0.211421 | ||||||||
\(845\) | 1.34315 | 0.0462056 | ||||||||
\(846\) | −5.65685 | −0.194487 | ||||||||
\(847\) | −33.7990 | −1.16135 | ||||||||
\(848\) | −7.65685 | −0.262937 | ||||||||
\(849\) | −15.6569 | −0.537342 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.48528 | −0.153753 | ||||||||
\(852\) | 10.0000 | 0.342594 | ||||||||
\(853\) | 4.20101 | 0.143840 | 0.0719199 | − | 0.997410i | \(-0.477087\pi\) | ||||
0.0719199 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(854\) | −28.9706 | −0.991352 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | −6.82843 | −0.233391 | ||||||||
\(857\) | −12.2426 | −0.418201 | −0.209100 | − | 0.977894i | \(-0.567054\pi\) | ||||
−0.209100 | + | 0.977894i | \(0.567054\pi\) | |||||||
\(858\) | −6.82843 | −0.233119 | ||||||||
\(859\) | −34.4264 | −1.17461 | −0.587307 | − | 0.809364i | \(-0.699812\pi\) | ||||
−0.587307 | + | 0.809364i | \(0.699812\pi\) | |||||||
\(860\) | −8.24264 | −0.281072 | ||||||||
\(861\) | 32.9706 | 1.12363 | ||||||||
\(862\) | 20.3431 | 0.692890 | ||||||||
\(863\) | −28.4264 | −0.967646 | −0.483823 | − | 0.875166i | \(-0.660752\pi\) | ||||
−0.483823 | + | 0.875166i | \(0.660752\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.4853 | 0.356510 | ||||||||
\(866\) | 20.3431 | 0.691288 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −30.1421 | −1.02309 | ||||||||
\(869\) | −20.4853 | −0.694916 | ||||||||
\(870\) | 1.17157 | 0.0397200 | ||||||||
\(871\) | 51.4558 | 1.74351 | ||||||||
\(872\) | 9.31371 | 0.315402 | ||||||||
\(873\) | 13.6569 | 0.462214 | ||||||||
\(874\) | 6.34315 | 0.214560 | ||||||||
\(875\) | −4.82843 | −0.163231 | ||||||||
\(876\) | 15.3137 | 0.517402 | ||||||||
\(877\) | 32.6274 | 1.10175 | 0.550875 | − | 0.834588i | \(-0.314294\pi\) | ||||
0.550875 | + | 0.834588i | \(0.314294\pi\) | |||||||
\(878\) | 38.7279 | 1.30700 | ||||||||
\(879\) | −20.6274 | −0.695746 | ||||||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | −20.4853 | −0.690167 | −0.345083 | − | 0.938572i | \(-0.612149\pi\) | ||||
−0.345083 | + | 0.938572i | \(0.612149\pi\) | |||||||
\(882\) | −16.3137 | −0.549311 | ||||||||
\(883\) | −27.7574 | −0.934110 | −0.467055 | − | 0.884228i | \(-0.654685\pi\) | ||||
−0.467055 | + | 0.884228i | \(0.654685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.2426 | −0.411532 | ||||||||
\(886\) | −33.4558 | −1.12397 | ||||||||
\(887\) | 45.3553 | 1.52288 | 0.761442 | − | 0.648233i | \(-0.224492\pi\) | ||||
0.761442 | + | 0.648233i | \(0.224492\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −90.9117 | −3.04908 | ||||||||
\(890\) | −10.4853 | −0.351467 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | −22.1421 | −0.741374 | ||||||||
\(893\) | 16.0000 | 0.535420 | ||||||||
\(894\) | 23.2132 | 0.776366 | ||||||||
\(895\) | 5.41421 | 0.180977 | ||||||||
\(896\) | −4.82843 | −0.161306 | ||||||||
\(897\) | −7.65685 | −0.255655 | ||||||||
\(898\) | −6.62742 | −0.221160 | ||||||||
\(899\) | 7.31371 | 0.243926 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 13.6569 | 0.454724 | ||||||||
\(903\) | −39.7990 | −1.32443 | ||||||||
\(904\) | −7.75736 | −0.258006 | ||||||||
\(905\) | −18.4853 | −0.614472 | ||||||||
\(906\) | −2.48528 | −0.0825679 | ||||||||
\(907\) | 45.2548 | 1.50266 | 0.751331 | − | 0.659925i | \(-0.229412\pi\) | ||||
0.751331 | + | 0.659925i | \(0.229412\pi\) | |||||||
\(908\) | 4.97056 | 0.164954 | ||||||||
\(909\) | −15.4142 | −0.511257 | ||||||||
\(910\) | −16.4853 | −0.546482 | ||||||||
\(911\) | 9.02944 | 0.299159 | 0.149579 | − | 0.988750i | \(-0.452208\pi\) | ||||
0.149579 | + | 0.988750i | \(0.452208\pi\) | |||||||
\(912\) | −2.82843 | −0.0936586 | ||||||||
\(913\) | 4.68629 | 0.155094 | ||||||||
\(914\) | −29.3137 | −0.969611 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 25.3137 | 0.836388 | ||||||||
\(917\) | −11.3137 | −0.373612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.51472 | 0.0499660 | 0.0249830 | − | 0.999688i | \(-0.492047\pi\) | ||||
0.0249830 | + | 0.999688i | \(0.492047\pi\) | |||||||
\(920\) | −2.24264 | −0.0739377 | ||||||||
\(921\) | −7.75736 | −0.255614 | ||||||||
\(922\) | −10.0416 | −0.330703 | ||||||||
\(923\) | 34.1421 | 1.12380 | ||||||||
\(924\) | −9.65685 | −0.317687 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | −23.7990 | −0.782083 | ||||||||
\(927\) | 2.82843 | 0.0928977 | ||||||||
\(928\) | 1.17157 | 0.0384588 | ||||||||
\(929\) | 43.7990 | 1.43700 | 0.718499 | − | 0.695528i | \(-0.244829\pi\) | ||||
0.718499 | + | 0.695528i | \(0.244829\pi\) | |||||||
\(930\) | 6.24264 | 0.204704 | ||||||||
\(931\) | 46.1421 | 1.51225 | ||||||||
\(932\) | 6.38478 | 0.209140 | ||||||||
\(933\) | 23.6569 | 0.774491 | ||||||||
\(934\) | 24.9706 | 0.817062 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.41421 | 0.111597 | ||||||||
\(937\) | −48.1421 | −1.57274 | −0.786368 | − | 0.617759i | \(-0.788041\pi\) | ||||
−0.786368 | + | 0.617759i | \(0.788041\pi\) | |||||||
\(938\) | 72.7696 | 2.37601 | ||||||||
\(939\) | 1.65685 | 0.0540694 | ||||||||
\(940\) | −5.65685 | −0.184506 | ||||||||
\(941\) | 18.8284 | 0.613789 | 0.306895 | − | 0.951744i | \(-0.400710\pi\) | ||||
0.306895 | + | 0.951744i | \(0.400710\pi\) | |||||||
\(942\) | −1.07107 | −0.0348973 | ||||||||
\(943\) | 15.3137 | 0.498683 | ||||||||
\(944\) | −12.2426 | −0.398464 | ||||||||
\(945\) | 4.82843 | 0.157069 | ||||||||
\(946\) | −16.4853 | −0.535983 | ||||||||
\(947\) | −45.4558 | −1.47712 | −0.738558 | − | 0.674190i | \(-0.764493\pi\) | ||||
−0.738558 | + | 0.674190i | \(0.764493\pi\) | |||||||
\(948\) | 10.2426 | 0.332666 | ||||||||
\(949\) | 52.2843 | 1.69722 | ||||||||
\(950\) | −2.82843 | −0.0917663 | ||||||||
\(951\) | −13.3137 | −0.431727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.2548 | 1.53073 | 0.765367 | − | 0.643594i | \(-0.222557\pi\) | ||||
0.765367 | + | 0.643594i | \(0.222557\pi\) | |||||||
\(954\) | 7.65685 | 0.247900 | ||||||||
\(955\) | 10.1421 | 0.328192 | ||||||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | 2.34315 | 0.0757431 | ||||||||
\(958\) | 38.0000 | 1.22772 | ||||||||
\(959\) | −57.9411 | −1.87102 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 7.97056 | 0.257115 | ||||||||
\(962\) | 6.82843 | 0.220157 | ||||||||
\(963\) | 6.82843 | 0.220043 | ||||||||
\(964\) | 2.58579 | 0.0832826 | ||||||||
\(965\) | −21.6569 | −0.697159 | ||||||||
\(966\) | −10.8284 | −0.348399 | ||||||||
\(967\) | −12.6863 | −0.407964 | −0.203982 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203982 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.6569 | 0.438495 | ||||||||
\(971\) | −13.6152 | −0.436933 | −0.218467 | − | 0.975844i | \(-0.570105\pi\) | ||||
−0.218467 | + | 0.975844i | \(0.570105\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 52.2843 | 1.67616 | ||||||||
\(974\) | −26.0000 | −0.833094 | ||||||||
\(975\) | 3.41421 | 0.109342 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 35.9411 | 1.14986 | 0.574929 | − | 0.818203i | \(-0.305030\pi\) | ||||
0.574929 | + | 0.818203i | \(0.305030\pi\) | |||||||
\(978\) | 2.00000 | 0.0639529 | ||||||||
\(979\) | −20.9706 | −0.670222 | ||||||||
\(980\) | −16.3137 | −0.521122 | ||||||||
\(981\) | −9.31371 | −0.297364 | ||||||||
\(982\) | −32.2426 | −1.02890 | ||||||||
\(983\) | −30.0416 | −0.958179 | −0.479090 | − | 0.877766i | \(-0.659033\pi\) | ||||
−0.479090 | + | 0.877766i | \(0.659033\pi\) | |||||||
\(984\) | −6.82843 | −0.217682 | ||||||||
\(985\) | 6.97056 | 0.222101 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.3137 | −0.869405 | ||||||||
\(988\) | −9.65685 | −0.307225 | ||||||||
\(989\) | −18.4853 | −0.587798 | ||||||||
\(990\) | 2.00000 | 0.0635642 | ||||||||
\(991\) | 49.3553 | 1.56782 | 0.783912 | − | 0.620872i | \(-0.213221\pi\) | ||||
0.783912 | + | 0.620872i | \(0.213221\pi\) | |||||||
\(992\) | 6.24264 | 0.198204 | ||||||||
\(993\) | 13.1716 | 0.417987 | ||||||||
\(994\) | 48.2843 | 1.53148 | ||||||||
\(995\) | −17.5563 | −0.556574 | ||||||||
\(996\) | −2.34315 | −0.0742454 | ||||||||
\(997\) | −40.3431 | −1.27768 | −0.638840 | − | 0.769340i | \(-0.720585\pi\) | ||||
−0.638840 | + | 0.769340i | \(0.720585\pi\) | |||||||
\(998\) | 17.1716 | 0.543557 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 8670.2.a.bc.1.2 | 2 | ||
17.8 | even | 8 | 510.2.p.b.421.2 | yes | 4 | ||
17.15 | even | 8 | 510.2.p.b.361.2 | ✓ | 4 | ||
17.16 | even | 2 | 8670.2.a.bg.1.1 | 2 | |||
51.8 | odd | 8 | 1530.2.q.e.1441.2 | 4 | |||
51.32 | odd | 8 | 1530.2.q.e.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
510.2.p.b.361.2 | ✓ | 4 | 17.15 | even | 8 | ||
510.2.p.b.421.2 | yes | 4 | 17.8 | even | 8 | ||
1530.2.q.e.361.2 | 4 | 51.32 | odd | 8 | |||
1530.2.q.e.1441.2 | 4 | 51.8 | odd | 8 | |||
8670.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8670.2.a.bg.1.1 | 2 | 17.16 | even | 2 |