Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.68 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.97722 | 1.39810 | 0.699051 | − | 0.715072i | \(-0.253606\pi\) | ||||
0.699051 | + | 0.715072i | \(0.253606\pi\) | |||||||
\(3\) | −0.844659 | −0.487664 | −0.243832 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243832 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(4\) | 1.90938 | 0.954691 | ||||||||
\(5\) | 0.614325 | 0.274735 | 0.137367 | − | 0.990520i | \(-0.456136\pi\) | ||||
0.137367 | + | 0.990520i | \(0.456136\pi\) | |||||||
\(6\) | −1.67007 | −0.681804 | ||||||||
\(7\) | 1.36766 | 0.516926 | 0.258463 | − | 0.966021i | \(-0.416784\pi\) | ||||
0.258463 | + | 0.966021i | \(0.416784\pi\) | |||||||
\(8\) | −0.179172 | −0.0633467 | ||||||||
\(9\) | −2.28655 | −0.762184 | ||||||||
\(10\) | 1.21465 | 0.384107 | ||||||||
\(11\) | −2.63598 | −0.794779 | −0.397389 | − | 0.917650i | \(-0.630084\pi\) | ||||
−0.397389 | + | 0.917650i | \(0.630084\pi\) | |||||||
\(12\) | −1.61278 | −0.465568 | ||||||||
\(13\) | 4.87808 | 1.35294 | 0.676468 | − | 0.736472i | \(-0.263510\pi\) | ||||
0.676468 | + | 0.736472i | \(0.263510\pi\) | |||||||
\(14\) | 2.70415 | 0.722716 | ||||||||
\(15\) | −0.518895 | −0.133978 | ||||||||
\(16\) | −4.17302 | −1.04326 | ||||||||
\(17\) | −7.57566 | −1.83737 | −0.918683 | − | 0.394995i | \(-0.870746\pi\) | ||||
−0.918683 | + | 0.394995i | \(0.870746\pi\) | |||||||
\(18\) | −4.52100 | −1.06561 | ||||||||
\(19\) | 3.99555 | 0.916641 | 0.458321 | − | 0.888787i | \(-0.348451\pi\) | ||||
0.458321 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(20\) | 1.17298 | 0.262287 | ||||||||
\(21\) | −1.15520 | −0.252086 | ||||||||
\(22\) | −5.21191 | −1.11118 | ||||||||
\(23\) | 2.88047 | 0.600619 | 0.300310 | − | 0.953842i | \(-0.402910\pi\) | ||||
0.300310 | + | 0.953842i | \(0.402910\pi\) | |||||||
\(24\) | 0.151339 | 0.0308919 | ||||||||
\(25\) | −4.62260 | −0.924521 | ||||||||
\(26\) | 9.64502 | 1.89154 | ||||||||
\(27\) | 4.46533 | 0.859354 | ||||||||
\(28\) | 2.61138 | 0.493505 | ||||||||
\(29\) | −7.60523 | −1.41226 | −0.706128 | − | 0.708085i | \(-0.749560\pi\) | ||||
−0.706128 | + | 0.708085i | \(0.749560\pi\) | |||||||
\(30\) | −1.02597 | −0.187315 | ||||||||
\(31\) | −1.29815 | −0.233155 | −0.116577 | − | 0.993182i | \(-0.537192\pi\) | ||||
−0.116577 | + | 0.993182i | \(0.537192\pi\) | |||||||
\(32\) | −7.89263 | −1.39523 | ||||||||
\(33\) | 2.22651 | 0.387585 | ||||||||
\(34\) | −14.9787 | −2.56883 | ||||||||
\(35\) | 0.840186 | 0.142017 | ||||||||
\(36\) | −4.36590 | −0.727650 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 7.90006 | 1.28156 | ||||||||
\(39\) | −4.12032 | −0.659779 | ||||||||
\(40\) | −0.110070 | −0.0174035 | ||||||||
\(41\) | 3.56060 | 0.556072 | 0.278036 | − | 0.960571i | \(-0.410317\pi\) | ||||
0.278036 | + | 0.960571i | \(0.410317\pi\) | |||||||
\(42\) | −2.28409 | −0.352442 | ||||||||
\(43\) | 0.705969 | 0.107659 | 0.0538296 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538296 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(44\) | −5.03310 | −0.758768 | ||||||||
\(45\) | −1.40469 | −0.209398 | ||||||||
\(46\) | 5.69531 | 0.839728 | ||||||||
\(47\) | 4.33906 | 0.632917 | 0.316459 | − | 0.948606i | \(-0.397506\pi\) | ||||
0.316459 | + | 0.948606i | \(0.397506\pi\) | |||||||
\(48\) | 3.52478 | 0.508759 | ||||||||
\(49\) | −5.12951 | −0.732788 | ||||||||
\(50\) | −9.13989 | −1.29258 | ||||||||
\(51\) | 6.39885 | 0.896018 | ||||||||
\(52\) | 9.31412 | 1.29164 | ||||||||
\(53\) | −7.77401 | −1.06784 | −0.533921 | − | 0.845534i | \(-0.679282\pi\) | ||||
−0.533921 | + | 0.845534i | \(0.679282\pi\) | |||||||
\(54\) | 8.82893 | 1.20146 | ||||||||
\(55\) | −1.61935 | −0.218353 | ||||||||
\(56\) | −0.245045 | −0.0327456 | ||||||||
\(57\) | −3.37488 | −0.447013 | ||||||||
\(58\) | −15.0372 | −1.97448 | ||||||||
\(59\) | −6.16758 | −0.802950 | −0.401475 | − | 0.915870i | \(-0.631502\pi\) | ||||
−0.401475 | + | 0.915870i | \(0.631502\pi\) | |||||||
\(60\) | −0.990769 | −0.127908 | ||||||||
\(61\) | −12.5683 | −1.60921 | −0.804603 | − | 0.593813i | \(-0.797622\pi\) | ||||
−0.804603 | + | 0.593813i | \(0.797622\pi\) | |||||||
\(62\) | −2.56673 | −0.325974 | ||||||||
\(63\) | −3.12722 | −0.393993 | ||||||||
\(64\) | −7.25938 | −0.907422 | ||||||||
\(65\) | 2.99673 | 0.371698 | ||||||||
\(66\) | 4.40228 | 0.541884 | ||||||||
\(67\) | −0.139780 | −0.0170769 | −0.00853843 | − | 0.999964i | \(-0.502718\pi\) | ||||
−0.00853843 | + | 0.999964i | \(0.502718\pi\) | |||||||
\(68\) | −14.4648 | −1.75412 | ||||||||
\(69\) | −2.43301 | −0.292901 | ||||||||
\(70\) | 1.66123 | 0.198555 | ||||||||
\(71\) | −10.7372 | −1.27428 | −0.637138 | − | 0.770750i | \(-0.719882\pi\) | ||||
−0.637138 | + | 0.770750i | \(0.719882\pi\) | |||||||
\(72\) | 0.409685 | 0.0482818 | ||||||||
\(73\) | 1.91378 | 0.223991 | 0.111995 | − | 0.993709i | \(-0.464276\pi\) | ||||
0.111995 | + | 0.993709i | \(0.464276\pi\) | |||||||
\(74\) | −1.97722 | −0.229847 | ||||||||
\(75\) | 3.90452 | 0.450856 | ||||||||
\(76\) | 7.62903 | 0.875109 | ||||||||
\(77\) | −3.60512 | −0.410842 | ||||||||
\(78\) | −8.14675 | −0.922438 | ||||||||
\(79\) | −13.8909 | −1.56285 | −0.781425 | − | 0.624000i | \(-0.785507\pi\) | ||||
−0.781425 | + | 0.624000i | \(0.785507\pi\) | |||||||
\(80\) | −2.56359 | −0.286619 | ||||||||
\(81\) | 3.08797 | 0.343108 | ||||||||
\(82\) | 7.04007 | 0.777446 | ||||||||
\(83\) | 12.3001 | 1.35011 | 0.675056 | − | 0.737766i | \(-0.264119\pi\) | ||||
0.675056 | + | 0.737766i | \(0.264119\pi\) | |||||||
\(84\) | −2.20573 | −0.240664 | ||||||||
\(85\) | −4.65392 | −0.504788 | ||||||||
\(86\) | 1.39585 | 0.150519 | ||||||||
\(87\) | 6.42382 | 0.688706 | ||||||||
\(88\) | 0.472293 | 0.0503466 | ||||||||
\(89\) | −2.29695 | −0.243477 | −0.121738 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121738 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(90\) | −2.77737 | −0.292760 | ||||||||
\(91\) | 6.67155 | 0.699368 | ||||||||
\(92\) | 5.49992 | 0.573406 | ||||||||
\(93\) | 1.09650 | 0.113701 | ||||||||
\(94\) | 8.57926 | 0.884883 | ||||||||
\(95\) | 2.45457 | 0.251833 | ||||||||
\(96\) | 6.66658 | 0.680405 | ||||||||
\(97\) | −2.63289 | −0.267329 | −0.133665 | − | 0.991027i | \(-0.542674\pi\) | ||||
−0.133665 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(98\) | −10.1422 | −1.02451 | ||||||||
\(99\) | 6.02731 | 0.605767 | ||||||||
\(100\) | −8.82632 | −0.882632 | ||||||||
\(101\) | 3.99977 | 0.397992 | 0.198996 | − | 0.980000i | \(-0.436232\pi\) | ||||
0.198996 | + | 0.980000i | \(0.436232\pi\) | |||||||
\(102\) | 12.6519 | 1.25272 | ||||||||
\(103\) | 6.72618 | 0.662751 | 0.331375 | − | 0.943499i | \(-0.392487\pi\) | ||||
0.331375 | + | 0.943499i | \(0.392487\pi\) | |||||||
\(104\) | −0.874014 | −0.0857041 | ||||||||
\(105\) | −0.709671 | −0.0692568 | ||||||||
\(106\) | −15.3709 | −1.49295 | ||||||||
\(107\) | −8.33461 | −0.805737 | −0.402869 | − | 0.915258i | \(-0.631987\pi\) | ||||
−0.402869 | + | 0.915258i | \(0.631987\pi\) | |||||||
\(108\) | 8.52603 | 0.820417 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −3.20180 | −0.305280 | ||||||||
\(111\) | 0.844659 | 0.0801715 | ||||||||
\(112\) | −5.70727 | −0.539286 | ||||||||
\(113\) | 5.53501 | 0.520690 | 0.260345 | − | 0.965516i | \(-0.416164\pi\) | ||||
0.260345 | + | 0.965516i | \(0.416164\pi\) | |||||||
\(114\) | −6.67286 | −0.624970 | ||||||||
\(115\) | 1.76954 | 0.165011 | ||||||||
\(116\) | −14.5213 | −1.34827 | ||||||||
\(117\) | −11.1540 | −1.03119 | ||||||||
\(118\) | −12.1946 | −1.12261 | ||||||||
\(119\) | −10.3609 | −0.949783 | ||||||||
\(120\) | 0.0929713 | 0.00848708 | ||||||||
\(121\) | −4.05160 | −0.368327 | ||||||||
\(122\) | −24.8502 | −2.24983 | ||||||||
\(123\) | −3.00749 | −0.271176 | ||||||||
\(124\) | −2.47867 | −0.222591 | ||||||||
\(125\) | −5.91141 | −0.528732 | ||||||||
\(126\) | −6.18319 | −0.550842 | ||||||||
\(127\) | 4.89305 | 0.434188 | 0.217094 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217094 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(128\) | 1.43190 | 0.126563 | ||||||||
\(129\) | −0.596303 | −0.0525015 | ||||||||
\(130\) | 5.92518 | 0.519673 | ||||||||
\(131\) | 12.6143 | 1.10212 | 0.551060 | − | 0.834466i | \(-0.314223\pi\) | ||||
0.551060 | + | 0.834466i | \(0.314223\pi\) | |||||||
\(132\) | 4.25125 | 0.370024 | ||||||||
\(133\) | 5.46454 | 0.473836 | ||||||||
\(134\) | −0.276375 | −0.0238752 | ||||||||
\(135\) | 2.74317 | 0.236094 | ||||||||
\(136\) | 1.35734 | 0.116391 | ||||||||
\(137\) | 10.5449 | 0.900908 | 0.450454 | − | 0.892800i | \(-0.351262\pi\) | ||||
0.450454 | + | 0.892800i | \(0.351262\pi\) | |||||||
\(138\) | −4.81059 | −0.409505 | ||||||||
\(139\) | 6.88657 | 0.584112 | 0.292056 | − | 0.956401i | \(-0.405661\pi\) | ||||
0.292056 | + | 0.956401i | \(0.405661\pi\) | |||||||
\(140\) | 1.60424 | 0.135583 | ||||||||
\(141\) | −3.66503 | −0.308651 | ||||||||
\(142\) | −21.2298 | −1.78157 | ||||||||
\(143\) | −12.8585 | −1.07528 | ||||||||
\(144\) | 9.54183 | 0.795153 | ||||||||
\(145\) | −4.67208 | −0.387995 | ||||||||
\(146\) | 3.78395 | 0.313162 | ||||||||
\(147\) | 4.33269 | 0.357354 | ||||||||
\(148\) | −1.90938 | −0.156950 | ||||||||
\(149\) | −15.4273 | −1.26385 | −0.631926 | − | 0.775029i | \(-0.717735\pi\) | ||||
−0.631926 | + | 0.775029i | \(0.717735\pi\) | |||||||
\(150\) | 7.72009 | 0.630342 | ||||||||
\(151\) | −3.82152 | −0.310991 | −0.155495 | − | 0.987837i | \(-0.549697\pi\) | ||||
−0.155495 | + | 0.987837i | \(0.549697\pi\) | |||||||
\(152\) | −0.715889 | −0.0580662 | ||||||||
\(153\) | 17.3221 | 1.40041 | ||||||||
\(154\) | −7.12810 | −0.574399 | ||||||||
\(155\) | −0.797487 | −0.0640557 | ||||||||
\(156\) | −7.86726 | −0.629885 | ||||||||
\(157\) | −22.6141 | −1.80480 | −0.902399 | − | 0.430901i | \(-0.858196\pi\) | ||||
−0.902399 | + | 0.430901i | \(0.858196\pi\) | |||||||
\(158\) | −27.4653 | −2.18502 | ||||||||
\(159\) | 6.56639 | 0.520749 | ||||||||
\(160\) | −4.84864 | −0.383319 | ||||||||
\(161\) | 3.93950 | 0.310476 | ||||||||
\(162\) | 6.10558 | 0.479700 | ||||||||
\(163\) | 2.70258 | 0.211682 | 0.105841 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105841 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(164\) | 6.79854 | 0.530877 | ||||||||
\(165\) | 1.36780 | 0.106483 | ||||||||
\(166\) | 24.3200 | 1.88760 | ||||||||
\(167\) | 13.8911 | 1.07492 | 0.537461 | − | 0.843288i | \(-0.319383\pi\) | ||||
0.537461 | + | 0.843288i | \(0.319383\pi\) | |||||||
\(168\) | 0.206980 | 0.0159688 | ||||||||
\(169\) | 10.7957 | 0.830437 | ||||||||
\(170\) | −9.20180 | −0.705746 | ||||||||
\(171\) | −9.13602 | −0.698649 | ||||||||
\(172\) | 1.34796 | 0.102781 | ||||||||
\(173\) | 10.4477 | 0.794326 | 0.397163 | − | 0.917748i | \(-0.369995\pi\) | ||||
0.397163 | + | 0.917748i | \(0.369995\pi\) | |||||||
\(174\) | 12.7013 | 0.962882 | ||||||||
\(175\) | −6.32214 | −0.477909 | ||||||||
\(176\) | 11.0000 | 0.829158 | ||||||||
\(177\) | 5.20950 | 0.391570 | ||||||||
\(178\) | −4.54157 | −0.340405 | ||||||||
\(179\) | −15.2361 | −1.13880 | −0.569400 | − | 0.822061i | \(-0.692824\pi\) | ||||
−0.569400 | + | 0.822061i | \(0.692824\pi\) | |||||||
\(180\) | −2.68208 | −0.199911 | ||||||||
\(181\) | 23.5119 | 1.74763 | 0.873813 | − | 0.486262i | \(-0.161640\pi\) | ||||
0.873813 | + | 0.486262i | \(0.161640\pi\) | |||||||
\(182\) | 13.1911 | 0.977788 | ||||||||
\(183\) | 10.6159 | 0.784752 | ||||||||
\(184\) | −0.516098 | −0.0380473 | ||||||||
\(185\) | −0.614325 | −0.0451661 | ||||||||
\(186\) | 2.16801 | 0.158966 | ||||||||
\(187\) | 19.9693 | 1.46030 | ||||||||
\(188\) | 8.28493 | 0.604240 | ||||||||
\(189\) | 6.10705 | 0.444222 | ||||||||
\(190\) | 4.85321 | 0.352089 | ||||||||
\(191\) | −21.6380 | −1.56567 | −0.782835 | − | 0.622229i | \(-0.786227\pi\) | ||||
−0.782835 | + | 0.622229i | \(0.786227\pi\) | |||||||
\(192\) | 6.13170 | 0.442517 | ||||||||
\(193\) | 13.0907 | 0.942290 | 0.471145 | − | 0.882056i | \(-0.343841\pi\) | ||||
0.471145 | + | 0.882056i | \(0.343841\pi\) | |||||||
\(194\) | −5.20579 | −0.373754 | ||||||||
\(195\) | −2.53121 | −0.181264 | ||||||||
\(196\) | −9.79420 | −0.699586 | ||||||||
\(197\) | −19.6322 | −1.39873 | −0.699367 | − | 0.714762i | \(-0.746535\pi\) | ||||
−0.699367 | + | 0.714762i | \(0.746535\pi\) | |||||||
\(198\) | 11.9173 | 0.846925 | ||||||||
\(199\) | −13.8508 | −0.981855 | −0.490927 | − | 0.871201i | \(-0.663342\pi\) | ||||
−0.490927 | + | 0.871201i | \(0.663342\pi\) | |||||||
\(200\) | 0.828239 | 0.0585654 | ||||||||
\(201\) | 0.118067 | 0.00832777 | ||||||||
\(202\) | 7.90841 | 0.556433 | ||||||||
\(203\) | −10.4013 | −0.730031 | ||||||||
\(204\) | 12.2178 | 0.855420 | ||||||||
\(205\) | 2.18736 | 0.152772 | ||||||||
\(206\) | 13.2991 | 0.926593 | ||||||||
\(207\) | −6.58634 | −0.457782 | ||||||||
\(208\) | −20.3564 | −1.41146 | ||||||||
\(209\) | −10.5322 | −0.728527 | ||||||||
\(210\) | −1.40317 | −0.0968281 | ||||||||
\(211\) | −23.3036 | −1.60429 | −0.802144 | − | 0.597131i | \(-0.796307\pi\) | ||||
−0.802144 | + | 0.597131i | \(0.796307\pi\) | |||||||
\(212\) | −14.8436 | −1.01946 | ||||||||
\(213\) | 9.06930 | 0.621418 | ||||||||
\(214\) | −16.4793 | −1.12650 | ||||||||
\(215\) | 0.433694 | 0.0295777 | ||||||||
\(216\) | −0.800061 | −0.0544372 | ||||||||
\(217\) | −1.77543 | −0.120524 | ||||||||
\(218\) | −1.97722 | −0.133914 | ||||||||
\(219\) | −1.61649 | −0.109232 | ||||||||
\(220\) | −3.09196 | −0.208460 | ||||||||
\(221\) | −36.9547 | −2.48584 | ||||||||
\(222\) | 1.67007 | 0.112088 | ||||||||
\(223\) | 12.6935 | 0.850019 | 0.425009 | − | 0.905189i | \(-0.360271\pi\) | ||||
0.425009 | + | 0.905189i | \(0.360271\pi\) | |||||||
\(224\) | −10.7944 | −0.721232 | ||||||||
\(225\) | 10.5698 | 0.704655 | ||||||||
\(226\) | 10.9439 | 0.727978 | ||||||||
\(227\) | 0.524762 | 0.0348297 | 0.0174148 | − | 0.999848i | \(-0.494456\pi\) | ||||
0.0174148 | + | 0.999848i | \(0.494456\pi\) | |||||||
\(228\) | −6.44393 | −0.426759 | ||||||||
\(229\) | 18.8504 | 1.24567 | 0.622834 | − | 0.782354i | \(-0.285981\pi\) | ||||
0.622834 | + | 0.782354i | \(0.285981\pi\) | |||||||
\(230\) | 3.49877 | 0.230702 | ||||||||
\(231\) | 3.04510 | 0.200353 | ||||||||
\(232\) | 1.36264 | 0.0894617 | ||||||||
\(233\) | 11.5693 | 0.757932 | 0.378966 | − | 0.925411i | \(-0.376280\pi\) | ||||
0.378966 | + | 0.925411i | \(0.376280\pi\) | |||||||
\(234\) | −22.0538 | −1.44170 | ||||||||
\(235\) | 2.66560 | 0.173884 | ||||||||
\(236\) | −11.7763 | −0.766569 | ||||||||
\(237\) | 11.7331 | 0.762145 | ||||||||
\(238\) | −20.4857 | −1.32789 | ||||||||
\(239\) | −1.00425 | −0.0649593 | −0.0324797 | − | 0.999472i | \(-0.510340\pi\) | ||||
−0.0324797 | + | 0.999472i | \(0.510340\pi\) | |||||||
\(240\) | 2.16536 | 0.139774 | ||||||||
\(241\) | −15.1149 | −0.973636 | −0.486818 | − | 0.873503i | \(-0.661842\pi\) | ||||
−0.486818 | + | 0.873503i | \(0.661842\pi\) | |||||||
\(242\) | −8.01088 | −0.514959 | ||||||||
\(243\) | −16.0043 | −1.02668 | ||||||||
\(244\) | −23.9977 | −1.53629 | ||||||||
\(245\) | −3.15119 | −0.201322 | ||||||||
\(246\) | −5.94646 | −0.379132 | ||||||||
\(247\) | 19.4906 | 1.24016 | ||||||||
\(248\) | 0.232592 | 0.0147696 | ||||||||
\(249\) | −10.3894 | −0.658401 | ||||||||
\(250\) | −11.6881 | −0.739222 | ||||||||
\(251\) | −13.5726 | −0.856697 | −0.428349 | − | 0.903614i | \(-0.640904\pi\) | ||||
−0.428349 | + | 0.903614i | \(0.640904\pi\) | |||||||
\(252\) | −5.97106 | −0.376141 | ||||||||
\(253\) | −7.59287 | −0.477359 | ||||||||
\(254\) | 9.67461 | 0.607039 | ||||||||
\(255\) | 3.93097 | 0.246167 | ||||||||
\(256\) | 17.3499 | 1.08437 | ||||||||
\(257\) | −0.604706 | −0.0377205 | −0.0188603 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188603 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(258\) | −1.17902 | −0.0734025 | ||||||||
\(259\) | −1.36766 | −0.0849821 | ||||||||
\(260\) | 5.72190 | 0.354857 | ||||||||
\(261\) | 17.3897 | 1.07640 | ||||||||
\(262\) | 24.9413 | 1.54088 | ||||||||
\(263\) | −29.1636 | −1.79830 | −0.899152 | − | 0.437636i | \(-0.855816\pi\) | ||||
−0.899152 | + | 0.437636i | \(0.855816\pi\) | |||||||
\(264\) | −0.398927 | −0.0245522 | ||||||||
\(265\) | −4.77577 | −0.293373 | ||||||||
\(266\) | 10.8046 | 0.662471 | ||||||||
\(267\) | 1.94014 | 0.118735 | ||||||||
\(268\) | −0.266894 | −0.0163031 | ||||||||
\(269\) | 6.62883 | 0.404167 | 0.202084 | − | 0.979368i | \(-0.435229\pi\) | ||||
0.202084 | + | 0.979368i | \(0.435229\pi\) | |||||||
\(270\) | 5.42383 | 0.330084 | ||||||||
\(271\) | 16.0290 | 0.973693 | 0.486846 | − | 0.873488i | \(-0.338147\pi\) | ||||
0.486846 | + | 0.873488i | \(0.338147\pi\) | |||||||
\(272\) | 31.6134 | 1.91684 | ||||||||
\(273\) | −5.63518 | −0.341057 | ||||||||
\(274\) | 20.8495 | 1.25956 | ||||||||
\(275\) | 12.1851 | 0.734789 | ||||||||
\(276\) | −4.64555 | −0.279629 | ||||||||
\(277\) | −4.96847 | −0.298527 | −0.149263 | − | 0.988797i | \(-0.547690\pi\) | ||||
−0.149263 | + | 0.988797i | \(0.547690\pi\) | |||||||
\(278\) | 13.6162 | 0.816648 | ||||||||
\(279\) | 2.96829 | 0.177707 | ||||||||
\(280\) | −0.150538 | −0.00899634 | ||||||||
\(281\) | −26.6508 | −1.58985 | −0.794927 | − | 0.606705i | \(-0.792491\pi\) | ||||
−0.794927 | + | 0.606705i | \(0.792491\pi\) | |||||||
\(282\) | −7.24655 | −0.431526 | ||||||||
\(283\) | −2.66611 | −0.158484 | −0.0792418 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792418 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(284\) | −20.5015 | −1.21654 | ||||||||
\(285\) | −2.07327 | −0.122810 | ||||||||
\(286\) | −25.4241 | −1.50336 | ||||||||
\(287\) | 4.86968 | 0.287448 | ||||||||
\(288\) | 18.0469 | 1.06342 | ||||||||
\(289\) | 40.3906 | 2.37592 | ||||||||
\(290\) | −9.23772 | −0.542457 | ||||||||
\(291\) | 2.22389 | 0.130367 | ||||||||
\(292\) | 3.65413 | 0.213842 | ||||||||
\(293\) | −15.4102 | −0.900276 | −0.450138 | − | 0.892959i | \(-0.648625\pi\) | ||||
−0.450138 | + | 0.892959i | \(0.648625\pi\) | |||||||
\(294\) | 8.56666 | 0.499618 | ||||||||
\(295\) | −3.78890 | −0.220598 | ||||||||
\(296\) | 0.179172 | 0.0104141 | ||||||||
\(297\) | −11.7705 | −0.682996 | ||||||||
\(298\) | −30.5030 | −1.76699 | ||||||||
\(299\) | 14.0512 | 0.812600 | ||||||||
\(300\) | 7.45523 | 0.430428 | ||||||||
\(301\) | 0.965523 | 0.0556518 | ||||||||
\(302\) | −7.55597 | −0.434797 | ||||||||
\(303\) | −3.37844 | −0.194086 | ||||||||
\(304\) | −16.6735 | −0.956292 | ||||||||
\(305\) | −7.72102 | −0.442104 | ||||||||
\(306\) | 34.2496 | 1.95792 | ||||||||
\(307\) | 33.2685 | 1.89873 | 0.949366 | − | 0.314173i | \(-0.101727\pi\) | ||||
0.949366 | + | 0.314173i | \(0.101727\pi\) | |||||||
\(308\) | −6.88355 | −0.392227 | ||||||||
\(309\) | −5.68133 | −0.323200 | ||||||||
\(310\) | −1.57680 | −0.0895564 | ||||||||
\(311\) | 25.6595 | 1.45502 | 0.727508 | − | 0.686100i | \(-0.240679\pi\) | ||||
0.727508 | + | 0.686100i | \(0.240679\pi\) | |||||||
\(312\) | 0.738244 | 0.0417948 | ||||||||
\(313\) | 26.6015 | 1.50360 | 0.751802 | − | 0.659389i | \(-0.229185\pi\) | ||||
0.751802 | + | 0.659389i | \(0.229185\pi\) | |||||||
\(314\) | −44.7129 | −2.52329 | ||||||||
\(315\) | −1.92113 | −0.108243 | ||||||||
\(316\) | −26.5230 | −1.49204 | ||||||||
\(317\) | 9.63243 | 0.541011 | 0.270506 | − | 0.962718i | \(-0.412809\pi\) | ||||
0.270506 | + | 0.962718i | \(0.412809\pi\) | |||||||
\(318\) | 12.9832 | 0.728060 | ||||||||
\(319\) | 20.0472 | 1.12243 | ||||||||
\(320\) | −4.45962 | −0.249300 | ||||||||
\(321\) | 7.03990 | 0.392929 | ||||||||
\(322\) | 7.78923 | 0.434077 | ||||||||
\(323\) | −30.2689 | −1.68421 | ||||||||
\(324\) | 5.89611 | 0.327562 | ||||||||
\(325\) | −22.5494 | −1.25082 | ||||||||
\(326\) | 5.34358 | 0.295954 | ||||||||
\(327\) | 0.844659 | 0.0467097 | ||||||||
\(328\) | −0.637958 | −0.0352253 | ||||||||
\(329\) | 5.93435 | 0.327171 | ||||||||
\(330\) | 2.70443 | 0.148874 | ||||||||
\(331\) | −13.6059 | −0.747846 | −0.373923 | − | 0.927460i | \(-0.621988\pi\) | ||||
−0.373923 | + | 0.927460i | \(0.621988\pi\) | |||||||
\(332\) | 23.4856 | 1.28894 | ||||||||
\(333\) | 2.28655 | 0.125302 | ||||||||
\(334\) | 27.4656 | 1.50285 | ||||||||
\(335\) | −0.0858705 | −0.00469160 | ||||||||
\(336\) | 4.82070 | 0.262991 | ||||||||
\(337\) | 13.6237 | 0.742130 | 0.371065 | − | 0.928607i | \(-0.378993\pi\) | ||||
0.371065 | + | 0.928607i | \(0.378993\pi\) | |||||||
\(338\) | 21.3454 | 1.16104 | ||||||||
\(339\) | −4.67519 | −0.253922 | ||||||||
\(340\) | −8.88610 | −0.481917 | ||||||||
\(341\) | 3.42190 | 0.185306 | ||||||||
\(342\) | −18.0639 | −0.976783 | ||||||||
\(343\) | −16.5890 | −0.895723 | ||||||||
\(344\) | −0.126490 | −0.00681986 | ||||||||
\(345\) | −1.49466 | −0.0804699 | ||||||||
\(346\) | 20.6574 | 1.11055 | ||||||||
\(347\) | 23.3582 | 1.25393 | 0.626966 | − | 0.779047i | \(-0.284296\pi\) | ||||
0.626966 | + | 0.779047i | \(0.284296\pi\) | |||||||
\(348\) | 12.2655 | 0.657502 | ||||||||
\(349\) | 27.8488 | 1.49071 | 0.745357 | − | 0.666665i | \(-0.232279\pi\) | ||||
0.745357 | + | 0.666665i | \(0.232279\pi\) | |||||||
\(350\) | −12.5002 | −0.668166 | ||||||||
\(351\) | 21.7823 | 1.16265 | ||||||||
\(352\) | 20.8048 | 1.10890 | ||||||||
\(353\) | 10.7822 | 0.573877 | 0.286939 | − | 0.957949i | \(-0.407362\pi\) | ||||
0.286939 | + | 0.957949i | \(0.407362\pi\) | |||||||
\(354\) | 10.3003 | 0.547455 | ||||||||
\(355\) | −6.59615 | −0.350087 | ||||||||
\(356\) | −4.38576 | −0.232445 | ||||||||
\(357\) | 8.75143 | 0.463175 | ||||||||
\(358\) | −30.1251 | −1.59216 | ||||||||
\(359\) | 29.7902 | 1.57227 | 0.786134 | − | 0.618056i | \(-0.212080\pi\) | ||||
0.786134 | + | 0.618056i | \(0.212080\pi\) | |||||||
\(360\) | 0.251680 | 0.0132647 | ||||||||
\(361\) | −3.03560 | −0.159768 | ||||||||
\(362\) | 46.4881 | 2.44336 | ||||||||
\(363\) | 3.42222 | 0.179620 | ||||||||
\(364\) | 12.7385 | 0.667680 | ||||||||
\(365\) | 1.17568 | 0.0615380 | ||||||||
\(366\) | 20.9900 | 1.09716 | ||||||||
\(367\) | 9.50922 | 0.496377 | 0.248189 | − | 0.968712i | \(-0.420165\pi\) | ||||
0.248189 | + | 0.968712i | \(0.420165\pi\) | |||||||
\(368\) | −12.0203 | −0.626600 | ||||||||
\(369\) | −8.14149 | −0.423829 | ||||||||
\(370\) | −1.21465 | −0.0631468 | ||||||||
\(371\) | −10.6322 | −0.551996 | ||||||||
\(372\) | 2.09363 | 0.108550 | ||||||||
\(373\) | 27.4998 | 1.42389 | 0.711944 | − | 0.702236i | \(-0.247815\pi\) | ||||
0.711944 | + | 0.702236i | \(0.247815\pi\) | |||||||
\(374\) | 39.4836 | 2.04165 | ||||||||
\(375\) | 4.99312 | 0.257844 | ||||||||
\(376\) | −0.777437 | −0.0400932 | ||||||||
\(377\) | −37.0989 | −1.91069 | ||||||||
\(378\) | 12.0749 | 0.621068 | ||||||||
\(379\) | 18.8466 | 0.968086 | 0.484043 | − | 0.875044i | \(-0.339168\pi\) | ||||
0.484043 | + | 0.875044i | \(0.339168\pi\) | |||||||
\(380\) | 4.68670 | 0.240423 | ||||||||
\(381\) | −4.13296 | −0.211738 | ||||||||
\(382\) | −42.7830 | −2.18897 | ||||||||
\(383\) | −23.3183 | −1.19151 | −0.595754 | − | 0.803167i | \(-0.703147\pi\) | ||||
−0.595754 | + | 0.803167i | \(0.703147\pi\) | |||||||
\(384\) | −1.20947 | −0.0617204 | ||||||||
\(385\) | −2.21472 | −0.112872 | ||||||||
\(386\) | 25.8832 | 1.31742 | ||||||||
\(387\) | −1.61423 | −0.0820561 | ||||||||
\(388\) | −5.02719 | −0.255217 | ||||||||
\(389\) | −5.99151 | −0.303781 | −0.151891 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151891 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(390\) | −5.00476 | −0.253426 | ||||||||
\(391\) | −21.8214 | −1.10356 | ||||||||
\(392\) | 0.919063 | 0.0464197 | ||||||||
\(393\) | −10.6548 | −0.537464 | ||||||||
\(394\) | −38.8171 | −1.95557 | ||||||||
\(395\) | −8.53353 | −0.429369 | ||||||||
\(396\) | 11.5084 | 0.578321 | ||||||||
\(397\) | 21.3616 | 1.07211 | 0.536054 | − | 0.844184i | \(-0.319914\pi\) | ||||
0.536054 | + | 0.844184i | \(0.319914\pi\) | |||||||
\(398\) | −27.3859 | −1.37273 | ||||||||
\(399\) | −4.61567 | −0.231073 | ||||||||
\(400\) | 19.2902 | 0.964512 | ||||||||
\(401\) | −16.9527 | −0.846578 | −0.423289 | − | 0.905995i | \(-0.639124\pi\) | ||||
−0.423289 | + | 0.905995i | \(0.639124\pi\) | |||||||
\(402\) | 0.233443 | 0.0116431 | ||||||||
\(403\) | −6.33249 | −0.315444 | ||||||||
\(404\) | 7.63709 | 0.379959 | ||||||||
\(405\) | 1.89702 | 0.0942636 | ||||||||
\(406\) | −20.5657 | −1.02066 | ||||||||
\(407\) | 2.63598 | 0.130661 | ||||||||
\(408\) | −1.14649 | −0.0567598 | ||||||||
\(409\) | 29.7384 | 1.47047 | 0.735234 | − | 0.677814i | \(-0.237072\pi\) | ||||
0.735234 | + | 0.677814i | \(0.237072\pi\) | |||||||
\(410\) | 4.32489 | 0.213591 | ||||||||
\(411\) | −8.90681 | −0.439341 | ||||||||
\(412\) | 12.8429 | 0.632722 | ||||||||
\(413\) | −8.43513 | −0.415066 | ||||||||
\(414\) | −13.0226 | −0.640027 | ||||||||
\(415\) | 7.55627 | 0.370923 | ||||||||
\(416\) | −38.5009 | −1.88766 | ||||||||
\(417\) | −5.81681 | −0.284850 | ||||||||
\(418\) | −20.8244 | −1.01856 | ||||||||
\(419\) | −30.1939 | −1.47507 | −0.737535 | − | 0.675309i | \(-0.764010\pi\) | ||||
−0.737535 | + | 0.675309i | \(0.764010\pi\) | |||||||
\(420\) | −1.35503 | −0.0661188 | ||||||||
\(421\) | 0.316198 | 0.0154105 | 0.00770527 | − | 0.999970i | \(-0.497547\pi\) | ||||
0.00770527 | + | 0.999970i | \(0.497547\pi\) | |||||||
\(422\) | −46.0763 | −2.24296 | ||||||||
\(423\) | −9.92149 | −0.482399 | ||||||||
\(424\) | 1.39288 | 0.0676443 | ||||||||
\(425\) | 35.0193 | 1.69868 | ||||||||
\(426\) | 17.9320 | 0.868806 | ||||||||
\(427\) | −17.1891 | −0.831840 | ||||||||
\(428\) | −15.9140 | −0.769230 | ||||||||
\(429\) | 10.8611 | 0.524378 | ||||||||
\(430\) | 0.857507 | 0.0413527 | ||||||||
\(431\) | 17.3643 | 0.836410 | 0.418205 | − | 0.908353i | \(-0.362659\pi\) | ||||
0.418205 | + | 0.908353i | \(0.362659\pi\) | |||||||
\(432\) | −18.6339 | −0.896526 | ||||||||
\(433\) | 18.6070 | 0.894198 | 0.447099 | − | 0.894485i | \(-0.352457\pi\) | ||||
0.447099 | + | 0.894485i | \(0.352457\pi\) | |||||||
\(434\) | −3.51040 | −0.168505 | ||||||||
\(435\) | 3.94632 | 0.189211 | ||||||||
\(436\) | −1.90938 | −0.0914428 | ||||||||
\(437\) | 11.5091 | 0.550553 | ||||||||
\(438\) | −3.19615 | −0.152718 | ||||||||
\(439\) | −12.8933 | −0.615366 | −0.307683 | − | 0.951489i | \(-0.599554\pi\) | ||||
−0.307683 | + | 0.951489i | \(0.599554\pi\) | |||||||
\(440\) | 0.290142 | 0.0138320 | ||||||||
\(441\) | 11.7289 | 0.558519 | ||||||||
\(442\) | −73.0674 | −3.47546 | ||||||||
\(443\) | −39.0619 | −1.85588 | −0.927942 | − | 0.372724i | \(-0.878424\pi\) | ||||
−0.927942 | + | 0.372724i | \(0.878424\pi\) | |||||||
\(444\) | 1.61278 | 0.0765390 | ||||||||
\(445\) | −1.41108 | −0.0668914 | ||||||||
\(446\) | 25.0978 | 1.18841 | ||||||||
\(447\) | 13.0308 | 0.616335 | ||||||||
\(448\) | −9.92834 | −0.469070 | ||||||||
\(449\) | 31.3696 | 1.48042 | 0.740211 | − | 0.672374i | \(-0.234726\pi\) | ||||
0.740211 | + | 0.672374i | \(0.234726\pi\) | |||||||
\(450\) | 20.8988 | 0.985180 | ||||||||
\(451\) | −9.38567 | −0.441954 | ||||||||
\(452\) | 10.5684 | 0.497098 | ||||||||
\(453\) | 3.22788 | 0.151659 | ||||||||
\(454\) | 1.03757 | 0.0486955 | ||||||||
\(455\) | 4.09850 | 0.192141 | ||||||||
\(456\) | 0.604682 | 0.0283168 | ||||||||
\(457\) | −1.36468 | −0.0638370 | −0.0319185 | − | 0.999490i | \(-0.510162\pi\) | ||||
−0.0319185 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(458\) | 37.2712 | 1.74157 | ||||||||
\(459\) | −33.8278 | −1.57895 | ||||||||
\(460\) | 3.37874 | 0.157534 | ||||||||
\(461\) | −23.7309 | −1.10526 | −0.552629 | − | 0.833427i | \(-0.686375\pi\) | ||||
−0.552629 | + | 0.833427i | \(0.686375\pi\) | |||||||
\(462\) | 6.02082 | 0.280114 | ||||||||
\(463\) | −8.14141 | −0.378363 | −0.189182 | − | 0.981942i | \(-0.560584\pi\) | ||||
−0.189182 | + | 0.981942i | \(0.560584\pi\) | |||||||
\(464\) | 31.7368 | 1.47334 | ||||||||
\(465\) | 0.673605 | 0.0312377 | ||||||||
\(466\) | 22.8751 | 1.05967 | ||||||||
\(467\) | 41.2670 | 1.90961 | 0.954804 | − | 0.297237i | \(-0.0960653\pi\) | ||||
0.954804 | + | 0.297237i | \(0.0960653\pi\) | |||||||
\(468\) | −21.2972 | −0.984464 | ||||||||
\(469\) | −0.191171 | −0.00882747 | ||||||||
\(470\) | 5.27046 | 0.243108 | ||||||||
\(471\) | 19.1012 | 0.880135 | ||||||||
\(472\) | 1.10505 | 0.0508642 | ||||||||
\(473\) | −1.86092 | −0.0855652 | ||||||||
\(474\) | 23.1988 | 1.06556 | ||||||||
\(475\) | −18.4698 | −0.847454 | ||||||||
\(476\) | −19.7829 | −0.906749 | ||||||||
\(477\) | 17.7757 | 0.813892 | ||||||||
\(478\) | −1.98561 | −0.0908198 | ||||||||
\(479\) | −32.1366 | −1.46836 | −0.734180 | − | 0.678955i | \(-0.762433\pi\) | ||||
−0.734180 | + | 0.678955i | \(0.762433\pi\) | |||||||
\(480\) | 4.09545 | 0.186931 | ||||||||
\(481\) | −4.87808 | −0.222421 | ||||||||
\(482\) | −29.8854 | −1.36124 | ||||||||
\(483\) | −3.32753 | −0.151408 | ||||||||
\(484\) | −7.73605 | −0.351639 | ||||||||
\(485\) | −1.61745 | −0.0734446 | ||||||||
\(486\) | −31.6439 | −1.43540 | ||||||||
\(487\) | −12.1022 | −0.548403 | −0.274201 | − | 0.961672i | \(-0.588413\pi\) | ||||
−0.274201 | + | 0.961672i | \(0.588413\pi\) | |||||||
\(488\) | 2.25188 | 0.101938 | ||||||||
\(489\) | −2.28276 | −0.103230 | ||||||||
\(490\) | −6.23058 | −0.281469 | ||||||||
\(491\) | −30.7004 | −1.38549 | −0.692744 | − | 0.721183i | \(-0.743598\pi\) | ||||
−0.692744 | + | 0.721183i | \(0.743598\pi\) | |||||||
\(492\) | −5.74245 | −0.258890 | ||||||||
\(493\) | 57.6146 | 2.59483 | ||||||||
\(494\) | 38.5371 | 1.73387 | ||||||||
\(495\) | 3.70273 | 0.166425 | ||||||||
\(496\) | 5.41722 | 0.243240 | ||||||||
\(497\) | −14.6849 | −0.658706 | ||||||||
\(498\) | −20.5421 | −0.920513 | ||||||||
\(499\) | 19.8952 | 0.890630 | 0.445315 | − | 0.895374i | \(-0.353092\pi\) | ||||
0.445315 | + | 0.895374i | \(0.353092\pi\) | |||||||
\(500\) | −11.2871 | −0.504776 | ||||||||
\(501\) | −11.7332 | −0.524201 | ||||||||
\(502\) | −26.8360 | −1.19775 | ||||||||
\(503\) | 12.9014 | 0.575244 | 0.287622 | − | 0.957744i | \(-0.407135\pi\) | ||||
0.287622 | + | 0.957744i | \(0.407135\pi\) | |||||||
\(504\) | 0.560309 | 0.0249581 | ||||||||
\(505\) | 2.45716 | 0.109342 | ||||||||
\(506\) | −15.0127 | −0.667397 | ||||||||
\(507\) | −9.11867 | −0.404975 | ||||||||
\(508\) | 9.34270 | 0.414515 | ||||||||
\(509\) | −9.57963 | −0.424610 | −0.212305 | − | 0.977203i | \(-0.568097\pi\) | ||||
−0.212305 | + | 0.977203i | \(0.568097\pi\) | |||||||
\(510\) | 7.77238 | 0.344167 | ||||||||
\(511\) | 2.61739 | 0.115787 | ||||||||
\(512\) | 31.4408 | 1.38950 | ||||||||
\(513\) | 17.8415 | 0.787719 | ||||||||
\(514\) | −1.19563 | −0.0527372 | ||||||||
\(515\) | 4.13206 | 0.182081 | ||||||||
\(516\) | −1.13857 | −0.0501227 | ||||||||
\(517\) | −11.4377 | −0.503029 | ||||||||
\(518\) | −2.70415 | −0.118814 | ||||||||
\(519\) | −8.82477 | −0.387364 | ||||||||
\(520\) | −0.536929 | −0.0235459 | ||||||||
\(521\) | −42.8130 | −1.87567 | −0.937835 | − | 0.347081i | \(-0.887173\pi\) | ||||
−0.937835 | + | 0.347081i | \(0.887173\pi\) | |||||||
\(522\) | 34.3833 | 1.50491 | ||||||||
\(523\) | −32.1467 | −1.40568 | −0.702838 | − | 0.711350i | \(-0.748084\pi\) | ||||
−0.702838 | + | 0.711350i | \(0.748084\pi\) | |||||||
\(524\) | 24.0856 | 1.05218 | ||||||||
\(525\) | 5.34005 | 0.233059 | ||||||||
\(526\) | −57.6627 | −2.51421 | ||||||||
\(527\) | 9.83435 | 0.428391 | ||||||||
\(528\) | −9.29126 | −0.404350 | ||||||||
\(529\) | −14.7029 | −0.639256 | ||||||||
\(530\) | −9.44273 | −0.410166 | ||||||||
\(531\) | 14.1025 | 0.611995 | ||||||||
\(532\) | 10.4339 | 0.452367 | ||||||||
\(533\) | 17.3689 | 0.752330 | ||||||||
\(534\) | 3.83608 | 0.166003 | ||||||||
\(535\) | −5.12016 | −0.221364 | ||||||||
\(536\) | 0.0250446 | 0.00108176 | ||||||||
\(537\) | 12.8693 | 0.555352 | ||||||||
\(538\) | 13.1066 | 0.565067 | ||||||||
\(539\) | 13.5213 | 0.582404 | ||||||||
\(540\) | 5.23775 | 0.225397 | ||||||||
\(541\) | −14.2474 | −0.612545 | −0.306273 | − | 0.951944i | \(-0.599082\pi\) | ||||
−0.306273 | + | 0.951944i | \(0.599082\pi\) | |||||||
\(542\) | 31.6928 | 1.36132 | ||||||||
\(543\) | −19.8595 | −0.852255 | ||||||||
\(544\) | 59.7918 | 2.56355 | ||||||||
\(545\) | −0.614325 | −0.0263148 | ||||||||
\(546\) | −11.1420 | −0.476832 | ||||||||
\(547\) | −24.4814 | −1.04675 | −0.523375 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523375 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(548\) | 20.1342 | 0.860089 | ||||||||
\(549\) | 28.7381 | 1.22651 | ||||||||
\(550\) | 24.0926 | 1.02731 | ||||||||
\(551\) | −30.3870 | −1.29453 | ||||||||
\(552\) | 0.435927 | 0.0185543 | ||||||||
\(553\) | −18.9980 | −0.807877 | ||||||||
\(554\) | −9.82374 | −0.417371 | ||||||||
\(555\) | 0.518895 | 0.0220259 | ||||||||
\(556\) | 13.1491 | 0.557646 | ||||||||
\(557\) | 37.4969 | 1.58879 | 0.794396 | − | 0.607400i | \(-0.207787\pi\) | ||||
0.794396 | + | 0.607400i | \(0.207787\pi\) | |||||||
\(558\) | 5.86895 | 0.248452 | ||||||||
\(559\) | 3.44377 | 0.145656 | ||||||||
\(560\) | −3.50612 | −0.148161 | ||||||||
\(561\) | −16.8672 | −0.712136 | ||||||||
\(562\) | −52.6944 | −2.22278 | ||||||||
\(563\) | −8.86803 | −0.373743 | −0.186872 | − | 0.982384i | \(-0.559835\pi\) | ||||
−0.186872 | + | 0.982384i | \(0.559835\pi\) | |||||||
\(564\) | −6.99794 | −0.294666 | ||||||||
\(565\) | 3.40030 | 0.143051 | ||||||||
\(566\) | −5.27147 | −0.221576 | ||||||||
\(567\) | 4.22329 | 0.177361 | ||||||||
\(568\) | 1.92381 | 0.0807211 | ||||||||
\(569\) | −19.5351 | −0.818953 | −0.409476 | − | 0.912321i | \(-0.634289\pi\) | ||||
−0.409476 | + | 0.912321i | \(0.634289\pi\) | |||||||
\(570\) | −4.09930 | −0.171701 | ||||||||
\(571\) | 41.7209 | 1.74596 | 0.872982 | − | 0.487752i | \(-0.162183\pi\) | ||||
0.872982 | + | 0.487752i | \(0.162183\pi\) | |||||||
\(572\) | −24.5519 | −1.02656 | ||||||||
\(573\) | 18.2767 | 0.763521 | ||||||||
\(574\) | 9.62840 | 0.401882 | ||||||||
\(575\) | −13.3153 | −0.555285 | ||||||||
\(576\) | 16.5989 | 0.691622 | ||||||||
\(577\) | 13.0856 | 0.544760 | 0.272380 | − | 0.962190i | \(-0.412189\pi\) | ||||
0.272380 | + | 0.962190i | \(0.412189\pi\) | |||||||
\(578\) | 79.8609 | 3.32177 | ||||||||
\(579\) | −11.0572 | −0.459521 | ||||||||
\(580\) | −8.92079 | −0.370416 | ||||||||
\(581\) | 16.8223 | 0.697908 | ||||||||
\(582\) | 4.39711 | 0.182266 | ||||||||
\(583\) | 20.4922 | 0.848698 | ||||||||
\(584\) | −0.342894 | −0.0141891 | ||||||||
\(585\) | −6.85217 | −0.283303 | ||||||||
\(586\) | −30.4694 | −1.25868 | ||||||||
\(587\) | −30.6343 | −1.26441 | −0.632206 | − | 0.774800i | \(-0.717850\pi\) | ||||
−0.632206 | + | 0.774800i | \(0.717850\pi\) | |||||||
\(588\) | 8.27276 | 0.341163 | ||||||||
\(589\) | −5.18683 | −0.213719 | ||||||||
\(590\) | −7.49147 | −0.308419 | ||||||||
\(591\) | 16.5825 | 0.682113 | ||||||||
\(592\) | 4.17302 | 0.171510 | ||||||||
\(593\) | 8.30041 | 0.340857 | 0.170428 | − | 0.985370i | \(-0.445485\pi\) | ||||
0.170428 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(594\) | −23.2729 | −0.954898 | ||||||||
\(595\) | −6.36496 | −0.260938 | ||||||||
\(596\) | −29.4565 | −1.20659 | ||||||||
\(597\) | 11.6992 | 0.478815 | ||||||||
\(598\) | 27.7822 | 1.13610 | ||||||||
\(599\) | 26.5007 | 1.08279 | 0.541394 | − | 0.840769i | \(-0.317897\pi\) | ||||
0.541394 | + | 0.840769i | \(0.317897\pi\) | |||||||
\(600\) | −0.699580 | −0.0285602 | ||||||||
\(601\) | −13.8654 | −0.565582 | −0.282791 | − | 0.959182i | \(-0.591260\pi\) | ||||
−0.282791 | + | 0.959182i | \(0.591260\pi\) | |||||||
\(602\) | 1.90905 | 0.0778070 | ||||||||
\(603\) | 0.319614 | 0.0130157 | ||||||||
\(604\) | −7.29674 | −0.296900 | ||||||||
\(605\) | −2.48900 | −0.101192 | ||||||||
\(606\) | −6.67991 | −0.271353 | ||||||||
\(607\) | 2.94292 | 0.119449 | 0.0597246 | − | 0.998215i | \(-0.480978\pi\) | ||||
0.0597246 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(608\) | −31.5354 | −1.27893 | ||||||||
\(609\) | 8.78559 | 0.356010 | ||||||||
\(610\) | −15.2661 | −0.618107 | ||||||||
\(611\) | 21.1663 | 0.856297 | ||||||||
\(612\) | 33.0746 | 1.33696 | ||||||||
\(613\) | −4.91720 | −0.198604 | −0.0993019 | − | 0.995057i | \(-0.531661\pi\) | ||||
−0.0993019 | + | 0.995057i | \(0.531661\pi\) | |||||||
\(614\) | 65.7789 | 2.65462 | ||||||||
\(615\) | −1.84758 | −0.0745015 | ||||||||
\(616\) | 0.645935 | 0.0260255 | ||||||||
\(617\) | 32.2975 | 1.30025 | 0.650124 | − | 0.759828i | \(-0.274717\pi\) | ||||
0.650124 | + | 0.759828i | \(0.274717\pi\) | |||||||
\(618\) | −11.2332 | −0.451866 | ||||||||
\(619\) | 3.76428 | 0.151299 | 0.0756496 | − | 0.997134i | \(-0.475897\pi\) | ||||
0.0756496 | + | 0.997134i | \(0.475897\pi\) | |||||||
\(620\) | −1.52271 | −0.0611534 | ||||||||
\(621\) | 12.8623 | 0.516145 | ||||||||
\(622\) | 50.7343 | 2.03426 | ||||||||
\(623\) | −3.14145 | −0.125859 | ||||||||
\(624\) | 17.1942 | 0.688318 | ||||||||
\(625\) | 19.4815 | 0.779260 | ||||||||
\(626\) | 52.5968 | 2.10219 | ||||||||
\(627\) | 8.89611 | 0.355276 | ||||||||
\(628\) | −43.1789 | −1.72302 | ||||||||
\(629\) | 7.57566 | 0.302061 | ||||||||
\(630\) | −3.79849 | −0.151335 | ||||||||
\(631\) | 14.7105 | 0.585618 | 0.292809 | − | 0.956171i | \(-0.405410\pi\) | ||||
0.292809 | + | 0.956171i | \(0.405410\pi\) | |||||||
\(632\) | 2.48886 | 0.0990014 | ||||||||
\(633\) | 19.6836 | 0.782353 | ||||||||
\(634\) | 19.0454 | 0.756389 | ||||||||
\(635\) | 3.00592 | 0.119286 | ||||||||
\(636\) | 12.5377 | 0.497154 | ||||||||
\(637\) | −25.0222 | −0.991415 | ||||||||
\(638\) | 39.6377 | 1.56927 | ||||||||
\(639\) | 24.5512 | 0.971232 | ||||||||
\(640\) | 0.879653 | 0.0347713 | ||||||||
\(641\) | 29.3084 | 1.15761 | 0.578806 | − | 0.815465i | \(-0.303519\pi\) | ||||
0.578806 | + | 0.815465i | \(0.303519\pi\) | |||||||
\(642\) | 13.9194 | 0.549355 | ||||||||
\(643\) | 38.6280 | 1.52334 | 0.761670 | − | 0.647965i | \(-0.224380\pi\) | ||||
0.761670 | + | 0.647965i | \(0.224380\pi\) | |||||||
\(644\) | 7.52200 | 0.296408 | ||||||||
\(645\) | −0.366324 | −0.0144240 | ||||||||
\(646\) | −59.8481 | −2.35469 | ||||||||
\(647\) | −47.1484 | −1.85360 | −0.926798 | − | 0.375559i | \(-0.877451\pi\) | ||||
−0.926798 | + | 0.375559i | \(0.877451\pi\) | |||||||
\(648\) | −0.553276 | −0.0217347 | ||||||||
\(649\) | 16.2576 | 0.638167 | ||||||||
\(650\) | −44.5851 | −1.74877 | ||||||||
\(651\) | 1.49963 | 0.0587751 | ||||||||
\(652\) | 5.16026 | 0.202091 | ||||||||
\(653\) | 29.3785 | 1.14967 | 0.574835 | − | 0.818269i | \(-0.305066\pi\) | ||||
0.574835 | + | 0.818269i | \(0.305066\pi\) | |||||||
\(654\) | 1.67007 | 0.0653050 | ||||||||
\(655\) | 7.74931 | 0.302791 | ||||||||
\(656\) | −14.8585 | −0.580125 | ||||||||
\(657\) | −4.37595 | −0.170722 | ||||||||
\(658\) | 11.7335 | 0.457419 | ||||||||
\(659\) | −33.2185 | −1.29401 | −0.647005 | − | 0.762485i | \(-0.723979\pi\) | ||||
−0.647005 | + | 0.762485i | \(0.723979\pi\) | |||||||
\(660\) | 2.61165 | 0.101658 | ||||||||
\(661\) | −26.8289 | −1.04352 | −0.521761 | − | 0.853092i | \(-0.674725\pi\) | ||||
−0.521761 | + | 0.853092i | \(0.674725\pi\) | |||||||
\(662\) | −26.9017 | −1.04557 | ||||||||
\(663\) | 31.2141 | 1.21226 | ||||||||
\(664\) | −2.20383 | −0.0855252 | ||||||||
\(665\) | 3.35701 | 0.130179 | ||||||||
\(666\) | 4.52100 | 0.175185 | ||||||||
\(667\) | −21.9066 | −0.848228 | ||||||||
\(668\) | 26.5233 | 1.02622 | ||||||||
\(669\) | −10.7217 | −0.414524 | ||||||||
\(670\) | −0.169784 | −0.00655934 | ||||||||
\(671\) | 33.1298 | 1.27896 | ||||||||
\(672\) | 9.11760 | 0.351719 | ||||||||
\(673\) | −36.9022 | −1.42247 | −0.711237 | − | 0.702953i | \(-0.751865\pi\) | ||||
−0.711237 | + | 0.702953i | \(0.751865\pi\) | |||||||
\(674\) | 26.9370 | 1.03757 | ||||||||
\(675\) | −20.6415 | −0.794491 | ||||||||
\(676\) | 20.6131 | 0.792811 | ||||||||
\(677\) | 36.7750 | 1.41338 | 0.706689 | − | 0.707525i | \(-0.250188\pi\) | ||||
0.706689 | + | 0.707525i | \(0.250188\pi\) | |||||||
\(678\) | −9.24387 | −0.355009 | ||||||||
\(679\) | −3.60089 | −0.138189 | ||||||||
\(680\) | 0.833850 | 0.0319767 | ||||||||
\(681\) | −0.443245 | −0.0169852 | ||||||||
\(682\) | 6.76584 | 0.259077 | ||||||||
\(683\) | −43.0319 | −1.64657 | −0.823284 | − | 0.567629i | \(-0.807861\pi\) | ||||
−0.823284 | + | 0.567629i | \(0.807861\pi\) | |||||||
\(684\) | −17.4442 | −0.666994 | ||||||||
\(685\) | 6.47797 | 0.247511 | ||||||||
\(686\) | −32.8001 | −1.25231 | ||||||||
\(687\) | −15.9221 | −0.607467 | ||||||||
\(688\) | −2.94602 | −0.112316 | ||||||||
\(689\) | −37.9223 | −1.44472 | ||||||||
\(690\) | −2.95527 | −0.112505 | ||||||||
\(691\) | −31.8018 | −1.20980 | −0.604898 | − | 0.796303i | \(-0.706786\pi\) | ||||
−0.604898 | + | 0.796303i | \(0.706786\pi\) | |||||||
\(692\) | 19.9487 | 0.758336 | ||||||||
\(693\) | 8.24329 | 0.313137 | ||||||||
\(694\) | 46.1841 | 1.75313 | ||||||||
\(695\) | 4.23060 | 0.160476 | ||||||||
\(696\) | −1.15097 | −0.0436273 | ||||||||
\(697\) | −26.9739 | −1.02171 | ||||||||
\(698\) | 55.0632 | 2.08417 | ||||||||
\(699\) | −9.77214 | −0.369616 | ||||||||
\(700\) | −12.0714 | −0.456255 | ||||||||
\(701\) | −14.7074 | −0.555492 | −0.277746 | − | 0.960654i | \(-0.589587\pi\) | ||||
−0.277746 | + | 0.960654i | \(0.589587\pi\) | |||||||
\(702\) | 43.0682 | 1.62551 | ||||||||
\(703\) | −3.99555 | −0.150695 | ||||||||
\(704\) | 19.1356 | 0.721200 | ||||||||
\(705\) | −2.25152 | −0.0847971 | ||||||||
\(706\) | 21.3187 | 0.802339 | ||||||||
\(707\) | 5.47031 | 0.205732 | ||||||||
\(708\) | 9.94692 | 0.373828 | ||||||||
\(709\) | −35.8182 | −1.34518 | −0.672590 | − | 0.740015i | \(-0.734818\pi\) | ||||
−0.672590 | + | 0.740015i | \(0.734818\pi\) | |||||||
\(710\) | −13.0420 | −0.489458 | ||||||||
\(711\) | 31.7623 | 1.19118 | ||||||||
\(712\) | 0.411549 | 0.0154234 | ||||||||
\(713\) | −3.73929 | −0.140037 | ||||||||
\(714\) | 17.3035 | 0.647566 | ||||||||
\(715\) | −7.89932 | −0.295418 | ||||||||
\(716\) | −29.0915 | −1.08720 | ||||||||
\(717\) | 0.848246 | 0.0316783 | ||||||||
\(718\) | 58.9017 | 2.19819 | ||||||||
\(719\) | 26.4644 | 0.986957 | 0.493479 | − | 0.869758i | \(-0.335725\pi\) | ||||
0.493479 | + | 0.869758i | \(0.335725\pi\) | |||||||
\(720\) | 5.86179 | 0.218456 | ||||||||
\(721\) | 9.19912 | 0.342593 | ||||||||
\(722\) | −6.00203 | −0.223373 | ||||||||
\(723\) | 12.7669 | 0.474807 | ||||||||
\(724\) | 44.8932 | 1.66844 | ||||||||
\(725\) | 35.1560 | 1.30566 | ||||||||
\(726\) | 6.76646 | 0.251127 | ||||||||
\(727\) | −32.0684 | −1.18935 | −0.594676 | − | 0.803966i | \(-0.702720\pi\) | ||||
−0.594676 | + | 0.803966i | \(0.702720\pi\) | |||||||
\(728\) | −1.19535 | −0.0443027 | ||||||||
\(729\) | 4.25425 | 0.157565 | ||||||||
\(730\) | 2.32458 | 0.0860364 | ||||||||
\(731\) | −5.34818 | −0.197809 | ||||||||
\(732\) | 20.2699 | 0.749196 | ||||||||
\(733\) | −11.2067 | −0.413930 | −0.206965 | − | 0.978348i | \(-0.566359\pi\) | ||||
−0.206965 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(734\) | 18.8018 | 0.693986 | ||||||||
\(735\) | 2.66168 | 0.0981775 | ||||||||
\(736\) | −22.7345 | −0.838004 | ||||||||
\(737\) | 0.368458 | 0.0135723 | ||||||||
\(738\) | −16.0975 | −0.592556 | ||||||||
\(739\) | 26.7846 | 0.985286 | 0.492643 | − | 0.870231i | \(-0.336031\pi\) | ||||
0.492643 | + | 0.870231i | \(0.336031\pi\) | |||||||
\(740\) | −1.17298 | −0.0431197 | ||||||||
\(741\) | −16.4629 | −0.604780 | ||||||||
\(742\) | −21.0221 | −0.771746 | ||||||||
\(743\) | 8.47336 | 0.310857 | 0.155429 | − | 0.987847i | \(-0.450324\pi\) | ||||
0.155429 | + | 0.987847i | \(0.450324\pi\) | |||||||
\(744\) | −0.196461 | −0.00720260 | ||||||||
\(745\) | −9.47736 | −0.347224 | ||||||||
\(746\) | 54.3731 | 1.99074 | ||||||||
\(747\) | −28.1248 | −1.02903 | ||||||||
\(748\) | 38.1290 | 1.39413 | ||||||||
\(749\) | −11.3989 | −0.416507 | ||||||||
\(750\) | 9.87248 | 0.360492 | ||||||||
\(751\) | 9.62853 | 0.351350 | 0.175675 | − | 0.984448i | \(-0.443789\pi\) | ||||
0.175675 | + | 0.984448i | \(0.443789\pi\) | |||||||
\(752\) | −18.1070 | −0.660295 | ||||||||
\(753\) | 11.4642 | 0.417780 | ||||||||
\(754\) | −73.3526 | −2.67134 | ||||||||
\(755\) | −2.34766 | −0.0854400 | ||||||||
\(756\) | 11.6607 | 0.424095 | ||||||||
\(757\) | 12.8991 | 0.468825 | 0.234412 | − | 0.972137i | \(-0.424683\pi\) | ||||
0.234412 | + | 0.972137i | \(0.424683\pi\) | |||||||
\(758\) | 37.2638 | 1.35348 | ||||||||
\(759\) | 6.41338 | 0.232791 | ||||||||
\(760\) | −0.439788 | −0.0159528 | ||||||||
\(761\) | 11.9093 | 0.431712 | 0.215856 | − | 0.976425i | \(-0.430746\pi\) | ||||
0.215856 | + | 0.976425i | \(0.430746\pi\) | |||||||
\(762\) | −8.17175 | −0.296031 | ||||||||
\(763\) | −1.36766 | −0.0495125 | ||||||||
\(764\) | −41.3152 | −1.49473 | ||||||||
\(765\) | 10.6414 | 0.384741 | ||||||||
\(766\) | −46.1052 | −1.66585 | ||||||||
\(767\) | −30.0859 | −1.08634 | ||||||||
\(768\) | −14.6548 | −0.528809 | ||||||||
\(769\) | 41.2287 | 1.48675 | 0.743373 | − | 0.668877i | \(-0.233225\pi\) | ||||
0.743373 | + | 0.668877i | \(0.233225\pi\) | |||||||
\(770\) | −4.37897 | −0.157807 | ||||||||
\(771\) | 0.510770 | 0.0183949 | ||||||||
\(772\) | 24.9952 | 0.899596 | ||||||||
\(773\) | 15.2584 | 0.548806 | 0.274403 | − | 0.961615i | \(-0.411520\pi\) | ||||
0.274403 | + | 0.961615i | \(0.411520\pi\) | |||||||
\(774\) | −3.19169 | −0.114723 | ||||||||
\(775\) | 6.00084 | 0.215557 | ||||||||
\(776\) | 0.471739 | 0.0169344 | ||||||||
\(777\) | 1.15520 | 0.0414427 | ||||||||
\(778\) | −11.8465 | −0.424718 | ||||||||
\(779\) | 14.2265 | 0.509719 | ||||||||
\(780\) | −4.83305 | −0.173051 | ||||||||
\(781\) | 28.3032 | 1.01277 | ||||||||
\(782\) | −43.1457 | −1.54289 | ||||||||
\(783\) | −33.9599 | −1.21363 | ||||||||
\(784\) | 21.4056 | 0.764485 | ||||||||
\(785\) | −13.8924 | −0.495840 | ||||||||
\(786\) | −21.0669 | −0.751430 | ||||||||
\(787\) | −11.3788 | −0.405610 | −0.202805 | − | 0.979219i | \(-0.565006\pi\) | ||||
−0.202805 | + | 0.979219i | \(0.565006\pi\) | |||||||
\(788\) | −37.4853 | −1.33536 | ||||||||
\(789\) | 24.6333 | 0.876969 | ||||||||
\(790\) | −16.8726 | −0.600301 | ||||||||
\(791\) | 7.57000 | 0.269158 | ||||||||
\(792\) | −1.07992 | −0.0383734 | ||||||||
\(793\) | −61.3092 | −2.17715 | ||||||||
\(794\) | 42.2365 | 1.49892 | ||||||||
\(795\) | 4.03390 | 0.143068 | ||||||||
\(796\) | −26.4464 | −0.937368 | ||||||||
\(797\) | −3.51128 | −0.124376 | −0.0621880 | − | 0.998064i | \(-0.519808\pi\) | ||||
−0.0621880 | + | 0.998064i | \(0.519808\pi\) | |||||||
\(798\) | −9.12618 | −0.323063 | ||||||||
\(799\) | −32.8712 | −1.16290 | ||||||||
\(800\) | 36.4845 | 1.28992 | ||||||||
\(801\) | 5.25210 | 0.185574 | ||||||||
\(802\) | −33.5192 | −1.18360 | ||||||||
\(803\) | −5.04468 | −0.178023 | ||||||||
\(804\) | 0.225434 | 0.00795045 | ||||||||
\(805\) | 2.42013 | 0.0852984 | ||||||||
\(806\) | −12.5207 | −0.441023 | ||||||||
\(807\) | −5.59910 | −0.197098 | ||||||||
\(808\) | −0.716645 | −0.0252115 | ||||||||
\(809\) | 20.6324 | 0.725396 | 0.362698 | − | 0.931907i | \(-0.381856\pi\) | ||||
0.362698 | + | 0.931907i | \(0.381856\pi\) | |||||||
\(810\) | 3.75081 | 0.131790 | ||||||||
\(811\) | 1.40042 | 0.0491753 | 0.0245876 | − | 0.999698i | \(-0.492173\pi\) | ||||
0.0245876 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(812\) | −19.8601 | −0.696954 | ||||||||
\(813\) | −13.5390 | −0.474835 | ||||||||
\(814\) | 5.21191 | 0.182677 | ||||||||
\(815\) | 1.66026 | 0.0581565 | ||||||||
\(816\) | −26.7025 | −0.934776 | ||||||||
\(817\) | 2.82073 | 0.0986849 | ||||||||
\(818\) | 58.7991 | 2.05586 | ||||||||
\(819\) | −15.2548 | −0.533047 | ||||||||
\(820\) | 4.17651 | 0.145850 | ||||||||
\(821\) | −45.8252 | −1.59931 | −0.799655 | − | 0.600460i | \(-0.794984\pi\) | ||||
−0.799655 | + | 0.600460i | \(0.794984\pi\) | |||||||
\(822\) | −17.6107 | −0.614243 | ||||||||
\(823\) | 28.8121 | 1.00433 | 0.502163 | − | 0.864773i | \(-0.332538\pi\) | ||||
0.502163 | + | 0.864773i | \(0.332538\pi\) | |||||||
\(824\) | −1.20514 | −0.0419831 | ||||||||
\(825\) | −10.2923 | −0.358330 | ||||||||
\(826\) | −16.6781 | −0.580304 | ||||||||
\(827\) | −28.5376 | −0.992349 | −0.496174 | − | 0.868223i | \(-0.665262\pi\) | ||||
−0.496174 | + | 0.868223i | \(0.665262\pi\) | |||||||
\(828\) | −12.5758 | −0.437041 | ||||||||
\(829\) | −33.7211 | −1.17118 | −0.585592 | − | 0.810606i | \(-0.699138\pi\) | ||||
−0.585592 | + | 0.810606i | \(0.699138\pi\) | |||||||
\(830\) | 14.9404 | 0.518588 | ||||||||
\(831\) | 4.19666 | 0.145581 | ||||||||
\(832\) | −35.4118 | −1.22768 | ||||||||
\(833\) | 38.8594 | 1.34640 | ||||||||
\(834\) | −11.5011 | −0.398250 | ||||||||
\(835\) | 8.53363 | 0.295318 | ||||||||
\(836\) | −20.1100 | −0.695518 | ||||||||
\(837\) | −5.79668 | −0.200362 | ||||||||
\(838\) | −59.6999 | −2.06230 | ||||||||
\(839\) | 27.3746 | 0.945075 | 0.472537 | − | 0.881311i | \(-0.343338\pi\) | ||||
0.472537 | + | 0.881311i | \(0.343338\pi\) | |||||||
\(840\) | 0.127153 | 0.00438719 | ||||||||
\(841\) | 28.8395 | 0.994465 | ||||||||
\(842\) | 0.625192 | 0.0215455 | ||||||||
\(843\) | 22.5109 | 0.775315 | ||||||||
\(844\) | −44.4955 | −1.53160 | ||||||||
\(845\) | 6.63206 | 0.228150 | ||||||||
\(846\) | −19.6169 | −0.674444 | ||||||||
\(847\) | −5.54120 | −0.190398 | ||||||||
\(848\) | 32.4411 | 1.11403 | ||||||||
\(849\) | 2.25195 | 0.0772867 | ||||||||
\(850\) | 69.2406 | 2.37493 | ||||||||
\(851\) | −2.88047 | −0.0987412 | ||||||||
\(852\) | 17.3168 | 0.593262 | ||||||||
\(853\) | 53.2490 | 1.82321 | 0.911605 | − | 0.411067i | \(-0.134844\pi\) | ||||
0.911605 | + | 0.411067i | \(0.134844\pi\) | |||||||
\(854\) | −33.9866 | −1.16300 | ||||||||
\(855\) | −5.61249 | −0.191943 | ||||||||
\(856\) | 1.49333 | 0.0510408 | ||||||||
\(857\) | −35.9158 | −1.22686 | −0.613431 | − | 0.789749i | \(-0.710211\pi\) | ||||
−0.613431 | + | 0.789749i | \(0.710211\pi\) | |||||||
\(858\) | 21.4747 | 0.733134 | ||||||||
\(859\) | −6.46786 | −0.220681 | −0.110340 | − | 0.993894i | \(-0.535194\pi\) | ||||
−0.110340 | + | 0.993894i | \(0.535194\pi\) | |||||||
\(860\) | 0.828088 | 0.0282376 | ||||||||
\(861\) | −4.11322 | −0.140178 | ||||||||
\(862\) | 34.3330 | 1.16939 | ||||||||
\(863\) | 48.6565 | 1.65629 | 0.828143 | − | 0.560517i | \(-0.189397\pi\) | ||||
0.828143 | + | 0.560517i | \(0.189397\pi\) | |||||||
\(864\) | −35.2432 | −1.19900 | ||||||||
\(865\) | 6.41830 | 0.218229 | ||||||||
\(866\) | 36.7901 | 1.25018 | ||||||||
\(867\) | −34.1163 | −1.15865 | ||||||||
\(868\) | −3.38997 | −0.115063 | ||||||||
\(869\) | 36.6162 | 1.24212 | ||||||||
\(870\) | 7.80272 | 0.264537 | ||||||||
\(871\) | −0.681859 | −0.0231039 | ||||||||
\(872\) | 0.179172 | 0.00606751 | ||||||||
\(873\) | 6.02023 | 0.203754 | ||||||||
\(874\) | 22.7559 | 0.769729 | ||||||||
\(875\) | −8.08478 | −0.273316 | ||||||||
\(876\) | −3.08649 | −0.104283 | ||||||||
\(877\) | −11.2955 | −0.381424 | −0.190712 | − | 0.981646i | \(-0.561080\pi\) | ||||
−0.190712 | + | 0.981646i | \(0.561080\pi\) | |||||||
\(878\) | −25.4929 | −0.860345 | ||||||||
\(879\) | 13.0164 | 0.439032 | ||||||||
\(880\) | 6.75759 | 0.227798 | ||||||||
\(881\) | −6.96989 | −0.234821 | −0.117411 | − | 0.993083i | \(-0.537459\pi\) | ||||
−0.117411 | + | 0.993083i | \(0.537459\pi\) | |||||||
\(882\) | 23.1906 | 0.780867 | ||||||||
\(883\) | 40.8259 | 1.37390 | 0.686951 | − | 0.726704i | \(-0.258949\pi\) | ||||
0.686951 | + | 0.726704i | \(0.258949\pi\) | |||||||
\(884\) | −70.5606 | −2.37321 | ||||||||
\(885\) | 3.20033 | 0.107578 | ||||||||
\(886\) | −77.2337 | −2.59472 | ||||||||
\(887\) | −19.3940 | −0.651187 | −0.325594 | − | 0.945510i | \(-0.605564\pi\) | ||||
−0.325594 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(888\) | −0.151339 | −0.00507860 | ||||||||
\(889\) | 6.69201 | 0.224443 | ||||||||
\(890\) | −2.79000 | −0.0935211 | ||||||||
\(891\) | −8.13983 | −0.272695 | ||||||||
\(892\) | 24.2367 | 0.811505 | ||||||||
\(893\) | 17.3369 | 0.580158 | ||||||||
\(894\) | 25.7647 | 0.861699 | ||||||||
\(895\) | −9.35992 | −0.312868 | ||||||||
\(896\) | 1.95835 | 0.0654239 | ||||||||
\(897\) | −11.8684 | −0.396276 | ||||||||
\(898\) | 62.0244 | 2.06978 | ||||||||
\(899\) | 9.87274 | 0.329274 | ||||||||
\(900\) | 20.1818 | 0.672728 | ||||||||
\(901\) | 58.8932 | 1.96202 | ||||||||
\(902\) | −18.5575 | −0.617897 | ||||||||
\(903\) | −0.815538 | −0.0271394 | ||||||||
\(904\) | −0.991716 | −0.0329840 | ||||||||
\(905\) | 14.4440 | 0.480133 | ||||||||
\(906\) | 6.38222 | 0.212035 | ||||||||
\(907\) | 19.9551 | 0.662599 | 0.331300 | − | 0.943526i | \(-0.392513\pi\) | ||||
0.331300 | + | 0.943526i | \(0.392513\pi\) | |||||||
\(908\) | 1.00197 | 0.0332516 | ||||||||
\(909\) | −9.14568 | −0.303343 | ||||||||
\(910\) | 8.10362 | 0.268632 | ||||||||
\(911\) | −44.6129 | −1.47809 | −0.739045 | − | 0.673656i | \(-0.764723\pi\) | ||||
−0.739045 | + | 0.673656i | \(0.764723\pi\) | |||||||
\(912\) | 14.0834 | 0.466349 | ||||||||
\(913\) | −32.4229 | −1.07304 | ||||||||
\(914\) | −2.69826 | −0.0892507 | ||||||||
\(915\) | 6.52163 | 0.215598 | ||||||||
\(916\) | 35.9925 | 1.18923 | ||||||||
\(917\) | 17.2521 | 0.569715 | ||||||||
\(918\) | −66.8849 | −2.20753 | ||||||||
\(919\) | 51.1995 | 1.68891 | 0.844457 | − | 0.535623i | \(-0.179923\pi\) | ||||
0.844457 | + | 0.535623i | \(0.179923\pi\) | |||||||
\(920\) | −0.317052 | −0.0104529 | ||||||||
\(921\) | −28.1005 | −0.925943 | ||||||||
\(922\) | −46.9211 | −1.54526 | ||||||||
\(923\) | −52.3771 | −1.72401 | ||||||||
\(924\) | 5.81425 | 0.191275 | ||||||||
\(925\) | 4.62260 | 0.151990 | ||||||||
\(926\) | −16.0973 | −0.528991 | ||||||||
\(927\) | −15.3798 | −0.505138 | ||||||||
\(928\) | 60.0252 | 1.97042 | ||||||||
\(929\) | 1.55058 | 0.0508727 | 0.0254364 | − | 0.999676i | \(-0.491902\pi\) | ||||
0.0254364 | + | 0.999676i | \(0.491902\pi\) | |||||||
\(930\) | 1.33186 | 0.0436735 | ||||||||
\(931\) | −20.4952 | −0.671703 | ||||||||
\(932\) | 22.0903 | 0.723591 | ||||||||
\(933\) | −21.6735 | −0.709559 | ||||||||
\(934\) | 81.5937 | 2.66983 | ||||||||
\(935\) | 12.2676 | 0.401195 | ||||||||
\(936\) | 1.99848 | 0.0653223 | ||||||||
\(937\) | −3.88918 | −0.127054 | −0.0635270 | − | 0.997980i | \(-0.520235\pi\) | ||||
−0.0635270 | + | 0.997980i | \(0.520235\pi\) | |||||||
\(938\) | −0.377987 | −0.0123417 | ||||||||
\(939\) | −22.4692 | −0.733253 | ||||||||
\(940\) | 5.08964 | 0.166006 | ||||||||
\(941\) | −42.9524 | −1.40021 | −0.700104 | − | 0.714040i | \(-0.746863\pi\) | ||||
−0.700104 | + | 0.714040i | \(0.746863\pi\) | |||||||
\(942\) | 37.7671 | 1.23052 | ||||||||
\(943\) | 10.2562 | 0.333988 | ||||||||
\(944\) | 25.7374 | 0.837683 | ||||||||
\(945\) | 3.75171 | 0.122043 | ||||||||
\(946\) | −3.67944 | −0.119629 | ||||||||
\(947\) | 35.5186 | 1.15420 | 0.577100 | − | 0.816674i | \(-0.304184\pi\) | ||||
0.577100 | + | 0.816674i | \(0.304184\pi\) | |||||||
\(948\) | 22.4029 | 0.727613 | ||||||||
\(949\) | 9.33556 | 0.303045 | ||||||||
\(950\) | −36.5189 | −1.18483 | ||||||||
\(951\) | −8.13612 | −0.263832 | ||||||||
\(952\) | 1.85638 | 0.0601656 | ||||||||
\(953\) | 28.4921 | 0.922951 | 0.461476 | − | 0.887153i | \(-0.347320\pi\) | ||||
0.461476 | + | 0.887153i | \(0.347320\pi\) | |||||||
\(954\) | 35.1463 | 1.13790 | ||||||||
\(955\) | −13.2928 | −0.430144 | ||||||||
\(956\) | −1.91749 | −0.0620161 | ||||||||
\(957\) | −16.9331 | −0.547369 | ||||||||
\(958\) | −63.5411 | −2.05292 | ||||||||
\(959\) | 14.4218 | 0.465703 | ||||||||
\(960\) | 3.76686 | 0.121575 | ||||||||
\(961\) | −29.3148 | −0.945639 | ||||||||
\(962\) | −9.64502 | −0.310968 | ||||||||
\(963\) | 19.0575 | 0.614120 | ||||||||
\(964\) | −28.8601 | −0.929521 | ||||||||
\(965\) | 8.04195 | 0.258880 | ||||||||
\(966\) | −6.57925 | −0.211684 | ||||||||
\(967\) | 40.9049 | 1.31541 | 0.657706 | − | 0.753275i | \(-0.271527\pi\) | ||||
0.657706 | + | 0.753275i | \(0.271527\pi\) | |||||||
\(968\) | 0.725931 | 0.0233323 | ||||||||
\(969\) | 25.5669 | 0.821327 | ||||||||
\(970\) | −3.19805 | −0.102683 | ||||||||
\(971\) | −5.68275 | −0.182368 | −0.0911840 | − | 0.995834i | \(-0.529065\pi\) | ||||
−0.0911840 | + | 0.995834i | \(0.529065\pi\) | |||||||
\(972\) | −30.5583 | −0.980157 | ||||||||
\(973\) | 9.41848 | 0.301942 | ||||||||
\(974\) | −23.9286 | −0.766723 | ||||||||
\(975\) | 19.0466 | 0.609979 | ||||||||
\(976\) | 52.4478 | 1.67881 | ||||||||
\(977\) | 43.6482 | 1.39643 | 0.698215 | − | 0.715888i | \(-0.253978\pi\) | ||||
0.698215 | + | 0.715888i | \(0.253978\pi\) | |||||||
\(978\) | −4.51351 | −0.144326 | ||||||||
\(979\) | 6.05473 | 0.193510 | ||||||||
\(980\) | −6.01682 | −0.192200 | ||||||||
\(981\) | 2.28655 | 0.0730040 | ||||||||
\(982\) | −60.7013 | −1.93705 | ||||||||
\(983\) | −50.9660 | −1.62556 | −0.812781 | − | 0.582570i | \(-0.802047\pi\) | ||||
−0.812781 | + | 0.582570i | \(0.802047\pi\) | |||||||
\(984\) | 0.538857 | 0.0171781 | ||||||||
\(985\) | −12.0605 | −0.384281 | ||||||||
\(986\) | 113.916 | 3.62784 | ||||||||
\(987\) | −5.01250 | −0.159550 | ||||||||
\(988\) | 37.2150 | 1.18397 | ||||||||
\(989\) | 2.03352 | 0.0646622 | ||||||||
\(990\) | 7.32109 | 0.232680 | ||||||||
\(991\) | −57.4663 | −1.82548 | −0.912738 | − | 0.408544i | \(-0.866036\pi\) | ||||
−0.912738 | + | 0.408544i | \(0.866036\pi\) | |||||||
\(992\) | 10.2458 | 0.325305 | ||||||||
\(993\) | 11.4923 | 0.364698 | ||||||||
\(994\) | −29.0351 | −0.920938 | ||||||||
\(995\) | −8.50887 | −0.269749 | ||||||||
\(996\) | −19.8373 | −0.628570 | ||||||||
\(997\) | −33.2477 | −1.05297 | −0.526483 | − | 0.850186i | \(-0.676490\pi\) | ||||
−0.526483 | + | 0.850186i | \(0.676490\pi\) | |||||||
\(998\) | 39.3370 | 1.24519 | ||||||||
\(999\) | −4.46533 | −0.141277 |
(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 | 4033.2.a.d.1.68 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.68 | ✓ | 79 | 1.1 | even | 1 | trivial |