Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(557,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.bk (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1745.4 | ||
Root | \(2.23256 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1745 |
Dual form | 1764.3.bk.d.557.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 4.46512 | + | 2.57794i | 0.893023 | + | 0.515587i | 0.874930 | − | 0.484249i | \(-0.160907\pi\) |
0.0180929 | + | 0.999836i | \(0.494241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.25600 | + | 3.03455i | −0.477818 | + | 0.275868i | −0.719507 | − | 0.694486i | \(-0.755632\pi\) |
0.241689 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.5830 | −0.967923 | −0.483962 | − | 0.875089i | \(-0.660803\pi\) | ||||
−0.483962 | + | 0.875089i | \(0.660803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.9771 | + | 8.64704i | −0.881006 | + | 0.508649i | −0.870990 | − | 0.491301i | \(-0.836522\pi\) |
−0.0100162 | + | 0.999950i | \(0.503188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.9373 | − | 22.4080i | 0.680908 | − | 1.17937i | −0.293796 | − | 0.955868i | \(-0.594919\pi\) |
0.974704 | − | 0.223499i | \(-0.0717480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.09247 | − | 1.20809i | −0.0909771 | − | 0.0525257i | 0.453821 | − | 0.891093i | \(-0.350060\pi\) |
−0.544798 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.791503 | + | 1.37092i | 0.0316601 | + | 0.0548369i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 55.8014i | − | 1.92418i | −0.272724 | − | 0.962092i | \(-0.587925\pi\) | ||
0.272724 | − | 0.962092i | \(-0.412075\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.64575 | − | 13.2428i | −0.246637 | − | 0.427188i | 0.715953 | − | 0.698148i | \(-0.245992\pi\) |
−0.962591 | + | 0.270960i | \(0.912659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8745 | − | 20.5673i | 0.320933 | − | 0.555872i | −0.659748 | − | 0.751487i | \(-0.729337\pi\) |
0.980681 | + | 0.195615i | \(0.0626704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 15.4676i | − | 0.377259i | −0.982048 | − | 0.188629i | \(-0.939596\pi\) | ||
0.982048 | − | 0.188629i | \(-0.0604045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.7490 | 0.645326 | 0.322663 | − | 0.946514i | \(-0.395422\pi\) | ||||
0.322663 | + | 0.946514i | \(0.395422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.6486 | + | 14.2309i | 0.524438 | + | 0.302785i | 0.738749 | − | 0.673981i | \(-0.235417\pi\) |
−0.214310 | + | 0.976766i | \(0.568750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.4166 | − | 23.3345i | 0.762577 | − | 0.440274i | −0.0676432 | − | 0.997710i | \(-0.521548\pi\) |
0.830220 | + | 0.557436i | \(0.188215\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −31.2915 | −0.568936 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 69.8601 | − | 40.3337i | 1.18407 | − | 0.683623i | 0.227117 | − | 0.973868i | \(-0.427070\pi\) |
0.956952 | + | 0.290245i | \(0.0937368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31.3542 | − | 54.3072i | 0.514004 | − | 0.890281i | −0.485864 | − | 0.874034i | \(-0.661495\pi\) |
0.999868 | − | 0.0162467i | \(-0.00517172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −56.1846 | − | 32.4382i | −0.864378 | − | 0.499049i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −58.0405 | − | 100.529i | −0.866276 | − | 1.50043i | −0.865774 | − | 0.500435i | \(-0.833173\pi\) |
−0.000502198 | − | 1.00000i | \(-0.500160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.7896i | 0.701261i | 0.936514 | + | 0.350631i | \(0.114033\pi\) | ||||
−0.936514 | + | 0.350631i | \(0.885967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.3542 | − | 26.5943i | −0.210332 | − | 0.364306i | 0.741486 | − | 0.670968i | \(-0.234121\pi\) |
−0.951818 | + | 0.306662i | \(0.900788\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −71.3320 | + | 123.551i | −0.902937 | + | 1.56393i | −0.0792742 | + | 0.996853i | \(0.525260\pi\) |
−0.823663 | + | 0.567080i | \(0.808073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28.5763i | 0.344293i | 0.985071 | + | 0.172147i | \(0.0550703\pi\) | ||||
−0.985071 | + | 0.172147i | \(0.944930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −89.1660 | −1.04901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 145.668 | + | 84.1013i | 1.63672 | + | 0.944959i | 0.981953 | + | 0.189125i | \(0.0605652\pi\) |
0.654764 | + | 0.755834i | \(0.272768\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 115.533 | − | 66.7028i | 1.21613 | − | 0.702135i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 113.956 | 1.17480 | 0.587400 | − | 0.809297i | \(-0.300152\pi\) | ||||
0.587400 | + | 0.809297i | \(0.300152\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34.8804 | − | 20.1382i | 0.345351 | − | 0.199388i | −0.317285 | − | 0.948330i | \(-0.602771\pi\) |
0.662636 | + | 0.748942i | \(0.269438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5608 | + | 25.2200i | −0.141367 | + | 0.244854i | −0.928012 | − | 0.372551i | \(-0.878483\pi\) |
0.786645 | + | 0.617406i | \(0.211816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −157.531 | − | 90.9506i | −1.47225 | − | 0.850005i | −0.472739 | − | 0.881202i | \(-0.656735\pi\) |
−0.999513 | + | 0.0311972i | \(0.990068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 44.0810 | + | 76.3506i | 0.404413 | + | 0.700464i | 0.994253 | − | 0.107056i | \(-0.0341424\pi\) |
−0.589840 | + | 0.807520i | \(0.700809\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 64.8190i | − | 0.573620i | −0.957988 | − | 0.286810i | \(-0.907405\pi\) | ||
0.957988 | − | 0.286810i | \(-0.0925948\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.22876 | − | 10.7885i | −0.0541631 | − | 0.0938132i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −42.0830 | + | 72.8899i | −0.347793 | + | 0.602396i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 120.735i | − | 0.965880i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −223.579 | −1.76047 | −0.880233 | − | 0.474543i | \(-0.842613\pi\) | ||||
−0.880233 | + | 0.474543i | \(0.842613\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 179.527 | + | 103.650i | 1.37043 | + | 0.791220i | 0.990982 | − | 0.133992i | \(-0.0427795\pi\) |
0.379451 | + | 0.925212i | \(0.376113\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 152.225 | − | 87.8874i | 1.11113 | − | 0.641514i | 0.172011 | − | 0.985095i | \(-0.444973\pi\) |
0.939123 | + | 0.343581i | \(0.111640\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −117.166 | −0.842921 | −0.421460 | − | 0.906847i | \(-0.638482\pi\) | ||||
−0.421460 | + | 0.906847i | \(0.638482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 66.1362 | − | 38.1838i | 0.462491 | − | 0.267019i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 143.852 | − | 249.159i | 0.992085 | − | 1.71834i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 161.354 | + | 93.1578i | 1.08291 | + | 0.625220i | 0.931681 | − | 0.363278i | \(-0.118342\pi\) |
0.151233 | + | 0.988498i | \(0.451676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −91.0405 | − | 157.687i | −0.602917 | − | 1.04428i | −0.992377 | − | 0.123240i | \(-0.960672\pi\) |
0.389460 | − | 0.921044i | \(-0.372662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 78.8410i | − | 0.508652i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34.1882 | − | 59.2158i | −0.217759 | − | 0.377170i | 0.736363 | − | 0.676586i | \(-0.236542\pi\) |
−0.954123 | + | 0.299416i | \(0.903208\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3725 | − | 31.8222i | 0.112715 | − | 0.195228i | −0.804149 | − | 0.594428i | \(-0.797379\pi\) |
0.916864 | + | 0.399200i | \(0.130712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 240.708i | − | 1.44137i | −0.693264 | − | 0.720684i | \(-0.743828\pi\) | ||
0.693264 | − | 0.720684i | \(-0.256172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6680 | −0.0631241 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 295.340 | + | 170.514i | 1.70717 | + | 0.985632i | 0.938035 | + | 0.346540i | \(0.112644\pi\) |
0.769130 | + | 0.639092i | \(0.220690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −119.866 | + | 69.2049i | −0.669645 | + | 0.386620i | −0.795942 | − | 0.605373i | \(-0.793024\pi\) |
0.126297 | + | 0.991992i | \(0.459691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −135.328 | −0.747669 | −0.373834 | − | 0.927495i | \(-0.621957\pi\) | ||||
−0.373834 | + | 0.927495i | \(0.621957\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 106.042 | − | 61.2234i | 0.573200 | − | 0.330937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52.4797 | − | 90.8976i | 0.280640 | − | 0.486083i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −145.898 | − | 84.2344i | −0.763866 | − | 0.441018i | 0.0668163 | − | 0.997765i | \(-0.478716\pi\) |
−0.830682 | + | 0.556747i | \(0.812049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −71.7490 | − | 124.273i | −0.371757 | − | 0.643901i | 0.618079 | − | 0.786116i | \(-0.287911\pi\) |
−0.989836 | + | 0.142215i | \(0.954578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 296.510i | − | 1.50513i | −0.658521 | − | 0.752563i | \(-0.728817\pi\) | ||
0.658521 | − | 0.752563i | \(-0.271183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71.1216 | + | 123.186i | 0.357395 | + | 0.619026i | 0.987525 | − | 0.157464i | \(-0.0503318\pi\) |
−0.630130 | + | 0.776490i | \(0.716998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.8745 | − | 69.0647i | 0.194510 | − | 0.336901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 157.035i | 0.751364i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 110.996 | 0.526048 | 0.263024 | − | 0.964789i | \(-0.415280\pi\) | ||||
0.263024 | + | 0.964789i | \(0.415280\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.903 | + | 71.5352i | 0.576291 | + | 0.332722i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 188.457 | − | 108.806i | 0.852747 | − | 0.492334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −104.251 | −0.467493 | −0.233747 | − | 0.972298i | \(-0.575099\pi\) | ||||
−0.233747 | + | 0.972298i | \(0.575099\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −141.302 | + | 81.5807i | −0.622475 | + | 0.359386i | −0.777832 | − | 0.628472i | \(-0.783681\pi\) |
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 139.207 | − | 241.113i | 0.607889 | − | 1.05289i | −0.383699 | − | 0.923458i | \(-0.625350\pi\) |
0.991588 | − | 0.129436i | \(-0.0413167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −349.910 | − | 202.021i | −1.50176 | − | 0.867042i | −0.999998 | − | 0.00203732i | \(-0.999352\pi\) |
−0.501763 | − | 0.865005i | \(-0.667315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 73.3725 | + | 127.085i | 0.312224 | + | 0.540787i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 257.204i | − | 1.07617i | −0.842892 | − | 0.538083i | \(-0.819149\pi\) | ||
0.842892 | − | 0.538083i | \(-0.180851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −124.808 | − | 216.173i | −0.517875 | − | 0.896985i | −0.999784 | − | 0.0207645i | \(-0.993390\pi\) |
0.481910 | − | 0.876221i | \(-0.339943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −162.790 | + | 281.960i | −0.659067 | + | 1.14154i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 69.2909i | 0.276059i | 0.990428 | + | 0.138030i | \(0.0440769\pi\) | ||||
−0.990428 | + | 0.138030i | \(0.955923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6640 | 0.0579606 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −221.592 | − | 127.936i | −0.862227 | − | 0.497807i | 0.00253044 | − | 0.999997i | \(-0.499195\pi\) |
−0.864757 | + | 0.502190i | \(0.832528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7037 | − | 7.33449i | 0.0483031 | − | 0.0278878i | −0.475654 | − | 0.879632i | \(-0.657789\pi\) |
0.523957 | + | 0.851745i | \(0.324455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 240.620 | 0.907998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −64.9339 | + | 37.4896i | −0.241390 | + | 0.139367i | −0.615815 | − | 0.787890i | \(-0.711173\pi\) |
0.374425 | + | 0.927257i | \(0.377840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 105.601 | − | 182.907i | 0.389673 | − | 0.674933i | −0.602733 | − | 0.797943i | \(-0.705921\pi\) |
0.992405 | + | 0.123010i | \(0.0392548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.32027 | − | 4.80371i | −0.0302555 | − | 0.0174680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −204.247 | − | 353.766i | −0.737354 | − | 1.27713i | −0.953683 | − | 0.300814i | \(-0.902742\pi\) |
0.216329 | − | 0.976321i | \(-0.430592\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 200.395i | 0.713149i | 0.934267 | + | 0.356575i | \(0.116055\pi\) | ||||
−0.934267 | + | 0.356575i | \(0.883945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −179.225 | − | 310.426i | −0.633303 | − | 1.09691i | −0.986872 | − | 0.161505i | \(-0.948365\pi\) |
0.353569 | − | 0.935409i | \(-0.384968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.04249 | − | 8.73384i | 0.0174481 | − | 0.0302209i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 325.352i | 1.11042i | 0.831711 | + | 0.555209i | \(0.187362\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 415.911 | 1.40987 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.3296 | + | 15.2014i | 0.0880589 | + | 0.0508408i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 280.001 | − | 161.658i | 0.918035 | − | 0.530028i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −338.037 | −1.10110 | −0.550548 | − | 0.834803i | \(-0.685581\pi\) | ||||
−0.550548 | + | 0.834803i | \(0.685581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.489 | − | 155.589i | 0.866523 | − | 0.500287i | 0.000331809 | − | 1.00000i | \(-0.499894\pi\) |
0.866191 | + | 0.499713i | \(0.166561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −200.535 | + | 347.336i | −0.640686 | + | 1.10970i | 0.344594 | + | 0.938752i | \(0.388016\pi\) |
−0.985280 | + | 0.170948i | \(0.945317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 72.8747 | + | 42.0742i | 0.229889 | + | 0.132726i | 0.610521 | − | 0.792000i | \(-0.290960\pi\) |
−0.380632 | + | 0.924727i | \(0.624294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 169.332 | + | 293.292i | 0.530821 | + | 0.919410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 447.476i | 1.38537i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.95948 | − | 17.2503i | −0.0306446 | − | 0.0530779i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 111.749 | − | 193.555i | 0.337610 | − | 0.584758i | −0.646372 | − | 0.763022i | \(-0.723715\pi\) |
0.983983 | + | 0.178264i | \(0.0570481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 598.499i | − | 1.78656i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −234.583 | −0.696092 | −0.348046 | − | 0.937477i | \(-0.613155\pi\) | ||||
−0.348046 | + | 0.937477i | \(0.613155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 80.3721 | + | 46.4028i | 0.235695 | + | 0.136079i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −72.4136 | + | 41.8080i | −0.208685 | + | 0.120484i | −0.600700 | − | 0.799474i | \(-0.705111\pi\) |
0.392015 | + | 0.919959i | \(0.371778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 298.959 | 0.856617 | 0.428309 | − | 0.903632i | \(-0.359110\pi\) | ||||
0.428309 | + | 0.903632i | \(0.359110\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 370.704 | − | 214.026i | 1.05015 | − | 0.606306i | 0.127460 | − | 0.991844i | \(-0.459317\pi\) |
0.922692 | + | 0.385538i | \(0.125984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −128.354 | + | 222.316i | −0.361561 | + | 0.626242i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 125.172 | + | 72.2681i | 0.348669 | + | 0.201304i | 0.664099 | − | 0.747645i | \(-0.268815\pi\) |
−0.315430 | + | 0.948949i | \(0.602149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −154.245 | − | 267.160i | −0.427272 | − | 0.740056i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 158.329i | − | 0.433778i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 305.122 | + | 528.486i | 0.831394 | + | 1.44002i | 0.896933 | + | 0.442166i | \(0.145790\pi\) |
−0.0655391 | + | 0.997850i | \(0.520877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.166010 | + | 0.287539i | −0.000445068 | + | 0.000770881i | −0.866248 | − | 0.499615i | \(-0.833475\pi\) |
0.865803 | + | 0.500385i | \(0.166808\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 702.149i | 1.86246i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −393.652 | −1.03866 | −0.519330 | − | 0.854574i | \(-0.673818\pi\) | ||||
−0.519330 | + | 0.854574i | \(0.673818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −468.259 | − | 270.350i | −1.22261 | − | 0.705874i | −0.257135 | − | 0.966375i | \(-0.582779\pi\) |
−0.965473 | + | 0.260502i | \(0.916112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −410.840 | + | 237.199i | −1.05614 | + | 0.609765i | −0.924363 | − | 0.381513i | \(-0.875403\pi\) |
−0.131781 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.7856 | 0.106869 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −637.011 | + | 367.779i | −1.61269 | + | 0.931085i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −200.144 | + | 346.659i | −0.504141 | + | 0.873197i | 0.495848 | + | 0.868409i | \(0.334857\pi\) |
−0.999989 | + | 0.00478767i | \(0.998476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 563.839 | + | 325.533i | 1.40608 | + | 0.811802i | 0.995008 | − | 0.0997999i | \(-0.0318203\pi\) |
0.411075 | + | 0.911602i | \(0.365154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 96.2065 | + | 166.635i | 0.238726 | + | 0.413485i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 144.135i | 0.354140i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 94.5568 | + | 163.777i | 0.231190 | + | 0.400433i | 0.958159 | − | 0.286238i | \(-0.0924047\pi\) |
−0.726968 | + | 0.686671i | \(0.759071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73.6680 | + | 127.597i | −0.177513 | + | 0.307462i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 829.772i | − | 1.98036i | −0.139791 | − | 0.990181i | \(-0.544643\pi\) | ||
0.139791 | − | 0.990181i | \(-0.455357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −226.324 | −0.537587 | −0.268794 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268794 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.7088 | − | 13.6883i | −0.0557855 | − | 0.0322078i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −377.985 | + | 218.230i | −0.876996 | + | 0.506334i | −0.869667 | − | 0.493640i | \(-0.835666\pi\) |
−0.00732893 | + | 0.999973i | \(0.502333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 404.243 | 0.933587 | 0.466793 | − | 0.884366i | \(-0.345409\pi\) | ||||
0.466793 | + | 0.884366i | \(0.345409\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54.1417 | + | 31.2587i | −0.123894 | + | 0.0715303i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 91.4091 | − | 158.325i | 0.208221 | − | 0.360650i | −0.742933 | − | 0.669366i | \(-0.766566\pi\) |
0.951154 | + | 0.308716i | \(0.0998993\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −286.838 | − | 165.606i | −0.647491 | − | 0.373829i | 0.140003 | − | 0.990151i | \(-0.455289\pi\) |
−0.787494 | + | 0.616322i | \(0.788622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 433.616 | + | 751.044i | 0.974417 | + | 1.68774i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.8425i | − | 0.0286025i | −0.999898 | − | 0.0143013i | \(-0.995448\pi\) | ||
0.999898 | − | 0.0143013i | \(-0.00455239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.9373 | + | 81.2977i | 0.104074 | + | 0.180261i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 155.336 | − | 269.050i | 0.339904 | − | 0.588730i | −0.644511 | − | 0.764595i | \(-0.722939\pi\) |
0.984414 | + | 0.175865i | \(0.0562722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 389.770i | 0.845489i | 0.906249 | + | 0.422744i | \(0.138933\pi\) | ||||
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 152.081 | 0.328469 | 0.164234 | − | 0.986421i | \(-0.447485\pi\) | ||||
0.164234 | + | 0.986421i | \(0.447485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −75.2298 | − | 43.4339i | −0.161092 | − | 0.0930063i | 0.417287 | − | 0.908775i | \(-0.362981\pi\) |
−0.578379 | + | 0.815768i | \(0.696314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −145.849 | + | 84.2058i | −0.308348 | + | 0.178025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.9595 | 0.0862305 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −476.005 | + | 274.821i | −0.993747 | + | 0.573740i | −0.906392 | − | 0.422437i | \(-0.861175\pi\) |
−0.0873545 | + | 0.996177i | \(0.527841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −149.417 | + | 258.798i | −0.310638 | + | 0.538041i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 508.825 | + | 293.770i | 1.04912 | + | 0.605711i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 345.373 | + | 598.203i | 0.709184 | + | 1.22834i | 0.965160 | + | 0.261659i | \(0.0842697\pi\) |
−0.255976 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 732.380i | 1.49161i | 0.666165 | + | 0.745804i | \(0.267934\pi\) | ||||
−0.666165 | + | 0.745804i | \(0.732066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 482.516 | + | 835.743i | 0.978735 | + | 1.69522i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 227.203 | − | 393.526i | 0.455316 | − | 0.788630i | −0.543390 | − | 0.839480i | \(-0.682860\pi\) |
0.998706 | + | 0.0508499i | \(0.0161930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 304.594i | − | 0.605554i | −0.953061 | − | 0.302777i | \(-0.902086\pi\) | ||
0.953061 | − | 0.302777i | \(-0.0979138\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 207.660 | 0.411208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 64.2102 | + | 37.0718i | 0.126150 | + | 0.0728326i | 0.561747 | − | 0.827309i | \(-0.310129\pi\) |
−0.435597 | + | 0.900142i | \(0.643463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −130.031 | + | 75.0735i | −0.252488 | + | 0.145774i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −172.737 | −0.334115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 185.772 | − | 107.256i | 0.356568 | − | 0.205865i | −0.311006 | − | 0.950408i | \(-0.600666\pi\) |
0.667574 | + | 0.744543i | \(0.267333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −466.243 | + | 807.557i | −0.891478 | + | 1.54409i | −0.0533746 | + | 0.998575i | \(0.516998\pi\) |
−0.838104 | + | 0.545511i | \(0.816336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 229.022 | + | 132.226i | 0.434578 | + | 0.250904i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −261.581 | − | 453.072i | −0.494482 | − | 0.856468i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 194.629i | 0.365158i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −468.929 | − | 812.210i | −0.876504 | − | 1.51815i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 93.1699 | − | 161.375i | 0.172218 | − | 0.298290i | −0.766977 | − | 0.641675i | \(-0.778240\pi\) |
0.939195 | + | 0.343384i | \(0.111573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 454.552i | 0.834041i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 792.170 | 1.44821 | 0.724104 | − | 0.689691i | \(-0.242253\pi\) | ||||
0.724104 | + | 0.689691i | \(0.242253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1250.40 | − | 721.916i | −2.26932 | − | 1.31019i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −346.087 | + | 199.814i | −0.621342 | + | 0.358732i | −0.777391 | − | 0.629017i | \(-0.783457\pi\) |
0.156050 | + | 0.987749i | \(0.450124\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −349.166 | −0.624626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −302.571 | + | 174.690i | −0.537427 | + | 0.310283i | −0.744035 | − | 0.668140i | \(-0.767091\pi\) |
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 167.099 | − | 289.425i | 0.295751 | − | 0.512256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 654.163 | + | 377.681i | 1.14967 | + | 0.663763i | 0.948807 | − | 0.315856i | \(-0.102292\pi\) |
0.200864 | + | 0.979619i | \(0.435625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.5751 | − | 82.4025i | −0.0833190 | − | 0.144313i | 0.821355 | − | 0.570418i | \(-0.193219\pi\) |
−0.904674 | + | 0.426105i | \(0.859885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.82483i | − | 0.00665187i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −378.033 | − | 654.772i | −0.655169 | − | 1.13479i | −0.981851 | − | 0.189652i | \(-0.939264\pi\) |
0.326682 | − | 0.945134i | \(-0.394069\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −141.620 | + | 245.292i | −0.242915 | + | 0.420742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 688.642i | 1.17316i | 0.809893 | + | 0.586578i | \(0.199525\pi\) | ||||
−0.809893 | + | 0.586578i | \(0.800475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −395.660 | −0.671749 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −879.890 | − | 508.005i | −1.48379 | − | 0.856669i | −0.483964 | − | 0.875088i | \(-0.660804\pi\) |
−0.999830 | + | 0.0184184i | \(0.994137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −511.180 | + | 295.130i | −0.853388 | + | 0.492704i | −0.861793 | − | 0.507261i | \(-0.830658\pi\) |
0.00840423 | + | 0.999965i | \(0.497325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 300.761 | 0.500434 | 0.250217 | − | 0.968190i | \(-0.419498\pi\) | ||||
0.250217 | + | 0.968190i | \(0.419498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −375.811 | + | 216.975i | −0.621175 | + | 0.358636i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −348.207 | + | 603.111i | −0.573652 | + | 0.993594i | 0.422535 | + | 0.906347i | \(0.361140\pi\) |
−0.996187 | + | 0.0872472i | \(0.972193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −310.153 | − | 179.067i | −0.507616 | − | 0.293072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −278.697 | − | 482.717i | −0.454644 | − | 0.787466i | 0.544024 | − | 0.839070i | \(-0.316900\pi\) |
−0.998668 | + | 0.0516035i | \(0.983567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 91.9868i | − | 0.149087i | −0.997218 | − | 0.0745436i | \(-0.976250\pi\) | ||
0.997218 | − | 0.0745436i | \(-0.0237500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 558.708 | + | 967.712i | 0.902599 | + | 1.56335i | 0.824109 | + | 0.566432i | \(0.191676\pi\) |
0.0784898 | + | 0.996915i | \(0.474990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 331.035 | − | 573.369i | 0.529655 | − | 0.917390i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 410.717i | 0.652969i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 962.219 | 1.52491 | 0.762456 | − | 0.647040i | \(-0.223993\pi\) | ||||
0.762456 | + | 0.647040i | \(0.223993\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −998.306 | − | 576.372i | −1.57214 | − | 0.907673i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 194.373 | − | 112.221i | 0.303233 | − | 0.175072i | −0.340661 | − | 0.940186i | \(-0.610651\pi\) |
0.643895 | + | 0.765114i | \(0.277318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −332.384 | −0.516927 | −0.258464 | − | 0.966021i | \(-0.583216\pi\) | ||||
−0.258464 | + | 0.966021i | \(0.583216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 788.563 | − | 455.277i | 1.21880 | − | 0.703674i | 0.254138 | − | 0.967168i | \(-0.418208\pi\) |
0.964661 | + | 0.263494i | \(0.0848750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −244.790 | + | 423.988i | −0.377180 | + | 0.653294i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −128.435 | − | 74.1519i | −0.196684 | − | 0.113556i | 0.398424 | − | 0.917202i | \(-0.369557\pi\) |
−0.595108 | + | 0.803646i | \(0.702891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 534.405 | + | 925.617i | 0.815886 | + | 1.41316i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.5636i | 0.0691405i | 0.999402 | + | 0.0345703i | \(0.0110063\pi\) | ||||
−0.999402 | + | 0.0345703i | \(0.988994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −202.107 | − | 350.060i | −0.305760 | − | 0.529591i | 0.671670 | − | 0.740850i | \(-0.265577\pi\) |
−0.977430 | + | 0.211259i | \(0.932244\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −67.4131 | + | 116.763i | −0.101069 | + | 0.175057i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 380.584i | 0.567190i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1016.49 | 1.51038 | 0.755190 | − | 0.655506i | \(-0.227544\pi\) | ||||
0.755190 | + | 0.655506i | \(0.227544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −201.391 | − | 116.273i | −0.297476 | − | 0.171748i | 0.343832 | − | 0.939031i | \(-0.388275\pi\) |
−0.641308 | + | 0.767283i | \(0.721608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 102.403 | − | 59.1224i | 0.149931 | − | 0.0865628i | −0.423158 | − | 0.906056i | \(-0.639078\pi\) |
0.573089 | + | 0.819493i | \(0.305745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 906.272 | 1.32302 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −508.562 | + | 293.618i | −0.738116 | + | 0.426152i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1255 | + | 41.7866i | −0.0349139 | + | 0.0604726i | −0.882954 | − | 0.469459i | \(-0.844449\pi\) |
0.848040 | + | 0.529931i | \(0.177782\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −523.160 | − | 302.046i | −0.752748 | − | 0.434599i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 133.749 | + | 231.660i | 0.191892 | + | 0.332367i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 236.466i | − | 0.337326i | −0.985674 | − | 0.168663i | \(-0.946055\pi\) | ||
0.985674 | − | 0.168663i | \(-0.0539450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −307.247 | − | 532.167i | −0.437051 | − | 0.756995i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 670.988 | − | 1162.19i | 0.946387 | − | 1.63919i | 0.193436 | − | 0.981113i | \(-0.438037\pi\) |
0.752951 | − | 0.658077i | \(-0.228630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.9470i | 0.0518191i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 393.741 | 0.550687 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −246.486 | − | 142.309i | −0.342818 | − | 0.197926i | 0.318700 | − | 0.947856i | \(-0.396754\pi\) |
−0.661517 | + | 0.749930i | \(0.730087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 76.4993 | − | 44.1669i | 0.105516 | − | 0.0609199i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 430.450 | 0.592090 | 0.296045 | − | 0.955174i | \(-0.404332\pi\) | ||||
0.296045 | + | 0.955174i | \(0.404332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −415.600 | + | 239.947i | −0.568536 | + | 0.328245i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 193.907 | − | 335.857i | 0.264539 | − | 0.458195i | −0.702904 | − | 0.711285i | \(-0.748114\pi\) |
0.967443 | + | 0.253090i | \(0.0814468\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 610.121 | + | 352.254i | 0.827845 | + | 0.477956i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −176.454 | − | 305.627i | −0.238773 | − | 0.413568i | 0.721589 | − | 0.692322i | \(-0.243412\pi\) |
−0.960363 | + | 0.278754i | \(0.910079\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1068.60i | 1.43822i | 0.694897 | + | 0.719109i | \(0.255450\pi\) | ||||
−0.694897 | + | 0.719109i | \(0.744550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 480.310 | + | 831.921i | 0.644711 | + | 1.11667i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −612.073 | + | 1060.14i | −0.815011 | + | 1.41164i | 0.0943092 | + | 0.995543i | \(0.469936\pi\) |
−0.909320 | + | 0.416097i | \(0.863398\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 938.786i | − | 1.24343i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −96.3399 | −0.127265 | −0.0636327 | − | 0.997973i | \(-0.520269\pi\) | ||||
−0.0636327 | + | 0.997973i | \(0.520269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 821.762 | + | 474.445i | 1.07985 | + | 0.623449i | 0.930855 | − | 0.365390i | \(-0.119064\pi\) |
0.148990 | + | 0.988839i | \(0.452398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −879.050 | + | 507.520i | −1.14609 | + | 0.661694i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −998.633 | −1.29861 | −0.649306 | − | 0.760527i | \(-0.724941\pi\) | ||||
−0.649306 | + | 0.760527i | \(0.724941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −74.8855 | + | 43.2352i | −0.0968765 | + | 0.0559317i | −0.547656 | − | 0.836704i | \(-0.684480\pi\) |
0.450779 | + | 0.892636i | \(0.351146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1033 | − | 20.9635i | 0.0156171 | − | 0.0270496i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −346.598 | − | 200.108i | −0.444927 | − | 0.256879i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −151.089 | − | 261.694i | −0.193456 | − | 0.335075i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 352.540i | − | 0.449096i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 244.907 | + | 424.192i | 0.311191 | + | 0.538998i | 0.978620 | − | 0.205675i | \(-0.0659388\pi\) |
−0.667430 | + | 0.744673i | \(0.732606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −394.531 | + | 683.347i | −0.497517 | + | 0.861724i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 500.193i | 0.627595i | 0.949490 | + | 0.313798i | \(0.101601\pi\) | ||||
−0.949490 | + | 0.313798i | \(0.898399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −492.219 | −0.616044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 161.404 | + | 93.1865i | 0.201001 | + | 0.116048i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −268.914 | + | 155.257i | −0.332403 | + | 0.191913i | −0.656907 | − | 0.753971i | \(-0.728136\pi\) |
0.324505 | + | 0.945884i | \(0.394802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.9190 | −0.0566202 | −0.0283101 | − | 0.999599i | \(-0.509013\pi\) | ||||
−0.0283101 | + | 0.999599i | \(0.509013\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 164.071 | − | 94.7264i | 0.201314 | − | 0.116229i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 358.996 | − | 621.799i | 0.439408 | − | 0.761076i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1046.73 | + | 604.330i | 1.27495 | + | 0.736091i | 0.975915 | − | 0.218153i | \(-0.0700030\pi\) |
0.299032 | + | 0.954243i | \(0.403336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 59.5909 | + | 103.214i | 0.0724069 | + | 0.125412i | 0.899956 | − | 0.435981i | \(-0.143599\pi\) |
−0.827549 | + | 0.561394i | \(0.810265\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 872.026i | 1.05445i | 0.849727 | + | 0.527223i | \(0.176767\pi\) | ||||
−0.849727 | + | 0.527223i | \(0.823233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −368.911 | − | 638.973i | −0.445007 | − | 0.770775i | 0.553045 | − | 0.833151i | \(-0.313466\pi\) |
−0.998053 | + | 0.0623758i | \(0.980132\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 620.531 | − | 1074.79i | 0.743151 | − | 1.28717i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 896.131i | − | 1.06809i | −0.845455 | − | 0.534047i | \(-0.820671\pi\) | ||
0.845455 | − | 0.534047i | \(-0.179329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2272.79 | −2.70249 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.6338 | − | 27.5014i | −0.0563713 | − | 0.0325460i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.6942 | + | 28.6910i | −0.0583950 | + | 0.0337144i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 311.875 | 0.365621 | 0.182810 | − | 0.983148i | \(-0.441481\pi\) | ||||
0.182810 | + | 0.983148i | \(0.441481\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 312.540 | − | 180.445i | 0.364691 | − | 0.210555i | −0.306445 | − | 0.951888i | \(-0.599140\pi\) |
0.671137 | + | 0.741334i | \(0.265806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −605.549 | + | 1048.84i | −0.704946 | + | 1.22100i | 0.261764 | + | 0.965132i | \(0.415696\pi\) |
−0.966711 | + | 0.255871i | \(0.917638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 442.972 | + | 255.750i | 0.513293 | + | 0.296350i | 0.734186 | − | 0.678948i | \(-0.237564\pi\) |
−0.220893 | + | 0.975298i | \(0.570897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 879.150 | + | 1522.73i | 1.01636 | + | 1.76038i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 865.843i | − | 0.996367i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 730.324 | + | 1264.96i | 0.838489 | + | 1.45231i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −67.2954 | + | 116.559i | −0.0767337 | + | 0.132907i | −0.901839 | − | 0.432072i | \(-0.857782\pi\) |
0.825105 | + | 0.564979i | \(0.191116\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 405.447i | 0.460212i | 0.973166 | + | 0.230106i | \(0.0739073\pi\) | ||||
−0.973166 | + | 0.230106i | \(0.926093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −552.235 | −0.625408 | −0.312704 | − | 0.949851i | \(-0.601235\pi\) | ||||
−0.312704 | + | 0.949851i | \(0.601235\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1042.69 | + | 602.000i | 1.17553 | + | 0.678692i | 0.954976 | − | 0.296682i | \(-0.0958803\pi\) |
0.220554 | + | 0.975375i | \(0.429214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 637.770 | − | 368.217i | 0.714188 | − | 0.412337i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −713.624 | −0.797345 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −738.968 | + | 426.643i | −0.821989 | + | 0.474575i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −403.549 | + | 698.967i | −0.447890 | + | 0.775768i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −604.255 | − | 348.867i | −0.667686 | − | 0.385488i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −660.207 | − | 1143.51i | −0.727901 | − | 1.26076i | −0.957769 | − | 0.287540i | \(-0.907163\pi\) |
0.229867 | − | 0.973222i | \(-0.426171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 965.020i | − | 1.05930i | −0.848217 | − | 0.529649i | \(-0.822324\pi\) | ||
0.848217 | − | 0.529649i | \(-0.177676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86.7164 | − | 150.197i | −0.0949796 | − | 0.164509i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −360.044 | + | 623.615i | −0.391779 | + | 0.678580i | −0.992684 | − | 0.120740i | \(-0.961473\pi\) |
0.600906 | + | 0.799320i | \(0.294807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 626.502i | − | 0.678767i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.5948 | 0.0406430 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 806.867 | + | 465.845i | 0.868532 | + | 0.501447i | 0.866860 | − | 0.498551i | \(-0.166134\pi\) |
0.00167220 | + | 0.999999i | \(0.499468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 468.656 | − | 270.579i | 0.501237 | − | 0.289389i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1370.97 | 1.46315 | 0.731575 | − | 0.681760i | \(-0.238785\pi\) | ||||
0.731575 | + | 0.681760i | \(0.238785\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 197.008 | − | 113.743i | 0.209360 | − | 0.120874i | −0.391654 | − | 0.920113i | \(-0.628097\pi\) |
0.601014 | + | 0.799239i | \(0.294764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.6863 | + | 32.3656i | −0.0198158 | + | 0.0343219i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 570.662 | + | 329.472i | 0.602600 | + | 0.347911i | 0.770064 | − | 0.637967i | \(-0.220224\pi\) |
−0.167464 | + | 0.985878i | \(0.553558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 193.203 | + | 334.637i | 0.203585 | + | 0.352620i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 217.669i | − | 0.228404i | −0.993458 | − | 0.114202i | \(-0.963569\pi\) | ||
0.993458 | − | 0.114202i | \(-0.0364311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −434.302 | − | 752.233i | −0.454766 | − | 0.787679i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 363.585 | − | 629.748i | 0.378340 | − | 0.655305i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 739.857i | − | 0.766692i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1018.75 | −1.05352 | −0.526760 | − | 0.850014i | \(-0.676593\pi\) | ||||
−0.526760 | + | 0.850014i | \(0.676593\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 353.812 | + | 204.273i | 0.364379 | + | 0.210374i | 0.671000 | − | 0.741457i | \(-0.265865\pi\) |
−0.306621 | + | 0.951832i | \(0.599198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 391.760 | − | 226.183i | 0.400982 | − | 0.231507i | −0.285925 | − | 0.958252i | \(-0.592301\pi\) |
0.686908 | + | 0.726745i | \(0.258968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1020.84 | −1.04274 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1500.44 | − | 866.281i | 1.52639 | − | 0.881262i | 0.526881 | − | 0.849939i | \(-0.323361\pi\) |
0.999509 | − | 0.0313233i | \(-0.00997213\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 764.383 | − | 1323.95i | 0.776023 | − | 1.34411i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.0641 | − | 33.5233i | −0.0587099 | − | 0.0338962i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −197.373 | − | 341.859i | −0.199165 | − | 0.344964i | 0.749093 | − | 0.662465i | \(-0.230490\pi\) |
−0.948258 | + | 0.317501i | \(0.897156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 733.387i | 0.737072i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −82.6745 | − | 143.196i | −0.0829232 | − | 0.143627i | 0.821581 | − | 0.570092i | \(-0.193092\pi\) |
−0.904504 | + | 0.426464i | \(0.859759\pi\) | |||||||
\(998\) | 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 | 1764.3.bk.d.1745.4 | 8 | ||
3.2 | odd | 2 | inner | 1764.3.bk.d.1745.1 | 8 | ||
7.2 | even | 3 | 252.3.c.a.197.1 | ✓ | 4 | ||
7.3 | odd | 6 | 1764.3.bk.e.557.4 | 8 | |||
7.4 | even | 3 | inner | 1764.3.bk.d.557.1 | 8 | ||
7.5 | odd | 6 | 1764.3.c.f.197.4 | 4 | |||
7.6 | odd | 2 | 1764.3.bk.e.1745.1 | 8 | |||
21.2 | odd | 6 | 252.3.c.a.197.4 | yes | 4 | ||
21.5 | even | 6 | 1764.3.c.f.197.1 | 4 | |||
21.11 | odd | 6 | inner | 1764.3.bk.d.557.4 | 8 | ||
21.17 | even | 6 | 1764.3.bk.e.557.1 | 8 | |||
21.20 | even | 2 | 1764.3.bk.e.1745.4 | 8 | |||
28.23 | odd | 6 | 1008.3.d.c.449.1 | 4 | |||
56.37 | even | 6 | 4032.3.d.h.449.4 | 4 | |||
56.51 | odd | 6 | 4032.3.d.e.449.4 | 4 | |||
63.2 | odd | 6 | 2268.3.bg.c.701.1 | 8 | |||
63.16 | even | 3 | 2268.3.bg.c.701.4 | 8 | |||
63.23 | odd | 6 | 2268.3.bg.c.2213.4 | 8 | |||
63.58 | even | 3 | 2268.3.bg.c.2213.1 | 8 | |||
84.23 | even | 6 | 1008.3.d.c.449.4 | 4 | |||
168.107 | even | 6 | 4032.3.d.e.449.1 | 4 | |||
168.149 | odd | 6 | 4032.3.d.h.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.3.c.a.197.1 | ✓ | 4 | 7.2 | even | 3 | ||
252.3.c.a.197.4 | yes | 4 | 21.2 | odd | 6 | ||
1008.3.d.c.449.1 | 4 | 28.23 | odd | 6 | |||
1008.3.d.c.449.4 | 4 | 84.23 | even | 6 | |||
1764.3.c.f.197.1 | 4 | 21.5 | even | 6 | |||
1764.3.c.f.197.4 | 4 | 7.5 | odd | 6 | |||
1764.3.bk.d.557.1 | 8 | 7.4 | even | 3 | inner | ||
1764.3.bk.d.557.4 | 8 | 21.11 | odd | 6 | inner | ||
1764.3.bk.d.1745.1 | 8 | 3.2 | odd | 2 | inner | ||
1764.3.bk.d.1745.4 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.bk.e.557.1 | 8 | 21.17 | even | 6 | |||
1764.3.bk.e.557.4 | 8 | 7.3 | odd | 6 | |||
1764.3.bk.e.1745.1 | 8 | 7.6 | odd | 2 | |||
1764.3.bk.e.1745.4 | 8 | 21.20 | even | 2 | |||
2268.3.bg.c.701.1 | 8 | 63.2 | odd | 6 | |||
2268.3.bg.c.701.4 | 8 | 63.16 | even | 3 | |||
2268.3.bg.c.2213.1 | 8 | 63.58 | even | 3 | |||
2268.3.bg.c.2213.4 | 8 | 63.23 | odd | 6 | |||
4032.3.d.e.449.1 | 4 | 168.107 | even | 6 | |||
4032.3.d.e.449.4 | 4 | 56.51 | odd | 6 | |||
4032.3.d.h.449.1 | 4 | 168.149 | odd | 6 | |||
4032.3.d.h.449.4 | 4 | 56.37 | even | 6 |