Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(362,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.362");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3588489216.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 10x^{6} - 8x^{5} + 8x^{4} + 4x^{3} + 16x^{2} + 32x + 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 362.7 | ||
Root | \(1.69709 + 1.58558i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.362 |
Dual form | 363.2.d.e.362.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39417 | 1.69293 | 0.846467 | − | 0.532441i | \(-0.178725\pi\) | ||||
0.846467 | + | 0.532441i | \(0.178725\pi\) | |||||||
\(3\) | 0.366025 | − | 1.69293i | 0.211325 | − | 0.977416i | ||||
\(4\) | 3.73205 | 1.86603 | ||||||||
\(5\) | − | 1.23931i | − | 0.554238i | −0.960836 | − | 0.277119i | \(-0.910620\pi\) | ||
0.960836 | − | 0.277119i | \(-0.0893796\pi\) | |||||||
\(6\) | 0.876327 | − | 4.05317i | 0.357759 | − | 1.65470i | ||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 4.14682 | 1.46612 | ||||||||
\(9\) | −2.73205 | − | 1.23931i | −0.910684 | − | 0.413105i | ||||
\(10\) | − | 2.96713i | − | 0.938288i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.36603 | − | 6.31812i | 0.394338 | − | 1.82388i | ||||
\(13\) | 3.34607i | 0.928032i | 0.885827 | + | 0.464016i | \(0.153592\pi\) | ||||
−0.885827 | + | 0.464016i | \(0.846408\pi\) | |||||||
\(14\) | 6.77174i | 1.80982i | ||||||||
\(15\) | −2.09808 | − | 0.453620i | −0.541721 | − | 0.117124i | ||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | −4.14682 | −1.00575 | −0.502876 | − | 0.864358i | \(-0.667725\pi\) | ||||
−0.502876 | + | 0.864358i | \(0.667725\pi\) | |||||||
\(18\) | −6.54099 | − | 2.96713i | −1.54173 | − | 0.699359i | ||||
\(19\) | − | 2.44949i | − | 0.561951i | −0.959715 | − | 0.280976i | \(-0.909342\pi\) | ||
0.959715 | − | 0.280976i | \(-0.0906580\pi\) | |||||||
\(20\) | − | 4.62518i | − | 1.03422i | ||||||
\(21\) | 4.78834 | + | 1.03528i | 1.04490 | + | 0.225916i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 1.51784 | − | 7.02030i | 0.309828 | − | 1.43301i | ||||
\(25\) | 3.46410 | 0.692820 | ||||||||
\(26\) | 8.01105i | 1.57110i | ||||||||
\(27\) | −3.09808 | + | 4.17156i | −0.596225 | + | 0.802817i | ||||
\(28\) | 10.5558i | 1.99487i | ||||||||
\(29\) | 5.42986 | 1.00830 | 0.504150 | − | 0.863616i | \(-0.331806\pi\) | ||||
0.504150 | + | 0.863616i | \(0.331806\pi\) | |||||||
\(30\) | −5.02315 | − | 1.08604i | −0.917098 | − | 0.198284i | ||||
\(31\) | 0.196152 | 0.0352300 | 0.0176150 | − | 0.999845i | \(-0.494393\pi\) | ||||
0.0176150 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(32\) | −2.39417 | −0.423233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.92820 | −1.70267 | ||||||||
\(35\) | 3.50531 | 0.592505 | ||||||||
\(36\) | −10.1962 | − | 4.62518i | −1.69936 | − | 0.770864i | ||||
\(37\) | −10.4641 | −1.72029 | −0.860144 | − | 0.510052i | \(-0.829626\pi\) | ||||
−0.860144 | + | 0.510052i | \(0.829626\pi\) | |||||||
\(38\) | − | 5.86450i | − | 0.951347i | ||||||
\(39\) | 5.66467 | + | 1.22474i | 0.907073 | + | 0.196116i | ||||
\(40\) | − | 5.13922i | − | 0.812581i | ||||||
\(41\) | 7.18251 | 1.12172 | 0.560860 | − | 0.827911i | \(-0.310471\pi\) | ||||
0.560860 | + | 0.827911i | \(0.310471\pi\) | |||||||
\(42\) | 11.4641 | + | 2.47863i | 1.76895 | + | 0.382461i | ||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.53590 | + | 3.38587i | −0.228958 | + | 0.504735i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.38587i | − | 0.493880i | −0.969031 | − | 0.246940i | \(-0.920575\pi\) | ||
0.969031 | − | 0.246940i | \(-0.0794250\pi\) | |||||||
\(48\) | 0.901924 | − | 4.17156i | 0.130181 | − | 0.602113i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 8.29365 | 1.17290 | ||||||||
\(51\) | −1.51784 | + | 7.02030i | −0.212541 | + | 0.983039i | ||||
\(52\) | 12.4877i | 1.73173i | ||||||||
\(53\) | 7.10381i | 0.975783i | 0.872904 | + | 0.487892i | \(0.162234\pi\) | ||||
−0.872904 | + | 0.487892i | \(0.837766\pi\) | |||||||
\(54\) | −7.41732 | + | 9.98743i | −1.00937 | + | 1.35912i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.7290i | 1.56735i | ||||||||
\(57\) | −4.14682 | − | 0.896575i | −0.549260 | − | 0.118754i | ||||
\(58\) | 13.0000 | 1.70698 | ||||||||
\(59\) | − | 12.6362i | − | 1.64510i | −0.568695 | − | 0.822549i | \(-0.692551\pi\) | ||
0.568695 | − | 0.822549i | \(-0.307449\pi\) | |||||||
\(60\) | −7.83013 | − | 1.69293i | −1.01087 | − | 0.218557i | ||||
\(61\) | − | 4.52004i | − | 0.578732i | −0.957219 | − | 0.289366i | \(-0.906556\pi\) | ||
0.957219 | − | 0.289366i | \(-0.0934445\pi\) | |||||||
\(62\) | 0.469622 | 0.0596421 | ||||||||
\(63\) | 3.50531 | − | 7.72741i | 0.441627 | − | 0.973562i | ||||
\(64\) | −10.6603 | −1.33253 | ||||||||
\(65\) | 4.14682 | 0.514350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −15.4762 | −1.87676 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.39230 | 1.00307 | ||||||||
\(71\) | 8.34312i | 0.990146i | 0.868851 | + | 0.495073i | \(0.164859\pi\) | ||||
−0.868851 | + | 0.495073i | \(0.835141\pi\) | |||||||
\(72\) | −11.3293 | − | 5.13922i | −1.33517 | − | 0.605662i | ||||
\(73\) | − | 8.10634i | − | 0.948776i | −0.880316 | − | 0.474388i | \(-0.842669\pi\) | ||
0.880316 | − | 0.474388i | \(-0.157331\pi\) | |||||||
\(74\) | −25.0528 | −2.91233 | ||||||||
\(75\) | 1.26795 | − | 5.86450i | 0.146410 | − | 0.677174i | ||||
\(76\) | − | 9.14162i | − | 1.04862i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.5622 | + | 2.93225i | 1.53561 | + | 0.332012i | ||||
\(79\) | 7.34847i | 0.826767i | 0.910557 | + | 0.413384i | \(0.135653\pi\) | ||||
−0.910557 | + | 0.413384i | \(0.864347\pi\) | |||||||
\(80\) | − | 3.05379i | − | 0.341425i | ||||||
\(81\) | 5.92820 | + | 6.77174i | 0.658689 | + | 0.752415i | ||||
\(82\) | 17.1962 | 1.89900 | ||||||||
\(83\) | −14.8346 | −1.62831 | −0.814157 | − | 0.580645i | \(-0.802800\pi\) | ||||
−0.814157 | + | 0.580645i | \(0.802800\pi\) | |||||||
\(84\) | 17.8703 | + | 3.86370i | 1.94981 | + | 0.421565i | ||||
\(85\) | 5.13922i | 0.557426i | ||||||||
\(86\) | 10.1576i | 1.09532i | ||||||||
\(87\) | 1.98747 | − | 9.19239i | 0.213079 | − | 0.985527i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.58244i | − | 1.01574i | −0.861435 | − | 0.507868i | \(-0.830434\pi\) | ||
0.861435 | − | 0.507868i | \(-0.169566\pi\) | |||||||
\(90\) | −3.67720 | + | 8.10634i | −0.387611 | + | 0.854484i | ||||
\(91\) | −9.46410 | −0.992107 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0717968 | − | 0.332073i | 0.00744498 | − | 0.0344344i | ||||
\(94\) | − | 8.10634i | − | 0.836106i | ||||||
\(95\) | −3.03569 | −0.311455 | ||||||||
\(96\) | −0.876327 | + | 4.05317i | −0.0894398 | + | 0.413675i | ||||
\(97\) | 2.26795 | 0.230275 | 0.115138 | − | 0.993350i | \(-0.463269\pi\) | ||||
0.115138 | + | 0.993350i | \(0.463269\pi\) | |||||||
\(98\) | −2.39417 | −0.241848 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.9282 | 1.29282 | ||||||||
\(101\) | −0.469622 | −0.0467292 | −0.0233646 | − | 0.999727i | \(-0.507438\pi\) | ||||
−0.0233646 | + | 0.999727i | \(0.507438\pi\) | |||||||
\(102\) | −3.63397 | + | 16.8078i | −0.359817 | + | 1.66422i | ||||
\(103\) | 12.7321 | 1.25453 | 0.627263 | − | 0.778807i | \(-0.284175\pi\) | ||||
0.627263 | + | 0.778807i | \(0.284175\pi\) | |||||||
\(104\) | 13.8755i | 1.36061i | ||||||||
\(105\) | 1.28303 | − | 5.93426i | 0.125211 | − | 0.579124i | ||||
\(106\) | 17.0077i | 1.65194i | ||||||||
\(107\) | −3.50531 | −0.338871 | −0.169435 | − | 0.985541i | \(-0.554194\pi\) | ||||
−0.169435 | + | 0.985541i | \(0.554194\pi\) | |||||||
\(108\) | −11.5622 | + | 15.5685i | −1.11257 | + | 1.49808i | ||||
\(109\) | − | 10.6945i | − | 1.02435i | −0.858881 | − | 0.512175i | \(-0.828840\pi\) | ||
0.858881 | − | 0.512175i | \(-0.171160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.83013 | + | 17.7150i | −0.363540 | + | 1.68144i | ||||
\(112\) | 6.96953i | 0.658559i | ||||||||
\(113\) | − | 12.9683i | − | 1.21996i | −0.792419 | − | 0.609978i | \(-0.791178\pi\) | ||
0.792419 | − | 0.609978i | \(-0.208822\pi\) | |||||||
\(114\) | −9.92820 | − | 2.14655i | −0.929861 | − | 0.201043i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.2645 | 1.88151 | ||||||||
\(117\) | 4.14682 | − | 9.14162i | 0.383374 | − | 0.845143i | ||||
\(118\) | − | 30.2533i | − | 2.78504i | ||||||
\(119\) | − | 11.7290i | − | 1.07519i | ||||||
\(120\) | −8.70035 | − | 1.88108i | −0.794230 | − | 0.171719i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 10.8217i | − | 0.979755i | ||||||
\(123\) | 2.62898 | − | 12.1595i | 0.237047 | − | 1.09639i | ||||
\(124\) | 0.732051 | 0.0657401 | ||||||||
\(125\) | − | 10.4897i | − | 0.938225i | ||||||
\(126\) | 8.39230 | − | 18.5007i | 0.747646 | − | 1.64818i | ||||
\(127\) | 14.4195i | 1.27953i | 0.768572 | + | 0.639764i | \(0.220968\pi\) | ||||
−0.768572 | + | 0.639764i | \(0.779032\pi\) | |||||||
\(128\) | −20.7341 | −1.83265 | ||||||||
\(129\) | 7.18251 | + | 1.55291i | 0.632385 | + | 0.136726i | ||||
\(130\) | 9.92820 | 0.870761 | ||||||||
\(131\) | −13.5516 | −1.18401 | −0.592005 | − | 0.805934i | \(-0.701663\pi\) | ||||
−0.592005 | + | 0.805934i | \(0.701663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | 4.78834 | 0.413650 | ||||||||
\(135\) | 5.16987 | + | 3.83949i | 0.444952 | + | 0.330451i | ||||
\(136\) | −17.1962 | −1.47456 | ||||||||
\(137\) | − | 17.8366i | − | 1.52388i | −0.647647 | − | 0.761941i | \(-0.724247\pi\) | ||
0.647647 | − | 0.761941i | \(-0.275753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.17638i | − | 0.439055i | −0.975606 | − | 0.219527i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219527i | \(-0.0704516\pi\) | |||||||
\(140\) | 13.0820 | 1.10563 | ||||||||
\(141\) | −5.73205 | − | 1.23931i | −0.482726 | − | 0.104369i | ||||
\(142\) | 19.9749i | 1.67625i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.73205 | − | 3.05379i | −0.561004 | − | 0.254483i | ||||
\(145\) | − | 6.72930i | − | 0.558838i | ||||||
\(146\) | − | 19.4080i | − | 1.60621i | ||||||
\(147\) | −0.366025 | + | 1.69293i | −0.0301893 | + | 0.139631i | ||||
\(148\) | −39.0526 | −3.21010 | ||||||||
\(149\) | 9.40479 | 0.770470 | 0.385235 | − | 0.922818i | \(-0.374120\pi\) | ||||
0.385235 | + | 0.922818i | \(0.374120\pi\) | |||||||
\(150\) | 3.03569 | − | 14.0406i | 0.247863 | − | 1.14641i | ||||
\(151\) | 16.4901i | 1.34194i | 0.741482 | + | 0.670972i | \(0.234123\pi\) | ||||
−0.741482 | + | 0.670972i | \(0.765877\pi\) | |||||||
\(152\) | − | 10.1576i | − | 0.823890i | ||||||
\(153\) | 11.3293 | + | 5.13922i | 0.915922 | + | 0.415481i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.243094i | − | 0.0195258i | ||||||
\(156\) | 21.1408 | + | 4.57081i | 1.69262 | + | 0.365958i | ||||
\(157\) | −11.4641 | −0.914935 | −0.457467 | − | 0.889226i | \(-0.651243\pi\) | ||||
−0.457467 | + | 0.889226i | \(0.651243\pi\) | |||||||
\(158\) | 17.5935i | 1.39966i | ||||||||
\(159\) | 12.0263 | + | 2.60017i | 0.953746 | + | 0.206207i | ||||
\(160\) | 2.96713i | 0.234572i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 14.1931 | + | 16.2127i | 1.11512 | + | 1.27379i | ||||
\(163\) | 12.3923 | 0.970640 | 0.485320 | − | 0.874337i | \(-0.338703\pi\) | ||||
0.485320 | + | 0.874337i | \(0.338703\pi\) | |||||||
\(164\) | 26.8055 | 2.09316 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.5167 | −2.75663 | ||||||||
\(167\) | 5.25796 | 0.406873 | 0.203437 | − | 0.979088i | \(-0.434789\pi\) | ||||
0.203437 | + | 0.979088i | \(0.434789\pi\) | |||||||
\(168\) | 19.8564 | + | 4.29311i | 1.53196 | + | 0.331221i | ||||
\(169\) | 1.80385 | 0.138758 | ||||||||
\(170\) | 12.3042i | 0.943686i | ||||||||
\(171\) | −3.03569 | + | 6.69213i | −0.232145 | + | 0.511760i | ||||
\(172\) | 15.8338i | 1.20731i | ||||||||
\(173\) | −11.3293 | −0.861353 | −0.430677 | − | 0.902506i | \(-0.641725\pi\) | ||||
−0.430677 | + | 0.902506i | \(0.641725\pi\) | |||||||
\(174\) | 4.75833 | − | 22.0081i | 0.360728 | − | 1.66843i | ||||
\(175\) | 9.79796i | 0.740656i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.3923 | − | 4.62518i | −1.60794 | − | 0.347650i | ||||
\(178\) | − | 22.9420i | − | 1.71957i | ||||||
\(179\) | 22.7938i | 1.70369i | 0.523793 | + | 0.851846i | \(0.324517\pi\) | ||||
−0.523793 | + | 0.851846i | \(0.675483\pi\) | |||||||
\(180\) | −5.73205 | + | 12.6362i | −0.427242 | + | 0.941849i | ||||
\(181\) | 12.8564 | 0.955609 | 0.477805 | − | 0.878466i | \(-0.341433\pi\) | ||||
0.477805 | + | 0.878466i | \(0.341433\pi\) | |||||||
\(182\) | −22.6587 | −1.67957 | ||||||||
\(183\) | −7.65213 | − | 1.65445i | −0.565662 | − | 0.122300i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.9683i | 0.953449i | ||||||||
\(186\) | 0.171894 | − | 0.795040i | 0.0126039 | − | 0.0582951i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 12.6362i | − | 0.921592i | ||||||
\(189\) | −11.7990 | − | 8.76268i | −0.858248 | − | 0.637391i | ||||
\(190\) | −7.26795 | −0.527272 | ||||||||
\(191\) | 2.47863i | 0.179347i | 0.995971 | + | 0.0896736i | \(0.0285824\pi\) | ||||
−0.995971 | + | 0.0896736i | \(0.971418\pi\) | |||||||
\(192\) | −3.90192 | + | 18.0471i | −0.281597 | + | 1.30244i | ||||
\(193\) | 2.86559i | 0.206270i | 0.994667 | + | 0.103135i | \(0.0328873\pi\) | ||||
−0.994667 | + | 0.103135i | \(0.967113\pi\) | |||||||
\(194\) | 5.42986 | 0.389841 | ||||||||
\(195\) | 1.51784 | − | 7.02030i | 0.108695 | − | 0.502734i | ||||
\(196\) | −3.73205 | −0.266575 | ||||||||
\(197\) | 10.6878 | 0.761476 | 0.380738 | − | 0.924683i | \(-0.375670\pi\) | ||||
0.380738 | + | 0.924683i | \(0.375670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.66025 | 0.543021 | 0.271511 | − | 0.962435i | \(-0.412477\pi\) | ||||
0.271511 | + | 0.962435i | \(0.412477\pi\) | |||||||
\(200\) | 14.3650 | 1.01576 | ||||||||
\(201\) | 0.732051 | − | 3.38587i | 0.0516349 | − | 0.238821i | ||||
\(202\) | −1.12436 | −0.0791094 | ||||||||
\(203\) | 15.3580i | 1.07792i | ||||||||
\(204\) | −5.66467 | + | 26.2001i | −0.396606 | + | 1.83438i | ||||
\(205\) | − | 8.90138i | − | 0.621700i | ||||||
\(206\) | 30.4827 | 2.12383 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.24504i | 0.571691i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.07180 | − | 14.2076i | 0.211974 | − | 0.980419i | ||||
\(211\) | − | 1.89469i | − | 0.130436i | −0.997871 | − | 0.0652178i | \(-0.979226\pi\) | ||
0.997871 | − | 0.0652178i | \(-0.0207742\pi\) | |||||||
\(212\) | 26.5118i | 1.82084i | ||||||||
\(213\) | 14.1244 | + | 3.05379i | 0.967785 | + | 0.209243i | ||||
\(214\) | −8.39230 | −0.573686 | ||||||||
\(215\) | 5.25796 | 0.358590 | ||||||||
\(216\) | −12.8472 | + | 17.2987i | −0.874140 | + | 1.17703i | ||||
\(217\) | 0.554803i | 0.0376625i | ||||||||
\(218\) | − | 25.6045i | − | 1.73416i | ||||||
\(219\) | −13.7235 | − | 2.96713i | −0.927349 | − | 0.200500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.8755i | − | 0.933370i | ||||||
\(222\) | −9.16998 | + | 42.4128i | −0.615448 | + | 2.84656i | ||||
\(223\) | 12.9282 | 0.865737 | 0.432868 | − | 0.901457i | \(-0.357502\pi\) | ||||
0.432868 | + | 0.901457i | \(0.357502\pi\) | |||||||
\(224\) | − | 6.77174i | − | 0.452456i | ||||||
\(225\) | −9.46410 | − | 4.29311i | −0.630940 | − | 0.286207i | ||||
\(226\) | − | 31.0483i | − | 2.06530i | ||||||
\(227\) | −5.25796 | −0.348983 | −0.174492 | − | 0.984659i | \(-0.555828\pi\) | ||||
−0.174492 | + | 0.984659i | \(0.555828\pi\) | |||||||
\(228\) | −15.4762 | − | 3.34607i | −1.02493 | − | 0.221599i | ||||
\(229\) | 5.53590 | 0.365822 | 0.182911 | − | 0.983129i | \(-0.441448\pi\) | ||||
0.182911 | + | 0.983129i | \(0.441448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.5167 | 1.47829 | ||||||||
\(233\) | −5.42986 | −0.355722 | −0.177861 | − | 0.984056i | \(-0.556918\pi\) | ||||
−0.177861 | + | 0.984056i | \(0.556918\pi\) | |||||||
\(234\) | 9.92820 | − | 21.8866i | 0.649027 | − | 1.43077i | ||||
\(235\) | −4.19615 | −0.273727 | ||||||||
\(236\) | − | 47.1591i | − | 3.06979i | ||||||
\(237\) | 12.4405 | + | 2.68973i | 0.808096 | + | 0.174717i | ||||
\(238\) | − | 28.0812i | − | 1.82023i | ||||||
\(239\) | 10.0463 | 0.649841 | 0.324921 | − | 0.945741i | \(-0.394662\pi\) | ||||
0.324921 | + | 0.945741i | \(0.394662\pi\) | |||||||
\(240\) | −5.16987 | − | 1.11777i | −0.333714 | − | 0.0721515i | ||||
\(241\) | − | 3.76217i | − | 0.242343i | −0.992632 | − | 0.121171i | \(-0.961335\pi\) | ||
0.992632 | − | 0.121171i | \(-0.0386650\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6340 | − | 7.55743i | 0.874620 | − | 0.484809i | ||||
\(244\) | − | 16.8690i | − | 1.07993i | ||||||
\(245\) | 1.23931i | 0.0791768i | ||||||||
\(246\) | 6.29423 | − | 29.1120i | 0.401305 | − | 1.85611i | ||||
\(247\) | 8.19615 | 0.521509 | ||||||||
\(248\) | 0.813410 | 0.0516516 | ||||||||
\(249\) | −5.42986 | + | 25.1141i | −0.344103 | + | 1.59154i | ||||
\(250\) | − | 25.1141i | − | 1.58835i | ||||||
\(251\) | 8.58622i | 0.541957i | 0.962585 | + | 0.270979i | \(0.0873473\pi\) | ||||
−0.962585 | + | 0.270979i | \(0.912653\pi\) | |||||||
\(252\) | 13.0820 | − | 28.8391i | 0.824088 | − | 1.81669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.5228i | 2.16615i | ||||||||
\(255\) | 8.70035 | + | 1.88108i | 0.544837 | + | 0.117798i | ||||
\(256\) | −28.3205 | −1.77003 | ||||||||
\(257\) | 23.1259i | 1.44255i | 0.692646 | + | 0.721277i | \(0.256445\pi\) | ||||
−0.692646 | + | 0.721277i | \(0.743555\pi\) | |||||||
\(258\) | 17.1962 | + | 3.71794i | 1.07059 | + | 0.231469i | ||||
\(259\) | − | 29.5969i | − | 1.83906i | ||||||
\(260\) | 15.4762 | 0.959791 | ||||||||
\(261\) | −14.8346 | − | 6.72930i | −0.918241 | − | 0.416533i | ||||
\(262\) | −32.4449 | −2.00445 | ||||||||
\(263\) | −23.4721 | −1.44735 | −0.723675 | − | 0.690141i | \(-0.757549\pi\) | ||||
−0.723675 | + | 0.690141i | \(0.757549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.80385 | 0.540816 | ||||||||
\(266\) | 16.5873 | 1.01703 | ||||||||
\(267\) | −16.2224 | − | 3.50742i | −0.992797 | − | 0.214650i | ||||
\(268\) | 7.46410 | 0.455943 | ||||||||
\(269\) | − | 16.3542i | − | 0.997131i | −0.866852 | − | 0.498566i | \(-0.833860\pi\) | ||
0.866852 | − | 0.498566i | \(-0.166140\pi\) | |||||||
\(270\) | 12.3776 | + | 9.19239i | 0.753274 | + | 0.559431i | ||||
\(271\) | 9.14162i | 0.555314i | 0.960680 | + | 0.277657i | \(0.0895579\pi\) | ||||
−0.960680 | + | 0.277657i | \(0.910442\pi\) | |||||||
\(272\) | −10.2182 | −0.619569 | ||||||||
\(273\) | −3.46410 | + | 16.0221i | −0.209657 | + | 0.969702i | ||||
\(274\) | − | 42.7038i | − | 2.57983i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.27603i | 0.377090i | 0.982065 | + | 0.188545i | \(0.0603771\pi\) | ||||
−0.982065 | + | 0.188545i | \(0.939623\pi\) | |||||||
\(278\) | − | 12.3931i | − | 0.743291i | ||||||
\(279\) | −0.535898 | − | 0.243094i | −0.0320834 | − | 0.0145537i | ||||
\(280\) | 14.5359 | 0.868686 | ||||||||
\(281\) | 0.813410 | 0.0485240 | 0.0242620 | − | 0.999706i | \(-0.492276\pi\) | ||||
0.0242620 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(282\) | −13.7235 | − | 2.96713i | −0.817223 | − | 0.176690i | ||||
\(283\) | 6.79367i | 0.403842i | 0.979402 | + | 0.201921i | \(0.0647184\pi\) | ||||
−0.979402 | + | 0.201921i | \(0.935282\pi\) | |||||||
\(284\) | 31.1370i | 1.84764i | ||||||||
\(285\) | −1.11114 | + | 5.13922i | −0.0658181 | + | 0.304421i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.3152i | 1.19917i | ||||||||
\(288\) | 6.54099 | + | 2.96713i | 0.385432 | + | 0.174840i | ||||
\(289\) | 0.196152 | 0.0115384 | ||||||||
\(290\) | − | 16.1111i | − | 0.946075i | ||||||
\(291\) | 0.830127 | − | 3.83949i | 0.0486629 | − | 0.225075i | ||||
\(292\) | − | 30.2533i | − | 1.77044i | ||||||
\(293\) | 32.5331 | 1.90060 | 0.950301 | − | 0.311331i | \(-0.100775\pi\) | ||||
0.950301 | + | 0.311331i | \(0.100775\pi\) | |||||||
\(294\) | −0.876327 | + | 4.05317i | −0.0511084 | + | 0.236386i | ||||
\(295\) | −15.6603 | −0.911775 | ||||||||
\(296\) | −43.3928 | −2.52215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5167 | 1.30436 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.73205 | − | 21.8866i | 0.273205 | − | 1.26362i | ||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 39.4801i | 2.27182i | ||||||||
\(303\) | −0.171894 | + | 0.795040i | −0.00987503 | + | 0.0456738i | ||||
\(304\) | − | 6.03579i | − | 0.346176i | ||||||
\(305\) | −5.60175 | −0.320755 | ||||||||
\(306\) | 27.1244 | + | 12.3042i | 1.55060 | + | 0.703382i | ||||
\(307\) | 31.1870i | 1.77994i | 0.456021 | + | 0.889969i | \(0.349274\pi\) | ||||
−0.456021 | + | 0.889969i | \(0.650726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.66025 | − | 21.5545i | 0.265113 | − | 1.22619i | ||||
\(310\) | − | 0.582009i | − | 0.0330559i | ||||||
\(311\) | 0.664146i | 0.0376603i | 0.999823 | + | 0.0188301i | \(0.00599417\pi\) | ||||
−0.999823 | + | 0.0188301i | \(0.994006\pi\) | |||||||
\(312\) | 23.4904 | + | 5.07880i | 1.32988 | + | 0.287531i | ||||
\(313\) | −7.39230 | −0.417838 | −0.208919 | − | 0.977933i | \(-0.566994\pi\) | ||||
−0.208919 | + | 0.977933i | \(0.566994\pi\) | |||||||
\(314\) | −27.4470 | −1.54892 | ||||||||
\(315\) | −9.57668 | − | 4.34418i | −0.539585 | − | 0.244767i | ||||
\(316\) | 27.4249i | 1.54277i | ||||||||
\(317\) | − | 24.6083i | − | 1.38214i | −0.722787 | − | 0.691070i | \(-0.757139\pi\) | ||
0.722787 | − | 0.691070i | \(-0.242861\pi\) | |||||||
\(318\) | 28.7930 | + | 6.22526i | 1.61463 | + | 0.349095i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.2114i | 0.738540i | ||||||||
\(321\) | −1.28303 | + | 5.93426i | −0.0716119 | + | 0.331218i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1576i | 0.565184i | ||||||||
\(324\) | 22.1244 | + | 25.2725i | 1.22913 | + | 1.40403i | ||||
\(325\) | 11.5911i | 0.642959i | ||||||||
\(326\) | 29.6693 | 1.64323 | ||||||||
\(327\) | −18.1051 | − | 3.91447i | −1.00122 | − | 0.216471i | ||||
\(328\) | 29.7846 | 1.64458 | ||||||||
\(329\) | 9.57668 | 0.527979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.392305 | −0.0215630 | −0.0107815 | − | 0.999942i | \(-0.503432\pi\) | ||||
−0.0107815 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(332\) | −55.3636 | −3.03847 | ||||||||
\(333\) | 28.5885 | + | 12.9683i | 1.56664 | + | 0.710659i | ||||
\(334\) | 12.5885 | 0.688810 | ||||||||
\(335\) | − | 2.47863i | − | 0.135422i | ||||||
\(336\) | 11.7990 | + | 2.55103i | 0.643686 | + | 0.139170i | ||||
\(337\) | 8.52245i | 0.464247i | 0.972686 | + | 0.232124i | \(0.0745674\pi\) | ||||
−0.972686 | + | 0.232124i | \(0.925433\pi\) | |||||||
\(338\) | 4.31872 | 0.234907 | ||||||||
\(339\) | −21.9545 | − | 4.74673i | −1.19240 | − | 0.257807i | ||||
\(340\) | 19.1798i | 1.04017i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.26795 | + | 16.0221i | −0.393006 | + | 0.866376i | ||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 17.5935i | 0.948577i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.1244 | −1.45821 | ||||||||
\(347\) | −1.28303 | −0.0688768 | −0.0344384 | − | 0.999407i | \(-0.510964\pi\) | ||||
−0.0344384 | + | 0.999407i | \(0.510964\pi\) | |||||||
\(348\) | 7.41732 | − | 34.3065i | 0.397610 | − | 1.83902i | ||||
\(349\) | − | 20.3166i | − | 1.08752i | −0.839239 | − | 0.543762i | \(-0.816999\pi\) | ||
0.839239 | − | 0.543762i | \(-0.183001\pi\) | |||||||
\(350\) | 23.4580i | 1.25388i | ||||||||
\(351\) | −13.9583 | − | 10.3664i | −0.745040 | − | 0.553316i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.58244i | 0.510022i | 0.966938 | + | 0.255011i | \(0.0820790\pi\) | ||||
−0.966938 | + | 0.255011i | \(0.917921\pi\) | |||||||
\(354\) | −51.2168 | − | 11.0735i | −2.72214 | − | 0.588548i | ||||
\(355\) | 10.3397 | 0.548777 | ||||||||
\(356\) | − | 35.7621i | − | 1.89539i | ||||||
\(357\) | −19.8564 | − | 4.29311i | −1.05091 | − | 0.227215i | ||||
\(358\) | 54.5723i | 2.88424i | ||||||||
\(359\) | −34.4576 | −1.81860 | −0.909302 | − | 0.416137i | \(-0.863384\pi\) | ||||
−0.909302 | + | 0.416137i | \(0.863384\pi\) | |||||||
\(360\) | −6.36910 | + | 14.0406i | −0.335681 | + | 0.740005i | ||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 30.7804 | 1.61778 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −35.3205 | −1.85130 | ||||||||
\(365\) | −10.0463 | −0.525848 | ||||||||
\(366\) | −18.3205 | − | 3.96104i | −0.957628 | − | 0.207047i | ||||
\(367\) | −23.8564 | −1.24529 | −0.622647 | − | 0.782503i | \(-0.713943\pi\) | ||||
−0.622647 | + | 0.782503i | \(0.713943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.6230 | − | 8.90138i | −1.02153 | − | 0.463388i | ||||
\(370\) | 31.0483i | 1.61413i | ||||||||
\(371\) | −20.0926 | −1.04316 | ||||||||
\(372\) | 0.267949 | − | 1.23931i | 0.0138925 | − | 0.0642554i | ||||
\(373\) | − | 9.62209i | − | 0.498213i | −0.968476 | − | 0.249107i | \(-0.919863\pi\) | ||
0.968476 | − | 0.249107i | \(-0.0801369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.7583 | − | 3.83949i | −0.917036 | − | 0.198270i | ||||
\(376\) | − | 14.0406i | − | 0.724089i | ||||||
\(377\) | 18.1687i | 0.935733i | ||||||||
\(378\) | −28.2487 | − | 20.9794i | −1.45296 | − | 1.07906i | ||||
\(379\) | −30.5885 | −1.57122 | −0.785612 | − | 0.618720i | \(-0.787652\pi\) | ||||
−0.785612 | + | 0.618720i | \(0.787652\pi\) | |||||||
\(380\) | −11.3293 | −0.581183 | ||||||||
\(381\) | 24.4113 | + | 5.27792i | 1.25063 | + | 0.270396i | ||||
\(382\) | 5.93426i | 0.303623i | ||||||||
\(383\) | − | 9.49346i | − | 0.485093i | −0.970140 | − | 0.242547i | \(-0.922017\pi\) | ||
0.970140 | − | 0.242547i | \(-0.0779827\pi\) | |||||||
\(384\) | −7.58922 | + | 35.1015i | −0.387286 | + | 1.79127i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.86071i | 0.349201i | ||||||||
\(387\) | 5.25796 | − | 11.5911i | 0.267277 | − | 0.589209i | ||||
\(388\) | 8.46410 | 0.429700 | ||||||||
\(389\) | 19.0759i | 0.967186i | 0.875293 | + | 0.483593i | \(0.160669\pi\) | ||||
−0.875293 | + | 0.483593i | \(0.839331\pi\) | |||||||
\(390\) | 3.63397 | − | 16.8078i | 0.184013 | − | 0.851096i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.14682 | −0.209446 | ||||||||
\(393\) | −4.96023 | + | 22.9420i | −0.250211 | + | 1.15727i | ||||
\(394\) | 25.5885 | 1.28913 | ||||||||
\(395\) | 9.10706 | 0.458226 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1962 | −1.06380 | −0.531902 | − | 0.846806i | \(-0.678523\pi\) | ||||
−0.531902 | + | 0.846806i | \(0.678523\pi\) | |||||||
\(398\) | 18.3400 | 0.919299 | ||||||||
\(399\) | 2.53590 | − | 11.7290i | 0.126954 | − | 0.587184i | ||||
\(400\) | 8.53590 | 0.426795 | ||||||||
\(401\) | − | 1.23931i | − | 0.0618884i | −0.999521 | − | 0.0309442i | \(-0.990149\pi\) | ||
0.999521 | − | 0.0309442i | \(-0.00985141\pi\) | |||||||
\(402\) | 1.75265 | − | 8.10634i | 0.0874144 | − | 0.404308i | ||||
\(403\) | 0.656339i | 0.0326946i | ||||||||
\(404\) | −1.75265 | −0.0871978 | ||||||||
\(405\) | 8.39230 | − | 7.34690i | 0.417017 | − | 0.365071i | ||||
\(406\) | 36.7696i | 1.82484i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.29423 | + | 29.1120i | −0.311611 | + | 1.44126i | ||||
\(409\) | 33.2204i | 1.64264i | 0.570465 | + | 0.821322i | \(0.306763\pi\) | ||||
−0.570465 | + | 0.821322i | \(0.693237\pi\) | |||||||
\(410\) | − | 21.3114i | − | 1.05250i | ||||||
\(411\) | −30.1962 | − | 6.52864i | −1.48947 | − | 0.322034i | ||||
\(412\) | 47.5167 | 2.34098 | ||||||||
\(413\) | 35.7407 | 1.75868 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3848i | 0.902473i | ||||||||
\(416\) | − | 8.01105i | − | 0.392774i | ||||||
\(417\) | −8.76327 | − | 1.89469i | −0.429139 | − | 0.0927832i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0648i | 0.540553i | 0.962783 | + | 0.270277i | \(0.0871151\pi\) | ||||
−0.962783 | + | 0.270277i | \(0.912885\pi\) | |||||||
\(420\) | 4.78834 | − | 22.1469i | 0.233647 | − | 1.08066i | ||||
\(421\) | −19.1962 | −0.935563 | −0.467782 | − | 0.883844i | \(-0.654947\pi\) | ||||
−0.467782 | + | 0.883844i | \(0.654947\pi\) | |||||||
\(422\) | − | 4.53620i | − | 0.220819i | ||||||
\(423\) | −4.19615 | + | 9.25036i | −0.204024 | + | 0.449768i | ||||
\(424\) | 29.4582i | 1.43062i | ||||||||
\(425\) | −14.3650 | −0.696806 | ||||||||
\(426\) | 33.8161 | + | 7.31130i | 1.63840 | + | 0.354234i | ||||
\(427\) | 12.7846 | 0.618691 | ||||||||
\(428\) | −13.0820 | −0.632342 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5885 | 0.607069 | ||||||||
\(431\) | 20.9060 | 1.00701 | 0.503504 | − | 0.863993i | \(-0.332044\pi\) | ||||
0.503504 | + | 0.863993i | \(0.332044\pi\) | |||||||
\(432\) | −7.63397 | + | 10.2792i | −0.367290 | + | 0.494556i | ||||
\(433\) | 13.0526 | 0.627266 | 0.313633 | − | 0.949544i | \(-0.398454\pi\) | ||||
0.313633 | + | 0.949544i | \(0.398454\pi\) | |||||||
\(434\) | 1.32829i | 0.0637601i | ||||||||
\(435\) | −11.3923 | − | 2.46309i | −0.546217 | − | 0.118096i | ||||
\(436\) | − | 39.9125i | − | 1.91146i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −32.8564 | − | 7.10381i | −1.56994 | − | 0.339433i | ||||
\(439\) | − | 8.38375i | − | 0.400134i | −0.979782 | − | 0.200067i | \(-0.935884\pi\) | ||
0.979782 | − | 0.200067i | \(-0.0641160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.73205 | + | 1.23931i | 0.130098 | + | 0.0590149i | ||||
\(442\) | − | 33.2204i | − | 1.58013i | ||||||
\(443\) | − | 25.5156i | − | 1.21228i | −0.795358 | − | 0.606140i | \(-0.792717\pi\) | ||
0.795358 | − | 0.606140i | \(-0.207283\pi\) | |||||||
\(444\) | −14.2942 | + | 66.1134i | −0.678374 | + | 3.13760i | ||||
\(445\) | −11.8756 | −0.562960 | ||||||||
\(446\) | 30.9523 | 1.46563 | ||||||||
\(447\) | 3.44239 | − | 15.9217i | 0.162820 | − | 0.753070i | ||||
\(448\) | − | 30.1518i | − | 1.42454i | ||||||
\(449\) | 40.2983i | 1.90180i | 0.309504 | + | 0.950898i | \(0.399837\pi\) | ||||
−0.309504 | + | 0.950898i | \(0.600163\pi\) | |||||||
\(450\) | −22.6587 | − | 10.2784i | −1.06814 | − | 0.484530i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 48.3984i | − | 2.27647i | ||||||
\(453\) | 27.9166 | + | 6.03579i | 1.31164 | + | 0.283586i | ||||
\(454\) | −12.5885 | −0.590806 | ||||||||
\(455\) | 11.7290i | 0.549864i | ||||||||
\(456\) | −17.1962 | − | 3.71794i | −0.805284 | − | 0.174109i | ||||
\(457\) | 18.4219i | 0.861742i | 0.902414 | + | 0.430871i | \(0.141794\pi\) | ||||
−0.902414 | + | 0.430871i | \(0.858206\pi\) | |||||||
\(458\) | 13.2539 | 0.619313 | ||||||||
\(459\) | 12.8472 | − | 17.2987i | 0.599655 | − | 0.807436i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.86379 | −0.133380 | −0.0666901 | − | 0.997774i | \(-0.521244\pi\) | ||||
−0.0666901 | + | 0.997774i | \(0.521244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.26795 | −0.0589266 | −0.0294633 | − | 0.999566i | \(-0.509380\pi\) | ||||
−0.0294633 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(464\) | 13.3797 | 0.621138 | ||||||||
\(465\) | −0.411543 | − | 0.0889787i | −0.0190848 | − | 0.00412629i | ||||
\(466\) | −13.0000 | −0.602213 | ||||||||
\(467\) | 19.4080i | 0.898094i | 0.893508 | + | 0.449047i | \(0.148236\pi\) | ||||
−0.893508 | + | 0.449047i | \(0.851764\pi\) | |||||||
\(468\) | 15.4762 | − | 34.1170i | 0.715386 | − | 1.57706i | ||||
\(469\) | 5.65685i | 0.261209i | ||||||||
\(470\) | −10.0463 | −0.463401 | ||||||||
\(471\) | −4.19615 | + | 19.4080i | −0.193348 | + | 0.894272i | ||||
\(472\) | − | 52.4002i | − | 2.41192i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 29.7846 | + | 6.43966i | 1.36805 | + | 0.295784i | ||||
\(475\) | − | 8.48528i | − | 0.389331i | ||||||
\(476\) | − | 43.7732i | − | 2.00634i | ||||||
\(477\) | 8.80385 | − | 19.4080i | 0.403100 | − | 0.888630i | ||||
\(478\) | 24.0526 | 1.10014 | ||||||||
\(479\) | 6.54099 | 0.298866 | 0.149433 | − | 0.988772i | \(-0.452255\pi\) | ||||
0.149433 | + | 0.988772i | \(0.452255\pi\) | |||||||
\(480\) | 5.02315 | + | 1.08604i | 0.229274 | + | 0.0495709i | ||||
\(481\) | − | 35.0136i | − | 1.59648i | ||||||
\(482\) | − | 9.00727i | − | 0.410270i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.81070i | − | 0.127627i | ||||||
\(486\) | 32.6421 | − | 18.0938i | 1.48067 | − | 0.820750i | ||||
\(487\) | 33.1769 | 1.50339 | 0.751695 | − | 0.659511i | \(-0.229237\pi\) | ||||
0.751695 | + | 0.659511i | \(0.229237\pi\) | |||||||
\(488\) | − | 18.7438i | − | 0.848493i | ||||||
\(489\) | 4.53590 | − | 20.9794i | 0.205120 | − | 0.948719i | ||||
\(490\) | 2.96713i | 0.134041i | ||||||||
\(491\) | −20.9060 | −0.943475 | −0.471738 | − | 0.881739i | \(-0.656373\pi\) | ||||
−0.471738 | + | 0.881739i | \(0.656373\pi\) | |||||||
\(492\) | 9.81149 | − | 45.3799i | 0.442336 | − | 2.04589i | ||||
\(493\) | −22.5167 | −1.01410 | ||||||||
\(494\) | 19.6230 | 0.882880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.483340 | 0.0217026 | ||||||||
\(497\) | −23.5979 | −1.05851 | ||||||||
\(498\) | −13.0000 | + | 60.1274i | −0.582544 | + | 2.69437i | ||||
\(499\) | 25.8038 | 1.15514 | 0.577569 | − | 0.816342i | \(-0.304001\pi\) | ||||
0.577569 | + | 0.816342i | \(0.304001\pi\) | |||||||
\(500\) | − | 39.1480i | − | 1.75075i | ||||||
\(501\) | 1.92455 | − | 8.90138i | 0.0859825 | − | 0.397684i | ||||
\(502\) | 20.5569i | 0.917498i | ||||||||
\(503\) | −3.50531 | −0.156294 | −0.0781470 | − | 0.996942i | \(-0.524900\pi\) | ||||
−0.0781470 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(504\) | 14.5359 | − | 32.0442i | 0.647480 | − | 1.42736i | ||||
\(505\) | 0.582009i | 0.0258991i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.660254 | − | 3.05379i | 0.0293229 | − | 0.135624i | ||||
\(508\) | 53.8144i | 2.38763i | ||||||||
\(509\) | 11.7290i | 0.519878i | 0.965625 | + | 0.259939i | \(0.0837025\pi\) | ||||
−0.965625 | + | 0.259939i | \(0.916297\pi\) | |||||||
\(510\) | 20.8301 | + | 4.50363i | 0.922374 | + | 0.199424i | ||||
\(511\) | 22.9282 | 1.01428 | ||||||||
\(512\) | −26.3359 | −1.16389 | ||||||||
\(513\) | 10.2182 | + | 7.58871i | 0.451144 | + | 0.335050i | ||||
\(514\) | 55.3674i | 2.44215i | ||||||||
\(515\) | − | 15.7790i | − | 0.695306i | ||||||
\(516\) | 26.8055 | + | 5.79555i | 1.18005 | + | 0.255135i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 70.8601i | − | 3.11342i | ||||||
\(519\) | −4.14682 | + | 19.1798i | −0.182025 | + | 0.841900i | ||||
\(520\) | 17.1962 | 0.754101 | ||||||||
\(521\) | 2.47863i | 0.108591i | 0.998525 | + | 0.0542953i | \(0.0172912\pi\) | ||||
−0.998525 | + | 0.0542953i | \(0.982709\pi\) | |||||||
\(522\) | −35.5167 | − | 16.1111i | −1.55452 | − | 0.705163i | ||||
\(523\) | − | 36.0860i | − | 1.57793i | −0.614438 | − | 0.788965i | \(-0.710617\pi\) | ||
0.614438 | − | 0.788965i | \(-0.289383\pi\) | |||||||
\(524\) | −50.5753 | −2.20939 | ||||||||
\(525\) | 16.5873 | + | 3.58630i | 0.723929 | + | 0.156519i | ||||
\(526\) | −56.1962 | −2.45027 | ||||||||
\(527\) | −0.813410 | −0.0354327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 21.0779 | 0.915566 | ||||||||
\(531\) | −15.6603 | + | 34.5228i | −0.679597 | + | 1.49816i | ||||
\(532\) | 25.8564 | 1.12102 | ||||||||
\(533\) | 24.0331i | 1.04099i | ||||||||
\(534\) | −38.8393 | − | 8.39735i | −1.68074 | − | 0.363389i | ||||
\(535\) | 4.34418i | 0.187815i | ||||||||
\(536\) | 8.29365 | 0.358231 | ||||||||
\(537\) | 38.5885 | + | 8.34312i | 1.66521 | + | 0.360032i | ||||
\(538\) | − | 39.1547i | − | 1.68808i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.2942 | + | 14.3292i | 0.830291 | + | 0.616629i | ||||
\(541\) | − | 5.27792i | − | 0.226915i | −0.993543 | − | 0.113458i | \(-0.963807\pi\) | ||
0.993543 | − | 0.113458i | \(-0.0361926\pi\) | |||||||
\(542\) | 21.8866i | 0.940110i | ||||||||
\(543\) | 4.70577 | − | 21.7650i | 0.201944 | − | 0.934028i | ||||
\(544\) | 9.92820 | 0.425668 | ||||||||
\(545\) | −13.2539 | −0.567734 | ||||||||
\(546\) | −8.29365 | + | 38.3596i | −0.354935 | + | 1.64164i | ||||
\(547\) | 21.1117i | 0.902670i | 0.892355 | + | 0.451335i | \(0.149052\pi\) | ||||
−0.892355 | + | 0.451335i | \(0.850948\pi\) | |||||||
\(548\) | − | 66.5670i | − | 2.84360i | ||||||
\(549\) | −5.60175 | + | 12.3490i | −0.239077 | + | 0.527042i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.3004i | − | 0.566615i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.7846 | −0.883852 | ||||||||
\(554\) | 15.0259i | 0.638388i | ||||||||
\(555\) | 21.9545 | + | 4.74673i | 0.931916 | + | 0.201487i | ||||
\(556\) | − | 19.3185i | − | 0.819288i | ||||||
\(557\) | 10.3901 | 0.440242 | 0.220121 | − | 0.975473i | \(-0.429355\pi\) | ||||
0.220121 | + | 0.975473i | \(0.429355\pi\) | |||||||
\(558\) | −1.28303 | − | 0.582009i | −0.0543151 | − | 0.0246384i | ||||
\(559\) | −14.1962 | −0.600433 | ||||||||
\(560\) | 8.63744 | 0.364998 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.94744 | 0.0821478 | ||||||||
\(563\) | −35.3969 | −1.49180 | −0.745900 | − | 0.666058i | \(-0.767980\pi\) | ||||
−0.745900 | + | 0.666058i | \(0.767980\pi\) | |||||||
\(564\) | −21.3923 | − | 4.62518i | −0.900779 | − | 0.194755i | ||||
\(565\) | −16.0718 | −0.676146 | ||||||||
\(566\) | 16.2652i | 0.683677i | ||||||||
\(567\) | −19.1534 | + | 16.7675i | −0.804366 | + | 0.704168i | ||||
\(568\) | 34.5975i | 1.45168i | ||||||||
\(569\) | 31.4219 | 1.31728 | 0.658638 | − | 0.752460i | \(-0.271133\pi\) | ||||
0.658638 | + | 0.752460i | \(0.271133\pi\) | |||||||
\(570\) | −2.66025 | + | 12.3042i | −0.111426 | + | 0.515364i | ||||
\(571\) | − | 27.3233i | − | 1.14345i | −0.820447 | − | 0.571723i | \(-0.806275\pi\) | ||
0.820447 | − | 0.571723i | \(-0.193725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.19615 | + | 0.907241i | 0.175297 | + | 0.0379005i | ||||
\(574\) | 48.6381i | 2.03011i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 29.1244 | + | 13.2114i | 1.21351 | + | 0.550475i | ||||
\(577\) | 4.80385 | 0.199987 | 0.0999934 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999934 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(578\) | 0.469622 | 0.0195337 | ||||||||
\(579\) | 4.85126 | + | 1.04888i | 0.201611 | + | 0.0435899i | ||||
\(580\) | − | 25.1141i | − | 1.04281i | ||||||
\(581\) | − | 41.9587i | − | 1.74074i | ||||||
\(582\) | 1.98747 | − | 9.19239i | 0.0823831 | − | 0.381037i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 33.6156i | − | 1.39102i | ||||||
\(585\) | −11.3293 | − | 5.13922i | −0.468410 | − | 0.212480i | ||||
\(586\) | 77.8897 | 3.21759 | ||||||||
\(587\) | 6.52864i | 0.269466i | 0.990882 | + | 0.134733i | \(0.0430177\pi\) | ||||
−0.990882 | + | 0.134733i | \(0.956982\pi\) | |||||||
\(588\) | −1.36603 | + | 6.31812i | −0.0563339 | + | 0.260555i | ||||
\(589\) | − | 0.480473i | − | 0.0197976i | ||||||
\(590\) | −37.4933 | −1.54358 | ||||||||
\(591\) | 3.91201 | − | 18.0938i | 0.160919 | − | 0.744278i | ||||
\(592\) | −25.7846 | −1.05974 | ||||||||
\(593\) | 26.3359 | 1.08148 | 0.540742 | − | 0.841188i | \(-0.318143\pi\) | ||||
0.540742 | + | 0.841188i | \(0.318143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.5359 | −0.595914 | ||||||||
\(596\) | 35.0991 | 1.43772 | ||||||||
\(597\) | 2.80385 | − | 12.9683i | 0.114754 | − | 0.530757i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.72172i | − | 0.111207i | −0.998453 | − | 0.0556033i | \(-0.982292\pi\) | ||
0.998453 | − | 0.0556033i | \(-0.0177082\pi\) | |||||||
\(600\) | 5.25796 | − | 24.3190i | 0.214655 | − | 0.992820i | ||||
\(601\) | − | 41.5298i | − | 1.69404i | −0.531563 | − | 0.847019i | \(-0.678395\pi\) | ||
0.531563 | − | 0.847019i | \(-0.321605\pi\) | |||||||
\(602\) | −28.7300 | −1.17095 | ||||||||
\(603\) | −5.46410 | − | 2.47863i | −0.222515 | − | 0.100938i | ||||
\(604\) | 61.5419i | 2.50410i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.411543 | + | 1.90346i | −0.0167178 | + | 0.0773228i | ||||
\(607\) | − | 44.3954i | − | 1.80195i | −0.433866 | − | 0.900977i | \(-0.642851\pi\) | ||
0.433866 | − | 0.900977i | \(-0.357149\pi\) | |||||||
\(608\) | 5.86450i | 0.237837i | ||||||||
\(609\) | 26.0000 | + | 5.62140i | 1.05357 | + | 0.227791i | ||||
\(610\) | −13.4115 | −0.543017 | ||||||||
\(611\) | 11.3293 | 0.458336 | ||||||||
\(612\) | 42.2817 | + | 19.1798i | 1.70913 | + | 0.775298i | ||||
\(613\) | 15.4176i | 0.622713i | 0.950293 | + | 0.311356i | \(0.100783\pi\) | ||||
−0.950293 | + | 0.311356i | \(0.899217\pi\) | |||||||
\(614\) | 74.6671i | 3.01332i | ||||||||
\(615\) | −15.0695 | − | 3.25813i | −0.607659 | − | 0.131381i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6325i | 0.548822i | 0.961613 | + | 0.274411i | \(0.0884828\pi\) | ||||
−0.961613 | + | 0.274411i | \(0.911517\pi\) | |||||||
\(618\) | 11.1574 | − | 51.6052i | 0.448818 | − | 2.07587i | ||||
\(619\) | −0.143594 | −0.00577151 | −0.00288576 | − | 0.999996i | \(-0.500919\pi\) | ||||
−0.00288576 | + | 0.999996i | \(0.500919\pi\) | |||||||
\(620\) | − | 0.907241i | − | 0.0364357i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.59008i | 0.0637564i | ||||||||
\(623\) | 27.1032 | 1.08587 | ||||||||
\(624\) | 13.9583 | + | 3.01790i | 0.558780 | + | 0.120813i | ||||
\(625\) | 4.32051 | 0.172820 | ||||||||
\(626\) | −17.6984 | −0.707372 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42.7846 | −1.70729 | ||||||||
\(629\) | 43.3928 | 1.73018 | ||||||||
\(630\) | −22.9282 | − | 10.4007i | −0.913481 | − | 0.414374i | ||||
\(631\) | 27.3205 | 1.08761 | 0.543806 | − | 0.839211i | \(-0.316983\pi\) | ||||
0.543806 | + | 0.839211i | \(0.316983\pi\) | |||||||
\(632\) | 30.4728i | 1.21214i | ||||||||
\(633\) | −3.20758 | − | 0.693504i | −0.127490 | − | 0.0275643i | ||||
\(634\) | − | 58.9165i | − | 2.33987i | ||||||
\(635\) | 17.8703 | 0.709162 | ||||||||
\(636\) | 44.8827 | + | 9.70398i | 1.77971 | + | 0.384788i | ||||
\(637\) | − | 3.34607i | − | 0.132576i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3397 | − | 22.7938i | 0.409034 | − | 0.901710i | ||||
\(640\) | 25.6961i | 1.01573i | ||||||||
\(641\) | − | 47.2480i | − | 1.86619i | −0.359636 | − | 0.933093i | \(-0.617099\pi\) | ||
0.359636 | − | 0.933093i | \(-0.382901\pi\) | |||||||
\(642\) | −3.07180 | + | 14.2076i | −0.121234 | + | 0.560730i | ||||
\(643\) | −3.80385 | −0.150009 | −0.0750046 | − | 0.997183i | \(-0.523897\pi\) | ||||
−0.0750046 | + | 0.997183i | \(0.523897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.92455 | − | 8.90138i | 0.0757790 | − | 0.350492i | ||||
\(646\) | 24.3190i | 0.956820i | ||||||||
\(647\) | 16.6862i | 0.656004i | 0.944677 | + | 0.328002i | \(0.106375\pi\) | ||||
−0.944677 | + | 0.328002i | \(0.893625\pi\) | |||||||
\(648\) | 24.5832 | + | 28.0812i | 0.965720 | + | 1.10313i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 27.7511i | 1.08849i | ||||||||
\(651\) | 0.939245 | + | 0.203072i | 0.0368119 | + | 0.00795902i | ||||
\(652\) | 46.2487 | 1.81124 | ||||||||
\(653\) | − | 38.8159i | − | 1.51898i | −0.650516 | − | 0.759492i | \(-0.725447\pi\) | ||
0.650516 | − | 0.759492i | \(-0.274553\pi\) | |||||||
\(654\) | −43.3468 | − | 9.37191i | −1.69499 | − | 0.366471i | ||||
\(655\) | 16.7947i | 0.656223i | ||||||||
\(656\) | 17.6984 | 0.691008 | ||||||||
\(657\) | −10.0463 | + | 22.1469i | −0.391944 | + | 0.864035i | ||||
\(658\) | 22.9282 | 0.893834 | ||||||||
\(659\) | 13.5516 | 0.527896 | 0.263948 | − | 0.964537i | \(-0.414975\pi\) | ||||
0.263948 | + | 0.964537i | \(0.414975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.19615 | 0.124316 | 0.0621580 | − | 0.998066i | \(-0.480202\pi\) | ||||
0.0621580 | + | 0.998066i | \(0.480202\pi\) | |||||||
\(662\) | −0.939245 | −0.0365048 | ||||||||
\(663\) | −23.4904 | − | 5.07880i | −0.912291 | − | 0.197244i | ||||
\(664\) | −61.5167 | −2.38731 | ||||||||
\(665\) | − | 8.58622i | − | 0.332959i | ||||||
\(666\) | 68.4456 | + | 31.0483i | 2.65221 | + | 1.20310i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 19.6230 | 0.759236 | ||||||||
\(669\) | 4.73205 | − | 21.8866i | 0.182952 | − | 0.846185i | ||||
\(670\) | − | 5.93426i | − | 0.229260i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4641 | − | 2.47863i | −0.442237 | − | 0.0956151i | ||||
\(673\) | − | 36.3906i | − | 1.40276i | −0.712790 | − | 0.701378i | \(-0.752569\pi\) | ||
0.712790 | − | 0.701378i | \(-0.247431\pi\) | |||||||
\(674\) | 20.4042i | 0.785940i | ||||||||
\(675\) | −10.7321 | + | 14.4507i | −0.413077 | + | 0.556208i | ||||
\(676\) | 6.73205 | 0.258925 | ||||||||
\(677\) | 11.5012 | 0.442028 | 0.221014 | − | 0.975271i | \(-0.429063\pi\) | ||||
0.221014 | + | 0.975271i | \(0.429063\pi\) | |||||||
\(678\) | −52.5628 | − | 11.3645i | −2.01866 | − | 0.436450i | ||||
\(679\) | 6.41473i | 0.246175i | ||||||||
\(680\) | 21.3114i | 0.817256i | ||||||||
\(681\) | −1.92455 | + | 8.90138i | −0.0737488 | + | 0.341102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.2946i | 1.58009i | 0.613047 | + | 0.790046i | \(0.289944\pi\) | ||||
−0.613047 | + | 0.790046i | \(0.710056\pi\) | |||||||
\(684\) | −11.3293 | + | 24.9754i | −0.433188 | + | 0.954957i | ||||
\(685\) | −22.1051 | −0.844593 | ||||||||
\(686\) | 40.6304i | 1.55128i | ||||||||
\(687\) | 2.02628 | − | 9.37191i | 0.0773074 | − | 0.357561i | ||||
\(688\) | 10.4543i | 0.398566i | ||||||||
\(689\) | −23.7698 | −0.905558 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.58846 | 0.0984696 | 0.0492348 | − | 0.998787i | \(-0.484322\pi\) | ||||
0.0492348 | + | 0.998787i | \(0.484322\pi\) | |||||||
\(692\) | −42.2817 | −1.60731 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.07180 | −0.116604 | ||||||||
\(695\) | −6.41516 | −0.243341 | ||||||||
\(696\) | 8.24167 | − | 38.1192i | 0.312400 | − | 1.44491i | ||||
\(697\) | −29.7846 | −1.12817 | ||||||||
\(698\) | − | 48.6415i | − | 1.84111i | ||||||
\(699\) | −1.98747 | + | 9.19239i | −0.0751728 | + | 0.347688i | ||||
\(700\) | 36.5665i | 1.38208i | ||||||||
\(701\) | −19.9207 | −0.752395 | −0.376197 | − | 0.926540i | \(-0.622769\pi\) | ||||
−0.376197 | + | 0.926540i | \(0.622769\pi\) | |||||||
\(702\) | −33.4186 | − | 24.8188i | −1.26130 | − | 0.936727i | ||||
\(703\) | 25.6317i | 0.966718i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.53590 | + | 7.10381i | −0.0578453 | + | 0.267545i | ||||
\(706\) | 22.9420i | 0.863433i | ||||||||
\(707\) | − | 1.32829i | − | 0.0499556i | ||||||
\(708\) | −79.8372 | − | 17.2614i | −3.00046 | − | 0.648724i | ||||
\(709\) | 39.3205 | 1.47671 | 0.738356 | − | 0.674411i | \(-0.235602\pi\) | ||||
0.738356 | + | 0.674411i | \(0.235602\pi\) | |||||||
\(710\) | 24.7551 | 0.929043 | ||||||||
\(711\) | 9.10706 | − | 20.0764i | 0.341541 | − | 0.752923i | ||||
\(712\) | − | 39.7367i | − | 1.48920i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −47.5396 | − | 10.2784i | −1.77913 | − | 0.384661i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 85.0677i | 3.17913i | ||||||||
\(717\) | 3.67720 | − | 17.0077i | 0.137328 | − | 0.635165i | ||||
\(718\) | −82.4974 | −3.07878 | ||||||||
\(719\) | − | 35.8511i | − | 1.33702i | −0.743703 | − | 0.668511i | \(-0.766932\pi\) | ||
0.743703 | − | 0.668511i | \(-0.233068\pi\) | |||||||
\(720\) | −3.78461 | + | 8.34312i | −0.141044 | + | 0.310930i | ||||
\(721\) | 36.0117i | 1.34114i | ||||||||
\(722\) | 31.1242 | 1.15832 | ||||||||
\(723\) | −6.36910 | − | 1.37705i | −0.236869 | − | 0.0512130i | ||||
\(724\) | 47.9808 | 1.78319 | ||||||||
\(725\) | 18.8096 | 0.698570 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9282 | −1.07289 | −0.536444 | − | 0.843936i | \(-0.680233\pi\) | ||||
−0.536444 | + | 0.843936i | \(0.680233\pi\) | |||||||
\(728\) | −39.2460 | −1.45455 | ||||||||
\(729\) | −7.80385 | − | 25.8476i | −0.289031 | − | 0.957320i | ||||
\(730\) | −24.0526 | −0.890225 | ||||||||
\(731\) | − | 17.5935i | − | 0.650719i | ||||||
\(732\) | −28.5581 | − | 6.17449i | −1.05554 | − | 0.228216i | ||||
\(733\) | 28.7004i | 1.06007i | 0.847975 | + | 0.530036i | \(0.177822\pi\) | ||||
−0.847975 | + | 0.530036i | \(0.822178\pi\) | |||||||
\(734\) | −57.1163 | −2.10820 | ||||||||
\(735\) | 2.09808 | + | 0.453620i | 0.0773887 | + | 0.0167320i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −46.9808 | − | 21.3114i | −1.72939 | − | 0.784484i | ||||
\(739\) | − | 22.5259i | − | 0.828628i | −0.910134 | − | 0.414314i | \(-0.864022\pi\) | ||
0.910134 | − | 0.414314i | \(-0.135978\pi\) | |||||||
\(740\) | 48.3984i | 1.77916i | ||||||||
\(741\) | 3.00000 | − | 13.8755i | 0.110208 | − | 0.509731i | ||||
\(742\) | −48.1051 | −1.76599 | ||||||||
\(743\) | −28.3863 | −1.04139 | −0.520695 | − | 0.853743i | \(-0.674327\pi\) | ||||
−0.520695 | + | 0.853743i | \(0.674327\pi\) | |||||||
\(744\) | 0.297729 | − | 1.37705i | 0.0109153 | − | 0.0504851i | ||||
\(745\) | − | 11.6555i | − | 0.427024i | ||||||
\(746\) | − | 23.0369i | − | 0.843442i | ||||||
\(747\) | 40.5290 | + | 18.3848i | 1.48288 | + | 0.672664i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 9.91451i | − | 0.362268i | ||||||
\(750\) | −42.5165 | − | 9.19239i | −1.55248 | − | 0.335659i | ||||
\(751\) | 4.87564 | 0.177915 | 0.0889574 | − | 0.996035i | \(-0.471647\pi\) | ||||
0.0889574 | + | 0.996035i | \(0.471647\pi\) | |||||||
\(752\) | − | 8.34312i | − | 0.304242i | ||||||
\(753\) | 14.5359 | + | 3.14277i | 0.529718 | + | 0.114529i | ||||
\(754\) | 43.4988i | 1.58413i | ||||||||
\(755\) | 20.4364 | 0.743757 | ||||||||
\(756\) | −44.0343 | − | 32.7028i | −1.60151 | − | 1.18939i | ||||
\(757\) | −6.66025 | −0.242071 | −0.121036 | − | 0.992648i | \(-0.538621\pi\) | ||||
−0.121036 | + | 0.992648i | \(0.538621\pi\) | |||||||
\(758\) | −73.2340 | −2.65998 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.5885 | −0.456631 | ||||||||
\(761\) | −28.9019 | −1.04769 | −0.523847 | − | 0.851812i | \(-0.675504\pi\) | ||||
−0.523847 | + | 0.851812i | \(0.675504\pi\) | |||||||
\(762\) | 58.4449 | + | 12.6362i | 2.11723 | + | 0.457762i | ||||
\(763\) | 30.2487 | 1.09508 | ||||||||
\(764\) | 9.25036i | 0.334666i | ||||||||
\(765\) | 6.36910 | − | 14.0406i | 0.230275 | − | 0.507639i | ||||
\(766\) | − | 22.7290i | − | 0.821230i | ||||||
\(767\) | 42.2817 | 1.52670 | ||||||||
\(768\) | −10.3660 | + | 47.9447i | −0.374052 | + | 1.73006i | ||||
\(769\) | − | 11.9329i | − | 0.430311i | −0.976580 | − | 0.215155i | \(-0.930974\pi\) | ||
0.976580 | − | 0.215155i | \(-0.0690258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.1506 | + | 8.46467i | 1.40998 | + | 0.304848i | ||||
\(772\) | 10.6945i | 0.384905i | ||||||||
\(773\) | 30.8939i | 1.11118i | 0.831458 | + | 0.555588i | \(0.187507\pi\) | ||||
−0.831458 | + | 0.555588i | \(0.812493\pi\) | |||||||
\(774\) | 12.5885 | − | 27.7511i | 0.452483 | − | 0.997492i | ||||
\(775\) | 0.679492 | 0.0244081 | ||||||||
\(776\) | 9.40479 | 0.337612 | ||||||||
\(777\) | −50.1057 | − | 10.8332i | −1.79753 | − | 0.388640i | ||||
\(778\) | 45.6709i | 1.63738i | ||||||||
\(779\) | − | 17.5935i | − | 0.630352i | ||||||
\(780\) | 5.66467 | − | 26.2001i | 0.202828 | − | 0.938115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.8221 | + | 22.6510i | −0.601173 | + | 0.809480i | ||||
\(784\) | −2.46410 | −0.0880036 | ||||||||
\(785\) | 14.2076i | 0.507092i | ||||||||
\(786\) | −11.8756 | + | 54.9270i | −0.423590 | + | 1.95918i | ||||
\(787\) | 45.5322i | 1.62305i | 0.584318 | + | 0.811524i | \(0.301362\pi\) | ||||
−0.584318 | + | 0.811524i | \(0.698638\pi\) | |||||||
\(788\) | 39.8875 | 1.42093 | ||||||||
\(789\) | −8.59138 | + | 39.7367i | −0.305861 | + | 1.41466i | ||||
\(790\) | 21.8038 | 0.775746 | ||||||||
\(791\) | 36.6799 | 1.30419 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1244 | 0.537082 | ||||||||
\(794\) | −50.7472 | −1.80095 | ||||||||
\(795\) | 3.22243 | − | 14.9043i | 0.114288 | − | 0.528602i | ||||
\(796\) | 28.5885 | 1.01329 | ||||||||
\(797\) | 15.3580i | 0.544007i | 0.962296 | + | 0.272003i | \(0.0876862\pi\) | ||||
−0.962296 | + | 0.272003i | \(0.912314\pi\) | |||||||
\(798\) | 6.07137 | − | 28.0812i | 0.214924 | − | 0.994064i | ||||
\(799\) | 14.0406i | 0.496721i | ||||||||
\(800\) | −8.29365 | −0.293225 | ||||||||
\(801\) | −11.8756 | + | 26.1797i | −0.419605 | + | 0.925014i | ||||
\(802\) | − | 2.96713i | − | 0.104773i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.73205 | − | 12.6362i | 0.0963520 | − | 0.445646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.57139i | 0.0553497i | ||||||||
\(807\) | −27.6865 | − | 5.98604i | −0.974612 | − | 0.210719i | ||||
\(808\) | −1.94744 | −0.0685107 | ||||||||
\(809\) | −51.8583 | −1.82324 | −0.911621 | − | 0.411032i | \(-0.865168\pi\) | ||||
−0.911621 | + | 0.411032i | \(0.865168\pi\) | |||||||
\(810\) | 20.0926 | − | 17.5897i | 0.705982 | − | 0.618040i | ||||
\(811\) | − | 26.0106i | − | 0.913357i | −0.889632 | − | 0.456679i | \(-0.849039\pi\) | ||
0.889632 | − | 0.456679i | \(-0.150961\pi\) | |||||||
\(812\) | 57.3167i | 2.01142i | ||||||||
\(813\) | 15.4762 | + | 3.34607i | 0.542773 | + | 0.117352i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.3580i | − | 0.537966i | ||||||
\(816\) | −3.74012 | + | 17.2987i | −0.130930 | + | 0.605577i | ||||
\(817\) | 10.3923 | 0.363581 | ||||||||
\(818\) | 79.5353i | 2.78089i | ||||||||
\(819\) | 25.8564 | + | 11.7290i | 0.903496 | + | 0.409844i | ||||
\(820\) | − | 33.2204i | − | 1.16011i | ||||||
\(821\) | 21.8453 | 0.762405 | 0.381202 | − | 0.924492i | \(-0.375510\pi\) | ||||
0.381202 | + | 0.924492i | \(0.375510\pi\) | |||||||
\(822\) | −72.2947 | − | 15.6307i | −2.52157 | − | 0.545183i | ||||
\(823\) | 32.8756 | 1.14597 | 0.572986 | − | 0.819565i | \(-0.305785\pi\) | ||||
0.572986 | + | 0.819565i | \(0.305785\pi\) | |||||||
\(824\) | 52.7976 | 1.83929 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 85.5692 | 2.97733 | ||||||||
\(827\) | 18.8096 | 0.654073 | 0.327036 | − | 0.945012i | \(-0.393950\pi\) | ||||
0.327036 | + | 0.945012i | \(0.393950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5885 | 0.680335 | 0.340168 | − | 0.940365i | \(-0.389516\pi\) | ||||
0.340168 | + | 0.940365i | \(0.389516\pi\) | |||||||
\(830\) | 44.0163i | 1.52783i | ||||||||
\(831\) | 10.6249 | + | 2.29719i | 0.368574 | + | 0.0796885i | ||||
\(832\) | − | 35.6699i | − | 1.23663i | ||||||
\(833\) | 4.14682 | 0.143679 | ||||||||
\(834\) | −20.9808 | − | 4.53620i | −0.726504 | − | 0.157076i | ||||
\(835\) | − | 6.51626i | − | 0.225505i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.607695 | + | 0.818262i | −0.0210050 | + | 0.0282833i | ||||
\(838\) | 26.4911i | 0.915121i | ||||||||
\(839\) | 18.7438i | 0.647109i | 0.946210 | + | 0.323554i | \(0.104878\pi\) | ||||
−0.946210 | + | 0.323554i | \(0.895122\pi\) | |||||||
\(840\) | 5.32051 | − | 24.6083i | 0.183575 | − | 0.849068i | ||||
\(841\) | 0.483340 | 0.0166669 | ||||||||
\(842\) | −45.9589 | −1.58385 | ||||||||
\(843\) | 0.297729 | − | 1.37705i | 0.0102543 | − | 0.0474281i | ||||
\(844\) | − | 7.07107i | − | 0.243396i | ||||||
\(845\) | − | 2.23553i | − | 0.0769047i | ||||||
\(846\) | −10.0463 | + | 22.1469i | −0.345399 | + | 0.761428i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.5045i | 0.601107i | ||||||||
\(849\) | 11.5012 | + | 2.48665i | 0.394721 | + | 0.0853418i | ||||
\(850\) | −34.3923 | −1.17965 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 52.7128 | + | 11.3969i | 1.80591 | + | 0.390452i | ||||
\(853\) | − | 42.5651i | − | 1.45740i | −0.684832 | − | 0.728701i | \(-0.740125\pi\) | ||
0.684832 | − | 0.728701i | \(-0.259875\pi\) | |||||||
\(854\) | 30.6085 | 1.04740 | ||||||||
\(855\) | 8.29365 | + | 3.76217i | 0.283637 | + | 0.128663i | ||||
\(856\) | −14.5359 | −0.496827 | ||||||||
\(857\) | −56.3029 | −1.92327 | −0.961635 | − | 0.274332i | \(-0.911543\pi\) | ||||
−0.961635 | + | 0.274332i | \(0.911543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.12436 | 0.0383625 | 0.0191813 | − | 0.999816i | \(-0.493894\pi\) | ||||
0.0191813 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(860\) | 19.6230 | 0.669138 | ||||||||
\(861\) | 34.3923 | + | 7.43588i | 1.17209 | + | 0.253414i | ||||
\(862\) | 50.0526 | 1.70480 | ||||||||
\(863\) | − | 28.9014i | − | 0.983816i | −0.870647 | − | 0.491908i | \(-0.836300\pi\) | ||
0.870647 | − | 0.491908i | \(-0.163700\pi\) | |||||||
\(864\) | 7.41732 | − | 9.98743i | 0.252342 | − | 0.339779i | ||||
\(865\) | 14.0406i | 0.477395i | ||||||||
\(866\) | 31.2500 | 1.06192 | ||||||||
\(867\) | 0.0717968 | − | 0.332073i | 0.00243835 | − | 0.0112778i | ||||
\(868\) | 2.07055i | 0.0702791i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −27.2750 | − | 5.89706i | −0.924709 | − | 0.199929i | ||||
\(871\) | 6.69213i | 0.226754i | ||||||||
\(872\) | − | 44.3484i | − | 1.50182i | ||||||
\(873\) | −6.19615 | − | 2.81070i | −0.209708 | − | 0.0951278i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.6693 | 1.00300 | ||||||||
\(876\) | −51.2168 | − | 11.0735i | −1.73046 | − | 0.374138i | ||||
\(877\) | − | 28.7747i | − | 0.971653i | −0.874055 | − | 0.485826i | \(-0.838519\pi\) | ||
0.874055 | − | 0.485826i | \(-0.161481\pi\) | |||||||
\(878\) | − | 20.0721i | − | 0.677401i | ||||||
\(879\) | 11.9079 | − | 55.0764i | 0.401645 | − | 1.85768i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6325i | 0.459289i | 0.973275 | + | 0.229644i | \(0.0737563\pi\) | ||||
−0.973275 | + | 0.229644i | \(0.926244\pi\) | |||||||
\(882\) | 6.54099 | + | 2.96713i | 0.220247 | + | 0.0999084i | ||||
\(883\) | −11.4641 | −0.385798 | −0.192899 | − | 0.981219i | \(-0.561789\pi\) | ||||
−0.192899 | + | 0.981219i | \(0.561789\pi\) | |||||||
\(884\) | − | 51.7842i | − | 1.74169i | ||||||
\(885\) | −5.73205 | + | 26.5118i | −0.192681 | + | 0.891184i | ||||
\(886\) | − | 61.0886i | − | 2.05231i | ||||||
\(887\) | 45.3173 | 1.52161 | 0.760804 | − | 0.648982i | \(-0.224805\pi\) | ||||
0.760804 | + | 0.648982i | \(0.224805\pi\) | |||||||
\(888\) | −15.8829 | + | 73.4611i | −0.532994 | + | 2.46519i | ||||
\(889\) | −40.7846 | −1.36787 | ||||||||
\(890\) | −28.4323 | −0.953053 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48.2487 | 1.61549 | ||||||||
\(893\) | −8.29365 | −0.277536 | ||||||||
\(894\) | 8.24167 | − | 38.1192i | 0.275643 | − | 1.27490i | ||||
\(895\) | 28.2487 | 0.944250 | ||||||||
\(896\) | − | 58.6450i | − | 1.95919i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 96.4811i | 3.21962i | ||||||||
\(899\) | 1.06508 | 0.0355224 | ||||||||
\(900\) | −35.3205 | − | 16.0221i | −1.17735 | − | 0.534070i | ||||
\(901\) | − | 29.4582i | − | 0.981397i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.39230 | + | 20.3152i | −0.146167 | + | 0.676048i | ||||
\(904\) | − | 53.7773i | − | 1.78861i | ||||||
\(905\) | − | 15.9331i | − | 0.529635i | ||||||
\(906\) | 66.8372 | + | 14.4507i | 2.22052 | + | 0.480093i | ||||
\(907\) | −26.4449 | −0.878087 | −0.439044 | − | 0.898466i | \(-0.644683\pi\) | ||||
−0.439044 | + | 0.898466i | \(0.644683\pi\) | |||||||
\(908\) | −19.6230 | −0.651212 | ||||||||
\(909\) | 1.28303 | + | 0.582009i | 0.0425555 | + | 0.0193040i | ||||
\(910\) | 28.0812i | 0.930883i | ||||||||
\(911\) | 31.8011i | 1.05362i | 0.849984 | + | 0.526809i | \(0.176612\pi\) | ||||
−0.849984 | + | 0.526809i | \(0.823388\pi\) | |||||||
\(912\) | −10.2182 | − | 2.20925i | −0.338358 | − | 0.0731557i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 44.1053i | 1.45887i | ||||||||
\(915\) | −2.05038 | + | 9.48339i | −0.0677836 | + | 0.313511i | ||||
\(916\) | 20.6603 | 0.682634 | ||||||||
\(917\) | − | 38.3297i | − | 1.26576i | ||||||
\(918\) | 30.7583 | − | 41.4161i | 1.01518 | − | 1.36694i | ||||
\(919\) | − | 39.0160i | − | 1.28702i | −0.765438 | − | 0.643509i | \(-0.777478\pi\) | ||
0.765438 | − | 0.643509i | \(-0.222522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 52.7976 | + | 11.4152i | 1.73974 | + | 0.376145i | ||||
\(922\) | −6.85641 | −0.225804 | ||||||||
\(923\) | −27.9166 | −0.918887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2487 | −1.19185 | ||||||||
\(926\) | −3.03569 | −0.0997588 | ||||||||
\(927\) | −34.7846 | − | 15.7790i | −1.14248 | − | 0.518251i | ||||
\(928\) | −13.0000 | −0.426746 | ||||||||
\(929\) | 31.9552i | 1.04842i | 0.851590 | + | 0.524208i | \(0.175639\pi\) | ||||
−0.851590 | + | 0.524208i | \(0.824361\pi\) | |||||||
\(930\) | −0.985303 | − | 0.213030i | −0.0323094 | − | 0.00698554i | ||||
\(931\) | 2.44949i | 0.0802788i | ||||||||
\(932\) | −20.2645 | −0.663786 | ||||||||
\(933\) | 1.12436 | + | 0.243094i | 0.0368098 | + | 0.00795855i | ||||
\(934\) | 46.4660i | 1.52041i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.1962 | − | 37.9087i | 0.562074 | − | 1.23908i | ||||
\(937\) | 28.5988i | 0.934283i | 0.884182 | + | 0.467142i | \(0.154716\pi\) | ||||
−0.884182 | + | 0.467142i | \(0.845284\pi\) | |||||||
\(938\) | 13.5435i | 0.442210i | ||||||||
\(939\) | −2.70577 | + | 12.5147i | −0.0882995 | + | 0.408401i | ||||
\(940\) | −15.6603 | −0.510781 | ||||||||
\(941\) | −2.05038 | −0.0668406 | −0.0334203 | − | 0.999441i | \(-0.510640\pi\) | ||||
−0.0334203 | + | 0.999441i | \(0.510640\pi\) | |||||||
\(942\) | −10.0463 | + | 46.4660i | −0.327326 | + | 1.51394i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 31.1370i | − | 1.01342i | ||||||
\(945\) | −10.8597 | + | 14.6226i | −0.353266 | + | 0.475674i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.2297i | − | 0.982334i | −0.871065 | − | 0.491167i | \(-0.836571\pi\) | ||
0.871065 | − | 0.491167i | \(-0.163429\pi\) | |||||||
\(948\) | 46.4285 | + | 10.0382i | 1.50793 | + | 0.326025i | ||||
\(949\) | 27.1244 | 0.880494 | ||||||||
\(950\) | − | 20.3152i | − | 0.659112i | ||||||
\(951\) | −41.6603 | − | 9.00727i | −1.35093 | − | 0.292081i | ||||
\(952\) | − | 48.6381i | − | 1.57637i | ||||||
\(953\) | −55.0659 | −1.78376 | −0.891880 | − | 0.452272i | \(-0.850614\pi\) | ||||
−0.891880 | + | 0.452272i | \(0.850614\pi\) | |||||||
\(954\) | 21.0779 | − | 46.4660i | 0.682423 | − | 1.50439i | ||||
\(955\) | 3.07180 | 0.0994010 | ||||||||
\(956\) | 37.4933 | 1.21262 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.6603 | 0.505960 | ||||||||
\(959\) | 50.4495 | 1.62910 | ||||||||
\(960\) | 22.3660 | + | 4.83571i | 0.721860 | + | 0.156072i | ||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | − | 83.8284i | − | 2.70274i | ||||||
\(963\) | 9.57668 | + | 4.34418i | 0.308604 | + | 0.139989i | ||||
\(964\) | − | 14.0406i | − | 0.452217i | ||||||
\(965\) | 3.55137 | 0.114323 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0518i | 1.44877i | 0.689397 | + | 0.724383i | \(0.257875\pi\) | ||||
−0.689397 | + | 0.724383i | \(0.742125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1962 | + | 3.71794i | 0.552420 | + | 0.119437i | ||||
\(970\) | − | 6.72930i | − | 0.216065i | ||||||
\(971\) | − | 7.43588i | − | 0.238629i | −0.992857 | − | 0.119314i | \(-0.961930\pi\) | ||
0.992857 | − | 0.119314i | \(-0.0380696\pi\) | |||||||
\(972\) | 50.8827 | − | 28.2047i | 1.63206 | − | 0.904666i | ||||
\(973\) | 14.6410 | 0.469369 | ||||||||
\(974\) | 79.4312 | 2.54514 | ||||||||
\(975\) | 19.6230 | + | 4.24264i | 0.628438 | + | 0.135873i | ||||
\(976\) | − | 11.1378i | − | 0.356514i | ||||||
\(977\) | 11.1538i | 0.356842i | 0.983954 | + | 0.178421i | \(0.0570990\pi\) | ||||
−0.983954 | + | 0.178421i | \(0.942901\pi\) | |||||||
\(978\) | 10.8597 | − | 50.2281i | 0.347255 | − | 1.60612i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.62518i | 0.147746i | ||||||||
\(981\) | −13.2539 | + | 29.2180i | −0.423164 | + | 0.932859i | ||||
\(982\) | −50.0526 | −1.59724 | ||||||||
\(983\) | − | 0.486189i | − | 0.0155070i | −0.999970 | − | 0.00775351i | \(-0.997532\pi\) | ||
0.999970 | − | 0.00775351i | \(-0.00246804\pi\) | |||||||
\(984\) | 10.9019 | − | 50.4234i | 0.347541 | − | 1.60744i | ||||
\(985\) | − | 13.2456i | − | 0.422039i | ||||||
\(986\) | −53.9087 | −1.71680 | ||||||||
\(987\) | 3.50531 | − | 16.2127i | 0.111575 | − | 0.516056i | ||||
\(988\) | 30.5885 | 0.973148 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8564 | 0.630760 | 0.315380 | − | 0.948966i | \(-0.397868\pi\) | ||||
0.315380 | + | 0.948966i | \(0.397868\pi\) | |||||||
\(992\) | −0.469622 | −0.0149105 | ||||||||
\(993\) | −0.143594 | + | 0.664146i | −0.00455680 | + | 0.0210760i | ||||
\(994\) | −56.4974 | −1.79199 | ||||||||
\(995\) | − | 9.49346i | − | 0.300963i | ||||||
\(996\) | −20.2645 | + | 93.7270i | −0.642105 | + | 2.96985i | ||||
\(997\) | − | 60.4694i | − | 1.91509i | −0.288291 | − | 0.957543i | \(-0.593087\pi\) | ||
0.288291 | − | 0.957543i | \(-0.406913\pi\) | |||||||
\(998\) | 61.7788 | 1.95557 | ||||||||
\(999\) | 32.4186 | − | 43.6516i | 1.02568 | − | 1.38108i |
(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 | 363.2.d.e.362.7 | yes | 8 | |
3.2 | odd | 2 | inner | 363.2.d.e.362.2 | yes | 8 | |
11.2 | odd | 10 | 363.2.f.i.161.7 | 32 | |||
11.3 | even | 5 | 363.2.f.i.233.8 | 32 | |||
11.4 | even | 5 | 363.2.f.i.215.7 | 32 | |||
11.5 | even | 5 | 363.2.f.i.239.2 | 32 | |||
11.6 | odd | 10 | 363.2.f.i.239.8 | 32 | |||
11.7 | odd | 10 | 363.2.f.i.215.1 | 32 | |||
11.8 | odd | 10 | 363.2.f.i.233.2 | 32 | |||
11.9 | even | 5 | 363.2.f.i.161.1 | 32 | |||
11.10 | odd | 2 | inner | 363.2.d.e.362.1 | ✓ | 8 | |
33.2 | even | 10 | 363.2.f.i.161.2 | 32 | |||
33.5 | odd | 10 | 363.2.f.i.239.7 | 32 | |||
33.8 | even | 10 | 363.2.f.i.233.7 | 32 | |||
33.14 | odd | 10 | 363.2.f.i.233.1 | 32 | |||
33.17 | even | 10 | 363.2.f.i.239.1 | 32 | |||
33.20 | odd | 10 | 363.2.f.i.161.8 | 32 | |||
33.26 | odd | 10 | 363.2.f.i.215.2 | 32 | |||
33.29 | even | 10 | 363.2.f.i.215.8 | 32 | |||
33.32 | even | 2 | inner | 363.2.d.e.362.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.e.362.1 | ✓ | 8 | 11.10 | odd | 2 | inner | |
363.2.d.e.362.2 | yes | 8 | 3.2 | odd | 2 | inner | |
363.2.d.e.362.7 | yes | 8 | 1.1 | even | 1 | trivial | |
363.2.d.e.362.8 | yes | 8 | 33.32 | even | 2 | inner | |
363.2.f.i.161.1 | 32 | 11.9 | even | 5 | |||
363.2.f.i.161.2 | 32 | 33.2 | even | 10 | |||
363.2.f.i.161.7 | 32 | 11.2 | odd | 10 | |||
363.2.f.i.161.8 | 32 | 33.20 | odd | 10 | |||
363.2.f.i.215.1 | 32 | 11.7 | odd | 10 | |||
363.2.f.i.215.2 | 32 | 33.26 | odd | 10 | |||
363.2.f.i.215.7 | 32 | 11.4 | even | 5 | |||
363.2.f.i.215.8 | 32 | 33.29 | even | 10 | |||
363.2.f.i.233.1 | 32 | 33.14 | odd | 10 | |||
363.2.f.i.233.2 | 32 | 11.8 | odd | 10 | |||
363.2.f.i.233.7 | 32 | 33.8 | even | 10 | |||
363.2.f.i.233.8 | 32 | 11.3 | even | 5 | |||
363.2.f.i.239.1 | 32 | 33.17 | even | 10 | |||
363.2.f.i.239.2 | 32 | 11.5 | even | 5 | |||
363.2.f.i.239.7 | 32 | 33.5 | odd | 10 | |||
363.2.f.i.239.8 | 32 | 11.6 | odd | 10 |