Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(4049,4140)]
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, 1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.4049");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.2 | ||
Character | \(\chi\) | \(=\) | 4140.4049 |
Dual form | 4140.3.c.a.4049.1 |
$q$-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 | ||||||||
\(5\) | −4.99275 | + | 0.269219i | −0.998549 | + | 0.0538437i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.6272i | 1.94674i | 0.229231 | + | 0.973372i | \(0.426379\pi\) | ||||
−0.229231 | + | 0.973372i | \(0.573621\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.9107i | 0.991881i | 0.868356 | + | 0.495941i | \(0.165177\pi\) | ||||
−0.868356 | + | 0.495941i | \(0.834823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.5051i | − | 1.42347i | −0.702448 | − | 0.711735i | \(-0.747910\pi\) | ||
0.702448 | − | 0.711735i | \(-0.252090\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.61399 | −0.389058 | −0.194529 | − | 0.980897i | \(-0.562318\pi\) | ||||
−0.194529 | + | 0.980897i | \(0.562318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.6941 | −0.983899 | −0.491949 | − | 0.870624i | \(-0.663716\pi\) | ||||
−0.491949 | + | 0.870624i | \(0.663716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.8550 | − | 2.68828i | 0.994202 | − | 0.107531i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 24.3559i | − | 0.839860i | −0.907556 | − | 0.419930i | \(-0.862055\pi\) | ||
0.907556 | − | 0.419930i | \(-0.137945\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8615 | −0.350372 | −0.175186 | − | 0.984535i | \(-0.556053\pi\) | ||||
−0.175186 | + | 0.984535i | \(0.556053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.66870 | − | 68.0372i | −0.104820 | − | 1.94392i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.5811i | 1.09679i | 0.836221 | + | 0.548393i | \(0.184760\pi\) | ||||
−0.836221 | + | 0.548393i | \(0.815240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8964i | 0.265765i | 0.991132 | + | 0.132882i | \(0.0424233\pi\) | ||||
−0.991132 | + | 0.132882i | \(0.957577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.6214i | 0.456310i | 0.973625 | + | 0.228155i | \(0.0732694\pi\) | ||||
−0.973625 | + | 0.228155i | \(0.926731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −55.1384 | −1.17316 | −0.586578 | − | 0.809892i | \(-0.699525\pi\) | ||||
−0.586578 | + | 0.809892i | \(0.699525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −136.701 | −2.78981 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −83.1263 | −1.56842 | −0.784210 | − | 0.620495i | \(-0.786932\pi\) | ||||
−0.784210 | + | 0.620495i | \(0.786932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.93736 | − | 54.4743i | −0.0534066 | − | 0.990443i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.74614i | − | 0.0804431i | −0.999191 | − | 0.0402215i | \(-0.987194\pi\) | ||
0.999191 | − | 0.0402215i | \(-0.0128064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 55.7886 | 0.914567 | 0.457284 | − | 0.889321i | \(-0.348822\pi\) | ||||
0.457284 | + | 0.889321i | \(0.348822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.98192 | + | 92.3913i | 0.0766449 | + | 1.42140i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.6610i | 1.11434i | 0.830397 | + | 0.557172i | \(0.188114\pi\) | ||||
−0.830397 | + | 0.557172i | \(0.811886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 51.0055i | − | 0.718387i | −0.933263 | − | 0.359194i | \(-0.883052\pi\) | ||
0.933263 | − | 0.359194i | \(-0.116948\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 129.217i | − | 1.77010i | −0.465496 | − | 0.885050i | \(-0.654124\pi\) | ||
0.465496 | − | 0.885050i | \(-0.345876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −148.682 | −1.93094 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 112.870 | 1.42873 | 0.714367 | − | 0.699771i | \(-0.246715\pi\) | ||||
0.714367 | + | 0.699771i | \(0.246715\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −156.983 | −1.89136 | −0.945680 | − | 0.325100i | \(-0.894602\pi\) | ||||
−0.945680 | + | 0.325100i | \(0.894602\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33.0220 | − | 1.78061i | 0.388494 | − | 0.0209484i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 119.858i | − | 1.34672i | −0.739313 | − | 0.673362i | \(-0.764850\pi\) | ||
0.739313 | − | 0.673362i | \(-0.235150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 252.173 | 2.77113 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 93.3348 | − | 5.03279i | 0.982472 | − | 0.0529768i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 109.487i | − | 1.12873i | −0.825524 | − | 0.564366i | \(-0.809121\pi\) | ||
0.825524 | − | 0.564366i | \(-0.190879\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 44.7777i | − | 0.443344i | −0.975121 | − | 0.221672i | \(-0.928849\pi\) | ||
0.975121 | − | 0.221672i | \(-0.0711514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 171.082i | 1.66099i | 0.557024 | + | 0.830496i | \(0.311943\pi\) | ||||
−0.557024 | + | 0.830496i | \(0.688057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 142.700 | 1.33365 | 0.666825 | − | 0.745215i | \(-0.267653\pi\) | ||||
0.666825 | + | 0.745215i | \(0.267653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −45.6967 | −0.419236 | −0.209618 | − | 0.977783i | \(-0.567222\pi\) | ||||
−0.209618 | + | 0.977783i | \(0.567222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −101.184 | −0.895436 | −0.447718 | − | 0.894175i | \(-0.647763\pi\) | ||||
−0.447718 | + | 0.894175i | \(0.647763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.9444 | + | 1.29113i | −0.208212 | + | 0.0112272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 90.1303i | − | 0.757397i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.95674 | 0.0161714 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −123.371 | + | 20.1133i | −0.986970 | + | 0.160907i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 144.502i | 1.13781i | 0.822404 | + | 0.568904i | \(0.192633\pi\) | ||||
−0.822404 | + | 0.568904i | \(0.807367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 103.500i | 0.790073i | 0.918665 | + | 0.395037i | \(0.129268\pi\) | ||||
−0.918665 | + | 0.395037i | \(0.870732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 254.748i | − | 1.91540i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 94.6970 | 0.691219 | 0.345610 | − | 0.938378i | \(-0.387672\pi\) | ||||
0.345610 | + | 0.938378i | \(0.387672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38.3831 | −0.276138 | −0.138069 | − | 0.990423i | \(-0.544090\pi\) | ||||
−0.138069 | + | 0.990423i | \(0.544090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 201.904 | 1.41191 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.55707 | + | 121.603i | 0.0452212 | + | 0.838642i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 138.799i | − | 0.931535i | −0.884907 | − | 0.465767i | \(-0.845778\pi\) | ||
0.884907 | − | 0.465767i | \(-0.154222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 43.0538 | 0.285124 | 0.142562 | − | 0.989786i | \(-0.454466\pi\) | ||||
0.142562 | + | 0.989786i | \(0.454466\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 54.2289 | − | 2.92413i | 0.349864 | − | 0.0188653i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 56.2911i | 0.358542i | 0.983800 | + | 0.179271i | \(0.0573739\pi\) | ||||
−0.983800 | + | 0.179271i | \(0.942626\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 65.3538i | 0.405924i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.418i | 1.68968i | 0.535019 | + | 0.844840i | \(0.320304\pi\) | ||||
−0.535019 | + | 0.844840i | \(0.679696\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 103.602 | 0.620372 | 0.310186 | − | 0.950676i | \(-0.399609\pi\) | ||||
0.310186 | + | 0.950676i | \(0.399609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −173.439 | −1.02627 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9240 | 0.132509 | 0.0662543 | − | 0.997803i | \(-0.478895\pi\) | ||||
0.0662543 | + | 0.997803i | \(0.478895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.6338 | + | 338.705i | 0.209336 | + | 1.93546i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 38.1958i | 0.213385i | 0.994292 | + | 0.106692i | \(0.0340260\pi\) | ||||
−0.994292 | + | 0.106692i | \(0.965974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 273.993 | 1.51377 | 0.756887 | − | 0.653546i | \(-0.226719\pi\) | ||||
0.756887 | + | 0.653546i | \(0.226719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.9252 | − | 202.611i | −0.0590551 | − | 1.09520i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 72.1633i | − | 0.385900i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7276i | 0.103286i | 0.998666 | + | 0.0516428i | \(0.0164457\pi\) | ||||
−0.998666 | + | 0.0516428i | \(0.983554\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 91.3081i | − | 0.473099i | −0.971619 | − | 0.236549i | \(-0.923983\pi\) | ||
0.971619 | − | 0.236549i | \(-0.0760165\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 62.5057 | 0.317288 | 0.158644 | − | 0.987336i | \(-0.449288\pi\) | ||||
0.158644 | + | 0.987336i | \(0.449288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −132.469 | −0.665672 | −0.332836 | − | 0.942985i | \(-0.608006\pi\) | ||||
−0.332836 | + | 0.942985i | \(0.608006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 331.904 | 1.63499 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.93350 | − | 54.4028i | −0.0143098 | − | 0.265379i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 203.965i | − | 0.975911i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 166.955 | 0.791255 | 0.395628 | − | 0.918411i | \(-0.370527\pi\) | ||||
0.395628 | + | 0.918411i | \(0.370527\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.28243 | − | 97.9644i | −0.0245695 | − | 0.455649i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 148.012i | − | 0.682085i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 122.393i | 0.553813i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 293.697i | − | 1.31703i | −0.752568 | − | 0.658514i | \(-0.771185\pi\) | ||
0.752568 | − | 0.658514i | \(-0.228815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 388.268 | 1.71043 | 0.855216 | − | 0.518272i | \(-0.173425\pi\) | ||||
0.855216 | + | 0.518272i | \(0.173425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 97.2207 | 0.424545 | 0.212272 | − | 0.977211i | \(-0.431914\pi\) | ||||
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 261.348 | 1.12166 | 0.560832 | − | 0.827930i | \(-0.310481\pi\) | ||||
0.560832 | + | 0.827930i | \(0.310481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 275.292 | − | 14.8443i | 1.17146 | − | 0.0631671i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 422.986i | − | 1.76982i | −0.465765 | − | 0.884909i | \(-0.654221\pi\) | ||
0.465765 | − | 0.884909i | \(-0.345779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 344.752 | 1.43051 | 0.715253 | − | 0.698866i | \(-0.246312\pi\) | ||||
0.715253 | + | 0.698866i | \(0.246312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 682.512 | − | 36.8024i | 2.78576 | − | 0.150214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 345.936i | 1.40055i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 252.361i | − | 1.00542i | −0.864455 | − | 0.502711i | \(-0.832336\pi\) | ||
0.864455 | − | 0.502711i | \(-0.167664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 52.3259i | 0.206822i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −267.765 | −1.04189 | −0.520944 | − | 0.853591i | \(-0.674420\pi\) | ||||
−0.520944 | + | 0.853591i | \(0.674420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −553.007 | −2.13516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −111.829 | −0.425205 | −0.212603 | − | 0.977139i | \(-0.568194\pi\) | ||||
−0.212603 | + | 0.977139i | \(0.568194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 415.028 | − | 22.3791i | 1.56615 | − | 0.0844496i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 423.875i | − | 1.57574i | −0.615839 | − | 0.787872i | \(-0.711183\pi\) | ||
0.615839 | − | 0.787872i | \(-0.288817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 187.453 | 0.691708 | 0.345854 | − | 0.938288i | \(-0.387589\pi\) | ||||
0.345854 | + | 0.938288i | \(0.387589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.3310 | + | 271.186i | 0.106658 | + | 0.986130i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 227.548i | 0.821473i | 0.911754 | + | 0.410736i | \(0.134728\pi\) | ||||
−0.911754 | + | 0.410736i | \(0.865272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 268.943i | − | 0.957093i | −0.878062 | − | 0.478546i | \(-0.841164\pi\) | ||
0.878062 | − | 0.478546i | \(-0.158836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 359.867i | 1.27161i | 0.771848 | + | 0.635807i | \(0.219333\pi\) | ||||
−0.771848 | + | 0.635807i | \(0.780667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −148.487 | −0.517376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −245.255 | −0.848634 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.848990 | −0.00289758 | −0.00144879 | − | 0.999999i | \(-0.500461\pi\) | ||||
−0.00144879 | + | 0.999999i | \(0.500461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27775 | + | 23.6963i | 0.00433135 | + | 0.0803264i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 88.7474i | − | 0.296814i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −267.384 | −0.888320 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −278.538 | + | 15.0193i | −0.913240 | + | 0.0492437i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 348.180i | − | 1.13414i | −0.823670 | − | 0.567069i | \(-0.808077\pi\) | ||
0.823670 | − | 0.567069i | \(-0.191923\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 254.597i | 0.818638i | 0.912391 | + | 0.409319i | \(0.134234\pi\) | ||||
−0.912391 | + | 0.409319i | \(0.865766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 462.281i | − | 1.47693i | −0.674289 | − | 0.738467i | \(-0.735550\pi\) | ||
0.674289 | − | 0.738467i | \(-0.264450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 139.176 | 0.439042 | 0.219521 | − | 0.975608i | \(-0.429551\pi\) | ||||
0.219521 | + | 0.975608i | \(0.429551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 265.740 | 0.833042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 123.643 | 0.382794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −49.7469 | − | 459.945i | −0.153067 | − | 1.41522i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 751.382i | − | 2.28384i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6330 | −0.0381662 | −0.0190831 | − | 0.999818i | \(-0.506075\pi\) | ||||
−0.0190831 | + | 0.999818i | \(0.506075\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.1001 | − | 372.764i | −0.0600004 | − | 1.11273i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 145.961i | − | 0.433119i | −0.976269 | − | 0.216560i | \(-0.930516\pi\) | ||
0.976269 | − | 0.216560i | \(-0.0694836\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 118.507i | − | 0.347528i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1195.12i | − | 3.48431i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −146.681 | −0.422710 | −0.211355 | − | 0.977409i | \(-0.567788\pi\) | ||||
−0.211355 | + | 0.977409i | \(0.567788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 436.675 | 1.25122 | 0.625608 | − | 0.780137i | \(-0.284851\pi\) | ||||
0.625608 | + | 0.780137i | \(0.284851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −461.875 | −1.30843 | −0.654213 | − | 0.756310i | \(-0.727000\pi\) | ||||
−0.654213 | + | 0.756310i | \(0.727000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.7316 | + | 254.658i | 0.0386807 | + | 0.717345i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 380.063i | − | 1.05867i | −0.848413 | − | 0.529336i | \(-0.822441\pi\) | ||
0.848413 | − | 0.529336i | \(-0.177559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5314 | −0.0319430 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.7877 | + | 645.149i | 0.0953088 | + | 1.76753i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 435.265i | − | 1.18601i | −0.805200 | − | 0.593004i | \(-0.797942\pi\) | ||
0.805200 | − | 0.593004i | \(-0.202058\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1132.78i | − | 3.05331i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 158.241i | 0.424238i | 0.977244 | + | 0.212119i | \(0.0680365\pi\) | ||||
−0.977244 | + | 0.212119i | \(0.931964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −450.709 | −1.19552 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 245.573 | 0.647949 | 0.323975 | − | 0.946066i | \(-0.394981\pi\) | ||||
0.323975 | + | 0.946066i | \(0.394981\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −485.878 | −1.26861 | −0.634305 | − | 0.773083i | \(-0.718714\pi\) | ||||
−0.634305 | + | 0.773083i | \(0.718714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 742.333 | − | 40.0280i | 1.92814 | − | 0.103969i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 370.231i | 0.951750i | 0.879513 | + | 0.475875i | \(0.157868\pi\) | ||||
−0.879513 | + | 0.475875i | \(0.842132\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7196 | −0.0811243 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −563.531 | + | 30.3867i | −1.42666 | + | 0.0769283i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 336.618i | − | 0.847903i | −0.905685 | − | 0.423952i | \(-0.860643\pi\) | ||
0.905685 | − | 0.423952i | \(-0.139357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 216.118i | 0.538947i | 0.963008 | + | 0.269473i | \(0.0868497\pi\) | ||||
−0.963008 | + | 0.269473i | \(0.913150\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 200.994i | 0.498744i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −442.768 | −1.08788 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 109.277 | 0.267181 | 0.133591 | − | 0.991037i | \(-0.457349\pi\) | ||||
0.133591 | + | 0.991037i | \(0.457349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 64.6766 | 0.156602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 783.776 | − | 42.2627i | 1.88862 | − | 0.101838i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 414.301i | 0.988784i | 0.869239 | + | 0.494392i | \(0.164609\pi\) | ||||
−0.869239 | + | 0.494392i | \(0.835391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −409.425 | −0.972506 | −0.486253 | − | 0.873818i | \(-0.661637\pi\) | ||||
−0.486253 | + | 0.873818i | \(0.661637\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −164.391 | + | 17.7803i | −0.386803 | + | 0.0418359i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 760.243i | 1.78043i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 80.9100i | − | 0.187726i | −0.995585 | − | 0.0938631i | \(-0.970078\pi\) | ||
0.995585 | − | 0.0938631i | \(-0.0299216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 90.4630i | 0.208921i | 0.994529 | + | 0.104461i | \(0.0333117\pi\) | ||||
−0.994529 | + | 0.104461i | \(0.966688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −89.6537 | −0.205157 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 299.175 | 0.681492 | 0.340746 | − | 0.940155i | \(-0.389320\pi\) | ||||
0.340746 | + | 0.940155i | \(0.389320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 489.134 | 1.10414 | 0.552069 | − | 0.833798i | \(-0.313838\pi\) | ||||
0.552069 | + | 0.833798i | \(0.313838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.2681 | + | 598.423i | 0.0725126 | + | 1.34477i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 316.630i | 0.705189i | 0.935776 | + | 0.352594i | \(0.114700\pi\) | ||||
−0.935776 | + | 0.352594i | \(0.885300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −118.887 | −0.263607 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1259.04 | + | 67.8896i | −2.76711 | + | 0.149208i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 689.747i | − | 1.50929i | −0.656131 | − | 0.754647i | \(-0.727808\pi\) | ||
0.656131 | − | 0.754647i | \(-0.272192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 835.305i | 1.81194i | 0.423340 | + | 0.905971i | \(0.360858\pi\) | ||||
−0.423340 | + | 0.905971i | \(0.639142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 96.5034i | 0.208431i | 0.994555 | + | 0.104215i | \(0.0332331\pi\) | ||||
−0.994555 | + | 0.104215i | \(0.966767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 624.883 | 1.33808 | 0.669040 | − | 0.743226i | \(-0.266705\pi\) | ||||
0.669040 | + | 0.743226i | \(0.266705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1017.42 | −2.16934 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −214.083 | −0.452606 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −464.642 | + | 50.2549i | −0.978194 | + | 0.105800i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 845.372i | − | 1.76487i | −0.470435 | − | 0.882435i | \(-0.655903\pi\) | ||
0.470435 | − | 0.882435i | \(-0.344097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 750.957 | 1.56124 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.4760 | + | 546.641i | 0.0607752 | + | 1.12710i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 154.626i | 0.317508i | 0.987318 | + | 0.158754i | \(0.0507477\pi\) | ||||
−0.987318 | + | 0.158754i | \(0.949252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 494.309i | − | 1.00674i | −0.864071 | − | 0.503370i | \(-0.832093\pi\) | ||
0.864071 | − | 0.503370i | \(-0.167907\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 161.090i | 0.326755i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 695.063 | 1.39852 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 143.978 | 0.288533 | 0.144267 | − | 0.989539i | \(-0.453918\pi\) | ||||
0.144267 | + | 0.989539i | \(0.453918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −567.447 | −1.12813 | −0.564063 | − | 0.825732i | \(-0.690763\pi\) | ||||
−0.564063 | + | 0.825732i | \(0.690763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0550 | + | 223.564i | 0.0238713 | + | 0.442700i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.9057i | − | 0.0332135i | −0.999862 | − | 0.0166068i | \(-0.994714\pi\) | ||
0.999862 | − | 0.0166068i | \(-0.00528634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1760.87 | 3.44593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −46.0585 | − | 854.170i | −0.0894340 | − | 1.65858i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 601.598i | − | 1.16363i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 946.617i | − | 1.81692i | −0.417969 | − | 0.908461i | \(-0.637258\pi\) | ||
0.417969 | − | 0.908461i | \(-0.362742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.3619i | − | 0.0446690i | −0.999751 | − | 0.0223345i | \(-0.992890\pi\) | ||
0.999751 | − | 0.0223345i | \(-0.00710988\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 71.8381 | 0.136315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 201.638 | 0.378308 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −712.467 | + | 38.4176i | −1.33171 | + | 0.0718087i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1491.50i | − | 2.76716i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −157.058 | −0.290311 | −0.145155 | − | 0.989409i | \(-0.546368\pi\) | ||||
−0.145155 | + | 0.989409i | \(0.546368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 228.152 | − | 12.3024i | 0.418628 | − | 0.0225732i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 426.038i | 0.778862i | 0.921056 | + | 0.389431i | \(0.127328\pi\) | ||||
−0.921056 | + | 0.389431i | \(0.872672\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 455.312i | 0.826338i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1538.10i | 2.78138i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 90.6387 | 0.162727 | 0.0813633 | − | 0.996685i | \(-0.474073\pi\) | ||||
0.0813633 | + | 0.996685i | \(0.474073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 363.095 | 0.649544 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 93.6335 | 0.166312 | 0.0831559 | − | 0.996537i | \(-0.473500\pi\) | ||||
0.0831559 | + | 0.996537i | \(0.473500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 505.187 | − | 27.2407i | 0.894137 | − | 0.0482136i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9284i | 0.0332661i | 0.999862 | + | 0.0166330i | \(0.00529471\pi\) | ||||
−0.999862 | + | 0.0166330i | \(0.994705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −129.940 | −0.227566 | −0.113783 | − | 0.993506i | \(-0.536297\pi\) | ||||
−0.113783 | + | 0.993506i | \(0.536297\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 119.201 | − | 12.8925i | 0.207305 | − | 0.0224218i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 509.890i | − | 0.883691i | −0.897091 | − | 0.441846i | \(-0.854324\pi\) | ||
0.897091 | − | 0.441846i | \(-0.145676\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2139.24i | − | 3.68199i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 906.965i | − | 1.55569i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −616.914 | −1.05096 | −0.525480 | − | 0.850806i | \(-0.676114\pi\) | ||||
−0.525480 | + | 0.850806i | \(0.676114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 203.046 | 0.344731 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1137.91 | 1.91891 | 0.959455 | − | 0.281862i | \(-0.0909521\pi\) | ||||
0.959455 | + | 0.281862i | \(0.0909521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.2647 | + | 449.998i | 0.0407811 | + | 0.756298i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 384.422i | 0.641774i | 0.947118 | + | 0.320887i | \(0.103981\pi\) | ||||
−0.947118 | + | 0.320887i | \(0.896019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −746.538 | −1.24216 | −0.621080 | − | 0.783747i | \(-0.713306\pi\) | ||||
−0.621080 | + | 0.783747i | \(0.713306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.76950 | + | 0.526790i | −0.0161479 | + | 0.000870728i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 922.940i | 1.52049i | 0.649634 | + | 0.760247i | \(0.274922\pi\) | ||||
−0.649634 | + | 0.760247i | \(0.725078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1020.34i | 1.66995i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 791.954i | 1.29193i | 0.763367 | + | 0.645965i | \(0.223545\pi\) | ||||
−0.763367 | + | 0.645965i | \(0.776455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 347.501 | 0.563211 | 0.281606 | − | 0.959530i | \(-0.409133\pi\) | ||||
0.281606 | + | 0.959530i | \(0.409133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 745.764 | 1.20479 | 0.602394 | − | 0.798199i | \(-0.294213\pi\) | ||||
0.602394 | + | 0.798199i | \(0.294213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1633.33 | 2.62173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 610.546 | − | 133.635i | 0.976874 | − | 0.213815i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 268.403i | − | 0.426714i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1163.24 | −1.84349 | −0.921744 | − | 0.387800i | \(-0.873235\pi\) | ||||
−0.921744 | + | 0.387800i | \(0.873235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.9026 | − | 721.460i | −0.0612639 | − | 1.13616i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2529.66i | 3.97121i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 164.410i | − | 0.256490i | −0.991743 | − | 0.128245i | \(-0.959066\pi\) | ||
0.991743 | − | 0.128245i | \(-0.0409344\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 255.319i | 0.397075i | 0.980093 | + | 0.198538i | \(0.0636192\pi\) | ||||
−0.980093 | + | 0.198538i | \(0.936381\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1238.64 | −1.91443 | −0.957215 | − | 0.289377i | \(-0.906552\pi\) | ||||
−0.957215 | + | 0.289377i | \(0.906552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.7837 | 0.0797900 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1002.98 | 1.53595 | 0.767976 | − | 0.640478i | \(-0.221264\pi\) | ||||
0.767976 | + | 0.640478i | \(0.221264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.8640 | − | 516.747i | −0.0425405 | − | 0.788927i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 615.722i | 0.934327i | 0.884171 | + | 0.467164i | \(0.154724\pi\) | ||||
−0.884171 | + | 0.467164i | \(0.845276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −377.413 | −0.570972 | −0.285486 | − | 0.958383i | \(-0.592155\pi\) | ||||
−0.285486 | + | 0.958383i | \(0.592155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 68.5829 | + | 1271.89i | 0.103132 | + | 1.91262i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 116.807i | − | 0.175123i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 608.692i | 0.907142i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 954.784i | − | 1.41870i | −0.704857 | − | 0.709349i | \(-0.748989\pi\) | ||
0.704857 | − | 0.709349i | \(-0.251011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −140.861 | −0.208066 | −0.104033 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104033 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1492.00 | 2.19735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.4201 | −0.0269694 | −0.0134847 | − | 0.999909i | \(-0.504292\pi\) | ||||
−0.0134847 | + | 0.999909i | \(0.504292\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −472.798 | + | 25.4942i | −0.690216 | + | 0.0372178i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1538.26i | 2.23260i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −627.126 | −0.907564 | −0.453782 | − | 0.891113i | \(-0.649925\pi\) | ||||
−0.453782 | + | 0.891113i | \(0.649925\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 191.637 | − | 10.3335i | 0.275737 | − | 0.0148683i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 72.0685i | − | 0.103398i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 708.842i | − | 1.01119i | −0.862772 | − | 0.505593i | \(-0.831274\pi\) | ||
0.862772 | − | 0.505593i | \(-0.168726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 758.626i | − | 1.07913i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 610.195 | 0.863076 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 294.963 | 0.416026 | 0.208013 | − | 0.978126i | \(-0.433300\pi\) | ||||
0.208013 | + | 0.978126i | \(0.433300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.0901 | −0.0730577 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1008.05 | + | 54.3562i | −1.40986 | + | 0.0760227i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 822.939i | − | 1.14456i | −0.820058 | − | 0.572280i | \(-0.806059\pi\) | ||
0.820058 | − | 0.572280i | \(-0.193941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2331.37 | −3.23353 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −65.4756 | − | 605.368i | −0.0903112 | − | 0.834990i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 443.780i | 0.610426i | 0.952284 | + | 0.305213i | \(0.0987276\pi\) | ||||
−0.952284 | + | 0.305213i | \(0.901272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 129.775i | − | 0.177531i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 130.278i | − | 0.177733i | −0.996044 | − | 0.0888666i | \(-0.971676\pi\) | ||
0.996044 | − | 0.0888666i | \(-0.0283245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −814.604 | −1.10530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −805.386 | −1.08983 | −0.544916 | − | 0.838490i | \(-0.683439\pi\) | ||||
−0.544916 | + | 0.838490i | \(0.683439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 284.424 | 0.382805 | 0.191402 | − | 0.981512i | \(-0.438696\pi\) | ||||
0.191402 | + | 0.981512i | \(0.438696\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.3672 | + | 692.987i | 0.0501573 | + | 0.930183i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1944.61i | 2.59627i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 72.2500 | 0.0962050 | 0.0481025 | − | 0.998842i | \(-0.484683\pi\) | ||||
0.0481025 | + | 0.998842i | \(0.484683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −214.957 | + | 11.5909i | −0.284711 | + | 0.0153522i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1268.09i | 1.67515i | 0.546321 | + | 0.837576i | \(0.316028\pi\) | ||||
−0.546321 | + | 0.837576i | \(0.683972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 115.653i | − | 0.151976i | −0.997109 | − | 0.0759878i | \(-0.975789\pi\) | ||
0.997109 | − | 0.0759878i | \(-0.0242110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 622.719i | − | 0.816146i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −87.8278 | −0.114508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 779.540 | 1.01371 | 0.506853 | − | 0.862032i | \(-0.330809\pi\) | ||||
0.506853 | + | 0.862032i | \(0.330809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −78.4368 | −0.101471 | −0.0507353 | − | 0.998712i | \(-0.516156\pi\) | ||||
−0.0507353 | + | 0.998712i | \(0.516156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −269.964 | + | 29.1989i | −0.348341 | + | 0.0376760i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 203.697i | − | 0.261486i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 556.506 | 0.712555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1546 | − | 281.047i | −0.0193052 | − | 0.358022i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 257.400i | 0.327065i | 0.986538 | + | 0.163532i | \(0.0522888\pi\) | ||||
−0.986538 | + | 0.163532i | \(0.947711\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1378.86i | − | 1.74318i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1032.37i | − | 1.30186i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1458.64 | −1.83017 | −0.915083 | − | 0.403266i | \(-0.867875\pi\) | ||||
−0.915083 | + | 0.403266i | \(0.867875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 364.685 | 0.456427 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1409.85 | 1.75573 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.5945 | − | 326.295i | −0.0218565 | − | 0.405335i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 275.824i | 0.340945i | 0.985362 | + | 0.170472i | \(0.0545294\pi\) | ||||
−0.985362 | + | 0.170472i | \(0.945471\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 265.225 | 0.327034 | 0.163517 | − | 0.986540i | \(-0.447716\pi\) | ||||
0.163517 | + | 0.986540i | \(0.447716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −74.1476 | − | 1375.09i | −0.0909787 | − | 1.68723i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 366.803i | − | 0.448963i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 889.794i | 1.08379i | 0.840445 | + | 0.541897i | \(0.182294\pi\) | ||||
−0.840445 | + | 0.541897i | \(0.817706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 70.0990i | − | 0.0851750i | −0.999093 | − | 0.0425875i | \(-0.986440\pi\) | ||
0.999093 | − | 0.0425875i | \(-0.0135601\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 369.845 | 0.447213 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1366.23 | 1.64804 | 0.824020 | − | 0.566561i | \(-0.191726\pi\) | ||||
0.824020 | + | 0.566561i | \(0.191726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 904.138 | 1.08540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −517.260 | + | 27.8916i | −0.619472 | + | 0.0334032i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 916.900i | 1.09285i | 0.837508 | + | 0.546425i | \(0.184012\pi\) | ||||
−0.837508 | + | 0.546425i | \(0.815988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 247.788 | 0.294635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 865.936 | − | 46.6930i | 1.02478 | − | 0.0552580i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.6649i | 0.0314815i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 194.620i | 0.228696i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 272.464i | 0.319419i | 0.987164 | + | 0.159709i | \(0.0510557\pi\) | ||||
−0.987164 | + | 0.159709i | \(0.948944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1474.04 | 1.72000 | 0.860002 | − | 0.510290i | \(-0.170462\pi\) | ||||
0.860002 | + | 0.510290i | \(0.170462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −923.505 | −1.07509 | −0.537547 | − | 0.843234i | \(-0.680649\pi\) | ||||
−0.537547 | + | 0.843234i | \(0.680649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1226.67 | −1.42140 | −0.710699 | − | 0.703496i | \(-0.751621\pi\) | ||||
−0.710699 | + | 0.703496i | \(0.751621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −114.454 | + | 6.17156i | −0.132316 | + | 0.00713475i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1231.49i | 1.41713i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1381.61 | 1.58623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −274.089 | − | 1681.20i | −0.313244 | − | 1.92138i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.67098i | 0.00190534i | 1.00000 | 0.000952669i | \(0.000303244\pi\) | |||||
−1.00000 | 0.000952669i | \(0.999697\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1360.29i | 1.54403i | 0.635604 | + | 0.772015i | \(0.280751\pi\) | ||||
−0.635604 | + | 0.772015i | \(0.719249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 758.529i | − | 0.859037i | −0.903058 | − | 0.429518i | \(-0.858683\pi\) | ||
0.903058 | − | 0.429518i | \(-0.141317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1066.21 | −1.20204 | −0.601018 | − | 0.799236i | \(-0.705238\pi\) | ||||
−0.601018 | + | 0.799236i | \(0.705238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1969.15 | −2.21502 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1030.76 | 1.15427 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.2830 | − | 190.702i | −0.0114894 | − | 0.213075i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 264.543i | 0.294264i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 549.797 | 0.610207 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1367.98 | + | 73.7641i | −1.51158 | + | 0.0815073i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 968.211i | − | 1.06749i | −0.845646 | − | 0.533744i | \(-0.820785\pi\) | ||
0.845646 | − | 0.533744i | \(-0.179215\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 559.212i | 0.613844i | 0.951735 | + | 0.306922i | \(0.0992990\pi\) | ||||
−0.951735 | + | 0.306922i | \(0.900701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1712.79i | − | 1.87600i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1410.41 | −1.53807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1047.46 | 1.13978 | 0.569889 | − | 0.821722i | \(-0.306986\pi\) | ||||
0.569889 | + | 0.821722i | \(0.306986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −943.862 | −1.02260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 109.093 | + | 1008.64i | 0.117939 | + | 1.09043i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1171.93i | − | 1.26149i | −0.775990 | − | 0.630746i | \(-0.782749\pi\) | ||
0.775990 | − | 0.630746i | \(-0.217251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2555.50 | 2.74489 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.4277 | + | 360.293i | 0.0207783 | + | 0.385340i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 694.182i | − | 0.740856i | −0.928861 | − | 0.370428i | \(-0.879211\pi\) | ||
0.928861 | − | 0.370428i | \(-0.120789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 643.730i | − | 0.684092i | −0.939683 | − | 0.342046i | \(-0.888880\pi\) | ||
0.939683 | − | 0.342046i | \(-0.111120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.2571i | 0.0554158i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 668.516 | 0.705930 | 0.352965 | − | 0.935637i | \(-0.385173\pi\) | ||||
0.352965 | + | 0.935637i | \(0.385173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2391.18 | −2.51968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1159.32 | −1.21650 | −0.608249 | − | 0.793747i | \(-0.708128\pi\) | ||||
−0.608249 | + | 0.793747i | \(0.708128\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.31102 | − | 98.4947i | −0.00556128 | − | 0.103136i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1290.46i | 1.34563i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −843.027 | −0.877239 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.5818 | + | 455.878i | 0.0254734 | + | 0.472412i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1838.49i | − | 1.90123i | −0.310379 | − | 0.950613i | \(-0.600456\pi\) | ||
0.310379 | − | 0.950613i | \(-0.399544\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 693.313i | 0.714019i | 0.934101 | + | 0.357010i | \(0.116204\pi\) | ||||
−0.934101 | + | 0.357010i | \(0.883796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 523.055i | − | 0.537569i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1157.04 | −1.18428 | −0.592139 | − | 0.805835i | \(-0.701717\pi\) | ||||
−0.592139 | + | 0.805835i | \(0.701717\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1307.74 | 1.33579 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1346.71 | −1.37000 | −0.685001 | − | 0.728542i | \(-0.740198\pi\) | ||||
−0.685001 | + | 0.728542i | \(0.740198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −312.075 | + | 16.8277i | −0.316828 | + | 0.0170840i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 94.1007i | 0.0951473i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −788.614 | −0.795776 | −0.397888 | − | 0.917434i | \(-0.630257\pi\) | ||||
−0.397888 | + | 0.917434i | \(0.630257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 661.383 | − | 35.6631i | 0.664707 | − | 0.0358423i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 569.209i | 0.570922i | 0.958390 | + | 0.285461i | \(0.0921467\pi\) | ||||
−0.958390 | + | 0.285461i | \(0.907853\pi\) | |||||||
\(998\) | 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 | 4140.3.c.a.4049.2 | yes | 88 | |
3.2 | odd | 2 | inner | 4140.3.c.a.4049.87 | yes | 88 | |
5.4 | even | 2 | inner | 4140.3.c.a.4049.88 | yes | 88 | |
15.14 | odd | 2 | inner | 4140.3.c.a.4049.1 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.c.a.4049.1 | ✓ | 88 | 15.14 | odd | 2 | inner | |
4140.3.c.a.4049.2 | yes | 88 | 1.1 | even | 1 | trivial | |
4140.3.c.a.4049.87 | yes | 88 | 3.2 | odd | 2 | inner | |
4140.3.c.a.4049.88 | yes | 88 | 5.4 | even | 2 | inner |