Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1881,2,Mod(1,1881)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1881, 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("1881.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1881 = 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1881.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: | \(15.0198606202\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 209) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.51908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1881.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82669 | −1.29166 | −0.645832 | − | 0.763479i | \(-0.723489\pi\) | ||||
−0.645832 | + | 0.763479i | \(0.723489\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.33679 | 0.668396 | ||||||||
\(5\) | −2.34577 | −1.04906 | −0.524530 | − | 0.851392i | \(-0.675759\pi\) | ||||
−0.524530 | + | 0.851392i | \(0.675759\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69239 | 0.639664 | 0.319832 | − | 0.947474i | \(-0.396374\pi\) | ||||
0.319832 | + | 0.947474i | \(0.396374\pi\) | |||||||
\(8\) | 1.21147 | 0.428321 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.28499 | 1.35503 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11168 | 1.14038 | 0.570188 | − | 0.821514i | \(-0.306870\pi\) | ||||
0.570188 | + | 0.821514i | \(0.306870\pi\) | |||||||
\(14\) | −3.09147 | −0.826231 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88657 | −1.22164 | ||||||||
\(17\) | 6.16499 | 1.49523 | 0.747615 | − | 0.664132i | \(-0.231199\pi\) | ||||
0.747615 | + | 0.664132i | \(0.231199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −3.13581 | −0.701188 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.82669 | 0.389451 | ||||||||
\(23\) | −3.52199 | −0.734386 | −0.367193 | − | 0.930145i | \(-0.619681\pi\) | ||||
−0.367193 | + | 0.930145i | \(0.619681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.502638 | 0.100528 | ||||||||
\(26\) | −7.51076 | −1.47298 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.26238 | 0.427549 | ||||||||
\(29\) | 8.10336 | 1.50476 | 0.752378 | − | 0.658731i | \(-0.228906\pi\) | ||||
0.752378 | + | 0.658731i | \(0.228906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.30144 | −0.413350 | −0.206675 | − | 0.978410i | \(-0.566264\pi\) | ||||
−0.206675 | + | 0.978410i | \(0.566264\pi\) | |||||||
\(32\) | 6.50330 | 1.14963 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.2615 | −1.93134 | ||||||||
\(35\) | −3.96996 | −0.671046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.56016 | −1.07848 | −0.539242 | − | 0.842151i | \(-0.681289\pi\) | ||||
−0.539242 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(38\) | 1.82669 | 0.296328 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.84184 | −0.449334 | ||||||||
\(41\) | −7.75013 | −1.21037 | −0.605183 | − | 0.796086i | \(-0.706900\pi\) | ||||
−0.605183 | + | 0.796086i | \(0.706900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.75102 | 1.18202 | 0.591010 | − | 0.806664i | \(-0.298729\pi\) | ||||
0.591010 | + | 0.806664i | \(0.298729\pi\) | |||||||
\(44\) | −1.33679 | −0.201529 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.43359 | 0.948581 | ||||||||
\(47\) | 10.8969 | 1.58948 | 0.794742 | − | 0.606948i | \(-0.207606\pi\) | ||||
0.794742 | + | 0.606948i | \(0.207606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.13581 | −0.590830 | ||||||||
\(50\) | −0.918163 | −0.129848 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.49647 | 0.762223 | ||||||||
\(53\) | −7.93511 | −1.08997 | −0.544986 | − | 0.838445i | \(-0.683465\pi\) | ||||
−0.544986 | + | 0.838445i | \(0.683465\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.34577 | 0.316304 | ||||||||
\(56\) | 2.05029 | 0.273981 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.8023 | −1.94364 | ||||||||
\(59\) | −10.9247 | −1.42228 | −0.711140 | − | 0.703051i | \(-0.751821\pi\) | ||||
−0.711140 | + | 0.703051i | \(0.751821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.51162 | −0.577653 | −0.288827 | − | 0.957381i | \(-0.593265\pi\) | ||||
−0.288827 | + | 0.957381i | \(0.593265\pi\) | |||||||
\(62\) | 4.20401 | 0.533910 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.10636 | −0.263295 | ||||||||
\(65\) | −9.64506 | −1.19632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7201 | 1.79835 | 0.899173 | − | 0.437594i | \(-0.144169\pi\) | ||||
0.899173 | + | 0.437594i | \(0.144169\pi\) | |||||||
\(68\) | 8.24132 | 0.999407 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.25189 | 0.866766 | ||||||||
\(71\) | −3.12026 | −0.370307 | −0.185153 | − | 0.982710i | \(-0.559278\pi\) | ||||
−0.185153 | + | 0.982710i | \(0.559278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5827 | 1.35565 | 0.677824 | − | 0.735224i | \(-0.262923\pi\) | ||||
0.677824 | + | 0.735224i | \(0.262923\pi\) | |||||||
\(74\) | 11.9834 | 1.39304 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.33679 | −0.153341 | ||||||||
\(77\) | −1.69239 | −0.192866 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.96184 | 0.558250 | 0.279125 | − | 0.960255i | \(-0.409956\pi\) | ||||
0.279125 | + | 0.960255i | \(0.409956\pi\) | |||||||
\(80\) | 11.4628 | 1.28158 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.1571 | 1.56339 | ||||||||
\(83\) | 1.82905 | 0.200765 | 0.100382 | − | 0.994949i | \(-0.467993\pi\) | ||||
0.100382 | + | 0.994949i | \(0.467993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4617 | −1.56859 | ||||||||
\(86\) | −14.1587 | −1.52677 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.21147 | −0.129144 | ||||||||
\(89\) | 9.37496 | 0.993743 | 0.496872 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496872 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.95858 | 0.729457 | ||||||||
\(92\) | −4.70818 | −0.490861 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −19.9053 | −2.05308 | ||||||||
\(95\) | 2.34577 | 0.240671 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9937 | −1.11625 | −0.558123 | − | 0.829758i | \(-0.688478\pi\) | ||||
−0.558123 | + | 0.829758i | \(0.688478\pi\) | |||||||
\(98\) | 7.55484 | 0.763154 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.671923 | 0.0671923 | ||||||||
\(101\) | −2.30621 | −0.229476 | −0.114738 | − | 0.993396i | \(-0.536603\pi\) | ||||
−0.114738 | + | 0.993396i | \(0.536603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.12000 | 0.603021 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(104\) | 4.98119 | 0.488446 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.4950 | 1.40788 | ||||||||
\(107\) | −0.422947 | −0.0408878 | −0.0204439 | − | 0.999791i | \(-0.506508\pi\) | ||||
−0.0204439 | + | 0.999791i | \(0.506508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0180 | 1.34268 | 0.671338 | − | 0.741151i | \(-0.265720\pi\) | ||||
0.671338 | + | 0.741151i | \(0.265720\pi\) | |||||||
\(110\) | −4.28499 | −0.408558 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.26999 | −0.781441 | ||||||||
\(113\) | 2.53638 | 0.238602 | 0.119301 | − | 0.992858i | \(-0.461935\pi\) | ||||
0.119301 | + | 0.992858i | \(0.461935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.26179 | 0.770416 | ||||||||
\(116\) | 10.8325 | 1.00577 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19.9561 | 1.83711 | ||||||||
\(119\) | 10.4336 | 0.956445 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.24132 | 0.746134 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.07654 | −0.276282 | ||||||||
\(125\) | 10.5498 | 0.943601 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.07275 | 0.0951914 | 0.0475957 | − | 0.998867i | \(-0.484844\pi\) | ||||
0.0475957 | + | 0.998867i | \(0.484844\pi\) | |||||||
\(128\) | −9.15893 | −0.809543 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.6185 | 1.54525 | ||||||||
\(131\) | 7.82709 | 0.683856 | 0.341928 | − | 0.939726i | \(-0.388920\pi\) | ||||
0.341928 | + | 0.939726i | \(0.388920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.69239 | −0.146749 | ||||||||
\(134\) | −26.8890 | −2.32286 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.46873 | 0.640438 | ||||||||
\(137\) | 11.2473 | 0.960919 | 0.480460 | − | 0.877017i | \(-0.340470\pi\) | ||||
0.480460 | + | 0.877017i | \(0.340470\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.905926 | −0.0768397 | −0.0384198 | − | 0.999262i | \(-0.512232\pi\) | ||||
−0.0384198 | + | 0.999262i | \(0.512232\pi\) | |||||||
\(140\) | −5.30702 | −0.448525 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.69975 | 0.478312 | ||||||||
\(143\) | −4.11168 | −0.343836 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.0086 | −1.57858 | ||||||||
\(146\) | −21.1579 | −1.75104 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.76957 | −0.720854 | ||||||||
\(149\) | −10.5174 | −0.861622 | −0.430811 | − | 0.902442i | \(-0.641772\pi\) | ||||
−0.430811 | + | 0.902442i | \(0.641772\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2436 | 1.07775 | 0.538873 | − | 0.842387i | \(-0.318850\pi\) | ||||
0.538873 | + | 0.842387i | \(0.318850\pi\) | |||||||
\(152\) | −1.21147 | −0.0982635 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.09147 | 0.249118 | ||||||||
\(155\) | 5.39864 | 0.433629 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.99915 | 0.159549 | 0.0797747 | − | 0.996813i | \(-0.474580\pi\) | ||||
0.0797747 | + | 0.996813i | \(0.474580\pi\) | |||||||
\(158\) | −9.06373 | −0.721072 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.2552 | −1.20603 | ||||||||
\(161\) | −5.96059 | −0.469761 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.7557 | −1.46906 | −0.734531 | − | 0.678575i | \(-0.762598\pi\) | ||||
−0.734531 | + | 0.678575i | \(0.762598\pi\) | |||||||
\(164\) | −10.3603 | −0.809005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.34111 | −0.259320 | ||||||||
\(167\) | 6.31203 | 0.488440 | 0.244220 | − | 0.969720i | \(-0.421468\pi\) | ||||
0.244220 | + | 0.969720i | \(0.421468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.90593 | 0.300456 | ||||||||
\(170\) | 26.4170 | 2.02609 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.3615 | 0.790058 | ||||||||
\(173\) | 21.5269 | 1.63666 | 0.818328 | − | 0.574751i | \(-0.194901\pi\) | ||||
0.818328 | + | 0.574751i | \(0.194901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.850661 | 0.0643039 | ||||||||
\(176\) | 4.88657 | 0.368339 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.1251 | −1.28358 | ||||||||
\(179\) | 7.97018 | 0.595719 | 0.297860 | − | 0.954610i | \(-0.403727\pi\) | ||||
0.297860 | + | 0.954610i | \(0.403727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.16955 | −0.0869317 | −0.0434659 | − | 0.999055i | \(-0.513840\pi\) | ||||
−0.0434659 | + | 0.999055i | \(0.513840\pi\) | |||||||
\(182\) | −12.7112 | −0.942214 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.26680 | −0.314553 | ||||||||
\(185\) | 15.3886 | 1.13139 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.16499 | −0.450829 | ||||||||
\(188\) | 14.5670 | 1.06240 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.28499 | −0.310866 | ||||||||
\(191\) | 15.6673 | 1.13365 | 0.566824 | − | 0.823839i | \(-0.308172\pi\) | ||||
0.566824 | + | 0.823839i | \(0.308172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6769 | 1.56034 | 0.780169 | − | 0.625568i | \(-0.215133\pi\) | ||||
0.780169 | + | 0.625568i | \(0.215133\pi\) | |||||||
\(194\) | 20.0821 | 1.44181 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.52872 | −0.394908 | ||||||||
\(197\) | −4.58794 | −0.326877 | −0.163439 | − | 0.986554i | \(-0.552259\pi\) | ||||
−0.163439 | + | 0.986554i | \(0.552259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0619 | 0.925937 | 0.462968 | − | 0.886375i | \(-0.346784\pi\) | ||||
0.462968 | + | 0.886375i | \(0.346784\pi\) | |||||||
\(200\) | 0.608933 | 0.0430580 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.21272 | 0.296406 | ||||||||
\(203\) | 13.7141 | 0.962539 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.1800 | 1.26975 | ||||||||
\(206\) | −11.1793 | −0.778901 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.0920 | −1.39313 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.91188 | 0.200462 | 0.100231 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100231 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(212\) | −10.6076 | −0.728533 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.772592 | 0.0528133 | ||||||||
\(215\) | −18.1821 | −1.24001 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.89493 | −0.264405 | ||||||||
\(218\) | −25.6064 | −1.73429 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.13581 | 0.211416 | ||||||||
\(221\) | 25.3485 | 1.70512 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.34161 | 0.424665 | 0.212333 | − | 0.977197i | \(-0.431894\pi\) | ||||
0.212333 | + | 0.977197i | \(0.431894\pi\) | |||||||
\(224\) | 11.0061 | 0.735378 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.63317 | −0.308194 | ||||||||
\(227\) | 2.00429 | 0.133029 | 0.0665147 | − | 0.997785i | \(-0.478812\pi\) | ||||
0.0665147 | + | 0.997785i | \(0.478812\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.9893 | −1.38701 | −0.693507 | − | 0.720450i | \(-0.743935\pi\) | ||||
−0.693507 | + | 0.720450i | \(0.743935\pi\) | |||||||
\(230\) | −15.0917 | −0.995118 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.81701 | 0.644518 | ||||||||
\(233\) | 17.6006 | 1.15305 | 0.576527 | − | 0.817078i | \(-0.304407\pi\) | ||||
0.576527 | + | 0.817078i | \(0.304407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.5617 | −1.66746 | ||||||||
\(236\) | −14.6041 | −0.950646 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −19.0589 | −1.23541 | ||||||||
\(239\) | −26.6207 | −1.72195 | −0.860975 | − | 0.508647i | \(-0.830146\pi\) | ||||
−0.860975 | + | 0.508647i | \(0.830146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1342 | 0.846049 | 0.423024 | − | 0.906118i | \(-0.360968\pi\) | ||||
0.423024 | + | 0.906118i | \(0.360968\pi\) | |||||||
\(242\) | −1.82669 | −0.117424 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.03109 | −0.386101 | ||||||||
\(245\) | 9.70166 | 0.619816 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.11168 | −0.261620 | ||||||||
\(248\) | −2.78813 | −0.177046 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −19.2712 | −1.21882 | ||||||||
\(251\) | 26.1636 | 1.65143 | 0.825715 | − | 0.564087i | \(-0.190772\pi\) | ||||
0.825715 | + | 0.564087i | \(0.190772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.52199 | 0.221426 | ||||||||
\(254\) | −1.95959 | −0.122955 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9432 | 1.30895 | ||||||||
\(257\) | −12.6117 | −0.786697 | −0.393349 | − | 0.919389i | \(-0.628683\pi\) | ||||
−0.393349 | + | 0.919389i | \(0.628683\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.1024 | −0.689867 | ||||||||
\(260\) | −12.8934 | −0.799618 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.2977 | −0.883312 | ||||||||
\(263\) | 20.0550 | 1.23664 | 0.618322 | − | 0.785925i | \(-0.287813\pi\) | ||||
0.618322 | + | 0.785925i | \(0.287813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.6139 | 1.14345 | ||||||||
\(266\) | 3.09147 | 0.189550 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.6777 | 1.20201 | ||||||||
\(269\) | 20.1150 | 1.22644 | 0.613218 | − | 0.789914i | \(-0.289875\pi\) | ||||
0.613218 | + | 0.789914i | \(0.289875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5586 | 0.945117 | 0.472558 | − | 0.881299i | \(-0.343331\pi\) | ||||
0.472558 | + | 0.881299i | \(0.343331\pi\) | |||||||
\(272\) | −30.1257 | −1.82664 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.5453 | −1.24119 | ||||||||
\(275\) | −0.502638 | −0.0303102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.89211 | 0.113686 | 0.0568429 | − | 0.998383i | \(-0.481897\pi\) | ||||
0.0568429 | + | 0.998383i | \(0.481897\pi\) | |||||||
\(278\) | 1.65485 | 0.0992510 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.80951 | −0.287423 | ||||||||
\(281\) | −4.59299 | −0.273995 | −0.136997 | − | 0.990571i | \(-0.543745\pi\) | ||||
−0.136997 | + | 0.990571i | \(0.543745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.17798 | −0.0700234 | −0.0350117 | − | 0.999387i | \(-0.511147\pi\) | ||||
−0.0350117 | + | 0.999387i | \(0.511147\pi\) | |||||||
\(284\) | −4.17114 | −0.247512 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.51076 | 0.444121 | ||||||||
\(287\) | −13.1163 | −0.774228 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.0071 | 1.23571 | ||||||||
\(290\) | 34.7229 | 2.03900 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.4836 | 0.906110 | ||||||||
\(293\) | 11.2606 | 0.657851 | 0.328925 | − | 0.944356i | \(-0.393314\pi\) | ||||
0.328925 | + | 0.944356i | \(0.393314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.6269 | 1.49206 | ||||||||
\(296\) | −7.94745 | −0.461936 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.2121 | 1.11293 | ||||||||
\(299\) | −14.4813 | −0.837476 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.1178 | 0.756096 | ||||||||
\(302\) | −24.1919 | −1.39209 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.88657 | 0.280264 | ||||||||
\(305\) | 10.5832 | 0.605993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.35245 | 0.248407 | 0.124204 | − | 0.992257i | \(-0.460362\pi\) | ||||
0.124204 | + | 0.992257i | \(0.460362\pi\) | |||||||
\(308\) | −2.26238 | −0.128911 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.86164 | −0.560103 | ||||||||
\(311\) | −7.61725 | −0.431935 | −0.215967 | − | 0.976401i | \(-0.569291\pi\) | ||||
−0.215967 | + | 0.976401i | \(0.569291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5654 | −0.992855 | −0.496427 | − | 0.868078i | \(-0.665355\pi\) | ||||
−0.496427 | + | 0.868078i | \(0.665355\pi\) | |||||||
\(314\) | −3.65182 | −0.206084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.63295 | 0.373132 | ||||||||
\(317\) | 1.94192 | 0.109069 | 0.0545345 | − | 0.998512i | \(-0.482633\pi\) | ||||
0.0545345 | + | 0.998512i | \(0.482633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.10336 | −0.453701 | ||||||||
\(320\) | 4.94104 | 0.276213 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.8882 | 0.606773 | ||||||||
\(323\) | −6.16499 | −0.343029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.06669 | 0.114639 | ||||||||
\(326\) | 34.2609 | 1.89754 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.38907 | −0.518425 | ||||||||
\(329\) | 18.4419 | 1.01674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3988 | 0.736462 | 0.368231 | − | 0.929734i | \(-0.379964\pi\) | ||||
0.368231 | + | 0.929734i | \(0.379964\pi\) | |||||||
\(332\) | 2.44506 | 0.134190 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.5301 | −0.630900 | ||||||||
\(335\) | −34.5300 | −1.88657 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.1631 | 1.80651 | 0.903254 | − | 0.429107i | \(-0.141172\pi\) | ||||
0.903254 | + | 0.429107i | \(0.141172\pi\) | |||||||
\(338\) | −7.13491 | −0.388088 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.3322 | −1.04844 | ||||||||
\(341\) | 2.30144 | 0.124630 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8462 | −1.01760 | ||||||||
\(344\) | 9.39016 | 0.506283 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −39.3229 | −2.11401 | ||||||||
\(347\) | −18.0268 | −0.967730 | −0.483865 | − | 0.875143i | \(-0.660767\pi\) | ||||
−0.483865 | + | 0.875143i | \(0.660767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.81411 | 0.471808 | 0.235904 | − | 0.971776i | \(-0.424195\pi\) | ||||
0.235904 | + | 0.971776i | \(0.424195\pi\) | |||||||
\(350\) | −1.55389 | −0.0830590 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.50330 | −0.346627 | ||||||||
\(353\) | 1.59249 | 0.0847599 | 0.0423799 | − | 0.999102i | \(-0.486506\pi\) | ||||
0.0423799 | + | 0.999102i | \(0.486506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.31942 | 0.388474 | ||||||||
\(356\) | 12.5324 | 0.664214 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.5590 | −0.769469 | ||||||||
\(359\) | −36.3774 | −1.91993 | −0.959963 | − | 0.280126i | \(-0.909624\pi\) | ||||
−0.959963 | + | 0.280126i | \(0.909624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.13640 | 0.112287 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.30218 | 0.487567 | ||||||||
\(365\) | −27.1703 | −1.42216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.00276 | −0.261142 | −0.130571 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130571 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(368\) | 17.2105 | 0.897158 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.1102 | −1.46138 | ||||||||
\(371\) | −13.4293 | −0.697216 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.1313 | −1.76725 | −0.883625 | − | 0.468195i | \(-0.844904\pi\) | ||||
−0.883625 | + | 0.468195i | \(0.844904\pi\) | |||||||
\(374\) | 11.2615 | 0.582320 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.2014 | 0.680808 | ||||||||
\(377\) | 33.3185 | 1.71599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7749 | 0.810302 | 0.405151 | − | 0.914250i | \(-0.367219\pi\) | ||||
0.405151 | + | 0.914250i | \(0.367219\pi\) | |||||||
\(380\) | 3.13581 | 0.160864 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −28.6193 | −1.46429 | ||||||||
\(383\) | 22.4260 | 1.14592 | 0.572958 | − | 0.819585i | \(-0.305796\pi\) | ||||
0.572958 | + | 0.819585i | \(0.305796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.96996 | 0.202328 | ||||||||
\(386\) | −39.5970 | −2.01543 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.6964 | −0.746094 | ||||||||
\(389\) | 18.3488 | 0.930321 | 0.465160 | − | 0.885226i | \(-0.345997\pi\) | ||||
0.465160 | + | 0.885226i | \(0.345997\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.7131 | −1.09808 | ||||||||
\(392\) | −5.01042 | −0.253065 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.38074 | 0.422216 | ||||||||
\(395\) | −11.6393 | −0.585638 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.511483 | −0.0256706 | −0.0128353 | − | 0.999918i | \(-0.504086\pi\) | ||||
−0.0128353 | + | 0.999918i | \(0.504086\pi\) | |||||||
\(398\) | −23.8601 | −1.19600 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.45618 | −0.122809 | ||||||||
\(401\) | −18.9824 | −0.947935 | −0.473967 | − | 0.880542i | \(-0.657179\pi\) | ||||
−0.473967 | + | 0.880542i | \(0.657179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.46277 | −0.471374 | ||||||||
\(404\) | −3.08292 | −0.153381 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.0513 | −1.24328 | ||||||||
\(407\) | 6.56016 | 0.325175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.10089 | 0.0544355 | 0.0272177 | − | 0.999630i | \(-0.491335\pi\) | ||||
0.0272177 | + | 0.999630i | \(0.491335\pi\) | |||||||
\(410\) | −33.2092 | −1.64009 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.18117 | 0.403057 | ||||||||
\(413\) | −18.4889 | −0.909781 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.29054 | −0.210614 | ||||||||
\(416\) | 26.7395 | 1.31101 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.82669 | −0.0893463 | ||||||||
\(419\) | 18.7929 | 0.918094 | 0.459047 | − | 0.888412i | \(-0.348191\pi\) | ||||
0.459047 | + | 0.888412i | \(0.348191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.7618 | −1.20682 | −0.603408 | − | 0.797433i | \(-0.706191\pi\) | ||||
−0.603408 | + | 0.797433i | \(0.706191\pi\) | |||||||
\(422\) | −5.31910 | −0.258930 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.61318 | −0.466857 | ||||||||
\(425\) | 3.09876 | 0.150312 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.63542 | −0.369504 | ||||||||
\(428\) | −0.565392 | −0.0273293 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.2131 | 1.60168 | ||||||||
\(431\) | 32.1985 | 1.55095 | 0.775474 | − | 0.631380i | \(-0.217511\pi\) | ||||
0.775474 | + | 0.631380i | \(0.217511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3042 | −0.735475 | −0.367737 | − | 0.929930i | \(-0.619867\pi\) | ||||
−0.367737 | + | 0.929930i | \(0.619867\pi\) | |||||||
\(434\) | 7.11483 | 0.341523 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.7391 | 0.897440 | ||||||||
\(437\) | 3.52199 | 0.168480 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1812 | 1.24956 | 0.624781 | − | 0.780800i | \(-0.285188\pi\) | ||||
0.624781 | + | 0.780800i | \(0.285188\pi\) | |||||||
\(440\) | 2.84184 | 0.135479 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −46.3038 | −2.20245 | ||||||||
\(443\) | −21.5579 | −1.02425 | −0.512123 | − | 0.858912i | \(-0.671141\pi\) | ||||
−0.512123 | + | 0.858912i | \(0.671141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.9915 | −1.04250 | ||||||||
\(446\) | −11.5841 | −0.548525 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.56479 | −0.168420 | ||||||||
\(449\) | −11.7990 | −0.556829 | −0.278415 | − | 0.960461i | \(-0.589809\pi\) | ||||
−0.278415 | + | 0.960461i | \(0.589809\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.75013 | 0.364939 | ||||||||
\(452\) | 3.39061 | 0.159481 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.66122 | −0.171829 | ||||||||
\(455\) | −16.3232 | −0.765245 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.6863 | −0.733773 | −0.366886 | − | 0.930266i | \(-0.619576\pi\) | ||||
−0.366886 | + | 0.930266i | \(0.619576\pi\) | |||||||
\(458\) | 38.3410 | 1.79156 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.0443 | 0.514943 | ||||||||
\(461\) | −27.2451 | −1.26893 | −0.634466 | − | 0.772951i | \(-0.718780\pi\) | ||||
−0.634466 | + | 0.772951i | \(0.718780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9364 | −0.833573 | −0.416787 | − | 0.909004i | \(-0.636844\pi\) | ||||
−0.416787 | + | 0.909004i | \(0.636844\pi\) | |||||||
\(464\) | −39.5977 | −1.83828 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.1509 | −1.48936 | ||||||||
\(467\) | −29.0100 | −1.34242 | −0.671211 | − | 0.741266i | \(-0.734226\pi\) | ||||
−0.671211 | + | 0.741266i | \(0.734226\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9122 | 1.15034 | ||||||||
\(470\) | 46.6933 | 2.15380 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.2350 | −0.609191 | ||||||||
\(473\) | −7.75102 | −0.356392 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.502638 | −0.0230626 | ||||||||
\(476\) | 13.9475 | 0.639285 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 48.6277 | 2.22418 | ||||||||
\(479\) | −34.0896 | −1.55759 | −0.778797 | − | 0.627276i | \(-0.784170\pi\) | ||||
−0.778797 | + | 0.627276i | \(0.784170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.9733 | −1.22988 | ||||||||
\(482\) | −23.9921 | −1.09281 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.33679 | 0.0607633 | ||||||||
\(485\) | 25.7888 | 1.17101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.38349 | 0.289264 | 0.144632 | − | 0.989486i | \(-0.453800\pi\) | ||||
0.144632 | + | 0.989486i | \(0.453800\pi\) | |||||||
\(488\) | −5.46570 | −0.247421 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.7219 | −0.800594 | ||||||||
\(491\) | 31.4552 | 1.41956 | 0.709778 | − | 0.704426i | \(-0.248795\pi\) | ||||
0.709778 | + | 0.704426i | \(0.248795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49.9572 | 2.24996 | ||||||||
\(494\) | 7.51076 | 0.337925 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.2461 | 0.504966 | ||||||||
\(497\) | −5.28071 | −0.236872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.9667 | −1.43103 | −0.715514 | − | 0.698599i | \(-0.753807\pi\) | ||||
−0.715514 | + | 0.698599i | \(0.753807\pi\) | |||||||
\(500\) | 14.1029 | 0.630699 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −47.7927 | −2.13309 | ||||||||
\(503\) | 34.0522 | 1.51831 | 0.759157 | − | 0.650907i | \(-0.225611\pi\) | ||||
0.759157 | + | 0.650907i | \(0.225611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.40983 | 0.240734 | ||||||||
\(506\) | −6.43359 | −0.286008 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.43405 | 0.0636256 | ||||||||
\(509\) | −25.7904 | −1.14314 | −0.571569 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571569 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.6024 | 0.867160 | ||||||||
\(512\) | −19.9389 | −0.881184 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.0377 | 1.01615 | ||||||||
\(515\) | −14.3561 | −0.632606 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8969 | −0.479247 | ||||||||
\(518\) | 20.2806 | 0.891076 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.6847 | −0.512410 | ||||||||
\(521\) | −31.3774 | −1.37467 | −0.687334 | − | 0.726342i | \(-0.741219\pi\) | ||||
−0.687334 | + | 0.726342i | \(0.741219\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2388 | −1.01616 | −0.508082 | − | 0.861309i | \(-0.669645\pi\) | ||||
−0.508082 | + | 0.861309i | \(0.669645\pi\) | |||||||
\(524\) | 10.4632 | 0.457087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.6343 | −1.59733 | ||||||||
\(527\) | −14.1883 | −0.618054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5956 | −0.460677 | ||||||||
\(530\) | −34.0019 | −1.47695 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.26238 | −0.0980865 | ||||||||
\(533\) | −31.8661 | −1.38027 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.992136 | 0.0428938 | ||||||||
\(536\) | 17.8330 | 0.770268 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.7439 | −1.58414 | ||||||||
\(539\) | 4.13581 | 0.178142 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.0085 | 1.54812 | 0.774062 | − | 0.633109i | \(-0.218222\pi\) | ||||
0.774062 | + | 0.633109i | \(0.218222\pi\) | |||||||
\(542\) | −28.4207 | −1.22077 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 40.0928 | 1.71896 | ||||||||
\(545\) | −32.8829 | −1.40855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.1855 | −1.20513 | −0.602563 | − | 0.798071i | \(-0.705854\pi\) | ||||
−0.602563 | + | 0.798071i | \(0.705854\pi\) | |||||||
\(548\) | 15.0353 | 0.642275 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.918163 | 0.0391506 | ||||||||
\(551\) | −8.10336 | −0.345215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.39738 | 0.357093 | ||||||||
\(554\) | −3.45629 | −0.146844 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.21104 | −0.0513594 | ||||||||
\(557\) | −21.6248 | −0.916274 | −0.458137 | − | 0.888882i | \(-0.651483\pi\) | ||||
−0.458137 | + | 0.888882i | \(0.651483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.8697 | 1.34795 | ||||||||
\(560\) | 19.3995 | 0.819779 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.38997 | 0.353909 | ||||||||
\(563\) | −13.1791 | −0.555434 | −0.277717 | − | 0.960663i | \(-0.589578\pi\) | ||||
−0.277717 | + | 0.960663i | \(0.589578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.94976 | −0.250308 | ||||||||
\(566\) | 2.15179 | 0.0904467 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.78011 | −0.158610 | ||||||||
\(569\) | −8.61143 | −0.361010 | −0.180505 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180505 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6546 | −0.738821 | −0.369410 | − | 0.929266i | \(-0.620440\pi\) | ||||
−0.369410 | + | 0.929266i | \(0.620440\pi\) | |||||||
\(572\) | −5.49647 | −0.229819 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 23.9593 | 1.00004 | ||||||||
\(575\) | −1.77029 | −0.0738261 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0907 | −1.29432 | −0.647162 | − | 0.762352i | \(-0.724044\pi\) | ||||
−0.647162 | + | 0.762352i | \(0.724044\pi\) | |||||||
\(578\) | −38.3735 | −1.59613 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.4106 | −1.05512 | ||||||||
\(581\) | 3.09547 | 0.128422 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.93511 | 0.328639 | ||||||||
\(584\) | 14.0321 | 0.580652 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.5696 | −0.849722 | ||||||||
\(587\) | 26.7211 | 1.10290 | 0.551450 | − | 0.834208i | \(-0.314075\pi\) | ||||
0.551450 | + | 0.834208i | \(0.314075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.30144 | 0.0948290 | ||||||||
\(590\) | −46.8124 | −1.92724 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32.0567 | 1.31752 | ||||||||
\(593\) | 24.2460 | 0.995666 | 0.497833 | − | 0.867273i | \(-0.334129\pi\) | ||||
0.497833 | + | 0.867273i | \(0.334129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.4748 | −1.00337 | ||||||||
\(596\) | −14.0596 | −0.575905 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.4529 | 1.08174 | ||||||||
\(599\) | 18.2095 | 0.744019 | 0.372009 | − | 0.928229i | \(-0.378669\pi\) | ||||
0.372009 | + | 0.928229i | \(0.378669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.9824 | 1.54934 | 0.774668 | − | 0.632368i | \(-0.217917\pi\) | ||||
0.774668 | + | 0.632368i | \(0.217917\pi\) | |||||||
\(602\) | −23.9621 | −0.976622 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.7039 | 0.720362 | ||||||||
\(605\) | −2.34577 | −0.0953691 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0130 | −0.812301 | −0.406151 | − | 0.913806i | \(-0.633129\pi\) | ||||
−0.406151 | + | 0.913806i | \(0.633129\pi\) | |||||||
\(608\) | −6.50330 | −0.263744 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.3322 | −0.782739 | ||||||||
\(611\) | 44.8048 | 1.81261 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.1414 | −1.70208 | −0.851038 | − | 0.525105i | \(-0.824026\pi\) | ||||
−0.851038 | + | 0.525105i | \(0.824026\pi\) | |||||||
\(614\) | −7.95057 | −0.320859 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.05029 | −0.0826085 | ||||||||
\(617\) | −16.9044 | −0.680545 | −0.340273 | − | 0.940327i | \(-0.610519\pi\) | ||||
−0.340273 | + | 0.940327i | \(0.610519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.31177 | 0.213498 | 0.106749 | − | 0.994286i | \(-0.465956\pi\) | ||||
0.106749 | + | 0.994286i | \(0.465956\pi\) | |||||||
\(620\) | 7.21686 | 0.289836 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.9144 | 0.557915 | ||||||||
\(623\) | 15.8661 | 0.635662 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2605 | −1.09042 | ||||||||
\(626\) | 32.0865 | 1.28243 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.67245 | 0.106642 | ||||||||
\(629\) | −40.4433 | −1.61258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0425 | 1.35521 | 0.677604 | − | 0.735427i | \(-0.263018\pi\) | ||||
0.677604 | + | 0.735427i | \(0.263018\pi\) | |||||||
\(632\) | 6.01113 | 0.239110 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.54728 | −0.140880 | ||||||||
\(635\) | −2.51643 | −0.0998615 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.0051 | −0.673768 | ||||||||
\(638\) | 14.8023 | 0.586030 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.4847 | 0.849259 | ||||||||
\(641\) | 15.0405 | 0.594063 | 0.297031 | − | 0.954868i | \(-0.404003\pi\) | ||||
0.297031 | + | 0.954868i | \(0.404003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.3618 | 1.27622 | 0.638112 | − | 0.769943i | \(-0.279715\pi\) | ||||
0.638112 | + | 0.769943i | \(0.279715\pi\) | |||||||
\(644\) | −7.96808 | −0.313986 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2615 | 0.443079 | ||||||||
\(647\) | 49.0042 | 1.92655 | 0.963276 | − | 0.268512i | \(-0.0865319\pi\) | ||||
0.963276 | + | 0.268512i | \(0.0865319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9247 | 0.428833 | ||||||||
\(650\) | −3.77520 | −0.148075 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.0725 | −0.981916 | ||||||||
\(653\) | −31.1992 | −1.22092 | −0.610460 | − | 0.792047i | \(-0.709016\pi\) | ||||
−0.610460 | + | 0.792047i | \(0.709016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.3605 | −0.717406 | ||||||||
\(656\) | 37.8715 | 1.47864 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.6876 | −1.31328 | ||||||||
\(659\) | 35.7237 | 1.39160 | 0.695799 | − | 0.718237i | \(-0.255050\pi\) | ||||
0.695799 | + | 0.718237i | \(0.255050\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.8677 | 1.31730 | 0.658651 | − | 0.752449i | \(-0.271128\pi\) | ||||
0.658651 | + | 0.752449i | \(0.271128\pi\) | |||||||
\(662\) | −24.4754 | −0.951262 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.21585 | 0.0859916 | ||||||||
\(665\) | 3.96996 | 0.153949 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.5400 | −1.10507 | ||||||||
\(668\) | 8.43788 | 0.326471 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 63.0755 | 2.43682 | ||||||||
\(671\) | 4.51162 | 0.174169 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1648 | 0.815842 | 0.407921 | − | 0.913017i | \(-0.366254\pi\) | ||||
0.407921 | + | 0.913017i | \(0.366254\pi\) | |||||||
\(674\) | −60.5786 | −2.33340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.22141 | 0.200824 | ||||||||
\(677\) | 34.5239 | 1.32686 | 0.663431 | − | 0.748238i | \(-0.269100\pi\) | ||||
0.663431 | + | 0.748238i | \(0.269100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.6057 | −0.714022 | ||||||||
\(680\) | −17.5199 | −0.671858 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.20401 | −0.160980 | ||||||||
\(683\) | −12.8022 | −0.489862 | −0.244931 | − | 0.969540i | \(-0.578765\pi\) | ||||
−0.244931 | + | 0.969540i | \(0.578765\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.3835 | −1.00806 | ||||||||
\(686\) | 34.4261 | 1.31439 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.8759 | −1.44401 | ||||||||
\(689\) | −32.6267 | −1.24298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5406 | 1.50419 | 0.752097 | − | 0.659052i | \(-0.229042\pi\) | ||||
0.752097 | + | 0.659052i | \(0.229042\pi\) | |||||||
\(692\) | 28.7769 | 1.09394 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.9294 | 1.24998 | ||||||||
\(695\) | 2.12510 | 0.0806094 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47.7795 | −1.80978 | ||||||||
\(698\) | −16.1006 | −0.609418 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.13716 | 0.0429805 | ||||||||
\(701\) | −22.4546 | −0.848097 | −0.424049 | − | 0.905639i | \(-0.639391\pi\) | ||||
−0.424049 | + | 0.905639i | \(0.639391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.56016 | 0.247421 | ||||||||
\(704\) | 2.10636 | 0.0793865 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.90899 | −0.109481 | ||||||||
\(707\) | −3.90301 | −0.146788 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.41244 | −0.0530451 | −0.0265226 | − | 0.999648i | \(-0.508443\pi\) | ||||
−0.0265226 | + | 0.999648i | \(0.508443\pi\) | |||||||
\(710\) | −13.3703 | −0.501778 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.3575 | 0.425641 | ||||||||
\(713\) | 8.10564 | 0.303559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.64506 | 0.360705 | ||||||||
\(716\) | 10.6545 | 0.398177 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 66.4502 | 2.47990 | ||||||||
\(719\) | 39.0879 | 1.45773 | 0.728867 | − | 0.684655i | \(-0.240047\pi\) | ||||
0.728867 | + | 0.684655i | \(0.240047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3574 | 0.385731 | ||||||||
\(722\) | −1.82669 | −0.0679823 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.56344 | −0.0581049 | ||||||||
\(725\) | 4.07306 | 0.151270 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.42098 | 0.349405 | 0.174702 | − | 0.984621i | \(-0.444104\pi\) | ||||
0.174702 | + | 0.984621i | \(0.444104\pi\) | |||||||
\(728\) | 8.43013 | 0.312442 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 49.6316 | 1.83695 | ||||||||
\(731\) | 47.7850 | 1.76739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.63361 | 0.171146 | 0.0855731 | − | 0.996332i | \(-0.472728\pi\) | ||||
0.0855731 | + | 0.996332i | \(0.472728\pi\) | |||||||
\(734\) | 9.13849 | 0.337308 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.9046 | −0.844274 | ||||||||
\(737\) | −14.7201 | −0.542222 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1654 | −0.484298 | −0.242149 | − | 0.970239i | \(-0.577852\pi\) | ||||
−0.242149 | + | 0.970239i | \(0.577852\pi\) | |||||||
\(740\) | 20.5714 | 0.756219 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.5312 | 0.900568 | ||||||||
\(743\) | 14.7689 | 0.541817 | 0.270909 | − | 0.962605i | \(-0.412676\pi\) | ||||
0.270909 | + | 0.962605i | \(0.412676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.6715 | 0.903894 | ||||||||
\(746\) | 62.3472 | 2.28269 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.24132 | −0.301332 | ||||||||
\(749\) | −0.715792 | −0.0261545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0415 | 1.27868 | 0.639341 | − | 0.768924i | \(-0.279207\pi\) | ||||
0.639341 | + | 0.768924i | \(0.279207\pi\) | |||||||
\(752\) | −53.2487 | −1.94178 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −60.8625 | −2.21648 | ||||||||
\(755\) | −31.0664 | −1.13062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.8005 | −0.865044 | −0.432522 | − | 0.901623i | \(-0.642376\pi\) | ||||
−0.432522 | + | 0.901623i | \(0.642376\pi\) | |||||||
\(758\) | −28.8158 | −1.04664 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.84184 | 0.103084 | ||||||||
\(761\) | 39.0282 | 1.41477 | 0.707386 | − | 0.706827i | \(-0.249874\pi\) | ||||
0.707386 | + | 0.706827i | \(0.249874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.7239 | 0.858862 | ||||||||
\(764\) | 20.9440 | 0.757726 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.9654 | −1.48014 | ||||||||
\(767\) | −44.9190 | −1.62193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.84757 | 0.355113 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(770\) | −7.25189 | −0.261340 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.9776 | 1.04292 | ||||||||
\(773\) | 42.9837 | 1.54602 | 0.773008 | − | 0.634396i | \(-0.218751\pi\) | ||||
0.773008 | + | 0.634396i | \(0.218751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.15679 | −0.0415531 | ||||||||
\(776\) | −13.3186 | −0.478111 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.5175 | −1.20166 | ||||||||
\(779\) | 7.75013 | 0.277677 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.12026 | 0.111652 | ||||||||
\(782\) | 39.6630 | 1.41835 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.2099 | 0.721783 | ||||||||
\(785\) | −4.68954 | −0.167377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8709 | −0.922199 | −0.461099 | − | 0.887349i | \(-0.652545\pi\) | ||||
−0.461099 | + | 0.887349i | \(0.652545\pi\) | |||||||
\(788\) | −6.13313 | −0.218484 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.2614 | 0.756448 | ||||||||
\(791\) | 4.29254 | 0.152625 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.5503 | −0.658741 | ||||||||
\(794\) | 0.934320 | 0.0331578 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4611 | 0.618893 | ||||||||
\(797\) | −3.62989 | −0.128577 | −0.0642886 | − | 0.997931i | \(-0.520478\pi\) | ||||
−0.0642886 | + | 0.997931i | \(0.520478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.1796 | 2.37664 | ||||||||
\(800\) | 3.26880 | 0.115570 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.6749 | 1.22441 | ||||||||
\(803\) | −11.5827 | −0.408743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.9822 | 0.492807 | ||||||||
\(806\) | 17.2855 | 0.608857 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.79391 | −0.0982894 | ||||||||
\(809\) | 13.1327 | 0.461720 | 0.230860 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230860 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.40230 | 0.330160 | 0.165080 | − | 0.986280i | \(-0.447212\pi\) | ||||
0.165080 | + | 0.986280i | \(0.447212\pi\) | |||||||
\(812\) | 18.3329 | 0.643358 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.9834 | −0.420017 | ||||||||
\(815\) | 43.9966 | 1.54114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.75102 | −0.271174 | ||||||||
\(818\) | −2.01098 | −0.0703124 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.3029 | 0.848695 | ||||||||
\(821\) | 21.1701 | 0.738843 | 0.369422 | − | 0.929262i | \(-0.379556\pi\) | ||||
0.369422 | + | 0.929262i | \(0.379556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2277 | 0.879384 | 0.439692 | − | 0.898149i | \(-0.355088\pi\) | ||||
0.439692 | + | 0.898149i | \(0.355088\pi\) | |||||||
\(824\) | 7.41422 | 0.258286 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.7735 | 1.17513 | ||||||||
\(827\) | 39.4460 | 1.37167 | 0.685836 | − | 0.727756i | \(-0.259437\pi\) | ||||
0.685836 | + | 0.727756i | \(0.259437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.5068 | −1.26793 | −0.633967 | − | 0.773360i | \(-0.718574\pi\) | ||||
−0.633967 | + | 0.773360i | \(0.718574\pi\) | |||||||
\(830\) | 7.83748 | 0.272043 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.66069 | −0.300255 | ||||||||
\(833\) | −25.4972 | −0.883427 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8066 | −0.512403 | ||||||||
\(836\) | 1.33679 | 0.0462339 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −34.3288 | −1.18587 | ||||||||
\(839\) | −42.4670 | −1.46612 | −0.733061 | − | 0.680163i | \(-0.761909\pi\) | ||||
−0.733061 | + | 0.680163i | \(0.761909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.6645 | 1.26429 | ||||||||
\(842\) | 45.2321 | 1.55880 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.89258 | 0.133988 | ||||||||
\(845\) | −9.16241 | −0.315196 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.69239 | 0.0581513 | ||||||||
\(848\) | 38.7755 | 1.33156 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.66047 | −0.194153 | ||||||||
\(851\) | 23.1048 | 0.792023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5088 | 0.736446 | 0.368223 | − | 0.929738i | \(-0.379966\pi\) | ||||
0.368223 | + | 0.929738i | \(0.379966\pi\) | |||||||
\(854\) | 13.9475 | 0.477275 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.512389 | −0.0175131 | ||||||||
\(857\) | 12.6370 | 0.431670 | 0.215835 | − | 0.976430i | \(-0.430753\pi\) | ||||
0.215835 | + | 0.976430i | \(0.430753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.39720 | −0.115911 | −0.0579555 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579555 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(860\) | −24.3057 | −0.828818 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −58.8167 | −2.00330 | ||||||||
\(863\) | 10.9308 | 0.372088 | 0.186044 | − | 0.982541i | \(-0.440433\pi\) | ||||
0.186044 | + | 0.982541i | \(0.440433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.4971 | −1.71695 | ||||||||
\(866\) | 27.9561 | 0.949987 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.20672 | −0.176727 | ||||||||
\(869\) | −4.96184 | −0.168319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.5243 | 2.05079 | ||||||||
\(872\) | 16.9824 | 0.575096 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.43359 | −0.217619 | ||||||||
\(875\) | 17.8544 | 0.603588 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.7230 | 1.07121 | 0.535605 | − | 0.844468i | \(-0.320083\pi\) | ||||
0.535605 | + | 0.844468i | \(0.320083\pi\) | |||||||
\(878\) | −47.8250 | −1.61402 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.4628 | −0.386410 | ||||||||
\(881\) | 6.45839 | 0.217589 | 0.108794 | − | 0.994064i | \(-0.465301\pi\) | ||||
0.108794 | + | 0.994064i | \(0.465301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.5242 | −1.63297 | −0.816485 | − | 0.577367i | \(-0.804080\pi\) | ||||
−0.816485 | + | 0.577367i | \(0.804080\pi\) | |||||||
\(884\) | 33.8857 | 1.13970 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.3796 | 1.32298 | ||||||||
\(887\) | 44.0097 | 1.47770 | 0.738851 | − | 0.673869i | \(-0.235369\pi\) | ||||
0.738851 | + | 0.673869i | \(0.235369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.81552 | 0.0608905 | ||||||||
\(890\) | 40.1716 | 1.34656 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.47742 | 0.283845 | ||||||||
\(893\) | −10.8969 | −0.364652 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.6962 | −0.624946 | ||||||||
\(896\) | −15.5005 | −0.517835 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.5531 | 0.719236 | ||||||||
\(899\) | −18.6494 | −0.621991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.9199 | −1.62976 | ||||||||
\(902\) | −14.1571 | −0.471379 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.07275 | 0.102198 | ||||||||
\(905\) | 2.74349 | 0.0911966 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.05084 | −0.0680971 | −0.0340485 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340485 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(908\) | 2.67932 | 0.0889164 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.8175 | 0.988439 | ||||||||
\(911\) | 16.8417 | 0.557990 | 0.278995 | − | 0.960293i | \(-0.409999\pi\) | ||||
0.278995 | + | 0.960293i | \(0.409999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.82905 | −0.0605328 | ||||||||
\(914\) | 28.6539 | 0.947788 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.0584 | −0.927075 | ||||||||
\(917\) | 13.2465 | 0.437438 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.01221 | 0.264299 | 0.132149 | − | 0.991230i | \(-0.457812\pi\) | ||||
0.132149 | + | 0.991230i | \(0.457812\pi\) | |||||||
\(920\) | 10.0089 | 0.329985 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 49.7683 | 1.63903 | ||||||||
\(923\) | −12.8295 | −0.422289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.29738 | −0.108417 | ||||||||
\(926\) | 32.7641 | 1.07670 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 52.6986 | 1.72992 | ||||||||
\(929\) | −16.7897 | −0.550853 | −0.275426 | − | 0.961322i | \(-0.588819\pi\) | ||||
−0.275426 | + | 0.961322i | \(0.588819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.13581 | 0.135546 | ||||||||
\(932\) | 23.5284 | 0.770698 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52.9922 | 1.73396 | ||||||||
\(935\) | 14.4617 | 0.472947 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.8471 | 0.713713 | 0.356856 | − | 0.934159i | \(-0.383849\pi\) | ||||
0.356856 | + | 0.934159i | \(0.383849\pi\) | |||||||
\(938\) | −45.5068 | −1.48585 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −34.1707 | −1.11453 | ||||||||
\(941\) | −17.8421 | −0.581635 | −0.290817 | − | 0.956779i | \(-0.593927\pi\) | ||||
−0.290817 | + | 0.956779i | \(0.593927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.2959 | 0.888877 | ||||||||
\(944\) | 53.3845 | 1.73752 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.1587 | 0.460339 | ||||||||
\(947\) | −41.9736 | −1.36396 | −0.681980 | − | 0.731371i | \(-0.738881\pi\) | ||||
−0.681980 | + | 0.731371i | \(0.738881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.6242 | 1.54595 | ||||||||
\(950\) | 0.918163 | 0.0297892 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.6400 | 0.409665 | ||||||||
\(953\) | 8.06945 | 0.261395 | 0.130697 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130697 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7520 | −1.18927 | ||||||||
\(956\) | −35.5864 | −1.15094 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 62.2711 | 2.01189 | ||||||||
\(959\) | 19.0348 | 0.614666 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7034 | −0.829142 | ||||||||
\(962\) | 49.2718 | 1.58859 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.5577 | 0.565496 | ||||||||
\(965\) | −50.8491 | −1.63689 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.86360 | −0.124245 | −0.0621225 | − | 0.998069i | \(-0.519787\pi\) | ||||
−0.0621225 | + | 0.998069i | \(0.519787\pi\) | |||||||
\(968\) | 1.21147 | 0.0389382 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −47.1081 | −1.51255 | ||||||||
\(971\) | −42.7787 | −1.37283 | −0.686417 | − | 0.727208i | \(-0.740818\pi\) | ||||
−0.686417 | + | 0.727208i | \(0.740818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.53318 | −0.0491516 | ||||||||
\(974\) | −11.6607 | −0.373631 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.0463 | 0.705686 | ||||||||
\(977\) | −54.5146 | −1.74408 | −0.872039 | − | 0.489437i | \(-0.837202\pi\) | ||||
−0.872039 | + | 0.489437i | \(0.837202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.37496 | −0.299625 | ||||||||
\(980\) | 12.9691 | 0.414283 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −57.4590 | −1.83359 | ||||||||
\(983\) | −33.5422 | −1.06983 | −0.534916 | − | 0.844905i | \(-0.679657\pi\) | ||||
−0.534916 | + | 0.844905i | \(0.679657\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7623 | 0.342914 | ||||||||
\(986\) | −91.2562 | −2.90619 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.49647 | −0.174866 | ||||||||
\(989\) | −27.2991 | −0.868060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.7767 | 1.00942 | 0.504710 | − | 0.863289i | \(-0.331600\pi\) | ||||
0.504710 | + | 0.863289i | \(0.331600\pi\) | |||||||
\(992\) | −14.9669 | −0.475200 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.64621 | 0.305959 | ||||||||
\(995\) | −30.6403 | −0.971363 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.5668 | −1.50646 | −0.753228 | − | 0.657759i | \(-0.771504\pi\) | ||||
−0.753228 | + | 0.657759i | \(0.771504\pi\) | |||||||
\(998\) | 58.3933 | 1.84841 | ||||||||
\(999\) | 0 | 0 |
(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 | 1881.2.a.k.1.2 | 5 | ||
3.2 | odd | 2 | 209.2.a.c.1.4 | ✓ | 5 | ||
12.11 | even | 2 | 3344.2.a.t.1.4 | 5 | |||
15.14 | odd | 2 | 5225.2.a.h.1.2 | 5 | |||
33.32 | even | 2 | 2299.2.a.n.1.2 | 5 | |||
57.56 | even | 2 | 3971.2.a.h.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.c.1.4 | ✓ | 5 | 3.2 | odd | 2 | ||
1881.2.a.k.1.2 | 5 | 1.1 | even | 1 | trivial | ||
2299.2.a.n.1.2 | 5 | 33.32 | even | 2 | |||
3344.2.a.t.1.4 | 5 | 12.11 | even | 2 | |||
3971.2.a.h.1.2 | 5 | 57.56 | even | 2 | |||
5225.2.a.h.1.2 | 5 | 15.14 | odd | 2 |