Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.81361 | 1.98952 | 0.994760 | − | 0.102237i | \(-0.0325999\pi\) | ||||
0.994760 | + | 0.102237i | \(0.0325999\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.91638 | 2.95819 | ||||||||
\(5\) | 1.28917 | 0.576534 | 0.288267 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288267 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(6\) | −2.81361 | −1.14865 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 11.0192 | 3.89586 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.62721 | 1.14703 | ||||||||
\(11\) | −4.20555 | −1.26802 | −0.634011 | − | 0.773324i | \(-0.718592\pi\) | ||||
−0.634011 | + | 0.773324i | \(0.718592\pi\) | |||||||
\(12\) | −5.91638 | −1.70791 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.81361 | 0.751968 | ||||||||
\(15\) | −1.28917 | −0.332862 | ||||||||
\(16\) | 19.1708 | 4.79270 | ||||||||
\(17\) | 1.62721 | 0.394657 | 0.197329 | − | 0.980337i | \(-0.436773\pi\) | ||||
0.197329 | + | 0.980337i | \(0.436773\pi\) | |||||||
\(18\) | 2.81361 | 0.663173 | ||||||||
\(19\) | 6.33804 | 1.45405 | 0.727024 | − | 0.686613i | \(-0.240903\pi\) | ||||
0.727024 | + | 0.686613i | \(0.240903\pi\) | |||||||
\(20\) | 7.62721 | 1.70550 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −11.8328 | −2.52275 | ||||||||
\(23\) | −2.71083 | −0.565247 | −0.282624 | − | 0.959231i | \(-0.591205\pi\) | ||||
−0.282624 | + | 0.959231i | \(0.591205\pi\) | |||||||
\(24\) | −11.0192 | −2.24928 | ||||||||
\(25\) | −3.33804 | −0.667609 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.91638 | 1.11809 | ||||||||
\(29\) | −4.33804 | −0.805555 | −0.402777 | − | 0.915298i | \(-0.631955\pi\) | ||||
−0.402777 | + | 0.915298i | \(0.631955\pi\) | |||||||
\(30\) | −3.62721 | −0.662235 | ||||||||
\(31\) | 7.49472 | 1.34609 | 0.673046 | − | 0.739601i | \(-0.264986\pi\) | ||||
0.673046 | + | 0.739601i | \(0.264986\pi\) | |||||||
\(32\) | 31.9008 | 5.63932 | ||||||||
\(33\) | 4.20555 | 0.732092 | ||||||||
\(34\) | 4.57834 | 0.785178 | ||||||||
\(35\) | 1.28917 | 0.217909 | ||||||||
\(36\) | 5.91638 | 0.986064 | ||||||||
\(37\) | −3.42166 | −0.562518 | −0.281259 | − | 0.959632i | \(-0.590752\pi\) | ||||
−0.281259 | + | 0.959632i | \(0.590752\pi\) | |||||||
\(38\) | 17.8328 | 2.89286 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.2056 | 2.24609 | ||||||||
\(41\) | 7.62721 | 1.19117 | 0.595585 | − | 0.803292i | \(-0.296920\pi\) | ||||
0.595585 | + | 0.803292i | \(0.296920\pi\) | |||||||
\(42\) | −2.81361 | −0.434149 | ||||||||
\(43\) | −4.91638 | −0.749741 | −0.374871 | − | 0.927077i | \(-0.622313\pi\) | ||||
−0.374871 | + | 0.927077i | \(0.622313\pi\) | |||||||
\(44\) | −24.8816 | −3.75105 | ||||||||
\(45\) | 1.28917 | 0.192178 | ||||||||
\(46\) | −7.62721 | −1.12457 | ||||||||
\(47\) | 1.08362 | 0.158062 | 0.0790310 | − | 0.996872i | \(-0.474817\pi\) | ||||
0.0790310 | + | 0.996872i | \(0.474817\pi\) | |||||||
\(48\) | −19.1708 | −2.76707 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.39194 | −1.32822 | ||||||||
\(51\) | −1.62721 | −0.227855 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.75971 | 0.241714 | 0.120857 | − | 0.992670i | \(-0.461436\pi\) | ||||
0.120857 | + | 0.992670i | \(0.461436\pi\) | |||||||
\(54\) | −2.81361 | −0.382883 | ||||||||
\(55\) | −5.42166 | −0.731057 | ||||||||
\(56\) | 11.0192 | 1.47250 | ||||||||
\(57\) | −6.33804 | −0.839494 | ||||||||
\(58\) | −12.2056 | −1.60267 | ||||||||
\(59\) | 4.57834 | 0.596049 | 0.298024 | − | 0.954558i | \(-0.403672\pi\) | ||||
0.298024 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(60\) | −7.62721 | −0.984669 | ||||||||
\(61\) | −5.25443 | −0.672760 | −0.336380 | − | 0.941726i | \(-0.609203\pi\) | ||||
−0.336380 | + | 0.941726i | \(0.609203\pi\) | |||||||
\(62\) | 21.0872 | 2.67808 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 51.4147 | 6.42683 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.8328 | 1.45651 | ||||||||
\(67\) | −8.67609 | −1.05995 | −0.529976 | − | 0.848012i | \(-0.677799\pi\) | ||||
−0.529976 | + | 0.848012i | \(0.677799\pi\) | |||||||
\(68\) | 9.62721 | 1.16747 | ||||||||
\(69\) | 2.71083 | 0.326346 | ||||||||
\(70\) | 3.62721 | 0.433535 | ||||||||
\(71\) | 6.78389 | 0.805099 | 0.402550 | − | 0.915398i | \(-0.368124\pi\) | ||||
0.402550 | + | 0.915398i | \(0.368124\pi\) | |||||||
\(72\) | 11.0192 | 1.29862 | ||||||||
\(73\) | −4.07306 | −0.476715 | −0.238358 | − | 0.971177i | \(-0.576609\pi\) | ||||
−0.238358 | + | 0.971177i | \(0.576609\pi\) | |||||||
\(74\) | −9.62721 | −1.11914 | ||||||||
\(75\) | 3.33804 | 0.385444 | ||||||||
\(76\) | 37.4983 | 4.30135 | ||||||||
\(77\) | −4.20555 | −0.479267 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.91638 | −1.00317 | −0.501586 | − | 0.865108i | \(-0.667250\pi\) | ||||
−0.501586 | + | 0.865108i | \(0.667250\pi\) | |||||||
\(80\) | 24.7144 | 2.76315 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 21.4600 | 2.36986 | ||||||||
\(83\) | 4.33804 | 0.476162 | 0.238081 | − | 0.971245i | \(-0.423482\pi\) | ||||
0.238081 | + | 0.971245i | \(0.423482\pi\) | |||||||
\(84\) | −5.91638 | −0.645530 | ||||||||
\(85\) | 2.09775 | 0.227533 | ||||||||
\(86\) | −13.8328 | −1.49163 | ||||||||
\(87\) | 4.33804 | 0.465087 | ||||||||
\(88\) | −46.3416 | −4.94003 | ||||||||
\(89\) | −4.54359 | −0.481620 | −0.240810 | − | 0.970572i | \(-0.577413\pi\) | ||||
−0.240810 | + | 0.970572i | \(0.577413\pi\) | |||||||
\(90\) | 3.62721 | 0.382342 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16.0383 | −1.67211 | ||||||||
\(93\) | −7.49472 | −0.777166 | ||||||||
\(94\) | 3.04888 | 0.314468 | ||||||||
\(95\) | 8.17081 | 0.838307 | ||||||||
\(96\) | −31.9008 | −3.25586 | ||||||||
\(97\) | −11.3275 | −1.15013 | −0.575066 | − | 0.818107i | \(-0.695024\pi\) | ||||
−0.575066 | + | 0.818107i | \(0.695024\pi\) | |||||||
\(98\) | 2.81361 | 0.284217 | ||||||||
\(99\) | −4.20555 | −0.422674 | ||||||||
\(100\) | −19.7491 | −1.97491 | ||||||||
\(101\) | 14.3033 | 1.42323 | 0.711616 | − | 0.702569i | \(-0.247964\pi\) | ||||
0.711616 | + | 0.702569i | \(0.247964\pi\) | |||||||
\(102\) | −4.57834 | −0.453323 | ||||||||
\(103\) | −19.6655 | −1.93770 | −0.968851 | − | 0.247645i | \(-0.920343\pi\) | ||||
−0.968851 | + | 0.247645i | \(0.920343\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.28917 | −0.125810 | ||||||||
\(106\) | 4.95112 | 0.480896 | ||||||||
\(107\) | 2.20555 | 0.213219 | 0.106609 | − | 0.994301i | \(-0.466001\pi\) | ||||
0.106609 | + | 0.994301i | \(0.466001\pi\) | |||||||
\(108\) | −5.91638 | −0.569304 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | −15.2544 | −1.45445 | ||||||||
\(111\) | 3.42166 | 0.324770 | ||||||||
\(112\) | 19.1708 | 1.81147 | ||||||||
\(113\) | −2.17081 | −0.204212 | −0.102106 | − | 0.994774i | \(-0.532558\pi\) | ||||
−0.102106 | + | 0.994774i | \(0.532558\pi\) | |||||||
\(114\) | −17.8328 | −1.67019 | ||||||||
\(115\) | −3.49472 | −0.325884 | ||||||||
\(116\) | −25.6655 | −2.38298 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.8816 | 1.18585 | ||||||||
\(119\) | 1.62721 | 0.149166 | ||||||||
\(120\) | −14.2056 | −1.29678 | ||||||||
\(121\) | 6.68665 | 0.607877 | ||||||||
\(122\) | −14.7839 | −1.33847 | ||||||||
\(123\) | −7.62721 | −0.687723 | ||||||||
\(124\) | 44.3416 | 3.98199 | ||||||||
\(125\) | −10.7491 | −0.961433 | ||||||||
\(126\) | 2.81361 | 0.250656 | ||||||||
\(127\) | −0.745574 | −0.0661590 | −0.0330795 | − | 0.999453i | \(-0.510531\pi\) | ||||
−0.0330795 | + | 0.999453i | \(0.510531\pi\) | |||||||
\(128\) | 80.8591 | 7.14700 | ||||||||
\(129\) | 4.91638 | 0.432863 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5089 | −1.26764 | −0.633822 | − | 0.773479i | \(-0.718515\pi\) | ||||
−0.633822 | + | 0.773479i | \(0.718515\pi\) | |||||||
\(132\) | 24.8816 | 2.16567 | ||||||||
\(133\) | 6.33804 | 0.549578 | ||||||||
\(134\) | −24.4111 | −2.10880 | ||||||||
\(135\) | −1.28917 | −0.110954 | ||||||||
\(136\) | 17.9305 | 1.53753 | ||||||||
\(137\) | −4.41110 | −0.376866 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(138\) | 7.62721 | 0.649271 | ||||||||
\(139\) | 18.9894 | 1.61066 | 0.805332 | − | 0.592825i | \(-0.201987\pi\) | ||||
0.805332 | + | 0.592825i | \(0.201987\pi\) | |||||||
\(140\) | 7.62721 | 0.644617 | ||||||||
\(141\) | −1.08362 | −0.0912571 | ||||||||
\(142\) | 19.0872 | 1.60176 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 19.1708 | 1.59757 | ||||||||
\(145\) | −5.59247 | −0.464429 | ||||||||
\(146\) | −11.4600 | −0.948434 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −20.2439 | −1.66404 | ||||||||
\(149\) | 9.42166 | 0.771853 | 0.385926 | − | 0.922530i | \(-0.373882\pi\) | ||||
0.385926 | + | 0.922530i | \(0.373882\pi\) | |||||||
\(150\) | 9.39194 | 0.766849 | ||||||||
\(151\) | 16.4111 | 1.33552 | 0.667758 | − | 0.744378i | \(-0.267254\pi\) | ||||
0.667758 | + | 0.744378i | \(0.267254\pi\) | |||||||
\(152\) | 69.8399 | 5.66476 | ||||||||
\(153\) | 1.62721 | 0.131552 | ||||||||
\(154\) | −11.8328 | −0.953511 | ||||||||
\(155\) | 9.66196 | 0.776067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.51941 | −0.759732 | −0.379866 | − | 0.925042i | \(-0.624030\pi\) | ||||
−0.379866 | + | 0.925042i | \(0.624030\pi\) | |||||||
\(158\) | −25.0872 | −1.99583 | ||||||||
\(159\) | −1.75971 | −0.139554 | ||||||||
\(160\) | 41.1255 | 3.25126 | ||||||||
\(161\) | −2.71083 | −0.213643 | ||||||||
\(162\) | 2.81361 | 0.221058 | ||||||||
\(163\) | 0.745574 | 0.0583979 | 0.0291989 | − | 0.999574i | \(-0.490704\pi\) | ||||
0.0291989 | + | 0.999574i | \(0.490704\pi\) | |||||||
\(164\) | 45.1255 | 3.52371 | ||||||||
\(165\) | 5.42166 | 0.422076 | ||||||||
\(166\) | 12.2056 | 0.947334 | ||||||||
\(167\) | −3.59247 | −0.277994 | −0.138997 | − | 0.990293i | \(-0.544388\pi\) | ||||
−0.138997 | + | 0.990293i | \(0.544388\pi\) | |||||||
\(168\) | −11.0192 | −0.850146 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.90225 | 0.452682 | ||||||||
\(171\) | 6.33804 | 0.484682 | ||||||||
\(172\) | −29.0872 | −2.21788 | ||||||||
\(173\) | −15.7250 | −1.19555 | −0.597773 | − | 0.801665i | \(-0.703948\pi\) | ||||
−0.597773 | + | 0.801665i | \(0.703948\pi\) | |||||||
\(174\) | 12.2056 | 0.925300 | ||||||||
\(175\) | −3.33804 | −0.252332 | ||||||||
\(176\) | −80.6238 | −6.07725 | ||||||||
\(177\) | −4.57834 | −0.344129 | ||||||||
\(178\) | −12.7839 | −0.958193 | ||||||||
\(179\) | 24.9547 | 1.86520 | 0.932601 | − | 0.360910i | \(-0.117534\pi\) | ||||
0.932601 | + | 0.360910i | \(0.117534\pi\) | |||||||
\(180\) | 7.62721 | 0.568499 | ||||||||
\(181\) | 10.9411 | 0.813244 | 0.406622 | − | 0.913597i | \(-0.366707\pi\) | ||||
0.406622 | + | 0.913597i | \(0.366707\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.25443 | 0.388418 | ||||||||
\(184\) | −29.8711 | −2.20212 | ||||||||
\(185\) | −4.41110 | −0.324311 | ||||||||
\(186\) | −21.0872 | −1.54619 | ||||||||
\(187\) | −6.84333 | −0.500434 | ||||||||
\(188\) | 6.41110 | 0.467578 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 22.9894 | 1.66783 | ||||||||
\(191\) | 5.04888 | 0.365324 | 0.182662 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182662 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(192\) | −51.4147 | −3.71053 | ||||||||
\(193\) | −2.74557 | −0.197631 | −0.0988154 | − | 0.995106i | \(-0.531505\pi\) | ||||
−0.0988154 | + | 0.995106i | \(0.531505\pi\) | |||||||
\(194\) | −31.8711 | −2.28821 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.91638 | 0.422599 | ||||||||
\(197\) | −5.42166 | −0.386277 | −0.193139 | − | 0.981171i | \(-0.561867\pi\) | ||||
−0.193139 | + | 0.981171i | \(0.561867\pi\) | |||||||
\(198\) | −11.8328 | −0.840918 | ||||||||
\(199\) | −20.4111 | −1.44690 | −0.723452 | − | 0.690374i | \(-0.757446\pi\) | ||||
−0.723452 | + | 0.690374i | \(0.757446\pi\) | |||||||
\(200\) | −36.7824 | −2.60091 | ||||||||
\(201\) | 8.67609 | 0.611964 | ||||||||
\(202\) | 40.2439 | 2.83155 | ||||||||
\(203\) | −4.33804 | −0.304471 | ||||||||
\(204\) | −9.62721 | −0.674040 | ||||||||
\(205\) | 9.83276 | 0.686750 | ||||||||
\(206\) | −55.3311 | −3.85510 | ||||||||
\(207\) | −2.71083 | −0.188416 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.6550 | −1.84376 | ||||||||
\(210\) | −3.62721 | −0.250301 | ||||||||
\(211\) | −14.4842 | −0.997130 | −0.498565 | − | 0.866852i | \(-0.666140\pi\) | ||||
−0.498565 | + | 0.866852i | \(0.666140\pi\) | |||||||
\(212\) | 10.4111 | 0.715037 | ||||||||
\(213\) | −6.78389 | −0.464824 | ||||||||
\(214\) | 6.20555 | 0.424203 | ||||||||
\(215\) | −6.33804 | −0.432251 | ||||||||
\(216\) | −11.0192 | −0.749759 | ||||||||
\(217\) | 7.49472 | 0.508775 | ||||||||
\(218\) | −28.1361 | −1.90561 | ||||||||
\(219\) | 4.07306 | 0.275232 | ||||||||
\(220\) | −32.0766 | −2.16261 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.62721 | 0.646136 | ||||||||
\(223\) | −16.8469 | −1.12815 | −0.564076 | − | 0.825723i | \(-0.690767\pi\) | ||||
−0.564076 | + | 0.825723i | \(0.690767\pi\) | |||||||
\(224\) | 31.9008 | 2.13146 | ||||||||
\(225\) | −3.33804 | −0.222536 | ||||||||
\(226\) | −6.10780 | −0.406285 | ||||||||
\(227\) | 21.9305 | 1.45558 | 0.727790 | − | 0.685800i | \(-0.240548\pi\) | ||||
0.727790 | + | 0.685800i | \(0.240548\pi\) | |||||||
\(228\) | −37.4983 | −2.48338 | ||||||||
\(229\) | 5.25443 | 0.347222 | 0.173611 | − | 0.984814i | \(-0.444456\pi\) | ||||
0.173611 | + | 0.984814i | \(0.444456\pi\) | |||||||
\(230\) | −9.83276 | −0.648353 | ||||||||
\(231\) | 4.20555 | 0.276705 | ||||||||
\(232\) | −47.8016 | −3.13833 | ||||||||
\(233\) | 4.07306 | 0.266835 | 0.133417 | − | 0.991060i | \(-0.457405\pi\) | ||||
0.133417 | + | 0.991060i | \(0.457405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.39697 | 0.0911281 | ||||||||
\(236\) | 27.0872 | 1.76323 | ||||||||
\(237\) | 8.91638 | 0.579181 | ||||||||
\(238\) | 4.57834 | 0.296770 | ||||||||
\(239\) | 2.37279 | 0.153483 | 0.0767414 | − | 0.997051i | \(-0.475548\pi\) | ||||
0.0767414 | + | 0.997051i | \(0.475548\pi\) | |||||||
\(240\) | −24.7144 | −1.59531 | ||||||||
\(241\) | −14.9164 | −0.960849 | −0.480424 | − | 0.877036i | \(-0.659517\pi\) | ||||
−0.480424 | + | 0.877036i | \(0.659517\pi\) | |||||||
\(242\) | 18.8136 | 1.20938 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −31.0872 | −1.99015 | ||||||||
\(245\) | 1.28917 | 0.0823620 | ||||||||
\(246\) | −21.4600 | −1.36824 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 82.5855 | 5.24418 | ||||||||
\(249\) | −4.33804 | −0.274912 | ||||||||
\(250\) | −30.2439 | −1.91279 | ||||||||
\(251\) | −1.08719 | −0.0686228 | −0.0343114 | − | 0.999411i | \(-0.510924\pi\) | ||||
−0.0343114 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(252\) | 5.91638 | 0.372697 | ||||||||
\(253\) | 11.4005 | 0.716746 | ||||||||
\(254\) | −2.09775 | −0.131625 | ||||||||
\(255\) | −2.09775 | −0.131366 | ||||||||
\(256\) | 124.676 | 7.79226 | ||||||||
\(257\) | −16.6167 | −1.03652 | −0.518259 | − | 0.855224i | \(-0.673420\pi\) | ||||
−0.518259 | + | 0.855224i | \(0.673420\pi\) | |||||||
\(258\) | 13.8328 | 0.861190 | ||||||||
\(259\) | −3.42166 | −0.212612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.33804 | −0.268518 | ||||||||
\(262\) | −40.8222 | −2.52200 | ||||||||
\(263\) | −27.0524 | −1.66813 | −0.834063 | − | 0.551670i | \(-0.813991\pi\) | ||||
−0.834063 | + | 0.551670i | \(0.813991\pi\) | |||||||
\(264\) | 46.3416 | 2.85213 | ||||||||
\(265\) | 2.26856 | 0.139356 | ||||||||
\(266\) | 17.8328 | 1.09340 | ||||||||
\(267\) | 4.54359 | 0.278063 | ||||||||
\(268\) | −51.3311 | −3.13554 | ||||||||
\(269\) | 7.52946 | 0.459079 | 0.229540 | − | 0.973299i | \(-0.426278\pi\) | ||||
0.229540 | + | 0.973299i | \(0.426278\pi\) | |||||||
\(270\) | −3.62721 | −0.220745 | ||||||||
\(271\) | −16.8222 | −1.02188 | −0.510938 | − | 0.859618i | \(-0.670702\pi\) | ||||
−0.510938 | + | 0.859618i | \(0.670702\pi\) | |||||||
\(272\) | 31.1950 | 1.89147 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4111 | −0.749782 | ||||||||
\(275\) | 14.0383 | 0.846542 | ||||||||
\(276\) | 16.0383 | 0.965393 | ||||||||
\(277\) | 17.4947 | 1.05116 | 0.525578 | − | 0.850745i | \(-0.323849\pi\) | ||||
0.525578 | + | 0.850745i | \(0.323849\pi\) | |||||||
\(278\) | 53.4288 | 3.20445 | ||||||||
\(279\) | 7.49472 | 0.448697 | ||||||||
\(280\) | 14.2056 | 0.848944 | ||||||||
\(281\) | −27.4005 | −1.63458 | −0.817290 | − | 0.576227i | \(-0.804524\pi\) | ||||
−0.817290 | + | 0.576227i | \(0.804524\pi\) | |||||||
\(282\) | −3.04888 | −0.181558 | ||||||||
\(283\) | 20.0766 | 1.19343 | 0.596716 | − | 0.802453i | \(-0.296472\pi\) | ||||
0.596716 | + | 0.802453i | \(0.296472\pi\) | |||||||
\(284\) | 40.1361 | 2.38164 | ||||||||
\(285\) | −8.17081 | −0.483997 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.62721 | 0.450220 | ||||||||
\(288\) | 31.9008 | 1.87977 | ||||||||
\(289\) | −14.3522 | −0.844246 | ||||||||
\(290\) | −15.7350 | −0.923992 | ||||||||
\(291\) | 11.3275 | 0.664029 | ||||||||
\(292\) | −24.0978 | −1.41021 | ||||||||
\(293\) | 27.0524 | 1.58042 | 0.790210 | − | 0.612836i | \(-0.209971\pi\) | ||||
0.790210 | + | 0.612836i | \(0.209971\pi\) | |||||||
\(294\) | −2.81361 | −0.164093 | ||||||||
\(295\) | 5.90225 | 0.343642 | ||||||||
\(296\) | −37.7038 | −2.19149 | ||||||||
\(297\) | 4.20555 | 0.244031 | ||||||||
\(298\) | 26.5089 | 1.53562 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 19.7491 | 1.14022 | ||||||||
\(301\) | −4.91638 | −0.283376 | ||||||||
\(302\) | 46.1744 | 2.65704 | ||||||||
\(303\) | −14.3033 | −0.821703 | ||||||||
\(304\) | 121.505 | 6.96881 | ||||||||
\(305\) | −6.77384 | −0.387869 | ||||||||
\(306\) | 4.57834 | 0.261726 | ||||||||
\(307\) | 20.1708 | 1.15121 | 0.575604 | − | 0.817728i | \(-0.304767\pi\) | ||||
0.575604 | + | 0.817728i | \(0.304767\pi\) | |||||||
\(308\) | −24.8816 | −1.41776 | ||||||||
\(309\) | 19.6655 | 1.11873 | ||||||||
\(310\) | 27.1849 | 1.54400 | ||||||||
\(311\) | −6.57834 | −0.373023 | −0.186512 | − | 0.982453i | \(-0.559718\pi\) | ||||
−0.186512 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7456 | −0.607376 | −0.303688 | − | 0.952772i | \(-0.598218\pi\) | ||||
−0.303688 | + | 0.952772i | \(0.598218\pi\) | |||||||
\(314\) | −26.7839 | −1.51150 | ||||||||
\(315\) | 1.28917 | 0.0726364 | ||||||||
\(316\) | −52.7527 | −2.96757 | ||||||||
\(317\) | −24.6066 | −1.38204 | −0.691022 | − | 0.722833i | \(-0.742839\pi\) | ||||
−0.691022 | + | 0.722833i | \(0.742839\pi\) | |||||||
\(318\) | −4.95112 | −0.277645 | ||||||||
\(319\) | 18.2439 | 1.02146 | ||||||||
\(320\) | 66.2822 | 3.70529 | ||||||||
\(321\) | −2.20555 | −0.123102 | ||||||||
\(322\) | −7.62721 | −0.425048 | ||||||||
\(323\) | 10.3133 | 0.573850 | ||||||||
\(324\) | 5.91638 | 0.328688 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.09775 | 0.116184 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | 84.0455 | 4.64063 | ||||||||
\(329\) | 1.08362 | 0.0597418 | ||||||||
\(330\) | 15.2544 | 0.839729 | ||||||||
\(331\) | −30.6550 | −1.68495 | −0.842475 | − | 0.538736i | \(-0.818902\pi\) | ||||
−0.842475 | + | 0.538736i | \(0.818902\pi\) | |||||||
\(332\) | 25.6655 | 1.40858 | ||||||||
\(333\) | −3.42166 | −0.187506 | ||||||||
\(334\) | −10.1078 | −0.553074 | ||||||||
\(335\) | −11.1849 | −0.611099 | ||||||||
\(336\) | −19.1708 | −1.04585 | ||||||||
\(337\) | −6.50528 | −0.354365 | −0.177183 | − | 0.984178i | \(-0.556698\pi\) | ||||
−0.177183 | + | 0.984178i | \(0.556698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.17081 | 0.117902 | ||||||||
\(340\) | 12.4111 | 0.673086 | ||||||||
\(341\) | −31.5194 | −1.70687 | ||||||||
\(342\) | 17.8328 | 0.964285 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −54.1744 | −2.92089 | ||||||||
\(345\) | 3.49472 | 0.188149 | ||||||||
\(346\) | −44.2439 | −2.37856 | ||||||||
\(347\) | 24.3033 | 1.30467 | 0.652335 | − | 0.757931i | \(-0.273790\pi\) | ||||
0.652335 | + | 0.757931i | \(0.273790\pi\) | |||||||
\(348\) | 25.6655 | 1.37582 | ||||||||
\(349\) | −17.7597 | −0.950655 | −0.475328 | − | 0.879809i | \(-0.657670\pi\) | ||||
−0.475328 | + | 0.879809i | \(0.657670\pi\) | |||||||
\(350\) | −9.39194 | −0.502021 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −134.160 | −7.15077 | ||||||||
\(353\) | −1.94056 | −0.103286 | −0.0516428 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516428 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(354\) | −12.8816 | −0.684651 | ||||||||
\(355\) | 8.74557 | 0.464167 | ||||||||
\(356\) | −26.8816 | −1.42472 | ||||||||
\(357\) | −1.62721 | −0.0861212 | ||||||||
\(358\) | 70.2127 | 3.71086 | ||||||||
\(359\) | 33.6272 | 1.77478 | 0.887388 | − | 0.461023i | \(-0.152517\pi\) | ||||
0.887388 | + | 0.461023i | \(0.152517\pi\) | |||||||
\(360\) | 14.2056 | 0.748698 | ||||||||
\(361\) | 21.1708 | 1.11425 | ||||||||
\(362\) | 30.7839 | 1.61797 | ||||||||
\(363\) | −6.68665 | −0.350958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.25086 | −0.274842 | ||||||||
\(366\) | 14.7839 | 0.772766 | ||||||||
\(367\) | −10.5783 | −0.552185 | −0.276092 | − | 0.961131i | \(-0.589040\pi\) | ||||
−0.276092 | + | 0.961131i | \(0.589040\pi\) | |||||||
\(368\) | −51.9688 | −2.70906 | ||||||||
\(369\) | 7.62721 | 0.397057 | ||||||||
\(370\) | −12.4111 | −0.645222 | ||||||||
\(371\) | 1.75971 | 0.0913595 | ||||||||
\(372\) | −44.3416 | −2.29901 | ||||||||
\(373\) | −5.47002 | −0.283227 | −0.141614 | − | 0.989922i | \(-0.545229\pi\) | ||||
−0.141614 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(374\) | −19.2544 | −0.995623 | ||||||||
\(375\) | 10.7491 | 0.555083 | ||||||||
\(376\) | 11.9406 | 0.615787 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.81361 | −0.144716 | ||||||||
\(379\) | 5.42166 | 0.278492 | 0.139246 | − | 0.990258i | \(-0.455532\pi\) | ||||
0.139246 | + | 0.990258i | \(0.455532\pi\) | |||||||
\(380\) | 48.3416 | 2.47987 | ||||||||
\(381\) | 0.745574 | 0.0381969 | ||||||||
\(382\) | 14.2056 | 0.726819 | ||||||||
\(383\) | −14.1461 | −0.722833 | −0.361416 | − | 0.932405i | \(-0.617707\pi\) | ||||
−0.361416 | + | 0.932405i | \(0.617707\pi\) | |||||||
\(384\) | −80.8591 | −4.12632 | ||||||||
\(385\) | −5.42166 | −0.276314 | ||||||||
\(386\) | −7.72496 | −0.393190 | ||||||||
\(387\) | −4.91638 | −0.249914 | ||||||||
\(388\) | −67.0177 | −3.40231 | ||||||||
\(389\) | 0.313348 | 0.0158874 | 0.00794370 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794370 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.41110 | −0.223079 | ||||||||
\(392\) | 11.0192 | 0.556551 | ||||||||
\(393\) | 14.5089 | 0.731875 | ||||||||
\(394\) | −15.2544 | −0.768507 | ||||||||
\(395\) | −11.4947 | −0.578362 | ||||||||
\(396\) | −24.8816 | −1.25035 | ||||||||
\(397\) | −20.6797 | −1.03788 | −0.518941 | − | 0.854810i | \(-0.673674\pi\) | ||||
−0.518941 | + | 0.854810i | \(0.673674\pi\) | |||||||
\(398\) | −57.4288 | −2.87865 | ||||||||
\(399\) | −6.33804 | −0.317299 | ||||||||
\(400\) | −63.9930 | −3.19965 | ||||||||
\(401\) | 12.7456 | 0.636484 | 0.318242 | − | 0.948010i | \(-0.396908\pi\) | ||||
0.318242 | + | 0.948010i | \(0.396908\pi\) | |||||||
\(402\) | 24.4111 | 1.21752 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 84.6238 | 4.21019 | ||||||||
\(405\) | 1.28917 | 0.0640593 | ||||||||
\(406\) | −12.2056 | −0.605751 | ||||||||
\(407\) | 14.3900 | 0.713285 | ||||||||
\(408\) | −17.9305 | −0.887693 | ||||||||
\(409\) | 18.6514 | 0.922252 | 0.461126 | − | 0.887335i | \(-0.347446\pi\) | ||||
0.461126 | + | 0.887335i | \(0.347446\pi\) | |||||||
\(410\) | 27.6655 | 1.36630 | ||||||||
\(411\) | 4.41110 | 0.217584 | ||||||||
\(412\) | −116.349 | −5.73209 | ||||||||
\(413\) | 4.57834 | 0.225285 | ||||||||
\(414\) | −7.62721 | −0.374857 | ||||||||
\(415\) | 5.59247 | 0.274524 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.9894 | −0.929917 | ||||||||
\(418\) | −74.9966 | −3.66820 | ||||||||
\(419\) | 3.10831 | 0.151851 | 0.0759256 | − | 0.997113i | \(-0.475809\pi\) | ||||
0.0759256 | + | 0.997113i | \(0.475809\pi\) | |||||||
\(420\) | −7.62721 | −0.372170 | ||||||||
\(421\) | −13.4005 | −0.653102 | −0.326551 | − | 0.945180i | \(-0.605887\pi\) | ||||
−0.326551 | + | 0.945180i | \(0.605887\pi\) | |||||||
\(422\) | −40.7527 | −1.98381 | ||||||||
\(423\) | 1.08362 | 0.0526873 | ||||||||
\(424\) | 19.3905 | 0.941685 | ||||||||
\(425\) | −5.43171 | −0.263477 | ||||||||
\(426\) | −19.0872 | −0.924777 | ||||||||
\(427\) | −5.25443 | −0.254279 | ||||||||
\(428\) | 13.0489 | 0.630741 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.8328 | −0.859972 | ||||||||
\(431\) | −9.89220 | −0.476491 | −0.238245 | − | 0.971205i | \(-0.576572\pi\) | ||||
−0.238245 | + | 0.971205i | \(0.576572\pi\) | |||||||
\(432\) | −19.1708 | −0.922356 | ||||||||
\(433\) | 0.578337 | 0.0277931 | 0.0138966 | − | 0.999903i | \(-0.495576\pi\) | ||||
0.0138966 | + | 0.999903i | \(0.495576\pi\) | |||||||
\(434\) | 21.0872 | 1.01222 | ||||||||
\(435\) | 5.59247 | 0.268138 | ||||||||
\(436\) | −59.1638 | −2.83343 | ||||||||
\(437\) | −17.1814 | −0.821896 | ||||||||
\(438\) | 11.4600 | 0.547579 | ||||||||
\(439\) | 23.7350 | 1.13281 | 0.566405 | − | 0.824127i | \(-0.308334\pi\) | ||||
0.566405 | + | 0.824127i | \(0.308334\pi\) | |||||||
\(440\) | −59.7422 | −2.84810 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.86751 | −0.183751 | −0.0918754 | − | 0.995771i | \(-0.529286\pi\) | ||||
−0.0918754 | + | 0.995771i | \(0.529286\pi\) | |||||||
\(444\) | 20.2439 | 0.960731 | ||||||||
\(445\) | −5.85746 | −0.277670 | ||||||||
\(446\) | −47.4005 | −2.24448 | ||||||||
\(447\) | −9.42166 | −0.445629 | ||||||||
\(448\) | 51.4147 | 2.42911 | ||||||||
\(449\) | −1.68665 | −0.0795980 | −0.0397990 | − | 0.999208i | \(-0.512672\pi\) | ||||
−0.0397990 | + | 0.999208i | \(0.512672\pi\) | |||||||
\(450\) | −9.39194 | −0.442740 | ||||||||
\(451\) | −32.0766 | −1.51043 | ||||||||
\(452\) | −12.8433 | −0.604099 | ||||||||
\(453\) | −16.4111 | −0.771061 | ||||||||
\(454\) | 61.7038 | 2.89590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −69.8399 | −3.27055 | ||||||||
\(457\) | 3.83276 | 0.179289 | 0.0896445 | − | 0.995974i | \(-0.471427\pi\) | ||||
0.0896445 | + | 0.995974i | \(0.471427\pi\) | |||||||
\(458\) | 14.7839 | 0.690806 | ||||||||
\(459\) | −1.62721 | −0.0759518 | ||||||||
\(460\) | −20.6761 | −0.964028 | ||||||||
\(461\) | 11.2161 | 0.522386 | 0.261193 | − | 0.965287i | \(-0.415884\pi\) | ||||
0.261193 | + | 0.965287i | \(0.415884\pi\) | |||||||
\(462\) | 11.8328 | 0.550510 | ||||||||
\(463\) | 25.8328 | 1.20055 | 0.600275 | − | 0.799794i | \(-0.295058\pi\) | ||||
0.600275 | + | 0.799794i | \(0.295058\pi\) | |||||||
\(464\) | −83.1638 | −3.86078 | ||||||||
\(465\) | −9.66196 | −0.448062 | ||||||||
\(466\) | 11.4600 | 0.530873 | ||||||||
\(467\) | 41.0872 | 1.90129 | 0.950644 | − | 0.310283i | \(-0.100424\pi\) | ||||
0.950644 | + | 0.310283i | \(0.100424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.67609 | −0.400625 | ||||||||
\(470\) | 3.93051 | 0.181301 | ||||||||
\(471\) | 9.51941 | 0.438631 | ||||||||
\(472\) | 50.4494 | 2.32212 | ||||||||
\(473\) | 20.6761 | 0.950688 | ||||||||
\(474\) | 25.0872 | 1.15229 | ||||||||
\(475\) | −21.1567 | −0.970735 | ||||||||
\(476\) | 9.62721 | 0.441263 | ||||||||
\(477\) | 1.75971 | 0.0805715 | ||||||||
\(478\) | 6.67609 | 0.305357 | ||||||||
\(479\) | −2.43580 | −0.111294 | −0.0556472 | − | 0.998450i | \(-0.517722\pi\) | ||||
−0.0556472 | + | 0.998450i | \(0.517722\pi\) | |||||||
\(480\) | −41.1255 | −1.87711 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −41.9688 | −1.91163 | ||||||||
\(483\) | 2.71083 | 0.123347 | ||||||||
\(484\) | 39.5608 | 1.79822 | ||||||||
\(485\) | −14.6030 | −0.663090 | ||||||||
\(486\) | −2.81361 | −0.127628 | ||||||||
\(487\) | 6.57834 | 0.298093 | 0.149046 | − | 0.988830i | \(-0.452380\pi\) | ||||
0.149046 | + | 0.988830i | \(0.452380\pi\) | |||||||
\(488\) | −57.8993 | −2.62098 | ||||||||
\(489\) | −0.745574 | −0.0337160 | ||||||||
\(490\) | 3.62721 | 0.163861 | ||||||||
\(491\) | 28.3033 | 1.27731 | 0.638655 | − | 0.769493i | \(-0.279491\pi\) | ||||
0.638655 | + | 0.769493i | \(0.279491\pi\) | |||||||
\(492\) | −45.1255 | −2.03441 | ||||||||
\(493\) | −7.05892 | −0.317918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.42166 | −0.243686 | ||||||||
\(496\) | 143.680 | 6.45141 | ||||||||
\(497\) | 6.78389 | 0.304299 | ||||||||
\(498\) | −12.2056 | −0.546944 | ||||||||
\(499\) | −28.8222 | −1.29026 | −0.645129 | − | 0.764073i | \(-0.723197\pi\) | ||||
−0.645129 | + | 0.764073i | \(0.723197\pi\) | |||||||
\(500\) | −63.5960 | −2.84410 | ||||||||
\(501\) | 3.59247 | 0.160500 | ||||||||
\(502\) | −3.05892 | −0.136526 | ||||||||
\(503\) | 8.67609 | 0.386848 | 0.193424 | − | 0.981115i | \(-0.438041\pi\) | ||||
0.193424 | + | 0.981115i | \(0.438041\pi\) | |||||||
\(504\) | 11.0192 | 0.490832 | ||||||||
\(505\) | 18.4394 | 0.820541 | ||||||||
\(506\) | 32.0766 | 1.42598 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.41110 | −0.195711 | ||||||||
\(509\) | 9.28917 | 0.411735 | 0.205868 | − | 0.978580i | \(-0.433998\pi\) | ||||
0.205868 | + | 0.978580i | \(0.433998\pi\) | |||||||
\(510\) | −5.90225 | −0.261356 | ||||||||
\(511\) | −4.07306 | −0.180181 | ||||||||
\(512\) | 189.072 | 8.35587 | ||||||||
\(513\) | −6.33804 | −0.279831 | ||||||||
\(514\) | −46.7527 | −2.06217 | ||||||||
\(515\) | −25.3522 | −1.11715 | ||||||||
\(516\) | 29.0872 | 1.28049 | ||||||||
\(517\) | −4.55721 | −0.200426 | ||||||||
\(518\) | −9.62721 | −0.422995 | ||||||||
\(519\) | 15.7250 | 0.690249 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7250 | −0.513680 | −0.256840 | − | 0.966454i | \(-0.582681\pi\) | ||||
−0.256840 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(522\) | −12.2056 | −0.534222 | ||||||||
\(523\) | 0.676089 | 0.0295633 | 0.0147817 | − | 0.999891i | \(-0.495295\pi\) | ||||
0.0147817 | + | 0.999891i | \(0.495295\pi\) | |||||||
\(524\) | −85.8399 | −3.74993 | ||||||||
\(525\) | 3.33804 | 0.145684 | ||||||||
\(526\) | −76.1149 | −3.31877 | ||||||||
\(527\) | 12.1955 | 0.531244 | ||||||||
\(528\) | 80.6238 | 3.50870 | ||||||||
\(529\) | −15.6514 | −0.680495 | ||||||||
\(530\) | 6.38283 | 0.277253 | ||||||||
\(531\) | 4.57834 | 0.198683 | ||||||||
\(532\) | 37.4983 | 1.62576 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.7839 | 0.553213 | ||||||||
\(535\) | 2.84333 | 0.122928 | ||||||||
\(536\) | −95.6032 | −4.12943 | ||||||||
\(537\) | −24.9547 | −1.07687 | ||||||||
\(538\) | 21.1849 | 0.913348 | ||||||||
\(539\) | −4.20555 | −0.181146 | ||||||||
\(540\) | −7.62721 | −0.328223 | ||||||||
\(541\) | 0.578337 | 0.0248647 | 0.0124323 | − | 0.999923i | \(-0.496043\pi\) | ||||
0.0124323 | + | 0.999923i | \(0.496043\pi\) | |||||||
\(542\) | −47.3311 | −2.03304 | ||||||||
\(543\) | −10.9411 | −0.469527 | ||||||||
\(544\) | 51.9094 | 2.22560 | ||||||||
\(545\) | −12.8917 | −0.552219 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.985867 | −0.0421526 | −0.0210763 | − | 0.999778i | \(-0.506709\pi\) | ||||
−0.0210763 | + | 0.999778i | \(0.506709\pi\) | |||||||
\(548\) | −26.0978 | −1.11484 | ||||||||
\(549\) | −5.25443 | −0.224253 | ||||||||
\(550\) | 39.4983 | 1.68421 | ||||||||
\(551\) | −27.4947 | −1.17131 | ||||||||
\(552\) | 29.8711 | 1.27140 | ||||||||
\(553\) | −8.91638 | −0.379163 | ||||||||
\(554\) | 49.2233 | 2.09130 | ||||||||
\(555\) | 4.41110 | 0.187241 | ||||||||
\(556\) | 112.349 | 4.76465 | ||||||||
\(557\) | −41.2333 | −1.74711 | −0.873556 | − | 0.486725i | \(-0.838192\pi\) | ||||
−0.873556 | + | 0.486725i | \(0.838192\pi\) | |||||||
\(558\) | 21.0872 | 0.892692 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24.7144 | 1.04437 | ||||||||
\(561\) | 6.84333 | 0.288925 | ||||||||
\(562\) | −77.0943 | −3.25203 | ||||||||
\(563\) | 6.91995 | 0.291641 | 0.145821 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145821 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(564\) | −6.41110 | −0.269956 | ||||||||
\(565\) | −2.79854 | −0.117735 | ||||||||
\(566\) | 56.4877 | 2.37436 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 74.7527 | 3.13655 | ||||||||
\(569\) | −29.5713 | −1.23970 | −0.619848 | − | 0.784722i | \(-0.712806\pi\) | ||||
−0.619848 | + | 0.784722i | \(0.712806\pi\) | |||||||
\(570\) | −22.9894 | −0.962922 | ||||||||
\(571\) | −19.4252 | −0.812921 | −0.406460 | − | 0.913668i | \(-0.633237\pi\) | ||||
−0.406460 | + | 0.913668i | \(0.633237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.04888 | −0.210920 | ||||||||
\(574\) | 21.4600 | 0.895722 | ||||||||
\(575\) | 9.04888 | 0.377364 | ||||||||
\(576\) | 51.4147 | 2.14228 | ||||||||
\(577\) | 38.8222 | 1.61619 | 0.808095 | − | 0.589053i | \(-0.200499\pi\) | ||||
0.808095 | + | 0.589053i | \(0.200499\pi\) | |||||||
\(578\) | −40.3814 | −1.67964 | ||||||||
\(579\) | 2.74557 | 0.114102 | ||||||||
\(580\) | −33.0872 | −1.37387 | ||||||||
\(581\) | 4.33804 | 0.179972 | ||||||||
\(582\) | 31.8711 | 1.32110 | ||||||||
\(583\) | −7.40054 | −0.306499 | ||||||||
\(584\) | −44.8816 | −1.85722 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 76.1149 | 3.14428 | ||||||||
\(587\) | −24.0731 | −0.993601 | −0.496801 | − | 0.867865i | \(-0.665492\pi\) | ||||
−0.496801 | + | 0.867865i | \(0.665492\pi\) | |||||||
\(588\) | −5.91638 | −0.243987 | ||||||||
\(589\) | 47.5019 | 1.95728 | ||||||||
\(590\) | 16.6066 | 0.683683 | ||||||||
\(591\) | 5.42166 | 0.223017 | ||||||||
\(592\) | −65.5960 | −2.69598 | ||||||||
\(593\) | −40.4741 | −1.66207 | −0.831036 | − | 0.556218i | \(-0.812252\pi\) | ||||
−0.831036 | + | 0.556218i | \(0.812252\pi\) | |||||||
\(594\) | 11.8328 | 0.485504 | ||||||||
\(595\) | 2.09775 | 0.0859994 | ||||||||
\(596\) | 55.7422 | 2.28329 | ||||||||
\(597\) | 20.4111 | 0.835371 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.49523 | −0.101953 | −0.0509763 | − | 0.998700i | \(-0.516233\pi\) | ||||
−0.0509763 | + | 0.998700i | \(0.516233\pi\) | |||||||
\(600\) | 36.7824 | 1.50164 | ||||||||
\(601\) | 35.2333 | 1.43720 | 0.718598 | − | 0.695426i | \(-0.244784\pi\) | ||||
0.718598 | + | 0.695426i | \(0.244784\pi\) | |||||||
\(602\) | −13.8328 | −0.563781 | ||||||||
\(603\) | −8.67609 | −0.353318 | ||||||||
\(604\) | 97.0943 | 3.95071 | ||||||||
\(605\) | 8.62022 | 0.350462 | ||||||||
\(606\) | −40.2439 | −1.63480 | ||||||||
\(607\) | 4.89169 | 0.198547 | 0.0992737 | − | 0.995060i | \(-0.468348\pi\) | ||||
0.0992737 | + | 0.995060i | \(0.468348\pi\) | |||||||
\(608\) | 202.189 | 8.19983 | ||||||||
\(609\) | 4.33804 | 0.175786 | ||||||||
\(610\) | −19.0589 | −0.771673 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 9.62721 | 0.389157 | ||||||||
\(613\) | −7.83276 | −0.316362 | −0.158181 | − | 0.987410i | \(-0.550563\pi\) | ||||
−0.158181 | + | 0.987410i | \(0.550563\pi\) | |||||||
\(614\) | 56.7527 | 2.29035 | ||||||||
\(615\) | −9.83276 | −0.396495 | ||||||||
\(616\) | −46.3416 | −1.86716 | ||||||||
\(617\) | −15.7350 | −0.633468 | −0.316734 | − | 0.948514i | \(-0.602586\pi\) | ||||
−0.316734 | + | 0.948514i | \(0.602586\pi\) | |||||||
\(618\) | 55.3311 | 2.22574 | ||||||||
\(619\) | 41.0177 | 1.64864 | 0.824320 | − | 0.566124i | \(-0.191558\pi\) | ||||
0.824320 | + | 0.566124i | \(0.191558\pi\) | |||||||
\(620\) | 57.1638 | 2.29575 | ||||||||
\(621\) | 2.71083 | 0.108782 | ||||||||
\(622\) | −18.5089 | −0.742137 | ||||||||
\(623\) | −4.54359 | −0.182035 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.83276 | 0.113311 | ||||||||
\(626\) | −30.2338 | −1.20839 | ||||||||
\(627\) | 26.6550 | 1.06450 | ||||||||
\(628\) | −56.3205 | −2.24743 | ||||||||
\(629\) | −5.56777 | −0.222002 | ||||||||
\(630\) | 3.62721 | 0.144512 | ||||||||
\(631\) | 19.5960 | 0.780106 | 0.390053 | − | 0.920792i | \(-0.372457\pi\) | ||||
0.390053 | + | 0.920792i | \(0.372457\pi\) | |||||||
\(632\) | −98.2510 | −3.90822 | ||||||||
\(633\) | 14.4842 | 0.575694 | ||||||||
\(634\) | −69.2333 | −2.74961 | ||||||||
\(635\) | −0.961171 | −0.0381429 | ||||||||
\(636\) | −10.4111 | −0.412827 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 51.3311 | 2.03222 | ||||||||
\(639\) | 6.78389 | 0.268366 | ||||||||
\(640\) | 104.241 | 4.12049 | ||||||||
\(641\) | −20.8953 | −0.825313 | −0.412656 | − | 0.910887i | \(-0.635399\pi\) | ||||
−0.412656 | + | 0.910887i | \(0.635399\pi\) | |||||||
\(642\) | −6.20555 | −0.244914 | ||||||||
\(643\) | 9.15667 | 0.361104 | 0.180552 | − | 0.983565i | \(-0.442212\pi\) | ||||
0.180552 | + | 0.983565i | \(0.442212\pi\) | |||||||
\(644\) | −16.0383 | −0.631998 | ||||||||
\(645\) | 6.33804 | 0.249560 | ||||||||
\(646\) | 29.0177 | 1.14169 | ||||||||
\(647\) | −6.24386 | −0.245472 | −0.122736 | − | 0.992439i | \(-0.539167\pi\) | ||||
−0.122736 | + | 0.992439i | \(0.539167\pi\) | |||||||
\(648\) | 11.0192 | 0.432873 | ||||||||
\(649\) | −19.2544 | −0.755802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.49472 | −0.293741 | ||||||||
\(652\) | 4.41110 | 0.172752 | ||||||||
\(653\) | −38.8222 | −1.51923 | −0.759615 | − | 0.650373i | \(-0.774613\pi\) | ||||
−0.759615 | + | 0.650373i | \(0.774613\pi\) | |||||||
\(654\) | 28.1361 | 1.10021 | ||||||||
\(655\) | −18.7044 | −0.730840 | ||||||||
\(656\) | 146.220 | 5.70893 | ||||||||
\(657\) | −4.07306 | −0.158905 | ||||||||
\(658\) | 3.04888 | 0.118858 | ||||||||
\(659\) | −0.954695 | −0.0371896 | −0.0185948 | − | 0.999827i | \(-0.505919\pi\) | ||||
−0.0185948 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(660\) | 32.0766 | 1.24858 | ||||||||
\(661\) | −2.28968 | −0.0890584 | −0.0445292 | − | 0.999008i | \(-0.514179\pi\) | ||||
−0.0445292 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(662\) | −86.2510 | −3.35224 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 47.8016 | 1.85506 | ||||||||
\(665\) | 8.17081 | 0.316850 | ||||||||
\(666\) | −9.62721 | −0.373047 | ||||||||
\(667\) | 11.7597 | 0.455338 | ||||||||
\(668\) | −21.2544 | −0.822358 | ||||||||
\(669\) | 16.8469 | 0.651339 | ||||||||
\(670\) | −31.4700 | −1.21579 | ||||||||
\(671\) | 22.0978 | 0.853074 | ||||||||
\(672\) | −31.9008 | −1.23060 | ||||||||
\(673\) | −44.6797 | −1.72227 | −0.861137 | − | 0.508373i | \(-0.830247\pi\) | ||||
−0.861137 | + | 0.508373i | \(0.830247\pi\) | |||||||
\(674\) | −18.3033 | −0.705017 | ||||||||
\(675\) | 3.33804 | 0.128481 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.0278 | −1.42309 | −0.711546 | − | 0.702639i | \(-0.752005\pi\) | ||||
−0.711546 | + | 0.702639i | \(0.752005\pi\) | |||||||
\(678\) | 6.10780 | 0.234569 | ||||||||
\(679\) | −11.3275 | −0.434709 | ||||||||
\(680\) | 23.1155 | 0.886437 | ||||||||
\(681\) | −21.9305 | −0.840379 | ||||||||
\(682\) | −88.6832 | −3.39586 | ||||||||
\(683\) | 26.8605 | 1.02779 | 0.513894 | − | 0.857853i | \(-0.328202\pi\) | ||||
0.513894 | + | 0.857853i | \(0.328202\pi\) | |||||||
\(684\) | 37.4983 | 1.43378 | ||||||||
\(685\) | −5.68665 | −0.217276 | ||||||||
\(686\) | 2.81361 | 0.107424 | ||||||||
\(687\) | −5.25443 | −0.200469 | ||||||||
\(688\) | −94.2510 | −3.59329 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 9.83276 | 0.374327 | ||||||||
\(691\) | −2.86802 | −0.109105 | −0.0545523 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545523 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(692\) | −93.0349 | −3.53666 | ||||||||
\(693\) | −4.20555 | −0.159756 | ||||||||
\(694\) | 68.3799 | 2.59567 | ||||||||
\(695\) | 24.4806 | 0.928602 | ||||||||
\(696\) | 47.8016 | 1.81191 | ||||||||
\(697\) | 12.4111 | 0.470104 | ||||||||
\(698\) | −49.9688 | −1.89135 | ||||||||
\(699\) | −4.07306 | −0.154057 | ||||||||
\(700\) | −19.7491 | −0.746448 | ||||||||
\(701\) | −42.9930 | −1.62382 | −0.811912 | − | 0.583780i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583780i | \(0.801573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6867 | −0.817928 | ||||||||
\(704\) | −216.227 | −8.14936 | ||||||||
\(705\) | −1.39697 | −0.0526128 | ||||||||
\(706\) | −5.45998 | −0.205489 | ||||||||
\(707\) | 14.3033 | 0.537931 | ||||||||
\(708\) | −27.0872 | −1.01800 | ||||||||
\(709\) | −3.49115 | −0.131113 | −0.0655564 | − | 0.997849i | \(-0.520882\pi\) | ||||
−0.0655564 | + | 0.997849i | \(0.520882\pi\) | |||||||
\(710\) | 24.6066 | 0.923469 | ||||||||
\(711\) | −8.91638 | −0.334390 | ||||||||
\(712\) | −50.0666 | −1.87632 | ||||||||
\(713\) | −20.3169 | −0.760875 | ||||||||
\(714\) | −4.57834 | −0.171340 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 147.641 | 5.51762 | ||||||||
\(717\) | −2.37279 | −0.0886134 | ||||||||
\(718\) | 94.6137 | 3.53095 | ||||||||
\(719\) | 27.5194 | 1.02630 | 0.513150 | − | 0.858299i | \(-0.328478\pi\) | ||||
0.513150 | + | 0.858299i | \(0.328478\pi\) | |||||||
\(720\) | 24.7144 | 0.921051 | ||||||||
\(721\) | −19.6655 | −0.732382 | ||||||||
\(722\) | 59.5663 | 2.21683 | ||||||||
\(723\) | 14.9164 | 0.554746 | ||||||||
\(724\) | 64.7316 | 2.40573 | ||||||||
\(725\) | 14.4806 | 0.537795 | ||||||||
\(726\) | −18.8136 | −0.698238 | ||||||||
\(727\) | 13.4983 | 0.500624 | 0.250312 | − | 0.968165i | \(-0.419467\pi\) | ||||
0.250312 | + | 0.968165i | \(0.419467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.7738 | −0.546804 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 31.0872 | 1.14902 | ||||||||
\(733\) | 5.08362 | 0.187768 | 0.0938839 | − | 0.995583i | \(-0.470072\pi\) | ||||
0.0938839 | + | 0.995583i | \(0.470072\pi\) | |||||||
\(734\) | −29.7633 | −1.09858 | ||||||||
\(735\) | −1.28917 | −0.0475517 | ||||||||
\(736\) | −86.4777 | −3.18761 | ||||||||
\(737\) | 36.4877 | 1.34404 | ||||||||
\(738\) | 21.4600 | 0.789953 | ||||||||
\(739\) | 53.1638 | 1.95566 | 0.977831 | − | 0.209394i | \(-0.0671492\pi\) | ||||
0.977831 | + | 0.209394i | \(0.0671492\pi\) | |||||||
\(740\) | −26.0978 | −0.959372 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.95112 | 0.181761 | ||||||||
\(743\) | 46.1149 | 1.69179 | 0.845897 | − | 0.533347i | \(-0.179066\pi\) | ||||
0.845897 | + | 0.533347i | \(0.179066\pi\) | |||||||
\(744\) | −82.5855 | −3.02773 | ||||||||
\(745\) | 12.1461 | 0.444999 | ||||||||
\(746\) | −15.3905 | −0.563486 | ||||||||
\(747\) | 4.33804 | 0.158721 | ||||||||
\(748\) | −40.4877 | −1.48038 | ||||||||
\(749\) | 2.20555 | 0.0805890 | ||||||||
\(750\) | 30.2439 | 1.10435 | ||||||||
\(751\) | −32.7774 | −1.19606 | −0.598032 | − | 0.801472i | \(-0.704051\pi\) | ||||
−0.598032 | + | 0.801472i | \(0.704051\pi\) | |||||||
\(752\) | 20.7738 | 0.757544 | ||||||||
\(753\) | 1.08719 | 0.0396194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.1567 | 0.769970 | ||||||||
\(756\) | −5.91638 | −0.215177 | ||||||||
\(757\) | −30.1708 | −1.09658 | −0.548288 | − | 0.836289i | \(-0.684720\pi\) | ||||
−0.548288 | + | 0.836289i | \(0.684720\pi\) | |||||||
\(758\) | 15.2544 | 0.554066 | ||||||||
\(759\) | −11.4005 | −0.413813 | ||||||||
\(760\) | 90.0354 | 3.26593 | ||||||||
\(761\) | 1.81915 | 0.0659440 | 0.0329720 | − | 0.999456i | \(-0.489503\pi\) | ||||
0.0329720 | + | 0.999456i | \(0.489503\pi\) | |||||||
\(762\) | 2.09775 | 0.0759935 | ||||||||
\(763\) | −10.0000 | −0.362024 | ||||||||
\(764\) | 29.8711 | 1.08070 | ||||||||
\(765\) | 2.09775 | 0.0758444 | ||||||||
\(766\) | −39.8016 | −1.43809 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −124.676 | −4.49887 | ||||||||
\(769\) | 0.937507 | 0.0338074 | 0.0169037 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169037 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(770\) | −15.2544 | −0.549731 | ||||||||
\(771\) | 16.6167 | 0.598434 | ||||||||
\(772\) | −16.2439 | −0.584629 | ||||||||
\(773\) | 8.03831 | 0.289118 | 0.144559 | − | 0.989496i | \(-0.453824\pi\) | ||||
0.144559 | + | 0.989496i | \(0.453824\pi\) | |||||||
\(774\) | −13.8328 | −0.497208 | ||||||||
\(775\) | −25.0177 | −0.898662 | ||||||||
\(776\) | −124.819 | −4.48075 | ||||||||
\(777\) | 3.42166 | 0.122751 | ||||||||
\(778\) | 0.881639 | 0.0316083 | ||||||||
\(779\) | 48.3416 | 1.73202 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.5300 | −1.02088 | ||||||||
\(782\) | −12.4111 | −0.443820 | ||||||||
\(783\) | 4.33804 | 0.155029 | ||||||||
\(784\) | 19.1708 | 0.684672 | ||||||||
\(785\) | −12.2721 | −0.438011 | ||||||||
\(786\) | 40.8222 | 1.45608 | ||||||||
\(787\) | −25.3275 | −0.902827 | −0.451414 | − | 0.892315i | \(-0.649080\pi\) | ||||
−0.451414 | + | 0.892315i | \(0.649080\pi\) | |||||||
\(788\) | −32.0766 | −1.14268 | ||||||||
\(789\) | 27.0524 | 0.963093 | ||||||||
\(790\) | −32.3416 | −1.15066 | ||||||||
\(791\) | −2.17081 | −0.0771850 | ||||||||
\(792\) | −46.3416 | −1.64668 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −58.1844 | −2.06489 | ||||||||
\(795\) | −2.26856 | −0.0804575 | ||||||||
\(796\) | −120.760 | −4.28022 | ||||||||
\(797\) | 40.8122 | 1.44564 | 0.722820 | − | 0.691036i | \(-0.242845\pi\) | ||||
0.722820 | + | 0.691036i | \(0.242845\pi\) | |||||||
\(798\) | −17.8328 | −0.631273 | ||||||||
\(799\) | 1.76328 | 0.0623803 | ||||||||
\(800\) | −106.486 | −3.76486 | ||||||||
\(801\) | −4.54359 | −0.160540 | ||||||||
\(802\) | 35.8610 | 1.26630 | ||||||||
\(803\) | 17.1294 | 0.604485 | ||||||||
\(804\) | 51.3311 | 1.81031 | ||||||||
\(805\) | −3.49472 | −0.123173 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.52946 | −0.265050 | ||||||||
\(808\) | 157.610 | 5.54471 | ||||||||
\(809\) | 25.4947 | 0.896347 | 0.448173 | − | 0.893947i | \(-0.352075\pi\) | ||||
0.448173 | + | 0.893947i | \(0.352075\pi\) | |||||||
\(810\) | 3.62721 | 0.127447 | ||||||||
\(811\) | 13.1567 | 0.461993 | 0.230997 | − | 0.972955i | \(-0.425801\pi\) | ||||
0.230997 | + | 0.972955i | \(0.425801\pi\) | |||||||
\(812\) | −25.6655 | −0.900683 | ||||||||
\(813\) | 16.8222 | 0.589980 | ||||||||
\(814\) | 40.4877 | 1.41909 | ||||||||
\(815\) | 0.961171 | 0.0336683 | ||||||||
\(816\) | −31.1950 | −1.09204 | ||||||||
\(817\) | −31.1602 | −1.09016 | ||||||||
\(818\) | 52.4777 | 1.83484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 58.1744 | 2.03154 | ||||||||
\(821\) | 23.1083 | 0.806486 | 0.403243 | − | 0.915093i | \(-0.367883\pi\) | ||||
0.403243 | + | 0.915093i | \(0.367883\pi\) | |||||||
\(822\) | 12.4111 | 0.432887 | ||||||||
\(823\) | −17.4911 | −0.609703 | −0.304852 | − | 0.952400i | \(-0.598607\pi\) | ||||
−0.304852 | + | 0.952400i | \(0.598607\pi\) | |||||||
\(824\) | −216.698 | −7.54902 | ||||||||
\(825\) | −14.0383 | −0.488751 | ||||||||
\(826\) | 12.8816 | 0.448210 | ||||||||
\(827\) | −39.3905 | −1.36974 | −0.684871 | − | 0.728665i | \(-0.740141\pi\) | ||||
−0.684871 | + | 0.728665i | \(0.740141\pi\) | |||||||
\(828\) | −16.0383 | −0.557370 | ||||||||
\(829\) | 10.8222 | 0.375871 | 0.187935 | − | 0.982181i | \(-0.439820\pi\) | ||||
0.187935 | + | 0.982181i | \(0.439820\pi\) | |||||||
\(830\) | 15.7350 | 0.546170 | ||||||||
\(831\) | −17.4947 | −0.606885 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.62721 | 0.0563796 | ||||||||
\(834\) | −53.4288 | −1.85009 | ||||||||
\(835\) | −4.63130 | −0.160273 | ||||||||
\(836\) | −157.701 | −5.45420 | ||||||||
\(837\) | −7.49472 | −0.259055 | ||||||||
\(838\) | 8.74557 | 0.302111 | ||||||||
\(839\) | −4.57834 | −0.158062 | −0.0790309 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790309 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(840\) | −14.2056 | −0.490138 | ||||||||
\(841\) | −10.1814 | −0.351082 | ||||||||
\(842\) | −37.7038 | −1.29936 | ||||||||
\(843\) | 27.4005 | 0.943725 | ||||||||
\(844\) | −85.6938 | −2.94970 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.04888 | 0.104823 | ||||||||
\(847\) | 6.68665 | 0.229756 | ||||||||
\(848\) | 33.7350 | 1.15847 | ||||||||
\(849\) | −20.0766 | −0.689028 | ||||||||
\(850\) | −15.2827 | −0.524192 | ||||||||
\(851\) | 9.27555 | 0.317962 | ||||||||
\(852\) | −40.1361 | −1.37504 | ||||||||
\(853\) | 54.6585 | 1.87147 | 0.935736 | − | 0.352700i | \(-0.114737\pi\) | ||||
0.935736 | + | 0.352700i | \(0.114737\pi\) | |||||||
\(854\) | −14.7839 | −0.505894 | ||||||||
\(855\) | 8.17081 | 0.279436 | ||||||||
\(856\) | 24.3033 | 0.830670 | ||||||||
\(857\) | 8.20555 | 0.280296 | 0.140148 | − | 0.990131i | \(-0.455242\pi\) | ||||
0.140148 | + | 0.990131i | \(0.455242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.20503 | −0.109354 | −0.0546772 | − | 0.998504i | \(-0.517413\pi\) | ||||
−0.0546772 | + | 0.998504i | \(0.517413\pi\) | |||||||
\(860\) | −37.4983 | −1.27868 | ||||||||
\(861\) | −7.62721 | −0.259935 | ||||||||
\(862\) | −27.8328 | −0.947988 | ||||||||
\(863\) | 21.7038 | 0.738807 | 0.369404 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369404 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(864\) | −31.9008 | −1.08529 | ||||||||
\(865\) | −20.2721 | −0.689273 | ||||||||
\(866\) | 1.62721 | 0.0552949 | ||||||||
\(867\) | 14.3522 | 0.487426 | ||||||||
\(868\) | 44.3416 | 1.50505 | ||||||||
\(869\) | 37.4983 | 1.27204 | ||||||||
\(870\) | 15.7350 | 0.533467 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −110.192 | −3.73156 | ||||||||
\(873\) | −11.3275 | −0.383377 | ||||||||
\(874\) | −48.3416 | −1.63518 | ||||||||
\(875\) | −10.7491 | −0.363387 | ||||||||
\(876\) | 24.0978 | 0.814188 | ||||||||
\(877\) | 38.5371 | 1.30131 | 0.650653 | − | 0.759375i | \(-0.274495\pi\) | ||||
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(878\) | 66.7810 | 2.25375 | ||||||||
\(879\) | −27.0524 | −0.912456 | ||||||||
\(880\) | −103.938 | −3.50374 | ||||||||
\(881\) | −20.2056 | −0.680742 | −0.340371 | − | 0.940291i | \(-0.610553\pi\) | ||||
−0.340371 | + | 0.940291i | \(0.610553\pi\) | |||||||
\(882\) | 2.81361 | 0.0947391 | ||||||||
\(883\) | 5.49115 | 0.184792 | 0.0923959 | − | 0.995722i | \(-0.470547\pi\) | ||||
0.0923959 | + | 0.995722i | \(0.470547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.90225 | −0.198402 | ||||||||
\(886\) | −10.8816 | −0.365576 | ||||||||
\(887\) | 45.7633 | 1.53658 | 0.768290 | − | 0.640102i | \(-0.221108\pi\) | ||||
0.768290 | + | 0.640102i | \(0.221108\pi\) | |||||||
\(888\) | 37.7038 | 1.26526 | ||||||||
\(889\) | −0.745574 | −0.0250057 | ||||||||
\(890\) | −16.4806 | −0.552430 | ||||||||
\(891\) | −4.20555 | −0.140891 | ||||||||
\(892\) | −99.6727 | −3.33729 | ||||||||
\(893\) | 6.86802 | 0.229830 | ||||||||
\(894\) | −26.5089 | −0.886589 | ||||||||
\(895\) | 32.1708 | 1.07535 | ||||||||
\(896\) | 80.8591 | 2.70131 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.74557 | −0.158362 | ||||||||
\(899\) | −32.5124 | −1.08435 | ||||||||
\(900\) | −19.7491 | −0.658305 | ||||||||
\(901\) | 2.86342 | 0.0953943 | ||||||||
\(902\) | −90.2510 | −3.00503 | ||||||||
\(903\) | 4.91638 | 0.163607 | ||||||||
\(904\) | −23.9205 | −0.795583 | ||||||||
\(905\) | 14.1049 | 0.468863 | ||||||||
\(906\) | −46.1744 | −1.53404 | ||||||||
\(907\) | 6.67252 | 0.221557 | 0.110779 | − | 0.993845i | \(-0.464666\pi\) | ||||
0.110779 | + | 0.993845i | \(0.464666\pi\) | |||||||
\(908\) | 129.749 | 4.30588 | ||||||||
\(909\) | 14.3033 | 0.474411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5330 | 0.779684 | 0.389842 | − | 0.920882i | \(-0.372530\pi\) | ||||
0.389842 | + | 0.920882i | \(0.372530\pi\) | |||||||
\(912\) | −121.505 | −4.02345 | ||||||||
\(913\) | −18.2439 | −0.603784 | ||||||||
\(914\) | 10.7839 | 0.356699 | ||||||||
\(915\) | 6.77384 | 0.223936 | ||||||||
\(916\) | 31.0872 | 1.02715 | ||||||||
\(917\) | −14.5089 | −0.479125 | ||||||||
\(918\) | −4.57834 | −0.151108 | ||||||||
\(919\) | −28.1955 | −0.930084 | −0.465042 | − | 0.885289i | \(-0.653961\pi\) | ||||
−0.465042 | + | 0.885289i | \(0.653961\pi\) | |||||||
\(920\) | −38.5089 | −1.26960 | ||||||||
\(921\) | −20.1708 | −0.664651 | ||||||||
\(922\) | 31.5577 | 1.03930 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 24.8816 | 0.818546 | ||||||||
\(925\) | 11.4217 | 0.375542 | ||||||||
\(926\) | 72.6832 | 2.38852 | ||||||||
\(927\) | −19.6655 | −0.645901 | ||||||||
\(928\) | −138.387 | −4.54278 | ||||||||
\(929\) | 6.97582 | 0.228869 | 0.114435 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114435 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(930\) | −27.1849 | −0.891429 | ||||||||
\(931\) | 6.33804 | 0.207721 | ||||||||
\(932\) | 24.0978 | 0.789348 | ||||||||
\(933\) | 6.57834 | 0.215365 | ||||||||
\(934\) | 115.603 | 3.78265 | ||||||||
\(935\) | −8.82220 | −0.288517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.5960 | 1.48956 | 0.744779 | − | 0.667311i | \(-0.232555\pi\) | ||||
0.744779 | + | 0.667311i | \(0.232555\pi\) | |||||||
\(938\) | −24.4111 | −0.797051 | ||||||||
\(939\) | 10.7456 | 0.350669 | ||||||||
\(940\) | 8.26499 | 0.269574 | ||||||||
\(941\) | 52.8086 | 1.72151 | 0.860755 | − | 0.509019i | \(-0.169992\pi\) | ||||
0.860755 | + | 0.509019i | \(0.169992\pi\) | |||||||
\(942\) | 26.7839 | 0.872666 | ||||||||
\(943\) | −20.6761 | −0.673306 | ||||||||
\(944\) | 87.7704 | 2.85668 | ||||||||
\(945\) | −1.28917 | −0.0419367 | ||||||||
\(946\) | 58.1744 | 1.89141 | ||||||||
\(947\) | −8.73553 | −0.283867 | −0.141933 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141933 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(948\) | 52.7527 | 1.71333 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −59.5266 | −1.93130 | ||||||||
\(951\) | 24.6066 | 0.797924 | ||||||||
\(952\) | 17.9305 | 0.581131 | ||||||||
\(953\) | 56.0036 | 1.81413 | 0.907067 | − | 0.420987i | \(-0.138316\pi\) | ||||
0.907067 | + | 0.420987i | \(0.138316\pi\) | |||||||
\(954\) | 4.95112 | 0.160299 | ||||||||
\(955\) | 6.50885 | 0.210622 | ||||||||
\(956\) | 14.0383 | 0.454031 | ||||||||
\(957\) | −18.2439 | −0.589740 | ||||||||
\(958\) | −6.85337 | −0.221422 | ||||||||
\(959\) | −4.41110 | −0.142442 | ||||||||
\(960\) | −66.2822 | −2.13925 | ||||||||
\(961\) | 25.1708 | 0.811962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.20555 | 0.0710729 | ||||||||
\(964\) | −88.2510 | −2.84237 | ||||||||
\(965\) | −3.53951 | −0.113941 | ||||||||
\(966\) | 7.62721 | 0.245402 | ||||||||
\(967\) | −29.9094 | −0.961821 | −0.480911 | − | 0.876770i | \(-0.659694\pi\) | ||||
−0.480911 | + | 0.876770i | \(0.659694\pi\) | |||||||
\(968\) | 73.6813 | 2.36821 | ||||||||
\(969\) | −10.3133 | −0.331312 | ||||||||
\(970\) | −41.0872 | −1.31923 | ||||||||
\(971\) | 11.5194 | 0.369676 | 0.184838 | − | 0.982769i | \(-0.440824\pi\) | ||||
0.184838 | + | 0.982769i | \(0.440824\pi\) | |||||||
\(972\) | −5.91638 | −0.189768 | ||||||||
\(973\) | 18.9894 | 0.608773 | ||||||||
\(974\) | 18.5089 | 0.593062 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −100.732 | −3.22434 | ||||||||
\(977\) | 36.4182 | 1.16512 | 0.582561 | − | 0.812787i | \(-0.302051\pi\) | ||||
0.582561 | + | 0.812787i | \(0.302051\pi\) | |||||||
\(978\) | −2.09775 | −0.0670787 | ||||||||
\(979\) | 19.1083 | 0.610704 | ||||||||
\(980\) | 7.62721 | 0.243642 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 79.6344 | 2.54123 | ||||||||
\(983\) | −17.6902 | −0.564230 | −0.282115 | − | 0.959381i | \(-0.591036\pi\) | ||||
−0.282115 | + | 0.959381i | \(0.591036\pi\) | |||||||
\(984\) | −84.0455 | −2.67927 | ||||||||
\(985\) | −6.98944 | −0.222702 | ||||||||
\(986\) | −19.8610 | −0.632504 | ||||||||
\(987\) | −1.08362 | −0.0344920 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.3275 | 0.423789 | ||||||||
\(990\) | −15.2544 | −0.484817 | ||||||||
\(991\) | −11.0589 | −0.351298 | −0.175649 | − | 0.984453i | \(-0.556202\pi\) | ||||
−0.175649 | + | 0.984453i | \(0.556202\pi\) | |||||||
\(992\) | 239.087 | 7.59104 | ||||||||
\(993\) | 30.6550 | 0.972806 | ||||||||
\(994\) | 19.0872 | 0.605409 | ||||||||
\(995\) | −26.3133 | −0.834189 | ||||||||
\(996\) | −25.6655 | −0.813243 | ||||||||
\(997\) | −49.6727 | −1.57315 | −0.786575 | − | 0.617495i | \(-0.788147\pi\) | ||||
−0.786575 | + | 0.617495i | \(0.788147\pi\) | |||||||
\(998\) | −81.0943 | −2.56700 | ||||||||
\(999\) | 3.42166 | 0.108257 |
(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 | 3549.2.a.t.1.3 | 3 | ||
13.12 | even | 2 | 273.2.a.d.1.1 | ✓ | 3 | ||
39.38 | odd | 2 | 819.2.a.j.1.3 | 3 | |||
52.51 | odd | 2 | 4368.2.a.bq.1.2 | 3 | |||
65.64 | even | 2 | 6825.2.a.bd.1.3 | 3 | |||
91.90 | odd | 2 | 1911.2.a.n.1.1 | 3 | |||
273.272 | even | 2 | 5733.2.a.bc.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.a.d.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
819.2.a.j.1.3 | 3 | 39.38 | odd | 2 | |||
1911.2.a.n.1.1 | 3 | 91.90 | odd | 2 | |||
3549.2.a.t.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4368.2.a.bq.1.2 | 3 | 52.51 | odd | 2 | |||
5733.2.a.bc.1.3 | 3 | 273.272 | even | 2 | |||
6825.2.a.bd.1.3 | 3 | 65.64 | even | 2 |