Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,3,Mod(728,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.728");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.b (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: | \(19.8638112719\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 728.19 | ||
Character | \(\chi\) | \(=\) | 729.728 |
Dual form | 729.3.b.a.728.12 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16096i | 0.580481i | 0.956954 | + | 0.290241i | \(0.0937353\pi\) | ||||
−0.956954 | + | 0.290241i | \(0.906265\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.65217 | 0.663042 | ||||||||
\(5\) | − 5.38300i | − 1.07660i | −0.842753 | − | 0.538300i | \(-0.819067\pi\) | ||||
0.842753 | − | 0.538300i | \(-0.180933\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.5344 | −1.50491 | −0.752455 | − | 0.658644i | \(-0.771130\pi\) | ||||
−0.752455 | + | 0.658644i | \(0.771130\pi\) | |||||||
\(8\) | 7.72291i | 0.965364i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.24946 | 0.624946 | ||||||||
\(11\) | 11.7440i | 1.06763i | 0.845600 | + | 0.533817i | \(0.179243\pi\) | ||||
−0.845600 | + | 0.533817i | \(0.820757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.2329 | 0.864067 | 0.432033 | − | 0.901858i | \(-0.357796\pi\) | ||||
0.432033 | + | 0.901858i | \(0.357796\pi\) | |||||||
\(14\) | − 12.2300i | − 0.873572i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.64265 | 0.102666 | ||||||||
\(17\) | 3.15961i | 0.185859i | 0.995673 | + | 0.0929296i | \(0.0296231\pi\) | ||||
−0.995673 | + | 0.0929296i | \(0.970377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.52102 | −0.237948 | −0.118974 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118974 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(20\) | − 14.2766i | − 0.713831i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.6343 | −0.619741 | ||||||||
\(23\) | 19.9076i | 0.865548i | 0.901502 | + | 0.432774i | \(0.142465\pi\) | ||||
−0.901502 | + | 0.432774i | \(0.857535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.97672 | −0.159069 | ||||||||
\(26\) | 13.0409i | 0.501575i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −27.9389 | −0.997818 | ||||||||
\(29\) | 25.3597i | 0.874472i | 0.899347 | + | 0.437236i | \(0.144043\pi\) | ||||
−0.899347 | + | 0.437236i | \(0.855957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.1215 | 0.713595 | 0.356798 | − | 0.934182i | \(-0.383869\pi\) | ||||
0.356798 | + | 0.934182i | \(0.383869\pi\) | |||||||
\(32\) | 32.7987i | 1.02496i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.66818 | −0.107888 | ||||||||
\(35\) | 56.7065i | 1.62019i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.6561 | 0.477193 | 0.238596 | − | 0.971119i | \(-0.423313\pi\) | ||||
0.238596 | + | 0.971119i | \(0.423313\pi\) | |||||||
\(38\) | − 5.24873i | − 0.138125i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 41.5725 | 1.03931 | ||||||||
\(41\) | 12.4448i | 0.303531i | 0.988417 | + | 0.151765i | \(0.0484958\pi\) | ||||
−0.988417 | + | 0.151765i | \(0.951504\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.4484 | 0.847638 | 0.423819 | − | 0.905747i | \(-0.360689\pi\) | ||||
0.423819 | + | 0.905747i | \(0.360689\pi\) | |||||||
\(44\) | 31.1470i | 0.707886i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.1120 | −0.502434 | ||||||||
\(47\) | 12.3996i | 0.263821i | 0.991262 | + | 0.131910i | \(0.0421111\pi\) | ||||
−0.991262 | + | 0.131910i | \(0.957889\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 61.9729 | 1.26475 | ||||||||
\(50\) | − 4.61682i | − 0.0923364i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29.7914 | 0.572912 | ||||||||
\(53\) | 84.6210i | 1.59662i | 0.602245 | + | 0.798311i | \(0.294273\pi\) | ||||
−0.602245 | + | 0.798311i | \(0.705727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.2178 | 1.14942 | ||||||||
\(56\) | − 81.3560i | − 1.45279i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −29.4417 | −0.507615 | ||||||||
\(59\) | − 68.2736i | − 1.15718i | −0.815619 | − | 0.578590i | \(-0.803603\pi\) | ||||
0.815619 | − | 0.578590i | \(-0.196397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 78.0720 | 1.27987 | 0.639935 | − | 0.768429i | \(-0.278961\pi\) | ||||
0.639935 | + | 0.768429i | \(0.278961\pi\) | |||||||
\(62\) | 25.6822i | 0.414229i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −31.5075 | −0.492304 | ||||||||
\(65\) | − 60.4666i | − 0.930255i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −97.1238 | −1.44961 | −0.724804 | − | 0.688955i | \(-0.758070\pi\) | ||||
−0.724804 | + | 0.688955i | \(0.758070\pi\) | |||||||
\(68\) | 8.37980i | 0.123232i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −65.8341 | −0.940488 | ||||||||
\(71\) | 121.664i | 1.71358i | 0.515663 | + | 0.856791i | \(0.327545\pi\) | ||||
−0.515663 | + | 0.856791i | \(0.672455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 91.1410 | 1.24851 | 0.624254 | − | 0.781222i | \(-0.285403\pi\) | ||||
0.624254 | + | 0.781222i | \(0.285403\pi\) | |||||||
\(74\) | 20.4981i | 0.277001i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.9905 | −0.157770 | ||||||||
\(77\) | − 123.715i | − 1.60669i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20.3879 | −0.258074 | −0.129037 | − | 0.991640i | \(-0.541189\pi\) | ||||
−0.129037 | + | 0.991640i | \(0.541189\pi\) | |||||||
\(80\) | − 8.84240i | − 0.110530i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.4479 | −0.176194 | ||||||||
\(83\) | 31.6020i | 0.380747i | 0.981712 | + | 0.190374i | \(0.0609700\pi\) | ||||
−0.981712 | + | 0.190374i | \(0.939030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.0082 | 0.200096 | ||||||||
\(86\) | 42.3153i | 0.492038i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −90.6977 | −1.03066 | ||||||||
\(89\) | − 69.0229i | − 0.775538i | −0.921757 | − | 0.387769i | \(-0.873246\pi\) | ||||
0.921757 | − | 0.387769i | \(-0.126754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −118.331 | −1.30034 | ||||||||
\(92\) | 52.7983i | 0.573894i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.3954 | −0.153143 | ||||||||
\(95\) | 24.3367i | 0.256175i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79.8042 | −0.822724 | −0.411362 | − | 0.911472i | \(-0.634947\pi\) | ||||
−0.411362 | + | 0.911472i | \(0.634947\pi\) | |||||||
\(98\) | 71.9482i | 0.734165i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.5469 | −0.105469 | ||||||||
\(101\) | 4.77669i | 0.0472939i | 0.999720 | + | 0.0236470i | \(0.00752776\pi\) | ||||
−0.999720 | + | 0.0236470i | \(0.992472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −72.2928 | −0.701872 | −0.350936 | − | 0.936400i | \(-0.614136\pi\) | ||||
−0.350936 | + | 0.936400i | \(0.614136\pi\) | |||||||
\(104\) | 86.7505i | 0.834139i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −98.2418 | −0.926809 | ||||||||
\(107\) | 158.133i | 1.47788i | 0.673773 | + | 0.738938i | \(0.264672\pi\) | ||||
−0.673773 | + | 0.738938i | \(0.735328\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.5788 | −0.170448 | −0.0852240 | − | 0.996362i | \(-0.527161\pi\) | ||||
−0.0852240 | + | 0.996362i | \(0.527161\pi\) | |||||||
\(110\) | 73.3935i | 0.667214i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.3043 | −0.154503 | ||||||||
\(113\) | − 18.0161i | − 0.159435i | −0.996817 | − | 0.0797175i | \(-0.974598\pi\) | ||||
0.996817 | − | 0.0797175i | \(-0.0254018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 107.163 | 0.931850 | ||||||||
\(116\) | 67.2581i | 0.579811i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 79.2631 | 0.671721 | ||||||||
\(119\) | − 33.2844i | − 0.279701i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.9209 | −0.139842 | ||||||||
\(122\) | 90.6387i | 0.742940i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 58.6698 | 0.473143 | ||||||||
\(125\) | − 113.168i | − 0.905347i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −156.213 | −1.23003 | −0.615013 | − | 0.788517i | \(-0.710849\pi\) | ||||
−0.615013 | + | 0.788517i | \(0.710849\pi\) | |||||||
\(128\) | 94.6159i | 0.739187i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 70.1994 | 0.539996 | ||||||||
\(131\) | 98.5190i | 0.752054i | 0.926609 | + | 0.376027i | \(0.122710\pi\) | ||||
−0.926609 | + | 0.376027i | \(0.877290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.6261 | 0.358091 | ||||||||
\(134\) | − 112.757i | − 0.841471i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.4014 | −0.179422 | ||||||||
\(137\) | − 65.6564i | − 0.479244i | −0.970866 | − | 0.239622i | \(-0.922976\pi\) | ||||
0.970866 | − | 0.239622i | \(-0.0770235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −125.301 | −0.901443 | −0.450722 | − | 0.892664i | \(-0.648833\pi\) | ||||
−0.450722 | + | 0.892664i | \(0.648833\pi\) | |||||||
\(140\) | 150.395i | 1.07425i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −141.248 | −0.994702 | ||||||||
\(143\) | 131.919i | 0.922507i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 136.511 | 0.941457 | ||||||||
\(146\) | 105.811i | 0.724735i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 46.8270 | 0.316399 | ||||||||
\(149\) | − 201.756i | − 1.35407i | −0.735951 | − | 0.677035i | \(-0.763264\pi\) | ||||
0.735951 | − | 0.677035i | \(-0.236736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 128.141 | 0.848613 | 0.424306 | − | 0.905519i | \(-0.360518\pi\) | ||||
0.424306 | + | 0.905519i | \(0.360518\pi\) | |||||||
\(152\) | − 34.9154i | − 0.229707i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 143.629 | 0.932655 | ||||||||
\(155\) | − 119.080i | − 0.768257i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −138.946 | −0.885008 | −0.442504 | − | 0.896767i | \(-0.645910\pi\) | ||||
−0.442504 | + | 0.896767i | \(0.645910\pi\) | |||||||
\(158\) | − 23.6696i | − 0.149807i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 176.556 | 1.10347 | ||||||||
\(161\) | − 209.714i | − 1.30257i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 39.8569 | 0.244521 | 0.122261 | − | 0.992498i | \(-0.460986\pi\) | ||||
0.122261 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(164\) | 33.0056i | 0.201254i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.6888 | −0.221017 | ||||||||
\(167\) | − 165.953i | − 0.993730i | −0.867828 | − | 0.496865i | \(-0.834484\pi\) | ||||
0.867828 | − | 0.496865i | \(-0.165516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42.8226 | −0.253388 | ||||||||
\(170\) | 19.7458i | 0.116152i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 96.6674 | 0.562019 | ||||||||
\(173\) | 10.8902i | 0.0629489i | 0.999505 | + | 0.0314744i | \(0.0100203\pi\) | ||||
−0.999505 | + | 0.0314744i | \(0.989980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41.8922 | 0.239384 | ||||||||
\(176\) | 19.2913i | 0.109609i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 80.1330 | 0.450185 | ||||||||
\(179\) | − 282.579i | − 1.57865i | −0.613974 | − | 0.789326i | \(-0.710430\pi\) | ||||
0.613974 | − | 0.789326i | \(-0.289570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −108.799 | −0.601100 | −0.300550 | − | 0.953766i | \(-0.597170\pi\) | ||||
−0.300550 | + | 0.953766i | \(0.597170\pi\) | |||||||
\(182\) | − 137.378i | − 0.754824i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −153.745 | −0.835569 | ||||||||
\(185\) | − 95.0430i | − 0.513746i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.1063 | −0.198429 | ||||||||
\(188\) | 32.8857i | 0.174924i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −28.2539 | −0.148705 | ||||||||
\(191\) | 108.629i | 0.568740i | 0.958715 | + | 0.284370i | \(0.0917844\pi\) | ||||
−0.958715 | + | 0.284370i | \(0.908216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 200.108 | 1.03683 | 0.518415 | − | 0.855129i | \(-0.326522\pi\) | ||||
0.518415 | + | 0.855129i | \(0.326522\pi\) | |||||||
\(194\) | − 92.6496i | − 0.477576i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 164.362 | 0.838584 | ||||||||
\(197\) | − 292.710i | − 1.48584i | −0.669383 | − | 0.742918i | \(-0.733441\pi\) | ||||
0.669383 | − | 0.742918i | \(-0.266559\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −82.3096 | −0.413616 | −0.206808 | − | 0.978382i | \(-0.566308\pi\) | ||||
−0.206808 | + | 0.978382i | \(0.566308\pi\) | |||||||
\(200\) | − 30.7119i | − 0.153559i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.54555 | −0.0274532 | ||||||||
\(203\) | − 267.148i | − 1.31600i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 66.9902 | 0.326781 | ||||||||
\(206\) | − 83.9292i | − 0.407423i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.4517 | 0.0887101 | ||||||||
\(209\) | − 53.0947i | − 0.254042i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 115.845 | 0.549029 | 0.274515 | − | 0.961583i | \(-0.411483\pi\) | ||||
0.274515 | + | 0.961583i | \(0.411483\pi\) | |||||||
\(212\) | 224.429i | 1.05863i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −183.586 | −0.857879 | ||||||||
\(215\) | − 196.202i | − 0.912568i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233.036 | −1.07390 | ||||||||
\(218\) | − 21.5693i | − 0.0989418i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 167.664 | 0.762110 | ||||||||
\(221\) | 35.4914i | 0.160595i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −198.236 | −0.888951 | −0.444476 | − | 0.895791i | \(-0.646610\pi\) | ||||
−0.444476 | + | 0.895791i | \(0.646610\pi\) | |||||||
\(224\) | − 345.514i | − 1.54247i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.9161 | 0.0925490 | ||||||||
\(227\) | 5.15186i | 0.0226954i | 0.999936 | + | 0.0113477i | \(0.00361216\pi\) | ||||
−0.999936 | + | 0.0113477i | \(0.996388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 353.347 | 1.54300 | 0.771500 | − | 0.636229i | \(-0.219507\pi\) | ||||
0.771500 | + | 0.636229i | \(0.219507\pi\) | |||||||
\(230\) | 124.412i | 0.540921i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −195.851 | −0.844184 | ||||||||
\(233\) | 140.561i | 0.603265i | 0.953424 | + | 0.301632i | \(0.0975315\pi\) | ||||
−0.953424 | + | 0.301632i | \(0.902469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 66.7470 | 0.284030 | ||||||||
\(236\) | − 181.073i | − 0.767258i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 38.6420 | 0.162361 | ||||||||
\(239\) | − 147.674i | − 0.617882i | −0.951081 | − | 0.308941i | \(-0.900025\pi\) | ||||
0.951081 | − | 0.308941i | \(-0.0999746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 304.414 | 1.26313 | 0.631563 | − | 0.775324i | \(-0.282414\pi\) | ||||
0.631563 | + | 0.775324i | \(0.282414\pi\) | |||||||
\(242\) | − 19.6445i | − 0.0811755i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 207.060 | 0.848606 | ||||||||
\(245\) | − 333.600i | − 1.36163i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −50.7840 | −0.205603 | ||||||||
\(248\) | 170.842i | 0.688880i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 131.384 | 0.525537 | ||||||||
\(251\) | 124.791i | 0.497175i | 0.968609 | + | 0.248588i | \(0.0799664\pi\) | ||||
−0.968609 | + | 0.248588i | \(0.920034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −233.794 | −0.924088 | ||||||||
\(254\) | − 181.358i | − 0.714007i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −235.875 | −0.921388 | ||||||||
\(257\) | 457.031i | 1.77833i | 0.457585 | + | 0.889166i | \(0.348715\pi\) | ||||
−0.457585 | + | 0.889166i | \(0.651285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −185.996 | −0.718132 | ||||||||
\(260\) | − 160.367i | − 0.616798i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −114.377 | −0.436553 | ||||||||
\(263\) | 467.947i | 1.77927i | 0.456677 | + | 0.889633i | \(0.349040\pi\) | ||||
−0.456677 | + | 0.889633i | \(0.650960\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 455.515 | 1.71892 | ||||||||
\(266\) | 55.2921i | 0.207865i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −257.588 | −0.961151 | ||||||||
\(269\) | − 317.049i | − 1.17862i | −0.807907 | − | 0.589310i | \(-0.799399\pi\) | ||||
0.807907 | − | 0.589310i | \(-0.200601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 115.698 | 0.426931 | 0.213465 | − | 0.976951i | \(-0.431525\pi\) | ||||
0.213465 | + | 0.976951i | \(0.431525\pi\) | |||||||
\(272\) | 5.19013i | 0.0190814i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 76.2247 | 0.278192 | ||||||||
\(275\) | − 46.7025i | − 0.169827i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −115.306 | −0.416267 | −0.208133 | − | 0.978100i | \(-0.566739\pi\) | ||||
−0.208133 | + | 0.978100i | \(0.566739\pi\) | |||||||
\(278\) | − 145.469i | − 0.523271i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −437.940 | −1.56407 | ||||||||
\(281\) | 81.5920i | 0.290363i | 0.989405 | + | 0.145181i | \(0.0463766\pi\) | ||||
−0.989405 | + | 0.145181i | \(0.953623\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −417.139 | −1.47399 | −0.736995 | − | 0.675898i | \(-0.763756\pi\) | ||||
−0.736995 | + | 0.675898i | \(0.763756\pi\) | |||||||
\(284\) | 322.674i | 1.13618i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −153.152 | −0.535498 | ||||||||
\(287\) | − 131.098i | − 0.456786i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 279.017 | 0.965456 | ||||||||
\(290\) | 158.484i | 0.546498i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 241.721 | 0.827812 | ||||||||
\(293\) | − 345.833i | − 1.18032i | −0.807287 | − | 0.590159i | \(-0.799065\pi\) | ||||
0.807287 | − | 0.590159i | \(-0.200935\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −367.517 | −1.24582 | ||||||||
\(296\) | 136.357i | 0.460665i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 234.232 | 0.786012 | ||||||||
\(299\) | 223.620i | 0.747892i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −383.961 | −1.27562 | ||||||||
\(302\) | 148.766i | 0.492604i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.42646 | −0.0244291 | ||||||||
\(305\) | − 420.262i | − 1.37791i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 577.336 | 1.88057 | 0.940286 | − | 0.340384i | \(-0.110557\pi\) | ||||
0.940286 | + | 0.340384i | \(0.110557\pi\) | |||||||
\(308\) | − 328.114i | − 1.06530i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 138.247 | 0.445959 | ||||||||
\(311\) | − 449.103i | − 1.44406i | −0.691861 | − | 0.722030i | \(-0.743209\pi\) | ||||
0.691861 | − | 0.722030i | \(-0.256791\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8376 | 0.0346248 | 0.0173124 | − | 0.999850i | \(-0.494489\pi\) | ||||
0.0173124 | + | 0.999850i | \(0.494489\pi\) | |||||||
\(314\) | − 161.311i | − 0.513730i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −54.0721 | −0.171114 | ||||||||
\(317\) | 218.233i | 0.688433i | 0.938890 | + | 0.344217i | \(0.111855\pi\) | ||||
−0.938890 | + | 0.344217i | \(0.888145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −297.824 | −0.933616 | ||||||||
\(320\) | 169.605i | 0.530015i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 243.470 | 0.756118 | ||||||||
\(323\) | − 14.2846i | − 0.0442249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.6700 | −0.137446 | ||||||||
\(326\) | 46.2724i | 0.141940i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −96.1099 | −0.293018 | ||||||||
\(329\) | − 130.622i | − 0.397026i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 600.678 | 1.81474 | 0.907369 | − | 0.420335i | \(-0.138087\pi\) | ||||
0.907369 | + | 0.420335i | \(0.138087\pi\) | |||||||
\(332\) | 83.8138i | 0.252451i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 192.665 | 0.576841 | ||||||||
\(335\) | 522.818i | 1.56065i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 449.269 | 1.33314 | 0.666571 | − | 0.745442i | \(-0.267761\pi\) | ||||
0.666571 | + | 0.745442i | \(0.267761\pi\) | |||||||
\(338\) | − 49.7154i | − 0.147087i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 45.1085 | 0.132672 | ||||||||
\(341\) | 259.794i | 0.761859i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −136.661 | −0.398429 | ||||||||
\(344\) | 281.488i | 0.818280i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.6431 | −0.0365406 | ||||||||
\(347\) | − 236.161i | − 0.680578i | −0.940321 | − | 0.340289i | \(-0.889475\pi\) | ||||
0.940321 | − | 0.340289i | \(-0.110525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 239.784 | 0.687060 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(350\) | 48.6353i | 0.138958i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −385.187 | −1.09428 | ||||||||
\(353\) | 25.5908i | 0.0724951i | 0.999343 | + | 0.0362475i | \(0.0115405\pi\) | ||||
−0.999343 | + | 0.0362475i | \(0.988460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 654.920 | 1.84484 | ||||||||
\(356\) | − 183.060i | − 0.514214i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 328.063 | 0.916378 | ||||||||
\(359\) | − 19.3755i | − 0.0539706i | −0.999636 | − | 0.0269853i | \(-0.991409\pi\) | ||||
0.999636 | − | 0.0269853i | \(-0.00859074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −340.560 | −0.943381 | ||||||||
\(362\) | − 126.312i | − 0.348927i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −313.834 | −0.862181 | ||||||||
\(365\) | − 490.612i | − 1.34414i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 390.715 | 1.06462 | 0.532309 | − | 0.846550i | \(-0.321324\pi\) | ||||
0.532309 | + | 0.846550i | \(0.321324\pi\) | |||||||
\(368\) | 32.7013i | 0.0888622i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 110.341 | 0.298220 | ||||||||
\(371\) | − 891.428i | − 2.40277i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −178.823 | −0.479418 | −0.239709 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239709 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(374\) | − 43.0790i | − 0.115185i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −95.7609 | −0.254683 | ||||||||
\(377\) | 284.862i | 0.755603i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.48118 | 0.00918518 | 0.00459259 | − | 0.999989i | \(-0.498538\pi\) | ||||
0.00459259 | + | 0.999989i | \(0.498538\pi\) | |||||||
\(380\) | 64.5449i | 0.169855i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −126.115 | −0.330143 | ||||||||
\(383\) | 17.2265i | 0.0449778i | 0.999747 | + | 0.0224889i | \(0.00715904\pi\) | ||||
−0.999747 | + | 0.0224889i | \(0.992841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −665.960 | −1.72977 | ||||||||
\(386\) | 232.318i | 0.601860i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −211.654 | −0.545500 | ||||||||
\(389\) | − 316.773i | − 0.814326i | −0.913356 | − | 0.407163i | \(-0.866518\pi\) | ||||
0.913356 | − | 0.407163i | \(-0.133482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −62.9002 | −0.160870 | ||||||||
\(392\) | 478.611i | 1.22095i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 339.825 | 0.862500 | ||||||||
\(395\) | 109.748i | 0.277843i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.082 | 0.675269 | 0.337634 | − | 0.941277i | \(-0.390373\pi\) | ||||
0.337634 | + | 0.941277i | \(0.390373\pi\) | |||||||
\(398\) | − 95.5584i | − 0.240096i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.53237 | −0.0163309 | ||||||||
\(401\) | 97.4667i | 0.243059i | 0.992588 | + | 0.121530i | \(0.0387799\pi\) | ||||
−0.992588 | + | 0.121530i | \(0.961220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 248.487 | 0.616594 | ||||||||
\(404\) | 12.6686i | 0.0313578i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 310.149 | 0.763914 | ||||||||
\(407\) | 207.353i | 0.509467i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −405.343 | −0.991060 | −0.495530 | − | 0.868591i | \(-0.665026\pi\) | ||||
−0.495530 | + | 0.868591i | \(0.665026\pi\) | |||||||
\(410\) | 77.7731i | 0.189691i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −191.732 | −0.465370 | ||||||||
\(413\) | 719.219i | 1.74145i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 170.114 | 0.409913 | ||||||||
\(416\) | 368.424i | 0.885634i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 61.6410 | 0.147466 | ||||||||
\(419\) | − 117.335i | − 0.280036i | −0.990149 | − | 0.140018i | \(-0.955284\pi\) | ||||
0.990149 | − | 0.140018i | \(-0.0447160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −521.334 | −1.23832 | −0.619161 | − | 0.785264i | \(-0.712527\pi\) | ||||
−0.619161 | + | 0.785264i | \(0.712527\pi\) | |||||||
\(422\) | 134.492i | 0.318701i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −653.521 | −1.54132 | ||||||||
\(425\) | − 12.5649i | − 0.0295644i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −822.439 | −1.92609 | ||||||||
\(428\) | 419.394i | 0.979893i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 227.783 | 0.529729 | ||||||||
\(431\) | − 263.580i | − 0.611555i | −0.952103 | − | 0.305777i | \(-0.901084\pi\) | ||||
0.952103 | − | 0.305777i | \(-0.0989163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −702.013 | −1.62128 | −0.810639 | − | 0.585547i | \(-0.800880\pi\) | ||||
−0.810639 | + | 0.585547i | \(0.800880\pi\) | |||||||
\(434\) | − 270.545i | − 0.623377i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −49.2741 | −0.113014 | ||||||||
\(437\) | − 90.0027i | − 0.205956i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −442.915 | −1.00892 | −0.504459 | − | 0.863436i | \(-0.668308\pi\) | ||||
−0.504459 | + | 0.863436i | \(0.668308\pi\) | |||||||
\(440\) | 488.226i | 1.10960i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −41.2042 | −0.0932222 | ||||||||
\(443\) | 606.842i | 1.36985i | 0.728615 | + | 0.684923i | \(0.240164\pi\) | ||||
−0.728615 | + | 0.684923i | \(0.759836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −371.550 | −0.834945 | ||||||||
\(446\) | − 230.145i | − 0.516019i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 331.911 | 0.740873 | ||||||||
\(449\) | 401.541i | 0.894302i | 0.894459 | + | 0.447151i | \(0.147561\pi\) | ||||
−0.894459 | + | 0.447151i | \(0.852439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −146.151 | −0.324060 | ||||||||
\(452\) | − 47.7818i | − 0.105712i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.98111 | −0.0131743 | ||||||||
\(455\) | 636.977i | 1.39995i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −147.113 | −0.321909 | −0.160955 | − | 0.986962i | \(-0.551457\pi\) | ||||
−0.160955 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(458\) | 410.223i | 0.895683i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 284.213 | 0.617855 | ||||||||
\(461\) | − 785.412i | − 1.70371i | −0.523774 | − | 0.851857i | \(-0.675476\pi\) | ||||
0.523774 | − | 0.851857i | \(-0.324524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −358.453 | −0.774196 | −0.387098 | − | 0.922039i | \(-0.626523\pi\) | ||||
−0.387098 | + | 0.922039i | \(0.626523\pi\) | |||||||
\(464\) | 41.6572i | 0.0897783i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −163.186 | −0.350184 | ||||||||
\(467\) | 101.929i | 0.218263i | 0.994027 | + | 0.109131i | \(0.0348069\pi\) | ||||
−0.994027 | + | 0.109131i | \(0.965193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1023.14 | 2.18153 | ||||||||
\(470\) | 77.4907i | 0.164874i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 527.271 | 1.11710 | ||||||||
\(473\) | 428.050i | 0.904967i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.9788 | 0.0378502 | ||||||||
\(476\) | − 88.2759i | − 0.185453i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 171.444 | 0.358669 | ||||||||
\(479\) | − 126.370i | − 0.263820i | −0.991262 | − | 0.131910i | \(-0.957889\pi\) | ||||
0.991262 | − | 0.131910i | \(-0.0421110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 198.329 | 0.412326 | ||||||||
\(482\) | 353.413i | 0.733221i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.8769 | −0.0927209 | ||||||||
\(485\) | 429.586i | 0.885745i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 454.010 | 0.932258 | 0.466129 | − | 0.884717i | \(-0.345648\pi\) | ||||
0.466129 | + | 0.884717i | \(0.345648\pi\) | |||||||
\(488\) | 602.944i | 1.23554i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 387.297 | 0.790403 | ||||||||
\(491\) | 316.087i | 0.643763i | 0.946780 | + | 0.321881i | \(0.104315\pi\) | ||||
−0.946780 | + | 0.321881i | \(0.895685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −80.1266 | −0.162529 | ||||||||
\(494\) | − 58.9583i | − 0.119349i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.3379 | 0.0732618 | ||||||||
\(497\) | − 1281.66i | − 2.57879i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 122.272 | 0.245034 | 0.122517 | − | 0.992466i | \(-0.460903\pi\) | ||||
0.122517 | + | 0.992466i | \(0.460903\pi\) | |||||||
\(500\) | − 300.141i | − 0.600283i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −144.878 | −0.288601 | ||||||||
\(503\) | − 451.536i | − 0.897685i | −0.893611 | − | 0.448843i | \(-0.851836\pi\) | ||||
0.893611 | − | 0.448843i | \(-0.148164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.7129 | 0.0509167 | ||||||||
\(506\) | − 271.426i | − 0.536416i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −414.304 | −0.815559 | ||||||||
\(509\) | − 499.710i | − 0.981748i | −0.871231 | − | 0.490874i | \(-0.836678\pi\) | ||||
0.871231 | − | 0.490874i | \(-0.163322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −960.113 | −1.87889 | ||||||||
\(512\) | 104.621i | 0.204338i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −530.596 | −1.03229 | ||||||||
\(515\) | 389.152i | 0.755635i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −145.620 | −0.281664 | ||||||||
\(518\) | − 215.935i | − 0.416862i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 466.978 | 0.898035 | ||||||||
\(521\) | 687.777i | 1.32011i | 0.751218 | + | 0.660054i | \(0.229467\pi\) | ||||
−0.751218 | + | 0.660054i | \(0.770533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −520.436 | −0.995098 | −0.497549 | − | 0.867436i | \(-0.665767\pi\) | ||||
−0.497549 | + | 0.867436i | \(0.665767\pi\) | |||||||
\(524\) | 261.289i | 0.498643i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −543.269 | −1.03283 | ||||||||
\(527\) | 69.8951i | 0.132628i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 132.687 | 0.250826 | ||||||||
\(530\) | 528.836i | 0.997803i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 126.312 | 0.237429 | ||||||||
\(533\) | 139.790i | 0.262271i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 851.229 | 1.59108 | ||||||||
\(536\) | − 750.079i | − 1.39940i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 368.082 | 0.684167 | ||||||||
\(539\) | 727.808i | 1.35029i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 803.120 | 1.48451 | 0.742255 | − | 0.670117i | \(-0.233756\pi\) | ||||
0.742255 | + | 0.670117i | \(0.233756\pi\) | |||||||
\(542\) | 134.321i | 0.247825i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −103.631 | −0.190498 | ||||||||
\(545\) | 100.010i | 0.183504i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −68.6886 | −0.125573 | −0.0627866 | − | 0.998027i | \(-0.519999\pi\) | ||||
−0.0627866 | + | 0.998027i | \(0.519999\pi\) | |||||||
\(548\) | − 174.132i | − 0.317759i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 54.2198 | 0.0985815 | ||||||||
\(551\) | − 114.652i | − 0.208079i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 214.773 | 0.388379 | ||||||||
\(554\) | − 133.866i | − 0.241635i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −332.318 | −0.597695 | ||||||||
\(557\) | 664.091i | 1.19226i | 0.802886 | + | 0.596132i | \(0.203296\pi\) | ||||
−0.802886 | + | 0.596132i | \(0.796704\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 409.421 | 0.732416 | ||||||||
\(560\) | 93.1491i | 0.166338i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −94.7252 | −0.168550 | ||||||||
\(563\) | − 347.655i | − 0.617504i | −0.951143 | − | 0.308752i | \(-0.900089\pi\) | ||||
0.951143 | − | 0.308752i | \(-0.0999114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −96.9810 | −0.171648 | ||||||||
\(566\) | − 484.283i | − 0.855623i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −939.603 | −1.65423 | ||||||||
\(569\) | − 391.019i | − 0.687203i | −0.939115 | − | 0.343602i | \(-0.888353\pi\) | ||||
0.939115 | − | 0.343602i | \(-0.111647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 855.725 | 1.49864 | 0.749321 | − | 0.662207i | \(-0.230380\pi\) | ||||
0.749321 | + | 0.662207i | \(0.230380\pi\) | |||||||
\(572\) | 349.870i | 0.611661i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 152.200 | 0.265156 | ||||||||
\(575\) | − 79.1670i | − 0.137682i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −627.491 | −1.08751 | −0.543753 | − | 0.839245i | \(-0.682997\pi\) | ||||
−0.543753 | + | 0.839245i | \(0.682997\pi\) | |||||||
\(578\) | 323.928i | 0.560429i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 362.051 | 0.624225 | ||||||||
\(581\) | − 332.907i | − 0.572990i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −993.786 | −1.70461 | ||||||||
\(584\) | 703.874i | 1.20526i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 401.499 | 0.685152 | ||||||||
\(587\) | 744.557i | 1.26841i | 0.773165 | + | 0.634205i | \(0.218673\pi\) | ||||
−0.773165 | + | 0.634205i | \(0.781327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −100.012 | −0.169799 | ||||||||
\(590\) | − 426.673i | − 0.723175i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 29.0029 | 0.0489913 | ||||||||
\(593\) | 625.722i | 1.05518i | 0.849499 | + | 0.527591i | \(0.176904\pi\) | ||||
−0.849499 | + | 0.527591i | \(0.823096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −179.170 | −0.301126 | ||||||||
\(596\) | − 535.092i | − 0.897805i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −259.614 | −0.434137 | ||||||||
\(599\) | − 573.042i | − 0.956664i | −0.878179 | − | 0.478332i | \(-0.841242\pi\) | ||||
0.878179 | − | 0.478332i | \(-0.158758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1131.48 | 1.88266 | 0.941330 | − | 0.337487i | \(-0.109577\pi\) | ||||
0.941330 | + | 0.337487i | \(0.109577\pi\) | |||||||
\(602\) | − 445.765i | − 0.740473i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 339.850 | 0.562666 | ||||||||
\(605\) | 91.0850i | 0.150554i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −232.474 | −0.382988 | −0.191494 | − | 0.981494i | \(-0.561333\pi\) | ||||
−0.191494 | + | 0.981494i | \(0.561333\pi\) | |||||||
\(608\) | − 148.284i | − 0.243888i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 487.908 | 0.799850 | ||||||||
\(611\) | 139.283i | 0.227959i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1067.78 | −1.74189 | −0.870945 | − | 0.491380i | \(-0.836493\pi\) | ||||
−0.870945 | + | 0.491380i | \(0.836493\pi\) | |||||||
\(614\) | 670.265i | 1.09164i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 955.443 | 1.55104 | ||||||||
\(617\) | 421.751i | 0.683552i | 0.939782 | + | 0.341776i | \(0.111028\pi\) | ||||
−0.939782 | + | 0.341776i | \(0.888972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 600.839 | 0.970661 | 0.485331 | − | 0.874331i | \(-0.338699\pi\) | ||||
0.485331 | + | 0.874331i | \(0.338699\pi\) | |||||||
\(620\) | − 315.820i | − 0.509386i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 521.392 | 0.838250 | ||||||||
\(623\) | 727.112i | 1.16711i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −708.604 | −1.13377 | ||||||||
\(626\) | 12.5820i | 0.0200990i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −368.509 | −0.586797 | ||||||||
\(629\) | 55.7864i | 0.0886906i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1109.24 | −1.75791 | −0.878956 | − | 0.476903i | \(-0.841759\pi\) | ||||
−0.878956 | + | 0.476903i | \(0.841759\pi\) | |||||||
\(632\) | − 157.454i | − 0.249136i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −253.361 | −0.399623 | ||||||||
\(635\) | 840.897i | 1.32425i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 696.133 | 1.09283 | ||||||||
\(638\) | − 345.762i | − 0.541947i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 509.318 | 0.795809 | ||||||||
\(641\) | 165.270i | 0.257832i | 0.991656 | + | 0.128916i | \(0.0411497\pi\) | ||||
−0.991656 | + | 0.128916i | \(0.958850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 794.624 | 1.23581 | 0.617904 | − | 0.786254i | \(-0.287982\pi\) | ||||
0.617904 | + | 0.786254i | \(0.287982\pi\) | |||||||
\(644\) | − 556.197i | − 0.863659i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.5839 | 0.0256717 | ||||||||
\(647\) | 222.504i | 0.343900i | 0.985106 | + | 0.171950i | \(0.0550068\pi\) | ||||
−0.985106 | + | 0.171950i | \(0.944993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 801.803 | 1.23544 | ||||||||
\(650\) | − 51.8602i | − 0.0797849i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 105.707 | 0.162128 | ||||||||
\(653\) | − 466.485i | − 0.714373i | −0.934033 | − | 0.357186i | \(-0.883736\pi\) | ||||
0.934033 | − | 0.357186i | \(-0.116264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 530.328 | 0.809661 | ||||||||
\(656\) | 20.4424i | 0.0311622i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 151.647 | 0.230466 | ||||||||
\(659\) | 208.274i | 0.316045i | 0.987436 | + | 0.158022i | \(0.0505118\pi\) | ||||
−0.987436 | + | 0.158022i | \(0.949488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −633.782 | −0.958823 | −0.479411 | − | 0.877590i | \(-0.659150\pi\) | ||||
−0.479411 | + | 0.877590i | \(0.659150\pi\) | |||||||
\(662\) | 697.365i | 1.05342i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −244.060 | −0.367560 | ||||||||
\(665\) | − 256.371i | − 0.385521i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −504.851 | −0.756898 | ||||||||
\(668\) | − 440.135i | − 0.658884i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −606.972 | −0.905928 | ||||||||
\(671\) | 916.876i | 1.36643i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 110.021 | 0.163478 | 0.0817390 | − | 0.996654i | \(-0.473953\pi\) | ||||
0.0817390 | + | 0.996654i | \(0.473953\pi\) | |||||||
\(674\) | 521.584i | 0.773864i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −113.573 | −0.168007 | ||||||||
\(677\) | − 143.039i | − 0.211283i | −0.994404 | − | 0.105642i | \(-0.966310\pi\) | ||||
0.994404 | − | 0.105642i | \(-0.0336896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 840.686 | 1.23812 | ||||||||
\(680\) | 131.353i | 0.193166i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −301.611 | −0.442245 | ||||||||
\(683\) | − 905.343i | − 1.32554i | −0.748824 | − | 0.662769i | \(-0.769381\pi\) | ||||
0.748824 | − | 0.662769i | \(-0.230619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −353.429 | −0.515954 | ||||||||
\(686\) | − 158.658i | − 0.231280i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 59.8721 | 0.0870234 | ||||||||
\(689\) | 950.537i | 1.37959i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 532.010 | 0.769913 | 0.384957 | − | 0.922935i | \(-0.374216\pi\) | ||||
0.384957 | + | 0.922935i | \(0.374216\pi\) | |||||||
\(692\) | 28.8825i | 0.0417377i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 274.173 | 0.395063 | ||||||||
\(695\) | 674.494i | 0.970495i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.3205 | −0.0564140 | ||||||||
\(698\) | 278.380i | 0.398826i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 111.105 | 0.158722 | ||||||||
\(701\) | − 905.026i | − 1.29105i | −0.763739 | − | 0.645525i | \(-0.776639\pi\) | ||||
0.763739 | − | 0.645525i | \(-0.223361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −79.8237 | −0.113547 | ||||||||
\(704\) | − 370.023i | − 0.525601i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.7099 | −0.0420820 | ||||||||
\(707\) | − 50.3194i | − 0.0711731i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −363.866 | −0.513211 | −0.256605 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256605 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(710\) | 760.337i | 1.07090i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 533.058 | 0.748677 | ||||||||
\(713\) | 440.385i | 0.617651i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 710.118 | 0.993172 | ||||||||
\(716\) | − 749.446i | − 1.04671i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.4942 | 0.0313289 | ||||||||
\(719\) | − 449.557i | − 0.625253i | −0.949876 | − | 0.312626i | \(-0.898791\pi\) | ||||
0.949876 | − | 0.312626i | \(-0.101209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 761.559 | 1.05625 | ||||||||
\(722\) | − 395.378i | − 0.547615i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −288.553 | −0.398555 | ||||||||
\(725\) | − 100.848i | − 0.139101i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 579.366 | 0.796927 | 0.398463 | − | 0.917184i | \(-0.369544\pi\) | ||||
0.398463 | + | 0.917184i | \(0.369544\pi\) | |||||||
\(728\) | − 913.862i | − 1.25530i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 569.582 | 0.780250 | ||||||||
\(731\) | 115.163i | 0.157541i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 936.322 | 1.27738 | 0.638691 | − | 0.769463i | \(-0.279476\pi\) | ||||
0.638691 | + | 0.769463i | \(0.279476\pi\) | |||||||
\(734\) | 453.605i | 0.617991i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −652.944 | −0.887152 | ||||||||
\(737\) | − 1140.62i | − 1.54765i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 527.835 | 0.714256 | 0.357128 | − | 0.934055i | \(-0.383756\pi\) | ||||
0.357128 | + | 0.934055i | \(0.383756\pi\) | |||||||
\(740\) | − 252.070i | − 0.340635i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1034.91 | 1.39476 | ||||||||
\(743\) | 36.8321i | 0.0495721i | 0.999693 | + | 0.0247861i | \(0.00789045\pi\) | ||||
−0.999693 | + | 0.0247861i | \(0.992110\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1086.06 | −1.45779 | ||||||||
\(746\) | − 207.607i | − 0.278293i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −98.4121 | −0.131567 | ||||||||
\(749\) | − 1665.83i | − 2.22407i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 98.5014 | 0.131160 | 0.0655802 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655802 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(752\) | 20.3682i | 0.0270854i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −330.714 | −0.438613 | ||||||||
\(755\) | − 689.781i | − 0.913617i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1385.09 | −1.82971 | −0.914857 | − | 0.403779i | \(-0.867697\pi\) | ||||
−0.914857 | + | 0.403779i | \(0.867697\pi\) | |||||||
\(758\) | 4.04152i | 0.00533182i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −187.950 | −0.247303 | ||||||||
\(761\) | 1454.92i | 1.91185i | 0.293608 | + | 0.955926i | \(0.405144\pi\) | ||||
−0.293608 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 195.716 | 0.256509 | ||||||||
\(764\) | 288.103i | 0.377098i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.9993 | −0.0261088 | ||||||||
\(767\) | − 766.908i | − 0.999880i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −100.066 | −0.130125 | −0.0650624 | − | 0.997881i | \(-0.520725\pi\) | ||||
−0.0650624 | + | 0.997881i | \(0.520725\pi\) | |||||||
\(770\) | − 773.154i | − 1.00410i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 530.720 | 0.687461 | ||||||||
\(773\) | − 632.693i | − 0.818491i | −0.912424 | − | 0.409245i | \(-0.865792\pi\) | ||||
0.912424 | − | 0.409245i | \(-0.134208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −87.9708 | −0.113511 | ||||||||
\(776\) | − 616.321i | − 0.794228i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 367.761 | 0.472701 | ||||||||
\(779\) | − 56.2630i | − 0.0722247i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1428.82 | −1.82948 | ||||||||
\(782\) | − 73.0247i | − 0.0933820i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 101.800 | 0.129847 | ||||||||
\(785\) | 747.948i | 0.952800i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −815.667 | −1.03643 | −0.518213 | − | 0.855252i | \(-0.673402\pi\) | ||||
−0.518213 | + | 0.855252i | \(0.673402\pi\) | |||||||
\(788\) | − 776.315i | − 0.985171i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −127.413 | −0.161283 | ||||||||
\(791\) | 189.789i | 0.239935i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 876.973 | 1.10589 | ||||||||
\(794\) | 311.233i | 0.391981i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −218.299 | −0.274245 | ||||||||
\(797\) | − 1252.70i | − 1.57177i | −0.618375 | − | 0.785883i | \(-0.712209\pi\) | ||||
0.618375 | − | 0.785883i | \(-0.287791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.1778 | −0.0490335 | ||||||||
\(800\) | − 130.431i | − 0.163039i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −113.155 | −0.141091 | ||||||||
\(803\) | 1070.36i | 1.33295i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1128.89 | −1.40235 | ||||||||
\(806\) | 288.485i | 0.357921i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.8899 | −0.0456559 | ||||||||
\(809\) | 1021.88i | 1.26313i | 0.775321 | + | 0.631567i | \(0.217588\pi\) | ||||
−0.775321 | + | 0.631567i | \(0.782412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −365.788 | −0.451034 | −0.225517 | − | 0.974239i | \(-0.572407\pi\) | ||||
−0.225517 | + | 0.974239i | \(0.572407\pi\) | |||||||
\(812\) | − 708.522i | − 0.872564i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −240.729 | −0.295736 | ||||||||
\(815\) | − 214.550i | − 0.263252i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −164.784 | −0.201694 | ||||||||
\(818\) | − 470.589i | − 0.575292i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 177.669 | 0.216670 | ||||||||
\(821\) | 9.69598i | 0.0118100i | 0.999983 | + | 0.00590498i | \(0.00187962\pi\) | ||||
−0.999983 | + | 0.00590498i | \(0.998120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.893888 | 0.00108613 | 0.000543067 | − | 1.00000i | \(-0.499827\pi\) | ||||
0.000543067 | 1.00000i | \(0.499827\pi\) | ||||||||
\(824\) | − 558.311i | − 0.677562i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −834.986 | −1.01088 | ||||||||
\(827\) | − 673.895i | − 0.814868i | −0.913235 | − | 0.407434i | \(-0.866424\pi\) | ||||
0.913235 | − | 0.407434i | \(-0.133576\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.9608 | 0.0349346 | 0.0174673 | − | 0.999847i | \(-0.494440\pi\) | ||||
0.0174673 | + | 0.999847i | \(0.494440\pi\) | |||||||
\(830\) | 197.496i | 0.237947i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −353.919 | −0.425384 | ||||||||
\(833\) | 195.810i | 0.235066i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −893.325 | −1.06985 | ||||||||
\(836\) | − 140.816i | − 0.168440i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 136.221 | 0.162555 | ||||||||
\(839\) | 638.715i | 0.761282i | 0.924723 | + | 0.380641i | \(0.124297\pi\) | ||||
−0.924723 | + | 0.380641i | \(0.875703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 197.886 | 0.235298 | ||||||||
\(842\) | − 605.249i | − 0.718823i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 307.241 | 0.364029 | ||||||||
\(845\) | 230.514i | 0.272798i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 178.251 | 0.210449 | ||||||||
\(848\) | 139.003i | 0.163918i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.5873 | 0.0171616 | ||||||||
\(851\) | 351.491i | 0.413033i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 777.081 | 0.910998 | 0.455499 | − | 0.890236i | \(-0.349461\pi\) | ||||
0.455499 | + | 0.890236i | \(0.349461\pi\) | |||||||
\(854\) | − 954.821i | − 1.11806i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1221.25 | −1.42669 | ||||||||
\(857\) | − 1076.82i | − 1.25650i | −0.778010 | − | 0.628252i | \(-0.783771\pi\) | ||||
0.778010 | − | 0.628252i | \(-0.216229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −80.9841 | −0.0942772 | −0.0471386 | − | 0.998888i | \(-0.515010\pi\) | ||||
−0.0471386 | + | 0.998888i | \(0.515010\pi\) | |||||||
\(860\) | − 520.361i | − 0.605070i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 306.007 | 0.354996 | ||||||||
\(863\) | − 1599.17i | − 1.85304i | −0.376244 | − | 0.926520i | \(-0.622785\pi\) | ||||
0.376244 | − | 0.926520i | \(-0.377215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.6217 | 0.0677708 | ||||||||
\(866\) | − 815.011i | − 0.941121i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −618.049 | −0.712038 | ||||||||
\(869\) | − 239.435i | − 0.275529i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1090.98 | −1.25256 | ||||||||
\(872\) | − 143.483i | − 0.164544i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 104.490 | 0.119553 | ||||||||
\(875\) | 1192.16i | 1.36247i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −378.583 | −0.431679 | −0.215840 | − | 0.976429i | \(-0.569249\pi\) | ||||
−0.215840 | + | 0.976429i | \(0.569249\pi\) | |||||||
\(878\) | − 514.208i | − 0.585658i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 103.845 | 0.118006 | ||||||||
\(881\) | − 1208.75i | − 1.37202i | −0.727593 | − | 0.686009i | \(-0.759361\pi\) | ||||
0.727593 | − | 0.686009i | \(-0.240639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −596.289 | −0.675299 | −0.337649 | − | 0.941272i | \(-0.609632\pi\) | ||||
−0.337649 | + | 0.941272i | \(0.609632\pi\) | |||||||
\(884\) | 94.1292i | 0.106481i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −704.521 | −0.795170 | ||||||||
\(887\) | 101.561i | 0.114500i | 0.998360 | + | 0.0572499i | \(0.0182332\pi\) | ||||
−0.998360 | + | 0.0572499i | \(0.981767\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1645.61 | 1.85108 | ||||||||
\(890\) | − 431.356i | − 0.484670i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −525.755 | −0.589412 | ||||||||
\(893\) | − 56.0587i | − 0.0627757i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1521.12 | −1.69958 | ||||||||
\(896\) | − 996.718i | − 1.11241i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −466.174 | −0.519125 | ||||||||
\(899\) | 560.993i | 0.624019i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −267.369 | −0.296747 | ||||||||
\(902\) | − 169.676i | − 0.188111i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 139.137 | 0.153913 | ||||||||
\(905\) | 585.666i | 0.647145i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1725.63 | 1.90257 | 0.951285 | − | 0.308313i | \(-0.0997644\pi\) | ||||
0.951285 | + | 0.308313i | \(0.0997644\pi\) | |||||||
\(908\) | 13.6636i | 0.0150480i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −739.506 | −0.812644 | ||||||||
\(911\) | − 312.709i | − 0.343259i | −0.985162 | − | 0.171629i | \(-0.945097\pi\) | ||||
0.985162 | − | 0.171629i | \(-0.0549032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −371.133 | −0.406499 | ||||||||
\(914\) | − 170.792i | − 0.186862i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 937.135 | 1.02307 | ||||||||
\(917\) | − 1037.84i | − 1.13177i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 198.504 | 0.216000 | 0.108000 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108000 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(920\) | 827.609i | 0.899574i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 911.834 | 0.988974 | ||||||||
\(923\) | 1366.64i | 1.48065i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.2135 | −0.0759065 | ||||||||
\(926\) | − 416.150i | − 0.449406i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −831.765 | −0.896299 | ||||||||
\(929\) | − 1329.75i | − 1.43138i | −0.698420 | − | 0.715688i | \(-0.746113\pi\) | ||||
0.698420 | − | 0.715688i | \(-0.253887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −280.181 | −0.300946 | ||||||||
\(932\) | 372.790i | 0.399990i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −118.335 | −0.126697 | ||||||||
\(935\) | 199.743i | 0.213629i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1351.34 | 1.44220 | 0.721100 | − | 0.692831i | \(-0.243637\pi\) | ||||
0.721100 | + | 0.692831i | \(0.243637\pi\) | |||||||
\(938\) | 1187.82i | 1.26634i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 177.024 | 0.188323 | ||||||||
\(941\) | 777.265i | 0.825999i | 0.910731 | + | 0.413000i | \(0.135519\pi\) | ||||
−0.910731 | + | 0.413000i | \(0.864481\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −247.746 | −0.262721 | ||||||||
\(944\) | − 112.150i | − 0.118803i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −496.949 | −0.525316 | ||||||||
\(947\) | − 274.291i | − 0.289642i | −0.989458 | − | 0.144821i | \(-0.953739\pi\) | ||||
0.989458 | − | 0.144821i | \(-0.0462606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1023.78 | 1.07879 | ||||||||
\(950\) | 20.8727i | 0.0219713i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 257.053 | 0.270014 | ||||||||
\(953\) | − 991.095i | − 1.03997i | −0.854174 | − | 0.519987i | \(-0.825937\pi\) | ||||
0.854174 | − | 0.519987i | \(-0.174063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 584.752 | 0.612306 | ||||||||
\(956\) | − 391.655i | − 0.409681i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 146.711 | 0.153143 | ||||||||
\(959\) | 691.649i | 0.721219i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −471.641 | −0.490782 | ||||||||
\(962\) | 230.253i | 0.239348i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 807.355 | 0.837506 | ||||||||
\(965\) | − 1077.18i | − 1.11625i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 312.452 | 0.323115 | 0.161557 | − | 0.986863i | \(-0.448348\pi\) | ||||
0.161557 | + | 0.986863i | \(0.448348\pi\) | |||||||
\(968\) | − 130.678i | − 0.134998i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −498.733 | −0.514158 | ||||||||
\(971\) | 487.838i | 0.502407i | 0.967934 | + | 0.251204i | \(0.0808264\pi\) | ||||
−0.967934 | + | 0.251204i | \(0.919174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1319.96 | 1.35659 | ||||||||
\(974\) | 527.088i | 0.541158i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 128.245 | 0.131399 | ||||||||
\(977\) | − 643.819i | − 0.658976i | −0.944160 | − | 0.329488i | \(-0.893124\pi\) | ||||
0.944160 | − | 0.329488i | \(-0.106876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 810.603 | 0.827991 | ||||||||
\(980\) | − 884.763i | − 0.902820i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −366.966 | −0.373692 | ||||||||
\(983\) | 1539.82i | 1.56645i | 0.621737 | + | 0.783226i | \(0.286427\pi\) | ||||
−0.621737 | + | 0.783226i | \(0.713573\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1575.66 | −1.59965 | ||||||||
\(986\) | − 93.0240i | − 0.0943448i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −134.688 | −0.136324 | ||||||||
\(989\) | 725.601i | 0.733672i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 311.141 | 0.313967 | 0.156984 | − | 0.987601i | \(-0.449823\pi\) | ||||
0.156984 | + | 0.987601i | \(0.449823\pi\) | |||||||
\(992\) | 725.555i | 0.731407i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1487.96 | 1.49694 | ||||||||
\(995\) | 443.073i | 0.445300i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.2298 | −0.0483749 | −0.0241875 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241875 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(998\) | 141.953i | 0.142238i | ||||||||
\(999\) | 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 | 729.3.b.a.728.19 | 30 | ||
3.2 | odd | 2 | inner | 729.3.b.a.728.12 | 30 | ||
27.2 | odd | 18 | 243.3.f.c.53.2 | 30 | |||
27.4 | even | 9 | 243.3.f.d.107.2 | 30 | |||
27.5 | odd | 18 | 81.3.f.a.8.2 | 30 | |||
27.7 | even | 9 | 243.3.f.a.134.4 | 30 | |||
27.11 | odd | 18 | 27.3.f.a.14.4 | yes | 30 | ||
27.13 | even | 9 | 243.3.f.c.188.2 | 30 | |||
27.14 | odd | 18 | 243.3.f.b.188.4 | 30 | |||
27.16 | even | 9 | 81.3.f.a.71.2 | 30 | |||
27.20 | odd | 18 | 243.3.f.d.134.2 | 30 | |||
27.22 | even | 9 | 27.3.f.a.2.4 | ✓ | 30 | ||
27.23 | odd | 18 | 243.3.f.a.107.4 | 30 | |||
27.25 | even | 9 | 243.3.f.b.53.4 | 30 | |||
108.11 | even | 18 | 432.3.bc.a.257.3 | 30 | |||
108.103 | odd | 18 | 432.3.bc.a.353.3 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.2.4 | ✓ | 30 | 27.22 | even | 9 | ||
27.3.f.a.14.4 | yes | 30 | 27.11 | odd | 18 | ||
81.3.f.a.8.2 | 30 | 27.5 | odd | 18 | |||
81.3.f.a.71.2 | 30 | 27.16 | even | 9 | |||
243.3.f.a.107.4 | 30 | 27.23 | odd | 18 | |||
243.3.f.a.134.4 | 30 | 27.7 | even | 9 | |||
243.3.f.b.53.4 | 30 | 27.25 | even | 9 | |||
243.3.f.b.188.4 | 30 | 27.14 | odd | 18 | |||
243.3.f.c.53.2 | 30 | 27.2 | odd | 18 | |||
243.3.f.c.188.2 | 30 | 27.13 | even | 9 | |||
243.3.f.d.107.2 | 30 | 27.4 | even | 9 | |||
243.3.f.d.134.2 | 30 | 27.20 | odd | 18 | |||
432.3.bc.a.257.3 | 30 | 108.11 | even | 18 | |||
432.3.bc.a.353.3 | 30 | 108.103 | odd | 18 | |||
729.3.b.a.728.12 | 30 | 3.2 | odd | 2 | inner | ||
729.3.b.a.728.19 | 30 | 1.1 | even | 1 | trivial |