Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.2 | ||
Root | \(-1.80194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.t.1351.5 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 1.35690i | − 0.512858i | −0.966563 | − | 0.256429i | \(-0.917454\pi\) | ||||
0.966563 | − | 0.256429i | \(-0.0825461\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − 5.29590i | − 1.59677i | −0.602145 | − | 0.798387i | \(-0.705687\pi\) | ||||
0.602145 | − | 0.798387i | \(-0.294313\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35690 | −0.362646 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.04892 | 0.496935 | 0.248468 | − | 0.968640i | \(-0.420073\pi\) | ||||
0.248468 | + | 0.968640i | \(0.420073\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 3.24698i | − 0.744908i | −0.928051 | − | 0.372454i | \(-0.878516\pi\) | ||||
0.928051 | − | 0.372454i | \(-0.121484\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 1.35690i | 0.296099i | ||||||||
\(22\) | −5.29590 | −1.12909 | ||||||||
\(23\) | −1.33513 | −0.278393 | −0.139196 | − | 0.990265i | \(-0.544452\pi\) | ||||
−0.139196 | + | 0.990265i | \(0.544452\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.35690i | 0.256429i | ||||||||
\(29\) | −5.13706 | −0.953929 | −0.476964 | − | 0.878923i | \(-0.658263\pi\) | ||||
−0.476964 | + | 0.878923i | \(0.658263\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 2.80194i | − 0.503243i | −0.967826 | − | 0.251621i | \(-0.919036\pi\) | ||||
0.967826 | − | 0.251621i | \(-0.0809638\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 5.29590i | 0.921897i | ||||||||
\(34\) | − 2.04892i | − 0.351386i | ||||||||
\(35\) | −1.35690 | −0.229357 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 2.24698i | − 0.369401i | −0.982795 | − | 0.184701i | \(-0.940868\pi\) | ||||
0.982795 | − | 0.184701i | \(-0.0591315\pi\) | |||||||
\(38\) | −3.24698 | −0.526730 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 10.6310i | − 1.66029i | −0.557550 | − | 0.830143i | \(-0.688258\pi\) | ||||
0.557550 | − | 0.830143i | \(-0.311742\pi\) | |||||||
\(42\) | 1.35690 | 0.209374 | ||||||||
\(43\) | −4.41789 | −0.673723 | −0.336861 | − | 0.941554i | \(-0.609365\pi\) | ||||
−0.336861 | + | 0.941554i | \(0.609365\pi\) | |||||||
\(44\) | 5.29590i | 0.798387i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 1.33513i | 0.196854i | ||||||||
\(47\) | 4.82371i | 0.703610i | 0.936073 | + | 0.351805i | \(0.114432\pi\) | ||||
−0.936073 | + | 0.351805i | \(0.885568\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.15883 | 0.736976 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −2.04892 | −0.286906 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.2349 | 1.95531 | 0.977657 | − | 0.210207i | \(-0.0674139\pi\) | ||||
0.977657 | + | 0.210207i | \(0.0674139\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −5.29590 | −0.714099 | ||||||||
\(56\) | 1.35690 | 0.181323 | ||||||||
\(57\) | 3.24698i | 0.430073i | ||||||||
\(58\) | 5.13706i | 0.674529i | ||||||||
\(59\) | 13.8998i | 1.80960i | 0.425841 | + | 0.904798i | \(0.359978\pi\) | ||||
−0.425841 | + | 0.904798i | \(0.640022\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | −3.62565 | −0.464216 | −0.232108 | − | 0.972690i | \(-0.574562\pi\) | ||||
−0.232108 | + | 0.972690i | \(0.574562\pi\) | |||||||
\(62\) | −2.80194 | −0.355846 | ||||||||
\(63\) | − 1.35690i | − 0.170953i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.29590 | 0.651880 | ||||||||
\(67\) | − 9.03684i | − 1.10403i | −0.833836 | − | 0.552013i | \(-0.813860\pi\) | ||||
0.833836 | − | 0.552013i | \(-0.186140\pi\) | |||||||
\(68\) | −2.04892 | −0.248468 | ||||||||
\(69\) | 1.33513 | 0.160730 | ||||||||
\(70\) | 1.35690i | 0.162180i | ||||||||
\(71\) | − 11.7506i | − 1.39454i | −0.716807 | − | 0.697271i | \(-0.754397\pi\) | ||||
0.716807 | − | 0.697271i | \(-0.245603\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 12.1032i | − 1.41657i | −0.705925 | − | 0.708287i | \(-0.749468\pi\) | ||||
0.705925 | − | 0.708287i | \(-0.250532\pi\) | |||||||
\(74\) | −2.24698 | −0.261206 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 3.24698i | 0.372454i | ||||||||
\(77\) | −7.18598 | −0.818919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.259061 | 0.0291467 | 0.0145733 | − | 0.999894i | \(-0.495361\pi\) | ||||
0.0145733 | + | 0.999894i | \(0.495361\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.6310 | −1.17400 | ||||||||
\(83\) | − 3.02177i | − 0.331682i | −0.986152 | − | 0.165841i | \(-0.946966\pi\) | ||||
0.986152 | − | 0.165841i | \(-0.0530339\pi\) | |||||||
\(84\) | − 1.35690i | − 0.148049i | ||||||||
\(85\) | − 2.04892i | − 0.222236i | ||||||||
\(86\) | 4.41789i | 0.476394i | ||||||||
\(87\) | 5.13706 | 0.550751 | ||||||||
\(88\) | 5.29590 | 0.564545 | ||||||||
\(89\) | − 5.47650i | − 0.580508i | −0.956950 | − | 0.290254i | \(-0.906260\pi\) | ||||
0.956950 | − | 0.290254i | \(-0.0937398\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.33513 | 0.139196 | ||||||||
\(93\) | 2.80194i | 0.290547i | ||||||||
\(94\) | 4.82371 | 0.497527 | ||||||||
\(95\) | −3.24698 | −0.333133 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 5.85086i | 0.594064i | 0.954867 | + | 0.297032i | \(0.0959969\pi\) | ||||
−0.954867 | + | 0.297032i | \(0.904003\pi\) | |||||||
\(98\) | − 5.15883i | − 0.521121i | ||||||||
\(99\) | − 5.29590i | − 0.532258i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.39612 | 0.835446 | 0.417723 | − | 0.908575i | \(-0.362828\pi\) | ||||
0.417723 | + | 0.908575i | \(0.362828\pi\) | |||||||
\(102\) | 2.04892i | 0.202873i | ||||||||
\(103\) | −13.6353 | −1.34353 | −0.671765 | − | 0.740765i | \(-0.734463\pi\) | ||||
−0.671765 | + | 0.740765i | \(0.734463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.35690 | 0.132419 | ||||||||
\(106\) | − 14.2349i | − 1.38262i | ||||||||
\(107\) | 3.92394 | 0.379341 | 0.189671 | − | 0.981848i | \(-0.439258\pi\) | ||||
0.189671 | + | 0.981848i | \(0.439258\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.554958i | 0.0531553i | 0.999647 | + | 0.0265777i | \(0.00846093\pi\) | ||||
−0.999647 | + | 0.0265777i | \(0.991539\pi\) | |||||||
\(110\) | 5.29590i | 0.504944i | ||||||||
\(111\) | 2.24698i | 0.213274i | ||||||||
\(112\) | − 1.35690i | − 0.128215i | ||||||||
\(113\) | 4.39373 | 0.413328 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(114\) | 3.24698 | 0.304108 | ||||||||
\(115\) | 1.33513i | 0.124501i | ||||||||
\(116\) | 5.13706 | 0.476964 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.8998 | 1.27958 | ||||||||
\(119\) | − 2.78017i | − 0.254858i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −17.0465 | −1.54968 | ||||||||
\(122\) | 3.62565i | 0.328251i | ||||||||
\(123\) | 10.6310i | 0.958567i | ||||||||
\(124\) | 2.80194i | 0.251621i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.35690 | −0.120882 | ||||||||
\(127\) | 2.23490 | 0.198315 | 0.0991576 | − | 0.995072i | \(-0.468385\pi\) | ||||
0.0991576 | + | 0.995072i | \(0.468385\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 4.41789 | 0.388974 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.51573 | −0.744023 | −0.372011 | − | 0.928228i | \(-0.621332\pi\) | ||||
−0.372011 | + | 0.928228i | \(0.621332\pi\) | |||||||
\(132\) | − 5.29590i | − 0.460949i | ||||||||
\(133\) | −4.40581 | −0.382032 | ||||||||
\(134\) | −9.03684 | −0.780664 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 2.04892i | 0.175693i | ||||||||
\(137\) | 13.1685i | 1.12506i | 0.826776 | + | 0.562531i | \(0.190172\pi\) | ||||
−0.826776 | + | 0.562531i | \(0.809828\pi\) | |||||||
\(138\) | − 1.33513i | − 0.113653i | ||||||||
\(139\) | 7.17629 | 0.608685 | 0.304343 | − | 0.952563i | \(-0.401563\pi\) | ||||
0.304343 | + | 0.952563i | \(0.401563\pi\) | |||||||
\(140\) | 1.35690 | 0.114679 | ||||||||
\(141\) | − 4.82371i | − 0.406229i | ||||||||
\(142\) | −11.7506 | −0.986091 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.13706i | 0.426610i | ||||||||
\(146\) | −12.1032 | −1.00167 | ||||||||
\(147\) | −5.15883 | −0.425493 | ||||||||
\(148\) | 2.24698i | 0.184701i | ||||||||
\(149\) | 9.66248i | 0.791581i | 0.918341 | + | 0.395791i | \(0.129529\pi\) | ||||
−0.918341 | + | 0.395791i | \(0.870471\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 7.35152i | 0.598258i | 0.954213 | + | 0.299129i | \(0.0966961\pi\) | ||||
−0.954213 | + | 0.299129i | \(0.903304\pi\) | |||||||
\(152\) | 3.24698 | 0.263365 | ||||||||
\(153\) | 2.04892 | 0.165645 | ||||||||
\(154\) | 7.18598i | 0.579063i | ||||||||
\(155\) | −2.80194 | −0.225057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.85325 | 0.227714 | 0.113857 | − | 0.993497i | \(-0.463679\pi\) | ||||
0.113857 | + | 0.993497i | \(0.463679\pi\) | |||||||
\(158\) | − 0.259061i | − 0.0206098i | ||||||||
\(159\) | −14.2349 | −1.12890 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.81163i | 0.142776i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 15.1075i | 1.18331i | 0.806190 | + | 0.591656i | \(0.201526\pi\) | ||||
−0.806190 | + | 0.591656i | \(0.798474\pi\) | |||||||
\(164\) | 10.6310i | 0.830143i | ||||||||
\(165\) | 5.29590 | 0.412285 | ||||||||
\(166\) | −3.02177 | −0.234535 | ||||||||
\(167\) | 16.0881i | 1.24494i | 0.782644 | + | 0.622469i | \(0.213870\pi\) | ||||
−0.782644 | + | 0.622469i | \(0.786130\pi\) | |||||||
\(168\) | −1.35690 | −0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.04892 | −0.157145 | ||||||||
\(171\) | − 3.24698i | − 0.248303i | ||||||||
\(172\) | 4.41789 | 0.336861 | ||||||||
\(173\) | 15.4795 | 1.17688 | 0.588442 | − | 0.808540i | \(-0.299742\pi\) | ||||
0.588442 | + | 0.808540i | \(0.299742\pi\) | |||||||
\(174\) | − 5.13706i | − 0.389440i | ||||||||
\(175\) | 1.35690i | 0.102572i | ||||||||
\(176\) | − 5.29590i | − 0.399193i | ||||||||
\(177\) | − 13.8998i | − 1.04477i | ||||||||
\(178\) | −5.47650 | −0.410481 | ||||||||
\(179\) | −19.0737 | −1.42563 | −0.712817 | − | 0.701351i | \(-0.752581\pi\) | ||||
−0.712817 | + | 0.701351i | \(0.752581\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −2.16852 | −0.161185 | −0.0805925 | − | 0.996747i | \(-0.525681\pi\) | ||||
−0.0805925 | + | 0.996747i | \(0.525681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.62565 | 0.268015 | ||||||||
\(184\) | − 1.33513i | − 0.0984268i | ||||||||
\(185\) | −2.24698 | −0.165201 | ||||||||
\(186\) | 2.80194 | 0.205448 | ||||||||
\(187\) | − 10.8509i | − 0.793493i | ||||||||
\(188\) | − 4.82371i | − 0.351805i | ||||||||
\(189\) | 1.35690i | 0.0986997i | ||||||||
\(190\) | 3.24698i | 0.235561i | ||||||||
\(191\) | −11.7409 | −0.849545 | −0.424772 | − | 0.905300i | \(-0.639646\pi\) | ||||
−0.424772 | + | 0.905300i | \(0.639646\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 24.6722i | − 1.77594i | −0.459900 | − | 0.887971i | \(-0.652115\pi\) | ||||
0.459900 | − | 0.887971i | \(-0.347885\pi\) | |||||||
\(194\) | 5.85086 | 0.420067 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.15883 | −0.368488 | ||||||||
\(197\) | − 26.2010i | − 1.86675i | −0.358906 | − | 0.933374i | \(-0.616850\pi\) | ||||
0.358906 | − | 0.933374i | \(-0.383150\pi\) | |||||||
\(198\) | −5.29590 | −0.376363 | ||||||||
\(199\) | −19.6722 | −1.39452 | −0.697262 | − | 0.716817i | \(-0.745598\pi\) | ||||
−0.697262 | + | 0.716817i | \(0.745598\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 9.03684i | 0.637409i | ||||||||
\(202\) | − 8.39612i | − 0.590749i | ||||||||
\(203\) | 6.97046i | 0.489230i | ||||||||
\(204\) | 2.04892 | 0.143453 | ||||||||
\(205\) | −10.6310 | −0.742503 | ||||||||
\(206\) | 13.6353i | 0.950019i | ||||||||
\(207\) | −1.33513 | −0.0927976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.1957 | −1.18945 | ||||||||
\(210\) | − 1.35690i | − 0.0936347i | ||||||||
\(211\) | −16.2935 | −1.12169 | −0.560846 | − | 0.827920i | \(-0.689524\pi\) | ||||
−0.560846 | + | 0.827920i | \(0.689524\pi\) | |||||||
\(212\) | −14.2349 | −0.977657 | ||||||||
\(213\) | 11.7506i | 0.805140i | ||||||||
\(214\) | − 3.92394i | − 0.268235i | ||||||||
\(215\) | 4.41789i | 0.301298i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | −3.80194 | −0.258092 | ||||||||
\(218\) | 0.554958 | 0.0375865 | ||||||||
\(219\) | 12.1032i | 0.817859i | ||||||||
\(220\) | 5.29590 | 0.357049 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.24698 | 0.150807 | ||||||||
\(223\) | 2.28083i | 0.152736i | 0.997080 | + | 0.0763679i | \(0.0243323\pi\) | ||||
−0.997080 | + | 0.0763679i | \(0.975668\pi\) | |||||||
\(224\) | −1.35690 | −0.0906614 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 4.39373i | − 0.292267i | ||||||||
\(227\) | 3.37196i | 0.223805i | 0.993719 | + | 0.111902i | \(0.0356944\pi\) | ||||
−0.993719 | + | 0.111902i | \(0.964306\pi\) | |||||||
\(228\) | − 3.24698i | − 0.215036i | ||||||||
\(229\) | 18.3763i | 1.21434i | 0.794573 | + | 0.607169i | \(0.207695\pi\) | ||||
−0.794573 | + | 0.607169i | \(0.792305\pi\) | |||||||
\(230\) | 1.33513 | 0.0880356 | ||||||||
\(231\) | 7.18598 | 0.472803 | ||||||||
\(232\) | − 5.13706i | − 0.337265i | ||||||||
\(233\) | −10.0858 | −0.660740 | −0.330370 | − | 0.943852i | \(-0.607173\pi\) | ||||
−0.330370 | + | 0.943852i | \(0.607173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82371 | 0.314664 | ||||||||
\(236\) | − 13.8998i | − 0.904798i | ||||||||
\(237\) | −0.259061 | −0.0168278 | ||||||||
\(238\) | −2.78017 | −0.180211 | ||||||||
\(239\) | 20.0834i | 1.29908i | 0.760325 | + | 0.649542i | \(0.225039\pi\) | ||||
−0.760325 | + | 0.649542i | \(0.774961\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 2.99462i | 0.192901i | 0.995338 | + | 0.0964503i | \(0.0307489\pi\) | ||||
−0.995338 | + | 0.0964503i | \(0.969251\pi\) | |||||||
\(242\) | 17.0465i | 1.09579i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.62565 | 0.232108 | ||||||||
\(245\) | − 5.15883i | − 0.329586i | ||||||||
\(246\) | 10.6310 | 0.677809 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.80194 | 0.177923 | ||||||||
\(249\) | 3.02177i | 0.191497i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 7.20237 | 0.454610 | 0.227305 | − | 0.973824i | \(-0.427009\pi\) | ||||
0.227305 | + | 0.973824i | \(0.427009\pi\) | |||||||
\(252\) | 1.35690i | 0.0854764i | ||||||||
\(253\) | 7.07069i | 0.444530i | ||||||||
\(254\) | − 2.23490i | − 0.140230i | ||||||||
\(255\) | 2.04892i | 0.128308i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.8291 | 1.17453 | 0.587263 | − | 0.809396i | \(-0.300205\pi\) | ||||
0.587263 | + | 0.809396i | \(0.300205\pi\) | |||||||
\(258\) | − 4.41789i | − 0.275046i | ||||||||
\(259\) | −3.04892 | −0.189451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.13706 | −0.317976 | ||||||||
\(262\) | 8.51573i | 0.526104i | ||||||||
\(263\) | −17.9245 | −1.10527 | −0.552637 | − | 0.833422i | \(-0.686378\pi\) | ||||
−0.552637 | + | 0.833422i | \(0.686378\pi\) | |||||||
\(264\) | −5.29590 | −0.325940 | ||||||||
\(265\) | − 14.2349i | − 0.874443i | ||||||||
\(266\) | 4.40581i | 0.270138i | ||||||||
\(267\) | 5.47650i | 0.335156i | ||||||||
\(268\) | 9.03684i | 0.552013i | ||||||||
\(269\) | −22.4045 | −1.36603 | −0.683013 | − | 0.730406i | \(-0.739331\pi\) | ||||
−0.683013 | + | 0.730406i | \(0.739331\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 23.2325i | − 1.41127i | −0.708573 | − | 0.705637i | \(-0.750661\pi\) | ||||
0.708573 | − | 0.705637i | \(-0.249339\pi\) | |||||||
\(272\) | 2.04892 | 0.124234 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.1685 | 0.795540 | ||||||||
\(275\) | 5.29590i | 0.319355i | ||||||||
\(276\) | −1.33513 | −0.0803651 | ||||||||
\(277\) | 9.78448 | 0.587892 | 0.293946 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293946 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(278\) | − 7.17629i | − 0.430405i | ||||||||
\(279\) | − 2.80194i | − 0.167748i | ||||||||
\(280\) | − 1.35690i | − 0.0810900i | ||||||||
\(281\) | 21.6286i | 1.29026i | 0.764075 | + | 0.645128i | \(0.223196\pi\) | ||||
−0.764075 | + | 0.645128i | \(0.776804\pi\) | |||||||
\(282\) | −4.82371 | −0.287248 | ||||||||
\(283\) | −3.38942 | −0.201480 | −0.100740 | − | 0.994913i | \(-0.532121\pi\) | ||||
−0.100740 | + | 0.994913i | \(0.532121\pi\) | |||||||
\(284\) | 11.7506i | 0.697271i | ||||||||
\(285\) | 3.24698 | 0.192334 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.4252 | −0.851492 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −12.8019 | −0.753055 | ||||||||
\(290\) | 5.13706 | 0.301659 | ||||||||
\(291\) | − 5.85086i | − 0.342983i | ||||||||
\(292\) | 12.1032i | 0.708287i | ||||||||
\(293\) | 34.1280i | 1.99378i | 0.0788243 | + | 0.996889i | \(0.474883\pi\) | ||||
−0.0788243 | + | 0.996889i | \(0.525117\pi\) | |||||||
\(294\) | 5.15883i | 0.300869i | ||||||||
\(295\) | 13.8998 | 0.809276 | ||||||||
\(296\) | 2.24698 | 0.130603 | ||||||||
\(297\) | 5.29590i | 0.307299i | ||||||||
\(298\) | 9.66248 | 0.559733 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 5.99462i | 0.345524i | ||||||||
\(302\) | 7.35152 | 0.423032 | ||||||||
\(303\) | −8.39612 | −0.482345 | ||||||||
\(304\) | − 3.24698i | − 0.186227i | ||||||||
\(305\) | 3.62565i | 0.207604i | ||||||||
\(306\) | − 2.04892i | − 0.117129i | ||||||||
\(307\) | − 15.6601i | − 0.893768i | −0.894592 | − | 0.446884i | \(-0.852534\pi\) | ||||
0.894592 | − | 0.446884i | \(-0.147466\pi\) | |||||||
\(308\) | 7.18598 | 0.409459 | ||||||||
\(309\) | 13.6353 | 0.775687 | ||||||||
\(310\) | 2.80194i | 0.159139i | ||||||||
\(311\) | −25.7972 | −1.46282 | −0.731411 | − | 0.681937i | \(-0.761138\pi\) | ||||
−0.731411 | + | 0.681937i | \(0.761138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6243 | −0.883139 | −0.441569 | − | 0.897227i | \(-0.645578\pi\) | ||||
−0.441569 | + | 0.897227i | \(0.645578\pi\) | |||||||
\(314\) | − 2.85325i | − 0.161018i | ||||||||
\(315\) | −1.35690 | −0.0764524 | ||||||||
\(316\) | −0.259061 | −0.0145733 | ||||||||
\(317\) | 9.25965i | 0.520074i | 0.965599 | + | 0.260037i | \(0.0837347\pi\) | ||||
−0.965599 | + | 0.260037i | \(0.916265\pi\) | |||||||
\(318\) | 14.2349i | 0.798253i | ||||||||
\(319\) | 27.2054i | 1.52321i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −3.92394 | −0.219013 | ||||||||
\(322\) | 1.81163 | 0.100958 | ||||||||
\(323\) | − 6.65279i | − 0.370171i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.1075 | 0.836728 | ||||||||
\(327\) | − 0.554958i | − 0.0306893i | ||||||||
\(328\) | 10.6310 | 0.587000 | ||||||||
\(329\) | 6.54527 | 0.360852 | ||||||||
\(330\) | − 5.29590i | − 0.291530i | ||||||||
\(331\) | − 21.8582i | − 1.20143i | −0.799462 | − | 0.600716i | \(-0.794882\pi\) | ||||
0.799462 | − | 0.600716i | \(-0.205118\pi\) | |||||||
\(332\) | 3.02177i | 0.165841i | ||||||||
\(333\) | − 2.24698i | − 0.123134i | ||||||||
\(334\) | 16.0881 | 0.880304 | ||||||||
\(335\) | −9.03684 | −0.493735 | ||||||||
\(336\) | 1.35690i | 0.0740247i | ||||||||
\(337\) | −14.5013 | −0.789934 | −0.394967 | − | 0.918695i | \(-0.629244\pi\) | ||||
−0.394967 | + | 0.918695i | \(0.629244\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.39373 | −0.238635 | ||||||||
\(340\) | 2.04892i | 0.111118i | ||||||||
\(341\) | −14.8388 | −0.803565 | ||||||||
\(342\) | −3.24698 | −0.175577 | ||||||||
\(343\) | − 16.4983i | − 0.890823i | ||||||||
\(344\) | − 4.41789i | − 0.238197i | ||||||||
\(345\) | − 1.33513i | − 0.0718807i | ||||||||
\(346\) | − 15.4795i | − 0.832182i | ||||||||
\(347\) | 7.84117 | 0.420936 | 0.210468 | − | 0.977601i | \(-0.432501\pi\) | ||||
0.210468 | + | 0.977601i | \(0.432501\pi\) | |||||||
\(348\) | −5.13706 | −0.275375 | ||||||||
\(349\) | 20.4252i | 1.09334i | 0.837350 | + | 0.546668i | \(0.184104\pi\) | ||||
−0.837350 | + | 0.546668i | \(0.815896\pi\) | |||||||
\(350\) | 1.35690 | 0.0725291 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.29590 | −0.282272 | ||||||||
\(353\) | − 13.2905i | − 0.707383i | −0.935362 | − | 0.353692i | \(-0.884926\pi\) | ||||
0.935362 | − | 0.353692i | \(-0.115074\pi\) | |||||||
\(354\) | −13.8998 | −0.738765 | ||||||||
\(355\) | −11.7506 | −0.623659 | ||||||||
\(356\) | 5.47650i | 0.290254i | ||||||||
\(357\) | 2.78017i | 0.147142i | ||||||||
\(358\) | 19.0737i | 1.00807i | ||||||||
\(359\) | − 12.8267i | − 0.676967i | −0.940972 | − | 0.338483i | \(-0.890086\pi\) | ||||
0.940972 | − | 0.338483i | \(-0.109914\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 8.45712 | 0.445112 | ||||||||
\(362\) | 2.16852i | 0.113975i | ||||||||
\(363\) | 17.0465 | 0.894710 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1032 | −0.633511 | ||||||||
\(366\) | − 3.62565i | − 0.189516i | ||||||||
\(367\) | −17.9554 | −0.937264 | −0.468632 | − | 0.883393i | \(-0.655253\pi\) | ||||
−0.468632 | + | 0.883393i | \(0.655253\pi\) | |||||||
\(368\) | −1.33513 | −0.0695982 | ||||||||
\(369\) | − 10.6310i | − 0.553429i | ||||||||
\(370\) | 2.24698i | 0.116815i | ||||||||
\(371\) | − 19.3153i | − 1.00280i | ||||||||
\(372\) | − 2.80194i | − 0.145274i | ||||||||
\(373\) | 27.8732 | 1.44322 | 0.721610 | − | 0.692300i | \(-0.243402\pi\) | ||||
0.721610 | + | 0.692300i | \(0.243402\pi\) | |||||||
\(374\) | −10.8509 | −0.561084 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −4.82371 | −0.248764 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.35690 | 0.0697912 | ||||||||
\(379\) | 13.8702i | 0.712466i | 0.934397 | + | 0.356233i | \(0.115939\pi\) | ||||
−0.934397 | + | 0.356233i | \(0.884061\pi\) | |||||||
\(380\) | 3.24698 | 0.166567 | ||||||||
\(381\) | −2.23490 | −0.114497 | ||||||||
\(382\) | 11.7409i | 0.600719i | ||||||||
\(383\) | − 26.8984i | − 1.37445i | −0.726446 | − | 0.687223i | \(-0.758829\pi\) | ||||
0.726446 | − | 0.687223i | \(-0.241171\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 7.18598i | 0.366231i | ||||||||
\(386\) | −24.6722 | −1.25578 | ||||||||
\(387\) | −4.41789 | −0.224574 | ||||||||
\(388\) | − 5.85086i | − 0.297032i | ||||||||
\(389\) | 0.187309 | 0.00949693 | 0.00474846 | − | 0.999989i | \(-0.498489\pi\) | ||||
0.00474846 | + | 0.999989i | \(0.498489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.73556 | −0.138343 | ||||||||
\(392\) | 5.15883i | 0.260560i | ||||||||
\(393\) | 8.51573 | 0.429562 | ||||||||
\(394\) | −26.2010 | −1.31999 | ||||||||
\(395\) | − 0.259061i | − 0.0130348i | ||||||||
\(396\) | 5.29590i | 0.266129i | ||||||||
\(397\) | 8.58211i | 0.430724i | 0.976534 | + | 0.215362i | \(0.0690931\pi\) | ||||
−0.976534 | + | 0.215362i | \(0.930907\pi\) | |||||||
\(398\) | 19.6722i | 0.986077i | ||||||||
\(399\) | 4.40581 | 0.220567 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 23.9748i | 1.19724i | 0.801032 | + | 0.598621i | \(0.204285\pi\) | ||||
−0.801032 | + | 0.598621i | \(0.795715\pi\) | |||||||
\(402\) | 9.03684 | 0.450716 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.39612 | −0.417723 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 6.97046 | 0.345938 | ||||||||
\(407\) | −11.8998 | −0.589850 | ||||||||
\(408\) | − 2.04892i | − 0.101437i | ||||||||
\(409\) | 8.37926i | 0.414328i | 0.978306 | + | 0.207164i | \(0.0664233\pi\) | ||||
−0.978306 | + | 0.207164i | \(0.933577\pi\) | |||||||
\(410\) | 10.6310i | 0.525029i | ||||||||
\(411\) | − 13.1685i | − 0.649555i | ||||||||
\(412\) | 13.6353 | 0.671765 | ||||||||
\(413\) | 18.8605 | 0.928067 | ||||||||
\(414\) | 1.33513i | 0.0656178i | ||||||||
\(415\) | −3.02177 | −0.148333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.17629 | −0.351425 | ||||||||
\(418\) | 17.1957i | 0.841068i | ||||||||
\(419\) | 37.0887 | 1.81190 | 0.905952 | − | 0.423381i | \(-0.139157\pi\) | ||||
0.905952 | + | 0.423381i | \(0.139157\pi\) | |||||||
\(420\) | −1.35690 | −0.0662097 | ||||||||
\(421\) | − 4.90515i | − 0.239062i | −0.992830 | − | 0.119531i | \(-0.961861\pi\) | ||||
0.992830 | − | 0.119531i | \(-0.0381391\pi\) | |||||||
\(422\) | 16.2935i | 0.793155i | ||||||||
\(423\) | 4.82371i | 0.234537i | ||||||||
\(424\) | 14.2349i | 0.691308i | ||||||||
\(425\) | −2.04892 | −0.0993871 | ||||||||
\(426\) | 11.7506 | 0.569320 | ||||||||
\(427\) | 4.91962i | 0.238077i | ||||||||
\(428\) | −3.92394 | −0.189671 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.41789 | 0.213050 | ||||||||
\(431\) | 6.06531i | 0.292156i | 0.989273 | + | 0.146078i | \(0.0466650\pi\) | ||||
−0.989273 | + | 0.146078i | \(0.953335\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.8877 | 0.715457 | 0.357728 | − | 0.933826i | \(-0.383551\pi\) | ||||
0.357728 | + | 0.933826i | \(0.383551\pi\) | |||||||
\(434\) | 3.80194i | 0.182499i | ||||||||
\(435\) | − 5.13706i | − 0.246303i | ||||||||
\(436\) | − 0.554958i | − 0.0265777i | ||||||||
\(437\) | 4.33513i | 0.207377i | ||||||||
\(438\) | 12.1032 | 0.578314 | ||||||||
\(439\) | 21.1336 | 1.00865 | 0.504326 | − | 0.863513i | \(-0.331741\pi\) | ||||
0.504326 | + | 0.863513i | \(0.331741\pi\) | |||||||
\(440\) | − 5.29590i | − 0.252472i | ||||||||
\(441\) | 5.15883 | 0.245659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0683 | 1.33356 | 0.666782 | − | 0.745252i | \(-0.267671\pi\) | ||||
0.666782 | + | 0.745252i | \(0.267671\pi\) | |||||||
\(444\) | − 2.24698i | − 0.106637i | ||||||||
\(445\) | −5.47650 | −0.259611 | ||||||||
\(446\) | 2.28083 | 0.108000 | ||||||||
\(447\) | − 9.66248i | − 0.457020i | ||||||||
\(448\) | 1.35690i | 0.0641073i | ||||||||
\(449\) | 19.2446i | 0.908208i | 0.890949 | + | 0.454104i | \(0.150041\pi\) | ||||
−0.890949 | + | 0.454104i | \(0.849959\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −56.3008 | −2.65110 | ||||||||
\(452\) | −4.39373 | −0.206664 | ||||||||
\(453\) | − 7.35152i | − 0.345404i | ||||||||
\(454\) | 3.37196 | 0.158254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.24698 | −0.152054 | ||||||||
\(457\) | 37.8485i | 1.77048i | 0.465138 | + | 0.885238i | \(0.346005\pi\) | ||||
−0.465138 | + | 0.885238i | \(0.653995\pi\) | |||||||
\(458\) | 18.3763 | 0.858667 | ||||||||
\(459\) | −2.04892 | −0.0956353 | ||||||||
\(460\) | − 1.33513i | − 0.0622506i | ||||||||
\(461\) | 11.2228i | 0.522699i | 0.965244 | + | 0.261349i | \(0.0841675\pi\) | ||||
−0.965244 | + | 0.261349i | \(0.915833\pi\) | |||||||
\(462\) | − 7.18598i | − 0.334322i | ||||||||
\(463\) | 25.0726i | 1.16522i | 0.812751 | + | 0.582611i | \(0.197969\pi\) | ||||
−0.812751 | + | 0.582611i | \(0.802031\pi\) | |||||||
\(464\) | −5.13706 | −0.238482 | ||||||||
\(465\) | 2.80194 | 0.129937 | ||||||||
\(466\) | 10.0858i | 0.467213i | ||||||||
\(467\) | −36.9657 | −1.71057 | −0.855284 | − | 0.518160i | \(-0.826617\pi\) | ||||
−0.855284 | + | 0.518160i | \(0.826617\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2620 | −0.566209 | ||||||||
\(470\) | − 4.82371i | − 0.222501i | ||||||||
\(471\) | −2.85325 | −0.131471 | ||||||||
\(472\) | −13.8998 | −0.639789 | ||||||||
\(473\) | 23.3967i | 1.07578i | ||||||||
\(474\) | 0.259061i | 0.0118991i | ||||||||
\(475\) | 3.24698i | 0.148982i | ||||||||
\(476\) | 2.78017i | 0.127429i | ||||||||
\(477\) | 14.2349 | 0.651771 | ||||||||
\(478\) | 20.0834 | 0.918592 | ||||||||
\(479\) | 31.4590i | 1.43740i | 0.695320 | + | 0.718700i | \(0.255263\pi\) | ||||
−0.695320 | + | 0.718700i | \(0.744737\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.99462 | 0.136401 | ||||||||
\(483\) | − 1.81163i | − 0.0824319i | ||||||||
\(484\) | 17.0465 | 0.774842 | ||||||||
\(485\) | 5.85086 | 0.265674 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 18.8713i | − 0.855140i | −0.903982 | − | 0.427570i | \(-0.859370\pi\) | ||||
0.903982 | − | 0.427570i | \(-0.140630\pi\) | |||||||
\(488\) | − 3.62565i | − 0.164125i | ||||||||
\(489\) | − 15.1075i | − 0.683186i | ||||||||
\(490\) | −5.15883 | −0.233052 | ||||||||
\(491\) | 16.3961 | 0.739947 | 0.369973 | − | 0.929042i | \(-0.379367\pi\) | ||||
0.369973 | + | 0.929042i | \(0.379367\pi\) | |||||||
\(492\) | − 10.6310i | − 0.479284i | ||||||||
\(493\) | −10.5254 | −0.474041 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.29590 | −0.238033 | ||||||||
\(496\) | − 2.80194i | − 0.125811i | ||||||||
\(497\) | −15.9444 | −0.715203 | ||||||||
\(498\) | 3.02177 | 0.135409 | ||||||||
\(499\) | − 40.2452i | − 1.80162i | −0.434212 | − | 0.900811i | \(-0.642973\pi\) | ||||
0.434212 | − | 0.900811i | \(-0.357027\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 16.0881i | − 0.718765i | ||||||||
\(502\) | − 7.20237i | − 0.321458i | ||||||||
\(503\) | 18.4004 | 0.820435 | 0.410217 | − | 0.911988i | \(-0.365453\pi\) | ||||
0.410217 | + | 0.911988i | \(0.365453\pi\) | |||||||
\(504\) | 1.35690 | 0.0604409 | ||||||||
\(505\) | − 8.39612i | − 0.373623i | ||||||||
\(506\) | 7.07069 | 0.314330 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.23490 | −0.0991576 | ||||||||
\(509\) | 35.1377i | 1.55745i | 0.627366 | + | 0.778725i | \(0.284133\pi\) | ||||
−0.627366 | + | 0.778725i | \(0.715867\pi\) | |||||||
\(510\) | 2.04892 | 0.0907276 | ||||||||
\(511\) | −16.4228 | −0.726502 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 3.24698i | 0.143358i | ||||||||
\(514\) | − 18.8291i | − 0.830515i | ||||||||
\(515\) | 13.6353i | 0.600845i | ||||||||
\(516\) | −4.41789 | −0.194487 | ||||||||
\(517\) | 25.5459 | 1.12351 | ||||||||
\(518\) | 3.04892i | 0.133962i | ||||||||
\(519\) | −15.4795 | −0.679474 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2610 | −1.54481 | −0.772406 | − | 0.635129i | \(-0.780947\pi\) | ||||
−0.772406 | + | 0.635129i | \(0.780947\pi\) | |||||||
\(522\) | 5.13706i | 0.224843i | ||||||||
\(523\) | 14.3043 | 0.625482 | 0.312741 | − | 0.949839i | \(-0.398753\pi\) | ||||
0.312741 | + | 0.949839i | \(0.398753\pi\) | |||||||
\(524\) | 8.51573 | 0.372011 | ||||||||
\(525\) | − 1.35690i | − 0.0592198i | ||||||||
\(526\) | 17.9245i | 0.781546i | ||||||||
\(527\) | − 5.74094i | − 0.250079i | ||||||||
\(528\) | 5.29590i | 0.230474i | ||||||||
\(529\) | −21.2174 | −0.922497 | ||||||||
\(530\) | −14.2349 | −0.618324 | ||||||||
\(531\) | 13.8998i | 0.603199i | ||||||||
\(532\) | 4.40581 | 0.191016 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.47650 | 0.236991 | ||||||||
\(535\) | − 3.92394i | − 0.169647i | ||||||||
\(536\) | 9.03684 | 0.390332 | ||||||||
\(537\) | 19.0737 | 0.823090 | ||||||||
\(538\) | 22.4045i | 0.965926i | ||||||||
\(539\) | − 27.3207i | − 1.17678i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | − 44.2422i | − 1.90212i | −0.309006 | − | 0.951060i | \(-0.599996\pi\) | ||||
0.309006 | − | 0.951060i | \(-0.400004\pi\) | |||||||
\(542\) | −23.2325 | −0.997922 | ||||||||
\(543\) | 2.16852 | 0.0930602 | ||||||||
\(544\) | − 2.04892i | − 0.0878466i | ||||||||
\(545\) | 0.554958 | 0.0237718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.34481 | 0.271285 | 0.135642 | − | 0.990758i | \(-0.456690\pi\) | ||||
0.135642 | + | 0.990758i | \(0.456690\pi\) | |||||||
\(548\) | − 13.1685i | − 0.562531i | ||||||||
\(549\) | −3.62565 | −0.154739 | ||||||||
\(550\) | 5.29590 | 0.225818 | ||||||||
\(551\) | 16.6799i | 0.710589i | ||||||||
\(552\) | 1.33513i | 0.0568267i | ||||||||
\(553\) | − 0.351519i | − 0.0149481i | ||||||||
\(554\) | − 9.78448i | − 0.415703i | ||||||||
\(555\) | 2.24698 | 0.0953790 | ||||||||
\(556\) | −7.17629 | −0.304343 | ||||||||
\(557\) | 31.3884i | 1.32997i | 0.746858 | + | 0.664984i | \(0.231562\pi\) | ||||
−0.746858 | + | 0.664984i | \(0.768438\pi\) | |||||||
\(558\) | −2.80194 | −0.118615 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.35690 | −0.0573393 | ||||||||
\(561\) | 10.8509i | 0.458123i | ||||||||
\(562\) | 21.6286 | 0.912349 | ||||||||
\(563\) | 44.4989 | 1.87540 | 0.937702 | − | 0.347441i | \(-0.112949\pi\) | ||||
0.937702 | + | 0.347441i | \(0.112949\pi\) | |||||||
\(564\) | 4.82371i | 0.203115i | ||||||||
\(565\) | − 4.39373i | − 0.184846i | ||||||||
\(566\) | 3.38942i | 0.142468i | ||||||||
\(567\) | − 1.35690i | − 0.0569843i | ||||||||
\(568\) | 11.7506 | 0.493045 | ||||||||
\(569\) | −30.5394 | −1.28028 | −0.640140 | − | 0.768259i | \(-0.721123\pi\) | ||||
−0.640140 | + | 0.768259i | \(0.721123\pi\) | |||||||
\(570\) | − 3.24698i | − 0.136001i | ||||||||
\(571\) | 32.7614 | 1.37102 | 0.685511 | − | 0.728063i | \(-0.259579\pi\) | ||||
0.685511 | + | 0.728063i | \(0.259579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.7409 | 0.490485 | ||||||||
\(574\) | 14.4252i | 0.602096i | ||||||||
\(575\) | 1.33513 | 0.0556786 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 36.5870i | − 1.52314i | −0.648084 | − | 0.761569i | \(-0.724430\pi\) | ||||
0.648084 | − | 0.761569i | \(-0.275570\pi\) | |||||||
\(578\) | 12.8019i | 0.532490i | ||||||||
\(579\) | 24.6722i | 1.02534i | ||||||||
\(580\) | − 5.13706i | − 0.213305i | ||||||||
\(581\) | −4.10023 | −0.170106 | ||||||||
\(582\) | −5.85086 | −0.242526 | ||||||||
\(583\) | − 75.3866i | − 3.12219i | ||||||||
\(584\) | 12.1032 | 0.500834 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.1280 | 1.40981 | ||||||||
\(587\) | − 22.4873i | − 0.928148i | −0.885796 | − | 0.464074i | \(-0.846387\pi\) | ||||
0.885796 | − | 0.464074i | \(-0.153613\pi\) | |||||||
\(588\) | 5.15883 | 0.212747 | ||||||||
\(589\) | −9.09783 | −0.374870 | ||||||||
\(590\) | − 13.8998i | − 0.572245i | ||||||||
\(591\) | 26.2010i | 1.07777i | ||||||||
\(592\) | − 2.24698i | − 0.0923503i | ||||||||
\(593\) | 39.5749i | 1.62515i | 0.582858 | + | 0.812574i | \(0.301934\pi\) | ||||
−0.582858 | + | 0.812574i | \(0.698066\pi\) | |||||||
\(594\) | 5.29590 | 0.217293 | ||||||||
\(595\) | −2.78017 | −0.113976 | ||||||||
\(596\) | − 9.66248i | − 0.395791i | ||||||||
\(597\) | 19.6722 | 0.805128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.3424 | −1.28062 | −0.640308 | − | 0.768118i | \(-0.721193\pi\) | ||||
−0.640308 | + | 0.768118i | \(0.721193\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −32.9487 | −1.34401 | −0.672003 | − | 0.740549i | \(-0.734566\pi\) | ||||
−0.672003 | + | 0.740549i | \(0.734566\pi\) | |||||||
\(602\) | 5.99462 | 0.244323 | ||||||||
\(603\) | − 9.03684i | − 0.368008i | ||||||||
\(604\) | − 7.35152i | − 0.299129i | ||||||||
\(605\) | 17.0465i | 0.693040i | ||||||||
\(606\) | 8.39612i | 0.341069i | ||||||||
\(607\) | −40.1739 | −1.63061 | −0.815304 | − | 0.579033i | \(-0.803430\pi\) | ||||
−0.815304 | + | 0.579033i | \(0.803430\pi\) | |||||||
\(608\) | −3.24698 | −0.131682 | ||||||||
\(609\) | − 6.97046i | − 0.282457i | ||||||||
\(610\) | 3.62565 | 0.146798 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.04892 | −0.0828226 | ||||||||
\(613\) | − 11.3588i | − 0.458778i | −0.973335 | − | 0.229389i | \(-0.926327\pi\) | ||||
0.973335 | − | 0.229389i | \(-0.0736728\pi\) | |||||||
\(614\) | −15.6601 | −0.631990 | ||||||||
\(615\) | 10.6310 | 0.428684 | ||||||||
\(616\) | − 7.18598i | − 0.289531i | ||||||||
\(617\) | − 20.9172i | − 0.842096i | −0.907038 | − | 0.421048i | \(-0.861662\pi\) | ||||
0.907038 | − | 0.421048i | \(-0.138338\pi\) | |||||||
\(618\) | − 13.6353i | − 0.548494i | ||||||||
\(619\) | − 14.0562i | − 0.564967i | −0.959272 | − | 0.282483i | \(-0.908842\pi\) | ||||
0.959272 | − | 0.282483i | \(-0.0911582\pi\) | |||||||
\(620\) | 2.80194 | 0.112529 | ||||||||
\(621\) | 1.33513 | 0.0535767 | ||||||||
\(622\) | 25.7972i | 1.03437i | ||||||||
\(623\) | −7.43104 | −0.297718 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 15.6243i | 0.624473i | ||||||||
\(627\) | 17.1957 | 0.686729 | ||||||||
\(628\) | −2.85325 | −0.113857 | ||||||||
\(629\) | − 4.60388i | − 0.183569i | ||||||||
\(630\) | 1.35690i | 0.0540600i | ||||||||
\(631\) | − 40.6601i | − 1.61865i | −0.587359 | − | 0.809326i | \(-0.699832\pi\) | ||||
0.587359 | − | 0.809326i | \(-0.300168\pi\) | |||||||
\(632\) | 0.259061i | 0.0103049i | ||||||||
\(633\) | 16.2935 | 0.647609 | ||||||||
\(634\) | 9.25965 | 0.367748 | ||||||||
\(635\) | − 2.23490i | − 0.0886892i | ||||||||
\(636\) | 14.2349 | 0.564450 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 27.2054 | 1.07707 | ||||||||
\(639\) | − 11.7506i | − 0.464848i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 1.92633 | 0.0760854 | 0.0380427 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380427 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(642\) | 3.92394i | 0.154865i | ||||||||
\(643\) | − 3.37973i | − 0.133284i | −0.997777 | − | 0.0666418i | \(-0.978772\pi\) | ||||
0.997777 | − | 0.0666418i | \(-0.0212285\pi\) | |||||||
\(644\) | − 1.81163i | − 0.0713881i | ||||||||
\(645\) | − 4.41789i | − 0.173954i | ||||||||
\(646\) | −6.65279 | −0.261751 | ||||||||
\(647\) | 10.8181 | 0.425302 | 0.212651 | − | 0.977128i | \(-0.431790\pi\) | ||||
0.212651 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 73.6118 | 2.88951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.80194 | 0.149010 | ||||||||
\(652\) | − 15.1075i | − 0.591656i | ||||||||
\(653\) | 33.7646 | 1.32131 | 0.660656 | − | 0.750689i | \(-0.270278\pi\) | ||||
0.660656 | + | 0.750689i | \(0.270278\pi\) | |||||||
\(654\) | −0.554958 | −0.0217006 | ||||||||
\(655\) | 8.51573i | 0.332737i | ||||||||
\(656\) | − 10.6310i | − 0.415072i | ||||||||
\(657\) | − 12.1032i | − 0.472191i | ||||||||
\(658\) | − 6.54527i | − 0.255161i | ||||||||
\(659\) | −16.8592 | −0.656742 | −0.328371 | − | 0.944549i | \(-0.606500\pi\) | ||||
−0.328371 | + | 0.944549i | \(0.606500\pi\) | |||||||
\(660\) | −5.29590 | −0.206143 | ||||||||
\(661\) | − 4.71140i | − 0.183252i | −0.995793 | − | 0.0916261i | \(-0.970794\pi\) | ||||
0.995793 | − | 0.0916261i | \(-0.0292065\pi\) | |||||||
\(662\) | −21.8582 | −0.849541 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.02177 | 0.117267 | ||||||||
\(665\) | 4.40581i | 0.170850i | ||||||||
\(666\) | −2.24698 | −0.0870687 | ||||||||
\(667\) | 6.85862 | 0.265567 | ||||||||
\(668\) | − 16.0881i | − 0.622469i | ||||||||
\(669\) | − 2.28083i | − 0.0881820i | ||||||||
\(670\) | 9.03684i | 0.349123i | ||||||||
\(671\) | 19.2010i | 0.741248i | ||||||||
\(672\) | 1.35690 | 0.0523434 | ||||||||
\(673\) | −3.12797 | −0.120574 | −0.0602871 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602871 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(674\) | 14.5013i | 0.558567i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.50737 | −0.0579329 | −0.0289664 | − | 0.999580i | \(-0.509222\pi\) | ||||
−0.0289664 | + | 0.999580i | \(0.509222\pi\) | |||||||
\(678\) | 4.39373i | 0.168740i | ||||||||
\(679\) | 7.93900 | 0.304671 | ||||||||
\(680\) | 2.04892 | 0.0785724 | ||||||||
\(681\) | − 3.37196i | − 0.129214i | ||||||||
\(682\) | 14.8388i | 0.568206i | ||||||||
\(683\) | − 31.0726i | − 1.18896i | −0.804110 | − | 0.594480i | \(-0.797358\pi\) | ||||
0.804110 | − | 0.594480i | \(-0.202642\pi\) | |||||||
\(684\) | 3.24698i | 0.124151i | ||||||||
\(685\) | 13.1685 | 0.503143 | ||||||||
\(686\) | −16.4983 | −0.629907 | ||||||||
\(687\) | − 18.3763i | − 0.701099i | ||||||||
\(688\) | −4.41789 | −0.168431 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.33513 | −0.0508274 | ||||||||
\(691\) | − 26.7469i | − 1.01750i | −0.860914 | − | 0.508750i | \(-0.830108\pi\) | ||||
0.860914 | − | 0.508750i | \(-0.169892\pi\) | |||||||
\(692\) | −15.4795 | −0.588442 | ||||||||
\(693\) | −7.18598 | −0.272973 | ||||||||
\(694\) | − 7.84117i | − 0.297647i | ||||||||
\(695\) | − 7.17629i | − 0.272212i | ||||||||
\(696\) | 5.13706i | 0.194720i | ||||||||
\(697\) | − 21.7821i | − 0.825055i | ||||||||
\(698\) | 20.4252 | 0.773105 | ||||||||
\(699\) | 10.0858 | 0.381478 | ||||||||
\(700\) | − 1.35690i | − 0.0512858i | ||||||||
\(701\) | −11.2054 | −0.423221 | −0.211610 | − | 0.977354i | \(-0.567871\pi\) | ||||
−0.211610 | + | 0.977354i | \(0.567871\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.29590 | −0.275170 | ||||||||
\(704\) | 5.29590i | 0.199597i | ||||||||
\(705\) | −4.82371 | −0.181671 | ||||||||
\(706\) | −13.2905 | −0.500195 | ||||||||
\(707\) | − 11.3927i | − 0.428465i | ||||||||
\(708\) | 13.8998i | 0.522385i | ||||||||
\(709\) | − 26.9933i | − 1.01375i | −0.862018 | − | 0.506877i | \(-0.830800\pi\) | ||||
0.862018 | − | 0.506877i | \(-0.169200\pi\) | |||||||
\(710\) | 11.7506i | 0.440993i | ||||||||
\(711\) | 0.259061 | 0.00971555 | ||||||||
\(712\) | 5.47650 | 0.205241 | ||||||||
\(713\) | 3.74094i | 0.140099i | ||||||||
\(714\) | 2.78017 | 0.104045 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.0737 | 0.712817 | ||||||||
\(717\) | − 20.0834i | − 0.750027i | ||||||||
\(718\) | −12.8267 | −0.478688 | ||||||||
\(719\) | 15.4601 | 0.576565 | 0.288282 | − | 0.957545i | \(-0.406916\pi\) | ||||
0.288282 | + | 0.957545i | \(0.406916\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 18.5017i | 0.689040i | ||||||||
\(722\) | − 8.45712i | − 0.314742i | ||||||||
\(723\) | − 2.99462i | − 0.111371i | ||||||||
\(724\) | 2.16852 | 0.0805925 | ||||||||
\(725\) | 5.13706 | 0.190786 | ||||||||
\(726\) | − 17.0465i | − 0.632656i | ||||||||
\(727\) | 10.9148 | 0.404809 | 0.202404 | − | 0.979302i | \(-0.435124\pi\) | ||||
0.202404 | + | 0.979302i | \(0.435124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.1032i | 0.447960i | ||||||||
\(731\) | −9.05190 | −0.334797 | ||||||||
\(732\) | −3.62565 | −0.134008 | ||||||||
\(733\) | − 13.5539i | − 0.500624i | −0.968165 | − | 0.250312i | \(-0.919467\pi\) | ||||
0.968165 | − | 0.250312i | \(-0.0805333\pi\) | |||||||
\(734\) | 17.9554i | 0.662746i | ||||||||
\(735\) | 5.15883i | 0.190286i | ||||||||
\(736\) | 1.33513i | 0.0492134i | ||||||||
\(737\) | −47.8582 | −1.76288 | ||||||||
\(738\) | −10.6310 | −0.391333 | ||||||||
\(739\) | − 15.4679i | − 0.568995i | −0.958677 | − | 0.284498i | \(-0.908173\pi\) | ||||
0.958677 | − | 0.284498i | \(-0.0918268\pi\) | |||||||
\(740\) | 2.24698 | 0.0826006 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.3153 | −0.709086 | ||||||||
\(743\) | 40.2040i | 1.47494i | 0.675378 | + | 0.737471i | \(0.263980\pi\) | ||||
−0.675378 | + | 0.737471i | \(0.736020\pi\) | |||||||
\(744\) | −2.80194 | −0.102724 | ||||||||
\(745\) | 9.66248 | 0.354006 | ||||||||
\(746\) | − 27.8732i | − 1.02051i | ||||||||
\(747\) | − 3.02177i | − 0.110561i | ||||||||
\(748\) | 10.8509i | 0.396747i | ||||||||
\(749\) | − 5.32437i | − 0.194548i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 19.8465 | 0.724211 | 0.362105 | − | 0.932137i | \(-0.382058\pi\) | ||||
0.362105 | + | 0.932137i | \(0.382058\pi\) | |||||||
\(752\) | 4.82371i | 0.175903i | ||||||||
\(753\) | −7.20237 | −0.262469 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.35152 | 0.267549 | ||||||||
\(756\) | − 1.35690i | − 0.0493498i | ||||||||
\(757\) | 39.8883 | 1.44976 | 0.724882 | − | 0.688873i | \(-0.241894\pi\) | ||||
0.724882 | + | 0.688873i | \(0.241894\pi\) | |||||||
\(758\) | 13.8702 | 0.503790 | ||||||||
\(759\) | − 7.07069i | − 0.256650i | ||||||||
\(760\) | − 3.24698i | − 0.117780i | ||||||||
\(761\) | − 31.8756i | − 1.15549i | −0.816217 | − | 0.577745i | \(-0.803933\pi\) | ||||
0.816217 | − | 0.577745i | \(-0.196067\pi\) | |||||||
\(762\) | 2.23490i | 0.0809618i | ||||||||
\(763\) | 0.753020 | 0.0272612 | ||||||||
\(764\) | 11.7409 | 0.424772 | ||||||||
\(765\) | − 2.04892i | − 0.0740788i | ||||||||
\(766\) | −26.8984 | −0.971880 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − 43.0672i | − 1.55304i | −0.630090 | − | 0.776522i | \(-0.716982\pi\) | ||||
0.630090 | − | 0.776522i | \(-0.283018\pi\) | |||||||
\(770\) | 7.18598 | 0.258965 | ||||||||
\(771\) | −18.8291 | −0.678113 | ||||||||
\(772\) | 24.6722i | 0.887971i | ||||||||
\(773\) | 33.1282i | 1.19154i | 0.803155 | + | 0.595770i | \(0.203153\pi\) | ||||
−0.803155 | + | 0.595770i | \(0.796847\pi\) | |||||||
\(774\) | 4.41789i | 0.158798i | ||||||||
\(775\) | 2.80194i | 0.100649i | ||||||||
\(776\) | −5.85086 | −0.210033 | ||||||||
\(777\) | 3.04892 | 0.109379 | ||||||||
\(778\) | − 0.187309i | − 0.00671534i | ||||||||
\(779\) | −34.5187 | −1.23676 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.2301 | −2.22677 | ||||||||
\(782\) | 2.73556i | 0.0978235i | ||||||||
\(783\) | 5.13706 | 0.183584 | ||||||||
\(784\) | 5.15883 | 0.184244 | ||||||||
\(785\) | − 2.85325i | − 0.101837i | ||||||||
\(786\) | − 8.51573i | − 0.303746i | ||||||||
\(787\) | − 35.9138i | − 1.28019i | −0.768297 | − | 0.640094i | \(-0.778895\pi\) | ||||
0.768297 | − | 0.640094i | \(-0.221105\pi\) | |||||||
\(788\) | 26.2010i | 0.933374i | ||||||||
\(789\) | 17.9245 | 0.638130 | ||||||||
\(790\) | −0.259061 | −0.00921698 | ||||||||
\(791\) | − 5.96184i | − 0.211978i | ||||||||
\(792\) | 5.29590 | 0.188182 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.58211 | 0.304568 | ||||||||
\(795\) | 14.2349i | 0.504860i | ||||||||
\(796\) | 19.6722 | 0.697262 | ||||||||
\(797\) | 29.7918 | 1.05528 | 0.527639 | − | 0.849468i | \(-0.323077\pi\) | ||||
0.527639 | + | 0.849468i | \(0.323077\pi\) | |||||||
\(798\) | − 4.40581i | − 0.155964i | ||||||||
\(799\) | 9.88338i | 0.349649i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 5.47650i | − 0.193503i | ||||||||
\(802\) | 23.9748 | 0.846579 | ||||||||
\(803\) | −64.0974 | −2.26195 | ||||||||
\(804\) | − 9.03684i | − 0.318705i | ||||||||
\(805\) | 1.81163 | 0.0638514 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.4045 | 0.788675 | ||||||||
\(808\) | 8.39612i | 0.295375i | ||||||||
\(809\) | 1.52648 | 0.0536683 | 0.0268341 | − | 0.999640i | \(-0.491457\pi\) | ||||
0.0268341 | + | 0.999640i | \(0.491457\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 51.6039i | 1.81206i | 0.423217 | + | 0.906029i | \(0.360901\pi\) | ||||
−0.423217 | + | 0.906029i | \(0.639099\pi\) | |||||||
\(812\) | − 6.97046i | − 0.244615i | ||||||||
\(813\) | 23.2325i | 0.814800i | ||||||||
\(814\) | 11.8998i | 0.417087i | ||||||||
\(815\) | 15.1075 | 0.529193 | ||||||||
\(816\) | −2.04892 | −0.0717265 | ||||||||
\(817\) | 14.3448i | 0.501862i | ||||||||
\(818\) | 8.37926 | 0.292974 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.6310 | 0.371251 | ||||||||
\(821\) | − 17.4795i | − 0.610038i | −0.952346 | − | 0.305019i | \(-0.901337\pi\) | ||||
0.952346 | − | 0.305019i | \(-0.0986629\pi\) | |||||||
\(822\) | −13.1685 | −0.459305 | ||||||||
\(823\) | 25.5566 | 0.890848 | 0.445424 | − | 0.895320i | \(-0.353053\pi\) | ||||
0.445424 | + | 0.895320i | \(0.353053\pi\) | |||||||
\(824\) | − 13.6353i | − 0.475009i | ||||||||
\(825\) | − 5.29590i | − 0.184379i | ||||||||
\(826\) | − 18.8605i | − 0.656242i | ||||||||
\(827\) | − 9.16182i | − 0.318588i | −0.987231 | − | 0.159294i | \(-0.949078\pi\) | ||||
0.987231 | − | 0.159294i | \(-0.0509217\pi\) | |||||||
\(828\) | 1.33513 | 0.0463988 | ||||||||
\(829\) | −48.6493 | −1.68966 | −0.844831 | − | 0.535034i | \(-0.820299\pi\) | ||||
−0.844831 | + | 0.535034i | \(0.820299\pi\) | |||||||
\(830\) | 3.02177i | 0.104887i | ||||||||
\(831\) | −9.78448 | −0.339420 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5700 | 0.366230 | ||||||||
\(834\) | 7.17629i | 0.248495i | ||||||||
\(835\) | 16.0881 | 0.556753 | ||||||||
\(836\) | 17.1957 | 0.594725 | ||||||||
\(837\) | 2.80194i | 0.0968491i | ||||||||
\(838\) | − 37.0887i | − 1.28121i | ||||||||
\(839\) | − 8.71246i | − 0.300788i | −0.988626 | − | 0.150394i | \(-0.951946\pi\) | ||||
0.988626 | − | 0.150394i | \(-0.0480542\pi\) | |||||||
\(840\) | 1.35690i | 0.0468174i | ||||||||
\(841\) | −2.61058 | −0.0900200 | ||||||||
\(842\) | −4.90515 | −0.169043 | ||||||||
\(843\) | − 21.6286i | − 0.744930i | ||||||||
\(844\) | 16.2935 | 0.560846 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.82371 | 0.165842 | ||||||||
\(847\) | 23.1304i | 0.794769i | ||||||||
\(848\) | 14.2349 | 0.488828 | ||||||||
\(849\) | 3.38942 | 0.116325 | ||||||||
\(850\) | 2.04892i | 0.0702773i | ||||||||
\(851\) | 3.00000i | 0.102839i | ||||||||
\(852\) | − 11.7506i | − 0.402570i | ||||||||
\(853\) | − 5.41060i | − 0.185255i | −0.995701 | − | 0.0926277i | \(-0.970473\pi\) | ||||
0.995701 | − | 0.0926277i | \(-0.0295266\pi\) | |||||||
\(854\) | 4.91962 | 0.168346 | ||||||||
\(855\) | −3.24698 | −0.111044 | ||||||||
\(856\) | 3.92394i | 0.134117i | ||||||||
\(857\) | −0.165275 | −0.00564570 | −0.00282285 | − | 0.999996i | \(-0.500899\pi\) | ||||
−0.00282285 | + | 0.999996i | \(0.500899\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.0853 | 1.60653 | 0.803264 | − | 0.595622i | \(-0.203095\pi\) | ||||
0.803264 | + | 0.595622i | \(0.203095\pi\) | |||||||
\(860\) | − 4.41789i | − 0.150649i | ||||||||
\(861\) | 14.4252 | 0.491609 | ||||||||
\(862\) | 6.06531 | 0.206585 | ||||||||
\(863\) | 31.2553i | 1.06394i | 0.846762 | + | 0.531972i | \(0.178549\pi\) | ||||
−0.846762 | + | 0.531972i | \(0.821451\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 15.4795i | − 0.526318i | ||||||||
\(866\) | − 14.8877i | − 0.505904i | ||||||||
\(867\) | 12.8019 | 0.434777 | ||||||||
\(868\) | 3.80194 | 0.129046 | ||||||||
\(869\) | − 1.37196i | − 0.0465406i | ||||||||
\(870\) | −5.13706 | −0.174163 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.554958 | −0.0187933 | ||||||||
\(873\) | 5.85086i | 0.198021i | ||||||||
\(874\) | 4.33513 | 0.146638 | ||||||||
\(875\) | 1.35690 | 0.0458715 | ||||||||
\(876\) | − 12.1032i | − 0.408930i | ||||||||
\(877\) | − 16.9898i | − 0.573706i | −0.957975 | − | 0.286853i | \(-0.907391\pi\) | ||||
0.957975 | − | 0.286853i | \(-0.0926091\pi\) | |||||||
\(878\) | − 21.1336i | − 0.713225i | ||||||||
\(879\) | − 34.1280i | − 1.15111i | ||||||||
\(880\) | −5.29590 | −0.178525 | ||||||||
\(881\) | 3.29159 | 0.110896 | 0.0554482 | − | 0.998462i | \(-0.482341\pi\) | ||||
0.0554482 | + | 0.998462i | \(0.482341\pi\) | |||||||
\(882\) | − 5.15883i | − 0.173707i | ||||||||
\(883\) | −17.3157 | −0.582721 | −0.291361 | − | 0.956613i | \(-0.594108\pi\) | ||||
−0.291361 | + | 0.956613i | \(0.594108\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.8998 | −0.467236 | ||||||||
\(886\) | − 28.0683i | − 0.942973i | ||||||||
\(887\) | 15.6775 | 0.526401 | 0.263200 | − | 0.964741i | \(-0.415222\pi\) | ||||
0.263200 | + | 0.964741i | \(0.415222\pi\) | |||||||
\(888\) | −2.24698 | −0.0754037 | ||||||||
\(889\) | − 3.03252i | − 0.101708i | ||||||||
\(890\) | 5.47650i | 0.183573i | ||||||||
\(891\) | − 5.29590i | − 0.177419i | ||||||||
\(892\) | − 2.28083i | − 0.0763679i | ||||||||
\(893\) | 15.6625 | 0.524125 | ||||||||
\(894\) | −9.66248 | −0.323162 | ||||||||
\(895\) | 19.0737i | 0.637563i | ||||||||
\(896\) | 1.35690 | 0.0453307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.2446 | 0.642200 | ||||||||
\(899\) | 14.3937i | 0.480058i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 29.1661 | 0.971665 | ||||||||
\(902\) | 56.3008i | 1.87461i | ||||||||
\(903\) | − 5.99462i | − 0.199489i | ||||||||
\(904\) | 4.39373i | 0.146133i | ||||||||
\(905\) | 2.16852i | 0.0720841i | ||||||||
\(906\) | −7.35152 | −0.244238 | ||||||||
\(907\) | 25.8877 | 0.859587 | 0.429793 | − | 0.902927i | \(-0.358586\pi\) | ||||
0.429793 | + | 0.902927i | \(0.358586\pi\) | |||||||
\(908\) | − 3.37196i | − 0.111902i | ||||||||
\(909\) | 8.39612 | 0.278482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5220 | −1.24316 | −0.621579 | − | 0.783351i | \(-0.713509\pi\) | ||||
−0.621579 | + | 0.783351i | \(0.713509\pi\) | |||||||
\(912\) | 3.24698i | 0.107518i | ||||||||
\(913\) | −16.0030 | −0.529621 | ||||||||
\(914\) | 37.8485 | 1.25192 | ||||||||
\(915\) | − 3.62565i | − 0.119860i | ||||||||
\(916\) | − 18.3763i | − 0.607169i | ||||||||
\(917\) | 11.5550i | 0.381578i | ||||||||
\(918\) | 2.04892i | 0.0676243i | ||||||||
\(919\) | −5.56358 | −0.183526 | −0.0917628 | − | 0.995781i | \(-0.529250\pi\) | ||||
−0.0917628 | + | 0.995781i | \(0.529250\pi\) | |||||||
\(920\) | −1.33513 | −0.0440178 | ||||||||
\(921\) | 15.6601i | 0.516017i | ||||||||
\(922\) | 11.2228 | 0.369604 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.18598 | −0.236401 | ||||||||
\(925\) | 2.24698i | 0.0738802i | ||||||||
\(926\) | 25.0726 | 0.823937 | ||||||||
\(927\) | −13.6353 | −0.447843 | ||||||||
\(928\) | 5.13706i | 0.168632i | ||||||||
\(929\) | − 40.2602i | − 1.32090i | −0.750872 | − | 0.660448i | \(-0.770366\pi\) | ||||
0.750872 | − | 0.660448i | \(-0.229634\pi\) | |||||||
\(930\) | − 2.80194i | − 0.0918792i | ||||||||
\(931\) | − 16.7506i | − 0.548980i | ||||||||
\(932\) | 10.0858 | 0.330370 | ||||||||
\(933\) | 25.7972 | 0.844561 | ||||||||
\(934\) | 36.9657i | 1.20955i | ||||||||
\(935\) | −10.8509 | −0.354861 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5356 | −0.997554 | −0.498777 | − | 0.866730i | \(-0.666217\pi\) | ||||
−0.498777 | + | 0.866730i | \(0.666217\pi\) | |||||||
\(938\) | 12.2620i | 0.400370i | ||||||||
\(939\) | 15.6243 | 0.509880 | ||||||||
\(940\) | −4.82371 | −0.157332 | ||||||||
\(941\) | 41.6461i | 1.35762i | 0.734312 | + | 0.678812i | \(0.237505\pi\) | ||||
−0.734312 | + | 0.678812i | \(0.762495\pi\) | |||||||
\(942\) | 2.85325i | 0.0929638i | ||||||||
\(943\) | 14.1938i | 0.462212i | ||||||||
\(944\) | 13.8998i | 0.452399i | ||||||||
\(945\) | 1.35690 | 0.0441398 | ||||||||
\(946\) | 23.3967 | 0.760693 | ||||||||
\(947\) | − 21.7724i | − 0.707508i | −0.935339 | − | 0.353754i | \(-0.884905\pi\) | ||||
0.935339 | − | 0.353754i | \(-0.115095\pi\) | |||||||
\(948\) | 0.259061 | 0.00841392 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.24698 | 0.105346 | ||||||||
\(951\) | − 9.25965i | − 0.300265i | ||||||||
\(952\) | 2.78017 | 0.0901057 | ||||||||
\(953\) | 41.9560 | 1.35909 | 0.679544 | − | 0.733635i | \(-0.262178\pi\) | ||||
0.679544 | + | 0.733635i | \(0.262178\pi\) | |||||||
\(954\) | − 14.2349i | − 0.460872i | ||||||||
\(955\) | 11.7409i | 0.379928i | ||||||||
\(956\) | − 20.0834i | − 0.649542i | ||||||||
\(957\) | − 27.2054i | − 0.879424i | ||||||||
\(958\) | 31.4590 | 1.01640 | ||||||||
\(959\) | 17.8683 | 0.576998 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 23.1491 | 0.746747 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.92394 | 0.126447 | ||||||||
\(964\) | − 2.99462i | − 0.0964503i | ||||||||
\(965\) | −24.6722 | −0.794225 | ||||||||
\(966\) | −1.81163 | −0.0582881 | ||||||||
\(967\) | 16.7041i | 0.537168i | 0.963256 | + | 0.268584i | \(0.0865556\pi\) | ||||
−0.963256 | + | 0.268584i | \(0.913444\pi\) | |||||||
\(968\) | − 17.0465i | − 0.547896i | ||||||||
\(969\) | 6.65279i | 0.213718i | ||||||||
\(970\) | − 5.85086i | − 0.187860i | ||||||||
\(971\) | −20.7275 | −0.665178 | −0.332589 | − | 0.943072i | \(-0.607922\pi\) | ||||
−0.332589 | + | 0.943072i | \(0.607922\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 9.73748i | − 0.312169i | ||||||||
\(974\) | −18.8713 | −0.604675 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.62565 | −0.116054 | ||||||||
\(977\) | − 33.4547i | − 1.07031i | −0.844753 | − | 0.535156i | \(-0.820253\pi\) | ||||
0.844753 | − | 0.535156i | \(-0.179747\pi\) | |||||||
\(978\) | −15.1075 | −0.483085 | ||||||||
\(979\) | −29.0030 | −0.926939 | ||||||||
\(980\) | 5.15883i | 0.164793i | ||||||||
\(981\) | 0.554958i | 0.0177184i | ||||||||
\(982\) | − 16.3961i | − 0.523221i | ||||||||
\(983\) | − 31.8605i | − 1.01619i | −0.861300 | − | 0.508097i | \(-0.830349\pi\) | ||||
0.861300 | − | 0.508097i | \(-0.169651\pi\) | |||||||
\(984\) | −10.6310 | −0.338905 | ||||||||
\(985\) | −26.2010 | −0.834835 | ||||||||
\(986\) | 10.5254i | 0.335198i | ||||||||
\(987\) | −6.54527 | −0.208338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.89844 | 0.187560 | ||||||||
\(990\) | 5.29590i | 0.168315i | ||||||||
\(991\) | −21.0925 | −0.670024 | −0.335012 | − | 0.942214i | \(-0.608740\pi\) | ||||
−0.335012 | + | 0.942214i | \(0.608740\pi\) | |||||||
\(992\) | −2.80194 | −0.0889616 | ||||||||
\(993\) | 21.8582i | 0.693647i | ||||||||
\(994\) | 15.9444i | 0.505725i | ||||||||
\(995\) | 19.6722i | 0.623650i | ||||||||
\(996\) | − 3.02177i | − 0.0957485i | ||||||||
\(997\) | 17.7832 | 0.563198 | 0.281599 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281599 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(998\) | −40.2452 | −1.27394 | ||||||||
\(999\) | 2.24698i | 0.0710913i |
(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 | 5070.2.b.t.1351.2 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bj.1.2 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.bu.1.2 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.t.1351.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.2 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.bu.1.2 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.t.1351.2 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.t.1351.5 | 6 | 13.12 | even | 2 | inner |