Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, 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("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.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: | \(64.1837531447\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.41917 | −1.39671 | −0.698354 | − | 0.715752i | \(-0.746084\pi\) | ||||
−0.698354 | + | 0.715752i | \(0.746084\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.79360 | 1.24933 | 0.624667 | − | 0.780891i | \(-0.285235\pi\) | ||||
0.624667 | + | 0.780891i | \(0.285235\pi\) | |||||||
\(6\) | −2.41917 | −0.987622 | ||||||||
\(7\) | 0.842715 | 0.318516 | 0.159258 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159258 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.85238 | 0.950794 | ||||||||
\(10\) | 2.79360 | 0.883412 | ||||||||
\(11\) | −3.67980 | −1.10950 | −0.554751 | − | 0.832016i | \(-0.687187\pi\) | ||||
−0.554751 | + | 0.832016i | \(0.687187\pi\) | |||||||
\(12\) | −2.41917 | −0.698354 | ||||||||
\(13\) | −1.86090 | −0.516121 | −0.258060 | − | 0.966129i | \(-0.583083\pi\) | ||||
−0.258060 | + | 0.966129i | \(0.583083\pi\) | |||||||
\(14\) | 0.842715 | 0.225225 | ||||||||
\(15\) | −6.75818 | −1.74496 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.11357 | 1.24022 | 0.620111 | − | 0.784514i | \(-0.287087\pi\) | ||||
0.620111 | + | 0.784514i | \(0.287087\pi\) | |||||||
\(18\) | 2.85238 | 0.672313 | ||||||||
\(19\) | 6.79587 | 1.55908 | 0.779540 | − | 0.626352i | \(-0.215453\pi\) | ||||
0.779540 | + | 0.626352i | \(0.215453\pi\) | |||||||
\(20\) | 2.79360 | 0.624667 | ||||||||
\(21\) | −2.03867 | −0.444874 | ||||||||
\(22\) | −3.67980 | −0.784537 | ||||||||
\(23\) | 8.42119 | 1.75594 | 0.877970 | − | 0.478716i | \(-0.158898\pi\) | ||||
0.877970 | + | 0.478716i | \(0.158898\pi\) | |||||||
\(24\) | −2.41917 | −0.493811 | ||||||||
\(25\) | 2.80418 | 0.560835 | ||||||||
\(26\) | −1.86090 | −0.364952 | ||||||||
\(27\) | 0.357110 | 0.0687258 | ||||||||
\(28\) | 0.842715 | 0.159258 | ||||||||
\(29\) | 3.74696 | 0.695792 | 0.347896 | − | 0.937533i | \(-0.386896\pi\) | ||||
0.347896 | + | 0.937533i | \(0.386896\pi\) | |||||||
\(30\) | −6.75818 | −1.23387 | ||||||||
\(31\) | −3.61114 | −0.648579 | −0.324290 | − | 0.945958i | \(-0.605125\pi\) | ||||
−0.324290 | + | 0.945958i | \(0.605125\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.90207 | 1.54965 | ||||||||
\(34\) | 5.11357 | 0.876970 | ||||||||
\(35\) | 2.35420 | 0.397933 | ||||||||
\(36\) | 2.85238 | 0.475397 | ||||||||
\(37\) | −9.86990 | −1.62260 | −0.811301 | − | 0.584629i | \(-0.801240\pi\) | ||||
−0.811301 | + | 0.584629i | \(0.801240\pi\) | |||||||
\(38\) | 6.79587 | 1.10244 | ||||||||
\(39\) | 4.50183 | 0.720870 | ||||||||
\(40\) | 2.79360 | 0.441706 | ||||||||
\(41\) | 1.78244 | 0.278370 | 0.139185 | − | 0.990266i | \(-0.455552\pi\) | ||||
0.139185 | + | 0.990266i | \(0.455552\pi\) | |||||||
\(42\) | −2.03867 | −0.314574 | ||||||||
\(43\) | −4.12943 | −0.629732 | −0.314866 | − | 0.949136i | \(-0.601960\pi\) | ||||
−0.314866 | + | 0.949136i | \(0.601960\pi\) | |||||||
\(44\) | −3.67980 | −0.554751 | ||||||||
\(45\) | 7.96841 | 1.18786 | ||||||||
\(46\) | 8.42119 | 1.24164 | ||||||||
\(47\) | 0.876797 | 0.127894 | 0.0639470 | − | 0.997953i | \(-0.479631\pi\) | ||||
0.0639470 | + | 0.997953i | \(0.479631\pi\) | |||||||
\(48\) | −2.41917 | −0.349177 | ||||||||
\(49\) | −6.28983 | −0.898547 | ||||||||
\(50\) | 2.80418 | 0.396570 | ||||||||
\(51\) | −12.3706 | −1.73223 | ||||||||
\(52\) | −1.86090 | −0.258060 | ||||||||
\(53\) | −4.42347 | −0.607611 | −0.303805 | − | 0.952734i | \(-0.598257\pi\) | ||||
−0.303805 | + | 0.952734i | \(0.598257\pi\) | |||||||
\(54\) | 0.357110 | 0.0485965 | ||||||||
\(55\) | −10.2799 | −1.38614 | ||||||||
\(56\) | 0.842715 | 0.112613 | ||||||||
\(57\) | −16.4404 | −2.17758 | ||||||||
\(58\) | 3.74696 | 0.491999 | ||||||||
\(59\) | 6.65122 | 0.865915 | 0.432957 | − | 0.901414i | \(-0.357470\pi\) | ||||
0.432957 | + | 0.901414i | \(0.357470\pi\) | |||||||
\(60\) | −6.75818 | −0.872478 | ||||||||
\(61\) | −5.63927 | −0.722034 | −0.361017 | − | 0.932559i | \(-0.617570\pi\) | ||||
−0.361017 | + | 0.932559i | \(0.617570\pi\) | |||||||
\(62\) | −3.61114 | −0.458615 | ||||||||
\(63\) | 2.40375 | 0.302844 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.19860 | −0.644807 | ||||||||
\(66\) | 8.90207 | 1.09577 | ||||||||
\(67\) | 12.9969 | 1.58782 | 0.793912 | − | 0.608033i | \(-0.208041\pi\) | ||||
0.793912 | + | 0.608033i | \(0.208041\pi\) | |||||||
\(68\) | 5.11357 | 0.620111 | ||||||||
\(69\) | −20.3723 | −2.45254 | ||||||||
\(70\) | 2.35420 | 0.281381 | ||||||||
\(71\) | 4.51649 | 0.536008 | 0.268004 | − | 0.963418i | \(-0.413636\pi\) | ||||
0.268004 | + | 0.963418i | \(0.413636\pi\) | |||||||
\(72\) | 2.85238 | 0.336157 | ||||||||
\(73\) | 10.9440 | 1.28090 | 0.640451 | − | 0.767999i | \(-0.278748\pi\) | ||||
0.640451 | + | 0.767999i | \(0.278748\pi\) | |||||||
\(74\) | −9.86990 | −1.14735 | ||||||||
\(75\) | −6.78378 | −0.783323 | ||||||||
\(76\) | 6.79587 | 0.779540 | ||||||||
\(77\) | −3.10103 | −0.353395 | ||||||||
\(78\) | 4.50183 | 0.509732 | ||||||||
\(79\) | 9.36761 | 1.05394 | 0.526969 | − | 0.849884i | \(-0.323328\pi\) | ||||
0.526969 | + | 0.849884i | \(0.323328\pi\) | |||||||
\(80\) | 2.79360 | 0.312333 | ||||||||
\(81\) | −9.42106 | −1.04678 | ||||||||
\(82\) | 1.78244 | 0.196837 | ||||||||
\(83\) | −5.58958 | −0.613536 | −0.306768 | − | 0.951784i | \(-0.599248\pi\) | ||||
−0.306768 | + | 0.951784i | \(0.599248\pi\) | |||||||
\(84\) | −2.03867 | −0.222437 | ||||||||
\(85\) | 14.2852 | 1.54945 | ||||||||
\(86\) | −4.12943 | −0.445288 | ||||||||
\(87\) | −9.06452 | −0.971819 | ||||||||
\(88\) | −3.67980 | −0.392268 | ||||||||
\(89\) | −10.2932 | −1.09108 | −0.545539 | − | 0.838085i | \(-0.683675\pi\) | ||||
−0.545539 | + | 0.838085i | \(0.683675\pi\) | |||||||
\(90\) | 7.96841 | 0.839944 | ||||||||
\(91\) | −1.56821 | −0.164393 | ||||||||
\(92\) | 8.42119 | 0.877970 | ||||||||
\(93\) | 8.73595 | 0.905876 | ||||||||
\(94\) | 0.876797 | 0.0904347 | ||||||||
\(95\) | 18.9849 | 1.94781 | ||||||||
\(96\) | −2.41917 | −0.246906 | ||||||||
\(97\) | 4.84073 | 0.491501 | 0.245751 | − | 0.969333i | \(-0.420966\pi\) | ||||
0.245751 | + | 0.969333i | \(0.420966\pi\) | |||||||
\(98\) | −6.28983 | −0.635369 | ||||||||
\(99\) | −10.4962 | −1.05491 | ||||||||
\(100\) | 2.80418 | 0.280418 | ||||||||
\(101\) | 6.86476 | 0.683069 | 0.341535 | − | 0.939869i | \(-0.389053\pi\) | ||||
0.341535 | + | 0.939869i | \(0.389053\pi\) | |||||||
\(102\) | −12.3706 | −1.22487 | ||||||||
\(103\) | −6.85383 | −0.675328 | −0.337664 | − | 0.941267i | \(-0.609637\pi\) | ||||
−0.337664 | + | 0.941267i | \(0.609637\pi\) | |||||||
\(104\) | −1.86090 | −0.182476 | ||||||||
\(105\) | −5.69522 | −0.555797 | ||||||||
\(106\) | −4.42347 | −0.429646 | ||||||||
\(107\) | 3.28550 | 0.317622 | 0.158811 | − | 0.987309i | \(-0.449234\pi\) | ||||
0.158811 | + | 0.987309i | \(0.449234\pi\) | |||||||
\(108\) | 0.357110 | 0.0343629 | ||||||||
\(109\) | 19.2307 | 1.84197 | 0.920985 | − | 0.389597i | \(-0.127386\pi\) | ||||
0.920985 | + | 0.389597i | \(0.127386\pi\) | |||||||
\(110\) | −10.2799 | −0.980149 | ||||||||
\(111\) | 23.8770 | 2.26630 | ||||||||
\(112\) | 0.842715 | 0.0796291 | ||||||||
\(113\) | −9.87276 | −0.928751 | −0.464375 | − | 0.885638i | \(-0.653721\pi\) | ||||
−0.464375 | + | 0.885638i | \(0.653721\pi\) | |||||||
\(114\) | −16.4404 | −1.53978 | ||||||||
\(115\) | 23.5254 | 2.19376 | ||||||||
\(116\) | 3.74696 | 0.347896 | ||||||||
\(117\) | −5.30800 | −0.490725 | ||||||||
\(118\) | 6.65122 | 0.612294 | ||||||||
\(119\) | 4.30928 | 0.395031 | ||||||||
\(120\) | −6.75818 | −0.616935 | ||||||||
\(121\) | 2.54096 | 0.230996 | ||||||||
\(122\) | −5.63927 | −0.510555 | ||||||||
\(123\) | −4.31201 | −0.388801 | ||||||||
\(124\) | −3.61114 | −0.324290 | ||||||||
\(125\) | −6.13425 | −0.548664 | ||||||||
\(126\) | 2.40375 | 0.214143 | ||||||||
\(127\) | 13.2507 | 1.17581 | 0.587903 | − | 0.808932i | \(-0.299954\pi\) | ||||
0.587903 | + | 0.808932i | \(0.299954\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.98978 | 0.879551 | ||||||||
\(130\) | −5.19860 | −0.455947 | ||||||||
\(131\) | −19.2692 | −1.68355 | −0.841777 | − | 0.539826i | \(-0.818490\pi\) | ||||
−0.841777 | + | 0.539826i | \(0.818490\pi\) | |||||||
\(132\) | 8.90207 | 0.774826 | ||||||||
\(133\) | 5.72699 | 0.496593 | ||||||||
\(134\) | 12.9969 | 1.12276 | ||||||||
\(135\) | 0.997620 | 0.0858615 | ||||||||
\(136\) | 5.11357 | 0.438485 | ||||||||
\(137\) | 9.03398 | 0.771825 | 0.385912 | − | 0.922535i | \(-0.373887\pi\) | ||||
0.385912 | + | 0.922535i | \(0.373887\pi\) | |||||||
\(138\) | −20.3723 | −1.73420 | ||||||||
\(139\) | 20.5078 | 1.73945 | 0.869724 | − | 0.493538i | \(-0.164297\pi\) | ||||
0.869724 | + | 0.493538i | \(0.164297\pi\) | |||||||
\(140\) | 2.35420 | 0.198967 | ||||||||
\(141\) | −2.12112 | −0.178631 | ||||||||
\(142\) | 4.51649 | 0.379015 | ||||||||
\(143\) | 6.84774 | 0.572637 | ||||||||
\(144\) | 2.85238 | 0.237699 | ||||||||
\(145\) | 10.4675 | 0.869277 | ||||||||
\(146\) | 10.9440 | 0.905734 | ||||||||
\(147\) | 15.2162 | 1.25501 | ||||||||
\(148\) | −9.86990 | −0.811301 | ||||||||
\(149\) | −8.54883 | −0.700348 | −0.350174 | − | 0.936685i | \(-0.613878\pi\) | ||||
−0.350174 | + | 0.936685i | \(0.613878\pi\) | |||||||
\(150\) | −6.78378 | −0.553893 | ||||||||
\(151\) | 8.98631 | 0.731296 | 0.365648 | − | 0.930753i | \(-0.380847\pi\) | ||||
0.365648 | + | 0.930753i | \(0.380847\pi\) | |||||||
\(152\) | 6.79587 | 0.551218 | ||||||||
\(153\) | 14.5859 | 1.17920 | ||||||||
\(154\) | −3.10103 | −0.249888 | ||||||||
\(155\) | −10.0881 | −0.810292 | ||||||||
\(156\) | 4.50183 | 0.360435 | ||||||||
\(157\) | −22.7106 | −1.81250 | −0.906250 | − | 0.422742i | \(-0.861068\pi\) | ||||
−0.906250 | + | 0.422742i | \(0.861068\pi\) | |||||||
\(158\) | 9.36761 | 0.745247 | ||||||||
\(159\) | 10.7011 | 0.848655 | ||||||||
\(160\) | 2.79360 | 0.220853 | ||||||||
\(161\) | 7.09666 | 0.559295 | ||||||||
\(162\) | −9.42106 | −0.740188 | ||||||||
\(163\) | 8.96046 | 0.701837 | 0.350919 | − | 0.936406i | \(-0.385869\pi\) | ||||
0.350919 | + | 0.936406i | \(0.385869\pi\) | |||||||
\(164\) | 1.78244 | 0.139185 | ||||||||
\(165\) | 24.8688 | 1.93603 | ||||||||
\(166\) | −5.58958 | −0.433835 | ||||||||
\(167\) | −16.9775 | −1.31376 | −0.656879 | − | 0.753996i | \(-0.728124\pi\) | ||||
−0.656879 | + | 0.753996i | \(0.728124\pi\) | |||||||
\(168\) | −2.03867 | −0.157287 | ||||||||
\(169\) | −9.53705 | −0.733620 | ||||||||
\(170\) | 14.2852 | 1.09563 | ||||||||
\(171\) | 19.3844 | 1.48237 | ||||||||
\(172\) | −4.12943 | −0.314866 | ||||||||
\(173\) | 5.08477 | 0.386588 | 0.193294 | − | 0.981141i | \(-0.438083\pi\) | ||||
0.193294 | + | 0.981141i | \(0.438083\pi\) | |||||||
\(174\) | −9.06452 | −0.687180 | ||||||||
\(175\) | 2.36312 | 0.178635 | ||||||||
\(176\) | −3.67980 | −0.277376 | ||||||||
\(177\) | −16.0904 | −1.20943 | ||||||||
\(178\) | −10.2932 | −0.771509 | ||||||||
\(179\) | 11.0419 | 0.825314 | 0.412657 | − | 0.910886i | \(-0.364601\pi\) | ||||
0.412657 | + | 0.910886i | \(0.364601\pi\) | |||||||
\(180\) | 7.96841 | 0.593930 | ||||||||
\(181\) | −1.93916 | −0.144136 | −0.0720682 | − | 0.997400i | \(-0.522960\pi\) | ||||
−0.0720682 | + | 0.997400i | \(0.522960\pi\) | |||||||
\(182\) | −1.56821 | −0.116243 | ||||||||
\(183\) | 13.6423 | 1.00847 | ||||||||
\(184\) | 8.42119 | 0.620818 | ||||||||
\(185\) | −27.5725 | −2.02717 | ||||||||
\(186\) | 8.73595 | 0.640551 | ||||||||
\(187\) | −18.8169 | −1.37603 | ||||||||
\(188\) | 0.876797 | 0.0639470 | ||||||||
\(189\) | 0.300942 | 0.0218903 | ||||||||
\(190\) | 18.9849 | 1.37731 | ||||||||
\(191\) | −11.4895 | −0.831352 | −0.415676 | − | 0.909513i | \(-0.636455\pi\) | ||||
−0.415676 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(192\) | −2.41917 | −0.174589 | ||||||||
\(193\) | 10.9398 | 0.787464 | 0.393732 | − | 0.919225i | \(-0.371184\pi\) | ||||
0.393732 | + | 0.919225i | \(0.371184\pi\) | |||||||
\(194\) | 4.84073 | 0.347544 | ||||||||
\(195\) | 12.5763 | 0.900607 | ||||||||
\(196\) | −6.28983 | −0.449274 | ||||||||
\(197\) | −8.25382 | −0.588060 | −0.294030 | − | 0.955796i | \(-0.594997\pi\) | ||||
−0.294030 | + | 0.955796i | \(0.594997\pi\) | |||||||
\(198\) | −10.4962 | −0.745933 | ||||||||
\(199\) | 18.6100 | 1.31923 | 0.659614 | − | 0.751604i | \(-0.270720\pi\) | ||||
0.659614 | + | 0.751604i | \(0.270720\pi\) | |||||||
\(200\) | 2.80418 | 0.198285 | ||||||||
\(201\) | −31.4417 | −2.21773 | ||||||||
\(202\) | 6.86476 | 0.483003 | ||||||||
\(203\) | 3.15762 | 0.221621 | ||||||||
\(204\) | −12.3706 | −0.866115 | ||||||||
\(205\) | 4.97940 | 0.347777 | ||||||||
\(206\) | −6.85383 | −0.477529 | ||||||||
\(207\) | 24.0205 | 1.66954 | ||||||||
\(208\) | −1.86090 | −0.129030 | ||||||||
\(209\) | −25.0075 | −1.72980 | ||||||||
\(210\) | −5.69522 | −0.393008 | ||||||||
\(211\) | −9.86959 | −0.679451 | −0.339725 | − | 0.940525i | \(-0.610334\pi\) | ||||
−0.339725 | + | 0.940525i | \(0.610334\pi\) | |||||||
\(212\) | −4.42347 | −0.303805 | ||||||||
\(213\) | −10.9261 | −0.748647 | ||||||||
\(214\) | 3.28550 | 0.224592 | ||||||||
\(215\) | −11.5359 | −0.786745 | ||||||||
\(216\) | 0.357110 | 0.0242982 | ||||||||
\(217\) | −3.04316 | −0.206583 | ||||||||
\(218\) | 19.2307 | 1.30247 | ||||||||
\(219\) | −26.4755 | −1.78905 | ||||||||
\(220\) | −10.2799 | −0.693070 | ||||||||
\(221\) | −9.51583 | −0.640104 | ||||||||
\(222\) | 23.8770 | 1.60252 | ||||||||
\(223\) | 6.05175 | 0.405255 | 0.202627 | − | 0.979256i | \(-0.435052\pi\) | ||||
0.202627 | + | 0.979256i | \(0.435052\pi\) | |||||||
\(224\) | 0.842715 | 0.0563063 | ||||||||
\(225\) | 7.99858 | 0.533239 | ||||||||
\(226\) | −9.87276 | −0.656726 | ||||||||
\(227\) | −13.2276 | −0.877950 | −0.438975 | − | 0.898499i | \(-0.644658\pi\) | ||||
−0.438975 | + | 0.898499i | \(0.644658\pi\) | |||||||
\(228\) | −16.4404 | −1.08879 | ||||||||
\(229\) | 16.1571 | 1.06769 | 0.533845 | − | 0.845582i | \(-0.320747\pi\) | ||||
0.533845 | + | 0.845582i | \(0.320747\pi\) | |||||||
\(230\) | 23.5254 | 1.55122 | ||||||||
\(231\) | 7.50191 | 0.493589 | ||||||||
\(232\) | 3.74696 | 0.246000 | ||||||||
\(233\) | 10.0916 | 0.661125 | 0.330563 | − | 0.943784i | \(-0.392762\pi\) | ||||
0.330563 | + | 0.943784i | \(0.392762\pi\) | |||||||
\(234\) | −5.30800 | −0.346995 | ||||||||
\(235\) | 2.44942 | 0.159782 | ||||||||
\(236\) | 6.65122 | 0.432957 | ||||||||
\(237\) | −22.6618 | −1.47204 | ||||||||
\(238\) | 4.30928 | 0.279329 | ||||||||
\(239\) | 22.6209 | 1.46323 | 0.731613 | − | 0.681720i | \(-0.238768\pi\) | ||||
0.731613 | + | 0.681720i | \(0.238768\pi\) | |||||||
\(240\) | −6.75818 | −0.436239 | ||||||||
\(241\) | 17.0708 | 1.09962 | 0.549812 | − | 0.835288i | \(-0.314699\pi\) | ||||
0.549812 | + | 0.835288i | \(0.314699\pi\) | |||||||
\(242\) | 2.54096 | 0.163339 | ||||||||
\(243\) | 21.7198 | 1.39333 | ||||||||
\(244\) | −5.63927 | −0.361017 | ||||||||
\(245\) | −17.5712 | −1.12259 | ||||||||
\(246\) | −4.31201 | −0.274924 | ||||||||
\(247\) | −12.6464 | −0.804674 | ||||||||
\(248\) | −3.61114 | −0.229307 | ||||||||
\(249\) | 13.5221 | 0.856931 | ||||||||
\(250\) | −6.13425 | −0.387964 | ||||||||
\(251\) | −5.94256 | −0.375091 | −0.187546 | − | 0.982256i | \(-0.560053\pi\) | ||||
−0.187546 | + | 0.982256i | \(0.560053\pi\) | |||||||
\(252\) | 2.40375 | 0.151422 | ||||||||
\(253\) | −30.9883 | −1.94822 | ||||||||
\(254\) | 13.2507 | 0.831420 | ||||||||
\(255\) | −34.5584 | −2.16413 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.582514 | 0.0363362 | 0.0181681 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181681 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(258\) | 9.98978 | 0.621937 | ||||||||
\(259\) | −8.31751 | −0.516825 | ||||||||
\(260\) | −5.19860 | −0.322403 | ||||||||
\(261\) | 10.6878 | 0.661555 | ||||||||
\(262\) | −19.2692 | −1.19045 | ||||||||
\(263\) | 7.64410 | 0.471356 | 0.235678 | − | 0.971831i | \(-0.424269\pi\) | ||||
0.235678 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(264\) | 8.90207 | 0.547885 | ||||||||
\(265\) | −12.3574 | −0.759108 | ||||||||
\(266\) | 5.72699 | 0.351144 | ||||||||
\(267\) | 24.9010 | 1.52392 | ||||||||
\(268\) | 12.9969 | 0.793912 | ||||||||
\(269\) | 1.56036 | 0.0951368 | 0.0475684 | − | 0.998868i | \(-0.484853\pi\) | ||||
0.0475684 | + | 0.998868i | \(0.484853\pi\) | |||||||
\(270\) | 0.997620 | 0.0607132 | ||||||||
\(271\) | 6.91822 | 0.420252 | 0.210126 | − | 0.977674i | \(-0.432613\pi\) | ||||
0.210126 | + | 0.977674i | \(0.432613\pi\) | |||||||
\(272\) | 5.11357 | 0.310056 | ||||||||
\(273\) | 3.79376 | 0.229609 | ||||||||
\(274\) | 9.03398 | 0.545763 | ||||||||
\(275\) | −10.3188 | −0.622248 | ||||||||
\(276\) | −20.3723 | −1.22627 | ||||||||
\(277\) | 7.48585 | 0.449781 | 0.224891 | − | 0.974384i | \(-0.427798\pi\) | ||||
0.224891 | + | 0.974384i | \(0.427798\pi\) | |||||||
\(278\) | 20.5078 | 1.22998 | ||||||||
\(279\) | −10.3003 | −0.616666 | ||||||||
\(280\) | 2.35420 | 0.140691 | ||||||||
\(281\) | 26.1553 | 1.56029 | 0.780146 | − | 0.625598i | \(-0.215145\pi\) | ||||
0.780146 | + | 0.625598i | \(0.215145\pi\) | |||||||
\(282\) | −2.12112 | −0.126311 | ||||||||
\(283\) | 6.31827 | 0.375582 | 0.187791 | − | 0.982209i | \(-0.439867\pi\) | ||||
0.187791 | + | 0.982209i | \(0.439867\pi\) | |||||||
\(284\) | 4.51649 | 0.268004 | ||||||||
\(285\) | −45.9278 | −2.72053 | ||||||||
\(286\) | 6.84774 | 0.404916 | ||||||||
\(287\) | 1.50208 | 0.0886653 | ||||||||
\(288\) | 2.85238 | 0.168078 | ||||||||
\(289\) | 9.14858 | 0.538152 | ||||||||
\(290\) | 10.4675 | 0.614671 | ||||||||
\(291\) | −11.7105 | −0.686484 | ||||||||
\(292\) | 10.9440 | 0.640451 | ||||||||
\(293\) | 18.9286 | 1.10582 | 0.552910 | − | 0.833241i | \(-0.313517\pi\) | ||||
0.552910 | + | 0.833241i | \(0.313517\pi\) | |||||||
\(294\) | 15.2162 | 0.887425 | ||||||||
\(295\) | 18.5808 | 1.08182 | ||||||||
\(296\) | −9.86990 | −0.573676 | ||||||||
\(297\) | −1.31409 | −0.0762515 | ||||||||
\(298\) | −8.54883 | −0.495221 | ||||||||
\(299\) | −15.6710 | −0.906277 | ||||||||
\(300\) | −6.78378 | −0.391662 | ||||||||
\(301\) | −3.47993 | −0.200580 | ||||||||
\(302\) | 8.98631 | 0.517104 | ||||||||
\(303\) | −16.6070 | −0.954048 | ||||||||
\(304\) | 6.79587 | 0.389770 | ||||||||
\(305\) | −15.7538 | −0.902061 | ||||||||
\(306\) | 14.5859 | 0.833818 | ||||||||
\(307\) | 27.9385 | 1.59453 | 0.797267 | − | 0.603627i | \(-0.206278\pi\) | ||||
0.797267 | + | 0.603627i | \(0.206278\pi\) | |||||||
\(308\) | −3.10103 | −0.176697 | ||||||||
\(309\) | 16.5806 | 0.943237 | ||||||||
\(310\) | −10.0881 | −0.572963 | ||||||||
\(311\) | 7.63033 | 0.432676 | 0.216338 | − | 0.976319i | \(-0.430589\pi\) | ||||
0.216338 | + | 0.976319i | \(0.430589\pi\) | |||||||
\(312\) | 4.50183 | 0.254866 | ||||||||
\(313\) | 16.7916 | 0.949115 | 0.474558 | − | 0.880224i | \(-0.342608\pi\) | ||||
0.474558 | + | 0.880224i | \(0.342608\pi\) | |||||||
\(314\) | −22.7106 | −1.28163 | ||||||||
\(315\) | 6.71509 | 0.378353 | ||||||||
\(316\) | 9.36761 | 0.526969 | ||||||||
\(317\) | −21.8726 | −1.22849 | −0.614244 | − | 0.789116i | \(-0.710539\pi\) | ||||
−0.614244 | + | 0.789116i | \(0.710539\pi\) | |||||||
\(318\) | 10.7011 | 0.600090 | ||||||||
\(319\) | −13.7881 | −0.771983 | ||||||||
\(320\) | 2.79360 | 0.156167 | ||||||||
\(321\) | −7.94819 | −0.443625 | ||||||||
\(322\) | 7.09666 | 0.395482 | ||||||||
\(323\) | 34.7512 | 1.93361 | ||||||||
\(324\) | −9.42106 | −0.523392 | ||||||||
\(325\) | −5.21829 | −0.289459 | ||||||||
\(326\) | 8.96046 | 0.496274 | ||||||||
\(327\) | −46.5224 | −2.57270 | ||||||||
\(328\) | 1.78244 | 0.0984185 | ||||||||
\(329\) | 0.738890 | 0.0407363 | ||||||||
\(330\) | 24.8688 | 1.36898 | ||||||||
\(331\) | 27.1766 | 1.49376 | 0.746881 | − | 0.664958i | \(-0.231550\pi\) | ||||
0.746881 | + | 0.664958i | \(0.231550\pi\) | |||||||
\(332\) | −5.58958 | −0.306768 | ||||||||
\(333\) | −28.1527 | −1.54276 | ||||||||
\(334\) | −16.9775 | −0.928967 | ||||||||
\(335\) | 36.3081 | 1.98372 | ||||||||
\(336\) | −2.03867 | −0.111219 | ||||||||
\(337\) | −20.9394 | −1.14064 | −0.570320 | − | 0.821423i | \(-0.693181\pi\) | ||||
−0.570320 | + | 0.821423i | \(0.693181\pi\) | |||||||
\(338\) | −9.53705 | −0.518747 | ||||||||
\(339\) | 23.8839 | 1.29719 | ||||||||
\(340\) | 14.2852 | 0.774726 | ||||||||
\(341\) | 13.2883 | 0.719601 | ||||||||
\(342\) | 19.3844 | 1.04819 | ||||||||
\(343\) | −11.1995 | −0.604718 | ||||||||
\(344\) | −4.12943 | −0.222644 | ||||||||
\(345\) | −56.9119 | −3.06404 | ||||||||
\(346\) | 5.08477 | 0.273359 | ||||||||
\(347\) | −2.21501 | −0.118908 | −0.0594539 | − | 0.998231i | \(-0.518936\pi\) | ||||
−0.0594539 | + | 0.998231i | \(0.518936\pi\) | |||||||
\(348\) | −9.06452 | −0.485909 | ||||||||
\(349\) | −26.1240 | −1.39839 | −0.699193 | − | 0.714933i | \(-0.746457\pi\) | ||||
−0.699193 | + | 0.714933i | \(0.746457\pi\) | |||||||
\(350\) | 2.36312 | 0.126314 | ||||||||
\(351\) | −0.664545 | −0.0354708 | ||||||||
\(352\) | −3.67980 | −0.196134 | ||||||||
\(353\) | 17.6451 | 0.939155 | 0.469578 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469578 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(354\) | −16.0904 | −0.855196 | ||||||||
\(355\) | 12.6172 | 0.669653 | ||||||||
\(356\) | −10.2932 | −0.545539 | ||||||||
\(357\) | −10.4249 | −0.551743 | ||||||||
\(358\) | 11.0419 | 0.583585 | ||||||||
\(359\) | 12.1707 | 0.642343 | 0.321172 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321172 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(360\) | 7.96841 | 0.419972 | ||||||||
\(361\) | 27.1839 | 1.43073 | ||||||||
\(362\) | −1.93916 | −0.101920 | ||||||||
\(363\) | −6.14701 | −0.322635 | ||||||||
\(364\) | −1.56821 | −0.0821964 | ||||||||
\(365\) | 30.5732 | 1.60027 | ||||||||
\(366\) | 13.6423 | 0.713097 | ||||||||
\(367\) | −16.8722 | −0.880723 | −0.440361 | − | 0.897821i | \(-0.645150\pi\) | ||||
−0.440361 | + | 0.897821i | \(0.645150\pi\) | |||||||
\(368\) | 8.42119 | 0.438985 | ||||||||
\(369\) | 5.08419 | 0.264672 | ||||||||
\(370\) | −27.5725 | −1.43343 | ||||||||
\(371\) | −3.72773 | −0.193534 | ||||||||
\(372\) | 8.73595 | 0.452938 | ||||||||
\(373\) | −15.6919 | −0.812493 | −0.406247 | − | 0.913763i | \(-0.633163\pi\) | ||||
−0.406247 | + | 0.913763i | \(0.633163\pi\) | |||||||
\(374\) | −18.8169 | −0.973000 | ||||||||
\(375\) | 14.8398 | 0.766323 | ||||||||
\(376\) | 0.876797 | 0.0452173 | ||||||||
\(377\) | −6.97271 | −0.359113 | ||||||||
\(378\) | 0.300942 | 0.0154788 | ||||||||
\(379\) | 10.6109 | 0.545044 | 0.272522 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(380\) | 18.9849 | 0.973906 | ||||||||
\(381\) | −32.0556 | −1.64226 | ||||||||
\(382\) | −11.4895 | −0.587855 | ||||||||
\(383\) | 2.07089 | 0.105817 | 0.0529087 | − | 0.998599i | \(-0.483151\pi\) | ||||
0.0529087 | + | 0.998599i | \(0.483151\pi\) | |||||||
\(384\) | −2.41917 | −0.123453 | ||||||||
\(385\) | −8.66301 | −0.441508 | ||||||||
\(386\) | 10.9398 | 0.556821 | ||||||||
\(387\) | −11.7787 | −0.598745 | ||||||||
\(388\) | 4.84073 | 0.245751 | ||||||||
\(389\) | −10.6659 | −0.540782 | −0.270391 | − | 0.962751i | \(-0.587153\pi\) | ||||
−0.270391 | + | 0.962751i | \(0.587153\pi\) | |||||||
\(390\) | 12.5763 | 0.636825 | ||||||||
\(391\) | 43.0623 | 2.17776 | ||||||||
\(392\) | −6.28983 | −0.317684 | ||||||||
\(393\) | 46.6154 | 2.35143 | ||||||||
\(394\) | −8.25382 | −0.415821 | ||||||||
\(395\) | 26.1693 | 1.31672 | ||||||||
\(396\) | −10.4962 | −0.527455 | ||||||||
\(397\) | −28.4239 | −1.42656 | −0.713278 | − | 0.700881i | \(-0.752790\pi\) | ||||
−0.713278 | + | 0.700881i | \(0.752790\pi\) | |||||||
\(398\) | 18.6100 | 0.932835 | ||||||||
\(399\) | −13.8546 | −0.693595 | ||||||||
\(400\) | 2.80418 | 0.140209 | ||||||||
\(401\) | 27.7211 | 1.38432 | 0.692162 | − | 0.721742i | \(-0.256658\pi\) | ||||
0.692162 | + | 0.721742i | \(0.256658\pi\) | |||||||
\(402\) | −31.4417 | −1.56817 | ||||||||
\(403\) | 6.71996 | 0.334745 | ||||||||
\(404\) | 6.86476 | 0.341535 | ||||||||
\(405\) | −26.3186 | −1.30778 | ||||||||
\(406\) | 3.15762 | 0.156710 | ||||||||
\(407\) | 36.3193 | 1.80028 | ||||||||
\(408\) | −12.3706 | −0.612436 | ||||||||
\(409\) | −6.29387 | −0.311212 | −0.155606 | − | 0.987819i | \(-0.549733\pi\) | ||||
−0.155606 | + | 0.987819i | \(0.549733\pi\) | |||||||
\(410\) | 4.97940 | 0.245915 | ||||||||
\(411\) | −21.8547 | −1.07801 | ||||||||
\(412\) | −6.85383 | −0.337664 | ||||||||
\(413\) | 5.60508 | 0.275808 | ||||||||
\(414\) | 24.0205 | 1.18054 | ||||||||
\(415\) | −15.6150 | −0.766511 | ||||||||
\(416\) | −1.86090 | −0.0912381 | ||||||||
\(417\) | −49.6118 | −2.42950 | ||||||||
\(418\) | −25.0075 | −1.22316 | ||||||||
\(419\) | −4.13463 | −0.201990 | −0.100995 | − | 0.994887i | \(-0.532203\pi\) | ||||
−0.100995 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(420\) | −5.69522 | −0.277898 | ||||||||
\(421\) | −2.38583 | −0.116278 | −0.0581391 | − | 0.998308i | \(-0.518517\pi\) | ||||
−0.0581391 | + | 0.998308i | \(0.518517\pi\) | |||||||
\(422\) | −9.86959 | −0.480444 | ||||||||
\(423\) | 2.50096 | 0.121601 | ||||||||
\(424\) | −4.42347 | −0.214823 | ||||||||
\(425\) | 14.3393 | 0.695560 | ||||||||
\(426\) | −10.9261 | −0.529373 | ||||||||
\(427\) | −4.75229 | −0.229980 | ||||||||
\(428\) | 3.28550 | 0.158811 | ||||||||
\(429\) | −16.5659 | −0.799807 | ||||||||
\(430\) | −11.5359 | −0.556313 | ||||||||
\(431\) | −23.7381 | −1.14343 | −0.571713 | − | 0.820454i | \(-0.693721\pi\) | ||||
−0.571713 | + | 0.820454i | \(0.693721\pi\) | |||||||
\(432\) | 0.357110 | 0.0171815 | ||||||||
\(433\) | −14.5976 | −0.701515 | −0.350758 | − | 0.936466i | \(-0.614076\pi\) | ||||
−0.350758 | + | 0.936466i | \(0.614076\pi\) | |||||||
\(434\) | −3.04316 | −0.146076 | ||||||||
\(435\) | −25.3226 | −1.21413 | ||||||||
\(436\) | 19.2307 | 0.920985 | ||||||||
\(437\) | 57.2294 | 2.73765 | ||||||||
\(438\) | −26.4755 | −1.26505 | ||||||||
\(439\) | −18.0585 | −0.861886 | −0.430943 | − | 0.902379i | \(-0.641819\pi\) | ||||
−0.430943 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(440\) | −10.2799 | −0.490074 | ||||||||
\(441\) | −17.9410 | −0.854334 | ||||||||
\(442\) | −9.51583 | −0.452622 | ||||||||
\(443\) | 22.3392 | 1.06137 | 0.530684 | − | 0.847570i | \(-0.321935\pi\) | ||||
0.530684 | + | 0.847570i | \(0.321935\pi\) | |||||||
\(444\) | 23.8770 | 1.13315 | ||||||||
\(445\) | −28.7551 | −1.36312 | ||||||||
\(446\) | 6.05175 | 0.286558 | ||||||||
\(447\) | 20.6811 | 0.978182 | ||||||||
\(448\) | 0.842715 | 0.0398145 | ||||||||
\(449\) | −23.4665 | −1.10745 | −0.553727 | − | 0.832698i | \(-0.686795\pi\) | ||||
−0.553727 | + | 0.832698i | \(0.686795\pi\) | |||||||
\(450\) | 7.99858 | 0.377057 | ||||||||
\(451\) | −6.55901 | −0.308852 | ||||||||
\(452\) | −9.87276 | −0.464375 | ||||||||
\(453\) | −21.7394 | −1.02141 | ||||||||
\(454\) | −13.2276 | −0.620804 | ||||||||
\(455\) | −4.38094 | −0.205382 | ||||||||
\(456\) | −16.4404 | −0.769891 | ||||||||
\(457\) | 38.5252 | 1.80213 | 0.901066 | − | 0.433681i | \(-0.142786\pi\) | ||||
0.901066 | + | 0.433681i | \(0.142786\pi\) | |||||||
\(458\) | 16.1571 | 0.754971 | ||||||||
\(459\) | 1.82611 | 0.0852353 | ||||||||
\(460\) | 23.5254 | 1.09688 | ||||||||
\(461\) | 16.4972 | 0.768352 | 0.384176 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384176 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(462\) | 7.50191 | 0.349020 | ||||||||
\(463\) | 7.94502 | 0.369236 | 0.184618 | − | 0.982810i | \(-0.440895\pi\) | ||||
0.184618 | + | 0.982810i | \(0.440895\pi\) | |||||||
\(464\) | 3.74696 | 0.173948 | ||||||||
\(465\) | 24.4047 | 1.13174 | ||||||||
\(466\) | 10.0916 | 0.467486 | ||||||||
\(467\) | −13.0541 | −0.604070 | −0.302035 | − | 0.953297i | \(-0.597666\pi\) | ||||
−0.302035 | + | 0.953297i | \(0.597666\pi\) | |||||||
\(468\) | −5.30800 | −0.245362 | ||||||||
\(469\) | 10.9527 | 0.505748 | ||||||||
\(470\) | 2.44942 | 0.112983 | ||||||||
\(471\) | 54.9407 | 2.53153 | ||||||||
\(472\) | 6.65122 | 0.306147 | ||||||||
\(473\) | 15.1955 | 0.698689 | ||||||||
\(474\) | −22.6618 | −1.04089 | ||||||||
\(475\) | 19.0568 | 0.874387 | ||||||||
\(476\) | 4.30928 | 0.197516 | ||||||||
\(477\) | −12.6174 | −0.577713 | ||||||||
\(478\) | 22.6209 | 1.03466 | ||||||||
\(479\) | 33.5455 | 1.53273 | 0.766367 | − | 0.642403i | \(-0.222063\pi\) | ||||
0.766367 | + | 0.642403i | \(0.222063\pi\) | |||||||
\(480\) | −6.75818 | −0.308467 | ||||||||
\(481\) | 18.3669 | 0.837458 | ||||||||
\(482\) | 17.0708 | 0.777552 | ||||||||
\(483\) | −17.1680 | −0.781173 | ||||||||
\(484\) | 2.54096 | 0.115498 | ||||||||
\(485\) | 13.5230 | 0.614049 | ||||||||
\(486\) | 21.7198 | 0.985231 | ||||||||
\(487\) | −31.8262 | −1.44218 | −0.721091 | − | 0.692840i | \(-0.756359\pi\) | ||||
−0.721091 | + | 0.692840i | \(0.756359\pi\) | |||||||
\(488\) | −5.63927 | −0.255278 | ||||||||
\(489\) | −21.6769 | −0.980262 | ||||||||
\(490\) | −17.5712 | −0.793788 | ||||||||
\(491\) | −7.28748 | −0.328879 | −0.164440 | − | 0.986387i | \(-0.552582\pi\) | ||||
−0.164440 | + | 0.986387i | \(0.552582\pi\) | |||||||
\(492\) | −4.31201 | −0.194401 | ||||||||
\(493\) | 19.1603 | 0.862937 | ||||||||
\(494\) | −12.6464 | −0.568990 | ||||||||
\(495\) | −29.3222 | −1.31793 | ||||||||
\(496\) | −3.61114 | −0.162145 | ||||||||
\(497\) | 3.80611 | 0.170727 | ||||||||
\(498\) | 13.5221 | 0.605941 | ||||||||
\(499\) | −21.8055 | −0.976149 | −0.488074 | − | 0.872802i | \(-0.662300\pi\) | ||||
−0.488074 | + | 0.872802i | \(0.662300\pi\) | |||||||
\(500\) | −6.13425 | −0.274332 | ||||||||
\(501\) | 41.0714 | 1.83494 | ||||||||
\(502\) | −5.94256 | −0.265229 | ||||||||
\(503\) | −24.7440 | −1.10328 | −0.551641 | − | 0.834081i | \(-0.685998\pi\) | ||||
−0.551641 | + | 0.834081i | \(0.685998\pi\) | |||||||
\(504\) | 2.40375 | 0.107071 | ||||||||
\(505\) | 19.1774 | 0.853381 | ||||||||
\(506\) | −30.9883 | −1.37760 | ||||||||
\(507\) | 23.0718 | 1.02465 | ||||||||
\(508\) | 13.2507 | 0.587903 | ||||||||
\(509\) | 2.17944 | 0.0966020 | 0.0483010 | − | 0.998833i | \(-0.484619\pi\) | ||||
0.0483010 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(510\) | −34.5584 | −1.53027 | ||||||||
\(511\) | 9.22270 | 0.407988 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.42687 | 0.107149 | ||||||||
\(514\) | 0.582514 | 0.0256936 | ||||||||
\(515\) | −19.1468 | −0.843710 | ||||||||
\(516\) | 9.98978 | 0.439776 | ||||||||
\(517\) | −3.22644 | −0.141899 | ||||||||
\(518\) | −8.31751 | −0.365450 | ||||||||
\(519\) | −12.3009 | −0.539950 | ||||||||
\(520\) | −5.19860 | −0.227974 | ||||||||
\(521\) | −28.4321 | −1.24563 | −0.622816 | − | 0.782369i | \(-0.714011\pi\) | ||||
−0.622816 | + | 0.782369i | \(0.714011\pi\) | |||||||
\(522\) | 10.6878 | 0.467790 | ||||||||
\(523\) | 18.5870 | 0.812754 | 0.406377 | − | 0.913706i | \(-0.366792\pi\) | ||||
0.406377 | + | 0.913706i | \(0.366792\pi\) | |||||||
\(524\) | −19.2692 | −0.841777 | ||||||||
\(525\) | −5.71679 | −0.249501 | ||||||||
\(526\) | 7.64410 | 0.333299 | ||||||||
\(527\) | −18.4658 | −0.804383 | ||||||||
\(528\) | 8.90207 | 0.387413 | ||||||||
\(529\) | 47.9165 | 2.08332 | ||||||||
\(530\) | −12.3574 | −0.536771 | ||||||||
\(531\) | 18.9718 | 0.823307 | ||||||||
\(532\) | 5.72699 | 0.248296 | ||||||||
\(533\) | −3.31693 | −0.143672 | ||||||||
\(534\) | 24.9010 | 1.07757 | ||||||||
\(535\) | 9.17836 | 0.396815 | ||||||||
\(536\) | 12.9969 | 0.561380 | ||||||||
\(537\) | −26.7123 | −1.15272 | ||||||||
\(538\) | 1.56036 | 0.0672719 | ||||||||
\(539\) | 23.1453 | 0.996941 | ||||||||
\(540\) | 0.997620 | 0.0429307 | ||||||||
\(541\) | −13.6590 | −0.587247 | −0.293623 | − | 0.955921i | \(-0.594861\pi\) | ||||
−0.293623 | + | 0.955921i | \(0.594861\pi\) | |||||||
\(542\) | 6.91822 | 0.297163 | ||||||||
\(543\) | 4.69115 | 0.201316 | ||||||||
\(544\) | 5.11357 | 0.219242 | ||||||||
\(545\) | 53.7229 | 2.30124 | ||||||||
\(546\) | 3.79376 | 0.162358 | ||||||||
\(547\) | −10.5516 | −0.451152 | −0.225576 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225576 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(548\) | 9.03398 | 0.385912 | ||||||||
\(549\) | −16.0853 | −0.686506 | ||||||||
\(550\) | −10.3188 | −0.439996 | ||||||||
\(551\) | 25.4638 | 1.08480 | ||||||||
\(552\) | −20.3723 | −0.867102 | ||||||||
\(553\) | 7.89423 | 0.335697 | ||||||||
\(554\) | 7.48585 | 0.318043 | ||||||||
\(555\) | 66.7026 | 2.83137 | ||||||||
\(556\) | 20.5078 | 0.869724 | ||||||||
\(557\) | 37.2798 | 1.57959 | 0.789797 | − | 0.613368i | \(-0.210186\pi\) | ||||
0.789797 | + | 0.613368i | \(0.210186\pi\) | |||||||
\(558\) | −10.3003 | −0.436048 | ||||||||
\(559\) | 7.68445 | 0.325017 | ||||||||
\(560\) | 2.35420 | 0.0994833 | ||||||||
\(561\) | 45.5214 | 1.92191 | ||||||||
\(562\) | 26.1553 | 1.10329 | ||||||||
\(563\) | 8.91337 | 0.375654 | 0.187827 | − | 0.982202i | \(-0.439856\pi\) | ||||
0.187827 | + | 0.982202i | \(0.439856\pi\) | |||||||
\(564\) | −2.12112 | −0.0893153 | ||||||||
\(565\) | −27.5805 | −1.16032 | ||||||||
\(566\) | 6.31827 | 0.265577 | ||||||||
\(567\) | −7.93927 | −0.333418 | ||||||||
\(568\) | 4.51649 | 0.189508 | ||||||||
\(569\) | 34.9216 | 1.46399 | 0.731995 | − | 0.681310i | \(-0.238589\pi\) | ||||
0.731995 | + | 0.681310i | \(0.238589\pi\) | |||||||
\(570\) | −45.9278 | −1.92370 | ||||||||
\(571\) | −5.47098 | −0.228954 | −0.114477 | − | 0.993426i | \(-0.536519\pi\) | ||||
−0.114477 | + | 0.993426i | \(0.536519\pi\) | |||||||
\(572\) | 6.84774 | 0.286319 | ||||||||
\(573\) | 27.7951 | 1.16116 | ||||||||
\(574\) | 1.50208 | 0.0626958 | ||||||||
\(575\) | 23.6145 | 0.984793 | ||||||||
\(576\) | 2.85238 | 0.118849 | ||||||||
\(577\) | 14.5236 | 0.604627 | 0.302313 | − | 0.953209i | \(-0.402241\pi\) | ||||
0.302313 | + | 0.953209i | \(0.402241\pi\) | |||||||
\(578\) | 9.14858 | 0.380531 | ||||||||
\(579\) | −26.4652 | −1.09986 | ||||||||
\(580\) | 10.4675 | 0.434638 | ||||||||
\(581\) | −4.71042 | −0.195421 | ||||||||
\(582\) | −11.7105 | −0.485418 | ||||||||
\(583\) | 16.2775 | 0.674146 | ||||||||
\(584\) | 10.9440 | 0.452867 | ||||||||
\(585\) | −14.8284 | −0.613079 | ||||||||
\(586\) | 18.9286 | 0.781933 | ||||||||
\(587\) | 14.3448 | 0.592072 | 0.296036 | − | 0.955177i | \(-0.404335\pi\) | ||||
0.296036 | + | 0.955177i | \(0.404335\pi\) | |||||||
\(588\) | 15.2162 | 0.627504 | ||||||||
\(589\) | −24.5408 | −1.01119 | ||||||||
\(590\) | 18.5808 | 0.764960 | ||||||||
\(591\) | 19.9674 | 0.821349 | ||||||||
\(592\) | −9.86990 | −0.405650 | ||||||||
\(593\) | 13.9969 | 0.574782 | 0.287391 | − | 0.957813i | \(-0.407212\pi\) | ||||
0.287391 | + | 0.957813i | \(0.407212\pi\) | |||||||
\(594\) | −1.31409 | −0.0539179 | ||||||||
\(595\) | 12.0384 | 0.493526 | ||||||||
\(596\) | −8.54883 | −0.350174 | ||||||||
\(597\) | −45.0208 | −1.84258 | ||||||||
\(598\) | −15.6710 | −0.640834 | ||||||||
\(599\) | −13.4346 | −0.548921 | −0.274461 | − | 0.961598i | \(-0.588499\pi\) | ||||
−0.274461 | + | 0.961598i | \(0.588499\pi\) | |||||||
\(600\) | −6.78378 | −0.276947 | ||||||||
\(601\) | 33.5650 | 1.36914 | 0.684572 | − | 0.728945i | \(-0.259989\pi\) | ||||
0.684572 | + | 0.728945i | \(0.259989\pi\) | |||||||
\(602\) | −3.47993 | −0.141831 | ||||||||
\(603\) | 37.0721 | 1.50969 | ||||||||
\(604\) | 8.98631 | 0.365648 | ||||||||
\(605\) | 7.09841 | 0.288592 | ||||||||
\(606\) | −16.6070 | −0.674614 | ||||||||
\(607\) | 23.1932 | 0.941382 | 0.470691 | − | 0.882298i | \(-0.344005\pi\) | ||||
0.470691 | + | 0.882298i | \(0.344005\pi\) | |||||||
\(608\) | 6.79587 | 0.275609 | ||||||||
\(609\) | −7.63881 | −0.309540 | ||||||||
\(610\) | −15.7538 | −0.637854 | ||||||||
\(611\) | −1.63163 | −0.0660087 | ||||||||
\(612\) | 14.5859 | 0.589598 | ||||||||
\(613\) | 44.2697 | 1.78803 | 0.894017 | − | 0.448033i | \(-0.147875\pi\) | ||||
0.894017 | + | 0.448033i | \(0.147875\pi\) | |||||||
\(614\) | 27.9385 | 1.12751 | ||||||||
\(615\) | −12.0460 | −0.485743 | ||||||||
\(616\) | −3.10103 | −0.124944 | ||||||||
\(617\) | −12.2658 | −0.493803 | −0.246902 | − | 0.969041i | \(-0.579412\pi\) | ||||
−0.246902 | + | 0.969041i | \(0.579412\pi\) | |||||||
\(618\) | 16.5806 | 0.666969 | ||||||||
\(619\) | −4.52193 | −0.181752 | −0.0908758 | − | 0.995862i | \(-0.528967\pi\) | ||||
−0.0908758 | + | 0.995862i | \(0.528967\pi\) | |||||||
\(620\) | −10.0881 | −0.405146 | ||||||||
\(621\) | 3.00729 | 0.120678 | ||||||||
\(622\) | 7.63033 | 0.305948 | ||||||||
\(623\) | −8.67424 | −0.347526 | ||||||||
\(624\) | 4.50183 | 0.180217 | ||||||||
\(625\) | −31.1575 | −1.24630 | ||||||||
\(626\) | 16.7916 | 0.671126 | ||||||||
\(627\) | 60.4974 | 2.41603 | ||||||||
\(628\) | −22.7106 | −0.906250 | ||||||||
\(629\) | −50.4704 | −2.01239 | ||||||||
\(630\) | 6.71509 | 0.267536 | ||||||||
\(631\) | 28.8137 | 1.14706 | 0.573528 | − | 0.819186i | \(-0.305574\pi\) | ||||
0.573528 | + | 0.819186i | \(0.305574\pi\) | |||||||
\(632\) | 9.36761 | 0.372624 | ||||||||
\(633\) | 23.8762 | 0.948995 | ||||||||
\(634\) | −21.8726 | −0.868672 | ||||||||
\(635\) | 37.0170 | 1.46897 | ||||||||
\(636\) | 10.7011 | 0.424327 | ||||||||
\(637\) | 11.7047 | 0.463759 | ||||||||
\(638\) | −13.7881 | −0.545875 | ||||||||
\(639\) | 12.8827 | 0.509634 | ||||||||
\(640\) | 2.79360 | 0.110427 | ||||||||
\(641\) | −44.3055 | −1.74996 | −0.874982 | − | 0.484156i | \(-0.839127\pi\) | ||||
−0.874982 | + | 0.484156i | \(0.839127\pi\) | |||||||
\(642\) | −7.94819 | −0.313690 | ||||||||
\(643\) | 3.92968 | 0.154972 | 0.0774858 | − | 0.996993i | \(-0.475311\pi\) | ||||
0.0774858 | + | 0.996993i | \(0.475311\pi\) | |||||||
\(644\) | 7.09666 | 0.279648 | ||||||||
\(645\) | 27.9074 | 1.09885 | ||||||||
\(646\) | 34.7512 | 1.36727 | ||||||||
\(647\) | −3.40195 | −0.133745 | −0.0668723 | − | 0.997762i | \(-0.521302\pi\) | ||||
−0.0668723 | + | 0.997762i | \(0.521302\pi\) | |||||||
\(648\) | −9.42106 | −0.370094 | ||||||||
\(649\) | −24.4752 | −0.960735 | ||||||||
\(650\) | −5.21829 | −0.204678 | ||||||||
\(651\) | 7.36192 | 0.288536 | ||||||||
\(652\) | 8.96046 | 0.350919 | ||||||||
\(653\) | 28.2526 | 1.10561 | 0.552805 | − | 0.833311i | \(-0.313557\pi\) | ||||
0.552805 | + | 0.833311i | \(0.313557\pi\) | |||||||
\(654\) | −46.5224 | −1.81917 | ||||||||
\(655\) | −53.8302 | −2.10332 | ||||||||
\(656\) | 1.78244 | 0.0695924 | ||||||||
\(657\) | 31.2166 | 1.21787 | ||||||||
\(658\) | 0.738890 | 0.0288049 | ||||||||
\(659\) | −14.2526 | −0.555204 | −0.277602 | − | 0.960696i | \(-0.589540\pi\) | ||||
−0.277602 | + | 0.960696i | \(0.589540\pi\) | |||||||
\(660\) | 24.8688 | 0.968016 | ||||||||
\(661\) | −23.9811 | −0.932757 | −0.466378 | − | 0.884585i | \(-0.654441\pi\) | ||||
−0.466378 | + | 0.884585i | \(0.654441\pi\) | |||||||
\(662\) | 27.1766 | 1.05625 | ||||||||
\(663\) | 23.0204 | 0.894039 | ||||||||
\(664\) | −5.58958 | −0.216918 | ||||||||
\(665\) | 15.9989 | 0.620410 | ||||||||
\(666\) | −28.1527 | −1.09090 | ||||||||
\(667\) | 31.5538 | 1.22177 | ||||||||
\(668\) | −16.9775 | −0.656879 | ||||||||
\(669\) | −14.6402 | −0.566023 | ||||||||
\(670\) | 36.3081 | 1.40270 | ||||||||
\(671\) | 20.7514 | 0.801099 | ||||||||
\(672\) | −2.03867 | −0.0786434 | ||||||||
\(673\) | 23.6826 | 0.912896 | 0.456448 | − | 0.889750i | \(-0.349121\pi\) | ||||
0.456448 | + | 0.889750i | \(0.349121\pi\) | |||||||
\(674\) | −20.9394 | −0.806554 | ||||||||
\(675\) | 1.00140 | 0.0385439 | ||||||||
\(676\) | −9.53705 | −0.366810 | ||||||||
\(677\) | −14.9125 | −0.573134 | −0.286567 | − | 0.958060i | \(-0.592514\pi\) | ||||
−0.286567 | + | 0.958060i | \(0.592514\pi\) | |||||||
\(678\) | 23.8839 | 0.917255 | ||||||||
\(679\) | 4.07935 | 0.156551 | ||||||||
\(680\) | 14.2852 | 0.547814 | ||||||||
\(681\) | 31.9999 | 1.22624 | ||||||||
\(682\) | 13.2883 | 0.508834 | ||||||||
\(683\) | 1.63412 | 0.0625277 | 0.0312639 | − | 0.999511i | \(-0.490047\pi\) | ||||
0.0312639 | + | 0.999511i | \(0.490047\pi\) | |||||||
\(684\) | 19.3844 | 0.741183 | ||||||||
\(685\) | 25.2373 | 0.964267 | ||||||||
\(686\) | −11.1995 | −0.427600 | ||||||||
\(687\) | −39.0867 | −1.49125 | ||||||||
\(688\) | −4.12943 | −0.157433 | ||||||||
\(689\) | 8.23163 | 0.313600 | ||||||||
\(690\) | −56.9119 | −2.16660 | ||||||||
\(691\) | −29.3989 | −1.11839 | −0.559193 | − | 0.829038i | \(-0.688889\pi\) | ||||
−0.559193 | + | 0.829038i | \(0.688889\pi\) | |||||||
\(692\) | 5.08477 | 0.193294 | ||||||||
\(693\) | −8.84532 | −0.336006 | ||||||||
\(694\) | −2.21501 | −0.0840806 | ||||||||
\(695\) | 57.2905 | 2.17315 | ||||||||
\(696\) | −9.06452 | −0.343590 | ||||||||
\(697\) | 9.11461 | 0.345240 | ||||||||
\(698\) | −26.1240 | −0.988808 | ||||||||
\(699\) | −24.4134 | −0.923399 | ||||||||
\(700\) | 2.36312 | 0.0893176 | ||||||||
\(701\) | −46.1423 | −1.74277 | −0.871384 | − | 0.490601i | \(-0.836777\pi\) | ||||
−0.871384 | + | 0.490601i | \(0.836777\pi\) | |||||||
\(702\) | −0.664545 | −0.0250816 | ||||||||
\(703\) | −67.0746 | −2.52977 | ||||||||
\(704\) | −3.67980 | −0.138688 | ||||||||
\(705\) | −5.92555 | −0.223169 | ||||||||
\(706\) | 17.6451 | 0.664083 | ||||||||
\(707\) | 5.78504 | 0.217569 | ||||||||
\(708\) | −16.0904 | −0.604715 | ||||||||
\(709\) | −41.2886 | −1.55063 | −0.775313 | − | 0.631577i | \(-0.782408\pi\) | ||||
−0.775313 | + | 0.631577i | \(0.782408\pi\) | |||||||
\(710\) | 12.6172 | 0.473516 | ||||||||
\(711\) | 26.7200 | 1.00208 | ||||||||
\(712\) | −10.2932 | −0.385754 | ||||||||
\(713\) | −30.4101 | −1.13887 | ||||||||
\(714\) | −10.4249 | −0.390141 | ||||||||
\(715\) | 19.1298 | 0.715415 | ||||||||
\(716\) | 11.0419 | 0.412657 | ||||||||
\(717\) | −54.7239 | −2.04370 | ||||||||
\(718\) | 12.1707 | 0.454205 | ||||||||
\(719\) | 27.0402 | 1.00843 | 0.504214 | − | 0.863579i | \(-0.331782\pi\) | ||||
0.504214 | + | 0.863579i | \(0.331782\pi\) | |||||||
\(720\) | 7.96841 | 0.296965 | ||||||||
\(721\) | −5.77583 | −0.215103 | ||||||||
\(722\) | 27.1839 | 1.01168 | ||||||||
\(723\) | −41.2971 | −1.53586 | ||||||||
\(724\) | −1.93916 | −0.0720682 | ||||||||
\(725\) | 10.5071 | 0.390225 | ||||||||
\(726\) | −6.14701 | −0.228137 | ||||||||
\(727\) | −1.80457 | −0.0669277 | −0.0334639 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334639 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(728\) | −1.56821 | −0.0581216 | ||||||||
\(729\) | −24.2807 | −0.899287 | ||||||||
\(730\) | 30.5732 | 1.13156 | ||||||||
\(731\) | −21.1161 | −0.781007 | ||||||||
\(732\) | 13.6423 | 0.504235 | ||||||||
\(733\) | −16.6822 | −0.616170 | −0.308085 | − | 0.951359i | \(-0.599688\pi\) | ||||
−0.308085 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(734\) | −16.8722 | −0.622765 | ||||||||
\(735\) | 42.5078 | 1.56792 | ||||||||
\(736\) | 8.42119 | 0.310409 | ||||||||
\(737\) | −47.8260 | −1.76169 | ||||||||
\(738\) | 5.08419 | 0.187152 | ||||||||
\(739\) | −31.1134 | −1.14452 | −0.572262 | − | 0.820071i | \(-0.693934\pi\) | ||||
−0.572262 | + | 0.820071i | \(0.693934\pi\) | |||||||
\(740\) | −27.5725 | −1.01359 | ||||||||
\(741\) | 30.5939 | 1.12389 | ||||||||
\(742\) | −3.72773 | −0.136849 | ||||||||
\(743\) | 24.5738 | 0.901526 | 0.450763 | − | 0.892644i | \(-0.351152\pi\) | ||||
0.450763 | + | 0.892644i | \(0.351152\pi\) | |||||||
\(744\) | 8.73595 | 0.320276 | ||||||||
\(745\) | −23.8820 | −0.874968 | ||||||||
\(746\) | −15.6919 | −0.574520 | ||||||||
\(747\) | −15.9436 | −0.583346 | ||||||||
\(748\) | −18.8169 | −0.688015 | ||||||||
\(749\) | 2.76874 | 0.101168 | ||||||||
\(750\) | 14.8398 | 0.541872 | ||||||||
\(751\) | −24.4679 | −0.892847 | −0.446423 | − | 0.894822i | \(-0.647302\pi\) | ||||
−0.446423 | + | 0.894822i | \(0.647302\pi\) | |||||||
\(752\) | 0.876797 | 0.0319735 | ||||||||
\(753\) | 14.3761 | 0.523893 | ||||||||
\(754\) | −6.97271 | −0.253931 | ||||||||
\(755\) | 25.1041 | 0.913633 | ||||||||
\(756\) | 0.300942 | 0.0109451 | ||||||||
\(757\) | −2.70227 | −0.0982158 | −0.0491079 | − | 0.998793i | \(-0.515638\pi\) | ||||
−0.0491079 | + | 0.998793i | \(0.515638\pi\) | |||||||
\(758\) | 10.6109 | 0.385405 | ||||||||
\(759\) | 74.9661 | 2.72110 | ||||||||
\(760\) | 18.9849 | 0.688656 | ||||||||
\(761\) | 38.8424 | 1.40804 | 0.704018 | − | 0.710182i | \(-0.251388\pi\) | ||||
0.704018 | + | 0.710182i | \(0.251388\pi\) | |||||||
\(762\) | −32.0556 | −1.16125 | ||||||||
\(763\) | 16.2060 | 0.586698 | ||||||||
\(764\) | −11.4895 | −0.415676 | ||||||||
\(765\) | 40.7470 | 1.47321 | ||||||||
\(766\) | 2.07089 | 0.0748243 | ||||||||
\(767\) | −12.3772 | −0.446916 | ||||||||
\(768\) | −2.41917 | −0.0872943 | ||||||||
\(769\) | −49.1490 | −1.77236 | −0.886179 | − | 0.463343i | \(-0.846650\pi\) | ||||
−0.886179 | + | 0.463343i | \(0.846650\pi\) | |||||||
\(770\) | −8.66301 | −0.312193 | ||||||||
\(771\) | −1.40920 | −0.0507511 | ||||||||
\(772\) | 10.9398 | 0.393732 | ||||||||
\(773\) | −21.5096 | −0.773645 | −0.386823 | − | 0.922154i | \(-0.626427\pi\) | ||||
−0.386823 | + | 0.922154i | \(0.626427\pi\) | |||||||
\(774\) | −11.7787 | −0.423377 | ||||||||
\(775\) | −10.1263 | −0.363746 | ||||||||
\(776\) | 4.84073 | 0.173772 | ||||||||
\(777\) | 20.1215 | 0.721854 | ||||||||
\(778\) | −10.6659 | −0.382390 | ||||||||
\(779\) | 12.1132 | 0.434001 | ||||||||
\(780\) | 12.5763 | 0.450304 | ||||||||
\(781\) | −16.6198 | −0.594703 | ||||||||
\(782\) | 43.0623 | 1.53991 | ||||||||
\(783\) | 1.33807 | 0.0478189 | ||||||||
\(784\) | −6.28983 | −0.224637 | ||||||||
\(785\) | −63.4441 | −2.26442 | ||||||||
\(786\) | 46.6154 | 1.66271 | ||||||||
\(787\) | 34.2989 | 1.22263 | 0.611313 | − | 0.791389i | \(-0.290642\pi\) | ||||
0.611313 | + | 0.791389i | \(0.290642\pi\) | |||||||
\(788\) | −8.25382 | −0.294030 | ||||||||
\(789\) | −18.4924 | −0.658346 | ||||||||
\(790\) | 26.1693 | 0.931062 | ||||||||
\(791\) | −8.31992 | −0.295822 | ||||||||
\(792\) | −10.4962 | −0.372967 | ||||||||
\(793\) | 10.4941 | 0.372657 | ||||||||
\(794\) | −28.4239 | −1.00873 | ||||||||
\(795\) | 29.8946 | 1.06025 | ||||||||
\(796\) | 18.6100 | 0.659614 | ||||||||
\(797\) | −35.8883 | −1.27123 | −0.635615 | − | 0.772006i | \(-0.719253\pi\) | ||||
−0.635615 | + | 0.772006i | \(0.719253\pi\) | |||||||
\(798\) | −13.8546 | −0.490446 | ||||||||
\(799\) | 4.48356 | 0.158617 | ||||||||
\(800\) | 2.80418 | 0.0991426 | ||||||||
\(801\) | −29.3602 | −1.03739 | ||||||||
\(802\) | 27.7211 | 0.978865 | ||||||||
\(803\) | −40.2719 | −1.42116 | ||||||||
\(804\) | −31.4417 | −1.10886 | ||||||||
\(805\) | 19.8252 | 0.698747 | ||||||||
\(806\) | 6.71996 | 0.236701 | ||||||||
\(807\) | −3.77477 | −0.132878 | ||||||||
\(808\) | 6.86476 | 0.241501 | ||||||||
\(809\) | −12.5378 | −0.440806 | −0.220403 | − | 0.975409i | \(-0.570737\pi\) | ||||
−0.220403 | + | 0.975409i | \(0.570737\pi\) | |||||||
\(810\) | −26.3186 | −0.924742 | ||||||||
\(811\) | 42.5345 | 1.49359 | 0.746795 | − | 0.665055i | \(-0.231592\pi\) | ||||
0.746795 | + | 0.665055i | \(0.231592\pi\) | |||||||
\(812\) | 3.15762 | 0.110811 | ||||||||
\(813\) | −16.7364 | −0.586970 | ||||||||
\(814\) | 36.3193 | 1.27299 | ||||||||
\(815\) | 25.0319 | 0.876829 | ||||||||
\(816\) | −12.3706 | −0.433057 | ||||||||
\(817\) | −28.0631 | −0.981802 | ||||||||
\(818\) | −6.29387 | −0.220060 | ||||||||
\(819\) | −4.47313 | −0.156304 | ||||||||
\(820\) | 4.97940 | 0.173888 | ||||||||
\(821\) | −3.80109 | −0.132659 | −0.0663294 | − | 0.997798i | \(-0.521129\pi\) | ||||
−0.0663294 | + | 0.997798i | \(0.521129\pi\) | |||||||
\(822\) | −21.8547 | −0.762271 | ||||||||
\(823\) | −49.7181 | −1.73306 | −0.866532 | − | 0.499122i | \(-0.833656\pi\) | ||||
−0.866532 | + | 0.499122i | \(0.833656\pi\) | |||||||
\(824\) | −6.85383 | −0.238765 | ||||||||
\(825\) | 24.9630 | 0.869099 | ||||||||
\(826\) | 5.60508 | 0.195026 | ||||||||
\(827\) | 46.7135 | 1.62439 | 0.812193 | − | 0.583388i | \(-0.198273\pi\) | ||||
0.812193 | + | 0.583388i | \(0.198273\pi\) | |||||||
\(828\) | 24.0205 | 0.834769 | ||||||||
\(829\) | 47.3406 | 1.64421 | 0.822104 | − | 0.569337i | \(-0.192800\pi\) | ||||
0.822104 | + | 0.569337i | \(0.192800\pi\) | |||||||
\(830\) | −15.6150 | −0.542005 | ||||||||
\(831\) | −18.1095 | −0.628213 | ||||||||
\(832\) | −1.86090 | −0.0645151 | ||||||||
\(833\) | −32.1635 | −1.11440 | ||||||||
\(834\) | −49.6118 | −1.71792 | ||||||||
\(835\) | −47.4283 | −1.64132 | ||||||||
\(836\) | −25.0075 | −0.864902 | ||||||||
\(837\) | −1.28957 | −0.0445742 | ||||||||
\(838\) | −4.13463 | −0.142828 | ||||||||
\(839\) | 28.4914 | 0.983632 | 0.491816 | − | 0.870699i | \(-0.336333\pi\) | ||||
0.491816 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(840\) | −5.69522 | −0.196504 | ||||||||
\(841\) | −14.9603 | −0.515873 | ||||||||
\(842\) | −2.38583 | −0.0822211 | ||||||||
\(843\) | −63.2740 | −2.17927 | ||||||||
\(844\) | −9.86959 | −0.339725 | ||||||||
\(845\) | −26.6427 | −0.916536 | ||||||||
\(846\) | 2.50096 | 0.0859848 | ||||||||
\(847\) | 2.14130 | 0.0735761 | ||||||||
\(848\) | −4.42347 | −0.151903 | ||||||||
\(849\) | −15.2850 | −0.524579 | ||||||||
\(850\) | 14.3393 | 0.491835 | ||||||||
\(851\) | −83.1163 | −2.84919 | ||||||||
\(852\) | −10.9261 | −0.374324 | ||||||||
\(853\) | 38.0377 | 1.30239 | 0.651193 | − | 0.758912i | \(-0.274269\pi\) | ||||
0.651193 | + | 0.758912i | \(0.274269\pi\) | |||||||
\(854\) | −4.75229 | −0.162620 | ||||||||
\(855\) | 54.1523 | 1.85197 | ||||||||
\(856\) | 3.28550 | 0.112296 | ||||||||
\(857\) | 26.8011 | 0.915508 | 0.457754 | − | 0.889079i | \(-0.348654\pi\) | ||||
0.457754 | + | 0.889079i | \(0.348654\pi\) | |||||||
\(858\) | −16.5659 | −0.565549 | ||||||||
\(859\) | −26.8221 | −0.915159 | −0.457580 | − | 0.889169i | \(-0.651284\pi\) | ||||
−0.457580 | + | 0.889169i | \(0.651284\pi\) | |||||||
\(860\) | −11.5359 | −0.393373 | ||||||||
\(861\) | −3.63380 | −0.123840 | ||||||||
\(862\) | −23.7381 | −0.808524 | ||||||||
\(863\) | 15.8736 | 0.540345 | 0.270172 | − | 0.962812i | \(-0.412919\pi\) | ||||
0.270172 | + | 0.962812i | \(0.412919\pi\) | |||||||
\(864\) | 0.357110 | 0.0121491 | ||||||||
\(865\) | 14.2048 | 0.482977 | ||||||||
\(866\) | −14.5976 | −0.496046 | ||||||||
\(867\) | −22.1320 | −0.751641 | ||||||||
\(868\) | −3.04316 | −0.103292 | ||||||||
\(869\) | −34.4710 | −1.16935 | ||||||||
\(870\) | −25.3226 | −0.858517 | ||||||||
\(871\) | −24.1859 | −0.819508 | ||||||||
\(872\) | 19.2307 | 0.651235 | ||||||||
\(873\) | 13.8076 | 0.467317 | ||||||||
\(874\) | 57.2294 | 1.93581 | ||||||||
\(875\) | −5.16942 | −0.174758 | ||||||||
\(876\) | −26.4755 | −0.894523 | ||||||||
\(877\) | 25.6418 | 0.865861 | 0.432931 | − | 0.901427i | \(-0.357479\pi\) | ||||
0.432931 | + | 0.901427i | \(0.357479\pi\) | |||||||
\(878\) | −18.0585 | −0.609445 | ||||||||
\(879\) | −45.7915 | −1.54451 | ||||||||
\(880\) | −10.2799 | −0.346535 | ||||||||
\(881\) | 50.7600 | 1.71015 | 0.855073 | − | 0.518507i | \(-0.173512\pi\) | ||||
0.855073 | + | 0.518507i | \(0.173512\pi\) | |||||||
\(882\) | −17.9410 | −0.604105 | ||||||||
\(883\) | 15.4942 | 0.521421 | 0.260710 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260710 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(884\) | −9.51583 | −0.320052 | ||||||||
\(885\) | −44.9501 | −1.51098 | ||||||||
\(886\) | 22.3392 | 0.750500 | ||||||||
\(887\) | 37.9254 | 1.27341 | 0.636705 | − | 0.771108i | \(-0.280297\pi\) | ||||
0.636705 | + | 0.771108i | \(0.280297\pi\) | |||||||
\(888\) | 23.8770 | 0.801258 | ||||||||
\(889\) | 11.1665 | 0.374513 | ||||||||
\(890\) | −28.7551 | −0.963872 | ||||||||
\(891\) | 34.6677 | 1.16141 | ||||||||
\(892\) | 6.05175 | 0.202627 | ||||||||
\(893\) | 5.95860 | 0.199397 | ||||||||
\(894\) | 20.6811 | 0.691679 | ||||||||
\(895\) | 30.8467 | 1.03109 | ||||||||
\(896\) | 0.842715 | 0.0281531 | ||||||||
\(897\) | 37.9108 | 1.26580 | ||||||||
\(898\) | −23.4665 | −0.783088 | ||||||||
\(899\) | −13.5308 | −0.451276 | ||||||||
\(900\) | 7.99858 | 0.266619 | ||||||||
\(901\) | −22.6197 | −0.753572 | ||||||||
\(902\) | −6.55901 | −0.218391 | ||||||||
\(903\) | 8.41854 | 0.280151 | ||||||||
\(904\) | −9.87276 | −0.328363 | ||||||||
\(905\) | −5.41722 | −0.180074 | ||||||||
\(906\) | −21.7394 | −0.722244 | ||||||||
\(907\) | 15.1805 | 0.504062 | 0.252031 | − | 0.967719i | \(-0.418902\pi\) | ||||
0.252031 | + | 0.967719i | \(0.418902\pi\) | |||||||
\(908\) | −13.2276 | −0.438975 | ||||||||
\(909\) | 19.5809 | 0.649458 | ||||||||
\(910\) | −4.38094 | −0.145227 | ||||||||
\(911\) | −42.3483 | −1.40306 | −0.701532 | − | 0.712638i | \(-0.747500\pi\) | ||||
−0.701532 | + | 0.712638i | \(0.747500\pi\) | |||||||
\(912\) | −16.4404 | −0.544395 | ||||||||
\(913\) | 20.5685 | 0.680720 | ||||||||
\(914\) | 38.5252 | 1.27430 | ||||||||
\(915\) | 38.1112 | 1.25992 | ||||||||
\(916\) | 16.1571 | 0.533845 | ||||||||
\(917\) | −16.2384 | −0.536239 | ||||||||
\(918\) | 1.82611 | 0.0602705 | ||||||||
\(919\) | −32.0102 | −1.05592 | −0.527960 | − | 0.849270i | \(-0.677043\pi\) | ||||
−0.527960 | + | 0.849270i | \(0.677043\pi\) | |||||||
\(920\) | 23.5254 | 0.775610 | ||||||||
\(921\) | −67.5879 | −2.22710 | ||||||||
\(922\) | 16.4972 | 0.543307 | ||||||||
\(923\) | −8.40472 | −0.276645 | ||||||||
\(924\) | 7.50191 | 0.246795 | ||||||||
\(925\) | −27.6769 | −0.910012 | ||||||||
\(926\) | 7.94502 | 0.261090 | ||||||||
\(927\) | −19.5498 | −0.642098 | ||||||||
\(928\) | 3.74696 | 0.123000 | ||||||||
\(929\) | 56.3336 | 1.84824 | 0.924122 | − | 0.382097i | \(-0.124798\pi\) | ||||
0.924122 | + | 0.382097i | \(0.124798\pi\) | |||||||
\(930\) | 24.4047 | 0.800262 | ||||||||
\(931\) | −42.7449 | −1.40091 | ||||||||
\(932\) | 10.0916 | 0.330563 | ||||||||
\(933\) | −18.4591 | −0.604322 | ||||||||
\(934\) | −13.0541 | −0.427142 | ||||||||
\(935\) | −52.5669 | −1.71912 | ||||||||
\(936\) | −5.30800 | −0.173497 | ||||||||
\(937\) | −44.5931 | −1.45679 | −0.728397 | − | 0.685156i | \(-0.759734\pi\) | ||||
−0.728397 | + | 0.685156i | \(0.759734\pi\) | |||||||
\(938\) | 10.9527 | 0.357618 | ||||||||
\(939\) | −40.6216 | −1.32564 | ||||||||
\(940\) | 2.44942 | 0.0798911 | ||||||||
\(941\) | −25.2209 | −0.822179 | −0.411090 | − | 0.911595i | \(-0.634852\pi\) | ||||
−0.411090 | + | 0.911595i | \(0.634852\pi\) | |||||||
\(942\) | 54.9407 | 1.79006 | ||||||||
\(943\) | 15.0102 | 0.488800 | ||||||||
\(944\) | 6.65122 | 0.216479 | ||||||||
\(945\) | 0.840710 | 0.0273483 | ||||||||
\(946\) | 15.1955 | 0.494048 | ||||||||
\(947\) | 19.9357 | 0.647823 | 0.323912 | − | 0.946087i | \(-0.395002\pi\) | ||||
0.323912 | + | 0.946087i | \(0.395002\pi\) | |||||||
\(948\) | −22.6618 | −0.736022 | ||||||||
\(949\) | −20.3657 | −0.661100 | ||||||||
\(950\) | 19.0568 | 0.618285 | ||||||||
\(951\) | 52.9136 | 1.71584 | ||||||||
\(952\) | 4.30928 | 0.139665 | ||||||||
\(953\) | −57.0318 | −1.84744 | −0.923720 | − | 0.383068i | \(-0.874868\pi\) | ||||
−0.923720 | + | 0.383068i | \(0.874868\pi\) | |||||||
\(954\) | −12.6174 | −0.408505 | ||||||||
\(955\) | −32.0971 | −1.03864 | ||||||||
\(956\) | 22.6209 | 0.731613 | ||||||||
\(957\) | 33.3557 | 1.07824 | ||||||||
\(958\) | 33.5455 | 1.08381 | ||||||||
\(959\) | 7.61307 | 0.245839 | ||||||||
\(960\) | −6.75818 | −0.218119 | ||||||||
\(961\) | −17.9597 | −0.579345 | ||||||||
\(962\) | 18.3669 | 0.592172 | ||||||||
\(963\) | 9.37151 | 0.301993 | ||||||||
\(964\) | 17.0708 | 0.549812 | ||||||||
\(965\) | 30.5614 | 0.983806 | ||||||||
\(966\) | −17.1680 | −0.552373 | ||||||||
\(967\) | 27.8890 | 0.896850 | 0.448425 | − | 0.893820i | \(-0.351985\pi\) | ||||
0.448425 | + | 0.893820i | \(0.351985\pi\) | |||||||
\(968\) | 2.54096 | 0.0816695 | ||||||||
\(969\) | −84.0690 | −2.70068 | ||||||||
\(970\) | 13.5230 | 0.434199 | ||||||||
\(971\) | −43.9258 | −1.40965 | −0.704824 | − | 0.709382i | \(-0.748974\pi\) | ||||
−0.704824 | + | 0.709382i | \(0.748974\pi\) | |||||||
\(972\) | 21.7198 | 0.696663 | ||||||||
\(973\) | 17.2822 | 0.554043 | ||||||||
\(974\) | −31.8262 | −1.01978 | ||||||||
\(975\) | 12.6239 | 0.404289 | ||||||||
\(976\) | −5.63927 | −0.180508 | ||||||||
\(977\) | 9.57667 | 0.306385 | 0.153192 | − | 0.988196i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(978\) | −21.6769 | −0.693150 | ||||||||
\(979\) | 37.8770 | 1.21055 | ||||||||
\(980\) | −17.5712 | −0.561293 | ||||||||
\(981\) | 54.8534 | 1.75134 | ||||||||
\(982\) | −7.28748 | −0.232553 | ||||||||
\(983\) | −11.0213 | −0.351525 | −0.175763 | − | 0.984433i | \(-0.556239\pi\) | ||||
−0.175763 | + | 0.984433i | \(0.556239\pi\) | |||||||
\(984\) | −4.31201 | −0.137462 | ||||||||
\(985\) | −23.0578 | −0.734684 | ||||||||
\(986\) | 19.1603 | 0.610189 | ||||||||
\(987\) | −1.78750 | −0.0568968 | ||||||||
\(988\) | −12.6464 | −0.402337 | ||||||||
\(989\) | −34.7747 | −1.10577 | ||||||||
\(990\) | −29.3222 | −0.931920 | ||||||||
\(991\) | 4.24190 | 0.134748 | 0.0673742 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673742 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(992\) | −3.61114 | −0.114654 | ||||||||
\(993\) | −65.7449 | −2.08635 | ||||||||
\(994\) | 3.80611 | 0.120722 | ||||||||
\(995\) | 51.9888 | 1.64816 | ||||||||
\(996\) | 13.5221 | 0.428465 | ||||||||
\(997\) | −50.6449 | −1.60394 | −0.801971 | − | 0.597363i | \(-0.796215\pi\) | ||||
−0.801971 | + | 0.597363i | \(0.796215\pi\) | |||||||
\(998\) | −21.8055 | −0.690241 | ||||||||
\(999\) | −3.52464 | −0.111515 |
(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 | 8038.2.a.d.1.12 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.d.1.12 | ✓ | 92 | 1.1 | even | 1 | trivial |