Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6035,2,Mod(1,6035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6035, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6035 = 5 \cdot 17 \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6035.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: | \(48.1897176198\) |
Analytic rank: | \(0\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27257 | −0.899844 | −0.449922 | − | 0.893068i | \(-0.648548\pi\) | ||||
−0.449922 | + | 0.893068i | \(0.648548\pi\) | |||||||
\(3\) | 0.337599 | 0.194913 | 0.0974566 | − | 0.995240i | \(-0.468929\pi\) | ||||
0.0974566 | + | 0.995240i | \(0.468929\pi\) | |||||||
\(4\) | −0.380563 | −0.190281 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.429619 | −0.175391 | ||||||||
\(7\) | −3.22826 | −1.22017 | −0.610085 | − | 0.792336i | \(-0.708865\pi\) | ||||
−0.610085 | + | 0.792336i | \(0.708865\pi\) | |||||||
\(8\) | 3.02944 | 1.07107 | ||||||||
\(9\) | −2.88603 | −0.962009 | ||||||||
\(10\) | −1.27257 | −0.402422 | ||||||||
\(11\) | 5.86941 | 1.76969 | 0.884846 | − | 0.465883i | \(-0.154263\pi\) | ||||
0.884846 | + | 0.465883i | \(0.154263\pi\) | |||||||
\(12\) | −0.128478 | −0.0370883 | ||||||||
\(13\) | 5.87183 | 1.62855 | 0.814277 | − | 0.580477i | \(-0.197134\pi\) | ||||
0.814277 | + | 0.580477i | \(0.197134\pi\) | |||||||
\(14\) | 4.10820 | 1.09796 | ||||||||
\(15\) | 0.337599 | 0.0871678 | ||||||||
\(16\) | −3.09405 | −0.773512 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 3.67267 | 0.865658 | ||||||||
\(19\) | −1.15278 | −0.264467 | −0.132233 | − | 0.991219i | \(-0.542215\pi\) | ||||
−0.132233 | + | 0.991219i | \(0.542215\pi\) | |||||||
\(20\) | −0.380563 | −0.0850964 | ||||||||
\(21\) | −1.08986 | −0.237827 | ||||||||
\(22\) | −7.46924 | −1.59245 | ||||||||
\(23\) | 5.98677 | 1.24833 | 0.624164 | − | 0.781293i | \(-0.285440\pi\) | ||||
0.624164 | + | 0.781293i | \(0.285440\pi\) | |||||||
\(24\) | 1.02274 | 0.208765 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.47233 | −1.46544 | ||||||||
\(27\) | −1.98712 | −0.382421 | ||||||||
\(28\) | 1.22856 | 0.232175 | ||||||||
\(29\) | −5.17557 | −0.961078 | −0.480539 | − | 0.876973i | \(-0.659559\pi\) | ||||
−0.480539 | + | 0.876973i | \(0.659559\pi\) | |||||||
\(30\) | −0.429619 | −0.0784374 | ||||||||
\(31\) | −4.45421 | −0.800000 | −0.400000 | − | 0.916515i | \(-0.630990\pi\) | ||||
−0.400000 | + | 0.916515i | \(0.630990\pi\) | |||||||
\(32\) | −2.12148 | −0.375028 | ||||||||
\(33\) | 1.98151 | 0.344936 | ||||||||
\(34\) | 1.27257 | 0.218244 | ||||||||
\(35\) | −3.22826 | −0.545676 | ||||||||
\(36\) | 1.09831 | 0.183052 | ||||||||
\(37\) | 9.18517 | 1.51003 | 0.755017 | − | 0.655706i | \(-0.227629\pi\) | ||||
0.755017 | + | 0.655706i | \(0.227629\pi\) | |||||||
\(38\) | 1.46700 | 0.237979 | ||||||||
\(39\) | 1.98233 | 0.317427 | ||||||||
\(40\) | 3.02944 | 0.478996 | ||||||||
\(41\) | 0.830550 | 0.129710 | 0.0648551 | − | 0.997895i | \(-0.479341\pi\) | ||||
0.0648551 | + | 0.997895i | \(0.479341\pi\) | |||||||
\(42\) | 1.38692 | 0.214007 | ||||||||
\(43\) | 3.80639 | 0.580470 | 0.290235 | − | 0.956955i | \(-0.406267\pi\) | ||||
0.290235 | + | 0.956955i | \(0.406267\pi\) | |||||||
\(44\) | −2.23368 | −0.336739 | ||||||||
\(45\) | −2.88603 | −0.430223 | ||||||||
\(46\) | −7.61859 | −1.12330 | ||||||||
\(47\) | 1.20804 | 0.176210 | 0.0881052 | − | 0.996111i | \(-0.471919\pi\) | ||||
0.0881052 | + | 0.996111i | \(0.471919\pi\) | |||||||
\(48\) | −1.04455 | −0.150768 | ||||||||
\(49\) | 3.42169 | 0.488813 | ||||||||
\(50\) | −1.27257 | −0.179969 | ||||||||
\(51\) | −0.337599 | −0.0472734 | ||||||||
\(52\) | −2.23460 | −0.309883 | ||||||||
\(53\) | 10.7170 | 1.47209 | 0.736043 | − | 0.676935i | \(-0.236692\pi\) | ||||
0.736043 | + | 0.676935i | \(0.236692\pi\) | |||||||
\(54\) | 2.52875 | 0.344119 | ||||||||
\(55\) | 5.86941 | 0.791430 | ||||||||
\(56\) | −9.77982 | −1.30688 | ||||||||
\(57\) | −0.389179 | −0.0515481 | ||||||||
\(58\) | 6.58628 | 0.864820 | ||||||||
\(59\) | 10.2801 | 1.33836 | 0.669179 | − | 0.743101i | \(-0.266646\pi\) | ||||
0.669179 | + | 0.743101i | \(0.266646\pi\) | |||||||
\(60\) | −0.128478 | −0.0165864 | ||||||||
\(61\) | 3.99447 | 0.511439 | 0.255719 | − | 0.966751i | \(-0.417688\pi\) | ||||
0.255719 | + | 0.966751i | \(0.417688\pi\) | |||||||
\(62\) | 5.66830 | 0.719875 | ||||||||
\(63\) | 9.31686 | 1.17381 | ||||||||
\(64\) | 8.88782 | 1.11098 | ||||||||
\(65\) | 5.87183 | 0.728311 | ||||||||
\(66\) | −2.52161 | −0.310389 | ||||||||
\(67\) | −3.74312 | −0.457295 | −0.228647 | − | 0.973509i | \(-0.573430\pi\) | ||||
−0.228647 | + | 0.973509i | \(0.573430\pi\) | |||||||
\(68\) | 0.380563 | 0.0461500 | ||||||||
\(69\) | 2.02113 | 0.243316 | ||||||||
\(70\) | 4.10820 | 0.491023 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −8.74303 | −1.03038 | ||||||||
\(73\) | −12.5152 | −1.46479 | −0.732394 | − | 0.680881i | \(-0.761597\pi\) | ||||
−0.732394 | + | 0.680881i | \(0.761597\pi\) | |||||||
\(74\) | −11.6888 | −1.35879 | ||||||||
\(75\) | 0.337599 | 0.0389826 | ||||||||
\(76\) | 0.438707 | 0.0503231 | ||||||||
\(77\) | −18.9480 | −2.15932 | ||||||||
\(78\) | −2.52265 | −0.285634 | ||||||||
\(79\) | −16.5348 | −1.86031 | −0.930155 | − | 0.367168i | \(-0.880327\pi\) | ||||
−0.930155 | + | 0.367168i | \(0.880327\pi\) | |||||||
\(80\) | −3.09405 | −0.345925 | ||||||||
\(81\) | 7.98723 | 0.887470 | ||||||||
\(82\) | −1.05693 | −0.116719 | ||||||||
\(83\) | 5.36542 | 0.588931 | 0.294465 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294465 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(84\) | 0.414760 | 0.0452541 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | −4.84391 | −0.522332 | ||||||||
\(87\) | −1.74727 | −0.187327 | ||||||||
\(88\) | 17.7810 | 1.89546 | ||||||||
\(89\) | 16.4034 | 1.73875 | 0.869376 | − | 0.494151i | \(-0.164521\pi\) | ||||
0.869376 | + | 0.494151i | \(0.164521\pi\) | |||||||
\(90\) | 3.67267 | 0.387134 | ||||||||
\(91\) | −18.9558 | −1.98711 | ||||||||
\(92\) | −2.27834 | −0.237534 | ||||||||
\(93\) | −1.50374 | −0.155931 | ||||||||
\(94\) | −1.53731 | −0.158562 | ||||||||
\(95\) | −1.15278 | −0.118273 | ||||||||
\(96\) | −0.716209 | −0.0730978 | ||||||||
\(97\) | −12.0695 | −1.22547 | −0.612734 | − | 0.790290i | \(-0.709930\pi\) | ||||
−0.612734 | + | 0.790290i | \(0.709930\pi\) | |||||||
\(98\) | −4.35435 | −0.439855 | ||||||||
\(99\) | −16.9393 | −1.70246 | ||||||||
\(100\) | −0.380563 | −0.0380563 | ||||||||
\(101\) | 3.19386 | 0.317801 | 0.158901 | − | 0.987295i | \(-0.449205\pi\) | ||||
0.158901 | + | 0.987295i | \(0.449205\pi\) | |||||||
\(102\) | 0.429619 | 0.0425387 | ||||||||
\(103\) | −10.8152 | −1.06565 | −0.532827 | − | 0.846224i | \(-0.678870\pi\) | ||||
−0.532827 | + | 0.846224i | \(0.678870\pi\) | |||||||
\(104\) | 17.7883 | 1.74429 | ||||||||
\(105\) | −1.08986 | −0.106359 | ||||||||
\(106\) | −13.6381 | −1.32465 | ||||||||
\(107\) | 5.76952 | 0.557761 | 0.278880 | − | 0.960326i | \(-0.410037\pi\) | ||||
0.278880 | + | 0.960326i | \(0.410037\pi\) | |||||||
\(108\) | 0.756224 | 0.0727676 | ||||||||
\(109\) | −4.47956 | −0.429064 | −0.214532 | − | 0.976717i | \(-0.568823\pi\) | ||||
−0.214532 | + | 0.976717i | \(0.568823\pi\) | |||||||
\(110\) | −7.46924 | −0.712164 | ||||||||
\(111\) | 3.10091 | 0.294325 | ||||||||
\(112\) | 9.98840 | 0.943815 | ||||||||
\(113\) | −17.8871 | −1.68267 | −0.841336 | − | 0.540512i | \(-0.818231\pi\) | ||||
−0.841336 | + | 0.540512i | \(0.818231\pi\) | |||||||
\(114\) | 0.495258 | 0.0463852 | ||||||||
\(115\) | 5.98677 | 0.558269 | ||||||||
\(116\) | 1.96963 | 0.182875 | ||||||||
\(117\) | −16.9463 | −1.56668 | ||||||||
\(118\) | −13.0822 | −1.20431 | ||||||||
\(119\) | 3.22826 | 0.295935 | ||||||||
\(120\) | 1.02274 | 0.0933626 | ||||||||
\(121\) | 23.4499 | 2.13181 | ||||||||
\(122\) | −5.08324 | −0.460215 | ||||||||
\(123\) | 0.280393 | 0.0252822 | ||||||||
\(124\) | 1.69511 | 0.152225 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −11.8564 | −1.05625 | ||||||||
\(127\) | −4.04593 | −0.359018 | −0.179509 | − | 0.983756i | \(-0.557451\pi\) | ||||
−0.179509 | + | 0.983756i | \(0.557451\pi\) | |||||||
\(128\) | −7.06743 | −0.624679 | ||||||||
\(129\) | 1.28504 | 0.113141 | ||||||||
\(130\) | −7.47233 | −0.655366 | ||||||||
\(131\) | −13.9551 | −1.21926 | −0.609631 | − | 0.792685i | \(-0.708683\pi\) | ||||
−0.609631 | + | 0.792685i | \(0.708683\pi\) | |||||||
\(132\) | −0.754088 | −0.0656349 | ||||||||
\(133\) | 3.72149 | 0.322694 | ||||||||
\(134\) | 4.76339 | 0.411494 | ||||||||
\(135\) | −1.98712 | −0.171024 | ||||||||
\(136\) | −3.02944 | −0.259772 | ||||||||
\(137\) | 3.39428 | 0.289993 | 0.144997 | − | 0.989432i | \(-0.453683\pi\) | ||||
0.144997 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(138\) | −2.57203 | −0.218946 | ||||||||
\(139\) | −0.911726 | −0.0773316 | −0.0386658 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386658 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(140\) | 1.22856 | 0.103832 | ||||||||
\(141\) | 0.407833 | 0.0343457 | ||||||||
\(142\) | 1.27257 | 0.106792 | ||||||||
\(143\) | 34.4642 | 2.88204 | ||||||||
\(144\) | 8.92950 | 0.744125 | ||||||||
\(145\) | −5.17557 | −0.429807 | ||||||||
\(146\) | 15.9264 | 1.31808 | ||||||||
\(147\) | 1.15516 | 0.0952761 | ||||||||
\(148\) | −3.49553 | −0.287331 | ||||||||
\(149\) | 7.69870 | 0.630702 | 0.315351 | − | 0.948975i | \(-0.397878\pi\) | ||||
0.315351 | + | 0.948975i | \(0.397878\pi\) | |||||||
\(150\) | −0.429619 | −0.0350783 | ||||||||
\(151\) | −14.1874 | −1.15455 | −0.577276 | − | 0.816549i | \(-0.695884\pi\) | ||||
−0.577276 | + | 0.816549i | \(0.695884\pi\) | |||||||
\(152\) | −3.49229 | −0.283262 | ||||||||
\(153\) | 2.88603 | 0.233321 | ||||||||
\(154\) | 24.1127 | 1.94305 | ||||||||
\(155\) | −4.45421 | −0.357771 | ||||||||
\(156\) | −0.754400 | −0.0604004 | ||||||||
\(157\) | −3.39395 | −0.270867 | −0.135433 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135433 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(158\) | 21.0417 | 1.67399 | ||||||||
\(159\) | 3.61804 | 0.286929 | ||||||||
\(160\) | −2.12148 | −0.167717 | ||||||||
\(161\) | −19.3269 | −1.52317 | ||||||||
\(162\) | −10.1643 | −0.798584 | ||||||||
\(163\) | 14.4047 | 1.12827 | 0.564133 | − | 0.825684i | \(-0.309210\pi\) | ||||
0.564133 | + | 0.825684i | \(0.309210\pi\) | |||||||
\(164\) | −0.316076 | −0.0246814 | ||||||||
\(165\) | 1.98151 | 0.154260 | ||||||||
\(166\) | −6.82787 | −0.529946 | ||||||||
\(167\) | −5.75602 | −0.445414 | −0.222707 | − | 0.974885i | \(-0.571489\pi\) | ||||
−0.222707 | + | 0.974885i | \(0.571489\pi\) | |||||||
\(168\) | −3.30166 | −0.254729 | ||||||||
\(169\) | 21.4784 | 1.65219 | ||||||||
\(170\) | 1.27257 | 0.0976018 | ||||||||
\(171\) | 3.32697 | 0.254419 | ||||||||
\(172\) | −1.44857 | −0.110453 | ||||||||
\(173\) | −17.5794 | −1.33654 | −0.668270 | − | 0.743919i | \(-0.732965\pi\) | ||||
−0.668270 | + | 0.743919i | \(0.732965\pi\) | |||||||
\(174\) | 2.22352 | 0.168565 | ||||||||
\(175\) | −3.22826 | −0.244034 | ||||||||
\(176\) | −18.1602 | −1.36888 | ||||||||
\(177\) | 3.47056 | 0.260864 | ||||||||
\(178\) | −20.8744 | −1.56460 | ||||||||
\(179\) | 6.73734 | 0.503573 | 0.251786 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251786 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(180\) | 1.09831 | 0.0818635 | ||||||||
\(181\) | 7.56702 | 0.562452 | 0.281226 | − | 0.959642i | \(-0.409259\pi\) | ||||
0.281226 | + | 0.959642i | \(0.409259\pi\) | |||||||
\(182\) | 24.1226 | 1.78809 | ||||||||
\(183\) | 1.34853 | 0.0996862 | ||||||||
\(184\) | 18.1365 | 1.33704 | ||||||||
\(185\) | 9.18517 | 0.675307 | ||||||||
\(186\) | 1.91362 | 0.140313 | ||||||||
\(187\) | −5.86941 | −0.429213 | ||||||||
\(188\) | −0.459734 | −0.0335295 | ||||||||
\(189\) | 6.41495 | 0.466619 | ||||||||
\(190\) | 1.46700 | 0.106427 | ||||||||
\(191\) | 16.9482 | 1.22633 | 0.613164 | − | 0.789956i | \(-0.289897\pi\) | ||||
0.613164 | + | 0.789956i | \(0.289897\pi\) | |||||||
\(192\) | 3.00052 | 0.216544 | ||||||||
\(193\) | −22.1445 | −1.59400 | −0.796998 | − | 0.603982i | \(-0.793580\pi\) | ||||
−0.796998 | + | 0.603982i | \(0.793580\pi\) | |||||||
\(194\) | 15.3592 | 1.10273 | ||||||||
\(195\) | 1.98233 | 0.141957 | ||||||||
\(196\) | −1.30217 | −0.0930120 | ||||||||
\(197\) | 17.8575 | 1.27229 | 0.636146 | − | 0.771568i | \(-0.280527\pi\) | ||||
0.636146 | + | 0.771568i | \(0.280527\pi\) | |||||||
\(198\) | 21.5564 | 1.53195 | ||||||||
\(199\) | 13.3543 | 0.946658 | 0.473329 | − | 0.880886i | \(-0.343052\pi\) | ||||
0.473329 | + | 0.880886i | \(0.343052\pi\) | |||||||
\(200\) | 3.02944 | 0.214213 | ||||||||
\(201\) | −1.26368 | −0.0891328 | ||||||||
\(202\) | −4.06442 | −0.285971 | ||||||||
\(203\) | 16.7081 | 1.17268 | ||||||||
\(204\) | 0.128478 | 0.00899524 | ||||||||
\(205\) | 0.830550 | 0.0580081 | ||||||||
\(206\) | 13.7631 | 0.958922 | ||||||||
\(207\) | −17.2780 | −1.20090 | ||||||||
\(208\) | −18.1677 | −1.25971 | ||||||||
\(209\) | −6.76616 | −0.468025 | ||||||||
\(210\) | 1.38692 | 0.0957069 | ||||||||
\(211\) | −5.21992 | −0.359354 | −0.179677 | − | 0.983726i | \(-0.557505\pi\) | ||||
−0.179677 | + | 0.983726i | \(0.557505\pi\) | |||||||
\(212\) | −4.07847 | −0.280111 | ||||||||
\(213\) | −0.337599 | −0.0231319 | ||||||||
\(214\) | −7.34213 | −0.501897 | ||||||||
\(215\) | 3.80639 | 0.259594 | ||||||||
\(216\) | −6.01985 | −0.409599 | ||||||||
\(217\) | 14.3794 | 0.976135 | ||||||||
\(218\) | 5.70056 | 0.386090 | ||||||||
\(219\) | −4.22511 | −0.285506 | ||||||||
\(220\) | −2.23368 | −0.150594 | ||||||||
\(221\) | −5.87183 | −0.394982 | ||||||||
\(222\) | −3.94613 | −0.264847 | ||||||||
\(223\) | −0.885735 | −0.0593132 | −0.0296566 | − | 0.999560i | \(-0.509441\pi\) | ||||
−0.0296566 | + | 0.999560i | \(0.509441\pi\) | |||||||
\(224\) | 6.84869 | 0.457597 | ||||||||
\(225\) | −2.88603 | −0.192402 | ||||||||
\(226\) | 22.7625 | 1.51414 | ||||||||
\(227\) | 13.7887 | 0.915187 | 0.457593 | − | 0.889162i | \(-0.348712\pi\) | ||||
0.457593 | + | 0.889162i | \(0.348712\pi\) | |||||||
\(228\) | 0.148107 | 0.00980864 | ||||||||
\(229\) | 7.08786 | 0.468379 | 0.234190 | − | 0.972191i | \(-0.424756\pi\) | ||||
0.234190 | + | 0.972191i | \(0.424756\pi\) | |||||||
\(230\) | −7.61859 | −0.502355 | ||||||||
\(231\) | −6.39683 | −0.420881 | ||||||||
\(232\) | −15.6790 | −1.02938 | ||||||||
\(233\) | 7.66767 | 0.502326 | 0.251163 | − | 0.967945i | \(-0.419187\pi\) | ||||
0.251163 | + | 0.967945i | \(0.419187\pi\) | |||||||
\(234\) | 21.5653 | 1.40977 | ||||||||
\(235\) | 1.20804 | 0.0788036 | ||||||||
\(236\) | −3.91223 | −0.254665 | ||||||||
\(237\) | −5.58214 | −0.362599 | ||||||||
\(238\) | −4.10820 | −0.266295 | ||||||||
\(239\) | 17.6920 | 1.14440 | 0.572199 | − | 0.820115i | \(-0.306090\pi\) | ||||
0.572199 | + | 0.820115i | \(0.306090\pi\) | |||||||
\(240\) | −1.04455 | −0.0674253 | ||||||||
\(241\) | 8.20554 | 0.528565 | 0.264283 | − | 0.964445i | \(-0.414865\pi\) | ||||
0.264283 | + | 0.964445i | \(0.414865\pi\) | |||||||
\(242\) | −29.8417 | −1.91830 | ||||||||
\(243\) | 8.65784 | 0.555401 | ||||||||
\(244\) | −1.52014 | −0.0973173 | ||||||||
\(245\) | 3.42169 | 0.218604 | ||||||||
\(246\) | −0.356820 | −0.0227500 | ||||||||
\(247\) | −6.76896 | −0.430699 | ||||||||
\(248\) | −13.4937 | −0.856854 | ||||||||
\(249\) | 1.81136 | 0.114790 | ||||||||
\(250\) | −1.27257 | −0.0804845 | ||||||||
\(251\) | 31.6059 | 1.99495 | 0.997474 | − | 0.0710310i | \(-0.0226289\pi\) | ||||
0.997474 | + | 0.0710310i | \(0.0226289\pi\) | |||||||
\(252\) | −3.54565 | −0.223355 | ||||||||
\(253\) | 35.1388 | 2.20916 | ||||||||
\(254\) | 5.14873 | 0.323060 | ||||||||
\(255\) | −0.337599 | −0.0211413 | ||||||||
\(256\) | −8.78183 | −0.548865 | ||||||||
\(257\) | 2.79029 | 0.174054 | 0.0870268 | − | 0.996206i | \(-0.472263\pi\) | ||||
0.0870268 | + | 0.996206i | \(0.472263\pi\) | |||||||
\(258\) | −1.63530 | −0.101809 | ||||||||
\(259\) | −29.6522 | −1.84250 | ||||||||
\(260\) | −2.23460 | −0.138584 | ||||||||
\(261\) | 14.9368 | 0.924566 | ||||||||
\(262\) | 17.7589 | 1.09715 | ||||||||
\(263\) | −10.3937 | −0.640904 | −0.320452 | − | 0.947265i | \(-0.603835\pi\) | ||||
−0.320452 | + | 0.947265i | \(0.603835\pi\) | |||||||
\(264\) | 6.00285 | 0.369450 | ||||||||
\(265\) | 10.7170 | 0.658337 | ||||||||
\(266\) | −4.73586 | −0.290374 | ||||||||
\(267\) | 5.53776 | 0.338906 | ||||||||
\(268\) | 1.42449 | 0.0870147 | ||||||||
\(269\) | −17.6866 | −1.07837 | −0.539185 | − | 0.842188i | \(-0.681267\pi\) | ||||
−0.539185 | + | 0.842188i | \(0.681267\pi\) | |||||||
\(270\) | 2.52875 | 0.153895 | ||||||||
\(271\) | −4.35618 | −0.264619 | −0.132310 | − | 0.991208i | \(-0.542239\pi\) | ||||
−0.132310 | + | 0.991208i | \(0.542239\pi\) | |||||||
\(272\) | 3.09405 | 0.187604 | ||||||||
\(273\) | −6.39948 | −0.387314 | ||||||||
\(274\) | −4.31947 | −0.260948 | ||||||||
\(275\) | 5.86941 | 0.353938 | ||||||||
\(276\) | −0.769167 | −0.0462984 | ||||||||
\(277\) | 20.1846 | 1.21278 | 0.606389 | − | 0.795168i | \(-0.292618\pi\) | ||||
0.606389 | + | 0.795168i | \(0.292618\pi\) | |||||||
\(278\) | 1.16024 | 0.0695863 | ||||||||
\(279\) | 12.8550 | 0.769607 | ||||||||
\(280\) | −9.77982 | −0.584456 | ||||||||
\(281\) | 9.95562 | 0.593902 | 0.296951 | − | 0.954893i | \(-0.404030\pi\) | ||||
0.296951 | + | 0.954893i | \(0.404030\pi\) | |||||||
\(282\) | −0.518996 | −0.0309058 | ||||||||
\(283\) | 7.96809 | 0.473654 | 0.236827 | − | 0.971552i | \(-0.423893\pi\) | ||||
0.236827 | + | 0.971552i | \(0.423893\pi\) | |||||||
\(284\) | 0.380563 | 0.0225822 | ||||||||
\(285\) | −0.389179 | −0.0230530 | ||||||||
\(286\) | −43.8581 | −2.59339 | ||||||||
\(287\) | −2.68124 | −0.158268 | ||||||||
\(288\) | 6.12264 | 0.360780 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.58628 | 0.386759 | ||||||||
\(291\) | −4.07464 | −0.238860 | ||||||||
\(292\) | 4.76280 | 0.278722 | ||||||||
\(293\) | 19.8259 | 1.15824 | 0.579120 | − | 0.815242i | \(-0.303396\pi\) | ||||
0.579120 | + | 0.815242i | \(0.303396\pi\) | |||||||
\(294\) | −1.47003 | −0.0857336 | ||||||||
\(295\) | 10.2801 | 0.598532 | ||||||||
\(296\) | 27.8259 | 1.61735 | ||||||||
\(297\) | −11.6632 | −0.676768 | ||||||||
\(298\) | −9.79714 | −0.567533 | ||||||||
\(299\) | 35.1533 | 2.03297 | ||||||||
\(300\) | −0.128478 | −0.00741767 | ||||||||
\(301\) | −12.2880 | −0.708271 | ||||||||
\(302\) | 18.0544 | 1.03892 | ||||||||
\(303\) | 1.07825 | 0.0619436 | ||||||||
\(304\) | 3.56677 | 0.204568 | ||||||||
\(305\) | 3.99447 | 0.228722 | ||||||||
\(306\) | −3.67267 | −0.209953 | ||||||||
\(307\) | −32.2798 | −1.84231 | −0.921153 | − | 0.389201i | \(-0.872751\pi\) | ||||
−0.921153 | + | 0.389201i | \(0.872751\pi\) | |||||||
\(308\) | 7.21090 | 0.410879 | ||||||||
\(309\) | −3.65121 | −0.207710 | ||||||||
\(310\) | 5.66830 | 0.321938 | ||||||||
\(311\) | 30.2566 | 1.71569 | 0.857847 | − | 0.513904i | \(-0.171801\pi\) | ||||
0.857847 | + | 0.513904i | \(0.171801\pi\) | |||||||
\(312\) | 6.00534 | 0.339985 | ||||||||
\(313\) | 5.12744 | 0.289820 | 0.144910 | − | 0.989445i | \(-0.453711\pi\) | ||||
0.144910 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(314\) | 4.31905 | 0.243738 | ||||||||
\(315\) | 9.31686 | 0.524945 | ||||||||
\(316\) | 6.29252 | 0.353982 | ||||||||
\(317\) | 18.2026 | 1.02236 | 0.511179 | − | 0.859474i | \(-0.329209\pi\) | ||||
0.511179 | + | 0.859474i | \(0.329209\pi\) | |||||||
\(318\) | −4.60421 | −0.258191 | ||||||||
\(319\) | −30.3775 | −1.70081 | ||||||||
\(320\) | 8.88782 | 0.496844 | ||||||||
\(321\) | 1.94779 | 0.108715 | ||||||||
\(322\) | 24.5948 | 1.37062 | ||||||||
\(323\) | 1.15278 | 0.0641426 | ||||||||
\(324\) | −3.03964 | −0.168869 | ||||||||
\(325\) | 5.87183 | 0.325711 | ||||||||
\(326\) | −18.3311 | −1.01526 | ||||||||
\(327\) | −1.51230 | −0.0836302 | ||||||||
\(328\) | 2.51610 | 0.138928 | ||||||||
\(329\) | −3.89986 | −0.215006 | ||||||||
\(330\) | −2.52161 | −0.138810 | ||||||||
\(331\) | 24.1254 | 1.32605 | 0.663025 | − | 0.748597i | \(-0.269272\pi\) | ||||
0.663025 | + | 0.748597i | \(0.269272\pi\) | |||||||
\(332\) | −2.04188 | −0.112063 | ||||||||
\(333\) | −26.5087 | −1.45267 | ||||||||
\(334\) | 7.32494 | 0.400803 | ||||||||
\(335\) | −3.74312 | −0.204508 | ||||||||
\(336\) | 3.37208 | 0.183962 | ||||||||
\(337\) | −17.9452 | −0.977537 | −0.488769 | − | 0.872413i | \(-0.662554\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(338\) | −27.3328 | −1.48671 | ||||||||
\(339\) | −6.03866 | −0.327975 | ||||||||
\(340\) | 0.380563 | 0.0206389 | ||||||||
\(341\) | −26.1436 | −1.41575 | ||||||||
\(342\) | −4.23380 | −0.228938 | ||||||||
\(343\) | 11.5517 | 0.623734 | ||||||||
\(344\) | 11.5312 | 0.621722 | ||||||||
\(345\) | 2.02113 | 0.108814 | ||||||||
\(346\) | 22.3711 | 1.20268 | ||||||||
\(347\) | 32.5771 | 1.74883 | 0.874414 | − | 0.485180i | \(-0.161246\pi\) | ||||
0.874414 | + | 0.485180i | \(0.161246\pi\) | |||||||
\(348\) | 0.664945 | 0.0356448 | ||||||||
\(349\) | 13.1267 | 0.702658 | 0.351329 | − | 0.936252i | \(-0.385730\pi\) | ||||
0.351329 | + | 0.936252i | \(0.385730\pi\) | |||||||
\(350\) | 4.10820 | 0.219592 | ||||||||
\(351\) | −11.6680 | −0.622794 | ||||||||
\(352\) | −12.4518 | −0.663683 | ||||||||
\(353\) | 16.3060 | 0.867881 | 0.433940 | − | 0.900942i | \(-0.357123\pi\) | ||||
0.433940 | + | 0.900942i | \(0.357123\pi\) | |||||||
\(354\) | −4.41654 | −0.234736 | ||||||||
\(355\) | −1.00000 | −0.0530745 | ||||||||
\(356\) | −6.24250 | −0.330852 | ||||||||
\(357\) | 1.08986 | 0.0576815 | ||||||||
\(358\) | −8.57375 | −0.453137 | ||||||||
\(359\) | −28.1828 | −1.48743 | −0.743715 | − | 0.668497i | \(-0.766938\pi\) | ||||
−0.743715 | + | 0.668497i | \(0.766938\pi\) | |||||||
\(360\) | −8.74303 | −0.460798 | ||||||||
\(361\) | −17.6711 | −0.930057 | ||||||||
\(362\) | −9.62957 | −0.506119 | ||||||||
\(363\) | 7.91668 | 0.415518 | ||||||||
\(364\) | 7.21388 | 0.378110 | ||||||||
\(365\) | −12.5152 | −0.655073 | ||||||||
\(366\) | −1.71610 | −0.0897020 | ||||||||
\(367\) | −2.14334 | −0.111882 | −0.0559408 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559408 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(368\) | −18.5234 | −0.965596 | ||||||||
\(369\) | −2.39699 | −0.124782 | ||||||||
\(370\) | −11.6888 | −0.607671 | ||||||||
\(371\) | −34.5972 | −1.79619 | ||||||||
\(372\) | 0.572267 | 0.0296707 | ||||||||
\(373\) | −23.8548 | −1.23515 | −0.617577 | − | 0.786511i | \(-0.711885\pi\) | ||||
−0.617577 | + | 0.786511i | \(0.711885\pi\) | |||||||
\(374\) | 7.46924 | 0.386225 | ||||||||
\(375\) | 0.337599 | 0.0174336 | ||||||||
\(376\) | 3.65967 | 0.188733 | ||||||||
\(377\) | −30.3901 | −1.56517 | ||||||||
\(378\) | −8.16348 | −0.419884 | ||||||||
\(379\) | 0.237486 | 0.0121988 | 0.00609941 | − | 0.999981i | \(-0.498058\pi\) | ||||
0.00609941 | + | 0.999981i | \(0.498058\pi\) | |||||||
\(380\) | 0.438707 | 0.0225052 | ||||||||
\(381\) | −1.36590 | −0.0699773 | ||||||||
\(382\) | −21.5678 | −1.10350 | ||||||||
\(383\) | −17.5382 | −0.896162 | −0.448081 | − | 0.893993i | \(-0.647892\pi\) | ||||
−0.448081 | + | 0.893993i | \(0.647892\pi\) | |||||||
\(384\) | −2.38596 | −0.121758 | ||||||||
\(385\) | −18.9480 | −0.965679 | ||||||||
\(386\) | 28.1804 | 1.43435 | ||||||||
\(387\) | −10.9854 | −0.558417 | ||||||||
\(388\) | 4.59318 | 0.233184 | ||||||||
\(389\) | 17.1988 | 0.872013 | 0.436007 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436007 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(390\) | −2.52265 | −0.127740 | ||||||||
\(391\) | −5.98677 | −0.302764 | ||||||||
\(392\) | 10.3658 | 0.523552 | ||||||||
\(393\) | −4.71123 | −0.237650 | ||||||||
\(394\) | −22.7249 | −1.14486 | ||||||||
\(395\) | −16.5348 | −0.831955 | ||||||||
\(396\) | 6.44645 | 0.323946 | ||||||||
\(397\) | 14.2319 | 0.714279 | 0.357139 | − | 0.934051i | \(-0.383752\pi\) | ||||
0.357139 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(398\) | −16.9942 | −0.851844 | ||||||||
\(399\) | 1.25637 | 0.0628974 | ||||||||
\(400\) | −3.09405 | −0.154702 | ||||||||
\(401\) | 7.19842 | 0.359472 | 0.179736 | − | 0.983715i | \(-0.442476\pi\) | ||||
0.179736 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(402\) | 1.60812 | 0.0802056 | ||||||||
\(403\) | −26.1544 | −1.30284 | ||||||||
\(404\) | −1.21546 | −0.0604716 | ||||||||
\(405\) | 7.98723 | 0.396889 | ||||||||
\(406\) | −21.2622 | −1.05523 | ||||||||
\(407\) | 53.9115 | 2.67229 | ||||||||
\(408\) | −1.02274 | −0.0506330 | ||||||||
\(409\) | −7.04846 | −0.348524 | −0.174262 | − | 0.984699i | \(-0.555754\pi\) | ||||
−0.174262 | + | 0.984699i | \(0.555754\pi\) | |||||||
\(410\) | −1.05693 | −0.0521983 | ||||||||
\(411\) | 1.14591 | 0.0565235 | ||||||||
\(412\) | 4.11587 | 0.202774 | ||||||||
\(413\) | −33.1870 | −1.63302 | ||||||||
\(414\) | 21.9875 | 1.08062 | ||||||||
\(415\) | 5.36542 | 0.263378 | ||||||||
\(416\) | −12.4570 | −0.610753 | ||||||||
\(417\) | −0.307798 | −0.0150729 | ||||||||
\(418\) | 8.61042 | 0.421149 | ||||||||
\(419\) | −31.3895 | −1.53348 | −0.766740 | − | 0.641958i | \(-0.778122\pi\) | ||||
−0.766740 | + | 0.641958i | \(0.778122\pi\) | |||||||
\(420\) | 0.414760 | 0.0202382 | ||||||||
\(421\) | 12.2569 | 0.597367 | 0.298683 | − | 0.954352i | \(-0.403453\pi\) | ||||
0.298683 | + | 0.954352i | \(0.403453\pi\) | |||||||
\(422\) | 6.64272 | 0.323363 | ||||||||
\(423\) | −3.48643 | −0.169516 | ||||||||
\(424\) | 32.4663 | 1.57670 | ||||||||
\(425\) | −1.00000 | −0.0485071 | ||||||||
\(426\) | 0.429619 | 0.0208151 | ||||||||
\(427\) | −12.8952 | −0.624042 | ||||||||
\(428\) | −2.19566 | −0.106131 | ||||||||
\(429\) | 11.6351 | 0.561747 | ||||||||
\(430\) | −4.84391 | −0.233594 | ||||||||
\(431\) | 11.4468 | 0.551374 | 0.275687 | − | 0.961247i | \(-0.411095\pi\) | ||||
0.275687 | + | 0.961247i | \(0.411095\pi\) | |||||||
\(432\) | 6.14824 | 0.295807 | ||||||||
\(433\) | 21.5457 | 1.03542 | 0.517711 | − | 0.855556i | \(-0.326784\pi\) | ||||
0.517711 | + | 0.855556i | \(0.326784\pi\) | |||||||
\(434\) | −18.2988 | −0.878369 | ||||||||
\(435\) | −1.74727 | −0.0837751 | ||||||||
\(436\) | 1.70475 | 0.0816429 | ||||||||
\(437\) | −6.90146 | −0.330141 | ||||||||
\(438\) | 5.37675 | 0.256911 | ||||||||
\(439\) | 11.1990 | 0.534498 | 0.267249 | − | 0.963628i | \(-0.413885\pi\) | ||||
0.267249 | + | 0.963628i | \(0.413885\pi\) | |||||||
\(440\) | 17.7810 | 0.847675 | ||||||||
\(441\) | −9.87510 | −0.470243 | ||||||||
\(442\) | 7.47233 | 0.355422 | ||||||||
\(443\) | 23.4136 | 1.11241 | 0.556206 | − | 0.831044i | \(-0.312257\pi\) | ||||
0.556206 | + | 0.831044i | \(0.312257\pi\) | |||||||
\(444\) | −1.18009 | −0.0560046 | ||||||||
\(445\) | 16.4034 | 0.777593 | ||||||||
\(446\) | 1.12716 | 0.0533726 | ||||||||
\(447\) | 2.59908 | 0.122932 | ||||||||
\(448\) | −28.6922 | −1.35558 | ||||||||
\(449\) | −13.1544 | −0.620794 | −0.310397 | − | 0.950607i | \(-0.600462\pi\) | ||||
−0.310397 | + | 0.950607i | \(0.600462\pi\) | |||||||
\(450\) | 3.67267 | 0.173132 | ||||||||
\(451\) | 4.87484 | 0.229547 | ||||||||
\(452\) | 6.80715 | 0.320181 | ||||||||
\(453\) | −4.78965 | −0.225037 | ||||||||
\(454\) | −17.5471 | −0.823525 | ||||||||
\(455\) | −18.9558 | −0.888663 | ||||||||
\(456\) | −1.17899 | −0.0552114 | ||||||||
\(457\) | 11.3029 | 0.528728 | 0.264364 | − | 0.964423i | \(-0.414838\pi\) | ||||
0.264364 | + | 0.964423i | \(0.414838\pi\) | |||||||
\(458\) | −9.01981 | −0.421468 | ||||||||
\(459\) | 1.98712 | 0.0927508 | ||||||||
\(460\) | −2.27834 | −0.106228 | ||||||||
\(461\) | 35.2666 | 1.64253 | 0.821264 | − | 0.570549i | \(-0.193270\pi\) | ||||
0.821264 | + | 0.570549i | \(0.193270\pi\) | |||||||
\(462\) | 8.14042 | 0.378727 | ||||||||
\(463\) | −10.4005 | −0.483353 | −0.241677 | − | 0.970357i | \(-0.577697\pi\) | ||||
−0.241677 | + | 0.970357i | \(0.577697\pi\) | |||||||
\(464\) | 16.0134 | 0.743405 | ||||||||
\(465\) | −1.50374 | −0.0697342 | ||||||||
\(466\) | −9.75766 | −0.452015 | ||||||||
\(467\) | 21.7086 | 1.00455 | 0.502276 | − | 0.864707i | \(-0.332496\pi\) | ||||
0.502276 | + | 0.864707i | \(0.332496\pi\) | |||||||
\(468\) | 6.44912 | 0.298111 | ||||||||
\(469\) | 12.0838 | 0.557977 | ||||||||
\(470\) | −1.53731 | −0.0709110 | ||||||||
\(471\) | −1.14580 | −0.0527955 | ||||||||
\(472\) | 31.1430 | 1.43347 | ||||||||
\(473\) | 22.3413 | 1.02725 | ||||||||
\(474\) | 7.10366 | 0.326282 | ||||||||
\(475\) | −1.15278 | −0.0528934 | ||||||||
\(476\) | −1.22856 | −0.0563108 | ||||||||
\(477\) | −30.9294 | −1.41616 | ||||||||
\(478\) | −22.5143 | −1.02978 | ||||||||
\(479\) | 22.7469 | 1.03933 | 0.519666 | − | 0.854370i | \(-0.326056\pi\) | ||||
0.519666 | + | 0.854370i | \(0.326056\pi\) | |||||||
\(480\) | −0.716209 | −0.0326903 | ||||||||
\(481\) | 53.9338 | 2.45917 | ||||||||
\(482\) | −10.4421 | −0.475626 | ||||||||
\(483\) | −6.52474 | −0.296886 | ||||||||
\(484\) | −8.92417 | −0.405644 | ||||||||
\(485\) | −12.0695 | −0.548046 | ||||||||
\(486\) | −11.0177 | −0.499774 | ||||||||
\(487\) | 10.9760 | 0.497369 | 0.248684 | − | 0.968585i | \(-0.420002\pi\) | ||||
0.248684 | + | 0.968585i | \(0.420002\pi\) | |||||||
\(488\) | 12.1010 | 0.547785 | ||||||||
\(489\) | 4.86303 | 0.219914 | ||||||||
\(490\) | −4.35435 | −0.196709 | ||||||||
\(491\) | −2.80460 | −0.126570 | −0.0632849 | − | 0.997996i | \(-0.520158\pi\) | ||||
−0.0632849 | + | 0.997996i | \(0.520158\pi\) | |||||||
\(492\) | −0.106707 | −0.00481073 | ||||||||
\(493\) | 5.17557 | 0.233096 | ||||||||
\(494\) | 8.61398 | 0.387561 | ||||||||
\(495\) | −16.9393 | −0.761363 | ||||||||
\(496\) | 13.7815 | 0.618809 | ||||||||
\(497\) | 3.22826 | 0.144807 | ||||||||
\(498\) | −2.30509 | −0.103293 | ||||||||
\(499\) | −9.89967 | −0.443170 | −0.221585 | − | 0.975141i | \(-0.571123\pi\) | ||||
−0.221585 | + | 0.975141i | \(0.571123\pi\) | |||||||
\(500\) | −0.380563 | −0.0170193 | ||||||||
\(501\) | −1.94323 | −0.0868170 | ||||||||
\(502\) | −40.2208 | −1.79514 | ||||||||
\(503\) | −26.2041 | −1.16838 | −0.584192 | − | 0.811615i | \(-0.698589\pi\) | ||||
−0.584192 | + | 0.811615i | \(0.698589\pi\) | |||||||
\(504\) | 28.2248 | 1.25723 | ||||||||
\(505\) | 3.19386 | 0.142125 | ||||||||
\(506\) | −44.7166 | −1.98790 | ||||||||
\(507\) | 7.25111 | 0.322033 | ||||||||
\(508\) | 1.53973 | 0.0683144 | ||||||||
\(509\) | −9.96280 | −0.441593 | −0.220797 | − | 0.975320i | \(-0.570866\pi\) | ||||
−0.220797 | + | 0.975320i | \(0.570866\pi\) | |||||||
\(510\) | 0.429619 | 0.0190239 | ||||||||
\(511\) | 40.4022 | 1.78729 | ||||||||
\(512\) | 25.3104 | 1.11857 | ||||||||
\(513\) | 2.29072 | 0.101138 | ||||||||
\(514\) | −3.55084 | −0.156621 | ||||||||
\(515\) | −10.8152 | −0.476575 | ||||||||
\(516\) | −0.489037 | −0.0215287 | ||||||||
\(517\) | 7.09046 | 0.311838 | ||||||||
\(518\) | 37.7345 | 1.65796 | ||||||||
\(519\) | −5.93481 | −0.260509 | ||||||||
\(520\) | 17.7883 | 0.780070 | ||||||||
\(521\) | 21.8350 | 0.956608 | 0.478304 | − | 0.878194i | \(-0.341252\pi\) | ||||
0.478304 | + | 0.878194i | \(0.341252\pi\) | |||||||
\(522\) | −19.0082 | −0.831965 | ||||||||
\(523\) | 6.74454 | 0.294918 | 0.147459 | − | 0.989068i | \(-0.452891\pi\) | ||||
0.147459 | + | 0.989068i | \(0.452891\pi\) | |||||||
\(524\) | 5.31079 | 0.232003 | ||||||||
\(525\) | −1.08986 | −0.0475654 | ||||||||
\(526\) | 13.2267 | 0.576713 | ||||||||
\(527\) | 4.45421 | 0.194029 | ||||||||
\(528\) | −6.13088 | −0.266812 | ||||||||
\(529\) | 12.8414 | 0.558323 | ||||||||
\(530\) | −13.6381 | −0.592400 | ||||||||
\(531\) | −29.6687 | −1.28751 | ||||||||
\(532\) | −1.41626 | −0.0614027 | ||||||||
\(533\) | 4.87685 | 0.211240 | ||||||||
\(534\) | −7.04720 | −0.304962 | ||||||||
\(535\) | 5.76952 | 0.249438 | ||||||||
\(536\) | −11.3395 | −0.489794 | ||||||||
\(537\) | 2.27452 | 0.0981529 | ||||||||
\(538\) | 22.5074 | 0.970364 | ||||||||
\(539\) | 20.0833 | 0.865049 | ||||||||
\(540\) | 0.756224 | 0.0325427 | ||||||||
\(541\) | −18.2284 | −0.783700 | −0.391850 | − | 0.920029i | \(-0.628165\pi\) | ||||
−0.391850 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(542\) | 5.54355 | 0.238116 | ||||||||
\(543\) | 2.55462 | 0.109629 | ||||||||
\(544\) | 2.12148 | 0.0909576 | ||||||||
\(545\) | −4.47956 | −0.191883 | ||||||||
\(546\) | 8.14379 | 0.348522 | ||||||||
\(547\) | 27.0661 | 1.15726 | 0.578631 | − | 0.815589i | \(-0.303587\pi\) | ||||
0.578631 | + | 0.815589i | \(0.303587\pi\) | |||||||
\(548\) | −1.29174 | −0.0551803 | ||||||||
\(549\) | −11.5281 | −0.492009 | ||||||||
\(550\) | −7.46924 | −0.318489 | ||||||||
\(551\) | 5.96631 | 0.254173 | ||||||||
\(552\) | 6.12289 | 0.260607 | ||||||||
\(553\) | 53.3787 | 2.26989 | ||||||||
\(554\) | −25.6864 | −1.09131 | ||||||||
\(555\) | 3.10091 | 0.131626 | ||||||||
\(556\) | 0.346969 | 0.0147148 | ||||||||
\(557\) | 23.8903 | 1.01226 | 0.506132 | − | 0.862456i | \(-0.331075\pi\) | ||||
0.506132 | + | 0.862456i | \(0.331075\pi\) | |||||||
\(558\) | −16.3589 | −0.692526 | ||||||||
\(559\) | 22.3505 | 0.945326 | ||||||||
\(560\) | 9.98840 | 0.422087 | ||||||||
\(561\) | −1.98151 | −0.0836593 | ||||||||
\(562\) | −12.6692 | −0.534419 | ||||||||
\(563\) | −1.17816 | −0.0496536 | −0.0248268 | − | 0.999692i | \(-0.507903\pi\) | ||||
−0.0248268 | + | 0.999692i | \(0.507903\pi\) | |||||||
\(564\) | −0.155206 | −0.00653535 | ||||||||
\(565\) | −17.8871 | −0.752514 | ||||||||
\(566\) | −10.1400 | −0.426214 | ||||||||
\(567\) | −25.7849 | −1.08286 | ||||||||
\(568\) | −3.02944 | −0.127112 | ||||||||
\(569\) | 10.7108 | 0.449021 | 0.224511 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224511 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(570\) | 0.495258 | 0.0207441 | ||||||||
\(571\) | 32.0002 | 1.33917 | 0.669584 | − | 0.742737i | \(-0.266473\pi\) | ||||
0.669584 | + | 0.742737i | \(0.266473\pi\) | |||||||
\(572\) | −13.1158 | −0.548398 | ||||||||
\(573\) | 5.72170 | 0.239027 | ||||||||
\(574\) | 3.41206 | 0.142417 | ||||||||
\(575\) | 5.98677 | 0.249666 | ||||||||
\(576\) | −25.6505 | −1.06877 | ||||||||
\(577\) | −7.78397 | −0.324051 | −0.162025 | − | 0.986787i | \(-0.551803\pi\) | ||||
−0.162025 | + | 0.986787i | \(0.551803\pi\) | |||||||
\(578\) | −1.27257 | −0.0529320 | ||||||||
\(579\) | −7.47597 | −0.310691 | ||||||||
\(580\) | 1.96963 | 0.0817843 | ||||||||
\(581\) | −17.3210 | −0.718596 | ||||||||
\(582\) | 5.18527 | 0.214936 | ||||||||
\(583\) | 62.9021 | 2.60514 | ||||||||
\(584\) | −37.9138 | −1.56889 | ||||||||
\(585\) | −16.9463 | −0.700642 | ||||||||
\(586\) | −25.2298 | −1.04223 | ||||||||
\(587\) | −17.1422 | −0.707536 | −0.353768 | − | 0.935333i | \(-0.615100\pi\) | ||||
−0.353768 | + | 0.935333i | \(0.615100\pi\) | |||||||
\(588\) | −0.439611 | −0.0181293 | ||||||||
\(589\) | 5.13475 | 0.211573 | ||||||||
\(590\) | −13.0822 | −0.538585 | ||||||||
\(591\) | 6.02868 | 0.247987 | ||||||||
\(592\) | −28.4194 | −1.16803 | ||||||||
\(593\) | 12.7502 | 0.523588 | 0.261794 | − | 0.965124i | \(-0.415686\pi\) | ||||
0.261794 | + | 0.965124i | \(0.415686\pi\) | |||||||
\(594\) | 14.8423 | 0.608985 | ||||||||
\(595\) | 3.22826 | 0.132346 | ||||||||
\(596\) | −2.92984 | −0.120011 | ||||||||
\(597\) | 4.50839 | 0.184516 | ||||||||
\(598\) | −44.7351 | −1.82935 | ||||||||
\(599\) | −30.0767 | −1.22890 | −0.614449 | − | 0.788956i | \(-0.710622\pi\) | ||||
−0.614449 | + | 0.788956i | \(0.710622\pi\) | |||||||
\(600\) | 1.02274 | 0.0417530 | ||||||||
\(601\) | 41.1510 | 1.67858 | 0.839291 | − | 0.543682i | \(-0.182970\pi\) | ||||
0.839291 | + | 0.543682i | \(0.182970\pi\) | |||||||
\(602\) | 15.6374 | 0.637334 | ||||||||
\(603\) | 10.8027 | 0.439922 | ||||||||
\(604\) | 5.39919 | 0.219690 | ||||||||
\(605\) | 23.4499 | 0.953375 | ||||||||
\(606\) | −1.37214 | −0.0557396 | ||||||||
\(607\) | −14.8488 | −0.602694 | −0.301347 | − | 0.953515i | \(-0.597436\pi\) | ||||
−0.301347 | + | 0.953515i | \(0.597436\pi\) | |||||||
\(608\) | 2.44560 | 0.0991824 | ||||||||
\(609\) | 5.64064 | 0.228570 | ||||||||
\(610\) | −5.08324 | −0.205814 | ||||||||
\(611\) | 7.09339 | 0.286968 | ||||||||
\(612\) | −1.09831 | −0.0443967 | ||||||||
\(613\) | −39.2117 | −1.58375 | −0.791874 | − | 0.610685i | \(-0.790894\pi\) | ||||
−0.791874 | + | 0.610685i | \(0.790894\pi\) | |||||||
\(614\) | 41.0784 | 1.65779 | ||||||||
\(615\) | 0.280393 | 0.0113065 | ||||||||
\(616\) | −57.4017 | −2.31278 | ||||||||
\(617\) | −35.4969 | −1.42905 | −0.714525 | − | 0.699610i | \(-0.753357\pi\) | ||||
−0.714525 | + | 0.699610i | \(0.753357\pi\) | |||||||
\(618\) | 4.64642 | 0.186907 | ||||||||
\(619\) | 10.8519 | 0.436173 | 0.218087 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218087 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(620\) | 1.69511 | 0.0680771 | ||||||||
\(621\) | −11.8964 | −0.477387 | ||||||||
\(622\) | −38.5037 | −1.54386 | ||||||||
\(623\) | −52.9544 | −2.12157 | ||||||||
\(624\) | −6.13342 | −0.245533 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.52503 | −0.260793 | ||||||||
\(627\) | −2.28425 | −0.0912242 | ||||||||
\(628\) | 1.29161 | 0.0515409 | ||||||||
\(629\) | −9.18517 | −0.366237 | ||||||||
\(630\) | −11.8564 | −0.472369 | ||||||||
\(631\) | 6.96650 | 0.277332 | 0.138666 | − | 0.990339i | \(-0.455719\pi\) | ||||
0.138666 | + | 0.990339i | \(0.455719\pi\) | |||||||
\(632\) | −50.0911 | −1.99252 | ||||||||
\(633\) | −1.76224 | −0.0700428 | ||||||||
\(634\) | −23.1641 | −0.919962 | ||||||||
\(635\) | −4.04593 | −0.160558 | ||||||||
\(636\) | −1.37689 | −0.0545972 | ||||||||
\(637\) | 20.0916 | 0.796059 | ||||||||
\(638\) | 38.6575 | 1.53047 | ||||||||
\(639\) | 2.88603 | 0.114169 | ||||||||
\(640\) | −7.06743 | −0.279365 | ||||||||
\(641\) | −35.2341 | −1.39166 | −0.695831 | − | 0.718206i | \(-0.744964\pi\) | ||||
−0.695831 | + | 0.718206i | \(0.744964\pi\) | |||||||
\(642\) | −2.47870 | −0.0978264 | ||||||||
\(643\) | −5.44519 | −0.214737 | −0.107369 | − | 0.994219i | \(-0.534243\pi\) | ||||
−0.107369 | + | 0.994219i | \(0.534243\pi\) | |||||||
\(644\) | 7.35509 | 0.289831 | ||||||||
\(645\) | 1.28504 | 0.0505983 | ||||||||
\(646\) | −1.46700 | −0.0577183 | ||||||||
\(647\) | −48.6119 | −1.91113 | −0.955566 | − | 0.294778i | \(-0.904754\pi\) | ||||
−0.955566 | + | 0.294778i | \(0.904754\pi\) | |||||||
\(648\) | 24.1968 | 0.950540 | ||||||||
\(649\) | 60.3382 | 2.36848 | ||||||||
\(650\) | −7.47233 | −0.293089 | ||||||||
\(651\) | 4.85447 | 0.190262 | ||||||||
\(652\) | −5.48191 | −0.214688 | ||||||||
\(653\) | 3.91385 | 0.153161 | 0.0765803 | − | 0.997063i | \(-0.475600\pi\) | ||||
0.0765803 | + | 0.997063i | \(0.475600\pi\) | |||||||
\(654\) | 1.92451 | 0.0752541 | ||||||||
\(655\) | −13.9551 | −0.545271 | ||||||||
\(656\) | −2.56976 | −0.100332 | ||||||||
\(657\) | 36.1191 | 1.40914 | ||||||||
\(658\) | 4.96285 | 0.193472 | ||||||||
\(659\) | −9.49337 | −0.369809 | −0.184905 | − | 0.982756i | \(-0.559198\pi\) | ||||
−0.184905 | + | 0.982756i | \(0.559198\pi\) | |||||||
\(660\) | −0.754088 | −0.0293528 | ||||||||
\(661\) | 20.9295 | 0.814064 | 0.407032 | − | 0.913414i | \(-0.366564\pi\) | ||||
0.407032 | + | 0.913414i | \(0.366564\pi\) | |||||||
\(662\) | −30.7012 | −1.19324 | ||||||||
\(663\) | −1.98233 | −0.0769872 | ||||||||
\(664\) | 16.2542 | 0.630785 | ||||||||
\(665\) | 3.72149 | 0.144313 | ||||||||
\(666\) | 33.7341 | 1.30717 | ||||||||
\(667\) | −30.9849 | −1.19974 | ||||||||
\(668\) | 2.19052 | 0.0847539 | ||||||||
\(669\) | −0.299024 | −0.0115609 | ||||||||
\(670\) | 4.76339 | 0.184026 | ||||||||
\(671\) | 23.4451 | 0.905090 | ||||||||
\(672\) | 2.31211 | 0.0891917 | ||||||||
\(673\) | 30.6986 | 1.18334 | 0.591672 | − | 0.806179i | \(-0.298468\pi\) | ||||
0.591672 | + | 0.806179i | \(0.298468\pi\) | |||||||
\(674\) | 22.8365 | 0.879631 | ||||||||
\(675\) | −1.98712 | −0.0764843 | ||||||||
\(676\) | −8.17389 | −0.314381 | ||||||||
\(677\) | −3.29935 | −0.126804 | −0.0634022 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634022 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(678\) | 7.68462 | 0.295126 | ||||||||
\(679\) | 38.9634 | 1.49528 | ||||||||
\(680\) | −3.02944 | −0.116174 | ||||||||
\(681\) | 4.65505 | 0.178382 | ||||||||
\(682\) | 33.2696 | 1.27396 | ||||||||
\(683\) | −2.75054 | −0.105246 | −0.0526232 | − | 0.998614i | \(-0.516758\pi\) | ||||
−0.0526232 | + | 0.998614i | \(0.516758\pi\) | |||||||
\(684\) | −1.26612 | −0.0484113 | ||||||||
\(685\) | 3.39428 | 0.129689 | ||||||||
\(686\) | −14.7004 | −0.561264 | ||||||||
\(687\) | 2.39286 | 0.0912932 | ||||||||
\(688\) | −11.7772 | −0.449000 | ||||||||
\(689\) | 62.9282 | 2.39737 | ||||||||
\(690\) | −2.57203 | −0.0979156 | ||||||||
\(691\) | 47.7193 | 1.81533 | 0.907664 | − | 0.419697i | \(-0.137864\pi\) | ||||
0.907664 | + | 0.419697i | \(0.137864\pi\) | |||||||
\(692\) | 6.69008 | 0.254319 | ||||||||
\(693\) | 54.6844 | 2.07729 | ||||||||
\(694\) | −41.4566 | −1.57367 | ||||||||
\(695\) | −0.911726 | −0.0345837 | ||||||||
\(696\) | −5.29324 | −0.200640 | ||||||||
\(697\) | −0.830550 | −0.0314593 | ||||||||
\(698\) | −16.7047 | −0.632282 | ||||||||
\(699\) | 2.58860 | 0.0979099 | ||||||||
\(700\) | 1.22856 | 0.0464351 | ||||||||
\(701\) | 8.50339 | 0.321169 | 0.160584 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160584 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(702\) | 14.8484 | 0.560417 | ||||||||
\(703\) | −10.5885 | −0.399354 | ||||||||
\(704\) | 52.1662 | 1.96609 | ||||||||
\(705\) | 0.407833 | 0.0153599 | ||||||||
\(706\) | −20.7505 | −0.780957 | ||||||||
\(707\) | −10.3106 | −0.387771 | ||||||||
\(708\) | −1.32077 | −0.0496375 | ||||||||
\(709\) | −28.2298 | −1.06019 | −0.530096 | − | 0.847938i | \(-0.677844\pi\) | ||||
−0.530096 | + | 0.847938i | \(0.677844\pi\) | |||||||
\(710\) | 1.27257 | 0.0477587 | ||||||||
\(711\) | 47.7198 | 1.78963 | ||||||||
\(712\) | 49.6929 | 1.86232 | ||||||||
\(713\) | −26.6663 | −0.998663 | ||||||||
\(714\) | −1.38692 | −0.0519044 | ||||||||
\(715\) | 34.4642 | 1.28889 | ||||||||
\(716\) | −2.56398 | −0.0958205 | ||||||||
\(717\) | 5.97280 | 0.223058 | ||||||||
\(718\) | 35.8646 | 1.33845 | ||||||||
\(719\) | 29.0258 | 1.08248 | 0.541240 | − | 0.840868i | \(-0.317955\pi\) | ||||
0.541240 | + | 0.840868i | \(0.317955\pi\) | |||||||
\(720\) | 8.92950 | 0.332783 | ||||||||
\(721\) | 34.9144 | 1.30028 | ||||||||
\(722\) | 22.4877 | 0.836906 | ||||||||
\(723\) | 2.77019 | 0.103024 | ||||||||
\(724\) | −2.87972 | −0.107024 | ||||||||
\(725\) | −5.17557 | −0.192216 | ||||||||
\(726\) | −10.0745 | −0.373901 | ||||||||
\(727\) | 40.1887 | 1.49052 | 0.745258 | − | 0.666776i | \(-0.232326\pi\) | ||||
0.745258 | + | 0.666776i | \(0.232326\pi\) | |||||||
\(728\) | −57.4255 | −2.12833 | ||||||||
\(729\) | −21.0388 | −0.779215 | ||||||||
\(730\) | 15.9264 | 0.589463 | ||||||||
\(731\) | −3.80639 | −0.140785 | ||||||||
\(732\) | −0.513200 | −0.0189684 | ||||||||
\(733\) | 24.2480 | 0.895621 | 0.447810 | − | 0.894129i | \(-0.352204\pi\) | ||||
0.447810 | + | 0.894129i | \(0.352204\pi\) | |||||||
\(734\) | 2.72756 | 0.100676 | ||||||||
\(735\) | 1.15516 | 0.0426088 | ||||||||
\(736\) | −12.7008 | −0.468158 | ||||||||
\(737\) | −21.9699 | −0.809271 | ||||||||
\(738\) | 3.05034 | 0.112285 | ||||||||
\(739\) | −16.7701 | −0.616898 | −0.308449 | − | 0.951241i | \(-0.599810\pi\) | ||||
−0.308449 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(740\) | −3.49553 | −0.128498 | ||||||||
\(741\) | −2.28520 | −0.0839488 | ||||||||
\(742\) | 44.0273 | 1.61629 | ||||||||
\(743\) | 24.8609 | 0.912057 | 0.456028 | − | 0.889965i | \(-0.349272\pi\) | ||||
0.456028 | + | 0.889965i | \(0.349272\pi\) | |||||||
\(744\) | −4.55548 | −0.167012 | ||||||||
\(745\) | 7.69870 | 0.282059 | ||||||||
\(746\) | 30.3569 | 1.11144 | ||||||||
\(747\) | −15.4847 | −0.566557 | ||||||||
\(748\) | 2.23368 | 0.0816713 | ||||||||
\(749\) | −18.6255 | −0.680562 | ||||||||
\(750\) | −0.429619 | −0.0156875 | ||||||||
\(751\) | 31.6001 | 1.15310 | 0.576552 | − | 0.817060i | \(-0.304398\pi\) | ||||
0.576552 | + | 0.817060i | \(0.304398\pi\) | |||||||
\(752\) | −3.73772 | −0.136301 | ||||||||
\(753\) | 10.6701 | 0.388842 | ||||||||
\(754\) | 38.6735 | 1.40841 | ||||||||
\(755\) | −14.1874 | −0.516332 | ||||||||
\(756\) | −2.44129 | −0.0887888 | ||||||||
\(757\) | 51.0067 | 1.85387 | 0.926935 | − | 0.375223i | \(-0.122434\pi\) | ||||
0.926935 | + | 0.375223i | \(0.122434\pi\) | |||||||
\(758\) | −0.302217 | −0.0109770 | ||||||||
\(759\) | 11.8628 | 0.430594 | ||||||||
\(760\) | −3.49229 | −0.126679 | ||||||||
\(761\) | 36.4452 | 1.32114 | 0.660569 | − | 0.750765i | \(-0.270315\pi\) | ||||
0.660569 | + | 0.750765i | \(0.270315\pi\) | |||||||
\(762\) | 1.73821 | 0.0629687 | ||||||||
\(763\) | 14.4612 | 0.523531 | ||||||||
\(764\) | −6.44985 | −0.233347 | ||||||||
\(765\) | 2.88603 | 0.104345 | ||||||||
\(766\) | 22.3187 | 0.806406 | ||||||||
\(767\) | 60.3632 | 2.17959 | ||||||||
\(768\) | −2.96474 | −0.106981 | ||||||||
\(769\) | 24.1240 | 0.869933 | 0.434967 | − | 0.900447i | \(-0.356760\pi\) | ||||
0.434967 | + | 0.900447i | \(0.356760\pi\) | |||||||
\(770\) | 24.1127 | 0.868960 | ||||||||
\(771\) | 0.942001 | 0.0339253 | ||||||||
\(772\) | 8.42737 | 0.303308 | ||||||||
\(773\) | −15.2051 | −0.546890 | −0.273445 | − | 0.961888i | \(-0.588163\pi\) | ||||
−0.273445 | + | 0.961888i | \(0.588163\pi\) | |||||||
\(774\) | 13.9796 | 0.502488 | ||||||||
\(775\) | −4.45421 | −0.160000 | ||||||||
\(776\) | −36.5636 | −1.31256 | ||||||||
\(777\) | −10.0106 | −0.359127 | ||||||||
\(778\) | −21.8867 | −0.784676 | ||||||||
\(779\) | −0.957445 | −0.0343040 | ||||||||
\(780\) | −0.754400 | −0.0270119 | ||||||||
\(781\) | −5.86941 | −0.210024 | ||||||||
\(782\) | 7.61859 | 0.272440 | ||||||||
\(783\) | 10.2845 | 0.367537 | ||||||||
\(784\) | −10.5869 | −0.378103 | ||||||||
\(785\) | −3.39395 | −0.121135 | ||||||||
\(786\) | 5.99538 | 0.213848 | ||||||||
\(787\) | −43.2331 | −1.54109 | −0.770547 | − | 0.637383i | \(-0.780017\pi\) | ||||
−0.770547 | + | 0.637383i | \(0.780017\pi\) | |||||||
\(788\) | −6.79589 | −0.242094 | ||||||||
\(789\) | −3.50891 | −0.124921 | ||||||||
\(790\) | 21.0417 | 0.748630 | ||||||||
\(791\) | 57.7441 | 2.05315 | ||||||||
\(792\) | −51.3164 | −1.82345 | ||||||||
\(793\) | 23.4548 | 0.832906 | ||||||||
\(794\) | −18.1111 | −0.642739 | ||||||||
\(795\) | 3.61804 | 0.128319 | ||||||||
\(796\) | −5.08213 | −0.180131 | ||||||||
\(797\) | −11.0646 | −0.391928 | −0.195964 | − | 0.980611i | \(-0.562784\pi\) | ||||
−0.195964 | + | 0.980611i | \(0.562784\pi\) | |||||||
\(798\) | −1.59883 | −0.0565978 | ||||||||
\(799\) | −1.20804 | −0.0427373 | ||||||||
\(800\) | −2.12148 | −0.0750055 | ||||||||
\(801\) | −47.3405 | −1.67269 | ||||||||
\(802\) | −9.16050 | −0.323468 | ||||||||
\(803\) | −73.4565 | −2.59222 | ||||||||
\(804\) | 0.480908 | 0.0169603 | ||||||||
\(805\) | −19.3269 | −0.681183 | ||||||||
\(806\) | 33.2833 | 1.17236 | ||||||||
\(807\) | −5.97098 | −0.210188 | ||||||||
\(808\) | 9.67560 | 0.340386 | ||||||||
\(809\) | 14.9362 | 0.525131 | 0.262565 | − | 0.964914i | \(-0.415431\pi\) | ||||
0.262565 | + | 0.964914i | \(0.415431\pi\) | |||||||
\(810\) | −10.1643 | −0.357138 | ||||||||
\(811\) | −12.6566 | −0.444433 | −0.222216 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222216 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(812\) | −6.35848 | −0.223139 | ||||||||
\(813\) | −1.47064 | −0.0515777 | ||||||||
\(814\) | −68.6062 | −2.40465 | ||||||||
\(815\) | 14.4047 | 0.504576 | ||||||||
\(816\) | 1.04455 | 0.0365665 | ||||||||
\(817\) | −4.38795 | −0.153515 | ||||||||
\(818\) | 8.96967 | 0.313617 | ||||||||
\(819\) | 54.7070 | 1.91162 | ||||||||
\(820\) | −0.316076 | −0.0110379 | ||||||||
\(821\) | −6.96528 | −0.243090 | −0.121545 | − | 0.992586i | \(-0.538785\pi\) | ||||
−0.121545 | + | 0.992586i | \(0.538785\pi\) | |||||||
\(822\) | −1.45825 | −0.0508623 | ||||||||
\(823\) | −55.3958 | −1.93098 | −0.965488 | − | 0.260449i | \(-0.916130\pi\) | ||||
−0.965488 | + | 0.260449i | \(0.916130\pi\) | |||||||
\(824\) | −32.7640 | −1.14139 | ||||||||
\(825\) | 1.98151 | 0.0689873 | ||||||||
\(826\) | 42.2328 | 1.46947 | ||||||||
\(827\) | −44.2933 | −1.54023 | −0.770115 | − | 0.637905i | \(-0.779801\pi\) | ||||
−0.770115 | + | 0.637905i | \(0.779801\pi\) | |||||||
\(828\) | 6.57536 | 0.228509 | ||||||||
\(829\) | −54.2801 | −1.88522 | −0.942612 | − | 0.333889i | \(-0.891639\pi\) | ||||
−0.942612 | + | 0.333889i | \(0.891639\pi\) | |||||||
\(830\) | −6.82787 | −0.236999 | ||||||||
\(831\) | 6.81432 | 0.236386 | ||||||||
\(832\) | 52.1878 | 1.80929 | ||||||||
\(833\) | −3.42169 | −0.118555 | ||||||||
\(834\) | 0.391695 | 0.0135633 | ||||||||
\(835\) | −5.75602 | −0.199195 | ||||||||
\(836\) | 2.57495 | 0.0890564 | ||||||||
\(837\) | 8.85105 | 0.305937 | ||||||||
\(838\) | 39.9454 | 1.37989 | ||||||||
\(839\) | 15.9942 | 0.552181 | 0.276091 | − | 0.961132i | \(-0.410961\pi\) | ||||
0.276091 | + | 0.961132i | \(0.410961\pi\) | |||||||
\(840\) | −3.30166 | −0.113918 | ||||||||
\(841\) | −2.21352 | −0.0763282 | ||||||||
\(842\) | −15.5978 | −0.537537 | ||||||||
\(843\) | 3.36101 | 0.115759 | ||||||||
\(844\) | 1.98651 | 0.0683784 | ||||||||
\(845\) | 21.4784 | 0.738881 | ||||||||
\(846\) | 4.43673 | 0.152538 | ||||||||
\(847\) | −75.7026 | −2.60117 | ||||||||
\(848\) | −33.1587 | −1.13868 | ||||||||
\(849\) | 2.69002 | 0.0923214 | ||||||||
\(850\) | 1.27257 | 0.0436488 | ||||||||
\(851\) | 54.9895 | 1.88502 | ||||||||
\(852\) | 0.128478 | 0.00440158 | ||||||||
\(853\) | −14.9503 | −0.511888 | −0.255944 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255944 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(854\) | 16.4100 | 0.561540 | ||||||||
\(855\) | 3.32697 | 0.113780 | ||||||||
\(856\) | 17.4784 | 0.597399 | ||||||||
\(857\) | −11.1088 | −0.379470 | −0.189735 | − | 0.981835i | \(-0.560763\pi\) | ||||
−0.189735 | + | 0.981835i | \(0.560763\pi\) | |||||||
\(858\) | −14.8065 | −0.505485 | ||||||||
\(859\) | 39.6451 | 1.35267 | 0.676337 | − | 0.736592i | \(-0.263566\pi\) | ||||
0.676337 | + | 0.736592i | \(0.263566\pi\) | |||||||
\(860\) | −1.44857 | −0.0493959 | ||||||||
\(861\) | −0.905184 | −0.0308486 | ||||||||
\(862\) | −14.5669 | −0.496150 | ||||||||
\(863\) | 8.52322 | 0.290134 | 0.145067 | − | 0.989422i | \(-0.453660\pi\) | ||||
0.145067 | + | 0.989422i | \(0.453660\pi\) | |||||||
\(864\) | 4.21563 | 0.143419 | ||||||||
\(865\) | −17.5794 | −0.597719 | ||||||||
\(866\) | −27.4185 | −0.931717 | ||||||||
\(867\) | 0.337599 | 0.0114655 | ||||||||
\(868\) | −5.47225 | −0.185740 | ||||||||
\(869\) | −97.0494 | −3.29217 | ||||||||
\(870\) | 2.22352 | 0.0753845 | ||||||||
\(871\) | −21.9790 | −0.744729 | ||||||||
\(872\) | −13.5705 | −0.459556 | ||||||||
\(873\) | 34.8328 | 1.17891 | ||||||||
\(874\) | 8.78259 | 0.297076 | ||||||||
\(875\) | −3.22826 | −0.109135 | ||||||||
\(876\) | 1.60792 | 0.0543265 | ||||||||
\(877\) | 7.66079 | 0.258686 | 0.129343 | − | 0.991600i | \(-0.458713\pi\) | ||||
0.129343 | + | 0.991600i | \(0.458713\pi\) | |||||||
\(878\) | −14.2515 | −0.480964 | ||||||||
\(879\) | 6.69320 | 0.225756 | ||||||||
\(880\) | −18.1602 | −0.612181 | ||||||||
\(881\) | −14.3327 | −0.482880 | −0.241440 | − | 0.970416i | \(-0.577620\pi\) | ||||
−0.241440 | + | 0.970416i | \(0.577620\pi\) | |||||||
\(882\) | 12.5668 | 0.423145 | ||||||||
\(883\) | −10.4269 | −0.350893 | −0.175446 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175446 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(884\) | 2.23460 | 0.0751578 | ||||||||
\(885\) | 3.47056 | 0.116662 | ||||||||
\(886\) | −29.7954 | −1.00100 | ||||||||
\(887\) | −5.95401 | −0.199916 | −0.0999580 | − | 0.994992i | \(-0.531871\pi\) | ||||
−0.0999580 | + | 0.994992i | \(0.531871\pi\) | |||||||
\(888\) | 9.39400 | 0.315242 | ||||||||
\(889\) | 13.0613 | 0.438063 | ||||||||
\(890\) | −20.8744 | −0.699713 | ||||||||
\(891\) | 46.8803 | 1.57055 | ||||||||
\(892\) | 0.337078 | 0.0112862 | ||||||||
\(893\) | −1.39261 | −0.0466018 | ||||||||
\(894\) | −3.30751 | −0.110620 | ||||||||
\(895\) | 6.73734 | 0.225205 | ||||||||
\(896\) | 22.8155 | 0.762214 | ||||||||
\(897\) | 11.8677 | 0.396253 | ||||||||
\(898\) | 16.7399 | 0.558617 | ||||||||
\(899\) | 23.0531 | 0.768863 | ||||||||
\(900\) | 1.09831 | 0.0366105 | ||||||||
\(901\) | −10.7170 | −0.357033 | ||||||||
\(902\) | −6.20358 | −0.206556 | ||||||||
\(903\) | −4.14844 | −0.138051 | ||||||||
\(904\) | −54.1877 | −1.80226 | ||||||||
\(905\) | 7.56702 | 0.251536 | ||||||||
\(906\) | 6.09517 | 0.202499 | ||||||||
\(907\) | −3.87371 | −0.128624 | −0.0643122 | − | 0.997930i | \(-0.520485\pi\) | ||||
−0.0643122 | + | 0.997930i | \(0.520485\pi\) | |||||||
\(908\) | −5.24746 | −0.174143 | ||||||||
\(909\) | −9.21757 | −0.305728 | ||||||||
\(910\) | 24.1226 | 0.799658 | ||||||||
\(911\) | −39.2971 | −1.30197 | −0.650985 | − | 0.759091i | \(-0.725644\pi\) | ||||
−0.650985 | + | 0.759091i | \(0.725644\pi\) | |||||||
\(912\) | 1.20414 | 0.0398730 | ||||||||
\(913\) | 31.4918 | 1.04223 | ||||||||
\(914\) | −14.3838 | −0.475773 | ||||||||
\(915\) | 1.34853 | 0.0445810 | ||||||||
\(916\) | −2.69738 | −0.0891238 | ||||||||
\(917\) | 45.0508 | 1.48771 | ||||||||
\(918\) | −2.52875 | −0.0834612 | ||||||||
\(919\) | 7.26096 | 0.239517 | 0.119759 | − | 0.992803i | \(-0.461788\pi\) | ||||
0.119759 | + | 0.992803i | \(0.461788\pi\) | |||||||
\(920\) | 18.1365 | 0.597944 | ||||||||
\(921\) | −10.8976 | −0.359090 | ||||||||
\(922\) | −44.8792 | −1.47802 | ||||||||
\(923\) | −5.87183 | −0.193274 | ||||||||
\(924\) | 2.43440 | 0.0800857 | ||||||||
\(925\) | 9.18517 | 0.302007 | ||||||||
\(926\) | 13.2354 | 0.434942 | ||||||||
\(927\) | 31.2130 | 1.02517 | ||||||||
\(928\) | 10.9798 | 0.360431 | ||||||||
\(929\) | 47.2676 | 1.55080 | 0.775400 | − | 0.631470i | \(-0.217548\pi\) | ||||
0.775400 | + | 0.631470i | \(0.217548\pi\) | |||||||
\(930\) | 1.91362 | 0.0627499 | ||||||||
\(931\) | −3.94447 | −0.129275 | ||||||||
\(932\) | −2.91803 | −0.0955833 | ||||||||
\(933\) | 10.2146 | 0.334411 | ||||||||
\(934\) | −27.6257 | −0.903940 | ||||||||
\(935\) | −5.86941 | −0.191950 | ||||||||
\(936\) | −51.3376 | −1.67802 | ||||||||
\(937\) | −8.70300 | −0.284315 | −0.142157 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142157 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(938\) | −15.3775 | −0.502092 | ||||||||
\(939\) | 1.73102 | 0.0564897 | ||||||||
\(940\) | −0.459734 | −0.0149949 | ||||||||
\(941\) | 34.4777 | 1.12394 | 0.561971 | − | 0.827157i | \(-0.310043\pi\) | ||||
0.561971 | + | 0.827157i | \(0.310043\pi\) | |||||||
\(942\) | 1.45811 | 0.0475077 | ||||||||
\(943\) | 4.97231 | 0.161921 | ||||||||
\(944\) | −31.8072 | −1.03524 | ||||||||
\(945\) | 6.41495 | 0.208678 | ||||||||
\(946\) | −28.4309 | −0.924367 | ||||||||
\(947\) | −26.2627 | −0.853423 | −0.426712 | − | 0.904388i | \(-0.640328\pi\) | ||||
−0.426712 | + | 0.904388i | \(0.640328\pi\) | |||||||
\(948\) | 2.12435 | 0.0689958 | ||||||||
\(949\) | −73.4869 | −2.38549 | ||||||||
\(950\) | 1.46700 | 0.0475958 | ||||||||
\(951\) | 6.14518 | 0.199271 | ||||||||
\(952\) | 9.77982 | 0.316966 | ||||||||
\(953\) | −52.2036 | −1.69104 | −0.845520 | − | 0.533943i | \(-0.820710\pi\) | ||||
−0.845520 | + | 0.533943i | \(0.820710\pi\) | |||||||
\(954\) | 39.3599 | 1.27432 | ||||||||
\(955\) | 16.9482 | 0.548430 | ||||||||
\(956\) | −6.73290 | −0.217758 | ||||||||
\(957\) | −10.2554 | −0.331511 | ||||||||
\(958\) | −28.9470 | −0.935236 | ||||||||
\(959\) | −10.9576 | −0.353841 | ||||||||
\(960\) | 3.00052 | 0.0968415 | ||||||||
\(961\) | −11.1600 | −0.360000 | ||||||||
\(962\) | −68.6346 | −2.21287 | ||||||||
\(963\) | −16.6510 | −0.536571 | ||||||||
\(964\) | −3.12272 | −0.100576 | ||||||||
\(965\) | −22.1445 | −0.712857 | ||||||||
\(966\) | 8.30320 | 0.267151 | ||||||||
\(967\) | −6.63601 | −0.213400 | −0.106700 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106700 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(968\) | 71.0400 | 2.28331 | ||||||||
\(969\) | 0.389179 | 0.0125022 | ||||||||
\(970\) | 15.3592 | 0.493155 | ||||||||
\(971\) | −28.2267 | −0.905838 | −0.452919 | − | 0.891552i | \(-0.649617\pi\) | ||||
−0.452919 | + | 0.891552i | \(0.649617\pi\) | |||||||
\(972\) | −3.29485 | −0.105682 | ||||||||
\(973\) | 2.94329 | 0.0943576 | ||||||||
\(974\) | −13.9677 | −0.447554 | ||||||||
\(975\) | 1.98233 | 0.0634853 | ||||||||
\(976\) | −12.3591 | −0.395604 | ||||||||
\(977\) | −22.0592 | −0.705738 | −0.352869 | − | 0.935673i | \(-0.614794\pi\) | ||||
−0.352869 | + | 0.935673i | \(0.614794\pi\) | |||||||
\(978\) | −6.18856 | −0.197888 | ||||||||
\(979\) | 96.2779 | 3.07706 | ||||||||
\(980\) | −1.30217 | −0.0415962 | ||||||||
\(981\) | 12.9281 | 0.412763 | ||||||||
\(982\) | 3.56905 | 0.113893 | ||||||||
\(983\) | 19.2776 | 0.614859 | 0.307429 | − | 0.951571i | \(-0.400531\pi\) | ||||
0.307429 | + | 0.951571i | \(0.400531\pi\) | |||||||
\(984\) | 0.849433 | 0.0270789 | ||||||||
\(985\) | 17.8575 | 0.568987 | ||||||||
\(986\) | −6.58628 | −0.209750 | ||||||||
\(987\) | −1.31659 | −0.0419076 | ||||||||
\(988\) | 2.57601 | 0.0819539 | ||||||||
\(989\) | 22.7880 | 0.724617 | ||||||||
\(990\) | 21.5564 | 0.685108 | ||||||||
\(991\) | 15.0669 | 0.478617 | 0.239309 | − | 0.970944i | \(-0.423079\pi\) | ||||
0.239309 | + | 0.970944i | \(0.423079\pi\) | |||||||
\(992\) | 9.44950 | 0.300022 | ||||||||
\(993\) | 8.14471 | 0.258465 | ||||||||
\(994\) | −4.10820 | −0.130304 | ||||||||
\(995\) | 13.3543 | 0.423358 | ||||||||
\(996\) | −0.689337 | −0.0218425 | ||||||||
\(997\) | 32.8272 | 1.03965 | 0.519825 | − | 0.854273i | \(-0.325997\pi\) | ||||
0.519825 | + | 0.854273i | \(0.325997\pi\) | |||||||
\(998\) | 12.5980 | 0.398784 | ||||||||
\(999\) | −18.2520 | −0.577469 |
(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 | 6035.2.a.h.1.18 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6035.2.a.h.1.18 | ✓ | 59 | 1.1 | even | 1 | trivial |