Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 2.56155 | 1.14556 | 0.572781 | − | 0.819709i | \(-0.305865\pi\) | ||||
0.572781 | + | 0.819709i | \(0.305865\pi\) | |||||||
\(6\) | 1.56155 | 0.637501 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.00000 | 1.26491 | ||||||||
\(11\) | −6.56155 | −1.97838 | −0.989191 | − | 0.146631i | \(-0.953157\pi\) | ||||
−0.989191 | + | 0.146631i | \(0.953157\pi\) | |||||||
\(12\) | 0.438447 | 0.126569 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | −6.56155 | −1.50532 | −0.752662 | − | 0.658407i | \(-0.771230\pi\) | ||||
−0.752662 | + | 0.658407i | \(0.771230\pi\) | |||||||
\(20\) | 1.12311 | 0.251134 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −10.2462 | −2.18450 | ||||||||
\(23\) | 5.12311 | 1.06824 | 0.534121 | − | 0.845408i | \(-0.320643\pi\) | ||||
0.534121 | + | 0.845408i | \(0.320643\pi\) | |||||||
\(24\) | −2.43845 | −0.497746 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 3.12311 | 0.612491 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.438447 | 0.0828587 | ||||||||
\(29\) | −7.12311 | −1.32273 | −0.661364 | − | 0.750065i | \(-0.730022\pi\) | ||||
−0.661364 | + | 0.750065i | \(0.730022\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | −2.56155 | −0.460068 | −0.230034 | − | 0.973183i | \(-0.573884\pi\) | ||||
−0.230034 | + | 0.973183i | \(0.573884\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | −6.56155 | −1.14222 | ||||||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | 2.56155 | 0.432981 | ||||||||
\(36\) | 0.438447 | 0.0730745 | ||||||||
\(37\) | −8.24621 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(38\) | −10.2462 | −1.66215 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | −6.24621 | −0.987613 | ||||||||
\(41\) | 3.68466 | 0.575447 | 0.287723 | − | 0.957714i | \(-0.407102\pi\) | ||||
0.287723 | + | 0.957714i | \(0.407102\pi\) | |||||||
\(42\) | 1.56155 | 0.240953 | ||||||||
\(43\) | −7.68466 | −1.17190 | −0.585950 | − | 0.810347i | \(-0.699278\pi\) | ||||
−0.585950 | + | 0.810347i | \(0.699278\pi\) | |||||||
\(44\) | −2.87689 | −0.433708 | ||||||||
\(45\) | 2.56155 | 0.381854 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 5.43845 | 0.793279 | 0.396640 | − | 0.917974i | \(-0.370176\pi\) | ||||
0.396640 | + | 0.917974i | \(0.370176\pi\) | |||||||
\(48\) | −4.68466 | −0.676172 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.43845 | 0.344849 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0.876894 | 0.121603 | ||||||||
\(53\) | −1.12311 | −0.154270 | −0.0771352 | − | 0.997021i | \(-0.524577\pi\) | ||||
−0.0771352 | + | 0.997021i | \(0.524577\pi\) | |||||||
\(54\) | 1.56155 | 0.212500 | ||||||||
\(55\) | −16.8078 | −2.26636 | ||||||||
\(56\) | −2.43845 | −0.325851 | ||||||||
\(57\) | −6.56155 | −0.869099 | ||||||||
\(58\) | −11.1231 | −1.46054 | ||||||||
\(59\) | 3.68466 | 0.479702 | 0.239851 | − | 0.970810i | \(-0.422901\pi\) | ||||
0.239851 | + | 0.970810i | \(0.422901\pi\) | |||||||
\(60\) | 1.12311 | 0.144992 | ||||||||
\(61\) | −12.2462 | −1.56797 | −0.783983 | − | 0.620782i | \(-0.786815\pi\) | ||||
−0.783983 | + | 0.620782i | \(0.786815\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 5.12311 | 0.635443 | ||||||||
\(66\) | −10.2462 | −1.26122 | ||||||||
\(67\) | −7.68466 | −0.938830 | −0.469415 | − | 0.882978i | \(-0.655535\pi\) | ||||
−0.469415 | + | 0.882978i | \(0.655535\pi\) | |||||||
\(68\) | −0.876894 | −0.106339 | ||||||||
\(69\) | 5.12311 | 0.616749 | ||||||||
\(70\) | 4.00000 | 0.478091 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −2.43845 | −0.287374 | ||||||||
\(73\) | 4.56155 | 0.533889 | 0.266945 | − | 0.963712i | \(-0.413986\pi\) | ||||
0.266945 | + | 0.963712i | \(0.413986\pi\) | |||||||
\(74\) | −12.8769 | −1.49691 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | −2.87689 | −0.330002 | ||||||||
\(77\) | −6.56155 | −0.747758 | ||||||||
\(78\) | 3.12311 | 0.353622 | ||||||||
\(79\) | 3.12311 | 0.351377 | 0.175688 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175688 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(80\) | −12.0000 | −1.34164 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.75379 | 0.635400 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0.438447 | 0.0478385 | ||||||||
\(85\) | −5.12311 | −0.555679 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | −7.12311 | −0.763677 | ||||||||
\(88\) | 16.0000 | 1.70561 | ||||||||
\(89\) | −14.5616 | −1.54352 | −0.771761 | − | 0.635913i | \(-0.780624\pi\) | ||||
−0.771761 | + | 0.635913i | \(0.780624\pi\) | |||||||
\(90\) | 4.00000 | 0.421637 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 2.24621 | 0.234184 | ||||||||
\(93\) | −2.56155 | −0.265621 | ||||||||
\(94\) | 8.49242 | 0.875927 | ||||||||
\(95\) | −16.8078 | −1.72444 | ||||||||
\(96\) | −2.43845 | −0.248873 | ||||||||
\(97\) | −11.1231 | −1.12938 | −0.564690 | − | 0.825303i | \(-0.691004\pi\) | ||||
−0.564690 | + | 0.825303i | \(0.691004\pi\) | |||||||
\(98\) | 1.56155 | 0.157741 | ||||||||
\(99\) | −6.56155 | −0.659461 | ||||||||
\(100\) | 0.684658 | 0.0684658 | ||||||||
\(101\) | 4.87689 | 0.485269 | 0.242635 | − | 0.970118i | \(-0.421988\pi\) | ||||
0.242635 | + | 0.970118i | \(0.421988\pi\) | |||||||
\(102\) | −3.12311 | −0.309234 | ||||||||
\(103\) | −5.43845 | −0.535866 | −0.267933 | − | 0.963438i | \(-0.586341\pi\) | ||||
−0.267933 | + | 0.963438i | \(0.586341\pi\) | |||||||
\(104\) | −4.87689 | −0.478219 | ||||||||
\(105\) | 2.56155 | 0.249982 | ||||||||
\(106\) | −1.75379 | −0.170343 | ||||||||
\(107\) | 14.2462 | 1.37723 | 0.688617 | − | 0.725126i | \(-0.258218\pi\) | ||||
0.688617 | + | 0.725126i | \(0.258218\pi\) | |||||||
\(108\) | 0.438447 | 0.0421896 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −26.2462 | −2.50248 | ||||||||
\(111\) | −8.24621 | −0.782696 | ||||||||
\(112\) | −4.68466 | −0.442659 | ||||||||
\(113\) | 5.36932 | 0.505103 | 0.252551 | − | 0.967583i | \(-0.418730\pi\) | ||||
0.252551 | + | 0.967583i | \(0.418730\pi\) | |||||||
\(114\) | −10.2462 | −0.959646 | ||||||||
\(115\) | 13.1231 | 1.22374 | ||||||||
\(116\) | −3.12311 | −0.289973 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 5.75379 | 0.529679 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | −6.24621 | −0.570198 | ||||||||
\(121\) | 32.0540 | 2.91400 | ||||||||
\(122\) | −19.1231 | −1.73132 | ||||||||
\(123\) | 3.68466 | 0.332234 | ||||||||
\(124\) | −1.12311 | −0.100858 | ||||||||
\(125\) | −8.80776 | −0.787790 | ||||||||
\(126\) | 1.56155 | 0.139114 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | −7.68466 | −0.676596 | ||||||||
\(130\) | 8.00000 | 0.701646 | ||||||||
\(131\) | −16.8078 | −1.46850 | −0.734251 | − | 0.678879i | \(-0.762466\pi\) | ||||
−0.734251 | + | 0.678879i | \(0.762466\pi\) | |||||||
\(132\) | −2.87689 | −0.250402 | ||||||||
\(133\) | −6.56155 | −0.568959 | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 2.56155 | 0.220463 | ||||||||
\(136\) | 4.87689 | 0.418190 | ||||||||
\(137\) | −4.24621 | −0.362778 | −0.181389 | − | 0.983411i | \(-0.558059\pi\) | ||||
−0.181389 | + | 0.983411i | \(0.558059\pi\) | |||||||
\(138\) | 8.00000 | 0.681005 | ||||||||
\(139\) | 5.43845 | 0.461283 | 0.230642 | − | 0.973039i | \(-0.425918\pi\) | ||||
0.230642 | + | 0.973039i | \(0.425918\pi\) | |||||||
\(140\) | 1.12311 | 0.0949197 | ||||||||
\(141\) | 5.43845 | 0.458000 | ||||||||
\(142\) | 12.4924 | 1.04834 | ||||||||
\(143\) | −13.1231 | −1.09741 | ||||||||
\(144\) | −4.68466 | −0.390388 | ||||||||
\(145\) | −18.2462 | −1.51527 | ||||||||
\(146\) | 7.12311 | 0.589512 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −3.61553 | −0.297195 | ||||||||
\(149\) | −5.36932 | −0.439872 | −0.219936 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219936 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(150\) | 2.43845 | 0.199098 | ||||||||
\(151\) | 16.2462 | 1.32210 | 0.661049 | − | 0.750343i | \(-0.270112\pi\) | ||||
0.661049 | + | 0.750343i | \(0.270112\pi\) | |||||||
\(152\) | 16.0000 | 1.29777 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | −10.2462 | −0.825663 | ||||||||
\(155\) | −6.56155 | −0.527037 | ||||||||
\(156\) | 0.876894 | 0.0702077 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 4.87689 | 0.387985 | ||||||||
\(159\) | −1.12311 | −0.0890681 | ||||||||
\(160\) | −6.24621 | −0.493806 | ||||||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 1.56155 | 0.122687 | ||||||||
\(163\) | −12.8769 | −1.00860 | −0.504298 | − | 0.863530i | \(-0.668249\pi\) | ||||
−0.504298 | + | 0.863530i | \(0.668249\pi\) | |||||||
\(164\) | 1.61553 | 0.126152 | ||||||||
\(165\) | −16.8078 | −1.30848 | ||||||||
\(166\) | 6.24621 | 0.484800 | ||||||||
\(167\) | −1.75379 | −0.135712 | −0.0678561 | − | 0.997695i | \(-0.521616\pi\) | ||||
−0.0678561 | + | 0.997695i | \(0.521616\pi\) | |||||||
\(168\) | −2.43845 | −0.188130 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −8.00000 | −0.613572 | ||||||||
\(171\) | −6.56155 | −0.501774 | ||||||||
\(172\) | −3.36932 | −0.256908 | ||||||||
\(173\) | −10.0000 | −0.760286 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(174\) | −11.1231 | −0.843240 | ||||||||
\(175\) | 1.56155 | 0.118042 | ||||||||
\(176\) | 30.7386 | 2.31701 | ||||||||
\(177\) | 3.68466 | 0.276956 | ||||||||
\(178\) | −22.7386 | −1.70433 | ||||||||
\(179\) | 0.807764 | 0.0603751 | 0.0301876 | − | 0.999544i | \(-0.490390\pi\) | ||||
0.0301876 | + | 0.999544i | \(0.490390\pi\) | |||||||
\(180\) | 1.12311 | 0.0837114 | ||||||||
\(181\) | −0.876894 | −0.0651790 | −0.0325895 | − | 0.999469i | \(-0.510375\pi\) | ||||
−0.0325895 | + | 0.999469i | \(0.510375\pi\) | |||||||
\(182\) | 3.12311 | 0.231500 | ||||||||
\(183\) | −12.2462 | −0.905266 | ||||||||
\(184\) | −12.4924 | −0.920954 | ||||||||
\(185\) | −21.1231 | −1.55300 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 13.1231 | 0.959657 | ||||||||
\(188\) | 2.38447 | 0.173905 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −26.2462 | −1.90410 | ||||||||
\(191\) | −9.75379 | −0.705759 | −0.352880 | − | 0.935669i | \(-0.614798\pi\) | ||||
−0.352880 | + | 0.935669i | \(0.614798\pi\) | |||||||
\(192\) | 5.56155 | 0.401371 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | −17.3693 | −1.24704 | ||||||||
\(195\) | 5.12311 | 0.366873 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | 23.0540 | 1.64253 | 0.821264 | − | 0.570549i | \(-0.193269\pi\) | ||||
0.821264 | + | 0.570549i | \(0.193269\pi\) | |||||||
\(198\) | −10.2462 | −0.728167 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | −3.80776 | −0.269250 | ||||||||
\(201\) | −7.68466 | −0.542034 | ||||||||
\(202\) | 7.61553 | 0.535827 | ||||||||
\(203\) | −7.12311 | −0.499944 | ||||||||
\(204\) | −0.876894 | −0.0613949 | ||||||||
\(205\) | 9.43845 | 0.659210 | ||||||||
\(206\) | −8.49242 | −0.591695 | ||||||||
\(207\) | 5.12311 | 0.356080 | ||||||||
\(208\) | −9.36932 | −0.649645 | ||||||||
\(209\) | 43.0540 | 2.97811 | ||||||||
\(210\) | 4.00000 | 0.276026 | ||||||||
\(211\) | 15.1231 | 1.04112 | 0.520559 | − | 0.853826i | \(-0.325724\pi\) | ||||
0.520559 | + | 0.853826i | \(0.325724\pi\) | |||||||
\(212\) | −0.492423 | −0.0338197 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 22.2462 | 1.52072 | ||||||||
\(215\) | −19.6847 | −1.34248 | ||||||||
\(216\) | −2.43845 | −0.165915 | ||||||||
\(217\) | −2.56155 | −0.173890 | ||||||||
\(218\) | −3.12311 | −0.211523 | ||||||||
\(219\) | 4.56155 | 0.308241 | ||||||||
\(220\) | −7.36932 | −0.496839 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | −12.8769 | −0.864241 | ||||||||
\(223\) | 7.68466 | 0.514603 | 0.257301 | − | 0.966331i | \(-0.417167\pi\) | ||||
0.257301 | + | 0.966331i | \(0.417167\pi\) | |||||||
\(224\) | −2.43845 | −0.162926 | ||||||||
\(225\) | 1.56155 | 0.104104 | ||||||||
\(226\) | 8.38447 | 0.557727 | ||||||||
\(227\) | −6.24621 | −0.414576 | −0.207288 | − | 0.978280i | \(-0.566464\pi\) | ||||
−0.207288 | + | 0.978280i | \(0.566464\pi\) | |||||||
\(228\) | −2.87689 | −0.190527 | ||||||||
\(229\) | 12.5616 | 0.830091 | 0.415045 | − | 0.909801i | \(-0.363766\pi\) | ||||
0.415045 | + | 0.909801i | \(0.363766\pi\) | |||||||
\(230\) | 20.4924 | 1.35123 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 17.3693 | 1.14035 | ||||||||
\(233\) | −5.43845 | −0.356285 | −0.178142 | − | 0.984005i | \(-0.557009\pi\) | ||||
−0.178142 | + | 0.984005i | \(0.557009\pi\) | |||||||
\(234\) | 3.12311 | 0.204164 | ||||||||
\(235\) | 13.9309 | 0.908750 | ||||||||
\(236\) | 1.61553 | 0.105162 | ||||||||
\(237\) | 3.12311 | 0.202868 | ||||||||
\(238\) | −3.12311 | −0.202441 | ||||||||
\(239\) | −23.6847 | −1.53203 | −0.766017 | − | 0.642821i | \(-0.777764\pi\) | ||||
−0.766017 | + | 0.642821i | \(0.777764\pi\) | |||||||
\(240\) | −12.0000 | −0.774597 | ||||||||
\(241\) | −16.2462 | −1.04651 | −0.523255 | − | 0.852176i | \(-0.675283\pi\) | ||||
−0.523255 | + | 0.852176i | \(0.675283\pi\) | |||||||
\(242\) | 50.0540 | 3.21759 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.36932 | −0.343735 | ||||||||
\(245\) | 2.56155 | 0.163652 | ||||||||
\(246\) | 5.75379 | 0.366848 | ||||||||
\(247\) | −13.1231 | −0.835003 | ||||||||
\(248\) | 6.24621 | 0.396635 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | −13.7538 | −0.869866 | ||||||||
\(251\) | 1.12311 | 0.0708898 | 0.0354449 | − | 0.999372i | \(-0.488715\pi\) | ||||
0.0354449 | + | 0.999372i | \(0.488715\pi\) | |||||||
\(252\) | 0.438447 | 0.0276196 | ||||||||
\(253\) | −33.6155 | −2.11339 | ||||||||
\(254\) | −9.36932 | −0.587883 | ||||||||
\(255\) | −5.12311 | −0.320821 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −22.5616 | −1.40735 | −0.703675 | − | 0.710521i | \(-0.748459\pi\) | ||||
−0.703675 | + | 0.710521i | \(0.748459\pi\) | |||||||
\(258\) | −12.0000 | −0.747087 | ||||||||
\(259\) | −8.24621 | −0.512395 | ||||||||
\(260\) | 2.24621 | 0.139304 | ||||||||
\(261\) | −7.12311 | −0.440909 | ||||||||
\(262\) | −26.2462 | −1.62150 | ||||||||
\(263\) | 31.3693 | 1.93431 | 0.967157 | − | 0.254178i | \(-0.0818049\pi\) | ||||
0.967157 | + | 0.254178i | \(0.0818049\pi\) | |||||||
\(264\) | 16.0000 | 0.984732 | ||||||||
\(265\) | −2.87689 | −0.176726 | ||||||||
\(266\) | −10.2462 | −0.628236 | ||||||||
\(267\) | −14.5616 | −0.891153 | ||||||||
\(268\) | −3.36932 | −0.205814 | ||||||||
\(269\) | 0.315342 | 0.0192267 | 0.00961336 | − | 0.999954i | \(-0.496940\pi\) | ||||
0.00961336 | + | 0.999954i | \(0.496940\pi\) | |||||||
\(270\) | 4.00000 | 0.243432 | ||||||||
\(271\) | 11.7538 | 0.713992 | 0.356996 | − | 0.934106i | \(-0.383801\pi\) | ||||
0.356996 | + | 0.934106i | \(0.383801\pi\) | |||||||
\(272\) | 9.36932 | 0.568098 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | −6.63068 | −0.400574 | ||||||||
\(275\) | −10.2462 | −0.617870 | ||||||||
\(276\) | 2.24621 | 0.135206 | ||||||||
\(277\) | −0.0691303 | −0.00415364 | −0.00207682 | − | 0.999998i | \(-0.500661\pi\) | ||||
−0.00207682 | + | 0.999998i | \(0.500661\pi\) | |||||||
\(278\) | 8.49242 | 0.509342 | ||||||||
\(279\) | −2.56155 | −0.153356 | ||||||||
\(280\) | −6.24621 | −0.373283 | ||||||||
\(281\) | 15.0540 | 0.898045 | 0.449022 | − | 0.893520i | \(-0.351772\pi\) | ||||
0.449022 | + | 0.893520i | \(0.351772\pi\) | |||||||
\(282\) | 8.49242 | 0.505716 | ||||||||
\(283\) | 12.8769 | 0.765452 | 0.382726 | − | 0.923862i | \(-0.374985\pi\) | ||||
0.382726 | + | 0.923862i | \(0.374985\pi\) | |||||||
\(284\) | 3.50758 | 0.208136 | ||||||||
\(285\) | −16.8078 | −0.995606 | ||||||||
\(286\) | −20.4924 | −1.21174 | ||||||||
\(287\) | 3.68466 | 0.217499 | ||||||||
\(288\) | −2.43845 | −0.143687 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −28.4924 | −1.67313 | ||||||||
\(291\) | −11.1231 | −0.652048 | ||||||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 1.56155 | 0.0910716 | ||||||||
\(295\) | 9.43845 | 0.549528 | ||||||||
\(296\) | 20.1080 | 1.16875 | ||||||||
\(297\) | −6.56155 | −0.380740 | ||||||||
\(298\) | −8.38447 | −0.485699 | ||||||||
\(299\) | 10.2462 | 0.592554 | ||||||||
\(300\) | 0.684658 | 0.0395288 | ||||||||
\(301\) | −7.68466 | −0.442936 | ||||||||
\(302\) | 25.3693 | 1.45984 | ||||||||
\(303\) | 4.87689 | 0.280170 | ||||||||
\(304\) | 30.7386 | 1.76298 | ||||||||
\(305\) | −31.3693 | −1.79620 | ||||||||
\(306\) | −3.12311 | −0.178536 | ||||||||
\(307\) | 0.246211 | 0.0140520 | 0.00702601 | − | 0.999975i | \(-0.497764\pi\) | ||||
0.00702601 | + | 0.999975i | \(0.497764\pi\) | |||||||
\(308\) | −2.87689 | −0.163926 | ||||||||
\(309\) | −5.43845 | −0.309382 | ||||||||
\(310\) | −10.2462 | −0.581946 | ||||||||
\(311\) | −33.3002 | −1.88828 | −0.944140 | − | 0.329544i | \(-0.893105\pi\) | ||||
−0.944140 | + | 0.329544i | \(0.893105\pi\) | |||||||
\(312\) | −4.87689 | −0.276100 | ||||||||
\(313\) | 18.1771 | 1.02743 | 0.513715 | − | 0.857961i | \(-0.328269\pi\) | ||||
0.513715 | + | 0.857961i | \(0.328269\pi\) | |||||||
\(314\) | 21.8617 | 1.23373 | ||||||||
\(315\) | 2.56155 | 0.144327 | ||||||||
\(316\) | 1.36932 | 0.0770301 | ||||||||
\(317\) | 6.63068 | 0.372416 | 0.186208 | − | 0.982510i | \(-0.440380\pi\) | ||||
0.186208 | + | 0.982510i | \(0.440380\pi\) | |||||||
\(318\) | −1.75379 | −0.0983476 | ||||||||
\(319\) | 46.7386 | 2.61686 | ||||||||
\(320\) | 14.2462 | 0.796387 | ||||||||
\(321\) | 14.2462 | 0.795146 | ||||||||
\(322\) | 8.00000 | 0.445823 | ||||||||
\(323\) | 13.1231 | 0.730189 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | 3.12311 | 0.173239 | ||||||||
\(326\) | −20.1080 | −1.11368 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | −8.98485 | −0.496105 | ||||||||
\(329\) | 5.43845 | 0.299831 | ||||||||
\(330\) | −26.2462 | −1.44481 | ||||||||
\(331\) | 10.2462 | 0.563183 | 0.281591 | − | 0.959534i | \(-0.409138\pi\) | ||||
0.281591 | + | 0.959534i | \(0.409138\pi\) | |||||||
\(332\) | 1.75379 | 0.0962517 | ||||||||
\(333\) | −8.24621 | −0.451890 | ||||||||
\(334\) | −2.73863 | −0.149851 | ||||||||
\(335\) | −19.6847 | −1.07549 | ||||||||
\(336\) | −4.68466 | −0.255569 | ||||||||
\(337\) | 13.3693 | 0.728273 | 0.364137 | − | 0.931346i | \(-0.381364\pi\) | ||||
0.364137 | + | 0.931346i | \(0.381364\pi\) | |||||||
\(338\) | −14.0540 | −0.764435 | ||||||||
\(339\) | 5.36932 | 0.291621 | ||||||||
\(340\) | −2.24621 | −0.121818 | ||||||||
\(341\) | 16.8078 | 0.910191 | ||||||||
\(342\) | −10.2462 | −0.554052 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 18.7386 | 1.01032 | ||||||||
\(345\) | 13.1231 | 0.706524 | ||||||||
\(346\) | −15.6155 | −0.839496 | ||||||||
\(347\) | −12.8078 | −0.687557 | −0.343778 | − | 0.939051i | \(-0.611707\pi\) | ||||
−0.343778 | + | 0.939051i | \(0.611707\pi\) | |||||||
\(348\) | −3.12311 | −0.167416 | ||||||||
\(349\) | 25.8617 | 1.38435 | 0.692174 | − | 0.721731i | \(-0.256653\pi\) | ||||
0.692174 | + | 0.721731i | \(0.256653\pi\) | |||||||
\(350\) | 2.43845 | 0.130340 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 16.0000 | 0.852803 | ||||||||
\(353\) | −15.1231 | −0.804922 | −0.402461 | − | 0.915437i | \(-0.631845\pi\) | ||||
−0.402461 | + | 0.915437i | \(0.631845\pi\) | |||||||
\(354\) | 5.75379 | 0.305810 | ||||||||
\(355\) | 20.4924 | 1.08762 | ||||||||
\(356\) | −6.38447 | −0.338376 | ||||||||
\(357\) | −2.00000 | −0.105851 | ||||||||
\(358\) | 1.26137 | 0.0666653 | ||||||||
\(359\) | −16.3153 | −0.861091 | −0.430545 | − | 0.902569i | \(-0.641679\pi\) | ||||
−0.430545 | + | 0.902569i | \(0.641679\pi\) | |||||||
\(360\) | −6.24621 | −0.329204 | ||||||||
\(361\) | 24.0540 | 1.26600 | ||||||||
\(362\) | −1.36932 | −0.0719697 | ||||||||
\(363\) | 32.0540 | 1.68240 | ||||||||
\(364\) | 0.876894 | 0.0459618 | ||||||||
\(365\) | 11.6847 | 0.611603 | ||||||||
\(366\) | −19.1231 | −0.999581 | ||||||||
\(367\) | 23.6155 | 1.23272 | 0.616360 | − | 0.787464i | \(-0.288607\pi\) | ||||
0.616360 | + | 0.787464i | \(0.288607\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 3.68466 | 0.191816 | ||||||||
\(370\) | −32.9848 | −1.71480 | ||||||||
\(371\) | −1.12311 | −0.0583087 | ||||||||
\(372\) | −1.12311 | −0.0582303 | ||||||||
\(373\) | −13.6847 | −0.708565 | −0.354282 | − | 0.935138i | \(-0.615275\pi\) | ||||
−0.354282 | + | 0.935138i | \(0.615275\pi\) | |||||||
\(374\) | 20.4924 | 1.05964 | ||||||||
\(375\) | −8.80776 | −0.454831 | ||||||||
\(376\) | −13.2614 | −0.683903 | ||||||||
\(377\) | −14.2462 | −0.733717 | ||||||||
\(378\) | 1.56155 | 0.0803176 | ||||||||
\(379\) | 10.4924 | 0.538960 | 0.269480 | − | 0.963006i | \(-0.413148\pi\) | ||||
0.269480 | + | 0.963006i | \(0.413148\pi\) | |||||||
\(380\) | −7.36932 | −0.378038 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | −15.2311 | −0.779289 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 13.5616 | 0.692060 | ||||||||
\(385\) | −16.8078 | −0.856603 | ||||||||
\(386\) | 3.12311 | 0.158962 | ||||||||
\(387\) | −7.68466 | −0.390633 | ||||||||
\(388\) | −4.87689 | −0.247587 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 8.00000 | 0.405096 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | −2.43845 | −0.123160 | ||||||||
\(393\) | −16.8078 | −0.847840 | ||||||||
\(394\) | 36.0000 | 1.81365 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | −2.87689 | −0.144569 | ||||||||
\(397\) | −22.8078 | −1.14469 | −0.572344 | − | 0.820013i | \(-0.693966\pi\) | ||||
−0.572344 | + | 0.820013i | \(0.693966\pi\) | |||||||
\(398\) | 15.6155 | 0.782736 | ||||||||
\(399\) | −6.56155 | −0.328489 | ||||||||
\(400\) | −7.31534 | −0.365767 | ||||||||
\(401\) | 4.87689 | 0.243540 | 0.121770 | − | 0.992558i | \(-0.461143\pi\) | ||||
0.121770 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | −5.12311 | −0.255200 | ||||||||
\(404\) | 2.13826 | 0.106382 | ||||||||
\(405\) | 2.56155 | 0.127285 | ||||||||
\(406\) | −11.1231 | −0.552030 | ||||||||
\(407\) | 54.1080 | 2.68203 | ||||||||
\(408\) | 4.87689 | 0.241442 | ||||||||
\(409\) | −10.4924 | −0.518817 | −0.259408 | − | 0.965768i | \(-0.583528\pi\) | ||||
−0.259408 | + | 0.965768i | \(0.583528\pi\) | |||||||
\(410\) | 14.7386 | 0.727889 | ||||||||
\(411\) | −4.24621 | −0.209450 | ||||||||
\(412\) | −2.38447 | −0.117474 | ||||||||
\(413\) | 3.68466 | 0.181310 | ||||||||
\(414\) | 8.00000 | 0.393179 | ||||||||
\(415\) | 10.2462 | 0.502967 | ||||||||
\(416\) | −4.87689 | −0.239109 | ||||||||
\(417\) | 5.43845 | 0.266322 | ||||||||
\(418\) | 67.2311 | 3.28838 | ||||||||
\(419\) | −22.2462 | −1.08680 | −0.543399 | − | 0.839474i | \(-0.682863\pi\) | ||||
−0.543399 | + | 0.839474i | \(0.682863\pi\) | |||||||
\(420\) | 1.12311 | 0.0548019 | ||||||||
\(421\) | −16.2462 | −0.791792 | −0.395896 | − | 0.918295i | \(-0.629566\pi\) | ||||
−0.395896 | + | 0.918295i | \(0.629566\pi\) | |||||||
\(422\) | 23.6155 | 1.14959 | ||||||||
\(423\) | 5.43845 | 0.264426 | ||||||||
\(424\) | 2.73863 | 0.133000 | ||||||||
\(425\) | −3.12311 | −0.151493 | ||||||||
\(426\) | 12.4924 | 0.605260 | ||||||||
\(427\) | −12.2462 | −0.592636 | ||||||||
\(428\) | 6.24621 | 0.301922 | ||||||||
\(429\) | −13.1231 | −0.633590 | ||||||||
\(430\) | −30.7386 | −1.48235 | ||||||||
\(431\) | 18.8769 | 0.909268 | 0.454634 | − | 0.890678i | \(-0.349770\pi\) | ||||
0.454634 | + | 0.890678i | \(0.349770\pi\) | |||||||
\(432\) | −4.68466 | −0.225391 | ||||||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | −4.00000 | −0.192006 | ||||||||
\(435\) | −18.2462 | −0.874839 | ||||||||
\(436\) | −0.876894 | −0.0419956 | ||||||||
\(437\) | −33.6155 | −1.60805 | ||||||||
\(438\) | 7.12311 | 0.340355 | ||||||||
\(439\) | −11.6847 | −0.557678 | −0.278839 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278839 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(440\) | 40.9848 | 1.95388 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −6.24621 | −0.297102 | ||||||||
\(443\) | −27.0540 | −1.28537 | −0.642687 | − | 0.766129i | \(-0.722180\pi\) | ||||
−0.642687 | + | 0.766129i | \(0.722180\pi\) | |||||||
\(444\) | −3.61553 | −0.171585 | ||||||||
\(445\) | −37.3002 | −1.76820 | ||||||||
\(446\) | 12.0000 | 0.568216 | ||||||||
\(447\) | −5.36932 | −0.253960 | ||||||||
\(448\) | 5.56155 | 0.262759 | ||||||||
\(449\) | 11.3693 | 0.536551 | 0.268276 | − | 0.963342i | \(-0.413546\pi\) | ||||
0.268276 | + | 0.963342i | \(0.413546\pi\) | |||||||
\(450\) | 2.43845 | 0.114950 | ||||||||
\(451\) | −24.1771 | −1.13845 | ||||||||
\(452\) | 2.35416 | 0.110730 | ||||||||
\(453\) | 16.2462 | 0.763314 | ||||||||
\(454\) | −9.75379 | −0.457768 | ||||||||
\(455\) | 5.12311 | 0.240175 | ||||||||
\(456\) | 16.0000 | 0.749269 | ||||||||
\(457\) | 0.246211 | 0.0115173 | 0.00575864 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575864 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(458\) | 19.6155 | 0.916573 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 5.75379 | 0.268272 | ||||||||
\(461\) | −2.87689 | −0.133990 | −0.0669952 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669952 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(462\) | −10.2462 | −0.476697 | ||||||||
\(463\) | 30.0000 | 1.39422 | 0.697109 | − | 0.716965i | \(-0.254469\pi\) | ||||
0.697109 | + | 0.716965i | \(0.254469\pi\) | |||||||
\(464\) | 33.3693 | 1.54913 | ||||||||
\(465\) | −6.56155 | −0.304285 | ||||||||
\(466\) | −8.49242 | −0.393404 | ||||||||
\(467\) | −29.6155 | −1.37044 | −0.685222 | − | 0.728335i | \(-0.740295\pi\) | ||||
−0.685222 | + | 0.728335i | \(0.740295\pi\) | |||||||
\(468\) | 0.876894 | 0.0405345 | ||||||||
\(469\) | −7.68466 | −0.354845 | ||||||||
\(470\) | 21.7538 | 1.00343 | ||||||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | −8.98485 | −0.413561 | ||||||||
\(473\) | 50.4233 | 2.31847 | ||||||||
\(474\) | 4.87689 | 0.224003 | ||||||||
\(475\) | −10.2462 | −0.470128 | ||||||||
\(476\) | −0.876894 | −0.0401924 | ||||||||
\(477\) | −1.12311 | −0.0514235 | ||||||||
\(478\) | −36.9848 | −1.69165 | ||||||||
\(479\) | 0.630683 | 0.0288166 | 0.0144083 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144083 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(480\) | −6.24621 | −0.285099 | ||||||||
\(481\) | −16.4924 | −0.751990 | ||||||||
\(482\) | −25.3693 | −1.15554 | ||||||||
\(483\) | 5.12311 | 0.233109 | ||||||||
\(484\) | 14.0540 | 0.638817 | ||||||||
\(485\) | −28.4924 | −1.29377 | ||||||||
\(486\) | 1.56155 | 0.0708335 | ||||||||
\(487\) | 36.2462 | 1.64247 | 0.821236 | − | 0.570588i | \(-0.193285\pi\) | ||||
0.821236 | + | 0.570588i | \(0.193285\pi\) | |||||||
\(488\) | 29.8617 | 1.35178 | ||||||||
\(489\) | −12.8769 | −0.582313 | ||||||||
\(490\) | 4.00000 | 0.180702 | ||||||||
\(491\) | 14.8769 | 0.671385 | 0.335692 | − | 0.941972i | \(-0.391030\pi\) | ||||
0.335692 | + | 0.941972i | \(0.391030\pi\) | |||||||
\(492\) | 1.61553 | 0.0728336 | ||||||||
\(493\) | 14.2462 | 0.641617 | ||||||||
\(494\) | −20.4924 | −0.921998 | ||||||||
\(495\) | −16.8078 | −0.755453 | ||||||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 6.24621 | 0.279899 | ||||||||
\(499\) | −22.7386 | −1.01792 | −0.508961 | − | 0.860790i | \(-0.669970\pi\) | ||||
−0.508961 | + | 0.860790i | \(0.669970\pi\) | |||||||
\(500\) | −3.86174 | −0.172702 | ||||||||
\(501\) | −1.75379 | −0.0783535 | ||||||||
\(502\) | 1.75379 | 0.0782754 | ||||||||
\(503\) | −23.6847 | −1.05605 | −0.528023 | − | 0.849230i | \(-0.677067\pi\) | ||||
−0.528023 | + | 0.849230i | \(0.677067\pi\) | |||||||
\(504\) | −2.43845 | −0.108617 | ||||||||
\(505\) | 12.4924 | 0.555906 | ||||||||
\(506\) | −52.4924 | −2.33357 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | −2.63068 | −0.116718 | ||||||||
\(509\) | −21.3693 | −0.947178 | −0.473589 | − | 0.880746i | \(-0.657042\pi\) | ||||
−0.473589 | + | 0.880746i | \(0.657042\pi\) | |||||||
\(510\) | −8.00000 | −0.354246 | ||||||||
\(511\) | 4.56155 | 0.201791 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | −6.56155 | −0.289700 | ||||||||
\(514\) | −35.2311 | −1.55398 | ||||||||
\(515\) | −13.9309 | −0.613867 | ||||||||
\(516\) | −3.36932 | −0.148326 | ||||||||
\(517\) | −35.6847 | −1.56941 | ||||||||
\(518\) | −12.8769 | −0.565778 | ||||||||
\(519\) | −10.0000 | −0.438951 | ||||||||
\(520\) | −12.4924 | −0.547829 | ||||||||
\(521\) | 4.24621 | 0.186030 | 0.0930149 | − | 0.995665i | \(-0.470350\pi\) | ||||
0.0930149 | + | 0.995665i | \(0.470350\pi\) | |||||||
\(522\) | −11.1231 | −0.486845 | ||||||||
\(523\) | 11.6155 | 0.507912 | 0.253956 | − | 0.967216i | \(-0.418268\pi\) | ||||
0.253956 | + | 0.967216i | \(0.418268\pi\) | |||||||
\(524\) | −7.36932 | −0.321930 | ||||||||
\(525\) | 1.56155 | 0.0681518 | ||||||||
\(526\) | 48.9848 | 2.13584 | ||||||||
\(527\) | 5.12311 | 0.223166 | ||||||||
\(528\) | 30.7386 | 1.33773 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | −4.49242 | −0.195138 | ||||||||
\(531\) | 3.68466 | 0.159901 | ||||||||
\(532\) | −2.87689 | −0.124729 | ||||||||
\(533\) | 7.36932 | 0.319201 | ||||||||
\(534\) | −22.7386 | −0.983997 | ||||||||
\(535\) | 36.4924 | 1.57771 | ||||||||
\(536\) | 18.7386 | 0.809386 | ||||||||
\(537\) | 0.807764 | 0.0348576 | ||||||||
\(538\) | 0.492423 | 0.0212298 | ||||||||
\(539\) | −6.56155 | −0.282626 | ||||||||
\(540\) | 1.12311 | 0.0483308 | ||||||||
\(541\) | −32.7386 | −1.40754 | −0.703772 | − | 0.710426i | \(-0.748502\pi\) | ||||
−0.703772 | + | 0.710426i | \(0.748502\pi\) | |||||||
\(542\) | 18.3542 | 0.788379 | ||||||||
\(543\) | −0.876894 | −0.0376311 | ||||||||
\(544\) | 4.87689 | 0.209095 | ||||||||
\(545\) | −5.12311 | −0.219450 | ||||||||
\(546\) | 3.12311 | 0.133657 | ||||||||
\(547\) | −3.75379 | −0.160500 | −0.0802502 | − | 0.996775i | \(-0.525572\pi\) | ||||
−0.0802502 | + | 0.996775i | \(0.525572\pi\) | |||||||
\(548\) | −1.86174 | −0.0795296 | ||||||||
\(549\) | −12.2462 | −0.522656 | ||||||||
\(550\) | −16.0000 | −0.682242 | ||||||||
\(551\) | 46.7386 | 1.99113 | ||||||||
\(552\) | −12.4924 | −0.531713 | ||||||||
\(553\) | 3.12311 | 0.132808 | ||||||||
\(554\) | −0.107951 | −0.00458638 | ||||||||
\(555\) | −21.1231 | −0.896626 | ||||||||
\(556\) | 2.38447 | 0.101124 | ||||||||
\(557\) | 2.00000 | 0.0847427 | 0.0423714 | − | 0.999102i | \(-0.486509\pi\) | ||||
0.0423714 | + | 0.999102i | \(0.486509\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | −15.3693 | −0.650053 | ||||||||
\(560\) | −12.0000 | −0.507093 | ||||||||
\(561\) | 13.1231 | 0.554058 | ||||||||
\(562\) | 23.5076 | 0.991607 | ||||||||
\(563\) | 12.4924 | 0.526493 | 0.263246 | − | 0.964729i | \(-0.415207\pi\) | ||||
0.263246 | + | 0.964729i | \(0.415207\pi\) | |||||||
\(564\) | 2.38447 | 0.100404 | ||||||||
\(565\) | 13.7538 | 0.578626 | ||||||||
\(566\) | 20.1080 | 0.845200 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −19.5076 | −0.818520 | ||||||||
\(569\) | −11.6155 | −0.486948 | −0.243474 | − | 0.969907i | \(-0.578287\pi\) | ||||
−0.243474 | + | 0.969907i | \(0.578287\pi\) | |||||||
\(570\) | −26.2462 | −1.09933 | ||||||||
\(571\) | −45.3693 | −1.89865 | −0.949323 | − | 0.314301i | \(-0.898230\pi\) | ||||
−0.949323 | + | 0.314301i | \(0.898230\pi\) | |||||||
\(572\) | −5.75379 | −0.240578 | ||||||||
\(573\) | −9.75379 | −0.407470 | ||||||||
\(574\) | 5.75379 | 0.240159 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 5.56155 | 0.231731 | ||||||||
\(577\) | −28.8769 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(578\) | −20.3002 | −0.844376 | ||||||||
\(579\) | 2.00000 | 0.0831172 | ||||||||
\(580\) | −8.00000 | −0.332182 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | −17.3693 | −0.719981 | ||||||||
\(583\) | 7.36932 | 0.305206 | ||||||||
\(584\) | −11.1231 | −0.460277 | ||||||||
\(585\) | 5.12311 | 0.211814 | ||||||||
\(586\) | −21.8617 | −0.903100 | ||||||||
\(587\) | 47.2311 | 1.94943 | 0.974717 | − | 0.223442i | \(-0.0717294\pi\) | ||||
0.974717 | + | 0.223442i | \(0.0717294\pi\) | |||||||
\(588\) | 0.438447 | 0.0180813 | ||||||||
\(589\) | 16.8078 | 0.692552 | ||||||||
\(590\) | 14.7386 | 0.606780 | ||||||||
\(591\) | 23.0540 | 0.948314 | ||||||||
\(592\) | 38.6307 | 1.58771 | ||||||||
\(593\) | 11.6847 | 0.479831 | 0.239916 | − | 0.970794i | \(-0.422880\pi\) | ||||
0.239916 | + | 0.970794i | \(0.422880\pi\) | |||||||
\(594\) | −10.2462 | −0.420407 | ||||||||
\(595\) | −5.12311 | −0.210027 | ||||||||
\(596\) | −2.35416 | −0.0964302 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 16.0000 | 0.654289 | ||||||||
\(599\) | 47.3693 | 1.93546 | 0.967729 | − | 0.251994i | \(-0.0810862\pi\) | ||||
0.967729 | + | 0.251994i | \(0.0810862\pi\) | |||||||
\(600\) | −3.80776 | −0.155451 | ||||||||
\(601\) | 18.4924 | 0.754322 | 0.377161 | − | 0.926148i | \(-0.376900\pi\) | ||||
0.377161 | + | 0.926148i | \(0.376900\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | −7.68466 | −0.312943 | ||||||||
\(604\) | 7.12311 | 0.289835 | ||||||||
\(605\) | 82.1080 | 3.33816 | ||||||||
\(606\) | 7.61553 | 0.309360 | ||||||||
\(607\) | 17.4384 | 0.707805 | 0.353902 | − | 0.935282i | \(-0.384855\pi\) | ||||
0.353902 | + | 0.935282i | \(0.384855\pi\) | |||||||
\(608\) | 16.0000 | 0.648886 | ||||||||
\(609\) | −7.12311 | −0.288643 | ||||||||
\(610\) | −48.9848 | −1.98334 | ||||||||
\(611\) | 10.8769 | 0.440032 | ||||||||
\(612\) | −0.876894 | −0.0354464 | ||||||||
\(613\) | 12.8769 | 0.520093 | 0.260046 | − | 0.965596i | \(-0.416262\pi\) | ||||
0.260046 | + | 0.965596i | \(0.416262\pi\) | |||||||
\(614\) | 0.384472 | 0.0155160 | ||||||||
\(615\) | 9.43845 | 0.380595 | ||||||||
\(616\) | 16.0000 | 0.644658 | ||||||||
\(617\) | −12.1771 | −0.490231 | −0.245115 | − | 0.969494i | \(-0.578826\pi\) | ||||
−0.245115 | + | 0.969494i | \(0.578826\pi\) | |||||||
\(618\) | −8.49242 | −0.341615 | ||||||||
\(619\) | −10.4924 | −0.421726 | −0.210863 | − | 0.977516i | \(-0.567627\pi\) | ||||
−0.210863 | + | 0.977516i | \(0.567627\pi\) | |||||||
\(620\) | −2.87689 | −0.115539 | ||||||||
\(621\) | 5.12311 | 0.205583 | ||||||||
\(622\) | −52.0000 | −2.08501 | ||||||||
\(623\) | −14.5616 | −0.583396 | ||||||||
\(624\) | −9.36932 | −0.375073 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 28.3845 | 1.13447 | ||||||||
\(627\) | 43.0540 | 1.71941 | ||||||||
\(628\) | 6.13826 | 0.244943 | ||||||||
\(629\) | 16.4924 | 0.657596 | ||||||||
\(630\) | 4.00000 | 0.159364 | ||||||||
\(631\) | 1.75379 | 0.0698172 | 0.0349086 | − | 0.999391i | \(-0.488886\pi\) | ||||
0.0349086 | + | 0.999391i | \(0.488886\pi\) | |||||||
\(632\) | −7.61553 | −0.302929 | ||||||||
\(633\) | 15.1231 | 0.601089 | ||||||||
\(634\) | 10.3542 | 0.411216 | ||||||||
\(635\) | −15.3693 | −0.609913 | ||||||||
\(636\) | −0.492423 | −0.0195258 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 72.9848 | 2.88950 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 34.7386 | 1.37317 | ||||||||
\(641\) | −2.49242 | −0.0984448 | −0.0492224 | − | 0.998788i | \(-0.515674\pi\) | ||||
−0.0492224 | + | 0.998788i | \(0.515674\pi\) | |||||||
\(642\) | 22.2462 | 0.877988 | ||||||||
\(643\) | 8.17708 | 0.322473 | 0.161236 | − | 0.986916i | \(-0.448452\pi\) | ||||
0.161236 | + | 0.986916i | \(0.448452\pi\) | |||||||
\(644\) | 2.24621 | 0.0885131 | ||||||||
\(645\) | −19.6847 | −0.775083 | ||||||||
\(646\) | 20.4924 | 0.806264 | ||||||||
\(647\) | −9.43845 | −0.371064 | −0.185532 | − | 0.982638i | \(-0.559401\pi\) | ||||
−0.185532 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(648\) | −2.43845 | −0.0957913 | ||||||||
\(649\) | −24.1771 | −0.949033 | ||||||||
\(650\) | 4.87689 | 0.191288 | ||||||||
\(651\) | −2.56155 | −0.100395 | ||||||||
\(652\) | −5.64584 | −0.221108 | ||||||||
\(653\) | 5.61553 | 0.219753 | 0.109876 | − | 0.993945i | \(-0.464955\pi\) | ||||
0.109876 | + | 0.993945i | \(0.464955\pi\) | |||||||
\(654\) | −3.12311 | −0.122123 | ||||||||
\(655\) | −43.0540 | −1.68226 | ||||||||
\(656\) | −17.2614 | −0.673943 | ||||||||
\(657\) | 4.56155 | 0.177963 | ||||||||
\(658\) | 8.49242 | 0.331069 | ||||||||
\(659\) | −47.8617 | −1.86443 | −0.932214 | − | 0.361907i | \(-0.882126\pi\) | ||||
−0.932214 | + | 0.361907i | \(0.882126\pi\) | |||||||
\(660\) | −7.36932 | −0.286850 | ||||||||
\(661\) | 42.0000 | 1.63361 | 0.816805 | − | 0.576913i | \(-0.195743\pi\) | ||||
0.816805 | + | 0.576913i | \(0.195743\pi\) | |||||||
\(662\) | 16.0000 | 0.621858 | ||||||||
\(663\) | −4.00000 | −0.155347 | ||||||||
\(664\) | −9.75379 | −0.378520 | ||||||||
\(665\) | −16.8078 | −0.651777 | ||||||||
\(666\) | −12.8769 | −0.498970 | ||||||||
\(667\) | −36.4924 | −1.41299 | ||||||||
\(668\) | −0.768944 | −0.0297513 | ||||||||
\(669\) | 7.68466 | 0.297106 | ||||||||
\(670\) | −30.7386 | −1.18754 | ||||||||
\(671\) | 80.3542 | 3.10204 | ||||||||
\(672\) | −2.43845 | −0.0940651 | ||||||||
\(673\) | −28.7386 | −1.10779 | −0.553896 | − | 0.832586i | \(-0.686860\pi\) | ||||
−0.553896 | + | 0.832586i | \(0.686860\pi\) | |||||||
\(674\) | 20.8769 | 0.804148 | ||||||||
\(675\) | 1.56155 | 0.0601042 | ||||||||
\(676\) | −3.94602 | −0.151770 | ||||||||
\(677\) | 21.8617 | 0.840215 | 0.420107 | − | 0.907474i | \(-0.361992\pi\) | ||||
0.420107 | + | 0.907474i | \(0.361992\pi\) | |||||||
\(678\) | 8.38447 | 0.322004 | ||||||||
\(679\) | −11.1231 | −0.426866 | ||||||||
\(680\) | 12.4924 | 0.479063 | ||||||||
\(681\) | −6.24621 | −0.239355 | ||||||||
\(682\) | 26.2462 | 1.00502 | ||||||||
\(683\) | 31.2311 | 1.19502 | 0.597512 | − | 0.801860i | \(-0.296156\pi\) | ||||
0.597512 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(684\) | −2.87689 | −0.110001 | ||||||||
\(685\) | −10.8769 | −0.415585 | ||||||||
\(686\) | 1.56155 | 0.0596204 | ||||||||
\(687\) | 12.5616 | 0.479253 | ||||||||
\(688\) | 36.0000 | 1.37249 | ||||||||
\(689\) | −2.24621 | −0.0855738 | ||||||||
\(690\) | 20.4924 | 0.780133 | ||||||||
\(691\) | −37.3693 | −1.42160 | −0.710798 | − | 0.703396i | \(-0.751666\pi\) | ||||
−0.710798 | + | 0.703396i | \(0.751666\pi\) | |||||||
\(692\) | −4.38447 | −0.166673 | ||||||||
\(693\) | −6.56155 | −0.249253 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 13.9309 | 0.528428 | ||||||||
\(696\) | 17.3693 | 0.658382 | ||||||||
\(697\) | −7.36932 | −0.279133 | ||||||||
\(698\) | 40.3845 | 1.52857 | ||||||||
\(699\) | −5.43845 | −0.205701 | ||||||||
\(700\) | 0.684658 | 0.0258777 | ||||||||
\(701\) | −40.8078 | −1.54129 | −0.770644 | − | 0.637266i | \(-0.780065\pi\) | ||||
−0.770644 | + | 0.637266i | \(0.780065\pi\) | |||||||
\(702\) | 3.12311 | 0.117874 | ||||||||
\(703\) | 54.1080 | 2.04072 | ||||||||
\(704\) | −36.4924 | −1.37536 | ||||||||
\(705\) | 13.9309 | 0.524667 | ||||||||
\(706\) | −23.6155 | −0.888782 | ||||||||
\(707\) | 4.87689 | 0.183414 | ||||||||
\(708\) | 1.61553 | 0.0607153 | ||||||||
\(709\) | 27.1231 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(710\) | 32.0000 | 1.20094 | ||||||||
\(711\) | 3.12311 | 0.117126 | ||||||||
\(712\) | 35.5076 | 1.33070 | ||||||||
\(713\) | −13.1231 | −0.491464 | ||||||||
\(714\) | −3.12311 | −0.116879 | ||||||||
\(715\) | −33.6155 | −1.25715 | ||||||||
\(716\) | 0.354162 | 0.0132357 | ||||||||
\(717\) | −23.6847 | −0.884520 | ||||||||
\(718\) | −25.4773 | −0.950803 | ||||||||
\(719\) | −10.8769 | −0.405640 | −0.202820 | − | 0.979216i | \(-0.565011\pi\) | ||||
−0.202820 | + | 0.979216i | \(0.565011\pi\) | |||||||
\(720\) | −12.0000 | −0.447214 | ||||||||
\(721\) | −5.43845 | −0.202538 | ||||||||
\(722\) | 37.5616 | 1.39790 | ||||||||
\(723\) | −16.2462 | −0.604203 | ||||||||
\(724\) | −0.384472 | −0.0142888 | ||||||||
\(725\) | −11.1231 | −0.413102 | ||||||||
\(726\) | 50.0540 | 1.85768 | ||||||||
\(727\) | 2.56155 | 0.0950027 | 0.0475014 | − | 0.998871i | \(-0.484874\pi\) | ||||
0.0475014 | + | 0.998871i | \(0.484874\pi\) | |||||||
\(728\) | −4.87689 | −0.180750 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.2462 | 0.675323 | ||||||||
\(731\) | 15.3693 | 0.568455 | ||||||||
\(732\) | −5.36932 | −0.198456 | ||||||||
\(733\) | −48.7386 | −1.80020 | −0.900101 | − | 0.435681i | \(-0.856508\pi\) | ||||
−0.900101 | + | 0.435681i | \(0.856508\pi\) | |||||||
\(734\) | 36.8769 | 1.36115 | ||||||||
\(735\) | 2.56155 | 0.0944843 | ||||||||
\(736\) | −12.4924 | −0.460477 | ||||||||
\(737\) | 50.4233 | 1.85737 | ||||||||
\(738\) | 5.75379 | 0.211800 | ||||||||
\(739\) | 50.9848 | 1.87551 | 0.937754 | − | 0.347300i | \(-0.112902\pi\) | ||||
0.937754 | + | 0.347300i | \(0.112902\pi\) | |||||||
\(740\) | −9.26137 | −0.340455 | ||||||||
\(741\) | −13.1231 | −0.482089 | ||||||||
\(742\) | −1.75379 | −0.0643836 | ||||||||
\(743\) | −1.43845 | −0.0527715 | −0.0263858 | − | 0.999652i | \(-0.508400\pi\) | ||||
−0.0263858 | + | 0.999652i | \(0.508400\pi\) | |||||||
\(744\) | 6.24621 | 0.228997 | ||||||||
\(745\) | −13.7538 | −0.503900 | ||||||||
\(746\) | −21.3693 | −0.782386 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 5.75379 | 0.210379 | ||||||||
\(749\) | 14.2462 | 0.520545 | ||||||||
\(750\) | −13.7538 | −0.502217 | ||||||||
\(751\) | −43.6847 | −1.59408 | −0.797038 | − | 0.603929i | \(-0.793601\pi\) | ||||
−0.797038 | + | 0.603929i | \(0.793601\pi\) | |||||||
\(752\) | −25.4773 | −0.929060 | ||||||||
\(753\) | 1.12311 | 0.0409282 | ||||||||
\(754\) | −22.2462 | −0.810159 | ||||||||
\(755\) | 41.6155 | 1.51454 | ||||||||
\(756\) | 0.438447 | 0.0159462 | ||||||||
\(757\) | −46.4924 | −1.68980 | −0.844898 | − | 0.534928i | \(-0.820339\pi\) | ||||
−0.844898 | + | 0.534928i | \(0.820339\pi\) | |||||||
\(758\) | 16.3845 | 0.595111 | ||||||||
\(759\) | −33.6155 | −1.22017 | ||||||||
\(760\) | 40.9848 | 1.48668 | ||||||||
\(761\) | −7.75379 | −0.281075 | −0.140537 | − | 0.990075i | \(-0.544883\pi\) | ||||
−0.140537 | + | 0.990075i | \(0.544883\pi\) | |||||||
\(762\) | −9.36932 | −0.339415 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | −4.27652 | −0.154719 | ||||||||
\(765\) | −5.12311 | −0.185226 | ||||||||
\(766\) | −1.56155 | −0.0564212 | ||||||||
\(767\) | 7.36932 | 0.266091 | ||||||||
\(768\) | 10.0540 | 0.362792 | ||||||||
\(769\) | 14.8078 | 0.533982 | 0.266991 | − | 0.963699i | \(-0.413971\pi\) | ||||
0.266991 | + | 0.963699i | \(0.413971\pi\) | |||||||
\(770\) | −26.2462 | −0.945848 | ||||||||
\(771\) | −22.5616 | −0.812534 | ||||||||
\(772\) | 0.876894 | 0.0315601 | ||||||||
\(773\) | −50.9848 | −1.83380 | −0.916899 | − | 0.399120i | \(-0.869316\pi\) | ||||
−0.916899 | + | 0.399120i | \(0.869316\pi\) | |||||||
\(774\) | −12.0000 | −0.431331 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 27.1231 | 0.973663 | ||||||||
\(777\) | −8.24621 | −0.295831 | ||||||||
\(778\) | 21.8617 | 0.783781 | ||||||||
\(779\) | −24.1771 | −0.866234 | ||||||||
\(780\) | 2.24621 | 0.0804273 | ||||||||
\(781\) | −52.4924 | −1.87833 | ||||||||
\(782\) | −16.0000 | −0.572159 | ||||||||
\(783\) | −7.12311 | −0.254559 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | 35.8617 | 1.27996 | ||||||||
\(786\) | −26.2462 | −0.936171 | ||||||||
\(787\) | 42.2462 | 1.50591 | 0.752957 | − | 0.658069i | \(-0.228627\pi\) | ||||
0.752957 | + | 0.658069i | \(0.228627\pi\) | |||||||
\(788\) | 10.1080 | 0.360081 | ||||||||
\(789\) | 31.3693 | 1.11678 | ||||||||
\(790\) | 12.4924 | 0.444460 | ||||||||
\(791\) | 5.36932 | 0.190911 | ||||||||
\(792\) | 16.0000 | 0.568535 | ||||||||
\(793\) | −24.4924 | −0.869751 | ||||||||
\(794\) | −35.6155 | −1.26395 | ||||||||
\(795\) | −2.87689 | −0.102033 | ||||||||
\(796\) | 4.38447 | 0.155403 | ||||||||
\(797\) | −20.2462 | −0.717158 | −0.358579 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358579 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(798\) | −10.2462 | −0.362712 | ||||||||
\(799\) | −10.8769 | −0.384797 | ||||||||
\(800\) | −3.80776 | −0.134625 | ||||||||
\(801\) | −14.5616 | −0.514507 | ||||||||
\(802\) | 7.61553 | 0.268914 | ||||||||
\(803\) | −29.9309 | −1.05624 | ||||||||
\(804\) | −3.36932 | −0.118827 | ||||||||
\(805\) | 13.1231 | 0.462529 | ||||||||
\(806\) | −8.00000 | −0.281788 | ||||||||
\(807\) | 0.315342 | 0.0111005 | ||||||||
\(808\) | −11.8920 | −0.418361 | ||||||||
\(809\) | −52.1080 | −1.83202 | −0.916009 | − | 0.401158i | \(-0.868608\pi\) | ||||
−0.916009 | + | 0.401158i | \(0.868608\pi\) | |||||||
\(810\) | 4.00000 | 0.140546 | ||||||||
\(811\) | 18.9848 | 0.666648 | 0.333324 | − | 0.942812i | \(-0.391830\pi\) | ||||
0.333324 | + | 0.942812i | \(0.391830\pi\) | |||||||
\(812\) | −3.12311 | −0.109600 | ||||||||
\(813\) | 11.7538 | 0.412223 | ||||||||
\(814\) | 84.4924 | 2.96146 | ||||||||
\(815\) | −32.9848 | −1.15541 | ||||||||
\(816\) | 9.36932 | 0.327992 | ||||||||
\(817\) | 50.4233 | 1.76409 | ||||||||
\(818\) | −16.3845 | −0.572870 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 4.13826 | 0.144514 | ||||||||
\(821\) | −44.1080 | −1.53938 | −0.769689 | − | 0.638419i | \(-0.779589\pi\) | ||||
−0.769689 | + | 0.638419i | \(0.779589\pi\) | |||||||
\(822\) | −6.63068 | −0.231272 | ||||||||
\(823\) | 41.3002 | 1.43963 | 0.719817 | − | 0.694164i | \(-0.244226\pi\) | ||||
0.719817 | + | 0.694164i | \(0.244226\pi\) | |||||||
\(824\) | 13.2614 | 0.461982 | ||||||||
\(825\) | −10.2462 | −0.356727 | ||||||||
\(826\) | 5.75379 | 0.200200 | ||||||||
\(827\) | −30.2462 | −1.05176 | −0.525882 | − | 0.850558i | \(-0.676265\pi\) | ||||
−0.525882 | + | 0.850558i | \(0.676265\pi\) | |||||||
\(828\) | 2.24621 | 0.0780612 | ||||||||
\(829\) | −11.9309 | −0.414376 | −0.207188 | − | 0.978301i | \(-0.566431\pi\) | ||||
−0.207188 | + | 0.978301i | \(0.566431\pi\) | |||||||
\(830\) | 16.0000 | 0.555368 | ||||||||
\(831\) | −0.0691303 | −0.00239810 | ||||||||
\(832\) | 11.1231 | 0.385624 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 8.49242 | 0.294069 | ||||||||
\(835\) | −4.49242 | −0.155467 | ||||||||
\(836\) | 18.8769 | 0.652871 | ||||||||
\(837\) | −2.56155 | −0.0885402 | ||||||||
\(838\) | −34.7386 | −1.20003 | ||||||||
\(839\) | 2.24621 | 0.0775478 | 0.0387739 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387739 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(840\) | −6.24621 | −0.215515 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | −25.3693 | −0.874284 | ||||||||
\(843\) | 15.0540 | 0.518486 | ||||||||
\(844\) | 6.63068 | 0.228238 | ||||||||
\(845\) | −23.0540 | −0.793081 | ||||||||
\(846\) | 8.49242 | 0.291976 | ||||||||
\(847\) | 32.0540 | 1.10139 | ||||||||
\(848\) | 5.26137 | 0.180676 | ||||||||
\(849\) | 12.8769 | 0.441934 | ||||||||
\(850\) | −4.87689 | −0.167276 | ||||||||
\(851\) | −42.2462 | −1.44818 | ||||||||
\(852\) | 3.50758 | 0.120168 | ||||||||
\(853\) | 46.1771 | 1.58107 | 0.790537 | − | 0.612415i | \(-0.209802\pi\) | ||||
0.790537 | + | 0.612415i | \(0.209802\pi\) | |||||||
\(854\) | −19.1231 | −0.654379 | ||||||||
\(855\) | −16.8078 | −0.574813 | ||||||||
\(856\) | −34.7386 | −1.18734 | ||||||||
\(857\) | 43.3693 | 1.48147 | 0.740734 | − | 0.671799i | \(-0.234478\pi\) | ||||
0.740734 | + | 0.671799i | \(0.234478\pi\) | |||||||
\(858\) | −20.4924 | −0.699600 | ||||||||
\(859\) | −15.5076 | −0.529112 | −0.264556 | − | 0.964370i | \(-0.585225\pi\) | ||||
−0.264556 | + | 0.964370i | \(0.585225\pi\) | |||||||
\(860\) | −8.63068 | −0.294304 | ||||||||
\(861\) | 3.68466 | 0.125573 | ||||||||
\(862\) | 29.4773 | 1.00400 | ||||||||
\(863\) | −12.8078 | −0.435981 | −0.217991 | − | 0.975951i | \(-0.569950\pi\) | ||||
−0.217991 | + | 0.975951i | \(0.569950\pi\) | |||||||
\(864\) | −2.43845 | −0.0829577 | ||||||||
\(865\) | −25.6155 | −0.870954 | ||||||||
\(866\) | −28.1080 | −0.955147 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | −1.12311 | −0.0381207 | ||||||||
\(869\) | −20.4924 | −0.695158 | ||||||||
\(870\) | −28.4924 | −0.965984 | ||||||||
\(871\) | −15.3693 | −0.520769 | ||||||||
\(872\) | 4.87689 | 0.165152 | ||||||||
\(873\) | −11.1231 | −0.376460 | ||||||||
\(874\) | −52.4924 | −1.77558 | ||||||||
\(875\) | −8.80776 | −0.297757 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −35.1231 | −1.18602 | −0.593012 | − | 0.805194i | \(-0.702061\pi\) | ||||
−0.593012 | + | 0.805194i | \(0.702061\pi\) | |||||||
\(878\) | −18.2462 | −0.615780 | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | 78.7386 | 2.65428 | ||||||||
\(881\) | −24.8078 | −0.835795 | −0.417897 | − | 0.908494i | \(-0.637233\pi\) | ||||
−0.417897 | + | 0.908494i | \(0.637233\pi\) | |||||||
\(882\) | 1.56155 | 0.0525802 | ||||||||
\(883\) | −28.7386 | −0.967132 | −0.483566 | − | 0.875308i | \(-0.660659\pi\) | ||||
−0.483566 | + | 0.875308i | \(0.660659\pi\) | |||||||
\(884\) | −1.75379 | −0.0589863 | ||||||||
\(885\) | 9.43845 | 0.317270 | ||||||||
\(886\) | −42.2462 | −1.41929 | ||||||||
\(887\) | 4.49242 | 0.150841 | 0.0754204 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754204 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(888\) | 20.1080 | 0.674779 | ||||||||
\(889\) | −6.00000 | −0.201234 | ||||||||
\(890\) | −58.2462 | −1.95242 | ||||||||
\(891\) | −6.56155 | −0.219820 | ||||||||
\(892\) | 3.36932 | 0.112813 | ||||||||
\(893\) | −35.6847 | −1.19414 | ||||||||
\(894\) | −8.38447 | −0.280419 | ||||||||
\(895\) | 2.06913 | 0.0691634 | ||||||||
\(896\) | 13.5616 | 0.453060 | ||||||||
\(897\) | 10.2462 | 0.342111 | ||||||||
\(898\) | 17.7538 | 0.592452 | ||||||||
\(899\) | 18.2462 | 0.608545 | ||||||||
\(900\) | 0.684658 | 0.0228219 | ||||||||
\(901\) | 2.24621 | 0.0748321 | ||||||||
\(902\) | −37.7538 | −1.25706 | ||||||||
\(903\) | −7.68466 | −0.255729 | ||||||||
\(904\) | −13.0928 | −0.435460 | ||||||||
\(905\) | −2.24621 | −0.0746666 | ||||||||
\(906\) | 25.3693 | 0.842839 | ||||||||
\(907\) | 47.4773 | 1.57646 | 0.788228 | − | 0.615383i | \(-0.210999\pi\) | ||||
0.788228 | + | 0.615383i | \(0.210999\pi\) | |||||||
\(908\) | −2.73863 | −0.0908848 | ||||||||
\(909\) | 4.87689 | 0.161756 | ||||||||
\(910\) | 8.00000 | 0.265197 | ||||||||
\(911\) | −29.9309 | −0.991654 | −0.495827 | − | 0.868421i | \(-0.665135\pi\) | ||||
−0.495827 | + | 0.868421i | \(0.665135\pi\) | |||||||
\(912\) | 30.7386 | 1.01786 | ||||||||
\(913\) | −26.2462 | −0.868623 | ||||||||
\(914\) | 0.384472 | 0.0127172 | ||||||||
\(915\) | −31.3693 | −1.03704 | ||||||||
\(916\) | 5.50758 | 0.181975 | ||||||||
\(917\) | −16.8078 | −0.555041 | ||||||||
\(918\) | −3.12311 | −0.103078 | ||||||||
\(919\) | 23.0540 | 0.760480 | 0.380240 | − | 0.924888i | \(-0.375841\pi\) | ||||
0.380240 | + | 0.924888i | \(0.375841\pi\) | |||||||
\(920\) | −32.0000 | −1.05501 | ||||||||
\(921\) | 0.246211 | 0.00811294 | ||||||||
\(922\) | −4.49242 | −0.147950 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | −2.87689 | −0.0946429 | ||||||||
\(925\) | −12.8769 | −0.423390 | ||||||||
\(926\) | 46.8466 | 1.53947 | ||||||||
\(927\) | −5.43845 | −0.178622 | ||||||||
\(928\) | 17.3693 | 0.570176 | ||||||||
\(929\) | −49.1231 | −1.61168 | −0.805838 | − | 0.592136i | \(-0.798285\pi\) | ||||
−0.805838 | + | 0.592136i | \(0.798285\pi\) | |||||||
\(930\) | −10.2462 | −0.335987 | ||||||||
\(931\) | −6.56155 | −0.215046 | ||||||||
\(932\) | −2.38447 | −0.0781060 | ||||||||
\(933\) | −33.3002 | −1.09020 | ||||||||
\(934\) | −46.2462 | −1.51322 | ||||||||
\(935\) | 33.6155 | 1.09935 | ||||||||
\(936\) | −4.87689 | −0.159406 | ||||||||
\(937\) | 10.4924 | 0.342773 | 0.171386 | − | 0.985204i | \(-0.445175\pi\) | ||||
0.171386 | + | 0.985204i | \(0.445175\pi\) | |||||||
\(938\) | −12.0000 | −0.391814 | ||||||||
\(939\) | 18.1771 | 0.593187 | ||||||||
\(940\) | 6.10795 | 0.199219 | ||||||||
\(941\) | 41.2311 | 1.34409 | 0.672047 | − | 0.740508i | \(-0.265415\pi\) | ||||
0.672047 | + | 0.740508i | \(0.265415\pi\) | |||||||
\(942\) | 21.8617 | 0.712294 | ||||||||
\(943\) | 18.8769 | 0.614716 | ||||||||
\(944\) | −17.2614 | −0.561810 | ||||||||
\(945\) | 2.56155 | 0.0833273 | ||||||||
\(946\) | 78.7386 | 2.56001 | ||||||||
\(947\) | −2.06913 | −0.0672377 | −0.0336189 | − | 0.999435i | \(-0.510703\pi\) | ||||
−0.0336189 | + | 0.999435i | \(0.510703\pi\) | |||||||
\(948\) | 1.36932 | 0.0444733 | ||||||||
\(949\) | 9.12311 | 0.296149 | ||||||||
\(950\) | −16.0000 | −0.519109 | ||||||||
\(951\) | 6.63068 | 0.215015 | ||||||||
\(952\) | 4.87689 | 0.158061 | ||||||||
\(953\) | 19.3693 | 0.627434 | 0.313717 | − | 0.949517i | \(-0.398426\pi\) | ||||
0.313717 | + | 0.949517i | \(0.398426\pi\) | |||||||
\(954\) | −1.75379 | −0.0567810 | ||||||||
\(955\) | −24.9848 | −0.808491 | ||||||||
\(956\) | −10.3845 | −0.335858 | ||||||||
\(957\) | 46.7386 | 1.51085 | ||||||||
\(958\) | 0.984845 | 0.0318189 | ||||||||
\(959\) | −4.24621 | −0.137117 | ||||||||
\(960\) | 14.2462 | 0.459794 | ||||||||
\(961\) | −24.4384 | −0.788337 | ||||||||
\(962\) | −25.7538 | −0.830335 | ||||||||
\(963\) | 14.2462 | 0.459078 | ||||||||
\(964\) | −7.12311 | −0.229420 | ||||||||
\(965\) | 5.12311 | 0.164919 | ||||||||
\(966\) | 8.00000 | 0.257396 | ||||||||
\(967\) | −6.73863 | −0.216700 | −0.108350 | − | 0.994113i | \(-0.534557\pi\) | ||||
−0.108350 | + | 0.994113i | \(0.534557\pi\) | |||||||
\(968\) | −78.1619 | −2.51222 | ||||||||
\(969\) | 13.1231 | 0.421575 | ||||||||
\(970\) | −44.4924 | −1.42857 | ||||||||
\(971\) | −42.7386 | −1.37155 | −0.685774 | − | 0.727815i | \(-0.740536\pi\) | ||||
−0.685774 | + | 0.727815i | \(0.740536\pi\) | |||||||
\(972\) | 0.438447 | 0.0140632 | ||||||||
\(973\) | 5.43845 | 0.174349 | ||||||||
\(974\) | 56.6004 | 1.81359 | ||||||||
\(975\) | 3.12311 | 0.100019 | ||||||||
\(976\) | 57.3693 | 1.83635 | ||||||||
\(977\) | −55.6847 | −1.78151 | −0.890755 | − | 0.454484i | \(-0.849824\pi\) | ||||
−0.890755 | + | 0.454484i | \(0.849824\pi\) | |||||||
\(978\) | −20.1080 | −0.642981 | ||||||||
\(979\) | 95.5464 | 3.05368 | ||||||||
\(980\) | 1.12311 | 0.0358763 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 23.2311 | 0.741333 | ||||||||
\(983\) | 52.4924 | 1.67425 | 0.837124 | − | 0.547013i | \(-0.184235\pi\) | ||||
0.837124 | + | 0.547013i | \(0.184235\pi\) | |||||||
\(984\) | −8.98485 | −0.286426 | ||||||||
\(985\) | 59.0540 | 1.88162 | ||||||||
\(986\) | 22.2462 | 0.708464 | ||||||||
\(987\) | 5.43845 | 0.173108 | ||||||||
\(988\) | −5.75379 | −0.183052 | ||||||||
\(989\) | −39.3693 | −1.25187 | ||||||||
\(990\) | −26.2462 | −0.834159 | ||||||||
\(991\) | 24.9848 | 0.793670 | 0.396835 | − | 0.917890i | \(-0.370109\pi\) | ||||
0.396835 | + | 0.917890i | \(0.370109\pi\) | |||||||
\(992\) | 6.24621 | 0.198317 | ||||||||
\(993\) | 10.2462 | 0.325154 | ||||||||
\(994\) | 12.4924 | 0.396236 | ||||||||
\(995\) | 25.6155 | 0.812067 | ||||||||
\(996\) | 1.75379 | 0.0555709 | ||||||||
\(997\) | 47.6155 | 1.50800 | 0.753999 | − | 0.656875i | \(-0.228122\pi\) | ||||
0.753999 | + | 0.656875i | \(0.228122\pi\) | |||||||
\(998\) | −35.5076 | −1.12397 | ||||||||
\(999\) | −8.24621 | −0.260899 |
(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 | 8043.2.a.l.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.l.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |