Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3971,2,Mod(1,3971)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3971, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3971.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3971 = 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3971.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: | \(31.7085946427\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 3971.1 |
$q$-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 | \(0.723489\pi\) | |||||||
\(3\) | 0.563416 | 0.325288 | 0.162644 | − | 0.986685i | \(-0.447998\pi\) | ||||
0.162644 | + | 0.986685i | \(0.447998\pi\) | |||||||
\(4\) | 1.33679 | 0.668396 | ||||||||
\(5\) | 2.34577 | 1.04906 | 0.524530 | − | 0.851392i | \(-0.324241\pi\) | ||||
0.524530 | + | 0.851392i | \(0.324241\pi\) | |||||||
\(6\) | −1.02918 | −0.420163 | ||||||||
\(7\) | 1.69239 | 0.639664 | 0.319832 | − | 0.947474i | \(-0.396374\pi\) | ||||
0.319832 | + | 0.947474i | \(0.396374\pi\) | |||||||
\(8\) | 1.21147 | 0.428321 | ||||||||
\(9\) | −2.68256 | −0.894188 | ||||||||
\(10\) | −4.28499 | −1.35503 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.753170 | 0.217421 | ||||||||
\(13\) | −4.11168 | −1.14038 | −0.570188 | − | 0.821514i | \(-0.693130\pi\) | ||||
−0.570188 | + | 0.821514i | \(0.693130\pi\) | |||||||
\(14\) | −3.09147 | −0.826231 | ||||||||
\(15\) | 1.32164 | 0.341247 | ||||||||
\(16\) | −4.88657 | −1.22164 | ||||||||
\(17\) | −6.16499 | −1.49523 | −0.747615 | − | 0.664132i | \(-0.768801\pi\) | ||||
−0.747615 | + | 0.664132i | \(0.768801\pi\) | |||||||
\(18\) | 4.90021 | 1.15499 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.13581 | 0.701188 | ||||||||
\(21\) | 0.953520 | 0.208075 | ||||||||
\(22\) | −1.82669 | −0.389451 | ||||||||
\(23\) | 3.52199 | 0.734386 | 0.367193 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367193 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(24\) | 0.682563 | 0.139328 | ||||||||
\(25\) | 0.502638 | 0.100528 | ||||||||
\(26\) | 7.51076 | 1.47298 | ||||||||
\(27\) | −3.20164 | −0.616157 | ||||||||
\(28\) | 2.26238 | 0.427549 | ||||||||
\(29\) | 8.10336 | 1.50476 | 0.752378 | − | 0.658731i | \(-0.228906\pi\) | ||||
0.752378 | + | 0.658731i | \(0.228906\pi\) | |||||||
\(30\) | −2.41423 | −0.440776 | ||||||||
\(31\) | 2.30144 | 0.413350 | 0.206675 | − | 0.978410i | \(-0.433736\pi\) | ||||
0.206675 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(32\) | 6.50330 | 1.14963 | ||||||||
\(33\) | 0.563416 | 0.0980781 | ||||||||
\(34\) | 11.2615 | 1.93134 | ||||||||
\(35\) | 3.96996 | 0.671046 | ||||||||
\(36\) | −3.58603 | −0.597672 | ||||||||
\(37\) | 6.56016 | 1.07848 | 0.539242 | − | 0.842151i | \(-0.318711\pi\) | ||||
0.539242 | + | 0.842151i | \(0.318711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.31659 | −0.370951 | ||||||||
\(40\) | 2.84184 | 0.449334 | ||||||||
\(41\) | −7.75013 | −1.21037 | −0.605183 | − | 0.796086i | \(-0.706900\pi\) | ||||
−0.605183 | + | 0.796086i | \(0.706900\pi\) | |||||||
\(42\) | −1.74178 | −0.268763 | ||||||||
\(43\) | 7.75102 | 1.18202 | 0.591010 | − | 0.806664i | \(-0.298729\pi\) | ||||
0.591010 | + | 0.806664i | \(0.298729\pi\) | |||||||
\(44\) | 1.33679 | 0.201529 | ||||||||
\(45\) | −6.29268 | −0.938057 | ||||||||
\(46\) | −6.43359 | −0.948581 | ||||||||
\(47\) | −10.8969 | −1.58948 | −0.794742 | − | 0.606948i | \(-0.792394\pi\) | ||||
−0.794742 | + | 0.606948i | \(0.792394\pi\) | |||||||
\(48\) | −2.75317 | −0.397386 | ||||||||
\(49\) | −4.13581 | −0.590830 | ||||||||
\(50\) | −0.918163 | −0.129848 | ||||||||
\(51\) | −3.47345 | −0.486381 | ||||||||
\(52\) | −5.49647 | −0.762223 | ||||||||
\(53\) | −7.93511 | −1.08997 | −0.544986 | − | 0.838445i | \(-0.683465\pi\) | ||||
−0.544986 | + | 0.838445i | \(0.683465\pi\) | |||||||
\(54\) | 5.84841 | 0.795868 | ||||||||
\(55\) | 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 | \(0.751821\pi\) | |||||||
\(60\) | 1.76676 | 0.228088 | ||||||||
\(61\) | −4.51162 | −0.577653 | −0.288827 | − | 0.957381i | \(-0.593265\pi\) | ||||
−0.288827 | + | 0.957381i | \(0.593265\pi\) | |||||||
\(62\) | −4.20401 | −0.533910 | ||||||||
\(63\) | −4.53995 | −0.571980 | ||||||||
\(64\) | −2.10636 | −0.263295 | ||||||||
\(65\) | −9.64506 | −1.19632 | ||||||||
\(66\) | −1.02918 | −0.126684 | ||||||||
\(67\) | −14.7201 | −1.79835 | −0.899173 | − | 0.437594i | \(-0.855831\pi\) | ||||
−0.899173 | + | 0.437594i | \(0.855831\pi\) | |||||||
\(68\) | −8.24132 | −0.999407 | ||||||||
\(69\) | 1.98435 | 0.238887 | ||||||||
\(70\) | −7.25189 | −0.866766 | ||||||||
\(71\) | −3.12026 | −0.370307 | −0.185153 | − | 0.982710i | \(-0.559278\pi\) | ||||
−0.185153 | + | 0.982710i | \(0.559278\pi\) | |||||||
\(72\) | −3.24985 | −0.382999 | ||||||||
\(73\) | 11.5827 | 1.35565 | 0.677824 | − | 0.735224i | \(-0.262923\pi\) | ||||
0.677824 | + | 0.735224i | \(0.262923\pi\) | |||||||
\(74\) | −11.9834 | −1.39304 | ||||||||
\(75\) | 0.283194 | 0.0327004 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.69239 | 0.192866 | ||||||||
\(78\) | 4.23168 | 0.479144 | ||||||||
\(79\) | −4.96184 | −0.558250 | −0.279125 | − | 0.960255i | \(-0.590044\pi\) | ||||
−0.279125 | + | 0.960255i | \(0.590044\pi\) | |||||||
\(80\) | −11.4628 | −1.28158 | ||||||||
\(81\) | 6.24383 | 0.693759 | ||||||||
\(82\) | 14.1571 | 1.56339 | ||||||||
\(83\) | −1.82905 | −0.200765 | −0.100382 | − | 0.994949i | \(-0.532007\pi\) | ||||
−0.100382 | + | 0.994949i | \(0.532007\pi\) | |||||||
\(84\) | 1.27466 | 0.139077 | ||||||||
\(85\) | −14.4617 | −1.56859 | ||||||||
\(86\) | −14.1587 | −1.52677 | ||||||||
\(87\) | 4.56556 | 0.489480 | ||||||||
\(88\) | 1.21147 | 0.129144 | ||||||||
\(89\) | 9.37496 | 0.993743 | 0.496872 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496872 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(90\) | 11.4948 | 1.21165 | ||||||||
\(91\) | −6.95858 | −0.729457 | ||||||||
\(92\) | 4.70818 | 0.490861 | ||||||||
\(93\) | 1.29666 | 0.134458 | ||||||||
\(94\) | 19.9053 | 2.05308 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.66406 | 0.373961 | ||||||||
\(97\) | 10.9937 | 1.11625 | 0.558123 | − | 0.829758i | \(-0.311522\pi\) | ||||
0.558123 | + | 0.829758i | \(0.311522\pi\) | |||||||
\(98\) | 7.55484 | 0.763154 | ||||||||
\(99\) | −2.68256 | −0.269608 | ||||||||
\(100\) | 0.671923 | 0.0671923 | ||||||||
\(101\) | 2.30621 | 0.229476 | 0.114738 | − | 0.993396i | \(-0.463397\pi\) | ||||
0.114738 | + | 0.993396i | \(0.463397\pi\) | |||||||
\(102\) | 6.34492 | 0.628241 | ||||||||
\(103\) | −6.12000 | −0.603021 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(104\) | −4.98119 | −0.488446 | ||||||||
\(105\) | 2.23674 | 0.218283 | ||||||||
\(106\) | 14.4950 | 1.40788 | ||||||||
\(107\) | −0.422947 | −0.0408878 | −0.0204439 | − | 0.999791i | \(-0.506508\pi\) | ||||
−0.0204439 | + | 0.999791i | \(0.506508\pi\) | |||||||
\(108\) | −4.27993 | −0.411837 | ||||||||
\(109\) | −14.0180 | −1.34268 | −0.671338 | − | 0.741151i | \(-0.734280\pi\) | ||||
−0.671338 | + | 0.741151i | \(0.734280\pi\) | |||||||
\(110\) | −4.28499 | −0.408558 | ||||||||
\(111\) | 3.69609 | 0.350818 | ||||||||
\(112\) | −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 | ||||||||
\(117\) | 11.0298 | 1.01971 | ||||||||
\(118\) | 19.9561 | 1.83711 | ||||||||
\(119\) | −10.4336 | −0.956445 | ||||||||
\(120\) | 1.60114 | 0.146163 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.24132 | 0.746134 | ||||||||
\(123\) | −4.36654 | −0.393718 | ||||||||
\(124\) | 3.07654 | 0.276282 | ||||||||
\(125\) | −10.5498 | −0.943601 | ||||||||
\(126\) | 8.29307 | 0.738806 | ||||||||
\(127\) | −1.07275 | −0.0951914 | −0.0475957 | − | 0.998867i | \(-0.515156\pi\) | ||||
−0.0475957 | + | 0.998867i | \(0.515156\pi\) | |||||||
\(128\) | −9.15893 | −0.809543 | ||||||||
\(129\) | 4.36705 | 0.384497 | ||||||||
\(130\) | 17.6185 | 1.54525 | ||||||||
\(131\) | −7.82709 | −0.683856 | −0.341928 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341928 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(132\) | 0.753170 | 0.0655550 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 26.8890 | 2.32286 | ||||||||
\(135\) | −7.51032 | −0.646386 | ||||||||
\(136\) | −7.46873 | −0.640438 | ||||||||
\(137\) | −11.2473 | −0.960919 | −0.480460 | − | 0.877017i | \(-0.659530\pi\) | ||||
−0.480460 | + | 0.877017i | \(0.659530\pi\) | |||||||
\(138\) | −3.62478 | −0.308562 | ||||||||
\(139\) | −0.905926 | −0.0768397 | −0.0384198 | − | 0.999262i | \(-0.512232\pi\) | ||||
−0.0384198 | + | 0.999262i | \(0.512232\pi\) | |||||||
\(140\) | 5.30702 | 0.448525 | ||||||||
\(141\) | −6.13951 | −0.517040 | ||||||||
\(142\) | 5.69975 | 0.478312 | ||||||||
\(143\) | −4.11168 | −0.343836 | ||||||||
\(144\) | 13.1085 | 1.09238 | ||||||||
\(145\) | 19.0086 | 1.57858 | ||||||||
\(146\) | −21.1579 | −1.75104 | ||||||||
\(147\) | −2.33018 | −0.192190 | ||||||||
\(148\) | 8.76957 | 0.720854 | ||||||||
\(149\) | 10.5174 | 0.861622 | 0.430811 | − | 0.902442i | \(-0.358228\pi\) | ||||
0.430811 | + | 0.902442i | \(0.358228\pi\) | |||||||
\(150\) | −0.517307 | −0.0422380 | ||||||||
\(151\) | −13.2436 | −1.07775 | −0.538873 | − | 0.842387i | \(-0.681150\pi\) | ||||
−0.538873 | + | 0.842387i | \(0.681150\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.5380 | 1.33702 | ||||||||
\(154\) | −3.09147 | −0.249118 | ||||||||
\(155\) | 5.39864 | 0.433629 | ||||||||
\(156\) | −3.09679 | −0.247942 | ||||||||
\(157\) | 1.99915 | 0.159549 | 0.0797747 | − | 0.996813i | \(-0.474580\pi\) | ||||
0.0797747 | + | 0.996813i | \(0.474580\pi\) | |||||||
\(158\) | 9.06373 | 0.721072 | ||||||||
\(159\) | −4.47076 | −0.354555 | ||||||||
\(160\) | 15.2552 | 1.20603 | ||||||||
\(161\) | 5.96059 | 0.469761 | ||||||||
\(162\) | −11.4055 | −0.896104 | ||||||||
\(163\) | −18.7557 | −1.46906 | −0.734531 | − | 0.678575i | \(-0.762598\pi\) | ||||
−0.734531 | + | 0.678575i | \(0.762598\pi\) | |||||||
\(164\) | −10.3603 | −0.809005 | ||||||||
\(165\) | 1.32164 | 0.102890 | ||||||||
\(166\) | 3.34111 | 0.259320 | ||||||||
\(167\) | 6.31203 | 0.488440 | 0.244220 | − | 0.969720i | \(-0.421468\pi\) | ||||
0.244220 | + | 0.969720i | \(0.421468\pi\) | |||||||
\(168\) | 1.15516 | 0.0891229 | ||||||||
\(169\) | 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 | \(0.194901\pi\) | |||||||
\(174\) | −8.33986 | −0.632243 | ||||||||
\(175\) | 0.850661 | 0.0643039 | ||||||||
\(176\) | −4.88657 | −0.368339 | ||||||||
\(177\) | −6.15516 | −0.462650 | ||||||||
\(178\) | −17.1251 | −1.28358 | ||||||||
\(179\) | 7.97018 | 0.595719 | 0.297860 | − | 0.954610i | \(-0.403727\pi\) | ||||
0.297860 | + | 0.954610i | \(0.403727\pi\) | |||||||
\(180\) | −8.41200 | −0.626994 | ||||||||
\(181\) | 1.16955 | 0.0869317 | 0.0434659 | − | 0.999055i | \(-0.486160\pi\) | ||||
0.0434659 | + | 0.999055i | \(0.486160\pi\) | |||||||
\(182\) | 12.7112 | 0.942214 | ||||||||
\(183\) | −2.54191 | −0.187904 | ||||||||
\(184\) | 4.26680 | 0.314553 | ||||||||
\(185\) | 15.3886 | 1.13139 | ||||||||
\(186\) | −2.36860 | −0.173674 | ||||||||
\(187\) | −6.16499 | −0.450829 | ||||||||
\(188\) | −14.5670 | −1.06240 | ||||||||
\(189\) | −5.41844 | −0.394133 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6673 | −1.13365 | −0.566824 | − | 0.823839i | \(-0.691828\pi\) | ||||
−0.566824 | + | 0.823839i | \(0.691828\pi\) | |||||||
\(192\) | −1.18676 | −0.0856468 | ||||||||
\(193\) | −21.6769 | −1.56034 | −0.780169 | − | 0.625568i | \(-0.784867\pi\) | ||||
−0.780169 | + | 0.625568i | \(0.784867\pi\) | |||||||
\(194\) | −20.0821 | −1.44181 | ||||||||
\(195\) | −5.43418 | −0.389149 | ||||||||
\(196\) | −5.52872 | −0.394908 | ||||||||
\(197\) | 4.58794 | 0.326877 | 0.163439 | − | 0.986554i | \(-0.447741\pi\) | ||||
0.163439 | + | 0.986554i | \(0.447741\pi\) | |||||||
\(198\) | 4.90021 | 0.348243 | ||||||||
\(199\) | 13.0619 | 0.925937 | 0.462968 | − | 0.886375i | \(-0.346784\pi\) | ||||
0.462968 | + | 0.886375i | \(0.346784\pi\) | |||||||
\(200\) | 0.608933 | 0.0430580 | ||||||||
\(201\) | −8.29353 | −0.584980 | ||||||||
\(202\) | −4.21272 | −0.296406 | ||||||||
\(203\) | 13.7141 | 0.962539 | ||||||||
\(204\) | −4.64329 | −0.325095 | ||||||||
\(205\) | −18.1800 | −1.26975 | ||||||||
\(206\) | 11.1793 | 0.778901 | ||||||||
\(207\) | −9.44797 | −0.656679 | ||||||||
\(208\) | 20.0920 | 1.39313 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.08583 | −0.281949 | ||||||||
\(211\) | −2.91188 | −0.200462 | −0.100231 | − | 0.994964i | \(-0.531958\pi\) | ||||
−0.100231 | + | 0.994964i | \(0.531958\pi\) | |||||||
\(212\) | −10.6076 | −0.728533 | ||||||||
\(213\) | −1.75800 | −0.120456 | ||||||||
\(214\) | 0.772592 | 0.0528133 | ||||||||
\(215\) | 18.1821 | 1.24001 | ||||||||
\(216\) | −3.87871 | −0.263913 | ||||||||
\(217\) | 3.89493 | 0.264405 | ||||||||
\(218\) | 25.6064 | 1.73429 | ||||||||
\(219\) | 6.52585 | 0.440976 | ||||||||
\(220\) | 3.13581 | 0.211416 | ||||||||
\(221\) | 25.3485 | 1.70512 | ||||||||
\(222\) | −6.75161 | −0.453139 | ||||||||
\(223\) | −6.34161 | −0.424665 | −0.212333 | − | 0.977197i | \(-0.568106\pi\) | ||||
−0.212333 | + | 0.977197i | \(0.568106\pi\) | |||||||
\(224\) | 11.0061 | 0.735378 | ||||||||
\(225\) | −1.34836 | −0.0898905 | ||||||||
\(226\) | −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 | ||||||||
\(231\) | 0.953520 | 0.0627370 | ||||||||
\(232\) | 9.81701 | 0.644518 | ||||||||
\(233\) | −17.6006 | −1.15305 | −0.576527 | − | 0.817078i | \(-0.695593\pi\) | ||||
−0.576527 | + | 0.817078i | \(0.695593\pi\) | |||||||
\(234\) | −20.1481 | −1.31712 | ||||||||
\(235\) | −25.5617 | −1.66746 | ||||||||
\(236\) | −14.6041 | −0.950646 | ||||||||
\(237\) | −2.79558 | −0.181592 | ||||||||
\(238\) | 19.0589 | 1.23541 | ||||||||
\(239\) | 26.6207 | 1.72195 | 0.860975 | − | 0.508647i | \(-0.169854\pi\) | ||||
0.860975 | + | 0.508647i | \(0.169854\pi\) | |||||||
\(240\) | −6.45830 | −0.416882 | ||||||||
\(241\) | −13.1342 | −0.846049 | −0.423024 | − | 0.906118i | \(-0.639032\pi\) | ||||
−0.423024 | + | 0.906118i | \(0.639032\pi\) | |||||||
\(242\) | −1.82669 | −0.117424 | ||||||||
\(243\) | 13.1228 | 0.841828 | ||||||||
\(244\) | −6.03109 | −0.386101 | ||||||||
\(245\) | −9.70166 | −0.619816 | ||||||||
\(246\) | 7.97632 | 0.508551 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.78813 | 0.177046 | ||||||||
\(249\) | −1.03052 | −0.0653063 | ||||||||
\(250\) | 19.2712 | 1.21882 | ||||||||
\(251\) | −26.1636 | −1.65143 | −0.825715 | − | 0.564087i | \(-0.809228\pi\) | ||||
−0.825715 | + | 0.564087i | \(0.809228\pi\) | |||||||
\(252\) | −6.06897 | −0.382309 | ||||||||
\(253\) | 3.52199 | 0.221426 | ||||||||
\(254\) | 1.95959 | 0.122955 | ||||||||
\(255\) | −8.14792 | −0.510243 | ||||||||
\(256\) | 20.9432 | 1.30895 | ||||||||
\(257\) | −12.6117 | −0.786697 | −0.393349 | − | 0.919389i | \(-0.628683\pi\) | ||||
−0.393349 | + | 0.919389i | \(0.628683\pi\) | |||||||
\(258\) | −7.97724 | −0.496641 | ||||||||
\(259\) | 11.1024 | 0.689867 | ||||||||
\(260\) | −12.8934 | −0.799618 | ||||||||
\(261\) | −21.7378 | −1.34554 | ||||||||
\(262\) | 14.2977 | 0.883312 | ||||||||
\(263\) | −20.0550 | −1.23664 | −0.618322 | − | 0.785925i | \(-0.712187\pi\) | ||||
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(264\) | 0.682563 | 0.0420088 | ||||||||
\(265\) | −18.6139 | −1.14345 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.28200 | 0.323253 | ||||||||
\(268\) | −19.6777 | −1.20201 | ||||||||
\(269\) | 20.1150 | 1.22644 | 0.613218 | − | 0.789914i | \(-0.289875\pi\) | ||||
0.613218 | + | 0.789914i | \(0.289875\pi\) | |||||||
\(270\) | 13.7190 | 0.834913 | ||||||||
\(271\) | 15.5586 | 0.945117 | 0.472558 | − | 0.881299i | \(-0.343331\pi\) | ||||
0.472558 | + | 0.881299i | \(0.343331\pi\) | |||||||
\(272\) | 30.1257 | 1.82664 | ||||||||
\(273\) | −3.92057 | −0.237284 | ||||||||
\(274\) | 20.5453 | 1.24119 | ||||||||
\(275\) | 0.502638 | 0.0303102 | ||||||||
\(276\) | 2.65266 | 0.159671 | ||||||||
\(277\) | 1.89211 | 0.113686 | 0.0568429 | − | 0.998383i | \(-0.481897\pi\) | ||||
0.0568429 | + | 0.998383i | \(0.481897\pi\) | |||||||
\(278\) | 1.65485 | 0.0992510 | ||||||||
\(279\) | −6.17375 | −0.369613 | ||||||||
\(280\) | 4.80951 | 0.287423 | ||||||||
\(281\) | −4.59299 | −0.273995 | −0.136997 | − | 0.990571i | \(-0.543745\pi\) | ||||
−0.136997 | + | 0.990571i | \(0.543745\pi\) | |||||||
\(282\) | 11.2150 | 0.667842 | ||||||||
\(283\) | −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 | ||||||||
\(288\) | −17.4455 | −1.02799 | ||||||||
\(289\) | 21.0071 | 1.23571 | ||||||||
\(290\) | −34.7229 | −2.03900 | ||||||||
\(291\) | 6.19405 | 0.363101 | ||||||||
\(292\) | 15.4836 | 0.906110 | ||||||||
\(293\) | 11.2606 | 0.657851 | 0.328925 | − | 0.944356i | \(-0.393314\pi\) | ||||
0.328925 | + | 0.944356i | \(0.393314\pi\) | |||||||
\(294\) | 4.25651 | 0.248245 | ||||||||
\(295\) | −25.6269 | −1.49206 | ||||||||
\(296\) | 7.94745 | 0.461936 | ||||||||
\(297\) | −3.20164 | −0.185778 | ||||||||
\(298\) | −19.2121 | −1.11293 | ||||||||
\(299\) | −14.4813 | −0.837476 | ||||||||
\(300\) | 0.378572 | 0.0218568 | ||||||||
\(301\) | 13.1178 | 0.756096 | ||||||||
\(302\) | 24.1919 | 1.39209 | ||||||||
\(303\) | 1.29935 | 0.0746459 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.5832 | −0.605993 | ||||||||
\(306\) | −30.2098 | −1.72698 | ||||||||
\(307\) | −4.35245 | −0.248407 | −0.124204 | − | 0.992257i | \(-0.539638\pi\) | ||||
−0.124204 | + | 0.992257i | \(0.539638\pi\) | |||||||
\(308\) | 2.26238 | 0.128911 | ||||||||
\(309\) | −3.44810 | −0.196156 | ||||||||
\(310\) | −9.86164 | −0.560103 | ||||||||
\(311\) | 7.61725 | 0.431935 | 0.215967 | − | 0.976401i | \(-0.430709\pi\) | ||||
0.215967 | + | 0.976401i | \(0.430709\pi\) | |||||||
\(312\) | −2.80648 | −0.158886 | ||||||||
\(313\) | −17.5654 | −0.992855 | −0.496427 | − | 0.868078i | \(-0.665355\pi\) | ||||
−0.496427 | + | 0.868078i | \(0.665355\pi\) | |||||||
\(314\) | −3.65182 | −0.206084 | ||||||||
\(315\) | −10.6497 | −0.600041 | ||||||||
\(316\) | −6.63295 | −0.373132 | ||||||||
\(317\) | 1.94192 | 0.109069 | 0.0545345 | − | 0.998512i | \(-0.482633\pi\) | ||||
0.0545345 | + | 0.998512i | \(0.482633\pi\) | |||||||
\(318\) | 8.16670 | 0.457966 | ||||||||
\(319\) | 8.10336 | 0.453701 | ||||||||
\(320\) | −4.94104 | −0.276213 | ||||||||
\(321\) | −0.238295 | −0.0133003 | ||||||||
\(322\) | −10.8882 | −0.606773 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.34671 | 0.463706 | ||||||||
\(325\) | −2.06669 | −0.114639 | ||||||||
\(326\) | 34.2609 | 1.89754 | ||||||||
\(327\) | −7.89793 | −0.436757 | ||||||||
\(328\) | −9.38907 | −0.518425 | ||||||||
\(329\) | −18.4419 | −1.01674 | ||||||||
\(330\) | −2.41423 | −0.132899 | ||||||||
\(331\) | −13.3988 | −0.736462 | −0.368231 | − | 0.929734i | \(-0.620036\pi\) | ||||
−0.368231 | + | 0.929734i | \(0.620036\pi\) | |||||||
\(332\) | −2.44506 | −0.134190 | ||||||||
\(333\) | −17.5980 | −0.964366 | ||||||||
\(334\) | −11.5301 | −0.630900 | ||||||||
\(335\) | −34.5300 | −1.88657 | ||||||||
\(336\) | −4.65944 | −0.254193 | ||||||||
\(337\) | −33.1631 | −1.80651 | −0.903254 | − | 0.429107i | \(-0.858828\pi\) | ||||
−0.903254 | + | 0.429107i | \(0.858828\pi\) | |||||||
\(338\) | −7.13491 | −0.388088 | ||||||||
\(339\) | 1.42903 | 0.0776145 | ||||||||
\(340\) | −19.3322 | −1.04844 | ||||||||
\(341\) | 2.30144 | 0.124630 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8462 | −1.01760 | ||||||||
\(344\) | 9.39016 | 0.506283 | ||||||||
\(345\) | 4.65482 | 0.250607 | ||||||||
\(346\) | −39.3229 | −2.11401 | ||||||||
\(347\) | 18.0268 | 0.967730 | 0.483865 | − | 0.875143i | \(-0.339233\pi\) | ||||
0.483865 | + | 0.875143i | \(0.339233\pi\) | |||||||
\(348\) | 6.10321 | 0.327166 | ||||||||
\(349\) | 8.81411 | 0.471808 | 0.235904 | − | 0.971776i | \(-0.424195\pi\) | ||||
0.235904 | + | 0.971776i | \(0.424195\pi\) | |||||||
\(350\) | −1.55389 | −0.0830590 | ||||||||
\(351\) | 13.1641 | 0.702650 | ||||||||
\(352\) | 6.50330 | 0.346627 | ||||||||
\(353\) | −1.59249 | −0.0847599 | −0.0423799 | − | 0.999102i | \(-0.513494\pi\) | ||||
−0.0423799 | + | 0.999102i | \(0.513494\pi\) | |||||||
\(354\) | 11.2436 | 0.597589 | ||||||||
\(355\) | −7.31942 | −0.388474 | ||||||||
\(356\) | 12.5324 | 0.664214 | ||||||||
\(357\) | −5.87844 | −0.311120 | ||||||||
\(358\) | −14.5590 | −0.769469 | ||||||||
\(359\) | 36.3774 | 1.91993 | 0.959963 | − | 0.280126i | \(-0.0903763\pi\) | ||||
0.959963 | + | 0.280126i | \(0.0903763\pi\) | |||||||
\(360\) | −7.62341 | −0.401789 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −2.13640 | −0.112287 | ||||||||
\(363\) | 0.563416 | 0.0295716 | ||||||||
\(364\) | −9.30218 | −0.487567 | ||||||||
\(365\) | 27.1703 | 1.42216 | ||||||||
\(366\) | 4.64329 | 0.242708 | ||||||||
\(367\) | −5.00276 | −0.261142 | −0.130571 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130571 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(368\) | −17.2105 | −0.897158 | ||||||||
\(369\) | 20.7902 | 1.08229 | ||||||||
\(370\) | −28.1102 | −1.46138 | ||||||||
\(371\) | −13.4293 | −0.697216 | ||||||||
\(372\) | 1.73337 | 0.0898712 | ||||||||
\(373\) | 34.1313 | 1.76725 | 0.883625 | − | 0.468195i | \(-0.155096\pi\) | ||||
0.883625 | + | 0.468195i | \(0.155096\pi\) | |||||||
\(374\) | 11.2615 | 0.582320 | ||||||||
\(375\) | −5.94391 | −0.306942 | ||||||||
\(376\) | −13.2014 | −0.680808 | ||||||||
\(377\) | −33.3185 | −1.71599 | ||||||||
\(378\) | 9.89780 | 0.509088 | ||||||||
\(379\) | −15.7749 | −0.810302 | −0.405151 | − | 0.914250i | \(-0.632781\pi\) | ||||
−0.405151 | + | 0.914250i | \(0.632781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.604405 | −0.0309646 | ||||||||
\(382\) | 28.6193 | 1.46429 | ||||||||
\(383\) | 22.4260 | 1.14592 | 0.572958 | − | 0.819585i | \(-0.305796\pi\) | ||||
0.572958 | + | 0.819585i | \(0.305796\pi\) | |||||||
\(384\) | −5.16028 | −0.263335 | ||||||||
\(385\) | 3.96996 | 0.202328 | ||||||||
\(386\) | 39.5970 | 2.01543 | ||||||||
\(387\) | −20.7926 | −1.05695 | ||||||||
\(388\) | 14.6964 | 0.746094 | ||||||||
\(389\) | −18.3488 | −0.930321 | −0.465160 | − | 0.885226i | \(-0.654003\pi\) | ||||
−0.465160 | + | 0.885226i | \(0.654003\pi\) | |||||||
\(390\) | 9.92655 | 0.502650 | ||||||||
\(391\) | −21.7131 | −1.09808 | ||||||||
\(392\) | −5.01042 | −0.253065 | ||||||||
\(393\) | −4.40990 | −0.222450 | ||||||||
\(394\) | −8.38074 | −0.422216 | ||||||||
\(395\) | −11.6393 | −0.585638 | ||||||||
\(396\) | −3.58603 | −0.180205 | ||||||||
\(397\) | −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 | \(0.657179\pi\) | |||||||
\(402\) | 15.1497 | 0.755598 | ||||||||
\(403\) | −9.46277 | −0.471374 | ||||||||
\(404\) | 3.08292 | 0.153381 | ||||||||
\(405\) | 14.6466 | 0.727795 | ||||||||
\(406\) | −25.0513 | −1.24328 | ||||||||
\(407\) | 6.56016 | 0.325175 | ||||||||
\(408\) | −4.20800 | −0.208327 | ||||||||
\(409\) | −1.10089 | −0.0544355 | −0.0272177 | − | 0.999630i | \(-0.508665\pi\) | ||||
−0.0272177 | + | 0.999630i | \(0.508665\pi\) | |||||||
\(410\) | 33.2092 | 1.64009 | ||||||||
\(411\) | −6.33689 | −0.312576 | ||||||||
\(412\) | −8.18117 | −0.403057 | ||||||||
\(413\) | −18.4889 | −0.909781 | ||||||||
\(414\) | 17.2585 | 0.848209 | ||||||||
\(415\) | −4.29054 | −0.210614 | ||||||||
\(416\) | −26.7395 | −1.31101 | ||||||||
\(417\) | −0.510413 | −0.0249950 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7929 | −0.918094 | −0.459047 | − | 0.888412i | \(-0.651809\pi\) | ||||
−0.459047 | + | 0.888412i | \(0.651809\pi\) | |||||||
\(420\) | 2.99006 | 0.145900 | ||||||||
\(421\) | 24.7618 | 1.20682 | 0.603408 | − | 0.797433i | \(-0.293809\pi\) | ||||
0.603408 | + | 0.797433i | \(0.293809\pi\) | |||||||
\(422\) | 5.31910 | 0.258930 | ||||||||
\(423\) | 29.2318 | 1.42130 | ||||||||
\(424\) | −9.61318 | −0.466857 | ||||||||
\(425\) | −3.09876 | −0.150312 | ||||||||
\(426\) | 3.21133 | 0.155589 | ||||||||
\(427\) | −7.63542 | −0.369504 | ||||||||
\(428\) | −0.565392 | −0.0273293 | ||||||||
\(429\) | −2.31659 | −0.111846 | ||||||||
\(430\) | −33.2131 | −1.60168 | ||||||||
\(431\) | 32.1985 | 1.55095 | 0.775474 | − | 0.631380i | \(-0.217511\pi\) | ||||
0.775474 | + | 0.631380i | \(0.217511\pi\) | |||||||
\(432\) | 15.6451 | 0.752723 | ||||||||
\(433\) | 15.3042 | 0.735475 | 0.367737 | − | 0.929930i | \(-0.380133\pi\) | ||||
0.367737 | + | 0.929930i | \(0.380133\pi\) | |||||||
\(434\) | −7.11483 | −0.341523 | ||||||||
\(435\) | 10.7098 | 0.513494 | ||||||||
\(436\) | −18.7391 | −0.897440 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −11.9207 | −0.569593 | ||||||||
\(439\) | −26.1812 | −1.24956 | −0.624781 | − | 0.780800i | \(-0.714812\pi\) | ||||
−0.624781 | + | 0.780800i | \(0.714812\pi\) | |||||||
\(440\) | 2.84184 | 0.135479 | ||||||||
\(441\) | 11.0946 | 0.528313 | ||||||||
\(442\) | −46.3038 | −2.20245 | ||||||||
\(443\) | 21.5579 | 1.02425 | 0.512123 | − | 0.858912i | \(-0.328859\pi\) | ||||
0.512123 | + | 0.858912i | \(0.328859\pi\) | |||||||
\(444\) | 4.94091 | 0.234485 | ||||||||
\(445\) | 21.9915 | 1.04250 | ||||||||
\(446\) | 11.5841 | 0.548525 | ||||||||
\(447\) | 5.92569 | 0.280275 | ||||||||
\(448\) | −3.56479 | −0.168420 | ||||||||
\(449\) | −11.7990 | −0.556829 | −0.278415 | − | 0.960461i | \(-0.589809\pi\) | ||||
−0.278415 | + | 0.960461i | \(0.589809\pi\) | |||||||
\(450\) | 2.46303 | 0.116108 | ||||||||
\(451\) | −7.75013 | −0.364939 | ||||||||
\(452\) | 3.39061 | 0.159481 | ||||||||
\(453\) | −7.46163 | −0.350578 | ||||||||
\(454\) | −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 | ||||||||
\(459\) | 19.7381 | 0.921296 | ||||||||
\(460\) | 11.0443 | 0.514943 | ||||||||
\(461\) | 27.2451 | 1.26893 | 0.634466 | − | 0.772951i | \(-0.281220\pi\) | ||||
0.634466 | + | 0.772951i | \(0.281220\pi\) | |||||||
\(462\) | −1.74178 | −0.0810352 | ||||||||
\(463\) | −17.9364 | −0.833573 | −0.416787 | − | 0.909004i | \(-0.636844\pi\) | ||||
−0.416787 | + | 0.909004i | \(0.636844\pi\) | |||||||
\(464\) | −39.5977 | −1.83828 | ||||||||
\(465\) | 3.04168 | 0.141054 | ||||||||
\(466\) | 32.1509 | 1.48936 | ||||||||
\(467\) | 29.0100 | 1.34242 | 0.671211 | − | 0.741266i | \(-0.265774\pi\) | ||||
0.671211 | + | 0.741266i | \(0.265774\pi\) | |||||||
\(468\) | 14.7446 | 0.681570 | ||||||||
\(469\) | −24.9122 | −1.15034 | ||||||||
\(470\) | 46.6933 | 2.15380 | ||||||||
\(471\) | 1.12635 | 0.0518995 | ||||||||
\(472\) | −13.2350 | −0.609191 | ||||||||
\(473\) | 7.75102 | 0.356392 | ||||||||
\(474\) | 5.10665 | 0.234556 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.9475 | −0.639285 | ||||||||
\(477\) | 21.2864 | 0.974639 | ||||||||
\(478\) | −48.6277 | −2.22418 | ||||||||
\(479\) | 34.0896 | 1.55759 | 0.778797 | − | 0.627276i | \(-0.215830\pi\) | ||||
0.778797 | + | 0.627276i | \(0.215830\pi\) | |||||||
\(480\) | 8.59504 | 0.392308 | ||||||||
\(481\) | −26.9733 | −1.22988 | ||||||||
\(482\) | 23.9921 | 1.09281 | ||||||||
\(483\) | 3.35829 | 0.152808 | ||||||||
\(484\) | 1.33679 | 0.0607633 | ||||||||
\(485\) | 25.7888 | 1.17101 | ||||||||
\(486\) | −23.9713 | −1.08736 | ||||||||
\(487\) | −6.38349 | −0.289264 | −0.144632 | − | 0.989486i | \(-0.546200\pi\) | ||||
−0.144632 | + | 0.989486i | \(0.546200\pi\) | |||||||
\(488\) | −5.46570 | −0.247421 | ||||||||
\(489\) | −10.5673 | −0.477869 | ||||||||
\(490\) | 17.7219 | 0.800594 | ||||||||
\(491\) | −31.4552 | −1.41956 | −0.709778 | − | 0.704426i | \(-0.751205\pi\) | ||||
−0.709778 | + | 0.704426i | \(0.751205\pi\) | |||||||
\(492\) | −5.83716 | −0.263160 | ||||||||
\(493\) | −49.9572 | −2.24996 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.29268 | −0.282835 | ||||||||
\(496\) | −11.2461 | −0.504966 | ||||||||
\(497\) | −5.28071 | −0.236872 | ||||||||
\(498\) | 1.88243 | 0.0843539 | ||||||||
\(499\) | −31.9667 | −1.43103 | −0.715514 | − | 0.698599i | \(-0.753807\pi\) | ||||
−0.715514 | + | 0.698599i | \(0.753807\pi\) | |||||||
\(500\) | −14.1029 | −0.630699 | ||||||||
\(501\) | 3.55630 | 0.158884 | ||||||||
\(502\) | 47.7927 | 2.13309 | ||||||||
\(503\) | −34.0522 | −1.51831 | −0.759157 | − | 0.650907i | \(-0.774389\pi\) | ||||
−0.759157 | + | 0.650907i | \(0.774389\pi\) | |||||||
\(504\) | −5.50003 | −0.244991 | ||||||||
\(505\) | 5.40983 | 0.240734 | ||||||||
\(506\) | −6.43359 | −0.286008 | ||||||||
\(507\) | 2.20066 | 0.0977347 | ||||||||
\(508\) | −1.43405 | −0.0636256 | ||||||||
\(509\) | −25.7904 | −1.14314 | −0.571569 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571569 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(510\) | 14.8837 | 0.659062 | ||||||||
\(511\) | 19.6024 | 0.867160 | ||||||||
\(512\) | −19.9389 | −0.881184 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.0377 | 1.01615 | ||||||||
\(515\) | −14.3561 | −0.632606 | ||||||||
\(516\) | 5.83784 | 0.256996 | ||||||||
\(517\) | −10.8969 | −0.479247 | ||||||||
\(518\) | −20.2806 | −0.891076 | ||||||||
\(519\) | 12.1286 | 0.532385 | ||||||||
\(520\) | −11.6847 | −0.512410 | ||||||||
\(521\) | −31.3774 | −1.37467 | −0.687334 | − | 0.726342i | \(-0.741219\pi\) | ||||
−0.687334 | + | 0.726342i | \(0.741219\pi\) | |||||||
\(522\) | 39.7082 | 1.73798 | ||||||||
\(523\) | 23.2388 | 1.01616 | 0.508082 | − | 0.861309i | \(-0.330355\pi\) | ||||
0.508082 | + | 0.861309i | \(0.330355\pi\) | |||||||
\(524\) | −10.4632 | −0.457087 | ||||||||
\(525\) | 0.479275 | 0.0209173 | ||||||||
\(526\) | 36.6343 | 1.59733 | ||||||||
\(527\) | −14.1883 | −0.618054 | ||||||||
\(528\) | −2.75317 | −0.119816 | ||||||||
\(529\) | −10.5956 | −0.460677 | ||||||||
\(530\) | 34.0019 | 1.47695 | ||||||||
\(531\) | 29.3063 | 1.27178 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.8661 | 1.38027 | ||||||||
\(534\) | −9.64856 | −0.417534 | ||||||||
\(535\) | −0.992136 | −0.0428938 | ||||||||
\(536\) | −17.8330 | −0.770268 | ||||||||
\(537\) | 4.49052 | 0.193780 | ||||||||
\(538\) | −36.7439 | −1.58414 | ||||||||
\(539\) | −4.13581 | −0.178142 | ||||||||
\(540\) | −10.0397 | −0.432042 | ||||||||
\(541\) | 36.0085 | 1.54812 | 0.774062 | − | 0.633109i | \(-0.218222\pi\) | ||||
0.774062 | + | 0.633109i | \(0.218222\pi\) | |||||||
\(542\) | −28.4207 | −1.22077 | ||||||||
\(543\) | 0.658941 | 0.0282779 | ||||||||
\(544\) | −40.0928 | −1.71896 | ||||||||
\(545\) | −32.8829 | −1.40855 | ||||||||
\(546\) | 7.16166 | 0.306491 | ||||||||
\(547\) | 28.1855 | 1.20513 | 0.602563 | − | 0.798071i | \(-0.294146\pi\) | ||||
0.602563 | + | 0.798071i | \(0.294146\pi\) | |||||||
\(548\) | −15.0353 | −0.642275 | ||||||||
\(549\) | 12.1027 | 0.516530 | ||||||||
\(550\) | −0.918163 | −0.0391506 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.40398 | 0.102320 | ||||||||
\(553\) | −8.39738 | −0.357093 | ||||||||
\(554\) | −3.45629 | −0.146844 | ||||||||
\(555\) | 8.67019 | 0.368029 | ||||||||
\(556\) | −1.21104 | −0.0513594 | ||||||||
\(557\) | 21.6248 | 0.916274 | 0.458137 | − | 0.888882i | \(-0.348517\pi\) | ||||
0.458137 | + | 0.888882i | \(0.348517\pi\) | |||||||
\(558\) | 11.2775 | 0.477415 | ||||||||
\(559\) | −31.8697 | −1.34795 | ||||||||
\(560\) | −19.3995 | −0.819779 | ||||||||
\(561\) | −3.47345 | −0.146649 | ||||||||
\(562\) | 8.38997 | 0.353909 | ||||||||
\(563\) | −13.1791 | −0.555434 | −0.277717 | − | 0.960663i | \(-0.589578\pi\) | ||||
−0.277717 | + | 0.960663i | \(0.589578\pi\) | |||||||
\(564\) | −8.20725 | −0.345588 | ||||||||
\(565\) | 5.94976 | 0.250308 | ||||||||
\(566\) | 2.15179 | 0.0904467 | ||||||||
\(567\) | 10.5670 | 0.443773 | ||||||||
\(568\) | −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 | ||||||||
\(573\) | −8.82722 | −0.368762 | ||||||||
\(574\) | 23.9593 | 1.00004 | ||||||||
\(575\) | 1.77029 | 0.0738261 | ||||||||
\(576\) | 5.65045 | 0.235435 | ||||||||
\(577\) | −31.0907 | −1.29432 | −0.647162 | − | 0.762352i | \(-0.724044\pi\) | ||||
−0.647162 | + | 0.762352i | \(0.724044\pi\) | |||||||
\(578\) | −38.3735 | −1.59613 | ||||||||
\(579\) | −12.2131 | −0.507560 | ||||||||
\(580\) | 25.4106 | 1.05512 | ||||||||
\(581\) | −3.09547 | −0.128422 | ||||||||
\(582\) | −11.3146 | −0.469005 | ||||||||
\(583\) | −7.93511 | −0.328639 | ||||||||
\(584\) | 14.0321 | 0.580652 | ||||||||
\(585\) | 25.8735 | 1.06974 | ||||||||
\(586\) | −20.5696 | −0.849722 | ||||||||
\(587\) | −26.7211 | −1.10290 | −0.551450 | − | 0.834208i | \(-0.685925\pi\) | ||||
−0.551450 | + | 0.834208i | \(0.685925\pi\) | |||||||
\(588\) | −3.11497 | −0.128459 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 46.8124 | 1.92724 | ||||||||
\(591\) | 2.58492 | 0.106329 | ||||||||
\(592\) | −32.0567 | −1.31752 | ||||||||
\(593\) | −24.2460 | −0.995666 | −0.497833 | − | 0.867273i | \(-0.665871\pi\) | ||||
−0.497833 | + | 0.867273i | \(0.665871\pi\) | |||||||
\(594\) | 5.84841 | 0.239963 | ||||||||
\(595\) | −24.4748 | −1.00337 | ||||||||
\(596\) | 14.0596 | 0.575905 | ||||||||
\(597\) | 7.35930 | 0.301196 | ||||||||
\(598\) | 26.4529 | 1.08174 | ||||||||
\(599\) | 18.2095 | 0.744019 | 0.372009 | − | 0.928229i | \(-0.378669\pi\) | ||||
0.372009 | + | 0.928229i | \(0.378669\pi\) | |||||||
\(600\) | 0.343082 | 0.0140063 | ||||||||
\(601\) | −37.9824 | −1.54934 | −0.774668 | − | 0.632368i | \(-0.782083\pi\) | ||||
−0.774668 | + | 0.632368i | \(0.782083\pi\) | |||||||
\(602\) | −23.9621 | −0.976622 | ||||||||
\(603\) | 39.4876 | 1.60806 | ||||||||
\(604\) | −17.7039 | −0.720362 | ||||||||
\(605\) | 2.34577 | 0.0953691 | ||||||||
\(606\) | −2.37351 | −0.0964174 | ||||||||
\(607\) | 20.0130 | 0.812301 | 0.406151 | − | 0.913806i | \(-0.366871\pi\) | ||||
0.406151 | + | 0.913806i | \(0.366871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.72672 | 0.313103 | ||||||||
\(610\) | 19.3322 | 0.782739 | ||||||||
\(611\) | 44.8048 | 1.81261 | ||||||||
\(612\) | 22.1079 | 0.893657 | ||||||||
\(613\) | −42.1414 | −1.70208 | −0.851038 | − | 0.525105i | \(-0.824026\pi\) | ||||
−0.851038 | + | 0.525105i | \(0.824026\pi\) | |||||||
\(614\) | 7.95057 | 0.320859 | ||||||||
\(615\) | −10.2429 | −0.413034 | ||||||||
\(616\) | 2.05029 | 0.0826085 | ||||||||
\(617\) | 16.9044 | 0.680545 | 0.340273 | − | 0.940327i | \(-0.389481\pi\) | ||||
0.340273 | + | 0.940327i | \(0.389481\pi\) | |||||||
\(618\) | 6.29861 | 0.253367 | ||||||||
\(619\) | 5.31177 | 0.213498 | 0.106749 | − | 0.994286i | \(-0.465956\pi\) | ||||
0.106749 | + | 0.994286i | \(0.465956\pi\) | |||||||
\(620\) | 7.21686 | 0.289836 | ||||||||
\(621\) | −11.2762 | −0.452497 | ||||||||
\(622\) | −13.9144 | −0.557915 | ||||||||
\(623\) | 15.8661 | 0.635662 | ||||||||
\(624\) | 11.3202 | 0.453169 | ||||||||
\(625\) | −27.2605 | −1.09042 | ||||||||
\(626\) | 32.0865 | 1.28243 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.67245 | 0.106642 | ||||||||
\(629\) | −40.4433 | −1.61258 | ||||||||
\(630\) | 19.4536 | 0.775052 | ||||||||
\(631\) | 34.0425 | 1.35521 | 0.677604 | − | 0.735427i | \(-0.263018\pi\) | ||||
0.677604 | + | 0.735427i | \(0.263018\pi\) | |||||||
\(632\) | −6.01113 | −0.239110 | ||||||||
\(633\) | −1.64060 | −0.0652079 | ||||||||
\(634\) | −3.54728 | −0.140880 | ||||||||
\(635\) | −2.51643 | −0.0998615 | ||||||||
\(636\) | −5.97649 | −0.236983 | ||||||||
\(637\) | 17.0051 | 0.673768 | ||||||||
\(638\) | −14.8023 | −0.586030 | ||||||||
\(639\) | 8.37030 | 0.331124 | ||||||||
\(640\) | −21.4847 | −0.849259 | ||||||||
\(641\) | 15.0405 | 0.594063 | 0.297031 | − | 0.954868i | \(-0.404003\pi\) | ||||
0.297031 | + | 0.954868i | \(0.404003\pi\) | |||||||
\(642\) | 0.435291 | 0.0171795 | ||||||||
\(643\) | 32.3618 | 1.27622 | 0.638112 | − | 0.769943i | \(-0.279715\pi\) | ||||
0.638112 | + | 0.769943i | \(0.279715\pi\) | |||||||
\(644\) | 7.96808 | 0.313986 | ||||||||
\(645\) | 10.2441 | 0.403361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −49.0042 | −1.92655 | −0.963276 | − | 0.268512i | \(-0.913468\pi\) | ||||
−0.963276 | + | 0.268512i | \(0.913468\pi\) | |||||||
\(648\) | 7.56424 | 0.297151 | ||||||||
\(649\) | −10.9247 | −0.428833 | ||||||||
\(650\) | 3.77520 | 0.148075 | ||||||||
\(651\) | 2.19447 | 0.0860079 | ||||||||
\(652\) | −25.0725 | −0.981916 | ||||||||
\(653\) | 31.1992 | 1.22092 | 0.610460 | − | 0.792047i | \(-0.290984\pi\) | ||||
0.610460 | + | 0.792047i | \(0.290984\pi\) | |||||||
\(654\) | 14.4271 | 0.564143 | ||||||||
\(655\) | −18.3605 | −0.717406 | ||||||||
\(656\) | 37.8715 | 1.47864 | ||||||||
\(657\) | −31.0712 | −1.21220 | ||||||||
\(658\) | 33.6876 | 1.31328 | ||||||||
\(659\) | 35.7237 | 1.39160 | 0.695799 | − | 0.718237i | \(-0.255050\pi\) | ||||
0.695799 | + | 0.718237i | \(0.255050\pi\) | |||||||
\(660\) | 1.76676 | 0.0687712 | ||||||||
\(661\) | −33.8677 | −1.31730 | −0.658651 | − | 0.752449i | \(-0.728872\pi\) | ||||
−0.658651 | + | 0.752449i | \(0.728872\pi\) | |||||||
\(662\) | 24.4754 | 0.951262 | ||||||||
\(663\) | 14.2817 | 0.554657 | ||||||||
\(664\) | −2.21585 | −0.0859916 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 32.1461 | 1.24564 | ||||||||
\(667\) | 28.5400 | 1.10507 | ||||||||
\(668\) | 8.43788 | 0.326471 | ||||||||
\(669\) | −3.57296 | −0.138139 | ||||||||
\(670\) | 63.0755 | 2.43682 | ||||||||
\(671\) | −4.51162 | −0.174169 | ||||||||
\(672\) | 6.20103 | 0.239210 | ||||||||
\(673\) | −21.1648 | −0.815842 | −0.407921 | − | 0.913017i | \(-0.633746\pi\) | ||||
−0.407921 | + | 0.913017i | \(0.633746\pi\) | |||||||
\(674\) | 60.5786 | 2.33340 | ||||||||
\(675\) | −1.60927 | −0.0619408 | ||||||||
\(676\) | 5.22141 | 0.200824 | ||||||||
\(677\) | 34.5239 | 1.32686 | 0.663431 | − | 0.748238i | \(-0.269100\pi\) | ||||
0.663431 | + | 0.748238i | \(0.269100\pi\) | |||||||
\(678\) | −2.61040 | −0.100252 | ||||||||
\(679\) | 18.6057 | 0.714022 | ||||||||
\(680\) | −17.5199 | −0.671858 | ||||||||
\(681\) | 1.12925 | 0.0432729 | ||||||||
\(682\) | −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 | ||||||||
\(687\) | −11.8257 | −0.451179 | ||||||||
\(688\) | −37.8759 | −1.44401 | ||||||||
\(689\) | 32.6267 | 1.24298 | ||||||||
\(690\) | −8.50291 | −0.323700 | ||||||||
\(691\) | 39.5406 | 1.50419 | 0.752097 | − | 0.659052i | \(-0.229042\pi\) | ||||
0.752097 | + | 0.659052i | \(0.229042\pi\) | |||||||
\(692\) | 28.7769 | 1.09394 | ||||||||
\(693\) | −4.53995 | −0.172458 | ||||||||
\(694\) | −32.9294 | −1.24998 | ||||||||
\(695\) | −2.12510 | −0.0806094 | ||||||||
\(696\) | 5.53106 | 0.209654 | ||||||||
\(697\) | 47.7795 | 1.80978 | ||||||||
\(698\) | −16.1006 | −0.609418 | ||||||||
\(699\) | −9.91646 | −0.375075 | ||||||||
\(700\) | 1.13716 | 0.0429805 | ||||||||
\(701\) | 22.4546 | 0.848097 | 0.424049 | − | 0.905639i | \(-0.360609\pi\) | ||||
0.424049 | + | 0.905639i | \(0.360609\pi\) | |||||||
\(702\) | −24.0468 | −0.907588 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.10636 | −0.0793865 | ||||||||
\(705\) | −14.4019 | −0.542406 | ||||||||
\(706\) | 2.90899 | 0.109481 | ||||||||
\(707\) | 3.90301 | 0.146788 | ||||||||
\(708\) | −8.22818 | −0.309234 | ||||||||
\(709\) | −1.41244 | −0.0530451 | −0.0265226 | − | 0.999648i | \(-0.508443\pi\) | ||||
−0.0265226 | + | 0.999648i | \(0.508443\pi\) | |||||||
\(710\) | 13.3703 | 0.501778 | ||||||||
\(711\) | 13.3104 | 0.499181 | ||||||||
\(712\) | 11.3575 | 0.425641 | ||||||||
\(713\) | 8.10564 | 0.303559 | ||||||||
\(714\) | 10.7381 | 0.401863 | ||||||||
\(715\) | −9.64506 | −0.360705 | ||||||||
\(716\) | 10.6545 | 0.398177 | ||||||||
\(717\) | 14.9985 | 0.560130 | ||||||||
\(718\) | −66.4502 | −2.47990 | ||||||||
\(719\) | −39.0879 | −1.45773 | −0.728867 | − | 0.684655i | \(-0.759953\pi\) | ||||
−0.728867 | + | 0.684655i | \(0.759953\pi\) | |||||||
\(720\) | 30.7496 | 1.14597 | ||||||||
\(721\) | −10.3574 | −0.385731 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.40002 | −0.275210 | ||||||||
\(724\) | 1.56344 | 0.0581049 | ||||||||
\(725\) | 4.07306 | 0.151270 | ||||||||
\(726\) | −1.02918 | −0.0381966 | ||||||||
\(727\) | 9.42098 | 0.349405 | 0.174702 | − | 0.984621i | \(-0.444104\pi\) | ||||
0.174702 | + | 0.984621i | \(0.444104\pi\) | |||||||
\(728\) | −8.43013 | −0.312442 | ||||||||
\(729\) | −11.3379 | −0.419922 | ||||||||
\(730\) | −49.6316 | −1.83695 | ||||||||
\(731\) | −47.7850 | −1.76739 | ||||||||
\(732\) | −3.39801 | −0.125594 | ||||||||
\(733\) | 4.63361 | 0.171146 | 0.0855731 | − | 0.996332i | \(-0.472728\pi\) | ||||
0.0855731 | + | 0.996332i | \(0.472728\pi\) | |||||||
\(734\) | 9.13849 | 0.337308 | ||||||||
\(735\) | −5.46606 | −0.201619 | ||||||||
\(736\) | 22.9046 | 0.844274 | ||||||||
\(737\) | −14.7201 | −0.542222 | ||||||||
\(738\) | −37.9772 | −1.39796 | ||||||||
\(739\) | −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 | \(0.412676\pi\) | |||||||
\(744\) | 1.57087 | 0.0575911 | ||||||||
\(745\) | 24.6715 | 0.903894 | ||||||||
\(746\) | −62.3472 | −2.28269 | ||||||||
\(747\) | 4.90655 | 0.179521 | ||||||||
\(748\) | −8.24132 | −0.301332 | ||||||||
\(749\) | −0.715792 | −0.0261545 | ||||||||
\(750\) | 10.8577 | 0.396466 | ||||||||
\(751\) | −35.0415 | −1.27868 | −0.639341 | − | 0.768924i | \(-0.720793\pi\) | ||||
−0.639341 | + | 0.768924i | \(0.720793\pi\) | |||||||
\(752\) | 53.2487 | 1.94178 | ||||||||
\(753\) | −14.7410 | −0.537191 | ||||||||
\(754\) | 60.8625 | 2.21648 | ||||||||
\(755\) | −31.0664 | −1.13062 | ||||||||
\(756\) | −7.24333 | −0.263437 | ||||||||
\(757\) | −23.8005 | −0.865044 | −0.432522 | − | 0.901623i | \(-0.642376\pi\) | ||||
−0.432522 | + | 0.901623i | \(0.642376\pi\) | |||||||
\(758\) | 28.8158 | 1.04664 | ||||||||
\(759\) | 1.98435 | 0.0720272 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.0282 | −1.41477 | −0.707386 | − | 0.706827i | \(-0.750126\pi\) | ||||
−0.707386 | + | 0.706827i | \(0.750126\pi\) | |||||||
\(762\) | 1.10406 | 0.0399959 | ||||||||
\(763\) | −23.7239 | −0.858862 | ||||||||
\(764\) | −20.9440 | −0.757726 | ||||||||
\(765\) | 38.7943 | 1.40261 | ||||||||
\(766\) | −40.9654 | −1.48014 | ||||||||
\(767\) | 44.9190 | 1.62193 | ||||||||
\(768\) | 11.7997 | 0.425787 | ||||||||
\(769\) | 9.84757 | 0.355113 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(770\) | −7.25189 | −0.261340 | ||||||||
\(771\) | −7.10564 | −0.255903 | ||||||||
\(772\) | −28.9776 | −1.04292 | ||||||||
\(773\) | 42.9837 | 1.54602 | 0.773008 | − | 0.634396i | \(-0.218751\pi\) | ||||
0.773008 | + | 0.634396i | \(0.218751\pi\) | |||||||
\(774\) | 37.9816 | 1.36522 | ||||||||
\(775\) | 1.15679 | 0.0415531 | ||||||||
\(776\) | 13.3186 | 0.478111 | ||||||||
\(777\) | 6.25524 | 0.224405 | ||||||||
\(778\) | 33.5175 | 1.20166 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −7.26437 | −0.260106 | ||||||||
\(781\) | −3.12026 | −0.111652 | ||||||||
\(782\) | 39.6630 | 1.41835 | ||||||||
\(783\) | −25.9441 | −0.927166 | ||||||||
\(784\) | 20.2099 | 0.721783 | ||||||||
\(785\) | 4.68954 | 0.167377 | ||||||||
\(786\) | 8.05552 | 0.287331 | ||||||||
\(787\) | 25.8709 | 0.922199 | 0.461099 | − | 0.887349i | \(-0.347455\pi\) | ||||
0.461099 | + | 0.887349i | \(0.347455\pi\) | |||||||
\(788\) | 6.13313 | 0.218484 | ||||||||
\(789\) | −11.2993 | −0.402266 | ||||||||
\(790\) | 21.2614 | 0.756448 | ||||||||
\(791\) | 4.29254 | 0.152625 | ||||||||
\(792\) | −3.24985 | −0.115479 | ||||||||
\(793\) | 18.5503 | 0.658741 | ||||||||
\(794\) | 0.934320 | 0.0331578 | ||||||||
\(795\) | −10.4874 | −0.371949 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | −25.1489 | −0.888593 | ||||||||
\(802\) | 34.6749 | 1.22441 | ||||||||
\(803\) | 11.5827 | 0.408743 | ||||||||
\(804\) | −11.0867 | −0.390999 | ||||||||
\(805\) | 13.9822 | 0.492807 | ||||||||
\(806\) | 17.2855 | 0.608857 | ||||||||
\(807\) | 11.3331 | 0.398945 | ||||||||
\(808\) | 2.79391 | 0.0982894 | ||||||||
\(809\) | −13.1327 | −0.461720 | −0.230860 | − | 0.972987i | \(-0.574154\pi\) | ||||
−0.230860 | + | 0.972987i | \(0.574154\pi\) | |||||||
\(810\) | −26.7548 | −0.940067 | ||||||||
\(811\) | −9.40230 | −0.330160 | −0.165080 | − | 0.986280i | \(-0.552788\pi\) | ||||
−0.165080 | + | 0.986280i | \(0.552788\pi\) | |||||||
\(812\) | 18.3329 | 0.643358 | ||||||||
\(813\) | 8.76595 | 0.307435 | ||||||||
\(814\) | −11.9834 | −0.420017 | ||||||||
\(815\) | −43.9966 | −1.54114 | ||||||||
\(816\) | 16.9733 | 0.594183 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.01098 | 0.0703124 | ||||||||
\(819\) | 18.6668 | 0.652272 | ||||||||
\(820\) | −24.3029 | −0.848695 | ||||||||
\(821\) | −21.1701 | −0.738843 | −0.369422 | − | 0.929262i | \(-0.620444\pi\) | ||||
−0.369422 | + | 0.929262i | \(0.620444\pi\) | |||||||
\(822\) | 11.5755 | 0.403743 | ||||||||
\(823\) | 25.2277 | 0.879384 | 0.439692 | − | 0.898149i | \(-0.355088\pi\) | ||||
0.439692 | + | 0.898149i | \(0.355088\pi\) | |||||||
\(824\) | −7.41422 | −0.258286 | ||||||||
\(825\) | 0.283194 | 0.00985955 | ||||||||
\(826\) | 33.7735 | 1.17513 | ||||||||
\(827\) | 39.4460 | 1.37167 | 0.685836 | − | 0.727756i | \(-0.259437\pi\) | ||||
0.685836 | + | 0.727756i | \(0.259437\pi\) | |||||||
\(828\) | −12.6300 | −0.438922 | ||||||||
\(829\) | 36.5068 | 1.26793 | 0.633967 | − | 0.773360i | \(-0.281426\pi\) | ||||
0.633967 | + | 0.773360i | \(0.281426\pi\) | |||||||
\(830\) | 7.83748 | 0.272043 | ||||||||
\(831\) | 1.06604 | 0.0369806 | ||||||||
\(832\) | 8.66069 | 0.300255 | ||||||||
\(833\) | 25.4972 | 0.883427 | ||||||||
\(834\) | 0.932366 | 0.0322852 | ||||||||
\(835\) | 14.8066 | 0.512403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.36838 | −0.254688 | ||||||||
\(838\) | 34.3288 | 1.18587 | ||||||||
\(839\) | −42.4670 | −1.46612 | −0.733061 | − | 0.680163i | \(-0.761909\pi\) | ||||
−0.733061 | + | 0.680163i | \(0.761909\pi\) | |||||||
\(840\) | 2.70975 | 0.0934953 | ||||||||
\(841\) | 36.6645 | 1.26429 | ||||||||
\(842\) | −45.2321 | −1.55880 | ||||||||
\(843\) | −2.58776 | −0.0891273 | ||||||||
\(844\) | −3.89258 | −0.133988 | ||||||||
\(845\) | 9.16241 | 0.315196 | ||||||||
\(846\) | −53.3973 | −1.83584 | ||||||||
\(847\) | 1.69239 | 0.0581513 | ||||||||
\(848\) | 38.7755 | 1.33156 | ||||||||
\(849\) | −0.663690 | −0.0227778 | ||||||||
\(850\) | 5.66047 | 0.194153 | ||||||||
\(851\) | 23.1048 | 0.792023 | ||||||||
\(852\) | −2.35009 | −0.0805126 | ||||||||
\(853\) | 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 | \(0.430753\pi\) | |||||||
\(858\) | 4.23168 | 0.144467 | ||||||||
\(859\) | −3.39720 | −0.115911 | −0.0579555 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579555 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(860\) | 24.3057 | 0.828818 | ||||||||
\(861\) | −7.38990 | −0.251847 | ||||||||
\(862\) | −58.8167 | −2.00330 | ||||||||
\(863\) | 10.9308 | 0.372088 | 0.186044 | − | 0.982541i | \(-0.440433\pi\) | ||||
0.186044 | + | 0.982541i | \(0.440433\pi\) | |||||||
\(864\) | −20.8212 | −0.708353 | ||||||||
\(865\) | 50.4971 | 1.71695 | ||||||||
\(866\) | −27.9561 | −0.949987 | ||||||||
\(867\) | 11.8358 | 0.401963 | ||||||||
\(868\) | 5.20672 | 0.176727 | ||||||||
\(869\) | −4.96184 | −0.168319 | ||||||||
\(870\) | −19.5634 | −0.663261 | ||||||||
\(871\) | 60.5243 | 2.05079 | ||||||||
\(872\) | −16.9824 | −0.575096 | ||||||||
\(873\) | −29.4914 | −0.998133 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.8544 | −0.603588 | ||||||||
\(876\) | 8.72371 | 0.294747 | ||||||||
\(877\) | −31.7230 | −1.07121 | −0.535605 | − | 0.844468i | \(-0.679917\pi\) | ||||
−0.535605 | + | 0.844468i | \(0.679917\pi\) | |||||||
\(878\) | 47.8250 | 1.61402 | ||||||||
\(879\) | 6.34439 | 0.213991 | ||||||||
\(880\) | −11.4628 | −0.386410 | ||||||||
\(881\) | −6.45839 | −0.217589 | −0.108794 | − | 0.994064i | \(-0.534699\pi\) | ||||
−0.108794 | + | 0.994064i | \(0.534699\pi\) | |||||||
\(882\) | −20.2663 | −0.682403 | ||||||||
\(883\) | −48.5242 | −1.63297 | −0.816485 | − | 0.577367i | \(-0.804080\pi\) | ||||
−0.816485 | + | 0.577367i | \(0.804080\pi\) | |||||||
\(884\) | 33.8857 | 1.13970 | ||||||||
\(885\) | −14.4386 | −0.485348 | ||||||||
\(886\) | −39.3796 | −1.32298 | ||||||||
\(887\) | 44.0097 | 1.47770 | 0.738851 | − | 0.673869i | \(-0.235369\pi\) | ||||
0.738851 | + | 0.673869i | \(0.235369\pi\) | |||||||
\(888\) | 4.47772 | 0.150262 | ||||||||
\(889\) | −1.81552 | −0.0608905 | ||||||||
\(890\) | −40.1716 | −1.34656 | ||||||||
\(891\) | 6.24383 | 0.209176 | ||||||||
\(892\) | −8.47742 | −0.283845 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −10.8244 | −0.362022 | ||||||||
\(895\) | 18.6962 | 0.624946 | ||||||||
\(896\) | −15.5005 | −0.517835 | ||||||||
\(897\) | −8.15900 | −0.272421 | ||||||||
\(898\) | 21.5531 | 0.719236 | ||||||||
\(899\) | 18.6494 | 0.621991 | ||||||||
\(900\) | −1.80248 | −0.0600825 | ||||||||
\(901\) | 48.9199 | 1.62976 | ||||||||
\(902\) | 14.1571 | 0.471379 | ||||||||
\(903\) | 7.39076 | 0.245949 | ||||||||
\(904\) | 3.07275 | 0.102198 | ||||||||
\(905\) | 2.74349 | 0.0911966 | ||||||||
\(906\) | 13.6301 | 0.452829 | ||||||||
\(907\) | 2.05084 | 0.0680971 | 0.0340485 | − | 0.999420i | \(-0.489160\pi\) | ||||
0.0340485 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(908\) | 2.67932 | 0.0889164 | ||||||||
\(909\) | −6.18655 | −0.205195 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | −5.96275 | −0.197122 | ||||||||
\(916\) | −28.0584 | −0.927075 | ||||||||
\(917\) | −13.2465 | −0.437438 | ||||||||
\(918\) | −36.0554 | −1.19001 | ||||||||
\(919\) | 8.01221 | 0.264299 | 0.132149 | − | 0.991230i | \(-0.457812\pi\) | ||||
0.132149 | + | 0.991230i | \(0.457812\pi\) | |||||||
\(920\) | 10.0089 | 0.329985 | ||||||||
\(921\) | −2.45224 | −0.0808039 | ||||||||
\(922\) | −49.7683 | −1.63903 | ||||||||
\(923\) | 12.8295 | 0.422289 | ||||||||
\(924\) | 1.27466 | 0.0419332 | ||||||||
\(925\) | 3.29738 | 0.108417 | ||||||||
\(926\) | 32.7641 | 1.07670 | ||||||||
\(927\) | 16.4173 | 0.539214 | ||||||||
\(928\) | 52.6986 | 1.72992 | ||||||||
\(929\) | 16.7897 | 0.550853 | 0.275426 | − | 0.961322i | \(-0.411181\pi\) | ||||
0.275426 | + | 0.961322i | \(0.411181\pi\) | |||||||
\(930\) | −5.55620 | −0.182195 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.5284 | −0.770698 | ||||||||
\(933\) | 4.29168 | 0.140503 | ||||||||
\(934\) | −52.9922 | −1.73396 | ||||||||
\(935\) | −14.4617 | −0.472947 | ||||||||
\(936\) | 13.3624 | 0.436763 | ||||||||
\(937\) | 21.8471 | 0.713713 | 0.356856 | − | 0.934159i | \(-0.383849\pi\) | ||||
0.356856 | + | 0.934159i | \(0.383849\pi\) | |||||||
\(938\) | 45.5068 | 1.48585 | ||||||||
\(939\) | −9.89661 | −0.322964 | ||||||||
\(940\) | −34.1707 | −1.11453 | ||||||||
\(941\) | −17.8421 | −0.581635 | −0.290817 | − | 0.956779i | \(-0.593927\pi\) | ||||
−0.290817 | + | 0.956779i | \(0.593927\pi\) | |||||||
\(942\) | −2.05749 | −0.0670368 | ||||||||
\(943\) | −27.2959 | −0.888877 | ||||||||
\(944\) | 53.3845 | 1.73752 | ||||||||
\(945\) | −12.7104 | −0.413470 | ||||||||
\(946\) | −14.1587 | −0.460339 | ||||||||
\(947\) | 41.9736 | 1.36396 | 0.681980 | − | 0.731371i | \(-0.261119\pi\) | ||||
0.681980 | + | 0.731371i | \(0.261119\pi\) | |||||||
\(948\) | −3.73711 | −0.121376 | ||||||||
\(949\) | −47.6242 | −1.54595 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.09411 | 0.0354788 | ||||||||
\(952\) | −12.6400 | −0.409665 | ||||||||
\(953\) | 8.06945 | 0.261395 | 0.130697 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130697 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(954\) | −38.8837 | −1.25891 | ||||||||
\(955\) | −36.7520 | −1.18927 | ||||||||
\(956\) | 35.5864 | 1.15094 | ||||||||
\(957\) | 4.56556 | 0.147584 | ||||||||
\(958\) | −62.2711 | −2.01189 | ||||||||
\(959\) | −19.0348 | −0.614666 | ||||||||
\(960\) | −2.78386 | −0.0898487 | ||||||||
\(961\) | −25.7034 | −0.829142 | ||||||||
\(962\) | 49.2718 | 1.58859 | ||||||||
\(963\) | 1.13458 | 0.0365614 | ||||||||
\(964\) | −17.5577 | −0.565496 | ||||||||
\(965\) | −50.8491 | −1.63689 | ||||||||
\(966\) | −6.13455 | −0.197376 | ||||||||
\(967\) | −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 | \(0.740818\pi\) | |||||||
\(972\) | 17.5425 | 0.562675 | ||||||||
\(973\) | −1.53318 | −0.0491516 | ||||||||
\(974\) | 11.6607 | 0.373631 | ||||||||
\(975\) | −1.16440 | −0.0372908 | ||||||||
\(976\) | 22.0463 | 0.705686 | ||||||||
\(977\) | −54.5146 | −1.74408 | −0.872039 | − | 0.489437i | \(-0.837202\pi\) | ||||
−0.872039 | + | 0.489437i | \(0.837202\pi\) | |||||||
\(978\) | 19.3031 | 0.617246 | ||||||||
\(979\) | 9.37496 | 0.299625 | ||||||||
\(980\) | −12.9691 | −0.414283 | ||||||||
\(981\) | 37.6040 | 1.20060 | ||||||||
\(982\) | 57.4590 | 1.83359 | ||||||||
\(983\) | −33.5422 | −1.06983 | −0.534916 | − | 0.844905i | \(-0.679657\pi\) | ||||
−0.534916 | + | 0.844905i | \(0.679657\pi\) | |||||||
\(984\) | −5.28995 | −0.168637 | ||||||||
\(985\) | 10.7623 | 0.342914 | ||||||||
\(986\) | 91.2562 | 2.90619 | ||||||||
\(987\) | −10.3905 | −0.330732 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.2991 | 0.868060 | ||||||||
\(990\) | 11.4948 | 0.365328 | ||||||||
\(991\) | −31.7767 | −1.00942 | −0.504710 | − | 0.863289i | \(-0.668400\pi\) | ||||
−0.504710 | + | 0.863289i | \(0.668400\pi\) | |||||||
\(992\) | 14.9669 | 0.475200 | ||||||||
\(993\) | −7.54907 | −0.239562 | ||||||||
\(994\) | 9.64621 | 0.305959 | ||||||||
\(995\) | 30.6403 | 0.971363 | ||||||||
\(996\) | −1.37759 | −0.0436505 | ||||||||
\(997\) | −47.5668 | −1.50646 | −0.753228 | − | 0.657759i | \(-0.771504\pi\) | ||||
−0.753228 | + | 0.657759i | \(0.771504\pi\) | |||||||
\(998\) | 58.3933 | 1.84841 | ||||||||
\(999\) | −21.0033 | −0.664515 |
(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 | 3971.2.a.h.1.2 | 5 | ||
19.18 | odd | 2 | 209.2.a.c.1.4 | ✓ | 5 | ||
57.56 | even | 2 | 1881.2.a.k.1.2 | 5 | |||
76.75 | even | 2 | 3344.2.a.t.1.4 | 5 | |||
95.94 | odd | 2 | 5225.2.a.h.1.2 | 5 | |||
209.208 | even | 2 | 2299.2.a.n.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.c.1.4 | ✓ | 5 | 19.18 | odd | 2 | ||
1881.2.a.k.1.2 | 5 | 57.56 | even | 2 | |||
2299.2.a.n.1.2 | 5 | 209.208 | even | 2 | |||
3344.2.a.t.1.4 | 5 | 76.75 | even | 2 | |||
3971.2.a.h.1.2 | 5 | 1.1 | even | 1 | trivial | ||
5225.2.a.h.1.2 | 5 | 95.94 | odd | 2 |