Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, 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("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 | ||||||||
\(3\) | −2.35142 | −1.35759 | −0.678797 | − | 0.734326i | \(-0.737498\pi\) | ||||
−0.678797 | + | 0.734326i | \(0.737498\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.94455 | −1.76406 | −0.882029 | − | 0.471196i | \(-0.843823\pi\) | ||||
−0.882029 | + | 0.471196i | \(0.843823\pi\) | |||||||
\(6\) | 2.35142 | 0.959964 | ||||||||
\(7\) | −0.732372 | −0.276810 | −0.138405 | − | 0.990376i | \(-0.544198\pi\) | ||||
−0.138405 | + | 0.990376i | \(0.544198\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.52919 | 0.843063 | ||||||||
\(10\) | 3.94455 | 1.24738 | ||||||||
\(11\) | −5.60227 | −1.68915 | −0.844574 | − | 0.535440i | \(-0.820146\pi\) | ||||
−0.844574 | + | 0.535440i | \(0.820146\pi\) | |||||||
\(12\) | −2.35142 | −0.678797 | ||||||||
\(13\) | −6.57678 | −1.82407 | −0.912035 | − | 0.410112i | \(-0.865490\pi\) | ||||
−0.912035 | + | 0.410112i | \(0.865490\pi\) | |||||||
\(14\) | 0.732372 | 0.195735 | ||||||||
\(15\) | 9.27531 | 2.39487 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.88851 | 1.91324 | 0.956622 | − | 0.291331i | \(-0.0940980\pi\) | ||||
0.956622 | + | 0.291331i | \(0.0940980\pi\) | |||||||
\(18\) | −2.52919 | −0.596135 | ||||||||
\(19\) | −3.58994 | −0.823588 | −0.411794 | − | 0.911277i | \(-0.635098\pi\) | ||||
−0.411794 | + | 0.911277i | \(0.635098\pi\) | |||||||
\(20\) | −3.94455 | −0.882029 | ||||||||
\(21\) | 1.72211 | 0.375796 | ||||||||
\(22\) | 5.60227 | 1.19441 | ||||||||
\(23\) | 0.597342 | 0.124554 | 0.0622772 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622772 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(24\) | 2.35142 | 0.479982 | ||||||||
\(25\) | 10.5595 | 2.11190 | ||||||||
\(26\) | 6.57678 | 1.28981 | ||||||||
\(27\) | 1.10708 | 0.213057 | ||||||||
\(28\) | −0.732372 | −0.138405 | ||||||||
\(29\) | −5.16201 | −0.958561 | −0.479281 | − | 0.877662i | \(-0.659102\pi\) | ||||
−0.479281 | + | 0.877662i | \(0.659102\pi\) | |||||||
\(30\) | −9.27531 | −1.69343 | ||||||||
\(31\) | 2.38291 | 0.427984 | 0.213992 | − | 0.976835i | \(-0.431353\pi\) | ||||
0.213992 | + | 0.976835i | \(0.431353\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 13.1733 | 2.29318 | ||||||||
\(34\) | −7.88851 | −1.35287 | ||||||||
\(35\) | 2.88888 | 0.488309 | ||||||||
\(36\) | 2.52919 | 0.421531 | ||||||||
\(37\) | −8.53492 | −1.40313 | −0.701566 | − | 0.712604i | \(-0.747516\pi\) | ||||
−0.701566 | + | 0.712604i | \(0.747516\pi\) | |||||||
\(38\) | 3.58994 | 0.582365 | ||||||||
\(39\) | 15.4648 | 2.47635 | ||||||||
\(40\) | 3.94455 | 0.623688 | ||||||||
\(41\) | 5.16216 | 0.806194 | 0.403097 | − | 0.915157i | \(-0.367934\pi\) | ||||
0.403097 | + | 0.915157i | \(0.367934\pi\) | |||||||
\(42\) | −1.72211 | −0.265728 | ||||||||
\(43\) | 4.23985 | 0.646571 | 0.323286 | − | 0.946301i | \(-0.395213\pi\) | ||||
0.323286 | + | 0.946301i | \(0.395213\pi\) | |||||||
\(44\) | −5.60227 | −0.844574 | ||||||||
\(45\) | −9.97651 | −1.48721 | ||||||||
\(46\) | −0.597342 | −0.0880733 | ||||||||
\(47\) | −2.11544 | −0.308569 | −0.154284 | − | 0.988026i | \(-0.549307\pi\) | ||||
−0.154284 | + | 0.988026i | \(0.549307\pi\) | |||||||
\(48\) | −2.35142 | −0.339399 | ||||||||
\(49\) | −6.46363 | −0.923376 | ||||||||
\(50\) | −10.5595 | −1.49334 | ||||||||
\(51\) | −18.5492 | −2.59741 | ||||||||
\(52\) | −6.57678 | −0.912035 | ||||||||
\(53\) | 13.3381 | 1.83213 | 0.916063 | − | 0.401034i | \(-0.131349\pi\) | ||||
0.916063 | + | 0.401034i | \(0.131349\pi\) | |||||||
\(54\) | −1.10708 | −0.150654 | ||||||||
\(55\) | 22.0984 | 2.97975 | ||||||||
\(56\) | 0.732372 | 0.0978673 | ||||||||
\(57\) | 8.44146 | 1.11810 | ||||||||
\(58\) | 5.16201 | 0.677805 | ||||||||
\(59\) | 14.6005 | 1.90083 | 0.950413 | − | 0.310991i | \(-0.100661\pi\) | ||||
0.950413 | + | 0.310991i | \(0.100661\pi\) | |||||||
\(60\) | 9.27531 | 1.19744 | ||||||||
\(61\) | 3.15824 | 0.404372 | 0.202186 | − | 0.979347i | \(-0.435195\pi\) | ||||
0.202186 | + | 0.979347i | \(0.435195\pi\) | |||||||
\(62\) | −2.38291 | −0.302630 | ||||||||
\(63\) | −1.85231 | −0.233369 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 25.9425 | 3.21776 | ||||||||
\(66\) | −13.1733 | −1.62152 | ||||||||
\(67\) | 15.0462 | 1.83818 | 0.919091 | − | 0.394045i | \(-0.128925\pi\) | ||||
0.919091 | + | 0.394045i | \(0.128925\pi\) | |||||||
\(68\) | 7.88851 | 0.956622 | ||||||||
\(69\) | −1.40460 | −0.169094 | ||||||||
\(70\) | −2.88888 | −0.345287 | ||||||||
\(71\) | −0.278234 | −0.0330203 | −0.0165102 | − | 0.999864i | \(-0.505256\pi\) | ||||
−0.0165102 | + | 0.999864i | \(0.505256\pi\) | |||||||
\(72\) | −2.52919 | −0.298068 | ||||||||
\(73\) | −15.4340 | −1.80641 | −0.903205 | − | 0.429209i | \(-0.858792\pi\) | ||||
−0.903205 | + | 0.429209i | \(0.858792\pi\) | |||||||
\(74\) | 8.53492 | 0.992165 | ||||||||
\(75\) | −24.8298 | −2.86710 | ||||||||
\(76\) | −3.58994 | −0.411794 | ||||||||
\(77\) | 4.10294 | 0.467573 | ||||||||
\(78\) | −15.4648 | −1.75104 | ||||||||
\(79\) | −3.94569 | −0.443925 | −0.221962 | − | 0.975055i | \(-0.571246\pi\) | ||||
−0.221962 | + | 0.975055i | \(0.571246\pi\) | |||||||
\(80\) | −3.94455 | −0.441014 | ||||||||
\(81\) | −10.1908 | −1.13231 | ||||||||
\(82\) | −5.16216 | −0.570065 | ||||||||
\(83\) | −13.3933 | −1.47010 | −0.735052 | − | 0.678010i | \(-0.762842\pi\) | ||||
−0.735052 | + | 0.678010i | \(0.762842\pi\) | |||||||
\(84\) | 1.72211 | 0.187898 | ||||||||
\(85\) | −31.1166 | −3.37507 | ||||||||
\(86\) | −4.23985 | −0.457195 | ||||||||
\(87\) | 12.1381 | 1.30134 | ||||||||
\(88\) | 5.60227 | 0.597204 | ||||||||
\(89\) | 1.59595 | 0.169170 | 0.0845850 | − | 0.996416i | \(-0.473044\pi\) | ||||
0.0845850 | + | 0.996416i | \(0.473044\pi\) | |||||||
\(90\) | 9.97651 | 1.05162 | ||||||||
\(91\) | 4.81665 | 0.504922 | ||||||||
\(92\) | 0.597342 | 0.0622772 | ||||||||
\(93\) | −5.60324 | −0.581029 | ||||||||
\(94\) | 2.11544 | 0.218191 | ||||||||
\(95\) | 14.1607 | 1.45286 | ||||||||
\(96\) | 2.35142 | 0.239991 | ||||||||
\(97\) | −11.1601 | −1.13314 | −0.566569 | − | 0.824014i | \(-0.691729\pi\) | ||||
−0.566569 | + | 0.824014i | \(0.691729\pi\) | |||||||
\(98\) | 6.46363 | 0.652925 | ||||||||
\(99\) | −14.1692 | −1.42406 | ||||||||
\(100\) | 10.5595 | 1.05595 | ||||||||
\(101\) | 15.8952 | 1.58163 | 0.790815 | − | 0.612055i | \(-0.209657\pi\) | ||||
0.790815 | + | 0.612055i | \(0.209657\pi\) | |||||||
\(102\) | 18.5492 | 1.83665 | ||||||||
\(103\) | 4.52520 | 0.445881 | 0.222940 | − | 0.974832i | \(-0.428434\pi\) | ||||
0.222940 | + | 0.974832i | \(0.428434\pi\) | |||||||
\(104\) | 6.57678 | 0.644906 | ||||||||
\(105\) | −6.79297 | −0.662926 | ||||||||
\(106\) | −13.3381 | −1.29551 | ||||||||
\(107\) | −2.00963 | −0.194278 | −0.0971392 | − | 0.995271i | \(-0.530969\pi\) | ||||
−0.0971392 | + | 0.995271i | \(0.530969\pi\) | |||||||
\(108\) | 1.10708 | 0.106529 | ||||||||
\(109\) | 3.39488 | 0.325170 | 0.162585 | − | 0.986695i | \(-0.448017\pi\) | ||||
0.162585 | + | 0.986695i | \(0.448017\pi\) | |||||||
\(110\) | −22.0984 | −2.10700 | ||||||||
\(111\) | 20.0692 | 1.90489 | ||||||||
\(112\) | −0.732372 | −0.0692026 | ||||||||
\(113\) | −2.44327 | −0.229843 | −0.114922 | − | 0.993375i | \(-0.536662\pi\) | ||||
−0.114922 | + | 0.993375i | \(0.536662\pi\) | |||||||
\(114\) | −8.44146 | −0.790615 | ||||||||
\(115\) | −2.35625 | −0.219721 | ||||||||
\(116\) | −5.16201 | −0.479281 | ||||||||
\(117\) | −16.6339 | −1.53781 | ||||||||
\(118\) | −14.6005 | −1.34409 | ||||||||
\(119\) | −5.77732 | −0.529606 | ||||||||
\(120\) | −9.27531 | −0.846716 | ||||||||
\(121\) | 20.3854 | 1.85322 | ||||||||
\(122\) | −3.15824 | −0.285934 | ||||||||
\(123\) | −12.1384 | −1.09448 | ||||||||
\(124\) | 2.38291 | 0.213992 | ||||||||
\(125\) | −21.9297 | −1.96145 | ||||||||
\(126\) | 1.85231 | 0.165016 | ||||||||
\(127\) | 5.11200 | 0.453616 | 0.226808 | − | 0.973939i | \(-0.427171\pi\) | ||||
0.226808 | + | 0.973939i | \(0.427171\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.96968 | −0.877782 | ||||||||
\(130\) | −25.9425 | −2.27530 | ||||||||
\(131\) | 7.31053 | 0.638724 | 0.319362 | − | 0.947633i | \(-0.396531\pi\) | ||||
0.319362 | + | 0.947633i | \(0.396531\pi\) | |||||||
\(132\) | 13.1733 | 1.14659 | ||||||||
\(133\) | 2.62917 | 0.227978 | ||||||||
\(134\) | −15.0462 | −1.29979 | ||||||||
\(135\) | −4.36693 | −0.375845 | ||||||||
\(136\) | −7.88851 | −0.676434 | ||||||||
\(137\) | 12.7625 | 1.09038 | 0.545189 | − | 0.838313i | \(-0.316458\pi\) | ||||
0.545189 | + | 0.838313i | \(0.316458\pi\) | |||||||
\(138\) | 1.40460 | 0.119568 | ||||||||
\(139\) | 5.16815 | 0.438357 | 0.219179 | − | 0.975685i | \(-0.429662\pi\) | ||||
0.219179 | + | 0.975685i | \(0.429662\pi\) | |||||||
\(140\) | 2.88888 | 0.244155 | ||||||||
\(141\) | 4.97429 | 0.418911 | ||||||||
\(142\) | 0.278234 | 0.0233489 | ||||||||
\(143\) | 36.8449 | 3.08112 | ||||||||
\(144\) | 2.52919 | 0.210766 | ||||||||
\(145\) | 20.3618 | 1.69096 | ||||||||
\(146\) | 15.4340 | 1.27732 | ||||||||
\(147\) | 15.1987 | 1.25357 | ||||||||
\(148\) | −8.53492 | −0.701566 | ||||||||
\(149\) | 11.8339 | 0.969471 | 0.484735 | − | 0.874661i | \(-0.338916\pi\) | ||||
0.484735 | + | 0.874661i | \(0.338916\pi\) | |||||||
\(150\) | 24.8298 | 2.02735 | ||||||||
\(151\) | 2.37792 | 0.193512 | 0.0967561 | − | 0.995308i | \(-0.469153\pi\) | ||||
0.0967561 | + | 0.995308i | \(0.469153\pi\) | |||||||
\(152\) | 3.58994 | 0.291182 | ||||||||
\(153\) | 19.9515 | 1.61299 | ||||||||
\(154\) | −4.10294 | −0.330624 | ||||||||
\(155\) | −9.39953 | −0.754988 | ||||||||
\(156\) | 15.4648 | 1.23817 | ||||||||
\(157\) | −3.17462 | −0.253362 | −0.126681 | − | 0.991943i | \(-0.540432\pi\) | ||||
−0.126681 | + | 0.991943i | \(0.540432\pi\) | |||||||
\(158\) | 3.94569 | 0.313902 | ||||||||
\(159\) | −31.3635 | −2.48728 | ||||||||
\(160\) | 3.94455 | 0.311844 | ||||||||
\(161\) | −0.437476 | −0.0344780 | ||||||||
\(162\) | 10.1908 | 0.800663 | ||||||||
\(163\) | 0.771085 | 0.0603961 | 0.0301980 | − | 0.999544i | \(-0.490386\pi\) | ||||
0.0301980 | + | 0.999544i | \(0.490386\pi\) | |||||||
\(164\) | 5.16216 | 0.403097 | ||||||||
\(165\) | −51.9628 | −4.04530 | ||||||||
\(166\) | 13.3933 | 1.03952 | ||||||||
\(167\) | 4.40690 | 0.341016 | 0.170508 | − | 0.985356i | \(-0.445459\pi\) | ||||
0.170508 | + | 0.985356i | \(0.445459\pi\) | |||||||
\(168\) | −1.72211 | −0.132864 | ||||||||
\(169\) | 30.2540 | 2.32723 | ||||||||
\(170\) | 31.1166 | 2.38654 | ||||||||
\(171\) | −9.07963 | −0.694337 | ||||||||
\(172\) | 4.23985 | 0.323286 | ||||||||
\(173\) | −9.05042 | −0.688091 | −0.344045 | − | 0.938953i | \(-0.611797\pi\) | ||||
−0.344045 | + | 0.938953i | \(0.611797\pi\) | |||||||
\(174\) | −12.1381 | −0.920184 | ||||||||
\(175\) | −7.73347 | −0.584595 | ||||||||
\(176\) | −5.60227 | −0.422287 | ||||||||
\(177\) | −34.3320 | −2.58055 | ||||||||
\(178\) | −1.59595 | −0.119621 | ||||||||
\(179\) | −8.97070 | −0.670502 | −0.335251 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335251 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(180\) | −9.97651 | −0.743605 | ||||||||
\(181\) | −3.91600 | −0.291074 | −0.145537 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145537 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(182\) | −4.81665 | −0.357034 | ||||||||
\(183\) | −7.42637 | −0.548973 | ||||||||
\(184\) | −0.597342 | −0.0440367 | ||||||||
\(185\) | 33.6665 | 2.47521 | ||||||||
\(186\) | 5.60324 | 0.410849 | ||||||||
\(187\) | −44.1935 | −3.23175 | ||||||||
\(188\) | −2.11544 | −0.154284 | ||||||||
\(189\) | −0.810793 | −0.0589765 | ||||||||
\(190\) | −14.1607 | −1.02733 | ||||||||
\(191\) | 10.4873 | 0.758836 | 0.379418 | − | 0.925225i | \(-0.376124\pi\) | ||||
0.379418 | + | 0.925225i | \(0.376124\pi\) | |||||||
\(192\) | −2.35142 | −0.169699 | ||||||||
\(193\) | −22.1435 | −1.59393 | −0.796963 | − | 0.604028i | \(-0.793562\pi\) | ||||
−0.796963 | + | 0.604028i | \(0.793562\pi\) | |||||||
\(194\) | 11.1601 | 0.801249 | ||||||||
\(195\) | −61.0017 | −4.36842 | ||||||||
\(196\) | −6.46363 | −0.461688 | ||||||||
\(197\) | 6.89885 | 0.491523 | 0.245761 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245761 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(198\) | 14.1692 | 1.00696 | ||||||||
\(199\) | −7.26553 | −0.515040 | −0.257520 | − | 0.966273i | \(-0.582905\pi\) | ||||
−0.257520 | + | 0.966273i | \(0.582905\pi\) | |||||||
\(200\) | −10.5595 | −0.746669 | ||||||||
\(201\) | −35.3799 | −2.49551 | ||||||||
\(202\) | −15.8952 | −1.11838 | ||||||||
\(203\) | 3.78051 | 0.265340 | ||||||||
\(204\) | −18.5492 | −1.29871 | ||||||||
\(205\) | −20.3624 | −1.42217 | ||||||||
\(206\) | −4.52520 | −0.315285 | ||||||||
\(207\) | 1.51079 | 0.105007 | ||||||||
\(208\) | −6.57678 | −0.456018 | ||||||||
\(209\) | 20.1118 | 1.39116 | ||||||||
\(210\) | 6.79297 | 0.468760 | ||||||||
\(211\) | 15.9296 | 1.09664 | 0.548320 | − | 0.836269i | \(-0.315268\pi\) | ||||
0.548320 | + | 0.836269i | \(0.315268\pi\) | |||||||
\(212\) | 13.3381 | 0.916063 | ||||||||
\(213\) | 0.654246 | 0.0448282 | ||||||||
\(214\) | 2.00963 | 0.137376 | ||||||||
\(215\) | −16.7243 | −1.14059 | ||||||||
\(216\) | −1.10708 | −0.0753271 | ||||||||
\(217\) | −1.74518 | −0.118470 | ||||||||
\(218\) | −3.39488 | −0.229930 | ||||||||
\(219\) | 36.2918 | 2.45237 | ||||||||
\(220\) | 22.0984 | 1.48988 | ||||||||
\(221\) | −51.8810 | −3.48989 | ||||||||
\(222\) | −20.0692 | −1.34696 | ||||||||
\(223\) | −27.6617 | −1.85236 | −0.926182 | − | 0.377078i | \(-0.876929\pi\) | ||||
−0.926182 | + | 0.377078i | \(0.876929\pi\) | |||||||
\(224\) | 0.732372 | 0.0489336 | ||||||||
\(225\) | 26.7069 | 1.78046 | ||||||||
\(226\) | 2.44327 | 0.162524 | ||||||||
\(227\) | −3.93286 | −0.261033 | −0.130517 | − | 0.991446i | \(-0.541664\pi\) | ||||
−0.130517 | + | 0.991446i | \(0.541664\pi\) | |||||||
\(228\) | 8.44146 | 0.559049 | ||||||||
\(229\) | −8.11720 | −0.536400 | −0.268200 | − | 0.963363i | \(-0.586429\pi\) | ||||
−0.268200 | + | 0.963363i | \(0.586429\pi\) | |||||||
\(230\) | 2.35625 | 0.155366 | ||||||||
\(231\) | −9.64775 | −0.634775 | ||||||||
\(232\) | 5.16201 | 0.338903 | ||||||||
\(233\) | −5.35936 | −0.351103 | −0.175552 | − | 0.984470i | \(-0.556171\pi\) | ||||
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(234\) | 16.6339 | 1.08739 | ||||||||
\(235\) | 8.34446 | 0.544333 | ||||||||
\(236\) | 14.6005 | 0.950413 | ||||||||
\(237\) | 9.27798 | 0.602670 | ||||||||
\(238\) | 5.77732 | 0.374488 | ||||||||
\(239\) | −19.4979 | −1.26121 | −0.630607 | − | 0.776102i | \(-0.717194\pi\) | ||||
−0.630607 | + | 0.776102i | \(0.717194\pi\) | |||||||
\(240\) | 9.27531 | 0.598719 | ||||||||
\(241\) | 0.671107 | 0.0432298 | 0.0216149 | − | 0.999766i | \(-0.493119\pi\) | ||||
0.0216149 | + | 0.999766i | \(0.493119\pi\) | |||||||
\(242\) | −20.3854 | −1.31042 | ||||||||
\(243\) | 20.6416 | 1.32416 | ||||||||
\(244\) | 3.15824 | 0.202186 | ||||||||
\(245\) | 25.4961 | 1.62889 | ||||||||
\(246\) | 12.1384 | 0.773917 | ||||||||
\(247\) | 23.6102 | 1.50228 | ||||||||
\(248\) | −2.38291 | −0.151315 | ||||||||
\(249\) | 31.4933 | 1.99581 | ||||||||
\(250\) | 21.9297 | 1.38696 | ||||||||
\(251\) | 24.4575 | 1.54374 | 0.771871 | − | 0.635779i | \(-0.219321\pi\) | ||||
0.771871 | + | 0.635779i | \(0.219321\pi\) | |||||||
\(252\) | −1.85231 | −0.116684 | ||||||||
\(253\) | −3.34647 | −0.210391 | ||||||||
\(254\) | −5.11200 | −0.320755 | ||||||||
\(255\) | 73.1684 | 4.58198 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.94806 | 0.121516 | 0.0607582 | − | 0.998153i | \(-0.480648\pi\) | ||||
0.0607582 | + | 0.998153i | \(0.480648\pi\) | |||||||
\(258\) | 9.96968 | 0.620685 | ||||||||
\(259\) | 6.25074 | 0.388402 | ||||||||
\(260\) | 25.9425 | 1.60888 | ||||||||
\(261\) | −13.0557 | −0.808127 | ||||||||
\(262\) | −7.31053 | −0.451646 | ||||||||
\(263\) | −9.59385 | −0.591582 | −0.295791 | − | 0.955253i | \(-0.595583\pi\) | ||||
−0.295791 | + | 0.955253i | \(0.595583\pi\) | |||||||
\(264\) | −13.1733 | −0.810760 | ||||||||
\(265\) | −52.6128 | −3.23198 | ||||||||
\(266\) | −2.62917 | −0.161205 | ||||||||
\(267\) | −3.75274 | −0.229664 | ||||||||
\(268\) | 15.0462 | 0.919091 | ||||||||
\(269\) | −24.0217 | −1.46463 | −0.732315 | − | 0.680966i | \(-0.761560\pi\) | ||||
−0.732315 | + | 0.680966i | \(0.761560\pi\) | |||||||
\(270\) | 4.36693 | 0.265763 | ||||||||
\(271\) | 25.6421 | 1.55765 | 0.778823 | − | 0.627243i | \(-0.215817\pi\) | ||||
0.778823 | + | 0.627243i | \(0.215817\pi\) | |||||||
\(272\) | 7.88851 | 0.478311 | ||||||||
\(273\) | −11.3260 | −0.685479 | ||||||||
\(274\) | −12.7625 | −0.771013 | ||||||||
\(275\) | −59.1571 | −3.56731 | ||||||||
\(276\) | −1.40460 | −0.0845472 | ||||||||
\(277\) | −15.9545 | −0.958610 | −0.479305 | − | 0.877648i | \(-0.659111\pi\) | ||||
−0.479305 | + | 0.877648i | \(0.659111\pi\) | |||||||
\(278\) | −5.16815 | −0.309965 | ||||||||
\(279\) | 6.02684 | 0.360817 | ||||||||
\(280\) | −2.88888 | −0.172643 | ||||||||
\(281\) | −9.92019 | −0.591789 | −0.295894 | − | 0.955221i | \(-0.595618\pi\) | ||||
−0.295894 | + | 0.955221i | \(0.595618\pi\) | |||||||
\(282\) | −4.97429 | −0.296215 | ||||||||
\(283\) | −14.0807 | −0.837011 | −0.418505 | − | 0.908214i | \(-0.637446\pi\) | ||||
−0.418505 | + | 0.908214i | \(0.637446\pi\) | |||||||
\(284\) | −0.278234 | −0.0165102 | ||||||||
\(285\) | −33.2978 | −1.97239 | ||||||||
\(286\) | −36.8449 | −2.17868 | ||||||||
\(287\) | −3.78062 | −0.223163 | ||||||||
\(288\) | −2.52919 | −0.149034 | ||||||||
\(289\) | 45.2286 | 2.66051 | ||||||||
\(290\) | −20.3618 | −1.19569 | ||||||||
\(291\) | 26.2421 | 1.53834 | ||||||||
\(292\) | −15.4340 | −0.903205 | ||||||||
\(293\) | −11.4487 | −0.668840 | −0.334420 | − | 0.942424i | \(-0.608540\pi\) | ||||
−0.334420 | + | 0.942424i | \(0.608540\pi\) | |||||||
\(294\) | −15.1987 | −0.886408 | ||||||||
\(295\) | −57.5925 | −3.35317 | ||||||||
\(296\) | 8.53492 | 0.496082 | ||||||||
\(297\) | −6.20215 | −0.359885 | ||||||||
\(298\) | −11.8339 | −0.685519 | ||||||||
\(299\) | −3.92859 | −0.227196 | ||||||||
\(300\) | −24.8298 | −1.43355 | ||||||||
\(301\) | −3.10515 | −0.178978 | ||||||||
\(302\) | −2.37792 | −0.136834 | ||||||||
\(303\) | −37.3763 | −2.14721 | ||||||||
\(304\) | −3.58994 | −0.205897 | ||||||||
\(305\) | −12.4579 | −0.713335 | ||||||||
\(306\) | −19.9515 | −1.14055 | ||||||||
\(307\) | −8.16040 | −0.465739 | −0.232869 | − | 0.972508i | \(-0.574811\pi\) | ||||
−0.232869 | + | 0.972508i | \(0.574811\pi\) | |||||||
\(308\) | 4.10294 | 0.233787 | ||||||||
\(309\) | −10.6407 | −0.605325 | ||||||||
\(310\) | 9.39953 | 0.533857 | ||||||||
\(311\) | 7.06502 | 0.400621 | 0.200310 | − | 0.979733i | \(-0.435805\pi\) | ||||
0.200310 | + | 0.979733i | \(0.435805\pi\) | |||||||
\(312\) | −15.4648 | −0.875521 | ||||||||
\(313\) | −11.0683 | −0.625616 | −0.312808 | − | 0.949816i | \(-0.601270\pi\) | ||||
−0.312808 | + | 0.949816i | \(0.601270\pi\) | |||||||
\(314\) | 3.17462 | 0.179154 | ||||||||
\(315\) | 7.30651 | 0.411675 | ||||||||
\(316\) | −3.94569 | −0.221962 | ||||||||
\(317\) | 14.8709 | 0.835231 | 0.417616 | − | 0.908624i | \(-0.362866\pi\) | ||||
0.417616 | + | 0.908624i | \(0.362866\pi\) | |||||||
\(318\) | 31.3635 | 1.75878 | ||||||||
\(319\) | 28.9190 | 1.61915 | ||||||||
\(320\) | −3.94455 | −0.220507 | ||||||||
\(321\) | 4.72549 | 0.263751 | ||||||||
\(322\) | 0.437476 | 0.0243796 | ||||||||
\(323\) | −28.3193 | −1.57573 | ||||||||
\(324\) | −10.1908 | −0.566154 | ||||||||
\(325\) | −69.4474 | −3.85225 | ||||||||
\(326\) | −0.771085 | −0.0427065 | ||||||||
\(327\) | −7.98279 | −0.441449 | ||||||||
\(328\) | −5.16216 | −0.285033 | ||||||||
\(329\) | 1.54929 | 0.0854150 | ||||||||
\(330\) | 51.9628 | 2.86046 | ||||||||
\(331\) | 16.8787 | 0.927735 | 0.463868 | − | 0.885905i | \(-0.346461\pi\) | ||||
0.463868 | + | 0.885905i | \(0.346461\pi\) | |||||||
\(332\) | −13.3933 | −0.735052 | ||||||||
\(333\) | −21.5864 | −1.18293 | ||||||||
\(334\) | −4.40690 | −0.241135 | ||||||||
\(335\) | −59.3504 | −3.24266 | ||||||||
\(336\) | 1.72211 | 0.0939491 | ||||||||
\(337\) | 26.6008 | 1.44904 | 0.724519 | − | 0.689255i | \(-0.242062\pi\) | ||||
0.724519 | + | 0.689255i | \(0.242062\pi\) | |||||||
\(338\) | −30.2540 | −1.64560 | ||||||||
\(339\) | 5.74515 | 0.312034 | ||||||||
\(340\) | −31.1166 | −1.68754 | ||||||||
\(341\) | −13.3497 | −0.722928 | ||||||||
\(342\) | 9.07963 | 0.490970 | ||||||||
\(343\) | 9.86038 | 0.532411 | ||||||||
\(344\) | −4.23985 | −0.228598 | ||||||||
\(345\) | 5.54053 | 0.298292 | ||||||||
\(346\) | 9.05042 | 0.486553 | ||||||||
\(347\) | 22.9759 | 1.23341 | 0.616705 | − | 0.787194i | \(-0.288467\pi\) | ||||
0.616705 | + | 0.787194i | \(0.288467\pi\) | |||||||
\(348\) | 12.1381 | 0.650669 | ||||||||
\(349\) | −18.5403 | −0.992440 | −0.496220 | − | 0.868197i | \(-0.665279\pi\) | ||||
−0.496220 | + | 0.868197i | \(0.665279\pi\) | |||||||
\(350\) | 7.73347 | 0.413371 | ||||||||
\(351\) | −7.28101 | −0.388632 | ||||||||
\(352\) | 5.60227 | 0.298602 | ||||||||
\(353\) | 22.9134 | 1.21956 | 0.609778 | − | 0.792572i | \(-0.291258\pi\) | ||||
0.609778 | + | 0.792572i | \(0.291258\pi\) | |||||||
\(354\) | 34.3320 | 1.82472 | ||||||||
\(355\) | 1.09751 | 0.0582497 | ||||||||
\(356\) | 1.59595 | 0.0845850 | ||||||||
\(357\) | 13.5849 | 0.718990 | ||||||||
\(358\) | 8.97070 | 0.474116 | ||||||||
\(359\) | −25.6182 | −1.35208 | −0.676039 | − | 0.736866i | \(-0.736305\pi\) | ||||
−0.676039 | + | 0.736866i | \(0.736305\pi\) | |||||||
\(360\) | 9.97651 | 0.525808 | ||||||||
\(361\) | −6.11234 | −0.321702 | ||||||||
\(362\) | 3.91600 | 0.205820 | ||||||||
\(363\) | −47.9347 | −2.51592 | ||||||||
\(364\) | 4.81665 | 0.252461 | ||||||||
\(365\) | 60.8801 | 3.18661 | ||||||||
\(366\) | 7.42637 | 0.388182 | ||||||||
\(367\) | −23.9395 | −1.24963 | −0.624817 | − | 0.780771i | \(-0.714826\pi\) | ||||
−0.624817 | + | 0.780771i | \(0.714826\pi\) | |||||||
\(368\) | 0.597342 | 0.0311386 | ||||||||
\(369\) | 13.0561 | 0.679672 | ||||||||
\(370\) | −33.6665 | −1.75024 | ||||||||
\(371\) | −9.76843 | −0.507152 | ||||||||
\(372\) | −5.60324 | −0.290514 | ||||||||
\(373\) | −11.4642 | −0.593595 | −0.296798 | − | 0.954940i | \(-0.595919\pi\) | ||||
−0.296798 | + | 0.954940i | \(0.595919\pi\) | |||||||
\(374\) | 44.1935 | 2.28519 | ||||||||
\(375\) | 51.5660 | 2.66286 | ||||||||
\(376\) | 2.11544 | 0.109095 | ||||||||
\(377\) | 33.9494 | 1.74848 | ||||||||
\(378\) | 0.810793 | 0.0417027 | ||||||||
\(379\) | −21.4613 | −1.10239 | −0.551195 | − | 0.834376i | \(-0.685828\pi\) | ||||
−0.551195 | + | 0.834376i | \(0.685828\pi\) | |||||||
\(380\) | 14.1607 | 0.726429 | ||||||||
\(381\) | −12.0205 | −0.615827 | ||||||||
\(382\) | −10.4873 | −0.536578 | ||||||||
\(383\) | −26.2934 | −1.34353 | −0.671764 | − | 0.740765i | \(-0.734463\pi\) | ||||
−0.671764 | + | 0.740765i | \(0.734463\pi\) | |||||||
\(384\) | 2.35142 | 0.119996 | ||||||||
\(385\) | −16.1843 | −0.824826 | ||||||||
\(386\) | 22.1435 | 1.12708 | ||||||||
\(387\) | 10.7234 | 0.545100 | ||||||||
\(388\) | −11.1601 | −0.566569 | ||||||||
\(389\) | −11.3139 | −0.573638 | −0.286819 | − | 0.957985i | \(-0.592598\pi\) | ||||
−0.286819 | + | 0.957985i | \(0.592598\pi\) | |||||||
\(390\) | 61.0017 | 3.08894 | ||||||||
\(391\) | 4.71214 | 0.238303 | ||||||||
\(392\) | 6.46363 | 0.326463 | ||||||||
\(393\) | −17.1901 | −0.867128 | ||||||||
\(394\) | −6.89885 | −0.347559 | ||||||||
\(395\) | 15.5640 | 0.783109 | ||||||||
\(396\) | −14.1692 | −0.712028 | ||||||||
\(397\) | −7.68422 | −0.385660 | −0.192830 | − | 0.981232i | \(-0.561767\pi\) | ||||
−0.192830 | + | 0.981232i | \(0.561767\pi\) | |||||||
\(398\) | 7.26553 | 0.364188 | ||||||||
\(399\) | −6.18229 | −0.309501 | ||||||||
\(400\) | 10.5595 | 0.527975 | ||||||||
\(401\) | −1.72129 | −0.0859573 | −0.0429786 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429786 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(402\) | 35.3799 | 1.76459 | ||||||||
\(403\) | −15.6719 | −0.780673 | ||||||||
\(404\) | 15.8952 | 0.790815 | ||||||||
\(405\) | 40.1980 | 1.99746 | ||||||||
\(406\) | −3.78051 | −0.187623 | ||||||||
\(407\) | 47.8149 | 2.37010 | ||||||||
\(408\) | 18.5492 | 0.918323 | ||||||||
\(409\) | 11.0519 | 0.546482 | 0.273241 | − | 0.961946i | \(-0.411904\pi\) | ||||
0.273241 | + | 0.961946i | \(0.411904\pi\) | |||||||
\(410\) | 20.3624 | 1.00563 | ||||||||
\(411\) | −30.0101 | −1.48029 | ||||||||
\(412\) | 4.52520 | 0.222940 | ||||||||
\(413\) | −10.6930 | −0.526168 | ||||||||
\(414\) | −1.51079 | −0.0742513 | ||||||||
\(415\) | 52.8305 | 2.59335 | ||||||||
\(416\) | 6.57678 | 0.322453 | ||||||||
\(417\) | −12.1525 | −0.595111 | ||||||||
\(418\) | −20.1118 | −0.983700 | ||||||||
\(419\) | −14.5494 | −0.710783 | −0.355391 | − | 0.934718i | \(-0.615652\pi\) | ||||
−0.355391 | + | 0.934718i | \(0.615652\pi\) | |||||||
\(420\) | −6.79297 | −0.331463 | ||||||||
\(421\) | −3.33663 | −0.162617 | −0.0813087 | − | 0.996689i | \(-0.525910\pi\) | ||||
−0.0813087 | + | 0.996689i | \(0.525910\pi\) | |||||||
\(422\) | −15.9296 | −0.775442 | ||||||||
\(423\) | −5.35035 | −0.260143 | ||||||||
\(424\) | −13.3381 | −0.647755 | ||||||||
\(425\) | 83.2987 | 4.04058 | ||||||||
\(426\) | −0.654246 | −0.0316983 | ||||||||
\(427\) | −2.31301 | −0.111934 | ||||||||
\(428\) | −2.00963 | −0.0971392 | ||||||||
\(429\) | −86.6379 | −4.18292 | ||||||||
\(430\) | 16.7243 | 0.806518 | ||||||||
\(431\) | 19.7302 | 0.950372 | 0.475186 | − | 0.879885i | \(-0.342381\pi\) | ||||
0.475186 | + | 0.879885i | \(0.342381\pi\) | |||||||
\(432\) | 1.10708 | 0.0532643 | ||||||||
\(433\) | −17.5306 | −0.842465 | −0.421232 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421232 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(434\) | 1.74518 | 0.0837713 | ||||||||
\(435\) | −47.8792 | −2.29563 | ||||||||
\(436\) | 3.39488 | 0.162585 | ||||||||
\(437\) | −2.14442 | −0.102582 | ||||||||
\(438\) | −36.2918 | −1.73409 | ||||||||
\(439\) | 33.2764 | 1.58820 | 0.794099 | − | 0.607789i | \(-0.207943\pi\) | ||||
0.794099 | + | 0.607789i | \(0.207943\pi\) | |||||||
\(440\) | −22.0984 | −1.05350 | ||||||||
\(441\) | −16.3477 | −0.778464 | ||||||||
\(442\) | 51.8810 | 2.46773 | ||||||||
\(443\) | 11.2269 | 0.533408 | 0.266704 | − | 0.963778i | \(-0.414065\pi\) | ||||
0.266704 | + | 0.963778i | \(0.414065\pi\) | |||||||
\(444\) | 20.0692 | 0.952443 | ||||||||
\(445\) | −6.29529 | −0.298426 | ||||||||
\(446\) | 27.6617 | 1.30982 | ||||||||
\(447\) | −27.8265 | −1.31615 | ||||||||
\(448\) | −0.732372 | −0.0346013 | ||||||||
\(449\) | 37.8756 | 1.78746 | 0.893730 | − | 0.448606i | \(-0.148079\pi\) | ||||
0.893730 | + | 0.448606i | \(0.148079\pi\) | |||||||
\(450\) | −26.7069 | −1.25898 | ||||||||
\(451\) | −28.9198 | −1.36178 | ||||||||
\(452\) | −2.44327 | −0.114922 | ||||||||
\(453\) | −5.59149 | −0.262711 | ||||||||
\(454\) | 3.93286 | 0.184578 | ||||||||
\(455\) | −18.9995 | −0.890711 | ||||||||
\(456\) | −8.44146 | −0.395308 | ||||||||
\(457\) | −8.93795 | −0.418100 | −0.209050 | − | 0.977905i | \(-0.567037\pi\) | ||||
−0.209050 | + | 0.977905i | \(0.567037\pi\) | |||||||
\(458\) | 8.11720 | 0.379292 | ||||||||
\(459\) | 8.73320 | 0.407631 | ||||||||
\(460\) | −2.35625 | −0.109861 | ||||||||
\(461\) | −9.44331 | −0.439819 | −0.219909 | − | 0.975520i | \(-0.570576\pi\) | ||||
−0.219909 | + | 0.975520i | \(0.570576\pi\) | |||||||
\(462\) | 9.64775 | 0.448854 | ||||||||
\(463\) | −2.79255 | −0.129781 | −0.0648903 | − | 0.997892i | \(-0.520670\pi\) | ||||
−0.0648903 | + | 0.997892i | \(0.520670\pi\) | |||||||
\(464\) | −5.16201 | −0.239640 | ||||||||
\(465\) | 22.1023 | 1.02497 | ||||||||
\(466\) | 5.35936 | 0.248268 | ||||||||
\(467\) | 20.4023 | 0.944104 | 0.472052 | − | 0.881571i | \(-0.343513\pi\) | ||||
0.472052 | + | 0.881571i | \(0.343513\pi\) | |||||||
\(468\) | −16.6339 | −0.768903 | ||||||||
\(469\) | −11.0194 | −0.508828 | ||||||||
\(470\) | −8.34446 | −0.384901 | ||||||||
\(471\) | 7.46487 | 0.343963 | ||||||||
\(472\) | −14.6005 | −0.672043 | ||||||||
\(473\) | −23.7528 | −1.09215 | ||||||||
\(474\) | −9.27798 | −0.426152 | ||||||||
\(475\) | −37.9079 | −1.73933 | ||||||||
\(476\) | −5.77732 | −0.264803 | ||||||||
\(477\) | 33.7345 | 1.54460 | ||||||||
\(478\) | 19.4979 | 0.891813 | ||||||||
\(479\) | 35.9555 | 1.64285 | 0.821425 | − | 0.570317i | \(-0.193180\pi\) | ||||
0.821425 | + | 0.570317i | \(0.193180\pi\) | |||||||
\(480\) | −9.27531 | −0.423358 | ||||||||
\(481\) | 56.1323 | 2.55941 | ||||||||
\(482\) | −0.671107 | −0.0305681 | ||||||||
\(483\) | 1.02869 | 0.0468071 | ||||||||
\(484\) | 20.3854 | 0.926609 | ||||||||
\(485\) | 44.0216 | 1.99892 | ||||||||
\(486\) | −20.6416 | −0.936321 | ||||||||
\(487\) | −4.43948 | −0.201172 | −0.100586 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(488\) | −3.15824 | −0.142967 | ||||||||
\(489\) | −1.81315 | −0.0819934 | ||||||||
\(490\) | −25.4961 | −1.15180 | ||||||||
\(491\) | 32.9313 | 1.48617 | 0.743085 | − | 0.669198i | \(-0.233362\pi\) | ||||
0.743085 | + | 0.669198i | \(0.233362\pi\) | |||||||
\(492\) | −12.1384 | −0.547242 | ||||||||
\(493\) | −40.7206 | −1.83396 | ||||||||
\(494\) | −23.6102 | −1.06227 | ||||||||
\(495\) | 55.8911 | 2.51212 | ||||||||
\(496\) | 2.38291 | 0.106996 | ||||||||
\(497\) | 0.203771 | 0.00914037 | ||||||||
\(498\) | −31.4933 | −1.41125 | ||||||||
\(499\) | 13.2766 | 0.594342 | 0.297171 | − | 0.954824i | \(-0.403957\pi\) | ||||
0.297171 | + | 0.954824i | \(0.403957\pi\) | |||||||
\(500\) | −21.9297 | −0.980726 | ||||||||
\(501\) | −10.3625 | −0.462962 | ||||||||
\(502\) | −24.4575 | −1.09159 | ||||||||
\(503\) | −31.0346 | −1.38377 | −0.691883 | − | 0.722010i | \(-0.743218\pi\) | ||||
−0.691883 | + | 0.722010i | \(0.743218\pi\) | |||||||
\(504\) | 1.85231 | 0.0825082 | ||||||||
\(505\) | −62.6994 | −2.79009 | ||||||||
\(506\) | 3.34647 | 0.148769 | ||||||||
\(507\) | −71.1400 | −3.15944 | ||||||||
\(508\) | 5.11200 | 0.226808 | ||||||||
\(509\) | −12.9425 | −0.573668 | −0.286834 | − | 0.957980i | \(-0.592603\pi\) | ||||
−0.286834 | + | 0.957980i | \(0.592603\pi\) | |||||||
\(510\) | −73.1684 | −3.23995 | ||||||||
\(511\) | 11.3034 | 0.500033 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.97434 | −0.175472 | ||||||||
\(514\) | −1.94806 | −0.0859251 | ||||||||
\(515\) | −17.8499 | −0.786560 | ||||||||
\(516\) | −9.96968 | −0.438891 | ||||||||
\(517\) | 11.8513 | 0.521218 | ||||||||
\(518\) | −6.25074 | −0.274642 | ||||||||
\(519\) | 21.2814 | 0.934148 | ||||||||
\(520\) | −25.9425 | −1.13765 | ||||||||
\(521\) | −2.99380 | −0.131161 | −0.0655803 | − | 0.997847i | \(-0.520890\pi\) | ||||
−0.0655803 | + | 0.997847i | \(0.520890\pi\) | |||||||
\(522\) | 13.0557 | 0.571432 | ||||||||
\(523\) | 33.6906 | 1.47319 | 0.736593 | − | 0.676336i | \(-0.236433\pi\) | ||||
0.736593 | + | 0.676336i | \(0.236433\pi\) | |||||||
\(524\) | 7.31053 | 0.319362 | ||||||||
\(525\) | 18.1847 | 0.793644 | ||||||||
\(526\) | 9.59385 | 0.418312 | ||||||||
\(527\) | 18.7976 | 0.818838 | ||||||||
\(528\) | 13.1733 | 0.573294 | ||||||||
\(529\) | −22.6432 | −0.984486 | ||||||||
\(530\) | 52.6128 | 2.28535 | ||||||||
\(531\) | 36.9275 | 1.60252 | ||||||||
\(532\) | 2.62917 | 0.113989 | ||||||||
\(533\) | −33.9504 | −1.47055 | ||||||||
\(534\) | 3.75274 | 0.162397 | ||||||||
\(535\) | 7.92710 | 0.342718 | ||||||||
\(536\) | −15.0462 | −0.649896 | ||||||||
\(537\) | 21.0939 | 0.910269 | ||||||||
\(538\) | 24.0217 | 1.03565 | ||||||||
\(539\) | 36.2110 | 1.55972 | ||||||||
\(540\) | −4.36693 | −0.187923 | ||||||||
\(541\) | 2.49802 | 0.107398 | 0.0536991 | − | 0.998557i | \(-0.482899\pi\) | ||||
0.0536991 | + | 0.998557i | \(0.482899\pi\) | |||||||
\(542\) | −25.6421 | −1.10142 | ||||||||
\(543\) | 9.20817 | 0.395160 | ||||||||
\(544\) | −7.88851 | −0.338217 | ||||||||
\(545\) | −13.3913 | −0.573619 | ||||||||
\(546\) | 11.3260 | 0.484707 | ||||||||
\(547\) | 25.4749 | 1.08923 | 0.544615 | − | 0.838686i | \(-0.316676\pi\) | ||||
0.544615 | + | 0.838686i | \(0.316676\pi\) | |||||||
\(548\) | 12.7625 | 0.545189 | ||||||||
\(549\) | 7.98779 | 0.340911 | ||||||||
\(550\) | 59.1571 | 2.52247 | ||||||||
\(551\) | 18.5313 | 0.789460 | ||||||||
\(552\) | 1.40460 | 0.0597839 | ||||||||
\(553\) | 2.88971 | 0.122883 | ||||||||
\(554\) | 15.9545 | 0.677840 | ||||||||
\(555\) | −79.1641 | −3.36033 | ||||||||
\(556\) | 5.16815 | 0.219179 | ||||||||
\(557\) | 29.6288 | 1.25541 | 0.627707 | − | 0.778450i | \(-0.283994\pi\) | ||||
0.627707 | + | 0.778450i | \(0.283994\pi\) | |||||||
\(558\) | −6.02684 | −0.255136 | ||||||||
\(559\) | −27.8846 | −1.17939 | ||||||||
\(560\) | 2.88888 | 0.122077 | ||||||||
\(561\) | 103.918 | 4.38741 | ||||||||
\(562\) | 9.92019 | 0.418458 | ||||||||
\(563\) | 3.05150 | 0.128606 | 0.0643028 | − | 0.997930i | \(-0.479518\pi\) | ||||
0.0643028 | + | 0.997930i | \(0.479518\pi\) | |||||||
\(564\) | 4.97429 | 0.209456 | ||||||||
\(565\) | 9.63760 | 0.405457 | ||||||||
\(566\) | 14.0807 | 0.591856 | ||||||||
\(567\) | 7.46343 | 0.313435 | ||||||||
\(568\) | 0.278234 | 0.0116744 | ||||||||
\(569\) | −34.2607 | −1.43628 | −0.718142 | − | 0.695897i | \(-0.755007\pi\) | ||||
−0.718142 | + | 0.695897i | \(0.755007\pi\) | |||||||
\(570\) | 33.2978 | 1.39469 | ||||||||
\(571\) | 1.81874 | 0.0761117 | 0.0380559 | − | 0.999276i | \(-0.487884\pi\) | ||||
0.0380559 | + | 0.999276i | \(0.487884\pi\) | |||||||
\(572\) | 36.8449 | 1.54056 | ||||||||
\(573\) | −24.6601 | −1.03019 | ||||||||
\(574\) | 3.78062 | 0.157800 | ||||||||
\(575\) | 6.30763 | 0.263046 | ||||||||
\(576\) | 2.52919 | 0.105383 | ||||||||
\(577\) | −37.1690 | −1.54736 | −0.773682 | − | 0.633574i | \(-0.781587\pi\) | ||||
−0.773682 | + | 0.633574i | \(0.781587\pi\) | |||||||
\(578\) | −45.2286 | −1.88126 | ||||||||
\(579\) | 52.0688 | 2.16391 | ||||||||
\(580\) | 20.3618 | 0.845478 | ||||||||
\(581\) | 9.80886 | 0.406940 | ||||||||
\(582\) | −26.2421 | −1.08777 | ||||||||
\(583\) | −74.7235 | −3.09473 | ||||||||
\(584\) | 15.4340 | 0.638662 | ||||||||
\(585\) | 65.6133 | 2.71278 | ||||||||
\(586\) | 11.4487 | 0.472942 | ||||||||
\(587\) | −6.79243 | −0.280354 | −0.140177 | − | 0.990126i | \(-0.544767\pi\) | ||||
−0.140177 | + | 0.990126i | \(0.544767\pi\) | |||||||
\(588\) | 15.1987 | 0.626785 | ||||||||
\(589\) | −8.55452 | −0.352483 | ||||||||
\(590\) | 57.5925 | 2.37105 | ||||||||
\(591\) | −16.2221 | −0.667289 | ||||||||
\(592\) | −8.53492 | −0.350783 | ||||||||
\(593\) | −13.8884 | −0.570329 | −0.285164 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285164 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(594\) | 6.20215 | 0.254477 | ||||||||
\(595\) | 22.7889 | 0.934255 | ||||||||
\(596\) | 11.8339 | 0.484735 | ||||||||
\(597\) | 17.0843 | 0.699215 | ||||||||
\(598\) | 3.92859 | 0.160652 | ||||||||
\(599\) | 8.75043 | 0.357533 | 0.178767 | − | 0.983892i | \(-0.442789\pi\) | ||||
0.178767 | + | 0.983892i | \(0.442789\pi\) | |||||||
\(600\) | 24.8298 | 1.01367 | ||||||||
\(601\) | 9.32602 | 0.380416 | 0.190208 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190208 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(602\) | 3.10515 | 0.126556 | ||||||||
\(603\) | 38.0546 | 1.54970 | ||||||||
\(604\) | 2.37792 | 0.0967561 | ||||||||
\(605\) | −80.4113 | −3.26918 | ||||||||
\(606\) | 37.3763 | 1.51831 | ||||||||
\(607\) | −47.1463 | −1.91361 | −0.956804 | − | 0.290732i | \(-0.906101\pi\) | ||||
−0.956804 | + | 0.290732i | \(0.906101\pi\) | |||||||
\(608\) | 3.58994 | 0.145591 | ||||||||
\(609\) | −8.88957 | −0.360224 | ||||||||
\(610\) | 12.4579 | 0.504404 | ||||||||
\(611\) | 13.9128 | 0.562851 | ||||||||
\(612\) | 19.9515 | 0.806493 | ||||||||
\(613\) | −24.0231 | −0.970285 | −0.485143 | − | 0.874435i | \(-0.661232\pi\) | ||||
−0.485143 | + | 0.874435i | \(0.661232\pi\) | |||||||
\(614\) | 8.16040 | 0.329327 | ||||||||
\(615\) | 47.8806 | 1.93073 | ||||||||
\(616\) | −4.10294 | −0.165312 | ||||||||
\(617\) | 32.1413 | 1.29396 | 0.646981 | − | 0.762507i | \(-0.276031\pi\) | ||||
0.646981 | + | 0.762507i | \(0.276031\pi\) | |||||||
\(618\) | 10.6407 | 0.428030 | ||||||||
\(619\) | 4.93499 | 0.198354 | 0.0991770 | − | 0.995070i | \(-0.468379\pi\) | ||||
0.0991770 | + | 0.995070i | \(0.468379\pi\) | |||||||
\(620\) | −9.39953 | −0.377494 | ||||||||
\(621\) | 0.661305 | 0.0265372 | ||||||||
\(622\) | −7.06502 | −0.283282 | ||||||||
\(623\) | −1.16883 | −0.0468280 | ||||||||
\(624\) | 15.4648 | 0.619087 | ||||||||
\(625\) | 33.7054 | 1.34822 | ||||||||
\(626\) | 11.0683 | 0.442377 | ||||||||
\(627\) | −47.2913 | −1.88863 | ||||||||
\(628\) | −3.17462 | −0.126681 | ||||||||
\(629\) | −67.3278 | −2.68454 | ||||||||
\(630\) | −7.30651 | −0.291098 | ||||||||
\(631\) | 35.8146 | 1.42576 | 0.712878 | − | 0.701288i | \(-0.247391\pi\) | ||||
0.712878 | + | 0.701288i | \(0.247391\pi\) | |||||||
\(632\) | 3.94569 | 0.156951 | ||||||||
\(633\) | −37.4573 | −1.48879 | ||||||||
\(634\) | −14.8709 | −0.590598 | ||||||||
\(635\) | −20.1645 | −0.800205 | ||||||||
\(636\) | −31.3635 | −1.24364 | ||||||||
\(637\) | 42.5099 | 1.68430 | ||||||||
\(638\) | −28.9190 | −1.14491 | ||||||||
\(639\) | −0.703706 | −0.0278382 | ||||||||
\(640\) | 3.94455 | 0.155922 | ||||||||
\(641\) | 19.2972 | 0.762192 | 0.381096 | − | 0.924535i | \(-0.375547\pi\) | ||||
0.381096 | + | 0.924535i | \(0.375547\pi\) | |||||||
\(642\) | −4.72549 | −0.186500 | ||||||||
\(643\) | 49.8612 | 1.96633 | 0.983166 | − | 0.182713i | \(-0.0584880\pi\) | ||||
0.983166 | + | 0.182713i | \(0.0584880\pi\) | |||||||
\(644\) | −0.437476 | −0.0172390 | ||||||||
\(645\) | 39.3259 | 1.54846 | ||||||||
\(646\) | 28.3193 | 1.11421 | ||||||||
\(647\) | −2.26143 | −0.0889060 | −0.0444530 | − | 0.999011i | \(-0.514154\pi\) | ||||
−0.0444530 | + | 0.999011i | \(0.514154\pi\) | |||||||
\(648\) | 10.1908 | 0.400331 | ||||||||
\(649\) | −81.7960 | −3.21077 | ||||||||
\(650\) | 69.4474 | 2.72395 | ||||||||
\(651\) | 4.10365 | 0.160835 | ||||||||
\(652\) | 0.771085 | 0.0301980 | ||||||||
\(653\) | −47.5403 | −1.86040 | −0.930198 | − | 0.367059i | \(-0.880365\pi\) | ||||
−0.930198 | + | 0.367059i | \(0.880365\pi\) | |||||||
\(654\) | 7.98279 | 0.312152 | ||||||||
\(655\) | −28.8368 | −1.12675 | ||||||||
\(656\) | 5.16216 | 0.201548 | ||||||||
\(657\) | −39.0354 | −1.52292 | ||||||||
\(658\) | −1.54929 | −0.0603975 | ||||||||
\(659\) | 27.6405 | 1.07672 | 0.538361 | − | 0.842714i | \(-0.319044\pi\) | ||||
0.538361 | + | 0.842714i | \(0.319044\pi\) | |||||||
\(660\) | −51.9628 | −2.02265 | ||||||||
\(661\) | 43.9554 | 1.70967 | 0.854834 | − | 0.518902i | \(-0.173659\pi\) | ||||
0.854834 | + | 0.518902i | \(0.173659\pi\) | |||||||
\(662\) | −16.8787 | −0.656008 | ||||||||
\(663\) | 121.994 | 4.73786 | ||||||||
\(664\) | 13.3933 | 0.519761 | ||||||||
\(665\) | −10.3709 | −0.402166 | ||||||||
\(666\) | 21.5864 | 0.836457 | ||||||||
\(667\) | −3.08349 | −0.119393 | ||||||||
\(668\) | 4.40690 | 0.170508 | ||||||||
\(669\) | 65.0443 | 2.51476 | ||||||||
\(670\) | 59.3504 | 2.29291 | ||||||||
\(671\) | −17.6933 | −0.683043 | ||||||||
\(672\) | −1.72211 | −0.0664320 | ||||||||
\(673\) | 20.3098 | 0.782885 | 0.391442 | − | 0.920203i | \(-0.371976\pi\) | ||||
0.391442 | + | 0.920203i | \(0.371976\pi\) | |||||||
\(674\) | −26.6008 | −1.02462 | ||||||||
\(675\) | 11.6902 | 0.449955 | ||||||||
\(676\) | 30.2540 | 1.16362 | ||||||||
\(677\) | 3.67264 | 0.141151 | 0.0705755 | − | 0.997506i | \(-0.477516\pi\) | ||||
0.0705755 | + | 0.997506i | \(0.477516\pi\) | |||||||
\(678\) | −5.74515 | −0.220641 | ||||||||
\(679\) | 8.17335 | 0.313664 | ||||||||
\(680\) | 31.1166 | 1.19327 | ||||||||
\(681\) | 9.24782 | 0.354377 | ||||||||
\(682\) | 13.3497 | 0.511187 | ||||||||
\(683\) | −6.18538 | −0.236677 | −0.118339 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118339 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(684\) | −9.07963 | −0.347168 | ||||||||
\(685\) | −50.3425 | −1.92349 | ||||||||
\(686\) | −9.86038 | −0.376471 | ||||||||
\(687\) | 19.0870 | 0.728213 | ||||||||
\(688\) | 4.23985 | 0.161643 | ||||||||
\(689\) | −87.7216 | −3.34193 | ||||||||
\(690\) | −5.54053 | −0.210924 | ||||||||
\(691\) | −28.0612 | −1.06750 | −0.533749 | − | 0.845643i | \(-0.679217\pi\) | ||||
−0.533749 | + | 0.845643i | \(0.679217\pi\) | |||||||
\(692\) | −9.05042 | −0.344045 | ||||||||
\(693\) | 10.3771 | 0.394194 | ||||||||
\(694\) | −22.9759 | −0.872153 | ||||||||
\(695\) | −20.3860 | −0.773287 | ||||||||
\(696\) | −12.1381 | −0.460092 | ||||||||
\(697\) | 40.7218 | 1.54245 | ||||||||
\(698\) | 18.5403 | 0.701761 | ||||||||
\(699\) | 12.6021 | 0.476656 | ||||||||
\(700\) | −7.73347 | −0.292298 | ||||||||
\(701\) | 44.9400 | 1.69736 | 0.848681 | − | 0.528906i | \(-0.177397\pi\) | ||||
0.848681 | + | 0.528906i | \(0.177397\pi\) | |||||||
\(702\) | 7.28101 | 0.274804 | ||||||||
\(703\) | 30.6398 | 1.15560 | ||||||||
\(704\) | −5.60227 | −0.211143 | ||||||||
\(705\) | −19.6214 | −0.738983 | ||||||||
\(706\) | −22.9134 | −0.862357 | ||||||||
\(707\) | −11.6412 | −0.437812 | ||||||||
\(708\) | −34.3320 | −1.29028 | ||||||||
\(709\) | −37.3761 | −1.40369 | −0.701845 | − | 0.712330i | \(-0.747640\pi\) | ||||
−0.701845 | + | 0.712330i | \(0.747640\pi\) | |||||||
\(710\) | −1.09751 | −0.0411888 | ||||||||
\(711\) | −9.97939 | −0.374256 | ||||||||
\(712\) | −1.59595 | −0.0598106 | ||||||||
\(713\) | 1.42342 | 0.0533073 | ||||||||
\(714\) | −13.5849 | −0.508403 | ||||||||
\(715\) | −145.337 | −5.43528 | ||||||||
\(716\) | −8.97070 | −0.335251 | ||||||||
\(717\) | 45.8478 | 1.71222 | ||||||||
\(718\) | 25.6182 | 0.956064 | ||||||||
\(719\) | 38.1675 | 1.42341 | 0.711704 | − | 0.702479i | \(-0.247924\pi\) | ||||
0.711704 | + | 0.702479i | \(0.247924\pi\) | |||||||
\(720\) | −9.97651 | −0.371803 | ||||||||
\(721\) | −3.31413 | −0.123424 | ||||||||
\(722\) | 6.11234 | 0.227478 | ||||||||
\(723\) | −1.57806 | −0.0586886 | ||||||||
\(724\) | −3.91600 | −0.145537 | ||||||||
\(725\) | −54.5082 | −2.02438 | ||||||||
\(726\) | 47.9347 | 1.77902 | ||||||||
\(727\) | 12.9750 | 0.481216 | 0.240608 | − | 0.970622i | \(-0.422653\pi\) | ||||
0.240608 | + | 0.970622i | \(0.422653\pi\) | |||||||
\(728\) | −4.81665 | −0.178517 | ||||||||
\(729\) | −17.9647 | −0.665361 | ||||||||
\(730\) | −60.8801 | −2.25327 | ||||||||
\(731\) | 33.4461 | 1.23705 | ||||||||
\(732\) | −7.42637 | −0.274486 | ||||||||
\(733\) | 39.9082 | 1.47404 | 0.737022 | − | 0.675869i | \(-0.236232\pi\) | ||||
0.737022 | + | 0.675869i | \(0.236232\pi\) | |||||||
\(734\) | 23.9395 | 0.883625 | ||||||||
\(735\) | −59.9522 | −2.21137 | ||||||||
\(736\) | −0.597342 | −0.0220183 | ||||||||
\(737\) | −84.2927 | −3.10496 | ||||||||
\(738\) | −13.0561 | −0.480601 | ||||||||
\(739\) | −4.55175 | −0.167439 | −0.0837194 | − | 0.996489i | \(-0.526680\pi\) | ||||
−0.0837194 | + | 0.996489i | \(0.526680\pi\) | |||||||
\(740\) | 33.6665 | 1.23760 | ||||||||
\(741\) | −55.5176 | −2.03949 | ||||||||
\(742\) | 9.76843 | 0.358610 | ||||||||
\(743\) | 34.2614 | 1.25693 | 0.628464 | − | 0.777839i | \(-0.283684\pi\) | ||||
0.628464 | + | 0.777839i | \(0.283684\pi\) | |||||||
\(744\) | 5.60324 | 0.205425 | ||||||||
\(745\) | −46.6794 | −1.71020 | ||||||||
\(746\) | 11.4642 | 0.419735 | ||||||||
\(747\) | −33.8741 | −1.23939 | ||||||||
\(748\) | −44.1935 | −1.61588 | ||||||||
\(749\) | 1.47180 | 0.0537783 | ||||||||
\(750\) | −51.5660 | −1.88292 | ||||||||
\(751\) | 32.0113 | 1.16811 | 0.584054 | − | 0.811715i | \(-0.301466\pi\) | ||||
0.584054 | + | 0.811715i | \(0.301466\pi\) | |||||||
\(752\) | −2.11544 | −0.0771422 | ||||||||
\(753\) | −57.5099 | −2.09578 | ||||||||
\(754\) | −33.9494 | −1.23636 | ||||||||
\(755\) | −9.37982 | −0.341366 | ||||||||
\(756\) | −0.810793 | −0.0294882 | ||||||||
\(757\) | −8.45348 | −0.307247 | −0.153624 | − | 0.988129i | \(-0.549094\pi\) | ||||
−0.153624 | + | 0.988129i | \(0.549094\pi\) | |||||||
\(758\) | 21.4613 | 0.779508 | ||||||||
\(759\) | 7.86897 | 0.285625 | ||||||||
\(760\) | −14.1607 | −0.513663 | ||||||||
\(761\) | 36.8514 | 1.33586 | 0.667932 | − | 0.744223i | \(-0.267180\pi\) | ||||
0.667932 | + | 0.744223i | \(0.267180\pi\) | |||||||
\(762\) | 12.0205 | 0.435455 | ||||||||
\(763\) | −2.48631 | −0.0900105 | ||||||||
\(764\) | 10.4873 | 0.379418 | ||||||||
\(765\) | −78.6998 | −2.84540 | ||||||||
\(766\) | 26.2934 | 0.950018 | ||||||||
\(767\) | −96.0244 | −3.46724 | ||||||||
\(768\) | −2.35142 | −0.0848497 | ||||||||
\(769\) | 16.7762 | 0.604965 | 0.302483 | − | 0.953155i | \(-0.402185\pi\) | ||||
0.302483 | + | 0.953155i | \(0.402185\pi\) | |||||||
\(770\) | 16.1843 | 0.583240 | ||||||||
\(771\) | −4.58070 | −0.164970 | ||||||||
\(772\) | −22.1435 | −0.796963 | ||||||||
\(773\) | −7.81619 | −0.281129 | −0.140564 | − | 0.990072i | \(-0.544892\pi\) | ||||
−0.140564 | + | 0.990072i | \(0.544892\pi\) | |||||||
\(774\) | −10.7234 | −0.385444 | ||||||||
\(775\) | 25.1624 | 0.903859 | ||||||||
\(776\) | 11.1601 | 0.400625 | ||||||||
\(777\) | −14.6981 | −0.527292 | ||||||||
\(778\) | 11.3139 | 0.405623 | ||||||||
\(779\) | −18.5318 | −0.663972 | ||||||||
\(780\) | −61.0017 | −2.18421 | ||||||||
\(781\) | 1.55874 | 0.0557762 | ||||||||
\(782\) | −4.71214 | −0.168506 | ||||||||
\(783\) | −5.71475 | −0.204228 | ||||||||
\(784\) | −6.46363 | −0.230844 | ||||||||
\(785\) | 12.5225 | 0.446946 | ||||||||
\(786\) | 17.1901 | 0.613152 | ||||||||
\(787\) | 20.7337 | 0.739077 | 0.369538 | − | 0.929216i | \(-0.379516\pi\) | ||||
0.369538 | + | 0.929216i | \(0.379516\pi\) | |||||||
\(788\) | 6.89885 | 0.245761 | ||||||||
\(789\) | 22.5592 | 0.803129 | ||||||||
\(790\) | −15.5640 | −0.553741 | ||||||||
\(791\) | 1.78938 | 0.0636230 | ||||||||
\(792\) | 14.1692 | 0.503480 | ||||||||
\(793\) | −20.7711 | −0.737603 | ||||||||
\(794\) | 7.68422 | 0.272703 | ||||||||
\(795\) | 123.715 | 4.38771 | ||||||||
\(796\) | −7.26553 | −0.257520 | ||||||||
\(797\) | 15.1196 | 0.535563 | 0.267782 | − | 0.963480i | \(-0.413709\pi\) | ||||
0.267782 | + | 0.963480i | \(0.413709\pi\) | |||||||
\(798\) | 6.18229 | 0.218851 | ||||||||
\(799\) | −16.6877 | −0.590367 | ||||||||
\(800\) | −10.5595 | −0.373334 | ||||||||
\(801\) | 4.03645 | 0.142621 | ||||||||
\(802\) | 1.72129 | 0.0607810 | ||||||||
\(803\) | 86.4653 | 3.05129 | ||||||||
\(804\) | −35.3799 | −1.24775 | ||||||||
\(805\) | 1.72565 | 0.0608211 | ||||||||
\(806\) | 15.6719 | 0.552019 | ||||||||
\(807\) | 56.4852 | 1.98837 | ||||||||
\(808\) | −15.8952 | −0.559191 | ||||||||
\(809\) | −19.0803 | −0.670828 | −0.335414 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335414 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(810\) | −40.1980 | −1.41241 | ||||||||
\(811\) | 1.02027 | 0.0358264 | 0.0179132 | − | 0.999840i | \(-0.494298\pi\) | ||||
0.0179132 | + | 0.999840i | \(0.494298\pi\) | |||||||
\(812\) | 3.78051 | 0.132670 | ||||||||
\(813\) | −60.2954 | −2.11465 | ||||||||
\(814\) | −47.8149 | −1.67591 | ||||||||
\(815\) | −3.04159 | −0.106542 | ||||||||
\(816\) | −18.5492 | −0.649353 | ||||||||
\(817\) | −15.2208 | −0.532509 | ||||||||
\(818\) | −11.0519 | −0.386421 | ||||||||
\(819\) | 12.1822 | 0.425681 | ||||||||
\(820\) | −20.3624 | −0.711086 | ||||||||
\(821\) | 17.6393 | 0.615617 | 0.307809 | − | 0.951448i | \(-0.400404\pi\) | ||||
0.307809 | + | 0.951448i | \(0.400404\pi\) | |||||||
\(822\) | 30.0101 | 1.04672 | ||||||||
\(823\) | 22.0045 | 0.767028 | 0.383514 | − | 0.923535i | \(-0.374714\pi\) | ||||
0.383514 | + | 0.923535i | \(0.374714\pi\) | |||||||
\(824\) | −4.52520 | −0.157643 | ||||||||
\(825\) | 139.103 | 4.84296 | ||||||||
\(826\) | 10.6930 | 0.372057 | ||||||||
\(827\) | 20.8310 | 0.724364 | 0.362182 | − | 0.932107i | \(-0.382032\pi\) | ||||
0.362182 | + | 0.932107i | \(0.382032\pi\) | |||||||
\(828\) | 1.51079 | 0.0525036 | ||||||||
\(829\) | 6.45825 | 0.224304 | 0.112152 | − | 0.993691i | \(-0.464226\pi\) | ||||
0.112152 | + | 0.993691i | \(0.464226\pi\) | |||||||
\(830\) | −52.8305 | −1.83377 | ||||||||
\(831\) | 37.5157 | 1.30140 | ||||||||
\(832\) | −6.57678 | −0.228009 | ||||||||
\(833\) | −50.9884 | −1.76664 | ||||||||
\(834\) | 12.1525 | 0.420807 | ||||||||
\(835\) | −17.3832 | −0.601572 | ||||||||
\(836\) | 20.1118 | 0.695581 | ||||||||
\(837\) | 2.63807 | 0.0911851 | ||||||||
\(838\) | 14.5494 | 0.502599 | ||||||||
\(839\) | 15.3261 | 0.529115 | 0.264558 | − | 0.964370i | \(-0.414774\pi\) | ||||
0.264558 | + | 0.964370i | \(0.414774\pi\) | |||||||
\(840\) | 6.79297 | 0.234380 | ||||||||
\(841\) | −2.35366 | −0.0811606 | ||||||||
\(842\) | 3.33663 | 0.114988 | ||||||||
\(843\) | 23.3266 | 0.803409 | ||||||||
\(844\) | 15.9296 | 0.548320 | ||||||||
\(845\) | −119.339 | −4.10537 | ||||||||
\(846\) | 5.35035 | 0.183949 | ||||||||
\(847\) | −14.9297 | −0.512990 | ||||||||
\(848\) | 13.3381 | 0.458032 | ||||||||
\(849\) | 33.1097 | 1.13632 | ||||||||
\(850\) | −83.2987 | −2.85712 | ||||||||
\(851\) | −5.09827 | −0.174766 | ||||||||
\(852\) | 0.654246 | 0.0224141 | ||||||||
\(853\) | −3.33584 | −0.114217 | −0.0571086 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571086 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(854\) | 2.31301 | 0.0791495 | ||||||||
\(855\) | 35.8151 | 1.22485 | ||||||||
\(856\) | 2.00963 | 0.0686878 | ||||||||
\(857\) | −4.55116 | −0.155465 | −0.0777324 | − | 0.996974i | \(-0.524768\pi\) | ||||
−0.0777324 | + | 0.996974i | \(0.524768\pi\) | |||||||
\(858\) | 86.6379 | 2.95777 | ||||||||
\(859\) | 11.6336 | 0.396933 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(860\) | −16.7243 | −0.570295 | ||||||||
\(861\) | 8.88983 | 0.302965 | ||||||||
\(862\) | −19.7302 | −0.672014 | ||||||||
\(863\) | 24.9565 | 0.849529 | 0.424765 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424765 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(864\) | −1.10708 | −0.0376636 | ||||||||
\(865\) | 35.6998 | 1.21383 | ||||||||
\(866\) | 17.5306 | 0.595713 | ||||||||
\(867\) | −106.352 | −3.61189 | ||||||||
\(868\) | −1.74518 | −0.0592352 | ||||||||
\(869\) | 22.1048 | 0.749854 | ||||||||
\(870\) | 47.8792 | 1.62326 | ||||||||
\(871\) | −98.9553 | −3.35297 | ||||||||
\(872\) | −3.39488 | −0.114965 | ||||||||
\(873\) | −28.2260 | −0.955306 | ||||||||
\(874\) | 2.14442 | 0.0725361 | ||||||||
\(875\) | 16.0607 | 0.542950 | ||||||||
\(876\) | 36.2918 | 1.22619 | ||||||||
\(877\) | 53.4352 | 1.80438 | 0.902189 | − | 0.431342i | \(-0.141960\pi\) | ||||
0.902189 | + | 0.431342i | \(0.141960\pi\) | |||||||
\(878\) | −33.2764 | −1.12303 | ||||||||
\(879\) | 26.9207 | 0.908014 | ||||||||
\(880\) | 22.0984 | 0.744938 | ||||||||
\(881\) | −32.1974 | −1.08476 | −0.542378 | − | 0.840134i | \(-0.682476\pi\) | ||||
−0.542378 | + | 0.840134i | \(0.682476\pi\) | |||||||
\(882\) | 16.3477 | 0.550457 | ||||||||
\(883\) | 8.65897 | 0.291398 | 0.145699 | − | 0.989329i | \(-0.453457\pi\) | ||||
0.145699 | + | 0.989329i | \(0.453457\pi\) | |||||||
\(884\) | −51.8810 | −1.74495 | ||||||||
\(885\) | 135.424 | 4.55224 | ||||||||
\(886\) | −11.2269 | −0.377177 | ||||||||
\(887\) | 39.5447 | 1.32778 | 0.663890 | − | 0.747830i | \(-0.268904\pi\) | ||||
0.663890 | + | 0.747830i | \(0.268904\pi\) | |||||||
\(888\) | −20.0692 | −0.673479 | ||||||||
\(889\) | −3.74388 | −0.125566 | ||||||||
\(890\) | 6.29529 | 0.211019 | ||||||||
\(891\) | 57.0914 | 1.91263 | ||||||||
\(892\) | −27.6617 | −0.926182 | ||||||||
\(893\) | 7.59430 | 0.254134 | ||||||||
\(894\) | 27.8265 | 0.930657 | ||||||||
\(895\) | 35.3854 | 1.18280 | ||||||||
\(896\) | 0.732372 | 0.0244668 | ||||||||
\(897\) | 9.23777 | 0.308440 | ||||||||
\(898\) | −37.8756 | −1.26392 | ||||||||
\(899\) | −12.3006 | −0.410249 | ||||||||
\(900\) | 26.7069 | 0.890231 | ||||||||
\(901\) | 105.218 | 3.50531 | ||||||||
\(902\) | 28.9198 | 0.962924 | ||||||||
\(903\) | 7.30151 | 0.242979 | ||||||||
\(904\) | 2.44327 | 0.0812619 | ||||||||
\(905\) | 15.4469 | 0.513471 | ||||||||
\(906\) | 5.59149 | 0.185765 | ||||||||
\(907\) | −37.6257 | −1.24934 | −0.624671 | − | 0.780888i | \(-0.714767\pi\) | ||||
−0.624671 | + | 0.780888i | \(0.714767\pi\) | |||||||
\(908\) | −3.93286 | −0.130517 | ||||||||
\(909\) | 40.2019 | 1.33341 | ||||||||
\(910\) | 18.9995 | 0.629828 | ||||||||
\(911\) | −25.5304 | −0.845859 | −0.422930 | − | 0.906162i | \(-0.638998\pi\) | ||||
−0.422930 | + | 0.906162i | \(0.638998\pi\) | |||||||
\(912\) | 8.44146 | 0.279525 | ||||||||
\(913\) | 75.0328 | 2.48322 | ||||||||
\(914\) | 8.93795 | 0.295641 | ||||||||
\(915\) | 29.2937 | 0.968420 | ||||||||
\(916\) | −8.11720 | −0.268200 | ||||||||
\(917\) | −5.35403 | −0.176805 | ||||||||
\(918\) | −8.73320 | −0.288239 | ||||||||
\(919\) | 24.4882 | 0.807792 | 0.403896 | − | 0.914805i | \(-0.367656\pi\) | ||||
0.403896 | + | 0.914805i | \(0.367656\pi\) | |||||||
\(920\) | 2.35625 | 0.0776832 | ||||||||
\(921\) | 19.1885 | 0.632284 | ||||||||
\(922\) | 9.44331 | 0.310999 | ||||||||
\(923\) | 1.82988 | 0.0602314 | ||||||||
\(924\) | −9.64775 | −0.317388 | ||||||||
\(925\) | −90.1245 | −2.96327 | ||||||||
\(926\) | 2.79255 | 0.0917687 | ||||||||
\(927\) | 11.4451 | 0.375906 | ||||||||
\(928\) | 5.16201 | 0.169451 | ||||||||
\(929\) | −41.9376 | −1.37593 | −0.687965 | − | 0.725744i | \(-0.741496\pi\) | ||||
−0.687965 | + | 0.725744i | \(0.741496\pi\) | |||||||
\(930\) | −22.1023 | −0.724762 | ||||||||
\(931\) | 23.2040 | 0.760482 | ||||||||
\(932\) | −5.35936 | −0.175552 | ||||||||
\(933\) | −16.6129 | −0.543880 | ||||||||
\(934\) | −20.4023 | −0.667583 | ||||||||
\(935\) | 174.324 | 5.70100 | ||||||||
\(936\) | 16.6339 | 0.543696 | ||||||||
\(937\) | 17.2560 | 0.563730 | 0.281865 | − | 0.959454i | \(-0.409047\pi\) | ||||
0.281865 | + | 0.959454i | \(0.409047\pi\) | |||||||
\(938\) | 11.0194 | 0.359796 | ||||||||
\(939\) | 26.0262 | 0.849333 | ||||||||
\(940\) | 8.34446 | 0.272166 | ||||||||
\(941\) | −16.3442 | −0.532805 | −0.266402 | − | 0.963862i | \(-0.585835\pi\) | ||||
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(942\) | −7.46487 | −0.243219 | ||||||||
\(943\) | 3.08358 | 0.100415 | ||||||||
\(944\) | 14.6005 | 0.475206 | ||||||||
\(945\) | 3.19821 | 0.104038 | ||||||||
\(946\) | 23.7528 | 0.772270 | ||||||||
\(947\) | −12.5846 | −0.408946 | −0.204473 | − | 0.978872i | \(-0.565548\pi\) | ||||
−0.204473 | + | 0.978872i | \(0.565548\pi\) | |||||||
\(948\) | 9.27798 | 0.301335 | ||||||||
\(949\) | 101.506 | 3.29502 | ||||||||
\(950\) | 37.9079 | 1.22990 | ||||||||
\(951\) | −34.9677 | −1.13391 | ||||||||
\(952\) | 5.77732 | 0.187244 | ||||||||
\(953\) | −32.6168 | −1.05656 | −0.528281 | − | 0.849069i | \(-0.677163\pi\) | ||||
−0.528281 | + | 0.849069i | \(0.677163\pi\) | |||||||
\(954\) | −33.7345 | −1.09220 | ||||||||
\(955\) | −41.3678 | −1.33863 | ||||||||
\(956\) | −19.4979 | −0.630607 | ||||||||
\(957\) | −68.0007 | −2.19815 | ||||||||
\(958\) | −35.9555 | −1.16167 | ||||||||
\(959\) | −9.34692 | −0.301828 | ||||||||
\(960\) | 9.27531 | 0.299359 | ||||||||
\(961\) | −25.3217 | −0.816830 | ||||||||
\(962\) | −56.1323 | −1.80978 | ||||||||
\(963\) | −5.08274 | −0.163789 | ||||||||
\(964\) | 0.671107 | 0.0216149 | ||||||||
\(965\) | 87.3463 | 2.81178 | ||||||||
\(966\) | −1.02869 | −0.0330976 | ||||||||
\(967\) | −17.1058 | −0.550087 | −0.275043 | − | 0.961432i | \(-0.588692\pi\) | ||||
−0.275043 | + | 0.961432i | \(0.588692\pi\) | |||||||
\(968\) | −20.3854 | −0.655211 | ||||||||
\(969\) | 66.5906 | 2.13920 | ||||||||
\(970\) | −44.0216 | −1.41345 | ||||||||
\(971\) | −46.2310 | −1.48362 | −0.741811 | − | 0.670609i | \(-0.766033\pi\) | ||||
−0.741811 | + | 0.670609i | \(0.766033\pi\) | |||||||
\(972\) | 20.6416 | 0.662079 | ||||||||
\(973\) | −3.78501 | −0.121342 | ||||||||
\(974\) | 4.43948 | 0.142250 | ||||||||
\(975\) | 163.300 | 5.22979 | ||||||||
\(976\) | 3.15824 | 0.101093 | ||||||||
\(977\) | −49.2388 | −1.57529 | −0.787645 | − | 0.616129i | \(-0.788700\pi\) | ||||
−0.787645 | + | 0.616129i | \(0.788700\pi\) | |||||||
\(978\) | 1.81315 | 0.0579781 | ||||||||
\(979\) | −8.94092 | −0.285753 | ||||||||
\(980\) | 25.4961 | 0.814444 | ||||||||
\(981\) | 8.58628 | 0.274139 | ||||||||
\(982\) | −32.9313 | −1.05088 | ||||||||
\(983\) | 26.3514 | 0.840479 | 0.420240 | − | 0.907413i | \(-0.361946\pi\) | ||||
0.420240 | + | 0.907413i | \(0.361946\pi\) | |||||||
\(984\) | 12.1384 | 0.386959 | ||||||||
\(985\) | −27.2129 | −0.867074 | ||||||||
\(986\) | 40.7206 | 1.29681 | ||||||||
\(987\) | −3.64303 | −0.115959 | ||||||||
\(988\) | 23.6102 | 0.751142 | ||||||||
\(989\) | 2.53264 | 0.0805333 | ||||||||
\(990\) | −55.8911 | −1.77634 | ||||||||
\(991\) | 52.6326 | 1.67193 | 0.835964 | − | 0.548784i | \(-0.184909\pi\) | ||||
0.835964 | + | 0.548784i | \(0.184909\pi\) | |||||||
\(992\) | −2.38291 | −0.0756576 | ||||||||
\(993\) | −39.6889 | −1.25949 | ||||||||
\(994\) | −0.203771 | −0.00646321 | ||||||||
\(995\) | 28.6593 | 0.908560 | ||||||||
\(996\) | 31.4933 | 0.997903 | ||||||||
\(997\) | −24.0893 | −0.762917 | −0.381459 | − | 0.924386i | \(-0.624578\pi\) | ||||
−0.381459 | + | 0.924386i | \(0.624578\pi\) | |||||||
\(998\) | −13.2766 | −0.420264 | ||||||||
\(999\) | −9.44883 | −0.298948 |
(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 | 4022.2.a.d.1.7 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.7 | ✓ | 37 | 1.1 | even | 1 | trivial |