Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1557568940\) |
Analytic rank: | \(0\) |
Dimension: | \(174\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66961 | −1.88770 | −0.943849 | − | 0.330378i | \(-0.892824\pi\) | ||||
−0.943849 | + | 0.330378i | \(0.892824\pi\) | |||||||
\(3\) | −0.492916 | −0.284585 | −0.142293 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142293 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(4\) | 5.12680 | 2.56340 | ||||||||
\(5\) | 2.37281 | 1.06115 | 0.530576 | − | 0.847637i | \(-0.321976\pi\) | ||||
0.530576 | + | 0.847637i | \(0.321976\pi\) | |||||||
\(6\) | 1.31589 | 0.537211 | ||||||||
\(7\) | 1.32431 | 0.500543 | 0.250271 | − | 0.968176i | \(-0.419480\pi\) | ||||
0.250271 | + | 0.968176i | \(0.419480\pi\) | |||||||
\(8\) | −8.34733 | −2.95123 | ||||||||
\(9\) | −2.75703 | −0.919011 | ||||||||
\(10\) | −6.33447 | −2.00314 | ||||||||
\(11\) | 0.0220541 | 0.00664956 | 0.00332478 | − | 0.999994i | \(-0.498942\pi\) | ||||
0.00332478 | + | 0.999994i | \(0.498942\pi\) | |||||||
\(12\) | −2.52708 | −0.729506 | ||||||||
\(13\) | −4.40501 | −1.22173 | −0.610865 | − | 0.791735i | \(-0.709178\pi\) | ||||
−0.610865 | + | 0.791735i | \(0.709178\pi\) | |||||||
\(14\) | −3.53539 | −0.944873 | ||||||||
\(15\) | −1.16960 | −0.301988 | ||||||||
\(16\) | 12.0305 | 3.00762 | ||||||||
\(17\) | 1.88399 | 0.456936 | 0.228468 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228468 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(18\) | 7.36020 | 1.73482 | ||||||||
\(19\) | 2.05105 | 0.470543 | 0.235271 | − | 0.971930i | \(-0.424402\pi\) | ||||
0.235271 | + | 0.971930i | \(0.424402\pi\) | |||||||
\(20\) | 12.1649 | 2.72016 | ||||||||
\(21\) | −0.652774 | −0.142447 | ||||||||
\(22\) | −0.0588757 | −0.0125524 | ||||||||
\(23\) | 3.94541 | 0.822674 | 0.411337 | − | 0.911483i | \(-0.365062\pi\) | ||||
0.411337 | + | 0.911483i | \(0.365062\pi\) | |||||||
\(24\) | 4.11453 | 0.839876 | ||||||||
\(25\) | 0.630226 | 0.126045 | ||||||||
\(26\) | 11.7596 | 2.30626 | ||||||||
\(27\) | 2.83773 | 0.546122 | ||||||||
\(28\) | 6.78948 | 1.28309 | ||||||||
\(29\) | −8.40013 | −1.55986 | −0.779932 | − | 0.625864i | \(-0.784747\pi\) | ||||
−0.779932 | + | 0.625864i | \(0.784747\pi\) | |||||||
\(30\) | 3.12236 | 0.570063 | ||||||||
\(31\) | −5.95042 | −1.06873 | −0.534364 | − | 0.845255i | \(-0.679449\pi\) | ||||
−0.534364 | + | 0.845255i | \(0.679449\pi\) | |||||||
\(32\) | −15.4220 | −2.72626 | ||||||||
\(33\) | −0.0108708 | −0.00189237 | ||||||||
\(34\) | −5.02952 | −0.862556 | ||||||||
\(35\) | 3.14234 | 0.531152 | ||||||||
\(36\) | −14.1348 | −2.35579 | ||||||||
\(37\) | −6.74280 | −1.10851 | −0.554255 | − | 0.832347i | \(-0.686997\pi\) | ||||
−0.554255 | + | 0.832347i | \(0.686997\pi\) | |||||||
\(38\) | −5.47550 | −0.888243 | ||||||||
\(39\) | 2.17130 | 0.347686 | ||||||||
\(40\) | −19.8066 | −3.13170 | ||||||||
\(41\) | −1.19570 | −0.186738 | −0.0933688 | − | 0.995632i | \(-0.529764\pi\) | ||||
−0.0933688 | + | 0.995632i | \(0.529764\pi\) | |||||||
\(42\) | 1.74265 | 0.268897 | ||||||||
\(43\) | 9.27473 | 1.41438 | 0.707192 | − | 0.707022i | \(-0.249962\pi\) | ||||
0.707192 | + | 0.707022i | \(0.249962\pi\) | |||||||
\(44\) | 0.113067 | 0.0170455 | ||||||||
\(45\) | −6.54192 | −0.975211 | ||||||||
\(46\) | −10.5327 | −1.55296 | ||||||||
\(47\) | 3.38827 | 0.494230 | 0.247115 | − | 0.968986i | \(-0.420517\pi\) | ||||
0.247115 | + | 0.968986i | \(0.420517\pi\) | |||||||
\(48\) | −5.93002 | −0.855925 | ||||||||
\(49\) | −5.24620 | −0.749457 | ||||||||
\(50\) | −1.68246 | −0.237935 | ||||||||
\(51\) | −0.928651 | −0.130037 | ||||||||
\(52\) | −22.5836 | −3.13178 | ||||||||
\(53\) | −8.44209 | −1.15961 | −0.579805 | − | 0.814755i | \(-0.696871\pi\) | ||||
−0.579805 | + | 0.814755i | \(0.696871\pi\) | |||||||
\(54\) | −7.57564 | −1.03091 | ||||||||
\(55\) | 0.0523301 | 0.00705620 | ||||||||
\(56\) | −11.0545 | −1.47722 | ||||||||
\(57\) | −1.01100 | −0.133910 | ||||||||
\(58\) | 22.4250 | 2.94455 | ||||||||
\(59\) | 8.17842 | 1.06474 | 0.532370 | − | 0.846512i | \(-0.321302\pi\) | ||||
0.532370 | + | 0.846512i | \(0.321302\pi\) | |||||||
\(60\) | −5.99629 | −0.774117 | ||||||||
\(61\) | 7.87505 | 1.00830 | 0.504148 | − | 0.863617i | \(-0.331806\pi\) | ||||
0.504148 | + | 0.863617i | \(0.331806\pi\) | |||||||
\(62\) | 15.8853 | 2.01743 | ||||||||
\(63\) | −3.65117 | −0.460004 | ||||||||
\(64\) | 17.1098 | 2.13872 | ||||||||
\(65\) | −10.4523 | −1.29644 | ||||||||
\(66\) | 0.0290208 | 0.00357221 | ||||||||
\(67\) | 11.0828 | 1.35398 | 0.676992 | − | 0.735990i | \(-0.263283\pi\) | ||||
0.676992 | + | 0.735990i | \(0.263283\pi\) | |||||||
\(68\) | 9.65887 | 1.17131 | ||||||||
\(69\) | −1.94475 | −0.234121 | ||||||||
\(70\) | −8.38881 | −1.00265 | ||||||||
\(71\) | 12.4430 | 1.47671 | 0.738355 | − | 0.674413i | \(-0.235603\pi\) | ||||
0.738355 | + | 0.674413i | \(0.235603\pi\) | |||||||
\(72\) | 23.0139 | 2.71221 | ||||||||
\(73\) | 8.53257 | 0.998661 | 0.499331 | − | 0.866412i | \(-0.333579\pi\) | ||||
0.499331 | + | 0.866412i | \(0.333579\pi\) | |||||||
\(74\) | 18.0006 | 2.09253 | ||||||||
\(75\) | −0.310649 | −0.0358706 | ||||||||
\(76\) | 10.5153 | 1.20619 | ||||||||
\(77\) | 0.0292065 | 0.00332839 | ||||||||
\(78\) | −5.79652 | −0.656326 | ||||||||
\(79\) | 2.13340 | 0.240027 | 0.120013 | − | 0.992772i | \(-0.461706\pi\) | ||||
0.120013 | + | 0.992772i | \(0.461706\pi\) | |||||||
\(80\) | 28.5461 | 3.19155 | ||||||||
\(81\) | 6.87234 | 0.763593 | ||||||||
\(82\) | 3.19206 | 0.352504 | ||||||||
\(83\) | −9.19652 | −1.00945 | −0.504725 | − | 0.863280i | \(-0.668406\pi\) | ||||
−0.504725 | + | 0.863280i | \(0.668406\pi\) | |||||||
\(84\) | −3.34664 | −0.365149 | ||||||||
\(85\) | 4.47036 | 0.484879 | ||||||||
\(86\) | −24.7599 | −2.66993 | ||||||||
\(87\) | 4.14056 | 0.443914 | ||||||||
\(88\) | −0.184093 | −0.0196244 | ||||||||
\(89\) | 16.1600 | 1.71296 | 0.856479 | − | 0.516182i | \(-0.172647\pi\) | ||||
0.856479 | + | 0.516182i | \(0.172647\pi\) | |||||||
\(90\) | 17.4643 | 1.84090 | ||||||||
\(91\) | −5.83360 | −0.611528 | ||||||||
\(92\) | 20.2273 | 2.10884 | ||||||||
\(93\) | 2.93306 | 0.304144 | ||||||||
\(94\) | −9.04535 | −0.932956 | ||||||||
\(95\) | 4.86675 | 0.499318 | ||||||||
\(96\) | 7.60177 | 0.775852 | ||||||||
\(97\) | −10.1958 | −1.03522 | −0.517612 | − | 0.855616i | \(-0.673179\pi\) | ||||
−0.517612 | + | 0.855616i | \(0.673179\pi\) | |||||||
\(98\) | 14.0053 | 1.41475 | ||||||||
\(99\) | −0.0608039 | −0.00611102 | ||||||||
\(100\) | 3.23104 | 0.323104 | ||||||||
\(101\) | 9.17371 | 0.912818 | 0.456409 | − | 0.889770i | \(-0.349135\pi\) | ||||
0.456409 | + | 0.889770i | \(0.349135\pi\) | |||||||
\(102\) | 2.47913 | 0.245471 | ||||||||
\(103\) | −10.2688 | −1.01182 | −0.505908 | − | 0.862588i | \(-0.668842\pi\) | ||||
−0.505908 | + | 0.862588i | \(0.668842\pi\) | |||||||
\(104\) | 36.7701 | 3.60560 | ||||||||
\(105\) | −1.54891 | −0.151158 | ||||||||
\(106\) | 22.5371 | 2.18899 | ||||||||
\(107\) | 14.2555 | 1.37813 | 0.689065 | − | 0.724700i | \(-0.258022\pi\) | ||||
0.689065 | + | 0.724700i | \(0.258022\pi\) | |||||||
\(108\) | 14.5485 | 1.39993 | ||||||||
\(109\) | 10.0984 | 0.967255 | 0.483627 | − | 0.875274i | \(-0.339319\pi\) | ||||
0.483627 | + | 0.875274i | \(0.339319\pi\) | |||||||
\(110\) | −0.139701 | −0.0133200 | ||||||||
\(111\) | 3.32363 | 0.315465 | ||||||||
\(112\) | 15.9321 | 1.50544 | ||||||||
\(113\) | −0.296080 | −0.0278528 | −0.0139264 | − | 0.999903i | \(-0.504433\pi\) | ||||
−0.0139264 | + | 0.999903i | \(0.504433\pi\) | |||||||
\(114\) | 2.69896 | 0.252781 | ||||||||
\(115\) | 9.36170 | 0.872983 | ||||||||
\(116\) | −43.0658 | −3.99856 | ||||||||
\(117\) | 12.1448 | 1.12278 | ||||||||
\(118\) | −21.8332 | −2.00991 | ||||||||
\(119\) | 2.49500 | 0.228716 | ||||||||
\(120\) | 9.76301 | 0.891237 | ||||||||
\(121\) | −10.9995 | −0.999956 | ||||||||
\(122\) | −21.0233 | −1.90336 | ||||||||
\(123\) | 0.589382 | 0.0531428 | ||||||||
\(124\) | −30.5066 | −2.73958 | ||||||||
\(125\) | −10.3686 | −0.927400 | ||||||||
\(126\) | 9.74719 | 0.868349 | ||||||||
\(127\) | 7.28789 | 0.646695 | 0.323348 | − | 0.946280i | \(-0.395192\pi\) | ||||
0.323348 | + | 0.946280i | \(0.395192\pi\) | |||||||
\(128\) | −14.8323 | −1.31100 | ||||||||
\(129\) | −4.57166 | −0.402513 | ||||||||
\(130\) | 27.9034 | 2.44729 | ||||||||
\(131\) | 20.0345 | 1.75042 | 0.875212 | − | 0.483739i | \(-0.160722\pi\) | ||||
0.875212 | + | 0.483739i | \(0.160722\pi\) | |||||||
\(132\) | −0.0557325 | −0.00485089 | ||||||||
\(133\) | 2.71623 | 0.235527 | ||||||||
\(134\) | −29.5868 | −2.55591 | ||||||||
\(135\) | 6.73340 | 0.579519 | ||||||||
\(136\) | −15.7263 | −1.34852 | ||||||||
\(137\) | 20.2975 | 1.73413 | 0.867066 | − | 0.498193i | \(-0.166003\pi\) | ||||
0.867066 | + | 0.498193i | \(0.166003\pi\) | |||||||
\(138\) | 5.19173 | 0.441949 | ||||||||
\(139\) | −13.9576 | −1.18387 | −0.591933 | − | 0.805987i | \(-0.701635\pi\) | ||||
−0.591933 | + | 0.805987i | \(0.701635\pi\) | |||||||
\(140\) | 16.1101 | 1.36156 | ||||||||
\(141\) | −1.67013 | −0.140651 | ||||||||
\(142\) | −33.2178 | −2.78758 | ||||||||
\(143\) | −0.0971485 | −0.00812396 | ||||||||
\(144\) | −33.1685 | −2.76404 | ||||||||
\(145\) | −19.9319 | −1.65525 | ||||||||
\(146\) | −22.7786 | −1.88517 | ||||||||
\(147\) | 2.58594 | 0.213284 | ||||||||
\(148\) | −34.5690 | −2.84155 | ||||||||
\(149\) | −15.9273 | −1.30482 | −0.652409 | − | 0.757867i | \(-0.726242\pi\) | ||||
−0.652409 | + | 0.757867i | \(0.726242\pi\) | |||||||
\(150\) | 0.829310 | 0.0677128 | ||||||||
\(151\) | −10.0185 | −0.815296 | −0.407648 | − | 0.913139i | \(-0.633651\pi\) | ||||
−0.407648 | + | 0.913139i | \(0.633651\pi\) | |||||||
\(152\) | −17.1208 | −1.38868 | ||||||||
\(153\) | −5.19424 | −0.419929 | ||||||||
\(154\) | −0.0779698 | −0.00628299 | ||||||||
\(155\) | −14.1192 | −1.13408 | ||||||||
\(156\) | 11.1318 | 0.891259 | ||||||||
\(157\) | −2.64432 | −0.211040 | −0.105520 | − | 0.994417i | \(-0.533651\pi\) | ||||
−0.105520 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(158\) | −5.69535 | −0.453098 | ||||||||
\(159\) | 4.16124 | 0.330008 | ||||||||
\(160\) | −36.5935 | −2.89297 | ||||||||
\(161\) | 5.22495 | 0.411783 | ||||||||
\(162\) | −18.3464 | −1.44143 | ||||||||
\(163\) | 20.5807 | 1.61201 | 0.806003 | − | 0.591911i | \(-0.201626\pi\) | ||||
0.806003 | + | 0.591911i | \(0.201626\pi\) | |||||||
\(164\) | −6.13014 | −0.478683 | ||||||||
\(165\) | −0.0257944 | −0.00200809 | ||||||||
\(166\) | 24.5511 | 1.90554 | ||||||||
\(167\) | 24.7481 | 1.91507 | 0.957534 | − | 0.288320i | \(-0.0930965\pi\) | ||||
0.957534 | + | 0.288320i | \(0.0930965\pi\) | |||||||
\(168\) | 5.44892 | 0.420394 | ||||||||
\(169\) | 6.40411 | 0.492624 | ||||||||
\(170\) | −11.9341 | −0.915304 | ||||||||
\(171\) | −5.65481 | −0.432434 | ||||||||
\(172\) | 47.5497 | 3.62563 | ||||||||
\(173\) | 18.9480 | 1.44059 | 0.720294 | − | 0.693668i | \(-0.244007\pi\) | ||||
0.720294 | + | 0.693668i | \(0.244007\pi\) | |||||||
\(174\) | −11.0537 | −0.837976 | ||||||||
\(175\) | 0.834615 | 0.0630910 | ||||||||
\(176\) | 0.265322 | 0.0199994 | ||||||||
\(177\) | −4.03127 | −0.303009 | ||||||||
\(178\) | −43.1409 | −3.23355 | ||||||||
\(179\) | −23.0060 | −1.71955 | −0.859775 | − | 0.510672i | \(-0.829397\pi\) | ||||
−0.859775 | + | 0.510672i | \(0.829397\pi\) | |||||||
\(180\) | −33.5391 | −2.49986 | ||||||||
\(181\) | 15.1869 | 1.12884 | 0.564418 | − | 0.825489i | \(-0.309101\pi\) | ||||
0.564418 | + | 0.825489i | \(0.309101\pi\) | |||||||
\(182\) | 15.5734 | 1.15438 | ||||||||
\(183\) | −3.88174 | −0.286946 | ||||||||
\(184\) | −32.9336 | −2.42790 | ||||||||
\(185\) | −15.9994 | −1.17630 | ||||||||
\(186\) | −7.83011 | −0.574132 | ||||||||
\(187\) | 0.0415498 | 0.00303842 | ||||||||
\(188\) | 17.3710 | 1.26691 | ||||||||
\(189\) | 3.75804 | 0.273357 | ||||||||
\(190\) | −12.9923 | −0.942561 | ||||||||
\(191\) | 12.0887 | 0.874709 | 0.437354 | − | 0.899289i | \(-0.355916\pi\) | ||||
0.437354 | + | 0.899289i | \(0.355916\pi\) | |||||||
\(192\) | −8.43368 | −0.608649 | ||||||||
\(193\) | −12.5731 | −0.905033 | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||||
−0.452517 | + | 0.891756i | \(0.649474\pi\) | |||||||
\(194\) | 27.2187 | 1.95419 | ||||||||
\(195\) | 5.15208 | 0.368948 | ||||||||
\(196\) | −26.8962 | −1.92116 | ||||||||
\(197\) | 22.3065 | 1.58927 | 0.794635 | − | 0.607088i | \(-0.207662\pi\) | ||||
0.794635 | + | 0.607088i | \(0.207662\pi\) | |||||||
\(198\) | 0.162322 | 0.0115358 | ||||||||
\(199\) | −6.79573 | −0.481737 | −0.240868 | − | 0.970558i | \(-0.577432\pi\) | ||||
−0.240868 | + | 0.970558i | \(0.577432\pi\) | |||||||
\(200\) | −5.26071 | −0.371988 | ||||||||
\(201\) | −5.46291 | −0.385324 | ||||||||
\(202\) | −24.4902 | −1.72312 | ||||||||
\(203\) | −11.1244 | −0.780779 | ||||||||
\(204\) | −4.76101 | −0.333337 | ||||||||
\(205\) | −2.83718 | −0.198157 | ||||||||
\(206\) | 27.4137 | 1.91000 | ||||||||
\(207\) | −10.8776 | −0.756047 | ||||||||
\(208\) | −52.9945 | −3.67450 | ||||||||
\(209\) | 0.0452340 | 0.00312890 | ||||||||
\(210\) | 4.13498 | 0.285341 | ||||||||
\(211\) | −4.85204 | −0.334028 | −0.167014 | − | 0.985954i | \(-0.553413\pi\) | ||||
−0.167014 | + | 0.985954i | \(0.553413\pi\) | |||||||
\(212\) | −43.2809 | −2.97255 | ||||||||
\(213\) | −6.13334 | −0.420250 | ||||||||
\(214\) | −38.0565 | −2.60149 | ||||||||
\(215\) | 22.0072 | 1.50088 | ||||||||
\(216\) | −23.6875 | −1.61173 | ||||||||
\(217\) | −7.88021 | −0.534944 | ||||||||
\(218\) | −26.9589 | −1.82588 | ||||||||
\(219\) | −4.20584 | −0.284204 | ||||||||
\(220\) | 0.268286 | 0.0180879 | ||||||||
\(221\) | −8.29901 | −0.558252 | ||||||||
\(222\) | −8.87280 | −0.595503 | ||||||||
\(223\) | 10.7977 | 0.723070 | 0.361535 | − | 0.932359i | \(-0.382253\pi\) | ||||
0.361535 | + | 0.932359i | \(0.382253\pi\) | |||||||
\(224\) | −20.4236 | −1.36461 | ||||||||
\(225\) | −1.73755 | −0.115837 | ||||||||
\(226\) | 0.790416 | 0.0525777 | ||||||||
\(227\) | −19.5689 | −1.29884 | −0.649418 | − | 0.760432i | \(-0.724987\pi\) | ||||
−0.649418 | + | 0.760432i | \(0.724987\pi\) | |||||||
\(228\) | −5.18317 | −0.343264 | ||||||||
\(229\) | 0.850754 | 0.0562194 | 0.0281097 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281097 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(230\) | −24.9921 | −1.64793 | ||||||||
\(231\) | −0.0143963 | −0.000947210 0 | ||||||||
\(232\) | 70.1187 | 4.60352 | ||||||||
\(233\) | 25.9394 | 1.69935 | 0.849673 | − | 0.527309i | \(-0.176799\pi\) | ||||
0.849673 | + | 0.527309i | \(0.176799\pi\) | |||||||
\(234\) | −32.4217 | −2.11948 | ||||||||
\(235\) | 8.03972 | 0.524453 | ||||||||
\(236\) | 41.9291 | 2.72935 | ||||||||
\(237\) | −1.05159 | −0.0683081 | ||||||||
\(238\) | −6.66066 | −0.431746 | ||||||||
\(239\) | 5.87878 | 0.380267 | 0.190133 | − | 0.981758i | \(-0.439108\pi\) | ||||
0.190133 | + | 0.981758i | \(0.439108\pi\) | |||||||
\(240\) | −14.0708 | −0.908268 | ||||||||
\(241\) | 14.2429 | 0.917469 | 0.458734 | − | 0.888573i | \(-0.348303\pi\) | ||||
0.458734 | + | 0.888573i | \(0.348303\pi\) | |||||||
\(242\) | 29.3644 | 1.88761 | ||||||||
\(243\) | −11.9007 | −0.763429 | ||||||||
\(244\) | 40.3738 | 2.58467 | ||||||||
\(245\) | −12.4482 | −0.795288 | ||||||||
\(246\) | −1.57342 | −0.100317 | ||||||||
\(247\) | −9.03489 | −0.574876 | ||||||||
\(248\) | 49.6702 | 3.15406 | ||||||||
\(249\) | 4.53311 | 0.287274 | ||||||||
\(250\) | 27.6802 | 1.75065 | ||||||||
\(251\) | −10.9668 | −0.692219 | −0.346110 | − | 0.938194i | \(-0.612497\pi\) | ||||
−0.346110 | + | 0.938194i | \(0.612497\pi\) | |||||||
\(252\) | −18.7188 | −1.17918 | ||||||||
\(253\) | 0.0870123 | 0.00547042 | ||||||||
\(254\) | −19.4558 | −1.22077 | ||||||||
\(255\) | −2.20351 | −0.137989 | ||||||||
\(256\) | 5.37689 | 0.336056 | ||||||||
\(257\) | 21.3539 | 1.33202 | 0.666008 | − | 0.745944i | \(-0.268002\pi\) | ||||
0.666008 | + | 0.745944i | \(0.268002\pi\) | |||||||
\(258\) | 12.2045 | 0.759822 | ||||||||
\(259\) | −8.92957 | −0.554856 | ||||||||
\(260\) | −53.5866 | −3.32330 | ||||||||
\(261\) | 23.1594 | 1.43353 | ||||||||
\(262\) | −53.4843 | −3.30427 | ||||||||
\(263\) | 9.63154 | 0.593906 | 0.296953 | − | 0.954892i | \(-0.404029\pi\) | ||||
0.296953 | + | 0.954892i | \(0.404029\pi\) | |||||||
\(264\) | 0.0907423 | 0.00558480 | ||||||||
\(265\) | −20.0315 | −1.23052 | ||||||||
\(266\) | −7.25126 | −0.444603 | ||||||||
\(267\) | −7.96553 | −0.487482 | ||||||||
\(268\) | 56.8195 | 3.47081 | ||||||||
\(269\) | −2.12980 | −0.129856 | −0.0649282 | − | 0.997890i | \(-0.520682\pi\) | ||||
−0.0649282 | + | 0.997890i | \(0.520682\pi\) | |||||||
\(270\) | −17.9755 | −1.09396 | ||||||||
\(271\) | 1.52317 | 0.0925262 | 0.0462631 | − | 0.998929i | \(-0.485269\pi\) | ||||
0.0462631 | + | 0.998929i | \(0.485269\pi\) | |||||||
\(272\) | 22.6654 | 1.37429 | ||||||||
\(273\) | 2.87548 | 0.174032 | ||||||||
\(274\) | −54.1864 | −3.27352 | ||||||||
\(275\) | 0.0138991 | 0.000838145 0 | ||||||||
\(276\) | −9.97037 | −0.600146 | ||||||||
\(277\) | −11.6260 | −0.698536 | −0.349268 | − | 0.937023i | \(-0.613570\pi\) | ||||
−0.349268 | + | 0.937023i | \(0.613570\pi\) | |||||||
\(278\) | 37.2613 | 2.23478 | ||||||||
\(279\) | 16.4055 | 0.982172 | ||||||||
\(280\) | −26.2301 | −1.56755 | ||||||||
\(281\) | −24.5100 | −1.46215 | −0.731073 | − | 0.682300i | \(-0.760980\pi\) | ||||
−0.731073 | + | 0.682300i | \(0.760980\pi\) | |||||||
\(282\) | 4.45860 | 0.265506 | ||||||||
\(283\) | −6.50918 | −0.386931 | −0.193465 | − | 0.981107i | \(-0.561973\pi\) | ||||
−0.193465 | + | 0.981107i | \(0.561973\pi\) | |||||||
\(284\) | 63.7927 | 3.78540 | ||||||||
\(285\) | −2.39890 | −0.142099 | ||||||||
\(286\) | 0.259348 | 0.0153356 | ||||||||
\(287\) | −1.58348 | −0.0934701 | ||||||||
\(288\) | 42.5191 | 2.50546 | ||||||||
\(289\) | −13.4506 | −0.791210 | ||||||||
\(290\) | 53.2104 | 3.12462 | ||||||||
\(291\) | 5.02566 | 0.294609 | ||||||||
\(292\) | 43.7448 | 2.55997 | ||||||||
\(293\) | 11.4226 | 0.667314 | 0.333657 | − | 0.942695i | \(-0.391717\pi\) | ||||
0.333657 | + | 0.942695i | \(0.391717\pi\) | |||||||
\(294\) | −6.90343 | −0.402616 | ||||||||
\(295\) | 19.4058 | 1.12985 | ||||||||
\(296\) | 56.2844 | 3.27146 | ||||||||
\(297\) | 0.0625836 | 0.00363147 | ||||||||
\(298\) | 42.5197 | 2.46310 | ||||||||
\(299\) | −17.3796 | −1.00509 | ||||||||
\(300\) | −1.59263 | −0.0919507 | ||||||||
\(301\) | 12.2826 | 0.707959 | ||||||||
\(302\) | 26.7455 | 1.53903 | ||||||||
\(303\) | −4.52187 | −0.259775 | ||||||||
\(304\) | 24.6751 | 1.41522 | ||||||||
\(305\) | 18.6860 | 1.06996 | ||||||||
\(306\) | 13.8666 | 0.792699 | ||||||||
\(307\) | −3.66332 | −0.209077 | −0.104538 | − | 0.994521i | \(-0.533336\pi\) | ||||
−0.104538 | + | 0.994521i | \(0.533336\pi\) | |||||||
\(308\) | 0.149736 | 0.00853199 | ||||||||
\(309\) | 5.06166 | 0.287948 | ||||||||
\(310\) | 37.6928 | 2.14081 | ||||||||
\(311\) | −18.6634 | −1.05830 | −0.529152 | − | 0.848527i | \(-0.677490\pi\) | ||||
−0.529152 | + | 0.848527i | \(0.677490\pi\) | |||||||
\(312\) | −18.1246 | −1.02610 | ||||||||
\(313\) | 21.5401 | 1.21752 | 0.608759 | − | 0.793355i | \(-0.291667\pi\) | ||||
0.608759 | + | 0.793355i | \(0.291667\pi\) | |||||||
\(314\) | 7.05930 | 0.398380 | ||||||||
\(315\) | −8.66353 | −0.488135 | ||||||||
\(316\) | 10.9375 | 0.615285 | ||||||||
\(317\) | 17.0387 | 0.956991 | 0.478495 | − | 0.878090i | \(-0.341182\pi\) | ||||
0.478495 | + | 0.878090i | \(0.341182\pi\) | |||||||
\(318\) | −11.1089 | −0.622955 | ||||||||
\(319\) | −0.185257 | −0.0103724 | ||||||||
\(320\) | 40.5982 | 2.26951 | ||||||||
\(321\) | −7.02676 | −0.392195 | ||||||||
\(322\) | −13.9486 | −0.777323 | ||||||||
\(323\) | 3.86417 | 0.215008 | ||||||||
\(324\) | 35.2331 | 1.95739 | ||||||||
\(325\) | −2.77615 | −0.153993 | ||||||||
\(326\) | −54.9424 | −3.04298 | ||||||||
\(327\) | −4.97768 | −0.275266 | ||||||||
\(328\) | 9.98094 | 0.551105 | ||||||||
\(329\) | 4.48712 | 0.247383 | ||||||||
\(330\) | 0.0688608 | 0.00379066 | ||||||||
\(331\) | −27.5665 | −1.51519 | −0.757595 | − | 0.652725i | \(-0.773626\pi\) | ||||
−0.757595 | + | 0.652725i | \(0.773626\pi\) | |||||||
\(332\) | −47.1488 | −2.58762 | ||||||||
\(333\) | 18.5901 | 1.01873 | ||||||||
\(334\) | −66.0678 | −3.61507 | ||||||||
\(335\) | 26.2975 | 1.43678 | ||||||||
\(336\) | −7.85320 | −0.428427 | ||||||||
\(337\) | 8.06440 | 0.439296 | 0.219648 | − | 0.975579i | \(-0.429509\pi\) | ||||
0.219648 | + | 0.975579i | \(0.429509\pi\) | |||||||
\(338\) | −17.0965 | −0.929925 | ||||||||
\(339\) | 0.145942 | 0.00792650 | ||||||||
\(340\) | 22.9187 | 1.24294 | ||||||||
\(341\) | −0.131231 | −0.00710656 | ||||||||
\(342\) | 15.0961 | 0.816305 | ||||||||
\(343\) | −16.2178 | −0.875678 | ||||||||
\(344\) | −77.4193 | −4.17417 | ||||||||
\(345\) | −4.61453 | −0.248438 | ||||||||
\(346\) | −50.5837 | −2.71940 | ||||||||
\(347\) | 20.8078 | 1.11702 | 0.558511 | − | 0.829497i | \(-0.311373\pi\) | ||||
0.558511 | + | 0.829497i | \(0.311373\pi\) | |||||||
\(348\) | 21.2278 | 1.13793 | ||||||||
\(349\) | 1.36090 | 0.0728471 | 0.0364236 | − | 0.999336i | \(-0.488403\pi\) | ||||
0.0364236 | + | 0.999336i | \(0.488403\pi\) | |||||||
\(350\) | −2.22810 | −0.119097 | ||||||||
\(351\) | −12.5002 | −0.667214 | ||||||||
\(352\) | −0.340119 | −0.0181284 | ||||||||
\(353\) | 4.77241 | 0.254010 | 0.127005 | − | 0.991902i | \(-0.459464\pi\) | ||||
0.127005 | + | 0.991902i | \(0.459464\pi\) | |||||||
\(354\) | 10.7619 | 0.571989 | ||||||||
\(355\) | 29.5248 | 1.56701 | ||||||||
\(356\) | 82.8492 | 4.39100 | ||||||||
\(357\) | −1.22982 | −0.0650891 | ||||||||
\(358\) | 61.4170 | 3.24599 | ||||||||
\(359\) | −27.8749 | −1.47118 | −0.735591 | − | 0.677426i | \(-0.763096\pi\) | ||||
−0.735591 | + | 0.677426i | \(0.763096\pi\) | |||||||
\(360\) | 54.6076 | 2.87807 | ||||||||
\(361\) | −14.7932 | −0.778589 | ||||||||
\(362\) | −40.5431 | −2.13090 | ||||||||
\(363\) | 5.42184 | 0.284573 | ||||||||
\(364\) | −29.9077 | −1.56759 | ||||||||
\(365\) | 20.2462 | 1.05973 | ||||||||
\(366\) | 10.3627 | 0.541668 | ||||||||
\(367\) | −7.67869 | −0.400825 | −0.200412 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200412 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(368\) | 47.4652 | 2.47429 | ||||||||
\(369\) | 3.29660 | 0.171614 | ||||||||
\(370\) | 42.7121 | 2.22049 | ||||||||
\(371\) | −11.1800 | −0.580435 | ||||||||
\(372\) | 15.0372 | 0.779643 | ||||||||
\(373\) | 1.29300 | 0.0669492 | 0.0334746 | − | 0.999440i | \(-0.489343\pi\) | ||||
0.0334746 | + | 0.999440i | \(0.489343\pi\) | |||||||
\(374\) | −0.110922 | −0.00573562 | ||||||||
\(375\) | 5.11087 | 0.263924 | ||||||||
\(376\) | −28.2830 | −1.45859 | ||||||||
\(377\) | 37.0026 | 1.90573 | ||||||||
\(378\) | −10.0325 | −0.516016 | ||||||||
\(379\) | −16.1562 | −0.829889 | −0.414944 | − | 0.909847i | \(-0.636199\pi\) | ||||
−0.414944 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(380\) | 24.9509 | 1.27995 | ||||||||
\(381\) | −3.59232 | −0.184040 | ||||||||
\(382\) | −32.2721 | −1.65119 | ||||||||
\(383\) | 6.91868 | 0.353528 | 0.176764 | − | 0.984253i | \(-0.443437\pi\) | ||||
0.176764 | + | 0.984253i | \(0.443437\pi\) | |||||||
\(384\) | 7.31108 | 0.373092 | ||||||||
\(385\) | 0.0693014 | 0.00353193 | ||||||||
\(386\) | 33.5653 | 1.70843 | ||||||||
\(387\) | −25.5708 | −1.29983 | ||||||||
\(388\) | −52.2717 | −2.65369 | ||||||||
\(389\) | 28.0120 | 1.42027 | 0.710133 | − | 0.704067i | \(-0.248635\pi\) | ||||
0.710133 | + | 0.704067i | \(0.248635\pi\) | |||||||
\(390\) | −13.7540 | −0.696463 | ||||||||
\(391\) | 7.43312 | 0.375909 | ||||||||
\(392\) | 43.7918 | 2.21182 | ||||||||
\(393\) | −9.87534 | −0.498145 | ||||||||
\(394\) | −59.5495 | −3.00006 | ||||||||
\(395\) | 5.06216 | 0.254705 | ||||||||
\(396\) | −0.311729 | −0.0156650 | ||||||||
\(397\) | 8.03898 | 0.403465 | 0.201732 | − | 0.979441i | \(-0.435343\pi\) | ||||
0.201732 | + | 0.979441i | \(0.435343\pi\) | |||||||
\(398\) | 18.1419 | 0.909373 | ||||||||
\(399\) | −1.33887 | −0.0670275 | ||||||||
\(400\) | 7.58193 | 0.379097 | ||||||||
\(401\) | −27.1278 | −1.35470 | −0.677349 | − | 0.735662i | \(-0.736871\pi\) | ||||
−0.677349 | + | 0.735662i | \(0.736871\pi\) | |||||||
\(402\) | 14.5838 | 0.727375 | ||||||||
\(403\) | 26.2117 | 1.30570 | ||||||||
\(404\) | 47.0318 | 2.33992 | ||||||||
\(405\) | 16.3067 | 0.810289 | ||||||||
\(406\) | 29.6977 | 1.47387 | ||||||||
\(407\) | −0.148706 | −0.00737110 | ||||||||
\(408\) | 7.75176 | 0.383769 | ||||||||
\(409\) | −38.9578 | −1.92634 | −0.963169 | − | 0.268896i | \(-0.913341\pi\) | ||||
−0.963169 | + | 0.268896i | \(0.913341\pi\) | |||||||
\(410\) | 7.57415 | 0.374061 | ||||||||
\(411\) | −10.0050 | −0.493508 | ||||||||
\(412\) | −52.6461 | −2.59369 | ||||||||
\(413\) | 10.8308 | 0.532947 | ||||||||
\(414\) | 29.0390 | 1.42719 | ||||||||
\(415\) | −21.8216 | −1.07118 | ||||||||
\(416\) | 67.9342 | 3.33075 | ||||||||
\(417\) | 6.87992 | 0.336911 | ||||||||
\(418\) | −0.120757 | −0.00590642 | ||||||||
\(419\) | −0.585367 | −0.0285970 | −0.0142985 | − | 0.999898i | \(-0.504552\pi\) | ||||
−0.0142985 | + | 0.999898i | \(0.504552\pi\) | |||||||
\(420\) | −7.94095 | −0.387479 | ||||||||
\(421\) | 13.8168 | 0.673389 | 0.336695 | − | 0.941614i | \(-0.390691\pi\) | ||||
0.336695 | + | 0.941614i | \(0.390691\pi\) | |||||||
\(422\) | 12.9531 | 0.630545 | ||||||||
\(423\) | −9.34157 | −0.454203 | ||||||||
\(424\) | 70.4690 | 3.42228 | ||||||||
\(425\) | 1.18734 | 0.0575946 | ||||||||
\(426\) | 16.3736 | 0.793304 | ||||||||
\(427\) | 10.4290 | 0.504695 | ||||||||
\(428\) | 73.0850 | 3.53270 | ||||||||
\(429\) | 0.0478860 | 0.00231196 | ||||||||
\(430\) | −58.7505 | −2.83320 | ||||||||
\(431\) | −6.20793 | −0.299026 | −0.149513 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149513 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(432\) | 34.1394 | 1.64253 | ||||||||
\(433\) | −31.4001 | −1.50899 | −0.754495 | − | 0.656306i | \(-0.772118\pi\) | ||||
−0.754495 | + | 0.656306i | \(0.772118\pi\) | |||||||
\(434\) | 21.0371 | 1.00981 | ||||||||
\(435\) | 9.82476 | 0.471061 | ||||||||
\(436\) | 51.7727 | 2.47946 | ||||||||
\(437\) | 8.09222 | 0.387103 | ||||||||
\(438\) | 11.2279 | 0.536492 | ||||||||
\(439\) | 23.4294 | 1.11822 | 0.559111 | − | 0.829093i | \(-0.311142\pi\) | ||||
0.559111 | + | 0.829093i | \(0.311142\pi\) | |||||||
\(440\) | −0.436817 | −0.0208244 | ||||||||
\(441\) | 14.4639 | 0.688759 | ||||||||
\(442\) | 22.1551 | 1.05381 | ||||||||
\(443\) | −18.1083 | −0.860349 | −0.430175 | − | 0.902746i | \(-0.641548\pi\) | ||||
−0.430175 | + | 0.902746i | \(0.641548\pi\) | |||||||
\(444\) | 17.0396 | 0.808664 | ||||||||
\(445\) | 38.3446 | 1.81771 | ||||||||
\(446\) | −28.8257 | −1.36494 | ||||||||
\(447\) | 7.85084 | 0.371332 | ||||||||
\(448\) | 22.6587 | 1.07052 | ||||||||
\(449\) | −5.18463 | −0.244678 | −0.122339 | − | 0.992488i | \(-0.539039\pi\) | ||||
−0.122339 | + | 0.992488i | \(0.539039\pi\) | |||||||
\(450\) | 4.63859 | 0.218665 | ||||||||
\(451\) | −0.0263702 | −0.00124172 | ||||||||
\(452\) | −1.51794 | −0.0713980 | ||||||||
\(453\) | 4.93829 | 0.232021 | ||||||||
\(454\) | 52.2414 | 2.45181 | ||||||||
\(455\) | −13.8420 | −0.648925 | ||||||||
\(456\) | 8.43911 | 0.395198 | ||||||||
\(457\) | 33.6054 | 1.57200 | 0.785998 | − | 0.618229i | \(-0.212150\pi\) | ||||
0.785998 | + | 0.618229i | \(0.212150\pi\) | |||||||
\(458\) | −2.27118 | −0.106125 | ||||||||
\(459\) | 5.34628 | 0.249543 | ||||||||
\(460\) | 47.9956 | 2.23781 | ||||||||
\(461\) | 10.0720 | 0.469100 | 0.234550 | − | 0.972104i | \(-0.424638\pi\) | ||||
0.234550 | + | 0.972104i | \(0.424638\pi\) | |||||||
\(462\) | 0.0384326 | 0.00178805 | ||||||||
\(463\) | −2.62919 | −0.122189 | −0.0610945 | − | 0.998132i | \(-0.519459\pi\) | ||||
−0.0610945 | + | 0.998132i | \(0.519459\pi\) | |||||||
\(464\) | −101.058 | −4.69149 | ||||||||
\(465\) | 6.95959 | 0.322743 | ||||||||
\(466\) | −69.2480 | −3.20785 | ||||||||
\(467\) | −21.1690 | −0.979584 | −0.489792 | − | 0.871839i | \(-0.662927\pi\) | ||||
−0.489792 | + | 0.871839i | \(0.662927\pi\) | |||||||
\(468\) | 62.2638 | 2.87814 | ||||||||
\(469\) | 14.6771 | 0.677727 | ||||||||
\(470\) | −21.4629 | −0.990009 | ||||||||
\(471\) | 1.30343 | 0.0600589 | ||||||||
\(472\) | −68.2680 | −3.14229 | ||||||||
\(473\) | 0.204546 | 0.00940502 | ||||||||
\(474\) | 2.80733 | 0.128945 | ||||||||
\(475\) | 1.29262 | 0.0593097 | ||||||||
\(476\) | 12.7913 | 0.586290 | ||||||||
\(477\) | 23.2751 | 1.06570 | ||||||||
\(478\) | −15.6940 | −0.717829 | ||||||||
\(479\) | 22.3250 | 1.02005 | 0.510027 | − | 0.860159i | \(-0.329635\pi\) | ||||
0.510027 | + | 0.860159i | \(0.329635\pi\) | |||||||
\(480\) | 18.0375 | 0.823298 | ||||||||
\(481\) | 29.7021 | 1.35430 | ||||||||
\(482\) | −38.0231 | −1.73190 | ||||||||
\(483\) | −2.57546 | −0.117187 | ||||||||
\(484\) | −56.3923 | −2.56329 | ||||||||
\(485\) | −24.1926 | −1.09853 | ||||||||
\(486\) | 31.7702 | 1.44112 | ||||||||
\(487\) | −12.3971 | −0.561765 | −0.280882 | − | 0.959742i | \(-0.590627\pi\) | ||||
−0.280882 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(488\) | −65.7357 | −2.97571 | ||||||||
\(489\) | −10.1446 | −0.458753 | ||||||||
\(490\) | 33.2319 | 1.50126 | ||||||||
\(491\) | 21.6477 | 0.976948 | 0.488474 | − | 0.872578i | \(-0.337554\pi\) | ||||
0.488474 | + | 0.872578i | \(0.337554\pi\) | |||||||
\(492\) | 3.02164 | 0.136226 | ||||||||
\(493\) | −15.8258 | −0.712758 | ||||||||
\(494\) | 24.1196 | 1.08519 | ||||||||
\(495\) | −0.144276 | −0.00648472 | ||||||||
\(496\) | −71.5865 | −3.21433 | ||||||||
\(497\) | 16.4784 | 0.739156 | ||||||||
\(498\) | −12.1016 | −0.542287 | ||||||||
\(499\) | 36.3551 | 1.62748 | 0.813739 | − | 0.581230i | \(-0.197428\pi\) | ||||
0.813739 | + | 0.581230i | \(0.197428\pi\) | |||||||
\(500\) | −53.1580 | −2.37730 | ||||||||
\(501\) | −12.1988 | −0.545000 | ||||||||
\(502\) | 29.2771 | 1.30670 | ||||||||
\(503\) | 5.55810 | 0.247823 | 0.123912 | − | 0.992293i | \(-0.460456\pi\) | ||||
0.123912 | + | 0.992293i | \(0.460456\pi\) | |||||||
\(504\) | 30.4775 | 1.35758 | ||||||||
\(505\) | 21.7675 | 0.968640 | ||||||||
\(506\) | −0.232289 | −0.0103265 | ||||||||
\(507\) | −3.15669 | −0.140194 | ||||||||
\(508\) | 37.3636 | 1.65774 | ||||||||
\(509\) | 4.79382 | 0.212483 | 0.106241 | − | 0.994340i | \(-0.466118\pi\) | ||||
0.106241 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(510\) | 5.88251 | 0.260482 | ||||||||
\(511\) | 11.2998 | 0.499873 | ||||||||
\(512\) | 15.3104 | 0.676632 | ||||||||
\(513\) | 5.82033 | 0.256974 | ||||||||
\(514\) | −57.0064 | −2.51444 | ||||||||
\(515\) | −24.3659 | −1.07369 | ||||||||
\(516\) | −23.4380 | −1.03180 | ||||||||
\(517\) | 0.0747252 | 0.00328641 | ||||||||
\(518\) | 23.8384 | 1.04740 | ||||||||
\(519\) | −9.33977 | −0.409970 | ||||||||
\(520\) | 87.2484 | 3.82610 | ||||||||
\(521\) | 7.89807 | 0.346021 | 0.173010 | − | 0.984920i | \(-0.444651\pi\) | ||||
0.173010 | + | 0.984920i | \(0.444651\pi\) | |||||||
\(522\) | −61.8266 | −2.70608 | ||||||||
\(523\) | −7.69827 | −0.336622 | −0.168311 | − | 0.985734i | \(-0.553831\pi\) | ||||
−0.168311 | + | 0.985734i | \(0.553831\pi\) | |||||||
\(524\) | 102.713 | 4.48704 | ||||||||
\(525\) | −0.411395 | −0.0179548 | ||||||||
\(526\) | −25.7124 | −1.12112 | ||||||||
\(527\) | −11.2106 | −0.488340 | ||||||||
\(528\) | −0.130781 | −0.00569152 | ||||||||
\(529\) | −7.43377 | −0.323207 | ||||||||
\(530\) | 53.4762 | 2.32286 | ||||||||
\(531\) | −22.5482 | −0.978507 | ||||||||
\(532\) | 13.9256 | 0.603750 | ||||||||
\(533\) | 5.26709 | 0.228143 | ||||||||
\(534\) | 21.2648 | 0.920219 | ||||||||
\(535\) | 33.8255 | 1.46241 | ||||||||
\(536\) | −92.5122 | −3.99592 | ||||||||
\(537\) | 11.3400 | 0.489359 | ||||||||
\(538\) | 5.68573 | 0.245129 | ||||||||
\(539\) | −0.115700 | −0.00498356 | ||||||||
\(540\) | 34.5208 | 1.48554 | ||||||||
\(541\) | −9.72119 | −0.417947 | −0.208973 | − | 0.977921i | \(-0.567012\pi\) | ||||
−0.208973 | + | 0.977921i | \(0.567012\pi\) | |||||||
\(542\) | −4.06627 | −0.174661 | ||||||||
\(543\) | −7.48588 | −0.321250 | ||||||||
\(544\) | −29.0550 | −1.24572 | ||||||||
\(545\) | 23.9617 | 1.02641 | ||||||||
\(546\) | −7.67640 | −0.328519 | ||||||||
\(547\) | 44.4771 | 1.90170 | 0.950851 | − | 0.309649i | \(-0.100212\pi\) | ||||
0.950851 | + | 0.309649i | \(0.100212\pi\) | |||||||
\(548\) | 104.061 | 4.44528 | ||||||||
\(549\) | −21.7118 | −0.926636 | ||||||||
\(550\) | −0.0371050 | −0.00158216 | ||||||||
\(551\) | −17.2291 | −0.733983 | ||||||||
\(552\) | 16.2335 | 0.690944 | ||||||||
\(553\) | 2.82529 | 0.120144 | ||||||||
\(554\) | 31.0367 | 1.31862 | ||||||||
\(555\) | 7.88635 | 0.334757 | ||||||||
\(556\) | −71.5578 | −3.03473 | ||||||||
\(557\) | 13.1352 | 0.556558 | 0.278279 | − | 0.960500i | \(-0.410236\pi\) | ||||
0.278279 | + | 0.960500i | \(0.410236\pi\) | |||||||
\(558\) | −43.7963 | −1.85404 | ||||||||
\(559\) | −40.8553 | −1.72799 | ||||||||
\(560\) | 37.8039 | 1.59751 | ||||||||
\(561\) | −0.0204805 | −0.000864689 0 | ||||||||
\(562\) | 65.4321 | 2.76009 | ||||||||
\(563\) | 25.1592 | 1.06033 | 0.530167 | − | 0.847893i | \(-0.322129\pi\) | ||||
0.530167 | + | 0.847893i | \(0.322129\pi\) | |||||||
\(564\) | −8.56244 | −0.360544 | ||||||||
\(565\) | −0.702541 | −0.0295561 | ||||||||
\(566\) | 17.3770 | 0.730408 | ||||||||
\(567\) | 9.10111 | 0.382211 | ||||||||
\(568\) | −103.866 | −4.35811 | ||||||||
\(569\) | −13.6901 | −0.573919 | −0.286960 | − | 0.957943i | \(-0.592645\pi\) | ||||
−0.286960 | + | 0.957943i | \(0.592645\pi\) | |||||||
\(570\) | 6.40412 | 0.268239 | ||||||||
\(571\) | 35.9345 | 1.50381 | 0.751907 | − | 0.659269i | \(-0.229134\pi\) | ||||
0.751907 | + | 0.659269i | \(0.229134\pi\) | |||||||
\(572\) | −0.498061 | −0.0208250 | ||||||||
\(573\) | −5.95872 | −0.248929 | ||||||||
\(574\) | 4.22728 | 0.176443 | ||||||||
\(575\) | 2.48650 | 0.103694 | ||||||||
\(576\) | −47.1722 | −1.96551 | ||||||||
\(577\) | −24.9740 | −1.03968 | −0.519840 | − | 0.854264i | \(-0.674008\pi\) | ||||
−0.519840 | + | 0.854264i | \(0.674008\pi\) | |||||||
\(578\) | 35.9077 | 1.49356 | ||||||||
\(579\) | 6.19749 | 0.257559 | ||||||||
\(580\) | −102.187 | −4.24308 | ||||||||
\(581\) | −12.1791 | −0.505273 | ||||||||
\(582\) | −13.4165 | −0.556133 | ||||||||
\(583\) | −0.186183 | −0.00771090 | ||||||||
\(584\) | −71.2242 | −2.94728 | ||||||||
\(585\) | 28.8172 | 1.19144 | ||||||||
\(586\) | −30.4938 | −1.25969 | ||||||||
\(587\) | −11.5977 | −0.478689 | −0.239344 | − | 0.970935i | \(-0.576933\pi\) | ||||
−0.239344 | + | 0.970935i | \(0.576933\pi\) | |||||||
\(588\) | 13.2576 | 0.546733 | ||||||||
\(589\) | −12.2046 | −0.502882 | ||||||||
\(590\) | −51.8059 | −2.13282 | ||||||||
\(591\) | −10.9952 | −0.452283 | ||||||||
\(592\) | −81.1192 | −3.33398 | ||||||||
\(593\) | 1.85002 | 0.0759711 | 0.0379856 | − | 0.999278i | \(-0.487906\pi\) | ||||
0.0379856 | + | 0.999278i | \(0.487906\pi\) | |||||||
\(594\) | −0.167074 | −0.00685512 | ||||||||
\(595\) | 5.92015 | 0.242702 | ||||||||
\(596\) | −81.6563 | −3.34477 | ||||||||
\(597\) | 3.34973 | 0.137095 | ||||||||
\(598\) | 46.3966 | 1.89730 | ||||||||
\(599\) | 20.0959 | 0.821098 | 0.410549 | − | 0.911839i | \(-0.365337\pi\) | ||||
0.410549 | + | 0.911839i | \(0.365337\pi\) | |||||||
\(600\) | 2.59309 | 0.105862 | ||||||||
\(601\) | 43.0798 | 1.75726 | 0.878631 | − | 0.477501i | \(-0.158457\pi\) | ||||
0.878631 | + | 0.477501i | \(0.158457\pi\) | |||||||
\(602\) | −32.7898 | −1.33641 | ||||||||
\(603\) | −30.5558 | −1.24433 | ||||||||
\(604\) | −51.3630 | −2.08993 | ||||||||
\(605\) | −26.0998 | −1.06111 | ||||||||
\(606\) | 12.0716 | 0.490376 | ||||||||
\(607\) | 9.31075 | 0.377912 | 0.188956 | − | 0.981986i | \(-0.439490\pi\) | ||||
0.188956 | + | 0.981986i | \(0.439490\pi\) | |||||||
\(608\) | −31.6313 | −1.28282 | ||||||||
\(609\) | 5.48339 | 0.222198 | ||||||||
\(610\) | −49.8843 | −2.01975 | ||||||||
\(611\) | −14.9254 | −0.603815 | ||||||||
\(612\) | −26.6298 | −1.07645 | ||||||||
\(613\) | 23.7679 | 0.959978 | 0.479989 | − | 0.877274i | \(-0.340641\pi\) | ||||
0.479989 | + | 0.877274i | \(0.340641\pi\) | |||||||
\(614\) | 9.77962 | 0.394673 | ||||||||
\(615\) | 1.39849 | 0.0563926 | ||||||||
\(616\) | −0.243796 | −0.00982283 | ||||||||
\(617\) | −30.2247 | −1.21680 | −0.608400 | − | 0.793630i | \(-0.708188\pi\) | ||||
−0.608400 | + | 0.793630i | \(0.708188\pi\) | |||||||
\(618\) | −13.5126 | −0.543558 | ||||||||
\(619\) | 19.0637 | 0.766234 | 0.383117 | − | 0.923700i | \(-0.374851\pi\) | ||||
0.383117 | + | 0.923700i | \(0.374851\pi\) | |||||||
\(620\) | −72.3864 | −2.90711 | ||||||||
\(621\) | 11.1960 | 0.449281 | ||||||||
\(622\) | 49.8240 | 1.99776 | ||||||||
\(623\) | 21.4009 | 0.857408 | ||||||||
\(624\) | 26.1218 | 1.04571 | ||||||||
\(625\) | −27.7539 | −1.11016 | ||||||||
\(626\) | −57.5036 | −2.29831 | ||||||||
\(627\) | −0.0222966 | −0.000890439 0 | ||||||||
\(628\) | −13.5569 | −0.540980 | ||||||||
\(629\) | −12.7034 | −0.506518 | ||||||||
\(630\) | 23.1282 | 0.921451 | ||||||||
\(631\) | 36.3233 | 1.44601 | 0.723005 | − | 0.690843i | \(-0.242761\pi\) | ||||
0.723005 | + | 0.690843i | \(0.242761\pi\) | |||||||
\(632\) | −17.8082 | −0.708374 | ||||||||
\(633\) | 2.39165 | 0.0950596 | ||||||||
\(634\) | −45.4867 | −1.80651 | ||||||||
\(635\) | 17.2928 | 0.686243 | ||||||||
\(636\) | 21.3339 | 0.845943 | ||||||||
\(637\) | 23.1096 | 0.915634 | ||||||||
\(638\) | 0.494564 | 0.0195800 | ||||||||
\(639\) | −34.3057 | −1.35711 | ||||||||
\(640\) | −35.1942 | −1.39117 | ||||||||
\(641\) | −23.0023 | −0.908537 | −0.454269 | − | 0.890865i | \(-0.650099\pi\) | ||||
−0.454269 | + | 0.890865i | \(0.650099\pi\) | |||||||
\(642\) | 18.7587 | 0.740346 | ||||||||
\(643\) | 39.3735 | 1.55274 | 0.776369 | − | 0.630279i | \(-0.217059\pi\) | ||||
0.776369 | + | 0.630279i | \(0.217059\pi\) | |||||||
\(644\) | 26.7873 | 1.05557 | ||||||||
\(645\) | −10.8477 | −0.427127 | ||||||||
\(646\) | −10.3158 | −0.405870 | ||||||||
\(647\) | 11.3424 | 0.445915 | 0.222958 | − | 0.974828i | \(-0.428429\pi\) | ||||
0.222958 | + | 0.974828i | \(0.428429\pi\) | |||||||
\(648\) | −57.3657 | −2.25354 | ||||||||
\(649\) | 0.180368 | 0.00708004 | ||||||||
\(650\) | 7.41124 | 0.290693 | ||||||||
\(651\) | 3.88428 | 0.152237 | ||||||||
\(652\) | 105.513 | 4.13222 | ||||||||
\(653\) | 33.8088 | 1.32304 | 0.661519 | − | 0.749928i | \(-0.269912\pi\) | ||||
0.661519 | + | 0.749928i | \(0.269912\pi\) | |||||||
\(654\) | 13.2885 | 0.519620 | ||||||||
\(655\) | 47.5381 | 1.85747 | ||||||||
\(656\) | −14.3849 | −0.561637 | ||||||||
\(657\) | −23.5246 | −0.917781 | ||||||||
\(658\) | −11.9789 | −0.466984 | ||||||||
\(659\) | 38.8880 | 1.51486 | 0.757430 | − | 0.652916i | \(-0.226455\pi\) | ||||
0.757430 | + | 0.652916i | \(0.226455\pi\) | |||||||
\(660\) | −0.132243 | −0.00514754 | ||||||||
\(661\) | 48.7096 | 1.89458 | 0.947292 | − | 0.320371i | \(-0.103808\pi\) | ||||
0.947292 | + | 0.320371i | \(0.103808\pi\) | |||||||
\(662\) | 73.5917 | 2.86022 | ||||||||
\(663\) | 4.09072 | 0.158870 | ||||||||
\(664\) | 76.7665 | 2.97912 | ||||||||
\(665\) | 6.44509 | 0.249930 | ||||||||
\(666\) | −49.6283 | −1.92306 | ||||||||
\(667\) | −33.1419 | −1.28326 | ||||||||
\(668\) | 126.879 | 4.90909 | ||||||||
\(669\) | −5.32238 | −0.205775 | ||||||||
\(670\) | −70.2039 | −2.71221 | ||||||||
\(671\) | 0.173677 | 0.00670473 | ||||||||
\(672\) | 10.0671 | 0.388347 | ||||||||
\(673\) | 11.3809 | 0.438702 | 0.219351 | − | 0.975646i | \(-0.429606\pi\) | ||||
0.219351 | + | 0.975646i | \(0.429606\pi\) | |||||||
\(674\) | −21.5288 | −0.829258 | ||||||||
\(675\) | 1.78841 | 0.0688361 | ||||||||
\(676\) | 32.8326 | 1.26279 | ||||||||
\(677\) | −24.3824 | −0.937093 | −0.468546 | − | 0.883439i | \(-0.655222\pi\) | ||||
−0.468546 | + | 0.883439i | \(0.655222\pi\) | |||||||
\(678\) | −0.389609 | −0.0149628 | ||||||||
\(679\) | −13.5024 | −0.518173 | ||||||||
\(680\) | −37.3156 | −1.43099 | ||||||||
\(681\) | 9.64584 | 0.369630 | ||||||||
\(682\) | 0.350335 | 0.0134150 | ||||||||
\(683\) | 14.6937 | 0.562240 | 0.281120 | − | 0.959673i | \(-0.409294\pi\) | ||||
0.281120 | + | 0.959673i | \(0.409294\pi\) | |||||||
\(684\) | −28.9911 | −1.10850 | ||||||||
\(685\) | 48.1621 | 1.84018 | ||||||||
\(686\) | 43.2951 | 1.65301 | ||||||||
\(687\) | −0.419350 | −0.0159992 | ||||||||
\(688\) | 111.580 | 4.25393 | ||||||||
\(689\) | 37.1875 | 1.41673 | ||||||||
\(690\) | 12.3190 | 0.468976 | ||||||||
\(691\) | 5.65759 | 0.215225 | 0.107612 | − | 0.994193i | \(-0.465679\pi\) | ||||
0.107612 | + | 0.994193i | \(0.465679\pi\) | |||||||
\(692\) | 97.1426 | 3.69281 | ||||||||
\(693\) | −0.0805232 | −0.00305882 | ||||||||
\(694\) | −55.5487 | −2.10860 | ||||||||
\(695\) | −33.1187 | −1.25626 | ||||||||
\(696\) | −34.5626 | −1.31009 | ||||||||
\(697\) | −2.25270 | −0.0853271 | ||||||||
\(698\) | −3.63306 | −0.137513 | ||||||||
\(699\) | −12.7859 | −0.483609 | ||||||||
\(700\) | 4.27891 | 0.161728 | ||||||||
\(701\) | −25.4597 | −0.961600 | −0.480800 | − | 0.876830i | \(-0.659654\pi\) | ||||
−0.480800 | + | 0.876830i | \(0.659654\pi\) | |||||||
\(702\) | 33.3708 | 1.25950 | ||||||||
\(703\) | −13.8298 | −0.521601 | ||||||||
\(704\) | 0.377340 | 0.0142216 | ||||||||
\(705\) | −3.96291 | −0.149252 | ||||||||
\(706\) | −12.7405 | −0.479494 | ||||||||
\(707\) | 12.1488 | 0.456905 | ||||||||
\(708\) | −20.6675 | −0.776734 | ||||||||
\(709\) | 43.0961 | 1.61851 | 0.809254 | − | 0.587459i | \(-0.199872\pi\) | ||||
0.809254 | + | 0.587459i | \(0.199872\pi\) | |||||||
\(710\) | −78.8196 | −2.95805 | ||||||||
\(711\) | −5.88187 | −0.220587 | ||||||||
\(712\) | −134.893 | −5.05533 | ||||||||
\(713\) | −23.4768 | −0.879214 | ||||||||
\(714\) | 3.28314 | 0.122869 | ||||||||
\(715\) | −0.230515 | −0.00862077 | ||||||||
\(716\) | −117.947 | −4.40790 | ||||||||
\(717\) | −2.89775 | −0.108218 | ||||||||
\(718\) | 74.4151 | 2.77715 | ||||||||
\(719\) | −14.5383 | −0.542186 | −0.271093 | − | 0.962553i | \(-0.587385\pi\) | ||||
−0.271093 | + | 0.962553i | \(0.587385\pi\) | |||||||
\(720\) | −78.7025 | −2.93307 | ||||||||
\(721\) | −13.5991 | −0.506457 | ||||||||
\(722\) | 39.4920 | 1.46974 | ||||||||
\(723\) | −7.02058 | −0.261098 | ||||||||
\(724\) | 77.8603 | 2.89366 | ||||||||
\(725\) | −5.29398 | −0.196613 | ||||||||
\(726\) | −14.4742 | −0.537187 | ||||||||
\(727\) | −19.3707 | −0.718420 | −0.359210 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359210 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(728\) | 48.6950 | 1.80476 | ||||||||
\(729\) | −14.7510 | −0.546332 | ||||||||
\(730\) | −54.0493 | −2.00045 | ||||||||
\(731\) | 17.4735 | 0.646282 | ||||||||
\(732\) | −19.9009 | −0.735559 | ||||||||
\(733\) | 11.1626 | 0.412301 | 0.206150 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206150 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(734\) | 20.4991 | 0.756635 | ||||||||
\(735\) | 6.13593 | 0.226327 | ||||||||
\(736\) | −60.8462 | −2.24282 | ||||||||
\(737\) | 0.244422 | 0.00900340 | ||||||||
\(738\) | −8.80062 | −0.323955 | ||||||||
\(739\) | −4.41772 | −0.162509 | −0.0812543 | − | 0.996693i | \(-0.525893\pi\) | ||||
−0.0812543 | + | 0.996693i | \(0.525893\pi\) | |||||||
\(740\) | −82.0257 | −3.01532 | ||||||||
\(741\) | 4.45344 | 0.163601 | ||||||||
\(742\) | 29.8461 | 1.09568 | ||||||||
\(743\) | 30.8234 | 1.13080 | 0.565400 | − | 0.824817i | \(-0.308722\pi\) | ||||
0.565400 | + | 0.824817i | \(0.308722\pi\) | |||||||
\(744\) | −24.4832 | −0.897598 | ||||||||
\(745\) | −37.7925 | −1.38461 | ||||||||
\(746\) | −3.45181 | −0.126380 | ||||||||
\(747\) | 25.3551 | 0.927696 | ||||||||
\(748\) | 0.213017 | 0.00778869 | ||||||||
\(749\) | 18.8787 | 0.689813 | ||||||||
\(750\) | −13.6440 | −0.498209 | ||||||||
\(751\) | 15.9352 | 0.581483 | 0.290742 | − | 0.956802i | \(-0.406098\pi\) | ||||
0.290742 | + | 0.956802i | \(0.406098\pi\) | |||||||
\(752\) | 40.7626 | 1.48646 | ||||||||
\(753\) | 5.40572 | 0.196995 | ||||||||
\(754\) | −98.7825 | −3.59745 | ||||||||
\(755\) | −23.7720 | −0.865153 | ||||||||
\(756\) | 19.2667 | 0.700725 | ||||||||
\(757\) | −30.7460 | −1.11748 | −0.558741 | − | 0.829342i | \(-0.688716\pi\) | ||||
−0.558741 | + | 0.829342i | \(0.688716\pi\) | |||||||
\(758\) | 43.1307 | 1.56658 | ||||||||
\(759\) | −0.0428898 | −0.00155680 | ||||||||
\(760\) | −40.6244 | −1.47360 | ||||||||
\(761\) | 0.105709 | 0.00383195 | 0.00191598 | − | 0.999998i | \(-0.499390\pi\) | ||||
0.00191598 | + | 0.999998i | \(0.499390\pi\) | |||||||
\(762\) | 9.59007 | 0.347412 | ||||||||
\(763\) | 13.3735 | 0.484152 | ||||||||
\(764\) | 61.9765 | 2.24223 | ||||||||
\(765\) | −12.3249 | −0.445609 | ||||||||
\(766\) | −18.4701 | −0.667354 | ||||||||
\(767\) | −36.0260 | −1.30082 | ||||||||
\(768\) | −2.65035 | −0.0956364 | ||||||||
\(769\) | −44.3309 | −1.59861 | −0.799306 | − | 0.600924i | \(-0.794800\pi\) | ||||
−0.799306 | + | 0.600924i | \(0.794800\pi\) | |||||||
\(770\) | −0.185008 | −0.00666721 | ||||||||
\(771\) | −10.5257 | −0.379072 | ||||||||
\(772\) | −64.4599 | −2.31996 | ||||||||
\(773\) | −1.75128 | −0.0629892 | −0.0314946 | − | 0.999504i | \(-0.510027\pi\) | ||||
−0.0314946 | + | 0.999504i | \(0.510027\pi\) | |||||||
\(774\) | 68.2639 | 2.45369 | ||||||||
\(775\) | −3.75011 | −0.134708 | ||||||||
\(776\) | 85.1075 | 3.05518 | ||||||||
\(777\) | 4.40153 | 0.157904 | ||||||||
\(778\) | −74.7811 | −2.68103 | ||||||||
\(779\) | −2.45245 | −0.0878681 | ||||||||
\(780\) | 26.4137 | 0.945762 | ||||||||
\(781\) | 0.274418 | 0.00981946 | ||||||||
\(782\) | −19.8435 | −0.709603 | ||||||||
\(783\) | −23.8373 | −0.851877 | ||||||||
\(784\) | −63.1144 | −2.25409 | ||||||||
\(785\) | −6.27448 | −0.223946 | ||||||||
\(786\) | 26.3633 | 0.940347 | ||||||||
\(787\) | −25.1571 | −0.896754 | −0.448377 | − | 0.893845i | \(-0.647998\pi\) | ||||
−0.448377 | + | 0.893845i | \(0.647998\pi\) | |||||||
\(788\) | 114.361 | 4.07393 | ||||||||
\(789\) | −4.74754 | −0.169017 | ||||||||
\(790\) | −13.5140 | −0.480806 | ||||||||
\(791\) | −0.392102 | −0.0139415 | ||||||||
\(792\) | 0.507550 | 0.0180350 | ||||||||
\(793\) | −34.6897 | −1.23187 | ||||||||
\(794\) | −21.4609 | −0.761620 | ||||||||
\(795\) | 9.87384 | 0.350189 | ||||||||
\(796\) | −34.8404 | −1.23488 | ||||||||
\(797\) | 16.2960 | 0.577235 | 0.288617 | − | 0.957445i | \(-0.406804\pi\) | ||||
0.288617 | + | 0.957445i | \(0.406804\pi\) | |||||||
\(798\) | 3.57426 | 0.126528 | ||||||||
\(799\) | 6.38348 | 0.225831 | ||||||||
\(800\) | −9.71937 | −0.343631 | ||||||||
\(801\) | −44.5537 | −1.57423 | ||||||||
\(802\) | 72.4206 | 2.55726 | ||||||||
\(803\) | 0.188178 | 0.00664065 | ||||||||
\(804\) | −28.0073 | −0.987740 | ||||||||
\(805\) | 12.3978 | 0.436965 | ||||||||
\(806\) | −69.9749 | −2.46476 | ||||||||
\(807\) | 1.04981 | 0.0369552 | ||||||||
\(808\) | −76.5760 | −2.69394 | ||||||||
\(809\) | −21.8305 | −0.767518 | −0.383759 | − | 0.923433i | \(-0.625371\pi\) | ||||
−0.383759 | + | 0.923433i | \(0.625371\pi\) | |||||||
\(810\) | −43.5326 | −1.52958 | ||||||||
\(811\) | −49.5710 | −1.74067 | −0.870337 | − | 0.492456i | \(-0.836099\pi\) | ||||
−0.870337 | + | 0.492456i | \(0.836099\pi\) | |||||||
\(812\) | −57.0325 | −2.00145 | ||||||||
\(813\) | −0.750797 | −0.0263316 | ||||||||
\(814\) | 0.396987 | 0.0139144 | ||||||||
\(815\) | 48.8341 | 1.71058 | ||||||||
\(816\) | −11.1721 | −0.391103 | ||||||||
\(817\) | 19.0229 | 0.665528 | ||||||||
\(818\) | 104.002 | 3.63634 | ||||||||
\(819\) | 16.0834 | 0.562001 | ||||||||
\(820\) | −14.5457 | −0.507956 | ||||||||
\(821\) | −28.7693 | −1.00405 | −0.502027 | − | 0.864852i | \(-0.667412\pi\) | ||||
−0.502027 | + | 0.864852i | \(0.667412\pi\) | |||||||
\(822\) | 26.7093 | 0.931595 | ||||||||
\(823\) | 28.2424 | 0.984468 | 0.492234 | − | 0.870463i | \(-0.336180\pi\) | ||||
0.492234 | + | 0.870463i | \(0.336180\pi\) | |||||||
\(824\) | 85.7171 | 2.98610 | ||||||||
\(825\) | −0.00685107 | −0.000238524 0 | ||||||||
\(826\) | −28.9139 | −1.00604 | ||||||||
\(827\) | −22.4252 | −0.779801 | −0.389901 | − | 0.920857i | \(-0.627491\pi\) | ||||
−0.389901 | + | 0.920857i | \(0.627491\pi\) | |||||||
\(828\) | −55.7674 | −1.93805 | ||||||||
\(829\) | −44.5840 | −1.54847 | −0.774233 | − | 0.632901i | \(-0.781864\pi\) | ||||
−0.774233 | + | 0.632901i | \(0.781864\pi\) | |||||||
\(830\) | 58.2551 | 2.02206 | ||||||||
\(831\) | 5.73062 | 0.198793 | ||||||||
\(832\) | −75.3687 | −2.61294 | ||||||||
\(833\) | −9.88381 | −0.342454 | ||||||||
\(834\) | −18.3667 | −0.635986 | ||||||||
\(835\) | 58.7226 | 2.03218 | ||||||||
\(836\) | 0.231906 | 0.00802063 | ||||||||
\(837\) | −16.8857 | −0.583656 | ||||||||
\(838\) | 1.56270 | 0.0539826 | ||||||||
\(839\) | −8.59628 | −0.296777 | −0.148388 | − | 0.988929i | \(-0.547409\pi\) | ||||
−0.148388 | + | 0.988929i | \(0.547409\pi\) | |||||||
\(840\) | 12.9293 | 0.446102 | ||||||||
\(841\) | 41.5621 | 1.43318 | ||||||||
\(842\) | −36.8854 | −1.27116 | ||||||||
\(843\) | 12.0814 | 0.416105 | ||||||||
\(844\) | −24.8755 | −0.856249 | ||||||||
\(845\) | 15.1957 | 0.522749 | ||||||||
\(846\) | 24.9383 | 0.857397 | ||||||||
\(847\) | −14.5668 | −0.500521 | ||||||||
\(848\) | −101.563 | −3.48767 | ||||||||
\(849\) | 3.20848 | 0.110115 | ||||||||
\(850\) | −3.16974 | −0.108721 | ||||||||
\(851\) | −26.6031 | −0.911942 | ||||||||
\(852\) | −31.4444 | −1.07727 | ||||||||
\(853\) | 3.97518 | 0.136108 | 0.0680538 | − | 0.997682i | \(-0.478321\pi\) | ||||
0.0680538 | + | 0.997682i | \(0.478321\pi\) | |||||||
\(854\) | −27.8414 | −0.952712 | ||||||||
\(855\) | −13.4178 | −0.458879 | ||||||||
\(856\) | −118.995 | −4.06717 | ||||||||
\(857\) | −35.9946 | −1.22955 | −0.614776 | − | 0.788701i | \(-0.710754\pi\) | ||||
−0.614776 | + | 0.788701i | \(0.710754\pi\) | |||||||
\(858\) | −0.127837 | −0.00436428 | ||||||||
\(859\) | −40.1751 | −1.37076 | −0.685379 | − | 0.728186i | \(-0.740363\pi\) | ||||
−0.685379 | + | 0.728186i | \(0.740363\pi\) | |||||||
\(860\) | 112.826 | 3.84735 | ||||||||
\(861\) | 0.780525 | 0.0266002 | ||||||||
\(862\) | 16.5727 | 0.564470 | ||||||||
\(863\) | −22.6578 | −0.771282 | −0.385641 | − | 0.922649i | \(-0.626020\pi\) | ||||
−0.385641 | + | 0.922649i | \(0.626020\pi\) | |||||||
\(864\) | −43.7636 | −1.48887 | ||||||||
\(865\) | 44.9600 | 1.52868 | ||||||||
\(866\) | 83.8258 | 2.84852 | ||||||||
\(867\) | 6.63000 | 0.225167 | ||||||||
\(868\) | −40.4003 | −1.37127 | ||||||||
\(869\) | 0.0470503 | 0.00159607 | ||||||||
\(870\) | −26.2282 | −0.889220 | ||||||||
\(871\) | −48.8200 | −1.65420 | ||||||||
\(872\) | −84.2950 | −2.85459 | ||||||||
\(873\) | 28.1101 | 0.951382 | ||||||||
\(874\) | −21.6031 | −0.730734 | ||||||||
\(875\) | −13.7313 | −0.464203 | ||||||||
\(876\) | −21.5625 | −0.728529 | ||||||||
\(877\) | 12.1004 | 0.408602 | 0.204301 | − | 0.978908i | \(-0.434508\pi\) | ||||
0.204301 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(878\) | −62.5472 | −2.11087 | ||||||||
\(879\) | −5.63037 | −0.189908 | ||||||||
\(880\) | 0.629558 | 0.0212224 | ||||||||
\(881\) | −14.9641 | −0.504153 | −0.252077 | − | 0.967707i | \(-0.581113\pi\) | ||||
−0.252077 | + | 0.967707i | \(0.581113\pi\) | |||||||
\(882\) | −38.6131 | −1.30017 | ||||||||
\(883\) | 4.27924 | 0.144008 | 0.0720039 | − | 0.997404i | \(-0.477061\pi\) | ||||
0.0720039 | + | 0.997404i | \(0.477061\pi\) | |||||||
\(884\) | −42.5474 | −1.43102 | ||||||||
\(885\) | −9.56544 | −0.321539 | ||||||||
\(886\) | 48.3419 | 1.62408 | ||||||||
\(887\) | 14.5774 | 0.489462 | 0.244731 | − | 0.969591i | \(-0.421300\pi\) | ||||
0.244731 | + | 0.969591i | \(0.421300\pi\) | |||||||
\(888\) | −27.7435 | −0.931010 | ||||||||
\(889\) | 9.65143 | 0.323699 | ||||||||
\(890\) | −102.365 | −3.43129 | ||||||||
\(891\) | 0.151563 | 0.00507755 | ||||||||
\(892\) | 55.3578 | 1.85352 | ||||||||
\(893\) | 6.94951 | 0.232556 | ||||||||
\(894\) | −20.9587 | −0.700962 | ||||||||
\(895\) | −54.5889 | −1.82471 | ||||||||
\(896\) | −19.6426 | −0.656213 | ||||||||
\(897\) | 8.56666 | 0.286032 | ||||||||
\(898\) | 13.8409 | 0.461878 | ||||||||
\(899\) | 49.9843 | 1.66707 | ||||||||
\(900\) | −8.90810 | −0.296937 | ||||||||
\(901\) | −15.9049 | −0.529868 | ||||||||
\(902\) | 0.0703980 | 0.00234400 | ||||||||
\(903\) | −6.05431 | −0.201475 | ||||||||
\(904\) | 2.47148 | 0.0822001 | ||||||||
\(905\) | 36.0357 | 1.19787 | ||||||||
\(906\) | −13.1833 | −0.437986 | ||||||||
\(907\) | 4.14976 | 0.137791 | 0.0688953 | − | 0.997624i | \(-0.478053\pi\) | ||||
0.0688953 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(908\) | −100.326 | −3.32944 | ||||||||
\(909\) | −25.2922 | −0.838890 | ||||||||
\(910\) | 36.9528 | 1.22497 | ||||||||
\(911\) | 16.3301 | 0.541041 | 0.270520 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270520 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(912\) | −12.1628 | −0.402750 | ||||||||
\(913\) | −0.202821 | −0.00671239 | ||||||||
\(914\) | −89.7133 | −2.96745 | ||||||||
\(915\) | −9.21063 | −0.304494 | ||||||||
\(916\) | 4.36165 | 0.144113 | ||||||||
\(917\) | 26.5319 | 0.876162 | ||||||||
\(918\) | −14.2725 | −0.471061 | ||||||||
\(919\) | 25.3757 | 0.837067 | 0.418533 | − | 0.908201i | \(-0.362544\pi\) | ||||
0.418533 | + | 0.908201i | \(0.362544\pi\) | |||||||
\(920\) | −78.1452 | −2.57637 | ||||||||
\(921\) | 1.80571 | 0.0595001 | ||||||||
\(922\) | −26.8883 | −0.885520 | ||||||||
\(923\) | −54.8114 | −1.80414 | ||||||||
\(924\) | −0.0738072 | −0.00242808 | ||||||||
\(925\) | −4.24949 | −0.139722 | ||||||||
\(926\) | 7.01891 | 0.230656 | ||||||||
\(927\) | 28.3114 | 0.929870 | ||||||||
\(928\) | 129.547 | 4.25259 | ||||||||
\(929\) | 30.1512 | 0.989228 | 0.494614 | − | 0.869113i | \(-0.335309\pi\) | ||||
0.494614 | + | 0.869113i | \(0.335309\pi\) | |||||||
\(930\) | −18.5794 | −0.609241 | ||||||||
\(931\) | −10.7602 | −0.352652 | ||||||||
\(932\) | 132.986 | 4.35611 | ||||||||
\(933\) | 9.19949 | 0.301178 | ||||||||
\(934\) | 56.5129 | 1.84916 | ||||||||
\(935\) | 0.0985897 | 0.00322423 | ||||||||
\(936\) | −101.376 | −3.31359 | ||||||||
\(937\) | 7.63452 | 0.249409 | 0.124704 | − | 0.992194i | \(-0.460202\pi\) | ||||
0.124704 | + | 0.992194i | \(0.460202\pi\) | |||||||
\(938\) | −39.1822 | −1.27934 | ||||||||
\(939\) | −10.6175 | −0.346488 | ||||||||
\(940\) | 41.2180 | 1.34438 | ||||||||
\(941\) | 35.0964 | 1.14411 | 0.572055 | − | 0.820215i | \(-0.306146\pi\) | ||||
0.572055 | + | 0.820215i | \(0.306146\pi\) | |||||||
\(942\) | −3.47964 | −0.113373 | ||||||||
\(943\) | −4.71754 | −0.153624 | ||||||||
\(944\) | 98.3904 | 3.20234 | ||||||||
\(945\) | 8.91712 | 0.290074 | ||||||||
\(946\) | −0.546057 | −0.0177538 | ||||||||
\(947\) | −7.54860 | −0.245297 | −0.122648 | − | 0.992450i | \(-0.539139\pi\) | ||||
−0.122648 | + | 0.992450i | \(0.539139\pi\) | |||||||
\(948\) | −5.39129 | −0.175101 | ||||||||
\(949\) | −37.5860 | −1.22009 | ||||||||
\(950\) | −3.45080 | −0.111959 | ||||||||
\(951\) | −8.39867 | −0.272345 | ||||||||
\(952\) | −20.8266 | −0.674993 | ||||||||
\(953\) | 43.1692 | 1.39839 | 0.699194 | − | 0.714932i | \(-0.253542\pi\) | ||||
0.699194 | + | 0.714932i | \(0.253542\pi\) | |||||||
\(954\) | −62.1355 | −2.01171 | ||||||||
\(955\) | 28.6842 | 0.928200 | ||||||||
\(956\) | 30.1394 | 0.974776 | ||||||||
\(957\) | 0.0913162 | 0.00295183 | ||||||||
\(958\) | −59.5989 | −1.92555 | ||||||||
\(959\) | 26.8802 | 0.868007 | ||||||||
\(960\) | −20.0115 | −0.645869 | ||||||||
\(961\) | 4.40752 | 0.142178 | ||||||||
\(962\) | −79.2929 | −2.55651 | ||||||||
\(963\) | −39.3028 | −1.26652 | ||||||||
\(964\) | 73.0208 | 2.35184 | ||||||||
\(965\) | −29.8336 | −0.960378 | ||||||||
\(966\) | 6.87547 | 0.221214 | ||||||||
\(967\) | −53.3958 | −1.71709 | −0.858547 | − | 0.512735i | \(-0.828632\pi\) | ||||
−0.858547 | + | 0.512735i | \(0.828632\pi\) | |||||||
\(968\) | 91.8166 | 2.95110 | ||||||||
\(969\) | −1.90471 | −0.0611881 | ||||||||
\(970\) | 64.5848 | 2.07369 | ||||||||
\(971\) | −59.1605 | −1.89855 | −0.949276 | − | 0.314445i | \(-0.898182\pi\) | ||||
−0.949276 | + | 0.314445i | \(0.898182\pi\) | |||||||
\(972\) | −61.0125 | −1.95698 | ||||||||
\(973\) | −18.4842 | −0.592576 | ||||||||
\(974\) | 33.0953 | 1.06044 | ||||||||
\(975\) | 1.36841 | 0.0438242 | ||||||||
\(976\) | 94.7407 | 3.03258 | ||||||||
\(977\) | 54.9861 | 1.75916 | 0.879580 | − | 0.475750i | \(-0.157823\pi\) | ||||
0.879580 | + | 0.475750i | \(0.157823\pi\) | |||||||
\(978\) | 27.0820 | 0.865987 | ||||||||
\(979\) | 0.356394 | 0.0113904 | ||||||||
\(980\) | −63.8196 | −2.03864 | ||||||||
\(981\) | −27.8417 | −0.888918 | ||||||||
\(982\) | −57.7909 | −1.84418 | ||||||||
\(983\) | 8.21767 | 0.262103 | 0.131051 | − | 0.991376i | \(-0.458165\pi\) | ||||
0.131051 | + | 0.991376i | \(0.458165\pi\) | |||||||
\(984\) | −4.91977 | −0.156836 | ||||||||
\(985\) | 52.9290 | 1.68646 | ||||||||
\(986\) | 42.2486 | 1.34547 | ||||||||
\(987\) | −2.21178 | −0.0704016 | ||||||||
\(988\) | −46.3201 | −1.47364 | ||||||||
\(989\) | 36.5926 | 1.16358 | ||||||||
\(990\) | 0.385160 | 0.0122412 | ||||||||
\(991\) | −11.8354 | −0.375964 | −0.187982 | − | 0.982173i | \(-0.560195\pi\) | ||||
−0.187982 | + | 0.982173i | \(0.560195\pi\) | |||||||
\(992\) | 91.7676 | 2.91362 | ||||||||
\(993\) | 13.5880 | 0.431201 | ||||||||
\(994\) | −43.9908 | −1.39530 | ||||||||
\(995\) | −16.1250 | −0.511196 | ||||||||
\(996\) | 23.2404 | 0.736400 | ||||||||
\(997\) | 21.6250 | 0.684872 | 0.342436 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342436 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(998\) | −97.0539 | −3.07219 | ||||||||
\(999\) | −19.1343 | −0.605382 |
(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 | 4027.2.a.c.1.4 | ✓ | 174 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.c.1.4 | ✓ | 174 | 1.1 | even | 1 | trivial |