Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28251 | −1.61398 | −0.806988 | − | 0.590567i | \(-0.798904\pi\) | ||||
−0.806988 | + | 0.590567i | \(0.798904\pi\) | |||||||
\(3\) | −0.277049 | −0.159954 | −0.0799770 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799770 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(4\) | 3.20984 | 1.60492 | ||||||||
\(5\) | 0.585497 | 0.261842 | 0.130921 | − | 0.991393i | \(-0.458207\pi\) | ||||
0.130921 | + | 0.991393i | \(0.458207\pi\) | |||||||
\(6\) | 0.632366 | 0.258162 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.76147 | −0.976328 | ||||||||
\(9\) | −2.92324 | −0.974415 | ||||||||
\(10\) | −1.33640 | −0.422608 | ||||||||
\(11\) | 3.59107 | 1.08275 | 0.541374 | − | 0.840782i | \(-0.317904\pi\) | ||||
0.541374 | + | 0.840782i | \(0.317904\pi\) | |||||||
\(12\) | −0.889282 | −0.256714 | ||||||||
\(13\) | 0.558307 | 0.154846 | 0.0774232 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774232 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(14\) | −2.28251 | −0.610026 | ||||||||
\(15\) | −0.162211 | −0.0418828 | ||||||||
\(16\) | −0.116600 | −0.0291500 | ||||||||
\(17\) | 2.03684 | 0.494006 | 0.247003 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247003 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(18\) | 6.67233 | 1.57268 | ||||||||
\(19\) | 5.46372 | 1.25346 | 0.626732 | − | 0.779235i | \(-0.284392\pi\) | ||||
0.626732 | + | 0.779235i | \(0.284392\pi\) | |||||||
\(20\) | 1.87935 | 0.420236 | ||||||||
\(21\) | −0.277049 | −0.0604570 | ||||||||
\(22\) | −8.19664 | −1.74753 | ||||||||
\(23\) | 3.31065 | 0.690319 | 0.345159 | − | 0.938544i | \(-0.387825\pi\) | ||||
0.345159 | + | 0.938544i | \(0.387825\pi\) | |||||||
\(24\) | 0.765062 | 0.156168 | ||||||||
\(25\) | −4.65719 | −0.931439 | ||||||||
\(26\) | −1.27434 | −0.249919 | ||||||||
\(27\) | 1.64103 | 0.315816 | ||||||||
\(28\) | 3.20984 | 0.606603 | ||||||||
\(29\) | 3.76294 | 0.698761 | 0.349380 | − | 0.936981i | \(-0.386392\pi\) | ||||
0.349380 | + | 0.936981i | \(0.386392\pi\) | |||||||
\(30\) | 0.370248 | 0.0675978 | ||||||||
\(31\) | 6.60139 | 1.18564 | 0.592822 | − | 0.805333i | \(-0.298014\pi\) | ||||
0.592822 | + | 0.805333i | \(0.298014\pi\) | |||||||
\(32\) | 5.78909 | 1.02338 | ||||||||
\(33\) | −0.994900 | −0.173190 | ||||||||
\(34\) | −4.64910 | −0.797314 | ||||||||
\(35\) | 0.585497 | 0.0989671 | ||||||||
\(36\) | −9.38315 | −1.56386 | ||||||||
\(37\) | 5.38098 | 0.884628 | 0.442314 | − | 0.896860i | \(-0.354158\pi\) | ||||
0.442314 | + | 0.896860i | \(0.354158\pi\) | |||||||
\(38\) | −12.4710 | −2.02306 | ||||||||
\(39\) | −0.154678 | −0.0247683 | ||||||||
\(40\) | −1.61684 | −0.255644 | ||||||||
\(41\) | −4.04781 | −0.632161 | −0.316081 | − | 0.948732i | \(-0.602367\pi\) | ||||
−0.316081 | + | 0.948732i | \(0.602367\pi\) | |||||||
\(42\) | 0.632366 | 0.0975761 | ||||||||
\(43\) | 1.09056 | 0.166308 | 0.0831542 | − | 0.996537i | \(-0.473501\pi\) | ||||
0.0831542 | + | 0.996537i | \(0.473501\pi\) | |||||||
\(44\) | 11.5268 | 1.73772 | ||||||||
\(45\) | −1.71155 | −0.255143 | ||||||||
\(46\) | −7.55659 | −1.11416 | ||||||||
\(47\) | −1.70506 | −0.248708 | −0.124354 | − | 0.992238i | \(-0.539686\pi\) | ||||
−0.124354 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(48\) | 0.0323038 | 0.00466266 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.6301 | 1.50332 | ||||||||
\(51\) | −0.564303 | −0.0790182 | ||||||||
\(52\) | 1.79208 | 0.248516 | ||||||||
\(53\) | 5.93502 | 0.815238 | 0.407619 | − | 0.913152i | \(-0.366359\pi\) | ||||
0.407619 | + | 0.913152i | \(0.366359\pi\) | |||||||
\(54\) | −3.74566 | −0.509719 | ||||||||
\(55\) | 2.10256 | 0.283509 | ||||||||
\(56\) | −2.76147 | −0.369017 | ||||||||
\(57\) | −1.51372 | −0.200497 | ||||||||
\(58\) | −8.58895 | −1.12778 | ||||||||
\(59\) | −6.28870 | −0.818718 | −0.409359 | − | 0.912373i | \(-0.634248\pi\) | ||||
−0.409359 | + | 0.912373i | \(0.634248\pi\) | |||||||
\(60\) | −0.520672 | −0.0672185 | ||||||||
\(61\) | 6.18002 | 0.791271 | 0.395635 | − | 0.918408i | \(-0.370524\pi\) | ||||
0.395635 | + | 0.918408i | \(0.370524\pi\) | |||||||
\(62\) | −15.0677 | −1.91360 | ||||||||
\(63\) | −2.92324 | −0.368294 | ||||||||
\(64\) | −12.9804 | −1.62255 | ||||||||
\(65\) | 0.326887 | 0.0405454 | ||||||||
\(66\) | 2.27087 | 0.279524 | ||||||||
\(67\) | −6.69246 | −0.817615 | −0.408807 | − | 0.912621i | \(-0.634055\pi\) | ||||
−0.408807 | + | 0.912621i | \(0.634055\pi\) | |||||||
\(68\) | 6.53793 | 0.792840 | ||||||||
\(69\) | −0.917212 | −0.110419 | ||||||||
\(70\) | −1.33640 | −0.159731 | ||||||||
\(71\) | −3.98312 | −0.472710 | −0.236355 | − | 0.971667i | \(-0.575953\pi\) | ||||
−0.236355 | + | 0.971667i | \(0.575953\pi\) | |||||||
\(72\) | 8.07246 | 0.951348 | ||||||||
\(73\) | 0.643838 | 0.0753555 | 0.0376777 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376777 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(74\) | −12.2821 | −1.42777 | ||||||||
\(75\) | 1.29027 | 0.148987 | ||||||||
\(76\) | 17.5377 | 2.01171 | ||||||||
\(77\) | 3.59107 | 0.409240 | ||||||||
\(78\) | 0.353054 | 0.0399755 | ||||||||
\(79\) | 4.71689 | 0.530691 | 0.265346 | − | 0.964153i | \(-0.414514\pi\) | ||||
0.265346 | + | 0.964153i | \(0.414514\pi\) | |||||||
\(80\) | −0.0682689 | −0.00763270 | ||||||||
\(81\) | 8.31509 | 0.923899 | ||||||||
\(82\) | 9.23915 | 1.02029 | ||||||||
\(83\) | 0.483915 | 0.0531166 | 0.0265583 | − | 0.999647i | \(-0.491545\pi\) | ||||
0.0265583 | + | 0.999647i | \(0.491545\pi\) | |||||||
\(84\) | −0.889282 | −0.0970286 | ||||||||
\(85\) | 1.19256 | 0.129352 | ||||||||
\(86\) | −2.48921 | −0.268418 | ||||||||
\(87\) | −1.04252 | −0.111770 | ||||||||
\(88\) | −9.91664 | −1.05712 | ||||||||
\(89\) | 7.45128 | 0.789834 | 0.394917 | − | 0.918717i | \(-0.370773\pi\) | ||||
0.394917 | + | 0.918717i | \(0.370773\pi\) | |||||||
\(90\) | 3.90663 | 0.411795 | ||||||||
\(91\) | 0.558307 | 0.0585265 | ||||||||
\(92\) | 10.6267 | 1.10791 | ||||||||
\(93\) | −1.82891 | −0.189649 | ||||||||
\(94\) | 3.89181 | 0.401410 | ||||||||
\(95\) | 3.19900 | 0.328210 | ||||||||
\(96\) | −1.60386 | −0.163693 | ||||||||
\(97\) | 12.0197 | 1.22042 | 0.610209 | − | 0.792241i | \(-0.291086\pi\) | ||||
0.610209 | + | 0.792241i | \(0.291086\pi\) | |||||||
\(98\) | −2.28251 | −0.230568 | ||||||||
\(99\) | −10.4976 | −1.05505 | ||||||||
\(100\) | −14.9489 | −1.49489 | ||||||||
\(101\) | −12.3084 | −1.22474 | −0.612368 | − | 0.790573i | \(-0.709783\pi\) | ||||
−0.612368 | + | 0.790573i | \(0.709783\pi\) | |||||||
\(102\) | 1.28803 | 0.127534 | ||||||||
\(103\) | −9.60351 | −0.946262 | −0.473131 | − | 0.880992i | \(-0.656876\pi\) | ||||
−0.473131 | + | 0.880992i | \(0.656876\pi\) | |||||||
\(104\) | −1.54175 | −0.151181 | ||||||||
\(105\) | −0.162211 | −0.0158302 | ||||||||
\(106\) | −13.5467 | −1.31578 | ||||||||
\(107\) | 7.82807 | 0.756768 | 0.378384 | − | 0.925649i | \(-0.376480\pi\) | ||||
0.378384 | + | 0.925649i | \(0.376480\pi\) | |||||||
\(108\) | 5.26744 | 0.506859 | ||||||||
\(109\) | 8.24191 | 0.789432 | 0.394716 | − | 0.918803i | \(-0.370843\pi\) | ||||
0.394716 | + | 0.918803i | \(0.370843\pi\) | |||||||
\(110\) | −4.79911 | −0.457577 | ||||||||
\(111\) | −1.49079 | −0.141500 | ||||||||
\(112\) | −0.116600 | −0.0110177 | ||||||||
\(113\) | −13.8053 | −1.29869 | −0.649345 | − | 0.760494i | \(-0.724957\pi\) | ||||
−0.649345 | + | 0.760494i | \(0.724957\pi\) | |||||||
\(114\) | 3.45507 | 0.323597 | ||||||||
\(115\) | 1.93838 | 0.180755 | ||||||||
\(116\) | 12.0785 | 1.12146 | ||||||||
\(117\) | −1.63207 | −0.150885 | ||||||||
\(118\) | 14.3540 | 1.32139 | ||||||||
\(119\) | 2.03684 | 0.186717 | ||||||||
\(120\) | 0.447942 | 0.0408913 | ||||||||
\(121\) | 1.89577 | 0.172342 | ||||||||
\(122\) | −14.1060 | −1.27709 | ||||||||
\(123\) | 1.12144 | 0.101117 | ||||||||
\(124\) | 21.1894 | 1.90287 | ||||||||
\(125\) | −5.65426 | −0.505732 | ||||||||
\(126\) | 6.67233 | 0.594418 | ||||||||
\(127\) | −12.7291 | −1.12953 | −0.564764 | − | 0.825252i | \(-0.691033\pi\) | ||||
−0.564764 | + | 0.825252i | \(0.691033\pi\) | |||||||
\(128\) | 18.0498 | 1.59539 | ||||||||
\(129\) | −0.302138 | −0.0266017 | ||||||||
\(130\) | −0.746123 | −0.0654393 | ||||||||
\(131\) | 9.78851 | 0.855226 | 0.427613 | − | 0.903962i | \(-0.359355\pi\) | ||||
0.427613 | + | 0.903962i | \(0.359355\pi\) | |||||||
\(132\) | −3.19347 | −0.277956 | ||||||||
\(133\) | 5.46372 | 0.473765 | ||||||||
\(134\) | 15.2756 | 1.31961 | ||||||||
\(135\) | 0.960817 | 0.0826939 | ||||||||
\(136\) | −5.62467 | −0.482312 | ||||||||
\(137\) | 10.4659 | 0.894161 | 0.447081 | − | 0.894494i | \(-0.352464\pi\) | ||||
0.447081 | + | 0.894494i | \(0.352464\pi\) | |||||||
\(138\) | 2.09354 | 0.178214 | ||||||||
\(139\) | 3.70442 | 0.314205 | 0.157102 | − | 0.987582i | \(-0.449785\pi\) | ||||
0.157102 | + | 0.987582i | \(0.449785\pi\) | |||||||
\(140\) | 1.87935 | 0.158834 | ||||||||
\(141\) | 0.472384 | 0.0397819 | ||||||||
\(142\) | 9.09151 | 0.762942 | ||||||||
\(143\) | 2.00492 | 0.167660 | ||||||||
\(144\) | 0.340850 | 0.0284042 | ||||||||
\(145\) | 2.20319 | 0.182965 | ||||||||
\(146\) | −1.46956 | −0.121622 | ||||||||
\(147\) | −0.277049 | −0.0228506 | ||||||||
\(148\) | 17.2721 | 1.41976 | ||||||||
\(149\) | 11.3829 | 0.932525 | 0.466262 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466262 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(150\) | −2.94505 | −0.240462 | ||||||||
\(151\) | −8.15733 | −0.663834 | −0.331917 | − | 0.943309i | \(-0.607695\pi\) | ||||
−0.331917 | + | 0.943309i | \(0.607695\pi\) | |||||||
\(152\) | −15.0879 | −1.22379 | ||||||||
\(153\) | −5.95417 | −0.481366 | ||||||||
\(154\) | −8.19664 | −0.660504 | ||||||||
\(155\) | 3.86510 | 0.310452 | ||||||||
\(156\) | −0.496492 | −0.0397512 | ||||||||
\(157\) | −8.93067 | −0.712745 | −0.356372 | − | 0.934344i | \(-0.615987\pi\) | ||||
−0.356372 | + | 0.934344i | \(0.615987\pi\) | |||||||
\(158\) | −10.7663 | −0.856523 | ||||||||
\(159\) | −1.64429 | −0.130401 | ||||||||
\(160\) | 3.38949 | 0.267963 | ||||||||
\(161\) | 3.31065 | 0.260916 | ||||||||
\(162\) | −18.9793 | −1.49115 | ||||||||
\(163\) | −6.95852 | −0.545033 | −0.272516 | − | 0.962151i | \(-0.587856\pi\) | ||||
−0.272516 | + | 0.962151i | \(0.587856\pi\) | |||||||
\(164\) | −12.9928 | −1.01457 | ||||||||
\(165\) | −0.582512 | −0.0453485 | ||||||||
\(166\) | −1.10454 | −0.0857289 | ||||||||
\(167\) | 20.1003 | 1.55541 | 0.777704 | − | 0.628631i | \(-0.216384\pi\) | ||||
0.777704 | + | 0.628631i | \(0.216384\pi\) | |||||||
\(168\) | 0.765062 | 0.0590258 | ||||||||
\(169\) | −12.6883 | −0.976023 | ||||||||
\(170\) | −2.72203 | −0.208770 | ||||||||
\(171\) | −15.9718 | −1.22139 | ||||||||
\(172\) | 3.50052 | 0.266912 | ||||||||
\(173\) | 18.1769 | 1.38196 | 0.690981 | − | 0.722873i | \(-0.257179\pi\) | ||||
0.690981 | + | 0.722873i | \(0.257179\pi\) | |||||||
\(174\) | 2.37956 | 0.180394 | ||||||||
\(175\) | −4.65719 | −0.352051 | ||||||||
\(176\) | −0.418718 | −0.0315621 | ||||||||
\(177\) | 1.74227 | 0.130957 | ||||||||
\(178\) | −17.0076 | −1.27477 | ||||||||
\(179\) | −11.2057 | −0.837556 | −0.418778 | − | 0.908089i | \(-0.637541\pi\) | ||||
−0.418778 | + | 0.908089i | \(0.637541\pi\) | |||||||
\(180\) | −5.49381 | −0.409484 | ||||||||
\(181\) | 2.27379 | 0.169009 | 0.0845047 | − | 0.996423i | \(-0.473069\pi\) | ||||
0.0845047 | + | 0.996423i | \(0.473069\pi\) | |||||||
\(182\) | −1.27434 | −0.0944604 | ||||||||
\(183\) | −1.71217 | −0.126567 | ||||||||
\(184\) | −9.14228 | −0.673978 | ||||||||
\(185\) | 3.15055 | 0.231633 | ||||||||
\(186\) | 4.17449 | 0.306089 | ||||||||
\(187\) | 7.31442 | 0.534883 | ||||||||
\(188\) | −5.47297 | −0.399157 | ||||||||
\(189\) | 1.64103 | 0.119367 | ||||||||
\(190\) | −7.30173 | −0.529723 | ||||||||
\(191\) | 24.8406 | 1.79740 | 0.898700 | − | 0.438563i | \(-0.144512\pi\) | ||||
0.898700 | + | 0.438563i | \(0.144512\pi\) | |||||||
\(192\) | 3.59621 | 0.259534 | ||||||||
\(193\) | 15.2276 | 1.09611 | 0.548055 | − | 0.836443i | \(-0.315369\pi\) | ||||
0.548055 | + | 0.836443i | \(0.315369\pi\) | |||||||
\(194\) | −27.4351 | −1.96973 | ||||||||
\(195\) | −0.0905637 | −0.00648540 | ||||||||
\(196\) | 3.20984 | 0.229274 | ||||||||
\(197\) | −6.88856 | −0.490790 | −0.245395 | − | 0.969423i | \(-0.578918\pi\) | ||||
−0.245395 | + | 0.969423i | \(0.578918\pi\) | |||||||
\(198\) | 23.9608 | 1.70282 | ||||||||
\(199\) | −20.6946 | −1.46700 | −0.733500 | − | 0.679689i | \(-0.762115\pi\) | ||||
−0.733500 | + | 0.679689i | \(0.762115\pi\) | |||||||
\(200\) | 12.8607 | 0.909390 | ||||||||
\(201\) | 1.85414 | 0.130781 | ||||||||
\(202\) | 28.0941 | 1.97669 | ||||||||
\(203\) | 3.76294 | 0.264107 | ||||||||
\(204\) | −1.81132 | −0.126818 | ||||||||
\(205\) | −2.36998 | −0.165527 | ||||||||
\(206\) | 21.9201 | 1.52724 | ||||||||
\(207\) | −9.67784 | −0.672657 | ||||||||
\(208\) | −0.0650985 | −0.00451377 | ||||||||
\(209\) | 19.6206 | 1.35719 | ||||||||
\(210\) | 0.370248 | 0.0255496 | ||||||||
\(211\) | 0.540588 | 0.0372156 | 0.0186078 | − | 0.999827i | \(-0.494077\pi\) | ||||
0.0186078 | + | 0.999827i | \(0.494077\pi\) | |||||||
\(212\) | 19.0505 | 1.30839 | ||||||||
\(213\) | 1.10352 | 0.0756118 | ||||||||
\(214\) | −17.8676 | −1.22141 | ||||||||
\(215\) | 0.638519 | 0.0435466 | ||||||||
\(216\) | −4.53165 | −0.308340 | ||||||||
\(217\) | 6.60139 | 0.448132 | ||||||||
\(218\) | −18.8122 | −1.27412 | ||||||||
\(219\) | −0.178374 | −0.0120534 | ||||||||
\(220\) | 6.74889 | 0.455010 | ||||||||
\(221\) | 1.13718 | 0.0764950 | ||||||||
\(222\) | 3.40275 | 0.228377 | ||||||||
\(223\) | 3.83858 | 0.257050 | 0.128525 | − | 0.991706i | \(-0.458976\pi\) | ||||
0.128525 | + | 0.991706i | \(0.458976\pi\) | |||||||
\(224\) | 5.78909 | 0.386800 | ||||||||
\(225\) | 13.6141 | 0.907607 | ||||||||
\(226\) | 31.5106 | 2.09606 | ||||||||
\(227\) | −22.3502 | −1.48344 | −0.741719 | − | 0.670711i | \(-0.765989\pi\) | ||||
−0.741719 | + | 0.670711i | \(0.765989\pi\) | |||||||
\(228\) | −4.85879 | −0.321781 | ||||||||
\(229\) | −4.90371 | −0.324046 | −0.162023 | − | 0.986787i | \(-0.551802\pi\) | ||||
−0.162023 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(230\) | −4.42436 | −0.291734 | ||||||||
\(231\) | −0.994900 | −0.0654596 | ||||||||
\(232\) | −10.3913 | −0.682220 | ||||||||
\(233\) | 11.6431 | 0.762765 | 0.381383 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381383 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(234\) | 3.72521 | 0.243524 | ||||||||
\(235\) | −0.998307 | −0.0651224 | ||||||||
\(236\) | −20.1857 | −1.31398 | ||||||||
\(237\) | −1.30681 | −0.0848862 | ||||||||
\(238\) | −4.64910 | −0.301356 | ||||||||
\(239\) | 17.3436 | 1.12187 | 0.560933 | − | 0.827861i | \(-0.310443\pi\) | ||||
0.560933 | + | 0.827861i | \(0.310443\pi\) | |||||||
\(240\) | 0.0189138 | 0.00122088 | ||||||||
\(241\) | −19.5006 | −1.25614 | −0.628072 | − | 0.778155i | \(-0.716156\pi\) | ||||
−0.628072 | + | 0.778155i | \(0.716156\pi\) | |||||||
\(242\) | −4.32710 | −0.278157 | ||||||||
\(243\) | −7.22676 | −0.463597 | ||||||||
\(244\) | 19.8369 | 1.26993 | ||||||||
\(245\) | 0.585497 | 0.0374061 | ||||||||
\(246\) | −2.55969 | −0.163200 | ||||||||
\(247\) | 3.05043 | 0.194095 | ||||||||
\(248\) | −18.2296 | −1.15758 | ||||||||
\(249\) | −0.134068 | −0.00849621 | ||||||||
\(250\) | 12.9059 | 0.816240 | ||||||||
\(251\) | −14.6005 | −0.921573 | −0.460787 | − | 0.887511i | \(-0.652433\pi\) | ||||
−0.460787 | + | 0.887511i | \(0.652433\pi\) | |||||||
\(252\) | −9.38315 | −0.591083 | ||||||||
\(253\) | 11.8888 | 0.747441 | ||||||||
\(254\) | 29.0544 | 1.82303 | ||||||||
\(255\) | −0.330398 | −0.0206903 | ||||||||
\(256\) | −15.2379 | −0.952367 | ||||||||
\(257\) | −9.93889 | −0.619971 | −0.309985 | − | 0.950741i | \(-0.600324\pi\) | ||||
−0.309985 | + | 0.950741i | \(0.600324\pi\) | |||||||
\(258\) | 0.689631 | 0.0429346 | ||||||||
\(259\) | 5.38098 | 0.334358 | ||||||||
\(260\) | 1.04926 | 0.0650721 | ||||||||
\(261\) | −11.0000 | −0.680883 | ||||||||
\(262\) | −22.3423 | −1.38031 | ||||||||
\(263\) | 11.2040 | 0.690870 | 0.345435 | − | 0.938443i | \(-0.387731\pi\) | ||||
0.345435 | + | 0.938443i | \(0.387731\pi\) | |||||||
\(264\) | 2.74739 | 0.169090 | ||||||||
\(265\) | 3.47494 | 0.213464 | ||||||||
\(266\) | −12.4710 | −0.764646 | ||||||||
\(267\) | −2.06437 | −0.126337 | ||||||||
\(268\) | −21.4817 | −1.31221 | ||||||||
\(269\) | −10.6131 | −0.647091 | −0.323546 | − | 0.946213i | \(-0.604875\pi\) | ||||
−0.323546 | + | 0.946213i | \(0.604875\pi\) | |||||||
\(270\) | −2.19307 | −0.133466 | ||||||||
\(271\) | −28.0823 | −1.70588 | −0.852938 | − | 0.522012i | \(-0.825182\pi\) | ||||
−0.852938 | + | 0.522012i | \(0.825182\pi\) | |||||||
\(272\) | −0.237495 | −0.0144002 | ||||||||
\(273\) | −0.154678 | −0.00936155 | ||||||||
\(274\) | −23.8885 | −1.44316 | ||||||||
\(275\) | −16.7243 | −1.00851 | ||||||||
\(276\) | −2.94410 | −0.177214 | ||||||||
\(277\) | 1.71708 | 0.103169 | 0.0515847 | − | 0.998669i | \(-0.483573\pi\) | ||||
0.0515847 | + | 0.998669i | \(0.483573\pi\) | |||||||
\(278\) | −8.45536 | −0.507119 | ||||||||
\(279\) | −19.2975 | −1.15531 | ||||||||
\(280\) | −1.61684 | −0.0966244 | ||||||||
\(281\) | 17.9840 | 1.07284 | 0.536418 | − | 0.843953i | \(-0.319777\pi\) | ||||
0.536418 | + | 0.843953i | \(0.319777\pi\) | |||||||
\(282\) | −1.07822 | −0.0642071 | ||||||||
\(283\) | 2.60980 | 0.155136 | 0.0775682 | − | 0.996987i | \(-0.475284\pi\) | ||||
0.0775682 | + | 0.996987i | \(0.475284\pi\) | |||||||
\(284\) | −12.7852 | −0.758661 | ||||||||
\(285\) | −0.886277 | −0.0524985 | ||||||||
\(286\) | −4.57624 | −0.270599 | ||||||||
\(287\) | −4.04781 | −0.238935 | ||||||||
\(288\) | −16.9229 | −0.997192 | ||||||||
\(289\) | −12.8513 | −0.755958 | ||||||||
\(290\) | −5.02881 | −0.295302 | ||||||||
\(291\) | −3.33005 | −0.195211 | ||||||||
\(292\) | 2.06662 | 0.120940 | ||||||||
\(293\) | 0.229207 | 0.0133904 | 0.00669520 | − | 0.999978i | \(-0.497869\pi\) | ||||
0.00669520 | + | 0.999978i | \(0.497869\pi\) | |||||||
\(294\) | 0.632366 | 0.0368803 | ||||||||
\(295\) | −3.68201 | −0.214375 | ||||||||
\(296\) | −14.8594 | −0.863687 | ||||||||
\(297\) | 5.89304 | 0.341949 | ||||||||
\(298\) | −25.9816 | −1.50507 | ||||||||
\(299\) | 1.84836 | 0.106893 | ||||||||
\(300\) | 4.14156 | 0.239113 | ||||||||
\(301\) | 1.09056 | 0.0628587 | ||||||||
\(302\) | 18.6192 | 1.07141 | ||||||||
\(303\) | 3.41003 | 0.195901 | ||||||||
\(304\) | −0.637069 | −0.0365384 | ||||||||
\(305\) | 3.61839 | 0.207188 | ||||||||
\(306\) | 13.5904 | 0.776914 | ||||||||
\(307\) | −24.9663 | −1.42490 | −0.712450 | − | 0.701722i | \(-0.752415\pi\) | ||||
−0.712450 | + | 0.701722i | \(0.752415\pi\) | |||||||
\(308\) | 11.5268 | 0.656798 | ||||||||
\(309\) | 2.66064 | 0.151358 | ||||||||
\(310\) | −8.82211 | −0.501062 | ||||||||
\(311\) | 5.57802 | 0.316301 | 0.158150 | − | 0.987415i | \(-0.449447\pi\) | ||||
0.158150 | + | 0.987415i | \(0.449447\pi\) | |||||||
\(312\) | 0.427140 | 0.0241820 | ||||||||
\(313\) | 5.94741 | 0.336168 | 0.168084 | − | 0.985773i | \(-0.446242\pi\) | ||||
0.168084 | + | 0.985773i | \(0.446242\pi\) | |||||||
\(314\) | 20.3843 | 1.15035 | ||||||||
\(315\) | −1.71155 | −0.0964350 | ||||||||
\(316\) | 15.1405 | 0.851717 | ||||||||
\(317\) | −4.11641 | −0.231200 | −0.115600 | − | 0.993296i | \(-0.536879\pi\) | ||||
−0.115600 | + | 0.993296i | \(0.536879\pi\) | |||||||
\(318\) | 3.75310 | 0.210464 | ||||||||
\(319\) | 13.5130 | 0.756582 | ||||||||
\(320\) | −7.60001 | −0.424853 | ||||||||
\(321\) | −2.16876 | −0.121048 | ||||||||
\(322\) | −7.55659 | −0.421112 | ||||||||
\(323\) | 11.1287 | 0.619218 | ||||||||
\(324\) | 26.6901 | 1.48278 | ||||||||
\(325\) | −2.60014 | −0.144230 | ||||||||
\(326\) | 15.8829 | 0.879671 | ||||||||
\(327\) | −2.28341 | −0.126273 | ||||||||
\(328\) | 11.1779 | 0.617197 | ||||||||
\(329\) | −1.70506 | −0.0940029 | ||||||||
\(330\) | 1.32959 | 0.0731914 | ||||||||
\(331\) | −23.5068 | −1.29205 | −0.646025 | − | 0.763316i | \(-0.723570\pi\) | ||||
−0.646025 | + | 0.763316i | \(0.723570\pi\) | |||||||
\(332\) | 1.55329 | 0.0852479 | ||||||||
\(333\) | −15.7299 | −0.861994 | ||||||||
\(334\) | −45.8791 | −2.51039 | ||||||||
\(335\) | −3.91842 | −0.214086 | ||||||||
\(336\) | 0.0323038 | 0.00176232 | ||||||||
\(337\) | −25.1793 | −1.37160 | −0.685801 | − | 0.727789i | \(-0.740548\pi\) | ||||
−0.685801 | + | 0.727789i | \(0.740548\pi\) | |||||||
\(338\) | 28.9611 | 1.57528 | ||||||||
\(339\) | 3.82473 | 0.207731 | ||||||||
\(340\) | 3.82794 | 0.207599 | ||||||||
\(341\) | 23.7060 | 1.28375 | ||||||||
\(342\) | 36.4558 | 1.97130 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.01155 | −0.162372 | ||||||||
\(345\) | −0.537025 | −0.0289125 | ||||||||
\(346\) | −41.4889 | −2.23046 | ||||||||
\(347\) | 12.6313 | 0.678084 | 0.339042 | − | 0.940771i | \(-0.389897\pi\) | ||||
0.339042 | + | 0.940771i | \(0.389897\pi\) | |||||||
\(348\) | −3.34632 | −0.179381 | ||||||||
\(349\) | 12.2189 | 0.654063 | 0.327032 | − | 0.945013i | \(-0.393952\pi\) | ||||
0.327032 | + | 0.945013i | \(0.393952\pi\) | |||||||
\(350\) | 10.6301 | 0.568202 | ||||||||
\(351\) | 0.916197 | 0.0489030 | ||||||||
\(352\) | 20.7890 | 1.10806 | ||||||||
\(353\) | 19.4614 | 1.03583 | 0.517914 | − | 0.855433i | \(-0.326709\pi\) | ||||
0.517914 | + | 0.855433i | \(0.326709\pi\) | |||||||
\(354\) | −3.97675 | −0.211362 | ||||||||
\(355\) | −2.33211 | −0.123775 | ||||||||
\(356\) | 23.9174 | 1.26762 | ||||||||
\(357\) | −0.564303 | −0.0298661 | ||||||||
\(358\) | 25.5772 | 1.35180 | ||||||||
\(359\) | 15.8495 | 0.836507 | 0.418253 | − | 0.908330i | \(-0.362642\pi\) | ||||
0.418253 | + | 0.908330i | \(0.362642\pi\) | |||||||
\(360\) | 4.72640 | 0.249103 | ||||||||
\(361\) | 10.8523 | 0.571172 | ||||||||
\(362\) | −5.18994 | −0.272777 | ||||||||
\(363\) | −0.525219 | −0.0275669 | ||||||||
\(364\) | 1.79208 | 0.0939304 | ||||||||
\(365\) | 0.376965 | 0.0197313 | ||||||||
\(366\) | 3.90803 | 0.204276 | ||||||||
\(367\) | 7.25773 | 0.378850 | 0.189425 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189425 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(368\) | −0.386022 | −0.0201228 | ||||||||
\(369\) | 11.8327 | 0.615987 | ||||||||
\(370\) | −7.19115 | −0.373850 | ||||||||
\(371\) | 5.93502 | 0.308131 | ||||||||
\(372\) | −5.87050 | −0.304371 | ||||||||
\(373\) | −14.9680 | −0.775014 | −0.387507 | − | 0.921867i | \(-0.626664\pi\) | ||||
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(374\) | −16.6952 | −0.863289 | ||||||||
\(375\) | 1.56651 | 0.0808940 | ||||||||
\(376\) | 4.70847 | 0.242821 | ||||||||
\(377\) | 2.10088 | 0.108201 | ||||||||
\(378\) | −3.74566 | −0.192656 | ||||||||
\(379\) | −34.7623 | −1.78562 | −0.892810 | − | 0.450434i | \(-0.851269\pi\) | ||||
−0.892810 | + | 0.450434i | \(0.851269\pi\) | |||||||
\(380\) | 10.2683 | 0.526751 | ||||||||
\(381\) | 3.52659 | 0.180673 | ||||||||
\(382\) | −56.6988 | −2.90096 | ||||||||
\(383\) | −9.00283 | −0.460023 | −0.230011 | − | 0.973188i | \(-0.573876\pi\) | ||||
−0.230011 | + | 0.973188i | \(0.573876\pi\) | |||||||
\(384\) | −5.00066 | −0.255189 | ||||||||
\(385\) | 2.10256 | 0.107156 | ||||||||
\(386\) | −34.7572 | −1.76909 | ||||||||
\(387\) | −3.18797 | −0.162053 | ||||||||
\(388\) | 38.5814 | 1.95867 | ||||||||
\(389\) | 25.3095 | 1.28324 | 0.641622 | − | 0.767021i | \(-0.278262\pi\) | ||||
0.641622 | + | 0.767021i | \(0.278262\pi\) | |||||||
\(390\) | 0.206712 | 0.0104673 | ||||||||
\(391\) | 6.74326 | 0.341021 | ||||||||
\(392\) | −2.76147 | −0.139475 | ||||||||
\(393\) | −2.71189 | −0.136797 | ||||||||
\(394\) | 15.7232 | 0.792123 | ||||||||
\(395\) | 2.76172 | 0.138957 | ||||||||
\(396\) | −33.6955 | −1.69326 | ||||||||
\(397\) | 34.7997 | 1.74655 | 0.873273 | − | 0.487230i | \(-0.161993\pi\) | ||||
0.873273 | + | 0.487230i | \(0.161993\pi\) | |||||||
\(398\) | 47.2356 | 2.36770 | ||||||||
\(399\) | −1.51372 | −0.0757806 | ||||||||
\(400\) | 0.543028 | 0.0271514 | ||||||||
\(401\) | 4.37821 | 0.218638 | 0.109319 | − | 0.994007i | \(-0.465133\pi\) | ||||
0.109319 | + | 0.994007i | \(0.465133\pi\) | |||||||
\(402\) | −4.23208 | −0.211077 | ||||||||
\(403\) | 3.68560 | 0.183593 | ||||||||
\(404\) | −39.5081 | −1.96560 | ||||||||
\(405\) | 4.86846 | 0.241916 | ||||||||
\(406\) | −8.58895 | −0.426262 | ||||||||
\(407\) | 19.3235 | 0.957829 | ||||||||
\(408\) | 1.55831 | 0.0771477 | ||||||||
\(409\) | 5.24544 | 0.259370 | 0.129685 | − | 0.991555i | \(-0.458603\pi\) | ||||
0.129685 | + | 0.991555i | \(0.458603\pi\) | |||||||
\(410\) | 5.40950 | 0.267156 | ||||||||
\(411\) | −2.89956 | −0.143025 | ||||||||
\(412\) | −30.8257 | −1.51867 | ||||||||
\(413\) | −6.28870 | −0.309446 | ||||||||
\(414\) | 22.0898 | 1.08565 | ||||||||
\(415\) | 0.283331 | 0.0139082 | ||||||||
\(416\) | 3.23209 | 0.158466 | ||||||||
\(417\) | −1.02630 | −0.0502583 | ||||||||
\(418\) | −44.7842 | −2.19047 | ||||||||
\(419\) | 1.81371 | 0.0886055 | 0.0443028 | − | 0.999018i | \(-0.485893\pi\) | ||||
0.0443028 | + | 0.999018i | \(0.485893\pi\) | |||||||
\(420\) | −0.520672 | −0.0254062 | ||||||||
\(421\) | −12.3131 | −0.600104 | −0.300052 | − | 0.953923i | \(-0.597004\pi\) | ||||
−0.300052 | + | 0.953923i | \(0.597004\pi\) | |||||||
\(422\) | −1.23390 | −0.0600651 | ||||||||
\(423\) | 4.98430 | 0.242345 | ||||||||
\(424\) | −16.3894 | −0.795940 | ||||||||
\(425\) | −9.48594 | −0.460136 | ||||||||
\(426\) | −2.51879 | −0.122036 | ||||||||
\(427\) | 6.18002 | 0.299072 | ||||||||
\(428\) | 25.1269 | 1.21455 | ||||||||
\(429\) | −0.555460 | −0.0268179 | ||||||||
\(430\) | −1.45742 | −0.0702832 | ||||||||
\(431\) | −19.7490 | −0.951277 | −0.475639 | − | 0.879641i | \(-0.657783\pi\) | ||||
−0.475639 | + | 0.879641i | \(0.657783\pi\) | |||||||
\(432\) | −0.191343 | −0.00920602 | ||||||||
\(433\) | 11.6397 | 0.559369 | 0.279684 | − | 0.960092i | \(-0.409770\pi\) | ||||
0.279684 | + | 0.960092i | \(0.409770\pi\) | |||||||
\(434\) | −15.0677 | −0.723274 | ||||||||
\(435\) | −0.610392 | −0.0292660 | ||||||||
\(436\) | 26.4552 | 1.26698 | ||||||||
\(437\) | 18.0885 | 0.865290 | ||||||||
\(438\) | 0.407141 | 0.0194539 | ||||||||
\(439\) | 25.3971 | 1.21214 | 0.606069 | − | 0.795412i | \(-0.292746\pi\) | ||||
0.606069 | + | 0.795412i | \(0.292746\pi\) | |||||||
\(440\) | −5.80616 | −0.276798 | ||||||||
\(441\) | −2.92324 | −0.139202 | ||||||||
\(442\) | −2.59562 | −0.123461 | ||||||||
\(443\) | 24.7323 | 1.17507 | 0.587534 | − | 0.809199i | \(-0.300099\pi\) | ||||
0.587534 | + | 0.809199i | \(0.300099\pi\) | |||||||
\(444\) | −4.78521 | −0.227096 | ||||||||
\(445\) | 4.36271 | 0.206812 | ||||||||
\(446\) | −8.76159 | −0.414873 | ||||||||
\(447\) | −3.15362 | −0.149161 | ||||||||
\(448\) | −12.9804 | −0.613268 | ||||||||
\(449\) | −7.72381 | −0.364509 | −0.182255 | − | 0.983251i | \(-0.558340\pi\) | ||||
−0.182255 | + | 0.983251i | \(0.558340\pi\) | |||||||
\(450\) | −31.0743 | −1.46486 | ||||||||
\(451\) | −14.5359 | −0.684471 | ||||||||
\(452\) | −44.3127 | −2.08430 | ||||||||
\(453\) | 2.25998 | 0.106183 | ||||||||
\(454\) | 51.0146 | 2.39423 | ||||||||
\(455\) | 0.326887 | 0.0153247 | ||||||||
\(456\) | 4.18009 | 0.195751 | ||||||||
\(457\) | 10.5209 | 0.492147 | 0.246073 | − | 0.969251i | \(-0.420860\pi\) | ||||
0.246073 | + | 0.969251i | \(0.420860\pi\) | |||||||
\(458\) | 11.1928 | 0.523003 | ||||||||
\(459\) | 3.34250 | 0.156015 | ||||||||
\(460\) | 6.22189 | 0.290097 | ||||||||
\(461\) | −3.21031 | −0.149519 | −0.0747595 | − | 0.997202i | \(-0.523819\pi\) | ||||
−0.0747595 | + | 0.997202i | \(0.523819\pi\) | |||||||
\(462\) | 2.27087 | 0.105650 | ||||||||
\(463\) | −12.2505 | −0.569329 | −0.284664 | − | 0.958627i | \(-0.591882\pi\) | ||||
−0.284664 | + | 0.958627i | \(0.591882\pi\) | |||||||
\(464\) | −0.438759 | −0.0203689 | ||||||||
\(465\) | −1.07082 | −0.0496581 | ||||||||
\(466\) | −26.5755 | −1.23109 | ||||||||
\(467\) | −9.45148 | −0.437362 | −0.218681 | − | 0.975796i | \(-0.570175\pi\) | ||||
−0.218681 | + | 0.975796i | \(0.570175\pi\) | |||||||
\(468\) | −5.23868 | −0.242158 | ||||||||
\(469\) | −6.69246 | −0.309029 | ||||||||
\(470\) | 2.27864 | 0.105106 | ||||||||
\(471\) | 2.47423 | 0.114006 | ||||||||
\(472\) | 17.3661 | 0.799338 | ||||||||
\(473\) | 3.91627 | 0.180070 | ||||||||
\(474\) | 2.98280 | 0.137004 | ||||||||
\(475\) | −25.4456 | −1.16752 | ||||||||
\(476\) | 6.53793 | 0.299665 | ||||||||
\(477\) | −17.3495 | −0.794380 | ||||||||
\(478\) | −39.5870 | −1.81067 | ||||||||
\(479\) | −2.32011 | −0.106009 | −0.0530043 | − | 0.998594i | \(-0.516880\pi\) | ||||
−0.0530043 | + | 0.998594i | \(0.516880\pi\) | |||||||
\(480\) | −0.939055 | −0.0428618 | ||||||||
\(481\) | 3.00424 | 0.136982 | ||||||||
\(482\) | 44.5103 | 2.02739 | ||||||||
\(483\) | −0.917212 | −0.0417346 | ||||||||
\(484\) | 6.08511 | 0.276596 | ||||||||
\(485\) | 7.03752 | 0.319557 | ||||||||
\(486\) | 16.4951 | 0.748235 | ||||||||
\(487\) | 18.1997 | 0.824708 | 0.412354 | − | 0.911024i | \(-0.364707\pi\) | ||||
0.412354 | + | 0.911024i | \(0.364707\pi\) | |||||||
\(488\) | −17.0660 | −0.772540 | ||||||||
\(489\) | 1.92785 | 0.0871803 | ||||||||
\(490\) | −1.33640 | −0.0603725 | ||||||||
\(491\) | 20.3167 | 0.916880 | 0.458440 | − | 0.888725i | \(-0.348408\pi\) | ||||
0.458440 | + | 0.888725i | \(0.348408\pi\) | |||||||
\(492\) | 3.59964 | 0.162284 | ||||||||
\(493\) | 7.66450 | 0.345192 | ||||||||
\(494\) | −6.96264 | −0.313264 | ||||||||
\(495\) | −6.14630 | −0.276256 | ||||||||
\(496\) | −0.769721 | −0.0345615 | ||||||||
\(497\) | −3.98312 | −0.178667 | ||||||||
\(498\) | 0.306011 | 0.0137127 | ||||||||
\(499\) | −13.6957 | −0.613104 | −0.306552 | − | 0.951854i | \(-0.599175\pi\) | ||||
−0.306552 | + | 0.951854i | \(0.599175\pi\) | |||||||
\(500\) | −18.1493 | −0.811661 | ||||||||
\(501\) | −5.56876 | −0.248794 | ||||||||
\(502\) | 33.3257 | 1.48740 | ||||||||
\(503\) | 30.6505 | 1.36664 | 0.683318 | − | 0.730120i | \(-0.260536\pi\) | ||||
0.683318 | + | 0.730120i | \(0.260536\pi\) | |||||||
\(504\) | 8.07246 | 0.359576 | ||||||||
\(505\) | −7.20656 | −0.320688 | ||||||||
\(506\) | −27.1362 | −1.20635 | ||||||||
\(507\) | 3.51527 | 0.156119 | ||||||||
\(508\) | −40.8585 | −1.81280 | ||||||||
\(509\) | 20.3721 | 0.902977 | 0.451488 | − | 0.892277i | \(-0.350893\pi\) | ||||
0.451488 | + | 0.892277i | \(0.350893\pi\) | |||||||
\(510\) | 0.754136 | 0.0333937 | ||||||||
\(511\) | 0.643838 | 0.0284817 | ||||||||
\(512\) | −1.31898 | −0.0582913 | ||||||||
\(513\) | 8.96612 | 0.395864 | ||||||||
\(514\) | 22.6856 | 1.00062 | ||||||||
\(515\) | −5.62283 | −0.247771 | ||||||||
\(516\) | −0.969814 | −0.0426937 | ||||||||
\(517\) | −6.12298 | −0.269288 | ||||||||
\(518\) | −12.2821 | −0.539646 | ||||||||
\(519\) | −5.03588 | −0.221051 | ||||||||
\(520\) | −0.902690 | −0.0395856 | ||||||||
\(521\) | 32.3581 | 1.41763 | 0.708817 | − | 0.705392i | \(-0.249229\pi\) | ||||
0.708817 | + | 0.705392i | \(0.249229\pi\) | |||||||
\(522\) | 25.1076 | 1.09893 | ||||||||
\(523\) | 30.7731 | 1.34562 | 0.672808 | − | 0.739817i | \(-0.265088\pi\) | ||||
0.672808 | + | 0.739817i | \(0.265088\pi\) | |||||||
\(524\) | 31.4196 | 1.37257 | ||||||||
\(525\) | 1.29027 | 0.0563119 | ||||||||
\(526\) | −25.5733 | −1.11505 | ||||||||
\(527\) | 13.4460 | 0.585715 | ||||||||
\(528\) | 0.116005 | 0.00504848 | ||||||||
\(529\) | −12.0396 | −0.523460 | ||||||||
\(530\) | −7.93158 | −0.344526 | ||||||||
\(531\) | 18.3834 | 0.797771 | ||||||||
\(532\) | 17.5377 | 0.760355 | ||||||||
\(533\) | −2.25992 | −0.0978880 | ||||||||
\(534\) | 4.71193 | 0.203905 | ||||||||
\(535\) | 4.58331 | 0.198154 | ||||||||
\(536\) | 18.4811 | 0.798260 | ||||||||
\(537\) | 3.10453 | 0.133970 | ||||||||
\(538\) | 24.2245 | 1.04439 | ||||||||
\(539\) | 3.59107 | 0.154678 | ||||||||
\(540\) | 3.08407 | 0.132717 | ||||||||
\(541\) | 28.8613 | 1.24084 | 0.620422 | − | 0.784268i | \(-0.286961\pi\) | ||||
0.620422 | + | 0.784268i | \(0.286961\pi\) | |||||||
\(542\) | 64.0980 | 2.75324 | ||||||||
\(543\) | −0.629950 | −0.0270337 | ||||||||
\(544\) | 11.7914 | 0.505553 | ||||||||
\(545\) | 4.82562 | 0.206707 | ||||||||
\(546\) | 0.353054 | 0.0151093 | ||||||||
\(547\) | 3.61721 | 0.154661 | 0.0773303 | − | 0.997006i | \(-0.475360\pi\) | ||||
0.0773303 | + | 0.997006i | \(0.475360\pi\) | |||||||
\(548\) | 33.5938 | 1.43506 | ||||||||
\(549\) | −18.0657 | −0.771026 | ||||||||
\(550\) | 38.1733 | 1.62772 | ||||||||
\(551\) | 20.5597 | 0.875872 | ||||||||
\(552\) | 2.53286 | 0.107805 | ||||||||
\(553\) | 4.71689 | 0.200582 | ||||||||
\(554\) | −3.91925 | −0.166513 | ||||||||
\(555\) | −0.872856 | −0.0370507 | ||||||||
\(556\) | 11.8906 | 0.504273 | ||||||||
\(557\) | −18.0993 | −0.766893 | −0.383447 | − | 0.923563i | \(-0.625263\pi\) | ||||
−0.383447 | + | 0.923563i | \(0.625263\pi\) | |||||||
\(558\) | 44.0466 | 1.86464 | ||||||||
\(559\) | 0.608866 | 0.0257523 | ||||||||
\(560\) | −0.0682689 | −0.00288489 | ||||||||
\(561\) | −2.02645 | −0.0855568 | ||||||||
\(562\) | −41.0486 | −1.73153 | ||||||||
\(563\) | −6.55280 | −0.276168 | −0.138084 | − | 0.990421i | \(-0.544094\pi\) | ||||
−0.138084 | + | 0.990421i | \(0.544094\pi\) | |||||||
\(564\) | 1.51628 | 0.0638468 | ||||||||
\(565\) | −8.08295 | −0.340052 | ||||||||
\(566\) | −5.95689 | −0.250387 | ||||||||
\(567\) | 8.31509 | 0.349201 | ||||||||
\(568\) | 10.9993 | 0.461520 | ||||||||
\(569\) | −14.9359 | −0.626145 | −0.313072 | − | 0.949729i | \(-0.601358\pi\) | ||||
−0.313072 | + | 0.949729i | \(0.601358\pi\) | |||||||
\(570\) | 2.02294 | 0.0847314 | ||||||||
\(571\) | −1.88374 | −0.0788320 | −0.0394160 | − | 0.999223i | \(-0.512550\pi\) | ||||
−0.0394160 | + | 0.999223i | \(0.512550\pi\) | |||||||
\(572\) | 6.43547 | 0.269080 | ||||||||
\(573\) | −6.88205 | −0.287502 | ||||||||
\(574\) | 9.23915 | 0.385635 | ||||||||
\(575\) | −15.4183 | −0.642989 | ||||||||
\(576\) | 37.9450 | 1.58104 | ||||||||
\(577\) | −33.2528 | −1.38433 | −0.692166 | − | 0.721739i | \(-0.743343\pi\) | ||||
−0.692166 | + | 0.721739i | \(0.743343\pi\) | |||||||
\(578\) | 29.3332 | 1.22010 | ||||||||
\(579\) | −4.21879 | −0.175327 | ||||||||
\(580\) | 7.07190 | 0.293645 | ||||||||
\(581\) | 0.483915 | 0.0200762 | ||||||||
\(582\) | 7.60086 | 0.315066 | ||||||||
\(583\) | 21.3131 | 0.882697 | ||||||||
\(584\) | −1.77794 | −0.0735717 | ||||||||
\(585\) | −0.955571 | −0.0395080 | ||||||||
\(586\) | −0.523166 | −0.0216118 | ||||||||
\(587\) | −7.81534 | −0.322574 | −0.161287 | − | 0.986908i | \(-0.551564\pi\) | ||||
−0.161287 | + | 0.986908i | \(0.551564\pi\) | |||||||
\(588\) | −0.889282 | −0.0366734 | ||||||||
\(589\) | 36.0682 | 1.48616 | ||||||||
\(590\) | 8.40423 | 0.345997 | ||||||||
\(591\) | 1.90847 | 0.0785038 | ||||||||
\(592\) | −0.627422 | −0.0257869 | ||||||||
\(593\) | 21.2241 | 0.871569 | 0.435784 | − | 0.900051i | \(-0.356471\pi\) | ||||
0.435784 | + | 0.900051i | \(0.356471\pi\) | |||||||
\(594\) | −13.4509 | −0.551897 | ||||||||
\(595\) | 1.19256 | 0.0488903 | ||||||||
\(596\) | 36.5374 | 1.49663 | ||||||||
\(597\) | 5.73341 | 0.234653 | ||||||||
\(598\) | −4.21890 | −0.172524 | ||||||||
\(599\) | 29.5623 | 1.20788 | 0.603942 | − | 0.797028i | \(-0.293596\pi\) | ||||
0.603942 | + | 0.797028i | \(0.293596\pi\) | |||||||
\(600\) | −3.56304 | −0.145461 | ||||||||
\(601\) | 8.62122 | 0.351667 | 0.175834 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175834 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(602\) | −2.48921 | −0.101452 | ||||||||
\(603\) | 19.5637 | 0.796696 | ||||||||
\(604\) | −26.1837 | −1.06540 | ||||||||
\(605\) | 1.10997 | 0.0451265 | ||||||||
\(606\) | −7.78343 | −0.316180 | ||||||||
\(607\) | 30.1109 | 1.22216 | 0.611082 | − | 0.791567i | \(-0.290735\pi\) | ||||
0.611082 | + | 0.791567i | \(0.290735\pi\) | |||||||
\(608\) | 31.6300 | 1.28276 | ||||||||
\(609\) | −1.04252 | −0.0422450 | ||||||||
\(610\) | −8.25900 | −0.334397 | ||||||||
\(611\) | −0.951946 | −0.0385116 | ||||||||
\(612\) | −19.1120 | −0.772555 | ||||||||
\(613\) | 41.1352 | 1.66143 | 0.830717 | − | 0.556696i | \(-0.187931\pi\) | ||||
0.830717 | + | 0.556696i | \(0.187931\pi\) | |||||||
\(614\) | 56.9857 | 2.29976 | ||||||||
\(615\) | 0.656600 | 0.0264767 | ||||||||
\(616\) | −9.91664 | −0.399553 | ||||||||
\(617\) | 23.9281 | 0.963310 | 0.481655 | − | 0.876361i | \(-0.340036\pi\) | ||||
0.481655 | + | 0.876361i | \(0.340036\pi\) | |||||||
\(618\) | −6.07293 | −0.244289 | ||||||||
\(619\) | −18.8193 | −0.756411 | −0.378206 | − | 0.925722i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925722i | \(0.623459\pi\) | |||||||
\(620\) | 12.4063 | 0.498251 | ||||||||
\(621\) | 5.43287 | 0.218014 | ||||||||
\(622\) | −12.7319 | −0.510502 | ||||||||
\(623\) | 7.45128 | 0.298529 | ||||||||
\(624\) | 0.0180355 | 0.000721996 0 | ||||||||
\(625\) | 19.9754 | 0.799016 | ||||||||
\(626\) | −13.5750 | −0.542567 | ||||||||
\(627\) | −5.43586 | −0.217087 | ||||||||
\(628\) | −28.6660 | −1.14390 | ||||||||
\(629\) | 10.9602 | 0.437011 | ||||||||
\(630\) | 3.90663 | 0.155644 | ||||||||
\(631\) | 28.5364 | 1.13602 | 0.568008 | − | 0.823023i | \(-0.307714\pi\) | ||||
0.568008 | + | 0.823023i | \(0.307714\pi\) | |||||||
\(632\) | −13.0256 | −0.518129 | ||||||||
\(633\) | −0.149769 | −0.00595278 | ||||||||
\(634\) | 9.39573 | 0.373152 | ||||||||
\(635\) | −7.45288 | −0.295759 | ||||||||
\(636\) | −5.27791 | −0.209283 | ||||||||
\(637\) | 0.558307 | 0.0221209 | ||||||||
\(638\) | −30.8435 | −1.22111 | ||||||||
\(639\) | 11.6436 | 0.460615 | ||||||||
\(640\) | 10.5681 | 0.417741 | ||||||||
\(641\) | −19.2987 | −0.762254 | −0.381127 | − | 0.924523i | \(-0.624464\pi\) | ||||
−0.381127 | + | 0.924523i | \(0.624464\pi\) | |||||||
\(642\) | 4.95020 | 0.195369 | ||||||||
\(643\) | 26.2181 | 1.03394 | 0.516970 | − | 0.856004i | \(-0.327060\pi\) | ||||
0.516970 | + | 0.856004i | \(0.327060\pi\) | |||||||
\(644\) | 10.6267 | 0.418749 | ||||||||
\(645\) | −0.176901 | −0.00696546 | ||||||||
\(646\) | −25.4014 | −0.999404 | ||||||||
\(647\) | −9.26466 | −0.364231 | −0.182116 | − | 0.983277i | \(-0.558295\pi\) | ||||
−0.182116 | + | 0.983277i | \(0.558295\pi\) | |||||||
\(648\) | −22.9619 | −0.902028 | ||||||||
\(649\) | −22.5831 | −0.886465 | ||||||||
\(650\) | 5.93485 | 0.232784 | ||||||||
\(651\) | −1.82891 | −0.0716805 | ||||||||
\(652\) | −22.3357 | −0.874735 | ||||||||
\(653\) | 30.7628 | 1.20384 | 0.601922 | − | 0.798555i | \(-0.294402\pi\) | ||||
0.601922 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(654\) | 5.21190 | 0.203801 | ||||||||
\(655\) | 5.73115 | 0.223934 | ||||||||
\(656\) | 0.471974 | 0.0184275 | ||||||||
\(657\) | −1.88209 | −0.0734275 | ||||||||
\(658\) | 3.89181 | 0.151719 | ||||||||
\(659\) | 41.8557 | 1.63047 | 0.815234 | − | 0.579132i | \(-0.196609\pi\) | ||||
0.815234 | + | 0.579132i | \(0.196609\pi\) | |||||||
\(660\) | −1.86977 | −0.0727807 | ||||||||
\(661\) | −44.7404 | −1.74020 | −0.870099 | − | 0.492877i | \(-0.835945\pi\) | ||||
−0.870099 | + | 0.492877i | \(0.835945\pi\) | |||||||
\(662\) | 53.6545 | 2.08534 | ||||||||
\(663\) | −0.315054 | −0.0122357 | ||||||||
\(664\) | −1.33632 | −0.0518592 | ||||||||
\(665\) | 3.19900 | 0.124052 | ||||||||
\(666\) | 35.9037 | 1.39124 | ||||||||
\(667\) | 12.4578 | 0.482368 | ||||||||
\(668\) | 64.5187 | 2.49631 | ||||||||
\(669\) | −1.06347 | −0.0411162 | ||||||||
\(670\) | 8.94382 | 0.345530 | ||||||||
\(671\) | 22.1929 | 0.856747 | ||||||||
\(672\) | −1.60386 | −0.0618702 | ||||||||
\(673\) | 28.1938 | 1.08679 | 0.543395 | − | 0.839477i | \(-0.317139\pi\) | ||||
0.543395 | + | 0.839477i | \(0.317139\pi\) | |||||||
\(674\) | 57.4719 | 2.21373 | ||||||||
\(675\) | −7.64258 | −0.294163 | ||||||||
\(676\) | −40.7274 | −1.56644 | ||||||||
\(677\) | −13.2041 | −0.507474 | −0.253737 | − | 0.967273i | \(-0.581660\pi\) | ||||
−0.253737 | + | 0.967273i | \(0.581660\pi\) | |||||||
\(678\) | −8.72998 | −0.335273 | ||||||||
\(679\) | 12.0197 | 0.461275 | ||||||||
\(680\) | −3.29323 | −0.126290 | ||||||||
\(681\) | 6.19210 | 0.237282 | ||||||||
\(682\) | −54.1092 | −2.07195 | ||||||||
\(683\) | −13.9598 | −0.534157 | −0.267079 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267079 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(684\) | −51.2669 | −1.96024 | ||||||||
\(685\) | 6.12775 | 0.234129 | ||||||||
\(686\) | −2.28251 | −0.0871466 | ||||||||
\(687\) | 1.35857 | 0.0518325 | ||||||||
\(688\) | −0.127159 | −0.00484789 | ||||||||
\(689\) | 3.31356 | 0.126237 | ||||||||
\(690\) | 1.22576 | 0.0466640 | ||||||||
\(691\) | 45.5447 | 1.73260 | 0.866301 | − | 0.499522i | \(-0.166491\pi\) | ||||
0.866301 | + | 0.499522i | \(0.166491\pi\) | |||||||
\(692\) | 58.3449 | 2.21794 | ||||||||
\(693\) | −10.4976 | −0.398770 | ||||||||
\(694\) | −28.8311 | −1.09441 | ||||||||
\(695\) | 2.16893 | 0.0822721 | ||||||||
\(696\) | 2.87889 | 0.109124 | ||||||||
\(697\) | −8.24473 | −0.312291 | ||||||||
\(698\) | −27.8898 | −1.05564 | ||||||||
\(699\) | −3.22571 | −0.122007 | ||||||||
\(700\) | −14.9489 | −0.565013 | ||||||||
\(701\) | −33.3591 | −1.25996 | −0.629979 | − | 0.776612i | \(-0.716936\pi\) | ||||
−0.629979 | + | 0.776612i | \(0.716936\pi\) | |||||||
\(702\) | −2.09123 | −0.0789282 | ||||||||
\(703\) | 29.4002 | 1.10885 | ||||||||
\(704\) | −46.6136 | −1.75682 | ||||||||
\(705\) | 0.276580 | 0.0104166 | ||||||||
\(706\) | −44.4209 | −1.67180 | ||||||||
\(707\) | −12.3084 | −0.462906 | ||||||||
\(708\) | 5.59243 | 0.210176 | ||||||||
\(709\) | −11.0538 | −0.415133 | −0.207567 | − | 0.978221i | \(-0.566554\pi\) | ||||
−0.207567 | + | 0.978221i | \(0.566554\pi\) | |||||||
\(710\) | 5.32305 | 0.199771 | ||||||||
\(711\) | −13.7886 | −0.517113 | ||||||||
\(712\) | −20.5765 | −0.771137 | ||||||||
\(713\) | 21.8549 | 0.818473 | ||||||||
\(714\) | 1.28803 | 0.0482032 | ||||||||
\(715\) | 1.17387 | 0.0439004 | ||||||||
\(716\) | −35.9686 | −1.34421 | ||||||||
\(717\) | −4.80503 | −0.179447 | ||||||||
\(718\) | −36.1767 | −1.35010 | ||||||||
\(719\) | −30.1215 | −1.12334 | −0.561671 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561671 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(720\) | 0.199567 | 0.00743741 | ||||||||
\(721\) | −9.60351 | −0.357653 | ||||||||
\(722\) | −24.7704 | −0.921859 | ||||||||
\(723\) | 5.40261 | 0.200925 | ||||||||
\(724\) | 7.29850 | 0.271247 | ||||||||
\(725\) | −17.5247 | −0.650853 | ||||||||
\(726\) | 1.19882 | 0.0444923 | ||||||||
\(727\) | 13.8529 | 0.513774 | 0.256887 | − | 0.966441i | \(-0.417303\pi\) | ||||
0.256887 | + | 0.966441i | \(0.417303\pi\) | |||||||
\(728\) | −1.54175 | −0.0571410 | ||||||||
\(729\) | −22.9431 | −0.849744 | ||||||||
\(730\) | −0.860426 | −0.0318458 | ||||||||
\(731\) | 2.22129 | 0.0821573 | ||||||||
\(732\) | −5.49578 | −0.203130 | ||||||||
\(733\) | −6.44859 | −0.238184 | −0.119092 | − | 0.992883i | \(-0.537998\pi\) | ||||
−0.119092 | + | 0.992883i | \(0.537998\pi\) | |||||||
\(734\) | −16.5658 | −0.611456 | ||||||||
\(735\) | −0.162211 | −0.00598325 | ||||||||
\(736\) | 19.1657 | 0.706455 | ||||||||
\(737\) | −24.0331 | −0.885270 | ||||||||
\(738\) | −27.0083 | −0.994189 | ||||||||
\(739\) | 6.67572 | 0.245570 | 0.122785 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122785 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(740\) | 10.1128 | 0.371753 | ||||||||
\(741\) | −0.845119 | −0.0310462 | ||||||||
\(742\) | −13.5467 | −0.497316 | ||||||||
\(743\) | 32.6741 | 1.19870 | 0.599349 | − | 0.800488i | \(-0.295426\pi\) | ||||
0.599349 | + | 0.800488i | \(0.295426\pi\) | |||||||
\(744\) | 5.05047 | 0.185159 | ||||||||
\(745\) | 6.66467 | 0.244174 | ||||||||
\(746\) | 34.1646 | 1.25085 | ||||||||
\(747\) | −1.41460 | −0.0517576 | ||||||||
\(748\) | 23.4781 | 0.858446 | ||||||||
\(749\) | 7.82807 | 0.286031 | ||||||||
\(750\) | −3.57556 | −0.130561 | ||||||||
\(751\) | 20.1994 | 0.737088 | 0.368544 | − | 0.929610i | \(-0.379856\pi\) | ||||
0.368544 | + | 0.929610i | \(0.379856\pi\) | |||||||
\(752\) | 0.198810 | 0.00724984 | ||||||||
\(753\) | 4.04504 | 0.147409 | ||||||||
\(754\) | −4.79527 | −0.174633 | ||||||||
\(755\) | −4.77610 | −0.173820 | ||||||||
\(756\) | 5.26744 | 0.191575 | ||||||||
\(757\) | 17.5831 | 0.639068 | 0.319534 | − | 0.947575i | \(-0.396474\pi\) | ||||
0.319534 | + | 0.947575i | \(0.396474\pi\) | |||||||
\(758\) | 79.3452 | 2.88195 | ||||||||
\(759\) | −3.29377 | −0.119556 | ||||||||
\(760\) | −8.83394 | −0.320441 | ||||||||
\(761\) | −3.10123 | −0.112419 | −0.0562097 | − | 0.998419i | \(-0.517902\pi\) | ||||
−0.0562097 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(762\) | −8.04947 | −0.291602 | ||||||||
\(763\) | 8.24191 | 0.298377 | ||||||||
\(764\) | 79.7343 | 2.88469 | ||||||||
\(765\) | −3.48615 | −0.126042 | ||||||||
\(766\) | 20.5490 | 0.742466 | ||||||||
\(767\) | −3.51102 | −0.126776 | ||||||||
\(768\) | 4.22163 | 0.152335 | ||||||||
\(769\) | −17.2489 | −0.622011 | −0.311005 | − | 0.950408i | \(-0.600666\pi\) | ||||
−0.311005 | + | 0.950408i | \(0.600666\pi\) | |||||||
\(770\) | −4.79911 | −0.172948 | ||||||||
\(771\) | 2.75356 | 0.0991669 | ||||||||
\(772\) | 48.8783 | 1.75917 | ||||||||
\(773\) | 3.26386 | 0.117393 | 0.0586964 | − | 0.998276i | \(-0.481306\pi\) | ||||
0.0586964 | + | 0.998276i | \(0.481306\pi\) | |||||||
\(774\) | 7.27656 | 0.261550 | ||||||||
\(775\) | −30.7439 | −1.10436 | ||||||||
\(776\) | −33.1921 | −1.19153 | ||||||||
\(777\) | −1.49079 | −0.0534819 | ||||||||
\(778\) | −57.7692 | −2.07112 | ||||||||
\(779\) | −22.1161 | −0.792392 | ||||||||
\(780\) | −0.290695 | −0.0104086 | ||||||||
\(781\) | −14.3037 | −0.511825 | ||||||||
\(782\) | −15.3915 | −0.550401 | ||||||||
\(783\) | 6.17509 | 0.220680 | ||||||||
\(784\) | −0.116600 | −0.00416428 | ||||||||
\(785\) | −5.22888 | −0.186627 | ||||||||
\(786\) | 6.18992 | 0.220787 | ||||||||
\(787\) | 40.9928 | 1.46123 | 0.730617 | − | 0.682788i | \(-0.239233\pi\) | ||||
0.730617 | + | 0.682788i | \(0.239233\pi\) | |||||||
\(788\) | −22.1112 | −0.787678 | ||||||||
\(789\) | −3.10406 | −0.110508 | ||||||||
\(790\) | −6.30366 | −0.224274 | ||||||||
\(791\) | −13.8053 | −0.490859 | ||||||||
\(792\) | 28.9887 | 1.03007 | ||||||||
\(793\) | 3.45035 | 0.122526 | ||||||||
\(794\) | −79.4306 | −2.81889 | ||||||||
\(795\) | −0.962727 | −0.0341444 | ||||||||
\(796\) | −66.4264 | −2.35442 | ||||||||
\(797\) | 40.3799 | 1.43033 | 0.715165 | − | 0.698955i | \(-0.246351\pi\) | ||||
0.715165 | + | 0.698955i | \(0.246351\pi\) | |||||||
\(798\) | 3.45507 | 0.122308 | ||||||||
\(799\) | −3.47293 | −0.122863 | ||||||||
\(800\) | −26.9609 | −0.953211 | ||||||||
\(801\) | −21.7819 | −0.769626 | ||||||||
\(802\) | −9.99331 | −0.352876 | ||||||||
\(803\) | 2.31206 | 0.0815910 | ||||||||
\(804\) | 5.95149 | 0.209893 | ||||||||
\(805\) | 1.93838 | 0.0683189 | ||||||||
\(806\) | −8.41242 | −0.296315 | ||||||||
\(807\) | 2.94034 | 0.103505 | ||||||||
\(808\) | 33.9894 | 1.19574 | ||||||||
\(809\) | 7.01714 | 0.246710 | 0.123355 | − | 0.992363i | \(-0.460635\pi\) | ||||
0.123355 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(810\) | −11.1123 | −0.390447 | ||||||||
\(811\) | −28.5862 | −1.00380 | −0.501899 | − | 0.864926i | \(-0.667365\pi\) | ||||
−0.501899 | + | 0.864926i | \(0.667365\pi\) | |||||||
\(812\) | 12.0785 | 0.423870 | ||||||||
\(813\) | 7.78015 | 0.272862 | ||||||||
\(814\) | −44.1060 | −1.54591 | ||||||||
\(815\) | −4.07419 | −0.142713 | ||||||||
\(816\) | 0.0657976 | 0.00230338 | ||||||||
\(817\) | 5.95851 | 0.208462 | ||||||||
\(818\) | −11.9728 | −0.418618 | ||||||||
\(819\) | −1.63207 | −0.0570291 | ||||||||
\(820\) | −7.60726 | −0.265657 | ||||||||
\(821\) | −10.2753 | −0.358611 | −0.179305 | − | 0.983793i | \(-0.557385\pi\) | ||||
−0.179305 | + | 0.983793i | \(0.557385\pi\) | |||||||
\(822\) | 6.61827 | 0.230839 | ||||||||
\(823\) | 50.9387 | 1.77561 | 0.887806 | − | 0.460219i | \(-0.152229\pi\) | ||||
0.887806 | + | 0.460219i | \(0.152229\pi\) | |||||||
\(824\) | 26.5198 | 0.923862 | ||||||||
\(825\) | 4.63344 | 0.161316 | ||||||||
\(826\) | 14.3540 | 0.499439 | ||||||||
\(827\) | 7.44497 | 0.258887 | 0.129443 | − | 0.991587i | \(-0.458681\pi\) | ||||
0.129443 | + | 0.991587i | \(0.458681\pi\) | |||||||
\(828\) | −31.0643 | −1.07956 | ||||||||
\(829\) | −38.8390 | −1.34893 | −0.674467 | − | 0.738305i | \(-0.735627\pi\) | ||||
−0.674467 | + | 0.738305i | \(0.735627\pi\) | |||||||
\(830\) | −0.646705 | −0.0224475 | ||||||||
\(831\) | −0.475715 | −0.0165024 | ||||||||
\(832\) | −7.24707 | −0.251247 | ||||||||
\(833\) | 2.03684 | 0.0705722 | ||||||||
\(834\) | 2.34255 | 0.0811157 | ||||||||
\(835\) | 11.7687 | 0.407271 | ||||||||
\(836\) | 62.9790 | 2.17818 | ||||||||
\(837\) | 10.8331 | 0.374445 | ||||||||
\(838\) | −4.13981 | −0.143007 | ||||||||
\(839\) | 8.88145 | 0.306622 | 0.153311 | − | 0.988178i | \(-0.451006\pi\) | ||||
0.153311 | + | 0.988178i | \(0.451006\pi\) | |||||||
\(840\) | 0.447942 | 0.0154555 | ||||||||
\(841\) | −14.8403 | −0.511733 | ||||||||
\(842\) | 28.1048 | 0.968554 | ||||||||
\(843\) | −4.98244 | −0.171604 | ||||||||
\(844\) | 1.73520 | 0.0597281 | ||||||||
\(845\) | −7.42896 | −0.255564 | ||||||||
\(846\) | −11.3767 | −0.391139 | ||||||||
\(847\) | 1.89577 | 0.0651393 | ||||||||
\(848\) | −0.692023 | −0.0237642 | ||||||||
\(849\) | −0.723041 | −0.0248147 | ||||||||
\(850\) | 21.6517 | 0.742649 | ||||||||
\(851\) | 17.8146 | 0.610675 | ||||||||
\(852\) | 3.54212 | 0.121351 | ||||||||
\(853\) | −23.7391 | −0.812813 | −0.406406 | − | 0.913692i | \(-0.633218\pi\) | ||||
−0.406406 | + | 0.913692i | \(0.633218\pi\) | |||||||
\(854\) | −14.1060 | −0.482696 | ||||||||
\(855\) | −9.35145 | −0.319813 | ||||||||
\(856\) | −21.6170 | −0.738854 | ||||||||
\(857\) | 37.9001 | 1.29464 | 0.647321 | − | 0.762218i | \(-0.275889\pi\) | ||||
0.647321 | + | 0.762218i | \(0.275889\pi\) | |||||||
\(858\) | 1.26784 | 0.0432834 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 2.04954 | 0.0698889 | ||||||||
\(861\) | 1.12144 | 0.0382186 | ||||||||
\(862\) | 45.0773 | 1.53534 | ||||||||
\(863\) | −30.0303 | −1.02224 | −0.511121 | − | 0.859509i | \(-0.670770\pi\) | ||||
−0.511121 | + | 0.859509i | \(0.670770\pi\) | |||||||
\(864\) | 9.50004 | 0.323198 | ||||||||
\(865\) | 10.6425 | 0.361856 | ||||||||
\(866\) | −26.5677 | −0.902808 | ||||||||
\(867\) | 3.56043 | 0.120919 | ||||||||
\(868\) | 21.1894 | 0.719216 | ||||||||
\(869\) | 16.9387 | 0.574605 | ||||||||
\(870\) | 1.39322 | 0.0472347 | ||||||||
\(871\) | −3.73645 | −0.126605 | ||||||||
\(872\) | −22.7598 | −0.770744 | ||||||||
\(873\) | −35.1366 | −1.18919 | ||||||||
\(874\) | −41.2871 | −1.39656 | ||||||||
\(875\) | −5.65426 | −0.191149 | ||||||||
\(876\) | −0.572553 | −0.0193448 | ||||||||
\(877\) | 42.6373 | 1.43976 | 0.719880 | − | 0.694099i | \(-0.244197\pi\) | ||||
0.719880 | + | 0.694099i | \(0.244197\pi\) | |||||||
\(878\) | −57.9691 | −1.95636 | ||||||||
\(879\) | −0.0635014 | −0.00214185 | ||||||||
\(880\) | −0.245158 | −0.00826428 | ||||||||
\(881\) | 5.82844 | 0.196365 | 0.0981826 | − | 0.995168i | \(-0.468697\pi\) | ||||
0.0981826 | + | 0.995168i | \(0.468697\pi\) | |||||||
\(882\) | 6.67233 | 0.224669 | ||||||||
\(883\) | 30.1977 | 1.01623 | 0.508117 | − | 0.861288i | \(-0.330342\pi\) | ||||
0.508117 | + | 0.861288i | \(0.330342\pi\) | |||||||
\(884\) | 3.65017 | 0.122768 | ||||||||
\(885\) | 1.02010 | 0.0342902 | ||||||||
\(886\) | −56.4517 | −1.89653 | ||||||||
\(887\) | 56.7148 | 1.90430 | 0.952148 | − | 0.305638i | \(-0.0988696\pi\) | ||||
0.952148 | + | 0.305638i | \(0.0988696\pi\) | |||||||
\(888\) | 4.11679 | 0.138150 | ||||||||
\(889\) | −12.7291 | −0.426922 | ||||||||
\(890\) | −9.95791 | −0.333790 | ||||||||
\(891\) | 29.8600 | 1.00035 | ||||||||
\(892\) | 12.3212 | 0.412545 | ||||||||
\(893\) | −9.31597 | −0.311747 | ||||||||
\(894\) | 7.19816 | 0.240743 | ||||||||
\(895\) | −6.56093 | −0.219308 | ||||||||
\(896\) | 18.0498 | 0.603000 | ||||||||
\(897\) | −0.512086 | −0.0170980 | ||||||||
\(898\) | 17.6297 | 0.588309 | ||||||||
\(899\) | 24.8407 | 0.828482 | ||||||||
\(900\) | 43.6991 | 1.45664 | ||||||||
\(901\) | 12.0887 | 0.402732 | ||||||||
\(902\) | 33.1784 | 1.10472 | ||||||||
\(903\) | −0.302138 | −0.0100545 | ||||||||
\(904\) | 38.1229 | 1.26795 | ||||||||
\(905\) | 1.33130 | 0.0442538 | ||||||||
\(906\) | −5.15842 | −0.171377 | ||||||||
\(907\) | −11.4679 | −0.380786 | −0.190393 | − | 0.981708i | \(-0.560976\pi\) | ||||
−0.190393 | + | 0.981708i | \(0.560976\pi\) | |||||||
\(908\) | −71.7407 | −2.38080 | ||||||||
\(909\) | 35.9806 | 1.19340 | ||||||||
\(910\) | −0.746123 | −0.0247337 | ||||||||
\(911\) | 22.9295 | 0.759688 | 0.379844 | − | 0.925051i | \(-0.375978\pi\) | ||||
0.379844 | + | 0.925051i | \(0.375978\pi\) | |||||||
\(912\) | 0.176499 | 0.00584447 | ||||||||
\(913\) | 1.73777 | 0.0575118 | ||||||||
\(914\) | −24.0140 | −0.794313 | ||||||||
\(915\) | −1.00247 | −0.0331406 | ||||||||
\(916\) | −15.7401 | −0.520068 | ||||||||
\(917\) | 9.78851 | 0.323245 | ||||||||
\(918\) | −7.62929 | −0.251804 | ||||||||
\(919\) | 15.7261 | 0.518756 | 0.259378 | − | 0.965776i | \(-0.416482\pi\) | ||||
0.259378 | + | 0.965776i | \(0.416482\pi\) | |||||||
\(920\) | −5.35278 | −0.176476 | ||||||||
\(921\) | 6.91687 | 0.227919 | ||||||||
\(922\) | 7.32756 | 0.241320 | ||||||||
\(923\) | −2.22380 | −0.0731974 | ||||||||
\(924\) | −3.19347 | −0.105058 | ||||||||
\(925\) | −25.0603 | −0.823976 | ||||||||
\(926\) | 27.9618 | 0.918883 | ||||||||
\(927\) | 28.0734 | 0.922051 | ||||||||
\(928\) | 21.7840 | 0.715095 | ||||||||
\(929\) | −4.00588 | −0.131429 | −0.0657144 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657144 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(930\) | 2.44415 | 0.0801470 | ||||||||
\(931\) | 5.46372 | 0.179066 | ||||||||
\(932\) | 37.3725 | 1.22418 | ||||||||
\(933\) | −1.54538 | −0.0505936 | ||||||||
\(934\) | 21.5731 | 0.705893 | ||||||||
\(935\) | 4.28257 | 0.140055 | ||||||||
\(936\) | 4.50691 | 0.147313 | ||||||||
\(937\) | 5.37073 | 0.175454 | 0.0877271 | − | 0.996145i | \(-0.472040\pi\) | ||||
0.0877271 | + | 0.996145i | \(0.472040\pi\) | |||||||
\(938\) | 15.2756 | 0.498766 | ||||||||
\(939\) | −1.64772 | −0.0537714 | ||||||||
\(940\) | −3.20441 | −0.104516 | ||||||||
\(941\) | 8.96604 | 0.292285 | 0.146142 | − | 0.989264i | \(-0.453314\pi\) | ||||
0.146142 | + | 0.989264i | \(0.453314\pi\) | |||||||
\(942\) | −5.64745 | −0.184004 | ||||||||
\(943\) | −13.4009 | −0.436393 | ||||||||
\(944\) | 0.733261 | 0.0238656 | ||||||||
\(945\) | 0.960817 | 0.0312554 | ||||||||
\(946\) | −8.93891 | −0.290629 | ||||||||
\(947\) | −47.6901 | −1.54972 | −0.774861 | − | 0.632132i | \(-0.782180\pi\) | ||||
−0.774861 | + | 0.632132i | \(0.782180\pi\) | |||||||
\(948\) | −4.19464 | −0.136236 | ||||||||
\(949\) | 0.359459 | 0.0116685 | ||||||||
\(950\) | 58.0798 | 1.88436 | ||||||||
\(951\) | 1.14044 | 0.0369814 | ||||||||
\(952\) | −5.62467 | −0.182297 | ||||||||
\(953\) | −15.9135 | −0.515488 | −0.257744 | − | 0.966213i | \(-0.582979\pi\) | ||||
−0.257744 | + | 0.966213i | \(0.582979\pi\) | |||||||
\(954\) | 39.6004 | 1.28211 | ||||||||
\(955\) | 14.5441 | 0.470636 | ||||||||
\(956\) | 55.6703 | 1.80051 | ||||||||
\(957\) | −3.74375 | −0.121018 | ||||||||
\(958\) | 5.29567 | 0.171095 | ||||||||
\(959\) | 10.4659 | 0.337961 | ||||||||
\(960\) | 2.10557 | 0.0679571 | ||||||||
\(961\) | 12.5784 | 0.405753 | ||||||||
\(962\) | −6.85720 | −0.221085 | ||||||||
\(963\) | −22.8834 | −0.737406 | ||||||||
\(964\) | −62.5938 | −2.01601 | ||||||||
\(965\) | 8.91574 | 0.287008 | ||||||||
\(966\) | 2.09354 | 0.0673586 | ||||||||
\(967\) | −55.6860 | −1.79074 | −0.895371 | − | 0.445322i | \(-0.853089\pi\) | ||||
−0.895371 | + | 0.445322i | \(0.853089\pi\) | |||||||
\(968\) | −5.23511 | −0.168263 | ||||||||
\(969\) | −3.08320 | −0.0990465 | ||||||||
\(970\) | −16.0632 | −0.515758 | ||||||||
\(971\) | 50.7158 | 1.62755 | 0.813774 | − | 0.581181i | \(-0.197409\pi\) | ||||
0.813774 | + | 0.581181i | \(0.197409\pi\) | |||||||
\(972\) | −23.1968 | −0.744037 | ||||||||
\(973\) | 3.70442 | 0.118758 | ||||||||
\(974\) | −41.5410 | −1.33106 | ||||||||
\(975\) | 0.720366 | 0.0230702 | ||||||||
\(976\) | −0.720590 | −0.0230655 | ||||||||
\(977\) | −53.1145 | −1.69928 | −0.849641 | − | 0.527362i | \(-0.823181\pi\) | ||||
−0.849641 | + | 0.527362i | \(0.823181\pi\) | |||||||
\(978\) | −4.40033 | −0.140707 | ||||||||
\(979\) | 26.7581 | 0.855191 | ||||||||
\(980\) | 1.87935 | 0.0600338 | ||||||||
\(981\) | −24.0931 | −0.769234 | ||||||||
\(982\) | −46.3730 | −1.47982 | ||||||||
\(983\) | 47.7346 | 1.52250 | 0.761248 | − | 0.648461i | \(-0.224587\pi\) | ||||
0.761248 | + | 0.648461i | \(0.224587\pi\) | |||||||
\(984\) | −3.09682 | −0.0987232 | ||||||||
\(985\) | −4.03323 | −0.128510 | ||||||||
\(986\) | −17.4943 | −0.557132 | ||||||||
\(987\) | 0.472384 | 0.0150362 | ||||||||
\(988\) | 9.79141 | 0.311506 | ||||||||
\(989\) | 3.61046 | 0.114806 | ||||||||
\(990\) | 14.0290 | 0.445870 | ||||||||
\(991\) | −14.7354 | −0.468086 | −0.234043 | − | 0.972226i | \(-0.575196\pi\) | ||||
−0.234043 | + | 0.972226i | \(0.575196\pi\) | |||||||
\(992\) | 38.2160 | 1.21336 | ||||||||
\(993\) | 6.51253 | 0.206669 | ||||||||
\(994\) | 9.09151 | 0.288365 | ||||||||
\(995\) | −12.1166 | −0.384123 | ||||||||
\(996\) | −0.430337 | −0.0136357 | ||||||||
\(997\) | −16.4851 | −0.522088 | −0.261044 | − | 0.965327i | \(-0.584067\pi\) | ||||
−0.261044 | + | 0.965327i | \(0.584067\pi\) | |||||||
\(998\) | 31.2606 | 0.989536 | ||||||||
\(999\) | 8.83033 | 0.279379 |
(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 | 6013.2.a.e.1.11 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.11 | ✓ | 109 | 1.1 | even | 1 | trivial |