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 | 353.3 | ||
Root | \(1.38255 - 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.a.161.3 |
$q$-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 | \(-0.916142\pi\) | ||
0.965498 | − | 0.260411i | \(-0.0838580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.91094 | − | 4.29150i | −0.878994 | − | 0.476834i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19038 | − | 1.19038i | 0.108216 | − | 0.108216i | −0.650926 | − | 0.759142i | \(-0.725619\pi\) |
0.759142 | + | 0.650926i | \(0.225619\pi\) | |||||||
\(12\) | 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 | −0.955913 | − | 0.293650i | \(-0.905130\pi\) |
0.293650 | + | 0.955913i | \(0.405130\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.6012 | + | 2.69028i | 0.504820 | + | 0.128109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.2630 | 1.27231 | 0.636153 | − | 0.771563i | \(-0.280525\pi\) | ||||
0.636153 | + | 0.771563i | \(0.280525\pi\) | |||||||
\(24\) | 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 | \(-0.439853\pi\) | ||||
0.187835 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(32\) | 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 | 0.998502 | − | 0.0547114i | \(-0.0174239\pi\) |
−0.0547114 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19.2154 | + | 5.69960i | −0.427009 | + | 0.126658i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 50.2681i | − | 1.06953i | −0.845000 | − | 0.534767i | \(-0.820399\pi\) | ||
0.845000 | − | 0.534767i | \(-0.179601\pi\) | |||||||
\(48\) | 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 | −0.487483 | − | 0.873132i | \(-0.662085\pi\) |
0.873132 | + | 0.487483i | \(0.162085\pi\) | |||||||
\(60\) | 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 | −0.782344 | − | 0.622847i | \(-0.785976\pi\) |
0.622847 | + | 0.782344i | \(0.285976\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.5938 | + | 85.0919i | −0.312954 | + | 1.23322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −122.086 | −1.71952 | −0.859760 | − | 0.510699i | \(-0.829387\pi\) | ||||
−0.859760 | + | 0.510699i | \(0.829387\pi\) | |||||||
\(72\) | 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 | \(-0.605460\pi\) | ||||
−0.325283 | + | 0.945617i | \(0.605460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 44.1660 | + | 67.8997i | 0.545259 | + | 0.838267i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −37.8680 | − | 37.8680i | −0.456240 | − | 0.456240i | 0.441179 | − | 0.897419i | \(-0.354560\pi\) |
−0.897419 | + | 0.441179i | \(0.854560\pi\) | |||||||
\(84\) | 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 | \(-0.920067\pi\) | ||
0.968635 | − | 0.248487i | \(-0.0799332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.9304 | − | 12.4575i | 0.199337 | − | 0.118643i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −85.4698 | + | 85.4698i | −0.798783 | + | 0.798783i | −0.982904 | − | 0.184121i | \(-0.941056\pi\) |
0.184121 | + | 0.982904i | \(0.441056\pi\) | |||||||
\(108\) | 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 | \(-0.405987\pi\) | ||||
0.291076 | + | 0.956700i | \(0.405987\pi\) | |||||||
\(128\) | 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 | \(-0.923455\pi\) |
−0.238161 | − | 0.971226i | \(-0.576545\pi\) | |||||||
\(132\) | 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 | 0.638314 | − | 0.769776i | \(-0.279632\pi\) |
−0.769776 | + | 0.638314i | \(0.779632\pi\) | |||||||
\(140\) | 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 | \(-0.970336\pi\) | ||
0.995661 | − | 0.0930572i | \(-0.0296639\pi\) | |||||||
\(152\) | 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 | −0.848199 | − | 0.529678i | \(-0.822313\pi\) |
0.529678 | + | 0.848199i | \(0.322313\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9015 | + | 2.76648i | 0.0660697 | + | 0.0167666i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −57.5333 | −0.344511 | −0.172255 | − | 0.985052i | \(-0.555105\pi\) | ||||
−0.172255 | + | 0.985052i | \(0.555105\pi\) | |||||||
\(168\) | 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 | 0.767109 | − | 0.641517i | \(-0.221695\pi\) |
−0.641517 | + | 0.767109i | \(0.721695\pi\) | |||||||
\(180\) | 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 | \(-0.832686\pi\) | ||
0.865007 | − | 0.501760i | \(-0.167314\pi\) | |||||||
\(192\) | 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 | \(0.118499\pi\) | ||||
−0.931502 | + | 0.363737i | \(0.881501\pi\) | |||||||
\(200\) | 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 | −0.0671538 | − | 0.997743i | \(-0.521392\pi\) |
0.997743 | + | 0.0671538i | \(0.0213918\pi\) | |||||||
\(212\) | 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 | \(-0.818264\pi\) | ||||
−0.841393 | + | 0.540423i | \(0.818264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 86.0039 | − | 158.539i | 0.382240 | − | 0.704619i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 181.108 | + | 181.108i | 0.797834 | + | 0.797834i | 0.982754 | − | 0.184920i | \(-0.0592025\pi\) |
−0.184920 | + | 0.982754i | \(0.559203\pi\) | |||||||
\(228\) | 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 | \(0.175113\pi\) | ||||
−0.852454 | + | 0.522802i | \(0.824887\pi\) | |||||||
\(240\) | 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 | −0.615519 | − | 0.788122i | \(-0.711053\pi\) |
0.788122 | + | 0.615519i | \(0.211053\pi\) | |||||||
\(252\) | 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 | \(-0.206163\pi\) | ||||
0.797486 | + | 0.603338i | \(0.206163\pi\) | |||||||
\(264\) | 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 | \(-0.292169\pi\) | ||||
0.607508 | + | 0.794314i | \(0.292169\pi\) | |||||||
\(272\) | 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 | 0.960823 | − | 0.277163i | \(-0.0893942\pi\) |
−0.277163 | + | 0.960823i | \(0.589394\pi\) | |||||||
\(284\) | 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 | −0.997171 | − | 0.0751680i | \(-0.976051\pi\) |
0.0751680 | + | 0.997171i | \(0.476051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 148.847 | + | 37.7729i | 0.481704 | + | 0.122242i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 54.0368 | 0.173752 | 0.0868759 | − | 0.996219i | \(-0.472312\pi\) | ||||
0.0868759 | + | 0.996219i | \(0.472312\pi\) | |||||||
\(312\) | 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 | 0.985230 | − | 0.171238i | \(-0.0547766\pi\) |
−0.171238 | + | 0.985230i | \(0.554777\pi\) | |||||||
\(332\) | 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 | −0.865932 | − | 0.500162i | \(-0.833274\pi\) |
0.500162 | + | 0.865932i | \(0.333274\pi\) | |||||||
\(348\) | 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 | \(-0.517898\pi\) | ||||
−0.0561976 | + | 0.998420i | \(0.517898\pi\) | |||||||
\(360\) | 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 | \(-0.346364\pi\) | ||||
0.464140 | + | 0.885762i | \(0.346364\pi\) | |||||||
\(368\) | 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 | 0.144327 | − | 0.989530i | \(-0.453898\pi\) |
−0.989530 | + | 0.144327i | \(0.953898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54.5570 | + | 214.985i | −0.143194 | + | 0.564266i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 632.700i | 1.65196i | 0.563702 | + | 0.825978i | \(0.309377\pi\) | ||||
−0.563702 | + | 0.825978i | \(0.690623\pi\) | |||||||
\(384\) | 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 | 0.725016 | − | 0.688733i | \(-0.241833\pi\) |
−0.688733 | + | 0.725016i | \(0.741833\pi\) | |||||||
\(420\) | 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 | \(0.0605943\pi\) | ||||
−0.981936 | + | 0.189215i | \(0.939406\pi\) | |||||||
\(432\) | 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 | \(0.164950\pi\) | ||||
−0.868709 | + | 0.495322i | \(0.835050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −282.488 | − | 153.243i | −0.640562 | − | 0.347490i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −260.367 | + | 260.367i | −0.587736 | + | 0.587736i | −0.937018 | − | 0.349282i | \(-0.886426\pi\) |
0.349282 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(444\) | 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 | \(-0.868782\pi\) | ||||
−0.916228 | + | 0.400657i | \(0.868782\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 39.7935 | + | 66.8587i | 0.0855774 | + | 0.143782i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 56.0706 | + | 56.0706i | 0.120066 | + | 0.120066i | 0.764587 | − | 0.644521i | \(-0.222943\pi\) |
−0.644521 | + | 0.764587i | \(0.722943\pi\) | |||||||
\(468\) | 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 | \(-0.763177\pi\) | ||
0.735764 | − | 0.677238i | \(-0.236823\pi\) | |||||||
\(480\) | 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 | \(-0.941904\pi\) | ||
0.983391 | − | 0.181502i | \(-0.0580959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −112.659 | − | 189.284i | −0.230387 | − | 0.387083i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −317.369 | + | 317.369i | −0.646373 | + | 0.646373i | −0.952114 | − | 0.305742i | \(-0.901096\pi\) |
0.305742 | + | 0.952114i | \(0.401096\pi\) | |||||||
\(492\) | 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 | −0.224250 | − | 0.974532i | \(-0.571993\pi\) |
0.974532 | + | 0.224250i | \(0.0719931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.4551 | − | 167.297i | 0.0847407 | − | 0.333926i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −386.094 | −0.767583 | −0.383791 | − | 0.923420i | \(-0.625382\pi\) | ||||
−0.383791 | + | 0.923420i | \(0.625382\pi\) | |||||||
\(504\) | 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 | 0.885102 | − | 0.465397i | \(-0.154088\pi\) |
−0.465397 | + | 0.885102i | \(0.654088\pi\) | |||||||
\(524\) | 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 | −0.708475 | − | 0.705736i | \(-0.750616\pi\) |
0.705736 | + | 0.708475i | \(0.250616\pi\) | |||||||
\(548\) | 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 | 0.997746 | − | 0.0671003i | \(-0.0213748\pi\) |
−0.0671003 | + | 0.997746i | \(0.521375\pi\) | |||||||
\(564\) | 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 | 0.710112 | − | 0.704089i | \(-0.248644\pi\) |
−0.704089 | + | 0.710112i | \(0.748644\pi\) | |||||||
\(572\) | 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 | −0.215522 | − | 0.976499i | \(-0.569145\pi\) |
0.976499 | + | 0.215522i | \(0.0691453\pi\) | |||||||
\(588\) | 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 | \(-0.387615\pi\) | ||||
0.345777 | + | 0.938317i | \(0.387615\pi\) | |||||||
\(600\) | 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 | \(-0.527096\pi\) | ||||
−0.0850222 | + | 0.996379i | \(0.527096\pi\) | |||||||
\(608\) | 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 | 0.951980 | − | 0.306159i | \(-0.0990440\pi\) |
−0.306159 | + | 0.951980i | \(0.599044\pi\) | |||||||
\(620\) | 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 | \(0.265310\pi\) | ||||
−0.672291 | + | 0.740287i | \(0.734690\pi\) | |||||||
\(632\) | 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 | −0.999633 | − | 0.0271039i | \(-0.991371\pi\) |
0.0271039 | + | 0.999633i | \(0.491371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −94.3165 | + | 371.660i | −0.146227 | + | 0.576218i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 97.2591 | 0.150323 | 0.0751616 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751616 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(648\) | 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 | 0.704743 | − | 0.709462i | \(-0.251062\pi\) |
−0.709462 | + | 0.704743i | \(0.751062\pi\) | |||||||
\(660\) | 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 | −0.946986 | − | 0.321273i | \(-0.895889\pi\) |
0.321273 | + | 0.946986i | \(0.395889\pi\) | |||||||
\(684\) | 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 | −0.334378 | − | 0.942439i | \(-0.608526\pi\) |
0.942439 | + | 0.334378i | \(0.108526\pi\) | |||||||
\(692\) | 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 | \(-0.853375\pi\) | ||
0.895770 | − | 0.444519i | \(-0.146625\pi\) | |||||||
\(720\) | 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 | \(-0.817389\pi\) | ||
0.839904 | − | 0.542734i | \(-0.182611\pi\) | |||||||
\(728\) | 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 | −0.805647 | − | 0.592395i | \(-0.798182\pi\) |
0.592395 | + | 0.805647i | \(0.298182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1071.75 | − | 271.980i | −1.44636 | − | 0.367044i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1305.03 | −1.75643 | −0.878216 | − | 0.478265i | \(-0.841266\pi\) | ||||
−0.878216 | + | 0.478265i | \(0.841266\pi\) | |||||||
\(744\) | 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 | \(-0.322756\pi\) | ||||
0.528495 | + | 0.848936i | \(0.322756\pi\) | |||||||
\(752\) | 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 | −0.00992500 | − | 0.999951i | \(-0.503159\pi\) |
0.999951 | + | 0.00992500i | \(0.00315928\pi\) | |||||||
\(788\) | 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 | 0.839006 | − | 0.544123i | \(-0.183137\pi\) |
−0.544123 | + | 0.839006i | \(0.683137\pi\) | |||||||
\(812\) | 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 | \(0.280763\pi\) | ||||
−0.635576 | + | 0.772038i | \(0.719237\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −86.9721 | + | 51.7648i | −0.105421 | + | 0.0627452i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −113.766 | + | 113.766i | −0.137565 | + | 0.137565i | −0.772536 | − | 0.634971i | \(-0.781012\pi\) |
0.634971 | + | 0.772536i | \(0.281012\pi\) | |||||||
\(828\) | 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 | \(-0.487620\pi\) | ||||
0.0388836 | + | 0.999244i | \(0.487620\pi\) | |||||||
\(840\) | 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 | 0.735702 | − | 0.677306i | \(-0.236853\pi\) |
−0.677306 | + | 0.735702i | \(0.736853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 272.365 | + | 69.1184i | 0.316336 | + | 0.0802769i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1027.80i | 1.19096i | 0.803370 | + | 0.595480i | \(0.203038\pi\) | ||||
−0.803370 | + | 0.595480i | \(0.796962\pi\) | |||||||
\(864\) | 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 | −0.450588 | − | 0.892732i | \(-0.648786\pi\) |
0.892732 | + | 0.450588i | \(0.148786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 208.375 | + | 52.8796i | 0.235452 | + | 0.0597509i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1446.61 | −1.63090 | −0.815450 | − | 0.578827i | \(-0.803511\pi\) | ||||
−0.815450 | + | 0.578827i | \(0.803511\pi\) | |||||||
\(888\) | 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 | 0.937866 | − | 0.346997i | \(-0.112798\pi\) |
−0.346997 | + | 0.937866i | \(0.612798\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −395.967 | + | 117.450i | −0.435607 | + | 0.129208i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1580.22i | − | 1.73460i | −0.497786 | − | 0.867300i | \(-0.665854\pi\) | ||
0.497786 | − | 0.867300i | \(-0.334146\pi\) | |||||||
\(912\) | 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 | \(-0.700033\pi\) | ||
0.587869 | − | 0.808956i | \(-0.299967\pi\) | |||||||
\(920\) | 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 | \(-0.911390\pi\) |
−0.274796 | − | 0.961502i | \(-0.588610\pi\) | |||||||
\(948\) | 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 | \(-0.659324\pi\) | ||
0.479892 | − | 0.877328i | \(-0.340676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1287.82 | + | 766.494i | −1.32902 | + | 0.791016i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −119.876 | + | 119.876i | −0.123457 | + | 0.123457i | −0.766136 | − | 0.642679i | \(-0.777823\pi\) |
0.642679 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(972\) | 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 | \(-0.272539\pi\) | ||||
0.655309 | + | 0.755361i | \(0.272539\pi\) | |||||||
\(984\) | 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 | \(-0.670815\pi\) | ||||
−0.511242 | + | 0.859437i | \(0.670815\pi\) | |||||||
\(992\) | 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.a.353.3 | 8 | ||
3.2 | odd | 2 | inner | 384.3.i.a.353.1 | 8 | ||
4.3 | odd | 2 | 384.3.i.b.353.2 | 8 | |||
8.3 | odd | 2 | 192.3.i.a.113.3 | 8 | |||
8.5 | even | 2 | 48.3.i.a.5.4 | yes | 8 | ||
12.11 | even | 2 | 384.3.i.b.353.4 | 8 | |||
16.3 | odd | 4 | 384.3.i.b.161.4 | 8 | |||
16.5 | even | 4 | 48.3.i.a.29.1 | yes | 8 | ||
16.11 | odd | 4 | 192.3.i.a.17.1 | 8 | |||
16.13 | even | 4 | inner | 384.3.i.a.161.1 | 8 | ||
24.5 | odd | 2 | 48.3.i.a.5.1 | ✓ | 8 | ||
24.11 | even | 2 | 192.3.i.a.113.1 | 8 | |||
48.5 | odd | 4 | 48.3.i.a.29.4 | yes | 8 | ||
48.11 | even | 4 | 192.3.i.a.17.3 | 8 | |||
48.29 | odd | 4 | inner | 384.3.i.a.161.3 | 8 | ||
48.35 | even | 4 | 384.3.i.b.161.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.a.5.1 | ✓ | 8 | 24.5 | odd | 2 | ||
48.3.i.a.5.4 | yes | 8 | 8.5 | even | 2 | ||
48.3.i.a.29.1 | yes | 8 | 16.5 | even | 4 | ||
48.3.i.a.29.4 | yes | 8 | 48.5 | odd | 4 | ||
192.3.i.a.17.1 | 8 | 16.11 | odd | 4 | |||
192.3.i.a.17.3 | 8 | 48.11 | even | 4 | |||
192.3.i.a.113.1 | 8 | 24.11 | even | 2 | |||
192.3.i.a.113.3 | 8 | 8.3 | odd | 2 | |||
384.3.i.a.161.1 | 8 | 16.13 | even | 4 | inner | ||
384.3.i.a.161.3 | 8 | 48.29 | odd | 4 | inner | ||
384.3.i.a.353.1 | 8 | 3.2 | odd | 2 | inner | ||
384.3.i.a.353.3 | 8 | 1.1 | even | 1 | trivial | ||
384.3.i.b.161.2 | 8 | 48.35 | even | 4 | |||
384.3.i.b.161.4 | 8 | 16.3 | odd | 4 | |||
384.3.i.b.353.2 | 8 | 4.3 | odd | 2 | |||
384.3.i.b.353.4 | 8 | 12.11 | even | 2 |