Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.15 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.34 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.96436 | + | 1.06831i | 0.878488 | + | 0.477764i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.03191i | − | 1.14595i | −0.819572 | − | 0.572977i | \(-0.805788\pi\) | ||
0.819572 | − | 0.572977i | \(-0.194212\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.01519 | 0.607603 | 0.303801 | − | 0.952735i | \(-0.401744\pi\) | ||||
0.303801 | + | 0.952735i | \(0.401744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13975i | 0.316110i | 0.987430 | + | 0.158055i | \(0.0505224\pi\) | ||||
−0.987430 | + | 0.158055i | \(0.949478\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.06831 | − | 1.96436i | 0.275837 | − | 0.507195i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.286135i | 0.0693979i | 0.999398 | + | 0.0346989i | \(0.0110472\pi\) | ||||
−0.999398 | + | 0.0346989i | \(0.988953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.78093 | −0.408574 | −0.204287 | − | 0.978911i | \(-0.565488\pi\) | ||||
−0.204287 | + | 0.978911i | \(0.565488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.03191 | −0.661617 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.18704i | 1.49860i | 0.662230 | + | 0.749301i | \(0.269610\pi\) | ||||
−0.662230 | + | 0.749301i | \(0.730390\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.71741 | + | 4.19710i | 0.543483 | + | 0.839420i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.82296 | 1.63838 | 0.819192 | − | 0.573520i | \(-0.194422\pi\) | ||||
0.819192 | + | 0.573520i | \(0.194422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.29610 | 0.412392 | 0.206196 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206196 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.01519i | − | 0.350800i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.23903 | − | 5.95576i | 0.547496 | − | 1.00671i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.36755i | 0.389223i | 0.980880 | + | 0.194612i | \(0.0623446\pi\) | ||||
−0.980880 | + | 0.194612i | \(0.937655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.13975 | 0.182506 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.15374 | 0.804879 | 0.402440 | − | 0.915446i | \(-0.368162\pi\) | ||||
0.402440 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.11893i | − | 0.323134i | −0.986862 | − | 0.161567i | \(-0.948345\pi\) | ||
0.986862 | − | 0.161567i | \(-0.0516548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.96436 | − | 1.06831i | −0.292829 | − | 0.159255i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.00381i | − | 0.875746i | −0.899037 | − | 0.437873i | \(-0.855732\pi\) | ||
0.899037 | − | 0.437873i | \(-0.144268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.19247 | −0.313210 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.286135 | 0.0400669 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.22119i | 1.26663i | 0.773895 | + | 0.633314i | \(0.218306\pi\) | ||||
−0.773895 | + | 0.633314i | \(0.781694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.95856 | + | 2.15285i | 0.533772 | + | 0.290291i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.78093i | 0.235890i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.81688 | 0.757294 | 0.378647 | − | 0.925541i | \(-0.376390\pi\) | ||||
0.378647 | + | 0.925541i | \(0.376390\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.84468 | 1.00441 | 0.502204 | − | 0.864749i | \(-0.332523\pi\) | ||||
0.502204 | + | 0.864749i | \(0.332523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.03191i | 0.381985i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.21761 | + | 2.23888i | −0.151026 | + | 0.277699i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.18704 | 0.865218 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.24595 | 0.622579 | 0.311290 | − | 0.950315i | \(-0.399239\pi\) | ||||
0.311290 | + | 0.950315i | \(0.399239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.12823i | − | 0.951337i | −0.879625 | − | 0.475669i | \(-0.842206\pi\) | ||
0.879625 | − | 0.475669i | \(-0.157794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.19710 | − | 2.71741i | 0.484640 | − | 0.313780i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.10987i | − | 0.696285i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3077 | −1.49723 | −0.748615 | − | 0.663004i | \(-0.769281\pi\) | ||||
−0.748615 | + | 0.663004i | \(0.769281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.42607i | − | 1.03465i | −0.855791 | − | 0.517323i | \(-0.826929\pi\) | ||
0.855791 | − | 0.517323i | \(-0.173071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.305682 | + | 0.562071i | −0.0331558 | + | 0.0609652i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.82296i | − | 0.945921i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.93173 | 0.204763 | 0.102382 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102382 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.45562 | 0.362248 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.29610i | − | 0.238094i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.49839 | − | 1.90259i | −0.358927 | − | 0.195202i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.99160i | 0.608355i | 0.952615 | + | 0.304178i | \(0.0983816\pi\) | ||||
−0.952615 | + | 0.304178i | \(0.901618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.01519 | −0.202534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.706768 | −0.0703261 | −0.0351630 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351630 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.437107i | − | 0.0430694i | −0.999768 | − | 0.0215347i | \(-0.993145\pi\) | ||
0.999768 | − | 0.0215347i | \(-0.00685524\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.95576 | − | 3.23903i | −0.581222 | − | 0.316097i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16.8841i | − | 1.63225i | −0.577878 | − | 0.816123i | \(-0.696119\pi\) | ||
0.577878 | − | 0.816123i | \(-0.303881\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00505 | 0.0962667 | 0.0481334 | − | 0.998841i | \(-0.484673\pi\) | ||||
0.0481334 | + | 0.998841i | \(0.484673\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.36755 | 0.224718 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.58363i | − | 0.713407i | −0.934218 | − | 0.356704i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356704i | \(-0.116099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.67801 | + | 14.1179i | −0.715978 | + | 1.31650i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.13975i | − | 0.105370i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.867535 | 0.0795268 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.93901 | −0.630819 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.15374i | − | 0.464697i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.854158 | + | 11.1477i | 0.0763983 | + | 0.997077i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.38467i | − | 0.832755i | −0.909192 | − | 0.416377i | \(-0.863300\pi\) | ||
0.909192 | − | 0.416377i | \(-0.136700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.11893 | −0.186561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3056 | 1.42462 | 0.712312 | − | 0.701863i | \(-0.247648\pi\) | ||||
0.712312 | + | 0.701863i | \(0.247648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.39963i | 0.468207i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.06831 | + | 1.96436i | −0.0919458 | + | 0.169065i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0046i | 1.36736i | 0.729781 | + | 0.683681i | \(0.239622\pi\) | ||||
−0.729781 | + | 0.683681i | \(0.760378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.81926 | −0.578402 | −0.289201 | − | 0.957268i | \(-0.593390\pi\) | ||||
−0.289201 | + | 0.957268i | \(0.593390\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00381 | −0.505612 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.29682i | 0.192069i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.3315 | + | 9.42569i | 1.43930 | + | 0.782761i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.19247i | 0.180832i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6381 | −1.52689 | −0.763447 | − | 0.645870i | \(-0.776495\pi\) | ||||
−0.763447 | + | 0.645870i | \(0.776495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.11827 | 0.0910037 | 0.0455018 | − | 0.998964i | \(-0.485511\pi\) | ||||
0.0455018 | + | 0.998964i | \(0.485511\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.286135i | − | 0.0231326i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.51036 | + | 2.45295i | 0.362281 | + | 0.197026i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.581889i | 0.0464398i | 0.999730 | + | 0.0232199i | \(0.00739179\pi\) | ||||
−0.999730 | + | 0.0232199i | \(0.992608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.22119 | 0.731288 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.7904 | 1.71733 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.09462i | − | 0.477367i | −0.971097 | − | 0.238684i | \(-0.923284\pi\) | ||
0.971097 | − | 0.238684i | \(-0.0767159\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.15285 | − | 3.95856i | 0.167599 | − | 0.308173i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.44027i | − | 0.111451i | −0.998446 | − | 0.0557257i | \(-0.982253\pi\) | ||
0.998446 | − | 0.0557257i | \(-0.0177472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7010 | 0.900074 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.78093 | 0.136191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1024i | 1.14821i | 0.818781 | + | 0.574106i | \(0.194650\pi\) | ||||
−0.818781 | + | 0.574106i | \(0.805350\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7252 | − | 8.23895i | 0.961937 | − | 0.622806i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.81688i | − | 0.437224i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0255 | −0.898825 | −0.449412 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449412 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1277 | 1.42175 | 0.710876 | − | 0.703317i | \(-0.248299\pi\) | ||||
0.710876 | + | 0.703317i | \(0.248299\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.84468i | − | 0.579895i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.52929 | + | 4.65072i | −0.185957 | + | 0.341928i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.576616i | 0.0421663i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.03191 | 0.220539 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.785469 | 0.0568345 | 0.0284173 | − | 0.999596i | \(-0.490953\pi\) | ||||
0.0284173 | + | 0.999596i | \(0.490953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.88940i | 0.279965i | 0.990154 | + | 0.139983i | \(0.0447046\pi\) | ||||
−0.990154 | + | 0.139983i | \(0.955295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.23888 | + | 1.21761i | 0.160330 | + | 0.0871950i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.5055i | − | 1.24721i | −0.781738 | − | 0.623607i | \(-0.785667\pi\) | ||
0.781738 | − | 0.623607i | \(-0.214333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.28359 | 0.516320 | 0.258160 | − | 0.966102i | \(-0.416884\pi\) | ||||
0.258160 | + | 0.966102i | \(0.416884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 26.7504i | − | 1.87751i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1238 | + | 5.50581i | 0.707077 | + | 0.384543i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.18704i | − | 0.499534i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.58892 | −0.248251 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.44237 | −0.236982 | −0.118491 | − | 0.992955i | \(-0.537806\pi\) | ||||
−0.118491 | + | 0.992955i | \(0.537806\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 5.24595i | − | 0.359446i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.26368 | − | 4.16234i | 0.154382 | − | 0.283869i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.96156i | − | 0.472582i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.12823 | −0.549255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.326123 | −0.0219374 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.03546i | 0.136304i | 0.997675 | + | 0.0681521i | \(0.0217103\pi\) | ||||
−0.997675 | + | 0.0681521i | \(0.978290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.71741 | − | 4.19710i | −0.181161 | − | 0.279807i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.69664i | 0.178982i | 0.995988 | + | 0.0894910i | \(0.0285240\pi\) | ||||
−0.995988 | + | 0.0894910i | \(0.971476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5001 | −1.35468 | −0.677342 | − | 0.735668i | \(-0.736868\pi\) | ||||
−0.677342 | + | 0.735668i | \(0.736868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.10987 | −0.402000 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.0115i | − | 0.917927i | −0.888455 | − | 0.458964i | \(-0.848221\pi\) | ||
0.888455 | − | 0.458964i | \(-0.151779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.41395 | − | 11.7936i | 0.418400 | − | 0.769332i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.3077i | 0.864427i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8898 | 1.22188 | 0.610940 | − | 0.791677i | \(-0.290792\pi\) | ||||
0.610940 | + | 0.791677i | \(0.290792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.81348 | −0.374479 | −0.187240 | − | 0.982314i | \(-0.559954\pi\) | ||||
−0.187240 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.30680 | − | 2.34224i | −0.275151 | − | 0.149641i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.02982i | − | 0.129154i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.42607 | −0.597353 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5194 | 1.35829 | 0.679147 | − | 0.734002i | \(-0.262350\pi\) | ||||
0.679147 | + | 0.734002i | \(0.262350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.4832i | 0.910554i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.562071 | + | 0.305682i | 0.0351983 | + | 0.0191425i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8474i | 1.36281i | 0.731909 | + | 0.681403i | \(0.238630\pi\) | ||||
−0.731909 | + | 0.681403i | \(0.761370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.17820 | 0.446032 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.82296 | −0.546128 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.11910i | − | 0.253994i | −0.991903 | − | 0.126997i | \(-0.959466\pi\) | ||
0.991903 | − | 0.126997i | \(-0.0405339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.85112 | + | 18.1137i | −0.605149 | + | 1.11272i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.93173i | − | 0.118220i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.3683 | −1.18090 | −0.590452 | − | 0.807073i | \(-0.701050\pi\) | ||||
−0.590452 | + | 0.807073i | \(0.701050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.63445 | −0.281523 | −0.140761 | − | 0.990044i | \(-0.544955\pi\) | ||||
−0.140761 | + | 0.990044i | \(0.544955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 3.45562i | − | 0.209144i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.47611 | + | 8.45796i | 0.330222 | + | 0.510034i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.126860i | − | 0.00762231i | −0.999993 | − | 0.00381115i | \(-0.998787\pi\) | ||
0.999993 | − | 0.00381115i | \(-0.00121313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.29610 | −0.137464 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0912 | −1.13888 | −0.569442 | − | 0.822032i | \(-0.692841\pi\) | ||||
−0.569442 | + | 0.822032i | \(0.692841\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.07191i | 0.0637185i | 0.999492 | + | 0.0318592i | \(0.0101428\pi\) | ||||
−0.999492 | + | 0.0318592i | \(0.989857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.90259 | + | 3.49839i | −0.112700 | + | 0.207227i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 15.6257i | − | 0.922355i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9181 | 0.995184 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.99160 | 0.351234 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 27.5814i | − | 1.61132i | −0.592378 | − | 0.805660i | \(-0.701811\pi\) | ||
0.592378 | − | 0.805660i | \(-0.298189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.4264 | + | 6.21425i | 0.665273 | + | 0.361808i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.01519i | 0.116933i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.19144 | −0.473723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.42440 | −0.370296 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.706768i | 0.0406028i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.4098 | + | 8.38057i | 0.882360 | + | 0.479870i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.66181i | 0.551429i | 0.961240 | + | 0.275714i | \(0.0889144\pi\) | ||||
−0.961240 | + | 0.275714i | \(0.911086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.437107 | −0.0248661 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.912234 | 0.0517280 | 0.0258640 | − | 0.999665i | \(-0.491766\pi\) | ||||
0.0258640 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.74134i | 0.0984263i | 0.998788 | + | 0.0492131i | \(0.0156714\pi\) | ||||
−0.998788 | + | 0.0492131i | \(0.984329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.23903 | + | 5.95576i | −0.182499 | + | 0.335569i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.5696i | − | 1.37997i | −0.723825 | − | 0.689984i | \(-0.757618\pi\) | ||
0.723825 | − | 0.689984i | \(-0.242382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.7799 | 0.995486 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8841 | −0.942378 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.509587i | − | 0.0283542i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.78365 | + | 3.09718i | −0.265349 | + | 0.171800i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.00505i | − | 0.0555796i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.2030 | −1.00356 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.1837 | 1.54911 | 0.774557 | − | 0.632504i | \(-0.217973\pi\) | ||||
0.774557 | + | 0.632504i | \(0.217973\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.36755i | − | 0.129741i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.06831 | − | 1.96436i | 0.0583682 | − | 0.107324i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0449i | 1.03744i | 0.854944 | + | 0.518721i | \(0.173592\pi\) | ||||
−0.854944 | + | 0.518721i | \(0.826408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.58363 | −0.411886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.62708 | 0.250570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.5760i | − | 0.787030i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.1179 | + | 7.67801i | 0.760084 | + | 0.413370i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 10.2409i | − | 0.549762i | −0.961478 | − | 0.274881i | \(-0.911362\pi\) | ||
0.961478 | − | 0.274881i | \(-0.0886385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.2558 | 1.19132 | 0.595662 | − | 0.803235i | \(-0.296890\pi\) | ||||
0.595662 | + | 0.803235i | \(0.296890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.13975 | −0.0608354 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.04721i | − | 0.215411i | −0.994183 | − | 0.107706i | \(-0.965650\pi\) | ||
0.994183 | − | 0.107706i | \(-0.0343504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3049 | + | 5.60432i | 0.546929 | + | 0.297446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.867535i | − | 0.0459148i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.41735 | −0.497029 | −0.248514 | − | 0.968628i | \(-0.579942\pi\) | ||||
−0.248514 | + | 0.968628i | \(0.579942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8283 | −0.833067 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.93901i | 0.364204i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.68350 | − | 15.9668i | 0.454515 | − | 0.835739i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.5169i | 1.54077i | 0.637581 | + | 0.770384i | \(0.279935\pi\) | ||||
−0.637581 | + | 0.770384i | \(0.720065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.15374 | −0.268293 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.9578 | 1.45150 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.77992i | − | 0.299273i | −0.988741 | − | 0.149636i | \(-0.952190\pi\) | ||
0.988741 | − | 0.149636i | \(-0.0478103\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1477 | − | 0.854158i | 0.575663 | − | 0.0441086i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.0560i | 0.517910i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.4720 | 0.897478 | 0.448739 | − | 0.893663i | \(-0.351873\pi\) | ||||
0.448739 | + | 0.893663i | \(0.351873\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.38467 | −0.480791 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.6307i | 1.36076i | 0.732858 | + | 0.680382i | \(0.238186\pi\) | ||||
−0.732858 | + | 0.680382i | \(0.761814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.52726 | − | 12.0020i | 0.332660 | − | 0.611678i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.11893i | 0.107711i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5671 | −0.890687 | −0.445343 | − | 0.895360i | \(-0.646918\pi\) | ||||
−0.445343 | + | 0.895360i | \(0.646918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.05646 | −0.104000 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.3056i | − | 0.822507i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.1411 | − | 14.2168i | −1.31530 | − | 0.715323i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6927i | 1.08872i | 0.838851 | + | 0.544362i | \(0.183228\pi\) | ||||
−0.838851 | + | 0.544362i | \(0.816772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.39963 | 0.270319 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.1350 | −0.605992 | −0.302996 | − | 0.952992i | \(-0.597987\pi\) | ||||
−0.302996 | + | 0.952992i | \(0.597987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.61698i | 0.130361i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96436 | + | 1.06831i | 0.0976098 | + | 0.0530849i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.77107i | 0.236493i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.20024 | −0.0593481 | −0.0296740 | − | 0.999560i | \(-0.509447\pi\) | ||||
−0.0296740 | + | 0.999560i | \(0.509447\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.0046 | 0.789447 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 17.6363i | − | 0.867824i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0700 | − | 18.5162i | 0.494316 | − | 0.908923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.81926i | 0.333941i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.86288 | 0.0910077 | 0.0455038 | − | 0.998964i | \(-0.485511\pi\) | ||||
0.0455038 | + | 0.998964i | \(0.485511\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6384 | 1.29828 | 0.649139 | − | 0.760670i | \(-0.275130\pi\) | ||||
0.649139 | + | 0.760670i | \(0.275130\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00381i | 0.291915i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20094 | + | 0.777547i | −0.0582540 | + | 0.0377166i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 23.7843i | − | 1.15101i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.29682 | 0.110891 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.88140 | −0.0906237 | −0.0453118 | − | 0.998973i | \(-0.514428\pi\) | ||||
−0.0453118 | + | 0.998973i | \(0.514428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.6245i | − | 0.750866i | −0.926849 | − | 0.375433i | \(-0.877494\pi\) | ||
0.926849 | − | 0.375433i | \(-0.122506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.42569 | − | 17.3315i | 0.451927 | − | 0.830980i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 12.7996i | − | 0.612289i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.78323 | 0.419201 | 0.209600 | − | 0.977787i | \(-0.432784\pi\) | ||||
0.209600 | + | 0.977787i | \(0.432784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.19247 | 0.104403 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.2846i | − | 0.488636i | −0.969695 | − | 0.244318i | \(-0.921436\pi\) | ||
0.969695 | − | 0.244318i | \(-0.0785640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.79461 | + | 2.06369i | 0.179882 | + | 0.0978285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.6381i | 0.881553i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0066 | 0.755396 | 0.377698 | − | 0.925929i | \(-0.376716\pi\) | ||||
0.377698 | + | 0.925929i | \(0.376716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3858 | 0.489047 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.11827i | − | 0.0525410i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.78808 | + | 3.69169i | 0.318230 | + | 0.173069i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.8643i | − | 0.742101i | −0.928613 | − | 0.371050i | \(-0.878998\pi\) | ||
0.928613 | − | 0.371050i | \(-0.121002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.286135 | −0.0133556 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6941 | −0.591225 | −0.295613 | − | 0.955308i | \(-0.595524\pi\) | ||||
−0.295613 | + | 0.955308i | \(0.595524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.01404i | 0.0471264i | 0.999722 | + | 0.0235632i | \(0.00750109\pi\) | ||||
−0.999722 | + | 0.0235632i | \(0.992499\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.45295 | − | 4.51036i | 0.113753 | − | 0.209163i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.0950i | − | 0.559690i | −0.960045 | − | 0.279845i | \(-0.909717\pi\) | ||
0.960045 | − | 0.279845i | \(-0.0902831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.03191 | −0.140001 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.581889 | 0.0268120 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.27005i | − | 0.196337i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.83953 | − | 7.47475i | −0.222053 | − | 0.342965i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 9.22119i | − | 0.422209i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1334 | −1.28545 | −0.642724 | − | 0.766097i | \(-0.722196\pi\) | ||||
−0.642724 | + | 0.766097i | \(0.722196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69842 | −0.123037 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 21.7904i | − | 0.991500i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.40091 | + | 11.7697i | −0.290650 | + | 0.534433i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.12111i | − | 0.186745i | −0.995631 | − | 0.0933726i | \(-0.970235\pi\) | ||
0.995631 | − | 0.0933726i | \(-0.0297648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.09462 | −0.275608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.7563 | −1.61366 | −0.806830 | − | 0.590784i | \(-0.798818\pi\) | ||||
−0.806830 | + | 0.590784i | \(0.798818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.52456i | 0.113700i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.95856 | − | 2.15285i | −0.177924 | − | 0.0967636i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15.9052i | − | 0.713447i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.35528 | 0.150203 | 0.0751014 | − | 0.997176i | \(-0.476072\pi\) | ||||
0.0751014 | + | 0.997176i | \(0.476072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.44027 | −0.0643465 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.41068i | 0.241250i | 0.992698 | + | 0.120625i | \(0.0384899\pi\) | ||||
−0.992698 | + | 0.120625i | \(0.961510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.38835 | − | 0.755050i | −0.0617806 | − | 0.0335993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.7010i | − | 0.519658i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.12069 | −0.138322 | −0.0691611 | − | 0.997606i | \(-0.522032\pi\) | ||||
−0.0691611 | + | 0.997606i | \(0.522032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.6441 | −1.09019 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.78093i | − | 0.0786301i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.466967 | − | 0.858634i | 0.0205770 | − | 0.0378359i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.0988i | − | 0.532105i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.1024 | 0.662920 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5687 | 0.769698 | 0.384849 | − | 0.922980i | \(-0.374254\pi\) | ||||
0.384849 | + | 0.922980i | \(0.374254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.2164i | 0.534185i | 0.963671 | + | 0.267093i | \(0.0860630\pi\) | ||||
−0.963671 | + | 0.267093i | \(0.913937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.23895 | − | 12.7252i | −0.359577 | − | 0.555375i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.656994i | 0.0286191i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.6535 | −1.24581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.81688 | −0.252431 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.87399i | 0.254431i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0375 | − | 33.1664i | 0.779829 | − | 1.43391i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0255i | 0.518937i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.41824 | −0.190307 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0129 | 0.645457 | 0.322728 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322728 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 19.1277i | − | 0.820849i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.97429 | + | 1.07371i | 0.0845692 | + | 0.0459928i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6577i | 1.22531i | 0.790349 | + | 0.612657i | \(0.209899\pi\) | ||||
−0.790349 | + | 0.612657i | \(0.790101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.84468 | −0.334803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.7131 | −0.669401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.3477i | 1.71576i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.65072 | + | 2.52929i | 0.197412 | + | 0.107362i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.1937i | − | 0.474294i | −0.971474 | − | 0.237147i | \(-0.923788\pi\) | ||
0.971474 | − | 0.237147i | \(-0.0762123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.41505 | 0.102146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.576616 | 0.0243447 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.1174i | 0.426397i | 0.977009 | + | 0.213198i | \(0.0683881\pi\) | ||||
−0.977009 | + | 0.213198i | \(0.931612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.10169 | − | 14.8970i | 0.340841 | − | 0.626720i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.03191i | − | 0.127328i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.0516 | −1.30175 | −0.650875 | − | 0.759185i | \(-0.725598\pi\) | ||||
−0.650875 | + | 0.759185i | \(0.725598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.08661 | −0.0454731 | −0.0227366 | − | 0.999741i | \(-0.507238\pi\) | ||||
−0.0227366 | + | 0.999741i | \(0.507238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.785469i | − | 0.0328134i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.1647 | + | 19.5302i | −1.25796 | + | 0.814464i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2750i | 0.427754i | 0.976861 | + | 0.213877i | \(0.0686092\pi\) | ||||
−0.976861 | + | 0.213877i | \(0.931391\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.88940 | 0.161638 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.5790 | −1.18566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.5825i | 0.769607i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.21761 | − | 2.23888i | 0.0503420 | − | 0.0925663i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.27942i | − | 0.0528072i | −0.999651 | − | 0.0264036i | \(-0.991594\pi\) | ||
0.999651 | − | 0.0264036i | \(-0.00840550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.08920 | −0.168493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5055 | −0.720079 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.8438i | − | 0.732757i | −0.930466 | − | 0.366378i | \(-0.880598\pi\) | ||
0.930466 | − | 0.366378i | \(-0.119402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.70415 | + | 0.926799i | 0.0698633 | + | 0.0379950i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.28359i | − | 0.298098i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5071 | −0.470167 | −0.235084 | − | 0.971975i | \(-0.575536\pi\) | ||||
−0.235084 | + | 0.971975i | \(0.575536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.9325 | 1.18018 | 0.590090 | − | 0.807337i | \(-0.299092\pi\) | ||||
0.590090 | + | 0.807337i | \(0.299092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.6307 | − | 7.41303i | −0.554167 | − | 0.301383i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9942i | 0.527418i | 0.964602 | + | 0.263709i | \(0.0849458\pi\) | ||||
−0.964602 | + | 0.263709i | \(0.915054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.7504 | −1.08398 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.84285 | 0.276832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.0239i | 1.73772i | 0.495059 | + | 0.868859i | \(0.335146\pi\) | ||||
−0.495059 | + | 0.868859i | \(0.664854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.50581 | − | 10.1238i | 0.222016 | − | 0.408231i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0193i | 1.53060i | 0.643675 | + | 0.765299i | \(0.277409\pi\) | ||||
−0.643675 | + | 0.765299i | \(0.722591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5438 | −1.30804 | −0.654022 | − | 0.756475i | \(-0.726920\pi\) | ||||
−0.654022 | + | 0.756475i | \(0.726920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.18704 | −0.288406 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 5.85683i | − | 0.234649i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.2313 | + | 22.8105i | −0.409253 | + | 0.912421i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.58892i | 0.143328i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.677439 | −0.0270113 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9220 | 0.793082 | 0.396541 | − | 0.918017i | \(-0.370210\pi\) | ||||
0.396541 | + | 0.918017i | \(0.370210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.44237i | 0.136822i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0258 | − | 18.4349i | 0.397860 | − | 0.731565i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.49887i | − | 0.0990089i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.24595 | −0.207526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.5081 | 1.83696 | 0.918479 | − | 0.395470i | \(-0.129418\pi\) | ||||
0.918479 | + | 0.395470i | \(0.129418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6172i | 0.773627i | 0.922158 | + | 0.386813i | \(0.126424\pi\) | ||||
−0.922158 | + | 0.386813i | \(0.873576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.16234 | − | 2.26368i | −0.163892 | − | 0.0891324i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8812i | 0.899551i | 0.893142 | + | 0.449776i | \(0.148496\pi\) | ||||
−0.893142 | + | 0.449776i | \(0.851504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.7221 | 0.460134 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.96156 | −0.272845 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.4979i | 0.684747i | 0.939564 | + | 0.342373i | \(0.111231\pi\) | ||||
−0.939564 | + | 0.342373i | \(0.888769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.0300 | + | 17.4194i | 1.25151 | + | 0.680634i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.12823i | 0.317112i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.7414 | −1.31438 | −0.657190 | − | 0.753725i | \(-0.728255\pi\) | ||||
−0.657190 | + | 0.753725i | \(0.728255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.3764 | −0.636967 | −0.318484 | − | 0.947928i | \(-0.603174\pi\) | ||||
−0.318484 | + | 0.947928i | \(0.603174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.326123i | 0.0126656i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.76849 | + | 10.6068i | −0.223692 | + | 0.411314i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.4110i | 2.45528i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.03546 | 0.0786953 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.8085 | 0.610281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 6.66168i | − | 0.256789i | −0.991723 | − | 0.128395i | \(-0.959018\pi\) | ||
0.991723 | − | 0.128395i | \(-0.0409824\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.19710 | + | 2.71741i | −0.161547 | + | 0.104593i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 17.0720i | − | 0.656129i | −0.944655 | − | 0.328064i | \(-0.893604\pi\) | ||
0.944655 | − | 0.328064i | \(-0.106396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.1660 | 0.697147 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.69664 | 0.103335 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.3173i | − | 0.777420i | −0.921360 | − | 0.388710i | \(-0.872921\pi\) | ||
0.921360 | − | 0.388710i | \(-0.127079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0979 | + | 31.4387i | −0.653276 | + | 1.20121i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.5001i | 0.782127i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5099 | −0.400394 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0742 | −0.801700 | −0.400850 | − | 0.916144i | \(-0.631285\pi\) | ||||
−0.400850 | + | 0.916144i | \(0.631285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.10987i | 0.232095i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.3955 | − | 7.28511i | −0.508120 | − | 0.276340i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.47467i | 0.0558569i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0115 | −0.529965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.1935 | 1.93355 | 0.966775 | − | 0.255628i | \(-0.0822824\pi\) | ||||
0.966775 | + | 0.255628i | \(0.0822824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.21645i | − | 0.159026i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.7936 | − | 6.41395i | −0.444174 | − | 0.241563i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.14286i | 0.0805905i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.5172 | −1.37143 | −0.685717 | − | 0.727869i | \(-0.740511\pi\) | ||||
−0.685717 | + | 0.727869i | \(0.740511\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3077 | 0.499077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.5022i | 0.618011i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.45372 | + | 4.51177i | −0.0917639 | + | 0.168731i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18.8898i | − | 0.705453i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.7800 | 0.998724 | 0.499362 | − | 0.866393i | \(-0.333568\pi\) | ||||
0.499362 | + | 0.866393i | \(0.333568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.32527 | −0.0493555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.81348i | 0.216206i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.9756 | + | 37.0309i | 0.890433 | + | 1.37529i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.7238i | 1.17657i | 0.808653 | + | 0.588286i | \(0.200197\pi\) | ||||
−0.808653 | + | 0.588286i | \(0.799803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.606300 | 0.0224248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.7555i | − | 1.02517i | −0.858636 | − | 0.512586i | \(-0.828688\pi\) | ||
0.858636 | − | 0.512586i | \(-0.171312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.34224 | + | 4.30680i | −0.0863950 | + | 0.158859i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.01519i | − | 0.0742305i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.32633 | 0.269503 | 0.134752 | − | 0.990879i | \(-0.456976\pi\) | ||||
0.134752 | + | 0.990879i | \(0.456976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.02982 | −0.0745673 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.64123i | 0.280329i | 0.990128 | + | 0.140165i | \(0.0447632\pi\) | ||||
−0.990128 | + | 0.140165i | \(0.955237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.6120 | − | 19.9114i | −1.34136 | − | 0.729496i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.42607i | 0.344882i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −51.1910 | −1.87048 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.7049 | −0.500098 | −0.250049 | − | 0.968233i | \(-0.580447\pi\) | ||||
−0.250049 | + | 0.968233i | \(0.580447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.5194i | − | 0.784211i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.19669 | + | 1.19466i | 0.0799456 | + | 0.0434783i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.05817i | 0.220188i | 0.993921 | + | 0.110094i | \(0.0351152\pi\) | ||||
−0.993921 | + | 0.110094i | \(0.964885\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.4832 | 0.525709 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.7656 | 0.499004 | 0.249502 | − | 0.968374i | \(-0.419733\pi\) | ||||
0.249502 | + | 0.968374i | \(0.419733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.04723i | − | 0.110317i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.305682 | − | 0.562071i | 0.0110519 | − | 0.0203217i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.62980i | 0.239388i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.3289 | −1.88703 | −0.943515 | − | 0.331330i | \(-0.892503\pi\) | ||||
−0.943515 | + | 0.331330i | \(0.892503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.8474 | 0.786816 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13.6707i | − | 0.491700i | −0.969308 | − | 0.245850i | \(-0.920933\pi\) | ||
0.969308 | − | 0.245850i | \(-0.0790670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.23945 | + | 9.63696i | 0.224128 | + | 0.346170i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.17820i | − | 0.257516i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.17847 | −0.328853 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5716 | 0.378281 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.82296i | 0.315307i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.621640 | + | 1.14304i | −0.0221873 | + | 0.0407968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.49527i | 0.338470i | 0.985576 | + | 0.169235i | \(0.0541297\pi\) | ||||
−0.985576 | + | 0.169235i | \(0.945870\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.11910 | −0.146644 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.9929 | −0.817532 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.94098i | 0.317504i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.1137 | + | 9.85112i | 0.642428 | + | 0.349383i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.58612i | 0.0916050i | 0.998951 | + | 0.0458025i | \(0.0145845\pi\) | ||||
−0.998951 | + | 0.0458025i | \(0.985416\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.71790 | 0.0607749 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.93173 | −0.0682544 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16.3799i | − | 0.578035i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 42.8043 | + | 23.2790i | 1.50865 | + | 0.820478i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.3683i | 0.681795i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.1635 | −1.09565 | −0.547826 | − | 0.836592i | \(-0.684544\pi\) | ||||
−0.547826 | + | 0.836592i | \(0.684544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4220 | −1.41941 | −0.709703 | − | 0.704501i | \(-0.751171\pi\) | ||||
−0.709703 | + | 0.704501i | \(0.751171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.63445i | 0.162537i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.51096 | − | 11.9720i | 0.228069 | − | 0.419361i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.77367i | 0.132024i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.45562 | −0.120749 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3251 | −0.779152 | −0.389576 | − | 0.920994i | \(-0.627378\pi\) | ||||
−0.389576 | + | 0.920994i | \(0.627378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.9279i | − | 0.764360i | −0.924088 | − | 0.382180i | \(-0.875173\pi\) | ||
0.924088 | − | 0.382180i | \(-0.124827\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.45796 | − | 5.47611i | 0.294468 | − | 0.190654i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.3645i | − | 0.847237i | −0.905841 | − | 0.423619i | \(-0.860760\pi\) | ||
0.905841 | − | 0.423619i | \(-0.139240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.41852 | −0.118730 | −0.0593651 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593651 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.126860 | −0.00440074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.627342i | − | 0.0217361i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53866 | − | 2.82921i | 0.0532475 | − | 0.0979087i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.29610i | 0.0793648i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.4072 | −0.359297 | −0.179648 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179648 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.8447 | 1.68430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.0912i | 0.657535i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.9849 | + | 12.5003i | 0.790705 | + | 0.430023i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0384i | 0.722889i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.07191 | 0.0367879 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.0157 | −0.583290 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.1207i | 1.37371i | 0.726796 | + | 0.686853i | \(0.241008\pi\) | ||||
−0.726796 | + | 0.686853i | \(0.758992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.49839 | + | 1.90259i | 0.119642 | + | 0.0650673i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.5663i | 1.52236i | 0.648544 | + | 0.761178i | \(0.275378\pi\) | ||||
−0.648544 | + | 0.761178i | \(0.724622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.7135 | −1.93504 | −0.967519 | − | 0.252797i | \(-0.918649\pi\) | ||||
−0.967519 | + | 0.252797i | \(0.918649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.6257 | −0.532522 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.2026i | 0.925989i | 0.886361 | + | 0.462994i | \(0.153225\pi\) | ||||
−0.886361 | + | 0.462994i | \(0.846775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1341 | + | 29.6665i | −0.548574 | + | 1.00869i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.9181i | − | 0.574570i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.8175 | −0.909722 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.13975 | 0.0386190 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.99160i | − | 0.202785i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.7987 | − | 2.58973i | 1.14260 | − | 0.0875489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.6770i | 1.64371i | 0.569700 | + | 0.821853i | \(0.307060\pi\) | ||||
−0.569700 | + | 0.821853i | \(0.692940\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.5814 | −0.930296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1239 | −0.947518 | −0.473759 | − | 0.880655i | \(-0.657103\pi\) | ||||
−0.473759 | + | 0.880655i | \(0.657103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.261513i | − | 0.00880061i | −0.999990 | − | 0.00440030i | \(-0.998599\pi\) | ||
0.999990 | − | 0.00440030i | \(-0.00140066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.21425 | − | 11.4264i | 0.208890 | − | 0.384096i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.6938i | 0.594101i | 0.954862 | + | 0.297050i | \(0.0960029\pi\) | ||||
−0.954862 | + | 0.297050i | \(0.903997\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4535 | −0.954298 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.01519 | 0.0675114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6924i | 0.357807i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.6223 | − | 12.8469i | −0.789607 | − | 0.429426i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.19144i | 0.273504i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.2584 | 0.675656 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.63850 | −0.0879013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.42440i | 0.213791i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.5737 | + | 20.4344i | 1.24899 | + | 0.679262i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.3723i | 0.776064i | 0.921646 | + | 0.388032i | \(0.126845\pi\) | ||||
−0.921646 | + | 0.388032i | \(0.873155\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.706768 | 0.0234420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3867 | −1.03989 | −0.519944 | − | 0.854200i | \(-0.674047\pi\) | ||||
−0.519944 | + | 0.854200i | \(0.674047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.9953i | − | 0.628653i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.38057 | − | 15.4098i | 0.277053 | − | 0.509431i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 49.4370i | − | 1.63255i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.5680 | −0.579516 | −0.289758 | − | 0.957100i | \(-0.593575\pi\) | ||||
−0.289758 | + | 0.957100i | \(0.593575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.66181 | 0.318367 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.97908i | 0.196804i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.93685 | + | 6.43362i | −0.326722 | + | 0.211536i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.437107i | 0.0143565i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0493 | −0.657798 | −0.328899 | − | 0.944365i | \(-0.606677\pi\) | ||||
−0.328899 | + | 0.944365i | \(0.606677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.90464 | 0.127969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 0.912234i | − | 0.0298652i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.616006 | + | 1.13268i | −0.0201456 | + | 0.0370426i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9084i | 1.10774i | 0.832604 | + | 0.553869i | \(0.186849\pi\) | ||||
−0.832604 | + | 0.553869i | \(0.813151\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.74134 | 0.0568264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.6922 | −1.16353 | −0.581766 | − | 0.813356i | \(-0.697638\pi\) | ||||
−0.581766 | + | 0.813356i | \(0.697638\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.0401i | 1.20619i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.95576 | + | 3.23903i | 0.193741 | + | 0.105366i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 21.3769i | − | 0.694656i | −0.937744 | − | 0.347328i | \(-0.887089\pi\) | ||
0.937744 | − | 0.347328i | \(-0.112911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.26416 | 0.300727 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.5696 | −0.796725 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.7544i | − | 1.02862i | −0.857603 | − | 0.514312i | \(-0.828047\pi\) | ||
0.857603 | − | 0.514312i | \(-0.171953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.54294 | + | 0.839127i | 0.0499285 | + | 0.0271535i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.7799i | − | 0.574744i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.5244 | 1.56693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7279 | −0.829933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.8841i | 0.544082i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.15510 | + | 7.64018i | −0.133757 | + | 0.245946i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.15208i | 0.262153i | 0.991372 | + | 0.131077i | \(0.0418434\pi\) | ||||
−0.991372 | + | 0.131077i | \(0.958157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.509587 | −0.0163703 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.1720 | 1.35336 | 0.676682 | − | 0.736275i | \(-0.263417\pi\) | ||||
0.676682 | + | 0.736275i | \(0.263417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.6754i | 0.662822i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.09718 | + | 4.78365i | 0.0991890 | + | 0.153199i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 44.2793i | − | 1.41662i | −0.705901 | − | 0.708310i | \(-0.749458\pi\) | ||
0.705901 | − | 0.708310i | \(-0.250542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.89281 | 0.124415 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00505 | −0.0320889 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 16.8150i | − | 0.536315i | −0.963375 | − | 0.268157i | \(-0.913585\pi\) | ||
0.963375 | − | 0.268157i | \(-0.0864147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7013 | − | 34.3870i | 0.595874 | − | 1.09566i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.2030i | 0.579408i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.2288 | 0.484249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.34170 | −0.201451 | −0.100725 | − | 0.994914i | \(-0.532116\pi\) | ||||
−0.100725 | + | 0.994914i | \(0.532116\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 28.1837i | − | 0.894382i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3076 | + | 7.78116i | 0.453581 | + | 0.246679i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.3096i | 1.40330i | 0.712522 | + | 0.701650i | \(0.247553\pi\) | ||||
−0.712522 | + | 0.701650i | \(0.752447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.36755 | −0.0749060 |
(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 | 4020.2.g.c.1609.15 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.34 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.15 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.34 | yes | 38 | 5.4 | even | 2 | inner |