Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(829,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.f (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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.1 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.829 |
Dual form | 4140.2.f.a.829.2 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.21432 | − | 0.311108i | −0.990274 | − | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.21432 | −0.667643 | −0.333821 | − | 0.942636i | \(-0.608338\pi\) | ||||
−0.333821 | + | 0.942636i | \(0.608338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.11753i | 1.41935i | 0.704530 | + | 0.709674i | \(0.251158\pi\) | ||||
−0.704530 | + | 0.709674i | \(0.748842\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.11753i | − | 0.998648i | −0.866415 | − | 0.499324i | \(-0.833582\pi\) | ||
0.866415 | − | 0.499324i | \(-0.166418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.11753 | 1.17404 | 0.587021 | − | 0.809572i | \(-0.300301\pi\) | ||||
0.587021 | + | 0.809572i | \(0.300301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.80642 | + | 1.37778i | 0.961285 | + | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.93332 | −0.544704 | −0.272352 | − | 0.962198i | \(-0.587802\pi\) | ||||
−0.272352 | + | 0.962198i | \(0.587802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.09679 | −0.376594 | −0.188297 | − | 0.982112i | \(-0.560297\pi\) | ||||
−0.188297 | + | 0.982112i | \(0.560297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.311108 | + | 2.21432i | −0.0525868 | + | 0.374288i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.28100i | 0.210594i | 0.994441 | + | 0.105297i | \(0.0335794\pi\) | ||||
−0.994441 | + | 0.105297i | \(0.966421\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.458751 | −0.0716449 | −0.0358224 | − | 0.999358i | \(-0.511405\pi\) | ||||
−0.0358224 | + | 0.999358i | \(0.511405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.14764i | − | 0.327513i | −0.986501 | − | 0.163756i | \(-0.947639\pi\) | ||
0.986501 | − | 0.163756i | \(-0.0523611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.40790i | 0.351228i | 0.984459 | + | 0.175614i | \(0.0561910\pi\) | ||||
−0.984459 | + | 0.175614i | \(0.943809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.83654i | 0.526989i | 0.964661 | + | 0.263494i | \(0.0848750\pi\) | ||||
−0.964661 | + | 0.263494i | \(0.915125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.90321 | + | 0.688892i | 0.661149 | + | 0.0928902i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.68889 | 0.219875 | 0.109938 | − | 0.993939i | \(-0.464935\pi\) | ||||
0.109938 | + | 0.993939i | \(0.464935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.5462 | −1.99048 | −0.995242 | − | 0.0974377i | \(-0.968935\pi\) | ||||
−0.995242 | + | 0.0974377i | \(0.968935\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.59210 | − | 11.3319i | 0.197476 | − | 1.40554i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.76986i | − | 0.216223i | −0.994139 | − | 0.108111i | \(-0.965520\pi\) | ||
0.994139 | − | 0.108111i | \(-0.0344803\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.39853 | −0.522009 | −0.261005 | − | 0.965338i | \(-0.584054\pi\) | ||||
−0.261005 | + | 0.965338i | \(0.584054\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.7397i | − | 1.37403i | −0.726642 | − | 0.687017i | \(-0.758920\pi\) | ||
0.726642 | − | 0.687017i | \(-0.241080\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.21432i | 0.252345i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6637 | 1.64980 | 0.824898 | − | 0.565282i | \(-0.191233\pi\) | ||||
0.824898 | + | 0.565282i | \(0.191233\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.4953i | − | 1.26177i | −0.775874 | − | 0.630887i | \(-0.782691\pi\) | ||
0.775874 | − | 0.630887i | \(-0.217309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.28100 | + | 9.11753i | −0.138944 | + | 0.988935i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.755569 | 0.0800901 | 0.0400451 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400451 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.11753 | 0.536463 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3319 | − | 1.59210i | −1.16262 | − | 0.163346i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.8938i | − | 1.20764i | −0.797122 | − | 0.603818i | \(-0.793645\pi\) | ||
0.797122 | − | 0.603818i | \(-0.206355\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.59210 | 0.854946 | 0.427473 | − | 0.904028i | \(-0.359404\pi\) | ||||
0.427473 | + | 0.904028i | \(0.359404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.90321i | − | 0.483128i | −0.970385 | − | 0.241564i | \(-0.922340\pi\) | ||
0.970385 | − | 0.241564i | \(-0.0776603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.82717i | − | 0.853354i | −0.904404 | − | 0.426677i | \(-0.859684\pi\) | ||
0.904404 | − | 0.426677i | \(-0.140316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.822245 | 0.0787568 | 0.0393784 | − | 0.999224i | \(-0.487462\pi\) | ||||
0.0393784 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.26517i | − | 0.589378i | −0.955593 | − | 0.294689i | \(-0.904784\pi\) | ||
0.955593 | − | 0.294689i | \(-0.0952161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.311108 | − | 2.21432i | 0.0290110 | − | 0.206486i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.11753 | −0.377454 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.09679 | −0.554253 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2143 | − | 4.54617i | −0.913597 | − | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.1590i | − | 1.70009i | −0.526712 | − | 0.850044i | \(-0.676575\pi\) | ||
0.526712 | − | 0.850044i | \(-0.323425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1526 | −1.14914 | −0.574572 | − | 0.818454i | \(-0.694832\pi\) | ||||
−0.574572 | + | 0.818454i | \(0.694832\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.11753i | − | 0.443746i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.76049i | − | 0.492152i | −0.969251 | − | 0.246076i | \(-0.920859\pi\) | ||
0.969251 | − | 0.246076i | \(-0.0791413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.42864 | 0.121176 | 0.0605878 | − | 0.998163i | \(-0.480702\pi\) | ||||
0.0605878 | + | 0.998163i | \(0.480702\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.3319i | − | 0.947617i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.49532 | + | 0.912580i | 0.539407 | + | 0.0757856i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.78568 | −0.473981 | −0.236991 | − | 0.971512i | \(-0.576161\pi\) | ||||
−0.236991 | + | 0.971512i | \(0.576161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.52543 | −0.286895 | −0.143448 | − | 0.989658i | \(-0.545819\pi\) | ||||
−0.143448 | + | 0.989658i | \(0.545819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.64296 | + | 0.652327i | 0.372931 | + | 0.0523962i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.81579i | − | 0.304533i | −0.988339 | − | 0.152267i | \(-0.951343\pi\) | ||
0.988339 | − | 0.152267i | \(-0.0486573\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.05086i | − | 0.552266i | −0.961119 | − | 0.276133i | \(-0.910947\pi\) | ||
0.961119 | − | 0.276133i | \(-0.0890530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.3892i | 1.42300i | 0.702688 | + | 0.711498i | \(0.251983\pi\) | ||||
−0.702688 | + | 0.711498i | \(0.748017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.1891 | −1.01455 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 0.0602231i | − | 0.00457867i | −0.999997 | − | 0.00228934i | \(-0.999271\pi\) | ||
0.999997 | − | 0.00228934i | \(-0.000728719\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.37778 | − | 4.80642i | 0.104151 | − | 0.363331i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.33185 | −0.548008 | −0.274004 | − | 0.961729i | \(-0.588348\pi\) | ||||
−0.274004 | + | 0.961729i | \(0.588348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.04149 | 0.597719 | 0.298860 | − | 0.954297i | \(-0.403394\pi\) | ||||
0.298860 | + | 0.954297i | \(0.403394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.398528 | − | 2.83654i | 0.0293004 | − | 0.208546i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.11753i | 0.666740i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.59210 | 0.549345 | 0.274673 | − | 0.961538i | \(-0.411431\pi\) | ||||
0.274673 | + | 0.961538i | \(0.411431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7239i | 0.915888i | 0.888981 | + | 0.457944i | \(0.151414\pi\) | ||||
−0.888981 | + | 0.457944i | \(0.848586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.1526i | − | 1.22207i | −0.791604 | − | 0.611035i | \(-0.790754\pi\) | ||
0.791604 | − | 0.611035i | \(-0.209246\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.69535 | −0.191068 | −0.0955340 | − | 0.995426i | \(-0.530456\pi\) | ||||
−0.0955340 | + | 0.995426i | \(0.530456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.93332i | 0.205879i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.01582 | + | 0.142721i | 0.0709480 | + | 0.00996807i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3319 | −0.783841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3684 | −1.47106 | −0.735531 | − | 0.677491i | \(-0.763067\pi\) | ||||
−0.735531 | + | 0.677491i | \(0.763067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.668149 | + | 4.75557i | −0.0455674 | + | 0.324327i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.09679i | 0.142339i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.0716 | 1.41743 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.7556i | − | 0.720246i | −0.932905 | − | 0.360123i | \(-0.882735\pi\) | ||
0.932905 | − | 0.360123i | \(-0.117265\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.36842i | − | 0.422687i | −0.977412 | − | 0.211343i | \(-0.932216\pi\) | ||
0.977412 | − | 0.211343i | \(-0.0677838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.1432 | −1.19894 | −0.599468 | − | 0.800399i | \(-0.704621\pi\) | ||||
−0.599468 | + | 0.800399i | \(0.704621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 25.3274i | − | 1.65925i | −0.558318 | − | 0.829627i | \(-0.688553\pi\) | ||
0.558318 | − | 0.829627i | \(-0.311447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.749115 | − | 5.33185i | 0.0488669 | − | 0.347812i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.8178 | 1.02317 | 0.511584 | − | 0.859233i | \(-0.329059\pi\) | ||||
0.511584 | + | 0.859233i | \(0.329059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8415 | −1.66459 | −0.832297 | − | 0.554330i | \(-0.812975\pi\) | ||||
−0.832297 | + | 0.554330i | \(0.812975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.2859 | − | 1.86665i | −0.848806 | − | 0.119256i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.1891i | 1.66637i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4795 | 0.724579 | 0.362290 | − | 0.932066i | \(-0.381995\pi\) | ||||
0.362290 | + | 0.932066i | \(0.381995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.21432i | − | 0.139213i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 24.7447i | − | 1.54353i | −0.635908 | − | 0.771765i | \(-0.719374\pi\) | ||
0.635908 | − | 0.771765i | \(-0.280626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.28100 | 0.0795972 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.3985i | − | 1.25783i | −0.777475 | − | 0.628914i | \(-0.783500\pi\) | ||
0.777475 | − | 0.628914i | \(-0.216500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.19358 | − | 8.49532i | 0.0733208 | − | 0.521863i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6702 | 0.955426 | 0.477713 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477713 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.37778 | −0.387423 | −0.193711 | − | 0.981059i | \(-0.562053\pi\) | ||||
−0.193711 | + | 0.981059i | \(0.562053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.6430 | − | 3.05086i | −0.641795 | − | 0.183973i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.80642i | − | 0.589211i | −0.955619 | − | 0.294605i | \(-0.904812\pi\) | ||
0.955619 | − | 0.294605i | \(-0.0951882\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.4306 | 1.93465 | 0.967325 | − | 0.253539i | \(-0.0815947\pi\) | ||||
0.967325 | + | 0.253539i | \(0.0815947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.2859i | − | 0.849210i | −0.905379 | − | 0.424605i | \(-0.860413\pi\) | ||
0.905379 | − | 0.424605i | \(-0.139587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.458751i | 0.0270792i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0459330 | 0.00270194 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 15.1684i | − | 0.886147i | −0.896485 | − | 0.443073i | \(-0.853888\pi\) | ||
0.896485 | − | 0.443073i | \(-0.146112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.73975 | − | 0.525428i | −0.217737 | − | 0.0305916i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.11753 | −0.295954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.14764 | −0.123788 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.4242 | + | 4.83654i | 1.97112 | + | 0.276939i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4035i | 1.39278i | 0.717664 | + | 0.696389i | \(0.245211\pi\) | ||||
−0.717664 | + | 0.696389i | \(0.754789\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.2351 | 1.48765 | 0.743827 | − | 0.668372i | \(-0.233009\pi\) | ||||
0.743827 | + | 0.668372i | \(0.233009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 30.3733i | − | 1.71680i | −0.512979 | − | 0.858401i | \(-0.671458\pi\) | ||
0.512979 | − | 0.858401i | \(-0.328542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.85881i | 0.553726i | 0.960909 | + | 0.276863i | \(0.0892948\pi\) | ||||
−0.960909 | + | 0.276863i | \(0.910705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.49532 | 0.363668 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.0716i | − | 1.17246i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.05086 | + | 24.5970i | −0.391111 | + | 1.36440i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.40790 | 0.132752 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.90321 | 0.324470 | 0.162235 | − | 0.986752i | \(-0.448130\pi\) | ||||
0.162235 | + | 0.986752i | \(0.448130\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.550617 | + | 3.91903i | −0.0300834 | + | 0.214120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1017i | 0.877116i | 0.898703 | + | 0.438558i | \(0.144511\pi\) | ||||
−0.898703 | + | 0.438558i | \(0.855489\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.64296 | 0.251430 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.5303i | 0.780030i | 0.920808 | + | 0.390015i | \(0.127530\pi\) | ||||
−0.920808 | + | 0.390015i | \(0.872470\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.32693 | 0.392202 | 0.196101 | − | 0.980584i | \(-0.437172\pi\) | ||||
0.196101 | + | 0.980584i | \(0.437172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5827i | 0.776161i | 0.921626 | + | 0.388080i | \(0.126862\pi\) | ||||
−0.921626 | + | 0.388080i | \(0.873138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.73975 | + | 1.36842i | 0.516932 | + | 0.0726280i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.3289 | −1.60070 | −0.800350 | − | 0.599533i | \(-0.795353\pi\) | ||||
−0.800350 | + | 0.599533i | \(0.795353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.18913 | 0.378375 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.65233 | + | 25.9956i | −0.191172 | + | 1.36067i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.94470i | − | 0.414710i | −0.978266 | − | 0.207355i | \(-0.933514\pi\) | ||
0.978266 | − | 0.207355i | \(-0.0664855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.83654 | 0.199183 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.2716i | − | 1.51563i | −0.652471 | − | 0.757814i | \(-0.726268\pi\) | ||
0.652471 | − | 0.757814i | \(-0.273732\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.0114i | − | 0.773125i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.48886 | −0.333310 | −0.166655 | − | 0.986015i | \(-0.553297\pi\) | ||||
−0.166655 | + | 0.986015i | \(0.553297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.13981i | 0.262632i | 0.991341 | + | 0.131316i | \(0.0419202\pi\) | ||||
−0.991341 | + | 0.131316i | \(0.958080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.688892 | − | 4.90321i | 0.0351092 | − | 0.249891i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.9813 | −1.31730 | −0.658651 | − | 0.752448i | \(-0.728873\pi\) | ||||
−0.658651 | + | 0.752448i | \(0.728873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.11753 | 0.208233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.4701 | − | 4.56199i | −1.63375 | − | 0.229539i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.663703i | − | 0.0333103i | −0.999861 | − | 0.0166551i | \(-0.994698\pi\) | ||
0.999861 | − | 0.0166551i | \(-0.00530174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2351 | 1.21024 | 0.605121 | − | 0.796134i | \(-0.293125\pi\) | ||||
0.605121 | + | 0.796134i | \(0.293125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.7304i | − | 0.534518i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.83654i | − | 0.140602i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0192 | 1.18767 | 0.593837 | − | 0.804586i | \(-0.297612\pi\) | ||||
0.593837 | + | 0.804586i | \(0.297612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.68889i | − | 0.0831050i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.57628 | + | 25.4543i | −0.175553 | + | 1.24950i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.9605 | 1.46367 | 0.731834 | − | 0.681483i | \(-0.238665\pi\) | ||||
0.731834 | + | 0.681483i | \(0.238665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.04440 | −0.245849 | −0.122925 | − | 0.992416i | \(-0.539227\pi\) | ||||
−0.122925 | + | 0.992416i | \(0.539227\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.67307 | − | 19.7906i | 0.275184 | − | 0.959985i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.5462i | 0.752332i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1017 | 0.775592 | 0.387796 | − | 0.921745i | \(-0.373236\pi\) | ||||
0.387796 | + | 0.921745i | \(0.373236\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0321i | 0.866568i | 0.901257 | + | 0.433284i | \(0.142645\pi\) | ||||
−0.901257 | + | 0.433284i | \(0.857355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.11753i | 0.244805i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.1575 | −1.53479 | −0.767397 | − | 0.641173i | \(-0.778448\pi\) | ||||
−0.767397 | + | 0.641173i | \(0.778448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.3481i | 1.67944i | 0.543019 | + | 0.839721i | \(0.317281\pi\) | ||||
−0.543019 | + | 0.839721i | \(0.682719\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.67307 | − | 0.235063i | −0.0793112 | − | 0.0111431i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2603 | −0.814562 | −0.407281 | − | 0.913303i | \(-0.633523\pi\) | ||||
−0.407281 | + | 0.913303i | \(0.633523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01582 | 0.0478332 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3319 | − | 1.59210i | −0.531245 | − | 0.0746390i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.38271i | − | 0.158236i | −0.996865 | − | 0.0791182i | \(-0.974790\pi\) | ||
0.996865 | − | 0.0791182i | \(-0.0252104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.94914 | 0.323654 | 0.161827 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161827 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.6800i | 1.33287i | 0.745562 | + | 0.666436i | \(0.232181\pi\) | ||||
−0.745562 | + | 0.666436i | \(0.767819\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.7862i | 1.56344i | 0.623632 | + | 0.781718i | \(0.285657\pi\) | ||||
−0.623632 | + | 0.781718i | \(0.714343\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.76986 | −0.0817245 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.75557i | 0.218661i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.5970 | + | 7.05086i | 1.12859 | + | 0.323515i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.78568 | 0.355737 | 0.177868 | − | 0.984054i | \(-0.443080\pi\) | ||||
0.177868 | + | 0.984054i | \(0.443080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.55554 | −0.298907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.70027 | + | 26.3368i | −0.168021 | + | 1.19589i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.7397i | − | 0.531979i | −0.963976 | − | 0.265989i | \(-0.914301\pi\) | ||
0.963976 | − | 0.265989i | \(-0.0856986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −43.9610 | −1.98393 | −0.991966 | − | 0.126505i | \(-0.959624\pi\) | ||||
−0.991966 | + | 0.126505i | \(0.959624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0781i | 0.543968i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.39853i | 0.197301i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.7382 | 0.525475 | 0.262737 | − | 0.964867i | \(-0.415375\pi\) | ||||
0.262737 | + | 0.964867i | \(0.415375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 19.7304i | − | 0.879734i | −0.898063 | − | 0.439867i | \(-0.855026\pi\) | ||
0.898063 | − | 0.439867i | \(-0.144974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.0257 | − | 2.67307i | −0.846631 | − | 0.118950i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.1289 | 0.537604 | 0.268802 | − | 0.963195i | \(-0.413372\pi\) | ||||
0.268802 | + | 0.963195i | \(0.413372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7397 | −0.519336 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.52543 | + | 10.8573i | −0.0672184 | + | 0.478429i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.33185i | − | 0.234495i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5605 | −0.944581 | −0.472290 | − | 0.881443i | \(-0.656573\pi\) | ||||
−0.472290 | + | 0.881443i | \(0.656573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.9684i | − | 1.31042i | −0.755445 | − | 0.655212i | \(-0.772579\pi\) | ||
0.755445 | − | 0.655212i | \(-0.227421\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.63359i | 0.376085i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.34767i | − | 0.101689i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.74620 | + | 19.5462i | −0.118729 | + | 0.845055i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2859 | −0.572265 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1985 | −1.16935 | −0.584677 | − | 0.811266i | \(-0.698779\pi\) | ||||
−0.584677 | + | 0.811266i | \(0.698779\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.82071 | − | 0.255807i | −0.0779908 | − | 0.0109576i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5433i | 1.22042i | 0.792239 | + | 0.610211i | \(0.208915\pi\) | ||||
−0.792239 | + | 0.610211i | \(0.791085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0114 | −0.639506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.6637i | − | 0.623564i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.87755i | − | 0.206668i | −0.994647 | − | 0.103334i | \(-0.967049\pi\) | ||
0.994647 | − | 0.103334i | \(-0.0329511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.9906 | 0.464854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.5195i | 1.41268i | 0.707875 | + | 0.706338i | \(0.249654\pi\) | ||||
−0.707875 | + | 0.706338i | \(0.750346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94914 | + | 13.8731i | −0.0820011 | + | 0.583646i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.44738 | −0.186444 | −0.0932218 | − | 0.995645i | \(-0.529717\pi\) | ||||
−0.0932218 | + | 0.995645i | \(0.529717\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3718 | 1.68951 | 0.844754 | − | 0.535155i | \(-0.179747\pi\) | ||||
0.844754 | + | 0.535155i | \(0.179747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.37778 | + | 4.80642i | −0.0574576 | + | 0.200442i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.9403i | − | 0.955015i | −0.878628 | − | 0.477508i | \(-0.841540\pi\) | ||
0.878628 | − | 0.477508i | \(-0.158460\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4953 | −0.476906 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.49532i | − | 0.351840i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0509i | 0.538666i | 0.963047 | + | 0.269333i | \(0.0868033\pi\) | ||||
−0.963047 | + | 0.269333i | \(0.913197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7304 | −0.442138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 43.3165i | − | 1.77880i | −0.457134 | − | 0.889398i | \(-0.651124\pi\) | ||
0.457134 | − | 0.889398i | \(-0.348876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.11753 | + | 1.28100i | 0.373782 | + | 0.0525157i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.7560 | 1.37923 | 0.689617 | − | 0.724174i | \(-0.257779\pi\) | ||||
0.689617 | + | 0.724174i | \(0.257779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.2114 | −1.06919 | −0.534593 | − | 0.845110i | \(-0.679535\pi\) | ||||
−0.534593 | + | 0.845110i | \(0.679535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.5002 | + | 1.89676i | 0.548863 | + | 0.0771142i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1367i | 0.898503i | 0.893405 | + | 0.449251i | \(0.148309\pi\) | ||||
−0.893405 | + | 0.449251i | \(0.851691\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3225 | −0.498514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.65433i | 0.0668180i | 0.999442 | + | 0.0334090i | \(0.0106364\pi\) | ||||
−0.999442 | + | 0.0334090i | \(0.989364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.6608i | − | 1.47591i | −0.674851 | − | 0.737954i | \(-0.735792\pi\) | ||
0.674851 | − | 0.737954i | \(-0.264208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.13383 | 0.367120 | 0.183560 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183560 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.755569i | − | 0.0302712i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.27454 | 0.210310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7620 | −0.428429 | −0.214215 | − | 0.976787i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976787i | \(0.568719\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.96052 | + | 42.4242i | −0.236536 | + | 1.68355i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.7052i | 1.21658i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4177 | −0.727457 | −0.363729 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363729 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4750i | 0.491968i | 0.969274 | + | 0.245984i | \(0.0791111\pi\) | ||||
−0.969274 | + | 0.245984i | \(0.920889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.78568i | 0.0702023i | 0.999384 | + | 0.0351012i | \(0.0111753\pi\) | ||||
−0.999384 | + | 0.0351012i | \(0.988825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.73975 | −0.146798 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 10.3793i | − | 0.406174i | −0.979161 | − | 0.203087i | \(-0.934903\pi\) | ||
0.979161 | − | 0.203087i | \(-0.0650974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.1240 | + | 4.09187i | 1.13797 | + | 0.159882i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.7353 | −0.612960 | −0.306480 | − | 0.951877i | \(-0.599151\pi\) | ||||
−0.306480 | + | 0.951877i | \(0.599151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.6829 | 1.77686 | 0.888430 | − | 0.459013i | \(-0.151797\pi\) | ||||
0.888430 | + | 0.459013i | \(0.151797\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.59210 | + | 11.3319i | −0.0617391 | + | 0.439430i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.93332i | − | 0.113579i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4242 | 1.32893 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.7906i | − | 1.41817i | −0.705121 | − | 0.709087i | \(-0.749107\pi\) | ||
0.705121 | − | 0.709087i | \(-0.250893\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7032i | 0.603522i | 0.953384 | + | 0.301761i | \(0.0975745\pi\) | ||||
−0.953384 | + | 0.301761i | \(0.902425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8938 | −0.456444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 23.7067i | − | 0.907112i | −0.891228 | − | 0.453556i | \(-0.850155\pi\) | ||
0.891228 | − | 0.453556i | \(-0.149845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.79213 | + | 12.7556i | −0.0684739 | + | 0.487365i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6336 | −0.747980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2810 | 0.847609 | 0.423805 | − | 0.905754i | \(-0.360694\pi\) | ||||
0.423805 | + | 0.905754i | \(0.360694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.16346 | − | 0.444461i | −0.119997 | − | 0.0168594i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.88892i | 0.0715480i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.7955 | 1.27644 | 0.638220 | − | 0.769854i | \(-0.279671\pi\) | ||||
0.638220 | + | 0.769854i | \(0.279671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.55554i | 0.247247i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 8.59210i | − | 0.323139i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.7817 | 1.90715 | 0.953574 | − | 0.301160i | \(-0.0973739\pi\) | ||||
0.953574 | + | 0.301160i | \(0.0973739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.09679i | − | 0.0785253i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52543 | + | 25.0923i | −0.131844 | + | 0.938400i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.3812 | 1.20761 | 0.603807 | − | 0.797131i | \(-0.293650\pi\) | ||||
0.603807 | + | 0.797131i | \(0.293650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.90321 | −0.182605 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.0988 | − | 4.04149i | −0.523616 | − | 0.150097i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.3783i | − | 0.718700i | −0.933203 | − | 0.359350i | \(-0.882998\pi\) | ||
0.933203 | − | 0.359350i | \(-0.117002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.84299 | −0.327070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.9857i | − | 0.627382i | −0.949525 | − | 0.313691i | \(-0.898434\pi\) | ||
0.949525 | − | 0.313691i | \(-0.101566\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.91903i | 0.144359i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.6271 | 0.464497 | 0.232248 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232248 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.8484i | 1.05834i | 0.848514 | + | 0.529172i | \(0.177498\pi\) | ||||
−0.848514 | + | 0.529172i | \(0.822502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.8113 | + | 1.79997i | 0.469371 | + | 0.0659458i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.82717 | −0.322538 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.6099 | −0.606105 | −0.303053 | − | 0.952974i | \(-0.598006\pi\) | ||||
−0.303053 | + | 0.952974i | \(0.598006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.80642 | + | 1.09679i | 0.284105 | + | 0.0399162i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.0098i | − | 0.908998i | −0.890747 | − | 0.454499i | \(-0.849818\pi\) | ||
0.890747 | − | 0.454499i | \(-0.150182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2830 | −0.989008 | −0.494504 | − | 0.869175i | \(-0.664650\pi\) | ||||
−0.494504 | + | 0.869175i | \(0.664650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.822245i | − | 0.0297673i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.64296i | 0.312079i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.8736 | 1.11333 | 0.556665 | − | 0.830737i | \(-0.312081\pi\) | ||||
0.556665 | + | 0.830737i | \(0.312081\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.0513i | 1.15281i | 0.817165 | + | 0.576403i | \(0.195544\pi\) | ||||
−0.817165 | + | 0.576403i | \(0.804456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0781 | − | 2.88892i | −0.362014 | − | 0.103773i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.34767 | −0.0841141 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.73975 | 0.348516 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.18712 | + | 8.44938i | −0.0423702 | + | 0.301571i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.9452i | 1.67341i | 0.547650 | + | 0.836707i | \(0.315522\pi\) | ||||
−0.547650 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.26517 | −0.222764 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 79.5580i | − | 2.82519i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.7955i | − | 0.453241i | −0.973983 | − | 0.226620i | \(-0.927232\pi\) | ||
0.973983 | − | 0.226620i | \(-0.0727677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.91459 | 0.350753 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9956i | 0.917363i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.21432 | − | 0.311108i | −0.0780445 | − | 0.0109651i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.6528 | −1.18317 | −0.591585 | − | 0.806243i | \(-0.701498\pi\) | ||||
−0.591585 | + | 0.806243i | \(0.701498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.49240 | 0.298209 | 0.149104 | − | 0.988821i | \(-0.452361\pi\) | ||||
0.149104 | + | 0.988821i | \(0.452361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.19358 | + | 15.6128i | −0.0768376 | + | 0.546894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.9906i | − | 0.384514i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0558 | −0.909353 | −0.454676 | − | 0.890657i | \(-0.650245\pi\) | ||||
−0.454676 | + | 0.890657i | \(0.650245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.03212i | 0.245124i | 0.992461 | + | 0.122562i | \(0.0391111\pi\) | ||||
−0.992461 | + | 0.122562i | \(0.960889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.0622i | 0.662859i | 0.943480 | + | 0.331429i | \(0.107531\pi\) | ||||
−0.943480 | + | 0.331429i | \(0.892469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.73191 | −0.233809 | −0.116904 | − | 0.993143i | \(-0.537297\pi\) | ||||
−0.116904 | + | 0.993143i | \(0.537297\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 24.7052i | − | 0.855984i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.72101 | − | 40.7195i | 0.197984 | − | 1.40916i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.5812 | 0.606971 | 0.303485 | − | 0.952836i | \(-0.401850\pi\) | ||||
0.303485 | + | 0.952836i | \(0.401850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.3956 | −0.703297 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.2050 | + | 4.10324i | 1.00468 | + | 0.141156i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.09679i | 0.209488i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.28100 | −0.0439120 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.8069i | − | 1.46568i | −0.680401 | − | 0.732840i | \(-0.738194\pi\) | ||
0.680401 | − | 0.732840i | \(-0.261806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 26.1146i | − | 0.892058i | −0.895018 | − | 0.446029i | \(-0.852838\pi\) | ||
0.895018 | − | 0.446029i | \(-0.147162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.3497 | −1.13788 | −0.568938 | − | 0.822380i | \(-0.692646\pi\) | ||||
−0.568938 | + | 0.822380i | \(0.692646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.2864i | 1.09904i | 0.835480 | + | 0.549521i | \(0.185190\pi\) | ||||
−0.835480 | + | 0.549521i | \(0.814810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0187359 | + | 0.133353i | −0.000637038 | + | 0.00453414i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.4701 | −1.10147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.05731 | 0.306895 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.54617 | + | 10.2143i | −0.153689 | + | 0.345307i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3466i | 0.889662i | 0.895615 | + | 0.444831i | \(0.146736\pi\) | ||||
−0.895615 | + | 0.444831i | \(0.853264\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7576 | −1.23839 | −0.619197 | − | 0.785236i | \(-0.712542\pi\) | ||||
−0.619197 | + | 0.785236i | \(0.712542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5560i | 1.19656i | 0.801289 | + | 0.598278i | \(0.204148\pi\) | ||||
−0.801289 | + | 0.598278i | \(0.795852\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.9906i | 0.906257i | 0.891445 | + | 0.453128i | \(0.149692\pi\) | ||||
−0.891445 | + | 0.453128i | \(0.850308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.1590 | −0.642573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.3225i | 0.412356i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.2351 | + | 2.28100i | 0.542678 | + | 0.0762453i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.15056 | 0.205133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7971 | 0.526276 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.8064 | − | 2.50177i | −0.591906 | − | 0.0831616i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.6780i | − | 0.586988i | −0.955961 | − | 0.293494i | \(-0.905182\pi\) | ||
0.955961 | − | 0.293494i | \(-0.0948181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.8448 | 1.32012 | 0.660059 | − | 0.751213i | \(-0.270531\pi\) | ||||
0.660059 | + | 0.751213i | \(0.270531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4543i | 0.842415i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1526i | 0.434336i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.7877 | −1.24650 | −0.623250 | − | 0.782022i | \(-0.714188\pi\) | ||||
−0.623250 | + | 0.782022i | \(0.714188\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 22.5096i | − | 0.740913i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.76494 | + | 6.15701i | −0.0580308 | + | 0.202441i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.1684 | −0.956984 | −0.478492 | − | 0.878092i | \(-0.658816\pi\) | ||||
−0.478492 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.7052 | 1.00632 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.83654 | − | 20.1891i | 0.0927646 | − | 0.660255i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.7511i | 0.547235i | 0.961839 | + | 0.273618i | \(0.0882203\pi\) | ||||
−0.961839 | + | 0.273618i | \(0.911780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.85881 | −0.125794 | −0.0628968 | − | 0.998020i | \(-0.520034\pi\) | ||||
−0.0628968 | + | 0.998020i | \(0.520034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.458751i | − | 0.0149390i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2953i | 1.11445i | 0.830363 | + | 0.557224i | \(0.188133\pi\) | ||||
−0.830363 | + | 0.557224i | \(0.811867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0785 | 1.95023 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0830i | 0.715338i | 0.933848 | + | 0.357669i | \(0.116428\pi\) | ||||
−0.933848 | + | 0.357669i | \(0.883572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.8113 | − | 2.36196i | −0.544002 | − | 0.0764313i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.76049 | −0.186016 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6035 | −0.858177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.95851 | − | 28.1748i | 0.127429 | − | 0.906980i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.1274i | 1.32257i | 0.750136 | + | 0.661284i | \(0.229988\pi\) | ||||
−0.750136 | + | 0.661284i | \(0.770012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.2948 | −0.555017 | −0.277508 | − | 0.960723i | \(-0.589509\pi\) | ||||
−0.277508 | + | 0.960723i | \(0.589509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.42864i | − | 0.0458001i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.3531i | 1.57894i | 0.613786 | + | 0.789472i | \(0.289646\pi\) | ||||
−0.613786 | + | 0.789472i | \(0.710354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.67307 | −0.0534716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.7719i | 0.503044i | 0.967852 | + | 0.251522i | \(0.0809311\pi\) | ||||
−0.967852 | + | 0.251522i | \(0.919069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.33630 | + | 37.9813i | −0.170029 | + | 1.21018i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.14764 | 0.0682911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.0928 | −0.924164 | −0.462082 | − | 0.886837i | \(-0.652897\pi\) | ||||
−0.462082 | + | 0.886837i | \(0.652897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.96836 | + | 0.838543i | 0.189210 | + | 0.0265836i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.0415i | − | 0.698061i | −0.937111 | − | 0.349030i | \(-0.886511\pi\) | ||
0.937111 | − | 0.349030i | \(-0.113489\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4140.2.f.a.829.1 | 6 | ||
3.2 | odd | 2 | 1380.2.f.a.829.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 4140.2.f.a.829.2 | 6 | ||
15.2 | even | 4 | 6900.2.a.y.1.3 | 3 | |||
15.8 | even | 4 | 6900.2.a.z.1.3 | 3 | |||
15.14 | odd | 2 | 1380.2.f.a.829.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.f.a.829.3 | ✓ | 6 | 3.2 | odd | 2 | ||
1380.2.f.a.829.6 | yes | 6 | 15.14 | odd | 2 | ||
4140.2.f.a.829.1 | 6 | 1.1 | even | 1 | trivial | ||
4140.2.f.a.829.2 | 6 | 5.4 | even | 2 | inner | ||
6900.2.a.y.1.3 | 3 | 15.2 | even | 4 | |||
6900.2.a.z.1.3 | 3 | 15.8 | even | 4 |