Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,3,Mod(323,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.323");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.c (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: | \(11.2806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 19x^{6} - 88x^{5} + 301x^{4} - 1010x^{3} + 2713x^{2} - 7044x + 9558 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Root | \(-1.93130 + 3.33657i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.323 |
Dual form | 414.3.c.b.323.5 |
$q$-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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(235\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 5.46255i | 1.09251i | 0.837619 | + | 0.546255i | \(0.183947\pi\) | ||||
−0.837619 | + | 0.546255i | \(0.816053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.65490 | 0.379272 | 0.189636 | − | 0.981854i | \(-0.439269\pi\) | ||||
0.189636 | + | 0.981854i | \(0.439269\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.72521 | 0.772521 | ||||||||
\(11\) | 3.75460i | 0.341327i | 0.985329 | + | 0.170664i | \(0.0545912\pi\) | ||||
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.2899 | −1.79153 | −0.895764 | − | 0.444529i | \(-0.853371\pi\) | ||||
−0.895764 | + | 0.444529i | \(0.853371\pi\) | |||||||
\(14\) | − 3.75460i | − 0.268186i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 19.2161i | − 1.13036i | −0.824969 | − | 0.565179i | \(-0.808807\pi\) | ||||
0.824969 | − | 0.565179i | \(-0.191193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0940 | −1.84705 | −0.923527 | − | 0.383533i | \(-0.874707\pi\) | ||||
−0.923527 | + | 0.383533i | \(0.874707\pi\) | |||||||
\(20\) | − 10.9251i | − 0.546255i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.30981 | 0.241355 | ||||||||
\(23\) | 4.79583i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.83945 | −0.193578 | ||||||||
\(26\) | 32.9369i | 1.26680i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.30981 | −0.189636 | ||||||||
\(29\) | 45.2762i | 1.56125i | 0.625002 | + | 0.780624i | \(0.285098\pi\) | ||||
−0.625002 | + | 0.780624i | \(0.714902\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −32.4391 | −1.04642 | −0.523212 | − | 0.852203i | \(-0.675266\pi\) | ||||
−0.523212 | + | 0.852203i | \(0.675266\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −27.1756 | −0.799283 | ||||||||
\(35\) | 14.5025i | 0.414359i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.5797 | −1.09675 | −0.548375 | − | 0.836233i | \(-0.684753\pi\) | ||||
−0.548375 | + | 0.836233i | \(0.684753\pi\) | |||||||
\(38\) | 49.6305i | 1.30606i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15.4504 | −0.386261 | ||||||||
\(41\) | − 41.1112i | − 1.00271i | −0.865241 | − | 0.501357i | \(-0.832834\pi\) | ||||
0.865241 | − | 0.501357i | \(-0.167166\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.0062 | 1.32573 | 0.662863 | − | 0.748741i | \(-0.269341\pi\) | ||||
0.662863 | + | 0.748741i | \(0.269341\pi\) | |||||||
\(44\) | − 7.50920i | − 0.170664i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 58.8804i | 1.25277i | 0.779512 | + | 0.626387i | \(0.215467\pi\) | ||||
−0.779512 | + | 0.626387i | \(0.784533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.9515 | −0.856153 | ||||||||
\(50\) | 6.84401i | 0.136880i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46.5797 | 0.895764 | ||||||||
\(53\) | 32.3166i | 0.609748i | 0.952393 | + | 0.304874i | \(0.0986143\pi\) | ||||
−0.952393 | + | 0.304874i | \(0.901386\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.5097 | −0.372904 | ||||||||
\(56\) | 7.50920i | 0.134093i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 64.0302 | 1.10397 | ||||||||
\(59\) | 41.6865i | 0.706551i | 0.935519 | + | 0.353275i | \(0.114932\pi\) | ||||
−0.935519 | + | 0.353275i | \(0.885068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 97.7791 | 1.60294 | 0.801468 | − | 0.598038i | \(-0.204053\pi\) | ||||
0.801468 | + | 0.598038i | \(0.204053\pi\) | |||||||
\(62\) | 45.8759i | 0.739933i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 127.222i | − 1.95726i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −35.0235 | −0.522738 | −0.261369 | − | 0.965239i | \(-0.584174\pi\) | ||||
−0.261369 | + | 0.965239i | \(0.584174\pi\) | |||||||
\(68\) | 38.4322i | 0.565179i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 20.5097 | 0.292996 | ||||||||
\(71\) | − 60.7708i | − 0.855926i | −0.903796 | − | 0.427963i | \(-0.859231\pi\) | ||||
0.903796 | − | 0.427963i | \(-0.140769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.2521 | 0.455508 | 0.227754 | − | 0.973719i | \(-0.426862\pi\) | ||||
0.227754 | + | 0.973719i | \(0.426862\pi\) | |||||||
\(74\) | 57.3884i | 0.775519i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 70.1881 | 0.923527 | ||||||||
\(77\) | 9.96811i | 0.129456i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −139.994 | −1.77208 | −0.886040 | − | 0.463608i | \(-0.846554\pi\) | ||||
−0.886040 | + | 0.463608i | \(0.846554\pi\) | |||||||
\(80\) | 21.8502i | 0.273127i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −58.1401 | −0.709025 | ||||||||
\(83\) | 67.4528i | 0.812685i | 0.913721 | + | 0.406342i | \(0.133196\pi\) | ||||
−0.913721 | + | 0.406342i | \(0.866804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 104.969 | 1.23493 | ||||||||
\(86\) | − 80.6189i | − 0.937429i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.6196 | −0.120677 | ||||||||
\(89\) | 45.1603i | 0.507419i | 0.967280 | + | 0.253710i | \(0.0816508\pi\) | ||||
−0.967280 | + | 0.253710i | \(0.918349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61.8324 | −0.679477 | ||||||||
\(92\) | − 9.59166i | − 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 83.2694 | 0.885845 | ||||||||
\(95\) | − 191.703i | − 2.01793i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2522 | 0.126311 | 0.0631557 | − | 0.998004i | \(-0.479884\pi\) | ||||
0.0631557 | + | 0.998004i | \(0.479884\pi\) | |||||||
\(98\) | 59.3284i | 0.605391i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.67890 | 0.0967890 | ||||||||
\(101\) | 25.4147i | 0.251630i | 0.992054 | + | 0.125815i | \(0.0401546\pi\) | ||||
−0.992054 | + | 0.125815i | \(0.959845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −149.727 | −1.45366 | −0.726828 | − | 0.686820i | \(-0.759006\pi\) | ||||
−0.726828 | + | 0.686820i | \(0.759006\pi\) | |||||||
\(104\) | − 65.8737i | − 0.633401i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 45.7026 | 0.431157 | ||||||||
\(107\) | − 103.893i | − 0.970958i | −0.874248 | − | 0.485479i | \(-0.838645\pi\) | ||||
0.874248 | − | 0.485479i | \(-0.161355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.2974 | 0.222912 | 0.111456 | − | 0.993769i | \(-0.464449\pi\) | ||||
0.111456 | + | 0.993769i | \(0.464449\pi\) | |||||||
\(110\) | 29.0051i | 0.263683i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.6196 | 0.0948180 | ||||||||
\(113\) | − 136.200i | − 1.20531i | −0.798001 | − | 0.602656i | \(-0.794109\pi\) | ||||
0.798001 | − | 0.602656i | \(-0.205891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.1975 | −0.227804 | ||||||||
\(116\) | − 90.5523i | − 0.780624i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 58.9536 | 0.499607 | ||||||||
\(119\) | − 51.0169i | − 0.428713i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 106.903 | 0.883496 | ||||||||
\(122\) | − 138.281i | − 1.13345i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 64.8783 | 0.523212 | ||||||||
\(125\) | 110.128i | 0.881024i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 137.362 | 1.08159 | 0.540793 | − | 0.841155i | \(-0.318124\pi\) | ||||
0.540793 | + | 0.841155i | \(0.318124\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −179.919 | −1.38399 | ||||||||
\(131\) | 43.8314i | 0.334591i | 0.985907 | + | 0.167295i | \(0.0535034\pi\) | ||||
−0.985907 | + | 0.167295i | \(0.946497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −93.1713 | −0.700536 | ||||||||
\(134\) | 49.5307i | 0.369632i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 54.3513 | 0.399642 | ||||||||
\(137\) | 129.400i | 0.944524i | 0.881458 | + | 0.472262i | \(0.156562\pi\) | ||||
−0.881458 | + | 0.472262i | \(0.843438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.3050 | −0.138885 | −0.0694426 | − | 0.997586i | \(-0.522122\pi\) | ||||
−0.0694426 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(140\) | − 29.0051i | − 0.207179i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −85.9428 | −0.605231 | ||||||||
\(143\) | − 87.4442i | − 0.611498i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −247.323 | −1.70568 | ||||||||
\(146\) | − 47.0256i | − 0.322093i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 81.1595 | 0.548375 | ||||||||
\(149\) | 49.5264i | 0.332392i | 0.986093 | + | 0.166196i | \(0.0531484\pi\) | ||||
−0.986093 | + | 0.166196i | \(0.946852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 52.3158 | 0.346462 | 0.173231 | − | 0.984881i | \(-0.444579\pi\) | ||||
0.173231 | + | 0.984881i | \(0.444579\pi\) | |||||||
\(152\) | − 99.2609i | − 0.653032i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.0970 | 0.0915392 | ||||||||
\(155\) | − 177.200i | − 1.14323i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 109.378 | 0.696677 | 0.348338 | − | 0.937369i | \(-0.386746\pi\) | ||||
0.348338 | + | 0.937369i | \(0.386746\pi\) | |||||||
\(158\) | 197.982i | 1.25305i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 30.9008 | 0.193130 | ||||||||
\(161\) | 12.7325i | 0.0790837i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 175.252 | 1.07516 | 0.537582 | − | 0.843212i | \(-0.319338\pi\) | ||||
0.537582 | + | 0.843212i | \(0.319338\pi\) | |||||||
\(164\) | 82.2225i | 0.501357i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 95.3927 | 0.574655 | ||||||||
\(167\) | − 188.781i | − 1.13042i | −0.824946 | − | 0.565212i | \(-0.808794\pi\) | ||||
0.824946 | − | 0.565212i | \(-0.191206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 373.418 | 2.20957 | ||||||||
\(170\) | − 148.448i | − 0.873225i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −114.012 | −0.662863 | ||||||||
\(173\) | − 239.909i | − 1.38676i | −0.720574 | − | 0.693378i | \(-0.756122\pi\) | ||||
0.720574 | − | 0.693378i | \(-0.243878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.8483 | −0.0734187 | ||||||||
\(176\) | 15.0184i | 0.0853319i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 63.8664 | 0.358800 | ||||||||
\(179\) | − 233.807i | − 1.30618i | −0.757279 | − | 0.653092i | \(-0.773471\pi\) | ||||
0.757279 | − | 0.653092i | \(-0.226529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −73.0872 | −0.403797 | −0.201898 | − | 0.979406i | \(-0.564711\pi\) | ||||
−0.201898 | + | 0.979406i | \(0.564711\pi\) | |||||||
\(182\) | 87.4442i | 0.480463i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.5647 | −0.0737210 | ||||||||
\(185\) | − 221.669i | − 1.19821i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.1487 | 0.385822 | ||||||||
\(188\) | − 117.761i | − 0.626387i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −271.109 | −1.42689 | ||||||||
\(191\) | 104.577i | 0.547526i | 0.961797 | + | 0.273763i | \(0.0882684\pi\) | ||||
−0.961797 | + | 0.273763i | \(0.911732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −90.8156 | −0.470547 | −0.235274 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235274 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(194\) | − 17.3272i | − 0.0893156i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 83.9030 | 0.428076 | ||||||||
\(197\) | 285.721i | 1.45036i | 0.688558 | + | 0.725181i | \(0.258244\pi\) | ||||
−0.688558 | + | 0.725181i | \(0.741756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −158.601 | −0.796988 | −0.398494 | − | 0.917171i | \(-0.630467\pi\) | ||||
−0.398494 | + | 0.917171i | \(0.630467\pi\) | |||||||
\(200\) | − 13.6880i | − 0.0684401i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 35.9418 | 0.177930 | ||||||||
\(203\) | 120.204i | 0.592137i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 224.572 | 1.09547 | ||||||||
\(206\) | 211.745i | 1.02789i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −93.1595 | −0.447882 | ||||||||
\(209\) | − 131.764i | − 0.630450i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −140.519 | −0.665966 | −0.332983 | − | 0.942933i | \(-0.608055\pi\) | ||||
−0.332983 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(212\) | − 64.6333i | − 0.304874i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −146.926 | −0.686571 | ||||||||
\(215\) | 311.399i | 1.44837i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −86.1228 | −0.396879 | ||||||||
\(218\) | − 34.3617i | − 0.157622i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 41.0194 | 0.186452 | ||||||||
\(221\) | 447.540i | 2.02507i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 45.7694 | 0.205244 | 0.102622 | − | 0.994720i | \(-0.467277\pi\) | ||||
0.102622 | + | 0.994720i | \(0.467277\pi\) | |||||||
\(224\) | − 15.0184i | − 0.0670465i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −192.616 | −0.852285 | ||||||||
\(227\) | 13.9578i | 0.0614879i | 0.999527 | + | 0.0307440i | \(0.00978765\pi\) | ||||
−0.999527 | + | 0.0307440i | \(0.990212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.5010 | −0.128825 | −0.0644126 | − | 0.997923i | \(-0.520517\pi\) | ||||
−0.0644126 | + | 0.997923i | \(0.520517\pi\) | |||||||
\(230\) | 37.0488i | 0.161082i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −128.060 | −0.551984 | ||||||||
\(233\) | 350.404i | 1.50388i | 0.659233 | + | 0.751939i | \(0.270881\pi\) | ||||
−0.659233 | + | 0.751939i | \(0.729119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −321.637 | −1.36867 | ||||||||
\(236\) | − 83.3730i | − 0.353275i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −72.1487 | −0.303146 | ||||||||
\(239\) | − 27.0749i | − 0.113284i | −0.998395 | − | 0.0566421i | \(-0.981961\pi\) | ||||
0.998395 | − | 0.0566421i | \(-0.0180394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 370.823 | 1.53869 | 0.769343 | − | 0.638836i | \(-0.220584\pi\) | ||||
0.769343 | + | 0.638836i | \(0.220584\pi\) | |||||||
\(242\) | − 151.184i | − 0.624726i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −195.558 | −0.801468 | ||||||||
\(245\) | − 229.162i | − 0.935355i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 817.336 | 3.30905 | ||||||||
\(248\) | − 91.7517i | − 0.369967i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 155.745 | 0.622978 | ||||||||
\(251\) | − 183.177i | − 0.729789i | −0.931049 | − | 0.364895i | \(-0.881105\pi\) | ||||
0.931049 | − | 0.364895i | \(-0.118895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0064 | −0.0711717 | ||||||||
\(254\) | − 194.259i | − 0.764797i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 179.627i | 0.698936i | 0.936948 | + | 0.349468i | \(0.113638\pi\) | ||||
−0.936948 | + | 0.349468i | \(0.886362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −107.735 | −0.415967 | ||||||||
\(260\) | 254.444i | 0.978631i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 61.9870 | 0.236591 | ||||||||
\(263\) | 372.423i | 1.41606i | 0.706183 | + | 0.708029i | \(0.250415\pi\) | ||||
−0.706183 | + | 0.708029i | \(0.749585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −176.531 | −0.666156 | ||||||||
\(266\) | 131.764i | 0.495354i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 70.0469 | 0.261369 | ||||||||
\(269\) | 436.192i | 1.62153i | 0.585371 | + | 0.810766i | \(0.300949\pi\) | ||||
−0.585371 | + | 0.810766i | \(0.699051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −361.492 | −1.33392 | −0.666959 | − | 0.745094i | \(-0.732405\pi\) | ||||
−0.666959 | + | 0.745094i | \(0.732405\pi\) | |||||||
\(272\) | − 76.8643i | − 0.282589i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 182.999 | 0.667879 | ||||||||
\(275\) | − 18.1702i | − 0.0660735i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 218.004 | 0.787019 | 0.393510 | − | 0.919320i | \(-0.371261\pi\) | ||||
0.393510 | + | 0.919320i | \(0.371261\pi\) | |||||||
\(278\) | 27.3014i | 0.0982066i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −41.0194 | −0.146498 | ||||||||
\(281\) | 195.789i | 0.696756i | 0.937354 | + | 0.348378i | \(0.113268\pi\) | ||||
−0.937354 | + | 0.348378i | \(0.886732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −36.7055 | −0.129702 | −0.0648508 | − | 0.997895i | \(-0.520657\pi\) | ||||
−0.0648508 | + | 0.997895i | \(0.520657\pi\) | |||||||
\(284\) | 121.542i | 0.427963i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −123.665 | −0.432394 | ||||||||
\(287\) | − 109.146i | − 0.380301i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −80.2576 | −0.277708 | ||||||||
\(290\) | 349.768i | 1.20610i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −66.5042 | −0.227754 | ||||||||
\(293\) | 474.261i | 1.61864i | 0.587370 | + | 0.809319i | \(0.300164\pi\) | ||||
−0.587370 | + | 0.809319i | \(0.699836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −227.715 | −0.771914 | ||||||||
\(296\) | − 114.777i | − 0.387760i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 70.0408 | 0.235036 | ||||||||
\(299\) | − 111.694i | − 0.373560i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 151.346 | 0.502811 | ||||||||
\(302\) | − 73.9857i | − 0.244986i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −140.376 | −0.461764 | ||||||||
\(305\) | 534.123i | 1.75122i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −70.4059 | −0.229335 | −0.114668 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114668 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(308\) | − 19.9362i | − 0.0647280i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −250.599 | −0.808384 | ||||||||
\(311\) | − 375.724i | − 1.20812i | −0.796941 | − | 0.604058i | \(-0.793550\pi\) | ||||
0.796941 | − | 0.604058i | \(-0.206450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 317.485 | 1.01433 | 0.507164 | − | 0.861849i | \(-0.330694\pi\) | ||||
0.507164 | + | 0.861849i | \(0.330694\pi\) | |||||||
\(314\) | − 154.684i | − 0.492625i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 279.989 | 0.886040 | ||||||||
\(317\) | 228.905i | 0.722097i | 0.932547 | + | 0.361048i | \(0.117581\pi\) | ||||
−0.932547 | + | 0.361048i | \(0.882419\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −169.994 | −0.532897 | ||||||||
\(320\) | − 43.7004i | − 0.136564i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.0064 | 0.0559206 | ||||||||
\(323\) | 674.370i | 2.08783i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 112.710 | 0.346800 | ||||||||
\(326\) | − 247.843i | − 0.760255i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 116.280 | 0.354513 | ||||||||
\(329\) | 156.322i | 0.475142i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −643.371 | −1.94372 | −0.971860 | − | 0.235560i | \(-0.924308\pi\) | ||||
−0.971860 | + | 0.235560i | \(0.924308\pi\) | |||||||
\(332\) | − 134.906i | − 0.406342i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −266.976 | −0.799330 | ||||||||
\(335\) | − 191.317i | − 0.571097i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 217.354 | 0.644966 | 0.322483 | − | 0.946575i | \(-0.395482\pi\) | ||||
0.322483 | + | 0.946575i | \(0.395482\pi\) | |||||||
\(338\) | − 528.093i | − 1.56241i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −209.938 | −0.617463 | ||||||||
\(341\) | − 121.796i | − 0.357173i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −241.468 | −0.703987 | ||||||||
\(344\) | 161.238i | 0.468715i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −339.282 | −0.980584 | ||||||||
\(347\) | − 376.022i | − 1.08364i | −0.840496 | − | 0.541818i | \(-0.817736\pi\) | ||||
0.840496 | − | 0.541818i | \(-0.182264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −431.406 | −1.23612 | −0.618061 | − | 0.786130i | \(-0.712081\pi\) | ||||
−0.618061 | + | 0.786130i | \(0.712081\pi\) | |||||||
\(350\) | 18.1702i | 0.0519149i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.2392 | 0.0603387 | ||||||||
\(353\) | − 335.644i | − 0.950834i | −0.879761 | − | 0.475417i | \(-0.842297\pi\) | ||||
0.879761 | − | 0.475417i | \(-0.157703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 331.963 | 0.935108 | ||||||||
\(356\) | − 90.3207i | − 0.253710i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −330.653 | −0.923612 | ||||||||
\(359\) | − 250.032i | − 0.696468i | −0.937408 | − | 0.348234i | \(-0.886781\pi\) | ||||
0.937408 | − | 0.348234i | \(-0.113219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 870.591 | 2.41161 | ||||||||
\(362\) | 103.361i | 0.285528i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 123.665 | 0.339738 | ||||||||
\(365\) | 181.641i | 0.497648i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −460.168 | −1.25386 | −0.626932 | − | 0.779074i | \(-0.715690\pi\) | ||||
−0.626932 | + | 0.779074i | \(0.715690\pi\) | |||||||
\(368\) | 19.1833i | 0.0521286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −313.487 | −0.847262 | ||||||||
\(371\) | 85.7976i | 0.231260i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −162.929 | −0.436806 | −0.218403 | − | 0.975859i | \(-0.570085\pi\) | ||||
−0.218403 | + | 0.975859i | \(0.570085\pi\) | |||||||
\(374\) | − 102.034i | − 0.272817i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −166.539 | −0.442922 | ||||||||
\(377\) | − 1054.48i | − 2.79702i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −369.874 | −0.975920 | −0.487960 | − | 0.872866i | \(-0.662259\pi\) | ||||
−0.487960 | + | 0.872866i | \(0.662259\pi\) | |||||||
\(380\) | 383.406i | 1.00896i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 147.895 | 0.387159 | ||||||||
\(383\) | 579.820i | 1.51389i | 0.653479 | + | 0.756945i | \(0.273309\pi\) | ||||
−0.653479 | + | 0.756945i | \(0.726691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −54.4513 | −0.141432 | ||||||||
\(386\) | 128.433i | 0.332727i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.5044 | −0.0631557 | ||||||||
\(389\) | − 415.995i | − 1.06939i | −0.845044 | − | 0.534697i | \(-0.820426\pi\) | ||||
0.845044 | − | 0.534697i | \(-0.179574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 92.1571 | 0.235696 | ||||||||
\(392\) | − 118.657i | − 0.302696i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 404.071 | 1.02556 | ||||||||
\(395\) | − 764.726i | − 1.93602i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −144.905 | −0.365000 | −0.182500 | − | 0.983206i | \(-0.558419\pi\) | ||||
−0.182500 | + | 0.983206i | \(0.558419\pi\) | |||||||
\(398\) | 224.295i | 0.563555i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.3578 | −0.0483945 | ||||||||
\(401\) | − 181.675i | − 0.453056i | −0.974005 | − | 0.226528i | \(-0.927263\pi\) | ||||
0.974005 | − | 0.226528i | \(-0.0727375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 755.503 | 1.87470 | ||||||||
\(404\) | − 50.8294i | − 0.125815i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 169.994 | 0.418704 | ||||||||
\(407\) | − 152.361i | − 0.374351i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3610 | −0.0742322 | −0.0371161 | − | 0.999311i | \(-0.511817\pi\) | ||||
−0.0371161 | + | 0.999311i | \(0.511817\pi\) | |||||||
\(410\) | − 317.593i | − 0.774617i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 299.453 | 0.726828 | ||||||||
\(413\) | 110.674i | 0.267975i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −368.465 | −0.887866 | ||||||||
\(416\) | 131.747i | 0.316701i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −186.343 | −0.445796 | ||||||||
\(419\) | 653.899i | 1.56062i | 0.625394 | + | 0.780309i | \(0.284938\pi\) | ||||
−0.625394 | + | 0.780309i | \(0.715062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 516.420 | 1.22665 | 0.613326 | − | 0.789830i | \(-0.289831\pi\) | ||||
0.613326 | + | 0.789830i | \(0.289831\pi\) | |||||||
\(422\) | 198.724i | 0.470909i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −91.4052 | −0.215578 | ||||||||
\(425\) | 92.9952i | 0.218812i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 259.594 | 0.607949 | ||||||||
\(428\) | 207.785i | 0.485479i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 440.385 | 1.02415 | ||||||||
\(431\) | − 59.2387i | − 0.137445i | −0.997636 | − | 0.0687224i | \(-0.978108\pi\) | ||||
0.997636 | − | 0.0687224i | \(-0.0218923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −785.285 | −1.81359 | −0.906796 | − | 0.421569i | \(-0.861479\pi\) | ||||
−0.906796 | + | 0.421569i | \(0.861479\pi\) | |||||||
\(434\) | 121.796i | 0.280636i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.5948 | −0.111456 | ||||||||
\(437\) | − 168.305i | − 0.385137i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 322.100 | 0.733713 | 0.366857 | − | 0.930278i | \(-0.380434\pi\) | ||||
0.366857 | + | 0.930278i | \(0.380434\pi\) | |||||||
\(440\) | − 58.0102i | − 0.131841i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 632.917 | 1.43194 | ||||||||
\(443\) | − 112.614i | − 0.254207i | −0.991889 | − | 0.127103i | \(-0.959432\pi\) | ||||
0.991889 | − | 0.127103i | \(-0.0405680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −246.691 | −0.554361 | ||||||||
\(446\) | − 64.7277i | − 0.145129i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.2392 | −0.0474090 | ||||||||
\(449\) | 32.4842i | 0.0723480i | 0.999346 | + | 0.0361740i | \(0.0115170\pi\) | ||||
−0.999346 | + | 0.0361740i | \(0.988483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 154.356 | 0.342254 | ||||||||
\(452\) | 272.401i | 0.602656i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.7392 | 0.0434785 | ||||||||
\(455\) | − 337.762i | − 0.742335i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −63.4223 | −0.138780 | −0.0693898 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693898 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(458\) | 41.7207i | 0.0910932i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 52.3949 | 0.113902 | ||||||||
\(461\) | − 768.616i | − 1.66728i | −0.552308 | − | 0.833640i | \(-0.686253\pi\) | ||||
0.552308 | − | 0.833640i | \(-0.313747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −453.446 | −0.979365 | −0.489683 | − | 0.871901i | \(-0.662887\pi\) | ||||
−0.489683 | + | 0.871901i | \(0.662887\pi\) | |||||||
\(464\) | 181.105i | 0.390312i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 495.545 | 1.06340 | ||||||||
\(467\) | − 65.6087i | − 0.140490i | −0.997530 | − | 0.0702449i | \(-0.977622\pi\) | ||||
0.997530 | − | 0.0702449i | \(-0.0223781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −92.9840 | −0.198260 | ||||||||
\(470\) | 454.863i | 0.967794i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −117.907 | −0.249803 | ||||||||
\(473\) | 214.036i | 0.452506i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 169.836 | 0.357549 | ||||||||
\(476\) | 102.034i | 0.214357i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.2897 | −0.0801040 | ||||||||
\(479\) | − 157.516i | − 0.328843i | −0.986390 | − | 0.164421i | \(-0.947424\pi\) | ||||
0.986390 | − | 0.164421i | \(-0.0525757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 945.097 | 1.96486 | ||||||||
\(482\) | − 524.423i | − 1.08802i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −213.806 | −0.441748 | ||||||||
\(485\) | 66.9283i | 0.137996i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 196.013 | 0.402491 | 0.201245 | − | 0.979541i | \(-0.435501\pi\) | ||||
0.201245 | + | 0.979541i | \(0.435501\pi\) | |||||||
\(488\) | 276.561i | 0.566724i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −324.084 | −0.661396 | ||||||||
\(491\) | 897.356i | 1.82761i | 0.406155 | + | 0.913804i | \(0.366869\pi\) | ||||
−0.406155 | + | 0.913804i | \(0.633131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 870.030 | 1.76477 | ||||||||
\(494\) | − 1155.89i | − 2.33985i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −129.757 | −0.261606 | ||||||||
\(497\) | − 161.341i | − 0.324629i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 521.387 | 1.04486 | 0.522432 | − | 0.852681i | \(-0.325025\pi\) | ||||
0.522432 | + | 0.852681i | \(0.325025\pi\) | |||||||
\(500\) | − 220.256i | − 0.440512i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −259.052 | −0.516039 | ||||||||
\(503\) | 830.919i | 1.65193i | 0.563724 | + | 0.825963i | \(0.309368\pi\) | ||||
−0.563724 | + | 0.825963i | \(0.690632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −138.829 | −0.274909 | ||||||||
\(506\) | 25.4650i | 0.0503260i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −274.723 | −0.540793 | ||||||||
\(509\) | − 1001.93i | − 1.96843i | −0.176986 | − | 0.984213i | \(-0.556635\pi\) | ||||
0.176986 | − | 0.984213i | \(-0.443365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 88.2812 | 0.172762 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 254.030 | 0.494222 | ||||||||
\(515\) | − 817.889i | − 1.58813i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −221.072 | −0.427606 | ||||||||
\(518\) | 152.361i | 0.294133i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 359.838 | 0.691997 | ||||||||
\(521\) | − 726.690i | − 1.39480i | −0.716683 | − | 0.697399i | \(-0.754341\pi\) | ||||
0.716683 | − | 0.697399i | \(-0.245659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −394.541 | −0.754380 | −0.377190 | − | 0.926136i | \(-0.623110\pi\) | ||||
−0.377190 | + | 0.926136i | \(0.623110\pi\) | |||||||
\(524\) | − 87.6628i | − 0.167295i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 526.686 | 1.00130 | ||||||||
\(527\) | 623.353i | 1.18283i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | 249.653i | 0.471043i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 186.343 | 0.350268 | ||||||||
\(533\) | 957.476i | 1.79639i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 567.518 | 1.06078 | ||||||||
\(536\) | − 99.0613i | − 0.184816i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 616.869 | 1.14660 | ||||||||
\(539\) | − 157.511i | − 0.292228i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 116.598 | 0.215524 | 0.107762 | − | 0.994177i | \(-0.465632\pi\) | ||||
0.107762 | + | 0.994177i | \(0.465632\pi\) | |||||||
\(542\) | 511.227i | 0.943223i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −108.703 | −0.199821 | ||||||||
\(545\) | 132.726i | 0.243533i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −344.108 | −0.629082 | −0.314541 | − | 0.949244i | \(-0.601851\pi\) | ||||
−0.314541 | + | 0.949244i | \(0.601851\pi\) | |||||||
\(548\) | − 258.799i | − 0.472262i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25.6965 | −0.0467210 | ||||||||
\(551\) | − 1588.92i | − 2.88371i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −371.672 | −0.672101 | ||||||||
\(554\) | − 308.305i | − 0.556507i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.6101 | 0.0694426 | ||||||||
\(557\) | 401.523i | 0.720867i | 0.932785 | + | 0.360434i | \(0.117371\pi\) | ||||
−0.932785 | + | 0.360434i | \(0.882629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1327.67 | −2.37507 | ||||||||
\(560\) | 58.0102i | 0.103590i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 276.887 | 0.492681 | ||||||||
\(563\) | − 605.143i | − 1.07485i | −0.843310 | − | 0.537427i | \(-0.819396\pi\) | ||||
0.843310 | − | 0.537427i | \(-0.180604\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 744.001 | 1.31682 | ||||||||
\(566\) | 51.9095i | 0.0917129i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 171.886 | 0.302616 | ||||||||
\(569\) | 129.848i | 0.228204i | 0.993469 | + | 0.114102i | \(0.0363991\pi\) | ||||
−0.993469 | + | 0.114102i | \(0.963601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −540.155 | −0.945981 | −0.472991 | − | 0.881067i | \(-0.656826\pi\) | ||||
−0.472991 | + | 0.881067i | \(0.656826\pi\) | |||||||
\(572\) | 174.888i | 0.305749i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −154.356 | −0.268914 | ||||||||
\(575\) | − 23.2092i | − 0.0403638i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −767.951 | −1.33094 | −0.665469 | − | 0.746425i | \(-0.731769\pi\) | ||||
−0.665469 | + | 0.746425i | \(0.731769\pi\) | |||||||
\(578\) | 113.501i | 0.196369i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 494.647 | 0.852839 | ||||||||
\(581\) | 179.081i | 0.308229i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −121.336 | −0.208124 | ||||||||
\(584\) | 94.0512i | 0.161047i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 670.706 | 1.14455 | ||||||||
\(587\) | 361.967i | 0.616639i | 0.951283 | + | 0.308319i | \(0.0997665\pi\) | ||||
−0.951283 | + | 0.308319i | \(0.900233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1138.42 | 1.93280 | ||||||||
\(590\) | 322.037i | 0.545825i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −162.319 | −0.274187 | ||||||||
\(593\) | − 685.417i | − 1.15585i | −0.816091 | − | 0.577923i | \(-0.803863\pi\) | ||||
0.816091 | − | 0.577923i | \(-0.196137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 278.682 | 0.468373 | ||||||||
\(596\) | − 99.0527i | − 0.166196i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −157.960 | −0.264146 | ||||||||
\(599\) | − 888.738i | − 1.48370i | −0.670564 | − | 0.741851i | \(-0.733948\pi\) | ||||
0.670564 | − | 0.741851i | \(-0.266052\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −911.130 | −1.51602 | −0.758012 | − | 0.652241i | \(-0.773829\pi\) | ||||
−0.758012 | + | 0.652241i | \(0.773829\pi\) | |||||||
\(602\) | − 214.036i | − 0.355541i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −104.632 | −0.173231 | ||||||||
\(605\) | 583.963i | 0.965228i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −331.088 | −0.545450 | −0.272725 | − | 0.962092i | \(-0.587925\pi\) | ||||
−0.272725 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(608\) | 198.522i | 0.326516i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 755.364 | 1.23830 | ||||||||
\(611\) | − 1371.32i | − 2.24438i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 516.088 | 0.841906 | 0.420953 | − | 0.907083i | \(-0.361696\pi\) | ||||
0.420953 | + | 0.907083i | \(0.361696\pi\) | |||||||
\(614\) | 99.5690i | 0.162165i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.1941 | −0.0457696 | ||||||||
\(617\) | 53.3362i | 0.0864444i | 0.999065 | + | 0.0432222i | \(0.0137623\pi\) | ||||
−0.999065 | + | 0.0432222i | \(0.986238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −568.724 | −0.918778 | −0.459389 | − | 0.888235i | \(-0.651932\pi\) | ||||
−0.459389 | + | 0.888235i | \(0.651932\pi\) | |||||||
\(620\) | 354.401i | 0.571614i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −531.354 | −0.854266 | ||||||||
\(623\) | 119.896i | 0.192450i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −722.566 | −1.15611 | ||||||||
\(626\) | − 448.991i | − 0.717239i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −218.757 | −0.348338 | ||||||||
\(629\) | 779.783i | 1.23972i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 65.0487 | 0.103088 | 0.0515441 | − | 0.998671i | \(-0.483586\pi\) | ||||
0.0515441 | + | 0.998671i | \(0.483586\pi\) | |||||||
\(632\) | − 395.964i | − 0.626525i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 323.720 | 0.510599 | ||||||||
\(635\) | 750.344i | 1.18164i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 977.045 | 1.53382 | ||||||||
\(638\) | 240.408i | 0.376815i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −61.8017 | −0.0965651 | ||||||||
\(641\) | 149.022i | 0.232483i | 0.993221 | + | 0.116242i | \(0.0370847\pi\) | ||||
−0.993221 | + | 0.116242i | \(0.962915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −500.221 | −0.777948 | −0.388974 | − | 0.921249i | \(-0.627170\pi\) | ||||
−0.388974 | + | 0.921249i | \(0.627170\pi\) | |||||||
\(644\) | − 25.4650i | − 0.0395419i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 953.703 | 1.47632 | ||||||||
\(647\) | 805.794i | 1.24543i | 0.782448 | + | 0.622716i | \(0.213971\pi\) | ||||
−0.782448 | + | 0.622716i | \(0.786029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −156.516 | −0.241165 | ||||||||
\(650\) | − 159.396i | − 0.245225i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −350.503 | −0.537582 | ||||||||
\(653\) | 601.044i | 0.920435i | 0.887806 | + | 0.460217i | \(0.152229\pi\) | ||||
−0.887806 | + | 0.460217i | \(0.847771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −239.431 | −0.365544 | ||||||||
\(656\) | − 164.445i | − 0.250678i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 221.072 | 0.335976 | ||||||||
\(659\) | 607.968i | 0.922562i | 0.887254 | + | 0.461281i | \(0.152610\pi\) | ||||
−0.887254 | + | 0.461281i | \(0.847390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 290.913 | 0.440110 | 0.220055 | − | 0.975487i | \(-0.429376\pi\) | ||||
0.220055 | + | 0.975487i | \(0.429376\pi\) | |||||||
\(662\) | 909.864i | 1.37442i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −190.785 | −0.287328 | ||||||||
\(665\) | − 508.953i | − 0.765343i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −217.137 | −0.325543 | ||||||||
\(668\) | 377.562i | 0.565212i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −270.564 | −0.403826 | ||||||||
\(671\) | 367.122i | 0.547126i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −481.374 | −0.715267 | −0.357633 | − | 0.933862i | \(-0.616416\pi\) | ||||
−0.357633 | + | 0.933862i | \(0.616416\pi\) | |||||||
\(674\) | − 307.384i | − 0.456060i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −746.836 | −1.10479 | ||||||||
\(677\) | 870.332i | 1.28557i | 0.766046 | + | 0.642786i | \(0.222222\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.5284 | 0.0479064 | ||||||||
\(680\) | 296.897i | 0.436613i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −172.246 | −0.252560 | ||||||||
\(683\) | 102.178i | 0.149602i | 0.997198 | + | 0.0748008i | \(0.0238321\pi\) | ||||
−0.997198 | + | 0.0748008i | \(0.976168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −706.852 | −1.03190 | ||||||||
\(686\) | 341.487i | 0.497794i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 228.025 | 0.331431 | ||||||||
\(689\) | − 752.650i | − 1.09238i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1291.14 | −1.86851 | −0.934256 | − | 0.356603i | \(-0.883935\pi\) | ||||
−0.934256 | + | 0.356603i | \(0.883935\pi\) | |||||||
\(692\) | 479.817i | 0.693378i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −531.775 | −0.766246 | ||||||||
\(695\) | − 105.455i | − 0.151733i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −789.997 | −1.13342 | ||||||||
\(698\) | 610.101i | 0.874070i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.6965 | 0.0367094 | ||||||||
\(701\) | − 412.010i | − 0.587747i | −0.955844 | − | 0.293873i | \(-0.905056\pi\) | ||||
0.955844 | − | 0.293873i | \(-0.0949444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1424.11 | 2.02576 | ||||||||
\(704\) | − 30.0368i | − 0.0426659i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −474.673 | −0.672341 | ||||||||
\(707\) | 67.4735i | 0.0954364i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −937.381 | −1.32212 | −0.661059 | − | 0.750334i | \(-0.729893\pi\) | ||||
−0.661059 | + | 0.750334i | \(0.729893\pi\) | |||||||
\(710\) | − 469.467i | − 0.661221i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −127.733 | −0.179400 | ||||||||
\(713\) | − 155.573i | − 0.218194i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 477.668 | 0.668068 | ||||||||
\(716\) | 467.614i | 0.653092i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −353.599 | −0.492477 | ||||||||
\(719\) | 352.526i | 0.490300i | 0.969485 | + | 0.245150i | \(0.0788372\pi\) | ||||
−0.969485 | + | 0.245150i | \(0.921163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −397.510 | −0.551331 | ||||||||
\(722\) | − 1231.20i | − 1.70527i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 146.174 | 0.201898 | ||||||||
\(725\) | − 219.112i | − 0.302223i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 665.087 | 0.914838 | 0.457419 | − | 0.889251i | \(-0.348774\pi\) | ||||
0.457419 | + | 0.889251i | \(0.348774\pi\) | |||||||
\(728\) | − 174.888i | − 0.240231i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 256.880 | 0.351890 | ||||||||
\(731\) | − 1095.43i | − 1.49854i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −821.098 | −1.12019 | −0.560094 | − | 0.828429i | \(-0.689235\pi\) | ||||
−0.560094 | + | 0.828429i | \(0.689235\pi\) | |||||||
\(734\) | 650.776i | 0.886616i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | − 131.499i | − 0.178425i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1282.72 | 1.73574 | 0.867872 | − | 0.496787i | \(-0.165487\pi\) | ||||
0.867872 | + | 0.496787i | \(0.165487\pi\) | |||||||
\(740\) | 443.338i | 0.599105i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 121.336 | 0.163526 | ||||||||
\(743\) | − 45.8919i | − 0.0617657i | −0.999523 | − | 0.0308828i | \(-0.990168\pi\) | ||||
0.999523 | − | 0.0308828i | \(-0.00983187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −270.540 | −0.363141 | ||||||||
\(746\) | 230.416i | 0.308869i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −144.297 | −0.192911 | ||||||||
\(749\) | − 275.825i | − 0.368257i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 434.621 | 0.578724 | 0.289362 | − | 0.957220i | \(-0.406557\pi\) | ||||
0.289362 | + | 0.957220i | \(0.406557\pi\) | |||||||
\(752\) | 235.521i | 0.313193i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1491.25 | −1.97779 | ||||||||
\(755\) | 285.778i | 0.378513i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 517.650 | 0.683817 | 0.341909 | − | 0.939733i | \(-0.388927\pi\) | ||||
0.341909 | + | 0.939733i | \(0.388927\pi\) | |||||||
\(758\) | 523.081i | 0.690080i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 542.218 | 0.713444 | ||||||||
\(761\) | 1191.22i | 1.56534i | 0.622437 | + | 0.782670i | \(0.286143\pi\) | ||||
−0.622437 | + | 0.782670i | \(0.713857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.5072 | 0.0845442 | ||||||||
\(764\) | − 209.155i | − 0.273763i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 819.989 | 1.07048 | ||||||||
\(767\) | − 970.873i | − 1.26581i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 295.214 | 0.383894 | 0.191947 | − | 0.981405i | \(-0.438520\pi\) | ||||
0.191947 | + | 0.981405i | \(0.438520\pi\) | |||||||
\(770\) | 77.0058i | 0.100007i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 181.631 | 0.235274 | ||||||||
\(773\) | 582.034i | 0.752955i | 0.926426 | + | 0.376478i | \(0.122865\pi\) | ||||
−0.926426 | + | 0.376478i | \(0.877135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 156.987 | 0.202564 | ||||||||
\(776\) | 34.6545i | 0.0446578i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −588.305 | −0.756176 | ||||||||
\(779\) | 1442.76i | 1.85207i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 228.170 | 0.292151 | ||||||||
\(782\) | − 130.330i | − 0.166662i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −167.806 | −0.214038 | ||||||||
\(785\) | 597.484i | 0.761126i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −466.725 | −0.593043 | −0.296522 | − | 0.955026i | \(-0.595827\pi\) | ||||
−0.296522 | + | 0.955026i | \(0.595827\pi\) | |||||||
\(788\) | − 571.443i | − 0.725181i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1081.49 | −1.36897 | ||||||||
\(791\) | − 361.599i | − 0.457141i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2277.26 | −2.87171 | ||||||||
\(794\) | 204.927i | 0.258094i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 317.201 | 0.398494 | ||||||||
\(797\) | − 631.543i | − 0.792401i | −0.918164 | − | 0.396200i | \(-0.870329\pi\) | ||||
0.918164 | − | 0.396200i | \(-0.129671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1131.45 | 1.41608 | ||||||||
\(800\) | 27.3761i | 0.0342201i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −256.928 | −0.320359 | ||||||||
\(803\) | 124.848i | 0.155478i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −69.5518 | −0.0863997 | ||||||||
\(806\) | − 1068.44i | − 1.32561i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −71.8836 | −0.0889648 | ||||||||
\(809\) | − 617.910i | − 0.763794i | −0.924205 | − | 0.381897i | \(-0.875271\pi\) | ||||
0.924205 | − | 0.381897i | \(-0.124729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −674.261 | −0.831394 | −0.415697 | − | 0.909503i | \(-0.636462\pi\) | ||||
−0.415697 | + | 0.909503i | \(0.636462\pi\) | |||||||
\(812\) | − 240.408i | − 0.296069i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −215.471 | −0.264706 | ||||||||
\(815\) | 957.320i | 1.17463i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2000.58 | −2.44869 | ||||||||
\(818\) | 42.9369i | 0.0524901i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −449.144 | −0.547737 | ||||||||
\(821\) | − 1164.86i | − 1.41883i | −0.704790 | − | 0.709416i | \(-0.748959\pi\) | ||||
0.704790 | − | 0.709416i | \(-0.251041\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1028.04 | −1.24913 | −0.624566 | − | 0.780972i | \(-0.714724\pi\) | ||||
−0.624566 | + | 0.780972i | \(0.714724\pi\) | |||||||
\(824\) | − 423.491i | − 0.513945i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 156.516 | 0.189487 | ||||||||
\(827\) | 789.195i | 0.954287i | 0.878825 | + | 0.477143i | \(0.158328\pi\) | ||||
−0.878825 | + | 0.477143i | \(0.841672\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 475.254 | 0.573285 | 0.286643 | − | 0.958038i | \(-0.407461\pi\) | ||||
0.286643 | + | 0.958038i | \(0.407461\pi\) | |||||||
\(830\) | 521.088i | 0.627816i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 186.319 | 0.223941 | ||||||||
\(833\) | 806.143i | 0.967759i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1031.22 | 1.23500 | ||||||||
\(836\) | 263.528i | 0.315225i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 924.753 | 1.10352 | ||||||||
\(839\) | 217.224i | 0.258908i | 0.991585 | + | 0.129454i | \(0.0413224\pi\) | ||||
−0.991585 | + | 0.129454i | \(0.958678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1208.93 | −1.43749 | ||||||||
\(842\) | − 730.329i | − 0.867374i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 281.038 | 0.332983 | ||||||||
\(845\) | 2039.82i | 2.41398i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 283.817 | 0.335085 | ||||||||
\(848\) | 129.267i | 0.152437i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 131.515 | 0.154724 | ||||||||
\(851\) | − 194.614i | − 0.228688i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 341.028 | 0.399798 | 0.199899 | − | 0.979816i | \(-0.435939\pi\) | ||||
0.199899 | + | 0.979816i | \(0.435939\pi\) | |||||||
\(854\) | − 367.122i | − 0.429885i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 293.852 | 0.343286 | ||||||||
\(857\) | − 897.544i | − 1.04731i | −0.851931 | − | 0.523655i | \(-0.824568\pi\) | ||||
0.851931 | − | 0.523655i | \(-0.175432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 180.587 | 0.210230 | 0.105115 | − | 0.994460i | \(-0.466479\pi\) | ||||
0.105115 | + | 0.994460i | \(0.466479\pi\) | |||||||
\(860\) | − 622.798i | − 0.724184i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −83.7762 | −0.0971882 | ||||||||
\(863\) | 1121.05i | 1.29902i | 0.760353 | + | 0.649510i | \(0.225026\pi\) | ||||
−0.760353 | + | 0.649510i | \(0.774974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1310.51 | 1.51504 | ||||||||
\(866\) | 1110.56i | 1.28240i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 172.246 | 0.198440 | ||||||||
\(869\) | − 525.623i | − 0.604860i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 815.692 | 0.936501 | ||||||||
\(872\) | 68.7234i | 0.0788112i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −238.019 | −0.272333 | ||||||||
\(875\) | 292.379i | 0.334148i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1613.95 | 1.84031 | 0.920156 | − | 0.391552i | \(-0.128062\pi\) | ||||
0.920156 | + | 0.391552i | \(0.128062\pi\) | |||||||
\(878\) | − 455.518i | − 0.518813i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −82.0388 | −0.0932259 | ||||||||
\(881\) | − 26.7686i | − 0.0303843i | −0.999885 | − | 0.0151921i | \(-0.995164\pi\) | ||||
0.999885 | − | 0.0151921i | \(-0.00483600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −104.854 | −0.118747 | −0.0593737 | − | 0.998236i | \(-0.518910\pi\) | ||||
−0.0593737 | + | 0.998236i | \(0.518910\pi\) | |||||||
\(884\) | − 895.080i | − 1.01253i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −159.260 | −0.179751 | ||||||||
\(887\) | 463.704i | 0.522778i | 0.965234 | + | 0.261389i | \(0.0841806\pi\) | ||||
−0.965234 | + | 0.261389i | \(0.915819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 364.682 | 0.410216 | ||||||||
\(890\) | 348.873i | 0.391992i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −91.5388 | −0.102622 | ||||||||
\(893\) | − 2066.35i | − 2.31394i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1277.18 | 1.42702 | ||||||||
\(896\) | 30.0368i | 0.0335232i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.9396 | 0.0511577 | ||||||||
\(899\) | − 1468.72i | − 1.63373i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 620.999 | 0.689233 | ||||||||
\(902\) | − 218.293i | − 0.242010i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 385.233 | 0.426142 | ||||||||
\(905\) | − 399.243i | − 0.441152i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −93.5538 | −0.103146 | −0.0515732 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515732 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(908\) | − 27.9155i | − 0.0307440i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −477.668 | −0.524910 | ||||||||
\(911\) | 1308.79i | 1.43665i | 0.695705 | + | 0.718327i | \(0.255092\pi\) | ||||
−0.695705 | + | 0.718327i | \(0.744908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −253.259 | −0.277392 | ||||||||
\(914\) | 89.6927i | 0.0981320i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59.0020 | 0.0644126 | ||||||||
\(917\) | 116.368i | 0.126901i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1146.21 | 1.24723 | 0.623616 | − | 0.781731i | \(-0.285663\pi\) | ||||
0.623616 | + | 0.781731i | \(0.285663\pi\) | |||||||
\(920\) | − 74.0976i | − 0.0805409i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1086.99 | −1.17895 | ||||||||
\(923\) | 1415.34i | 1.53342i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 196.384 | 0.212307 | ||||||||
\(926\) | 641.269i | 0.692516i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 256.121 | 0.275992 | ||||||||
\(929\) | 402.392i | 0.433145i | 0.976267 | + | 0.216573i | \(0.0694878\pi\) | ||||
−0.976267 | + | 0.216573i | \(0.930512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1472.25 | 1.58136 | ||||||||
\(932\) | − 700.807i | − 0.751939i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −92.7847 | −0.0993413 | ||||||||
\(935\) | 394.116i | 0.421514i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1315.29 | 1.40373 | 0.701863 | − | 0.712312i | \(-0.252352\pi\) | ||||
0.701863 | + | 0.712312i | \(0.252352\pi\) | |||||||
\(938\) | 131.499i | 0.140191i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 643.274 | 0.684334 | ||||||||
\(941\) | 1057.80i | 1.12412i | 0.827095 | + | 0.562062i | \(0.189992\pi\) | ||||
−0.827095 | + | 0.562062i | \(0.810008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 197.163 | 0.209080 | ||||||||
\(944\) | 166.746i | 0.176638i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 302.692 | 0.319970 | ||||||||
\(947\) | − 942.801i | − 0.995566i | −0.867302 | − | 0.497783i | \(-0.834148\pi\) | ||||
0.867302 | − | 0.497783i | \(-0.165852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −774.438 | −0.816056 | ||||||||
\(950\) | − 240.184i | − 0.252825i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 144.297 | 0.151573 | ||||||||
\(953\) | 1019.03i | 1.06928i | 0.845079 | + | 0.534642i | \(0.179554\pi\) | ||||
−0.845079 | + | 0.534642i | \(0.820446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −571.260 | −0.598178 | ||||||||
\(956\) | 54.1498i | 0.0566421i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −222.761 | −0.232527 | ||||||||
\(959\) | 343.544i | 0.358231i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 91.2971 | 0.0950022 | ||||||||
\(962\) | − 1336.57i | − 1.38936i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −741.647 | −0.769343 | ||||||||
\(965\) | − 496.085i | − 0.514078i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1197.09 | −1.23795 | −0.618974 | − | 0.785412i | \(-0.712451\pi\) | ||||
−0.618974 | + | 0.785412i | \(0.712451\pi\) | |||||||
\(968\) | 302.367i | 0.312363i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 94.6508 | 0.0975782 | ||||||||
\(971\) | − 282.153i | − 0.290580i | −0.989389 | − | 0.145290i | \(-0.953589\pi\) | ||||
0.989389 | − | 0.145290i | \(-0.0464114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.2530 | −0.0526753 | ||||||||
\(974\) | − 277.204i | − 0.284604i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 391.116 | 0.400734 | ||||||||
\(977\) | 72.9646i | 0.0746823i | 0.999303 | + | 0.0373411i | \(0.0118888\pi\) | ||||
−0.999303 | + | 0.0373411i | \(0.988111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −169.559 | −0.173196 | ||||||||
\(980\) | 458.324i | 0.467678i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1269.05 | 1.29231 | ||||||||
\(983\) | 1345.86i | 1.36913i | 0.728951 | + | 0.684566i | \(0.240008\pi\) | ||||
−0.728951 | + | 0.684566i | \(0.759992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1560.77 | −1.58454 | ||||||||
\(986\) | − 1230.41i | − 1.24788i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1634.67 | −1.65453 | ||||||||
\(989\) | 273.392i | 0.276433i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1316.06 | 1.32802 | 0.664008 | − | 0.747726i | \(-0.268854\pi\) | ||||
0.664008 | + | 0.747726i | \(0.268854\pi\) | |||||||
\(992\) | 183.503i | 0.184983i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −228.170 | −0.229547 | ||||||||
\(995\) | − 866.363i | − 0.870717i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1880.80 | 1.88646 | 0.943229 | − | 0.332144i | \(-0.107772\pi\) | ||||
0.943229 | + | 0.332144i | \(0.107772\pi\) | |||||||
\(998\) | − 737.353i | − 0.738831i | ||||||||
\(999\) | 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 | 414.3.c.b.323.4 | ✓ | 8 | |
3.2 | odd | 2 | inner | 414.3.c.b.323.5 | yes | 8 | |
4.3 | odd | 2 | 3312.3.g.b.737.7 | 8 | |||
12.11 | even | 2 | 3312.3.g.b.737.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.3.c.b.323.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
414.3.c.b.323.5 | yes | 8 | 3.2 | odd | 2 | inner | |
3312.3.g.b.737.2 | 8 | 12.11 | even | 2 | |||
3312.3.g.b.737.7 | 8 | 4.3 | odd | 2 |