Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93894 | −1.37104 | −0.685520 | − | 0.728054i | \(-0.740425\pi\) | ||||
−0.685520 | + | 0.728054i | \(0.740425\pi\) | |||||||
\(3\) | −1.61421 | −0.931965 | −0.465983 | − | 0.884794i | \(-0.654299\pi\) | ||||
−0.465983 | + | 0.884794i | \(0.654299\pi\) | |||||||
\(4\) | 1.75950 | 0.879748 | ||||||||
\(5\) | −0.710068 | −0.317552 | −0.158776 | − | 0.987315i | \(-0.550755\pi\) | ||||
−0.158776 | + | 0.987315i | \(0.550755\pi\) | |||||||
\(6\) | 3.12986 | 1.27776 | ||||||||
\(7\) | −1.51648 | −0.573175 | −0.286588 | − | 0.958054i | \(-0.592521\pi\) | ||||
−0.286588 | + | 0.958054i | \(0.592521\pi\) | |||||||
\(8\) | 0.466323 | 0.164870 | ||||||||
\(9\) | −0.394323 | −0.131441 | ||||||||
\(10\) | 1.37678 | 0.435376 | ||||||||
\(11\) | 4.83786 | 1.45867 | 0.729335 | − | 0.684157i | \(-0.239830\pi\) | ||||
0.729335 | + | 0.684157i | \(0.239830\pi\) | |||||||
\(12\) | −2.84020 | −0.819894 | ||||||||
\(13\) | −3.42790 | −0.950728 | −0.475364 | − | 0.879789i | \(-0.657684\pi\) | ||||
−0.475364 | + | 0.879789i | \(0.657684\pi\) | |||||||
\(14\) | 2.94037 | 0.785846 | ||||||||
\(15\) | 1.14620 | 0.295948 | ||||||||
\(16\) | −4.42317 | −1.10579 | ||||||||
\(17\) | 2.25296 | 0.546423 | 0.273212 | − | 0.961954i | \(-0.411914\pi\) | ||||
0.273212 | + | 0.961954i | \(0.411914\pi\) | |||||||
\(18\) | 0.764570 | 0.180211 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.24936 | −0.279366 | ||||||||
\(21\) | 2.44792 | 0.534179 | ||||||||
\(22\) | −9.38033 | −1.99989 | ||||||||
\(23\) | 5.02944 | 1.04871 | 0.524356 | − | 0.851499i | \(-0.324306\pi\) | ||||
0.524356 | + | 0.851499i | \(0.324306\pi\) | |||||||
\(24\) | −0.752744 | −0.153653 | ||||||||
\(25\) | −4.49580 | −0.899161 | ||||||||
\(26\) | 6.64650 | 1.30349 | ||||||||
\(27\) | 5.47915 | 1.05446 | ||||||||
\(28\) | −2.66824 | −0.504250 | ||||||||
\(29\) | −9.09232 | −1.68840 | −0.844200 | − | 0.536028i | \(-0.819924\pi\) | ||||
−0.844200 | + | 0.536028i | \(0.819924\pi\) | |||||||
\(30\) | −2.22241 | −0.405756 | ||||||||
\(31\) | −7.95846 | −1.42938 | −0.714691 | − | 0.699440i | \(-0.753433\pi\) | ||||
−0.714691 | + | 0.699440i | \(0.753433\pi\) | |||||||
\(32\) | 7.64362 | 1.35121 | ||||||||
\(33\) | −7.80933 | −1.35943 | ||||||||
\(34\) | −4.36836 | −0.749168 | ||||||||
\(35\) | 1.07680 | 0.182013 | ||||||||
\(36\) | −0.693810 | −0.115635 | ||||||||
\(37\) | 0.118446 | 0.0194724 | 0.00973618 | − | 0.999953i | \(-0.496901\pi\) | ||||
0.00973618 | + | 0.999953i | \(0.496901\pi\) | |||||||
\(38\) | −1.93894 | −0.314538 | ||||||||
\(39\) | 5.53335 | 0.886045 | ||||||||
\(40\) | −0.331121 | −0.0523549 | ||||||||
\(41\) | 4.81219 | 0.751538 | 0.375769 | − | 0.926713i | \(-0.377379\pi\) | ||||
0.375769 | + | 0.926713i | \(0.377379\pi\) | |||||||
\(42\) | −4.74637 | −0.732381 | ||||||||
\(43\) | 7.87596 | 1.20107 | 0.600537 | − | 0.799597i | \(-0.294954\pi\) | ||||
0.600537 | + | 0.799597i | \(0.294954\pi\) | |||||||
\(44\) | 8.51220 | 1.28326 | ||||||||
\(45\) | 0.279996 | 0.0417394 | ||||||||
\(46\) | −9.75180 | −1.43782 | ||||||||
\(47\) | −4.37650 | −0.638379 | −0.319189 | − | 0.947691i | \(-0.603411\pi\) | ||||
−0.319189 | + | 0.947691i | \(0.603411\pi\) | |||||||
\(48\) | 7.13992 | 1.03056 | ||||||||
\(49\) | −4.70029 | −0.671470 | ||||||||
\(50\) | 8.71710 | 1.23278 | ||||||||
\(51\) | −3.63675 | −0.509248 | ||||||||
\(52\) | −6.03137 | −0.836401 | ||||||||
\(53\) | −2.80310 | −0.385036 | −0.192518 | − | 0.981293i | \(-0.561665\pi\) | ||||
−0.192518 | + | 0.981293i | \(0.561665\pi\) | |||||||
\(54\) | −10.6238 | −1.44571 | ||||||||
\(55\) | −3.43521 | −0.463204 | ||||||||
\(56\) | −0.707169 | −0.0944995 | ||||||||
\(57\) | −1.61421 | −0.213807 | ||||||||
\(58\) | 17.6295 | 2.31486 | ||||||||
\(59\) | 13.7278 | 1.78721 | 0.893607 | − | 0.448851i | \(-0.148167\pi\) | ||||
0.893607 | + | 0.448851i | \(0.148167\pi\) | |||||||
\(60\) | 2.01673 | 0.260359 | ||||||||
\(61\) | 5.59544 | 0.716423 | 0.358211 | − | 0.933640i | \(-0.383387\pi\) | ||||
0.358211 | + | 0.933640i | \(0.383387\pi\) | |||||||
\(62\) | 15.4310 | 1.95974 | ||||||||
\(63\) | 0.597983 | 0.0753388 | ||||||||
\(64\) | −5.97420 | −0.746774 | ||||||||
\(65\) | 2.43404 | 0.301906 | ||||||||
\(66\) | 15.1418 | 1.86383 | ||||||||
\(67\) | −4.65901 | −0.569189 | −0.284594 | − | 0.958648i | \(-0.591859\pi\) | ||||
−0.284594 | + | 0.958648i | \(0.591859\pi\) | |||||||
\(68\) | 3.96408 | 0.480715 | ||||||||
\(69\) | −8.11858 | −0.977362 | ||||||||
\(70\) | −2.08786 | −0.249547 | ||||||||
\(71\) | 4.73205 | 0.561591 | 0.280795 | − | 0.959768i | \(-0.409402\pi\) | ||||
0.280795 | + | 0.959768i | \(0.409402\pi\) | |||||||
\(72\) | −0.183882 | −0.0216707 | ||||||||
\(73\) | 8.30981 | 0.972589 | 0.486295 | − | 0.873795i | \(-0.338348\pi\) | ||||
0.486295 | + | 0.873795i | \(0.338348\pi\) | |||||||
\(74\) | −0.229659 | −0.0266974 | ||||||||
\(75\) | 7.25717 | 0.837986 | ||||||||
\(76\) | 1.75950 | 0.201828 | ||||||||
\(77\) | −7.33651 | −0.836073 | ||||||||
\(78\) | −10.7288 | −1.21480 | ||||||||
\(79\) | −1.73416 | −0.195108 | −0.0975539 | − | 0.995230i | \(-0.531102\pi\) | ||||
−0.0975539 | + | 0.995230i | \(0.531102\pi\) | |||||||
\(80\) | 3.14075 | 0.351146 | ||||||||
\(81\) | −7.66154 | −0.851282 | ||||||||
\(82\) | −9.33056 | −1.03039 | ||||||||
\(83\) | −10.6561 | −1.16966 | −0.584831 | − | 0.811155i | \(-0.698839\pi\) | ||||
−0.584831 | + | 0.811155i | \(0.698839\pi\) | |||||||
\(84\) | 4.30710 | 0.469943 | ||||||||
\(85\) | −1.59976 | −0.173518 | ||||||||
\(86\) | −15.2710 | −1.64672 | ||||||||
\(87\) | 14.6769 | 1.57353 | ||||||||
\(88\) | 2.25601 | 0.240491 | ||||||||
\(89\) | −0.175995 | −0.0186555 | −0.00932773 | − | 0.999956i | \(-0.502969\pi\) | ||||
−0.00932773 | + | 0.999956i | \(0.502969\pi\) | |||||||
\(90\) | −0.542897 | −0.0572263 | ||||||||
\(91\) | 5.19834 | 0.544934 | ||||||||
\(92\) | 8.84929 | 0.922602 | ||||||||
\(93\) | 12.8466 | 1.33213 | ||||||||
\(94\) | 8.48579 | 0.875242 | ||||||||
\(95\) | −0.710068 | −0.0728515 | ||||||||
\(96\) | −12.3384 | −1.25928 | ||||||||
\(97\) | −6.23723 | −0.633295 | −0.316648 | − | 0.948543i | \(-0.602557\pi\) | ||||
−0.316648 | + | 0.948543i | \(0.602557\pi\) | |||||||
\(98\) | 9.11359 | 0.920612 | ||||||||
\(99\) | −1.90768 | −0.191729 | ||||||||
\(100\) | −7.91035 | −0.791035 | ||||||||
\(101\) | 10.6438 | 1.05910 | 0.529551 | − | 0.848278i | \(-0.322360\pi\) | ||||
0.529551 | + | 0.848278i | \(0.322360\pi\) | |||||||
\(102\) | 7.05146 | 0.698198 | ||||||||
\(103\) | 10.3097 | 1.01585 | 0.507923 | − | 0.861402i | \(-0.330413\pi\) | ||||
0.507923 | + | 0.861402i | \(0.330413\pi\) | |||||||
\(104\) | −1.59851 | −0.156747 | ||||||||
\(105\) | −1.73819 | −0.169630 | ||||||||
\(106\) | 5.43505 | 0.527899 | ||||||||
\(107\) | −11.2971 | −1.09213 | −0.546065 | − | 0.837743i | \(-0.683875\pi\) | ||||
−0.546065 | + | 0.837743i | \(0.683875\pi\) | |||||||
\(108\) | 9.64055 | 0.927662 | ||||||||
\(109\) | −8.43282 | −0.807717 | −0.403859 | − | 0.914821i | \(-0.632331\pi\) | ||||
−0.403859 | + | 0.914821i | \(0.632331\pi\) | |||||||
\(110\) | 6.66067 | 0.635070 | ||||||||
\(111\) | −0.191196 | −0.0181476 | ||||||||
\(112\) | 6.70764 | 0.633812 | ||||||||
\(113\) | 1.82578 | 0.171755 | 0.0858774 | − | 0.996306i | \(-0.472631\pi\) | ||||
0.0858774 | + | 0.996306i | \(0.472631\pi\) | |||||||
\(114\) | 3.12986 | 0.293138 | ||||||||
\(115\) | −3.57125 | −0.333021 | ||||||||
\(116\) | −15.9979 | −1.48537 | ||||||||
\(117\) | 1.35170 | 0.124965 | ||||||||
\(118\) | −26.6175 | −2.45034 | ||||||||
\(119\) | −3.41657 | −0.313196 | ||||||||
\(120\) | 0.534499 | 0.0487929 | ||||||||
\(121\) | 12.4049 | 1.12772 | ||||||||
\(122\) | −10.8492 | −0.982244 | ||||||||
\(123\) | −7.76789 | −0.700407 | ||||||||
\(124\) | −14.0029 | −1.25750 | ||||||||
\(125\) | 6.74267 | 0.603083 | ||||||||
\(126\) | −1.15945 | −0.103292 | ||||||||
\(127\) | 18.6381 | 1.65387 | 0.826933 | − | 0.562300i | \(-0.190083\pi\) | ||||
0.826933 | + | 0.562300i | \(0.190083\pi\) | |||||||
\(128\) | −3.70361 | −0.327356 | ||||||||
\(129\) | −12.7135 | −1.11936 | ||||||||
\(130\) | −4.71947 | −0.413925 | ||||||||
\(131\) | 13.0963 | 1.14423 | 0.572113 | − | 0.820174i | \(-0.306124\pi\) | ||||
0.572113 | + | 0.820174i | \(0.306124\pi\) | |||||||
\(132\) | −13.7405 | −1.19596 | ||||||||
\(133\) | −1.51648 | −0.131495 | ||||||||
\(134\) | 9.03356 | 0.780380 | ||||||||
\(135\) | −3.89057 | −0.334847 | ||||||||
\(136\) | 1.05061 | 0.0900889 | ||||||||
\(137\) | 12.1805 | 1.04065 | 0.520325 | − | 0.853968i | \(-0.325811\pi\) | ||||
0.520325 | + | 0.853968i | \(0.325811\pi\) | |||||||
\(138\) | 15.7415 | 1.34000 | ||||||||
\(139\) | 6.69201 | 0.567609 | 0.283804 | − | 0.958882i | \(-0.408403\pi\) | ||||
0.283804 | + | 0.958882i | \(0.408403\pi\) | |||||||
\(140\) | 1.89463 | 0.160126 | ||||||||
\(141\) | 7.06460 | 0.594947 | ||||||||
\(142\) | −9.17517 | −0.769963 | ||||||||
\(143\) | −16.5837 | −1.38680 | ||||||||
\(144\) | 1.74416 | 0.145346 | ||||||||
\(145\) | 6.45616 | 0.536155 | ||||||||
\(146\) | −16.1122 | −1.33346 | ||||||||
\(147\) | 7.58726 | 0.625787 | ||||||||
\(148\) | 0.208405 | 0.0171308 | ||||||||
\(149\) | 15.0153 | 1.23010 | 0.615050 | − | 0.788488i | \(-0.289136\pi\) | ||||
0.615050 | + | 0.788488i | \(0.289136\pi\) | |||||||
\(150\) | −14.0712 | −1.14891 | ||||||||
\(151\) | −1.59359 | −0.129685 | −0.0648423 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648423 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(152\) | 0.466323 | 0.0378238 | ||||||||
\(153\) | −0.888395 | −0.0718225 | ||||||||
\(154\) | 14.2251 | 1.14629 | ||||||||
\(155\) | 5.65105 | 0.453903 | ||||||||
\(156\) | 9.73591 | 0.779497 | ||||||||
\(157\) | −18.4721 | −1.47423 | −0.737115 | − | 0.675767i | \(-0.763812\pi\) | ||||
−0.737115 | + | 0.675767i | \(0.763812\pi\) | |||||||
\(158\) | 3.36243 | 0.267500 | ||||||||
\(159\) | 4.52480 | 0.358840 | ||||||||
\(160\) | −5.42749 | −0.429081 | ||||||||
\(161\) | −7.62705 | −0.601095 | ||||||||
\(162\) | 14.8553 | 1.16714 | ||||||||
\(163\) | 19.3453 | 1.51524 | 0.757621 | − | 0.652695i | \(-0.226362\pi\) | ||||
0.757621 | + | 0.652695i | \(0.226362\pi\) | |||||||
\(164\) | 8.46703 | 0.661164 | ||||||||
\(165\) | 5.54515 | 0.431690 | ||||||||
\(166\) | 20.6616 | 1.60365 | ||||||||
\(167\) | 22.4293 | 1.73563 | 0.867817 | − | 0.496884i | \(-0.165523\pi\) | ||||
0.867817 | + | 0.496884i | \(0.165523\pi\) | |||||||
\(168\) | 1.14152 | 0.0880702 | ||||||||
\(169\) | −1.24951 | −0.0961161 | ||||||||
\(170\) | 3.10183 | 0.237900 | ||||||||
\(171\) | −0.394323 | −0.0301546 | ||||||||
\(172\) | 13.8577 | 1.05664 | ||||||||
\(173\) | −6.57092 | −0.499578 | −0.249789 | − | 0.968300i | \(-0.580361\pi\) | ||||
−0.249789 | + | 0.968300i | \(0.580361\pi\) | |||||||
\(174\) | −28.4577 | −2.15737 | ||||||||
\(175\) | 6.81779 | 0.515377 | ||||||||
\(176\) | −21.3987 | −1.61298 | ||||||||
\(177\) | −22.1596 | −1.66562 | ||||||||
\(178\) | 0.341245 | 0.0255774 | ||||||||
\(179\) | −19.4022 | −1.45019 | −0.725096 | − | 0.688648i | \(-0.758205\pi\) | ||||
−0.725096 | + | 0.688648i | \(0.758205\pi\) | |||||||
\(180\) | 0.492652 | 0.0367201 | ||||||||
\(181\) | −22.0532 | −1.63920 | −0.819600 | − | 0.572936i | \(-0.805804\pi\) | ||||
−0.819600 | + | 0.572936i | \(0.805804\pi\) | |||||||
\(182\) | −10.0793 | −0.747126 | ||||||||
\(183\) | −9.03222 | −0.667681 | ||||||||
\(184\) | 2.34535 | 0.172901 | ||||||||
\(185\) | −0.0841046 | −0.00618349 | ||||||||
\(186\) | −24.9089 | −1.82641 | ||||||||
\(187\) | 10.8995 | 0.797051 | ||||||||
\(188\) | −7.70044 | −0.561613 | ||||||||
\(189\) | −8.30902 | −0.604392 | ||||||||
\(190\) | 1.37678 | 0.0998822 | ||||||||
\(191\) | 5.74002 | 0.415334 | 0.207667 | − | 0.978200i | \(-0.433413\pi\) | ||||
0.207667 | + | 0.978200i | \(0.433413\pi\) | |||||||
\(192\) | 9.64361 | 0.695968 | ||||||||
\(193\) | 12.5726 | 0.904995 | 0.452497 | − | 0.891766i | \(-0.350533\pi\) | ||||
0.452497 | + | 0.891766i | \(0.350533\pi\) | |||||||
\(194\) | 12.0936 | 0.868272 | ||||||||
\(195\) | −3.92906 | −0.281366 | ||||||||
\(196\) | −8.27014 | −0.590724 | ||||||||
\(197\) | −22.4687 | −1.60083 | −0.800414 | − | 0.599448i | \(-0.795387\pi\) | ||||
−0.800414 | + | 0.599448i | \(0.795387\pi\) | |||||||
\(198\) | 3.69888 | 0.262868 | ||||||||
\(199\) | −14.4119 | −1.02163 | −0.510816 | − | 0.859690i | \(-0.670657\pi\) | ||||
−0.510816 | + | 0.859690i | \(0.670657\pi\) | |||||||
\(200\) | −2.09650 | −0.148245 | ||||||||
\(201\) | 7.52063 | 0.530464 | ||||||||
\(202\) | −20.6378 | −1.45207 | ||||||||
\(203\) | 13.7883 | 0.967750 | ||||||||
\(204\) | −6.39886 | −0.448010 | ||||||||
\(205\) | −3.41699 | −0.238653 | ||||||||
\(206\) | −19.9899 | −1.39277 | ||||||||
\(207\) | −1.98323 | −0.137844 | ||||||||
\(208\) | 15.1622 | 1.05131 | ||||||||
\(209\) | 4.83786 | 0.334642 | ||||||||
\(210\) | 3.37025 | 0.232569 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −4.93205 | −0.338734 | ||||||||
\(213\) | −7.63852 | −0.523383 | ||||||||
\(214\) | 21.9044 | 1.49735 | ||||||||
\(215\) | −5.59247 | −0.381403 | ||||||||
\(216\) | 2.55506 | 0.173850 | ||||||||
\(217\) | 12.0688 | 0.819287 | ||||||||
\(218\) | 16.3507 | 1.10741 | ||||||||
\(219\) | −13.4138 | −0.906419 | ||||||||
\(220\) | −6.04424 | −0.407503 | ||||||||
\(221\) | −7.72292 | −0.519500 | ||||||||
\(222\) | 0.370719 | 0.0248810 | ||||||||
\(223\) | 22.4017 | 1.50013 | 0.750065 | − | 0.661364i | \(-0.230022\pi\) | ||||
0.750065 | + | 0.661364i | \(0.230022\pi\) | |||||||
\(224\) | −11.5914 | −0.774482 | ||||||||
\(225\) | 1.77280 | 0.118187 | ||||||||
\(226\) | −3.54008 | −0.235482 | ||||||||
\(227\) | 4.24493 | 0.281746 | 0.140873 | − | 0.990028i | \(-0.455009\pi\) | ||||
0.140873 | + | 0.990028i | \(0.455009\pi\) | |||||||
\(228\) | −2.84020 | −0.188097 | ||||||||
\(229\) | 24.9751 | 1.65040 | 0.825199 | − | 0.564842i | \(-0.191063\pi\) | ||||
0.825199 | + | 0.564842i | \(0.191063\pi\) | |||||||
\(230\) | 6.92444 | 0.456584 | ||||||||
\(231\) | 11.8427 | 0.779191 | ||||||||
\(232\) | −4.23996 | −0.278367 | ||||||||
\(233\) | −9.42191 | −0.617250 | −0.308625 | − | 0.951184i | \(-0.599869\pi\) | ||||
−0.308625 | + | 0.951184i | \(0.599869\pi\) | |||||||
\(234\) | −2.62087 | −0.171332 | ||||||||
\(235\) | 3.10762 | 0.202719 | ||||||||
\(236\) | 24.1541 | 1.57230 | ||||||||
\(237\) | 2.79929 | 0.181834 | ||||||||
\(238\) | 6.62453 | 0.429405 | ||||||||
\(239\) | −16.2998 | −1.05435 | −0.527173 | − | 0.849758i | \(-0.676748\pi\) | ||||
−0.527173 | + | 0.849758i | \(0.676748\pi\) | |||||||
\(240\) | −5.06983 | −0.327256 | ||||||||
\(241\) | −12.7871 | −0.823690 | −0.411845 | − | 0.911254i | \(-0.635115\pi\) | ||||
−0.411845 | + | 0.911254i | \(0.635115\pi\) | |||||||
\(242\) | −24.0524 | −1.54614 | ||||||||
\(243\) | −4.07012 | −0.261098 | ||||||||
\(244\) | 9.84516 | 0.630272 | ||||||||
\(245\) | 3.33753 | 0.213227 | ||||||||
\(246\) | 15.0615 | 0.960286 | ||||||||
\(247\) | −3.42790 | −0.218112 | ||||||||
\(248\) | −3.71122 | −0.235662 | ||||||||
\(249\) | 17.2012 | 1.09008 | ||||||||
\(250\) | −13.0736 | −0.826850 | ||||||||
\(251\) | −23.6809 | −1.49472 | −0.747362 | − | 0.664417i | \(-0.768680\pi\) | ||||
−0.747362 | + | 0.664417i | \(0.768680\pi\) | |||||||
\(252\) | 1.05215 | 0.0662791 | ||||||||
\(253\) | 24.3317 | 1.52972 | ||||||||
\(254\) | −36.1383 | −2.26752 | ||||||||
\(255\) | 2.58234 | 0.161713 | ||||||||
\(256\) | 19.1295 | 1.19559 | ||||||||
\(257\) | −3.38495 | −0.211147 | −0.105574 | − | 0.994411i | \(-0.533668\pi\) | ||||
−0.105574 | + | 0.994411i | \(0.533668\pi\) | |||||||
\(258\) | 24.6507 | 1.53468 | ||||||||
\(259\) | −0.179621 | −0.0111611 | ||||||||
\(260\) | 4.28269 | 0.265601 | ||||||||
\(261\) | 3.58531 | 0.221925 | ||||||||
\(262\) | −25.3929 | −1.56878 | ||||||||
\(263\) | 27.4938 | 1.69534 | 0.847670 | − | 0.530524i | \(-0.178005\pi\) | ||||
0.847670 | + | 0.530524i | \(0.178005\pi\) | |||||||
\(264\) | −3.64167 | −0.224129 | ||||||||
\(265\) | 1.99039 | 0.122269 | ||||||||
\(266\) | 2.94037 | 0.180285 | ||||||||
\(267\) | 0.284093 | 0.0173862 | ||||||||
\(268\) | −8.19751 | −0.500743 | ||||||||
\(269\) | −26.1034 | −1.59155 | −0.795775 | − | 0.605592i | \(-0.792936\pi\) | ||||
−0.795775 | + | 0.605592i | \(0.792936\pi\) | |||||||
\(270\) | 7.54359 | 0.459089 | ||||||||
\(271\) | −19.7467 | −1.19953 | −0.599763 | − | 0.800177i | \(-0.704739\pi\) | ||||
−0.599763 | + | 0.800177i | \(0.704739\pi\) | |||||||
\(272\) | −9.96522 | −0.604230 | ||||||||
\(273\) | −8.39121 | −0.507859 | ||||||||
\(274\) | −23.6173 | −1.42677 | ||||||||
\(275\) | −21.7501 | −1.31158 | ||||||||
\(276\) | −14.2846 | −0.859833 | ||||||||
\(277\) | 22.9531 | 1.37912 | 0.689558 | − | 0.724230i | \(-0.257805\pi\) | ||||
0.689558 | + | 0.724230i | \(0.257805\pi\) | |||||||
\(278\) | −12.9754 | −0.778214 | ||||||||
\(279\) | 3.13821 | 0.187880 | ||||||||
\(280\) | 0.502138 | 0.0300085 | ||||||||
\(281\) | −14.0236 | −0.836576 | −0.418288 | − | 0.908314i | \(-0.637370\pi\) | ||||
−0.418288 | + | 0.908314i | \(0.637370\pi\) | |||||||
\(282\) | −13.6979 | −0.815695 | ||||||||
\(283\) | −14.4795 | −0.860716 | −0.430358 | − | 0.902658i | \(-0.641613\pi\) | ||||
−0.430358 | + | 0.902658i | \(0.641613\pi\) | |||||||
\(284\) | 8.32602 | 0.494058 | ||||||||
\(285\) | 1.14620 | 0.0678950 | ||||||||
\(286\) | 32.1548 | 1.90135 | ||||||||
\(287\) | −7.29759 | −0.430763 | ||||||||
\(288\) | −3.01405 | −0.177605 | ||||||||
\(289\) | −11.9242 | −0.701421 | ||||||||
\(290\) | −12.5181 | −0.735090 | ||||||||
\(291\) | 10.0682 | 0.590209 | ||||||||
\(292\) | 14.6211 | 0.855634 | ||||||||
\(293\) | −26.4389 | −1.54458 | −0.772288 | − | 0.635273i | \(-0.780888\pi\) | ||||
−0.772288 | + | 0.635273i | \(0.780888\pi\) | |||||||
\(294\) | −14.7113 | −0.857978 | ||||||||
\(295\) | −9.74771 | −0.567533 | ||||||||
\(296\) | 0.0552340 | 0.00321041 | ||||||||
\(297\) | 26.5074 | 1.53811 | ||||||||
\(298\) | −29.1137 | −1.68651 | ||||||||
\(299\) | −17.2404 | −0.997039 | ||||||||
\(300\) | 12.7690 | 0.737217 | ||||||||
\(301\) | −11.9437 | −0.688426 | ||||||||
\(302\) | 3.08988 | 0.177803 | ||||||||
\(303\) | −17.1814 | −0.987046 | ||||||||
\(304\) | −4.42317 | −0.253686 | ||||||||
\(305\) | −3.97315 | −0.227502 | ||||||||
\(306\) | 1.72255 | 0.0984714 | ||||||||
\(307\) | −2.14032 | −0.122155 | −0.0610773 | − | 0.998133i | \(-0.519454\pi\) | ||||
−0.0610773 | + | 0.998133i | \(0.519454\pi\) | |||||||
\(308\) | −12.9086 | −0.735534 | ||||||||
\(309\) | −16.6421 | −0.946734 | ||||||||
\(310\) | −10.9571 | −0.622319 | ||||||||
\(311\) | −16.8102 | −0.953217 | −0.476609 | − | 0.879116i | \(-0.658134\pi\) | ||||
−0.476609 | + | 0.879116i | \(0.658134\pi\) | |||||||
\(312\) | 2.58033 | 0.146082 | ||||||||
\(313\) | 19.2019 | 1.08536 | 0.542678 | − | 0.839941i | \(-0.317410\pi\) | ||||
0.542678 | + | 0.839941i | \(0.317410\pi\) | |||||||
\(314\) | 35.8162 | 2.02123 | ||||||||
\(315\) | −0.424609 | −0.0239240 | ||||||||
\(316\) | −3.05124 | −0.171646 | ||||||||
\(317\) | −7.18411 | −0.403500 | −0.201750 | − | 0.979437i | \(-0.564663\pi\) | ||||
−0.201750 | + | 0.979437i | \(0.564663\pi\) | |||||||
\(318\) | −8.77332 | −0.491983 | ||||||||
\(319\) | −43.9874 | −2.46282 | ||||||||
\(320\) | 4.24209 | 0.237140 | ||||||||
\(321\) | 18.2359 | 1.01783 | ||||||||
\(322\) | 14.7884 | 0.824125 | ||||||||
\(323\) | 2.25296 | 0.125358 | ||||||||
\(324\) | −13.4804 | −0.748914 | ||||||||
\(325\) | 15.4112 | 0.854857 | ||||||||
\(326\) | −37.5094 | −2.07746 | ||||||||
\(327\) | 13.6123 | 0.752764 | ||||||||
\(328\) | 2.24404 | 0.123906 | ||||||||
\(329\) | 6.63688 | 0.365903 | ||||||||
\(330\) | −10.7517 | −0.591863 | ||||||||
\(331\) | −22.1654 | −1.21832 | −0.609162 | − | 0.793046i | \(-0.708494\pi\) | ||||
−0.609162 | + | 0.793046i | \(0.708494\pi\) | |||||||
\(332\) | −18.7494 | −1.02901 | ||||||||
\(333\) | −0.0467059 | −0.00255947 | ||||||||
\(334\) | −43.4892 | −2.37962 | ||||||||
\(335\) | 3.30822 | 0.180747 | ||||||||
\(336\) | −10.8275 | −0.590691 | ||||||||
\(337\) | 21.0069 | 1.14432 | 0.572159 | − | 0.820143i | \(-0.306106\pi\) | ||||
0.572159 | + | 0.820143i | \(0.306106\pi\) | |||||||
\(338\) | 2.42273 | 0.131779 | ||||||||
\(339\) | −2.94719 | −0.160069 | ||||||||
\(340\) | −2.81476 | −0.152652 | ||||||||
\(341\) | −38.5019 | −2.08500 | ||||||||
\(342\) | 0.764570 | 0.0413432 | ||||||||
\(343\) | 17.7432 | 0.958045 | ||||||||
\(344\) | 3.67274 | 0.198021 | ||||||||
\(345\) | 5.76475 | 0.310364 | ||||||||
\(346\) | 12.7406 | 0.684941 | ||||||||
\(347\) | 9.85372 | 0.528975 | 0.264488 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264488 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(348\) | 25.8240 | 1.38431 | ||||||||
\(349\) | −14.4455 | −0.773250 | −0.386625 | − | 0.922237i | \(-0.626359\pi\) | ||||
−0.386625 | + | 0.922237i | \(0.626359\pi\) | |||||||
\(350\) | −13.2193 | −0.706602 | ||||||||
\(351\) | −18.7820 | −1.00251 | ||||||||
\(352\) | 36.9787 | 1.97097 | ||||||||
\(353\) | 3.85238 | 0.205041 | 0.102521 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102521 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(354\) | 42.9663 | 2.28363 | ||||||||
\(355\) | −3.36008 | −0.178334 | ||||||||
\(356\) | −0.309663 | −0.0164121 | ||||||||
\(357\) | 5.51506 | 0.291888 | ||||||||
\(358\) | 37.6198 | 1.98827 | ||||||||
\(359\) | −15.9317 | −0.840840 | −0.420420 | − | 0.907329i | \(-0.638117\pi\) | ||||
−0.420420 | + | 0.907329i | \(0.638117\pi\) | |||||||
\(360\) | 0.130569 | 0.00688158 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 42.7598 | 2.24741 | ||||||||
\(363\) | −20.0241 | −1.05099 | ||||||||
\(364\) | 9.14646 | 0.479405 | ||||||||
\(365\) | −5.90053 | −0.308848 | ||||||||
\(366\) | 17.5130 | 0.915417 | ||||||||
\(367\) | −25.5007 | −1.33112 | −0.665562 | − | 0.746343i | \(-0.731808\pi\) | ||||
−0.665562 | + | 0.746343i | \(0.731808\pi\) | |||||||
\(368\) | −22.2461 | −1.15966 | ||||||||
\(369\) | −1.89756 | −0.0987830 | ||||||||
\(370\) | 0.163074 | 0.00847781 | ||||||||
\(371\) | 4.25085 | 0.220693 | ||||||||
\(372\) | 22.6036 | 1.17194 | ||||||||
\(373\) | 28.4844 | 1.47486 | 0.737432 | − | 0.675421i | \(-0.236038\pi\) | ||||
0.737432 | + | 0.675421i | \(0.236038\pi\) | |||||||
\(374\) | −21.1335 | −1.09279 | ||||||||
\(375\) | −10.8841 | −0.562052 | ||||||||
\(376\) | −2.04087 | −0.105250 | ||||||||
\(377\) | 31.1675 | 1.60521 | ||||||||
\(378\) | 16.1107 | 0.828646 | ||||||||
\(379\) | 16.3569 | 0.840200 | 0.420100 | − | 0.907478i | \(-0.361995\pi\) | ||||
0.420100 | + | 0.907478i | \(0.361995\pi\) | |||||||
\(380\) | −1.24936 | −0.0640909 | ||||||||
\(381\) | −30.0859 | −1.54135 | ||||||||
\(382\) | −11.1296 | −0.569439 | ||||||||
\(383\) | −3.96299 | −0.202499 | −0.101250 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101250 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(384\) | 5.97841 | 0.305084 | ||||||||
\(385\) | 5.20943 | 0.265497 | ||||||||
\(386\) | −24.3775 | −1.24078 | ||||||||
\(387\) | −3.10568 | −0.157870 | ||||||||
\(388\) | −10.9744 | −0.557140 | ||||||||
\(389\) | 2.67002 | 0.135375 | 0.0676877 | − | 0.997707i | \(-0.478438\pi\) | ||||
0.0676877 | + | 0.997707i | \(0.478438\pi\) | |||||||
\(390\) | 7.61821 | 0.385763 | ||||||||
\(391\) | 11.3311 | 0.573040 | ||||||||
\(392\) | −2.19185 | −0.110705 | ||||||||
\(393\) | −21.1402 | −1.06638 | ||||||||
\(394\) | 43.5655 | 2.19480 | ||||||||
\(395\) | 1.23137 | 0.0619569 | ||||||||
\(396\) | −3.35656 | −0.168673 | ||||||||
\(397\) | −1.51398 | −0.0759846 | −0.0379923 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379923 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(398\) | 27.9438 | 1.40070 | ||||||||
\(399\) | 2.44792 | 0.122549 | ||||||||
\(400\) | 19.8857 | 0.994284 | ||||||||
\(401\) | 34.0918 | 1.70246 | 0.851232 | − | 0.524790i | \(-0.175856\pi\) | ||||
0.851232 | + | 0.524790i | \(0.175856\pi\) | |||||||
\(402\) | −14.5821 | −0.727287 | ||||||||
\(403\) | 27.2808 | 1.35895 | ||||||||
\(404\) | 18.7278 | 0.931743 | ||||||||
\(405\) | 5.44022 | 0.270326 | ||||||||
\(406\) | −26.7347 | −1.32682 | ||||||||
\(407\) | 0.573024 | 0.0284037 | ||||||||
\(408\) | −1.69590 | −0.0839597 | ||||||||
\(409\) | −30.4921 | −1.50774 | −0.753869 | − | 0.657024i | \(-0.771815\pi\) | ||||
−0.753869 | + | 0.657024i | \(0.771815\pi\) | |||||||
\(410\) | 6.62534 | 0.327202 | ||||||||
\(411\) | −19.6619 | −0.969849 | ||||||||
\(412\) | 18.1399 | 0.893689 | ||||||||
\(413\) | −20.8180 | −1.02439 | ||||||||
\(414\) | 3.84536 | 0.188989 | ||||||||
\(415\) | 7.56658 | 0.371429 | ||||||||
\(416\) | −26.2015 | −1.28464 | ||||||||
\(417\) | −10.8023 | −0.528991 | ||||||||
\(418\) | −9.38033 | −0.458807 | ||||||||
\(419\) | 24.0107 | 1.17300 | 0.586499 | − | 0.809950i | \(-0.300506\pi\) | ||||
0.586499 | + | 0.809950i | \(0.300506\pi\) | |||||||
\(420\) | −3.05834 | −0.149231 | ||||||||
\(421\) | −23.6431 | −1.15230 | −0.576148 | − | 0.817346i | \(-0.695445\pi\) | ||||
−0.576148 | + | 0.817346i | \(0.695445\pi\) | |||||||
\(422\) | −1.93894 | −0.0943862 | ||||||||
\(423\) | 1.72576 | 0.0839092 | ||||||||
\(424\) | −1.30715 | −0.0634809 | ||||||||
\(425\) | −10.1289 | −0.491322 | ||||||||
\(426\) | 14.8107 | 0.717579 | ||||||||
\(427\) | −8.48537 | −0.410636 | ||||||||
\(428\) | −19.8772 | −0.960799 | ||||||||
\(429\) | 26.7696 | 1.29245 | ||||||||
\(430\) | 10.8435 | 0.522919 | ||||||||
\(431\) | −35.5519 | −1.71247 | −0.856237 | − | 0.516583i | \(-0.827204\pi\) | ||||
−0.856237 | + | 0.516583i | \(0.827204\pi\) | |||||||
\(432\) | −24.2352 | −1.16602 | ||||||||
\(433\) | −22.7300 | −1.09233 | −0.546166 | − | 0.837677i | \(-0.683913\pi\) | ||||
−0.546166 | + | 0.837677i | \(0.683913\pi\) | |||||||
\(434\) | −23.4008 | −1.12327 | ||||||||
\(435\) | −10.4216 | −0.499678 | ||||||||
\(436\) | −14.8375 | −0.710588 | ||||||||
\(437\) | 5.02944 | 0.240591 | ||||||||
\(438\) | 26.0085 | 1.24274 | ||||||||
\(439\) | −34.1119 | −1.62807 | −0.814036 | − | 0.580814i | \(-0.802734\pi\) | ||||
−0.814036 | + | 0.580814i | \(0.802734\pi\) | |||||||
\(440\) | −1.60192 | −0.0763684 | ||||||||
\(441\) | 1.85343 | 0.0882587 | ||||||||
\(442\) | 14.9743 | 0.712255 | ||||||||
\(443\) | −27.3154 | −1.29779 | −0.648897 | − | 0.760876i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760876i | \(0.724769\pi\) | |||||||
\(444\) | −0.336409 | −0.0159653 | ||||||||
\(445\) | 0.124969 | 0.00592408 | ||||||||
\(446\) | −43.4356 | −2.05674 | ||||||||
\(447\) | −24.2378 | −1.14641 | ||||||||
\(448\) | 9.05974 | 0.428033 | ||||||||
\(449\) | −26.5782 | −1.25430 | −0.627151 | − | 0.778897i | \(-0.715779\pi\) | ||||
−0.627151 | + | 0.778897i | \(0.715779\pi\) | |||||||
\(450\) | −3.43736 | −0.162038 | ||||||||
\(451\) | 23.2807 | 1.09625 | ||||||||
\(452\) | 3.21245 | 0.151101 | ||||||||
\(453\) | 2.57239 | 0.120862 | ||||||||
\(454\) | −8.23067 | −0.386284 | ||||||||
\(455\) | −3.69117 | −0.173045 | ||||||||
\(456\) | −0.752744 | −0.0352505 | ||||||||
\(457\) | −11.0655 | −0.517624 | −0.258812 | − | 0.965928i | \(-0.583331\pi\) | ||||
−0.258812 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(458\) | −48.4252 | −2.26276 | ||||||||
\(459\) | 12.3443 | 0.576184 | ||||||||
\(460\) | −6.28360 | −0.292974 | ||||||||
\(461\) | 20.9443 | 0.975473 | 0.487737 | − | 0.872991i | \(-0.337823\pi\) | ||||
0.487737 | + | 0.872991i | \(0.337823\pi\) | |||||||
\(462\) | −22.9623 | −1.06830 | ||||||||
\(463\) | −30.7131 | −1.42736 | −0.713680 | − | 0.700472i | \(-0.752973\pi\) | ||||
−0.713680 | + | 0.700472i | \(0.752973\pi\) | |||||||
\(464\) | 40.2168 | 1.86702 | ||||||||
\(465\) | −9.12199 | −0.423022 | ||||||||
\(466\) | 18.2685 | 0.846273 | ||||||||
\(467\) | −15.3672 | −0.711111 | −0.355555 | − | 0.934655i | \(-0.615708\pi\) | ||||
−0.355555 | + | 0.934655i | \(0.615708\pi\) | |||||||
\(468\) | 2.37831 | 0.109937 | ||||||||
\(469\) | 7.06530 | 0.326245 | ||||||||
\(470\) | −6.02549 | −0.277935 | ||||||||
\(471\) | 29.8178 | 1.37393 | ||||||||
\(472\) | 6.40161 | 0.294658 | ||||||||
\(473\) | 38.1028 | 1.75197 | ||||||||
\(474\) | −5.42767 | −0.249301 | ||||||||
\(475\) | −4.49580 | −0.206282 | ||||||||
\(476\) | −6.01144 | −0.275534 | ||||||||
\(477\) | 1.10533 | 0.0506095 | ||||||||
\(478\) | 31.6043 | 1.44555 | ||||||||
\(479\) | −21.2338 | −0.970196 | −0.485098 | − | 0.874460i | \(-0.661216\pi\) | ||||
−0.485098 | + | 0.874460i | \(0.661216\pi\) | |||||||
\(480\) | 8.76111 | 0.399888 | ||||||||
\(481\) | −0.406020 | −0.0185129 | ||||||||
\(482\) | 24.7935 | 1.12931 | ||||||||
\(483\) | 12.3117 | 0.560200 | ||||||||
\(484\) | 21.8264 | 0.992107 | ||||||||
\(485\) | 4.42886 | 0.201104 | ||||||||
\(486\) | 7.89173 | 0.357976 | ||||||||
\(487\) | −16.8974 | −0.765696 | −0.382848 | − | 0.923811i | \(-0.625057\pi\) | ||||
−0.382848 | + | 0.923811i | \(0.625057\pi\) | |||||||
\(488\) | 2.60928 | 0.118117 | ||||||||
\(489\) | −31.2274 | −1.41215 | ||||||||
\(490\) | −6.47127 | −0.292342 | ||||||||
\(491\) | −22.5677 | −1.01847 | −0.509234 | − | 0.860628i | \(-0.670071\pi\) | ||||
−0.509234 | + | 0.860628i | \(0.670071\pi\) | |||||||
\(492\) | −13.6676 | −0.616182 | ||||||||
\(493\) | −20.4846 | −0.922582 | ||||||||
\(494\) | 6.64650 | 0.299040 | ||||||||
\(495\) | 1.35458 | 0.0608840 | ||||||||
\(496\) | 35.2016 | 1.58060 | ||||||||
\(497\) | −7.17605 | −0.321890 | ||||||||
\(498\) | −33.3522 | −1.49455 | ||||||||
\(499\) | −13.4511 | −0.602156 | −0.301078 | − | 0.953600i | \(-0.597346\pi\) | ||||
−0.301078 | + | 0.953600i | \(0.597346\pi\) | |||||||
\(500\) | 11.8637 | 0.530561 | ||||||||
\(501\) | −36.2057 | −1.61755 | ||||||||
\(502\) | 45.9159 | 2.04933 | ||||||||
\(503\) | −4.75979 | −0.212228 | −0.106114 | − | 0.994354i | \(-0.533841\pi\) | ||||
−0.106114 | + | 0.994354i | \(0.533841\pi\) | |||||||
\(504\) | 0.278853 | 0.0124211 | ||||||||
\(505\) | −7.55786 | −0.336320 | ||||||||
\(506\) | −47.1778 | −2.09731 | ||||||||
\(507\) | 2.01697 | 0.0895768 | ||||||||
\(508\) | 32.7937 | 1.45499 | ||||||||
\(509\) | −1.27382 | −0.0564612 | −0.0282306 | − | 0.999601i | \(-0.508987\pi\) | ||||
−0.0282306 | + | 0.999601i | \(0.508987\pi\) | |||||||
\(510\) | −5.00702 | −0.221714 | ||||||||
\(511\) | −12.6017 | −0.557464 | ||||||||
\(512\) | −29.6837 | −1.31185 | ||||||||
\(513\) | 5.47915 | 0.241911 | ||||||||
\(514\) | 6.56322 | 0.289491 | ||||||||
\(515\) | −7.32060 | −0.322584 | ||||||||
\(516\) | −22.3693 | −0.984753 | ||||||||
\(517\) | −21.1729 | −0.931184 | ||||||||
\(518\) | 0.348274 | 0.0153023 | ||||||||
\(519\) | 10.6068 | 0.465589 | ||||||||
\(520\) | 1.13505 | 0.0497752 | ||||||||
\(521\) | −12.1115 | −0.530616 | −0.265308 | − | 0.964164i | \(-0.585474\pi\) | ||||
−0.265308 | + | 0.964164i | \(0.585474\pi\) | |||||||
\(522\) | −6.95171 | −0.304268 | ||||||||
\(523\) | 35.7349 | 1.56258 | 0.781288 | − | 0.624170i | \(-0.214563\pi\) | ||||
0.781288 | + | 0.624170i | \(0.214563\pi\) | |||||||
\(524\) | 23.0428 | 1.00663 | ||||||||
\(525\) | −11.0054 | −0.480313 | ||||||||
\(526\) | −53.3089 | −2.32438 | ||||||||
\(527\) | −17.9301 | −0.781048 | ||||||||
\(528\) | 34.5419 | 1.50325 | ||||||||
\(529\) | 2.29530 | 0.0997956 | ||||||||
\(530\) | −3.85926 | −0.167635 | ||||||||
\(531\) | −5.41321 | −0.234913 | ||||||||
\(532\) | −2.66824 | −0.115683 | ||||||||
\(533\) | −16.4957 | −0.714509 | ||||||||
\(534\) | −0.550841 | −0.0238372 | ||||||||
\(535\) | 8.02170 | 0.346808 | ||||||||
\(536\) | −2.17261 | −0.0938423 | ||||||||
\(537\) | 31.3193 | 1.35153 | ||||||||
\(538\) | 50.6129 | 2.18208 | ||||||||
\(539\) | −22.7393 | −0.979453 | ||||||||
\(540\) | −6.84545 | −0.294581 | ||||||||
\(541\) | 1.29855 | 0.0558291 | 0.0279145 | − | 0.999610i | \(-0.491113\pi\) | ||||
0.0279145 | + | 0.999610i | \(0.491113\pi\) | |||||||
\(542\) | 38.2877 | 1.64460 | ||||||||
\(543\) | 35.5985 | 1.52768 | ||||||||
\(544\) | 17.2208 | 0.738334 | ||||||||
\(545\) | 5.98788 | 0.256492 | ||||||||
\(546\) | 16.2701 | 0.696295 | ||||||||
\(547\) | −25.5778 | −1.09363 | −0.546814 | − | 0.837254i | \(-0.684160\pi\) | ||||
−0.546814 | + | 0.837254i | \(0.684160\pi\) | |||||||
\(548\) | 21.4315 | 0.915509 | ||||||||
\(549\) | −2.20641 | −0.0941674 | ||||||||
\(550\) | 42.1721 | 1.79823 | ||||||||
\(551\) | −9.09232 | −0.387346 | ||||||||
\(552\) | −3.78588 | −0.161138 | ||||||||
\(553\) | 2.62981 | 0.111831 | ||||||||
\(554\) | −44.5047 | −1.89082 | ||||||||
\(555\) | 0.135762 | 0.00576280 | ||||||||
\(556\) | 11.7746 | 0.499353 | ||||||||
\(557\) | −39.8206 | −1.68725 | −0.843626 | − | 0.536931i | \(-0.819583\pi\) | ||||
−0.843626 | + | 0.536931i | \(0.819583\pi\) | |||||||
\(558\) | −6.08480 | −0.257590 | ||||||||
\(559\) | −26.9980 | −1.14189 | ||||||||
\(560\) | −4.76288 | −0.201268 | ||||||||
\(561\) | −17.5941 | −0.742824 | ||||||||
\(562\) | 27.1909 | 1.14698 | ||||||||
\(563\) | 11.4528 | 0.482680 | 0.241340 | − | 0.970441i | \(-0.422413\pi\) | ||||
0.241340 | + | 0.970441i | \(0.422413\pi\) | |||||||
\(564\) | 12.4301 | 0.523403 | ||||||||
\(565\) | −1.29643 | −0.0545411 | ||||||||
\(566\) | 28.0749 | 1.18008 | ||||||||
\(567\) | 11.6186 | 0.487934 | ||||||||
\(568\) | 2.20666 | 0.0925895 | ||||||||
\(569\) | −2.46885 | −0.103500 | −0.0517498 | − | 0.998660i | \(-0.516480\pi\) | ||||
−0.0517498 | + | 0.998660i | \(0.516480\pi\) | |||||||
\(570\) | −2.22241 | −0.0930867 | ||||||||
\(571\) | −28.1346 | −1.17739 | −0.588697 | − | 0.808354i | \(-0.700359\pi\) | ||||
−0.588697 | + | 0.808354i | \(0.700359\pi\) | |||||||
\(572\) | −29.1789 | −1.22003 | ||||||||
\(573\) | −9.26561 | −0.387076 | ||||||||
\(574\) | 14.1496 | 0.590593 | ||||||||
\(575\) | −22.6114 | −0.942960 | ||||||||
\(576\) | 2.35576 | 0.0981568 | ||||||||
\(577\) | 20.2880 | 0.844603 | 0.422301 | − | 0.906456i | \(-0.361222\pi\) | ||||
0.422301 | + | 0.906456i | \(0.361222\pi\) | |||||||
\(578\) | 23.1203 | 0.961676 | ||||||||
\(579\) | −20.2948 | −0.843423 | ||||||||
\(580\) | 11.3596 | 0.471682 | ||||||||
\(581\) | 16.1598 | 0.670422 | ||||||||
\(582\) | −19.5217 | −0.809199 | ||||||||
\(583\) | −13.5610 | −0.561640 | ||||||||
\(584\) | 3.87506 | 0.160351 | ||||||||
\(585\) | −0.959799 | −0.0396828 | ||||||||
\(586\) | 51.2634 | 2.11767 | ||||||||
\(587\) | 15.9598 | 0.658730 | 0.329365 | − | 0.944203i | \(-0.393165\pi\) | ||||
0.329365 | + | 0.944203i | \(0.393165\pi\) | |||||||
\(588\) | 13.3498 | 0.550535 | ||||||||
\(589\) | −7.95846 | −0.327923 | ||||||||
\(590\) | 18.9002 | 0.778111 | ||||||||
\(591\) | 36.2692 | 1.49192 | ||||||||
\(592\) | −0.523905 | −0.0215324 | ||||||||
\(593\) | 15.8008 | 0.648860 | 0.324430 | − | 0.945910i | \(-0.394827\pi\) | ||||
0.324430 | + | 0.945910i | \(0.394827\pi\) | |||||||
\(594\) | −51.3963 | −2.10881 | ||||||||
\(595\) | 2.42600 | 0.0994562 | ||||||||
\(596\) | 26.4193 | 1.08218 | ||||||||
\(597\) | 23.2638 | 0.952125 | ||||||||
\(598\) | 33.4282 | 1.36698 | ||||||||
\(599\) | −4.63147 | −0.189237 | −0.0946184 | − | 0.995514i | \(-0.530163\pi\) | ||||
−0.0946184 | + | 0.995514i | \(0.530163\pi\) | |||||||
\(600\) | 3.38419 | 0.138159 | ||||||||
\(601\) | −12.3540 | −0.503929 | −0.251964 | − | 0.967737i | \(-0.581077\pi\) | ||||
−0.251964 | + | 0.967737i | \(0.581077\pi\) | |||||||
\(602\) | 23.1582 | 0.943858 | ||||||||
\(603\) | 1.83716 | 0.0748148 | ||||||||
\(604\) | −2.80392 | −0.114090 | ||||||||
\(605\) | −8.80832 | −0.358109 | ||||||||
\(606\) | 33.3138 | 1.35328 | ||||||||
\(607\) | −11.3892 | −0.462274 | −0.231137 | − | 0.972921i | \(-0.574245\pi\) | ||||
−0.231137 | + | 0.972921i | \(0.574245\pi\) | |||||||
\(608\) | 7.64362 | 0.309990 | ||||||||
\(609\) | −22.2572 | −0.901909 | ||||||||
\(610\) | 7.70370 | 0.311914 | ||||||||
\(611\) | 15.0022 | 0.606925 | ||||||||
\(612\) | −1.56313 | −0.0631857 | ||||||||
\(613\) | 10.3331 | 0.417350 | 0.208675 | − | 0.977985i | \(-0.433085\pi\) | ||||
0.208675 | + | 0.977985i | \(0.433085\pi\) | |||||||
\(614\) | 4.14996 | 0.167479 | ||||||||
\(615\) | 5.51573 | 0.222416 | ||||||||
\(616\) | −3.42119 | −0.137844 | ||||||||
\(617\) | −5.53466 | −0.222817 | −0.111408 | − | 0.993775i | \(-0.535536\pi\) | ||||
−0.111408 | + | 0.993775i | \(0.535536\pi\) | |||||||
\(618\) | 32.2680 | 1.29801 | ||||||||
\(619\) | 14.9342 | 0.600256 | 0.300128 | − | 0.953899i | \(-0.402971\pi\) | ||||
0.300128 | + | 0.953899i | \(0.402971\pi\) | |||||||
\(620\) | 9.94300 | 0.399321 | ||||||||
\(621\) | 27.5571 | 1.10583 | ||||||||
\(622\) | 32.5939 | 1.30690 | ||||||||
\(623\) | 0.266893 | 0.0106928 | ||||||||
\(624\) | −24.4749 | −0.979781 | ||||||||
\(625\) | 17.6913 | 0.707650 | ||||||||
\(626\) | −37.2314 | −1.48807 | ||||||||
\(627\) | −7.80933 | −0.311874 | ||||||||
\(628\) | −32.5015 | −1.29695 | ||||||||
\(629\) | 0.266854 | 0.0106402 | ||||||||
\(630\) | 0.823292 | 0.0328007 | ||||||||
\(631\) | −22.5759 | −0.898732 | −0.449366 | − | 0.893348i | \(-0.648350\pi\) | ||||
−0.449366 | + | 0.893348i | \(0.648350\pi\) | |||||||
\(632\) | −0.808677 | −0.0321674 | ||||||||
\(633\) | −1.61421 | −0.0641591 | ||||||||
\(634\) | 13.9296 | 0.553214 | ||||||||
\(635\) | −13.2343 | −0.525189 | ||||||||
\(636\) | 7.96136 | 0.315689 | ||||||||
\(637\) | 16.1121 | 0.638385 | ||||||||
\(638\) | 85.2889 | 3.37662 | ||||||||
\(639\) | −1.86596 | −0.0738161 | ||||||||
\(640\) | 2.62982 | 0.103953 | ||||||||
\(641\) | 7.33130 | 0.289569 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(642\) | −35.3583 | −1.39548 | ||||||||
\(643\) | 31.4635 | 1.24080 | 0.620399 | − | 0.784286i | \(-0.286971\pi\) | ||||
0.620399 | + | 0.784286i | \(0.286971\pi\) | |||||||
\(644\) | −13.4198 | −0.528813 | ||||||||
\(645\) | 9.02743 | 0.355455 | ||||||||
\(646\) | −4.36836 | −0.171871 | ||||||||
\(647\) | −32.1732 | −1.26486 | −0.632429 | − | 0.774618i | \(-0.717942\pi\) | ||||
−0.632429 | + | 0.774618i | \(0.717942\pi\) | |||||||
\(648\) | −3.57275 | −0.140351 | ||||||||
\(649\) | 66.4134 | 2.60695 | ||||||||
\(650\) | −29.8813 | −1.17204 | ||||||||
\(651\) | −19.4817 | −0.763546 | ||||||||
\(652\) | 34.0380 | 1.33303 | ||||||||
\(653\) | −40.2209 | −1.57396 | −0.786982 | − | 0.616976i | \(-0.788358\pi\) | ||||
−0.786982 | + | 0.616976i | \(0.788358\pi\) | |||||||
\(654\) | −26.3936 | −1.03207 | ||||||||
\(655\) | −9.29925 | −0.363352 | ||||||||
\(656\) | −21.2851 | −0.831045 | ||||||||
\(657\) | −3.27675 | −0.127838 | ||||||||
\(658\) | −12.8685 | −0.501667 | ||||||||
\(659\) | −41.6504 | −1.62247 | −0.811235 | − | 0.584720i | \(-0.801204\pi\) | ||||
−0.811235 | + | 0.584720i | \(0.801204\pi\) | |||||||
\(660\) | 9.75668 | 0.379778 | ||||||||
\(661\) | −15.5677 | −0.605513 | −0.302757 | − | 0.953068i | \(-0.597907\pi\) | ||||
−0.302757 | + | 0.953068i | \(0.597907\pi\) | |||||||
\(662\) | 42.9775 | 1.67037 | ||||||||
\(663\) | 12.4664 | 0.484156 | ||||||||
\(664\) | −4.96920 | −0.192842 | ||||||||
\(665\) | 1.07680 | 0.0417567 | ||||||||
\(666\) | 0.0905600 | 0.00350913 | ||||||||
\(667\) | −45.7293 | −1.77064 | ||||||||
\(668\) | 39.4643 | 1.52692 | ||||||||
\(669\) | −36.1611 | −1.39807 | ||||||||
\(670\) | −6.41444 | −0.247811 | ||||||||
\(671\) | 27.0700 | 1.04502 | ||||||||
\(672\) | 18.7109 | 0.721790 | ||||||||
\(673\) | −21.7671 | −0.839059 | −0.419530 | − | 0.907742i | \(-0.637805\pi\) | ||||
−0.419530 | + | 0.907742i | \(0.637805\pi\) | |||||||
\(674\) | −40.7311 | −1.56890 | ||||||||
\(675\) | −24.6332 | −0.948132 | ||||||||
\(676\) | −2.19851 | −0.0845579 | ||||||||
\(677\) | 14.2408 | 0.547319 | 0.273659 | − | 0.961827i | \(-0.411766\pi\) | ||||
0.273659 | + | 0.961827i | \(0.411766\pi\) | |||||||
\(678\) | 5.71443 | 0.219461 | ||||||||
\(679\) | 9.45863 | 0.362989 | ||||||||
\(680\) | −0.746003 | −0.0286079 | ||||||||
\(681\) | −6.85221 | −0.262577 | ||||||||
\(682\) | 74.6530 | 2.85861 | ||||||||
\(683\) | −27.6097 | −1.05646 | −0.528228 | − | 0.849102i | \(-0.677144\pi\) | ||||
−0.528228 | + | 0.849102i | \(0.677144\pi\) | |||||||
\(684\) | −0.693810 | −0.0265285 | ||||||||
\(685\) | −8.64898 | −0.330460 | ||||||||
\(686\) | −34.4031 | −1.31352 | ||||||||
\(687\) | −40.3150 | −1.53811 | ||||||||
\(688\) | −34.8367 | −1.32814 | ||||||||
\(689\) | 9.60875 | 0.366064 | ||||||||
\(690\) | −11.1775 | −0.425521 | ||||||||
\(691\) | 30.2222 | 1.14971 | 0.574854 | − | 0.818256i | \(-0.305059\pi\) | ||||
0.574854 | + | 0.818256i | \(0.305059\pi\) | |||||||
\(692\) | −11.5615 | −0.439503 | ||||||||
\(693\) | 2.89296 | 0.109894 | ||||||||
\(694\) | −19.1058 | −0.725246 | ||||||||
\(695\) | −4.75178 | −0.180245 | ||||||||
\(696\) | 6.84418 | 0.259428 | ||||||||
\(697\) | 10.8417 | 0.410658 | ||||||||
\(698\) | 28.0090 | 1.06016 | ||||||||
\(699\) | 15.2089 | 0.575255 | ||||||||
\(700\) | 11.9959 | 0.453402 | ||||||||
\(701\) | 49.8089 | 1.88126 | 0.940628 | − | 0.339438i | \(-0.110237\pi\) | ||||
0.940628 | + | 0.339438i | \(0.110237\pi\) | |||||||
\(702\) | 36.4172 | 1.37448 | ||||||||
\(703\) | 0.118446 | 0.00446727 | ||||||||
\(704\) | −28.9023 | −1.08930 | ||||||||
\(705\) | −5.01635 | −0.188927 | ||||||||
\(706\) | −7.46954 | −0.281120 | ||||||||
\(707\) | −16.1412 | −0.607051 | ||||||||
\(708\) | −38.9898 | −1.46533 | ||||||||
\(709\) | 33.8181 | 1.27007 | 0.635033 | − | 0.772485i | \(-0.280987\pi\) | ||||
0.635033 | + | 0.772485i | \(0.280987\pi\) | |||||||
\(710\) | 6.51499 | 0.244503 | ||||||||
\(711\) | 0.683818 | 0.0256452 | ||||||||
\(712\) | −0.0820706 | −0.00307573 | ||||||||
\(713\) | −40.0266 | −1.49901 | ||||||||
\(714\) | −10.6934 | −0.400190 | ||||||||
\(715\) | 11.7756 | 0.440381 | ||||||||
\(716\) | −34.1382 | −1.27580 | ||||||||
\(717\) | 26.3113 | 0.982613 | ||||||||
\(718\) | 30.8906 | 1.15283 | ||||||||
\(719\) | −18.0136 | −0.671794 | −0.335897 | − | 0.941899i | \(-0.609039\pi\) | ||||
−0.335897 | + | 0.941899i | \(0.609039\pi\) | |||||||
\(720\) | −1.23847 | −0.0461551 | ||||||||
\(721\) | −15.6345 | −0.582258 | ||||||||
\(722\) | −1.93894 | −0.0721599 | ||||||||
\(723\) | 20.6411 | 0.767650 | ||||||||
\(724\) | −38.8025 | −1.44208 | ||||||||
\(725\) | 40.8773 | 1.51814 | ||||||||
\(726\) | 38.8256 | 1.44095 | ||||||||
\(727\) | 27.6422 | 1.02519 | 0.512595 | − | 0.858630i | \(-0.328684\pi\) | ||||
0.512595 | + | 0.858630i | \(0.328684\pi\) | |||||||
\(728\) | 2.42411 | 0.0898433 | ||||||||
\(729\) | 29.5547 | 1.09462 | ||||||||
\(730\) | 11.4408 | 0.423442 | ||||||||
\(731\) | 17.7442 | 0.656295 | ||||||||
\(732\) | −15.8922 | −0.587391 | ||||||||
\(733\) | 32.4675 | 1.19922 | 0.599608 | − | 0.800294i | \(-0.295323\pi\) | ||||
0.599608 | + | 0.800294i | \(0.295323\pi\) | |||||||
\(734\) | 49.4443 | 1.82502 | ||||||||
\(735\) | −5.38747 | −0.198720 | ||||||||
\(736\) | 38.4431 | 1.41703 | ||||||||
\(737\) | −22.5397 | −0.830259 | ||||||||
\(738\) | 3.67926 | 0.135435 | ||||||||
\(739\) | 8.02656 | 0.295262 | 0.147631 | − | 0.989043i | \(-0.452835\pi\) | ||||
0.147631 | + | 0.989043i | \(0.452835\pi\) | |||||||
\(740\) | −0.147982 | −0.00543991 | ||||||||
\(741\) | 5.53335 | 0.203273 | ||||||||
\(742\) | −8.24214 | −0.302579 | ||||||||
\(743\) | 45.1744 | 1.65729 | 0.828644 | − | 0.559776i | \(-0.189113\pi\) | ||||
0.828644 | + | 0.559776i | \(0.189113\pi\) | |||||||
\(744\) | 5.99068 | 0.219629 | ||||||||
\(745\) | −10.6619 | −0.390621 | ||||||||
\(746\) | −55.2295 | −2.02210 | ||||||||
\(747\) | 4.20196 | 0.153742 | ||||||||
\(748\) | 19.1776 | 0.701204 | ||||||||
\(749\) | 17.1318 | 0.625982 | ||||||||
\(750\) | 21.1036 | 0.770595 | ||||||||
\(751\) | 29.4782 | 1.07568 | 0.537838 | − | 0.843048i | \(-0.319241\pi\) | ||||
0.537838 | + | 0.843048i | \(0.319241\pi\) | |||||||
\(752\) | 19.3580 | 0.705914 | ||||||||
\(753\) | 38.2260 | 1.39303 | ||||||||
\(754\) | −60.4321 | −2.20081 | ||||||||
\(755\) | 1.13156 | 0.0411816 | ||||||||
\(756\) | −14.6197 | −0.531713 | ||||||||
\(757\) | −22.6655 | −0.823793 | −0.411896 | − | 0.911231i | \(-0.635133\pi\) | ||||
−0.411896 | + | 0.911231i | \(0.635133\pi\) | |||||||
\(758\) | −31.7152 | −1.15195 | ||||||||
\(759\) | −39.2766 | −1.42565 | ||||||||
\(760\) | −0.331121 | −0.0120110 | ||||||||
\(761\) | 23.1047 | 0.837543 | 0.418772 | − | 0.908092i | \(-0.362461\pi\) | ||||
0.418772 | + | 0.908092i | \(0.362461\pi\) | |||||||
\(762\) | 58.3348 | 2.11325 | ||||||||
\(763\) | 12.7882 | 0.462964 | ||||||||
\(764\) | 10.0996 | 0.365389 | ||||||||
\(765\) | 0.630821 | 0.0228074 | ||||||||
\(766\) | 7.68401 | 0.277635 | ||||||||
\(767\) | −47.0577 | −1.69915 | ||||||||
\(768\) | −30.8790 | −1.11425 | ||||||||
\(769\) | 20.8502 | 0.751877 | 0.375939 | − | 0.926645i | \(-0.377320\pi\) | ||||
0.375939 | + | 0.926645i | \(0.377320\pi\) | |||||||
\(770\) | −10.1008 | −0.364007 | ||||||||
\(771\) | 5.46402 | 0.196782 | ||||||||
\(772\) | 22.1214 | 0.796167 | ||||||||
\(773\) | 34.7891 | 1.25128 | 0.625639 | − | 0.780113i | \(-0.284838\pi\) | ||||
0.625639 | + | 0.780113i | \(0.284838\pi\) | |||||||
\(774\) | 6.02172 | 0.216446 | ||||||||
\(775\) | 35.7797 | 1.28524 | ||||||||
\(776\) | −2.90857 | −0.104411 | ||||||||
\(777\) | 0.289945 | 0.0104017 | ||||||||
\(778\) | −5.17701 | −0.185605 | ||||||||
\(779\) | 4.81219 | 0.172415 | ||||||||
\(780\) | −6.91316 | −0.247531 | ||||||||
\(781\) | 22.8930 | 0.819175 | ||||||||
\(782\) | −21.9704 | −0.785661 | ||||||||
\(783\) | −49.8182 | −1.78036 | ||||||||
\(784\) | 20.7902 | 0.742506 | ||||||||
\(785\) | 13.1164 | 0.468145 | ||||||||
\(786\) | 40.9895 | 1.46205 | ||||||||
\(787\) | −9.81657 | −0.349923 | −0.174961 | − | 0.984575i | \(-0.555980\pi\) | ||||
−0.174961 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(788\) | −39.5336 | −1.40832 | ||||||||
\(789\) | −44.3808 | −1.58000 | ||||||||
\(790\) | −2.38755 | −0.0849453 | ||||||||
\(791\) | −2.76875 | −0.0984456 | ||||||||
\(792\) | −0.889596 | −0.0316104 | ||||||||
\(793\) | −19.1806 | −0.681123 | ||||||||
\(794\) | 2.93552 | 0.104178 | ||||||||
\(795\) | −3.21291 | −0.113950 | ||||||||
\(796\) | −25.3577 | −0.898778 | ||||||||
\(797\) | 29.2697 | 1.03679 | 0.518393 | − | 0.855143i | \(-0.326531\pi\) | ||||
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(798\) | −4.74637 | −0.168020 | ||||||||
\(799\) | −9.86010 | −0.348825 | ||||||||
\(800\) | −34.3642 | −1.21496 | ||||||||
\(801\) | 0.0693990 | 0.00245209 | ||||||||
\(802\) | −66.1020 | −2.33414 | ||||||||
\(803\) | 40.2017 | 1.41869 | ||||||||
\(804\) | 13.2325 | 0.466675 | ||||||||
\(805\) | 5.41572 | 0.190879 | ||||||||
\(806\) | −52.8959 | −1.86318 | ||||||||
\(807\) | 42.1364 | 1.48327 | ||||||||
\(808\) | 4.96347 | 0.174614 | ||||||||
\(809\) | 44.9580 | 1.58064 | 0.790320 | − | 0.612695i | \(-0.209915\pi\) | ||||
0.790320 | + | 0.612695i | \(0.209915\pi\) | |||||||
\(810\) | −10.5483 | −0.370628 | ||||||||
\(811\) | 12.0436 | 0.422908 | 0.211454 | − | 0.977388i | \(-0.432180\pi\) | ||||
0.211454 | + | 0.977388i | \(0.432180\pi\) | |||||||
\(812\) | 24.2605 | 0.851376 | ||||||||
\(813\) | 31.8753 | 1.11792 | ||||||||
\(814\) | −1.11106 | −0.0389426 | ||||||||
\(815\) | −13.7365 | −0.481168 | ||||||||
\(816\) | 16.0860 | 0.563122 | ||||||||
\(817\) | 7.87596 | 0.275545 | ||||||||
\(818\) | 59.1225 | 2.06717 | ||||||||
\(819\) | −2.04983 | −0.0716267 | ||||||||
\(820\) | −6.01217 | −0.209954 | ||||||||
\(821\) | 9.76338 | 0.340744 | 0.170372 | − | 0.985380i | \(-0.445503\pi\) | ||||
0.170372 | + | 0.985380i | \(0.445503\pi\) | |||||||
\(822\) | 38.1232 | 1.32970 | ||||||||
\(823\) | 6.09808 | 0.212566 | 0.106283 | − | 0.994336i | \(-0.466105\pi\) | ||||
0.106283 | + | 0.994336i | \(0.466105\pi\) | |||||||
\(824\) | 4.80766 | 0.167483 | ||||||||
\(825\) | 35.1092 | 1.22235 | ||||||||
\(826\) | 40.3649 | 1.40447 | ||||||||
\(827\) | 7.68780 | 0.267331 | 0.133666 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133666 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(828\) | −3.48948 | −0.121268 | ||||||||
\(829\) | −41.3837 | −1.43731 | −0.718657 | − | 0.695365i | \(-0.755243\pi\) | ||||
−0.718657 | + | 0.695365i | \(0.755243\pi\) | |||||||
\(830\) | −14.6712 | −0.509243 | ||||||||
\(831\) | −37.0511 | −1.28529 | ||||||||
\(832\) | 20.4789 | 0.709979 | ||||||||
\(833\) | −10.5896 | −0.366907 | ||||||||
\(834\) | 20.9451 | 0.725268 | ||||||||
\(835\) | −15.9264 | −0.551154 | ||||||||
\(836\) | 8.51220 | 0.294400 | ||||||||
\(837\) | −43.6056 | −1.50723 | ||||||||
\(838\) | −46.5553 | −1.60823 | ||||||||
\(839\) | −26.4281 | −0.912399 | −0.456199 | − | 0.889878i | \(-0.650790\pi\) | ||||
−0.456199 | + | 0.889878i | \(0.650790\pi\) | |||||||
\(840\) | −0.810557 | −0.0279669 | ||||||||
\(841\) | 53.6702 | 1.85070 | ||||||||
\(842\) | 45.8426 | 1.57984 | ||||||||
\(843\) | 22.6370 | 0.779660 | ||||||||
\(844\) | 1.75950 | 0.0605644 | ||||||||
\(845\) | 0.887237 | 0.0305219 | ||||||||
\(846\) | −3.34614 | −0.115043 | ||||||||
\(847\) | −18.8118 | −0.646380 | ||||||||
\(848\) | 12.3986 | 0.425769 | ||||||||
\(849\) | 23.3729 | 0.802157 | ||||||||
\(850\) | 19.6393 | 0.673622 | ||||||||
\(851\) | 0.595716 | 0.0204209 | ||||||||
\(852\) | −13.4400 | −0.460445 | ||||||||
\(853\) | 44.8321 | 1.53502 | 0.767510 | − | 0.641037i | \(-0.221495\pi\) | ||||
0.767510 | + | 0.641037i | \(0.221495\pi\) | |||||||
\(854\) | 16.4526 | 0.562998 | ||||||||
\(855\) | 0.279996 | 0.00957567 | ||||||||
\(856\) | −5.26809 | −0.180060 | ||||||||
\(857\) | 36.7482 | 1.25529 | 0.627647 | − | 0.778498i | \(-0.284018\pi\) | ||||
0.627647 | + | 0.778498i | \(0.284018\pi\) | |||||||
\(858\) | −51.9047 | −1.77200 | ||||||||
\(859\) | −43.4808 | −1.48355 | −0.741774 | − | 0.670650i | \(-0.766015\pi\) | ||||
−0.741774 | + | 0.670650i | \(0.766015\pi\) | |||||||
\(860\) | −9.83993 | −0.335539 | ||||||||
\(861\) | 11.7799 | 0.401456 | ||||||||
\(862\) | 68.9330 | 2.34787 | ||||||||
\(863\) | 9.85100 | 0.335332 | 0.167666 | − | 0.985844i | \(-0.446377\pi\) | ||||
0.167666 | + | 0.985844i | \(0.446377\pi\) | |||||||
\(864\) | 41.8805 | 1.42480 | ||||||||
\(865\) | 4.66580 | 0.158642 | ||||||||
\(866\) | 44.0721 | 1.49763 | ||||||||
\(867\) | 19.2481 | 0.653700 | ||||||||
\(868\) | 21.2351 | 0.720766 | ||||||||
\(869\) | −8.38960 | −0.284598 | ||||||||
\(870\) | 20.2069 | 0.685078 | ||||||||
\(871\) | 15.9706 | 0.541144 | ||||||||
\(872\) | −3.93242 | −0.133168 | ||||||||
\(873\) | 2.45949 | 0.0832410 | ||||||||
\(874\) | −9.75180 | −0.329860 | ||||||||
\(875\) | −10.2251 | −0.345672 | ||||||||
\(876\) | −23.6015 | −0.797421 | ||||||||
\(877\) | −46.1145 | −1.55718 | −0.778589 | − | 0.627534i | \(-0.784064\pi\) | ||||
−0.778589 | + | 0.627534i | \(0.784064\pi\) | |||||||
\(878\) | 66.1410 | 2.23215 | ||||||||
\(879\) | 42.6779 | 1.43949 | ||||||||
\(880\) | 15.1945 | 0.512207 | ||||||||
\(881\) | 18.8370 | 0.634634 | 0.317317 | − | 0.948319i | \(-0.397218\pi\) | ||||
0.317317 | + | 0.948319i | \(0.397218\pi\) | |||||||
\(882\) | −3.59370 | −0.121006 | ||||||||
\(883\) | 15.8320 | 0.532789 | 0.266394 | − | 0.963864i | \(-0.414168\pi\) | ||||
0.266394 | + | 0.963864i | \(0.414168\pi\) | |||||||
\(884\) | −13.5885 | −0.457029 | ||||||||
\(885\) | 15.7349 | 0.528921 | ||||||||
\(886\) | 52.9630 | 1.77933 | ||||||||
\(887\) | −38.9792 | −1.30879 | −0.654397 | − | 0.756151i | \(-0.727077\pi\) | ||||
−0.654397 | + | 0.756151i | \(0.727077\pi\) | |||||||
\(888\) | −0.0891593 | −0.00299199 | ||||||||
\(889\) | −28.2643 | −0.947956 | ||||||||
\(890\) | −0.242307 | −0.00812215 | ||||||||
\(891\) | −37.0655 | −1.24174 | ||||||||
\(892\) | 39.4157 | 1.31974 | ||||||||
\(893\) | −4.37650 | −0.146454 | ||||||||
\(894\) | 46.9957 | 1.57177 | ||||||||
\(895\) | 13.7769 | 0.460512 | ||||||||
\(896\) | 5.61645 | 0.187632 | ||||||||
\(897\) | 27.8297 | 0.929206 | ||||||||
\(898\) | 51.5336 | 1.71970 | ||||||||
\(899\) | 72.3609 | 2.41337 | ||||||||
\(900\) | 3.11923 | 0.103974 | ||||||||
\(901\) | −6.31528 | −0.210392 | ||||||||
\(902\) | −45.1400 | −1.50300 | ||||||||
\(903\) | 19.2797 | 0.641589 | ||||||||
\(904\) | 0.851402 | 0.0283172 | ||||||||
\(905\) | 15.6593 | 0.520532 | ||||||||
\(906\) | −4.98772 | −0.165706 | ||||||||
\(907\) | 16.2101 | 0.538246 | 0.269123 | − | 0.963106i | \(-0.413266\pi\) | ||||
0.269123 | + | 0.963106i | \(0.413266\pi\) | |||||||
\(908\) | 7.46893 | 0.247865 | ||||||||
\(909\) | −4.19712 | −0.139210 | ||||||||
\(910\) | 7.15697 | 0.237251 | ||||||||
\(911\) | −1.93959 | −0.0642616 | −0.0321308 | − | 0.999484i | \(-0.510229\pi\) | ||||
−0.0321308 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(912\) | 7.13992 | 0.236426 | ||||||||
\(913\) | −51.5529 | −1.70615 | ||||||||
\(914\) | 21.4554 | 0.709683 | ||||||||
\(915\) | 6.41349 | 0.212024 | ||||||||
\(916\) | 43.9435 | 1.45193 | ||||||||
\(917\) | −19.8602 | −0.655843 | ||||||||
\(918\) | −23.9349 | −0.789970 | ||||||||
\(919\) | −14.6607 | −0.483613 | −0.241807 | − | 0.970324i | \(-0.577740\pi\) | ||||
−0.241807 | + | 0.970324i | \(0.577740\pi\) | |||||||
\(920\) | −1.66536 | −0.0549051 | ||||||||
\(921\) | 3.45493 | 0.113844 | ||||||||
\(922\) | −40.6098 | −1.33741 | ||||||||
\(923\) | −16.2210 | −0.533920 | ||||||||
\(924\) | 20.8372 | 0.685492 | ||||||||
\(925\) | −0.532509 | −0.0175088 | ||||||||
\(926\) | 59.5509 | 1.95696 | ||||||||
\(927\) | −4.06536 | −0.133524 | ||||||||
\(928\) | −69.4982 | −2.28139 | ||||||||
\(929\) | 25.6528 | 0.841642 | 0.420821 | − | 0.907144i | \(-0.361742\pi\) | ||||
0.420821 | + | 0.907144i | \(0.361742\pi\) | |||||||
\(930\) | 17.6870 | 0.579980 | ||||||||
\(931\) | −4.70029 | −0.154046 | ||||||||
\(932\) | −16.5778 | −0.543024 | ||||||||
\(933\) | 27.1352 | 0.888365 | ||||||||
\(934\) | 29.7962 | 0.974961 | ||||||||
\(935\) | −7.73940 | −0.253105 | ||||||||
\(936\) | 0.630329 | 0.0206029 | ||||||||
\(937\) | −24.2289 | −0.791525 | −0.395763 | − | 0.918353i | \(-0.629520\pi\) | ||||
−0.395763 | + | 0.918353i | \(0.629520\pi\) | |||||||
\(938\) | −13.6992 | −0.447295 | ||||||||
\(939\) | −30.9959 | −1.01151 | ||||||||
\(940\) | 5.46784 | 0.178341 | ||||||||
\(941\) | −54.4971 | −1.77655 | −0.888277 | − | 0.459308i | \(-0.848097\pi\) | ||||
−0.888277 | + | 0.459308i | \(0.848097\pi\) | |||||||
\(942\) | −57.8150 | −1.88371 | ||||||||
\(943\) | 24.2027 | 0.788147 | ||||||||
\(944\) | −60.7205 | −1.97629 | ||||||||
\(945\) | 5.89997 | 0.191926 | ||||||||
\(946\) | −73.8791 | −2.40202 | ||||||||
\(947\) | 6.51946 | 0.211854 | 0.105927 | − | 0.994374i | \(-0.466219\pi\) | ||||
0.105927 | + | 0.994374i | \(0.466219\pi\) | |||||||
\(948\) | 4.92535 | 0.159968 | ||||||||
\(949\) | −28.4852 | −0.924668 | ||||||||
\(950\) | 8.71710 | 0.282820 | ||||||||
\(951\) | 11.5967 | 0.376048 | ||||||||
\(952\) | −1.59323 | −0.0516367 | ||||||||
\(953\) | −36.3798 | −1.17846 | −0.589229 | − | 0.807966i | \(-0.700569\pi\) | ||||
−0.589229 | + | 0.807966i | \(0.700569\pi\) | |||||||
\(954\) | −2.14317 | −0.0693876 | ||||||||
\(955\) | −4.07581 | −0.131890 | ||||||||
\(956\) | −28.6794 | −0.927558 | ||||||||
\(957\) | 71.0049 | 2.29526 | ||||||||
\(958\) | 41.1711 | 1.33018 | ||||||||
\(959\) | −18.4715 | −0.596475 | ||||||||
\(960\) | −6.84762 | −0.221006 | ||||||||
\(961\) | 32.3371 | 1.04313 | ||||||||
\(962\) | 0.787249 | 0.0253819 | ||||||||
\(963\) | 4.45470 | 0.143551 | ||||||||
\(964\) | −22.4989 | −0.724640 | ||||||||
\(965\) | −8.92739 | −0.287383 | ||||||||
\(966\) | −23.8716 | −0.768056 | ||||||||
\(967\) | 18.2294 | 0.586219 | 0.293110 | − | 0.956079i | \(-0.405310\pi\) | ||||
0.293110 | + | 0.956079i | \(0.405310\pi\) | |||||||
\(968\) | 5.78469 | 0.185927 | ||||||||
\(969\) | −3.63675 | −0.116829 | ||||||||
\(970\) | −8.58730 | −0.275722 | ||||||||
\(971\) | −41.7816 | −1.34084 | −0.670418 | − | 0.741984i | \(-0.733885\pi\) | ||||
−0.670418 | + | 0.741984i | \(0.733885\pi\) | |||||||
\(972\) | −7.16136 | −0.229701 | ||||||||
\(973\) | −10.1483 | −0.325339 | ||||||||
\(974\) | 32.7631 | 1.04980 | ||||||||
\(975\) | −24.8769 | −0.796697 | ||||||||
\(976\) | −24.7496 | −0.792214 | ||||||||
\(977\) | 19.6861 | 0.629813 | 0.314906 | − | 0.949123i | \(-0.398027\pi\) | ||||
0.314906 | + | 0.949123i | \(0.398027\pi\) | |||||||
\(978\) | 60.5481 | 1.93612 | ||||||||
\(979\) | −0.851440 | −0.0272122 | ||||||||
\(980\) | 5.87237 | 0.187586 | ||||||||
\(981\) | 3.32526 | 0.106167 | ||||||||
\(982\) | 43.7576 | 1.39636 | ||||||||
\(983\) | −49.8680 | −1.59054 | −0.795271 | − | 0.606254i | \(-0.792671\pi\) | ||||
−0.795271 | + | 0.606254i | \(0.792671\pi\) | |||||||
\(984\) | −3.62235 | −0.115476 | ||||||||
\(985\) | 15.9543 | 0.508346 | ||||||||
\(986\) | 39.7185 | 1.26490 | ||||||||
\(987\) | −10.7133 | −0.341009 | ||||||||
\(988\) | −6.03137 | −0.191884 | ||||||||
\(989\) | 39.6117 | 1.25958 | ||||||||
\(990\) | −2.62646 | −0.0834743 | ||||||||
\(991\) | −4.85857 | −0.154337 | −0.0771687 | − | 0.997018i | \(-0.524588\pi\) | ||||
−0.0771687 | + | 0.997018i | \(0.524588\pi\) | |||||||
\(992\) | −60.8314 | −1.93140 | ||||||||
\(993\) | 35.7797 | 1.13543 | ||||||||
\(994\) | 13.9140 | 0.441324 | ||||||||
\(995\) | 10.2334 | 0.324421 | ||||||||
\(996\) | 30.2655 | 0.959000 | ||||||||
\(997\) | −7.93651 | −0.251352 | −0.125676 | − | 0.992071i | \(-0.540110\pi\) | ||||
−0.125676 | + | 0.992071i | \(0.540110\pi\) | |||||||
\(998\) | 26.0810 | 0.825579 | ||||||||
\(999\) | 0.648982 | 0.0205329 |
(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 | 4009.2.a.c.1.16 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.16 | ✓ | 71 | 1.1 | even | 1 | trivial |