Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.36 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.615616 | 0.435307 | 0.217653 | − | 0.976026i | \(-0.430160\pi\) | ||||
0.217653 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(3\) | −0.601096 | −0.347043 | −0.173521 | − | 0.984830i | \(-0.555515\pi\) | ||||
−0.173521 | + | 0.984830i | \(0.555515\pi\) | |||||||
\(4\) | −1.62102 | −0.810508 | ||||||||
\(5\) | −3.97491 | −1.77764 | −0.888818 | − | 0.458261i | \(-0.848473\pi\) | ||||
−0.888818 | + | 0.458261i | \(0.848473\pi\) | |||||||
\(6\) | −0.370044 | −0.151070 | ||||||||
\(7\) | 2.02870 | 0.766776 | 0.383388 | − | 0.923587i | \(-0.374757\pi\) | ||||
0.383388 | + | 0.923587i | \(0.374757\pi\) | |||||||
\(8\) | −2.22916 | −0.788126 | ||||||||
\(9\) | −2.63868 | −0.879561 | ||||||||
\(10\) | −2.44702 | −0.773816 | ||||||||
\(11\) | −1.11202 | −0.335288 | −0.167644 | − | 0.985848i | \(-0.553616\pi\) | ||||
−0.167644 | + | 0.985848i | \(0.553616\pi\) | |||||||
\(12\) | 0.974386 | 0.281281 | ||||||||
\(13\) | 3.85425 | 1.06898 | 0.534488 | − | 0.845176i | \(-0.320505\pi\) | ||||
0.534488 | + | 0.845176i | \(0.320505\pi\) | |||||||
\(14\) | 1.24890 | 0.333783 | ||||||||
\(15\) | 2.38930 | 0.616915 | ||||||||
\(16\) | 1.86973 | 0.467432 | ||||||||
\(17\) | 5.07668 | 1.23128 | 0.615638 | − | 0.788029i | \(-0.288899\pi\) | ||||
0.615638 | + | 0.788029i | \(0.288899\pi\) | |||||||
\(18\) | −1.62442 | −0.382879 | ||||||||
\(19\) | −3.93973 | −0.903836 | −0.451918 | − | 0.892059i | \(-0.649260\pi\) | ||||
−0.451918 | + | 0.892059i | \(0.649260\pi\) | |||||||
\(20\) | 6.44340 | 1.44079 | ||||||||
\(21\) | −1.21944 | −0.266104 | ||||||||
\(22\) | −0.684580 | −0.145953 | ||||||||
\(23\) | 1.65525 | 0.345143 | 0.172571 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172571 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(24\) | 1.33994 | 0.273513 | ||||||||
\(25\) | 10.7999 | 2.15999 | ||||||||
\(26\) | 2.37274 | 0.465332 | ||||||||
\(27\) | 3.38939 | 0.652288 | ||||||||
\(28\) | −3.28855 | −0.621478 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 1.47089 | 0.268547 | ||||||||
\(31\) | −1.06636 | −0.191524 | −0.0957622 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957622 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(32\) | 5.60935 | 0.991602 | ||||||||
\(33\) | 0.668432 | 0.116359 | ||||||||
\(34\) | 3.12529 | 0.535982 | ||||||||
\(35\) | −8.06390 | −1.36305 | ||||||||
\(36\) | 4.27735 | 0.712892 | ||||||||
\(37\) | −1.15005 | −0.189067 | −0.0945334 | − | 0.995522i | \(-0.530136\pi\) | ||||
−0.0945334 | + | 0.995522i | \(0.530136\pi\) | |||||||
\(38\) | −2.42536 | −0.393446 | ||||||||
\(39\) | −2.31677 | −0.370980 | ||||||||
\(40\) | 8.86071 | 1.40100 | ||||||||
\(41\) | −2.93208 | −0.457914 | −0.228957 | − | 0.973437i | \(-0.573531\pi\) | ||||
−0.228957 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(42\) | −0.750708 | −0.115837 | ||||||||
\(43\) | 4.25294 | 0.648567 | 0.324284 | − | 0.945960i | \(-0.394877\pi\) | ||||
0.324284 | + | 0.945960i | \(0.394877\pi\) | |||||||
\(44\) | 1.80261 | 0.271753 | ||||||||
\(45\) | 10.4885 | 1.56354 | ||||||||
\(46\) | 1.01900 | 0.150243 | ||||||||
\(47\) | 2.70624 | 0.394746 | 0.197373 | − | 0.980328i | \(-0.436759\pi\) | ||||
0.197373 | + | 0.980328i | \(0.436759\pi\) | |||||||
\(48\) | −1.12388 | −0.162219 | ||||||||
\(49\) | −2.88438 | −0.412055 | ||||||||
\(50\) | 6.64862 | 0.940257 | ||||||||
\(51\) | −3.05157 | −0.427305 | ||||||||
\(52\) | −6.24779 | −0.866413 | ||||||||
\(53\) | 9.71282 | 1.33416 | 0.667079 | − | 0.744987i | \(-0.267544\pi\) | ||||
0.667079 | + | 0.744987i | \(0.267544\pi\) | |||||||
\(54\) | 2.08656 | 0.283945 | ||||||||
\(55\) | 4.42020 | 0.596019 | ||||||||
\(56\) | −4.52229 | −0.604316 | ||||||||
\(57\) | 2.36816 | 0.313670 | ||||||||
\(58\) | −0.615616 | −0.0808344 | ||||||||
\(59\) | 7.35669 | 0.957760 | 0.478880 | − | 0.877880i | \(-0.341043\pi\) | ||||
0.478880 | + | 0.877880i | \(0.341043\pi\) | |||||||
\(60\) | −3.87310 | −0.500015 | ||||||||
\(61\) | −12.1435 | −1.55481 | −0.777406 | − | 0.628999i | \(-0.783465\pi\) | ||||
−0.777406 | + | 0.628999i | \(0.783465\pi\) | |||||||
\(62\) | −0.656470 | −0.0833718 | ||||||||
\(63\) | −5.35309 | −0.674427 | ||||||||
\(64\) | −0.286248 | −0.0357810 | ||||||||
\(65\) | −15.3203 | −1.90025 | ||||||||
\(66\) | 0.411498 | 0.0506519 | ||||||||
\(67\) | −7.65775 | −0.935543 | −0.467772 | − | 0.883849i | \(-0.654943\pi\) | ||||
−0.467772 | + | 0.883849i | \(0.654943\pi\) | |||||||
\(68\) | −8.22938 | −0.997959 | ||||||||
\(69\) | −0.994962 | −0.119779 | ||||||||
\(70\) | −4.96427 | −0.593344 | ||||||||
\(71\) | −3.84285 | −0.456063 | −0.228031 | − | 0.973654i | \(-0.573229\pi\) | ||||
−0.228031 | + | 0.973654i | \(0.573229\pi\) | |||||||
\(72\) | 5.88204 | 0.693205 | ||||||||
\(73\) | 7.70041 | 0.901265 | 0.450633 | − | 0.892710i | \(-0.351198\pi\) | ||||
0.450633 | + | 0.892710i | \(0.351198\pi\) | |||||||
\(74\) | −0.707989 | −0.0823020 | ||||||||
\(75\) | −6.49180 | −0.749608 | ||||||||
\(76\) | 6.38637 | 0.732567 | ||||||||
\(77\) | −2.25596 | −0.257090 | ||||||||
\(78\) | −1.42624 | −0.161490 | ||||||||
\(79\) | 2.65058 | 0.298214 | 0.149107 | − | 0.988821i | \(-0.452360\pi\) | ||||
0.149107 | + | 0.988821i | \(0.452360\pi\) | |||||||
\(80\) | −7.43201 | −0.830924 | ||||||||
\(81\) | 5.87871 | 0.653190 | ||||||||
\(82\) | −1.80503 | −0.199333 | ||||||||
\(83\) | 12.8977 | 1.41571 | 0.707855 | − | 0.706358i | \(-0.249663\pi\) | ||||
0.707855 | + | 0.706358i | \(0.249663\pi\) | |||||||
\(84\) | 1.97674 | 0.215679 | ||||||||
\(85\) | −20.1794 | −2.18876 | ||||||||
\(86\) | 2.61818 | 0.282326 | ||||||||
\(87\) | 0.601096 | 0.0644442 | ||||||||
\(88\) | 2.47887 | 0.264249 | ||||||||
\(89\) | −1.51478 | −0.160566 | −0.0802832 | − | 0.996772i | \(-0.525582\pi\) | ||||
−0.0802832 | + | 0.996772i | \(0.525582\pi\) | |||||||
\(90\) | 6.45692 | 0.680619 | ||||||||
\(91\) | 7.81910 | 0.819665 | ||||||||
\(92\) | −2.68318 | −0.279741 | ||||||||
\(93\) | 0.640986 | 0.0664671 | ||||||||
\(94\) | 1.66601 | 0.171835 | ||||||||
\(95\) | 15.6601 | 1.60669 | ||||||||
\(96\) | −3.37175 | −0.344128 | ||||||||
\(97\) | −13.5584 | −1.37665 | −0.688325 | − | 0.725402i | \(-0.741654\pi\) | ||||
−0.688325 | + | 0.725402i | \(0.741654\pi\) | |||||||
\(98\) | −1.77567 | −0.179370 | ||||||||
\(99\) | 2.93428 | 0.294906 | ||||||||
\(100\) | −17.5069 | −1.75069 | ||||||||
\(101\) | 8.99135 | 0.894673 | 0.447336 | − | 0.894366i | \(-0.352373\pi\) | ||||
0.447336 | + | 0.894366i | \(0.352373\pi\) | |||||||
\(102\) | −1.87860 | −0.186009 | ||||||||
\(103\) | −18.1518 | −1.78855 | −0.894276 | − | 0.447517i | \(-0.852309\pi\) | ||||
−0.894276 | + | 0.447517i | \(0.852309\pi\) | |||||||
\(104\) | −8.59172 | −0.842487 | ||||||||
\(105\) | 4.84718 | 0.473036 | ||||||||
\(106\) | 5.97937 | 0.580768 | ||||||||
\(107\) | −5.50313 | −0.532008 | −0.266004 | − | 0.963972i | \(-0.585703\pi\) | ||||
−0.266004 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(108\) | −5.49425 | −0.528685 | ||||||||
\(109\) | −7.87069 | −0.753875 | −0.376938 | − | 0.926239i | \(-0.623023\pi\) | ||||
−0.376938 | + | 0.926239i | \(0.623023\pi\) | |||||||
\(110\) | 2.72115 | 0.259451 | ||||||||
\(111\) | 0.691289 | 0.0656143 | ||||||||
\(112\) | 3.79311 | 0.358416 | ||||||||
\(113\) | −7.01168 | −0.659603 | −0.329802 | − | 0.944050i | \(-0.606982\pi\) | ||||
−0.329802 | + | 0.944050i | \(0.606982\pi\) | |||||||
\(114\) | 1.45788 | 0.136543 | ||||||||
\(115\) | −6.57947 | −0.613539 | ||||||||
\(116\) | 1.62102 | 0.150508 | ||||||||
\(117\) | −10.1701 | −0.940229 | ||||||||
\(118\) | 4.52890 | 0.416919 | ||||||||
\(119\) | 10.2990 | 0.944112 | ||||||||
\(120\) | −5.32613 | −0.486207 | ||||||||
\(121\) | −9.76340 | −0.887582 | ||||||||
\(122\) | −7.47572 | −0.676820 | ||||||||
\(123\) | 1.76246 | 0.158916 | ||||||||
\(124\) | 1.72859 | 0.155232 | ||||||||
\(125\) | −23.0543 | −2.06204 | ||||||||
\(126\) | −3.29545 | −0.293582 | ||||||||
\(127\) | −14.5986 | −1.29542 | −0.647710 | − | 0.761887i | \(-0.724273\pi\) | ||||
−0.647710 | + | 0.761887i | \(0.724273\pi\) | |||||||
\(128\) | −11.3949 | −1.00718 | ||||||||
\(129\) | −2.55642 | −0.225081 | ||||||||
\(130\) | −9.43142 | −0.827191 | ||||||||
\(131\) | −0.715609 | −0.0625231 | −0.0312615 | − | 0.999511i | \(-0.509952\pi\) | ||||
−0.0312615 | + | 0.999511i | \(0.509952\pi\) | |||||||
\(132\) | −1.08354 | −0.0943100 | ||||||||
\(133\) | −7.99253 | −0.693040 | ||||||||
\(134\) | −4.71424 | −0.407248 | ||||||||
\(135\) | −13.4725 | −1.15953 | ||||||||
\(136\) | −11.3167 | −0.970400 | ||||||||
\(137\) | −16.0288 | −1.36944 | −0.684718 | − | 0.728808i | \(-0.740075\pi\) | ||||
−0.684718 | + | 0.728808i | \(0.740075\pi\) | |||||||
\(138\) | −0.612515 | −0.0521407 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 13.0717 | 1.10476 | ||||||||
\(141\) | −1.62671 | −0.136994 | ||||||||
\(142\) | −2.36572 | −0.198527 | ||||||||
\(143\) | −4.28601 | −0.358414 | ||||||||
\(144\) | −4.93362 | −0.411135 | ||||||||
\(145\) | 3.97491 | 0.330099 | ||||||||
\(146\) | 4.74050 | 0.392327 | ||||||||
\(147\) | 1.73379 | 0.143001 | ||||||||
\(148\) | 1.86425 | 0.153240 | ||||||||
\(149\) | 6.35112 | 0.520304 | 0.260152 | − | 0.965568i | \(-0.416227\pi\) | ||||
0.260152 | + | 0.965568i | \(0.416227\pi\) | |||||||
\(150\) | −3.99646 | −0.326309 | ||||||||
\(151\) | 18.4580 | 1.50209 | 0.751044 | − | 0.660253i | \(-0.229551\pi\) | ||||
0.751044 | + | 0.660253i | \(0.229551\pi\) | |||||||
\(152\) | 8.78228 | 0.712337 | ||||||||
\(153\) | −13.3958 | −1.08298 | ||||||||
\(154\) | −1.38881 | −0.111913 | ||||||||
\(155\) | 4.23870 | 0.340461 | ||||||||
\(156\) | 3.75552 | 0.300682 | ||||||||
\(157\) | −3.16247 | −0.252392 | −0.126196 | − | 0.992005i | \(-0.540277\pi\) | ||||
−0.126196 | + | 0.992005i | \(0.540277\pi\) | |||||||
\(158\) | 1.63174 | 0.129814 | ||||||||
\(159\) | −5.83834 | −0.463010 | ||||||||
\(160\) | −22.2967 | −1.76271 | ||||||||
\(161\) | 3.35800 | 0.264647 | ||||||||
\(162\) | 3.61903 | 0.284338 | ||||||||
\(163\) | 19.0835 | 1.49474 | 0.747369 | − | 0.664409i | \(-0.231317\pi\) | ||||
0.747369 | + | 0.664409i | \(0.231317\pi\) | |||||||
\(164\) | 4.75295 | 0.371143 | ||||||||
\(165\) | −2.65696 | −0.206844 | ||||||||
\(166\) | 7.94005 | 0.616268 | ||||||||
\(167\) | −11.0288 | −0.853434 | −0.426717 | − | 0.904385i | \(-0.640330\pi\) | ||||
−0.426717 | + | 0.904385i | \(0.640330\pi\) | |||||||
\(168\) | 2.71833 | 0.209723 | ||||||||
\(169\) | 1.85521 | 0.142708 | ||||||||
\(170\) | −12.4227 | −0.952781 | ||||||||
\(171\) | 10.3957 | 0.794980 | ||||||||
\(172\) | −6.89409 | −0.525669 | ||||||||
\(173\) | −5.76735 | −0.438483 | −0.219242 | − | 0.975671i | \(-0.570358\pi\) | ||||
−0.219242 | + | 0.975671i | \(0.570358\pi\) | |||||||
\(174\) | 0.370044 | 0.0280530 | ||||||||
\(175\) | 21.9098 | 1.65623 | ||||||||
\(176\) | −2.07918 | −0.156724 | ||||||||
\(177\) | −4.42207 | −0.332383 | ||||||||
\(178\) | −0.932524 | −0.0698956 | ||||||||
\(179\) | −21.4899 | −1.60623 | −0.803117 | − | 0.595822i | \(-0.796826\pi\) | ||||
−0.803117 | + | 0.595822i | \(0.796826\pi\) | |||||||
\(180\) | −17.0021 | −1.26726 | ||||||||
\(181\) | 11.9839 | 0.890756 | 0.445378 | − | 0.895343i | \(-0.353069\pi\) | ||||
0.445378 | + | 0.895343i | \(0.353069\pi\) | |||||||
\(182\) | 4.81357 | 0.356805 | ||||||||
\(183\) | 7.29939 | 0.539586 | ||||||||
\(184\) | −3.68981 | −0.272016 | ||||||||
\(185\) | 4.57135 | 0.336092 | ||||||||
\(186\) | 0.394601 | 0.0289336 | ||||||||
\(187\) | −5.64538 | −0.412831 | ||||||||
\(188\) | −4.38686 | −0.319945 | ||||||||
\(189\) | 6.87605 | 0.500159 | ||||||||
\(190\) | 9.64061 | 0.699403 | ||||||||
\(191\) | 17.1105 | 1.23807 | 0.619036 | − | 0.785362i | \(-0.287523\pi\) | ||||
0.619036 | + | 0.785362i | \(0.287523\pi\) | |||||||
\(192\) | 0.172062 | 0.0124175 | ||||||||
\(193\) | −20.0620 | −1.44409 | −0.722046 | − | 0.691845i | \(-0.756798\pi\) | ||||
−0.722046 | + | 0.691845i | \(0.756798\pi\) | |||||||
\(194\) | −8.34679 | −0.599265 | ||||||||
\(195\) | 9.20896 | 0.659467 | ||||||||
\(196\) | 4.67563 | 0.333974 | ||||||||
\(197\) | 21.6008 | 1.53900 | 0.769498 | − | 0.638650i | \(-0.220507\pi\) | ||||
0.769498 | + | 0.638650i | \(0.220507\pi\) | |||||||
\(198\) | 1.80639 | 0.128374 | ||||||||
\(199\) | −14.8104 | −1.04988 | −0.524940 | − | 0.851139i | \(-0.675912\pi\) | ||||
−0.524940 | + | 0.851139i | \(0.675912\pi\) | |||||||
\(200\) | −24.0748 | −1.70234 | ||||||||
\(201\) | 4.60304 | 0.324673 | ||||||||
\(202\) | 5.53522 | 0.389457 | ||||||||
\(203\) | −2.02870 | −0.142387 | ||||||||
\(204\) | 4.94664 | 0.346334 | ||||||||
\(205\) | 11.6548 | 0.814003 | ||||||||
\(206\) | −11.1746 | −0.778568 | ||||||||
\(207\) | −4.36768 | −0.303574 | ||||||||
\(208\) | 7.20639 | 0.499673 | ||||||||
\(209\) | 4.38107 | 0.303045 | ||||||||
\(210\) | 2.98400 | 0.205916 | ||||||||
\(211\) | 7.22427 | 0.497339 | 0.248670 | − | 0.968588i | \(-0.420007\pi\) | ||||
0.248670 | + | 0.968588i | \(0.420007\pi\) | |||||||
\(212\) | −15.7446 | −1.08135 | ||||||||
\(213\) | 2.30992 | 0.158273 | ||||||||
\(214\) | −3.38782 | −0.231587 | ||||||||
\(215\) | −16.9051 | −1.15292 | ||||||||
\(216\) | −7.55548 | −0.514085 | ||||||||
\(217\) | −2.16333 | −0.146856 | ||||||||
\(218\) | −4.84532 | −0.328167 | ||||||||
\(219\) | −4.62868 | −0.312777 | ||||||||
\(220\) | −7.16521 | −0.483078 | ||||||||
\(221\) | 19.5668 | 1.31620 | ||||||||
\(222\) | 0.425569 | 0.0285623 | ||||||||
\(223\) | −21.2526 | −1.42318 | −0.711591 | − | 0.702594i | \(-0.752025\pi\) | ||||
−0.711591 | + | 0.702594i | \(0.752025\pi\) | |||||||
\(224\) | 11.3797 | 0.760337 | ||||||||
\(225\) | −28.4976 | −1.89984 | ||||||||
\(226\) | −4.31651 | −0.287130 | ||||||||
\(227\) | 10.6364 | 0.705961 | 0.352980 | − | 0.935631i | \(-0.385168\pi\) | ||||
0.352980 | + | 0.935631i | \(0.385168\pi\) | |||||||
\(228\) | −3.83882 | −0.254232 | ||||||||
\(229\) | −5.26420 | −0.347868 | −0.173934 | − | 0.984757i | \(-0.555648\pi\) | ||||
−0.173934 | + | 0.984757i | \(0.555648\pi\) | |||||||
\(230\) | −4.05043 | −0.267077 | ||||||||
\(231\) | 1.35605 | 0.0892214 | ||||||||
\(232\) | 2.22916 | 0.146351 | ||||||||
\(233\) | 14.1390 | 0.926278 | 0.463139 | − | 0.886286i | \(-0.346723\pi\) | ||||
0.463139 | + | 0.886286i | \(0.346723\pi\) | |||||||
\(234\) | −6.26090 | −0.409288 | ||||||||
\(235\) | −10.7571 | −0.701714 | ||||||||
\(236\) | −11.9253 | −0.776272 | ||||||||
\(237\) | −1.59325 | −0.103493 | ||||||||
\(238\) | 6.34026 | 0.410978 | ||||||||
\(239\) | −19.8238 | −1.28230 | −0.641149 | − | 0.767417i | \(-0.721542\pi\) | ||||
−0.641149 | + | 0.767417i | \(0.721542\pi\) | |||||||
\(240\) | 4.46735 | 0.288366 | ||||||||
\(241\) | 27.6751 | 1.78271 | 0.891356 | − | 0.453304i | \(-0.149755\pi\) | ||||
0.891356 | + | 0.453304i | \(0.149755\pi\) | |||||||
\(242\) | −6.01051 | −0.386370 | ||||||||
\(243\) | −13.7018 | −0.878973 | ||||||||
\(244\) | 19.6848 | 1.26019 | ||||||||
\(245\) | 11.4652 | 0.732483 | ||||||||
\(246\) | 1.08500 | 0.0691770 | ||||||||
\(247\) | −15.1847 | −0.966179 | ||||||||
\(248\) | 2.37709 | 0.150945 | ||||||||
\(249\) | −7.75277 | −0.491312 | ||||||||
\(250\) | −14.1926 | −0.897618 | ||||||||
\(251\) | 14.0246 | 0.885222 | 0.442611 | − | 0.896714i | \(-0.354052\pi\) | ||||
0.442611 | + | 0.896714i | \(0.354052\pi\) | |||||||
\(252\) | 8.67745 | 0.546628 | ||||||||
\(253\) | −1.84067 | −0.115722 | ||||||||
\(254\) | −8.98716 | −0.563905 | ||||||||
\(255\) | 12.1297 | 0.759593 | ||||||||
\(256\) | −6.44240 | −0.402650 | ||||||||
\(257\) | −23.3636 | −1.45738 | −0.728692 | − | 0.684842i | \(-0.759871\pi\) | ||||
−0.728692 | + | 0.684842i | \(0.759871\pi\) | |||||||
\(258\) | −1.57378 | −0.0979790 | ||||||||
\(259\) | −2.33310 | −0.144972 | ||||||||
\(260\) | 24.8344 | 1.54017 | ||||||||
\(261\) | 2.63868 | 0.163330 | ||||||||
\(262\) | −0.440541 | −0.0272167 | ||||||||
\(263\) | 2.28010 | 0.140597 | 0.0702984 | − | 0.997526i | \(-0.477605\pi\) | ||||
0.0702984 | + | 0.997526i | \(0.477605\pi\) | |||||||
\(264\) | −1.49004 | −0.0917056 | ||||||||
\(265\) | −38.6076 | −2.37165 | ||||||||
\(266\) | −4.92033 | −0.301685 | ||||||||
\(267\) | 0.910528 | 0.0557234 | ||||||||
\(268\) | 12.4133 | 0.758265 | ||||||||
\(269\) | 14.6816 | 0.895153 | 0.447577 | − | 0.894246i | \(-0.352287\pi\) | ||||
0.447577 | + | 0.894246i | \(0.352287\pi\) | |||||||
\(270\) | −8.29391 | −0.504751 | ||||||||
\(271\) | −21.5027 | −1.30620 | −0.653099 | − | 0.757273i | \(-0.726531\pi\) | ||||
−0.653099 | + | 0.757273i | \(0.726531\pi\) | |||||||
\(272\) | 9.49200 | 0.575537 | ||||||||
\(273\) | −4.70003 | −0.284459 | ||||||||
\(274\) | −9.86762 | −0.596125 | ||||||||
\(275\) | −12.0098 | −0.724217 | ||||||||
\(276\) | 1.61285 | 0.0970822 | ||||||||
\(277\) | 12.4775 | 0.749698 | 0.374849 | − | 0.927086i | \(-0.377695\pi\) | ||||
0.374849 | + | 0.927086i | \(0.377695\pi\) | |||||||
\(278\) | −0.615616 | −0.0369222 | ||||||||
\(279\) | 2.81379 | 0.168457 | ||||||||
\(280\) | 17.9757 | 1.07425 | ||||||||
\(281\) | 13.1413 | 0.783945 | 0.391973 | − | 0.919977i | \(-0.371793\pi\) | ||||
0.391973 | + | 0.919977i | \(0.371793\pi\) | |||||||
\(282\) | −1.00143 | −0.0596342 | ||||||||
\(283\) | −5.10844 | −0.303665 | −0.151833 | − | 0.988406i | \(-0.548517\pi\) | ||||
−0.151833 | + | 0.988406i | \(0.548517\pi\) | |||||||
\(284\) | 6.22933 | 0.369642 | ||||||||
\(285\) | −9.41321 | −0.557591 | ||||||||
\(286\) | −2.63854 | −0.156020 | ||||||||
\(287\) | −5.94830 | −0.351117 | ||||||||
\(288\) | −14.8013 | −0.872175 | ||||||||
\(289\) | 8.77266 | 0.516039 | ||||||||
\(290\) | 2.44702 | 0.143694 | ||||||||
\(291\) | 8.14991 | 0.477756 | ||||||||
\(292\) | −12.4825 | −0.730483 | ||||||||
\(293\) | 16.6263 | 0.971318 | 0.485659 | − | 0.874148i | \(-0.338580\pi\) | ||||
0.485659 | + | 0.874148i | \(0.338580\pi\) | |||||||
\(294\) | 1.06735 | 0.0622491 | ||||||||
\(295\) | −29.2422 | −1.70255 | ||||||||
\(296\) | 2.56364 | 0.149009 | ||||||||
\(297\) | −3.76908 | −0.218704 | ||||||||
\(298\) | 3.90985 | 0.226492 | ||||||||
\(299\) | 6.37973 | 0.368949 | ||||||||
\(300\) | 10.5233 | 0.607564 | ||||||||
\(301\) | 8.62793 | 0.497306 | ||||||||
\(302\) | 11.3630 | 0.653868 | ||||||||
\(303\) | −5.40466 | −0.310490 | ||||||||
\(304\) | −7.36622 | −0.422482 | ||||||||
\(305\) | 48.2693 | 2.76389 | ||||||||
\(306\) | −8.24664 | −0.471429 | ||||||||
\(307\) | 12.6283 | 0.720733 | 0.360366 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360366 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(308\) | 3.65695 | 0.208374 | ||||||||
\(309\) | 10.9110 | 0.620704 | ||||||||
\(310\) | 2.60941 | 0.148205 | ||||||||
\(311\) | 14.6237 | 0.829235 | 0.414618 | − | 0.909996i | \(-0.363915\pi\) | ||||
0.414618 | + | 0.909996i | \(0.363915\pi\) | |||||||
\(312\) | 5.16444 | 0.292379 | ||||||||
\(313\) | −23.5069 | −1.32869 | −0.664346 | − | 0.747426i | \(-0.731290\pi\) | ||||
−0.664346 | + | 0.747426i | \(0.731290\pi\) | |||||||
\(314\) | −1.94687 | −0.109868 | ||||||||
\(315\) | 21.2781 | 1.19888 | ||||||||
\(316\) | −4.29664 | −0.241705 | ||||||||
\(317\) | 30.3158 | 1.70271 | 0.851353 | − | 0.524594i | \(-0.175783\pi\) | ||||
0.851353 | + | 0.524594i | \(0.175783\pi\) | |||||||
\(318\) | −3.59417 | −0.201551 | ||||||||
\(319\) | 1.11202 | 0.0622613 | ||||||||
\(320\) | 1.13781 | 0.0636055 | ||||||||
\(321\) | 3.30791 | 0.184629 | ||||||||
\(322\) | 2.06724 | 0.115203 | ||||||||
\(323\) | −20.0007 | −1.11287 | ||||||||
\(324\) | −9.52948 | −0.529416 | ||||||||
\(325\) | 41.6256 | 2.30897 | ||||||||
\(326\) | 11.7481 | 0.650670 | ||||||||
\(327\) | 4.73104 | 0.261627 | ||||||||
\(328\) | 6.53606 | 0.360894 | ||||||||
\(329\) | 5.49015 | 0.302682 | ||||||||
\(330\) | −1.63567 | −0.0900406 | ||||||||
\(331\) | −12.0201 | −0.660683 | −0.330342 | − | 0.943861i | \(-0.607164\pi\) | ||||
−0.330342 | + | 0.943861i | \(0.607164\pi\) | |||||||
\(332\) | −20.9074 | −1.14744 | ||||||||
\(333\) | 3.03462 | 0.166296 | ||||||||
\(334\) | −6.78951 | −0.371505 | ||||||||
\(335\) | 30.4389 | 1.66305 | ||||||||
\(336\) | −2.28002 | −0.124385 | ||||||||
\(337\) | −4.57770 | −0.249363 | −0.124682 | − | 0.992197i | \(-0.539791\pi\) | ||||
−0.124682 | + | 0.992197i | \(0.539791\pi\) | |||||||
\(338\) | 1.14209 | 0.0621218 | ||||||||
\(339\) | 4.21469 | 0.228911 | ||||||||
\(340\) | 32.7111 | 1.77401 | ||||||||
\(341\) | 1.18582 | 0.0642157 | ||||||||
\(342\) | 6.39977 | 0.346060 | ||||||||
\(343\) | −20.0524 | −1.08273 | ||||||||
\(344\) | −9.48047 | −0.511153 | ||||||||
\(345\) | 3.95489 | 0.212924 | ||||||||
\(346\) | −3.55047 | −0.190875 | ||||||||
\(347\) | −13.5257 | −0.726100 | −0.363050 | − | 0.931770i | \(-0.618265\pi\) | ||||
−0.363050 | + | 0.931770i | \(0.618265\pi\) | |||||||
\(348\) | −0.974386 | −0.0522326 | ||||||||
\(349\) | −36.2039 | −1.93795 | −0.968975 | − | 0.247160i | \(-0.920503\pi\) | ||||
−0.968975 | + | 0.247160i | \(0.920503\pi\) | |||||||
\(350\) | 13.4880 | 0.720967 | ||||||||
\(351\) | 13.0635 | 0.697280 | ||||||||
\(352\) | −6.23773 | −0.332472 | ||||||||
\(353\) | −26.9850 | −1.43627 | −0.718135 | − | 0.695904i | \(-0.755004\pi\) | ||||
−0.718135 | + | 0.695904i | \(0.755004\pi\) | |||||||
\(354\) | −2.72230 | −0.144689 | ||||||||
\(355\) | 15.2750 | 0.810713 | ||||||||
\(356\) | 2.45548 | 0.130140 | ||||||||
\(357\) | −6.19071 | −0.327647 | ||||||||
\(358\) | −13.2296 | −0.699204 | ||||||||
\(359\) | −1.11856 | −0.0590353 | −0.0295176 | − | 0.999564i | \(-0.509397\pi\) | ||||
−0.0295176 | + | 0.999564i | \(0.509397\pi\) | |||||||
\(360\) | −23.3806 | −1.23227 | ||||||||
\(361\) | −3.47852 | −0.183080 | ||||||||
\(362\) | 7.37748 | 0.387752 | ||||||||
\(363\) | 5.86874 | 0.308029 | ||||||||
\(364\) | −12.6749 | −0.664345 | ||||||||
\(365\) | −30.6085 | −1.60212 | ||||||||
\(366\) | 4.49362 | 0.234885 | ||||||||
\(367\) | 8.60130 | 0.448984 | 0.224492 | − | 0.974476i | \(-0.427928\pi\) | ||||
0.224492 | + | 0.974476i | \(0.427928\pi\) | |||||||
\(368\) | 3.09486 | 0.161331 | ||||||||
\(369\) | 7.73683 | 0.402763 | ||||||||
\(370\) | 2.81420 | 0.146303 | ||||||||
\(371\) | 19.7044 | 1.02300 | ||||||||
\(372\) | −1.03905 | −0.0538722 | ||||||||
\(373\) | −15.1345 | −0.783634 | −0.391817 | − | 0.920043i | \(-0.628153\pi\) | ||||
−0.391817 | + | 0.920043i | \(0.628153\pi\) | |||||||
\(374\) | −3.47539 | −0.179708 | ||||||||
\(375\) | 13.8578 | 0.715615 | ||||||||
\(376\) | −6.03263 | −0.311109 | ||||||||
\(377\) | −3.85425 | −0.198504 | ||||||||
\(378\) | 4.23301 | 0.217722 | ||||||||
\(379\) | −37.1079 | −1.90611 | −0.953053 | − | 0.302804i | \(-0.902077\pi\) | ||||
−0.953053 | + | 0.302804i | \(0.902077\pi\) | |||||||
\(380\) | −25.3853 | −1.30224 | ||||||||
\(381\) | 8.77518 | 0.449566 | ||||||||
\(382\) | 10.5335 | 0.538941 | ||||||||
\(383\) | −28.1644 | −1.43913 | −0.719566 | − | 0.694424i | \(-0.755659\pi\) | ||||
−0.719566 | + | 0.694424i | \(0.755659\pi\) | |||||||
\(384\) | 6.84943 | 0.349534 | ||||||||
\(385\) | 8.96725 | 0.457013 | ||||||||
\(386\) | −12.3505 | −0.628623 | ||||||||
\(387\) | −11.2222 | −0.570455 | ||||||||
\(388\) | 21.9784 | 1.11579 | ||||||||
\(389\) | −17.7910 | −0.902042 | −0.451021 | − | 0.892513i | \(-0.648940\pi\) | ||||
−0.451021 | + | 0.892513i | \(0.648940\pi\) | |||||||
\(390\) | 5.66919 | 0.287070 | ||||||||
\(391\) | 8.40316 | 0.424966 | ||||||||
\(392\) | 6.42974 | 0.324751 | ||||||||
\(393\) | 0.430150 | 0.0216982 | ||||||||
\(394\) | 13.2978 | 0.669935 | ||||||||
\(395\) | −10.5358 | −0.530116 | ||||||||
\(396\) | −4.75651 | −0.239024 | ||||||||
\(397\) | 7.57846 | 0.380352 | 0.190176 | − | 0.981750i | \(-0.439094\pi\) | ||||
0.190176 | + | 0.981750i | \(0.439094\pi\) | |||||||
\(398\) | −9.11751 | −0.457019 | ||||||||
\(399\) | 4.80427 | 0.240514 | ||||||||
\(400\) | 20.1930 | 1.00965 | ||||||||
\(401\) | 15.8085 | 0.789437 | 0.394718 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394718 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(402\) | 2.83371 | 0.141332 | ||||||||
\(403\) | −4.11002 | −0.204735 | ||||||||
\(404\) | −14.5751 | −0.725140 | ||||||||
\(405\) | −23.3674 | −1.16113 | ||||||||
\(406\) | −1.24890 | −0.0619819 | ||||||||
\(407\) | 1.27888 | 0.0633918 | ||||||||
\(408\) | 6.80243 | 0.336770 | ||||||||
\(409\) | −10.3518 | −0.511863 | −0.255932 | − | 0.966695i | \(-0.582382\pi\) | ||||
−0.255932 | + | 0.966695i | \(0.582382\pi\) | |||||||
\(410\) | 7.17486 | 0.354341 | ||||||||
\(411\) | 9.63487 | 0.475253 | ||||||||
\(412\) | 29.4244 | 1.44964 | ||||||||
\(413\) | 14.9245 | 0.734387 | ||||||||
\(414\) | −2.68881 | −0.132148 | ||||||||
\(415\) | −51.2674 | −2.51662 | ||||||||
\(416\) | 21.6198 | 1.06000 | ||||||||
\(417\) | 0.601096 | 0.0294358 | ||||||||
\(418\) | 2.69706 | 0.131918 | ||||||||
\(419\) | 27.5104 | 1.34397 | 0.671986 | − | 0.740564i | \(-0.265442\pi\) | ||||
0.671986 | + | 0.740564i | \(0.265442\pi\) | |||||||
\(420\) | −7.85735 | −0.383400 | ||||||||
\(421\) | 19.2900 | 0.940139 | 0.470070 | − | 0.882629i | \(-0.344229\pi\) | ||||
0.470070 | + | 0.882629i | \(0.344229\pi\) | |||||||
\(422\) | 4.44738 | 0.216495 | ||||||||
\(423\) | −7.14091 | −0.347203 | ||||||||
\(424\) | −21.6514 | −1.05149 | ||||||||
\(425\) | 54.8278 | 2.65954 | ||||||||
\(426\) | 1.42203 | 0.0688974 | ||||||||
\(427\) | −24.6354 | −1.19219 | ||||||||
\(428\) | 8.92067 | 0.431197 | ||||||||
\(429\) | 2.57630 | 0.124385 | ||||||||
\(430\) | −10.4070 | −0.501872 | ||||||||
\(431\) | −25.2094 | −1.21430 | −0.607148 | − | 0.794589i | \(-0.707687\pi\) | ||||
−0.607148 | + | 0.794589i | \(0.707687\pi\) | |||||||
\(432\) | 6.33723 | 0.304900 | ||||||||
\(433\) | 14.0514 | 0.675266 | 0.337633 | − | 0.941278i | \(-0.390374\pi\) | ||||
0.337633 | + | 0.941278i | \(0.390374\pi\) | |||||||
\(434\) | −1.33178 | −0.0639275 | ||||||||
\(435\) | −2.38930 | −0.114558 | ||||||||
\(436\) | 12.7585 | 0.611022 | ||||||||
\(437\) | −6.52123 | −0.311953 | ||||||||
\(438\) | −2.84949 | −0.136154 | ||||||||
\(439\) | −19.5953 | −0.935233 | −0.467616 | − | 0.883932i | \(-0.654887\pi\) | ||||
−0.467616 | + | 0.883932i | \(0.654887\pi\) | |||||||
\(440\) | −9.85331 | −0.469738 | ||||||||
\(441\) | 7.61097 | 0.362427 | ||||||||
\(442\) | 12.0456 | 0.572952 | ||||||||
\(443\) | 27.3631 | 1.30006 | 0.650031 | − | 0.759908i | \(-0.274756\pi\) | ||||
0.650031 | + | 0.759908i | \(0.274756\pi\) | |||||||
\(444\) | −1.12059 | −0.0531809 | ||||||||
\(445\) | 6.02112 | 0.285429 | ||||||||
\(446\) | −13.0835 | −0.619520 | ||||||||
\(447\) | −3.81763 | −0.180568 | ||||||||
\(448\) | −0.580711 | −0.0274360 | ||||||||
\(449\) | 1.72837 | 0.0815668 | 0.0407834 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407834 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(450\) | −17.5436 | −0.827014 | ||||||||
\(451\) | 3.26054 | 0.153533 | ||||||||
\(452\) | 11.3660 | 0.534614 | ||||||||
\(453\) | −11.0950 | −0.521288 | ||||||||
\(454\) | 6.54793 | 0.307309 | ||||||||
\(455\) | −31.0803 | −1.45706 | ||||||||
\(456\) | −5.27899 | −0.247211 | ||||||||
\(457\) | −13.7529 | −0.643333 | −0.321666 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321666 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(458\) | −3.24073 | −0.151429 | ||||||||
\(459\) | 17.2068 | 0.803146 | ||||||||
\(460\) | 10.6654 | 0.497278 | ||||||||
\(461\) | 0.0328874 | 0.00153172 | 0.000765860 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000765860 | 1.00000i | \(0.499756\pi\) | ||||||||
\(462\) | 0.834805 | 0.0388386 | ||||||||
\(463\) | 27.5517 | 1.28044 | 0.640219 | − | 0.768192i | \(-0.278844\pi\) | ||||
0.640219 | + | 0.768192i | \(0.278844\pi\) | |||||||
\(464\) | −1.86973 | −0.0867999 | ||||||||
\(465\) | −2.54786 | −0.118154 | ||||||||
\(466\) | 8.70421 | 0.403215 | ||||||||
\(467\) | 37.1987 | 1.72135 | 0.860676 | − | 0.509154i | \(-0.170041\pi\) | ||||
0.860676 | + | 0.509154i | \(0.170041\pi\) | |||||||
\(468\) | 16.4860 | 0.762064 | ||||||||
\(469\) | −15.5353 | −0.717352 | ||||||||
\(470\) | −6.62223 | −0.305461 | ||||||||
\(471\) | 1.90095 | 0.0875909 | ||||||||
\(472\) | −16.3992 | −0.754835 | ||||||||
\(473\) | −4.72937 | −0.217457 | ||||||||
\(474\) | −0.980833 | −0.0450512 | ||||||||
\(475\) | −42.5489 | −1.95228 | ||||||||
\(476\) | −16.6949 | −0.765211 | ||||||||
\(477\) | −25.6291 | −1.17347 | ||||||||
\(478\) | −12.2039 | −0.558192 | ||||||||
\(479\) | −6.60073 | −0.301595 | −0.150798 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150798 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(480\) | 13.4024 | 0.611735 | ||||||||
\(481\) | −4.43257 | −0.202108 | ||||||||
\(482\) | 17.0373 | 0.776026 | ||||||||
\(483\) | −2.01848 | −0.0918439 | ||||||||
\(484\) | 15.8266 | 0.719393 | ||||||||
\(485\) | 53.8936 | 2.44718 | ||||||||
\(486\) | −8.43507 | −0.382623 | ||||||||
\(487\) | 9.97276 | 0.451909 | 0.225954 | − | 0.974138i | \(-0.427450\pi\) | ||||
0.225954 | + | 0.974138i | \(0.427450\pi\) | |||||||
\(488\) | 27.0697 | 1.22539 | ||||||||
\(489\) | −11.4710 | −0.518738 | ||||||||
\(490\) | 7.05815 | 0.318855 | ||||||||
\(491\) | −34.0992 | −1.53887 | −0.769437 | − | 0.638722i | \(-0.779463\pi\) | ||||
−0.769437 | + | 0.638722i | \(0.779463\pi\) | |||||||
\(492\) | −2.85697 | −0.128802 | ||||||||
\(493\) | −5.07668 | −0.228642 | ||||||||
\(494\) | −9.34794 | −0.420584 | ||||||||
\(495\) | −11.6635 | −0.524235 | ||||||||
\(496\) | −1.99381 | −0.0895246 | ||||||||
\(497\) | −7.79599 | −0.349698 | ||||||||
\(498\) | −4.77273 | −0.213871 | ||||||||
\(499\) | −2.80683 | −0.125651 | −0.0628254 | − | 0.998025i | \(-0.520011\pi\) | ||||
−0.0628254 | + | 0.998025i | \(0.520011\pi\) | |||||||
\(500\) | 37.3714 | 1.67130 | ||||||||
\(501\) | 6.62936 | 0.296178 | ||||||||
\(502\) | 8.63374 | 0.385343 | ||||||||
\(503\) | −30.9422 | −1.37964 | −0.689821 | − | 0.723980i | \(-0.742311\pi\) | ||||
−0.689821 | + | 0.723980i | \(0.742311\pi\) | |||||||
\(504\) | 11.9329 | 0.531533 | ||||||||
\(505\) | −35.7399 | −1.59040 | ||||||||
\(506\) | −1.13315 | −0.0503746 | ||||||||
\(507\) | −1.11516 | −0.0495258 | ||||||||
\(508\) | 23.6646 | 1.04995 | ||||||||
\(509\) | 4.18478 | 0.185487 | 0.0927436 | − | 0.995690i | \(-0.470436\pi\) | ||||
0.0927436 | + | 0.995690i | \(0.470436\pi\) | |||||||
\(510\) | 7.46726 | 0.330656 | ||||||||
\(511\) | 15.6218 | 0.691068 | ||||||||
\(512\) | 18.8238 | 0.831902 | ||||||||
\(513\) | −13.3533 | −0.589562 | ||||||||
\(514\) | −14.3830 | −0.634408 | ||||||||
\(515\) | 72.1519 | 3.17939 | ||||||||
\(516\) | 4.14400 | 0.182430 | ||||||||
\(517\) | −3.00940 | −0.132353 | ||||||||
\(518\) | −1.43630 | −0.0631072 | ||||||||
\(519\) | 3.46673 | 0.152172 | ||||||||
\(520\) | 34.1513 | 1.49764 | ||||||||
\(521\) | 20.2995 | 0.889336 | 0.444668 | − | 0.895696i | \(-0.353322\pi\) | ||||
0.444668 | + | 0.895696i | \(0.353322\pi\) | |||||||
\(522\) | 1.62442 | 0.0710988 | ||||||||
\(523\) | 2.31065 | 0.101038 | 0.0505188 | − | 0.998723i | \(-0.483913\pi\) | ||||
0.0505188 | + | 0.998723i | \(0.483913\pi\) | |||||||
\(524\) | 1.16001 | 0.0506755 | ||||||||
\(525\) | −13.1699 | −0.574782 | ||||||||
\(526\) | 1.40366 | 0.0612027 | ||||||||
\(527\) | −5.41358 | −0.235819 | ||||||||
\(528\) | 1.24979 | 0.0543900 | ||||||||
\(529\) | −20.2602 | −0.880876 | ||||||||
\(530\) | −23.7675 | −1.03239 | ||||||||
\(531\) | −19.4120 | −0.842408 | ||||||||
\(532\) | 12.9560 | 0.561715 | ||||||||
\(533\) | −11.3009 | −0.489498 | ||||||||
\(534\) | 0.560536 | 0.0242568 | ||||||||
\(535\) | 21.8745 | 0.945716 | ||||||||
\(536\) | 17.0703 | 0.737326 | ||||||||
\(537\) | 12.9175 | 0.557432 | ||||||||
\(538\) | 9.03824 | 0.389666 | ||||||||
\(539\) | 3.20750 | 0.138157 | ||||||||
\(540\) | 21.8392 | 0.939809 | ||||||||
\(541\) | −10.2859 | −0.442225 | −0.221112 | − | 0.975248i | \(-0.570969\pi\) | ||||
−0.221112 | + | 0.975248i | \(0.570969\pi\) | |||||||
\(542\) | −13.2374 | −0.568596 | ||||||||
\(543\) | −7.20346 | −0.309130 | ||||||||
\(544\) | 28.4769 | 1.22094 | ||||||||
\(545\) | 31.2853 | 1.34012 | ||||||||
\(546\) | −2.89341 | −0.123827 | ||||||||
\(547\) | −31.8539 | −1.36198 | −0.680988 | − | 0.732295i | \(-0.738449\pi\) | ||||
−0.680988 | + | 0.732295i | \(0.738449\pi\) | |||||||
\(548\) | 25.9830 | 1.10994 | ||||||||
\(549\) | 32.0428 | 1.36755 | ||||||||
\(550\) | −7.39342 | −0.315257 | ||||||||
\(551\) | 3.93973 | 0.167838 | ||||||||
\(552\) | 2.21793 | 0.0944012 | ||||||||
\(553\) | 5.37724 | 0.228663 | ||||||||
\(554\) | 7.68133 | 0.326348 | ||||||||
\(555\) | −2.74782 | −0.116638 | ||||||||
\(556\) | 1.62102 | 0.0687464 | ||||||||
\(557\) | −14.6446 | −0.620513 | −0.310256 | − | 0.950653i | \(-0.600415\pi\) | ||||
−0.310256 | + | 0.950653i | \(0.600415\pi\) | |||||||
\(558\) | 1.73222 | 0.0733306 | ||||||||
\(559\) | 16.3919 | 0.693302 | ||||||||
\(560\) | −15.0773 | −0.637132 | ||||||||
\(561\) | 3.39341 | 0.143270 | ||||||||
\(562\) | 8.09001 | 0.341256 | ||||||||
\(563\) | −42.4379 | −1.78855 | −0.894273 | − | 0.447522i | \(-0.852307\pi\) | ||||
−0.894273 | + | 0.447522i | \(0.852307\pi\) | |||||||
\(564\) | 2.63692 | 0.111034 | ||||||||
\(565\) | 27.8708 | 1.17253 | ||||||||
\(566\) | −3.14484 | −0.132188 | ||||||||
\(567\) | 11.9261 | 0.500850 | ||||||||
\(568\) | 8.56632 | 0.359435 | ||||||||
\(569\) | 3.05541 | 0.128089 | 0.0640446 | − | 0.997947i | \(-0.479600\pi\) | ||||
0.0640446 | + | 0.997947i | \(0.479600\pi\) | |||||||
\(570\) | −5.79493 | −0.242723 | ||||||||
\(571\) | 37.7646 | 1.58040 | 0.790199 | − | 0.612850i | \(-0.209977\pi\) | ||||
0.790199 | + | 0.612850i | \(0.209977\pi\) | |||||||
\(572\) | 6.94769 | 0.290498 | ||||||||
\(573\) | −10.2850 | −0.429664 | ||||||||
\(574\) | −3.66187 | −0.152844 | ||||||||
\(575\) | 17.8766 | 0.745505 | ||||||||
\(576\) | 0.755318 | 0.0314716 | ||||||||
\(577\) | 38.5479 | 1.60477 | 0.802384 | − | 0.596808i | \(-0.203565\pi\) | ||||
0.802384 | + | 0.596808i | \(0.203565\pi\) | |||||||
\(578\) | 5.40059 | 0.224635 | ||||||||
\(579\) | 12.0592 | 0.501162 | ||||||||
\(580\) | −6.44340 | −0.267548 | ||||||||
\(581\) | 26.1656 | 1.08553 | ||||||||
\(582\) | 5.01722 | 0.207970 | ||||||||
\(583\) | −10.8009 | −0.447327 | ||||||||
\(584\) | −17.1654 | −0.710311 | ||||||||
\(585\) | 40.4254 | 1.67139 | ||||||||
\(586\) | 10.2354 | 0.422821 | ||||||||
\(587\) | −31.2128 | −1.28829 | −0.644146 | − | 0.764903i | \(-0.722787\pi\) | ||||
−0.644146 | + | 0.764903i | \(0.722787\pi\) | |||||||
\(588\) | −2.81050 | −0.115903 | ||||||||
\(589\) | 4.20118 | 0.173107 | ||||||||
\(590\) | −18.0020 | −0.741130 | ||||||||
\(591\) | −12.9842 | −0.534097 | ||||||||
\(592\) | −2.15028 | −0.0883759 | ||||||||
\(593\) | 37.0761 | 1.52253 | 0.761267 | − | 0.648439i | \(-0.224578\pi\) | ||||
0.761267 | + | 0.648439i | \(0.224578\pi\) | |||||||
\(594\) | −2.32031 | −0.0952033 | ||||||||
\(595\) | −40.9378 | −1.67829 | ||||||||
\(596\) | −10.2953 | −0.421710 | ||||||||
\(597\) | 8.90245 | 0.364353 | ||||||||
\(598\) | 3.92747 | 0.160606 | ||||||||
\(599\) | 5.32743 | 0.217673 | 0.108836 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108836 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(600\) | 14.4712 | 0.590786 | ||||||||
\(601\) | −16.1212 | −0.657599 | −0.328800 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328800 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(602\) | 5.31150 | 0.216480 | ||||||||
\(603\) | 20.2064 | 0.822868 | ||||||||
\(604\) | −29.9207 | −1.21745 | ||||||||
\(605\) | 38.8087 | 1.57780 | ||||||||
\(606\) | −3.32720 | −0.135158 | ||||||||
\(607\) | −9.46080 | −0.384002 | −0.192001 | − | 0.981395i | \(-0.561498\pi\) | ||||
−0.192001 | + | 0.981395i | \(0.561498\pi\) | |||||||
\(608\) | −22.0993 | −0.896246 | ||||||||
\(609\) | 1.21944 | 0.0494143 | ||||||||
\(610\) | 29.7153 | 1.20314 | ||||||||
\(611\) | 10.4305 | 0.421973 | ||||||||
\(612\) | 21.7147 | 0.877766 | ||||||||
\(613\) | −6.21076 | −0.250850 | −0.125425 | − | 0.992103i | \(-0.540029\pi\) | ||||
−0.125425 | + | 0.992103i | \(0.540029\pi\) | |||||||
\(614\) | 7.77416 | 0.313740 | ||||||||
\(615\) | −7.00562 | −0.282494 | ||||||||
\(616\) | 5.02889 | 0.202620 | ||||||||
\(617\) | −10.8486 | −0.436749 | −0.218374 | − | 0.975865i | \(-0.570075\pi\) | ||||
−0.218374 | + | 0.975865i | \(0.570075\pi\) | |||||||
\(618\) | 6.71697 | 0.270196 | ||||||||
\(619\) | −10.6805 | −0.429286 | −0.214643 | − | 0.976693i | \(-0.568859\pi\) | ||||
−0.214643 | + | 0.976693i | \(0.568859\pi\) | |||||||
\(620\) | −6.87100 | −0.275946 | ||||||||
\(621\) | 5.61028 | 0.225133 | ||||||||
\(622\) | 9.00260 | 0.360972 | ||||||||
\(623\) | −3.07303 | −0.123118 | ||||||||
\(624\) | −4.33173 | −0.173408 | ||||||||
\(625\) | 37.6391 | 1.50556 | ||||||||
\(626\) | −14.4713 | −0.578388 | ||||||||
\(627\) | −2.63344 | −0.105170 | ||||||||
\(628\) | 5.12641 | 0.204566 | ||||||||
\(629\) | −5.83843 | −0.232793 | ||||||||
\(630\) | 13.0991 | 0.521882 | ||||||||
\(631\) | −4.98594 | −0.198487 | −0.0992436 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992436 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(632\) | −5.90857 | −0.235030 | ||||||||
\(633\) | −4.34248 | −0.172598 | ||||||||
\(634\) | 18.6629 | 0.741199 | ||||||||
\(635\) | 58.0284 | 2.30279 | ||||||||
\(636\) | 9.46404 | 0.375274 | ||||||||
\(637\) | −11.1171 | −0.440476 | ||||||||
\(638\) | 0.684580 | 0.0271028 | ||||||||
\(639\) | 10.1401 | 0.401135 | ||||||||
\(640\) | 45.2938 | 1.79040 | ||||||||
\(641\) | 0.148411 | 0.00586187 | 0.00293094 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00293094 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(642\) | 2.03640 | 0.0803704 | ||||||||
\(643\) | 8.24633 | 0.325203 | 0.162602 | − | 0.986692i | \(-0.448011\pi\) | ||||
0.162602 | + | 0.986692i | \(0.448011\pi\) | |||||||
\(644\) | −5.44337 | −0.214499 | ||||||||
\(645\) | 10.1616 | 0.400111 | ||||||||
\(646\) | −12.3128 | −0.484440 | ||||||||
\(647\) | 7.51637 | 0.295499 | 0.147750 | − | 0.989025i | \(-0.452797\pi\) | ||||
0.147750 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(648\) | −13.1046 | −0.514796 | ||||||||
\(649\) | −8.18081 | −0.321125 | ||||||||
\(650\) | 25.6254 | 1.00511 | ||||||||
\(651\) | 1.30037 | 0.0509654 | ||||||||
\(652\) | −30.9347 | −1.21150 | ||||||||
\(653\) | −22.7328 | −0.889604 | −0.444802 | − | 0.895629i | \(-0.646726\pi\) | ||||
−0.444802 | + | 0.895629i | \(0.646726\pi\) | |||||||
\(654\) | 2.91250 | 0.113888 | ||||||||
\(655\) | 2.84449 | 0.111143 | ||||||||
\(656\) | −5.48219 | −0.214043 | ||||||||
\(657\) | −20.3190 | −0.792718 | ||||||||
\(658\) | 3.37982 | 0.131759 | ||||||||
\(659\) | 2.90476 | 0.113153 | 0.0565766 | − | 0.998398i | \(-0.481981\pi\) | ||||
0.0565766 | + | 0.998398i | \(0.481981\pi\) | |||||||
\(660\) | 4.30698 | 0.167649 | ||||||||
\(661\) | −22.2795 | −0.866571 | −0.433286 | − | 0.901257i | \(-0.642646\pi\) | ||||
−0.433286 | + | 0.901257i | \(0.642646\pi\) | |||||||
\(662\) | −7.39976 | −0.287600 | ||||||||
\(663\) | −11.7615 | −0.456779 | ||||||||
\(664\) | −28.7511 | −1.11576 | ||||||||
\(665\) | 31.7696 | 1.23197 | ||||||||
\(666\) | 1.86816 | 0.0723897 | ||||||||
\(667\) | −1.65525 | −0.0640914 | ||||||||
\(668\) | 17.8779 | 0.691715 | ||||||||
\(669\) | 12.7749 | 0.493905 | ||||||||
\(670\) | 18.7387 | 0.723939 | ||||||||
\(671\) | 13.5038 | 0.521309 | ||||||||
\(672\) | −6.84027 | −0.263869 | ||||||||
\(673\) | 2.12558 | 0.0819353 | 0.0409676 | − | 0.999160i | \(-0.486956\pi\) | ||||
0.0409676 | + | 0.999160i | \(0.486956\pi\) | |||||||
\(674\) | −2.81811 | −0.108549 | ||||||||
\(675\) | 36.6052 | 1.40893 | ||||||||
\(676\) | −3.00732 | −0.115666 | ||||||||
\(677\) | 10.6579 | 0.409617 | 0.204809 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204809 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(678\) | 2.59463 | 0.0996462 | ||||||||
\(679\) | −27.5060 | −1.05558 | ||||||||
\(680\) | 44.9830 | 1.72502 | ||||||||
\(681\) | −6.39348 | −0.244999 | ||||||||
\(682\) | 0.730010 | 0.0279535 | ||||||||
\(683\) | −20.9959 | −0.803386 | −0.401693 | − | 0.915774i | \(-0.631578\pi\) | ||||
−0.401693 | + | 0.915774i | \(0.631578\pi\) | |||||||
\(684\) | −16.8516 | −0.644337 | ||||||||
\(685\) | 63.7133 | 2.43436 | ||||||||
\(686\) | −12.3446 | −0.471319 | ||||||||
\(687\) | 3.16429 | 0.120725 | ||||||||
\(688\) | 7.95184 | 0.303161 | ||||||||
\(689\) | 37.4356 | 1.42618 | ||||||||
\(690\) | 2.43469 | 0.0926872 | ||||||||
\(691\) | 35.1483 | 1.33711 | 0.668553 | − | 0.743664i | \(-0.266914\pi\) | ||||
0.668553 | + | 0.743664i | \(0.266914\pi\) | |||||||
\(692\) | 9.34897 | 0.355394 | ||||||||
\(693\) | 5.95276 | 0.226127 | ||||||||
\(694\) | −8.32667 | −0.316076 | ||||||||
\(695\) | 3.97491 | 0.150777 | ||||||||
\(696\) | −1.33994 | −0.0507902 | ||||||||
\(697\) | −14.8852 | −0.563818 | ||||||||
\(698\) | −22.2877 | −0.843602 | ||||||||
\(699\) | −8.49890 | −0.321458 | ||||||||
\(700\) | −35.5162 | −1.34239 | ||||||||
\(701\) | −40.7904 | −1.54063 | −0.770316 | − | 0.637663i | \(-0.779901\pi\) | ||||
−0.770316 | + | 0.637663i | \(0.779901\pi\) | |||||||
\(702\) | 8.04212 | 0.303530 | ||||||||
\(703\) | 4.53088 | 0.170886 | ||||||||
\(704\) | 0.318314 | 0.0119969 | ||||||||
\(705\) | 6.46603 | 0.243525 | ||||||||
\(706\) | −16.6124 | −0.625217 | ||||||||
\(707\) | 18.2407 | 0.686014 | ||||||||
\(708\) | 7.16826 | 0.269400 | ||||||||
\(709\) | 44.6748 | 1.67780 | 0.838898 | − | 0.544289i | \(-0.183200\pi\) | ||||
0.838898 | + | 0.544289i | \(0.183200\pi\) | |||||||
\(710\) | 9.40354 | 0.352909 | ||||||||
\(711\) | −6.99405 | −0.262297 | ||||||||
\(712\) | 3.37668 | 0.126547 | ||||||||
\(713\) | −1.76509 | −0.0661033 | ||||||||
\(714\) | −3.81110 | −0.142627 | ||||||||
\(715\) | 17.0365 | 0.637130 | ||||||||
\(716\) | 34.8355 | 1.30187 | ||||||||
\(717\) | 11.9160 | 0.445012 | ||||||||
\(718\) | −0.688603 | −0.0256984 | ||||||||
\(719\) | −35.3292 | −1.31756 | −0.658778 | − | 0.752338i | \(-0.728926\pi\) | ||||
−0.658778 | + | 0.752338i | \(0.728926\pi\) | |||||||
\(720\) | 19.6107 | 0.730848 | ||||||||
\(721\) | −36.8246 | −1.37142 | ||||||||
\(722\) | −2.14143 | −0.0796958 | ||||||||
\(723\) | −16.6354 | −0.618677 | ||||||||
\(724\) | −19.4261 | −0.721965 | ||||||||
\(725\) | −10.7999 | −0.401100 | ||||||||
\(726\) | 3.61289 | 0.134087 | ||||||||
\(727\) | −19.6178 | −0.727585 | −0.363793 | − | 0.931480i | \(-0.618518\pi\) | ||||
−0.363793 | + | 0.931480i | \(0.618518\pi\) | |||||||
\(728\) | −17.4300 | −0.645999 | ||||||||
\(729\) | −9.40001 | −0.348149 | ||||||||
\(730\) | −18.8431 | −0.697414 | ||||||||
\(731\) | 21.5908 | 0.798565 | ||||||||
\(732\) | −11.8324 | −0.437339 | ||||||||
\(733\) | −29.6250 | −1.09422 | −0.547112 | − | 0.837059i | \(-0.684273\pi\) | ||||
−0.547112 | + | 0.837059i | \(0.684273\pi\) | |||||||
\(734\) | 5.29510 | 0.195446 | ||||||||
\(735\) | −6.89167 | −0.254203 | ||||||||
\(736\) | 9.28486 | 0.342245 | ||||||||
\(737\) | 8.51560 | 0.313676 | ||||||||
\(738\) | 4.76292 | 0.175325 | ||||||||
\(739\) | 32.8693 | 1.20912 | 0.604558 | − | 0.796561i | \(-0.293350\pi\) | ||||
0.604558 | + | 0.796561i | \(0.293350\pi\) | |||||||
\(740\) | −7.41023 | −0.272405 | ||||||||
\(741\) | 9.12745 | 0.335305 | ||||||||
\(742\) | 12.1303 | 0.445319 | ||||||||
\(743\) | −33.8805 | −1.24296 | −0.621478 | − | 0.783432i | \(-0.713467\pi\) | ||||
−0.621478 | + | 0.783432i | \(0.713467\pi\) | |||||||
\(744\) | −1.42886 | −0.0523845 | ||||||||
\(745\) | −25.2451 | −0.924911 | ||||||||
\(746\) | −9.31704 | −0.341121 | ||||||||
\(747\) | −34.0330 | −1.24520 | ||||||||
\(748\) | 9.15126 | 0.334603 | ||||||||
\(749\) | −11.1642 | −0.407931 | ||||||||
\(750\) | 8.53110 | 0.311512 | ||||||||
\(751\) | 30.8934 | 1.12732 | 0.563658 | − | 0.826008i | \(-0.309394\pi\) | ||||
0.563658 | + | 0.826008i | \(0.309394\pi\) | |||||||
\(752\) | 5.05993 | 0.184517 | ||||||||
\(753\) | −8.43010 | −0.307210 | ||||||||
\(754\) | −2.37274 | −0.0864100 | ||||||||
\(755\) | −73.3688 | −2.67016 | ||||||||
\(756\) | −11.1462 | −0.405383 | ||||||||
\(757\) | −49.7854 | −1.80948 | −0.904741 | − | 0.425961i | \(-0.859936\pi\) | ||||
−0.904741 | + | 0.425961i | \(0.859936\pi\) | |||||||
\(758\) | −22.8442 | −0.829740 | ||||||||
\(759\) | 1.10642 | 0.0401605 | ||||||||
\(760\) | −34.9088 | −1.26628 | ||||||||
\(761\) | −15.5545 | −0.563849 | −0.281924 | − | 0.959437i | \(-0.590973\pi\) | ||||
−0.281924 | + | 0.959437i | \(0.590973\pi\) | |||||||
\(762\) | 5.40214 | 0.195699 | ||||||||
\(763\) | −15.9673 | −0.578053 | ||||||||
\(764\) | −27.7364 | −1.00347 | ||||||||
\(765\) | 53.2470 | 1.92515 | ||||||||
\(766\) | −17.3384 | −0.626464 | ||||||||
\(767\) | 28.3545 | 1.02382 | ||||||||
\(768\) | 3.87250 | 0.139737 | ||||||||
\(769\) | −26.8281 | −0.967447 | −0.483724 | − | 0.875221i | \(-0.660716\pi\) | ||||
−0.483724 | + | 0.875221i | \(0.660716\pi\) | |||||||
\(770\) | 5.52038 | 0.198941 | ||||||||
\(771\) | 14.0438 | 0.505774 | ||||||||
\(772\) | 32.5208 | 1.17045 | ||||||||
\(773\) | −31.8644 | −1.14608 | −0.573042 | − | 0.819526i | \(-0.694237\pi\) | ||||
−0.573042 | + | 0.819526i | \(0.694237\pi\) | |||||||
\(774\) | −6.90855 | −0.248323 | ||||||||
\(775\) | −11.5167 | −0.413690 | ||||||||
\(776\) | 30.2239 | 1.08497 | ||||||||
\(777\) | 1.40242 | 0.0503115 | ||||||||
\(778\) | −10.9525 | −0.392665 | ||||||||
\(779\) | 11.5516 | 0.413879 | ||||||||
\(780\) | −14.9279 | −0.534504 | ||||||||
\(781\) | 4.27334 | 0.152912 | ||||||||
\(782\) | 5.17312 | 0.184990 | ||||||||
\(783\) | −3.38939 | −0.121127 | ||||||||
\(784\) | −5.39301 | −0.192607 | ||||||||
\(785\) | 12.5705 | 0.448662 | ||||||||
\(786\) | 0.264807 | 0.00944536 | ||||||||
\(787\) | 7.31493 | 0.260749 | 0.130374 | − | 0.991465i | \(-0.458382\pi\) | ||||
0.130374 | + | 0.991465i | \(0.458382\pi\) | |||||||
\(788\) | −35.0153 | −1.24737 | ||||||||
\(789\) | −1.37056 | −0.0487931 | ||||||||
\(790\) | −6.48604 | −0.230763 | ||||||||
\(791\) | −14.2246 | −0.505768 | ||||||||
\(792\) | −6.54097 | −0.232423 | ||||||||
\(793\) | −46.8039 | −1.66206 | ||||||||
\(794\) | 4.66542 | 0.165570 | ||||||||
\(795\) | 23.2069 | 0.823063 | ||||||||
\(796\) | 24.0079 | 0.850936 | ||||||||
\(797\) | −50.0545 | −1.77302 | −0.886511 | − | 0.462707i | \(-0.846878\pi\) | ||||
−0.886511 | + | 0.462707i | \(0.846878\pi\) | |||||||
\(798\) | 2.95759 | 0.104698 | ||||||||
\(799\) | 13.7387 | 0.486041 | ||||||||
\(800\) | 60.5807 | 2.14185 | ||||||||
\(801\) | 3.99703 | 0.141228 | ||||||||
\(802\) | 9.73195 | 0.343647 | ||||||||
\(803\) | −8.56304 | −0.302183 | ||||||||
\(804\) | −7.46160 | −0.263150 | ||||||||
\(805\) | −13.3478 | −0.470447 | ||||||||
\(806\) | −2.53020 | −0.0891224 | ||||||||
\(807\) | −8.82505 | −0.310656 | ||||||||
\(808\) | −20.0431 | −0.705115 | ||||||||
\(809\) | −6.08205 | −0.213833 | −0.106917 | − | 0.994268i | \(-0.534098\pi\) | ||||
−0.106917 | + | 0.994268i | \(0.534098\pi\) | |||||||
\(810\) | −14.3853 | −0.505449 | ||||||||
\(811\) | 15.0138 | 0.527206 | 0.263603 | − | 0.964631i | \(-0.415089\pi\) | ||||
0.263603 | + | 0.964631i | \(0.415089\pi\) | |||||||
\(812\) | 3.28855 | 0.115406 | ||||||||
\(813\) | 12.9252 | 0.453306 | ||||||||
\(814\) | 0.787300 | 0.0275949 | ||||||||
\(815\) | −75.8555 | −2.65710 | ||||||||
\(816\) | −5.70560 | −0.199736 | ||||||||
\(817\) | −16.7554 | −0.586199 | ||||||||
\(818\) | −6.37273 | −0.222817 | ||||||||
\(819\) | −20.6321 | −0.720945 | ||||||||
\(820\) | −18.8926 | −0.659756 | ||||||||
\(821\) | −5.33220 | −0.186095 | −0.0930475 | − | 0.995662i | \(-0.529661\pi\) | ||||
−0.0930475 | + | 0.995662i | \(0.529661\pi\) | |||||||
\(822\) | 5.93138 | 0.206881 | ||||||||
\(823\) | 38.9628 | 1.35816 | 0.679080 | − | 0.734065i | \(-0.262379\pi\) | ||||
0.679080 | + | 0.734065i | \(0.262379\pi\) | |||||||
\(824\) | 40.4632 | 1.40960 | ||||||||
\(825\) | 7.21903 | 0.251334 | ||||||||
\(826\) | 9.18777 | 0.319683 | ||||||||
\(827\) | 23.3030 | 0.810326 | 0.405163 | − | 0.914245i | \(-0.367215\pi\) | ||||
0.405163 | + | 0.914245i | \(0.367215\pi\) | |||||||
\(828\) | 7.08007 | 0.246050 | ||||||||
\(829\) | −5.21237 | −0.181033 | −0.0905165 | − | 0.995895i | \(-0.528852\pi\) | ||||
−0.0905165 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(830\) | −31.5610 | −1.09550 | ||||||||
\(831\) | −7.50015 | −0.260177 | ||||||||
\(832\) | −1.10327 | −0.0382490 | ||||||||
\(833\) | −14.6431 | −0.507353 | ||||||||
\(834\) | 0.370044 | 0.0128136 | ||||||||
\(835\) | 43.8385 | 1.51709 | ||||||||
\(836\) | −7.10179 | −0.245621 | ||||||||
\(837\) | −3.61432 | −0.124929 | ||||||||
\(838\) | 16.9359 | 0.585040 | ||||||||
\(839\) | 46.8673 | 1.61804 | 0.809019 | − | 0.587782i | \(-0.199999\pi\) | ||||
0.809019 | + | 0.587782i | \(0.199999\pi\) | |||||||
\(840\) | −10.8051 | −0.372812 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 11.8753 | 0.409249 | ||||||||
\(843\) | −7.89919 | −0.272062 | ||||||||
\(844\) | −11.7107 | −0.403097 | ||||||||
\(845\) | −7.37428 | −0.253683 | ||||||||
\(846\) | −4.39606 | −0.151140 | ||||||||
\(847\) | −19.8070 | −0.680577 | ||||||||
\(848\) | 18.1603 | 0.623628 | ||||||||
\(849\) | 3.07066 | 0.105385 | ||||||||
\(850\) | 33.7529 | 1.15772 | ||||||||
\(851\) | −1.90362 | −0.0652551 | ||||||||
\(852\) | −3.74442 | −0.128282 | ||||||||
\(853\) | 37.2671 | 1.27600 | 0.638000 | − | 0.770036i | \(-0.279762\pi\) | ||||
0.638000 | + | 0.770036i | \(0.279762\pi\) | |||||||
\(854\) | −15.1660 | −0.518969 | ||||||||
\(855\) | −41.3220 | −1.41318 | ||||||||
\(856\) | 12.2673 | 0.419289 | ||||||||
\(857\) | 29.4433 | 1.00576 | 0.502882 | − | 0.864355i | \(-0.332273\pi\) | ||||
0.502882 | + | 0.864355i | \(0.332273\pi\) | |||||||
\(858\) | 1.58601 | 0.0541456 | ||||||||
\(859\) | −26.6031 | −0.907687 | −0.453844 | − | 0.891081i | \(-0.649948\pi\) | ||||
−0.453844 | + | 0.891081i | \(0.649948\pi\) | |||||||
\(860\) | 27.4034 | 0.934448 | ||||||||
\(861\) | 3.57550 | 0.121853 | ||||||||
\(862\) | −15.5193 | −0.528591 | ||||||||
\(863\) | −4.62917 | −0.157579 | −0.0787893 | − | 0.996891i | \(-0.525105\pi\) | ||||
−0.0787893 | + | 0.996891i | \(0.525105\pi\) | |||||||
\(864\) | 19.0123 | 0.646810 | ||||||||
\(865\) | 22.9247 | 0.779464 | ||||||||
\(866\) | 8.65026 | 0.293948 | ||||||||
\(867\) | −5.27321 | −0.179088 | ||||||||
\(868\) | 3.50679 | 0.119028 | ||||||||
\(869\) | −2.94751 | −0.0999874 | ||||||||
\(870\) | −1.47089 | −0.0498680 | ||||||||
\(871\) | −29.5148 | −1.00007 | ||||||||
\(872\) | 17.5450 | 0.594149 | ||||||||
\(873\) | 35.7764 | 1.21085 | ||||||||
\(874\) | −4.01458 | −0.135795 | ||||||||
\(875\) | −46.7702 | −1.58112 | ||||||||
\(876\) | 7.50317 | 0.253509 | ||||||||
\(877\) | −37.9500 | −1.28148 | −0.640741 | − | 0.767757i | \(-0.721373\pi\) | ||||
−0.640741 | + | 0.767757i | \(0.721373\pi\) | |||||||
\(878\) | −12.0632 | −0.407113 | ||||||||
\(879\) | −9.99398 | −0.337089 | ||||||||
\(880\) | 8.26456 | 0.278598 | ||||||||
\(881\) | −36.9384 | −1.24449 | −0.622243 | − | 0.782824i | \(-0.713779\pi\) | ||||
−0.622243 | + | 0.782824i | \(0.713779\pi\) | |||||||
\(882\) | 4.68544 | 0.157767 | ||||||||
\(883\) | 6.62091 | 0.222811 | 0.111406 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111406 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(884\) | −31.7180 | −1.06679 | ||||||||
\(885\) | 17.5774 | 0.590857 | ||||||||
\(886\) | 16.8452 | 0.565925 | ||||||||
\(887\) | −31.5031 | −1.05777 | −0.528886 | − | 0.848693i | \(-0.677390\pi\) | ||||
−0.528886 | + | 0.848693i | \(0.677390\pi\) | |||||||
\(888\) | −1.54099 | −0.0517123 | ||||||||
\(889\) | −29.6162 | −0.993297 | ||||||||
\(890\) | 3.70670 | 0.124249 | ||||||||
\(891\) | −6.53726 | −0.219006 | ||||||||
\(892\) | 34.4509 | 1.15350 | ||||||||
\(893\) | −10.6619 | −0.356786 | ||||||||
\(894\) | −2.35019 | −0.0786023 | ||||||||
\(895\) | 85.4207 | 2.85530 | ||||||||
\(896\) | −23.1168 | −0.772280 | ||||||||
\(897\) | −3.83483 | −0.128041 | ||||||||
\(898\) | 1.06401 | 0.0355066 | ||||||||
\(899\) | 1.06636 | 0.0355652 | ||||||||
\(900\) | 46.1951 | 1.53984 | ||||||||
\(901\) | 49.3089 | 1.64272 | ||||||||
\(902\) | 2.00724 | 0.0668338 | ||||||||
\(903\) | −5.18621 | −0.172586 | ||||||||
\(904\) | 15.6301 | 0.519851 | ||||||||
\(905\) | −47.6349 | −1.58344 | ||||||||
\(906\) | −6.83026 | −0.226920 | ||||||||
\(907\) | −35.3168 | −1.17267 | −0.586337 | − | 0.810067i | \(-0.699431\pi\) | ||||
−0.586337 | + | 0.810067i | \(0.699431\pi\) | |||||||
\(908\) | −17.2417 | −0.572187 | ||||||||
\(909\) | −23.7253 | −0.786920 | ||||||||
\(910\) | −19.1335 | −0.634270 | ||||||||
\(911\) | −41.4212 | −1.37235 | −0.686173 | − | 0.727439i | \(-0.740711\pi\) | ||||
−0.686173 | + | 0.727439i | \(0.740711\pi\) | |||||||
\(912\) | 4.42780 | 0.146619 | ||||||||
\(913\) | −14.3426 | −0.474670 | ||||||||
\(914\) | −8.46650 | −0.280047 | ||||||||
\(915\) | −29.0144 | −0.959188 | ||||||||
\(916\) | 8.53335 | 0.281950 | ||||||||
\(917\) | −1.45176 | −0.0479412 | ||||||||
\(918\) | 10.5928 | 0.349615 | ||||||||
\(919\) | −26.9177 | −0.887934 | −0.443967 | − | 0.896043i | \(-0.646429\pi\) | ||||
−0.443967 | + | 0.896043i | \(0.646429\pi\) | |||||||
\(920\) | 14.6667 | 0.483546 | ||||||||
\(921\) | −7.59079 | −0.250125 | ||||||||
\(922\) | 0.0202460 | 0.000666767 0 | ||||||||
\(923\) | −14.8113 | −0.487520 | ||||||||
\(924\) | −2.19818 | −0.0723146 | ||||||||
\(925\) | −12.4205 | −0.408382 | ||||||||
\(926\) | 16.9613 | 0.557383 | ||||||||
\(927\) | 47.8969 | 1.57314 | ||||||||
\(928\) | −5.60935 | −0.184136 | ||||||||
\(929\) | −12.8312 | −0.420977 | −0.210488 | − | 0.977596i | \(-0.567505\pi\) | ||||
−0.210488 | + | 0.977596i | \(0.567505\pi\) | |||||||
\(930\) | −1.56851 | −0.0514334 | ||||||||
\(931\) | 11.3637 | 0.372430 | ||||||||
\(932\) | −22.9196 | −0.750756 | ||||||||
\(933\) | −8.79026 | −0.287780 | ||||||||
\(934\) | 22.9001 | 0.749315 | ||||||||
\(935\) | 22.4399 | 0.733864 | ||||||||
\(936\) | 22.6708 | 0.741019 | ||||||||
\(937\) | −15.6452 | −0.511106 | −0.255553 | − | 0.966795i | \(-0.582258\pi\) | ||||
−0.255553 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(938\) | −9.56377 | −0.312268 | ||||||||
\(939\) | 14.1299 | 0.461113 | ||||||||
\(940\) | 17.4374 | 0.568745 | ||||||||
\(941\) | −21.1585 | −0.689748 | −0.344874 | − | 0.938649i | \(-0.612078\pi\) | ||||
−0.344874 | + | 0.938649i | \(0.612078\pi\) | |||||||
\(942\) | 1.17025 | 0.0381289 | ||||||||
\(943\) | −4.85331 | −0.158046 | ||||||||
\(944\) | 13.7550 | 0.447687 | ||||||||
\(945\) | −27.3317 | −0.889100 | ||||||||
\(946\) | −2.91148 | −0.0946603 | ||||||||
\(947\) | −3.97387 | −0.129133 | −0.0645666 | − | 0.997913i | \(-0.520567\pi\) | ||||
−0.0645666 | + | 0.997913i | \(0.520567\pi\) | |||||||
\(948\) | 2.58269 | 0.0838819 | ||||||||
\(949\) | 29.6793 | 0.963430 | ||||||||
\(950\) | −26.1938 | −0.849839 | ||||||||
\(951\) | −18.2227 | −0.590911 | ||||||||
\(952\) | −22.9582 | −0.744079 | ||||||||
\(953\) | 6.48506 | 0.210072 | 0.105036 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105036 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(954\) | −15.7777 | −0.510821 | ||||||||
\(955\) | −68.0128 | −2.20084 | ||||||||
\(956\) | 32.1348 | 1.03931 | ||||||||
\(957\) | −0.668432 | −0.0216073 | ||||||||
\(958\) | −4.06352 | −0.131286 | ||||||||
\(959\) | −32.5177 | −1.05005 | ||||||||
\(960\) | −0.683933 | −0.0220738 | ||||||||
\(961\) | −29.8629 | −0.963318 | ||||||||
\(962\) | −2.72876 | −0.0879789 | ||||||||
\(963\) | 14.5210 | 0.467934 | ||||||||
\(964\) | −44.8619 | −1.44490 | ||||||||
\(965\) | 79.7446 | 2.56707 | ||||||||
\(966\) | −1.24261 | −0.0399803 | ||||||||
\(967\) | −8.77847 | −0.282297 | −0.141148 | − | 0.989988i | \(-0.545079\pi\) | ||||
−0.141148 | + | 0.989988i | \(0.545079\pi\) | |||||||
\(968\) | 21.7642 | 0.699527 | ||||||||
\(969\) | 12.0224 | 0.386214 | ||||||||
\(970\) | 33.1778 | 1.06527 | ||||||||
\(971\) | −32.5946 | −1.04601 | −0.523006 | − | 0.852329i | \(-0.675189\pi\) | ||||
−0.523006 | + | 0.852329i | \(0.675189\pi\) | |||||||
\(972\) | 22.2109 | 0.712415 | ||||||||
\(973\) | −2.02870 | −0.0650371 | ||||||||
\(974\) | 6.13939 | 0.196719 | ||||||||
\(975\) | −25.0210 | −0.801313 | ||||||||
\(976\) | −22.7050 | −0.726769 | ||||||||
\(977\) | −39.0187 | −1.24832 | −0.624159 | − | 0.781297i | \(-0.714558\pi\) | ||||
−0.624159 | + | 0.781297i | \(0.714558\pi\) | |||||||
\(978\) | −7.06176 | −0.225810 | ||||||||
\(979\) | 1.68447 | 0.0538359 | ||||||||
\(980\) | −18.5852 | −0.593684 | ||||||||
\(981\) | 20.7683 | 0.663079 | ||||||||
\(982\) | −20.9920 | −0.669882 | ||||||||
\(983\) | 25.7395 | 0.820962 | 0.410481 | − | 0.911869i | \(-0.365361\pi\) | ||||
0.410481 | + | 0.911869i | \(0.365361\pi\) | |||||||
\(984\) | −3.92880 | −0.125245 | ||||||||
\(985\) | −85.8615 | −2.73577 | ||||||||
\(986\) | −3.12529 | −0.0995294 | ||||||||
\(987\) | −3.30010 | −0.105043 | ||||||||
\(988\) | 24.6146 | 0.783096 | ||||||||
\(989\) | 7.03967 | 0.223848 | ||||||||
\(990\) | −7.18024 | −0.228203 | ||||||||
\(991\) | −13.8592 | −0.440251 | −0.220125 | − | 0.975472i | \(-0.570647\pi\) | ||||
−0.220125 | + | 0.975472i | \(0.570647\pi\) | |||||||
\(992\) | −5.98160 | −0.189916 | ||||||||
\(993\) | 7.22522 | 0.229285 | ||||||||
\(994\) | −4.79934 | −0.152226 | ||||||||
\(995\) | 58.8700 | 1.86630 | ||||||||
\(996\) | 12.5674 | 0.398212 | ||||||||
\(997\) | 35.1566 | 1.11342 | 0.556710 | − | 0.830707i | \(-0.312063\pi\) | ||||
0.556710 | + | 0.830707i | \(0.312063\pi\) | |||||||
\(998\) | −1.72793 | −0.0546966 | ||||||||
\(999\) | −3.89796 | −0.123326 |
(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 | 4031.2.a.c.1.36 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.36 | ✓ | 61 | 1.1 | even | 1 | trivial |