Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.67396\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.72927 | 1.22056 | 0.610282 | − | 0.792184i | \(-0.291056\pi\) | ||||
0.610282 | + | 0.792184i | \(0.291056\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.673957 | −0.254732 | −0.127366 | − | 0.991856i | \(-0.540652\pi\) | ||||
−0.127366 | + | 0.991856i | \(0.540652\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.72927 | 0.863069 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.59767 | 0.997814 | 0.498907 | − | 0.866656i | \(-0.333735\pi\) | ||||
0.498907 | + | 0.866656i | \(0.333735\pi\) | |||||||
\(14\) | −0.673957 | −0.180123 | ||||||||
\(15\) | 2.72927 | 0.704693 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.25138 | 1.03111 | 0.515556 | − | 0.856856i | \(-0.327586\pi\) | ||||
0.515556 | + | 0.856856i | \(0.327586\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.82526 | 1.33641 | 0.668204 | − | 0.743978i | \(-0.267063\pi\) | ||||
0.668204 | + | 0.743978i | \(0.267063\pi\) | |||||||
\(20\) | 2.72927 | 0.610282 | ||||||||
\(21\) | −0.673957 | −0.147070 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.69468 | −0.561879 | −0.280940 | − | 0.959725i | \(-0.590646\pi\) | ||||
−0.280940 | + | 0.959725i | \(0.590646\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.44889 | 0.489778 | ||||||||
\(26\) | 3.59767 | 0.705561 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.673957 | −0.127366 | ||||||||
\(29\) | −7.00036 | −1.29993 | −0.649967 | − | 0.759963i | \(-0.725217\pi\) | ||||
−0.649967 | + | 0.759963i | \(0.725217\pi\) | |||||||
\(30\) | 2.72927 | 0.498293 | ||||||||
\(31\) | 1.96541 | 0.352999 | 0.176499 | − | 0.984301i | \(-0.443523\pi\) | ||||
0.176499 | + | 0.984301i | \(0.443523\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 4.25138 | 0.729106 | ||||||||
\(35\) | −1.83941 | −0.310917 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.3558 | 1.70248 | 0.851239 | − | 0.524779i | \(-0.175852\pi\) | ||||
0.851239 | + | 0.524779i | \(0.175852\pi\) | |||||||
\(38\) | 5.82526 | 0.944983 | ||||||||
\(39\) | 3.59767 | 0.576088 | ||||||||
\(40\) | 2.72927 | 0.431535 | ||||||||
\(41\) | −3.88057 | −0.606044 | −0.303022 | − | 0.952984i | \(-0.597996\pi\) | ||||
−0.303022 | + | 0.952984i | \(0.597996\pi\) | |||||||
\(42\) | −0.673957 | −0.103994 | ||||||||
\(43\) | −9.14034 | −1.39389 | −0.696944 | − | 0.717125i | \(-0.745458\pi\) | ||||
−0.696944 | + | 0.717125i | \(0.745458\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.72927 | 0.406855 | ||||||||
\(46\) | −2.69468 | −0.397309 | ||||||||
\(47\) | −10.6370 | −1.55156 | −0.775779 | − | 0.631004i | \(-0.782643\pi\) | ||||
−0.775779 | + | 0.631004i | \(0.782643\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.54578 | −0.935112 | ||||||||
\(50\) | 2.44889 | 0.346325 | ||||||||
\(51\) | 4.25138 | 0.595312 | ||||||||
\(52\) | 3.59767 | 0.498907 | ||||||||
\(53\) | −3.56328 | −0.489454 | −0.244727 | − | 0.969592i | \(-0.578698\pi\) | ||||
−0.244727 | + | 0.969592i | \(0.578698\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.72927 | −0.368014 | ||||||||
\(56\) | −0.673957 | −0.0900614 | ||||||||
\(57\) | 5.82526 | 0.771575 | ||||||||
\(58\) | −7.00036 | −0.919192 | ||||||||
\(59\) | 3.91975 | 0.510307 | 0.255154 | − | 0.966900i | \(-0.417874\pi\) | ||||
0.255154 | + | 0.966900i | \(0.417874\pi\) | |||||||
\(60\) | 2.72927 | 0.352347 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 1.96541 | 0.249608 | ||||||||
\(63\) | −0.673957 | −0.0849107 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.81900 | 1.21790 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 6.94252 | 0.848164 | 0.424082 | − | 0.905624i | \(-0.360597\pi\) | ||||
0.424082 | + | 0.905624i | \(0.360597\pi\) | |||||||
\(68\) | 4.25138 | 0.515556 | ||||||||
\(69\) | −2.69468 | −0.324401 | ||||||||
\(70\) | −1.83941 | −0.219851 | ||||||||
\(71\) | 0.365213 | 0.0433428 | 0.0216714 | − | 0.999765i | \(-0.493101\pi\) | ||||
0.0216714 | + | 0.999765i | \(0.493101\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.95939 | −0.580453 | −0.290226 | − | 0.956958i | \(-0.593731\pi\) | ||||
−0.290226 | + | 0.956958i | \(0.593731\pi\) | |||||||
\(74\) | 10.3558 | 1.20383 | ||||||||
\(75\) | 2.44889 | 0.282773 | ||||||||
\(76\) | 5.82526 | 0.668204 | ||||||||
\(77\) | 0.673957 | 0.0768046 | ||||||||
\(78\) | 3.59767 | 0.407356 | ||||||||
\(79\) | −2.75204 | −0.309629 | −0.154814 | − | 0.987944i | \(-0.549478\pi\) | ||||
−0.154814 | + | 0.987944i | \(0.549478\pi\) | |||||||
\(80\) | 2.72927 | 0.305141 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.88057 | −0.428538 | ||||||||
\(83\) | −0.156532 | −0.0171816 | −0.00859082 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859082 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(84\) | −0.673957 | −0.0735348 | ||||||||
\(85\) | 11.6031 | 1.25854 | ||||||||
\(86\) | −9.14034 | −0.985628 | ||||||||
\(87\) | −7.00036 | −0.750517 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 16.9930 | 1.80125 | 0.900626 | − | 0.434595i | \(-0.143109\pi\) | ||||
0.900626 | + | 0.434595i | \(0.143109\pi\) | |||||||
\(90\) | 2.72927 | 0.287690 | ||||||||
\(91\) | −2.42468 | −0.254175 | ||||||||
\(92\) | −2.69468 | −0.280940 | ||||||||
\(93\) | 1.96541 | 0.203804 | ||||||||
\(94\) | −10.6370 | −1.09712 | ||||||||
\(95\) | 15.8987 | 1.63117 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.2082 | −1.13802 | −0.569010 | − | 0.822330i | \(-0.692674\pi\) | ||||
−0.569010 | + | 0.822330i | \(0.692674\pi\) | |||||||
\(98\) | −6.54578 | −0.661224 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.44889 | 0.244889 | ||||||||
\(101\) | 7.44745 | 0.741049 | 0.370524 | − | 0.928823i | \(-0.379178\pi\) | ||||
0.370524 | + | 0.928823i | \(0.379178\pi\) | |||||||
\(102\) | 4.25138 | 0.420949 | ||||||||
\(103\) | −6.91858 | −0.681708 | −0.340854 | − | 0.940116i | \(-0.610716\pi\) | ||||
−0.340854 | + | 0.940116i | \(0.610716\pi\) | |||||||
\(104\) | 3.59767 | 0.352781 | ||||||||
\(105\) | −1.83941 | −0.179508 | ||||||||
\(106\) | −3.56328 | −0.346096 | ||||||||
\(107\) | 4.35224 | 0.420747 | 0.210374 | − | 0.977621i | \(-0.432532\pi\) | ||||
0.210374 | + | 0.977621i | \(0.432532\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 18.7692 | 1.79776 | 0.898879 | − | 0.438196i | \(-0.144382\pi\) | ||||
0.898879 | + | 0.438196i | \(0.144382\pi\) | |||||||
\(110\) | −2.72927 | −0.260225 | ||||||||
\(111\) | 10.3558 | 0.982926 | ||||||||
\(112\) | −0.673957 | −0.0636830 | ||||||||
\(113\) | −3.45468 | −0.324989 | −0.162495 | − | 0.986709i | \(-0.551954\pi\) | ||||
−0.162495 | + | 0.986709i | \(0.551954\pi\) | |||||||
\(114\) | 5.82526 | 0.545586 | ||||||||
\(115\) | −7.35449 | −0.685810 | ||||||||
\(116\) | −7.00036 | −0.649967 | ||||||||
\(117\) | 3.59767 | 0.332605 | ||||||||
\(118\) | 3.91975 | 0.360842 | ||||||||
\(119\) | −2.86525 | −0.262657 | ||||||||
\(120\) | 2.72927 | 0.249147 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | −3.88057 | −0.349899 | ||||||||
\(124\) | 1.96541 | 0.176499 | ||||||||
\(125\) | −6.96266 | −0.622759 | ||||||||
\(126\) | −0.673957 | −0.0600409 | ||||||||
\(127\) | −2.79518 | −0.248032 | −0.124016 | − | 0.992280i | \(-0.539577\pi\) | ||||
−0.124016 | + | 0.992280i | \(0.539577\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.14034 | −0.804762 | ||||||||
\(130\) | 9.81900 | 0.861183 | ||||||||
\(131\) | 1.56261 | 0.136526 | 0.0682629 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682629 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −3.92598 | −0.340426 | ||||||||
\(134\) | 6.94252 | 0.599742 | ||||||||
\(135\) | 2.72927 | 0.234898 | ||||||||
\(136\) | 4.25138 | 0.364553 | ||||||||
\(137\) | −11.8420 | −1.01173 | −0.505867 | − | 0.862612i | \(-0.668827\pi\) | ||||
−0.505867 | + | 0.862612i | \(0.668827\pi\) | |||||||
\(138\) | −2.69468 | −0.229386 | ||||||||
\(139\) | 18.4081 | 1.56136 | 0.780678 | − | 0.624933i | \(-0.214874\pi\) | ||||
0.780678 | + | 0.624933i | \(0.214874\pi\) | |||||||
\(140\) | −1.83941 | −0.155458 | ||||||||
\(141\) | −10.6370 | −0.895793 | ||||||||
\(142\) | 0.365213 | 0.0306480 | ||||||||
\(143\) | −3.59767 | −0.300852 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −19.1058 | −1.58665 | ||||||||
\(146\) | −4.95939 | −0.410442 | ||||||||
\(147\) | −6.54578 | −0.539887 | ||||||||
\(148\) | 10.3558 | 0.851239 | ||||||||
\(149\) | 11.4006 | 0.933975 | 0.466988 | − | 0.884264i | \(-0.345339\pi\) | ||||
0.466988 | + | 0.884264i | \(0.345339\pi\) | |||||||
\(150\) | 2.44889 | 0.199951 | ||||||||
\(151\) | −4.24190 | −0.345201 | −0.172600 | − | 0.984992i | \(-0.555217\pi\) | ||||
−0.172600 | + | 0.984992i | \(0.555217\pi\) | |||||||
\(152\) | 5.82526 | 0.472491 | ||||||||
\(153\) | 4.25138 | 0.343704 | ||||||||
\(154\) | 0.673957 | 0.0543090 | ||||||||
\(155\) | 5.36413 | 0.430858 | ||||||||
\(156\) | 3.59767 | 0.288044 | ||||||||
\(157\) | 21.8267 | 1.74196 | 0.870981 | − | 0.491316i | \(-0.163484\pi\) | ||||
0.870981 | + | 0.491316i | \(0.163484\pi\) | |||||||
\(158\) | −2.75204 | −0.218941 | ||||||||
\(159\) | −3.56328 | −0.282586 | ||||||||
\(160\) | 2.72927 | 0.215767 | ||||||||
\(161\) | 1.81610 | 0.143129 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.27864 | 0.100150 | 0.0500752 | − | 0.998745i | \(-0.484054\pi\) | ||||
0.0500752 | + | 0.998745i | \(0.484054\pi\) | |||||||
\(164\) | −3.88057 | −0.303022 | ||||||||
\(165\) | −2.72927 | −0.212473 | ||||||||
\(166\) | −0.156532 | −0.0121493 | ||||||||
\(167\) | 13.8118 | 1.06879 | 0.534396 | − | 0.845234i | \(-0.320539\pi\) | ||||
0.534396 | + | 0.845234i | \(0.320539\pi\) | |||||||
\(168\) | −0.673957 | −0.0519969 | ||||||||
\(169\) | −0.0567725 | −0.00436712 | ||||||||
\(170\) | 11.6031 | 0.889921 | ||||||||
\(171\) | 5.82526 | 0.445469 | ||||||||
\(172\) | −9.14034 | −0.696944 | ||||||||
\(173\) | 6.63267 | 0.504273 | 0.252136 | − | 0.967692i | \(-0.418867\pi\) | ||||
0.252136 | + | 0.967692i | \(0.418867\pi\) | |||||||
\(174\) | −7.00036 | −0.530696 | ||||||||
\(175\) | −1.65045 | −0.124762 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 3.91975 | 0.294626 | ||||||||
\(178\) | 16.9930 | 1.27368 | ||||||||
\(179\) | −13.7972 | −1.03125 | −0.515624 | − | 0.856815i | \(-0.672440\pi\) | ||||
−0.515624 | + | 0.856815i | \(0.672440\pi\) | |||||||
\(180\) | 2.72927 | 0.203427 | ||||||||
\(181\) | −10.3165 | −0.766819 | −0.383409 | − | 0.923579i | \(-0.625250\pi\) | ||||
−0.383409 | + | 0.923579i | \(0.625250\pi\) | |||||||
\(182\) | −2.42468 | −0.179729 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −2.69468 | −0.198654 | ||||||||
\(185\) | 28.2636 | 2.07798 | ||||||||
\(186\) | 1.96541 | 0.144111 | ||||||||
\(187\) | −4.25138 | −0.310892 | ||||||||
\(188\) | −10.6370 | −0.775779 | ||||||||
\(189\) | −0.673957 | −0.0490232 | ||||||||
\(190\) | 15.8987 | 1.15341 | ||||||||
\(191\) | −3.66910 | −0.265486 | −0.132743 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132743 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.96138 | 0.573073 | 0.286536 | − | 0.958069i | \(-0.407496\pi\) | ||||
0.286536 | + | 0.958069i | \(0.407496\pi\) | |||||||
\(194\) | −11.2082 | −0.804702 | ||||||||
\(195\) | 9.81900 | 0.703153 | ||||||||
\(196\) | −6.54578 | −0.467556 | ||||||||
\(197\) | −3.60611 | −0.256924 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −16.6285 | −1.17877 | −0.589383 | − | 0.807854i | \(-0.700629\pi\) | ||||
−0.589383 | + | 0.807854i | \(0.700629\pi\) | |||||||
\(200\) | 2.44889 | 0.173163 | ||||||||
\(201\) | 6.94252 | 0.489688 | ||||||||
\(202\) | 7.44745 | 0.524001 | ||||||||
\(203\) | 4.71794 | 0.331135 | ||||||||
\(204\) | 4.25138 | 0.297656 | ||||||||
\(205\) | −10.5911 | −0.739715 | ||||||||
\(206\) | −6.91858 | −0.482041 | ||||||||
\(207\) | −2.69468 | −0.187293 | ||||||||
\(208\) | 3.59767 | 0.249454 | ||||||||
\(209\) | −5.82526 | −0.402942 | ||||||||
\(210\) | −1.83941 | −0.126931 | ||||||||
\(211\) | −22.5841 | −1.55475 | −0.777376 | − | 0.629036i | \(-0.783450\pi\) | ||||
−0.777376 | + | 0.629036i | \(0.783450\pi\) | |||||||
\(212\) | −3.56328 | −0.244727 | ||||||||
\(213\) | 0.365213 | 0.0250240 | ||||||||
\(214\) | 4.35224 | 0.297513 | ||||||||
\(215\) | −24.9464 | −1.70133 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.32460 | −0.0899200 | ||||||||
\(218\) | 18.7692 | 1.27121 | ||||||||
\(219\) | −4.95939 | −0.335125 | ||||||||
\(220\) | −2.72927 | −0.184007 | ||||||||
\(221\) | 15.2951 | 1.02886 | ||||||||
\(222\) | 10.3558 | 0.695033 | ||||||||
\(223\) | −0.596137 | −0.0399203 | −0.0199601 | − | 0.999801i | \(-0.506354\pi\) | ||||
−0.0199601 | + | 0.999801i | \(0.506354\pi\) | |||||||
\(224\) | −0.673957 | −0.0450307 | ||||||||
\(225\) | 2.44889 | 0.163259 | ||||||||
\(226\) | −3.45468 | −0.229802 | ||||||||
\(227\) | −25.8235 | −1.71397 | −0.856983 | − | 0.515345i | \(-0.827664\pi\) | ||||
−0.856983 | + | 0.515345i | \(0.827664\pi\) | |||||||
\(228\) | 5.82526 | 0.385788 | ||||||||
\(229\) | −24.1601 | −1.59654 | −0.798271 | − | 0.602299i | \(-0.794252\pi\) | ||||
−0.798271 | + | 0.602299i | \(0.794252\pi\) | |||||||
\(230\) | −7.35449 | −0.484941 | ||||||||
\(231\) | 0.673957 | 0.0443431 | ||||||||
\(232\) | −7.00036 | −0.459596 | ||||||||
\(233\) | 4.62550 | 0.303027 | 0.151513 | − | 0.988455i | \(-0.451585\pi\) | ||||
0.151513 | + | 0.988455i | \(0.451585\pi\) | |||||||
\(234\) | 3.59767 | 0.235187 | ||||||||
\(235\) | −29.0311 | −1.89378 | ||||||||
\(236\) | 3.91975 | 0.255154 | ||||||||
\(237\) | −2.75204 | −0.178764 | ||||||||
\(238\) | −2.86525 | −0.185727 | ||||||||
\(239\) | −24.4212 | −1.57967 | −0.789837 | − | 0.613316i | \(-0.789835\pi\) | ||||
−0.789837 | + | 0.613316i | \(0.789835\pi\) | |||||||
\(240\) | 2.72927 | 0.176173 | ||||||||
\(241\) | 12.0073 | 0.773457 | 0.386729 | − | 0.922194i | \(-0.373605\pi\) | ||||
0.386729 | + | 0.922194i | \(0.373605\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −17.8652 | −1.14136 | ||||||||
\(246\) | −3.88057 | −0.247416 | ||||||||
\(247\) | 20.9574 | 1.33349 | ||||||||
\(248\) | 1.96541 | 0.124804 | ||||||||
\(249\) | −0.156532 | −0.00991983 | ||||||||
\(250\) | −6.96266 | −0.440357 | ||||||||
\(251\) | −28.8035 | −1.81806 | −0.909029 | − | 0.416732i | \(-0.863175\pi\) | ||||
−0.909029 | + | 0.416732i | \(0.863175\pi\) | |||||||
\(252\) | −0.673957 | −0.0424553 | ||||||||
\(253\) | 2.69468 | 0.169413 | ||||||||
\(254\) | −2.79518 | −0.175385 | ||||||||
\(255\) | 11.6031 | 0.726617 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.26066 | 0.203395 | 0.101697 | − | 0.994815i | \(-0.467573\pi\) | ||||
0.101697 | + | 0.994815i | \(0.467573\pi\) | |||||||
\(258\) | −9.14034 | −0.569053 | ||||||||
\(259\) | −6.97935 | −0.433675 | ||||||||
\(260\) | 9.81900 | 0.608948 | ||||||||
\(261\) | −7.00036 | −0.433311 | ||||||||
\(262\) | 1.56261 | 0.0965383 | ||||||||
\(263\) | 2.24512 | 0.138440 | 0.0692199 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692199 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | −9.72513 | −0.597410 | ||||||||
\(266\) | −3.92598 | −0.240717 | ||||||||
\(267\) | 16.9930 | 1.03995 | ||||||||
\(268\) | 6.94252 | 0.424082 | ||||||||
\(269\) | 23.6005 | 1.43895 | 0.719474 | − | 0.694519i | \(-0.244383\pi\) | ||||
0.719474 | + | 0.694519i | \(0.244383\pi\) | |||||||
\(270\) | 2.72927 | 0.166098 | ||||||||
\(271\) | −7.54489 | −0.458320 | −0.229160 | − | 0.973389i | \(-0.573598\pi\) | ||||
−0.229160 | + | 0.973389i | \(0.573598\pi\) | |||||||
\(272\) | 4.25138 | 0.257778 | ||||||||
\(273\) | −2.42468 | −0.146748 | ||||||||
\(274\) | −11.8420 | −0.715403 | ||||||||
\(275\) | −2.44889 | −0.147674 | ||||||||
\(276\) | −2.69468 | −0.162201 | ||||||||
\(277\) | 20.2982 | 1.21960 | 0.609800 | − | 0.792556i | \(-0.291250\pi\) | ||||
0.609800 | + | 0.792556i | \(0.291250\pi\) | |||||||
\(278\) | 18.4081 | 1.10405 | ||||||||
\(279\) | 1.96541 | 0.117666 | ||||||||
\(280\) | −1.83941 | −0.109926 | ||||||||
\(281\) | 4.38450 | 0.261557 | 0.130779 | − | 0.991412i | \(-0.458252\pi\) | ||||
0.130779 | + | 0.991412i | \(0.458252\pi\) | |||||||
\(282\) | −10.6370 | −0.633421 | ||||||||
\(283\) | 10.5547 | 0.627409 | 0.313704 | − | 0.949521i | \(-0.398430\pi\) | ||||
0.313704 | + | 0.949521i | \(0.398430\pi\) | |||||||
\(284\) | 0.365213 | 0.0216714 | ||||||||
\(285\) | 15.8987 | 0.941757 | ||||||||
\(286\) | −3.59767 | −0.212735 | ||||||||
\(287\) | 2.61534 | 0.154379 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.07423 | 0.0631903 | ||||||||
\(290\) | −19.1058 | −1.12193 | ||||||||
\(291\) | −11.2082 | −0.657037 | ||||||||
\(292\) | −4.95939 | −0.290226 | ||||||||
\(293\) | −31.7323 | −1.85382 | −0.926911 | − | 0.375282i | \(-0.877546\pi\) | ||||
−0.926911 | + | 0.375282i | \(0.877546\pi\) | |||||||
\(294\) | −6.54578 | −0.381758 | ||||||||
\(295\) | 10.6980 | 0.622863 | ||||||||
\(296\) | 10.3558 | 0.601917 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 11.4006 | 0.660420 | ||||||||
\(299\) | −9.69456 | −0.560651 | ||||||||
\(300\) | 2.44889 | 0.141387 | ||||||||
\(301\) | 6.16020 | 0.355068 | ||||||||
\(302\) | −4.24190 | −0.244094 | ||||||||
\(303\) | 7.44745 | 0.427845 | ||||||||
\(304\) | 5.82526 | 0.334102 | ||||||||
\(305\) | 2.72927 | 0.156277 | ||||||||
\(306\) | 4.25138 | 0.243035 | ||||||||
\(307\) | −0.998640 | −0.0569954 | −0.0284977 | − | 0.999594i | \(-0.509072\pi\) | ||||
−0.0284977 | + | 0.999594i | \(0.509072\pi\) | |||||||
\(308\) | 0.673957 | 0.0384023 | ||||||||
\(309\) | −6.91858 | −0.393584 | ||||||||
\(310\) | 5.36413 | 0.304662 | ||||||||
\(311\) | 3.92585 | 0.222614 | 0.111307 | − | 0.993786i | \(-0.464496\pi\) | ||||
0.111307 | + | 0.993786i | \(0.464496\pi\) | |||||||
\(312\) | 3.59767 | 0.203678 | ||||||||
\(313\) | −20.3307 | −1.14916 | −0.574578 | − | 0.818450i | \(-0.694834\pi\) | ||||
−0.574578 | + | 0.818450i | \(0.694834\pi\) | |||||||
\(314\) | 21.8267 | 1.23175 | ||||||||
\(315\) | −1.83941 | −0.103639 | ||||||||
\(316\) | −2.75204 | −0.154814 | ||||||||
\(317\) | −19.7540 | −1.10949 | −0.554747 | − | 0.832019i | \(-0.687185\pi\) | ||||
−0.554747 | + | 0.832019i | \(0.687185\pi\) | |||||||
\(318\) | −3.56328 | −0.199819 | ||||||||
\(319\) | 7.00036 | 0.391945 | ||||||||
\(320\) | 2.72927 | 0.152571 | ||||||||
\(321\) | 4.35224 | 0.242918 | ||||||||
\(322\) | 1.81610 | 0.101207 | ||||||||
\(323\) | 24.7654 | 1.37798 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.81030 | 0.488707 | ||||||||
\(326\) | 1.27864 | 0.0708171 | ||||||||
\(327\) | 18.7692 | 1.03794 | ||||||||
\(328\) | −3.88057 | −0.214269 | ||||||||
\(329\) | 7.16885 | 0.395232 | ||||||||
\(330\) | −2.72927 | −0.150241 | ||||||||
\(331\) | −4.11510 | −0.226186 | −0.113093 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113093 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(332\) | −0.156532 | −0.00859082 | ||||||||
\(333\) | 10.3558 | 0.567492 | ||||||||
\(334\) | 13.8118 | 0.755750 | ||||||||
\(335\) | 18.9480 | 1.03524 | ||||||||
\(336\) | −0.673957 | −0.0367674 | ||||||||
\(337\) | −11.6712 | −0.635769 | −0.317884 | − | 0.948129i | \(-0.602972\pi\) | ||||
−0.317884 | + | 0.948129i | \(0.602972\pi\) | |||||||
\(338\) | −0.0567725 | −0.00308802 | ||||||||
\(339\) | −3.45468 | −0.187633 | ||||||||
\(340\) | 11.6031 | 0.629269 | ||||||||
\(341\) | −1.96541 | −0.106433 | ||||||||
\(342\) | 5.82526 | 0.314994 | ||||||||
\(343\) | 9.12928 | 0.492935 | ||||||||
\(344\) | −9.14034 | −0.492814 | ||||||||
\(345\) | −7.35449 | −0.395953 | ||||||||
\(346\) | 6.63267 | 0.356575 | ||||||||
\(347\) | 8.20412 | 0.440420 | 0.220210 | − | 0.975452i | \(-0.429326\pi\) | ||||
0.220210 | + | 0.975452i | \(0.429326\pi\) | |||||||
\(348\) | −7.00036 | −0.375259 | ||||||||
\(349\) | −1.81610 | −0.0972134 | −0.0486067 | − | 0.998818i | \(-0.515478\pi\) | ||||
−0.0486067 | + | 0.998818i | \(0.515478\pi\) | |||||||
\(350\) | −1.65045 | −0.0882201 | ||||||||
\(351\) | 3.59767 | 0.192029 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 14.3060 | 0.761432 | 0.380716 | − | 0.924692i | \(-0.375678\pi\) | ||||
0.380716 | + | 0.924692i | \(0.375678\pi\) | |||||||
\(354\) | 3.91975 | 0.208332 | ||||||||
\(355\) | 0.996762 | 0.0529026 | ||||||||
\(356\) | 16.9930 | 0.900626 | ||||||||
\(357\) | −2.86525 | −0.151645 | ||||||||
\(358\) | −13.7972 | −0.729203 | ||||||||
\(359\) | 5.14351 | 0.271464 | 0.135732 | − | 0.990746i | \(-0.456661\pi\) | ||||
0.135732 | + | 0.990746i | \(0.456661\pi\) | |||||||
\(360\) | 2.72927 | 0.143845 | ||||||||
\(361\) | 14.9337 | 0.785985 | ||||||||
\(362\) | −10.3165 | −0.542223 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −2.42468 | −0.127088 | ||||||||
\(365\) | −13.5355 | −0.708480 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −31.4881 | −1.64367 | −0.821834 | − | 0.569727i | \(-0.807049\pi\) | ||||
−0.821834 | + | 0.569727i | \(0.807049\pi\) | |||||||
\(368\) | −2.69468 | −0.140470 | ||||||||
\(369\) | −3.88057 | −0.202015 | ||||||||
\(370\) | 28.2636 | 1.46936 | ||||||||
\(371\) | 2.40150 | 0.124680 | ||||||||
\(372\) | 1.96541 | 0.101902 | ||||||||
\(373\) | 7.12105 | 0.368714 | 0.184357 | − | 0.982859i | \(-0.440980\pi\) | ||||
0.184357 | + | 0.982859i | \(0.440980\pi\) | |||||||
\(374\) | −4.25138 | −0.219834 | ||||||||
\(375\) | −6.96266 | −0.359550 | ||||||||
\(376\) | −10.6370 | −0.548559 | ||||||||
\(377\) | −25.1850 | −1.29709 | ||||||||
\(378\) | −0.673957 | −0.0346646 | ||||||||
\(379\) | 14.0522 | 0.721815 | 0.360907 | − | 0.932602i | \(-0.382467\pi\) | ||||
0.360907 | + | 0.932602i | \(0.382467\pi\) | |||||||
\(380\) | 15.8987 | 0.815586 | ||||||||
\(381\) | −2.79518 | −0.143201 | ||||||||
\(382\) | −3.66910 | −0.187727 | ||||||||
\(383\) | −18.2433 | −0.932187 | −0.466094 | − | 0.884735i | \(-0.654339\pi\) | ||||
−0.466094 | + | 0.884735i | \(0.654339\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.83941 | 0.0937450 | ||||||||
\(386\) | 7.96138 | 0.405224 | ||||||||
\(387\) | −9.14034 | −0.464630 | ||||||||
\(388\) | −11.2082 | −0.569010 | ||||||||
\(389\) | 38.2158 | 1.93762 | 0.968808 | − | 0.247813i | \(-0.0797120\pi\) | ||||
0.968808 | + | 0.247813i | \(0.0797120\pi\) | |||||||
\(390\) | 9.81900 | 0.497204 | ||||||||
\(391\) | −11.4561 | −0.579360 | ||||||||
\(392\) | −6.54578 | −0.330612 | ||||||||
\(393\) | 1.56261 | 0.0788232 | ||||||||
\(394\) | −3.60611 | −0.181673 | ||||||||
\(395\) | −7.51105 | −0.377922 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 35.0350 | 1.75836 | 0.879179 | − | 0.476491i | \(-0.158092\pi\) | ||||
0.879179 | + | 0.476491i | \(0.158092\pi\) | |||||||
\(398\) | −16.6285 | −0.833513 | ||||||||
\(399\) | −3.92598 | −0.196545 | ||||||||
\(400\) | 2.44889 | 0.122444 | ||||||||
\(401\) | 10.5478 | 0.526734 | 0.263367 | − | 0.964696i | \(-0.415167\pi\) | ||||
0.263367 | + | 0.964696i | \(0.415167\pi\) | |||||||
\(402\) | 6.94252 | 0.346261 | ||||||||
\(403\) | 7.07091 | 0.352227 | ||||||||
\(404\) | 7.44745 | 0.370524 | ||||||||
\(405\) | 2.72927 | 0.135618 | ||||||||
\(406\) | 4.71794 | 0.234148 | ||||||||
\(407\) | −10.3558 | −0.513316 | ||||||||
\(408\) | 4.25138 | 0.210475 | ||||||||
\(409\) | −23.1673 | −1.14555 | −0.572774 | − | 0.819713i | \(-0.694133\pi\) | ||||
−0.572774 | + | 0.819713i | \(0.694133\pi\) | |||||||
\(410\) | −10.5911 | −0.523058 | ||||||||
\(411\) | −11.8420 | −0.584124 | ||||||||
\(412\) | −6.91858 | −0.340854 | ||||||||
\(413\) | −2.64174 | −0.129992 | ||||||||
\(414\) | −2.69468 | −0.132436 | ||||||||
\(415\) | −0.427218 | −0.0209713 | ||||||||
\(416\) | 3.59767 | 0.176390 | ||||||||
\(417\) | 18.4081 | 0.901449 | ||||||||
\(418\) | −5.82526 | −0.284923 | ||||||||
\(419\) | −35.4669 | −1.73267 | −0.866336 | − | 0.499461i | \(-0.833531\pi\) | ||||
−0.866336 | + | 0.499461i | \(0.833531\pi\) | |||||||
\(420\) | −1.83941 | −0.0897540 | ||||||||
\(421\) | 21.2987 | 1.03803 | 0.519017 | − | 0.854764i | \(-0.326298\pi\) | ||||
0.519017 | + | 0.854764i | \(0.326298\pi\) | |||||||
\(422\) | −22.5841 | −1.09938 | ||||||||
\(423\) | −10.6370 | −0.517186 | ||||||||
\(424\) | −3.56328 | −0.173048 | ||||||||
\(425\) | 10.4112 | 0.505015 | ||||||||
\(426\) | 0.365213 | 0.0176946 | ||||||||
\(427\) | −0.673957 | −0.0326151 | ||||||||
\(428\) | 4.35224 | 0.210374 | ||||||||
\(429\) | −3.59767 | −0.173697 | ||||||||
\(430\) | −24.9464 | −1.20302 | ||||||||
\(431\) | −3.83729 | −0.184836 | −0.0924179 | − | 0.995720i | \(-0.529460\pi\) | ||||
−0.0924179 | + | 0.995720i | \(0.529460\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −18.4484 | −0.886575 | −0.443288 | − | 0.896379i | \(-0.646188\pi\) | ||||
−0.443288 | + | 0.896379i | \(0.646188\pi\) | |||||||
\(434\) | −1.32460 | −0.0635831 | ||||||||
\(435\) | −19.1058 | −0.916055 | ||||||||
\(436\) | 18.7692 | 0.898879 | ||||||||
\(437\) | −15.6972 | −0.750900 | ||||||||
\(438\) | −4.95939 | −0.236969 | ||||||||
\(439\) | −17.1275 | −0.817450 | −0.408725 | − | 0.912658i | \(-0.634026\pi\) | ||||
−0.408725 | + | 0.912658i | \(0.634026\pi\) | |||||||
\(440\) | −2.72927 | −0.130113 | ||||||||
\(441\) | −6.54578 | −0.311704 | ||||||||
\(442\) | 15.2951 | 0.727512 | ||||||||
\(443\) | −5.95809 | −0.283077 | −0.141539 | − | 0.989933i | \(-0.545205\pi\) | ||||
−0.141539 | + | 0.989933i | \(0.545205\pi\) | |||||||
\(444\) | 10.3558 | 0.491463 | ||||||||
\(445\) | 46.3783 | 2.19854 | ||||||||
\(446\) | −0.596137 | −0.0282279 | ||||||||
\(447\) | 11.4006 | 0.539231 | ||||||||
\(448\) | −0.673957 | −0.0318415 | ||||||||
\(449\) | −15.5422 | −0.733480 | −0.366740 | − | 0.930323i | \(-0.619526\pi\) | ||||
−0.366740 | + | 0.930323i | \(0.619526\pi\) | |||||||
\(450\) | 2.44889 | 0.115442 | ||||||||
\(451\) | 3.88057 | 0.182729 | ||||||||
\(452\) | −3.45468 | −0.162495 | ||||||||
\(453\) | −4.24190 | −0.199302 | ||||||||
\(454\) | −25.8235 | −1.21196 | ||||||||
\(455\) | −6.61759 | −0.310237 | ||||||||
\(456\) | 5.82526 | 0.272793 | ||||||||
\(457\) | 7.16430 | 0.335132 | 0.167566 | − | 0.985861i | \(-0.446409\pi\) | ||||
0.167566 | + | 0.985861i | \(0.446409\pi\) | |||||||
\(458\) | −24.1601 | −1.12893 | ||||||||
\(459\) | 4.25138 | 0.198437 | ||||||||
\(460\) | −7.35449 | −0.342905 | ||||||||
\(461\) | −19.2505 | −0.896583 | −0.448292 | − | 0.893887i | \(-0.647967\pi\) | ||||
−0.448292 | + | 0.893887i | \(0.647967\pi\) | |||||||
\(462\) | 0.673957 | 0.0313553 | ||||||||
\(463\) | 24.3868 | 1.13335 | 0.566674 | − | 0.823942i | \(-0.308230\pi\) | ||||
0.566674 | + | 0.823942i | \(0.308230\pi\) | |||||||
\(464\) | −7.00036 | −0.324983 | ||||||||
\(465\) | 5.36413 | 0.248756 | ||||||||
\(466\) | 4.62550 | 0.214272 | ||||||||
\(467\) | 9.41440 | 0.435647 | 0.217823 | − | 0.975988i | \(-0.430104\pi\) | ||||
0.217823 | + | 0.975988i | \(0.430104\pi\) | |||||||
\(468\) | 3.59767 | 0.166302 | ||||||||
\(469\) | −4.67896 | −0.216054 | ||||||||
\(470\) | −29.0311 | −1.33910 | ||||||||
\(471\) | 21.8267 | 1.00572 | ||||||||
\(472\) | 3.91975 | 0.180421 | ||||||||
\(473\) | 9.14034 | 0.420273 | ||||||||
\(474\) | −2.75204 | −0.126405 | ||||||||
\(475\) | 14.2654 | 0.654543 | ||||||||
\(476\) | −2.86525 | −0.131328 | ||||||||
\(477\) | −3.56328 | −0.163151 | ||||||||
\(478\) | −24.4212 | −1.11700 | ||||||||
\(479\) | −21.7380 | −0.993236 | −0.496618 | − | 0.867969i | \(-0.665425\pi\) | ||||
−0.496618 | + | 0.867969i | \(0.665425\pi\) | |||||||
\(480\) | 2.72927 | 0.124573 | ||||||||
\(481\) | 37.2566 | 1.69876 | ||||||||
\(482\) | 12.0073 | 0.546917 | ||||||||
\(483\) | 1.81610 | 0.0826353 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −30.5902 | −1.38903 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 17.5946 | 0.797288 | 0.398644 | − | 0.917106i | \(-0.369481\pi\) | ||||
0.398644 | + | 0.917106i | \(0.369481\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | 1.27864 | 0.0578219 | ||||||||
\(490\) | −17.8652 | −0.807066 | ||||||||
\(491\) | 39.4366 | 1.77975 | 0.889875 | − | 0.456205i | \(-0.150792\pi\) | ||||
0.889875 | + | 0.456205i | \(0.150792\pi\) | |||||||
\(492\) | −3.88057 | −0.174950 | ||||||||
\(493\) | −29.7612 | −1.34038 | ||||||||
\(494\) | 20.9574 | 0.942917 | ||||||||
\(495\) | −2.72927 | −0.122671 | ||||||||
\(496\) | 1.96541 | 0.0882496 | ||||||||
\(497\) | −0.246138 | −0.0110408 | ||||||||
\(498\) | −0.156532 | −0.00701438 | ||||||||
\(499\) | 29.9798 | 1.34208 | 0.671041 | − | 0.741420i | \(-0.265847\pi\) | ||||
0.671041 | + | 0.741420i | \(0.265847\pi\) | |||||||
\(500\) | −6.96266 | −0.311380 | ||||||||
\(501\) | 13.8118 | 0.617067 | ||||||||
\(502\) | −28.8035 | −1.28556 | ||||||||
\(503\) | −26.5171 | −1.18234 | −0.591170 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591170 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(504\) | −0.673957 | −0.0300205 | ||||||||
\(505\) | 20.3261 | 0.904498 | ||||||||
\(506\) | 2.69468 | 0.119793 | ||||||||
\(507\) | −0.0567725 | −0.00252136 | ||||||||
\(508\) | −2.79518 | −0.124016 | ||||||||
\(509\) | 1.49678 | 0.0663434 | 0.0331717 | − | 0.999450i | \(-0.489439\pi\) | ||||
0.0331717 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(510\) | 11.6031 | 0.513796 | ||||||||
\(511\) | 3.34242 | 0.147860 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.82526 | 0.257192 | ||||||||
\(514\) | 3.26066 | 0.143822 | ||||||||
\(515\) | −18.8826 | −0.832069 | ||||||||
\(516\) | −9.14034 | −0.402381 | ||||||||
\(517\) | 10.6370 | 0.467813 | ||||||||
\(518\) | −6.97935 | −0.306655 | ||||||||
\(519\) | 6.63267 | 0.291142 | ||||||||
\(520\) | 9.81900 | 0.430591 | ||||||||
\(521\) | −28.0423 | −1.22856 | −0.614278 | − | 0.789090i | \(-0.710553\pi\) | ||||
−0.614278 | + | 0.789090i | \(0.710553\pi\) | |||||||
\(522\) | −7.00036 | −0.306397 | ||||||||
\(523\) | 20.9384 | 0.915570 | 0.457785 | − | 0.889063i | \(-0.348643\pi\) | ||||
0.457785 | + | 0.889063i | \(0.348643\pi\) | |||||||
\(524\) | 1.56261 | 0.0682629 | ||||||||
\(525\) | −1.65045 | −0.0720314 | ||||||||
\(526\) | 2.24512 | 0.0978917 | ||||||||
\(527\) | 8.35572 | 0.363981 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −15.7387 | −0.684292 | ||||||||
\(530\) | −9.72513 | −0.422433 | ||||||||
\(531\) | 3.91975 | 0.170102 | ||||||||
\(532\) | −3.92598 | −0.170213 | ||||||||
\(533\) | −13.9610 | −0.604719 | ||||||||
\(534\) | 16.9930 | 0.735358 | ||||||||
\(535\) | 11.8784 | 0.513549 | ||||||||
\(536\) | 6.94252 | 0.299871 | ||||||||
\(537\) | −13.7972 | −0.595391 | ||||||||
\(538\) | 23.6005 | 1.01749 | ||||||||
\(539\) | 6.54578 | 0.281947 | ||||||||
\(540\) | 2.72927 | 0.117449 | ||||||||
\(541\) | 19.0512 | 0.819077 | 0.409539 | − | 0.912293i | \(-0.365690\pi\) | ||||
0.409539 | + | 0.912293i | \(0.365690\pi\) | |||||||
\(542\) | −7.54489 | −0.324081 | ||||||||
\(543\) | −10.3165 | −0.442723 | ||||||||
\(544\) | 4.25138 | 0.182276 | ||||||||
\(545\) | 51.2260 | 2.19428 | ||||||||
\(546\) | −2.42468 | −0.103767 | ||||||||
\(547\) | −18.5438 | −0.792878 | −0.396439 | − | 0.918061i | \(-0.629754\pi\) | ||||
−0.396439 | + | 0.918061i | \(0.629754\pi\) | |||||||
\(548\) | −11.8420 | −0.505867 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.44889 | −0.104421 | ||||||||
\(551\) | −40.7789 | −1.73724 | ||||||||
\(552\) | −2.69468 | −0.114693 | ||||||||
\(553\) | 1.85476 | 0.0788724 | ||||||||
\(554\) | 20.2982 | 0.862387 | ||||||||
\(555\) | 28.2636 | 1.19972 | ||||||||
\(556\) | 18.4081 | 0.780678 | ||||||||
\(557\) | 19.5596 | 0.828768 | 0.414384 | − | 0.910102i | \(-0.363997\pi\) | ||||
0.414384 | + | 0.910102i | \(0.363997\pi\) | |||||||
\(558\) | 1.96541 | 0.0832026 | ||||||||
\(559\) | −32.8839 | −1.39084 | ||||||||
\(560\) | −1.83941 | −0.0777292 | ||||||||
\(561\) | −4.25138 | −0.179493 | ||||||||
\(562\) | 4.38450 | 0.184949 | ||||||||
\(563\) | −12.7296 | −0.536487 | −0.268244 | − | 0.963351i | \(-0.586443\pi\) | ||||
−0.268244 | + | 0.963351i | \(0.586443\pi\) | |||||||
\(564\) | −10.6370 | −0.447896 | ||||||||
\(565\) | −9.42874 | −0.396670 | ||||||||
\(566\) | 10.5547 | 0.443645 | ||||||||
\(567\) | −0.673957 | −0.0283036 | ||||||||
\(568\) | 0.365213 | 0.0153240 | ||||||||
\(569\) | −28.2675 | −1.18503 | −0.592517 | − | 0.805558i | \(-0.701866\pi\) | ||||
−0.592517 | + | 0.805558i | \(0.701866\pi\) | |||||||
\(570\) | 15.8987 | 0.665923 | ||||||||
\(571\) | 16.4863 | 0.689932 | 0.344966 | − | 0.938615i | \(-0.387890\pi\) | ||||
0.344966 | + | 0.938615i | \(0.387890\pi\) | |||||||
\(572\) | −3.59767 | −0.150426 | ||||||||
\(573\) | −3.66910 | −0.153279 | ||||||||
\(574\) | 2.61534 | 0.109162 | ||||||||
\(575\) | −6.59897 | −0.275196 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 23.9235 | 0.995949 | 0.497975 | − | 0.867192i | \(-0.334077\pi\) | ||||
0.497975 | + | 0.867192i | \(0.334077\pi\) | |||||||
\(578\) | 1.07423 | 0.0446823 | ||||||||
\(579\) | 7.96138 | 0.330864 | ||||||||
\(580\) | −19.1058 | −0.793327 | ||||||||
\(581\) | 0.105496 | 0.00437671 | ||||||||
\(582\) | −11.2082 | −0.464595 | ||||||||
\(583\) | 3.56328 | 0.147576 | ||||||||
\(584\) | −4.95939 | −0.205221 | ||||||||
\(585\) | 9.81900 | 0.405965 | ||||||||
\(586\) | −31.7323 | −1.31085 | ||||||||
\(587\) | 19.1867 | 0.791919 | 0.395959 | − | 0.918268i | \(-0.370412\pi\) | ||||
0.395959 | + | 0.918268i | \(0.370412\pi\) | |||||||
\(588\) | −6.54578 | −0.269943 | ||||||||
\(589\) | 11.4490 | 0.471750 | ||||||||
\(590\) | 10.6980 | 0.440431 | ||||||||
\(591\) | −3.60611 | −0.148335 | ||||||||
\(592\) | 10.3558 | 0.425619 | ||||||||
\(593\) | 35.1543 | 1.44362 | 0.721808 | − | 0.692094i | \(-0.243311\pi\) | ||||
0.721808 | + | 0.692094i | \(0.243311\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −7.82003 | −0.320590 | ||||||||
\(596\) | 11.4006 | 0.466988 | ||||||||
\(597\) | −16.6285 | −0.680561 | ||||||||
\(598\) | −9.69456 | −0.396440 | ||||||||
\(599\) | −38.0017 | −1.55271 | −0.776353 | − | 0.630299i | \(-0.782932\pi\) | ||||
−0.776353 | + | 0.630299i | \(0.782932\pi\) | |||||||
\(600\) | 2.44889 | 0.0999755 | ||||||||
\(601\) | −11.9234 | −0.486364 | −0.243182 | − | 0.969981i | \(-0.578191\pi\) | ||||
−0.243182 | + | 0.969981i | \(0.578191\pi\) | |||||||
\(602\) | 6.16020 | 0.251071 | ||||||||
\(603\) | 6.94252 | 0.282721 | ||||||||
\(604\) | −4.24190 | −0.172600 | ||||||||
\(605\) | 2.72927 | 0.110960 | ||||||||
\(606\) | 7.44745 | 0.302532 | ||||||||
\(607\) | 2.10367 | 0.0853854 | 0.0426927 | − | 0.999088i | \(-0.486406\pi\) | ||||
0.0426927 | + | 0.999088i | \(0.486406\pi\) | |||||||
\(608\) | 5.82526 | 0.236246 | ||||||||
\(609\) | 4.71794 | 0.191181 | ||||||||
\(610\) | 2.72927 | 0.110505 | ||||||||
\(611\) | −38.2682 | −1.54817 | ||||||||
\(612\) | 4.25138 | 0.171852 | ||||||||
\(613\) | 43.7062 | 1.76528 | 0.882639 | − | 0.470052i | \(-0.155765\pi\) | ||||
0.882639 | + | 0.470052i | \(0.155765\pi\) | |||||||
\(614\) | −0.998640 | −0.0403018 | ||||||||
\(615\) | −10.5911 | −0.427075 | ||||||||
\(616\) | 0.673957 | 0.0271545 | ||||||||
\(617\) | −36.2925 | −1.46108 | −0.730540 | − | 0.682870i | \(-0.760731\pi\) | ||||
−0.730540 | + | 0.682870i | \(0.760731\pi\) | |||||||
\(618\) | −6.91858 | −0.278306 | ||||||||
\(619\) | −11.9174 | −0.479002 | −0.239501 | − | 0.970896i | \(-0.576984\pi\) | ||||
−0.239501 | + | 0.970896i | \(0.576984\pi\) | |||||||
\(620\) | 5.36413 | 0.215429 | ||||||||
\(621\) | −2.69468 | −0.108134 | ||||||||
\(622\) | 3.92585 | 0.157412 | ||||||||
\(623\) | −11.4525 | −0.458836 | ||||||||
\(624\) | 3.59767 | 0.144022 | ||||||||
\(625\) | −31.2474 | −1.24990 | ||||||||
\(626\) | −20.3307 | −0.812576 | ||||||||
\(627\) | −5.82526 | −0.232639 | ||||||||
\(628\) | 21.8267 | 0.870981 | ||||||||
\(629\) | 44.0263 | 1.75544 | ||||||||
\(630\) | −1.83941 | −0.0732838 | ||||||||
\(631\) | −3.06591 | −0.122052 | −0.0610260 | − | 0.998136i | \(-0.519437\pi\) | ||||
−0.0610260 | + | 0.998136i | \(0.519437\pi\) | |||||||
\(632\) | −2.75204 | −0.109470 | ||||||||
\(633\) | −22.5841 | −0.897637 | ||||||||
\(634\) | −19.7540 | −0.784530 | ||||||||
\(635\) | −7.62878 | −0.302739 | ||||||||
\(636\) | −3.56328 | −0.141293 | ||||||||
\(637\) | −23.5496 | −0.933068 | ||||||||
\(638\) | 7.00036 | 0.277147 | ||||||||
\(639\) | 0.365213 | 0.0144476 | ||||||||
\(640\) | 2.72927 | 0.107884 | ||||||||
\(641\) | −6.11169 | −0.241397 | −0.120699 | − | 0.992689i | \(-0.538513\pi\) | ||||
−0.120699 | + | 0.992689i | \(0.538513\pi\) | |||||||
\(642\) | 4.35224 | 0.171769 | ||||||||
\(643\) | 1.41675 | 0.0558711 | 0.0279356 | − | 0.999610i | \(-0.491107\pi\) | ||||
0.0279356 | + | 0.999610i | \(0.491107\pi\) | |||||||
\(644\) | 1.81610 | 0.0715643 | ||||||||
\(645\) | −24.9464 | −0.982264 | ||||||||
\(646\) | 24.7654 | 0.974382 | ||||||||
\(647\) | −3.11439 | −0.122439 | −0.0612197 | − | 0.998124i | \(-0.519499\pi\) | ||||
−0.0612197 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.91975 | −0.153863 | ||||||||
\(650\) | 8.81030 | 0.345568 | ||||||||
\(651\) | −1.32460 | −0.0519153 | ||||||||
\(652\) | 1.27864 | 0.0500752 | ||||||||
\(653\) | −39.3794 | −1.54103 | −0.770517 | − | 0.637419i | \(-0.780002\pi\) | ||||
−0.770517 | + | 0.637419i | \(0.780002\pi\) | |||||||
\(654\) | 18.7692 | 0.733932 | ||||||||
\(655\) | 4.26477 | 0.166639 | ||||||||
\(656\) | −3.88057 | −0.151511 | ||||||||
\(657\) | −4.95939 | −0.193484 | ||||||||
\(658\) | 7.16885 | 0.279471 | ||||||||
\(659\) | 19.6845 | 0.766800 | 0.383400 | − | 0.923582i | \(-0.374753\pi\) | ||||
0.383400 | + | 0.923582i | \(0.374753\pi\) | |||||||
\(660\) | −2.72927 | −0.106237 | ||||||||
\(661\) | −44.7958 | −1.74236 | −0.871178 | − | 0.490967i | \(-0.836643\pi\) | ||||
−0.871178 | + | 0.490967i | \(0.836643\pi\) | |||||||
\(662\) | −4.11510 | −0.159938 | ||||||||
\(663\) | 15.2951 | 0.594011 | ||||||||
\(664\) | −0.156532 | −0.00607463 | ||||||||
\(665\) | −10.7150 | −0.415512 | ||||||||
\(666\) | 10.3558 | 0.401278 | ||||||||
\(667\) | 18.8637 | 0.730406 | ||||||||
\(668\) | 13.8118 | 0.534396 | ||||||||
\(669\) | −0.596137 | −0.0230480 | ||||||||
\(670\) | 18.9480 | 0.732024 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −0.673957 | −0.0259985 | ||||||||
\(673\) | 1.26117 | 0.0486145 | 0.0243073 | − | 0.999705i | \(-0.492262\pi\) | ||||
0.0243073 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(674\) | −11.6712 | −0.449556 | ||||||||
\(675\) | 2.44889 | 0.0942578 | ||||||||
\(676\) | −0.0567725 | −0.00218356 | ||||||||
\(677\) | −37.5710 | −1.44397 | −0.721985 | − | 0.691909i | \(-0.756770\pi\) | ||||
−0.721985 | + | 0.691909i | \(0.756770\pi\) | |||||||
\(678\) | −3.45468 | −0.132676 | ||||||||
\(679\) | 7.55385 | 0.289890 | ||||||||
\(680\) | 11.6031 | 0.444960 | ||||||||
\(681\) | −25.8235 | −0.989559 | ||||||||
\(682\) | −1.96541 | −0.0752595 | ||||||||
\(683\) | 3.43910 | 0.131594 | 0.0657968 | − | 0.997833i | \(-0.479041\pi\) | ||||
0.0657968 | + | 0.997833i | \(0.479041\pi\) | |||||||
\(684\) | 5.82526 | 0.222735 | ||||||||
\(685\) | −32.3201 | −1.23489 | ||||||||
\(686\) | 9.12928 | 0.348558 | ||||||||
\(687\) | −24.1601 | −0.921764 | ||||||||
\(688\) | −9.14034 | −0.348472 | ||||||||
\(689\) | −12.8195 | −0.488384 | ||||||||
\(690\) | −7.35449 | −0.279981 | ||||||||
\(691\) | 19.0866 | 0.726087 | 0.363044 | − | 0.931772i | \(-0.381738\pi\) | ||||
0.363044 | + | 0.931772i | \(0.381738\pi\) | |||||||
\(692\) | 6.63267 | 0.252136 | ||||||||
\(693\) | 0.673957 | 0.0256015 | ||||||||
\(694\) | 8.20412 | 0.311424 | ||||||||
\(695\) | 50.2406 | 1.90574 | ||||||||
\(696\) | −7.00036 | −0.265348 | ||||||||
\(697\) | −16.4978 | −0.624898 | ||||||||
\(698\) | −1.81610 | −0.0687403 | ||||||||
\(699\) | 4.62550 | 0.174953 | ||||||||
\(700\) | −1.65045 | −0.0623810 | ||||||||
\(701\) | 19.4078 | 0.733021 | 0.366510 | − | 0.930414i | \(-0.380552\pi\) | ||||
0.366510 | + | 0.930414i | \(0.380552\pi\) | |||||||
\(702\) | 3.59767 | 0.135785 | ||||||||
\(703\) | 60.3251 | 2.27520 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −29.0311 | −1.09337 | ||||||||
\(706\) | 14.3060 | 0.538414 | ||||||||
\(707\) | −5.01926 | −0.188769 | ||||||||
\(708\) | 3.91975 | 0.147313 | ||||||||
\(709\) | −4.02286 | −0.151082 | −0.0755408 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755408 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(710\) | 0.996762 | 0.0374078 | ||||||||
\(711\) | −2.75204 | −0.103210 | ||||||||
\(712\) | 16.9930 | 0.636839 | ||||||||
\(713\) | −5.29615 | −0.198343 | ||||||||
\(714\) | −2.86525 | −0.107229 | ||||||||
\(715\) | −9.81900 | −0.367210 | ||||||||
\(716\) | −13.7972 | −0.515624 | ||||||||
\(717\) | −24.4212 | −0.912026 | ||||||||
\(718\) | 5.14351 | 0.191954 | ||||||||
\(719\) | −35.7621 | −1.33370 | −0.666850 | − | 0.745192i | \(-0.732358\pi\) | ||||
−0.666850 | + | 0.745192i | \(0.732358\pi\) | |||||||
\(720\) | 2.72927 | 0.101714 | ||||||||
\(721\) | 4.66283 | 0.173653 | ||||||||
\(722\) | 14.9337 | 0.555775 | ||||||||
\(723\) | 12.0073 | 0.446556 | ||||||||
\(724\) | −10.3165 | −0.383409 | ||||||||
\(725\) | −17.1431 | −0.636679 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 2.06808 | 0.0767008 | 0.0383504 | − | 0.999264i | \(-0.487790\pi\) | ||||
0.0383504 | + | 0.999264i | \(0.487790\pi\) | |||||||
\(728\) | −2.42468 | −0.0898645 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.5355 | −0.500971 | ||||||||
\(731\) | −38.8591 | −1.43725 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 5.39491 | 0.199266 | 0.0996329 | − | 0.995024i | \(-0.468233\pi\) | ||||
0.0996329 | + | 0.995024i | \(0.468233\pi\) | |||||||
\(734\) | −31.4881 | −1.16225 | ||||||||
\(735\) | −17.8652 | −0.658967 | ||||||||
\(736\) | −2.69468 | −0.0993272 | ||||||||
\(737\) | −6.94252 | −0.255731 | ||||||||
\(738\) | −3.88057 | −0.142846 | ||||||||
\(739\) | −2.31206 | −0.0850505 | −0.0425252 | − | 0.999095i | \(-0.513540\pi\) | ||||
−0.0425252 | + | 0.999095i | \(0.513540\pi\) | |||||||
\(740\) | 28.2636 | 1.03899 | ||||||||
\(741\) | 20.9574 | 0.769889 | ||||||||
\(742\) | 2.40150 | 0.0881618 | ||||||||
\(743\) | −3.98719 | −0.146276 | −0.0731380 | − | 0.997322i | \(-0.523301\pi\) | ||||
−0.0731380 | + | 0.997322i | \(0.523301\pi\) | |||||||
\(744\) | 1.96541 | 0.0720555 | ||||||||
\(745\) | 31.1153 | 1.13998 | ||||||||
\(746\) | 7.12105 | 0.260720 | ||||||||
\(747\) | −0.156532 | −0.00572722 | ||||||||
\(748\) | −4.25138 | −0.155446 | ||||||||
\(749\) | −2.93323 | −0.107178 | ||||||||
\(750\) | −6.96266 | −0.254240 | ||||||||
\(751\) | −6.45422 | −0.235518 | −0.117759 | − | 0.993042i | \(-0.537571\pi\) | ||||
−0.117759 | + | 0.993042i | \(0.537571\pi\) | |||||||
\(752\) | −10.6370 | −0.387890 | ||||||||
\(753\) | −28.8035 | −1.04966 | ||||||||
\(754\) | −25.1850 | −0.917183 | ||||||||
\(755\) | −11.5773 | −0.421340 | ||||||||
\(756\) | −0.673957 | −0.0245116 | ||||||||
\(757\) | −23.2343 | −0.844463 | −0.422232 | − | 0.906488i | \(-0.638753\pi\) | ||||
−0.422232 | + | 0.906488i | \(0.638753\pi\) | |||||||
\(758\) | 14.0522 | 0.510400 | ||||||||
\(759\) | 2.69468 | 0.0978106 | ||||||||
\(760\) | 15.8987 | 0.576706 | ||||||||
\(761\) | 29.5065 | 1.06961 | 0.534804 | − | 0.844976i | \(-0.320385\pi\) | ||||
0.534804 | + | 0.844976i | \(0.320385\pi\) | |||||||
\(762\) | −2.79518 | −0.101259 | ||||||||
\(763\) | −12.6496 | −0.457947 | ||||||||
\(764\) | −3.66910 | −0.132743 | ||||||||
\(765\) | 11.6031 | 0.419513 | ||||||||
\(766\) | −18.2433 | −0.659156 | ||||||||
\(767\) | 14.1020 | 0.509192 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 33.7110 | 1.21565 | 0.607825 | − | 0.794071i | \(-0.292042\pi\) | ||||
0.607825 | + | 0.794071i | \(0.292042\pi\) | |||||||
\(770\) | 1.83941 | 0.0662877 | ||||||||
\(771\) | 3.26066 | 0.117430 | ||||||||
\(772\) | 7.96138 | 0.286536 | ||||||||
\(773\) | −9.58341 | −0.344691 | −0.172346 | − | 0.985037i | \(-0.555135\pi\) | ||||
−0.172346 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(774\) | −9.14034 | −0.328543 | ||||||||
\(775\) | 4.81308 | 0.172891 | ||||||||
\(776\) | −11.2082 | −0.402351 | ||||||||
\(777\) | −6.97935 | −0.250383 | ||||||||
\(778\) | 38.2158 | 1.37010 | ||||||||
\(779\) | −22.6054 | −0.809921 | ||||||||
\(780\) | 9.81900 | 0.351576 | ||||||||
\(781\) | −0.365213 | −0.0130683 | ||||||||
\(782\) | −11.4561 | −0.409669 | ||||||||
\(783\) | −7.00036 | −0.250172 | ||||||||
\(784\) | −6.54578 | −0.233778 | ||||||||
\(785\) | 59.5709 | 2.12618 | ||||||||
\(786\) | 1.56261 | 0.0557364 | ||||||||
\(787\) | −20.2864 | −0.723131 | −0.361565 | − | 0.932347i | \(-0.617758\pi\) | ||||
−0.361565 | + | 0.932347i | \(0.617758\pi\) | |||||||
\(788\) | −3.60611 | −0.128462 | ||||||||
\(789\) | 2.24512 | 0.0799282 | ||||||||
\(790\) | −7.51105 | −0.267231 | ||||||||
\(791\) | 2.32831 | 0.0827851 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 3.59767 | 0.127757 | ||||||||
\(794\) | 35.0350 | 1.24335 | ||||||||
\(795\) | −9.72513 | −0.344915 | ||||||||
\(796\) | −16.6285 | −0.589383 | ||||||||
\(797\) | 19.8303 | 0.702426 | 0.351213 | − | 0.936296i | \(-0.385769\pi\) | ||||
0.351213 | + | 0.936296i | \(0.385769\pi\) | |||||||
\(798\) | −3.92598 | −0.138978 | ||||||||
\(799\) | −45.2217 | −1.59983 | ||||||||
\(800\) | 2.44889 | 0.0865813 | ||||||||
\(801\) | 16.9930 | 0.600417 | ||||||||
\(802\) | 10.5478 | 0.372457 | ||||||||
\(803\) | 4.95939 | 0.175013 | ||||||||
\(804\) | 6.94252 | 0.244844 | ||||||||
\(805\) | 4.95661 | 0.174698 | ||||||||
\(806\) | 7.07091 | 0.249062 | ||||||||
\(807\) | 23.6005 | 0.830777 | ||||||||
\(808\) | 7.44745 | 0.262000 | ||||||||
\(809\) | −34.0922 | −1.19862 | −0.599309 | − | 0.800518i | \(-0.704558\pi\) | ||||
−0.599309 | + | 0.800518i | \(0.704558\pi\) | |||||||
\(810\) | 2.72927 | 0.0958966 | ||||||||
\(811\) | −13.5287 | −0.475056 | −0.237528 | − | 0.971381i | \(-0.576337\pi\) | ||||
−0.237528 | + | 0.971381i | \(0.576337\pi\) | |||||||
\(812\) | 4.71794 | 0.165567 | ||||||||
\(813\) | −7.54489 | −0.264611 | ||||||||
\(814\) | −10.3558 | −0.362969 | ||||||||
\(815\) | 3.48973 | 0.122240 | ||||||||
\(816\) | 4.25138 | 0.148828 | ||||||||
\(817\) | −53.2449 | −1.86280 | ||||||||
\(818\) | −23.1673 | −0.810025 | ||||||||
\(819\) | −2.42468 | −0.0847250 | ||||||||
\(820\) | −10.5911 | −0.369858 | ||||||||
\(821\) | 17.4642 | 0.609506 | 0.304753 | − | 0.952431i | \(-0.401426\pi\) | ||||
0.304753 | + | 0.952431i | \(0.401426\pi\) | |||||||
\(822\) | −11.8420 | −0.413038 | ||||||||
\(823\) | 50.1561 | 1.74833 | 0.874165 | − | 0.485629i | \(-0.161409\pi\) | ||||
0.874165 | + | 0.485629i | \(0.161409\pi\) | |||||||
\(824\) | −6.91858 | −0.241020 | ||||||||
\(825\) | −2.44889 | −0.0852594 | ||||||||
\(826\) | −2.64174 | −0.0919180 | ||||||||
\(827\) | 28.8166 | 1.00205 | 0.501025 | − | 0.865433i | \(-0.332956\pi\) | ||||
0.501025 | + | 0.865433i | \(0.332956\pi\) | |||||||
\(828\) | −2.69468 | −0.0936465 | ||||||||
\(829\) | −17.2738 | −0.599946 | −0.299973 | − | 0.953948i | \(-0.596978\pi\) | ||||
−0.299973 | + | 0.953948i | \(0.596978\pi\) | |||||||
\(830\) | −0.427218 | −0.0148290 | ||||||||
\(831\) | 20.2982 | 0.704136 | ||||||||
\(832\) | 3.59767 | 0.124727 | ||||||||
\(833\) | −27.8286 | −0.964204 | ||||||||
\(834\) | 18.4081 | 0.637421 | ||||||||
\(835\) | 37.6962 | 1.30453 | ||||||||
\(836\) | −5.82526 | −0.201471 | ||||||||
\(837\) | 1.96541 | 0.0679346 | ||||||||
\(838\) | −35.4669 | −1.22518 | ||||||||
\(839\) | 32.4044 | 1.11872 | 0.559362 | − | 0.828924i | \(-0.311046\pi\) | ||||
0.559362 | + | 0.828924i | \(0.311046\pi\) | |||||||
\(840\) | −1.83941 | −0.0634656 | ||||||||
\(841\) | 20.0050 | 0.689828 | ||||||||
\(842\) | 21.2987 | 0.734001 | ||||||||
\(843\) | 4.38450 | 0.151010 | ||||||||
\(844\) | −22.5841 | −0.777376 | ||||||||
\(845\) | −0.154947 | −0.00533035 | ||||||||
\(846\) | −10.6370 | −0.365706 | ||||||||
\(847\) | −0.673957 | −0.0231575 | ||||||||
\(848\) | −3.56328 | −0.122363 | ||||||||
\(849\) | 10.5547 | 0.362235 | ||||||||
\(850\) | 10.4112 | 0.357100 | ||||||||
\(851\) | −27.9055 | −0.956587 | ||||||||
\(852\) | 0.365213 | 0.0125120 | ||||||||
\(853\) | 38.8126 | 1.32892 | 0.664458 | − | 0.747325i | \(-0.268662\pi\) | ||||
0.664458 | + | 0.747325i | \(0.268662\pi\) | |||||||
\(854\) | −0.673957 | −0.0230623 | ||||||||
\(855\) | 15.8987 | 0.543724 | ||||||||
\(856\) | 4.35224 | 0.148757 | ||||||||
\(857\) | −8.39669 | −0.286825 | −0.143413 | − | 0.989663i | \(-0.545808\pi\) | ||||
−0.143413 | + | 0.989663i | \(0.545808\pi\) | |||||||
\(858\) | −3.59767 | −0.122822 | ||||||||
\(859\) | −21.0504 | −0.718231 | −0.359115 | − | 0.933293i | \(-0.616922\pi\) | ||||
−0.359115 | + | 0.933293i | \(0.616922\pi\) | |||||||
\(860\) | −24.9464 | −0.850666 | ||||||||
\(861\) | 2.61534 | 0.0891306 | ||||||||
\(862\) | −3.83729 | −0.130699 | ||||||||
\(863\) | 10.7011 | 0.364270 | 0.182135 | − | 0.983273i | \(-0.441699\pi\) | ||||
0.182135 | + | 0.983273i | \(0.441699\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 18.1023 | 0.615498 | ||||||||
\(866\) | −18.4484 | −0.626904 | ||||||||
\(867\) | 1.07423 | 0.0364829 | ||||||||
\(868\) | −1.32460 | −0.0449600 | ||||||||
\(869\) | 2.75204 | 0.0933566 | ||||||||
\(870\) | −19.1058 | −0.647748 | ||||||||
\(871\) | 24.9769 | 0.846310 | ||||||||
\(872\) | 18.7692 | 0.635604 | ||||||||
\(873\) | −11.2082 | −0.379340 | ||||||||
\(874\) | −15.6972 | −0.530966 | ||||||||
\(875\) | 4.69254 | 0.158637 | ||||||||
\(876\) | −4.95939 | −0.167562 | ||||||||
\(877\) | −29.0313 | −0.980317 | −0.490159 | − | 0.871633i | \(-0.663061\pi\) | ||||
−0.490159 | + | 0.871633i | \(0.663061\pi\) | |||||||
\(878\) | −17.1275 | −0.578024 | ||||||||
\(879\) | −31.7323 | −1.07030 | ||||||||
\(880\) | −2.72927 | −0.0920035 | ||||||||
\(881\) | −26.9938 | −0.909445 | −0.454723 | − | 0.890633i | \(-0.650262\pi\) | ||||
−0.454723 | + | 0.890633i | \(0.650262\pi\) | |||||||
\(882\) | −6.54578 | −0.220408 | ||||||||
\(883\) | −3.19215 | −0.107425 | −0.0537123 | − | 0.998556i | \(-0.517105\pi\) | ||||
−0.0537123 | + | 0.998556i | \(0.517105\pi\) | |||||||
\(884\) | 15.2951 | 0.514429 | ||||||||
\(885\) | 10.6980 | 0.359610 | ||||||||
\(886\) | −5.95809 | −0.200166 | ||||||||
\(887\) | −20.1739 | −0.677374 | −0.338687 | − | 0.940899i | \(-0.609983\pi\) | ||||
−0.338687 | + | 0.940899i | \(0.609983\pi\) | |||||||
\(888\) | 10.3558 | 0.347517 | ||||||||
\(889\) | 1.88383 | 0.0631817 | ||||||||
\(890\) | 46.3783 | 1.55461 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −0.596137 | −0.0199601 | ||||||||
\(893\) | −61.9631 | −2.07351 | ||||||||
\(894\) | 11.4006 | 0.381294 | ||||||||
\(895\) | −37.6561 | −1.25871 | ||||||||
\(896\) | −0.673957 | −0.0225153 | ||||||||
\(897\) | −9.69456 | −0.323692 | ||||||||
\(898\) | −15.5422 | −0.518649 | ||||||||
\(899\) | −13.7586 | −0.458875 | ||||||||
\(900\) | 2.44889 | 0.0816296 | ||||||||
\(901\) | −15.1489 | −0.504681 | ||||||||
\(902\) | 3.88057 | 0.129209 | ||||||||
\(903\) | 6.16020 | 0.204999 | ||||||||
\(904\) | −3.45468 | −0.114901 | ||||||||
\(905\) | −28.1564 | −0.935952 | ||||||||
\(906\) | −4.24190 | −0.140928 | ||||||||
\(907\) | −25.4686 | −0.845670 | −0.422835 | − | 0.906207i | \(-0.638965\pi\) | ||||
−0.422835 | + | 0.906207i | \(0.638965\pi\) | |||||||
\(908\) | −25.8235 | −0.856983 | ||||||||
\(909\) | 7.44745 | 0.247016 | ||||||||
\(910\) | −6.61759 | −0.219371 | ||||||||
\(911\) | −44.0589 | −1.45974 | −0.729868 | − | 0.683589i | \(-0.760418\pi\) | ||||
−0.729868 | + | 0.683589i | \(0.760418\pi\) | |||||||
\(912\) | 5.82526 | 0.192894 | ||||||||
\(913\) | 0.156532 | 0.00518046 | ||||||||
\(914\) | 7.16430 | 0.236974 | ||||||||
\(915\) | 2.72927 | 0.0902267 | ||||||||
\(916\) | −24.1601 | −0.798271 | ||||||||
\(917\) | −1.05313 | −0.0347775 | ||||||||
\(918\) | 4.25138 | 0.140316 | ||||||||
\(919\) | −34.8564 | −1.14981 | −0.574903 | − | 0.818221i | \(-0.694960\pi\) | ||||
−0.574903 | + | 0.818221i | \(0.694960\pi\) | |||||||
\(920\) | −7.35449 | −0.242470 | ||||||||
\(921\) | −0.998640 | −0.0329063 | ||||||||
\(922\) | −19.2505 | −0.633980 | ||||||||
\(923\) | 1.31391 | 0.0432480 | ||||||||
\(924\) | 0.673957 | 0.0221716 | ||||||||
\(925\) | 25.3601 | 0.833836 | ||||||||
\(926\) | 24.3868 | 0.801399 | ||||||||
\(927\) | −6.91858 | −0.227236 | ||||||||
\(928\) | −7.00036 | −0.229798 | ||||||||
\(929\) | 24.6179 | 0.807687 | 0.403843 | − | 0.914828i | \(-0.367674\pi\) | ||||
0.403843 | + | 0.914828i | \(0.367674\pi\) | |||||||
\(930\) | 5.36413 | 0.175897 | ||||||||
\(931\) | −38.1309 | −1.24969 | ||||||||
\(932\) | 4.62550 | 0.151513 | ||||||||
\(933\) | 3.92585 | 0.128526 | ||||||||
\(934\) | 9.41440 | 0.308049 | ||||||||
\(935\) | −11.6031 | −0.379463 | ||||||||
\(936\) | 3.59767 | 0.117594 | ||||||||
\(937\) | 24.8911 | 0.813157 | 0.406579 | − | 0.913616i | \(-0.366722\pi\) | ||||
0.406579 | + | 0.913616i | \(0.366722\pi\) | |||||||
\(938\) | −4.67896 | −0.152774 | ||||||||
\(939\) | −20.3307 | −0.663466 | ||||||||
\(940\) | −29.0311 | −0.946889 | ||||||||
\(941\) | 13.5673 | 0.442282 | 0.221141 | − | 0.975242i | \(-0.429022\pi\) | ||||
0.221141 | + | 0.975242i | \(0.429022\pi\) | |||||||
\(942\) | 21.8267 | 0.711153 | ||||||||
\(943\) | 10.4569 | 0.340523 | ||||||||
\(944\) | 3.91975 | 0.127577 | ||||||||
\(945\) | −1.83941 | −0.0598360 | ||||||||
\(946\) | 9.14034 | 0.297178 | ||||||||
\(947\) | −37.8393 | −1.22961 | −0.614806 | − | 0.788678i | \(-0.710766\pi\) | ||||
−0.614806 | + | 0.788678i | \(0.710766\pi\) | |||||||
\(948\) | −2.75204 | −0.0893822 | ||||||||
\(949\) | −17.8422 | −0.579184 | ||||||||
\(950\) | 14.2654 | 0.462832 | ||||||||
\(951\) | −19.7540 | −0.640566 | ||||||||
\(952\) | −2.86525 | −0.0928633 | ||||||||
\(953\) | −10.1723 | −0.329514 | −0.164757 | − | 0.986334i | \(-0.552684\pi\) | ||||
−0.164757 | + | 0.986334i | \(0.552684\pi\) | |||||||
\(954\) | −3.56328 | −0.115365 | ||||||||
\(955\) | −10.0139 | −0.324043 | ||||||||
\(956\) | −24.4212 | −0.789837 | ||||||||
\(957\) | 7.00036 | 0.226289 | ||||||||
\(958\) | −21.7380 | −0.702324 | ||||||||
\(959\) | 7.98103 | 0.257721 | ||||||||
\(960\) | 2.72927 | 0.0880867 | ||||||||
\(961\) | −27.1372 | −0.875392 | ||||||||
\(962\) | 37.2566 | 1.20120 | ||||||||
\(963\) | 4.35224 | 0.140249 | ||||||||
\(964\) | 12.0073 | 0.386729 | ||||||||
\(965\) | 21.7287 | 0.699473 | ||||||||
\(966\) | 1.81610 | 0.0584320 | ||||||||
\(967\) | −19.8780 | −0.639232 | −0.319616 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319616 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 24.7654 | 0.795580 | ||||||||
\(970\) | −30.5902 | −0.982191 | ||||||||
\(971\) | 33.2038 | 1.06556 | 0.532780 | − | 0.846254i | \(-0.321147\pi\) | ||||
0.532780 | + | 0.846254i | \(0.321147\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −12.4063 | −0.397727 | ||||||||
\(974\) | 17.5946 | 0.563768 | ||||||||
\(975\) | 8.81030 | 0.282155 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −32.6561 | −1.04476 | −0.522381 | − | 0.852712i | \(-0.674956\pi\) | ||||
−0.522381 | + | 0.852712i | \(0.674956\pi\) | |||||||
\(978\) | 1.27864 | 0.0408862 | ||||||||
\(979\) | −16.9930 | −0.543098 | ||||||||
\(980\) | −17.8652 | −0.570682 | ||||||||
\(981\) | 18.7692 | 0.599253 | ||||||||
\(982\) | 39.4366 | 1.25847 | ||||||||
\(983\) | 30.3201 | 0.967060 | 0.483530 | − | 0.875328i | \(-0.339354\pi\) | ||||
0.483530 | + | 0.875328i | \(0.339354\pi\) | |||||||
\(984\) | −3.88057 | −0.123708 | ||||||||
\(985\) | −9.84202 | −0.313593 | ||||||||
\(986\) | −29.7612 | −0.947789 | ||||||||
\(987\) | 7.16885 | 0.228187 | ||||||||
\(988\) | 20.9574 | 0.666743 | ||||||||
\(989\) | 24.6303 | 0.783197 | ||||||||
\(990\) | −2.72927 | −0.0867417 | ||||||||
\(991\) | −13.7111 | −0.435547 | −0.217773 | − | 0.975999i | \(-0.569879\pi\) | ||||
−0.217773 | + | 0.975999i | \(0.569879\pi\) | |||||||
\(992\) | 1.96541 | 0.0624019 | ||||||||
\(993\) | −4.11510 | −0.130589 | ||||||||
\(994\) | −0.246138 | −0.00780702 | ||||||||
\(995\) | −45.3837 | −1.43876 | ||||||||
\(996\) | −0.156532 | −0.00495991 | ||||||||
\(997\) | −30.2370 | −0.957615 | −0.478807 | − | 0.877920i | \(-0.658931\pi\) | ||||
−0.478807 | + | 0.877920i | \(0.658931\pi\) | |||||||
\(998\) | 29.9798 | 0.948995 | ||||||||
\(999\) | 10.3558 | 0.327642 |
(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 | 4026.2.a.bb.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bb.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial |