Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.2 | ||
Root | \(1.38255 - 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.b.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.737922 | − | 2.90783i | 0.245974 | − | 0.969276i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.57472 | − | 1.57472i | 0.314944 | − | 0.314944i | −0.531877 | − | 0.846821i | \(-0.678513\pi\) |
0.846821 | + | 0.531877i | \(0.178513\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64575i | 0.520822i | 0.965498 | + | 0.260411i | \(0.0838580\pi\) | ||||
−0.965498 | + | 0.260411i | \(0.916142\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.91094 | − | 4.29150i | −0.878994 | − | 0.476834i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.19038 | + | 1.19038i | −0.108216 | + | 0.108216i | −0.759142 | − | 0.650926i | \(-0.774381\pi\) |
0.650926 | + | 0.759142i | \(0.274381\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.6458 | − | 14.6458i | 1.12660 | − | 1.12660i | 0.135870 | − | 0.990727i | \(-0.456617\pi\) |
0.990727 | − | 0.135870i | \(-0.0433828\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41699 | − | 5.74103i | −0.227800 | − | 0.382736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 28.0726i | − | 1.65133i | −0.564159 | − | 0.825666i | \(-0.690800\pi\) | ||
0.564159 | − | 0.825666i | \(-0.309200\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.5830 | − | 12.5830i | 0.662263 | − | 0.662263i | −0.293650 | − | 0.955913i | \(-0.594870\pi\) |
0.955913 | + | 0.293650i | \(0.0948699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.6012 | + | 2.69028i | 0.504820 | + | 0.128109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −29.2630 | −1.27231 | −0.636153 | − | 0.771563i | \(-0.719475\pi\) | ||||
−0.636153 | + | 0.771563i | \(0.719475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.0405i | 0.801621i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.3166 | + | 19.8369i | −0.678393 | + | 0.734699i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19.3557 | − | 19.3557i | −0.667437 | − | 0.667437i | 0.289685 | − | 0.957122i | \(-0.406449\pi\) |
−0.957122 | + | 0.289685i | \(0.906449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.6458 | −0.375669 | −0.187835 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187835 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.58301 | + | 4.33981i | 0.0782729 | + | 0.131510i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.74103 | + | 5.74103i | 0.164030 | + | 0.164030i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.771243 | − | 0.771243i | −0.0208444 | − | 0.0208444i | 0.696608 | − | 0.717452i | \(-0.254692\pi\) |
−0.717452 | + | 0.696608i | \(0.754692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −31.7799 | − | 53.3948i | −0.814870 | − | 1.36910i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 25.6919 | 0.626631 | 0.313316 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313316 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −40.5830 | − | 40.5830i | −0.943791 | − | 0.943791i | 0.0547114 | − | 0.998502i | \(-0.482576\pi\) |
−0.998502 | + | 0.0547114i | \(0.982576\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19.2154 | + | 5.69960i | −0.427009 | + | 0.126658i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 50.2681i | 1.06953i | 0.845000 | + | 0.534767i | \(0.179601\pi\) | ||||
−0.845000 | + | 0.534767i | \(0.820399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.7085 | 0.728745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −81.6304 | − | 20.7154i | −1.60060 | − | 0.406185i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.2379 | − | 46.2379i | 0.872414 | − | 0.872414i | −0.120321 | − | 0.992735i | \(-0.538392\pi\) |
0.992735 | + | 0.120321i | \(0.0383925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.74902i | 0.0681639i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.3040 | − | 45.8745i | −0.479017 | − | 0.804816i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −22.7533 | + | 22.7533i | −0.385649 | + | 0.385649i | −0.873132 | − | 0.487483i | \(-0.837915\pi\) |
0.487483 | + | 0.873132i | \(0.337915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7712 | + | 12.7712i | −0.209365 | + | 0.209365i | −0.803997 | − | 0.594633i | \(-0.797297\pi\) |
0.594633 | + | 0.803997i | \(0.297297\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.6458 | − | 28.8413i | 0.248345 | − | 0.457799i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 46.1259i | − | 0.709629i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6863 | − | 10.6863i | 0.159497 | − | 0.159497i | −0.622847 | − | 0.782344i | \(-0.714024\pi\) |
0.782344 | + | 0.622847i | \(0.214024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.5938 | + | 85.0919i | −0.312954 | + | 1.23322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 122.086 | 1.71952 | 0.859760 | − | 0.510699i | \(-0.170613\pi\) | ||||
0.859760 | + | 0.510699i | \(0.170613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.0405i | − | 0.206034i | −0.994680 | − | 0.103017i | \(-0.967150\pi\) | ||
0.994680 | − | 0.103017i | \(-0.0328497\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 58.2744 | + | 14.7883i | 0.776992 | + | 0.197178i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.33981 | − | 4.33981i | −0.0563612 | − | 0.0563612i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.3948 | 0.650567 | 0.325283 | − | 0.945617i | \(-0.394540\pi\) | ||||
0.325283 | + | 0.945617i | \(0.394540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 44.1660 | + | 67.8997i | 0.545259 | + | 0.838267i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37.8680 | + | 37.8680i | 0.456240 | + | 0.456240i | 0.897419 | − | 0.441179i | \(-0.145440\pi\) |
−0.441179 | + | 0.897419i | \(0.645440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44.2065 | − | 44.2065i | −0.520077 | − | 0.520077i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −70.5659 | + | 42.0000i | −0.811103 | + | 0.482759i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.45550 | −0.0612977 | −0.0306489 | − | 0.999530i | \(-0.509757\pi\) | ||||
−0.0306489 | + | 0.999530i | \(0.509757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 53.3948 | + | 53.3948i | 0.586756 | + | 0.586756i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.59366 | + | 33.8639i | −0.0924049 | + | 0.364127i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 39.6294i | − | 0.417152i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −81.1660 | −0.836763 | −0.418381 | − | 0.908271i | \(-0.637402\pi\) | ||||
−0.418381 | + | 0.908271i | \(0.637402\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.5255 | − | 4.30849i | 0.146722 | − | 0.0435201i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 32.4498 | − | 32.4498i | 0.321285 | − | 0.321285i | −0.527975 | − | 0.849260i | \(-0.677048\pi\) |
0.849260 | + | 0.527975i | \(0.177048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 51.1882i | 0.496973i | 0.968635 | + | 0.248487i | \(0.0799332\pi\) | ||||
−0.968635 | + | 0.248487i | \(0.920067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.9304 | − | 12.4575i | 0.199337 | − | 0.118643i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 85.4698 | − | 85.4698i | 0.798783 | − | 0.798783i | −0.184121 | − | 0.982904i | \(-0.558944\pi\) |
0.982904 | + | 0.184121i | \(0.0589438\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 52.8523 | − | 52.8523i | 0.484883 | − | 0.484883i | −0.421804 | − | 0.906687i | \(-0.638603\pi\) |
0.906687 | + | 0.421804i | \(0.138603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81176 | + | 1.67353i | −0.0253312 | + | 0.0150768i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 73.5045i | 0.650483i | 0.945631 | + | 0.325241i | \(0.105446\pi\) | ||||
−0.945631 | + | 0.325241i | \(0.894554\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −46.0810 | + | 46.0810i | −0.400705 | + | 0.400705i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −178.714 | + | 53.0094i | −1.52747 | + | 0.453072i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 102.346 | 0.860049 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 118.166i | 0.976579i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.9586 | − | 74.7076i | 0.154135 | − | 0.607379i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 70.9262 | + | 70.9262i | 0.567409 | + | 0.567409i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −73.9333 | −0.582152 | −0.291076 | − | 0.956700i | \(-0.594013\pi\) | ||||
−0.291076 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −147.956 | + | 88.0614i | −1.14694 | + | 0.682646i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 158.430 | + | 158.430i | 1.20939 | + | 1.20939i | 0.971226 | + | 0.238161i | \(0.0765447\pi\) |
0.238161 | + | 0.971226i | \(0.423455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 45.8745 | + | 45.8745i | 0.344921 | + | 0.344921i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.39398 | + | 60.0810i | 0.0177332 | + | 0.445045i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 100.734 | 0.735283 | 0.367642 | − | 0.929968i | \(-0.380165\pi\) | ||||
0.367642 | + | 0.929968i | \(0.380165\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.2732 | + | 18.2732i | 0.131462 | + | 0.131462i | 0.769776 | − | 0.638314i | \(-0.220368\pi\) |
−0.638314 | + | 0.769776i | \(0.720368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 146.171 | + | 37.0939i | 1.03667 | + | 0.263078i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34.8679i | 0.243831i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −60.9595 | −0.420410 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.3501 | − | 103.834i | 0.179252 | − | 0.706355i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 44.9729 | − | 44.9729i | 0.301831 | − | 0.301831i | −0.539899 | − | 0.841730i | \(-0.681537\pi\) |
0.841730 | + | 0.539899i | \(0.181537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 28.1033i | 0.186114i | 0.995661 | + | 0.0930572i | \(0.0296639\pi\) | ||||
−0.995661 | + | 0.0930572i | \(0.970336\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −120.474 | + | 222.081i | −0.787411 | + | 1.45151i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.3388 | + | 18.3388i | −0.118315 | + | 0.118315i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −173.265 | + | 173.265i | −1.10360 | + | 1.10360i | −0.109628 | + | 0.993973i | \(0.534966\pi\) |
−0.993973 | + | 0.109628i | \(0.965034\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −100.332 | − | 168.572i | −0.631019 | − | 1.06020i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 106.686i | − | 0.662644i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 51.9190 | − | 51.9190i | 0.318521 | − | 0.318521i | −0.529678 | − | 0.848199i | \(-0.677687\pi\) |
0.848199 | + | 0.529678i | \(0.177687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9015 | + | 2.76648i | 0.0660697 | + | 0.0167666i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 57.5333 | 0.344511 | 0.172255 | − | 0.985052i | \(-0.444895\pi\) | ||||
0.172255 | + | 0.985052i | \(0.444895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 259.996i | − | 1.53844i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −153.543 | + | 45.5434i | −0.897915 | + | 0.266336i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 112.600 | + | 112.600i | 0.650868 | + | 0.650868i | 0.953202 | − | 0.302334i | \(-0.0977657\pi\) |
−0.302334 | + | 0.953202i | \(0.597766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −73.0627 | −0.417501 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 49.3725 | + | 82.9529i | 0.278941 | + | 0.468660i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.4810 | − | 22.4810i | −0.125592 | − | 0.125592i | 0.641517 | − | 0.767109i | \(-0.278305\pi\) |
−0.767109 | + | 0.641517i | \(0.778305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6013 | + | 18.6013i | 0.102770 | + | 0.102770i | 0.756622 | − | 0.653852i | \(-0.226848\pi\) |
−0.653852 | + | 0.756622i | \(0.726848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.7124 | + | 46.5608i | 0.151434 | + | 0.254430i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42898 | −0.0131296 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.4170 | + | 33.4170i | 0.178701 | + | 0.178701i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −72.3203 | − | 66.7778i | −0.382647 | − | 0.353322i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 191.672i | 1.00352i | 0.865007 | + | 0.501760i | \(0.167314\pi\) | ||||
−0.865007 | + | 0.501760i | \(0.832686\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 48.6275 | 0.251956 | 0.125978 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125978 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −134.126 | − | 34.0373i | −0.687827 | − | 0.174550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −136.258 | + | 136.258i | −0.691667 | + | 0.691667i | −0.962599 | − | 0.270932i | \(-0.912668\pi\) |
0.270932 | + | 0.962599i | \(0.412668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 144.767i | − | 0.727474i | −0.931502 | − | 0.363737i | \(-0.881501\pi\) | ||
0.931502 | − | 0.363737i | \(-0.118499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.1882 | − | 38.9595i | −0.115364 | − | 0.193828i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 70.5659 | − | 70.5659i | 0.347615 | − | 0.347615i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.4575 | − | 40.4575i | 0.197354 | − | 0.197354i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 231.498 | + | 125.582i | 1.11835 | + | 0.606678i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.9570i | 0.143335i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −196.354 | + | 196.354i | −0.930589 | + | 0.930589i | −0.997743 | − | 0.0671538i | \(-0.978608\pi\) |
0.0671538 | + | 0.997743i | \(0.478608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 90.0899 | − | 355.005i | 0.422957 | − | 1.66669i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −127.814 | −0.594482 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 42.4575i | − | 0.195657i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43.7353 | − | 11.0987i | −0.199704 | − | 0.0506791i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −411.145 | − | 411.145i | −1.86038 | − | 1.86038i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 375.261 | 1.68279 | 0.841393 | − | 0.540423i | \(-0.181736\pi\) | ||||
0.841393 | + | 0.540423i | \(0.181736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 86.0039 | − | 158.539i | 0.382240 | − | 0.704619i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −181.108 | − | 181.108i | −0.797834 | − | 0.797834i | 0.184920 | − | 0.982754i | \(-0.440797\pi\) |
−0.982754 | + | 0.184920i | \(0.940797\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 153.937 | + | 153.937i | 0.672215 | + | 0.672215i | 0.958226 | − | 0.286011i | \(-0.0923295\pi\) |
−0.286011 | + | 0.958226i | \(0.592329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.8219 | + | 9.41699i | −0.0684930 | + | 0.0407662i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 51.7790 | 0.222228 | 0.111114 | − | 0.993808i | \(-0.464558\pi\) | ||||
0.111114 | + | 0.993808i | \(0.464558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.1581 | + | 79.1581i | 0.336843 | + | 0.336843i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.9253 | − | 149.447i | 0.160022 | − | 0.630579i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 249.900i | − | 1.04560i | −0.852454 | − | 0.522802i | \(-0.824887\pi\) | ||
0.852454 | − | 0.522802i | \(-0.175113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 442.531 | 1.83623 | 0.918113 | − | 0.396318i | \(-0.129712\pi\) | ||||
0.918113 | + | 0.396318i | \(0.129712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 230.032 | − | 78.3226i | 0.946632 | − | 0.322315i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 56.2309 | − | 56.2309i | 0.229514 | − | 0.229514i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 368.575i | − | 1.49221i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 138.057 | − | 82.1699i | 0.554446 | − | 0.330000i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −43.3235 | + | 43.3235i | −0.172603 | + | 0.172603i | −0.788122 | − | 0.615519i | \(-0.788947\pi\) |
0.615519 | + | 0.788122i | \(0.288947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.8340 | − | 34.8340i | 0.137684 | − | 0.137684i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −161.166 | + | 95.9241i | −0.632024 | + | 0.376173i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 179.197i | − | 0.697266i | −0.937259 | − | 0.348633i | \(-0.886646\pi\) | ||
0.937259 | − | 0.348633i | \(-0.113354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.81176 | − | 2.81176i | 0.0108562 | − | 0.0108562i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 70.0567 | + | 236.186i | 0.268416 | + | 0.904929i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −419.478 | −1.59497 | −0.797486 | − | 0.603338i | \(-0.793837\pi\) | ||||
−0.797486 | + | 0.603338i | \(0.793837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 145.624i | − | 0.549523i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.02573 | + | 15.8637i | −0.0150777 | + | 0.0594145i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 33.7631 | + | 33.7631i | 0.125513 | + | 0.125513i | 0.767073 | − | 0.641560i | \(-0.221712\pi\) |
−0.641560 | + | 0.767073i | \(0.721712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −329.269 | −1.21502 | −0.607508 | − | 0.794314i | \(-0.707831\pi\) | ||||
−0.607508 | + | 0.794314i | \(0.707831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 194.664 | − | 115.862i | 0.713055 | − | 0.424402i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.8557 | − | 23.8557i | −0.0867482 | − | 0.0867482i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −251.265 | − | 251.265i | −0.907095 | − | 0.907095i | 0.0889417 | − | 0.996037i | \(-0.471652\pi\) |
−0.996037 | + | 0.0889417i | \(0.971652\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 92.1289 | + | 49.9778i | 0.330211 | + | 0.179132i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −171.809 | −0.611421 | −0.305711 | − | 0.952124i | \(-0.598894\pi\) | ||||
−0.305711 | + | 0.952124i | \(0.598894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −193.476 | − | 193.476i | −0.683660 | − | 0.683660i | 0.277163 | − | 0.960823i | \(-0.410606\pi\) |
−0.960823 | + | 0.277163i | \(0.910606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −115.236 | − | 29.2434i | −0.404335 | − | 0.102608i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 93.6662i | 0.326363i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −499.073 | −1.72690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −59.8942 | + | 236.017i | −0.205822 | + | 0.811055i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 73.4937 | − | 73.4937i | 0.250832 | − | 0.250832i | −0.570480 | − | 0.821312i | \(-0.693243\pi\) |
0.821312 | + | 0.570480i | \(0.193243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 71.6601i | 0.242916i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.80968 | − | 45.4170i | −0.00609320 | − | 0.152919i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −428.579 | + | 428.579i | −1.43337 | + | 1.43337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 147.956 | − | 147.956i | 0.491547 | − | 0.491547i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −70.4131 | − | 118.304i | −0.232386 | − | 0.390442i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 40.2222i | 0.131876i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 283.055 | − | 283.055i | 0.922003 | − | 0.922003i | −0.0751680 | − | 0.997171i | \(-0.523949\pi\) |
0.997171 | + | 0.0751680i | \(0.0239493\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 148.847 | + | 37.7729i | 0.481704 | + | 0.122242i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −54.0368 | −0.173752 | −0.0868759 | − | 0.996219i | \(-0.527688\pi\) | ||||
−0.0868759 | + | 0.996219i | \(0.527688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 490.280i | 1.56639i | 0.621777 | + | 0.783194i | \(0.286411\pi\) | ||||
−0.621777 | + | 0.783194i | \(0.713589\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.7793 | − | 70.0547i | −0.0659661 | − | 0.222396i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 319.550 | + | 319.550i | 1.00804 | + | 1.00804i | 0.999967 | + | 0.00807607i | \(0.00257072\pi\) |
0.00807607 | + | 0.999967i | \(0.497429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.0810 | 0.144455 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −185.461 | − | 311.601i | −0.577762 | − | 0.970721i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −353.238 | − | 353.238i | −1.09362 | − | 1.09362i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 293.508 | + | 293.508i | 0.903103 | + | 0.903103i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −114.685 | − | 192.686i | −0.350717 | − | 0.589255i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −183.265 | −0.557036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −269.431 | − | 269.431i | −0.813992 | − | 0.813992i | 0.171238 | − | 0.985230i | \(-0.445223\pi\) |
−0.985230 | + | 0.171238i | \(0.945223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.79147 | + | 9.41106i | 0.00838279 | + | 0.0282614i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 33.6557i | − | 0.100465i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 143.041 | 0.424453 | 0.212226 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212226 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 213.739 | + | 54.2406i | 0.630497 | + | 0.160002i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8628 | − | 13.8628i | 0.0406534 | − | 0.0406534i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 308.826i | 0.900368i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 99.9916 | + | 168.000i | 0.289831 | + | 0.486957i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 126.922 | − | 126.922i | 0.365770 | − | 0.365770i | −0.500162 | − | 0.865932i | \(-0.666726\pi\) |
0.865932 | + | 0.500162i | \(0.166726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −195.893 | + | 195.893i | −0.561297 | + | 0.561297i | −0.929676 | − | 0.368378i | \(-0.879913\pi\) |
0.368378 | + | 0.929676i | \(0.379913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.2653 | + | 558.787i | 0.0634340 | + | 1.59198i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 291.488i | 0.825745i | 0.910789 | + | 0.412873i | \(0.135475\pi\) | ||||
−0.910789 | + | 0.412873i | \(0.864525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 192.251 | − | 192.251i | 0.541552 | − | 0.541552i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 75.5233 | − | 297.604i | 0.211550 | − | 0.833626i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 40.3499 | 0.112395 | 0.0561976 | − | 0.998420i | \(-0.482102\pi\) | ||||
0.0561976 | + | 0.998420i | \(0.482102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.3360i | 0.122814i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 343.607 | + | 87.1973i | 0.946575 | + | 0.240213i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.6846 | − | 23.6846i | −0.0648893 | − | 0.0648893i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −340.678 | −0.928279 | −0.464140 | − | 0.885762i | \(-0.653636\pi\) | ||||
−0.464140 | + | 0.885762i | \(0.653636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −203.247 | − | 110.257i | −0.550805 | − | 0.298799i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 168.572 | + | 168.572i | 0.454372 | + | 0.454372i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −237.678 | − | 237.678i | −0.637207 | − | 0.637207i | 0.312658 | − | 0.949866i | \(-0.398781\pi\) |
−0.949866 | + | 0.312658i | \(0.898781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 258.579 | − | 153.903i | 0.689544 | − | 0.410409i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −566.957 | −1.50386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 320.332 | + | 320.332i | 0.845203 | + | 0.845203i | 0.989530 | − | 0.144327i | \(-0.0461017\pi\) |
−0.144327 | + | 0.989530i | \(0.546102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54.5570 | + | 214.985i | −0.143194 | + | 0.564266i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 632.700i | − | 1.65196i | −0.563702 | − | 0.825978i | \(-0.690623\pi\) | ||
0.563702 | − | 0.825978i | \(-0.309377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6680 | −0.0355012 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 146.888 | + | 495.212i | 0.379555 | + | 1.27962i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −424.351 | + | 424.351i | −1.09088 | + | 1.09088i | −0.0954418 | + | 0.995435i | \(0.530426\pi\) |
−0.995435 | + | 0.0954418i | \(0.969574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 821.490i | 2.10100i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 577.595 | − | 343.778i | 1.46971 | − | 0.874752i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 80.9323 | − | 80.9323i | 0.204892 | − | 0.204892i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 445.678 | − | 445.678i | 1.12262 | − | 1.12262i | 0.131269 | − | 0.991347i | \(-0.458095\pi\) |
0.991347 | − | 0.131269i | \(-0.0419051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 167.247 | − | 99.5434i | 0.419166 | − | 0.249482i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 555.896i | 1.38627i | 0.720806 | + | 0.693137i | \(0.243772\pi\) | ||||
−0.720806 | + | 0.693137i | \(0.756228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −170.561 | + | 170.561i | −0.423228 | + | 0.423228i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 176.472 | + | 37.3738i | 0.435733 | + | 0.0922811i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.83614 | 0.00451140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 44.8261i | 0.109599i | 0.998497 | + | 0.0547997i | \(0.0174520\pi\) | ||||
−0.998497 | + | 0.0547997i | \(0.982548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 74.3337 | − | 292.917i | 0.180861 | − | 0.712693i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −82.9529 | − | 82.9529i | −0.200854 | − | 0.200854i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 119.263 | 0.287380 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 66.6196 | − | 39.6512i | 0.159759 | − | 0.0950868i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2026 | − | 15.2026i | −0.0362830 | − | 0.0362830i | 0.688733 | − | 0.725016i | \(-0.258167\pi\) |
−0.725016 | + | 0.688733i | \(0.758167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −262.889 | − | 262.889i | −0.624439 | − | 0.624439i | 0.322224 | − | 0.946663i | \(-0.395569\pi\) |
−0.946663 | + | 0.322224i | \(0.895569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 215.726 | − | 397.668i | 0.509990 | − | 0.940113i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 562.590 | 1.32374 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −46.5608 | − | 46.5608i | −0.109042 | − | 0.109042i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 101.390 | + | 25.7298i | 0.236340 | + | 0.0599762i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 163.103i | − | 0.378430i | −0.981936 | − | 0.189215i | \(-0.939406\pi\) | ||
0.981936 | − | 0.189215i | \(-0.0605943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −140.737 | −0.325028 | −0.162514 | − | 0.986706i | \(-0.551960\pi\) | ||||
−0.162514 | + | 0.986706i | \(0.551960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −44.9833 | + | 177.260i | −0.103410 | + | 0.407494i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −368.217 | + | 368.217i | −0.842601 | + | 0.842601i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 434.893i | − | 0.990644i | −0.868709 | − | 0.495322i | \(-0.835050\pi\) | ||
0.868709 | − | 0.495322i | \(-0.164950\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −282.488 | − | 153.243i | −0.640562 | − | 0.347490i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 260.367 | − | 260.367i | 0.587736 | − | 0.587736i | −0.349282 | − | 0.937018i | \(-0.613574\pi\) |
0.937018 | + | 0.349282i | \(0.113574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.59088 | + | 8.59088i | −0.0193053 | + | 0.0193053i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −97.5869 | − | 163.960i | −0.218315 | − | 0.366801i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 98.9506i | 0.220380i | 0.993911 | + | 0.110190i | \(0.0351459\pi\) | ||||
−0.993911 | + | 0.110190i | \(0.964854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.5830 | + | 30.5830i | −0.0678115 | + | 0.0678115i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 81.7195 | + | 20.7380i | 0.180396 | + | 0.0457793i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 168.164 | 0.369590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.4209i | 0.0315556i | 0.999876 | + | 0.0157778i | \(0.00502245\pi\) | ||||
−0.999876 | + | 0.0157778i | \(0.994978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 556.873 | + | 514.196i | 1.21323 | + | 1.12025i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 328.278 | + | 328.278i | 0.712099 | + | 0.712099i | 0.966974 | − | 0.254875i | \(-0.0820343\pi\) |
−0.254875 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 848.427 | 1.83246 | 0.916228 | − | 0.400657i | \(-0.131218\pi\) | ||||
0.916228 | + | 0.400657i | \(0.131218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 39.7935 | + | 66.8587i | 0.0855774 | + | 0.143782i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −56.0706 | − | 56.0706i | −0.120066 | − | 0.120066i | 0.644521 | − | 0.764587i | \(-0.277057\pi\) |
−0.764587 | + | 0.644521i | \(0.777057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.9595 | + | 38.9595i | 0.0830693 | + | 0.0830693i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 375.970 | + | 631.682i | 0.798237 | + | 1.34115i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 96.6181 | 0.204267 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 252.170 | + | 252.170i | 0.530884 | + | 0.530884i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −564.216 | + | 167.355i | −1.18284 | + | 0.350850i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 648.794i | 1.35448i | 0.735764 | + | 0.677238i | \(0.236823\pi\) | ||||
−0.735764 | + | 0.677238i | \(0.763177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5909 | −0.0469665 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −310.224 | − | 78.7257i | −0.642285 | − | 0.162993i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −127.814 | + | 127.814i | −0.263533 | + | 0.263533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 176.783i | 0.363004i | 0.983391 | + | 0.181502i | \(0.0580959\pi\) | ||||
−0.983391 | + | 0.181502i | \(0.941904\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −112.659 | − | 189.284i | −0.230387 | − | 0.387083i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 317.369 | − | 317.369i | 0.646373 | − | 0.646373i | −0.305742 | − | 0.952114i | \(-0.598904\pi\) |
0.952114 | + | 0.305742i | \(0.0989044\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −543.365 | + | 543.365i | −1.10216 | + | 1.10216i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0889 | − | 29.6582i | 0.0325029 | − | 0.0599156i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 445.095i | 0.895563i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −374.391 | + | 374.391i | −0.750282 | + | 0.750282i | −0.974532 | − | 0.224250i | \(-0.928007\pi\) |
0.224250 | + | 0.974532i | \(0.428007\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.4551 | − | 167.297i | 0.0847407 | − | 0.333926i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 386.094 | 0.767583 | 0.383791 | − | 0.923420i | \(-0.374618\pi\) | ||||
0.383791 | + | 0.923420i | \(0.374618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 102.199i | − | 0.202374i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −756.024 | − | 191.857i | −1.49117 | − | 0.378416i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.6258 | + | 41.6258i | 0.0817796 | + | 0.0817796i | 0.746813 | − | 0.665034i | \(-0.231583\pi\) |
−0.665034 | + | 0.746813i | \(0.731583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.8340 | 0.107307 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.1294 | + | 480.086i | 0.0372893 | + | 0.935839i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 80.6071 | + | 80.6071i | 0.156519 | + | 0.156519i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −59.8379 | − | 59.8379i | −0.115741 | − | 0.115741i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 410.512 | − | 244.332i | 0.790968 | − | 0.470775i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −233.704 | −0.448569 | −0.224284 | − | 0.974524i | \(-0.572004\pi\) | ||||
−0.224284 | + | 0.974524i | \(0.572004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −219.506 | − | 219.506i | −0.419705 | − | 0.419705i | 0.465397 | − | 0.885102i | \(-0.345912\pi\) |
−0.885102 | + | 0.465397i | \(0.845912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −53.9146 | + | 212.454i | −0.102694 | + | 0.404674i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 326.927i | 0.620355i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 327.324 | 0.618760 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 277.646 | − | 82.3542i | 0.522873 | − | 0.155093i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 376.277 | − | 376.277i | 0.705961 | − | 0.705961i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 269.182i | − | 0.503143i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −81.9601 | + | 48.7817i | −0.152626 | + | 0.0908411i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −42.5065 | + | 42.5065i | −0.0788618 | + | 0.0788618i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −80.5203 | + | 80.5203i | −0.148836 | + | 0.148836i | −0.777598 | − | 0.628762i | \(-0.783562\pi\) |
0.628762 | + | 0.777598i | \(0.283562\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 67.8157 | − | 40.3631i | 0.124891 | − | 0.0743335i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 166.455i | − | 0.305422i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49803 | − | 1.49803i | 0.00273863 | − | 0.00273863i | −0.705736 | − | 0.708475i | \(-0.749384\pi\) |
0.708475 | + | 0.705736i | \(0.249384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 155.840 | − | 46.2247i | 0.283862 | − | 0.0841981i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −487.105 | −0.884038 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 187.373i | 0.338829i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.79240 | + | 7.06307i | −0.00322955 | + | 0.0127263i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −322.326 | − | 322.326i | −0.578682 | − | 0.578682i | 0.355858 | − | 0.934540i | \(-0.384189\pi\) |
−0.934540 | + | 0.355858i | \(0.884189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1188.74 | −2.12654 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 121.830 | − | 72.5118i | 0.217166 | − | 0.129255i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −523.954 | − | 523.954i | −0.930646 | − | 0.930646i | 0.0671003 | − | 0.997746i | \(-0.478625\pi\) |
−0.997746 | + | 0.0671003i | \(0.978625\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 115.749 | + | 115.749i | 0.204866 | + | 0.204866i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −247.545 | + | 161.018i | −0.436588 | + | 0.283983i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 767.880 | 1.34952 | 0.674762 | − | 0.738035i | \(-0.264246\pi\) | ||||
0.674762 | + | 0.738035i | \(0.264246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.43922 | − | 3.43922i | −0.00602316 | − | 0.00602316i | 0.704089 | − | 0.710112i | \(-0.251356\pi\) |
−0.710112 | + | 0.704089i | \(0.751356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 557.350 | + | 141.439i | 0.972688 | + | 0.246840i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 586.446i | − | 1.01991i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −572.442 | −0.992100 | −0.496050 | − | 0.868294i | \(-0.665217\pi\) | ||||
−0.496050 | + | 0.868294i | \(0.665217\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.8833 | − | 141.400i | 0.0619746 | − | 0.244215i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −138.057 | + | 138.057i | −0.237620 | + | 0.237620i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 110.081i | 0.188818i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −197.949 | + | 364.899i | −0.338375 | + | 0.623759i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −446.694 | + | 446.694i | −0.760977 | + | 0.760977i | −0.976499 | − | 0.215522i | \(-0.930855\pi\) |
0.215522 | + | 0.976499i | \(0.430855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −146.539 | + | 146.539i | −0.248792 | + | 0.248792i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 295.668 | + | 496.764i | 0.500284 | + | 0.840548i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 838.112i | − | 1.41334i | −0.707542 | − | 0.706671i | \(-0.750196\pi\) | ||
0.707542 | − | 0.706671i | \(-0.249804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 161.166 | − | 161.166i | 0.270867 | − | 0.270867i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −420.959 | − | 106.827i | −0.705123 | − | 0.178940i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −414.241 | −0.691555 | −0.345777 | − | 0.938317i | \(-0.612385\pi\) | ||||
−0.345777 | + | 0.938317i | \(0.612385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 305.786i | − | 0.508795i | −0.967100 | − | 0.254397i | \(-0.918123\pi\) | ||
0.967100 | − | 0.254397i | \(-0.0818771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −130.399 | + | 38.6783i | −0.216250 | + | 0.0641431i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 186.078 | + | 186.078i | 0.307567 | + | 0.307567i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 103.217 | 0.170044 | 0.0850222 | − | 0.996379i | \(-0.472904\pi\) | ||||
0.0850222 | + | 0.996379i | \(0.472904\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −153.122 | − | 257.266i | −0.251431 | − | 0.422440i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 736.214 | + | 736.214i | 1.20493 | + | 1.20493i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 391.273 | + | 391.273i | 0.638292 | + | 0.638292i | 0.950134 | − | 0.311842i | \(-0.100946\pi\) |
−0.311842 | + | 0.950134i | \(0.600946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −87.7891 | − | 147.498i | −0.142746 | − | 0.239834i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −713.373 | −1.15620 | −0.578098 | − | 0.815967i | \(-0.696205\pi\) | ||||
−0.578098 | + | 0.815967i | \(0.696205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −399.763 | − | 399.763i | −0.645821 | − | 0.645821i | 0.306159 | − | 0.951980i | \(-0.400956\pi\) |
−0.951980 | + | 0.306159i | \(0.900956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 535.999 | − | 580.487i | 0.863123 | − | 0.934761i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 19.8894i | − | 0.0319252i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −277.635 | −0.444217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 87.1099 | + | 22.1059i | 0.138931 | + | 0.0352567i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.6508 | + | 21.6508i | −0.0344210 | + | 0.0344210i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 934.242i | − | 1.48057i | −0.672291 | − | 0.740287i | \(-0.734690\pi\) | ||
0.672291 | − | 0.740287i | \(-0.265310\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 426.071 | + | 715.859i | 0.673097 | + | 1.13090i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −116.424 | + | 116.424i | −0.183345 | + | 0.183345i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 522.978 | − | 522.978i | 0.821001 | − | 0.821001i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −965.814 | − | 523.932i | −1.51145 | − | 0.819925i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 26.1836i | − | 0.0408480i | −0.999791 | − | 0.0204240i | \(-0.993498\pi\) | ||
0.999791 | − | 0.0204240i | \(-0.00650162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 625.336 | − | 625.336i | 0.972529 | − | 0.972529i | −0.0271039 | − | 0.999633i | \(-0.508629\pi\) |
0.999633 | + | 0.0271039i | \(0.00862850\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −94.3165 | + | 371.660i | −0.146227 | + | 0.576218i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −97.2591 | −0.150323 | −0.0751616 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751616 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 54.1699i | − | 0.0834668i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −123.459 | − | 31.3303i | −0.189645 | − | 0.0481265i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −129.213 | − | 129.213i | −0.197875 | − | 0.197875i | 0.601213 | − | 0.799089i | \(-0.294684\pi\) |
−0.799089 | + | 0.601213i | \(0.794684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 498.965 | 0.761778 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −64.5464 | + | 118.985i | −0.0982442 | + | 0.181103i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.10975 | + | 3.10975i | 0.00471889 | + | 0.00471889i | 0.709462 | − | 0.704743i | \(-0.248938\pi\) |
−0.704743 | + | 0.709462i | \(0.748938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3424 | + | 22.3424i | 0.0338010 | + | 0.0338010i | 0.723805 | − | 0.690004i | \(-0.242391\pi\) |
−0.690004 | + | 0.723805i | \(0.742391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1498.93 | + | 892.146i | −2.26083 | + | 1.34562i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 144.479 | 0.217262 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 566.405 | + | 566.405i | 0.849183 | + | 0.849183i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 276.914 | − | 1091.20i | 0.413922 | − | 1.63109i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 30.4052i | − | 0.0453132i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1085.74 | 1.61329 | 0.806643 | − | 0.591039i | \(-0.201282\pi\) | ||||
0.806643 | + | 0.591039i | \(0.201282\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −397.541 | − | 367.074i | −0.588950 | − | 0.543814i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 813.520 | − | 813.520i | 1.20165 | − | 1.20165i | 0.227991 | − | 0.973663i | \(-0.426784\pi\) |
0.973663 | − | 0.227991i | \(-0.0732157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 295.911i | − | 0.435804i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −660.276 | + | 392.988i | −0.969568 | + | 0.577075i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 427.362 | − | 427.362i | 0.625713 | − | 0.625713i | −0.321273 | − | 0.946986i | \(-0.604111\pi\) |
0.946986 | + | 0.321273i | \(0.104111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 158.627 | − | 158.627i | 0.231573 | − | 0.231573i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 561.217 | − | 334.030i | 0.816910 | − | 0.486215i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1354.38i | − | 1.96572i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −420.170 | + | 420.170i | −0.608061 | + | 0.608061i | −0.942439 | − | 0.334378i | \(-0.891474\pi\) |
0.334378 | + | 0.942439i | \(0.391474\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.7077 | + | 52.9563i | 0.0226662 | + | 0.0764161i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 57.5504 | 0.0828063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 721.239i | − | 1.03478i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.2089 | − | 150.565i | 0.0546622 | − | 0.215400i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −774.018 | − | 774.018i | −1.10416 | − | 1.10416i | −0.993903 | − | 0.110260i | \(-0.964832\pi\) |
−0.110260 | − | 0.993903i | \(-0.535168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.4091 | −0.0276090 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 288.591 | − | 171.766i | 0.409349 | − | 0.243639i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 118.304 | + | 118.304i | 0.167332 | + | 0.167332i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −198.261 | − | 198.261i | −0.279635 | − | 0.279635i | 0.553328 | − | 0.832963i | \(-0.313358\pi\) |
−0.832963 | + | 0.553328i | \(0.813358\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −406.581 | − | 220.561i | −0.571844 | − | 0.310212i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 340.790 | 0.477966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 54.9072 | + | 54.9072i | 0.0767932 | + | 0.0767932i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −726.665 | − | 184.406i | −1.01348 | − | 0.257192i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 639.218i | 0.889037i | 0.895770 | + | 0.444519i | \(0.146625\pi\) | ||||
−0.895770 | + | 0.444519i | \(0.853375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −186.620 | −0.258834 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 326.553 | − | 1286.80i | 0.451664 | − | 1.77981i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 387.898 | − | 387.898i | 0.535031 | − | 0.535031i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 789.136i | 1.08547i | 0.839904 | + | 0.542734i | \(0.182611\pi\) | ||||
−0.839904 | + | 0.542734i | \(0.817389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −58.0032 | − | 726.689i | −0.0795654 | − | 0.996830i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1139.27 | + | 1139.27i | −1.55851 | + | 1.55851i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.8641 | − | 49.8641i | 0.0680274 | − | 0.0680274i | −0.672275 | − | 0.740302i | \(-0.734683\pi\) |
0.740302 | + | 0.672275i | \(0.234683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −122.016 | − | 205.004i | −0.166008 | − | 0.278917i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.4414i | 0.0345202i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 157.593 | − | 157.593i | 0.213252 | − | 0.213252i | −0.592395 | − | 0.805647i | \(-0.701818\pi\) |
0.805647 | + | 0.592395i | \(0.201818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1071.75 | − | 271.980i | −1.44636 | − | 0.367044i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1305.03 | 1.75643 | 0.878216 | − | 0.478265i | \(-0.158734\pi\) | ||||
0.878216 | + | 0.478265i | \(0.158734\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 141.639i | − | 0.190120i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −137.061 | − | 462.082i | −0.183482 | − | 0.618583i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 311.601 | + | 311.601i | 0.416023 | + | 0.416023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −793.800 | −1.05699 | −0.528495 | − | 0.848936i | \(-0.677244\pi\) | ||||
−0.528495 | + | 0.848936i | \(0.677244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 94.0079 | + | 157.947i | 0.124844 | + | 0.209756i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.2548 | + | 44.2548i | 0.0586156 | + | 0.0586156i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 750.497 | + | 750.497i | 0.991409 | + | 0.991409i | 0.999963 | − | 0.00855438i | \(-0.00272298\pi\) |
−0.00855438 | + | 0.999963i | \(0.502723\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −75.5865 | − | 126.996i | −0.0995870 | − | 0.167320i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1055.45 | −1.38692 | −0.693462 | − | 0.720493i | \(-0.743916\pi\) | ||||
−0.693462 | + | 0.720493i | \(0.743916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 192.686 | + | 192.686i | 0.252538 | + | 0.252538i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 160.003 | + | 539.428i | 0.209154 | + | 0.705134i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 666.478i | 0.868942i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 883.681 | 1.14913 | 0.574565 | − | 0.818459i | \(-0.305171\pi\) | ||||
0.574565 | + | 0.818459i | \(0.305171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −521.076 | − | 132.234i | −0.675844 | − | 0.171509i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 894.518 | − | 894.518i | 1.15720 | − | 1.15720i | 0.172129 | − | 0.985074i | \(-0.444935\pi\) |
0.985074 | − | 0.172129i | \(-0.0550647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 233.387i | − | 0.301144i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.10126 | − | 10.2510i | −0.00785233 | − | 0.0131930i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 323.281 | − | 323.281i | 0.414995 | − | 0.414995i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −145.328 | + | 145.328i | −0.186079 | + | 0.186079i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 738.486 | − | 29.4256i | 0.943150 | − | 0.0375806i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 545.689i | 0.695145i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −779.150 | + | 779.150i | −0.990026 | + | 0.990026i | −0.999951 | − | 0.00992500i | \(-0.996841\pi\) |
0.00992500 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −309.542 | + | 1219.77i | −0.392322 | + | 1.54597i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −267.979 | −0.338785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 374.089i | 0.471739i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −423.448 | − | 107.459i | −0.532639 | − | 0.135168i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 149.801 | + | 149.801i | 0.187956 | + | 0.187956i | 0.794812 | − | 0.606856i | \(-0.207570\pi\) |
−0.606856 | + | 0.794812i | \(0.707570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1411.16 | 1.76616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43.1581 | + | 23.4123i | 0.0538803 | + | 0.0292288i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.9039 | + | 17.9039i | 0.0222962 | + | 0.0222962i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −168.000 | − | 168.000i | −0.208696 | − | 0.208696i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 123.092 | − | 73.2628i | 0.152530 | − | 0.0907841i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 373.773 | 0.462019 | 0.231009 | − | 0.972951i | \(-0.425797\pi\) | ||||
0.231009 | + | 0.972951i | \(0.425797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −239.150 | − | 239.150i | −0.294883 | − | 0.294883i | 0.544123 | − | 0.839006i | \(-0.316863\pi\) |
−0.839006 | + | 0.544123i | \(0.816863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −242.975 | + | 957.459i | −0.298862 | + | 1.17769i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 163.516i | − | 0.200633i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1021.31 | −1.25008 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −193.259 | − | 651.547i | −0.235970 | − | 0.795539i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −385.069 | + | 385.069i | −0.469024 | + | 0.469024i | −0.901598 | − | 0.432574i | \(-0.857605\pi\) |
0.432574 | + | 0.901598i | \(0.357605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1270.78i | − | 1.54408i | −0.635576 | − | 0.772038i | \(-0.719237\pi\) | ||
0.635576 | − | 0.772038i | \(-0.280763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −86.9721 | + | 51.7648i | −0.105421 | + | 0.0627452i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 113.766 | − | 113.766i | 0.137565 | − | 0.137565i | −0.634971 | − | 0.772536i | \(-0.718988\pi\) |
0.772536 | + | 0.634971i | \(0.218988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −238.593 | + | 238.593i | −0.287809 | + | 0.287809i | −0.836213 | − | 0.548404i | \(-0.815235\pi\) |
0.548404 | + | 0.836213i | \(0.315235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −916.051 | + | 545.222i | −1.10235 | + | 0.656104i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1002.43i | − | 1.20340i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 90.5988 | − | 90.5988i | 0.108502 | − | 0.108502i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 213.311 | − | 231.015i | 0.254852 | − | 0.276004i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −65.2466 | −0.0777671 | −0.0388836 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388836 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 91.7164i | − | 0.109056i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −126.782 | + | 499.592i | −0.150394 | + | 0.592636i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −409.421 | − | 409.421i | −0.484522 | − | 0.484522i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −430.804 | −0.508623 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −705.365 | + | 419.825i | −0.830818 | + | 0.494493i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.5689 | + | 22.5689i | 0.0265205 | + | 0.0265205i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 245.067 | + | 245.067i | 0.287300 | + | 0.287300i | 0.836012 | − | 0.548712i | \(-0.184882\pi\) |
−0.548712 | + | 0.836012i | \(0.684882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −170.070 | + | 313.506i | −0.198912 | + | 0.366674i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1408.63 | 1.64368 | 0.821841 | − | 0.569718i | \(-0.192947\pi\) | ||||
0.821841 | + | 0.569718i | \(0.192947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.1621 | − | 50.1621i | −0.0583959 | − | 0.0583959i | 0.677306 | − | 0.735702i | \(-0.263147\pi\) |
−0.735702 | + | 0.677306i | \(0.763147\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 272.365 | + | 69.1184i | 0.316336 | + | 0.0802769i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1027.80i | − | 1.19096i | −0.803370 | − | 0.595480i | \(-0.796962\pi\) | ||
0.803370 | − | 0.595480i | \(-0.203038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 354.627 | 0.409974 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −368.277 | + | 1451.22i | −0.424772 | + | 1.67384i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.1791 | + | 61.1791i | −0.0704017 | + | 0.0704017i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 313.017i | − | 0.359376i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 642.100 | + | 348.324i | 0.735509 | + | 0.398997i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −258.579 | + | 258.579i | −0.295519 | + | 0.295519i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −600.071 | + | 600.071i | −0.684231 | + | 0.684231i | −0.960951 | − | 0.276720i | \(-0.910753\pi\) |
0.276720 | + | 0.960951i | \(0.410753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −159.474 | − | 267.940i | −0.181427 | − | 0.304823i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 786.482i | 0.892715i | 0.894855 | + | 0.446358i | \(0.147279\pi\) | ||||
−0.894855 | + | 0.446358i | \(0.852721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −390.413 | + | 390.413i | −0.442144 | + | 0.442144i | −0.892732 | − | 0.450588i | \(-0.851214\pi\) |
0.450588 | + | 0.892732i | \(0.351214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 208.375 | + | 52.8796i | 0.235452 | + | 0.0597509i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1446.61 | 1.63090 | 0.815450 | − | 0.578827i | \(-0.196489\pi\) | ||||
0.815450 | + | 0.578827i | \(0.196489\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 269.542i | − | 0.303197i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −133.400 | − | 28.2520i | −0.149720 | − | 0.0317081i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 632.524 | + | 632.524i | 0.708313 | + | 0.708313i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −70.8025 | −0.0791089 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 929.976 | + | 1562.49i | 1.03676 | + | 1.74191i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 225.411 | + | 225.411i | 0.250736 | + | 0.250736i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1298.02 | − | 1298.02i | −1.44064 | − | 1.44064i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −321.050 | − | 539.409i | −0.355537 | − | 0.597352i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 58.5836 | 0.0647333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −535.919 | − | 535.919i | −0.590870 | − | 0.590870i | 0.346997 | − | 0.937866i | \(-0.387202\pi\) |
−0.937866 | + | 0.346997i | \(0.887202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −395.967 | + | 117.450i | −0.435607 | + | 0.129208i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1580.22i | 1.73460i | 0.497786 | + | 0.867300i | \(0.334146\pi\) | ||||
−0.497786 | + | 0.867300i | \(0.665854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −90.1542 | −0.0987450 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 116.959 | + | 29.6809i | 0.127825 | + | 0.0324381i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −577.595 | + | 577.595i | −0.629875 | + | 0.629875i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1486.86i | 1.61791i | 0.587869 | + | 0.808956i | \(0.299967\pi\) | ||||
−0.587869 | + | 0.808956i | \(0.700033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −614.203 | − | 1031.95i | −0.666887 | − | 1.12046i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1788.04 | − | 1788.04i | 1.93720 | − | 1.93720i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4561 | − | 15.4561i | 0.0167093 | − | 0.0167093i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 219.674 | − | 404.947i | 0.236974 | − | 0.436836i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1091.41i | 1.17482i | 0.809290 | + | 0.587409i | \(0.199852\pi\) | ||||
−0.809290 | + | 0.587409i | \(0.800148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 449.320 | − | 449.320i | 0.482621 | − | 0.482621i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.8750 | + | 157.130i | −0.0427384 | + | 0.168414i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 105.245 | 0.112561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 887.919i | 0.947619i | 0.880627 | + | 0.473809i | \(0.157121\pi\) | ||||
−0.880627 | + | 0.473809i | \(0.842879\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1425.65 | + | 361.788i | 1.51826 | + | 0.385291i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −790.753 | − | 790.753i | −0.840333 | − | 0.840333i | 0.148569 | − | 0.988902i | \(-0.452533\pi\) |
−0.988902 | + | 0.148569i | \(0.952533\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −751.822 | −0.797266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −219.041 | + | 8.72786i | −0.231789 | + | 0.00923583i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1170.78 | + | 1170.78i | 1.23630 | + | 1.23630i | 0.961502 | + | 0.274796i | \(0.0886105\pi\) |
0.274796 | + | 0.961502i | \(0.411390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −220.280 | − | 220.280i | −0.232118 | − | 0.232118i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1165.00 | − | 693.393i | 1.22503 | − | 0.729120i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1148.50 | 1.20514 | 0.602571 | − | 0.798065i | \(-0.294143\pi\) | ||||
0.602571 | + | 0.798065i | \(0.294143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 301.830 | + | 301.830i | 0.316052 | + | 0.316052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.0042 | − | 133.996i | 0.0355321 | − | 0.140016i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 367.250i | 0.382951i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −825.376 | −0.858873 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1042.94 | + | 309.353i | −1.08301 | + | 0.321238i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 76.5746 | − | 76.5746i | 0.0793519 | − | 0.0793519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1696.75i | 1.75466i | 0.479892 | + | 0.877328i | \(0.340676\pi\) | ||||
−0.479892 | + | 0.877328i | \(0.659324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1287.82 | + | 766.494i | −1.32902 | + | 0.791016i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 119.876 | − | 119.876i | 0.123457 | − | 0.123457i | −0.642679 | − | 0.766136i | \(-0.722177\pi\) |
0.766136 | + | 0.642679i | \(0.222177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −66.6196 | + | 66.6196i | −0.0684682 | + | 0.0684682i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1070.06 | − | 636.886i | 1.09750 | − | 0.653217i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1408.74i | − | 1.44190i | −0.692985 | − | 0.720952i | \(-0.743705\pi\) | ||
0.692985 | − | 0.720952i | \(-0.256295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.49409 | − | 6.49409i | 0.00663340 | − | 0.00663340i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −644.927 | + | 191.296i | −0.657418 | + | 0.195001i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1288.34 | −1.31062 | −0.655309 | − | 0.755361i | \(-0.727461\pi\) | ||||
−0.655309 | + | 0.755361i | \(0.727461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 429.137i | 0.435672i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −135.235 | + | 532.903i | −0.137016 | + | 0.539922i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1187.58 | + | 1187.58i | 1.20079 | + | 1.20079i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1013.28 | 1.02248 | 0.511242 | − | 0.859437i | \(-0.329185\pi\) | ||||
0.511242 | + | 0.859437i | \(0.329185\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −982.280 | + | 584.641i | −0.989204 | + | 0.588762i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −227.968 | − | 227.968i | −0.229113 | − | 0.229113i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 537.885 | + | 537.885i | 0.539503 | + | 0.539503i | 0.923383 | − | 0.383880i | \(-0.125412\pi\) |
−0.383880 | + | 0.923383i | \(0.625412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.4256 | − | 1.17249i | 0.0294551 | − | 0.00117366i |
(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 | 384.3.i.b.353.2 | 8 | ||
3.2 | odd | 2 | inner | 384.3.i.b.353.4 | 8 | ||
4.3 | odd | 2 | 384.3.i.a.353.3 | 8 | |||
8.3 | odd | 2 | 48.3.i.a.5.4 | yes | 8 | ||
8.5 | even | 2 | 192.3.i.a.113.3 | 8 | |||
12.11 | even | 2 | 384.3.i.a.353.1 | 8 | |||
16.3 | odd | 4 | 384.3.i.a.161.1 | 8 | |||
16.5 | even | 4 | 192.3.i.a.17.1 | 8 | |||
16.11 | odd | 4 | 48.3.i.a.29.1 | yes | 8 | ||
16.13 | even | 4 | inner | 384.3.i.b.161.4 | 8 | ||
24.5 | odd | 2 | 192.3.i.a.113.1 | 8 | |||
24.11 | even | 2 | 48.3.i.a.5.1 | ✓ | 8 | ||
48.5 | odd | 4 | 192.3.i.a.17.3 | 8 | |||
48.11 | even | 4 | 48.3.i.a.29.4 | yes | 8 | ||
48.29 | odd | 4 | inner | 384.3.i.b.161.2 | 8 | ||
48.35 | even | 4 | 384.3.i.a.161.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.a.5.1 | ✓ | 8 | 24.11 | even | 2 | ||
48.3.i.a.5.4 | yes | 8 | 8.3 | odd | 2 | ||
48.3.i.a.29.1 | yes | 8 | 16.11 | odd | 4 | ||
48.3.i.a.29.4 | yes | 8 | 48.11 | even | 4 | ||
192.3.i.a.17.1 | 8 | 16.5 | even | 4 | |||
192.3.i.a.17.3 | 8 | 48.5 | odd | 4 | |||
192.3.i.a.113.1 | 8 | 24.5 | odd | 2 | |||
192.3.i.a.113.3 | 8 | 8.5 | even | 2 | |||
384.3.i.a.161.1 | 8 | 16.3 | odd | 4 | |||
384.3.i.a.161.3 | 8 | 48.35 | even | 4 | |||
384.3.i.a.353.1 | 8 | 12.11 | even | 2 | |||
384.3.i.a.353.3 | 8 | 4.3 | odd | 2 | |||
384.3.i.b.161.2 | 8 | 48.29 | odd | 4 | inner | ||
384.3.i.b.161.4 | 8 | 16.13 | even | 4 | inner | ||
384.3.i.b.353.2 | 8 | 1.1 | even | 1 | trivial | ||
384.3.i.b.353.4 | 8 | 3.2 | odd | 2 | inner |