Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38697 | −1.68784 | −0.843920 | − | 0.536468i | \(-0.819758\pi\) | ||||
−0.843920 | + | 0.536468i | \(0.819758\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.69761 | 1.84881 | ||||||||
\(5\) | 2.25593 | 1.00888 | 0.504441 | − | 0.863446i | \(-0.331699\pi\) | ||||
0.504441 | + | 0.863446i | \(0.331699\pi\) | |||||||
\(6\) | 2.38697 | 0.974475 | ||||||||
\(7\) | −4.86795 | −1.83991 | −0.919956 | − | 0.392022i | \(-0.871776\pi\) | ||||
−0.919956 | + | 0.392022i | \(0.871776\pi\) | |||||||
\(8\) | −4.05215 | −1.43265 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.38482 | −1.70283 | ||||||||
\(11\) | 1.03520 | 0.312126 | 0.156063 | − | 0.987747i | \(-0.450120\pi\) | ||||
0.156063 | + | 0.987747i | \(0.450120\pi\) | |||||||
\(12\) | −3.69761 | −1.06741 | ||||||||
\(13\) | −0.688087 | −0.190841 | −0.0954205 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954205 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(14\) | 11.6196 | 3.10548 | ||||||||
\(15\) | −2.25593 | −0.582478 | ||||||||
\(16\) | 2.27712 | 0.569280 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.38697 | −0.562614 | ||||||||
\(19\) | −8.17166 | −1.87471 | −0.937354 | − | 0.348379i | \(-0.886732\pi\) | ||||
−0.937354 | + | 0.348379i | \(0.886732\pi\) | |||||||
\(20\) | 8.34155 | 1.86523 | ||||||||
\(21\) | 4.86795 | 1.06227 | ||||||||
\(22\) | −2.47100 | −0.526819 | ||||||||
\(23\) | 7.38826 | 1.54056 | 0.770280 | − | 0.637706i | \(-0.220117\pi\) | ||||
0.770280 | + | 0.637706i | \(0.220117\pi\) | |||||||
\(24\) | 4.05215 | 0.827141 | ||||||||
\(25\) | 0.0892066 | 0.0178413 | ||||||||
\(26\) | 1.64244 | 0.322109 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −17.9998 | −3.40164 | ||||||||
\(29\) | 2.85376 | 0.529930 | 0.264965 | − | 0.964258i | \(-0.414640\pi\) | ||||
0.264965 | + | 0.964258i | \(0.414640\pi\) | |||||||
\(30\) | 5.38482 | 0.983130 | ||||||||
\(31\) | −10.3049 | −1.85081 | −0.925406 | − | 0.378978i | \(-0.876276\pi\) | ||||
−0.925406 | + | 0.378978i | \(0.876276\pi\) | |||||||
\(32\) | 2.66889 | 0.471797 | ||||||||
\(33\) | −1.03520 | −0.180206 | ||||||||
\(34\) | −2.38697 | −0.409362 | ||||||||
\(35\) | −10.9817 | −1.85625 | ||||||||
\(36\) | 3.69761 | 0.616269 | ||||||||
\(37\) | 1.32195 | 0.217327 | 0.108664 | − | 0.994079i | \(-0.465343\pi\) | ||||
0.108664 | + | 0.994079i | \(0.465343\pi\) | |||||||
\(38\) | 19.5055 | 3.16421 | ||||||||
\(39\) | 0.688087 | 0.110182 | ||||||||
\(40\) | −9.14135 | −1.44537 | ||||||||
\(41\) | 8.69790 | 1.35838 | 0.679192 | − | 0.733961i | \(-0.262330\pi\) | ||||
0.679192 | + | 0.733961i | \(0.262330\pi\) | |||||||
\(42\) | −11.6196 | −1.79295 | ||||||||
\(43\) | 4.03880 | 0.615912 | 0.307956 | − | 0.951401i | \(-0.400355\pi\) | ||||
0.307956 | + | 0.951401i | \(0.400355\pi\) | |||||||
\(44\) | 3.82779 | 0.577061 | ||||||||
\(45\) | 2.25593 | 0.336294 | ||||||||
\(46\) | −17.6355 | −2.60022 | ||||||||
\(47\) | −12.0312 | −1.75493 | −0.877464 | − | 0.479643i | \(-0.840766\pi\) | ||||
−0.877464 | + | 0.479643i | \(0.840766\pi\) | |||||||
\(48\) | −2.27712 | −0.328674 | ||||||||
\(49\) | 16.6969 | 2.38527 | ||||||||
\(50\) | −0.212933 | −0.0301133 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −2.54428 | −0.352828 | ||||||||
\(53\) | −8.62613 | −1.18489 | −0.592445 | − | 0.805611i | \(-0.701837\pi\) | ||||
−0.592445 | + | 0.805611i | \(0.701837\pi\) | |||||||
\(54\) | 2.38697 | 0.324825 | ||||||||
\(55\) | 2.33535 | 0.314898 | ||||||||
\(56\) | 19.7256 | 2.63595 | ||||||||
\(57\) | 8.17166 | 1.08236 | ||||||||
\(58\) | −6.81184 | −0.894438 | ||||||||
\(59\) | −2.74590 | −0.357486 | −0.178743 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178743 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(60\) | −8.34155 | −1.07689 | ||||||||
\(61\) | −10.2874 | −1.31717 | −0.658586 | − | 0.752505i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752505i | \(0.728845\pi\) | |||||||
\(62\) | 24.5974 | 3.12387 | ||||||||
\(63\) | −4.86795 | −0.613304 | ||||||||
\(64\) | −10.9248 | −1.36560 | ||||||||
\(65\) | −1.55227 | −0.192536 | ||||||||
\(66\) | 2.47100 | 0.304159 | ||||||||
\(67\) | 15.1775 | 1.85423 | 0.927114 | − | 0.374780i | \(-0.122282\pi\) | ||||
0.927114 | + | 0.374780i | \(0.122282\pi\) | |||||||
\(68\) | 3.69761 | 0.448402 | ||||||||
\(69\) | −7.38826 | −0.889443 | ||||||||
\(70\) | 26.2130 | 3.13306 | ||||||||
\(71\) | −3.50593 | −0.416078 | −0.208039 | − | 0.978121i | \(-0.566708\pi\) | ||||
−0.208039 | + | 0.978121i | \(0.566708\pi\) | |||||||
\(72\) | −4.05215 | −0.477550 | ||||||||
\(73\) | 5.22796 | 0.611886 | 0.305943 | − | 0.952050i | \(-0.401028\pi\) | ||||
0.305943 | + | 0.952050i | \(0.401028\pi\) | |||||||
\(74\) | −3.15545 | −0.366814 | ||||||||
\(75\) | −0.0892066 | −0.0103007 | ||||||||
\(76\) | −30.2156 | −3.46597 | ||||||||
\(77\) | −5.03932 | −0.574284 | ||||||||
\(78\) | −1.64244 | −0.185970 | ||||||||
\(79\) | 4.50555 | 0.506914 | 0.253457 | − | 0.967347i | \(-0.418432\pi\) | ||||
0.253457 | + | 0.967347i | \(0.418432\pi\) | |||||||
\(80\) | 5.13702 | 0.574336 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −20.7616 | −2.29274 | ||||||||
\(83\) | −7.62159 | −0.836578 | −0.418289 | − | 0.908314i | \(-0.637370\pi\) | ||||
−0.418289 | + | 0.908314i | \(0.637370\pi\) | |||||||
\(84\) | 17.9998 | 1.96394 | ||||||||
\(85\) | 2.25593 | 0.244690 | ||||||||
\(86\) | −9.64049 | −1.03956 | ||||||||
\(87\) | −2.85376 | −0.305955 | ||||||||
\(88\) | −4.19480 | −0.447168 | ||||||||
\(89\) | −3.63646 | −0.385464 | −0.192732 | − | 0.981251i | \(-0.561735\pi\) | ||||
−0.192732 | + | 0.981251i | \(0.561735\pi\) | |||||||
\(90\) | −5.38482 | −0.567610 | ||||||||
\(91\) | 3.34957 | 0.351131 | ||||||||
\(92\) | 27.3189 | 2.84820 | ||||||||
\(93\) | 10.3049 | 1.06857 | ||||||||
\(94\) | 28.7180 | 2.96204 | ||||||||
\(95\) | −18.4347 | −1.89136 | ||||||||
\(96\) | −2.66889 | −0.272392 | ||||||||
\(97\) | −4.49489 | −0.456387 | −0.228194 | − | 0.973616i | \(-0.573282\pi\) | ||||
−0.228194 | + | 0.973616i | \(0.573282\pi\) | |||||||
\(98\) | −39.8550 | −4.02596 | ||||||||
\(99\) | 1.03520 | 0.104042 | ||||||||
\(100\) | 0.329852 | 0.0329852 | ||||||||
\(101\) | −14.1289 | −1.40588 | −0.702938 | − | 0.711251i | \(-0.748129\pi\) | ||||
−0.702938 | + | 0.711251i | \(0.748129\pi\) | |||||||
\(102\) | 2.38697 | 0.236345 | ||||||||
\(103\) | 2.40939 | 0.237404 | 0.118702 | − | 0.992930i | \(-0.462127\pi\) | ||||
0.118702 | + | 0.992930i | \(0.462127\pi\) | |||||||
\(104\) | 2.78823 | 0.273409 | ||||||||
\(105\) | 10.9817 | 1.07171 | ||||||||
\(106\) | 20.5903 | 1.99991 | ||||||||
\(107\) | 7.48379 | 0.723486 | 0.361743 | − | 0.932278i | \(-0.382182\pi\) | ||||
0.361743 | + | 0.932278i | \(0.382182\pi\) | |||||||
\(108\) | −3.69761 | −0.355803 | ||||||||
\(109\) | −8.01499 | −0.767697 | −0.383848 | − | 0.923396i | \(-0.625401\pi\) | ||||
−0.383848 | + | 0.923396i | \(0.625401\pi\) | |||||||
\(110\) | −5.57439 | −0.531498 | ||||||||
\(111\) | −1.32195 | −0.125474 | ||||||||
\(112\) | −11.0849 | −1.04742 | ||||||||
\(113\) | 6.04782 | 0.568931 | 0.284465 | − | 0.958686i | \(-0.408184\pi\) | ||||
0.284465 | + | 0.958686i | \(0.408184\pi\) | |||||||
\(114\) | −19.5055 | −1.82686 | ||||||||
\(115\) | 16.6674 | 1.55424 | ||||||||
\(116\) | 10.5521 | 0.979739 | ||||||||
\(117\) | −0.688087 | −0.0636137 | ||||||||
\(118\) | 6.55437 | 0.603379 | ||||||||
\(119\) | −4.86795 | −0.446244 | ||||||||
\(120\) | 9.14135 | 0.834487 | ||||||||
\(121\) | −9.92835 | −0.902577 | ||||||||
\(122\) | 24.5558 | 2.22318 | ||||||||
\(123\) | −8.69790 | −0.784263 | ||||||||
\(124\) | −38.1035 | −3.42179 | ||||||||
\(125\) | −11.0784 | −0.990881 | ||||||||
\(126\) | 11.6196 | 1.03516 | ||||||||
\(127\) | −15.1142 | −1.34117 | −0.670585 | − | 0.741833i | \(-0.733957\pi\) | ||||
−0.670585 | + | 0.741833i | \(0.733957\pi\) | |||||||
\(128\) | 20.7393 | 1.83312 | ||||||||
\(129\) | −4.03880 | −0.355597 | ||||||||
\(130\) | 3.70523 | 0.324970 | ||||||||
\(131\) | −3.12398 | −0.272943 | −0.136471 | − | 0.990644i | \(-0.543576\pi\) | ||||
−0.136471 | + | 0.990644i | \(0.543576\pi\) | |||||||
\(132\) | −3.82779 | −0.333166 | ||||||||
\(133\) | 39.7792 | 3.44930 | ||||||||
\(134\) | −36.2282 | −3.12964 | ||||||||
\(135\) | −2.25593 | −0.194159 | ||||||||
\(136\) | −4.05215 | −0.347469 | ||||||||
\(137\) | 14.0665 | 1.20179 | 0.600893 | − | 0.799329i | \(-0.294812\pi\) | ||||
0.600893 | + | 0.799329i | \(0.294812\pi\) | |||||||
\(138\) | 17.6355 | 1.50124 | ||||||||
\(139\) | 1.39970 | 0.118721 | 0.0593603 | − | 0.998237i | \(-0.481094\pi\) | ||||
0.0593603 | + | 0.998237i | \(0.481094\pi\) | |||||||
\(140\) | −40.6062 | −3.43185 | ||||||||
\(141\) | 12.0312 | 1.01321 | ||||||||
\(142\) | 8.36855 | 0.702273 | ||||||||
\(143\) | −0.712311 | −0.0595664 | ||||||||
\(144\) | 2.27712 | 0.189760 | ||||||||
\(145\) | 6.43788 | 0.534637 | ||||||||
\(146\) | −12.4790 | −1.03277 | ||||||||
\(147\) | −16.6969 | −1.37714 | ||||||||
\(148\) | 4.88806 | 0.401796 | ||||||||
\(149\) | 23.2464 | 1.90442 | 0.952208 | − | 0.305451i | \(-0.0988071\pi\) | ||||
0.952208 | + | 0.305451i | \(0.0988071\pi\) | |||||||
\(150\) | 0.212933 | 0.0173859 | ||||||||
\(151\) | −18.3008 | −1.48930 | −0.744650 | − | 0.667456i | \(-0.767383\pi\) | ||||
−0.744650 | + | 0.667456i | \(0.767383\pi\) | |||||||
\(152\) | 33.1128 | 2.68580 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 12.0287 | 0.969300 | ||||||||
\(155\) | −23.2471 | −1.86725 | ||||||||
\(156\) | 2.54428 | 0.203705 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −10.7546 | −0.855590 | ||||||||
\(159\) | 8.62613 | 0.684096 | ||||||||
\(160\) | 6.02081 | 0.475987 | ||||||||
\(161\) | −35.9657 | −2.83449 | ||||||||
\(162\) | −2.38697 | −0.187538 | ||||||||
\(163\) | 23.0881 | 1.80840 | 0.904201 | − | 0.427107i | \(-0.140467\pi\) | ||||
0.904201 | + | 0.427107i | \(0.140467\pi\) | |||||||
\(164\) | 32.1615 | 2.51139 | ||||||||
\(165\) | −2.33535 | −0.181806 | ||||||||
\(166\) | 18.1925 | 1.41201 | ||||||||
\(167\) | −5.92527 | −0.458511 | −0.229255 | − | 0.973366i | \(-0.573629\pi\) | ||||
−0.229255 | + | 0.973366i | \(0.573629\pi\) | |||||||
\(168\) | −19.7256 | −1.52187 | ||||||||
\(169\) | −12.5265 | −0.963580 | ||||||||
\(170\) | −5.38482 | −0.412997 | ||||||||
\(171\) | −8.17166 | −0.624903 | ||||||||
\(172\) | 14.9339 | 1.13870 | ||||||||
\(173\) | 9.10713 | 0.692402 | 0.346201 | − | 0.938160i | \(-0.387472\pi\) | ||||
0.346201 | + | 0.938160i | \(0.387472\pi\) | |||||||
\(174\) | 6.81184 | 0.516404 | ||||||||
\(175\) | −0.434253 | −0.0328265 | ||||||||
\(176\) | 2.35729 | 0.177687 | ||||||||
\(177\) | 2.74590 | 0.206394 | ||||||||
\(178\) | 8.68011 | 0.650602 | ||||||||
\(179\) | 8.84444 | 0.661064 | 0.330532 | − | 0.943795i | \(-0.392772\pi\) | ||||
0.330532 | + | 0.943795i | \(0.392772\pi\) | |||||||
\(180\) | 8.34155 | 0.621742 | ||||||||
\(181\) | 4.37866 | 0.325463 | 0.162732 | − | 0.986670i | \(-0.447970\pi\) | ||||
0.162732 | + | 0.986670i | \(0.447970\pi\) | |||||||
\(182\) | −7.99532 | −0.592653 | ||||||||
\(183\) | 10.2874 | 0.760470 | ||||||||
\(184\) | −29.9383 | −2.20708 | ||||||||
\(185\) | 2.98222 | 0.219257 | ||||||||
\(186\) | −24.5974 | −1.80357 | ||||||||
\(187\) | 1.03520 | 0.0757017 | ||||||||
\(188\) | −44.4866 | −3.24452 | ||||||||
\(189\) | 4.86795 | 0.354091 | ||||||||
\(190\) | 44.0030 | 3.19231 | ||||||||
\(191\) | 23.8655 | 1.72684 | 0.863422 | − | 0.504483i | \(-0.168317\pi\) | ||||
0.863422 | + | 0.504483i | \(0.168317\pi\) | |||||||
\(192\) | 10.9248 | 0.788428 | ||||||||
\(193\) | 25.8382 | 1.85987 | 0.929936 | − | 0.367722i | \(-0.119862\pi\) | ||||
0.929936 | + | 0.367722i | \(0.119862\pi\) | |||||||
\(194\) | 10.7292 | 0.770309 | ||||||||
\(195\) | 1.55227 | 0.111161 | ||||||||
\(196\) | 61.7388 | 4.40991 | ||||||||
\(197\) | −11.8190 | −0.842072 | −0.421036 | − | 0.907044i | \(-0.638333\pi\) | ||||
−0.421036 | + | 0.907044i | \(0.638333\pi\) | |||||||
\(198\) | −2.47100 | −0.175606 | ||||||||
\(199\) | −8.56448 | −0.607120 | −0.303560 | − | 0.952812i | \(-0.598175\pi\) | ||||
−0.303560 | + | 0.952812i | \(0.598175\pi\) | |||||||
\(200\) | −0.361478 | −0.0255604 | ||||||||
\(201\) | −15.1775 | −1.07054 | ||||||||
\(202\) | 33.7252 | 2.37290 | ||||||||
\(203\) | −13.8920 | −0.975025 | ||||||||
\(204\) | −3.69761 | −0.258885 | ||||||||
\(205\) | 19.6218 | 1.37045 | ||||||||
\(206\) | −5.75112 | −0.400700 | ||||||||
\(207\) | 7.38826 | 0.513520 | ||||||||
\(208\) | −1.56686 | −0.108642 | ||||||||
\(209\) | −8.45934 | −0.585145 | ||||||||
\(210\) | −26.2130 | −1.80887 | ||||||||
\(211\) | −19.5382 | −1.34506 | −0.672532 | − | 0.740068i | \(-0.734793\pi\) | ||||
−0.672532 | + | 0.740068i | \(0.734793\pi\) | |||||||
\(212\) | −31.8961 | −2.19063 | ||||||||
\(213\) | 3.50593 | 0.240223 | ||||||||
\(214\) | −17.8636 | −1.22113 | ||||||||
\(215\) | 9.11125 | 0.621382 | ||||||||
\(216\) | 4.05215 | 0.275714 | ||||||||
\(217\) | 50.1636 | 3.40533 | ||||||||
\(218\) | 19.1315 | 1.29575 | ||||||||
\(219\) | −5.22796 | −0.353273 | ||||||||
\(220\) | 8.63521 | 0.582186 | ||||||||
\(221\) | −0.688087 | −0.0462858 | ||||||||
\(222\) | 3.15545 | 0.211780 | ||||||||
\(223\) | 16.2790 | 1.09012 | 0.545060 | − | 0.838397i | \(-0.316507\pi\) | ||||
0.545060 | + | 0.838397i | \(0.316507\pi\) | |||||||
\(224\) | −12.9920 | −0.868064 | ||||||||
\(225\) | 0.0892066 | 0.00594711 | ||||||||
\(226\) | −14.4359 | −0.960265 | ||||||||
\(227\) | 1.57421 | 0.104484 | 0.0522420 | − | 0.998634i | \(-0.483363\pi\) | ||||
0.0522420 | + | 0.998634i | \(0.483363\pi\) | |||||||
\(228\) | 30.2156 | 2.00108 | ||||||||
\(229\) | 1.72625 | 0.114074 | 0.0570368 | − | 0.998372i | \(-0.481835\pi\) | ||||
0.0570368 | + | 0.998372i | \(0.481835\pi\) | |||||||
\(230\) | −39.7845 | −2.62331 | ||||||||
\(231\) | 5.03932 | 0.331563 | ||||||||
\(232\) | −11.5639 | −0.759205 | ||||||||
\(233\) | 8.90826 | 0.583600 | 0.291800 | − | 0.956479i | \(-0.405746\pi\) | ||||
0.291800 | + | 0.956479i | \(0.405746\pi\) | |||||||
\(234\) | 1.64244 | 0.107370 | ||||||||
\(235\) | −27.1415 | −1.77051 | ||||||||
\(236\) | −10.1533 | −0.660922 | ||||||||
\(237\) | −4.50555 | −0.292667 | ||||||||
\(238\) | 11.6196 | 0.753189 | ||||||||
\(239\) | 12.7409 | 0.824140 | 0.412070 | − | 0.911152i | \(-0.364806\pi\) | ||||
0.412070 | + | 0.911152i | \(0.364806\pi\) | |||||||
\(240\) | −5.13702 | −0.331593 | ||||||||
\(241\) | −5.25252 | −0.338344 | −0.169172 | − | 0.985587i | \(-0.554109\pi\) | ||||
−0.169172 | + | 0.985587i | \(0.554109\pi\) | |||||||
\(242\) | 23.6987 | 1.52341 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −38.0390 | −2.43520 | ||||||||
\(245\) | 37.6670 | 2.40646 | ||||||||
\(246\) | 20.7616 | 1.32371 | ||||||||
\(247\) | 5.62282 | 0.357771 | ||||||||
\(248\) | 41.7569 | 2.65157 | ||||||||
\(249\) | 7.62159 | 0.482999 | ||||||||
\(250\) | 26.4438 | 1.67245 | ||||||||
\(251\) | −0.517752 | −0.0326802 | −0.0163401 | − | 0.999866i | \(-0.505201\pi\) | ||||
−0.0163401 | + | 0.999866i | \(0.505201\pi\) | |||||||
\(252\) | −17.9998 | −1.13388 | ||||||||
\(253\) | 7.64837 | 0.480849 | ||||||||
\(254\) | 36.0771 | 2.26368 | ||||||||
\(255\) | −2.25593 | −0.141272 | ||||||||
\(256\) | −27.6545 | −1.72841 | ||||||||
\(257\) | 23.9250 | 1.49240 | 0.746200 | − | 0.665722i | \(-0.231876\pi\) | ||||
0.746200 | + | 0.665722i | \(0.231876\pi\) | |||||||
\(258\) | 9.64049 | 0.600191 | ||||||||
\(259\) | −6.43518 | −0.399863 | ||||||||
\(260\) | −5.73971 | −0.355962 | ||||||||
\(261\) | 2.85376 | 0.176643 | ||||||||
\(262\) | 7.45683 | 0.460684 | ||||||||
\(263\) | −24.0357 | −1.48211 | −0.741053 | − | 0.671447i | \(-0.765673\pi\) | ||||
−0.741053 | + | 0.671447i | \(0.765673\pi\) | |||||||
\(264\) | 4.19480 | 0.258172 | ||||||||
\(265\) | −19.4599 | −1.19541 | ||||||||
\(266\) | −94.9517 | −5.82186 | ||||||||
\(267\) | 3.63646 | 0.222548 | ||||||||
\(268\) | 56.1206 | 3.42811 | ||||||||
\(269\) | 1.15181 | 0.0702268 | 0.0351134 | − | 0.999383i | \(-0.488821\pi\) | ||||
0.0351134 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(270\) | 5.38482 | 0.327710 | ||||||||
\(271\) | 6.73126 | 0.408895 | 0.204447 | − | 0.978878i | \(-0.434460\pi\) | ||||
0.204447 | + | 0.978878i | \(0.434460\pi\) | |||||||
\(272\) | 2.27712 | 0.138071 | ||||||||
\(273\) | −3.34957 | −0.202725 | ||||||||
\(274\) | −33.5764 | −2.02842 | ||||||||
\(275\) | 0.0923471 | 0.00556874 | ||||||||
\(276\) | −27.3189 | −1.64441 | ||||||||
\(277\) | −19.6709 | −1.18191 | −0.590955 | − | 0.806705i | \(-0.701249\pi\) | ||||
−0.590955 | + | 0.806705i | \(0.701249\pi\) | |||||||
\(278\) | −3.34103 | −0.200382 | ||||||||
\(279\) | −10.3049 | −0.616937 | ||||||||
\(280\) | 44.4996 | 2.65936 | ||||||||
\(281\) | 14.5307 | 0.866831 | 0.433415 | − | 0.901194i | \(-0.357308\pi\) | ||||
0.433415 | + | 0.901194i | \(0.357308\pi\) | |||||||
\(282\) | −28.7180 | −1.71013 | ||||||||
\(283\) | 1.06397 | 0.0632463 | 0.0316232 | − | 0.999500i | \(-0.489932\pi\) | ||||
0.0316232 | + | 0.999500i | \(0.489932\pi\) | |||||||
\(284\) | −12.9636 | −0.769247 | ||||||||
\(285\) | 18.4347 | 1.09198 | ||||||||
\(286\) | 1.70026 | 0.100539 | ||||||||
\(287\) | −42.3409 | −2.49931 | ||||||||
\(288\) | 2.66889 | 0.157266 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −15.3670 | −0.902382 | ||||||||
\(291\) | 4.49489 | 0.263495 | ||||||||
\(292\) | 19.3310 | 1.13126 | ||||||||
\(293\) | −16.5473 | −0.966706 | −0.483353 | − | 0.875426i | \(-0.660581\pi\) | ||||
−0.483353 | + | 0.875426i | \(0.660581\pi\) | |||||||
\(294\) | 39.8550 | 2.32439 | ||||||||
\(295\) | −6.19455 | −0.360661 | ||||||||
\(296\) | −5.35674 | −0.311354 | ||||||||
\(297\) | −1.03520 | −0.0600687 | ||||||||
\(298\) | −55.4883 | −3.21435 | ||||||||
\(299\) | −5.08377 | −0.294002 | ||||||||
\(300\) | −0.329852 | −0.0190440 | ||||||||
\(301\) | −19.6607 | −1.13322 | ||||||||
\(302\) | 43.6834 | 2.51370 | ||||||||
\(303\) | 14.1289 | 0.811683 | ||||||||
\(304\) | −18.6079 | −1.06723 | ||||||||
\(305\) | −23.2077 | −1.32887 | ||||||||
\(306\) | −2.38697 | −0.136454 | ||||||||
\(307\) | −12.0964 | −0.690377 | −0.345188 | − | 0.938533i | \(-0.612185\pi\) | ||||
−0.345188 | + | 0.938533i | \(0.612185\pi\) | |||||||
\(308\) | −18.6335 | −1.06174 | ||||||||
\(309\) | −2.40939 | −0.137065 | ||||||||
\(310\) | 55.4900 | 3.15162 | ||||||||
\(311\) | −20.6007 | −1.16816 | −0.584079 | − | 0.811697i | \(-0.698544\pi\) | ||||
−0.584079 | + | 0.811697i | \(0.698544\pi\) | |||||||
\(312\) | −2.78823 | −0.157853 | ||||||||
\(313\) | 19.8787 | 1.12361 | 0.561804 | − | 0.827270i | \(-0.310108\pi\) | ||||
0.561804 | + | 0.827270i | \(0.310108\pi\) | |||||||
\(314\) | 2.38697 | 0.134704 | ||||||||
\(315\) | −10.9817 | −0.618751 | ||||||||
\(316\) | 16.6598 | 0.937186 | ||||||||
\(317\) | 12.4872 | 0.701351 | 0.350676 | − | 0.936497i | \(-0.385952\pi\) | ||||
0.350676 | + | 0.936497i | \(0.385952\pi\) | |||||||
\(318\) | −20.5903 | −1.15465 | ||||||||
\(319\) | 2.95423 | 0.165405 | ||||||||
\(320\) | −24.6455 | −1.37773 | ||||||||
\(321\) | −7.48379 | −0.417705 | ||||||||
\(322\) | 85.8489 | 4.78417 | ||||||||
\(323\) | −8.17166 | −0.454683 | ||||||||
\(324\) | 3.69761 | 0.205423 | ||||||||
\(325\) | −0.0613819 | −0.00340486 | ||||||||
\(326\) | −55.1106 | −3.05230 | ||||||||
\(327\) | 8.01499 | 0.443230 | ||||||||
\(328\) | −35.2452 | −1.94609 | ||||||||
\(329\) | 58.5671 | 3.22891 | ||||||||
\(330\) | 5.57439 | 0.306860 | ||||||||
\(331\) | −32.9406 | −1.81058 | −0.905291 | − | 0.424792i | \(-0.860347\pi\) | ||||
−0.905291 | + | 0.424792i | \(0.860347\pi\) | |||||||
\(332\) | −28.1817 | −1.54667 | ||||||||
\(333\) | 1.32195 | 0.0724424 | ||||||||
\(334\) | 14.1434 | 0.773893 | ||||||||
\(335\) | 34.2393 | 1.87070 | ||||||||
\(336\) | 11.0849 | 0.604731 | ||||||||
\(337\) | 30.3454 | 1.65302 | 0.826510 | − | 0.562922i | \(-0.190323\pi\) | ||||
0.826510 | + | 0.562922i | \(0.190323\pi\) | |||||||
\(338\) | 29.9004 | 1.62637 | ||||||||
\(339\) | −6.04782 | −0.328472 | ||||||||
\(340\) | 8.34155 | 0.452384 | ||||||||
\(341\) | −10.6677 | −0.577686 | ||||||||
\(342\) | 19.5055 | 1.05474 | ||||||||
\(343\) | −47.2041 | −2.54878 | ||||||||
\(344\) | −16.3658 | −0.882387 | ||||||||
\(345\) | −16.6674 | −0.897342 | ||||||||
\(346\) | −21.7384 | −1.16866 | ||||||||
\(347\) | −4.53769 | −0.243596 | −0.121798 | − | 0.992555i | \(-0.538866\pi\) | ||||
−0.121798 | + | 0.992555i | \(0.538866\pi\) | |||||||
\(348\) | −10.5521 | −0.565653 | ||||||||
\(349\) | −23.4313 | −1.25425 | −0.627126 | − | 0.778918i | \(-0.715769\pi\) | ||||
−0.627126 | + | 0.778918i | \(0.715769\pi\) | |||||||
\(350\) | 1.03655 | 0.0554058 | ||||||||
\(351\) | 0.688087 | 0.0367274 | ||||||||
\(352\) | 2.76284 | 0.147260 | ||||||||
\(353\) | −24.5331 | −1.30577 | −0.652883 | − | 0.757458i | \(-0.726441\pi\) | ||||
−0.652883 | + | 0.757458i | \(0.726441\pi\) | |||||||
\(354\) | −6.55437 | −0.348361 | ||||||||
\(355\) | −7.90913 | −0.419773 | ||||||||
\(356\) | −13.4462 | −0.712648 | ||||||||
\(357\) | 4.86795 | 0.257639 | ||||||||
\(358\) | −21.1114 | −1.11577 | ||||||||
\(359\) | −16.6243 | −0.877399 | −0.438700 | − | 0.898634i | \(-0.644561\pi\) | ||||
−0.438700 | + | 0.898634i | \(0.644561\pi\) | |||||||
\(360\) | −9.14135 | −0.481792 | ||||||||
\(361\) | 47.7760 | 2.51453 | ||||||||
\(362\) | −10.4517 | −0.549330 | ||||||||
\(363\) | 9.92835 | 0.521103 | ||||||||
\(364\) | 12.3854 | 0.649173 | ||||||||
\(365\) | 11.7939 | 0.617320 | ||||||||
\(366\) | −24.5558 | −1.28355 | ||||||||
\(367\) | 30.8098 | 1.60826 | 0.804129 | − | 0.594455i | \(-0.202632\pi\) | ||||
0.804129 | + | 0.594455i | \(0.202632\pi\) | |||||||
\(368\) | 16.8240 | 0.877010 | ||||||||
\(369\) | 8.69790 | 0.452795 | ||||||||
\(370\) | −7.11846 | −0.370071 | ||||||||
\(371\) | 41.9915 | 2.18009 | ||||||||
\(372\) | 38.1035 | 1.97557 | ||||||||
\(373\) | −27.8694 | −1.44302 | −0.721510 | − | 0.692404i | \(-0.756552\pi\) | ||||
−0.721510 | + | 0.692404i | \(0.756552\pi\) | |||||||
\(374\) | −2.47100 | −0.127772 | ||||||||
\(375\) | 11.0784 | 0.572086 | ||||||||
\(376\) | 48.7521 | 2.51420 | ||||||||
\(377\) | −1.96364 | −0.101132 | ||||||||
\(378\) | −11.6196 | −0.597649 | ||||||||
\(379\) | 0.141939 | 0.00729092 | 0.00364546 | − | 0.999993i | \(-0.498840\pi\) | ||||
0.00364546 | + | 0.999993i | \(0.498840\pi\) | |||||||
\(380\) | −68.1643 | −3.49675 | ||||||||
\(381\) | 15.1142 | 0.774325 | ||||||||
\(382\) | −56.9661 | −2.91464 | ||||||||
\(383\) | −18.9612 | −0.968872 | −0.484436 | − | 0.874827i | \(-0.660975\pi\) | ||||
−0.484436 | + | 0.874827i | \(0.660975\pi\) | |||||||
\(384\) | −20.7393 | −1.05835 | ||||||||
\(385\) | −11.3683 | −0.579384 | ||||||||
\(386\) | −61.6748 | −3.13917 | ||||||||
\(387\) | 4.03880 | 0.205304 | ||||||||
\(388\) | −16.6204 | −0.843772 | ||||||||
\(389\) | 14.6757 | 0.744086 | 0.372043 | − | 0.928216i | \(-0.378657\pi\) | ||||
0.372043 | + | 0.928216i | \(0.378657\pi\) | |||||||
\(390\) | −3.70523 | −0.187622 | ||||||||
\(391\) | 7.38826 | 0.373641 | ||||||||
\(392\) | −67.6584 | −3.41727 | ||||||||
\(393\) | 3.12398 | 0.157584 | ||||||||
\(394\) | 28.2117 | 1.42128 | ||||||||
\(395\) | 10.1642 | 0.511416 | ||||||||
\(396\) | 3.82779 | 0.192354 | ||||||||
\(397\) | −6.47396 | −0.324919 | −0.162459 | − | 0.986715i | \(-0.551943\pi\) | ||||
−0.162459 | + | 0.986715i | \(0.551943\pi\) | |||||||
\(398\) | 20.4431 | 1.02472 | ||||||||
\(399\) | −39.7792 | −1.99145 | ||||||||
\(400\) | 0.203134 | 0.0101567 | ||||||||
\(401\) | 26.7107 | 1.33387 | 0.666934 | − | 0.745117i | \(-0.267606\pi\) | ||||
0.666934 | + | 0.745117i | \(0.267606\pi\) | |||||||
\(402\) | 36.2282 | 1.80690 | ||||||||
\(403\) | 7.09066 | 0.353211 | ||||||||
\(404\) | −52.2432 | −2.59919 | ||||||||
\(405\) | 2.25593 | 0.112098 | ||||||||
\(406\) | 33.1597 | 1.64569 | ||||||||
\(407\) | 1.36849 | 0.0678334 | ||||||||
\(408\) | 4.05215 | 0.200611 | ||||||||
\(409\) | −4.47245 | −0.221148 | −0.110574 | − | 0.993868i | \(-0.535269\pi\) | ||||
−0.110574 | + | 0.993868i | \(0.535269\pi\) | |||||||
\(410\) | −46.8367 | −2.31310 | ||||||||
\(411\) | −14.0665 | −0.693852 | ||||||||
\(412\) | 8.90898 | 0.438914 | ||||||||
\(413\) | 13.3669 | 0.657742 | ||||||||
\(414\) | −17.6355 | −0.866740 | ||||||||
\(415\) | −17.1938 | −0.844008 | ||||||||
\(416\) | −1.83643 | −0.0900382 | ||||||||
\(417\) | −1.39970 | −0.0685434 | ||||||||
\(418\) | 20.1922 | 0.987631 | ||||||||
\(419\) | −4.70265 | −0.229739 | −0.114870 | − | 0.993381i | \(-0.536645\pi\) | ||||
−0.114870 | + | 0.993381i | \(0.536645\pi\) | |||||||
\(420\) | 40.6062 | 1.98138 | ||||||||
\(421\) | 23.6631 | 1.15327 | 0.576633 | − | 0.817003i | \(-0.304366\pi\) | ||||
0.576633 | + | 0.817003i | \(0.304366\pi\) | |||||||
\(422\) | 46.6370 | 2.27025 | ||||||||
\(423\) | −12.0312 | −0.584976 | ||||||||
\(424\) | 34.9544 | 1.69753 | ||||||||
\(425\) | 0.0892066 | 0.00432716 | ||||||||
\(426\) | −8.36855 | −0.405458 | ||||||||
\(427\) | 50.0788 | 2.42348 | ||||||||
\(428\) | 27.6722 | 1.33759 | ||||||||
\(429\) | 0.712311 | 0.0343907 | ||||||||
\(430\) | −21.7482 | −1.04879 | ||||||||
\(431\) | −16.0270 | −0.771992 | −0.385996 | − | 0.922501i | \(-0.626142\pi\) | ||||
−0.385996 | + | 0.922501i | \(0.626142\pi\) | |||||||
\(432\) | −2.27712 | −0.109558 | ||||||||
\(433\) | 8.77716 | 0.421803 | 0.210902 | − | 0.977507i | \(-0.432360\pi\) | ||||
0.210902 | + | 0.977507i | \(0.432360\pi\) | |||||||
\(434\) | −119.739 | −5.74765 | ||||||||
\(435\) | −6.43788 | −0.308673 | ||||||||
\(436\) | −29.6363 | −1.41932 | ||||||||
\(437\) | −60.3744 | −2.88810 | ||||||||
\(438\) | 12.4790 | 0.596268 | ||||||||
\(439\) | −32.1966 | −1.53666 | −0.768330 | − | 0.640054i | \(-0.778912\pi\) | ||||
−0.768330 | + | 0.640054i | \(0.778912\pi\) | |||||||
\(440\) | −9.46317 | −0.451139 | ||||||||
\(441\) | 16.6969 | 0.795091 | ||||||||
\(442\) | 1.64244 | 0.0781230 | ||||||||
\(443\) | 28.9989 | 1.37778 | 0.688890 | − | 0.724866i | \(-0.258098\pi\) | ||||
0.688890 | + | 0.724866i | \(0.258098\pi\) | |||||||
\(444\) | −4.88806 | −0.231977 | ||||||||
\(445\) | −8.20359 | −0.388887 | ||||||||
\(446\) | −38.8574 | −1.83995 | ||||||||
\(447\) | −23.2464 | −1.09951 | ||||||||
\(448\) | 53.1813 | 2.51258 | ||||||||
\(449\) | 6.15803 | 0.290615 | 0.145308 | − | 0.989387i | \(-0.453583\pi\) | ||||
0.145308 | + | 0.989387i | \(0.453583\pi\) | |||||||
\(450\) | −0.212933 | −0.0100378 | ||||||||
\(451\) | 9.00410 | 0.423987 | ||||||||
\(452\) | 22.3625 | 1.05184 | ||||||||
\(453\) | 18.3008 | 0.859847 | ||||||||
\(454\) | −3.75759 | −0.176352 | ||||||||
\(455\) | 7.55639 | 0.354249 | ||||||||
\(456\) | −33.1128 | −1.55065 | ||||||||
\(457\) | −4.17338 | −0.195222 | −0.0976112 | − | 0.995225i | \(-0.531120\pi\) | ||||
−0.0976112 | + | 0.995225i | \(0.531120\pi\) | |||||||
\(458\) | −4.12050 | −0.192538 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 61.6296 | 2.87349 | ||||||||
\(461\) | 13.6076 | 0.633770 | 0.316885 | − | 0.948464i | \(-0.397363\pi\) | ||||
0.316885 | + | 0.948464i | \(0.397363\pi\) | |||||||
\(462\) | −12.0287 | −0.559626 | ||||||||
\(463\) | −17.9595 | −0.834648 | −0.417324 | − | 0.908758i | \(-0.637032\pi\) | ||||
−0.417324 | + | 0.908758i | \(0.637032\pi\) | |||||||
\(464\) | 6.49836 | 0.301679 | ||||||||
\(465\) | 23.2471 | 1.07806 | ||||||||
\(466\) | −21.2637 | −0.985023 | ||||||||
\(467\) | −20.2696 | −0.937963 | −0.468982 | − | 0.883208i | \(-0.655379\pi\) | ||||
−0.468982 | + | 0.883208i | \(0.655379\pi\) | |||||||
\(468\) | −2.54428 | −0.117609 | ||||||||
\(469\) | −73.8833 | −3.41161 | ||||||||
\(470\) | 64.7858 | 2.98835 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 11.1268 | 0.512152 | ||||||||
\(473\) | 4.18099 | 0.192242 | ||||||||
\(474\) | 10.7546 | 0.493975 | ||||||||
\(475\) | −0.728966 | −0.0334473 | ||||||||
\(476\) | −17.9998 | −0.825019 | ||||||||
\(477\) | −8.62613 | −0.394963 | ||||||||
\(478\) | −30.4121 | −1.39102 | ||||||||
\(479\) | 29.2474 | 1.33635 | 0.668175 | − | 0.744004i | \(-0.267076\pi\) | ||||
0.668175 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(480\) | −6.02081 | −0.274811 | ||||||||
\(481\) | −0.909616 | −0.0414749 | ||||||||
\(482\) | 12.5376 | 0.571071 | ||||||||
\(483\) | 35.9657 | 1.63650 | ||||||||
\(484\) | −36.7112 | −1.66869 | ||||||||
\(485\) | −10.1401 | −0.460440 | ||||||||
\(486\) | 2.38697 | 0.108275 | ||||||||
\(487\) | −27.1984 | −1.23248 | −0.616239 | − | 0.787559i | \(-0.711345\pi\) | ||||
−0.616239 | + | 0.787559i | \(0.711345\pi\) | |||||||
\(488\) | 41.6863 | 1.88705 | ||||||||
\(489\) | −23.0881 | −1.04408 | ||||||||
\(490\) | −89.9100 | −4.06172 | ||||||||
\(491\) | 18.3532 | 0.828270 | 0.414135 | − | 0.910215i | \(-0.364084\pi\) | ||||
0.414135 | + | 0.910215i | \(0.364084\pi\) | |||||||
\(492\) | −32.1615 | −1.44995 | ||||||||
\(493\) | 2.85376 | 0.128527 | ||||||||
\(494\) | −13.4215 | −0.603861 | ||||||||
\(495\) | 2.33535 | 0.104966 | ||||||||
\(496\) | −23.4654 | −1.05363 | ||||||||
\(497\) | 17.0667 | 0.765546 | ||||||||
\(498\) | −18.1925 | −0.815225 | ||||||||
\(499\) | 38.9303 | 1.74276 | 0.871381 | − | 0.490608i | \(-0.163225\pi\) | ||||
0.871381 | + | 0.490608i | \(0.163225\pi\) | |||||||
\(500\) | −40.9636 | −1.83195 | ||||||||
\(501\) | 5.92527 | 0.264721 | ||||||||
\(502\) | 1.23586 | 0.0551590 | ||||||||
\(503\) | −16.4097 | −0.731671 | −0.365835 | − | 0.930680i | \(-0.619217\pi\) | ||||
−0.365835 | + | 0.930680i | \(0.619217\pi\) | |||||||
\(504\) | 19.7256 | 0.878650 | ||||||||
\(505\) | −31.8737 | −1.41836 | ||||||||
\(506\) | −18.2564 | −0.811596 | ||||||||
\(507\) | 12.5265 | 0.556323 | ||||||||
\(508\) | −55.8865 | −2.47956 | ||||||||
\(509\) | 29.0100 | 1.28585 | 0.642923 | − | 0.765931i | \(-0.277722\pi\) | ||||
0.642923 | + | 0.765931i | \(0.277722\pi\) | |||||||
\(510\) | 5.38482 | 0.238444 | ||||||||
\(511\) | −25.4494 | −1.12582 | ||||||||
\(512\) | 24.5318 | 1.08416 | ||||||||
\(513\) | 8.17166 | 0.360788 | ||||||||
\(514\) | −57.1082 | −2.51893 | ||||||||
\(515\) | 5.43540 | 0.239512 | ||||||||
\(516\) | −14.9339 | −0.657430 | ||||||||
\(517\) | −12.4547 | −0.547758 | ||||||||
\(518\) | 15.3606 | 0.674905 | ||||||||
\(519\) | −9.10713 | −0.399758 | ||||||||
\(520\) | 6.29005 | 0.275837 | ||||||||
\(521\) | −26.2257 | −1.14897 | −0.574485 | − | 0.818515i | \(-0.694798\pi\) | ||||
−0.574485 | + | 0.818515i | \(0.694798\pi\) | |||||||
\(522\) | −6.81184 | −0.298146 | ||||||||
\(523\) | −15.9597 | −0.697868 | −0.348934 | − | 0.937147i | \(-0.613456\pi\) | ||||
−0.348934 | + | 0.937147i | \(0.613456\pi\) | |||||||
\(524\) | −11.5513 | −0.504619 | ||||||||
\(525\) | 0.434253 | 0.0189524 | ||||||||
\(526\) | 57.3725 | 2.50156 | ||||||||
\(527\) | −10.3049 | −0.448888 | ||||||||
\(528\) | −2.35729 | −0.102588 | ||||||||
\(529\) | 31.5865 | 1.37332 | ||||||||
\(530\) | 46.4502 | 2.01767 | ||||||||
\(531\) | −2.74590 | −0.119162 | ||||||||
\(532\) | 147.088 | 6.37708 | ||||||||
\(533\) | −5.98491 | −0.259235 | ||||||||
\(534\) | −8.68011 | −0.375625 | ||||||||
\(535\) | 16.8829 | 0.729911 | ||||||||
\(536\) | −61.5015 | −2.65646 | ||||||||
\(537\) | −8.84444 | −0.381666 | ||||||||
\(538\) | −2.74932 | −0.118532 | ||||||||
\(539\) | 17.2847 | 0.744506 | ||||||||
\(540\) | −8.34155 | −0.358963 | ||||||||
\(541\) | −18.9157 | −0.813251 | −0.406626 | − | 0.913595i | \(-0.633295\pi\) | ||||
−0.406626 | + | 0.913595i | \(0.633295\pi\) | |||||||
\(542\) | −16.0673 | −0.690150 | ||||||||
\(543\) | −4.37866 | −0.187906 | ||||||||
\(544\) | 2.66889 | 0.114428 | ||||||||
\(545\) | −18.0812 | −0.774515 | ||||||||
\(546\) | 7.99532 | 0.342168 | ||||||||
\(547\) | −14.0848 | −0.602225 | −0.301112 | − | 0.953589i | \(-0.597358\pi\) | ||||
−0.301112 | + | 0.953589i | \(0.597358\pi\) | |||||||
\(548\) | 52.0127 | 2.22187 | ||||||||
\(549\) | −10.2874 | −0.439058 | ||||||||
\(550\) | −0.220430 | −0.00939915 | ||||||||
\(551\) | −23.3200 | −0.993465 | ||||||||
\(552\) | 29.9383 | 1.27426 | ||||||||
\(553\) | −21.9328 | −0.932677 | ||||||||
\(554\) | 46.9538 | 1.99488 | ||||||||
\(555\) | −2.98222 | −0.126588 | ||||||||
\(556\) | 5.17553 | 0.219492 | ||||||||
\(557\) | 25.0666 | 1.06210 | 0.531052 | − | 0.847339i | \(-0.321797\pi\) | ||||
0.531052 | + | 0.847339i | \(0.321797\pi\) | |||||||
\(558\) | 24.5974 | 1.04129 | ||||||||
\(559\) | −2.77905 | −0.117541 | ||||||||
\(560\) | −25.0067 | −1.05673 | ||||||||
\(561\) | −1.03520 | −0.0437064 | ||||||||
\(562\) | −34.6844 | −1.46307 | ||||||||
\(563\) | 20.9268 | 0.881961 | 0.440980 | − | 0.897517i | \(-0.354631\pi\) | ||||
0.440980 | + | 0.897517i | \(0.354631\pi\) | |||||||
\(564\) | 44.4866 | 1.87323 | ||||||||
\(565\) | 13.6434 | 0.573984 | ||||||||
\(566\) | −2.53966 | −0.106750 | ||||||||
\(567\) | −4.86795 | −0.204435 | ||||||||
\(568\) | 14.2066 | 0.596094 | ||||||||
\(569\) | −20.2596 | −0.849328 | −0.424664 | − | 0.905351i | \(-0.639608\pi\) | ||||
−0.424664 | + | 0.905351i | \(0.639608\pi\) | |||||||
\(570\) | −44.0030 | −1.84308 | ||||||||
\(571\) | −11.9229 | −0.498958 | −0.249479 | − | 0.968380i | \(-0.580259\pi\) | ||||
−0.249479 | + | 0.968380i | \(0.580259\pi\) | |||||||
\(572\) | −2.63385 | −0.110127 | ||||||||
\(573\) | −23.8655 | −0.996994 | ||||||||
\(574\) | 101.066 | 4.21843 | ||||||||
\(575\) | 0.659082 | 0.0274856 | ||||||||
\(576\) | −10.9248 | −0.455199 | ||||||||
\(577\) | 24.8018 | 1.03251 | 0.516256 | − | 0.856434i | \(-0.327325\pi\) | ||||
0.516256 | + | 0.856434i | \(0.327325\pi\) | |||||||
\(578\) | −2.38697 | −0.0992848 | ||||||||
\(579\) | −25.8382 | −1.07380 | ||||||||
\(580\) | 23.8048 | 0.988440 | ||||||||
\(581\) | 37.1015 | 1.53923 | ||||||||
\(582\) | −10.7292 | −0.444738 | ||||||||
\(583\) | −8.92981 | −0.369835 | ||||||||
\(584\) | −21.1845 | −0.876619 | ||||||||
\(585\) | −1.55227 | −0.0641786 | ||||||||
\(586\) | 39.4980 | 1.63165 | ||||||||
\(587\) | −42.9454 | −1.77255 | −0.886273 | − | 0.463163i | \(-0.846714\pi\) | ||||
−0.886273 | + | 0.463163i | \(0.846714\pi\) | |||||||
\(588\) | −61.7388 | −2.54606 | ||||||||
\(589\) | 84.2080 | 3.46973 | ||||||||
\(590\) | 14.7862 | 0.608738 | ||||||||
\(591\) | 11.8190 | 0.486171 | ||||||||
\(592\) | 3.01024 | 0.123720 | ||||||||
\(593\) | 4.33274 | 0.177924 | 0.0889621 | − | 0.996035i | \(-0.471645\pi\) | ||||
0.0889621 | + | 0.996035i | \(0.471645\pi\) | |||||||
\(594\) | 2.47100 | 0.101386 | ||||||||
\(595\) | −10.9817 | −0.450207 | ||||||||
\(596\) | 85.9560 | 3.52090 | ||||||||
\(597\) | 8.56448 | 0.350521 | ||||||||
\(598\) | 12.1348 | 0.496229 | ||||||||
\(599\) | −2.55928 | −0.104569 | −0.0522847 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522847 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(600\) | 0.361478 | 0.0147573 | ||||||||
\(601\) | 48.9485 | 1.99665 | 0.998325 | − | 0.0578602i | \(-0.0184278\pi\) | ||||
0.998325 | + | 0.0578602i | \(0.0184278\pi\) | |||||||
\(602\) | 46.9294 | 1.91270 | ||||||||
\(603\) | 15.1775 | 0.618076 | ||||||||
\(604\) | −67.6693 | −2.75343 | ||||||||
\(605\) | −22.3976 | −0.910593 | ||||||||
\(606\) | −33.7252 | −1.36999 | ||||||||
\(607\) | 12.1269 | 0.492217 | 0.246109 | − | 0.969242i | \(-0.420848\pi\) | ||||
0.246109 | + | 0.969242i | \(0.420848\pi\) | |||||||
\(608\) | −21.8092 | −0.884481 | ||||||||
\(609\) | 13.8920 | 0.562931 | ||||||||
\(610\) | 55.3961 | 2.24292 | ||||||||
\(611\) | 8.27850 | 0.334912 | ||||||||
\(612\) | 3.69761 | 0.149467 | ||||||||
\(613\) | 44.0029 | 1.77726 | 0.888631 | − | 0.458623i | \(-0.151657\pi\) | ||||
0.888631 | + | 0.458623i | \(0.151657\pi\) | |||||||
\(614\) | 28.8737 | 1.16525 | ||||||||
\(615\) | −19.6218 | −0.791228 | ||||||||
\(616\) | 20.4201 | 0.822749 | ||||||||
\(617\) | 20.8755 | 0.840416 | 0.420208 | − | 0.907428i | \(-0.361957\pi\) | ||||
0.420208 | + | 0.907428i | \(0.361957\pi\) | |||||||
\(618\) | 5.75112 | 0.231344 | ||||||||
\(619\) | −0.996380 | −0.0400479 | −0.0200239 | − | 0.999800i | \(-0.506374\pi\) | ||||
−0.0200239 | + | 0.999800i | \(0.506374\pi\) | |||||||
\(620\) | −85.9586 | −3.45218 | ||||||||
\(621\) | −7.38826 | −0.296481 | ||||||||
\(622\) | 49.1731 | 1.97166 | ||||||||
\(623\) | 17.7021 | 0.709219 | ||||||||
\(624\) | 1.56686 | 0.0627245 | ||||||||
\(625\) | −25.4381 | −1.01752 | ||||||||
\(626\) | −47.4497 | −1.89647 | ||||||||
\(627\) | 8.45934 | 0.337834 | ||||||||
\(628\) | −3.69761 | −0.147551 | ||||||||
\(629\) | 1.32195 | 0.0527096 | ||||||||
\(630\) | 26.2130 | 1.04435 | ||||||||
\(631\) | 8.38733 | 0.333894 | 0.166947 | − | 0.985966i | \(-0.446609\pi\) | ||||
0.166947 | + | 0.985966i | \(0.446609\pi\) | |||||||
\(632\) | −18.2572 | −0.726231 | ||||||||
\(633\) | 19.5382 | 0.776573 | ||||||||
\(634\) | −29.8065 | −1.18377 | ||||||||
\(635\) | −34.0966 | −1.35308 | ||||||||
\(636\) | 31.8961 | 1.26476 | ||||||||
\(637\) | −11.4889 | −0.455208 | ||||||||
\(638\) | −7.05165 | −0.279177 | ||||||||
\(639\) | −3.50593 | −0.138693 | ||||||||
\(640\) | 46.7864 | 1.84940 | ||||||||
\(641\) | 35.4979 | 1.40208 | 0.701042 | − | 0.713120i | \(-0.252719\pi\) | ||||
0.701042 | + | 0.713120i | \(0.252719\pi\) | |||||||
\(642\) | 17.8636 | 0.705019 | ||||||||
\(643\) | 21.1198 | 0.832883 | 0.416442 | − | 0.909162i | \(-0.363277\pi\) | ||||
0.416442 | + | 0.909162i | \(0.363277\pi\) | |||||||
\(644\) | −132.987 | −5.24043 | ||||||||
\(645\) | −9.11125 | −0.358755 | ||||||||
\(646\) | 19.5055 | 0.767433 | ||||||||
\(647\) | 21.1705 | 0.832297 | 0.416148 | − | 0.909297i | \(-0.363380\pi\) | ||||
0.416148 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(648\) | −4.05215 | −0.159183 | ||||||||
\(649\) | −2.84257 | −0.111581 | ||||||||
\(650\) | 0.146517 | 0.00574686 | ||||||||
\(651\) | −50.1636 | −1.96607 | ||||||||
\(652\) | 85.3710 | 3.34339 | ||||||||
\(653\) | 28.6436 | 1.12091 | 0.560456 | − | 0.828185i | \(-0.310626\pi\) | ||||
0.560456 | + | 0.828185i | \(0.310626\pi\) | |||||||
\(654\) | −19.1315 | −0.748101 | ||||||||
\(655\) | −7.04746 | −0.275367 | ||||||||
\(656\) | 19.8062 | 0.773301 | ||||||||
\(657\) | 5.22796 | 0.203962 | ||||||||
\(658\) | −139.798 | −5.44989 | ||||||||
\(659\) | 5.58343 | 0.217499 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(660\) | −8.63521 | −0.336125 | ||||||||
\(661\) | −25.2857 | −0.983499 | −0.491749 | − | 0.870737i | \(-0.663642\pi\) | ||||
−0.491749 | + | 0.870737i | \(0.663642\pi\) | |||||||
\(662\) | 78.6283 | 3.05597 | ||||||||
\(663\) | 0.688087 | 0.0267231 | ||||||||
\(664\) | 30.8838 | 1.19852 | ||||||||
\(665\) | 89.7390 | 3.47993 | ||||||||
\(666\) | −3.15545 | −0.122271 | ||||||||
\(667\) | 21.0844 | 0.816389 | ||||||||
\(668\) | −21.9093 | −0.847698 | ||||||||
\(669\) | −16.2790 | −0.629381 | ||||||||
\(670\) | −81.7282 | −3.15744 | ||||||||
\(671\) | −10.6496 | −0.411124 | ||||||||
\(672\) | 12.9920 | 0.501177 | ||||||||
\(673\) | −6.22366 | −0.239904 | −0.119952 | − | 0.992780i | \(-0.538274\pi\) | ||||
−0.119952 | + | 0.992780i | \(0.538274\pi\) | |||||||
\(674\) | −72.4335 | −2.79003 | ||||||||
\(675\) | −0.0892066 | −0.00343356 | ||||||||
\(676\) | −46.3183 | −1.78147 | ||||||||
\(677\) | 24.4292 | 0.938890 | 0.469445 | − | 0.882962i | \(-0.344454\pi\) | ||||
0.469445 | + | 0.882962i | \(0.344454\pi\) | |||||||
\(678\) | 14.4359 | 0.554409 | ||||||||
\(679\) | 21.8809 | 0.839712 | ||||||||
\(680\) | −9.14135 | −0.350555 | ||||||||
\(681\) | −1.57421 | −0.0603238 | ||||||||
\(682\) | 25.4634 | 0.975042 | ||||||||
\(683\) | 50.5092 | 1.93268 | 0.966340 | − | 0.257268i | \(-0.0828222\pi\) | ||||
0.966340 | + | 0.257268i | \(0.0828222\pi\) | |||||||
\(684\) | −30.2156 | −1.15532 | ||||||||
\(685\) | 31.7331 | 1.21246 | ||||||||
\(686\) | 112.675 | 4.30194 | ||||||||
\(687\) | −1.72625 | −0.0658605 | ||||||||
\(688\) | 9.19684 | 0.350626 | ||||||||
\(689\) | 5.93553 | 0.226126 | ||||||||
\(690\) | 39.7845 | 1.51457 | ||||||||
\(691\) | 16.7000 | 0.635298 | 0.317649 | − | 0.948208i | \(-0.397107\pi\) | ||||
0.317649 | + | 0.948208i | \(0.397107\pi\) | |||||||
\(692\) | 33.6746 | 1.28012 | ||||||||
\(693\) | −5.03932 | −0.191428 | ||||||||
\(694\) | 10.8313 | 0.411151 | ||||||||
\(695\) | 3.15761 | 0.119775 | ||||||||
\(696\) | 11.5639 | 0.438327 | ||||||||
\(697\) | 8.69790 | 0.329456 | ||||||||
\(698\) | 55.9299 | 2.11698 | ||||||||
\(699\) | −8.90826 | −0.336941 | ||||||||
\(700\) | −1.60570 | −0.0606898 | ||||||||
\(701\) | −11.9214 | −0.450265 | −0.225133 | − | 0.974328i | \(-0.572282\pi\) | ||||
−0.225133 | + | 0.974328i | \(0.572282\pi\) | |||||||
\(702\) | −1.64244 | −0.0619900 | ||||||||
\(703\) | −10.8025 | −0.407425 | ||||||||
\(704\) | −11.3094 | −0.426239 | ||||||||
\(705\) | 27.1415 | 1.02221 | ||||||||
\(706\) | 58.5598 | 2.20393 | ||||||||
\(707\) | 68.7787 | 2.58669 | ||||||||
\(708\) | 10.1533 | 0.381584 | ||||||||
\(709\) | −3.68560 | −0.138416 | −0.0692078 | − | 0.997602i | \(-0.522047\pi\) | ||||
−0.0692078 | + | 0.997602i | \(0.522047\pi\) | |||||||
\(710\) | 18.8788 | 0.708510 | ||||||||
\(711\) | 4.50555 | 0.168971 | ||||||||
\(712\) | 14.7355 | 0.552235 | ||||||||
\(713\) | −76.1352 | −2.85129 | ||||||||
\(714\) | −11.6196 | −0.434854 | ||||||||
\(715\) | −1.60692 | −0.0600955 | ||||||||
\(716\) | 32.7033 | 1.22218 | ||||||||
\(717\) | −12.7409 | −0.475818 | ||||||||
\(718\) | 39.6818 | 1.48091 | ||||||||
\(719\) | 19.9854 | 0.745330 | 0.372665 | − | 0.927966i | \(-0.378444\pi\) | ||||
0.372665 | + | 0.927966i | \(0.378444\pi\) | |||||||
\(720\) | 5.13702 | 0.191445 | ||||||||
\(721\) | −11.7288 | −0.436802 | ||||||||
\(722\) | −114.040 | −4.24412 | ||||||||
\(723\) | 5.25252 | 0.195343 | ||||||||
\(724\) | 16.1906 | 0.601718 | ||||||||
\(725\) | 0.254574 | 0.00945466 | ||||||||
\(726\) | −23.6987 | −0.879539 | ||||||||
\(727\) | 48.8817 | 1.81292 | 0.906460 | − | 0.422291i | \(-0.138774\pi\) | ||||
0.906460 | + | 0.422291i | \(0.138774\pi\) | |||||||
\(728\) | −13.5730 | −0.503048 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.1516 | −1.04194 | ||||||||
\(731\) | 4.03880 | 0.149381 | ||||||||
\(732\) | 38.0390 | 1.40596 | ||||||||
\(733\) | −48.1988 | −1.78026 | −0.890132 | − | 0.455704i | \(-0.849388\pi\) | ||||
−0.890132 | + | 0.455704i | \(0.849388\pi\) | |||||||
\(734\) | −73.5420 | −2.71448 | ||||||||
\(735\) | −37.6670 | −1.38937 | ||||||||
\(736\) | 19.7184 | 0.726831 | ||||||||
\(737\) | 15.7118 | 0.578752 | ||||||||
\(738\) | −20.7616 | −0.764245 | ||||||||
\(739\) | 10.8723 | 0.399944 | 0.199972 | − | 0.979802i | \(-0.435915\pi\) | ||||
0.199972 | + | 0.979802i | \(0.435915\pi\) | |||||||
\(740\) | 11.0271 | 0.405364 | ||||||||
\(741\) | −5.62282 | −0.206559 | ||||||||
\(742\) | −100.232 | −3.67965 | ||||||||
\(743\) | −4.04041 | −0.148228 | −0.0741141 | − | 0.997250i | \(-0.523613\pi\) | ||||
−0.0741141 | + | 0.997250i | \(0.523613\pi\) | |||||||
\(744\) | −41.7569 | −1.53088 | ||||||||
\(745\) | 52.4421 | 1.92133 | ||||||||
\(746\) | 66.5233 | 2.43559 | ||||||||
\(747\) | −7.62159 | −0.278859 | ||||||||
\(748\) | 3.82779 | 0.139958 | ||||||||
\(749\) | −36.4307 | −1.33115 | ||||||||
\(750\) | −26.4438 | −0.965590 | ||||||||
\(751\) | 50.6975 | 1.84998 | 0.924989 | − | 0.379993i | \(-0.124074\pi\) | ||||
0.924989 | + | 0.379993i | \(0.124074\pi\) | |||||||
\(752\) | −27.3964 | −0.999045 | ||||||||
\(753\) | 0.517752 | 0.0188679 | ||||||||
\(754\) | 4.68714 | 0.170696 | ||||||||
\(755\) | −41.2853 | −1.50253 | ||||||||
\(756\) | 17.9998 | 0.654646 | ||||||||
\(757\) | 15.8022 | 0.574340 | 0.287170 | − | 0.957880i | \(-0.407286\pi\) | ||||
0.287170 | + | 0.957880i | \(0.407286\pi\) | |||||||
\(758\) | −0.338804 | −0.0123059 | ||||||||
\(759\) | −7.64837 | −0.277618 | ||||||||
\(760\) | 74.7000 | 2.70965 | ||||||||
\(761\) | 32.2278 | 1.16826 | 0.584129 | − | 0.811661i | \(-0.301436\pi\) | ||||
0.584129 | + | 0.811661i | \(0.301436\pi\) | |||||||
\(762\) | −36.0771 | −1.30694 | ||||||||
\(763\) | 39.0165 | 1.41249 | ||||||||
\(764\) | 88.2452 | 3.19260 | ||||||||
\(765\) | 2.25593 | 0.0815632 | ||||||||
\(766\) | 45.2598 | 1.63530 | ||||||||
\(767\) | 1.88942 | 0.0682229 | ||||||||
\(768\) | 27.6545 | 0.997897 | ||||||||
\(769\) | 0.0266519 | 0.000961094 0 | 0.000480547 | − | 1.00000i | \(-0.499847\pi\) | ||||
0.000480547 | 1.00000i | \(0.499847\pi\) | ||||||||
\(770\) | 27.1359 | 0.977909 | ||||||||
\(771\) | −23.9250 | −0.861637 | ||||||||
\(772\) | 95.5395 | 3.43854 | ||||||||
\(773\) | 8.33097 | 0.299644 | 0.149822 | − | 0.988713i | \(-0.452130\pi\) | ||||
0.149822 | + | 0.988713i | \(0.452130\pi\) | |||||||
\(774\) | −9.64049 | −0.346520 | ||||||||
\(775\) | −0.919263 | −0.0330209 | ||||||||
\(776\) | 18.2140 | 0.653844 | ||||||||
\(777\) | 6.43518 | 0.230861 | ||||||||
\(778\) | −35.0303 | −1.25590 | ||||||||
\(779\) | −71.0763 | −2.54657 | ||||||||
\(780\) | 5.73971 | 0.205515 | ||||||||
\(781\) | −3.62936 | −0.129869 | ||||||||
\(782\) | −17.6355 | −0.630646 | ||||||||
\(783\) | −2.85376 | −0.101985 | ||||||||
\(784\) | 38.0209 | 1.35789 | ||||||||
\(785\) | −2.25593 | −0.0805175 | ||||||||
\(786\) | −7.45683 | −0.265976 | ||||||||
\(787\) | 6.96595 | 0.248309 | 0.124155 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124155 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(788\) | −43.7023 | −1.55683 | ||||||||
\(789\) | 24.0357 | 0.855694 | ||||||||
\(790\) | −24.2616 | −0.863189 | ||||||||
\(791\) | −29.4405 | −1.04678 | ||||||||
\(792\) | −4.19480 | −0.149056 | ||||||||
\(793\) | 7.07866 | 0.251371 | ||||||||
\(794\) | 15.4531 | 0.548411 | ||||||||
\(795\) | 19.4599 | 0.690172 | ||||||||
\(796\) | −31.6681 | −1.12245 | ||||||||
\(797\) | −50.1632 | −1.77687 | −0.888436 | − | 0.459001i | \(-0.848207\pi\) | ||||
−0.888436 | + | 0.459001i | \(0.848207\pi\) | |||||||
\(798\) | 94.9517 | 3.36125 | ||||||||
\(799\) | −12.0312 | −0.425632 | ||||||||
\(800\) | 0.238082 | 0.00841748 | ||||||||
\(801\) | −3.63646 | −0.128488 | ||||||||
\(802\) | −63.7576 | −2.25136 | ||||||||
\(803\) | 5.41201 | 0.190986 | ||||||||
\(804\) | −56.1206 | −1.97922 | ||||||||
\(805\) | −81.1360 | −2.85967 | ||||||||
\(806\) | −16.9252 | −0.596164 | ||||||||
\(807\) | −1.15181 | −0.0405455 | ||||||||
\(808\) | 57.2523 | 2.01413 | ||||||||
\(809\) | 22.7875 | 0.801165 | 0.400583 | − | 0.916261i | \(-0.368808\pi\) | ||||
0.400583 | + | 0.916261i | \(0.368808\pi\) | |||||||
\(810\) | −5.38482 | −0.189203 | ||||||||
\(811\) | 22.7928 | 0.800363 | 0.400181 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400181 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(812\) | −51.3671 | −1.80263 | ||||||||
\(813\) | −6.73126 | −0.236076 | ||||||||
\(814\) | −3.26654 | −0.114492 | ||||||||
\(815\) | 52.0852 | 1.82446 | ||||||||
\(816\) | −2.27712 | −0.0797151 | ||||||||
\(817\) | −33.0037 | −1.15465 | ||||||||
\(818\) | 10.6756 | 0.373263 | ||||||||
\(819\) | 3.34957 | 0.117044 | ||||||||
\(820\) | 72.5539 | 2.53369 | ||||||||
\(821\) | −31.5337 | −1.10053 | −0.550266 | − | 0.834989i | \(-0.685474\pi\) | ||||
−0.550266 | + | 0.834989i | \(0.685474\pi\) | |||||||
\(822\) | 33.5764 | 1.17111 | ||||||||
\(823\) | 48.0071 | 1.67342 | 0.836712 | − | 0.547643i | \(-0.184475\pi\) | ||||
0.836712 | + | 0.547643i | \(0.184475\pi\) | |||||||
\(824\) | −9.76319 | −0.340117 | ||||||||
\(825\) | −0.0923471 | −0.00321511 | ||||||||
\(826\) | −31.9063 | −1.11016 | ||||||||
\(827\) | 33.5928 | 1.16814 | 0.584068 | − | 0.811705i | \(-0.301460\pi\) | ||||
0.584068 | + | 0.811705i | \(0.301460\pi\) | |||||||
\(828\) | 27.3189 | 0.949399 | ||||||||
\(829\) | −44.4695 | −1.54449 | −0.772245 | − | 0.635325i | \(-0.780866\pi\) | ||||
−0.772245 | + | 0.635325i | \(0.780866\pi\) | |||||||
\(830\) | 41.0409 | 1.42455 | ||||||||
\(831\) | 19.6709 | 0.682376 | ||||||||
\(832\) | 7.51720 | 0.260612 | ||||||||
\(833\) | 16.6969 | 0.578514 | ||||||||
\(834\) | 3.34103 | 0.115690 | ||||||||
\(835\) | −13.3670 | −0.462583 | ||||||||
\(836\) | −31.2794 | −1.08182 | ||||||||
\(837\) | 10.3049 | 0.356189 | ||||||||
\(838\) | 11.2251 | 0.387763 | ||||||||
\(839\) | 7.51957 | 0.259604 | 0.129802 | − | 0.991540i | \(-0.458566\pi\) | ||||
0.129802 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(840\) | −44.4996 | −1.53538 | ||||||||
\(841\) | −20.8560 | −0.719174 | ||||||||
\(842\) | −56.4829 | −1.94653 | ||||||||
\(843\) | −14.5307 | −0.500465 | ||||||||
\(844\) | −72.2446 | −2.48676 | ||||||||
\(845\) | −28.2590 | −0.972137 | ||||||||
\(846\) | 28.7180 | 0.987346 | ||||||||
\(847\) | 48.3307 | 1.66066 | ||||||||
\(848\) | −19.6427 | −0.674534 | ||||||||
\(849\) | −1.06397 | −0.0365153 | ||||||||
\(850\) | −0.212933 | −0.00730355 | ||||||||
\(851\) | 9.76691 | 0.334805 | ||||||||
\(852\) | 12.9636 | 0.444125 | ||||||||
\(853\) | −11.9113 | −0.407834 | −0.203917 | − | 0.978988i | \(-0.565367\pi\) | ||||
−0.203917 | + | 0.978988i | \(0.565367\pi\) | |||||||
\(854\) | −119.536 | −4.09045 | ||||||||
\(855\) | −18.4347 | −0.630452 | ||||||||
\(856\) | −30.3254 | −1.03650 | ||||||||
\(857\) | −25.0072 | −0.854230 | −0.427115 | − | 0.904197i | \(-0.640470\pi\) | ||||
−0.427115 | + | 0.904197i | \(0.640470\pi\) | |||||||
\(858\) | −1.70026 | −0.0580460 | ||||||||
\(859\) | 40.2573 | 1.37356 | 0.686780 | − | 0.726865i | \(-0.259023\pi\) | ||||
0.686780 | + | 0.726865i | \(0.259023\pi\) | |||||||
\(860\) | 33.6899 | 1.14882 | ||||||||
\(861\) | 42.3409 | 1.44297 | ||||||||
\(862\) | 38.2558 | 1.30300 | ||||||||
\(863\) | 11.4655 | 0.390291 | 0.195146 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195146 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(864\) | −2.66889 | −0.0907974 | ||||||||
\(865\) | 20.5450 | 0.698551 | ||||||||
\(866\) | −20.9508 | −0.711937 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 185.486 | 6.29579 | ||||||||
\(869\) | 4.66417 | 0.158221 | ||||||||
\(870\) | 15.3670 | 0.520990 | ||||||||
\(871\) | −10.4434 | −0.353863 | ||||||||
\(872\) | 32.4779 | 1.09984 | ||||||||
\(873\) | −4.49489 | −0.152129 | ||||||||
\(874\) | 144.112 | 4.87465 | ||||||||
\(875\) | 53.9290 | 1.82313 | ||||||||
\(876\) | −19.3310 | −0.653133 | ||||||||
\(877\) | −8.02608 | −0.271022 | −0.135511 | − | 0.990776i | \(-0.543268\pi\) | ||||
−0.135511 | + | 0.990776i | \(0.543268\pi\) | |||||||
\(878\) | 76.8523 | 2.59364 | ||||||||
\(879\) | 16.5473 | 0.558128 | ||||||||
\(880\) | 5.31786 | 0.179265 | ||||||||
\(881\) | −1.37081 | −0.0461836 | −0.0230918 | − | 0.999733i | \(-0.507351\pi\) | ||||
−0.0230918 | + | 0.999733i | \(0.507351\pi\) | |||||||
\(882\) | −39.8550 | −1.34199 | ||||||||
\(883\) | 46.8654 | 1.57715 | 0.788573 | − | 0.614941i | \(-0.210820\pi\) | ||||
0.788573 | + | 0.614941i | \(0.210820\pi\) | |||||||
\(884\) | −2.54428 | −0.0855734 | ||||||||
\(885\) | 6.19455 | 0.208228 | ||||||||
\(886\) | −69.2194 | −2.32547 | ||||||||
\(887\) | 44.6925 | 1.50063 | 0.750314 | − | 0.661082i | \(-0.229902\pi\) | ||||
0.750314 | + | 0.661082i | \(0.229902\pi\) | |||||||
\(888\) | 5.35674 | 0.179760 | ||||||||
\(889\) | 73.5752 | 2.46763 | ||||||||
\(890\) | 19.5817 | 0.656380 | ||||||||
\(891\) | 1.03520 | 0.0346807 | ||||||||
\(892\) | 60.1933 | 2.01542 | ||||||||
\(893\) | 98.3147 | 3.28998 | ||||||||
\(894\) | 55.4883 | 1.85581 | ||||||||
\(895\) | 19.9524 | 0.666935 | ||||||||
\(896\) | −100.958 | −3.37277 | ||||||||
\(897\) | 5.08377 | 0.169742 | ||||||||
\(898\) | −14.6990 | −0.490512 | ||||||||
\(899\) | −29.4077 | −0.980801 | ||||||||
\(900\) | 0.329852 | 0.0109951 | ||||||||
\(901\) | −8.62613 | −0.287378 | ||||||||
\(902\) | −21.4925 | −0.715622 | ||||||||
\(903\) | 19.6607 | 0.654267 | ||||||||
\(904\) | −24.5067 | −0.815079 | ||||||||
\(905\) | 9.87793 | 0.328354 | ||||||||
\(906\) | −43.6834 | −1.45129 | ||||||||
\(907\) | 16.8013 | 0.557877 | 0.278939 | − | 0.960309i | \(-0.410017\pi\) | ||||
0.278939 | + | 0.960309i | \(0.410017\pi\) | |||||||
\(908\) | 5.82082 | 0.193171 | ||||||||
\(909\) | −14.1289 | −0.468626 | ||||||||
\(910\) | −18.0369 | −0.597916 | ||||||||
\(911\) | −25.4071 | −0.841774 | −0.420887 | − | 0.907113i | \(-0.638281\pi\) | ||||
−0.420887 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(912\) | 18.6079 | 0.616168 | ||||||||
\(913\) | −7.88991 | −0.261118 | ||||||||
\(914\) | 9.96172 | 0.329504 | ||||||||
\(915\) | 23.2077 | 0.767224 | ||||||||
\(916\) | 6.38300 | 0.210900 | ||||||||
\(917\) | 15.2073 | 0.502191 | ||||||||
\(918\) | 2.38697 | 0.0787817 | ||||||||
\(919\) | 3.57057 | 0.117782 | 0.0588912 | − | 0.998264i | \(-0.481244\pi\) | ||||
0.0588912 | + | 0.998264i | \(0.481244\pi\) | |||||||
\(920\) | −67.5387 | −2.22669 | ||||||||
\(921\) | 12.0964 | 0.398589 | ||||||||
\(922\) | −32.4809 | −1.06970 | ||||||||
\(923\) | 2.41239 | 0.0794047 | ||||||||
\(924\) | 18.6335 | 0.612996 | ||||||||
\(925\) | 0.117927 | 0.00387740 | ||||||||
\(926\) | 42.8687 | 1.40875 | ||||||||
\(927\) | 2.40939 | 0.0791346 | ||||||||
\(928\) | 7.61637 | 0.250020 | ||||||||
\(929\) | −0.00949945 | −0.000311667 0 | −0.000155833 | − | 1.00000i | \(-0.500050\pi\) | ||||
−0.000155833 | 1.00000i | \(0.500050\pi\) | ||||||||
\(930\) | −55.4900 | −1.81959 | ||||||||
\(931\) | −136.442 | −4.47169 | ||||||||
\(932\) | 32.9393 | 1.07896 | ||||||||
\(933\) | 20.6007 | 0.674436 | ||||||||
\(934\) | 48.3828 | 1.58313 | ||||||||
\(935\) | 2.33535 | 0.0763740 | ||||||||
\(936\) | 2.78823 | 0.0911362 | ||||||||
\(937\) | 11.8867 | 0.388320 | 0.194160 | − | 0.980970i | \(-0.437802\pi\) | ||||
0.194160 | + | 0.980970i | \(0.437802\pi\) | |||||||
\(938\) | 176.357 | 5.75826 | ||||||||
\(939\) | −19.8787 | −0.648715 | ||||||||
\(940\) | −100.359 | −3.27334 | ||||||||
\(941\) | 1.27612 | 0.0416005 | 0.0208002 | − | 0.999784i | \(-0.493379\pi\) | ||||
0.0208002 | + | 0.999784i | \(0.493379\pi\) | |||||||
\(942\) | −2.38697 | −0.0777716 | ||||||||
\(943\) | 64.2624 | 2.09267 | ||||||||
\(944\) | −6.25274 | −0.203509 | ||||||||
\(945\) | 10.9817 | 0.357236 | ||||||||
\(946\) | −9.97988 | −0.324474 | ||||||||
\(947\) | −14.2844 | −0.464180 | −0.232090 | − | 0.972694i | \(-0.574556\pi\) | ||||
−0.232090 | + | 0.972694i | \(0.574556\pi\) | |||||||
\(948\) | −16.6598 | −0.541085 | ||||||||
\(949\) | −3.59729 | −0.116773 | ||||||||
\(950\) | 1.74002 | 0.0564537 | ||||||||
\(951\) | −12.4872 | −0.404925 | ||||||||
\(952\) | 19.7256 | 0.639312 | ||||||||
\(953\) | 1.39435 | 0.0451674 | 0.0225837 | − | 0.999745i | \(-0.492811\pi\) | ||||
0.0225837 | + | 0.999745i | \(0.492811\pi\) | |||||||
\(954\) | 20.5903 | 0.666635 | ||||||||
\(955\) | 53.8387 | 1.74218 | ||||||||
\(956\) | 47.1109 | 1.52368 | ||||||||
\(957\) | −2.95423 | −0.0954966 | ||||||||
\(958\) | −69.8127 | −2.25555 | ||||||||
\(959\) | −68.4752 | −2.21118 | ||||||||
\(960\) | 24.6455 | 0.795431 | ||||||||
\(961\) | 75.1906 | 2.42550 | ||||||||
\(962\) | 2.17122 | 0.0700031 | ||||||||
\(963\) | 7.48379 | 0.241162 | ||||||||
\(964\) | −19.4218 | −0.625533 | ||||||||
\(965\) | 58.2890 | 1.87639 | ||||||||
\(966\) | −85.8489 | −2.76214 | ||||||||
\(967\) | 32.5456 | 1.04660 | 0.523298 | − | 0.852150i | \(-0.324702\pi\) | ||||
0.523298 | + | 0.852150i | \(0.324702\pi\) | |||||||
\(968\) | 40.2312 | 1.29308 | ||||||||
\(969\) | 8.17166 | 0.262512 | ||||||||
\(970\) | 24.2042 | 0.777150 | ||||||||
\(971\) | 23.2256 | 0.745346 | 0.372673 | − | 0.927963i | \(-0.378441\pi\) | ||||
0.372673 | + | 0.927963i | \(0.378441\pi\) | |||||||
\(972\) | −3.69761 | −0.118601 | ||||||||
\(973\) | −6.81364 | −0.218435 | ||||||||
\(974\) | 64.9218 | 2.08023 | ||||||||
\(975\) | 0.0613819 | 0.00196579 | ||||||||
\(976\) | −23.4258 | −0.749840 | ||||||||
\(977\) | −50.8529 | −1.62693 | −0.813465 | − | 0.581614i | \(-0.802421\pi\) | ||||
−0.813465 | + | 0.581614i | \(0.802421\pi\) | |||||||
\(978\) | 55.1106 | 1.76224 | ||||||||
\(979\) | −3.76448 | −0.120313 | ||||||||
\(980\) | 139.278 | 4.44908 | ||||||||
\(981\) | −8.01499 | −0.255899 | ||||||||
\(982\) | −43.8086 | −1.39799 | ||||||||
\(983\) | 0.196709 | 0.00627403 | 0.00313702 | − | 0.999995i | \(-0.499001\pi\) | ||||
0.00313702 | + | 0.999995i | \(0.499001\pi\) | |||||||
\(984\) | 35.2452 | 1.12358 | ||||||||
\(985\) | −26.6629 | −0.849551 | ||||||||
\(986\) | −6.81184 | −0.216933 | ||||||||
\(987\) | −58.5671 | −1.86421 | ||||||||
\(988\) | 20.7910 | 0.661450 | ||||||||
\(989\) | 29.8398 | 0.948849 | ||||||||
\(990\) | −5.57439 | −0.177166 | ||||||||
\(991\) | 42.1068 | 1.33757 | 0.668784 | − | 0.743457i | \(-0.266815\pi\) | ||||
0.668784 | + | 0.743457i | \(0.266815\pi\) | |||||||
\(992\) | −27.5026 | −0.873207 | ||||||||
\(993\) | 32.9406 | 1.04534 | ||||||||
\(994\) | −40.7377 | −1.29212 | ||||||||
\(995\) | −19.3208 | −0.612512 | ||||||||
\(996\) | 28.1817 | 0.892971 | ||||||||
\(997\) | 43.7861 | 1.38672 | 0.693360 | − | 0.720592i | \(-0.256130\pi\) | ||||
0.693360 | + | 0.720592i | \(0.256130\pi\) | |||||||
\(998\) | −92.9255 | −2.94150 | ||||||||
\(999\) | −1.32195 | −0.0418246 |
(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 | 8007.2.a.j.1.6 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.6 | ✓ | 64 | 1.1 | even | 1 | trivial |