Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(71,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.71");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.e (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.17 | ||
Character | \(\chi\) | \(=\) | 252.71 |
Dual form | 252.4.e.a.71.18 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.614971 | − | 2.76076i | −0.217425 | − | 0.976077i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.24362 | + | 3.39558i | −0.905453 | + | 0.424447i | ||||
\(5\) | 2.97985i | 0.266526i | 0.991081 | + | 0.133263i | \(0.0425454\pi\) | ||||
−0.991081 | + | 0.133263i | \(0.957455\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 13.8290 | + | 17.9097i | 0.611161 | + | 0.791506i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.22665 | − | 1.83252i | 0.260150 | − | 0.0579494i | ||||
\(11\) | 14.5861 | 0.399806 | 0.199903 | − | 0.979816i | \(-0.435937\pi\) | ||||
0.199903 | + | 0.979816i | \(0.435937\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27.9716 | 0.596763 | 0.298381 | − | 0.954447i | \(-0.403553\pi\) | ||||
0.298381 | + | 0.954447i | \(0.403553\pi\) | |||||||
\(14\) | −19.3253 | + | 4.30480i | −0.368922 | + | 0.0821790i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 40.9401 | − | 49.1926i | 0.639689 | − | 0.768634i | ||||
\(17\) | 47.0690i | 0.671525i | 0.941947 | + | 0.335762i | \(0.108994\pi\) | ||||
−0.941947 | + | 0.335762i | \(0.891006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 148.649i | − | 1.79487i | −0.441151 | − | 0.897433i | \(-0.645430\pi\) | ||
0.441151 | − | 0.897433i | \(-0.354570\pi\) | |||||||
\(20\) | −10.1183 | − | 21.5849i | −0.113126 | − | 0.241326i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.97001 | − | 40.2687i | −0.0869279 | − | 0.390241i | ||||
\(23\) | −85.1221 | −0.771704 | −0.385852 | − | 0.922561i | \(-0.626092\pi\) | ||||
−0.385852 | + | 0.922561i | \(0.626092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 116.121 | 0.928964 | ||||||||
\(26\) | −17.2017 | − | 77.2228i | −0.129751 | − | 0.582486i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 23.7690 | + | 50.7053i | 0.160426 | + | 0.342229i | ||||
\(29\) | − | 197.212i | − | 1.26280i | −0.775455 | − | 0.631402i | \(-0.782480\pi\) | ||
0.775455 | − | 0.631402i | \(-0.217520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 213.574i | − | 1.23739i | −0.785631 | − | 0.618695i | \(-0.787662\pi\) | ||
0.785631 | − | 0.618695i | \(-0.212338\pi\) | |||||||
\(32\) | −160.986 | − | 82.7739i | −0.889330 | − | 0.457265i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 129.946 | − | 28.9461i | 0.655460 | − | 0.146006i | ||||
\(35\) | 20.8589 | 0.100737 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00048 | −0.0133318 | −0.00666589 | − | 0.999978i | \(-0.502122\pi\) | ||||
−0.00666589 | + | 0.999978i | \(0.502122\pi\) | |||||||
\(38\) | −410.385 | + | 91.4149i | −1.75193 | + | 0.390249i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −53.3683 | + | 41.2083i | −0.210957 | + | 0.162890i | ||||
\(41\) | − | 4.26768i | − | 0.0162561i | −0.999967 | − | 0.00812805i | \(-0.997413\pi\) | ||
0.999967 | − | 0.00812805i | \(-0.00258727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 261.825i | − | 0.928556i | −0.885689 | − | 0.464278i | \(-0.846314\pi\) | ||
0.885689 | − | 0.464278i | \(-0.153686\pi\) | |||||||
\(44\) | −105.656 | + | 49.5281i | −0.362005 | + | 0.169697i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 52.3476 | + | 235.002i | 0.167788 | + | 0.753242i | ||||
\(47\) | 96.0780 | 0.298179 | 0.149090 | − | 0.988824i | \(-0.452366\pi\) | ||||
0.149090 | + | 0.988824i | \(0.452366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −71.4108 | − | 320.581i | −0.201980 | − | 0.906740i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −202.615 | + | 94.9796i | −0.540340 | + | 0.253294i | ||||
\(53\) | 131.677i | 0.341268i | 0.985334 | + | 0.170634i | \(0.0545816\pi\) | ||||
−0.985334 | + | 0.170634i | \(0.945418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.4643i | 0.106559i | ||||||||
\(56\) | 125.368 | − | 96.8030i | 0.299161 | − | 0.230997i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −544.455 | + | 121.280i | −1.23259 | + | 0.274565i | ||||
\(59\) | −294.327 | −0.649460 | −0.324730 | − | 0.945807i | \(-0.605273\pi\) | ||||
−0.324730 | + | 0.945807i | \(0.605273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 134.782 | 0.282904 | 0.141452 | − | 0.989945i | \(-0.454823\pi\) | ||||
0.141452 | + | 0.989945i | \(0.454823\pi\) | |||||||
\(62\) | −589.628 | + | 131.342i | −1.20779 | + | 0.269040i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −129.517 | + | 495.348i | −0.252963 | + | 0.967476i | ||||
\(65\) | 83.3510i | 0.159053i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 148.648i | − | 0.271049i | −0.990774 | − | 0.135525i | \(-0.956728\pi\) | ||
0.990774 | − | 0.135525i | \(-0.0432720\pi\) | |||||||
\(68\) | −159.827 | − | 340.950i | −0.285027 | − | 0.608034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.8276 | − | 57.5866i | −0.0219028 | − | 0.0983273i | ||||
\(71\) | 796.550 | 1.33145 | 0.665726 | − | 0.746197i | \(-0.268122\pi\) | ||||
0.665726 | + | 0.746197i | \(0.268122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −163.335 | −0.261875 | −0.130938 | − | 0.991391i | \(-0.541799\pi\) | ||||
−0.130938 | + | 0.991391i | \(0.541799\pi\) | |||||||
\(74\) | 1.84521 | + | 8.28361i | 0.00289866 | + | 0.0130128i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 504.750 | + | 1076.76i | 0.761826 | + | 1.62517i | ||||
\(77\) | − | 102.102i | − | 0.151112i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1347.64i | − | 1.91925i | −0.281275 | − | 0.959627i | \(-0.590757\pi\) | ||
0.281275 | − | 0.959627i | \(-0.409243\pi\) | |||||||
\(80\) | 146.586 | + | 121.995i | 0.204861 | + | 0.170494i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.7821 | + | 2.62450i | −0.0158672 | + | 0.00353448i | ||||
\(83\) | 534.740 | 0.707173 | 0.353586 | − | 0.935402i | \(-0.384962\pi\) | ||||
0.353586 | + | 0.935402i | \(0.384962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −140.259 | −0.178979 | ||||||||
\(86\) | −722.836 | + | 161.015i | −0.906342 | + | 0.201891i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 201.711 | + | 261.233i | 0.244346 | + | 0.316449i | ||||
\(89\) | − | 398.405i | − | 0.474504i | −0.971448 | − | 0.237252i | \(-0.923753\pi\) | ||
0.971448 | − | 0.237252i | \(-0.0762466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 195.801i | − | 0.225555i | ||||||
\(92\) | 616.592 | − | 289.039i | 0.698741 | − | 0.327548i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −59.0852 | − | 265.249i | −0.0648316 | − | 0.291046i | ||||
\(95\) | 442.952 | 0.478378 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1711.36 | 1.79137 | 0.895684 | − | 0.444691i | \(-0.146686\pi\) | ||||
0.895684 | + | 0.444691i | \(0.146686\pi\) | |||||||
\(98\) | 30.1336 | + | 135.277i | 0.0310607 | + | 0.139440i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −841.133 | + | 394.296i | −0.841133 | + | 0.394296i | ||||
\(101\) | 1871.61i | 1.84388i | 0.387333 | + | 0.921940i | \(0.373396\pi\) | ||||
−0.387333 | + | 0.921940i | \(0.626604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8187i | 0.0113061i | 0.999984 | + | 0.00565306i | \(0.00179944\pi\) | ||||
−0.999984 | + | 0.00565306i | \(0.998201\pi\) | |||||||
\(104\) | 386.819 | + | 500.963i | 0.364718 | + | 0.472341i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 363.529 | − | 80.9775i | 0.333104 | − | 0.0742003i | ||||
\(107\) | 1350.29 | 1.21998 | 0.609990 | − | 0.792409i | \(-0.291173\pi\) | ||||
0.609990 | + | 0.792409i | \(0.291173\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −571.162 | −0.501903 | −0.250951 | − | 0.968000i | \(-0.580743\pi\) | ||||
−0.250951 | + | 0.968000i | \(0.580743\pi\) | |||||||
\(110\) | 119.994 | − | 26.7293i | 0.104009 | − | 0.0231685i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −344.348 | − | 286.581i | −0.290516 | − | 0.241780i | ||||
\(113\) | − | 967.624i | − | 0.805544i | −0.915300 | − | 0.402772i | \(-0.868047\pi\) | ||
0.915300 | − | 0.402772i | \(-0.131953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 253.651i | − | 0.205679i | ||||||
\(116\) | 669.649 | + | 1428.53i | 0.535994 | + | 1.14341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 181.003 | + | 812.567i | 0.141209 | + | 0.633923i | ||||
\(119\) | 329.483 | 0.253812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1118.25 | −0.840155 | ||||||||
\(122\) | −82.8873 | − | 372.102i | −0.0615104 | − | 0.276136i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 725.209 | + | 1547.05i | 0.525207 | + | 1.12040i | ||||
\(125\) | 718.502i | 0.514118i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 208.578i | − | 0.145734i | −0.997342 | − | 0.0728672i | \(-0.976785\pi\) | ||
0.997342 | − | 0.0728672i | \(-0.0232149\pi\) | |||||||
\(128\) | 1447.19 | + | 52.9421i | 0.999332 | + | 0.0365583i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 230.112 | − | 51.2584i | 0.155248 | − | 0.0345820i | ||||
\(131\) | 1680.47 | 1.12079 | 0.560393 | − | 0.828227i | \(-0.310650\pi\) | ||||
0.560393 | + | 0.828227i | \(0.310650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1040.54 | −0.678396 | ||||||||
\(134\) | −410.383 | + | 91.4145i | −0.264565 | + | 0.0589329i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −842.994 | + | 650.918i | −0.531516 | + | 0.410410i | ||||
\(137\) | 1504.86i | 0.938460i | 0.883076 | + | 0.469230i | \(0.155469\pi\) | ||||
−0.883076 | + | 0.469230i | \(0.844531\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1613.01i | 0.984273i | 0.870518 | + | 0.492136i | \(0.163784\pi\) | ||||
−0.870518 | + | 0.492136i | \(0.836216\pi\) | |||||||
\(140\) | −151.094 | + | 70.8281i | −0.0912128 | + | 0.0427576i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −489.855 | − | 2199.08i | −0.289491 | − | 1.29960i | ||||
\(143\) | 407.995 | 0.238589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 587.661 | 0.336570 | ||||||||
\(146\) | 100.446 | + | 450.929i | 0.0569382 | + | 0.255610i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 21.7343 | − | 10.1884i | 0.0120713 | − | 0.00565864i | ||||
\(149\) | − | 50.6741i | − | 0.0278616i | −0.999903 | − | 0.0139308i | \(-0.995566\pi\) | ||
0.999903 | − | 0.0139308i | \(-0.00443446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 99.3618i | − | 0.0535493i | −0.999641 | − | 0.0267747i | \(-0.991476\pi\) | ||
0.999641 | − | 0.0267747i | \(-0.00852366\pi\) | |||||||
\(152\) | 2662.27 | − | 2055.67i | 1.42065 | − | 1.09695i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −281.881 | + | 62.7901i | −0.147497 | + | 0.0328556i | ||||
\(155\) | 636.419 | 0.329796 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2638.39 | 1.34119 | 0.670593 | − | 0.741825i | \(-0.266040\pi\) | ||||
0.670593 | + | 0.741825i | \(0.266040\pi\) | |||||||
\(158\) | −3720.51 | + | 828.758i | −1.87334 | + | 0.417294i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 246.654 | − | 479.714i | 0.121873 | − | 0.237029i | ||||
\(161\) | 595.855i | 0.291677i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2611.58i | 1.25494i | 0.778642 | + | 0.627468i | \(0.215909\pi\) | ||||
−0.778642 | + | 0.627468i | \(0.784091\pi\) | |||||||
\(164\) | 14.4912 | + | 30.9135i | 0.00689986 | + | 0.0147191i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −328.850 | − | 1476.29i | −0.153757 | − | 0.690255i | ||||
\(167\) | −3438.19 | −1.59314 | −0.796572 | − | 0.604544i | \(-0.793355\pi\) | ||||
−0.796572 | + | 0.604544i | \(0.793355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1414.59 | −0.643874 | ||||||||
\(170\) | 86.2549 | + | 387.221i | 0.0389144 | + | 0.174697i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 889.047 | + | 1896.56i | 0.394123 | + | 0.840764i | ||||
\(173\) | − | 3976.76i | − | 1.74767i | −0.486219 | − | 0.873837i | \(-0.661624\pi\) | ||
0.486219 | − | 0.873837i | \(-0.338376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 812.844i | − | 0.351115i | ||||||
\(176\) | 597.155 | − | 717.526i | 0.255751 | − | 0.307304i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1099.90 | + | 245.007i | −0.463152 | + | 0.103169i | ||||
\(179\) | −3605.92 | −1.50569 | −0.752846 | − | 0.658197i | \(-0.771319\pi\) | ||||
−0.752846 | + | 0.658197i | \(0.771319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1160.80 | −0.476693 | −0.238346 | − | 0.971180i | \(-0.576605\pi\) | ||||
−0.238346 | + | 0.971180i | \(0.576605\pi\) | |||||||
\(182\) | −540.560 | + | 120.412i | −0.220159 | + | 0.0490413i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1177.15 | − | 1524.51i | −0.471635 | − | 0.610808i | ||||
\(185\) | − | 8.94097i | − | 0.00355326i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 686.552i | 0.268480i | ||||||||
\(188\) | −695.953 | + | 326.241i | −0.269987 | + | 0.126561i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −272.403 | − | 1222.88i | −0.104011 | − | 0.466934i | ||||
\(191\) | −4106.76 | −1.55578 | −0.777891 | − | 0.628399i | \(-0.783710\pi\) | ||||
−0.777891 | + | 0.628399i | \(0.783710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2388.95 | −0.890987 | −0.445494 | − | 0.895285i | \(-0.646972\pi\) | ||||
−0.445494 | + | 0.895285i | \(0.646972\pi\) | |||||||
\(194\) | −1052.44 | − | 4724.67i | −0.389488 | − | 1.74851i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 354.937 | − | 166.383i | 0.129350 | − | 0.0606353i | ||||
\(197\) | − | 3236.10i | − | 1.17037i | −0.810901 | − | 0.585184i | \(-0.801022\pi\) | ||
0.810901 | − | 0.585184i | \(-0.198978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3509.90i | 1.25030i | 0.780503 | + | 0.625152i | \(0.214963\pi\) | ||||
−0.780503 | + | 0.625152i | \(0.785037\pi\) | |||||||
\(200\) | 1605.83 | + | 2079.69i | 0.567747 | + | 0.735281i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5167.06 | − | 1150.98i | 1.79977 | − | 0.400906i | ||||
\(203\) | −1380.48 | −0.477295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.7170 | 0.00433267 | ||||||||
\(206\) | 32.6286 | − | 7.26816i | 0.0110357 | − | 0.00245824i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1145.16 | − | 1375.99i | 0.381743 | − | 0.458692i | ||||
\(209\) | − | 2168.21i | − | 0.717598i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 485.243i | 0.158320i | 0.996862 | + | 0.0791599i | \(0.0252238\pi\) | ||||
−0.996862 | + | 0.0791599i | \(0.974776\pi\) | |||||||
\(212\) | −447.119 | − | 953.818i | −0.144850 | − | 0.309002i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −830.392 | − | 3727.84i | −0.265254 | − | 1.19079i | ||||
\(215\) | 780.198 | 0.247484 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1495.02 | −0.467690 | ||||||||
\(218\) | 351.248 | + | 1576.84i | 0.109126 | + | 0.489896i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −147.586 | − | 314.839i | −0.0452285 | − | 0.0964837i | ||||
\(221\) | 1316.59i | 0.400741i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 96.8412i | − | 0.0290806i | −0.999894 | − | 0.0145403i | \(-0.995372\pi\) | ||
0.999894 | − | 0.0145403i | \(-0.00462848\pi\) | |||||||
\(224\) | −579.417 | + | 1126.90i | −0.172830 | + | 0.336135i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2671.38 | + | 595.061i | −0.786273 | + | 0.175145i | ||||
\(227\) | −3635.58 | −1.06300 | −0.531502 | − | 0.847057i | \(-0.678372\pi\) | ||||
−0.531502 | + | 0.847057i | \(0.678372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4587.11 | 1.32369 | 0.661845 | − | 0.749641i | \(-0.269774\pi\) | ||||
0.661845 | + | 0.749641i | \(0.269774\pi\) | |||||||
\(230\) | −700.270 | + | 155.988i | −0.200758 | + | 0.0447197i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3532.01 | − | 2727.24i | 0.999518 | − | 0.771778i | ||||
\(233\) | 4490.81i | 1.26267i | 0.775509 | + | 0.631336i | \(0.217493\pi\) | ||||
−0.775509 | + | 0.631336i | \(0.782507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 286.298i | 0.0794724i | ||||||||
\(236\) | 2131.99 | − | 999.411i | 0.588055 | − | 0.275661i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −202.623 | − | 909.625i | −0.0551852 | − | 0.247741i | ||||
\(239\) | −3218.42 | −0.871057 | −0.435528 | − | 0.900175i | \(-0.643438\pi\) | ||||
−0.435528 | + | 0.900175i | \(0.643438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2254.22 | 0.602520 | 0.301260 | − | 0.953542i | \(-0.402593\pi\) | ||||
0.301260 | + | 0.953542i | \(0.402593\pi\) | |||||||
\(242\) | 687.689 | + | 3087.21i | 0.182671 | + | 0.820056i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −976.313 | + | 457.665i | −0.256156 | + | 0.120078i | ||||
\(245\) | − | 146.013i | − | 0.0380751i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4157.95i | − | 1.07111i | ||||||
\(248\) | 3825.06 | − | 2953.52i | 0.979402 | − | 0.756245i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1983.61 | − | 441.858i | 0.501819 | − | 0.111782i | ||||
\(251\) | 3998.17 | 1.00543 | 0.502714 | − | 0.864453i | \(-0.332335\pi\) | ||||
0.502714 | + | 0.864453i | \(0.332335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1241.60 | −0.308532 | ||||||||
\(254\) | −575.834 | + | 128.269i | −0.142248 | + | 0.0316863i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −743.817 | − | 4027.90i | −0.181596 | − | 0.983373i | ||||
\(257\) | − | 3387.39i | − | 0.822177i | −0.911595 | − | 0.411088i | \(-0.865149\pi\) | ||
0.911595 | − | 0.411088i | \(-0.134851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.0033i | 0.00503894i | ||||||||
\(260\) | −283.025 | − | 603.763i | −0.0675094 | − | 0.144015i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1033.44 | − | 4639.37i | −0.243687 | − | 1.09397i | ||||
\(263\) | −3331.72 | −0.781151 | −0.390575 | − | 0.920571i | \(-0.627724\pi\) | ||||
−0.390575 | + | 0.920571i | \(0.627724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −392.377 | −0.0909567 | ||||||||
\(266\) | 639.905 | + | 2872.70i | 0.147500 | + | 0.662166i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 504.748 | + | 1076.75i | 0.115046 | + | 0.245422i | ||||
\(269\) | 5844.63i | 1.32473i | 0.749180 | + | 0.662367i | \(0.230448\pi\) | ||||
−0.749180 | + | 0.662367i | \(0.769552\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6710.76i | 1.50424i | 0.659025 | + | 0.752121i | \(0.270969\pi\) | ||||
−0.659025 | + | 0.752121i | \(0.729031\pi\) | |||||||
\(272\) | 2315.45 | + | 1927.01i | 0.516157 | + | 0.429567i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4154.57 | − | 925.447i | 0.916009 | − | 0.204045i | ||||
\(275\) | 1693.74 | 0.371405 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4400.29 | −0.954469 | −0.477235 | − | 0.878776i | \(-0.658361\pi\) | ||||
−0.477235 | + | 0.878776i | \(0.658361\pi\) | |||||||
\(278\) | 4453.14 | − | 991.956i | 0.960726 | − | 0.214006i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 288.458 | + | 373.578i | 0.0615667 | + | 0.0797341i | ||||
\(281\) | − | 4749.75i | − | 1.00835i | −0.863601 | − | 0.504175i | \(-0.831797\pi\) | ||
0.863601 | − | 0.504175i | \(-0.168203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1497.32i | 0.314510i | 0.987558 | + | 0.157255i | \(0.0502645\pi\) | ||||
−0.987558 | + | 0.157255i | \(0.949735\pi\) | |||||||
\(284\) | −5769.90 | + | 2704.75i | −1.20557 | + | 0.565131i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −250.905 | − | 1126.38i | −0.0518753 | − | 0.232881i | ||||
\(287\) | −29.8738 | −0.00614423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2697.51 | 0.549055 | ||||||||
\(290\) | −361.395 | − | 1622.39i | −0.0731787 | − | 0.328518i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1183.14 | − | 554.616i | 0.237116 | − | 0.111152i | ||||
\(293\) | − | 3651.08i | − | 0.727982i | −0.931403 | − | 0.363991i | \(-0.881414\pi\) | ||
0.931403 | − | 0.363991i | \(-0.118586\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 877.050i | − | 0.173098i | ||||||
\(296\) | −41.4936 | − | 53.7378i | −0.00814786 | − | 0.0105522i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −139.899 | + | 31.1631i | −0.0271951 | + | 0.00605781i | ||||
\(299\) | −2381.00 | −0.460524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1832.77 | −0.350961 | ||||||||
\(302\) | −274.314 | + | 61.1046i | −0.0522683 | + | 0.0116430i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7312.43 | − | 6085.71i | −1.37959 | − | 1.14816i | ||||
\(305\) | 401.631i | 0.0754011i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 210.827i | 0.0391940i | 0.999808 | + | 0.0195970i | \(0.00623832\pi\) | ||||
−0.999808 | + | 0.0195970i | \(0.993762\pi\) | |||||||
\(308\) | 346.697 | + | 739.592i | 0.0641393 | + | 0.136825i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −391.379 | − | 1757.00i | −0.0717060 | − | 0.321907i | ||||
\(311\) | −724.581 | −0.132113 | −0.0660566 | − | 0.997816i | \(-0.521042\pi\) | ||||
−0.0660566 | + | 0.997816i | \(0.521042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8805.01 | 1.59006 | 0.795030 | − | 0.606571i | \(-0.207455\pi\) | ||||
0.795030 | + | 0.606571i | \(0.207455\pi\) | |||||||
\(314\) | −1622.53 | − | 7283.96i | −0.291608 | − | 1.30910i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4576.01 | + | 9761.78i | 0.814622 | + | 1.73779i | ||||
\(317\) | 6348.48i | 1.12481i | 0.826860 | + | 0.562407i | \(0.190125\pi\) | ||||
−0.826860 | + | 0.562407i | \(0.809875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2876.55i | − | 0.504877i | ||||||
\(320\) | −1476.06 | − | 385.942i | −0.257857 | − | 0.0674213i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1645.01 | − | 366.433i | 0.284699 | − | 0.0634178i | ||||
\(323\) | 6996.77 | 1.20530 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3248.07 | 0.554371 | ||||||||
\(326\) | 7209.95 | − | 1606.05i | 1.22491 | − | 0.272855i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 76.4331 | − | 59.0178i | 0.0128668 | − | 0.00993510i | ||||
\(329\) | − | 672.546i | − | 0.112701i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5556.10i | 0.922631i | 0.887236 | + | 0.461315i | \(0.152622\pi\) | ||||
−0.887236 | + | 0.461315i | \(0.847378\pi\) | |||||||
\(332\) | −3873.45 | + | 1815.75i | −0.640312 | + | 0.300158i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2114.39 | + | 9492.02i | 0.346390 | + | 1.55503i | ||||
\(335\) | 442.950 | 0.0722416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3816.67 | −0.616936 | −0.308468 | − | 0.951235i | \(-0.599816\pi\) | ||||
−0.308468 | + | 0.951235i | \(0.599816\pi\) | |||||||
\(338\) | 869.933 | + | 3905.35i | 0.139994 | + | 0.628471i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1015.98 | − | 476.259i | 0.162057 | − | 0.0759670i | ||||
\(341\) | − | 3115.21i | − | 0.494716i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 4689.21 | − | 3620.78i | 0.734958 | − | 0.567498i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10978.9 | + | 2445.59i | −1.70586 | + | 0.379988i | ||||
\(347\) | 12314.6 | 1.90514 | 0.952571 | − | 0.304317i | \(-0.0984281\pi\) | ||||
0.952571 | + | 0.304317i | \(0.0984281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8216.49 | −1.26023 | −0.630113 | − | 0.776503i | \(-0.716991\pi\) | ||||
−0.630113 | + | 0.776503i | \(0.716991\pi\) | |||||||
\(350\) | −2244.07 | + | 499.875i | −0.342716 | + | 0.0763413i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2348.15 | − | 1207.35i | −0.355560 | − | 0.182817i | ||||
\(353\) | 9603.40i | 1.44798i | 0.689810 | + | 0.723990i | \(0.257694\pi\) | ||||
−0.689810 | + | 0.723990i | \(0.742306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2373.60i | 0.354866i | ||||||||
\(356\) | 1352.81 | + | 2885.89i | 0.201402 | + | 0.429640i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2217.53 | + | 9955.08i | 0.327375 | + | 1.46967i | ||||
\(359\) | −7618.71 | −1.12006 | −0.560028 | − | 0.828474i | \(-0.689210\pi\) | ||||
−0.560028 | + | 0.828474i | \(0.689210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15237.6 | −2.22154 | ||||||||
\(362\) | 713.856 | + | 3204.68i | 0.103645 | + | 0.465289i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 664.857 | + | 1418.31i | 0.0957363 | + | 0.204229i | ||||
\(365\) | − | 486.713i | − | 0.0697965i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7619.79i | − | 1.08379i | −0.840447 | − | 0.541894i | \(-0.817708\pi\) | ||
0.840447 | − | 0.541894i | \(-0.182292\pi\) | |||||||
\(368\) | −3484.91 | + | 4187.37i | −0.493650 | + | 0.593158i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.6839 | + | 5.49844i | −0.00346825 | + | 0.000772568i | ||||
\(371\) | 921.739 | 0.128987 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −102.877 | −0.0142809 | −0.00714045 | − | 0.999975i | \(-0.502273\pi\) | ||||
−0.00714045 | + | 0.999975i | \(0.502273\pi\) | |||||||
\(374\) | 1895.41 | − | 422.210i | 0.262057 | − | 0.0583742i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1328.66 | + | 1720.73i | 0.182236 | + | 0.236011i | ||||
\(377\) | − | 5516.33i | − | 0.753595i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10008.1i | 1.35641i | 0.734871 | + | 0.678207i | \(0.237243\pi\) | ||||
−0.734871 | + | 0.678207i | \(0.762757\pi\) | |||||||
\(380\) | −3208.57 | + | 1504.08i | −0.433148 | + | 0.203046i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2525.54 | + | 11337.8i | 0.338266 | + | 1.51856i | ||||
\(383\) | 6622.81 | 0.883576 | 0.441788 | − | 0.897119i | \(-0.354344\pi\) | ||||
0.441788 | + | 0.897119i | \(0.354344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 304.250 | 0.0402753 | ||||||||
\(386\) | 1469.14 | + | 6595.33i | 0.193723 | + | 0.869672i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12396.5 | + | 5811.07i | −1.62200 | + | 0.760341i | ||||
\(389\) | − | 10793.4i | − | 1.40681i | −0.710791 | − | 0.703403i | \(-0.751663\pi\) | ||
0.710791 | − | 0.703403i | \(-0.248337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4006.62i | − | 0.518218i | ||||||
\(392\) | −677.621 | − | 877.577i | −0.0873088 | − | 0.113072i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8934.10 | + | 1990.11i | −1.14237 | + | 0.254467i | ||||
\(395\) | 4015.75 | 0.511530 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4491.35 | 0.567795 | 0.283897 | − | 0.958855i | \(-0.408373\pi\) | ||||
0.283897 | + | 0.958855i | \(0.408373\pi\) | |||||||
\(398\) | 9690.01 | − | 2158.49i | 1.22039 | − | 0.271847i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4753.98 | − | 5712.27i | 0.594248 | − | 0.714033i | ||||
\(401\) | 14004.7i | 1.74404i | 0.489467 | + | 0.872022i | \(0.337191\pi\) | ||||
−0.489467 | + | 0.872022i | \(0.662809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5974.01i | − | 0.738428i | ||||||
\(404\) | −6355.19 | − | 13557.2i | −0.782630 | − | 1.66955i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 848.957 | + | 3811.19i | 0.103776 | + | 0.465877i | ||||
\(407\) | −43.7652 | −0.00533012 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14406.8 | 1.74173 | 0.870867 | − | 0.491519i | \(-0.163558\pi\) | ||||
0.870867 | + | 0.491519i | \(0.163558\pi\) | |||||||
\(410\) | −7.82061 | − | 35.1087i | −0.000942030 | − | 0.00422902i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −40.1313 | − | 85.6102i | −0.00479886 | − | 0.0102372i | ||||
\(413\) | 2060.29i | 0.245473i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1593.44i | 0.188480i | ||||||||
\(416\) | −4503.03 | − | 2315.31i | −0.530719 | − | 0.272879i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5985.90 | + | 1333.38i | −0.700431 | + | 0.156024i | ||||
\(419\) | 13240.1 | 1.54372 | 0.771862 | − | 0.635790i | \(-0.219326\pi\) | ||||
0.771862 | + | 0.635790i | \(0.219326\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4321.30 | 0.500255 | 0.250128 | − | 0.968213i | \(-0.419527\pi\) | ||||
0.250128 | + | 0.968213i | \(0.419527\pi\) | |||||||
\(422\) | 1339.64 | − | 298.410i | 0.154532 | − | 0.0344227i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2358.30 | + | 1820.96i | −0.270116 | + | 0.208570i | ||||
\(425\) | 5465.68i | 0.623822i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 943.477i | − | 0.106928i | ||||||
\(428\) | −9781.02 | + | 4585.03i | −1.10463 | + | 0.517817i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −479.799 | − | 2153.94i | −0.0538092 | − | 0.241564i | ||||
\(431\) | −1296.30 | −0.144874 | −0.0724371 | − | 0.997373i | \(-0.523078\pi\) | ||||
−0.0724371 | + | 0.997373i | \(0.523078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10543.7 | −1.17020 | −0.585101 | − | 0.810961i | \(-0.698945\pi\) | ||||
−0.585101 | + | 0.810961i | \(0.698945\pi\) | |||||||
\(434\) | 919.395 | + | 4127.40i | 0.101687 | + | 0.456501i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4137.28 | − | 1939.43i | 0.454449 | − | 0.213031i | ||||
\(437\) | 12653.3i | 1.38510i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13198.6i | − | 1.43493i | −0.696595 | − | 0.717465i | \(-0.745302\pi\) | ||
0.696595 | − | 0.717465i | \(-0.254698\pi\) | |||||||
\(440\) | −778.433 | + | 601.067i | −0.0843417 | + | 0.0651245i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3634.80 | − | 809.668i | 0.391154 | − | 0.0871311i | ||||
\(443\) | −2362.08 | −0.253331 | −0.126666 | − | 0.991945i | \(-0.540427\pi\) | ||||
−0.126666 | + | 0.991945i | \(0.540427\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1187.19 | 0.126467 | ||||||||
\(446\) | −267.355 | + | 59.5545i | −0.0283849 | + | 0.00632284i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3467.43 | + | 906.621i | 0.365671 | + | 0.0956112i | ||||
\(449\) | − | 12464.5i | − | 1.31010i | −0.755583 | − | 0.655052i | \(-0.772647\pi\) | ||
0.755583 | − | 0.655052i | \(-0.227353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 62.2487i | − | 0.00649928i | ||||||
\(452\) | 3285.64 | + | 7009.11i | 0.341911 | + | 0.729382i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2235.78 | + | 10037.0i | 0.231124 | + | 1.03757i | ||||
\(455\) | 583.457 | 0.0601162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14842.4 | 1.51925 | 0.759627 | − | 0.650359i | \(-0.225381\pi\) | ||||
0.759627 | + | 0.650359i | \(0.225381\pi\) | |||||||
\(458\) | −2820.94 | − | 12663.9i | −0.287803 | − | 1.29202i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 861.291 | + | 1837.35i | 0.0872998 | + | 0.186232i | ||||
\(461\) | − | 9687.52i | − | 0.978727i | −0.872080 | − | 0.489363i | \(-0.837229\pi\) | ||
0.872080 | − | 0.489363i | \(-0.162771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15024.8i | − | 1.50812i | −0.656803 | − | 0.754062i | \(-0.728092\pi\) | ||
0.656803 | − | 0.754062i | \(-0.271908\pi\) | |||||||
\(464\) | −9701.36 | − | 8073.88i | −0.970635 | − | 0.807802i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12398.1 | − | 2761.72i | 1.23246 | − | 0.274537i | ||||
\(467\) | 10567.3 | 1.04710 | 0.523549 | − | 0.851995i | \(-0.324608\pi\) | ||||
0.523549 | + | 0.851995i | \(0.324608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1040.54 | −0.102447 | ||||||||
\(470\) | 790.400 | − | 176.065i | 0.0775712 | − | 0.0172793i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4070.25 | − | 5271.32i | −0.396925 | − | 0.514051i | ||||
\(473\) | − | 3819.00i | − | 0.371242i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 17261.2i | − | 1.66737i | ||||||
\(476\) | −2386.65 | + | 1118.79i | −0.229815 | + | 0.107730i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1979.24 | + | 8885.31i | 0.189390 | + | 0.850219i | ||||
\(479\) | −18844.8 | −1.79758 | −0.898788 | − | 0.438384i | \(-0.855551\pi\) | ||||
−0.898788 | + | 0.438384i | \(0.855551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −83.9281 | −0.00795590 | ||||||||
\(482\) | −1386.28 | − | 6223.38i | −0.131003 | − | 0.588106i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8100.15 | − | 3797.09i | 0.760721 | − | 0.356602i | ||||
\(485\) | 5099.60i | 0.477446i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9562.33i | − | 0.889755i | −0.895591 | − | 0.444878i | \(-0.853247\pi\) | ||
0.895591 | − | 0.444878i | \(-0.146753\pi\) | |||||||
\(488\) | 1863.91 | + | 2413.92i | 0.172900 | + | 0.223920i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −403.106 | + | 89.7935i | −0.0371642 | + | 0.00827848i | ||||
\(491\) | 10643.7 | 0.978298 | 0.489149 | − | 0.872200i | \(-0.337307\pi\) | ||||
0.489149 | + | 0.872200i | \(0.337307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9282.58 | 0.848005 | ||||||||
\(494\) | −11479.1 | + | 2557.02i | −1.04548 | + | 0.232886i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10506.3 | − | 8743.76i | −0.951100 | − | 0.791545i | ||||
\(497\) | − | 5575.85i | − | 0.503241i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 7550.79i | − | 0.677394i | −0.940895 | − | 0.338697i | \(-0.890014\pi\) | ||
0.940895 | − | 0.338697i | \(-0.109986\pi\) | |||||||
\(500\) | −2439.73 | − | 5204.56i | −0.218216 | − | 0.465510i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2458.76 | − | 11038.0i | −0.218605 | − | 0.981374i | ||||
\(503\) | −1090.04 | −0.0966255 | −0.0483127 | − | 0.998832i | \(-0.515384\pi\) | ||||
−0.0483127 | + | 0.998832i | \(0.515384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5577.10 | −0.491441 | ||||||||
\(506\) | 763.546 | + | 3427.75i | 0.0670825 | + | 0.301151i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 708.242 | + | 1510.86i | 0.0618566 | + | 0.131956i | ||||
\(509\) | 7957.32i | 0.692931i | 0.938063 | + | 0.346465i | \(0.112618\pi\) | ||||
−0.938063 | + | 0.346465i | \(0.887382\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1143.34i | 0.0989795i | ||||||||
\(512\) | −10662.6 | + | 4530.54i | −0.920364 | + | 0.391062i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9351.77 | + | 2083.15i | −0.802508 | + | 0.178762i | ||||
\(515\) | −35.2179 | −0.00301337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1401.40 | 0.119214 | ||||||||
\(518\) | 57.9853 | − | 12.9165i | 0.00491839 | − | 0.00109559i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1492.79 | + | 1152.66i | −0.125891 | + | 0.0972068i | ||||
\(521\) | 6770.45i | 0.569326i | 0.958628 | + | 0.284663i | \(0.0918816\pi\) | ||||
−0.958628 | + | 0.284663i | \(0.908118\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9837.70i | 0.822510i | 0.911520 | + | 0.411255i | \(0.134909\pi\) | ||||
−0.911520 | + | 0.411255i | \(0.865091\pi\) | |||||||
\(524\) | −12172.7 | + | 5706.15i | −1.01482 | + | 0.475714i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2048.91 | + | 9198.09i | 0.169842 | + | 0.762463i | ||||
\(527\) | 10052.7 | 0.830938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4921.23 | −0.404474 | ||||||||
\(530\) | 241.301 | + | 1083.26i | 0.0197763 | + | 0.0887808i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7537.31 | − | 3533.25i | 0.614255 | − | 0.287943i | ||||
\(533\) | − | 119.374i | − | 0.00970103i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4023.67i | 0.325156i | ||||||||
\(536\) | 2662.25 | − | 2055.66i | 0.214537 | − | 0.165655i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16135.6 | − | 3594.28i | 1.29304 | − | 0.288030i | ||||
\(539\) | −714.717 | −0.0571151 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11900.7 | 0.945749 | 0.472874 | − | 0.881130i | \(-0.343216\pi\) | ||||
0.472874 | + | 0.881130i | \(0.343216\pi\) | |||||||
\(542\) | 18526.8 | − | 4126.92i | 1.46826 | − | 0.327060i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3896.09 | − | 7577.46i | 0.307065 | − | 0.597207i | ||||
\(545\) | − | 1701.98i | − | 0.133770i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4883.36i | − | 0.381714i | −0.981618 | − | 0.190857i | \(-0.938873\pi\) | ||
0.981618 | − | 0.190857i | \(-0.0611267\pi\) | |||||||
\(548\) | −5109.88 | − | 10900.7i | −0.398327 | − | 0.849731i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1041.60 | − | 4676.02i | −0.0807529 | − | 0.362520i | ||||
\(551\) | −29315.4 | −2.26657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9433.46 | −0.725410 | ||||||||
\(554\) | 2706.05 | + | 12148.2i | 0.207526 | + | 0.931636i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5477.11 | − | 11684.0i | −0.417772 | − | 0.891212i | ||||
\(557\) | 1481.08i | 0.112667i | 0.998412 | + | 0.0563334i | \(0.0179410\pi\) | ||||
−0.998412 | + | 0.0563334i | \(0.982059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7323.65i | − | 0.554128i | ||||||
\(560\) | 853.967 | − | 1026.10i | 0.0644405 | − | 0.0774300i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13112.9 | + | 2920.96i | −0.984228 | + | 0.219241i | ||||
\(563\) | 20443.6 | 1.53037 | 0.765183 | − | 0.643813i | \(-0.222649\pi\) | ||||
0.765183 | + | 0.643813i | \(0.222649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2883.37 | 0.214698 | ||||||||
\(566\) | 4133.74 | − | 920.808i | 0.306986 | − | 0.0683824i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11015.5 | + | 14266.0i | 0.813732 | + | 1.05385i | ||||
\(569\) | − | 17488.2i | − | 1.28848i | −0.764824 | − | 0.644240i | \(-0.777174\pi\) | ||
0.764824 | − | 0.644240i | \(-0.222826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6945.88i | 0.509065i | 0.967064 | + | 0.254532i | \(0.0819215\pi\) | ||||
−0.967064 | + | 0.254532i | \(0.918078\pi\) | |||||||
\(572\) | −2955.36 | + | 1385.38i | −0.216031 | + | 0.101269i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.3715 | + | 82.4744i | 0.00133591 | + | 0.00599724i | ||||
\(575\) | −9884.42 | −0.716885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24227.0 | 1.74797 | 0.873987 | − | 0.485949i | \(-0.161526\pi\) | ||||
0.873987 | + | 0.485949i | \(0.161526\pi\) | |||||||
\(578\) | −1658.89 | − | 7447.17i | −0.119378 | − | 0.535920i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4256.80 | + | 1995.45i | −0.304748 | + | 0.142856i | ||||
\(581\) | − | 3743.18i | − | 0.267286i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1920.65i | 0.136441i | ||||||||
\(584\) | −2258.76 | − | 2925.28i | −0.160048 | − | 0.207276i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10079.8 | + | 2245.31i | −0.710566 | + | 0.158281i | ||||
\(587\) | −15665.7 | −1.10152 | −0.550760 | − | 0.834663i | \(-0.685662\pi\) | ||||
−0.550760 | + | 0.834663i | \(0.685662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31747.7 | −2.22095 | ||||||||
\(590\) | −2421.33 | + | 539.360i | −0.168957 | + | 0.0376358i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −122.840 | + | 147.601i | −0.00852819 | + | 0.0102473i | ||||
\(593\) | − | 3668.32i | − | 0.254030i | −0.991901 | − | 0.127015i | \(-0.959460\pi\) | ||
0.991901 | − | 0.127015i | \(-0.0405397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 981.810i | 0.0676475i | ||||||||
\(596\) | 172.068 | + | 367.064i | 0.0118258 | + | 0.0252274i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1464.24 | + | 6573.37i | 0.100129 | + | 0.449507i | ||||
\(599\) | −11412.5 | −0.778469 | −0.389235 | − | 0.921139i | \(-0.627260\pi\) | ||||
−0.389235 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10557.7 | −0.716566 | −0.358283 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358283 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(602\) | 1127.10 | + | 5059.85i | 0.0763078 | + | 0.342565i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 337.391 | + | 719.739i | 0.0227289 | + | 0.0484864i | ||||
\(605\) | − | 3332.20i | − | 0.223923i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6370.55i | − | 0.425985i | −0.977054 | − | 0.212992i | \(-0.931679\pi\) | ||
0.977054 | − | 0.212992i | \(-0.0683209\pi\) | |||||||
\(608\) | −12304.3 | + | 23930.4i | −0.820730 | + | 1.59623i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1108.81 | − | 246.992i | 0.0735973 | − | 0.0163941i | ||||
\(611\) | 2687.45 | 0.177942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11921.8 | −0.785506 | −0.392753 | − | 0.919644i | \(-0.628477\pi\) | ||||
−0.392753 | + | 0.919644i | \(0.628477\pi\) | |||||||
\(614\) | 582.045 | − | 129.653i | 0.0382564 | − | 0.00852176i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1828.63 | − | 1411.98i | 0.119606 | − | 0.0923541i | ||||
\(617\) | 10885.0i | 0.710233i | 0.934822 | + | 0.355117i | \(0.115559\pi\) | ||||
−0.934822 | + | 0.355117i | \(0.884441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22866.9i | 1.48481i | 0.669949 | + | 0.742407i | \(0.266316\pi\) | ||||
−0.669949 | + | 0.742407i | \(0.733684\pi\) | |||||||
\(620\) | −4609.98 | + | 2161.01i | −0.298615 | + | 0.139981i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 445.596 | + | 2000.40i | 0.0287247 | + | 0.128953i | ||||
\(623\) | −2788.83 | −0.179345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12374.0 | 0.791938 | ||||||||
\(626\) | −5414.83 | − | 24308.5i | −0.345719 | − | 1.55202i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19111.5 | + | 8958.85i | −1.21438 | + | 0.569263i | ||||
\(629\) | − | 141.230i | − | 0.00895261i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 627.472i | 0.0395868i | 0.999804 | + | 0.0197934i | \(0.00630085\pi\) | ||||
−0.999804 | + | 0.0197934i | \(0.993699\pi\) | |||||||
\(632\) | 24135.8 | − | 18636.5i | 1.51910 | − | 1.17297i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17526.6 | − | 3904.13i | 1.09791 | − | 0.244563i | ||||
\(635\) | 621.530 | 0.0388420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1370.61 | −0.0852518 | ||||||||
\(638\) | −7941.46 | + | 1768.99i | −0.492799 | + | 0.109773i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −157.759 | + | 4312.39i | −0.00974373 | + | 0.266347i | ||||
\(641\) | − | 12854.0i | − | 0.792047i | −0.918240 | − | 0.396024i | \(-0.870390\pi\) | ||
0.918240 | − | 0.396024i | \(-0.129610\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31056.4i | 1.90473i | 0.304956 | + | 0.952366i | \(0.401358\pi\) | ||||
−0.304956 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(644\) | −2023.27 | − | 4316.15i | −0.123801 | − | 0.264099i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4302.81 | − | 19316.4i | −0.262062 | − | 1.17646i | ||||
\(647\) | −9340.79 | −0.567580 | −0.283790 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283790 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4293.07 | −0.259658 | ||||||||
\(650\) | −1997.47 | − | 8967.16i | −0.120534 | − | 0.541109i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8867.82 | − | 18917.3i | −0.532654 | − | 1.13629i | ||||
\(653\) | − | 4651.62i | − | 0.278763i | −0.990239 | − | 0.139381i | \(-0.955489\pi\) | ||
0.990239 | − | 0.139381i | \(-0.0445114\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5007.53i | 0.298718i | ||||||||
\(656\) | −209.938 | − | 174.719i | −0.0124950 | − | 0.0103988i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1856.74 | + | 413.597i | −0.110005 | + | 0.0245041i | ||||
\(659\) | −30458.7 | −1.80046 | −0.900231 | − | 0.435413i | \(-0.856602\pi\) | ||||
−0.900231 | + | 0.435413i | \(0.856602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22311.1 | 1.31286 | 0.656431 | − | 0.754386i | \(-0.272065\pi\) | ||||
0.656431 | + | 0.754386i | \(0.272065\pi\) | |||||||
\(662\) | 15339.1 | − | 3416.84i | 0.900559 | − | 0.200603i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7394.92 | + | 9577.05i | 0.432197 | + | 0.559732i | ||||
\(665\) | − | 3100.66i | − | 0.180810i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16787.1i | 0.974511i | ||||||||
\(668\) | 24904.9 | − | 11674.6i | 1.44252 | − | 0.676206i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −272.401 | − | 1222.88i | −0.0157071 | − | 0.0705133i | ||||
\(671\) | 1965.95 | 0.113107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12390.1 | −0.709661 | −0.354831 | − | 0.934931i | \(-0.615461\pi\) | ||||
−0.354831 | + | 0.934931i | \(0.615461\pi\) | |||||||
\(674\) | 2347.14 | + | 10536.9i | 0.134137 | + | 0.602177i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10246.8 | − | 4803.36i | 0.582998 | − | 0.273291i | ||||
\(677\) | 32115.6i | 1.82319i | 0.411084 | + | 0.911597i | \(0.365150\pi\) | ||||
−0.411084 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11979.5i | − | 0.677074i | ||||||
\(680\) | −1939.64 | − | 2511.99i | −0.109385 | − | 0.141663i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8600.36 | + | 1915.77i | −0.482881 | + | 0.107564i | ||||
\(683\) | 22387.2 | 1.25421 | 0.627104 | − | 0.778936i | \(-0.284240\pi\) | ||||
0.627104 | + | 0.778936i | \(0.284240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4484.26 | −0.250124 | ||||||||
\(686\) | 946.942 | − | 210.935i | 0.0527032 | − | 0.0117399i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12879.8 | − | 10719.1i | −0.713720 | − | 0.593987i | ||||
\(689\) | 3683.21i | 0.203656i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18455.0i | 1.01601i | 0.861354 | + | 0.508005i | \(0.169617\pi\) | ||||
−0.861354 | + | 0.508005i | \(0.830383\pi\) | |||||||
\(692\) | 13503.4 | + | 28806.1i | 0.741795 | + | 1.58244i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7573.14 | − | 33997.8i | −0.414226 | − | 1.85957i | ||||
\(695\) | −4806.53 | −0.262334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 200.876 | 0.0109164 | ||||||||
\(698\) | 5052.91 | + | 22683.8i | 0.274005 | + | 1.23008i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2760.07 | + | 5887.93i | 0.149030 | + | 0.317918i | ||||
\(701\) | − | 19758.3i | − | 1.06457i | −0.846566 | − | 0.532283i | \(-0.821334\pi\) | ||
0.846566 | − | 0.532283i | \(-0.178666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 446.019i | 0.0239287i | ||||||||
\(704\) | −1889.15 | + | 7225.17i | −0.101136 | + | 0.386803i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26512.7 | − | 5905.81i | 1.41334 | − | 0.314827i | ||||
\(707\) | 13101.2 | 0.696921 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5354.63 | −0.283635 | −0.141818 | − | 0.989893i | \(-0.545295\pi\) | ||||
−0.141818 | + | 0.989893i | \(0.545295\pi\) | |||||||
\(710\) | 6552.94 | − | 1459.69i | 0.346376 | − | 0.0771568i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7135.32 | − | 5509.54i | 0.375572 | − | 0.289998i | ||||
\(713\) | 18179.9i | 0.954899i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1215.76i | 0.0635902i | ||||||||
\(716\) | 26119.9 | − | 12244.2i | 1.36333 | − | 0.639087i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4685.29 | + | 21033.5i | 0.243528 | + | 1.09326i | ||||
\(719\) | 6327.40 | 0.328195 | 0.164097 | − | 0.986444i | \(-0.447529\pi\) | ||||
0.164097 | + | 0.986444i | \(0.447529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 82.7309 | 0.00427331 | ||||||||
\(722\) | 9370.67 | + | 42067.3i | 0.483019 | + | 2.16840i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8408.37 | − | 3941.58i | 0.431622 | − | 0.202331i | ||||
\(725\) | − | 22900.4i | − | 1.17310i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17148.8i | 0.874846i | 0.899256 | + | 0.437423i | \(0.144109\pi\) | ||||
−0.899256 | + | 0.437423i | \(0.855891\pi\) | |||||||
\(728\) | 3506.74 | − | 2707.73i | 0.178528 | − | 0.137851i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1343.70 | + | 299.314i | −0.0681267 | + | 0.0151755i | ||||
\(731\) | 12323.8 | 0.623548 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14960.0 | −0.753832 | −0.376916 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376916 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(734\) | −21036.4 | + | 4685.95i | −1.05786 | + | 0.235643i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13703.5 | + | 7045.89i | 0.686299 | + | 0.352873i | ||||
\(737\) | − | 2168.20i | − | 0.108367i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11540.8i | 0.574470i | 0.957860 | + | 0.287235i | \(0.0927361\pi\) | ||||
−0.957860 | + | 0.287235i | \(0.907264\pi\) | |||||||
\(740\) | 30.3598 | + | 64.7650i | 0.00150817 | + | 0.00321731i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −566.843 | − | 2544.70i | −0.0280451 | − | 0.125902i | ||||
\(743\) | 22310.2 | 1.10159 | 0.550795 | − | 0.834640i | \(-0.314325\pi\) | ||||
0.550795 | + | 0.834640i | \(0.314325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 151.001 | 0.00742583 | ||||||||
\(746\) | 63.2665 | + | 284.019i | 0.00310503 | + | 0.0139393i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2331.24 | − | 4973.12i | −0.113955 | − | 0.243096i | ||||
\(749\) | − | 9452.06i | − | 0.461109i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21276.7i | 1.03382i | 0.856040 | + | 0.516909i | \(0.172917\pi\) | ||||
−0.856040 | + | 0.516909i | \(0.827083\pi\) | |||||||
\(752\) | 3933.44 | − | 4726.33i | 0.190742 | − | 0.229191i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15229.3 | + | 3392.38i | −0.735567 | + | 0.163850i | ||||
\(755\) | 296.083 | 0.0142723 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18995.8 | −0.912042 | −0.456021 | − | 0.889969i | \(-0.650726\pi\) | ||||
−0.456021 | + | 0.889969i | \(0.650726\pi\) | |||||||
\(758\) | 27629.9 | − | 6154.68i | 1.32396 | − | 0.294918i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6125.58 | + | 7933.15i | 0.292366 | + | 0.378639i | ||||
\(761\) | 24525.2i | 1.16825i | 0.811664 | + | 0.584124i | \(0.198562\pi\) | ||||
−0.811664 | + | 0.584124i | \(0.801438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3998.13i | 0.189701i | ||||||||
\(764\) | 29747.8 | − | 13944.8i | 1.40869 | − | 0.660348i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4072.84 | − | 18284.0i | −0.192112 | − | 0.862438i | ||||
\(767\) | −8232.79 | −0.387573 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12318.1 | 0.577636 | 0.288818 | − | 0.957384i | \(-0.406738\pi\) | ||||
0.288818 | + | 0.957384i | \(0.406738\pi\) | |||||||
\(770\) | −187.105 | − | 839.961i | −0.00875687 | − | 0.0393118i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17304.7 | − | 8111.88i | 0.806747 | − | 0.378177i | ||||
\(773\) | 29609.2i | 1.37771i | 0.724901 | + | 0.688853i | \(0.241886\pi\) | ||||
−0.724901 | + | 0.688853i | \(0.758114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 24800.4i | − | 1.14949i | ||||||
\(776\) | 23666.5 | + | 30650.1i | 1.09482 | + | 1.41788i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29798.0 | + | 6637.64i | −1.37315 | + | 0.305875i | ||||
\(779\) | −634.387 | −0.0291775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11618.5 | 0.532322 | ||||||||
\(782\) | −11061.3 | + | 2463.95i | −0.505821 | + | 0.112674i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2006.06 | + | 2410.44i | −0.0913841 | + | 0.109805i | ||||
\(785\) | 7861.99i | 0.357461i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23458.7i | 1.06253i | 0.847206 | + | 0.531265i | \(0.178283\pi\) | ||||
−0.847206 | + | 0.531265i | \(0.821717\pi\) | |||||||
\(788\) | 10988.4 | + | 23441.1i | 0.496759 | + | 1.05971i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2469.57 | − | 11086.5i | −0.111220 | − | 0.499293i | ||||
\(791\) | −6773.37 | −0.304467 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3770.08 | 0.168826 | ||||||||
\(794\) | −2762.05 | − | 12399.6i | −0.123453 | − | 0.554211i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11918.2 | − | 25424.4i | −0.530688 | − | 1.13209i | ||||
\(797\) | 11962.9i | 0.531680i | 0.964017 | + | 0.265840i | \(0.0856492\pi\) | ||||
−0.964017 | + | 0.265840i | \(0.914351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4522.30i | 0.200235i | ||||||||
\(800\) | −18693.8 | − | 9611.74i | −0.826156 | − | 0.424783i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38663.7 | − | 8612.49i | 1.70232 | − | 0.379199i | ||||
\(803\) | −2382.41 | −0.104699 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1775.56 | −0.0777393 | ||||||||
\(806\) | −16492.8 | + | 3673.84i | −0.720763 | + | 0.160553i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33520.0 | + | 25882.5i | −1.45944 | + | 1.12691i | ||||
\(809\) | 3777.90i | 0.164183i | 0.996625 | + | 0.0820914i | \(0.0261600\pi\) | ||||
−0.996625 | + | 0.0820914i | \(0.973840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 133.384i | 0.00577527i | 0.999996 | + | 0.00288763i | \(0.000919164\pi\) | ||||
−0.999996 | + | 0.00288763i | \(0.999081\pi\) | |||||||
\(812\) | 9999.70 | − | 4687.54i | 0.432168 | − | 0.202587i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.9143 | + | 120.825i | 0.00115890 | + | 0.00520261i | ||||
\(815\) | −7782.10 | −0.334473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38920.0 | −1.66663 | ||||||||
\(818\) | −8859.75 | − | 39773.7i | −0.378697 | − | 1.70007i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −92.1174 | + | 43.1817i | −0.00392302 | + | 0.00183899i | ||||
\(821\) | − | 19162.7i | − | 0.814595i | −0.913296 | − | 0.407298i | \(-0.866471\pi\) | ||
0.913296 | − | 0.407298i | \(-0.133529\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7574.02i | 0.320794i | 0.987053 | + | 0.160397i | \(0.0512775\pi\) | ||||
−0.987053 | + | 0.160397i | \(0.948722\pi\) | |||||||
\(824\) | −211.670 | + | 163.441i | −0.00894887 | + | 0.00690987i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5687.97 | − | 1267.02i | 0.239600 | − | 0.0533719i | ||||
\(827\) | 34129.2 | 1.43505 | 0.717527 | − | 0.696531i | \(-0.245274\pi\) | ||||
0.717527 | + | 0.696531i | \(0.245274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34706.3 | 1.45404 | 0.727021 | − | 0.686615i | \(-0.240904\pi\) | ||||
0.727021 | + | 0.686615i | \(0.240904\pi\) | |||||||
\(830\) | 4399.12 | − | 979.922i | 0.183971 | − | 0.0409802i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3622.80 | + | 13855.6i | −0.150959 | + | 0.577353i | ||||
\(833\) | − | 2306.38i | − | 0.0959321i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 10245.3i | − | 0.424614i | ||||||
\(836\) | 7362.32 | + | 15705.7i | 0.304583 | + | 0.649751i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8142.27 | − | 36552.7i | −0.335644 | − | 1.50679i | ||||
\(839\) | −39467.7 | −1.62405 | −0.812025 | − | 0.583623i | \(-0.801635\pi\) | ||||
−0.812025 | + | 0.583623i | \(0.801635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14503.5 | −0.594676 | ||||||||
\(842\) | −2657.48 | − | 11930.1i | −0.108768 | − | 0.488287i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1647.68 | − | 3514.91i | −0.0671984 | − | 0.143351i | ||||
\(845\) | − | 4215.27i | − | 0.171609i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7827.73i | 0.317549i | ||||||||
\(848\) | 6477.53 | + | 5390.87i | 0.262310 | + | 0.218306i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15089.4 | − | 3361.24i | 0.608899 | − | 0.135635i | ||||
\(851\) | 255.407 | 0.0102882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15904.1 | 0.638389 | 0.319194 | − | 0.947689i | \(-0.396588\pi\) | ||||
0.319194 | + | 0.947689i | \(0.396588\pi\) | |||||||
\(854\) | −2604.72 | + | 580.211i | −0.104370 | + | 0.0232487i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18673.2 | + | 24183.4i | 0.745605 | + | 0.965621i | ||||
\(857\) | − | 21592.9i | − | 0.860677i | −0.902668 | − | 0.430338i | \(-0.858394\pi\) | ||
0.902668 | − | 0.430338i | \(-0.141606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9787.59i | − | 0.388764i | −0.980926 | − | 0.194382i | \(-0.937730\pi\) | ||
0.980926 | − | 0.194382i | \(-0.0622701\pi\) | |||||||
\(860\) | −5651.46 | + | 2649.22i | −0.224085 | + | 0.105044i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 797.189 | + | 3578.79i | 0.0314993 | + | 0.141408i | ||||
\(863\) | 15577.8 | 0.614455 | 0.307227 | − | 0.951636i | \(-0.400599\pi\) | ||||
0.307227 | + | 0.951636i | \(0.400599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11850.1 | 0.465800 | ||||||||
\(866\) | 6484.06 | + | 29108.6i | 0.254431 | + | 1.14221i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10829.4 | − | 5076.46i | 0.423471 | − | 0.198510i | ||||
\(869\) | − | 19656.7i | − | 0.767329i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4157.93i | − | 0.161752i | ||||||
\(872\) | −7898.60 | − | 10229.4i | −0.306744 | − | 0.397259i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34932.8 | − | 7781.43i | 1.35197 | − | 0.301157i | ||||
\(875\) | 5029.52 | 0.194318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9974.67 | 0.384060 | 0.192030 | − | 0.981389i | \(-0.438493\pi\) | ||||
0.192030 | + | 0.981389i | \(0.438493\pi\) | |||||||
\(878\) | −36438.2 | + | 8116.75i | −1.40060 | + | 0.311990i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2138.12 | + | 1779.43i | 0.0819045 | + | 0.0681643i | ||||
\(881\) | 8716.38i | 0.333328i | 0.986014 | + | 0.166664i | \(0.0532996\pi\) | ||||
−0.986014 | + | 0.166664i | \(0.946700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31703.2i | − | 1.20826i | −0.796884 | − | 0.604132i | \(-0.793520\pi\) | ||
0.796884 | − | 0.604132i | \(-0.206480\pi\) | |||||||
\(884\) | −4470.60 | − | 9536.91i | −0.170093 | − | 0.362852i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1452.61 | + | 6521.13i | 0.0550805 | + | 0.247271i | ||||
\(887\) | −46045.2 | −1.74301 | −0.871503 | − | 0.490390i | \(-0.836854\pi\) | ||||
−0.871503 | + | 0.490390i | \(0.836854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1460.04 | −0.0550825 | ||||||||
\(890\) | −730.085 | − | 3277.54i | −0.0274972 | − | 0.123442i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 328.832 | + | 701.481i | 0.0123432 | + | 0.0263311i | ||||
\(893\) | − | 14281.9i | − | 0.535192i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10745.1i | − | 0.401305i | ||||||
\(896\) | 370.595 | − | 10130.3i | 0.0138177 | − | 0.377712i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34411.6 | + | 7665.32i | −1.27876 | + | 0.284850i | ||||
\(899\) | −42119.4 | −1.56258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6197.91 | −0.229170 | ||||||||
\(902\) | −171.854 | + | 38.2812i | −0.00634380 | + | 0.00141311i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17329.9 | − | 13381.3i | 0.637593 | − | 0.492317i | ||||
\(905\) | − | 3459.00i | − | 0.127051i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30436.7i | 1.11426i | 0.830425 | + | 0.557131i | \(0.188098\pi\) | ||||
−0.830425 | + | 0.557131i | \(0.811902\pi\) | |||||||
\(908\) | 26334.8 | − | 12344.9i | 0.962500 | − | 0.451189i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −358.809 | − | 1610.79i | −0.0130708 | − | 0.0586781i | ||||
\(911\) | −33110.9 | −1.20419 | −0.602093 | − | 0.798426i | \(-0.705666\pi\) | ||||
−0.602093 | + | 0.798426i | \(0.705666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7799.76 | 0.282732 | ||||||||
\(914\) | −9127.66 | − | 40976.4i | −0.330324 | − | 1.48291i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33227.3 | + | 15575.9i | −1.19854 | + | 0.561836i | ||||
\(917\) | − | 11763.3i | − | 0.423617i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36489.9i | − | 1.30978i | −0.755723 | − | 0.654891i | \(-0.772715\pi\) | ||
0.755723 | − | 0.654891i | \(-0.227285\pi\) | |||||||
\(920\) | 4542.82 | − | 3507.74i | 0.162796 | − | 0.125703i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26745.0 | + | 5957.55i | −0.955312 | + | 0.212800i | ||||
\(923\) | 22280.7 | 0.794561 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −348.417 | −0.0123847 | ||||||||
\(926\) | −41479.9 | + | 9239.82i | −1.47205 | + | 0.327904i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16324.0 | + | 31748.4i | −0.577437 | + | 1.12305i | ||||
\(929\) | 1922.94i | 0.0679113i | 0.999423 | + | 0.0339556i | \(0.0108105\pi\) | ||||
−0.999423 | + | 0.0339556i | \(0.989190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7283.81i | 0.256409i | ||||||||
\(932\) | −15248.9 | − | 32529.7i | −0.535938 | − | 1.14329i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6498.57 | − | 29173.7i | −0.227665 | − | 1.02205i | ||||
\(935\) | −2045.82 | −0.0715567 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 820.948 | 0.0286224 | 0.0143112 | − | 0.999898i | \(-0.495444\pi\) | ||||
0.0143112 | + | 0.999898i | \(0.495444\pi\) | |||||||
\(938\) | 639.902 | + | 2872.68i | 0.0222745 | + | 0.0999962i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −972.147 | − | 2073.83i | −0.0337318 | − | 0.0719585i | ||||
\(941\) | − | 2949.16i | − | 0.102168i | −0.998694 | − | 0.0510839i | \(-0.983732\pi\) | ||
0.998694 | − | 0.0510839i | \(-0.0162676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 363.274i | 0.0125449i | ||||||||
\(944\) | −12049.8 | + | 14478.7i | −0.415452 | + | 0.499197i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10543.3 | + | 2348.57i | −0.362361 | + | 0.0807174i | ||||
\(947\) | 14834.6 | 0.509038 | 0.254519 | − | 0.967068i | \(-0.418083\pi\) | ||||
0.254519 | + | 0.967068i | \(0.418083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4568.73 | −0.156277 | ||||||||
\(950\) | −47654.1 | + | 10615.1i | −1.62748 | + | 0.362527i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4556.43 | + | 5900.96i | 0.155120 | + | 0.200894i | ||||
\(953\) | 23219.2i | 0.789237i | 0.918845 | + | 0.394619i | \(0.129123\pi\) | ||||
−0.918845 | + | 0.394619i | \(0.870877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12237.5i | − | 0.414656i | ||||||
\(956\) | 23313.0 | − | 10928.4i | 0.788701 | − | 0.369718i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11589.0 | + | 52025.9i | 0.390838 | + | 1.75457i | ||||
\(959\) | 10534.0 | 0.354705 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15823.0 | −0.531135 | ||||||||
\(962\) | 51.6133 | + | 231.705i | 0.00172981 | + | 0.00776558i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16328.7 | + | 7654.39i | −0.545553 | + | 0.255738i | ||||
\(965\) | − | 7118.71i | − | 0.237471i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8504.08i | − | 0.282805i | −0.989952 | − | 0.141403i | \(-0.954839\pi\) | ||
0.989952 | − | 0.141403i | \(-0.0451613\pi\) | |||||||
\(968\) | −15464.2 | − | 20027.5i | −0.513470 | − | 0.664988i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14078.8 | − | 3136.11i | 0.466024 | − | 0.103809i | ||||
\(971\) | 23347.8 | 0.771645 | 0.385822 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385822 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11291.1 | 0.372020 | ||||||||
\(974\) | −26399.3 | + | 5880.56i | −0.868470 | + | 0.193455i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5518.01 | − | 6630.30i | 0.180970 | − | 0.217449i | ||||
\(977\) | − | 38899.9i | − | 1.27382i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) | ||
0.770940 | − | 0.636908i | \(-0.219787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5811.16i | − | 0.189709i | ||||||
\(980\) | 495.797 | + | 1057.66i | 0.0161609 | + | 0.0344752i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6545.58 | − | 29384.8i | −0.212707 | − | 0.954894i | ||||
\(983\) | 9378.14 | 0.304289 | 0.152145 | − | 0.988358i | \(-0.451382\pi\) | ||||
0.152145 | + | 0.988358i | \(0.451382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9643.08 | 0.311933 | ||||||||
\(986\) | −5708.52 | − | 25627.0i | −0.184377 | − | 0.827718i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14118.6 | + | 30118.6i | 0.454629 | + | 0.969839i | ||||
\(989\) | 22287.1i | 0.716570i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 30417.6i | − | 0.975023i | −0.873117 | − | 0.487511i | \(-0.837905\pi\) | ||
0.873117 | − | 0.487511i | \(-0.162095\pi\) | |||||||
\(992\) | −17678.4 | + | 34382.5i | −0.565816 | + | 1.10045i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15393.6 | + | 3428.99i | −0.491202 | + | 0.109417i | ||||
\(995\) | −10459.0 | −0.333238 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42253.4 | −1.34221 | −0.671103 | − | 0.741364i | \(-0.734179\pi\) | ||||
−0.671103 | + | 0.741364i | \(0.734179\pi\) | |||||||
\(998\) | −20845.9 | + | 4643.52i | −0.661189 | + | 0.147282i | ||||
\(999\) | 0 | 0 |
(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 | 252.4.e.a.71.17 | ✓ | 36 | |
3.2 | odd | 2 | inner | 252.4.e.a.71.20 | yes | 36 | |
4.3 | odd | 2 | inner | 252.4.e.a.71.19 | yes | 36 | |
12.11 | even | 2 | inner | 252.4.e.a.71.18 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.e.a.71.17 | ✓ | 36 | 1.1 | even | 1 | trivial | |
252.4.e.a.71.18 | yes | 36 | 12.11 | even | 2 | inner | |
252.4.e.a.71.19 | yes | 36 | 4.3 | odd | 2 | inner | |
252.4.e.a.71.20 | yes | 36 | 3.2 | odd | 2 | inner |