Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.352076.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.567739\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52275 | −1.78385 | −0.891926 | − | 0.452181i | \(-0.850646\pi\) | ||||
−0.891926 | + | 0.452181i | \(0.850646\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.36426 | 2.18213 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.52275 | −1.02991 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.96443 | −2.10874 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.52275 | 0.797763 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 4.36426 | 1.25985 | ||||||||
\(13\) | 5.44168 | 1.50925 | 0.754625 | − | 0.656156i | \(-0.227819\pi\) | ||||
0.754625 | + | 0.656156i | \(0.227819\pi\) | |||||||
\(14\) | −2.52275 | −0.674233 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 6.31823 | 1.57956 | ||||||||
\(17\) | 1.41028 | 0.342044 | 0.171022 | − | 0.985267i | \(-0.445293\pi\) | ||||
0.171022 | + | 0.985267i | \(0.445293\pi\) | |||||||
\(18\) | −2.52275 | −0.594617 | ||||||||
\(19\) | −1.36426 | −0.312982 | −0.156491 | − | 0.987679i | \(-0.550018\pi\) | ||||
−0.156491 | + | 0.987679i | \(0.550018\pi\) | |||||||
\(20\) | −4.36426 | −0.975878 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.52275 | −0.537852 | ||||||||
\(23\) | −8.40975 | −1.75355 | −0.876777 | − | 0.480896i | \(-0.840311\pi\) | ||||
−0.876777 | + | 0.480896i | \(0.840311\pi\) | |||||||
\(24\) | −5.96443 | −1.21748 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.7280 | −2.69228 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.36426 | 0.824767 | ||||||||
\(29\) | 8.75991 | 1.62667 | 0.813337 | − | 0.581792i | \(-0.197648\pi\) | ||||
0.813337 | + | 0.581792i | \(0.197648\pi\) | |||||||
\(30\) | 2.52275 | 0.460589 | ||||||||
\(31\) | 3.60382 | 0.647265 | 0.323632 | − | 0.946183i | \(-0.395096\pi\) | ||||
0.323632 | + | 0.946183i | \(0.395096\pi\) | |||||||
\(32\) | −4.01045 | −0.708955 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −3.55779 | −0.610156 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.36426 | 0.727376 | ||||||||
\(37\) | 3.48771 | 0.573375 | 0.286688 | − | 0.958024i | \(-0.407446\pi\) | ||||
0.286688 | + | 0.958024i | \(0.407446\pi\) | |||||||
\(38\) | 3.44168 | 0.558314 | ||||||||
\(39\) | 5.44168 | 0.871366 | ||||||||
\(40\) | 5.96443 | 0.943059 | ||||||||
\(41\) | 10.4411 | 1.63063 | 0.815317 | − | 0.579015i | \(-0.196563\pi\) | ||||
0.815317 | + | 0.579015i | \(0.196563\pi\) | |||||||
\(42\) | −2.52275 | −0.389268 | ||||||||
\(43\) | −11.5345 | −1.75899 | −0.879494 | − | 0.475910i | \(-0.842119\pi\) | ||||
−0.879494 | + | 0.475910i | \(0.842119\pi\) | |||||||
\(44\) | 4.36426 | 0.657937 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 21.2157 | 3.12808 | ||||||||
\(47\) | −8.21622 | −1.19846 | −0.599230 | − | 0.800577i | \(-0.704526\pi\) | ||||
−0.599230 | + | 0.800577i | \(0.704526\pi\) | |||||||
\(48\) | 6.31823 | 0.911958 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.52275 | −0.356770 | ||||||||
\(51\) | 1.41028 | 0.197479 | ||||||||
\(52\) | 23.7489 | 3.29338 | ||||||||
\(53\) | −5.31823 | −0.730515 | −0.365258 | − | 0.930906i | \(-0.619019\pi\) | ||||
−0.365258 | + | 0.930906i | \(0.619019\pi\) | |||||||
\(54\) | −2.52275 | −0.343303 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −5.96443 | −0.797030 | ||||||||
\(57\) | −1.36426 | −0.180700 | ||||||||
\(58\) | −22.0991 | −2.90175 | ||||||||
\(59\) | 7.07689 | 0.921333 | 0.460666 | − | 0.887573i | \(-0.347610\pi\) | ||||
0.460666 | + | 0.887573i | \(0.347610\pi\) | |||||||
\(60\) | −4.36426 | −0.563423 | ||||||||
\(61\) | 3.52640 | 0.451509 | 0.225754 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225754 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(62\) | −9.09152 | −1.15462 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −2.51910 | −0.314888 | ||||||||
\(65\) | −5.44168 | −0.674957 | ||||||||
\(66\) | −2.52275 | −0.310529 | ||||||||
\(67\) | −1.09152 | −0.133351 | −0.0666753 | − | 0.997775i | \(-0.521239\pi\) | ||||
−0.0666753 | + | 0.997775i | \(0.521239\pi\) | |||||||
\(68\) | 6.15484 | 0.746384 | ||||||||
\(69\) | −8.40975 | −1.01242 | ||||||||
\(70\) | 2.52275 | 0.301526 | ||||||||
\(71\) | 4.69534 | 0.557234 | 0.278617 | − | 0.960402i | \(-0.410124\pi\) | ||||
0.278617 | + | 0.960402i | \(0.410124\pi\) | |||||||
\(72\) | −5.96443 | −0.702915 | ||||||||
\(73\) | 7.31645 | 0.856326 | 0.428163 | − | 0.903702i | \(-0.359161\pi\) | ||||
0.428163 | + | 0.903702i | \(0.359161\pi\) | |||||||
\(74\) | −8.79860 | −1.02282 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −5.95397 | −0.682968 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −13.7280 | −1.55439 | ||||||||
\(79\) | 4.55832 | 0.512851 | 0.256426 | − | 0.966564i | \(-0.417455\pi\) | ||||
0.256426 | + | 0.966564i | \(0.417455\pi\) | |||||||
\(80\) | −6.31823 | −0.706400 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −26.3404 | −2.90881 | ||||||||
\(83\) | −9.51910 | −1.04486 | −0.522429 | − | 0.852683i | \(-0.674974\pi\) | ||||
−0.522429 | + | 0.852683i | \(0.674974\pi\) | |||||||
\(84\) | 4.36426 | 0.476180 | ||||||||
\(85\) | −1.41028 | −0.152967 | ||||||||
\(86\) | 29.0985 | 3.13777 | ||||||||
\(87\) | 8.75991 | 0.939161 | ||||||||
\(88\) | −5.96443 | −0.635810 | ||||||||
\(89\) | −16.7421 | −1.77466 | −0.887329 | − | 0.461137i | \(-0.847442\pi\) | ||||
−0.887329 | + | 0.461137i | \(0.847442\pi\) | |||||||
\(90\) | 2.52275 | 0.265921 | ||||||||
\(91\) | 5.44168 | 0.570443 | ||||||||
\(92\) | −36.7023 | −3.82648 | ||||||||
\(93\) | 3.60382 | 0.373698 | ||||||||
\(94\) | 20.7275 | 2.13787 | ||||||||
\(95\) | 1.36426 | 0.139970 | ||||||||
\(96\) | −4.01045 | −0.409315 | ||||||||
\(97\) | 16.2630 | 1.65125 | 0.825627 | − | 0.564216i | \(-0.190821\pi\) | ||||
0.825627 | + | 0.564216i | \(0.190821\pi\) | |||||||
\(98\) | −2.52275 | −0.254836 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 4.36426 | 0.436426 | ||||||||
\(101\) | 14.9816 | 1.49073 | 0.745365 | − | 0.666657i | \(-0.232275\pi\) | ||||
0.745365 | + | 0.666657i | \(0.232275\pi\) | |||||||
\(102\) | −3.55779 | −0.352274 | ||||||||
\(103\) | 2.07742 | 0.204694 | 0.102347 | − | 0.994749i | \(-0.467365\pi\) | ||||
0.102347 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(104\) | −32.4565 | −3.18262 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 13.4166 | 1.30313 | ||||||||
\(107\) | 13.3778 | 1.29328 | 0.646642 | − | 0.762794i | \(-0.276173\pi\) | ||||
0.646642 | + | 0.762794i | \(0.276173\pi\) | |||||||
\(108\) | 4.36426 | 0.419951 | ||||||||
\(109\) | −10.2790 | −0.984551 | −0.492275 | − | 0.870439i | \(-0.663835\pi\) | ||||
−0.492275 | + | 0.870439i | \(0.663835\pi\) | |||||||
\(110\) | 2.52275 | 0.240535 | ||||||||
\(111\) | 3.48771 | 0.331038 | ||||||||
\(112\) | 6.31823 | 0.597017 | ||||||||
\(113\) | 8.29364 | 0.780200 | 0.390100 | − | 0.920772i | \(-0.372440\pi\) | ||||
0.390100 | + | 0.920772i | \(0.372440\pi\) | |||||||
\(114\) | 3.44168 | 0.322343 | ||||||||
\(115\) | 8.40975 | 0.784214 | ||||||||
\(116\) | 38.2305 | 3.54961 | ||||||||
\(117\) | 5.44168 | 0.503083 | ||||||||
\(118\) | −17.8532 | −1.64352 | ||||||||
\(119\) | 1.41028 | 0.129281 | ||||||||
\(120\) | 5.96443 | 0.544475 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.89621 | −0.805425 | ||||||||
\(123\) | 10.4411 | 0.941447 | ||||||||
\(124\) | 15.7280 | 1.41241 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.52275 | −0.224744 | ||||||||
\(127\) | 12.8687 | 1.14192 | 0.570958 | − | 0.820980i | \(-0.306572\pi\) | ||||
0.570958 | + | 0.820980i | \(0.306572\pi\) | |||||||
\(128\) | 14.3760 | 1.27067 | ||||||||
\(129\) | −11.5345 | −1.01555 | ||||||||
\(130\) | 13.7280 | 1.20402 | ||||||||
\(131\) | 11.4239 | 0.998107 | 0.499053 | − | 0.866571i | \(-0.333681\pi\) | ||||
0.499053 | + | 0.866571i | \(0.333681\pi\) | |||||||
\(132\) | 4.36426 | 0.379860 | ||||||||
\(133\) | −1.36426 | −0.118296 | ||||||||
\(134\) | 2.75364 | 0.237878 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −8.41154 | −0.721283 | ||||||||
\(137\) | 7.61187 | 0.650326 | 0.325163 | − | 0.945658i | \(-0.394581\pi\) | ||||
0.325163 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(138\) | 21.2157 | 1.80600 | ||||||||
\(139\) | −9.31645 | −0.790211 | −0.395106 | − | 0.918636i | \(-0.629292\pi\) | ||||
−0.395106 | + | 0.918636i | \(0.629292\pi\) | |||||||
\(140\) | −4.36426 | −0.368847 | ||||||||
\(141\) | −8.21622 | −0.691931 | ||||||||
\(142\) | −11.8452 | −0.994024 | ||||||||
\(143\) | 5.44168 | 0.455056 | ||||||||
\(144\) | 6.31823 | 0.526519 | ||||||||
\(145\) | −8.75991 | −0.727471 | ||||||||
\(146\) | −18.4576 | −1.52756 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 15.2212 | 1.25118 | ||||||||
\(149\) | 14.1370 | 1.15815 | 0.579075 | − | 0.815274i | \(-0.303414\pi\) | ||||
0.579075 | + | 0.815274i | \(0.303414\pi\) | |||||||
\(150\) | −2.52275 | −0.205982 | ||||||||
\(151\) | −7.56585 | −0.615700 | −0.307850 | − | 0.951435i | \(-0.599610\pi\) | ||||
−0.307850 | + | 0.951435i | \(0.599610\pi\) | |||||||
\(152\) | 8.13702 | 0.659999 | ||||||||
\(153\) | 1.41028 | 0.114015 | ||||||||
\(154\) | −2.52275 | −0.203289 | ||||||||
\(155\) | −3.60382 | −0.289466 | ||||||||
\(156\) | 23.7489 | 1.90143 | ||||||||
\(157\) | −21.5972 | −1.72365 | −0.861824 | − | 0.507208i | \(-0.830678\pi\) | ||||
−0.861824 | + | 0.507208i | \(0.830678\pi\) | |||||||
\(158\) | −11.4995 | −0.914851 | ||||||||
\(159\) | −5.31823 | −0.421763 | ||||||||
\(160\) | 4.01045 | 0.317054 | ||||||||
\(161\) | −8.40975 | −0.662781 | ||||||||
\(162\) | −2.52275 | −0.198206 | ||||||||
\(163\) | 17.0608 | 1.33631 | 0.668154 | − | 0.744023i | \(-0.267085\pi\) | ||||
0.668154 | + | 0.744023i | \(0.267085\pi\) | |||||||
\(164\) | 45.5679 | 3.55825 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 24.0143 | 1.86387 | ||||||||
\(167\) | 0.866594 | 0.0670590 | 0.0335295 | − | 0.999438i | \(-0.489325\pi\) | ||||
0.0335295 | + | 0.999438i | \(0.489325\pi\) | |||||||
\(168\) | −5.96443 | −0.460166 | ||||||||
\(169\) | 16.6119 | 1.27784 | ||||||||
\(170\) | 3.55779 | 0.272870 | ||||||||
\(171\) | −1.36426 | −0.104327 | ||||||||
\(172\) | −50.3393 | −3.83834 | ||||||||
\(173\) | 10.0628 | 0.765060 | 0.382530 | − | 0.923943i | \(-0.375053\pi\) | ||||
0.382530 | + | 0.923943i | \(0.375053\pi\) | |||||||
\(174\) | −22.0991 | −1.67532 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 6.31823 | 0.476255 | ||||||||
\(177\) | 7.07689 | 0.531932 | ||||||||
\(178\) | 42.2361 | 3.16573 | ||||||||
\(179\) | 2.42024 | 0.180897 | 0.0904487 | − | 0.995901i | \(-0.471170\pi\) | ||||
0.0904487 | + | 0.995901i | \(0.471170\pi\) | |||||||
\(180\) | −4.36426 | −0.325293 | ||||||||
\(181\) | 2.54191 | 0.188939 | 0.0944693 | − | 0.995528i | \(-0.469885\pi\) | ||||
0.0944693 | + | 0.995528i | \(0.469885\pi\) | |||||||
\(182\) | −13.7280 | −1.01759 | ||||||||
\(183\) | 3.52640 | 0.260679 | ||||||||
\(184\) | 50.1594 | 3.69780 | ||||||||
\(185\) | −3.48771 | −0.256421 | ||||||||
\(186\) | −9.09152 | −0.666623 | ||||||||
\(187\) | 1.41028 | 0.103130 | ||||||||
\(188\) | −35.8577 | −2.61519 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −3.44168 | −0.249686 | ||||||||
\(191\) | 24.0899 | 1.74309 | 0.871543 | − | 0.490319i | \(-0.163120\pi\) | ||||
0.871543 | + | 0.490319i | \(0.163120\pi\) | |||||||
\(192\) | −2.51910 | −0.181800 | ||||||||
\(193\) | 7.77401 | 0.559586 | 0.279793 | − | 0.960060i | \(-0.409734\pi\) | ||||
0.279793 | + | 0.960060i | \(0.409734\pi\) | |||||||
\(194\) | −41.0274 | −2.94559 | ||||||||
\(195\) | −5.44168 | −0.389687 | ||||||||
\(196\) | 4.36426 | 0.311733 | ||||||||
\(197\) | −0.425797 | −0.0303368 | −0.0151684 | − | 0.999885i | \(-0.504828\pi\) | ||||
−0.0151684 | + | 0.999885i | \(0.504828\pi\) | |||||||
\(198\) | −2.52275 | −0.179284 | ||||||||
\(199\) | 11.8200 | 0.837900 | 0.418950 | − | 0.908009i | \(-0.362398\pi\) | ||||
0.418950 | + | 0.908009i | \(0.362398\pi\) | |||||||
\(200\) | −5.96443 | −0.421749 | ||||||||
\(201\) | −1.09152 | −0.0769900 | ||||||||
\(202\) | −37.7949 | −2.65924 | ||||||||
\(203\) | 8.75991 | 0.614825 | ||||||||
\(204\) | 6.15484 | 0.430925 | ||||||||
\(205\) | −10.4411 | −0.729242 | ||||||||
\(206\) | −5.24081 | −0.365145 | ||||||||
\(207\) | −8.40975 | −0.584518 | ||||||||
\(208\) | 34.3818 | 2.38395 | ||||||||
\(209\) | −1.36426 | −0.0943677 | ||||||||
\(210\) | 2.52275 | 0.174086 | ||||||||
\(211\) | −24.2305 | −1.66810 | −0.834049 | − | 0.551691i | \(-0.813983\pi\) | ||||
−0.834049 | + | 0.551691i | \(0.813983\pi\) | |||||||
\(212\) | −23.2101 | −1.59408 | ||||||||
\(213\) | 4.69534 | 0.321719 | ||||||||
\(214\) | −33.7489 | −2.30703 | ||||||||
\(215\) | 11.5345 | 0.786643 | ||||||||
\(216\) | −5.96443 | −0.405828 | ||||||||
\(217\) | 3.60382 | 0.244643 | ||||||||
\(218\) | 25.9314 | 1.75629 | ||||||||
\(219\) | 7.31645 | 0.494400 | ||||||||
\(220\) | −4.36426 | −0.294238 | ||||||||
\(221\) | 7.67431 | 0.516230 | ||||||||
\(222\) | −8.79860 | −0.590523 | ||||||||
\(223\) | 2.62289 | 0.175642 | 0.0878210 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878210 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(224\) | −4.01045 | −0.267960 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −20.9228 | −1.39176 | ||||||||
\(227\) | −3.02281 | −0.200631 | −0.100315 | − | 0.994956i | \(-0.531985\pi\) | ||||
−0.100315 | + | 0.994956i | \(0.531985\pi\) | |||||||
\(228\) | −5.95397 | −0.394312 | ||||||||
\(229\) | −3.23725 | −0.213923 | −0.106962 | − | 0.994263i | \(-0.534112\pi\) | ||||
−0.106962 | + | 0.994263i | \(0.534112\pi\) | |||||||
\(230\) | −21.2157 | −1.39892 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −52.2479 | −3.43024 | ||||||||
\(233\) | −18.0363 | −1.18159 | −0.590797 | − | 0.806820i | \(-0.701187\pi\) | ||||
−0.590797 | + | 0.806820i | \(0.701187\pi\) | |||||||
\(234\) | −13.7280 | −0.897427 | ||||||||
\(235\) | 8.21622 | 0.535967 | ||||||||
\(236\) | 30.8854 | 2.01047 | ||||||||
\(237\) | 4.55832 | 0.296095 | ||||||||
\(238\) | −3.55779 | −0.230617 | ||||||||
\(239\) | 9.44346 | 0.610847 | 0.305423 | − | 0.952217i | \(-0.401202\pi\) | ||||
0.305423 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(240\) | −6.31823 | −0.407840 | ||||||||
\(241\) | 16.7662 | 1.08001 | 0.540003 | − | 0.841663i | \(-0.318423\pi\) | ||||
0.540003 | + | 0.841663i | \(0.318423\pi\) | |||||||
\(242\) | −2.52275 | −0.162168 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.3901 | 0.985250 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −26.3404 | −1.67940 | ||||||||
\(247\) | −7.42385 | −0.472369 | ||||||||
\(248\) | −21.4947 | −1.36492 | ||||||||
\(249\) | −9.51910 | −0.603249 | ||||||||
\(250\) | 2.52275 | 0.159553 | ||||||||
\(251\) | −27.8200 | −1.75599 | −0.877993 | − | 0.478674i | \(-0.841118\pi\) | ||||
−0.877993 | + | 0.478674i | \(0.841118\pi\) | |||||||
\(252\) | 4.36426 | 0.274922 | ||||||||
\(253\) | −8.40975 | −0.528717 | ||||||||
\(254\) | −32.4646 | −2.03701 | ||||||||
\(255\) | −1.41028 | −0.0883154 | ||||||||
\(256\) | −31.2287 | −1.95180 | ||||||||
\(257\) | −13.5159 | −0.843099 | −0.421550 | − | 0.906805i | \(-0.638514\pi\) | ||||
−0.421550 | + | 0.906805i | \(0.638514\pi\) | |||||||
\(258\) | 29.0985 | 1.81159 | ||||||||
\(259\) | 3.48771 | 0.216715 | ||||||||
\(260\) | −23.7489 | −1.47284 | ||||||||
\(261\) | 8.75991 | 0.542225 | ||||||||
\(262\) | −28.8195 | −1.78048 | ||||||||
\(263\) | −1.95397 | −0.120487 | −0.0602436 | − | 0.998184i | \(-0.519188\pi\) | ||||
−0.0602436 | + | 0.998184i | \(0.519188\pi\) | |||||||
\(264\) | −5.96443 | −0.367085 | ||||||||
\(265\) | 5.31823 | 0.326696 | ||||||||
\(266\) | 3.44168 | 0.211023 | ||||||||
\(267\) | −16.7421 | −1.02460 | ||||||||
\(268\) | −4.76368 | −0.290988 | ||||||||
\(269\) | −12.2323 | −0.745814 | −0.372907 | − | 0.927869i | \(-0.621639\pi\) | ||||
−0.372907 | + | 0.927869i | \(0.621639\pi\) | |||||||
\(270\) | 2.52275 | 0.153530 | ||||||||
\(271\) | −27.8877 | −1.69406 | −0.847028 | − | 0.531548i | \(-0.821611\pi\) | ||||
−0.847028 | + | 0.531548i | \(0.821611\pi\) | |||||||
\(272\) | 8.91050 | 0.540278 | ||||||||
\(273\) | 5.44168 | 0.329345 | ||||||||
\(274\) | −19.2028 | −1.16009 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −36.7023 | −2.20922 | ||||||||
\(277\) | −8.34518 | −0.501413 | −0.250707 | − | 0.968063i | \(-0.580663\pi\) | ||||
−0.250707 | + | 0.968063i | \(0.580663\pi\) | |||||||
\(278\) | 23.5031 | 1.40962 | ||||||||
\(279\) | 3.60382 | 0.215755 | ||||||||
\(280\) | 5.96443 | 0.356443 | ||||||||
\(281\) | 18.1998 | 1.08571 | 0.542855 | − | 0.839827i | \(-0.317343\pi\) | ||||
0.542855 | + | 0.839827i | \(0.317343\pi\) | |||||||
\(282\) | 20.7275 | 1.23430 | ||||||||
\(283\) | −7.49021 | −0.445247 | −0.222623 | − | 0.974905i | \(-0.571462\pi\) | ||||
−0.222623 | + | 0.974905i | \(0.571462\pi\) | |||||||
\(284\) | 20.4917 | 1.21596 | ||||||||
\(285\) | 1.36426 | 0.0808117 | ||||||||
\(286\) | −13.7280 | −0.811753 | ||||||||
\(287\) | 10.4411 | 0.616322 | ||||||||
\(288\) | −4.01045 | −0.236318 | ||||||||
\(289\) | −15.0111 | −0.883006 | ||||||||
\(290\) | 22.0991 | 1.29770 | ||||||||
\(291\) | 16.2630 | 0.953352 | ||||||||
\(292\) | 31.9309 | 1.86861 | ||||||||
\(293\) | −5.15983 | −0.301440 | −0.150720 | − | 0.988576i | \(-0.548159\pi\) | ||||
−0.150720 | + | 0.988576i | \(0.548159\pi\) | |||||||
\(294\) | −2.52275 | −0.147130 | ||||||||
\(295\) | −7.07689 | −0.412033 | ||||||||
\(296\) | −20.8022 | −1.20910 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −35.6641 | −2.06597 | ||||||||
\(299\) | −45.7632 | −2.64655 | ||||||||
\(300\) | 4.36426 | 0.251971 | ||||||||
\(301\) | −11.5345 | −0.664835 | ||||||||
\(302\) | 19.0867 | 1.09832 | ||||||||
\(303\) | 14.9816 | 0.860673 | ||||||||
\(304\) | −8.61970 | −0.494374 | ||||||||
\(305\) | −3.52640 | −0.201921 | ||||||||
\(306\) | −3.55779 | −0.203385 | ||||||||
\(307\) | 16.8859 | 0.963727 | 0.481864 | − | 0.876246i | \(-0.339960\pi\) | ||||
0.481864 | + | 0.876246i | \(0.339960\pi\) | |||||||
\(308\) | 4.36426 | 0.248677 | ||||||||
\(309\) | 2.07742 | 0.118180 | ||||||||
\(310\) | 9.09152 | 0.516364 | ||||||||
\(311\) | −15.0633 | −0.854163 | −0.427081 | − | 0.904213i | \(-0.640458\pi\) | ||||
−0.427081 | + | 0.904213i | \(0.640458\pi\) | |||||||
\(312\) | −32.4565 | −1.83749 | ||||||||
\(313\) | −14.8687 | −0.840430 | −0.420215 | − | 0.907425i | \(-0.638045\pi\) | ||||
−0.420215 | + | 0.907425i | \(0.638045\pi\) | |||||||
\(314\) | 54.4844 | 3.07473 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 19.8937 | 1.11911 | ||||||||
\(317\) | 31.0015 | 1.74122 | 0.870609 | − | 0.491976i | \(-0.163725\pi\) | ||||
0.870609 | + | 0.491976i | \(0.163725\pi\) | |||||||
\(318\) | 13.4166 | 0.752363 | ||||||||
\(319\) | 8.75991 | 0.490461 | ||||||||
\(320\) | 2.51910 | 0.140822 | ||||||||
\(321\) | 13.3778 | 0.746678 | ||||||||
\(322\) | 21.2157 | 1.18230 | ||||||||
\(323\) | −1.92399 | −0.107054 | ||||||||
\(324\) | 4.36426 | 0.242459 | ||||||||
\(325\) | 5.44168 | 0.301850 | ||||||||
\(326\) | −43.0402 | −2.38378 | ||||||||
\(327\) | −10.2790 | −0.568431 | ||||||||
\(328\) | −62.2755 | −3.43859 | ||||||||
\(329\) | −8.21622 | −0.452975 | ||||||||
\(330\) | 2.52275 | 0.138873 | ||||||||
\(331\) | 13.6597 | 0.750804 | 0.375402 | − | 0.926862i | \(-0.377505\pi\) | ||||
0.375402 | + | 0.926862i | \(0.377505\pi\) | |||||||
\(332\) | −41.5438 | −2.28001 | ||||||||
\(333\) | 3.48771 | 0.191125 | ||||||||
\(334\) | −2.18620 | −0.119623 | ||||||||
\(335\) | 1.09152 | 0.0596362 | ||||||||
\(336\) | 6.31823 | 0.344688 | ||||||||
\(337\) | −21.3060 | −1.16061 | −0.580305 | − | 0.814399i | \(-0.697067\pi\) | ||||
−0.580305 | + | 0.814399i | \(0.697067\pi\) | |||||||
\(338\) | −41.9076 | −2.27947 | ||||||||
\(339\) | 8.29364 | 0.450449 | ||||||||
\(340\) | −6.15484 | −0.333793 | ||||||||
\(341\) | 3.60382 | 0.195158 | ||||||||
\(342\) | 3.44168 | 0.186105 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 68.7964 | 3.70925 | ||||||||
\(345\) | 8.40975 | 0.452766 | ||||||||
\(346\) | −25.3859 | −1.36475 | ||||||||
\(347\) | −28.6358 | −1.53725 | −0.768626 | − | 0.639699i | \(-0.779059\pi\) | ||||
−0.768626 | + | 0.639699i | \(0.779059\pi\) | |||||||
\(348\) | 38.2305 | 2.04937 | ||||||||
\(349\) | −4.50075 | −0.240919 | −0.120460 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120460 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(350\) | −2.52275 | −0.134847 | ||||||||
\(351\) | 5.44168 | 0.290455 | ||||||||
\(352\) | −4.01045 | −0.213758 | ||||||||
\(353\) | −7.51838 | −0.400163 | −0.200081 | − | 0.979779i | \(-0.564121\pi\) | ||||
−0.200081 | + | 0.979779i | \(0.564121\pi\) | |||||||
\(354\) | −17.8532 | −0.948888 | ||||||||
\(355\) | −4.69534 | −0.249203 | ||||||||
\(356\) | −73.0668 | −3.87253 | ||||||||
\(357\) | 1.41028 | 0.0746401 | ||||||||
\(358\) | −6.10566 | −0.322694 | ||||||||
\(359\) | −24.7410 | −1.30578 | −0.652891 | − | 0.757452i | \(-0.726444\pi\) | ||||
−0.652891 | + | 0.757452i | \(0.726444\pi\) | |||||||
\(360\) | 5.96443 | 0.314353 | ||||||||
\(361\) | −17.1388 | −0.902042 | ||||||||
\(362\) | −6.41260 | −0.337039 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 23.7489 | 1.24478 | ||||||||
\(365\) | −7.31645 | −0.382961 | ||||||||
\(366\) | −8.89621 | −0.465012 | ||||||||
\(367\) | 16.6782 | 0.870597 | 0.435298 | − | 0.900286i | \(-0.356643\pi\) | ||||
0.435298 | + | 0.900286i | \(0.356643\pi\) | |||||||
\(368\) | −53.1348 | −2.76984 | ||||||||
\(369\) | 10.4411 | 0.543545 | ||||||||
\(370\) | 8.79860 | 0.457418 | ||||||||
\(371\) | −5.31823 | −0.276109 | ||||||||
\(372\) | 15.7280 | 0.815458 | ||||||||
\(373\) | −18.1757 | −0.941103 | −0.470551 | − | 0.882373i | \(-0.655945\pi\) | ||||
−0.470551 | + | 0.882373i | \(0.655945\pi\) | |||||||
\(374\) | −3.55779 | −0.183969 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 49.0051 | 2.52724 | ||||||||
\(377\) | 47.6686 | 2.45506 | ||||||||
\(378\) | −2.52275 | −0.129756 | ||||||||
\(379\) | −3.31823 | −0.170446 | −0.0852231 | − | 0.996362i | \(-0.527160\pi\) | ||||
−0.0852231 | + | 0.996362i | \(0.527160\pi\) | |||||||
\(380\) | 5.95397 | 0.305432 | ||||||||
\(381\) | 12.8687 | 0.659285 | ||||||||
\(382\) | −60.7728 | −3.10941 | ||||||||
\(383\) | 18.6205 | 0.951461 | 0.475731 | − | 0.879591i | \(-0.342184\pi\) | ||||
0.475731 | + | 0.879591i | \(0.342184\pi\) | |||||||
\(384\) | 14.3760 | 0.733620 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −19.6119 | −0.998218 | ||||||||
\(387\) | −11.5345 | −0.586329 | ||||||||
\(388\) | 70.9758 | 3.60325 | ||||||||
\(389\) | −9.64505 | −0.489024 | −0.244512 | − | 0.969646i | \(-0.578628\pi\) | ||||
−0.244512 | + | 0.969646i | \(0.578628\pi\) | |||||||
\(390\) | 13.7280 | 0.695144 | ||||||||
\(391\) | −11.8601 | −0.599793 | ||||||||
\(392\) | −5.96443 | −0.301249 | ||||||||
\(393\) | 11.4239 | 0.576257 | ||||||||
\(394\) | 1.07418 | 0.0541163 | ||||||||
\(395\) | −4.55832 | −0.229354 | ||||||||
\(396\) | 4.36426 | 0.219312 | ||||||||
\(397\) | −22.9451 | −1.15158 | −0.575791 | − | 0.817597i | \(-0.695306\pi\) | ||||
−0.575791 | + | 0.817597i | \(0.695306\pi\) | |||||||
\(398\) | −29.8190 | −1.49469 | ||||||||
\(399\) | −1.36426 | −0.0682983 | ||||||||
\(400\) | 6.31823 | 0.315912 | ||||||||
\(401\) | 17.4239 | 0.870106 | 0.435053 | − | 0.900405i | \(-0.356730\pi\) | ||||
0.435053 | + | 0.900405i | \(0.356730\pi\) | |||||||
\(402\) | 2.75364 | 0.137339 | ||||||||
\(403\) | 19.6108 | 0.976884 | ||||||||
\(404\) | 65.3838 | 3.25296 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −22.0991 | −1.09676 | ||||||||
\(407\) | 3.48771 | 0.172879 | ||||||||
\(408\) | −8.41154 | −0.416433 | ||||||||
\(409\) | −1.21816 | −0.0602343 | −0.0301172 | − | 0.999546i | \(-0.509588\pi\) | ||||
−0.0301172 | + | 0.999546i | \(0.509588\pi\) | |||||||
\(410\) | 26.3404 | 1.30086 | ||||||||
\(411\) | 7.61187 | 0.375466 | ||||||||
\(412\) | 9.06640 | 0.446670 | ||||||||
\(413\) | 7.07689 | 0.348231 | ||||||||
\(414\) | 21.2157 | 1.04269 | ||||||||
\(415\) | 9.51910 | 0.467274 | ||||||||
\(416\) | −21.8236 | −1.06999 | ||||||||
\(417\) | −9.31645 | −0.456229 | ||||||||
\(418\) | 3.44168 | 0.168338 | ||||||||
\(419\) | 2.35088 | 0.114848 | 0.0574240 | − | 0.998350i | \(-0.481711\pi\) | ||||
0.0574240 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(420\) | −4.36426 | −0.212954 | ||||||||
\(421\) | −18.9572 | −0.923920 | −0.461960 | − | 0.886901i | \(-0.652854\pi\) | ||||
−0.461960 | + | 0.886901i | \(0.652854\pi\) | |||||||
\(422\) | 61.1275 | 2.97564 | ||||||||
\(423\) | −8.21622 | −0.399486 | ||||||||
\(424\) | 31.7202 | 1.54047 | ||||||||
\(425\) | 1.41028 | 0.0684088 | ||||||||
\(426\) | −11.8452 | −0.573900 | ||||||||
\(427\) | 3.52640 | 0.170654 | ||||||||
\(428\) | 58.3843 | 2.82211 | ||||||||
\(429\) | 5.44168 | 0.262727 | ||||||||
\(430\) | −29.0985 | −1.40326 | ||||||||
\(431\) | 32.8823 | 1.58388 | 0.791942 | − | 0.610596i | \(-0.209070\pi\) | ||||
0.791942 | + | 0.610596i | \(0.209070\pi\) | |||||||
\(432\) | 6.31823 | 0.303986 | ||||||||
\(433\) | −9.33322 | −0.448526 | −0.224263 | − | 0.974529i | \(-0.571997\pi\) | ||||
−0.224263 | + | 0.974529i | \(0.571997\pi\) | |||||||
\(434\) | −9.09152 | −0.436407 | ||||||||
\(435\) | −8.75991 | −0.420006 | ||||||||
\(436\) | −44.8603 | −2.14842 | ||||||||
\(437\) | 11.4731 | 0.548832 | ||||||||
\(438\) | −18.4576 | −0.881936 | ||||||||
\(439\) | 16.7010 | 0.797097 | 0.398549 | − | 0.917147i | \(-0.369514\pi\) | ||||
0.398549 | + | 0.917147i | \(0.369514\pi\) | |||||||
\(440\) | 5.96443 | 0.284343 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −19.3604 | −0.920878 | ||||||||
\(443\) | −9.79184 | −0.465224 | −0.232612 | − | 0.972570i | \(-0.574727\pi\) | ||||
−0.232612 | + | 0.972570i | \(0.574727\pi\) | |||||||
\(444\) | 15.2212 | 0.722368 | ||||||||
\(445\) | 16.7421 | 0.793651 | ||||||||
\(446\) | −6.61690 | −0.313319 | ||||||||
\(447\) | 14.1370 | 0.668658 | ||||||||
\(448\) | −2.51910 | −0.119016 | ||||||||
\(449\) | −36.5556 | −1.72516 | −0.862582 | − | 0.505918i | \(-0.831154\pi\) | ||||
−0.862582 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(450\) | −2.52275 | −0.118923 | ||||||||
\(451\) | 10.4411 | 0.491655 | ||||||||
\(452\) | 36.1956 | 1.70250 | ||||||||
\(453\) | −7.56585 | −0.355475 | ||||||||
\(454\) | 7.62578 | 0.357896 | ||||||||
\(455\) | −5.44168 | −0.255110 | ||||||||
\(456\) | 8.13702 | 0.381051 | ||||||||
\(457\) | −18.7986 | −0.879363 | −0.439682 | − | 0.898154i | \(-0.644909\pi\) | ||||
−0.439682 | + | 0.898154i | \(0.644909\pi\) | |||||||
\(458\) | 8.16676 | 0.381608 | ||||||||
\(459\) | 1.41028 | 0.0658264 | ||||||||
\(460\) | 36.7023 | 1.71126 | ||||||||
\(461\) | 34.0972 | 1.58807 | 0.794033 | − | 0.607875i | \(-0.207978\pi\) | ||||
0.794033 | + | 0.607875i | \(0.207978\pi\) | |||||||
\(462\) | −2.52275 | −0.117369 | ||||||||
\(463\) | −6.20816 | −0.288518 | −0.144259 | − | 0.989540i | \(-0.546080\pi\) | ||||
−0.144259 | + | 0.989540i | \(0.546080\pi\) | |||||||
\(464\) | 55.3472 | 2.56943 | ||||||||
\(465\) | −3.60382 | −0.167123 | ||||||||
\(466\) | 45.5009 | 2.10779 | ||||||||
\(467\) | 3.20763 | 0.148432 | 0.0742158 | − | 0.997242i | \(-0.476355\pi\) | ||||
0.0742158 | + | 0.997242i | \(0.476355\pi\) | |||||||
\(468\) | 23.7489 | 1.09779 | ||||||||
\(469\) | −1.09152 | −0.0504018 | ||||||||
\(470\) | −20.7275 | −0.956086 | ||||||||
\(471\) | −21.5972 | −0.995149 | ||||||||
\(472\) | −42.2096 | −1.94285 | ||||||||
\(473\) | −11.5345 | −0.530355 | ||||||||
\(474\) | −11.4995 | −0.528189 | ||||||||
\(475\) | −1.36426 | −0.0625965 | ||||||||
\(476\) | 6.15484 | 0.282107 | ||||||||
\(477\) | −5.31823 | −0.243505 | ||||||||
\(478\) | −23.8235 | −1.08966 | ||||||||
\(479\) | −10.1252 | −0.462634 | −0.231317 | − | 0.972878i | \(-0.574303\pi\) | ||||
−0.231317 | + | 0.972878i | \(0.574303\pi\) | |||||||
\(480\) | 4.01045 | 0.183051 | ||||||||
\(481\) | 18.9790 | 0.865367 | ||||||||
\(482\) | −42.2969 | −1.92657 | ||||||||
\(483\) | −8.40975 | −0.382657 | ||||||||
\(484\) | 4.36426 | 0.198375 | ||||||||
\(485\) | −16.2630 | −0.738463 | ||||||||
\(486\) | −2.52275 | −0.114434 | ||||||||
\(487\) | −25.5721 | −1.15878 | −0.579391 | − | 0.815050i | \(-0.696710\pi\) | ||||
−0.579391 | + | 0.815050i | \(0.696710\pi\) | |||||||
\(488\) | −21.0329 | −0.952116 | ||||||||
\(489\) | 17.0608 | 0.771518 | ||||||||
\(490\) | 2.52275 | 0.113966 | ||||||||
\(491\) | −15.4681 | −0.698066 | −0.349033 | − | 0.937111i | \(-0.613490\pi\) | ||||
−0.349033 | + | 0.937111i | \(0.613490\pi\) | |||||||
\(492\) | 45.5679 | 2.05436 | ||||||||
\(493\) | 12.3540 | 0.556394 | ||||||||
\(494\) | 18.7285 | 0.842636 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 22.7698 | 1.02239 | ||||||||
\(497\) | 4.69534 | 0.210615 | ||||||||
\(498\) | 24.0143 | 1.07611 | ||||||||
\(499\) | −0.712473 | −0.0318947 | −0.0159473 | − | 0.999873i | \(-0.505076\pi\) | ||||
−0.0159473 | + | 0.999873i | \(0.505076\pi\) | |||||||
\(500\) | −4.36426 | −0.195176 | ||||||||
\(501\) | 0.866594 | 0.0387165 | ||||||||
\(502\) | 70.1829 | 3.13242 | ||||||||
\(503\) | −41.8595 | −1.86642 | −0.933211 | − | 0.359328i | \(-0.883006\pi\) | ||||
−0.933211 | + | 0.359328i | \(0.883006\pi\) | |||||||
\(504\) | −5.96443 | −0.265677 | ||||||||
\(505\) | −14.9816 | −0.666674 | ||||||||
\(506\) | 21.2157 | 0.943153 | ||||||||
\(507\) | 16.6119 | 0.737759 | ||||||||
\(508\) | 56.1625 | 2.49181 | ||||||||
\(509\) | 5.35247 | 0.237244 | 0.118622 | − | 0.992939i | \(-0.462152\pi\) | ||||
0.118622 | + | 0.992939i | \(0.462152\pi\) | |||||||
\(510\) | 3.55779 | 0.157542 | ||||||||
\(511\) | 7.31645 | 0.323661 | ||||||||
\(512\) | 50.0303 | 2.21105 | ||||||||
\(513\) | −1.36426 | −0.0602335 | ||||||||
\(514\) | 34.0972 | 1.50396 | ||||||||
\(515\) | −2.07742 | −0.0915421 | ||||||||
\(516\) | −50.3393 | −2.21607 | ||||||||
\(517\) | −8.21622 | −0.361349 | ||||||||
\(518\) | −8.79860 | −0.386588 | ||||||||
\(519\) | 10.0628 | 0.441708 | ||||||||
\(520\) | 32.4565 | 1.42331 | ||||||||
\(521\) | −18.6511 | −0.817119 | −0.408560 | − | 0.912732i | \(-0.633969\pi\) | ||||
−0.408560 | + | 0.912732i | \(0.633969\pi\) | |||||||
\(522\) | −22.0991 | −0.967249 | ||||||||
\(523\) | −26.2494 | −1.14781 | −0.573903 | − | 0.818923i | \(-0.694571\pi\) | ||||
−0.573903 | + | 0.818923i | \(0.694571\pi\) | |||||||
\(524\) | 49.8567 | 2.17800 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 4.92938 | 0.214931 | ||||||||
\(527\) | 5.08240 | 0.221393 | ||||||||
\(528\) | 6.31823 | 0.274966 | ||||||||
\(529\) | 47.7240 | 2.07496 | ||||||||
\(530\) | −13.4166 | −0.582778 | ||||||||
\(531\) | 7.07689 | 0.307111 | ||||||||
\(532\) | −5.95397 | −0.258138 | ||||||||
\(533\) | 56.8174 | 2.46103 | ||||||||
\(534\) | 42.2361 | 1.82773 | ||||||||
\(535\) | −13.3778 | −0.578374 | ||||||||
\(536\) | 6.51030 | 0.281202 | ||||||||
\(537\) | 2.42024 | 0.104441 | ||||||||
\(538\) | 30.8589 | 1.33042 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −4.36426 | −0.187808 | ||||||||
\(541\) | 23.0714 | 0.991916 | 0.495958 | − | 0.868346i | \(-0.334817\pi\) | ||||
0.495958 | + | 0.868346i | \(0.334817\pi\) | |||||||
\(542\) | 70.3536 | 3.02195 | ||||||||
\(543\) | 2.54191 | 0.109084 | ||||||||
\(544\) | −5.65588 | −0.242494 | ||||||||
\(545\) | 10.2790 | 0.440305 | ||||||||
\(546\) | −13.7280 | −0.587504 | ||||||||
\(547\) | 43.1117 | 1.84332 | 0.921662 | − | 0.387993i | \(-0.126831\pi\) | ||||
0.921662 | + | 0.387993i | \(0.126831\pi\) | |||||||
\(548\) | 33.2202 | 1.41910 | ||||||||
\(549\) | 3.52640 | 0.150503 | ||||||||
\(550\) | −2.52275 | −0.107570 | ||||||||
\(551\) | −11.9508 | −0.509120 | ||||||||
\(552\) | 50.1594 | 2.13492 | ||||||||
\(553\) | 4.55832 | 0.193840 | ||||||||
\(554\) | 21.0528 | 0.894447 | ||||||||
\(555\) | −3.48771 | −0.148045 | ||||||||
\(556\) | −40.6594 | −1.72434 | ||||||||
\(557\) | 5.15537 | 0.218440 | 0.109220 | − | 0.994018i | \(-0.465165\pi\) | ||||
0.109220 | + | 0.994018i | \(0.465165\pi\) | |||||||
\(558\) | −9.09152 | −0.384875 | ||||||||
\(559\) | −62.7668 | −2.65475 | ||||||||
\(560\) | −6.31823 | −0.266994 | ||||||||
\(561\) | 1.41028 | 0.0595422 | ||||||||
\(562\) | −45.9135 | −1.93675 | ||||||||
\(563\) | −31.7624 | −1.33863 | −0.669313 | − | 0.742980i | \(-0.733412\pi\) | ||||
−0.669313 | + | 0.742980i | \(0.733412\pi\) | |||||||
\(564\) | −35.8577 | −1.50988 | ||||||||
\(565\) | −8.29364 | −0.348916 | ||||||||
\(566\) | 18.8959 | 0.794254 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −28.0050 | −1.17506 | ||||||||
\(569\) | −24.5256 | −1.02817 | −0.514083 | − | 0.857741i | \(-0.671868\pi\) | ||||
−0.514083 | + | 0.857741i | \(0.671868\pi\) | |||||||
\(570\) | −3.44168 | −0.144156 | ||||||||
\(571\) | 14.8077 | 0.619684 | 0.309842 | − | 0.950788i | \(-0.399724\pi\) | ||||
0.309842 | + | 0.950788i | \(0.399724\pi\) | |||||||
\(572\) | 23.7489 | 0.992991 | ||||||||
\(573\) | 24.0899 | 1.00637 | ||||||||
\(574\) | −26.3404 | −1.09943 | ||||||||
\(575\) | −8.40975 | −0.350711 | ||||||||
\(576\) | −2.51910 | −0.104963 | ||||||||
\(577\) | −17.3304 | −0.721474 | −0.360737 | − | 0.932668i | \(-0.617475\pi\) | ||||
−0.360737 | + | 0.932668i | \(0.617475\pi\) | |||||||
\(578\) | 37.8692 | 1.57515 | ||||||||
\(579\) | 7.77401 | 0.323077 | ||||||||
\(580\) | −38.2305 | −1.58744 | ||||||||
\(581\) | −9.51910 | −0.394919 | ||||||||
\(582\) | −41.0274 | −1.70064 | ||||||||
\(583\) | −5.31823 | −0.220259 | ||||||||
\(584\) | −43.6384 | −1.80577 | ||||||||
\(585\) | −5.44168 | −0.224986 | ||||||||
\(586\) | 13.0169 | 0.537725 | ||||||||
\(587\) | 45.9180 | 1.89524 | 0.947620 | − | 0.319400i | \(-0.103481\pi\) | ||||
0.947620 | + | 0.319400i | \(0.103481\pi\) | |||||||
\(588\) | 4.36426 | 0.179979 | ||||||||
\(589\) | −4.91654 | −0.202582 | ||||||||
\(590\) | 17.8532 | 0.735005 | ||||||||
\(591\) | −0.425797 | −0.0175150 | ||||||||
\(592\) | 22.0361 | 0.905679 | ||||||||
\(593\) | 1.54658 | 0.0635104 | 0.0317552 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317552 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(594\) | −2.52275 | −0.103510 | ||||||||
\(595\) | −1.41028 | −0.0578160 | ||||||||
\(596\) | 61.6976 | 2.52723 | ||||||||
\(597\) | 11.8200 | 0.483762 | ||||||||
\(598\) | 115.449 | 4.72106 | ||||||||
\(599\) | −18.2604 | −0.746101 | −0.373050 | − | 0.927811i | \(-0.621688\pi\) | ||||
−0.373050 | + | 0.927811i | \(0.621688\pi\) | |||||||
\(600\) | −5.96443 | −0.243497 | ||||||||
\(601\) | −20.0990 | −0.819856 | −0.409928 | − | 0.912118i | \(-0.634446\pi\) | ||||
−0.409928 | + | 0.912118i | \(0.634446\pi\) | |||||||
\(602\) | 29.0985 | 1.18597 | ||||||||
\(603\) | −1.09152 | −0.0444502 | ||||||||
\(604\) | −33.0193 | −1.34354 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −37.7949 | −1.53531 | ||||||||
\(607\) | 19.3368 | 0.784856 | 0.392428 | − | 0.919783i | \(-0.371635\pi\) | ||||
0.392428 | + | 0.919783i | \(0.371635\pi\) | |||||||
\(608\) | 5.47129 | 0.221890 | ||||||||
\(609\) | 8.75991 | 0.354970 | ||||||||
\(610\) | 8.89621 | 0.360197 | ||||||||
\(611\) | −44.7100 | −1.80877 | ||||||||
\(612\) | 6.15484 | 0.248795 | ||||||||
\(613\) | 41.1982 | 1.66398 | 0.831990 | − | 0.554790i | \(-0.187202\pi\) | ||||
0.831990 | + | 0.554790i | \(0.187202\pi\) | |||||||
\(614\) | −42.5988 | −1.71915 | ||||||||
\(615\) | −10.4411 | −0.421028 | ||||||||
\(616\) | −5.96443 | −0.240314 | ||||||||
\(617\) | −3.17943 | −0.127999 | −0.0639996 | − | 0.997950i | \(-0.520386\pi\) | ||||
−0.0639996 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(618\) | −5.24081 | −0.210816 | ||||||||
\(619\) | −36.5831 | −1.47040 | −0.735200 | − | 0.677850i | \(-0.762912\pi\) | ||||
−0.735200 | + | 0.677850i | \(0.762912\pi\) | |||||||
\(620\) | −15.7280 | −0.631651 | ||||||||
\(621\) | −8.40975 | −0.337472 | ||||||||
\(622\) | 38.0010 | 1.52370 | ||||||||
\(623\) | −16.7421 | −0.670758 | ||||||||
\(624\) | 34.3818 | 1.37637 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 37.5101 | 1.49920 | ||||||||
\(627\) | −1.36426 | −0.0544832 | ||||||||
\(628\) | −94.2559 | −3.76122 | ||||||||
\(629\) | 4.91865 | 0.196120 | ||||||||
\(630\) | 2.52275 | 0.100509 | ||||||||
\(631\) | 26.8209 | 1.06772 | 0.533861 | − | 0.845572i | \(-0.320740\pi\) | ||||
0.533861 | + | 0.845572i | \(0.320740\pi\) | |||||||
\(632\) | −27.1878 | −1.08147 | ||||||||
\(633\) | −24.2305 | −0.963077 | ||||||||
\(634\) | −78.2090 | −3.10607 | ||||||||
\(635\) | −12.8687 | −0.510680 | ||||||||
\(636\) | −23.2101 | −0.920342 | ||||||||
\(637\) | 5.44168 | 0.215607 | ||||||||
\(638\) | −22.0991 | −0.874910 | ||||||||
\(639\) | 4.69534 | 0.185745 | ||||||||
\(640\) | −14.3760 | −0.568260 | ||||||||
\(641\) | 10.1841 | 0.402248 | 0.201124 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201124 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(642\) | −33.7489 | −1.33196 | ||||||||
\(643\) | −15.3525 | −0.605442 | −0.302721 | − | 0.953079i | \(-0.597895\pi\) | ||||
−0.302721 | + | 0.953079i | \(0.597895\pi\) | |||||||
\(644\) | −36.7023 | −1.44627 | ||||||||
\(645\) | 11.5345 | 0.454169 | ||||||||
\(646\) | 4.85374 | 0.190968 | ||||||||
\(647\) | −38.5234 | −1.51451 | −0.757256 | − | 0.653118i | \(-0.773461\pi\) | ||||
−0.757256 | + | 0.653118i | \(0.773461\pi\) | |||||||
\(648\) | −5.96443 | −0.234305 | ||||||||
\(649\) | 7.07689 | 0.277792 | ||||||||
\(650\) | −13.7280 | −0.538456 | ||||||||
\(651\) | 3.60382 | 0.141245 | ||||||||
\(652\) | 74.4579 | 2.91600 | ||||||||
\(653\) | 4.17089 | 0.163219 | 0.0816097 | − | 0.996664i | \(-0.473994\pi\) | ||||
0.0816097 | + | 0.996664i | \(0.473994\pi\) | |||||||
\(654\) | 25.9314 | 1.01400 | ||||||||
\(655\) | −11.4239 | −0.446367 | ||||||||
\(656\) | 65.9696 | 2.57568 | ||||||||
\(657\) | 7.31645 | 0.285442 | ||||||||
\(658\) | 20.7275 | 0.808040 | ||||||||
\(659\) | −38.1242 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(660\) | −4.36426 | −0.169879 | ||||||||
\(661\) | −28.4621 | −1.10705 | −0.553523 | − | 0.832834i | \(-0.686717\pi\) | ||||
−0.553523 | + | 0.832834i | \(0.686717\pi\) | |||||||
\(662\) | −34.4599 | −1.33932 | ||||||||
\(663\) | 7.67431 | 0.298046 | ||||||||
\(664\) | 56.7760 | 2.20334 | ||||||||
\(665\) | 1.36426 | 0.0529037 | ||||||||
\(666\) | −8.79860 | −0.340939 | ||||||||
\(667\) | −73.6687 | −2.85246 | ||||||||
\(668\) | 3.78204 | 0.146331 | ||||||||
\(669\) | 2.62289 | 0.101407 | ||||||||
\(670\) | −2.75364 | −0.106382 | ||||||||
\(671\) | 3.52640 | 0.136135 | ||||||||
\(672\) | −4.01045 | −0.154707 | ||||||||
\(673\) | −18.4890 | −0.712697 | −0.356348 | − | 0.934353i | \(-0.615978\pi\) | ||||
−0.356348 | + | 0.934353i | \(0.615978\pi\) | |||||||
\(674\) | 53.7496 | 2.07036 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 72.4985 | 2.78840 | ||||||||
\(677\) | 8.58721 | 0.330033 | 0.165017 | − | 0.986291i | \(-0.447232\pi\) | ||||
0.165017 | + | 0.986291i | \(0.447232\pi\) | |||||||
\(678\) | −20.9228 | −0.803534 | ||||||||
\(679\) | 16.2630 | 0.624115 | ||||||||
\(680\) | 8.41154 | 0.322568 | ||||||||
\(681\) | −3.02281 | −0.115834 | ||||||||
\(682\) | −9.09152 | −0.348132 | ||||||||
\(683\) | 4.05226 | 0.155055 | 0.0775277 | − | 0.996990i | \(-0.475297\pi\) | ||||
0.0775277 | + | 0.996990i | \(0.475297\pi\) | |||||||
\(684\) | −5.95397 | −0.227656 | ||||||||
\(685\) | −7.61187 | −0.290835 | ||||||||
\(686\) | −2.52275 | −0.0963190 | ||||||||
\(687\) | −3.23725 | −0.123509 | ||||||||
\(688\) | −72.8774 | −2.77842 | ||||||||
\(689\) | −28.9401 | −1.10253 | ||||||||
\(690\) | −21.2157 | −0.807668 | ||||||||
\(691\) | −0.408622 | −0.0155447 | −0.00777235 | − | 0.999970i | \(-0.502474\pi\) | ||||
−0.00777235 | + | 0.999970i | \(0.502474\pi\) | |||||||
\(692\) | 43.9166 | 1.66946 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 72.2409 | 2.74223 | ||||||||
\(695\) | 9.31645 | 0.353393 | ||||||||
\(696\) | −52.2479 | −1.98045 | ||||||||
\(697\) | 14.7250 | 0.557749 | ||||||||
\(698\) | 11.3543 | 0.429765 | ||||||||
\(699\) | −18.0363 | −0.682194 | ||||||||
\(700\) | 4.36426 | 0.164953 | ||||||||
\(701\) | −37.1239 | −1.40215 | −0.701075 | − | 0.713088i | \(-0.747296\pi\) | ||||
−0.701075 | + | 0.713088i | \(0.747296\pi\) | |||||||
\(702\) | −13.7280 | −0.518129 | ||||||||
\(703\) | −4.75813 | −0.179456 | ||||||||
\(704\) | −2.51910 | −0.0949422 | ||||||||
\(705\) | 8.21622 | 0.309441 | ||||||||
\(706\) | 18.9670 | 0.713832 | ||||||||
\(707\) | 14.9816 | 0.563443 | ||||||||
\(708\) | 30.8854 | 1.16074 | ||||||||
\(709\) | −3.88834 | −0.146030 | −0.0730149 | − | 0.997331i | \(-0.523262\pi\) | ||||
−0.0730149 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(710\) | 11.8452 | 0.444541 | ||||||||
\(711\) | 4.55832 | 0.170950 | ||||||||
\(712\) | 99.8570 | 3.74230 | ||||||||
\(713\) | −30.3072 | −1.13501 | ||||||||
\(714\) | −3.55779 | −0.133147 | ||||||||
\(715\) | −5.44168 | −0.203507 | ||||||||
\(716\) | 10.5626 | 0.394742 | ||||||||
\(717\) | 9.44346 | 0.352673 | ||||||||
\(718\) | 62.4154 | 2.32932 | ||||||||
\(719\) | −25.8792 | −0.965132 | −0.482566 | − | 0.875860i | \(-0.660295\pi\) | ||||
−0.482566 | + | 0.875860i | \(0.660295\pi\) | |||||||
\(720\) | −6.31823 | −0.235467 | ||||||||
\(721\) | 2.07742 | 0.0773672 | ||||||||
\(722\) | 43.2369 | 1.60911 | ||||||||
\(723\) | 16.7662 | 0.623541 | ||||||||
\(724\) | 11.0935 | 0.412288 | ||||||||
\(725\) | 8.75991 | 0.325335 | ||||||||
\(726\) | −2.52275 | −0.0936280 | ||||||||
\(727\) | −12.9315 | −0.479604 | −0.239802 | − | 0.970822i | \(-0.577082\pi\) | ||||
−0.239802 | + | 0.970822i | \(0.577082\pi\) | |||||||
\(728\) | −32.4565 | −1.20292 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.4576 | 0.683145 | ||||||||
\(731\) | −16.2669 | −0.601651 | ||||||||
\(732\) | 15.3901 | 0.568834 | ||||||||
\(733\) | 34.2270 | 1.26420 | 0.632101 | − | 0.774886i | \(-0.282193\pi\) | ||||
0.632101 | + | 0.774886i | \(0.282193\pi\) | |||||||
\(734\) | −42.0750 | −1.55302 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 33.7269 | 1.24319 | ||||||||
\(737\) | −1.09152 | −0.0402067 | ||||||||
\(738\) | −26.3404 | −0.969603 | ||||||||
\(739\) | −12.1741 | −0.447832 | −0.223916 | − | 0.974608i | \(-0.571884\pi\) | ||||
−0.223916 | + | 0.974608i | \(0.571884\pi\) | |||||||
\(740\) | −15.2212 | −0.559544 | ||||||||
\(741\) | −7.42385 | −0.272722 | ||||||||
\(742\) | 13.4166 | 0.492537 | ||||||||
\(743\) | −14.2672 | −0.523414 | −0.261707 | − | 0.965147i | \(-0.584285\pi\) | ||||
−0.261707 | + | 0.965147i | \(0.584285\pi\) | |||||||
\(744\) | −21.4947 | −0.788034 | ||||||||
\(745\) | −14.1370 | −0.517940 | ||||||||
\(746\) | 45.8527 | 1.67879 | ||||||||
\(747\) | −9.51910 | −0.348286 | ||||||||
\(748\) | 6.15484 | 0.225043 | ||||||||
\(749\) | 13.3778 | 0.488815 | ||||||||
\(750\) | 2.52275 | 0.0921177 | ||||||||
\(751\) | −31.9793 | −1.16694 | −0.583471 | − | 0.812134i | \(-0.698306\pi\) | ||||
−0.583471 | + | 0.812134i | \(0.698306\pi\) | |||||||
\(752\) | −51.9120 | −1.89304 | ||||||||
\(753\) | −27.8200 | −1.01382 | ||||||||
\(754\) | −120.256 | −4.37946 | ||||||||
\(755\) | 7.56585 | 0.275349 | ||||||||
\(756\) | 4.36426 | 0.158727 | ||||||||
\(757\) | 14.4681 | 0.525852 | 0.262926 | − | 0.964816i | \(-0.415313\pi\) | ||||
0.262926 | + | 0.964816i | \(0.415313\pi\) | |||||||
\(758\) | 8.37106 | 0.304051 | ||||||||
\(759\) | −8.40975 | −0.305255 | ||||||||
\(760\) | −8.13702 | −0.295161 | ||||||||
\(761\) | −26.5297 | −0.961700 | −0.480850 | − | 0.876803i | \(-0.659672\pi\) | ||||
−0.480850 | + | 0.876803i | \(0.659672\pi\) | |||||||
\(762\) | −32.4646 | −1.17607 | ||||||||
\(763\) | −10.2790 | −0.372125 | ||||||||
\(764\) | 105.135 | 3.80364 | ||||||||
\(765\) | −1.41028 | −0.0509889 | ||||||||
\(766\) | −46.9747 | −1.69727 | ||||||||
\(767\) | 38.5102 | 1.39052 | ||||||||
\(768\) | −31.2287 | −1.12687 | ||||||||
\(769\) | −36.1744 | −1.30448 | −0.652240 | − | 0.758012i | \(-0.726171\pi\) | ||||
−0.652240 | + | 0.758012i | \(0.726171\pi\) | |||||||
\(770\) | 2.52275 | 0.0909135 | ||||||||
\(771\) | −13.5159 | −0.486763 | ||||||||
\(772\) | 33.9278 | 1.22109 | ||||||||
\(773\) | 4.48162 | 0.161193 | 0.0805964 | − | 0.996747i | \(-0.474318\pi\) | ||||
0.0805964 | + | 0.996747i | \(0.474318\pi\) | |||||||
\(774\) | 29.0985 | 1.04592 | ||||||||
\(775\) | 3.60382 | 0.129453 | ||||||||
\(776\) | −96.9993 | −3.48207 | ||||||||
\(777\) | 3.48771 | 0.125121 | ||||||||
\(778\) | 24.3320 | 0.872346 | ||||||||
\(779\) | −14.2444 | −0.510359 | ||||||||
\(780\) | −23.7489 | −0.850347 | ||||||||
\(781\) | 4.69534 | 0.168012 | ||||||||
\(782\) | 29.9201 | 1.06994 | ||||||||
\(783\) | 8.75991 | 0.313054 | ||||||||
\(784\) | 6.31823 | 0.225651 | ||||||||
\(785\) | 21.5972 | 0.770839 | ||||||||
\(786\) | −28.8195 | −1.02796 | ||||||||
\(787\) | 32.7728 | 1.16823 | 0.584113 | − | 0.811673i | \(-0.301443\pi\) | ||||
0.584113 | + | 0.811673i | \(0.301443\pi\) | |||||||
\(788\) | −1.85829 | −0.0661988 | ||||||||
\(789\) | −1.95397 | −0.0695633 | ||||||||
\(790\) | 11.4995 | 0.409134 | ||||||||
\(791\) | 8.29364 | 0.294888 | ||||||||
\(792\) | −5.96443 | −0.211937 | ||||||||
\(793\) | 19.1895 | 0.681440 | ||||||||
\(794\) | 57.8847 | 2.05425 | ||||||||
\(795\) | 5.31823 | 0.188618 | ||||||||
\(796\) | 51.5857 | 1.82841 | ||||||||
\(797\) | 1.56756 | 0.0555257 | 0.0277629 | − | 0.999615i | \(-0.491162\pi\) | ||||
0.0277629 | + | 0.999615i | \(0.491162\pi\) | |||||||
\(798\) | 3.44168 | 0.121834 | ||||||||
\(799\) | −11.5872 | −0.409926 | ||||||||
\(800\) | −4.01045 | −0.141791 | ||||||||
\(801\) | −16.7421 | −0.591553 | ||||||||
\(802\) | −43.9560 | −1.55214 | ||||||||
\(803\) | 7.31645 | 0.258192 | ||||||||
\(804\) | −4.76368 | −0.168002 | ||||||||
\(805\) | 8.40975 | 0.296405 | ||||||||
\(806\) | −49.4731 | −1.74262 | ||||||||
\(807\) | −12.2323 | −0.430596 | ||||||||
\(808\) | −89.3569 | −3.14357 | ||||||||
\(809\) | 48.0083 | 1.68788 | 0.843940 | − | 0.536437i | \(-0.180230\pi\) | ||||
0.843940 | + | 0.536437i | \(0.180230\pi\) | |||||||
\(810\) | 2.52275 | 0.0886403 | ||||||||
\(811\) | 23.0204 | 0.808355 | 0.404177 | − | 0.914681i | \(-0.367558\pi\) | ||||
0.404177 | + | 0.914681i | \(0.367558\pi\) | |||||||
\(812\) | 38.2305 | 1.34163 | ||||||||
\(813\) | −27.8877 | −0.978064 | ||||||||
\(814\) | −8.79860 | −0.308391 | ||||||||
\(815\) | −17.0608 | −0.597615 | ||||||||
\(816\) | 8.91050 | 0.311930 | ||||||||
\(817\) | 15.7360 | 0.550532 | ||||||||
\(818\) | 3.07312 | 0.107449 | ||||||||
\(819\) | 5.44168 | 0.190148 | ||||||||
\(820\) | −45.5679 | −1.59130 | ||||||||
\(821\) | 47.4418 | 1.65573 | 0.827864 | − | 0.560928i | \(-0.189556\pi\) | ||||
0.827864 | + | 0.560928i | \(0.189556\pi\) | |||||||
\(822\) | −19.2028 | −0.669776 | ||||||||
\(823\) | 48.0905 | 1.67633 | 0.838165 | − | 0.545416i | \(-0.183628\pi\) | ||||
0.838165 | + | 0.545416i | \(0.183628\pi\) | |||||||
\(824\) | −12.3906 | −0.431648 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | −17.8532 | −0.621193 | ||||||||
\(827\) | 26.9026 | 0.935496 | 0.467748 | − | 0.883862i | \(-0.345065\pi\) | ||||
0.467748 | + | 0.883862i | \(0.345065\pi\) | |||||||
\(828\) | −36.7023 | −1.27549 | ||||||||
\(829\) | 18.0592 | 0.627223 | 0.313611 | − | 0.949551i | \(-0.398461\pi\) | ||||
0.313611 | + | 0.949551i | \(0.398461\pi\) | |||||||
\(830\) | −24.0143 | −0.833548 | ||||||||
\(831\) | −8.34518 | −0.289491 | ||||||||
\(832\) | −13.7081 | −0.475244 | ||||||||
\(833\) | 1.41028 | 0.0488634 | ||||||||
\(834\) | 23.5031 | 0.813844 | ||||||||
\(835\) | −0.866594 | −0.0299897 | ||||||||
\(836\) | −5.95397 | −0.205923 | ||||||||
\(837\) | 3.60382 | 0.124566 | ||||||||
\(838\) | −5.93068 | −0.204872 | ||||||||
\(839\) | 6.74623 | 0.232906 | 0.116453 | − | 0.993196i | \(-0.462848\pi\) | ||||
0.116453 | + | 0.993196i | \(0.462848\pi\) | |||||||
\(840\) | 5.96443 | 0.205792 | ||||||||
\(841\) | 47.7361 | 1.64607 | ||||||||
\(842\) | 47.8244 | 1.64814 | ||||||||
\(843\) | 18.1998 | 0.626835 | ||||||||
\(844\) | −105.748 | −3.64000 | ||||||||
\(845\) | −16.6119 | −0.571466 | ||||||||
\(846\) | 20.7275 | 0.712625 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −33.6018 | −1.15389 | ||||||||
\(849\) | −7.49021 | −0.257063 | ||||||||
\(850\) | −3.55779 | −0.122031 | ||||||||
\(851\) | −29.3307 | −1.00544 | ||||||||
\(852\) | 20.4917 | 0.702033 | ||||||||
\(853\) | 9.12097 | 0.312296 | 0.156148 | − | 0.987734i | \(-0.450092\pi\) | ||||
0.156148 | + | 0.987734i | \(0.450092\pi\) | |||||||
\(854\) | −8.89621 | −0.304422 | ||||||||
\(855\) | 1.36426 | 0.0466566 | ||||||||
\(856\) | −79.7911 | −2.72720 | ||||||||
\(857\) | −40.8651 | −1.39593 | −0.697963 | − | 0.716134i | \(-0.745910\pi\) | ||||
−0.697963 | + | 0.716134i | \(0.745910\pi\) | |||||||
\(858\) | −13.7280 | −0.468666 | ||||||||
\(859\) | −6.54852 | −0.223433 | −0.111716 | − | 0.993740i | \(-0.535635\pi\) | ||||
−0.111716 | + | 0.993740i | \(0.535635\pi\) | |||||||
\(860\) | 50.3393 | 1.71656 | ||||||||
\(861\) | 10.4411 | 0.355833 | ||||||||
\(862\) | −82.9538 | −2.82542 | ||||||||
\(863\) | 32.9504 | 1.12164 | 0.560822 | − | 0.827937i | \(-0.310485\pi\) | ||||
0.560822 | + | 0.827937i | \(0.310485\pi\) | |||||||
\(864\) | −4.01045 | −0.136438 | ||||||||
\(865\) | −10.0628 | −0.342145 | ||||||||
\(866\) | 23.5454 | 0.800104 | ||||||||
\(867\) | −15.0111 | −0.509804 | ||||||||
\(868\) | 15.7280 | 0.533843 | ||||||||
\(869\) | 4.55832 | 0.154630 | ||||||||
\(870\) | 22.0991 | 0.749228 | ||||||||
\(871\) | −5.93971 | −0.201260 | ||||||||
\(872\) | 61.3084 | 2.07617 | ||||||||
\(873\) | 16.2630 | 0.550418 | ||||||||
\(874\) | −28.9437 | −0.979035 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 31.9309 | 1.07884 | ||||||||
\(877\) | 44.4377 | 1.50055 | 0.750277 | − | 0.661124i | \(-0.229920\pi\) | ||||
0.750277 | + | 0.661124i | \(0.229920\pi\) | |||||||
\(878\) | −42.1325 | −1.42190 | ||||||||
\(879\) | −5.15983 | −0.174037 | ||||||||
\(880\) | −6.31823 | −0.212988 | ||||||||
\(881\) | 48.6954 | 1.64059 | 0.820295 | − | 0.571941i | \(-0.193809\pi\) | ||||
0.820295 | + | 0.571941i | \(0.193809\pi\) | |||||||
\(882\) | −2.52275 | −0.0849453 | ||||||||
\(883\) | 14.7954 | 0.497906 | 0.248953 | − | 0.968516i | \(-0.419913\pi\) | ||||
0.248953 | + | 0.968516i | \(0.419913\pi\) | |||||||
\(884\) | 33.4927 | 1.12648 | ||||||||
\(885\) | −7.07689 | −0.237887 | ||||||||
\(886\) | 24.7023 | 0.829891 | ||||||||
\(887\) | −21.0707 | −0.707484 | −0.353742 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353742 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(888\) | −20.8022 | −0.698075 | ||||||||
\(889\) | 12.8687 | 0.431603 | ||||||||
\(890\) | −42.2361 | −1.41576 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 11.4470 | 0.383273 | ||||||||
\(893\) | 11.2090 | 0.375096 | ||||||||
\(894\) | −35.6641 | −1.19279 | ||||||||
\(895\) | −2.42024 | −0.0808998 | ||||||||
\(896\) | 14.3760 | 0.480267 | ||||||||
\(897\) | −45.7632 | −1.52799 | ||||||||
\(898\) | 92.2205 | 3.07744 | ||||||||
\(899\) | 31.5691 | 1.05289 | ||||||||
\(900\) | 4.36426 | 0.145475 | ||||||||
\(901\) | −7.50022 | −0.249868 | ||||||||
\(902\) | −26.3404 | −0.877039 | ||||||||
\(903\) | −11.5345 | −0.383843 | ||||||||
\(904\) | −49.4668 | −1.64524 | ||||||||
\(905\) | −2.54191 | −0.0844959 | ||||||||
\(906\) | 19.0867 | 0.634114 | ||||||||
\(907\) | 7.04732 | 0.234002 | 0.117001 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.117001 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(908\) | −13.1923 | −0.437802 | ||||||||
\(909\) | 14.9816 | 0.496910 | ||||||||
\(910\) | 13.7280 | 0.455078 | ||||||||
\(911\) | 41.7472 | 1.38315 | 0.691573 | − | 0.722307i | \(-0.256918\pi\) | ||||
0.691573 | + | 0.722307i | \(0.256918\pi\) | |||||||
\(912\) | −8.61970 | −0.285427 | ||||||||
\(913\) | −9.51910 | −0.315036 | ||||||||
\(914\) | 47.4242 | 1.56865 | ||||||||
\(915\) | −3.52640 | −0.116579 | ||||||||
\(916\) | −14.1282 | −0.466808 | ||||||||
\(917\) | 11.4239 | 0.377249 | ||||||||
\(918\) | −3.55779 | −0.117425 | ||||||||
\(919\) | −2.65284 | −0.0875092 | −0.0437546 | − | 0.999042i | \(-0.513932\pi\) | ||||
−0.0437546 | + | 0.999042i | \(0.513932\pi\) | |||||||
\(920\) | −50.1594 | −1.65371 | ||||||||
\(921\) | 16.8859 | 0.556408 | ||||||||
\(922\) | −86.0187 | −2.83288 | ||||||||
\(923\) | 25.5505 | 0.841006 | ||||||||
\(924\) | 4.36426 | 0.143574 | ||||||||
\(925\) | 3.48771 | 0.114675 | ||||||||
\(926\) | 15.6616 | 0.514673 | ||||||||
\(927\) | 2.07742 | 0.0682315 | ||||||||
\(928\) | −35.1312 | −1.15324 | ||||||||
\(929\) | −33.7286 | −1.10660 | −0.553299 | − | 0.832983i | \(-0.686631\pi\) | ||||
−0.553299 | + | 0.832983i | \(0.686631\pi\) | |||||||
\(930\) | 9.09152 | 0.298123 | ||||||||
\(931\) | −1.36426 | −0.0447118 | ||||||||
\(932\) | −78.7149 | −2.57839 | ||||||||
\(933\) | −15.0633 | −0.493151 | ||||||||
\(934\) | −8.09205 | −0.264780 | ||||||||
\(935\) | −1.41028 | −0.0461212 | ||||||||
\(936\) | −32.4565 | −1.06087 | ||||||||
\(937\) | −27.4371 | −0.896330 | −0.448165 | − | 0.893951i | \(-0.647922\pi\) | ||||
−0.448165 | + | 0.893951i | \(0.647922\pi\) | |||||||
\(938\) | 2.75364 | 0.0899094 | ||||||||
\(939\) | −14.8687 | −0.485223 | ||||||||
\(940\) | 35.8577 | 1.16955 | ||||||||
\(941\) | 11.5725 | 0.377251 | 0.188626 | − | 0.982049i | \(-0.439597\pi\) | ||||
0.188626 | + | 0.982049i | \(0.439597\pi\) | |||||||
\(942\) | 54.4844 | 1.77520 | ||||||||
\(943\) | −87.8075 | −2.85941 | ||||||||
\(944\) | 44.7134 | 1.45530 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 29.0985 | 0.946075 | ||||||||
\(947\) | 11.0719 | 0.359789 | 0.179894 | − | 0.983686i | \(-0.442424\pi\) | ||||
0.179894 | + | 0.983686i | \(0.442424\pi\) | |||||||
\(948\) | 19.8937 | 0.646117 | ||||||||
\(949\) | 39.8138 | 1.29241 | ||||||||
\(950\) | 3.44168 | 0.111663 | ||||||||
\(951\) | 31.0015 | 1.00529 | ||||||||
\(952\) | −8.41154 | −0.272619 | ||||||||
\(953\) | −48.3609 | −1.56656 | −0.783281 | − | 0.621667i | \(-0.786456\pi\) | ||||
−0.783281 | + | 0.621667i | \(0.786456\pi\) | |||||||
\(954\) | 13.4166 | 0.434377 | ||||||||
\(955\) | −24.0899 | −0.779532 | ||||||||
\(956\) | 41.2137 | 1.33295 | ||||||||
\(957\) | 8.75991 | 0.283168 | ||||||||
\(958\) | 25.5434 | 0.825270 | ||||||||
\(959\) | 7.61187 | 0.245800 | ||||||||
\(960\) | 2.51910 | 0.0813036 | ||||||||
\(961\) | −18.0125 | −0.581049 | ||||||||
\(962\) | −47.8792 | −1.54369 | ||||||||
\(963\) | 13.3778 | 0.431095 | ||||||||
\(964\) | 73.1720 | 2.35671 | ||||||||
\(965\) | −7.77401 | −0.250254 | ||||||||
\(966\) | 21.2157 | 0.682604 | ||||||||
\(967\) | −38.9904 | −1.25385 | −0.626924 | − | 0.779081i | \(-0.715686\pi\) | ||||
−0.626924 | + | 0.779081i | \(0.715686\pi\) | |||||||
\(968\) | −5.96443 | −0.191704 | ||||||||
\(969\) | −1.92399 | −0.0618075 | ||||||||
\(970\) | 41.0274 | 1.31731 | ||||||||
\(971\) | −56.7487 | −1.82115 | −0.910577 | − | 0.413340i | \(-0.864362\pi\) | ||||
−0.910577 | + | 0.413340i | \(0.864362\pi\) | |||||||
\(972\) | 4.36426 | 0.139984 | ||||||||
\(973\) | −9.31645 | −0.298672 | ||||||||
\(974\) | 64.5119 | 2.06710 | ||||||||
\(975\) | 5.44168 | 0.174273 | ||||||||
\(976\) | 22.2806 | 0.713184 | ||||||||
\(977\) | −33.9990 | −1.08772 | −0.543862 | − | 0.839174i | \(-0.683039\pi\) | ||||
−0.543862 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(978\) | −43.0402 | −1.37627 | ||||||||
\(979\) | −16.7421 | −0.535079 | ||||||||
\(980\) | −4.36426 | −0.139411 | ||||||||
\(981\) | −10.2790 | −0.328184 | ||||||||
\(982\) | 39.0221 | 1.24525 | ||||||||
\(983\) | −3.52088 | −0.112299 | −0.0561494 | − | 0.998422i | \(-0.517882\pi\) | ||||
−0.0561494 | + | 0.998422i | \(0.517882\pi\) | |||||||
\(984\) | −62.2755 | −1.98527 | ||||||||
\(985\) | 0.425797 | 0.0135670 | ||||||||
\(986\) | −31.1659 | −0.992526 | ||||||||
\(987\) | −8.21622 | −0.261525 | ||||||||
\(988\) | −32.3996 | −1.03077 | ||||||||
\(989\) | 97.0019 | 3.08448 | ||||||||
\(990\) | 2.52275 | 0.0801782 | ||||||||
\(991\) | 35.2790 | 1.12068 | 0.560338 | − | 0.828264i | \(-0.310671\pi\) | ||||
0.560338 | + | 0.828264i | \(0.310671\pi\) | |||||||
\(992\) | −14.4529 | −0.458881 | ||||||||
\(993\) | 13.6597 | 0.433477 | ||||||||
\(994\) | −11.8452 | −0.375706 | ||||||||
\(995\) | −11.8200 | −0.374720 | ||||||||
\(996\) | −41.5438 | −1.31637 | ||||||||
\(997\) | 22.6176 | 0.716306 | 0.358153 | − | 0.933663i | \(-0.383407\pi\) | ||||
0.358153 | + | 0.933663i | \(0.383407\pi\) | |||||||
\(998\) | 1.79739 | 0.0568954 | ||||||||
\(999\) | 3.48771 | 0.110346 |
(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 | 1155.2.a.w.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 3465.2.a.bm.1.5 | 5 | |||
5.4 | even | 2 | 5775.2.a.cg.1.5 | 5 | |||
7.6 | odd | 2 | 8085.2.a.bv.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.w.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
3465.2.a.bm.1.5 | 5 | 3.2 | odd | 2 | |||
5775.2.a.cg.1.5 | 5 | 5.4 | even | 2 | |||
8085.2.a.bv.1.1 | 5 | 7.6 | odd | 2 |