Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(545,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.k (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.4 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.545 |
Dual form | 672.2.k.c.545.2 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.58114 | + | 0.707107i | −0.912871 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | 0.632456 | 0.316228 | − | 0.948683i | \(-0.397584\pi\) | ||||
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | + | 1.41421i | −0.845154 | + | 0.534522i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | − | 2.23607i | 0.666667 | − | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.16228i | 0.877058i | 0.898717 | + | 0.438529i | \(0.144500\pi\) | ||||
−0.898717 | + | 0.438529i | \(0.855500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.23607 | + | 1.00000i | −0.577350 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264i | 0.973329i | 0.873589 | + | 0.486664i | \(0.161786\pi\) | ||||
−0.873589 | + | 0.486664i | \(0.838214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53553 | − | 3.81721i | 0.553299 | − | 0.832983i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.58114 | + | 4.94975i | −0.304290 | + | 0.952579i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214i | 0.830455i | 0.909718 | + | 0.415227i | \(0.136298\pi\) | ||||
−0.909718 | + | 0.415227i | \(0.863702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685i | 1.01600i | 0.861357 | + | 0.508001i | \(0.169615\pi\) | ||||
−0.861357 | + | 0.508001i | \(0.830385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.16228 | + | 2.00000i | −0.534522 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.23607 | − | 5.00000i | −0.358057 | − | 0.800641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.48528 | −1.32518 | −0.662589 | − | 0.748983i | \(-0.730542\pi\) | ||||
−0.662589 | + | 0.748983i | \(0.730542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.94427 | −1.36399 | −0.681994 | − | 0.731357i | \(-0.738887\pi\) | ||||
−0.681994 | + | 0.731357i | \(0.738887\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | − | 3.16228i | 0.421637 | − | 0.471405i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.32456 | −0.922531 | −0.461266 | − | 0.887262i | \(-0.652604\pi\) | ||||
−0.461266 | + | 0.887262i | \(0.652604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 6.32456i | 0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.47214 | − | 2.00000i | 0.626224 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4164i | 1.84289i | 0.388514 | + | 0.921443i | \(0.372988\pi\) | ||||
−0.388514 | + | 0.921443i | \(0.627012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.00000 | − | 6.70820i | −0.397360 | − | 0.888523i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.16228 | 0.411693 | 0.205847 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205847 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.16228i | 0.404888i | 0.979294 | + | 0.202444i | \(0.0648884\pi\) | ||||
−0.979294 | + | 0.202444i | \(0.935112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.30986 | + | 7.82843i | −0.165027 | + | 0.986289i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214i | 0.554700i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.24264 | + | 9.48683i | 0.510754 | + | 1.14208i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000i | 0.949425i | 0.880141 | + | 0.474713i | \(0.157448\pi\) | ||||
−0.880141 | + | 0.474713i | \(0.842552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.6491i | − | 1.48047i | −0.672350 | − | 0.740233i | \(-0.734715\pi\) | ||
0.672350 | − | 0.740233i | \(-0.265285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.74342 | − | 2.12132i | 0.547723 | − | 0.244949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4164 | 1.50946 | 0.754732 | − | 0.656033i | \(-0.227767\pi\) | ||||
0.754732 | + | 0.656033i | \(0.227767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.16228 | −0.347105 | −0.173553 | − | 0.984825i | \(-0.555525\pi\) | ||||
−0.173553 | + | 0.984825i | \(0.555525\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.16228 | − | 7.07107i | −0.339032 | − | 0.758098i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.3137 | −1.19925 | −0.599625 | − | 0.800281i | \(-0.704684\pi\) | ||||
−0.599625 | + | 0.800281i | \(0.704684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | − | 7.07107i | −0.468807 | − | 0.741249i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | − | 8.94427i | −0.414781 | − | 0.927478i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.9737i | 1.92648i | 0.268635 | + | 0.963242i | \(0.413427\pi\) | ||||
−0.268635 | + | 0.963242i | \(0.586573\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7279 | 1.26648 | 0.633238 | − | 0.773957i | \(-0.281726\pi\) | ||||
0.633238 | + | 0.773957i | \(0.281726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.58579 | − | 5.39835i | 0.349937 | − | 0.526825i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.16228 | − | 1.41421i | 0.300150 | − | 0.134231i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.47214i | 0.420703i | 0.977626 | + | 0.210352i | \(0.0674609\pi\) | ||||
−0.977626 | + | 0.210352i | \(0.932539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.48528i | − | 0.791257i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.07107 | + | 6.32456i | 0.653720 | + | 0.584705i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.32456 | − | 4.00000i | 0.579771 | − | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4164 | − | 6.00000i | 1.20972 | − | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3137 | −1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94427 | 0.793676 | 0.396838 | − | 0.917889i | \(-0.370108\pi\) | ||||
0.396838 | + | 0.917889i | \(0.370108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.1421 | − | 6.32456i | 1.24515 | − | 0.556846i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8114 | 1.38145 | 0.690724 | − | 0.723119i | \(-0.257292\pi\) | ||||
0.690724 | + | 0.723119i | \(0.257292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 9.48683i | −0.520266 | − | 0.822613i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.23607 | + | 7.00000i | −0.192450 | + | 0.602464i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.94427i | − | 0.764161i | −0.924129 | − | 0.382080i | \(-0.875208\pi\) | ||
0.924129 | − | 0.382080i | \(-0.124792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.3848i | − | 1.55938i | −0.626168 | − | 0.779688i | \(-0.715378\pi\) | ||
0.626168 | − | 0.779688i | \(-0.284622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0000 | − | 4.47214i | 0.842152 | − | 0.376622i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.32456i | 0.525226i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.271281 | + | 12.1213i | −0.0223748 | + | 0.999750i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.47214i | 0.366372i | 0.983078 | + | 0.183186i | \(0.0586410\pi\) | ||||
−0.983078 | + | 0.183186i | \(0.941359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427 | 0.727875 | 0.363937 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363937 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.65685 | + | 6.32456i | −0.457330 | + | 0.511310i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000i | 0.642575i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.8114i | − | 1.26189i | −0.775829 | − | 0.630943i | \(-0.782668\pi\) | ||
0.775829 | − | 0.630943i | \(-0.217332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.48683 | − | 21.2132i | −0.752355 | − | 1.68232i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.48528 | + | 13.4164i | 0.668734 | + | 1.05736i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9737 | 1.46823 | 0.734113 | − | 0.679027i | \(-0.237598\pi\) | ||||
0.734113 | + | 0.679027i | \(0.237598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.48683 | + | 8.48528i | 0.725476 | + | 0.648886i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5563 | −1.18273 | −0.591364 | − | 0.806405i | \(-0.701410\pi\) | ||||
−0.591364 | + | 0.806405i | \(0.701410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.70820 | − | 4.24264i | 0.507093 | − | 0.320713i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.00000 | + | 2.23607i | −0.375823 | + | 0.168073i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.0000i | 1.19590i | 0.801535 | + | 0.597948i | \(0.204017\pi\) | ||||
−0.801535 | + | 0.597948i | \(0.795983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1359i | 1.64535i | 0.568511 | + | 0.822676i | \(0.307520\pi\) | ||||
−0.568511 | + | 0.822676i | \(0.692480\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.23607 | − | 5.00000i | −0.165295 | − | 0.369611i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | −0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.46447 | − | 13.3040i | −0.252003 | − | 0.967726i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.16228 | − | 7.07107i | −0.226455 | − | 0.506370i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.47214i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509280\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.3137i | − | 0.802008i | −0.916076 | − | 0.401004i | \(-0.868661\pi\) | ||
0.916076 | − | 0.401004i | \(-0.131339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.32456 | − | 10.0000i | −0.443897 | − | 0.701862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | −0.838116 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.4164 | − | 12.0000i | −0.932505 | − | 0.834058i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.65685 | − | 12.6491i | −0.387601 | − | 0.866703i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.6491 | −0.862662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | − | 12.6491i | −0.543075 | − | 0.858678i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.94427 | + | 20.0000i | 0.604398 | + | 1.35147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.94427i | − | 0.601657i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1421i | 0.947027i | 0.880786 | + | 0.473514i | \(0.157015\pi\) | ||||
−0.880786 | + | 0.473514i | \(0.842985\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 6.70820i | −0.400000 | + | 0.447214i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.16228 | −0.209888 | −0.104944 | − | 0.994478i | \(-0.533466\pi\) | ||||
−0.104944 | + | 0.994478i | \(0.533466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.16228i | 0.208969i | 0.994527 | + | 0.104485i | \(0.0333193\pi\) | ||||
−0.994527 | + | 0.104485i | \(0.966681\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8885i | 1.17192i | 0.810341 | + | 0.585959i | \(0.199282\pi\) | ||||
−0.810341 | + | 0.585959i | \(0.800718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.94427 | −0.583460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.2132 | + | 9.48683i | −1.37795 | + | 0.616236i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.0000i | − | 0.646846i | −0.946254 | − | 0.323423i | \(-0.895166\pi\) | ||
0.946254 | − | 0.323423i | \(-0.104834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.32456i | − | 0.407400i | −0.979033 | − | 0.203700i | \(-0.934703\pi\) | ||
0.979033 | − | 0.203700i | \(-0.0652968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.90569 | + | 13.4350i | 0.507151 | + | 0.861858i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.24264 | − | 8.94427i | 0.271052 | − | 0.571429i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.4164 | −0.853666 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.00000 | − | 2.23607i | 0.316862 | − | 0.141705i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.4605 | −1.79641 | −0.898205 | − | 0.439576i | \(-0.855129\pi\) | ||||
−0.898205 | + | 0.439576i | \(0.855129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.32456 | − | 2.82843i | 0.396059 | − | 0.177123i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.2843 | 1.76432 | 0.882162 | − | 0.470946i | \(-0.156087\pi\) | ||||
0.882162 | + | 0.470946i | \(0.156087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | − | 2.82843i | 0.277885 | − | 0.175750i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | + | 8.94427i | 0.618984 | + | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0000i | 0.986602i | 0.869859 | + | 0.493301i | \(0.164210\pi\) | ||||
−0.869859 | + | 0.493301i | \(0.835790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.9737i | 1.16554i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.8885 | − | 8.00000i | 1.09476 | − | 0.489592i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.89949 | −0.603583 | −0.301791 | − | 0.953374i | \(-0.597585\pi\) | ||||
−0.301791 | + | 0.953374i | \(0.597585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.48528i | 0.515444i | 0.966219 | + | 0.257722i | \(0.0829719\pi\) | ||||
−0.966219 | + | 0.257722i | \(0.917028\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0711 | + | 8.01806i | 0.730574 | + | 0.485275i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0000 | 1.08152 | 0.540758 | − | 0.841178i | \(-0.318138\pi\) | ||||
0.540758 | + | 0.841178i | \(0.318138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.6491 | + | 11.3137i | 0.757282 | + | 0.677334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.8885i | − | 1.06714i | −0.845756 | − | 0.533571i | \(-0.820850\pi\) | ||
0.845756 | − | 0.533571i | \(-0.179150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.2132i | 1.26099i | 0.776192 | + | 0.630497i | \(0.217149\pi\) | ||||
−0.776192 | + | 0.630497i | \(0.782851\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.24264 | − | 9.48683i | −0.251312 | − | 0.561951i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9737 | − | 12.0000i | 1.11998 | − | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4164 | − | 30.0000i | −0.786484 | − | 1.75863i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.07107 | −0.413096 | −0.206548 | − | 0.978436i | \(-0.566223\pi\) | ||||
−0.206548 | + | 0.978436i | \(0.566223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.47214 | 0.260378 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.9737 | 1.09728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 12.6491i | 1.15278 | − | 0.729083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.1246 | + | 9.00000i | −1.15613 | + | 0.517036i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214i | 0.256074i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.24264i | 0.242140i | 0.992644 | + | 0.121070i | \(0.0386326\pi\) | ||||
−0.992644 | + | 0.121070i | \(0.961367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.2982 | −1.43453 | −0.717265 | − | 0.696800i | \(-0.754606\pi\) | ||||
−0.717265 | + | 0.696800i | \(0.754606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.32456i | 0.357485i | 0.983896 | + | 0.178743i | \(0.0572029\pi\) | ||||
−0.983896 | + | 0.178743i | \(0.942797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.85242 | + | 11.0711i | −0.104372 | + | 0.623784i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 31.3050i | − | 1.75826i | −0.476581 | − | 0.879131i | \(-0.658124\pi\) | ||
0.476581 | − | 0.879131i | \(-0.341876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.48528 | + | 18.9737i | 0.473602 | + | 1.05901i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 9.48683i | − | 0.526235i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.8114 | + | 7.07107i | −0.874372 | + | 0.391031i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.1421 | − | 8.94427i | 0.779681 | − | 0.493114i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.7771 | −1.96649 | −0.983243 | − | 0.182298i | \(-0.941646\pi\) | ||||
−0.983243 | + | 0.182298i | \(0.941646\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | + | 4.47214i | −0.219199 | + | 0.245072i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0000 | 0.653682 | 0.326841 | − | 0.945079i | \(-0.394016\pi\) | ||||
0.326841 | + | 0.945079i | \(0.394016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.16228 | − | 7.07107i | −0.171751 | − | 0.384048i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | + | 18.3848i | 0.120736 | + | 0.992685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | + | 13.4164i | 0.323029 | + | 0.722315i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0000i | 1.50312i | 0.659665 | + | 0.751559i | \(0.270698\pi\) | ||||
−0.659665 | + | 0.751559i | \(0.729302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.48683i | 0.507819i | 0.967228 | + | 0.253909i | \(0.0817165\pi\) | ||||
−0.967228 | + | 0.253909i | \(0.918284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6525 | − | 5.00000i | −0.835467 | − | 0.266880i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.2843 | 1.50542 | 0.752710 | − | 0.658352i | \(-0.228746\pi\) | ||||
0.752710 | + | 0.658352i | \(0.228746\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137i | 0.600469i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.17157 | + | 10.7967i | −0.379560 | + | 0.571421i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10.0000i | − | 0.527780i | −0.964553 | − | 0.263890i | \(-0.914994\pi\) | ||
0.964553 | − | 0.263890i | \(-0.0850056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.3925 | + | 7.77817i | −0.912871 | + | 0.408248i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 17.8885i | − | 0.936329i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1421i | 0.738213i | 0.929387 | + | 0.369107i | \(0.120336\pi\) | ||||
−0.929387 | + | 0.369107i | \(0.879664\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.9706 | + | 18.9737i | −0.883452 | + | 0.987730i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.9737 | − | 30.0000i | −0.985064 | − | 1.55752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.8885 | − | 8.00000i | 0.923760 | − | 0.413118i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.1421 | −0.728357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.94427 | 0.459436 | 0.229718 | − | 0.973257i | \(-0.426220\pi\) | ||||
0.229718 | + | 0.973257i | \(0.426220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1421 | + | 6.32456i | −0.724524 | + | 0.324017i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.6228 | −1.61585 | −0.807924 | − | 0.589286i | \(-0.799409\pi\) | ||||
−0.807924 | + | 0.589286i | \(0.799409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.8885 | + | 20.0000i | −0.909326 | + | 1.01666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.4164i | − | 0.680239i | −0.940382 | − | 0.340119i | \(-0.889532\pi\) | ||
0.940382 | − | 0.340119i | \(-0.110468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9706i | 0.858238i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.0000 | + | 11.1803i | −1.26108 | + | 0.563974i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.9737 | 0.954669 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.16228i | − | 0.158710i | −0.996846 | − | 0.0793551i | \(-0.974714\pi\) | ||
0.996846 | − | 0.0793551i | \(-0.0252861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.1950 | + | 10.7574i | 0.810766 | + | 0.538542i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.3050i | − | 1.56329i | −0.623721 | − | 0.781647i | \(-0.714380\pi\) | ||
0.623721 | − | 0.781647i | \(-0.285620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.8885 | −0.891092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.41421 | − | 12.6491i | −0.0702728 | − | 0.628539i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.32456i | − | 0.312729i | −0.987699 | − | 0.156365i | \(-0.950023\pi\) | ||
0.987699 | − | 0.156365i | \(-0.0499775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.32456 | + | 14.1421i | 0.311967 | + | 0.697580i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.07107 | + | 4.47214i | −0.347945 | + | 0.220059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.47214 | −0.219529 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0000 | + | 29.0689i | 0.636613 | + | 1.42351i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.48683 | 0.463462 | 0.231731 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231731 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.6491 | + | 14.1421i | −0.615021 | + | 0.687614i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.48528 | 0.411597 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.47214 | − | 7.07107i | −0.216422 | − | 0.342193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000i | 0.867029i | 0.901146 | + | 0.433515i | \(0.142727\pi\) | ||||
−0.901146 | + | 0.433515i | \(0.857273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.32456i | − | 0.303939i | −0.988385 | − | 0.151969i | \(-0.951438\pi\) | ||
0.988385 | − | 0.151969i | \(-0.0485615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.47214 | − | 10.0000i | −0.214423 | − | 0.479463i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.4558 | 1.21772 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.4558i | − | 1.21494i | −0.794342 | − | 0.607471i | \(-0.792184\pi\) | ||
0.794342 | − | 0.607471i | \(-0.207816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.14214 | − | 19.3573i | −0.387721 | − | 0.921777i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.00000i | − | 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | −0.758473 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.16228 | − | 7.07107i | −0.149571 | − | 0.334450i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8328i | 1.26632i | 0.774021 | + | 0.633159i | \(0.218242\pi\) | ||||
−0.774021 | + | 0.633159i | \(0.781758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1421 | + | 6.32456i | −0.664455 | + | 0.297154i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.32456 | − | 10.0000i | −0.296500 | − | 0.468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.47214 | − | 14.0000i | 0.208741 | − | 0.653464i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5563 | 0.724531 | 0.362266 | − | 0.932075i | \(-0.382003\pi\) | ||||
0.362266 | + | 0.932075i | \(0.382003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.47214 | −0.207838 | −0.103919 | − | 0.994586i | \(-0.533138\pi\) | ||||
−0.103919 | + | 0.994586i | \(0.533138\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.65685 | − | 12.6491i | −0.262330 | − | 0.586588i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1359 | 1.02433 | 0.512165 | − | 0.858887i | \(-0.328844\pi\) | ||||
0.512165 | + | 0.858887i | \(0.328844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.1803 | + | 25.0000i | 0.515163 | + | 1.15194i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 12.7279i | − | 0.583997i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.0000 | + | 26.8328i | 1.37361 | + | 1.22859i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9737 | 0.866929 | 0.433464 | − | 0.901171i | \(-0.357291\pi\) | ||||
0.433464 | + | 0.901171i | \(0.357291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.32456i | − | 0.288375i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.9032 | − | 15.2132i | −1.04213 | − | 0.692225i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.8328i | 1.21842i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.94427 | −0.405304 | −0.202652 | − | 0.979251i | \(-0.564956\pi\) | ||||
−0.202652 | + | 0.979251i | \(0.564956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000i | 0.361035i | 0.983572 | + | 0.180517i | \(0.0577772\pi\) | ||||
−0.983572 | + | 0.180517i | \(0.942223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.6491i | − | 0.569687i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.3137 | − | 17.8885i | −0.507489 | − | 0.802411i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8328 | 1.20120 | 0.600601 | − | 0.799549i | \(-0.294928\pi\) | ||||
0.600601 | + | 0.799549i | \(0.294928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.0000 | + | 13.4164i | −1.34030 | + | 0.599401i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.2982 | 1.12799 | 0.563996 | − | 0.825778i | \(-0.309263\pi\) | ||||
0.563996 | + | 0.825778i | \(0.309263\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.74342 | + | 2.12132i | −0.210663 | + | 0.0942111i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.24264 | −0.188052 | −0.0940259 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940259 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.8885 | + | 28.2843i | 0.791343 | + | 1.25122i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.0000 | − | 6.70820i | −0.927173 | − | 0.296174i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.5967 | − | 11.0000i | 1.07968 | − | 0.482846i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.48528 | −0.371747 | −0.185873 | − | 0.982574i | \(-0.559511\pi\) | ||||
−0.185873 | + | 0.982574i | \(0.559511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.07107i | 0.309196i | 0.987977 | + | 0.154598i | \(0.0494083\pi\) | ||||
−0.987977 | + | 0.154598i | \(0.950592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.60660 | + | 11.4516i | −0.331979 | + | 0.499790i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.0000i | − | 0.696971i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.32456 | − | 7.07107i | 0.274462 | − | 0.306858i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.8328i | − | 1.16226i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.9706i | − | 0.733701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.3137 | − | 25.2982i | −0.488223 | − | 1.09170i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.6525 | − | 35.0000i | −0.671712 | − | 1.50199i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.1421 | 0.605783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8885 | 0.764859 | 0.382429 | − | 0.923985i | \(-0.375088\pi\) | ||||
0.382429 | + | 0.923985i | \(0.375088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.07107 | + | 6.32456i | 0.301786 | + | 0.269925i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9737 | −0.808305 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 18.9737i | −1.27573 | + | 0.806842i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.47214 | − | 2.00000i | 0.189832 | − | 0.0848953i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.47214i | 0.189490i | 0.995502 | + | 0.0947452i | \(0.0302037\pi\) | ||||
−0.995502 | + | 0.0947452i | \(0.969796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.2843i | − | 1.19630i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.48683 | −0.399822 | −0.199911 | − | 0.979814i | \(-0.564065\pi\) | ||||
−0.199911 | + | 0.979814i | \(0.564065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32456i | 0.266076i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.8852 | + | 18.5858i | 0.625119 | + | 0.780530i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.3607i | − | 0.937408i | −0.883355 | − | 0.468704i | \(-0.844721\pi\) | ||
0.883355 | − | 0.468704i | \(-0.155279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.8885 | 0.748612 | 0.374306 | − | 0.927305i | \(-0.377881\pi\) | ||||
0.374306 | + | 0.927305i | \(0.377881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000i | 0.750652i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.2982i | 1.05318i | 0.850120 | + | 0.526589i | \(0.176529\pi\) | ||||
−0.850120 | + | 0.526589i | \(0.823471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.2982 | − | 11.3137i | 1.05136 | − | 0.470182i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.07107 | − | 4.47214i | 0.293357 | − | 0.185535i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0000 | + | 8.94427i | 0.413449 | + | 0.369800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.4605 | −1.17469 | −0.587345 | − | 0.809336i | \(-0.699827\pi\) | ||||
−0.587345 | + | 0.809336i | \(0.699827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.16228 | − | 7.07107i | −0.130079 | − | 0.290865i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.6274 | −0.929197 | −0.464598 | − | 0.885522i | \(-0.653801\pi\) | ||||
−0.464598 | + | 0.885522i | \(0.653801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.94427 | − | 5.65685i | 0.366679 | − | 0.231908i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | + | 17.8885i | 0.327418 | + | 0.732129i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000i | 1.63436i | 0.576386 | + | 0.817178i | \(0.304463\pi\) | ||||
−0.576386 | + | 0.817178i | \(0.695537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.2982i | − | 1.03194i | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||
0.856608 | − | 0.515968i | \(-0.172568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.5563 | 0.632456 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 42.4264i | − | 1.72203i | −0.508576 | − | 0.861017i | \(-0.669828\pi\) | ||
0.508576 | − | 0.861017i | \(-0.330172\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0711 | + | 11.3393i | 0.691755 | + | 0.459490i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 20.0000i | − | 0.809113i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000 | 0.242338 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.9737 | − | 8.48528i | 0.765092 | − | 0.342160i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.3607i | − | 0.900207i | −0.892976 | − | 0.450104i | \(-0.851387\pi\) | ||
0.892976 | − | 0.450104i | \(-0.148613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.1838i | − | 1.53474i | −0.641207 | − | 0.767368i | \(-0.721566\pi\) | ||
0.641207 | − | 0.767368i | \(-0.278434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.6985 | + | 9.48683i | 1.19176 | + | 0.380693i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.2982 | − | 16.0000i | 1.01355 | − | 0.641026i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65685 | 0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.3050 | −1.24623 | −0.623115 | − | 0.782130i | \(-0.714133\pi\) | ||||
−0.623115 | + | 0.782130i | \(0.714133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.6491 | 0.501965 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.0000 | + | 9.48683i | 0.792429 | + | 0.375882i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.8885 | + | 16.0000i | 0.707660 | + | 0.632950i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.47214i | − | 0.176639i | −0.996092 | − | 0.0883194i | \(-0.971850\pi\) | ||
0.996092 | − | 0.0883194i | \(-0.0281496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8701i | 1.05965i | 0.848106 | + | 0.529826i | \(0.177743\pi\) | ||||
−0.848106 | + | 0.529826i | \(0.822257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.0000 | − | 8.94427i | 0.787499 | − | 0.352180i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.32456 | 0.248644 | 0.124322 | − | 0.992242i | \(-0.460324\pi\) | ||||
0.124322 | + | 0.992242i | \(0.460324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.5934 | + | 14.3431i | 0.846311 | + | 0.562152i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 4.47214i | − | 0.175008i | −0.996164 | − | 0.0875041i | \(-0.972111\pi\) | ||
0.996164 | − | 0.0875041i | \(-0.0278891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3607 | 0.873704 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.2843 | − | 25.2982i | −1.10347 | − | 0.986978i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0000i | 1.71400i | 0.515319 | + | 0.856998i | \(0.327673\pi\) | ||||
−0.515319 | + | 0.856998i | \(0.672327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7851i | 1.35298i | 0.736451 | + | 0.676491i | \(0.236500\pi\) | ||||
−0.736451 | + | 0.676491i | \(0.763500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.32456 | + | 14.1421i | 0.245625 | + | 0.549235i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.48528 | − | 13.4164i | −0.329045 | − | 0.520266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8328 | 1.03897 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.0000 | − | 22.3607i | −0.386622 | − | 0.864514i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.74342 | − | 14.8492i | 0.182574 | − | 0.571548i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.1838 | 1.46752 | 0.733761 | − | 0.679408i | \(-0.237763\pi\) | ||||
0.733761 | + | 0.679408i | \(0.237763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.8328 | − | 42.4264i | −1.02975 | − | 1.62818i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.00000 | − | 2.23607i | 0.191600 | − | 0.0856863i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.6491i | − | 0.483298i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.23607 | − | 5.00000i | −0.0853113 | − | 0.190762i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.4264 | −1.61632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.41421i | − | 0.0537992i | −0.999638 | − | 0.0268996i | \(-0.991437\pi\) | ||
0.999638 | − | 0.0268996i | \(-0.00856344\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 26.0000i | − | 0.986236i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.6491 | − | 28.2843i | −0.478433 | − | 1.06981i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.1935i | 1.85801i | 0.370064 | + | 0.929006i | \(0.379336\pi\) | ||||
−0.370064 | + | 0.929006i | \(0.620664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.48528i | − | 0.320028i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.1421 | − | 6.32456i | 0.532624 | − | 0.238197i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.4605 | + | 18.0000i | −1.07037 | + | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.8328 | − | 30.0000i | 1.00631 | − | 1.12509i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.9411 | 1.27111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.07107 | + | 15.8114i | 0.264074 | + | 0.590487i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.32456 | −0.235866 | −0.117933 | − | 0.993022i | \(-0.537627\pi\) | ||||
−0.117933 | + | 0.993022i | \(0.537627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.47214 | + | 10.0000i | 0.166321 | + | 0.371904i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 13.4164i | − | 0.498273i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.3137i | 0.419602i | 0.977744 | + | 0.209801i | \(0.0672817\pi\) | ||||
−0.977744 | + | 0.209801i | \(0.932718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0000 | − | 15.6525i | −0.814815 | − | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.2982 | 0.935689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.48683i | 0.350404i | 0.984532 | + | 0.175202i | \(0.0560579\pi\) | ||||
−0.984532 | + | 0.175202i | \(0.943942\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.383649 | + | 17.1421i | −0.0141511 | + | 0.632297i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.7214 | 1.64510 | 0.822551 | − | 0.568691i | \(-0.192550\pi\) | ||||
0.822551 | + | 0.568691i | \(0.192550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.2132 | − | 9.48683i | 0.779287 | − | 0.348508i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.00000i | − | 0.220119i | −0.993925 | − | 0.110059i | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.32456i | 0.231714i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.32456 | + | 7.07107i | −0.231403 | + | 0.258717i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706 | + | 26.8328i | 0.620091 | + | 0.980450i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.94427 | 0.326381 | 0.163191 | − | 0.986595i | \(-0.447821\pi\) | ||||
0.163191 | + | 0.986595i | \(0.447821\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.0000 | − | 20.1246i | 1.63989 | − | 0.733382i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.6491 | 0.460348 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.0000 | −1.52652 | −0.763258 | − | 0.646094i | \(-0.776401\pi\) | ||||
−0.763258 | + | 0.646094i | \(0.776401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.7990 | −0.717713 | −0.358856 | − | 0.933393i | \(-0.616833\pi\) | ||||
−0.358856 | + | 0.933393i | \(0.616833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.3607 | + | 14.1421i | −0.809511 | + | 0.511980i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.00000 | + | 8.94427i | −0.289241 | + | 0.323381i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0000i | 0.361079i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.6228i | − | 1.14035i | −0.821524 | − | 0.570173i | \(-0.806876\pi\) | ||
0.821524 | − | 0.570173i | \(-0.193124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.7214 | + | 20.0000i | −1.61060 | + | 0.720282i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.4975 | −1.78030 | −0.890150 | − | 0.455667i | \(-0.849401\pi\) | ||||
−0.890150 | + | 0.455667i | \(0.849401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.9706i | − | 0.609601i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.07107 | + | 7.63441i | −0.181924 | + | 0.273883i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 36.0000i | − | 1.28983i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.1359 | − | 7.07107i | −0.791074 | − | 0.252699i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.3607i | − | 0.798087i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.3553i | 1.26028i | 0.776481 | + | 0.630141i | \(0.217003\pi\) | ||||
−0.776481 | + | 0.630141i | \(0.782997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.3137 | − | 25.2982i | −0.402779 | − | 0.900641i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.32456 | − | 10.0000i | −0.224875 | − | 0.355559i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | −0.355110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.4164 | − | 30.0000i | −0.475831 | − | 1.06399i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5269 | 1.15216 | 0.576081 | − | 0.817392i | \(-0.304581\pi\) | ||||
0.576081 | + | 0.817392i | \(0.304581\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.8885 | 0.632851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.6274 | + | 25.2982i | −0.799500 | + | 0.893869i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | + | 18.9737i | 0.422944 | + | 0.668734i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.6525 | − | 7.00000i | 0.550993 | − | 0.246412i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.1935i | 1.72955i | 0.502159 | + | 0.864776i | \(0.332539\pi\) | ||||
−0.502159 | + | 0.864776i | \(0.667461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.41421i | − | 0.0496598i | −0.999692 | − | 0.0248299i | \(-0.992096\pi\) | ||
0.999692 | − | 0.0248299i | \(-0.00790441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.00000 | − | 13.4164i | −0.210429 | − | 0.470534i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 37.9473i | − | 1.32761i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.7557 | − | 4.14214i | −0.865033 | − | 0.144738i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3607i | 0.780393i | 0.920732 | + | 0.390197i | \(0.127593\pi\) | ||||
−0.920732 | + | 0.390197i | \(0.872407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.2492 | −1.40300 | −0.701500 | − | 0.712670i | \(-0.747486\pi\) | ||||
−0.701500 | + | 0.712670i | \(0.747486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.0000i | − | 0.973655i | −0.873498 | − | 0.486828i | \(-0.838154\pi\) | ||
0.873498 | − | 0.486828i | \(-0.161846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.4605i | 0.988474i | 0.869327 | + | 0.494237i | \(0.164552\pi\) | ||||
−0.869327 | + | 0.494237i | \(0.835448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.4605 | + | 12.7279i | −0.987284 | + | 0.441527i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.48528 | + | 17.8885i | −0.293998 | + | 0.619801i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.8328 | 0.928588 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.0000 | − | 8.94427i | −0.967822 | − | 0.309159i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.6228 | 1.09174 | 0.545870 | − | 0.837870i | \(-0.316199\pi\) | ||||
0.545870 | + | 0.837870i | \(0.316199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.6491 | + | 28.2843i | 0.435659 | + | 0.974162i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.24264 | 0.145951 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.5967 | + | 15.5563i | −0.845154 | + | 0.534522i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.0000 | − | 33.5410i | −0.514799 | − | 1.15112i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47.4342i | − | 1.62411i | −0.583578 | − | 0.812057i | \(-0.698348\pi\) | ||
0.583578 | − | 0.812057i | \(-0.301652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4164 | + | 12.0000i | 0.458831 | + | 0.410391i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.1421 | −0.483086 | −0.241543 | − | 0.970390i | \(-0.577654\pi\) | ||||
−0.241543 | + | 0.970390i | \(0.577654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.24264i | − | 0.144757i | −0.997377 | − | 0.0723785i | \(-0.976941\pi\) | ||
0.997377 | − | 0.0723785i | \(-0.0230590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.5147 | + | 32.3901i | −0.733220 | + | 1.10385i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.0000 | −0.748022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.2302 | − | 6.36396i | 0.483285 | − | 0.216131i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.4264 | + | 37.9473i | 1.43592 | + | 1.28432i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.2982 | − | 16.0000i | 0.855236 | − | 0.540899i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.0000 | −1.28317 | −0.641584 | − | 0.767052i | \(-0.721723\pi\) | ||||
−0.641584 | + | 0.767052i | \(0.721723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.1803 | − | 5.00000i | 0.377104 | − | 0.168646i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.9117 | −1.71526 | −0.857629 | − | 0.514269i | \(-0.828063\pi\) | ||||
−0.857629 | + | 0.514269i | \(0.828063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.8885 | −0.601997 | −0.300999 | − | 0.953625i | \(-0.597320\pi\) | ||||
−0.300999 | + | 0.953625i | \(0.597320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.07107 | + | 3.16228i | −0.237691 | + | 0.106299i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9737 | 0.637073 | 0.318537 | − | 0.947911i | \(-0.396809\pi\) | ||||
0.318537 | + | 0.947911i | \(0.396809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | + | 12.6491i | −0.670778 | + | 0.424238i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 26.8328i | − | 0.897926i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.6274i | 0.756351i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.0000 | + | 13.4164i | −1.00167 | + | 0.447961i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.2982 | −0.843743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 37.9473i | − | 1.26421i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.6785 | + | 34.1421i | −0.754693 | + | 1.13618i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.3050i | 1.04061i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8328 | −0.890969 | −0.445485 | − | 0.895290i | \(-0.646969\pi\) | ||||
−0.445485 | + | 0.895290i | \(0.646969\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.4558 | − | 28.4605i | 0.844317 | − | 0.943975i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.0000i | 1.65657i | 0.560304 | + | 0.828287i | \(0.310684\pi\) | ||||
−0.560304 | + | 0.828287i | \(0.689316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.16228 | − | 7.07107i | −0.104542 | − | 0.233762i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.3553 | + | 22.3607i | −1.16754 | + | 0.738415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.4164 | −0.442566 | −0.221283 | − | 0.975210i | \(-0.571025\pi\) | ||||
−0.221283 | + | 0.975210i | \(0.571025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00000 | − | 6.70820i | −0.0988534 | − | 0.221043i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.2982 | −0.832701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.82843 | 0.0927977 | 0.0463988 | − | 0.998923i | \(-0.485225\pi\) | ||||
0.0463988 | + | 0.998923i | \(0.485225\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8328 | + | 12.7279i | 0.879410 | + | 0.417141i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 40.0000 | − | 17.8885i | 1.30954 | − | 0.585645i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25.2982i | − | 0.826457i | −0.910627 | − | 0.413228i | \(-0.864401\pi\) | ||
0.910627 | − | 0.413228i | \(-0.135599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.47214 | − | 10.0000i | −0.145943 | − | 0.326338i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.41421 | −0.0461020 | −0.0230510 | − | 0.999734i | \(-0.507338\pi\) | ||||
−0.0230510 | + | 0.999734i | \(0.507338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.9117i | 1.65791i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.89949 | − | 18.8148i | −0.159381 | − | 0.612044i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 28.0000i | − | 0.909878i | −0.890523 | − | 0.454939i | \(-0.849661\pi\) | ||
0.890523 | − | 0.454939i | \(-0.150339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0000 | 1.29845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.1359 | + | 49.4975i | 0.717807 | + | 1.60507i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.7214i | 1.44867i | 0.689450 | + | 0.724333i | \(0.257852\pi\) | ||||
−0.689450 | + | 0.724333i | \(0.742148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6491 | + | 20.0000i | 0.408461 | + | 0.645834i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.8328 | − | 24.0000i | −0.864675 | − | 0.773389i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.6274 | −0.728402 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8328 | −0.862885 | −0.431443 | − | 0.902140i | \(-0.641995\pi\) | ||||
−0.431443 | + | 0.902140i | \(0.641995\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.48528 | + | 18.9737i | 0.272587 | + | 0.609522i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.48683 | −0.304447 | −0.152223 | − | 0.988346i | \(-0.548643\pi\) | ||||
−0.152223 | + | 0.988346i | \(0.548643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0000 | + | 41.1096i | 0.833522 | + | 1.31791i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.70820 | + | 15.0000i | 0.214834 | + | 0.480384i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.8328i | − | 0.858458i | −0.903196 | − | 0.429229i | \(-0.858785\pi\) | ||
0.903196 | − | 0.429229i | \(-0.141215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.0000 | − | 22.3607i | 0.638551 | − | 0.713922i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.9210 | −1.81550 | −0.907749 | − | 0.419514i | \(-0.862201\pi\) | ||||
−0.907749 | + | 0.419514i | \(0.862201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.32456i | 0.201517i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0361 | + | 24.1421i | −0.510435 | + | 0.768453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.6656i | 1.70647i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.4164 | −0.426186 | −0.213093 | − | 0.977032i | \(-0.568354\pi\) | ||||
−0.213093 | + | 0.977032i | \(0.568354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 56.5685 | − | 25.2982i | 1.79515 | − | 0.802815i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 16.0000i | − | 0.507234i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.1359i | 0.701052i | 0.936553 | + | 0.350526i | \(0.113997\pi\) | ||||
−0.936553 | + | 0.350526i | \(0.886003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.16228 | − | 9.89949i | 0.100050 | − | 0.313206i |
(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 | 672.2.k.c.545.4 | yes | 8 | |
3.2 | odd | 2 | inner | 672.2.k.c.545.7 | yes | 8 | |
4.3 | odd | 2 | inner | 672.2.k.c.545.6 | yes | 8 | |
7.6 | odd | 2 | inner | 672.2.k.c.545.5 | yes | 8 | |
8.3 | odd | 2 | 1344.2.k.h.1217.3 | 8 | |||
8.5 | even | 2 | 1344.2.k.h.1217.5 | 8 | |||
12.11 | even | 2 | inner | 672.2.k.c.545.1 | ✓ | 8 | |
21.20 | even | 2 | inner | 672.2.k.c.545.2 | yes | 8 | |
24.5 | odd | 2 | 1344.2.k.h.1217.2 | 8 | |||
24.11 | even | 2 | 1344.2.k.h.1217.8 | 8 | |||
28.27 | even | 2 | inner | 672.2.k.c.545.3 | yes | 8 | |
56.13 | odd | 2 | 1344.2.k.h.1217.4 | 8 | |||
56.27 | even | 2 | 1344.2.k.h.1217.6 | 8 | |||
84.83 | odd | 2 | inner | 672.2.k.c.545.8 | yes | 8 | |
168.83 | odd | 2 | 1344.2.k.h.1217.1 | 8 | |||
168.125 | even | 2 | 1344.2.k.h.1217.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.k.c.545.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
672.2.k.c.545.2 | yes | 8 | 21.20 | even | 2 | inner | |
672.2.k.c.545.3 | yes | 8 | 28.27 | even | 2 | inner | |
672.2.k.c.545.4 | yes | 8 | 1.1 | even | 1 | trivial | |
672.2.k.c.545.5 | yes | 8 | 7.6 | odd | 2 | inner | |
672.2.k.c.545.6 | yes | 8 | 4.3 | odd | 2 | inner | |
672.2.k.c.545.7 | yes | 8 | 3.2 | odd | 2 | inner | |
672.2.k.c.545.8 | yes | 8 | 84.83 | odd | 2 | inner | |
1344.2.k.h.1217.1 | 8 | 168.83 | odd | 2 | |||
1344.2.k.h.1217.2 | 8 | 24.5 | odd | 2 | |||
1344.2.k.h.1217.3 | 8 | 8.3 | odd | 2 | |||
1344.2.k.h.1217.4 | 8 | 56.13 | odd | 2 | |||
1344.2.k.h.1217.5 | 8 | 8.5 | even | 2 | |||
1344.2.k.h.1217.6 | 8 | 56.27 | even | 2 | |||
1344.2.k.h.1217.7 | 8 | 168.125 | even | 2 | |||
1344.2.k.h.1217.8 | 8 | 24.11 | even | 2 |